************** MAGMA ***************** Host janssons.medic.chalmers.se. (129.16.32.56) Time: Fri Feb 13 08:50:09 2004 Input: 1+2 Output: Magma V2.10-6 Fri Feb 13 2004 08:50:04 on modular [Seed = 1845688440] ------------------------------------- 3 Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host janssons.medic.chalmers.se. (129.16.32.56) Time: Fri Feb 13 08:50:39 2004 Input: 1+2 Output: Magma V2.10-6 Fri Feb 13 2004 08:50:36 on modular [Seed = 2632977066] ------------------------------------- 3 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathl30.sogang.ac.kr. (163.239.42.230) Time: Fri Feb 13 20:36:47 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Fri Feb 13 2004 20:36:44 on modular [Seed = 3316186696] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (218.79.220.21) Time: Mon Feb 16 00:18:41 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Mon Feb 16 2004 00:18:37 on modular [Seed = 3049629541] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.099 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host classic.univ-ab.pt. (193.136.111.1) Time: Mon Feb 16 07:29:48 2004 Input: (a+b)+c=a+(b+c). a+a=a. (a+b)+(a+d)!=(a+b)+d. Output: Magma V2.10-6 Mon Feb 16 2004 07:29:44 on modular [Seed = 4119134799] ------------------------------------- >> (a+b)+(a+d)!=(a+b)+d.; ^ User error: bad syntax Total time: 3.119 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host classic.univ-ab.pt. (193.136.111.1) Time: Mon Feb 16 07:32:06 2004 Input: (a+b)+c=a+(b+c). a+a=a. (a+b)+(a+d)>(a+b)+d. Output: Magma V2.10-6 Mon Feb 16 2004 07:32:03 on modular [Seed = 74775620] ------------------------------------- >> (a+b)+(a+d)>(a+b)+d.; ^ User error: bad syntax Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host classic.univ-ab.pt. (193.136.111.1) Time: Mon Feb 16 07:37:36 2004 Input: (a+b)+c=a+(b+c) & a+a=a -> (a+b)+(a+d)(a+b)+d. Output: Magma V2.10-6 Mon Feb 16 2004 07:37:33 on modular [Seed = 359001243] ------------------------------------- >> (a+b)+c=a+(b+c) & a+a=a -> (a+b)+(a+d)(a+b)+d.; ^ User error: Bad reduction operator Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host classic.univ-ab.pt. (193.136.111.1) Time: Mon Feb 16 07:52:55 2004 Input: (a+b)+c=a+(b+c) and a+a=a and (a+b)+(a+d) ne (a+b)+d. Output: Magma V2.10-6 Mon Feb 16 2004 07:52:52 on modular [Seed = 927451664] ------------------------------------- >> (a+b)+c=a+(b+c) and a+a=a and (a+b)+(a+d) ne (a+b)+d.; ^ User error: bad syntax Total time: 3.099 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host classic.univ-ab.pt. (193.136.111.1) Time: Mon Feb 16 07:54:21 2004 Input: (a+b)+c=a+(b+c) and a+a=a and (a+b)+(a+d) ne (a+b)+d Output: Magma V2.10-6 Mon Feb 16 2004 07:54:18 on modular [Seed = 1045349191] ------------------------------------- >> (a+b)+c=a+(b+c) and a+a=a and (a+b)+(a+d) ne (a+b)+d; ^ User error: Identifier 'a' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host classic.univ-ab.pt. (193.136.111.1) Time: Mon Feb 16 08:00:10 2004 Input: (a+b)+c=a+(b+c) a+a=a (a+b)+(a+d) ne (a+b)+d Output: Magma V2.10-6 Mon Feb 16 2004 08:00:07 on modular [Seed = 1580114058] ------------------------------------- >> a+a=a ^ User error: bad syntax >> (a+b)+(a+d) ne (a+b)+d; ^ User error: Identifier 'a' has not been declared or assigned Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (12.104.244.38) Time: Mon Feb 16 12:01:13 2004 Input: GetSeed(); Output: Magma V2.10-6 Mon Feb 16 2004 12:01:09 on modular [Seed = 2314813145] ------------------------------------- 2314813145 0 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (12.104.244.38) Time: Mon Feb 16 12:02:01 2004 Input: K := GF(RandomPrime(40)); E := EllipticCurve([Random(K), Random(K)]); E; Output: Magma V2.10-6 Mon Feb 16 2004 12:01:56 on modular [Seed = 2481136658] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 95578316362*x + 101604805736 over GF(430691276293) Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (12.104.244.38) Time: Mon Feb 16 12:03:48 2004 Input: GetSeed(); K := GF(RandomPrime(40)); E := EllipticCurve([Random(K), Random(K)]); E; Q := Random(E); Q; FactoredOrder(Q); P := Random(Order(Q))*Q; P; m := Log(Q, P); m; m*Q - P; Output: Magma V2.10-6 Mon Feb 16 2004 12:03:44 on modular [Seed = 2782204496] ------------------------------------- 2782204496 0 Elliptic Curve defined by y^2 = x^3 + 39359586944*x + 190995520634 over GF(957632693371) (613100332250 : 469510526239 : 1) [ <2, 4>, <2621, 1>, <22835569, 1> ] (160753340997 : 392177928413 : 1) 829514499424 (0 : 1 : 0) Total time: 3.369 seconds, Total memory usage: 2.85MB ************** MAGMA ***************** Host m157.tnt04-bp.pool.eol.hu. (212.108.246.157) Time: Mon Feb 16 14:30:57 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Mon Feb 16 2004 14:30:54 on modular [Seed = 910650463] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (140.115.25.8) Time: Mon Feb 16 20:07:17 2004 Input: 1 Output: Magma V2.10-6 Mon Feb 16 2004 20:07:14 on modular [Seed = 3818048171] ------------------------------------- 1 Total time: 3.109 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (140.115.25.8) Time: Mon Feb 16 20:07:32 2004 Input: 1 + 1 Output: Magma V2.10-6 Mon Feb 16 2004 20:07:29 on modular [Seed = 4186493090] ------------------------------------- 2 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (140.115.25.8) Time: Mon Feb 16 20:07:47 2004 Input: 1/2 * 2 Output: Magma V2.10-6 Mon Feb 16 2004 20:07:44 on modular [Seed = 4136099740] ------------------------------------- 1 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (140.115.25.8) Time: Mon Feb 16 20:08:00 2004 Input: 1/123456789 * 2 Output: Magma V2.10-6 Mon Feb 16 2004 20:07:57 on modular [Seed = 243214184] ------------------------------------- 2/123456789 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (140.115.25.8) Time: Mon Feb 16 20:08:12 2004 Input: 2**2 * 2 Output: Magma V2.10-6 Mon Feb 16 2004 20:08:09 on modular [Seed = 91499639] ------------------------------------- >> 2**2 * 2; ^ User error: bad syntax Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (140.115.25.8) Time: Mon Feb 16 20:08:22 2004 Input: 2^2 * 2 Output: Magma V2.10-6 Mon Feb 16 2004 20:08:19 on modular [Seed = 476919188] ------------------------------------- 8 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (140.115.25.8) Time: Mon Feb 16 20:08:32 2004 Input: 2^2048 * 2 Output: Magma V2.10-6 Mon Feb 16 2004 20:08:29 on modular [Seed = 727319213] ------------------------------------- 6463401214262201460142975337733990392088820533943096806426069085504931027773578\ 1786394402823045826927377435921843796038988239118300981842190176304772896566241\ 2617547346019921835003955007793042135921152767681351365535844372852395123236761\ 8867695234094116329170407261008577515178308213161721510479824786077104382866677\ 9336684841369949573129138989712352070652644116155611318662052385416920628300517\ 1857283542334518872074369237147151967023046032918088073952264665744624542513694\ 2164041945031420345386264693935708516131339587009199453670599727643105033277887\ 4671087204270866459209290636957209904296387111707222119192461312 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (140.115.25.8) Time: Mon Feb 16 20:08:51 2004 Input: atan(1) Output: Magma V2.10-6 Mon Feb 16 2004 20:08:48 on modular [Seed = 575867785] ------------------------------------- >> atan(1); ^ User error: Identifier 'atan' has not been declared or assigned Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (140.115.25.8) Time: Mon Feb 16 20:09:04 2004 Input: tan(1) Output: Magma V2.10-6 Mon Feb 16 2004 20:09:01 on modular [Seed = 961024159] ------------------------------------- >> tan(1); ^ User error: Identifier 'tan' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (140.115.25.8) Time: Mon Feb 16 20:09:27 2004 Input: 2^(-100) Output: Magma V2.10-6 Mon Feb 16 2004 20:09:24 on modular [Seed = 809572863] ------------------------------------- 1/1267650600228229401496703205376 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam145-177.student.harvard.edu. (140.247.145.177) Time: Mon Feb 16 23:26:18 2004 Input: Factorial(10000) Output: Magma V2.10-6 Mon Feb 16 2004 23:26:14 on modular [Seed = 4152762397] ------------------------------------- 2846259680917054518906413212119868890148051401702799230794179994274411340003764\ 4437729907867577847758158840621423175288300423399401535187390524211613827161748\ 1982419982759241828925978789812425312059465996259867065601615720360323979263287\ 3671705574197596209947972034615369811989709261127750048419884541047554464244213\ 6573303076703628825803548967461117097369578603670191071512730587281041158640561\ 2811653853259684258259955846881464304255898366493170592517172042765974074461334\ 0005419405246230343686915405940406622782824837151203832217864462718382292389963\ 8992827221879702459387693803094627332292570555459690027875282242544348021127559\ 0191694254290289169072190970836905398737474524833728995218023632827412170402680\ 8676921045155584056717255537201585213282903427998981844931361064038148930449962\ 1599999359670892980190336998484404665419236258424947163178961192041233108268651\ 0713545168455409360330096072103469443779823494307806260694223026818852275920570\ 2923084312618849760656074258627944882715595683153344053442544664841689458042570\ 9461673613187605234982286326452921529423479870603344290737158688499178932580691\ 4831688542519560061723726363239744207869246429560123062887201226529529640915083\ 0133663098273380635397290150658182257429547589439976511386554120812578868370423\ 9208764484761569001264889271590706306409661628038784044485191643790807186112370\ 6221334154150659918438759610239267132765469861636577066264386380298480519527695\ 3619525924093090861447190739076858575593478698172073437209310482547562856777769\ 4081564074962275254993384112809289637516990219870492405617531786346939798024619\ 7370790418683299310165541507423083931768783669236948490259996077296842939774275\ 3626311982541668153189176323483919082100014717893218422780513518173492190114624\ 6875769835373441456013122615221391178759688367364087207937002992038279198038702\ 3720780391403123689976081528403060511167094847222248703891999934420713958369830\ 6396223207911562404425080891991431983712044559834404755675948921210149815245454\ 3594285414390843564419984224855478532163624030098442855331829253154206551237079\ 7058163934602962476970103887422064415366267337154287007891227493406843364428898\ 4710084064160009362393526124803797529334392876439831639031277645072247926785170\ 0826669598389526150759007349215197592659192708873202594066382118801988854748266\ 0483422564577057439731222597006719360617635135795298217942907977053272832675014\ 8802444352868164502616566283754651900617187344226043891929850607151539003110668\ 4727360135816706437861756757439184376479658136100599638689552334648781746143243\ 5732248643267984819814584327030358955084205347884933645824825920332880890257823\ 8823326577020524897093704721021424841334246526820680673231421448385407418213962\ 1846870108359582946965235632764870475718351616879235068366271743711915723361143\ 0701211207676086978515597218464859859186436417168508996255168209107935702311185\ 1817477501080462258552131476489749066075287708289766751495100968232968973200062\ 2392888056658036140311285465929084078033974900664953205873164948093883816198658\ 8508273824680348978647571166798904235680183035041338757319726308979094357106877\ 9730163391808786847494363353389337358690640584841782806519627582643442925805842\ 2212947649402948622670761832988229004072390403733168207417413251656688443079339\ 4470192089056207883875853425128209573593070181977083401638176382785625395168254\ 2664461494104471157953326237281546879408042371858742302620026422182269418862621\ 2107297776657401018376182280136857586442185863011539843712299107010094061929413\ 2232027731939594670067136953770978977781182882424429208648161341795620174718316\ 0968766104314049795819823644580736820940402221118153005143338707660706314961610\ 7771117448059552764348333385744040212757031851527298377435921878558552795591028\ 6644579173620072218581433099772947789237207179428577562713009239823979219575811\ 9726474264287826668235391568785727162014619224426626670840076566562580710947439\ 8740110772811669918806268726626565583345665007890309050656074633078027158530817\ 6912237728135105845273265916262196476205714348802156308152590053437211410003030\ 3924286645720732847348171203416818632896886504828736793339844397123673508452734\ 0196309427697652684170174990756947982757825835229994315633322107439131550124459\ 0053247026803129123922979790304175878233986223735350546426469135025039510092392\ 8658510868208807066273473320035499572039708648806604092985460700633940988583634\ 9865466136727880748764700702458790118046518296111277090609016152022111461543158\ 3176699570609746180853593904000678928785488278509386373537039040494126846189912\ 7287156265500127083303995025787993170543188275265922581494895074663997600731692\ 7310831735883056612614782997663188070063044632429112260691931278881566221591523\ 2704576958675128219909389426866019639044897189185974729253103224802105438410443\ 2582847283058429780416240510811032691400190056878439634150269652104892027214023\ 2160234898588827371428695339681755106287470907473718188014223487248498558198439\ 0946517083643689943061896502432883532796671901845276205510857076262042445096233\ 2320474470783119043449935144262550170177101737955112474615947173186270156557126\ 6295855125077711738338208419705893367323724453280456537178514960308802580284067\ 8478094146418386592266528068679788432506605379430462502871051049293472674712674\ 9989263462735816714693506049511034075540465817039348104675848562596776795976829\ 9409334026387269378365320912287718077451152622642548771835461108886360843272806\ 2277766430972838790567286180360486334648933714394152502594596525015209595361579\ 7713559579496572977565090269442808847976127666484700361964890604376193469427044\ 4070215317943583831051404915462608728486678750541674146731648999356381312866931\ 4276168635373056345866269578945682750658102359508148887789550739393653419373657\ 0084831850447568221544406759920313807707353997803633926733454954929666875992253\ 0893898086430606532961793164029612492673080638031873912596151131890359351266480\ 8185683667702865377423907465823909109555171797705807977892897524902307378017531\ 4268036391424472025772889178495007811788933662975043680421466819782427298069757\ 9391742229456683185815676816288797870624531246651727622758295493421483658868919\ 2995874020956960002435603052898298663868920769928340305497102665143223061252319\ 1513184387690382370620539920693394371688046642971147674356448637502684769814885\ 3105354063328845062012173302630676481322931561043551941761050712449024873277273\ 1120919458651374931909651624976916575538121985664322079786663003989386602386073\ 5785811439471587280089337416503379296583261843607313332752602360511552422722844\ 7251463863269369763762510196714380125691227784428426999440829152215904694437282\ 4986580852051865762929927755088331286726384187132777808744466438753526447335624\ 4113944762878097465068395298210817496795883645227334469487379347179071006497823\ 6466016680572034297929207446822322848665839522211446859572858403863377278030227\ 5915304978658739195136502462741958990883743873315942873720297706202071202130385\ 7217593321116241333042277374241635355358797706530964768588607730143277829032889\ 4795818404378858567772932094476778669357537460048142376741194182671636870481056\ 9111562156143575162905273512243500806046536689174581965494826086122607502930627\ 6147881326895528073614902252581968281505103331813212965966495815903042123877564\ 5990973296728066683849166257949747922905361845563741034791430771561168650484292\ 4902811029925296787352987678292690407887784802624792227507359484058174390862518\ 7794689004594206016860514277224448627246991114620014988066272353883780938062854\ 4384763053235070132028029488392008132135446450056134987017834271106158177289819\ 2906564986880810455622337030672542512772773302834984335957725759562247037077933\ 8714659303308862969944031833266579751467650271734629888377739784821870071802674\ 1265997158728035440478432478674907127921672898523588486943546692255101337606377\ 9151645972542571169684773399511589983490818882812639844005055462100669887926145\ 5821456531969690982725393451576040861347625877816586729441077535882416231577908\ 2538054746933540582469717674324523451498483027170396543887737637358191736582454\ 2733474904242629460112998819165637138471118491569150547681404117498014542657123\ 9420442544102807580600138819865061375928853903892264432294799028648284009959867\ 5963580999112695367601527173086852756572147583507122298296529564917835071750835\ 7413622825450556202709694174767992592297748886274113145876761475314568953280931\ 1705269648641018740767329698664923643738256547502281647192681555988319662984830\ 7776666840622314315884384910519058281816740764463033300119710293036455866594651\ 8690744752508378419876229904159117936827997606541860887216266548864923443910309\ 2325691063377596973905178112276466848679173604940439370333935190060938726839729\ 9246478483727274770977466693599784857120156789000241947269220974984127323147401\ 5499809203814598214164811763571478015542315996678385348544864069364105569135313\ 3523118405358134894093819182189869482538396098994282202759933963520621770534357\ 2073396250574216769465101608495601439303244304271576099527308684609204422226103\ 1542299844448021100981613338248273752189987382053151649271344981059501599748005\ 7159191220215448774875010347324619063394130303089239941198500622590218416440998\ 8173214324422108554248620896250260604398180189026317781146617454999771440665232\ 8638463638470016556181538610981881111817341913055050248603458567555856375117297\ 7429932907494423657966833270091836733897734790175924888566037995277154056908301\ 7311723894140326159612292912225191095948743805673381278538616491842786938417556\ 8980471008598683720336151751580970225662752001609561922299254017598785220385459\ 1377178397638981119848580329104875166692119510451489667776159824946872742066343\ 7593207852618922687285527671324883267794152912839165407968344190239094803676688\ 7 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host roam145-177.student.harvard.edu. (140.247.145.177) Time: Mon Feb 16 23:26:22 2004 Input: Factorial(10000) Output: Magma V2.10-6 Mon Feb 16 2004 23:26:19 on modular [Seed = 158916335] ------------------------------------- 2846259680917054518906413212119868890148051401702799230794179994274411340003764\ 4437729907867577847758158840621423175288300423399401535187390524211613827161748\ 1982419982759241828925978789812425312059465996259867065601615720360323979263287\ 3671705574197596209947972034615369811989709261127750048419884541047554464244213\ 6573303076703628825803548967461117097369578603670191071512730587281041158640561\ 2811653853259684258259955846881464304255898366493170592517172042765974074461334\ 0005419405246230343686915405940406622782824837151203832217864462718382292389963\ 8992827221879702459387693803094627332292570555459690027875282242544348021127559\ 0191694254290289169072190970836905398737474524833728995218023632827412170402680\ 8676921045155584056717255537201585213282903427998981844931361064038148930449962\ 1599999359670892980190336998484404665419236258424947163178961192041233108268651\ 0713545168455409360330096072103469443779823494307806260694223026818852275920570\ 2923084312618849760656074258627944882715595683153344053442544664841689458042570\ 9461673613187605234982286326452921529423479870603344290737158688499178932580691\ 4831688542519560061723726363239744207869246429560123062887201226529529640915083\ 0133663098273380635397290150658182257429547589439976511386554120812578868370423\ 9208764484761569001264889271590706306409661628038784044485191643790807186112370\ 6221334154150659918438759610239267132765469861636577066264386380298480519527695\ 3619525924093090861447190739076858575593478698172073437209310482547562856777769\ 4081564074962275254993384112809289637516990219870492405617531786346939798024619\ 7370790418683299310165541507423083931768783669236948490259996077296842939774275\ 3626311982541668153189176323483919082100014717893218422780513518173492190114624\ 6875769835373441456013122615221391178759688367364087207937002992038279198038702\ 3720780391403123689976081528403060511167094847222248703891999934420713958369830\ 6396223207911562404425080891991431983712044559834404755675948921210149815245454\ 3594285414390843564419984224855478532163624030098442855331829253154206551237079\ 7058163934602962476970103887422064415366267337154287007891227493406843364428898\ 4710084064160009362393526124803797529334392876439831639031277645072247926785170\ 0826669598389526150759007349215197592659192708873202594066382118801988854748266\ 0483422564577057439731222597006719360617635135795298217942907977053272832675014\ 8802444352868164502616566283754651900617187344226043891929850607151539003110668\ 4727360135816706437861756757439184376479658136100599638689552334648781746143243\ 5732248643267984819814584327030358955084205347884933645824825920332880890257823\ 8823326577020524897093704721021424841334246526820680673231421448385407418213962\ 1846870108359582946965235632764870475718351616879235068366271743711915723361143\ 0701211207676086978515597218464859859186436417168508996255168209107935702311185\ 1817477501080462258552131476489749066075287708289766751495100968232968973200062\ 2392888056658036140311285465929084078033974900664953205873164948093883816198658\ 8508273824680348978647571166798904235680183035041338757319726308979094357106877\ 9730163391808786847494363353389337358690640584841782806519627582643442925805842\ 2212947649402948622670761832988229004072390403733168207417413251656688443079339\ 4470192089056207883875853425128209573593070181977083401638176382785625395168254\ 2664461494104471157953326237281546879408042371858742302620026422182269418862621\ 2107297776657401018376182280136857586442185863011539843712299107010094061929413\ 2232027731939594670067136953770978977781182882424429208648161341795620174718316\ 0968766104314049795819823644580736820940402221118153005143338707660706314961610\ 7771117448059552764348333385744040212757031851527298377435921878558552795591028\ 6644579173620072218581433099772947789237207179428577562713009239823979219575811\ 9726474264287826668235391568785727162014619224426626670840076566562580710947439\ 8740110772811669918806268726626565583345665007890309050656074633078027158530817\ 6912237728135105845273265916262196476205714348802156308152590053437211410003030\ 3924286645720732847348171203416818632896886504828736793339844397123673508452734\ 0196309427697652684170174990756947982757825835229994315633322107439131550124459\ 0053247026803129123922979790304175878233986223735350546426469135025039510092392\ 8658510868208807066273473320035499572039708648806604092985460700633940988583634\ 9865466136727880748764700702458790118046518296111277090609016152022111461543158\ 3176699570609746180853593904000678928785488278509386373537039040494126846189912\ 7287156265500127083303995025787993170543188275265922581494895074663997600731692\ 7310831735883056612614782997663188070063044632429112260691931278881566221591523\ 2704576958675128219909389426866019639044897189185974729253103224802105438410443\ 2582847283058429780416240510811032691400190056878439634150269652104892027214023\ 2160234898588827371428695339681755106287470907473718188014223487248498558198439\ 0946517083643689943061896502432883532796671901845276205510857076262042445096233\ 2320474470783119043449935144262550170177101737955112474615947173186270156557126\ 6295855125077711738338208419705893367323724453280456537178514960308802580284067\ 8478094146418386592266528068679788432506605379430462502871051049293472674712674\ 9989263462735816714693506049511034075540465817039348104675848562596776795976829\ 9409334026387269378365320912287718077451152622642548771835461108886360843272806\ 2277766430972838790567286180360486334648933714394152502594596525015209595361579\ 7713559579496572977565090269442808847976127666484700361964890604376193469427044\ 4070215317943583831051404915462608728486678750541674146731648999356381312866931\ 4276168635373056345866269578945682750658102359508148887789550739393653419373657\ 0084831850447568221544406759920313807707353997803633926733454954929666875992253\ 0893898086430606532961793164029612492673080638031873912596151131890359351266480\ 8185683667702865377423907465823909109555171797705807977892897524902307378017531\ 4268036391424472025772889178495007811788933662975043680421466819782427298069757\ 9391742229456683185815676816288797870624531246651727622758295493421483658868919\ 2995874020956960002435603052898298663868920769928340305497102665143223061252319\ 1513184387690382370620539920693394371688046642971147674356448637502684769814885\ 3105354063328845062012173302630676481322931561043551941761050712449024873277273\ 1120919458651374931909651624976916575538121985664322079786663003989386602386073\ 5785811439471587280089337416503379296583261843607313332752602360511552422722844\ 7251463863269369763762510196714380125691227784428426999440829152215904694437282\ 4986580852051865762929927755088331286726384187132777808744466438753526447335624\ 4113944762878097465068395298210817496795883645227334469487379347179071006497823\ 6466016680572034297929207446822322848665839522211446859572858403863377278030227\ 5915304978658739195136502462741958990883743873315942873720297706202071202130385\ 7217593321116241333042277374241635355358797706530964768588607730143277829032889\ 4795818404378858567772932094476778669357537460048142376741194182671636870481056\ 9111562156143575162905273512243500806046536689174581965494826086122607502930627\ 6147881326895528073614902252581968281505103331813212965966495815903042123877564\ 5990973296728066683849166257949747922905361845563741034791430771561168650484292\ 4902811029925296787352987678292690407887784802624792227507359484058174390862518\ 7794689004594206016860514277224448627246991114620014988066272353883780938062854\ 4384763053235070132028029488392008132135446450056134987017834271106158177289819\ 2906564986880810455622337030672542512772773302834984335957725759562247037077933\ 8714659303308862969944031833266579751467650271734629888377739784821870071802674\ 1265997158728035440478432478674907127921672898523588486943546692255101337606377\ 9151645972542571169684773399511589983490818882812639844005055462100669887926145\ 5821456531969690982725393451576040861347625877816586729441077535882416231577908\ 2538054746933540582469717674324523451498483027170396543887737637358191736582454\ 2733474904242629460112998819165637138471118491569150547681404117498014542657123\ 9420442544102807580600138819865061375928853903892264432294799028648284009959867\ 5963580999112695367601527173086852756572147583507122298296529564917835071750835\ 7413622825450556202709694174767992592297748886274113145876761475314568953280931\ 1705269648641018740767329698664923643738256547502281647192681555988319662984830\ 7776666840622314315884384910519058281816740764463033300119710293036455866594651\ 8690744752508378419876229904159117936827997606541860887216266548864923443910309\ 2325691063377596973905178112276466848679173604940439370333935190060938726839729\ 9246478483727274770977466693599784857120156789000241947269220974984127323147401\ 5499809203814598214164811763571478015542315996678385348544864069364105569135313\ 3523118405358134894093819182189869482538396098994282202759933963520621770534357\ 2073396250574216769465101608495601439303244304271576099527308684609204422226103\ 1542299844448021100981613338248273752189987382053151649271344981059501599748005\ 7159191220215448774875010347324619063394130303089239941198500622590218416440998\ 8173214324422108554248620896250260604398180189026317781146617454999771440665232\ 8638463638470016556181538610981881111817341913055050248603458567555856375117297\ 7429932907494423657966833270091836733897734790175924888566037995277154056908301\ 7311723894140326159612292912225191095948743805673381278538616491842786938417556\ 8980471008598683720336151751580970225662752001609561922299254017598785220385459\ 1377178397638981119848580329104875166692119510451489667776159824946872742066343\ 7593207852618922687285527671324883267794152912839165407968344190239094803676688\ 70 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 218-164-123-55.HINET-IP.hinet.net. (218.164.123.55) Time: Tue Feb 17 00:36:46 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Tue Feb 17 2004 00:36:42 on modular [Seed = 3500226743] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.6.87.13) Time: Tue Feb 17 05:22:49 2004 Input: ? hadamard Output: Magma V2.10-6 Tue Feb 17 2004 05:22:45 on modular [Seed = 1062114392] ------------------------------------- 9 matches: 1 S /magma/combinatorial-geometrical-incidence/\ incidence-structure-design/operation/hadamard 2 I /magma/combinatorial-geometrical-incidence/graph/\ group-code-design/code-design/HadamardGraph 3 I /magma/combinatorial-geometrical-incidence/\ incidence-structure-design/operation/hadamard/\ HadamardAutomorphismGroup 4 I /magma/combinatorial-geometrical-incidence/\ incidence-structure-design/operation/hadamard/HadamardColumnDesign 5 I /magma/combinatorial-geometrical-incidence/\ incidence-structure-design/operation/hadamard/HadamardNormalize 6 I /magma/combinatorial-geometrical-incidence/\ incidence-structure-design/operation/hadamard/HadamardRowDesign 7 I /magma/combinatorial-geometrical-incidence/\ incidence-structure-design/operation/hadamard/IsHadamard 8 I /magma/combinatorial-geometrical-incidence/\ incidence-structure-design/operation/hadamard/IsHadamardEquivalent 9 E /magma/combinatorial-geometrical-incidence/\ incidence-structure-design/operation/hadamard/Example-hadamard To view an entry, type ? followed by the number next to it Total time: 3.159 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Tue Feb 17 07:06:25 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f3:=630*x^8+630*y^8-322560+151*x^7-151*y^7+70*x^5-70*y^5+49*x^3-49*y^3+45*x-45*y; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Tue Feb 17 2004 07:06:21 on modular [Seed = 192497829] ------------------------------------- [ x^2 + 8*x + 31*y^2 - 8*y - 128, x*y + 2*x + 4*y^3 + 111*y^2 - 18*y - 448, 15*x + 60*y^2 - 15*y - 240, 4*y^4 + 20*y^2 - 144, 8*y^3 + 72*y^2 - 32*y - 288, 120*y^2 - 480 ] Total time: 3.089 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Tue Feb 17 07:07:29 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; Output: Magma V2.10-6 Tue Feb 17 2004 07:07:26 on modular [Seed = 910456283] ------------------------------------- Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ZWLEE.ECE.CMU.EDU. (128.2.132.182) Time: Tue Feb 17 10:35:47 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Tue Feb 17 2004 10:35:44 on modular [Seed = 3817969447] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9E0C8D5.dip.t-dialin.net. (217.224.200.213) Time: Tue Feb 17 12:14:47 2004 Input: > x := 1; > S := { }; > for i := 1 to 10 do > S join:= { x }; > x *:= 2; > end for; > S; Output: Magma V2.10-6 Tue Feb 17 2004 12:14:43 on modular [Seed = 4287493097] ------------------------------------- { 1, 2, 4, 8, 16, 32, 64, 128, 256, 512 } Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9E0C8D5.dip.t-dialin.net. (217.224.200.213) Time: Tue Feb 17 12:15:25 2004 Input: x := 1; S := { }; for i := 1 to 10 do S join:= { x }; x *:= 2; end for; S; Output: Magma V2.10-6 Tue Feb 17 2004 12:15:22 on modular [Seed = 3801149149] ------------------------------------- { 1, 2, 4, 8, 16, 32, 64, 128, 256, 512 } Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9E0C8D5.dip.t-dialin.net. (217.224.200.213) Time: Tue Feb 17 12:21:09 2004 Input: primeDivisors(120) Output: Magma V2.10-6 Tue Feb 17 2004 12:21:06 on modular [Seed = 510399370] ------------------------------------- >> primeDivisors(120); ^ User error: Identifier 'primeDivisors' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9E0C8D5.dip.t-dialin.net. (217.224.200.213) Time: Tue Feb 17 12:22:22 2004 Input: > primeDivisors := function(n) > if isPrime(n) then > return { n }; > else > return func< d | primeDivisors(d) join primeDivisors(n div d) > > ( rep{ d : d in [2..Isqrt(n)] | n mod d eq 0 }); > end if; > end function; > isPrime(1087); true; primeDivisors(120) Output: Magma V2.10-6 Tue Feb 17 2004 12:22:19 on modular [Seed = 125111002] ------------------------------------- >> if isPrime(n) then ^ User error: Identifier 'isPrime' has not been declared or assigned >> isPrime(1087); ^ User error: Identifier 'isPrime' has not been declared or assigned true >> primeDivisors(120); ^ User error: Identifier 'primeDivisors' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9E0C8D5.dip.t-dialin.net. (217.224.200.213) Time: Tue Feb 17 12:26:18 2004 Input: PrimeDivisors(120) Output: Magma V2.10-6 Tue Feb 17 2004 12:26:15 on modular [Seed = 159057832] ------------------------------------- [ 2, 3, 5 ] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9E0C8D5.dip.t-dialin.net. (217.224.200.213) Time: Tue Feb 17 12:26:37 2004 Input: PrimeDivisors(123456789) Output: Magma V2.10-6 Tue Feb 17 2004 12:26:34 on modular [Seed = 1045180642] ------------------------------------- [ 3, 3607, 3803 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9E0C8D5.dip.t-dialin.net. (217.224.200.213) Time: Tue Feb 17 12:27:54 2004 Input: PrimeBasis(123456789) Output: Magma V2.10-6 Tue Feb 17 2004 12:27:51 on modular [Seed = 609626917] ------------------------------------- [ 3, 3607, 3803 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9E0C8D5.dip.t-dialin.net. (217.224.200.213) Time: Tue Feb 17 12:30:18 2004 Input: SquarefreeFactorization(123456789) Output: Magma V2.10-6 Tue Feb 17 2004 12:30:15 on modular [Seed = 1411800037] ------------------------------------- 13717421 3 Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9E0C8D5.dip.t-dialin.net. (217.224.200.213) Time: Tue Feb 17 12:34:38 2004 Input: Facint(12) Output: Magma V2.10-6 Tue Feb 17 2004 12:34:35 on modular [Seed = 1512590055] ------------------------------------- >> Facint(12); ^ Runtime error in 'Facint': Bad argument types Argument types given: RngIntElt Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9E0C8D5.dip.t-dialin.net. (217.224.200.213) Time: Tue Feb 17 12:35:44 2004 Input: Divisors(12) Output: Magma V2.10-6 Tue Feb 17 2004 12:35:41 on modular [Seed = 1329422260] ------------------------------------- [ 1, 2, 3, 4, 6, 12 ] Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Feb 17 18:56:13 2004 Input: F := NumberField(x^3-2) Output: Magma V2.10-6 Tue Feb 17 2004 18:56:10 on modular [Seed = 2649716636] ------------------------------------- >> F := NumberField(x^3-2) ^ User error: Identifier 'x' has not been declared or assigned Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Feb 17 18:56:38 2004 Input: F := NumberField(x^3-2) R := RingOfIntegers(F) Output: Magma V2.10-6 Tue Feb 17 2004 18:56:35 on modular [Seed = 2498133692] ------------------------------------- >> R := RingOfIntegers(F); ^ User error: bad syntax Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Feb 17 18:56:49 2004 Input: F := NumberField(x^3-2); R := RingOfIntegers(F); Output: Magma V2.10-6 Tue Feb 17 2004 18:56:46 on modular [Seed = 2213636518] ------------------------------------- >> F := NumberField(x^3-2); ^ User error: Identifier 'x' has not been declared or assigned >> R := RingOfIntegers(F);; ^ User error: Identifier 'F' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Feb 17 18:59:03 2004 Input: Q := PolynomialRing(Rationals()); F := NumberField(x^3-2); R := RingOfIntegers(F); Output: Magma V2.10-6 Tue Feb 17 2004 18:58:59 on modular [Seed = 3184482149] ------------------------------------- Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Feb 17 18:59:14 2004 Input: Q := PolynomialRing(Rationals()); F := NumberField(x^3-2); R := RingOfIntegers(F); Output: Magma V2.10-6 Tue Feb 17 2004 18:59:11 on modular [Seed = 3032899168] ------------------------------------- Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Feb 17 19:02:11 2004 Input: Q := PolynomialRing(Rationals()); F := NumberField(x^3-2); R := RingOfIntegers(F); Integers(K) : FldNum -> RngOrd; Output: Magma V2.10-6 Tue Feb 17 2004 19:02:08 on modular [Seed = 3384484434] ------------------------------------- >> Integers(K) : FldNum -> RngOrd;; ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Feb 17 19:02:20 2004 Input: Q := PolynomialRing(Rationals()); F := NumberField(x^3-2); R := RingOfIntegers(F); Integers(K) : FldNum -> RngOrd Output: Magma V2.10-6 Tue Feb 17 2004 19:02:17 on modular [Seed = 3232901970] ------------------------------------- >> Integers(K) : FldNum -> RngOrd; ^ User error: bad syntax Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Feb 17 19:02:32 2004 Input: Q := PolynomialRing(Rationals()) F := NumberField(x^3-2) R := RingOfIntegers(F) Output: Magma V2.10-6 Tue Feb 17 2004 19:02:29 on modular [Seed = 4287435889] ------------------------------------- >> F := NumberField(x^3-2) ^ User error: bad syntax >> R := RingOfIntegers(F) ^ User error: Identifier 'F' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Feb 17 19:02:43 2004 Input: Q := PolynomialRing(Rationals()); F := NumberField(x^3-2); R := RingOfIntegers(F); Output: Magma V2.10-6 Tue Feb 17 2004 19:02:40 on modular [Seed = 4135853389] ------------------------------------- Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Feb 17 19:28:16 2004 Input: Q := PolynomialRing(Rationals()); F := NumberField(x^3-2); R := RingOfIntegers(F); Basis(R); Output: Magma V2.10-6 Tue Feb 17 2004 19:28:13 on modular [Seed = 74904965] ------------------------------------- [ R.1, R.2, R.3 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Feb 17 19:30:18 2004 Input: Q := PolynomialRing(Rationals()); F := NumberField(x^3-2); R := RingOfIntegers(F); Basis(R); R.1; Output: Magma V2.10-6 Tue Feb 17 2004 19:30:15 on modular [Seed = 877053503] ------------------------------------- [ R.1, R.2, R.3 ] R.1 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Feb 17 19:30:41 2004 Input: Q := PolynomialRing(Rationals()); F := NumberField(x^3-2); R := RingOfIntegers(F); Basis(R); R.1 =1; Output: Magma V2.10-6 Tue Feb 17 2004 19:30:37 on modular [Seed = 761257756] ------------------------------------- [ R.1, R.2, R.3 ] R.1 = R.1 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Feb 17 19:36:08 2004 Input: Q := PolynomialRing(Rationals()); F := NumberField(x^3-2); R := RingOfIntegers(F); MaximalOrder(F) Output: Magma V2.10-6 Tue Feb 17 2004 19:36:05 on modular [Seed = 592564298] ------------------------------------- Maximal Equation Order with defining polynomial x^3 - 2 over its ground order Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Feb 17 19:39:14 2004 Input: Q := PolynomialRing(Rationals()); K := AdjoinRoot(Q, 2^(1/3); R := RingOfIntegers(K); MaximalOrder(K) Output: Magma V2.10-6 Tue Feb 17 2004 19:39:10 on modular [Seed = 1428660582] ------------------------------------- >> K := AdjoinRoot(Q, 2^(1/3); ^ User error: bad syntax >> R := RingOfIntegers(K); ^ User error: Identifier 'K' has not been declared or assigned >> MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Feb 17 19:42:06 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^3-2); E := EquationOrder(K); O := MaximalOrder(K); Index(O, E); Output: Magma V2.10-6 Tue Feb 17 2004 19:42:03 on modular [Seed = 1194701696] ------------------------------------- 1 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Feb 17 19:42:16 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^3-2); E := EquationOrder(K); O := MaximalOrder(K); Output: Magma V2.10-6 Tue Feb 17 2004 19:42:13 on modular [Seed = 2013957249] ------------------------------------- Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Feb 17 19:42:26 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^3-2); E := EquationOrder(K); O := MaximalOrder(K); O Output: Magma V2.10-6 Tue Feb 17 2004 19:42:23 on modular [Seed = 1896056194] ------------------------------------- Maximal Equation Order with defining polynomial x^3 - 2 over its ground order Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Feb 17 19:54:44 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^3-2); E := EquationOrder(K); O := MaximalOrder(K); IntegralBasis(K); Output: Magma V2.10-6 Tue Feb 17 2004 19:54:41 on modular [Seed = 2565500757] ------------------------------------- [ 1, K.1, K.1^2 ] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Feb 17 20:05:34 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^3-2); E := EquationOrder(K); O := MaximalOrder(K); IntegralBasis(K); Output: Magma V2.10-6 Tue Feb 17 2004 20:05:30 on modular [Seed = 2900252395] ------------------------------------- >> E := EquationOrder(K); ^ User error: bad syntax >> O := MaximalOrder(K); ^ User error: bad syntax [ 1, y, y^2 ] Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Feb 17 20:06:27 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^3-2); E := EquationOrder(K); O := MaximalOrder(K); IntegralBasis(K); Output: Magma V2.10-6 Tue Feb 17 2004 20:06:24 on modular [Seed = 2798935082] ------------------------------------- >> E := EquationOrder(K); ^ User error: bad syntax >> O := MaximalOrder(K); ^ User error: bad syntax [ 1, x, x^2 ] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Feb 17 20:10:32 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^3-2); print IntegralBasis(K); Output: Magma V2.10-6 Tue Feb 17 2004 20:10:29 on modular [Seed = 4102426477] ------------------------------------- [ 1, y, y^2 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:02:38 2004 Input: d := 2 ; Output: Magma V2.10-6 Tue Feb 17 2004 21:02:34 on modular [Seed = 1980035537] ------------------------------------- Total time: 3.109 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:03:03 2004 Input: d := 2; Q(Sqrt(d)); Q; Output: Magma V2.10-6 Tue Feb 17 2004 21:03:00 on modular [Seed = 1696064172] ------------------------------------- >> Q(Sqrt(d)); ^ User error: Identifier 'Q' has not been declared or assigned >> Q; ^ User error: Identifier 'Q' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:06:44 2004 Input: d := 2; Q := RationalField(); F := Q(Sqrt(d)); Q; IntegerRing(F); Output: Magma V2.10-6 Tue Feb 17 2004 21:06:41 on modular [Seed = 2514951481] ------------------------------------- >> F := Q(Sqrt(d)); ^ Runtime error: Bad argument types Argument types given: FldPrElt, FldRat Rational Field >> IntegerRing(F);; ^ User error: Identifier 'F' has not been declared or assigned Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:10:23 2004 Input: d := 2; Q := RationalField(); R := QuadraticField(d); Q; IntegerRing(F); Output: Magma V2.10-6 Tue Feb 17 2004 21:10:20 on modular [Seed = 2280984086] ------------------------------------- Rational Field >> IntegerRing(F);; ^ User error: Identifier 'F' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:10:32 2004 Input: d := 2; Q := RationalField(); R := QuadraticField(d); Q; IntegerRing(R); Output: Magma V2.10-6 Tue Feb 17 2004 21:10:29 on modular [Seed = 3100258608] ------------------------------------- Rational Field Maximal Equation Order of R Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:11:16 2004 Input: d := 2; Q := RationalField(); R := QuadraticField(d); Q; IntegerRing(R); RingOfIntegers(R); Output: Magma V2.10-6 Tue Feb 17 2004 21:11:13 on modular [Seed = 3015785071] ------------------------------------- Rational Field Maximal Equation Order of R Maximal Equation Order of R Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:11:34 2004 Input: d := 2; Q := RationalField(); R := QuadraticField(d); Q; IntegerRing(R); RingOfIntegers(R); Output: Magma V2.10-6 Tue Feb 17 2004 21:11:31 on modular [Seed = 2866291556] ------------------------------------- Rational Field Maximal Equation Order of R >> RingOfIntegers(R);; ^ User error: bad syntax Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:11:49 2004 Input: d := 2; Q := RationalField(); R := QuadraticField(d); Q; IntegerRing(R); RingOfIntegers(R); Output: Magma V2.10-6 Tue Feb 17 2004 21:11:46 on modular [Seed = 3719255074] ------------------------------------- Rational Field Maximal Equation Order of R Maximal Equation Order of R Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host d66-222-151-70.abhsia.telus.net. (66.222.151.70) Time: Tue Feb 17 21:22:04 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Tue Feb 17 2004 21:22:01 on modular [Seed = 4270617258] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:40:36 2004 Input: N := NumberField(x^3 -2); Output: Magma V2.10-6 Tue Feb 17 2004 21:40:33 on modular [Seed = 2548369192] ------------------------------------- >> N := NumberField(x^3 -2);; ^ User error: Identifier 'x' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:41:32 2004 Input: N := NumberField(x^3 -2); Output: Magma V2.10-6 Tue Feb 17 2004 21:41:29 on modular [Seed = 2365463627] ------------------------------------- >> N := NumberField(x^3 -2);; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:43:01 2004 Input: PQ := PlynomialRing(RationalField()); N := NumberField(x^3 -2); Output: Magma V2.10-6 Tue Feb 17 2004 21:42:58 on modular [Seed = 2247562409] ------------------------------------- >> PQ := PlynomialRing(RationalField()); ^ User error: Identifier 'PlynomialRing' has not been declared or assigned >> N := NumberField(x^3 -2);; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:43:11 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^3 -2); Output: Magma V2.10-6 Tue Feb 17 2004 21:43:08 on modular [Seed = 3150523033] ------------------------------------- Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:43:30 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^3 -2); RingOfIntegers(N); Output: Magma V2.10-6 Tue Feb 17 2004 21:43:27 on modular [Seed = 2982355168] ------------------------------------- Maximal Equation Order with defining polynomial x^3 - 2 over its ground order Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:44:03 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^3 -2); print RingOfIntegers(N); Output: Magma V2.10-6 Tue Feb 17 2004 21:44:00 on modular [Seed = 2798925768] ------------------------------------- Maximal Equation Order with defining polynomial x^3 - 2 over its ground order Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:44:27 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^3 -2); P := RingOfIntegers(N); Output: Magma V2.10-6 Tue Feb 17 2004 21:44:24 on modular [Seed = 3752676937] ------------------------------------- >> P := RingOfIntegers(N);; ^ Runtime error in 'Name': Bad argument types Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:44:40 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^3 -2); P := RingOfIntegers(N); Output: Magma V2.10-6 Tue Feb 17 2004 21:44:37 on modular [Seed = 3567666527] ------------------------------------- Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:44:54 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^3 -2); P := RingOfIntegers(N); print P; Output: Magma V2.10-6 Tue Feb 17 2004 21:44:50 on modular [Seed = 3451870321] ------------------------------------- Maximal Equation Order with defining polynomial x^3 - 2 over its ground order Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:45:38 2004 Input: PQ := RationalField(); N := NumberField(x^3 -2); P := RingOfIntegers(N); print P; Output: Magma V2.10-6 Tue Feb 17 2004 21:45:35 on modular [Seed = 4270616367] ------------------------------------- >> PQ := RationalField(); ^ Runtime error in 'Name': Bad argument types >> N := NumberField(x^3 -2); ^ User error: Identifier 'x' has not been declared or assigned >> P := RingOfIntegers(N); ^ User error: Identifier 'N' has not been declared or assigned >> print P;; ^ User error: Identifier 'P' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:46:40 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 - 3); P := RingOfIntegers(N); print P; Output: Magma V2.10-6 Tue Feb 17 2004 21:46:37 on modular [Seed = 4102448871] ------------------------------------- Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:47:01 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 + 3); P := RingOfIntegers(N); print P; Output: Magma V2.10-6 Tue Feb 17 2004 21:46:58 on modular [Seed = 3986653137] ------------------------------------- Maximal Order of Equation Order with defining polynomial x^2 + 3 over its ground order Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:47:35 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^3 - 2); P := RingOfIntegers(N); print P; Output: Magma V2.10-6 Tue Feb 17 2004 21:47:32 on modular [Seed = 3817959865] ------------------------------------- Maximal Equation Order with defining polynomial x^3 - 2 over its ground order Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:56:13 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^3 - 2); w; P := RingOfIntegers(N); print P; Output: Magma V2.10-6 Tue Feb 17 2004 21:56:10 on modular [Seed = 159096156] ------------------------------------- w Maximal Equation Order with defining polynomial x^3 - 2 over its ground order Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:56:29 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^3 - 2); print w; P := RingOfIntegers(N); print P; Output: Magma V2.10-6 Tue Feb 17 2004 21:56:26 on modular [Seed = 7509061] ------------------------------------- w Maximal Equation Order with defining polynomial x^3 - 2 over its ground order Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:01:49 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^3 - 2); print w^3; P := RingOfIntegers(N); print P; Output: Magma V2.10-6 Tue Feb 17 2004 22:01:46 on modular [Seed = 1512624095] ------------------------------------- 2 Maximal Equation Order with defining polynomial x^3 - 2 over its ground order Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:02:43 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^3 - 2); print w^2; P := RingOfIntegers(N); print P; Output: Magma V2.10-6 Tue Feb 17 2004 22:02:40 on modular [Seed = 1344456095] ------------------------------------- w^2 Maximal Equation Order with defining polynomial x^3 - 2 over its ground order Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:06:42 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^3 - 2); print w^2; P := MaximalOrder(N); print P; Output: Magma V2.10-6 Tue Feb 17 2004 22:06:39 on modular [Seed = 2098195421] ------------------------------------- w^2 Maximal Equation Order with defining polynomial x^3 - 2 over its ground order Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:07:18 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 + 3); print w^2; P := MaximalOrder(N); print P; Output: Magma V2.10-6 Tue Feb 17 2004 22:07:15 on modular [Seed = 1946608264] ------------------------------------- -3 Maximal Order of Equation Order with defining polynomial x^2 + 3 over its ground order Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:07:47 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 - 3); print w^2; P := MaximalOrder(N); print P; Output: Magma V2.10-6 Tue Feb 17 2004 22:07:44 on modular [Seed = 1780022645] ------------------------------------- 3 Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:08:36 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 - 3); print w^2; P := IntegerRing(N); print P; Output: Magma V2.10-6 Tue Feb 17 2004 22:08:33 on modular [Seed = 1611855694] ------------------------------------- 3 Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:09:07 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 - 3); print w^2; P := IntegerRing(N); print P;print P;print P;print P;print P;print P; Output: Magma V2.10-6 Tue Feb 17 2004 22:09:04 on modular [Seed = 2548367576] ------------------------------------- 3 Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:12:27 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 - 3); print w^2; P := IntegerRing(N); IsIntegral(N, w); print P;print P;print P;print P;print P;print P; Output: Magma V2.10-6 Tue Feb 17 2004 22:12:24 on modular [Seed = 2230721667] ------------------------------------- 3 >> IsIntegral(N, w); ^ Runtime error in 'IsIntegral': Bad argument types Argument types given: FldNum, FldNumElt Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:12:47 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 - 3); print w^2; P := IntegerRing(N); IsIntegral(w); print P;print P;print P;print P;print P;print P; Output: Magma V2.10-6 Tue Feb 17 2004 22:12:43 on modular [Seed = 3150521231] ------------------------------------- 3 true Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:13:16 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 - 3); print w^2; P := IntegerRing(N); IsIntegral(w); IsIntegral(w/2); print P;print P;print P;print P;print P;print P; Output: Magma V2.10-6 Tue Feb 17 2004 22:13:13 on modular [Seed = 2982357479] ------------------------------------- 3 true false Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:13:41 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 - 3); print w^2; P := IntegerRing(N); IsIntegral(w); IsIntegral(w/3); print P;print P;print P;print P;print P;print P; Output: Magma V2.10-6 Tue Feb 17 2004 22:13:38 on modular [Seed = 2832871637] ------------------------------------- 3 true false Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:14:02 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 - 3); print w^2; P := IntegerRing(N); IsIntegral(w); IsIntegral(2w); IsIntegral(w + 2); IsIntegral(w + 3); IsIntegral(w/3); print P;print P;print P;print P;print P;print P; Output: Magma V2.10-6 Tue Feb 17 2004 22:13:59 on modular [Seed = 3735832246] ------------------------------------- 3 true >> IsIntegral(2w); ^ User error: bad syntax true true false Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:14:13 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 - 3); print w^2; P := IntegerRing(N); IsIntegral(w); IsIntegral(2*w); IsIntegral(w + 2); IsIntegral(w + 3); IsIntegral(w/3); print P;print P;print P;print P;print P;print P; Output: Magma V2.10-6 Tue Feb 17 2004 22:14:09 on modular [Seed = 3584511304] ------------------------------------- 3 true true true true false Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:14:35 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 - 3); print w^2; P := IntegerRing(N); IsIntegral(w); IsIntegral(2*w); IsIntegral(w + 2); IsIntegral(w + 3); IsIntegral(w div 3); print P;print P;print P;print P;print P;print P; Output: Magma V2.10-6 Tue Feb 17 2004 22:14:32 on modular [Seed = 3435025483] ------------------------------------- 3 true true true true >> IsIntegral(w div 3); ^ Runtime error in 'div': Bad argument types Argument types given: FldNumElt, FldNumElt Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:14:56 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 - 3); print w^2; P := IntegerRing(N); IsIntegral(w); IsIntegral(2*w); IsIntegral(w + 2); IsIntegral(w + 3); IsIntegral(w div 2); IsIntegral(w div 3); print P;print P;print P;print P;print P;print P; Output: Magma V2.10-6 Tue Feb 17 2004 22:14:53 on modular [Seed = 3283180401] ------------------------------------- 3 true true true true >> IsIntegral(w div 2); ^ Runtime error in 'div': Bad argument types Argument types given: FldNumElt, FldNumElt >> IsIntegral(w div 3); ^ Runtime error in 'div': Bad argument types Argument types given: FldNumElt, FldNumElt Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:15:11 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 - 3); print w^2; P := IntegerRing(N); IsIntegral(w); IsIntegral(2*w); IsIntegral(w + 2); IsIntegral(w + 3); IsIntegral(w / 2); IsIntegral(w div 3); print P;print P;print P;print P;print P;print P; Output: Magma V2.10-6 Tue Feb 17 2004 22:15:08 on modular [Seed = 4135874133] ------------------------------------- 3 true true true true false >> IsIntegral(w div 3); ^ Runtime error in 'div': Bad argument types Argument types given: FldNumElt, FldNumElt Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:17:23 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 - 3); print w^2; P := IntegerRing(N); IsIntegral(w); IsIntegral(2*w); IsIntegral(w + 1/2); IsIntegral(w + 3); IsIntegral(w / 2); IsIntegral(w div 3); print P;print P;print P;print P;print P;print P; Output: Magma V2.10-6 Tue Feb 17 2004 22:17:20 on modular [Seed = 3969807795] ------------------------------------- 3 true true false true false >> IsIntegral(w div 3); ^ Runtime error in 'div': Bad argument types Argument types given: FldNumElt, FldNumElt Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:17:41 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 - 3); print w^2; P := IntegerRing(N); IsIntegral(w^2); IsIntegral(2*w); IsIntegral(w + 1/2); IsIntegral(w + 3); IsIntegral(w / 2); IsIntegral(w div 3); print P;print P;print P;print P;print P;print P; Output: Magma V2.10-6 Tue Feb 17 2004 22:17:38 on modular [Seed = 3817962158] ------------------------------------- 3 true true false true false >> IsIntegral(w div 3); ^ Runtime error in 'div': Bad argument types Argument types given: FldNumElt, FldNumElt Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:21:16 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 - 3); print w^2; P := IntegerRing(N); Trace(1 + w + w^2); IsIntegral(w^2); IsIntegral(2*w); IsIntegral(w + 1/2); IsIntegral(w + 3); IsIntegral(w / 2); IsIntegral(w div 3); print P;print P;print P;print P;print P;print P; Output: Magma V2.10-6 Tue Feb 17 2004 22:21:13 on modular [Seed = 777827367] ------------------------------------- 3 8 true true false true false >> IsIntegral(w div 3); ^ Runtime error in 'div': Bad argument types Argument types given: FldNumElt, FldNumElt Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:21:52 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 - 3); print w^2; P := IntegerRing(N); Trace(1 + w + w^2); Trace(1); Trace(w); Trace(w^2); IsIntegral(w^2); IsIntegral(2*w); IsIntegral(w + 1/2); IsIntegral(w + 3); IsIntegral(w / 2); IsIntegral(w div 3); print P;print P;print P;print P;print P;print P; Output: Magma V2.10-6 Tue Feb 17 2004 22:21:49 on modular [Seed = 927313242] ------------------------------------- 3 8 1 0 6 true true false true false >> IsIntegral(w div 3); ^ Runtime error in 'div': Bad argument types Argument types given: FldNumElt, FldNumElt Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:29:30 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 - 3); print w^2; P := IntegerRing(N); Basis(P); Output: Magma V2.10-6 Tue Feb 17 2004 22:29:27 on modular [Seed = 226464058] ------------------------------------- 3 [ P.1, P.2 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:30:09 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 + 3); print w^2; P := IntegerRing(N); Basis(P); Output: Magma V2.10-6 Tue Feb 17 2004 22:30:06 on modular [Seed = 493846787] ------------------------------------- -3 [ P.1, P.2 ] Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:30:26 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^3 + 2); print w^2; P := IntegerRing(N); Basis(P); Output: Magma V2.10-6 Tue Feb 17 2004 22:30:23 on modular [Seed = 1712650761] ------------------------------------- w^2 [ P.1, P.2, P.3 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:30:45 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^3 + 2); print w^2; P := IntegerRing(N); Basis(P); P.1; P.2; Output: Magma V2.10-6 Tue Feb 17 2004 22:30:43 on modular [Seed = 1864233772] ------------------------------------- w^2 [ P.1, P.2, P.3 ] P.1 P.2 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:31:39 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^3 + 2); print w^2; P := IntegerRing(N); Basis(P); IntegralBasis(N); Output: Magma V2.10-6 Tue Feb 17 2004 22:31:36 on modular [Seed = 2013979840] ------------------------------------- w^2 [ P.1, P.2, P.3 ] [ 1, w, w^2 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:31:58 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^3 + 2); print w^2; P := IntegerRing(N); Basis(P); print w^2; IntegralBasis(N); Output: Magma V2.10-6 Tue Feb 17 2004 22:31:55 on modular [Seed = 1110499017] ------------------------------------- w^2 [ P.1, P.2, P.3 ] w^2 [ 1, w, w^2 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:32:25 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^3 - 2); print w^2; P := IntegerRing(N); Basis(P); print w^2; IntegralBasis(N); Output: Magma V2.10-6 Tue Feb 17 2004 22:32:22 on modular [Seed = 1329451945] ------------------------------------- w^2 [ P.1, P.2, P.3 ] w^2 [ 1, w, w^2 ] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:32:42 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 - 3); print w^2; P := IntegerRing(N); Basis(P); print w^2; IntegralBasis(N); Output: Magma V2.10-6 Tue Feb 17 2004 22:32:39 on modular [Seed = 1479197871] ------------------------------------- 3 [ P.1, P.2 ] 3 [ 1, w ] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:32:58 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 + 3); print w^2; P := IntegerRing(N); Basis(P); print w^2; IntegralBasis(N); Output: Magma V2.10-6 Tue Feb 17 2004 22:32:55 on modular [Seed = 2714975590] ------------------------------------- -3 [ P.1, P.2 ] -3 [ 1, 1/2*(w + 1) ] Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:33:48 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 + 2); IntegralBasis(N); Output: Magma V2.10-6 Tue Feb 17 2004 22:33:45 on modular [Seed = 2883139218] ------------------------------------- [ 1, w ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:34:01 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^3 + 2); IntegralBasis(N); Output: Magma V2.10-6 Tue Feb 17 2004 22:33:58 on modular [Seed = 3032885682] ------------------------------------- [ 1, w, w^2 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Wed Feb 18 02:50:41 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Wed Feb 18 2004 02:50:37 on modular [Seed = 826435679] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Wed Feb 18 02:53:01 2004 Input: E=EllipticCurve([1,2]); E=BaseChange(E, GF(17)); Order(E); Output: Magma V2.10-6 Wed Feb 18 2004 02:52:58 on modular [Seed = 1061971654] ------------------------------------- >> E=EllipticCurve([1,2]); ^ User error: Identifier 'E' has not been declared or assigned >> E=BaseChange(E, GF(17)); ^ User error: Identifier 'E' has not been declared or assigned >> Order(E);; ^ User error: Identifier 'E' has not been declared or assigned Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Wed Feb 18 02:53:19 2004 Input: E:=EllipticCurve([1,2]); E:=BaseChange(E, GF(17)); Order(E); Output: Magma V2.10-6 Wed Feb 18 2004 02:53:16 on modular [Seed = 108355529] ------------------------------------- >> E:=BaseChange(E, GF(17)); ^ Runtime error in 'BaseChange': Coercion of equations is not possible >> Order(E);; ^ Runtime error in 'Order': Algorithm does not work for this ring Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Wed Feb 18 02:53:46 2004 Input: E:=EllipticCurve([1,2]); E:=ChangeRing(E, GF(17)); Order(E); Output: Magma V2.10-6 Wed Feb 18 2004 02:53:43 on modular [Seed = 274942516] ------------------------------------- 24 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Wed Feb 18 02:54:21 2004 Input: E:=EllipticCurve([1,2]); E:=ChangeRing(E, GF(19)); Order(E); Output: Magma V2.10-6 Wed Feb 18 2004 02:54:18 on modular [Seed = 527189270] ------------------------------------- 12 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 03:42:46 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 18 2004 03:42:43 on modular [Seed = 2314923049] ------------------------------------- [ x^2 + 8*x + 232315781992*y^3 + 5693103461359*y^2 - 929263127976*y - 22772413845440, x*y + 2*x + 65228091924*y^3 + 4892924850951*y^2 - 260912367698*y - 19571699403808, 15*x + 75708865464*y^3 + 2052062158236*y^2 - 302835461871*y - 8208248632944, 4*y^4 + 30002386104*y^3 + 1969993642436*y^2 - 120009544416*y - 7879974569808, 388922698520*y^3 + 3500304286680*y^2 - 1555690794080*y - 14001217146720, 5833840477800*y^2 - 23335361911200 ] Total time: 3.039 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host unallocated.star.net.uk. (62.173.118.42) Time: Wed Feb 18 04:48:44 2004 Input: integrate( x ) Output: Magma V2.10-6 Wed Feb 18 2004 04:48:40 on modular [Seed = 1796743093] ------------------------------------- >> integrate( x ); ^ User error: Identifier 'x' has not been declared or assigned Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 05:26:52 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f3:=630*x^8+630*y^8-322560+151*x^7-151*y^7+70*x^5-70*y^5+49*x^3-49*y^3+45*x-45*y; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 18 2004 05:26:49 on modular [Seed = 2498226523] ------------------------------------- [ x^2 + 8*x + 31*y^2 - 8*y - 128, x*y + 2*x + 4*y^3 + 111*y^2 - 18*y - 448, 15*x + 60*y^2 - 15*y - 240, 4*y^4 + 20*y^2 - 144, 8*y^3 + 72*y^2 - 32*y - 288, 120*y^2 - 480 ] Total time: 2.979 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:02:30 2004 Input: Floor(3.141592); Output: Magma V2.10-6 Wed Feb 18 2004 06:02:27 on modular [Seed = 843134038] ------------------------------------- 3 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:04:37 2004 Input: x:=2; y:=3; assigned x; assigned y; Output: Magma V2.10-6 Wed Feb 18 2004 06:04:33 on modular [Seed = 125043169] ------------------------------------- true true Total time: 3.409 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:05:04 2004 Input: x:=2; y:=3; assigned x; assigned y; delete x; assigned x; assigned y; Output: Magma V2.10-6 Wed Feb 18 2004 06:05:01 on modular [Seed = 158994419] ------------------------------------- true true false true Total time: 3.179 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:05:17 2004 Input: x:=2; y:=3; assigned x; assigned y; x; delete x; assigned x; assigned y; Output: Magma V2.10-6 Wed Feb 18 2004 06:05:14 on modular [Seed = 274929373] ------------------------------------- true true 2 false true Total time: 3.189 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:07:25 2004 Input: x:=2; y:=3; assigned x; assigned y; x; print y; delete x; assigned x; assigned y; Output: Magma V2.10-6 Wed Feb 18 2004 06:07:22 on modular [Seed = 1662018606] ------------------------------------- true true 2 3 false true Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:07:40 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f3:=630*x^8+630*y^8-322560+151*x^7-151*y^7+70*x^5-70*y^5+49*x^3-49*y^3+45*x-45*y; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 18 2004 06:07:37 on modular [Seed = 1780051252] ------------------------------------- [ x^2 + 8*x + 31*y^2 - 8*y - 128, x*y + 2*x + 4*y^3 + 111*y^2 - 18*y - 448, 15*x + 60*y^2 - 15*y - 240, 4*y^4 + 20*y^2 - 144, 8*y^3 + 72*y^2 - 32*y - 288, 120*y^2 - 480 ] Total time: 2.959 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:08:22 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f3:=645120*x^8+645120*y^8-330303015+2251776*x^7-154624*y^7-1075200*x^5-71680*y^5+ 182784*x^3-50176*y^3+44280*x-46080*y+1835008*x^6-1003520*x^4+116032*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 18 2004 06:08:19 on modular [Seed = 1895986933] ------------------------------------- [ x^2 + 8*x + y^2 + 14549527*y + 2648015362, x*y + 2*x + 14549533*y + 14695030346, 15*x + 14549520*y + 14695030350, y^3 + 9*y^2 + 14549531*y + 11683276569, 15*y^2 + 3011753685, 14549535*y + 5659769115, 15058768725 ] Total time: 2.969 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:08:35 2004 Input: x:=2; y:=3; assigned x; assigned y; x; print y; x and y; Output: Magma V2.10-6 Wed Feb 18 2004 06:08:32 on modular [Seed = 2014019567] ------------------------------------- true true 2 3 >> x and y;; ^ Runtime error: Expected a logical for the 'and' operator Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:09:01 2004 Input: x:=true; y:=false; assigned x; assigned y; x; print y; x and y; Output: Magma V2.10-6 Wed Feb 18 2004 06:08:58 on modular [Seed = 1312639395] ------------------------------------- true true true false false Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:09:12 2004 Input: x:=true; y:=false; assigned x; assigned y; x; print y; x or y; Output: Magma V2.10-6 Wed Feb 18 2004 06:09:09 on modular [Seed = 1428574887] ------------------------------------- true true true false true Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:09:57 2004 Input: GCD(12,4); Output: Magma V2.10-6 Wed Feb 18 2004 06:09:54 on modular [Seed = 1529369470] ------------------------------------- 4 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:10:12 2004 Input: GCD(12,4); GCD(120,2); Output: Magma V2.10-6 Wed Feb 18 2004 06:10:09 on modular [Seed = 2883101597] ------------------------------------- 4 2 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:10:40 2004 Input: GCD(12,4); GCD(120,2); x:=[1,2,3,6,3]; Output: Magma V2.10-6 Wed Feb 18 2004 06:10:37 on modular [Seed = 2965616826] ------------------------------------- 4 2 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:10:50 2004 Input: GCD(12,4); GCD(120,2); x:=[1,2,3,6,3]; x; Output: Magma V2.10-6 Wed Feb 18 2004 06:10:47 on modular [Seed = 2280951703] ------------------------------------- 4 2 [ 1, 2, 3, 6, 3 ] Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:11:48 2004 Input: GCD(12,4); GCD(120,2); x:=[1,2,3,6,3]; x; Sort x; Output: Magma V2.10-6 Wed Feb 18 2004 06:11:45 on modular [Seed = 2398979800] ------------------------------------- 4 2 [ 1, 2, 3, 6, 3 ] >> Sort x;; ^ User error: bad syntax Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:12:02 2004 Input: GCD(12,4); GCD(120,2); x:=[1,2,3,6,3]; x; Sort (x); Output: Magma V2.10-6 Wed Feb 18 2004 06:11:59 on modular [Seed = 2514918861] ------------------------------------- 4 2 [ 1, 2, 3, 6, 3 ] [ 1, 2, 3, 3, 6 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:12:23 2004 Input: GCD(12,4); GCD(120,2); x:=[1,2,3,6,3]; x; Sort (x); Min (x); Output: Magma V2.10-6 Wed Feb 18 2004 06:12:20 on modular [Seed = 2615710504] ------------------------------------- 4 2 [ 1, 2, 3, 6, 3 ] [ 1, 2, 3, 3, 6 ] 1 1 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:12:51 2004 Input: GCD(12,4); GCD(120,2); x:=[1,2,3,6,3,6]; x; Sort (x); Min (x); Max (x); Output: Magma V2.10-6 Wed Feb 18 2004 06:12:48 on modular [Seed = 3801213557] ------------------------------------- 4 2 [ 1, 2, 3, 6, 3, 6 ] [ 1, 2, 3, 3, 6, 6 ] 1 1 6 4 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:13:23 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f3:=630*x^8+630*y^8-322560+151*x^7-151*y^7+70*x^5-70*y^5+49*x^3-49*y^3+45*x-45*y; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 18 2004 06:13:20 on modular [Seed = 3919241502] ------------------------------------- [ x^2 + 8*x + 31*y^2 - 8*y - 128, x*y + 2*x + 4*y^3 + 111*y^2 - 18*y - 448, 15*x + 60*y^2 - 15*y - 240, 4*y^4 + 20*y^2 - 144, 8*y^3 + 72*y^2 - 32*y - 288, 120*y^2 - 480 ] Total time: 3.009 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:13:49 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f3:=645120*x^8+645120*y^8-330303015+2251776*x^7-154624*y^7-1075200*x^5-71680*y^5+ 182784*x^3-50176*y^3+44280*x-46080*y+1835008*x^6-1003520*x^4+116032*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 18 2004 06:13:46 on modular [Seed = 4035180605] ------------------------------------- [ x^2 + 8*x + y^2 + 14549527*y + 2648015362, x*y + 2*x + 14549533*y + 14695030346, 15*x + 14549520*y + 14695030350, y^3 + 9*y^2 + 14549531*y + 11683276569, 15*y^2 + 3011753685, 14549535*y + 5659769115, 15058768725 ] Total time: 2.999 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:15:21 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f3:=645120*x^8+645120*y^8-330303015+2251776*x^7-154624*y^7-1075200*x^5-71680*y^5+ 182784*x^3-50176*y^3+44280*x-46080*y+1835008*x^6-1003520*x^4+116032*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(14549535); Factorization(15058768725); Output: Magma V2.10-6 Wed Feb 18 2004 06:15:18 on modular [Seed = 3249719456] ------------------------------------- [ x^2 + 8*x + y^2 + 14549527*y + 2648015362, x*y + 2*x + 14549533*y + 14695030346, 15*x + 14549520*y + 14695030350, y^3 + 9*y^2 + 14549531*y + 11683276569, 15*y^2 + 3011753685, 14549535*y + 5659769115, 15058768725 ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ <3, 4>, <5, 2>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1>, <23, 1> ] Total time: 3.039 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:15:39 2004 Input: GCD(12,4); GCD(120,2); x:=[1,2,3,6,3,6]; x; Sort (x); min,pos:=Min (x); Max (x); Output: Magma V2.10-6 Wed Feb 18 2004 06:15:36 on modular [Seed = 3367748023] ------------------------------------- 4 2 [ 1, 2, 3, 6, 3, 6 ] [ 1, 2, 3, 3, 6, 6 ] 6 4 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:15:51 2004 Input: GCD(12,4); GCD(120,2); x:=[1,2,3,6,3,6]; x; Sort (x); min,pos:=Min (x); min; pos; Max (x); Output: Magma V2.10-6 Wed Feb 18 2004 06:15:48 on modular [Seed = 3752646300] ------------------------------------- 4 2 [ 1, 2, 3, 6, 3, 6 ] [ 1, 2, 3, 3, 6, 6 ] 1 1 6 4 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:17:16 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f3:=645120*x^8+645120*y^8-330303015+2251776*x^7-154624*y^7-1075200*x^5-71680*y^5+ 182784*x^3-50176*y^3+44280*x-46080*y+1835008*x^6-1003520*x^4+116032*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(14549535); Factorization(15058768725); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23^2))); Bn; Output: Magma V2.10-6 Wed Feb 18 2004 06:17:13 on modular [Seed = 693772472] ------------------------------------- [ x^2 + 8*x + y^2 + 14549527*y + 2648015362, x*y + 2*x + 14549533*y + 14695030346, 15*x + 14549520*y + 14695030350, y^3 + 9*y^2 + 14549531*y + 11683276569, 15*y^2 + 3011753685, 14549535*y + 5659769115, 15058768725 ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ <3, 4>, <5, 2>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1>, <23, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 16*y, y^2 + 13 ] [ x + 16*y, y^2 + 13 ] [ x + 18*y, y^2 + 15 ] [ x + 18*y, y^2 + 15 ] [ x + 21, y + 21 ] [ x + 21, y + 21 ] Total time: 3.129 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:17:32 2004 Input: x:=[1,2,3,6,3,6]; x; min,pos:=Min (x); min; pos; print "hola"; Output: Magma V2.10-6 Wed Feb 18 2004 06:17:29 on modular [Seed = 575744963] ------------------------------------- [ 1, 2, 3, 6, 3, 6 ] 1 1 hola Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:18:54 2004 Input: x:=[1,2,3,6,3,6]; x; y:=true; min,pos:=Min (x); min; pos; print "hola"; if y then print x+2; Output: Magma V2.10-6 Wed Feb 18 2004 06:18:51 on modular [Seed = 1028536078] ------------------------------------- [ 1, 2, 3, 6, 3, 6 ] 1 1 hola User error: syntax error at end of input Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:19:07 2004 Input: x:=[1,2,3,6,3,6]; x; y:=true; min,pos:=Min (x); min; pos; print "hola"; if y then print (x+2); Output: Magma V2.10-6 Wed Feb 18 2004 06:19:04 on modular [Seed = 910507062] ------------------------------------- [ 1, 2, 3, 6, 3, 6 ] 1 1 hola User error: syntax error at end of input Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:19:27 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+2944*x^5-352*y^5-560*x^3-160*y^3+146*x-128*y+2160*x^4-600*x^2 -163825; f3:=645120*x^8+645120*y^8-330303015+2251776*x^7-154624*y^7-1075200*x^5-71680*y^5+ 182784*x^3-50176*y^3+44280*x-46080*y+1835008*x^6-1003520*x^4+116032*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 18 2004 06:19:24 on modular [Seed = 259786011] ------------------------------------- [ x^2 + 23*x + y^2 + 6412*y + 643492, x*y + 2*x + 6433*y + 643496, 45*x + 6390*y + 643500, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 765705, 6435*y + 643500, 765765 ] Total time: 3.049 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:20:33 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+2944*x^5-352*y^5-560*x^3-160*y^3+146*x-128*y+2160*x^4-600*x^2 -163825; f3:=645120*x^8+645120*y^8-330303015+2251776*x^7-154624*y^7-1075200*x^5-71680*y^5+ 182784*x^3-50176*y^3+44280*x-46080*y+1835008*x^6-1003520*x^4+116032*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(765765); Output: Magma V2.10-6 Wed Feb 18 2004 06:20:30 on modular [Seed = 527177033] ------------------------------------- [ x^2 + 23*x + y^2 + 6412*y + 643492, x*y + 2*x + 6433*y + 643496, 45*x + 6390*y + 643500, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 765705, 6435*y + 643500, 765765 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] Total time: 3.159 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:21:09 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+2944*x^5-352*y^5-560*x^3-160*y^3+146*x-128*y+2160*x^4-600*x^2 -163825; f3:=645120*x^8+645120*y^8-330303015+2251776*x^7-154624*y^7-1075200*x^5-71680*y^5+ 182784*x^3-50176*y^3+44280*x-46080*y+1835008*x^6-1003520*x^4+116032*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(765765); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^2))); Bn; Output: Magma V2.10-6 Wed Feb 18 2004 06:21:05 on modular [Seed = 1746625249] ------------------------------------- [ x^2 + 23*x + y^2 + 6412*y + 643492, x*y + 2*x + 6433*y + 643496, 45*x + 6390*y + 643500, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 765705, 6435*y + 643500, 765765 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 15, y + 15 ] [ x + 15, y + 15 ] Total time: 3.049 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:22:03 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+2944*x^5-352*y^5-560*x^3-160*y^3+146*x-128*y+2160*x^4-600*x^2 -163825; f3:=645120*x^8+645120*y^8-330290415+12288*x^7-154624*y^7+1102080*x^5-71680*y^5- 264768*x^3-50176*y^3+55080*x-46080*y-777728*x^6+1536640*x^4-406112*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 18 2004 06:22:00 on modular [Seed = 1645308050] ------------------------------------- [ x^2 + 248*x + y^2 + 6187*y + 643492, x*y + 317*x + 6118*y + 2175026, 495*x + 5940*y + 1409265, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 2297235, 6435*y + 2175030, 2297295 ] Total time: 3.019 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:24:03 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+2944*x^5-352*y^5-560*x^3-160*y^3+146*x-128*y+2160*x^4-600*x^2 -163825; f3:=645120*x^8+645120*y^8-330290415+12288*x^7-154624*y^7+1102080*x^5-71680*y^5- 264768*x^3-50176*y^3+55080*x-46080*y-777728*x^6+1536640*x^4-406112*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(2297295); Output: Magma V2.10-6 Wed Feb 18 2004 06:24:00 on modular [Seed = 2081388292] ------------------------------------- [ x^2 + 248*x + y^2 + 6187*y + 643492, x*y + 317*x + 6118*y + 2175026, 495*x + 5940*y + 1409265, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 2297235, 6435*y + 2175030, 2297295 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 3>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] Total time: 2.929 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:24:39 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+2944*x^5-352*y^5-560*x^3-160*y^3+146*x-128*y+2160*x^4-600*x^2 -163825; f3:=645120*x^8+645120*y^8-330290415+12288*x^7-154624*y^7+1102080*x^5-71680*y^5- 264768*x^3-50176*y^3+55080*x-46080*y-777728*x^6+1536640*x^4-406112*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(2297295); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^2))); Bn; Output: Magma V2.10-6 Wed Feb 18 2004 06:24:35 on modular [Seed = 1980071213] ------------------------------------- [ x^2 + 248*x + y^2 + 6187*y + 643492, x*y + 317*x + 6118*y + 2175026, 495*x + 5940*y + 1409265, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 2297235, 6435*y + 2175030, 2297295 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 3>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] [ x^2 + 6*x + 5*y + 7, x*y + 9*x + 2*y + 7, y^2 + 7 ] [ x^2 + 6*x + 5*y + 7, x*y + 9*x + 2*y + 7, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 15, y + 15 ] [ x + 15, y + 15 ] Total time: 3.069 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:26:58 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f3:=645120*x^8+645120*y^8-330303015+154624*x^7-2251776*y^7+71680*x^5+1075200*y^5+ 50176*x^3-182784*y^3+46080*x-44280*y+1835008*y^6-1003520*y^4+116032*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 18 2004 06:26:55 on modular [Seed = 1127237780] ------------------------------------- [ x^2 + 8*x + y^2 + 14549527*y + 363738367, x*y + 2*x + 14549533*y + 12410753351, 15*x + 14549520*y + 12410753355, y^3 + 9*y^2 + 14549531*y + 12410753319, 15*y^2 + 15058768665, 14549535*y + 3375492120, 15058768725 ] Total time: 2.959 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:27:42 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f3:=645120*x^8+645120*y^8-330303015+154624*x^7-2251776*y^7+71680*x^5+1075200*y^5+ 50176*x^3-182784*y^3+46080*x-44280*y+1835008*y^6-1003520*y^4+116032*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(14549535); Factorization(15058768725); Output: Magma V2.10-6 Wed Feb 18 2004 06:27:38 on modular [Seed = 1563316575] ------------------------------------- [ x^2 + 8*x + y^2 + 14549527*y + 363738367, x*y + 2*x + 14549533*y + 12410753351, 15*x + 14549520*y + 12410753355, y^3 + 9*y^2 + 14549531*y + 12410753319, 15*y^2 + 15058768665, 14549535*y + 3375492120, 15058768725 ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ <3, 4>, <5, 2>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1>, <23, 1> ] Total time: 3.099 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:28:38 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f3:=645120*x^8+645120*y^8-330303015+154624*x^7-2251776*y^7+71680*x^5+1075200*y^5+ 50176*x^3-182784*y^3+46080*x-44280*y+1835008*y^6-1003520*y^4+116032*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(14549535); Factorization(15058768725); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23^2))); Bn; Output: Magma V2.10-6 Wed Feb 18 2004 06:28:35 on modular [Seed = 1445288477] ------------------------------------- [ x^2 + 8*x + y^2 + 14549527*y + 363738367, x*y + 2*x + 14549533*y + 12410753351, 15*x + 14549520*y + 12410753355, y^3 + 9*y^2 + 14549531*y + 12410753319, 15*y^2 + 15058768665, 14549535*y + 3375492120, 15058768725 ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ <3, 4>, <5, 2>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1>, <23, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 16*y, y^2 + 13 ] [ x + 16*y, y^2 + 13 ] [ x + 18*y, y^2 + 15 ] [ x + 18*y, y^2 + 15 ] [ x + 2, y + 2 ] [ x + 2, y + 2 ] Total time: 2.999 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:29:33 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f3:=322560*x^8+322560*y^8-165152295+1125888*x^7-1125888*y^7-537600*x^5+537600*y^5+ 91392*x^3-91392*y^3+22140*x-22140*y+917504*y^6-501760*y^4+58016*y^2+917504*x^6- 501760*x^4+58016*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 18 2004 06:29:30 on modular [Seed = 2698226706] ------------------------------------- [ x^2 + 8*x + y^2 + 101846737*y + 101846737, x*y + 2*x + 101846743*y + 101846741, 15*x + 101846730*y, y^3 + 9*y^2 + 101846741*y + 101846709, 15*y^2 + 101846685, 101846745 ] Total time: 2.969 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:29:59 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f3:=322560*x^8+322560*y^8-165152295+1125888*x^7-1125888*y^7-537600*x^5+537600*y^5+ 91392*x^3-91392*y^3+22140*x-22140*y+917504*y^6-501760*y^4+58016*y^2+917504*x^6- 501760*x^4+58016*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(101846745); Output: Magma V2.10-6 Wed Feb 18 2004 06:29:55 on modular [Seed = 3117069602] ------------------------------------- [ x^2 + 8*x + y^2 + 101846737*y + 101846737, x*y + 2*x + 101846743*y + 101846741, 15*x + 101846730*y, y^3 + 9*y^2 + 101846741*y + 101846709, 15*y^2 + 101846685, 101846745 ] [ <3, 2>, <5, 1>, <7, 2>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] Total time: 3.069 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:30:54 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f3:=322560*x^8+322560*y^8-165152295+1125888*x^7-1125888*y^7-537600*x^5+537600*y^5+ 91392*x^3-91392*y^3+22140*x-22140*y+917504*y^6-501760*y^4+58016*y^2+917504*x^6- 501760*x^4+58016*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(101846745); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19^2))); Bn; Output: Magma V2.10-6 Wed Feb 18 2004 06:30:51 on modular [Seed = 2331608649] ------------------------------------- [ x^2 + 8*x + y^2 + 101846737*y + 101846737, x*y + 2*x + 101846743*y + 101846741, 15*x + 101846730*y, y^3 + 9*y^2 + 101846741*y + 101846709, 15*y^2 + 101846685, 101846745 ] [ <3, 2>, <5, 1>, <7, 2>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 16*y, y^2 + 13 ] [ x + 16*y, y^2 + 13 ] [ x + 18*y, y^2 + 15 ] [ x + 18*y, y^2 + 15 ] Total time: 3.069 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:31:35 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+2944*x^5-352*y^5-560*x^3-160*y^3+146*x-128*y+2160*x^4-600*x^2 -163825; f3:=322560*x^8+322560*y^8-165152295+1125888*x^7-1125888*y^7-537600*x^5+537600*y^5+ 91392*x^3-91392*y^3+22140*x-22140*y+917504*y^6-501760*y^4+58016*y^2+917504*x^6- 501760*x^4+58016*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 18 2004 06:31:32 on modular [Seed = 2213580479] ------------------------------------- [ x^2 + 23*x + y^2 + 6412*y + 643492, x*y + 2*x + 6433*y + 643496, 45*x + 6390*y + 643500, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 765705, 6435*y + 643500, 765765 ] Total time: 2.969 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:32:04 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+2944*x^5-352*y^5-560*x^3-160*y^3+146*x-128*y+2160*x^4-600*x^2 -163825; f3:=322560*x^8+322560*y^8-165152295+1125888*x^7-1125888*y^7-537600*x^5+537600*y^5+ 91392*x^3-91392*y^3+22140*x-22140*y+917504*y^6-501760*y^4+58016*y^2+917504*x^6- 501760*x^4+58016*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(765765); Output: Magma V2.10-6 Wed Feb 18 2004 06:32:01 on modular [Seed = 2632946053] ------------------------------------- [ x^2 + 23*x + y^2 + 6412*y + 643492, x*y + 2*x + 6433*y + 643496, 45*x + 6390*y + 643500, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 765705, 6435*y + 643500, 765765 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] Total time: 3.059 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:32:29 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+2944*x^5-352*y^5-560*x^3-160*y^3+146*x-128*y+2160*x^4-600*x^2 -163825; f3:=322560*x^8+322560*y^8-165152295+1125888*x^7-1125888*y^7-537600*x^5+537600*y^5+ 91392*x^3-91392*y^3+22140*x-22140*y+917504*y^6-501760*y^4+58016*y^2+917504*x^6- 501760*x^4+58016*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(765765); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^2))); Bn; Output: Magma V2.10-6 Wed Feb 18 2004 06:32:26 on modular [Seed = 2514917623] ------------------------------------- [ x^2 + 23*x + y^2 + 6412*y + 643492, x*y + 2*x + 6433*y + 643496, 45*x + 6390*y + 643500, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 765705, 6435*y + 643500, 765765 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 15, y + 15 ] [ x + 15, y + 15 ] Total time: 3.119 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:33:28 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+2944*x^5-352*y^5-560*x^3-160*y^3+146*x-128*y+2160*x^4-600*x^2 -163825; f3:=322560*x^8+322560*y^8-165145995+6144*x^7-1125888*y^7+551040*x^5+537600*y^5- 132384*x^3-91392*y^3+27540*x-22140*y+917504*y^6-501760*y^4+58016*y^2-388864*x^6 +768320*x^4-203056*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 18 2004 06:33:25 on modular [Seed = 4020036162] ------------------------------------- [ x^2 + 248*x + y^2 + 6187*y + 643492, x*y + 317*x + 6118*y + 643496, 495*x + 5940*y + 643500, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 765705, 6435*y + 643500, 765765 ] Total time: 3.009 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:34:07 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+2944*x^5-352*y^5-560*x^3-160*y^3+146*x-128*y+2160*x^4-600*x^2 -163825; f3:=322560*x^8+322560*y^8-165145995+6144*x^7-1125888*y^7+551040*x^5+537600*y^5- 132384*x^3-91392*y^3+27540*x-22140*y+917504*y^6-501760*y^4+58016*y^2-388864*x^6 +768320*x^4-203056*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(765765); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^2))); Bn; Output: Magma V2.10-6 Wed Feb 18 2004 06:34:04 on modular [Seed = 4186633341] ------------------------------------- [ x^2 + 248*x + y^2 + 6187*y + 643492, x*y + 317*x + 6118*y + 643496, 495*x + 5940*y + 643500, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 765705, 6435*y + 643500, 765765 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] [ x^2 + 6*x + 5*y + 7, x*y + 9*x + 2*y + 7, y^2 + 7 ] [ x^2 + 6*x + 5*y + 7, x*y + 9*x + 2*y + 7, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 15, y + 15 ] [ x + 15, y + 15 ] Total time: 3.049 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:34:53 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+352*x^5-2944*y^5+160*x^3+560*y^3+128*x-146*y+2160*y^4+600*y^2 -163825; f3:=645120*x^8+645120*y^8-330303015+154624*x^7-2251776*y^7+71680*x^5+1075200*y^5+ 50176*x^3-182784*y^3+46080*x-44280*y+1835008*y^6-1003520*y^4+116032*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 18 2004 06:34:50 on modular [Seed = 4068605696] ------------------------------------- [ x^2 + 8*x + y^2 + 7*y + 22, x*y + 2*x + 13*y + 716, 15*x + 375, y^3 + 9*y^2 + 11*y + 1029, 15*y + 720, 1035 ] Total time: 3.039 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:35:19 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+352*x^5-2944*y^5+160*x^3+560*y^3+128*x-146*y+2160*y^4+600*y^2 -163825; f3:=645120*x^8+645120*y^8-330303015+154624*x^7-2251776*y^7+71680*x^5+1075200*y^5+ 50176*x^3-182784*y^3+46080*x-44280*y+1835008*y^6-1003520*y^4+116032*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(1035); Output: Magma V2.10-6 Wed Feb 18 2004 06:35:15 on modular [Seed = 3485254164] ------------------------------------- [ x^2 + 8*x + y^2 + 7*y + 22, x*y + 2*x + 13*y + 716, 15*x + 375, y^3 + 9*y^2 + 11*y + 1029, 15*y + 720, 1035 ] [ <3, 2>, <5, 1>, <23, 1> ] Total time: 2.969 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:36:27 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+352*x^5-2944*y^5+160*x^3+560*y^3+128*x-146*y+2160*y^4+600*y^2 -163825; f3:=645120*x^8+645120*y^8-330303015+154624*x^7-2251776*y^7+71680*x^5+1075200*y^5+ 50176*x^3-182784*y^3+46080*x-44280*y+1835008*y^6-1003520*y^4+116032*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(1035); Bn:=GroebnerBasis(ChangeRing(I,GF(23))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23^2))); Bn; Output: Magma V2.10-6 Wed Feb 18 2004 06:36:24 on modular [Seed = 3651852233] ------------------------------------- [ x^2 + 8*x + y^2 + 7*y + 22, x*y + 2*x + 13*y + 716, 15*x + 375, y^3 + 9*y^2 + 11*y + 1029, 15*y + 720, 1035 ] [ <3, 2>, <5, 1>, <23, 1> ] [ x + 2, y + 2 ] [ x + 2, y + 2 ] Total time: 3.119 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:37:20 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+352*x^5-2944*y^5+160*x^3+560*y^3+128*x-146*y+2160*y^4+600*y^2 -163825; f3:=322560*x^8+322560*y^8-165152295+1125888*x^7-1125888*y^7-537600*x^5+537600*y^5+ 91392*x^3-91392*y^3+22140*x-22140*y+917504*y^6-501760*y^4+58016*y^2+917504*x^6- 501760*x^4+58016*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 18 2004 06:37:17 on modular [Seed = 3533823127] ------------------------------------- [ x^2 + 8*x + y^2 + 7*y + 22, x*y + 2*x + 13*y + 41, 15*x + 15, y^3 + 9*y^2 + 11*y + 39, 15*y, 45 ] Total time: 3.089 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:38:14 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=640*x^6+640*y^6+1472*x^5-1472*y^5+1080*x^4+1080*y^4-280*x^3+280*y^3; f3:=322560*x^8+322560*y^8-165152295+1125888*x^7-1125888*y^7-537600*x^5+537600*y^5+ 91392*x^3-91392*y^3+22140*x-22140*y+917504*y^6-501760*y^4+58016*y^2+917504*x^6- 501760*x^4+58016*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 18 2004 06:38:11 on modular [Seed = 710485152] ------------------------------------- [ x + 4094*y + 910, y^2 + 3185*y + 2271, 4095 ] Total time: 3.059 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:38:51 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=640*x^6+640*y^6+1472*x^5-1472*y^5+1080*x^4+1080*y^4-280*x^3+280*y^3; f3:=322560*x^8+322560*y^8-165152295+1125888*x^7-1125888*y^7-537600*x^5+537600*y^5+ 91392*x^3-91392*y^3+22140*x-22140*y+917504*y^6-501760*y^4+58016*y^2+917504*x^6- 501760*x^4+58016*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(4095); Output: Magma V2.10-6 Wed Feb 18 2004 06:38:48 on modular [Seed = 609692357] ------------------------------------- [ x + 4094*y + 910, y^2 + 3185*y + 2271, 4095 ] [ <3, 2>, <5, 1>, <7, 1>, <13, 1> ] Total time: 3.099 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:39:20 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=640*x^6+640*y^6+1472*x^5-1472*y^5+1080*x^4+1080*y^4-280*x^3+280*y^3; f3:=322560*x^8+322560*y^8-165152295+1125888*x^7-1125888*y^7-537600*x^5+537600*y^5+ 91392*x^3-91392*y^3+22140*x-22140*y+917504*y^6-501760*y^4+58016*y^2+917504*x^6- 501760*x^4+58016*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(4095); Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Output: Magma V2.10-6 Wed Feb 18 2004 06:39:17 on modular [Seed = 1045246194] ------------------------------------- [ x + 4094*y + 910, y^2 + 3185*y + 2271, 4095 ] [ <3, 2>, <5, 1>, <7, 1>, <13, 1> ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] Total time: 2.989 seconds, Total memory usage: 2.13MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:40:00 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=640*x^6+640*y^6+1472*x^5-1472*y^5+1080*x^4+1080*y^4-280*x^3+280*y^3; f3:=322560*x^8+322560*y^8-165145995+6144*x^7-1125888*y^7+551040*x^5+537600*y^5- 132384*x^3-91392*y^3+27540*x-22140*y+917504*y^6-501760*y^4+58016*y^2-388864*x^6 +768320*x^4-203056*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 18 2004 06:39:57 on modular [Seed = 158991917] ------------------------------------- [ x + 4094*y + 910, y^2 + 3185*y + 2271, 4095 ] Total time: 2.989 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:40:28 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=640*x^6+640*y^6+1472*x^5-1472*y^5+1080*x^4+1080*y^4-280*x^3+280*y^3; f3:=322560*x^8+322560*y^8-165145995+6144*x^7-1125888*y^7+551040*x^5+537600*y^5- 132384*x^3-91392*y^3+27540*x-22140*y+917504*y^6-501760*y^4+58016*y^2-388864*x^6 +768320*x^4-203056*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(4095); Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Output: Magma V2.10-6 Wed Feb 18 2004 06:40:25 on modular [Seed = 426382873] ------------------------------------- [ x + 4094*y + 910, y^2 + 3185*y + 2271, 4095 ] [ <3, 2>, <5, 1>, <7, 1>, <13, 1> ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] Total time: 2.949 seconds, Total memory usage: 2.13MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:41:26 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+352*x^5-2944*y^5+160*x^3+560*y^3+128*x-146*y+2160*y^4+600*y^2 -163825; f3:=645120*x^8+645120*y^8-330290415+154624*x^7-12288*y^7+71680*x^5-1102080*y^5+ 50176*x^3+264768*y^3+46080*x-55080*y-777728*y^6+1536640*y^4-406112*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 18 2004 06:41:23 on modular [Seed = 274931546] ------------------------------------- [ x^2 + 8*x + y^2 + 7*y + 22, x*y + 2*x + 13*y + 176, 15*x + 240, y^3 + 9*y^2 + 11*y + 354, 15*y + 225, 405 ] Total time: 3.059 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:41:54 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+352*x^5-2944*y^5+160*x^3+560*y^3+128*x-146*y+2160*y^4+600*y^2 -163825; f3:=645120*x^8+645120*y^8-330290415+154624*x^7-12288*y^7+71680*x^5-1102080*y^5+ 50176*x^3+264768*y^3+46080*x-55080*y-777728*y^6+1536640*y^4-406112*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(405); Output: Magma V2.10-6 Wed Feb 18 2004 06:41:51 on modular [Seed = 1796760637] ------------------------------------- [ x^2 + 8*x + y^2 + 7*y + 22, x*y + 2*x + 13*y + 176, 15*x + 240, y^3 + 9*y^2 + 11*y + 354, 15*y + 225, 405 ] [ <3, 4>, <5, 1> ] Total time: 2.919 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:42:19 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+352*x^5-2944*y^5+160*x^3+560*y^3+128*x-146*y+2160*y^4+600*y^2 -163825; f3:=645120*x^8+645120*y^8-330290415+154624*x^7-12288*y^7+71680*x^5-1102080*y^5+ 50176*x^3+264768*y^3+46080*x-55080*y-777728*y^6+1536640*y^4-406112*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 18 2004 06:42:16 on modular [Seed = 1695967956] ------------------------------------- [ x^2 + 8*x + y^2 + 7*y + 22, x*y + 2*x + 13*y + 176, 15*x + 240, y^3 + 9*y^2 + 11*y + 354, 15*y + 225, 405 ] Total time: 3.089 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:42:23 2004 Input: x:=[1,2,3,6,3,6]; x; y:=true; min,pos:=Min (x); min; pos; print "hola"; if y then print (x+2); Output: Magma V2.10-6 Wed Feb 18 2004 06:42:20 on modular [Seed = 2081387465] ------------------------------------- [ 1, 2, 3, 6, 3, 6 ] 1 1 hola User error: syntax error at end of input Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:42:35 2004 Input: x:=[1,2,3,6,3,6]; x; y:=true; min,pos:=Min (x); min; pos; print "hola"; if y then print x; Output: Magma V2.10-6 Wed Feb 18 2004 06:42:32 on modular [Seed = 1996781814] ------------------------------------- [ 1, 2, 3, 6, 3, 6 ] 1 1 hola User error: syntax error at end of input Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:42:53 2004 Input: x:=[1,2,3,6,3,6]; x; y:=true; min,pos:=Min (x); min; pos; print "hola"; if (y) then (print x); Output: Magma V2.10-6 Wed Feb 18 2004 06:42:50 on modular [Seed = 1312637405] ------------------------------------- [ 1, 2, 3, 6, 3, 6 ] 1 1 hola >> if (y) then (print x);; ^ User error: bad syntax Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:42:58 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+352*x^5-2944*y^5+160*x^3+560*y^3+128*x-146*y+2160*y^4+600*y^2 -163825; f3:=322560*x^8+322560*y^8-165145995+1125888*x^7-6144*y^7-537600*x^5-551040*y^5+ 91392*x^3+132384*y^3+22140*x-27540*y+917504*x^6-501760*x^4+58016*x^2-388864*y^6 +768320*y^4-203056*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 18 2004 06:42:55 on modular [Seed = 1495946959] ------------------------------------- [ x^2 + 8*x + y^2 + 7*y + 22, x*y + 2*x + 13*y + 41, 15*x + 15, y^3 + 9*y^2 + 11*y + 39, 15*y, 45 ] Total time: 3.049 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:43:27 2004 Input: x:=[1,2,3,6,3,6]; x; y:=true; min,pos:=Min (x); min; pos; print "hola"; if (y) then (print x) end if; Output: Magma V2.10-6 Wed Feb 18 2004 06:43:24 on modular [Seed = 1344495525] ------------------------------------- [ 1, 2, 3, 6, 3, 6 ] 1 1 hola >> if (y) then (print x) end if;; ^ User error: bad syntax Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:43:36 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=640*x^6+640*y^6+1472*x^5-1472*y^5+1080*x^4+1080*y^4-280*x^3+280*y^3; f3:=322560*x^8+322560*y^8-165145995+1125888*x^7-6144*y^7-537600*x^5-551040*y^5+ 91392*x^3+132384*y^3+22140*x-27540*y+917504*x^6-501760*x^4+58016*x^2-388864*y^6 +768320*y^4-203056*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 18 2004 06:43:32 on modular [Seed = 2883101798] ------------------------------------- [ x + 4094*y + 910, y^2 + 3185*y + 2271, 4095 ] Total time: 3.049 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:44:16 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=640*x^6+640*y^6+1472*x^5-1472*y^5+1080*x^4+1080*y^4-280*x^3+280*y^3; f3:=322560*x^8+322560*y^8-165145995+1125888*x^7-6144*y^7-537600*x^5-551040*y^5+ 91392*x^3+132384*y^3+22140*x-27540*y+917504*x^6-501760*x^4+58016*x^2-388864*y^6 +768320*y^4-203056*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(4095); Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Output: Magma V2.10-6 Wed Feb 18 2004 06:44:13 on modular [Seed = 2782311809] ------------------------------------- [ x + 4094*y + 910, y^2 + 3185*y + 2271, 4095 ] [ <3, 2>, <5, 1>, <7, 1>, <13, 1> ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] Total time: 3.039 seconds, Total memory usage: 2.13MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:44:48 2004 Input: x:=[1,2,3,6,3,6]; x; y:=true; min,pos:=Min (x); min; pos; print "hola"; IsPrime(2); if (y) then (print x) end if; Output: Magma V2.10-6 Wed Feb 18 2004 06:44:45 on modular [Seed = 3167726776] ------------------------------------- [ 1, 2, 3, 6, 3, 6 ] 1 1 hola true >> if (y) then (print x) end if;; ^ User error: bad syntax Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:44:52 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=640*x^6+640*y^6+1472*x^5-1472*y^5+1080*x^4+1080*y^4-280*x^3+280*y^3; f3:=322560*x^8+322560*y^8-165139695+6144*x^7-6144*y^7+551040*x^5-551040*y^5-132384* x^3+132384*y^3+27540*x-27540*y-388864*x^6+768320*x^4-203056*x^2-388864*y^6+ 768320*y^4-203056*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 18 2004 06:44:49 on modular [Seed = 3083118511] ------------------------------------- [ x + 4094*y + 910, y^2 + 3185*y + 2271, 4095 ] Total time: 2.949 seconds, Total memory usage: 1.94MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:44:56 2004 Input: x:=[1,2,3,6,3,6]; x; y:=true; min,pos:=Min (x); min; pos; print "hola"; IsPrime(20); if (y) then (print x) end if; Output: Magma V2.10-6 Wed Feb 18 2004 06:44:53 on modular [Seed = 2398985874] ------------------------------------- [ 1, 2, 3, 6, 3, 6 ] 1 1 hola false >> if (y) then (print x) end if;; ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:45:04 2004 Input: x:=[1,2,3,6,3,6]; x; y:=true; min,pos:=Min (x); min; pos; print "hola"; IsPrime(1); if (y) then (print x) end if; Output: Magma V2.10-6 Wed Feb 18 2004 06:45:01 on modular [Seed = 2649656713] ------------------------------------- [ 1, 2, 3, 6, 3, 6 ] 1 1 hola false >> if (y) then (print x) end if;; ^ User error: bad syntax Total time: 3.099 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:45:13 2004 Input: x:=[1,2,3,6,3,6]; x; y:=true; min,pos:=Min (x); min; pos; print "hola"; IsPrime(0); if (y) then (print x) end if; Output: Magma V2.10-6 Wed Feb 18 2004 06:45:10 on modular [Seed = 2498200827] ------------------------------------- [ 1, 2, 3, 6, 3, 6 ] 1 1 hola false >> if (y) then (print x) end if;; ^ User error: bad syntax Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:45:21 2004 Input: x:=[1,2,3,6,3,6]; x; y:=true; min,pos:=Min (x); min; pos; print "hola"; IsPrime(5); if (y) then (print x) end if; Output: Magma V2.10-6 Wed Feb 18 2004 06:45:18 on modular [Seed = 4003331721] ------------------------------------- [ 1, 2, 3, 6, 3, 6 ] 1 1 hola true >> if (y) then (print x) end if;; ^ User error: bad syntax Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:45:31 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=640*x^6+640*y^6+1472*x^5-1472*y^5+1080*x^4+1080*y^4-280*x^3+280*y^3; f3:=322560*x^8+322560*y^8-165139695+6144*x^7-6144*y^7+551040*x^5-551040*y^5-132384* x^3+132384*y^3+27540*x-27540*y-388864*x^6+768320*x^4-203056*x^2-388864*y^6+ 768320*y^4-203056*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(4095); Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Output: Magma V2.10-6 Wed Feb 18 2004 06:45:28 on modular [Seed = 4186630536] ------------------------------------- [ x + 4094*y + 910, y^2 + 3185*y + 2271, 4095 ] [ <3, 2>, <5, 1>, <7, 1>, <13, 1> ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] Total time: 3.039 seconds, Total memory usage: 2.14MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:45:42 2004 Input: x:=[1,2,3,6,3,6]; x; y:=true; min,pos:=Min (x); min; pos; print "hola"; IsPrime(5); if (min==1) then (print x) end if; Output: Magma V2.10-6 Wed Feb 18 2004 06:45:39 on modular [Seed = 4035174586] ------------------------------------- [ 1, 2, 3, 6, 3, 6 ] 1 1 hola true >> if (min==1) then (print x) end if;; ^ User error: bad syntax Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:48:12 2004 Input: x:=[1,2,3,6,3,6]; x; y:=true; min,pos:=Min (x); min; pos; print "hola"; IsPrime(5); if (min==1) then x; Output: Magma V2.10-6 Wed Feb 18 2004 06:48:09 on modular [Seed = 3417889563] ------------------------------------- [ 1, 2, 3, 6, 3, 6 ] 1 1 hola true >> if (min==1) then x;; ^ User error: bad syntax Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:49:56 2004 Input: x:=[1,2,3,6,3,6]; x; y:=true; min,pos:=Min (x); min; pos; print "hola"; IsPrime(5); if (min==1) then x; Output: Magma V2.10-6 Wed Feb 18 2004 06:49:53 on modular [Seed = 3317093517] ------------------------------------- [ 1, 2, 3, 6, 3, 6 ] 1 1 hola true >> if (min==1) then x;; ^ User error: bad syntax Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:57:08 2004 Input: Z4:=Integers(4); Output: Magma V2.10-6 Wed Feb 18 2004 06:57:05 on modular [Seed = 24252986] ------------------------------------- Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:57:21 2004 Input: Z4:=Integers(4); Z4; Output: Magma V2.10-6 Wed Feb 18 2004 06:57:18 on modular [Seed = 510463274] ------------------------------------- Residue class ring of integers modulo 4 Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:57:37 2004 Input: Z4:=Integers(4); Z4; Print(Z4); Output: Magma V2.10-6 Wed Feb 18 2004 06:57:34 on modular [Seed = 392430611] ------------------------------------- Residue class ring of integers modulo 4 >> Print(Z4);; ^ User error: Identifier 'Print' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:57:55 2004 Input: Z4:=Integers(4); Z4; Print Z4; Output: Magma V2.10-6 Wed Feb 18 2004 06:57:52 on modular [Seed = 1814003462] ------------------------------------- Residue class ring of integers modulo 4 >> Print Z4;; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:59:09 2004 Input: Z4:=Integers(4); Z4; IsField (Z4); Output: Magma V2.10-6 Wed Feb 18 2004 06:59:06 on modular [Seed = 2064148699] ------------------------------------- Residue class ring of integers modulo 4 false Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:59:38 2004 Input: Z4:=Integers(4); Z4; IsField (Z4); IsInvertible (Z4); Output: Magma V2.10-6 Wed Feb 18 2004 06:59:35 on modular [Seed = 1879270397] ------------------------------------- Residue class ring of integers modulo 4 false >> IsInvertible (Z4);; ^ Runtime error in 'IsInvertible': Bad argument types Argument types given: RngIntRes Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 07:00:26 2004 Input: Z4:=Integers(4); Z4; IsField (Z4); Z4!2; Output: Magma V2.10-6 Wed Feb 18 2004 07:00:22 on modular [Seed = 1093817021] ------------------------------------- Residue class ring of integers modulo 4 false 2 Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 07:00:50 2004 Input: Z4:=Integers(4); Z4; IsField (Z4); Z4!2; IsInvertible (Z4!2); Output: Magma V2.10-6 Wed Feb 18 2004 07:00:47 on modular [Seed = 1580027291] ------------------------------------- Residue class ring of integers modulo 4 false 2 false Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 07:01:00 2004 Input: Z4:=Integers(4); Z4; IsField (Z4); Z4!2; IsInvertible (Z4); Output: Magma V2.10-6 Wed Feb 18 2004 07:00:57 on modular [Seed = 1461994628] ------------------------------------- Residue class ring of integers modulo 4 false 2 >> IsInvertible (Z4); ^ Runtime error in 'IsInvertible': Bad argument types Argument types given: RngIntRes Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 07:01:09 2004 Input: Z4:=Integers(4); Z4; IsField (Z4); Z4!2; IsInvertible (Z4!2); Output: Magma V2.10-6 Wed Feb 18 2004 07:01:06 on modular [Seed = 2999035546] ------------------------------------- Residue class ring of integers modulo 4 false 2 false Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 07:01:41 2004 Input: Z4:=Integers(4); Z4; IsField (Z4); Z4!2; IsInvertible (Z4!2); IsInvertible (Z4!3); Output: Magma V2.10-6 Wed Feb 18 2004 07:01:38 on modular [Seed = 2298190976] ------------------------------------- Residue class ring of integers modulo 4 false 2 false true 3 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 07:02:06 2004 Input: Z4:=Integers(4); Z4; IsField (Z4); Z4!2; IsInvertible (Z4!2); IsInvertible (Z4!3); Z5:=Integers(41); Output: Magma V2.10-6 Wed Feb 18 2004 07:02:03 on modular [Seed = 2180158864] ------------------------------------- Residue class ring of integers modulo 4 false 2 false true 3 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:08:45 2004 Input: Sqrt(2); Output: Magma V2.10-6 Wed Feb 18 2004 07:08:42 on modular [Seed = 3902536968] ------------------------------------- 1.414213562373095048801688724198 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:08:48 2004 Input: Sqrt(2); Output: Magma V2.10-6 Wed Feb 18 2004 07:08:45 on modular [Seed = 3767792903] ------------------------------------- 1.414213562373095048801688724198 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:09:36 2004 Input: Sqrt(2); Sqrt(100); Output: Magma V2.10-6 Wed Feb 18 2004 07:09:33 on modular [Seed = 4270713641] ------------------------------------- 1.414213562373095048801688724198 10.00000000000000000000000000 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:10:26 2004 Input: Ceiling(Sqrt(100)); Floor(Sqrt(999)); Output: Magma V2.10-6 Wed Feb 18 2004 07:10:23 on modular [Seed = 3435125449] ------------------------------------- 10 31 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:18:40 2004 Input: print 2+4; 2+4; Output: Magma V2.10-6 Wed Feb 18 2004 07:18:37 on modular [Seed = 3533818597] ------------------------------------- 6 6 Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:23:49 2004 Input: P:=PolynomialRing(IntegerRing()); P; Output: Magma V2.10-6 Wed Feb 18 2004 07:23:46 on modular [Seed = 643120991] ------------------------------------- Univariate Polynomial Ring in x over Integer Ring Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:27:00 2004 Input: (x^6-5*x^2+2)*(17*x^3-1); Output: Magma V2.10-6 Wed Feb 18 2004 07:26:57 on modular [Seed = 809708042] ------------------------------------- >> (x^6-5*x^2+2)*(17*x^3-1); ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:27:39 2004 Input: P:=PolynomialRing(IntegerRing()); (x^6-5*x^2+2)*(17*x^3-1); Output: Magma V2.10-6 Wed Feb 18 2004 07:27:36 on modular [Seed = 259790108] ------------------------------------- 17*x^9 - x^6 - 85*x^5 + 34*x^3 + 5*x^2 - 2 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:28:12 2004 Input: P:=PolynomialRing(IntegerRing()); (x^6-5*x^2+2)*(17*x^3-1); Factorization(x^8-1); Output: Magma V2.10-6 Wed Feb 18 2004 07:28:09 on modular [Seed = 108338292] ------------------------------------- 17*x^9 - x^6 - 85*x^5 + 34*x^3 + 5*x^2 - 2 [ , , , ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:29:06 2004 Input: ?div Output: Magma V2.10-6 Wed Feb 18 2004 07:29:03 on modular [Seed = 477038264] ------------------------------------- 16 matches: 1 O /magma/ring-field-algebra 2 S /magma/ring-field-algebra/algebraic-field/divisors/div-arith 3 S /magma/ring-field-algebra/algebraic-field/divisors/div-create-e 4 S /magma/ring-field-algebra/algebraic-field/divisors/div-create-s 5 S /magma/ring-field-algebra/algebraic-field/divisors/div-other 6 I /magma/geometry/algebraic-curve/divisors/divisor-arithmetic/\ divisors-coeff-arith/+ 7 I /magma/group/braid/braid-groups-elements/braid-groups-arithmetic/\ LeftDiv 8 I /magma/group/braid/braid-groups-elements/braid-groups-arithmetic/\ LeftDiv 9 I /magma/module-lattice/lattice/element/operation/div 10 I /magma/module-lattice/modules-affine-algebras/element-access/\ arithmetic/div 11 I /magma/ring-field-algebra/algebraic-field/operation-element/\ field-element/div 12 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ operation-element/division/div 13 I /magma/ring-field-algebra/integer/operation-element/arithmetic/div 14 I /magma/ring-field-algebra/local/operation-element/arithmetic/div 15 I /magma/ring-field-algebra/univariate-polynomial/\ operation-element/division/div 16 I /magma/ring-field-algebra/valuation/element/arithmetic/div To view an entry, type ? followed by the number next to it Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:31:37 2004 Input: ?div ?15 Output: Magma V2.10-6 Wed Feb 18 2004 07:31:34 on modular [Seed = 1814001505] ------------------------------------- 16 matches: 1 O /magma/ring-field-algebra 2 S /magma/ring-field-algebra/algebraic-field/divisors/div-arith 3 S /magma/ring-field-algebra/algebraic-field/divisors/div-create-e 4 S /magma/ring-field-algebra/algebraic-field/divisors/div-create-s 5 S /magma/ring-field-algebra/algebraic-field/divisors/div-other 6 I /magma/geometry/algebraic-curve/divisors/divisor-arithmetic/\ divisors-coeff-arith/+ 7 I /magma/group/braid/braid-groups-elements/braid-groups-arithmetic/\ LeftDiv 8 I /magma/group/braid/braid-groups-elements/braid-groups-arithmetic/\ LeftDiv 9 I /magma/module-lattice/lattice/element/operation/div 10 I /magma/module-lattice/modules-affine-algebras/element-access/\ arithmetic/div 11 I /magma/ring-field-algebra/algebraic-field/operation-element/\ field-element/div 12 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ operation-element/division/div 13 I /magma/ring-field-algebra/integer/operation-element/arithmetic/div 14 I /magma/ring-field-algebra/local/operation-element/arithmetic/div 15 I /magma/ring-field-algebra/univariate-polynomial/\ operation-element/division/div 16 I /magma/ring-field-algebra/valuation/element/arithmetic/div To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/ring-field-algebra/univariate-polynomial/operation-element/\ division/div KIND: Intrinsic =============================================================================== f div g : RngUPolElt, RngUPolElt -> RngUPolElt The quotient q of f by g, where f and g are in the polynomial ring P=R[x]. Magma calculates the polynomials q (quotient) and r (remainder) in P such that f = q * g + r, and the degree of r is minimal. The leading coefficient of g has to be a unit. If the leading coefficient of g is a unit in R, then the degree of r will be strictly less than that of g (taking the degree of 0 to be -1). Over the integers (R=Z) this will be true in general when the leading coefficient of g divides that of f. To find r, use mod, and to find both q and r, use Quotrem. =============================================================================== Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:33:04 2004 Input: ?Quotrem Output: Magma V2.10-6 Wed Feb 18 2004 07:33:00 on modular [Seed = 2064146477] ------------------------------------- 5 matches: 1 I /magma/ring-field-algebra/function-field/Divisors/\ operation-element/arithmetic/Quotrem 2 I /magma/ring-field-algebra/function-field/Places/\ operation-element/arithmetic/Quotrem 3 I /magma/ring-field-algebra/integer/operation-element/simple/Quotrem 4 I /magma/ring-field-algebra/univariate-polynomial/\ operation-element/division/Quotrem 5 I /magma/ring-field-algebra/valuation/element/other/Quotrem To view an entry, type ? followed by the number next to it Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:33:21 2004 Input: ?Quotrem ?4 Output: Magma V2.10-6 Wed Feb 18 2004 07:33:18 on modular [Seed = 1912695255] ------------------------------------- 5 matches: 1 I /magma/ring-field-algebra/function-field/Divisors/\ operation-element/arithmetic/Quotrem 2 I /magma/ring-field-algebra/function-field/Places/\ operation-element/arithmetic/Quotrem 3 I /magma/ring-field-algebra/integer/operation-element/simple/Quotrem 4 I /magma/ring-field-algebra/univariate-polynomial/\ operation-element/division/Quotrem 5 I /magma/ring-field-algebra/valuation/element/other/Quotrem To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/ring-field-algebra/univariate-polynomial/operation-element/\ division/Quotrem KIND: Intrinsic =============================================================================== Quotrem(f, g) : RngUPolElt, RngUPolElt -> RngUPolElt, RngUPolElt Given elements f and g of the polynomial ring P=R[x], this function returns polynomials q (quotient) and r (remainder) in P such that f = q.g + r, and the degree of r is minimal. The leading coefficient of g has to be a non-zero divisor in R. If the leading coefficient of g is a unit, then the degree of r will be strictly less than that of g (taking the degree of 0 to be -1). Over the integers (R=Z) this will be true in general when the leading coefficient of g divides that of f. =============================================================================== Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:34:08 2004 Input: ? Output: Magma V2.10-6 Wed Feb 18 2004 07:34:04 on modular [Seed = 1211847647] ------------------------------------- =============================================================================== PATH: /language/statement KIND: Overview =============================================================================== A statement is a complete command to Magma. Every statement must end with a semicolon ( ; ). If you press the key before typing ; then Magma may give you a special prompt symbol such as print> or if> to remind you that the statement is not yet finished. EXAMPLE: > print 5+8; > DivBy3 := func< n | IsZero(n mod 3) >; =============================================================================== Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:36:27 2004 Input: 23 div 4; 23 mod 4; Output: Magma V2.10-6 Wed Feb 18 2004 07:36:24 on modular [Seed = 1529366328] ------------------------------------- 5 3 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:36:47 2004 Input: 23 div 4, 23 mod 4; Output: Magma V2.10-6 Wed Feb 18 2004 07:36:44 on modular [Seed = 1377914405] ------------------------------------- 5 3 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:38:28 2004 Input: (2/3)/(4+7/9); 4.7/2.6; Output: Magma V2.10-6 Wed Feb 18 2004 07:38:25 on modular [Seed = 2849682755] ------------------------------------- 6/43 1.80769230769230769230769230768 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:39:51 2004 Input: 2+4*9; (2+4)*9; 3^3^3; Output: Magma V2.10-6 Wed Feb 18 2004 07:39:48 on modular [Seed = 2815736472] ------------------------------------- 38 54 7625597484987 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:40:15 2004 Input: 2^2; 2^2^2; 2^2^2^2; 2^2^2^2^2; Output: Magma V2.10-6 Wed Feb 18 2004 07:40:11 on modular [Seed = 3083119287] ------------------------------------- 4 16 65536 2003529930406846464979072351560255750447825475569751419265016973710894059556311\ 4530895061308809333481010382343429072631818229493821188126688695063647615470291\ 6504187191635158796634721944293092798208430910485599057015931895963952486337236\ 7203002916969592156108764948889254090805911457037675208500206671563702366126359\ 7471448071117748158809141357427209671901518362825606180914588526998261414250301\ 2339110827360384376787644904320596037912449090570756031403507616256247603186379\ 3126484703743782954975613770981604614413308692118102485959152380195331030292162\ 8001605686701056516467505680387415294638422448452925373614425336143737290883037\ 9460127472495841486491593064725201515569392262818069165079638106413227530726714\ 3998158508811292628901134237782705567421080070065283963322155077831214288551675\ 5540733451072131124273995629827197691500548839052238043570458481979563931578535\ 1001899200002414196370681355984046403947219401606951769015611972698233789001764\ 1517190051133466306898140219383481435426387306539552969691388024158161859561100\ 6403621197961018595348027871672001226046424923851113934004643516238675670787452\ 5946467090388654774348321789701276445552940909202195958575162297333357615955239\ 4885297579954028471943529913543763705986928913757153740001986394332464890052543\ 1066296691652434191746913896324765602894151997754777031380647813423095961909606\ 5459130089018888758808473362595606544488850144733570605881709016210849971452956\ 8344061979690565469813631162053579369791403236328496233046421066136200220175787\ 8518574091620504897117818204001872829399434461862243280098373237649318147898481\ 1945271300744022076568091037620399920349202390662626449190916798546151577883906\ 0397720759279378852241294301017458086862263369284725851403039615558564330385450\ 6886522131148136384083847782637904596071868767285097634712719888906804782432303\ 9471865052566097815072986114143030581692792497140916105941718535227588750447759\ 2218301158780701975535722241400019548102005661773589781499532325208589753463547\ 0077866904064290167638081617405504051176700936732028045493390279924918673065399\ 3164072049223847481528061916690093380573212081635070763435166986962502096902316\ 2859350071874190579161241536897514808261904847946571736601005892476655445840838\ 3347905441448176842553272073155863493476051374197795251903650321980201087647383\ 6868253102518337753390886142618480037400808223810407646887847164755294532694766\ 1700424461063311238021134588694532200116564076327023074292426051582811070387018\ 3453245676356259514300320374327407808790562836634069650308442258559670392718694\ 6115851379338647569974856867007982396060439347885086164926030494506174341236582\ 8352144806726676841807083754862211408236579802961200027441324438432402331257403\ 5450193524287764308802328508558860899627744581646808578751158070147437638679769\ 5504999164399828435729041537814343884730348426190338884149403136613985425763557\ 7105335580206622185577060082551288893332226436281984838613239570676191409638533\ 8323743437588308592337222846442879962456054769324289984326526773783731732880632\ 1075321123868060467470842805116648870908477029120816110491255559832236624486855\ 6651402684641209694982590565519216188104341226838996283071654868525536914850299\ 5396755039549383718534059000961874894739928804324963731657538036735867101757839\ 9481847179849824694806053208199606618343401247609663951977802144119975254670408\ 0608499344178256285092726523709898651539462193004607364507926212975917698293892\ 3670151709920915315678144397912484757062378046000099182933213068805700465914583\ 8720808801688744583555792625846512476308714856631352893416611749061752667149267\ 2176128330845273936469244582892571388877839056300482483799839692029222215486145\ 9023734782226825216399574408017271441461795592261750838890200741699262383002822\ 8624928418267124340575142418856999427233160699871298688277182061721445314257494\ 4015066139463169197629181506579745526236191224848063890033669074365989226349564\ 1146655030629659601997206362026035219177767406687774635493753188995878662821254\ 6979710206574723272137291814466665942187200347450894283091153518927111428710837\ 6159222380276605327823351661555149369375778466670145717971901227117812780450240\ 0263847587883393968179629506907988171216906869295382485298300234760684541141781\ 3911064856023654975422749723100761513187002405391051091381784372179142252858743\ 2098524957878034683703337818421444017138688124249984418618129271198533315382567\ 3218704215306311977485352146709553346263366108646673322924098798492566911095161\ 4361860154890974024191350962304361219612816595051866602203071561368473236466086\ 8905014263913906515063908199378852318365059897299125404479443425166774299659811\ 8492331515552728832740283526884424087528112832899806259126736995462473415433335\ 0014723143061275039030739713525206933817384332295070104906186753943313078479801\ 5655130384758155685236218010419650255596181934986315913233036096461905990236112\ 6811960234418433633345949276319461017166529138237171823942992162725384617760656\ 9454229787707138319881703696458868981186321097690035573588462446483570629145305\ 2757101278872027965364479724025405448132748391794128826423835171949197209797145\ 9368875371987291308317380339110161285474153773777159517280841116275971863849242\ 2280237344192546999198367219213128703558530796694271341639103388275431861364349\ 0100943197409047331014476299861725424423355612237435715825933382804986243892498\ 2227807159517627578471094751190334822414120251826887137281931042534781961284401\ 7647953150505711072297431456991522345164312184865757578652819756484350895838472\ 2923534559464521215831657751471298708225909292655638836651120681943836904116252\ 6687100445602437042006637090019411855571604720446436969328500600469281405071190\ 6926139399390273553454556747031490388602202463994826050176243196930564066636662\ 6090207048887438898907498152865444381862917382901051820869936382661868303915273\ 2645812867828066013375000965933646251460917231803129303478774212346791184547913\ 1110989779464821692250562939995679348380169915743970053754213448587458685604728\ 6751065423341893839099110586465595113646061055156838541217459801807133163612573\ 0796111683438637676673073545834947897883163301292408008363568259391571131309780\ 3051644171668251834657367593419808495894794098329250008638977856349469321247342\ 6103062713745077286156922596628573857905533240641849018451328284632709269753830\ 8673084091422476594744399733481308109863994173797896570106870267341619671965915\ 9958853783482298827012560584236558953969030647496558414798131099715754204325639\ 5776070485100881578291408250777738559790129129407309462785944505859412273194812\ 7532251523248015034665190482289614066468903051025109162377704484862302294889667\ 1138055560795662073244937337402783676730020301161522700892184351565212137921574\ 8206859356920790214502277133099987729459596952817044582181956080965811702798062\ 6698912050615607423256868422713062950098644218534708104071289176469065508361299\ 1669477802382250278966784348919940965736170458678624255400694251669397929262471\ 4524945408858422726153755260071904336329196375777502176005195800693847635789586\ 8784895368721228985578068265181927036320994801558744555751753127364714212955364\ 9408438558661520801211507907506855334448925869328385965301327204697069457154695\ 9353658571788894862333292465202735853188533370948455403336565356988172582528918\ 0566354883637437933484118455801683318276768346462919956055134700391478768086403\ 2262961664156066750815371064672310846196424753749055374480531822600271021640098\ 0584497526023035640038083472053149941172965736785066421400842696497103241919182\ 1212132069397691439233683747092282677387081322366800869247034915868409911530983\ 1541206356612318750430546753698323082796645741762080659317726568584168183796610\ 6144963432544111706941700222657817358351259821080769101961052229263879745049019\ 2543119006205619065774524161919131875339840493439768233102984658933183730158095\ 9252282920682086223033258528011926649631444131644277300323779227471233069641714\ 9945532261035475145631290668854345426869788447742981777493710117614651624183616\ 6802548152963353084908499430067636548061029400946937506098455885580439704859144\ 4958444507997849704558355068540874516331646411808312307970438984919050658758642\ 5810738422420591191941674182490452700288263983057950057341711487031187142834184\ 4991534567029152801044851451760553069714417613685823841027876593246626899784183\ 1962031226242117739147720800488357833356920453393595325456489702855858973550575\ 1235129536540502842081022785248776603574246366673148680279486052445782673626230\ 8529782650571146248465959142102781227889414481639949738818846227682448516220518\ 1707672216986326570165431691974265123004175732990447353767253684579275436541282\ 6553581858046840069367718605020070547247548400805530424951854495267247261347318\ 1747421800785746934654471360369758841180294080396167469462885406791721386012254\ 1950381970453841726800639882065632879283958270851091995883944829777564715202613\ 2871089526163417707151642899487953564854553553148754978134009964854498635824847\ 6905900331169613037661279234643231297066284113074270462020320133683503854253603\ 1363676357521260470742531120923340283748294945310472741896928727557202761527226\ 8283376741393425652653283068469997597097750005560889932685025049212884068274139\ 8816315404564903507758716800740556857240217586854390532281337707074158307562696\ 2831695568742406052772648585305061135638485196591896864959633556821697543762143\ 0778665934730450164822432964891270709898076676625671517269062058815549666382573\ 8292741820822789606844882229833948166709840390242835143068137672534601260072692\ 6296946867275079434619043999661897961192875051944235640264430327173734159128149\ 6056168353988188569484045342311424613559925272330064881627466723523751234311893\ 44211888508507935816384899448754475633168921386967557430273795378526254 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:41:17 2004 Input: 3^3^3; 4^4^4; 5^5^5; 6^6^6; 7^7^7; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Wed Feb 18 2004 07:40:54 on modular [Seed = 2398983155] ------------------------------------- 7625597484987 1340780792994259709957402499820584612747936582059239337772356144372176403007354\ 6976801874298166903427690031858186486050853753882811946569946433649006084096 1911012597945477520356404559703964599198081048990094337139512789246520530242615\ 8030120593865197398502655864401557944622353592127886738069722884101469159866020\ 8796189675719570183928166033804761122597553362610100148265112341314776825241149\ 3094447176965282756285196737514395357542479093219206641883011787169122552421070\ 0507090646743828708514499502565861944615431835113798491336917799281274338404315\ 4923685552678359637410210533154603135372532574863690915977869032826645918298381\ 5230286936572873691422648131291743762136325730321645282979486862576245362218017\ 6732249405676428193600787207138370723553054463561539464011853484937927195145945\ 0550823274922160584891291094518995994868619954314766693801303717616359259447974\ 6164220050885079469804487133205133160739134230540198872570038329801246050197013\ 4673971759090273894939238173157869968458997947810680428224360937839463352654228\ 1570430283244238551508231649096728571217170812323279048181726832751011274678231\ 7410985888683708522000711733492253913322300756147180429007527677793352306200618\ 2860124552542430610068948054465847048206509826643193609603887362585107470743406\ 3628697657670269925864995355797631817390255089133122329474393034395616132833407\ 2831663498258145226862004307799084688103804187368324800903873596212919633602583\ 1207816736737425333228792969072054905956214068888259912445818423795978634764843\ 1567376092362509037151179894142426227022006628648686786871018298087280256069310\ 1949280830825044198424796792058908817112327192301455582916746795197430548026404\ 6468540027339938607985944659615017525869658114475685100415686877309037124825353\ 4383928539759874945849705003822501248928400182659005625128618762993804440734014\ 2347062055785305325034918189589707199305662188512963187501743535960282201038211\ 6160485451210393133122563322607664362366882968502088394961428304847391139916696\ 2264994856368523471287329479668088450940589395110465094413790950227654565313301\ 8670633521323028460519434381399810561400652595300731790772711065783494174642684\ 7209561346473277485842382748996687550525043942182321913572230540667153733742485\ 4364566378204570165459321815405354839361425066449858540330746646854189014813434\ 7714650315037954175778622811776585876941680908203125 2659119772153226779682489404387918594905342200269924300660432789497073559873882\ 9091213422929061755830324406828265067234256016357755902793896426126110930203989\ 3034777446061389442537960087466214788422902213385381919290542791575075927495293\ 5109319020362271989830578539328807633196834507090639946131138999460277671978289\ 4125322123292520329605118204879136400838954904436579209562671262919222892246094\ 4103484957826646121969087967503992005139138817452525944319386504163034800032329\ 5729231692725808120388628956451330203199414186213654593812478970390749485268614\ 9719642484285627826487208185484939372990256931327191655440604310691360290106405\ 5895953421212374607966076698330673506053248292555308212118869609719907808556324\ 6046013216102655431476452400396602364732664246252767374593256582134654265209220\ 0423701432404566464797038786340284767995163013023205896206379946238959999623765\ 3062587414899860913010693318793720947688749687131107213871394369489435728806106\ 1557708461902289692063089736008186036231141171109877425423962410946849388972369\ 2229868569843429449642470140802948317293238661862906599604019822684282364653842\ 2586113704883857989007702229553937496834838684871215875596667442178077474619334\ 1210284889327660838136389953101390774574758301775513253381447321315090878342620\ 2141074589657337735067867485009838541438860204109111373970447647124896178134657\ 6074509649789560993834854196961759483379704895730837108476073243820752302407048\ 5676366743247949452619568563043097519281279901865567251422836828609153126216460\ 7345315800880321538864368261641121986701237220967952805350151681595261506024638\ 5651031976562807101388014614012727625982704958770707410574826165853317280489979\ 6647665799512016121857794554314732807944463937679710202841966709590373326913064\ 8509487971165760759273875265486950175533115298307542310219922387378915117039469\ 8211199449920074131308554214681213100553681303428933484193987068952218348302678\ 8318279211074015593520658290920832202358534204685761697532570041173608482405870\ 8316251068319872736680439547350926932156113607132883103875634505032211015537060\ 5205773322174682858545420089112607776943756235718685791083329489150388849193534\ 3685602140772592750173300818010227855065558133740979531794020135520818832606782\ 0100816398249113946898528658683952592451639902206088916703402630725949553703103\ 6865710606177193275628159515876151135875206383384565803345010001967990900297897\ 7210476250415036861890539382236467101342139404047198098937821736422631345084415\ 5084928788944718684436772321138168459653343097848549218348328628086605976293753\ 3235790152346913482052907574065476985428074987463200630523320192960729488033220\ 1004717281324198437509334189946518277661952803985354578792105909387255417312074\ 7621525117838001854428727026143848075169886235092312850223508774079275269944791\ 6376634508067462510897466136541982989588498885556218913512465902304156653376336\ 8715666883872519670361529007800640686028880699319352079993106891407764243519484\ 1873000496551583222171096899743145933378494129522944030965551185586702844503519\ 8762119848288829295380202219936661078120427828843001276230841951275304807279299\ 9430981041279846531138489663915470801660511525166958395469518574113425090292056\ 5803702371824003777483260335454309351150011847970153429740074513674484611585461\ 8011592988204941297108616076522379205004659217817374565514468243397003282844487\ 4727091779059199199358992754255739644938275793654460000274764771917984145132545\ 8165027536733301982127884317270946575069275217180859490121750950120741742161758\ 6944497161282705033574579740947969818330006129341292987484417693746915156267819\ 6944190690705517408341270110116530574809547623023762237215060111172786568367816\ 8746764256566024505419592238301506354098330297656458503223221234832849268443851\ 7686135813543777864727386998363224693825363151801851106716453198841449354389812\ 1913341135214098433302365245387920761986009692225770264786814922275015405662983\ 5170763956641633686286846795059729747683692320947290092229370228618694089033287\ 8669151652070026861441427046793265655884082960714097320267268049408177667445088\ 4965348180178536723618226884857339133854002554565679342826314848719771140478757\ 0805868543619247666329872476144815634284283040260250502157420429656415893036607\ 8365481437442997463536675091000411699963360673064732160583745460680016965456758\ 5660962905152709201645875359613001828866538307844122009421906770504442910472440\ 0338945610254181442573942904470433088000869614865383635497648482086438633359077\ 2821957611006776947872616515008395331769033371947624815253698065061836502368055\ 4431459093152034405561484568860650743316691318968247599582565088000180171489431\ 1432338616140040591744676003585928270381442887477162496213203619776525245493346\ 7861555487197397619695431510692383342974202667545414955466938030160673169706724\ 4626258551370851645391322577304348105969848017839230034831055415640301000157431\ 8363088271619670316655426565096307103879220539680315920477904433236931651777785\ 9190655421620788215534975404890121605354486244302325493234970592691383707828560\ 1349377225336743205365375169877349183777799512554222275972716118029303245222040\ 2175805775241249712745521825292094227842847947169853969781345269676790717922850\ 8491839775153628228243052306992659549440199892772061036616473355839050070498310\ 4734871820642675450015770792062615402032657173010642210191250683502667912493991\ 7960929109036707635684925844071845295552207259748158406331181740311377161873180\ 1958998128677729597378367094064062033675539166479397859978760723803175210934594\ 3211213245184776643282291717067329390590611377334237254454253333764205685000119\ 3700991122080485436988881739995354037296008464004215102803014253112283196161957\ 1524522422266809290751616197961883530242609434051902857830543763397061153243582\ 4942105030926815212418399836123882923621685584810804537249260089845227867729237\ 3925746477183290922071023540633431838930936317317923907752973092138140886569986\ 9199075222777463146266117543342519940204770331943339078678783474761260772613750\ 6165832564303984452942500391460991393998606523780004197450420782411818751232638\ 0718368393963815092903223756458204021992572554406619436546545607277504604301995\ 3993748322983683489516208150738424224196778813811196748091317343045579356718550\ 3253077370951114339420093226364558981503238107164979185429453859587491416458261\ 1340382160163904914690554622878987393587127110178251704306000449333379035230261\ 3291297240328564529779500158901992057657168980489272863072158461749965174823389\ 9013735670497661974774566958118340094026521126535891155535929942925658149730479\ 9536927229726101711111934451119961877285162664439375171281088704824407739875503\ 2272241691310649437516764253759232572706022781934855221122174485770810461351760\ 7227866285161431584555506426114705436926937102207295289591203404452105297886929\ 0369227711092923808319201305155269917739063897908527599113641594775880324806565\ 8708433324533317375936823619422963019751271123958949266745154287327508514137369\ 6736275088647141468241347762353946251726651995399677652856675923289105145097886\ 7257444586595186908132381256973600847975826933474902529005843319787694328408058\ 0745193611989429990468280533178199550083230163227944716082271056280731820677005\ 3559618683620245098910221398201256238417876905853099286122673035956258245084360\ 1854424142186404275027338471616760698128093125032964959943475205297146297336367\ 2222035938392416581 ** WARNING: Output too long, hence truncated. Errors: /home/mfd/gomagma: line 2: 27557 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:42:52 2004 Input: Factorial(18); GCD(15130,3162); Output: Magma V2.10-6 Wed Feb 18 2004 07:42:49 on modular [Seed = 2247530599] ------------------------------------- 6402373705728000 34 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:46:31 2004 Input: "Number of permutations of five objects is",Factorial(5); Output: Magma V2.10-6 Wed Feb 18 2004 07:46:27 on modular [Seed = 2548336920] ------------------------------------- Number of permutations of five objects is 120 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:49:29 2004 Input: rqA5:=1492478; rqA5*10; rqA5:=rqA5+1; ShowIdentifiers(); ShowValues(); Output: Magma V2.10-6 Wed Feb 18 2004 07:49:26 on modular [Seed = 3986616976] ------------------------------------- 14924780 rqA5 rqA5: 1492479 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:57:09 2004 Input: IsPrime(257); IsPrime(2^59-1); IsPrime(2^61-1); IsPrime(2^67-1); Output: Magma V2.10-6 Wed Feb 18 2004 07:57:06 on modular [Seed = 4102542845] ------------------------------------- true false true false Total time: 3.019 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:57:34 2004 Input: IsPrime(2^521-1); Output: Magma V2.10-6 Wed Feb 18 2004 07:57:31 on modular [Seed = 3283149523] ------------------------------------- true Total time: 3.689 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:58:11 2004 Input: IsPrime(2^2281-1); Output: Magma V2.10-6 Wed Feb 18 2004 07:57:48 on modular [Seed = 3668573117] ------------------------------------- true Total time: 22.250 seconds, Total memory usage: 3.00MB ************** MAGMA ***************** Host 3(NXDOMAIN) (159.226.47.109) Time: Wed Feb 18 08:01:02 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Wed Feb 18 2004 08:00:59 on modular [Seed = 1045240857] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 08:01:12 2004 Input: a:=6; b:=8; c:=10; if (a gt (b+c)) and (b gt (c+a)) and (c gt (a+b)) then s:=(a+b+c)/2; "Area is", Sqrt(s*(s-a)*(s-b)*(s-c)), "square units."; else "Triangle is degenerate."; endif; Output: Magma V2.10-6 Wed Feb 18 2004 08:01:08 on modular [Seed = 24257337] ------------------------------------- User error: syntax error at end of input Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 08:01:24 2004 Input: a:=6; b:=8; c:=10; if (a gt (b+c)) and (b gt (c+a)) and (c gt (a+b)) then s:=(a+b+c)/2; "Area is", Sqrt(s*(s-a)*(s-b)*(s-c)), "square units."; else "Triangle is degenerate."; endif Output: Magma V2.10-6 Wed Feb 18 2004 08:01:21 on modular [Seed = 443103255] ------------------------------------- User error: syntax error at end of input Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 08:01:34 2004 Input: a:=6; b:=8; c:=10; if (a gt (b+c)) and (b gt (c+a)) and (c gt (a+b)) then s:=(a+b+c)/2; "Area is", Sqrt(s*(s-a)*(s-b)*(s-c)), "square units."; else "Triangle is degenerate."; end if Output: Magma V2.10-6 Wed Feb 18 2004 08:01:31 on modular [Seed = 1813991019] ------------------------------------- Triangle is degenerate. Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 08:03:27 2004 Input: a:=6; b:=8; c:=10; if ((a+b) gt c) and ((b+c) gt a) and ((c+a) gt b) then s:=(a+b+c)/2; "Area is", Sqrt(s*(s-a)*(s-b)*(s-c)), "square units."; else "Triangle is degenerate."; end if Output: Magma V2.10-6 Wed Feb 18 2004 08:03:24 on modular [Seed = 1712669910] ------------------------------------- Area is 24.00000000000000000000000000 square units. Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 08:03:46 2004 Input: a:=6; b:=8; c:=15; if ((a+b) gt c) and ((b+c) gt a) and ((c+a) gt b) then s:=(a+b+c)/2; "Area is", Sqrt(s*(s-a)*(s-b)*(s-c)), "square units."; else "Triangle is degenerate."; end if Output: Magma V2.10-6 Wed Feb 18 2004 08:03:43 on modular [Seed = 2131516924] ------------------------------------- Triangle is degenerate. Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host scylla.inria.fr. (138.96.81.2) Time: Wed Feb 18 08:18:03 2004 Input: 2+2; Output: Magma V2.10-6 Wed Feb 18 2004 08:18:00 on modular [Seed = 1462006131] ------------------------------------- 4 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host host250-185.pool81115.interbusiness.it. (81.115.185.250) Time: Wed Feb 18 09:47:30 2004 Input: a=1:100 Output: Magma V2.10-6 Wed Feb 18 2004 09:47:27 on modular [Seed = 7551698] ------------------------------------- >> a=1:100; ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host host250-185.pool81115.interbusiness.it. (81.115.185.250) Time: Wed Feb 18 09:47:47 2004 Input: a:=1 Output: Magma V2.10-6 Wed Feb 18 2004 09:47:44 on modular [Seed = 459808806] ------------------------------------- Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD95438A3.dip.t-dialin.net. (217.84.56.163) Time: Wed Feb 18 14:07:20 2004 Input: > t := { n^2 : n in [-11..11 by 2] | IsPrime(n) }; Output: Magma V2.10-6 Wed Feb 18 2004 14:07:17 on modular [Seed = 927252706] ------------------------------------- Total time: 3.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD95438A3.dip.t-dialin.net. (217.84.56.163) Time: Wed Feb 18 14:07:43 2004 Input: > t := { n^2 : n in [-11..11 by 2] | IsPrime(n) }; t Output: Magma V2.10-6 Wed Feb 18 2004 14:07:40 on modular [Seed = 542365676] ------------------------------------- { 9, 25, 49, 121 } Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD95438A3.dip.t-dialin.net. (217.84.56.163) Time: Wed Feb 18 14:08:17 2004 Input: t := { n^2 : n in [-11..11 by 2] | IsPrime(n) } t Output: Magma V2.10-6 Wed Feb 18 2004 14:08:14 on modular [Seed = 693817607] ------------------------------------- >> t; ^ User error: bad syntax Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD95438A3.dip.t-dialin.net. (217.84.56.163) Time: Wed Feb 18 14:08:29 2004 Input: t := { n^2 : n in [-11..11 by 2] | IsPrime(n) }; t Output: Magma V2.10-6 Wed Feb 18 2004 14:08:26 on modular [Seed = 308406792] ------------------------------------- { 9, 25, 49, 121 } Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD95438A3.dip.t-dialin.net. (217.84.56.163) Time: Wed Feb 18 14:11:28 2004 Input: XGCD(21, 27) Output: Magma V2.10-6 Wed Feb 18 2004 14:11:25 on modular [Seed = 91684328] ------------------------------------- 3 4 -3 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD95438A3.dip.t-dialin.net. (217.84.56.163) Time: Wed Feb 18 14:12:33 2004 Input: d, p, q := XGCD(21, 27); d, p, q; Output: Magma V2.10-6 Wed Feb 18 2004 14:12:30 on modular [Seed = 243136288] ------------------------------------- 3 4 -3 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD95438A3.dip.t-dialin.net. (217.84.56.163) Time: Wed Feb 18 14:13:02 2004 Input: d, p, q := XGCD(a, b); d, p, q; Output: Magma V2.10-6 Wed Feb 18 2004 14:12:59 on modular [Seed = 1996787324] ------------------------------------- >> d, p, q := XGCD(a, b); ^ User error: Identifier 'a' has not been declared or assigned >> d, p, q; ^ User error: Identifier 'd' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD95438A3.dip.t-dialin.net. (217.84.56.163) Time: Wed Feb 18 14:13:44 2004 Input: a, b := 12, 8; d, p, q := XGCD(a, b); d, p, q; Output: Magma V2.10-6 Wed Feb 18 2004 14:13:41 on modular [Seed = 1611897141] ------------------------------------- >> a, b := 12, 8; ^ User error: bad syntax >> d, p, q := XGCD(a, b); ^ User error: Identifier 'a' has not been declared or assigned >> d, p, q; ^ User error: Identifier 'd' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD95438A3.dip.t-dialin.net. (217.84.56.163) Time: Wed Feb 18 14:15:31 2004 Input: a := 12; b := 8; d, p, q := XGCD(a, b); d, p, q; Output: Magma V2.10-6 Wed Feb 18 2004 14:15:28 on modular [Seed = 1847433102] ------------------------------------- 4 1 -1 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD95438A3.dip.t-dialin.net. (217.84.56.163) Time: Wed Feb 18 14:27:22 2004 Input: // Cartesian product of all combinations > firstnames := {"Margie", "Marion", "Myrtle", "Martha", "Mary"}; > surnames := {"Brown", "Green", "Grey", "Black", "White"}; > dogbreeds := {"terrier", "poodle", "great dane", "basset", "setter"}; > dognames := {"Loopsie", "Mooksie", "Smooksie", "Woopsie", "Poopsie"}; > C := car; > // Some useful functions are defined: > iff := 'eq'; // the '...' treats this operator as a function > implies := func< A, B | B or not A >; > S := { a : a in C | > implies(sn eq "Brown", (dn in {"Loopsie","Mooksie"})) and > implies(sn eq "Brown", (db ne "terrier")) and > iff(dn eq "Woopsie", db eq "poodle") and > implies(dn eq "Woopsie", fn ne "Mary") and > iff(fn eq "Marion", db eq "setter") and > implies(fn eq "Marion", dn ne "Loopsie") and > iff(fn eq "Margie", db eq "basset") and > implies(fn eq "Margie", (dn in {"Smooksie","Mooksie"})) and > implies(fn eq "Myrtle", sn ne "Grey") and > implies(fn eq "Myrtle", (dn in {"Poopsie","Smooksie"})) and > iff(fn eq "Martha", sn eq "Black") and > implies(fn eq "Martha", db ne "great dane") and > implies(sn eq "Grey", dn ne "Poopsie") and > iff(dn eq "Mooksie", sn eq "White") and > implies(sn eq "White", fn ne "Marion") > where fn, sn, db, dn is Explode(a) }; > findsoln := function(S, n) > if n eq 1 then > return {S}; > end if; > soln := {}; > T := S; > while #T ge n do > ExtractRep(~T, ~x); > sol:=$$({a : a in T | forall{i : i in [1..4] | a[i] ne x[i] }}, n-1); > soln join:= { Include(U, x) : U in sol | #U eq n-1 }; > end while; > return soln; > end function; > findsoln(S, 5); Output: Magma V2.10-6 Wed Feb 18 2004 14:27:18 on modular [Seed = 1211872494] ------------------------------------- { { , , , , } } Total time: 3.119 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD95438A3.dip.t-dialin.net. (217.84.56.163) Time: Wed Feb 18 14:33:20 2004 Input: > PartitionWithSeq:=function(set) > > function partnsq(seq) //returns sequence of sets of sets > if #seq le 1 then > return [{Seqset(seq)}]; > else > x := seq[#seq]; > p := partnsq(Prune(seq)); > return [Include(y, {x}) : y in p] > cat [ {Include(z, x)} join Exclude(y, z) : z in y, y in p ]; > end if; > end function; > > return Seqset(partnsq(Setseq(set))); > > end function; > > PartitionWithSeq( {1..2} ); Output: Magma V2.10-6 Wed Feb 18 2004 14:33:17 on modular [Seed = 3117040756] ------------------------------------- >> > ^ User error: bad syntax >> > ^ User error: bad syntax >> return Seqset(partnsq(Setseq(set))); ^ User error: A 'return' can only be used inside a procedure or function >> > ^ User error: bad syntax >> end function; ^ User error: bad syntax >> > ^ User error: bad syntax >> PartitionWithSeq( {1..2} );; ^ User error: Identifier 'PartitionWithSeq' has not been declared or assigned Total time: 3.099 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD95438A3.dip.t-dialin.net. (217.84.56.163) Time: Wed Feb 18 14:34:31 2004 Input: > function PartitionSet(s) > if #s le 1 then > return {{s}}; > else > x := Rep(s); > p := PartitionSet(Exclude(s, x)); > return {Include(y, {x}) : y in p} > join { {Include(z, x)} join Exclude(y, z) : z in y, y in p }; > end if; > end function; > PartitionWithSeq:=function(set) > > function partnsq(seq) //returns sequence of sets of sets > if #seq le 1 then > return [{Seqset(seq)}]; > else > x := seq[#seq]; > p := partnsq(Prune(seq)); > return [Include(y, {x}) : y in p] > cat [ {Include(z, x)} join Exclude(y, z) : z in y, y in p ]; > end if; > end function; > > return Seqset(partnsq(Setseq(set))); > > end function; > > PartitionWithSeq( {1..2} ); Output: Magma V2.10-6 Wed Feb 18 2004 14:34:28 on modular [Seed = 2748341719] ------------------------------------- >> > ^ User error: bad syntax >> > ^ User error: bad syntax >> return Seqset(partnsq(Setseq(set))); ^ User error: A 'return' can only be used inside a procedure or function >> > ^ User error: bad syntax >> end function; ^ User error: bad syntax >> > ^ User error: bad syntax >> PartitionWithSeq( {1..2} );; ^ User error: Identifier 'PartitionWithSeq' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam240-180.fas.harvard.edu. (140.247.240.180) Time: Thu Feb 19 11:30:29 2004 Input: 2+2; Output: Magma V2.10-6 Thu Feb 19 2004 11:30:26 on modular [Seed = 3718871353] ------------------------------------- 4 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host form.fas.harvard.edu. (140.247.29.178) Time: Thu Feb 19 11:54:58 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(R); O := MaximalOrder(K); [K!b : b in Basis(O)]; Output: Magma V2.10-6 Thu Feb 19 2004 11:54:54 on modular [Seed = 3100381856] ------------------------------------- >> K := NumberField(R); ^ Runtime error in 'NumberField': Bad argument types Argument types given: RngUPol >> O := MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> [K!b : b in Basis(O)];; ^ User error: Identifier 'K' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host form.fas.harvard.edu. (140.247.29.178) Time: Thu Feb 19 11:55:12 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3-2); O := MaximalOrder(K); [K!b : b in Basis(O)]; Output: Magma V2.10-6 Thu Feb 19 2004 11:55:08 on modular [Seed = 1228792674] ------------------------------------- [ 1, a, a^2 ] Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9022C27.dip.t-dialin.net. (217.2.44.39) Time: Thu Feb 19 12:17:41 2004 Input: HomogeneousInvariantsBayer:=function(IG,A,d: P:=1); // Thomas Bayer's algorithm; same purpose and same input as // HomogeneousInvariants n:=#A; K:=CoefficientRing(Parent(A[1][1])); if Type(P) eq RngIntElt then P:=PolynomialRing(K,n); AssignNames(~P,["x"*IntegerToString(i): i in [1..n]]); end if; S:=Parent(A[1][1]); m:=Rank(S); degs:=[TotalDegree(A[i][j]): i,j in [1..n]]; delta:=Max(degs); // Homogenize A if {e in {-1,delta}: e in degs} ne {true} then Ss:=PolynomialRing(K,m+1); emb:=homSs | [Ss.i: i in [1..m]]>; Ah:=[[Ss.(m+1)^(delta-TotalDegree(a))*emb(a): a in l]: l in A]; IGh:=ideal; S:=Ss; m +:= 1; else Ah:=A; IGh:=IG; end if; delta +:= 1; // The degree of the psi's IGh:=Homogenization(IGh,false); // the homogenizing variable ("X") comes last Ss:=Parent(IGh.1); emb:=homSs | [Ss.i: i in [1..m]]>; Ah:=[[emb(a): a in l]: l in Ah]; m +:= 1; S:=Ss; PS:=PolynomialRing(K,n+m); embS:=homPS | [PS.i: i in [1..m]]>; embP:=homPS | [PS.(m+i): i in [1..n]]>; psi:=homPS | [&+[embS(Ah[i][j])*embP(P.j): j in [1..n]]: i in [1..n]]>; mons:=MonomialsOfDegree(P,d); I:=ideal + ideal; // time G:=GroebnerBasis(Basis(I),d*delta); J:=[f: f in G | {Exponents(LeadingMonomial(f))[i] eq 0: i in [1..m-1]} eq {true}]; B:=[f: f in J | TotalDegree(f) eq d*delta]; spec:=homP | [1: i in [1..m]] cat [P.i: i in [1..n]]>; return [spec(b): b in B]; end function; Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed. ************** MAGMA ***************** Host sv4.ictp.trieste.it. (140.105.16.64) Time: Thu Feb 19 12:44:49 2004 Input: R:= PolynomialRing(Rationals()); f:=x^2-x+1; K:=NumberField(f); P:=MaximalOrder(K); M:=MatrixRing( P , 15 ) ! [ 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, 1, 0, 0, w, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, 1-w, 0, 0, 1-w, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 1, 1-w, 0, 0, 1-w, -1+w, -1, 1+w, 3, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, w, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -w, 0, 0, 0, 0, 1-w, 1-w, 1, 0, -1+w, 3, 0, 0, 0, 0, 0, -w, 1-w, 1-w, 1-w, 0, -w, 0, 0, 1-2*w, -1, 3, 0, 0, 0, 0, 1, 1-w, 0, 0, 0, 1, 0, 0, 1-w, -1, w, 3, 0, 0, 1, 0, 1, 0, 0, -1+w, -1, 0, 1, 1, -w, w, w, 3, 0, 1-w, 0, 1-w, 1-w, 0, 1, 0, 0, 0, 1-w, w, 1, 0, 1-w, 3 ]; for i := 1 to 15 do for j := i+1 to 15 do M[i,j]:=Trace(M[j,i])-M[j,i]; end for; end for; N:= MatrixRing( Integers() , 30 ) ! [ 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; for i := 1 to 15 do for j := 1 to 15 do N[i,j]:=Trace(M[i,j]); N[15+i,15+j]:=N[i,j]; N[15+i,j]:=Trace(w*M[i,j]); N[j,15+i]:=N[15+i,j]; end for; end for; L := LatticeWithGram(N); S := ShortestVectors(L); d:=#S; d; G := EmptyGraph(d); for i := 1 to d do for j := i+1 to d do if not (S[i],S[j]) eq 0 then AddEdge(~G, i, j); end if; end for; end for; Components(G); T := sub< L | S >; r := Rank(T); r; Determinant(L); H := AutomorphismGroup(L); #H; FactoredOrder(H); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Feb 19 2004 12:44:26 on modular [Seed = 3801503568] ------------------------------------- 36 [ { 1, 2, 3, 36, 4, 27, 28, 29, 30 }, { 32, 33, 5, 34, 6, 7, 8, 9, 10, 15, 16, 17, 18, 19, 20, 21, 22, 23 }, { 35, 24, 25, 26, 11, 12, 13, 14, 31 } ] 14 14348907 Errors: /home/mfd/gomagma: line 2: 2218 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host sv4.ictp.trieste.it. (140.105.16.64) Time: Thu Feb 19 12:45:31 2004 Input: R:= PolynomialRing(Rationals()); f:=x^2-x+1; K:=NumberField(f); P:=MaximalOrder(K); M:=MatrixRing( P , 15 ) ! [ 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, 1, 0, 0, w, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, 1-w, 0, 0, 1-w, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 1, 1-w, 0, 0, 1-w, -1+w, -1, 1+w, 3, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, w, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -w, 0, 0, 0, 0, 1-w, 1-w, 1, 0, -1+w, 3, 0, 0, 0, 0, 0, -w, 1-w, 1-w, 1-w, 0, -w, 0, 0, 1-2*w, -1, 3, 0, 0, 0, 0, 1, 1-w, 0, 0, 0, 1, 0, 0, 1-w, -1, w, 3, 0, 0, 1, 0, 1, 0, 0, -1+w, -1, 0, 1, 1, -w, w, w, 3, 0, 1-w, 0, 1-w, 1-w, 0, 1, 0, 0, 0, 1-w, w, 1, 0, 1-w, 3 ]; for i := 1 to 15 do for j := i+1 to 15 do M[i,j]:=Trace(M[j,i])-M[j,i]; end for; end for; N:= MatrixRing( Integers() , 30 ) ! [ 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; for i := 1 to 15 do for j := 1 to 15 do N[i,j]:=Trace(M[i,j]); N[15+i,15+j]:=N[i,j]; N[15+i,j]:=Trace(w*M[i,j]); N[j,15+i]:=N[15+i,j]; end for; end for; L := LatticeWithGram(N); S := ShortestVectors(L); d:=#S; d; G := EmptyGraph(d); for i := 1 to d do for j := i+1 to d do if not (S[i],S[j]) eq 0 then AddEdge(~G, i, j); end if; end for; end for; Components(G); Output: Magma V2.10-6 Thu Feb 19 2004 12:45:27 on modular [Seed = 4287318400] ------------------------------------- 36 [ { 1, 2, 3, 36, 4, 27, 28, 29, 30 }, { 32, 33, 5, 34, 6, 7, 8, 9, 10, 15, 16, 17, 18, 19, 20, 21, 22, 23 }, { 35, 24, 25, 26, 11, 12, 13, 14, 31 } ] Total time: 3.239 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sv4.ictp.trieste.it. (140.105.16.64) Time: Thu Feb 19 12:49:17 2004 Input: R:= PolynomialRing(Rationals()); f:=x^2-x+1; K:=NumberField(f); P:=MaximalOrder(K); M:=MatrixRing( P , 15 ) ! [ 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1+w, -2+w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, 0, 1, 0, -w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1-w, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, -1, w, w, 0, 0, 1-w, 1-w, 3, 0, 0, 0, 0, 0, 0, 0, 0, -w, -w, 1, -w, -1+w, -1+w, -1, 3, 0, 0, 0, 0, 0, 0, 0, 1-w, 1, 0, 1-w, 0, -1+w, -w, w, 3, 0, 0, 0, 0, 0, 1, 0, -w, -w, -1+w, -1, 1-w, -w, 0, 0, 3, 0, 0, 0, 0, -1+w, 1-w, 0, -2+w, 1, 0, 0, -w, 0, 0, -w, 3, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 1, w, 0, w, -1, 3, 0, 0, 0, 0, -1, w, 1, -1, -1, 0, w, 0, -w, 0, 1, 3, 0, 1, -1+w, 0, 1-w, -1+w, w, 0, 0, -w, -1+w, 1, -1, -w, -1, 3 ]; for i := 1 to 15 do for j := i+1 to 15 do M[i,j]:=Trace(M[j,i])-M[j,i]; end for; end for; N:= MatrixRing( Integers() , 30 ) ! [ 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; for i := 1 to 15 do for j := 1 to 15 do N[i,j]:=Trace(M[i,j]); N[15+i,15+j]:=N[i,j]; N[15+i,j]:=Trace(w*M[i,j]); N[j,15+i]:=N[15+i,j]; end for; end for; L := LatticeWithGram(N); S := ShortestVectors(L); d:=#S; d; G := EmptyGraph(d); for i := 1 to d do for j := i+1 to d do if not (S[i],S[j]) eq 0 then AddEdge(~G, i, j); end if; end for; end for; Components(G); T := sub< L | S >; r := Rank(T); r; Determinant(L); H := AutomorphismGroup(L); #H; FactoredOrder(H); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Feb 19 2004 12:48:54 on modular [Seed = 2832998374] ------------------------------------- 36 [ { 1, 3, 23, 6, 24, 25, 11, 28, 29 }, { 2, 4, 26 }, { 17, 18, 20, 5, 7, 27, 15, 32, 16 }, { 33, 12, 13, 35, 14, 8, 19, 9, 10 }, { 22, 36, 21 }, { 34, 30, 31 } ] 18 14348907 Errors: /home/mfd/gomagma: line 2: 2272 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host sv4.ictp.trieste.it. (140.105.16.64) Time: Thu Feb 19 12:51:35 2004 Input: R:= PolynomialRing(Rationals()); f:=x^2-x+1; K:=NumberField(f); P:=MaximalOrder(K); M:=MatrixRing( P , 15 ) ! [ 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1+w, -2+w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, 0, 1, 0, -w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1-w, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, -1, w, w, 0, 0, 1-w, 1-w, 3, 0, 0, 0, 0, 0, 0, 0, 0, -w, -w, 1, -w, -1+w, -1+w, -1, 3, 0, 0, 0, 0, 0, 0, 0, 1-w, 1, 0, 1-w, 0, -1+w, -w, w, 3, 0, 0, 0, 0, 0, 1, 0, -w, -w, -1+w, -1, 1-w, -w, 0, 0, 3, 0, 0, 0, 0, -1+w, 1-w, 0, -2+w, 1, 0, 0, -w, 0, 0, -w, 3, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 1, w, 0, w, -1, 3, 0, 0, 0, 0, -1, w, 1, -1, -1, 0, w, 0, -w, 0, 1, 3, 0, 1, -1+w, 0, 1-w, -1+w, w, 0, 0, -w, -1+w, 1, -1, -w, -1, 3 ]; for i := 1 to 15 do for j := i+1 to 15 do M[i,j]:=Trace(M[j,i])-M[j,i]; end for; end for; N:= MatrixRing( Integers() , 30 ) ! [ 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; for i := 1 to 15 do for j := 1 to 15 do N[i,j]:=Trace(M[i,j]); N[15+i,15+j]:=N[i,j]; N[15+i,j]:=Trace(w*M[i,j]); N[j,15+i]:=N[15+i,j]; end for; end for; L := LatticeWithGram(N); S := ShortestVectors(L); d:=#S; d; G := EmptyGraph(d); for i := 1 to d do for j := i+1 to d do if not (S[i],S[j]) eq 0 then AddEdge(~G, i, j); end if; end for; end for; Components(G); T := sub< L | S >; r := Rank(T); r; Determinant(L); H := AutomorphismGroup(L); #H; FactoredOrder(H); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Feb 19 2004 12:51:12 on modular [Seed = 3134066018] ------------------------------------- 36 [ { 1, 3, 23, 6, 24, 25, 11, 28, 29 }, { 2, 4, 26 }, { 17, 18, 20, 5, 7, 27, 15, 32, 16 }, { 33, 12, 13, 35, 14, 8, 19, 9, 10 }, { 22, 36, 21 }, { 34, 30, 31 } ] 18 14348907 Errors: /home/mfd/gomagma: line 2: 2290 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host sv4.ictp.trieste.it. (140.105.16.64) Time: Thu Feb 19 12:52:38 2004 Input: R:= PolynomialRing(Rationals()); f:=x^2-x+1; K:=NumberField(f); P:=MaximalOrder(K); M:=MatrixRing( P , 15 ) ! [ 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, 1, 0, 0, w, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, 1-w, 0, 0, 1-w, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 1, 1-w, 0, 0, 1-w, -1+w, -1, 1+w, 3, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, w, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -w, 0, 0, 0, 0, 1-w, 1-w, 1, 0, -1+w, 3, 0, 0, 0, 0, 0, -w, 1-w, 1-w, 1-w, 0, -w, 0, 0, 1-2*w, -1, 3, 0, 0, 0, 0, 1, 1-w, 0, 0, 0, 1, 0, 0, 1-w, -1, w, 3, 0, 0, 1, 0, 1, 0, 0, -1+w, -1, 0, 1, 1, -w, w, w, 3, 0, 1-w, 0, 1-w, 1-w, 0, 1, 0, 0, 0, 1-w, w, 1, 0, 1-w, 3 ]; for i := 1 to 15 do for j := i+1 to 15 do M[i,j]:=Trace(M[j,i])-M[j,i]; end for; end for; N:= MatrixRing( Integers() , 30 ) ! [ 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; for i := 1 to 15 do for j := 1 to 15 do N[i,j]:=Trace(M[i,j]); N[15+i,15+j]:=N[i,j]; N[15+i,j]:=Trace(w*M[i,j]); N[j,15+i]:=N[15+i,j]; end for; end for; L := LatticeWithGram(N); S := ShortestVectors(L); d:=#S; d; G := EmptyGraph(d); for i := 1 to d do for j := i+1 to d do if not (S[i],S[j]) eq 0 then AddEdge(~G, i, j); end if; end for; end for; Components(G); T := sub< L | S >; r := Rank(T); r; Determinant(L); H := AutomorphismGroup(L); #H; FactoredOrder(H); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Feb 19 2004 12:52:15 on modular [Seed = 3016164404] ------------------------------------- 36 [ { 1, 2, 3, 36, 4, 27, 28, 29, 30 }, { 32, 33, 5, 34, 6, 7, 8, 9, 10, 15, 16, 17, 18, 19, 20, 21, 22, 23 }, { 35, 24, 25, 26, 11, 12, 13, 14, 31 } ] 14 14348907 Errors: /home/mfd/gomagma: line 2: 2299 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host sv4.ictp.trieste.it. (140.105.16.64) Time: Thu Feb 19 12:56:50 2004 Input: R:= PolynomialRing(Rationals()); f:=x^2-x+1; K:=NumberField(f); P:=MaximalOrder(K); M:=MatrixRing( P , 15 ) ! [ 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, 1, 0, 0, w, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, 1-w, 0, 0, 1-w, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 1, 1-w, 0, 0, 1-w, -1+w, -1, 1+w, 3, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, w, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -w, 0, 0, 0, 0, 1-w, 1-w, 1, 0, -1+w, 3, 0, 0, 0, 0, 0, -w, 1-w, 1-w, 1-w, 0, -w, 0, 0, 1-2*w, -1, 3, 0, 0, 0, 0, 1, 1-w, 0, 0, 0, 1, 0, 0, 1-w, -1, w, 3, 0, 0, 1, 0, 1, 0, 0, -1+w, -1, 0, 1, 1, -w, w, w, 3, 0, 1-w, 0, 1-w, 1-w, 0, 1, 0, 0, 0, 1-w, w, 1, 0, 1-w, 3 ]; for i := 1 to 15 do for j := i+1 to 15 do M[i,j]:=Trace(M[j,i])-M[j,i]; end for; end for; N:= MatrixRing( Integers() , 30 ) ! [ 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; for i := 1 to 15 do for j := 1 to 15 do N[i,j]:=Trace(M[i,j]); N[15+i,15+j]:=N[i,j]; N[15+i,j]:=Trace(w*M[i,j]); N[j,15+i]:=N[15+i,j]; end for; end for; L := LatticeWithGram(N); H := AutomorphismGroup(L); #H; FactoredOrder(H); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Feb 19 2004 12:56:27 on modular [Seed = 426615195] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 2384 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host pD9543BA3.dip.t-dialin.net. (217.84.59.163) Time: Thu Feb 19 14:35:19 2004 Input: bezout(8,12); 3 + 5 Output: Magma V2.10-6 Thu Feb 19 2004 14:35:16 on modular [Seed = 2748771357] ------------------------------------- >> bezout(8,12); ^ User error: Identifier 'bezout' has not been declared or assigned 8 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 212-14-109-104.dialupb.inicia.es. (212.14.109.104) Time: Thu Feb 19 16:36:37 2004 Input: 2*4; Output: Magma V2.10-6 Thu Feb 19 2004 16:36:34 on modular [Seed = 2599417524] ------------------------------------- 8 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dhcp9536062.columbus.rr.com. (24.95.36.62) Time: Thu Feb 19 16:43:33 2004 Input: x*(x+1)*(0.028x+1) Output: Magma V2.10-6 Thu Feb 19 2004 16:43:29 on modular [Seed = 3100497653] ------------------------------------- >> x*(x+1)*(0.028x+1) ^ User error: bad syntax Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dhcp9536062.columbus.rr.com. (24.95.36.62) Time: Thu Feb 19 16:43:42 2004 Input: x*(x+1)*(0.028*x+1) Output: Magma V2.10-6 Thu Feb 19 2004 16:43:39 on modular [Seed = 2982469622] ------------------------------------- >> x*(x+1)*(0.028*x+1) ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host grewebdproxy1.net.external.hp.com. (192.6.111.72) Time: Fri Feb 20 04:05:56 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Fri Feb 20 2004 04:05:53 on modular [Seed = 2365129003] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host grewebdproxy1.net.external.hp.com. (192.6.111.72) Time: Fri Feb 20 04:10:09 2004 Input: Floor(9); Output: Magma V2.10-6 Fri Feb 20 2004 04:10:06 on modular [Seed = 3851447132] ------------------------------------- 9 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host grewebdproxy1.net.external.hp.com. (192.6.111.72) Time: Fri Feb 20 04:10:30 2004 Input: GCD(9,3); Output: Magma V2.10-6 Fri Feb 20 2004 04:10:26 on modular [Seed = 3936314815] ------------------------------------- 3 Total time: 3.189 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sv4.ictp.trieste.it. (140.105.16.64) Time: Fri Feb 20 05:29:41 2004 Input: R:= PolynomialRing(Rationals()); f:=x^2-x+1; K:=NumberField(f); P:=MaximalOrder(K); M:=MatrixRing( P , 13 ) ! [ 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2-w, -1+w, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1-2w, 1, 0, 1-w, 3, 0, 0, 0, 0, 0, 0, 0, 0, w, -1+w, -1+w, -1+2w, -1+w, 3, 0, 0, 0, 0, 0, 0, 0, w, 1, w, w, w, 1-w, 3, 0, 0, 0, 0, 0, 0, 2-w, -1, 1-w, 1, w, 0, -w, 3, 0, 0, 0, 0, 0, -1+w, 0, w, -1+w, -w, 0, 1, -1, 3, 0, 0, 0, 0, 1-w, -w, 1, 1, 0, -1, -w, 1, -w, 3, 0, 0, 0, 0, w, 0, 0, -1+w, 0, 1, -1, 1-w, 0, 3, 0, 0, 0, 0, 1-w, 1-w, -w, -w, -w, 0, 0, 0, w, 3, 0, -1+w, -1, -1+w, w, -w, 1, 0, -w, 1, 0, 0, 0, 4 ]; for i := 1 to 13 do for j := i+1 to 13 do M[i,j]:=Trace(M[j,i])-M[j,i]; end for; end for; N:= MatrixRing( Integers() , 26 ) ! [ 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; for i := 1 to 13 do for j := 1 to 13 do N[i,j]:=Trace(M[i,j]); N[13+i,13+j]:=N[i,j]; N[13+i,j]:=Trace(w*M[i,j]); N[j,13+i]:=N[13+i,j]; end for; end for; L := LatticeWithGram(N); S := ShortestVectors(L); d:=#S; d; G := EmptyGraph(d); for i := 1 to d do for j := i+1 to d do if not (S[i],S[j]) eq 0 then AddEdge(~G, i, j); end if; end for; end for; Components(G); T := sub< L | S >; r := Rank(T); r; Determinant(L); H := AutomorphismGroup(L); #H; FactoredOrder(H); Output: Magma V2.10-6 Fri Feb 20 2004 05:29:36 on modular [Seed = 4051980345] ------------------------------------- >> 1-2w, 1, 0, 1-w, 3, 0, 0, ^ User error: bad syntax >> w, -1+w, -1+w, -1+2w, -1+w, 3, 0, ^ User error: bad syntax >> ]; ^ User error: bad syntax >> M[i,j]:=Trace(M[j,i])-M[j,i]; ^ User error: Identifier 'M' has not been declared or assigned >> N[i,j]:=Trace(M[i,j]); ^ User error: Identifier 'M' has not been declared or assigned >> L := LatticeWithGram(N); ^ Runtime error in 'LatticeWithGram': Inner product matrix argument is not symmetric and positive definite >> S := ShortestVectors(L); ^ User error: Identifier 'L' has not been declared or assigned >> d:=#S; ^ User error: Identifier 'S' has not been declared or assigned >> d; ^ User error: Identifier 'd' has not been declared or assigned >> G := EmptyGraph(d); ^ User error: Identifier 'd' has not been declared or assigned >> for i := 1 to d do ^ User error: Identifier 'd' has not been declared or assigned >> Components(G); ^ User error: Identifier 'G' has not been declared or assigned >> T := sub< L | S >; ^ User error: Identifier 'L' has not been declared or assigned >> r := Rank(T); ^ User error: Identifier 'T' has not been declared or assigned >> r; ^ User error: Identifier 'r' has not been declared or assigned >> Determinant(L); ^ User error: Identifier 'L' has not been declared or assigned >> H := AutomorphismGroup(L); ^ User error: Identifier 'L' has not been declared or assigned >> #H; FactoredOrder(H); ^ User error: Identifier 'H' has not been declared or assigned >> #H; FactoredOrder(H); ^ User error: Identifier 'H' has not been declared or assigned Total time: 3.129 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sv4.ictp.trieste.it. (140.105.16.64) Time: Fri Feb 20 05:30:47 2004 Input: R:= PolynomialRing(Rationals()); f:=x^2-x+1; K:=NumberField(f); P:=MaximalOrder(K); M:=MatrixRing( P , 13 ) ! [ 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2-w, -1+w, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1-2*w, 1, 0, 1-w, 3, 0, 0, 0, 0, 0, 0, 0, 0, w, -1+w, -1+w, -1+2*w, -1+w, 3, 0, 0, 0, 0, 0, 0, 0, w, 1, w, w, w, 1-w, 3, 0, 0, 0, 0, 0, 0, 2-w, -1, 1-w, 1, w, 0, -w, 3, 0, 0, 0, 0, 0, -1+w, 0, w, -1+w, -w, 0, 1, -1, 3, 0, 0, 0, 0, 1-w, -w, 1, 1, 0, -1, -w, 1, -w, 3, 0, 0, 0, 0, w, 0, 0, -1+w, 0, 1, -1, 1-w, 0, 3, 0, 0, 0, 0, 1-w, 1-w, -w, -w, -w, 0, 0, 0, w, 3, 0, -1+w, -1, -1+w, w, -w, 1, 0, -w, 1, 0, 0, 0, 4 ]; for i := 1 to 13 do for j := i+1 to 13 do M[i,j]:=Trace(M[j,i])-M[j,i]; end for; end for; N:= MatrixRing( Integers() , 26 ) ! [ 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; for i := 1 to 13 do for j := 1 to 13 do N[i,j]:=Trace(M[i,j]); N[13+i,13+j]:=N[i,j]; N[13+i,j]:=Trace(w*M[i,j]); N[j,13+i]:=N[13+i,j]; end for; end for; L := LatticeWithGram(N); S := ShortestVectors(L); d:=#S; d; G := EmptyGraph(d); for i := 1 to d do for j := i+1 to d do if not (S[i],S[j]) eq 0 then AddEdge(~G, i, j); end if; end for; end for; Components(G); T := sub< L | S >; r := Rank(T); r; Determinant(L); H := AutomorphismGroup(L); #H; FactoredOrder(H); Output: Magma V2.10-6 Fri Feb 20 2004 05:30:40 on modular [Seed = 3801564010] ------------------------------------- 261 [ { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261 } ] 26 3228504075 6 [ <2, 1>, <3, 1> ] Total time: 6.729 seconds, Total memory usage: 8.21MB ************** MAGMA ***************** Host sv4.ictp.trieste.it. (140.105.16.64) Time: Fri Feb 20 05:48:41 2004 Input: R:= PolynomialRing(Rationals()); f:=x^2-x+1; K:=NumberField(f); P:=MaximalOrder(K); M:=MatrixRing( P , 15 ) ! [ 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, -w, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, -w, 2-w, -1+w, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1-2*w, 1, 0, 1-w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, w, -1+w, -1+w, -1+2*w, -1+w, 3, 0, 0, 0, 0, 0, 0, 0, 1-w, 0, w, 1, w, w, w, 1-w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 2-w, -1, 1-w, 1, w, 0, -w, 3, 0, 0, 0, 0, 0, 1-w, 1-w, -1+w, 0, w, -1+w, -w, 0, 1, -1, 3, 0, 0, 0, 0, -w, -w, 1-w, -w, 1, 1, 0, -1, -w, 1, -w, 3, 0, 0, 0, -w, 0, 0, w, 0, 0, -1+w, 0, 1, -1, 1-w, 0, 3, 0, 0, -w, 0, 0, 0, 1-w, 1-w, -w, -w, -w, 0, 0, 0, w, 3, 0, -w, 1-w, -1+w, -1, -1+w, w, -w, 1, 0, -w, 1, 0, 0, 0, 4 ]; for i := 1 to 15 do for j := i+1 to 15 do M[i,j]:=Trace(M[j,i])-M[j,i]; end for; end for; N:= MatrixRing( Integers() , 30 ) ! [ 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; for i := 1 to 15 do for j := 1 to 15 do N[i,j]:=Trace(M[i,j]); N[15+i,15+j]:=N[i,j]; N[15+i,j]:=Trace(w*M[i,j]); N[j,15+i]:=N[15+i,j]; end for; end for; L := LatticeWithGram(N); S := ShortestVectors(L); d:=#S; d; G := EmptyGraph(d); for i := 1 to d do for j := i+1 to d do if not (S[i],S[j]) eq 0 then AddEdge(~G, i, j); end if; end for; end for; Components(G); T := sub< L | S >; r := Rank(T); r; Determinant(L); H := AutomorphismGroup(L); #H; FactoredOrder(H); Output: ** WARNING: Computation used more memory than allowed. ** Magma V2.10-6 Fri Feb 20 2004 05:48:20 on modular [Seed = 2213946927] ------------------------------------- 9 [ { 1, 2, 3, 4, 5, 6, 7, 8, 9 } ] 4 14348907 Current total memory usage: 83.5MB, failed memory request: 43.4MB System Error: User memory limit has been reached >> #H; FactoredOrder(H); ^ Runtime error: Variable 'H' has not been initialized >> #H; FactoredOrder(H); ^ User error: Identifier 'H' has not been declared or assigned Total time: 20.100 seconds, Total memory usage: 87.60MB ************** MAGMA ***************** Host sv4.ictp.trieste.it. (140.105.16.64) Time: Fri Feb 20 05:59:35 2004 Input: R:= PolynomialRing(Rationals()); f:=x^2-x+1; K:=NumberField(f); P:=MaximalOrder(K); M:=MatrixRing( P , 14 ) ! [ 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, 2-w, -1+w, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1-2*w, 1, 0, 1-w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1, w, -1+w, -1+w, -1+2*w, -1+w, 3, 0, 0, 0, 0, 0, 0, 0, 0, w, 1, w, w, w, 1-w, 3, 0, 0, 0, 0, 0, 0, 0, 2-w, -1, 1-w, 1, w, 0, -w, 3, 0, 0, 0, 0, 0, 1-w, -1+w, 0, w, -1+w, -w, 0, 1, -1, 3, 0, 0, 0, 0, -w, 1-w, -w, 1, 1, 0, -1, -w, 1, -w, 3, 0, 0, 0, 0, 0, w, 0, 0, -1+w, 0, 1, -1, 1-w, 0, 3, 0, 0, 0, 0, 0, 1-w, 1-w, -w, -w, -w, 0, 0, 0, w, 3, 0, 1-w, -1+w, -1, -1+w, w, -w, 1, 0, -w, 1, 0, 0, 0, 4 ]; for i := 1 to 14 do for j := i+1 to 14 do M[i,j]:=Trace(M[j,i])-M[j,i]; end for; end for; N:= MatrixRing( Integers() , 28 ) ! [ 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; for i := 1 to 14 do for j := 1 to 14 do N[i,j]:=Trace(M[i,j]); N[14+i,14+j]:=N[i,j]; N[14+i,j]:=Trace(w*M[i,j]); N[j,14+i]:=N[14+i,j]; end for; end for; L := LatticeWithGram(N); S := ShortestVectors(L); d:=#S; d; G := EmptyGraph(d); for i := 1 to d do for j := i+1 to d do if not (S[i],S[j]) eq 0 then AddEdge(~G, i, j); end if; end for; end for; Components(G); T := sub< L | S >; r := Rank(T); r; Determinant(L); H := AutomorphismGroup(L); #H; FactoredOrder(H); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Feb 20 2004 05:59:12 on modular [Seed = 2916615541] ------------------------------------- 3 [ { 1, 2, 3 } ] 2 234365481 Errors: /home/mfd/gomagma: line 2: 6389 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 06:06:13 2004 Input: C := CartanMatrix( "A_5" ); Output: Magma V2.10-6 Fri Feb 20 2004 06:06:05 on modular [Seed = 1896143669] ------------------------------------- Total time: 4.489 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 06:06:39 2004 Input: C := CartanMatrix( "A_5" ); C; Output: Magma V2.10-6 Fri Feb 20 2004 06:06:35 on modular [Seed = 1746780682] ------------------------------------- [ 2 -1 0 0 0] [-1 2 -1 0 0] [ 0 -1 2 -1 0] [ 0 0 -1 2 -1] [ 0 0 0 -1 2] Total time: 3.599 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 06:08:57 2004 Input: C := CartanMatrix( "A_5" ); C; C^-1; Output: Magma V2.10-6 Fri Feb 20 2004 06:08:54 on modular [Seed = 1729285624] ------------------------------------- [ 2 -1 0 0 0] [-1 2 -1 0 0] [ 0 -1 2 -1 0] [ 0 0 -1 2 -1] [ 0 0 0 -1 2] >> C^-1;; ^ Runtime error in '^': Argument 1 is not invertible Total time: 3.089 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 06:17:54 2004 Input: C := CartanMatrix( "A_5" ); C; Output: Magma V2.10-6 Fri Feb 20 2004 06:17:51 on modular [Seed = 995006397] ------------------------------------- [ 2 -1 0 0 0] [-1 2 -1 0 0] [ 0 -1 2 -1 0] [ 0 0 -1 2 -1] [ 0 0 0 -1 2] Total time: 3.049 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 06:19:08 2004 Input: C := CartanMatrix( "A_5" ); C; Inverse("C"); Output: Magma V2.10-6 Fri Feb 20 2004 06:19:05 on modular [Seed = 843554626] ------------------------------------- [ 2 -1 0 0 0] [-1 2 -1 0 0] [ 0 -1 2 -1 0] [ 0 0 -1 2 -1] [ 0 0 0 -1 2] >> Inverse("C");; ^ Runtime error in 'Inverse': Bad argument types Argument types given: MonStgElt Total time: 3.079 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 06:19:31 2004 Input: C := CartanMatrix( "A_5" ); C; InverseC; Output: Magma V2.10-6 Fri Feb 20 2004 06:19:28 on modular [Seed = 760774708] ------------------------------------- [ 2 -1 0 0 0] [-1 2 -1 0 0] [ 0 -1 2 -1 0] [ 0 0 -1 2 -1] [ 0 0 0 -1 2] >> InverseC;; ^ User error: Identifier 'InverseC' has not been declared or assigned Total time: 3.059 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 06:19:40 2004 Input: C := CartanMatrix( "A_5" ); C; Inverse C; Output: Magma V2.10-6 Fri Feb 20 2004 06:19:37 on modular [Seed = 609323316] ------------------------------------- [ 2 -1 0 0 0] [-1 2 -1 0 0] [ 0 -1 2 -1 0] [ 0 0 -1 2 -1] [ 0 0 0 -1 2] >> Inverse C;; ^ User error: bad syntax Total time: 3.049 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 06:19:50 2004 Input: C := CartanMatrix( "A_5" ); C; Inverse ; Output: Magma V2.10-6 Fri Feb 20 2004 06:19:47 on modular [Seed = 3752489685] ------------------------------------- [ 2 -1 0 0 0] [-1 2 -1 0 0] [ 0 -1 2 -1 0] [ 0 0 -1 2 -1] [ 0 0 0 -1 2] Intrinsic 'Inverse' Signatures: ( x) -> GrpSLPElt ( x) -> GrpPermElt ( x) -> GrpRWSElt ( x) -> GrpGPCElt ( x) -> GrpBrdElt The inverse of x. ( ~x) Replace x with x^-1. ( m) -> Map Returns the inverse of the map m, which must have a preimage or calculation of an inverse defined. ( w) -> GrpFPElt The inverse of w. ( x) -> GrpLieElt The inverse of x. Total time: 3.119 seconds, Total memory usage: 2.61MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 06:23:26 2004 Input: C := CartanMatrix( "A_5" ); C; Determinant(C); Output: Magma V2.10-6 Fri Feb 20 2004 06:23:23 on modular [Seed = 3233115826] ------------------------------------- [ 2 -1 0 0 0] [-1 2 -1 0 0] [ 0 -1 2 -1 0] [ 0 0 -1 2 -1] [ 0 0 0 -1 2] 6 Total time: 3.059 seconds, Total memory usage: 2.11MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 06:24:33 2004 Input: C := CartanMatrix( "A_5" ); C; Determinant(C); C^(-1); Output: Magma V2.10-6 Fri Feb 20 2004 06:24:30 on modular [Seed = 4220409292] ------------------------------------- [ 2 -1 0 0 0] [-1 2 -1 0 0] [ 0 -1 2 -1 0] [ 0 0 -1 2 -1] [ 0 0 0 -1 2] 6 >> C^(-1);; ^ Runtime error in '^': Argument 1 is not invertible Total time: 3.039 seconds, Total memory usage: 2.11MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 06:25:30 2004 Input: C := CartanMatrix( "A_5" ); C; Determinant(C); 1/C; Output: Magma V2.10-6 Fri Feb 20 2004 06:25:27 on modular [Seed = 3919333143] ------------------------------------- [ 2 -1 0 0 0] [-1 2 -1 0 0] [ 0 -1 2 -1 0] [ 0 0 -1 2 -1] [ 0 0 0 -1 2] 6 >> 1/C;; ^ Runtime error in '/': Arguments are not compatible Argument types given: AlgMatElt, AlgMatElt Total time: 3.029 seconds, Total memory usage: 2.11MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 06:26:31 2004 Input: C := CartanMatrix( "A_5" ); C; Determinant(C); D := C^(-1); D; Output: Magma V2.10-6 Fri Feb 20 2004 06:26:27 on modular [Seed = 3818278238] ------------------------------------- [ 2 -1 0 0 0] [-1 2 -1 0 0] [ 0 -1 2 -1 0] [ 0 0 -1 2 -1] [ 0 0 0 -1 2] 6 >> D := C^(-1); ^ Runtime error in '^': Argument 1 is not invertible >> D; ^ User error: Identifier 'D' has not been declared or assigned Total time: 3.079 seconds, Total memory usage: 2.11MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 06:27:07 2004 Input: C := CartanMatrix( "A_5" ); C; Determinant(C); D := C ^(-1); D; Output: Magma V2.10-6 Fri Feb 20 2004 06:27:03 on modular [Seed = 2599368132] ------------------------------------- [ 2 -1 0 0 0] [-1 2 -1 0 0] [ 0 -1 2 -1 0] [ 0 0 -1 2 -1] [ 0 0 0 -1 2] 6 >> D := C ^(-1); ^ Runtime error in '^': Argument 1 is not invertible >> D; ^ User error: Identifier 'D' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 2.11MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 06:27:51 2004 Input: C := CartanMatrix( "A_2" ); C; Output: Magma V2.10-6 Fri Feb 20 2004 06:27:48 on modular [Seed = 2514500344] ------------------------------------- [ 2 -1] [-1 2] Total time: 3.099 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 06:28:29 2004 Input: C := CartanMatrix( "A_2" ); C; D := CartanMatrix( "A_2" ); D; D*C; Output: Magma V2.10-6 Fri Feb 20 2004 06:28:26 on modular [Seed = 2365137807] ------------------------------------- [ 2 -1] [-1 2] [ 2 -1] [-1 2] [ 5 -4] [-4 5] Total time: 3.049 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 06:29:10 2004 Input: C := CartanMatrix( "A_2" ); C; D := CartanMatrix( "A_2" ); D; D^2; Output: Magma V2.10-6 Fri Feb 20 2004 06:29:07 on modular [Seed = 2264082780] ------------------------------------- [ 2 -1] [-1 2] [ 2 -1] [-1 2] [ 5 -4] [-4 5] Total time: 3.049 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 06:29:21 2004 Input: C := CartanMatrix( "A_2" ); C; D := CartanMatrix( "A_2" ); D; D^2; Output: Magma V2.10-6 Fri Feb 20 2004 06:29:18 on modular [Seed = 2982420070] ------------------------------------- [ 2 -1] [-1 2] [ 2 -1] [-1 2] [ 5 -4] [-4 5] Total time: 2.999 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 06:29:42 2004 Input: C := CartanMatrix( "A_2" ); C; C^-1; Output: Magma V2.10-6 Fri Feb 20 2004 06:29:39 on modular [Seed = 2833057618] ------------------------------------- [ 2 -1] [-1 2] >> C^-1; ^ Runtime error in '^': Argument 1 is not invertible Total time: 2.939 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 06:31:25 2004 Input: C := CartanMatrix( "A_2" ); C; D:=C^2; C^-1 *D; Output: Magma V2.10-6 Fri Feb 20 2004 06:31:21 on modular [Seed = 1479403531] ------------------------------------- [ 2 -1] [-1 2] >> C^-1 *D; ^ Runtime error in '^': Argument 1 is not invertible Total time: 3.079 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 06:33:25 2004 Input: C := CartanMatrix( "A_2") Output: Magma V2.10-6 Fri Feb 20 2004 06:33:22 on modular [Seed = 1445193358] ------------------------------------- Total time: 3.009 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 06:33:47 2004 Input: C := CartanMatrix( "A_2"); C; C^3; Output: Magma V2.10-6 Fri Feb 20 2004 06:33:44 on modular [Seed = 1329266573] ------------------------------------- [ 2 -1] [-1 2] [ 14 -13] [-13 14] Total time: 3.029 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 06:34:16 2004 Input: C := CartanMatrix( "A_2"); C; D:=C^3; D^-1; Output: Magma V2.10-6 Fri Feb 20 2004 06:34:12 on modular [Seed = 1144124586] ------------------------------------- [ 2 -1] [-1 2] >> D^-1; ^ Runtime error in '^': Argument 1 is not invertible Total time: 3.029 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 06:34:51 2004 Input: C := CartanMatrix( "A_2"); C; D:=C^3; C/C; Output: Magma V2.10-6 Fri Feb 20 2004 06:34:48 on modular [Seed = 2097729023] ------------------------------------- [ 2 -1] [-1 2] >> C/C; ^ Runtime error in '/': Arguments are not compatible Argument types given: AlgMatElt, AlgMatElt Total time: 2.949 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 06:36:34 2004 Input: C := CartanMatrix( "A_2"); C; D=C^3; Output: Magma V2.10-6 Fri Feb 20 2004 06:36:31 on modular [Seed = 1813634313] ------------------------------------- [ 2 -1] [-1 2] >> D=C^3; ^ User error: Identifier 'D' has not been declared or assigned Total time: 3.079 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 06:36:47 2004 Input: C := CartanMatrix( "A_2"); C; C^3; Output: Magma V2.10-6 Fri Feb 20 2004 06:36:44 on modular [Seed = 1695601779] ------------------------------------- [ 2 -1] [-1 2] [ 14 -13] [-13 14] Total time: 3.009 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 06:41:04 2004 Input: GL2 := GeneralLinearGroup(2, R) B := GL2 ! [1,0, 0,1]; Output: Magma V2.10-6 Fri Feb 20 2004 06:41:01 on modular [Seed = 142457375] ------------------------------------- >> B := GL2 ! [1,0, 0,1]; ^ User error: bad syntax Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 06:41:19 2004 Input: GL2 := GeneralLinearGroup(2, R) I := GL2 ! [1,0, 0,1]; Output: Magma V2.10-6 Fri Feb 20 2004 06:41:16 on modular [Seed = 24425223] ------------------------------------- >> I := GL2 ! [1,0, 0,1]; ^ User error: bad syntax Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 06:41:33 2004 Input: GL2 := GeneralLinearGroup(2, R) x := GL2 ! [1,0, 0,1]; Output: Magma V2.10-6 Fri Feb 20 2004 06:41:30 on modular [Seed = 927106311] ------------------------------------- >> x := GL2 ! [1,0, 0,1]; ^ User error: bad syntax Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 06:41:52 2004 Input: GL2 := GeneralLinearGroup(2, R) x := GL2 ! [1,0, 0,1]; x; Output: Magma V2.10-6 Fri Feb 20 2004 06:41:49 on modular [Seed = 744070667] ------------------------------------- >> x := GL2 ! [1,0, 0,1]; ^ User error: bad syntax >> x; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 06:42:17 2004 Input: GL2 := GeneralLinearGroup(2, R); Output: Magma V2.10-6 Fri Feb 20 2004 06:42:14 on modular [Seed = 626038761] ------------------------------------- >> GL2 := GeneralLinearGroup(2, R); ^ User error: Identifier 'R' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 07:02:07 2004 Input: GL2 := GeneralLinearGroup(2); Output: Magma V2.10-6 Fri Feb 20 2004 07:02:04 on modular [Seed = 3868414336] ------------------------------------- >> GL2 := GeneralLinearGroup(2); ^ Runtime error in 'GeneralLinearGroup': Bad argument types Argument types given: RngIntElt Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 07:05:08 2004 Input: C := Matrix( 2, 2, [2,-1, -1,2]); C; Output: Magma V2.10-6 Fri Feb 20 2004 07:05:05 on modular [Seed = 2447648314] ------------------------------------- [ 2 -1] [-1 2] Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 07:05:32 2004 Input: C := Matrix( 2, 2, [2,-1, -1,2]); C; C^-1; Output: Magma V2.10-6 Fri Feb 20 2004 07:05:29 on modular [Seed = 2398828253] ------------------------------------- [ 2 -1] [-1 2] >> C^-1;; ^ Runtime error in '^': Argument 1 is not invertible Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 07:05:55 2004 Input: C := Matrix( 2, 2, [1,0, 0,1]); C; C^-1; Output: Magma V2.10-6 Fri Feb 20 2004 07:05:52 on modular [Seed = 2280800253] ------------------------------------- [1 0] [0 1] [1 0] [0 1] Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 07:06:58 2004 Input: C := Matrix( 2, 2, [3,0, 5,1]); C; C^-1; Output: Magma V2.10-6 Fri Feb 20 2004 07:06:55 on modular [Seed = 3167290553] ------------------------------------- [3 0] [5 1] >> C^-1;; ^ Runtime error in '^': Argument 1 is not invertible Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 07:07:45 2004 Input: C := Matrix( 2, 2, [3,0, 0,3]); C; C^-1; Output: Magma V2.10-6 Fri Feb 20 2004 07:07:42 on modular [Seed = 3049262433] ------------------------------------- [3 0] [0 3] >> C^-1;; ^ Runtime error in '^': Argument 1 is not invertible Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 07:09:58 2004 Input: C := Matrix( 2, 2, [3,0, 0,3]); C; C*4; Output: Magma V2.10-6 Fri Feb 20 2004 07:09:55 on modular [Seed = 2698320361] ------------------------------------- [3 0] [0 3] [12 0] [ 0 12] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 07:10:50 2004 Input: C := Matrix( 2, 2, [3,0, 0,3]); C; D := Matrix( 2, 2, [1/3,0, 0,1/3]); D; C*D; Output: Magma V2.10-6 Fri Feb 20 2004 07:10:47 on modular [Seed = 1461907019] ------------------------------------- [3 0] [0 3] [1/3 0] [ 0 1/3] [1 0] [0 1] Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 07:11:14 2004 Input: C := Matrix( 2, 2, [3,0, 0,3]); C; D := Matrix( 2, 2, [1/3,0, 0,1/3]); D^-1; C*D; Output: Magma V2.10-6 Fri Feb 20 2004 07:11:11 on modular [Seed = 1295578185] ------------------------------------- [3 0] [0 3] [3 0] [0 3] [1 0] [0 1] Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 07:11:30 2004 Input: C := Matrix( 2, 2, [3,0, 0,3]); C; D := Matrix( 2, 2, [1/3,0, 0,1/3]); D^-1; C*D; Output: Magma V2.10-6 Fri Feb 20 2004 07:11:27 on modular [Seed = 1144126832] ------------------------------------- [3 0] [0 3] [3 0] [0 3] [1 0] [0 1] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 07:12:19 2004 Input: C := Matrix( 2, 2, [3,0, 0,3]); C^-1; D := Matrix( 2, 2, [1/3,0, 0,1/3]); D^-1; Output: Magma V2.10-6 Fri Feb 20 2004 07:12:15 on modular [Seed = 1929824951] ------------------------------------- >> C^-1; ^ Runtime error in '^': Argument 1 is not invertible [3 0] [0 3] Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 07:13:28 2004 Input: C := Matrix( 2, 2, [3,0, 0,3]); D := Matrix( 2, 2, [1/3,2, 2,1/3]); D^-1; Output: Magma V2.10-6 Fri Feb 20 2004 07:13:24 on modular [Seed = 1780470741] ------------------------------------- [-3/35 18/35] [18/35 -3/35] Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 07:14:06 2004 Input: C := Matrix( 2, 2, [3,0, 0,3]); D := Matrix( 2, 2, [1/3,2, 2,1/3]); D^-1; D*D^-1; Output: Magma V2.10-6 Fri Feb 20 2004 07:14:03 on modular [Seed = 1612044848] ------------------------------------- [-3/35 18/35] [18/35 -3/35] [1 0] [0 1] Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 07:14:49 2004 Input: C := Matrix( 2, 2, [3,0, 0,3]); D := Matrix( 2, 2, [1/3,2, 1/3,2]); D^-1; D*D^-1; Output: Magma V2.10-6 Fri Feb 20 2004 07:14:45 on modular [Seed = 527082866] ------------------------------------- >> D^-1; ^ Runtime error in '^': Argument 1 is not invertible >> D*D^-1; ^ Runtime error in '^': Argument 1 is not invertible Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 07:15:12 2004 Input: C := Matrix( 2, 2, [3,0, 0,3]); C^-1; D := Matrix( 2, 2, [1/3,2, 1/3,2]); D^-1; D*D^-1; Output: Magma V2.10-6 Fri Feb 20 2004 07:15:09 on modular [Seed = 159167263] ------------------------------------- >> C^-1; ^ Runtime error in '^': Argument 1 is not invertible >> D^-1; ^ Runtime error in '^': Argument 1 is not invertible >> D*D^-1; ^ Runtime error in '^': Argument 1 is not invertible Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 07:19:01 2004 Input: C := Matrix( 2, 2, [9/3,0, 0,9/3]); C^-1; D := Matrix( 2, 2, [1/3,2, 1/3,2]); D^-1; D*D^-1; Output: Magma V2.10-6 Fri Feb 20 2004 07:18:58 on modular [Seed = 124959854] ------------------------------------- [1/3 0] [ 0 1/3] >> D^-1; ^ Runtime error in '^': Argument 1 is not invertible >> D*D^-1; ^ Runtime error in '^': Argument 1 is not invertible Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 07:19:42 2004 Input: C := Matrix( 2, 2, [9/3,0, 0,9/3]); C^-1; Output: Magma V2.10-6 Fri Feb 20 2004 07:19:39 on modular [Seed = 1045136702] ------------------------------------- [1/3 0] [ 0 1/3] Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 07:20:10 2004 Input: C := Matrix( 2, 2, [3/1,0, 0,3/1]); C^-1; Output: Magma V2.10-6 Fri Feb 20 2004 07:20:06 on modular [Seed = 744068864] ------------------------------------- [1/3 0] [ 0 1/3] Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 07:20:26 2004 Input: C := Matrix( 2, 2, [4/1,0, 0,4/1]); C^-1; Output: Magma V2.10-6 Fri Feb 20 2004 07:20:22 on modular [Seed = 3685638150] ------------------------------------- [1/4 0] [ 0 1/4] Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 07:22:10 2004 Input: C := Matrix( 2, 2, [4,0, 0,4]); C*1/1; Output: Magma V2.10-6 Fri Feb 20 2004 07:22:07 on modular [Seed = 3534186854] ------------------------------------- >> C*1/1; ^ Runtime error in '/': Coefficient ring of argument 1 is not a field Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 07:22:31 2004 Input: C := Matrix( 2, 2, [4,0, 0,4]); C*1; Output: Magma V2.10-6 Fri Feb 20 2004 07:22:28 on modular [Seed = 3384571286] ------------------------------------- [4 0] [0 4] Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sv4.ictp.trieste.it. (140.105.16.64) Time: Fri Feb 20 07:24:52 2004 Input: R:= PolynomialRing(Rationals()); f:=x^2-x+1; K:=NumberField(f); P:=MaximalOrder(K); M:=MatrixRing( P , 15 ) ! [ 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, w, 0, -1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1+w, -1, 1-w, w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2-w, -1+w, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, 0, w, 1-2*w, -1, -1+w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, -w, -1, -w, -1, -w, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, w, 1-w, -1, 0, 1, 1-2*w, -1+w, 3, 0, 0, 0, 0, 0, 0, -w, 1-w, w, -w, -1, -1+w, 1, 0, 0, 3, 0, 0, 0, 0, 0, -w, 1-w, -1, 0, 0, 0, -w, w, 1-w, 0, 3, 0, 0, 0, 0, 0, 0, w, 0, 0, -1+w, w, -w, -1, 1, -1-w, 3, 0, 0, 0, 0, 0, -w, -1+w, w, -w, -1, 1-w, -w, -w, -1, 1, 3, 0, 0, -1+w, -w, 1, 0, 1, w, -w, -1+w, 0, 1-w, 1-w, 0, -1+w, 3, 0, -1, -1, -w, 1, 1, -w, 0, 0, -1+w, -1, 0, -w, 1-w, 0, 3 ]; for i := 1 to 15 do for j := i+1 to 15 do M[i,j]:=Trace(M[j,i])-M[j,i]; end for; end for; N:= MatrixRing( Integers() , 30 ) ! [ 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; for i := 1 to 15 do for j := 1 to 15 do N[i,j]:=Trace(M[i,j]); N[15+i,15+j]:=N[i,j]; N[15+i,j]:=Trace(w*M[i,j]); N[j,15+i]:=N[15+i,j]; end for; end for; L := LatticeWithGram(N); S := ShortestVectors(L); d:=#S; d; G := EmptyGraph(d); for i := 1 to d do for j := i+1 to d do if not (S[i],S[j]) eq 0 then AddEdge(~G, i, j); end if; end for; end for; Components(G); T := sub< L | S >; r := Rank(T); r; Determinant(L); H := AutomorphismGroup(L); #H; FactoredOrder(H); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Feb 20 2004 07:24:29 on modular [Seed = 3350363105] ------------------------------------- 3 [ { 1, 2, 3 } ] 2 14348907 Errors: /home/mfd/gomagma: line 2: 7068 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host sv4.ictp.trieste.it. (140.105.16.64) Time: Fri Feb 20 07:26:31 2004 Input: R:= PolynomialRing(Rationals()); f:=x^2-x+1; K:=NumberField(f); P:=MaximalOrder(K); M:=MatrixRing( P , 15 ) ! [ 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, w, 0, -1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1+w, -1, 1-w, w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2-w, -1+w, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, 0, w, 1-2*w, -1, -1+w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, -w, -1, -w, -1, -w, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, w, 1-w, -1, 0, 1, 1-2*w, -1+w, 3, 0, 0, 0, 0, 0, 0, -w, 1-w, w, -w, -1, -1+w, 1, 0, 0, 3, 0, 0, 0, 0, 0, -w, 1-w, -1, 0, 0, 0, -w, w, 1-w, 0, 3, 0, 0, 0, 0, 0, 0, w, 0, 0, -1+w, w, -w, -1, 1, -1-w, 3, 0, 0, 0, 0, 0, -w, -1+w, w, -w, -1, 1-w, -w, -w, -1, 1, 3, 0, 0, -1+w, -w, 1, 0, 1, w, -w, -1+w, 0, 1-w, 1-w, 0, -1+w, 3, 0, -1, -1, -w, 1, 1, -w, 0, 0, -1+w, -1, 0, -w, 1-w, 0, 3 ]; for i := 1 to 15 do for j := i+1 to 15 do M[i,j]:=Trace(M[j,i])-M[j,i]; end for; end for; N:= MatrixRing( Integers() , 30 ) ! [ 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; for i := 1 to 15 do for j := 1 to 15 do N[i,j]:=Trace(M[i,j]); N[15+i,15+j]:=N[i,j]; N[15+i,j]:=Trace(w*M[i,j]); N[j,15+i]:=N[15+i,j]; end for; end for; L := LatticeWithGram(N); H := AutomorphismGroup(L); #H; FactoredOrder(H); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Feb 20 2004 07:26:06 on modular [Seed = 4035267701] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 7083 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host sv4.ictp.trieste.it. (140.105.16.64) Time: Fri Feb 20 07:31:47 2004 Input: R:= PolynomialRing(Rationals()); f:=x^2-x+1; K:=NumberField(f); P:=MaximalOrder(K); M:=MatrixRing( P , 15 ) ! [ 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, w, 0, -1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1+w, -1, 1-w, w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2-w, -1+w, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, 0, w, 1-2*w, -1, -1+w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, -w, -1, -w, -1, -w, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, w, 1-w, -1, 0, 1, 1-2*w, -1+w, 3, 0, 0, 0, 0, 0, 0, -w, 1-w, w, -w, -1, -1+w, 1, 0, 0, 3, 0, 0, 0, 0, 0, -w, 1-w, -1, 0, 0, 0, -w, w, 1-w, 0, 3, 0, 0, 0, 0, 0, 0, w, 0, 0, -1+w, w, -w, -1, 1, -1-w, 3, 0, 0, 0, 0, 0, -w, -1+w, w, -w, -1, 1-w, -w, -w, -1, 1, 3, 0, 0, -1+w, -w, 1, 0, 1, w, -w, -1+w, 0, 1-w, 1-w, 0, -1+w, 3, 0, -1, -1, -w, 1, 1, -w, 0, 0, -1+w, -1, 0, -w, 1-w, 0, 3 ]; for i := 1 to 15 do for j := i+1 to 15 do M[i,j]:=Trace(M[j,i])-M[j,i]; end for; end for; N:= MatrixRing( Integers() , 30 ) ! [ 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; for i := 1 to 15 do for j := 1 to 15 do N[i,j]:=Trace(M[i,j]); N[15+i,15+j]:=N[i,j]; N[15+i,j]:=Trace(w*M[i,j]); N[j,15+i]:=N[15+i,j]; end for; end for; L := LatticeWithGram(N); H := AutomorphismGroup(L); #H; FactoredOrder(H); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Feb 20 2004 07:31:24 on modular [Seed = 3868416161] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 7101 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host sv4.ictp.trieste.it. (140.105.16.64) Time: Fri Feb 20 07:32:44 2004 Input: R:= PolynomialRing(Rationals()); f:=x^2-x+1; K:=NumberField(f); P:=MaximalOrder(K); M:=MatrixRing( P , 14 ) ! [ 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1-w, w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2-w, -1+w, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, w, 1-2*w, -1, -1+w, 3, 0, 0, 0, 0, 0, 0, 0, 0, -w, -1, -w, -1, -w, 0, 3, 0, 0, 0, 0, 0, 0, 0, w, 1-w, -1, 0, 1, 1-2*w, -1+w, 3, 0, 0, 0, 0, 0, 0, 1-w, w, -w, -1, -1+w, 1, 0, 0, 3, 0, 0, 0, 0, 0, 1-w, -1, 0, 0, 0, -w, w, 1-w, 0, 3, 0, 0, 0, 0, 0, w, 0, 0, -1+w, w, -w, -1, 1, -1-w, 3, 0, 0, 0, 0, -w, -1+w, w, -w, -1, 1-w, -w, -w, -1, 1, 3, 0, 0, -w, 1, 0, 1, w, -w, -1+w, 0, 1-w, 1-w, 0, -1+w, 3, 0, -1, -w, 1, 1, -w, 0, 0, -1+w, -1, 0, -w, 1-w, 0, 3 ]; for i := 1 to 14 do for j := i+1 to 14 do M[i,j]:=Trace(M[j,i])-M[j,i]; end for; end for; N:= MatrixRing( Integers() , 28 ) ! [ 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; for i := 1 to 14 do for j := 1 to 14 do N[i,j]:=Trace(M[i,j]); N[14+i,14+j]:=N[i,j]; N[14+i,j]:=Trace(w*M[i,j]); N[j,14+i]:=N[14+i,j]; end for; end for; L := LatticeWithGram(N); S := ShortestVectors(L); d:=#S; d; G := EmptyGraph(d); for i := 1 to d do for j := i+1 to d do if not (S[i],S[j]) eq 0 then AddEdge(~G, i, j); end if; end for; end for; Components(G); T := sub< L | S >; r := Rank(T); r; Determinant(L); H := AutomorphismGroup(L); #H; FactoredOrder(H); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Feb 20 2004 07:32:21 on modular [Seed = 2632524434] ------------------------------------- 3 [ { 1, 2, 3 } ] 2 76527504 Errors: /home/mfd/gomagma: line 2: 7111 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 07:50:52 2004 Input: Q := RationalField(); C := Matrix( Q 2, [4,0, 0,4]); C^-1; Output: Magma V2.10-6 Fri Feb 20 2004 07:50:49 on modular [Seed = 2866604120] ------------------------------------- >> C := Matrix( Q 2, [4,0, 0,4]); ^ User error: bad syntax >> C^-1; ^ User error: Identifier 'C' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 07:51:03 2004 Input: Q := RationalField(); C := Matrix( Q, 2, [4,0, 0,4]); C^-1; Output: Magma V2.10-6 Fri Feb 20 2004 07:51:00 on modular [Seed = 2715280206] ------------------------------------- [1/4 0] [ 0 1/4] Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 07:52:22 2004 Input: Q := RationalField(); C := Matrix( Q, 2, CartanMatrix( "A_2" )); C^-1; Output: Magma V2.10-6 Fri Feb 20 2004 07:52:19 on modular [Seed = 1596529664] ------------------------------------- >> C := Matrix( Q, 2, CartanMatrix( "A_2" )); ^ Runtime error in 'Matrix': Bad argument types Argument types given: FldRat, RngIntElt, AlgMatElt >> C^-1; ^ User error: Identifier 'C' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 07:52:58 2004 Input: Q := RationalField(); CartanMatrix(Q, "A_2" )); C^-1; Output: Magma V2.10-6 Fri Feb 20 2004 07:52:55 on modular [Seed = 1344672555] ------------------------------------- >> CartanMatrix(Q, "A_2" )); ^ User error: bad syntax >> C^-1; ^ User error: Identifier 'C' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 07:53:08 2004 Input: Q := RationalField(); CartanMatrix(Q, "A_2" ); C^-1; Output: Magma V2.10-6 Fri Feb 20 2004 07:53:04 on modular [Seed = 1245448486] ------------------------------------- >> CartanMatrix(Q, "A_2" ); ^ Runtime error in 'CartanMatrix': Bad argument types Argument types given: FldRat, MonStgElt >> C^-1; ^ User error: Identifier 'C' has not been declared or assigned Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 07:53:43 2004 Input: Q := RationalField(); C:=CartanMatrix("A_2" ); C^-1; Output: Magma V2.10-6 Fri Feb 20 2004 07:53:39 on modular [Seed = 1127546956] ------------------------------------- >> C^-1; ^ Runtime error in '^': Argument 1 is not invertible Total time: 3.039 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 07:53:53 2004 Input: Q := RationalField(); C:=CartanMatrix(Q, "A_2" ); C^-1; Output: Magma V2.10-6 Fri Feb 20 2004 07:53:50 on modular [Seed = 1946302326] ------------------------------------- >> C:=CartanMatrix(Q, "A_2" ); ^ Runtime error in 'CartanMatrix': Bad argument types Argument types given: FldRat, MonStgElt >> C^-1; ^ User error: Identifier 'C' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 07:54:45 2004 Input: Q := RationalField(); C:=CartanMatrix("A_2" ); B:=Matrix(Q C); Output: Magma V2.10-6 Fri Feb 20 2004 07:54:42 on modular [Seed = 1830497955] ------------------------------------- >> B:=Matrix(Q C);; ^ User error: bad syntax Total time: 3.019 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 07:55:17 2004 Input: Q := RationalField(); C:=CartanMatrix("A_2" ); B:=Matrix(Q! C); Output: Magma V2.10-6 Fri Feb 20 2004 07:55:13 on modular [Seed = 1662328973] ------------------------------------- >> B:=Matrix(Q! C);; ^ Runtime error in '!': Illegal coercion LHS: FldRat RHS: AlgMatElt Total time: 3.099 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sv4.ictp.trieste.it. (140.105.16.64) Time: Fri Feb 20 07:56:38 2004 Input: R:= PolynomialRing(Rationals()); f:=x^2-x+1; K:=NumberField(f); P:=MaximalOrder(K); M:=MatrixRing( P , 15 ) ! [ 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, w, 0, -1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1+w, -1, 1-w, w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2-w, -1+w, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, 0, w, 1-2*w, -1, -1+w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, -w, -1, -w, -1, -w, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, w, 1-w, -1, 0, 1, 1-2*w, -1+w, 3, 0, 0, 0, 0, 0, 0, -w, 1-w, w, -w, -1, -1+w, 1, 0, 0, 3, 0, 0, 0, 0, 0, -w, 1-w, -1, 0, 0, 0, -w, w, 1-w, 0, 3, 0, 0, 0, 0, 0, 0, w, 0, 0, -1+w, w, -w, -1, 1, -1-w, 3, 0, 0, 0, 0, 0, -w, -1+w, w, -w, -1, 1-w, -w, -w, -1, 1, 3, 0, 0, -1+w, -w, 1, 0, 1, w, -w, -1+w, 0, 1-w, 1-w, 0, -1+w, 3, 0, -1, -1, -w, 1, 1, -w, 0, 0, -1+w, -1, 0, -w, 1-w, 0, 3 ]; for i := 1 to 15 do for j := i+1 to 15 do M[i,j]:=Trace(M[j,i])-M[j,i]; end for; end for; N:= MatrixRing( Integers() , 30 ) ! [ 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; for i := 1 to 15 do for j := 1 to 15 do N[i,j]:=Trace(M[i,j]); N[15+i,15+j]:=N[i,j]; N[15+i,j]:=Trace(w*M[i,j]); N[j,15+i]:=N[15+i,j]; end for; end for; L := LatticeWithGram(N); S := ShortestVectors(L); d:=#S; d; G := EmptyGraph(d); for i := 1 to d do for j := i+1 to d do if not (S[i],S[j]) eq 0 then AddEdge(~G, i, j); end if; end for; end for; Components(G); T := sub< L | S >; r := Rank(T); r; Determinant(L); H := AutomorphismGroup(L); #H; FactoredOrder(H); X:=DerivedGroup(H); FactoredOrder(X); Y:=DerivedGroup(X); FactoredOrder(Y); Z:=DerivedGroup(Y); FactoredOrder(Z); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Feb 20 2004 07:56:15 on modular [Seed = 358831782] ------------------------------------- 3 [ { 1, 2, 3 } ] 2 14348907 Errors: /home/mfd/gomagma: line 2: 7241 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 07:57:05 2004 Input: Q := RationalField(); C:=CartanMatrix("A_2" ); C; B:=Matrix(Q! C); Output: Magma V2.10-6 Fri Feb 20 2004 07:57:02 on modular [Seed = 242764364] ------------------------------------- [ 2 -1] [-1 2] >> B:=Matrix(Q! C);; ^ Runtime error in '!': Illegal coercion LHS: FldRat RHS: AlgMatElt Total time: 3.049 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 07:57:34 2004 Input: Q := RationalField(); C:=CartanMatrix("A_2" ); C; B:=Matrix(Q, C); Output: Magma V2.10-6 Fri Feb 20 2004 07:57:30 on modular [Seed = 124863329] ------------------------------------- [ 2 -1] [-1 2] Total time: 3.029 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 07:57:57 2004 Input: Q := RationalField(); C:=CartanMatrix("A_2" ); C; B:=Matrix(Q, C); B^-1; Output: Magma V2.10-6 Fri Feb 20 2004 07:57:54 on modular [Seed = 944667702] ------------------------------------- [ 2 -1] [-1 2] [2/3 1/3] [1/3 2/3] Total time: 3.059 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 07:58:14 2004 Input: Q := RationalField(); C:=CartanMatrix("A_3" ); C; B:=Matrix(Q, C); B^-1; Output: Magma V2.10-6 Fri Feb 20 2004 07:58:11 on modular [Seed = 826766606] ------------------------------------- [ 2 -1 0] [-1 2 -1] [ 0 -1 2] [3/4 1/2 1/4] [1/2 1 1/2] [1/4 1/2 3/4] Total time: 3.039 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 08:00:19 2004 Input: Q := RationalField(); C:=CartanMatrix("A_2" ); C; B:=Matrix(Q, C); B^-1; Output: Magma V2.10-6 Fri Feb 20 2004 08:00:16 on modular [Seed = 3719010657] ------------------------------------- [ 2 -1] [-1 2] [2/3 1/3] [1/3 2/3] Total time: 3.029 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 08:00:55 2004 Input: Q := RationalField(); C:=CartanMatrix("A_4" ); C; B:=Matrix(Q, C); B^-1; Output: Magma V2.10-6 Fri Feb 20 2004 08:00:52 on modular [Seed = 3600847758] ------------------------------------- [ 2 -1 0 0] [-1 2 -1 0] [ 0 -1 2 -1] [ 0 0 -1 2] [4/5 3/5 2/5 1/5] [3/5 6/5 4/5 2/5] [2/5 4/5 6/5 3/5] [1/5 2/5 3/5 4/5] Total time: 3.049 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 08:01:40 2004 Input: Q := RationalField(); C:=CartanMatrix("A_4" ); C; Determinat(C); B:=Matrix(Q, C); B^-1; Output: Magma V2.10-6 Fri Feb 20 2004 08:01:36 on modular [Seed = 4186946708] ------------------------------------- [ 2 -1 0 0] [-1 2 -1 0] [ 0 -1 2 -1] [ 0 0 -1 2] >> Determinat(C); ^ User error: Identifier 'Determinat' has not been declared or assigned [4/5 3/5 2/5 1/5] [3/5 6/5 4/5 2/5] [2/5 4/5 6/5 3/5] [1/5 2/5 3/5 4/5] Total time: 2.989 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 08:01:52 2004 Input: Q := RationalField(); C:=CartanMatrix("A_4" ); C; determinat(C); B:=Matrix(Q, C); B^-1; Output: Magma V2.10-6 Fri Feb 20 2004 08:01:49 on modular [Seed = 4068784019] ------------------------------------- [ 2 -1 0 0] [-1 2 -1 0] [ 0 -1 2 -1] [ 0 0 -1 2] >> determinat(C); ^ User error: Identifier 'determinat' has not been declared or assigned [4/5 3/5 2/5 1/5] [3/5 6/5 4/5 2/5] [2/5 4/5 6/5 3/5] [1/5 2/5 3/5 4/5] Total time: 2.969 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 08:05:21 2004 Input: Q := RationalField(); C:=CartanMatrix("A_4" ); C; Determinant(C); B:=Matrix(Q, C); B^-1; Output: Magma V2.10-6 Fri Feb 20 2004 08:05:17 on modular [Seed = 3801392307] ------------------------------------- [ 2 -1 0 0] [-1 2 -1 0] [ 0 -1 2 -1] [ 0 0 -1 2] 5 [4/5 3/5 2/5 1/5] [3/5 6/5 4/5 2/5] [2/5 4/5 6/5 3/5] [1/5 2/5 3/5 4/5] Total time: 3.049 seconds, Total memory usage: 2.11MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 08:05:54 2004 Input: Q := RationalField(); C:=CartanMatrix("B2" ); C; Determinant(C); B:=Matrix(Q, C); B^-1; Output: Magma V2.10-6 Fri Feb 20 2004 08:05:51 on modular [Seed = 2616057320] ------------------------------------- [ 2 -2] [-1 2] 2 [ 1 1] [1/2 1] Total time: 3.129 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 08:06:33 2004 Input: Q := RationalField(); C:=CartanMatrix("B3" ); C; Determinant(C); B:=Matrix(Q, C); B^-1; Output: Magma V2.10-6 Fri Feb 20 2004 08:06:29 on modular [Seed = 2365246085] ------------------------------------- [ 2 -1 0] [-1 2 -2] [ 0 -1 2] 2 [ 1 1 1] [ 1 2 2] [1/2 1 3/2] Total time: 3.159 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 08:07:07 2004 Input: Q := RationalField(); C:=CartanMatrix("B4" ); C; Determinant(C); B:=Matrix(Q, C); B^-1; Output: Magma V2.10-6 Fri Feb 20 2004 08:07:04 on modular [Seed = 2247345057] ------------------------------------- [ 2 -1 0 0] [-1 2 -1 0] [ 0 -1 2 -2] [ 0 0 -1 2] 2 [ 1 1 1 1] [ 1 2 2 2] [ 1 2 3 3] [1/2 1 3/2 2] Total time: 3.079 seconds, Total memory usage: 2.11MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 08:08:05 2004 Input: Q := RationalField(); C:=CartanMatrix("C2" ); C; Determinant(C); B:=Matrix(Q, C); B^-1; Output: Magma V2.10-6 Fri Feb 20 2004 08:08:01 on modular [Seed = 3217684818] ------------------------------------- [ 2 -1] [-2 2] 2 [ 1 1/2] [ 1 1] Total time: 3.079 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 08:09:22 2004 Input: Q := RationalField(); C:=CartanMatrix("C2" ); C; DynkinDiagram( C ); Determinant(C); B:=Matrix(Q, C); B^-1; Output: Magma V2.10-6 Fri Feb 20 2004 08:09:19 on modular [Seed = 2965829139] ------------------------------------- [ 2 -1] [-2 2] C2 1 =<= 2 2 [ 1 1/2] [ 1 1] Total time: 3.049 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 08:10:18 2004 Input: Q := RationalField(); C:=CartanMatrix("C2" ); C; DynkinDiagram( C ); Determinant(C); B:=Matrix(Q, C); B^-1; Output: Magma V2.10-6 Fri Feb 20 2004 08:10:15 on modular [Seed = 2715281098] ------------------------------------- [ 2 -1] [-2 2] C2 1 =<= 2 2 [ 1 1/2] [ 1 1] Total time: 3.119 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 08:10:29 2004 Input: Q := RationalField(); C:=CartanMatrix("C3" ); C; DynkinDiagram( C ); Determinant(C); B:=Matrix(Q, C); B^-1; Output: Magma V2.10-6 Fri Feb 20 2004 08:10:26 on modular [Seed = 1428361802] ------------------------------------- [ 2 -1 0] [-1 2 -1] [ 0 -2 2] C3 1 - 2 =<= 3 2 [ 1 1 1/2] [ 1 2 1] [ 1 2 3/2] Total time: 3.079 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 08:11:07 2004 Input: Q := RationalField(); C:=CartanMatrix("C4" ); C; DynkinDiagram( C ); Determinant(C); B:=Matrix(Q, C); B^-1; Output: Magma V2.10-6 Fri Feb 20 2004 08:11:04 on modular [Seed = 1329137786] ------------------------------------- [ 2 -1 0 0] [-1 2 -1 0] [ 0 -1 2 -1] [ 0 0 -2 2] C4 1 - 2 - 3 =<= 4 2 [ 1 1 1 1/2] [ 1 2 2 1] [ 1 2 3 3/2] [ 1 2 3 2] Total time: 3.029 seconds, Total memory usage: 2.11MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 08:11:52 2004 Input: Q := RationalField(); C:=CartanMatrix("B2" ); C; DynkinDiagram( C ); Determinant(C); B:=Matrix(Q, C); B^-1; Output: Magma V2.10-6 Fri Feb 20 2004 08:11:49 on modular [Seed = 1177551246] ------------------------------------- [ 2 -2] [-1 2] B2 1 =>= 2 2 [ 1 1] [1/2 1] Total time: 3.059 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 08:12:18 2004 Input: Q := RationalField(); C:=CartanMatrix("B3" ); C; DynkinDiagram( C ); Determinant(C); B:=Matrix(Q, C); B^-1; Output: Magma V2.10-6 Fri Feb 20 2004 08:12:14 on modular [Seed = 2031042186] ------------------------------------- [ 2 -1 0] [-1 2 -2] [ 0 -1 2] B3 1 - 2 =>= 3 2 [ 1 1 1] [ 1 2 2] [1/2 1 3/2] Total time: 3.059 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 08:12:45 2004 Input: Q := RationalField(); C:=CartanMatrix("B4" ); C; DynkinDiagram( C ); Determinant(C); B:=Matrix(Q, C); B^-1; Output: Magma V2.10-6 Fri Feb 20 2004 08:12:42 on modular [Seed = 1879455719] ------------------------------------- [ 2 -1 0 0] [-1 2 -1 0] [ 0 -1 2 -2] [ 0 0 -1 2] B4 1 - 2 - 3 =>= 4 2 [ 1 1 1 1] [ 1 2 2 2] [ 1 2 3 3] [1/2 1 3/2 2] Total time: 3.070 seconds, Total memory usage: 2.11MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 08:13:22 2004 Input: Q := RationalField(); C:=CartanMatrix("D2" ); C; DynkinDiagram( C ); Determinant(C); B:=Matrix(Q, C); B^-1; Output: Magma V2.10-6 Fri Feb 20 2004 08:13:19 on modular [Seed = 1797074137] ------------------------------------- [2 0] [0 2] A1 1 A1 2 4 [1/2 0] [ 0 1/2] Total time: 3.119 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 08:14:41 2004 Input: Q := RationalField(); C:=CartanMatrix("D3" ); C; DynkinDiagram( C ); Determinant(C); B:=Matrix(Q, C); B^-1; Output: Magma V2.10-6 Fri Feb 20 2004 08:14:38 on modular [Seed = 493573502] ------------------------------------- [ 2 -1 -1] [-1 2 0] [-1 0 2] A3 2 - 1 - 3 4 [ 1 1/2 1/2] [1/2 3/4 1/4] [1/2 1/4 3/4] Total time: 3.119 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 08:16:48 2004 Input: Q := RationalField(); C:=CartanMatrix("D4" ); C; DynkinDiagram( C ); Determinant(C); B:=Matrix(Q, C); B^-1; Output: Magma V2.10-6 Fri Feb 20 2004 08:16:44 on modular [Seed = 325409778] ------------------------------------- [ 2 -1 0 0] [-1 2 -1 -1] [ 0 -1 2 0] [ 0 -1 0 2] D4 3 / 1 - 2 \ 4 4 [ 1 1 1/2 1/2] [ 1 2 1 1] [1/2 1 1 1/2] [1/2 1 1/2 1] Total time: 3.139 seconds, Total memory usage: 2.11MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 08:19:06 2004 Input: Q := RationalField(); C:=CartanMatrix("D5" ); C; DynkinDiagram( C ); Determinant(C); B:=Matrix(Q, C); B^-1; Output: Magma V2.10-6 Fri Feb 20 2004 08:19:03 on modular [Seed = 74599710] ------------------------------------- [ 2 -1 0 0 0] [-1 2 -1 0 0] [ 0 -1 2 -1 -1] [ 0 0 -1 2 0] [ 0 0 -1 0 2] D5 4 / 1 - 2 - 3 \ 5 4 [ 1 1 1 1/2 1/2] [ 1 2 2 1 1] [ 1 2 3 3/2 3/2] [1/2 1 3/2 5/4 3/4] [1/2 1 3/2 3/4 5/4] Total time: 3.149 seconds, Total memory usage: 2.11MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 08:21:36 2004 Input: Q := RationalField(); C:=CartanMatrix("E5" ); C; DynkinDiagram( C ); Determinant(C); B:=Matrix(Q, C); B^-1; Output: Magma V2.10-6 Fri Feb 20 2004 08:21:33 on modular [Seed = 826767537] ------------------------------------- CartanMatrix( N: E5 ) [/usr/local/magma/package/LieThry/Cartan.m:870]( type: false ) [/usr/local/magma/package/LieThry/Cartan.m:866]( type: false ) In file "/usr/local/magma/package/LieThry/Cartan.m", line 867, column 22: >> return forall{ t : t in type | t[1][1] in "ABCDEFG" }; ^ Runtime error in for: Iteration is not possible over this object >> C; ^ User error: Identifier 'C' has not been declared or assigned >> DynkinDiagram( C ); ^ User error: Identifier 'C' has not been declared or assigned >> Determinant(C); ^ User error: Identifier 'C' has not been declared or assigned >> B:=Matrix(Q, C); ^ User error: Identifier 'C' has not been declared or assigned >> B^-1;; ^ User error: Identifier 'B' has not been declared or assigned Total time: 3.229 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 08:22:53 2004 Input: DynkinDiagram("A2" ); Output: Magma V2.10-6 Fri Feb 20 2004 08:22:50 on modular [Seed = 677274207] ------------------------------------- A2 1 - 2 Total time: 3.119 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 08:23:15 2004 Input: DynkinDiagram("A3" ); Output: Magma V2.10-6 Fri Feb 20 2004 08:23:12 on modular [Seed = 575957055] ------------------------------------- A3 1 - 2 - 3 Total time: 3.109 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 08:23:34 2004 Input: DynkinDiagram("A4" ); Output: Magma V2.10-6 Fri Feb 20 2004 08:23:31 on modular [Seed = 3584270299] ------------------------------------- A4 1 - 2 - 3 - 4 Total time: 3.169 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 08:25:58 2004 Input: Q := RationalField(); C:=CartanMatrix("E6" ); C; DynkinDiagram( C ); Determinant(C); B:=Matrix(Q, C); B^-1; Output: Magma V2.10-6 Fri Feb 20 2004 08:25:55 on modular [Seed = 3418194293] ------------------------------------- [ 2 0 -1 0 0 0] [ 0 2 0 -1 0 0] [-1 0 2 -1 0 0] [ 0 -1 -1 2 -1 0] [ 0 0 0 -1 2 -1] [ 0 0 0 0 -1 2] E6 1 - 3 - 4 - 5 - 6 | 2 3 [ 4/3 1 5/3 2 4/3 2/3] [ 1 2 2 3 2 1] [ 5/3 2 10/3 4 8/3 4/3] [ 2 3 4 6 4 2] [ 4/3 2 8/3 4 10/3 5/3] [ 2/3 1 4/3 2 5/3 4/3] Total time: 3.279 seconds, Total memory usage: 2.11MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 08:31:09 2004 Input: Q := RationalField(); DynkinDiagram("E7" ); C:=CartanMatrix("E7" ); C; Determinant(C); B:=Matrix(Q, C); B^-1; Output: Magma V2.10-6 Fri Feb 20 2004 08:31:05 on modular [Seed = 4102207664] ------------------------------------- E7 1 - 3 - 4 - 5 - 6 - 7 | 2 [ 2 0 -1 0 0 0 0] [ 0 2 0 -1 0 0 0] [-1 0 2 -1 0 0 0] [ 0 -1 -1 2 -1 0 0] [ 0 0 0 -1 2 -1 0] [ 0 0 0 0 -1 2 -1] [ 0 0 0 0 0 -1 2] 2 [ 2 2 3 4 3 2 1] [ 2 7/2 4 6 9/2 3 3/2] [ 3 4 6 8 6 4 2] [ 4 6 8 12 9 6 3] [ 3 9/2 6 9 15/2 5 5/2] [ 2 3 4 6 5 4 2] [ 1 3/2 2 3 5/2 2 3/2] Total time: 3.089 seconds, Total memory usage: 2.11MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 08:33:09 2004 Input: Q := RationalField(); DynkinDiagram("E8" ); C:=CartanMatrix("E8" ); C; Determinant(C); B:=Matrix(Q, C); B^-1; Output: Magma V2.10-6 Fri Feb 20 2004 08:33:05 on modular [Seed = 4002980386] ------------------------------------- E8 1 - 3 - 4 - 5 - 6 - 7 - 8 | 2 [ 2 0 -1 0 0 0 0 0] [ 0 2 0 -1 0 0 0 0] [-1 0 2 -1 0 0 0 0] [ 0 -1 -1 2 -1 0 0 0] [ 0 0 0 -1 2 -1 0 0] [ 0 0 0 0 -1 2 -1 0] [ 0 0 0 0 0 -1 2 -1] [ 0 0 0 0 0 0 -1 2] 1 [ 4 5 7 10 8 6 4 2] [ 5 8 10 15 12 9 6 3] [ 7 10 14 20 16 12 8 4] [10 15 20 30 24 18 12 6] [ 8 12 16 24 20 15 10 5] [ 6 9 12 18 15 12 8 4] [ 4 6 8 12 10 8 6 3] [ 2 3 4 6 5 4 3 2] Total time: 3.169 seconds, Total memory usage: 2.11MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 08:36:04 2004 Input: Q := RationalField(); L:="A2" DynkinDiagram(L); C:=CartanMatrix(L); C; Determinant(C); B:=Matrix(Q, C); B^-1; Output: Magma V2.10-6 Fri Feb 20 2004 08:36:01 on modular [Seed = 2682901123] ------------------------------------- >> DynkinDiagram(L); ^ User error: bad syntax >> C:=CartanMatrix(L); ^ User error: Identifier 'L' has not been declared or assigned >> C; ^ User error: Identifier 'C' has not been declared or assigned >> Determinant(C); ^ User error: Identifier 'C' has not been declared or assigned >> B:=Matrix(Q, C); ^ User error: Identifier 'C' has not been declared or assigned >> B^-1; ^ User error: Identifier 'B' has not been declared or assigned Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 08:36:24 2004 Input: Q := RationalField(); L:="A2" DynkinDiagram("L"); C:=CartanMatrix("L"); C; Determinant(C); B:=Matrix(Q, C); B^-1; Output: Magma V2.10-6 Fri Feb 20 2004 08:36:21 on modular [Seed = 2531318686] ------------------------------------- >> DynkinDiagram("L"); ^ User error: bad syntax CartanMatrix( N: L ) [/usr/local/magma/package/LieThry/Cartan.m:870]( type: false ) [/usr/local/magma/package/LieThry/Cartan.m:866]( type: false ) In file "/usr/local/magma/package/LieThry/Cartan.m", line 867, column 22: >> return forall{ t : t in type | t[1][1] in "ABCDEFG" }; ^ Runtime error in for: Iteration is not possible over this object >> C; ^ User error: Identifier 'C' has not been declared or assigned >> Determinant(C); ^ User error: Identifier 'C' has not been declared or assigned >> B:=Matrix(Q, C); ^ User error: Identifier 'C' has not been declared or assigned >> B^-1; ^ User error: Identifier 'B' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 08:36:37 2004 Input: Q := RationalField(); L:="A2"; DynkinDiagram("L"); C:=CartanMatrix("L"); C; Determinant(C); B:=Matrix(Q, C); B^-1; Output: Magma V2.10-6 Fri Feb 20 2004 08:36:34 on modular [Seed = 2315240630] ------------------------------------- DynkinDiagram( N: L ) [/usr/local/magma/package/LieThry/Cartan.m:866]( type: false ) In file "/usr/local/magma/package/LieThry/Cartan.m", line 867, column 22: >> return forall{ t : t in type | t[1][1] in "ABCDEFG" }; ^ Runtime error in for: Iteration is not possible over this object CartanMatrix( N: L ) [/usr/local/magma/package/LieThry/Cartan.m:870]( type: false ) [/usr/local/magma/package/LieThry/Cartan.m:866]( type: false ) In file "/usr/local/magma/package/LieThry/Cartan.m", line 867, column 22: >> return forall{ t : t in type | t[1][1] in "ABCDEFG" }; ^ Runtime error in for: Iteration is not possible over this object >> C; ^ User error: Identifier 'C' has not been declared or assigned >> Determinant(C); ^ User error: Identifier 'C' has not been declared or assigned >> B:=Matrix(Q, C); ^ User error: Identifier 'C' has not been declared or assigned >> B^-1; ^ User error: Identifier 'B' has not been declared or assigned Total time: 3.109 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 08:36:49 2004 Input: Q := RationalField(); L:="A2"; DynkinDiagram(L); C:=CartanMatrix("L"); C; Determinant(C); B:=Matrix(Q, C); B^-1; Output: Magma V2.10-6 Fri Feb 20 2004 08:36:46 on modular [Seed = 2163658163] ------------------------------------- A2 1 - 2 CartanMatrix( N: L ) [/usr/local/magma/package/LieThry/Cartan.m:870]( type: false ) [/usr/local/magma/package/LieThry/Cartan.m:866]( type: false ) In file "/usr/local/magma/package/LieThry/Cartan.m", line 867, column 22: >> return forall{ t : t in type | t[1][1] in "ABCDEFG" }; ^ Runtime error in for: Iteration is not possible over this object >> C; ^ User error: Identifier 'C' has not been declared or assigned >> Determinant(C); ^ User error: Identifier 'C' has not been declared or assigned >> B:=Matrix(Q, C); ^ User error: Identifier 'C' has not been declared or assigned >> B^-1; ^ User error: Identifier 'B' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host sisiphos.math.unifi.it. (150.217.33.46) Time: Fri Feb 20 08:36:58 2004 Input: Q := RationalField(); L:="A2"; DynkinDiagram(L); C:=CartanMatrix(L); C; Determinant(C); B:=Matrix(Q, C); B^-1; Output: Magma V2.10-6 Fri Feb 20 2004 08:36:55 on modular [Seed = 3150837393] ------------------------------------- A2 1 - 2 [ 2 -1] [-1 2] 3 [2/3 1/3] [1/3 2/3] Total time: 3.099 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host MG001076.user.veloxzone.com.br. (200.165.1.76) Time: Fri Feb 20 11:50:10 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Fri Feb 20 2004 11:50:05 on modular [Seed = 1830492080] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathdhcp41.ces.clemson.edu. (130.127.112.170) Time: Fri Feb 20 12:07:57 2004 Input: S3:=Sym(3); S3; Output: Magma V2.10-6 Fri Feb 20 2004 12:07:53 on modular [Seed = 192771458] ------------------------------------- Symmetric group S3 acting on a set of cardinality 3 Order = 6 = 2 * 3 Total time: 3.219 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathdhcp41.ces.clemson.edu. (130.127.112.170) Time: Fri Feb 20 12:08:46 2004 Input: S3:=Sym(3); S3.1; Output: Magma V2.10-6 Fri Feb 20 2004 12:08:43 on modular [Seed = 409888611] ------------------------------------- (1, 2, 3) Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Sat Feb 21 02:56:06 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f3:=630*x^8+630*y^8-322560+151*x^7-151*y^7+70*x^5-70*y^5+49*x^3-49*y^3+45*x-45*y; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Bn:=GroebnerBasis(ChangeRing(I,GF(2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(2^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(2^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(2^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(2^5))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(3^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(3^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(3^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(3^5))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(5))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(5^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(5^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(5^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(5^5))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(7))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(7^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(7^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(7^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(7^5))); Bn; Output: Magma V2.10-6 Sat Feb 21 2004 02:56:03 on modular [Seed = 3784748675] ------------------------------------- [ x^2 + 8*x + 31*y^2 - 8*y - 128, x*y + 2*x + 4*y^3 + 111*y^2 - 18*y - 448, 15*x + 60*y^2 - 15*y - 240, 4*y^4 + 20*y^2 - 144, 8*y^3 + 72*y^2 - 32*y - 288, 120*y^2 - 480 ] [ x + y ] [ x + y ] [ x + y ] [ x + y ] [ x + y ] [ x^2 + 2*x + y^2 + y + 1, x*y + 2*x + y + 2, y^3 + 2*y ] [ x^2 + 2*x + y^2 + y + 1, x*y + 2*x + y + 2, y^3 + 2*y ] [ x^2 + 2*x + y^2 + y + 1, x*y + 2*x + y + 2, y^3 + 2*y ] [ x^2 + 2*x + y^2 + y + 1, x*y + 2*x + y + 2, y^3 + 2*y ] [ x^2 + 2*x + y^2 + y + 1, x*y + 2*x + y + 2, y^3 + 2*y ] [ x^2 + 3*x + y^2 + 2*y + 2, x*y + 2*x + 3*y + 1, y^3 + 4*y^2 + y + 4 ] [ x^2 + 3*x + y^2 + 2*y + 2, x*y + 2*x + 3*y + 1, y^3 + 4*y^2 + y + 4 ] [ x^2 + 3*x + y^2 + 2*y + 2, x*y + 2*x + 3*y + 1, y^3 + 4*y^2 + y + 4 ] [ x^2 + 3*x + y^2 + 2*y + 2, x*y + 2*x + 3*y + 1, y^3 + 4*y^2 + y + 4 ] [ x^2 + 3*x + y^2 + 2*y + 2, x*y + 2*x + 3*y + 1, y^3 + 4*y^2 + y + 4 ] [ x + 6*y, y^2 + 3 ] [ x + 6*y, y^2 + 3 ] [ x + 6*y, y^2 + 3 ] [ x + 6*y, y^2 + 3 ] [ x + 6*y, y^2 + 3 ] Total time: 3.089 seconds, Total memory usage: 2.29MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Sat Feb 21 02:58:13 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f3:=645120*x^8+645120*y^8-330303015+2251776*x^7-154624*y^7-1075200*x^5-71680*y^5+ 182784*x^3-50176*y^3+44280*x-46080*y+1835008*x^6-1003520*x^4+116032*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(14549535); Factorization(15058768725); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^5))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^5))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^5))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19^5))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(123^5))); Bn; Output: Magma V2.10-6 Sat Feb 21 2004 02:58:09 on modular [Seed = 3952911371] ------------------------------------- [ x^2 + 8*x + y^2 + 14549527*y + 2648015362, x*y + 2*x + 14549533*y + 14695030346, 15*x + 14549520*y + 14695030350, y^3 + 9*y^2 + 14549531*y + 11683276569, 15*y^2 + 3011753685, 14549535*y + 5659769115, 15058768725 ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ <3, 4>, <5, 2>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1>, <23, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 10*y, y^2 + 7 ] [ x + 10*y, y^2 + 7 ] [ x + 10*y, y^2 + 7 ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 16*y, y^2 + 13 ] [ x + 16*y, y^2 + 13 ] [ x + 16*y, y^2 + 13 ] [ x + 16*y, y^2 + 13 ] [ x + 16*y, y^2 + 13 ] [ x + 18*y, y^2 + 15 ] [ x + 18*y, y^2 + 15 ] [ x + 18*y, y^2 + 15 ] [ x + 18*y, y^2 + 15 ] [ x + 18*y, y^2 + 15 ] [ x + 21, y + 21 ] [ x + 21, y + 21 ] [ x + 21, y + 21 ] [ x + 21, y + 21 ] >> Bn:=GroebnerBasis(ChangeRing(I,GF(123^5))); ^ Runtime error in 'GF': Argument 1 (28153056843) is not a prime power [ x + 21, y + 21 ] Total time: 3.769 seconds, Total memory usage: 7.23MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Sat Feb 21 02:58:59 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f3:=645120*x^8+645120*y^8-330303015+2251776*x^7-154624*y^7-1075200*x^5-71680*y^5+ 182784*x^3-50176*y^3+44280*x-46080*y+1835008*x^6-1003520*x^4+116032*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(14549535); Factorization(15058768725); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^5))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^5))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^5))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19^5))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23^5))); Bn; Output: Magma V2.10-6 Sat Feb 21 2004 02:58:55 on modular [Seed = 3534069020] ------------------------------------- [ x^2 + 8*x + y^2 + 14549527*y + 2648015362, x*y + 2*x + 14549533*y + 14695030346, 15*x + 14549520*y + 14695030350, y^3 + 9*y^2 + 14549531*y + 11683276569, 15*y^2 + 3011753685, 14549535*y + 5659769115, 15058768725 ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ <3, 4>, <5, 2>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1>, <23, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 10*y, y^2 + 7 ] [ x + 10*y, y^2 + 7 ] [ x + 10*y, y^2 + 7 ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 16*y, y^2 + 13 ] [ x + 16*y, y^2 + 13 ] [ x + 16*y, y^2 + 13 ] [ x + 16*y, y^2 + 13 ] [ x + 16*y, y^2 + 13 ] [ x + 18*y, y^2 + 15 ] [ x + 18*y, y^2 + 15 ] [ x + 18*y, y^2 + 15 ] [ x + 18*y, y^2 + 15 ] [ x + 18*y, y^2 + 15 ] [ x + 21, y + 21 ] [ x + 21, y + 21 ] [ x + 21, y + 21 ] [ x + 21, y + 21 ] [ x + 21, y + 21 ] Total time: 3.669 seconds, Total memory usage: 7.23MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Sat Feb 21 02:59:54 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+2944*x^5-352*y^5-560*x^3-160*y^3+146*x-128*y+2160*x^4-600*x^2 -163825; f3:=645120*x^8+645120*y^8-330303015+2251776*x^7-154624*y^7-1075200*x^5-71680*y^5+ 182784*x^3-50176*y^3+44280*x-46080*y+1835008*x^6-1003520*x^4+116032*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(765765); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^5))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^5))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^5))); Bn; Output: Magma V2.10-6 Sat Feb 21 2004 02:59:50 on modular [Seed = 3718943322] ------------------------------------- [ x^2 + 23*x + y^2 + 6412*y + 643492, x*y + 2*x + 6433*y + 643496, 45*x + 6390*y + 643500, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 765705, 6435*y + 643500, 765765 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 10*y, y^2 + 7 ] [ x + 10*y, y^2 + 7 ] [ x + 10*y, y^2 + 7 ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 15, y + 15 ] [ x + 15, y + 15 ] [ x + 15, y + 15 ] [ x + 15, y + 15 ] [ x + 15, y + 15 ] Total time: 3.369 seconds, Total memory usage: 7.21MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Sat Feb 21 03:00:40 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+2944*x^5-352*y^5-560*x^3-160*y^3+146*x-128*y+2160*x^4-600*x^2 -163825; f3:=645120*x^8+645120*y^8-330290415+12288*x^7-154624*y^7+1102080*x^5-71680*y^5- 264768*x^3-50176*y^3+55080*x-46080*y-777728*x^6+1536640*x^4-406112*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(2297295); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^5))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^5))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^5))); Bn; Output: Magma V2.10-6 Sat Feb 21 2004 03:00:36 on modular [Seed = 3484983194] ------------------------------------- [ x^2 + 248*x + y^2 + 6187*y + 643492, x*y + 317*x + 6118*y + 2175026, 495*x + 5940*y + 1409265, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 2297235, 6435*y + 2175030, 2297295 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 3>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] [ x^2 + 6*x + 5*y + 7, x*y + 9*x + 2*y + 7, y^2 + 7 ] [ x^2 + 6*x + 5*y + 7, x*y + 9*x + 2*y + 7, y^2 + 7 ] [ x^2 + 6*x + 5*y + 7, x*y + 9*x + 2*y + 7, y^2 + 7 ] [ x^2 + 6*x + 5*y + 7, x*y + 9*x + 2*y + 7, y^2 + 7 ] [ x^2 + 6*x + 5*y + 7, x*y + 9*x + 2*y + 7, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 15, y + 15 ] [ x + 15, y + 15 ] [ x + 15, y + 15 ] [ x + 15, y + 15 ] [ x + 15, y + 15 ] Total time: 3.399 seconds, Total memory usage: 7.23MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Sat Feb 21 03:01:28 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f3:=645120*x^8+645120*y^8-330303015+154624*x^7-2251776*y^7+71680*x^5+1075200*y^5+ 50176*x^3-182784*y^3+46080*x-44280*y+1835008*y^6-1003520*y^4+116032*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(14549535); Factorization(15058768725); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^5))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^5))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^5))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19^5))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(123^5))); Bn; Output: Magma V2.10-6 Sat Feb 21 2004 03:01:24 on modular [Seed = 2833250445] ------------------------------------- [ x^2 + 8*x + y^2 + 14549527*y + 363738367, x*y + 2*x + 14549533*y + 12410753351, 15*x + 14549520*y + 12410753355, y^3 + 9*y^2 + 14549531*y + 12410753319, 15*y^2 + 15058768665, 14549535*y + 3375492120, 15058768725 ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ <3, 4>, <5, 2>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1>, <23, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 10*y, y^2 + 7 ] [ x + 10*y, y^2 + 7 ] [ x + 10*y, y^2 + 7 ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 16*y, y^2 + 13 ] [ x + 16*y, y^2 + 13 ] [ x + 16*y, y^2 + 13 ] [ x + 16*y, y^2 + 13 ] [ x + 16*y, y^2 + 13 ] [ x + 18*y, y^2 + 15 ] [ x + 18*y, y^2 + 15 ] [ x + 18*y, y^2 + 15 ] [ x + 18*y, y^2 + 15 ] [ x + 18*y, y^2 + 15 ] [ x + 2, y + 2 ] [ x + 2, y + 2 ] [ x + 2, y + 2 ] [ x + 2, y + 2 ] >> Bn:=GroebnerBasis(ChangeRing(I,GF(123^5))); ^ Runtime error in 'GF': Argument 1 (28153056843) is not a prime power [ x + 2, y + 2 ] Total time: 3.669 seconds, Total memory usage: 7.25MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Sat Feb 21 03:02:10 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f3:=322560*x^8+322560*y^8-165152295+1125888*x^7-1125888*y^7-537600*x^5+537600*y^5+ 91392*x^3-91392*y^3+22140*x-22140*y+917504*y^6-501760*y^4+58016*y^2+917504*x^6- 501760*x^4+58016*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(101846745); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^5))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^5))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^5))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19^5))); Bn; Output: Magma V2.10-6 Sat Feb 21 2004 03:02:06 on modular [Seed = 2481243036] ------------------------------------- [ x^2 + 8*x + y^2 + 101846737*y + 101846737, x*y + 2*x + 101846743*y + 101846741, 15*x + 101846730*y, y^3 + 9*y^2 + 101846741*y + 101846709, 15*y^2 + 101846685, 101846745 ] [ <3, 2>, <5, 1>, <7, 2>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 10*y, y^2 + 7 ] [ x + 10*y, y^2 + 7 ] [ x + 10*y, y^2 + 7 ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 16*y, y^2 + 13 ] [ x + 16*y, y^2 + 13 ] [ x + 16*y, y^2 + 13 ] [ x + 16*y, y^2 + 13 ] [ x + 16*y, y^2 + 13 ] [ x + 18*y, y^2 + 15 ] [ x + 18*y, y^2 + 15 ] [ x + 18*y, y^2 + 15 ] [ x + 18*y, y^2 + 15 ] [ x + 18*y, y^2 + 15 ] Total time: 3.509 seconds, Total memory usage: 7.89MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Sat Feb 21 03:02:49 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+2944*x^5-352*y^5-560*x^3-160*y^3+146*x-128*y+2160*x^4-600*x^2 -163825; f3:=322560*x^8+322560*y^8-165152295+1125888*x^7-1125888*y^7-537600*x^5+537600*y^5+ 91392*x^3-91392*y^3+22140*x-22140*y+917504*y^6-501760*y^4+58016*y^2+917504*x^6- 501760*x^4+58016*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(765765); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^5))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^5))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^5))); Bn; Output: Magma V2.10-6 Sat Feb 21 2004 03:02:46 on modular [Seed = 2599275085] ------------------------------------- [ x^2 + 23*x + y^2 + 6412*y + 643492, x*y + 2*x + 6433*y + 643496, 45*x + 6390*y + 643500, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 765705, 6435*y + 643500, 765765 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 10*y, y^2 + 7 ] [ x + 10*y, y^2 + 7 ] [ x + 10*y, y^2 + 7 ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 15, y + 15 ] [ x + 15, y + 15 ] [ x + 15, y + 15 ] [ x + 15, y + 15 ] [ x + 15, y + 15 ] Total time: 3.409 seconds, Total memory usage: 7.23MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Sat Feb 21 03:03:33 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+2944*x^5-352*y^5-560*x^3-160*y^3+146*x-128*y+2160*x^4-600*x^2 -163825; f3:=322560*x^8+322560*y^8-165145995+6144*x^7-1125888*y^7+551040*x^5+537600*y^5- 132384*x^3-91392*y^3+27540*x-22140*y+917504*y^6-501760*y^4+58016*y^2-388864*x^6 +768320*x^4-203056*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(765765); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^5))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^5))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^5))); Bn; Output: Magma V2.10-6 Sat Feb 21 2004 03:03:30 on modular [Seed = 2247284006] ------------------------------------- [ x^2 + 248*x + y^2 + 6187*y + 643492, x*y + 317*x + 6118*y + 643496, 495*x + 5940*y + 643500, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 765705, 6435*y + 643500, 765765 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] [ x^2 + 6*x + 5*y + 7, x*y + 9*x + 2*y + 7, y^2 + 7 ] [ x^2 + 6*x + 5*y + 7, x*y + 9*x + 2*y + 7, y^2 + 7 ] [ x^2 + 6*x + 5*y + 7, x*y + 9*x + 2*y + 7, y^2 + 7 ] [ x^2 + 6*x + 5*y + 7, x*y + 9*x + 2*y + 7, y^2 + 7 ] [ x^2 + 6*x + 5*y + 7, x*y + 9*x + 2*y + 7, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 15, y + 15 ] [ x + 15, y + 15 ] [ x + 15, y + 15 ] [ x + 15, y + 15 ] [ x + 15, y + 15 ] Total time: 3.319 seconds, Total memory usage: 7.23MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Sat Feb 21 03:04:31 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+352*x^5-2944*y^5+160*x^3+560*y^3+128*x-146*y+2160*y^4+600*y^2 -163825; f3:=645120*x^8+645120*y^8-330303015+154624*x^7-2251776*y^7+71680*x^5+1075200*y^5+ 50176*x^3-182784*y^3+46080*x-44280*y+1835008*y^6-1003520*y^4+116032*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(1035); Bn:=GroebnerBasis(ChangeRing(I,GF(23))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23^2))); Bn; Output: Magma V2.10-6 Sat Feb 21 2004 03:04:28 on modular [Seed = 2415451890] ------------------------------------- [ x^2 + 8*x + y^2 + 7*y + 22, x*y + 2*x + 13*y + 716, 15*x + 375, y^3 + 9*y^2 + 11*y + 1029, 15*y + 720, 1035 ] [ <3, 2>, <5, 1>, <23, 1> ] [ x + 2, y + 2 ] [ x + 2, y + 2 ] Total time: 2.939 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Sat Feb 21 03:05:04 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+352*x^5-2944*y^5+160*x^3+560*y^3+128*x-146*y+2160*y^4+600*y^2 -163825; f3:=322560*x^8+322560*y^8-165152295+1125888*x^7-1125888*y^7-537600*x^5+537600*y^5+ 91392*x^3-91392*y^3+22140*x-22140*y+917504*y^6-501760*y^4+58016*y^2+917504*x^6- 501760*x^4+58016*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Bn:=GroebnerBasis(ChangeRing(I,GF(23^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(123^5))); Bn; Output: Magma V2.10-6 Sat Feb 21 2004 03:05:01 on modular [Seed = 2030970918] ------------------------------------- [ x^2 + 8*x + y^2 + 7*y + 22, x*y + 2*x + 13*y + 41, 15*x + 15, y^3 + 9*y^2 + 11*y + 39, 15*y, 45 ] [ 1 ] [ 1 ] >> Bn:=GroebnerBasis(ChangeRing(I,GF(123^5))); ^ Runtime error in 'GF': Argument 1 (28153056843) is not a prime power [ 1 ] Total time: 3.219 seconds, Total memory usage: 5.39MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Sat Feb 21 03:05:32 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+352*x^5-2944*y^5+160*x^3+560*y^3+128*x-146*y+2160*y^4+600*y^2 -163825; f3:=322560*x^8+322560*y^8-165152295+1125888*x^7-1125888*y^7-537600*x^5+537600*y^5+ 91392*x^3-91392*y^3+22140*x-22140*y+917504*y^6-501760*y^4+58016*y^2+917504*x^6- 501760*x^4+58016*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Bn:=GroebnerBasis(ChangeRing(I,GF(23^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23^5))); Bn; Output: Magma V2.10-6 Sat Feb 21 2004 03:05:29 on modular [Seed = 1729115740] ------------------------------------- [ x^2 + 8*x + y^2 + 7*y + 22, x*y + 2*x + 13*y + 41, 15*x + 15, y^3 + 9*y^2 + 11*y + 39, 15*y, 45 ] [ 1 ] [ 1 ] [ 1 ] Total time: 3.169 seconds, Total memory usage: 5.39MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Sat Feb 21 03:06:11 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=640*x^6+640*y^6+1472*x^5-1472*y^5+1080*x^4+1080*y^4-280*x^3+280*y^3; f3:=322560*x^8+322560*y^8-165152295+1125888*x^7-1125888*y^7-537600*x^5+537600*y^5+ 91392*x^3-91392*y^3+22140*x-22140*y+917504*y^6-501760*y^4+58016*y^2+917504*x^6- 501760*x^4+58016*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(4095); Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^5))); Bn; Output: Magma V2.10-6 Sat Feb 21 2004 03:06:08 on modular [Seed = 1813724526] ------------------------------------- [ x + 4094*y + 910, y^2 + 3185*y + 2271, 4095 ] [ <3, 2>, <5, 1>, <7, 1>, <13, 1> ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] Total time: 3.219 seconds, Total memory usage: 6.91MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Sat Feb 21 03:06:49 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=640*x^6+640*y^6+1472*x^5-1472*y^5+1080*x^4+1080*y^4-280*x^3+280*y^3; f3:=322560*x^8+322560*y^8-165145995+6144*x^7-1125888*y^7+551040*x^5+537600*y^5- 132384*x^3-91392*y^3+27540*x-22140*y+917504*y^6-501760*y^4+58016*y^2-388864*x^6 +768320*x^4-203056*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(4095); Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^5))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^5))); Bn; Output: Magma V2.10-6 Sat Feb 21 2004 03:06:45 on modular [Seed = 1428292786] ------------------------------------- [ x + 4094*y + 910, y^2 + 3185*y + 2271, 4095 ] [ <3, 2>, <5, 1>, <7, 1>, <13, 1> ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ 1 ] [ 1 ] [ 1 ] Total time: 3.279 seconds, Total memory usage: 7.92MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Sat Feb 21 03:07:43 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+352*x^5-2944*y^5+160*x^3+560*y^3+128*x-146*y+2160*y^4+600*y^2 -163825; f3:=645120*x^8+645120*y^8-330290415+154624*x^7-12288*y^7+71680*x^5-1102080*y^5+ 50176*x^3+264768*y^3+46080*x-55080*y-777728*y^6+1536640*y^4-406112*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Bn:=GroebnerBasis(ChangeRing(I,GF(19^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19^5))); Bn; Output: Magma V2.10-6 Sat Feb 21 2004 03:07:40 on modular [Seed = 1127486205] ------------------------------------- [ x^2 + 8*x + y^2 + 7*y + 22, x*y + 2*x + 13*y + 176, 15*x + 240, y^3 + 9*y^2 + 11*y + 354, 15*y + 225, 405 ] [ 1 ] [ 1 ] [ 1 ] Total time: 2.989 seconds, Total memory usage: 3.50MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Sat Feb 21 03:08:18 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+352*x^5-2944*y^5+160*x^3+560*y^3+128*x-146*y+2160*y^4+600*y^2 -163825; f3:=322560*x^8+322560*y^8-165145995+1125888*x^7-6144*y^7-537600*x^5-551040*y^5+ 91392*x^3+132384*y^3+22140*x-27540*y+917504*x^6-501760*x^4+58016*x^2-388864*y^6 +768320*y^4-203056*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(765765); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^5))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^5))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^5))); Bn; Output: Magma V2.10-6 Sat Feb 21 2004 03:08:15 on modular [Seed = 1212094933] ------------------------------------- [ x^2 + 8*x + y^2 + 7*y + 22, x*y + 2*x + 13*y + 41, 15*x + 15, y^3 + 9*y^2 + 11*y + 39, 15*y, 45 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] [ 1 ] [ 1 ] [ 1 ] [ 1 ] [ 1 ] [ 1 ] [ 1 ] [ 1 ] [ 1 ] [ 1 ] [ 1 ] [ 1 ] [ 1 ] [ 1 ] [ 1 ] Total time: 3.380 seconds, Total memory usage: 7.30MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Sat Feb 21 03:08:49 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=640*x^6+640*y^6+1472*x^5-1472*y^5+1080*x^4+1080*y^4-280*x^3+280*y^3; f3:=322560*x^8+322560*y^8-165145995+1125888*x^7-6144*y^7-537600*x^5-551040*y^5+ 91392*x^3+132384*y^3+22140*x-27540*y+917504*x^6-501760*x^4+58016*x^2-388864*y^6 +768320*y^4-203056*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(4095); Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^5))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^5))); Bn; Output: Magma V2.10-6 Sat Feb 21 2004 03:08:45 on modular [Seed = 694057814] ------------------------------------- [ x + 4094*y + 910, y^2 + 3185*y + 2271, 4095 ] [ <3, 2>, <5, 1>, <7, 1>, <13, 1> ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ 1 ] [ 1 ] [ 1 ] Total time: 3.459 seconds, Total memory usage: 7.91MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Sat Feb 21 03:09:20 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=640*x^6+640*y^6+1472*x^5-1472*y^5+1080*x^4+1080*y^4-280*x^3+280*y^3; f3:=322560*x^8+322560*y^8-165139695+6144*x^7-6144*y^7+551040*x^5-551040*y^5-132384* x^3+132384*y^3+27540*x-27540*y-388864*x^6+768320*x^4-203056*x^2-388864*y^6+ 768320*y^4-203056*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(4095); Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^3))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^5))); Bn; Output: Magma V2.10-6 Sat Feb 21 2004 03:09:17 on modular [Seed = 242834513] ------------------------------------- [ x + 4094*y + 910, y^2 + 3185*y + 2271, 4095 ] [ <3, 2>, <5, 1>, <7, 1>, <13, 1> ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] Total time: 3.299 seconds, Total memory usage: 6.92MB ************** MAGMA ***************** Host cisco-cache-4.kuleuven.ac.be. (134.58.253.129) Time: Sat Feb 21 04:44:08 2004 Input: q:=2; F:=GF(q); K:=FunctionField(F,4); R:=MatrixRing(K,2); S:=MatrixRing(F,2); Z:=Matrix(K,2,2,[a1,a2,a3,a4]); Mi:=&+[(Z-lambda)^(-1) : lambda in S]; Mi; M:=Mi^(-1); Output: Magma V2.10-6 Sat Feb 21 2004 04:43:49 on modular [Seed = 3685528571] ------------------------------------- [(a1^12*a4^14 + a1^12*a4^13 + a1^12*a4^11 + a1^12*a4^9 + a1^12*a4^7 + a1^12*a4^6 + a1^10*a4^14 + a1^10*a4^13 + a1^10*a4^11 + a1^10*a4^9 + a1^10*a4^7 + a1^10*a4^6 + a1^8*a2^4*a3^4*a4^10 + a1^8*a2^4*a3^4*a4^9 + a1^8*a2^4*a3^4*a4^3 + a1^8*a2^4*a3^4*a4^2 + a1^8*a2^4*a3^2*a4^8 + a1^8*a2^4*a3^2*a4^2 + a1^8*a2^4*a3*a4^10 + a1^8*a2^4*a3*a4^9 + a1^8*a2^4*a3*a4^8 + a1^8*a2^4*a3*a4^3 + a1^8*a2^4*a4^10 + a1^8*a2^4*a4^9 + a1^8*a2^4*a4^6 + a1^8*a2^4*a4^5 + a1^8*a2^2*a3^4*a4^8 + a1^8*a2^2*a3^4*a4^2 + a1^8*a2^2*a3^2*a4^12 + a1^8*a2^2*a3^2*a4^10 + a1^8*a2^2*a3^2*a4^5 + a1^8*a2^2*a3^2*a4^4 + a1^8*a2^2*a3^2*a4^3 + a1^8*a2^2*a3^2*a4^2 + a1^8*a2^2*a3*a4^12 + a1^8*a2^2*a3*a4^10 + a1^8*a2^2*a3*a4^8 + a1^8*a2^2*a3*a4^5 + a1^8*a2^2*a3*a4^4 + a1^8*a2^2*a3*a4^3 + a1^8*a2^2*a4^12 + a1^8*a2^2*a4^9 + a1^8*a2^2*a4^8 + a1^8*a2^2*a4^5 + a1^8*a2*a3^4*a4^10 + a1^8*a2*a3^4*a4^9 + a1^8*a2*a3^4*a4^8 + a1^8*a2*a3^4*a4^3 + a1^8*a2*a3^2*a4^12 + a1^8*a2*a3^2*a4^10 + a1^8*a2*a3^2*a4^8 + a1^8*a2*a3^2*a4^5 + a1^8*a2*a3^2*a4^4 + a1^8*a2*a3^2*a4^3 + a1^8*a2*a3*a4^12 + a1^8*a2*a3*a4^9 + a1^8*a2*a3*a4^5 + a1^8*a2*a3*a4^4 + a1^8*a2*a4^12 + a1^8*a2*a4^10 + a1^8*a2*a4^8 + a1^8*a2*a4^6 + a1^8*a3^4*a4^10 + a1^8*a3^4*a4^9 + a1^8*a3^4*a4^6 + a1^8*a3^4*a4^5 + a1^8*a3^2*a4^12 + a1^8*a3^2*a4^9 + a1^8*a3^2*a4^8 + a1^8*a3^2*a4^5 + a1^8*a3*a4^12 + a1^8*a3*a4^10 + a1^8*a3*a4^8 + a1^8*a3*a4^6 + a1^8*a4^14 + a1^8*a4^13 + a1^8*a4^11 + a1^8*a4^9 + a1^8*a4^7 + a1^8*a4^6 + a1^6*a4^14 + a1^6*a4^13 + a1^6*a4^11 + a1^6*a4^9 + a1^6*a4^7 + a1^6*a4^6 + a1^4*a2^8*a3^8*a4^6 + a1^4*a2^8*a3^8*a4^5 + a1^4*a2^8*a3^8*a4^3 + a1^4*a2^8*a3^8*a4 + a1^4*a2^8*a3^4*a4^2 + a1^4*a2^8*a3^4*a4 + a1^4*a2^8*a3^2*a4^4 + a1^4*a2^8*a3^2*a4^2 + a1^4*a2^8*a3*a4^6 + a1^4*a2^8*a3*a4^5 + a1^4*a2^8*a3*a4^4 + a1^4*a2^8*a3*a4^3 + a1^4*a2^4*a3^8*a4^2 + a1^4*a2^4*a3^8*a4 + a1^4*a2^4*a3^4*a4^2 + a1^4*a2^4*a3^4*a4 + a1^4*a2^4*a3^2*a4^8 + a1^4*a2^4*a3^2*a4^4 + a1^4*a2^4*a3*a4^8 + a1^4*a2^4*a3*a4^4 + a1^4*a2^4*a4^10 + a1^4*a2^4*a4^9 + a1^4*a2^4*a4^6 + a1^4*a2^4*a4^5 + a1^4*a2^2*a3^8*a4^4 + a1^4*a2^2*a3^8*a4^2 + a1^4*a2^2*a3^4*a4^8 + a1^4*a2^2*a3^4*a4^4 + a1^4*a2^2*a3^2*a4^12 + a1^4*a2^2*a3^2*a4^9 + a1^4*a2^2*a3^2*a4^6 + a1^4*a2^2*a3^2*a4^4 + a1^4*a2^2*a3^2*a4^3 + a1^4*a2^2*a3^2*a4^2 + a1^4*a2^2*a3*a4^12 + a1^4*a2^2*a3*a4^9 + a1^4*a2^2*a3*a4^8 + a1^4*a2^2*a3*a4^6 + a1^4*a2^2*a3*a4^4 + a1^4*a2^2*a3*a4^3 + a1^4*a2^2*a4^12 + a1^4*a2^2*a4^9 + a1^4*a2^2*a4^8 + a1^4*a2^2*a4^5 + a1^4*a2*a3^8*a4^6 + a1^4*a2*a3^8*a4^5 + a1^4*a2*a3^8*a4^4 + a1^4*a2*a3^8*a4^3 + a1^4*a2*a3^4*a4^8 + a1^4*a2*a3^4*a4^4 + a1^4*a2*a3^2*a4^12 + a1^4*a2*a3^2*a4^9 + a1^4*a2*a3^2*a4^8 + a1^4*a2*a3^2*a4^6 + a1^4*a2*a3^2*a4^4 + a1^4*a2*a3^2*a4^3 + a1^4*a2*a3*a4^12 + a1^4*a2*a3*a4^9 + a1^4*a2*a3*a4^5 + a1^4*a2*a3*a4^4 + a1^4*a2*a4^12 + a1^4*a2*a4^10 + a1^4*a2*a4^8 + a1^4*a2*a4^6 + a1^4*a3^4*a4^10 + a1^4*a3^4*a4^9 + a1^4*a3^4*a4^6 + a1^4*a3^4*a4^5 + a1^4*a3^2*a4^12 + a1^4*a3^2*a4^9 + a1^4*a3^2*a4^8 + a1^4*a3^2*a4^5 + a1^4*a3*a4^12 + a1^4*a3*a4^10 + a1^4*a3*a4^8 + a1^4*a3*a4^6 + a1^2*a2^8*a3^8*a4^6 + a1^2*a2^8*a3^8*a4^5 + a1^2*a2^8*a3^8*a4^3 + a1^2*a2^8*a3^8*a4 + a1^2*a2^8*a3^4*a4^2 + a1^2*a2^8*a3^4*a4 + a1^2*a2^8*a3^2*a4^4 + a1^2*a2^8*a3^2*a4^2 + a1^2*a2^8*a3*a4^6 + a1^2*a2^8*a3*a4^5 + a1^2*a2^8*a3*a4^4 + a1^2*a2^8*a3*a4^3 + a1^2*a2^4*a3^8*a4^2 + a1^2*a2^4*a3^8*a4 + a1^2*a2^4*a3^4*a4^10 + a1^2*a2^4*a3^4*a4^9 + a1^2*a2^4*a3^4*a4^3 + a1^2*a2^4*a3^4*a4 + a1^2*a2^4*a3^2*a4^4 + a1^2*a2^4*a3^2*a4^2 + a1^2*a2^4*a3*a4^10 + a1^2*a2^4*a3*a4^9 + a1^2*a2^4*a3*a4^4 + a1^2*a2^4*a3*a4^3 + a1^2*a2^2*a3^8*a4^4 + a1^2*a2^2*a3^8*a4^2 + a1^2*a2^2*a3^4*a4^4 + a1^2*a2^2*a3^4*a4^2 + a1^2*a2^2*a3^2*a4^10 + a1^2*a2^2*a3^2*a4^9 + a1^2*a2^2*a3^2*a4^6 + a1^2*a2^2*a3^2*a4^5 + a1^2*a2^2*a3*a4^10 + a1^2*a2^2*a3*a4^9 + a1^2*a2^2*a3*a4^6 + a1^2*a2^2*a3*a4^5 + a1^2*a2*a3^8*a4^6 + a1^2*a2*a3^8*a4^5 + a1^2*a2*a3^8*a4^4 + a1^2*a2*a3^8*a4^3 + a1^2*a2*a3^4*a4^10 + a1^2*a2*a3^4*a4^9 + a1^2*a2*a3^4*a4^4 + a1^2*a2*a3^4*a4^3 + a1^2*a2*a3^2*a4^10 + a1^2*a2*a3^2*a4^9 + a1^2*a2*a3^2*a4^6 + a1^2*a2*a3^2*a4^5 + a2^12*a3^12*a4^2 + a2^12*a3^12*a4 + a2^12*a3^10 + a2^12*a3^9*a4^2 + a2^12*a3^9*a4 + a2^12*a3^9 + a2^12*a3^8*a4^2 + a2^12*a3^8*a4 + a2^12*a3^6 + a2^12*a3^5*a4^2 + a2^12*a3^5*a4 + a2^12*a3^5 + a2^10*a3^12 + a2^10*a3^10*a4^4 + a2^10*a3^10*a4^2 + a2^10*a3^9*a4^4 + a2^10*a3^9*a4^2 + a2^10*a3^9 + a2^10*a3^8*a4^4 + a2^10*a3^8*a4 + a2^10*a3^8 + a2^10*a3^5 + a2^10*a3^4*a4^2 + a2^10*a3^4*a4 + a2^10*a3^3*a4^4 + a2^10*a3^3*a4^2 + a2^9*a3^12*a4^2 + a2^9*a3^12*a4 + a2^9*a3^12 + a2^9*a3^10*a4^4 + a2^9*a3^10*a4^2 + a2^9*a3^10 + a2^9*a3^9*a4^4 + a2^9*a3^9*a4 + a2^9*a3^8*a4^4 + a2^9*a3^8*a4^2 + a2^9*a3^8 + a2^9*a3^6 + a2^9*a3^5*a4^2 + a2^9*a3^5*a4 + a2^9*a3^4*a4^2 + a2^9*a3^4*a4 + a2^9*a3^3*a4^4 + a2^9*a3^3*a4^2 + a2^8*a3^12*a4^2 + a2^8*a3^12*a4 + a2^8*a3^10*a4^4 + a2^8*a3^10*a4 + a2^8*a3^10 + a2^8*a3^9*a4^4 + a2^8*a3^9*a4^2 + a2^8*a3^9 + a2^8*a3^8*a4^6 + a2^8*a3^8*a4^5 + a2^8*a3^8*a4^3 + a2^8*a3^8*a4 + a2^8*a3^6*a4^4 + a2^8*a3^6*a4 + a2^8*a3^6 + a2^8*a3^5*a4^4 + a2^8*a3^5*a4^2 + a2^8*a3^5 + a2^8*a3^4*a4^6 + a2^8*a3^4*a4^5 + a2^8*a3^4*a4^3 + a2^8*a3^4*a4^2 + a2^6*a3^12 + a2^6*a3^9 + a2^6*a3^8*a4^4 + a2^6*a3^8*a4 + a2^6*a3^8 + a2^6*a3^6*a4^8 + a2^6*a3^6*a4^2 + a2^6*a3^5*a4^8 + a2^6*a3^5*a4^2 + a2^6*a3^5 + a2^6*a3^4*a4^8 + a2^6*a3^4*a4^4 + a2^6*a3^4*a4^2 + a2^6*a3^4*a4 + a2^6*a3^3*a4^8 + a2^6*a3^3*a4^2 + a2^5*a3^12*a4^2 + a2^5*a3^12*a4 + a2^5*a3^12 + a2^5*a3^10 + a2^5*a3^9*a4^2 + a2^5*a3^9*a4 + a2^5*a3^8*a4^4 + a2^5*a3^8*a4^2 + a2^5*a3^8 + a2^5*a3^6*a4^8 + a2^5*a3^6*a4^2 + a2^5*a3^6 + a2^5*a3^5*a4^8 + a2^5*a3^5*a4 + a2^5*a3^4*a4^8 + a2^5*a3^4*a4^4 + a2^5*a3^4*a4^2 + a2^5*a3^4*a4 + a2^5*a3^3*a4^8 + a2^5*a3^3*a4^2 + a2^4*a3^10*a4^2 + a2^4*a3^10*a4 + a2^4*a3^9*a4^2 + a2^4*a3^9*a4 + a2^4*a3^8*a4^6 + a2^4*a3^8*a4^5 + a2^4*a3^8*a4^3 + a2^4*a3^8*a4^2 + a2^4*a3^6*a4^8 + a2^4*a3^6*a4^4 + a2^4*a3^6*a4^2 + a2^4*a3^6*a4 + a2^4*a3^5*a4^8 + a2^4*a3^5*a4^4 + a2^4*a3^5*a4^2 + a2^4*a3^5*a4 + a2^4*a3^4*a4^8 + a2^4*a3^4*a4^6 + a2^4*a3^4*a4^5 + a2^4*a3^4*a4^4 + a2^4*a3^4*a4^3 + a2^4*a3^4*a4^2 + a2^4*a3^3*a4^8 + a2^4*a3^3*a4^4 + a2^3*a3^10*a4^4 + a2^3*a3^10*a4^2 + a2^3*a3^9*a4^4 + a2^3*a3^9*a4^2 + a2^3*a3^6*a4^8 + a2^3*a3^6*a4^2 + a2^3*a3^5*a4^8 + a2^3*a3^5*a4^2 + a2^3*a3^4*a4^8 + a2^3*a3^4*a4^4 + a2^3*a3^3*a4^8 + a2^3*a3^3*a4^4)/(a1^16*a4^16 + a1^16*a4^8 + a1^14*a4^14 + a1^14*a4^13 + a1^14*a4^11 + a1^14*a4^9 + a1^14*a4^7 + a1^14*a4^6 + a1^13*a4^14 + a1^13*a4^13 + a1^13*a4^11 + a1^13*a4^9 + a1^13*a4^7 + a1^13*a4^6 + a1^12*a2^4*a4^8 + a1^12*a2^4*a4^4 + a1^12*a2^2*a3^2*a4^12 + a1^12*a2^2*a3^2*a4^9 + a1^12*a2^2*a3^2*a4^8 + a1^12*a2^2*a3^2*a4^5 + a1^12*a2^2*a3*a4^12 + a1^12*a2^2*a3*a4^9 + a1^12*a2^2*a3*a4^8 + a1^12*a2^2*a3*a4^5 + a1^12*a2^2*a4^10 + a1^12*a2^2*a4^9 + a1^12*a2^2*a4^8 + a1^12*a2^2*a4^6 + a1^12*a2^2*a4^5 + a1^12*a2^2*a4^4 + a1^12*a2*a3^2*a4^12 + a1^12*a2*a3^2*a4^9 + a1^12*a2*a3^2*a4^8 + a1^12*a2*a3^2*a4^5 + a1^12*a2*a3*a4^12 + a1^12*a2*a3*a4^9 + a1^12*a2*a3*a4^8 + a1^12*a2*a3*a4^5 + a1^12*a2*a4^10 + a1^12*a2*a4^9 + a1^12*a2*a4^6 + a1^12*a2*a4^5 + a1^12*a3^4*a4^8 + a1^12*a3^4*a4^4 + a1^12*a3^2*a4^10 + a1^12*a3^2*a4^9 + a1^12*a3^2*a4^8 + a1^12*a3^2*a4^6 + a1^12*a3^2*a4^5 + a1^12*a3^2*a4^4 + a1^12*a3*a4^10 + a1^12*a3*a4^9 + a1^12*a3*a4^6 + a1^12*a3*a4^5 + a1^12*a4^12 + a1^12*a4^10 + a1^12*a4^8 + a1^12*a4^6 + a1^11*a4^14 + a1^11*a4^13 + a1^11*a4^11 + a1^11*a4^9 + a1^11*a4^7 + a1^11*a4^6 + a1^10*a2^4*a3^4*a4^10 + a1^10*a2^4*a3^4*a4^9 + a1^10*a2^4*a3^4*a4^3 + a1^10*a2^4*a3^4*a4^2 + a1^10*a2^4*a3^2*a4^8 + a1^10*a2^4*a3^2*a4^2 + a1^10*a2^4*a3*a4^10 + a1^10*a2^4*a3*a4^9 + a1^10*a2^4*a3*a4^8 + a1^10*a2^4*a3*a4^3 + a1^10*a2^4*a4^10 + a1^10*a2^4*a4^9 + a1^10*a2^4*a4^8 + a1^10*a2^4*a4^6 + a1^10*a2^4*a4^5 + a1^10*a2^4*a4^4 + a1^10*a2^2*a3^4*a4^8 + a1^10*a2^2*a3^4*a4^2 + a1^10*a2^2*a3^2*a4^10 + a1^10*a2^2*a3^2*a4^9 + a1^10*a2^2*a3^2*a4^8 + a1^10*a2^2*a3^2*a4^4 + a1^10*a2^2*a3^2*a4^3 + a1^10*a2^2*a3^2*a4^2 + a1^10*a2^2*a3*a4^10 + a1^10*a2^2*a3*a4^9 + a1^10*a2^2*a3*a4^4 + a1^10*a2^2*a3*a4^3 + a1^10*a2^2*a4^12 + a1^10*a2^2*a4^10 + a1^10*a2^2*a4^6 + a1^10*a2^2*a4^4 + a1^10*a2*a3^4*a4^10 + a1^10*a2*a3^4*a4^9 + a1^10*a2*a3^4*a4^8 + a1^10*a2*a3^4*a4^3 + a1^10*a2*a3^2*a4^10 + a1^10*a2*a3^2*a4^9 + a1^10*a2*a3^2*a4^4 + a1^10*a2*a3^2*a4^3 + a1^10*a2*a3*a4^8 + a1^10*a2*a3*a4^4 + a1^10*a2*a4^12 + a1^10*a2*a4^9 + a1^10*a2*a4^8 + a1^10*a2*a4^5 + a1^10*a3^4*a4^10 + a1^10*a3^4*a4^9 + a1^10*a3^4*a4^8 + a1^10*a3^4*a4^6 + a1^10*a3^4*a4^5 + a1^10*a3^4*a4^4 + a1^10*a3^2*a4^12 + a1^10*a3^2*a4^10 + a1^10*a3^2*a4^6 + a1^10*a3^2*a4^4 + a1^10*a3*a4^12 + a1^10*a3*a4^9 + a1^10*a3*a4^8 + a1^10*a3*a4^5 + a1^10*a4^12 + a1^10*a4^10 + a1^10*a4^8 + a1^10*a4^6 + a1^9*a2^4*a3^4*a4^10 + a1^9*a2^4*a3^4*a4^9 + a1^9*a2^4*a3^4*a4^3 + a1^9*a2^4*a3^4*a4^2 + a1^9*a2^4*a3^2*a4^8 + a1^9*a2^4*a3^2*a4^2 + a1^9*a2^4*a3*a4^10 + a1^9*a2^4*a3*a4^9 + a1^9*a2^4*a3*a4^8 + a1^9*a2^4*a3*a4^3 + a1^9*a2^4*a4^10 + a1^9*a2^4*a4^9 + a1^9*a2^4*a4^6 + a1^9*a2^4*a4^5 + a1^9*a2^2*a3^4*a4^8 + a1^9*a2^2*a3^4*a4^2 + a1^9*a2^2*a3^2*a4^12 + a1^9*a2^2*a3^2*a4^10 + a1^9*a2^2*a3^2*a4^5 + a1^9*a2^2*a3^2*a4^4 + a1^9*a2^2*a3^2*a4^3 + a1^9*a2^2*a3^2*a4^2 + a1^9*a2^2*a3*a4^12 + a1^9*a2^2*a3*a4^10 + a1^9*a2^2*a3*a4^8 + a1^9*a2^2*a3*a4^5 + a1^9*a2^2*a3*a4^4 + a1^9*a2^2*a3*a4^3 + a1^9*a2^2*a4^12 + a1^9*a2^2*a4^9 + a1^9*a2^2*a4^8 + a1^9*a2^2*a4^5 + a1^9*a2*a3^4 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Sat Feb 21 05:55:25 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Sat Feb 21 2004 05:55:22 on modular [Seed = 1212100900] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Sat Feb 21 05:55:47 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*x^2+29+x; f1:=x^4+3+2*x^3+x; f2:=x^5-x; f3:=x^7-x^3; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Sat Feb 21 2004 05:55:44 on modular [Seed = 1044989816] ------------------------------------- [ 1 ] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Sat Feb 21 05:56:42 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*x^2+x+1; f1:=6*x^4+2*x^3+x+7; f2:=7*x^6+5*x^3+4*x+10; f3:=3*x^8+10*x^7+10*x^6+6*x^5+10*x^4+8*x^3+4*x^2+5*x+5; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Sat Feb 21 2004 05:56:39 on modular [Seed = 609443125] ------------------------------------- [ x + 9, 11 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Sat Feb 21 05:57:36 2004 Input: :=PolynomialRing(IntegerRing(),2); f0:=2*x^2+x+1; f1:=6*x^4+2*x^3+x+7; f2:=4*x^6+7*x^5+4*x^4+x^3+5*x^2+3*x+5; f3:=3*x^8+10*x^7+10*x^6+6*x^5+10*x^4+8*x^3+4*x^2+5*x+5; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Sat Feb 21 2004 05:57:33 on modular [Seed = 760894662] ------------------------------------- >> :=PolynomialRing(IntegerRing(),2); ^ User error: Illegal left hand side of an assignment statement >> f0:=2*x^2+x+1; ^ User error: Identifier 'x' has not been declared or assigned >> f1:=6*x^4+2*x^3+x+7; ^ User error: Identifier 'x' has not been declared or assigned >> f2:=4*x^6+7*x^5+4*x^4+x^3+5*x^2+3*x+5; ^ User error: Identifier 'x' has not been declared or assigned >> f3:=3*x^8+10*x^7+10*x^6+6*x^5+10*x^4+8*x^3+4*x^2+5*x+5; ^ User error: Identifier 'x' has not been declared or assigned >> I:=ideal; ^ User error: Identifier 'P' has not been declared or assigned >> B:=GroebnerBasis(I:Al:="Direct"); ^ User error: Identifier 'I' has not been declared or assigned >> B; ^ User error: Identifier 'B' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Sat Feb 21 05:58:16 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*x^2+x+1; f1:=6*x^4+2*x^3+x+7; f2:=4*x^6+7*x^5+4*x^4+x^3+5*x^2+3*x+5; f3:=3*x^8+10*x^7+10*x^6+6*x^5+10*x^4+8*x^3+4*x^2+5*x+5; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Sat Feb 21 2004 05:58:13 on modular [Seed = 308636577] ------------------------------------- [ x + 9, 11 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Sat Feb 21 05:58:49 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*x^2+x+1; f1:=6*x^4+2*x^3+x+7; f2:=4*x^6+7*x^5+4*x^4+x^3+5*x^2+3*x+5; f3:=3*x^8+x^7+5*x^6+x^5+6*x^4+2*x^3+8*x^2+3*x+10; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Sat Feb 21 2004 05:58:46 on modular [Seed = 460087947] ------------------------------------- [ x^2 + 6*x + 6, 11 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Sat Feb 21 05:59:20 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*x^2+x+1; f1:=6*x^4+2*x^3+x+7; f2:=7*x^6+5*x^3+4*x+10; f3:=3*x^8+8*x^7+4*x^5+5*x^3+x+7; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Sat Feb 21 2004 05:59:17 on modular [Seed = 7830131] ------------------------------------- [ x + 9, 22 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Sat Feb 21 05:59:56 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*x^2+x+1; f1:=6*x^4+2*x^3+x+7; f2:=7*x^6+5*x^3+4*x+10; f3:=7*x^8+5*x^7+5*x^6+3*x^5+5*x^4+4*x^3+2*x^2+8*x+8; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Sat Feb 21 2004 05:59:53 on modular [Seed = 4135685289] ------------------------------------- [ x + 9, 11 ] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Sat Feb 21 06:00:26 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*x^2+x+1; f1:=6*x^4+2*x^3+x+7; f2:=4*x^6+7*x^5+4*x^4+x^3+5*x^2+3*x+5; f3:=7*x^8+5*x^7+5*x^6+3*x^5+5*x^4+4*x^3+2*x^2+8*x+8; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Sat Feb 21 2004 06:00:22 on modular [Seed = 3818166739] ------------------------------------- [ x + 9, 11 ] Total time: 3.259 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Sat Feb 21 06:01:08 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*x^2+x+1; f1:=6*x^4+2*x^3+x+7; f2:=4*x^6+7*x^5+4*x^4+x^3+5*x^2+3*x+5; f3:=7*x^8+6*x^7+8*x^6+6*x^5+3*x^4+x^3+4*x^2+7*x+5; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Sat Feb 21 2004 06:00:59 on modular [Seed = 3919483892] ------------------------------------- [ x^2 + 6*x + 6, 11 ] Total time: 3.289 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Sat Feb 21 06:01:41 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*x^2+x+1; f1:=6*x^4+2*x^3+x+7; f2:=4*x^6+6*x^3+7*x+5; f3:=3*x^8+8*x^7+4*x^5+5*x^3+x+7; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Sat Feb 21 2004 06:01:37 on modular [Seed = 3434853931] ------------------------------------- [ x + 1, 2 ] Total time: 3.219 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Sat Feb 21 06:02:25 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*x^2+x+1; f1:=6*x^4+2*x^3+x+7; f2:=4*x^6+6*x^3+7*x+5; f3:=7*x^8+5*x^7+5*x^6+3*x^5+5*x^4+4*x^3+2*x^2+8*x+8; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Sat Feb 21 2004 06:02:22 on modular [Seed = 3049443197] ------------------------------------- [ 1 ] Total time: 3.319 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Sat Feb 21 06:02:56 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*x^2+x+1; f1:=6*x^4+2*x^3+x+7; f2:=2*x^6+9*x^5+2*x^4+6*x^3; f3:=7*x^8+5*x^7+5*x^6+3*x^5+5*x^4+4*x^3+2*x^2+8*x+8; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Sat Feb 21 2004 06:02:53 on modular [Seed = 3134046225] ------------------------------------- [ 1 ] Total time: 3.209 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Sat Feb 21 06:03:25 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*x^2+x+1; f1:=6*x^4+2*x^3+x+7; f2:=2*x^6+9*x^5+2*x^4+6*x^3; f3:=7*x^8+6*x^7+8*x^6+6*x^5+3*x^4+x^3+4*x^2+7*x+5; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Sat Feb 21 2004 06:03:22 on modular [Seed = 2748635439] ------------------------------------- [ 1 ] Total time: 3.000 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Sat Feb 21 06:03:54 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*x^2+x+1; f1:=6*x^4+2*x^3+x+7; f2:=4*x^6+6*x^3+7*x+5; f3:=3*x^8+8*x^7+4*x^5+5*x^3+x+7; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Sat Feb 21 2004 06:03:50 on modular [Seed = 2849952457] ------------------------------------- [ x + 1, 2 ] Total time: 3.139 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Sat Feb 21 06:04:20 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*x^2+x+1; f1:=6*x^4+2*x^3+x+7; f2:=4*x^6+6*x^3+7*x+5; f3:=7*x^8+5*x^7+5*x^6+3*x^5+5*x^4+4*x^3+2*x^2+8*x+8; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Sat Feb 21 2004 06:04:15 on modular [Seed = 2666128839] ------------------------------------- [ 1 ] Total time: 5.209 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Sat Feb 21 06:04:40 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*x^2+x+1; f1:=6*x^4+2*x^3+x+7; f2:=2*x^6+9*x^5+2*x^4+6*x^3; f3:=7*x^8+5*x^7+5*x^6+3*x^5+5*x^4+4*x^3+2*x^2+8*x+8; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Sat Feb 21 2004 06:04:37 on modular [Seed = 2230583223] ------------------------------------- [ 1 ] Total time: 3.189 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Sat Feb 21 06:05:09 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*x^2+x+1; f1:=6*x^4+2*x^3+x+7; f2:=2*x^6+9*x^5+2*x^4+6*x^3; f3:=7*x^8+6*x^7+8*x^6+6*x^5+3*x^4+x^3+4*x^2+7*x+5; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Sat Feb 21 2004 06:05:06 on modular [Seed = 2315186845] ------------------------------------- [ 1 ] Total time: 3.499 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Feb 21 06:42:22 2004 Input: puta xD; Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed. ************** MAGMA ***************** Host cache-frr-ab01.proxy.aol.com. (195.93.73.6) Time: Sat Feb 21 08:00:44 2004 Input: 4+2 Output: Magma V2.10-6 Sat Feb 21 2004 08:00:41 on modular [Seed = 2415434113] ------------------------------------- 6 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (61.0.137.13) Time: Sat Feb 21 13:41:05 2004 Input: TAPAN GHOSH ACCOUNT NO.973692 ACCOUNT TYPE. CONSUMER LOAN ASSET FINANCED. ASSEMBLED PC PRODUCT.MD-MAGMA-DURABLE BOOKING DATE. 28-AUG-2002 Output: Magma V2.10-6 Sat Feb 21 2004 13:41:02 on modular [Seed = 1262267662] ------------------------------------- >> TAPAN GHOSH ^ User error: bad syntax >> ACCOUNT NO.973692 ^ User error: bad syntax >> ACCOUNT TYPE. CONSUMER LOAN ^ User error: bad syntax >> ASSET FINANCED. ASSEMBLED PC ^ User error: bad syntax >> BOOKING DATE. 28-AUG-2002; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Sat Feb 21 13:45:03 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Sat Feb 21 2004 13:45:00 on modular [Seed = 1061738600] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sv4.ictp.trieste.it. (140.105.16.64) Time: Sat Feb 21 14:23:49 2004 Input: R:= PolynomialRing(Rationals()); f:=x^2-x+1; K:=NumberField(f); P:=MaximalOrder(K); M:=MatrixRing( P , 15 ) ! [ 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, -w, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, -w, 2-w, -1+w, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1-2*w, 1, 0, 1-w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, w, -1+w, -1+w, -1+2*w, -1+w, 3, 0, 0, 0, 0, 0, 0, 0, 1-w, 0, w, 1, w, w, w, 1-w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 2-w, -1, 1-w, 1, w, 0, -w, 3, 0, 0, 0, 0, 0, 1-w, 1-w, -1+w, 0, w, -1+w, -w, 0, 1, -1, 3, 0, 0, 0, 0, -w, -w, 1-w, -w, 1, 1, 0, -1, -w, 1, -w, 3, 0, 0, 0, -w, 0, 0, w, 0, 0, -1+w, 0, 1, -1, 1-w, 0, 3, 0, 0, -w, 0, 0, 0, 1-w, 1-w, -w, -w, -w, 0, 0, 0, w, 3, 0, -w, 1-w, -1+w, -1, -1+w, w, -w, 1, 0, -w, 1, 0, 0, 0, 4 ]; for i := 1 to 15 do for j := i+1 to 15 do M[i,j]:=Trace(M[j,i])-M[j,i]; end for; end for; N:= MatrixRing( Integers() , 30 ) ! [ 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; for i := 1 to 15 do for j := 1 to 15 do N[i,j]:=Trace(M[i,j]); N[15+i,15+j]:=N[i,j]; N[15+i,j]:=Trace(w*M[i,j]); N[j,15+i]:=N[15+i,j]; end for; end for; L := LatticeWithGram(N); S := ShortestVectors(L); d:=#S; d; G := EmptyGraph(d); for i := 1 to d do for j := i+1 to d do if not (S[i],S[j]) eq 0 then AddEdge(~G, i, j); end if; end for; end for; Components(G); T := sub< L | S >; r := Rank(T); r; Determinant(L); H := AutomorphismGroup(L); #H; FactoredOrder(H); X:=DerivedGroup(H); FactoredOrder(X); Y:=DerivedGroup(X); FactoredOrder(Y); Z:=DerivedGroup(Y); FactoredOrder(Z); Output: ** WARNING: Computation used more memory than allowed. ** Magma V2.10-6 Sat Feb 21 2004 14:23:28 on modular [Seed = 3584173470] ------------------------------------- 9 [ { 1, 2, 3, 4, 5, 6, 7, 8, 9 } ] 4 14348907 Current total memory usage: 83.5MB, failed memory request: 43.4MB System Error: User memory limit has been reached >> #H; FactoredOrder(H); ^ Runtime error: Variable 'H' has not been initialized >> #H; FactoredOrder(H); ^ User error: Identifier 'H' has not been declared or assigned >> X:=DerivedGroup(H); FactoredOrder(X); ^ User error: Identifier 'H' has not been declared or assigned >> X:=DerivedGroup(H); FactoredOrder(X); ^ User error: Identifier 'X' has not been declared or assigned >> Y:=DerivedGroup(X); FactoredOrder(Y); ^ User error: Identifier 'X' has not been declared or assigned >> Y:=DerivedGroup(X); FactoredOrder(Y); ^ User error: Identifier 'Y' has not been declared or assigned >> Z:=DerivedGroup(Y); FactoredOrder(Z); ^ User error: Identifier 'Y' has not been declared or assigned >> Z:=DerivedGroup(Y); FactoredOrder(Z); ^ User error: Identifier 'Z' has not been declared or assigned Total time: 20.219 seconds, Total memory usage: 87.60MB ************** MAGMA ***************** Host sv4.ictp.trieste.it. (140.105.16.64) Time: Sat Feb 21 14:25:09 2004 Input: R:= PolynomialRing(Rationals()); f:=x^2-x+1; K:=NumberField(f); P:=MaximalOrder(K); M:=MatrixRing( P , 15 ) ! [ 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, w, 0, -1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1+w, -1, 1-w, w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2-w, -1+w, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, 0, w, 1-2*w, -1, -1+w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, -w, -1, -w, -1, -w, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, w, 1-w, -1, 0, 1, 1-2*w, -1+w, 3, 0, 0, 0, 0, 0, 0, -w, 1-w, w, -w, -1, -1+w, 1, 0, 0, 3, 0, 0, 0, 0, 0, -w, 1-w, -1, 0, 0, 0, -w, w, 1-w, 0, 3, 0, 0, 0, 0, 0, 0, w, 0, 0, -1+w, w, -w, -1, 1, -1-w, 3, 0, 0, 0, 0, 0, -w, -1+w, w, -w, -1, 1-w, -w, -w, -1, 1, 3, 0, 0, -1+w, -w, 1, 0, 1, w, -w, -1+w, 0, 1-w, 1-w, 0, -1+w, 3, 0, -1, -1, -w, 1, 1, -w, 0, 0, -1+w, -1, 0, -w, 1-w, 0, 3 ]; for i := 1 to 15 do for j := i+1 to 15 do M[i,j]:=Trace(M[j,i])-M[j,i]; end for; end for; N:= MatrixRing( Integers() , 30 ) ! [ 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; for i := 1 to 15 do for j := 1 to 15 do N[i,j]:=Trace(M[i,j]); N[15+i,15+j]:=N[i,j]; N[15+i,j]:=Trace(w*M[i,j]); N[j,15+i]:=N[15+i,j]; end for; end for; L := LatticeWithGram(N); S := ShortestVectors(L); d:=#S; d; G := EmptyGraph(d); for i := 1 to d do for j := i+1 to d do if not (S[i],S[j]) eq 0 then AddEdge(~G, i, j); end if; end for; end for; Components(G); T := sub< L | S >; r := Rank(T); r; Determinant(L); H := AutomorphismGroup(L); #H; FactoredOrder(H); X:=DerivedGroup(H); FactoredOrder(X); Y:=DerivedGroup(X); FactoredOrder(Y); Z:=DerivedGroup(Y); FactoredOrder(Z); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Feb 21 2004 14:24:44 on modular [Seed = 3434822859] ------------------------------------- 3 [ { 1, 2, 3 } ] 2 14348907 Errors: /home/mfd/gomagma: line 2: 15287 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host riemann.math.harvard.edu. (140.247.29.234) Time: Sat Feb 21 22:53:55 2004 Input: P:=PolynomialRing(RationalField()); Output: Magma V2.10-6 Sat Feb 21 2004 22:53:52 on modular [Seed = 3150175338] ------------------------------------- Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host riemann.math.harvard.edu. (140.247.29.234) Time: Sat Feb 21 22:55:11 2004 Input: 1+1; Output: Magma V2.10-6 Sat Feb 21 2004 22:55:08 on modular [Seed = 3451233744] ------------------------------------- 2 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host riemann.math.harvard.edu. (140.247.29.234) Time: Sat Feb 21 22:55:24 2004 Input: 1+1 Output: Magma V2.10-6 Sat Feb 21 2004 22:55:21 on modular [Seed = 3568090364] ------------------------------------- 2 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host riemann.math.harvard.edu. (140.247.29.234) Time: Sat Feb 21 22:55:49 2004 Input: 1+1; Output: Magma V2.10-6 Sat Feb 21 2004 22:55:46 on modular [Seed = 3735467677] ------------------------------------- 2 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host newproxy1.ictp.trieste.it. (140.105.16.2) Time: Sun Feb 22 07:20:51 2004 Input: R:= PolynomialRing(Rationals()); f:=x^2-x+1; K:=NumberField(f); P:=MaximalOrder(K); M:=MatrixRing( P , 15 ) ! [ 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, w, 0, -1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1+w, -1, 1-w, w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2-w, -1+w, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, 0, w, 1-2*w, -1, -1+w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, -w, -1, -w, -1, -w, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, w, 1-w, -1, 0, 1, 1-2*w, -1+w, 3, 0, 0, 0, 0, 0, 0, -w, 1-w, w, -w, -1, -1+w, 1, 0, 0, 3, 0, 0, 0, 0, 0, -w, 1-w, -1, 0, 0, 0, -w, w, 1-w, 0, 3, 0, 0, 0, 0, 0, 0, w, 0, 0, -1+w, w, -w, -1, 1, -1-w, 3, 0, 0, 0, 0, 0, -w, -1+w, w, -w, -1, 1-w, -w, -w, -1, 1, 3, 0, 0, -1+w, -w, 1, 0, 1, w, -w, -1+w, 0, 1-w, 1-w, 0, -1+w, 3, 0, -1, -1, -w, 1, 1, -w, 0, 0, -1+w, -1, 0, -w, 1-w, 0, 3 ]; for i := 1 to 15 do for j := i+1 to 15 do M[i,j]:=Trace(M[j,i])-M[j,i]; end for; end for; N:= MatrixRing( Integers() , 30 ) ! [ 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; for i := 1 to 15 do for j := 1 to 15 do N[i,j]:=Trace(M[i,j]); N[15+i,15+j]:=N[i,j]; N[15+i,j]:=Trace(w*M[i,j]); N[j,15+i]:=N[15+i,j]; end for; end for; L := LatticeWithGram(N); S := ShortestVectors(L); d:=#S; d; G := EmptyGraph(d); for i := 1 to d do for j := i+1 to d do if not (S[i],S[j]) eq 0 then AddEdge(~G, i, j); end if; end for; end for; Components(G); T := sub< L | S >; r := Rank(T); r; Determinant(L); H := AutomorphismGroup(L : Stabilizer :=1); #H; FactoredOrder(H); H1:=DerivedGroup(H); FactoredOrder(H1); H2:=DerivedGroup(H1); FactoredOrder(H2); H3:=DerivedGroup(H2); FactoredOrder(H3); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Feb 22 2004 07:20:26 on modular [Seed = 1361678236] ------------------------------------- 3 [ { 1, 2, 3 } ] 2 14348907 Errors: /home/mfd/gomagma: line 2: 1814 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host newproxy1.ictp.trieste.it. (140.105.16.2) Time: Sun Feb 22 07:22:15 2004 Input: R:= PolynomialRing(Rationals()); f:=x^2-x+1; K:=NumberField(f); P:=MaximalOrder(K); M:=MatrixRing( P , 15 ) ! [ 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, w, 0, -1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1+w, -1, 1-w, w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2-w, -1+w, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, 0, w, 1-2*w, -1, -1+w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, -w, -1, -w, -1, -w, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, w, 1-w, -1, 0, 1, 1-2*w, -1+w, 3, 0, 0, 0, 0, 0, 0, -w, 1-w, w, -w, -1, -1+w, 1, 0, 0, 3, 0, 0, 0, 0, 0, -w, 1-w, -1, 0, 0, 0, -w, w, 1-w, 0, 3, 0, 0, 0, 0, 0, 0, w, 0, 0, -1+w, w, -w, -1, 1, -1-w, 3, 0, 0, 0, 0, 0, -w, -1+w, w, -w, -1, 1-w, -w, -w, -1, 1, 3, 0, 0, -1+w, -w, 1, 0, 1, w, -w, -1+w, 0, 1-w, 1-w, 0, -1+w, 3, 0, -1, -1, -w, 1, 1, -w, 0, 0, -1+w, -1, 0, -w, 1-w, 0, 3 ]; for i := 1 to 15 do for j := i+1 to 15 do M[i,j]:=Trace(M[j,i])-M[j,i]; end for; end for; N:= MatrixRing( Integers() , 30 ) ! 0; for i := 1 to 15 do for j := 1 to 15 do N[i,j]:=Trace(M[i,j]); N[15+i,15+j]:=N[i,j]; N[15+i,j]:=Trace(w*M[i,j]); N[j,15+i]:=N[15+i,j]; end for; end for; L := LatticeWithGram(N); S := ShortestVectors(L); d:=#S; d; G := EmptyGraph(d); for i := 1 to d do for j := i+1 to d do if not (S[i],S[j]) eq 0 then AddEdge(~G, i, j); end if; end for; end for; Components(G); T := sub< L | S >; r := Rank(T); r; Determinant(L); H := AutomorphismGroup(L : Stabilizer :=1); #H; FactoredOrder(H); H1:=DerivedGroup(H); FactoredOrder(H1); H2:=DerivedGroup(H1); FactoredOrder(H2); H3:=DerivedGroup(H2); FactoredOrder(H3); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Feb 22 2004 07:21:52 on modular [Seed = 1730132416] ------------------------------------- 3 [ { 1, 2, 3 } ] 2 14348907 Errors: /home/mfd/gomagma: line 2: 1824 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host newproxy1.ictp.trieste.it. (140.105.16.2) Time: Sun Feb 22 07:23:00 2004 Input: R:= PolynomialRing(Rationals()); f:=x^2-x+1; K:=NumberField(f); P:=MaximalOrder(K); M:=MatrixRing( P , 15 ) ! [ 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, w, 0, -1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1+w, -1, 1-w, w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2-w, -1+w, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, 0, w, 1-2*w, -1, -1+w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, -w, -1, -w, -1, -w, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, w, 1-w, -1, 0, 1, 1-2*w, -1+w, 3, 0, 0, 0, 0, 0, 0, -w, 1-w, w, -w, -1, -1+w, 1, 0, 0, 3, 0, 0, 0, 0, 0, -w, 1-w, -1, 0, 0, 0, -w, w, 1-w, 0, 3, 0, 0, 0, 0, 0, 0, w, 0, 0, -1+w, w, -w, -1, 1, -1-w, 3, 0, 0, 0, 0, 0, -w, -1+w, w, -w, -1, 1-w, -w, -w, -1, 1, 3, 0, 0, -1+w, -w, 1, 0, 1, w, -w, -1+w, 0, 1-w, 1-w, 0, -1+w, 3, 0, -1, -1, -w, 1, 1, -w, 0, 0, -1+w, -1, 0, -w, 1-w, 0, 3 ]; for i := 1 to 15 do for j := i+1 to 15 do M[i,j]:=Trace(M[j,i])-M[j,i]; end for; end for; N:= MatrixRing( Integers() , 30 ) ! 0; for i := 1 to 15 do for j := 1 to 15 do N[i,j]:=Trace(M[i,j]); N[15+i,15+j]:=N[i,j]; N[15+i,j]:=Trace(w*M[i,j]); N[j,15+i]:=N[15+i,j]; end for; end for; L := LatticeWithGram(N); S := ShortestVectors(L); d:=#S; d; G := EmptyGraph(d); for i := 1 to d do for j := i+1 to d do if not (S[i],S[j]) eq 0 then AddEdge(~G, i, j); end if; end for; end for; Components(G); T := sub< L | S >; r := Rank(T); r; Determinant(L); H := AutomorphismGroup(L : Stabilizer :=2); #H; FactoredOrder(H); H1:=DerivedGroup(H); FactoredOrder(H1); H2:=DerivedGroup(H1); FactoredOrder(H2); H3:=DerivedGroup(H2); FactoredOrder(H3); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Feb 22 2004 07:22:37 on modular [Seed = 1846980900] ------------------------------------- 3 [ { 1, 2, 3 } ] 2 14348907 Errors: /home/mfd/gomagma: line 2: 1833 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host newproxy1.ictp.trieste.it. (140.105.16.2) Time: Sun Feb 22 07:23:58 2004 Input: R:= PolynomialRing(Rationals()); f:=x^2-x+1; K:=NumberField(f); P:=MaximalOrder(K); M:=MatrixRing( P , 15 ) ! [ 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, w, 0, -1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1+w, -1, 1-w, w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2-w, -1+w, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, 0, w, 1-2*w, -1, -1+w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, -w, -1, -w, -1, -w, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, w, 1-w, -1, 0, 1, 1-2*w, -1+w, 3, 0, 0, 0, 0, 0, 0, -w, 1-w, w, -w, -1, -1+w, 1, 0, 0, 3, 0, 0, 0, 0, 0, -w, 1-w, -1, 0, 0, 0, -w, w, 1-w, 0, 3, 0, 0, 0, 0, 0, 0, w, 0, 0, -1+w, w, -w, -1, 1, -1-w, 3, 0, 0, 0, 0, 0, -w, -1+w, w, -w, -1, 1-w, -w, -w, -1, 1, 3, 0, 0, -1+w, -w, 1, 0, 1, w, -w, -1+w, 0, 1-w, 1-w, 0, -1+w, 3, 0, -1, -1, -w, 1, 1, -w, 0, 0, -1+w, -1, 0, -w, 1-w, 0, 3 ]; for i := 1 to 15 do for j := i+1 to 15 do M[i,j]:=Trace(M[j,i])-M[j,i]; end for; end for; N:= MatrixRing( Integers() , 30 ) ! 0; for i := 1 to 15 do for j := 1 to 15 do N[i,j]:=Trace(M[i,j]); N[15+i,15+j]:=N[i,j]; N[15+i,j]:=Trace(w*M[i,j]); N[j,15+i]:=N[15+i,j]; end for; end for; L := LatticeWithGram(N); S := ShortestVectors(L); d:=#S; d; G := EmptyGraph(d); for i := 1 to d do for j := i+1 to d do if not (S[i],S[j]) eq 0 then AddEdge(~G, i, j); end if; end for; end for; Components(G); T := sub< L | S >; r := Rank(T); r; Determinant(L); H := AutomorphismGroup(L : Stabilizer :=3); #H; FactoredOrder(H); H1:=DerivedGroup(H); FactoredOrder(H1); H2:=DerivedGroup(H1); FactoredOrder(H2); H3:=DerivedGroup(H2); FactoredOrder(H3); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Feb 22 2004 07:23:35 on modular [Seed = 1963829877] ------------------------------------- 3 [ { 1, 2, 3 } ] 2 14348907 Errors: /home/mfd/gomagma: line 2: 1842 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host newproxy1.ictp.trieste.it. (140.105.16.2) Time: Sun Feb 22 07:24:38 2004 Input: R:= PolynomialRing(Rationals()); f:=x^2-x+1; K:=NumberField(f); P:=MaximalOrder(K); M:=MatrixRing( P , 15 ) ! [ 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, w, 0, -1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1+w, -1, 1-w, w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2-w, -1+w, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, 0, w, 1-2*w, -1, -1+w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, -w, -1, -w, -1, -w, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, w, 1-w, -1, 0, 1, 1-2*w, -1+w, 3, 0, 0, 0, 0, 0, 0, -w, 1-w, w, -w, -1, -1+w, 1, 0, 0, 3, 0, 0, 0, 0, 0, -w, 1-w, -1, 0, 0, 0, -w, w, 1-w, 0, 3, 0, 0, 0, 0, 0, 0, w, 0, 0, -1+w, w, -w, -1, 1, -1-w, 3, 0, 0, 0, 0, 0, -w, -1+w, w, -w, -1, 1-w, -w, -w, -1, 1, 3, 0, 0, -1+w, -w, 1, 0, 1, w, -w, -1+w, 0, 1-w, 1-w, 0, -1+w, 3, 0, -1, -1, -w, 1, 1, -w, 0, 0, -1+w, -1, 0, -w, 1-w, 0, 3 ]; for i := 1 to 15 do for j := i+1 to 15 do M[i,j]:=Trace(M[j,i])-M[j,i]; end for; end for; N:= MatrixRing( Integers() , 30 ) ! 0; for i := 1 to 15 do for j := 1 to 15 do N[i,j]:=Trace(M[i,j]); N[15+i,15+j]:=N[i,j]; N[15+i,j]:=Trace(w*M[i,j]); N[j,15+i]:=N[15+i,j]; end for; end for; L := LatticeWithGram(N); S := ShortestVectors(L); d:=#S; d; G := EmptyGraph(d); for i := 1 to d do for j := i+1 to d do if not (S[i],S[j]) eq 0 then AddEdge(~G, i, j); end if; end for; end for; Components(G); T := sub< L | S >; r := Rank(T); r; Determinant(L); H := AutomorphismGroup(L : Stabilizer :=4); #H; FactoredOrder(H); H1:=DerivedGroup(H); FactoredOrder(H1); H2:=DerivedGroup(H1); FactoredOrder(H2); H3:=DerivedGroup(H2); FactoredOrder(H3); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Feb 22 2004 07:24:15 on modular [Seed = 2080678740] ------------------------------------- 3 [ { 1, 2, 3 } ] 2 14348907 Errors: /home/mfd/gomagma: line 2: 1851 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host newproxy1.ictp.trieste.it. (140.105.16.2) Time: Sun Feb 22 07:25:18 2004 Input: R:= PolynomialRing(Rationals()); f:=x^2-x+1; K:=NumberField(f); P:=MaximalOrder(K); M:=MatrixRing( P , 15 ) ! [ 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, w, 0, -1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1+w, -1, 1-w, w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2-w, -1+w, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, 0, w, 1-2*w, -1, -1+w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, -w, -1, -w, -1, -w, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, w, 1-w, -1, 0, 1, 1-2*w, -1+w, 3, 0, 0, 0, 0, 0, 0, -w, 1-w, w, -w, -1, -1+w, 1, 0, 0, 3, 0, 0, 0, 0, 0, -w, 1-w, -1, 0, 0, 0, -w, w, 1-w, 0, 3, 0, 0, 0, 0, 0, 0, w, 0, 0, -1+w, w, -w, -1, 1, -1-w, 3, 0, 0, 0, 0, 0, -w, -1+w, w, -w, -1, 1-w, -w, -w, -1, 1, 3, 0, 0, -1+w, -w, 1, 0, 1, w, -w, -1+w, 0, 1-w, 1-w, 0, -1+w, 3, 0, -1, -1, -w, 1, 1, -w, 0, 0, -1+w, -1, 0, -w, 1-w, 0, 3 ]; for i := 1 to 15 do for j := i+1 to 15 do M[i,j]:=Trace(M[j,i])-M[j,i]; end for; end for; N:= MatrixRing( Integers() , 30 ) ! 0; for i := 1 to 15 do for j := 1 to 15 do N[i,j]:=Trace(M[i,j]); N[15+i,15+j]:=N[i,j]; N[15+i,j]:=Trace(w*M[i,j]); N[j,15+i]:=N[15+i,j]; end for; end for; L := LatticeWithGram(N); S := ShortestVectors(L); d:=#S; d; G := EmptyGraph(d); for i := 1 to d do for j := i+1 to d do if not (S[i],S[j]) eq 0 then AddEdge(~G, i, j); end if; end for; end for; Components(G); T := sub< L | S >; r := Rank(T); r; Determinant(L); H := AutomorphismGroup(L : Stabilizer :=5); #H; FactoredOrder(H); H1:=DerivedGroup(H); FactoredOrder(H1); H2:=DerivedGroup(H1); FactoredOrder(H2); H3:=DerivedGroup(H2); FactoredOrder(H3); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Feb 22 2004 07:24:55 on modular [Seed = 58449107] ------------------------------------- 3 [ { 1, 2, 3 } ] 2 14348907 Errors: /home/mfd/gomagma: line 2: 1860 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host newproxy1.ictp.trieste.it. (140.105.16.2) Time: Sun Feb 22 07:26:51 2004 Input: R:= PolynomialRing(Rationals()); f:=x^2-x+1; K:=NumberField(f); P:=MaximalOrder(K); M:=MatrixRing( P , 15 ) ! [ 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, w, 0, -1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1+w, -1, 1-w, w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2-w, -1+w, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, 0, w, 1-2*w, -1, -1+w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, -w, -1, -w, -1, -w, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, w, 1-w, -1, 0, 1, 1-2*w, -1+w, 3, 0, 0, 0, 0, 0, 0, -w, 1-w, w, -w, -1, -1+w, 1, 0, 0, 3, 0, 0, 0, 0, 0, -w, 1-w, -1, 0, 0, 0, -w, w, 1-w, 0, 3, 0, 0, 0, 0, 0, 0, w, 0, 0, -1+w, w, -w, -1, 1, -1-w, 3, 0, 0, 0, 0, 0, -w, -1+w, w, -w, -1, 1-w, -w, -w, -1, 1, 3, 0, 0, -1+w, -w, 1, 0, 1, w, -w, -1+w, 0, 1-w, 1-w, 0, -1+w, 3, 0, -1, -1, -w, 1, 1, -w, 0, 0, -1+w, -1, 0, -w, 1-w, 0, 3 ]; for i := 1 to 15 do for j := i+1 to 15 do M[i,j]:=Trace(M[j,i])-M[j,i]; end for; end for; N:= MatrixRing( Integers() , 30 ) ! 0; for i := 1 to 15 do for j := 1 to 15 do N[i,j]:=Trace(M[i,j]); N[15+i,15+j]:=N[i,j]; N[15+i,j]:=Trace(w*M[i,j]); N[j,15+i]:=N[15+i,j]; end for; end for; L := LatticeWithGram(N); H := AutomorphismGroup(L : Stabilizer :=5); #H; FactoredOrder(H); H1:=DerivedGroup(H); FactoredOrder(H1); H2:=DerivedGroup(H1); FactoredOrder(H2); H3:=DerivedGroup(H2); FactoredOrder(H3); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Feb 22 2004 07:26:28 on modular [Seed = 359516838] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 1874 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host newproxy1.ictp.trieste.it. (140.105.16.2) Time: Sun Feb 22 07:27:34 2004 Input: R:= PolynomialRing(Rationals()); f:=x^2-x+1; K:=NumberField(f); P:=MaximalOrder(K); M:=MatrixRing( P , 15 ) ! [ 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, w, 0, -1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1+w, -1, 1-w, w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2-w, -1+w, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, 0, w, 1-2*w, -1, -1+w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, -w, -1, -w, -1, -w, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, w, 1-w, -1, 0, 1, 1-2*w, -1+w, 3, 0, 0, 0, 0, 0, 0, -w, 1-w, w, -w, -1, -1+w, 1, 0, 0, 3, 0, 0, 0, 0, 0, -w, 1-w, -1, 0, 0, 0, -w, w, 1-w, 0, 3, 0, 0, 0, 0, 0, 0, w, 0, 0, -1+w, w, -w, -1, 1, -1-w, 3, 0, 0, 0, 0, 0, -w, -1+w, w, -w, -1, 1-w, -w, -w, -1, 1, 3, 0, 0, -1+w, -w, 1, 0, 1, w, -w, -1+w, 0, 1-w, 1-w, 0, -1+w, 3, 0, -1, -1, -w, 1, 1, -w, 0, 0, -1+w, -1, 0, -w, 1-w, 0, 3 ]; for i := 1 to 15 do for j := i+1 to 15 do M[i,j]:=Trace(M[j,i])-M[j,i]; end for; end for; N:= MatrixRing( Integers() , 30 ) ! 0; for i := 1 to 15 do for j := 1 to 15 do N[i,j]:=Trace(M[i,j]); N[15+i,15+j]:=N[i,j]; N[15+i,j]:=Trace(w*M[i,j]); N[j,15+i]:=N[15+i,j]; end for; end for; L := LatticeWithGram(N); H := AutomorphismGroup(L : Stabilizer :=6); #H; FactoredOrder(H); H1:=DerivedGroup(H); FactoredOrder(H1); H2:=DerivedGroup(H1); FactoredOrder(H2); H3:=DerivedGroup(H2); FactoredOrder(H3); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Feb 22 2004 07:27:11 on modular [Seed = 459537219] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 1884 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host newproxy1.ictp.trieste.it. (140.105.16.2) Time: Sun Feb 22 07:28:26 2004 Input: R:= PolynomialRing(Rationals()); f:=x^2-x+1; K:=NumberField(f); P:=MaximalOrder(K); M:=MatrixRing( P , 15 ) ! [ 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, w, 0, -1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1+w, -1, 1-w, w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2-w, -1+w, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, 0, w, 1-2*w, -1, -1+w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, -w, -1, -w, -1, -w, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, w, 1-w, -1, 0, 1, 1-2*w, -1+w, 3, 0, 0, 0, 0, 0, 0, -w, 1-w, w, -w, -1, -1+w, 1, 0, 0, 3, 0, 0, 0, 0, 0, -w, 1-w, -1, 0, 0, 0, -w, w, 1-w, 0, 3, 0, 0, 0, 0, 0, 0, w, 0, 0, -1+w, w, -w, -1, 1, -1-w, 3, 0, 0, 0, 0, 0, -w, -1+w, w, -w, -1, 1-w, -w, -w, -1, 1, 3, 0, 0, -1+w, -w, 1, 0, 1, w, -w, -1+w, 0, 1-w, 1-w, 0, -1+w, 3, 0, -1, -1, -w, 1, 1, -w, 0, 0, -1+w, -1, 0, -w, 1-w, 0, 3 ]; for i := 1 to 15 do for j := i+1 to 15 do M[i,j]:=Trace(M[j,i])-M[j,i]; end for; end for; N:= MatrixRing( Integers() , 30 ) ! 0; for i := 1 to 15 do for j := 1 to 15 do N[i,j]:=Trace(M[i,j]); N[15+i,15+j]:=N[i,j]; N[15+i,j]:=Trace(w*M[i,j]); N[j,15+i]:=N[15+i,j]; end for; end for; L := LatticeWithGram(N); H := AutomorphismGroup(L : Stabilizer :=7); #H; FactoredOrder(H); H1:=DerivedGroup(H); FactoredOrder(H1); H2:=DerivedGroup(H1); FactoredOrder(H2); H3:=DerivedGroup(H2); FactoredOrder(H3); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Feb 22 2004 07:28:03 on modular [Seed = 576373302] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 1893 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host newproxy1.ictp.trieste.it. (140.105.16.2) Time: Sun Feb 22 07:29:52 2004 Input: R:= PolynomialRing(Rationals()); f:=x^2-x+1; K:=NumberField(f); P:=MaximalOrder(K); M:=MatrixRing( P , 15 ) ! [ 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, w, 0, -1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1+w, -1, 1-w, w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2-w, -1+w, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, 0, w, 1-2*w, -1, -1+w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, -w, -1, -w, -1, -w, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, w, 1-w, -1, 0, 1, 1-2*w, -1+w, 3, 0, 0, 0, 0, 0, 0, -w, 1-w, w, -w, -1, -1+w, 1, 0, 0, 3, 0, 0, 0, 0, 0, -w, 1-w, -1, 0, 0, 0, -w, w, 1-w, 0, 3, 0, 0, 0, 0, 0, 0, w, 0, 0, -1+w, w, -w, -1, 1, -1-w, 3, 0, 0, 0, 0, 0, -w, -1+w, w, -w, -1, 1-w, -w, -w, -1, 1, 3, 0, 0, -1+w, -w, 1, 0, 1, w, -w, -1+w, 0, 1-w, 1-w, 0, -1+w, 3, 0, -1, -1, -w, 1, 1, -w, 0, 0, -1+w, -1, 0, -w, 1-w, 0, 3 ]; for i := 1 to 15 do for j := i+1 to 15 do M[i,j]:=Trace(M[j,i])-M[j,i]; end for; end for; N:= MatrixRing( Integers() , 30 ) ! 0; for i := 1 to 15 do for j := 1 to 15 do N[i,j]:=Trace(M[i,j]); N[15+i,15+j]:=N[i,j]; N[15+i,j]:=Trace(w*M[i,j]); N[j,15+i]:=N[15+i,j]; end for; end for; L := LatticeWithGram(N); H := AutomorphismGroup(L : Stabilizer :=10); #H; FactoredOrder(H); H1:=DerivedGroup(H); FactoredOrder(H1); H2:=DerivedGroup(H1); FactoredOrder(H2); H3:=DerivedGroup(H2); FactoredOrder(H3); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Feb 22 2004 07:29:29 on modular [Seed = 693225927] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 1902 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host newproxy1.ictp.trieste.it. (140.105.16.2) Time: Sun Feb 22 07:32:25 2004 Input: R:= PolynomialRing(Rationals()); f:=x^2-x+1; K:=NumberField(f); P:=MaximalOrder(K); M:=MatrixRing( P , 14 ) ! [ 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1-w, w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2-w, -1+w, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, w, 1-2*w, -1, -1+w, 3, 0, 0, 0, 0, 0, 0, 0, 0, -w, -1, -w, -1, -w, 0, 3, 0, 0, 0, 0, 0, 0, 0, w, 1-w, -1, 0, 1, 1-2*w, -1+w, 3, 0, 0, 0, 0, 0, 0, 1-w, w, -w, -1, -1+w, 1, 0, 0, 3, 0, 0, 0, 0, 0, 1-w, -1, 0, 0, 0, -w, w, 1-w, 0, 3, 0, 0, 0, 0, 0, w, 0, 0, -1+w, w, -w, -1, 1, -1-w, 3, 0, 0, 0, 0, -w, -1+w, w, -w, -1, 1-w, -w, -w, -1, 1, 3, 0, 0, -w, 1, 0, 1, w, -w, -1+w, 0, 1-w, 1-w, 0, -1+w, 3, 0, -1, -w, 1, 1, -w, 0, 0, -1+w, -1, 0, -w, 1-w, 0, 3 ]; for i := 1 to 14 do for j := i+1 to 14 do M[i,j]:=Trace(M[j,i])-M[j,i]; end for; end for; N:= MatrixRing( Integers() , 28 ) ! 0; for i := 1 to 14 do for j := 1 to 14 do N[i,j]:=Trace(M[i,j]); N[14+i,14+j]:=N[i,j]; N[14+i,j]:=Trace(w*M[i,j]); N[j,14+i]:=N[14+i,j]; end for; end for; L := LatticeWithGram(N); S := ShortestVectors(L); d:=#S; d; G := EmptyGraph(d); for i := 1 to d do for j := i+1 to d do if not (S[i],S[j]) eq 0 then AddEdge(~G, i, j); end if; end for; end for; Components(G); T := sub< L | S >; r := Rank(T); r; Determinant(L); H := AutomorphismGroup(L : Stabilizer :=1); #H; FactoredOrder(H); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Feb 22 2004 07:32:02 on modular [Seed = 943774013] ------------------------------------- 3 [ { 1, 2, 3 } ] 2 76527504 Errors: /home/mfd/gomagma: line 2: 1919 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host newproxy1.ictp.trieste.it. (140.105.16.2) Time: Sun Feb 22 07:34:47 2004 Input: R:= PolynomialRing(Rationals()); f:=x^2-x+1; K:=NumberField(f); P:=MaximalOrder(K); M:=MatrixRing( P , 14 ) ! [ 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1-w, w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2-w, -1+w, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, w, 1-2*w, -1, -1+w, 3, 0, 0, 0, 0, 0, 0, 0, 0, -w, -1, -w, -1, -w, 0, 3, 0, 0, 0, 0, 0, 0, 0, w, 1-w, -1, 0, 1, 1-2*w, -1+w, 3, 0, 0, 0, 0, 0, 0, 1-w, w, -w, -1, -1+w, 1, 0, 0, 3, 0, 0, 0, 0, 0, 1-w, -1, 0, 0, 0, -w, w, 1-w, 0, 3, 0, 0, 0, 0, 0, w, 0, 0, -1+w, w, -w, -1, 1, -1-w, 3, 0, 0, 0, 0, -w, -1+w, w, -w, -1, 1-w, -w, -w, -1, 1, 3, 0, 0, -w, 1, 0, 1, w, -w, -1+w, 0, 1-w, 1-w, 0, -1+w, 3, 0, -1, -w, 1, 1, -w, 0, 0, -1+w, -1, 0, -w, 1-w, 0, 3 ]; for i := 1 to 14 do for j := i+1 to 14 do M[i,j]:=Trace(M[j,i])-M[j,i]; end for; end for; N:= MatrixRing( Integers() , 28 ) ! 0; for i := 1 to 14 do for j := 1 to 14 do N[i,j]:=Trace(M[i,j]); N[14+i,14+j]:=N[i,j]; N[14+i,j]:=Trace(w*M[i,j]); N[j,14+i]:=N[14+i,j]; end for; end for; L := LatticeWithGram(N); S := ShortestVectors(L); d:=#S; d; G := EmptyGraph(d); for i := 1 to d do for j := i+1 to d do if not (S[i],S[j]) eq 0 then AddEdge(~G, i, j); end if; end for; end for; Components(G); T := sub< L | S >; r := Rank(T); r; Determinant(L); H := AutomorphismGroup(L : Stabilizer :=6); #H; FactoredOrder(H); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Feb 22 2004 07:34:23 on modular [Seed = 3484888647] ------------------------------------- 3 [ { 1, 2, 3 } ] 2 76527504 Errors: /home/mfd/gomagma: line 2: 1928 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host newproxy1.ictp.trieste.it. (140.105.16.2) Time: Sun Feb 22 07:37:25 2004 Input: R:= PolynomialRing(Rationals()); f:=x^2-x+1; K:=NumberField(f); P:=MaximalOrder(K); M:=MatrixRing( P , 14 ) ! [ 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, 2-w, -1+w, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1-2*w, 1, 0, 1-w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1, w, -1+w, -1+w, -1+2*w, -1+w, 3, 0, 0, 0, 0, 0, 0, 0, 0, w, 1, w, w, w, 1-w, 3, 0, 0, 0, 0, 0, 0, 0, 2-w, -1, 1-w, 1, w, 0, -w, 3, 0, 0, 0, 0, 0, 1-w, -1+w, 0, w, -1+w, -w, 0, 1, -1, 3, 0, 0, 0, 0, -w, 1-w, -w, 1, 1, 0, -1, -w, 1, -w, 3, 0, 0, 0, 0, 0, w, 0, 0, -1+w, 0, 1, -1, 1-w, 0, 3, 0, 0, 0, 0, 0, 1-w, 1-w, -w, -w, -w, 0, 0, 0, w, 3, 0, 1-w, -1+w, -1, -1+w, w, -w, 1, 0, -w, 1, 0, 0, 0, 4 ]; for i := 1 to 14 do for j := i+1 to 14 do M[i,j]:=Trace(M[j,i])-M[j,i]; end for; end for; N:= MatrixRing( Integers() , 28 ) ! 0; for i := 1 to 14 do for j := 1 to 14 do N[i,j]:=Trace(M[i,j]); N[14+i,14+j]:=N[i,j]; N[14+i,j]:=Trace(w*M[i,j]); N[j,14+i]:=N[14+i,j]; end for; end for; L := LatticeWithGram(N); S := ShortestVectors(L); d:=#S; d; G := EmptyGraph(d); for i := 1 to d do for j := i+1 to d do if not (S[i],S[j]) eq 0 then AddEdge(~G, i, j); end if; end for; end for; Components(G); T := sub< L | S >; r := Rank(T); r; Determinant(L); H := AutomorphismGroup(L : Stabilizer :=1); #H; FactoredOrder(H); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Feb 22 2004 07:37:02 on modular [Seed = 3517527032] ------------------------------------- 3 [ { 1, 2, 3 } ] 2 234365481 Errors: /home/mfd/gomagma: line 2: 1942 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host newproxy1.ictp.trieste.it. (140.105.16.2) Time: Sun Feb 22 07:38:18 2004 Input: R:= PolynomialRing(Rationals()); f:=x^2-x+1; K:=NumberField(f); P:=MaximalOrder(K); M:=MatrixRing( P , 14 ) ! [ 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, 2-w, -1+w, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1-2*w, 1, 0, 1-w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1, w, -1+w, -1+w, -1+2*w, -1+w, 3, 0, 0, 0, 0, 0, 0, 0, 0, w, 1, w, w, w, 1-w, 3, 0, 0, 0, 0, 0, 0, 0, 2-w, -1, 1-w, 1, w, 0, -w, 3, 0, 0, 0, 0, 0, 1-w, -1+w, 0, w, -1+w, -w, 0, 1, -1, 3, 0, 0, 0, 0, -w, 1-w, -w, 1, 1, 0, -1, -w, 1, -w, 3, 0, 0, 0, 0, 0, w, 0, 0, -1+w, 0, 1, -1, 1-w, 0, 3, 0, 0, 0, 0, 0, 1-w, 1-w, -w, -w, -w, 0, 0, 0, w, 3, 0, 1-w, -1+w, -1, -1+w, w, -w, 1, 0, -w, 1, 0, 0, 0, 4 ]; for i := 1 to 14 do for j := i+1 to 14 do M[i,j]:=Trace(M[j,i])-M[j,i]; end for; end for; N:= MatrixRing( Integers() , 28 ) ! 0; for i := 1 to 14 do for j := 1 to 14 do N[i,j]:=Trace(M[i,j]); N[14+i,14+j]:=N[i,j]; N[14+i,j]:=Trace(w*M[i,j]); N[j,14+i]:=N[14+i,j]; end for; end for; L := LatticeWithGram(N); S := ShortestVectors(L); d:=#S; d; G := EmptyGraph(d); for i := 1 to d do for j := i+1 to d do if not (S[i],S[j]) eq 0 then AddEdge(~G, i, j); end if; end for; end for; Components(G); T := sub< L | S >; r := Rank(T); r; Determinant(L); H := AutomorphismGroup(L : Stabilizer :=5); #H; FactoredOrder(H); Output: Magma V2.10-6 Sun Feb 22 2004 07:38:02 on modular [Seed = 3634379317] ------------------------------------- 3 [ { 1, 2, 3 } ] 2 234365481 1 [] Total time: 15.679 seconds, Total memory usage: 51.43MB ************** MAGMA ***************** Host newproxy1.ictp.trieste.it. (140.105.16.2) Time: Sun Feb 22 07:39:47 2004 Input: R:= PolynomialRing(Rationals()); f:=x^2-x+1; K:=NumberField(f); P:=MaximalOrder(K); M:=MatrixRing( P , 14 ) ! [ 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, 2-w, -1+w, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1-2*w, 1, 0, 1-w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1, w, -1+w, -1+w, -1+2*w, -1+w, 3, 0, 0, 0, 0, 0, 0, 0, 0, w, 1, w, w, w, 1-w, 3, 0, 0, 0, 0, 0, 0, 0, 2-w, -1, 1-w, 1, w, 0, -w, 3, 0, 0, 0, 0, 0, 1-w, -1+w, 0, w, -1+w, -w, 0, 1, -1, 3, 0, 0, 0, 0, -w, 1-w, -w, 1, 1, 0, -1, -w, 1, -w, 3, 0, 0, 0, 0, 0, w, 0, 0, -1+w, 0, 1, -1, 1-w, 0, 3, 0, 0, 0, 0, 0, 1-w, 1-w, -w, -w, -w, 0, 0, 0, w, 3, 0, 1-w, -1+w, -1, -1+w, w, -w, 1, 0, -w, 1, 0, 0, 0, 4 ]; for i := 1 to 14 do for j := i+1 to 14 do M[i,j]:=Trace(M[j,i])-M[j,i]; end for; end for; N:= MatrixRing( Integers() , 28 ) ! 0; for i := 1 to 14 do for j := 1 to 14 do N[i,j]:=Trace(M[i,j]); N[14+i,14+j]:=N[i,j]; N[14+i,j]:=Trace(w*M[i,j]); N[j,14+i]:=N[14+i,j]; end for; end for; L := LatticeWithGram(N); H := AutomorphismGroup(L : Stabilizer :=3); #H; FactoredOrder(H); Output: Magma V2.10-6 Sun Feb 22 2004 07:39:30 on modular [Seed = 4019653802] ------------------------------------- 1 [] Total time: 17.239 seconds, Total memory usage: 51.43MB ************** MAGMA ***************** Host newproxy1.ictp.trieste.it. (140.105.16.2) Time: Sun Feb 22 07:40:29 2004 Input: R:= PolynomialRing(Rationals()); f:=x^2-x+1; K:=NumberField(f); P:=MaximalOrder(K); M:=MatrixRing( P , 14 ) ! [ 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, 2-w, -1+w, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1-2*w, 1, 0, 1-w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1, w, -1+w, -1+w, -1+2*w, -1+w, 3, 0, 0, 0, 0, 0, 0, 0, 0, w, 1, w, w, w, 1-w, 3, 0, 0, 0, 0, 0, 0, 0, 2-w, -1, 1-w, 1, w, 0, -w, 3, 0, 0, 0, 0, 0, 1-w, -1+w, 0, w, -1+w, -w, 0, 1, -1, 3, 0, 0, 0, 0, -w, 1-w, -w, 1, 1, 0, -1, -w, 1, -w, 3, 0, 0, 0, 0, 0, w, 0, 0, -1+w, 0, 1, -1, 1-w, 0, 3, 0, 0, 0, 0, 0, 1-w, 1-w, -w, -w, -w, 0, 0, 0, w, 3, 0, 1-w, -1+w, -1, -1+w, w, -w, 1, 0, -w, 1, 0, 0, 0, 4 ]; for i := 1 to 14 do for j := i+1 to 14 do M[i,j]:=Trace(M[j,i])-M[j,i]; end for; end for; N:= MatrixRing( Integers() , 28 ) ! 0; for i := 1 to 14 do for j := 1 to 14 do N[i,j]:=Trace(M[i,j]); N[14+i,14+j]:=N[i,j]; N[14+i,j]:=Trace(w*M[i,j]); N[j,14+i]:=N[14+i,j]; end for; end for; L := LatticeWithGram(N); H := AutomorphismGroup(L : Stabilizer :=2); #H; FactoredOrder(H); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Feb 22 2004 07:40:06 on modular [Seed = 4287044766] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 1976 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host newproxy1.ictp.trieste.it. (140.105.16.2) Time: Sun Feb 22 07:41:18 2004 Input: R:= PolynomialRing(Rationals()); f:=x^2-x+1; K:=NumberField(f); P:=MaximalOrder(K); M:=MatrixRing( P , 14 ) ! [ 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, 2-w, -1+w, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1-2*w, 1, 0, 1-w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1, w, -1+w, -1+w, -1+2*w, -1+w, 3, 0, 0, 0, 0, 0, 0, 0, 0, w, 1, w, w, w, 1-w, 3, 0, 0, 0, 0, 0, 0, 0, 2-w, -1, 1-w, 1, w, 0, -w, 3, 0, 0, 0, 0, 0, 1-w, -1+w, 0, w, -1+w, -w, 0, 1, -1, 3, 0, 0, 0, 0, -w, 1-w, -w, 1, 1, 0, -1, -w, 1, -w, 3, 0, 0, 0, 0, 0, w, 0, 0, -1+w, 0, 1, -1, 1-w, 0, 3, 0, 0, 0, 0, 0, 1-w, 1-w, -w, -w, -w, 0, 0, 0, w, 3, 0, 1-w, -1+w, -1, -1+w, w, -w, 1, 0, -w, 1, 0, 0, 0, 4 ]; for i := 1 to 14 do for j := i+1 to 14 do M[i,j]:=Trace(M[j,i])-M[j,i]; end for; end for; N:= MatrixRing( Integers() , 28 ) ! 0; for i := 1 to 14 do for j := 1 to 14 do N[i,j]:=Trace(M[i,j]); N[14+i,14+j]:=N[i,j]; N[14+i,j]:=Trace(w*M[i,j]); N[j,14+i]:=N[14+i,j]; end for; end for; L := LatticeWithGram(N); H := AutomorphismGroup(L : Stabilizer :=3); #H; FactoredOrder(H); Output: Magma V2.10-6 Sun Feb 22 2004 07:41:00 on modular [Seed = 2264819101] ------------------------------------- 1 [] Total time: 17.350 seconds, Total memory usage: 51.43MB ************** MAGMA ***************** Host n137.ryd.student.liu.se. (130.236.215.137) Time: Sun Feb 22 11:44:55 2004 Input: FindGroupOrder(19259080382453841122679088710848926436527873,89213102615023533314496249400381124216642939896548619296666391544357403574914698073115920663355909193867030042795676972968093,45328869994094670844371176968552741890670519167427973231865925749226777118379116604766982911482838986736609871163771581552422); Output: Magma V2.10-6 Sun Feb 22 2004 11:44:52 on modular [Seed = 1879633063] ------------------------------------- >> FindGroupOrder(19259080382453841122679088710848926436527873,892131026150235 ^ User error: Identifier 'FindGroupOrder' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host n137.ryd.student.liu.se. (130.236.215.137) Time: Sun Feb 22 12:54:45 2004 Input: p:=3; Output: Magma V2.10-6 Sun Feb 22 2004 12:54:42 on modular [Seed = 1344863462] ------------------------------------- Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host n137.ryd.student.liu.se. (130.236.215.137) Time: Sun Feb 22 12:54:54 2004 Input: p:=3; print(p); Output: Magma V2.10-6 Sun Feb 22 2004 12:54:51 on modular [Seed = 1495397862] ------------------------------------- 3 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host csenh125pc12a.uta.edu. (129.107.55.36) Time: Sun Feb 22 15:35:10 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Sun Feb 22 2004 15:35:07 on modular [Seed = 559444751] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host n137.ryd.student.liu.se. (130.236.215.137) Time: Sun Feb 22 18:56:00 2004 Input: p:=19259080382453841122679088710848926436527873; E:=EllipticCurve(x^3+15861818589692588652817246278877135720068817*x+9126971811468968432031427267937836982986618); Order(E); Output: Magma V2.10-6 Sun Feb 22 2004 18:55:57 on modular [Seed = 3250110484] ------------------------------------- >> E:=EllipticCurve(x^3+15861818589692588652817246278877135720068817*x+9126971 ^ User error: Identifier 'x' has not been declared or assigned >> Order(E); ^ User error: Identifier 'E' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host n137.ryd.student.liu.se. (130.236.215.137) Time: Sun Feb 22 18:56:29 2004 Input: p:=19259080382453841122679088710848926436527873; E:=EllipticCurve([15861818589692588652817246278877135720068817,9126971811468968432031427267937836982986618]); Order(E); Output: Magma V2.10-6 Sun Feb 22 2004 18:56:26 on modular [Seed = 4202953480] ------------------------------------- >> Order(E); ^ Runtime error in 'Order': Algorithm does not work for this ring Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host n137.ryd.student.liu.se. (130.236.215.137) Time: Sun Feb 22 18:57:52 2004 Input: p:=19259080382453841122679088710848926436527873; E:=EllipticCurve([15861818589692588652817246278877135720068817,9126971811468968432031427267937836982986618]); print(E); Order(E); Output: Magma V2.10-6 Sun Feb 22 2004 18:57:49 on modular [Seed = 4102944081] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 15861818589692588652817246278877135720068\ 817*x + 9126971811468968432031427267937836982986618 over Rational Field >> Order(E); ^ Runtime error in 'Order': Algorithm does not work for this ring Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host n137.ryd.student.liu.se. (130.236.215.137) Time: Sun Feb 22 18:59:29 2004 Input: p:=19259080382453841122679088710848926436527873; E:=EllipticCurve([15861818589692588652817246278877135720068817,9126971811468968432031427267937836982986618]); BaseChange(E,GF(p)); print(E); Order(E); Output: Magma V2.10-6 Sun Feb 22 2004 18:59:26 on modular [Seed = 3985960939] ------------------------------------- >> BaseChange(E,GF(p)); ^ Runtime error in 'BaseChange': Coercion of equations is not possible Elliptic Curve defined by y^2 = x^3 + 15861818589692588652817246278877135720068\ 817*x + 9126971811468968432031427267937836982986618 over Rational Field >> Order(E); ^ Runtime error in 'Order': Algorithm does not work for this ring Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host n137.ryd.student.liu.se. (130.236.215.137) Time: Sun Feb 22 19:00:13 2004 Input: p:=19259080382453841122679088710848926436527873; E:=EllipticCurve([15861818589692588652817246278877135720068817,9126971811468968432031427267937836982986618]); ChangeRing(E,GF(p)); print(E); Order(E); Output: Magma V2.10-6 Sun Feb 22 2004 19:00:10 on modular [Seed = 2665978956] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 15861818589692588652817246278877135720068\ 817*x + 9126971811468968432031427267937836982986618 over GF(19259080382453841122679088710848926436527873) Elliptic Curve defined by y^2 = x^3 + 15861818589692588652817246278877135720068\ 817*x + 9126971811468968432031427267937836982986618 over Rational Field >> Order(E); ^ Runtime error in 'Order': Algorithm does not work for this ring Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host n137.ryd.student.liu.se. (130.236.215.137) Time: Sun Feb 22 19:00:52 2004 Input: p:=19259080382453841122679088710848926436527873; E:=EllipticCurve([15861818589692588652817246278877135720068817,9126971811468968432031427267937836982986618]); E:=ChangeRing(E,GF(p)); print(E); Order(E); Output: Magma V2.10-6 Sun Feb 22 2004 19:00:40 on modular [Seed = 2548995431] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 15861818589692588652817246278877135720068\ 817*x + 9126971811468968432031427267937836982986618 over GF(19259080382453841122679088710848926436527873) 19259080382453841122677309570934222539438716 Total time: 11.589 seconds, Total memory usage: 3.48MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Feb 23 00:08:45 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2+1); Output: Magma V2.10-6 Mon Feb 23 2004 00:08:42 on modular [Seed = 209045133] ------------------------------------- Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Feb 23 00:09:00 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2+1); K; Output: Magma V2.10-6 Mon Feb 23 2004 00:08:57 on modular [Seed = 994242953] ------------------------------------- Number Field with defining polynomial x^2 + 1 over the Rational Field Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Feb 23 00:10:00 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2+1); Factorization(2004*K); Output: Magma V2.10-6 Mon Feb 23 2004 00:09:57 on modular [Seed = 810154830] ------------------------------------- >> Factorization(2004*K); ^ Runtime error in '*': Bad argument types Argument types given: RngIntElt, FldNum Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Feb 23 00:13:16 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2+1); OK:=MaximalOrder(K); Factorization(2004*OK); Output: Magma V2.10-6 Mon Feb 23 2004 00:13:13 on modular [Seed = 610135958] ------------------------------------- [ , , ] Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Feb 23 00:16:50 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^6+x^5+x^4+x^3+x^2+x+1); OK:=MaximalOrder(K); Factorization(7*OK); Output: Magma V2.10-6 Mon Feb 23 2004 00:16:47 on modular [Seed = 3601799730] ------------------------------------- [ ] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Feb 23 00:18:03 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^6+x^5+x^4+x^3+x^2+x+1); OK:=MaximalOrder(K); Factorization(3*OK); Output: Magma V2.10-6 Mon Feb 23 2004 00:18:00 on modular [Seed = 3434414495] ------------------------------------- [ ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Feb 23 00:30:21 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField^2-5); OK:=MaximalOrder(K); I:=3*OK; J:=8*OK; K:=I/J; K; Output: Magma V2.10-6 Mon Feb 23 2004 00:30:18 on modular [Seed = 2965995265] ------------------------------------- >> K := NumberField^2-5); ^ User error: bad syntax >> OK:=MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> I:=3*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> J:=8*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> K:=I/J; ^ User error: Identifier 'I' has not been declared or assigned >> K; ^ User error: Identifier 'K' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Feb 23 00:30:37 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField^2-5); OK:=MaximalOrder(K); I:=3*OK; J:=8*OK; M:=I/J; M; Output: Magma V2.10-6 Mon Feb 23 2004 00:30:34 on modular [Seed = 2899665677] ------------------------------------- >> K := NumberField^2-5); ^ User error: bad syntax >> OK:=MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> I:=3*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> J:=8*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> M:=I/J; ^ User error: Identifier 'I' has not been declared or assigned >> M; ^ User error: Identifier 'M' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Feb 23 00:30:45 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField^2-5); OK:=MaximalOrder(K); I:=3*OK; J:=8*OK; M:=I/J; M; Output: Magma V2.10-6 Mon Feb 23 2004 00:30:42 on modular [Seed = 1545964546] ------------------------------------- >> K := NumberField^2-5); ^ User error: bad syntax >> OK:=MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> I:=3*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> J:=8*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> M:=I/J; ^ User error: Identifier 'I' has not been declared or assigned >> M; ^ User error: Identifier 'M' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Feb 23 00:31:14 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2-5); OK:=MaximalOrder(K); I:=3*OK; J:=8*OK; M:=I/J; M; Output: Magma V2.10-6 Mon Feb 23 2004 00:31:11 on modular [Seed = 1445955093] ------------------------------------- Principal Ideal of OK Generator: [3, 0] / 8 Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Feb 23 00:31:43 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2-5); OK:=MaximalOrder(K); I:=3*OK; J:=8*OK; M:=I/J; Factorization(M); Output: Magma V2.10-6 Mon Feb 23 2004 00:31:40 on modular [Seed = 1328979759] ------------------------------------- [ , ] Total time: 3.049 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Feb 23 00:35:53 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2-5); OK:=MaximalOrder(K); I:=sqrt[5]*OK; Factorization(I); Output: Magma V2.10-6 Mon Feb 23 2004 00:35:49 on modular [Seed = 7983465] ------------------------------------- >> I:=sqrt[5]*OK; ^ User error: Identifier 'sqrt' has not been declared or assigned >> Factorization(I); ^ User error: Identifier 'I' has not been declared or assigned Total time: 3.059 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Feb 23 00:36:57 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2-5); OK:=MaximalOrder(K); I:=y*OK; Factorization(I); Output: Magma V2.10-6 Mon Feb 23 2004 00:36:54 on modular [Seed = 810148122] ------------------------------------- [ ] Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Feb 23 00:39:18 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2-5); OK:=MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Mon Feb 23 2004 00:39:15 on modular [Seed = 3651144582] ------------------------------------- [ ] Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Feb 23 00:39:38 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2-5); OK:=MaximalOrder(K); I:=y*OK; Factorization(I); Output: Magma V2.10-6 Mon Feb 23 2004 00:39:35 on modular [Seed = 3534422169] ------------------------------------- [ ] Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Feb 23 00:46:43 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2-5); OK:=MaximalOrder(K); O:=Order([y]); Index(OK,O); Output: Magma V2.10-6 Mon Feb 23 2004 00:46:39 on modular [Seed = 4119602710] ------------------------------------- >> Index(OK,O); ^ Runtime error in 'Index': Argument is not a suborder Total time: 3.279 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Feb 23 00:47:06 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2-5); OK:=MaximalOrder(K); O:=Order([1+y]); Index(OK,O); Output: Magma V2.10-6 Mon Feb 23 2004 00:47:03 on modular [Seed = 3918543458] ------------------------------------- >> Index(OK,O); ^ Runtime error in 'Index': Argument is not a suborder Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Feb 23 00:47:41 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2-5); OK:=MaximalOrder(K); O:=Order(1+y); Index(OK,O); Output: Magma V2.10-6 Mon Feb 23 2004 00:47:37 on modular [Seed = 2297518893] ------------------------------------- >> O:=Order(1+y); ^ Runtime error in 'Order': Bad argument types Argument types given: FldNumElt >> Index(OK,O); ^ Runtime error in 'Index': Bad argument types Argument types given: RngOrd, Intrinsic Total time: 3.419 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Feb 23 00:50:42 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2-5); OK:=MaximalOrder(K); O:=Order([2*y]); Index(OK,O); Output: Magma V2.10-6 Mon Feb 23 2004 00:50:39 on modular [Seed = 1361610147] ------------------------------------- >> Index(OK,O); ^ Runtime error in 'Index': Argument is not a suborder Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Feb 23 00:51:18 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^3-2); OK:=MaximalOrder(K); O:=Order([2*y]); Index(OK,O); Output: Magma V2.10-6 Mon Feb 23 2004 00:51:15 on modular [Seed = 1211210950] ------------------------------------- >> Index(OK,O); ^ Runtime error in 'Index': Argument is not a suborder Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Feb 23 00:51:24 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^3-2); OK:=MaximalOrder(K); O:=Order([2*y]); Index(OK,O); Output: Magma V2.10-6 Mon Feb 23 2004 00:51:21 on modular [Seed = 1127913415] ------------------------------------- >> Index(OK,O); ^ Runtime error in 'Index': Argument is not a suborder Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Feb 23 00:52:10 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^3-2); OK:=MaximalOrder(K); O:=Order([2*y]); O; Output: Magma V2.10-6 Mon Feb 23 2004 00:52:07 on modular [Seed = 1963761711] ------------------------------------- Transformation of Order over Equation Order with defining polynomial x^3 - 2 over its ground order Transformation Matrix: [1 0 0] [0 2 0] [0 0 4] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Feb 23 00:52:49 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^3-2); OK:=MaximalOrder(K); O:=Order([2*y]); O; Index(OK,O); Output: Magma V2.10-6 Mon Feb 23 2004 00:52:46 on modular [Seed = 1863760412] ------------------------------------- Transformation of Order over Equation Order with defining polynomial x^3 - 2 over its ground order Transformation Matrix: [1 0 0] [0 2 0] [0 0 4] >> Index(OK,O); ^ Runtime error in 'Index': Argument is not a suborder Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Feb 23 00:53:05 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^3-2); O:=Order([2*y]); O; OK:=MaximalOrder(K); Index(OK,O); Output: Magma V2.10-6 Mon Feb 23 2004 00:53:03 on modular [Seed = 1713353476] ------------------------------------- Transformation of Order over Equation Order with defining polynomial x^3 - 2 over its ground order Transformation Matrix: [1 0 0] [0 2 0] [0 0 4] >> Index(OK,O); ^ Runtime error in 'Index': Argument is not a suborder Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Feb 23 00:53:49 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^3-2); O:=Order([2*y]); O; OK:=MaximalOrder(K); Fractorization(3*O); Output: Magma V2.10-6 Mon Feb 23 2004 00:53:46 on modular [Seed = 425774126] ------------------------------------- Transformation of Order over Equation Order with defining polynomial x^3 - 2 over its ground order Transformation Matrix: [1 0 0] [0 2 0] [0 0 4] >> Fractorization(3*O); ^ User error: Identifier 'Fractorization' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Feb 23 00:54:04 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^3-2); O:=Order([2*y]); O; OK:=MaximalOrder(K); Factorization(3*O); Output: Magma V2.10-6 Mon Feb 23 2004 00:54:01 on modular [Seed = 275367220] ------------------------------------- Transformation of Order over Equation Order with defining polynomial x^3 - 2 over its ground order Transformation Matrix: [1 0 0] [0 2 0] [0 0 4] >> Factorization(3*O); ^ Runtime error in 'Factorization': Order associated with ideal argument 1 is not known to be maximal Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Feb 23 00:54:49 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^3-2); O:=Order([2*y]); O; OK:=MaximalOrder(K); Factorization(y*O); Output: Magma V2.10-6 Mon Feb 23 2004 00:54:46 on modular [Seed = 192077552] ------------------------------------- Transformation of Order over Equation Order with defining polynomial x^3 - 2 over its ground order Transformation Matrix: [1 0 0] [0 2 0] [0 0 4] >> Factorization(y*O); ^ Runtime error in 'Factorization': Order associated with ideal argument 1 is not known to be maximal Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Feb 23 01:01:58 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2-5); O:=Order([1,y]); O; OK:=MaximalOrder(K); Factorization(6*O); Output: Magma V2.10-6 Mon Feb 23 2004 01:01:55 on modular [Seed = 3701803986] ------------------------------------- Equation Order with defining polynomial x^2 - 5 over its ground order >> Factorization(6*O); ^ Runtime error in 'Factorization': Order associated with ideal argument 1 is not known to be maximal Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 04:08:11 2004 Input: F:=FieldOfFractions(PolynomialRing(Rationals())); space:=MatrixAlgebra(F,2); M:=space![0,1,1/4,3/4]; Eigenvalues(M); Output: Magma V2.10-6 Mon Feb 23 2004 04:08:07 on modular [Seed = 2281571600] ------------------------------------- { <1, 1>, <-1/4, 1> } Total time: 3.589 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 04:09:06 2004 Input: F:=FieldOfFractions(PolynomialRing(Rationals())); space:=MatrixAlgebra(F,2); M:=space![0,1,1/4,3/4]; Eigenvalues(M); Eigenspace(M,1); Eigenspace(M,-1/4); Output: Magma V2.10-6 Mon Feb 23 2004 04:09:03 on modular [Seed = 2431194079] ------------------------------------- { <1, 1>, <-1/4, 1> } Vector space of degree 2, dimension 1 over Univariate rational function field over Rational Field Echelonized basis: (1 4) Vector space of degree 2, dimension 1 over Univariate rational function field over Rational Field Echelonized basis: ( 1 -1) Total time: 3.169 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 04:11:14 2004 Input: F:=FieldOfFractions(PolynomialRing(Rationals())); space:=MatrixAlgebra(F,3); M:=space![1/5,4/5,0,0,1/5,4/5,1/5,1/5,3/5]; Eigenvalues(M); Eigenspace(M,1); Output: Magma V2.10-6 Mon Feb 23 2004 04:11:10 on modular [Seed = 1645994413] ------------------------------------- { <1, 1> } Vector space of degree 3, dimension 1 over Univariate rational function field over Rational Field Echelonized basis: (1 2 4) Total time: 3.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9022D0B.dip.t-dialin.net. (217.2.45.11) Time: Mon Feb 23 04:12:24 2004 Input: K:=GF(2); Pa:=PolynomialRing(K,4); IG:=ideal; A:=[[a,b,0,0,0,0,0,0],[c,d,0,0,0,0,0,0],[0,0,a,b,0,0,0,0],[0,0,c,d,0,0,0,0],[0,0,0,0,a,b,0,0],[0,0,0,0,cd,0,0],[0,0,0,0,0,0,a,b],[0,0,0,0,c,d]]; P:=PolynomialRing(K,8); f1:=x2*y3+x3*y2; f2:=x1*y3+x3*y1; f3:=x1*y2+x2*y1; I:=ideal Dimension(I); // Falls Erg. 8-3=5, dann hurra Output: Magma V2.10-6 Mon Feb 23 2004 04:12:21 on modular [Seed = 1813377016] ------------------------------------- >> 0],[0,0,c,d,0,0,0,0],[0,0,0,0,a,b,0,0],[0,0,0,0,cd,0,0],[0,0,0,0,0,0,a,b],[ ^ User error: Identifier 'cd' has not been declared or assigned >> Dimension(I); ^ User error: bad syntax Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 04:12:54 2004 Input: G:= FielfofFractions(Integers()); space:=MatrixAlgebra(G,3); M:=space![1/5,4/5,0,0,1/5,4/5,1/5,1/5,3/5]; Eigenvalues(M); Eigenspace(M,1); Output: Magma V2.10-6 Mon Feb 23 2004 04:12:51 on modular [Seed = 1997468421] ------------------------------------- >> G:= FielfofFractions(Integers()); ^ User error: Identifier 'FielfofFractions' has not been declared or assigned >> space:=MatrixAlgebra(G,3); ^ User error: Identifier 'G' has not been declared or assigned >> M:=space![1/5,4/5,0,0,1/5,4/5,1/5,1/5,3/5]; ^ User error: Identifier 'space' has not been declared or assigned >> Eigenvalues(M); ^ User error: Identifier 'M' has not been declared or assigned >> Eigenspace(M,1); ^ User error: Identifier 'M' has not been declared or assigned Total time: 3.119 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9022D0B.dip.t-dialin.net. (217.2.45.11) Time: Mon Feb 23 04:13:05 2004 Input: K:=GF(2); Pa:=PolynomialRing(K,4); IG:=ideal; A:=[[a,b,0,0,0,0,0,0],[c,d,0,0,0,0,0,0],[0,0,a,b,0,0,0,0],[0,0,c,d,0,0,0,0],[0,0,0,0,a,b,0,0],[0,0,0,0,c,d,0,0],[0,0,0,0,0,0,a,b],[0,0,0,0,c,d]]; P:=PolynomialRing(K,8); f1:=x2*y3+x3*y2; f2:=x1*y3+x3*y1; f3:=x1*y2+x2*y1; I:=ideal Dimension(I); // Falls Erg. 8-3=5, dann hurra Output: Magma V2.10-6 Mon Feb 23 2004 04:13:02 on modular [Seed = 1094239550] ------------------------------------- >> Dimension(I); ^ User error: bad syntax Total time: 3.139 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9022D0B.dip.t-dialin.net. (217.2.45.11) Time: Mon Feb 23 04:13:41 2004 Input: K:=GF(2); Pa:=PolynomialRing(K,4); IG:=ideal; A:=[[a,b,0,0,0,0,0,0],[c,d,0,0,0,0,0,0],[0,0,a,b,0,0,0,0],[0,0,c,d,0,0,0,0],[0,0,0,0,a,b,0,0],[0,0,0,0,c,d,0,0],[0,0,0,0,0,0,a,b],[0,0,0,0,c,d]]; P:=PolynomialRing(K,8); f1:=x2*y3+x3*y2; f2:=x1*y3+x3*y1; f3:=x1*y2+x2*y1; I:=ideal dimension(I); // Falls Erg. 8-3=5, dann hurra Output: Magma V2.10-6 Mon Feb 23 2004 04:13:38 on modular [Seed = 1211223147] ------------------------------------- >> dimension(I); ^ User error: bad syntax Total time: 3.320 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9022D0B.dip.t-dialin.net. (217.2.45.11) Time: Mon Feb 23 04:14:23 2004 Input: K:=GF(2); Pa:=PolynomialRing(K,4); IG:=ideal; A:=[[a,b,0,0,0,0,0,0],[c,d,0,0,0,0,0,0],[0,0,a,b,0,0,0,0],[0,0,c,d,0,0,0,0],[0,0,0,0,a,b,0,0],[0,0,0,0,c,d,0,0],[0,0,0,0,0,0,a,b],[0,0,0,0,c,d]]; P:=PolynomialRing(K,8); f1:=x2*y3+x3*y2; f2:=x1*y3+x3*y1; f3:=x1*y2+x2*y1; I:=ideal; Dimension(I); // Falls Erg. 8-3=5, dann hurra Output: Magma V2.10-6 Mon Feb 23 2004 04:14:19 on modular [Seed = 1395316569] ------------------------------------- 6 [ 1, 3, 5, 6, 7, 8 ] Total time: 3.269 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9022D0B.dip.t-dialin.net. (217.2.45.11) Time: Mon Feb 23 04:17:48 2004 Input: K:=GF(2); Pa:=PolynomialRing(K,4); IG:=ideal; A:=[[a,b,0,0,0,0,0,0],[c,d,0,0,0,0,0,0],[0,0,a,b,0,0,0,0],[0,0,c,d,0,0,0,0],[0,0,0,0,a,b,0,0],[0,0,0,0,c,d,0,0],[0,0,0,0,0,0,a,b],[0,0,0,0,c,d]]; P:=PolynomialRing(K,8); f1:=x2*y3+x3*y2; f2:=x1*y3+x3*y1; f3:=x1*y2+x2*y1; I:=ideal; Dimension(I); // Falls Erg. 8-3=5, dann hurra Output: Magma V2.10-6 Mon Feb 23 2004 04:17:45 on modular [Seed = 325752395] ------------------------------------- 6 [ 1, 3, 5, 6, 7, 8 ] Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9022D0B.dip.t-dialin.net. (217.2.45.11) Time: Mon Feb 23 04:18:32 2004 Input: K:=GF(2); Pa:=PolynomialRing(K,4); IG:=ideal; A:=[[a,b,0,0,0,0,0,0],[c,d,0,0,0,0,0,0],[0,0,a,b,0,0,0,0],[0,0,c,d,0,0,0,0],[0,0,0,0,a,b,0,0],[0,0,0,0,c,d,0,0],[0,0,0,0,0,0,a,b],[0,0,0,0,c,d]]; P:=PolynomialRing(K,8); f1:=x2*y3+x3*y2; f2:=x1*y3+x3*y1; f3:=x1*y2+x2*y1; I:=ideal; Dimension(I); // Falls Erg. 8-3=5, dann hurra Output: Magma V2.10-6 Mon Feb 23 2004 04:18:29 on modular [Seed = 442736414] ------------------------------------- 6 [ 1, 3, 5, 6, 7, 8 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9022D0B.dip.t-dialin.net. (217.2.45.11) Time: Mon Feb 23 04:18:59 2004 Input: K:=GF(2); Pa:=PolynomialRing(K,4); IG:=ideal; A:=[[a,b,0,0,0,0,0,0],[c,d,0,0,0,0,0,0],[0,0,a,b,0,0,0,0],[0,0,c,d,0,0,0,0],[0,0,0,0,a,b,0,0],[0,0,0,0,c,d,0,0],[0,0,0,0,0,0,a,b],[0,0,0,0,c,d]]; P:=PolynomialRing(K,8); f1:=x2*y3+x3*y2; f2:=x1*y3+x3*y1; f3:=x1*y2+x2*y1; I:=ideal; Dimension(I); // Falls Erg. 8-3=5, dann hurra Output: Magma V2.10-6 Mon Feb 23 2004 04:18:56 on modular [Seed = 3835519237] ------------------------------------- 5 [ 3, 5, 6, 7, 8 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9022D0B.dip.t-dialin.net. (217.2.45.11) Time: Mon Feb 23 04:19:28 2004 Input: K:=GF(2); Pa:=PolynomialRing(K,4); IG:=ideal; A:=[[a,b,0,0,0,0,0,0],[c,d,0,0,0,0,0,0],[0,0,a,b,0,0,0,0],[0,0,c,d,0,0,0,0],[0,0,0,0,a,b,0,0],[0,0,0,0,c,d,0,0],[0,0,0,0,0,0,a,b],[0,0,0,0,c,d]]; P:=PolynomialRing(K,8); f1:=x2*y3+x3*y2; f2:=x1*y3+x3*y1; f3:=x1*y2+x2*y1; I:=ideal; Dimension(I); // Falls Erg. 8-3=5, dann hurra Output: Magma V2.10-6 Mon Feb 23 2004 04:19:25 on modular [Seed = 4019612179] ------------------------------------- 6 [ 1, 3, 5, 6, 7, 8 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9022D0B.dip.t-dialin.net. (217.2.45.11) Time: Mon Feb 23 04:19:52 2004 Input: K:=GF(2); Pa:=PolynomialRing(K,4); IG:=ideal; A:=[[a,b,0,0,0,0,0,0],[c,d,0,0,0,0,0,0],[0,0,a,b,0,0,0,0],[0,0,c,d,0,0,0,0],[0,0,0,0,a,b,0,0],[0,0,0,0,c,d,0,0],[0,0,0,0,0,0,a,b],[0,0,0,0,c,d]]; P:=PolynomialRing(K,8); f1:=x2*y3+x3*y2; f2:=x1*y3+x3*y1; f3:=x1*y2+x2*y1; I:=ideal; Dimension(I); // Falls Erg. 8-3=5, dann hurra Output: Magma V2.10-6 Mon Feb 23 2004 04:19:49 on modular [Seed = 4136596258] ------------------------------------- 5 [ 2, 5, 6, 7, 8 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9022D0B.dip.t-dialin.net. (217.2.45.11) Time: Mon Feb 23 04:21:05 2004 Input: K:=GF(2); Pa:=PolynomialRing(K,4); IG:=ideal; A:=[[a,b,0,0,0,0,0,0],[c,d,0,0,0,0,0,0],[0,0,a,b,0,0,0,0],[0,0,c,d,0,0,0,0],[0,0,0,0,a,b,0,0],[0,0,0,0,c,d,0,0],[0,0,0,0,0,0,a,b],[0,0,0,0,c,d]]; P:=PolynomialRing(K,8); f1:=x2*y3+x3*y2; f2:=x1*y3+x3*y1; f3:=x1*y2+x2*y1; I:=ideal; Dimension(I); // Falls Erg. 8-3=5, dann hurra Output: Magma V2.10-6 Mon Feb 23 2004 04:21:02 on modular [Seed = 3334423385] ------------------------------------- 6 [ 1, 3, 5, 6, 7, 8 ] Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9022D0B.dip.t-dialin.net. (217.2.45.11) Time: Mon Feb 23 04:23:06 2004 Input: K:=GF(2); Pa:=PolynomialRing(K,4); IG:=ideal; P:=PolynomialRing(K,8); f1:=x2*y3+x3*y2; f2:=x1*y3+x3*y1; f3:=x1*y2+x2*y1; I:=ideal; Dimension(I); // Falls Erg. 8-3=5, dann hurra Output: Magma V2.10-6 Mon Feb 23 2004 04:23:03 on modular [Seed = 3551155653] ------------------------------------- 6 [ 1, 3, 5, 6, 7, 8 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9022D0B.dip.t-dialin.net. (217.2.45.11) Time: Mon Feb 23 04:24:13 2004 Input: K:=GF(2); Pa:=PolynomialRing(K,4); IG:=ideal; A:=[[a,b,0,0,0,0,0,0],[c,d,0,0,0,0,0,0],[0,0,a,b,0,0,0,0],[0,0,c,d,0,0,0,0],[0,0,0,0,a,b,0,0],[0,0,0,0,c,d,0,0],[0,0,0,0,0,0,a,b],[0,0,0,0,c,d]]; P:=PolynomialRing(K,8); f1:=x2*y3+x3*y2; f2:=x1*y3+x3*y1; f3:=x1*y2+x2*y1; I:=ideal; Dimension(I); // Falls Erg. 8-3=5, dann phsop //Ergebnis: 6 Output: Magma V2.10-6 Mon Feb 23 2004 04:24:10 on modular [Seed = 3718535942] ------------------------------------- 6 [ 1, 3, 5, 6, 7, 8 ] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 04:31:27 2004 Input: G = Complex(); Output: Magma V2.10-6 Mon Feb 23 2004 04:31:24 on modular [Seed = 2999663295] ------------------------------------- >> G = Complex();; ^ User error: Identifier 'G' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 04:31:38 2004 Input: G := Complex(); Output: Magma V2.10-6 Mon Feb 23 2004 04:31:35 on modular [Seed = 3183752612] ------------------------------------- >> G := Complex();; ^ Runtime error in 'Complex': Bad argument types Argument types given: Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 04:33:52 2004 Input: G := ComplexField(); Output: Magma V2.10-6 Mon Feb 23 2004 04:33:49 on modular [Seed = 2264862234] ------------------------------------- Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 04:34:17 2004 Input: G:= ComplexField(); space:=MatrixAlgebra(G,3); M:=space![1/5,4/5,0,0,1/5,4/5,1/5,1/5,3/5]; Eigenvalues(M); Eigenspace(M,1); Output: Magma V2.10-6 Mon Feb 23 2004 04:34:14 on modular [Seed = 2447907046] ------------------------------------- { <0.999999999999999999999999999999999999994, 1>, < 0.E-30 - 0.346410161513775458705489268301174473410*i, 1>, < 0.E-30 + 0.346410161513775458705489268301174473410*i, 1> } Vector space of degree 3, dimension 1 over Complex Field Echelonized basis: (1 2 4) Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 04:35:27 2004 Input: G:= ComplexField(); space:=MatrixAlgebra(G,3); M:=space![1/5,4/5,0,0,1/5,4/5,1/5,1/5,3/5]; Eigenvalues(M); Eigenspace(M,1); Eigenspace(M,0.346410161513775458705489268301174473410*i); Output: Magma V2.10-6 Mon Feb 23 2004 04:35:24 on modular [Seed = 2682656418] ------------------------------------- { <0.999999999999999999999999999999999999994, 1>, < 0.E-30 - 0.346410161513775458705489268301174473410*i, 1>, < 0.E-30 + 0.346410161513775458705489268301174473410*i, 1> } Vector space of degree 3, dimension 1 over Complex Field Echelonized basis: (1 2 4) >> Eigenspace(M,0.346410161513775458705489268301174473410*i); ^ User error: Identifier 'i' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 04:36:32 2004 Input: G:= ComplexField(); space:=MatrixAlgebra(G,3); M:=space![1/5,4/5,0,0,1/5,4/5,1/5,1/5,3/5]; Eigenvalues(M); Eigenspace(M,1); Eigenspace(M,0.346410161513775458705489268301174473410*i); Output: Magma V2.10-6 Mon Feb 23 2004 04:36:29 on modular [Seed = 1796399764] ------------------------------------- { <0.999999999999999999999999999999999999994, 1>, < 0.E-30 - 0.346410161513775458705489268301174473410*i, 1>, < 0.E-30 + 0.346410161513775458705489268301174473410*i, 1> } Vector space of degree 3, dimension 1 over Complex Field Echelonized basis: (1 2 4) Vector space of degree 3, dimension 0 over Complex Field Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 04:37:03 2004 Input: G:= ComplexField(); space:=MatrixAlgebra(G,3); M:=space![1/5,4/5,0,0,1/5,4/5,1/5,1/5,3/5]; Eigenvalues(M); Eigenspace(M,1); Eigenspace(M,0.E-30 + 0.346410161513775458705489268301174473410*i); Output: Magma V2.10-6 Mon Feb 23 2004 04:37:00 on modular [Seed = 1879701934] ------------------------------------- { <0.999999999999999999999999999999999999994, 1>, < 0.E-30 - 0.346410161513775458705489268301174473410*i, 1>, < 0.E-30 + 0.346410161513775458705489268301174473410*i, 1> } Vector space of degree 3, dimension 1 over Complex Field Echelonized basis: (1 2 4) >> Eigenspace(M,0.E-30 + 0.346410161513775458705489268301174473410*i); ^ User error: Real literal has no digits after decimal point Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 04:37:35 2004 Input: G:= ComplexField(); space:=MatrixAlgebra(G,3); M:=space![1/5,4/5,0,0,1/5,4/5,1/5,1/5,3/5]; Eigenvalues(M); Eigenspace(M,1); Eigenspace(M,0 + 0.346410161513775458705489268301174473410*i); Output: Magma V2.10-6 Mon Feb 23 2004 04:37:32 on modular [Seed = 2114451392] ------------------------------------- { <0.999999999999999999999999999999999999994, 1>, < 0.E-30 - 0.346410161513775458705489268301174473410*i, 1>, < 0.E-30 + 0.346410161513775458705489268301174473410*i, 1> } Vector space of degree 3, dimension 1 over Complex Field Echelonized basis: (1 2 4) Vector space of degree 3, dimension 0 over Complex Field Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9022C5A.dip.t-dialin.net. (217.2.44.90) Time: Mon Feb 23 04:38:59 2004 Input: K:=GF(2); Pa:=PolynomialRing(K,4); IG:=ideal; A:=[[a,b,0,0,0,0,0,0],[c,d,0,0,0,0,0,0],[0,0,a,b,0,0,0,0],[0,0,c,d,0,0,0,0],[0,0,0,0,a,b,0,0],[0,0,0,0,c,d,0,0],[0,0,0,0,0,0,a,b],[0,0,0,0,c,d]]; P:=PolynomialRing(K,8); f1:=x2*y3+x3*y2; f2:=x1*y3+x3*y1; f3:=x1*y2+x2*y1; I:=ideal; Dimension(I); // Falls Erg. 8-3=5, dann phsop //Ergebnis: 6 Output: Magma V2.10-6 Mon Feb 23 2004 04:38:56 on modular [Seed = 1295304479] ------------------------------------- 6 [ 1, 3, 5, 6, 7, 8 ] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 04:40:05 2004 Input: G:= ComplexField(); space:=MatrixAlgebra(G,3); M:=space![1/5,4/5,0,0,1/5,4/5,1/5,1/5,3/5]; Eigenvalues(M); Eigenspace(M,1); Eigenspace(M,0 + 0.346410161513775458705489268301174473410*i); x:=3/7 x; Output: Magma V2.10-6 Mon Feb 23 2004 04:40:02 on modular [Seed = 576432178] ------------------------------------- { <0.999999999999999999999999999999999999994, 1>, < 0.E-30 - 0.346410161513775458705489268301174473410*i, 1>, < 0.E-30 + 0.346410161513775458705489268301174473410*i, 1> } Vector space of degree 3, dimension 1 over Complex Field Echelonized basis: (1 2 4) Vector space of degree 3, dimension 0 over Complex Field >> x;; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9022C5A.dip.t-dialin.net. (217.2.44.90) Time: Mon Feb 23 04:40:24 2004 Input: K:=GF(2); Pa:=PolynomialRing(K,4); IG:=ideal; P:=PolynomialRing(K,8); f1:=x2*y3+x3*y2; f2:=x1*y3+x3*y1; f3:=x1*y2+x2*y1; I:=ideal; Dimension(I); // Falls Erg. 8-3=5, dann phsop //Ergebnis: 6 Output: Magma V2.10-6 Mon Feb 23 2004 04:40:21 on modular [Seed = 726835660] ------------------------------------- 6 [ 1, 3, 5, 6, 7, 8 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 04:40:37 2004 Input: G:= ComplexField(); space:=MatrixAlgebra(G,3); M:=space![1/5,4/5,0,0,1/5,4/5,1/5,1/5,3/5]; Eigenvalues(M); Eigenspace(M,1); Eigenspace(M,0 + 0.346410161513775458705489268301174473410*i); x:=3/7*i; x - 0.346410161513775458705489268301174473410*i; Output: Magma V2.10-6 Mon Feb 23 2004 04:40:34 on modular [Seed = 810138304] ------------------------------------- { <0.999999999999999999999999999999999999994, 1>, < 0.E-30 - 0.346410161513775458705489268301174473410*i, 1>, < 0.E-30 + 0.346410161513775458705489268301174473410*i, 1> } Vector space of degree 3, dimension 1 over Complex Field Echelonized basis: (1 2 4) Vector space of degree 3, dimension 0 over Complex Field 0.08216126705765311272308216027025409801857142857155*i Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9022C5A.dip.t-dialin.net. (217.2.44.90) Time: Mon Feb 23 04:41:05 2004 Input: K:=GF(2); P:=PolynomialRing(K,8); f1:=x2*y3+x3*y2; f2:=x1*y3+x3*y1; f3:=x1*y2+x2*y1; I:=ideal; Dimension(I); // Falls Erg. 8-3=5, dann phsop //Ergebnis: 6 Output: Magma V2.10-6 Mon Feb 23 2004 04:41:02 on modular [Seed = 960541685] ------------------------------------- 6 [ 1, 3, 5, 6, 7, 8 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 04:42:17 2004 Input: x:=7/15*i; x - 0.346410161513775458705489268301174473410*i; Output: Magma V2.10-6 Mon Feb 23 2004 04:42:14 on modular [Seed = 125734291] ------------------------------------- >> x:=7/15*i; ^ User error: Identifier 'i' has not been declared or assigned >> x - 0.346410161513775458705489268301174473410*i;; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 04:42:35 2004 Input: G:=ComplexField(); x:=7/15*i; x - 0.346410161513775458705489268301174473410*i; Output: Magma V2.10-6 Mon Feb 23 2004 04:42:32 on modular [Seed = 309041528] ------------------------------------- 0.12025650515289120796117739836549219325666666666684*i Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 04:42:51 2004 Input: G:=ComplexField(); x:=13/30*i; x - 0.346410161513775458705489268301174473410*i; Output: Magma V2.10-6 Mon Feb 23 2004 04:42:48 on modular [Seed = 459444320] ------------------------------------- 0.08692317181955787462784406503215885992333333333347*i Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 04:45:13 2004 Input: G:= ComplexField(); space:=MatrixAlgebra(G,3); M:=space![1/5,4/5,0,0,1/5,4/5,1/5,1/5,3/5]; Eigenvalues(M); Eigenspace(M,1); CharacteristicPolynomial(M) Output: Magma V2.10-6 Mon Feb 23 2004 04:45:10 on modular [Seed = 3852234273] ------------------------------------- { <0.999999999999999999999999999999999999994, 1>, < 0.E-30 - 0.346410161513775458705489268301174473410*i, 1>, < 0.E-30 + 0.346410161513775458705489268301174473410*i, 1> } Vector space of degree 3, dimension 1 over Complex Field Echelonized basis: (1 2 4) $.1^3 - $.1^2 + 3/25*$.1 - 3/25 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 04:45:48 2004 Input: G:= ComplexField(); space:=MatrixAlgebra(G,3); M:=space![1/5,4/5,0,0,1/5,4/5,1/5,1/5,3/5]; Eigenvalues(M); Eigenspace(M,1); a:= CharacteristicPolynomial(M) Output: Magma V2.10-6 Mon Feb 23 2004 04:45:45 on modular [Seed = 4069226841] ------------------------------------- { <0.999999999999999999999999999999999999994, 1>, < 0.E-30 - 0.346410161513775458705489268301174473410*i, 1>, < 0.E-30 + 0.346410161513775458705489268301174473410*i, 1> } Vector space of degree 3, dimension 1 over Complex Field Echelonized basis: (1 2 4) Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 04:45:55 2004 Input: G:= ComplexField(); space:=MatrixAlgebra(G,3); M:=space![1/5,4/5,0,0,1/5,4/5,1/5,1/5,3/5]; Eigenvalues(M); Eigenspace(M,1); a:= CharacteristicPolynomial(M) Output: Magma V2.10-6 Mon Feb 23 2004 04:45:52 on modular [Seed = 4219629641] ------------------------------------- { <0.999999999999999999999999999999999999994, 1>, < 0.E-30 - 0.346410161513775458705489268301174473410*i, 1>, < 0.E-30 + 0.346410161513775458705489268301174473410*i, 1> } Vector space of degree 3, dimension 1 over Complex Field Echelonized basis: (1 2 4) Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 04:46:06 2004 Input: G:= ComplexField(); space:=MatrixAlgebra(G,3); M:=space![1/5,4/5,0,0,1/5,4/5,1/5,1/5,3/5]; Eigenvalues(M); Eigenspace(M,1); a:= CharacteristicPolynomial(M) Factorization(a); Output: Magma V2.10-6 Mon Feb 23 2004 04:46:04 on modular [Seed = 3233368958] ------------------------------------- { <0.999999999999999999999999999999999999994, 1>, < 0.E-30 - 0.346410161513775458705489268301174473410*i, 1>, < 0.E-30 + 0.346410161513775458705489268301174473410*i, 1> } Vector space of degree 3, dimension 1 over Complex Field Echelonized basis: (1 2 4) >> Factorization(a);; ^ User error: bad syntax Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 04:46:43 2004 Input: G:= ComplexField(); space:=MatrixAlgebra(G,3); M:=space![1/5,4/5,0,0,1/5,4/5,1/5,1/5,3/5]; Eigenvalues(M); Eigenspace(M,1); FactoredCharacteristicPolynomial(M) Output: Magma V2.10-6 Mon Feb 23 2004 04:46:40 on modular [Seed = 3468116652] ------------------------------------- { <0.999999999999999999999999999999999999994, 1>, < 0.E-30 - 0.346410161513775458705489268301174473410*i, 1>, < 0.E-30 + 0.346410161513775458705489268301174473410*i, 1> } Vector space of degree 3, dimension 1 over Complex Field Echelonized basis: (1 2 4) Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Wed Apr 23 11:13:24 EST 2003 Initial seed: 3468116652 Time to this point: 2.95 Internal error in vpoly_factorize() at vpoly/fact.c, line 949 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9022C5A.dip.t-dialin.net. (217.2.44.90) Time: Mon Feb 23 04:48:08 2004 Input: K:=GF(2); P:=PolynomialRing(K,8); f1:=x2*y3+x3*y2; f2:=x1*y3+x3*y1; f3:=x1*y2+x2*y1; I:=ideal; Dimension(I); // Falls Erg. 8-3=5, dann phsop //Ergebnis: 6 Output: Magma V2.10-6 Mon Feb 23 2004 04:48:05 on modular [Seed = 3584842210] ------------------------------------- 5 [ 1, 3, 5, 6, 7 ] Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 04:49:39 2004 Input: G:= ComplexField(); space:=MatrixAlgebra(G,3); M:=space![1/5,4/5,0,0,1/5,4/5,1/5,1/5,3/5]; Eigenvalues(M); Eigenspace(M,1); FactoredCharacteristicPolynomial(M) Output: Magma V2.10-6 Mon Feb 23 2004 04:49:36 on modular [Seed = 2732273264] ------------------------------------- { <0.999999999999999999999999999999999999994, 1>, < 0.E-30 - 0.346410161513775458705489268301174473410*i, 1>, < 0.E-30 + 0.346410161513775458705489268301174473410*i, 1> } Vector space of degree 3, dimension 1 over Complex Field Echelonized basis: (1 2 4) Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Wed Apr 23 11:13:24 EST 2003 Initial seed: 2732273264 Time to this point: 2.93 Internal error in vpoly_factorize() at vpoly/fact.c, line 949 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 04:50:34 2004 Input: G:= ComplexField(); space:=MatrixAlgebra(G,3); M:=space![1/5,4/5,0,0,1/5,4/5,1/5,1/5,3/5]; Eigenvalues(M); Eigenspace(M,1); FactoredMinimalPolynomial(M) Output: Magma V2.10-6 Mon Feb 23 2004 04:50:31 on modular [Seed = 3016376118] ------------------------------------- { <0.999999999999999999999999999999999999994, 1>, < 0.E-30 - 0.346410161513775458705489268301174473410*i, 1>, < 0.E-30 + 0.346410161513775458705489268301174473410*i, 1> } Vector space of degree 3, dimension 1 over Complex Field Echelonized basis: (1 2 4) Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Wed Apr 23 11:13:24 EST 2003 Initial seed: 3016376118 Time to this point: 2.94 Internal error in vpoly_factorize() at vpoly/fact.c, line 949 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 04:51:02 2004 Input: G:= ComplexField(); space:=MatrixAlgebra(G,3); M:=space![1/5,4/5,0,0,1/5,4/5,1/5,1/5,3/5]; Eigenvalues(M); Eigenspace(M,1); MinimalPolynomial(M) Output: Magma V2.10-6 Mon Feb 23 2004 04:50:59 on modular [Seed = 3099669977] ------------------------------------- { <0.999999999999999999999999999999999999994, 1>, < 0.E-30 - 0.346410161513775458705489268301174473410*i, 1>, < 0.E-30 + 0.346410161513775458705489268301174473410*i, 1> } Vector space of degree 3, dimension 1 over Complex Field Echelonized basis: (1 2 4) Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Wed Apr 23 11:13:24 EST 2003 Initial seed: 3099669977 Time to this point: 2.97 Segmentation fault Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 04:51:19 2004 Input: G:= ComplexField(); space:=MatrixAlgebra(G,3); M:=space![1/5,4/5,0,0,1/5,4/5,1/5,1/5,3/5]; Eigenvalues(M); Eigenspace(M,1); MinimalPolynomial(M) Output: Magma V2.10-6 Mon Feb 23 2004 04:51:16 on modular [Seed = 2180517111] ------------------------------------- { <0.999999999999999999999999999999999999994, 1>, < 0.E-30 - 0.346410161513775458705489268301174473410*i, 1>, < 0.E-30 + 0.346410161513775458705489268301174473410*i, 1> } Vector space of degree 3, dimension 1 over Complex Field Echelonized basis: (1 2 4) Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Wed Apr 23 11:13:24 EST 2003 Initial seed: 2180517111 Time to this point: 2.94 Segmentation fault Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 04:52:55 2004 Input: G:= ComplexField(); space:=MatrixAlgebra(G,3); M:=space![1/5,4/5,0,0,1/5,4/5,1/5,1/5,3/5]; Eigenvalues(M); Eigenspace(M,1); FactoredCharacteristicPolynomial(M) Output: Magma V2.10-6 Mon Feb 23 2004 04:52:52 on modular [Seed = 2364866970] ------------------------------------- { <0.999999999999999999999999999999999999994, 1>, < 0.E-30 - 0.346410161513775458705489268301174473410*i, 1>, < 0.E-30 + 0.346410161513775458705489268301174473410*i, 1> } Vector space of degree 3, dimension 1 over Complex Field Echelonized basis: (1 2 4) Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Wed Apr 23 11:13:24 EST 2003 Initial seed: 2364866970 Time to this point: 2.92 Internal error in vpoly_factorize() at vpoly/fact.c, line 949 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 04:55:15 2004 Input: G:= ComplexField(); space:=MatrixAlgebra(G,3); M:=space![1/5,4/5,0,0,1/5,4/5,1/5,1/5,3/5]; Eigenvalues(M); Eigenspace(M,1); CharacteristicPolynomial(M) FactoredCharacteristicPolynomial(M) Output: Magma V2.10-6 Mon Feb 23 2004 04:55:12 on modular [Seed = 2665943292] ------------------------------------- { <0.999999999999999999999999999999999999994, 1>, < 0.E-30 - 0.346410161513775458705489268301174473410*i, 1>, < 0.E-30 + 0.346410161513775458705489268301174473410*i, 1> } Vector space of degree 3, dimension 1 over Complex Field Echelonized basis: (1 2 4) >> FactoredCharacteristicPolynomial(M) ^ User error: bad syntax Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 04:55:32 2004 Input: G:= ComplexField(); space:=MatrixAlgebra(G,3); M:=space![1/5,4/5,0,0,1/5,4/5,1/5,1/5,3/5]; Eigenvalues(M); Eigenspace(M,1); CharacteristicPolynomial(M) Output: Magma V2.10-6 Mon Feb 23 2004 04:55:29 on modular [Seed = 1713367060] ------------------------------------- { <0.999999999999999999999999999999999999994, 1>, < 0.E-30 - 0.346410161513775458705489268301174473410*i, 1>, < 0.E-30 + 0.346410161513775458705489268301174473410*i, 1> } Vector space of degree 3, dimension 1 over Complex Field Echelonized basis: (1 2 4) $.1^3 - $.1^2 + 3/25*$.1 - 3/25 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 04:55:55 2004 Input: G:= ComplexField(); space:=MatrixAlgebra(G,3); M:=space![1/5,4/5,0,0,1/5,4/5,1/5,1/5,3/5]; Eigenvalues(M); Eigenspace(M,1); CharacteristicPolynomial(M) FactoredCharacteristicPolynomial(M) Output: Magma V2.10-6 Mon Feb 23 2004 04:55:52 on modular [Seed = 1830085414] ------------------------------------- { <0.999999999999999999999999999999999999994, 1>, < 0.E-30 - 0.346410161513775458705489268301174473410*i, 1>, < 0.E-30 + 0.346410161513775458705489268301174473410*i, 1> } Vector space of degree 3, dimension 1 over Complex Field Echelonized basis: (1 2 4) >> FactoredCharacteristicPolynomial(M); ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 04:56:06 2004 Input: G:= ComplexField(); space:=MatrixAlgebra(G,3); M:=space![1/5,4/5,0,0,1/5,4/5,1/5,1/5,3/5]; Eigenvalues(M); Eigenspace(M,1); CharacteristicPolynomial(M); FactoredCharacteristicPolynomial(M); Output: Magma V2.10-6 Mon Feb 23 2004 04:56:03 on modular [Seed = 1947073060] ------------------------------------- { <0.999999999999999999999999999999999999994, 1>, < 0.E-30 - 0.346410161513775458705489268301174473410*i, 1>, < 0.E-30 + 0.346410161513775458705489268301174473410*i, 1> } Vector space of degree 3, dimension 1 over Complex Field Echelonized basis: (1 2 4) $.1^3 - $.1^2 + 3/25*$.1 - 3/25 Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Wed Apr 23 11:13:24 EST 2003 Initial seed: 1947073060 Time to this point: 2.98 Internal error in vpoly_factorize() at vpoly/fact.c, line 949 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 04:56:32 2004 Input: G:=PolynomialRing(ComplexField())); p:=x^3-x^2+3/25*x -3/25 Output: Magma V2.10-6 Mon Feb 23 2004 04:56:29 on modular [Seed = 1111215212] ------------------------------------- >> G:=PolynomialRing(ComplexField())); ^ User error: bad syntax >> p:=x^3-x^2+3/25*x -3/25 ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 04:56:43 2004 Input: G:=PolynomialRing(ComplexField()); p:=x^3-x^2+3/25*x -3/25 Output: Magma V2.10-6 Mon Feb 23 2004 04:56:40 on modular [Seed = 1227933554] ------------------------------------- Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 04:56:53 2004 Input: G:=PolynomialRing(ComplexField()); p:=x^3-x^2+3/25*x -3/25 p; Output: Magma V2.10-6 Mon Feb 23 2004 04:56:50 on modular [Seed = 1596379486] ------------------------------------- >> p;; ^ User error: bad syntax Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 04:57:13 2004 Input: G:=PolynomialRing(ComplexField()); p:=x^3-x^2+3/25*x -3/25 p; Factorization(p); Output: Magma V2.10-6 Mon Feb 23 2004 04:57:09 on modular [Seed = 877509154] ------------------------------------- >> p; ^ User error: bad syntax >> Factorization(p); ^ User error: Identifier 'p' has not been declared or assigned Total time: 3.729 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 05:05:31 2004 Input: G:=PolynomialRing(ComplexField()); p:=x^3-x^2+3/25*x -3/25; p; Factorization(p); Output: Magma V2.10-6 Mon Feb 23 2004 05:05:28 on modular [Seed = 3869210349] ------------------------------------- x^3 - x^2 + 3/25*x - 3/25 >> Factorization(p); ^ Runtime error in 'Factorization': Algorithm is not available for this kind of coefficient ring Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 05:06:23 2004 Input: G:=PolynomialRing(Rationals()); p:=x^3-x^2+3/25*x -3/25; p; Factorization(p); Output: Magma V2.10-6 Mon Feb 23 2004 05:06:20 on modular [Seed = 3985931538] ------------------------------------- x^3 - x^2 + 3/25*x - 3/25 [ , ] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 05:19:29 2004 Input: G:= ComplexField(); space:=MatrixAlgebra(G,3); M:=space![1/5,0,4/5,3/5,0,4/5,0,0,1]; Eigenvalues(M); Output: Magma V2.10-6 Mon Feb 23 2004 05:19:26 on modular [Seed = 3534438687] ------------------------------------- { <0.E-28, 1>, <0.1999999999999999999999999999999999999994, 1>, <1.00000000000000000000000000000000000000, 1> } Total time: 3.169 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 05:20:28 2004 Input: G:= ComplexField(); space:=MatrixAlgebra(G,3); M:=space![1/5,0,4/5,3/5,0,4/5,0,0,1]; Eigenvalues(M); CharacteristicPolynomial(M); FactoredCharacteristicPolynomial(M); Output: Magma V2.10-6 Mon Feb 23 2004 05:20:25 on modular [Seed = 2715300395] ------------------------------------- { <0.E-28, 1>, <0.1999999999999999999999999999999999999994, 1>, <1.00000000000000000000000000000000000000, 1> } $.1^3 - 6/5*$.1^2 + 1/5*$.1 Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Wed Apr 23 11:13:24 EST 2003 Initial seed: 2715300395 Time to this point: 3.03 Internal error in vpoly_factorize() at vpoly/fact.c, line 949 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 05:20:43 2004 Input: G:= ComplexField(); space:=MatrixAlgebra(G,3); M:=space![1/5,0,4/5,3/5,0,4/5,0,0,1]; Eigenvalues(M); CharacteristicPolynomial(M); Output: Magma V2.10-6 Mon Feb 23 2004 05:20:39 on modular [Seed = 2832284476] ------------------------------------- { <0.E-28, 1>, <0.1999999999999999999999999999999999999994, 1>, <1.00000000000000000000000000000000000000, 1> } $.1^3 - 6/5*$.1^2 + 1/5*$.1 Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 05:21:42 2004 Input: G:=PolynomialRing(Rationals()); p:=x^3-6/5*x^2+1/5*x; p; Factorization(p); Output: Magma V2.10-6 Mon Feb 23 2004 05:21:39 on modular [Seed = 3083740135] ------------------------------------- x^3 - 6/5*x^2 + 1/5*x [ , , ] Total time: 3.129 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 05:22:45 2004 Input: G:= ComplexField(); space:=MatrixAlgebra(G,3); M:=space![1/5,0,4/5,3/5,0,4/5,0,0,1]; Eigenvalues(M); Eigenspace(M,1); Eigenspace(M,1/5); Eigenspace(M,0); CharacteristicPolynomial(M); Output: Magma V2.10-6 Mon Feb 23 2004 05:22:42 on modular [Seed = 3183749548] ------------------------------------- { <0.E-28, 1>, <0.1999999999999999999999999999999999999994, 1>, <1.00000000000000000000000000000000000000, 1> } Vector space of degree 3, dimension 1 over Complex Field Echelonized basis: (0 0 1) Vector space of degree 3, dimension 1 over Complex Field Echelonized basis: ( 1 0 -1) Vector space of degree 3, dimension 1 over Complex Field Echelonized basis: ( 1 -1/3 -8/15) $.1^3 - 6/5*$.1^2 + 1/5*$.1 Total time: 3.199 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 05:26:49 2004 Input: G:= ComplexField(); space:=MatrixAlgebra(G,3); M:=space![1/5,0,4/5,3/5,0,4/5,0,0,1]; Eigenvalues(M); Eigenspace(M,1); Eigenspace(M,1/5); Eigenspace(M,0); CharacteristicPolynomial(M); 1-1/3+8/15 Output: Magma V2.10-6 Mon Feb 23 2004 05:26:46 on modular [Seed = 2381584520] ------------------------------------- { <0.E-28, 1>, <0.1999999999999999999999999999999999999994, 1>, <1.00000000000000000000000000000000000000, 1> } Vector space of degree 3, dimension 1 over Complex Field Echelonized basis: (0 0 1) Vector space of degree 3, dimension 1 over Complex Field Echelonized basis: ( 1 0 -1) Vector space of degree 3, dimension 1 over Complex Field Echelonized basis: ( 1 -1/3 -8/15) $.1^3 - 6/5*$.1^2 + 1/5*$.1 6/5 Total time: 3.289 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 05:28:00 2004 Input: G:= ComplexField(); space:=MatrixAlgebra(G,3); M:=space![1/5,0,4/5,3/5,0,4/5,0,0,1]; Eigenvalues(M); Eigenspace(M,1); Eigenspace(M,1/5); Eigenspace(M,0); CharacteristicPolynomial(M); 1-1/3+8/15; 1/3*5/6; 8/15*5/6; Output: Magma V2.10-6 Mon Feb 23 2004 05:27:57 on modular [Seed = 2615283285] ------------------------------------- { <0.E-28, 1>, <0.1999999999999999999999999999999999999994, 1>, <1.00000000000000000000000000000000000000, 1> } Vector space of degree 3, dimension 1 over Complex Field Echelonized basis: (0 0 1) Vector space of degree 3, dimension 1 over Complex Field Echelonized basis: ( 1 0 -1) Vector space of degree 3, dimension 1 over Complex Field Echelonized basis: ( 1 -1/3 -8/15) $.1^3 - 6/5*$.1^2 + 1/5*$.1 6/5 5/18 4/9 Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host fondue.mat-stat.uit.no. (129.242.20.195) Time: Mon Feb 23 05:47:16 2004 Input: p:=1406019989634685423; Output: Magma V2.10-6 Mon Feb 23 2004 05:47:13 on modular [Seed = 1178590227] ------------------------------------- Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host fondue.mat-stat.uit.no. (129.242.20.195) Time: Mon Feb 23 05:47:28 2004 Input: p:=1406019989634685423; p; Output: Magma V2.10-6 Mon Feb 23 2004 05:47:25 on modular [Seed = 1211224593] ------------------------------------- 1406019989634685423 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host fondue.mat-stat.uit.no. (129.242.20.195) Time: Mon Feb 23 05:48:16 2004 Input: p:=1406019989634685423; p; D:=1-4*p; Output: Magma V2.10-6 Mon Feb 23 2004 05:48:13 on modular [Seed = 1361627992] ------------------------------------- 1406019989634685423 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 05:48:40 2004 Input: F:=FieldOfFractions(PolynomialRing(Rationals())); space:=MatrixAlgebra(F,2); M:=space![b,1-b,b/2,1-b/2]; Eigenvalues(M); Eigenspace(M,1); Eigenspace(M,-1/4); Output: Magma V2.10-6 Mon Feb 23 2004 05:48:37 on modular [Seed = 1512292539] ------------------------------------- { <1, 1>, <1/2*b, 1> } Vector space of degree 2, dimension 1 over Univariate rational function field over Rational Field Echelonized basis: ( 1 (-2*b + 2)/b) Vector space of degree 2, dimension 0 over Univariate rational function field over Rational Field Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host fondue.mat-stat.uit.no. (129.242.20.195) Time: Mon Feb 23 05:48:56 2004 Input: p:=1406019989634685423; p; D:=1-4*p; g:=HilbertClassPolynomial(D); Output: ** WARNING: Computation used more memory than allowed. ** Magma V2.10-6 Mon Feb 23 2004 05:48:41 on modular [Seed = 593148366] ------------------------------------- 1406019989634685423 Current total memory usage: 95.4MB, failed memory request: 0.0MB System Error: User memory limit has been reached Total time: 14.279 seconds, Total memory usage: 100.00MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 05:49:04 2004 Input: F:=FieldOfFractions(PolynomialRing(Rationals())); space:=MatrixAlgebra(F,2); M:=space![b,1-b,b/2,1-b/2]; Eigenvalues(M); Eigenspace(M,1); Eigenspace(M,b/2); Output: Magma V2.10-6 Mon Feb 23 2004 05:49:01 on modular [Seed = 877506253] ------------------------------------- { <1, 1>, <1/2*b, 1> } Vector space of degree 2, dimension 1 over Univariate rational function field over Rational Field Echelonized basis: ( 1 (-2*b + 2)/b) Vector space of degree 2, dimension 1 over Univariate rational function field over Rational Field Echelonized basis: ( 1 -1) Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host n137.ryd.student.liu.se. (130.236.215.137) Time: Mon Feb 23 06:15:58 2004 Input: p:=9834818944328567723398401275057520739; A:=812708013396563478897939064502400485; B:=9314324318399725412968518193528639157; E:=ChangeRing(EllipticCurve([A,B]),GF(p)); print(E); Order(E); Output: Magma V2.10-6 Mon Feb 23 2004 06:15:52 on modular [Seed = 3233374284] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 812708013396563478897939064502400485*x + 9314324318399725412968518193528639157 over GF(9834818944328567723398401275057520739) 9834818944328567721614012261818948512 Total time: 5.519 seconds, Total memory usage: 3.52MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 06:30:38 2004 Input: F:=FieldOfFractions(PolynomialRing(Rationals())); space:=MatrixAlgebra(F,3); M:=space![ (1+4*b^2)/5,4/5*b*(1-b),4/5*(1-b), 3/5*(1-b),b,2/5*(1-b), 0,-b*(2*b^2 + b - 3)/5,(2*b^3 + b^2 - 3*b + 5)/5]; Output: Magma V2.10-6 Mon Feb 23 2004 06:30:34 on modular [Seed = 2748975004] ------------------------------------- Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 06:31:00 2004 Input: F:=FieldOfFractions(PolynomialRing(Rationals())); space:=MatrixAlgebra(F,3); M:=space![ (1+4*b^2)/5,4/5*b*(1-b),4/5*(1-b), 3/5*(1-b),b,2/5*(1-b), 0,-b*(2*b^2 + b - 3)/5,(2*b^3 + b^2 - 3*b + 5)/5]; Eigenvalues(M); Eigenspace(M,1); Output: Magma V2.10-6 Mon Feb 23 2004 06:30:57 on modular [Seed = 3033338017] ------------------------------------- { <1, 1> } Vector space of degree 3, dimension 1 over Univariate rational function field over Rational Field Echelonized basis: (1 4/3*b + 4/3 (4/3*b + 10/3)/(b^2 + 3/2*b)) Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 06:31:48 2004 Input: F:=FieldOfFractions(PolynomialRing(Rationals())); space:=MatrixAlgebra(F,3); M:=space![ (1+4*b^2)/5,4/5*b*(1-b),4/5*(1-b), 3/5*(1-b),b,2/5*(1-b), 0,-b*(2*b^2 + b - 3)/5,(2*b^3 + b^2 - 3*b + 5)/5]; Eigenvalues(M); Eigenspace(M,1); CharacteristicPolynomial(M); Output: Magma V2.10-6 Mon Feb 23 2004 06:31:45 on modular [Seed = 3200719483] ------------------------------------- { <1, 1> } Vector space of degree 3, dimension 1 over Univariate rational function field over Rational Field Echelonized basis: (1 4/3*b + 4/3 (4/3*b + 10/3)/(b^2 + 3/2*b)) $.1^3 + (-2/5*b^3 - b^2 - 2/5*b - 6/5)*$.1^2 + (8/25*b^5 + 2/5*b^4 + 1/5*b^3 + 38/25*b^2 + 9/25*b + 1/5)*$.1 - 8/25*b^5 - 2/5*b^4 + 1/5*b^3 - 13/25*b^2 + 1/25*b Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9022C50.dip.t-dialin.net. (217.2.44.80) Time: Mon Feb 23 06:47:52 2004 Input: K:=GF(2); Pa:=PolynomialRing(K,4); IG:=ideal; A:=[[a,b,0,0,0,0,0,0],[c,d,0,0,0,0,0,0],[0,0,a,b,0,0,0,0],[0,0,c,d,0,0,0,0],[0,0,0,0,a,b,0,0],[0,0,0,0,c,d,0,0],[0,0,0,0,0,0,a,b],[0,0,0,0,c,d]]; P:=PolynomialRing(K,8); f1:=x2*y3+x3*y2; f2:=x1*y3+x3*y1; f3:=x1*y2+x2*y1; I:=ideal; Dimension(I); // Falls Erg. 8-3=5, dann phsop //Ergebnis: 6 Output: Magma V2.10-6 Mon Feb 23 2004 06:47:48 on modular [Seed = 1662700386] ------------------------------------- 6 [ 1, 3, 5, 6, 7, 8 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9022C50.dip.t-dialin.net. (217.2.44.80) Time: Mon Feb 23 06:48:14 2004 Input: K:=GF(2); Pa:=PolynomialRing(K,4); IG:=ideal; A:=[[a,b,0,0,0,0,0,0],[c,d,0,0,0,0,0,0],[0,0,a,b,0,0,0,0],[0,0,c,d,0,0,0,0],[0,0,0,0,a,b,0,0],[0,0,0,0,c,d,0,0],[0,0,0,0,0,0,a,b],[0,0,0,0,c,d]]; P:=PolynomialRing(K,8); f1:=x2*y3+x3*y2; f2:=x1*y3+x3*y1; f3:=x3*y4+x4*y3; I:=ideal; Dimension(I); // Falls Erg. 8-3=5, dann phsop //Ergebnis: 6 Output: Magma V2.10-6 Mon Feb 23 2004 06:48:11 on modular [Seed = 1779679860] ------------------------------------- 6 [ 1, 2, 3, 4, 7, 8 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9022C50.dip.t-dialin.net. (217.2.44.80) Time: Mon Feb 23 06:48:48 2004 Input: K:=GF(2); Pa:=PolynomialRing(K,4); IG:=ideal; A:=[[a,b,0,0,0,0,0,0],[c,d,0,0,0,0,0,0],[0,0,a,b,0,0,0,0],[0,0,c,d,0,0,0,0],[0,0,0,0,a,b,0,0],[0,0,0,0,c,d,0,0],[0,0,0,0,0,0,a,b],[0,0,0,0,c,d]]; P:=PolynomialRing(K,8); f1:=x2*y3+x3*y2; f2:=x1*y3+x3*y1; f3:=x1*y4+x4*y1; I:=ideal; Dimension(I); // Falls Erg. 8-3=5, dann phsop //Ergebnis: 6 Output: Magma V2.10-6 Mon Feb 23 2004 06:48:45 on modular [Seed = 2097468805] ------------------------------------- 5 [ 3, 5, 6, 7, 8 ] Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9022C50.dip.t-dialin.net. (217.2.44.80) Time: Mon Feb 23 06:51:07 2004 Input: K:=GF(2); Pa:=PolynomialRing(K,4); IG:=ideal; A:=[[a,b,0,0,0,0,0,0],[c,d,0,0,0,0,0,0],[0,0,a,b,0,0,0,0],[0,0,c,d,0,0,0,0],[0,0,0,0,a,b,0,0],[0,0,0,0,c,d,0,0],[0,0,0,0,0,0,a,b],[0,0,0,0,c,d]]; P:=PolynomialRing(K,8); f1:=x1*y2+x2*y1; f2:=x3*y4+x4*y1; f3:=x2*y3+x3*y4; I:=ideal; Dimension(I); // Falls Erg. 8-3=5, dann phsop //Ergebnis: 6 Output: Magma V2.10-6 Mon Feb 23 2004 06:51:04 on modular [Seed = 1278600449] ------------------------------------- 5 [ 4, 5, 6, 7, 8 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9022C50.dip.t-dialin.net. (217.2.44.80) Time: Mon Feb 23 06:51:30 2004 Input: K:=GF(2); P:=PolynomialRing(K,8); f1:=x1*y2+x2*y1; f2:=x3*y4+x4*y1; f3:=x2*y3+x3*y4; I:=ideal; Dimension(I); // Falls Erg. 8-3=5, dann phsop //Ergebnis: 6 Output: Magma V2.10-6 Mon Feb 23 2004 06:51:26 on modular [Seed = 1462697484] ------------------------------------- 5 [ 4, 5, 6, 7, 8 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host webgate.cscploenzke.de. (194.45.150.17) Time: Mon Feb 23 07:08:07 2004 Input: 100000! Output: Magma V2.10-6 Mon Feb 23 2004 07:08:04 on modular [Seed = 58371650] ------------------------------------- >> 100000!; ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host webgate.cscploenzke.de. (194.45.150.17) Time: Mon Feb 23 07:08:24 2004 Input: 100000!; Output: Magma V2.10-6 Mon Feb 23 2004 07:08:21 on modular [Seed = 393132615] ------------------------------------- >> 100000!;; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host webgate.cscploenzke.de. (194.45.150.17) Time: Mon Feb 23 07:08:43 2004 Input: fact(100000) Output: Magma V2.10-6 Mon Feb 23 2004 07:08:40 on modular [Seed = 409056565] ------------------------------------- >> fact(100000); ^ User error: Identifier 'fact' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host webgate.cscploenzke.de. (194.45.150.17) Time: Mon Feb 23 07:09:57 2004 Input: factorial(100000) Output: Magma V2.10-6 Mon Feb 23 2004 07:09:54 on modular [Seed = 3985915930] ------------------------------------- >> factorial(100000); ^ User error: Identifier 'factorial' has not been declared or assigned Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host webgate.cscploenzke.de. (194.45.150.17) Time: Mon Feb 23 07:10:29 2004 Input: Factorial(100000) Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Feb 23 2004 07:10:06 on modular [Seed = 4236595463] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 9625 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host webgate.cscploenzke.de. (194.45.150.17) Time: Mon Feb 23 07:10:48 2004 Input: Factorial(10000) Output: Magma V2.10-6 Mon Feb 23 2004 07:10:45 on modular [Seed = 3283775075] ------------------------------------- 2846259680917054518906413212119868890148051401702799230794179994274411340003764\ 4437729907867577847758158840621423175288300423399401535187390524211613827161748\ 1982419982759241828925978789812425312059465996259867065601615720360323979263287\ 3671705574197596209947972034615369811989709261127750048419884541047554464244213\ 6573303076703628825803548967461117097369578603670191071512730587281041158640561\ 2811653853259684258259955846881464304255898366493170592517172042765974074461334\ 0005419405246230343686915405940406622782824837151203832217864462718382292389963\ 8992827221879702459387693803094627332292570555459690027875282242544348021127559\ 0191694254290289169072190970836905398737474524833728995218023632827412170402680\ 8676921045155584056717255537201585213282903427998981844931361064038148930449962\ 1599999359670892980190336998484404665419236258424947163178961192041233108268651\ 0713545168455409360330096072103469443779823494307806260694223026818852275920570\ 2923084312618849760656074258627944882715595683153344053442544664841689458042570\ 9461673613187605234982286326452921529423479870603344290737158688499178932580691\ 4831688542519560061723726363239744207869246429560123062887201226529529640915083\ 0133663098273380635397290150658182257429547589439976511386554120812578868370423\ 9208764484761569001264889271590706306409661628038784044485191643790807186112370\ 6221334154150659918438759610239267132765469861636577066264386380298480519527695\ 3619525924093090861447190739076858575593478698172073437209310482547562856777769\ 4081564074962275254993384112809289637516990219870492405617531786346939798024619\ 7370790418683299310165541507423083931768783669236948490259996077296842939774275\ 3626311982541668153189176323483919082100014717893218422780513518173492190114624\ 6875769835373441456013122615221391178759688367364087207937002992038279198038702\ 3720780391403123689976081528403060511167094847222248703891999934420713958369830\ 6396223207911562404425080891991431983712044559834404755675948921210149815245454\ 3594285414390843564419984224855478532163624030098442855331829253154206551237079\ 7058163934602962476970103887422064415366267337154287007891227493406843364428898\ 4710084064160009362393526124803797529334392876439831639031277645072247926785170\ 0826669598389526150759007349215197592659192708873202594066382118801988854748266\ 0483422564577057439731222597006719360617635135795298217942907977053272832675014\ 8802444352868164502616566283754651900617187344226043891929850607151539003110668\ 4727360135816706437861756757439184376479658136100599638689552334648781746143243\ 5732248643267984819814584327030358955084205347884933645824825920332880890257823\ 8823326577020524897093704721021424841334246526820680673231421448385407418213962\ 1846870108359582946965235632764870475718351616879235068366271743711915723361143\ 0701211207676086978515597218464859859186436417168508996255168209107935702311185\ 1817477501080462258552131476489749066075287708289766751495100968232968973200062\ 2392888056658036140311285465929084078033974900664953205873164948093883816198658\ 8508273824680348978647571166798904235680183035041338757319726308979094357106877\ 9730163391808786847494363353389337358690640584841782806519627582643442925805842\ 2212947649402948622670761832988229004072390403733168207417413251656688443079339\ 4470192089056207883875853425128209573593070181977083401638176382785625395168254\ 2664461494104471157953326237281546879408042371858742302620026422182269418862621\ 2107297776657401018376182280136857586442185863011539843712299107010094061929413\ 2232027731939594670067136953770978977781182882424429208648161341795620174718316\ 0968766104314049795819823644580736820940402221118153005143338707660706314961610\ 7771117448059552764348333385744040212757031851527298377435921878558552795591028\ 6644579173620072218581433099772947789237207179428577562713009239823979219575811\ 9726474264287826668235391568785727162014619224426626670840076566562580710947439\ 8740110772811669918806268726626565583345665007890309050656074633078027158530817\ 6912237728135105845273265916262196476205714348802156308152590053437211410003030\ 3924286645720732847348171203416818632896886504828736793339844397123673508452734\ 0196309427697652684170174990756947982757825835229994315633322107439131550124459\ 0053247026803129123922979790304175878233986223735350546426469135025039510092392\ 8658510868208807066273473320035499572039708648806604092985460700633940988583634\ 9865466136727880748764700702458790118046518296111277090609016152022111461543158\ 3176699570609746180853593904000678928785488278509386373537039040494126846189912\ 7287156265500127083303995025787993170543188275265922581494895074663997600731692\ 7310831735883056612614782997663188070063044632429112260691931278881566221591523\ 2704576958675128219909389426866019639044897189185974729253103224802105438410443\ 2582847283058429780416240510811032691400190056878439634150269652104892027214023\ 2160234898588827371428695339681755106287470907473718188014223487248498558198439\ 0946517083643689943061896502432883532796671901845276205510857076262042445096233\ 2320474470783119043449935144262550170177101737955112474615947173186270156557126\ 6295855125077711738338208419705893367323724453280456537178514960308802580284067\ 8478094146418386592266528068679788432506605379430462502871051049293472674712674\ 9989263462735816714693506049511034075540465817039348104675848562596776795976829\ 9409334026387269378365320912287718077451152622642548771835461108886360843272806\ 2277766430972838790567286180360486334648933714394152502594596525015209595361579\ 7713559579496572977565090269442808847976127666484700361964890604376193469427044\ 4070215317943583831051404915462608728486678750541674146731648999356381312866931\ 4276168635373056345866269578945682750658102359508148887789550739393653419373657\ 0084831850447568221544406759920313807707353997803633926733454954929666875992253\ 0893898086430606532961793164029612492673080638031873912596151131890359351266480\ 8185683667702865377423907465823909109555171797705807977892897524902307378017531\ 4268036391424472025772889178495007811788933662975043680421466819782427298069757\ 9391742229456683185815676816288797870624531246651727622758295493421483658868919\ 2995874020956960002435603052898298663868920769928340305497102665143223061252319\ 1513184387690382370620539920693394371688046642971147674356448637502684769814885\ 3105354063328845062012173302630676481322931561043551941761050712449024873277273\ 1120919458651374931909651624976916575538121985664322079786663003989386602386073\ 5785811439471587280089337416503379296583261843607313332752602360511552422722844\ 7251463863269369763762510196714380125691227784428426999440829152215904694437282\ 4986580852051865762929927755088331286726384187132777808744466438753526447335624\ 4113944762878097465068395298210817496795883645227334469487379347179071006497823\ 6466016680572034297929207446822322848665839522211446859572858403863377278030227\ 5915304978658739195136502462741958990883743873315942873720297706202071202130385\ 7217593321116241333042277374241635355358797706530964768588607730143277829032889\ 4795818404378858567772932094476778669357537460048142376741194182671636870481056\ 9111562156143575162905273512243500806046536689174581965494826086122607502930627\ 6147881326895528073614902252581968281505103331813212965966495815903042123877564\ 5990973296728066683849166257949747922905361845563741034791430771561168650484292\ 4902811029925296787352987678292690407887784802624792227507359484058174390862518\ 7794689004594206016860514277224448627246991114620014988066272353883780938062854\ 4384763053235070132028029488392008132135446450056134987017834271106158177289819\ 2906564986880810455622337030672542512772773302834984335957725759562247037077933\ 8714659303308862969944031833266579751467650271734629888377739784821870071802674\ 1265997158728035440478432478674907127921672898523588486943546692255101337606377\ 9151645972542571169684773399511589983490818882812639844005055462100669887926145\ 5821456531969690982725393451576040861347625877816586729441077535882416231577908\ 2538054746933540582469717674324523451498483027170396543887737637358191736582454\ 2733474904242629460112998819165637138471118491569150547681404117498014542657123\ 9420442544102807580600138819865061375928853903892264432294799028648284009959867\ 5963580999112695367601527173086852756572147583507122298296529564917835071750835\ 7413622825450556202709694174767992592297748886274113145876761475314568953280931\ 1705269648641018740767329698664923643738256547502281647192681555988319662984830\ 7776666840622314315884384910519058281816740764463033300119710293036455866594651\ 8690744752508378419876229904159117936827997606541860887216266548864923443910309\ 2325691063377596973905178112276466848679173604940439370333935190060938726839729\ 9246478483727274770977466693599784857120156789000241947269220974984127323147401\ 5499809203814598214164811763571478015542315996678385348544864069364105569135313\ 3523118405358134894093819182189869482538396098994282202759933963520621770534357\ 2073396250574216769465101608495601439303244304271576099527308684609204422226103\ 1542299844448021100981613338248273752189987382053151649271344981059501599748005\ 7159191220215448774875010347324619063394130303089239941198500622590218416440998\ 8173214324422108554248620896250260604398180189026317781146617454999771440665232\ 8638463638470016556181538610981881111817341913055050248603458567555856375117297\ 7429932907494423657966833270091836733897734790175924888566037995277154056908301\ 7311723894140326159612292912225191095948743805673381278538616491842786938417556\ 8980471008598683720336151751580970225662752001609561922299254017598785220385459\ 1377178397638981119848580329104875166692119510451489667776159824946872742066343\ 7593207852618922687285527671324883267794152912839165407968344190239094803676688\ 7 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host webgate.cscploenzke.de. (194.45.150.17) Time: Mon Feb 23 07:11:53 2004 Input: 2^1000000 Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Feb 23 2004 07:11:30 on modular [Seed = 3618536000] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 9650 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host webgate.cscploenzke.de. (194.45.150.17) Time: Mon Feb 23 07:13:21 2004 Input: Factor(14324523532453462362346234656) Output: Magma V2.10-6 Mon Feb 23 2004 07:13:18 on modular [Seed = 2381587382] ------------------------------------- >> Factor(14324523532453462362346234656); ^ Runtime error in 'Factor': Bad argument types Argument types given: RngIntElt Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host webgate.cscploenzke.de. (194.45.150.17) Time: Mon Feb 23 07:13:55 2004 Input: Factorization(14324523532453462362346234656) Output: Magma V2.10-6 Mon Feb 23 2004 07:13:52 on modular [Seed = 2532259955] ------------------------------------- [ <2, 5>, <3, 2>, <17, 1>, <31, 2>, <311, 1>, <142559, 1>, <68668942465049, 1> ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host webgate.cscploenzke.de. (194.45.150.17) Time: Mon Feb 23 07:14:43 2004 Input: Factorization(x^8-1) Output: Magma V2.10-6 Mon Feb 23 2004 07:14:40 on modular [Seed = 2598581327] ------------------------------------- >> Factorization(x^8-1); ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host webgate.cscploenzke.de. (194.45.150.17) Time: Mon Feb 23 07:15:34 2004 Input: P := PolynomialRing(IntegerRing());Factorization(x^8-1) Output: Magma V2.10-6 Mon Feb 23 2004 07:15:31 on modular [Seed = 1745995501] ------------------------------------- [ , , , ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host webgate.cscploenzke.de. (194.45.150.17) Time: Mon Feb 23 07:16:59 2004 Input: Pi(1299); Output: Magma V2.10-6 Mon Feb 23 2004 07:16:56 on modular [Seed = 2131152929] ------------------------------------- >> Pi(1299);; ^ Runtime error in 'Pi': Bad argument types Argument types given: RngIntElt Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host webgate.cscploenzke.de. (194.45.150.17) Time: Mon Feb 23 07:17:15 2004 Input: Pi(C); Output: Magma V2.10-6 Mon Feb 23 2004 07:17:12 on modular [Seed = 1127935085] ------------------------------------- >> Pi(C);; ^ User error: Identifier 'C' has not been declared or assigned Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host webgate.cscploenzke.de. (194.45.150.17) Time: Mon Feb 23 07:17:24 2004 Input: Pi(); Output: Magma V2.10-6 Mon Feb 23 2004 07:17:21 on modular [Seed = 1445984610] ------------------------------------- >> Pi();; ^ Runtime error in 'Pi': Bad argument types Argument types given: Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD90223D3.dip.t-dialin.net. (217.2.35.211) Time: Mon Feb 23 07:22:02 2004 Input: K:=GF(2); P:=PolynomialRing(K,8); f1:=x1*y2+x2*y1; f2:=x1*y3+x3*y1; f3:=x1*y4+x4*y1; I:=ideal; Dimension(I); // Falls Erg. 8-3=5, dann phsop //Ergebnis: 6 Output: Magma V2.10-6 Mon Feb 23 2004 07:21:59 on modular [Seed = 576426531] ------------------------------------- 6 [ 3, 4, 5, 6, 7, 8 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD90223D3.dip.t-dialin.net. (217.2.35.211) Time: Mon Feb 23 07:29:56 2004 Input: K:=GF(2); P:=PolynomialRing(K,8); f1:=x1*y2+x2*y1; f2:=x1*y3+x3*y1; f3:=x1*y4; I:=ideal; Dimension(I); // Falls Erg. 8-3=5, dann phsop //Ergebnis: 6 Output: Magma V2.10-6 Mon Feb 23 2004 07:29:53 on modular [Seed = 1011191323] ------------------------------------- 6 [ 3, 4, 5, 6, 7, 8 ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ZE047070.ppp.dion.ne.jp. (220.217.47.70) Time: Mon Feb 23 07:32:25 2004 Input: 2^3; Output: Magma V2.10-6 Mon Feb 23 2004 07:32:22 on modular [Seed = 175356090] ------------------------------------- 8 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ZE047070.ppp.dion.ne.jp. (220.217.47.70) Time: Mon Feb 23 07:33:26 2004 Input: > c:=LinearCode [1,0,1,2,3], > [0,1,2,3,4]>; > g:=GeneratorMatrix(c); > g; Output: Magma V2.10-6 Mon Feb 23 2004 07:33:23 on modular [Seed = 275358565] ------------------------------------- [1 0 1 2 3] [0 1 2 3 4] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ZE047070.ppp.dion.ne.jp. (220.217.47.70) Time: Mon Feb 23 07:34:17 2004 Input: > c:=LinearCode [1,0,1,2,3], > [0,1,2,3,4]>; > g:=GeneratorMatrix(c); > g; s:=Sym({1,2,3,4,5}); a:=s!(1,2); b:=s!(1,2,3,4); G:=; Output: Magma V2.10-6 Mon Feb 23 2004 07:34:14 on modular [Seed = 3869201862] ------------------------------------- [1 0 1 2 3] [0 1 2 3 4] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ZE047070.ppp.dion.ne.jp. (220.217.47.70) Time: Mon Feb 23 07:34:52 2004 Input: s:=Sym({1,2,3,4,5}); a:=s!(1,2); b:=s!(1,2,3,4); G:=; Output: Magma V2.10-6 Mon Feb 23 2004 07:34:49 on modular [Seed = 3969212387] ------------------------------------- Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ZE047070.ppp.dion.ne.jp. (220.217.47.70) Time: Mon Feb 23 07:35:05 2004 Input: s:=Sym({1,2,3,4,5}); a:=s!(1,2); b:=s!(1,2,3,4); G:=; G; $G; Output: Magma V2.10-6 Mon Feb 23 2004 07:35:02 on modular [Seed = 4052239073] ------------------------------------- <(1, 2), (1, 2, 3, 4)> >> $G; ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ZE047070.ppp.dion.ne.jp. (220.217.47.70) Time: Mon Feb 23 07:35:16 2004 Input: s:=Sym({1,2,3,4,5}); a:=s!(1,2); b:=s!(1,2,3,4); G:=; G; #G; Output: Magma V2.10-6 Mon Feb 23 2004 07:35:13 on modular [Seed = 3351147552] ------------------------------------- <(1, 2), (1, 2, 3, 4)> 2 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 09:57:49 2004 Input: F:=FieldOfFractions(PolynomialRing(Rationals())); space:=MatrixAlgebra(F,3); M:=space![0,0,1,2/5,1/5,3/5,1/5,1/5,3/5]; Eigenvalues(M); Eigenspace(M,1); Output: Magma V2.10-6 Mon Feb 23 2004 09:57:46 on modular [Seed = 3467942477] ------------------------------------- {} Vector space of degree 3, dimension 0 over Univariate rational function field over Rational Field Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 09:58:11 2004 Input: F:=FieldOfFractions(PolynomialRing(Rationals())); space:=MatrixAlgebra(F,3); M:=space![0,0,1,2/5,1/5,2/5,1/5,1/5,3/5]; Eigenvalues(M); Eigenspace(M,1); Output: Magma V2.10-6 Mon Feb 23 2004 09:58:08 on modular [Seed = 3651374256] ------------------------------------- { <1, 1> } Vector space of degree 3, dimension 1 over Univariate rational function field over Rational Field Echelonized basis: ( 1 5/6 10/3) Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 09:59:07 2004 Input: 1+ 5/6 +10/3; Output: Magma V2.10-6 Mon Feb 23 2004 09:59:04 on modular [Seed = 3618472582] ------------------------------------- 31/6 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 10:05:44 2004 Input: F:=FieldOfFractions(PolynomialRing(Rationals())); space:=MatrixAlgebra(F,3); M:=space![1/5,0,4/5,2/5,1/5,2/5,1/5,1/5,3/5]; Eigenvalues(M); Eigenspace(M,1); Output: Magma V2.10-6 Mon Feb 23 2004 10:05:41 on modular [Seed = 2398410786] ------------------------------------- { <1, 1> } Vector space of degree 3, dimension 1 over Univariate rational function field over Rational Field Echelonized basis: ( 1 2/3 8/3) Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 10:07:36 2004 Input: 1+2/3+8/3 Output: Magma V2.10-6 Mon Feb 23 2004 10:07:33 on modular [Seed = 2581843653] ------------------------------------- 13/3 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 10:09:25 2004 Input: F:=FieldOfFractions(PolynomialRing(Rationals())); space:=MatrixAlgebra(F,3); M:=space![1/5,0,4/5,2/5,1/5,2/5,2/5,3/5]; Eigenvalues(M); Eigenspace(M,1); Output: Magma V2.10-6 Mon Feb 23 2004 10:09:22 on modular [Seed = 2464728409] ------------------------------------- >> M:=space![1/5,0,4/5,2/5,1/5,2/5,2/5,3/5]; ^ Runtime error in '!': Sequence argument length (8) should be 9 to be coerced into a matrix >> Eigenvalues(M); ^ User error: Identifier 'M' has not been declared or assigned >> Eigenspace(M,1); ^ User error: Identifier 'M' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 10:09:49 2004 Input: F:=FieldOfFractions(PolynomialRing(Rationals())); space:=MatrixAlgebra(F,3); M:=space![1/5,0,4/5,2/5,1/5,2/5,0,2/5,3/5]; Eigenvalues(M); Eigenspace(M,1); Output: Magma V2.10-6 Mon Feb 23 2004 10:09:46 on modular [Seed = 1846819262] ------------------------------------- { <1, 1> } Vector space of degree 3, dimension 1 over Univariate rational function field over Rational Field Echelonized basis: (1 2 4) Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 10:29:36 2004 Input: F:=FieldOfFractions(PolynomialRing(Rationals())); space:=MatrixAlgebra(F,3); M:=space![1/5,4/5,0,0,1/5,4/5,1/5,1/5,3/5]; Eigenvalues(M); Eigenspace(M,1); Output: Magma V2.10-6 Mon Feb 23 2004 10:29:33 on modular [Seed = 3634529519] ------------------------------------- { <1, 1> } Vector space of degree 3, dimension 1 over Univariate rational function field over Rational Field Echelonized basis: (1 2 4) Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 10:30:23 2004 Input: G:=ComplexField(); space:=MatrixAlgebra(G,3); M:=space![1/5,4/5,0,0,1/5,4/5,1/5,1/5,3/5]; Eigenvalues(M); Eigenspace(M,1); Output: Magma V2.10-6 Mon Feb 23 2004 10:30:19 on modular [Seed = 2966088790] ------------------------------------- { <0.999999999999999999999999999999999999994, 1>, < 0.E-30 - 0.346410161513775458705489268301174473410*i, 1>, < 0.E-30 + 0.346410161513775458705489268301174473410*i, 1> } Vector space of degree 3, dimension 1 over Complex Field Echelonized basis: (1 2 4) Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee108.uab.es. (158.109.66.108) Time: Mon Feb 23 11:52:51 2004 Input: hola Output: Magma V2.10-6 Mon Feb 23 2004 11:52:47 on modular [Seed = 3033455366] ------------------------------------- >> hola; ^ User error: Identifier 'hola' has not been declared or assigned Total time: 3.169 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee108.uab.es. (158.109.66.108) Time: Mon Feb 23 11:52:53 2004 Input: hola Output: Magma V2.10-6 Mon Feb 23 2004 11:52:49 on modular [Seed = 2966085436] ------------------------------------- >> hola; ^ User error: Identifier 'hola' has not been declared or assigned Total time: 3.689 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee108.uab.es. (158.109.66.108) Time: Mon Feb 23 11:52:55 2004 Input: hola Output: Magma V2.10-6 Mon Feb 23 2004 11:52:49 on modular [Seed = 2381832706] ------------------------------------- >> hola; ^ User error: Identifier 'hola' has not been declared or assigned Total time: 3.699 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee108.uab.es. (158.109.66.108) Time: Mon Feb 23 11:52:55 2004 Input: hola Output: Magma V2.10-6 Mon Feb 23 2004 11:52:50 on modular [Seed = 2398413057] ------------------------------------- >> hola; ^ User error: Identifier 'hola' has not been declared or assigned Total time: 3.599 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 12:07:43 2004 Input: F:=FieldOfFractions(PolynomialRing(Rationals())); space:=MatrixAlgebra(G,3); M:=space![(4*b^2 + 1)/(4*b^2 + 4*b + 5), 4*b/(4*b^2 + 4*b + 5), 4/(4*b^2 + 4*b + 5), 2/(b^2 + 5*b + 5), (b^2 + 3*b + 1)/(b^2 + 5*b + 5), 2*(b + 1)/(b^2 + 5*b + 5), b/(2*b^3 + 3*b^2 + 4*b + 5), 2/(2*b^3 + 3*b^2 + 4*b + 5), (2*b^3 + 3*b^2 + 3*b + 3)/(2*b^3 + 3*b^2 + 4*b + 5)] Eigenvalues(M); Eigenspace(M,1); Output: Magma V2.10-6 Mon Feb 23 2004 12:07:40 on modular [Seed = 1061506061] ------------------------------------- >> space:=MatrixAlgebra(G,3); ^ User error: Identifier 'G' has not been declared or assigned >> Eigenvalues(M); ^ User error: bad syntax >> Eigenspace(M,1); ^ User error: Identifier 'M' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 12:08:04 2004 Input: F:=FieldOfFractions(PolynomialRing(Rationals())); space:=MatrixAlgebra(G,3); M:=space![(4*b^2 + 1)/(4*b^2 + 4*b + 5), 4*b/(4*b^2 + 4*b + 5), 4/(4*b^2 + 4*b + 5), 2/(b^2 + 5*b + 5), (b^2 + 3*b + 1)/(b^2 + 5*b + 5), 2*(b + 1)/(b^2 + 5*b + 5), b/(2*b^3 + 3*b^2 + 4*b + 5), 2/(2*b^3 + 3*b^2 + 4*b + 5), (2*b^3 + 3*b^2 + 3*b + 3)/(2*b^3 + 3*b^2 + 4*b + 5)] Eigenvalues(M); Eigenspace(M,1); Output: Magma V2.10-6 Mon Feb 23 2004 12:08:01 on modular [Seed = 894387753] ------------------------------------- >> space:=MatrixAlgebra(G,3); ^ User error: Identifier 'G' has not been declared or assigned >> Eigenvalues(M); ^ User error: bad syntax >> Eigenspace(M,1); ^ User error: Identifier 'M' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 12:08:21 2004 Input: F:=FieldOfFractions(PolynomialRing(Rationals())); space:=MatrixAlgebra(F,3); M:=space![(4*b^2 + 1)/(4*b^2 + 4*b + 5), 4*b/(4*b^2 + 4*b + 5), 4/(4*b^2 + 4*b + 5), 2/(b^2 + 5*b + 5), (b^2 + 3*b + 1)/(b^2 + 5*b + 5), 2*(b + 1)/(b^2 + 5*b + 5), b/(2*b^3 + 3*b^2 + 4*b + 5), 2/(2*b^3 + 3*b^2 + 4*b + 5), (2*b^3 + 3*b^2 + 3*b + 3)/(2*b^3 + 3*b^2 + 4*b + 5)] Eigenvalues(M); Eigenspace(M,1); Output: Magma V2.10-6 Mon Feb 23 2004 12:08:18 on modular [Seed = 175143398] ------------------------------------- >> Eigenvalues(M); ^ User error: bad syntax >> Eigenspace(M,1);; ^ User error: Identifier 'M' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 12:08:40 2004 Input: F:=FieldOfFractions(PolynomialRing(Rationals())); space:=MatrixAlgebra(F,3); M:=space![(4*b^2 + 1)/(4*b^2 + 4*b + 5), 4*b/(4*b^2 + 4*b + 5), 4/(4*b^2 + 4*b + 5), 2/(b^2 + 5*b + 5), (b^2 + 3*b + 1)/(b^2 + 5*b + 5), 2*(b + 1)/(b^2 + 5*b + 5), b/(2*b^3 + 3*b^2 + 4*b + 5), 2/(2*b^3 + 3*b^2 + 4*b + 5), (2*b^3 + 3*b^2 + 3*b + 3)/(2*b^3 + 3*b^2 + 4*b + 5)]; Eigenvalues(M); Eigenspace(M,1); Output: Magma V2.10-6 Mon Feb 23 2004 12:08:37 on modular [Seed = 58290424] ------------------------------------- { <1, 1> } Vector space of degree 3, dimension 1 over Univariate rational function field over Rational Field Echelonized basis: (1 (1/2*b^2 + 5/2*b + 5/2)/(b^2 + b + 5/4) (2*b^3 + 3*b^2 + 4*b + 5)/(b^2 + b + 5/4)) Total time: 3.009 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 12:11:27 2004 Input: F:=FieldOfFractions(PolynomialRing(Rationals())); G:=ComplexField(); space:=MatrixAlgebra(G,3); M:=space![5/13,4/13,4/13,2/11,5/11,4/11,1/14,1/7,11/14]; Eigenvalues(M); Eigenspace(M,1); Output: Magma V2.10-6 Mon Feb 23 2004 12:11:24 on modular [Seed = 4002716348] ------------------------------------- { <0.999999999999999999999999999999999999994, 1>, <0.1775425995911080632132838517874383327021, 1>, <0.447332525284016811911591273087686542437, 1> } Vector space of degree 3, dimension 1 over Complex Field Echelonized basis: ( 1 22/13 56/13) Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 12:11:55 2004 Input: F:=FieldOfFractions(PolynomialRing(Rationals())); G:=ComplexField(); space:=MatrixAlgebra(G,3); M:=space![5/13,4/13,4/13,2/11,5/11,4/11,1/14,1/7,11/14]; Eigenvalues(M); Eigenspace(M,1); 13+22+56; Output: Magma V2.10-6 Mon Feb 23 2004 12:11:52 on modular [Seed = 3885863889] ------------------------------------- { <0.999999999999999999999999999999999999994, 1>, <0.1775425995911080632132838517874383327021, 1>, <0.447332525284016811911591273087686542437, 1> } Vector space of degree 3, dimension 1 over Complex Field Echelonized basis: ( 1 22/13 56/13) 91 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 12:12:59 2004 Input: F:=FieldOfFractions(PolynomialRing(Rationals())); G:=ComplexField(); space:=MatrixAlgebra(G,3); M:=space![1/4,1/4,1/2,8/31,11/31,12/31,1/16,1/4,11/16]; Eigenvalues(M); Eigenspace(M,1); Output: Magma V2.10-6 Mon Feb 23 2004 12:12:56 on modular [Seed = 4202728972] ------------------------------------- { <1.00000000000000000000000000000000000000, 1>, <0.1048387096774193548387096774193548390954, 1>, <0.1874999999999999999999999999999999996385, 1> } Vector space of degree 3, dimension 1 over Complex Field Echelonized basis: ( 1 31/16 4) Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 12:13:22 2004 Input: F:=FieldOfFractions(PolynomialRing(Rationals())); G:=ComplexField(); space:=MatrixAlgebra(F,3); M:=space![1/4,1/4,1/2,8/31,11/31,12/31,1/16,1/4,11/16]; Eigenvalues(M); Eigenspace(M,1); Output: Magma V2.10-6 Mon Feb 23 2004 12:13:19 on modular [Seed = 4035609649] ------------------------------------- { <1, 1>, <13/124, 1>, <3/16, 1> } Vector space of degree 3, dimension 1 over Univariate rational function field over Rational Field Echelonized basis: ( 1 31/16 4) Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Feb 23 12:14:31 2004 Input: F:=FieldOfFractions(PolynomialRing(Rationals())); G:=ComplexField(); space:=MatrixAlgebra(F,3); M:=space![1/4,1/4,1/2,8/31,11/31,12/31,1/16,1/4,11/16]; Eigenvalues(M); Eigenspace(M,1); 5*16+31 Output: Magma V2.10-6 Mon Feb 23 2004 12:14:28 on modular [Seed = 3334255196] ------------------------------------- { <1, 1>, <13/124, 1>, <3/16, 1> } Vector space of degree 3, dimension 1 over Univariate rational function field over Rational Field Echelonized basis: ( 1 31/16 4) 111 Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 13:57:52 2004 Input: 2+4; print 2+4; Output: Magma V2.10-6 Mon Feb 23 2004 13:57:49 on modular [Seed = 3701920158] ------------------------------------- 6 6 Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 14:03:56 2004 Input: x:=10; ShowIndentifiers(); ShowValues(); Output: Magma V2.10-6 Mon Feb 23 2004 14:03:53 on modular [Seed = 2297595518] ------------------------------------- >> ShowIndentifiers(); ^ User error: Identifier 'ShowIndentifiers' has not been declared or assigned x: 10 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 14:04:33 2004 Input: x:=10; ShowIdentifiers(); ShowValues(); Output: Magma V2.10-6 Mon Feb 23 2004 14:04:29 on modular [Seed = 2682622285] ------------------------------------- x x: 10 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 14:17:33 2004 Input: Qbar := AlgebraicClosure(RationalField()); Qbar; S := PolynomialRing(Qbar); r := Roots(x^3-2); r; Output: Magma V2.10-6 Mon Feb 23 2004 14:17:30 on modular [Seed = 542781850] ------------------------------------- >> Qbar := AlgebraicClosure(RationalField()); ^ Runtime error in 'AlgebraicClosure': Bad argument types Argument types given: FldRat >> Qbar; ^ User error: Identifier 'Qbar' has not been declared or assigned >> S := PolynomialRing(Qbar); ^ User error: Identifier 'Qbar' has not been declared or assigned >> r := Roots(x^3-2); ^ User error: Identifier 'x' has not been declared or assigned >> r;; ^ User error: Identifier 'r' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 14:22:01 2004 Input: Qbar := AlgebraicClosure(Rationals()); Qbar; S := PolynomialRing(Qbar); r := Roots(x^3-2); r; Output: Magma V2.10-6 Mon Feb 23 2004 14:21:58 on modular [Seed = 292225975] ------------------------------------- >> Qbar := AlgebraicClosure(Rationals()); ^ Runtime error in 'AlgebraicClosure': Bad argument types Argument types given: FldRat >> Qbar; ^ User error: Identifier 'Qbar' has not been declared or assigned >> S := PolynomialRing(Qbar); ^ User error: Identifier 'Qbar' has not been declared or assigned >> r := Roots(x^3-2); ^ User error: Identifier 'x' has not been declared or assigned >> r;; ^ User error: Identifier 'r' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 14:25:29 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3-2); O := MaximalOrder(K); [K!b : b in Basis(O)]; Output: Magma V2.10-6 Mon Feb 23 2004 14:25:25 on modular [Seed = 8000469] ------------------------------------- [ 1, a, a^2 ] Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 14:26:44 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3-2); O := MaximalOrder(K); [K!b : b in Basis(O)]; Qbar:=AlgebraicClosure(RationalField()); Output: Magma V2.10-6 Mon Feb 23 2004 14:26:41 on modular [Seed = 3601646935] ------------------------------------- [ 1, a, a^2 ] >> Qbar:=AlgebraicClosure(RationalField());; ^ Runtime error in 'AlgebraicClosure': Bad argument types Argument types given: FldRat Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 14:28:30 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3-2); O := Order([2*a]); O; Output: Magma V2.10-6 Mon Feb 23 2004 14:28:27 on modular [Seed = 3300839663] ------------------------------------- Transformation of Order over Equation Order with defining polynomial x^3 - 2 over its ground order Transformation Matrix: [1 0 0] [0 2 0] [0 0 4] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 14:29:18 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3-2); O := Order([2*a]); O; OK:=MaximalOrder(K); Index(OK,O); Output: Magma V2.10-6 Mon Feb 23 2004 14:29:15 on modular [Seed = 3451377974] ------------------------------------- Transformation of Order over Equation Order with defining polynomial x^3 - 2 over its ground order Transformation Matrix: [1 0 0] [0 2 0] [0 0 4] >> Index(OK,O);; ^ Runtime error in 'Index': Argument is not a suborder Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 14:29:57 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3-2); O := Order([2*a]); O; OK:=MaximalOrder(K); OK; Output: Magma V2.10-6 Mon Feb 23 2004 14:29:54 on modular [Seed = 3066864244] ------------------------------------- Transformation of Order over Equation Order with defining polynomial x^3 - 2 over its ground order Transformation Matrix: [1 0 0] [0 2 0] [0 0 4] Maximal Equation Order with defining polynomial x^3 - 2 over its ground order Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 14:35:55 2004 Input: Qbar:=AlgebraicClosure(); Output: Magma V2.10-6 Mon Feb 23 2004 14:35:52 on modular [Seed = 2882649539] ------------------------------------- Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 14:36:20 2004 Input: Qbar:=AlgebraicClosure(); Qbar; Output: Magma V2.10-6 Mon Feb 23 2004 14:36:16 on modular [Seed = 2498659028] ------------------------------------- Algebraically closed field with no variables Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 14:36:32 2004 Input: Qbar:=AlgebraicClosure; Qbar; Output: Magma V2.10-6 Mon Feb 23 2004 14:36:28 on modular [Seed = 2649197521] ------------------------------------- Intrinsic 'AlgebraicClosure' Signatures: () -> FldAC The algebraic closure of Q. Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 14:37:46 2004 Input: Qbar:=AlgebraicClosure(); Qbar; S;=PolynomialRing(Qbar); r:=Roots(x^3-2) r; Output: Magma V2.10-6 Mon Feb 23 2004 14:37:42 on modular [Seed = 2264698993] ------------------------------------- Algebraically closed field with no variables >> S;=PolynomialRing(Qbar); ^ User error: Bad print expression >> S;=PolynomialRing(Qbar); ^ User error: bad syntax >> r;; ^ User error: bad syntax Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 14:37:58 2004 Input: Qbar:=AlgebraicClosure(); Qbar; S:=PolynomialRing(Qbar); r:=Roots(x^3-2) r; Output: Magma V2.10-6 Mon Feb 23 2004 14:37:55 on modular [Seed = 1896572819] ------------------------------------- Algebraically closed field with no variables >> r;; ^ User error: bad syntax Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 14:38:18 2004 Input: Qbar:=AlgebraicClosure(); Qbar; S:=PolynomialRing(Qbar); r:=Roots(x^3-2); r; Output: Magma V2.10-6 Mon Feb 23 2004 14:38:15 on modular [Seed = 2013425326] ------------------------------------- Algebraically closed field with no variables [ , , ] Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 14:39:28 2004 Input: Qbar:=AlgebraicClosure(); Qbar; S:=PolynomialRing(Qbar); r:=Roots(x^3-2); r; a:=r[1][1]; a; Output: Magma V2.10-6 Mon Feb 23 2004 14:39:25 on modular [Seed = 1696560121] ------------------------------------- Algebraically closed field with no variables [ , , ] r1 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 14:39:41 2004 Input: Qbar:=AlgebraicClosure(); Qbar; S:=PolynomialRing(Qbar); r:=Roots(x^3-2); r; a:=r[2][1]; a; Output: Magma V2.10-6 Mon Feb 23 2004 14:39:37 on modular [Seed = 1813412580] ------------------------------------- Algebraically closed field with no variables [ , , ] r2 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 14:39:56 2004 Input: Qbar:=AlgebraicClosure(); Qbar; S:=PolynomialRing(Qbar); r:=Roots(x^3-2); r; a:=r[1][2]; a; Output: Magma V2.10-6 Mon Feb 23 2004 14:39:53 on modular [Seed = 1462583343] ------------------------------------- Algebraically closed field with no variables [ , , ] 1 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 14:40:38 2004 Input: Qbar:=AlgebraicClosure(); Qbar; S:=PolynomialRing(Qbar); r:=Roots(x^3-2); r; a:=r[1][1]; a; MinimalPolynomial(a); Output: Magma V2.10-6 Mon Feb 23 2004 14:40:35 on modular [Seed = 1195200517] ------------------------------------- Algebraically closed field with no variables [ , , ] r1 $.1^3 - 2 Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 14:45:53 2004 Input: Qbar:=AlgebraicClosure(); Qbar; S:=PolynomialRing(Qbar); r:=Roots(x^3-2); r; a:=r[1][1]; a; MinimalPolynomial(a); s:=Roots(x^3-1); s; Output: Magma V2.10-6 Mon Feb 23 2004 14:45:50 on modular [Seed = 927805224] ------------------------------------- Algebraically closed field with no variables [ , , ] r1 $.1^3 - 2 [ <1, 1>, , ] Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 14:47:44 2004 Input: Qbar:=AlgebraicClosure(); Qbar; S:=PolynomialRing(Qbar); r:=Roots(x^3-2); r; a:=r[1][1]; a; T:=PolynomialRing(RationalField()); MinimalPolynomial(a); s:=Roots(x^3-1); s; Output: Magma V2.10-6 Mon Feb 23 2004 14:47:41 on modular [Seed = 559626637] ------------------------------------- Algebraically closed field with no variables [ , , ] r1 X^3 - 2 [ <1, 1>, , ] Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 14:48:48 2004 Input: Qbar:=AlgebraicClosure(); S:=PolynomialRing(Qbar); r:=Roots(x^3-2); a:=r[1][1]; a; T:=PolynomialRing(RationalField()); MinimalPolynomial(a); s:=Roots(x^4-4); s; Output: Magma V2.10-6 Mon Feb 23 2004 14:48:45 on modular [Seed = 726741575] ------------------------------------- r1 X^3 - 2 [ , , , ] Total time: 2.909 seconds, Total memory usage: 1.91MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 14:49:54 2004 Input: Qbar:=AlgebraicClosure(); S:=PolynomialRing(Qbar); r:=Roots(x^3-2); a:=r[1][1]; T:=PolynomialRing(RationalField()); MinimalPolynomial(a); s:=Roots(x^4-4); s; b:=s[1][1]; MinimalPolynomial(b); c:=s[2][1]; MinimalPolynomial(c); Output: Magma V2.10-6 Mon Feb 23 2004 14:49:51 on modular [Seed = 376180536] ------------------------------------- X^3 - 2 [ , , , ] X^2 - 2 X^2 - 2 Total time: 2.989 seconds, Total memory usage: 1.91MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 14:50:10 2004 Input: Qbar:=AlgebraicClosure(); S:=PolynomialRing(Qbar); r:=Roots(x^3-2); a:=r[1][1]; T:=PolynomialRing(RationalField()); MinimalPolynomial(a); s:=Roots(x^4-4); s; b:=s[1][1]; MinimalPolynomial(b); c:=s[3][1]; MinimalPolynomial(c); Output: Magma V2.10-6 Mon Feb 23 2004 14:50:07 on modular [Seed = 108797720] ------------------------------------- X^3 - 2 [ , , , ] X^2 - 2 X^2 + 2 Total time: 2.979 seconds, Total memory usage: 1.91MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 14:51:23 2004 Input: Qbar:=AlgebraicClosure(); S:=PolynomialRing(Qbar); r:=Roots(x^3-2); a:=r[1][1]; T:=PolynomialRing(RationalField()); MinimalPolynomial(a); s:=Roots(x^4-4); b:=s[1][1]; MinimalPolynomial(b); c:=s[3][1]; MinimalPolynomial(c); Trace(a); Trace(b); Trace(a+b); Output: Magma V2.10-6 Mon Feb 23 2004 14:51:20 on modular [Seed = 4035635513] ------------------------------------- X^3 - 2 X^2 - 2 X^2 + 2 0 0 0 Total time: 3.109 seconds, Total memory usage: 1.91MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 14:51:52 2004 Input: Qbar:=AlgebraicClosure(); S:=PolynomialRing(Qbar); r:=Roots(x^3-2); a:=r[1][1]; T:=PolynomialRing(RationalField()); MinimalPolynomial(a); s:=Roots(x^4-4); b:=s[1][1]; MinimalPolynomial(b); c:=s[3][1]; MinimalPolynomial(c); Norm(a); Norm(b); Norm(a*b); Output: Magma V2.10-6 Mon Feb 23 2004 14:51:49 on modular [Seed = 4219593311] ------------------------------------- X^3 - 2 X^2 - 2 X^2 + 2 2 -2 -32 Total time: 2.989 seconds, Total memory usage: 1.91MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 14:52:27 2004 Input: Qbar:=AlgebraicClosure(); S:=PolynomialRing(Qbar); r:=Roots(x^3-2); a:=r[1][1]; T:=PolynomialRing(RationalField()); MinimalPolynomial(a); s:=Roots(x^4-4); b:=s[1][1]; MinimalPolynomial(b); c:=s[3][1]; MinimalPolynomial(c); Norm(a); Norm(b); Norm(a*b); Norm; Output: Magma V2.10-6 Mon Feb 23 2004 14:52:23 on modular [Seed = 3801676644] ------------------------------------- X^3 - 2 X^2 - 2 X^2 + 2 2 -2 -32 Intrinsic 'Norm' Signatures: ( x) -> FldFinElt The norm of the element x of F relative to the ground field of F. ( x, E) -> FldFinElt The norm of the element x of F relative to the subfield E of F. ( x) -> FldReElt ( x) -> FldReElt ( x) -> RngIntElt ( x) -> FldRatElt ( x) -> RngElt ( x) -> FldPrElt ( x) -> FldRatElt The absolute norm of x (over Q). ( a) -> RngElt ( a, R) -> RngElt ( a) -> RngElt ( a, R) -> RngElt The norm of a over R if given otherwise Subfield (Parent (a)); see also AbsoluteNorm. ( v) -> RngElt ( v) -> RngElt The norm of vector v (the inner product of v with itself). ( a) -> RngElt ( a) -> FldFunGElt ( a, R) -> RngElt ( a, R) -> FldFunGElt The norm of the element a. ( I) -> . ( I) -> . ( I) -> RngElt The norm of the ideal I. ( x) -> RngLocElt ( x) -> FldLocElt ( x) -> RngPadResElt ( x) -> RngPadResExtElt ( x) -> RngPadElt ( x) -> FldPadElt ( x) -> RngElt The norm of x. ( x, R) -> RngPadResElt ( x, R) -> RngPadResExtElt ( x, R) -> RngPadResExtElt ( x, R) -> RngPadElt ( x, R) -> FldPadElt The norm of x over R. ( x) -> RngElt ( x) -> RngElt The norm of the quaternion algebra element over the base field. ( I) -> RngElt The norm of the quaternion order or ideal I. ( x) -> RngElt Total time: 2.989 seconds, Total memory usage: 1.91MB ************** MAGMA ***************** Host mesaana.uchicago.edu. (128.135.72.137) Time: Mon Feb 23 17:10:32 2004 Input: R := PolynomialRing(GF(2)); F := FieldOfFractions(R); W := WittRing(F,5); v := [x,0,0,0,0]; w := [x+1,0,0,0,0]; a := W!v; b := W!w; Output: Magma V2.10-6 Mon Feb 23 2004 17:10:29 on modular [Seed = 3718768635] ------------------------------------- Total time: 2.989 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host mesaana.uchicago.edu. (128.135.72.137) Time: Mon Feb 23 17:11:11 2004 Input: R := PolynomialRing(GF(2)); F := FieldOfFractions(R); W := WittRing(F,5); v := [x,0,0,0,0]; w := [x+1,0,0,0,0]; a := W!v; b := W!w; a+b; Output: Magma V2.10-6 Mon Feb 23 2004 17:11:08 on modular [Seed = 3300851403] ------------------------------------- (1 x^2 + x x^2 + x x^2 + x x^12 + x^10 + x^6 + x^4 + x^2 + x) Total time: 3.019 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host p5085F740.dip0.t-ipconnect.de. (80.133.247.64) Time: Mon Feb 23 18:08:53 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Mon Feb 23 2004 18:08:49 on modular [Seed = 1127844662] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ip251-10.ct.co.cr. (196.40.10.251) Time: Mon Feb 23 20:30:42 2004 Input: (x=y)^(.5) Output: Magma V2.10-6 Mon Feb 23 2004 20:30:39 on modular [Seed = 2748926697] ------------------------------------- >> (x=y)^(.5); ^ User error: bad syntax Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-68-252-37-126.dsl.wotnoh.ameritech.net. (68.252.37.126) Time: Mon Feb 23 20:42:18 2004 Input: 17!+1 Output: Magma V2.10-6 Mon Feb 23 2004 20:42:15 on modular [Seed = 1662617826] ------------------------------------- >> 17!+1; ^ Runtime error in '!': Illegal coercion Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nom5070it.nomadic.ncsu.edu. (152.7.237.59) Time: Mon Feb 23 20:55:55 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Mon Feb 23 2004 20:55:51 on modular [Seed = 1211279129] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ip251-10.ct.co.cr. (196.40.10.251) Time: Mon Feb 23 21:23:45 2004 Input: ? Output: Magma V2.10-6 Mon Feb 23 2004 21:23:42 on modular [Seed = 209123797] ------------------------------------- =============================================================================== PATH: /language/statement KIND: Overview =============================================================================== A statement is a complete command to Magma. Every statement must end with a semicolon ( ; ). If you press the key before typing ; then Magma may give you a special prompt symbol such as print> or if> to remind you that the statement is not yet finished. EXAMPLE: > print 5+8; > DivBy3 := func< n | IsZero(n mod 3) >; =============================================================================== Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 22:51:39 2004 Input: R := PolynomialRing(RationalField()); R; Output: Magma V2.10-6 Mon Feb 23 2004 22:51:36 on modular [Seed = 158565177] ------------------------------------- >> R;; ^ User error: Bad print expression Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 22:52:29 2004 Input: R := PolynomialRing(RationalField()); Output: Magma V2.10-6 Mon Feb 23 2004 22:52:26 on modular [Seed = 41453568] ------------------------------------- Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 22:58:15 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3-2); O := Order([2*a]) O; Output: Magma V2.10-6 Mon Feb 23 2004 22:58:12 on modular [Seed = 4085872735] ------------------------------------- >> O;; ^ User error: bad syntax Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 22:58:22 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3-2); O := Order([2*a]); O; Output: Magma V2.10-6 Mon Feb 23 2004 22:58:19 on modular [Seed = 3969279823] ------------------------------------- Transformation of Order over Equation Order with defining polynomial x^3 - 2 over its ground order Transformation Matrix: [1 0 0] [0 2 0] [0 0 4] Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 23:01:00 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3-2); O := Order([2*a]); O; OK:= MaximalOrder(K); Output: Magma V2.10-6 Mon Feb 23 2004 23:00:57 on modular [Seed = 3334228679] ------------------------------------- Transformation of Order over Equation Order with defining polynomial x^3 - 2 over its ground order Transformation Matrix: [1 0 0] [0 2 0] [0 0 4] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 23:01:20 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3-2); O := Order([2*a]); O; OK:= MaximalOrder(K); Index(OK,O); Output: Magma V2.10-6 Mon Feb 23 2004 23:01:17 on modular [Seed = 2715495764] ------------------------------------- Transformation of Order over Equation Order with defining polynomial x^3 - 2 over its ground order Transformation Matrix: [1 0 0] [0 2 0] [0 0 4] >> Index(OK,O);; ^ Runtime error in 'Index': Argument is not a suborder Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 23:03:56 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3-2); O := Order([2*a]); O; OK:= MaximalOrder(K); Index; Output: Magma V2.10-6 Mon Feb 23 2004 23:03:53 on modular [Seed = 2649166028] ------------------------------------- Transformation of Order over Equation Order with defining polynomial x^3 - 2 over its ground order Transformation Matrix: [1 0 0] [0 2 0] [0 0 4] Intrinsic 'Index' Signatures: ( S, . x) -> RngIntElt ( S, . x) -> RngIntElt The index of x in S (i.e. the smallest integer i such that S[i] equals x), 0 if x is not in S. ( S, T) -> RngIntElt The index in S at which T is a substring of S (0 if T is not a substring of S). ( G, H) -> RngIntElt ( G, H) -> RngIntElt [ Strategy: Any, Compact: RngIntElt, CosetLimit: RngIntElt, FillFactor: RngIntElt, Style: "C" | "CR" | "Cr" | "R" | "R_CR" | "Rc" | "Rt", CTFactor: RngIntElt, RTFactor: RngIntElt, RelationsInSubgroup: RngIntElt, Print: Any, Messages: RngIntElt, TimeLimit: RngIntElt, Workspace: RngIntElt, Mendelsohn: BoolElt, RowFilling: BoolElt, PathCompression: BoolElt, Lookahead: RngIntElt, PrefDefMode: RngIntElt, PrefDefSize: RngIntElt, DeductionMode: RngIntElt, DeductionSize: RngIntElt, LoopLimit: RngIntElt, Grain: RngIntElt, Hard: BoolElt, SubgroupRelations: RngIntElt, Time: RngIntElt ] ( G, H) -> RngIntElt ( G, H) -> RngIntElt ( G, H) -> RngIntElt The index of the subgroup H in G. ( G, H) -> RngIntElt The index of the subgroup H in G, or zero if H is of infinite index. ( L, S) -> RngIntElt The index of the lattice S in the lattice L (0 if infinite). ( O, E) -> . ( O, E) -> . The index of the suborder E in O. ( O, I) -> RngIntElt The index of the ideal I in the order O. ( a) -> RngIntElt The module index (O:Z[a]) where a lies in the Z-order O. ( e) -> RngIntElt The index of e (the number of the constituent to which e belongs). ( v) -> RngIntElt The index of v. ( p) -> RngIntElt ( P, p) -> RngIntElt The index of the plane p in the plane P. ( l) -> RngIntElt ( P, l) -> RngIntElt The index of the line l in the plane P. ( G, H) -> RngIntElt The index of the subgroup H in G. ( F) -> RngIntElt The index of F in its table. ( w) -> RngIntElt The variable index of the single letter w. ( P) -> RngIntElt The index found in the enumeration in P. ( s, i, n) -> RngIntElt Return the index of the ith coefficient when the first n are asked for. ( e) -> RngIntElt Return the edge's index in the parent graph G's adjacency list. G cannot be a simple graph. ( v) -> RngIntElt The index of v in its resolution graph. ( v) -> RngIntElt The index of v in its splice diagram. ( G) -> RngIntElt returns index of G in SL_2(Z), if this is finite. ( G, H) -> RngIntElt returns index of G in H, if this is finite. ( FS) -> RngIntElt returns the index in PSL2(Z) of the congruence subgroup corresponding to the Farey Symbol FS. Total time: 2.999 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 23:05:04 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3-2); O := Order([2*a]); O; OK:= MaximalOrder(K); OK; Index; Output: Magma V2.10-6 Mon Feb 23 2004 23:05:01 on modular [Seed = 2347828894] ------------------------------------- Transformation of Order over Equation Order with defining polynomial x^3 - 2 over its ground order Transformation Matrix: [1 0 0] [0 2 0] [0 0 4] Maximal Equation Order with defining polynomial x^3 - 2 over its ground order Intrinsic 'Index' Signatures: ( S, . x) -> RngIntElt ( S, . x) -> RngIntElt The index of x in S (i.e. the smallest integer i such that S[i] equals x), 0 if x is not in S. ( S, T) -> RngIntElt The index in S at which T is a substring of S (0 if T is not a substring of S). ( G, H) -> RngIntElt ( G, H) -> RngIntElt [ Strategy: Any, Compact: RngIntElt, CosetLimit: RngIntElt, FillFactor: RngIntElt, Style: "C" | "CR" | "Cr" | "R" | "R_CR" | "Rc" | "Rt", CTFactor: RngIntElt, RTFactor: RngIntElt, RelationsInSubgroup: RngIntElt, Print: Any, Messages: RngIntElt, TimeLimit: RngIntElt, Workspace: RngIntElt, Mendelsohn: BoolElt, RowFilling: BoolElt, PathCompression: BoolElt, Lookahead: RngIntElt, PrefDefMode: RngIntElt, PrefDefSize: RngIntElt, DeductionMode: RngIntElt, DeductionSize: RngIntElt, LoopLimit: RngIntElt, Grain: RngIntElt, Hard: BoolElt, SubgroupRelations: RngIntElt, Time: RngIntElt ] ( G, H) -> RngIntElt ( G, H) -> RngIntElt ( G, H) -> RngIntElt The index of the subgroup H in G. ( G, H) -> RngIntElt The index of the subgroup H in G, or zero if H is of infinite index. ( L, S) -> RngIntElt The index of the lattice S in the lattice L (0 if infinite). ( O, E) -> . ( O, E) -> . The index of the suborder E in O. ( O, I) -> RngIntElt The index of the ideal I in the order O. ( a) -> RngIntElt The module index (O:Z[a]) where a lies in the Z-order O. ( e) -> RngIntElt The index of e (the number of the constituent to which e belongs). ( v) -> RngIntElt The index of v. ( p) -> RngIntElt ( P, p) -> RngIntElt The index of the plane p in the plane P. ( l) -> RngIntElt ( P, l) -> RngIntElt The index of the line l in the plane P. ( G, H) -> RngIntElt The index of the subgroup H in G. ( F) -> RngIntElt The index of F in its table. ( w) -> RngIntElt The variable index of the single letter w. ( P) -> RngIntElt The index found in the enumeration in P. ( s, i, n) -> RngIntElt Return the index of the ith coefficient when the first n are asked for. ( e) -> RngIntElt Return the edge's index in the parent graph G's adjacency list. G cannot be a simple graph. ( v) -> RngIntElt The index of v in its resolution graph. ( v) -> RngIntElt The index of v in its splice diagram. ( G) -> RngIntElt returns index of G in SL_2(Z), if this is finite. ( G, H) -> RngIntElt returns index of G in H, if this is finite. ( FS) -> RngIntElt returns the index in PSL2(Z) of the congruence subgroup corresponding to the Farey Symbol FS. Total time: 3.019 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 23:05:45 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3-2); O := Order([2*a]); O; OK:= MaximalOrder(K); OK; Index(OK , O); Output: Magma V2.10-6 Mon Feb 23 2004 23:05:42 on modular [Seed = 2231241066] ------------------------------------- Transformation of Order over Equation Order with defining polynomial x^3 - 2 over its ground order Transformation Matrix: [1 0 0] [0 2 0] [0 0 4] Maximal Equation Order with defining polynomial x^3 - 2 over its ground order >> Index(OK , O);; ^ Runtime error in 'Index': Argument is not a suborder Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 23:06:03 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3-2); O := Order([2*a]); O; OK:= MaximalOrder(K); OK; Index(O , OK); Output: Magma V2.10-6 Mon Feb 23 2004 23:06:00 on modular [Seed = 2080829869] ------------------------------------- Transformation of Order over Equation Order with defining polynomial x^3 - 2 over its ground order Transformation Matrix: [1 0 0] [0 2 0] [0 0 4] Maximal Equation Order with defining polynomial x^3 - 2 over its ground order >> Index(O , OK);; ^ Runtime error in 'Index': Argument is not a suborder Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 23:06:17 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3-2); O := Order([2*a]); O; OK:= MaximalOrder(K); OK; Index(OK); Output: Magma V2.10-6 Mon Feb 23 2004 23:06:14 on modular [Seed = 1997404856] ------------------------------------- Transformation of Order over Equation Order with defining polynomial x^3 - 2 over its ground order Transformation Matrix: [1 0 0] [0 2 0] [0 0 4] Maximal Equation Order with defining polynomial x^3 - 2 over its ground order >> Index(OK);; ^ Runtime error in 'Index': Bad argument types Argument types given: RngOrd Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 23:07:32 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3-2); O := Order([2*a]); O; OK:= MaximalOrder(K); OK; Discriminat(O); Output: Magma V2.10-6 Mon Feb 23 2004 23:07:29 on modular [Seed = 1846861846] ------------------------------------- Transformation of Order over Equation Order with defining polynomial x^3 - 2 over its ground order Transformation Matrix: [1 0 0] [0 2 0] [0 0 4] Maximal Equation Order with defining polynomial x^3 - 2 over its ground order >> Discriminat(O);; ^ User error: Identifier 'Discriminat' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 23:07:50 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3-2); O := Order([2*a]); OK:= MaximalOrder(K); Discriminant(O); Output: Magma V2.10-6 Mon Feb 23 2004 23:07:47 on modular [Seed = 1478678069] ------------------------------------- -6912 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 23:08:03 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3-2); O := Order([2*a]); OK:= MaximalOrder(K); Discriminant(OK); Output: Magma V2.10-6 Mon Feb 23 2004 23:08:00 on modular [Seed = 1395252490] ------------------------------------- -108 Total time: 2.859 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 23:09:05 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3-2); O := Order([2*a]); OK:= MaximalOrder(K); Discriminant(OK); Discriminant(K); Output: Magma V2.10-6 Mon Feb 23 2004 23:09:02 on modular [Seed = 1295500138] ------------------------------------- -108 -108 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 23:12:06 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3-2); O := Order([2*a]); OK:= MaximalOrder(K); Discriminant(OK); Discriminant(K); I:=6*O; Output: Magma V2.10-6 Mon Feb 23 2004 23:12:03 on modular [Seed = 1044689236] ------------------------------------- -108 -108 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 23:12:18 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3-2); O := Order([2*a]); OK:= MaximalOrder(K); Discriminant(OK); Discriminant(K); I:=6*O; I; Output: Magma V2.10-6 Mon Feb 23 2004 23:12:15 on modular [Seed = 693347919] ------------------------------------- -108 -108 Principal Ideal of O Generator: [6, 0, 0] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 23:13:35 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+1); K; Output: Magma V2.10-6 Mon Feb 23 2004 23:13:32 on modular [Seed = 593079350] ------------------------------------- >> K;; ^ User error: Bad print expression Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 23:13:46 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+1); K; Output: Magma V2.10-6 Mon Feb 23 2004 23:13:43 on modular [Seed = 442537236] ------------------------------------- Number Field with defining polynomial x^2 + 1 over the Rational Field Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 23:15:24 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+1); K; OK:= MaximalOrder(K); OK; Output: Magma V2.10-6 Mon Feb 23 2004 23:15:21 on modular [Seed = 141723560] ------------------------------------- Number Field with defining polynomial x^2 + 1 over the Rational Field Maximal Equation Order with defining polynomial x^2 + 1 over its ground order Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 23:17:13 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+1); K; OK:= MaximalOrder(K); OK; I:=6*K; I; Output: Magma V2.10-6 Mon Feb 23 2004 23:17:10 on modular [Seed = 125671224] ------------------------------------- Number Field with defining polynomial x^2 + 1 over the Rational Field Maximal Equation Order with defining polynomial x^2 + 1 over its ground order >> I:=6*K; ^ Runtime error in '*': Bad argument types Argument types given: RngIntElt, FldNum >> I;; ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 23:17:29 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+1); K; OK:= MaximalOrder(K); OK; I:=6*OK; I; Output: Magma V2.10-6 Mon Feb 23 2004 23:17:26 on modular [Seed = 4270091985] ------------------------------------- Number Field with defining polynomial x^2 + 1 over the Rational Field Maximal Equation Order with defining polynomial x^2 + 1 over its ground order Principal Ideal of OK Generator: [6, 0] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 23:19:10 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+1); K; OK:= MaximalOrder(K); OK; I:=6*OK; I; J=12*OK; J; I subset J; J subset I; Output: Magma V2.10-6 Mon Feb 23 2004 23:19:07 on modular [Seed = 3901913130] ------------------------------------- Number Field with defining polynomial x^2 + 1 over the Rational Field Maximal Equation Order with defining polynomial x^2 + 1 over its ground order Principal Ideal of OK Generator: [6, 0] >> J=12*OK; ^ User error: Identifier 'J' has not been declared or assigned >> J; ^ User error: Identifier 'J' has not been declared or assigned >> I subset J; ^ User error: Identifier 'J' has not been declared or assigned >> J subset I;; ^ User error: Identifier 'J' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 23:19:22 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+1); K; OK:= MaximalOrder(K); OK; I:=6*OK; I; J:=12*OK; J; I subset J; J subset I; Output: Magma V2.10-6 Mon Feb 23 2004 23:19:19 on modular [Seed = 3818484573] ------------------------------------- Number Field with defining polynomial x^2 + 1 over the Rational Field Maximal Equation Order with defining polynomial x^2 + 1 over its ground order Principal Ideal of OK Generator: [6, 0] Principal Ideal of OK Generator: [12, 0] false true Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 23:24:44 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+1); K; OK:= MaximalOrder(K); OK; I:=6*OK; I; J:=12*OK; J; I subset J; J subset I; I*J; Output: Magma V2.10-6 Mon Feb 23 2004 23:24:41 on modular [Seed = 3568191140] ------------------------------------- Number Field with defining polynomial x^2 + 1 over the Rational Field Maximal Equation Order with defining polynomial x^2 + 1 over its ground order Principal Ideal of OK Generator: [6, 0] Principal Ideal of OK Generator: [12, 0] false true Principal Ideal of OK Generator: [72, 0] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 23:25:50 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+1); K; OK:= MaximalOrder(K); I:=6*OK; J:=12*OK; I subset J; J subset I; I*J; I+J; Output: Magma V2.10-6 Mon Feb 23 2004 23:25:47 on modular [Seed = 3266859248] ------------------------------------- Number Field with defining polynomial x^2 + 1 over the Rational Field false true Principal Ideal of OK Generator: [72, 0] Principal Ideal of OK Generator: [6, 0] Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 23:26:51 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+1); K; OK:= MaximalOrder(K); I:=9*OK; J:=12*OK; I subset J; J subset I; I*J; I+J; I meet J; Output: Magma V2.10-6 Mon Feb 23 2004 23:26:48 on modular [Seed = 3183947596] ------------------------------------- Number Field with defining polynomial x^2 + 1 over the Rational Field false false Principal Ideal of OK Generator: [108, 0] Principal Ideal of OK Generator: [3, 0] Ideal of OK Basis: [36 0] [ 0 36] Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 23:29:59 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+1); OK:= MaximalOrder(K); I:=9*OK; J:=12*OK; I subset J; J subset I; I*J; I+J; I meet J; Factorization(I); Factorization(J); Output: Magma V2.10-6 Mon Feb 23 2004 23:29:56 on modular [Seed = 3066832266] ------------------------------------- false false Principal Ideal of OK Generator: [108, 0] Principal Ideal of OK Generator: [3, 0] Ideal of OK Basis: [36 0] [ 0 36] [ ] [ , ] Total time: 2.909 seconds, Total memory usage: 1.96MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 23:31:45 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+5); OK:= MaximalOrder(K); I:=2*OK; Factorization(I); Output: Magma V2.10-6 Mon Feb 23 2004 23:31:42 on modular [Seed = 2799449457] ------------------------------------- [ ] Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 23:35:47 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+1); OK:= MaximalOrder(K); I:=2*OK; Factorization(I); Output: Magma V2.10-6 Mon Feb 23 2004 23:35:44 on modular [Seed = 2532049487] ------------------------------------- [ ] Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 23:36:19 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+1); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Mon Feb 23 2004 23:36:16 on modular [Seed = 2180715832] ------------------------------------- [ ] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Feb 23 23:36:41 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+1); OK:= MaximalOrder(K); I:=5*OK; Factorization(I); Output: Magma V2.10-6 Mon Feb 23 2004 23:36:38 on modular [Seed = 2063724503] ------------------------------------- [ , ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (64.86.36.6) Time: Tue Feb 24 01:57:37 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Tue Feb 24 2004 01:57:34 on modular [Seed = 1061522074] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (64.86.36.6) Time: Tue Feb 24 01:58:52 2004 Input: 2+2 Output: Magma V2.10-6 Tue Feb 24 2004 01:58:49 on modular [Seed = 877560422] ------------------------------------- 4 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (64.86.36.6) Time: Tue Feb 24 01:59:24 2004 Input: 2+2 7*7 Output: Magma V2.10-6 Tue Feb 24 2004 01:59:21 on modular [Seed = 593073425] ------------------------------------- >> 7*7 ^ User error: bad syntax Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (195.219.172.3) Time: Tue Feb 24 03:33:25 2004 Input: a:=[[1 1 1 1 1],[0 1 1 1 1],[0 0 1 1 1],[0 0 0 1 1],[0 0 0 0 1]]; b:=[[1 1 1 1 1],[1 0 1 1 1],[0 0 1 1 1],[0 0 1 1 0],[0 0 0 1 0]]; Isequivalent(a,b) Output: Magma V2.10-6 Tue Feb 24 2004 03:33:21 on modular [Seed = 1295384928] ------------------------------------- >> a:=[[1 1 1 1 1],[0 1 1 1 1],[0 0 1 1 1],[0 0 0 1 1],[0 0 0 0 1]]; ^ User error: bad syntax >> b:=[[1 1 1 1 1],[1 0 1 1 1],[0 0 1 1 1],[0 0 1 1 0],[0 0 0 1 0]]; ^ User error: bad syntax >> Isequivalent(a,b) ^ User error: Identifier 'a' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (195.219.172.7) Time: Tue Feb 24 03:36:05 2004 Input: a:=[[1,1,1,1,1],[0,1,1,1,1],[0,0,1,1,1],[0,0,0,1,1],[0,0,0,0,1]]; b:=[[1,1,1,1,1],[1,0,1,1,1],[0,0,1,1,1],[0,0,1,1,0],[0,0,0,1,0]]; Isequivalent(a,b) Output: Magma V2.10-6 Tue Feb 24 2004 03:36:02 on modular [Seed = 1127747533] ------------------------------------- >> Isequivalent(a,b) ^ User error: Identifier 'Isequivalent' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (195.219.172.8) Time: Tue Feb 24 03:38:12 2004 Input: a:=[[1,1,1,1,1],[0,1,1,1,1],[0,0,1,1,1],[0,0,0,1,1],[0,0,0,0,1]]; b:=[[1,1,1,1,1],[1,0,1,1,1],[0,0,1,1,1],[0,0,1,1,0],[0,0,0,1,0]]; IsEquivalent(a,b) Output: Magma V2.10-6 Tue Feb 24 2004 03:38:09 on modular [Seed = 911047483] ------------------------------------- >> IsEquivalent(a,b) ^ Runtime error in 'IsEquivalent': Bad argument types Argument types given: SeqEnum[SeqEnum], SeqEnum[SeqEnum] Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Tue Feb 24 04:30:06 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Tue Feb 24 2004 04:30:02 on modular [Seed = 3033525584] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (195.219.172.6) Time: Tue Feb 24 04:52:06 2004 Input: R:=FiniteField(2); LinearCode; Output: Magma V2.10-6 Tue Feb 24 2004 04:52:03 on modular [Seed = 2381763376] ------------------------------------- [4, 3, 1] Linear Code over GF(2) Generator matrix: [1 0 0 0] [0 1 0 0] [0 0 1 1] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (195.219.172.5) Time: Tue Feb 24 04:59:04 2004 Input: R:=FiniteField(2); LinearCode; Output: Magma V2.10-6 Tue Feb 24 2004 04:59:01 on modular [Seed = 2046892640] ------------------------------------- [4, 3, 1] Linear Code over GF(2) Generator matrix: [1 0 0 0] [0 1 0 0] [0 0 1 1] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host n137.ryd.student.liu.se. (130.236.215.137) Time: Tue Feb 24 05:45:54 2004 Input: A:=61958849225446588963639911677884335233383559879931775643742884030195943972894055108248309605912; B:=12615021631686710153710203123097870818516849934564206509607106566339254615752561260699527866942; p:=2467181678764049224047570663031240703802631; E:=ChangeRing(EllipticCurve([A,B]),GF(p)); print(E); Order(E); Output: Magma V2.10-6 Tue Feb 24 2004 05:45:40 on modular [Seed = 308902201] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 19908771235585897371547216824850697102713\ 90*x + 1054018290005476490418827699092888550807365 over GF(2467181678764049224047570663031240703802631) 2467181678764049224047789949030001358995352 Total time: 12.649 seconds, Total memory usage: 3.48MB ************** MAGMA ***************** Host 2(SERVFAIL) (195.219.172.3) Time: Tue Feb 24 06:29:59 2004 Input: K := FiniteField(3); C := LinearCode; Output: Magma V2.10-6 Tue Feb 24 2004 06:29:56 on modular [Seed = 2649155670] ------------------------------------- Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (195.219.172.5) Time: Tue Feb 24 06:31:56 2004 Input: K := FiniteField(3); C := LinearCode Output: Magma V2.10-6 Tue Feb 24 2004 06:31:52 on modular [Seed = 2281501136] ------------------------------------- Total time: 3.469 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (195.219.172.5) Time: Tue Feb 24 06:31:57 2004 Input: K := FiniteField(3); C := LinearCode> ; ^ User error: bad syntax Total time: 3.389 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (195.219.172.3) Time: Tue Feb 24 06:32:19 2004 Input: K := FiniteField(3); C := LinearCode Output: Magma V2.10-6 Tue Feb 24 2004 06:32:16 on modular [Seed = 158498633] ------------------------------------- Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (195.219.172.9) Time: Tue Feb 24 06:32:46 2004 Input: K := FiniteField(3); C := LinearCode Output: Magma V2.10-6 Tue Feb 24 2004 06:32:43 on modular [Seed = 308896841] ------------------------------------- Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (195.219.172.3) Time: Tue Feb 24 06:34:42 2004 Input: K := FiniteField(3); C := LinearCode A:=FiniteField(2); c=:= Output: Magma V2.10-6 Tue Feb 24 2004 06:34:39 on modular [Seed = 476539603] ------------------------------------- >> A:=FiniteField(2); ^ User error: bad syntax >> c=:= ^ User error: bad syntax Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (195.219.172.9) Time: Tue Feb 24 06:35:02 2004 Input: K := FiniteField(3); C := LinearCode A:=FiniteField(2); c:= Output: Magma V2.10-6 Tue Feb 24 2004 06:34:59 on modular [Seed = 643649733] ------------------------------------- >> A:=FiniteField(2); ^ User error: bad syntax >> c:= ^ User error: bad syntax Total time: 3.099 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (195.219.172.7) Time: Tue Feb 24 06:35:21 2004 Input: K := FiniteField(3); C := LinearCode A:=FiniteField(2); c:= Output: Magma V2.10-6 Tue Feb 24 2004 06:35:18 on modular [Seed = 860374469] ------------------------------------- >> A:=FiniteField(2); ^ User error: bad syntax >> c:= ^ User error: Identifier 'A' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (195.219.172.4) Time: Tue Feb 24 06:35:46 2004 Input: K := FiniteField(3); C := LinearCode A:=FiniteField(2); c:= Output: Magma V2.10-6 Tue Feb 24 2004 06:35:43 on modular [Seed = 1011305267] ------------------------------------- >> A:=FiniteField(2); ^ User error: bad syntax >> c:= ^ User error: bad syntax Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (195.219.172.7) Time: Tue Feb 24 06:36:13 2004 Input: K := FiniteField(3); C := LinearCode A:=FiniteField(2); c:= Output: Magma V2.10-6 Tue Feb 24 2004 06:36:10 on modular [Seed = 1161704047] ------------------------------------- >> A:=FiniteField(2); ^ User error: bad syntax >> c:= ^ User error: bad syntax Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (195.219.172.3) Time: Tue Feb 24 06:36:44 2004 Input: K := FiniteField(3); C := LinearCode A:=FiniteField(2); c:= Output: Magma V2.10-6 Tue Feb 24 2004 06:36:41 on modular [Seed = 1312110855] ------------------------------------- >> A:=FiniteField(2); ^ User error: bad syntax >> c:= ^ User error: bad syntax Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (195.219.172.3) Time: Tue Feb 24 06:37:51 2004 Input: K := FiniteField(3); C := LinearCode A:=FiniteField(2); c:= Output: Magma V2.10-6 Tue Feb 24 2004 06:37:48 on modular [Seed = 1478701012] ------------------------------------- >> A:=FiniteField(2); ^ User error: bad syntax >> c:= ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (195.219.172.6) Time: Tue Feb 24 06:38:44 2004 Input: K := FiniteField(3); C := LinearCode A:=FiniteField(2); c:=LinearCode Output: Magma V2.10-6 Tue Feb 24 2004 06:38:41 on modular [Seed = 1645811107] ------------------------------------- >> A:=FiniteField(2); ^ User error: bad syntax >> c:=LinearCode ^ User error: Identifier 'A' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (195.219.172.4) Time: Tue Feb 24 06:39:47 2004 Input: K := FiniteField(3); C := LinearCode K:=FiniteField(2); c:=LinearCode Output: Magma V2.10-6 Tue Feb 24 2004 06:39:42 on modular [Seed = 1796218005] ------------------------------------- >> K:=FiniteField(2); ^ User error: bad syntax Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (195.219.172.3) Time: Tue Feb 24 06:40:17 2004 Input: K := FiniteField(3); C := LinearCode K :=FiniteField(2); c :=LinearCode Output: Magma V2.10-6 Tue Feb 24 2004 06:40:13 on modular [Seed = 2063598438] ------------------------------------- >> K :=FiniteField(2); ^ User error: bad syntax Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (195.219.172.4) Time: Tue Feb 24 06:40:45 2004 Input: K := FiniteField(3); C := LinearCode R :=FiniteField(2); c :=LinearCode Output: Magma V2.10-6 Tue Feb 24 2004 06:40:42 on modular [Seed = 2231368894] ------------------------------------- >> R :=FiniteField(2); ^ User error: bad syntax >> c :=LinearCode ^ User error: Identifier 'R' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (195.219.172.4) Time: Tue Feb 24 06:41:26 2004 Input: K := FiniteField(3); C := LinearCode R := FiniteField(2); c := LinearCode Output: Magma V2.10-6 Tue Feb 24 2004 06:41:23 on modular [Seed = 2398484205] ------------------------------------- >> R := FiniteField(2); ^ User error: bad syntax >> c := LinearCode ^ User error: Identifier 'R' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (195.219.172.6) Time: Tue Feb 24 06:42:12 2004 Input: K := FiniteField(3); C := LinearCode R := FiniteField(2) c := LinearCode Output: Magma V2.10-6 Tue Feb 24 2004 06:42:09 on modular [Seed = 2548887302] ------------------------------------- >> R := FiniteField(2) ^ User error: bad syntax >> c := LinearCode ^ User error: Identifier 'R' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (195.219.172.3) Time: Tue Feb 24 06:43:13 2004 Input: K := FiniteField(3); C := LinearCode R := FiniteField(2) c := LinearCode Output: Magma V2.10-6 Tue Feb 24 2004 06:43:10 on modular [Seed = 2715474287] ------------------------------------- >> R := FiniteField(2) ^ User error: bad syntax >> c := LinearCode ^ User error: Identifier 'R' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (195.219.172.4) Time: Tue Feb 24 06:43:52 2004 Input: K := FiniteField(3); C := LinearCode R := FiniteField(2) D := LinearCode Output: Magma V2.10-6 Tue Feb 24 2004 06:43:49 on modular [Seed = 2882589534] ------------------------------------- >> R := FiniteField(2) ^ User error: bad syntax >> D := LinearCode ^ User error: Identifier 'R' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (195.219.172.8) Time: Tue Feb 24 06:44:27 2004 Input: R := FiniteField(2) D := LinearCode Output: Magma V2.10-6 Tue Feb 24 2004 06:44:24 on modular [Seed = 3033517484] ------------------------------------- >> D := LinearCode ^ User error: bad syntax Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (195.219.172.5) Time: Tue Feb 24 06:45:23 2004 Input: R := FiniteField(2) D := LinearCode Output: Magma V2.10-6 Tue Feb 24 2004 06:45:20 on modular [Seed = 3400643482] ------------------------------------- >> D := LinearCode ^ User error: bad syntax Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (195.219.172.3) Time: Tue Feb 24 06:46:05 2004 Input: R := FiniteField(2); D := LinearCode; Output: Magma V2.10-6 Tue Feb 24 2004 06:46:02 on modular [Seed = 3551046313] ------------------------------------- Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (195.219.172.6) Time: Tue Feb 24 06:46:21 2004 Input: R := FiniteField(2); D := LinearCode Output: Magma V2.10-6 Tue Feb 24 2004 06:46:18 on modular [Seed = 3701974358] ------------------------------------- Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (195.219.172.6) Time: Tue Feb 24 06:48:19 2004 Input: R := FiniteField(2); D := LinearCode KMatrixSpace(FiniteField(5), 2, 4); G := M ! [1,1,1,2, 3,2,1,4] Output: Magma V2.10-6 Tue Feb 24 2004 06:48:16 on modular [Seed = 3885800935] ------------------------------------- >> KMatrixSpace(FiniteField(5), 2, 4); ^ User error: bad syntax >> G := M ! [1,1,1,2, 3,2,1,4] ^ User error: Identifier 'M' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (195.219.172.9) Time: Tue Feb 24 06:49:30 2004 Input: R := FiniteField(2); D := LinearCode M := KMatrixSpace(FiniteField(5), 2, 4); G := M ! [1,1,1,2, 3,2,1,4] Output: Magma V2.10-6 Tue Feb 24 2004 06:49:27 on modular [Seed = 4035676855] ------------------------------------- >> M := KMatrixSpace(FiniteField(5), 2, 4); ^ User error: bad syntax >> G := M ! [1,1,1,2, 3,2,1,4] ^ User error: Identifier 'M' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Tue Feb 24 09:33:55 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-65+16*y^2-8*y; f1:=-8097+768*y^4-256*y^3-128*y; f2:=-645545+40960*y^6-11264*y^5-5120*y^3-4096*y; f3:=1391737725+20643840*y^8-4947968*y^7-2293760*y^5-1605632*y^3-1474560*y; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Tue Feb 24 2004 09:33:52 on modular [Seed = 1612398772] ------------------------------------- [ y + 32, 255 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Tue Feb 24 09:36:15 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-65+16*y^2-8*y; f1:=-8097+768*y^4-256*y^3-128*y; f2:=-645545+40960*y^6-11264*y^5-5120*y^3-4096*y; f3:=-9316720035+20643840*y^8-4947968*y^7-2293760*y^5-1605632*y^3-1474560*y; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Tue Feb 24 2004 09:36:12 on modular [Seed = 1963873325] ------------------------------------- [ y + 32, 255 ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Tue Feb 24 09:36:52 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-65+16*y^2-8*y; f1:=-8097+768*y^4-256*y^3-128*y; f2:=-873155+10240*y^6-2816*y^5-1280*y^3-1024*y; f3:=-9316720035+20643840*y^8-4947968*y^7-2293760*y^5-1605632*y^3-1474560*y; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Tue Feb 24 2004 09:36:49 on modular [Seed = 2114281467] ------------------------------------- [ y + 32, 255 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Tue Feb 24 09:37:05 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-65+16*y^2-8*y; f1:=-8097+768*y^4-256*y^3-128*y; f2:=-873155+10240*y^6-2816*y^5-1280*y^3-1024*y; f3:=-9316720035+20643840*y^8-4947968*y^7-2293760*y^5-1605632*y^3-1474560*y; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Tue Feb 24 2004 09:37:02 on modular [Seed = 2281481741] ------------------------------------- [ y + 32, 255 ] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Tue Feb 24 09:37:47 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-65+16*y^2-8*y; f1:=-8097+768*y^4-256*y^3-128*y; f2:=-873155+10240*y^6-2816*y^5-1280*y^3-1024*y; f3:=-1100061585+20643840*y^8-4947968*y^7-2293760*y^5-1605632*y^3-1474560*y; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Tue Feb 24 2004 09:37:44 on modular [Seed = 2297669940] ------------------------------------- [ y + 32, 255 ] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Tue Feb 24 09:38:35 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-65+16*y^2-8*y; f1:=-8097+768*y^4-256*y^3-128*y; f2:=-645545+40960*y^6-11264*y^5-5120*y^3-4096*y; f3:=1391687325+20643840*y^8-72056832*y^7+34406400*y^5-5849088*y^3-1416960*y+ 58720256*y^6-32112640*y^4+3713024*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Tue Feb 24 2004 09:38:32 on modular [Seed = 2464789374] ------------------------------------- [ y + 32, 1275 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Tue Feb 24 09:39:07 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-65+16*y^2-8*y; f1:=-8097+768*y^4-256*y^3-128*y; f2:=-645545+40960*y^6-11264*y^5-5120*y^3-4096*y; f3:=-9316770435+20643840*y^8-72056832*y^7+34406400*y^5-5849088*y^3-1416960*y+ 58720256*y^6-32112640*y^4+3713024*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Tue Feb 24 2004 09:39:04 on modular [Seed = 2615196055] ------------------------------------- [ y + 32, 255 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Tue Feb 24 09:39:40 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-65+16*y^2-8*y; f1:=-8097+768*y^4-256*y^3-128*y; f2:=-873155+10240*y^6-2816*y^5-1280*y^3-1024*y; f3:=-9316770435+20643840*y^8-72056832*y^7+34406400*y^5-5849088*y^3-1416960*y+ 58720256*y^6-32112640*y^4+3713024*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Tue Feb 24 2004 09:39:37 on modular [Seed = 2899807873] ------------------------------------- [ y + 32, 255 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Tue Feb 24 09:40:13 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-65+16*y^2-8*y; f1:=-8097+768*y^4-256*y^3-128*y; f2:=-873155+10240*y^6-2816*y^5-1280*y^3-1024*y; f3:=-1100111985+20643840*y^8-72056832*y^7+34406400*y^5-5849088*y^3-1416960*y+ 58720256*y^6-32112640*y^4+3713024*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Tue Feb 24 2004 09:40:10 on modular [Seed = 3167198962] ------------------------------------- [ y + 32, 255 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Tue Feb 24 09:40:47 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-65+16*y^2-8*y; f1:=-8097+768*y^4-256*y^3-128*y; f2:=-645065+40960*y^6-94208*y^5+17920*y^3-4672*y+69120*y^4+19200*y^2; f3:=1391687325+20643840*y^8-72056832*y^7+34406400*y^5-5849088*y^3-1416960*y+ 58720256*y^6-32112640*y^4+3713024*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Tue Feb 24 2004 09:40:44 on modular [Seed = 3334333614] ------------------------------------- [ y + 2, 15 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Tue Feb 24 09:41:22 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-65+16*y^2-8*y; f1:=-8097+768*y^4-256*y^3-128*y; f2:=-645065+40960*y^6-94208*y^5+17920*y^3-4672*y+69120*y^4+19200*y^2; f3:=-9316770435+20643840*y^8-72056832*y^7+34406400*y^5-5849088*y^3-1416960*y+ 58720256*y^6-32112640*y^4+3713024*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B Output: Magma V2.10-6 Tue Feb 24 2004 09:41:19 on modular [Seed = 3484740932] ------------------------------------- [ y + 2, 15 ] Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Tue Feb 24 09:41:52 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-65+16*y^2-8*y; f1:=-8097+768*y^4-256*y^3-128*y; f2:=464373+10240*y^6-23552*y^5+17280*y^4+4480*y^3; f3:=-9316770435+20643840*y^8-72056832*y^7+34406400*y^5-5849088*y^3-1416960*y+ 58720256*y^6-32112640*y^4+3713024*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Tue Feb 24 2004 09:41:49 on modular [Seed = 3500929657] ------------------------------------- [ y + 2, 3 ] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Tue Feb 24 09:42:27 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-65+16*y^2-8*y; f1:=-8097+768*y^4-256*y^3-128*y; f2:=464373+10240*y^6-23552*y^5+17280*y^4+4480*y^3; f3:=-1100111985+20643840*y^8-72056832*y^7+34406400*y^5-5849088*y^3-1416960*y+ 58720256*y^6-32112640*y^4+3713024*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Tue Feb 24 2004 09:42:24 on modular [Seed = 3651336973] ------------------------------------- [ y + 2, 3 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Tue Feb 24 09:42:59 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-65+16*y^2-8*y; f1:=-8097+768*y^4-256*y^3-128*y; f2:=-645065+40960*y^6-94208*y^5+17920*y^3-4672*y+69120*y^4+19200*y^2; f3:=1392090525+20643840*y^8-393216*y^7-35266560*y^5+8472576*y^3-1762560*y-24887296* y^6+49172480*y^4-12995584*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Tue Feb 24 2004 09:42:56 on modular [Seed = 3801726998] ------------------------------------- [ y + 2, 15 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Tue Feb 24 09:43:30 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-65+16*y^2-8*y; f1:=-8097+768*y^4-256*y^3-128*y; f2:=-645065+40960*y^6-94208*y^5+17920*y^3-4672*y+69120*y^4+19200*y^2; f3:=-9316367235+20643840*y^8-393216*y^7-35266560*y^5+8472576*y^3-1762560*y-24887296 *y^6+49172480*y^4-12995584*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Tue Feb 24 2004 09:43:27 on modular [Seed = 4103067647] ------------------------------------- [ y + 2, 15 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Tue Feb 24 09:43:58 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-65+16*y^2-8*y; f1:=-8097+768*y^4-256*y^3-128*y; f2:=464373+10240*y^6-23552*y^5+17280*y^4+4480*y^3; f3:=-9316367235+20643840*y^8-393216*y^7-35266560*y^5+8472576*y^3-1762560*y-24887296 *y^6+49172480*y^4-12995584*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Tue Feb 24 2004 09:43:55 on modular [Seed = 4253474514] ------------------------------------- [ y + 2, 3 ] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Tue Feb 24 09:44:29 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-65+16*y^2-8*y; f1:=-8097+768*y^4-256*y^3-128*y; f2:=464373+10240*y^6-23552*y^5+17280*y^4+4480*y^3; f3:=-1099708785+20643840*y^8-393216*y^7-35266560*y^5+8472576*y^3-1762560*y-24887296 *y^6+49172480*y^4-12995584*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Tue Feb 24 2004 09:44:26 on modular [Seed = 125576264] ------------------------------------- [ y + 2, 3 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Tue Feb 24 09:45:22 2004 Input: Factorization(255); Output: Magma V2.10-6 Tue Feb 24 2004 09:45:19 on modular [Seed = 493239911] ------------------------------------- [ <3, 1>, <5, 1>, <17, 1> ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Tue Feb 24 09:45:48 2004 Input: Factorization(1275); Output: Magma V2.10-6 Tue Feb 24 2004 09:45:45 on modular [Seed = 610207672] ------------------------------------- [ <3, 1>, <5, 2>, <17, 1> ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sv4.ictp.trieste.it. (140.105.16.64) Time: Tue Feb 24 09:49:21 2004 Input: R:= PolynomialRing(Rationals()); f:=x^2-x+1; K:=NumberField(f); P:=MaximalOrder(K); M:=MatrixRing( P , 15 ) ! [ 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, w, 0, -1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1+w, -1, 1-w, w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2-w, -1+w, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, 0, w, 1-2*w, -1, -1+w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, -w, -1, -w, -1, -w, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, w, 1-w, -1, 0, 1, 1-2*w, -1+w, 3, 0, 0, 0, 0, 0, 0, -w, 1-w, w, -w, -1, -1+w, 1, 0, 0, 3, 0, 0, 0, 0, 0, -w, 1-w, -1, 0, 0, 0, -w, w, 1-w, 0, 3, 0, 0, 0, 0, 0, 0, w, 0, 0, -1+w, w, -w, -1, 1, -1-w, 3, 0, 0, 0, 0, 0, -w, -1+w, w, -w, -1, 1-w, -w, -w, -1, 1, 3, 0, 0, -1+w, -w, 1, 0, 1, w, -w, -1+w, 0, 1-w, 1-w, 0, -1+w, 3, 0, -1, -1, -w, 1, 1, -w, 0, 0, -1+w, -1, 0, -w, 1-w, 0, 3 ]; for i := 1 to 15 do for j := i+1 to 15 do M[i,j]:=Trace(M[j,i])-M[j,i]; end for; end for; N:= MatrixRing( Integers() , 30 ) ! 0; for i := 1 to 15 do for j := 1 to 15 do N[i,j]:=Trace(M[i,j]); N[15+i,15+j]:=N[i,j]; N[15+i,j]:=Trace(w*M[i,j]); N[j,15+i]:=N[15+i,j]; end for; end for; L := LatticeWithGram(N); S := ShortestVectors(L); d:=#S; d; G := EmptyGraph(d); for i := 1 to d do for j := i+1 to d do if not (S[i],S[j]) eq 0 then AddEdge(~G, i, j); end if; end for; end for; Components(G); T := sub< L | S >; r := Rank(T); r; Determinant(L); H := AutomorphismGroup(L); #H; FactoredOrder(H); H1:=DerivedGroup(H); FactoredOrder(H1); H2:=DerivedGroup(H1); FactoredOrder(H2); H3:=DerivedGroup(H2); FactoredOrder(H3); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Feb 24 2004 09:48:58 on modular [Seed = 1211329559] ------------------------------------- 3 [ { 1, 2, 3 } ] 2 14348907 Errors: /home/mfd/gomagma: line 2: 17741 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host sv4.ictp.trieste.it. (140.105.16.64) Time: Tue Feb 24 09:50:40 2004 Input: R:= PolynomialRing(Rationals()); f:=x^2-x+1; K:=NumberField(f); P:=MaximalOrder(K); M:=MatrixRing( P , 15 ) ! [ 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, -w, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, -w, 2-w, -1+w, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1-2*w, 1, 0, 1-w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, w, -1+w, -1+w, -1+2*w, -1+w, 3, 0, 0, 0, 0, 0, 0, 0, 1-w, 0, w, 1, w, w, w, 1-w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 2-w, -1, 1-w, 1, w, 0, -w, 3, 0, 0, 0, 0, 0, 1-w, 1-w, -1+w, 0, w, -1+w, -w, 0, 1, -1, 3, 0, 0, 0, 0, -w, -w, 1-w, -w, 1, 1, 0, -1, -w, 1, -w, 3, 0, 0, 0, -w, 0, 0, w, 0, 0, -1+w, 0, 1, -1, 1-w, 0, 3, 0, 0, -w, 0, 0, 0, 1-w, 1-w, -w, -w, -w, 0, 0, 0, w, 3, 0, -w, 1-w, -1+w, -1, -1+w, w, -w, 1, 0, -w, 1, 0, 0, 0, 4 ]; for i := 1 to 15 do for j := i+1 to 15 do M[i,j]:=Trace(M[j,i])-M[j,i]; end for; end for; N:= MatrixRing( Integers() , 30 ) ! 0; for i := 1 to 15 do for j := 1 to 15 do N[i,j]:=Trace(M[i,j]); N[15+i,15+j]:=N[i,j]; N[15+i,j]:=Trace(w*M[i,j]); N[j,15+i]:=N[15+i,j]; end for; end for; L := LatticeWithGram(N); S := ShortestVectors(L); d:=#S; d; G := EmptyGraph(d); for i := 1 to d do for j := i+1 to d do if not (S[i],S[j]) eq 0 then AddEdge(~G, i, j); end if; end for; end for; Components(G); T := sub< L | S >; r := Rank(T); r; Determinant(L); H := AutomorphismGroup(L); #H; FactoredOrder(H); H1:=DerivedGroup(H); FactoredOrder(H1); H2:=DerivedGroup(H1); FactoredOrder(H2); H3:=DerivedGroup(H2); FactoredOrder(H3); Output: ** WARNING: Computation used more memory than allowed. ** Magma V2.10-6 Tue Feb 24 2004 09:50:20 on modular [Seed = 2097568212] ------------------------------------- 9 [ { 1, 2, 3, 4, 5, 6, 7, 8, 9 } ] 4 14348907 Current total memory usage: 83.5MB, failed memory request: 43.4MB System Error: User memory limit has been reached >> #H; FactoredOrder(H); ^ Runtime error: Variable 'H' has not been initialized >> #H; FactoredOrder(H); ^ User error: Identifier 'H' has not been declared or assigned >> H1:=DerivedGroup(H); FactoredOrder(H1); ^ User error: Identifier 'H' has not been declared or assigned >> H1:=DerivedGroup(H); FactoredOrder(H1); ^ User error: Identifier 'H1' has not been declared or assigned >> H2:=DerivedGroup(H1); FactoredOrder(H2); ^ User error: Identifier 'H1' has not been declared or assigned >> H2:=DerivedGroup(H1); FactoredOrder(H2); ^ User error: Identifier 'H2' has not been declared or assigned >> H3:=DerivedGroup(H2); FactoredOrder(H3); ^ User error: Identifier 'H2' has not been declared or assigned >> H3:=DerivedGroup(H2); FactoredOrder(H3); ^ User error: Identifier 'H3' has not been declared or assigned Total time: 20.239 seconds, Total memory usage: 87.60MB ************** MAGMA ***************** Host sv4.ictp.trieste.it. (140.105.16.64) Time: Tue Feb 24 09:52:39 2004 Input: R:= PolynomialRing(Rationals()); f:=x^2-x+1; K:=NumberField(f); P:=MaximalOrder(K); M:=MatrixRing( P , 15 ) ! [ 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, w, 0, -1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1+w, -1, 1-w, w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2-w, -1+w, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, 0, w, 1-2*w, -1, -1+w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, -w, -1, -w, -1, -w, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, w, 1-w, -1, 0, 1, 1-2*w, -1+w, 3, 0, 0, 0, 0, 0, 0, -w, 1-w, w, -w, -1, -1+w, 1, 0, 0, 3, 0, 0, 0, 0, 0, -w, 1-w, -1, 0, 0, 0, -w, w, 1-w, 0, 3, 0, 0, 0, 0, 0, 0, w, 0, 0, -1+w, w, -w, -1, 1, -1-w, 3, 0, 0, 0, 0, 0, -w, -1+w, w, -w, -1, 1-w, -w, -w, -1, 1, 3, 0, 0, -1+w, -w, 1, 0, 1, w, -w, -1+w, 0, 1-w, 1-w, 0, -1+w, 3, 0, -1, -1, -w, 1, 1, -w, 0, 0, -1+w, -1, 0, -w, 1-w, 0, 3 ]; for i := 1 to 15 do for j := i+1 to 15 do M[i,j]:=Trace(M[j,i])-M[j,i]; end for; end for; N:= MatrixRing( Integers() , 30 ) ! 0; for i := 1 to 15 do for j := 1 to 15 do N[i,j]:=Trace(M[i,j]); N[15+i,15+j]:=N[i,j]; N[15+i,j]:=Trace(w*M[i,j]); N[j,15+i]:=N[15+i,j]; end for; end for; L := LatticeWithGram(N); S := ShortestVectors(L); d:=#S; d; G := EmptyGraph(d); for i := 1 to d do for j := i+1 to d do if not (S[i],S[j]) eq 0 then AddEdge(~G, i, j); end if; end for; end for; Components(G); T := sub< L | S >; r := Rank(T); r; Determinant(L); H := AutomorphismGroup(L); #H; FactoredOrder(H); H1:=DerivedGroup(H); FactoredOrder(H1); H2:=DerivedGroup(H1); FactoredOrder(H2); H3:=DerivedGroup(H2); FactoredOrder(H3); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Feb 24 2004 09:52:16 on modular [Seed = 2231345569] ------------------------------------- 3 [ { 1, 2, 3 } ] 2 14348907 Errors: /home/mfd/gomagma: line 2: 17793 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Feb 24 13:47:08 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); R; K; Output: Magma V2.10-6 Tue Feb 24 2004 13:47:05 on modular [Seed = 476561469] ------------------------------------- Univariate Polynomial Ring in x over Rational Field Number Field with defining polynomial x^5 + 7*x^4 + 3*x^2 - x + 1 over the Rational Field Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Feb 24 13:48:09 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); R; K; Output: Magma V2.10-6 Tue Feb 24 2004 13:48:06 on modular [Seed = 376294008] ------------------------------------- >> R := PolynomialRing(RationalField()); ^ Runtime error in 'AssignNames': Argument 2 must have length 1 >> K := NumberField(x^5+7*x^4+3*x^2-x+1); ^ User error: Identifier 'x' has not been declared or assigned Univariate Polynomial Ring over Rational Field >> K;; ^ User error: Identifier 'K' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Feb 24 13:48:28 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); R; K; Output: Magma V2.10-6 Tue Feb 24 2004 13:48:25 on modular [Seed = 542899281] ------------------------------------- Univariate Polynomial Ring in x over Rational Field Number Field with defining polynomial x^5 + 7*x^4 + 3*x^2 - x + 1 over the Rational Field Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Feb 24 13:50:03 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); R; K; Output: Magma V2.10-6 Tue Feb 24 2004 13:50:00 on modular [Seed = 960685545] ------------------------------------- >> R := PolynomialRing(RationalField()); ^ User error: bad syntax >> K := NumberField(x^5+7*x^4+3*x^2-x+1); ^ User error: Identifier 'x' has not been declared or assigned >> R; ^ User error: Identifier 'R' has not been declared or assigned >> K; ^ User error: Identifier 'K' has not been declared or assigned Total time: 3.099 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Feb 24 13:50:13 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); R; K; Output: Magma V2.10-6 Tue Feb 24 2004 13:50:10 on modular [Seed = 1228051875] ------------------------------------- Univariate Polynomial Ring in x over Rational Field Number Field with defining polynomial x^5 + 7*x^4 + 3*x^2 - x + 1 over the Rational Field Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Feb 24 13:50:59 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); R; K; OK:=MaximalOrder(K); I:=2*OK; Factorization(I); Output: Magma V2.10-6 Tue Feb 24 2004 13:50:56 on modular [Seed = 1111072602] ------------------------------------- Univariate Polynomial Ring in x over Rational Field Number Field with defining polynomial x^5 + 7*x^4 + 3*x^2 - x + 1 over the Rational Field [ ] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Feb 24 13:52:01 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); R; K; OK:=MaximalOrder(K); I:=2*OK; Factorization(I); [K!OK.i; i in [1..5]]; Output: Magma V2.10-6 Tue Feb 24 2004 13:51:58 on modular [Seed = 1546092826] ------------------------------------- Univariate Polynomial Ring in x over Rational Field Number Field with defining polynomial x^5 + 7*x^4 + 3*x^2 - x + 1 over the Rational Field [ ] >> [K!OK.i; i in [1..5]];; ^ User error: bad syntax Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Feb 24 13:52:23 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); R; K; OK:=MaximalOrder(K); I:=2*OK; Factorization(I); [K ! OK .i; i in [1..5]]; Output: Magma V2.10-6 Tue Feb 24 2004 13:52:20 on modular [Seed = 1429112889] ------------------------------------- Univariate Polynomial Ring in x over Rational Field Number Field with defining polynomial x^5 + 7*x^4 + 3*x^2 - x + 1 over the Rational Field [ ] >> [K ! OK .i; i in [1..5]];; ^ User error: bad syntax Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Feb 24 13:55:51 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); R; K; E:=EquationOrder(K); OK:=MaximalOrder(K); Index(OK, E); I:=2*OK; Factorization(I); Output: Magma V2.10-6 Tue Feb 24 2004 13:55:48 on modular [Seed = 1696512857] ------------------------------------- Univariate Polynomial Ring in x over Rational Field Number Field with defining polynomial x^5 + 7*x^4 + 3*x^2 - x + 1 over the Rational Field 1 [ ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Feb 24 13:56:25 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); R; K; E:=EquationOrder(K); E; OK:=MaximalOrder(K); OK; Index(OK, E); I:=2*OK; Factorization(I); Output: Magma V2.10-6 Tue Feb 24 2004 13:56:22 on modular [Seed = 2114297888] ------------------------------------- Univariate Polynomial Ring in x over Rational Field Number Field with defining polynomial x^5 + 7*x^4 + 3*x^2 - x + 1 over the Rational Field Equation Order with defining polynomial x^5 + 7*x^4 + 3*x^2 - x + 1 over its ground order Maximal Equation Order with defining polynomial x^5 + 7*x^4 + 3*x^2 - x + 1 over its ground order 1 [ ] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Feb 24 14:00:43 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); R; K; E:=EquationOrder(K); E; OK:=MaximalOrder(K); OK; Index(OK, E); I:=2*OK; Factorization(I); OK.1; Output: Magma V2.10-6 Tue Feb 24 2004 14:00:40 on modular [Seed = 2163957712] ------------------------------------- Univariate Polynomial Ring in x over Rational Field Number Field with defining polynomial x^5 + 7*x^4 + 3*x^2 - x + 1 over the Rational Field Equation Order with defining polynomial x^5 + 7*x^4 + 3*x^2 - x + 1 over its ground order Maximal Equation Order with defining polynomial x^5 + 7*x^4 + 3*x^2 - x + 1 over its ground order 1 [ ] E.1 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Feb 24 14:02:15 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); E:=EquationOrder(K); OK:=MaximalOrder(K); OK; Index(OK, E); I:=2*OK; Factorization(I); K!OK.1; Output: Magma V2.10-6 Tue Feb 24 2004 14:02:12 on modular [Seed = 2899800848] ------------------------------------- Maximal Equation Order with defining polynomial x^5 + 7*x^4 + 3*x^2 - x + 1 over its ground order 1 [ ] 1 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Feb 24 14:08:25 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); E:=EquationOrder(K); OK:=MaximalOrder(K); OK; Index(OK, E); I:=2*OK; Factorization(I); K!OK.2; Output: Magma V2.10-6 Tue Feb 24 2004 14:08:22 on modular [Seed = 3066910616] ------------------------------------- Maximal Equation Order with defining polynomial x^5 + 7*x^4 + 3*x^2 - x + 1 over its ground order 1 [ ] a Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Feb 24 14:09:02 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); E:=EquationOrder(K); OK:=MaximalOrder(K); Index(OK, E); I:=2*OK; Factorization(I); [K!OK.i : i in [1..5]];; Output: Magma V2.10-6 Tue Feb 24 2004 14:08:59 on modular [Seed = 3250200706] ------------------------------------- 1 [ ] [ 1, a, a^2, a^3, a^4 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Feb 24 14:10:29 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+1); E:=EquationOrder(K); OK:=MaximalOrder(K); Index(OK, E); Output: Magma V2.10-6 Tue Feb 24 2004 14:10:25 on modular [Seed = 3568252285] ------------------------------------- 1 Total time: 3.900 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Feb 24 14:10:53 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+1); E:=EquationOrder(K); OK:=MaximalOrder(K); Index(OK, E); I:=2004*OK; Factorization(I); [K!OK.i : i in [1..5]];; Output: Magma V2.10-6 Tue Feb 24 2004 14:10:50 on modular [Seed = 3986033759] ------------------------------------- 1 [ , , ] >> [K!OK.i : i in [1..5]];;; ^ Runtime error in '.': Value for name index (3) should be in the range [1..2] Total time: 3.209 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Feb 24 14:11:07 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+1); E:=EquationOrder(K); OK:=MaximalOrder(K); Index(OK, E); I:=2004*OK; Factorization(I); [K!OK.i : i in [1, 2]];; Output: Magma V2.10-6 Tue Feb 24 2004 14:11:03 on modular [Seed = 3885762087] ------------------------------------- 1 [ , , ] [ 1, a ] Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Feb 24 14:13:25 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^6+x^5+x^4+x^3+x^2+x+1); E:=EquationOrder(K); OK:=MaximalOrder(K); Index(OK, E); I:=7*OK; Factorization(I); [K!OK.i : i in [1, 2]];; Output: Magma V2.10-6 Tue Feb 24 2004 14:13:22 on modular [Seed = 4035646122] ------------------------------------- 1 [ ] [ 1, a ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Feb 24 14:13:38 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^6+x^5+x^4+x^3+x^2+x+1); E:=EquationOrder(K); OK:=MaximalOrder(K); Index(OK, E); I:=7*OK; Factorization(I); [K!OK.i : i in [1, 6]];; Output: Magma V2.10-6 Tue Feb 24 2004 14:13:35 on modular [Seed = 191949149] ------------------------------------- 1 [ ] [ 1, a^5 ] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Feb 24 14:14:12 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^6+x^5+x^4+x^3+x^2+x+1); E:=EquationOrder(K); OK:=MaximalOrder(K); Index(OK, E); I:=7*OK; Factorization(I); J:=3*OK; Factorization(J); [K!OK.i : i in [1..6]];; Output: Magma V2.10-6 Tue Feb 24 2004 14:14:09 on modular [Seed = 41541770] ------------------------------------- 1 [ ] [ ] [ 1, a, a^2, a^3, a^4, a^5 ] Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Feb 24 14:15:09 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-5); E:=EquationOrder(K); OK:=MaximalOrder(K); Index(OK, E); Output: Magma V2.10-6 Tue Feb 24 2004 14:15:06 on modular [Seed = 275509923] ------------------------------------- 2 Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Feb 24 14:15:45 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-5); E:=EquationOrder(K); OK:=MaximalOrder(K); Index(OK, E); I:=(3/8)*OK; I; Output: Magma V2.10-6 Tue Feb 24 2004 14:15:42 on modular [Seed = 726714876] ------------------------------------- 2 Fractional Principal Ideal of OK Generator: 3/8*OK.1 Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Feb 24 14:16:14 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-5); E:=EquationOrder(K); OK:=MaximalOrder(K); Index(OK, E); I:=(3/8)*OK; I; Factorization(I); Output: Magma V2.10-6 Tue Feb 24 2004 14:16:11 on modular [Seed = 576307408] ------------------------------------- 2 Fractional Principal Ideal of OK Generator: 3/8*OK.1 [ , ] Total time: 3.049 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Feb 24 14:16:39 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-5); E:=EquationOrder(K); OK:=MaximalOrder(K); Index(OK, E); I:=(3/8)*OK; I; Factorization(I); [K!OK.i : i in [1,2]];; Output: Magma V2.10-6 Tue Feb 24 2004 14:16:36 on modular [Seed = 1028054560] ------------------------------------- 2 Fractional Principal Ideal of OK Generator: 3/8*OK.1 [ , ] [ 1, 1/2*(a + 1) ] Total time: 3.039 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Feb 24 14:16:50 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-5); E:=EquationOrder(K); OK:=MaximalOrder(K); Index(OK, E); I:=(3/8)*OK; I; Factorization(I); [K!OK.i : i in [1,2]]; Output: Magma V2.10-6 Tue Feb 24 2004 14:16:47 on modular [Seed = 877647650] ------------------------------------- 2 Fractional Principal Ideal of OK Generator: 3/8*OK.1 [ , ] [ 1, 1/2*(a + 1) ] Total time: 3.019 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Feb 24 14:17:50 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+7); E:=EquationOrder(K); OK:=MaximalOrder(K); Index(OK, E); Output: Magma V2.10-6 Tue Feb 24 2004 14:17:47 on modular [Seed = 1328851997] ------------------------------------- 2 Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Feb 24 14:18:22 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+5); E:=EquationOrder(K); OK:=MaximalOrder(K); Index(OK, E); Output: Magma V2.10-6 Tue Feb 24 2004 14:18:19 on modular [Seed = 1495448107] ------------------------------------- 1 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Feb 24 14:18:32 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+7); E:=EquationOrder(K); OK:=MaximalOrder(K); Index(OK, E); Output: Magma V2.10-6 Tue Feb 24 2004 14:18:29 on modular [Seed = 1395175647] ------------------------------------- 2 Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Feb 24 14:19:16 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+7); E:=EquationOrder(K); OK:=MaximalOrder(K); Index(OK, E); I:=2*E; I; Output: Magma V2.10-6 Tue Feb 24 2004 14:19:13 on modular [Seed = 1779534290] ------------------------------------- 2 Principal Ideal of E Generator: [2, 0] Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Feb 24 14:19:45 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+7); E:=EquationOrder(K); OK:=MaximalOrder(K); Index(OK, E); I:=2*E; I; Factorization(I); Output: Magma V2.10-6 Tue Feb 24 2004 14:19:42 on modular [Seed = 1696499362] ------------------------------------- 2 Principal Ideal of E Generator: [2, 0] >> Factorization(I);; ^ Runtime error in 'Factorization': Order associated with ideal argument 1 is not known to be maximal Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Feb 24 15:28:32 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+1); E:=EquationOrder(K); OK:=MaximalOrder(K); Index(OK, E); I:=5*OK; Factorization(I); [K!OK.i : i in [1, 2]]; Output: Magma V2.10-6 Tue Feb 24 2004 15:28:29 on modular [Seed = 359589619] ------------------------------------- 1 [ , ] [ 1, a ] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h0050da316214.ne.client2.attbi.com. (65.96.168.112) Time: Tue Feb 24 18:07:34 2004 Input: D := LatticeDatabase(); Lat:=Lattice(D,2,16); dual_semigp_gens([[1,0],3,4]],Lat); Output: Magma V2.10-6 Tue Feb 24 2004 18:07:30 on modular [Seed = 1178460025] ------------------------------------- >> dual_semigp_gens([[1,0],3,4]],Lat);; ^ User error: Could not find a valid universe for the sequence Total time: 3.029 seconds, Total memory usage: 2.11MB ************** MAGMA ***************** Host h0050da316214.ne.client2.attbi.com. (65.96.168.112) Time: Tue Feb 24 18:07:49 2004 Input: D := LatticeDatabase(); Lat:=Lattice(D,2,16); dual_semigp_gens([[1,0],[3,4]],Lat); Output: Magma V2.10-6 Tue Feb 24 2004 18:07:46 on modular [Seed = 1495449622] ------------------------------------- >> dual_semigp_gens([[1,0],[3,4]],Lat);; ^ User error: Identifier 'dual_semigp_gens' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 2.11MB ************** MAGMA ***************** Host h0050da316214.ne.client2.attbi.com. (65.96.168.112) Time: Tue Feb 24 18:08:47 2004 Input: load "/home/wdj/magmafiles/toric.mag"' D := LatticeDatabase(); Lat:=Lattice(D,2,16); dual_semigp_gens([[1,0],[3,4]],Lat); Output: WARNING: MAGMA command contains unsafe command 'file', so it will not be executed. ************** MAGMA ***************** Host h0050da316214.ne.client2.attbi.com. (65.96.168.112) Time: Tue Feb 24 18:09:03 2004 Input: D := LatticeDatabase(); Lat:=Lattice(D,2,16); dual_semigp_gens([[1,0],[3,4]],Lat); Output: Magma V2.10-6 Tue Feb 24 2004 18:09:00 on modular [Seed = 1746137577] ------------------------------------- >> dual_semigp_gens([[1,0],[3,4]],Lat);; ^ User error: Identifier 'dual_semigp_gens' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 2.11MB ************** MAGMA ***************** Host roam149-56.student.harvard.edu. (140.247.149.56) Time: Tue Feb 24 20:49:21 2004 Input: Q:=RationalField(Rationals()); K:=NumberField(x^2+1); OK:=MaximalOrder(K); I:=2004*OK; Factorization(I); Output: Magma V2.10-6 Tue Feb 24 2004 20:49:18 on modular [Seed = 3969340412] ------------------------------------- >> Q:=RationalField(Rationals()); ^ Runtime error in 'RationalField': Bad argument types Argument types given: FldRat >> K:=NumberField(x^2+1); ^ User error: Identifier 'x' has not been declared or assigned >> OK:=MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> I:=2004*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I);; ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-56.student.harvard.edu. (140.247.149.56) Time: Tue Feb 24 20:51:58 2004 Input: Q:=PolynomialRing(RationalField()); K:=NumberFieldQ(x^2+1); OK:=MaximalOrder(K); I:=2004*OK; Factorization(I); Output: Magma V2.10-6 Tue Feb 24 2004 20:51:55 on modular [Seed = 4253434440] ------------------------------------- >> K:=NumberFieldQ(x^2+1); ^ User error: Identifier 'NumberFieldQ' has not been declared or assigned >> OK:=MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> I:=2004*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I);; ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-56.student.harvard.edu. (140.247.149.56) Time: Tue Feb 24 20:52:10 2004 Input: Q:=PolynomialRing(RationalField()); K:=NumberField(x^2+1); OK:=MaximalOrder(K); I:=2004*OK; Factorization(I); Output: Magma V2.10-6 Tue Feb 24 2004 20:52:07 on modular [Seed = 4085795898] ------------------------------------- [ , , ] Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-56.student.harvard.edu. (140.247.149.56) Time: Tue Feb 24 20:54:28 2004 Input: Q:=PolynomialRing(RationalField()); K:=NumberField(x^6+x^5+x^4+x^3+x^2+x+1); OK:=MaximalOrder(K); I:=7*OK; Factorization(I); Output: Magma V2.10-6 Tue Feb 24 2004 20:54:25 on modular [Seed = 141838422] ------------------------------------- [ ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-56.student.harvard.edu. (140.247.149.56) Time: Tue Feb 24 20:55:23 2004 Input: Q:=PolynomialRing(RationalField()); K:=NumberField(x^6+x^5+x^4+x^3+x^2+x+1); OK:=MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Tue Feb 24 2004 20:55:20 on modular [Seed = 459758492] ------------------------------------- [ ] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-56.student.harvard.edu. (140.247.149.56) Time: Tue Feb 24 20:55:27 2004 Input: Q:=PolynomialRing(RationalField()); K:=NumberField(x^6+x^5+x^4+x^3+x^2+x+1); OK:=MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Tue Feb 24 2004 20:55:24 on modular [Seed = 309219985] ------------------------------------- [ ] Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-56.student.harvard.edu. (140.247.149.56) Time: Tue Feb 24 20:57:22 2004 Input: Q:=PolynomialRing(RationalField()); K:=NumberField(x^6+x^5+x^4+x^3+x^2+x+1); OK:=MaximalOrder(K); I:=3*OK; J:=8*OK; M:=I/J Factorization(M); Output: Magma V2.10-6 Tue Feb 24 2004 20:57:19 on modular [Seed = 693463513] ------------------------------------- >> Factorization(M);; ^ User error: bad syntax Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-56.student.harvard.edu. (140.247.149.56) Time: Tue Feb 24 20:57:36 2004 Input: Q:=PolynomialRing(RationalField()); K:=NumberField(x^6+x^5+x^4+x^3+x^2+x+1); OK:=MaximalOrder(K); I:=3*OK; J:=8*OK; M:=I/J; Factorization(M); Output: Magma V2.10-6 Tue Feb 24 2004 20:57:33 on modular [Seed = 542925090] ------------------------------------- [ , , ] Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-56.student.harvard.edu. (140.247.149.56) Time: Tue Feb 24 20:59:37 2004 Input: Q:=PolynomialRing(RationalField()); K:=NumberField(x^6+x^5+x^4+x^3+x^2+x+1); OK:=MaximalOrder(K); I:=3*OK; J:=8*OK; M:=I/J; Factorization(M); Output: Magma V2.10-6 Tue Feb 24 2004 20:59:34 on modular [Seed = 810316217] ------------------------------------- [ , , ] Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-56.student.harvard.edu. (140.247.149.56) Time: Tue Feb 24 21:02:20 2004 Input: Q:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK:=MaximalOrder(K); I:=3*OK; J:=8*OK; M:=I/J; Factorization(M); Output: Magma V2.10-6 Tue Feb 24 2004 21:02:17 on modular [Seed = 1779837004] ------------------------------------- [ , ] Total time: 2.999 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Feb 24 21:11:23 2004 Input: Q:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK:=MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Tue Feb 24 2004 21:11:20 on modular [Seed = 2348273612] ------------------------------------- [ ] Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Feb 24 21:11:35 2004 Input: Q:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK:=MaximalOrder(K); I:=2*OK; Factorization(I); Output: Magma V2.10-6 Tue Feb 24 2004 21:11:32 on modular [Seed = 2197735129] ------------------------------------- [ ] Total time: 2.919 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 02:28:57 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-129+16*y^2-8*y; f1:=-24609+768*y^4-256*y^3-128*y; f2:=-5243985+40960*y^6-11264*y^5-5120*y^3-4096*y; f3:=-10570042035+20643840*y^8-4947968*y^7-2293760*y^5-1605632*y^3-1474560*y; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 02:28:54 on modular [Seed = 3968918088] ------------------------------------- [ 2*y^2 + 2*y + 24, 3*y + 48, 63 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 02:29:40 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-129+16*y^2-8*y; f1:=-24609+768*y^4-256*y^3-128*y; f2:=-5243985+40960*y^6-11264*y^5-5120*y^3-4096*y; f3:=-10569991635+20643840*y^8-4947968*y^7-2293760*y^5-1605632*y^3-1474560*y; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 02:29:37 on modular [Seed = 342366950] ------------------------------------- [ 2*y^2 + 2*y + 24, 3*y + 48, 63 ] Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 02:30:09 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-129+16*y^2-8*y; f1:=-24609+768*y^4-256*y^3-128*y; f2:=-1311075+10240*y^6-2816*y^5-1280*y^3-1024*y; f3:=-10569991635+20643840*y^8-4947968*y^7-2293760*y^5-1605632*y^3-1474560*y; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 02:30:06 on modular [Seed = 192349670] ------------------------------------- [ y^2 + y + 12, 3*y + 48, 63 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 02:30:45 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-129+16*y^2-8*y; f1:=-24609+768*y^4-256*y^3-128*y; f2:=-1311075+10240*y^6-2816*y^5-1280*y^3-1024*y; f3:=-10570261905+20643840*y^8-4947968*y^7-2293760*y^5-1605632*y^3-1474560*y; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 02:30:42 on modular [Seed = 843988227] ------------------------------------- [ y^2 + y + 12, 3*y + 48, 63 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 02:31:14 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-129+16*y^2-8*y; f1:=-24609+768*y^4-256*y^3-128*y; f2:=-5243985+40960*y^6-11264*y^5-5120*y^3-4096*y; f3:=-10570092435+20643840*y^8-72056832*y^7+34406400*y^5-5849088*y^3-1416960*y+ 58720256*y^6-32112640*y^4+3713024*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 02:31:11 on modular [Seed = 960837141] ------------------------------------- [ 2*y^2 + 2*y + 24, 3*y + 48, 63 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 02:31:44 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-129+16*y^2-8*y; f1:=-24609+768*y^4-256*y^3-128*y; f2:=-5243985+40960*y^6-11264*y^5-5120*y^3-4096*y f3:=-10570042035+20643840*y^8-72056832*y^7+34406400*y^5-5849088*y^3-1416960*y+ 58720256*y^6-32112640*y^4+3713024*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 02:31:41 on modular [Seed = 542912366] ------------------------------------- >> f3:=-10570042035+20643840*y^8-72056832*y^7+34406400*y^5-5849088*y^3-1416960 ^ User error: bad syntax 58720256*y^6 - 32112640*y^4 + 3713024*y^2 >> I:=ideal; ^ User error: Identifier 'f2' has not been declared or assigned >> B:=GroebnerBasis(I:Al:="Direct"); ^ User error: Identifier 'I' has not been declared or assigned >> B; ^ User error: Identifier 'B' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 02:32:20 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-129+16*y^2-8*y; f1:=-24609+768*y^4-256*y^3-128*y; f2:=-5243985+40960*y^6-11264*y^5-5120*y^3-4096*y f3:=-10570042035+20643840*y^8-72056832*y^7+34406400*y^5-5849088*y^3-1416960*y+ 58720256*y^6-32112640*y^4+3713024*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 02:32:17 on modular [Seed = 793977021] ------------------------------------- >> f3:=-10570042035+20643840*y^8-72056832*y^7+34406400*y^5-5849088*y^3-1416960 ^ User error: bad syntax 58720256*y^6 - 32112640*y^4 + 3713024*y^2 >> I:=ideal; ^ User error: Identifier 'f2' has not been declared or assigned >> B:=GroebnerBasis(I:Al:="Direct"); ^ User error: Identifier 'I' has not been declared or assigned >> B; ^ User error: Identifier 'B' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 02:32:55 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-129+16*y^2-8*y; f1:=-24609+768*y^4-256*y^3-128*y; f2:=-5243985+40960*y^6-11264*y^5-5120*y^3-4096*y; f3:=-10570042035+20643840*y^8-72056832*y^7+34406400*y^5-5849088*y^3-1416960*y+ 58720256*y^6-32112640*y^4+3713024*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 02:32:52 on modular [Seed = 1445616097] ------------------------------------- [ 2*y^2 + 2*y + 24, 3*y + 48, 63 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 02:33:28 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-129+16*y^2-8*y; f1:=-24609+768*y^4-256*y^3-128*y; f2:=-1311075+10240*y^6-2816*y^5-1280*y^3-1024*y; f3:=-10570042035+20643840*y^8-72056832*y^7+34406400*y^5-5849088*y^3-1416960*y+ 58720256*y^6-32112640*y^4+3713024*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 02:33:25 on modular [Seed = 1545622410] ------------------------------------- [ y^2 + y + 12, 3*y + 48, 63 ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 02:33:59 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-129+16*y^2-8*y; f1:=-24609+768*y^4-256*y^3-128*y; f2:=-1311075+10240*y^6-2816*y^5-1280*y^3-1024*y; f3:=-10570312305+20643840*y^8-72056832*y^7+34406400*y^5-5849088*y^3-1416960*y+ 58720256*y^6-32112640*y^4+3713024*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 02:33:56 on modular [Seed = 1245070781] ------------------------------------- [ y^2 + y + 12, 3*y + 48, 63 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam133-181.student.harvard.edu. (140.247.133.181) Time: Wed Feb 25 02:34:25 2004 Input: R := PolynomialRing( RationalField() ); R; Output: Magma V2.10-6 Wed Feb 25 2004 02:34:22 on modular [Seed = 1896709788] ------------------------------------- Univariate Polynomial Ring in x over Rational Field Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 02:34:29 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-129+16*y^2-8*y; f1:=-24609+768*y^4-256*y^3-128*y; f2:=-5243505+40960*y^6-94208*y^5+17920*y^3-4672*y+69120*y^4+19200*y^2; f3:=-10570092435+20643840*y^8-72056832*y^7+34406400*y^5-5849088*y^3-1416960*y+ 58720256*y^6-32112640*y^4+3713024*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 02:34:26 on modular [Seed = 2013554793] ------------------------------------- [ 2*y^2 + 2*y + 3, 3*y, 9 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam133-181.student.harvard.edu. (140.247.133.181) Time: Wed Feb 25 02:34:48 2004 Input: 1+1; Output: Magma V2.10-6 Wed Feb 25 2004 02:34:44 on modular [Seed = 1729853280] ------------------------------------- 2 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 02:35:00 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-129+16*y^2-8*y; f1:=-24609+768*y^4-256*y^3-128*y; f2:=-5243505+40960*y^6-94208*y^5+17920*y^3-4672*y+69120*y^4+19200*y^2; f3:=-10570042035+20643840*y^8-72056832*y^7+34406400*y^5-5849088*y^3-1416960*y+ 58720256*y^6-32112640*y^4+3713024*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 02:34:57 on modular [Seed = 1846705756] ------------------------------------- [ 2*y^2 + 2*y + 3, 3*y, 9 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 02:35:26 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-129+16*y^2-8*y; f1:=-24609+768*y^4-256*y^3-128*y; f2:=117+10240*y^6-23552*y^5+17280*y^4+4480*y^3; f3:=-10570042035+20643840*y^8-72056832*y^7+34406400*y^5-5849088*y^3-1416960*y+ 58720256*y^6-32112640*y^4+3713024*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 02:35:23 on modular [Seed = 2581957041] ------------------------------------- [ y + 51, 63 ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 02:35:54 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-129+16*y^2-8*y; f1:=-24609+768*y^4-256*y^3-128*y; f2:=117+10240*y^6-23552*y^5+17280*y^4+4480*y^3; f3:=-10570312305+20643840*y^8-72056832*y^7+34406400*y^5-5849088*y^3-1416960*y+ 58720256*y^6-32112640*y^4+3713024*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 02:35:51 on modular [Seed = 2164035780] ------------------------------------- [ y + 51, 63 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 02:36:23 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-129+16*y^2-8*y; f1:=-24609+768*y^4-256*y^3-128*y; f2:=-5243505+40960*y^6-94208*y^5+17920*y^3-4672*y+69120*y^4+19200*y^2; f3:=-10569689235+20643840*y^8-393216*y^7-35266560*y^5+8472576*y^3-1762560*y-24887296*y^6+49172480*y^4-12995584*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 02:36:20 on modular [Seed = 2398265065] ------------------------------------- [ 2*y^2 + 2*y + 3, 3*y, 9 ] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 02:36:53 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-129+16*y^2-8*y; f1:=-24609+768*y^4-256*y^3-128*y; f2:=-5243505+40960*y^6-94208*y^5+17920*y^3-4672*y+69120*y^4+19200*y^2; f3:=-10569638835+20643840*y^8-393216*y^7-35266560*y^5+8472576*y^3-1762560*y-24887296*y^6+49172480*y^4-12995584*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 02:36:50 on modular [Seed = 3049891124] ------------------------------------- [ 2*y^2 + 2*y + 3, 3*y, 9 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 02:37:24 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-129+16*y^2-8*y; f1:=-24609+768*y^4-256*y^3-128*y; f2:=117+10240*y^6-23552*y^5+17280*y^4+4480*y^3; f3:=-10569638835+20643840*y^8-393216*y^7-35266560*y^5+8472576*y^3-1762560*y-24887296*y^6+49172480*y^4-12995584*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 02:37:21 on modular [Seed = 3166743582] ------------------------------------- [ y + 51, 63 ] Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 02:37:51 2004 Input: //////////////////////// XVI P:=PolynomialRing(IntegerRing(),2); f0:=-129+16*y^2-8*y; f1:=-24609+768*y^4-256*y^3-128*y; f2:=117+10240*y^6-23552*y^5+17280*y^4+4480*y^3; f3:=-10569909105+20643840*y^8-393216*y^7-35266560*y^5+8472576*y^3-1762560*y-24887296*y^6+49172480*y^4-12995584*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 02:37:48 on modular [Seed = 2883042164] ------------------------------------- [ y + 51, 63 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 02:57:38 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*x^2-10+x; f1:=6*x^4-114+2*x^3+x; f2:=40*x^6-2960+11*x^5+5*x^3+4*x; f3:=630*x^8-183330+151*x^7+70*x^5+49*x^3+45*x; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 02:57:35 on modular [Seed = 4052608141] ------------------------------------- [ x - 2 ] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 02:58:05 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*x^2-10+x; f1:=6*x^4-114+2*x^3+x; f2:=40*x^6-2960+11*x^5+5*x^3+4*x; f3:=645120*x^8-187731495+2251776*x^7-1075200*x^5+182784*x^3+44280*x+1835008*x^6-1003520*x^4+116032*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 02:58:02 on modular [Seed = 4169461089] ------------------------------------- [ x + 334639303, 334639305 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 02:58:33 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*x^2-10+x; f1:=6*x^4-114+2*x^3+x; f2:=1280*x^6-94705+2944*x^5-560*x^3+146*x+2160*x^4-600*x^2; f3:=645120*x^8-187731495+2251776*x^7-1075200*x^5+182784*x^3+44280*x+1835008*x^6-1003520*x^4+116032*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 02:58:30 on modular [Seed = 3885757010] ------------------------------------- [ x + 109393, 109395 ] Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 02:58:58 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*x^2-10+x; f1:=6*x^4-114+2*x^3+x; f2:=1280*x^6-94705+2944*x^5-560*x^3+146*x+2160*x^4-600*x^2; f3:=645120*x^8-187718895+12288*x^7+1102080*x^5-264768*x^3+55080*x-777728*x^6+ 1536640*x^4-406112*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 02:58:55 on modular [Seed = 3985766465] ------------------------------------- [ x^2 + 6*x + 109379, 11*x + 109373, 109395 ] Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 02:59:27 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*x^2-10+x; f1:=6*x^4-114+2*x^3+x; f2:=40*x^6-2960+11*x^5+5*x^3+4*x; f3:=645120*x^8-318675735+154624*x^7+71680*x^5+50176*x^3+46080*x; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 02:59:24 on modular [Seed = 476056020] ------------------------------------- [ x + 130945813, 130945815 ] Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 02:59:48 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*x^2-10+x; f1:=6*x^4-114+2*x^3+x; f2:=40*x^6-2960+11*x^5+5*x^3+4*x; f3:=322560*x^8-159338655+1125888*x^7-537600*x^5+91392*x^3+22140*x+917504*x^6-501760 *x^4+58016*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 02:59:45 on modular [Seed = 91820256] ------------------------------------- [ x + 101846743, 101846745 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 03:00:11 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*x^2-10+x; f1:=6*x^4-114+2*x^3+x; f2:=1280*x^6-94705+2944*x^5-560*x^3+146*x+2160*x^4-600*x^2; f3:=322560*x^8-159338655+1125888*x^7-537600*x^5+91392*x^3+22140*x+917504*x^6-501760 *x^4+58016*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 03:00:08 on modular [Seed = 893985577] ------------------------------------- [ x + 109393, 109395 ] Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 03:00:32 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*x^2-10+x; f1:=6*x^4-114+2*x^3+x; f2:=1280*x^6-94705+2944*x^5-560*x^3+146*x+2160*x^4-600*x^2; f3:=322560*x^8-159332355+6144*x^7+551040*x^5-132384*x^3+27540*x-388864*x^6+768320*x ^4-203056*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 03:00:29 on modular [Seed = 1044523063] ------------------------------------- [ x^2 + 6*x + 109379, 11*x + 109373, 109395 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 03:00:56 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*x^2-10+x; f1:=6*x^4-114+2*x^3+x; f2:=1280*x^6-134965+352*x^5+160*x^3+128*x; f3:=645120*x^8-318675735+154624*x^7+71680*x^5+50176*x^3+46080*x; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 03:00:53 on modular [Seed = 660287750] ------------------------------------- [ x + 13, 15 ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 03:01:18 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*x^2-10+x; f1:=6*x^4-114+2*x^3+x; f2:=1280*x^6-134965+352*x^5+160*x^3+128*x; f3:=322560*x^8-159338655+1125888*x^7-537600*x^5+91392*x^3+22140*x+917504*x^6-501760 *x^4+58016*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 03:01:15 on modular [Seed = 1512459269] ------------------------------------- [ x + 13, 15 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 03:01:45 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*x^2-10+x; f1:=6*x^4-114+2*x^3+x; f2:=640*x^6+13376+1472*x^5+1080*x^4-280*x^3; f3:=322560*x^8-159338655+1125888*x^7-537600*x^5+91392*x^3+22140*x+917504*x^6-501760 *x^4+58016*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 03:01:42 on modular [Seed = 1128224049] ------------------------------------- [ x + 453, 455 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 03:02:11 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*x^2-10+x; f1:=6*x^4-114+2*x^3+x; f2:=640*x^6+13376+1472*x^5+1080*x^4-280*x^3; f3:=322560*x^8-159332355+6144*x^7+551040*x^5-132384*x^3+27540*x-388864*x^6+768320*x ^4-203056*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 03:02:08 on modular [Seed = 1946706656] ------------------------------------- [ x + 453, 455 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 03:02:33 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*x^2-10+x; f1:=6*x^4-114+2*x^3+x; f2:=1280*x^6-134965+352*x^5+160*x^3+128*x; f3:=645120*x^8-226783935+154624*x^7+71680*x^5+50176*x^3+46080*x; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 03:02:30 on modular [Seed = 2114087164] ------------------------------------- [ x + 13, 15 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 03:02:53 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*x^2-10+x; f1:=6*x^4-114+2*x^3+x; f2:=1280*x^6-134965+352*x^5+160*x^3+128*x; f3:=322560*x^8-113392755+1125888*x^7-537600*x^5+91392*x^3+22140*x+917504*x^6-501760 *x^4+58016*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 03:02:50 on modular [Seed = 1729851865] ------------------------------------- [ x + 13, 15 ] Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 03:03:12 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*x^2-10+x; f1:=6*x^4-114+2*x^3+x; f2:=640*x^6+13376+1472*x^5+1080*x^4-280*x^3; f3:=322560*x^8-113392755+1125888*x^7-537600*x^5+91392*x^3+22140*x+917504*x^6-501760 *x^4+58016*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 03:03:09 on modular [Seed = 1746173633] ------------------------------------- [ x + 453, 455 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 03:03:30 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*x^2-10+x; f1:=6*x^4-114+2*x^3+x; f2:=640*x^6+13376+1472*x^5+1080*x^4-280*x^3; f3:=322560*x^8-113386455+6144*x^7+551040*x^5-132384*x^3+27540*x-388864*x^6+768320*x ^4-203056*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 03:03:27 on modular [Seed = 2448262997] ------------------------------------- [ x + 453, 455 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 03:06:48 2004 Input: Factorization(334639305); Factorization(109395); Factorization(130945815); Factorization(101846745); Factorization(455); Output: Magma V2.10-6 Wed Feb 25 2004 03:06:45 on modular [Seed = 2164037377] ------------------------------------- [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1>, <23, 1> ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1>, <17, 1> ] [ <3, 4>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ <3, 2>, <5, 1>, <7, 2>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ <5, 1>, <7, 1>, <13, 1> ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 03:34:57 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-16+2*y^2-y; f1:=-192+6*y^4-2*y^3-y; f2:=-5120+40*y^6-11*y^5-5*y^3-4*y; f3:=-322560+630*y^8-151*y^7-70*y^5-49*y^3-45*y; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 03:34:53 on modular [Seed = 3668362467] ------------------------------------- [ y + 32, 48 ] Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 03:35:21 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-16+2*y^2-y; f1:=-192+6*y^4-2*y^3-y; f2:=-5120+40*y^6-11*y^5-5*y^3-4*y; f3:=-330303015+645120*y^8-154624*y^7-71680*y^5-50176*y^3-46080*y; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 03:35:18 on modular [Seed = 3484668317] ------------------------------------- [ y + 2, 3 ] Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 03:35:41 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-16+2*y^2-y; f1:=-192+6*y^4-2*y^3-y; f2:=-163825+1280*y^6-352*y^5-160*y^3-128*y; f3:=-330303015+645120*y^8-154624*y^7-71680*y^5-50176*y^3-46080*y; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 03:35:38 on modular [Seed = 4035767998] ------------------------------------- [ y + 2, 3 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 03:35:58 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-16+2*y^2-y; f1:=-192+6*y^4-2*y^3-y; f2:=-163825+1280*y^6-352*y^5-160*y^3-128*y; f3:=-330290415+645120*y^8-154624*y^7-71680*y^5-50176*y^3-46080*y; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 03:35:55 on modular [Seed = 4186302342] ------------------------------------- [ y + 2, 3 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 03:36:24 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-16+2*y^2-y; f1:=-192+6*y^4-2*y^3-y; f2:=-5120+40*y^6-11*y^5-5*y^3-4*y; f3:=-330303015+645120*y^8-2251776*y^7+1075200*y^5-182784*y^3-44280*y+1835008*y^6-1003520*y^4+116032*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 03:36:21 on modular [Seed = 3802070131] ------------------------------------- [ y + 2, 3 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 03:36:40 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-16+2*y^2-y; f1:=-192+6*y^4-2*y^3-y; f2:=-5120+40*y^6-11*y^5-5*y^3-4*y; f3:=-165152295+322560*y^8-1125888*y^7+537600*y^5-91392*y^3-22140*y+917504*y^6-501760*y^4+58016*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 03:36:37 on modular [Seed = 3952604522] ------------------------------------- [ y + 2, 3 ] Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 03:37:13 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-16+2*y^2-y; f1:=-192+6*y^4-2*y^3-y; f2:=-163825+1280*y^6-352*y^5-160*y^3-128*y; f3:=-165152295+322560*y^8-1125888*y^7+537600*y^5-91392*y^3-22140*y+917504*y^6-501760*y^4+58016*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 03:37:10 on modular [Seed = 492897214] ------------------------------------- [ y + 2, 3 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 03:37:30 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-16+2*y^2-y; f1:=-192+6*y^4-2*y^3-y; f2:=-163825+1280*y^6-352*y^5-160*y^3-128*y; f3:=-165145995+322560*y^8-1125888*y^7+537600*y^5-91392*y^3-22140*y+917504*y^6-501760*y^4+58016*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 03:37:27 on modular [Seed = 74980054] ------------------------------------- [ y + 2, 3 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 03:37:51 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-16+2*y^2-y; f1:=-192+6*y^4-2*y^3-y; f2:=-163825+1280*y^6-2944*y^5+560*y^3-146*y+2160*y^4+600*y^2; f3:=-330303015+645120*y^8-2251776*y^7+1075200*y^5-182784*y^3-44280*y+1835008*y^6-1003520*y^4+116032*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 03:37:48 on modular [Seed = 242356423] ------------------------------------- [ y + 2, 3 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 03:38:11 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-16+2*y^2-y; f1:=-192+6*y^4-2*y^3-y; f2:=-163825+1280*y^6-2944*y^5+560*y^3-146*y+2160*y^4+600*y^2; f3:=-165152295+322560*y^8-1125888*y^7+537600*y^5-91392*y^3-22140*y+917504*y^6-501760*y^4+58016*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 03:38:08 on modular [Seed = 827142100] ------------------------------------- [ y + 2, 3 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 03:38:46 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-16+2*y^2-y; f1:=-192+6*y^4-2*y^3-y; f2:=640*y^6-1472*y^5+1080*y^4+280*y^3; f3:=-165152295+322560*y^8-1125888*y^7+537600*y^5-91392*y^3-22140*y+917504*y^6-501760*y^4+58016*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 03:38:43 on modular [Seed = 943990590] ------------------------------------- [ y + 2, 3 ] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 03:39:04 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-16+2*y^2-y; f1:=-192+6*y^4-2*y^3-y; f2:=640*y^6-1472*y^5+1080*y^4+280*y^3; f3:=-165145995+322560*y^8-1125888*y^7+537600*y^5-91392*y^3-22140*y+917504*y^6-501760*y^4+58016*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 03:39:01 on modular [Seed = 576601362] ------------------------------------- [ y + 2, 3 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 03:39:24 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-16+2*y^2-y; f1:=-192+6*y^4-2*y^3-y; f2:=-163825+1280*y^6-2944*y^5+560*y^3-146*y+2160*y^4+600*y^2; f3:=-330290415+645120*y^8-12288*y^7-1102080*y^5+264768*y^3-55080*y-777728*y^6+ 1536640*y^4-406112*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 03:39:21 on modular [Seed = 1428769401] ------------------------------------- [ y + 2, 3 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 03:39:41 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-16+2*y^2-y; f1:=-192+6*y^4-2*y^3-y; f2:=-163825+1280*y^6-2944*y^5+560*y^3-146*y+2160*y^4+600*y^2; f3:=-165145995+322560*y^8-6144*y^7-551040*y^5+132384*y^3-27540*y-388864*y^6+768320* y^4-203056*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 03:39:38 on modular [Seed = 1545618179] ------------------------------------- [ y + 2, 3 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 03:39:58 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-16+2*y^2-y; f1:=-192+6*y^4-2*y^3-y; f2:=640*y^6-1472*y^5+1080*y^4+280*y^3; f3:=-165145995+322560*y^8-6144*y^7-551040*y^5+132384*y^3-27540*y-388864*y^6+768320* y^4-203056*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 03:39:55 on modular [Seed = 1195071497] ------------------------------------- [ y + 2, 3 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 03:40:18 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-16+2*y^2-y; f1:=-192+6*y^4-2*y^3-y; f2:=640*y^6-1472*y^5+1080*y^4+280*y^3; f3:=-165139695+322560*y^8-6144*y^7-551040*y^5+132384*y^3-27540*y-388864*y^6+768320* y^4-203056*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 03:40:15 on modular [Seed = 1997236237] ------------------------------------- [ y + 2, 3 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 03:53:39 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=-2160+40*y^6-11*y^5-5*y^3-4*y; f3:=-139230+630*y^8-151*y^7-70*y^5-49*y^3-45*y; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 03:53:36 on modular [Seed = 1746160365] ------------------------------------- [ y^2 + 7*y - 18, 15*y - 30 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 03:54:03 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=-2160+40*y^6-11*y^5-5*y^3-4*y; f3:=192067785+645120*y^8-154624*y^7-71680*y^5-50176*y^3-46080*y; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 03:54:00 on modular [Seed = 2465116207] ------------------------------------- [ y^2 + 7*y + 334639287, 15*y + 334639275, 334639305 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 03:54:29 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=40275+1280*y^6-352*y^5-160*y^3-128*y; f3:=192067785+645120*y^8-154624*y^7-71680*y^5-50176*y^3-46080*y; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 03:54:26 on modular [Seed = 2247731026] ------------------------------------- [ y^2 + 7*y + 109377, 15*y + 109365, 109395 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 03:54:57 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=40275+1280*y^6-352*y^5-160*y^3-128*y; f3:=-157121055+645120*y^8-154624*y^7-71680*y^5-50176*y^3-46080*y; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 03:54:54 on modular [Seed = 2364583495] ------------------------------------- [ y^2 + 7*y + 109377, 15*y + 109365, 109395 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 03:55:18 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=-2160+40*y^6-11*y^5-5*y^3-4*y; f3:=-142573095+645120*y^8-2251776*y^7+1075200*y^5-182784*y^3-44280*y+1835008*y^6-1003520*y^4+116032*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 03:55:15 on modular [Seed = 3016724821] ------------------------------------- [ y^2 + 7*y + 130945797, 15*y + 130945785, 130945815 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 03:55:38 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=-2160+40*y^6-11*y^5-5*y^3-4*y; f3:=96033105+322560*y^8-1125888*y^7+537600*y^5-91392*y^3-22140*y+917504*y^6-501760* y^4+58016*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B Output: Magma V2.10-6 Wed Feb 25 2004 03:55:35 on modular [Seed = 3133577640] ------------------------------------- [ y^2 + 7*y + 101846727, 15*y + 101846715, 101846745 ] Total time: 3.219 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 03:56:00 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=40275+1280*y^6-352*y^5-160*y^3-128*y; f3:=96033105+322560*y^8-1125888*y^7+537600*y^5-91392*y^3-22140*y+917504*y^6-501760* y^4+58016*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 03:55:57 on modular [Seed = 3618370783] ------------------------------------- [ y^2 + 7*y + 109377, 15*y + 109365, 109395 ] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 03:56:20 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=40275+1280*y^6-352*y^5-160*y^3-128*y; f3:=-78561315+322560*y^8-1125888*y^7+537600*y^5-91392*y^3-22140*y+917504*y^6-501760 *y^4+58016*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 03:56:17 on modular [Seed = 3735223802] ------------------------------------- [ y^2 + 7*y + 109377, 15*y + 109365, 109395 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 03:56:43 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=-69105+1280*y^6-2944*y^5+560*y^3-146*y+2160*y^4+600*y^2; f3:=-142573095+645120*y^8-2251776*y^7+1075200*y^5-182784*y^3-44280*y+1835008*y^6-1003520*y^4+116032*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B Output: Magma V2.10-6 Wed Feb 25 2004 03:56:40 on modular [Seed = 3250447004] ------------------------------------- [ y^2 + 7*y + 42, 15*y, 45 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 03:57:03 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=-69105+1280*y^6-2944*y^5+560*y^3-146*y+2160*y^4+600*y^2; f3:=96033105+322560*y^8-1125888*y^7+537600*y^5-91392*y^3-22140*y+917504*y^6-501760* y^4+58016*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 03:57:00 on modular [Seed = 3367299969] ------------------------------------- [ y^2 + 7*y + 42, 15*y, 45 ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 03:57:27 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=103104+640*y^6-1472*y^5+1080*y^4+280*y^3; f3:=96033105+322560*y^8-1125888*y^7+537600*y^5-91392*y^3-22140*y+917504*y^6-501760* y^4+58016*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 03:57:24 on modular [Seed = 4086288530] ------------------------------------- [ y + 3183, 4095 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 03:57:49 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=103104+640*y^6-1472*y^5+1080*y^4+280*y^3; f3:=-78561315+322560*y^8-1125888*y^7+537600*y^5-91392*y^3-22140*y+917504*y^6-501760 *y^4+58016*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 03:57:46 on modular [Seed = 4203141477] ------------------------------------- [ y + 3183, 4095 ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 03:58:10 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=-69105+1280*y^6-2944*y^5+560*y^3-146*y+2160*y^4+600*y^2; f3:=-142560495+645120*y^8-12288*y^7-1102080*y^5+264768*y^3-55080*y-777728*y^6+ 1536640*y^4-406112*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 03:58:07 on modular [Seed = 3985755751] ------------------------------------- [ y^2 + 7*y + 42, 15*y, 45 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (195.219.172.9) Time: Wed Feb 25 03:58:26 2004 Input: K := FiniteField(3); C := LinearCode Output: Magma V2.10-6 Wed Feb 25 2004 03:58:22 on modular [Seed = 392901806] ------------------------------------- Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 03:58:30 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=-69105+1280*y^6-2944*y^5+560*y^3-146*y+2160*y^4+600*y^2; f3:=96039405+322560*y^8-6144*y^7-551040*y^5+132384*y^3-27540*y-388864*y^6+768320*y^ 4-203056*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 03:58:27 on modular [Seed = 526597306] ------------------------------------- [ y^2 + 7*y + 42, 15*y, 45 ] Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 03:58:54 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=103104+640*y^6-1472*y^5+1080*y^4+280*y^3; f3:=96039405+322560*y^8-6144*y^7-551040*y^5+132384*y^3-27540*y-388864*y^6+768320*y^ 4-203056*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 03:58:50 on modular [Seed = 41820638] ------------------------------------- [ y + 3183, 4095 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 03:59:14 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=103104+640*y^6-1472*y^5+1080*y^4+280*y^3; f3:=-78555015+322560*y^8-6144*y^7-551040*y^5+132384*y^3-27540*y-388864*y^6+768320*y ^4-203056*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 03:59:10 on modular [Seed = 141831104] ------------------------------------- [ y + 3183, 4095 ] Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (195.219.172.6) Time: Wed Feb 25 04:00:22 2004 Input: K := FiniteField(3); C := LinearCode Output: Magma V2.10-6 Wed Feb 25 2004 04:00:19 on modular [Seed = 943987725] ------------------------------------- Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (195.219.172.10) Time: Wed Feb 25 04:00:39 2004 Input: K := FiniteField(3) C := LinearCode Output: Magma V2.10-6 Wed Feb 25 2004 04:00:36 on modular [Seed = 559744259] ------------------------------------- >> C := LinearCode> [0, 0, 1, 0, 0, 0, 1, 0, 1, 2, 2], [0, 0, 0, 1, 0, 0, 2, 1, 0, 1, 2]> ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 04:00:47 2004 Input: Factorization(334639305); Output: Magma V2.10-6 Wed Feb 25 2004 04:00:44 on modular [Seed = 1445622396] ------------------------------------- [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1>, <23, 1> ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 04:01:40 2004 Input: Factorization(109395); Output: Magma V2.10-6 Wed Feb 25 2004 04:01:37 on modular [Seed = 1295083818] ------------------------------------- [ <3, 2>, <5, 1>, <11, 1>, <13, 1>, <17, 1> ] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 04:02:08 2004 Input: Factorization(109395109395); Output: Magma V2.10-6 Wed Feb 25 2004 04:02:05 on modular [Seed = 1128228825] ------------------------------------- [ <3, 2>, <5, 1>, <11, 1>, <13, 1>, <17, 1>, <101, 1>, <9901, 1> ] Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (195.219.172.7) Time: Wed Feb 25 04:02:21 2004 Input: K := FiniteField(3) C := LinearCode Output: Magma V2.10-6 Wed Feb 25 2004 04:02:18 on modular [Seed = 1245081287] ------------------------------------- >> C := LinearCode, <5, 1>, <7, 2>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 04:03:23 2004 Input: Factorization(4095); Output: Magma V2.10-6 Wed Feb 25 2004 04:03:20 on modular [Seed = 1846692513] ------------------------------------- [ <3, 2>, <5, 1>, <7, 1>, <13, 1> ] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Wed Feb 25 04:47:54 2004 Input: magma Output: Magma V2.10-6 Wed Feb 25 2004 04:47:50 on modular [Seed = 3968910258] ------------------------------------- >> magma ^ User error: Identifier 'magma' has not been declared or assigned Total time: 3.149 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam133-22.student.harvard.edu. (140.247.133.22) Time: Wed Feb 25 05:17:41 2004 Input: R:=PolynomialRing( RationalField(), 4); I:=ideal< R | x3^2-x0^2-x2^2+x1^2, (x3+x0)*(x2-x1)-(x1+x2)^2, (x1+x2)*(x2-x0)-(x20x1)^2 >; EliminationIdeal(I, {x0, x1, x2}); Output: Magma V2.10-6 Wed Feb 25 2004 05:17:38 on modular [Seed = 1596156164] ------------------------------------- >> I:=ideal< R | x3^2-x0^2-x2^2+x1^2, (x3+x0)*(x2-x1)-(x1+x2)^2, (x1+x2)*(x2-x ^ User error: Identifier 'x3' has not been declared or assigned >> EliminationIdeal(I, {x0, x1, x2});; ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam133-22.student.harvard.edu. (140.247.133.22) Time: Wed Feb 25 05:18:27 2004 Input: R:=PolynomialRing( RationalField(), 4); R; Output: Magma V2.10-6 Wed Feb 25 2004 05:18:24 on modular [Seed = 1445617726] ------------------------------------- Polynomial ring of rank 4 over Rational Field Lexicographical Order Variables: $.1, $.2, $.3, $.4 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam133-22.student.harvard.edu. (140.247.133.22) Time: Wed Feb 25 05:19:47 2004 Input: R:=PolynomialRing( RationalField(), 4); R; Output: Magma V2.10-6 Wed Feb 25 2004 05:19:44 on modular [Seed = 1077704345] ------------------------------------- Polynomial ring of rank 4 over Rational Field Lexicographical Order Variables: x0, x1, x2, x3 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam133-22.student.harvard.edu. (140.247.133.22) Time: Wed Feb 25 05:20:04 2004 Input: R:=PolynomialRing( RationalField(), 4); I:=ideal< R | x3^2-x0^2-x2^2+x1^2, (x3+x0)*(x2-x1)-(x1+x2)^2, (x1+x2)*(x2-x0)-(x20x1)^2 >; EliminationIdeal(I, {x0, x1, x2}); Output: Magma V2.10-6 Wed Feb 25 2004 05:20:01 on modular [Seed = 1879852728] ------------------------------------- >> x2)^2, (x1+x2)*(x2-x0)-(x20x1)^2 >; ^ User error: Identifier 'x20x1' has not been declared or assigned >> EliminationIdeal(I, {x0, x1, x2});; ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam133-22.student.harvard.edu. (140.247.133.22) Time: Wed Feb 25 05:20:52 2004 Input: R:=PolynomialRing( RationalField(), 4); I:=ideal< R | x3^2-x0^2-x2^2+x1^2, (x3+x0)*(x2-x1)-(x1+x2)^2, (x1+x2)*(x2-x0)-(x2-x1)^2 >; EliminationIdeal(I, {x0, x1, x2}); Output: Magma V2.10-6 Wed Feb 25 2004 05:20:49 on modular [Seed = 1779850610] ------------------------------------- Ideal of Polynomial ring of rank 4 over Rational Field Lexicographical Order Variables: x0, x1, x2, x3 Basis: [ 1/4*x0^3*x1*x2 + 1/4*x0^3*x2^2 + x0^2*x2^3, -1/12*x0^2*x1*x2 - 1/12*x0^2*x2^2 - 1/3*x0*x2^3 + x1*x2^3, -1/4*x0^2*x1*x2 - 1/4*x0^2*x2^2 + x0*x1*x2^2, x0*x1 + x0*x2 + x1^2 - 3*x1*x2 ] Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Wed Feb 25 05:27:37 2004 Input: magma; Output: Magma V2.10-6 Wed Feb 25 2004 05:27:34 on modular [Seed = 2598806037] ------------------------------------- >> magma; ^ User error: Identifier 'magma' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Wed Feb 25 05:28:33 2004 Input: Floor(3.141592); Output: Magma V2.10-6 Wed Feb 25 2004 05:28:28 on modular [Seed = 2515119424] ------------------------------------- 3 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Wed Feb 25 05:29:34 2004 Input: Floor(3.141592); GCD(12,8); Output: Magma V2.10-6 Wed Feb 25 2004 05:29:31 on modular [Seed = 2398271388] ------------------------------------- 3 4 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Wed Feb 25 05:29:46 2004 Input: Floor(3.141592); GCD(12,8); Output: Magma V2.10-6 Wed Feb 25 2004 05:29:43 on modular [Seed = 2966194622] ------------------------------------- 3 4 Total time: 2.869 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Wed Feb 25 05:30:16 2004 Input: Floor(3.141592); GCD(12,8); Sort([3,2,5]); Output: Magma V2.10-6 Wed Feb 25 2004 05:30:13 on modular [Seed = 2698811788] ------------------------------------- 3 4 [ 2, 3, 5 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cflow1.csv.warwick.ac.uk. (137.205.8.2) Time: Wed Feb 25 05:33:16 2004 Input: k:=FunctionField(Rationals()); Factorization(x^3*(a+b)-x^2*a-b); Output: Magma V2.10-6 Wed Feb 25 2004 05:33:13 on modular [Seed = 3668370218] ------------------------------------- >> Factorization(x^3*(a+b)-x^2*a-b);; ^ User error: Identifier 'a' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cflow1.csv.warwick.ac.uk. (137.205.8.2) Time: Wed Feb 25 05:34:24 2004 Input: integer(a,b); k:=FunctionField(Rationals()); Factorization(x^3*(a+b)-x^2*a-b); Output: Magma V2.10-6 Wed Feb 25 2004 05:34:21 on modular [Seed = 3567840992] ------------------------------------- >> integer(a,b); ^ User error: Identifier 'a' has not been declared or assigned >> Factorization(x^3*(a+b)-x^2*a-b);; ^ User error: Identifier 'a' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cflow1.csv.warwick.ac.uk. (137.205.8.2) Time: Wed Feb 25 05:38:10 2004 Input: Factorization(x^3*(3/2*a+27/8)-x^2*3/2*a -27/8); Output: Magma V2.10-6 Wed Feb 25 2004 05:38:07 on modular [Seed = 3317300947] ------------------------------------- >> Factorization(x^3*(3/2*a+27/8)-x^2*3/2*a -27/8);; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cflow1.csv.warwick.ac.uk. (137.205.8.2) Time: Wed Feb 25 05:39:44 2004 Input: a:=Integrer(); k:=FunctionField(Rationals(a)); Factorization(x^3*(3/2*a+27/8)-x^2*3/2*a -27/8); Output: Magma V2.10-6 Wed Feb 25 2004 05:39:41 on modular [Seed = 4269983114] ------------------------------------- >> a:=Integrer(); ^ User error: Identifier 'Integrer' has not been declared or assigned >> k:=FunctionField(Rationals(a)); ^ User error: Identifier 'a' has not been declared or assigned >> Factorization(x^3*(3/2*a+27/8)-x^2*3/2*a -27/8);; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cflow1.csv.warwick.ac.uk. (137.205.8.2) Time: Wed Feb 25 05:40:06 2004 Input: a:=Integer(); k:=FunctionField(Rationals(a)); Factorization(x^3*(3/2*a+27/8)-x^2*3/2*a -27/8); Output: Magma V2.10-6 Wed Feb 25 2004 05:40:03 on modular [Seed = 4002600308] ------------------------------------- >> a:=Integer(); ^ User error: Identifier 'Integer' has not been declared or assigned >> k:=FunctionField(Rationals(a)); ^ User error: Identifier 'a' has not been declared or assigned >> Factorization(x^3*(3/2*a+27/8)-x^2*3/2*a -27/8);; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cflow1.csv.warwick.ac.uk. (137.205.8.2) Time: Wed Feb 25 05:40:21 2004 Input: a:=Integer(a); k:=FunctionField(Rationals(a)); Factorization(x^3*(3/2*a+27/8)-x^2*3/2*a -27/8); Output: Magma V2.10-6 Wed Feb 25 2004 05:40:18 on modular [Seed = 442900882] ------------------------------------- >> a:=Integer(a); ^ User error: Identifier 'a' has not been declared or assigned >> k:=FunctionField(Rationals(a)); ^ User error: Identifier 'a' has not been declared or assigned >> Factorization(x^3*(3/2*a+27/8)-x^2*3/2*a -27/8);; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cflow1.csv.warwick.ac.uk. (137.205.8.2) Time: Wed Feb 25 05:40:39 2004 Input: a:=a; k:=FunctionField(Rationals(a)); Factorization(x^3*(3/2*a+27/8)-x^2*3/2*a -27/8); Output: Magma V2.10-6 Wed Feb 25 2004 05:40:36 on modular [Seed = 326052013] ------------------------------------- >> a:=a; ^ User error: Identifier 'a' has not been declared or assigned >> k:=FunctionField(Rationals(a)); ^ User error: Identifier 'a' has not been declared or assigned >> Factorization(x^3*(3/2*a+27/8)-x^2*3/2*a -27/8);; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cflow1.csv.warwick.ac.uk. (137.205.8.2) Time: Wed Feb 25 05:40:51 2004 Input: a; k:=FunctionField(Rationals(a)); Factorization(x^3*(3/2*a+27/8)-x^2*3/2*a -27/8); Output: Magma V2.10-6 Wed Feb 25 2004 05:40:48 on modular [Seed = 141833122] ------------------------------------- >> a; ^ User error: Identifier 'a' has not been declared or assigned >> k:=FunctionField(Rationals(a)); ^ User error: Identifier 'a' has not been declared or assigned >> Factorization(x^3*(3/2*a+27/8)-x^2*3/2*a -27/8);; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cflow1.csv.warwick.ac.uk. (137.205.8.2) Time: Wed Feb 25 05:41:02 2004 Input: k:=FunctionField(Rationals(a)); Factorization(x^3*(3/2*a+27/8)-x^2*3/2*a -27/8); Output: Magma V2.10-6 Wed Feb 25 2004 05:40:59 on modular [Seed = 24984224] ------------------------------------- >> k:=FunctionField(Rationals(a)); ^ User error: Identifier 'a' has not been declared or assigned >> Factorization(x^3*(3/2*a+27/8)-x^2*3/2*a -27/8);; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cflow1.csv.warwick.ac.uk. (137.205.8.2) Time: Wed Feb 25 05:42:00 2004 Input: k:=FunctionField(Rationals()); Factorization(x^3*(3/2*a+27/8)-x^2*3/2*a -27/8); Output: Magma V2.10-6 Wed Feb 25 2004 05:41:57 on modular [Seed = 1061356752] ------------------------------------- >> k:=FunctionField(Rationals()); ^ Runtime error in 'AssignNames': Argument 2 should have length at most 1 >> Factorization(x^3*(3/2*a+27/8)-x^2*3/2*a -27/8);; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cflow1.csv.warwick.ac.uk. (137.205.8.2) Time: Wed Feb 25 05:46:23 2004 Input: k:=FunctionField(Rationals(),a); Factorization(x^3*(3/2*a+27/8)-x^2*3/2*a -27/8); Output: Magma V2.10-6 Wed Feb 25 2004 05:46:20 on modular [Seed = 777130696] ------------------------------------- >> k:=FunctionField(Rationals(),a); ^ User error: Identifier 'a' has not been declared or assigned >> Factorization(x^3*(3/2*a+27/8)-x^2*3/2*a -27/8);; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cflow1.csv.warwick.ac.uk. (137.205.8.2) Time: Wed Feb 25 05:47:18 2004 Input: k:=FunctionField(Rationals()); l:=FunctionField(Rationals()); Factorization(x^3*(3/2*a+27/8)-x^2*3/2*a -27/8); Output: Magma V2.10-6 Wed Feb 25 2004 05:47:15 on modular [Seed = 609753357] ------------------------------------- >> Factorization(x^3*(3/2*a+27/8)-x^2*3/2*a -27/8);; ^ Runtime error in 'Factorization': Bad argument types Argument types given: FldFunRatUElt Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cflow1.csv.warwick.ac.uk. (137.205.8.2) Time: Wed Feb 25 05:47:59 2004 Input: k:=FunctionField(Rationals()); Factorization(x^3*(3/2*a+27/8)-x^2*3/2*a -27/8,x); Output: Magma V2.10-6 Wed Feb 25 2004 05:47:56 on modular [Seed = 1562468379] ------------------------------------- >> Factorization(x^3*(3/2*a+27/8)-x^2*3/2*a -27/8,x);; ^ User error: Identifier 'a' has not been declared or assigned Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cflow1.csv.warwick.ac.uk. (137.205.8.2) Time: Wed Feb 25 05:48:14 2004 Input: k:=FunctionField(Rationals()); Factorization(x^3*(3/2*a+27/8)-x^2*3/2*a -27/8,a); Output: Magma V2.10-6 Wed Feb 25 2004 05:48:11 on modular [Seed = 1211397433] ------------------------------------- >> Factorization(x^3*(3/2*a+27/8)-x^2*3/2*a -27/8,a);; ^ User error: Identifier 'a' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cflow1.csv.warwick.ac.uk. (137.205.8.2) Time: Wed Feb 25 05:48:50 2004 Input: Rational(a); k:=FunctionField(Rationals()); Factorization(x^3*(3/2*a+27/8)-x^2*3/2*a -27/8,a); Output: Magma V2.10-6 Wed Feb 25 2004 05:48:47 on modular [Seed = 1178237907] ------------------------------------- >> Rational(a); ^ User error: Identifier 'a' has not been declared or assigned >> Factorization(x^3*(3/2*a+27/8)-x^2*3/2*a -27/8,a);; ^ User error: Identifier 'a' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cflow1.csv.warwick.ac.uk. (137.205.8.2) Time: Wed Feb 25 05:49:04 2004 Input: Rationals(a); k:=FunctionField(Rationals()); Factorization(x^3*(3/2*a+27/8)-x^2*3/2*a -27/8,a); Output: Magma V2.10-6 Wed Feb 25 2004 05:49:01 on modular [Seed = 2080391675] ------------------------------------- >> Rationals(a); ^ User error: Identifier 'a' has not been declared or assigned >> Factorization(x^3*(3/2*a+27/8)-x^2*3/2*a -27/8,a);; ^ User error: Identifier 'a' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cflow1.csv.warwick.ac.uk. (137.205.8.2) Time: Wed Feb 25 05:49:32 2004 Input: a:=1; k:=FunctionField(Rationals()); Factorization(x^3*(3/2*a+27/8)-x^2*3/2*a -27/8,a); Output: Magma V2.10-6 Wed Feb 25 2004 05:49:29 on modular [Seed = 1963542742] ------------------------------------- >> Factorization(x^3*(3/2*a+27/8)-x^2*3/2*a -27/8,a);; ^ Runtime error in 'Factorization': Bad argument types Argument types given: FldFunRatUElt, RngIntElt Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cflow1.csv.warwick.ac.uk. (137.205.8.2) Time: Wed Feb 25 05:50:21 2004 Input: a:=1; k:=FunctionField(Rationals()); Factorization(x^3*(3/2*a+27/8)-x^2*3/2*a-27/8,a); Output: Magma V2.10-6 Wed Feb 25 2004 05:50:18 on modular [Seed = 2598807402] ------------------------------------- >> Factorization(x^3*(3/2*a+27/8)-x^2*3/2*a-27/8,a);; ^ Runtime error in 'Factorization': Bad argument types Argument types given: FldFunRatUElt, RngIntElt Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cflow1.csv.warwick.ac.uk. (137.205.8.2) Time: Wed Feb 25 05:50:33 2004 Input: a:=1; k:=FunctionField(Rationals()); Factorization(x^3*(3/2*a+27/8)-x^2*3/2*a-27/8); Output: Magma V2.10-6 Wed Feb 25 2004 05:50:30 on modular [Seed = 2481958527] ------------------------------------- >> Factorization(x^3*(3/2*a+27/8)-x^2*3/2*a-27/8);; ^ Runtime error in 'Factorization': Bad argument types Argument types given: FldFunRatUElt Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cflow1.csv.warwick.ac.uk. (137.205.8.2) Time: Wed Feb 25 05:51:02 2004 Input: a:=a; k:=FunctionField(Rationals()); Factorization(x^3*(3/2*a+27/8)-x^2*3/2*a-27/8); Output: Magma V2.10-6 Wed Feb 25 2004 05:50:59 on modular [Seed = 2297738881] ------------------------------------- >> a:=a; ^ User error: Identifier 'a' has not been declared or assigned >> Factorization(x^3*(3/2*a+27/8)-x^2*3/2*a-27/8);; ^ User error: Identifier 'a' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cflow1.csv.warwick.ac.uk. (137.205.8.2) Time: Wed Feb 25 05:51:13 2004 Input: a:=a;; k:=FunctionField(Rationals());; Factorization(x^3*(3/2*a+27/8)-x^2*3/2*a-27/8);; Output: Magma V2.10-6 Wed Feb 25 2004 05:51:10 on modular [Seed = 2180890501] ------------------------------------- >> a:=a;; ^ User error: Identifier 'a' has not been declared or assigned >> Factorization(x^3*(3/2*a+27/8)-x^2*3/2*a-27/8);;; ^ User error: Identifier 'a' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cflow1.csv.warwick.ac.uk. (137.205.8.2) Time: Wed Feb 25 06:00:30 2004 Input: aInteger; k:=FunctionField(Rationals()); Factorization(x^3*(a+27/8)-x^2*a -27/8); Output: Magma V2.10-6 Wed Feb 25 2004 06:00:27 on modular [Seed = 3400927899] ------------------------------------- >> aInteger; ^ User error: Identifier 'aInteger' has not been declared or assigned >> Factorization(x^3*(a+27/8)-x^2*a -27/8);; ^ User error: Identifier 'a' has not been declared or assigned Total time: 3.169 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cflow1.csv.warwick.ac.uk. (137.205.8.2) Time: Wed Feb 25 06:01:31 2004 Input: a:=1; k:=FunctionField(Rationals()); Factorization(x^3*(a+27/8)-x^2*a -27/8); Output: Magma V2.10-6 Wed Feb 25 2004 06:01:06 on modular [Seed = 4136253086] ------------------------------------- >> Factorization(x^3*(a+27/8)-x^2*a -27/8);; ^ Runtime error in 'Factorization': Bad argument types Argument types given: FldFunRatUElt Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Wed Feb 25 06:01:50 2004 Input: Min([5,10,4,6,2,9,12,3,8,7,11]); Output: Magma V2.10-6 Wed Feb 25 2004 06:01:47 on modular [Seed = 4019400558] ------------------------------------- 2 5 Total time: 3.139 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cflow1.csv.warwick.ac.uk. (137.205.8.2) Time: Wed Feb 25 06:02:03 2004 Input: k:=FunctionField(Rationals()); Factorization(x^3*(27/8)-x^2-27/8); Output: Magma V2.10-6 Wed Feb 25 2004 06:02:00 on modular [Seed = 3835176022] ------------------------------------- >> Factorization(x^3*(27/8)-x^2-27/8);; ^ Runtime error in 'Factorization': Bad argument types Argument types given: FldFunRatUElt Total time: 3.099 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cflow1.csv.warwick.ac.uk. (137.205.8.2) Time: Wed Feb 25 06:04:18 2004 Input: k:=PolynomialRing(Rationals()); Factorization(x^3*(27/8)-x^2-27/8); Output: Magma V2.10-6 Wed Feb 25 2004 06:04:04 on modular [Seed = 309252909] ------------------------------------- [ ] Total time: 3.209 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host cflow1.csv.warwick.ac.uk. (137.205.8.2) Time: Wed Feb 25 06:04:37 2004 Input: k:=PolynomialRing(Rationals()); Factorization(x^3*(a+27/8)-x^2*a-27/8); Output: Magma V2.10-6 Wed Feb 25 2004 06:04:33 on modular [Seed = 158713939] ------------------------------------- >> Factorization(x^3*(a+27/8)-x^2*a-27/8);; ^ User error: Identifier 'a' has not been declared or assigned Total time: 3.239 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cflow1.csv.warwick.ac.uk. (137.205.8.2) Time: Wed Feb 25 06:04:49 2004 Input: k:=PolynomialRing(Rationals(a)); Factorization(x^3*(a+27/8)-x^2*a-27/8); Output: Magma V2.10-6 Wed Feb 25 2004 06:04:44 on modular [Seed = 8175959] ------------------------------------- >> k:=PolynomialRing(Rationals(a)); ^ User error: Identifier 'a' has not been declared or assigned >> Factorization(x^3*(a+27/8)-x^2*a-27/8);; ^ User error: Identifier 'x' has not been declared or assigned Total time: 4.679 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cflow1.csv.warwick.ac.uk. (137.205.8.2) Time: Wed Feb 25 06:06:29 2004 Input: e:=FunctionField(Rationals()); k:=PolynomialRing(e); Factorization(x^3*(a+27/8)-x^2*a-27/8); Output: Magma V2.10-6 Wed Feb 25 2004 06:06:23 on modular [Seed = 827191429] ------------------------------------- [ , ] Total time: 4.209 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cflow1.csv.warwick.ac.uk. (137.205.8.2) Time: Wed Feb 25 06:08:02 2004 Input: e:=FunctionField(Rationals()); k:=PolynomialRing(e); Factorization(x^3*(3/2*a+27/8)-x^2*3/2*a-27/8); Output: Magma V2.10-6 Wed Feb 25 2004 06:07:59 on modular [Seed = 1579326538] ------------------------------------- [ , ] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 06:20:36 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-128+31*y^2-8*y; f1:=-448+4*y^3+111*y^2-18*y; f2:=-240+60*y^2-15*y; f3:=4*y^4+20*y^2-144; f4:=8*y^3+72*y^2-32*y-288; f5:=120*y^2-480; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 06:20:33 on modular [Seed = 1896723563] ------------------------------------- [ y + 32, 48 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Wed Feb 25 06:22:50 2004 Input: Min([5,10,4,6,2,9,12,3,8,7,11]); Output: Magma V2.10-6 Wed Feb 25 2004 06:22:47 on modular [Seed = 1746185716] ------------------------------------- 2 5 Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Wed Feb 25 06:24:14 2004 Input: m,p:=Min([5,10,4,6,2,9,12,3,8,7,11]); Output: Magma V2.10-6 Wed Feb 25 2004 06:24:11 on modular [Seed = 1696178341] ------------------------------------- Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Wed Feb 25 06:24:23 2004 Input: m,p:=Min([5,10,4,6,2,9,12,3,8,7,11]); Output: Magma V2.10-6 Wed Feb 25 2004 06:24:20 on modular [Seed = 2631948643] ------------------------------------- Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Wed Feb 25 06:24:42 2004 Input: m,p:=Min([5,10,4,6,2,9,12,3,8,7,11]); m; p; Output: Magma V2.10-6 Wed Feb 25 2004 06:24:39 on modular [Seed = 2348240487] ------------------------------------- 2 5 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Wed Feb 25 06:25:20 2004 Input: min:=Min([5,10,4,6,2,9,12,3,8,7,11]); Output: Magma V2.10-6 Wed Feb 25 2004 06:25:17 on modular [Seed = 2264547456] ------------------------------------- Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Wed Feb 25 06:25:30 2004 Input: min:=Min([5,10,4,6,2,9,12,3,8,7,11]); min; Output: Magma V2.10-6 Wed Feb 25 2004 06:25:27 on modular [Seed = 3183573889] ------------------------------------- 2 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 06:25:42 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2648015362+y^2+14549527*y; f1:=14695030346+14549533*y; f2:=14695030350+14549520*y; f3:=y^3+9*y^2+14549531*y+11683276569; f4:=15*y^2+3011753685; f5:=14549535*y+5659769115; f6:=15058768725; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 06:25:39 on modular [Seed = 3033035420] ------------------------------------- [ y + 2, 3 ] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Wed Feb 25 06:25:54 2004 Input: min:=Min([5,10,4,6,2,9,12,3,8,7,11]); min; Output: Magma V2.10-6 Wed Feb 25 2004 06:25:51 on modular [Seed = 2749326727] ------------------------------------- 2 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 06:27:52 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=643492+y^2+6412*y; f1:=643496+6433*y; f2:=643500+6390*y; f3:=y^3+9*y^2+6431*y+643464; f4:=15*y^2+765705; f5:=6435*y+643500; f6:=765765; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 06:27:49 on modular [Seed = 3651477367] ------------------------------------- [ y + 2, 3 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 06:30:06 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=643492+y^2+6187*y; f1:=2175026+6118*y; f2:=1409265+5940*y; f3:=y^3+9*y^2+6431*y+643464; f4:=15*y^2+2297235; f5:=6435*y+2175030; f6:=2297295; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 06:30:03 on modular [Seed = 3367243759] ------------------------------------- [ y + 2, 3 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 06:31:42 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=363738367+y^2+14549527*y; f1:=12410753351+14549533*y; f2:=12410753355+14549520*y; f3:=y^3+9*y^2+14549531*y+12410753319; f4:=15*y^2+15058768665; f5:=14549535*y+3375492120; f6:=15058768725; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 06:31:39 on modular [Seed = 3350921287] ------------------------------------- [ y + 2, 3 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 06:33:31 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=101846737+y^2+101846737*y; f1:=101846741+101846743*y; f2:=101846730*y; f3:=y^3+9*y^2+101846741*y+101846709; f4:=15*y^2+101846685; f5:=101846745; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 06:33:28 on modular [Seed = 4253103598] ------------------------------------- [ y + 2, 3 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 06:35:42 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=643492+y^2+6412*y; f1:=643496+6433*y; f2:=643500+6390*y; f3:=y^3+9*y^2+6431*y+643464; f4:=15*y^2+765705; f5:=6435*y+643500; f6:=765765; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 06:35:39 on modular [Seed = 4002555518] ------------------------------------- [ y + 2, 3 ] Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 06:37:18 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=643492+y^2+6187*y; f1:=643496+6118*y; f2:=643500+5940*y; f3:=y^3+9*y^2+6431*y+643464; f4:=15*y^2+765705; f5:=6435*y+643500; f6:=765765; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 06:37:15 on modular [Seed = 3852021013] ------------------------------------- [ y + 2, 3 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 06:38:54 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=22+y^2+7*y; f1:=716+13*y; f2:=375; f3:=y^3+9*y^2+11*y+1029; f4:=15*y+720; f5:=1035; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 06:38:51 on modular [Seed = 342416707] ------------------------------------- [ y + 2, 3 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 06:40:30 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=22+y^2+7*y; f1:=41+13*y; f2:=15; f3:=y^3+9*y^2+11*y+39; f4:=15*y; f5:=45; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 06:40:27 on modular [Seed = 91868338] ------------------------------------- [ y + 2, 3 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 06:41:41 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=910+4094*y; f1:=y^2+3185*y+2271; f2:=4095; f3:=0; f4:=0; f5:=0; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 06:41:38 on modular [Seed = 1061418705] ------------------------------------- [ y + 2, 3 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Wed Feb 25 06:42:40 2004 Input: t := { (-11)ˆ2, (-7)ˆ2, (-5)ˆ2, (-3)ˆ2, 3ˆ2, 5ˆ2, 7ˆ2, 11ˆ2 }; q := [ (-11)ˆ2, (-7)ˆ2, (-5)ˆ2, (-3)ˆ2, 3ˆ2, 5ˆ2, 7ˆ2, 11ˆ2 ]; Output: Magma V2.10-6 Wed Feb 25 2004 06:42:37 on modular [Seed = 810351105] ------------------------------------- >> t := { (-11)^È2, (-7)^È2, (-5)^È2, (-3)^È2, 3^È2, 5^È2, 7^È2, 11^È2 }; ^ User error: Unknown character (ascii value -120) >> q := [ (-11)^È2, (-7)^È2, (-5)^È2, (-3)^È2, 3^È2, 5^È2, 7^È2, 11^È2 ];; ^ User error: Unknown character (ascii value -120) Total time: 3.579 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 06:42:41 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=910+4094*y; f1:=y^2+3185*y+2271; f2:=4095; f3:=0; f4:=0; f5:=0; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 06:42:37 on modular [Seed = 860879106] ------------------------------------- [ y + 2, 3 ] Total time: 3.559 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Wed Feb 25 06:43:38 2004 Input: t := { (-11)ˆ2, (-7)ˆ2, (-5)ˆ2, (-3)ˆ2, 3ˆ2, 5ˆ2, 7ˆ2, 11ˆ2 }; q := [ (-11)ˆ2, (-7)ˆ2, (-5)ˆ2, (-3)ˆ2, 3ˆ2, 5ˆ2, 7ˆ2, 11ˆ2 ]; t,q; Output: Magma V2.10-6 Wed Feb 25 2004 06:43:35 on modular [Seed = 576645209] ------------------------------------- >> t := { (-11)^È2, (-7)^È2, (-5)^È2, (-3)^È2, 3^È2, 5^È2, 7^È2, 11^È2 }; ^ User error: Unknown character (ascii value -120) >> q := [ (-11)^È2, (-7)^È2, (-5)^È2, (-3)^È2, 3^È2, 5^È2, 7^È2, 11^È2 ]; ^ User error: Unknown character (ascii value -120) >> t,q;; ^ User error: Identifier 't' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 06:44:13 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=22+y^2+7*y; f1:=176+13*y; f2:=405; f3:=y^3+9*y^2+11*y+354; f4:=15*y+225; f5:=240; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 06:44:10 on modular [Seed = 1428791235] ------------------------------------- [ y + 2, 3 ] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 06:45:34 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=22+y^2+7*y; f1:=41+13*y; f2:=45; f3:=y^3+9*y^2+11*y+39; f4:=15; f5:=15*y; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 06:45:31 on modular [Seed = 1245085837] ------------------------------------- [ y + 2, 3 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 06:46:54 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=910+4094*y; f1:=y^2+3185*y+2271; f2:=4095; f3:=0; f4:=0; f5:=0; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 06:46:51 on modular [Seed = 1128237172] ------------------------------------- [ y + 2, 3 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Wed Feb 25 06:49:10 2004 Input: t := { (-11)ˆ2, (-7)ˆ2, (-5)ˆ2, (-3)ˆ2, 3ˆ2, 5ˆ2, 7ˆ2, 11ˆ2 }; Output: Magma V2.10-6 Wed Feb 25 2004 06:49:07 on modular [Seed = 1980415449] ------------------------------------- >> t := { (-11)^È2, (-7)^È2, (-5)^È2, (-3)^È2, 3^È2, 5^È2, 7^È2, 11^È2 };; ^ User error: Unknown character (ascii value -120) Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Wed Feb 25 06:51:14 2004 Input: t := { 11ˆ2 }; Output: Magma V2.10-6 Wed Feb 25 2004 06:51:11 on modular [Seed = 1729866580] ------------------------------------- >> t := { 11^È2 };; ^ User error: Unknown character (ascii value -120) Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host n137.ryd.student.liu.se. (130.236.215.137) Time: Wed Feb 25 07:12:51 2004 Input: A:=8557279344828479648963919334598121952009051585815655260460872411637735753291478000525722754921813014836; B:=12208960125242227674248262376735924429540356305761754210277173125240299322804490361872161327366888857828; p:=10922739944516357003167494744127937; E:=ChangeRing(EllipticCurve([A,B]),GF(p)); print(E); Order(E); Output: Magma V2.10-6 Wed Feb 25 2004 07:12:45 on modular [Seed = 2799335303] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 6367337586593438131158097300977116*x + 2741074124936022891543123641128966 over GF(10922739944516357003167494744127937) 10922739944516357127569183414240820 Total time: 5.119 seconds, Total memory usage: 3.63MB ************** MAGMA ***************** Host mathpc2.ulb.ac.be. (164.15.127.82) Time: Wed Feb 25 07:25:12 2004 Input: g := Sym(5); l := SubgroupLattice(g); print l; Output: Magma V2.10-6 Wed Feb 25 2004 07:25:09 on modular [Seed = 3233551609] ------------------------------------- Partially ordered set of subgroup classes ----------------------------------------- [ 1] Order 1 Length 1 Maximal Subgroups: --- [ 2] Order 2 Length 10 Maximal Subgroups: 1 [ 3] Order 2 Length 15 Maximal Subgroups: 1 [ 4] Order 3 Length 10 Maximal Subgroups: 1 [ 5] Order 5 Length 6 Maximal Subgroups: 1 --- [ 6] Order 4 Length 5 Maximal Subgroups: 3 [ 7] Order 4 Length 15 Maximal Subgroups: 3 [ 8] Order 4 Length 15 Maximal Subgroups: 2 3 [ 9] Order 6 Length 10 Maximal Subgroups: 3 4 [10] Order 6 Length 10 Maximal Subgroups: 2 4 [11] Order 6 Length 10 Maximal Subgroups: 2 4 [12] Order 10 Length 6 Maximal Subgroups: 3 5 --- [13] Order 8 Length 15 Maximal Subgroups: 6 7 8 [14] Order 12 Length 5 Maximal Subgroups: 4 6 [15] Order 12 Length 10 Maximal Subgroups: 8 9 10 11 [16] Order 20 Length 6 Maximal Subgroups: 7 12 --- [17] Order 24 Length 5 Maximal Subgroups: 10 13 14 [18] Order 60 Length 1 Maximal Subgroups: 9 12 14 --- [19] Order 120 Length 1 Maximal Subgroups: 15 16 17 18 Total time: 2.949 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host dsl-58.16.240.220.rns02-kent-syd.dsl.comindico.com.au. (220.240.16.58) Time: Wed Feb 25 08:46:42 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Wed Feb 25 2004 08:46:38 on modular [Seed = 492960317] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee14.uab.es. (158.109.66.14) Time: Wed Feb 25 08:48:59 2004 Input: 21341242 Output: Magma V2.10-6 Wed Feb 25 2004 08:48:55 on modular [Seed = 242411991] ------------------------------------- 21341242 Total time: 3.809 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee14.uab.es. (158.109.66.14) Time: Wed Feb 25 08:49:01 2004 Input: 21341242 Output: Magma V2.10-6 Wed Feb 25 2004 08:48:56 on modular [Seed = 225569499] ------------------------------------- 21341242 Total time: 3.900 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee14.uab.es. (158.109.66.14) Time: Wed Feb 25 08:49:02 2004 Input: 21341242 Output: Magma V2.10-6 Wed Feb 25 2004 08:48:57 on modular [Seed = 141881311] ------------------------------------- 21341242 Total time: 3.709 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cache2.nottingham.ac.uk. (128.243.220.22) Time: Wed Feb 25 08:52:47 2004 Input: Q:=Rationals(); E:=EllipticCurve([Q|1,0,0,-3,4]); E; Output: Magma V2.10-6 Wed Feb 25 2004 08:52:43 on modular [Seed = 743490713] ------------------------------------- Elliptic Curve defined by y^2 + x*y = x^3 - 3*x + 4 over Rational Field Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cache2.nottingham.ac.uk. (128.243.220.22) Time: Wed Feb 25 08:53:34 2004 Input: Q:=Rationals(); E:=EllipticCurve([Q|1,0,0,-3,4]); E; Points(E); Rank(E); MordellWeilGroup(E); Output: Magma V2.10-6 Wed Feb 25 2004 08:53:30 on modular [Seed = 626642401] ------------------------------------- Elliptic Curve defined by y^2 + x*y = x^3 - 3*x + 4 over Rational Field >> Points(E); ^ Runtime error in 'Points': A positive height bound must be given 2 Abelian Group isomorphic to Z + Z Defined on 2 generators (free) Total time: 3.469 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host cache2.nottingham.ac.uk. (128.243.220.22) Time: Wed Feb 25 08:54:36 2004 Input: Q:=Rationals(); E:=EllipticCurve([Q|1,0,0,-3,4]); E; Rank(E); G:=MordellWeilGroup(E); Generators(G); Output: Magma V2.10-6 Wed Feb 25 2004 08:54:32 on modular [Seed = 1529328221] ------------------------------------- Elliptic Curve defined by y^2 + x*y = x^3 - 3*x + 4 over Rational Field 2 { G.2, G.1 } Total time: 3.509 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host cache2.nottingham.ac.uk. (128.243.220.22) Time: Wed Feb 25 08:55:15 2004 Input: Q:=Rationals(); E:=EllipticCurve([Q|1,0,0,-3,4]); E; Rank(E); G:=MordellWeilGroup(E); Gen:=E!Generators(G); Output: Magma V2.10-6 Wed Feb 25 2004 08:55:12 on modular [Seed = 1295098899] ------------------------------------- Elliptic Curve defined by y^2 + x*y = x^3 - 3*x + 4 over Rational Field 2 >> Gen:=E!Generators(G); ^ Runtime error in '!': Illegal coercion Total time: 3.469 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host cache2.nottingham.ac.uk. (128.243.220.22) Time: Wed Feb 25 08:56:00 2004 Input: Q:=Rationals(); E:=EllipticCurve([Q|1,0,0,-3,4]); E; Rank(E); G:=MordellWeilGroup(E); Gen:=E!Generators(G); ? Output: Magma V2.10-6 Wed Feb 25 2004 08:55:56 on modular [Seed = 1094559795] ------------------------------------- Elliptic Curve defined by y^2 + x*y = x^3 - 3*x + 4 over Rational Field 2 >> Gen:=E!Generators(G); ^ Runtime error in '!': Illegal coercion =============================================================================== PATH: /language/statement KIND: Overview =============================================================================== A statement is a complete command to Magma. Every statement must end with a semicolon ( ; ). If you press the key before typing ; then Magma may give you a special prompt symbol such as print> or if> to remind you that the statement is not yet finished. EXAMPLE: > print 5+8; > DivBy3 := func< n | IsZero(n mod 3) >; =============================================================================== Total time: 3.399 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host cache2.nottingham.ac.uk. (128.243.220.22) Time: Wed Feb 25 08:56:11 2004 Input: ? Output: Magma V2.10-6 Wed Feb 25 2004 08:56:08 on modular [Seed = 1913559828] ------------------------------------- =============================================================================== PATH: /language/statement KIND: Overview =============================================================================== A statement is a complete command to Magma. Every statement must end with a semicolon ( ; ). If you press the key before typing ; then Magma may give you a special prompt symbol such as print> or if> to remind you that the statement is not yet finished. EXAMPLE: > print 5+8; > DivBy3 := func< n | IsZero(n mod 3) >; =============================================================================== Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cache2.nottingham.ac.uk. (128.243.220.22) Time: Wed Feb 25 08:56:31 2004 Input: ?? Output: Magma V2.10-6 Wed Feb 25 2004 08:56:28 on modular [Seed = 1796702969] ------------------------------------- 2 matches: 1 O / 2 O /browser To view an entry, type ? followed by the number next to it Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cache2.nottingham.ac.uk. (128.243.220.22) Time: Wed Feb 25 08:56:47 2004 Input: ?2 Output: Magma V2.10-6 Wed Feb 25 2004 08:56:44 on modular [Seed = 1612483042] ------------------------------------- No numbers are defined Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 10:45:28 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-2079+496*y^2-128*y; f1:=-73*y-1794+16*y^3+444*y^2; f2:=-975+240*y^2-60*y; f3:=4*y^4+20*y^2-144; f4:=8*y^3+72*y^2-32*y-288; f5:=120*y^2-480; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 10:45:25 on modular [Seed = 3450949319] ------------------------------------- [ y^2 + y + 12, 3*y + 48, 63 ] Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 10:45:52 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=42368245761+16*y^2+232792432*y; f1:=58198131*y+58780121382; f2:=58780121385+58198080*y; f3:=y^3+9*y^2+14549531*y+11683276569; f4:=15*y^2+3011753685; f5:=14549535*y+5659769115; f6:=15058768725; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 10:45:49 on modular [Seed = 3300411382] ------------------------------------- [ y^2 + y + 12, 3*y + 48, 63 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 10:46:11 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=10295781+16*y^2+102592*y; f1:=25731*y+2573982; f2:=2573955+25560*y; f3:=y^3+9*y^2+6431*y+643464; f4:=15*y^2+765705; f5:=6435*y+643500; f6:=765765; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 10:46:09 on modular [Seed = 4219959461] ------------------------------------- [ y^2 + y + 12, 3*y + 48, 63 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 10:46:32 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=10294881+16*y^2+98992*y; f1:=24471*y+8699787; f2:=5636565+23760*y; f3:=y^3+9*y^2+6431*y+64346; f4:=15*y^2+2297235; f5:=6435*y+2175030; f6:=2297295; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 10:46:29 on modular [Seed = 4069421496] ------------------------------------- [ 1 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 10:46:59 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=5819813841+16*y^2+232792432*y; f1:=58198131*y+49643013402; f2:=49643013405+58198080*y; f3:=y^3+9*y^2+14549531*y+12410753319; f4:=15*y^2+15058768665; f5:=14549535*y+3375492120; f6:=15058768725; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 10:46:56 on modular [Seed = 3918883462] ------------------------------------- [ y^2 + y + 12, 3*y + 48, 63 ] Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 10:47:17 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=1629547761+16*y^2+1629547792*y; f1:=407386971*y+407386962; f2:=-15+407386920*y; f3:=y^3+9*y^2+101846741*y+101846709; f4:=15*y^2+101846685; f5:=101846745; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 10:47:14 on modular [Seed = 3768345469] ------------------------------------- [ y^2 + y + 12, 3*y + 48, 63 ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 10:47:41 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=10295781+16*y^2+102592*y; f1:=25731*y+2573982; f2:=2573955+25560*y; f3:=y^3+9*y^2+6431*y+643464; f4:=15*y^2+765705; f5:=6435*y+643500; f6:=765765; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 10:47:38 on modular [Seed = 676637586] ------------------------------------- [ y^2 + y + 12, 3*y + 48, 63 ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 10:48:02 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=10294881+16*y^2+98992*y; f1:=24471*y+2573667; f2:=2573505+23760*y; f3:=y^3+9*y^2+6431*y+643464; f4:=15*y^2+765705; f5:=6435*y+643500; f6:=765765; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 10:47:59 on modular [Seed = 844018109] ------------------------------------- [ y^2 + y + 12, 3*y + 48, 63 ] Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 10:48:19 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=321+16*y^2+112*y; f1:=51*y+2862; f2:=1485; f3:=y^3+9*y^2+11*y+1029; f4:=15*y+720; f5:=1035; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 10:48:16 on modular [Seed = 994556123] ------------------------------------- [ y^2 + y + 6, 3*y, 9 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 10:48:40 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=321+16*y^2+112*y; f1:=51*y+162; f2:=0; f3:=y^3+9*y^2+11*y+39; f4:=15*y; f5:=45; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 10:48:37 on modular [Seed = 75007985] ------------------------------------- [ y^2 + y + 6, 3*y, 9 ] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 10:49:01 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=3639+16376*y; f1:=y^2+3185*y+2271; f2:=4095; f3:=0; f4:=0; f5:=0; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 10:48:58 on modular [Seed = 225545927] ------------------------------------- [ y + 51, 63 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 10:49:22 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=3639+16376*y; f1:=y^2+3185*y+2271; f2:=4095; f3:=0; f4:=0; f5:=0; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 10:49:19 on modular [Seed = 392926408] ------------------------------------- [ y + 51, 63 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 10:49:42 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=321+16*y^2+112*y; f1:=51*y+702; f2:=405; f3:=y^3+9*y^2+11*y+354; f4:=15*y+225; f5:=945; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 10:49:39 on modular [Seed = 1612506195] ------------------------------------- [ y^2 + y + 6, 3*y, 9 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 10:50:01 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=321+16*y^2+112*y; f1:=51*y+162; f2:=45; f3:=y^3+9*y^2+11*y+39; f4:=0; f5:=15*y; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 10:49:58 on modular [Seed = 1763044719] ------------------------------------- [ y^2 + y + 6, 3*y, 9 ] Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 10:50:25 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=3639+16376*y; f1:=y^2+3185*y+2271; f2:=4095; f3:=0; f4:=0; f5:=0; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 10:50:22 on modular [Seed = 2080438370] ------------------------------------- [ y + 51, 63 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 10:50:41 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=3639+16376*y; f1:=y^2+3185*y+2271; f2:=4095; f3:=0; f4:=0; f5:=0; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 10:50:38 on modular [Seed = 1161412907] ------------------------------------- [ y + 51, 63 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 10:51:02 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=3639+16376*y; f1:=y^2+3185*y+2271; f2:=0; f3:=0; f4:=0; f5:=0; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 10:50:59 on modular [Seed = 1328794380] ------------------------------------- [ y + 230404407, 419233618377 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 10:52:06 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=3639+16376*y; f1:=y^2+3185*y+2271; f2:=0; f3:=0; f4:=0; f5:=0; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(419233618377); Output: Magma V2.10-6 Wed Feb 25 2004 10:52:03 on modular [Seed = 1478810843] ------------------------------------- [ y + 230404407, 419233618377 ] [ <3, 3>, <7, 1>, <17, 1>, <19, 1>, <79, 1>, <86929, 1> ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 10:53:06 2004 Input: Factorization(419233618377);P:=PolynomialRing(IntegerRing(),2); f0:=3639+16376*y; f1:=y^2+3185*y+2271; f2:=0; f3:=0; f4:=0; f5:=0; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 10:53:03 on modular [Seed = 2715624798] ------------------------------------- [ <3, 3>, <7, 1>, <17, 1>, <19, 1>, <79, 1>, <86929, 1> ] [ y + 230404407, 419233618377 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 10:54:30 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=321+16*y^2+112*y; f1:=51*y+162; f2:=0; f3:=y^3+9*y^2+11*y+39; f4:=0; f5:=15*y; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 10:54:27 on modular [Seed = 2899323327] ------------------------------------- [ y^2 + y + 6, 3*y, 9 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 10:55:33 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=321+16*y^2+112*y; f1:=51*y+702; f2:=0; f3:=y^3+9*y^2+11*y+354; f4:=15*y+225; f5:=0; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 10:55:30 on modular [Seed = 3116711147] ------------------------------------- [ y^2 + y + 6, 3*y, 9 ] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 10:56:21 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=3639+16376*y; f1:=y^2+3185*y+2271; f2:=0; f3:=0; f4:=0; f5:=0; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 10:56:18 on modular [Seed = 2197686016] ------------------------------------- [ y + 230404407, 419233618377 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 10:57:13 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=3639+16376*y; f1:=y^2+3185*y+2271; f2:=0; f3:=0; f4:=0; f5:=0; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B;Factorization(419233618377); Output: Magma V2.10-6 Wed Feb 25 2004 10:57:10 on modular [Seed = 2364541306] ------------------------------------- [ y + 230404407, 419233618377 ] [ <3, 3>, <7, 1>, <17, 1>, <19, 1>, <79, 1>, <86929, 1> ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 10:57:51 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=3639+16376*y; f1:=y^2+3185*y+2271; f2:=0; f3:=0; f4:=0; f5:=0; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 10:57:46 on modular [Seed = 2515079246] ------------------------------------- [ y + 230404407, 419233618377 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 10:59:02 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=321+16*y^2+112*y; f1:=51*y+162; f2:=0; f3:=y^3+9*y^2+11*y+39; f4:=15*y; f5:=0; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 10:59:00 on modular [Seed = 2682460667] ------------------------------------- [ y^2 + y + 6, 3*y, 9 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 10:59:50 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=321+16*y^2+112*y; f1:=51*y+2862; f2:=0; f3:=y^3+9*y^2+11*y+1029; f4:=15*y+720; f5:=0; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 10:59:47 on modular [Seed = 3918884794] ------------------------------------- [ y^2 + y + 159, 3*y + 144, 207 ] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:00:43 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=10294881+16*y^2+98992*y; f1:=24471*y+2573667; f2:=2573505+23760*y; f3:=y^3+9*y^2+6431*y+643464; f4:=15*y^2+765705; f5:=6435*y+643500; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 11:00:40 on modular [Seed = 4186275697] ------------------------------------- [ y^2 + y + 12, 3*y + 48, 63 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:01:16 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=10295781+16*y^2+102592*y; f1:=25731*y+2573982; f2:=2573955+25560*y; f3:=y^3+9*y^2+6431*y+643464; f4:=15*y^2+765705; f5:=6435*y+643500; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 11:01:13 on modular [Seed = 3567800893] ------------------------------------- [ y^2 + y + 12, 3*y + 48, 63 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:01:32 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=10295781+16*y^2+102592*y; f1:=25731*y+2573982; f2:=2573955+25560*y; f3:=y^3+9*y^2+6431*y+643464; f4:=15*y^2+765705; f5:=6435*y+643500; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 11:01:29 on modular [Seed = 3718339364] ------------------------------------- [ y^2 + y + 12, 3*y + 48, 63 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:02:06 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=1629547761+16*y^2+1629547792*y; f1:=407386971*y+407386962; f2:=-15+407386920*y; f3:=y^3+9*y^2+101846741*y+101846709; f4:=15*y^2+101846685; f5:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 11:02:03 on modular [Seed = 660316669] ------------------------------------- [ y^2 + y + 12, 3*y + 48, 63 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:02:40 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=5819813841+16*y^2+232792432*y; f1:=58198131*y+49643013402; f2:=49643013405+58198080*y; f3:=y^3+9*y^2+14549531*y+12410753319; f4:=15*y^2+15058768665; f5:=14549535*y+3375492120; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 11:02:37 on modular [Seed = 777169170] ------------------------------------- [ y^2 + y + 12, 3*y + 48, 63 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:03:13 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=10294881+16*y^2+98992*y; f1:=24471*y+8699787; f2:=5636565+23760*y; f3:=y^3+9*y^2+6431*y+64346; f4:=15*y^2+2297235; f5:=6435*y+2175030; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 11:03:10 on modular [Seed = 75006747] ------------------------------------- [ 1 ] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:03:48 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=10295781+16*y^2+102592*y; f1:=25731*y+2573982; f2:=2573955+25560*y; f3:=y^3+9*y^2+6431*y+643464; f4:=15*y^2+765705; f5:=6435*y+643500; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 11:03:44 on modular [Seed = 259229775] ------------------------------------- [ y^2 + y + 12, 3*y + 48, 63 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:04:26 2004 Input: ; P:=PolynomialRing(IntegerRing(),2); f0:=42368245761+16*y^2+232792432*y; f1:=58198131*y+58780121382; f2:=58780121385+58198080*y; f3:=y^3+9*y^2+14549531*y+11683276569; f4:=15*y^2+3011753685; f5:=14549535*y+5659769115; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 11:04:23 on modular [Seed = 409247678] ------------------------------------- [ y^2 + y + 12, 3*y + 48, 63 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:26:33 2004 Input: ; P:=PolynomialRing(IntegerRing(),2); f0:=-2255+496*y^2-128*y; f1:=-81*y-1810+16*y^3+444*y^2; f2:=-1095+240*y^2-60*y; f3:=4*y^4+20*y^2-144; f4:=8*y^3+72*y^2-32*y-288; f5:=120*y^2-480; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 11:26:30 on modular [Seed = 1278263515] ------------------------------------- [ y + 32, 255 ] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:27:02 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=42368245585+16*y^2+232792432*y; f1:=58198123*y+58780121366; f2:=58780121265+58198080*y; f3:=y^3+9*y^2+14549531*y+11683276569; f4:=15*y^2+3011753685; f5:=14549535*y+5659769115; f6:=15058768725; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 11:27:00 on modular [Seed = 1445649059] ------------------------------------- [ y + 32, 255 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:27:30 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=42368245585+16*y^2+232792432*y; f1:=58198123*y+58780121366; f2:=58780121265+58198080*y; f3:=y^3+9*y^2+14549531*y+11683276569; f4:=15*y^2+3011753685; f5:=14549535*y+5659769115; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 11:27:27 on modular [Seed = 2715626863] ------------------------------------- [ y + 32, 255 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:27:53 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=10295781+16*y^2+102592*y; f1:=25723*y+2573966; f2:=2573955+25560*y; f3:=y^3+9*y^2+6431*y+643464; f4:=15*y^2+765705; f5:=6435*y+643500; f6:=765765; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 11:27:49 on modular [Seed = 2832475532] ------------------------------------- [ y + 2, 7 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:28:18 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=10295781+16*y^2+102592*y; f1:=25723*y+2573966; f2:=2573955+25560*y; f3:=y^3+9*y^2+6431*y+643464; f4:=15*y^2+765705; f5:=6435*y+643500; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 11:28:14 on modular [Seed = 3016703628] ------------------------------------- [ y + 2, 7 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:28:40 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=10287025+16*y^2+98992*y; f1:=24463*y+8697251; f2:=5632605+23760*y; f3:=y^3+9*y^2+6431*y+643464; f4:=15*y^2+2297235; f5:=6435*y+2175030; f6:=2297295; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 11:28:37 on modular [Seed = 3133552558] ------------------------------------- [ y + 32, 255 ] Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:29:01 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=10287025+16*y^2+98992*y; f1:=24463*y+8697251; f2:=5632605+23760*y; f3:=y^3+9*y^2+6431*y+643464; f4:=15*y^2+2297235; f5:=6435*y+2175030; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 11:28:57 on modular [Seed = 2247690477] ------------------------------------- [ y + 32, 255 ] Total time: 3.329 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:29:24 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=5819813665+16*y^2+232792432*y; f1:=58198123*y+49643013386; f2:=49643013285+58198080*y; f3:=y^3+9*y^2+14549531*y+12410753319; f4:=15*y^2+15058768665; f5:=14549535*y+3375492120; f6:=15058768725; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 11:29:21 on modular [Seed = 2415067855] ------------------------------------- [ y + 32, 1275 ] Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:29:55 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=5819813665+16*y^2+232792432*y; f1:=58198123*y+49643013386; f2:=49643013285+58198080*y; f3:=y^3+9*y^2+14549531*y+12410753319; f4:=15*y^2+15058768665; f5:=14549535*y+3375492120; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B;Factorization(1275); Output: Magma V2.10-6 Wed Feb 25 2004 11:29:52 on modular [Seed = 2581926968] ------------------------------------- [ y + 32, 1275 ] [ <3, 1>, <5, 2>, <17, 1> ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:30:31 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=1629547585+16*y^2+1629547792*y; f1:=407386963*y+407386946; f2:=-135+407386920*y; f3:=y^3+9*y^2+101846741*y+101846709; f4:=15*y^2+101846685; f5:=101846745; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 11:30:28 on modular [Seed = 3918881900] ------------------------------------- [ y + 32, 255 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:30:54 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=1629547585+16*y^2+1629547792*y; f1:=407386963*y+407386946; f2:=-135+407386920*y; f3:=y^3+9*y^2+101846741*y+101846709; f4:=15*y^2+101846685; f5:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 11:30:51 on modular [Seed = 4035738986] ------------------------------------- [ y + 32, 255 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:31:11 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=10295125+16*y^2+102592*y; f1:=25723*y+2573966; f2:=2573595+25560*y; f3:=y^3+9*y^2+6431*y+643464; f4:=15*y^2+765705; f5:=6435*y+643500; f6:=765765; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 11:31:08 on modular [Seed = 4219958806] ------------------------------------- [ y + 32, 255 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:31:33 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=10295125+16*y^2+102592*y; f1:=25723*y+2573966; f2:=2573595+25560*y; f3:=y^3+9*y^2+6431*y+643464; f4:=15*y^2+765705; f5:=6435*y+643500; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 11:31:30 on modular [Seed = 3267251969] ------------------------------------- [ y + 32, 255 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:31:56 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=10287025+16*y^2+98992*y; f1:=24463*y+2571131; f2:=2569545+23760*y; f3:=y^3+9*y^2+6431*y+643464; f4:=15*y^2+765705; f5:=6435*y+643500; f6:=765765; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 11:31:53 on modular [Seed = 3450945557] ------------------------------------- [ y + 32, 255 ] Total time: 3.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:32:15 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=10287025+16*y^2+98992*y; f1:=24463*y+2571131; f2:=2569545+23760*y; f3:=y^3+9*y^2+6431*y+643464; f4:=15*y^2+765705; f5:=6435*y+643500; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 11:32:12 on modular [Seed = 3567803129] ------------------------------------- [ y + 32, 255 ] Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:32:34 2004 Input: PP:=PolynomialRing(IntegerRing(),2); f0:=145+16*y^2+112*y; f1:=43*y+2846; f2:=1365; f3:=y^3+9*y^2+11*y+1029; f4:=15*y+720; f5:=1035; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 11:32:31 on modular [Seed = 3752022497] ------------------------------------- >> I:=ideal; ^ User error: Identifier 'P' has not been declared or assigned >> B:=GroebnerBasis(I:Al:="Direct"); ^ User error: Identifier 'I' has not been declared or assigned >> B;; ^ User error: Identifier 'B' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:32:47 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=145+16*y^2+112*y; f1:=43*y+2846; f2:=1365; f3:=y^3+9*y^2+11*y+1029; f4:=15*y+720; f5:=1035; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 11:32:44 on modular [Seed = 626633515] ------------------------------------- [ y + 2, 15 ] Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:33:08 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=145+16*y^2+112*y; f1:=43*y+2846; f2:=1365; f3:=y^3+9*y^2+11*y+1029; f4:=15*y+720; f5:=0; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 11:33:05 on modular [Seed = 860863824] ------------------------------------- [ y + 2, 15 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:33:26 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=145+16*y^2+112*y; f1:=43*y+146; f2:=0; f3:=y^3+9*y^2+11*y+39; f4:=15*y; f5:=45; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 11:33:23 on modular [Seed = 944027209] ------------------------------------- [ y + 2, 15 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:33:45 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=145+16*y^2+112*y; f1:=43*y+146; f2:=0; f3:=y^3+9*y^2+11*y+39; f4:=15*y; f5:=0; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 11:33:42 on modular [Seed = 25005893] ------------------------------------- [ y + 2, 15 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:34:15 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=3631+16376*y; f1:=y^2+3185*y+2271; f2:=4095; f3:=0; f4:=0; f5:=0; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 11:34:12 on modular [Seed = 259228073] ------------------------------------- [ y + 2, 3 ] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:34:32 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=3631+16376*y; f1:=y^2+3185*y+2271; f2:=0; f3:=0; f4:=0; f5:=0; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 11:34:29 on modular [Seed = 342399651] ------------------------------------- [ y + 155216476610, 419650820697 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:35:08 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=3631+16376*y; f1:=y^2+3185*y+2271; f2:=0; f3:=0; f4:=0; f5:=0; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(419650820697); Output: Magma V2.10-6 Wed Feb 25 2004 11:35:05 on modular [Seed = 1629351930] ------------------------------------- [ y + 155216476610, 419650820697 ] [ <3, 1>, <139883606899, 1> ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:35:41 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=3631+16376*y; f1:=y^2+3185*y+2271; f2:=4095; f3:=0; f4:=0; f5:=0; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 11:35:37 on modular [Seed = 1846730902] ------------------------------------- [ y + 2, 3 ] Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:35:58 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=3631+16376*y; f1:=y^2+3185*y+2271; f2:=0; f3:=0; f4:=0; f5:=0; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 11:35:55 on modular [Seed = 1946745533] ------------------------------------- [ y + 155216476610, 419650820697 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:36:27 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=3631+16376*y; f1:=y^2+3185*y+2271; f2:=0; f3:=0; f4:=0; f5:=0; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(419650820697); Output: Magma V2.10-6 Wed Feb 25 2004 11:36:24 on modular [Seed = 2097279575] ------------------------------------- [ y + 155216476610, 419650820697 ] [ <3, 1>, <139883606899, 1> ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:36:54 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=145+16*y^2+112*y; f1:=43*y+686; f2:=825; f3:=y^3+9*y^2+11*y+354; f4:=15*y+225; f5:=945; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 11:36:51 on modular [Seed = 1245103435] ------------------------------------- [ y + 2, 15 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:37:17 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=145+16*y^2+112*y; f1:=43*y+686; f2:=0; f3:=y^3+9*y^2+11*y+354; f4:=15*y+225; f5:=0; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 11:37:14 on modular [Seed = 1395645515] ------------------------------------- [ y + 2, 15 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:37:39 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=145+16*y^2+112*y; f1:=43*y+146; f2:=75; f3:=y^3+9*y^2+11*y+39; f4:=0; f5:=15*y; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 11:37:36 on modular [Seed = 1478809386] ------------------------------------- [ y + 2, 15 ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:37:58 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=145+16*y^2+112*y; f1:=43*y+146; f2:=0; f3:=y^3+9*y^2+11*y+39; f4:=0; f5:=15*y; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 11:37:55 on modular [Seed = 2715627232] ------------------------------------- [ y + 2, 15 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:38:18 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=3631+16376*y; f1:=y^2+3185*y+2271; f2:=4095; f3:=0; f4:=0; f5:=0; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(419233618377); Output: Magma V2.10-6 Wed Feb 25 2004 11:38:15 on modular [Seed = 2933006843] ------------------------------------- [ y + 2, 3 ] [ <3, 3>, <7, 1>, <17, 1>, <19, 1>, <79, 1>, <86929, 1> ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:38:49 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=3631+16376*y; f1:=y^2+3185*y+2271; f2:=4095; f3:=0; f4:=0; f5:=0; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 11:38:46 on modular [Seed = 3033021184] ------------------------------------- [ y + 2, 3 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:39:07 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=3631+16376*y; f1:=y^2+3185*y+2271; f2:=0; f3:=0; f4:=0; f5:=0; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 11:39:04 on modular [Seed = 2197687560] ------------------------------------- [ y + 155216476610, 419650820697 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:39:42 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=3631+16376*y; f1:=y^2+3185*y+2271; f2:=0; f3:=0; f4:=0; f5:=0; f6:=0; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B;Factorization(419650820697); Output: Magma V2.10-6 Wed Feb 25 2004 11:39:39 on modular [Seed = 2348221538] ------------------------------------- [ y + 155216476610, 419650820697 ] [ <3, 1>, <139883606899, 1> ] Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:54:21 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f3:=630*x^8+630*y^8-322560+151*x^7-151*y^7+70*x^5-70*y^5+49*x^3-49*y^3+45*x-45*y; I:=ideal; B:=GroebnerBasis(I:Al:="Direct",RemoveRedundant:="False", ReduceInitial:="False"); B; C:=Coordinates(I, f5); &+[C[i]*I[i]: i in [1 .. #C]] Output: Magma V2.10-6 Wed Feb 25 2004 11:54:18 on modular [Seed = 3968892916] ------------------------------------- >> B:=GroebnerBasis(I:Al:="Direct",RemoveRedundant:="False", ReduceInitial:="F ^ Runtime error in 'GroebnerBasis': Bad type for parameter 'RemoveRedundant' Argument types given: RngMPol >> B; ^ User error: Identifier 'B' has not been declared or assigned >> C:=Coordinates(I, f5); ^ User error: Identifier 'f5' has not been declared or assigned >> &+[C[i]*I[i]: i in [1 .. #C]] ^ User error: Identifier 'C' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:55:10 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f3:=630*x^8+630*y^8-322560+151*x^7-151*y^7+70*x^5-70*y^5+49*x^3-49*y^3+45*x-45*y; I:=ideal; B:=GroebnerBasis(I:Al:="Direct",RemoveRedundant:="F", ReduceInitial:="F"); B; C:=Coordinates(I, f5); &+[C[i]*I[i]: i in [1 .. #C]] Output: Magma V2.10-6 Wed Feb 25 2004 11:55:07 on modular [Seed = 4186270384] ------------------------------------- >> B:=GroebnerBasis(I:Al:="Direct",RemoveRedundant:="F", ReduceInitial:="F"); ^ Runtime error in 'GroebnerBasis': Bad type for parameter 'RemoveRedundant' Argument types given: RngMPol >> B; ^ User error: Identifier 'B' has not been declared or assigned >> C:=Coordinates(I, f5); ^ User error: Identifier 'f5' has not been declared or assigned >> &+[C[i]*I[i]: i in [1 .. #C]] ^ User error: Identifier 'C' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:55:37 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f3:=630*x^8+630*y^8-322560+151*x^7-151*y^7+70*x^5-70*y^5+49*x^3-49*y^3+45*x-45*y; I:=ideal; B:=GroebnerBasis(I:Al:="Direct",RemoveRedundant:=False, ReduceInitial:="F"); B; C:=Coordinates(I, f5); &+[C[i]*I[i]: i in [1 .. #C]] Output: Magma V2.10-6 Wed Feb 25 2004 11:55:34 on modular [Seed = 3334100322] ------------------------------------- >> B:=GroebnerBasis(I:Al:="Direct",RemoveRedundant:=False, ReduceInitial:="F") ^ User error: Identifier 'False' has not been declared or assigned >> B; ^ User error: Identifier 'B' has not been declared or assigned >> C:=Coordinates(I, f5); ^ User error: Identifier 'f5' has not been declared or assigned >> &+[C[i]*I[i]: i in [1 .. #C]] ^ User error: Identifier 'C' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:57:48 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Wed Feb 25 2004 11:57:45 on modular [Seed = 3534636793] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:58:09 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f3:=630*x^8+630*y^8-322560+151*x^7-151*y^7+70*x^5-70*y^5+49*x^3-49*y^3+45*x-45*y; I:=ideal; B:=GroebnerBasis(I:Al:="Direct",RemoveRedundant:=false, ReduceInitial:=false); B; C:=Coordinates(I, f5); &+[C[i]*I[i]: i in [1 .. #C]] Output: Magma V2.10-6 Wed Feb 25 2004 11:58:06 on modular [Seed = 3685175271] ------------------------------------- [ x^2 + 8*x + 31*y^2 - 8*y - 128, x*y + 2*x + 4*y^3 + 111*y^2 - 18*y - 448, 15*x + 60*y^2 - 15*y - 240, 4*y^4 + 20*y^2 - 144, 8*y^3 + 72*y^2 - 32*y - 288, 120*y^2 - 480 ] >> C:=Coordinates(I, f5); ^ User error: Identifier 'f5' has not been declared or assigned >> &+[C[i]*I[i]: i in [1 .. #C]] ^ User error: Identifier 'C' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:58:38 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f3:=630*x^8+630*y^8-322560+151*x^7-151*y^7+70*x^5-70*y^5+49*x^3-49*y^3+45*x-45*y; I:=ideal; B:=GroebnerBasis(I:Al:="Direct",RemoveRedundant:=false, ReduceInitial:=false); B; C:=Coordinates(I, f3); &+[C[i]*I[i]: i in [1 .. #C]] Output: Magma V2.10-6 Wed Feb 25 2004 11:58:35 on modular [Seed = 559789369] ------------------------------------- [ x^2 + 8*x + 31*y^2 - 8*y - 128, x*y + 2*x + 4*y^3 + 111*y^2 - 18*y - 448, 15*x + 60*y^2 - 15*y - 240, 4*y^4 + 20*y^2 - 144, 8*y^3 + 72*y^2 - 32*y - 288, 120*y^2 - 480 ] >> &+[C[i]*I[i]: i in [1 .. #C]] ^ Runtime error in '[]': Bad argument types Total time: 2.979 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 11:59:25 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f3:=630*x^8+630*y^8-322560+151*x^7-151*y^7+70*x^5-70*y^5+49*x^3-49*y^3+45*x-45*y; I:=ideal; B:=GroebnerBasis(I:Al:="Direct",RemoveRedundant:=false, ReduceInitial:=false); B; C:=Coordinates(I, f3); C; &+[C[i]*I[i]: i in [1 .. #C]] Output: Magma V2.10-6 Wed Feb 25 2004 11:59:22 on modular [Seed = 794016614] ------------------------------------- [ x^2 + 8*x + 31*y^2 - 8*y - 128, x*y + 2*x + 4*y^3 + 111*y^2 - 18*y - 448, 15*x + 60*y^2 - 15*y - 240, 4*y^4 + 20*y^2 - 144, 8*y^3 + 72*y^2 - 32*y - 288, 120*y^2 - 480 ] [ -1109*x^5 + 8872*x^4 - 57598*x^3 + 354320*x^2, -2520*x^6*y + 5670*x^6 + 10080*x^5*y^3 + 236880*x^5*y^2 - 1148490*x^5*y + 1270080*x^5 - 40320*x^4*y^5 - 1985760*x^4*y^4 - 17546760*x^4*y^3 + 166275270*x^4*y^2 - 388045621*x^4*y + 284420290*x^4 + 161280*x^3*y^7 + 12096000*x^3*y^6 + 265688640*x^3*y^5 + 697404960*x^3*y^4 - 19504644566*x^3*y^3 + 76076678283*x^3*y^2 - 116217784006*x^3*y + 63710766000*x^3 - 645120*x^2*y^9 - 64995840*x^2*y^8 - 2272515840*x^2*y^7 - 27446045760*x^2*y^6 + 65700122744*x^2*y^5 + 1860890388206*x^2*y^4 - 11740067109909*x^2*y^3 + 28756764624010*x^2*y^2 - 32594990729806*x^2*y + 14271207552140*x^2 + 2580480*x*y^11 + 326430720*x*y^10 + 15640128000*x*y^9 + 329294246400*x*y^8 + 2055098674144*x*y^7 - 20358588445696*x*y^6 - 129994614050926*x*y^5 + 1511039300782731*x*y^4 - 5461341825973422*x*y^3 + 9741714490739698*x*y^2 - 8771212303757544*x*y + 3196750497191745*x + 9608212196855846*y^6 - 194083458873883757*y^5 + 919555211877484874*y^4 - 2192017751029310206*y^3 + 3073522788584162324*y^2 - 2295478611972998751*y, 42*x^7 - 142889*x^2 + 2322*x - 688128*y^14 - 106143744*y^13 - 6583191552*y^12 - 203079959040*y^11 + 47933041387473602*y + 95476281516163939, -11086073195104*x*y^6 - 33436881317000*x*y^5 + 796504709024958*x*y^4 - 6579048511979686623503, 5160960*y^13 + 748339200*y^12 + 42439864320*y^11 + 1128792268800*y^10 - 10540701420480*y^9 + 94816918203840*y^8 - 854878547839680*y^7 + 2889603253807277*y^6 - 62284749214718879*y^5 + 2796094391604790865*y^4 - 36871410392892689930*y^3 + 360862630561749941698*y^2 + 31732448250255228654, 1954627346502994768561 ] >> &+[C[i]*I[i]: i in [1 .. #C]] ^ Runtime error in '[]': Bad argument types Total time: 2.979 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 12:00:03 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f3:=630*x^8+630*y^8-322560+151*x^7-151*y^7+70*x^5-70*y^5+49*x^3-49*y^3+45*x-45*y; I:=ideal; B:=GroebnerBasis(I:Al:="Direct",RemoveRedundant:=false, ReduceInitial:=false); B; C:=Coordinates(I, f3); C; // &+[C[i]*I[i]: i in [1 .. #C]] Output: Magma V2.10-6 Wed Feb 25 2004 12:00:00 on modular [Seed = 894017926] ------------------------------------- [ x^2 + 8*x + 31*y^2 - 8*y - 128, x*y + 2*x + 4*y^3 + 111*y^2 - 18*y - 448, 15*x + 60*y^2 - 15*y - 240, 4*y^4 + 20*y^2 - 144, 8*y^3 + 72*y^2 - 32*y - 288, 120*y^2 - 480 ] [ -1109*x^5 + 8872*x^4 - 57598*x^3 + 354320*x^2, -2520*x^6*y + 5670*x^6 + 10080*x^5*y^3 + 236880*x^5*y^2 - 1148490*x^5*y + 1270080*x^5 - 40320*x^4*y^5 - 1985760*x^4*y^4 - 17546760*x^4*y^3 + 166275270*x^4*y^2 - 388045621*x^4*y + 284420290*x^4 + 161280*x^3*y^7 + 12096000*x^3*y^6 + 265688640*x^3*y^5 + 697404960*x^3*y^4 - 19504644566*x^3*y^3 + 76076678283*x^3*y^2 - 116217784006*x^3*y + 63710766000*x^3 - 645120*x^2*y^9 - 64995840*x^2*y^8 - 2272515840*x^2*y^7 - 27446045760*x^2*y^6 + 65700122744*x^2*y^5 + 1860890388206*x^2*y^4 - 11740067109909*x^2*y^3 + 28756764624010*x^2*y^2 - 32594990729806*x^2*y + 14271207552140*x^2 + 2580480*x*y^11 + 326430720*x*y^10 + 15640128000*x*y^9 + 329294246400*x*y^8 + 2055098674144*x*y^7 - 20358588445696*x*y^6 - 129994614050926*x*y^5 + 1511039300782731*x*y^4 - 5461341825973422*x*y^3 + 9741714490739698*x*y^2 - 8771212303757544*x*y + 3196750497191745*x + 9608212196855846*y^6 - 194083458873883757*y^5 + 919555211877484874*y^4 - 2192017751029310206*y^3 + 3073522788584162324*y^2 - 2295478611972998751*y, 42*x^7 - 142889*x^2 + 2322*x - 688128*y^14 - 106143744*y^13 - 6583191552*y^12 - 203079959040*y^11 + 47933041387473602*y + 95476281516163939, -11086073195104*x*y^6 - 33436881317000*x*y^5 + 796504709024958*x*y^4 - 6579048511979686623503, 5160960*y^13 + 748339200*y^12 + 42439864320*y^11 + 1128792268800*y^10 - 10540701420480*y^9 + 94816918203840*y^8 - 854878547839680*y^7 + 2889603253807277*y^6 - 62284749214718879*y^5 + 2796094391604790865*y^4 - 36871410392892689930*y^3 + 360862630561749941698*y^2 + 31732448250255228654, 1954627346502994768561 ] Total time: 3.169 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 12:00:51 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f3:=630*x^8+630*y^8-322560+151*x^7-151*y^7+70*x^5-70*y^5+49*x^3-49*y^3+45*x-45*y; I:=ideal; B:=GroebnerBasis(I:Al:="Direct",RemoveRedundant:=false, ReduceInitial:=false); B; C:=Coordinates(I, f3); C; &+[C[i]*B[i]: i in [1 .. #C]] Output: Magma V2.10-6 Wed Feb 25 2004 12:00:48 on modular [Seed = 192389096] ------------------------------------- [ x^2 + 8*x + 31*y^2 - 8*y - 128, x*y + 2*x + 4*y^3 + 111*y^2 - 18*y - 448, 15*x + 60*y^2 - 15*y - 240, 4*y^4 + 20*y^2 - 144, 8*y^3 + 72*y^2 - 32*y - 288, 120*y^2 - 480 ] [ -1109*x^5 + 8872*x^4 - 57598*x^3 + 354320*x^2, -2520*x^6*y + 5670*x^6 + 10080*x^5*y^3 + 236880*x^5*y^2 - 1148490*x^5*y + 1270080*x^5 - 40320*x^4*y^5 - 1985760*x^4*y^4 - 17546760*x^4*y^3 + 166275270*x^4*y^2 - 388045621*x^4*y + 284420290*x^4 + 161280*x^3*y^7 + 12096000*x^3*y^6 + 265688640*x^3*y^5 + 697404960*x^3*y^4 - 19504644566*x^3*y^3 + 76076678283*x^3*y^2 - 116217784006*x^3*y + 63710766000*x^3 - 645120*x^2*y^9 - 64995840*x^2*y^8 - 2272515840*x^2*y^7 - 27446045760*x^2*y^6 + 65700122744*x^2*y^5 + 1860890388206*x^2*y^4 - 11740067109909*x^2*y^3 + 28756764624010*x^2*y^2 - 32594990729806*x^2*y + 14271207552140*x^2 + 2580480*x*y^11 + 326430720*x*y^10 + 15640128000*x*y^9 + 329294246400*x*y^8 + 2055098674144*x*y^7 - 20358588445696*x*y^6 - 129994614050926*x*y^5 + 1511039300782731*x*y^4 - 5461341825973422*x*y^3 + 9741714490739698*x*y^2 - 8771212303757544*x*y + 3196750497191745*x + 9608212196855846*y^6 - 194083458873883757*y^5 + 919555211877484874*y^4 - 2192017751029310206*y^3 + 3073522788584162324*y^2 - 2295478611972998751*y, 42*x^7 - 142889*x^2 + 2322*x - 688128*y^14 - 106143744*y^13 - 6583191552*y^12 - 203079959040*y^11 + 47933041387473602*y + 95476281516163939, -11086073195104*x*y^6 - 33436881317000*x*y^5 + 796504709024958*x*y^4 - 6579048511979686623503, 5160960*y^13 + 748339200*y^12 + 42439864320*y^11 + 1128792268800*y^10 - 10540701420480*y^9 + 94816918203840*y^8 - 854878547839680*y^7 + 2889603253807277*y^6 - 62284749214718879*y^5 + 2796094391604790865*y^4 - 36871410392892689930*y^3 + 360862630561749941698*y^2 + 31732448250255228654, 1954627346502994768561 ] 630*x^8 + 151*x^7 + 70*x^5 + 49*x^3 + 45*x + 630*y^8 - 151*y^7 - 70*y^5 - 49*y^3 - 45*y - 322560 Total time: 2.919 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 12:18:00 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 12:17:57 on modular [Seed = 1128258469] ------------------------------------- [ y + 32, 48 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 12:28:57 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 12:28:54 on modular [Seed = 1512489263] ------------------------------------- >> ; ^ User error: bad syntax >> B:=GroebnerBasis(I:Al:="Direct"); ^ User error: Identifier 'I' has not been declared or assigned >> B; ^ User error: Identifier 'B' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 12:29:18 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 12:29:15 on modular [Seed = 2698787816] ------------------------------------- >> ; ^ User error: bad syntax >> B:=GroebnerBasis(I:Al:="Direct"); ^ User error: Identifier 'I' has not been declared or assigned >> B; ^ User error: Identifier 'B' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 12:30:09 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 12:30:06 on modular [Seed = 3083545610] ------------------------------------- [ y + 2, 3 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 12:30:48 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 12:30:45 on modular [Seed = 3200394584] ------------------------------------- [ y + 2, 3 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 12:31:15 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 12:31:12 on modular [Seed = 2247695942] ------------------------------------- [ y + 2, 3 ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 12:31:40 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 12:31:37 on modular [Seed = 2364544854] ------------------------------------- [ y + 2, 3 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 12:32:16 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 12:32:13 on modular [Seed = 2615609253] ------------------------------------- [ y + 2, 3 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 12:32:38 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 12:32:35 on modular [Seed = 3802038002] ------------------------------------- [ y + 2, 3 ] Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 12:33:07 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 12:33:04 on modular [Seed = 3902043291] ------------------------------------- [ y + 2, 3 ] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 12:33:28 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 12:33:25 on modular [Seed = 4153109425] ------------------------------------- [ y + 2, 3 ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 12:33:48 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 12:33:45 on modular [Seed = 4269957796] ------------------------------------- [ y + 2, 3 ] Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 12:34:08 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 12:34:05 on modular [Seed = 3300415594] ------------------------------------- [ y + 2, 3 ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 12:34:32 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 12:34:29 on modular [Seed = 3551481685] ------------------------------------- [ y + 2, 3 ] Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 12:34:55 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 12:34:52 on modular [Seed = 3668330053] ------------------------------------- [ y + 2, 3 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 12:35:13 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 12:35:10 on modular [Seed = 576634568] ------------------------------------- [ y + 2, 3 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 12:35:34 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 12:35:31 on modular [Seed = 727169004] ------------------------------------- [ y + 2, 3 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 25 12:35:55 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 25 2004 12:35:52 on modular [Seed = 1027711457] ------------------------------------- [ y + 2, 3 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cactus.lirmm.fr. (193.49.106.78) Time: Wed Feb 25 12:50:41 2004 Input: cvp Output: Magma V2.10-6 Wed Feb 25 2004 12:50:37 on modular [Seed = 459782993] ------------------------------------- >> cvp ^ User error: Identifier 'cvp' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cactus.lirmm.fr. (193.49.106.78) Time: Wed Feb 25 12:50:58 2004 Input: ? Output: Magma V2.10-6 Wed Feb 25 2004 12:50:54 on modular [Seed = 1829883191] ------------------------------------- =============================================================================== PATH: / KIND: Overview =============================================================================== You are reading about the Magma online help system. This system gives you information about Magma while you are at the computer. To see this help page at any time, all you have to do is to type ? ---------- The online help system comes in two modes: the single request mode and the Magma Help Browser. To enter the Browser, type ?? The Browser is useful if you intend to read several related help nodes, because you can exploit the tree structure of the online help. Once you are in the Browser, you can type help again to find out how to use the Browser, and for a more detailed explanation of the whole online help system. ---------- Single help requests begin with the ? character. Examples are: ?print ?magma ?ring ?example If your help request is ambiguous, Magma will return a numbered list of matches. To see the contents of one of them, type ? followed by its number. Some help pages suggest other pages that you might like to look at as well. They are prefixed by a code such as +3 or +5 . To read one of them, type ? followed by the code. You can also supply the full pathname of a help node, if you know it. For example: ?/system/quit ?/magma/module/homomorphism ---------- The online help system offers tab completion. If you type a few letters of your help request and then press the tab key, Magma will "complete" the request if there is a unique completion. Otherwise, it will complete the request as far as possible, and then emit a beep. Press the tab key again to see all the possibilities. ALWAYS PRESS TAB BEFORE THE END OF THE LINE, SO AS TO SEE EVERY RELEVANT HELP PAGE. (On a few operating systems, the tab completion feature cannot be made available.) ---------- The content of the online help system comes from two sources: the "Handbook of Magma Functions" (Bosma and Cannon) and specially-written overview nodes. You may also wish to consult the books "An Introduction to Algebraic Programming in Magma" (Cannon and Playoust) and "Solving Problems with Magma" (Bosma, Cannon, Playoust and Steel). ---------- The online help system is also available in an HTML form suitable for Internet browsers. To use this, move to a shell prompt (outside Magma) and type magmahelp ---------- To leave Magma, type quit; or -D. =============================================================================== Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cactus.lirmm.fr. (193.49.106.78) Time: Wed Feb 25 12:51:22 2004 Input: ?magma Output: Magma V2.10-6 Wed Feb 25 2004 12:51:19 on modular [Seed = 1980421829] ------------------------------------- 24 matches: 1 O /magma 2 O /system/Magma 3 O /system/Magma/update 4 S /magma/combinatorial-geometrical-incidence/plane/introduction/\ planes-in-magma 5 S /magma/group/automatic/creation/magma 6 S /magma/group/group-overview/creation-general/magma 7 S /magma/group/matrix/creation-general-linear-group/magma 8 S /magma/group/permutation/creation-symmetric/magma 9 S /magma/group/polycyclic/polycyclic-groups/magma 10 S /magma/group/rewrite-system/creation/magma 11 S /magma/module-lattice/vector-space-linear-transformation/\ creation-arithmetic/creation-magma 12 S /magma/ring-field-algebra/abelian-extension/introduction/magma 13 S /magma/ring-field-algebra/alg_grp/creation/complete-magma 14 S /magma/ring-field-algebra/algebraic-field/creation/magma 15 S /magma/ring-field-algebra/integer/nfs/nfs-data-files-formats/\ nfs-magma-native 16 S /magma/ring-field-algebra/matrix/creation/complete-magma 17 S /magma/ring-field-algebra/matrix/creation/general-magma 18 S /magma/ring-field-algebra/rational-function-field/operation/magma 19 S /magma/ring-field-algebra/rational/creation/magma 20 S /magma/ring-field-algebra/real-complex/creation/magma 21 S /magma/ring-field-algebra/univariate-polynomial/creation/magma 22 S /magma/semigroup/finitely-presented/presentation/general-magma 23 I /language/IO/print/printing-file/PrintFileMagma 24 I /magma/ring-field-algebra/detail/generic/predicate/\ IsMagmaEuclideanRing To view an entry, type ? followed by the number next to it Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cactus.lirmm.fr. (193.49.106.78) Time: Wed Feb 25 12:51:40 2004 Input: ?lattice Output: Magma V2.10-6 Wed Feb 25 2004 12:51:37 on modular [Seed = 2130960370] ------------------------------------- 72 matches: 1 O /magma/module-lattice 2 S /magma/group/braid/braid-groups-elements/braid-groups-lattice 3 S /magma/group/braid/braid-groups-introduction/\ braid-groups-introduction-lattice 4 S /magma/module-lattice/general/submodule-lattice 5 S /magma/module-lattice/general/submodule-lattice/lattice-element 6 S /magma/module-lattice/general/submodule-lattice/lattice-element 7 S /magma/module-lattice/lattice 8 S /magma/module-lattice/lattice/lattice-properties 9 S /magma/module-lattice/lattice/lattice-properties/\ lattice-attributes 10 S /magma/module-lattice/lattice/lattice-properties/\ lattice-predicates 11 S /magma/ring-field-algebra/algebraic-field/subfields/\ subfield-lattice 12 I /magma/combinatorial-geometrical-incidence/graph/\ group-code-design/constr-misc/SquareLatticeGraph 13 I /magma/combinatorial-geometrical-incidence/modular-symbol/\ l-series/winding/WindingLattice 14 I /magma/combinatorial-geometrical-incidence/modular-symbol/\ underlying-representation/Lattice 15 I /magma/combinatorial-geometrical-incidence/tableaux-chap/words/\ ordered-monoid/IsReverseLatticeWord 16 I /magma/group/databases-overview/quatgps/Lattice 17 I /magma/group/databases-overview/quatgps/Lattice 18 I /magma/group/databases-overview/ratgps/Lattice 19 I /magma/group/databases-overview/ratgps/Lattice 20 I /magma/group/fiurg/action/weights/WeightLattice 21 I /magma/group/fiurg/action/weights/WeightLattice 22 I /magma/group/group-overview/\ characteristic-subgroup-normal-structure/subgroup-series/\ NormalLattice 23 I /magma/group/group-overview/subgroup/subgroup-poset/creation/\ SubgroupLattice 24 I /magma/group/groups-lie-type/operations/WeightLattice 25 I /magma/group/groups-lie-type/operations/WeightLattice 26 I /magma/group/permutation/\ characteristic-subgroup-normal-structure/normal-subgroups/\ NormalLattice 27 I /magma/group/root-data/roots-coroots-weights/weights/\ CoweightLattice 28 I /magma/group/root-data/roots-coroots-weights/weights/WeightLattice 29 I /magma/group/soluble/normal-series/normals/NormalLattice 30 I /magma/group/soluble/subgroups/subgroup-classes/SubgroupLattice 31 I /magma/lie-theory/finite-coxeter-groups/root-data-roots/weights/\ WeightLattice 32 I /magma/lie-theory/finite-coxeter-groups/root-data-roots/weights/\ WeightLattice 33 I /magma/module-lattice/general/submodule-lattice/create/\ SubmoduleLattice 34 I /magma/module-lattice/general/submodule-lattice/create/\ SubmoduleLatticeAbort 35 I /magma/module-lattice/lattice/creation/anf/MinkowskiLattice 36 I /magma/module-lattice/lattice/creation/anf/MinkowskiLattice 37 I /magma/module-lattice/lattice/creation/anf/MinkowskiLattice 38 I /magma/module-lattice/lattice/creation/code/Lattice 39 I /magma/module-lattice/lattice/creation/code/Lattice 40 I /magma/module-lattice/lattice/creation/creation/CoordinateLattice 41 I /magma/module-lattice/lattice/creation/creation/Lattice 42 I /magma/module-lattice/lattice/creation/creation/Lattice 43 I /magma/module-lattice/lattice/creation/creation/LatticeWithBasis 44 I /magma/module-lattice/lattice/creation/creation/LatticeWithBasis 45 I /magma/module-lattice/lattice/creation/creation/LatticeWithBasis 46 I /magma/module-lattice/lattice/creation/creation/LatticeWithBasis 47 I /magma/module-lattice/lattice/creation/creation/LatticeWithBasis 48 I /magma/module-lattice/lattice/creation/creation/LatticeWithGram 49 I /magma/module-lattice/lattice/creation/creation/LatticeWithGram 50 I /magma/module-lattice/lattice/creation/creation/ScaledLattice 51 I /magma/module-lattice/lattice/creation/creation/ScaledLattice 52 I /magma/module-lattice/lattice/creation/creation/StandardLattice 53 I /magma/module-lattice/lattice/creation/special-lattices/Lattice 54 I /magma/module-lattice/lattice/G-lattices/create/Lattice 55 I /magma/module-lattice/lattice/G-lattices/create/LatticeWithBasis 56 I /magma/module-lattice/lattice/G-lattices/create/LatticeWithBasis 57 I /magma/module-lattice/lattice/G-lattices/create/LatticeWithGram 58 I /magma/module-lattice/lattice/latdb/access/Lattice 59 I /magma/module-lattice/lattice/latdb/access/LatticeData 60 I /magma/module-lattice/lattice/latdb/access/LatticeData 61 I /magma/module-lattice/lattice/latdb/access/LatticeData 62 I /magma/module-lattice/lattice/latdb/creation/LatticeDatabase 63 I /magma/module-lattice/lattice/latdb/information/LatticeName 64 I /magma/module-lattice/lattice/latdb/information/LatticeName 65 I /magma/module-lattice/lattice/latdb/information/LatticeName 66 I /magma/module-lattice/lattice/new-construction/construction/\ DualBasisLattice 67 I /magma/module-lattice/lattice/new-construction/construction/\ PureLattice 68 I /magma/module-lattice/quadratic/invar/Lattice 69 I /magma/ring-field-algebra/algebraic-field/ideal/ideal-other/\ Lattice 70 I /magma/ring-field-algebra/algebraic-field/ideal/ideal-other/\ Lattice 71 I /magma/ring-field-algebra/algebraic-field/operation/related/\ Lattice 72 I /magma/ring-field-algebra/algebraic-field/subfields/\ subfield-lattice/SubfieldLattice To view an entry, type ? followed by the number next to it Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Feb 25 13:49:03 2004 Input: A;=Matrix(2,2,[1,1,1,1]); A; Output: Magma V2.10-6 Wed Feb 25 2004 13:49:00 on modular [Seed = 4286796231] ------------------------------------- >> A;=Matrix(2,2,[1,1,1,1]); ^ User error: Identifier 'A' has not been declared or assigned >> A;=Matrix(2,2,[1,1,1,1]); ^ User error: bad syntax >> A;; ^ User error: Identifier 'A' has not been declared or assigned Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Feb 25 13:49:24 2004 Input: A:=Matrix(2,2,[1,1,1,1]); A; Output: Magma V2.10-6 Wed Feb 25 2004 13:49:21 on modular [Seed = 3250417620] ------------------------------------- [1 1] [1 1] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Feb 25 13:50:37 2004 Input: R:=PolynomialRing(RationalField()); Output: Magma V2.10-6 Wed Feb 25 2004 13:50:34 on modular [Seed = 3517808527] ------------------------------------- Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Feb 25 14:01:48 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2+1); OK:=MaximalOrder(K); I:=2004*OK; I; Output: Magma V2.10-6 Wed Feb 25 2004 14:01:45 on modular [Seed = 944015620] ------------------------------------- Principal Ideal of OK Generator: [2004, 0] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Feb 25 14:02:27 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2+1); OK:=MaximalOrder(K); I:=2004*OK; Factorization(I); Output: Magma V2.10-6 Wed Feb 25 2004 14:02:24 on modular [Seed = 58700390] ------------------------------------- [ , , ] Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Feb 25 14:05:25 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2+1); OK:=MaximalOrder(K); [K!x : x in Basis(OK)]; Output: Magma V2.10-6 Wed Feb 25 2004 14:05:21 on modular [Seed = 292397253] ------------------------------------- [ 1, a ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Feb 25 14:07:51 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^6+x^5+x^4+x^3+x^2+1); OK:=MaximalOrder(K); [K!x : x in Basis(OK)]; I:=7*OK; Factorization(I); J:=3*OK; Factorization(J); Output: Magma V2.10-6 Wed Feb 25 2004 14:07:48 on modular [Seed = 409250489] ------------------------------------- >> K:=NumberField(x^6+x^5+x^4+x^3+x^2+1); ^ Runtime error in 'NumberField': Argument 1 is not irreducible >> OK:=MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> [K!x : x in Basis(OK)]; ^ User error: Identifier 'OK' has not been declared or assigned >> I:=7*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I); ^ User error: Identifier 'I' has not been declared or assigned >> J:=3*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(J);; ^ User error: Identifier 'J' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Feb 25 14:08:13 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^6+x^5+x^4+x^3+x^2+x+1); OK:=MaximalOrder(K); [K!x : x in Basis(OK)]; I:=7*OK; Factorization(I); J:=3*OK; Factorization(J); Output: Magma V2.10-6 Wed Feb 25 2004 14:08:10 on modular [Seed = 1663029724] ------------------------------------- [ 1, a, a^2, a^3, a^4, a^5 ] [ ] [ ] Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Feb 25 14:11:04 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK:=MaximalOrder(K); I:=(3/8)*OK; Factorization(I); Output: Magma V2.10-6 Wed Feb 25 2004 14:11:01 on modular [Seed = 2080427804] ------------------------------------- [ , ] Total time: 3.039 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Feb 25 14:14:59 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK:=MaximalOrder(K); [K!x : x in Basis(OK)]; Output: Magma V2.10-6 Wed Feb 25 2004 14:14:56 on modular [Seed = 1278277721] ------------------------------------- [ 1, 1/2*(a + 1) ] Total time: 2.889 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Feb 25 14:15:42 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK:=MaximalOrder(K); [K!x : x in Basis(OK)]; I:=(3/8)*OK; Factorization(I); Output: Magma V2.10-6 Wed Feb 25 2004 14:15:39 on modular [Seed = 1395648301] ------------------------------------- [ 1, 1/2*(a + 1) ] [ , ] Total time: 2.939 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Wed Feb 25 17:26:50 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+1); OK := RingOfIntegers(K); Factorization(2004*OK); Output: Magma V2.10-6 Wed Feb 25 2004 17:26:47 on modular [Seed = 1378825055] ------------------------------------- [ , , ] Total time: 3.319 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Wed Feb 25 17:33:02 2004 Input: (2+3i)^4*3*167 Output: Magma V2.10-6 Wed Feb 25 2004 17:32:58 on modular [Seed = 2715599633] ------------------------------------- >> (2+3i)^4*3*167 ^ User error: bad syntax Total time: 3.869 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Wed Feb 25 17:35:43 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+1); OK := RingOfIntegers(K); Factorization(2004*OK); Output: Magma V2.10-6 Wed Feb 25 2004 17:35:38 on modular [Seed = 2498361220] ------------------------------------- [ , , ] Total time: 3.459 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Wed Feb 25 18:56:50 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(CyclotomicPolynomial(7)); OK := RingOfIntegers(K); Factorization(3*OK); Output: Magma V2.10-6 Wed Feb 25 2004 18:56:46 on modular [Seed = 1094465362] ------------------------------------- [ ] Total time: 3.040 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Wed Feb 25 18:57:08 2004 Input: R := PolynomialRing(RationalField()) K := NumberField(CyclotomicPolynomial(7)) OK := RingOfIntegers(K) Factorization(3*OK); Output: Magma V2.10-6 Wed Feb 25 2004 18:57:04 on modular [Seed = 1478831653] ------------------------------------- >> K := NumberField(CyclotomicPolynomial(7)) ^ User error: bad syntax >> Factorization(3*OK);; ^ User error: bad syntax Total time: 3.319 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Wed Feb 25 18:57:22 2004 Input: R := PolynomialRing(RationalField()), K := NumberField(CyclotomicPolynomial(7)), OK := RingOfIntegers(K), Factorization(3*OK); Output: Magma V2.10-6 Wed Feb 25 2004 18:57:18 on modular [Seed = 1395533088] ------------------------------------- >> R := PolynomialRing(RationalField()), ^ User error: bad syntax >> K := NumberField(CyclotomicPolynomial(7)), ^ User error: bad syntax >> OK := RingOfIntegers(K), ^ User error: bad syntax >> Factorization(3*OK);; ^ User error: Identifier 'OK' has not been declared or assigned Total time: 3.359 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Wed Feb 25 18:57:39 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(CyclotomicPolynomial(7)); OK := RingOfIntegers(K); Factorization(3*OK); Output: Magma V2.10-6 Wed Feb 25 2004 18:57:35 on modular [Seed = 2866273512] ------------------------------------- [ ] Total time: 3.759 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Wed Feb 25 18:58:22 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(CyclotomicPolynomial(7)); OK := RingOfIntegers(K); Factorization(7*OK); Output: Magma V2.10-6 Wed Feb 25 2004 18:58:19 on modular [Seed = 3183528715] ------------------------------------- [ ] Total time: 3.319 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Wed Feb 25 18:58:58 2004 Input: CyclotomicPolynomial(7); Output: Magma V2.10-6 Wed Feb 25 2004 18:58:54 on modular [Seed = 3033121319] ------------------------------------- $.1^6 + $.1^5 + $.1^4 + $.1^3 + $.1^2 + $.1 + 1 Total time: 3.349 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Wed Feb 25 18:59:49 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(CyclotomicPolynomial(7)); OK := RingOfIntegers(K); Factorization(7*OK); Output: Magma V2.10-6 Wed Feb 25 2004 18:59:41 on modular [Seed = 2314534729] ------------------------------------- [ ] Total time: 3.970 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Wed Feb 25 19:04:05 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-5); OK := RingOfIntegers(K); Factorization(3/7*OK); Output: Magma V2.10-6 Wed Feb 25 2004 19:04:01 on modular [Seed = 3835269944] ------------------------------------- [ , ] Total time: 3.269 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Wed Feb 25 19:11:18 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-5); OK := RingOfIntegers(K); I:=3*OK; J:=8*OK M:=I/J; Output: Magma V2.10-6 Wed Feb 25 2004 19:11:14 on modular [Seed = 3467884353] ------------------------------------- >> M:=I/J; ^ User error: bad syntax Total time: 3.449 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Wed Feb 25 19:11:35 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-5); OK := RingOfIntegers(K); I := 3*OK; J := 8*OK M := I/J; Output: Magma V2.10-6 Wed Feb 25 2004 19:11:32 on modular [Seed = 3250370648] ------------------------------------- >> M := I/J; ^ User error: bad syntax Total time: 3.379 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Wed Feb 25 19:11:52 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-5); OK := RingOfIntegers(K); I := 3*OK; J := 8*OK; M := I/J; Output: Magma V2.10-6 Wed Feb 25 2004 19:11:48 on modular [Seed = 3567889725] ------------------------------------- Total time: 3.299 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Wed Feb 25 19:12:14 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-5); OK := RingOfIntegers(K); I := 3*OK; J := 8*OK; M := I/J; Factorization(M); Output: Magma V2.10-6 Wed Feb 25 2004 19:12:11 on modular [Seed = 743527897] ------------------------------------- [ , ] Total time: 3.359 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Wed Feb 25 19:12:56 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-5); OK := RingOfIntegers(K); Factorization(3/8*OK); Output: Magma V2.10-6 Wed Feb 25 2004 19:12:52 on modular [Seed = 626548495] ------------------------------------- [ , ] Total time: 3.499 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host dsl-200-67-214-213.prod-infinitum.com.mx. (200.67.214.213) Time: Wed Feb 25 20:33:17 2004 Input: G := sub; Output: Magma V2.10-6 Wed Feb 25 2004 20:33:13 on modular [Seed = 309272292] ------------------------------------- >> ; ^ User error: bad syntax Total time: 3.529 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dsl-200-67-214-213.prod-infinitum.com.mx. (200.67.214.213) Time: Wed Feb 25 20:33:33 2004 Input: G := sub Output: Magma V2.10-6 Wed Feb 25 2004 20:33:29 on modular [Seed = 1762944431] ------------------------------------- Total time: 3.569 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dsl-200-67-214-213.prod-infinitum.com.mx. (200.67.214.213) Time: Wed Feb 25 20:34:09 2004 Input: Order(sub) Output: Magma V2.10-6 Wed Feb 25 2004 20:34:05 on modular [Seed = 1612541250] ------------------------------------- >> ) ^ User error: bad syntax Total time: 3.679 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dsl-200-67-214-213.prod-infinitum.com.mx. (200.67.214.213) Time: Wed Feb 25 20:35:07 2004 Input: FactoredOrder(sub) Output: Magma V2.10-6 Wed Feb 25 2004 20:35:04 on modular [Seed = 1913618197] ------------------------------------- >> ) ^ User error: bad syntax Total time: 3.399 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dsl-200-67-214-213.prod-infinitum.com.mx. (200.67.214.213) Time: Wed Feb 25 20:35:29 2004 Input: print FactoredOrder(sub) Output: Magma V2.10-6 Wed Feb 25 2004 20:35:25 on modular [Seed = 1228162107] ------------------------------------- >> ) ^ User error: bad syntax Total time: 3.449 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dsl-200-67-214-213.prod-infinitum.com.mx. (200.67.214.213) Time: Wed Feb 25 20:36:43 2004 Input: G:=sub print FactoredOrder(G) Output: Magma V2.10-6 Wed Feb 25 2004 20:36:10 on modular [Seed = 3183521822] ------------------------------------- >> print FactoredOrder(G) ^ User error: bad syntax Total time: 4.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dsl-200-67-214-213.prod-infinitum.com.mx. (200.67.214.213) Time: Wed Feb 25 20:38:07 2004 Input: G:=sub ; print FactoredOrder(G) ; Output: Magma V2.10-6 Wed Feb 25 2004 20:37:59 on modular [Seed = 2982984809] ------------------------------------- [ <2, 27>, <3, 14>, <5, 3>, <7, 2>, <11, 1> ] Total time: 3.419 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dsl-200-67-214-213.prod-infinitum.com.mx. (200.67.214.213) Time: Wed Feb 25 20:41:10 2004 Input: G:=sub ; print Order(G) ; Output: Magma V2.10-6 Wed Feb 25 2004 20:41:05 on modular [Seed = 2164100638] ------------------------------------- 43252003274489856000 Total time: 4.239 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dsl-200-67-214-213.prod-infinitum.com.mx. (200.67.214.213) Time: Wed Feb 25 20:42:53 2004 Input: G:=sub ; print Center(G) ; Output: Magma V2.10-6 Wed Feb 25 2004 20:42:09 on modular [Seed = 2532022700] ------------------------------------- Permutation group acting on a set of cardinality 48 Order = 2 (2, 47)(4, 10)(5, 16)(7, 13)(18, 44)(19, 20)(21, 22)(23, 45)(25, 36)(28, 34)(31, 37)(39, 42) Total time: 4.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Feb 26 02:05:27 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; [IsHomogeneous(f): f in S]; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; Write("resultMod2-3-2", S); Output: WARNING: MAGMA command contains unsafe command 'write', so it will not be executed. ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Feb 26 02:05:56 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; [IsHomogeneous(f): f in S]; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; Output: Magma V2.10-6 Thu Feb 26 2004 02:05:46 on modular [Seed = 2114167939] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 >> [IsHomogeneous(f): f in S]; ^ User error: Identifier 'S' has not been declared or assigned 0 [] Total time: 3.700 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Feb 26 02:06:37 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; Output: Magma V2.10-6 Thu Feb 26 2004 02:06:34 on modular [Seed = 1696120748] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] Total time: 3.509 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Feb 26 02:07:22 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; Output: Magma V2.10-6 Thu Feb 26 2004 02:07:19 on modular [Seed = 1395558471] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 Total time: 3.469 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Feb 26 02:10:45 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Feb 26 2004 02:10:41 on modular [Seed = 1111464320] ------------------------------------- [ 2*y^2 + 2*y + 24, 3*y + 48, 63 ] Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Feb 26 02:11:33 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Feb 26 2004 02:11:26 on modular [Seed = 1328714594] ------------------------------------- [ 2*y^2 + 2*y + 24, 3*y + 48, 63 ] Total time: 3.239 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Feb 26 02:11:52 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S; Output: Magma V2.10-6 Thu Feb 26 2004 02:11:48 on modular [Seed = 3066784433] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] [ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, y^11, y^12, y^13, y^14, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x*y^11, x*y^12, x*y^13, x*y^14, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^2*y^11, x^2*y^12, x^2*y^13, x^2*y^14, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^11*y^5, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ] Total time: 3.799 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Feb 26 02:11:57 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Feb 26 2004 02:11:53 on modular [Seed = 3183501751] ------------------------------------- [ y^2 + y + 12, 3*y + 48, 63 ] Total time: 3.319 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Feb 26 02:12:18 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Feb 26 2004 02:12:15 on modular [Seed = 2765715672] ------------------------------------- [ y^2 + y + 12, 3*y + 48, 63 ] Total time: 3.279 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Feb 26 02:12:41 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Feb 26 2004 02:12:38 on modular [Seed = 2481868742] ------------------------------------- [ 2*y^2 + 2*y + 24, 3*y + 48, 63 ] Total time: 3.459 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Feb 26 02:13:03 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Feb 26 2004 02:13:00 on modular [Seed = 2598848213] ------------------------------------- [ 4*y^2 + 73*y + 18, 105*y + 105, 315 ] Total time: 3.479 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Feb 26 02:13:24 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Feb 26 2004 02:13:20 on modular [Seed = 2164087843] ------------------------------------- [ y^2 + y + 12, 3*y + 48, 63 ] Total time: 3.279 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Feb 26 02:13:48 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Feb 26 2004 02:13:45 on modular [Seed = 2415022869] ------------------------------------- [ y^2 + y + 12, 3*y + 48, 63 ] Total time: 3.329 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Feb 26 02:14:12 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Feb 26 2004 02:14:09 on modular [Seed = 4136315396] ------------------------------------- [ 2*y^2 + 2*y + 3, 3*y, 9 ] Total time: 3.289 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Feb 26 02:14:39 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Feb 26 2004 02:14:32 on modular [Seed = 4253032726] ------------------------------------- [ 2*y^2 + 2*y + 3, 3*y, 9 ] Total time: 3.809 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Feb 26 02:15:03 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Feb 26 2004 02:14:55 on modular [Seed = 3835246628] ------------------------------------- [ y + 51, 63 ] Total time: 3.559 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Feb 26 02:15:41 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Feb 26 2004 02:15:22 on modular [Seed = 3618245358] ------------------------------------- [ y + 51, 63 ] Total time: 3.539 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Feb 26 02:16:02 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Feb 26 2004 02:15:56 on modular [Seed = 3735225280] ------------------------------------- [ 2*y^2 + 2*y + 3, 3*y, 9 ] Total time: 3.609 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Feb 26 02:16:22 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Feb 26 2004 02:16:17 on modular [Seed = 3300465078] ------------------------------------- [ 2*y^2 + 2*y + 3, 3*y, 9 ] Total time: 3.819 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Feb 26 02:16:42 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Feb 26 2004 02:16:39 on modular [Seed = 877259095] ------------------------------------- [ y + 51, 63 ] Total time: 3.499 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Feb 26 02:17:06 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Feb 26 2004 02:17:02 on modular [Seed = 1027661927] ------------------------------------- [ y + 51, 63 ] Total time: 3.409 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Feb 26 02:19:29 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Feb 26 2004 02:18:38 on modular [Seed = 643562460] ------------------------------------- [ y + 32, 255 ] Total time: 4.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Feb 26 02:20:11 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Feb 26 2004 02:20:08 on modular [Seed = 392874251] ------------------------------------- [ y + 32, 255 ] Total time: 3.389 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Feb 26 02:20:34 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Feb 26 2004 02:20:30 on modular [Seed = 409323027] ------------------------------------- [ y + 32, 255 ] Total time: 3.400 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Feb 26 02:20:58 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Feb 26 2004 02:20:55 on modular [Seed = 24960866] ------------------------------------- [ y + 32, 255 ] Total time: 3.459 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Feb 26 02:21:18 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Feb 26 2004 02:21:14 on modular [Seed = 175625300] ------------------------------------- [ y + 32, 1275 ] Total time: 3.419 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Feb 26 02:21:49 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Feb 26 2004 02:21:45 on modular [Seed = 1930341838] ------------------------------------- [ y + 32, 255 ] Total time: 3.329 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Feb 26 02:22:08 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Feb 26 2004 02:22:05 on modular [Seed = 1696119756] ------------------------------------- [ y + 32, 255 ] Total time: 3.369 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Feb 26 02:22:28 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Feb 26 2004 02:22:24 on modular [Seed = 1846784234] ------------------------------------- [ y + 32, 255 ] Total time: 3.389 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Feb 26 02:23:09 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Feb 26 2004 02:22:47 on modular [Seed = 1462405544] ------------------------------------- [ y + 2, 15 ] Total time: 4.329 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Feb 26 02:23:48 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Feb 26 2004 02:23:41 on modular [Seed = 1529251217] ------------------------------------- [ y + 2, 15 ] Total time: 4.229 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Feb 26 02:24:07 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Feb 26 2004 02:24:04 on modular [Seed = 1278317420] ------------------------------------- [ y + 2, 3 ] Total time: 3.449 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Feb 26 02:24:31 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Feb 26 2004 02:24:27 on modular [Seed = 3049810602] ------------------------------------- [ y + 2, 3 ] Total time: 3.759 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Feb 26 02:24:54 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Feb 26 2004 02:24:50 on modular [Seed = 3200475592] ------------------------------------- [ y + 2, 15 ] Total time: 3.699 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Feb 26 02:25:05 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Feb 26 2004 02:25:01 on modular [Seed = 2749267162] ------------------------------------- [ y + 2, 15 ] Total time: 3.539 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Feb 26 02:25:26 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Feb 26 2004 02:25:22 on modular [Seed = 2515028675] ------------------------------------- [ y + 2, 15 ] Total time: 3.629 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Feb 26 02:25:45 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Feb 26 2004 02:25:41 on modular [Seed = 2665693663] ------------------------------------- [ y + 2, 3 ] Total time: 3.519 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Feb 26 02:26:08 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Feb 26 2004 02:26:04 on modular [Seed = 2281330751] ------------------------------------- [ y + 2, 3 ] Total time: 3.499 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Feb 26 03:10:35 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S; Output: Magma V2.10-6 Thu Feb 26 2004 03:10:31 on modular [Seed = 660262629] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] [ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, y^11, y^12, y^13, y^14, y^15, y^16, y^17, y^18, y^19, y^20, y^21, y^22, y^23, y^24, y^25, y^26, y^27, y^28, y^29, y^30, y^31, y^32, y^33, y^34, y^35, y^36, y^37, y^38, y^39, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x*y^11, x*y^12, x*y^13, x*y^14, x*y^15, x*y^16, x*y^17, x*y^18, x*y^19, x*y^20, x*y^21, x*y^22, x*y^23, x*y^24, x*y^25, x*y^26, x*y^27, x*y^28, x*y^29, x*y^30, x*y^31, x*y^32, x*y^33, x*y^34, x*y^35, x*y^36, x*y^37, x*y^38, x*y^39, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^2*y^11, x^2*y^12, x^2*y^13, x^2*y^14, x^2*y^15, x^2*y^16, x^2*y^17, x^2*y^18, x^2*y^19, x^2*y^20, x^2*y^21, x^2*y^22, x^2*y^23, x^2*y^24, x^2*y^25, x^2*y^26, x^2*y^27, x^2*y^28, x^2*y^29, x^2*y^30, x^2*y^31, x^2*y^32, x^2*y^33, x^2*y^34, x^2*y^35, x^2*y^36, x^2*y^37, x^2*y^38, x^2*y^39, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^3*y^13, x^3*y^14, x^3*y^15, x^3*y^16, x^3*y^17, x^3*y^18, x^3*y^19, x^3*y^20, x^3*y^21, x^3*y^22, x^3*y^23, x^3*y^24, x^3*y^25, x^3*y^26, x^3*y^27, x^3*y^28, x^3*y^29, x^3*y^30, x^3*y^31, x^3*y^32, x^3*y^33, x^3*y^34, x^3*y^35, x^3*y^36, x^3*y^37, x^3*y^38, x^3*y^39, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^4*y^15, x^4*y^16, x^4*y^17, x^4*y^18, x^4*y^19, x^4*y^20, x^4*y^21, x^4*y^22, x^4*y^23, x^4*y^24, x^4*y^25, x^4*y^26, x^4*y^27, x^4*y^28, x^4*y^29, x^4*y^30, x^4*y^31, x^4*y^32, x^4*y^33, x^4*y^34, x^4*y^35, x^4*y^36, x^4*y^37, x^4*y^38, x^4*y^39, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^5*y^15, x^5*y^16, x^5*y^17, x^5*y^18, x^5*y^19, x^5*y^20, x^5*y^21, x^5*y^22, x^5*y^23, x^5*y^24, x^5*y^25, x^5*y^26, x^5*y^27, x^5*y^28, x^5*y^29, x^5*y^30, x^5*y^31, x^5*y^32, x^5*y^33, x^5*y^34, x^5*y^35, x^5*y^36, x^5*y^37, x^5*y^38, x^5*y^39, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^6*y^15, x^6*y^16, x^6*y^17, x^6*y^18, x^6*y^19, x^6*y^20, x^6*y^21, x^6*y^22, x^6*y^23, x^6*y^24, x^6*y^25, x^6*y^26, x^6*y^27, x^6*y^28, x^6*y^29, x^6*y^30, x^6*y^31, x^6*y^32, x^6*y^33, x^6*y^34, x^6*y^35, x^6*y^36, x^6*y^37, x^6*y^38, x^6*y^39, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^7*y^15, x^7*y^16, x^7*y^17, x^7*y^18, x^7*y^19, x^7*y^20, x^7*y^21, x^7*y^22, x^7*y^23, x^7*y^24, x^7*y^25, x^7*y^26, x^7*y^27, x^7*y^28, x^7*y^29, x^7*y^30, x^7*y^31, x^7*y^32, x^7*y^33, x^7*y^34, x^7*y^35, x^7*y^36, x^7*y^37, x^7*y^38, x^7*y^39, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^8*y^7, x^8*y^8, x^8*y^9, x^8*y^10, x^8*y^11, x^8*y^12, x^8*y^13, x^8*y^14, x^8*y^15, x^8*y^16, x^8*y^17, x^8*y^18, x^8*y^19, x^8*y^20, x^8*y^21, x^8*y^22, x^8*y^23, x^8*y^24, x^8*y^25, x^8*y^26, x^8*y^27, x^8*y^28, x^8*y^29, x^8*y^30, x^8*y^31, x^8*y^32, x^8*y^33, x^8*y^34, x^8*y^35, x^8*y^36, x^8*y^37, x^8*y^38, x^8*y^39, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^9*y^7, x^9*y^8, x^9*y^9, x^9*y^10, x^9*y^11, x^9*y^12, x^9*y^13, x^9*y^14, x^9*y^15, x^9*y^16, x^9*y^17, x^9*y^18, x^9*y^19, x^9*y^20, x^9*y^21, x^9*y^22, x^9*y^23, x^9*y^24, x^9*y^25, x^9*y^26, x^9*y^27, x^9*y^28, x^9*y^29, x^9*y^30, x^9*y^31, x^9*y^32, x^9*y^33, x^9*y^34, x^9*y^35, x^9*y^36, x^9*y^37, x^9*y^38, x^9*y^39, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^10*y^7, x^10*y^8, x^10*y^9, x^10*y^10, x^10*y^11, x^10*y^12, x^10*y^13, x^10*y^14, x^10*y^15, x^10*y^16, x^10*y^17, x^10*y^18, x^10*y^19, x^10*y^20, x^10*y^21, x^10*y^22, x^10*y^23, x^10*y^24, x^10*y^25, x^10*y^26, x^10*y^27, x^10*y^28, x^10*y^29, x^10*y^30, x^10*y^31, x^10*y^32, x^10*y^33, x^10*y^34, x^10*y^35, x^10*y^36, x^10*y^37, x^10*y^38, x^10*y^39, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^11*y^5, x^11*y^6, x^11*y^7, x^11*y^8, x^11*y^9, x^11*y^10, x^11*y^11, x^11*y^12, x^11*y^13, x^11*y^14, x^11*y^15, x^11*y^16, x^11*y^17, x^11*y^18, x^11*y^19, x^11*y^20, x^11*y^21, x^11*y^22, x^11*y^23, x^11*y^24, x^11*y^25, x^11*y^26, x^11*y^27, x^11*y^28, x^11*y^29, x^11*y^30, x^11*y^31, x^11*y^32, x^11*y^33, x^11*y^34, x^11*y^35, x^11*y^36, x^11*y^37, x^11*y^38, x^11*y^39, x^12, x^12*y, x^12*y^2, x^12*y^3, x^12*y^4, x^12*y^5, x^12*y^6, x^12*y^7, x^12*y^8, x^12*y^9, x^12*y^10, x^12*y^11, x^12*y^12, x^12*y^13, x^12*y^14, x^12*y^15, x^12*y^16, x^12*y^17, x^12*y^18, x^12*y^19, x^12*y^20, x^12*y^21, x^12*y^22, x^12*y^23, x^12*y^24, x^12*y^25, x^12*y^26, x^12*y^27, x^12*y^28, x^12*y^29, x^12*y^30, x^12*y^31, x^12*y^32, x^12*y^33, x^12*y^34, x^12*y^35, x^12*y^36, x^12*y^37, x^12*y^38, x^12*y^39, x^13, x^13*y, x^13*y^2, x^13*y^3, x^13*y^4, x^13*y^5, x^13*y^6, x^13*y^7, x^13*y^8, x^13*y^9, x^13*y^10, x^13*y^11, x^13*y^12, x^13*y^13, x^13*y^14, x^13*y^15, x^13*y^16, x^13*y^17, x^13*y^18, x^13*y^19, x^13*y^20, x^13*y^21, x^13*y^22, x^13*y^23, x^13*y^24, x^13*y^25, x^13*y^26, x^13*y^27, x^13*y^28, x^13*y^29, x^13*y^30, x^13*y^31, x^13*y^32, x^13*y^33, x^13*y^34, x^13*y^35, x^13*y^36, x^13*y^37, x^13*y^38, x^13*y^39, x^14, x^14*y, x^14*y^2, x^14*y^3, x^14*y^4, x^14*y^5, x^14*y^6, x^14*y^7, x^14*y^8, x^14*y^9, x^14*y^10, x^14*y^11, x^14*y^12, x^14*y^13, x^14*y^14, x^14*y^15, x^14*y^16, x^14*y^17, x^14*y^18, x^14*y^19, x^14*y^20, x^14*y^21, x^14*y^22, x^14*y^23, x^14*y^24, x^14*y^25, x^14*y^26, x^14*y^27, x^14*y^28, x^14*y^29, x^14*y^30, x^14*y^31, x^14*y^32, x^14*y^33, x^14*y^34, x^14*y^35, x^14*y^36, x^14*y^37, x^14*y^38, x^14*y^39, x^15, x^15*y, x^15*y^2, x^15*y^3, x^15*y^4, x^15*y^5, x^15*y^6, x^15*y^7, x^15*y^8, x^15*y^9, x^15*y^10, x^15*y^11, x^15*y^12, x^15*y^13, x^15*y^14, x^15*y^15, x^15*y^16, x^15*y^17, x^15*y^18, x^15*y^19, x^15*y^20, x^15*y^21, x^15*y^22, x^15*y^23, x^15*y^24, x^15*y^25, x^15*y^26, x^15*y^27, x^15*y^28, x^15*y^29, x^15*y^30, x^15*y^31, x^15*y^32, x^15*y^33, x^15*y^34, x^15*y^35, x^15*y^36, x^15*y^37, x^15*y^38, x^15*y^39, x^16, x^16*y, x^16*y^2, x^16*y^3, x^16*y^4, x^16*y^5, x^16*y^6, x^16*y^7, x^16*y^8, x^16*y^9, x^16*y^10, x^16*y^11, x^16*y^12, x^16*y^13, x^16*y^14, x^16*y^15, x^16*y^16, x^16*y^17, x^16*y^18, x^16*y^19, x^16*y^20, x^16*y^21, x^16*y^22, x^16*y^23, x^16*y^24, x^16*y^25, x^16*y^26, x^16*y^27, x^16*y^28, x^16*y^29, x^16*y^30, x^16*y^31, x^16*y^32, x^16*y^33, x^16*y^34, x^16*y^35, x^16*y^36, x^16*y^37, x^16*y^38, x^16*y^39, x^17, x^17*y, x^17*y^2, x^17*y^3, x^17*y^4, x^17*y^5, x^17*y^6, x^17*y^7, x^17*y^8, x^17*y^9, x^17*y^10, x^17*y^11, x^17*y^12, x^17*y^13, x^17*y^14, x^17*y^15, x^17*y^16, x^17*y^17, x^17*y^18, x^17*y^19, x^17*y^20, x^17*y^21, x^17*y^22, x^17*y^23, x^17*y^24, x^17*y^25, x^17*y^26, x^17*y^27, x^17*y^28, x^17*y^29, x^17*y^30, x^17*y^31 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Feb 26 03:19:20 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; L := [y^39]; HomogeneousModuleTestBasis(P, S, L ) ; Output: Magma V2.10-6 Thu Feb 26 2004 03:19:15 on modular [Seed = 292355367] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] [] Total time: 4.349 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Feb 26 03:19:48 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; L := [y^2]; HomogeneousModuleTestBasis(P, S, L ) ; Output: Magma V2.10-6 Thu Feb 26 2004 03:19:44 on modular [Seed = 409334797] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] [] Total time: 4.119 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Feb 26 03:20:48 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; L := [y^40]; HomogeneousModuleTestBasis(P, S, L ) ; Output: Magma V2.10-6 Thu Feb 26 2004 03:20:32 on modular [Seed = 141943916] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] [] Total time: 5.189 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Feb 26 03:29:39 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; L := [y^40]; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Thu Feb 26 2004 03:29:34 on modular [Seed = 2047317025] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] [ true ] Total time: 4.129 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Feb 26 03:39:01 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S' := [y^40]; S' subset S ; Output: Magma V2.10-6 Thu Feb 26 2004 03:38:06 on modular [Seed = 1395565337] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] >> S' := [y^40]; ^ User error: Unexpected newline in literal identifier >> S' subset S ;; ^ User error: Unexpected newline in literal identifier Total time: 5.429 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Feb 26 03:40:38 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S' := [y^40]; S'; Output: Magma V2.10-6 Thu Feb 26 2004 03:40:33 on modular [Seed = 1111470966] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] >> S' := [y^40]; ^ User error: Unexpected newline in literal identifier >> S';; ^ User error: Unexpected newline in literal identifier Total time: 4.589 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Feb 26 03:41:23 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S':= [y^40]; S'; Output: Magma V2.10-6 Thu Feb 26 2004 03:41:19 on modular [Seed = 3049800879] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] >> S':= [y^40]; ^ User error: Unexpected newline in literal identifier >> S';; ^ User error: Unexpected newline in literal identifier Total time: 4.009 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Feb 26 04:25:08 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S':={y^40}; S' meet S; Output: Magma V2.10-6 Thu Feb 26 2004 04:24:26 on modular [Seed = 2949797078] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] >> S':={y^40}; ^ User error: Unexpected newline in literal identifier >> S' meet S; ^ User error: Unexpected newline in literal identifier Total time: 5.129 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Feb 26 04:27:25 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S' := { y^40 }; S' meet S; Output: Magma V2.10-6 Thu Feb 26 2004 04:27:12 on modular [Seed = 2448190038] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] >> S' := { y^40 }; ^ User error: Unexpected newline in literal identifier >> S' meet S; ^ User error: Unexpected newline in literal identifier Total time: 5.009 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Feb 26 04:30:11 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; %I:=ideal; %Dimension(I); %V,phi:=VectorSpace(quo); %S:=[R!(v@@phi ): v in Basis(V)]; %S' := { y^40 }; %S' meet S; Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed. ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Feb 26 04:31:38 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; S' := { 1, 2, 3 }; S := { 1, 1/2, 1/3 }; S' join S; S' meet S; S' diff S; %I:=ideal; %Dimension(I); %V,phi:=VectorSpace(quo); %S:=[R!(v@@phi ): v in Basis(V)]; %S' := { y^40 }; %S' meet S; Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed. ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Feb 26 04:31:57 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; S' := { 1, 2, 3 }; S := { 1, 1/2, 1/3 }; S' join S; S' meet S; S' diff S; Output: Magma V2.10-6 Thu Feb 26 2004 04:31:54 on modular [Seed = 4069461967] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 >> S' := { 1, 2, 3 }; ^ User error: Unexpected newline in literal identifier >> S' join S; ^ User error: Unexpected newline in literal identifier >> S' meet S; ^ User error: Unexpected newline in literal identifier >> S' diff S; ^ User error: Unexpected newline in literal identifier Total time: 3.369 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Feb 26 04:34:57 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S' := { y^40 }; S' subset S; Output: Magma V2.10-6 Thu Feb 26 2004 04:34:50 on modular [Seed = 4169467252] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] >> S' := { y^40 }; ^ User error: Unexpected newline in literal identifier >> S' subset S; ^ User error: Unexpected newline in literal identifier Total time: 4.819 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Feb 26 04:39:20 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; { y^40 } subset S; Output: Magma V2.10-6 Thu Feb 26 2004 04:39:16 on modular [Seed = 3918796570] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] false Total time: 4.089 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Feb 26 04:40:46 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; { y^39 } subset S; Output: Magma V2.10-6 Thu Feb 26 2004 04:39:54 on modular [Seed = 3501010443] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] true Total time: 4.309 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Feb 26 04:50:14 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; { x^12*y^27 } subset S; Output: Magma V2.10-6 Thu Feb 26 2004 04:49:50 on modular [Seed = 960804927] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] true Total time: 5.189 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host dk285.clare.cam.ac.uk. (131.111.230.244) Time: Thu Feb 26 04:50:48 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Thu Feb 26 2004 04:50:44 on modular [Seed = 743550304] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.449 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dk285.clare.cam.ac.uk. (131.111.230.244) Time: Thu Feb 26 04:51:01 2004 Input: 3+4 Output: Magma V2.10-6 Thu Feb 26 2004 04:50:58 on modular [Seed = 626566303] ------------------------------------- 7 Total time: 3.629 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Feb 26 04:59:36 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; { x^13*y^27 } subset S; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Feb 26 2004 04:59:04 on modular [Seed = 141921112] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] Errors: /home/mfd/gomagma: line 2: 30768 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Feb 26 05:00:09 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; { x^13*y^27 } subset S; Output: Magma V2.10-6 Thu Feb 26 2004 05:00:04 on modular [Seed = 2030369509] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] true Total time: 4.129 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Feb 26 05:02:38 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; { x^27*y^13 } subset S; Output: Magma V2.10-6 Thu Feb 26 2004 05:01:27 on modular [Seed = 1997206347] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] false Total time: 5.919 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Feb 26 05:03:02 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; { x^27*y^12 } subset S; Output: Magma V2.10-6 Thu Feb 26 2004 05:02:57 on modular [Seed = 1361892664] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] true Total time: 4.099 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host roam23-100.fas.harvard.edu. (140.247.23.100) Time: Thu Feb 26 09:15:06 2004 Input: Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+1); OK := RingOfIntegers(K); Factorization(2004*OK); Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed. ************** MAGMA ***************** Host roam23-100.fas.harvard.edu. (140.247.23.100) Time: Thu Feb 26 09:15:28 2004 Input: Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+1); OK := RingOfIntegers(K); Factorization(2004*OK); Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed. ************** MAGMA ***************** Host roam23-100.fas.harvard.edu. (140.247.23.100) Time: Thu Feb 26 09:18:53 2004 Input: Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+1); OK := RingOfIntegers(K); Factorization(2004*OK); Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed. ************** MAGMA ***************** Host roam23-100.fas.harvard.edu. (140.247.23.100) Time: Thu Feb 26 09:20:08 2004 Input: Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+1); OK := RingOfIntegers(K); Factorization(2004*OK); Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed. ************** MAGMA ***************** Host roam23-100.fas.harvard.edu. (140.247.23.100) Time: Thu Feb 26 09:20:09 2004 Input: Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+1); OK := RingOfIntegers(K); Factorization(2004*OK); Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed. ************** MAGMA ***************** Host roam23-100.fas.harvard.edu. (140.247.23.100) Time: Thu Feb 26 09:20:32 2004 Input: Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+1); OK := RingOfIntegers(K); Factorization(2004*OK); Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed. ************** MAGMA ***************** Host roam23-100.fas.harvard.edu. (140.247.23.100) Time: Thu Feb 26 09:21:28 2004 Input: Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+1); OK := RingOfIntegers(K); Factorization(2004*OK); Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed. ************** MAGMA ***************** Host roam23-100.fas.harvard.edu. (140.247.23.100) Time: Thu Feb 26 09:22:57 2004 Input: Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+1); OK := RingOfIntegers(K); Factorization(2004*OK); Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed. ************** MAGMA ***************** Host roam23-100.fas.harvard.edu. (140.247.23.100) Time: Thu Feb 26 09:23:45 2004 Input: Input: R := PolynomialRing(RationalField); K := NumberField(x^2+1); OK := RingOfIntegers(K); Factorization(2004*OK); Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed. ************** MAGMA ***************** Host roam23-100.fas.harvard.edu. (140.247.23.100) Time: Thu Feb 26 09:26:35 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+1); OK := RingOfIntegers(K); Factorization(2004*OK); Output: Magma V2.10-6 Thu Feb 26 2004 09:26:28 on modular [Seed = 3333981417] ------------------------------------- [ , , ] Total time: 4.079 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam23-100.fas.harvard.edu. (140.247.23.100) Time: Thu Feb 26 09:31:05 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^6+x^5+x^4+x^3+x^2+x+1); OK := RingOfIntegers(K); Factorization(3*OK); Output: Magma V2.10-6 Thu Feb 26 2004 09:31:01 on modular [Seed = 843870507] ------------------------------------- [ ] Total time: 3.609 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam23-100.fas.harvard.edu. (140.247.23.100) Time: Thu Feb 26 09:33:03 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^6+x^5+x^4+x^3+x^2+x+1); OK := RingOfIntegers(K); Factorization(7*OK); Output: Magma V2.10-6 Thu Feb 26 2004 09:32:26 on modular [Seed = 609904483] ------------------------------------- [ ] Total time: 4.209 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam23-100.fas.harvard.edu. (140.247.23.100) Time: Thu Feb 26 09:36:52 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5-5); OK := RingOfIntegers(K); Factorization(3*OK); Output: Magma V2.10-6 Thu Feb 26 2004 09:36:44 on modular [Seed = 442785370] ------------------------------------- [ , ] Total time: 4.729 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host roam23-100.fas.harvard.edu. (140.247.23.100) Time: Thu Feb 26 09:37:32 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-5); OK := RingOfIntegers(K); Factorization(3*OK); Output: Magma V2.10-6 Thu Feb 26 2004 09:37:27 on modular [Seed = 325932936] ------------------------------------- [ ] Total time: 3.489 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam23-100.fas.harvard.edu. (140.247.23.100) Time: Thu Feb 26 09:38:19 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-5); OK := RingOfIntegers(K); Factorization(8*OK); Output: Magma V2.10-6 Thu Feb 26 2004 09:37:48 on modular [Seed = 91963896] ------------------------------------- [ ] Total time: 3.779 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam23-100.fas.harvard.edu. (140.247.23.100) Time: Thu Feb 26 09:39:44 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+1); OK := RingOfIntegers(K); Factorization(2004*OK); Output: Magma V2.10-6 Thu Feb 26 2004 09:39:40 on modular [Seed = 2130786927] ------------------------------------- [ , , ] Total time: 3.430 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam23-100.fas.harvard.edu. (140.247.23.100) Time: Thu Feb 26 09:45:37 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2+1); OK:=MaximalOrder(K); [K!x : x in Basis(OK)]; Output: Magma V2.10-6 Thu Feb 26 2004 09:45:22 on modular [Seed = 1111229688] ------------------------------------- [ 1, a ] Total time: 4.609 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam23-100.fas.harvard.edu. (140.247.23.100) Time: Thu Feb 26 09:48:45 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^6+x^5+x^4+x^3+x^2+x+1); OK:=MaximalOrder(K); [K!x : x in Basis(OK)]; Output: Magma V2.10-6 Thu Feb 26 2004 09:48:41 on modular [Seed = 2398145019] ------------------------------------- [ 1, a, a^2, a^3, a^4, a^5 ] Total time: 3.559 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam23-100.fas.harvard.edu. (140.247.23.100) Time: Thu Feb 26 09:49:26 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^5-5); OK:=MaximalOrder(K); [K!x : x in Basis(OK)]; Output: Magma V2.10-6 Thu Feb 26 2004 09:49:22 on modular [Seed = 2164180942] ------------------------------------- [ 1, a, a^2, a^3, a^4 ] Total time: 3.369 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Feb 26 10:32:55 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+2944*x^5-352*y^5-560*x^3-160*y^3+146*x-128*y+2160*x^4-600*x^2 -163825; f3:=645120*x^8+645120*y^8-330290415+12288*x^7-154624*y^7+1102080*x^5-71680*y^5- 264768*x^3-50176*y^3+55080*x-46080*y-777728*x^6+1536640*x^4-406112*x^2; f4:=-218639089123875-2113929216*y-9888071680*y^3-5295833088*y^5-9798942720*y^7-20466630656*y^9+95126814720*y^10; f5:=4*x+9; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Feb 26 2004 10:32:43 on modular [Seed = 593326725] ------------------------------------- [ x + 6, y + 2, 15 ] Total time: 4.549 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Feb 26 10:33:36 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+2944*x^5-352*y^5-560*x^3-160*y^3+146*x-128*y+2160*x^4-600*x^2 -163825; f3:=645120*x^8+645120*y^8-330290415+12288*x^7-154624*y^7+1102080*x^5-71680*y^5- 264768*x^3-50176*y^3+55080*x-46080*y-777728*x^6+1536640*x^4-406112*x^2; f4:=-218639038320675-2170377216*y-3275079680*y^3-106364633088*y^5-387072000000*y^6+ 420281057280*y^7+460800000000*y^8-5951692800*y^2+90961920000*y^4-532466630656*y ^9+95126814720*y^10; f5:=4*x+9; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Feb 26 2004 10:33:32 on modular [Seed = 442780651] ------------------------------------- [ x + 6, y + 2, 15 ] Total time: 3.309 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Feb 26 10:35:27 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+2944*x^5-352*y^5-560*x^3-160*y^3+146*x-128*y+2160*x^4-600*x^2 -163825; f3:=322560*x^8+322560*y^8-165145995+6144*x^7-1125888*y^7+551040*x^5+537600*y^5- 132384*x^3-91392*y^3+27540*x-22140*y+917504*y^6-501760*y^4+58016*y^2-388864*x^6 +768320*x^4-203056*x^2; f4:=8*y-9; f5:=4*x+9; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Feb 26 2004 10:34:00 on modular [Seed = 225664216] ------------------------------------- [ x + 1, y + 2, 5 ] Total time: 4.229 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Feb 26 10:35:36 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+2944*x^5-352*y^5-560*x^3-160*y^3+146*x-128*y+2160*x^4-600*x^2 -163825; f3:=322560*x^8+322560*y^8-165145995+6144*x^7-1125888*y^7+551040*x^5+537600*y^5- 132384*x^3-91392*y^3+27540*x-22140*y+917504*y^6-501760*y^4+58016*y^2-388864*x^6 +768320*x^4-203056*x^2; f4:=8*y-9; f5:=4*x+9; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Feb 26 2004 10:35:28 on modular [Seed = 25121660] ------------------------------------- [ x + 1, y + 2, 5 ] Total time: 3.759 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Feb 26 10:36:14 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+2944*x^5-352*y^5-560*x^3-160*y^3+146*x-128*y+2160*x^4-600*x^2 -163825; f3:=322560*x^8+322560*y^8-165145995+6144*x^7-1125888*y^7+551040*x^5+537600*y^5- 132384*x^3-91392*y^3+27540*x-22140*y+917504*y^6-501760*y^4+58016*y^2-388864*x^6 +768320*x^4-203056*x^2; f4:=-218639546352675-1718793216*y-37133598720*y^3+224817610752*y^5+627614023680*y^6 -481662074880*y^7-312294113280*y^8+32139141120*y^2-281618104320*y^4+ 154728136704*y^9+95126814720*y^10; f5:=4*x+9; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Feb 26 2004 10:36:10 on modular [Seed = 2013669935] ------------------------------------- [ x + 6, y + 2, 15 ] Total time: 4.169 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cache2.nottingham.ac.uk. (128.243.220.22) Time: Thu Feb 26 12:19:33 2004 Input: Q:=Rationals(); R:=PolynomialRing(Q); F:=NumberField([x^2+1,x^2+x+1]:Abs:=true); F; [i,i^2,r,r^2,r^3]; Output: Magma V2.10-6 Thu Feb 26 2004 12:19:24 on modular [Seed = 1027823519] ------------------------------------- Number Field with defining polynomial [ x^2 + 1, x^2 + x + 1] over the Rational Field [ i, -1, r, -r - 1, 1 ] Total time: 3.439 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host cache2.nottingham.ac.uk. (128.243.220.22) Time: Thu Feb 26 12:21:35 2004 Input: Q:=Rationals(); Q; Output: Magma V2.10-6 Thu Feb 26 2004 12:21:28 on modular [Seed = 760432139] ------------------------------------- Rational Field Total time: 3.579 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MusePSE9.library.mcgill.ca. (132.206.124.179) Time: Thu Feb 26 15:24:24 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Thu Feb 26 2004 15:24:20 on modular [Seed = 2448393254] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.499 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MusePSE9.library.mcgill.ca. (132.206.124.179) Time: Thu Feb 26 15:26:34 2004 Input: C:=ComplexField(); E:=EllipticCurve([0,-1,1,-10,-20]); Periods(E); Output: Magma V2.10-6 Thu Feb 26 2004 15:26:30 on modular [Seed = 2732373143] ------------------------------------- [ 1.26920930427955342168879461675454730521949224183025537695802, 0.6346046521397767108443973083772736526097461209151276884790 + 1.45881661693849522933088961290367525715924342895095414432485*i ] Total time: 3.639 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host MusePSE9.library.mcgill.ca. (132.206.124.179) Time: Thu Feb 26 15:26:51 2004 Input: C:=ComplexField(); E:=EllipticCurve([0,-1,1,-10,-20]); Periods(E)[1]*2; Output: Magma V2.10-6 Thu Feb 26 2004 15:26:47 on modular [Seed = 2849488749] ------------------------------------- 2.5384186085591068433775892335090946104389844836605107539160 Total time: 4.409 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (217.196.166.253) Time: Thu Feb 26 15:49:38 2004 Input: 32434 Output: Magma V2.10-6 Thu Feb 26 2004 15:49:35 on modular [Seed = 2231017247] ------------------------------------- 32434 Total time: 3.779 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (200.195.19.144) Time: Thu Feb 26 23:09:27 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Thu Feb 26 2004 23:08:39 on modular [Seed = 3183689488] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 4.900 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (200.195.19.144) Time: Thu Feb 26 23:09:51 2004 Input: a b 10 b c 20 a c 30 b d 40 Output: Magma V2.10-6 Thu Feb 26 2004 23:09:47 on modular [Seed = 1278398217] ------------------------------------- >> a b 10 ^ User error: bad syntax >> b c 20 ^ User error: bad syntax >> a c 30 ^ User error: bad syntax >> b d 40; ^ User error: bad syntax Total time: 3.289 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 04:41:24 2004 Input: t := { (-11)ˆ2, (-7)ˆ2, (-5)ˆ2, (-3)ˆ2, 3ˆ2, 5ˆ2, 7ˆ2, 11ˆ2 }; Output: Magma V2.10-6 Fri Feb 27 2004 04:41:14 on modular [Seed = 4269911574] ------------------------------------- >> t := { (-11)^È2, (-7)^È2, (-5)^È2, (-3)^È2, 3^È2, 5^È2, 7^È2, 11^È2 };; ^ User error: Unknown character (ascii value -120) Total time: 4.539 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 04:41:25 2004 Input: t := { (-11)ˆ2, (-7)ˆ2, (-5)ˆ2, (-3)ˆ2, 3ˆ2, 5ˆ2, 7ˆ2, 11ˆ2 }; Output: Magma V2.10-6 Fri Feb 27 2004 04:41:19 on modular [Seed = 4253199632] ------------------------------------- >> t := { (-11)^È2, (-7)^È2, (-5)^È2, (-3)^È2, 3^È2, 5^È2, 7^È2, 11^È2 };; ^ User error: Unknown character (ascii value -120) Total time: 4.759 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 04:41:27 2004 Input: t := { (-11)ˆ2, (-7)ˆ2, (-5)ˆ2, (-3)ˆ2, 3ˆ2, 5ˆ2, 7ˆ2, 11ˆ2 }; Output: Magma V2.10-6 Fri Feb 27 2004 04:41:24 on modular [Seed = 3852121459] ------------------------------------- >> t := { (-11)^È2, (-7)^È2, (-5)^È2, (-3)^È2, 3^È2, 5^È2, 7^È2, 11^È2 }; ^ User error: Unknown character (ascii value -120) Total time: 3.529 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 04:42:17 2004 Input: t := { (-11)ˆ2, (-7)ˆ2, (-5)ˆ2, (-3)ˆ2, 3ˆ2, 5ˆ2, 7ˆ2, 11ˆ2 }; q := [ (-11)ˆ2, (-7)ˆ2, (-5)ˆ2, (-3)ˆ2, 3ˆ2, 5ˆ2, 7ˆ2, 11ˆ2 ]; Output: Magma V2.10-6 Fri Feb 27 2004 04:42:13 on modular [Seed = 2548614963] ------------------------------------- >> t := { (-11)^È2, (-7)^È2, (-5)^È2, (-3)^È2, 3^È2, 5^È2, 7^È2, 11^È2 }; ^ User error: Unknown character (ascii value -120) >> q := [ (-11)^È2, (-7)^È2, (-5)^È2, (-3)^È2, 3^È2, 5^È2, 7^È2, 11^È2 ];; ^ User error: Unknown character (ascii value -120) Total time: 3.379 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 04:42:34 2004 Input: t := { (-11)ˆ2, (-7)ˆ2, (-5)ˆ2, (-3)ˆ2, 3ˆ2, 5ˆ2, 7ˆ2, 11ˆ2 }; q := [ (-11)ˆ2, (-7)ˆ2, (-5)ˆ2, (-3)ˆ2, 3ˆ2, 5ˆ2, 7ˆ2, 11ˆ2 ]; Output: Magma V2.10-6 Fri Feb 27 2004 04:42:30 on modular [Seed = 2632175048] ------------------------------------- >> t := { (-11)^È2, (-7)^È2, (-5)^È2, (-3)^È2, 3^È2, 5^È2, 7^È2, 11^È2 }; ^ User error: Unknown character (ascii value -120) >> q := [ (-11)^È2, (-7)^È2, (-5)^È2, (-3)^È2, 3^È2, 5^È2, 7^È2, 11^È2 ];; ^ User error: Unknown character (ascii value -120) Total time: 3.409 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 04:42:52 2004 Input: q := [ (-11)ˆ2, (-7)ˆ2, (-5)ˆ2, (-3)ˆ2, 3ˆ2, 5ˆ2, 7ˆ2, 11ˆ2 ]; Output: Magma V2.10-6 Fri Feb 27 2004 04:42:49 on modular [Seed = 2247808206] ------------------------------------- >> q := [ (-11)^È2, (-7)^È2, (-5)^È2, (-3)^È2, 3^È2, 5^È2, 7^È2, 11^È2 ];; ^ User error: Unknown character (ascii value -120) Total time: 3.289 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 04:44:42 2004 Input: q := [ (-11)ˆ2, (-7)ˆ2, (-5)ˆ2, (-3)ˆ2, 3ˆ2, 5ˆ2, 7ˆ2, 11ˆ2 ]; Output: Magma V2.10-6 Fri Feb 27 2004 04:44:37 on modular [Seed = 3016548967] ------------------------------------- >> q := [ (-11)^È2, (-7)^È2, (-5)^È2, (-3)^È2, 3^È2, 5^È2, 7^È2, 11^È2 ];; ^ User error: Unknown character (ascii value -120) Total time: 3.599 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 04:47:37 2004 Input: t := { nˆ2 : n in [-11..11 by 2] | IsPrime(n) }; Output: Magma V2.10-6 Fri Feb 27 2004 04:47:33 on modular [Seed = 3183669210] ------------------------------------- >> t := { n^È2 : n in [-11..11 by 2] | IsPrime(n) };; ^ User error: Unknown character (ascii value -120) Total time: 3.339 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 04:50:51 2004 Input: t := { nˆ2 : n in [-11..11 by 2] | IsPrime(n) }; Output: Magma V2.10-6 Fri Feb 27 2004 04:50:47 on modular [Seed = 1512376574] ------------------------------------- >> t := { n^È2 : n in [-11..11 by 2] | IsPrime(n) };; ^ User error: Unknown character (ascii value -120) Total time: 3.369 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 05:02:12 2004 Input: positiu:= func < x | x gt 0 select 1 else 0 >; Output: Magma V2.10-6 Fri Feb 27 2004 05:02:09 on modular [Seed = 1612658066] ------------------------------------- Total time: 3.379 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 05:02:31 2004 Input: positiu:= func < x | x gt 0 select 1 else 0 >; positiu(8); Output: Magma V2.10-6 Fri Feb 27 2004 05:02:28 on modular [Seed = 1863334536] ------------------------------------- 1 Total time: 3.379 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 05:02:58 2004 Input: positiu:= func < x | x gt 0 select 1 else 0 >; positiu(-8); Output: Magma V2.10-6 Fri Feb 27 2004 05:02:55 on modular [Seed = 375997322] ------------------------------------- 0 Total time: 3.339 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 05:06:49 2004 Input: suma_i_prod:= func < a,b | a+b, a*b >; Output: Magma V2.10-6 Fri Feb 27 2004 05:06:45 on modular [Seed = 259021289] ------------------------------------- Total time: 4.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 05:07:30 2004 Input: suma_i_prod:= func < a,b | a+b, a*b >; sum, prod:=suma_i_prod(3,4); Output: Magma V2.10-6 Fri Feb 27 2004 05:07:26 on modular [Seed = 910778555] ------------------------------------- Total time: 3.569 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 05:07:54 2004 Input: suma_i_prod:= func < a,b | a+b, a*b >; sum, prod:=suma_i_prod(3,4); sum; Output: Magma V2.10-6 Fri Feb 27 2004 05:07:51 on modular [Seed = 1027763097] ------------------------------------- 7 Total time: 3.289 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 05:08:48 2004 Input: suma_i_prod:= func < a,b | a+b, a*b >; sum; Output: Magma V2.10-6 Fri Feb 27 2004 05:08:45 on modular [Seed = 726957141] ------------------------------------- >> sum;; ^ User error: Identifier 'sum' has not been declared or assigned Total time: 3.319 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 05:09:01 2004 Input: suma_i_prod:= func < a,b | a+b, a*b >; sum, prod:=suma_i_prod(3,4); sum; Output: Magma V2.10-6 Fri Feb 27 2004 05:08:56 on modular [Seed = 3534587321] ------------------------------------- 7 Total time: 3.669 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 05:09:27 2004 Input: suma_i_prod:= func < a,b | a+b, a*b >; sum, prod:=suma_i_prod(3,4); sum; prod; Output: Magma V2.10-6 Fri Feb 27 2004 05:09:24 on modular [Seed = 3651571422] ------------------------------------- 7 12 Total time: 3.379 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 05:14:13 2004 Input: solucions_reals_equacio_segon_grau:=function(a,b,c) discriminant:=bˆ2-4.0*a*c; arrel_discr:=Sqrt(discriminant); if positiu(discriminant) eq 1 then print "hi ha dues solucions reals"; sol1:=(-b+arrel_discr)/(2*a); sol2:=(-b-arrel_discr)/(2*a); return {sol1,sol2}; elif discriminant eq 0 then print "hi ha una solucio real"; sol:=-b/(2.0*a); return {sol}; else print "no hi ha solucions reals"; return {}; end if; end function;; Output: Magma V2.10-6 Fri Feb 27 2004 05:14:09 on modular [Seed = 3467745004] ------------------------------------- >> discriminant:=b^È2-4.0*a*c; ^ User error: Unknown character (ascii value -120) >> arrel_discr:=Sqrt(discriminant); ^ User error: Identifier 'discriminant' has not been declared or assigned >> if positiu(discriminant) eq 1 then ^ User error: Identifier 'discriminant' has not been declared or assigned >> end function;;; ^ User error: bad syntax Total time: 3.369 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 05:15:11 2004 Input: solucions_reals_equacio_segon_grau:=function(a,b,c) discriminant:=b*2-4.0*a*c; arrel_discr:=Sqrt(discriminant); if positiu(discriminant) eq 1 then print "hi ha dues solucions reals"; sol1:=(-b+arrel_discr)/(2*a); sol2:=(-b-arrel_discr)/(2*a); return {sol1,sol2}; elif discriminant eq 0 then print "hi ha una solucio real"; sol:=-b/(2.0*a); return {sol}; else print "no hi ha solucions reals"; return {}; end if; end function;; Output: Magma V2.10-6 Fri Feb 27 2004 05:14:58 on modular [Seed = 4102794245] ------------------------------------- >> if positiu(discriminant) eq 1 then ^ User error: Identifier 'positiu' has not been declared or assigned Total time: 4.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 05:20:08 2004 Input: positiu:= func < x | x gt 0 select 1 else 0 >; solucions_reals_equacio_segon_grau:=function(a,b,c) discriminant:=bˆ2-4.0*a*c; arrel_discr:=Sqrt(discriminant); if positiu(discriminant) eq 1 then print "hi ha dues solucions reals"; sol1:=(-b+arrel_discr)/(2*a); sol2:=(-b-arrel_discr)/(2*a); return {sol1,sol2}; elif discriminant eq 0 then print "hi ha una solucio real"; sol:=-b/(2.0*a); return {sol}; else print "no hi ha solucions reals"; return {}; end if; end function; Output: Magma V2.10-6 Fri Feb 27 2004 05:20:05 on modular [Seed = 3902255470] ------------------------------------- >> discriminant:=b^È2-4.0*a*c; ^ User error: Unknown character (ascii value -120) >> arrel_discr:=Sqrt(discriminant); ^ User error: Identifier 'discriminant' has not been declared or assigned >> if positiu(discriminant) eq 1 then ^ User error: Identifier 'discriminant' has not been declared or assigned >> end function;; ^ User error: bad syntax Total time: 3.469 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 05:20:42 2004 Input: positiu:= func < x | x gt 0 select 1 else 0 >; solucions_reals_equacio_segon_grau:=function(a,b,c) discriminant:=b*2-4.0*a*c; arrel_discr:=Sqrt(discriminant); if positiu(discriminant) eq 1 then print "hi ha dues solucions reals"; sol1:=(-b+arrel_discr)/(2*a); sol2:=(-b-arrel_discr)/(2*a); return {sol1,sol2}; elif discriminant eq 0 then print "hi ha una solucio real"; sol:=-b/(2.0*a); return {sol}; else print "no hi ha solucions reals"; return {}; end if; end function; Output: Magma V2.10-6 Fri Feb 27 2004 05:20:39 on modular [Seed = 2548616755] ------------------------------------- Total time: 3.449 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 05:22:04 2004 Input: positiu:= func < x | x gt 0 select 1 else 0 >; solucions_reals_equacio_segon_grau:=function(a,b,c) discriminant:=b*2-4.0*a*c; arrel_discr:=Sqrt(discriminant); if positiu(discriminant) eq 1 then print "hi ha dues solucions reals"; sol1:=(-b+arrel_discr)/(2*a); sol2:=(-b-arrel_discr)/(2*a); return {sol1,sol2}; elif discriminant eq 0 then print "hi ha una solucio real"; sol:=-b/(2.0*a); return {sol}; else print "no hi ha solucions reals"; return {}; end if; end function; solucions_reals_equacio_segon_grau(9,-6,1); Output: Magma V2.10-6 Fri Feb 27 2004 05:22:00 on modular [Seed = 2665596037] ------------------------------------- no hi ha solucions reals {} Total time: 3.539 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 05:22:43 2004 Input: positiu:= func < x | x gt 0 select 1 else 0 >; solucions_reals_equacio_segon_grau:=function(a,b,c) discriminant:=b*b-4.0*a*c; arrel_discr:=Sqrt(discriminant); if positiu(discriminant) eq 1 then print "hi ha dues solucions reals"; sol1:=(-b+arrel_discr)/(2*a); sol2:=(-b-arrel_discr)/(2*a); return {sol1,sol2}; elif discriminant eq 0 then print "hi ha una solucio real"; sol:=-b/(2.0*a); return {sol}; else print "no hi ha solucions reals"; return {}; end if; end function; solucions_reals_equacio_segon_grau(9,-6,1); Output: Magma V2.10-6 Fri Feb 27 2004 05:22:39 on modular [Seed = 2247811001] ------------------------------------- hi ha una solucio real { 0.333333333333333333333333333329 } Total time: 3.509 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 05:24:13 2004 Input: repetirfrase := procedure (frase,n) for i in {1..n} do print frase; end for; end procedure; Output: Magma V2.10-6 Fri Feb 27 2004 05:24:09 on modular [Seed = 3016550697] ------------------------------------- Total time: 3.459 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 05:24:39 2004 Input: repetirfrase := procedure (frase,n) for i in {1..n} do print frase; end for; end procedure; repetirfrase("No copiare", 3); Output: Magma V2.10-6 Fri Feb 27 2004 05:24:35 on modular [Seed = 3133530122] ------------------------------------- No copiare No copiare No copiare Total time: 3.409 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 05:27:54 2004 Input: duplica:=procedure(˜x) x:=2*x; end procedure; Output: Magma V2.10-6 Fri Feb 27 2004 05:27:51 on modular [Seed = 2765881168] ------------------------------------- >> duplica:=procedure(^Øx) ^ User error: Unknown character (ascii value -104) >> x:=2*x; ^ User error: Identifier 'x' has not been declared or assigned >> end procedure; ^ User error: bad syntax Total time: 3.449 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 05:28:20 2004 Input: duplica:=procedure(~x) x:=2*x; end procedure; Output: Magma V2.10-6 Fri Feb 27 2004 05:28:16 on modular [Seed = 1412108224] ------------------------------------- Total time: 3.499 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 05:28:59 2004 Input: duplica:=procedure(~x) x:=2*x; end procedure; x:=4; duplica(˜x); x; Output: Magma V2.10-6 Fri Feb 27 2004 05:28:48 on modular [Seed = 1562511081] ------------------------------------- >> duplica(^Øx); ^ User error: Unknown character (ascii value -104) 4 Total time: 3.799 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 05:29:12 2004 Input: duplica:=procedure(~x) x:=2*x; end procedure; x:=4; duplica(˜x); x; Output: Magma V2.10-6 Fri Feb 27 2004 05:29:08 on modular [Seed = 1178148326] ------------------------------------- >> duplica(^Øx); ^ User error: Unknown character (ascii value -104) 4 Total time: 3.810 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 05:29:36 2004 Input: duplica:=procedure(~x) x:=2*x; end procedure; x:=4; duplica(~x); x; Output: Magma V2.10-6 Fri Feb 27 2004 05:29:33 on modular [Seed = 1211569169] ------------------------------------- 8 Total time: 3.239 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 05:32:37 2004 Input: duplica:=procedure(~x) x:=2*x; end procedure; x:=4; duplica(~x); x; Output: Magma V2.10-6 Fri Feb 27 2004 05:32:33 on modular [Seed = 2030446060] ------------------------------------- 8 Total time: 3.479 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 05:33:22 2004 Input: l:=[3,2,5]; Sort(l); [ 2, 3, 5 ] l; [ 3, 2, 5 ] Sort(˜l); l; [ 2, 3, 5 ] Output: Magma V2.10-6 Fri Feb 27 2004 05:33:18 on modular [Seed = 1646083800] ------------------------------------- [ 2, 3, 5 ] >> l; ^ User error: bad syntax >> Sort(^Øl); ^ User error: bad syntax [ 3, 2, 5 ] [ 2, 3, 5 ] Total time: 3.469 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 05:33:40 2004 Input: l:=[3,2,5]; Sort(l); l; Sort(˜l); l; Output: Magma V2.10-6 Fri Feb 27 2004 05:33:37 on modular [Seed = 1796486718] ------------------------------------- [ 2, 3, 5 ] [ 3, 2, 5 ] >> Sort(^Øl); ^ User error: Unknown character (ascii value -104) [ 3, 2, 5 ] Total time: 3.289 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 05:34:19 2004 Input: l:=[3,2,5]; Sort(l); Output: Magma V2.10-6 Fri Feb 27 2004 05:34:15 on modular [Seed = 476266863] ------------------------------------- [ 2, 3, 5 ] Total time: 3.569 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 05:35:27 2004 Input: f:= map < Integers() -> Integers() | x:-> 2*x >; Output: Magma V2.10-6 Fri Feb 27 2004 05:35:22 on modular [Seed = 41770813] ------------------------------------- Total time: 3.699 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 05:35:40 2004 Input: f:= map < Integers() -> Integers() | x:-> 2*x >; f(5); Output: Magma V2.10-6 Fri Feb 27 2004 05:35:37 on modular [Seed = 192173606] ------------------------------------- 10 Total time: 3.439 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 05:36:30 2004 Input: f:= map < Integers() -> Integers() | x:-> 2*x >; f(5); g:=map<[0,1,2,3]->[0,2,4,6]|x:->2*x>; g(2); Output: Magma V2.10-6 Fri Feb 27 2004 05:36:26 on modular [Seed = 1011048898] ------------------------------------- 10 4 Total time: 3.399 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 06:04:12 2004 Input: f:= map < Integers() -> Integers() | x:-> 2*x >; f(5); g:=map<[0,1,2,3]->[0,2,4,6]|x:->2*x>; g(2); Output: Magma V2.10-6 Fri Feb 27 2004 06:03:52 on modular [Seed = 4203060916] ------------------------------------- 10 4 Total time: 3.529 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 06:11:43 2004 Input: Z4:=Integers(4); [x: x in Z4]; Output: Magma V2.10-6 Fri Feb 27 2004 06:11:39 on modular [Seed = 2632186147] ------------------------------------- [ 0, 1, 2, 3 ] Total time: 3.449 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 06:12:15 2004 Input: Z4:=Integers(4); [x: x in Z4]; IsField(Z4); Output: Magma V2.10-6 Fri Feb 27 2004 06:12:12 on modular [Seed = 2247812061] ------------------------------------- [ 0, 1, 2, 3 ] false Total time: 3.349 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 06:17:05 2004 Input: P:=PolynomialRing(R); P:=PolynomialRing(R); Output: Magma V2.10-6 Fri Feb 27 2004 06:17:00 on modular [Seed = 3217086663] ------------------------------------- >> P:=PolynomialRing(R); ^ User error: Identifier 'R' has not been declared or assigned >> P:=PolynomialRing(R); ^ User error: Identifier 'R' has not been declared or assigned Total time: 3.459 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 06:17:21 2004 Input: P:=PolynomialRing(R); Output: Magma V2.10-6 Fri Feb 27 2004 06:17:18 on modular [Seed = 2715731659] ------------------------------------- >> P:=PolynomialRing(R); ^ User error: Identifier 'R' has not been declared or assigned Total time: 3.279 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 06:25:10 2004 Input: P:=PolynomialRing(GF(49)); f:=4*xˆ5+5*x+2; g:=xˆ8+6*xˆ7+xˆ2; d,a,b:=XGCD(f,g); d; Output: Magma V2.10-6 Fri Feb 27 2004 06:25:06 on modular [Seed = 1579235097] ------------------------------------- >> f:=4*x^È5+5*x+2; ^ User error: Unknown character (ascii value -120) >> g:=x^È8+6*x^È7+x^È2; ^ User error: Unknown character (ascii value -120) >> d,a,b:=XGCD(f,g); ^ User error: Identifier 'f' has not been declared or assigned >> d;; ^ User error: Identifier 'd' has not been declared or assigned Total time: 3.399 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 06:26:04 2004 Input: P:=PolynomialRing(GF(49)); f:=4*x^5+5*x+2; g:=x^8+6*x^7+x^2; d,a,b:=XGCD(f,g); d; Output: Magma V2.10-6 Fri Feb 27 2004 06:26:00 on modular [Seed = 1094592604] ------------------------------------- 1 Total time: 3.579 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 06:26:30 2004 Input: P:=PolynomialRing(GF(49)); f:=4*x^5+5*x+2; g:=x^8+6*x^7+x^2; d,a,b:=XGCD(f,g); d; d eq a*f+b*g; Output: Magma V2.10-6 Fri Feb 27 2004 06:26:27 on modular [Seed = 1261707901] ------------------------------------- 1 true Total time: 3.369 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host gate.mef-rd.com. (212.234.57.71) Time: Fri Feb 27 06:44:35 2004 Input: (1/3)*(1/sqrt(2))^3*sin(3*4*atan(1)/4) Output: Magma V2.10-6 Fri Feb 27 2004 06:44:31 on modular [Seed = 793789157] ------------------------------------- >> (1/3)*(1/sqrt(2))^3*sin(3*4*atan(1)/4); ^ User error: Identifier 'sqrt' has not been declared or assigned Total time: 3.349 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host gate.mef-rd.com. (212.234.57.71) Time: Fri Feb 27 06:45:35 2004 Input: (1/3)*(1/2^(1/2))^3*sin(3*4*atan(1)/4) Output: Magma V2.10-6 Fri Feb 27 2004 06:45:31 on modular [Seed = 3534602076] ------------------------------------- >> (1/3)*(1/2^(1/2))^3*sin(3*4*atan(1)/4); ^ User error: Identifier 'atan' has not been declared or assigned Total time: 3.419 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 06:56:43 2004 Input: F:=GF(27); 2*alphaˆ2+alpha+1; F![1,1,2]; elt; Output: Magma V2.10-6 Fri Feb 27 2004 06:56:26 on modular [Seed = 4152920009] ------------------------------------- >> 2*alpha^È2+alpha+1; ^ User error: Unknown character (ascii value -120) alpha^20 alpha^20 Total time: 4.259 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 06:56:43 2004 Input: F:=GF(27); 2*alphaˆ2+alpha+1; F![1,1,2]; elt; Output: Magma V2.10-6 Fri Feb 27 2004 06:56:19 on modular [Seed = 4102784194] ------------------------------------- >> 2*alpha^È2+alpha+1; ^ User error: Unknown character (ascii value -120) alpha^20 alpha^20 Total time: 4.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 06:56:52 2004 Input: F:=GF(27); 2*alphaˆ2+alpha+1; F![1,1,2]; elt; Output: Magma V2.10-6 Fri Feb 27 2004 06:56:43 on modular [Seed = 4069360348] ------------------------------------- >> 2*alpha^È2+alpha+1; ^ User error: Unknown character (ascii value -120) alpha^20 alpha^20 Total time: 4.549 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 06:57:17 2004 Input: F:=GF(27); 2*alphaˆ2+alpha+1; F![1,1,2]; elt; Output: Magma V2.10-6 Fri Feb 27 2004 06:57:14 on modular [Seed = 3801977389] ------------------------------------- >> 2*alpha^È2+alpha+1; ^ User error: Unknown character (ascii value -120) alpha^20 alpha^20 Total time: 3.329 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 06:58:27 2004 Input: F:=GF(27); 2*alpha^2+alpha+1; F![1,1,2]; elt; Output: Magma V2.10-6 Fri Feb 27 2004 06:57:39 on modular [Seed = 2515199347] ------------------------------------- alpha^20 alpha^20 alpha^20 Total time: 4.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 06:58:33 2004 Input: F:=GF(27); 2*alpha^2+alpha+1; F![1,1,2]; elt; Output: Magma V2.10-6 Fri Feb 27 2004 06:58:27 on modular [Seed = 2431639590] ------------------------------------- alpha^20 alpha^20 alpha^20 Total time: 4.349 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 06:58:40 2004 Input: F:=GF(27); 2*alpha^2+alpha+1; F![1,1,2]; elt; Output: Magma V2.10-6 Fri Feb 27 2004 06:58:36 on modular [Seed = 2231104573] ------------------------------------- alpha^20 alpha^20 alpha^20 Total time: 3.480 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 06:59:27 2004 Input: F:=GF(27); 2*alpha^2+alpha+1; F![1,1,2]; elt; ElementToSequence(alphaˆ20); Output: Magma V2.10-6 Fri Feb 27 2004 06:59:23 on modular [Seed = 2398224320] ------------------------------------- alpha^20 alpha^20 alpha^20 >> ElementToSequence(alpha^È20);; ^ User error: Unknown character (ascii value -120) Total time: 3.399 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Fri Feb 27 07:02:02 2004 Input: F:=GF(27); 2*alpha^2+alpha+1; F![1,1,2]; elt; ElementToSequence(alpha^20); Output: Magma V2.10-6 Fri Feb 27 2004 07:01:58 on modular [Seed = 2882853448] ------------------------------------- alpha^20 alpha^20 alpha^20 [ 1, 1, 2 ] Total time: 3.799 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 09:18:16 2004 Input: E:=EllipticCurve([-4,-8]); w1:=Periods(E)[1]; w2:=Periods(E)[2]; Eisenstein(4,[w1,w2])*2*ZetaFunction(4); Output: Magma V2.10-6 Fri Feb 27 2004 09:18:08 on modular [Seed = 1813216666] ------------------------------------- 1.55202693184857115074069760042 - 3.070378110668449156504 E-29*i Total time: 4.379 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 09:18:48 2004 Input: E:=EllipticCurve([-4,-8]); w1:=Periods(E)[1]; w2:=Periods(E)[2]; Eisenstein(4,[w1,2*w2])*2*ZetaFunction(4); Eisenstein(4,[w1,w2/2])*2*ZetaFunction(4); Eisenstein(4,[w1,w2/2])*2*ZetaFunction(4); Output: Magma V2.10-6 Fri Feb 27 2004 09:18:44 on modular [Seed = 325845632] ------------------------------------- 2.165384579645140412879511196175 + 7.45310527389640501598 E-32*i -3.354834250523982946369811166025 + 17.340682834472221469518522479880*i -3.354834250523982946369811166025 + 17.340682834472221469518522479880*i Total time: 3.849 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 09:19:03 2004 Input: E:=EllipticCurve([-4,-8]); w1:=Periods(E)[1]; w2:=Periods(E)[2]; Eisenstein(4,[w1,2*w2])*2*ZetaFunction(4); Eisenstein(4,[w1,w2/2])*2*ZetaFunction(4); Eisenstein(4,[w1,w2])*2*ZetaFunction(4); Output: Magma V2.10-6 Fri Feb 27 2004 09:18:59 on modular [Seed = 442829726] ------------------------------------- 2.165384579645140412879511196175 + 7.45310527389640501598 E-32*i -3.354834250523982946369811166025 + 17.340682834472221469518522479880*i 1.55202693184857115074069760042 - 3.070378110668449156504 E-29*i Total time: 3.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 09:19:29 2004 Input: E:=EllipticCurve([-4,-8]); w1:=Periods(E)[1]; w2:=Periods(E)[2]; Eisenstein(4,[w1,2*w2])*2*ZetaFunction(4); Eisenstein(4,[w1,w2/2])*2*ZetaFunction(4); Eisenstein(4,[w1,w2])*2*ZetaFunction(4); Eisenstein(6,[w1,2*w2])*2*ZetaFunction(6); Eisenstein(6,[w1,w2/2])*2*ZetaFunction(6); Eisenstein(6,[w1,w2])*2*ZetaFunction(6); Output: Magma V2.10-6 Fri Feb 27 2004 09:19:25 on modular [Seed = 25039035] ------------------------------------- 2.165384579645140412879511196175 + 7.45310527389640501598 E-32*i -3.354834250523982946369811166025 + 17.340682834472221469518522479880*i 1.55202693184857115074069760042 - 3.070378110668449156504 E-29*i 2.0332290991601951320733435098497 - 1.47127442261186123606 E-31*i 40.84537532240341027208794833743 - 25.263761859405528440686936203315*i 3.209354742288777409043483050105 + 5.76908704423330024636 E-29*i Total time: 4.089 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 09:20:08 2004 Input: E:=EllipticCurve([-4,-8]); w1:=Periods(E)[1]; w2:=Periods(E)[2]; 60*Eisenstein(4,[w1,2*w2])*2*ZetaFunction(4); 60*Eisenstein(4,[w1,w2/2])*2*ZetaFunction(4); 60*Eisenstein(4,[w1,w2])*2*ZetaFunction(4); 140*Eisenstein(6,[w1,2*w2])*2*ZetaFunction(6); 140*Eisenstein(6,[w1,w2/2])*2*ZetaFunction(6); 140*Eisenstein(6,[w1,w2])*2*ZetaFunction(6); Output: Magma V2.10-6 Fri Feb 27 2004 09:20:04 on modular [Seed = 810492531] ------------------------------------- 129.92307477870842477277067177091 + 4.47186316433784300950 E-30*i -201.290055031438976782188669959126 + 1040.440970068333288171111348778266*i 93.121615910914269044441856026001 - 1.84222686640106949381 E-27*i 284.65207388242731849026809137775 - 2.059784191656605730489 E-29*i 5718.352545136477438092312767282695 - 3536.92666031677398169617106843512*i 449.309663920428837266087627014175 + 8.076721861926620344394 E-27*i Total time: 4.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 09:21:16 2004 Input: E:=EllipticCurve([-4,-8]); w1:=Periods(E)[1]; w2:=Periods(E)[2]; 60*Eisenstein(4,[1.003847,1.09797*i])*2*ZetaFunction(4); 60*Eisenstein(4,[w1,2*w2])*2*ZetaFunction(4); 60*Eisenstein(4,[w1,w2/2])*2*ZetaFunction(4); 60*Eisenstein(4,[w1,w2])*2*ZetaFunction(4); 140*Eisenstein(6,[w1,2*w2])*2*ZetaFunction(6); 140*Eisenstein(6,[w1,w2/2])*2*ZetaFunction(6); 140*Eisenstein(6,[w1,w2])*2*ZetaFunction(6); Output: Magma V2.10-6 Fri Feb 27 2004 09:21:12 on modular [Seed = 660092200] ------------------------------------- >> 60*Eisenstein(4,[1.003847,1.09797*i])*2*ZetaFunction(4); ^ User error: Identifier 'i' has not been declared or assigned 129.92307477870842477277067177091 + 4.47186316433784300950 E-30*i -201.290055031438976782188669959126 + 1040.440970068333288171111348778266*i 93.121615910914269044441856026001 - 1.84222686640106949381 E-27*i 284.65207388242731849026809137775 - 2.059784191656605730489 E-29*i 5718.352545136477438092312767282695 - 3536.92666031677398169617106843512*i 449.309663920428837266087627014175 + 8.076721861926620344394 E-27*i Total time: 3.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 09:21:36 2004 Input: C:=ComplexField(); E:=EllipticCurve([-4,-8]); w1:=Periods(E)[1]; w2:=Periods(E)[2]; 60*Eisenstein(4,[1.003847,1.09797*i])*2*ZetaFunction(4); 60*Eisenstein(4,[w1,2*w2])*2*ZetaFunction(4); 60*Eisenstein(4,[w1,w2/2])*2*ZetaFunction(4); 60*Eisenstein(4,[w1,w2])*2*ZetaFunction(4); 140*Eisenstein(6,[w1,2*w2])*2*ZetaFunction(6); 140*Eisenstein(6,[w1,w2/2])*2*ZetaFunction(6); 140*Eisenstein(6,[w1,w2])*2*ZetaFunction(6); Output: Magma V2.10-6 Fri Feb 27 2004 09:21:32 on modular [Seed = 760364822] ------------------------------------- 162.476454955975383160926831345276 + 0.E-27*i 129.92307477870842477277067177091 + 4.47186316433784300950 E-30*i -201.290055031438976782188669959126 + 1040.440970068333288171111348778266*i 93.121615910914269044441856026001 - 1.84222686640106949381 E-27*i 284.65207388242731849026809137775 - 2.059784191656605730489 E-29*i 5718.352545136477438092312767282695 - 3536.92666031677398169617106843512*i 449.309663920428837266087627014175 + 8.076721861926620344394 E-27*i Total time: 3.789 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:02:28 2004 Input: C:=ComplexField(); R := PowerSeriesRing(C); tau:=1+i; z:=0.5+0.3*i; pi:=Pi(RealField()); g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[1,1+i]),Exp(2*i*pi*z); x1:=Evaluate(Derivative(WeierstrassSeries(z,[1,1+i])),Exp(2*i*pi*z); Output: Magma V2.10-6 Fri Feb 27 2004 11:02:25 on modular [Seed = 2465052891] ------------------------------------- >> x1:=Evaluate(WeierstrassSeries(z,[1,1+i]),Exp(2*i*pi*z); ^ User error: bad syntax >> x1:=Evaluate(Derivative(WeierstrassSeries(z,[1,1+i])),Exp(2*i*pi*z); ^ User error: bad syntax Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:02:46 2004 Input: C:=ComplexField(); R := PowerSeriesRing(C); tau:=1+i; z:=0.5+0.3*i; pi:=Pi(RealField()); g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[1,1+i]),Exp(2*i*pi*z)); x1:=Evaluate(Derivative(WeierstrassSeries(z,[1,1+i])),Exp(2*i*pi*z); Output: Magma V2.10-6 Fri Feb 27 2004 11:02:43 on modular [Seed = 2348065264] ------------------------------------- >> x1:=Evaluate(WeierstrassSeries(z,[1,1+i]),Exp(2*i*pi*z)); ^ Runtime error in 'WeierstrassSeries': Bad argument types Argument types given: FldPrElt, SeqEnum[FldPrElt] >> x1:=Evaluate(Derivative(WeierstrassSeries(z,[1,1+i])),Exp(2*i*pi*z); ^ User error: bad syntax Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:03:03 2004 Input: C:=ComplexField(); R := PowerSeriesRing(C); tau:=1+i; x:=0.5+0.3*i; pi:=Pi(RealField()); g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[1,1+i]),Exp(2*i*pi*x)); x1:=Evaluate(Derivative(WeierstrassSeries(z,[1,1+i])),Exp(2*i*pi*x); Output: Magma V2.10-6 Fri Feb 27 2004 11:03:00 on modular [Seed = 2231086824] ------------------------------------- >> x1:=Evaluate(Derivative(WeierstrassSeries(z,[1,1+i])),Exp(2*i*pi*x); ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:03:15 2004 Input: C:=ComplexField(); R := PowerSeriesRing(C); tau:=1+i; x:=0.5+0.3*i; pi:=Pi(RealField()); g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[1,1+i]),Exp(2*i*pi*x)); x1:=Evaluate(Derivative(WeierstrassSeries(z,[1,1+i])),Exp(2*i*pi*x)); Output: Magma V2.10-6 Fri Feb 27 2004 11:03:12 on modular [Seed = 3183646629] ------------------------------------- Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:03:25 2004 Input: C:=ComplexField(); R := PowerSeriesRing(C); tau:=1+i; x:=0.5+0.3*i; pi:=Pi(RealField()); g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[1,1+i]),Exp(2*i*pi*x)); x1:=Evaluate(Derivative(WeierstrassSeries(z,[1,1+i])),Exp(2*i*pi*x)); x1,x2; Output: Magma V2.10-6 Fri Feb 27 2004 11:03:22 on modular [Seed = 3066666148] ------------------------------------- >> x1,x2; ^ User error: Identifier 'x2' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:03:34 2004 Input: C:=ComplexField(); R := PowerSeriesRing(C); tau:=1+i; x:=0.5+0.3*i; pi:=Pi(RealField()); g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[1,1+i]),Exp(2*i*pi*x)); x2:=Evaluate(Derivative(WeierstrassSeries(z,[1,1+i])),Exp(2*i*pi*x)); x1,x2; Output: Magma V2.10-6 Fri Feb 27 2004 11:03:30 on modular [Seed = 2949678501] ------------------------------------- 43.376352015433578306901300107434 + 4.03896783292 E-27*i 571.355000221919130343405098609710 + 7.7548182420 E-26*i Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:04:06 2004 Input: C:=ComplexField(); R := PowerSeriesRing(C); tau:=1+i; x:=0.5+0.3*i; pi:=Pi(RealField()); g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[1,1+i]),Exp(2*i*pi*x)); x2:=Evaluate(Derivative(WeierstrassSeries(z,[1,1+i])),Exp(2*i*pi*x)); x1,x2; x2^2; 4*x3^3-g2*x-g3; Output: Magma V2.10-6 Fri Feb 27 2004 11:04:03 on modular [Seed = 1495692147] ------------------------------------- 43.376352015433578306901300107434 + 4.03896783292 E-27*i 571.355000221919130343405098609710 + 7.7548182420 E-26*i 326446.53627858920948396054064132065 + 8.6026783697 E-23*i >> 4*x3^3-g2*x-g3; ^ User error: Identifier 'x3' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:04:21 2004 Input: C:=ComplexField(); R := PowerSeriesRing(C); tau:=1+i; x:=0.5+0.3*i; pi:=Pi(RealField()); g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[1,1+i]),Exp(2*i*pi*x)); x2:=Evaluate(Derivative(WeierstrassSeries(z,[1,1+i])),Exp(2*i*pi*x)); x1,x2; x2^2; 4*x1^3-g2*x1-g3; Output: Magma V2.10-6 Fri Feb 27 2004 11:04:18 on modular [Seed = 1345288843] ------------------------------------- 43.376352015433578306901300107434 + 4.03896783292 E-27*i 571.355000221919130343405098609710 + 7.7548182420 E-26*i 326446.53627858920948396054064132065 + 8.6026783697 E-23*i 326315.110337814027226036564086759302 + 8.6007613278 E-23*i Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:04:57 2004 Input: AssertAttribute(FldPr,"Precision",100); C:=ComplexField(); R := PowerSeriesRing(C); tau:=1+i; x:=0.5+0.3*i; pi:=Pi(RealField()); g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[1,1+i]),Exp(2*i*pi*x)); x2:=Evaluate(Derivative(WeierstrassSeries(z,[1,1+i])),Exp(2*i*pi*x)); x1,x2; x2^2; 4*x1^3-g2*x1-g3; Output: Magma V2.10-6 Fri Feb 27 2004 11:04:54 on modular [Seed = 1245012149] ------------------------------------- 43.3763520154335783069013001082118783141598423950773982071754510021491742877622\ 5237457979232525136731828387732 + 3.4881207002 E-104*i 571.355000221919130343405098635308662287803448701744079391392914521423673550286\ 87818145688800287404388275926300 + 7.8133903685 E-103*i 326446.536278589209483960540673926783054246711867442350125121139905392824779020\ 0242673228399318406211431714991800 + 8.5724054314 E-100*i 326315.110337814027226036564108107909391266956485889336298533645920724448912455\ 52877716427419418788680883955544580 + 7.9998141061 E-100*i Total time: 2.989 seconds, Total memory usage: 1.91MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:05:21 2004 Input: AssertAttribute(FldPr,"Precision",50); C:=ComplexField(); R := PowerSeriesRing(C); tau:=1+i; x:=0.5+0.3*i; pi:=Pi(RealField()); g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[1,1+i]),Exp(2*i*pi*x)); x2:=Evaluate(Derivative(WeierstrassSeries(z,[1,1+i])),Exp(2*i*pi*x)); x1,x2; x2^2; 4*x1^3-g2*x1-g3; Output: Magma V2.10-6 Fri Feb 27 2004 11:05:18 on modular [Seed = 2030457758] ------------------------------------- 43.37635201543357830690130010821187831415984239507739820712946 + 0.E-56*i 571.35500022191913034340509863530866228780344870174407939039700 + 0.E-55*i 326446.5362785892094839605406739267830542467118674423501239462425 + 0.E-52*i 326315.11033781402722603656410810790939126695648588933629748388215 + 0.E-52*i Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:07:23 2004 Input: AssertAttribute(FldPr,"Precision",50); C:=ComplexField(); R := PowerSeriesRing(C); tau:=1+i; x:=0.5+0.3*i; pi:=Pi(RealField()); g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[1,1+i]),Exp(2*i*pi*x)); x2:=Evaluate(Derivative(WeierstrassSeries(z,[1,1+i])),Exp(2*i*pi*x)); g2,g3; x2^2; 4*x1^3-g2*x1-g3; Output: Magma V2.10-6 Fri Feb 27 2004 11:07:20 on modular [Seed = 1930188818] ------------------------------------- 3.15121200215389753821768994224868855664551935451485243846778 + 0.E-57*i 1.9330533697722892605969253989346656780509849166983488846857 E-58 + 0.E-57*i 326446.5362785892094839605406739267830542467118674423501239462425 + 0.E-52*i 326315.11033781402722603656410810790939126695648588933629748388215 + 0.E-52*i Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:07:49 2004 Input: AssertAttribute(FldPr,"Precision",50); C:=ComplexField(); R := PowerSeriesRing(C); tau:=0.2+12*i; x:=0.5+0.3*i; pi:=Pi(RealField()); g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[1,1+i]),Exp(2*i*pi*x)); x2:=Evaluate(Derivative(WeierstrassSeries(z,[1,1+i])),Exp(2*i*pi*x)); g2,g3; x2^2; 4*x1^3-g2*x1-g3; Output: Magma V2.10-6 Fri Feb 27 2004 11:07:46 on modular [Seed = 1829914214] ------------------------------------- 2.16464646742227638303200739308262457290163509459061876694782 + 8.8873452573401047330895707174478524982183634968831432395877 E-31*i 2.034686123968898279429035859581271051897734048056235038508524 - 1.7542916373168907224960586645018101826512622524147121602110 E-30*i 326446.5362785892094839605406739267830542467118674423501239462425 + 0.E-52*i 326355.8692656108715889502862932773087473615589766103675442728907 - 3.67957699991909598364025072817 E-29*i Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:09:00 2004 Input: AssertAttribute(FldPr,"Precision",50); C:=ComplexField(); R := PowerSeriesRing(C); tau:=1+12*i; x:=3+5*i; pi:=Pi(RealField()); g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[1,1+i]),Exp(2*i*pi*x)); x2:=Evaluate(Derivative(WeierstrassSeries(z,[1,1+i])),Exp(2*i*pi*x)); g2,g3; x2^2; 4*x1^3-g2*x1-g3; Output: Magma V2.10-6 Fri Feb 27 2004 11:08:57 on modular [Seed = 1679511460] ------------------------------------- 2.16464646742227638303200739308327027633068752801985895493883 - 4.7638330966286133032339486458047290030745912200058666625757 E-87*i 2.034686123968898279429035859579996484416699170576317978172614 + 9.40342961930818193319953925506489139209718673833767777405187 E-87*i 2.9150178724832101110202884061031552845680737904256590821515 E82 - 8.8976940289 E26*i 2.9150178724832101110202884061031552845680737904256590817545 E82 - 8.8976940289 E26*i Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:09:41 2004 Input: AssertAttribute(FldPr,"Precision",50); C:=ComplexField(); R := PowerSeriesRing(C); tau:=1+12*i; x:=0.5+5*i; pi:=Pi(RealField()); g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[1,1+i]),Exp(2*i*pi*x)); x2:=Evaluate(Derivative(WeierstrassSeries(z,[1,1+i])),Exp(2*i*pi*x)); g2,g3; x2^2; 4*x1^3-g2*x1-g3; Output: Magma V2.10-6 Fri Feb 27 2004 11:09:37 on modular [Seed = 526398599] ------------------------------------- 2.16464646742227638303200739308327027633068752801985895493883 - 4.7638330966286133032339486458047290030745912200058666625757 E-87*i 2.034686123968898279429035859579996484416699170576317978172614 + 9.40342961930818193319953925506489139209718673833767777405187 E-87*i 2.9150178724832101110202884061031552845680737904256590821515 E82 + 4.4488470144 E26*i 2.9150178724832101110202884061031552845680737904256590817545 E82 + 4.4004899822 E26*i Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:12:41 2004 Input: AssertAttribute(FldPr,"Precision",50); C:=ComplexField(); R := PowerSeriesRing(C); pi:=Pi(RealField()); E:=EllipticCurve([0,-1,1,-10,-20]); fo:=ModularForm(E); calc:=function(fo) Resul:=0; m:=mapC|j:->(Coefficient(fo,j)/j)*Exp(2*i*Pi(RealField())*j*((-9+Sqrt(-7))/22))>; for k in [1..100] do Resul+:=m(k); end for; return Resul; end function; zz:=calc(fo); w1:=Periods(E)[1]; w2:=Periods(E)[2]; tau:=w2/w1; g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[1,1+i]),Exp(2*i*pi*zz)); x2:=Evaluate(Derivative(WeierstrassSeries(z,[1,1+i])),Exp(2*i*pi*zz)); g2,g3; x2^2; 4*x1^3-g2*x1-g3; Output: Magma V2.10-6 Fri Feb 27 2004 11:12:35 on modular [Seed = 58470185] ------------------------------------- 1.7876486640085465927864938253018652243378838852716202318923 + 0.E-58*i 2.7658038371326492764144919381891037820073988643193766711360 + 0.E-58*i 418229925.7257510435903523844324878166020668290102110792661525219064 - 1232086426.1366616033185995296901389316994347252518000575485*i -62153608670264.5343447103597906977130483625856340779289897746326 - 134850106583630.4635413485548268567796611247676248140244296921949*i Total time: 4.759 seconds, Total memory usage: 2.51MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:13:37 2004 Input: AssertAttribute(FldPr,"Precision",50); C:=ComplexField(); R := PowerSeriesRing(C); pi:=Pi(RealField()); E:=EllipticCurve([0,-1,1,-10,-20]); fo:=ModularForm(E); calc:=function(fo) Resul:=0; m:=mapC|j:->(Coefficient(fo,j)/j)*Exp(2*i*Pi(RealField())*j*((-9+Sqrt(-7))/22))>; for k in [1..100] do Resul+:=m(k); end for; return Resul; end function; zz:=calc(fo); w1:=Periods(E)[1]; w2:=Periods(E)[2]; tau:=w2/w1; g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[w1,w2]),Exp(2*i*pi*zz)); x2:=Evaluate(Derivative(WeierstrassSeries(z,[w1,w2])),Exp(2*i*pi*zz)); g2,g3; x2^2; 4*x1^3-g2*x1-g3; Output: Magma V2.10-6 Fri Feb 27 2004 11:13:32 on modular [Seed = 1027740104] ------------------------------------- 1.7876486640085465927864938253018652243378838852716202318923 + 0.E-58*i 2.7658038371326492764144919381891037820073988643193766711360 + 0.E-58*i 508577423.9652127374993273535586711854694642402678932776816772127419 - 5801125818.06847939939480869111648408948265285542049597465795*i 607323449333981.03660784145119272394814914932990873757248399769463 + 583269573419718.6013784020572590557788162545107139911160926525016*i Total time: 4.919 seconds, Total memory usage: 2.51MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:14:37 2004 Input: zz; Output: Magma V2.10-6 Fri Feb 27 2004 11:14:34 on modular [Seed = 877336711] ------------------------------------- >> zz;; ^ User error: Identifier 'zz' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:16:12 2004 Input: C:=ComplexField(); R := PowerSeriesRing(C); pi:=Pi(RealField()); w1:=1; w2:=1+i; tau:=w2/w1; x:=0.2+2*i g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[w1,w2]),Exp(2*i*pi*x)); x2:=Evaluate(Derivative(WeierstrassSeries(z,[w1,w2])),Exp(2*i*pi*x)); x2^2; 4*x1^3-g2*x1-g3; Output: Magma V2.10-6 Fri Feb 27 2004 11:16:09 on modular [Seed = 593235507] ------------------------------------- >> g2:=Eisenstein(4,tau)*2*ZetaFunction(4); ^ User error: bad syntax >> x1:=Evaluate(WeierstrassSeries(z,[w1,w2]),Exp(2*i*pi*x)); ^ User error: Identifier 'x' has not been declared or assigned >> x2:=Evaluate(Derivative(WeierstrassSeries(z,[w1,w2])),Exp(2*i*pi*x)); ^ User error: Identifier 'x' has not been declared or assigned >> x2^2; ^ User error: Identifier 'x2' has not been declared or assigned >> 4*x1^3-g2*x1-g3;; ^ User error: Identifier 'x1' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:16:32 2004 Input: C:=ComplexField(); R := PowerSeriesRing(C); pi:=Pi(RealField()); w1:=1; w2:=1+i; tau:=w2/w1; x:=0.2+2*i; g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[w1,w2]),Exp(2*i*pi*x)); x2:=Evaluate(Derivative(WeierstrassSeries(z,[w1,w2])),Exp(2*i*pi*x)); x2^2; 4*x1^3-g2*x1-g3; Output: Magma V2.10-6 Fri Feb 27 2004 11:16:29 on modular [Seed = 3718443225] ------------------------------------- 6.87186861661470952375812786021 E32 - 2.114943691098637453038510112715 E33*i 6.87186861661470952376014342582 E32 - 2.114943691098637453038363673424 E33*i Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:17:39 2004 Input: C:=ComplexField(); R := PowerSeriesRing(C); pi:=Pi(RealField()); E:=EllipticCurve([0,-1,1,-10,-20]); fo:=ModularForm(E); calc:=function(fo) Resul:=0; m:=mapC|j:->(Coefficient(fo,j)/j)*Exp(2*i*Pi(RealField())*j*((-9+Sqrt(-7))/22))>; for k in [1..100] do Resul+:=m(k); end for; return Resul; end function; calc(fo); Periods(E); Output: Magma V2.10-6 Fri Feb 27 2004 11:17:34 on modular [Seed = 3618175504] ------------------------------------- -0.50768372171182136867551784671 - 0.405629044516045165291427536016*i [ 1.26920930427955342168879461675454730521949224183025537695802, 0.6346046521397767108443973083772736526097461209151276884790 + 1.45881661693849522933088961290367525715924342895095414432485*i ] Total time: 4.739 seconds, Total memory usage: 2.51MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:19:08 2004 Input: C:=ComplexField(); R := PowerSeriesRing(C); pi:=Pi(RealField()); w1:=1.26920930427955342168879461675454730521949224183025537695802; w2:=0.6346046521397767108443973083772736526097461209151276884790 + 1.45881661693849522933088961290367525715924342895095414432485*i; tau:=w2/w1; x:=-0.50768372171182136867551784671 - 0.405629044516045165291427536016*i; g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[w1,w2]),Exp(2*i*pi*x)); x2:=Evaluate(Derivative(WeierstrassSeries(z,[w1,w2])),Exp(2*i*pi*x)); x2^2; 4*x1^3-g2*x1-g3; Output: Magma V2.10-6 Fri Feb 27 2004 11:19:05 on modular [Seed = 3467764590] ------------------------------------- 508577423.96521273749932734377799531388 - 5801125818.068479399394808712891*i 607323449333981.036607841456515188838 + 583269573419718.60137840205847226116*i Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:19:37 2004 Input: C:=ComplexField(); R := PowerSeriesRing(C); pi:=Pi(RealField()); w1:=1.26920930427955342168879461675454730521949224183025537695802; w2:=0.6346046521397767108443973083772736526097461209151276884790 + 1.45881661693849522933088961290367525715924342895095414432485*i; tau:=w2/w1; x:=-0.50768372171182136867551784671 - 0.405629044516045165291427536016*i+w2; g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[w1,w2]),Exp(2*i*pi*x)); x2:=Evaluate(Derivative(WeierstrassSeries(z,[w1,w2])),Exp(2*i*pi*x)); x2^2; 4*x1^3-g2*x1-g3; Output: Magma V2.10-6 Fri Feb 27 2004 11:19:34 on modular [Seed = 4169651895] ------------------------------------- 50681997828651650.31880889848980586975 + 698635828924321440.60994018695782870054*i 50681997828674858.27771836396459548268 + 698635828925282793.75847480520315002650*i Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:20:36 2004 Input: C:=ComplexField(); R := PowerSeriesRing(C); pi:=Pi(RealField()); w1:=1.26920930427955342168879461675454730521949224183025537695802; w2:=0.6346046521397767108443973083772736526097461209151276884790 + 1.45881661693849522933088961290367525715924342895095414432485*i; tau:=w2/w1; x:=-0.50768372171182136867551784671 - 0.405629044516045165291427536016*i+w2+10*w1; g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[w1,w2]),Exp(2*i*pi*x)); x2:=Evaluate(Derivative(WeierstrassSeries(z,[w1,w2])),Exp(2*i*pi*x)); x2^2; 4*x1^3-g2*x1-g3; Output: Magma V2.10-6 Fri Feb 27 2004 11:20:33 on modular [Seed = 3902260960] ------------------------------------- 600862947326031414.64307602315966505557 + 360033894086840036.17659783938142936676*i 600862947326653513.68171429153881035745 + 360033894086106736.81664232010371051728*i Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:20:59 2004 Input: C:=ComplexField(); R := PowerSeriesRing(C); pi:=Pi(RealField()); w1:=1.26920930427955342168879461675454730521949224183025537695802; w2:=0.6346046521397767108443973083772736526097461209151276884790 + 1.45881661693849522933088961290367525715924342895095414432485*i; tau:=w2/w1; x:=-0.50768372171182136867551784671 - 0.405629044516045165291427536016*i+w2; g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[w1,w2]),Exp(2*i*pi*x)); x2:=Evaluate(Derivative(WeierstrassSeries(z,[w1,w2])),Exp(2*i*pi*x)); x2^2; 4*x1^3-g2*x1-g3; Output: Magma V2.10-6 Fri Feb 27 2004 11:20:56 on modular [Seed = 3818704339] ------------------------------------- 50681997828651650.31880889848980586975 + 698635828924321440.60994018695782870054*i 50681997828674858.27771836396459548268 + 698635828925282793.75847480520315002650*i Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:21:25 2004 Input: C:=ComplexField(); R := PowerSeriesRing(C); pi:=Pi(RealField()); w1:=1.26920930427955342168879461675454730521949224183025537695802; w2:=0.6346046521397767108443973083772736526097461209151276884790 + 1.45881661693849522933088961290367525715924342895095414432485*i; tau:=w2/w1; x:=-0.50768372171182136867551784671 - 0.405629044516045165291427536016*i+w2; g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[w1,w2]),Exp(2*i*pi*w1)); x2:=Evaluate(Derivative(WeierstrassSeries(z,[w1,w2])),Exp(2*i*pi*x)); x1; x2^2; 4*x1^3-g2*x1-g3; Output: Magma V2.10-6 Fri Feb 27 2004 11:21:22 on modular [Seed = 2598745153] ------------------------------------- -0.974549708291617928871839773477985768033 + 0.2381240383046843782813838195486048385480*i 50681997828651650.31880889848980586975 + 698635828924321440.60994018695782870054*i -4.062835143252742901434790551874 + 2.2341999115991090059772470743349798762640*\ i Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:23:14 2004 Input: C:=ComplexField(); R := PowerSeriesRing(C); pi:=Pi(RealField()); w1:=1.26920930427955342168879461675454730521949224183025537695802; w2:=0.6346046521397767108443973083772736526097461209151276884790 + 1.45881661693849522933088961290367525715924342895095414432485*i; tau:=w2/w1; x:=-0.50768372171182136867551784671 - 0.405629044516045165291427536016*i+3*w2; g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[w1,w2]),Exp(2*i*pi*x)); x2:=Evaluate(Derivative(WeierstrassSeries(z,[w1,w2])),Exp(2*i*pi*x)); x2^2; 4*x1^3-g2*x1-g3; Output: Magma V2.10-6 Fri Feb 27 2004 11:23:11 on modular [Seed = 2548611361] ------------------------------------- -2.94225405484677091268683612933 E65 - 2.87711560653191308496402172153 E65*i -2.94225405484677091268683612898 E65 - 2.87711560653191308496402172132 E65*i Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:23:26 2004 Input: C:=ComplexField(); R := PowerSeriesRing(C); pi:=Pi(RealField()); w1:=1.26920930427955342168879461675454730521949224183025537695802; w2:=0.6346046521397767108443973083772736526097461209151276884790 + 1.45881661693849522933088961290367525715924342895095414432485*i; tau:=w2/w1; x:=-0.50768372171182136867551784671 - 0.405629044516045165291427536016*i+w2; g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[w1,w2]),Exp(2*i*pi*x)); x2:=Evaluate(Derivative(WeierstrassSeries(z,[w1,w2])),Exp(2*i*pi*x)); x2^2; 4*x1^3-g2*x1-g3; Output: Magma V2.10-6 Fri Feb 27 2004 11:23:23 on modular [Seed = 2398199852] ------------------------------------- 50681997828651650.31880889848980586975 + 698635828924321440.60994018695782870054*i 50681997828674858.27771836396459548268 + 698635828925282793.75847480520315002650*i Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:26:46 2004 Input: C:=ComplexField(); R := PowerSeriesRing(C); pi:=Pi(RealField()); w1:=1.26920930427955342168879461675454730521949224183025537695802; w2:=0.6346046521397767108443973083772736526097461209151276884790 + 1.45881661693849522933088961290367525715924342895095414432485*i; tau:=w2/w1; x:=-0.50768372171182136867551784671 - 0.405629044516045165291427536016*i; g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[w1,w2]),Exp(2*i*pi*x)); x2:=Evaluate(Derivative(WeierstrassSeries(z,[w1,w2])),Exp(2*i*pi*x)); x2^2; 4*x1^3-g2*x1-g3; Output: Magma V2.10-6 Fri Feb 27 2004 11:26:43 on modular [Seed = 3166933798] ------------------------------------- 508577423.96521273749932734377799531388 - 5801125818.068479399394808712891*i 607323449333981.036607841456515188838 + 583269573419718.60137840205847226116*i Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:27:00 2004 Input: C:=ComplexField(); R := PowerSeriesRing(C); pi:=Pi(RealField()); w1:=1.26920930427955342168879461675454730521949224183025537695802; w2:=0.6346046521397767108443973083772736526097461209151276884790 + 1.45881661693849522933088961290367525715924342895095414432485*i; tau:=w2/w1; x:=-0.50768372171182136867551784671 - 0.405629044516045165291427536016*i-w2; g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[w1,w2]),Exp(2*i*pi*x)); x2:=Evaluate(Derivative(WeierstrassSeries(z,[w1,w2])),Exp(2*i*pi*x)); x2^2; 4*x1^3-g2*x1-g3; Output: Magma V2.10-6 Fri Feb 27 2004 11:26:57 on modular [Seed = 3083376703] ------------------------------------- -2.62674901390901135944126025282 E128 - 2.231192607505798325067325962352 E129*i -9.159297502126602505538759301568 E205 - 1.66999632377389333081306505910 E206*i Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:27:15 2004 Input: C:=ComplexField(); R := PowerSeriesRing(C); pi:=Pi(RealField()); w1:=1.26920930427955342168879461675454730521949224183025537695802; w2:=0.6346046521397767108443973083772736526097461209151276884790 + 1.45881661693849522933088961290367525715924342895095414432485*i; tau:=w2/w1; x:=-0.50768372171182136867551784671 - 0.405629044516045165291427536016*i+w1; g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[w1,w2]),Exp(2*i*pi*x)); x2:=Evaluate(Derivative(WeierstrassSeries(z,[w1,w2])),Exp(2*i*pi*x)); x2^2; 4*x1^3-g2*x1-g3; Output: Magma V2.10-6 Fri Feb 27 2004 11:27:12 on modular [Seed = 2932965655] ------------------------------------- 6600098721.44037518350127182213 - 11123521081.28717196045497417051*i 3250768735765710.18958163140018768899 + 715205752929469.77157106227633676098*i Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:27:30 2004 Input: C:=ComplexField(); R := PowerSeriesRing(C); pi:=Pi(RealField()); w1:=1.26920930427955342168879461675454730521949224183025537695802; w2:=0.6346046521397767108443973083772736526097461209151276884790 + 1.45881661693849522933088961290367525715924342895095414432485*i; tau:=w2/w1; x:=-0.50768372171182136867551784671 - 0.405629044516045165291427536016*i+w2; g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[w1,w2]),Exp(2*i*pi*x)); x2:=Evaluate(Derivative(WeierstrassSeries(z,[w1,w2])),Exp(2*i*pi*x)); x2^2; 4*x1^3-g2*x1-g3; Output: Magma V2.10-6 Fri Feb 27 2004 11:27:27 on modular [Seed = 1529115886] ------------------------------------- 50681997828651650.31880889848980586975 + 698635828924321440.60994018695782870054*i 50681997828674858.27771836396459548268 + 698635828925282793.75847480520315002650*i Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:29:42 2004 Input: C:=ComplexField(); R := PowerSeriesRing(C); pi:=Pi(RealField()); w1:=1.26920930427955342168879461675454730521949224183025537695802; w2:=0.6346046521397767108443973083772736526097461209151276884790 + 1.45881661693849522933088961290367525715924342895095414432485*i; tau:=w2/w1; x:=-0.50768372171182136867551784671 - 0.405629044516045165291427536016*i+w2; x:=tau; g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[w1,w2]),Exp(2*i*pi*x)); x2:=Evaluate(Derivative(WeierstrassSeries(z,[w1,w2])),Exp(2*i*pi*x)); x2^2; 4*x1^3-g2*x1-g3; Output: Magma V2.10-6 Fri Feb 27 2004 11:29:39 on modular [Seed = 1361994104] ------------------------------------- 26331049950381102698.3590633664 - 0.000000005587935447*i 26331049950377881364.6384037584 - 0.000000005587935447*i Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:30:09 2004 Input: C:=ComplexField(); R := PowerSeriesRing(C); pi:=Pi(RealField()); w1:=1.26920930427955342168879461675454730521949224183025537695802; w2:=0.6346046521397767108443973083772736526097461209151276884790 + 1.45881661693849522933088961290367525715924342895095414432485*i; tau:=w2/w1; x:=-0.50768372171182136867551784671 - 0.405629044516045165291427536016*i+w2; x:=w2; g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[w1,w2]),Exp(2*i*pi*x)); x2:=Evaluate(Derivative(WeierstrassSeries(z,[w1,w2])),Exp(2*i*pi*x)); x2^2; 4*x1^3-g2*x1-g3; Output: Magma V2.10-6 Fri Feb 27 2004 11:30:06 on modular [Seed = 1094611349] ------------------------------------- 1086025084809881384710923.7064819335 + 2867111005569903955067101.7701416015*i 1086025084809881403650432.2664337158 + 2867111005569904111224014.9918823242*i Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:30:31 2004 Input: C:=ComplexField(); R := PowerSeriesRing(C); pi:=Pi(RealField()); w1:=1.26920930427955342168879461675454730521949224183025537695802; w2:=0.6346046521397767108443973083772736526097461209151276884790 + 1.45881661693849522933088961290367525715924342895095414432485*i; tau:=w2/w1; x:=-0.50768372171182136867551784671 - 0.405629044516045165291427536016*i+w2; x:=w2; g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[w1,w2]),0); x2:=Evaluate(Derivative(WeierstrassSeries(z,[w1,w2])),Exp(2*i*pi*x)); x2^2; 4*x1^3-g2*x1-g3; Output: Magma V2.10-6 Fri Feb 27 2004 11:30:28 on modular [Seed = 2114014848] ------------------------------------- >> x1:=Evaluate(WeierstrassSeries(z,[w1,w2]),0); ^ Runtime error in 'Evaluate': Argument 2 is not invertible (needed since negative valuation) 1086025084809881384710923.7064819335 + 2867111005569903955067101.7701416015*i >> 4*x1^3-g2*x1-g3;; ^ User error: Identifier 'x1' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:31:34 2004 Input: C:=ComplexField(); R := PowerSeriesRing(C); pi:=Pi(RealField()); w1:=1.26920930427955342168879461675454730521949224183025537695802; w2:=0.6346046521397767108443973083772736526097461209151276884790 + 1.45881661693849522933088961290367525715924342895095414432485*i; tau:=w2/w1; x:=-0.50768372171182136867551784671 - 0.405629044516045165291427536016*i+w2; x:=w2; g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[w1,w2]),1); x2:=Evaluate(Derivative(WeierstrassSeries(z,[w1,w2])),Exp(2*i*pi*x)); x2^2; 4*x1^3-g2*x1-g3; Output: Magma V2.10-6 Fri Feb 27 2004 11:31:31 on modular [Seed = 1946895565] ------------------------------------- 1086025084809881384710923.7064819335 + 2867111005569903955067101.7701416015*i -0.52044438611401910758009817037 - 3.6606951486 E-29*i Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:33:24 2004 Input: C:=ComplexField(); R := PowerSeriesRing(C); pi:=Pi(RealField()); w1:=1.26920930427955342168879461675454730521949224183025537695802; w2:=0.6346046521397767108443973083772736526097461209151276884790 + 1.45881661693849522933088961290367525715924342895095414432485*i; tau:=w2/w1; x:=-0.50768372171182136867551784671 - 0.405629044516045165291427536016*i+w2; x:=w2; g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[w1,w2]),Exp(2*i*pi*x)); x2:=Evaluate(Derivative(WeierstrassSeries(z,[w1,w2])),Exp(2*i*pi*x)); x2^2; 4*x1^3-g2*x1-g3; WeierstrassSeries(z,[w1,w2]); Output: Magma V2.10-6 Fri Feb 27 2004 11:33:21 on modular [Seed = 1646089065] ------------------------------------- 1086025084809881384710923.7064819335 + 2867111005569903955067101.7701416015*i 1086025084809881403650432.2664337158 + 2867111005569904111224014.9918823242*i $.1^-2 + (0.00344099427418535600859399732276834155633 - 3.65551404786060381096 E-32*i)*$.1^2 + (-0.0002247564526624389049607390401076381000712 - 2.97477660956570758867 E-33*i)*$.1^4 + (0.00000394681386499213500149374533558542808563 - 8.38573527036165912440 E-35*i)*$.1^6 + (-0.0000002109233636448175324952696208933957909221 - 5.5095970351 E-37*i)*$.1^8 + (0.0000000059751839103715202192318317640581357\ 9914 + 3.62724972977683743488 E-38*i)*$.1^10 + (-1.612857970208295137545456263569720212797 E-10 + 1.2921075546 E-39*i)*$.1^12 + (5.347456267883206785118660570270080004356 E-12 + 2.30613206816839571774 E-41*i)*$.1^14 + (-1.437063105179485758258968961261666743274 E-13 - 3.8113676803 E-45*i)*$.1^16 + O($.1^18) Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:38:15 2004 Input: C:=ComplexField(); R := PowerSeriesRing(C); pi:=Pi(RealField()); w1:=1.26920930427955342168879461675454730521949224183025537695802; w2:=0.6346046521397767108443973083772736526097461209151276884790 + 1.45881661693849522933088961290367525715924342895095414432485*i; tau:=w2/w1; x:=-0.50768372171182136867551784671 - 0.405629044516045165291427536016*i+w2; x:=w2; g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[w1,w2]),Exp(2*i*pi*x)); x2:=Evaluate(Derivative(WeierstrassSeries(z,[w1,w2])),Exp(2*i*pi*x)); Trouver:=function(tau) A:= Matrix(Integers(),2,2,[1,0,0,1]); n:=Truncate(Real(tau)); tau-:=n; A:=Matrix(Integers(),2,2,[1,-n,0,1])*A; m:=Norm(tau); if m ge 1 then return tau,A; else tau:=-ComplexConjugate(tau)/m; A:=Matrix(Integers(),2,2,[0,-1,1,0])*A; n:=Truncate(Real(tau)); tau-:=n; A:=Matrix(Integers(),2,2,[1,-n,0,1])*A; return tau,A; end if; end function; Trouver(x); Output: Magma V2.10-6 Fri Feb 27 2004 11:38:12 on modular [Seed = 342566458] ------------------------------------- 0.63460465213977671084439730837727365260974612091512768847899999999997 + 1.45881661693849522933088961290367525715924342895095414432484999999993*i [1 0] [0 1] Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:38:33 2004 Input: C:=ComplexField(); R := PowerSeriesRing(C); pi:=Pi(RealField()); w1:=1.26920930427955342168879461675454730521949224183025537695802; w2:=0.6346046521397767108443973083772736526097461209151276884790 + 1.45881661693849522933088961290367525715924342895095414432485*i; tau:=w2/w1; x:=-0.50768372171182136867551784671 - 0.405629044516045165291427536016*i; g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[w1,w2]),Exp(2*i*pi*x)); x2:=Evaluate(Derivative(WeierstrassSeries(z,[w1,w2])),Exp(2*i*pi*x)); Trouver:=function(tau) A:= Matrix(Integers(),2,2,[1,0,0,1]); n:=Truncate(Real(tau)); tau-:=n; A:=Matrix(Integers(),2,2,[1,-n,0,1])*A; m:=Norm(tau); if m ge 1 then return tau,A; else tau:=-ComplexConjugate(tau)/m; A:=Matrix(Integers(),2,2,[0,-1,1,0])*A; n:=Truncate(Real(tau)); tau-:=n; A:=Matrix(Integers(),2,2,[1,-n,0,1])*A; return tau,A; end if; end function; Trouver(x); Output: Magma V2.10-6 Fri Feb 27 2004 11:38:30 on modular [Seed = 225591249] ------------------------------------- 0.2022508934158342753552882589036891392011 - 0.960574192768078289393850309397246122930*i [-1 -1] [ 1 0] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:38:52 2004 Input: C:=ComplexField(); R := PowerSeriesRing(C); pi:=Pi(RealField()); w1:=1.26920930427955342168879461675454730521949224183025537695802; w2:=0.6346046521397767108443973083772736526097461209151276884790 + 1.45881661693849522933088961290367525715924342895095414432485*i; tau:=w2/w1; x:=-0.50768372171182136867551784671 - 0.405629044516045165291427536016*i; g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[w1,w2]),Exp(2*i*pi*x)); x2:=Evaluate(Derivative(WeierstrassSeries(z,[w1,w2])),Exp(2*i*pi*x)); Trouver:=function(tau) A:= Matrix(Integers(),2,2,[1,0,0,1]); n:=Truncate(Real(tau)); tau-:=n; A:=Matrix(Integers(),2,2,[1,-n,0,1])*A; m:=Norm(tau); if m ge 1 then return tau,A; else tau:=-ComplexConjugate(tau)/m; A:=Matrix(Integers(),2,2,[0,-1,1,0])*A; n:=Truncate(Real(tau)); tau-:=n; A:=Matrix(Integers(),2,2,[1,-n,0,1])*A; return tau,A; end if; end function; Trouver(x); x+w2; Output: Magma V2.10-6 Fri Feb 27 2004 11:38:49 on modular [Seed = 977602809] ------------------------------------- 0.2022508934158342753552882589036891392011 - 0.960574192768078289393850309397246122930*i [-1 -1] [ 1 0] 0.1269209304279553421688794616672736526100 + 1.05318757242245006403946207688767525716046736686567*i Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:39:43 2004 Input: C:=ComplexField(); R := PowerSeriesRing(C); pi:=Pi(RealField()); w1:=1.26920930427955342168879461675454730521949224183025537695802; w2:=0.6346046521397767108443973083772736526097461209151276884790 + 1.45881661693849522933088961290367525715924342895095414432485*i; tau:=w2/w1; x:=-0.50768372171182136867551784671 - 0.405629044516045165291427536016*i; g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[w1,w2]),Exp(2*i*pi*x)); x2:=Evaluate(Derivative(WeierstrassSeries(z,[w1,w2])),Exp(2*i*pi*x)); Trouver:=function(tau) A:= Matrix(Integers(),2,2,[1,0,0,1]); n:=Truncate(Real(tau)); tau-:=n; A:=Matrix(Integers(),2,2,[1,-n,0,1])*A; m:=Norm(tau); if m ge 1 then return tau,A; else tau:=-ComplexConjugate(tau)/m; A:=Matrix(Integers(),2,2,[0,-1,1,0])*A; n:=Truncate(Real(tau)); tau-:=n; A:=Matrix(Integers(),2,2,[1,-n,0,1])*A; return tau,A; end if; end function; Trouver(x+w2); Output: Magma V2.10-6 Fri Feb 27 2004 11:39:40 on modular [Seed = 860619173] ------------------------------------- 0.1269209304279553421688794616672736526100 + 1.05318757242245006403946207688767525716046736686567*i [1 0] [0 1] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:39:58 2004 Input: C:=ComplexField(); R := PowerSeriesRing(C); pi:=Pi(RealField()); w1:=1.26920930427955342168879461675454730521949224183025537695802; w2:=0.6346046521397767108443973083772736526097461209151276884790 + 1.45881661693849522933088961290367525715924342895095414432485*i; tau:=w2/w1; x:=-0.50768372171182136867551784671 - 0.405629044516045165291427536016*i; g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[w1,w2]),Exp(2*i*pi*x)); x2:=Evaluate(Derivative(WeierstrassSeries(z,[w1,w2])),Exp(2*i*pi*x)); Trouver:=function(tau) A:= Matrix(Integers(),2,2,[1,0,0,1]); n:=Truncate(Real(tau)); tau-:=n; A:=Matrix(Integers(),2,2,[1,-n,0,1])*A; m:=Norm(tau); if m ge 1 then return tau,A; else tau:=-ComplexConjugate(tau)/m; A:=Matrix(Integers(),2,2,[0,-1,1,0])*A; n:=Truncate(Real(tau)); tau-:=n; A:=Matrix(Integers(),2,2,[1,-n,0,1])*A; return tau,A; end if; end function; Trouver(x+w2); x+w2; Output: Magma V2.10-6 Fri Feb 27 2004 11:39:55 on modular [Seed = 676797097] ------------------------------------- 0.1269209304279553421688794616672736526100 + 1.05318757242245006403946207688767525716046736686567*i [1 0] [0 1] 0.1269209304279553421688794616672736526100 + 1.05318757242245006403946207688767525716046736686567*i Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:40:07 2004 Input: C:=ComplexField(); R := PowerSeriesRing(C); pi:=Pi(RealField()); w1:=1.26920930427955342168879461675454730521949224183025537695802; w2:=0.6346046521397767108443973083772736526097461209151276884790 + 1.45881661693849522933088961290367525715924342895095414432485*i; tau:=w2/w1; x:=-0.50768372171182136867551784671 - 0.405629044516045165291427536016*i; g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[w1,w2]),Exp(2*i*pi*x)); x2:=Evaluate(Derivative(WeierstrassSeries(z,[w1,w2])),Exp(2*i*pi*x)); Trouver:=function(tau) A:= Matrix(Integers(),2,2,[1,0,0,1]); n:=Truncate(Real(tau)); tau-:=n; A:=Matrix(Integers(),2,2,[1,-n,0,1])*A; m:=Norm(tau); if m ge 1 then return tau,A; else tau:=-ComplexConjugate(tau)/m; A:=Matrix(Integers(),2,2,[0,-1,1,0])*A; n:=Truncate(Real(tau)); tau-:=n; A:=Matrix(Integers(),2,2,[1,-n,0,1])*A; return tau,A; end if; end function; Trouver(x+10*w2); x+w2; Output: Magma V2.10-6 Fri Feb 27 2004 11:40:04 on modular [Seed = 3634883174] ------------------------------------- 0.8383627996859457397684552370627365260981545935211 + 14.1825371248689071280174685930207525715936582274243*i [ 1 -5] [ 0 1] 0.1269209304279553421688794616672736526100 + 1.05318757242245006403946207688767525716046736686567*i Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:41:45 2004 Input: C:=ComplexField(); R := PowerSeriesRing(C); pi:=Pi(RealField()); w1:=1.26920930427955342168879461675454730521949224183025537695802; w2:=0.6346046521397767108443973083772736526097461209151276884790 + 1.45881661693849522933088961290367525715924342895095414432485*i; tau:=w2/w1; x:=-0.50768372171182136867551784671 - 0.405629044516045165291427536016*i; g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[w1,w2]),Exp(2*i*pi*x)); x2:=Evaluate(Derivative(WeierstrassSeries(z,[w1,w2])),Exp(2*i*pi*x)); Trouver:=function(tau) A:= Matrix(Integers(),2,2,[1,0,0,1]); n:=Truncate(Real(tau)); tau-:=n; A:=Matrix(Integers(),2,2,[1,-n,0,1])*A; m:=Norm(tau); if m ge 1 then return tau,A; else tau:=-ComplexConjugate(tau)/m; A:=Matrix(Integers(),2,2,[0,-1,1,0])*A; n:=Truncate(Real(tau)); tau-:=n; A:=Matrix(Integers(),2,2,[1,-n,0,1])*A; return tau,A; end if; end function; Weierstrass:=function(w1,w2,x) if Im(w2/w1) ge 0 then tau:=w2/w1; else tau:=w1/w2; end if; tau2,A:=Trouver(tau); w1:=A[2][1]*w2+A[2][2]*w1; x:=x/w1; n:=Truncate(Im(x)/Im(tau2)); x-:=n*tau2; x-:=Truncate(Re(x)); pi:=Pi(RealField()); q:=Exp(2*i*pi*tau2); u:=Exp(2*i*pi*x/w1); Res:=1/12+u/(1-u)^2; for k in [1..500] do Res+:=q^k*(u*(1/(1-q^k*u)^2+1/(q^k-u)^2)-2/(1-q^k)^2); end for; Res*:=(2*i*pi/w1)^2; return Res; end function; x1; Weierstrass(w1,w2,x); Output: Magma V2.10-6 Fri Feb 27 2004 11:41:42 on modular [Seed = 3601458634] ------------------------------------- -41779.81858253346824089321777848919 + 42346.290997563164447659379117962062*i 0.74739607023764227828916119692 - 3.120424095313850604212697917986*i Total time: 3.419 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:42:56 2004 Input: C:=ComplexField(); R := PowerSeriesRing(C); pi:=Pi(RealField()); w1:=1.26920930427955342168879461675454730521949224183025537695802; w2:=0.6346046521397767108443973083772736526097461209151276884790 + 1.45881661693849522933088961290367525715924342895095414432485*i; tau:=w2/w1; x:=-0.50768372171182136867551784671 - 0.405629044516045165291427536016*i; g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[w1,w2]),Exp(2*i*pi*x)); x2:=Evaluate(Derivative(WeierstrassSeries(z,[w1,w2])),Exp(2*i*pi*x)); Trouver:=function(tau) A:= Matrix(Integers(),2,2,[1,0,0,1]); n:=Truncate(Real(tau)); tau-:=n; A:=Matrix(Integers(),2,2,[1,-n,0,1])*A; m:=Norm(tau); if m ge 1 then return tau,A; else tau:=-ComplexConjugate(tau)/m; A:=Matrix(Integers(),2,2,[0,-1,1,0])*A; n:=Truncate(Real(tau)); tau-:=n; A:=Matrix(Integers(),2,2,[1,-n,0,1])*A; return tau,A; end if; end function; Weierstrass:=function(w1,w2,x) if Im(w2/w1) ge 0 then tau:=w2/w1; else tau:=w1/w2; end if; tau2,A:=Trouver(tau); w1:=A[2][1]*w2+A[2][2]*w1; x:=x/w1; n:=Truncate(Im(x)/Im(tau2)); x-:=n*tau2; x-:=Truncate(Re(x)); pi:=Pi(RealField()); q:=Exp(2*i*pi*tau2); u:=Exp(2*i*pi*x/w1); Res:=1/12+u/(1-u)^2; for k in [1..500] do Res+:=q^k*(u*(1/(1-q^k*u)^2+1/(q^k-u)^2)-2/(1-q^k)^2); end for; Res*:=(2*i*pi/w1)^2; return Res; end function; dWeierstrass:=function(w1,w2,x) if Im(w2/w1) ge 0 then tau:=w2/w1; else tau:=w1/w2; end if; tau2,A:=Trouver(tau); w1:=A[2][1]*w2+A[2][2]*w1; x:=x/w1; n:=Truncate(Im(x)/Im(tau2)); x-:=n*tau2; x-:=Truncate(Re(x)); pi:=Pi(RealField()); q:=Exp(2*i*pi*tau2); u:=Exp(2*i*pi*x/w1); Res:=(1+u)/(1-u)^3; for k in [1..500] do Res+:=q^k*((1+q^k*u)/(1-q^k*u)^3+(q^k+u)/(q^k-u)^3); end for; Res*:=(2*i*pi/w1)^3*u; return Res; end function; x1; y1:=Weierstrass(w1,w2,x); y2:=dWeierstrass(w1,w2,x); y2^2; 4*y1^3-g2*y1-g3; Output: Magma V2.10-6 Fri Feb 27 2004 11:42:51 on modular [Seed = 3434348317] ------------------------------------- -41779.81858253346824089321777848919 + 42346.290997563164447659379117962062*i -209.181179893562829252949436495586 + 229.59552780337772403686490821610*i -89.76106478435552713493838474931 + 106.196220495533115083453627363151*i Total time: 4.829 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:43:29 2004 Input: C:=ComplexField(); R := PowerSeriesRing(C); pi:=Pi(RealField()); w1:=1.26920930427955342168879461675454730521949224183025537695802; w2:=0.6346046521397767108443973083772736526097461209151276884790 + 1.45881661693849522933088961290367525715924342895095414432485*i; tau:=w2/w1; x:=-0.50768372171182136867551784671 - 0.405629044516045165291427536016*i; g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[w1,w2]),Exp(2*i*pi*x)); x2:=Evaluate(Derivative(WeierstrassSeries(z,[w1,w2])),Exp(2*i*pi*x)); Trouver:=function(tau) A:= Matrix(Integers(),2,2,[1,0,0,1]); n:=Truncate(Real(tau)); tau-:=n; A:=Matrix(Integers(),2,2,[1,-n,0,1])*A; m:=Norm(tau); if m ge 1 then return tau,A; else tau:=-ComplexConjugate(tau)/m; A:=Matrix(Integers(),2,2,[0,-1,1,0])*A; n:=Truncate(Real(tau)); tau-:=n; A:=Matrix(Integers(),2,2,[1,-n,0,1])*A; return tau,A; end if; end function; Weierstrass:=function(w1,w2,x) if Im(w2/w1) ge 0 then tau:=w2/w1; else tau:=w1/w2; end if; tau2,A:=Trouver(tau); w1:=A[2][1]*w2+A[2][2]*w1; x:=x/w1; n:=Truncate(Im(x)/Im(tau2)); x-:=n*tau2; x-:=Truncate(Re(x)); pi:=Pi(RealField()); q:=Exp(2*i*pi*tau2); u:=Exp(2*i*pi*x/w1); Res:=1/12+u/(1-u)^2; for k in [1..500] do Res+:=q^k*(u*(1/(1-q^k*u)^2+1/(q^k-u)^2)-2/(1-q^k)^2); end for; Res*:=(2*i*pi/w1)^2; return Res; end function; dWeierstrass:=function(w1,w2,x) if Im(w2/w1) ge 0 then tau:=w2/w1; else tau:=w1/w2; end if; tau2,A:=Trouver(tau); w1:=A[2][1]*w2+A[2][2]*w1; x:=x/w1; n:=Truncate(Im(x)/Im(tau2)); x-:=n*tau2; x-:=Truncate(Re(x)); pi:=Pi(RealField()); q:=Exp(2*i*pi*tau2); u:=Exp(2*i*pi*x/w1); Res:=(1+u)/(1-u)^3; for k in [1..500] do Res+:=q^k*((1+q^k*u)/(1-q^k*u)^3+(q^k+u)/(q^k-u)^3); end for; Res*:=(2*i*pi/w1)^3*u; return Res; end function; y1:=Weierstrass(w1,w2,x); y2:=dWeierstrass(w1,w2,x); y2^2; 4*y1^3-g2*y1-g3; x2^2 4*x1^3-g2*x1-g3; Output: Magma V2.10-6 Fri Feb 27 2004 11:43:25 on modular [Seed = 4286630920] ------------------------------------- -209.181179893562829252949436495586 + 229.59552780337772403686490821610*i -89.76106478435552713493838474931 + 106.196220495533115083453627363151*i >> 4*x1^3-g2*x1-g3;; ^ User error: bad syntax Total time: 3.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:43:32 2004 Input: C:=ComplexField(); R := PowerSeriesRing(C); pi:=Pi(RealField()); w1:=1.26920930427955342168879461675454730521949224183025537695802; w2:=0.6346046521397767108443973083772736526097461209151276884790 + 1.45881661693849522933088961290367525715924342895095414432485*i; tau:=w2/w1; x:=-0.50768372171182136867551784671 - 0.405629044516045165291427536016*i; g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[w1,w2]),Exp(2*i*pi*x)); x2:=Evaluate(Derivative(WeierstrassSeries(z,[w1,w2])),Exp(2*i*pi*x)); Trouver:=function(tau) A:= Matrix(Integers(),2,2,[1,0,0,1]); n:=Truncate(Real(tau)); tau-:=n; A:=Matrix(Integers(),2,2,[1,-n,0,1])*A; m:=Norm(tau); if m ge 1 then return tau,A; else tau:=-ComplexConjugate(tau)/m; A:=Matrix(Integers(),2,2,[0,-1,1,0])*A; n:=Truncate(Real(tau)); tau-:=n; A:=Matrix(Integers(),2,2,[1,-n,0,1])*A; return tau,A; end if; end function; Weierstrass:=function(w1,w2,x) if Im(w2/w1) ge 0 then tau:=w2/w1; else tau:=w1/w2; end if; tau2,A:=Trouver(tau); w1:=A[2][1]*w2+A[2][2]*w1; x:=x/w1; n:=Truncate(Im(x)/Im(tau2)); x-:=n*tau2; x-:=Truncate(Re(x)); pi:=Pi(RealField()); q:=Exp(2*i*pi*tau2); u:=Exp(2*i*pi*x/w1); Res:=1/12+u/(1-u)^2; for k in [1..500] do Res+:=q^k*(u*(1/(1-q^k*u)^2+1/(q^k-u)^2)-2/(1-q^k)^2); end for; Res*:=(2*i*pi/w1)^2; return Res; end function; dWeierstrass:=function(w1,w2,x) if Im(w2/w1) ge 0 then tau:=w2/w1; else tau:=w1/w2; end if; tau2,A:=Trouver(tau); w1:=A[2][1]*w2+A[2][2]*w1; x:=x/w1; n:=Truncate(Im(x)/Im(tau2)); x-:=n*tau2; x-:=Truncate(Re(x)); pi:=Pi(RealField()); q:=Exp(2*i*pi*tau2); u:=Exp(2*i*pi*x/w1); Res:=(1+u)/(1-u)^3; for k in [1..500] do Res+:=q^k*((1+q^k*u)/(1-q^k*u)^3+(q^k+u)/(q^k-u)^3); end for; Res*:=(2*i*pi/w1)^3*u; return Res; end function; y1:=Weierstrass(w1,w2,x); y2:=dWeierstrass(w1,w2,x); y2^2; 4*y1^3-g2*y1-g3; x2^2; 4*x1^3-g2*x1-g3; Output: Magma V2.10-6 Fri Feb 27 2004 11:43:28 on modular [Seed = 4086087705] ------------------------------------- -209.181179893562829252949436495586 + 229.59552780337772403686490821610*i -89.76106478435552713493838474931 + 106.196220495533115083453627363151*i 508577423.96521273749932734377799531388 - 5801125818.068479399394808712891*i 607323449333981.036607841456515188838 + 583269573419718.60137840205847226116*i Total time: 3.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD19.Math.McGill.CA. (132.206.150.219) Time: Fri Feb 27 11:43:52 2004 Input: C:=ComplexField(); R := PowerSeriesRing(C); pi:=Pi(RealField()); w1:=1.26920930427955342168879461675454730521949224183025537695802; w2:=0.6346046521397767108443973083772736526097461209151276884790 + 1.45881661693849522933088961290367525715924342895095414432485*i; tau:=w2/w1; x:=-0.50768372171182136867551784671 - 0.405629044516045165291427536016*i+w2; g2:=Eisenstein(4,tau)*2*ZetaFunction(4); g3:=Eisenstein(6,tau)*2*ZetaFunction(6); x1:=Evaluate(WeierstrassSeries(z,[w1,w2]),Exp(2*i*pi*x)); x2:=Evaluate(Derivative(WeierstrassSeries(z,[w1,w2])),Exp(2*i*pi*x)); Trouver:=function(tau) A:= Matrix(Integers(),2,2,[1,0,0,1]); n:=Truncate(Real(tau)); tau-:=n; A:=Matrix(Integers(),2,2,[1,-n,0,1])*A; m:=Norm(tau); if m ge 1 then return tau,A; else tau:=-ComplexConjugate(tau)/m; A:=Matrix(Integers(),2,2,[0,-1,1,0])*A; n:=Truncate(Real(tau)); tau-:=n; A:=Matrix(Integers(),2,2,[1,-n,0,1])*A; return tau,A; end if; end function; Weierstrass:=function(w1,w2,x) if Im(w2/w1) ge 0 then tau:=w2/w1; else tau:=w1/w2; end if; tau2,A:=Trouver(tau); w1:=A[2][1]*w2+A[2][2]*w1; x:=x/w1; n:=Truncate(Im(x)/Im(tau2)); x-:=n*tau2; x-:=Truncate(Re(x)); pi:=Pi(RealField()); q:=Exp(2*i*pi*tau2); u:=Exp(2*i*pi*x/w1); Res:=1/12+u/(1-u)^2; for k in [1..500] do Res+:=q^k*(u*(1/(1-q^k*u)^2+1/(q^k-u)^2)-2/(1-q^k)^2); end for; Res*:=(2*i*pi/w1)^2; return Res; end function; dWeierstrass:=function(w1,w2,x) if Im(w2/w1) ge 0 then tau:=w2/w1; else tau:=w1/w2; end if; tau2,A:=Trouver(tau); w1:=A[2][1]*w2+A[2][2]*w1; x:=x/w1; n:=Truncate(Im(x)/Im(tau2)); x-:=n*tau2; x-:=Truncate(Re(x)); pi:=Pi(RealField()); q:=Exp(2*i*pi*tau2); u:=Exp(2*i*pi*x/w1); Res:=(1+u)/(1-u)^3; for k in [1..500] do Res+:=q^k*((1+q^k*u)/(1-q^k*u)^3+(q^k+u)/(q^k-u)^3); end for; Res*:=(2*i*pi/w1)^3*u; return Res; end function; y1:=Weierstrass(w1,w2,x); y2:=dWeierstrass(w1,w2,x); y2^2; 4*y1^3-g2*y1-g3; x2^2; 4*x1^3-g2*x1-g3; Output: Magma V2.10-6 Fri Feb 27 2004 11:43:47 on modular [Seed = 3985825396] ------------------------------------- -35.99885419375764972402685762416 + 9.50033250566004743806154083637*i -6.82375095754560827847390355129 - 15.99747424297705097337366743400*i 50681997828651650.31880889848980586975 + 698635828924321440.60994018695782870054*i 50681997828674858.27771836396459548268 + 698635828925282793.75847480520315002650*i Total time: 3.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sab-combi-01.uab.es. (158.109.241.123) Time: Fri Feb 27 12:23:05 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsArf:=func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern>0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; if firstnongaps(semigrup) eq [0] then return true; if not IsStrongAdmissible(pattern) then return false; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; MAXGENUS=10; MAXLENGTHPATTERNS=5; Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)]); end if; end for; Output: Magma V2.10-6 Fri Feb 27 2004 12:23:02 on modular [Seed = 994314134] ------------------------------------- >> IsArf:=func; ^ User error: Identifier 'admits' has not been declared or assigned >> while IsAdmissible(pat) and #pattern>0 do ^ User error: bad syntax >> degree:=degree+1; ^ User error: Identifier 'degree' has not been declared or assigned >> pat:=PreviousPattern(pat); ^ User error: Identifier 'pat' has not been declared or assigned >> end while; ^ User error: bad syntax >> return degree; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> end function; ^ User error: bad syntax >> while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; ^ User error: Identifier 'admits' has not been declared or assigned >> MAXGENUS=10; ^ User error: Identifier 'MAXGENUS' has not been declared or assigned >> MAXLENGTHPATTERNS=5; ^ User error: Identifier 'MAXLENGTHPATTERNS' has not been declared or assigned >> Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); ^ User error: Identifier 'MAXGENUS' has not been declared or assigned >> l:=#Semigrups; ^ User error: Identifier 'Semigrups' has not been declared or assigned >> Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ^ User error: Identifier 'MAXLENGTHPATTERNS' has not been declared or assigned >> Append(~admdeg[pos],NonAdmissibleDegree(p)]); ^ User error: bad syntax >> end if; ^ User error: bad syntax >> end for; ^ User error: bad syntax Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sab-combi-01.uab.es. (158.109.241.123) Time: Fri Feb 27 12:24:04 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern>0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; if firstnongaps(semigrup) eq [0] then return true; if not IsStrongAdmissible(pattern) then return false; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS=10; MAXLENGTHPATTERNS=5; Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)]); end if; end for; Output: Magma V2.10-6 Fri Feb 27 2004 12:24:01 on modular [Seed = 843911000] ------------------------------------- >> while IsAdmissible(pat) and #pattern>0 do ^ User error: bad syntax >> degree:=degree+1; ^ User error: Identifier 'degree' has not been declared or assigned >> pat:=PreviousPattern(pat); ^ User error: Identifier 'pat' has not been declared or assigned >> end while; ^ User error: bad syntax >> return degree; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> end function; ^ User error: bad syntax >> while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; ^ User error: Identifier 'admits' has not been declared or assigned >> IsArf:=func; ^ User error: Identifier 'admits' has not been declared or assigned >> MAXGENUS=10; ^ User error: Identifier 'MAXGENUS' has not been declared or assigned >> MAXLENGTHPATTERNS=5; ^ User error: Identifier 'MAXLENGTHPATTERNS' has not been declared or assigned >> Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); ^ User error: Identifier 'MAXGENUS' has not been declared or assigned >> l:=#Semigrups; ^ User error: Identifier 'Semigrups' has not been declared or assigned >> Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ^ User error: Identifier 'MAXLENGTHPATTERNS' has not been declared or assigned >> Append(~admdeg[pos],NonAdmissibleDegree(p)]); ^ User error: bad syntax >> end if; ^ User error: bad syntax >> end for; ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sab-combi-01.uab.es. (158.109.241.123) Time: Fri Feb 27 12:24:50 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; if firstnongaps(semigrup) eq [0] then return true; if not IsStrongAdmissible(pattern) then return false; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS=10; MAXLENGTHPATTERNS=5; Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)]); end if; end for; Output: Magma V2.10-6 Fri Feb 27 2004 12:24:47 on modular [Seed = 693507117] ------------------------------------- >> end function; ^ User error: bad syntax >> while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; ^ User error: Identifier 'admits' has not been declared or assigned >> IsArf:=func; ^ User error: Identifier 'admits' has not been declared or assigned >> MAXGENUS=10; ^ User error: Identifier 'MAXGENUS' has not been declared or assigned >> MAXLENGTHPATTERNS=5; ^ User error: Identifier 'MAXLENGTHPATTERNS' has not been declared or assigned >> Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); ^ User error: Identifier 'MAXGENUS' has not been declared or assigned >> l:=#Semigrups; ^ User error: Identifier 'Semigrups' has not been declared or assigned >> Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ^ User error: Identifier 'MAXLENGTHPATTERNS' has not been declared or assigned >> Append(~admdeg[pos],NonAdmissibleDegree(p)]); ^ User error: bad syntax >> end if; ^ User error: bad syntax >> end for; ^ User error: bad syntax Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sab-combi-01.uab.es. (158.109.241.123) Time: Fri Feb 27 12:26:23 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS=10; MAXLENGTHPATTERNS=5; Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)]); end if; end for; Output: Magma V2.10-6 Fri Feb 27 2004 12:26:19 on modular [Seed = 3685017148] ------------------------------------- >> MAXGENUS=10; ^ User error: Identifier 'MAXGENUS' has not been declared or assigned >> MAXLENGTHPATTERNS=5; ^ User error: Identifier 'MAXLENGTHPATTERNS' has not been declared or assigned >> Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); ^ User error: Identifier 'MAXGENUS' has not been declared or assigned >> l:=#Semigrups; ^ User error: Identifier 'Semigrups' has not been declared or assigned >> Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ^ User error: Identifier 'MAXLENGTHPATTERNS' has not been declared or assigned >> Append(~admdeg[pos],NonAdmissibleDegree(p)]); ^ User error: bad syntax >> end if; ^ User error: bad syntax >> end for; ^ User error: bad syntax Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sab-combi-01.uab.es. (158.109.241.123) Time: Fri Feb 27 12:26:58 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=10; MAXLENGTHPATTERNS:=5; Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)]); end if; end for; Output: Magma V2.10-6 Fri Feb 27 2004 12:26:43 on modular [Seed = 3534614362] ------------------------------------- Semigrup: <0, ...> n Semigrup: <0, 2, ...> n Semigrup: <0, 2, 4, ...> n Semigrup: <0, 3, ...> n Semigrup: <0, 2, 4, 6, ...> n Semigrup: <0, 3, 4, 6, ...> n Semigrup: <0, 4, ...> n Semigrup: <0, 3, 5, ...> n Semigrup: <0, 3, 6, ...> n Semigrup: <0, 5, ...> n Semigrup: <0, 2, 4, 6, 8, ...> n Semigrup: <0, 4, 6, ...> n Semigrup: <0, 4, 5, 7, ...> n Semigrup: <0, 3, 5, 6, 8, ...> n Semigrup: <0, 4, 5, 6, 8, ...> n Semigrup: <0, 3, 6, 7, 9, ...> n Semigrup: <0, 3, 6, 8, ...> n Semigrup: <0, 2, 4, 6, 8, 10, ...> n Semigrup: <0, 4, 7, ...> n Semigrup: <0, 5, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, ...> n Semigrup: <0, 4, 6, 8, ...> n Semigrup: <0, 5, 6, 7, 8, 10, ...> n Semigrup: <0, 4, 6, 7, 8, 10, ...> n Semigrup: <0, 5, 6, 8, ...> n Semigrup: <0, 5, 7, ...> n Semigrup: <0, 6, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, ...> n Semigrup: <0, 5, 7, 8, 10, ...> n Semigrup: <0, 3, 6, 7, 9, 10, 12, ...> n Semigrup: <0, 4, 6, 8, 10, ...> n Semigrup: <0, 6, 8, ...> n Semigrup: <0, 5, 6, 8, 10, ...> n Semigrup: <0, 6, 7, 8, 9, 11, ...> n Semigrup: <0, 4, 8, ...> n Semigrup: <0, 5, 6, 9, ...> n Semigrup: <0, 4, 7, 8, 10, ...> n Semigrup: <0, 5, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 4, 7, 8, 9, 11, ...> n Semigrup: <0, 3, 6, 8, 9, 11, ...> n Semigrup: <0, 6, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 7, 10, ...> n Semigrup: <0, 5, 8, ...> n Semigrup: <0, 6, 7, 8, 10, ...> n Semigrup: <0, 7, ...> n Semigrup: <0, 3, 6, 9, ...> n Semigrup: <0, 4, 6, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 7, 9, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, 14, ...> n Semigrup: <0, 8, ...> n Semigrup: <0, 6, 7, 9, 10, 12, ...> n Semigrup: <0, 4, 7, 8, 11, ...> n Semigrup: <0, 6, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 9, 11, ...> n Semigrup: <0, 5, 6, 10, ...> n Semigrup: <0, 5, 7, 8, 10, 12, ...> n Semigrup: <0, 7, 8, 10, ...> n Semigrup: <0, 4, 8, 9, 11, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 5, 7, 9, 10, 12, ...> n Semigrup: <0, 5, 7, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 8, 10, 12, ...> n Semigrup: <0, 4, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 9, 11, ...> n Semigrup: <0, 7, 9, ...> n Semigrup: <0, 6, 9, ...> n Semigrup: <0, 6, 7, 8, 9, 12, ...> n Semigrup: <0, 3, 6, 9, 11, ...> n Semigrup: <0, 4, 6, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 7, 8, 9, 11, ...> n Semigrup: <0, 5, 8, 10, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 9, ...> n Semigrup: <0, 6, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 4, 6, 8, 10, 12, ...> n Semigrup: <0, 5, 7, 10, ...> n Semigrup: <0, 6, 8, 10, ...> n Semigrup: <0, 3, 6, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 10, ...> n Semigrup: <0, 3, 6, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 4, 7, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 8, 11, ...> n Semigrup: <0, 4, 8, 10, ...> n Semigrup: <0, 5, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 7, 10, ...> n Semigrup: <0, 4, 6, 8, 10, 12, 13, 14, 16, ...> n Semigrup: <0, 5, 7, 9, 10, 12, 14, ...> n Semigrup: <0, 6, 8, 11, ...> n Semigrup: <0, 5, 8, 9, 10, 13, ...> n Semigrup: <0, 4, 8, 10, 12, ...> n Semigrup: <0, 6, 9, 11, ...> n Semigrup: <0, 6, 7, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, 14, 16, ...> n Semigrup: <0, 3, 6, 9, 11, 12, 14, ...> n Semigrup: <0, 5, 10, ...> n Semigrup: <0, 7, 9, 11, ...> n Semigrup: <0, 7, 8, 11, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 5, 7, 10, 11, 12, 14, ...> n Semigrup: <0, 4, 6, 8, 10, 12, 14, ...> n Semigrup: <0, 6, 10, ...> n Semigrup: <0, 7, 8, 9, 10, 13, ...> n Semigrup: <0, 4, 8, 9, 12, ...> n Semigrup: <0, 7, 8, 9, 11, 13, ...> n Semigrup: <0, 5, 8, 10, 11, 13, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 7, 8, 10, 12, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 7, 9, 10, 12, ...> n Semigrup: <0, 5, 9, 10, 11, 13, ...> n Semigrup: <0, 6, 8, 9, 12, ...> n Semigrup: <0, 3, 6, 9, 10, 12, 13, 15, ...> n Semigrup: <0, 5, 8, 10, 12, ...> n Semigrup: <0, 7, 8, 9, 12, ...> n Semigrup: <0, 6, 9, 10, 12, ...> n Semigrup: <0, 4, 8, 11, ...> n Semigrup: <0, 7, 8, 10, 11, 13, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 10, 12, ...> n Semigrup: <0, 7, 9, 10, 11, 13, ...> n Semigrup: <0, 6, 9, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 5, 9, 10, 12, ...> n Semigrup: <0, 7, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 8, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 6, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 5, 7, 10, 12, ...> n Semigrup: <0, 7, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 10, 12, ...> n Semigrup: <0, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 7, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 8, 12, ...> n Semigrup: <0, 5, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 9, 12, ...> n Semigrup: <0, 4, 8, 9, 10, 12, 13, 14, 16, ...> n Semigrup: <0, 8, 9, 10, 12, ...> n Semigrup: <0, 8, 9, 11, ...> n Semigrup: <0, 7, 9, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 7, 8, 9, 10, 12, 14, ...> n Semigrup: <0, 4, 8, 9, 11, 12, 13, 15, ...> n Semigrup: <0, 4, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 9, 10, 12, 14, ...> n Semigrup: <0, 6, 7, 11, ...> n Semigrup: <0, 8, 10, ...> n Semigrup: <0, 6, 8, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 14, ...> n Semigrup: <0, 9, ...> n Semigrup: <0, 3, 6, 9, 12, ...> n Semigrup: <0, 4, 7, 8, 11, 12, 14, ...> n Semigrup: <0, 8, 10, 11, 13, ...> n Semigrup: <0, 4, 6, 8, 10, 12, 14, 16, ...> n Semigrup: <0, 8, 9, 12, ...> n Semigrup: <0, 9, 10, 11, 13, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 13, 16, ...> n Semigrup: <0, 8, 10, 12, ...> n Semigrup: <0, 8, 9, 11, 13, ...> n Semigrup: <0, 6, 7, 12, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 14, 16, ...> n Semigrup: <0, 9, 10, 12, ...> n Semigrup: <0, 9, 11, ...> n Semigrup: <0, 4, 8, 10, 11, 12, 14, 15, 16, 18, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 15, ...> n Semigrup: <0, 8, 9, 10, 13, ...> n Semigrup: <0, 8, 11, ...> n Semigrup: <0, 3, 6, 9, 11, 12, 14, 15, 17, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 15, ...> n Semigrup: <0, 10, ...> n Semigrup: <0, 6, 9, 10, 11, 12, 15, ...> n Semigrup: <0, 5, 8, 10, 13, ...> n Semigrup: <0, 7, 8, 9, 13, ...> n Semigrup: <0, 6, 11, ...> n Semigrup: <0, 5, 9, 10, 13, ...> n Semigrup: <0, 4, 7, 8, 11, 12, 14, 15, 16, 18, ...> n Semigrup: <0, 7, 8, 10, 13, ...> n Semigrup: <0, 4, 8, 12, ...> n Semigrup: <0, 7, 11, ...> n Semigrup: <0, 7, 9, 10, 13, ...> n Semigrup: <0, 5, 10, 11, 13, ...> n Semigrup: <0, 7, 9, 11, 13, ...> n Semigrup: <0, 6, 8, 12, ...> n Semigrup: <0, 7, 10, 12, ...> n Semigrup: <0, 4, 6, 8, 10, 12, 14, 15, 16, 18, ...> n Semigrup: <0, 7, 9, 10, 11, 12, 14, 16, ...> n Semigrup: <0, 7, 8, 11, 13, ...> n Semigrup: <0, 6, 9, 12, ...> n Semigrup: <0, 7, 9, 12, ...> n Semigrup: <0, 5, 10, 12, ...> n Semigrup: <0, 7, 10, 11, 13, ...> n Semigrup: <0, 6, 10, 12, ...> n Semigrup: <0, 6, 8, 10, 11, 12, 14, 16, ...> n Semigrup: <0, 3, 6, 9, 10, 12, 13, 15, 16, 18, ...> n Semigrup: <0, 7, 8, 12, ...> n Semigrup: <0, 7, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 11, 12, 14, ...> n Semigrup: <0, 5, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 5, 9, 10, 12, 13, 14, 15, 17, ...> n Semigrup: <0, 6, 9, 11, 12, 14, ...> n Semigrup: <0, 4, 8, 10, 12, 14, ...> n Semigrup: <0, 4, 8, 9, 12, 13, 15, ...> n Semigrup: <0, 6, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 7, 9, 10, 12, 13, 14, 16, ...> n Semigrup: <0, 6, 7, 9, 12, 13, 14, 15, 16, 18, ...> n Semigrup: <0, 7, 9, 11, 12, 14, ...> n Semigrup: <0, 5, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 9, 11, 12, 13, 15, ...> n Semigrup: <0, 7, 8, 11, 12, 14, ...> n Semigrup: <0, 7, 9, 10, 11, 13, 14, 16, ...> n Semigrup: <0, 6, 8, 10, 12, 13, 14, 16, ...> n Semigrup: <0, 6, 7, 8, 12, 13, 14, 15, 16, 18, ...> n Semigrup: <0, 7, 8, 9, 10, 14, ...> n Semigrup: <0, 6, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 8, 10, 12, 13, 15, ...> n Semigrup: <0, 6, 8, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 7, 8, 9, 11, 14, ...> n Semigrup: <0, 7, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 7, 8, 10, 12, 14, ...> n Semigrup: <0, 4, 8, 11, 12, 13, 15, ...> n Semigrup: <0, 6, 9, 10, 12, 13, 15, ...> n Semigrup: <0, 7, 9, 10, 12, 14, ...> n Semigrup: <0, 4, 8, 10, 12, 13, 14, 16, ...> n Semigrup: <0, 6, 8, 9, 12, 14, ...> n Semigrup: <0, 5, 9, 10, 11, 14, ...> n Semigrup: <0, 7, 9, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 7, 8, 9, 12, 14, ...> n Semigrup: <0, 9, 10, 11, 12, 13, 14, 15, 16, 18, ...> n Semigrup: <0, 5, 8, 10, 11, 13, 15, ...> n Semigrup: <0, 7, 10, 11, 12, 13, 14, 15, 17, ...> n Semigrup: <0, 7, 8, 10, 11, 14, ...> n Semigrup: <0, 4, 8, 11, 12, 14, ...> n Semigrup: <0, 6, 9, 10, 12, 14, ...> n Semigrup: <0, 4, 8, 9, 12, 13, 14, 16, ...> n Semigrup: <0, 6, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 7, 9, 10, 11, 14, ...> n Semigrup: <0, 6, 8, 10, 12, 14, ...> n Semigrup: <0, 6, 9, 11, 12, 13, 14, 15, 17, ...> n Semigrup: <0, 5, 9, 10, 12, 14, ...> n Semigrup: <0, 8, 10, 11, 12, 13, 14, 15, 16, 18, ...> n Semigrup: <0, 5, 7, 10, 12, 14, ...> n Semigrup: <0, 8, 9, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 6, 7, 11, 12, 13, 14, 15, 17, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, 14, 16, 18, ...> n Semigrup: <0, 8, 9, 10, 12, 13, 15, ...> n Semigrup: <0, 8, 9, 10, 11, 14, ...> n Semigrup: <0, 9, 10, 11, 12, 13, 14, 15, 17, ...> n Semigrup: <0, 7, 8, 11, 12, 13, 14, 15, 16, 18, ...> n Semigrup: <0, 8, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 6, 7, 11, ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host sab-combi-01.uab.es. (158.109.241.123) Time: Fri Feb 27 12:27:31 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=5; MAXLENGTHPATTERNS:=5; Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)]); end if; end for; Output: Magma V2.10-6 Fri Feb 27 2004 12:27:28 on modular [Seed = 3434345111] ------------------------------------- Semigrup: <0, ...> n Semigrup: <0, 2, ...> n Semigrup: <0, 2, 4, ...> n Semigrup: <0, 3, ...> n Semigrup: <0, 2, 4, 6, ...> n Semigrup: <0, 3, 4, 6, ...> n Semigrup: <0, 4, ...> n Semigrup: <0, 3, 5, ...> n Semigrup: <0, 3, 6, ...> n Semigrup: <0, 5, ...> n Semigrup: <0, 2, 4, 6, 8, ...> n Semigrup: <0, 4, 6, ...> n Semigrup: <0, 4, 5, 7, ...> n Semigrup: <0, 3, 5, 6, 8, ...> n Semigrup: <0, 4, 5, 6, 8, ...> n Semigrup: <0, 3, 6, 7, 9, ...> n Semigrup: <0, 3, 6, 8, ...> n Semigrup: <0, 2, 4, 6, 8, 10, ...> n Semigrup: <0, 4, 7, ...> n Semigrup: <0, 5, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, ...> n Semigrup: <0, 4, 6, 8, ...> n Semigrup: <0, 5, 6, 7, 8, 10, ...> n Semigrup: <0, 4, 6, 7, 8, 10, ...> n Semigrup: <0, 5, 6, 8, ...> n Semigrup: <0, 5, 7, ...> n Semigrup: <0, 6, ...> n >> Append(~admdeg[pos],NonAdmissibleDegree(p)]); ^ User error: bad syntax >> end if; ^ User error: bad syntax >> end for; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host sab-combi-01.uab.es. (158.109.241.123) Time: Fri Feb 27 12:28:27 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=5; MAXLENGTHPATTERNS:=5; Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; end for; Output: Magma V2.10-6 Fri Feb 27 2004 12:28:24 on modular [Seed = 4219782552] ------------------------------------- Semigrup: <0, ...> n Semigrup: <0, 2, ...> n Semigrup: <0, 2, 4, ...> n Semigrup: <0, 3, ...> n Semigrup: <0, 2, 4, 6, ...> n Semigrup: <0, 3, 4, 6, ...> n Semigrup: <0, 4, ...> n Semigrup: <0, 3, 5, ...> n Semigrup: <0, 3, 6, ...> n Semigrup: <0, 5, ...> n Semigrup: <0, 2, 4, 6, 8, ...> n Semigrup: <0, 4, 6, ...> n Semigrup: <0, 4, 5, 7, ...> n Semigrup: <0, 3, 5, 6, 8, ...> n Semigrup: <0, 4, 5, 6, 8, ...> n Semigrup: <0, 3, 6, 7, 9, ...> n Semigrup: <0, 3, 6, 8, ...> n Semigrup: <0, 2, 4, 6, 8, 10, ...> n Semigrup: <0, 4, 7, ...> n Semigrup: <0, 5, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, ...> n Semigrup: <0, 4, 6, 8, ...> n Semigrup: <0, 5, 6, 7, 8, 10, ...> n Semigrup: <0, 4, 6, 7, 8, 10, ...> n Semigrup: <0, 5, 6, 8, ...> n Semigrup: <0, 5, 7, ...> n Semigrup: <0, 6, ...> n [ 1, -1 ] [ 1, 1, -1 ] [ 1, 1, -1, -1 ] [ 1, -1, 1, -1 ] [ 1, 1, 1, -1 ] [ 1, -1, 1, 1, -1 ] [ 1, 1, 1, -1, -1 ] [ 1, 1, 1, 1, -1 ] [ 1, 1, -1, 1, -1 ] Total time: 3.259 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host sab-combi-01.uab.es. (158.109.241.123) Time: Fri Feb 27 12:29:24 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=4; MAXLENGTHPATTERNS:=4; Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; end for; [#s: s in ss]; pp; admdeg; Output: Magma V2.10-6 Fri Feb 27 2004 12:29:21 on modular [Seed = 4119514079] ------------------------------------- Semigrup: <0, ...> n Semigrup: <0, 2, ...> n Semigrup: <0, 2, 4, ...> n Semigrup: <0, 3, ...> n Semigrup: <0, 2, 4, 6, ...> n Semigrup: <0, 3, 4, 6, ...> n Semigrup: <0, 4, ...> n Semigrup: <0, 3, 5, ...> n Semigrup: <0, 3, 6, ...> n Semigrup: <0, 5, ...> n Semigrup: <0, 2, 4, 6, 8, ...> n Semigrup: <0, 4, 6, ...> n Semigrup: <0, 4, 5, 7, ...> n Semigrup: <0, 3, 5, 6, 8, ...> n Semigrup: <0, 4, 5, 6, 8, ...> n [ 1, -1 ] [ 1, 1, -1 ] [ 1, 1, -1, -1 ] [ 1, -1, 1, -1 ] [ 1, 1, 1, -1 ] [ 1, 11, 15 ] [ [ [ 1, -1 ], [ 1, 1, -1, -1 ], [ 1, -1, 1, -1 ] ], [ [ 1, 1, -1 ] ], [ [ 1, 1, 1, -1 ] ] ] [ [ 1, 1, 1 ], [ 2 ], [ 3 ] ] Total time: 2.969 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host sab-combi-01.uab.es. (158.109.241.123) Time: Fri Feb 27 12:32:57 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=4; MAXLENGTHPATTERNS:=8; Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; end for; [#s: s in ss]; pp; admdeg; Output: Magma V2.10-6 Fri Feb 27 2004 12:32:53 on modular [Seed = 2648875651] ------------------------------------- Semigrup: <0, ...> n Semigrup: <0, 2, ...> n Semigrup: <0, 2, 4, ...> n Semigrup: <0, 3, ...> n Semigrup: <0, 2, 4, 6, ...> n Semigrup: <0, 3, 4, 6, ...> n Semigrup: <0, 4, ...> n Semigrup: <0, 3, 5, ...> n Semigrup: <0, 3, 6, ...> n Semigrup: <0, 5, ...> n Semigrup: <0, 2, 4, 6, 8, ...> n Semigrup: <0, 4, 6, ...> n Semigrup: <0, 4, 5, 7, ...> n Semigrup: <0, 3, 5, 6, 8, ...> n Semigrup: <0, 4, 5, 6, 8, ...> n [ 1, -1 ] [ 1, 1, -1 ] [ 1, 1, -1, -1 ] [ 1, -1, 1, -1 ] [ 1, 1, 1, -1 ] [ 1, -1, 1, 1, -1 ] [ 1, 1, 1, -1, -1 ] [ 1, 1, 1, 1, -1 ] [ 1, 1, -1, 1, -1 ] [ 1, 1, 1, 1, 1, -1 ] [ 1, 1, 1, -1, -1, -1 ] [ 1, 1, -1, -1, 1, -1 ] [ 1, -1, 1, 1, 1, -1 ] [ 1, 1, -1, 1, -1, -1 ] [ 1, 1, 1, -1, 1, -1 ] [ 1, 1, 1, 1, -1, -1 ] [ 1, 1, -1, 1, 1, -1 ] [ 1, -1, 1, 1, -1, -1 ] [ 1, -1, 1, -1, 1, -1 ] [ 1, 1, 1, -1, 1, -1, -1 ] [ 1, -1, 1, -1, 1, 1, -1 ] [ 1, 1, 1, -1, 1, 1, -1 ] [ 1, 1, -1, 1, -1, 1, -1 ] [ 1, 1, -1, -1, 1, 1, -1 ] [ 1, 1, 1, 1, -1, -1, -1 ] [ 1, 1, -1, 1, 1, -1, -1 ] [ 1, 1, 1, -1, -1, 1, -1 ] [ 1, -1, 1, 1, 1, 1, -1 ] [ 1, -1, 1, 1, -1, 1, -1 ] [ 1, 1, 1, 1, 1, -1, -1 ] [ 1, -1, 1, 1, 1, -1, -1 ] [ 1, 1, 1, 1, -1, 1, -1 ] [ 1, 1, 1, 1, 1, 1, -1 ] [ 1, 1, -1, 1, 1, 1, -1 ] [ 1, 1, 1, -1, 1, -1, 1, -1 ] [ 1, -1, 1, -1, 1, 1, -1, -1 ] [ 1, 1, 1, -1, 1, -1, -1, -1 ] [ 1, 1, -1, 1, -1, 1, -1, -1 ] [ 1, 1, 1, -1, -1, 1, -1, -1 ] [ 1, 1, -1, -1, 1, 1, -1, -1 ] [ 1, 1, 1, 1, 1, 1, -1, -1 ] [ 1, 1, -1, 1, 1, -1, -1, -1 ] [ 1, 1, 1, 1, -1, -1, -1, -1 ] [ 1, 1, 1, 1, 1, -1, -1, -1 ] [ 1, 1, 1, 1, -1, 1, -1, -1 ] [ 1, -1, 1, 1, 1, 1, -1, -1 ] [ 1, -1, 1, 1, -1, 1, -1, -1 ] [ 1, -1, 1, 1, 1, -1, -1, -1 ] [ 1, 1, 1, -1, 1, 1, 1, -1 ] [ 1, -1, 1, 1, -1, 1, 1, -1 ] [ 1, 1, -1, 1, 1, 1, 1, -1 ] [ 1, 1, -1, 1, -1, -1, 1, -1 ] [ 1, 1, 1, -1, -1, -1, 1, -1 ] [ 1, -1, 1, 1, 1, -1, 1, -1 ] [ 1, 1, -1, 1, 1, 1, -1, -1 ] [ 1, 1, 1, -1, 1, 1, -1, -1 ] [ 1, -1, 1, -1, 1, -1, 1, -1 ] [ 1, 1, -1, -1, 1, -1, 1, -1 ] [ 1, 1, 1, 1, 1, -1, 1, -1 ] [ 1, 1, 1, -1, -1, 1, 1, -1 ] [ 1, 1, 1, 1, 1, 1, 1, -1 ] [ 1, 1, -1, -1, 1, 1, 1, -1 ] [ 1, 1, 1, 1, -1, -1, 1, -1 ] [ 1, 1, -1, 1, -1, 1, 1, -1 ] [ 1, -1, 1, 1, 1, 1, 1, -1 ] [ 1, -1, 1, 1, -1, -1, 1, -1 ] [ 1, 1, 1, 1, -1, 1, 1, -1 ] [ 1, -1, 1, -1, 1, 1, 1, -1 ] [ 1, 1, -1, 1, 1, -1, 1, -1 ] [ 1, 11, 15 ] [ [ [ 1, -1 ], [ 1, 1, -1, -1 ], [ 1, -1, 1, -1 ], [ 1, -1, 1, 1, -1 ], [ 1, 1, 1, -1, -1, -1 ], [ 1, 1, -1, -1, 1, -1 ], [ 1, -1, 1, 1, 1, -1 ], [ 1, 1, -1, 1, -1, -1 ], [ 1, -1, 1, 1, -1, -1 ], [ 1, -1, 1, -1, 1, -1 ], [ 1, -1, 1, -1, 1, 1, -1 ], [ 1, 1, -1, -1, 1, 1, -1 ], [ 1, -1, 1, 1, 1, 1, -1 ], [ 1, -1, 1, 1, -1, 1, -1 ], [ 1, -1, 1, 1, 1, -1, -1 ], [ 1, -1, 1, -1, 1, 1, -1, -1 ], [ 1, 1, 1, -1, 1, -1, -1, -1 ], [ 1, 1, -1, 1, -1, 1, -1, -1 ], [ 1, 1, 1, -1, -1, 1, -1, -1 ], [ 1, 1, -1, -1, 1, 1, -1, -1 ], [ 1, 1, -1, 1, 1, -1, -1, -1 ], [ 1, 1, 1, 1, -1, -1, -1, -1 ], [ 1, -1, 1, 1, 1, 1, -1, -1 ], [ 1, -1, 1, 1, -1, 1, -1, -1 ], [ 1, -1, 1, 1, 1, -1, -1, -1 ], [ 1, -1, 1, 1, -1, 1, 1, -1 ], [ 1, 1, -1, 1, -1, -1, 1, -1 ], [ 1, 1, 1, -1, -1, -1, 1, -1 ], [ 1, -1, 1, 1, 1, -1, 1, -1 ], [ 1, -1, 1, -1, 1, -1, 1, -1 ], [ 1, 1, -1, -1, 1, -1, 1, -1 ], [ 1, 1, -1, -1, 1, 1, 1, -1 ], [ 1, -1, 1, 1, 1, 1, 1, -1 ], [ 1, -1, 1, 1, -1, -1, 1, -1 ], [ 1, -1, 1, -1, 1, 1, 1, -1 ] ], [ [ 1, 1, -1 ], [ 1, 1, 1, -1, -1 ], [ 1, 1, -1, 1, -1 ], [ 1, 1, -1, 1, 1, -1 ], [ 1, 1, 1, -1, 1, -1, -1 ], [ 1, 1, -1, 1, -1, 1, -1 ], [ 1, 1, 1, 1, -1, -1, -1 ], [ 1, 1, -1, 1, 1, -1, -1 ], [ 1, 1, 1, -1, -1, 1, -1 ], [ 1, 1, -1, 1, 1, 1, -1 ], [ 1, 1, -1, 1, 1, 1, 1, -1 ], [ 1, 1, -1, 1, 1, 1, -1, -1 ], [ 1, 1, 1, -1, -1, 1, 1, -1 ], [ 1, 1, -1, 1, -1, 1, 1, -1 ], [ 1, 1, -1, 1, 1, -1, 1, -1 ] ], [ [ 1, 1, 1, -1 ], [ 1, 1, 1, 1, -1 ], [ 1, 1, 1, 1, 1, -1 ], [ 1, 1, 1, -1, 1, -1 ], [ 1, 1, 1, 1, -1, -1 ], [ 1, 1, 1, -1, 1, 1, -1 ], [ 1, 1, 1, 1, 1, -1, -1 ], [ 1, 1, 1, 1, -1, 1, -1 ], [ 1, 1, 1, 1, 1, 1, -1 ], [ 1, 1, 1, -1, 1, -1, 1, -1 ], [ 1, 1, 1, 1, 1, 1, -1, -1 ], [ 1, 1, 1, 1, 1, -1, -1, -1 ], [ 1, 1, 1, 1, -1, 1, -1, -1 ], [ 1, 1, 1, -1, 1, 1, 1, -1 ], [ 1, 1, 1, -1, 1, 1, -1, -1 ], [ 1, 1, 1, 1, 1, -1, 1, -1 ], [ 1, 1, 1, 1, 1, 1, 1, -1 ], [ 1, 1, 1, 1, -1, -1, 1, -1 ], [ 1, 1, 1, 1, -1, 1, 1, -1 ] ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ], [ 3, 4, 5, 3, 3, 3, 4, 4, 6, 3, 5, 3, 3, 3, 3, 5, 7, 3, 4 ] ] Total time: 4.189 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host sab-combi-01.uab.es. (158.109.241.123) Time: Fri Feb 27 12:34:49 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=5; MAXLENGTHPATTERNS:=8; Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; end for; [#s: s in ss]; pp; admdeg; Output: Magma V2.10-6 Fri Feb 27 2004 12:34:40 on modular [Seed = 2348069984] ------------------------------------- Semigrup: <0, ...> n Semigrup: <0, 2, ...> n Semigrup: <0, 2, 4, ...> n Semigrup: <0, 3, ...> n Semigrup: <0, 2, 4, 6, ...> n Semigrup: <0, 3, 4, 6, ...> n Semigrup: <0, 4, ...> n Semigrup: <0, 3, 5, ...> n Semigrup: <0, 3, 6, ...> n Semigrup: <0, 5, ...> n Semigrup: <0, 2, 4, 6, 8, ...> n Semigrup: <0, 4, 6, ...> n Semigrup: <0, 4, 5, 7, ...> n Semigrup: <0, 3, 5, 6, 8, ...> n Semigrup: <0, 4, 5, 6, 8, ...> n Semigrup: <0, 3, 6, 7, 9, ...> n Semigrup: <0, 3, 6, 8, ...> n Semigrup: <0, 2, 4, 6, 8, 10, ...> n Semigrup: <0, 4, 7, ...> n Semigrup: <0, 5, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, ...> n Semigrup: <0, 4, 6, 8, ...> n Semigrup: <0, 5, 6, 7, 8, 10, ...> n Semigrup: <0, 4, 6, 7, 8, 10, ...> n Semigrup: <0, 5, 6, 8, ...> n Semigrup: <0, 5, 7, ...> n Semigrup: <0, 6, ...> n [ 1, -1 ] [ 1, 1, -1 ] [ 1, 1, -1, -1 ] [ 1, -1, 1, -1 ] [ 1, 1, 1, -1 ] [ 1, -1, 1, 1, -1 ] [ 1, 1, 1, -1, -1 ] [ 1, 1, 1, 1, -1 ] [ 1, 1, -1, 1, -1 ] [ 1, 1, 1, 1, 1, -1 ] [ 1, 1, 1, -1, -1, -1 ] [ 1, 1, -1, -1, 1, -1 ] [ 1, -1, 1, 1, 1, -1 ] [ 1, 1, -1, 1, -1, -1 ] [ 1, 1, 1, -1, 1, -1 ] [ 1, 1, 1, 1, -1, -1 ] [ 1, 1, -1, 1, 1, -1 ] [ 1, -1, 1, 1, -1, -1 ] [ 1, -1, 1, -1, 1, -1 ] [ 1, 1, 1, -1, 1, -1, -1 ] [ 1, -1, 1, -1, 1, 1, -1 ] [ 1, 1, 1, -1, 1, 1, -1 ] [ 1, 1, -1, 1, -1, 1, -1 ] [ 1, 1, -1, -1, 1, 1, -1 ] [ 1, 1, 1, 1, -1, -1, -1 ] [ 1, 1, -1, 1, 1, -1, -1 ] [ 1, 1, 1, -1, -1, 1, -1 ] [ 1, -1, 1, 1, 1, 1, -1 ] [ 1, -1, 1, 1, -1, 1, -1 ] [ 1, 1, 1, 1, 1, -1, -1 ] [ 1, -1, 1, 1, 1, -1, -1 ] [ 1, 1, 1, 1, -1, 1, -1 ] [ 1, 1, 1, 1, 1, 1, -1 ] [ 1, 1, -1, 1, 1, 1, -1 ] [ 1, 1, 1, -1, 1, -1, 1, -1 ] [ 1, -1, 1, -1, 1, 1, -1, -1 ] [ 1, 1, 1, -1, 1, -1, -1, -1 ] [ 1, 1, -1, 1, -1, 1, -1, -1 ] [ 1, 1, 1, -1, -1, 1, -1, -1 ] [ 1, 1, -1, -1, 1, 1, -1, -1 ] [ 1, 1, 1, 1, 1, 1, -1, -1 ] [ 1, 1, -1, 1, 1, -1, -1, -1 ] [ 1, 1, 1, 1, -1, -1, -1, -1 ] [ 1, 1, 1, 1, 1, -1, -1, -1 ] [ 1, 1, 1, 1, -1, 1, -1, -1 ] [ 1, -1, 1, 1, 1, 1, -1, -1 ] [ 1, -1, 1, 1, -1, 1, -1, -1 ] [ 1, -1, 1, 1, 1, -1, -1, -1 ] [ 1, 1, 1, -1, 1, 1, 1, -1 ] [ 1, -1, 1, 1, -1, 1, 1, -1 ] [ 1, 1, -1, 1, 1, 1, 1, -1 ] [ 1, 1, -1, 1, -1, -1, 1, -1 ] [ 1, 1, 1, -1, -1, -1, 1, -1 ] [ 1, -1, 1, 1, 1, -1, 1, -1 ] [ 1, 1, -1, 1, 1, 1, -1, -1 ] [ 1, 1, 1, -1, 1, 1, -1, -1 ] [ 1, -1, 1, -1, 1, -1, 1, -1 ] [ 1, 1, -1, -1, 1, -1, 1, -1 ] [ 1, 1, 1, 1, 1, -1, 1, -1 ] [ 1, 1, 1, -1, -1, 1, 1, -1 ] [ 1, 1, 1, 1, 1, 1, 1, -1 ] [ 1, 1, -1, -1, 1, 1, 1, -1 ] [ 1, 1, 1, 1, -1, -1, 1, -1 ] [ 1, 1, -1, 1, -1, 1, 1, -1 ] [ 1, -1, 1, 1, 1, 1, 1, -1 ] [ 1, -1, 1, 1, -1, -1, 1, -1 ] [ 1, 1, 1, 1, -1, 1, 1, -1 ] [ 1, -1, 1, -1, 1, 1, 1, -1 ] [ 1, 1, -1, 1, 1, -1, 1, -1 ] [ 1, 17, 27 ] [ [ [ 1, -1 ], [ 1, 1, -1, -1 ], [ 1, -1, 1, -1 ], [ 1, -1, 1, 1, -1 ], [ 1, 1, 1, -1, -1, -1 ], [ 1, 1, -1, -1, 1, -1 ], [ 1, -1, 1, 1, 1, -1 ], [ 1, 1, -1, 1, -1, -1 ], [ 1, -1, 1, 1, -1, -1 ], [ 1, -1, 1, -1, 1, -1 ], [ 1, -1, 1, -1, 1, 1, -1 ], [ 1, 1, -1, -1, 1, 1, -1 ], [ 1, -1, 1, 1, 1, 1, -1 ], [ 1, -1, 1, 1, -1, 1, -1 ], [ 1, -1, 1, 1, 1, -1, -1 ], [ 1, -1, 1, -1, 1, 1, -1, -1 ], [ 1, 1, 1, -1, 1, -1, -1, -1 ], [ 1, 1, -1, 1, -1, 1, -1, -1 ], [ 1, 1, 1, -1, -1, 1, -1, -1 ], [ 1, 1, -1, -1, 1, 1, -1, -1 ], [ 1, 1, -1, 1, 1, -1, -1, -1 ], [ 1, 1, 1, 1, -1, -1, -1, -1 ], [ 1, -1, 1, 1, 1, 1, -1, -1 ], [ 1, -1, 1, 1, -1, 1, -1, -1 ], [ 1, -1, 1, 1, 1, -1, -1, -1 ], [ 1, -1, 1, 1, -1, 1, 1, -1 ], [ 1, 1, -1, 1, -1, -1, 1, -1 ], [ 1, 1, 1, -1, -1, -1, 1, -1 ], [ 1, -1, 1, 1, 1, -1, 1, -1 ], [ 1, -1, 1, -1, 1, -1, 1, -1 ], [ 1, 1, -1, -1, 1, -1, 1, -1 ], [ 1, 1, -1, -1, 1, 1, 1, -1 ], [ 1, -1, 1, 1, 1, 1, 1, -1 ], [ 1, -1, 1, 1, -1, -1, 1, -1 ], [ 1, -1, 1, -1, 1, 1, 1, -1 ] ], [ [ 1, 1, -1 ], [ 1, 1, 1, -1, -1 ], [ 1, 1, -1, 1, -1 ], [ 1, 1, -1, 1, 1, -1 ], [ 1, 1, 1, -1, 1, -1, -1 ], [ 1, 1, -1, 1, -1, 1, -1 ], [ 1, 1, 1, 1, -1, -1, -1 ], [ 1, 1, -1, 1, 1, -1, -1 ], [ 1, 1, 1, -1, -1, 1, -1 ], [ 1, 1, -1, 1, 1, 1, -1 ], [ 1, 1, -1, 1, 1, 1, 1, -1 ], [ 1, 1, -1, 1, 1, 1, -1, -1 ], [ 1, 1, 1, -1, -1, 1, 1, -1 ], [ 1, 1, -1, 1, -1, 1, 1, -1 ], [ 1, 1, -1, 1, 1, -1, 1, -1 ] ], [ [ 1, 1, 1, -1 ], [ 1, 1, 1, 1, -1 ], [ 1, 1, 1, 1, 1, -1 ], [ 1, 1, 1, -1, 1, -1 ], [ 1, 1, 1, 1, -1, -1 ], [ 1, 1, 1, -1, 1, 1, -1 ], [ 1, 1, 1, 1, 1, -1, -1 ], [ 1, 1, 1, 1, -1, 1, -1 ], [ 1, 1, 1, 1, 1, 1, -1 ], [ 1, 1, 1, -1, 1, -1, 1, -1 ], [ 1, 1, 1, 1, 1, 1, -1, -1 ], [ 1, 1, 1, 1, 1, -1, -1, -1 ], [ 1, 1, 1, 1, -1, 1, -1, -1 ], [ 1, 1, 1, -1, 1, 1, 1, -1 ], [ 1, 1, 1, -1, 1, 1, -1, -1 ], [ 1, 1, 1, 1, 1, -1, 1, -1 ], [ 1, 1, 1, 1, 1, 1, 1, -1 ], [ 1, 1, 1, 1, -1, -1, 1, -1 ], [ 1, 1, 1, 1, -1, 1, 1, -1 ] ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ], [ 3, 4, 5, 3, 3, 3, 4, 4, 6, 3, 5, 3, 3, 3, 3, 5, 7, 3, 4 ] ] Total time: 7.829 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host sab-combi-01.uab.es. (158.109.241.123) Time: Fri Feb 27 12:35:53 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=6; MAXLENGTHPATTERNS:=8; Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; end for; [#s: s in ss]; pp; admdeg; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Feb 27 2004 12:35:30 on modular [Seed = 2264512831] ------------------------------------- Semigrup: <0, ...> n Semigrup: <0, 2, ...> n Semigrup: <0, 2, 4, ...> n Semigrup: <0, 3, ...> n Semigrup: <0, 2, 4, 6, ...> n Semigrup: <0, 3, 4, 6, ...> n Semigrup: <0, 4, ...> n Semigrup: <0, 3, 5, ...> n Semigrup: <0, 3, 6, ...> n Semigrup: <0, 5, ...> n Semigrup: <0, 2, 4, 6, 8, ...> n Semigrup: <0, 4, 6, ...> n Semigrup: <0, 4, 5, 7, ...> n Semigrup: <0, 3, 5, 6, 8, ...> n Semigrup: <0, 4, 5, 6, 8, ...> n Semigrup: <0, 3, 6, 7, 9, ...> n Semigrup: <0, 3, 6, 8, ...> n Semigrup: <0, 2, 4, 6, 8, 10, ...> n Semigrup: <0, 4, 7, ...> n Semigrup: <0, 5, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, ...> n Semigrup: <0, 4, 6, 8, ...> n Semigrup: <0, 5, 6, 7, 8, 10, ...> n Semigrup: <0, 4, 6, 7, 8, 10, ...> n Semigrup: <0, 5, 6, 8, ...> n Semigrup: <0, 5, 7, ...> n Semigrup: <0, 6, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, ...> n Semigrup: <0, 5, 7, 8, 10, ...> n Semigrup: <0, 3, 6, 7, 9, 10, 12, ...> n Semigrup: <0, 4, 6, 8, 10, ...> n Semigrup: <0, 6, 8, ...> n Semigrup: <0, 5, 6, 8, 10, ...> n Semigrup: <0, 6, 7, 8, 9, 11, ...> n Semigrup: <0, 4, 8, ...> n Semigrup: <0, 5, 6, 9, ...> n Semigrup: <0, 4, 7, 8, 10, ...> n Semigrup: <0, 5, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 4, 7, 8, 9, 11, ...> n Semigrup: <0, 3, 6, 8, 9, 11, ...> n Semigrup: <0, 6, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 7, 10, ...> n Semigrup: <0, 5, 8, ...> n Semigrup: <0, 6, 7, 8, 10, ...> n Semigrup: <0, 7, ...> n Semigrup: <0, 3, 6, 9, ...> n Semigrup: <0, 4, 6, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 7, 9, ...> n [ 1, -1 ] [ 1, 1, -1 ] [ 1, 1, -1, -1 ] [ 1, -1, 1, -1 ] [ 1, 1, 1, -1 ] [ 1, -1, 1, 1, -1 ] [ 1, 1, 1, -1, -1 ] [ 1, 1, 1, 1, -1 ] [ 1, 1, -1, 1, -1 ] [ 1, 1, 1, 1, 1, -1 ] [ 1, 1, 1, -1, -1, -1 ] [ 1, 1, -1, -1, 1, -1 ] [ 1, -1, 1, 1, 1, -1 ] [ 1, 1, -1, 1, -1, -1 ] [ 1, 1, 1, -1, 1, -1 ] [ 1, 1, 1, 1, -1, -1 ] [ 1, 1, -1, 1, 1, -1 ] [ 1, -1, 1, 1, -1, -1 ] [ 1, -1, 1, -1, 1, -1 ] [ 1, 1, 1, -1, 1, -1, -1 ] [ 1, -1, 1, -1, 1, 1, -1 ] [ 1, 1, 1, -1, 1, 1, -1 ] [ 1, 1, -1, 1, -1, 1, -1 ] [ 1, 1, -1, -1, 1, 1, -1 ] [ 1, 1, 1, 1, -1, -1, -1 ] [ 1, 1, -1, 1, 1, -1, -1 ] [ 1, 1, 1, -1, -1, 1, -1 ] [ 1, -1, 1, 1, 1, 1, -1 ] [ 1, -1, 1, 1, -1, 1, -1 ] [ 1, 1, 1, 1, 1, -1, -1 ] [ 1, -1, 1, 1, 1, -1, -1 ] [ 1, 1, 1, 1, -1, 1, -1 ] [ 1, 1, 1, 1, 1, 1, -1 ] [ 1, 1, -1, 1, 1, 1, -1 ] [ 1, 1, 1, -1, 1, -1, 1, -1 ] [ 1, -1, 1, -1, 1, 1, -1, -1 ] [ 1, 1, 1, -1, 1, -1, -1, -1 ] [ 1, 1, -1, 1, -1, 1, -1, -1 ] [ 1, 1, 1, -1, -1, 1, -1, -1 ] [ 1, 1, -1, -1, 1, 1, -1, -1 ] [ 1, 1, 1, 1, 1, 1, -1, -1 ] [ 1, 1, -1, 1, 1, -1, -1, -1 ] [ 1, 1, 1, 1, -1, -1, -1, -1 ] [ 1, 1, 1, 1, 1, -1, -1, -1 ] [ 1, 1, 1, 1, -1, 1, -1, -1 ] [ 1, -1, 1, 1, 1, 1, -1, -1 ] [ 1, -1, 1, 1, -1, 1, -1, -1 ] [ 1, -1, 1, 1, 1, -1, -1, -1 ] [ 1, 1, 1, -1, 1, 1, 1, -1 ] [ 1, -1, 1, 1, -1, 1, 1, -1 ] [ 1, 1, -1, 1, 1, 1, 1, -1 ] [ 1, 1, -1, 1, -1, -1, 1, -1 ] [ 1, 1, 1, -1, -1, -1, 1, -1 ] [ 1, -1, 1, 1, 1, -1, 1, -1 ] [ 1, 1, -1, 1, 1, 1, -1, -1 ] [ 1, 1, 1, -1, 1, 1, -1, -1 ] [ 1, -1, 1, -1, 1, -1, 1, -1 ] [ 1, 1, -1, -1, 1, -1, 1, -1 ] [ 1, 1, 1, 1, 1, -1, 1, -1 ] [ 1, 1, 1, -1, -1, 1, 1, -1 ] [ 1, 1, 1, 1, 1, 1, 1, -1 ] [ 1, 1, -1, -1, 1, 1, 1, -1 ] [ 1, 1, 1, 1, -1, -1, 1, -1 ] [ 1, 1, -1, 1, -1, 1, 1, -1 ] Errors: /home/mfd/gomagma: line 2: 7133 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host sab-combi-01.uab.es. (158.109.241.123) Time: Fri Feb 27 12:36:22 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=6; MAXLENGTHPATTERNS:=7; Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; end for; [#s: s in ss]; pp; admdeg; Output: Magma V2.10-6 Fri Feb 27 2004 12:36:12 on modular [Seed = 3183640042] ------------------------------------- Semigrup: <0, ...> n Semigrup: <0, 2, ...> n Semigrup: <0, 2, 4, ...> n Semigrup: <0, 3, ...> n Semigrup: <0, 2, 4, 6, ...> n Semigrup: <0, 3, 4, 6, ...> n Semigrup: <0, 4, ...> n Semigrup: <0, 3, 5, ...> n Semigrup: <0, 3, 6, ...> n Semigrup: <0, 5, ...> n Semigrup: <0, 2, 4, 6, 8, ...> n Semigrup: <0, 4, 6, ...> n Semigrup: <0, 4, 5, 7, ...> n Semigrup: <0, 3, 5, 6, 8, ...> n Semigrup: <0, 4, 5, 6, 8, ...> n Semigrup: <0, 3, 6, 7, 9, ...> n Semigrup: <0, 3, 6, 8, ...> n Semigrup: <0, 2, 4, 6, 8, 10, ...> n Semigrup: <0, 4, 7, ...> n Semigrup: <0, 5, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, ...> n Semigrup: <0, 4, 6, 8, ...> n Semigrup: <0, 5, 6, 7, 8, 10, ...> n Semigrup: <0, 4, 6, 7, 8, 10, ...> n Semigrup: <0, 5, 6, 8, ...> n Semigrup: <0, 5, 7, ...> n Semigrup: <0, 6, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, ...> n Semigrup: <0, 5, 7, 8, 10, ...> n Semigrup: <0, 3, 6, 7, 9, 10, 12, ...> n Semigrup: <0, 4, 6, 8, 10, ...> n Semigrup: <0, 6, 8, ...> n Semigrup: <0, 5, 6, 8, 10, ...> n Semigrup: <0, 6, 7, 8, 9, 11, ...> n Semigrup: <0, 4, 8, ...> n Semigrup: <0, 5, 6, 9, ...> n Semigrup: <0, 4, 7, 8, 10, ...> n Semigrup: <0, 5, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 4, 7, 8, 9, 11, ...> n Semigrup: <0, 3, 6, 8, 9, 11, ...> n Semigrup: <0, 6, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 7, 10, ...> n Semigrup: <0, 5, 8, ...> n Semigrup: <0, 6, 7, 8, 10, ...> n Semigrup: <0, 7, ...> n Semigrup: <0, 3, 6, 9, ...> n Semigrup: <0, 4, 6, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 7, 9, ...> n [ 1, -1 ] [ 1, 1, -1 ] [ 1, 1, -1, -1 ] [ 1, -1, 1, -1 ] [ 1, 1, 1, -1 ] [ 1, -1, 1, 1, -1 ] [ 1, 1, 1, -1, -1 ] [ 1, 1, 1, 1, -1 ] [ 1, 1, -1, 1, -1 ] [ 1, 1, 1, 1, 1, -1 ] [ 1, 1, 1, -1, -1, -1 ] [ 1, 1, -1, -1, 1, -1 ] [ 1, -1, 1, 1, 1, -1 ] [ 1, 1, -1, 1, -1, -1 ] [ 1, 1, 1, -1, 1, -1 ] [ 1, 1, 1, 1, -1, -1 ] [ 1, 1, -1, 1, 1, -1 ] [ 1, -1, 1, 1, -1, -1 ] [ 1, -1, 1, -1, 1, -1 ] [ 1, 1, 1, -1, 1, -1, -1 ] [ 1, -1, 1, -1, 1, 1, -1 ] [ 1, 1, 1, -1, 1, 1, -1 ] [ 1, 1, -1, 1, -1, 1, -1 ] [ 1, 1, -1, -1, 1, 1, -1 ] [ 1, 1, 1, 1, -1, -1, -1 ] [ 1, 1, -1, 1, 1, -1, -1 ] [ 1, 1, 1, -1, -1, 1, -1 ] [ 1, -1, 1, 1, 1, 1, -1 ] [ 1, -1, 1, 1, -1, 1, -1 ] [ 1, 1, 1, 1, 1, -1, -1 ] [ 1, -1, 1, 1, 1, -1, -1 ] [ 1, 1, 1, 1, -1, 1, -1 ] [ 1, 1, 1, 1, 1, 1, -1 ] [ 1, 1, -1, 1, 1, 1, -1 ] [ 1, 25, 49, 50 ] [ [ [ 1, -1 ], [ 1, 1, -1, -1 ], [ 1, -1, 1, -1 ], [ 1, -1, 1, 1, -1 ], [ 1, 1, 1, -1, -1, -1 ], [ 1, 1, -1, -1, 1, -1 ], [ 1, -1, 1, 1, 1, -1 ], [ 1, 1, -1, 1, -1, -1 ], [ 1, -1, 1, 1, -1, -1 ], [ 1, -1, 1, -1, 1, -1 ], [ 1, -1, 1, -1, 1, 1, -1 ], [ 1, 1, -1, -1, 1, 1, -1 ], [ 1, -1, 1, 1, 1, 1, -1 ], [ 1, -1, 1, 1, -1, 1, -1 ], [ 1, -1, 1, 1, 1, -1, -1 ] ], [ [ 1, 1, -1 ], [ 1, 1, 1, -1, -1 ], [ 1, 1, -1, 1, -1 ], [ 1, 1, -1, 1, 1, -1 ], [ 1, 1, 1, -1, 1, -1, -1 ], [ 1, 1, -1, 1, -1, 1, -1 ], [ 1, 1, 1, 1, -1, -1, -1 ], [ 1, 1, -1, 1, 1, -1, -1 ], [ 1, 1, 1, -1, -1, 1, -1 ], [ 1, 1, -1, 1, 1, 1, -1 ] ], [ [ 1, 1, 1, -1 ], [ 1, 1, 1, -1, 1, -1 ], [ 1, 1, 1, 1, -1, -1 ], [ 1, 1, 1, -1, 1, 1, -1 ] ], [ [ 1, 1, 1, 1, -1 ], [ 1, 1, 1, 1, 1, -1 ], [ 1, 1, 1, 1, 1, -1, -1 ], [ 1, 1, 1, 1, -1, 1, -1 ], [ 1, 1, 1, 1, 1, 1, -1 ] ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ], [ 3, 3, 3, 3 ], [ 4, 5, 4, 4, 6 ] ] Total time: 10.219 seconds, Total memory usage: 2.33MB ************** MAGMA ***************** Host sab-combi-01.uab.es. (158.109.241.123) Time: Fri Feb 27 12:37:45 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=7; MAXLENGTHPATTERNS:=7; Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; end for; [#s: s in ss]; pp; admdeg; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Feb 27 2004 12:37:21 on modular [Seed = 3033232574] ------------------------------------- Semigrup: <0, ...> n Semigrup: <0, 2, ...> n Semigrup: <0, 2, 4, ...> n Semigrup: <0, 3, ...> n Semigrup: <0, 2, 4, 6, ...> n Semigrup: <0, 3, 4, 6, ...> n Semigrup: <0, 4, ...> n Semigrup: <0, 3, 5, ...> n Semigrup: <0, 3, 6, ...> n Semigrup: <0, 5, ...> n Semigrup: <0, 2, 4, 6, 8, ...> n Semigrup: <0, 4, 6, ...> n Semigrup: <0, 4, 5, 7, ...> n Semigrup: <0, 3, 5, 6, 8, ...> n Semigrup: <0, 4, 5, 6, 8, ...> n Semigrup: <0, 3, 6, 7, 9, ...> n Semigrup: <0, 3, 6, 8, ...> n Semigrup: <0, 2, 4, 6, 8, 10, ...> n Semigrup: <0, 4, 7, ...> n Semigrup: <0, 5, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, ...> n Semigrup: <0, 4, 6, 8, ...> n Semigrup: <0, 5, 6, 7, 8, 10, ...> n Semigrup: <0, 4, 6, 7, 8, 10, ...> n Semigrup: <0, 5, 6, 8, ...> n Semigrup: <0, 5, 7, ...> n Semigrup: <0, 6, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, ...> n Semigrup: <0, 5, 7, 8, 10, ...> n Semigrup: <0, 3, 6, 7, 9, 10, 12, ...> n Semigrup: <0, 4, 6, 8, 10, ...> n Semigrup: <0, 6, 8, ...> n Semigrup: <0, 5, 6, 8, 10, ...> n Semigrup: <0, 6, 7, 8, 9, 11, ...> n Semigrup: <0, 4, 8, ...> n Semigrup: <0, 5, 6, 9, ...> n Semigrup: <0, 4, 7, 8, 10, ...> n Semigrup: <0, 5, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 4, 7, 8, 9, 11, ...> n Semigrup: <0, 3, 6, 8, 9, 11, ...> n Semigrup: <0, 6, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 7, 10, ...> n Semigrup: <0, 5, 8, ...> n Semigrup: <0, 6, 7, 8, 10, ...> n Semigrup: <0, 7, ...> n Semigrup: <0, 3, 6, 9, ...> n Semigrup: <0, 4, 6, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 7, 9, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, 14, ...> n Semigrup: <0, 8, ...> n Semigrup: <0, 6, 7, 9, 10, 12, ...> n Semigrup: <0, 4, 7, 8, 11, ...> n Semigrup: <0, 6, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 9, 11, ...> n Semigrup: <0, 5, 6, 10, ...> n Semigrup: <0, 5, 7, 8, 10, 12, ...> n Semigrup: <0, 7, 8, 10, ...> n Semigrup: <0, 4, 8, 9, 11, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 5, 7, 9, 10, 12, ...> n Semigrup: <0, 5, 7, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 8, 10, 12, ...> n Semigrup: <0, 4, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 9, 11, ...> n Semigrup: <0, 7, 9, ...> n Semigrup: <0, 6, 9, ...> n Semigrup: <0, 6, 7, 8, 9, 12, ...> n Semigrup: <0, 3, 6, 9, 11, ...> n Semigrup: <0, 4, 6, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 7, 8, 9, 11, ...> n Semigrup: <0, 5, 8, 10, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 9, ...> n Semigrup: <0, 6, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 4, 6, 8, 10, 12, ...> n Semigrup: <0, 5, 7, 10, ...> n Semigrup: <0, 6, 8, 10, ...> n Semigrup: <0, 3, 6, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 10, ...> n Semigrup: <0, 3, 6, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 4, 7, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 8, 11, ...> n Semigrup: <0, 4, 8, 10, ...> n Semigrup: <0, 5, 8, 9, 10, 11, 13, ...> n [ 1, -1 ] [ 1, 1, -1 ] [ 1, 1, -1, -1 ] [ 1, -1, 1, -1 ] [ 1, 1, 1, -1 ] [ 1, -1, 1, 1, -1 ] [ 1, 1, 1, -1, -1 ] [ 1, 1, 1, 1, -1 ] [ 1, 1, -1, 1, -1 ] [ 1, 1, 1, 1, 1, -1 ] [ 1, 1, 1, -1, -1, -1 ] [ 1, 1, -1, -1, 1, -1 ] [ 1, -1, 1, 1, 1, -1 ] [ 1, 1, -1, 1, -1, -1 ] [ 1, 1, 1, -1, 1, -1 ] [ 1, 1, 1, 1, -1, -1 ] [ 1, 1, -1, 1, 1, -1 ] [ 1, -1, 1, 1, -1, -1 ] [ 1, -1, 1, -1, 1, -1 ] [ 1, 1, 1, -1, 1, -1, -1 ] [ 1, -1, 1, -1, 1, 1, -1 ] [ 1, 1, 1, -1, 1, 1, -1 ] [ 1, 1, -1, 1, -1, 1, -1 ] [ 1, 1, -1, -1, 1, 1, -1 ] [ 1, 1, 1, 1, -1, -1, -1 ] [ 1, 1, -1, 1, 1, -1, -1 ] [ 1, 1, 1, -1, -1, 1, -1 ] [ 1, -1, 1, 1, 1, 1, -1 ] [ 1, -1, 1, 1, -1, 1, -1 ] [ 1, 1, 1, 1, 1, -1, -1 ] [ 1, -1, 1, 1, 1, -1, -1 ] [ 1, 1, 1, 1, -1, 1, -1 ] Errors: /home/mfd/gomagma: line 2: 7151 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host sab-combi-01.uab.es. (158.109.241.123) Time: Fri Feb 27 12:39:20 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=7; MAXLENGTHPATTERNS:=7; Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; admdeg; end for; //[#s: s in ss]; //pp; admdeg; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Feb 27 2004 12:38:57 on modular [Seed = 2715705675] ------------------------------------- Semigrup: <0, ...> n Semigrup: <0, 2, ...> n Semigrup: <0, 2, 4, ...> n Semigrup: <0, 3, ...> n Semigrup: <0, 2, 4, 6, ...> n Semigrup: <0, 3, 4, 6, ...> n Semigrup: <0, 4, ...> n Semigrup: <0, 3, 5, ...> n Semigrup: <0, 3, 6, ...> n Semigrup: <0, 5, ...> n Semigrup: <0, 2, 4, 6, 8, ...> n Semigrup: <0, 4, 6, ...> n Semigrup: <0, 4, 5, 7, ...> n Semigrup: <0, 3, 5, 6, 8, ...> n Semigrup: <0, 4, 5, 6, 8, ...> n Semigrup: <0, 3, 6, 7, 9, ...> n Semigrup: <0, 3, 6, 8, ...> n Semigrup: <0, 2, 4, 6, 8, 10, ...> n Semigrup: <0, 4, 7, ...> n Semigrup: <0, 5, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, ...> n Semigrup: <0, 4, 6, 8, ...> n Semigrup: <0, 5, 6, 7, 8, 10, ...> n Semigrup: <0, 4, 6, 7, 8, 10, ...> n Semigrup: <0, 5, 6, 8, ...> n Semigrup: <0, 5, 7, ...> n Semigrup: <0, 6, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, ...> n Semigrup: <0, 5, 7, 8, 10, ...> n Semigrup: <0, 3, 6, 7, 9, 10, 12, ...> n Semigrup: <0, 4, 6, 8, 10, ...> n Semigrup: <0, 6, 8, ...> n Semigrup: <0, 5, 6, 8, 10, ...> n Semigrup: <0, 6, 7, 8, 9, 11, ...> n Semigrup: <0, 4, 8, ...> n Semigrup: <0, 5, 6, 9, ...> n Semigrup: <0, 4, 7, 8, 10, ...> n Semigrup: <0, 5, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 4, 7, 8, 9, 11, ...> n Semigrup: <0, 3, 6, 8, 9, 11, ...> n Semigrup: <0, 6, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 7, 10, ...> n Semigrup: <0, 5, 8, ...> n Semigrup: <0, 6, 7, 8, 10, ...> n Semigrup: <0, 7, ...> n Semigrup: <0, 3, 6, 9, ...> n Semigrup: <0, 4, 6, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 7, 9, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, 14, ...> n Semigrup: <0, 8, ...> n Semigrup: <0, 6, 7, 9, 10, 12, ...> n Semigrup: <0, 4, 7, 8, 11, ...> n Semigrup: <0, 6, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 9, 11, ...> n Semigrup: <0, 5, 6, 10, ...> n Semigrup: <0, 5, 7, 8, 10, 12, ...> n Semigrup: <0, 7, 8, 10, ...> n Semigrup: <0, 4, 8, 9, 11, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 5, 7, 9, 10, 12, ...> n Semigrup: <0, 5, 7, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 8, 10, 12, ...> n Semigrup: <0, 4, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 9, 11, ...> n Semigrup: <0, 7, 9, ...> n Semigrup: <0, 6, 9, ...> n Semigrup: <0, 6, 7, 8, 9, 12, ...> n Semigrup: <0, 3, 6, 9, 11, ...> n Semigrup: <0, 4, 6, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 7, 8, 9, 11, ...> n Semigrup: <0, 5, 8, 10, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 9, ...> n Semigrup: <0, 6, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 4, 6, 8, 10, 12, ...> n Semigrup: <0, 5, 7, 10, ...> n Semigrup: <0, 6, 8, 10, ...> n Semigrup: <0, 3, 6, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 10, ...> n Semigrup: <0, 3, 6, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 4, 7, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 8, 11, ...> n Semigrup: <0, 4, 8, 10, ...> n Semigrup: <0, 5, 8, 9, 10, 11, 13, ...> n [ 1, -1 ] [ [ 1 ] ] [ 1, 1, -1 ] [ [ 1 ], [ 2 ] ] [ 1, 1, -1, -1 ] [ [ 1, 1 ], [ 2 ] ] [ 1, -1, 1, -1 ] [ [ 1, 1, 1 ], [ 2 ] ] [ 1, 1, 1, -1 ] [ [ 1, 1, 1 ], [ 2 ], [ 3 ] ] [ 1, -1, 1, 1, -1 ] [ [ 1, 1, 1, 1 ], [ 2 ], [ 3 ] ] [ 1, 1, 1, -1, -1 ] [ [ 1, 1, 1, 1 ], [ 2, 2 ], [ 3 ] ] [ 1, 1, 1, 1, -1 ] [ [ 1, 1, 1, 1 ], [ 2, 2 ], [ 3 ], [ 4 ] ] [ 1, 1, -1, 1, -1 ] [ [ 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4 ] ] [ 1, 1, 1, 1, 1, -1 ] [ [ 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ 1, 1, 1, -1, -1, -1 ] [ [ 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ 1, 1, -1, -1, 1, -1 ] [ [ 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ 1, -1, 1, 1, 1, -1 ] [ [ 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ 1, 1, -1, 1, -1, -1 ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ 1, 1, 1, -1, 1, -1 ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3, 3 ], [ 4, 5 ] ] [ 1, 1, 1, 1, -1, -1 ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3, 3, 3 ], [ 4, 5 ] ] [ 1, 1, -1, 1, 1, -1 ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2, 2 ], [ 3, 3, 3 ], [ 4, 5 ] ] [ 1, -1, 1, 1, -1, -1 ] [ [ 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2, 2 ], [ 3, 3, 3 ], [ 4, 5 ] ] [ 1, -1, 1, -1, 1, -1 ] [ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2, 2 ], [ 3, 3, 3 ], [ 4, 5 ] ] [ 1, 1, 1, -1, 1, -1, -1 ] [ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2, 2, 2 ], [ 3, 3, 3 ], [ 4, 5 ] ] [ 1, -1, 1, -1, 1, 1, -1 ] [ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2, 2, 2 ], [ 3, 3, 3 ], [ 4, 5 ] ] [ 1, 1, 1, -1, 1, 1, -1 ] [ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2, 2, 2 ], [ 3, 3, 3, 3 ], [ 4, 5 ] ] [ 1, 1, -1, 1, -1, 1, -1 ] [ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2, 2, 2, 2 ], [ 3, 3, 3, 3 ], [ 4, 5 ] ] [ 1, 1, -1, -1, 1, 1, -1 ] [ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2, 2, 2, 2 ], [ 3, 3, 3, 3 ], [ 4, 5 ] ] [ 1, 1, 1, 1, -1, -1, -1 ] [ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2, 2, 2, 2, 2 ], [ 3, 3, 3, 3 ], [ 4, 5 ] ] [ 1, 1, -1, 1, 1, -1, -1 ] [ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2, 2, 2, 2, 2, 2 ], [ 3, 3, 3, 3 ], [ 4, 5 ] ] [ 1, 1, 1, -1, -1, 1, -1 ] [ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2, 2, 2, 2, 2, 2, 2 ], [ 3, 3, 3, 3 ], [ 4, 5 ] ] [ 1, -1, 1, 1, 1, 1, -1 ] [ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2, 2, 2, 2, 2, 2, 2 ], [ 3, 3, 3, 3 ], [ 4, 5 ] ] [ 1, -1, 1, 1, -1, 1, -1 ] [ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2, 2, 2, 2, 2, 2, 2 ], [ 3, 3, 3, 3 ], [ 4, 5 ] ] [ 1, 1, 1, 1, 1, -1, -1 ] [ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2, 2, 2, 2, 2, 2, 2 ], [ 3, 3, 3, 3 ], [ 4, 5, 4 ] ] [ 1, -1, 1, 1, 1, -1, -1 ] [ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2, 2, 2, 2, 2, 2, 2 ], [ 3, 3, 3, 3 ], [ 4, 5, 4 ] ] [ 1, 1, 1, 1, -1, 1, -1 ] Errors: /home/mfd/gomagma: line 2: 7162 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host sab-combi-01.uab.es. (158.109.241.123) Time: Fri Feb 27 12:40:07 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=7; MAXLENGTHPATTERNS:=7; Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do //print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; admdeg; end for; //[#s: s in ss]; //pp; admdeg; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Feb 27 2004 12:39:44 on modular [Seed = 1595973603] ------------------------------------- Semigrup: <0, ...> n Semigrup: <0, 2, ...> n Semigrup: <0, 2, 4, ...> n Semigrup: <0, 3, ...> n Semigrup: <0, 2, 4, 6, ...> n Semigrup: <0, 3, 4, 6, ...> n Semigrup: <0, 4, ...> n Semigrup: <0, 3, 5, ...> n Semigrup: <0, 3, 6, ...> n Semigrup: <0, 5, ...> n Semigrup: <0, 2, 4, 6, 8, ...> n Semigrup: <0, 4, 6, ...> n Semigrup: <0, 4, 5, 7, ...> n Semigrup: <0, 3, 5, 6, 8, ...> n Semigrup: <0, 4, 5, 6, 8, ...> n Semigrup: <0, 3, 6, 7, 9, ...> n Semigrup: <0, 3, 6, 8, ...> n Semigrup: <0, 2, 4, 6, 8, 10, ...> n Semigrup: <0, 4, 7, ...> n Semigrup: <0, 5, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, ...> n Semigrup: <0, 4, 6, 8, ...> n Semigrup: <0, 5, 6, 7, 8, 10, ...> n Semigrup: <0, 4, 6, 7, 8, 10, ...> n Semigrup: <0, 5, 6, 8, ...> n Semigrup: <0, 5, 7, ...> n Semigrup: <0, 6, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, ...> n Semigrup: <0, 5, 7, 8, 10, ...> n Semigrup: <0, 3, 6, 7, 9, 10, 12, ...> n Semigrup: <0, 4, 6, 8, 10, ...> n Semigrup: <0, 6, 8, ...> n Semigrup: <0, 5, 6, 8, 10, ...> n Semigrup: <0, 6, 7, 8, 9, 11, ...> n Semigrup: <0, 4, 8, ...> n Semigrup: <0, 5, 6, 9, ...> n Semigrup: <0, 4, 7, 8, 10, ...> n Semigrup: <0, 5, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 4, 7, 8, 9, 11, ...> n Semigrup: <0, 3, 6, 8, 9, 11, ...> n Semigrup: <0, 6, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 7, 10, ...> n Semigrup: <0, 5, 8, ...> n Semigrup: <0, 6, 7, 8, 10, ...> n Semigrup: <0, 7, ...> n Semigrup: <0, 3, 6, 9, ...> n Semigrup: <0, 4, 6, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 7, 9, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, 14, ...> n Semigrup: <0, 8, ...> n Semigrup: <0, 6, 7, 9, 10, 12, ...> n Semigrup: <0, 4, 7, 8, 11, ...> n Semigrup: <0, 6, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 9, 11, ...> n Semigrup: <0, 5, 6, 10, ...> n Semigrup: <0, 5, 7, 8, 10, 12, ...> n Semigrup: <0, 7, 8, 10, ...> n Semigrup: <0, 4, 8, 9, 11, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 5, 7, 9, 10, 12, ...> n Semigrup: <0, 5, 7, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 8, 10, 12, ...> n Semigrup: <0, 4, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 9, 11, ...> n Semigrup: <0, 7, 9, ...> n Semigrup: <0, 6, 9, ...> n Semigrup: <0, 6, 7, 8, 9, 12, ...> n Semigrup: <0, 3, 6, 9, 11, ...> n Semigrup: <0, 4, 6, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 7, 8, 9, 11, ...> n Semigrup: <0, 5, 8, 10, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 9, ...> n Semigrup: <0, 6, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 4, 6, 8, 10, 12, ...> n Semigrup: <0, 5, 7, 10, ...> n Semigrup: <0, 6, 8, 10, ...> n Semigrup: <0, 3, 6, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 10, ...> n Semigrup: <0, 3, 6, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 4, 7, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 8, 11, ...> n Semigrup: <0, 4, 8, 10, ...> n Semigrup: <0, 5, 8, 9, 10, 11, 13, ...> n [ [ 1 ] ] [ [ 1 ], [ 2 ] ] [ [ 1, 1 ], [ 2 ] ] [ [ 1, 1, 1 ], [ 2 ] ] [ [ 1, 1, 1 ], [ 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2 ], [ 3 ], [ 4 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3, 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3, 3, 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2, 2 ], [ 3, 3, 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2, 2 ], [ 3, 3, 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2, 2 ], [ 3, 3, 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2, 2, 2 ], [ 3, 3, 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2, 2, 2 ], [ 3, 3, 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2, 2, 2 ], [ 3, 3, 3, 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2, 2, 2, 2 ], [ 3, 3, 3, 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2, 2, 2, 2 ], [ 3, 3, 3, 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2, 2, 2, 2, 2 ], [ 3, 3, 3, 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2, 2, 2, 2, 2, 2 ], [ 3, 3, 3, 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2, 2, 2, 2, 2, 2, 2 ], [ 3, 3, 3, 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2, 2, 2, 2, 2, 2, 2 ], [ 3, 3, 3, 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2, 2, 2, 2, 2, 2, 2 ], [ 3, 3, 3, 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2, 2, 2, 2, 2, 2, 2 ], [ 3, 3, 3, 3 ], [ 4, 5, 4 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2, 2, 2, 2, 2, 2, 2 ], [ 3, 3, 3, 3 ], [ 4, 5, 4 ] ] Errors: /home/mfd/gomagma: line 2: 7171 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host sab-combi-01.uab.es. (158.109.241.123) Time: Fri Feb 27 12:41:16 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=8; MAXLENGTHPATTERNS:=7; Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do //print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; admdeg; end for; //[#s: s in ss]; //pp; admdeg; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Feb 27 2004 12:40:53 on modular [Seed = 1211599153] ------------------------------------- Semigrup: <0, ...> n Semigrup: <0, 2, ...> n Semigrup: <0, 2, 4, ...> n Semigrup: <0, 3, ...> n Semigrup: <0, 2, 4, 6, ...> n Semigrup: <0, 3, 4, 6, ...> n Semigrup: <0, 4, ...> n Semigrup: <0, 3, 5, ...> n Semigrup: <0, 3, 6, ...> n Semigrup: <0, 5, ...> n Semigrup: <0, 2, 4, 6, 8, ...> n Semigrup: <0, 4, 6, ...> n Semigrup: <0, 4, 5, 7, ...> n Semigrup: <0, 3, 5, 6, 8, ...> n Semigrup: <0, 4, 5, 6, 8, ...> n Semigrup: <0, 3, 6, 7, 9, ...> n Semigrup: <0, 3, 6, 8, ...> n Semigrup: <0, 2, 4, 6, 8, 10, ...> n Semigrup: <0, 4, 7, ...> n Semigrup: <0, 5, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, ...> n Semigrup: <0, 4, 6, 8, ...> n Semigrup: <0, 5, 6, 7, 8, 10, ...> n Semigrup: <0, 4, 6, 7, 8, 10, ...> n Semigrup: <0, 5, 6, 8, ...> n Semigrup: <0, 5, 7, ...> n Semigrup: <0, 6, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, ...> n Semigrup: <0, 5, 7, 8, 10, ...> n Semigrup: <0, 3, 6, 7, 9, 10, 12, ...> n Semigrup: <0, 4, 6, 8, 10, ...> n Semigrup: <0, 6, 8, ...> n Semigrup: <0, 5, 6, 8, 10, ...> n Semigrup: <0, 6, 7, 8, 9, 11, ...> n Semigrup: <0, 4, 8, ...> n Semigrup: <0, 5, 6, 9, ...> n Semigrup: <0, 4, 7, 8, 10, ...> n Semigrup: <0, 5, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 4, 7, 8, 9, 11, ...> n Semigrup: <0, 3, 6, 8, 9, 11, ...> n Semigrup: <0, 6, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 7, 10, ...> n Semigrup: <0, 5, 8, ...> n Semigrup: <0, 6, 7, 8, 10, ...> n Semigrup: <0, 7, ...> n Semigrup: <0, 3, 6, 9, ...> n Semigrup: <0, 4, 6, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 7, 9, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, 14, ...> n Semigrup: <0, 8, ...> n Semigrup: <0, 6, 7, 9, 10, 12, ...> n Semigrup: <0, 4, 7, 8, 11, ...> n Semigrup: <0, 6, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 9, 11, ...> n Semigrup: <0, 5, 6, 10, ...> n Semigrup: <0, 5, 7, 8, 10, 12, ...> n Semigrup: <0, 7, 8, 10, ...> n Semigrup: <0, 4, 8, 9, 11, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 5, 7, 9, 10, 12, ...> n Semigrup: <0, 5, 7, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 8, 10, 12, ...> n Semigrup: <0, 4, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 9, 11, ...> n Semigrup: <0, 7, 9, ...> n Semigrup: <0, 6, 9, ...> n Semigrup: <0, 6, 7, 8, 9, 12, ...> n Semigrup: <0, 3, 6, 9, 11, ...> n Semigrup: <0, 4, 6, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 7, 8, 9, 11, ...> n Semigrup: <0, 5, 8, 10, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 9, ...> n Semigrup: <0, 6, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 4, 6, 8, 10, 12, ...> n Semigrup: <0, 5, 7, 10, ...> n Semigrup: <0, 6, 8, 10, ...> n Semigrup: <0, 3, 6, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 10, ...> n Semigrup: <0, 3, 6, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 4, 7, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 8, 11, ...> n Semigrup: <0, 4, 8, 10, ...> n Semigrup: <0, 5, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 7, 10, ...> n Semigrup: <0, 4, 6, 8, 10, 12, 13, 14, 16, ...> n Semigrup: <0, 5, 7, 9, 10, 12, 14, ...> n Semigrup: <0, 6, 8, 11, ...> n Semigrup: <0, 5, 8, 9, 10, 13, ...> n Semigrup: <0, 4, 8, 10, 12, ...> n Semigrup: <0, 6, 9, 11, ...> n Semigrup: <0, 6, 7, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, 14, 16, ...> n Semigrup: <0, 3, 6, 9, 11, 12, 14, ...> n Semigrup: <0, 5, 10, ...> n Semigrup: <0, 7, 9, 11, ...> n Semigrup: <0, 7, 8, 11, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 5, 7, 10, 11, 12, 14, ...> n Semigrup: <0, 4, 6, 8, 10, 12, 14, ...> n Semigrup: <0, 6, 10, ...> n Semigrup: <0, 7, 8, 9, 10, 13, ...> n Semigrup: <0, 4, 8, 9, 12, ...> n Semigrup: <0, 7, 8, 9, 11, 13, ...> n Semigrup: <0, 5, 8, 10, 11, 13, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 7, 8, 10, 12, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 7, 9, 10, 12, ...> n Semigrup: <0, 5, 9, 10, 11, 13, ...> n Semigrup: <0, 6, 8, 9, 12, ...> n Semigrup: <0, 3, 6, 9, 10, 12, 13, 15, ...> n Semigrup: <0, 5, 8, 10, 12, ...> n Semigrup: <0, 7, 8, 9, 12, ...> n Semigrup: <0, 6, 9, 10, 12, ...> n Semigrup: <0, 4, 8, 11, ...> n Semigrup: <0, 7, 8, 10, 11, 13, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 10, 12, ...> n Semigrup: <0, 7, 9, 10, 11, 13, ...> n Semigrup: <0, 6, 9, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 5, 9, 10, 12, ...> n Semigrup: <0, 7, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 8, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 6, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 5, 7, 10, 12, ...> n Semigrup: <0, 7, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 10, 12, ...> n Semigrup: <0, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 7, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 8, 12, ...> n Semigrup: <0, 5, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 9, 12, ...> n Semigrup: <0, 4, 8, 9, 10, 12, 13, 14, 16, ...> n Semigrup: <0, 8, 9, 10, 12, ...> n Semigrup: <0, 8, 9, 11, ...> n Semigrup: <0, 7, 9, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 7, 8, 9, 10, 12, 14, ...> n Semigrup: <0, 4, 8, 9, 11, 12, 13, 15, ...> n Semigrup: <0, 4, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 9, 10, 12, 14, ...> n Semigrup: <0, 6, 7, 11, ...> n Semigrup: <0, 8, 10, ...> n Semigrup: <0, 6, 8, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 14, ...> n Semigrup: <0, 9, ...> n Semigrup: <0, 3, 6, 9, 12, ...> n Semigrup: <0, 4, 7, 8, 11, 12, 14, ...> n [ [ 1 ] ] [ [ 1 ], [ 2 ] ] [ [ 1, 1 ], [ 2 ] ] [ [ 1, 1, 1 ], [ 2 ] ] [ [ 1, 1, 1 ], [ 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2 ], [ 3 ], [ 4 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3, 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3, 3 ], [ 4, 5 ], [ 3 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2, 2 ], [ 3, 3 ], [ 4, 5 ], [ 3 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2, 2 ], [ 3, 3 ], [ 4, 5 ], [ 3 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2, 2 ], [ 3, 3 ], [ 4, 5 ], [ 3 ] ] Errors: /home/mfd/gomagma: line 2: 7188 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host sab-combi-01.uab.es. (158.109.241.123) Time: Fri Feb 27 12:44:16 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=8; MAXLENGTHPATTERNS:=7; Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); /* ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do //print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; admdeg; end for; //[#s: s in ss]; //pp; admdeg; */ p:=Patterns[16]; [i: i in [1..l]| admits(Semigrups[i],p)] p:=[1,1,-1]; [i: i in [1..l]| admits(Semigrups[i],p)] Output: Magma V2.10-6 Fri Feb 27 2004 12:44:10 on modular [Seed = 292475047] ------------------------------------- Semigrup: <0, ...> n Semigrup: <0, 2, ...> n Semigrup: <0, 2, 4, ...> n Semigrup: <0, 3, ...> n Semigrup: <0, 2, 4, 6, ...> n Semigrup: <0, 3, 4, 6, ...> n Semigrup: <0, 4, ...> n Semigrup: <0, 3, 5, ...> n Semigrup: <0, 3, 6, ...> n Semigrup: <0, 5, ...> n Semigrup: <0, 2, 4, 6, 8, ...> n Semigrup: <0, 4, 6, ...> n Semigrup: <0, 4, 5, 7, ...> n Semigrup: <0, 3, 5, 6, 8, ...> n Semigrup: <0, 4, 5, 6, 8, ...> n Semigrup: <0, 3, 6, 7, 9, ...> n Semigrup: <0, 3, 6, 8, ...> n Semigrup: <0, 2, 4, 6, 8, 10, ...> n Semigrup: <0, 4, 7, ...> n Semigrup: <0, 5, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, ...> n Semigrup: <0, 4, 6, 8, ...> n Semigrup: <0, 5, 6, 7, 8, 10, ...> n Semigrup: <0, 4, 6, 7, 8, 10, ...> n Semigrup: <0, 5, 6, 8, ...> n Semigrup: <0, 5, 7, ...> n Semigrup: <0, 6, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, ...> n Semigrup: <0, 5, 7, 8, 10, ...> n Semigrup: <0, 3, 6, 7, 9, 10, 12, ...> n Semigrup: <0, 4, 6, 8, 10, ...> n Semigrup: <0, 6, 8, ...> n Semigrup: <0, 5, 6, 8, 10, ...> n Semigrup: <0, 6, 7, 8, 9, 11, ...> n Semigrup: <0, 4, 8, ...> n Semigrup: <0, 5, 6, 9, ...> n Semigrup: <0, 4, 7, 8, 10, ...> n Semigrup: <0, 5, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 4, 7, 8, 9, 11, ...> n Semigrup: <0, 3, 6, 8, 9, 11, ...> n Semigrup: <0, 6, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 7, 10, ...> n Semigrup: <0, 5, 8, ...> n Semigrup: <0, 6, 7, 8, 10, ...> n Semigrup: <0, 7, ...> n Semigrup: <0, 3, 6, 9, ...> n Semigrup: <0, 4, 6, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 7, 9, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, 14, ...> n Semigrup: <0, 8, ...> n Semigrup: <0, 6, 7, 9, 10, 12, ...> n Semigrup: <0, 4, 7, 8, 11, ...> n Semigrup: <0, 6, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 9, 11, ...> n Semigrup: <0, 5, 6, 10, ...> n Semigrup: <0, 5, 7, 8, 10, 12, ...> n Semigrup: <0, 7, 8, 10, ...> n Semigrup: <0, 4, 8, 9, 11, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 5, 7, 9, 10, 12, ...> n Semigrup: <0, 5, 7, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 8, 10, 12, ...> n Semigrup: <0, 4, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 9, 11, ...> n Semigrup: <0, 7, 9, ...> n Semigrup: <0, 6, 9, ...> n Semigrup: <0, 6, 7, 8, 9, 12, ...> n Semigrup: <0, 3, 6, 9, 11, ...> n Semigrup: <0, 4, 6, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 7, 8, 9, 11, ...> n Semigrup: <0, 5, 8, 10, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 9, ...> n Semigrup: <0, 6, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 4, 6, 8, 10, 12, ...> n Semigrup: <0, 5, 7, 10, ...> n Semigrup: <0, 6, 8, 10, ...> n Semigrup: <0, 3, 6, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 10, ...> n Semigrup: <0, 3, 6, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 4, 7, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 8, 11, ...> n Semigrup: <0, 4, 8, 10, ...> n Semigrup: <0, 5, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 7, 10, ...> n Semigrup: <0, 4, 6, 8, 10, 12, 13, 14, 16, ...> n Semigrup: <0, 5, 7, 9, 10, 12, 14, ...> n Semigrup: <0, 6, 8, 11, ...> n Semigrup: <0, 5, 8, 9, 10, 13, ...> n Semigrup: <0, 4, 8, 10, 12, ...> n Semigrup: <0, 6, 9, 11, ...> n Semigrup: <0, 6, 7, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, 14, 16, ...> n Semigrup: <0, 3, 6, 9, 11, 12, 14, ...> n Semigrup: <0, 5, 10, ...> n Semigrup: <0, 7, 9, 11, ...> n Semigrup: <0, 7, 8, 11, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 5, 7, 10, 11, 12, 14, ...> n Semigrup: <0, 4, 6, 8, 10, 12, 14, ...> n Semigrup: <0, 6, 10, ...> n Semigrup: <0, 7, 8, 9, 10, 13, ...> n Semigrup: <0, 4, 8, 9, 12, ...> n Semigrup: <0, 7, 8, 9, 11, 13, ...> n Semigrup: <0, 5, 8, 10, 11, 13, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 7, 8, 10, 12, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 7, 9, 10, 12, ...> n Semigrup: <0, 5, 9, 10, 11, 13, ...> n Semigrup: <0, 6, 8, 9, 12, ...> n Semigrup: <0, 3, 6, 9, 10, 12, 13, 15, ...> n Semigrup: <0, 5, 8, 10, 12, ...> n Semigrup: <0, 7, 8, 9, 12, ...> n Semigrup: <0, 6, 9, 10, 12, ...> n Semigrup: <0, 4, 8, 11, ...> n Semigrup: <0, 7, 8, 10, 11, 13, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 10, 12, ...> n Semigrup: <0, 7, 9, 10, 11, 13, ...> n Semigrup: <0, 6, 9, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 5, 9, 10, 12, ...> n Semigrup: <0, 7, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 8, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 6, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 5, 7, 10, 12, ...> n Semigrup: <0, 7, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 10, 12, ...> n Semigrup: <0, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 7, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 8, 12, ...> n Semigrup: <0, 5, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 9, 12, ...> n Semigrup: <0, 4, 8, 9, 10, 12, 13, 14, 16, ...> n Semigrup: <0, 8, 9, 10, 12, ...> n Semigrup: <0, 8, 9, 11, ...> n Semigrup: <0, 7, 9, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 7, 8, 9, 10, 12, 14, ...> n Semigrup: <0, 4, 8, 9, 11, 12, 13, 15, ...> n Semigrup: <0, 4, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 9, 10, 12, 14, ...> n Semigrup: <0, 6, 7, 11, ...> n Semigrup: <0, 8, 10, ...> n Semigrup: <0, 6, 8, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 14, ...> n Semigrup: <0, 9, ...> n Semigrup: <0, 3, 6, 9, 12, ...> n Semigrup: <0, 4, 7, 8, 11, 12, 14, ...> n >> p:=[1,1,-1]; ^ User error: bad syntax [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156 ] Total time: 6.789 seconds, Total memory usage: 3.95MB ************** MAGMA ***************** Host ca-rennes-7-184.w80-8.abo.wanadoo.fr. (80.8.187.184) Time: Fri Feb 27 12:44:52 2004 Input: M8:=matrix(GF(2),28,28); Output: Magma V2.10-6 Fri Feb 27 2004 12:44:48 on modular [Seed = 91932489] ------------------------------------- >> M8:=matrix(GF(2),28,28); ^ User error: Identifier 'matrix' has not been declared or assigned Total time: 3.439 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sab-combi-01.uab.es. (158.109.241.123) Time: Fri Feb 27 12:44:55 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=8; MAXLENGTHPATTERNS:=7; Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); /* ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do //print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; admdeg; end for; //[#s: s in ss]; //pp; admdeg; */ p:=Patterns[16]; [i: i in [1..l]| admits(Semigrups[i],p)]; p:=[1,1,-1]; [i: i in [1..l]| admits(Semigrups[i],p)]; Output: Magma V2.10-6 Fri Feb 27 2004 12:44:47 on modular [Seed = 175491161] ------------------------------------- Semigrup: <0, ...> n Semigrup: <0, 2, ...> n Semigrup: <0, 2, 4, ...> n Semigrup: <0, 3, ...> n Semigrup: <0, 2, 4, 6, ...> n Semigrup: <0, 3, 4, 6, ...> n Semigrup: <0, 4, ...> n Semigrup: <0, 3, 5, ...> n Semigrup: <0, 3, 6, ...> n Semigrup: <0, 5, ...> n Semigrup: <0, 2, 4, 6, 8, ...> n Semigrup: <0, 4, 6, ...> n Semigrup: <0, 4, 5, 7, ...> n Semigrup: <0, 3, 5, 6, 8, ...> n Semigrup: <0, 4, 5, 6, 8, ...> n Semigrup: <0, 3, 6, 7, 9, ...> n Semigrup: <0, 3, 6, 8, ...> n Semigrup: <0, 2, 4, 6, 8, 10, ...> n Semigrup: <0, 4, 7, ...> n Semigrup: <0, 5, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, ...> n Semigrup: <0, 4, 6, 8, ...> n Semigrup: <0, 5, 6, 7, 8, 10, ...> n Semigrup: <0, 4, 6, 7, 8, 10, ...> n Semigrup: <0, 5, 6, 8, ...> n Semigrup: <0, 5, 7, ...> n Semigrup: <0, 6, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, ...> n Semigrup: <0, 5, 7, 8, 10, ...> n Semigrup: <0, 3, 6, 7, 9, 10, 12, ...> n Semigrup: <0, 4, 6, 8, 10, ...> n Semigrup: <0, 6, 8, ...> n Semigrup: <0, 5, 6, 8, 10, ...> n Semigrup: <0, 6, 7, 8, 9, 11, ...> n Semigrup: <0, 4, 8, ...> n Semigrup: <0, 5, 6, 9, ...> n Semigrup: <0, 4, 7, 8, 10, ...> n Semigrup: <0, 5, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 4, 7, 8, 9, 11, ...> n Semigrup: <0, 3, 6, 8, 9, 11, ...> n Semigrup: <0, 6, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 7, 10, ...> n Semigrup: <0, 5, 8, ...> n Semigrup: <0, 6, 7, 8, 10, ...> n Semigrup: <0, 7, ...> n Semigrup: <0, 3, 6, 9, ...> n Semigrup: <0, 4, 6, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 7, 9, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, 14, ...> n Semigrup: <0, 8, ...> n Semigrup: <0, 6, 7, 9, 10, 12, ...> n Semigrup: <0, 4, 7, 8, 11, ...> n Semigrup: <0, 6, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 9, 11, ...> n Semigrup: <0, 5, 6, 10, ...> n Semigrup: <0, 5, 7, 8, 10, 12, ...> n Semigrup: <0, 7, 8, 10, ...> n Semigrup: <0, 4, 8, 9, 11, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 5, 7, 9, 10, 12, ...> n Semigrup: <0, 5, 7, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 8, 10, 12, ...> n Semigrup: <0, 4, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 9, 11, ...> n Semigrup: <0, 7, 9, ...> n Semigrup: <0, 6, 9, ...> n Semigrup: <0, 6, 7, 8, 9, 12, ...> n Semigrup: <0, 3, 6, 9, 11, ...> n Semigrup: <0, 4, 6, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 7, 8, 9, 11, ...> n Semigrup: <0, 5, 8, 10, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 9, ...> n Semigrup: <0, 6, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 4, 6, 8, 10, 12, ...> n Semigrup: <0, 5, 7, 10, ...> n Semigrup: <0, 6, 8, 10, ...> n Semigrup: <0, 3, 6, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 10, ...> n Semigrup: <0, 3, 6, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 4, 7, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 8, 11, ...> n Semigrup: <0, 4, 8, 10, ...> n Semigrup: <0, 5, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 7, 10, ...> n Semigrup: <0, 4, 6, 8, 10, 12, 13, 14, 16, ...> n Semigrup: <0, 5, 7, 9, 10, 12, 14, ...> n Semigrup: <0, 6, 8, 11, ...> n Semigrup: <0, 5, 8, 9, 10, 13, ...> n Semigrup: <0, 4, 8, 10, 12, ...> n Semigrup: <0, 6, 9, 11, ...> n Semigrup: <0, 6, 7, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, 14, 16, ...> n Semigrup: <0, 3, 6, 9, 11, 12, 14, ...> n Semigrup: <0, 5, 10, ...> n Semigrup: <0, 7, 9, 11, ...> n Semigrup: <0, 7, 8, 11, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 5, 7, 10, 11, 12, 14, ...> n Semigrup: <0, 4, 6, 8, 10, 12, 14, ...> n Semigrup: <0, 6, 10, ...> n Semigrup: <0, 7, 8, 9, 10, 13, ...> n Semigrup: <0, 4, 8, 9, 12, ...> n Semigrup: <0, 7, 8, 9, 11, 13, ...> n Semigrup: <0, 5, 8, 10, 11, 13, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 7, 8, 10, 12, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 7, 9, 10, 12, ...> n Semigrup: <0, 5, 9, 10, 11, 13, ...> n Semigrup: <0, 6, 8, 9, 12, ...> n Semigrup: <0, 3, 6, 9, 10, 12, 13, 15, ...> n Semigrup: <0, 5, 8, 10, 12, ...> n Semigrup: <0, 7, 8, 9, 12, ...> n Semigrup: <0, 6, 9, 10, 12, ...> n Semigrup: <0, 4, 8, 11, ...> n Semigrup: <0, 7, 8, 10, 11, 13, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 10, 12, ...> n Semigrup: <0, 7, 9, 10, 11, 13, ...> n Semigrup: <0, 6, 9, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 5, 9, 10, 12, ...> n Semigrup: <0, 7, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 8, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 6, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 5, 7, 10, 12, ...> n Semigrup: <0, 7, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 10, 12, ...> n Semigrup: <0, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 7, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 8, 12, ...> n Semigrup: <0, 5, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 9, 12, ...> n Semigrup: <0, 4, 8, 9, 10, 12, 13, 14, 16, ...> n Semigrup: <0, 8, 9, 10, 12, ...> n Semigrup: <0, 8, 9, 11, ...> n Semigrup: <0, 7, 9, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 7, 8, 9, 10, 12, 14, ...> n Semigrup: <0, 4, 8, 9, 11, 12, 13, 15, ...> n Semigrup: <0, 4, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 9, 10, 12, 14, ...> n Semigrup: <0, 6, 7, 11, ...> n Semigrup: <0, 8, 10, ...> n Semigrup: <0, 6, 8, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 14, ...> n Semigrup: <0, 9, ...> n Semigrup: <0, 3, 6, 9, 12, ...> n Semigrup: <0, 4, 7, 8, 11, 12, 14, ...> n [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156 ] [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 17, 18, 19, 22, 26, 27, 28, 31, 32, 35, 45, 47, 48, 50, 51, 52, 69, 70, 72, 75, 77, 79, 81, 88, 90, 95, 96, 98, 100, 101, 105, 106, 121, 125, 151, 154, 155 ] Total time: 7.529 seconds, Total memory usage: 3.95MB ************** MAGMA ***************** Host ca-rennes-7-184.w80-8.abo.wanadoo.fr. (80.8.187.184) Time: Fri Feb 27 12:45:26 2004 Input: M8:=Matrix(GF(2),28,28); Output: Magma V2.10-6 Fri Feb 27 2004 12:45:23 on modular [Seed = 810545759] ------------------------------------- >> M8:=Matrix(GF(2),28,28); ^ Runtime error in 'Matrix': Bad argument types Argument types given: FldFin, RngIntElt, RngIntElt Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sab-combi-01.uab.es. (158.109.241.123) Time: Fri Feb 27 12:45:56 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=8; MAXLENGTHPATTERNS:=7; Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); /* ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do //print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; admdeg; end for; //[#s: s in ss]; //pp; admdeg; */ p1:=Patterns[16]; l1:=[i: i in [1..l]| admits(Semigrups[i],p1)]; p2:=[1,1,-1]; l2:=[i: i in [1..l]| admits(Semigrups[i],p2)]; l1 eq l2; l1 diff l2; l2 diff l1; Output: Magma V2.10-6 Fri Feb 27 2004 12:45:49 on modular [Seed = 693562168] ------------------------------------- Semigrup: <0, ...> n Semigrup: <0, 2, ...> n Semigrup: <0, 2, 4, ...> n Semigrup: <0, 3, ...> n Semigrup: <0, 2, 4, 6, ...> n Semigrup: <0, 3, 4, 6, ...> n Semigrup: <0, 4, ...> n Semigrup: <0, 3, 5, ...> n Semigrup: <0, 3, 6, ...> n Semigrup: <0, 5, ...> n Semigrup: <0, 2, 4, 6, 8, ...> n Semigrup: <0, 4, 6, ...> n Semigrup: <0, 4, 5, 7, ...> n Semigrup: <0, 3, 5, 6, 8, ...> n Semigrup: <0, 4, 5, 6, 8, ...> n Semigrup: <0, 3, 6, 7, 9, ...> n Semigrup: <0, 3, 6, 8, ...> n Semigrup: <0, 2, 4, 6, 8, 10, ...> n Semigrup: <0, 4, 7, ...> n Semigrup: <0, 5, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, ...> n Semigrup: <0, 4, 6, 8, ...> n Semigrup: <0, 5, 6, 7, 8, 10, ...> n Semigrup: <0, 4, 6, 7, 8, 10, ...> n Semigrup: <0, 5, 6, 8, ...> n Semigrup: <0, 5, 7, ...> n Semigrup: <0, 6, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, ...> n Semigrup: <0, 5, 7, 8, 10, ...> n Semigrup: <0, 3, 6, 7, 9, 10, 12, ...> n Semigrup: <0, 4, 6, 8, 10, ...> n Semigrup: <0, 6, 8, ...> n Semigrup: <0, 5, 6, 8, 10, ...> n Semigrup: <0, 6, 7, 8, 9, 11, ...> n Semigrup: <0, 4, 8, ...> n Semigrup: <0, 5, 6, 9, ...> n Semigrup: <0, 4, 7, 8, 10, ...> n Semigrup: <0, 5, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 4, 7, 8, 9, 11, ...> n Semigrup: <0, 3, 6, 8, 9, 11, ...> n Semigrup: <0, 6, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 7, 10, ...> n Semigrup: <0, 5, 8, ...> n Semigrup: <0, 6, 7, 8, 10, ...> n Semigrup: <0, 7, ...> n Semigrup: <0, 3, 6, 9, ...> n Semigrup: <0, 4, 6, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 7, 9, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, 14, ...> n Semigrup: <0, 8, ...> n Semigrup: <0, 6, 7, 9, 10, 12, ...> n Semigrup: <0, 4, 7, 8, 11, ...> n Semigrup: <0, 6, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 9, 11, ...> n Semigrup: <0, 5, 6, 10, ...> n Semigrup: <0, 5, 7, 8, 10, 12, ...> n Semigrup: <0, 7, 8, 10, ...> n Semigrup: <0, 4, 8, 9, 11, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 5, 7, 9, 10, 12, ...> n Semigrup: <0, 5, 7, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 8, 10, 12, ...> n Semigrup: <0, 4, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 9, 11, ...> n Semigrup: <0, 7, 9, ...> n Semigrup: <0, 6, 9, ...> n Semigrup: <0, 6, 7, 8, 9, 12, ...> n Semigrup: <0, 3, 6, 9, 11, ...> n Semigrup: <0, 4, 6, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 7, 8, 9, 11, ...> n Semigrup: <0, 5, 8, 10, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 9, ...> n Semigrup: <0, 6, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 4, 6, 8, 10, 12, ...> n Semigrup: <0, 5, 7, 10, ...> n Semigrup: <0, 6, 8, 10, ...> n Semigrup: <0, 3, 6, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 10, ...> n Semigrup: <0, 3, 6, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 4, 7, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 8, 11, ...> n Semigrup: <0, 4, 8, 10, ...> n Semigrup: <0, 5, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 7, 10, ...> n Semigrup: <0, 4, 6, 8, 10, 12, 13, 14, 16, ...> n Semigrup: <0, 5, 7, 9, 10, 12, 14, ...> n Semigrup: <0, 6, 8, 11, ...> n Semigrup: <0, 5, 8, 9, 10, 13, ...> n Semigrup: <0, 4, 8, 10, 12, ...> n Semigrup: <0, 6, 9, 11, ...> n Semigrup: <0, 6, 7, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, 14, 16, ...> n Semigrup: <0, 3, 6, 9, 11, 12, 14, ...> n Semigrup: <0, 5, 10, ...> n Semigrup: <0, 7, 9, 11, ...> n Semigrup: <0, 7, 8, 11, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 5, 7, 10, 11, 12, 14, ...> n Semigrup: <0, 4, 6, 8, 10, 12, 14, ...> n Semigrup: <0, 6, 10, ...> n Semigrup: <0, 7, 8, 9, 10, 13, ...> n Semigrup: <0, 4, 8, 9, 12, ...> n Semigrup: <0, 7, 8, 9, 11, 13, ...> n Semigrup: <0, 5, 8, 10, 11, 13, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 7, 8, 10, 12, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 7, 9, 10, 12, ...> n Semigrup: <0, 5, 9, 10, 11, 13, ...> n Semigrup: <0, 6, 8, 9, 12, ...> n Semigrup: <0, 3, 6, 9, 10, 12, 13, 15, ...> n Semigrup: <0, 5, 8, 10, 12, ...> n Semigrup: <0, 7, 8, 9, 12, ...> n Semigrup: <0, 6, 9, 10, 12, ...> n Semigrup: <0, 4, 8, 11, ...> n Semigrup: <0, 7, 8, 10, 11, 13, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 10, 12, ...> n Semigrup: <0, 7, 9, 10, 11, 13, ...> n Semigrup: <0, 6, 9, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 5, 9, 10, 12, ...> n Semigrup: <0, 7, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 8, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 6, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 5, 7, 10, 12, ...> n Semigrup: <0, 7, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 10, 12, ...> n Semigrup: <0, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 7, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 8, 12, ...> n Semigrup: <0, 5, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 9, 12, ...> n Semigrup: <0, 4, 8, 9, 10, 12, 13, 14, 16, ...> n Semigrup: <0, 8, 9, 10, 12, ...> n Semigrup: <0, 8, 9, 11, ...> n Semigrup: <0, 7, 9, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 7, 8, 9, 10, 12, 14, ...> n Semigrup: <0, 4, 8, 9, 11, 12, 13, 15, ...> n Semigrup: <0, 4, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 9, 10, 12, 14, ...> n Semigrup: <0, 6, 7, 11, ...> n Semigrup: <0, 8, 10, ...> n Semigrup: <0, 6, 8, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 14, ...> n Semigrup: <0, 9, ...> n Semigrup: <0, 3, 6, 9, 12, ...> n Semigrup: <0, 4, 7, 8, 11, 12, 14, ...> n false >> l1 diff l2; ^ Runtime error in 'diff': Bad argument types Argument types given: SeqEnum[RngIntElt], SeqEnum[RngIntElt] >> l2 diff l1; ^ Runtime error in 'diff': Bad argument types Argument types given: SeqEnum[RngIntElt], SeqEnum[RngIntElt] Total time: 6.949 seconds, Total memory usage: 3.95MB ************** MAGMA ***************** Host ca-rennes-7-184.w80-8.abo.wanadoo.fr. (80.8.187.184) Time: Fri Feb 27 12:48:11 2004 Input: M8:=Matrix(GF(2),28,28,[0,1,0,0,1,1,1,1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0,0,1,0,1,0,0,1,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0]); Output: Magma V2.10-6 Fri Feb 27 2004 12:48:08 on modular [Seed = 3718389593] ------------------------------------- >> M8:=Matrix(GF(2),28,28,[0,1,0,0,1,1,1,1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,1,1,0,0 ^ Runtime error in 'Matrix': Sequence should have length 784 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ca-rennes-7-184.w80-8.abo.wanadoo.fr. (80.8.187.184) Time: Fri Feb 27 12:48:45 2004 Input: M8:=matrix(GF(2),28,28,[0,1,0,0,1,1,1,1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0,0,1,0,1,0,0,1,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0]); Output: Magma V2.10-6 Fri Feb 27 2004 12:48:42 on modular [Seed = 3601405040] ------------------------------------- >> M8:=matrix(GF(2),28,28,[0,1,0,0,1,1,1,1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,1,1,0,0 ^ User error: Identifier 'matrix' has not been declared or assigned Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ca-rennes-7-184.w80-8.abo.wanadoo.fr. (80.8.187.184) Time: Fri Feb 27 12:50:03 2004 Input: M8:=Matrix[GF(2),28,28]; Output: Magma V2.10-6 Fri Feb 27 2004 12:50:00 on modular [Seed = 3484421339] ------------------------------------- >> M8:=Matrix[GF(2),28,28]; ^ Runtime error in '[]': Bad argument types Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ca-rennes-7-184.w80-8.abo.wanadoo.fr. (80.8.187.184) Time: Fri Feb 27 12:50:18 2004 Input: M8:=Matrix(GF(2),28,28); Output: Magma V2.10-6 Fri Feb 27 2004 12:50:15 on modular [Seed = 4169612275] ------------------------------------- >> M8:=Matrix(GF(2),28,28); ^ Runtime error in 'Matrix': Bad argument types Argument types given: FldFin, RngIntElt, RngIntElt Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ca-rennes-7-184.w80-8.abo.wanadoo.fr. (80.8.187.184) Time: Fri Feb 27 12:50:53 2004 Input: M8:=Matrix(28,28,[0,1,0,0,1,1,1,1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0,0,1,0,1,0,0,1,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0]); Output: Magma V2.10-6 Fri Feb 27 2004 12:50:48 on modular [Seed = 4069339606] ------------------------------------- >> M8:=Matrix(28,28,[0,1,0,0,1,1,1,1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1 ^ Runtime error in 'Matrix': Sequence should have length 784 Total time: 3.209 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sab-combi-01.uab.es. (158.109.241.123) Time: Fri Feb 27 12:53:39 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=4; MAXLENGTHPATTERNS:=4; Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; if Position(ss,semisp) gt NonAdmissibleDegree(p) then break; end if; end for; print p; [#s: s in ss]; pp; admdeg; Output: Magma V2.10-6 Fri Feb 27 2004 12:53:36 on modular [Seed = 2983097805] ------------------------------------- Semigrup: <0, ...> n Semigrup: <0, 2, ...> n Semigrup: <0, 2, 4, ...> n Semigrup: <0, 3, ...> n Semigrup: <0, 2, 4, 6, ...> n Semigrup: <0, 3, 4, 6, ...> n Semigrup: <0, 4, ...> n Semigrup: <0, 3, 5, ...> n Semigrup: <0, 3, 6, ...> n Semigrup: <0, 5, ...> n Semigrup: <0, 2, 4, 6, 8, ...> n Semigrup: <0, 4, 6, ...> n Semigrup: <0, 4, 5, 7, ...> n Semigrup: <0, 3, 5, 6, 8, ...> n Semigrup: <0, 4, 5, 6, 8, ...> n [ 1, -1 ] [ 1, 1, -1 ] [ 1, 1, -1, -1 ] [ 1, -1, 1, -1 ] [ 1, 1, 1, -1 ] >> print p; ^ User error: Identifier 'p' has not been declared or assigned [ 1, 11, 15 ] [ [ [ 1, -1 ], [ 1, 1, -1, -1 ], [ 1, -1, 1, -1 ] ], [ [ 1, 1, -1 ] ], [ [ 1, 1, 1, -1 ] ] ] [ [ 1, 1, 1 ], [ 2 ], [ 3 ] ] Total time: 2.969 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host sab-combi-01.uab.es. (158.109.241.123) Time: Fri Feb 27 12:54:12 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=4; MAXLENGTHPATTERNS:=4; Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; if Position(ss,semisp) gt NonAdmissibleDegree(p) then print "MERDA!"; break; end if; end for; print p; [#s: s in ss]; pp; admdeg; Output: Magma V2.10-6 Fri Feb 27 2004 12:54:09 on modular [Seed = 2866114231] ------------------------------------- Semigrup: <0, ...> n Semigrup: <0, 2, ...> n Semigrup: <0, 2, 4, ...> n Semigrup: <0, 3, ...> n Semigrup: <0, 2, 4, 6, ...> n Semigrup: <0, 3, 4, 6, ...> n Semigrup: <0, 4, ...> n Semigrup: <0, 3, 5, ...> n Semigrup: <0, 3, 6, ...> n Semigrup: <0, 5, ...> n Semigrup: <0, 2, 4, 6, 8, ...> n Semigrup: <0, 4, 6, ...> n Semigrup: <0, 4, 5, 7, ...> n Semigrup: <0, 3, 5, 6, 8, ...> n Semigrup: <0, 4, 5, 6, 8, ...> n [ 1, -1 ] [ 1, 1, -1 ] [ 1, 1, -1, -1 ] [ 1, -1, 1, -1 ] [ 1, 1, 1, -1 ] >> print p; ^ User error: Identifier 'p' has not been declared or assigned [ 1, 11, 15 ] [ [ [ 1, -1 ], [ 1, 1, -1, -1 ], [ 1, -1, 1, -1 ] ], [ [ 1, 1, -1 ] ], [ [ 1, 1, 1, -1 ] ] ] [ [ 1, 1, 1 ], [ 2 ], [ 3 ] ] Total time: 3.059 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host sab-combi-01.uab.es. (158.109.241.123) Time: Fri Feb 27 12:54:42 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=7; MAXLENGTHPATTERNS:=7; Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; if Position(ss,semisp) gt NonAdmissibleDegree(p) then print "MERDA!"; break; end if; end for; print p; [#s: s in ss]; pp; admdeg; Output: Magma V2.10-6 Fri Feb 27 2004 12:54:33 on modular [Seed = 2749130662] ------------------------------------- Semigrup: <0, ...> n Semigrup: <0, 2, ...> n Semigrup: <0, 2, 4, ...> n Semigrup: <0, 3, ...> n Semigrup: <0, 2, 4, 6, ...> n Semigrup: <0, 3, 4, 6, ...> n Semigrup: <0, 4, ...> n Semigrup: <0, 3, 5, ...> n Semigrup: <0, 3, 6, ...> n Semigrup: <0, 5, ...> n Semigrup: <0, 2, 4, 6, 8, ...> n Semigrup: <0, 4, 6, ...> n Semigrup: <0, 4, 5, 7, ...> n Semigrup: <0, 3, 5, 6, 8, ...> n Semigrup: <0, 4, 5, 6, 8, ...> n Semigrup: <0, 3, 6, 7, 9, ...> n Semigrup: <0, 3, 6, 8, ...> n Semigrup: <0, 2, 4, 6, 8, 10, ...> n Semigrup: <0, 4, 7, ...> n Semigrup: <0, 5, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, ...> n Semigrup: <0, 4, 6, 8, ...> n Semigrup: <0, 5, 6, 7, 8, 10, ...> n Semigrup: <0, 4, 6, 7, 8, 10, ...> n Semigrup: <0, 5, 6, 8, ...> n Semigrup: <0, 5, 7, ...> n Semigrup: <0, 6, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, ...> n Semigrup: <0, 5, 7, 8, 10, ...> n Semigrup: <0, 3, 6, 7, 9, 10, 12, ...> n Semigrup: <0, 4, 6, 8, 10, ...> n Semigrup: <0, 6, 8, ...> n Semigrup: <0, 5, 6, 8, 10, ...> n Semigrup: <0, 6, 7, 8, 9, 11, ...> n Semigrup: <0, 4, 8, ...> n Semigrup: <0, 5, 6, 9, ...> n Semigrup: <0, 4, 7, 8, 10, ...> n Semigrup: <0, 5, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 4, 7, 8, 9, 11, ...> n Semigrup: <0, 3, 6, 8, 9, 11, ...> n Semigrup: <0, 6, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 7, 10, ...> n Semigrup: <0, 5, 8, ...> n Semigrup: <0, 6, 7, 8, 10, ...> n Semigrup: <0, 7, ...> n Semigrup: <0, 3, 6, 9, ...> n Semigrup: <0, 4, 6, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 7, 9, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, 14, ...> n Semigrup: <0, 8, ...> n Semigrup: <0, 6, 7, 9, 10, 12, ...> n Semigrup: <0, 4, 7, 8, 11, ...> n Semigrup: <0, 6, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 9, 11, ...> n Semigrup: <0, 5, 6, 10, ...> n Semigrup: <0, 5, 7, 8, 10, 12, ...> n Semigrup: <0, 7, 8, 10, ...> n Semigrup: <0, 4, 8, 9, 11, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 5, 7, 9, 10, 12, ...> n Semigrup: <0, 5, 7, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 8, 10, 12, ...> n Semigrup: <0, 4, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 9, 11, ...> n Semigrup: <0, 7, 9, ...> n Semigrup: <0, 6, 9, ...> n Semigrup: <0, 6, 7, 8, 9, 12, ...> n Semigrup: <0, 3, 6, 9, 11, ...> n Semigrup: <0, 4, 6, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 7, 8, 9, 11, ...> n Semigrup: <0, 5, 8, 10, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 9, ...> n Semigrup: <0, 6, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 4, 6, 8, 10, 12, ...> n Semigrup: <0, 5, 7, 10, ...> n Semigrup: <0, 6, 8, 10, ...> n Semigrup: <0, 3, 6, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 10, ...> n Semigrup: <0, 3, 6, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 4, 7, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 8, 11, ...> n Semigrup: <0, 4, 8, 10, ...> n Semigrup: <0, 5, 8, 9, 10, 11, 13, ...> n [ 1, -1 ] [ 1, 1, -1 ] [ 1, 1, -1, -1 ] [ 1, -1, 1, -1 ] [ 1, 1, 1, -1 ] [ 1, -1, 1, 1, -1 ] [ 1, 1, 1, -1, -1 ] [ 1, 1, 1, 1, -1 ] [ 1, 1, -1, 1, -1 ] [ 1, 1, 1, 1, 1, -1 ] [ 1, 1, 1, -1, -1, -1 ] [ 1, 1, -1, -1, 1, -1 ] [ 1, -1, 1, 1, 1, -1 ] [ 1, 1, -1, 1, -1, -1 ] [ 1, 1, 1, -1, 1, -1 ] [ 1, 1, 1, 1, -1, -1 ] [ 1, 1, -1, 1, 1, -1 ] [ 1, -1, 1, 1, -1, -1 ] [ 1, -1, 1, -1, 1, -1 ] [ 1, 1, 1, -1, 1, -1, -1 ] Current total memory usage: 2.5MB, failed memory request: 16384.0MB System error: Out of memory. All virtual memory has been exhausted so Magma cannot perform this statement. >> print p; ^ User error: Identifier 'p' has not been declared or assigned [ 1, 35, 87, 89 ] [ [ [ 1, -1 ], [ 1, 1, -1, -1 ], [ 1, -1, 1, -1 ], [ 1, -1, 1, 1, -1 ], [ 1, 1, 1, -1, -1, -1 ], [ 1, 1, -1, -1, 1, -1 ], [ 1, -1, 1, 1, 1, -1 ], [ 1, 1, -1, 1, -1, -1 ], [ 1, -1, 1, 1, -1, -1 ], [ 1, -1, 1, -1, 1, -1 ] ], [ [ 1, 1, -1 ], [ 1, 1, 1, -1, -1 ], [ 1, 1, -1, 1, -1 ], [ 1, 1, -1, 1, 1, -1 ] ], [ [ 1, 1, 1, -1 ], [ 1, 1, 1, -1, 1, -1 ], [ 1, 1, 1, 1, -1, -1 ] ], [ [ 1, 1, 1, 1, -1 ], [ 1, 1, 1, 1, 1, -1 ] ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2, 2 ], [ 3, 3, 3 ], [ 4, 5 ] ] Total time: 9.489 seconds, Total memory usage: 2.63MB ************** MAGMA ***************** Host sab-combi-01.uab.es. (158.109.241.123) Time: Fri Feb 27 12:55:20 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=8; MAXLENGTHPATTERNS:=7; Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; if Position(ss,semisp) gt NonAdmissibleDegree(p) then print "MERDA!"; break; end if; end for; print p; [#s: s in ss]; pp; admdeg; Output: Magma V2.10-6 Fri Feb 27 2004 12:55:03 on modular [Seed = 1362007419] ------------------------------------- Semigrup: <0, ...> n Semigrup: <0, 2, ...> n Semigrup: <0, 2, 4, ...> n Semigrup: <0, 3, ...> n Semigrup: <0, 2, 4, 6, ...> n Semigrup: <0, 3, 4, 6, ...> n Semigrup: <0, 4, ...> n Semigrup: <0, 3, 5, ...> n Semigrup: <0, 3, 6, ...> n Semigrup: <0, 5, ...> n Semigrup: <0, 2, 4, 6, 8, ...> n Semigrup: <0, 4, 6, ...> n Semigrup: <0, 4, 5, 7, ...> n Semigrup: <0, 3, 5, 6, 8, ...> n Semigrup: <0, 4, 5, 6, 8, ...> n Semigrup: <0, 3, 6, 7, 9, ...> n Semigrup: <0, 3, 6, 8, ...> n Semigrup: <0, 2, 4, 6, 8, 10, ...> n Semigrup: <0, 4, 7, ...> n Semigrup: <0, 5, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, ...> n Semigrup: <0, 4, 6, 8, ...> n Semigrup: <0, 5, 6, 7, 8, 10, ...> n Semigrup: <0, 4, 6, 7, 8, 10, ...> n Semigrup: <0, 5, 6, 8, ...> n Semigrup: <0, 5, 7, ...> n Semigrup: <0, 6, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, ...> n Semigrup: <0, 5, 7, 8, 10, ...> n Semigrup: <0, 3, 6, 7, 9, 10, 12, ...> n Semigrup: <0, 4, 6, 8, 10, ...> n Semigrup: <0, 6, 8, ...> n Semigrup: <0, 5, 6, 8, 10, ...> n Semigrup: <0, 6, 7, 8, 9, 11, ...> n Semigrup: <0, 4, 8, ...> n Semigrup: <0, 5, 6, 9, ...> n Semigrup: <0, 4, 7, 8, 10, ...> n Semigrup: <0, 5, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 4, 7, 8, 9, 11, ...> n Semigrup: <0, 3, 6, 8, 9, 11, ...> n Semigrup: <0, 6, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 7, 10, ...> n Semigrup: <0, 5, 8, ...> n Semigrup: <0, 6, 7, 8, 10, ...> n Semigrup: <0, 7, ...> n Semigrup: <0, 3, 6, 9, ...> n Semigrup: <0, 4, 6, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 7, 9, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, 14, ...> n Semigrup: <0, 8, ...> n Semigrup: <0, 6, 7, 9, 10, 12, ...> n Semigrup: <0, 4, 7, 8, 11, ...> n Semigrup: <0, 6, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 9, 11, ...> n Semigrup: <0, 5, 6, 10, ...> n Semigrup: <0, 5, 7, 8, 10, 12, ...> n Semigrup: <0, 7, 8, 10, ...> n Semigrup: <0, 4, 8, 9, 11, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 5, 7, 9, 10, 12, ...> n Semigrup: <0, 5, 7, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 8, 10, 12, ...> n Semigrup: <0, 4, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 9, 11, ...> n Semigrup: <0, 7, 9, ...> n Semigrup: <0, 6, 9, ...> n Semigrup: <0, 6, 7, 8, 9, 12, ...> n Semigrup: <0, 3, 6, 9, 11, ...> n Semigrup: <0, 4, 6, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 7, 8, 9, 11, ...> n Semigrup: <0, 5, 8, 10, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 9, ...> n Semigrup: <0, 6, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 4, 6, 8, 10, 12, ...> n Semigrup: <0, 5, 7, 10, ...> n Semigrup: <0, 6, 8, 10, ...> n Semigrup: <0, 3, 6, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 10, ...> n Semigrup: <0, 3, 6, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 4, 7, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 8, 11, ...> n Semigrup: <0, 4, 8, 10, ...> n Semigrup: <0, 5, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 7, 10, ...> n Semigrup: <0, 4, 6, 8, 10, 12, 13, 14, 16, ...> n Semigrup: <0, 5, 7, 9, 10, 12, 14, ...> n Semigrup: <0, 6, 8, 11, ...> n Semigrup: <0, 5, 8, 9, 10, 13, ...> n Semigrup: <0, 4, 8, 10, 12, ...> n Semigrup: <0, 6, 9, 11, ...> n Semigrup: <0, 6, 7, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, 14, 16, ...> n Semigrup: <0, 3, 6, 9, 11, 12, 14, ...> n Semigrup: <0, 5, 10, ...> n Semigrup: <0, 7, 9, 11, ...> n Semigrup: <0, 7, 8, 11, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 5, 7, 10, 11, 12, 14, ...> n Semigrup: <0, 4, 6, 8, 10, 12, 14, ...> n Semigrup: <0, 6, 10, ...> n Semigrup: <0, 7, 8, 9, 10, 13, ...> n Semigrup: <0, 4, 8, 9, 12, ...> n Semigrup: <0, 7, 8, 9, 11, 13, ...> n Semigrup: <0, 5, 8, 10, 11, 13, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 7, 8, 10, 12, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 7, 9, 10, 12, ...> n Semigrup: <0, 5, 9, 10, 11, 13, ...> n Semigrup: <0, 6, 8, 9, 12, ...> n Semigrup: <0, 3, 6, 9, 10, 12, 13, 15, ...> n Semigrup: <0, 5, 8, 10, 12, ...> n Semigrup: <0, 7, 8, 9, 12, ...> n Semigrup: <0, 6, 9, 10, 12, ...> n Semigrup: <0, 4, 8, 11, ...> n Semigrup: <0, 7, 8, 10, 11, 13, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 10, 12, ...> n Semigrup: <0, 7, 9, 10, 11, 13, ...> n Semigrup: <0, 6, 9, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 5, 9, 10, 12, ...> n Semigrup: <0, 7, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 8, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 6, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 5, 7, 10, 12, ...> n Semigrup: <0, 7, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 10, 12, ...> n Semigrup: <0, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 7, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 8, 12, ...> n Semigrup: <0, 5, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 9, 12, ...> n Semigrup: <0, 4, 8, 9, 10, 12, 13, 14, 16, ...> n Semigrup: <0, 8, 9, 10, 12, ...> n Semigrup: <0, 8, 9, 11, ...> n Semigrup: <0, 7, 9, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 7, 8, 9, 10, 12, 14, ...> n Semigrup: <0, 4, 8, 9, 11, 12, 13, 15, ...> n Semigrup: <0, 4, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 9, 10, 12, 14, ...> n Semigrup: <0, 6, 7, 11, ...> n Semigrup: <0, 8, 10, ...> n Semigrup: <0, 6, 8, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 14, ...> n Semigrup: <0, 9, ...> n Semigrup: <0, 3, 6, 9, 12, ...> n Semigrup: <0, 4, 7, 8, 11, 12, 14, ...> n [ 1, -1 ] [ 1, 1, -1 ] [ 1, 1, -1, -1 ] [ 1, -1, 1, -1 ] [ 1, 1, 1, -1 ] [ 1, -1, 1, 1, -1 ] [ 1, 1, 1, -1, -1 ] [ 1, 1, 1, 1, -1 ] [ 1, 1, -1, 1, -1 ] [ 1, 1, 1, 1, 1, -1 ] [ 1, 1, 1, -1, -1, -1 ] [ 1, 1, -1, -1, 1, -1 ] [ 1, -1, 1, 1, 1, -1 ] [ 1, 1, -1, 1, -1, -1 ] [ 1, 1, 1, -1, 1, -1 ] [ 1, 1, 1, 1, -1, -1 ] MERDA! >> print p; ^ User error: Identifier 'p' has not been declared or assigned [ 1, 48, 152, 156, 151 ] [ [ [ 1, -1 ], [ 1, 1, -1, -1 ], [ 1, -1, 1, -1 ], [ 1, -1, 1, 1, -1 ], [ 1, 1, 1, -1, -1, -1 ], [ 1, 1, -1, -1, 1, -1 ], [ 1, -1, 1, 1, 1, -1 ], [ 1, 1, -1, 1, -1, -1 ] ], [ [ 1, 1, -1 ], [ 1, 1, 1, -1, -1 ], [ 1, 1, -1, 1, -1 ] ], [ [ 1, 1, 1, -1 ], [ 1, 1, 1, -1, 1, -1 ] ], [ [ 1, 1, 1, 1, -1 ], [ 1, 1, 1, 1, 1, -1 ] ], [ [ 1, 1, 1, 1, -1, -1 ] ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3, 3 ], [ 4, 5 ], [ 3 ] ] Total time: 17.039 seconds, Total memory usage: 3.95MB ************** MAGMA ***************** Host sab-combi-01.uab.es. (158.109.241.123) Time: Fri Feb 27 12:57:26 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=8; MAXLENGTHPATTERNS:=7; Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do //print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; if Position(ss,semisp) gt NonAdmissibleDegree(p) then admdeg; print "MERDA!"; break; end if; admdeg; end for; //print p; //[#s: s in ss]; //pp; //admdeg; Output: Magma V2.10-6 Fri Feb 27 2004 12:57:08 on modular [Seed = 1261735906] ------------------------------------- Semigrup: <0, ...> n Semigrup: <0, 2, ...> n Semigrup: <0, 2, 4, ...> n Semigrup: <0, 3, ...> n Semigrup: <0, 2, 4, 6, ...> n Semigrup: <0, 3, 4, 6, ...> n Semigrup: <0, 4, ...> n Semigrup: <0, 3, 5, ...> n Semigrup: <0, 3, 6, ...> n Semigrup: <0, 5, ...> n Semigrup: <0, 2, 4, 6, 8, ...> n Semigrup: <0, 4, 6, ...> n Semigrup: <0, 4, 5, 7, ...> n Semigrup: <0, 3, 5, 6, 8, ...> n Semigrup: <0, 4, 5, 6, 8, ...> n Semigrup: <0, 3, 6, 7, 9, ...> n Semigrup: <0, 3, 6, 8, ...> n Semigrup: <0, 2, 4, 6, 8, 10, ...> n Semigrup: <0, 4, 7, ...> n Semigrup: <0, 5, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, ...> n Semigrup: <0, 4, 6, 8, ...> n Semigrup: <0, 5, 6, 7, 8, 10, ...> n Semigrup: <0, 4, 6, 7, 8, 10, ...> n Semigrup: <0, 5, 6, 8, ...> n Semigrup: <0, 5, 7, ...> n Semigrup: <0, 6, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, ...> n Semigrup: <0, 5, 7, 8, 10, ...> n Semigrup: <0, 3, 6, 7, 9, 10, 12, ...> n Semigrup: <0, 4, 6, 8, 10, ...> n Semigrup: <0, 6, 8, ...> n Semigrup: <0, 5, 6, 8, 10, ...> n Semigrup: <0, 6, 7, 8, 9, 11, ...> n Semigrup: <0, 4, 8, ...> n Semigrup: <0, 5, 6, 9, ...> n Semigrup: <0, 4, 7, 8, 10, ...> n Semigrup: <0, 5, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 4, 7, 8, 9, 11, ...> n Semigrup: <0, 3, 6, 8, 9, 11, ...> n Semigrup: <0, 6, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 7, 10, ...> n Semigrup: <0, 5, 8, ...> n Semigrup: <0, 6, 7, 8, 10, ...> n Semigrup: <0, 7, ...> n Semigrup: <0, 3, 6, 9, ...> n Semigrup: <0, 4, 6, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 7, 9, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, 14, ...> n Semigrup: <0, 8, ...> n Semigrup: <0, 6, 7, 9, 10, 12, ...> n Semigrup: <0, 4, 7, 8, 11, ...> n Semigrup: <0, 6, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 9, 11, ...> n Semigrup: <0, 5, 6, 10, ...> n Semigrup: <0, 5, 7, 8, 10, 12, ...> n Semigrup: <0, 7, 8, 10, ...> n Semigrup: <0, 4, 8, 9, 11, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 5, 7, 9, 10, 12, ...> n Semigrup: <0, 5, 7, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 8, 10, 12, ...> n Semigrup: <0, 4, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 9, 11, ...> n Semigrup: <0, 7, 9, ...> n Semigrup: <0, 6, 9, ...> n Semigrup: <0, 6, 7, 8, 9, 12, ...> n Semigrup: <0, 3, 6, 9, 11, ...> n Semigrup: <0, 4, 6, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 7, 8, 9, 11, ...> n Semigrup: <0, 5, 8, 10, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 9, ...> n Semigrup: <0, 6, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 4, 6, 8, 10, 12, ...> n Semigrup: <0, 5, 7, 10, ...> n Semigrup: <0, 6, 8, 10, ...> n Semigrup: <0, 3, 6, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 10, ...> n Semigrup: <0, 3, 6, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 4, 7, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 8, 11, ...> n Semigrup: <0, 4, 8, 10, ...> n Semigrup: <0, 5, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 7, 10, ...> n Semigrup: <0, 4, 6, 8, 10, 12, 13, 14, 16, ...> n Semigrup: <0, 5, 7, 9, 10, 12, 14, ...> n Semigrup: <0, 6, 8, 11, ...> n Semigrup: <0, 5, 8, 9, 10, 13, ...> n Semigrup: <0, 4, 8, 10, 12, ...> n Semigrup: <0, 6, 9, 11, ...> n Semigrup: <0, 6, 7, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, 14, 16, ...> n Semigrup: <0, 3, 6, 9, 11, 12, 14, ...> n Semigrup: <0, 5, 10, ...> n Semigrup: <0, 7, 9, 11, ...> n Semigrup: <0, 7, 8, 11, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 5, 7, 10, 11, 12, 14, ...> n Semigrup: <0, 4, 6, 8, 10, 12, 14, ...> n Semigrup: <0, 6, 10, ...> n Semigrup: <0, 7, 8, 9, 10, 13, ...> n Semigrup: <0, 4, 8, 9, 12, ...> n Semigrup: <0, 7, 8, 9, 11, 13, ...> n Semigrup: <0, 5, 8, 10, 11, 13, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 7, 8, 10, 12, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 7, 9, 10, 12, ...> n Semigrup: <0, 5, 9, 10, 11, 13, ...> n Semigrup: <0, 6, 8, 9, 12, ...> n Semigrup: <0, 3, 6, 9, 10, 12, 13, 15, ...> n Semigrup: <0, 5, 8, 10, 12, ...> n Semigrup: <0, 7, 8, 9, 12, ...> n Semigrup: <0, 6, 9, 10, 12, ...> n Semigrup: <0, 4, 8, 11, ...> n Semigrup: <0, 7, 8, 10, 11, 13, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 10, 12, ...> n Semigrup: <0, 7, 9, 10, 11, 13, ...> n Semigrup: <0, 6, 9, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 5, 9, 10, 12, ...> n Semigrup: <0, 7, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 8, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 6, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 5, 7, 10, 12, ...> n Semigrup: <0, 7, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 10, 12, ...> n Semigrup: <0, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 7, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 8, 12, ...> n Semigrup: <0, 5, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 9, 12, ...> n Semigrup: <0, 4, 8, 9, 10, 12, 13, 14, 16, ...> n Semigrup: <0, 8, 9, 10, 12, ...> n Semigrup: <0, 8, 9, 11, ...> n Semigrup: <0, 7, 9, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 7, 8, 9, 10, 12, 14, ...> n Semigrup: <0, 4, 8, 9, 11, 12, 13, 15, ...> n Semigrup: <0, 4, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 9, 10, 12, 14, ...> n Semigrup: <0, 6, 7, 11, ...> n Semigrup: <0, 8, 10, ...> n Semigrup: <0, 6, 8, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 14, ...> n Semigrup: <0, 9, ...> n Semigrup: <0, 3, 6, 9, 12, ...> n Semigrup: <0, 4, 7, 8, 11, 12, 14, ...> n [ [ 1 ] ] [ [ 1 ], [ 2 ] ] [ [ 1, 1 ], [ 2 ] ] [ [ 1, 1, 1 ], [ 2 ] ] [ [ 1, 1, 1 ], [ 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2 ], [ 3 ], [ 4 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3, 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3, 3 ], [ 4, 5 ], [ 3 ] ] MERDA! Total time: 17.139 seconds, Total memory usage: 3.95MB ************** MAGMA ***************** Host sab-combi-01.uab.es. (158.109.241.123) Time: Fri Feb 27 12:58:08 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=8; MAXLENGTHPATTERNS:=7; Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do //print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; if Position(ss,semisp) gt NonAdmissibleDegree(p) then admdeg; print "MERDA!"; print p; break; end if; admdeg; end for; //print p; //[#s: s in ss]; //pp; //admdeg; Output: Magma V2.10-6 Fri Feb 27 2004 12:57:50 on modular [Seed = 2097330238] ------------------------------------- Semigrup: <0, ...> n Semigrup: <0, 2, ...> n Semigrup: <0, 2, 4, ...> n Semigrup: <0, 3, ...> n Semigrup: <0, 2, 4, 6, ...> n Semigrup: <0, 3, 4, 6, ...> n Semigrup: <0, 4, ...> n Semigrup: <0, 3, 5, ...> n Semigrup: <0, 3, 6, ...> n Semigrup: <0, 5, ...> n Semigrup: <0, 2, 4, 6, 8, ...> n Semigrup: <0, 4, 6, ...> n Semigrup: <0, 4, 5, 7, ...> n Semigrup: <0, 3, 5, 6, 8, ...> n Semigrup: <0, 4, 5, 6, 8, ...> n Semigrup: <0, 3, 6, 7, 9, ...> n Semigrup: <0, 3, 6, 8, ...> n Semigrup: <0, 2, 4, 6, 8, 10, ...> n Semigrup: <0, 4, 7, ...> n Semigrup: <0, 5, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, ...> n Semigrup: <0, 4, 6, 8, ...> n Semigrup: <0, 5, 6, 7, 8, 10, ...> n Semigrup: <0, 4, 6, 7, 8, 10, ...> n Semigrup: <0, 5, 6, 8, ...> n Semigrup: <0, 5, 7, ...> n Semigrup: <0, 6, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, ...> n Semigrup: <0, 5, 7, 8, 10, ...> n Semigrup: <0, 3, 6, 7, 9, 10, 12, ...> n Semigrup: <0, 4, 6, 8, 10, ...> n Semigrup: <0, 6, 8, ...> n Semigrup: <0, 5, 6, 8, 10, ...> n Semigrup: <0, 6, 7, 8, 9, 11, ...> n Semigrup: <0, 4, 8, ...> n Semigrup: <0, 5, 6, 9, ...> n Semigrup: <0, 4, 7, 8, 10, ...> n Semigrup: <0, 5, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 4, 7, 8, 9, 11, ...> n Semigrup: <0, 3, 6, 8, 9, 11, ...> n Semigrup: <0, 6, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 7, 10, ...> n Semigrup: <0, 5, 8, ...> n Semigrup: <0, 6, 7, 8, 10, ...> n Semigrup: <0, 7, ...> n Semigrup: <0, 3, 6, 9, ...> n Semigrup: <0, 4, 6, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 7, 9, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, 14, ...> n Semigrup: <0, 8, ...> n Semigrup: <0, 6, 7, 9, 10, 12, ...> n Semigrup: <0, 4, 7, 8, 11, ...> n Semigrup: <0, 6, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 9, 11, ...> n Semigrup: <0, 5, 6, 10, ...> n Semigrup: <0, 5, 7, 8, 10, 12, ...> n Semigrup: <0, 7, 8, 10, ...> n Semigrup: <0, 4, 8, 9, 11, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 5, 7, 9, 10, 12, ...> n Semigrup: <0, 5, 7, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 8, 10, 12, ...> n Semigrup: <0, 4, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 9, 11, ...> n Semigrup: <0, 7, 9, ...> n Semigrup: <0, 6, 9, ...> n Semigrup: <0, 6, 7, 8, 9, 12, ...> n Semigrup: <0, 3, 6, 9, 11, ...> n Semigrup: <0, 4, 6, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 7, 8, 9, 11, ...> n Semigrup: <0, 5, 8, 10, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 9, ...> n Semigrup: <0, 6, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 4, 6, 8, 10, 12, ...> n Semigrup: <0, 5, 7, 10, ...> n Semigrup: <0, 6, 8, 10, ...> n Semigrup: <0, 3, 6, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 10, ...> n Semigrup: <0, 3, 6, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 4, 7, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 8, 11, ...> n Semigrup: <0, 4, 8, 10, ...> n Semigrup: <0, 5, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 7, 10, ...> n Semigrup: <0, 4, 6, 8, 10, 12, 13, 14, 16, ...> n Semigrup: <0, 5, 7, 9, 10, 12, 14, ...> n Semigrup: <0, 6, 8, 11, ...> n Semigrup: <0, 5, 8, 9, 10, 13, ...> n Semigrup: <0, 4, 8, 10, 12, ...> n Semigrup: <0, 6, 9, 11, ...> n Semigrup: <0, 6, 7, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, 14, 16, ...> n Semigrup: <0, 3, 6, 9, 11, 12, 14, ...> n Semigrup: <0, 5, 10, ...> n Semigrup: <0, 7, 9, 11, ...> n Semigrup: <0, 7, 8, 11, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 5, 7, 10, 11, 12, 14, ...> n Semigrup: <0, 4, 6, 8, 10, 12, 14, ...> n Semigrup: <0, 6, 10, ...> n Semigrup: <0, 7, 8, 9, 10, 13, ...> n Semigrup: <0, 4, 8, 9, 12, ...> n Semigrup: <0, 7, 8, 9, 11, 13, ...> n Semigrup: <0, 5, 8, 10, 11, 13, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 7, 8, 10, 12, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 7, 9, 10, 12, ...> n Semigrup: <0, 5, 9, 10, 11, 13, ...> n Semigrup: <0, 6, 8, 9, 12, ...> n Semigrup: <0, 3, 6, 9, 10, 12, 13, 15, ...> n Semigrup: <0, 5, 8, 10, 12, ...> n Semigrup: <0, 7, 8, 9, 12, ...> n Semigrup: <0, 6, 9, 10, 12, ...> n Semigrup: <0, 4, 8, 11, ...> n Semigrup: <0, 7, 8, 10, 11, 13, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 10, 12, ...> n Semigrup: <0, 7, 9, 10, 11, 13, ...> n Semigrup: <0, 6, 9, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 5, 9, 10, 12, ...> n Semigrup: <0, 7, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 8, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 6, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 5, 7, 10, 12, ...> n Semigrup: <0, 7, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 10, 12, ...> n Semigrup: <0, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 7, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 8, 12, ...> n Semigrup: <0, 5, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 9, 12, ...> n Semigrup: <0, 4, 8, 9, 10, 12, 13, 14, 16, ...> n Semigrup: <0, 8, 9, 10, 12, ...> n Semigrup: <0, 8, 9, 11, ...> n Semigrup: <0, 7, 9, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 7, 8, 9, 10, 12, 14, ...> n Semigrup: <0, 4, 8, 9, 11, 12, 13, 15, ...> n Semigrup: <0, 4, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 9, 10, 12, 14, ...> n Semigrup: <0, 6, 7, 11, ...> n Semigrup: <0, 8, 10, ...> n Semigrup: <0, 6, 8, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 14, ...> n Semigrup: <0, 9, ...> n Semigrup: <0, 3, 6, 9, 12, ...> n Semigrup: <0, 4, 7, 8, 11, 12, 14, ...> n [ [ 1 ] ] [ [ 1 ], [ 2 ] ] [ [ 1, 1 ], [ 2 ] ] [ [ 1, 1, 1 ], [ 2 ] ] [ [ 1, 1, 1 ], [ 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2 ], [ 3 ], [ 4 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3, 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3, 3 ], [ 4, 5 ], [ 3 ] ] MERDA! [ 1, 1, 1, 1, -1, -1 ] Total time: 17.289 seconds, Total memory usage: 3.95MB ************** MAGMA ***************** Host sab-combi-01.uab.es. (158.109.241.123) Time: Fri Feb 27 12:59:00 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=8; MAXLENGTHPATTERNS:=7; Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do //print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; if Position(ss,semisp) gt NonAdmissibleDegree(p) then admdeg; print "MERDA!"; print p; break; end if; admdeg; end for; //print p; [#s: s in ss]; //pp; //admdeg; Output: Magma V2.10-6 Fri Feb 27 2004 12:58:43 on modular [Seed = 1997058681] ------------------------------------- Semigrup: <0, ...> n Semigrup: <0, 2, ...> n Semigrup: <0, 2, 4, ...> n Semigrup: <0, 3, ...> n Semigrup: <0, 2, 4, 6, ...> n Semigrup: <0, 3, 4, 6, ...> n Semigrup: <0, 4, ...> n Semigrup: <0, 3, 5, ...> n Semigrup: <0, 3, 6, ...> n Semigrup: <0, 5, ...> n Semigrup: <0, 2, 4, 6, 8, ...> n Semigrup: <0, 4, 6, ...> n Semigrup: <0, 4, 5, 7, ...> n Semigrup: <0, 3, 5, 6, 8, ...> n Semigrup: <0, 4, 5, 6, 8, ...> n Semigrup: <0, 3, 6, 7, 9, ...> n Semigrup: <0, 3, 6, 8, ...> n Semigrup: <0, 2, 4, 6, 8, 10, ...> n Semigrup: <0, 4, 7, ...> n Semigrup: <0, 5, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, ...> n Semigrup: <0, 4, 6, 8, ...> n Semigrup: <0, 5, 6, 7, 8, 10, ...> n Semigrup: <0, 4, 6, 7, 8, 10, ...> n Semigrup: <0, 5, 6, 8, ...> n Semigrup: <0, 5, 7, ...> n Semigrup: <0, 6, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, ...> n Semigrup: <0, 5, 7, 8, 10, ...> n Semigrup: <0, 3, 6, 7, 9, 10, 12, ...> n Semigrup: <0, 4, 6, 8, 10, ...> n Semigrup: <0, 6, 8, ...> n Semigrup: <0, 5, 6, 8, 10, ...> n Semigrup: <0, 6, 7, 8, 9, 11, ...> n Semigrup: <0, 4, 8, ...> n Semigrup: <0, 5, 6, 9, ...> n Semigrup: <0, 4, 7, 8, 10, ...> n Semigrup: <0, 5, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 4, 7, 8, 9, 11, ...> n Semigrup: <0, 3, 6, 8, 9, 11, ...> n Semigrup: <0, 6, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 7, 10, ...> n Semigrup: <0, 5, 8, ...> n Semigrup: <0, 6, 7, 8, 10, ...> n Semigrup: <0, 7, ...> n Semigrup: <0, 3, 6, 9, ...> n Semigrup: <0, 4, 6, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 7, 9, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, 14, ...> n Semigrup: <0, 8, ...> n Semigrup: <0, 6, 7, 9, 10, 12, ...> n Semigrup: <0, 4, 7, 8, 11, ...> n Semigrup: <0, 6, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 9, 11, ...> n Semigrup: <0, 5, 6, 10, ...> n Semigrup: <0, 5, 7, 8, 10, 12, ...> n Semigrup: <0, 7, 8, 10, ...> n Semigrup: <0, 4, 8, 9, 11, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 5, 7, 9, 10, 12, ...> n Semigrup: <0, 5, 7, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 8, 10, 12, ...> n Semigrup: <0, 4, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 9, 11, ...> n Semigrup: <0, 7, 9, ...> n Semigrup: <0, 6, 9, ...> n Semigrup: <0, 6, 7, 8, 9, 12, ...> n Semigrup: <0, 3, 6, 9, 11, ...> n Semigrup: <0, 4, 6, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 7, 8, 9, 11, ...> n Semigrup: <0, 5, 8, 10, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 9, ...> n Semigrup: <0, 6, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 4, 6, 8, 10, 12, ...> n Semigrup: <0, 5, 7, 10, ...> n Semigrup: <0, 6, 8, 10, ...> n Semigrup: <0, 3, 6, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 10, ...> n Semigrup: <0, 3, 6, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 4, 7, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 8, 11, ...> n Semigrup: <0, 4, 8, 10, ...> n Semigrup: <0, 5, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 7, 10, ...> n Semigrup: <0, 4, 6, 8, 10, 12, 13, 14, 16, ...> n Semigrup: <0, 5, 7, 9, 10, 12, 14, ...> n Semigrup: <0, 6, 8, 11, ...> n Semigrup: <0, 5, 8, 9, 10, 13, ...> n Semigrup: <0, 4, 8, 10, 12, ...> n Semigrup: <0, 6, 9, 11, ...> n Semigrup: <0, 6, 7, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, 14, 16, ...> n Semigrup: <0, 3, 6, 9, 11, 12, 14, ...> n Semigrup: <0, 5, 10, ...> n Semigrup: <0, 7, 9, 11, ...> n Semigrup: <0, 7, 8, 11, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 5, 7, 10, 11, 12, 14, ...> n Semigrup: <0, 4, 6, 8, 10, 12, 14, ...> n Semigrup: <0, 6, 10, ...> n Semigrup: <0, 7, 8, 9, 10, 13, ...> n Semigrup: <0, 4, 8, 9, 12, ...> n Semigrup: <0, 7, 8, 9, 11, 13, ...> n Semigrup: <0, 5, 8, 10, 11, 13, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 7, 8, 10, 12, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 7, 9, 10, 12, ...> n Semigrup: <0, 5, 9, 10, 11, 13, ...> n Semigrup: <0, 6, 8, 9, 12, ...> n Semigrup: <0, 3, 6, 9, 10, 12, 13, 15, ...> n Semigrup: <0, 5, 8, 10, 12, ...> n Semigrup: <0, 7, 8, 9, 12, ...> n Semigrup: <0, 6, 9, 10, 12, ...> n Semigrup: <0, 4, 8, 11, ...> n Semigrup: <0, 7, 8, 10, 11, 13, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 10, 12, ...> n Semigrup: <0, 7, 9, 10, 11, 13, ...> n Semigrup: <0, 6, 9, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 5, 9, 10, 12, ...> n Semigrup: <0, 7, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 8, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 6, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 5, 7, 10, 12, ...> n Semigrup: <0, 7, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 10, 12, ...> n Semigrup: <0, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 7, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 8, 12, ...> n Semigrup: <0, 5, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 9, 12, ...> n Semigrup: <0, 4, 8, 9, 10, 12, 13, 14, 16, ...> n Semigrup: <0, 8, 9, 10, 12, ...> n Semigrup: <0, 8, 9, 11, ...> n Semigrup: <0, 7, 9, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 7, 8, 9, 10, 12, 14, ...> n Semigrup: <0, 4, 8, 9, 11, 12, 13, 15, ...> n Semigrup: <0, 4, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 9, 10, 12, 14, ...> n Semigrup: <0, 6, 7, 11, ...> n Semigrup: <0, 8, 10, ...> n Semigrup: <0, 6, 8, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 14, ...> n Semigrup: <0, 9, ...> n Semigrup: <0, 3, 6, 9, 12, ...> n Semigrup: <0, 4, 7, 8, 11, 12, 14, ...> n [ [ 1 ] ] [ [ 1 ], [ 2 ] ] [ [ 1, 1 ], [ 2 ] ] [ [ 1, 1, 1 ], [ 2 ] ] [ [ 1, 1, 1 ], [ 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2 ], [ 3 ], [ 4 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3, 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3, 3 ], [ 4, 5 ], [ 3 ] ] MERDA! [ 1, 1, 1, 1, -1, -1 ] [ 1, 48, 152, 156, 151 ] Total time: 17.170 seconds, Total memory usage: 3.95MB ************** MAGMA ***************** Host sab-combi-01.uab.es. (158.109.241.123) Time: Fri Feb 27 13:00:39 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=8; MAXLENGTHPATTERNS:=7; Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do //print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; if Position(ss,semisp) gt NonAdmissibleDegree(p) then admdeg; print "MERDA!"; print p; break; end if; admdeg; end for; //print p; [#s: s in ss]; ss[3] diff ss[5]; //pp; //admdeg; Output: Magma V2.10-6 Fri Feb 27 2004 13:00:22 on modular [Seed = 1712956301] ------------------------------------- Semigrup: <0, ...> n Semigrup: <0, 2, ...> n Semigrup: <0, 2, 4, ...> n Semigrup: <0, 3, ...> n Semigrup: <0, 2, 4, 6, ...> n Semigrup: <0, 3, 4, 6, ...> n Semigrup: <0, 4, ...> n Semigrup: <0, 3, 5, ...> n Semigrup: <0, 3, 6, ...> n Semigrup: <0, 5, ...> n Semigrup: <0, 2, 4, 6, 8, ...> n Semigrup: <0, 4, 6, ...> n Semigrup: <0, 4, 5, 7, ...> n Semigrup: <0, 3, 5, 6, 8, ...> n Semigrup: <0, 4, 5, 6, 8, ...> n Semigrup: <0, 3, 6, 7, 9, ...> n Semigrup: <0, 3, 6, 8, ...> n Semigrup: <0, 2, 4, 6, 8, 10, ...> n Semigrup: <0, 4, 7, ...> n Semigrup: <0, 5, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, ...> n Semigrup: <0, 4, 6, 8, ...> n Semigrup: <0, 5, 6, 7, 8, 10, ...> n Semigrup: <0, 4, 6, 7, 8, 10, ...> n Semigrup: <0, 5, 6, 8, ...> n Semigrup: <0, 5, 7, ...> n Semigrup: <0, 6, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, ...> n Semigrup: <0, 5, 7, 8, 10, ...> n Semigrup: <0, 3, 6, 7, 9, 10, 12, ...> n Semigrup: <0, 4, 6, 8, 10, ...> n Semigrup: <0, 6, 8, ...> n Semigrup: <0, 5, 6, 8, 10, ...> n Semigrup: <0, 6, 7, 8, 9, 11, ...> n Semigrup: <0, 4, 8, ...> n Semigrup: <0, 5, 6, 9, ...> n Semigrup: <0, 4, 7, 8, 10, ...> n Semigrup: <0, 5, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 4, 7, 8, 9, 11, ...> n Semigrup: <0, 3, 6, 8, 9, 11, ...> n Semigrup: <0, 6, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 7, 10, ...> n Semigrup: <0, 5, 8, ...> n Semigrup: <0, 6, 7, 8, 10, ...> n Semigrup: <0, 7, ...> n Semigrup: <0, 3, 6, 9, ...> n Semigrup: <0, 4, 6, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 7, 9, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, 14, ...> n Semigrup: <0, 8, ...> n Semigrup: <0, 6, 7, 9, 10, 12, ...> n Semigrup: <0, 4, 7, 8, 11, ...> n Semigrup: <0, 6, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 9, 11, ...> n Semigrup: <0, 5, 6, 10, ...> n Semigrup: <0, 5, 7, 8, 10, 12, ...> n Semigrup: <0, 7, 8, 10, ...> n Semigrup: <0, 4, 8, 9, 11, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 5, 7, 9, 10, 12, ...> n Semigrup: <0, 5, 7, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 8, 10, 12, ...> n Semigrup: <0, 4, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 9, 11, ...> n Semigrup: <0, 7, 9, ...> n Semigrup: <0, 6, 9, ...> n Semigrup: <0, 6, 7, 8, 9, 12, ...> n Semigrup: <0, 3, 6, 9, 11, ...> n Semigrup: <0, 4, 6, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 7, 8, 9, 11, ...> n Semigrup: <0, 5, 8, 10, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 9, ...> n Semigrup: <0, 6, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 4, 6, 8, 10, 12, ...> n Semigrup: <0, 5, 7, 10, ...> n Semigrup: <0, 6, 8, 10, ...> n Semigrup: <0, 3, 6, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 10, ...> n Semigrup: <0, 3, 6, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 4, 7, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 8, 11, ...> n Semigrup: <0, 4, 8, 10, ...> n Semigrup: <0, 5, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 7, 10, ...> n Semigrup: <0, 4, 6, 8, 10, 12, 13, 14, 16, ...> n Semigrup: <0, 5, 7, 9, 10, 12, 14, ...> n Semigrup: <0, 6, 8, 11, ...> n Semigrup: <0, 5, 8, 9, 10, 13, ...> n Semigrup: <0, 4, 8, 10, 12, ...> n Semigrup: <0, 6, 9, 11, ...> n Semigrup: <0, 6, 7, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, 14, 16, ...> n Semigrup: <0, 3, 6, 9, 11, 12, 14, ...> n Semigrup: <0, 5, 10, ...> n Semigrup: <0, 7, 9, 11, ...> n Semigrup: <0, 7, 8, 11, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 5, 7, 10, 11, 12, 14, ...> n Semigrup: <0, 4, 6, 8, 10, 12, 14, ...> n Semigrup: <0, 6, 10, ...> n Semigrup: <0, 7, 8, 9, 10, 13, ...> n Semigrup: <0, 4, 8, 9, 12, ...> n Semigrup: <0, 7, 8, 9, 11, 13, ...> n Semigrup: <0, 5, 8, 10, 11, 13, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 7, 8, 10, 12, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 7, 9, 10, 12, ...> n Semigrup: <0, 5, 9, 10, 11, 13, ...> n Semigrup: <0, 6, 8, 9, 12, ...> n Semigrup: <0, 3, 6, 9, 10, 12, 13, 15, ...> n Semigrup: <0, 5, 8, 10, 12, ...> n Semigrup: <0, 7, 8, 9, 12, ...> n Semigrup: <0, 6, 9, 10, 12, ...> n Semigrup: <0, 4, 8, 11, ...> n Semigrup: <0, 7, 8, 10, 11, 13, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 10, 12, ...> n Semigrup: <0, 7, 9, 10, 11, 13, ...> n Semigrup: <0, 6, 9, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 5, 9, 10, 12, ...> n Semigrup: <0, 7, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 8, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 6, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 5, 7, 10, 12, ...> n Semigrup: <0, 7, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 10, 12, ...> n Semigrup: <0, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 7, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 8, 12, ...> n Semigrup: <0, 5, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 9, 12, ...> n Semigrup: <0, 4, 8, 9, 10, 12, 13, 14, 16, ...> n Semigrup: <0, 8, 9, 10, 12, ...> n Semigrup: <0, 8, 9, 11, ...> n Semigrup: <0, 7, 9, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 7, 8, 9, 10, 12, 14, ...> n Semigrup: <0, 4, 8, 9, 11, 12, 13, 15, ...> n Semigrup: <0, 4, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 9, 10, 12, 14, ...> n Semigrup: <0, 6, 7, 11, ...> n Semigrup: <0, 8, 10, ...> n Semigrup: <0, 6, 8, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 14, ...> n Semigrup: <0, 9, ...> n Semigrup: <0, 3, 6, 9, 12, ...> n Semigrup: <0, 4, 7, 8, 11, 12, 14, ...> n [ [ 1 ] ] [ [ 1 ], [ 2 ] ] [ [ 1, 1 ], [ 2 ] ] [ [ 1, 1, 1 ], [ 2 ] ] [ [ 1, 1, 1 ], [ 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2 ], [ 3 ], [ 4 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3, 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3, 3 ], [ 4, 5 ], [ 3 ] ] MERDA! [ 1, 1, 1, 1, -1, -1 ] [ 1, 48, 152, 156, 151 ] >> ss[3] diff ss[5]; ^ Runtime error in 'diff': Bad argument types Argument types given: SeqEnum[RngIntElt], SeqEnum[RngIntElt] Total time: 17.369 seconds, Total memory usage: 3.95MB ************** MAGMA ***************** Host sab-combi-01.uab.es. (158.109.241.123) Time: Fri Feb 27 13:01:45 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=8; MAXLENGTHPATTERNS:=7; Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do //print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; if Position(ss,semisp) gt NonAdmissibleDegree(p) then admdeg; print "MERDA!"; print p; break; end if; admdeg; end for; //print p; [#s: s in ss]; [s: s in ss[3]| s notin ss[5]; //pp; //admdeg; Output: Magma V2.10-6 Fri Feb 27 2004 13:01:27 on modular [Seed = 944242066] ------------------------------------- Semigrup: <0, ...> n Semigrup: <0, 2, ...> n Semigrup: <0, 2, 4, ...> n Semigrup: <0, 3, ...> n Semigrup: <0, 2, 4, 6, ...> n Semigrup: <0, 3, 4, 6, ...> n Semigrup: <0, 4, ...> n Semigrup: <0, 3, 5, ...> n Semigrup: <0, 3, 6, ...> n Semigrup: <0, 5, ...> n Semigrup: <0, 2, 4, 6, 8, ...> n Semigrup: <0, 4, 6, ...> n Semigrup: <0, 4, 5, 7, ...> n Semigrup: <0, 3, 5, 6, 8, ...> n Semigrup: <0, 4, 5, 6, 8, ...> n Semigrup: <0, 3, 6, 7, 9, ...> n Semigrup: <0, 3, 6, 8, ...> n Semigrup: <0, 2, 4, 6, 8, 10, ...> n Semigrup: <0, 4, 7, ...> n Semigrup: <0, 5, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, ...> n Semigrup: <0, 4, 6, 8, ...> n Semigrup: <0, 5, 6, 7, 8, 10, ...> n Semigrup: <0, 4, 6, 7, 8, 10, ...> n Semigrup: <0, 5, 6, 8, ...> n Semigrup: <0, 5, 7, ...> n Semigrup: <0, 6, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, ...> n Semigrup: <0, 5, 7, 8, 10, ...> n Semigrup: <0, 3, 6, 7, 9, 10, 12, ...> n Semigrup: <0, 4, 6, 8, 10, ...> n Semigrup: <0, 6, 8, ...> n Semigrup: <0, 5, 6, 8, 10, ...> n Semigrup: <0, 6, 7, 8, 9, 11, ...> n Semigrup: <0, 4, 8, ...> n Semigrup: <0, 5, 6, 9, ...> n Semigrup: <0, 4, 7, 8, 10, ...> n Semigrup: <0, 5, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 4, 7, 8, 9, 11, ...> n Semigrup: <0, 3, 6, 8, 9, 11, ...> n Semigrup: <0, 6, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 7, 10, ...> n Semigrup: <0, 5, 8, ...> n Semigrup: <0, 6, 7, 8, 10, ...> n Semigrup: <0, 7, ...> n Semigrup: <0, 3, 6, 9, ...> n Semigrup: <0, 4, 6, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 7, 9, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, 14, ...> n Semigrup: <0, 8, ...> n Semigrup: <0, 6, 7, 9, 10, 12, ...> n Semigrup: <0, 4, 7, 8, 11, ...> n Semigrup: <0, 6, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 9, 11, ...> n Semigrup: <0, 5, 6, 10, ...> n Semigrup: <0, 5, 7, 8, 10, 12, ...> n Semigrup: <0, 7, 8, 10, ...> n Semigrup: <0, 4, 8, 9, 11, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 5, 7, 9, 10, 12, ...> n Semigrup: <0, 5, 7, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 8, 10, 12, ...> n Semigrup: <0, 4, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 9, 11, ...> n Semigrup: <0, 7, 9, ...> n Semigrup: <0, 6, 9, ...> n Semigrup: <0, 6, 7, 8, 9, 12, ...> n Semigrup: <0, 3, 6, 9, 11, ...> n Semigrup: <0, 4, 6, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 7, 8, 9, 11, ...> n Semigrup: <0, 5, 8, 10, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 9, ...> n Semigrup: <0, 6, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 4, 6, 8, 10, 12, ...> n Semigrup: <0, 5, 7, 10, ...> n Semigrup: <0, 6, 8, 10, ...> n Semigrup: <0, 3, 6, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 10, ...> n Semigrup: <0, 3, 6, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 4, 7, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 8, 11, ...> n Semigrup: <0, 4, 8, 10, ...> n Semigrup: <0, 5, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 7, 10, ...> n Semigrup: <0, 4, 6, 8, 10, 12, 13, 14, 16, ...> n Semigrup: <0, 5, 7, 9, 10, 12, 14, ...> n Semigrup: <0, 6, 8, 11, ...> n Semigrup: <0, 5, 8, 9, 10, 13, ...> n Semigrup: <0, 4, 8, 10, 12, ...> n Semigrup: <0, 6, 9, 11, ...> n Semigrup: <0, 6, 7, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, 14, 16, ...> n Semigrup: <0, 3, 6, 9, 11, 12, 14, ...> n Semigrup: <0, 5, 10, ...> n Semigrup: <0, 7, 9, 11, ...> n Semigrup: <0, 7, 8, 11, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 5, 7, 10, 11, 12, 14, ...> n Semigrup: <0, 4, 6, 8, 10, 12, 14, ...> n Semigrup: <0, 6, 10, ...> n Semigrup: <0, 7, 8, 9, 10, 13, ...> n Semigrup: <0, 4, 8, 9, 12, ...> n Semigrup: <0, 7, 8, 9, 11, 13, ...> n Semigrup: <0, 5, 8, 10, 11, 13, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 7, 8, 10, 12, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 7, 9, 10, 12, ...> n Semigrup: <0, 5, 9, 10, 11, 13, ...> n Semigrup: <0, 6, 8, 9, 12, ...> n Semigrup: <0, 3, 6, 9, 10, 12, 13, 15, ...> n Semigrup: <0, 5, 8, 10, 12, ...> n Semigrup: <0, 7, 8, 9, 12, ...> n Semigrup: <0, 6, 9, 10, 12, ...> n Semigrup: <0, 4, 8, 11, ...> n Semigrup: <0, 7, 8, 10, 11, 13, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 10, 12, ...> n Semigrup: <0, 7, 9, 10, 11, 13, ...> n Semigrup: <0, 6, 9, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 5, 9, 10, 12, ...> n Semigrup: <0, 7, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 8, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 6, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 5, 7, 10, 12, ...> n Semigrup: <0, 7, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 10, 12, ...> n Semigrup: <0, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 7, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 8, 12, ...> n Semigrup: <0, 5, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 9, 12, ...> n Semigrup: <0, 4, 8, 9, 10, 12, 13, 14, 16, ...> n Semigrup: <0, 8, 9, 10, 12, ...> n Semigrup: <0, 8, 9, 11, ...> n Semigrup: <0, 7, 9, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 7, 8, 9, 10, 12, 14, ...> n Semigrup: <0, 4, 8, 9, 11, 12, 13, 15, ...> n Semigrup: <0, 4, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 9, 10, 12, 14, ...> n Semigrup: <0, 6, 7, 11, ...> n Semigrup: <0, 8, 10, ...> n Semigrup: <0, 6, 8, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 14, ...> n Semigrup: <0, 9, ...> n Semigrup: <0, 3, 6, 9, 12, ...> n Semigrup: <0, 4, 7, 8, 11, 12, 14, ...> n [ [ 1 ] ] [ [ 1 ], [ 2 ] ] [ [ 1, 1 ], [ 2 ] ] [ [ 1, 1, 1 ], [ 2 ] ] [ [ 1, 1, 1 ], [ 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2 ], [ 3 ], [ 4 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3, 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3, 3 ], [ 4, 5 ], [ 3 ] ] MERDA! [ 1, 1, 1, 1, -1, -1 ] [ 1, 48, 152, 156, 151 ] >> [s: s in ss[3]| s notin ss[5]; ^ User error: bad syntax Total time: 17.359 seconds, Total memory usage: 3.95MB ************** MAGMA ***************** Host sab-combi-01.uab.es. (158.109.241.123) Time: Fri Feb 27 13:02:14 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=8; MAXLENGTHPATTERNS:=7; Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do //print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; if Position(ss,semisp) gt NonAdmissibleDegree(p) then admdeg; print "MERDA!"; print p; break; end if; admdeg; end for; //print p; [#s: s in ss]; [s: s in ss[3]| s notin ss[5]]; //pp; //admdeg; Output: Magma V2.10-6 Fri Feb 27 2004 13:01:57 on modular [Seed = 860681595] ------------------------------------- Semigrup: <0, ...> n Semigrup: <0, 2, ...> n Semigrup: <0, 2, 4, ...> n Semigrup: <0, 3, ...> n Semigrup: <0, 2, 4, 6, ...> n Semigrup: <0, 3, 4, 6, ...> n Semigrup: <0, 4, ...> n Semigrup: <0, 3, 5, ...> n Semigrup: <0, 3, 6, ...> n Semigrup: <0, 5, ...> n Semigrup: <0, 2, 4, 6, 8, ...> n Semigrup: <0, 4, 6, ...> n Semigrup: <0, 4, 5, 7, ...> n Semigrup: <0, 3, 5, 6, 8, ...> n Semigrup: <0, 4, 5, 6, 8, ...> n Semigrup: <0, 3, 6, 7, 9, ...> n Semigrup: <0, 3, 6, 8, ...> n Semigrup: <0, 2, 4, 6, 8, 10, ...> n Semigrup: <0, 4, 7, ...> n Semigrup: <0, 5, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, ...> n Semigrup: <0, 4, 6, 8, ...> n Semigrup: <0, 5, 6, 7, 8, 10, ...> n Semigrup: <0, 4, 6, 7, 8, 10, ...> n Semigrup: <0, 5, 6, 8, ...> n Semigrup: <0, 5, 7, ...> n Semigrup: <0, 6, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, ...> n Semigrup: <0, 5, 7, 8, 10, ...> n Semigrup: <0, 3, 6, 7, 9, 10, 12, ...> n Semigrup: <0, 4, 6, 8, 10, ...> n Semigrup: <0, 6, 8, ...> n Semigrup: <0, 5, 6, 8, 10, ...> n Semigrup: <0, 6, 7, 8, 9, 11, ...> n Semigrup: <0, 4, 8, ...> n Semigrup: <0, 5, 6, 9, ...> n Semigrup: <0, 4, 7, 8, 10, ...> n Semigrup: <0, 5, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 4, 7, 8, 9, 11, ...> n Semigrup: <0, 3, 6, 8, 9, 11, ...> n Semigrup: <0, 6, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 7, 10, ...> n Semigrup: <0, 5, 8, ...> n Semigrup: <0, 6, 7, 8, 10, ...> n Semigrup: <0, 7, ...> n Semigrup: <0, 3, 6, 9, ...> n Semigrup: <0, 4, 6, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 7, 9, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, 14, ...> n Semigrup: <0, 8, ...> n Semigrup: <0, 6, 7, 9, 10, 12, ...> n Semigrup: <0, 4, 7, 8, 11, ...> n Semigrup: <0, 6, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 9, 11, ...> n Semigrup: <0, 5, 6, 10, ...> n Semigrup: <0, 5, 7, 8, 10, 12, ...> n Semigrup: <0, 7, 8, 10, ...> n Semigrup: <0, 4, 8, 9, 11, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 5, 7, 9, 10, 12, ...> n Semigrup: <0, 5, 7, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 8, 10, 12, ...> n Semigrup: <0, 4, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 9, 11, ...> n Semigrup: <0, 7, 9, ...> n Semigrup: <0, 6, 9, ...> n Semigrup: <0, 6, 7, 8, 9, 12, ...> n Semigrup: <0, 3, 6, 9, 11, ...> n Semigrup: <0, 4, 6, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 7, 8, 9, 11, ...> n Semigrup: <0, 5, 8, 10, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 9, ...> n Semigrup: <0, 6, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 4, 6, 8, 10, 12, ...> n Semigrup: <0, 5, 7, 10, ...> n Semigrup: <0, 6, 8, 10, ...> n Semigrup: <0, 3, 6, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 10, ...> n Semigrup: <0, 3, 6, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 4, 7, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 8, 11, ...> n Semigrup: <0, 4, 8, 10, ...> n Semigrup: <0, 5, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 7, 10, ...> n Semigrup: <0, 4, 6, 8, 10, 12, 13, 14, 16, ...> n Semigrup: <0, 5, 7, 9, 10, 12, 14, ...> n Semigrup: <0, 6, 8, 11, ...> n Semigrup: <0, 5, 8, 9, 10, 13, ...> n Semigrup: <0, 4, 8, 10, 12, ...> n Semigrup: <0, 6, 9, 11, ...> n Semigrup: <0, 6, 7, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, 14, 16, ...> n Semigrup: <0, 3, 6, 9, 11, 12, 14, ...> n Semigrup: <0, 5, 10, ...> n Semigrup: <0, 7, 9, 11, ...> n Semigrup: <0, 7, 8, 11, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 5, 7, 10, 11, 12, 14, ...> n Semigrup: <0, 4, 6, 8, 10, 12, 14, ...> n Semigrup: <0, 6, 10, ...> n Semigrup: <0, 7, 8, 9, 10, 13, ...> n Semigrup: <0, 4, 8, 9, 12, ...> n Semigrup: <0, 7, 8, 9, 11, 13, ...> n Semigrup: <0, 5, 8, 10, 11, 13, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 7, 8, 10, 12, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 7, 9, 10, 12, ...> n Semigrup: <0, 5, 9, 10, 11, 13, ...> n Semigrup: <0, 6, 8, 9, 12, ...> n Semigrup: <0, 3, 6, 9, 10, 12, 13, 15, ...> n Semigrup: <0, 5, 8, 10, 12, ...> n Semigrup: <0, 7, 8, 9, 12, ...> n Semigrup: <0, 6, 9, 10, 12, ...> n Semigrup: <0, 4, 8, 11, ...> n Semigrup: <0, 7, 8, 10, 11, 13, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 10, 12, ...> n Semigrup: <0, 7, 9, 10, 11, 13, ...> n Semigrup: <0, 6, 9, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 5, 9, 10, 12, ...> n Semigrup: <0, 7, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 8, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 6, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 5, 7, 10, 12, ...> n Semigrup: <0, 7, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 10, 12, ...> n Semigrup: <0, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 7, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 8, 12, ...> n Semigrup: <0, 5, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 9, 12, ...> n Semigrup: <0, 4, 8, 9, 10, 12, 13, 14, 16, ...> n Semigrup: <0, 8, 9, 10, 12, ...> n Semigrup: <0, 8, 9, 11, ...> n Semigrup: <0, 7, 9, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 7, 8, 9, 10, 12, 14, ...> n Semigrup: <0, 4, 8, 9, 11, 12, 13, 15, ...> n Semigrup: <0, 4, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 9, 10, 12, 14, ...> n Semigrup: <0, 6, 7, 11, ...> n Semigrup: <0, 8, 10, ...> n Semigrup: <0, 6, 8, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 14, ...> n Semigrup: <0, 9, ...> n Semigrup: <0, 3, 6, 9, 12, ...> n Semigrup: <0, 4, 7, 8, 11, 12, 14, ...> n [ [ 1 ] ] [ [ 1 ], [ 2 ] ] [ [ 1, 1 ], [ 2 ] ] [ [ 1, 1, 1 ], [ 2 ] ] [ [ 1, 1, 1 ], [ 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2 ], [ 3 ], [ 4 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3, 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3, 3 ], [ 4, 5 ], [ 3 ] ] MERDA! [ 1, 1, 1, 1, -1, -1 ] [ 1, 48, 152, 156, 151 ] [ 113 ] Total time: 17.010 seconds, Total memory usage: 3.95MB ************** MAGMA ***************** Host sab-combi-01.uab.es. (158.109.241.123) Time: Fri Feb 27 13:02:56 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=8; MAXLENGTHPATTERNS:=7; Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do //print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; if Position(ss,semisp) gt NonAdmissibleDegree(p) then admdeg; print "MERDA!"; print p; break; end if; admdeg; end for; //print p; [#s: s in ss]; [Semigroups[s]: s in ss[3]| s notin ss[5]]; //pp; //admdeg; Output: Magma V2.10-6 Fri Feb 27 2004 13:02:39 on modular [Seed = 626713415] ------------------------------------- Semigrup: <0, ...> n Semigrup: <0, 2, ...> n Semigrup: <0, 2, 4, ...> n Semigrup: <0, 3, ...> n Semigrup: <0, 2, 4, 6, ...> n Semigrup: <0, 3, 4, 6, ...> n Semigrup: <0, 4, ...> n Semigrup: <0, 3, 5, ...> n Semigrup: <0, 3, 6, ...> n Semigrup: <0, 5, ...> n Semigrup: <0, 2, 4, 6, 8, ...> n Semigrup: <0, 4, 6, ...> n Semigrup: <0, 4, 5, 7, ...> n Semigrup: <0, 3, 5, 6, 8, ...> n Semigrup: <0, 4, 5, 6, 8, ...> n Semigrup: <0, 3, 6, 7, 9, ...> n Semigrup: <0, 3, 6, 8, ...> n Semigrup: <0, 2, 4, 6, 8, 10, ...> n Semigrup: <0, 4, 7, ...> n Semigrup: <0, 5, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, ...> n Semigrup: <0, 4, 6, 8, ...> n Semigrup: <0, 5, 6, 7, 8, 10, ...> n Semigrup: <0, 4, 6, 7, 8, 10, ...> n Semigrup: <0, 5, 6, 8, ...> n Semigrup: <0, 5, 7, ...> n Semigrup: <0, 6, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, ...> n Semigrup: <0, 5, 7, 8, 10, ...> n Semigrup: <0, 3, 6, 7, 9, 10, 12, ...> n Semigrup: <0, 4, 6, 8, 10, ...> n Semigrup: <0, 6, 8, ...> n Semigrup: <0, 5, 6, 8, 10, ...> n Semigrup: <0, 6, 7, 8, 9, 11, ...> n Semigrup: <0, 4, 8, ...> n Semigrup: <0, 5, 6, 9, ...> n Semigrup: <0, 4, 7, 8, 10, ...> n Semigrup: <0, 5, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 4, 7, 8, 9, 11, ...> n Semigrup: <0, 3, 6, 8, 9, 11, ...> n Semigrup: <0, 6, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 7, 10, ...> n Semigrup: <0, 5, 8, ...> n Semigrup: <0, 6, 7, 8, 10, ...> n Semigrup: <0, 7, ...> n Semigrup: <0, 3, 6, 9, ...> n Semigrup: <0, 4, 6, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 7, 9, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, 14, ...> n Semigrup: <0, 8, ...> n Semigrup: <0, 6, 7, 9, 10, 12, ...> n Semigrup: <0, 4, 7, 8, 11, ...> n Semigrup: <0, 6, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 9, 11, ...> n Semigrup: <0, 5, 6, 10, ...> n Semigrup: <0, 5, 7, 8, 10, 12, ...> n Semigrup: <0, 7, 8, 10, ...> n Semigrup: <0, 4, 8, 9, 11, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 5, 7, 9, 10, 12, ...> n Semigrup: <0, 5, 7, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 8, 10, 12, ...> n Semigrup: <0, 4, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 9, 11, ...> n Semigrup: <0, 7, 9, ...> n Semigrup: <0, 6, 9, ...> n Semigrup: <0, 6, 7, 8, 9, 12, ...> n Semigrup: <0, 3, 6, 9, 11, ...> n Semigrup: <0, 4, 6, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 7, 8, 9, 11, ...> n Semigrup: <0, 5, 8, 10, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 9, ...> n Semigrup: <0, 6, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 4, 6, 8, 10, 12, ...> n Semigrup: <0, 5, 7, 10, ...> n Semigrup: <0, 6, 8, 10, ...> n Semigrup: <0, 3, 6, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 10, ...> n Semigrup: <0, 3, 6, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 4, 7, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 8, 11, ...> n Semigrup: <0, 4, 8, 10, ...> n Semigrup: <0, 5, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 7, 10, ...> n Semigrup: <0, 4, 6, 8, 10, 12, 13, 14, 16, ...> n Semigrup: <0, 5, 7, 9, 10, 12, 14, ...> n Semigrup: <0, 6, 8, 11, ...> n Semigrup: <0, 5, 8, 9, 10, 13, ...> n Semigrup: <0, 4, 8, 10, 12, ...> n Semigrup: <0, 6, 9, 11, ...> n Semigrup: <0, 6, 7, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, 14, 16, ...> n Semigrup: <0, 3, 6, 9, 11, 12, 14, ...> n Semigrup: <0, 5, 10, ...> n Semigrup: <0, 7, 9, 11, ...> n Semigrup: <0, 7, 8, 11, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 5, 7, 10, 11, 12, 14, ...> n Semigrup: <0, 4, 6, 8, 10, 12, 14, ...> n Semigrup: <0, 6, 10, ...> n Semigrup: <0, 7, 8, 9, 10, 13, ...> n Semigrup: <0, 4, 8, 9, 12, ...> n Semigrup: <0, 7, 8, 9, 11, 13, ...> n Semigrup: <0, 5, 8, 10, 11, 13, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 7, 8, 10, 12, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 7, 9, 10, 12, ...> n Semigrup: <0, 5, 9, 10, 11, 13, ...> n Semigrup: <0, 6, 8, 9, 12, ...> n Semigrup: <0, 3, 6, 9, 10, 12, 13, 15, ...> n Semigrup: <0, 5, 8, 10, 12, ...> n Semigrup: <0, 7, 8, 9, 12, ...> n Semigrup: <0, 6, 9, 10, 12, ...> n Semigrup: <0, 4, 8, 11, ...> n Semigrup: <0, 7, 8, 10, 11, 13, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 10, 12, ...> n Semigrup: <0, 7, 9, 10, 11, 13, ...> n Semigrup: <0, 6, 9, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 5, 9, 10, 12, ...> n Semigrup: <0, 7, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 8, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 6, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 5, 7, 10, 12, ...> n Semigrup: <0, 7, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 10, 12, ...> n Semigrup: <0, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 7, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 8, 12, ...> n Semigrup: <0, 5, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 9, 12, ...> n Semigrup: <0, 4, 8, 9, 10, 12, 13, 14, 16, ...> n Semigrup: <0, 8, 9, 10, 12, ...> n Semigrup: <0, 8, 9, 11, ...> n Semigrup: <0, 7, 9, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 7, 8, 9, 10, 12, 14, ...> n Semigrup: <0, 4, 8, 9, 11, 12, 13, 15, ...> n Semigrup: <0, 4, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 9, 10, 12, 14, ...> n Semigrup: <0, 6, 7, 11, ...> n Semigrup: <0, 8, 10, ...> n Semigrup: <0, 6, 8, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 14, ...> n Semigrup: <0, 9, ...> n Semigrup: <0, 3, 6, 9, 12, ...> n Semigrup: <0, 4, 7, 8, 11, 12, 14, ...> n [ [ 1 ] ] [ [ 1 ], [ 2 ] ] [ [ 1, 1 ], [ 2 ] ] [ [ 1, 1, 1 ], [ 2 ] ] [ [ 1, 1, 1 ], [ 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2 ], [ 3 ], [ 4 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3, 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3, 3 ], [ 4, 5 ], [ 3 ] ] MERDA! [ 1, 1, 1, 1, -1, -1 ] [ 1, 48, 152, 156, 151 ] >> [Semigroups[s]: s in ss[3]| s notin ss[5]]; ^ User error: Identifier 'Semigroups' has not been declared or assigned Total time: 17.109 seconds, Total memory usage: 3.95MB ************** MAGMA ***************** Host sab-combi-01.uab.es. (158.109.241.123) Time: Fri Feb 27 13:03:39 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=8; MAXLENGTHPATTERNS:=7; Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do //print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; if Position(ss,semisp) gt NonAdmissibleDegree(p) then admdeg; print "MERDA!"; print p; break; end if; admdeg; end for; //print p; [#s: s in ss]; [Semigrups[s]: s in ss[3]| s notin ss[5]]; //pp; //admdeg; Output: Magma V2.10-6 Fri Feb 27 2004 13:03:22 on modular [Seed = 3701676779] ------------------------------------- Semigrup: <0, ...> n Semigrup: <0, 2, ...> n Semigrup: <0, 2, 4, ...> n Semigrup: <0, 3, ...> n Semigrup: <0, 2, 4, 6, ...> n Semigrup: <0, 3, 4, 6, ...> n Semigrup: <0, 4, ...> n Semigrup: <0, 3, 5, ...> n Semigrup: <0, 3, 6, ...> n Semigrup: <0, 5, ...> n Semigrup: <0, 2, 4, 6, 8, ...> n Semigrup: <0, 4, 6, ...> n Semigrup: <0, 4, 5, 7, ...> n Semigrup: <0, 3, 5, 6, 8, ...> n Semigrup: <0, 4, 5, 6, 8, ...> n Semigrup: <0, 3, 6, 7, 9, ...> n Semigrup: <0, 3, 6, 8, ...> n Semigrup: <0, 2, 4, 6, 8, 10, ...> n Semigrup: <0, 4, 7, ...> n Semigrup: <0, 5, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, ...> n Semigrup: <0, 4, 6, 8, ...> n Semigrup: <0, 5, 6, 7, 8, 10, ...> n Semigrup: <0, 4, 6, 7, 8, 10, ...> n Semigrup: <0, 5, 6, 8, ...> n Semigrup: <0, 5, 7, ...> n Semigrup: <0, 6, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, ...> n Semigrup: <0, 5, 7, 8, 10, ...> n Semigrup: <0, 3, 6, 7, 9, 10, 12, ...> n Semigrup: <0, 4, 6, 8, 10, ...> n Semigrup: <0, 6, 8, ...> n Semigrup: <0, 5, 6, 8, 10, ...> n Semigrup: <0, 6, 7, 8, 9, 11, ...> n Semigrup: <0, 4, 8, ...> n Semigrup: <0, 5, 6, 9, ...> n Semigrup: <0, 4, 7, 8, 10, ...> n Semigrup: <0, 5, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 4, 7, 8, 9, 11, ...> n Semigrup: <0, 3, 6, 8, 9, 11, ...> n Semigrup: <0, 6, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 7, 10, ...> n Semigrup: <0, 5, 8, ...> n Semigrup: <0, 6, 7, 8, 10, ...> n Semigrup: <0, 7, ...> n Semigrup: <0, 3, 6, 9, ...> n Semigrup: <0, 4, 6, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 7, 9, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, 14, ...> n Semigrup: <0, 8, ...> n Semigrup: <0, 6, 7, 9, 10, 12, ...> n Semigrup: <0, 4, 7, 8, 11, ...> n Semigrup: <0, 6, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 9, 11, ...> n Semigrup: <0, 5, 6, 10, ...> n Semigrup: <0, 5, 7, 8, 10, 12, ...> n Semigrup: <0, 7, 8, 10, ...> n Semigrup: <0, 4, 8, 9, 11, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 5, 7, 9, 10, 12, ...> n Semigrup: <0, 5, 7, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 8, 10, 12, ...> n Semigrup: <0, 4, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 9, 11, ...> n Semigrup: <0, 7, 9, ...> n Semigrup: <0, 6, 9, ...> n Semigrup: <0, 6, 7, 8, 9, 12, ...> n Semigrup: <0, 3, 6, 9, 11, ...> n Semigrup: <0, 4, 6, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 7, 8, 9, 11, ...> n Semigrup: <0, 5, 8, 10, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 9, ...> n Semigrup: <0, 6, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 4, 6, 8, 10, 12, ...> n Semigrup: <0, 5, 7, 10, ...> n Semigrup: <0, 6, 8, 10, ...> n Semigrup: <0, 3, 6, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 10, ...> n Semigrup: <0, 3, 6, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 4, 7, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 8, 11, ...> n Semigrup: <0, 4, 8, 10, ...> n Semigrup: <0, 5, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 7, 10, ...> n Semigrup: <0, 4, 6, 8, 10, 12, 13, 14, 16, ...> n Semigrup: <0, 5, 7, 9, 10, 12, 14, ...> n Semigrup: <0, 6, 8, 11, ...> n Semigrup: <0, 5, 8, 9, 10, 13, ...> n Semigrup: <0, 4, 8, 10, 12, ...> n Semigrup: <0, 6, 9, 11, ...> n Semigrup: <0, 6, 7, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, 14, 16, ...> n Semigrup: <0, 3, 6, 9, 11, 12, 14, ...> n Semigrup: <0, 5, 10, ...> n Semigrup: <0, 7, 9, 11, ...> n Semigrup: <0, 7, 8, 11, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 5, 7, 10, 11, 12, 14, ...> n Semigrup: <0, 4, 6, 8, 10, 12, 14, ...> n Semigrup: <0, 6, 10, ...> n Semigrup: <0, 7, 8, 9, 10, 13, ...> n Semigrup: <0, 4, 8, 9, 12, ...> n Semigrup: <0, 7, 8, 9, 11, 13, ...> n Semigrup: <0, 5, 8, 10, 11, 13, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 7, 8, 10, 12, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 7, 9, 10, 12, ...> n Semigrup: <0, 5, 9, 10, 11, 13, ...> n Semigrup: <0, 6, 8, 9, 12, ...> n Semigrup: <0, 3, 6, 9, 10, 12, 13, 15, ...> n Semigrup: <0, 5, 8, 10, 12, ...> n Semigrup: <0, 7, 8, 9, 12, ...> n Semigrup: <0, 6, 9, 10, 12, ...> n Semigrup: <0, 4, 8, 11, ...> n Semigrup: <0, 7, 8, 10, 11, 13, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 10, 12, ...> n Semigrup: <0, 7, 9, 10, 11, 13, ...> n Semigrup: <0, 6, 9, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 5, 9, 10, 12, ...> n Semigrup: <0, 7, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 8, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 6, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 5, 7, 10, 12, ...> n Semigrup: <0, 7, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 10, 12, ...> n Semigrup: <0, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 7, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 8, 12, ...> n Semigrup: <0, 5, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 9, 12, ...> n Semigrup: <0, 4, 8, 9, 10, 12, 13, 14, 16, ...> n Semigrup: <0, 8, 9, 10, 12, ...> n Semigrup: <0, 8, 9, 11, ...> n Semigrup: <0, 7, 9, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 7, 8, 9, 10, 12, 14, ...> n Semigrup: <0, 4, 8, 9, 11, 12, 13, 15, ...> n Semigrup: <0, 4, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 9, 10, 12, 14, ...> n Semigrup: <0, 6, 7, 11, ...> n Semigrup: <0, 8, 10, ...> n Semigrup: <0, 6, 8, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 14, ...> n Semigrup: <0, 9, ...> n Semigrup: <0, 3, 6, 9, 12, ...> n Semigrup: <0, 4, 7, 8, 11, 12, 14, ...> n [ [ 1 ] ] [ [ 1 ], [ 2 ] ] [ [ 1, 1 ], [ 2 ] ] [ [ 1, 1, 1 ], [ 2 ] ] [ [ 1, 1, 1 ], [ 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2 ], [ 3 ], [ 4 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3, 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3, 3 ], [ 4, 5 ], [ 3 ] ] MERDA! [ 1, 1, 1, 1, -1, -1 ] [ 1, 48, 152, 156, 151 ] [ <[ 0, 5, 6, 10, 11, 12, 13, 15 ], 7, 15, 8, function(i) ... end function, [ 1, 2, 3, 4, 7, 8, 9, 14 ], function(i) ... end function, function(i) ... end function, function(i, j) ... end function, function(i, j) ... end function, function(j, i) ... end function, function(i) ... end function, function(i) ... end function, function(i) ... end function, 13, 10, 6> ] Total time: 17.100 seconds, Total memory usage: 3.95MB ************** MAGMA ***************** Host sab-combi-01.uab.es. (158.109.241.123) Time: Fri Feb 27 13:06:48 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=8; MAXLENGTHPATTERNS:=7; Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do //print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; if Position(ss,semisp) gt NonAdmissibleDegree(p) then admdeg; print "MERDA!"; print p; break; end if; admdeg; end for; //print p; [#s: s in ss]; ontafalles:=[Semigrups[s]: s in ss[3]| s notin ss[5]]; //pp; //admdeg; s:=ontafalles[1]; admits(s,p); Output: Magma V2.10-6 Fri Feb 27 2004 13:06:31 on modular [Seed = 4236458886] ------------------------------------- Semigrup: <0, ...> n Semigrup: <0, 2, ...> n Semigrup: <0, 2, 4, ...> n Semigrup: <0, 3, ...> n Semigrup: <0, 2, 4, 6, ...> n Semigrup: <0, 3, 4, 6, ...> n Semigrup: <0, 4, ...> n Semigrup: <0, 3, 5, ...> n Semigrup: <0, 3, 6, ...> n Semigrup: <0, 5, ...> n Semigrup: <0, 2, 4, 6, 8, ...> n Semigrup: <0, 4, 6, ...> n Semigrup: <0, 4, 5, 7, ...> n Semigrup: <0, 3, 5, 6, 8, ...> n Semigrup: <0, 4, 5, 6, 8, ...> n Semigrup: <0, 3, 6, 7, 9, ...> n Semigrup: <0, 3, 6, 8, ...> n Semigrup: <0, 2, 4, 6, 8, 10, ...> n Semigrup: <0, 4, 7, ...> n Semigrup: <0, 5, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, ...> n Semigrup: <0, 4, 6, 8, ...> n Semigrup: <0, 5, 6, 7, 8, 10, ...> n Semigrup: <0, 4, 6, 7, 8, 10, ...> n Semigrup: <0, 5, 6, 8, ...> n Semigrup: <0, 5, 7, ...> n Semigrup: <0, 6, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, ...> n Semigrup: <0, 5, 7, 8, 10, ...> n Semigrup: <0, 3, 6, 7, 9, 10, 12, ...> n Semigrup: <0, 4, 6, 8, 10, ...> n Semigrup: <0, 6, 8, ...> n Semigrup: <0, 5, 6, 8, 10, ...> n Semigrup: <0, 6, 7, 8, 9, 11, ...> n Semigrup: <0, 4, 8, ...> n Semigrup: <0, 5, 6, 9, ...> n Semigrup: <0, 4, 7, 8, 10, ...> n Semigrup: <0, 5, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 4, 7, 8, 9, 11, ...> n Semigrup: <0, 3, 6, 8, 9, 11, ...> n Semigrup: <0, 6, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 7, 10, ...> n Semigrup: <0, 5, 8, ...> n Semigrup: <0, 6, 7, 8, 10, ...> n Semigrup: <0, 7, ...> n Semigrup: <0, 3, 6, 9, ...> n Semigrup: <0, 4, 6, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 7, 9, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, 14, ...> n Semigrup: <0, 8, ...> n Semigrup: <0, 6, 7, 9, 10, 12, ...> n Semigrup: <0, 4, 7, 8, 11, ...> n Semigrup: <0, 6, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 9, 11, ...> n Semigrup: <0, 5, 6, 10, ...> n Semigrup: <0, 5, 7, 8, 10, 12, ...> n Semigrup: <0, 7, 8, 10, ...> n Semigrup: <0, 4, 8, 9, 11, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 5, 7, 9, 10, 12, ...> n Semigrup: <0, 5, 7, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 8, 10, 12, ...> n Semigrup: <0, 4, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 9, 11, ...> n Semigrup: <0, 7, 9, ...> n Semigrup: <0, 6, 9, ...> n Semigrup: <0, 6, 7, 8, 9, 12, ...> n Semigrup: <0, 3, 6, 9, 11, ...> n Semigrup: <0, 4, 6, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 7, 8, 9, 11, ...> n Semigrup: <0, 5, 8, 10, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 9, ...> n Semigrup: <0, 6, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 4, 6, 8, 10, 12, ...> n Semigrup: <0, 5, 7, 10, ...> n Semigrup: <0, 6, 8, 10, ...> n Semigrup: <0, 3, 6, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 10, ...> n Semigrup: <0, 3, 6, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 4, 7, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 8, 11, ...> n Semigrup: <0, 4, 8, 10, ...> n Semigrup: <0, 5, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 7, 10, ...> n Semigrup: <0, 4, 6, 8, 10, 12, 13, 14, 16, ...> n Semigrup: <0, 5, 7, 9, 10, 12, 14, ...> n Semigrup: <0, 6, 8, 11, ...> n Semigrup: <0, 5, 8, 9, 10, 13, ...> n Semigrup: <0, 4, 8, 10, 12, ...> n Semigrup: <0, 6, 9, 11, ...> n Semigrup: <0, 6, 7, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, 14, 16, ...> n Semigrup: <0, 3, 6, 9, 11, 12, 14, ...> n Semigrup: <0, 5, 10, ...> n Semigrup: <0, 7, 9, 11, ...> n Semigrup: <0, 7, 8, 11, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 5, 7, 10, 11, 12, 14, ...> n Semigrup: <0, 4, 6, 8, 10, 12, 14, ...> n Semigrup: <0, 6, 10, ...> n Semigrup: <0, 7, 8, 9, 10, 13, ...> n Semigrup: <0, 4, 8, 9, 12, ...> n Semigrup: <0, 7, 8, 9, 11, 13, ...> n Semigrup: <0, 5, 8, 10, 11, 13, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 7, 8, 10, 12, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 7, 9, 10, 12, ...> n Semigrup: <0, 5, 9, 10, 11, 13, ...> n Semigrup: <0, 6, 8, 9, 12, ...> n Semigrup: <0, 3, 6, 9, 10, 12, 13, 15, ...> n Semigrup: <0, 5, 8, 10, 12, ...> n Semigrup: <0, 7, 8, 9, 12, ...> n Semigrup: <0, 6, 9, 10, 12, ...> n Semigrup: <0, 4, 8, 11, ...> n Semigrup: <0, 7, 8, 10, 11, 13, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 10, 12, ...> n Semigrup: <0, 7, 9, 10, 11, 13, ...> n Semigrup: <0, 6, 9, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 5, 9, 10, 12, ...> n Semigrup: <0, 7, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 8, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 6, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 5, 7, 10, 12, ...> n Semigrup: <0, 7, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 10, 12, ...> n Semigrup: <0, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 7, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 8, 12, ...> n Semigrup: <0, 5, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 9, 12, ...> n Semigrup: <0, 4, 8, 9, 10, 12, 13, 14, 16, ...> n Semigrup: <0, 8, 9, 10, 12, ...> n Semigrup: <0, 8, 9, 11, ...> n Semigrup: <0, 7, 9, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 7, 8, 9, 10, 12, 14, ...> n Semigrup: <0, 4, 8, 9, 11, 12, 13, 15, ...> n Semigrup: <0, 4, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 9, 10, 12, 14, ...> n Semigrup: <0, 6, 7, 11, ...> n Semigrup: <0, 8, 10, ...> n Semigrup: <0, 6, 8, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 14, ...> n Semigrup: <0, 9, ...> n Semigrup: <0, 3, 6, 9, 12, ...> n Semigrup: <0, 4, 7, 8, 11, 12, 14, ...> n [ [ 1 ] ] [ [ 1 ], [ 2 ] ] [ [ 1, 1 ], [ 2 ] ] [ [ 1, 1, 1 ], [ 2 ] ] [ [ 1, 1, 1 ], [ 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2 ], [ 3 ], [ 4 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3, 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3, 3 ], [ 4, 5 ], [ 3 ] ] MERDA! [ 1, 1, 1, 1, -1, -1 ] [ 1, 48, 152, 156, 151 ] >> admits(s,p); ^ User error: Identifier 'p' has not been declared or assigned Total time: 17.190 seconds, Total memory usage: 3.95MB ************** MAGMA ***************** Host sab-combi-01.uab.es. (158.109.241.123) Time: Fri Feb 27 13:08:22 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=8; MAXLENGTHPATTERNS:=7; Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do //print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; if Position(ss,semisp) gt NonAdmissibleDegree(p) then admdeg; print "MERDA!"; print p; break; end if; admdeg; end for; //print p; [#s: s in ss]; ontafalles:=[Semigrups[s]: s in ss[3]| s notin ss[5]]; //pp; //admdeg; s:=ontafalles[1]; admits(s,[1,1,1,1,-1,-1]); admits(s,[1,1,1,-1]); Output: Magma V2.10-6 Fri Feb 27 2004 13:08:05 on modular [Seed = 4052629033] ------------------------------------- Semigrup: <0, ...> n Semigrup: <0, 2, ...> n Semigrup: <0, 2, 4, ...> n Semigrup: <0, 3, ...> n Semigrup: <0, 2, 4, 6, ...> n Semigrup: <0, 3, 4, 6, ...> n Semigrup: <0, 4, ...> n Semigrup: <0, 3, 5, ...> n Semigrup: <0, 3, 6, ...> n Semigrup: <0, 5, ...> n Semigrup: <0, 2, 4, 6, 8, ...> n Semigrup: <0, 4, 6, ...> n Semigrup: <0, 4, 5, 7, ...> n Semigrup: <0, 3, 5, 6, 8, ...> n Semigrup: <0, 4, 5, 6, 8, ...> n Semigrup: <0, 3, 6, 7, 9, ...> n Semigrup: <0, 3, 6, 8, ...> n Semigrup: <0, 2, 4, 6, 8, 10, ...> n Semigrup: <0, 4, 7, ...> n Semigrup: <0, 5, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, ...> n Semigrup: <0, 4, 6, 8, ...> n Semigrup: <0, 5, 6, 7, 8, 10, ...> n Semigrup: <0, 4, 6, 7, 8, 10, ...> n Semigrup: <0, 5, 6, 8, ...> n Semigrup: <0, 5, 7, ...> n Semigrup: <0, 6, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, ...> n Semigrup: <0, 5, 7, 8, 10, ...> n Semigrup: <0, 3, 6, 7, 9, 10, 12, ...> n Semigrup: <0, 4, 6, 8, 10, ...> n Semigrup: <0, 6, 8, ...> n Semigrup: <0, 5, 6, 8, 10, ...> n Semigrup: <0, 6, 7, 8, 9, 11, ...> n Semigrup: <0, 4, 8, ...> n Semigrup: <0, 5, 6, 9, ...> n Semigrup: <0, 4, 7, 8, 10, ...> n Semigrup: <0, 5, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 4, 7, 8, 9, 11, ...> n Semigrup: <0, 3, 6, 8, 9, 11, ...> n Semigrup: <0, 6, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 7, 10, ...> n Semigrup: <0, 5, 8, ...> n Semigrup: <0, 6, 7, 8, 10, ...> n Semigrup: <0, 7, ...> n Semigrup: <0, 3, 6, 9, ...> n Semigrup: <0, 4, 6, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 7, 9, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, 14, ...> n Semigrup: <0, 8, ...> n Semigrup: <0, 6, 7, 9, 10, 12, ...> n Semigrup: <0, 4, 7, 8, 11, ...> n Semigrup: <0, 6, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 9, 11, ...> n Semigrup: <0, 5, 6, 10, ...> n Semigrup: <0, 5, 7, 8, 10, 12, ...> n Semigrup: <0, 7, 8, 10, ...> n Semigrup: <0, 4, 8, 9, 11, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 5, 7, 9, 10, 12, ...> n Semigrup: <0, 5, 7, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 8, 10, 12, ...> n Semigrup: <0, 4, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 9, 11, ...> n Semigrup: <0, 7, 9, ...> n Semigrup: <0, 6, 9, ...> n Semigrup: <0, 6, 7, 8, 9, 12, ...> n Semigrup: <0, 3, 6, 9, 11, ...> n Semigrup: <0, 4, 6, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 7, 8, 9, 11, ...> n Semigrup: <0, 5, 8, 10, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 9, ...> n Semigrup: <0, 6, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 4, 6, 8, 10, 12, ...> n Semigrup: <0, 5, 7, 10, ...> n Semigrup: <0, 6, 8, 10, ...> n Semigrup: <0, 3, 6, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 10, ...> n Semigrup: <0, 3, 6, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 4, 7, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 8, 11, ...> n Semigrup: <0, 4, 8, 10, ...> n Semigrup: <0, 5, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 7, 10, ...> n Semigrup: <0, 4, 6, 8, 10, 12, 13, 14, 16, ...> n Semigrup: <0, 5, 7, 9, 10, 12, 14, ...> n Semigrup: <0, 6, 8, 11, ...> n Semigrup: <0, 5, 8, 9, 10, 13, ...> n Semigrup: <0, 4, 8, 10, 12, ...> n Semigrup: <0, 6, 9, 11, ...> n Semigrup: <0, 6, 7, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, 14, 16, ...> n Semigrup: <0, 3, 6, 9, 11, 12, 14, ...> n Semigrup: <0, 5, 10, ...> n Semigrup: <0, 7, 9, 11, ...> n Semigrup: <0, 7, 8, 11, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 5, 7, 10, 11, 12, 14, ...> n Semigrup: <0, 4, 6, 8, 10, 12, 14, ...> n Semigrup: <0, 6, 10, ...> n Semigrup: <0, 7, 8, 9, 10, 13, ...> n Semigrup: <0, 4, 8, 9, 12, ...> n Semigrup: <0, 7, 8, 9, 11, 13, ...> n Semigrup: <0, 5, 8, 10, 11, 13, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 7, 8, 10, 12, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 7, 9, 10, 12, ...> n Semigrup: <0, 5, 9, 10, 11, 13, ...> n Semigrup: <0, 6, 8, 9, 12, ...> n Semigrup: <0, 3, 6, 9, 10, 12, 13, 15, ...> n Semigrup: <0, 5, 8, 10, 12, ...> n Semigrup: <0, 7, 8, 9, 12, ...> n Semigrup: <0, 6, 9, 10, 12, ...> n Semigrup: <0, 4, 8, 11, ...> n Semigrup: <0, 7, 8, 10, 11, 13, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 10, 12, ...> n Semigrup: <0, 7, 9, 10, 11, 13, ...> n Semigrup: <0, 6, 9, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 5, 9, 10, 12, ...> n Semigrup: <0, 7, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 8, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 6, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 5, 7, 10, 12, ...> n Semigrup: <0, 7, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 10, 12, ...> n Semigrup: <0, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 7, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 8, 12, ...> n Semigrup: <0, 5, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 9, 12, ...> n Semigrup: <0, 4, 8, 9, 10, 12, 13, 14, 16, ...> n Semigrup: <0, 8, 9, 10, 12, ...> n Semigrup: <0, 8, 9, 11, ...> n Semigrup: <0, 7, 9, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 7, 8, 9, 10, 12, 14, ...> n Semigrup: <0, 4, 8, 9, 11, 12, 13, 15, ...> n Semigrup: <0, 4, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 9, 10, 12, 14, ...> n Semigrup: <0, 6, 7, 11, ...> n Semigrup: <0, 8, 10, ...> n Semigrup: <0, 6, 8, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 14, ...> n Semigrup: <0, 9, ...> n Semigrup: <0, 3, 6, 9, 12, ...> n Semigrup: <0, 4, 7, 8, 11, 12, 14, ...> n [ [ 1 ] ] [ [ 1 ], [ 2 ] ] [ [ 1, 1 ], [ 2 ] ] [ [ 1, 1, 1 ], [ 2 ] ] [ [ 1, 1, 1 ], [ 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2 ], [ 3 ], [ 4 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3, 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3, 3 ], [ 4, 5 ], [ 3 ] ] MERDA! [ 1, 1, 1, 1, -1, -1 ] [ 1, 48, 152, 156, 151 ] false [ 6, 6, 6, 6, 5, 5 ] true Total time: 17.260 seconds, Total memory usage: 3.95MB ************** MAGMA ***************** Host sab-combi-01.uab.es. (158.109.241.123) Time: Fri Feb 27 13:11:05 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=8; MAXLENGTHPATTERNS:=7; Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do //print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; if Position(ss,semisp) gt NonAdmissibleDegree(p) then admdeg; print "MERDA!"; print p; break; end if; admdeg; end for; //print p; [#s: s in ss]; ontafalles:=[Semigrups[s]: s in ss[3]| s notin ss[5]]; //pp; //admdeg; s:=ontafalles[1]; s; p1:=[1,1,1,-1]; p2:=[1,1,1,1,-1,-1]; NonAdmissionDegree(p1); NonAdmissionDegree(p2); admits(s,p1); admits(s,p2); Output: Magma V2.10-6 Fri Feb 27 2004 13:10:48 on modular [Seed = 3768526997] ------------------------------------- Semigrup: <0, ...> n Semigrup: <0, 2, ...> n Semigrup: <0, 2, 4, ...> n Semigrup: <0, 3, ...> n Semigrup: <0, 2, 4, 6, ...> n Semigrup: <0, 3, 4, 6, ...> n Semigrup: <0, 4, ...> n Semigrup: <0, 3, 5, ...> n Semigrup: <0, 3, 6, ...> n Semigrup: <0, 5, ...> n Semigrup: <0, 2, 4, 6, 8, ...> n Semigrup: <0, 4, 6, ...> n Semigrup: <0, 4, 5, 7, ...> n Semigrup: <0, 3, 5, 6, 8, ...> n Semigrup: <0, 4, 5, 6, 8, ...> n Semigrup: <0, 3, 6, 7, 9, ...> n Semigrup: <0, 3, 6, 8, ...> n Semigrup: <0, 2, 4, 6, 8, 10, ...> n Semigrup: <0, 4, 7, ...> n Semigrup: <0, 5, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, ...> n Semigrup: <0, 4, 6, 8, ...> n Semigrup: <0, 5, 6, 7, 8, 10, ...> n Semigrup: <0, 4, 6, 7, 8, 10, ...> n Semigrup: <0, 5, 6, 8, ...> n Semigrup: <0, 5, 7, ...> n Semigrup: <0, 6, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, ...> n Semigrup: <0, 5, 7, 8, 10, ...> n Semigrup: <0, 3, 6, 7, 9, 10, 12, ...> n Semigrup: <0, 4, 6, 8, 10, ...> n Semigrup: <0, 6, 8, ...> n Semigrup: <0, 5, 6, 8, 10, ...> n Semigrup: <0, 6, 7, 8, 9, 11, ...> n Semigrup: <0, 4, 8, ...> n Semigrup: <0, 5, 6, 9, ...> n Semigrup: <0, 4, 7, 8, 10, ...> n Semigrup: <0, 5, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 9, ...> n Semigrup: <0, 4, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 4, 7, 8, 9, 11, ...> n Semigrup: <0, 3, 6, 8, 9, 11, ...> n Semigrup: <0, 6, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 7, 10, ...> n Semigrup: <0, 5, 8, ...> n Semigrup: <0, 6, 7, 8, 10, ...> n Semigrup: <0, 7, ...> n Semigrup: <0, 3, 6, 9, ...> n Semigrup: <0, 4, 6, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 7, 9, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, 14, ...> n Semigrup: <0, 8, ...> n Semigrup: <0, 6, 7, 9, 10, 12, ...> n Semigrup: <0, 4, 7, 8, 11, ...> n Semigrup: <0, 6, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 9, 11, ...> n Semigrup: <0, 5, 6, 10, ...> n Semigrup: <0, 5, 7, 8, 10, 12, ...> n Semigrup: <0, 7, 8, 10, ...> n Semigrup: <0, 4, 8, 9, 11, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 5, 7, 9, 10, 12, ...> n Semigrup: <0, 5, 7, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 8, 10, 12, ...> n Semigrup: <0, 4, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 9, 11, ...> n Semigrup: <0, 7, 9, ...> n Semigrup: <0, 6, 9, ...> n Semigrup: <0, 6, 7, 8, 9, 12, ...> n Semigrup: <0, 3, 6, 9, 11, ...> n Semigrup: <0, 4, 6, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 7, 8, 9, 11, ...> n Semigrup: <0, 5, 8, 10, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 9, ...> n Semigrup: <0, 6, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 4, 6, 8, 10, 12, ...> n Semigrup: <0, 5, 7, 10, ...> n Semigrup: <0, 6, 8, 10, ...> n Semigrup: <0, 3, 6, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 10, ...> n Semigrup: <0, 3, 6, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 4, 7, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 7, 8, 9, 10, 12, ...> n Semigrup: <0, 6, 7, 8, 11, ...> n Semigrup: <0, 4, 8, 10, ...> n Semigrup: <0, 5, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 7, 10, ...> n Semigrup: <0, 4, 6, 8, 10, 12, 13, 14, 16, ...> n Semigrup: <0, 5, 7, 9, 10, 12, 14, ...> n Semigrup: <0, 6, 8, 11, ...> n Semigrup: <0, 5, 8, 9, 10, 13, ...> n Semigrup: <0, 4, 8, 10, 12, ...> n Semigrup: <0, 6, 9, 11, ...> n Semigrup: <0, 6, 7, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 2, 4, 6, 8, 10, 12, 14, 16, ...> n Semigrup: <0, 3, 6, 9, 11, 12, 14, ...> n Semigrup: <0, 5, 10, ...> n Semigrup: <0, 7, 9, 11, ...> n Semigrup: <0, 7, 8, 11, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 5, 7, 10, 11, 12, 14, ...> n Semigrup: <0, 4, 6, 8, 10, 12, 14, ...> n Semigrup: <0, 6, 10, ...> n Semigrup: <0, 7, 8, 9, 10, 13, ...> n Semigrup: <0, 4, 8, 9, 12, ...> n Semigrup: <0, 7, 8, 9, 11, 13, ...> n Semigrup: <0, 5, 8, 10, 11, 13, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 7, 8, 10, 12, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 7, 9, 10, 12, ...> n Semigrup: <0, 5, 9, 10, 11, 13, ...> n Semigrup: <0, 6, 8, 9, 12, ...> n Semigrup: <0, 3, 6, 9, 10, 12, 13, 15, ...> n Semigrup: <0, 5, 8, 10, 12, ...> n Semigrup: <0, 7, 8, 9, 12, ...> n Semigrup: <0, 6, 9, 10, 12, ...> n Semigrup: <0, 4, 8, 11, ...> n Semigrup: <0, 7, 8, 10, 11, 13, ...> n Semigrup: <0, 8, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 10, 12, ...> n Semigrup: <0, 7, 9, 10, 11, 13, ...> n Semigrup: <0, 6, 9, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 5, 9, 10, 12, ...> n Semigrup: <0, 7, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 5, 8, 10, 11, 12, 13, 15, ...> n Semigrup: <0, 6, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 5, 7, 10, 12, ...> n Semigrup: <0, 7, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 10, 12, ...> n Semigrup: <0, 8, 9, 10, 11, 13, ...> n Semigrup: <0, 7, 8, 9, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 8, 12, ...> n Semigrup: <0, 5, 9, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 7, 9, 12, ...> n Semigrup: <0, 4, 8, 9, 10, 12, 13, 14, 16, ...> n Semigrup: <0, 8, 9, 10, 12, ...> n Semigrup: <0, 8, 9, 11, ...> n Semigrup: <0, 7, 9, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 7, 8, 9, 10, 12, 14, ...> n Semigrup: <0, 4, 8, 9, 11, 12, 13, 15, ...> n Semigrup: <0, 4, 8, 10, 11, 12, 14, ...> n Semigrup: <0, 6, 8, 9, 10, 12, 14, ...> n Semigrup: <0, 6, 7, 11, ...> n Semigrup: <0, 8, 10, ...> n Semigrup: <0, 6, 8, 10, 11, 12, 13, 14, 16, ...> n Semigrup: <0, 7, 8, 9, 10, 11, 14, ...> n Semigrup: <0, 9, ...> n Semigrup: <0, 3, 6, 9, 12, ...> n Semigrup: <0, 4, 7, 8, 11, 12, 14, ...> n [ [ 1 ] ] [ [ 1 ], [ 2 ] ] [ [ 1, 1 ], [ 2 ] ] [ [ 1, 1, 1 ], [ 2 ] ] [ [ 1, 1, 1 ], [ 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2 ], [ 3 ], [ 4 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3, 3 ], [ 4, 5 ] ] [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3, 3 ], [ 4, 5 ], [ 3 ] ] MERDA! [ 1, 1, 1, 1, -1, -1 ] [ 1, 48, 152, 156, 151 ] <[ 0, 5, 6, 10, 11, 12, 13, 15 ], 7, 15, 8, function(i) ... end function, [ 1, 2, 3, 4, 7, 8, 9, 14 ], function(i) ... end function, function(i) ... end function, function(i, j) ... end function, function(i, j) ... end function, function(j, i) ... end function, function(i) ... end function, function(i) ... end function, function(i) ... end function, 13, 10, 6> >> NonAdmissionDegree(p1); ^ User error: Identifier 'NonAdmissionDegree' has not been declared or assigned >> NonAdmissionDegree(p2); ^ User error: Identifier 'NonAdmissionDegree' has not been declared or assigned true false [ 6, 6, 6, 6, 5, 5 ] Total time: 17.239 seconds, Total memory usage: 3.95MB ************** MAGMA ***************** Host sab-combi-01.uab.es. (158.109.241.123) Time: Fri Feb 27 13:12:46 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; /* MAXGENUS:=8; MAXLENGTHPATTERNS:=7; Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do //print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; if Position(ss,semisp) gt NonAdmissibleDegree(p) then admdeg; print "MERDA!"; print p; break; end if; admdeg; end for; //print p; [#s: s in ss]; ontafalles:=[Semigrups[s]: s in ss[3]| s notin ss[5]]; //pp; //admdeg; s:=ontafalles[1]; */ s:=semigrup([0,5,6,10,11,12,13,15]); p1:=[1,1,1,-1]; p2:=[1,1,1,1,-1,-1]; NonAdmissibleDegree(p1); NonAdmissibleDegree(p2); admits(s,p1); admits(s,p2); Output: Magma V2.10-6 Fri Feb 27 2004 13:12:42 on modular [Seed = 2164213831] ------------------------------------- Semigrup: <0, 5, 6, 10, 11, 12, 13, 15, ...> n 3 3 true false [ 6, 6, 6, 6, 5, 5 ] Total time: 3.029 seconds, Total memory usage: 2.39MB ************** MAGMA ***************** Host a-mi21-51.tin.it. (212.216.4.114) Time: Fri Feb 27 15:56:22 2004 Input: 2^11-1 Output: Magma V2.10-6 Fri Feb 27 2004 15:56:19 on modular [Seed = 41806993] ------------------------------------- 2047 Total time: 3.309 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host a-mi21-51.tin.it. (212.216.4.114) Time: Fri Feb 27 15:56:24 2004 Input: 2^11-1 Output: Magma V2.10-6 Fri Feb 27 2004 15:56:21 on modular [Seed = 91941776] ------------------------------------- 2047 Total time: 3.399 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Sat Feb 28 03:25:19 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Sat Feb 28 2004 03:25:16 on modular [Seed = 3200167604] ------------------------------------- [ y^2 + 7*y - 18, 15*y - 30 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Sat Feb 28 03:25:44 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Sat Feb 28 2004 03:25:41 on modular [Seed = 2273810276] ------------------------------------- [ y^2 + 7*y + 130945797, 15*y + 130945785, 130945815 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Sat Feb 28 03:26:11 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Sat Feb 28 2004 03:26:08 on modular [Seed = 2358025290] ------------------------------------- [ y^2 + 7*y + 42, 15*y, 45 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Sat Feb 28 03:26:40 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Sat Feb 28 2004 03:26:37 on modular [Seed = 2459075145] ------------------------------------- [ y^2 + 7*y + 42, 15*y, 45 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Sat Feb 28 03:27:48 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(130945815); Output: Magma V2.10-6 Sat Feb 28 2004 03:27:45 on modular [Seed = 1734833665] ------------------------------------- [ y^2 + 7*y + 130945797, 15*y + 130945785, 130945815 ] [ <3, 4>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Sat Feb 28 03:30:51 2004 Input: P:=PolynomialRing(IntegerRing(),2); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(130945815); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19))); Bn; Output: Magma V2.10-6 Sat Feb 28 2004 03:30:48 on modular [Seed = 1987471273] ------------------------------------- [ y^2 + 7*y + 130945797, 15*y + 130945785, 130945815 ] [ <3, 4>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ y + 9 ] [ y + 11 ] [ y + 15 ] [ y + 17 ] Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sat Feb 28 11:39:20 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=8; MAXLENGTHPATTERNS:=7; //Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); Semigrups:=[HermitianSemigroup(q): q in [1..10]]; l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do //print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; if Position(ss,semisp) gt NonAdmissibleDegree(p) then admdeg; print "MERDA!"; print p; break; end if; admdeg; end for; [#s: s in ss]; //pp; admdeg; /* s:=semigrup([0,5,6,10,11,12,13,15]); p1:=[1,1,1,-1]; p2:=[1,1,1,1,-1,-1]; NonAdmissibleDegree(p1); NonAdmissibleDegree(p2); admits(s,p1); admits(s,p2); */ Output: ** WARNING: Computation used more memory than allowed. ** Magma V2.10-6 Sat Feb 28 2004 11:39:00 on modular [Seed = 1701175596] ------------------------------------- Semigrup: <0, ...> n Semigrup: <0, 2, ...> n Semigrup: <0, 3, 4, 6, ...> n Semigrup: <0, 4, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 15, 16, 17, 18, 20, ...> n Semigrup: <0, 6, 7, 12, 13, 14, 18, 19, 20, 21, 24, 25, 26, 27, 28, 30, ...> n Semigrup: <0, 7, 8, 14, 15, 16, 21, 22, 23, 24, 28, 29, 30, 31, 32, 35, 36, 37, 38, 39, 40, 42, ...> n Semigrup: <0, 8, 9, 16, 17, 18, 24, 25, 26, 27, 32, 33, 34, 35, 36, 40, 41, 42, 43, 44, 45, 48, 49, 50, 51, 52, 53, 54, 56, ...> n Semigrup: <0, 9, 10, 18, 19, 20, 27, 28, 29, 30, 36, 37, 38, 39, 40, 45, 46, 47, 48, 49, 50, 54, 55, 56, 57, 58, 59, 60, 63, 64, 65, 66, 67, 68, 69, 70, 72, ...> n Semigrup: <0, 10, 11, 20, 21, 22, 30, 31, 32, 33, 40, 41, 42, 43, 44, 50, 51, 52, 53, 54, 55, 60, 61, 62, 63, 64, 65, 66, 70, 71, 72, 73, 74, 75, 76, 77, 80, 81, 82, 83, 84, 85, 86, 87, 88, 90, ...> n [ [ 1 ] ] [ [ 1 ], [ 2 ] ] [ [ 1, 1 ], [ 2 ] ] [ [ 1, 1, 1 ], [ 2 ] ] Current total memory usage: 90.7MB, failed memory request: 9.8MB System Error: User memory limit has been reached [ 1, 2 ] [ [ 1, 1, 1 ], [ 2 ] ] Total time: 19.639 seconds, Total memory usage: 95.14MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sat Feb 28 11:40:56 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=8; MAXLENGTHPATTERNS:=7; //Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); Semigrups:=[HermitianSemigroup(q): q in [1..5]]; l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do //print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; if Position(ss,semisp) gt NonAdmissibleDegree(p) then admdeg; print "MERDA!"; print p; break; end if; //admdeg; end for; [#s: s in ss]; //pp; admdeg; /* s:=semigrup([0,5,6,10,11,12,13,15]); p1:=[1,1,1,-1]; p2:=[1,1,1,1,-1,-1]; NonAdmissibleDegree(p1); NonAdmissibleDegree(p2); admits(s,p1); admits(s,p2); */ Output: Magma V2.10-6 Sat Feb 28 2004 11:40:44 on modular [Seed = 1970663828] ------------------------------------- Semigrup: <0, ...> n Semigrup: <0, 2, ...> n Semigrup: <0, 3, 4, 6, ...> n Semigrup: <0, 4, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 15, 16, 17, 18, 20, ...> n [ 1, 2, 3, 4, 5 ] [ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ], [ 3, 3, 3, 3 ], [ 4, 4, 4 ], [ 5, 6 ] ] Total time: 11.809 seconds, Total memory usage: 8.06MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sat Feb 28 11:42:04 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=8; MAXLENGTHPATTERNS:=7; //Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); Semigrups:=[HermitianSemigroup(q): q in [1..9]]; l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do //print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; if Position(ss,semisp) gt NonAdmissibleDegree(p) then admdeg; print "MERDA!"; print p; break; end if; //admdeg; end for; [#s: s in ss]; //pp; admdeg; /* s:=semigrup([0,5,6,10,11,12,13,15]); p1:=[1,1,1,-1]; p2:=[1,1,1,1,-1,-1]; NonAdmissibleDegree(p1); NonAdmissibleDegree(p2); admits(s,p1); admits(s,p2); */ Output: ** WARNING: Computation used more memory than allowed. ** ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Feb 28 2004 11:41:41 on modular [Seed = 1280100580] ------------------------------------- Semigrup: <0, ...> n Semigrup: <0, 2, ...> n Semigrup: <0, 3, 4, 6, ...> n Semigrup: <0, 4, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 15, 16, 17, 18, 20, ...> n Semigrup: <0, 6, 7, 12, 13, 14, 18, 19, 20, 21, 24, 25, 26, 27, 28, 30, ...> n Semigrup: <0, 7, 8, 14, 15, 16, 21, 22, 23, 24, 28, 29, 30, 31, 32, 35, 36, 37, 38, 39, 40, 42, ...> n Semigrup: <0, 8, 9, 16, 17, 18, 24, 25, 26, 27, 32, 33, 34, 35, 36, 40, 41, 42, 43, 44, 45, 48, 49, 50, 51, 52, 53, 54, 56, ...> n Semigrup: <0, 9, 10, 18, 19, 20, 27, 28, 29, 30, 36, 37, 38, 39, 40, 45, 46, 47, 48, 49, 50, 54, 55, 56, 57, 58, 59, 60, 63, 64, 65, 66, 67, 68, 69, 70, 72, ...> n Current total memory usage: 94.4MB, failed memory request: 9.8MB System Error: User memory limit has been reached Errors: /home/mfd/gomagma: line 2: 11553 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sat Feb 28 11:42:43 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=8; MAXLENGTHPATTERNS:=7; //Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); Semigrups:=[HermitianSemigroup(q): q in [1..8]]; l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do //print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; if Position(ss,semisp) gt NonAdmissibleDegree(p) then admdeg; print "MERDA!"; print p; break; end if; //admdeg; end for; [#s: s in ss]; //pp; admdeg; /* s:=semigrup([0,5,6,10,11,12,13,15]); p1:=[1,1,1,-1]; p2:=[1,1,1,1,-1,-1]; NonAdmissibleDegree(p1); NonAdmissibleDegree(p2); admits(s,p1); admits(s,p2); */ Output: ** WARNING: Computation used more memory than allowed. ** Magma V2.10-6 Sat Feb 28 2004 11:42:23 on modular [Seed = 1195885509] ------------------------------------- Semigrup: <0, ...> n Semigrup: <0, 2, ...> n Semigrup: <0, 3, 4, 6, ...> n Semigrup: <0, 4, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 15, 16, 17, 18, 20, ...> n Semigrup: <0, 6, 7, 12, 13, 14, 18, 19, 20, 21, 24, 25, 26, 27, 28, 30, ...> n Semigrup: <0, 7, 8, 14, 15, 16, 21, 22, 23, 24, 28, 29, 30, 31, 32, 35, 36, 37, 38, 39, 40, 42, ...> n Semigrup: <0, 8, 9, 16, 17, 18, 24, 25, 26, 27, 32, 33, 34, 35, 36, 40, 41, 42, 43, 44, 45, 48, 49, 50, 51, 52, 53, 54, 56, ...> n Current total memory usage: 94.3MB, failed memory request: 9.8MB System Error: User memory limit has been reached [ 1, 2, 3 ] [ [ 1, 1, 1, 1 ], [ 2 ], [ 3 ] ] Total time: 19.789 seconds, Total memory usage: 98.91MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sat Feb 28 11:43:34 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=8; MAXLENGTHPATTERNS:=6; //Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); Semigrups:=[HermitianSemigroup(q): q in [1..8]]; l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do //print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; if Position(ss,semisp) gt NonAdmissibleDegree(p) then admdeg; print "MERDA!"; print p; break; end if; //admdeg; end for; [#s: s in ss]; //pp; admdeg; /* s:=semigrup([0,5,6,10,11,12,13,15]); p1:=[1,1,1,-1]; p2:=[1,1,1,1,-1,-1]; NonAdmissibleDegree(p1); NonAdmissibleDegree(p2); admits(s,p1); admits(s,p2); */ Output: ** WARNING: Computation used more memory than allowed. ** Magma V2.10-6 Sat Feb 28 2004 11:43:15 on modular [Seed = 1499061271] ------------------------------------- Semigrup: <0, ...> n Semigrup: <0, 2, ...> n Semigrup: <0, 3, 4, 6, ...> n Semigrup: <0, 4, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 15, 16, 17, 18, 20, ...> n Semigrup: <0, 6, 7, 12, 13, 14, 18, 19, 20, 21, 24, 25, 26, 27, 28, 30, ...> n Semigrup: <0, 7, 8, 14, 15, 16, 21, 22, 23, 24, 28, 29, 30, 31, 32, 35, 36, 37, 38, 39, 40, 42, ...> n Semigrup: <0, 8, 9, 16, 17, 18, 24, 25, 26, 27, 32, 33, 34, 35, 36, 40, 41, 42, 43, 44, 45, 48, 49, 50, 51, 52, 53, 54, 56, ...> n Current total memory usage: 94.3MB, failed memory request: 9.8MB System Error: User memory limit has been reached [ 1, 2, 3 ] [ [ 1, 1, 1, 1 ], [ 2 ], [ 3 ] ] Total time: 19.549 seconds, Total memory usage: 98.90MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sat Feb 28 11:44:28 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=8; MAXLENGTHPATTERNS:=6; //Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); Semigrups:=[HermitianSemigroup(q): q in [1..8]]; l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do //print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; if Position(ss,semisp) gt NonAdmissibleDegree(p) then admdeg; print "MERDA!"; print p; break; end if; admdeg; end for; [#s: s in ss]; //pp; admdeg; /* s:=semigrup([0,5,6,10,11,12,13,15]); p1:=[1,1,1,-1]; p2:=[1,1,1,1,-1,-1]; NonAdmissibleDegree(p1); NonAdmissibleDegree(p2); admits(s,p1); admits(s,p2); */ Output: ** WARNING: Computation used more memory than allowed. ** Magma V2.10-6 Sat Feb 28 2004 11:44:08 on modular [Seed = 1347474789] ------------------------------------- Semigrup: <0, ...> n Semigrup: <0, 2, ...> n Semigrup: <0, 3, 4, 6, ...> n Semigrup: <0, 4, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 15, 16, 17, 18, 20, ...> n Semigrup: <0, 6, 7, 12, 13, 14, 18, 19, 20, 21, 24, 25, 26, 27, 28, 30, ...> n Semigrup: <0, 7, 8, 14, 15, 16, 21, 22, 23, 24, 28, 29, 30, 31, 32, 35, 36, 37, 38, 39, 40, 42, ...> n Semigrup: <0, 8, 9, 16, 17, 18, 24, 25, 26, 27, 32, 33, 34, 35, 36, 40, 41, 42, 43, 44, 45, 48, 49, 50, 51, 52, 53, 54, 56, ...> n [ [ 1 ] ] [ [ 1 ], [ 2 ] ] [ [ 1, 1 ], [ 2 ] ] [ [ 1, 1, 1 ], [ 2 ] ] [ [ 1, 1, 1 ], [ 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2 ], [ 3 ] ] Current total memory usage: 94.4MB, failed memory request: 9.8MB System Error: User memory limit has been reached [ 1, 2, 3 ] [ [ 1, 1, 1, 1 ], [ 2 ], [ 3 ] ] Total time: 19.549 seconds, Total memory usage: 98.95MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sat Feb 28 11:45:28 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=8; MAXLENGTHPATTERNS:=6; //Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); Semigrups:=[HermitianSemigroup(q): q in [1..7]]; l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do //print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; if Position(ss,semisp) gt NonAdmissibleDegree(p) then admdeg; print "MERDA!"; print p; break; end if; admdeg; end for; [#s: s in ss]; //pp; admdeg; /* s:=semigrup([0,5,6,10,11,12,13,15]); p1:=[1,1,1,-1]; p2:=[1,1,1,1,-1,-1]; NonAdmissibleDegree(p1); NonAdmissibleDegree(p2); admits(s,p1); admits(s,p2); */ Output: ** WARNING: Computation used more memory than allowed. ** ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Feb 28 2004 11:45:05 on modular [Seed = 656909019] ------------------------------------- Semigrup: <0, ...> n Semigrup: <0, 2, ...> n Semigrup: <0, 3, 4, 6, ...> n Semigrup: <0, 4, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 15, 16, 17, 18, 20, ...> n Semigrup: <0, 6, 7, 12, 13, 14, 18, 19, 20, 21, 24, 25, 26, 27, 28, 30, ...> n Semigrup: <0, 7, 8, 14, 15, 16, 21, 22, 23, 24, 28, 29, 30, 31, 32, 35, 36, 37, 38, 39, 40, 42, ...> n [ [ 1 ] ] [ [ 1 ], [ 2 ] ] [ [ 1, 1 ], [ 2 ] ] [ [ 1, 1, 1 ], [ 2 ] ] [ [ 1, 1, 1 ], [ 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2 ], [ 3 ], [ 4 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4 ] ] Current total memory usage: 95.4MB, failed memory request: 0.0MB System Error: User memory limit has been reached Errors: /home/mfd/gomagma: line 2: 11594 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sat Feb 28 11:47:28 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return< semi, i_cond, c, g, pertany, gaps, lambda, lambdainv, //oplus, //inferior, //ominus, //N, //nu, //dORD, //d, //subc, //subd >; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; /* oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; */ TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=8; MAXLENGTHPATTERNS:=6; //Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); Semigrups:=[HermitianSemigroup(q): q in [1..7]]; l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do //print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; if Position(ss,semisp) gt NonAdmissibleDegree(p) then admdeg; print "MERDA!"; print p; break; end if; admdeg; end for; [#s: s in ss]; //pp; admdeg; /* s:=semigrup([0,5,6,10,11,12,13,15]); p1:=[1,1,1,-1]; p2:=[1,1,1,1,-1,-1]; NonAdmissibleDegree(p1); NonAdmissibleDegree(p2); admits(s,p1); admits(s,p2); */ Output: Magma V2.10-6 Sat Feb 28 2004 11:47:25 on modular [Seed = 1044297806] ------------------------------------- >> ; ^ User error: bad syntax >> end function; ^ User error: bad syntax >> func<|semigrup([0])>; ^ User error: Identifier 'semigrup' has not been declared or assigned >> func; ^ User error: Identifier 'semigrup' has not been declared or assigned >> func<|semigrup([0,3,5])>; ^ User error: Identifier 'semigrup' has not been declared or assigned >> func> func> func> IsAcute:=func> if g eq 0 then return [TrivialSemigroup()]; end if; ^ User error: Identifier 'TrivialSemigroup' has not been declared or assigned >> AllSemigroupsWithGenus(h)]: h in ^ User error: Identifier 'AllSemigroupsWithGenus' has not been declared or assigned >> Semigrups:=[HermitianSemigroup(q): q in [1..7]]; ^ User error: Identifier 'HermitianSemigroup' has not been declared or assigned >> l:=#Semigrups; ^ User error: Identifier 'Semigrups' has not been declared or assigned >> semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; ^ User error: Identifier 'l' has not been declared or assigned [] [] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sat Feb 28 11:48:11 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return< semi, i_cond, c, g, pertany, gaps, lambda, lambdainv //oplus, //inferior, //ominus, //N, //nu, //dORD, //d, //subc, //subd >; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; /* oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; */ TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=8; MAXLENGTHPATTERNS:=6; //Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); Semigrups:=[HermitianSemigroup(q): q in [1..7]]; l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do //print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; if Position(ss,semisp) gt NonAdmissibleDegree(p) then admdeg; print "MERDA!"; print p; break; end if; admdeg; end for; [#s: s in ss]; //pp; admdeg; /* s:=semigrup([0,5,6,10,11,12,13,15]); p1:=[1,1,1,-1]; p2:=[1,1,1,1,-1,-1]; NonAdmissibleDegree(p1); NonAdmissibleDegree(p2); admits(s,p1); admits(s,p2); */ Output: Magma V2.10-6 Sat Feb 28 2004 11:48:08 on modular [Seed = 808498709] ------------------------------------- >> ; ^ User error: bad syntax >> end function; ^ User error: bad syntax >> func<|semigrup([0])>; ^ User error: Identifier 'semigrup' has not been declared or assigned >> func; ^ User error: Identifier 'semigrup' has not been declared or assigned >> func<|semigrup([0,3,5])>; ^ User error: Identifier 'semigrup' has not been declared or assigned >> func> func> func> IsAcute:=func> if g eq 0 then return [TrivialSemigroup()]; end if; ^ User error: Identifier 'TrivialSemigroup' has not been declared or assigned >> AllSemigroupsWithGenus(h)]: h in ^ User error: Identifier 'AllSemigroupsWithGenus' has not been declared or assigned >> Semigrups:=[HermitianSemigroup(q): q in [1..7]]; ^ User error: Identifier 'HermitianSemigroup' has not been declared or assigned >> l:=#Semigrups; ^ User error: Identifier 'Semigrups' has not been declared or assigned >> semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; ^ User error: Identifier 'l' has not been declared or assigned [] [] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sat Feb 28 11:49:18 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return< semi, i_cond, c, g, pertany, gaps, lambda, lambdainv //oplus, //inferior, //ominus, //N, //nu, //dORD, //d, //subc, //subd >; end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; /* oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; */ TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=8; MAXLENGTHPATTERNS:=6; //Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); Semigrups:=[HermitianSemigroup(q): q in [1..7]]; l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do //print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; if Position(ss,semisp) gt NonAdmissibleDegree(p) then admdeg; print "MERDA!"; print p; break; end if; admdeg; end for; [#s: s in ss]; //pp; admdeg; /* s:=semigrup([0,5,6,10,11,12,13,15]); p1:=[1,1,1,-1]; p2:=[1,1,1,1,-1,-1]; NonAdmissibleDegree(p1); NonAdmissibleDegree(p2); admits(s,p1); admits(s,p2); */ Output: Magma V2.10-6 Sat Feb 28 2004 11:49:15 on modular [Seed = 185306605] ------------------------------------- >> ; ^ User error: bad syntax >> end function; ^ User error: bad syntax >> func<|semigrup([0])>; ^ User error: Identifier 'semigrup' has not been declared or assigned >> func; ^ User error: Identifier 'semigrup' has not been declared or assigned >> func<|semigrup([0,3,5])>; ^ User error: Identifier 'semigrup' has not been declared or assigned >> func> func> func> IsAcute:=func> if g eq 0 then return [TrivialSemigroup()]; end if; ^ User error: Identifier 'TrivialSemigroup' has not been declared or assigned >> AllSemigroupsWithGenus(h)]: h in ^ User error: Identifier 'AllSemigroupsWithGenus' has not been declared or assigned >> Semigrups:=[HermitianSemigroup(q): q in [1..7]]; ^ User error: Identifier 'HermitianSemigroup' has not been declared or assigned >> l:=#Semigrups; ^ User error: Identifier 'Semigrups' has not been declared or assigned >> semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; ^ User error: Identifier 'l' has not been declared or assigned [] [] Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sat Feb 28 11:50:58 2004 Input: print "hola2"; semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return< semi, i_cond, c, g, pertany, gaps, lambda, lambdainv //oplus, //inferior, //ominus, //N, //nu, //dORD, //d, //subc, //subd >; end function; print "hola1"; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; /* oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; */ TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=8; MAXLENGTHPATTERNS:=6; //Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); Semigrups:=[HermitianSemigroup(q): q in [1..7]]; l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do //print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; if Position(ss,semisp) gt NonAdmissibleDegree(p) then admdeg; print "MERDA!"; print p; break; end if; admdeg; end for; [#s: s in ss]; //pp; admdeg; /* s:=semigrup([0,5,6,10,11,12,13,15]); p1:=[1,1,1,-1]; p2:=[1,1,1,1,-1,-1]; NonAdmissibleDegree(p1); NonAdmissibleDegree(p2); admits(s,p1); admits(s,p2); */ Output: Magma V2.10-6 Sat Feb 28 2004 11:50:55 on modular [Seed = 454794649] ------------------------------------- hola2 >> ; ^ User error: bad syntax >> end function; ^ User error: bad syntax hola1 >> func<|semigrup([0])>; ^ User error: Identifier 'semigrup' has not been declared or assigned >> func; ^ User error: Identifier 'semigrup' has not been declared or assigned >> func<|semigrup([0,3,5])>; ^ User error: Identifier 'semigrup' has not been declared or assigned >> func> func> func> IsAcute:=func> if g eq 0 then return [TrivialSemigroup()]; end if; ^ User error: Identifier 'TrivialSemigroup' has not been declared or assigned >> AllSemigroupsWithGenus(h)]: h in ^ User error: Identifier 'AllSemigroupsWithGenus' has not been declared or assigned >> Semigrups:=[HermitianSemigroup(q): q in [1..7]]; ^ User error: Identifier 'HermitianSemigroup' has not been declared or assigned >> l:=#Semigrups; ^ User error: Identifier 'Semigrups' has not been declared or assigned >> semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; ^ User error: Identifier 'l' has not been declared or assigned [] [] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sat Feb 28 11:53:37 2004 Input: print "hola2"; semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; /*return;*/ end function; print "hola1"; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; /* oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; */ TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=8; MAXLENGTHPATTERNS:=6; //Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); Semigrups:=[HermitianSemigroup(q): q in [1..7]]; l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do //print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; if Position(ss,semisp) gt NonAdmissibleDegree(p) then admdeg; print "MERDA!"; print p; break; end if; admdeg; end for; [#s: s in ss]; //pp; admdeg; /* s:=semigrup([0,5,6,10,11,12,13,15]); p1:=[1,1,1,-1]; p2:=[1,1,1,1,-1,-1]; NonAdmissibleDegree(p1); NonAdmissibleDegree(p2); admits(s,p1); admits(s,p2); */ Output: ** WARNING: Computation used more memory than allowed. ** ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Feb 28 2004 11:53:14 on modular [Seed = 3991759610] ------------------------------------- hola2 hola1 >> IsAcute:=func n Semigrup: <0, 2, ...> n Semigrup: <0, 3, 4, 6, ...> n Semigrup: <0, 4, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 15, 16, 17, 18, 20, ...> n Semigrup: <0, 6, 7, 12, 13, 14, 18, 19, 20, 21, 24, 25, 26, 27, 28, 30, ...> n Semigrup: <0, 7, 8, 14, 15, 16, 21, 22, 23, 24, 28, 29, 30, 31, 32, 35, 36, 37, 38, 39, 40, 42, ...> n [ [ 1 ] ] [ [ 1 ], [ 2 ] ] [ [ 1, 1 ], [ 2 ] ] [ [ 1, 1, 1 ], [ 2 ] ] [ [ 1, 1, 1 ], [ 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2 ], [ 3 ], [ 4 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4 ] ] Current total memory usage: 95.4MB, failed memory request: 0.0MB System Error: User memory limit has been reached Errors: /home/mfd/gomagma: line 2: 11648 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sat Feb 28 11:54:39 2004 Input: print "hola2"; semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; /*return;*/ end function; print "hola1"; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=8; MAXLENGTHPATTERNS:=6; //Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); Semigrups:=[HermitianSemigroup(q): q in [1..7]]; l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do //print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; if Position(ss,semisp) gt NonAdmissibleDegree(p) then admdeg; print "MERDA!"; print p; break; end if; admdeg; end for; [#s: s in ss]; //pp; admdeg; /* s:=semigrup([0,5,6,10,11,12,13,15]); p1:=[1,1,1,-1]; p2:=[1,1,1,1,-1,-1]; NonAdmissibleDegree(p1); NonAdmissibleDegree(p2); admits(s,p1); admits(s,p2); */ Output: ** WARNING: Computation used more memory than allowed. ** ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Feb 28 2004 11:54:16 on modular [Seed = 3840172849] ------------------------------------- hola2 hola1 Semigrup: <0, ...> n Semigrup: <0, 2, ...> n Semigrup: <0, 3, 4, 6, ...> n Semigrup: <0, 4, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 15, 16, 17, 18, 20, ...> n Semigrup: <0, 6, 7, 12, 13, 14, 18, 19, 20, 21, 24, 25, 26, 27, 28, 30, ...> n Semigrup: <0, 7, 8, 14, 15, 16, 21, 22, 23, 24, 28, 29, 30, 31, 32, 35, 36, 37, 38, 39, 40, 42, ...> n [ [ 1 ] ] [ [ 1 ], [ 2 ] ] [ [ 1, 1 ], [ 2 ] ] [ [ 1, 1, 1 ], [ 2 ] ] [ [ 1, 1, 1 ], [ 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2 ], [ 3 ], [ 4 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4 ] ] Current total memory usage: 95.4MB, failed memory request: 0.0MB System Error: User memory limit has been reached Errors: /home/mfd/gomagma: line 2: 11657 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sat Feb 28 11:57:03 2004 Input: print "hola2"; semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ while (semi[#semi-1]+1 eq semi[#semi]) do Prune(~semi); end while; i_cond:=#semi-1; c:=semi[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #semi gt 1 then d:=semi[i_cond]; i:=d; while i in semi do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; /*return;*/ end function; print "hola1"; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=8; MAXLENGTHPATTERNS:=5; //Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); Semigrups:=[HermitianSemigroup(q): q in [1..6]]; l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do //print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; if Position(ss,semisp) gt NonAdmissibleDegree(p) then admdeg; print "MERDA!"; print p; break; end if; admdeg; end for; [#s: s in ss]; //pp; admdeg; /* s:=semigrup([0,5,6,10,11,12,13,15]); p1:=[1,1,1,-1]; p2:=[1,1,1,1,-1,-1]; NonAdmissibleDegree(p1); NonAdmissibleDegree(p2); admits(s,p1); admits(s,p2); */ semigrup([0,1,2,3,4]); Output: Magma V2.10-6 Sat Feb 28 2004 11:57:00 on modular [Seed = 4227560394] ------------------------------------- hola2 hola1 [
:67]( q: 1 ) [
:4]( semi: [ 0 ] ) >> while (semi[#semi-1]+1 eq semi[#semi]) do Prune(~semi); end while; ^ Runtime error in '[]': Sequence element 0 not defined >> l:=#Semigrups; ^ User error: Identifier 'Semigrups' has not been declared or assigned >> semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; ^ User error: Identifier 'l' has not been declared or assigned [] [] [
:4]( semi: [ 0 ] ) >> while (semi[#semi-1]+1 eq semi[#semi]) do Prune(~semi); end while; ^ Runtime error in '[]': Sequence element 0 not defined Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sat Feb 28 12:02:58 2004 Input: print "hola2"; semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; while (semi[i_cond]+1 eq semi[i_cond+1]) do i_cond:=i_cond-1; end while; firstnongaps:=[semi[i]:i in [1..i_cond+1]]; c:=firstnongaps[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #firstnongaps gt 1 then d:=firstnongaps[i_cond]; i:=d; while i in firstnongaps do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; /*return;*/ end function; print "hola1"; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=8; MAXLENGTHPATTERNS:=5; //Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); Semigrups:=[HermitianSemigroup(q): q in [1..6]]; l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do //print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; if Position(ss,semisp) gt NonAdmissibleDegree(p) then admdeg; print "MERDA!"; print p; break; end if; admdeg; end for; [#s: s in ss]; //pp; admdeg; /* s:=semigrup([0,5,6,10,11,12,13,15]); p1:=[1,1,1,-1]; p2:=[1,1,1,1,-1,-1]; NonAdmissibleDegree(p1); NonAdmissibleDegree(p2); admits(s,p1); admits(s,p2); */ semigrup([0,1,2,3,4]); Output: Magma V2.10-6 Sat Feb 28 2004 12:02:55 on modular [Seed = 3604373252] ------------------------------------- hola2 hola1 [
:68]( q: 1 ) [
:4]( semi: [ 0 ] ) >> while (semi[i_cond]+1 eq semi[i_cond+1]) do i_cond:=i_cond-1; end while; ^ Runtime error in '[]': Sequence element 0 not defined >> l:=#Semigrups; ^ User error: Identifier 'Semigrups' has not been declared or assigned >> semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; ^ User error: Identifier 'l' has not been declared or assigned [] [] [
:4]( semi: [ 0, 1, 2, 3, 4 ] ) >> while (semi[i_cond]+1 eq semi[i_cond+1]) do i_cond:=i_cond-1; end while; ^ Runtime error in '[]': Sequence element 0 not defined Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sat Feb 28 12:03:57 2004 Input: print "hola2"; semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; while (i_cond gt 0 and semi[i_cond]+1 eq semi[i_cond+1]) do i_cond:=i_cond-1; end while; firstnongaps:=[semi[i]:i in [1..i_cond+1]]; c:=firstnongaps[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #firstnongaps gt 1 then d:=firstnongaps[i_cond]; i:=d; while i in firstnongaps do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; /*return;*/ end function; print "hola1"; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=8; MAXLENGTHPATTERNS:=5; //Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); Semigrups:=[HermitianSemigroup(q): q in [1..6]]; l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do //print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; if Position(ss,semisp) gt NonAdmissibleDegree(p) then admdeg; print "MERDA!"; print p; break; end if; admdeg; end for; [#s: s in ss]; //pp; admdeg; /* s:=semigrup([0,5,6,10,11,12,13,15]); p1:=[1,1,1,-1]; p2:=[1,1,1,1,-1,-1]; NonAdmissibleDegree(p1); NonAdmissibleDegree(p2); admits(s,p1); admits(s,p2); */ semigrup([0,1,2,3,4]); Output: Magma V2.10-6 Sat Feb 28 2004 12:03:52 on modular [Seed = 2829590845] ------------------------------------- hola2 hola1 Semigrup: <0, ...> n Semigrup: <0, 2, ...> n Semigrup: <0, 3, 4, 6, ...> n Semigrup: <0, 4, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 15, 16, 17, 18, 20, ...> n Semigrup: <0, 6, 7, 12, 13, 14, 18, 19, 20, 21, 24, 25, 26, 27, 28, 30, ...> n [ [ 1 ] ] [ [ 1 ], [ 2 ] ] [ [ 1, 1 ], [ 2 ] ] [ [ 1, 1, 1 ], [ 2 ] ] [ [ 1, 1, 1 ], [ 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2 ], [ 3 ], [ 4 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4 ] ] [ 1, 2, 3, 4 ] [ [ 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4 ] ] Semigrup: <0, ...> n <[ 0 ], 0, 0, 0, function(i) ... end function, [], function(i) ... end function, function(i) ... end function> Total time: 5.299 seconds, Total memory usage: 8.11MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sat Feb 28 12:04:39 2004 Input: print "hola2"; semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; while (i_cond gt 0 and semi[i_cond]+1 eq semi[i_cond+1]) do i_cond:=i_cond-1; end while; firstnongaps:=[semi[i]:i in [1..i_cond+1]]; c:=firstnongaps[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #firstnongaps gt 1 then d:=firstnongaps[i_cond]; i:=d; while i in firstnongaps do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; /*return;*/ end function; print "hola1"; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=8; MAXLENGTHPATTERNS:=5; //Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); Semigrups:=[HermitianSemigroup(q): q in [1..6]]; l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do //print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; if Position(ss,semisp) gt NonAdmissibleDegree(p) then admdeg; print "MERDA!"; print p; break; end if; admdeg; end for; [#s: s in ss]; //pp; admdeg; /* s:=semigrup([0,5,6,10,11,12,13,15]); p1:=[1,1,1,-1]; p2:=[1,1,1,1,-1,-1]; NonAdmissibleDegree(p1); NonAdmissibleDegree(p2); admits(s,p1); admits(s,p2); */ semigrup([0,1,2,3,4]) eq TrivialSemigroup(); Output: Magma V2.10-6 Sat Feb 28 2004 12:04:34 on modular [Seed = 2745379308] ------------------------------------- hola2 hola1 Semigrup: <0, ...> n Semigrup: <0, 2, ...> n Semigrup: <0, 3, 4, 6, ...> n Semigrup: <0, 4, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 15, 16, 17, 18, 20, ...> n Semigrup: <0, 6, 7, 12, 13, 14, 18, 19, 20, 21, 24, 25, 26, 27, 28, 30, ...> n [ [ 1 ] ] [ [ 1 ], [ 2 ] ] [ [ 1, 1 ], [ 2 ] ] [ [ 1, 1, 1 ], [ 2 ] ] [ [ 1, 1, 1 ], [ 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2 ], [ 3 ], [ 4 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4 ] ] [ 1, 2, 3, 4 ] [ [ 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4 ] ] Semigrup: <0, ...> n Semigrup: <0, ...> n >> semigrup([0,1,2,3,4]) eq TrivialSemigroup(); ^ Runtime error in 'eq': Component 5 has no equality algorithm Total time: 5.319 seconds, Total memory usage: 8.11MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sat Feb 28 12:05:40 2004 Input: print "hola2"; semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; while (i_cond gt 0 and semi[i_cond]+1 eq semi[i_cond+1]) do i_cond:=i_cond-1; end while; firstnongaps:=[semi[i]:i in [1..i_cond+1]]; c:=firstnongaps[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #firstnongaps gt 1 then d:=firstnongaps[i_cond]; i:=d; while i in firstnongaps do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; /*return;*/ end function; print "hola1"; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=8; MAXLENGTHPATTERNS:=5; //Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); Semigrups:=[HermitianSemigroup(q): q in [1..6]]; l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do //print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; if Position(ss,semisp) gt NonAdmissibleDegree(p) then admdeg; print "MERDA!"; print p; break; end if; admdeg; end for; [#s: s in ss]; //pp; admdeg; /* s:=semigrup([0,5,6,10,11,12,13,15]); p1:=[1,1,1,-1]; p2:=[1,1,1,1,-1,-1]; NonAdmissibleDegree(p1); NonAdmissibleDegree(p2); admits(s,p1); admits(s,p2); */ semigrup([0,1,2,3,4]); TrivialSemigroup(); Output: Magma V2.10-6 Sat Feb 28 2004 12:05:34 on modular [Seed = 3065396357] ------------------------------------- hola2 hola1 Semigrup: <0, ...> n Semigrup: <0, 2, ...> n Semigrup: <0, 3, 4, 6, ...> n Semigrup: <0, 4, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 15, 16, 17, 18, 20, ...> n Semigrup: <0, 6, 7, 12, 13, 14, 18, 19, 20, 21, 24, 25, 26, 27, 28, 30, ...> n [ [ 1 ] ] [ [ 1 ], [ 2 ] ] [ [ 1, 1 ], [ 2 ] ] [ [ 1, 1, 1 ], [ 2 ] ] [ [ 1, 1, 1 ], [ 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2 ], [ 3 ], [ 4 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4 ] ] [ 1, 2, 3, 4 ] [ [ 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4 ] ] Semigrup: <0, ...> n <[ 0 ], 0, 0, 0, function(i) ... end function, [], function(i) ... end function, function(i) ... end function> Semigrup: <0, ...> n <[ 0 ], 0, 0, 0, function(i) ... end function, [], function(i) ... end function, function(i) ... end function> Total time: 5.299 seconds, Total memory usage: 8.11MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sat Feb 28 12:07:04 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; while (i_cond gt 0 and semi[i_cond]+1 eq semi[i_cond+1]) do i_cond:=i_cond-1; end while; firstnongaps:=[semi[i]:i in [1..i_cond+1]]; c:=firstnongaps[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #firstnongaps gt 1 then d:=firstnongaps[i_cond]; i:=d; while i in firstnongaps do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; /*return;*/ end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; NonAdmissibleDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; return degree; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; MAXGENUS:=8; MAXLENGTHPATTERNS:=6; //Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); Semigrups:=[HermitianSemigroup(q): q in [1..7]]; l:=#Semigrups; Patterns:=AllAdmissiblePatternsWithLengthUpto(MAXLENGTHPATTERNS); ss:=[]; pp:=[]; admdeg:=[]; for p in Patterns do //print p; semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~admdeg,[NonAdmissibleDegree(p)]); else Append(~pp[pos],p); Append(~admdeg[pos],NonAdmissibleDegree(p)); end if; if Position(ss,semisp) gt NonAdmissibleDegree(p) then admdeg; print "MERDA!"; print p; break; end if; admdeg; end for; [#s: s in ss]; //pp; admdeg; /* s:=semigrup([0,5,6,10,11,12,13,15]); p1:=[1,1,1,-1]; p2:=[1,1,1,1,-1,-1]; NonAdmissibleDegree(p1); NonAdmissibleDegree(p2); admits(s,p1); admits(s,p2); */ Output: ** WARNING: Computation used more memory than allowed. ** ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Feb 28 2004 12:06:41 on modular [Seed = 2307457861] ------------------------------------- Semigrup: <0, ...> n Semigrup: <0, 2, ...> n Semigrup: <0, 3, 4, 6, ...> n Semigrup: <0, 4, 5, 8, 9, 10, 12, ...> n Semigrup: <0, 5, 6, 10, 11, 12, 15, 16, 17, 18, 20, ...> n Semigrup: <0, 6, 7, 12, 13, 14, 18, 19, 20, 21, 24, 25, 26, 27, 28, 30, ...> n Semigrup: <0, 7, 8, 14, 15, 16, 21, 22, 23, 24, 28, 29, 30, 31, 32, 35, 36, 37, 38, 39, 40, 42, ...> n [ [ 1 ] ] [ [ 1 ], [ 2 ] ] [ [ 1, 1 ], [ 2 ] ] [ [ 1, 1, 1 ], [ 2 ] ] [ [ 1, 1, 1 ], [ 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2 ], [ 3 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2 ], [ 3 ], [ 4 ] ] [ [ 1, 1, 1, 1 ], [ 2, 2, 2 ], [ 3 ], [ 4 ] ] Current total memory usage: 95.4MB, failed memory request: 0.0MB System Error: User memory limit has been reached Errors: /home/mfd/gomagma: line 2: 11748 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host adsl-67-122-208-92.dsl.pltn13.pacbell.net. (67.122.208.92) Time: Sat Feb 28 14:40:28 2004 Input: X:=Matrix([[1,0],[0,1]]); M:=Matrix([[3,4],[4,5]]); CheckPositive:=false; L:=Lattice(X,M); OrthogonalDecomposition(L); Output: Magma V2.10-6 Sat Feb 28 2004 14:40:25 on modular [Seed = 3435946506] ------------------------------------- >> L:=Lattice(X,M); ^ Runtime error in 'Lattice': Inner product matrix argument is not symmetric and positive definite >> OrthogonalDecomposition(L); ^ User error: Identifier 'L' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ool-44c1e5c3.dyn.optonline.net. (68.193.229.195) Time: Sat Feb 28 23:37:30 2004 Input: 1*1 Output: Magma V2.10-6 Sat Feb 28 2004 23:37:27 on modular [Seed = 3671848494] ------------------------------------- 1 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host n137.ryd.student.liu.se. (130.236.215.137) Time: Sun Feb 29 11:20:52 2004 Input: A:=6630266344492421510655417533975408280699114541037055412014729756283513277532538238251380911683448088469938171104853974381181461030694708079757267652927787330155544253858000367022785705355514415890664933631023320230267609169663354152; B:=1786898538033222544822377658654589094616277597934833272432743612014179728717274383622950999362513959929665111603325695973344596683416556386162365922654447705137091217162506300716384494673369690832522275939006920304016143507331214302; p:=195303555153105689394605664018778179073; E:=ChangeRing(EllipticCurve([A,B]),GF(p)); print(E); Order(E); Output: Magma V2.10-6 Sun Feb 29 2004 11:20:44 on modular [Seed = 1111495471] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 96969244432163517629402382751585239602*x + 106598328600354781932225432498148599643 over GF(195303555153105689394605664018778179073) 195303555153105689394562456737772994016 Total time: 6.089 seconds, Total memory usage: 3.12MB ************** MAGMA ***************** Host 80.58.35.42.proxycache.rima-tde.net. (80.58.35.42) Time: Sun Feb 29 12:18:16 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Sun Feb 29 2004 12:18:13 on modular [Seed = 3907696140] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.42.proxycache.rima-tde.net. (80.58.35.42) Time: Sun Feb 29 12:21:47 2004 Input: a=1; Output: Magma V2.10-6 Sun Feb 29 2004 12:21:44 on modular [Seed = 3638200129] ------------------------------------- >> a=1; ^ User error: Identifier 'a' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.42.proxycache.rima-tde.net. (80.58.35.42) Time: Sun Feb 29 12:22:08 2004 Input: a:=1; Output: Magma V2.10-6 Sun Feb 29 2004 12:22:05 on modular [Seed = 3284245583] ------------------------------------- Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.42.proxycache.rima-tde.net. (80.58.35.42) Time: Sun Feb 29 12:22:23 2004 Input: a:=1; a; Output: Magma V2.10-6 Sun Feb 29 2004 12:22:21 on modular [Seed = 3402143030] ------------------------------------- 1 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.42.proxycache.rima-tde.net. (80.58.35.42) Time: Sun Feb 29 12:22:48 2004 Input: a:=1; assigned a; Output: Magma V2.10-6 Sun Feb 29 2004 12:22:45 on modular [Seed = 909404641] ------------------------------------- true Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.42.proxycache.rima-tde.net. (80.58.35.42) Time: Sun Feb 29 12:23:33 2004 Input: a:=1; b:=2; assigned a; assigned b; a; b; a lt b; Output: Magma V2.10-6 Sun Feb 29 2004 12:23:30 on modular [Seed = 1010719772] ------------------------------------- true true 1 2 true Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.42.proxycache.rima-tde.net. (80.58.35.42) Time: Sun Feb 29 12:24:02 2004 Input: a:=1; b:=2; assigned a; assigned b; a; b; a lt b; b lt a; a gt b; Output: Magma V2.10-6 Sun Feb 29 2004 12:23:59 on modular [Seed = 623330616] ------------------------------------- true true 1 2 true false false Total time: 2.829 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.42.proxycache.rima-tde.net. (80.58.35.42) Time: Sun Feb 29 12:24:38 2004 Input: a:=1; b:=2; assigned a; assigned b; a; b; a lt b; b lt a; a gt b; b gt a; a in b; Output: Magma V2.10-6 Sun Feb 29 2004 12:24:35 on modular [Seed = 303067764] ------------------------------------- true true 1 2 true false false true >> a in b;; ^ Runtime error in 'in': Bad argument types Argument types given: RngIntElt, RngIntElt Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.42.proxycache.rima-tde.net. (80.58.35.42) Time: Sun Feb 29 12:25:18 2004 Input: a:=1; b:=2; assigned a; assigned b; a; b; a lt b; b lt a; a gt b; b gt a; a + b; Output: Magma V2.10-6 Sun Feb 29 2004 12:25:15 on modular [Seed = 522026838] ------------------------------------- true true 1 2 true false false true 3 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.42.proxycache.rima-tde.net. (80.58.35.42) Time: Sun Feb 29 12:25:48 2004 Input: a:=1; b:=2; assigned a; assigned b; a; b; a lt b; b lt a; a gt b; b gt a; a + b := q; Output: Magma V2.10-6 Sun Feb 29 2004 12:25:45 on modular [Seed = 67527855] ------------------------------------- true true 1 2 true false false true >> a + b := q;; ^ User error: Identifier 'q' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.42.proxycache.rima-tde.net. (80.58.35.42) Time: Sun Feb 29 12:26:22 2004 Input: a:=1; b:=2; assigned a; assigned b; a; b; a lt b; b lt a; a gt b; b gt a; q:=(a + b); Output: Magma V2.10-6 Sun Feb 29 2004 12:26:19 on modular [Seed = 219114884] ------------------------------------- true true 1 2 true false false true Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.42.proxycache.rima-tde.net. (80.58.35.42) Time: Sun Feb 29 12:26:59 2004 Input: a:=1; b:=2; assigned a; assigned b; a; b; a lt b; b lt a; a gt b; b gt a; q:=(a + b); q; vector:=[1,2,3,4,5,6,7,8,9,0]; Output: Magma V2.10-6 Sun Feb 29 2004 12:26:56 on modular [Seed = 2054691496] ------------------------------------- true true 1 2 true false false true 3 Total time: 2.839 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.42.proxycache.rima-tde.net. (80.58.35.42) Time: Sun Feb 29 12:27:50 2004 Input: a:=1; b:=2; assigned a; assigned b; a; b; a lt b; b lt a; a gt b; b gt a; q:=(a + b); q; vector:=[1,2,3,4,5,6,7,8,9,0]; m,p:=Min(vector); Output: Magma V2.10-6 Sun Feb 29 2004 12:27:47 on modular [Seed = 1667301954] ------------------------------------- true true 1 2 true false false true 3 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.42.proxycache.rima-tde.net. (80.58.35.42) Time: Sun Feb 29 12:28:08 2004 Input: a:=1; b:=2; assigned a; assigned b; a; b; a lt b; b lt a; a gt b; b gt a; q:=(a + b); q; vector:=[1,2,3,4,5,6,7,8,9,0]; m,p:=Min(vector); m,p; Output: Magma V2.10-6 Sun Feb 29 2004 12:28:05 on modular [Seed = 1751779711] ------------------------------------- true true 1 2 true false false true 3 0 10 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sun Feb 29 12:59:11 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+1); E:=EquationOrder(K); OK:=MaximalOrder(K); Index(OK, E); I:=2004*OK; Factorization(I); [K!OK.i : i in [1, 2]]; Output: Magma V2.10-6 Sun Feb 29 2004 12:59:08 on modular [Seed = 2745289725] ------------------------------------- 1 [ , , ] [ 1, a ] Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sun Feb 29 12:59:38 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^4+1); E:=EquationOrder(K); OK:=MaximalOrder(K); Index(OK, E); [K!OK.i : i in [1, 2]]; Output: Magma V2.10-6 Sun Feb 29 2004 12:59:35 on modular [Seed = 2829762589] ------------------------------------- 1 [ 1, a ] Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sun Feb 29 13:00:00 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^4+2); E:=EquationOrder(K); OK:=MaximalOrder(K); Index(OK, E); [K!OK.i : i in [1, 2, 3, 4]]; Output: Magma V2.10-6 Sun Feb 29 2004 12:59:57 on modular [Seed = 2442393918] ------------------------------------- 1 [ 1, a, a^2, a^3 ] Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sun Feb 29 13:02:20 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^4+7*x^3+2); E:=EquationOrder(K); OK:=MaximalOrder(K); Index(OK, E); [K!OK.i : i in [1, 2, 3, 4]]; Output: Magma V2.10-6 Sun Feb 29 2004 13:02:17 on modular [Seed = 4109802991] ------------------------------------- 1 [ 1, a, a^2, a^3 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sun Feb 29 13:04:32 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^4+8*x^3-2); E:=EquationOrder(K); OK:=MaximalOrder(K); OK; Index(OK, E); [K!OK.i : i in [1]]; Output: Magma V2.10-6 Sun Feb 29 2004 13:04:29 on modular [Seed = 3806366589] ------------------------------------- Maximal Equation Order with defining polynomial x^4 + 8*x^3 - 2 over its ground order 1 [ 1 ] Total time: 2.909 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sun Feb 29 13:05:52 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3+2); E:=EquationOrder(K); OK:=MaximalOrder(K); OK; Index(OK, E); Output: Magma V2.10-6 Sun Feb 29 2004 13:05:49 on modular [Seed = 4025320992] ------------------------------------- Maximal Equation Order with defining polynomial x^3 + 2 over its ground order 1 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sun Feb 29 13:06:47 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^7+32*x^2+2); E:=EquationOrder(K); OK:=MaximalOrder(K); OK; I:=2*OK; Index(OK, E); Output: Magma V2.10-6 Sun Feb 29 2004 13:06:44 on modular [Seed = 3570843346] ------------------------------------- Maximal Equation Order with defining polynomial x^7 + 32*x^2 + 2 over its ground order 1 Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sun Feb 29 13:07:05 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^7+32*x^2+2); E:=EquationOrder(K); E; OK:=MaximalOrder(K); OK; I:=2*OK; Index(OK, E); Output: Magma V2.10-6 Sun Feb 29 2004 13:07:02 on modular [Seed = 3722426281] ------------------------------------- Equation Order with defining polynomial x^7 + 32*x^2 + 2 over its ground order Maximal Equation Order with defining polynomial x^7 + 32*x^2 + 2 over its ground order 1 Total time: 3.039 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sun Feb 29 13:07:22 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^7+32*x^2+2); E:=EquationOrder(K); E; OK:=MaximalOrder(K); OK; I:=2*OK; I; Index(OK, E); Output: Magma V2.10-6 Sun Feb 29 2004 13:07:19 on modular [Seed = 3402145967] ------------------------------------- Equation Order with defining polynomial x^7 + 32*x^2 + 2 over its ground order Maximal Equation Order with defining polynomial x^7 + 32*x^2 + 2 over its ground order Principal Ideal of E Generator: [2, 0, 0, 0, 0, 0, 0] 1 Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sun Feb 29 13:07:56 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^7+32*x^2+2); OK:=MaximalOrder(K); OK; I:=2*OK; I; Index(OK, E); [K!OK.i : i in [1..7]]; Output: Magma V2.10-6 Sun Feb 29 2004 13:07:53 on modular [Seed = 842029176] ------------------------------------- Maximal Equation Order with defining polynomial x^7 + 32*x^2 + 2 over its ground order Principal Ideal of OK Generator: [2, 0, 0, 0, 0, 0, 0] >> Index(OK, E); ^ User error: Identifier 'E' has not been declared or assigned [ 1, a, a^2, a^3, a^4, a^5, a^6 ] Total time: 3.029 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sun Feb 29 13:08:21 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3+2); OK:=MaximalOrder(K); OK; I:=2*OK; I; Index(OK, E); [K!OK.i : i in [1..3]]; Output: Magma V2.10-6 Sun Feb 29 2004 13:08:18 on modular [Seed = 943346329] ------------------------------------- Maximal Equation Order with defining polynomial x^3 + 2 over its ground order Principal Ideal of OK Generator: [2, 0, 0] >> Index(OK, E); ^ User error: Identifier 'E' has not been declared or assigned [ 1, a, a^2 ] Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sun Feb 29 13:08:49 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^4+2); OK:=MaximalOrder(K); OK; I:=2*OK; I; [K!OK.i : i in [1..3]]; Output: Magma V2.10-6 Sun Feb 29 2004 13:08:46 on modular [Seed = 656756154] ------------------------------------- Maximal Equation Order with defining polynomial x^4 + 2 over its ground order Principal Ideal of OK Generator: [2, 0, 0, 0] [ 1, a, a^2 ] Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sun Feb 29 13:09:16 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^4+4*x^3+28); OK:=MaximalOrder(K); OK; I:=2*OK; I; [K!OK.i : i in [1..3]]; Output: Magma V2.10-6 Sun Feb 29 2004 13:09:13 on modular [Seed = 774653140] ------------------------------------- Maximal Order of Equation Order with defining polynomial x^4 + 4*x^3 + 28 over its ground order Principal Ideal of OK Generator: [2, 0, 0, 0] [ 1, a, 1/2*a^2 ] Total time: 3.029 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sun Feb 29 13:09:31 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^4+4*x^3+28); OK:=MaximalOrder(K); OK; I:=2*OK; I; [K!OK.i : i in [1..4]]; Output: Magma V2.10-6 Sun Feb 29 2004 13:09:28 on modular [Seed = 353861630] ------------------------------------- Maximal Order of Equation Order with defining polynomial x^4 + 4*x^3 + 28 over its ground order Principal Ideal of OK Generator: [2, 0, 0, 0] [ 1, a, 1/2*a^2, 1/4*(a^3 - 2*a) ] Total time: 3.009 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sun Feb 29 13:10:10 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^4+8*x^3-2); OK:=MaximalOrder(K); OK; I:=2*OK; I; [K!OK.i : i in [1..4]]; Output: Magma V2.10-6 Sun Feb 29 2004 13:10:07 on modular [Seed = 84373449] ------------------------------------- Maximal Equation Order with defining polynomial x^4 + 8*x^3 - 2 over its ground order Principal Ideal of OK Generator: [2, 0, 0, 0] [ 1, a, a^2, a^3 ] Total time: 2.979 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sun Feb 29 13:12:12 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^7+8*x^3-2); OK:=MaximalOrder(K); OK; I:=2*OK; I; [K!OK.i : i in [1..7]]; Output: Magma V2.10-6 Sun Feb 29 2004 13:12:09 on modular [Seed = 202270534] ------------------------------------- Maximal Equation Order with defining polynomial x^7 + 8*x^3 - 2 over its ground order Principal Ideal of OK Generator: [2, 0, 0, 0, 0, 0, 0] [ 1, a, a^2, a^3, a^4, a^5, a^6 ] Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sun Feb 29 13:12:49 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^6+5*x^5+3); OK:=MaximalOrder(K); OK; I:=2*OK; I; [K!OK.i : i in [1..6]]; Output: Magma V2.10-6 Sun Feb 29 2004 13:12:46 on modular [Seed = 2071531734] ------------------------------------- Maximal Equation Order with defining polynomial x^6 + 5*x^5 + 3 over its ground order Principal Ideal of OK Generator: [2, 0, 0, 0, 0, 0] [ 1, a, a^2, a^3, a^4, a^5 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sun Feb 29 13:13:01 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^6+5*x^5+10); OK:=MaximalOrder(K); OK; I:=2*OK; I; [K!OK.i : i in [1..6]]; Output: Magma V2.10-6 Sun Feb 29 2004 13:12:59 on modular [Seed = 1650461178] ------------------------------------- Maximal Equation Order with defining polynomial x^6 + 5*x^5 + 10 over its ground order Principal Ideal of OK Generator: [2, 0, 0, 0, 0, 0] [ 1, a, a^2, a^3, a^4, a^5 ] Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sun Feb 29 13:23:41 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^6+5*x^5+10); OK:=MaximalOrder(K); OK; I:=2*OK; I; [K!OK.i : i in [1..6]]; Output: Magma V2.10-6 Sun Feb 29 2004 13:23:38 on modular [Seed = 1499150144] ------------------------------------- Maximal Equation Order with defining polynomial x^6 + 5*x^5 + 10 over its ground order Principal Ideal of OK Generator: [2, 0, 0, 0, 0, 0] [ 1, a, a^2, a^3, a^4, a^5 ] Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 62-37-40-92.dialup.uni2.es. (62.37.40.92) Time: Sun Feb 29 14:54:00 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Sun Feb 29 2004 14:53:57 on modular [Seed = 303042931] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 62-37-40-92.dialup.uni2.es. (62.37.40.92) Time: Sun Feb 29 15:01:24 2004 Input: hello Output: Magma V2.10-6 Sun Feb 29 2004 15:01:21 on modular [Seed = 2038135900] ------------------------------------- >> hello; ^ User error: Identifier 'hello' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sun Feb 29 15:12:06 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+1); E:=EquationOrder(K); OK:=MaximalOrder(K); Index(OK, E); I:=2004*OK; Factorization(I); [K!OK.i : i in [1, 2]]; Output: Magma V2.10-6 Sun Feb 29 2004 15:12:03 on modular [Seed = 1465209072] ------------------------------------- 1 [ , , ] [ 1, a ] Total time: 3.049 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sun Feb 29 15:12:54 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); E:=EquationOrder(K); OK:=MaximalOrder(K); Index(OK, E); I:=2*OK; Factorization(I); [K!OK.i : i in [1..5]]; Output: Magma V2.10-6 Sun Feb 29 2004 15:12:51 on modular [Seed = 1482317743] ------------------------------------- 1 [ ] [ 1, a, a^2, a^3, a^4 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sun Feb 29 15:21:38 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); OK:=MaximalOrder(K); I:=2*OK; Factorization(I); [K!OK.i : i in [1..5]]; t:={2*OK, 3*OK} t; Output: Magma V2.10-6 Sun Feb 29 2004 15:21:35 on modular [Seed = 2964502859] ------------------------------------- [ ] [ 1, a, a^2, a^3, a^4 ] >> t;; ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sun Feb 29 15:21:50 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); OK:=MaximalOrder(K); I:=2*OK; Factorization(I); [K!OK.i : i in [1..5]]; t:={2*OK, 3*OK}; t; Output: Magma V2.10-6 Sun Feb 29 2004 15:21:47 on modular [Seed = 3116085334] ------------------------------------- [ ] [ 1, a, a^2, a^3, a^4 ] { Principal Ideal of OK Generator: [2, 0, 0, 0, 0], Principal Ideal of OK Generator: [3, 0, 0, 0, 0] } Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sun Feb 29 15:22:18 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); OK:=MaximalOrder(K); I:=2*OK; Factorization(I); [K!OK.i : i in [1..5]]; t:={2*OK, 3*OK}; t; Factorization(t); Output: Magma V2.10-6 Sun Feb 29 2004 15:22:15 on modular [Seed = 2728438625] ------------------------------------- [ ] [ 1, a, a^2, a^3, a^4 ] { Principal Ideal of OK Generator: [2, 0, 0, 0, 0], Principal Ideal of OK Generator: [3, 0, 0, 0, 0] } >> Factorization(t);; ^ Runtime error in 'Factorization': Bad argument types Argument types given: SetEnum[RngOrdIdl] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sun Feb 29 15:22:32 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); OK:=MaximalOrder(K); I:=2*OK; Factorization(I); [K!OK.i : i in [1..5]]; t:={2*OK, 3*OK}; t; Factorization; Output: Magma V2.10-6 Sun Feb 29 2004 15:22:29 on modular [Seed = 2880020890] ------------------------------------- [ ] [ 1, a, a^2, a^3, a^4 ] { Principal Ideal of OK Generator: [2, 0, 0, 0, 0], Principal Ideal of OK Generator: [3, 0, 0, 0, 0] } Intrinsic 'Factorization' Signatures: ( n) -> RngIntEltFact, RngIntElt, SeqEnum [ Proof: BoolElt, Bases: RngIntElt, TrialDivisionLimit: RngIntElt, PollardRhoLimit: RngIntElt, ECMLimit: RngIntElt, MPQSLimit: RngIntElt ] Attempt to find the prime factorization of the value of n; the factorization is returned, together with the appropriate unit and the sequence of composite factors which could not be factored. ( f) -> SeqEnum, RngElt [ Al: "BerlekampLarge" | "BerlekampSmall" | "Default" | "GKS", Certificates: BoolElt, IsSquarefree: BoolElt, Ideals: BoolElt, Extensions: BoolElt ] ( f) -> SeqEnum, RngElt Factorization of f into irreducible factors together with the appropriate unit. ( I) -> SeqEnum ( I) -> SeqEnum The factorization of I into prime ideals. ( n) -> SeqEnum, Tup Factorization of n in the maximal order of the quadratic number field Q(Sqrt(d)), where d is one of: -1, -2, -3, -7, or -11. Returns the factorization along with the appropriate power of a unit (the unit being -1, Sqrt(-1), or [1 + Sqrt(-3)]/2). ( f) -> SeqEnum, RngElt, . [ Certificates, IsSquarefree, Ideals, Extensions ] Factorization of f into irreducible factors together with the appropriate scalar and certifcates for the irreducibility of the factors if requested. Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sun Feb 29 15:24:23 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); OK:=MaximalOrder(K); I:=2*OK; Factorization(I); [K!OK.i : i in [1..5]]; t:=[2*OK, 3*OK]; t; Factorization(t[1]); Output: Magma V2.10-6 Sun Feb 29 2004 15:24:20 on modular [Seed = 2644482013] ------------------------------------- [ ] [ 1, a, a^2, a^3, a^4 ] [ Principal Ideal of OK Generator: [2, 0, 0, 0, 0], Principal Ideal of OK Generator: [3, 0, 0, 0, 0] ] [ ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sun Feb 29 15:25:56 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); OK:=MaximalOrder(K); I:=2*OK; Factorization(I); [K!OK.i : i in [1..5]]; t:=[2*OK, 3*OK]; t; [Factorization( t[i] ) : i in [1, 2] ]; Output: Magma V2.10-6 Sun Feb 29 2004 15:25:53 on modular [Seed = 2189461607] ------------------------------------- [ ] [ 1, a, a^2, a^3, a^4 ] [ Principal Ideal of OK Generator: [2, 0, 0, 0, 0], Principal Ideal of OK Generator: [3, 0, 0, 0, 0] ] [ [ ], [ ] ] Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sun Feb 29 15:27:12 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); OK:=MaximalOrder(K); I:=2*OK; Factorization(I); [K!OK.i : i in [1..5]]; t:=[p*OK: p in [1..100] | IsPrime(p)]; t; [Factorization( t[i] ) : i in [1, 2] ]; Output: Magma V2.10-6 Sun Feb 29 2004 15:27:09 on modular [Seed = 2341044386] ------------------------------------- [ ] [ 1, a, a^2, a^3, a^4 ] [ Principal Ideal of OK Generator: [2, 0, 0, 0, 0], Principal Ideal of OK Generator: [3, 0, 0, 0, 0], Principal Ideal of OK Generator: [5, 0, 0, 0, 0], Principal Ideal of OK Generator: [7, 0, 0, 0, 0], Principal Ideal of OK Generator: [11, 0, 0, 0, 0], Principal Ideal of OK Generator: [13, 0, 0, 0, 0], Principal Ideal of OK Generator: [17, 0, 0, 0, 0], Principal Ideal of OK Generator: [19, 0, 0, 0, 0], Principal Ideal of OK Generator: [23, 0, 0, 0, 0], Principal Ideal of OK Generator: [29, 0, 0, 0, 0], Principal Ideal of OK Generator: [31, 0, 0, 0, 0], Principal Ideal of OK Generator: [37, 0, 0, 0, 0], Principal Ideal of OK Generator: [41, 0, 0, 0, 0], Principal Ideal of OK Generator: [43, 0, 0, 0, 0], Principal Ideal of OK Generator: [47, 0, 0, 0, 0], Principal Ideal of OK Generator: [53, 0, 0, 0, 0], Principal Ideal of OK Generator: [59, 0, 0, 0, 0], Principal Ideal of OK Generator: [61, 0, 0, 0, 0], Principal Ideal of OK Generator: [67, 0, 0, 0, 0], Principal Ideal of OK Generator: [71, 0, 0, 0, 0], Principal Ideal of OK Generator: [73, 0, 0, 0, 0], Principal Ideal of OK Generator: [79, 0, 0, 0, 0], Principal Ideal of OK Generator: [83, 0, 0, 0, 0], Principal Ideal of OK Generator: [89, 0, 0, 0, 0], Principal Ideal of OK Generator: [97, 0, 0, 0, 0] ] [ [ ], [ ] ] Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sun Feb 29 15:28:21 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); OK:=MaximalOrder(K); I:=2*OK; Factorization(I); [K!OK.i : i in [1..5]]; t:=[p*OK: p in [1..100] | IsPrime(p)]; |t|; [Factorization( t[i] ) : i in [1, 2] ]; Output: Magma V2.10-6 Sun Feb 29 2004 15:28:18 on modular [Seed = 4261410475] ------------------------------------- [ ] [ 1, a, a^2, a^3, a^4 ] >> |t|; ^ User error: bad syntax [ [ ], [ ] ] Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sun Feb 29 15:28:36 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); OK:=MaximalOrder(K); I:=2*OK; Factorization(I); [K!OK.i : i in [1..5]]; t:=[p*OK: p in [1..100] | IsPrime(p)]; Size(t); [Factorization( t[i] ) : i in [1, 2] ]; Output: Magma V2.10-6 Sun Feb 29 2004 15:28:33 on modular [Seed = 3873762723] ------------------------------------- [ ] [ 1, a, a^2, a^3, a^4 ] >> Size(t); ^ Runtime error in 'Size': Bad argument types Argument types given: SeqEnum[RngOrdIdl] [ [ ], [ ] ] Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sun Feb 29 15:30:58 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); OK:=MaximalOrder(K); I:=2*OK; Factorization(I); [K!OK.i : i in [1..5]]; t:=[p*OK: p in [1..100] | IsPrime(p)]; P:=[p: p in [1..100] | IsPrime(p)]; [Factorization( t[i] ) : i in [1, 2] ]; Output: Magma V2.10-6 Sun Feb 29 2004 15:30:55 on modular [Seed = 3604274461] ------------------------------------- [ ] [ 1, a, a^2, a^3, a^4 ] [ [ ], [ ] ] Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sun Feb 29 15:31:10 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); OK:=MaximalOrder(K); I:=2*OK; Factorization(I); [K!OK.i : i in [1..5]]; t:=[p*OK: p in [1..100] | IsPrime(p)]; P:=[p: p in [1..100] | IsPrime(p)]; P; [Factorization( t[i] ) : i in [1, 2] ]; Output: Magma V2.10-6 Sun Feb 29 2004 15:31:07 on modular [Seed = 3755856864] ------------------------------------- [ ] [ 1, a, a^2, a^3, a^4 ] [ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 ] [ [ ], [ ] ] Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sun Feb 29 15:31:45 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); OK:=MaximalOrder(K); I:=2*OK; Factorization(I); [K!OK.i : i in [1..5]]; t:=[p*OK: p in [1..100] | IsPrime(p)]; [Factorization( t[i] ) : i in [1..25] ]; Output: Magma V2.10-6 Sun Feb 29 2004 15:31:42 on modular [Seed = 3233991898] ------------------------------------- [ ] [ 1, a, a^2, a^3, a^4 ] [ [ ], [ ], [ , , ], [ , ], [ , , , ], [ , ], [ , , ], [ , , ], [ , ], [ , , ], [ , , ], [ ], [ , ], [ , , , ], [ , ], [ , ], [ , ], [ ], [ , , , ], [ , , , ], [ ], [ , ], [ , , , ], [ , ], [ ] ] Total time: 3.089 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sun Feb 29 15:32:38 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); OK:=MaximalOrder(K); I:=2*OK; Factorization(I); [K!OK.i : i in [1..5]]; t:=[p*OK: p in [1..100] | IsPrime(p)]; t; [Factorization( t[i] ) : i in [1..25] ]; Output: Magma V2.10-6 Sun Feb 29 2004 15:32:35 on modular [Seed = 3385574814] ------------------------------------- [ ] [ 1, a, a^2, a^3, a^4 ] [ Principal Ideal of OK Generator: [2, 0, 0, 0, 0], Principal Ideal of OK Generator: [3, 0, 0, 0, 0], Principal Ideal of OK Generator: [5, 0, 0, 0, 0], Principal Ideal of OK Generator: [7, 0, 0, 0, 0], Principal Ideal of OK Generator: [11, 0, 0, 0, 0], Principal Ideal of OK Generator: [13, 0, 0, 0, 0], Principal Ideal of OK Generator: [17, 0, 0, 0, 0], Principal Ideal of OK Generator: [19, 0, 0, 0, 0], Principal Ideal of OK Generator: [23, 0, 0, 0, 0], Principal Ideal of OK Generator: [29, 0, 0, 0, 0], Principal Ideal of OK Generator: [31, 0, 0, 0, 0], Principal Ideal of OK Generator: [37, 0, 0, 0, 0], Principal Ideal of OK Generator: [41, 0, 0, 0, 0], Principal Ideal of OK Generator: [43, 0, 0, 0, 0], Principal Ideal of OK Generator: [47, 0, 0, 0, 0], Principal Ideal of OK Generator: [53, 0, 0, 0, 0], Principal Ideal of OK Generator: [59, 0, 0, 0, 0], Principal Ideal of OK Generator: [61, 0, 0, 0, 0], Principal Ideal of OK Generator: [67, 0, 0, 0, 0], Principal Ideal of OK Generator: [71, 0, 0, 0, 0], Principal Ideal of OK Generator: [73, 0, 0, 0, 0], Principal Ideal of OK Generator: [79, 0, 0, 0, 0], Principal Ideal of OK Generator: [83, 0, 0, 0, 0], Principal Ideal of OK Generator: [89, 0, 0, 0, 0], Principal Ideal of OK Generator: [97, 0, 0, 0, 0] ] [ [ ], [ ], [ , , ], [ , ], [ , , , ], [ , ], [ , , ], [ , , ], [ , ], [ , , ], [ , , ], [ ], [ , ], [ , , , ], [ , ], [ , ], [ , ], [ ], [ , , , ], [ , , , ], [ ], [ , ], [ , , , ], [ , ], [ ] ] Total time: 3.099 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host jcarlos.uab.es. (158.109.9.25) Time: Mon Mar 1 03:15:05 2004 Input: gfffff Output: Magma V2.10-6 Mon Mar 1 2004 03:15:02 on modular [Seed = 4126622920] ------------------------------------- >> gfffff; ^ User error: Identifier 'gfffff' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse008.uab.es. (158.109.66.73) Time: Mon Mar 1 05:52:22 2004 Input: GF(8) subset GF(16); Output: Magma V2.10-6 Mon Mar 1 2004 05:52:18 on modular [Seed = 4177243429] ------------------------------------- false Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse008.uab.es. (158.109.66.73) Time: Mon Mar 1 05:53:13 2004 Input: GF(8) meet GF(16); Output: Magma V2.10-6 Mon Mar 1 2004 05:53:10 on modular [Seed = 4025268678] ------------------------------------- Finite field of size 2 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse008.uab.es. (158.109.66.73) Time: Mon Mar 1 05:54:31 2004 Input: K:=GF(9); V3:=VectorSpace(K,3); v:=V3![K.1,0,1]; v; Output: Magma V2.10-6 Mon Mar 1 2004 05:54:28 on modular [Seed = 3840389823] ------------------------------------- ( K.1 0 1) Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-etse008.uab.es. (158.109.66.73) Time: Mon Mar 1 05:55:34 2004 Input: K:=GF(9); V3:=VectorSpace(K,3); v:=V3![K.1,0,1]; v; v[1]; Output: Magma V2.10-6 Mon Mar 1 2004 05:55:31 on modular [Seed = 3621028171] ------------------------------------- ( K.1 0 1) K.1 Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Mon Mar 1 06:27:45 2004 Input: M43:=KMatrixSpace(K,4,3); m:=M43![K.1, 2, 2*K.1, 1, 0, K.1, 2*K.1+1, 2*K.1+2, K.1, K.1+2, 0, 2*K.1+1]; m; Output: Magma V2.10-6 Mon Mar 1 2004 06:27:42 on modular [Seed = 3469578401] ------------------------------------- >> M43:=KMatrixSpace(K,4,3); ^ User error: Identifier 'K' has not been declared or assigned >> m:=M43![K.1, 2, 2*K.1, 1, 0, K.1, 2*K.1+1, 2*K.1+2, K.1, K.1+2, 0, 2*K.1+1] ^ User error: Identifier 'M43' has not been declared or assigned >> m;; ^ User error: Identifier 'm' has not been declared or assigned Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Mon Mar 1 06:28:31 2004 Input: K:=GF(9); M43:=KMatrixSpace(K,4,3); m:=M43![K.1, 2, 2*K.1, 1, 0, K.1, 2*K.1+1, 2*K.1+2, K.1, K.1+2, 0, 2*K.1+1]; m; Output: Magma V2.10-6 Mon Mar 1 2004 06:28:28 on modular [Seed = 3739058371] ------------------------------------- [ K.1 2 K.1^5] [ 1 0 K.1] [K.1^3 K.1^6 K.1] [K.1^7 0 K.1^3] Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Mon Mar 1 08:15:31 2004 Input: magma Output: Magma V2.10-6 Mon Mar 1 2004 08:15:28 on modular [Seed = 3469588988] ------------------------------------- >> magma ^ User error: Identifier 'magma' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Mon Mar 1 08:15:54 2004 Input: magma; Output: Magma V2.10-6 Mon Mar 1 2004 08:15:51 on modular [Seed = 3907755821] ------------------------------------- >> magma;; ^ User error: Identifier 'magma' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Mon Mar 1 08:16:58 2004 Input: Floor(3.444); Output: Magma V2.10-6 Mon Mar 1 2004 08:16:55 on modular [Seed = 4059203188] ------------------------------------- 3 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Mon Mar 1 08:17:17 2004 Input: Floor(3.444); Output: Magma V2.10-6 Mon Mar 1 2004 08:17:14 on modular [Seed = 2273636383] ------------------------------------- 3 Total time: 2.869 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Mon Mar 1 08:17:42 2004 Input: Sort([3,2,4]); Output: Magma V2.10-6 Mon Mar 1 2004 08:17:39 on modular [Seed = 2358246205] ------------------------------------- [ 2, 3, 4 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dirichlet.math.umass.edu. (128.119.47.126) Time: Mon Mar 1 14:26:32 2004 Input: > F:=FreeGroup(2); > a:=y^2*x*y*x*y; > G:=quo; > for i:=1 to 10 do for> print i,FactoredOrder(pQuotient(G,2,i)); for> end for; Output: Magma V2.10-6 Mon Mar 1 2004 14:26:29 on modular [Seed = 1364369266] ------------------------------------- >> for> print i,FactoredOrder(pQuotient(G,2,i)); ^ User error: bad syntax >> for> end for; ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dirichlet.math.umass.edu. (128.119.47.126) Time: Mon Mar 1 14:26:54 2004 Input: F:=FreeGroup(2); a:=y^2*x*y*x*y; G:=quo; for i:=1 to 10 do print i,FactoredOrder(pQuotient(G,2,i)); end for; Output: Magma V2.10-6 Mon Mar 1 2004 14:26:51 on modular [Seed = 1717938267] ------------------------------------- 1 [ <2, 2> ] 2 [ <2, 5> ] 3 [ <2, 8> ] 4 [ <2, 11> ] 5 [ <2, 14> ] 6 [ <2, 16> ] 7 [ <2, 20> ] 8 [ <2, 24> ] 9 [ <2, 30> ] 10 [ <2, 36> ] Total time: 2.939 seconds, Total memory usage: 21.80MB ************** MAGMA ***************** Host dirichlet.math.umass.edu. (128.119.47.126) Time: Mon Mar 1 14:28:01 2004 Input: F:=FreeGroup(2); a:=y^2*x*y*x^(-1)*y^(-1); G:=quo; for i:=1 to 10 do print i,FactoredOrder(pQuotient(G,2,i)); end for; Output: Magma V2.10-6 Mon Mar 1 2004 14:27:58 on modular [Seed = 1869390231] ------------------------------------- 1 [ <2, 2> ] 2 [ <2, 5> ] 3 [ <2, 8> ] 4 [ <2, 11> ] 5 [ <2, 14> ] 6 [ <2, 16> ] 7 [ <2, 20> ] 8 [ <2, 24> ] 9 [ <2, 30> ] 10 [ <2, 36> ] Total time: 2.979 seconds, Total memory usage: 41.69MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Mon Mar 1 16:48:04 2004 Input: if 5 = 5 then 3 + 4 end if; Output: Magma V2.10-6 Mon Mar 1 2004 16:48:00 on modular [Seed = 3654956558] ------------------------------------- >> if 5 = 5 then 3 + 4 end if; ^ User error: bad syntax Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Mon Mar 1 16:48:52 2004 Input: if 5 = 5 then 3 end if; Output: Magma V2.10-6 Mon Mar 1 2004 16:48:49 on modular [Seed = 4025221225] ------------------------------------- >> if 5 = 5 then 3 end if; ^ User error: bad syntax Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Mon Mar 1 16:49:13 2004 Input: if 5 = 5 then 3+4 else 4 + 5 end if; Output: Magma V2.10-6 Mon Mar 1 2004 16:49:10 on modular [Seed = 4143257959] ------------------------------------- >> if 5 = 5 then 3+4 else 4 + 5 end if; ^ User error: bad syntax Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Mon Mar 1 16:49:52 2004 Input: if 5 = 5 then 3+4; else 4 + 5; end if; Output: Magma V2.10-6 Mon Mar 1 2004 16:49:49 on modular [Seed = 4244575046] ------------------------------------- >> if 5 = 5 then 3+4; else 4 + 5; end if; ^ Runtime error in if: Logical expected Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Mon Mar 1 16:50:31 2004 Input: if 5 = 5 then 3+4 elif 4 = 4 then 4 + 5 else 6 + 4 end if; Output: Magma V2.10-6 Mon Mar 1 2004 16:50:28 on modular [Seed = 2358213871] ------------------------------------- >> if 5 = 5 then 3+4 elif 4 = 4 then 4 + 5 else 6 + 4 end if; ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Mon Mar 1 16:52:46 2004 Input: if true then false else true; Output: Magma V2.10-6 Mon Mar 1 2004 16:52:43 on modular [Seed = 2475713407] ------------------------------------- >> if true then false else true; ^ User error: bad syntax Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Mon Mar 1 16:52:58 2004 Input: if true then false else true end if; Output: Magma V2.10-6 Mon Mar 1 2004 16:52:55 on modular [Seed = 2593745514] ------------------------------------- >> if true then false else true end if; ^ User error: bad syntax Total time: 2.869 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Mon Mar 1 16:53:19 2004 Input: if (true) then (false) else (true); Output: Magma V2.10-6 Mon Mar 1 2004 16:53:16 on modular [Seed = 2913885478] ------------------------------------- >> if (true) then (false) else (true); ^ User error: bad syntax Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Mon Mar 1 17:13:43 2004 Input: m := Random( 2, 10000 ); if IsPrime(m) then print m, "is prime"; else print Factorization(m); end if; Output: Magma V2.10-6 Mon Mar 1 2004 17:13:40 on modular [Seed = 1617139132] ------------------------------------- [ <2, 5>, <193, 1> ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Mon Mar 1 17:14:29 2004 Input: m := Random( 2, 10000 ); print m, " is da numba"; if IsPrime(m) then print m, "is prime"; else print Factorization(m); end if; Output: Magma V2.10-6 Mon Mar 1 2004 17:14:26 on modular [Seed = 2038074611] ------------------------------------- 3218 is da numba [ <2, 1>, <1609, 1> ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Mon Mar 1 17:14:47 2004 Input: m := Random( 2, 10000 ); print m, " is da numba"; if IsPrime(m) then print m, "is prime"; else print Factorization(m); end if; Output: Magma V2.10-6 Mon Mar 1 2004 17:14:44 on modular [Seed = 1920042990] ------------------------------------- 8089 is da numba 8089 is prime Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Mon Mar 1 17:15:11 2004 Input: m := Random( 2, 10000 ); print m, " is da numba"; if IsPrime(m) then print m, "is prime"; else print Factorization(m); end if; Output: Magma V2.10-6 Mon Mar 1 2004 17:15:08 on modular [Seed = 252508843] ------------------------------------- 4608 is da numba [ <2, 9>, <3, 2> ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Mon Mar 1 17:17:04 2004 Input: m := Random( 2, 10000 ); print m, " is da numba"; if m = 3 then print m, "is prime"; else print Factorization(m); end if; Output: Magma V2.10-6 Mon Mar 1 2004 17:17:01 on modular [Seed = 437906447] ------------------------------------- 9567 is da numba >> if m = 3 then ^ Runtime error in if: Logical expected Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Mon Mar 1 17:17:16 2004 Input: m := Random( 2, 10000 ); print m, " is da numba"; if (m = 3) then print m, "is prime"; else print Factorization(m); end if; Output: Magma V2.10-6 Mon Mar 1 2004 17:17:13 on modular [Seed = 337109557] ------------------------------------- 9225 is da numba >> if (m = 3) then ^ Runtime error in if: Logical expected Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Mon Mar 1 17:17:34 2004 Input: m := Random( 2, 10000 ); print m, " is da numba"; if (m = m) then print m, "is prime"; else print Factorization(m); end if; Output: Magma V2.10-6 Mon Mar 1 2004 17:17:31 on modular [Seed = 758045470] ------------------------------------- 2275 is da numba >> if (m = m) then ^ Runtime error in if: Logical expected Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Mon Mar 1 17:18:03 2004 Input: m := Random( 2, 10000 ); print m, " is da numba"; if eq(m,3) then print m, "is prime"; else print Factorization(m); end if; Output: Magma V2.10-6 Mon Mar 1 2004 17:18:00 on modular [Seed = 656724471] ------------------------------------- 7134 is da numba >> if eq(m,3) then ^ User error: bad syntax 7134 is prime >> else ^ User error: bad syntax [ <2, 1>, <3, 1>, <29, 1>, <41, 1> ] >> end if;; ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Mon Mar 1 17:19:43 2004 Input: m := Random( 2, 10000 ); print m, " is da numba"; if (m eq 3) then print m, "is prime"; else print Factorization(m); end if; Output: Magma V2.10-6 Mon Mar 1 2004 17:19:40 on modular [Seed = 825411461] ------------------------------------- 6032 is da numba [ <2, 4>, <13, 1>, <29, 1> ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ca-rennes-4-29.w80-8.abo.wanadoo.fr. (80.8.3.29) Time: Mon Mar 1 18:09:03 2004 Input: M:=Matrix(GF(2),8,8,[0,1,0,0,1,1,1,1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0,0,1,0,1,0,0,1,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0]); Output: Magma V2.10-6 Mon Mar 1 2004 18:09:00 on modular [Seed = 2964533876] ------------------------------------- Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ca-rennes-4-29.w80-8.abo.wanadoo.fr. (80.8.3.29) Time: Mon Mar 1 18:09:21 2004 Input: M:=Matrix(GF(2),8,8,[0,1,0,0,1,1,1,1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0,0,1,0,1,0,0,1,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0]); M; Output: Magma V2.10-6 Mon Mar 1 2004 18:09:18 on modular [Seed = 1212926623] ------------------------------------- [0 1 0 0 1 1 1 1] [1 0 1 0 0 1 1 1] [0 1 0 1 0 0 1 1] [0 0 1 0 1 0 0 1] [0 0 0 1 0 1 0 0] [1 0 0 0 0 0 1 0] [1 1 0 0 1 0 0 1] [1 1 1 0 0 1 0 0] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ca-rennes-4-29.w80-8.abo.wanadoo.fr. (80.8.3.29) Time: Mon Mar 1 18:09:37 2004 Input: M:=Matrix(GF(2),8,8,[0,1,0,0,1,1,1,1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0,0,1,0,1,0,0,1,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0]); Kernel(M); Output: Magma V2.10-6 Mon Mar 1 2004 18:09:34 on modular [Seed = 1128317348] ------------------------------------- Vector space of degree 8, dimension 2 over GF(2) Echelonized basis: (1 0 0 1 0 1 0 1) (0 1 1 1 1 0 1 0) Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Mon Mar 1 18:17:35 2004 Input: m := Random( 2, 10000 ); print m, " is da numba"; if (m eq 3) then print m, "is prime"; else print Factorization(m); end if; 6 mod 4; Output: Magma V2.10-6 Mon Mar 1 2004 18:17:32 on modular [Seed = 1835985320] ------------------------------------- 5310 is da numba [ <2, 1>, <3, 2>, <5, 1>, <59, 1> ] 2 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Mon Mar 1 18:19:55 2004 Input: diumenges:=func < | 3 mod 2 >; Output: Magma V2.10-6 Mon Mar 1 2004 18:19:52 on modular [Seed = 1734664758] ------------------------------------- Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Mon Mar 1 18:20:27 2004 Input: diumenges:=func < | 3 mod 2 >; diumenges(); Output: Magma V2.10-6 Mon Mar 1 2004 18:20:24 on modular [Seed = 1987441415] ------------------------------------- 1 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Mon Mar 1 18:42:11 2004 Input: diumenges:=func < | for i:=1 to 3 do print "hola" end for >; diumenges(); Output: Magma V2.10-6 Mon Mar 1 2004 18:42:08 on modular [Seed = 589343034] ------------------------------------- >> diumenges:=func < | for i:=1 to 3 do print "hola" end for >; ^ User error: bad syntax >> diumenges();; ^ User error: Identifier 'diumenges' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Mon Mar 1 18:42:22 2004 Input: diumenges:=func < | for i:=1 to 3 do print "hola" end for; >; diumenges(); Output: Magma V2.10-6 Mon Mar 1 2004 18:42:19 on modular [Seed = 1027520303] ------------------------------------- >> diumenges:=func < | for i:=1 to 3 do print "hola" end for; >; ^ User error: bad syntax >> diumenges();; ^ User error: Identifier 'diumenges' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Mon Mar 1 18:42:58 2004 Input: diumenges:=func < | for i:=1 to 3 do print "hola"; end for; >; diumenges(); Output: Magma V2.10-6 Mon Mar 1 2004 18:42:55 on modular [Seed = 909491200] ------------------------------------- >> diumenges:=func < | for i:=1 to 3 do print "hola"; end for; >; ^ User error: bad syntax >> diumenges();; ^ User error: Identifier 'diumenges' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Mon Mar 1 18:44:40 2004 Input: diumenges:=func < | p := 10037; for x in [1..100] do for y in [1..100] do if x^2+y^2 eq p then print x, y; break x; end if; end for; end for; >; diumenges(); Output: Magma V2.10-6 Mon Mar 1 2004 18:44:37 on modular [Seed = 3284158831] ------------------------------------- >> p := 10037; ^ User error: bad syntax >> if x^2+y^2 eq p then ^ User error: Identifier 'p' has not been declared or assigned >> diumenges();; ^ User error: Identifier 'diumenges' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Mon Mar 1 18:50:34 2004 Input: diumenges := function() setmana := 7; diumenge := 4; any := 366; for dia in [1..any] do if (dia mod setmana) eq diumenge then print dia; end if; end for; return {}; end function; Output: Magma V2.10-6 Mon Mar 1 2004 18:50:31 on modular [Seed = 3907740902] ------------------------------------- Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Mon Mar 1 18:50:48 2004 Input: diumenges := function() setmana := 7; diumenge := 4; any := 366; for dia in [1..any] do if (dia mod setmana) eq diumenge then print dia; end if; end for; return {}; end function; diumenges(); Output: Magma V2.10-6 Mon Mar 1 2004 18:50:45 on modular [Seed = 3823136767] ------------------------------------- 4 11 18 25 32 39 46 53 60 67 74 81 88 95 102 109 116 123 130 137 144 151 158 165 172 179 186 193 200 207 214 221 228 235 242 249 256 263 270 277 284 291 298 305 312 319 326 333 340 347 354 361 {} Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (61.28.2.178) Time: Mon Mar 1 20:29:17 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Mon Mar 1 2004 20:29:14 on modular [Seed = 4210645466] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Mar 1 21:53:05 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^5+7x64+3x^2-x+1); OK:=MaximalOrder(K); I2:=2*OK; Factorization(I2); I3:=3*OK; Factorization(I3); I5:=5*OK; Factorization(I5); I7:=7*OK; Factorization(I7); I11:=11*OK; Factorization(I11); I13:=13*OK; Factorization(I13); I17:=17*OK; Factorization(I17); I19:=19*OK; Factorization(I19); I23:=23*OK; Factorization(I23); I29:=29*OK; Factorization(I29); I31:=31*OK; Factorization(I31); I37:=37*OK; Factorization(I37); I41:=41*OK; Factorization(I41); I43:=43*OK; Factorization(I43); I47:=47*OK; Factorization(I47); I53:=53*OK; Factorization(I53); I59:=59*OK; Factorization(I59); I61:=61*OK; Factorization(I61); I67:=67*OK; Factorization(I67); I71:=71*OK; Factorization(I71); I73:=73*OK; Factorization(I73); I79:=79*OK; Factorization(I79); I83:=83*OK; Factorization(I83); I89:=89*OK; Factorization(I89); I97:=97*OK; Factorization(I97); Output: Magma V2.10-6 Mon Mar 1 2004 21:53:02 on modular [Seed = 3284169862] ------------------------------------- >> K := NumberField(x^5+7x64+3x^2-x+1); ^ User error: bad syntax >> OK:=MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> I2:=2*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I2); ^ User error: Identifier 'I2' has not been declared or assigned >> I3:=3*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I3); ^ User error: Identifier 'I3' has not been declared or assigned >> I5:=5*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I5); ^ User error: Identifier 'I5' has not been declared or assigned >> I7:=7*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I7); ^ User error: Identifier 'I7' has not been declared or assigned >> I11:=11*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I11); ^ User error: Identifier 'I11' has not been declared or assigned >> I13:=13*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I13); ^ User error: Identifier 'I13' has not been declared or assigned >> I17:=17*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I17); ^ User error: Identifier 'I17' has not been declared or assigned >> I19:=19*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I19); ^ User error: Identifier 'I19' has not been declared or assigned >> I23:=23*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I23); ^ User error: Identifier 'I23' has not been declared or assigned >> I29:=29*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I29); ^ User error: Identifier 'I29' has not been declared or assigned >> I31:=31*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I31); ^ User error: Identifier 'I31' has not been declared or assigned >> I37:=37*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I37); ^ User error: Identifier 'I37' has not been declared or assigned >> I41:=41*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I41); ^ User error: Identifier 'I41' has not been declared or assigned >> I43:=43*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I43); ^ User error: Identifier 'I43' has not been declared or assigned >> I47:=47*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I47); ^ User error: Identifier 'I47' has not been declared or assigned >> I53:=53*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I53); ^ User error: Identifier 'I53' has not been declared or assigned >> I59:=59*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I59); ^ User error: Identifier 'I59' has not been declared or assigned >> I61:=61*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I61); ^ User error: Identifier 'I61' has not been declared or assigned >> I67:=67*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I67); ^ User error: Identifier 'I67' has not been declared or assigned >> I71:=71*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I71); ^ User error: Identifier 'I71' has not been declared or assigned >> I73:=73*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I73); ^ User error: Identifier 'I73' has not been declared or assigned >> I79:=79*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I79); ^ User error: Identifier 'I79' has not been declared or assigned >> I83:=83*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I83); ^ User error: Identifier 'I83' has not been declared or assigned >> I89:=89*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I89); ^ User error: Identifier 'I89' has not been declared or assigned >> I97:=97*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I97); ^ User error: Identifier 'I97' has not been declared or assigned Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Mar 1 21:53:37 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^5+7x^4+3x^2-x+1); OK:=MaximalOrder(K); I2:=2*OK; Factorization(I2); I3:=3*OK; Factorization(I3); I5:=5*OK; Factorization(I5); I7:=7*OK; Factorization(I7); I11:=11*OK; Factorization(I11); I13:=13*OK; Factorization(I13); I17:=17*OK; Factorization(I17); I19:=19*OK; Factorization(I19); I23:=23*OK; Factorization(I23); I29:=29*OK; Factorization(I29); I31:=31*OK; Factorization(I31); I37:=37*OK; Factorization(I37); I41:=41*OK; Factorization(I41); I43:=43*OK; Factorization(I43); I47:=47*OK; Factorization(I47); I53:=53*OK; Factorization(I53); I59:=59*OK; Factorization(I59); I61:=61*OK; Factorization(I61); I67:=67*OK; Factorization(I67); I71:=71*OK; Factorization(I71); I73:=73*OK; Factorization(I73); I79:=79*OK; Factorization(I79); I83:=83*OK; Factorization(I83); I89:=89*OK; Factorization(I89); I97:=97*OK; Factorization(I97); Output: Magma V2.10-6 Mon Mar 1 2004 21:53:34 on modular [Seed = 3654971068] ------------------------------------- >> K := NumberField(x^5+7x^4+3x^2-x+1); ^ User error: bad syntax >> OK:=MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> I2:=2*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I2); ^ User error: Identifier 'I2' has not been declared or assigned >> I3:=3*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I3); ^ User error: Identifier 'I3' has not been declared or assigned >> I5:=5*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I5); ^ User error: Identifier 'I5' has not been declared or assigned >> I7:=7*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I7); ^ User error: Identifier 'I7' has not been declared or assigned >> I11:=11*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I11); ^ User error: Identifier 'I11' has not been declared or assigned >> I13:=13*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I13); ^ User error: Identifier 'I13' has not been declared or assigned >> I17:=17*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I17); ^ User error: Identifier 'I17' has not been declared or assigned >> I19:=19*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I19); ^ User error: Identifier 'I19' has not been declared or assigned >> I23:=23*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I23); ^ User error: Identifier 'I23' has not been declared or assigned >> I29:=29*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I29); ^ User error: Identifier 'I29' has not been declared or assigned >> I31:=31*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I31); ^ User error: Identifier 'I31' has not been declared or assigned >> I37:=37*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I37); ^ User error: Identifier 'I37' has not been declared or assigned >> I41:=41*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I41); ^ User error: Identifier 'I41' has not been declared or assigned >> I43:=43*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I43); ^ User error: Identifier 'I43' has not been declared or assigned >> I47:=47*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I47); ^ User error: Identifier 'I47' has not been declared or assigned >> I53:=53*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I53); ^ User error: Identifier 'I53' has not been declared or assigned >> I59:=59*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I59); ^ User error: Identifier 'I59' has not been declared or assigned >> I61:=61*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I61); ^ User error: Identifier 'I61' has not been declared or assigned >> I67:=67*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I67); ^ User error: Identifier 'I67' has not been declared or assigned >> I71:=71*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I71); ^ User error: Identifier 'I71' has not been declared or assigned >> I73:=73*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I73); ^ User error: Identifier 'I73' has not been declared or assigned >> I79:=79*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I79); ^ User error: Identifier 'I79' has not been declared or assigned >> I83:=83*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I83); ^ User error: Identifier 'I83' has not been declared or assigned >> I89:=89*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I89); ^ User error: Identifier 'I89' has not been declared or assigned >> I97:=97*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I97); ^ User error: Identifier 'I97' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Mar 1 21:54:53 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^5+7x^4+3x^2-x+1); OK:=MaximalOrder(K); I2:=2*OK; Factorization(I2); I3:=3*OK; Factorization(I3); I5:=5*OK; Factorization(I5); I7:=7*OK; Factorization(I7); I11:=11*OK; Factorization(I11); I13:=13*OK; Factorization(I13); I17:=17*OK; Factorization(I17); I19:=19*OK; Factorization(I19); I23:=23*OK; Factorization(I23); I29:=29*OK; Factorization(I29); I31:=31*OK; Factorization(I31); I37:=37*OK; Factorization(I37); I41:=41*OK; Factorization(I41); I43:=43*OK; Factorization(I43); I47:=47*OK; Factorization(I47); I53:=53*OK; Factorization(I53); I59:=59*OK; Factorization(I59); I61:=61*OK; Factorization(I61); I67:=67*OK; Factorization(I67); I71:=71*OK; Factorization(I71); I73:=73*OK; Factorization(I73); I79:=79*OK; Factorization(I79); I83:=83*OK; Factorization(I83); I89:=89*OK; Factorization(I89); I97:=97*OK; Factorization(I97); Output: Magma V2.10-6 Mon Mar 1 2004 21:54:50 on modular [Seed = 3621019878] ------------------------------------- >> K := NumberField(x^5+7x^4+3x^2-x+1); ^ User error: bad syntax >> OK:=MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> I2:=2*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I2); ^ User error: Identifier 'I2' has not been declared or assigned >> I3:=3*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I3); ^ User error: Identifier 'I3' has not been declared or assigned >> I5:=5*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I5); ^ User error: Identifier 'I5' has not been declared or assigned >> I7:=7*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I7); ^ User error: Identifier 'I7' has not been declared or assigned >> I11:=11*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I11); ^ User error: Identifier 'I11' has not been declared or assigned >> I13:=13*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I13); ^ User error: Identifier 'I13' has not been declared or assigned >> I17:=17*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I17); ^ User error: Identifier 'I17' has not been declared or assigned >> I19:=19*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I19); ^ User error: Identifier 'I19' has not been declared or assigned >> I23:=23*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I23); ^ User error: Identifier 'I23' has not been declared or assigned >> I29:=29*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I29); ^ User error: Identifier 'I29' has not been declared or assigned >> I31:=31*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I31); ^ User error: Identifier 'I31' has not been declared or assigned >> I37:=37*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I37); ^ User error: Identifier 'I37' has not been declared or assigned >> I41:=41*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I41); ^ User error: Identifier 'I41' has not been declared or assigned >> I43:=43*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I43); ^ User error: Identifier 'I43' has not been declared or assigned >> I47:=47*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I47); ^ User error: Identifier 'I47' has not been declared or assigned >> I53:=53*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I53); ^ User error: Identifier 'I53' has not been declared or assigned >> I59:=59*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I59); ^ User error: Identifier 'I59' has not been declared or assigned >> I61:=61*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I61); ^ User error: Identifier 'I61' has not been declared or assigned >> I67:=67*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I67); ^ User error: Identifier 'I67' has not been declared or assigned >> I71:=71*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I71); ^ User error: Identifier 'I71' has not been declared or assigned >> I73:=73*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I73); ^ User error: Identifier 'I73' has not been declared or assigned >> I79:=79*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I79); ^ User error: Identifier 'I79' has not been declared or assigned >> I83:=83*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I83); ^ User error: Identifier 'I83' has not been declared or assigned >> I89:=89*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I89); ^ User error: Identifier 'I89' has not been declared or assigned >> I97:=97*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I97); ^ User error: Identifier 'I97' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Mar 1 21:56:16 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^5+7*x^4+3*x^2-x+1); OK:=MaximalOrder(K); I2:=2*OK; Factorization(I2); I3:=3*OK; Factorization(I3); I5:=5*OK; Factorization(I5); I7:=7*OK; Factorization(I7); I11:=11*OK; Factorization(I11); I13:=13*OK; Factorization(I13); I17:=17*OK; Factorization(I17); I19:=19*OK; Factorization(I19); I23:=23*OK; Factorization(I23); I29:=29*OK; Factorization(I29); I31:=31*OK; Factorization(I31); I37:=37*OK; Factorization(I37); I41:=41*OK; Factorization(I41); I43:=43*OK; Factorization(I43); I47:=47*OK; Factorization(I47); I53:=53*OK; Factorization(I53); I59:=59*OK; Factorization(I59); I61:=61*OK; Factorization(I61); I67:=67*OK; Factorization(I67); I71:=71*OK; Factorization(I71); I73:=73*OK; Factorization(I73); I79:=79*OK; Factorization(I79); I83:=83*OK; Factorization(I83); I89:=89*OK; Factorization(I89); I97:=97*OK; Factorization(I97); Output: Magma V2.10-6 Mon Mar 1 2004 21:56:13 on modular [Seed = 3806418276] ------------------------------------- [ ] [ ] [ , , ] [ , ] [ , , , ] [ , ] [ , , ] [ , , ] [ , ] [ , , ] [ , , ] [ ] [ , ] [ , , , ] [ , ] [ , ] [ , ] [ ] [ , , , ] [ , , , ] [ ] [ , ] [ , , , ] [ , ] [ ] Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 2 00:08:18 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4+1); OK:=MaximalOrder(K); Print IntegralBasis(K); Output: Magma V2.10-6 Tue Mar 2 2004 00:08:15 on modular [Seed = 67130102] ------------------------------------- >> Print IntegralBasis(K); ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 2 00:08:29 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4+1); OK:=MaximalOrder(K); IntegralBasis(K); Output: Magma V2.10-6 Tue Mar 2 2004 00:08:26 on modular [Seed = 521882008] ------------------------------------- [ 1, y, y^2, y^3 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 2 00:08:43 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4+1); OK:=MaximalOrder(K); IntegralBasis(OK); Output: Magma V2.10-6 Tue Mar 2 2004 00:08:40 on modular [Seed = 286607236] ------------------------------------- >> IntegralBasis(OK); ^ Runtime error in 'IntegralBasis': Bad argument types Argument types given: RngOrd Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 2 00:09:38 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4+1); OK:=MaximalOrder(K); print IntegralBasis(K); Output: Magma V2.10-6 Tue Mar 2 2004 00:09:35 on modular [Seed = 674004842] ------------------------------------- [ 1, y, y^2, y^3 ] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 2 00:10:32 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4+x^2-1); OK:=MaximalOrder(K); print IntegralBasis(K); Output: Magma V2.10-6 Tue Mar 2 2004 00:10:29 on modular [Seed = 994012211] ------------------------------------- [ 1, y, y^2, y^3 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Tue Mar 2 01:54:38 2004 Input: MatrixGroup(4, GF(2)) Output: Magma V2.10-6 Tue Mar 2 2004 01:54:35 on modular [Seed = 168715759] ------------------------------------- >> MatrixGroup(4, GF(2)); ^ Runtime error in 'MatrixGroup': Bad argument types Argument types given: RngIntElt, FldFin Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Tue Mar 2 01:56:01 2004 Input: A:=GL(4, 2); Output: Magma V2.10-6 Tue Mar 2 2004 01:55:58 on modular [Seed = 521892015] ------------------------------------- Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Tue Mar 2 01:56:44 2004 Input: A:=GeneralLinearGroup(4, FiniteField(2)); Output: Magma V2.10-6 Tue Mar 2 2004 01:56:41 on modular [Seed = 336618611] ------------------------------------- Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Tue Mar 2 01:57:36 2004 Input: A:=GeneralLinearGroup(4, FiniteField(2)); print A; Output: Magma V2.10-6 Tue Mar 2 2004 01:57:33 on modular [Seed = 943474731] ------------------------------------- GL(4, GF(2)) Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Tue Mar 2 02:00:49 2004 Input: A:=GeneralLinearGroup(4, FiniteField(2)); print Order(A); Output: Magma V2.10-6 Tue Mar 2 2004 02:00:46 on modular [Seed = 3334649750] ------------------------------------- 20160 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Tue Mar 2 02:02:15 2004 Input: A:=GeneralLinearGroup(4, FiniteField(2)); print Exponent(A); Output: Magma V2.10-6 Tue Mar 2 2004 02:02:12 on modular [Seed = 3991510231] ------------------------------------- 420 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Tue Mar 2 02:04:42 2004 Input: A:=GeneralLinearGroup(4, FiniteField(2)); print FactoredOrder(A); Output: Magma V2.10-6 Tue Mar 2 2004 02:04:39 on modular [Seed = 3773076137] ------------------------------------- [ <2, 6>, <3, 2>, <5, 1>, <7, 1> ] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Tue Mar 2 03:14:33 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=-2160+40*y^6-11*y^5-5*y^3-4*y; f3:=-139230+630*y^8-151*y^7-70*y^5-49*y^3-45*y; f4:=4032*y+18860*y^3+10101*y^5+18690*y^7+39037*y^9-22861440; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Tue Mar 2 2004 03:14:30 on modular [Seed = 218697508] ------------------------------------- [ y^2 + 7*y - 18, 15*y - 30 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Tue Mar 2 03:15:04 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=-2160+40*y^6-11*y^5-5*y^3-4*y; f3:=-139230+630*y^8-151*y^7-70*y^5-49*y^3-45*y; f4:=4239018*y+6396640*y^3+207743424*y^5-820861440*y^7+1039973888*y^9-900000000*y^8+ 756000000*y^6-177660000*y^4+11624400*y^2-23410213785; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Tue Mar 2 2004 03:15:01 on modular [Seed = 262858] ------------------------------------- [ y^2 + 7*y + 225881530857, 15*y + 225881530845, 225881530875 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Tue Mar 2 03:16:36 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=-2160+40*y^6-11*y^5-5*y^3-4*y; f3:=-139230+630*y^8-151*y^7-70*y^5-49*y^3-45*y; f4:=4239018*y+6396640*y^3+207743424*y^5-820861440*y^7+1039973888*y^9-900000000*y^8+ 756000000*y^6-177660000*y^4+11624400*y^2-23410213785; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(225881530875); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Output: Magma V2.10-6 Tue Mar 2 2004 03:16:33 on modular [Seed = 336598714] ------------------------------------- [ y^2 + 7*y + 225881530857, 15*y + 225881530845, 225881530875 ] [ <3, 5>, <5, 3>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1>, <23, 1> ] [ y + 9 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Tue Mar 2 03:17:37 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=-2160+40*y^6-11*y^5-5*y^3-4*y; f3:=-139230+630*y^8-151*y^7-70*y^5-49*y^3-45*y; f4:=4239018*y+6396640*y^3+207743424*y^5-820861440*y^7+1039973888*y^9-900000000*y^8+ 756000000*y^6-177660000*y^4+11624400*y^2-23410213785; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(225881530875); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23))); Bn; Output: Magma V2.10-6 Tue Mar 2 2004 03:17:34 on modular [Seed = 724510842] ------------------------------------- [ y^2 + 7*y + 225881530857, 15*y + 225881530845, 225881530875 ] [ <3, 5>, <5, 3>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1>, <23, 1> ] [ y + 9 ] [ y + 11 ] [ y + 15 ] [ y + 17 ] [ y + 21 ] Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Tue Mar 2 03:18:54 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=-2160+40*y^6-11*y^5-5*y^3-4*y; f3:=-142573095+645120*y^8-2251776*y^7+1075200*y^5-182784*y^3-44280*y+1835008*y^6-1003520*y^4+116032*y^2; f4:=4239018*y+6396640*y^3+207743424*y^5-820861440*y^7+1039973888*y^9-900000000*y^8+ 756000000*y^6-177660000*y^4+11624400*y^2-23410213785; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Tue Mar 2 2004 03:18:51 on modular [Seed = 539239172] ------------------------------------- [ y^2 + 7*y + 130945797, 15*y + 130945785, 130945815 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Tue Mar 2 03:19:39 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=-2160+40*y^6-11*y^5-5*y^3-4*y; f3:=-142573095+645120*y^8-2251776*y^7+1075200*y^5-182784*y^3-44280*y+1835008*y^6-1003520*y^4+116032*y^2; f4:=4239018*y+6396640*y^3+207743424*y^5-820861440*y^7+1039973888*y^9-900000000*y^8+ 756000000*y^6-177660000*y^4+11624400*y^2-23410213785; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(130945815); Output: Magma V2.10-6 Tue Mar 2 2004 03:19:36 on modular [Seed = 926102752] ------------------------------------- [ y^2 + 7*y + 130945797, 15*y + 130945785, 130945815 ] [ <3, 4>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Tue Mar 2 03:20:01 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=-2160+40*y^6-11*y^5-5*y^3-4*y; f3:=-142573095+645120*y^8-2251776*y^7+1075200*y^5-182784*y^3-44280*y+1835008*y^6-1003520*y^4+116032*y^2; f4:=4239018*y+6396640*y^3+207743424*y^5-820861440*y^7+1039973888*y^9-900000000*y^8+ 756000000*y^6-177660000*y^4+11624400*y^2-23410213785; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(130945815); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19))); Bn; Output: Magma V2.10-6 Tue Mar 2 2004 03:19:58 on modular [Seed = 3469397295] ------------------------------------- [ y^2 + 7*y + 130945797, 15*y + 130945785, 130945815 ] [ <3, 4>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ y + 9 ] [ y + 11 ] [ y + 15 ] [ y + 17 ] Total time: 3.129 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Tue Mar 2 03:21:35 2004 Input: P:=PolynomialRing(IntegerRing(),2);f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=-2160+40*y^6-11*y^5-5*y^3-4*y; f3:=-142573095+645120*y^8-2251776*y^7+1075200*y^5-182784*y^3-44280*y+1835008*y^6-1003520*y^4+116032*y^2; f4:=1119006*y+24175520*y^3-146365632*y^5+313582080*y^7-100734464*y^9+203316480*y^8-408602880*y^6+183345120*y^4-20923920*y^2-7803073845; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Tue Mar 2 2004 03:21:32 on modular [Seed = 3722041758] ------------------------------------- [ y^2 + 7*y + 43648587, 15*y + 43648575, 43648605 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Tue Mar 2 03:22:06 2004 Input: P:=PolynomialRing(IntegerRing(),2);f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=-2160+40*y^6-11*y^5-5*y^3-4*y; f3:=-142573095+645120*y^8-2251776*y^7+1075200*y^5-182784*y^3-44280*y+1835008*y^6-1003520*y^4+116032*y^2; f4:=1119006*y+24175520*y^3-146365632*y^5+313582080*y^7-100734464*y^9+203316480*y^8-408602880*y^6+183345120*y^4-20923920*y^2-7803073845; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(43648605); Output: Magma V2.10-6 Tue Mar 2 2004 03:22:03 on modular [Seed = 3570454704] ------------------------------------- [ y^2 + 7*y + 43648587, 15*y + 43648575, 43648605 ] [ <3, 3>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Tue Mar 2 03:22:25 2004 Input: P:=PolynomialRing(IntegerRing(),2);f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=-2160+40*y^6-11*y^5-5*y^3-4*y; f3:=-142573095+645120*y^8-2251776*y^7+1075200*y^5-182784*y^3-44280*y+1835008*y^6-1003520*y^4+116032*y^2; f4:=1119006*y+24175520*y^3-146365632*y^5+313582080*y^7-100734464*y^9+203316480*y^8-408602880*y^6+183345120*y^4-20923920*y^2-7803073845; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(43648605); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19))); Bn; Output: Magma V2.10-6 Tue Mar 2 2004 03:22:22 on modular [Seed = 3958370202] ------------------------------------- [ y^2 + 7*y + 43648587, 15*y + 43648575, 43648605 ] [ <3, 3>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ y + 9 ] [ y + 11 ] [ y + 15 ] [ y + 17 ] Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Tue Mar 2 03:23:06 2004 Input: P:=PolynomialRing(IntegerRing(),2);f0:=-6+2*y^2-y; f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=-69105+1280*y^6-2944*y^5+560*y^3-146*y+2160*y^4+600*y^2; f3:=-142573095+645120*y^8-2251776*y^7+1075200*y^5-182784*y^3-44280*y+1835008*y^6-1003520*y^4+116032*y^2; f4:=1119006*y+24175520*y^3-146365632*y^5+313582080*y^7-100734464*y^9+203316480*y^8-408602880*y^6+183345120*y^4-20923920*y^2-7803073845; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Tue Mar 2 2004 03:23:03 on modular [Seed = 3806783178] ------------------------------------- [ y^2 + 7*y + 42, 15*y, 45 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Tue Mar 2 03:23:36 2004 Input: P:=PolynomialRing(IntegerRing(),2);f0:=-6+2*y^2-y; f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=-69105+1280*y^6-2944*y^5+560*y^3-146*y+2160*y^4+600*y^2; f3:=-142560495+645120*y^8-12288*y^7-1102080*y^5+264768*y^3-55080*y-777728*y^6+ 1536640*y^4-406112*y^2; f4:=1119006*y+24175520*y^3-146365632*y^5+313582080*y^7-100734464*y^9+203316480*y^8-408602880*y^6+183345120*y^4-20923920*y^2-7803073845; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Tue Mar 2 2004 03:23:33 on modular [Seed = 4194172211] ------------------------------------- [ y^2 + 7*y + 42, 15*y, 45 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Tue Mar 2 03:24:04 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=-69105+1280*y^6-2944*y^5+560*y^3-146*y+2160*y^4+600*y^2; f3:=-142560495+645120*y^8-12288*y^7-1102080*y^5+264768*y^3-55080*y-777728*y^6+ 1536640*y^4-406112*y^2; f4:=527814*y-4418080*y^3+20970432*y^5-9784320*y^7+12607744*y^9-5857920*y^8+30119040 *y^6-40506480*y^4+10461960*y^2-1951140555; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Tue Mar 2 2004 03:24:01 on modular [Seed = 2408287073] ------------------------------------- [ y^2 + 7*y + 42, 15*y, 45 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Tue Mar 2 03:24:28 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=-69105+1280*y^6-2944*y^5+560*y^3-146*y+2160*y^4+600*y^2; f3:=-142560495+645120*y^8-12288*y^7-1102080*y^5+264768*y^3-55080*y-777728*y^6+ 1536640*y^4-406112*y^2; f4:=1122642*y+1849760*y^3-29488704*y^5+342357120*y^6+30647040*y^7-467573760*y^8+ 32422680*y^2-156799440*y^4+287823232*y^9-5853421665; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Tue Mar 2 2004 03:24:25 on modular [Seed = 2239857011] ------------------------------------- [ y^2 + 7*y + 42, 15*y, 45 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-15-12.go.retevision.es. (81.61.12.15) Time: Tue Mar 2 04:30:06 2004 Input: [3^i mod 7: i in [1..366]]; Output: Magma V2.10-6 Tue Mar 2 2004 04:30:03 on modular [Seed = 438177363] ------------------------------------- [ 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-15-12.go.retevision.es. (81.61.12.15) Time: Tue Mar 2 04:30:47 2004 Input: [i mod 7 = 3: i in [1..366]]; Output: Magma V2.10-6 Tue Mar 2 2004 04:30:44 on modular [Seed = 267286] ------------------------------------- [ 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3, 3 = 3, 4 = 3, 5 = 3, 6 = 3, 0 = 3, 1 = 3, 2 = 3 ] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-15-12.go.retevision.es. (81.61.12.15) Time: Tue Mar 2 04:30:58 2004 Input: [i mod 7 := 3: i in [1..366]]; Output: Magma V2.10-6 Tue Mar 2 2004 04:30:55 on modular [Seed = 151854356] ------------------------------------- >> [i mod 7 := 3: i in [1..366]];; ^ User error: bad syntax Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-15-12.go.retevision.es. (81.61.12.15) Time: Tue Mar 2 04:36:08 2004 Input: [i mod 7: i in [1..366]]; Output: Magma V2.10-6 Tue Mar 2 2004 04:36:05 on modular [Seed = 943468015] ------------------------------------- [ 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-15-12.go.retevision.es. (81.61.12.15) Time: Tue Mar 2 04:36:56 2004 Input: [if i mod 7=3 then print(i): i in [1..366]]; Output: Magma V2.10-6 Tue Mar 2 2004 04:36:53 on modular [Seed = 639775681] ------------------------------------- >> [if i mod 7=3 then print(i): i in [1..366]];; ^ User error: bad syntax Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-15-12.go.retevision.es. (81.61.12.15) Time: Tue Mar 2 04:39:30 2004 Input: for i:= 1 to 366 do if i mod 7 = 3 then print i; end for; Output: Magma V2.10-6 Tue Mar 2 2004 04:39:27 on modular [Seed = 757676848] ------------------------------------- >> end for;; ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-15-12.go.retevision.es. (81.61.12.15) Time: Tue Mar 2 04:39:50 2004 Input: for i:= 1 to 366 do if i mod 7 = 3 then print i end if; end for; Output: Magma V2.10-6 Tue Mar 2 2004 04:39:47 on modular [Seed = 3672034539] ------------------------------------- >> if i mod 7 = 3 then print i end if; ^ User error: bad syntax >> end for;; ^ User error: bad syntax Total time: 2.869 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-15-12.go.retevision.es. (81.61.12.15) Time: Tue Mar 2 04:40:32 2004 Input: for i:= 1 to 366 do if i mod 7 = 3 then print i; end if; end for; Output: Magma V2.10-6 Tue Mar 2 2004 04:40:28 on modular [Seed = 3402554388] ------------------------------------- >> if i mod 7 = 3 then ^ Runtime error in if: Logical expected Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-15-12.go.retevision.es. (81.61.12.15) Time: Tue Mar 2 04:41:39 2004 Input: for i in {1..366} do if (i mod 7) eq 3 then print i; end if; end for; Output: Magma V2.10-6 Tue Mar 2 2004 04:41:36 on modular [Seed = 4093109617] ------------------------------------- 3 10 17 24 31 38 45 52 59 66 73 80 87 94 101 108 115 122 129 136 143 150 157 164 171 178 185 192 199 206 213 220 227 234 241 248 255 262 269 276 283 290 297 304 311 318 325 332 339 346 353 360 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-15-12.go.retevision.es. (81.61.12.15) Time: Tue Mar 2 04:48:35 2004 Input: M:=MatrixRing(GF(4),2); Trace(0); Output: Magma V2.10-6 Tue Mar 2 2004 04:48:32 on modular [Seed = 3773102274] ------------------------------------- 0 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-15-12.go.retevision.es. (81.61.12.15) Time: Tue Mar 2 04:53:41 2004 Input: M:=MatrixRing(GF(4),2); Trace(M); Output: Magma V2.10-6 Tue Mar 2 2004 04:53:38 on modular [Seed = 2543029863] ------------------------------------- >> Trace(M);; ^ Runtime error in 'Trace': Bad argument types Argument types given: AlgMat Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Tue Mar 2 05:16:34 2004 Input: [1,2,3,4] Output: Magma V2.10-6 Tue Mar 2 2004 05:16:30 on modular [Seed = 1532970487] ------------------------------------- [ 1, 2, 3, 4 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee39.uab.es. (158.109.66.39) Time: Tue Mar 2 05:23:03 2004 Input: for i=1 to 366 do Include(X,i); Output: Magma V2.10-6 Tue Mar 2 2004 05:22:59 on modular [Seed = 1212967064] ------------------------------------- >> for i=1 to 366 do Include(X,i); ^ User error: bad syntax Total time: 3.349 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Tue Mar 2 05:23:04 2004 Input: for i=1 to 366 do Include ({},i); Output: Magma V2.10-6 Tue Mar 2 2004 05:23:00 on modular [Seed = 1296657818] ------------------------------------- >> for i=1 to 366 do Include ({},i);; ^ User error: bad syntax Total time: 3.579 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Tue Mar 2 05:23:28 2004 Input: for i:=1 to 366 do Include ({},i); Output: Magma V2.10-6 Tue Mar 2 2004 05:23:25 on modular [Seed = 2121948848] ------------------------------------- User error: syntax error at end of input Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Tue Mar 2 05:23:47 2004 Input: for i:=1 to 366 do Include ({},i) end for; Output: Magma V2.10-6 Tue Mar 2 2004 05:23:44 on modular [Seed = 1684030599] ------------------------------------- >> for i:=1 to 366 do Include ({},i) end for;; ^ User error: bad syntax Total time: 2.829 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee39.uab.es. (158.109.66.39) Time: Tue Mar 2 05:23:54 2004 Input: for i:=1 to 366 do Include(X,i) end for; Output: Magma V2.10-6 Tue Mar 2 2004 05:23:51 on modular [Seed = 320287735] ------------------------------------- >> for i:=1 to 366 do Include(X,i) end for; ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Tue Mar 2 05:24:11 2004 Input: for i:=1 to 366 do Include ({},i); end for; Output: Magma V2.10-6 Tue Mar 2 2004 05:24:08 on modular [Seed = 438188673] ------------------------------------- { 1 } { 2 } { 3 } { 4 } { 5 } { 6 } { 7 } { 8 } { 9 } { 10 } { 11 } { 12 } { 13 } { 14 } { 15 } { 16 } { 17 } { 18 } { 19 } { 20 } { 21 } { 22 } { 23 } { 24 } { 25 } { 26 } { 27 } { 28 } { 29 } { 30 } { 31 } { 32 } { 33 } { 34 } { 35 } { 36 } { 37 } { 38 } { 39 } { 40 } { 41 } { 42 } { 43 } { 44 } { 45 } { 46 } { 47 } { 48 } { 49 } { 50 } { 51 } { 52 } { 53 } { 54 } { 55 } { 56 } { 57 } { 58 } { 59 } { 60 } { 61 } { 62 } { 63 } { 64 } { 65 } { 66 } { 67 } { 68 } { 69 } { 70 } { 71 } { 72 } { 73 } { 74 } { 75 } { 76 } { 77 } { 78 } { 79 } { 80 } { 81 } { 82 } { 83 } { 84 } { 85 } { 86 } { 87 } { 88 } { 89 } { 90 } { 91 } { 92 } { 93 } { 94 } { 95 } { 96 } { 97 } { 98 } { 99 } { 100 } { 101 } { 102 } { 103 } { 104 } { 105 } { 106 } { 107 } { 108 } { 109 } { 110 } { 111 } { 112 } { 113 } { 114 } { 115 } { 116 } { 117 } { 118 } { 119 } { 120 } { 121 } { 122 } { 123 } { 124 } { 125 } { 126 } { 127 } { 128 } { 129 } { 130 } { 131 } { 132 } { 133 } { 134 } { 135 } { 136 } { 137 } { 138 } { 139 } { 140 } { 141 } { 142 } { 143 } { 144 } { 145 } { 146 } { 147 } { 148 } { 149 } { 150 } { 151 } { 152 } { 153 } { 154 } { 155 } { 156 } { 157 } { 158 } { 159 } { 160 } { 161 } { 162 } { 163 } { 164 } { 165 } { 166 } { 167 } { 168 } { 169 } { 170 } { 171 } { 172 } { 173 } { 174 } { 175 } { 176 } { 177 } { 178 } { 179 } { 180 } { 181 } { 182 } { 183 } { 184 } { 185 } { 186 } { 187 } { 188 } { 189 } { 190 } { 191 } { 192 } { 193 } { 194 } { 195 } { 196 } { 197 } { 198 } { 199 } { 200 } { 201 } { 202 } { 203 } { 204 } { 205 } { 206 } { 207 } { 208 } { 209 } { 210 } { 211 } { 212 } { 213 } { 214 } { 215 } { 216 } { 217 } { 218 } { 219 } { 220 } { 221 } { 222 } { 223 } { 224 } { 225 } { 226 } { 227 } { 228 } { 229 } { 230 } { 231 } { 232 } { 233 } { 234 } { 235 } { 236 } { 237 } { 238 } { 239 } { 240 } { 241 } { 242 } { 243 } { 244 } { 245 } { 246 } { 247 } { 248 } { 249 } { 250 } { 251 } { 252 } { 253 } { 254 } { 255 } { 256 } { 257 } { 258 } { 259 } { 260 } { 261 } { 262 } { 263 } { 264 } { 265 } { 266 } { 267 } { 268 } { 269 } { 270 } { 271 } { 272 } { 273 } { 274 } { 275 } { 276 } { 277 } { 278 } { 279 } { 280 } { 281 } { 282 } { 283 } { 284 } { 285 } { 286 } { 287 } { 288 } { 289 } { 290 } { 291 } { 292 } { 293 } { 294 } { 295 } { 296 } { 297 } { 298 } { 299 } { 300 } { 301 } { 302 } { 303 } { 304 } { 305 } { 306 } { 307 } { 308 } { 309 } { 310 } { 311 } { 312 } { 313 } { 314 } { 315 } { 316 } { 317 } { 318 } { 319 } { 320 } { 321 } { 322 } { 323 } { 324 } { 325 } { 326 } { 327 } { 328 } { 329 } { 330 } { 331 } { 332 } { 333 } { 334 } { 335 } { 336 } { 337 } { 338 } { 339 } { 340 } { 341 } { 342 } { 343 } { 344 } { 345 } { 346 } { 347 } { 348 } { 349 } { 350 } { 351 } { 352 } { 353 } { 354 } { 355 } { 356 } { 357 } { 358 } { 359 } { 360 } { 361 } { 362 } { 363 } { 364 } { 365 } { 366 } Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee39.uab.es. (158.109.66.39) Time: Tue Mar 2 05:24:17 2004 Input: for i:=1 to 366 do Include(X,i); end for; Output: Magma V2.10-6 Tue Mar 2 2004 05:24:14 on modular [Seed = 17113500] ------------------------------------- >> for i:=1 to 366 do Include(X,i); end for; ^ User error: Identifier 'X' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee39.uab.es. (158.109.66.39) Time: Tue Mar 2 05:24:42 2004 Input: X:=[]; for i:=1 to 366 do Include(X,i); end for; Output: Magma V2.10-6 Tue Mar 2 2004 05:24:39 on modular [Seed = 252391355] ------------------------------------- [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 6 ] [ 7 ] [ 8 ] [ 9 ] [ 10 ] [ 11 ] [ 12 ] [ 13 ] [ 14 ] [ 15 ] [ 16 ] [ 17 ] [ 18 ] [ 19 ] [ 20 ] [ 21 ] [ 22 ] [ 23 ] [ 24 ] [ 25 ] [ 26 ] [ 27 ] [ 28 ] [ 29 ] [ 30 ] [ 31 ] [ 32 ] [ 33 ] [ 34 ] [ 35 ] [ 36 ] [ 37 ] [ 38 ] [ 39 ] [ 40 ] [ 41 ] [ 42 ] [ 43 ] [ 44 ] [ 45 ] [ 46 ] [ 47 ] [ 48 ] [ 49 ] [ 50 ] [ 51 ] [ 52 ] [ 53 ] [ 54 ] [ 55 ] [ 56 ] [ 57 ] [ 58 ] [ 59 ] [ 60 ] [ 61 ] [ 62 ] [ 63 ] [ 64 ] [ 65 ] [ 66 ] [ 67 ] [ 68 ] [ 69 ] [ 70 ] [ 71 ] [ 72 ] [ 73 ] [ 74 ] [ 75 ] [ 76 ] [ 77 ] [ 78 ] [ 79 ] [ 80 ] [ 81 ] [ 82 ] [ 83 ] [ 84 ] [ 85 ] [ 86 ] [ 87 ] [ 88 ] [ 89 ] [ 90 ] [ 91 ] [ 92 ] [ 93 ] [ 94 ] [ 95 ] [ 96 ] [ 97 ] [ 98 ] [ 99 ] [ 100 ] [ 101 ] [ 102 ] [ 103 ] [ 104 ] [ 105 ] [ 106 ] [ 107 ] [ 108 ] [ 109 ] [ 110 ] [ 111 ] [ 112 ] [ 113 ] [ 114 ] [ 115 ] [ 116 ] [ 117 ] [ 118 ] [ 119 ] [ 120 ] [ 121 ] [ 122 ] [ 123 ] [ 124 ] [ 125 ] [ 126 ] [ 127 ] [ 128 ] [ 129 ] [ 130 ] [ 131 ] [ 132 ] [ 133 ] [ 134 ] [ 135 ] [ 136 ] [ 137 ] [ 138 ] [ 139 ] [ 140 ] [ 141 ] [ 142 ] [ 143 ] [ 144 ] [ 145 ] [ 146 ] [ 147 ] [ 148 ] [ 149 ] [ 150 ] [ 151 ] [ 152 ] [ 153 ] [ 154 ] [ 155 ] [ 156 ] [ 157 ] [ 158 ] [ 159 ] [ 160 ] [ 161 ] [ 162 ] [ 163 ] [ 164 ] [ 165 ] [ 166 ] [ 167 ] [ 168 ] [ 169 ] [ 170 ] [ 171 ] [ 172 ] [ 173 ] [ 174 ] [ 175 ] [ 176 ] [ 177 ] [ 178 ] [ 179 ] [ 180 ] [ 181 ] [ 182 ] [ 183 ] [ 184 ] [ 185 ] [ 186 ] [ 187 ] [ 188 ] [ 189 ] [ 190 ] [ 191 ] [ 192 ] [ 193 ] [ 194 ] [ 195 ] [ 196 ] [ 197 ] [ 198 ] [ 199 ] [ 200 ] [ 201 ] [ 202 ] [ 203 ] [ 204 ] [ 205 ] [ 206 ] [ 207 ] [ 208 ] [ 209 ] [ 210 ] [ 211 ] [ 212 ] [ 213 ] [ 214 ] [ 215 ] [ 216 ] [ 217 ] [ 218 ] [ 219 ] [ 220 ] [ 221 ] [ 222 ] [ 223 ] [ 224 ] [ 225 ] [ 226 ] [ 227 ] [ 228 ] [ 229 ] [ 230 ] [ 231 ] [ 232 ] [ 233 ] [ 234 ] [ 235 ] [ 236 ] [ 237 ] [ 238 ] [ 239 ] [ 240 ] [ 241 ] [ 242 ] [ 243 ] [ 244 ] [ 245 ] [ 246 ] [ 247 ] [ 248 ] [ 249 ] [ 250 ] [ 251 ] [ 252 ] [ 253 ] [ 254 ] [ 255 ] [ 256 ] [ 257 ] [ 258 ] [ 259 ] [ 260 ] [ 261 ] [ 262 ] [ 263 ] [ 264 ] [ 265 ] [ 266 ] [ 267 ] [ 268 ] [ 269 ] [ 270 ] [ 271 ] [ 272 ] [ 273 ] [ 274 ] [ 275 ] [ 276 ] [ 277 ] [ 278 ] [ 279 ] [ 280 ] [ 281 ] [ 282 ] [ 283 ] [ 284 ] [ 285 ] [ 286 ] [ 287 ] [ 288 ] [ 289 ] [ 290 ] [ 291 ] [ 292 ] [ 293 ] [ 294 ] [ 295 ] [ 296 ] [ 297 ] [ 298 ] [ 299 ] [ 300 ] [ 301 ] [ 302 ] [ 303 ] [ 304 ] [ 305 ] [ 306 ] [ 307 ] [ 308 ] [ 309 ] [ 310 ] [ 311 ] [ 312 ] [ 313 ] [ 314 ] [ 315 ] [ 316 ] [ 317 ] [ 318 ] [ 319 ] [ 320 ] [ 321 ] [ 322 ] [ 323 ] [ 324 ] [ 325 ] [ 326 ] [ 327 ] [ 328 ] [ 329 ] [ 330 ] [ 331 ] [ 332 ] [ 333 ] [ 334 ] [ 335 ] [ 336 ] [ 337 ] [ 338 ] [ 339 ] [ 340 ] [ 341 ] [ 342 ] [ 343 ] [ 344 ] [ 345 ] [ 346 ] [ 347 ] [ 348 ] [ 349 ] [ 350 ] [ 351 ] [ 352 ] [ 353 ] [ 354 ] [ 355 ] [ 356 ] [ 357 ] [ 358 ] [ 359 ] [ 360 ] [ 361 ] [ 362 ] [ 363 ] [ 364 ] [ 365 ] [ 366 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Tue Mar 2 05:24:56 2004 Input: for i:=1 to 366 do Include ([],i); end for; Output: Magma V2.10-6 Tue Mar 2 2004 05:24:53 on modular [Seed = 909252240] ------------------------------------- [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 6 ] [ 7 ] [ 8 ] [ 9 ] [ 10 ] [ 11 ] [ 12 ] [ 13 ] [ 14 ] [ 15 ] [ 16 ] [ 17 ] [ 18 ] [ 19 ] [ 20 ] [ 21 ] [ 22 ] [ 23 ] [ 24 ] [ 25 ] [ 26 ] [ 27 ] [ 28 ] [ 29 ] [ 30 ] [ 31 ] [ 32 ] [ 33 ] [ 34 ] [ 35 ] [ 36 ] [ 37 ] [ 38 ] [ 39 ] [ 40 ] [ 41 ] [ 42 ] [ 43 ] [ 44 ] [ 45 ] [ 46 ] [ 47 ] [ 48 ] [ 49 ] [ 50 ] [ 51 ] [ 52 ] [ 53 ] [ 54 ] [ 55 ] [ 56 ] [ 57 ] [ 58 ] [ 59 ] [ 60 ] [ 61 ] [ 62 ] [ 63 ] [ 64 ] [ 65 ] [ 66 ] [ 67 ] [ 68 ] [ 69 ] [ 70 ] [ 71 ] [ 72 ] [ 73 ] [ 74 ] [ 75 ] [ 76 ] [ 77 ] [ 78 ] [ 79 ] [ 80 ] [ 81 ] [ 82 ] [ 83 ] [ 84 ] [ 85 ] [ 86 ] [ 87 ] [ 88 ] [ 89 ] [ 90 ] [ 91 ] [ 92 ] [ 93 ] [ 94 ] [ 95 ] [ 96 ] [ 97 ] [ 98 ] [ 99 ] [ 100 ] [ 101 ] [ 102 ] [ 103 ] [ 104 ] [ 105 ] [ 106 ] [ 107 ] [ 108 ] [ 109 ] [ 110 ] [ 111 ] [ 112 ] [ 113 ] [ 114 ] [ 115 ] [ 116 ] [ 117 ] [ 118 ] [ 119 ] [ 120 ] [ 121 ] [ 122 ] [ 123 ] [ 124 ] [ 125 ] [ 126 ] [ 127 ] [ 128 ] [ 129 ] [ 130 ] [ 131 ] [ 132 ] [ 133 ] [ 134 ] [ 135 ] [ 136 ] [ 137 ] [ 138 ] [ 139 ] [ 140 ] [ 141 ] [ 142 ] [ 143 ] [ 144 ] [ 145 ] [ 146 ] [ 147 ] [ 148 ] [ 149 ] [ 150 ] [ 151 ] [ 152 ] [ 153 ] [ 154 ] [ 155 ] [ 156 ] [ 157 ] [ 158 ] [ 159 ] [ 160 ] [ 161 ] [ 162 ] [ 163 ] [ 164 ] [ 165 ] [ 166 ] [ 167 ] [ 168 ] [ 169 ] [ 170 ] [ 171 ] [ 172 ] [ 173 ] [ 174 ] [ 175 ] [ 176 ] [ 177 ] [ 178 ] [ 179 ] [ 180 ] [ 181 ] [ 182 ] [ 183 ] [ 184 ] [ 185 ] [ 186 ] [ 187 ] [ 188 ] [ 189 ] [ 190 ] [ 191 ] [ 192 ] [ 193 ] [ 194 ] [ 195 ] [ 196 ] [ 197 ] [ 198 ] [ 199 ] [ 200 ] [ 201 ] [ 202 ] [ 203 ] [ 204 ] [ 205 ] [ 206 ] [ 207 ] [ 208 ] [ 209 ] [ 210 ] [ 211 ] [ 212 ] [ 213 ] [ 214 ] [ 215 ] [ 216 ] [ 217 ] [ 218 ] [ 219 ] [ 220 ] [ 221 ] [ 222 ] [ 223 ] [ 224 ] [ 225 ] [ 226 ] [ 227 ] [ 228 ] [ 229 ] [ 230 ] [ 231 ] [ 232 ] [ 233 ] [ 234 ] [ 235 ] [ 236 ] [ 237 ] [ 238 ] [ 239 ] [ 240 ] [ 241 ] [ 242 ] [ 243 ] [ 244 ] [ 245 ] [ 246 ] [ 247 ] [ 248 ] [ 249 ] [ 250 ] [ 251 ] [ 252 ] [ 253 ] [ 254 ] [ 255 ] [ 256 ] [ 257 ] [ 258 ] [ 259 ] [ 260 ] [ 261 ] [ 262 ] [ 263 ] [ 264 ] [ 265 ] [ 266 ] [ 267 ] [ 268 ] [ 269 ] [ 270 ] [ 271 ] [ 272 ] [ 273 ] [ 274 ] [ 275 ] [ 276 ] [ 277 ] [ 278 ] [ 279 ] [ 280 ] [ 281 ] [ 282 ] [ 283 ] [ 284 ] [ 285 ] [ 286 ] [ 287 ] [ 288 ] [ 289 ] [ 290 ] [ 291 ] [ 292 ] [ 293 ] [ 294 ] [ 295 ] [ 296 ] [ 297 ] [ 298 ] [ 299 ] [ 300 ] [ 301 ] [ 302 ] [ 303 ] [ 304 ] [ 305 ] [ 306 ] [ 307 ] [ 308 ] [ 309 ] [ 310 ] [ 311 ] [ 312 ] [ 313 ] [ 314 ] [ 315 ] [ 316 ] [ 317 ] [ 318 ] [ 319 ] [ 320 ] [ 321 ] [ 322 ] [ 323 ] [ 324 ] [ 325 ] [ 326 ] [ 327 ] [ 328 ] [ 329 ] [ 330 ] [ 331 ] [ 332 ] [ 333 ] [ 334 ] [ 335 ] [ 336 ] [ 337 ] [ 338 ] [ 339 ] [ 340 ] [ 341 ] [ 342 ] [ 343 ] [ 344 ] [ 345 ] [ 346 ] [ 347 ] [ 348 ] [ 349 ] [ 350 ] [ 351 ] [ 352 ] [ 353 ] [ 354 ] [ 355 ] [ 356 ] [ 357 ] [ 358 ] [ 359 ] [ 360 ] [ 361 ] [ 362 ] [ 363 ] [ 364 ] [ 365 ] [ 366 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee39.uab.es. (158.109.66.39) Time: Tue Mar 2 05:25:09 2004 Input: X:=[]; for i:=1 to 366 do Include(X,i); end for; X; Output: Magma V2.10-6 Tue Mar 2 2004 05:25:06 on modular [Seed = 556073072] ------------------------------------- [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 6 ] [ 7 ] [ 8 ] [ 9 ] [ 10 ] [ 11 ] [ 12 ] [ 13 ] [ 14 ] [ 15 ] [ 16 ] [ 17 ] [ 18 ] [ 19 ] [ 20 ] [ 21 ] [ 22 ] [ 23 ] [ 24 ] [ 25 ] [ 26 ] [ 27 ] [ 28 ] [ 29 ] [ 30 ] [ 31 ] [ 32 ] [ 33 ] [ 34 ] [ 35 ] [ 36 ] [ 37 ] [ 38 ] [ 39 ] [ 40 ] [ 41 ] [ 42 ] [ 43 ] [ 44 ] [ 45 ] [ 46 ] [ 47 ] [ 48 ] [ 49 ] [ 50 ] [ 51 ] [ 52 ] [ 53 ] [ 54 ] [ 55 ] [ 56 ] [ 57 ] [ 58 ] [ 59 ] [ 60 ] [ 61 ] [ 62 ] [ 63 ] [ 64 ] [ 65 ] [ 66 ] [ 67 ] [ 68 ] [ 69 ] [ 70 ] [ 71 ] [ 72 ] [ 73 ] [ 74 ] [ 75 ] [ 76 ] [ 77 ] [ 78 ] [ 79 ] [ 80 ] [ 81 ] [ 82 ] [ 83 ] [ 84 ] [ 85 ] [ 86 ] [ 87 ] [ 88 ] [ 89 ] [ 90 ] [ 91 ] [ 92 ] [ 93 ] [ 94 ] [ 95 ] [ 96 ] [ 97 ] [ 98 ] [ 99 ] [ 100 ] [ 101 ] [ 102 ] [ 103 ] [ 104 ] [ 105 ] [ 106 ] [ 107 ] [ 108 ] [ 109 ] [ 110 ] [ 111 ] [ 112 ] [ 113 ] [ 114 ] [ 115 ] [ 116 ] [ 117 ] [ 118 ] [ 119 ] [ 120 ] [ 121 ] [ 122 ] [ 123 ] [ 124 ] [ 125 ] [ 126 ] [ 127 ] [ 128 ] [ 129 ] [ 130 ] [ 131 ] [ 132 ] [ 133 ] [ 134 ] [ 135 ] [ 136 ] [ 137 ] [ 138 ] [ 139 ] [ 140 ] [ 141 ] [ 142 ] [ 143 ] [ 144 ] [ 145 ] [ 146 ] [ 147 ] [ 148 ] [ 149 ] [ 150 ] [ 151 ] [ 152 ] [ 153 ] [ 154 ] [ 155 ] [ 156 ] [ 157 ] [ 158 ] [ 159 ] [ 160 ] [ 161 ] [ 162 ] [ 163 ] [ 164 ] [ 165 ] [ 166 ] [ 167 ] [ 168 ] [ 169 ] [ 170 ] [ 171 ] [ 172 ] [ 173 ] [ 174 ] [ 175 ] [ 176 ] [ 177 ] [ 178 ] [ 179 ] [ 180 ] [ 181 ] [ 182 ] [ 183 ] [ 184 ] [ 185 ] [ 186 ] [ 187 ] [ 188 ] [ 189 ] [ 190 ] [ 191 ] [ 192 ] [ 193 ] [ 194 ] [ 195 ] [ 196 ] [ 197 ] [ 198 ] [ 199 ] [ 200 ] [ 201 ] [ 202 ] [ 203 ] [ 204 ] [ 205 ] [ 206 ] [ 207 ] [ 208 ] [ 209 ] [ 210 ] [ 211 ] [ 212 ] [ 213 ] [ 214 ] [ 215 ] [ 216 ] [ 217 ] [ 218 ] [ 219 ] [ 220 ] [ 221 ] [ 222 ] [ 223 ] [ 224 ] [ 225 ] [ 226 ] [ 227 ] [ 228 ] [ 229 ] [ 230 ] [ 231 ] [ 232 ] [ 233 ] [ 234 ] [ 235 ] [ 236 ] [ 237 ] [ 238 ] [ 239 ] [ 240 ] [ 241 ] [ 242 ] [ 243 ] [ 244 ] [ 245 ] [ 246 ] [ 247 ] [ 248 ] [ 249 ] [ 250 ] [ 251 ] [ 252 ] [ 253 ] [ 254 ] [ 255 ] [ 256 ] [ 257 ] [ 258 ] [ 259 ] [ 260 ] [ 261 ] [ 262 ] [ 263 ] [ 264 ] [ 265 ] [ 266 ] [ 267 ] [ 268 ] [ 269 ] [ 270 ] [ 271 ] [ 272 ] [ 273 ] [ 274 ] [ 275 ] [ 276 ] [ 277 ] [ 278 ] [ 279 ] [ 280 ] [ 281 ] [ 282 ] [ 283 ] [ 284 ] [ 285 ] [ 286 ] [ 287 ] [ 288 ] [ 289 ] [ 290 ] [ 291 ] [ 292 ] [ 293 ] [ 294 ] [ 295 ] [ 296 ] [ 297 ] [ 298 ] [ 299 ] [ 300 ] [ 301 ] [ 302 ] [ 303 ] [ 304 ] [ 305 ] [ 306 ] [ 307 ] [ 308 ] [ 309 ] [ 310 ] [ 311 ] [ 312 ] [ 313 ] [ 314 ] [ 315 ] [ 316 ] [ 317 ] [ 318 ] [ 319 ] [ 320 ] [ 321 ] [ 322 ] [ 323 ] [ 324 ] [ 325 ] [ 326 ] [ 327 ] [ 328 ] [ 329 ] [ 330 ] [ 331 ] [ 332 ] [ 333 ] [ 334 ] [ 335 ] [ 336 ] [ 337 ] [ 338 ] [ 339 ] [ 340 ] [ 341 ] [ 342 ] [ 343 ] [ 344 ] [ 345 ] [ 346 ] [ 347 ] [ 348 ] [ 349 ] [ 350 ] [ 351 ] [ 352 ] [ 353 ] [ 354 ] [ 355 ] [ 356 ] [ 357 ] [ 358 ] [ 359 ] [ 360 ] [ 361 ] [ 362 ] [ 363 ] [ 364 ] [ 365 ] [ 366 ] [] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee39.uab.es. (158.109.66.39) Time: Tue Mar 2 05:25:36 2004 Input: X:=[]; for i:=1 to 366 do X:=Include(X,i); end for; Output: Magma V2.10-6 Tue Mar 2 2004 05:25:33 on modular [Seed = 673974630] ------------------------------------- Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee39.uab.es. (158.109.66.39) Time: Tue Mar 2 05:26:08 2004 Input: X:=[]; for i:=1 to 366 do X:=Include(X,i); end for; X; Output: Magma V2.10-6 Tue Mar 2 2004 05:26:05 on modular [Seed = 3620992697] ------------------------------------- [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366 ] Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Tue Mar 2 05:26:55 2004 Input: X:=[]; for i:=1 to 366 do X:=Include (X,i); end for; Output: Magma V2.10-6 Tue Mar 2 2004 05:26:52 on modular [Seed = 3738894305] ------------------------------------- Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Tue Mar 2 05:27:16 2004 Input: X:=[]; for i:=1 to 366 do X:=Include (X,i); end for; print X; Output: Magma V2.10-6 Tue Mar 2 2004 05:27:12 on modular [Seed = 3317818390] ------------------------------------- [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366 ] Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Tue Mar 2 05:35:40 2004 Input: X:=[]; for i:=1 to 366 do X:=Include (X,i); end for; print X; for i:=4 to 366 by 7 do print X[i]; Output: Magma V2.10-6 Tue Mar 2 2004 05:35:37 on modular [Seed = 3789931211] ------------------------------------- [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366 ] User error: syntax error at end of input Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee39.uab.es. (158.109.66.39) Time: Tue Mar 2 05:35:48 2004 Input: X:=[]; for i:=1 to 366 do X:=Include(X,i); end for; X; y:=[]; for i = 4 to 366 by 7 do print x[i]; end for; Output: Magma V2.10-6 Tue Mar 2 2004 05:35:45 on modular [Seed = 3907832634] ------------------------------------- [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366 ] >> for i = 4 to 366 by 7 do print x[i]; end for; ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Tue Mar 2 05:35:52 2004 Input: X:=[]; for i:=1 to 366 do X:=Include (X,i); end for; print X; for i:=4 to 366 by 7 do print X[i] end for; Output: Magma V2.10-6 Tue Mar 2 2004 05:35:49 on modular [Seed = 2543039553] ------------------------------------- [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366 ] >> for i:=4 to 366 by 7 do print X[i] end for; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee39.uab.es. (158.109.66.39) Time: Tue Mar 2 05:35:58 2004 Input: X:=[]; for i:=1 to 366 do X:=Include(X,i); end for; X; y:=[]; for i := 4 to 366 by 7 do print x[i]; end for; Output: Magma V2.10-6 Tue Mar 2 2004 05:35:55 on modular [Seed = 2660941126] ------------------------------------- [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366 ] >> for i := 4 to 366 by 7 do print x[i]; end for; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Tue Mar 2 05:36:10 2004 Input: X:=[]; for i:=1 to 366 do X:=Include (X,i); end for; print X; for i:=4 to 366 by 7 do print X[i]; end for; Output: Magma V2.10-6 Tue Mar 2 2004 05:36:06 on modular [Seed = 2239866432] ------------------------------------- [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366 ] 4 11 18 25 32 39 46 53 60 67 74 81 88 95 102 109 116 123 130 137 144 151 158 165 172 179 186 193 200 207 214 221 228 235 242 249 256 263 270 277 284 291 298 305 312 319 326 333 340 347 354 361 Total time: 3.619 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee39.uab.es. (158.109.66.39) Time: Tue Mar 2 05:36:10 2004 Input: X:=[]; for i:=1 to 366 do X:=Include(X,i); end for; X; y:=[]; for i := 4 to 366 by 7 do print X[i]; end for; Output: Magma V2.10-6 Tue Mar 2 2004 05:36:07 on modular [Seed = 2324605262] ------------------------------------- [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366 ] 4 11 18 25 32 39 46 53 60 67 74 81 88 95 102 109 116 123 130 137 144 151 158 165 172 179 186 193 200 207 214 221 228 235 242 249 256 263 270 277 284 291 298 305 312 319 326 333 340 347 354 361 Total time: 3.589 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee39.uab.es. (158.109.66.39) Time: Tue Mar 2 05:36:19 2004 Input: X:=[]; for i:=1 to 366 do X:=Include(X,i); end for; X; for i := 4 to 366 by 7 do print X[i]; end for; Output: Magma V2.10-6 Tue Mar 2 2004 05:36:16 on modular [Seed = 3133053257] ------------------------------------- [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366 ] 4 11 18 25 32 39 46 53 60 67 74 81 88 95 102 109 116 123 130 137 144 151 158 165 172 179 186 193 200 207 214 221 228 235 242 249 256 263 270 277 284 291 298 305 312 319 326 333 340 347 354 361 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Tue Mar 2 05:37:16 2004 Input: X:=[]; Y:=[]; for i:=1 to 366 do X:=Include (X,i); end for; print X; for i:=4 to 366 by 7 do Y:= Include (Y,X[i]); /*print X[i];*/ end for; Output: Magma V2.10-6 Tue Mar 2 2004 05:37:13 on modular [Seed = 2695136042] ------------------------------------- [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee39.uab.es. (158.109.66.39) Time: Tue Mar 2 05:37:32 2004 Input: X:=[]; Y:=[]; for i:=1 to 366 do X:=Include(X,i); end for; for i := 4 to 366 by 7 do Y:=Include(Y,X[i]); end for; Output: Magma V2.10-6 Tue Mar 2 2004 05:37:29 on modular [Seed = 2947255317] ------------------------------------- Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee39.uab.es. (158.109.66.39) Time: Tue Mar 2 05:37:45 2004 Input: X:=[]; Y:=[]; for i:=1 to 366 do X:=Include(X,i); end for; for i := 4 to 366 by 7 do Y:=Include(Y,X[i]); end for; Y; Output: Magma V2.10-6 Tue Mar 2 2004 05:37:42 on modular [Seed = 1364554483] ------------------------------------- [ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Tue Mar 2 05:37:53 2004 Input: X:=[]; Y:=[]; for i:=1 to 366 do X:=Include (X,i); end for; print X; for i:=4 to 366 by 7 do Y:= Include (Y,X[i]); /*print X[i];*/ end for; print Y; Output: Magma V2.10-6 Tue Mar 2 2004 05:37:50 on modular [Seed = 1516141040] ------------------------------------- [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366 ] [ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Tue Mar 2 05:38:06 2004 Input: X:=[]; Y:=[]; for i:=1 to 366 do X:=Include (X,i); end for; for i:=4 to 366 by 7 do Y:= Include (Y,X[i]); /*print X[i];*/ end for; print Y; Output: Magma V2.10-6 Tue Mar 2 2004 05:38:03 on modular [Seed = 1128752924] ------------------------------------- [ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee39.uab.es. (158.109.66.39) Time: Tue Mar 2 05:39:33 2004 Input: K:=GF(4); Output: Magma V2.10-6 Tue Mar 2 2004 05:39:30 on modular [Seed = 1987203648] ------------------------------------- Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee39.uab.es. (158.109.66.39) Time: Tue Mar 2 05:49:40 2004 Input: M:=GF(4); M22:=MatrixRing (M,2); Output: Magma V2.10-6 Tue Mar 2 2004 05:49:37 on modular [Seed = 1869302266] ------------------------------------- Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee39.uab.es. (158.109.66.39) Time: Tue Mar 2 05:49:51 2004 Input: M:=GF(4); M22:=MatrixRing (M,2); M22; Output: Magma V2.10-6 Tue Mar 2 2004 05:49:48 on modular [Seed = 269760136] ------------------------------------- Full Matrix Algebra of degree 2 over GF(2^2) Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Tue Mar 2 05:49:59 2004 Input: M:= GF(4); M22:= MatrixRing (M,2); print M22; /*tra (A) = a11 + a22 + a33 + ... + ann */ Output: Magma V2.10-6 Tue Mar 2 2004 05:49:56 on modular [Seed = 421347225] ------------------------------------- Full Matrix Algebra of degree 2 over GF(2^2) Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Tue Mar 2 05:50:11 2004 Input: M:= GF(4); M22:= MatrixRing (M,1); print M22; /*tra (A) = a11 + a22 + a33 + ... + ann */ Output: Magma V2.10-6 Tue Mar 2 2004 05:50:08 on modular [Seed = 151859133] ------------------------------------- Full Matrix Algebra of degree 1 over GF(2^2) Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Tue Mar 2 05:51:12 2004 Input: M:= GF(4); M22:= MatrixRing (M,2); print M22; a:= M22[1,1]; /*tra (A) = a11 + a22 + a33 + ... + ann */ Output: Magma V2.10-6 Tue Mar 2 2004 05:51:09 on modular [Seed = 842405243] ------------------------------------- Full Matrix Algebra of degree 2 over GF(2^2) >> a:= M22[1,1]; ^ Runtime error in '[]': Bad argument types Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Tue Mar 2 05:51:38 2004 Input: M:= GF(4); M22:= MatrixRing (M,2); print M22; a:= M22![1,1]; /*tra (A) = a11 + a22 + a33 + ... + ann */ Output: Magma V2.10-6 Tue Mar 2 2004 05:51:35 on modular [Seed = 606077767] ------------------------------------- Full Matrix Algebra of degree 2 over GF(2^2) >> a:= M22![1,1]; ^ Runtime error in '!': Sequence argument length (2) should be 4 to be coerced into a matrix Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Tue Mar 2 05:51:56 2004 Input: M:= GF(4); M22:= MatrixRing (M,2); print M22; M22![1,1]; /*tra (A) = a11 + a22 + a33 + ... + ann */ Output: Magma V2.10-6 Tue Mar 2 2004 05:51:53 on modular [Seed = 757664304] ------------------------------------- Full Matrix Algebra of degree 2 over GF(2^2) >> M22![1,1]; ^ Runtime error in '!': Sequence argument length (2) should be 4 to be coerced into a matrix Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Tue Mar 2 05:52:43 2004 Input: M:= GF(4); M22:= MatrixRing (M,2); print M22; M22[1,1]; /*tra (A) = a11 + a22 + a33 + ... + ann */ Output: Magma V2.10-6 Tue Mar 2 2004 05:52:40 on modular [Seed = 3604148730] ------------------------------------- Full Matrix Algebra of degree 2 over GF(2^2) >> M22[1,1]; ^ Runtime error in '[]': Bad argument types Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse011.uab.es. (158.109.66.133) Time: Tue Mar 2 05:59:00 2004 Input: MatrixRing(4,2); Output: Magma V2.10-6 Tue Mar 2 2004 05:58:57 on modular [Seed = 3351506786] ------------------------------------- >> MatrixRing(4,2); ^ Runtime error in 'MatrixRing': Bad argument types Argument types given: RngIntElt, RngIntElt Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Tue Mar 2 06:05:04 2004 Input: M:= Matrix (GF(4),2,[6,8, 1,9]); /*M22:= MatrixRing (M,2);*/ print M; /*tra (A) = a11 + a22 + a33 + ... + ann */ Output: Magma V2.10-6 Tue Mar 2 2004 06:05:01 on modular [Seed = 2425666201] ------------------------------------- [ 0 0] [ 1 1] Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 2 08:39:04 2004 Input: K:=GF(4); M:=MatrixRing(K,2); Mt:={x:x in M | Trace(x)}; Output: Magma V2.10-6 Tue Mar 2 2004 08:39:01 on modular [Seed = 1145080423] ------------------------------------- >> Mt:={x:x in M | Trace(x)};; ^ Runtime error in set construction: Logical expected Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 2 08:41:12 2004 Input: K:=GF(4); M:=MatrixRing(K,2); Mt := {x : x in M | Trace(x)}; Output: Magma V2.10-6 Tue Mar 2 2004 08:41:09 on modular [Seed = 1970387926] ------------------------------------- >> Mt := {x : x in M | Trace(x)};; ^ Runtime error in set construction: Logical expected Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 2 08:45:20 2004 Input: t:= { n^2 : n in [-11..11 by 2] | IsPrime(n) }; Output: Magma V2.10-6 Tue Mar 2 2004 08:45:17 on modular [Seed = 1684057055] ------------------------------------- Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 2 08:46:04 2004 Input: t:= { n^2 : n in [-11..11 by 2] | IsPrime(n) }; t; Output: Magma V2.10-6 Tue Mar 2 2004 08:46:00 on modular [Seed = 1835646242] ------------------------------------- { 9, 25, 49, 121 } Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 2 08:47:57 2004 Input: /*t:= { n^2 : n in [-11..11 by 2] | IsPrime(n) }; t;*/ K:=GF(4); M:=MatrixRing(K,2); Mt := {x : x in M | Trace(x)}; Output: Magma V2.10-6 Tue Mar 2 2004 08:47:54 on modular [Seed = 320324559] ------------------------------------- >> Mt := {x : x in M | Trace(x)};; ^ Runtime error in set construction: Logical expected Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 2 08:48:32 2004 Input: /*t:= { n^2 : n in [-11..11 by 2] | IsPrime(n) }; t;*/ K:=GF(4); M:=MatrixRing(K,2); M; /*Mt := {x : x in M | Trace(x)};*/ Output: Magma V2.10-6 Tue Mar 2 2004 08:48:29 on modular [Seed = 404539619] ------------------------------------- Full Matrix Algebra of degree 2 over GF(2^2) Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 2 08:54:43 2004 Input: /*t:= { n^2 : n in [-11..11 by 2] | IsPrime(n) }; t;*/ K:=GF(4); M:=MatrixRing(K,2); /*Mt := {x : x in M | Trace(x)};*/ Output: Magma V2.10-6 Tue Mar 2 2004 08:54:40 on modular [Seed = 875619906] ------------------------------------- Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 2 09:04:44 2004 Input: t := { nˆ2 : n in [-11..11 by 2] | IsPrime(n) }; Output: Magma V2.10-6 Tue Mar 2 2004 09:04:41 on modular [Seed = 3419348964] ------------------------------------- >> t := { n^È2 : n in [-11..11 by 2] | IsPrime(n) };; ^ User error: Unknown character (ascii value -120) Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 2 09:05:39 2004 Input: t := { n^2 : n in [-11..11 by 2] | IsPrime(n) }; Output: Magma V2.10-6 Tue Mar 2 2004 09:05:36 on modular [Seed = 4260964635] ------------------------------------- Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 2 09:06:28 2004 Input: t := { n^2 : n in [-11..11 by 2] | IsPrime(n) }; print t; Output: Magma V2.10-6 Tue Mar 2 2004 09:06:25 on modular [Seed = 3806738005] ------------------------------------- { 9, 25, 49, 121 } Total time: 2.839 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 2 09:09:19 2004 Input: t := { n^2 : n in [-11..11 by 2] | IsPrime(n) }; print t; dies := {n in [1..366]}; print dies; Output: Magma V2.10-6 Tue Mar 2 2004 09:09:16 on modular [Seed = 2543010381] ------------------------------------- { 9, 25, 49, 121 } >> dies := {n in [1..366]}; ^ User error: Identifier 'n' has not been declared or assigned >> print dies; ^ User error: Identifier 'dies' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 2 09:10:09 2004 Input: t := { n^2 : n in [-11..11 by 2] | IsPrime(n) }; print t; {dies : n in [1..366]}; print dies; Output: Magma V2.10-6 Tue Mar 2 2004 09:10:06 on modular [Seed = 2273530479] ------------------------------------- { 9, 25, 49, 121 } >> {dies : n in [1..366]}; ^ User error: Identifier 'dies' has not been declared or assigned >> print dies; ^ User error: Identifier 'dies' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 2 09:11:54 2004 Input: t := { n^2 : n in [-11..11 by 2] | IsPrime(n) }; print t; /*{dies : n in [1..366]};*/ dies in [1..366]; print dies; Output: Magma V2.10-6 Tue Mar 2 2004 09:11:51 on modular [Seed = 2374589436] ------------------------------------- { 9, 25, 49, 121 } >> dies in [1..366]; ^ User error: Identifier 'dies' has not been declared or assigned >> print dies; ^ User error: Identifier 'dies' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 2 09:13:40 2004 Input: t := { n^2 : n in [-11..11 by 2] | IsPrime(n) }; print t; dies := [1..366]; print dies; Output: Magma V2.10-6 Tue Mar 2 2004 09:13:37 on modular [Seed = 3015140724] ------------------------------------- { 9, 25, 49, 121 } [ 1 .. 366 ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 2 09:14:14 2004 Input: t := { n^2 : n in [-11..11 by 2] | IsPrime(n) }; print t; dies := [1..366 by 1]; print dies; Output: Magma V2.10-6 Tue Mar 2 2004 09:14:11 on modular [Seed = 3116199772] ------------------------------------- { 9, 25, 49, 121 } [ 1 .. 366 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 2 09:14:41 2004 Input: t := { n^2 : n in [-11..11 by 2] | IsPrime(n) }; print t; dies := [1..366 by 1]; print dies[3]; Output: Magma V2.10-6 Tue Mar 2 2004 09:14:38 on modular [Seed = 2930407478] ------------------------------------- { 9, 25, 49, 121 } 3 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 2 09:15:02 2004 Input: t := { n^2 : n in [-11..11 by 2] | IsPrime(n) }; print t; dies := [1..366 by 1]; print dies[63]; Output: Magma V2.10-6 Tue Mar 2 2004 09:14:59 on modular [Seed = 1448247522] ------------------------------------- { 9, 25, 49, 121 } 63 Total time: 3.129 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 2 09:18:54 2004 Input: t := { n^2 : n in [-11..11 by 2] | IsPrime(n) }; print t; dies := [1..366 by 1]; for i:=4 to 366 by 7 do Diumenges := Include (Diumenges,dies[i]); end for; print Diumenges; Output: Magma V2.10-6 Tue Mar 2 2004 09:18:51 on modular [Seed = 1161925337] ------------------------------------- { 9, 25, 49, 121 } >> Diumenges := Include (Diumenges,dies[i]); ^ User error: Identifier 'Diumenges' has not been declared or assigned >> print Diumenges;; ^ User error: Identifier 'Diumenges' has not been declared or assigned Total time: 2.839 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 2 09:19:26 2004 Input: t := { n^2 : n in [-11..11 by 2] | IsPrime(n) }; print t; Diumendes := []; dies := [1..366 by 1]; for i:=4 to 366 by 7 do Diumenges := Include (Diumenges,dies[i]); end for; print Diumenges; Output: Magma V2.10-6 Tue Mar 2 2004 09:19:23 on modular [Seed = 1279826928] ------------------------------------- { 9, 25, 49, 121 } >> Diumenges := Include (Diumenges,dies[i]); ^ User error: Identifier 'Diumenges' has not been declared or assigned >> print Diumenges;; ^ User error: Identifier 'Diumenges' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 2 09:20:02 2004 Input: t := { n^2 : n in [-11..11 by 2] | IsPrime(n) }; print t; Diumenges := []; dies := [1..366 by 1]; for i:=4 to 366 by 7 do Diumenges := Include (Diumenges,dies[i]); end for; print Diumenges; Output: Magma V2.10-6 Tue Mar 2 2004 09:19:59 on modular [Seed = 1937222443] ------------------------------------- { 9, 25, 49, 121 } [ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 2 09:21:24 2004 Input: t := { n^2 : n in [-11..11 by 2] | IsPrime(n) }; print t; Diumenges := []; dies := [1..366 by 1]; for i:=4 to 366 by 7 do Diumenges := Include (Diumenges,dies[i]); end for; print Diumenges; X:=[]; Y:=[]; for i:=1 to 366 do X:=Include (X,i); end for; for i:=4 to 366 by 7 do Y:= Include (Y,X[i]); end for; print Y; Output: Magma V2.10-6 Tue Mar 2 2004 09:21:21 on modular [Seed = 1650899540] ------------------------------------- { 9, 25, 49, 121 } [ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] [ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 2 09:21:51 2004 Input: t := { n^2 : n in [-11..11 by 2] | IsPrime(n) }; print t; /*Diumenges := []; dies := [1..366 by 1]; for i:=4 to 366 by 7 do Diumenges := Include (Diumenges,dies[i]); end for; print Diumenges;*/ X:=[]; Y:=[]; for i:=1 to 366 do X:=Include (X,i); end for; for i:=4 to 366 by 7 do Y:= Include (Y,X[i]); end for; print Y; Output: Magma V2.10-6 Tue Mar 2 2004 09:21:48 on modular [Seed = 269797435] ------------------------------------- { 9, 25, 49, 121 } [ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 2 09:31:51 2004 Input: /*t:= { n^2 : n in [-11..11 by 2] | IsPrime(n) }; t;*/ K:=GF(4); M:=MatrixRing(K,2); Mt := {x : x in M | Trace(x)=0}; Output: Magma V2.10-6 Tue Mar 2 2004 09:31:48 on modular [Seed = 2206685440] ------------------------------------- >> Mt := {x : x in M | Trace(x)=0};; ^ Runtime error in set construction: Logical expected Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 2 09:32:21 2004 Input: /*t:= { n^2 : n in [-11..11 by 2] | IsPrime(n) }; t;*/ K:=GF(4); M:=MatrixRing(K,2); Mt := { x : x in M | Trace(x)=0 }; Output: Magma V2.10-6 Tue Mar 2 2004 09:32:18 on modular [Seed = 2324582447] ------------------------------------- >> Mt := { x : x in M | Trace(x)=0 };; ^ Runtime error in set construction: Logical expected Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 2 09:33:48 2004 Input: /*t:= { n^2 : n in [-11..11 by 2] | IsPrime(n) }; t;*/ K:=GF(4); M:=MatrixRing(K,2); Mt := { x : x in M }; Output: Magma V2.10-6 Tue Mar 2 2004 09:33:45 on modular [Seed = 2964614062] ------------------------------------- Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 2 09:34:58 2004 Input: polinomi_t := function (a,b) expo := [] while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; print expo; end function; Output: Magma V2.10-6 Tue Mar 2 2004 09:34:55 on modular [Seed = 2795666814] ------------------------------------- >> while b ne 0 do ^ User error: bad syntax >> expo := Include (expo, a^(b-1)); ^ User error: Identifier 'expo' has not been declared or assigned >> b:= b-1; ^ User error: Identifier 'b' has not been declared or assigned >> end while; ^ User error: bad syntax >> print expo; ^ User error: Identifier 'expo' has not been declared or assigned >> end function;; ^ User error: bad syntax Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 2 09:35:41 2004 Input: polinomi_t := function (a,b) expo := [] while b ne 0 do expo[b] := Include (expo, a^(b-1)); b:= b-1; end while; end function; Output: Magma V2.10-6 Tue Mar 2 2004 09:35:38 on modular [Seed = 2846716484] ------------------------------------- >> while b ne 0 do ^ User error: bad syntax >> expo[b] := Include (expo, a^(b-1)); ^ User error: Identifier 'expo' has not been declared or assigned >> b:= b-1; ^ User error: Identifier 'b' has not been declared or assigned >> end while; ^ User error: bad syntax >> end function;; ^ User error: bad syntax Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 2 09:37:00 2004 Input: polinomi_t := function (a,b) expo := [] while b ne 0 do expo := Include (expo[b], a^(b-1)); b:= b-1; end while; end function; Output: Magma V2.10-6 Tue Mar 2 2004 09:36:57 on modular [Seed = 1599832845] ------------------------------------- >> while b ne 0 do ^ User error: bad syntax >> expo := Include (expo[b], a^(b-1)); ^ User error: Identifier 'expo' has not been declared or assigned >> b:= b-1; ^ User error: Identifier 'b' has not been declared or assigned >> end while; ^ User error: bad syntax >> end function;; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 2 09:37:05 2004 Input: /*t:= { n^2 : n in [-11..11 by 2] | IsPrime(n) }; t;*/ K:=GF(4); M:=MatrixRing(K,2); Mt := { x : x in M | Trace(x) == 0 }; Output: Magma V2.10-6 Tue Mar 2 2004 09:37:02 on modular [Seed = 1465092865] ------------------------------------- >> Mt := { x : x in M | Trace(x) == 0 }; ^ User error: bad syntax Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 2 09:37:57 2004 Input: polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo[b], a^(b-1)); b:= b-1; end while; end function; Output: Magma V2.10-6 Tue Mar 2 2004 09:37:53 on modular [Seed = 1111924315] ------------------------------------- Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 2 09:38:13 2004 Input: /*t:= { n^2 : n in [-11..11 by 2] | IsPrime(n) }; t;*/ K:=GF(4); M:=MatrixRing(K,2); Mt := { x : x in M | Trace(x) == 0 }; Output: Magma V2.10-6 Tue Mar 2 2004 09:38:08 on modular [Seed = 2071963507] ------------------------------------- >> Mt := { x : x in M | Trace(x) == 0 }; ^ User error: bad syntax Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 2 09:38:15 2004 Input: polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; end function; Output: Magma V2.10-6 Tue Mar 2 2004 09:38:11 on modular [Seed = 2121966197] ------------------------------------- Total time: 3.099 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 2 09:38:55 2004 Input: polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; end function; polinomi_t (7,3); Output: Magma V2.10-6 Tue Mar 2 2004 09:38:52 on modular [Seed = 1852486218] ------------------------------------- >> polinomi_t (7,3);; ^ Runtime error in procedure call: No return statement executed in user-defined function Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 2 09:39:11 2004 Input: /*t:= { n^2 : n in [-11..11 by 2] | IsPrime(n) }; t;*/ K:=GF(4); M:=MatrixRing(K,2); O:=K!0; Mt := { x : x in M | Trace(x) = O }; Output: Magma V2.10-6 Tue Mar 2 2004 09:39:08 on modular [Seed = 1734589363] ------------------------------------- >> Mt := { x : x in M | Trace(x) = O }; ^ Runtime error in set construction: Logical expected Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 2 09:39:39 2004 Input: polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; polinomi_t (7,3); Output: Magma V2.10-6 Tue Mar 2 2004 09:39:36 on modular [Seed = 269798624] ------------------------------------- [ 49, 7, 1 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 2 09:40:04 2004 Input: /*t:= { n^2 : n in [-11..11 by 2] | IsPrime(n) }; t;*/ K:=GF(4); M:=MatrixRing(K,2); Mt := { x : x in M | Trace(x) eq 0 }; Output: Magma V2.10-6 Tue Mar 2 2004 09:40:01 on modular [Seed = 318617] ------------------------------------- Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 2 09:42:41 2004 Input: polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; polinomi_t (7,3); P:=PolynomialRing(GF(49)); Output: Magma V2.10-6 Tue Mar 2 2004 09:42:38 on modular [Seed = 960357439] ------------------------------------- [ 49, 7, 1 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 2 09:43:19 2004 Input: polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; polinomi_t (7,3); P:=PolynomialRing(GF(49)); print P <3>; Output: Magma V2.10-6 Tue Mar 2 2004 09:43:16 on modular [Seed = 842461166] ------------------------------------- [ 49, 7, 1 ] >> print P <3>;; ^ User error: bad syntax Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 2 09:43:41 2004 Input: polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; polinomi_t (7,3); P:=PolynomialRing(GF(49)); print P<3>; Output: Magma V2.10-6 Tue Mar 2 2004 09:43:38 on modular [Seed = 740880878] ------------------------------------- [ 49, 7, 1 ] >> print P<3>;; ^ User error: bad syntax Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 2 09:44:09 2004 Input: P:=PolynomialRing(GF(49)); print P; Output: Magma V2.10-6 Tue Mar 2 2004 09:44:06 on modular [Seed = 622983371] ------------------------------------- >> print P;; ^ User error: bad syntax Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host n137.ryd.student.liu.se. (130.236.215.137) Time: Tue Mar 2 10:12:56 2004 Input: A:=33851236171239641265270800518600310290539375914384039323642361520363520546314650943398733920539217473681772837846957377454413104031165774; B:=39034508706847425235010450165099394176184094256982009273896067512886110799674958571370959830516545409668338961132498155256298007101774506; p:=3050544912062985183031836001189; E:=ChangeRing(EllipticCurve([A,B]),GF(p)); print(E); FactorOrder(E); Output: Magma V2.10-6 Tue Mar 2 2004 10:12:53 on modular [Seed = 3873571531] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 3028456474824639160704499041558*x + 2301387323192706015156203785484 over GF(3050544912062985183031836001189) >> print(E); FactorOrder(E);; ^ User error: Identifier 'FactorOrder' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host n137.ryd.student.liu.se. (130.236.215.137) Time: Tue Mar 2 10:13:11 2004 Input: A:=33851236171239641265270800518600310290539375914384039323642361520363520546314650943398733920539217473681772837846957377454413104031165774; B:=39034508706847425235010450165099394176184094256982009273896067512886110799674958571370959830516545409668338961132498155256298007101774506; p:=3050544912062985183031836001189; E:=ChangeRing(EllipticCurve([A,B]),GF(p)); print(E); Order(E); Output: Magma V2.10-6 Tue Mar 2 2004 10:13:06 on modular [Seed = 2677766981] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 3028456474824639160704499041558*x + 2301387323192706015156203785484 over GF(3050544912062985183031836001189) 3050544912062982631908884945436 Total time: 4.759 seconds, Total memory usage: 3.11MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 2 11:21:22 2004 Input: /*t:= { n^2 : n in [-11..11 by 2] | IsPrime(n) }; t;*/ K:=GF(4); M:=MatrixRing(K,2); Mt := { x : x in M | Trace(x) eq 0 }; Mf := { x : x in M | M[1,1]=M[2,1] AND M[1,2]=M[2,2]}; Output: Magma V2.10-6 Tue Mar 2 2004 11:21:19 on modular [Seed = 556127495] ------------------------------------- >> Mf := { x : x in M | M[1,1]=M[2,1] AND M[1,2]=M[2,2]};; ^ User error: bad syntax Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 2 11:21:41 2004 Input: /*t:= { n^2 : n in [-11..11 by 2] | IsPrime(n) }; t;*/ K:=GF(4); M:=MatrixRing(K,2); Mt := { x : x in M | Trace(x) eq 0 }; Mf := { x : x in M | M[1,1]=M[2,1] and M[1,2]=M[2,2]}; Output: Magma V2.10-6 Tue Mar 2 2004 11:21:38 on modular [Seed = 3638307859] ------------------------------------- >> Mf := { x : x in M | M[1,1]=M[2,1] and M[1,2]=M[2,2]};; ^ User error: relation chains can only be used inside a constructor Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 2 11:22:07 2004 Input: /*t:= { n^2 : n in [-11..11 by 2] | IsPrime(n) }; t;*/ K:=GF(4); M:=MatrixRing(K,2); Mt := { x : x in M | Trace(x) eq 0 }; Mf := { x : x in M | M[1,1] eq M[2,1] and M[1,2] eq M[2,2]}; Output: Magma V2.10-6 Tue Mar 2 2004 11:22:04 on modular [Seed = 3554092838] ------------------------------------- >> Mf := { x : x in M | M[1,1] eq M[2,1] and M[1,2] eq M[2,2]};; ^ Runtime error in '[]': Bad argument types Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 2 11:23:24 2004 Input: /*t:= { n^2 : n in [-11..11 by 2] | IsPrime(n) }; t;*/ K:=GF(4); M:=MatrixRing(K,2); Mt := { x : x in M | Trace(x) eq 0 }; Mf := { x : x in M | M![1,1] eq M![2,1] and M![1,2] eq M![2,2]}; Output: Magma V2.10-6 Tue Mar 2 2004 11:23:21 on modular [Seed = 3402514026] ------------------------------------- >> Mf := { x : x in M | M![1,1] eq M![2,1] and M![1,2] eq M![2,2]};; ^ Runtime error in '!': Sequence argument length (2) should be 4 to be coerced into a matrix Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 2 11:24:15 2004 Input: /*t:= { n^2 : n in [-11..11 by 2] | IsPrime(n) }; t;*/ K:=GF(4); M:=MatrixRing(K,2); Mt := { x : x in M | Trace(x) eq 0 }; Mf := { y : y in M | y[1,1] eq y[2,1] and y[1,2] eq y[2,2]}; Output: Magma V2.10-6 Tue Mar 2 2004 11:24:12 on modular [Seed = 3300929969] ------------------------------------- Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 2 11:24:34 2004 Input: /*t:= { n^2 : n in [-11..11 by 2] | IsPrime(n) }; t;*/ K:=GF(4); M:=MatrixRing(K,2); Mt := { x : x in M | Trace(x) eq 0 }; Mf := { y : y in M | y[1,1] eq y[2,1] and y[1,2] eq y[2,2]}; print Mf; Output: Magma V2.10-6 Tue Mar 2 2004 11:24:32 on modular [Seed = 4294642406] ------------------------------------- { [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ K.1 0] [ K.1 0], [ 0 K.1^2] [ 0 K.1^2], [ K.1 K.1^2] [ K.1 K.1^2], [ 0 K.1] [ 0 K.1], [ K.1 K.1] [ K.1 K.1], [ 0 1] [ 0 1], [ K.1 1] [ K.1 1], [K.1^2 0] [K.1^2 0], [ 1 0] [ 1 0], [K.1^2 K.1^2] [K.1^2 K.1^2], [ 1 K.1^2] [ 1 K.1^2], [K.1^2 K.1] [K.1^2 K.1], [ 1 K.1] [ 1 K.1], [K.1^2 1] [K.1^2 1] } Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 2 11:27:18 2004 Input: /*t:= { n^2 : n in [-11..11 by 2] | IsPrime(n) }; t;*/ K:=GF(4); M:=MatrixRing(K,2); Mt := { x : x in M | Trace(x) eq 0 }; Mf := { y : y in M | y[1,1] eq y[2,1] and y[1,2] eq y[2,2]}; Mtf := { z : z in Mt and Mf }; Output: Magma V2.10-6 Tue Mar 2 2004 11:27:15 on modular [Seed = 3941474128] ------------------------------------- >> Mtf := { z : z in Mt and Mf };; ^ Runtime error: Expected a logical for the 'and' operator Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 2 11:27:41 2004 Input: /*t:= { n^2 : n in [-11..11 by 2] | IsPrime(n) }; t;*/ K:=GF(4); M:=MatrixRing(K,2); Mt := { x : x in M | Trace(x) eq 0 }; Mf := { y : y in M | y[1,1] eq y[2,1] and y[1,2] eq y[2,2]}; Mtf := { z : z in {Mt,Mf} }; Output: Magma V2.10-6 Tue Mar 2 2004 11:27:37 on modular [Seed = 3856732229] ------------------------------------- Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 2 11:27:57 2004 Input: /*t:= { n^2 : n in [-11..11 by 2] | IsPrime(n) }; t;*/ K:=GF(4); M:=MatrixRing(K,2); Mt := { x : x in M | Trace(x) eq 0 }; Mf := { y : y in M | y[1,1] eq y[2,1] and y[1,2] eq y[2,2]}; Mtf := { z : z in {Mt,Mf} }; print Mtf; Output: Magma V2.10-6 Tue Mar 2 2004 11:27:54 on modular [Seed = 2627234511] ------------------------------------- { { [ 0 0] [ 0 0], [ 0 0] [K.1^2 0], [ 0 0] [ K.1 0], [ 0 0] [ 1 0], [K.1^2 0] [ 0 K.1^2], [K.1^2 0] [K.1^2 K.1^2], [K.1^2 0] [ K.1 K.1^2], [K.1^2 0] [ 1 K.1^2], [ 1 0] [ 0 1], [ 1 0] [K.1^2 1], [ 1 0] [ K.1 1], [ 1 0] [ 1 1], [ K.1 0] [ 0 K.1], [ K.1 0] [K.1^2 K.1], [ K.1 0] [ K.1 K.1], [ K.1 0] [ 1 K.1], [ 0 K.1^2] [ 0 0], [ 0 K.1^2] [K.1^2 0], [ 0 K.1^2] [ K.1 0], [ 0 K.1^2] [ 1 0], [K.1^2 K.1^2] [ 0 K.1^2], [K.1^2 K.1^2] [K.1^2 K.1^2], [K.1^2 K.1^2] [ K.1 K.1^2], [K.1^2 K.1^2] [ 1 K.1^2], [ 1 K.1^2] [ 0 1], [ 1 K.1^2] [K.1^2 1], [ 1 K.1^2] [ K.1 1], [ 1 K.1^2] [ 1 1], [ K.1 K.1^2] [ 0 K.1], [ K.1 K.1^2] [K.1^2 K.1], [ K.1 K.1^2] [ K.1 K.1], [ K.1 K.1^2] [ 1 K.1], [ 0 K.1] [ 0 0], [ 0 K.1] [K.1^2 0], [ 0 K.1] [ K.1 0], [ 0 K.1] [ 1 0], [K.1^2 K.1] [ 0 K.1^2], [K.1^2 K.1] [K.1^2 K.1^2], [K.1^2 K.1] [ K.1 K.1^2], [K.1^2 K.1] [ 1 K.1^2], [ 1 K.1] [ 0 1], [ 1 K.1] [K.1^2 1], [ 1 K.1] [ K.1 1], [ 1 K.1] [ 1 1], [ K.1 K.1] [ 0 K.1], [ K.1 K.1] [K.1^2 K.1], [ K.1 K.1] [ K.1 K.1], [ K.1 K.1] [ 1 K.1], [ 0 1] [ 0 0], [ 0 1] [K.1^2 0], [ 0 1] [ K.1 0], [ 0 1] [ 1 0], [K.1^2 1] [ 0 K.1^2], [K.1^2 1] [K.1^2 K.1^2], [K.1^2 1] [ K.1 K.1^2], [K.1^2 1] [ 1 K.1^2], [ 1 1] [ 0 1], [ 1 1] [K.1^2 1], [ 1 1] [ K.1 1], [ 1 1] [ 1 1], [ K.1 1] [ 0 K.1], [ K.1 1] [K.1^2 K.1], [ K.1 1] [ K.1 K.1], [ K.1 1] [ 1 K.1] }, { [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ K.1 0] [ K.1 0], [ 0 K.1^2] [ 0 K.1^2], [ K.1 K.1^2] [ K.1 K.1^2], [ 0 K.1] [ 0 K.1], [ K.1 K.1] [ K.1 K.1], [ 0 1] [ 0 1], [ K.1 1] [ K.1 1], [K.1^2 0] [K.1^2 0], [ 1 0] [ 1 0], [K.1^2 K.1^2] [K.1^2 K.1^2], [ 1 K.1^2] [ 1 K.1^2], [K.1^2 K.1] [K.1^2 K.1], [ 1 K.1] [ 1 K.1], [K.1^2 1] [K.1^2 1] } } Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 2 11:28:56 2004 Input: /*t:= { n^2 : n in [-11..11 by 2] | IsPrime(n) }; t;*/ K:=GF(4); M:=MatrixRing(K,2); Mt := { x : x in M | Trace(x) eq 0 }; Mf := { y : y in M | y[1,1] eq y[2,1] and y[1,2] eq y[2,2]}; Mtf := { z : z in {Mt,Mf} }; print Mt; Output: Magma V2.10-6 Tue Mar 2 2004 11:28:53 on modular [Seed = 2526175370] ------------------------------------- { [ 0 0] [ 0 0], [ 0 0] [K.1^2 0], [ 0 0] [ K.1 0], [ 0 0] [ 1 0], [K.1^2 0] [ 0 K.1^2], [K.1^2 0] [K.1^2 K.1^2], [K.1^2 0] [ K.1 K.1^2], [K.1^2 0] [ 1 K.1^2], [ 1 0] [ 0 1], [ 1 0] [K.1^2 1], [ 1 0] [ K.1 1], [ 1 0] [ 1 1], [ K.1 0] [ 0 K.1], [ K.1 0] [K.1^2 K.1], [ K.1 0] [ K.1 K.1], [ K.1 0] [ 1 K.1], [ 0 K.1^2] [ 0 0], [ 0 K.1^2] [K.1^2 0], [ 0 K.1^2] [ K.1 0], [ 0 K.1^2] [ 1 0], [K.1^2 K.1^2] [ 0 K.1^2], [K.1^2 K.1^2] [K.1^2 K.1^2], [K.1^2 K.1^2] [ K.1 K.1^2], [K.1^2 K.1^2] [ 1 K.1^2], [ 1 K.1^2] [ 0 1], [ 1 K.1^2] [K.1^2 1], [ 1 K.1^2] [ K.1 1], [ 1 K.1^2] [ 1 1], [ K.1 K.1^2] [ 0 K.1], [ K.1 K.1^2] [K.1^2 K.1], [ K.1 K.1^2] [ K.1 K.1], [ K.1 K.1^2] [ 1 K.1], [ 0 K.1] [ 0 0], [ 0 K.1] [K.1^2 0], [ 0 K.1] [ K.1 0], [ 0 K.1] [ 1 0], [K.1^2 K.1] [ 0 K.1^2], [K.1^2 K.1] [K.1^2 K.1^2], [K.1^2 K.1] [ K.1 K.1^2], [K.1^2 K.1] [ 1 K.1^2], [ 1 K.1] [ 0 1], [ 1 K.1] [K.1^2 1], [ 1 K.1] [ K.1 1], [ 1 K.1] [ 1 1], [ K.1 K.1] [ 0 K.1], [ K.1 K.1] [K.1^2 K.1], [ K.1 K.1] [ K.1 K.1], [ K.1 K.1] [ 1 K.1], [ 0 1] [ 0 0], [ 0 1] [K.1^2 0], [ 0 1] [ K.1 0], [ 0 1] [ 1 0], [K.1^2 1] [ 0 K.1^2], [K.1^2 1] [K.1^2 K.1^2], [K.1^2 1] [ K.1 K.1^2], [K.1^2 1] [ 1 K.1^2], [ 1 1] [ 0 1], [ 1 1] [K.1^2 1], [ 1 1] [ K.1 1], [ 1 1] [ 1 1], [ K.1 1] [ 0 K.1], [ K.1 1] [K.1^2 K.1], [ K.1 1] [ K.1 K.1], [ K.1 1] [ 1 K.1] } Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 2 11:29:51 2004 Input: /*t:= { n^2 : n in [-11..11 by 2] | IsPrime(n) }; t;*/ K:=GF(4); M:=MatrixRing(K,2); Mt := { x : x in M | Trace(x) eq 0 }; Mf := { y : y in M | y[1,1] eq y[2,1] and y[1,2] eq y[2,2]}; Mtf := { z : z in [Mt,Mf] }; print Mt; Output: Magma V2.10-6 Tue Mar 2 2004 11:29:48 on modular [Seed = 2173007780] ------------------------------------- { [ 0 0] [ 0 0], [ 0 0] [K.1^2 0], [ 0 0] [ K.1 0], [ 0 0] [ 1 0], [K.1^2 0] [ 0 K.1^2], [K.1^2 0] [K.1^2 K.1^2], [K.1^2 0] [ K.1 K.1^2], [K.1^2 0] [ 1 K.1^2], [ 1 0] [ 0 1], [ 1 0] [K.1^2 1], [ 1 0] [ K.1 1], [ 1 0] [ 1 1], [ K.1 0] [ 0 K.1], [ K.1 0] [K.1^2 K.1], [ K.1 0] [ K.1 K.1], [ K.1 0] [ 1 K.1], [ 0 K.1^2] [ 0 0], [ 0 K.1^2] [K.1^2 0], [ 0 K.1^2] [ K.1 0], [ 0 K.1^2] [ 1 0], [K.1^2 K.1^2] [ 0 K.1^2], [K.1^2 K.1^2] [K.1^2 K.1^2], [K.1^2 K.1^2] [ K.1 K.1^2], [K.1^2 K.1^2] [ 1 K.1^2], [ 1 K.1^2] [ 0 1], [ 1 K.1^2] [K.1^2 1], [ 1 K.1^2] [ K.1 1], [ 1 K.1^2] [ 1 1], [ K.1 K.1^2] [ 0 K.1], [ K.1 K.1^2] [K.1^2 K.1], [ K.1 K.1^2] [ K.1 K.1], [ K.1 K.1^2] [ 1 K.1], [ 0 K.1] [ 0 0], [ 0 K.1] [K.1^2 0], [ 0 K.1] [ K.1 0], [ 0 K.1] [ 1 0], [K.1^2 K.1] [ 0 K.1^2], [K.1^2 K.1] [K.1^2 K.1^2], [K.1^2 K.1] [ K.1 K.1^2], [K.1^2 K.1] [ 1 K.1^2], [ 1 K.1] [ 0 1], [ 1 K.1] [K.1^2 1], [ 1 K.1] [ K.1 1], [ 1 K.1] [ 1 1], [ K.1 K.1] [ 0 K.1], [ K.1 K.1] [K.1^2 K.1], [ K.1 K.1] [ K.1 K.1], [ K.1 K.1] [ 1 K.1], [ 0 1] [ 0 0], [ 0 1] [K.1^2 0], [ 0 1] [ K.1 0], [ 0 1] [ 1 0], [K.1^2 1] [ 0 K.1^2], [K.1^2 1] [K.1^2 K.1^2], [K.1^2 1] [ K.1 K.1^2], [K.1^2 1] [ 1 K.1^2], [ 1 1] [ 0 1], [ 1 1] [K.1^2 1], [ 1 1] [ K.1 1], [ 1 1] [ 1 1], [ K.1 1] [ 0 K.1], [ K.1 1] [K.1^2 K.1], [ K.1 1] [ K.1 K.1], [ K.1 1] [ 1 K.1] } Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 2 11:30:06 2004 Input: /*t:= { n^2 : n in [-11..11 by 2] | IsPrime(n) }; t;*/ K:=GF(4); M:=MatrixRing(K,2); Mt := { x : x in M | Trace(x) eq 0 }; Mf := { y : y in M | y[1,1] eq y[2,1] and y[1,2] eq y[2,2]}; Mtf := { z : z in [Mt,Mf] }; print Mtf print Mt; Output: Magma V2.10-6 Tue Mar 2 2004 11:30:03 on modular [Seed = 2981447523] ------------------------------------- >> print Mt;; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 2 11:30:17 2004 Input: /*t:= { n^2 : n in [-11..11 by 2] | IsPrime(n) }; t;*/ K:=GF(4); M:=MatrixRing(K,2); Mt := { x : x in M | Trace(x) eq 0 }; Mf := { y : y in M | y[1,1] eq y[2,1] and y[1,2] eq y[2,2]}; Mtf := { z : z in [Mt,Mf] }; print Mtf; print Mt; Output: Magma V2.10-6 Tue Mar 2 2004 11:30:14 on modular [Seed = 2829868647] ------------------------------------- { { [ 0 0] [ 0 0], [ 0 0] [K.1^2 0], [ 0 0] [ K.1 0], [ 0 0] [ 1 0], [K.1^2 0] [ 0 K.1^2], [K.1^2 0] [K.1^2 K.1^2], [K.1^2 0] [ K.1 K.1^2], [K.1^2 0] [ 1 K.1^2], [ 1 0] [ 0 1], [ 1 0] [K.1^2 1], [ 1 0] [ K.1 1], [ 1 0] [ 1 1], [ K.1 0] [ 0 K.1], [ K.1 0] [K.1^2 K.1], [ K.1 0] [ K.1 K.1], [ K.1 0] [ 1 K.1], [ 0 K.1^2] [ 0 0], [ 0 K.1^2] [K.1^2 0], [ 0 K.1^2] [ K.1 0], [ 0 K.1^2] [ 1 0], [K.1^2 K.1^2] [ 0 K.1^2], [K.1^2 K.1^2] [K.1^2 K.1^2], [K.1^2 K.1^2] [ K.1 K.1^2], [K.1^2 K.1^2] [ 1 K.1^2], [ 1 K.1^2] [ 0 1], [ 1 K.1^2] [K.1^2 1], [ 1 K.1^2] [ K.1 1], [ 1 K.1^2] [ 1 1], [ K.1 K.1^2] [ 0 K.1], [ K.1 K.1^2] [K.1^2 K.1], [ K.1 K.1^2] [ K.1 K.1], [ K.1 K.1^2] [ 1 K.1], [ 0 K.1] [ 0 0], [ 0 K.1] [K.1^2 0], [ 0 K.1] [ K.1 0], [ 0 K.1] [ 1 0], [K.1^2 K.1] [ 0 K.1^2], [K.1^2 K.1] [K.1^2 K.1^2], [K.1^2 K.1] [ K.1 K.1^2], [K.1^2 K.1] [ 1 K.1^2], [ 1 K.1] [ 0 1], [ 1 K.1] [K.1^2 1], [ 1 K.1] [ K.1 1], [ 1 K.1] [ 1 1], [ K.1 K.1] [ 0 K.1], [ K.1 K.1] [K.1^2 K.1], [ K.1 K.1] [ K.1 K.1], [ K.1 K.1] [ 1 K.1], [ 0 1] [ 0 0], [ 0 1] [K.1^2 0], [ 0 1] [ K.1 0], [ 0 1] [ 1 0], [K.1^2 1] [ 0 K.1^2], [K.1^2 1] [K.1^2 K.1^2], [K.1^2 1] [ K.1 K.1^2], [K.1^2 1] [ 1 K.1^2], [ 1 1] [ 0 1], [ 1 1] [K.1^2 1], [ 1 1] [ K.1 1], [ 1 1] [ 1 1], [ K.1 1] [ 0 K.1], [ K.1 1] [K.1^2 K.1], [ K.1 1] [ K.1 K.1], [ K.1 1] [ 1 K.1] }, { [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ K.1 0] [ K.1 0], [ 0 K.1^2] [ 0 K.1^2], [ K.1 K.1^2] [ K.1 K.1^2], [ 0 K.1] [ 0 K.1], [ K.1 K.1] [ K.1 K.1], [ 0 1] [ 0 1], [ K.1 1] [ K.1 1], [K.1^2 0] [K.1^2 0], [ 1 0] [ 1 0], [K.1^2 K.1^2] [K.1^2 K.1^2], [ 1 K.1^2] [ 1 K.1^2], [K.1^2 K.1] [K.1^2 K.1], [ 1 K.1] [ 1 K.1], [K.1^2 1] [K.1^2 1] } } { [ 0 0] [ 0 0], [ 0 0] [K.1^2 0], [ 0 0] [ K.1 0], [ 0 0] [ 1 0], [K.1^2 0] [ 0 K.1^2], [K.1^2 0] [K.1^2 K.1^2], [K.1^2 0] [ K.1 K.1^2], [K.1^2 0] [ 1 K.1^2], [ 1 0] [ 0 1], [ 1 0] [K.1^2 1], [ 1 0] [ K.1 1], [ 1 0] [ 1 1], [ K.1 0] [ 0 K.1], [ K.1 0] [K.1^2 K.1], [ K.1 0] [ K.1 K.1], [ K.1 0] [ 1 K.1], [ 0 K.1^2] [ 0 0], [ 0 K.1^2] [K.1^2 0], [ 0 K.1^2] [ K.1 0], [ 0 K.1^2] [ 1 0], [K.1^2 K.1^2] [ 0 K.1^2], [K.1^2 K.1^2] [K.1^2 K.1^2], [K.1^2 K.1^2] [ K.1 K.1^2], [K.1^2 K.1^2] [ 1 K.1^2], [ 1 K.1^2] [ 0 1], [ 1 K.1^2] [K.1^2 1], [ 1 K.1^2] [ K.1 1], [ 1 K.1^2] [ 1 1], [ K.1 K.1^2] [ 0 K.1], [ K.1 K.1^2] [K.1^2 K.1], [ K.1 K.1^2] [ K.1 K.1], [ K.1 K.1^2] [ 1 K.1], [ 0 K.1] [ 0 0], [ 0 K.1] [K.1^2 0], [ 0 K.1] [ K.1 0], [ 0 K.1] [ 1 0], [K.1^2 K.1] [ 0 K.1^2], [K.1^2 K.1] [K.1^2 K.1^2], [K.1^2 K.1] [ K.1 K.1^2], [K.1^2 K.1] [ 1 K.1^2], [ 1 K.1] [ 0 1], [ 1 K.1] [K.1^2 1], [ 1 K.1] [ K.1 1], [ 1 K.1] [ 1 1], [ K.1 K.1] [ 0 K.1], [ K.1 K.1] [K.1^2 K.1], [ K.1 K.1] [ K.1 K.1], [ K.1 K.1] [ 1 K.1], [ 0 1] [ 0 0], [ 0 1] [K.1^2 0], [ 0 1] [ K.1 0], [ 0 1] [ 1 0], [K.1^2 1] [ 0 K.1^2], [K.1^2 1] [K.1^2 K.1^2], [K.1^2 1] [ K.1 K.1^2], [K.1^2 1] [ 1 K.1^2], [ 1 1] [ 0 1], [ 1 1] [K.1^2 1], [ 1 1] [ K.1 1], [ 1 1] [ 1 1], [ K.1 1] [ 0 K.1], [ K.1 1] [K.1^2 K.1], [ K.1 1] [ K.1 K.1], [ K.1 1] [ 1 K.1] } Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 2 11:31:18 2004 Input: /*t:= { n^2 : n in [-11..11 by 2] | IsPrime(n) }; t;*/ K:=GF(4); M:=MatrixRing(K,2); Mt := { x : x in M | Trace(x) eq 0 }; Mf := { y : y in M | y[1,1] eq y[2,1] and y[1,2] eq y[2,2]}; Mtf := { z : z in Mt join Mf }; print Mtf; print Mt; Output: Magma V2.10-6 Tue Mar 2 2004 11:31:14 on modular [Seed = 2745652520] ------------------------------------- { [ 0 0] [ 0 0], [ 0 0] [K.1^2 0], [ 0 0] [ K.1 0], [ 0 0] [ 1 0], [K.1^2 0] [K.1^2 0], [K.1^2 0] [ 0 K.1^2], [K.1^2 0] [K.1^2 K.1^2], [K.1^2 0] [ K.1 K.1^2], [K.1^2 0] [ 1 K.1^2], [ K.1 0] [ K.1 0], [ 1 0] [ 0 1], [ 1 0] [K.1^2 1], [ 1 0] [ K.1 1], [ 1 0] [ 1 1], [ K.1 0] [ 0 K.1], [ K.1 0] [K.1^2 K.1], [ K.1 0] [ K.1 K.1], [ K.1 0] [ 1 K.1], [ 1 0] [ 1 0], [ 0 K.1^2] [ 0 0], [ 0 K.1^2] [K.1^2 0], [ 0 K.1^2] [ K.1 0], [ 0 K.1^2] [ 1 0], [ 0 K.1^2] [ 0 K.1^2], [K.1^2 K.1^2] [ 0 K.1^2], [K.1^2 K.1^2] [K.1^2 K.1^2], [K.1^2 K.1^2] [ K.1 K.1^2], [K.1^2 K.1^2] [ 1 K.1^2], [ 1 K.1^2] [ 0 1], [ 1 K.1^2] [K.1^2 1], [ 1 K.1^2] [ K.1 1], [ K.1 K.1^2] [ K.1 K.1^2], [ 1 K.1^2] [ 1 1], [ K.1 K.1^2] [ 0 K.1], [ K.1 K.1^2] [K.1^2 K.1], [ K.1 K.1^2] [ K.1 K.1], [ K.1 K.1^2] [ 1 K.1], [ 1 K.1^2] [ 1 K.1^2], [ 0 K.1] [ 0 0], [ 0 K.1] [K.1^2 0], [K.1^2 K.1] [K.1^2 K.1], [ 0 K.1] [ K.1 0], [ 0 K.1] [ 1 0], [ 0 K.1] [ 0 K.1], [K.1^2 K.1] [ 0 K.1^2], [K.1^2 K.1] [K.1^2 K.1^2], [K.1^2 K.1] [ K.1 K.1^2], [K.1^2 K.1] [ 1 K.1^2], [ 1 K.1] [ 1 K.1], [ 1 K.1] [ 0 1], [ 1 K.1] [K.1^2 1], [ 1 K.1] [ K.1 1], [ 1 K.1] [ 1 1], [ K.1 K.1] [ 0 K.1], [ K.1 K.1] [K.1^2 K.1], [ K.1 K.1] [ K.1 K.1], [ K.1 K.1] [ 1 K.1], [ 0 1] [ 0 0], [ 0 1] [K.1^2 0], [ 0 1] [ K.1 0], [ 0 1] [ 1 0], [K.1^2 1] [K.1^2 1], [K.1^2 1] [ 0 K.1^2], [ 0 1] [ 0 1], [K.1^2 1] [K.1^2 K.1^2], [K.1^2 1] [ K.1 K.1^2], [K.1^2 1] [ 1 K.1^2], [ 1 1] [ 0 1], [ 1 1] [K.1^2 1], [ 1 1] [ K.1 1], [ 1 1] [ 1 1], [ K.1 1] [ 0 K.1], [ K.1 1] [K.1^2 K.1], [ K.1 1] [ K.1 K.1], [ K.1 1] [ 1 K.1], [ K.1 1] [ K.1 1] } { [ 0 0] [ 0 0], [ 0 0] [K.1^2 0], [ 0 0] [ K.1 0], [ 0 0] [ 1 0], [K.1^2 0] [ 0 K.1^2], [K.1^2 0] [K.1^2 K.1^2], [K.1^2 0] [ K.1 K.1^2], [K.1^2 0] [ 1 K.1^2], [ 1 0] [ 0 1], [ 1 0] [K.1^2 1], [ 1 0] [ K.1 1], [ 1 0] [ 1 1], [ K.1 0] [ 0 K.1], [ K.1 0] [K.1^2 K.1], [ K.1 0] [ K.1 K.1], [ K.1 0] [ 1 K.1], [ 0 K.1^2] [ 0 0], [ 0 K.1^2] [K.1^2 0], [ 0 K.1^2] [ K.1 0], [ 0 K.1^2] [ 1 0], [K.1^2 K.1^2] [ 0 K.1^2], [K.1^2 K.1^2] [K.1^2 K.1^2], [K.1^2 K.1^2] [ K.1 K.1^2], [K.1^2 K.1^2] [ 1 K.1^2], [ 1 K.1^2] [ 0 1], [ 1 K.1^2] [K.1^2 1], [ 1 K.1^2] [ K.1 1], [ 1 K.1^2] [ 1 1], [ K.1 K.1^2] [ 0 K.1], [ K.1 K.1^2] [K.1^2 K.1], [ K.1 K.1^2] [ K.1 K.1], [ K.1 K.1^2] [ 1 K.1], [ 0 K.1] [ 0 0], [ 0 K.1] [K.1^2 0], [ 0 K.1] [ K.1 0], [ 0 K.1] [ 1 0], [K.1^2 K.1] [ 0 K.1^2], [K.1^2 K.1] [K.1^2 K.1^2], [K.1^2 K.1] [ K.1 K.1^2], [K.1^2 K.1] [ 1 K.1^2], [ 1 K.1] [ 0 1], [ 1 K.1] [K.1^2 1], [ 1 K.1] [ K.1 1], [ 1 K.1] [ 1 1], [ K.1 K.1] [ 0 K.1], [ K.1 K.1] [K.1^2 K.1], [ K.1 K.1] [ K.1 K.1], [ K.1 K.1] [ 1 K.1], [ 0 1] [ 0 0], [ 0 1] [K.1^2 0], [ 0 1] [ K.1 0], [ 0 1] [ 1 0], [K.1^2 1] [ 0 K.1^2], [K.1^2 1] [K.1^2 K.1^2], [K.1^2 1] [ K.1 K.1^2], [K.1^2 1] [ 1 K.1^2], [ 1 1] [ 0 1], [ 1 1] [K.1^2 1], [ 1 1] [ K.1 1], [ 1 1] [ 1 1], [ K.1 1] [ 0 K.1], [ K.1 1] [K.1^2 K.1], [ K.1 1] [ K.1 K.1], [ K.1 1] [ 1 K.1] } Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 2 12:26:44 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; while (i_cond gt 0 and semi[i_cond]+1 eq semi[i_cond+1]) do i_cond:=i_cond-1; end while; firstnongaps:=[semi[i]:i in [1..i_cond+1]]; c:=firstnongaps[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #firstnongaps gt 1 then d:=firstnongaps[i_cond]; i:=d; while i in firstnongaps do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; /*return;*/ end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; LockDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; relock:=1; sum:=1; max:=1; for i in [1..#pat] do sum:=sum+pat[i]; if sum eq 0 and max gt relock then relock:=max; max:=0; elif sum gt max then max:=sum; end if; end for; return degree, relock; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; AllArfSemigroupsWithGenus:=func; AllArfSemigroupsWithGenusUpto:=func; AllNonArfSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then s:=semigrup(semi); if not IsArf(s) then AS:=AS cat [s]; end if; end if; end for; return AS; end function; AllNonArfSemigroupsWithGenusUpto:=func; AllSemigroupsWithGenusAndSubstractionDegree:=function(g,sd) if g eq 0 or sd eq 1 then return [TrivialSemigroup()]; elif sd eq 1 then return AllArfSemigroupsWithGenus(g); endif; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then s:=semigrup(semi); if SubstractionDegree(s) eq sd then AS:=AS cat [s]; end if; end if; end for; return AS; end function; AllSemigroupsWithGenusUptoAndSubstractionDegree:= func; PatternSemigroupClassification:=function(Semigups,Patterns) t:=Cputime(); l:=#Semigrups; lp:=#Patterns; ss:=[]; pp:=[]; lockdeg:=[]; c:=0; for p in Patterns do tint:=Cputime(); c:=c+1; ld,rld:=LockDegree(p); semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~lockdeg,[]); else Append(~pp[pos],p); Append(~lockdeg[pos],); end if; print "---------------------------------------------------------------"; print " ",c,"/",lp," n=",#p," ---> ",p; print "---------------------------------------------------------------"; [#s: s in ss]; pp; lockdeg; print "TEMPS= ... + ",Cputime(tint)," = ",Cputime(t); end for; print "TEMPS TOTAL=",Cputime(t); return ss, pp, lockdeg; end function; FixedLockDegreePatternSemigroupCassification:= func; MAXGENUS:=10; MAXLENGTHPATTERNS:=20; //Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); //Semigrups:=[HermitianSemigroup(q): q in [1..7]]; /* s:=semigrup([0,5,6,10,11,12,13,15]); p1:=[1,1,1,-1]; p2:=[1,1,1,1,-1,-1]; LockDegree(p1); LockDegree(p2); admits(s,p1); admits(s,p2); */ Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed. ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 2 12:31:31 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; while (i_cond gt 0 and semi[i_cond]+1 eq semi[i_cond+1]) do i_cond:=i_cond-1; end while; firstnongaps:=[semi[i]:i in [1..i_cond+1]]; c:=firstnongaps[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #firstnongaps gt 1 then d:=firstnongaps[i_cond]; i:=d; while i in firstnongaps do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; /*return;*/ end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; LockDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; relock:=1; sum:=1; max:=1; for i in [1..#pat] do sum:=sum+pat[i]; if sum eq 0 and max gt relock then relock:=max; max:=0; elif sum gt max then max:=sum; end if; end for; return degree, relock; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; AllArfSemigroupsWithGenus:=func; AllArfSemigroupsWithGenusUpto:=func; AllNonArfSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then s:=semigrup(semi); if not IsArf(s) then AS:=AS cat [s]; end if; end if; end for; return AS; end function; AllNonArfSemigroupsWithGenusUpto:=func; AllSemigroupsWithGenusAndSubstractionDegree:=function(g,sd) if g eq 0 or sd eq 1 then return [TrivialSemigroup()]; elif sd eq 1 then return AllArfSemigroupsWithGenus(g); endif; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then s:=semigrup(semi); if SubstractionDegree(s) eq sd then AS:=AS cat [s]; end if; end if; end for; return AS; end function; AllSemigroupsWithGenusUptoAndSubstractionDegree:= func; PatternSemigroupClassification:=function(Semigups,Patterns) //t:=Cputime(); l:=#Semigrups; lp:=#Patterns; ss:=[]; pp:=[]; lockdeg:=[]; c:=0; for p in Patterns do //tint:=Cputime(); c:=c+1; ld,rld:=LockDegree(p); semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~lockdeg,[]); else Append(~pp[pos],p); Append(~lockdeg[pos],); end if; print "---------------------------------------------------------------"; print " ",c,"/",lp," n=",#p," ---> ",p; print "---------------------------------------------------------------"; [#s: s in ss]; pp; lockdeg; //print "TEMPS= ... + ",Cputime(tint)," = ",Cputime(t); end for; //print "TEMPS TOTAL=",Cputime(t); return ss, pp, lockdeg; end function; FixedLockDegreePatternSemigroupCassification:= func; MAXGENUS:=10; MAXLENGTHPATTERNS:=20; //Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); //Semigrups:=[HermitianSemigroup(q): q in [1..7]]; /* s:=semigrup([0,5,6,10,11,12,13,15]); p1:=[1,1,1,-1]; p2:=[1,1,1,1,-1,-1]; LockDegree(p1); LockDegree(p2); admits(s,p1); admits(s,p2); */ Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed. ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 2 12:31:55 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; while (i_cond gt 0 and semi[i_cond]+1 eq semi[i_cond+1]) do i_cond:=i_cond-1; end while; firstnongaps:=[semi[i]:i in [1..i_cond+1]]; c:=firstnongaps[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #firstnongaps gt 1 then d:=firstnongaps[i_cond]; i:=d; while i in firstnongaps do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; /*return;*/ end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; LockDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; relock:=1; sum:=1; max:=1; for i in [1..#pat] do sum:=sum+pat[i]; if sum eq 0 and max gt relock then relock:=max; max:=0; elif sum gt max then max:=sum; end if; end for; return degree, relock; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; AllArfSemigroupsWithGenus:=func; AllArfSemigroupsWithGenusUpto:=func; AllNonArfSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then s:=semigrup(semi); if not IsArf(s) then AS:=AS cat [s]; end if; end if; end for; return AS; end function; AllNonArfSemigroupsWithGenusUpto:=func; AllSemigroupsWithGenusAndSubstractionDegree:=function(g,sd) if g eq 0 or sd eq 1 then return [TrivialSemigroup()]; elif sd eq 1 then return AllArfSemigroupsWithGenus(g); endif; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then s:=semigrup(semi); if SubstractionDegree(s) eq sd then AS:=AS cat [s]; end if; end if; end for; return AS; end function; AllSemigroupsWithGenusUptoAndSubstractionDegree:= func; PatternSemigroupClassification:=function(Semigups,Patterns) //t:=Cputime(); l:=#Semigrups; lp:=#Patterns; ss:=[]; pp:=[]; lockdeg:=[]; c:=0; for p in Patterns do //tint:=Cputime(); c:=c+1; ld,rld:=LockDegree(p); semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~lockdeg,[]); else Append(~pp[pos],p); Append(~lockdeg[pos],); end if; print "---------------------------------------------------------------"; print " ",c,"/",lp," n=",#p," ---> ",p; print "---------------------------------------------------------------"; [#s: s in ss]; pp; lockdeg; //print "TEMPS= ... + ",Cputime(tint)," = ",Cputime(t); end for; //print "TEMPS TOTAL=",Cputime(t); return ss, pp, lockdeg; end function; FixedLockDegreePatternSemigroupCassification:= func; MAXGENUS:=10; MAXLENGTHPATTERNS:=20; //Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); //Semigrups:=[HermitianSemigroup(q): q in [1..7]]; /* s:=semigrup([0,5,6,10,11,12,13,15]); p1:=[1,1,1,-1]; p2:=[1,1,1,1,-1,-1]; LockDegree(p1); LockDegree(p2); admits(s,p1); admits(s,p2); */ Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed. ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 2 12:32:01 2004 Input: semigrup:=function(semi) /* semi conte tots els nogaps fins al conductor (inclos) */ i_cond:=#semi-1; while (i_cond gt 0 and semi[i_cond]+1 eq semi[i_cond+1]) do i_cond:=i_cond-1; end while; firstnongaps:=[semi[i]:i in [1..i_cond+1]]; c:=firstnongaps[i_cond+1]; g:=c-i_cond; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; dORD:=func; if #firstnongaps gt 1 then d:=firstnongaps[i_cond]; i:=d; while i in firstnongaps do i:=i-1; end while; subc:=i+1; if subc gt 0 then subd:=lambda(lambdainv(subc)-1); else subd:=-Infinity(); end if; else d:=-Infinity(); subc:=-Infinity(); subd:=-Infinity(); end if; print "Semigrup: ", Append(,"..."),"n"; return; /*return;*/ end function; firstnongaps:=func; i_cond :=func; conductor :=func; genus :=func; pertany :=func; gaps :=func; lambda :=func; lambdainv :=func; oplus :=func; inferior :=func; ominus :=func; N :=func; nu :=func; dORD :=func; dominant :=func; subconductor:=func; subdominant :=func; TrivialSemigroup:= func<|semigrup([0])>; OrdinarySemigroup:= func; KleinSemigroup:= func<|semigrup([0,3,5])>; HermitianSemigroup:= func; IntervalGeneratedSemigroup:= func; TwoGeneratedSemigroup:= func; IsSymmetric:=func; IsPseudosymmetric:=func; IsAcute:=func; IsOrdinary:=func; IsSemigroup:=function(semi) semiescapsat:=[semi[i]: i in [2..(#semi-1)]]; c:=semi[#semi]; r:=exists(a){[l,m]:l in semiescapsat, m in semiescapsat | (l+m lt c) and (l+m notin semi)}; if r eq true then return false,a; else return true; end if; end function; AllSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then AS:=AS cat [semigrup(semi)]; end if; end for; return AS; end function; AllSemigroupsWithGenusUpto:=func; /* PATTERNS */ PreviousPattern:= func; IsAdmissible:=function(pattern) sum:=pattern[1]; i:=2; while ((sum ge 0) and (i le #pattern)) do sum:=sum+pattern[i]; i:=i+1; end while; return (sum ge 0); end function; AllAdmissiblePatternsWithLength:=func; AllAdmissiblePatternsWithLengthUpto:=func; IsStrongAdmissible:= func; LockDegree:=function(pattern) degree:=0; pat:=pattern; while IsAdmissible(pat) and #pattern gt 0 do degree:=degree+1; pat:=PreviousPattern(pat); end while; relock:=1; sum:=1; max:=1; for i in [1..#pat] do sum:=sum+pat[i]; if sum eq 0 and max gt relock then relock:=max; max:=0; elif sum gt max then max:=sum; end if; end for; return degree, relock; end function; caudins:=function(semigrup,pattern,seq) /* seq es una sequencia d'indexos i no d'elements del semigrup ! */ lamb:=lambda(semigrup); pert:=pertany(semigrup); m:=Min(#pattern,#seq); seq:=Reverse(Sort(seq)); return pert(&+[pattern[i]*lamb(seq[i]): i in [1..m]]); end function; admits:=function(semigrup,pattern) if not IsAdmissible(pattern) then return false; end if; if firstnongaps(semigrup) eq [0] then return true; end if; if not IsStrongAdmissible(pattern) then return false; end if; subsemi:=Prune(firstnongaps(semigrup)); pert:=pertany(semigrup); totselscasos:={Reverse(Sort([i: i in m])):m in Multisets(SequenceToSet(subsemi),#pattern)}; r:=exists(a){seq:seq in totselscasos|not pert(&+[pattern[i]*seq[i]: i in [1..#pattern]])}; if r eq true then return false,a; else return true; end if; end function; SubstractionPattern:=func; SubstractionDegree:=function(semigrup) k:=1; while not admits(semigrup,SubstractionPattern(k)) do k:=k+1; end while; return(k); end function; IsArf:=func; AllArfSemigroupsWithGenus:=func; AllArfSemigroupsWithGenusUpto:=func; AllNonArfSemigroupsWithGenus:=function(g) if g eq 0 then return [TrivialSemigroup()]; end if; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then s:=semigrup(semi); if not IsArf(s) then AS:=AS cat [s]; end if; end if; end for; return AS; end function; AllNonArfSemigroupsWithGenusUpto:=func; AllSemigroupsWithGenusAndSubstractionDegree:=function(g,sd) if g eq 0 or sd eq 1 then return [TrivialSemigroup()]; elif sd eq 1 then return AllArfSemigroupsWithGenus(g); endif; AS:=[]; for gapset in Subsets({1..2*g-1},g) do semi:=Sort(SetToSequence({0..Max(gapset)+1} diff gapset)); if IsSemigroup(semi) then s:=semigrup(semi); if SubstractionDegree(s) eq sd then AS:=AS cat [s]; end if; end if; end for; return AS; end function; AllSemigroupsWithGenusUptoAndSubstractionDegree:= func; PatternSemigroupClassification:=function(Semigups,Patterns) //t:=Cputime(); l:=#Semigrups; lp:=#Patterns; ss:=[]; pp:=[]; lockdeg:=[]; c:=0; for p in Patterns do //tint:=Cputime(); c:=c+1; ld,rld:=LockDegree(p); semisp:=[i: i in [1..l]| admits(Semigrups[i],p)]; pos:=Position(ss,semisp); if pos eq 0 then Append(~ss,semisp); Append(~pp,[p]); Append(~lockdeg,[]); else Append(~pp[pos],p); Append(~lockdeg[pos],); end if; print "---------------------------------------------------------------"; print " ",c,"/",lp," n=",#p," ---> ",p; print "---------------------------------------------------------------"; [#s: s in ss]; pp; lockdeg; //print "TEMPS= ... + ",Cputime(tint)," = ",Cputime(t); end for; //print "TEMPS TOTAL=",Cputime(t); return ss, pp, lockdeg; end function; FixedLockDegreePatternSemigroupCassification:= func; MAXGENUS:=10; MAXLENGTHPATTERNS:=20; //Semigrups:=AllSemigroupsWithGenusUpto(MAXGENUS); //Semigrups:=[HermitianSemigroup(q): q in [1..7]]; /* s:=semigrup([0,5,6,10,11,12,13,15]); p1:=[1,1,1,-1]; p2:=[1,1,1,1,-1,-1]; LockDegree(p1); LockDegree(p2); admits(s,p1); admits(s,p2); */ Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed. ************** MAGMA ***************** Host nat1.na.baesystems.com. (208.19.133.131) Time: Tue Mar 2 13:42:30 2004 Input: 2+2= Output: Magma V2.10-6 Tue Mar 2 2004 13:42:27 on modular [Seed = 1802501796] ------------------------------------- >> 2+2=; ^ User error: bad syntax Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nat1.na.baesystems.com. (208.19.133.131) Time: Tue Mar 2 13:42:53 2004 Input: 2+2 Output: Magma V2.10-6 Tue Mar 2 2004 13:42:50 on modular [Seed = 471370218] ------------------------------------- 4 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nat1.na.baesystems.com. (208.19.133.131) Time: Tue Mar 2 13:43:34 2004 Input: (2+2/e3)-2 Output: Magma V2.10-6 Tue Mar 2 2004 13:43:31 on modular [Seed = 235576193] ------------------------------------- >> (2+2/e3)-2; ^ User error: Identifier 'e3' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nat1.na.baesystems.com. (208.19.133.131) Time: Tue Mar 2 13:43:52 2004 Input: (2+2/3)-2 Output: Magma V2.10-6 Tue Mar 2 2004 13:43:49 on modular [Seed = 17142968] ------------------------------------- 2/3 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nat1.na.baesystems.com. (208.19.133.131) Time: Tue Mar 2 13:44:28 2004 Input: (2+77788887777788888887788/3)-2 Output: Magma V2.10-6 Tue Mar 2 2004 13:44:25 on modular [Seed = 539276917] ------------------------------------- 25929629259262962962596 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Tue Mar 2 15:00:39 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Tue Mar 2 2004 15:00:36 on modular [Seed = 370323884] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.309 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Tue Mar 2 15:00:41 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Tue Mar 2 2004 15:00:38 on modular [Seed = 353481389] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.219 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Tue Mar 2 15:01:26 2004 Input: [-11..11 by 2]; Output: Magma V2.10-6 Tue Mar 2 2004 15:01:23 on modular [Seed = 842439295] ------------------------------------- [ -11 .. 11 by 2 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Tue Mar 2 15:01:34 2004 Input: [-11..11 by 2]; Output: Magma V2.10-6 Tue Mar 2 2004 15:01:31 on modular [Seed = 724534126] ------------------------------------- [ -11 .. 11 by 2 ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Tue Mar 2 15:01:46 2004 Input: r:=[-11..11 by 2]; Output: Magma V2.10-6 Tue Mar 2 2004 15:01:43 on modular [Seed = 539265113] ------------------------------------- Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Tue Mar 2 15:01:57 2004 Input: r:=[-11..11 by 2]; r; Output: Magma V2.10-6 Tue Mar 2 2004 15:01:54 on modular [Seed = 3655168436] ------------------------------------- [ -11 .. 11 by 2 ] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Tue Mar 2 15:02:13 2004 Input: r:=[-11..11 by 2]; r; 3+2; Output: Magma V2.10-6 Tue Mar 2 2004 15:02:10 on modular [Seed = 3469371090] ------------------------------------- [ -11 .. 11 by 2 ] 5 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Tue Mar 2 15:19:58 2004 Input: r:=[-11..11 by 2]; r; 3+2; t := {n^2 : n in [-11..11 by 2] | IsPrime(n)}; Output: Magma V2.10-6 Tue Mar 2 2004 15:19:55 on modular [Seed = 2594059951] ------------------------------------- [ -11 .. 11 by 2 ] 5 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Tue Mar 2 15:20:10 2004 Input: t := {n^2 : n in [-11..11 by 2] | IsPrime(n)}; Output: Magma V2.10-6 Tue Mar 2 2004 15:20:07 on modular [Seed = 2324571811] ------------------------------------- Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Tue Mar 2 15:20:19 2004 Input: t := {n^2 : n in [-11..11 by 2] | IsPrime(n)}; t; Output: Magma V2.10-6 Tue Mar 2 2004 15:20:16 on modular [Seed = 2206674781] ------------------------------------- { 9, 25, 49, 121 } Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Tue Mar 2 15:21:12 2004 Input: t := {n^2 : n in [-11..11 by 2] | IsPrime(n)}; t; Factorial(3); Output: Magma V2.10-6 Tue Mar 2 2004 15:21:09 on modular [Seed = 3099333715] ------------------------------------- { 9, 25, 49, 121 } 6 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Tue Mar 2 15:21:54 2004 Input: t := {n^2 : n in [-11..11 by 2] | IsPrime(n)}; t; Factorial(3); &+ [1,2,3]; Output: Magma V2.10-6 Tue Mar 2 2004 15:21:51 on modular [Seed = 2981436720] ------------------------------------- { 9, 25, 49, 121 } 6 6 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Tue Mar 2 15:23:42 2004 Input: t := {n^2 : n in [-11..11 by 2] | IsPrime(n)}; t; Factorial(3); &+ [1,2,3,20]; Output: Magma V2.10-6 Tue Mar 2 2004 15:23:39 on modular [Seed = 2812480178] ------------------------------------- { 9, 25, 49, 121 } 6 26 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Tue Mar 2 15:23:45 2004 Input: t := {n^2 : n in [-11..11 by 2] | IsPrime(n)}; t; Factorial(3); &+ [1,2,3,20]; Output: Magma V2.10-6 Tue Mar 2 2004 15:23:42 on modular [Seed = 1583018831] ------------------------------------- { 9, 25, 49, 121 } 6 26 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Tue Mar 2 15:24:33 2004 Input: &* [2,2,3]; Output: Magma V2.10-6 Tue Mar 2 2004 15:24:30 on modular [Seed = 1414592885] ------------------------------------- 12 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Tue Mar 2 15:25:53 2004 Input: {<{a,b},c> : a,b,c in [1..10] | a^2 + b^2 eq c^2}; Output: Magma V2.10-6 Tue Mar 2 2004 15:25:50 on modular [Seed = 1178790871] ------------------------------------- { <{ 6, 8 }, 10>, <{ 3, 4 }, 5> } Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Tue Mar 2 15:27:45 2004 Input: {<{a,b},c> : a,b,c in [1..10] | a^2 + b^2 eq c^2}; x^2 + y^6 eq 89; Output: Magma V2.10-6 Tue Mar 2 2004 15:27:42 on modular [Seed = 2105135900] ------------------------------------- { <{ 6, 8 }, 10>, <{ 3, 4 }, 5> } >> x^2 + y^6 eq 89;; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Tue Mar 2 15:29:52 2004 Input: hola := [1,2,3,4,5,6]; #(hola); Output: Magma V2.10-6 Tue Mar 2 2004 15:29:49 on modular [Seed = 1903550355] ------------------------------------- 6 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Tue Mar 2 15:30:08 2004 Input: hola := [1,2,3,4,5,6]; #(hola); print"adios"; Output: Magma V2.10-6 Tue Mar 2 2004 15:30:05 on modular [Seed = 1634062323] ------------------------------------- 6 adios Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Tue Mar 2 15:30:19 2004 Input: hola := [1,2,3,4,5,6]; #(hola); print"adios"; /* jajaja*/ Output: Magma V2.10-6 Tue Mar 2 2004 15:30:16 on modular [Seed = 404534943] ------------------------------------- 6 adios Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Tue Mar 2 15:30:49 2004 Input: hola := [1,2,3,4,5,6]; #(hola); print"adios"; /* jajaja*/ 8 lt 5; Output: Magma V2.10-6 Tue Mar 2 2004 15:30:46 on modular [Seed = 252420518] ------------------------------------- 6 adios false Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Tue Mar 2 15:31:14 2004 Input: 8 in [1,2,8,5]; Output: Magma V2.10-6 Tue Mar 2 2004 15:31:11 on modular [Seed = 926128248] ------------------------------------- true Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Tue Mar 2 15:31:34 2004 Input: 8 in {1,2,8,5}; Output: Magma V2.10-6 Tue Mar 2 2004 15:31:31 on modular [Seed = 774537554] ------------------------------------- true Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 2 15:37:19 2004 Input: K:=GF(4); M:=MatrixRing(K,2); Mt := { x : x in M | Trace(x) eq 0 }; /*Mf := { y : y in M | y[1,1] eq y[2,1] and y[1,2] eq y[2,2]};*/ Mf := { y : y in M | Submatrix(y,1,1,1,2) eq Submatrix(y,2,1,1,2)}; print Mf; /*Mtf:=*/ Output: Magma V2.10-6 Tue Mar 2 2004 15:37:15 on modular [Seed = 3738857213] ------------------------------------- { [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ K.1 0] [ K.1 0], [ 0 K.1^2] [ 0 K.1^2], [ K.1 K.1^2] [ K.1 K.1^2], [ 0 K.1] [ 0 K.1], [ K.1 K.1] [ K.1 K.1], [ 0 1] [ 0 1], [ K.1 1] [ K.1 1], [K.1^2 0] [K.1^2 0], [ 1 0] [ 1 0], [K.1^2 K.1^2] [K.1^2 K.1^2], [ 1 K.1^2] [ 1 K.1^2], [K.1^2 K.1] [K.1^2 K.1], [ 1 K.1] [ 1 K.1], [K.1^2 1] [K.1^2 1] } Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 2 15:39:02 2004 Input: K:=GF(4); M:=MatrixRing(K,2); Mt := { x : x in M | Trace(x) eq 0 }; /*Mf := { y : y in M | y[1,1] eq y[2,1] and y[1,2] eq y[2,2]};*/ Mf := { y : y in M | Submatrix(y,1,1,1,2) eq Submatrix(y,2,1,1,2)}; Mtf := Mt meet Mf; print Mtf; Output: Magma V2.10-6 Tue Mar 2 2004 15:38:59 on modular [Seed = 3570426984] ------------------------------------- { [ 0 0] [ 0 0], [K.1^2 K.1^2] [K.1^2 K.1^2], [ K.1 K.1] [ K.1 K.1], [ 1 1] [ 1 1] } Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 2 15:42:13 2004 Input: K:=GF(4); M:=MatrixRing(K,2); Random(M); Output: Magma V2.10-6 Tue Mar 2 2004 15:42:10 on modular [Seed = 3267785535] ------------------------------------- [K.1^2 K.1] [K.1^2 K.1^2] Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 2 15:44:54 2004 Input: K:=GF(4); M:=MatrixRing(K,2); {Random(M):n in [1..10]} Output: Magma V2.10-6 Tue Mar 2 2004 15:44:51 on modular [Seed = 4159915499] ------------------------------------- { [ 0 1] [ K.1 K.1^2], [ K.1 K.1] [ 0 K.1], [ 0 K.1] [K.1^2 K.1], [ 1 K.1] [ 1 0], [ 1 K.1^2] [ K.1 0], [K.1^2 0] [ 0 0], [K.1^2 1] [ K.1 K.1^2], [ 1 K.1^2] [K.1^2 K.1^2], [ K.1 K.1^2] [K.1^2 1], [K.1^2 K.1^2] [ K.1 K.1^2] } Total time: 2.879 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 2 15:45:05 2004 Input: K:=GF(4); M:=MatrixRing(K,2); {Random(M):n in [1..10]}; Output: Magma V2.10-6 Tue Mar 2 2004 15:45:02 on modular [Seed = 3806744819] ------------------------------------- { [ K.1 1] [K.1^2 K.1], [ K.1 1] [ K.1 K.1], [K.1^2 0] [ K.1 K.1], [ K.1 K.1^2] [ 0 0], [ 1 1] [ 1 K.1], [ 1 K.1^2] [ K.1 K.1], [ 1 K.1] [K.1^2 1], [K.1^2 1] [ 1 0], [ K.1 1] [ 0 K.1] } Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 2 15:45:51 2004 Input: K:=GF(4); M:=MatrixRing(K,2); L:=[Random(M):n in [1..10]]; Output: Magma V2.10-6 Tue Mar 2 2004 15:45:48 on modular [Seed = 2577214394] ------------------------------------- Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 2 15:48:53 2004 Input: K:=GF(4); M:=MatrixRing(K,2); Mt := { x : x in M | Trace(x) eq 0 }; Mf := { y : y in M | Submatrix(y,1,1,1,2) eq Submatrix(y,2,1,1,2)}; Mtf := Mt meet Mf; L:=[Random(M):n in [1..10]]; #([z : z in L | z in Mt]); Output: Magma V2.10-6 Tue Mar 2 2004 15:48:50 on modular [Seed = 2391424483] ------------------------------------- 2 Total time: 3.049 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 2 15:49:48 2004 Input: K:=GF(4); M:=MatrixRing(K,2); Mt := { x : x in M | Trace(x) eq 0 }; Mf := { y : y in M | Submatrix(y,1,1,1,2) eq Submatrix(y,2,1,1,2)}; Mtf := Mt meet Mf; L:=[Random(M):n in [1..10]]; #([z : z in L | z in Mt]); #([z : z in L | z in Mf]); #([z : z in L | z in Mtf]); Output: Magma V2.10-6 Tue Mar 2 2004 15:49:45 on modular [Seed = 2222995378] ------------------------------------- 3 1 1 Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 2 15:50:18 2004 Input: K:=GF(4); M:=MatrixRing(K,2); Mt := { x : x in M | Trace(x) eq 0 }; Mf := { y : y in M | Submatrix(y,1,1,1,2) eq Submatrix(y,2,1,1,2)}; Mtf := Mt meet Mf; L:=[Random(M):n in [1..10]]; #([z : z in L | z in Mt]); #([z : z in L | z in Mf]); #([z : z in L | z in Mtf]); Output: Magma V2.10-6 Tue Mar 2 2004 15:50:15 on modular [Seed = 3031435116] ------------------------------------- 2 0 0 Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host DIFFUSE.TAMU.EDU. (128.194.105.7) Time: Tue Mar 2 16:05:00 2004 Input: k = (b*c^1/2)/a a+b+c = 1 q = (2*a + b + 2*c)/(a+b) Output: Magma V2.10-6 Tue Mar 2 2004 16:04:57 on modular [Seed = 2812481854] ------------------------------------- >> a+b+c = 1 ^ User error: bad syntax >> q = (2*a + b + 2*c)/(a+b); ^ User error: Identifier 'a' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Tue Mar 2 16:40:58 2004 Input: a:={1,2,8,5}; b:={1,3,7}; a join b; Output: Magma V2.10-6 Tue Mar 2 2004 16:40:55 on modular [Seed = 2105131643] ------------------------------------- { 1, 2, 3, 5, 7, 8 } Total time: 3.129 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Tue Mar 2 16:41:30 2004 Input: a:={1,2,8,5}; b:={1,3,7}; a join b; a meet b; Output: Magma V2.10-6 Tue Mar 2 2004 16:41:27 on modular [Seed = 1145109410] ------------------------------------- { 1, 2, 3, 5, 7, 8 } { 1 } Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host zeno.pims.ubc.ca. (137.82.175.1) Time: Tue Mar 2 16:41:53 2004 Input: > F := EllipticCurve([-1,1]); > F; Output: Magma V2.10-6 Tue Mar 2 2004 16:41:49 on modular [Seed = 1330376883] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - x + 1 over Rational Field Total time: 3.269 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Tue Mar 2 16:41:55 2004 Input: a:={1,2,8,5}; b:={1,3,7}; a join b; a meet b; a diff b; Output: Magma V2.10-6 Tue Mar 2 2004 16:41:52 on modular [Seed = 1347743633] ------------------------------------- { 1, 2, 3, 5, 7, 8 } { 1 } { 2, 5, 8 } Total time: 3.179 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host zeno.pims.ubc.ca. (137.82.175.1) Time: Tue Mar 2 16:42:37 2004 Input: > F := EllipticCurve([-1,1]); > F; > MW, f := MordellWeilGroup(F); > MW; Output: Magma V2.10-6 Tue Mar 2 2004 16:42:34 on modular [Seed = 556113546] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - x + 1 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) Total time: 3.149 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Tue Mar 2 16:42:52 2004 Input: a:=[l,r,m]; b:=[p,q]; a cat b; Output: Magma V2.10-6 Tue Mar 2 2004 16:42:49 on modular [Seed = 674011024] ------------------------------------- >> a:=[l,r,m]; ^ User error: Identifier 'l' has not been declared or assigned >> b:=[p,q]; ^ User error: Identifier 'p' has not been declared or assigned >> a cat b;; ^ User error: Identifier 'a' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Tue Mar 2 16:43:07 2004 Input: a:=[2,4,6]; b:=[1,3]; a cat b; Output: Magma V2.10-6 Tue Mar 2 2004 16:43:04 on modular [Seed = 842436027] ------------------------------------- [ 2, 4, 6, 1, 3 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Tue Mar 2 16:43:21 2004 Input: a:=[2,4,6]; b:=[1,3]; a cat b; b cat a; Output: Magma V2.10-6 Tue Mar 2 2004 16:43:18 on modular [Seed = 1027179178] ------------------------------------- [ 2, 4, 6, 1, 3 ] [ 1, 3, 2, 4, 6 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Tue Mar 2 16:43:40 2004 Input: a:=[2,4,6]; b:=[1,3]; a cat b; b cat a; Min(a); Output: Magma V2.10-6 Tue Mar 2 2004 16:43:37 on modular [Seed = 67191916] ------------------------------------- [ 2, 4, 6, 1, 3 ] [ 1, 3, 2, 4, 6 ] 2 1 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Tue Mar 2 16:44:06 2004 Input: a:=[2,4,6]; b:=[1,3]; a cat b; b cat a; Min(a); Include(a,99); Output: Magma V2.10-6 Tue Mar 2 2004 16:44:03 on modular [Seed = 235621964] ------------------------------------- [ 2, 4, 6, 1, 3 ] [ 1, 3, 2, 4, 6 ] 2 1 [ 2, 4, 6, 99 ] Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host zeno.pims.ubc.ca. (137.82.175.1) Time: Tue Mar 2 16:44:29 2004 Input: > F := EllipticCurve([-1,1]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; Output: Magma V2.10-6 Tue Mar 2 2004 16:44:26 on modular [Seed = 421288258] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - x + 1 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (1 : 1 : 1) Total time: 3.209 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Tue Mar 2 16:45:35 2004 Input: a:=[2,4,6]; b:=[1,3]; a cat b; b cat a; Min(a); Include(a,99); Position(4,a); Output: Magma V2.10-6 Tue Mar 2 2004 16:45:32 on modular [Seed = 3924601332] ------------------------------------- [ 2, 4, 6, 1, 3 ] [ 1, 3, 2, 4, 6 ] 2 1 [ 2, 4, 6, 99 ] >> Position(4,a);; ^ Runtime error in 'Position': Bad argument types Argument types given: RngIntElt, SeqEnum[RngIntElt] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Tue Mar 2 16:45:49 2004 Input: a:=[2,4,6]; b:=[1,3]; a cat b; b cat a; Min(a); Include(a,99); Position(a,4); Output: Magma V2.10-6 Tue Mar 2 2004 16:45:46 on modular [Seed = 4042633243] ------------------------------------- [ 2, 4, 6, 1, 3 ] [ 1, 3, 2, 4, 6 ] 2 1 [ 2, 4, 6, 99 ] 2 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Tue Mar 2 16:47:49 2004 Input: a:=[2,4,6]; b:=[1,3]; a cat b; b cat a; Min(a); Include(a,99); Position(a,4); Remove(a,6); Output: Magma V2.10-6 Tue Mar 2 2004 16:47:46 on modular [Seed = 4211063705] ------------------------------------- [ 2, 4, 6, 1, 3 ] [ 1, 3, 2, 4, 6 ] 2 1 [ 2, 4, 6, 99 ] 2 >> Remove(a,6);; ^ Runtime error in 'Remove': Illegal sequence position Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host zeno.pims.ubc.ca. (137.82.175.1) Time: Tue Mar 2 16:48:36 2004 Input: > F := EllipticCurve([-1,1]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i in [-4..4] | > IsIntegral(pt) where pt is i*a] ; > intpts; Output: Magma V2.10-6 Tue Mar 2 2004 16:48:32 on modular [Seed = 3317728404] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - x + 1 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (1 : 1 : 1) [ (3 : 5 : 1), (0 : 1 : 1), (-1 : -1 : 1), (1 : -1 : 1), (1 : 1 : 1), (-1 : 1 : 1), (0 : -1 : 1), (3 : -5 : 1) ] Total time: 3.179 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Tue Mar 2 16:49:11 2004 Input: a:=[2,4,6]; b:=[1,3]; a cat b; b cat a; Min(a); Include(a,99); Position(a,4); Remove(a,3); Output: Magma V2.10-6 Tue Mar 2 2004 16:49:08 on modular [Seed = 3469447163] ------------------------------------- [ 2, 4, 6, 1, 3 ] [ 1, 3, 2, 4, 6 ] 2 1 [ 2, 4, 6, 99 ] 2 [ 2, 4 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host zeno.pims.ubc.ca. (137.82.175.1) Time: Tue Mar 2 16:49:16 2004 Input: > F := EllipticCurve([-1,1]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i in [-4..60] | > IsIntegral(pt) where pt is i*a] ; > intpts; Output: Magma V2.10-6 Tue Mar 2 2004 16:49:13 on modular [Seed = 3655112929] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - x + 1 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (1 : 1 : 1) [ (3 : 5 : 1), (0 : 1 : 1), (-1 : -1 : 1), (1 : -1 : 1), (1 : 1 : 1), (-1 : 1 : 1), (0 : -1 : 1), (3 : -5 : 1), (5 : 11 : 1), (56 : -419 : 1) ] Total time: 3.239 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host zeno.pims.ubc.ca. (137.82.175.1) Time: Tue Mar 2 16:50:06 2004 Input: > F := EllipticCurve([-1,1]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i in [-60..60] | > IsIntegral(pt) where pt is i*a] ; > intpts; Output: Magma V2.10-6 Tue Mar 2 2004 16:50:02 on modular [Seed = 2846681154] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - x + 1 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (1 : 1 : 1) [ (56 : 419 : 1), (5 : -11 : 1), (3 : 5 : 1), (0 : 1 : 1), (-1 : -1 : 1), (1 : -1 : 1), (1 : 1 : 1), (-1 : 1 : 1), (0 : -1 : 1), (3 : -5 : 1), (5 : 11 : 1), (56 : -419 : 1) ] Total time: 3.259 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Tue Mar 2 16:50:29 2004 Input: a:=[2,4,6]; b:=[1,3]; a cat b; b cat a; Min(a); Include(a,99); Position(a,4); Remove(a,3); tuple:=<[1,2],36>; Prune(tuple); Output: Magma V2.10-6 Tue Mar 2 2004 16:50:26 on modular [Seed = 2964713843] ------------------------------------- [ 2, 4, 6, 1, 3 ] [ 1, 3, 2, 4, 6 ] 2 1 [ 2, 4, 6, 99 ] 2 [ 2, 4 ] <[ 1, 2 ]> Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Tue Mar 2 17:19:29 2004 Input: a:=[2,4,6]; b:=[1,3]; a cat b; b cat a; Min(a); Include(a,99); Position(a,4); Remove(a,3); tuple:=<[1,2],36>; Prune(tuple); Random(a); Output: Magma V2.10-6 Tue Mar 2 2004 17:19:26 on modular [Seed = 2038182261] ------------------------------------- [ 2, 4, 6, 1, 3 ] [ 1, 3, 2, 4, 6 ] 2 1 [ 2, 4, 6, 99 ] 2 [ 2, 4 ] <[ 1, 2 ]> 2 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.33.44.proxycache.rima-tde.net. (80.58.33.44) Time: Tue Mar 2 17:54:38 2004 Input: i=366; assigned i; Output: Magma V2.10-6 Tue Mar 2 2004 17:54:35 on modular [Seed = 471420117] ------------------------------------- >> i=366; ^ User error: Identifier 'i' has not been declared or assigned false Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.33.44.proxycache.rima-tde.net. (80.58.33.44) Time: Tue Mar 2 17:56:09 2004 Input: i:=366; assigned i; Output: Magma V2.10-6 Tue Mar 2 2004 17:56:06 on modular [Seed = 4076315542] ------------------------------------- true Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.33.44.proxycache.rima-tde.net. (80.58.33.44) Time: Tue Mar 2 17:59:55 2004 Input: vec:=[1..366 by 1]; Output: Magma V2.10-6 Tue Mar 2 2004 17:59:52 on modular [Seed = 4194084979] ------------------------------------- Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.33.44.proxycache.rima-tde.net. (80.58.33.44) Time: Tue Mar 2 18:00:35 2004 Input: vec:=[1..366 by 1]; print vec; Output: Magma V2.10-6 Tue Mar 2 2004 18:00:32 on modular [Seed = 3385629627] ------------------------------------- [ 1 .. 366 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.33.44.proxycache.rima-tde.net. (80.58.33.44) Time: Tue Mar 2 18:00:56 2004 Input: vec:=[1..366 by 1]; print vec[78]; Output: Magma V2.10-6 Tue Mar 2 2004 18:00:52 on modular [Seed = 3604186256] ------------------------------------- 78 Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.33.44.proxycache.rima-tde.net. (80.58.33.44) Time: Tue Mar 2 18:07:59 2004 Input: vec:=[1..366 by 1]; print vec[78]; resultat=[n+4 : n in vec | true]; Output: Magma V2.10-6 Tue Mar 2 2004 18:07:56 on modular [Seed = 1802385604] ------------------------------------- 78 >> resultat=[n+4 : n in vec | true]; ^ User error: Identifier 'resultat' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 2 18:08:19 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField((x^2_10)*(x^2-7)); K; Output: Magma V2.10-6 Tue Mar 2 2004 18:08:16 on modular [Seed = 1920410097] ------------------------------------- >> K:=NumberField((x^2_10)*(x^2-7)); ^ User error: bad syntax >> K;; ^ User error: Identifier 'K' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.33.44.proxycache.rima-tde.net. (80.58.33.44) Time: Tue Mar 2 18:08:30 2004 Input: vec:=[1..366 by 1]; print vec[78]; resultat:=[n+4 : n in vec | true]; Output: Magma V2.10-6 Tue Mar 2 2004 18:08:27 on modular [Seed = 2038180598] ------------------------------------- 78 Total time: 2.859 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 2 18:08:44 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-10); K; Output: Magma V2.10-6 Tue Mar 2 2004 18:08:41 on modular [Seed = 1078268890] ------------------------------------- Number Field with defining polynomial x^2 - 10 over the Rational Field Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 2 18:09:04 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField((x^2-10)*(x^2-7)); K; Output: Magma V2.10-6 Tue Mar 2 2004 18:09:01 on modular [Seed = 1313544736] ------------------------------------- >> K:=NumberField((x^2-10)*(x^2-7)); ^ Runtime error in 'NumberField': Argument 1 is not irreducible >> K;; ^ User error: Identifier 'K' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.33.44.proxycache.rima-tde.net. (80.58.33.44) Time: Tue Mar 2 18:09:20 2004 Input: vec:=[1..366 by 1]; print vec[78]; resultat:=[n+4 : n in vec | true]; print resultat; print resultat[1]; Output: Magma V2.10-6 Tue Mar 2 2004 18:09:17 on modular [Seed = 1431306539] ------------------------------------- 78 [ 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 370 ] 5 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 2 18:09:30 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-10); K; Output: Magma V2.10-6 Tue Mar 2 2004 18:09:27 on modular [Seed = 1549338648] ------------------------------------- Number Field with defining polynomial x^2 - 10 over the Rational Field Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.33.44.proxycache.rima-tde.net. (80.58.33.44) Time: Tue Mar 2 18:12:29 2004 Input: vec:=[1..366 by 1]; print vec[78]; resultat:=[n+4 : n in vec | n/4=0]; print resultat; print resultat[1]; Output: Magma V2.10-6 Tue Mar 2 2004 18:12:26 on modular [Seed = 842491531] ------------------------------------- 78 >> resultat:=[n+4 : n in vec | n/4=0]; ^ Runtime error in sequence construction: Logical expected >> print resultat; ^ User error: Identifier 'resultat' has not been declared or assigned >> print resultat[1]; ^ User error: Identifier 'resultat' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.33.44.proxycache.rima-tde.net. (80.58.33.44) Time: Tue Mar 2 18:12:46 2004 Input: vec:=[1..366 by 1]; print vec[78]; resultat:=[n : n in vec | n/4=0]; print resultat; print resultat[1]; Output: Magma V2.10-6 Tue Mar 2 2004 18:12:43 on modular [Seed = 960261553] ------------------------------------- 78 >> resultat:=[n : n in vec | n/4=0]; ^ Runtime error in sequence construction: Logical expected >> print resultat; ^ User error: Identifier 'resultat' has not been declared or assigned >> print resultat[1]; ^ User error: Identifier 'resultat' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.33.44.proxycache.rima-tde.net. (80.58.33.44) Time: Tue Mar 2 18:13:58 2004 Input: vec:=[1..366 by 1]; print vec[78]; /*resultat:=[n : n in vec | n/4=0]; print resultat; print resultat[1];*/ n:=8/4; print n; Output: Magma V2.10-6 Tue Mar 2 2004 18:13:55 on modular [Seed = 100881238] ------------------------------------- 78 2 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.33.44.proxycache.rima-tde.net. (80.58.33.44) Time: Tue Mar 2 18:14:37 2004 Input: vec:=[1..366 by 1]; print vec[78]; resultat:=[n : n in vec | n/4 eq 0]; print resultat; print resultat[1]; n:=8/4; print n; Output: Magma V2.10-6 Tue Mar 2 2004 18:14:34 on modular [Seed = 218650676] ------------------------------------- 78 [] >> print resultat[1]; ^ Runtime error in '[]': Sequence element 1 not defined 2 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 2 18:15:38 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-10); K; K:=NumberField(x^2-7); K; Output: Magma V2.10-6 Tue Mar 2 2004 18:15:35 on modular [Seed = 521816811] ------------------------------------- Number Field with defining polynomial x^2 - 10 over the Rational Field Number Field with defining polynomial x^2 - 7 over the Rational Field Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.33.44.proxycache.rima-tde.net. (80.58.33.44) Time: Tue Mar 2 18:18:24 2004 Input: vec:=[1..366 by 1]; /*resultat:=[n : n in vec | n/4 eq 0];*/ for i:=4 to 366 by 4 do resultat:=vec[i] endfor; print resultat; Output: Magma V2.10-6 Tue Mar 2 2004 18:18:21 on modular [Seed = 3924606903] ------------------------------------- >> for i:=4 to 366 by 4 do resultat:=vec[i] endfor; ^ User error: bad syntax >> print resultat; ^ User error: Identifier 'resultat' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.33.44.proxycache.rima-tde.net. (80.58.33.44) Time: Tue Mar 2 18:18:34 2004 Input: vec:=[1..366 by 1]; /*resultat:=[n : n in vec | n/4 eq 0];*/ for i:=4 to 366 by 4 do resultat:=vec[i] end for; print resultat; Output: Magma V2.10-6 Tue Mar 2 2004 18:18:31 on modular [Seed = 4042630868] ------------------------------------- >> for i:=4 to 366 by 4 do resultat:=vec[i] end for; ^ User error: bad syntax >> print resultat; ^ User error: Identifier 'resultat' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 2 18:18:44 2004 Input: R:=PolynomialRing(RationalField()); u:= Sqrt(7) +Sqrt(10); u; Output: Magma V2.10-6 Tue Mar 2 2004 18:18:41 on modular [Seed = 4294617549] ------------------------------------- 5.80802897123296992250050929795 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 2 18:19:01 2004 Input: R:=PolynomialRing(RationalField()); u:= Sqrt(7) +Sqrt(10); u; MinimalPolynomial(u); Output: Magma V2.10-6 Tue Mar 2 2004 18:18:58 on modular [Seed = 3317732292] ------------------------------------- 5.80802897123296992250050929795 >> MinimalPolynomial(u);; ^ Runtime error in 'MinimalPolynomial': Bad argument types Argument types given: FldPrElt Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.33.44.proxycache.rima-tde.net. (80.58.33.44) Time: Tue Mar 2 18:19:31 2004 Input: vec:=[1..366 by 1]; /*resultat:=[n : n in vec | n/4 eq 0];*/ for i:=4 to 366 by 4 do resultat:=vec[i]; end for; print resultat; Output: Magma V2.10-6 Tue Mar 2 2004 18:19:28 on modular [Seed = 3435764271] ------------------------------------- 364 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 2 18:19:50 2004 Input: R:=PolynomialRing(RationalField()); u:= Sqrt(7) +Sqrt(10); u; f:=MinimalPolynomial(u); Output: Magma V2.10-6 Tue Mar 2 2004 18:19:47 on modular [Seed = 3688795435] ------------------------------------- 5.80802897123296992250050929795 >> f:=MinimalPolynomial(u);; ^ Runtime error in 'MinimalPolynomial': Bad argument types Argument types given: FldPrElt Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 2 18:20:06 2004 Input: R:=PolynomialRing(RationalField()); u:= Sqrt(7) +Sqrt(10); u; MinimalPolynomial; Output: Magma V2.10-6 Tue Mar 2 2004 18:20:03 on modular [Seed = 2880372075] ------------------------------------- 5.80802897123296992250050929795 Intrinsic 'MinimalPolynomial' Signatures: ( X) -> RngUPolElt [ Proof: BoolElt ] ( X) -> RngUPolElt [ Proof: BoolElt ] ( X) -> RngUPolElt [ Proof: BoolElt ] The minimal polynomial of X; over Z and Q, proof of correctness can be suppressed for efficiency. ( x) -> RngUPolElt The minimal polynomial of x in F with respect to the ground field of F. ( x, E) -> RngUPolElt The minimal polynomial of x in F with respect to the subfield E of F. ( a) -> RngUPolElt ( a) -> RngUPolElt The minimal polynomial of the field element a over Q. ( a) -> RngUPolElt ( a, R) -> RngUPolElt The minimal polynomial of the field element a over R if given or CoefficientField(Parent(a)). ( a) -> RngUPolElt The minimal polynomial of the field element a over the coefficient field. ( a) -> RngUPolElt ( a, R) -> RngUPolElt ( a) -> RngUPolElt The minimal polynomial of the order element a over its coefficient ring or R if given. ( x) -> RngUPolElt ( x) -> RngUPolElt The minimal polynomial of x with respect to the base field. ( a) -> RngUPolElt The minimal polynomial of a over Z. ( x) -> RngUPolElt ( x) -> RngUPolElt ( x) -> RngUPolElt ( x) -> RngUPolElt ( x) -> RngUPolElt ( x) -> RngUPolElt The minimal polynomial of x. ( x, R) -> RngUPolElt ( x, R) -> RngUPolElt ( x, R) -> RngUPolElt ( x, R) -> RngUPolElt ( x, R) -> RngUPolElt The minimal polynomial of x over R. ( v) -> RngUPolElt Return the minimal polynomial of v. ( e, K) -> RngUPolElt Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.33.44.proxycache.rima-tde.net. (80.58.33.44) Time: Tue Mar 2 18:21:00 2004 Input: vec:=[1..366 by 1]; /*resultat:=[n : n in vec | n/4 eq 0];*/ cont:=1; for i:=4 to 366 by 4 do cont:=cont+1; resultat[cont]:=vec[i]; end for; print resultat; Output: Magma V2.10-6 Tue Mar 2 2004 18:20:57 on modular [Seed = 2998395912] ------------------------------------- >> resultat[cont]:=vec[i]; ^ User error: Identifier 'resultat' has not been declared or assigned >> print resultat; ^ User error: Identifier 'resultat' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 2 18:21:33 2004 Input: R:=PolynomialRing(RationalField()); u:= Sqrt(7); u; MinimalPolynomial(u); Output: Magma V2.10-6 Tue Mar 2 2004 18:21:30 on modular [Seed = 3116166944] ------------------------------------- 2.64575131106459059050161575359 >> MinimalPolynomial(u);; ^ Runtime error in 'MinimalPolynomial': Bad argument types Argument types given: FldPrElt Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 2 18:21:46 2004 Input: R:=PolynomialRing(RationalField()); u:= Sqrt(7); u; MinimalPolynomial; Output: Magma V2.10-6 Tue Mar 2 2004 18:21:43 on modular [Seed = 2156255204] ------------------------------------- 2.64575131106459059050161575359 Intrinsic 'MinimalPolynomial' Signatures: ( X) -> RngUPolElt [ Proof: BoolElt ] ( X) -> RngUPolElt [ Proof: BoolElt ] ( X) -> RngUPolElt [ Proof: BoolElt ] The minimal polynomial of X; over Z and Q, proof of correctness can be suppressed for efficiency. ( x) -> RngUPolElt The minimal polynomial of x in F with respect to the ground field of F. ( x, E) -> RngUPolElt The minimal polynomial of x in F with respect to the subfield E of F. ( a) -> RngUPolElt ( a) -> RngUPolElt The minimal polynomial of the field element a over Q. ( a) -> RngUPolElt ( a, R) -> RngUPolElt The minimal polynomial of the field element a over R if given or CoefficientField(Parent(a)). ( a) -> RngUPolElt The minimal polynomial of the field element a over the coefficient field. ( a) -> RngUPolElt ( a, R) -> RngUPolElt ( a) -> RngUPolElt The minimal polynomial of the order element a over its coefficient ring or R if given. ( x) -> RngUPolElt ( x) -> RngUPolElt The minimal polynomial of x with respect to the base field. ( a) -> RngUPolElt The minimal polynomial of a over Z. ( x) -> RngUPolElt ( x) -> RngUPolElt ( x) -> RngUPolElt ( x) -> RngUPolElt ( x) -> RngUPolElt ( x) -> RngUPolElt The minimal polynomial of x. ( x, R) -> RngUPolElt ( x, R) -> RngUPolElt ( x, R) -> RngUPolElt ( x, R) -> RngUPolElt ( x, R) -> RngUPolElt The minimal polynomial of x over R. ( v) -> RngUPolElt Return the minimal polynomial of v. ( e, K) -> RngUPolElt Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 2 18:22:58 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-7); L:=NumberField(x^2-10); u:= a+b; u; Output: Magma V2.10-6 Tue Mar 2 2004 18:22:55 on modular [Seed = 2408241315] ------------------------------------- >> u:= a+b; ^ Runtime error in '+': Arguments are not compatible Argument types given: FldNumElt, FldNumElt >> u;; ^ User error: Identifier 'u' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.33.44.proxycache.rima-tde.net. (80.58.33.44) Time: Tue Mar 2 18:25:41 2004 Input: vec:=[4..366 by 7]; print vec; Output: Magma V2.10-6 Tue Mar 2 2004 18:25:38 on modular [Seed = 1751990270] ------------------------------------- [ 4 .. 361 by 7 ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.33.44.proxycache.rima-tde.net. (80.58.33.44) Time: Tue Mar 2 18:27:38 2004 Input: vec:=[4..366 by 7]; for i:=4 to 361 by 1 do print[i]; end for; print vec; Output: Magma V2.10-6 Tue Mar 2 2004 18:27:35 on modular [Seed = 1903438194] ------------------------------------- [ 4 ] [ 5 ] [ 6 ] [ 7 ] [ 8 ] [ 9 ] [ 10 ] [ 11 ] [ 12 ] [ 13 ] [ 14 ] [ 15 ] [ 16 ] [ 17 ] [ 18 ] [ 19 ] [ 20 ] [ 21 ] [ 22 ] [ 23 ] [ 24 ] [ 25 ] [ 26 ] [ 27 ] [ 28 ] [ 29 ] [ 30 ] [ 31 ] [ 32 ] [ 33 ] [ 34 ] [ 35 ] [ 36 ] [ 37 ] [ 38 ] [ 39 ] [ 40 ] [ 41 ] [ 42 ] [ 43 ] [ 44 ] [ 45 ] [ 46 ] [ 47 ] [ 48 ] [ 49 ] [ 50 ] [ 51 ] [ 52 ] [ 53 ] [ 54 ] [ 55 ] [ 56 ] [ 57 ] [ 58 ] [ 59 ] [ 60 ] [ 61 ] [ 62 ] [ 63 ] [ 64 ] [ 65 ] [ 66 ] [ 67 ] [ 68 ] [ 69 ] [ 70 ] [ 71 ] [ 72 ] [ 73 ] [ 74 ] [ 75 ] [ 76 ] [ 77 ] [ 78 ] [ 79 ] [ 80 ] [ 81 ] [ 82 ] [ 83 ] [ 84 ] [ 85 ] [ 86 ] [ 87 ] [ 88 ] [ 89 ] [ 90 ] [ 91 ] [ 92 ] [ 93 ] [ 94 ] [ 95 ] [ 96 ] [ 97 ] [ 98 ] [ 99 ] [ 100 ] [ 101 ] [ 102 ] [ 103 ] [ 104 ] [ 105 ] [ 106 ] [ 107 ] [ 108 ] [ 109 ] [ 110 ] [ 111 ] [ 112 ] [ 113 ] [ 114 ] [ 115 ] [ 116 ] [ 117 ] [ 118 ] [ 119 ] [ 120 ] [ 121 ] [ 122 ] [ 123 ] [ 124 ] [ 125 ] [ 126 ] [ 127 ] [ 128 ] [ 129 ] [ 130 ] [ 131 ] [ 132 ] [ 133 ] [ 134 ] [ 135 ] [ 136 ] [ 137 ] [ 138 ] [ 139 ] [ 140 ] [ 141 ] [ 142 ] [ 143 ] [ 144 ] [ 145 ] [ 146 ] [ 147 ] [ 148 ] [ 149 ] [ 150 ] [ 151 ] [ 152 ] [ 153 ] [ 154 ] [ 155 ] [ 156 ] [ 157 ] [ 158 ] [ 159 ] [ 160 ] [ 161 ] [ 162 ] [ 163 ] [ 164 ] [ 165 ] [ 166 ] [ 167 ] [ 168 ] [ 169 ] [ 170 ] [ 171 ] [ 172 ] [ 173 ] [ 174 ] [ 175 ] [ 176 ] [ 177 ] [ 178 ] [ 179 ] [ 180 ] [ 181 ] [ 182 ] [ 183 ] [ 184 ] [ 185 ] [ 186 ] [ 187 ] [ 188 ] [ 189 ] [ 190 ] [ 191 ] [ 192 ] [ 193 ] [ 194 ] [ 195 ] [ 196 ] [ 197 ] [ 198 ] [ 199 ] [ 200 ] [ 201 ] [ 202 ] [ 203 ] [ 204 ] [ 205 ] [ 206 ] [ 207 ] [ 208 ] [ 209 ] [ 210 ] [ 211 ] [ 212 ] [ 213 ] [ 214 ] [ 215 ] [ 216 ] [ 217 ] [ 218 ] [ 219 ] [ 220 ] [ 221 ] [ 222 ] [ 223 ] [ 224 ] [ 225 ] [ 226 ] [ 227 ] [ 228 ] [ 229 ] [ 230 ] [ 231 ] [ 232 ] [ 233 ] [ 234 ] [ 235 ] [ 236 ] [ 237 ] [ 238 ] [ 239 ] [ 240 ] [ 241 ] [ 242 ] [ 243 ] [ 244 ] [ 245 ] [ 246 ] [ 247 ] [ 248 ] [ 249 ] [ 250 ] [ 251 ] [ 252 ] [ 253 ] [ 254 ] [ 255 ] [ 256 ] [ 257 ] [ 258 ] [ 259 ] [ 260 ] [ 261 ] [ 262 ] [ 263 ] [ 264 ] [ 265 ] [ 266 ] [ 267 ] [ 268 ] [ 269 ] [ 270 ] [ 271 ] [ 272 ] [ 273 ] [ 274 ] [ 275 ] [ 276 ] [ 277 ] [ 278 ] [ 279 ] [ 280 ] [ 281 ] [ 282 ] [ 283 ] [ 284 ] [ 285 ] [ 286 ] [ 287 ] [ 288 ] [ 289 ] [ 290 ] [ 291 ] [ 292 ] [ 293 ] [ 294 ] [ 295 ] [ 296 ] [ 297 ] [ 298 ] [ 299 ] [ 300 ] [ 301 ] [ 302 ] [ 303 ] [ 304 ] [ 305 ] [ 306 ] [ 307 ] [ 308 ] [ 309 ] [ 310 ] [ 311 ] [ 312 ] [ 313 ] [ 314 ] [ 315 ] [ 316 ] [ 317 ] [ 318 ] [ 319 ] [ 320 ] [ 321 ] [ 322 ] [ 323 ] [ 324 ] [ 325 ] [ 326 ] [ 327 ] [ 328 ] [ 329 ] [ 330 ] [ 331 ] [ 332 ] [ 333 ] [ 334 ] [ 335 ] [ 336 ] [ 337 ] [ 338 ] [ 339 ] [ 340 ] [ 341 ] [ 342 ] [ 343 ] [ 344 ] [ 345 ] [ 346 ] [ 347 ] [ 348 ] [ 349 ] [ 350 ] [ 351 ] [ 352 ] [ 353 ] [ 354 ] [ 355 ] [ 356 ] [ 357 ] [ 358 ] [ 359 ] [ 360 ] [ 361 ] [ 4 .. 361 by 7 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host babbage.bham.ac.uk. (147.188.56.114) Time: Tue Mar 2 18:27:57 2004 Input: G:=PermutationGroup<7|(1,2,3,4,5,6,7),(2,6)(4,5)>; print #G; su:=Subgroups(G); su:=[u`subgroup:u in su]; #su; [#u:u in su]; Output: Magma V2.10-6 Tue Mar 2 2004 18:27:53 on modular [Seed = 2055152231] ------------------------------------- 168 15 [ 1, 2, 3, 7, 4, 4, 4, 6, 21, 8, 12, 12, 24, 24, 168 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.33.44.proxycache.rima-tde.net. (80.58.33.44) Time: Tue Mar 2 18:28:14 2004 Input: vec:=[4..366 by 7]; for i:=4 to 361 by 1 do print vec[i]; end for; print vec; Output: Magma V2.10-6 Tue Mar 2 2004 18:28:11 on modular [Seed = 1279857827] ------------------------------------- 25 32 39 46 53 60 67 74 81 88 95 102 109 116 123 130 137 144 151 158 165 172 179 186 193 200 207 214 221 228 235 242 249 256 263 270 277 284 291 298 305 312 319 326 333 340 347 354 361 >> for i:=4 to 361 by 1 do print vec[i]; end for; ^ Runtime error in '[]': Sequence element 53 not defined [ 4 .. 361 by 7 ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.33.44.proxycache.rima-tde.net. (80.58.33.44) Time: Tue Mar 2 18:28:29 2004 Input: vec:=[4..366 by 7]; for i:=1 to 361 by 1 do print vec[i]; end for; print vec; Output: Magma V2.10-6 Tue Mar 2 2004 18:28:25 on modular [Seed = 1431309739] ------------------------------------- 4 11 18 25 32 39 46 53 60 67 74 81 88 95 102 109 116 123 130 137 144 151 158 165 172 179 186 193 200 207 214 221 228 235 242 249 256 263 270 277 284 291 298 305 312 319 326 333 340 347 354 361 >> for i:=1 to 361 by 1 do print vec[i]; end for; ^ Runtime error in '[]': Sequence element 53 not defined [ 4 .. 361 by 7 ] Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.33.44.proxycache.rima-tde.net. (80.58.33.44) Time: Tue Mar 2 18:29:34 2004 Input: vec:=[4..366 by 7]; for i:=1 to 366 by 1 do print vec[i]; end for; print vec; Output: Magma V2.10-6 Tue Mar 2 2004 18:29:31 on modular [Seed = 1599735776] ------------------------------------- 4 11 18 25 32 39 46 53 60 67 74 81 88 95 102 109 116 123 130 137 144 151 158 165 172 179 186 193 200 207 214 221 228 235 242 249 256 263 270 277 284 291 298 305 312 319 326 333 340 347 354 361 >> for i:=1 to 366 by 1 do print vec[i]; end for; ^ Runtime error in '[]': Sequence element 53 not defined [ 4 .. 361 by 7 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host babbage.bham.ac.uk. (147.188.56.114) Time: Tue Mar 2 18:30:00 2004 Input: G:=PermutationGroup<7|(1,2,3,4,5,6,7),(2,6)(4,5)>; print #G; su:=Subgroups(G); su:=[u`subgroup:u in su]; #su; [#u:u in su]; Output: Magma V2.10-6 Tue Mar 2 2004 18:29:57 on modular [Seed = 539326641] ------------------------------------- 168 15 [ 1, 2, 3, 7, 4, 4, 4, 6, 21, 8, 12, 12, 24, 24, 168 ] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.33.44.proxycache.rima-tde.net. (80.58.33.44) Time: Tue Mar 2 18:31:29 2004 Input: vec:=[4..366 by 7]; for i:=1 to 52 by 1 do print vec[i]; end for; print vec; Output: Magma V2.10-6 Tue Mar 2 2004 18:31:26 on modular [Seed = 808806682] ------------------------------------- 4 11 18 25 32 39 46 53 60 67 74 81 88 95 102 109 116 123 130 137 144 151 158 165 172 179 186 193 200 207 214 221 228 235 242 249 256 263 270 277 284 291 298 305 312 319 326 333 340 347 354 361 [ 4 .. 361 by 7 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 2 19:09:34 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^4 + x^3 + x^2 + 2x + 1); O := MaximalOrder(N); I := 2 * O; Factorization(I); I := 3 * O; Factorization(I); Output: Magma V2.10-6 Tue Mar 2 2004 19:09:31 on modular [Seed = 3385633686] ------------------------------------- >> N := NumberField(x^4 + x^3 + x^2 + 2x + 1); ^ User error: bad syntax >> O := MaximalOrder(N); ^ User error: Identifier 'N' has not been declared or assigned >> I := 2 * O; ^ Runtime error in '*': Bad argument types Argument types given: RngIntElt, Intrinsic >> Factorization(I); ^ User error: Identifier 'I' has not been declared or assigned >> I := 3 * O; ^ Runtime error in '*': Bad argument types Argument types given: RngIntElt, Intrinsic >> Factorization(I);; ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 2 19:09:58 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^4 + x^3 + x^2 + 2*x + 1); O := MaximalOrder(N); I := 2 * O; Factorization(I); I := 3 * O; Factorization(I); Output: Magma V2.10-6 Tue Mar 2 2004 19:09:55 on modular [Seed = 3537350885] ------------------------------------- >> N := NumberField(x^4 + x^3 + x^2 + 2*x + 1); ^ Runtime error in 'NumberField': Argument 1 is not irreducible >> O := MaximalOrder(N); ^ User error: Identifier 'N' has not been declared or assigned >> I := 2 * O; ^ Runtime error in '*': Bad argument types Argument types given: RngIntElt, Intrinsic >> Factorization(I); ^ User error: Identifier 'I' has not been declared or assigned >> I := 3 * O; ^ Runtime error in '*': Bad argument types Argument types given: RngIntElt, Intrinsic >> Factorization(I);; ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 2 19:10:17 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^4 + 4*x^3 + x^2 + 2*x + 1); O := MaximalOrder(N); I := 2 * O; Factorization(I); I := 3 * O; Factorization(I); Output: Magma V2.10-6 Tue Mar 2 2004 19:10:14 on modular [Seed = 2728902816] ------------------------------------- [ ] [ , , ] Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 2 19:11:30 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^4 + 5*x^3 + x^2 + 2*x + 1); O := MaximalOrder(N); I := 2 * O; Factorization(I); I := 3 * O; Factorization(I); Output: Magma V2.10-6 Tue Mar 2 2004 19:11:27 on modular [Seed = 2880358752] ------------------------------------- [ , ] [ ] Total time: 2.989 seconds, Total memory usage: 2.10MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 2 19:11:45 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^4 + 7*x^3 + x^2 + 2*x + 1); O := MaximalOrder(N); I := 2 * O; Factorization(I); I := 3 * O; Factorization(I); Output: Magma V2.10-6 Tue Mar 2 2004 19:11:42 on modular [Seed = 2239817567] ------------------------------------- [ , ] [ , , ] Total time: 2.949 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 2 19:12:07 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^4 + 8*x^3 + x^2 + 2*x + 1); O := MaximalOrder(N); I := 2 * O; Factorization(I); I := 3 * O; Factorization(I); Output: Magma V2.10-6 Tue Mar 2 2004 19:12:04 on modular [Seed = 2391534654] ------------------------------------- [ ] [ ] Total time: 2.909 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 2 19:12:28 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^4 + 9*x^3 + x^2 + 2*x + 1); O := MaximalOrder(N); I := 2 * O; Factorization(I); I := 3 * O; Factorization(I); Output: Magma V2.10-6 Tue Mar 2 2004 19:12:25 on modular [Seed = 2542990618] ------------------------------------- [ , ] [ ] Total time: 2.939 seconds, Total memory usage: 2.10MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 2 19:12:52 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^4 + 5*x^3 + x^2 + 5*x + 1); O := MaximalOrder(N); I := 2 * O; Factorization(I); I := 3 * O; Factorization(I); Output: Magma V2.10-6 Tue Mar 2 2004 19:12:49 on modular [Seed = 2560490493] ------------------------------------- [ ] [ ] Total time: 3.079 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 2 19:13:03 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^4 + 5*x^3 + 2x^2 + 5*x + 1); O := MaximalOrder(N); I := 2 * O; Factorization(I); I := 3 * O; Factorization(I); Output: Magma V2.10-6 Tue Mar 2 2004 19:13:00 on modular [Seed = 1617232649] ------------------------------------- >> N := NumberField(x^4 + 5*x^3 + 2x^2 + 5*x + 1); ^ User error: bad syntax >> O := MaximalOrder(N); ^ User error: Identifier 'N' has not been declared or assigned >> I := 2 * O; ^ Runtime error in '*': Bad argument types Argument types given: RngIntElt, Intrinsic >> Factorization(I); ^ User error: Identifier 'I' has not been declared or assigned >> I := 3 * O; ^ Runtime error in '*': Bad argument types Argument types given: RngIntElt, Intrinsic >> Factorization(I);; ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 2 19:13:11 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^4 + 5*x^3 + 2*x^2 + 5*x + 1); O := MaximalOrder(N); I := 2 * O; Factorization(I); I := 3 * O; Factorization(I); Output: Magma V2.10-6 Tue Mar 2 2004 19:13:08 on modular [Seed = 1802373146] ------------------------------------- >> N := NumberField(x^4 + 5*x^3 + 2*x^2 + 5*x + 1); ^ Runtime error in 'NumberField': Argument 1 is not irreducible >> O := MaximalOrder(N); ^ User error: Identifier 'N' has not been declared or assigned >> I := 2 * O; ^ Runtime error in '*': Bad argument types Argument types given: RngIntElt, Intrinsic >> Factorization(I); ^ User error: Identifier 'I' has not been declared or assigned >> I := 3 * O; ^ Runtime error in '*': Bad argument types Argument types given: RngIntElt, Intrinsic >> Factorization(I);; ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 2 19:13:26 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^4 + 5*x^3 + 2*x^2 + 5*x + 7); O := MaximalOrder(N); I := 2 * O; Factorization(I); I := 3 * O; Factorization(I); Output: Magma V2.10-6 Tue Mar 2 2004 19:13:23 on modular [Seed = 1920405812] ------------------------------------- >> N := NumberField(x^4 + 5*x^3 + 2*x^2 + 5*x + 7); ^ Runtime error in 'NumberField': Argument 1 is not irreducible >> O := MaximalOrder(N); ^ User error: Identifier 'N' has not been declared or assigned >> I := 2 * O; ^ Runtime error in '*': Bad argument types Argument types given: RngIntElt, Intrinsic >> Factorization(I); ^ User error: Identifier 'I' has not been declared or assigned >> I := 3 * O; ^ Runtime error in '*': Bad argument types Argument types given: RngIntElt, Intrinsic >> Factorization(I);; ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 2 19:18:02 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^2 - 2); K := RadicalExtention(N, 2, 3); O1 := MaximalOrder(N); O2 := MaximalOrder(K); I := 2 * O2; Factorization(I); I := 3 * O2; Factorization(I); Output: Magma V2.10-6 Tue Mar 2 2004 19:17:59 on modular [Seed = 1111959056] ------------------------------------- >> K := RadicalExtention(N, 2, 3); ^ User error: Identifier 'RadicalExtention' has not been declared or assigned >> O2 := MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> I := 2 * O2; ^ User error: Identifier 'O2' has not been declared or assigned >> Factorization(I); ^ User error: Identifier 'I' has not been declared or assigned >> I := 3 * O2; ^ User error: Identifier 'O2' has not been declared or assigned >> Factorization(I);; ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 2 19:18:19 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^2 - 2); K := RadicalExtension(N, 2, 3); O1 := MaximalOrder(N); O2 := MaximalOrder(K); I := 2 * O2; Factorization(I); I := 3 * O2; Factorization(I); Output: Magma V2.10-6 Tue Mar 2 2004 19:18:15 on modular [Seed = 1431318903] ------------------------------------- [ ] [ ] Total time: 3.889 seconds, Total memory usage: 2.07MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 2 19:18:40 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^2 - 5); K := RadicalExtension(N, 2, 7); O1 := MaximalOrder(N); O2 := MaximalOrder(K); I := 2 * O2; Factorization(I); I := 3 * O2; Factorization(I); Output: Magma V2.10-6 Tue Mar 2 2004 19:18:37 on modular [Seed = 1549351012] ------------------------------------- [ ] [ , ] Total time: 3.049 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 2 19:27:33 2004 Input: F := PolynomialRing(RationalField()); For x in [[1...100] do a := random(1000); b := random(1000); c := random(1000); d := random(1000); N := NumberField(x^4 + a*x^3 + b*x^2 + c^x + d); O2 := MaximalOrder(N); I := 2 * O2; Factorization(I); I := 3 * O2; Factorization(I); end for; Output: Magma V2.10-6 Tue Mar 2 2004 19:27:30 on modular [Seed = 707742781] ------------------------------------- >> For x in [[1...100] do ^ User error: bad syntax >> a := random(1000); ^ User error: bad syntax >> b := random(1000); ^ User error: bad syntax >> c := random(1000); ^ User error: bad syntax >> d := random(1000); ^ User error: bad syntax >> N := NumberField(x^4 + a*x^3 + b*x^2 + c^x + d); ^ User error: Identifier 'a' has not been declared or assigned >> O2 := MaximalOrder(N); ^ User error: Identifier 'N' has not been declared or assigned >> I := 2 * O2; ^ User error: Identifier 'O2' has not been declared or assigned >> Factorization(I); ^ User error: Identifier 'I' has not been declared or assigned >> I := 3 * O2; ^ User error: Identifier 'O2' has not been declared or assigned >> Factorization(I); ^ User error: Identifier 'I' has not been declared or assigned >> end for;; ^ User error: bad syntax Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 2 19:27:54 2004 Input: F := PolynomialRing(RationalField()); For l in [[1...100] do a := random(1000); b := random(1000); c := random(1000); d := random(1000); N := NumberField(x^4 + a*x^3 + b*x^2 + c^x + d); O2 := MaximalOrder(N); I := 2 * O2; Factorization(I); I := 3 * O2; Factorization(I); end for; Output: Magma V2.10-6 Tue Mar 2 2004 19:27:51 on modular [Seed = 1027103711] ------------------------------------- >> For l in [[1...100] do ^ User error: bad syntax >> a := random(1000); ^ User error: bad syntax >> b := random(1000); ^ User error: bad syntax >> c := random(1000); ^ User error: bad syntax >> d := random(1000); ^ User error: bad syntax >> N := NumberField(x^4 + a*x^3 + b*x^2 + c^x + d); ^ User error: Identifier 'a' has not been declared or assigned >> O2 := MaximalOrder(N); ^ User error: Identifier 'N' has not been declared or assigned >> I := 2 * O2; ^ User error: Identifier 'O2' has not been declared or assigned >> Factorization(I); ^ User error: Identifier 'I' has not been declared or assigned >> I := 3 * O2; ^ User error: Identifier 'O2' has not been declared or assigned >> Factorization(I); ^ User error: Identifier 'I' has not been declared or assigned >> end for;; ^ User error: bad syntax Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 2 19:28:33 2004 Input: F := PolynomialRing(RationalField()); For mom in [1...100] do a := random(1000); b := random(1000); c := random(1000); d := random(1000); N := NumberField(x^4 + a*x^3 + b*x^2 + c^x + d); O2 := MaximalOrder(N); I := 2 * O2; Factorization(I); I := 3 * O2; Factorization(I); end for; Output: Magma V2.10-6 Tue Mar 2 2004 19:28:30 on modular [Seed = 67199695] ------------------------------------- >> For mom in [1...100] do ^ User error: bad syntax >> a := random(1000); ^ User error: bad syntax >> b := random(1000); ^ User error: bad syntax >> c := random(1000); ^ User error: bad syntax >> d := random(1000); ^ User error: bad syntax >> N := NumberField(x^4 + a*x^3 + b*x^2 + c^x + d); ^ User error: Identifier 'a' has not been declared or assigned >> O2 := MaximalOrder(N); ^ User error: Identifier 'N' has not been declared or assigned >> I := 2 * O2; ^ User error: Identifier 'O2' has not been declared or assigned >> Factorization(I); ^ User error: Identifier 'I' has not been declared or assigned >> I := 3 * O2; ^ User error: Identifier 'O2' has not been declared or assigned >> Factorization(I); ^ User error: Identifier 'I' has not been declared or assigned >> end for;; ^ User error: bad syntax Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 2 19:29:30 2004 Input: F := PolynomialRing(RationalField()); For mom in [1...100] do a := Random(1000); b := Random(1000); c := Random(1000); d := Random(1000); N := NumberField(x^4 + a*x^3 + b*x^2 + c^x + d); O2 := MaximalOrder(N); I := 2 * O2; Factorization(I); I := 3 * O2; Factorization(I); end for; Output: Magma V2.10-6 Tue Mar 2 2004 19:29:27 on modular [Seed = 235628684] ------------------------------------- >> For mom in [1...100] do ^ User error: bad syntax >> N := NumberField(x^4 + a*x^3 + b*x^2 + c^x + d); ^ Runtime error in '^': Bad argument types Argument types given: RngUPolElt, RngUPolElt >> O2 := MaximalOrder(N); ^ User error: Identifier 'N' has not been declared or assigned >> I := 2 * O2; ^ User error: Identifier 'O2' has not been declared or assigned >> Factorization(I); ^ User error: Identifier 'I' has not been declared or assigned >> I := 3 * O2; ^ User error: Identifier 'O2' has not been declared or assigned >> Factorization(I); ^ User error: Identifier 'I' has not been declared or assigned >> end for;; ^ User error: bad syntax Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 2 19:29:58 2004 Input: F := PolynomialRing(RationalField()); for mom in [1...100] do a := Random(1000); b := Random(1000); c := Random(1000); d := Random(1000); N := NumberField(x^4 + a*x^3 + b*x^2 + c^x + d); O2 := MaximalOrder(N); I := 2 * O2; Factorization(I); I := 3 * O2; Factorization(I); end for; Output: Magma V2.10-6 Tue Mar 2 2004 19:29:55 on modular [Seed = 286553719] ------------------------------------- >> for mom in [1...100] do ^ User error: bad syntax >> N := NumberField(x^4 + a*x^3 + b*x^2 + c^x + d); ^ Runtime error in '^': Bad argument types Argument types given: RngUPolElt, RngUPolElt >> O2 := MaximalOrder(N); ^ User error: Identifier 'N' has not been declared or assigned >> I := 2 * O2; ^ User error: Identifier 'O2' has not been declared or assigned >> Factorization(I); ^ User error: Identifier 'I' has not been declared or assigned >> I := 3 * O2; ^ User error: Identifier 'O2' has not been declared or assigned >> Factorization(I); ^ User error: Identifier 'I' has not been declared or assigned >> end for;; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 2 19:30:07 2004 Input: F := PolynomialRing(RationalField()); for mom in [1..100] do a := Random(1000); b := Random(1000); c := Random(1000); d := Random(1000); N := NumberField(x^4 + a*x^3 + b*x^2 + c^x + d); O2 := MaximalOrder(N); I := 2 * O2; Factorization(I); I := 3 * O2; Factorization(I); end for; Output: Magma V2.10-6 Tue Mar 2 2004 19:30:04 on modular [Seed = 3789850248] ------------------------------------- >> N := NumberField(x^4 + a*x^3 + b*x^2 + c^x + d); ^ Runtime error in '^': Bad argument types Argument types given: RngUPolElt, RngUPolElt Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 2 19:30:30 2004 Input: F := PolynomialRing(RationalField()); for mom in [1..100] do a := Random(1000); b := Random(1000); c := Random(1000); d := Random(1000); N := NumberField(x^4 + a*x^3 + b*x^2 + c*x + d); O2 := MaximalOrder(N); I := 2 * O2; Factorization(I); I := 3 * O2; Factorization(I); end for; Output: Magma V2.10-6 Tue Mar 2 2004 19:30:20 on modular [Seed = 3907882897] ------------------------------------- [ ] [ , , ] [ , ] [ , ] [ , ] [ , , ] [ , ] [ , , ] [ , ] [ , ] [ , ] [ ] [ , ] [ , , ] [ ] [ , ] [ , , , ] [ , ] [ , ] [ , ] [ ] [ , , ] [ , ] [ , ] [ ] [ , ] [ ] [ ] [ , ] [ , ] [ , ] [ ] [ ] [ ] [ ] [ ] [ , , ] [ , , ] [ , ] [ , ] [ ] [ , ] [ , ] [ ] [ ] [ ] [ , , ] [ ] [ ] [ , ] [ , ] [ , , ] [ , , ] [ , ] [ := PolynomialRing(RationalField()); for mom in [1..100] do a := Random(1000); b := Random(1000); c := Random(1000); d := Random(1000); N := NumberField(x^4 + a*x^3 + b*x^2 + c*x + d); x^4 + a*x^3 + b*x^2 + c*x + d; O2 := MaximalOrder(N); I := 2 * O2; print("I = 2"); Factorization(I); print("I = 3"); I := 3 * O2; Factorization(I); end for; Output: Magma V2.10-6 Tue Mar 2 2004 19:32:19 on modular [Seed = 4093023237] ------------------------------------- x^4 + 971*x^3 + 179*x^2 + 100*x + 904 I = 2 [ , ] I = 3 [ ] x^4 + 204*x^3 + 180*x^2 + 626*x + 662 I = 2 [ ] I = 3 [ ] x^4 + 117*x^3 + 49*x^2 + 996*x + 990 I = 2 [ , ] I = 3 [ , ] x^4 + 380*x^3 + 167*x^2 + 196*x + 480 I = 2 [ , , , ] I = 3 [ , , , ] x^4 + 342*x^3 + 731*x^2 + 549*x + 221 I = 2 [ , ] I = 3 [ ] x^4 + 508*x^3 + 640*x^2 + 835*x + 236 I = 2 [ , , ] I = 3 [ , ] x^4 + 156*x^3 + 475*x^2 + 481*x + 536 I = 2 [ , ] I = 3 [ , ] x^4 + 92*x^3 + 715*x^2 + 127*x + 252 I = 2 [ , ] I = 3 [ , ] x^4 + 490*x^3 + 898*x^2 + 78*x + 856 I = 2 [ , ] I = 3 [ ] x^4 + 594*x^3 + 979*x^2 + 527*x + 726 I = 2 [ , ] I = 3 [ , , ] x^4 + 730*x^3 + 525*x^2 + 301*x + 898 I = 2 [ , ] I = 3 [ ] x^4 + 439*x^3 + 24*x^2 + 204*x + 55 I = 2 [ ] I = 3 [ , ] x^4 + 76*x^3 + 140*x^2 + 297*x + 160 I = 2 [ , , ] I = 3 [ , ] x^4 + 59*x^3 + 283*x^2 + 458*x + 325 I = 2 [ , ] I = 3 [ ] x^4 + 638*x^3 + 943*x^2 + 116*x + 239 I = 2 [ ] I = 3 [ , ] x^4 + 40*x^3 + 930*x^2 + 396*x + 968 I = 2 [ , ] I = 3 [ ] x^4 + 1000*x^3 + 397*x^2 + 683*x + 969 I = 2 [ , ] I = 3 [ , ] x^4 + 152*x^3 + 70*x^2 + 450*x + 759 I = 2 [ , ] I = 3 [ , ] x^4 + 174*x^3 + 257*x^2 + 611*x + 219 I = 2 [ , ] I = 3 [ , ] x^4 + 898*x^3 + 858*x^2 + 140*x + 562 I = 2 [ ] I = 3 [ ] x^4 + 705*x^3 + 403*x^2 + 31*x + 288 I = 2 [ , ] I = 3 [ , , ] x^4 + 904*x^3 + 832*x^2 + 916*x + 699 I = 2 [ , ] I = 3 [ , , ] x^4 + 221*x^3 + 175*x^2 + 150*x + 186 I = 2 [ , ] I = 3 [ , , := PolynomialRing(RationalField()); N := NumberField(x^5 + 7*x^4 + 3*x^2 - x + 1); O2 := MaximalOrder(N); for mom in [1..100] do if IsPrime(mom) do mom; I := mom * O2; if IsRamified(I) do Factorization(I); end if; end if; end for; Output: Magma V2.10-6 Tue Mar 2 2004 19:40:14 on modular [Seed = 3385630914] ------------------------------------- >> if IsPrime(mom) do ^ User error: bad syntax >> mom; ^ User error: Identifier 'mom' has not been declared or assigned >> I := mom * O2; ^ User error: Identifier 'mom' has not been declared or assigned >> if IsRamified(I) do ^ User error: bad syntax >> Factorization(I); ^ User error: Identifier 'I' has not been declared or assigned >> end if; ^ User error: bad syntax >> end if; ^ User error: bad syntax >> end for;; ^ User error: bad syntax Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 2 19:40:57 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^5 + 7*x^4 + 3*x^2 - x + 1); O2 := MaximalOrder(N); for mom in [1..100] do if IsPrime(mom) then mom; I := mom * O2; if IsRamified(I) then Factorization(I); end if; end if; end for; Output: Magma V2.10-6 Tue Mar 2 2004 19:40:54 on modular [Seed = 3503667491] ------------------------------------- 2 3 5 >> if IsRamified(I) then ^ Runtime error in 'IsRamified': The ideal must be a prime ideal Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 2 19:41:42 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^5 + 7*x^4 + 3*x^2 - x + 1); O2 := MaximalOrder(N); for mom in [1..100] do if IsPrime(mom) then mom; I := mom * O2; Factorization(I); end if; end for; Output: Magma V2.10-6 Tue Mar 2 2004 19:41:38 on modular [Seed = 3688804988] ------------------------------------- 2 [ ] 3 [ ] 5 [ , , ] 7 [ , ] 11 [ , , , ] 13 [ , ] 17 [ , , ] 19 [ , , ] 23 [ , ] 29 [ , , ] 31 [ , , ] 37 [ ] 41 [ , ] 43 [ , , , ] 47 [ , ] 53 [ , ] 59 [ , ] 61 [ ] 67 [ , , , ] 71 [ , , , ] 73 [ ] 79 [ , ] 83 [ , , , ] 89 [ , ] 97 [ ] Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 2 19:50:23 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^2 -5); O := MaximalOrder(N); I := ideal(2, 2 + w); J := ideal(209, (389 + w)/2); b := ChineseRemainderTheorem(I, J, O!w, O!(1 - w)); b - w in I; b - (1 + w) in J; Norm(I); Norm(J); Output: Magma V2.10-6 Tue Mar 2 2004 19:50:20 on modular [Seed = 2981419544] ------------------------------------- >> I := ideal(2, 2 + w); ^ User error: Identifier 'ideal' has not been declared or assigned >> J := ideal(209, (389 + w)/2); ^ User error: Identifier 'ideal' has not been declared or assigned >> b := ChineseRemainderTheorem(I, J, O!w, O!(1 - w)); ^ User error: Identifier 'I' has not been declared or assigned >> b - w in I; ^ User error: Identifier 'b' has not been declared or assigned >> b - (1 + w) in J; ^ User error: Identifier 'b' has not been declared or assigned >> Norm(I); ^ User error: Identifier 'I' has not been declared or assigned >> Norm(J);; ^ User error: Identifier 'J' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 2 19:50:39 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^2 -5); O := MaximalOrder(N); I := Ideal(2, 2 + w); J := Ideal(209, (389 + w)/2); b := ChineseRemainderTheorem(I, J, O!w, O!(1 - w)); b - w in I; b - (1 + w) in J; Norm(I); Norm(J); Output: Magma V2.10-6 Tue Mar 2 2004 19:50:36 on modular [Seed = 3099448065] ------------------------------------- >> I := Ideal(2, 2 + w); ^ Runtime error in 'Ideal': Bad argument types Argument types given: RngIntElt, FldNumElt >> J := Ideal(209, (389 + w)/2); ^ Runtime error in 'Ideal': Bad argument types Argument types given: RngIntElt, FldNumElt >> b := ChineseRemainderTheorem(I, J, O!w, O!(1 - w)); ^ User error: Identifier 'I' has not been declared or assigned >> b - w in I; ^ User error: Identifier 'b' has not been declared or assigned >> b - (1 + w) in J; ^ User error: Identifier 'b' has not been declared or assigned >> Norm(I); ^ User error: Identifier 'I' has not been declared or assigned >> Norm(J);; ^ User error: Identifier 'J' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 2 19:51:40 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^2 -5); O := MaximalOrder(N); I := ideal; J := ideal; b := ChineseRemainderTheorem(I, J, O!w, O!(1 - w)); b - w in I; b - (1 + w) in J; Norm(I); Norm(J); Output: Magma V2.10-6 Tue Mar 2 2004 19:51:37 on modular [Seed = 2206658559] ------------------------------------- true false 1 209 Total time: 2.929 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 2 19:52:16 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^2 -5); O := MaximalOrder(N); I := ideal; J := ideal; b := ChineseRemainderTheorem(I, J, O!w, O!(1 - w)); b; b - w in I; b - (1 - w) in J; Norm(I); Norm(J); Output: Magma V2.10-6 Tue Mar 2 2004 19:52:13 on modular [Seed = 2324686546] ------------------------------------- [-28, 0] true true 1 209 Total time: 2.959 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 2 19:52:45 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^2 -5); O := MaximalOrder(N); I := ideal; J := ideal; b := ChineseRemainderTheorem(I, J, O!w, O!(1 - w)); b; b - w in I; b - (1 - w) in J; Norm(I); Norm(J); Output: Magma V2.10-6 Tue Mar 2 2004 19:52:42 on modular [Seed = 2644046242] ------------------------------------- [-28, 0] true true 1 209 Total time: 2.949 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 2 19:55:29 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^2 -5); O := MaximalOrder(N); I := ideal; J := ideal; b := ChineseRemainderTheorem(I, J, O!w, O!(1 - w)); b; b - w in I; b - (1 - w) in J; Index(O, I); Index(O, J); Output: Magma V2.10-6 Tue Mar 2 2004 19:55:26 on modular [Seed = 1617235192] ------------------------------------- [-28, 0] true true 1 209 Total time: 2.999 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 2 19:57:08 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^2 -5); O := MaximalOrder(N); I := ideal; Basis(I); J := ideal; b := ChineseRemainderTheorem(I, J, O!w, O!(1 - w)); b; b - w in I; b - (1 - w) in J; Index(O, I); Index(O, J); Output: Magma V2.10-6 Tue Mar 2 2004 19:57:05 on modular [Seed = 1768686702] ------------------------------------- [ [1, 0], [0, 1] ] [-28, 0] true true 1 209 Total time: 2.949 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 2 19:59:13 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^2 -5); O := MaximalOrder(N); Basis(O); I := ideal; Basis(I); J := ideal; b := ChineseRemainderTheorem(I, J, O!w, O!(1 - w)); b; b - w in I; b - (1 - w) in J; Index(O, I); Index(O, J); Output: Magma V2.10-6 Tue Mar 2 2004 19:59:10 on modular [Seed = 2138706631] ------------------------------------- [ O.1, O.2 ] [ [1, 0], [0, 1] ] [-28, 0] true true 1 209 Total time: 2.989 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 2 19:59:51 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^2 -5); O := MaximalOrder(N); Basis(O); I := ideal; Basis(I); J := ideal; Basis(J); b := ChineseRemainderTheorem(I, J, O!w, O!(1 - w)); b; b - w in I; b - (1 - w) in J; Index(O, I); Index(O, J); Output: Magma V2.10-6 Tue Mar 2 2004 19:59:48 on modular [Seed = 1145121318] ------------------------------------- [ O.1, O.2 ] [ [1, 0], [0, 1] ] [ [209, 0], [194, 1] ] [-28, 0] true true 1 209 Total time: 3.009 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host c-24-12-5-43.client.comcast.net. (24.12.5.43) Time: Tue Mar 2 20:45:02 2004 Input: ;lkjhoysfd sarA'KLGDF":l ?: '; ';F ;ALDF Output: Magma V2.10-6 Tue Mar 2 2004 20:44:59 on modular [Seed = 3301030969] ------------------------------------- >> ;lkjhoysfd sarA'KLGDF":l ?: ^ User error: bad syntax >> '; ^ User error: Unexpected newline in literal identifier >> ';F ^ User error: Unexpected newline in literal identifier >> ;ALDF; ^ User error: Identifier 'ALDF' has not been declared or assigned Total time: 3.119 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host babbage.bham.ac.uk. (147.188.56.114) Time: Tue Mar 2 21:04:26 2004 Input: 2^10; Output: Magma V2.10-6 Tue Mar 2 2004 21:04:23 on modular [Seed = 3216687870] ------------------------------------- 1024 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-67-65-250-154.dsl.okcyok.swbell.net. (67.65.250.154) Time: Tue Mar 2 22:00:07 2004 Input: Mod(448842263^1973583573927159327592375937593759173513759375397539573958739583958395839531753751973597356837583918738519357,77038717908638071813880096581303102604552018462668921038977313239022513085916778273471467501239472111546684987) Output: Magma V2.10-6 Tue Mar 2 2004 22:00:04 on modular [Seed = 4227789224] ------------------------------------- >> Mod(448842263^1973583573927159327592375937593759173513759375397539573958739 ^ Runtime error in '^': Argument 2 (197358357392715932759237593759375917351375937\ 5397539573958739583958395839531753751973597356837583918738519357) is too large Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 2 22:03:54 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^2 -5); O := MaximalOrder(N); Basis(O); I := ideal; Basis(I); J := ideal; Basis(J); b := ChineseRemainderTheorem(I, J, O!w, O!(1 - w)); b; b - w in I; b - (1 - w) in J; Index(O, I); Index(O, J); Output: Magma V2.10-6 Tue Mar 2 2004 22:03:51 on modular [Seed = 3738949038] ------------------------------------- [ O.1, O.2 ] [ [1, 0], [0, 1] ] [ [209, 0], [194, 1] ] [-28, 0] true true 1 209 Total time: 2.979 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Tue Mar 2 23:16:03 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^5+7*x^4+3*x^2-x+1); OK:=MaximalOrder(K); Output: Magma V2.10-6 Tue Mar 2 2004 23:16:00 on modular [Seed = 1027088725] ------------------------------------- Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 00:00:45 2004 Input: Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^5+7*x^4+3*x^2-x+1); OK:=MaximalOrder(K); for p in [1..100] do if IsPrime(p) then p; I := p * O2; Factorization(I); end if; end for; Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed. ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 00:04:16 2004 Input: Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^5+7*x^4+3*x^2-x+1); OK:=MaximalOrder(K); S := [ [ 1..100 ] | x : x isPrime ]; Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed. ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 00:04:22 2004 Input: Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^5+7*x^4+3*x^2-x+1); OK:=MaximalOrder(K); S := [ [ 1..100 ] | x : x isPrime ]; Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed. ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 00:04:36 2004 Input: Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^5+7*x^4+3*x^2-x+1); OK:=MaximalOrder(K); S := [ [ 1..100 ] | x : x isPrime ]; S; Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed. ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 00:04:45 2004 Input: Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^5+7*x^4+3*x^2-x+1); OK:=MaximalOrder(K); Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed. ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 00:05:26 2004 Input: S := [ [ 1..10 ] | x^2+x+1 : x in { -3 .. 3 by 1} ]; Output: Magma V2.10-6 Wed Mar 3 2004 00:05:23 on modular [Seed = 2172954234] ------------------------------------- >> S := [ [ 1..10 ] | x^2+x+1 : x in { -3 .. 3 by 1} ];; ^ Runtime error in sequence construction: Can't coerce element into the universe Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 00:06:42 2004 Input: Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^5+7*x^4+3*x^2-x+1); OK:=MaximalOrder(K); for p in [1..100] do p; end for; Output: WARNING: MAGMA command contains unsafe command 'open', so it will not be executed. ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 00:07:03 2004 Input: Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^5+7*x^4+3*x^2-x+1); OK:=MaximalOrder(K); for p in [1..100] do p; end for; Output: WARNING: MAGMA command contains unsafe command 'open', so it will not be executed. ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 00:19:05 2004 Input: S := [ [ 1..10 ] | x^2+x+1 : x in { -3 .. 2 by 1 } ]; Output: Magma V2.10-6 Wed Mar 3 2004 00:19:02 on modular [Seed = 1937136092] ------------------------------------- Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 00:19:19 2004 Input: S := [ [ 1..10 ] | x^2+x+1 : x in { -3 .. 2 by 1 } ]; S; Output: Magma V2.10-6 Wed Mar 3 2004 00:19:16 on modular [Seed = 1246716151] ------------------------------------- [ 7, 3, 1, 1, 3, 7 ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 00:19:57 2004 Input: S := [ [ 1..100 ] | x : x isPrime ]; S; Output: Magma V2.10-6 Wed Mar 3 2004 00:19:54 on modular [Seed = 1161850838] ------------------------------------- >> S := [ [ 1..100 ] | x : x isPrime ]; ^ User error: bad syntax >> S;; ^ User error: Identifier 'S' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 00:20:15 2004 Input: S := [ [ 1..100 ] | x : isPrime(x) ]; S; Output: Magma V2.10-6 Wed Mar 3 2004 00:20:12 on modular [Seed = 1431338544] ------------------------------------- >> S := [ [ 1..100 ] | x : isPrime(x) ]; ^ User error: bad syntax >> S;; ^ User error: Identifier 'S' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 00:21:23 2004 Input: S := [ [ 1..10 ] | x : x in { -3 .. 2 by 1 } ]; Output: Magma V2.10-6 Wed Mar 3 2004 00:21:20 on modular [Seed = 740886293] ------------------------------------- >> S := [ [ 1..10 ] | x : x in { -3 .. 2 by 1 } ]; ^ Runtime error in sequence construction: Can't coerce element into the universe Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 00:21:38 2004 Input: S := [ [ 1..10 ] | x^2 : x in { -3 .. 2 by 1 } ]; Output: Magma V2.10-6 Wed Mar 3 2004 00:21:35 on modular [Seed = 656542737] ------------------------------------- >> S := [ [ 1..10 ] | x^2 : x in { -3 .. 2 by 1 } ];; ^ Runtime error in sequence construction: Can't coerce element into the universe Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 00:21:49 2004 Input: S := [ [ 1..10 ] | x^2+x+1 : x in { -3 .. 2 by 1 } ]; Output: Magma V2.10-6 Wed Mar 3 2004 00:21:46 on modular [Seed = 1044059453] ------------------------------------- Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 00:24:57 2004 Input: S := [ x in [ 1..100 ] | isPrime(x) ]; Output: Magma V2.10-6 Wed Mar 3 2004 00:24:54 on modular [Seed = 135078983] ------------------------------------- >> S := [ x in [ 1..100 ] | isPrime(x) ];; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 00:25:11 2004 Input: S := [ x in [ 1..100 ] : isPrime(x) ]; Output: Magma V2.10-6 Wed Mar 3 2004 00:25:08 on modular [Seed = 117582682] ------------------------------------- >> S := [ x in [ 1..100 ] : isPrime(x) ];; ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 00:26:08 2004 Input: S := { x in [ 1..100] : isPrime(x) }; Output: Magma V2.10-6 Wed Mar 3 2004 00:26:05 on modular [Seed = 505098778] ------------------------------------- >> S := { x in [ 1..100] : isPrime(x) };; ^ User error: bad syntax Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 00:28:01 2004 Input: S := { x in [ 1..100] }; Output: Magma V2.10-6 Wed Mar 3 2004 00:27:58 on modular [Seed = 3924608350] ------------------------------------- >> S := { x in [ 1..100] };; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 00:28:38 2004 Input: Input: R:=PolynomialRing(RationalField()); S := { x in [ 1..100] }; Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed. ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 00:29:14 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^5 + 7*x^4 + 3*x^2 - x + 1); O2 := MaximalOrder(N); for mom in [1..100] do if IsPrime(mom) then mom; I := mom * O2; Factorization(I); end if; end for; Output: Magma V2.10-6 Wed Mar 3 2004 00:29:11 on modular [Seed = 4177384886] ------------------------------------- 2 [ ] 3 [ ] 5 [ , , ] 7 [ , ] 11 [ , , , ] 13 [ , ] 17 [ , , ] 19 [ , , ] 23 [ , ] 29 [ , , ] 31 [ , , ] 37 [ ] 41 [ , ] 43 [ , , , ] 47 [ , ] 53 [ , ] 59 [ , ] 61 [ ] 67 [ , , , ] 71 [ , , , ] 73 [ ] 79 [ , ] 83 [ , , , ] 89 [ , ] 97 [ ] Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 00:29:55 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5 + 7*x^4 + 3*x^2 - x + 1); OK := MaximalOrder(K); for mom in [1..100] do if IsPrime(mom) then mom; I := mom * OK; Factorization(I); end if; end for; Output: Magma V2.10-6 Wed Mar 3 2004 00:29:52 on modular [Seed = 4093042378] ------------------------------------- 2 [ ] 3 [ ] 5 [ , , ] 7 [ , ] 11 [ , , , ] 13 [ , ] 17 [ , , ] 19 [ , , ] 23 [ , ] 29 [ , , ] 31 [ , , ] 37 [ ] 41 [ , ] 43 [ , , , ] 47 [ , ] 53 [ , ] 59 [ , ] 61 [ ] 67 [ , , , ] 71 [ , , , ] 73 [ ] 79 [ , ] 83 [ , , , ] 89 [ , ] 97 [ ] Total time: 3.029 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 00:30:20 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5 + 7*x^4 + 3*x^2 - x + 1); OK := MaximalOrder(K); for p in [1..100] do if IsPrime(p) then p; I := p * OK; Factorization(I); end if; end for; Output: Magma V2.10-6 Wed Mar 3 2004 00:30:17 on modular [Seed = 3284594371] ------------------------------------- 2 [ ] 3 [ ] 5 [ , , ] 7 [ , ] 11 [ , , , ] 13 [ , ] 17 [ , , ] 19 [ , , ] 23 [ , ] 29 [ , , ] 31 [ , , ] 37 [ ] 41 [ , ] 43 [ , , , ] 47 [ , ] 53 [ , ] 59 [ , ] 61 [ ] 67 [ , , , ] 71 [ , , , ] 73 [ ] 79 [ , ] 83 [ , , , ] 89 [ , ] 97 [ ] Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 00:55:17 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5 + 7*x^4 + 3*x^2 - x + 1); OK := MaximalOrder(K); Basis(OK); for p in [1..100] do if IsPrime(p) then p; I := p * OK; Factorization(I); end if; end for; Output: Magma V2.10-6 Wed Mar 3 2004 00:55:14 on modular [Seed = 1768708673] ------------------------------------- [ OK.1, OK.2, OK.3, OK.4, OK.5 ] 2 [ ] 3 [ ] 5 [ , , ] 7 [ , ] 11 [ , , , ] 13 [ , ] 17 [ , , ] 19 [ , , ] 23 [ , ] 29 [ , , ] 31 [ , , ] 37 [ ] 41 [ , ] 43 [ , , , ] 47 [ , ] 53 [ , ] 59 [ , ] 61 [ ] 67 [ , , , ] 71 [ , , , ] 73 [ ] 79 [ , ] 83 [ , , , ] 89 [ , ] 97 [ ] Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 00:56:35 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5 + 7*x^4 + 3*x^2 - x + 1); OK := MaximalOrder(K); K!Basis(OK); for p in [1..100] do if IsPrime(p) then p; I := p * OK; Factorization(I); end if; end for; Output: Magma V2.10-6 Wed Mar 3 2004 00:56:32 on modular [Seed = 1717786012] ------------------------------------- >> K!Basis(OK); ^ Runtime error in '!': Illegal coercion 2 [ ] 3 [ ] 5 [ , , ] 7 [ , ] 11 [ , , , ] 13 [ , ] 17 [ , , ] 19 [ , , ] 23 [ , ] 29 [ , , ] 31 [ , , ] 37 [ ] 41 [ , ] 43 [ , , , ] 47 [ , ] 53 [ , ] 59 [ , ] 61 [ ] 67 [ , , , ] 71 [ , , , ] 73 [ ] 79 [ , ] 83 [ , , , ] 89 [ , ] 97 [ ] Total time: 3.029 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 00:57:44 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5 + 7*x^4 + 3*x^2 - x + 1); OK := MaximalOrder(K); [K!x : x in Basis(OK)]; for p in [1..100] do if IsPrime(p) then p; I := p * OK; Factorization(I); end if; end for; Output: Magma V2.10-6 Wed Mar 3 2004 00:57:40 on modular [Seed = 2138721472] ------------------------------------- [ 1, a, a^2, a^3, a^4 ] 2 [ ] 3 [ ] 5 [ , , ] 7 [ , ] 11 [ , , , ] 13 [ , ] 17 [ , , ] 19 [ , , ] 23 [ , ] 29 [ , , ] 31 [ , , ] 37 [ ] 41 [ , ] 43 [ , , , ] 47 [ , ] 53 [ , ] 59 [ , ] 61 [ ] 67 [ , , , ] 71 [ , , , ] 73 [ ] 79 [ , ] 83 [ , , , ] 89 [ , ] 97 [ ] Total time: 3.119 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Wed Mar 3 01:43:35 2004 Input: ModularCurve(X, Classical, 5); Output: Magma V2.10-6 Wed Mar 3 2004 01:43:31 on modular [Seed = 3958297874] ------------------------------------- >> ModularCurve(X, Classical, 5);; ^ User error: Identifier 'X' has not been declared or assigned Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Wed Mar 3 01:44:20 2004 Input: A2:=AffineSpace(RationalField(), 2); ModularCurve(X, Classical, 5); Output: Magma V2.10-6 Wed Mar 3 2004 01:44:17 on modular [Seed = 3789872970] ------------------------------------- >> ModularCurve(X, Classical, 5);; ^ User error: Identifier 'X' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Wed Mar 3 01:44:32 2004 Input: A2:=AffineSpace(RationalField(), 2); ModularCurve(A2, Classical, 5); Output: Magma V2.10-6 Wed Mar 3 2004 01:44:29 on modular [Seed = 4194092894] ------------------------------------- >> ModularCurve(A2, Classical, 5);; ^ User error: Identifier 'Classical' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Wed Mar 3 01:44:52 2004 Input: A2:=AffineSpace(RationalField(), 2); ModularCurve(A2, "Classical", 5); Output: Magma V2.10-6 Wed Mar 3 2004 01:44:49 on modular [Seed = 4059352954] ------------------------------------- Modular Curve over Rational Field defined by $.1^6 - $.1^5*$.2^5 + 3720*$.1^5*$.2^4 - 4550940*$.1^5*$.2^3 + 2028551200*$.1^5*$.2^2 - 246683410950*$.1^5*$.2 + 1963211489280*$.1^5 + 3720*$.1^4*$.2^5 + 1665999364600*$.1^4*$.2^4 + 107878928185336800*$.1^4*$.2^3 + 383083609779811215375*$.1^4*$.2^2 + 128541798906828816384000*$.1^4*$.2 + 1284733132841424456253440*$.1^4 - 4550940*$.1^3*$.2^5 + 107878928185336800*$.1^3*$.2^4 - 441206965512914835246100*$.1^3*$.2^3 + 26898488858380731577417728000*$.1^3*$.2^2 - 192457934618928299655108231168000*$.1^3*$.2 + 280244777828439527804321565297868800*$.1^3 + 2028551200*$.1^2*$.2^5 + 383083609779811215375*$.1^2*$.2^4 + 26898488858380731577417728000*$.1^2*$.2\ ^3 + 5110941777552418083110765199360000*$.1^2*$.2^2 + 36554736583949629295706472332656640000*$.1^2*$.2 + 6692500042627997708487149415015068467200*$.1^2 - 246683410950*$.1*$.2^5 + 128541798906828816384000*$.1*$.2^4 - 192457934618928299655108231168000*$.1*\ $.2^3 + 36554736583949629295706472332656640000*$.1*$.2^2 - 264073457076620596259715790247978782949376*$.1*$.2 + 53274330803424425450420160273356509151232000*$.1 + $.2^6 + 1963211489280*$.2^5 + 1284733132841424456253440*$.2^4 + 280244777828439527804321565297868800*$.2^3 + 6692500042627997708487149415015068467200*$.2^2 + 53274330803424425450420160273356509151232000*$.2 + 141359947154721358697753474691071362751004672000 Total time: 2.999 seconds, Total memory usage: 4.70MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Wed Mar 3 01:45:36 2004 Input: A2:=AffineSpace(RationalField(), 2); ModularCurve(A2, "Classical", 5); Output: Magma V2.10-6 Wed Mar 3 2004 01:45:33 on modular [Seed = 3452498602] ------------------------------------- Modular Curve over Rational Field defined by x^6 - x^5*y^5 + 3720*x^5*y^4 - 4550940*x^5*y^3 + 2028551200*x^5*y^2 - 246683410950*x^5*y + 1963211489280*x^5 + 3720*x^4*y^5 + 1665999364600*x^4*y^4 + 107878928185336800*x^4*y^3 + 383083609779811215375*x^4*y^2 + 128541798906828816384000*x^4*y + 1284733132841424456253440*x^4 - 4550940*x^3*y^5 + 107878928185336800*x^3*y^4 - 441206965512914835246100*x^3*y^3 + 26898488858380731577417728000*x^3*y^2 - 192457934618928299655108231168000*x^3*y + 280244777828439527804321565297868800*x^3 + 2028551200*x^2*y^5 + 383083609779811215375*x^2*y^4 + 26898488858380731577417728000*x^2*y^3 + 5110941777552418083110765199360000*x^2*y^2 + 36554736583949629295706472332656640000*x^2*y + 6692500042627997708487149415015068467200*x^2 - 246683410950*x*y^5 + 128541798906828816384000*x*y^4 - 192457934618928299655108231168000*x*y^3 + 36554736583949629295706472332656640000*x*y^2 - 264073457076620596259715790247978782949376*x*y + 53274330803424425450420160273356509151232000*x + y^6 + 1963211489280*y^5 + 1284733132841424456253440*y^4 + 280244777828439527804321565297868800*y^3 + 6692500042627997708487149415015068467200*y^2 + 53274330803424425450420160273356509151232000*y + 141359947154721358697753474691071362751004672000 Total time: 2.999 seconds, Total memory usage: 4.70MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Wed Mar 3 01:46:14 2004 Input: A2:=AffineSpace(RationalField(), 2); ModularCurve(A2, "Classical", 2); Output: Magma V2.10-6 Wed Mar 3 2004 01:46:11 on modular [Seed = 3317758620] ------------------------------------- Modular Curve over Rational Field defined by x^3 - x^2*y^2 + 1488*x^2*y - 162000*x^2 + 1488*x*y^2 + 40773375*x*y + 8748000000*x + y^3 - 162000*y^2 + 8748000000*y - 157464000000000 Total time: 2.909 seconds, Total memory usage: 4.70MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Wed Mar 3 01:47:09 2004 Input: A2:=AffineSpace(RationalField(), 2); X:=ModularCurve(A2, "Classical", 2); X;Genus(X); Output: Magma V2.10-6 Wed Mar 3 2004 01:47:06 on modular [Seed = 3721978589] ------------------------------------- Modular Curve over Rational Field defined by x^3 - x^2*y^2 + 1488*x^2*y - 162000*x^2 + 1488*x*y^2 + 40773375*x*y + 8748000000*x + y^3 - 162000*y^2 + 8748000000*y - 157464000000000 0 Total time: 3.039 seconds, Total memory usage: 4.70MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Wed Mar 3 01:48:34 2004 Input: A2:=AffineSpace(RationalField(), 2); X:=ModularCurve(A2, "Classical", 11); X;Genus(X); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Wed Mar 3 2004 01:48:11 on modular [Seed = 3587238420] ------------------------------------- Modular Curve over Rational Field defined by x^12 - x^11*y^11 + 8184*x^11*y^10 - 28278756*x^11*y^9 + 53686822816*x^11*y^8 - 61058988656490*x^11*y^7 + 42570393135641712*x^11*y^6 - 17899526272883039048*x^11*y^5 + 4297837238774928467520*x^11*y^4 - 529134841844639613861795*x^11*y^3 + 27209811658056645815522600*x^11*y^2 - 374642006356701393515817612*x^11*y + 296470902355240575283200000*x^11 + 8184*x^10*y^11 + 1608331026427734378*x^10*y^10 + 30134971854812981978547264*x^10*y^9 + 12407796387712093514736413264496*x^10\ *y^8 + 645470833566425875717489618904152240*x^10*y^7 + 7848482999227584325448694633580010490867*x^10*y^6 + 28890545335855949285086003898461917345026160*x^10*y^5 + 35372414460361796790312007060191890803134127320*x^10*y^4 + 14131378888778142661582693947549844785863493325800*x^10*y^3 + 1587728122949690904187089204116332301200302760915266*x^10*y^2 + 33446467926379842030532687838341039552110187929600000*x^10*y + 29298331981110197366602526090413106879319244800000000*x^10 - 28278756*x^9*y^11 + 30134971854812981978547264*x^9*y^10 - 573388748843683532691009051194955437*x^9*y^9 + 24228593349948582884094197811518266845689352*x^9*y^8 - 51135193038502008150804190472844550800569441050500*x^9*y^7 + 14690460927260804690751501000083244161647396386205851440*x^9*y^6 - 994774826102691960922410649494629085486856242714439003812180*x^9*y^5 + 22148485195925584385790489089697473918894904664093860668378292000*x^9*y^4 - 199188452917764242987050083089364860927274115441197382331866126825820*x^9*y\ ^3 + 8044364183079957387401325981668933650994688420897059005250506278912000\ 00*x^9*y^2 - 14581782545972952078399807867686230186502343069323313930136349\ 52069120000000*x^9*y + 9651225466603492984067240639408842527438736331761292\ 90337528305418240000000000*x^9 + 53686822816*x^8*y^11 + 12407796387712093514736413264496*x^8*y^10 + 24228593349948582884094197811518266845689352*x^8*y^9 + 29211180544704743418963619709378403797452606969172658*x^8*y^8 + 636861023141767565580039581191818069063579259290464688398880*x^8*y^7 + 987807801334019988631500819088661487281712947788833523552559299560*x^8*y^6 + 208334210762751500564946204497082337222910461284651050215872586641463200*x^\ 8*y^5 + 8498500708725193890718329655230574962816784139443636591086906768989\ 729050095*x^8*y^4 + 7951324712505790649284198939520744230013378175092486044\ 9090230806481243648000000*x^8*y^3 + 171790435018380416903247878610824648919\ 543398246401012395341432490921925017600000000*x^8*y^2 + 668063044679983105817933911947911151848051275284130912352843152941437367091\ 20000000000*x^8*y + 1338586400912357073420399795635643400599836918986297982\ 928179335149920452608000000000000*x^8 - 61058988656490*x^7*y^11 + 645470833566425875717489618904152240*x^7*y^10 - 51135193038502008150804190472844550800569441050500*x^7*y^9 + 636861023141767565580039581191818069063579259290464688398880*x^7*y^8 - 64999046469909490143435875140651300541119093852394968074094803537810*x^7*y^\ 7 + 24790023356193929438861279985747642436485625176909488028808653790427939\ 6400*x^7*y^6 - 759485852012679734036275336311389950898826472843074845794136\ 91458563029509971992*x^7*y^5 + 29731196727162122194564718811128885698355755\ 78534065127175856819648732682854604800000*x^7*y^4 - 220932496966279334196552268236040576388972225626826358002699091783257109851\ 17040640000000*x^7*y^3 + 44681231489418997440503069818655052635806384532381\ 152777755381649015689662976491520000000000*x^7*y^2 - 241559572537644189753077428231295861870612436207563395156025710750612369922\ 94518784000000000000*x^7*y + 6188407231077618898963630168852515740786353884\ 43306832549992828319945330157158400000000000000000*x^7 + 42570393135641712*x^6*y^11 + 7848482999227584325448694633580010490867*x^6*y\ ^10 + 14690460927260804690751501000083244161647396386205851440*x^6*y^9 + 987807801334019988631500819088661487281712947788833523552559299560*x^6*y^8 + 247900233561939294388612799857476424364856251769094880288086537904279396400\ *x^6*y^7 + 1168150167526575837857761510359647773943258089269992605255478096\ 499695783789300124*x^6*y^6 + 2240803998866274951497716546923691770940596499\ 40825305182078225594292057242702643200000*x^6*y^5 + 193873837382174012147044636866579741283308287387546853037164291333930267899\ 9680942080000000*x^6*y^4 - 721191229974600751053515948619991969748296038927\ 8446632552985263875183091897870581760000000000*x^6*y^3 + 304940442465503101178718956284212733791730506305683970723911106883665585358\ 04457582592000000000000*x^6*y^2 - 95333447356443287210404497374050404132491\ 763274506548619337189691919811046970438451200000000000000000*x^6*y + 953562665947317950794933099657566747110587348311644892128115531290587730803\ 52804044800000000000000000000*x^6 - 17899526272883039048*x^5*y^11 + 28890545335855949285086003898461917345026160*x^5*y^10 - 994774826102691960922410649494629085486856242714439003812180*x^5*y^9 + 208334210762751500564946204497082337222910461284651050215872586641463200*x^\ 5*y^8 - 7594858520126797340362753363113899508988264728430748457941369145856\ 3029509971992*x^5*y^7 + 224080399886627495149771654692369177094059649940825\ 305182078225594292057242702643200000*x^5*y^6 - 150572973117089225265805144105638484783346937586249997741086009686674872608\ 27388477440000000*x^5*y^5 - 17799464186707526269518498092046260860406035746\ 6681128822395417442867019643767352197120000000000*x^5*y^4 - 132899390746510815213576388699982507144408409988109860756557471614019142636\ 9978927939584000000000000*x^5*y^3 + 971814871813934664738444920164383351748\ 8848029697396574289278515913329360524510494720000000000000000000*x^5*y^2 - 784037924821419672964306279649326942508185993010014130404793290934602248317\ 1510017064960000000000000000000*x^5*y - 311135714890286591241798839183635025168280538591757187756842266421807890101\ 0004935966720000000000000000000000*x^5 + 4297837238774928467520*x^4*y^11 + 35372414460361796790312007060191890803134127320*x^4*y^10 + 22148485195925584385790489089697473918894904664093860668378292000*x^4*y^9 + 849850070872519389071832965523057496281678413944363659108690676898972905009\ 5*x^4*y^8 + 297311967271621221945647188111288856983557557853406512717585681\ 9648732682854604800000*x^4*y^7 + 193873837382174012147044636866579741283308\ 2873875468530371642913339302678999680942080000000*x^4*y^6 - 177994641867075262695184980920462608604060357466681128822395417442867019643\ 767352197120000000000*x^4*y^5 + 1504342316556396664561828460973036017600526\ 5392518745580151910727157028699006028388237312000000000000*x^4*y^4 - 510387788704673753171746274142812030167891533922654498803534638710043488164\ 11677478092800000000000000000*x^4*y^3 + 378494977797549959360178068152933818044335078157093771639955480261351930169\ 113765048483840000000000000000000*x^4*y^2 + 596596095770309616375411102891120210780911047671877878225490788693942054393\ 02452893450240000000000000000000000*x^4*y + 437146826371712360213676049668333053099237469748508946653253316043623031097\ 15777067941888000000000000000000000000*x^4 - 529134841844639613861795*x^3*y^11 + 141313788887781426615826939475498447858\ 63493325800*x^3*y^10 - 1991884529177642429870500830893648609272741154411973\ 82331866126825820*x^3*y^9 + 79513247125057906492841989395207442300133781750\ 924860449090230806481243648000000*x^3*y^8 - 220932496966279334196552268236040576388972225626826358002699091783257109851\ 17040640000000*x^3*y^7 - 72119122997460075105351594861999196974829603892784\ 46632552985263875183091897870581760000000000*x^3*y^6 - 132899390746510815213576388699982507144408409988109860756557471614019142636\ 9978927939584000000000000*x^3*y^5 - 510387788704673753171746274142812030167\ 89153392265449880353463871004348816411677478092800000000000000000*x^3*y^4 - 925461466455522523607980072366478440235575959511945288268604770825451300845\ 059605937520640000000000000000000*x^3*y^3 + 103867720178991499136209046596137730276914706598548722228567268915891817571\ 6097236444119040000000000000000000000*x^3*y^2 + 493751729222149651035457063068642305508233453469401395944974296438196687728\ 770695603159040000000000000000000000000*x^3*y - 337500037290942764495395868386562971754016116785390841072048221617443316658\ 082155384012800000000000000000000000000000*x^3 + 27209811658056645815522600*x^2*y^11 + 1587728122949690904187089204116332301\ 200302760915266*x^2*y^10 + 804436418307995738740132598166893365099468842089\ 705900525050627891200000*x^2*y^9 + 1717904350183804169032478786108246489195\ 43398246401012395341432490921925017600000000*x^2*y^8 + 446812314894189974405030698186550526358063845323811527777553816490156896629\ 76491520000000000*x^2*y^7 + 30494044246550310117871895628421273379173050630\ 568397072391110688366558535804457582592000000000000*x^2*y^6 + 971814871813934664738444920164383351748884802969739657428927851591332936052\ 4510494720000000000000000000*x^2*y^5 + 378494977797549959360178068152933818044335078157093771639955480261351930169\ 113765048483840000000000000000000*x^2*y^4 + 103867720178991499136209046596137730276914706598548722228567268915891817571\ 6097236444119040000000000000000000000*x^2*y^3 - 301851634381591833346238394387907563828793379391119445614595161272769455527\ 698270716428288000000000000000000000000*x^2*y^2 - 417519094737708994161145213538320499717294846522136843211955441884544692965\ 5566146994176000 ** WARNING: Output too long, hence truncated. Errors: /home/mfd/gomagma: line 2: 10943 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Wed Mar 3 01:50:11 2004 Input: A2:=AffineSpace(RationalField(), 2); X:=ModularCurve(A2, "Classical", 13); X;Genus(X); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Wed Mar 3 2004 01:49:48 on modular [Seed = 2728878788] ------------------------------------- Modular Curve over Rational Field defined by x^14 - x^13*y^13 + 9672*x^13*y^12 - 40616316*x^13*y^11 + 97116140576*x^13*y^10 - 145742356534710*x^13*y^9 + 142727120530755696*x^13*y^8 - 91944131414745883208*x^13*y^7 + 38373375189621696878784*x^13*y^6 - 9980376107988974265288009*x^13*y^5 + 1508484527780717514871680200*x^13*y^4 - 117589277940072151921466095740*x^13*y^3 + 3813066975450671721121304807712*x^13*y^2 - 32685702714621175092948209889806*x^13*y + 15787756016985099663979167744000*x^13 + 9672*x^12*y^13 + 63336131453282305176*x^12*y^12 + 5339704017492387472276862944*x^12*y^11 + 7038227861570702862399825051262104*x^12*y^10 + 1017131468961830048705766611220442641072*x^12*y^9 + 32988905472599070890328795217808043240900816*x^12*y^8 + 333551826778342195432371586876023049547129080896*x^12*y^7 + 1234257162452453722866237618078783279952599399679176*x^12*y^6 + 1787206767475651398304042906319887696372425891847417480*x^12*y^5 + 1010922460622081033367079280521141037085193349093095277208*x^12*y^4 + 207577177886168263601723424708043354620195244558620874018272*x^12*y^3 + 12893770087100209197778927627416397147602669299324665034127451*x^12*y^2 + 157870586217596053304332218736965888119051656824626442141696000*x^12*y + 83084413350616406183495875982586495825900375128760385536000000*x^12 - 40616316*x^11*y^13 + 5339704017492387472276862944*x^11*y^12 - 936062849021824119784660671862200161988*x^11*y^11 + 214191411057420328765018422101187988893741675744*x^11*y^10 - 1967575998834670421411906070499119710120923910594022072*x^11*y^9 + 2117324199178304244393290847066787694415213468957410146838208*x^11*y^8 - 481806591005250661668209263946913789583739163176277250633369496316*x^11*y^7 + 33157532644992168541479115114277423707920632043639237944990254217082784*x\ ^11*y^6 - 87417469046345585847874003497367779787464972072491120720290834965\ 3368101836*x^11*y^5 + 10335702376336052876569385632176208762756384874046214\ 470799722804104208232161120*x^11*y^4 - 602590848803086525607541259573769559230947018312350973789324240925928462880\ 59835756*x^11*y^3 + 1793126194379952688627855688925381405873166359324729346\ 86318597956817819648897662976000*x^11*y^2 - 260241334661897724169148477062778090370575619826743149104887568856318553170\ 833833984000000*x^11*y + 14574627186598570130300696869072707362311015418915\ 1557978520314340489760352149438464000000000*x^11 + 97116140576*x^10*y^13 + 7038227861570702862399825051262104*x^10*y^12 + 214191411057420328765018422101187988893741675744*x^10*y^11 + 2303156526339236416244981158503557124969923397655602595936*x^10*y^10 + 333376714930461597630366410672145363642373801348744230962709165120*x^10*y^9 + 2965269806029300518982153645576999878343315273199400249881587616072766840\ *x^10*y^8 + 331907401512677500334062749845196660862177698561706846404048127\ 3875824853713440*x^10*y^7 + 70760230695433596126438774739283071460912495129\ 4341249227988393380722334150416923424*x^10*y^6 + 368775623989661147432548958525081545138173437545718898205962050939974691231\ 13726984508320*x^10*y^5 + 5394340669528386336010583140803518297287681856138\ 81497302494155281483862817525900116623514601*x^10*y^4 + 230891658037370536354632112034652186513764908871370896095056481488595059679\ 3631208268755124224000*x^10*y^3 + 26786657366897690499000181091405982640357\ 50069305308244518131035743577819824227828206936260608000000*x^10*y^2 + 618365025729687208026621844082518672586866478732183940869747889968364543178\ 129991952544825344000000000*x^10*y + 76053487350172126258758371849784576150\ 81634815943367015020891775626681233374752203029348352000000000000*x^10 - 145742356534710*x^9*y^13 + 1017131468961830048705766611220442641072*x^9*y^1\ 2 - 1967575998834670421411906070499119710120923910594022072*x^9*y^11 + 333376714930461597630366410672145363642373801348744230962709165120*x^9*y^10 - 3446428446108873653338438122607890222998287145071532602786604033089435617\ 18*x^9*y^9 + 11510485988607799847944664306226745280653016997751179971212105\ 953518910829665118960*x^9*y^8 - 2897183372200476960821835189860299702387371\ 8918496584569542741468721604925350565276800952*x^9*y^7 + 896870705987792979395381663999962505308565678114644405791268638870640408275\ 3228694260847129920*x^9*y^6 - 474980656775733704222417133934306465523573652\ 393831168608700490473956434788522583600537536840594898*x^9*y^5 + 571667792098574365520150012010167700719010260891251508120687682964279392933\ 7037298192242022307430400000*x^9*y^4 - 206780785372128827616941538480266841615104256198673928826284179715898085131\ 39875419201055859633291264000000*x^9*y^3 + 258724639084492890167506285555673727101853288484834630834940771825704443391\ 88517407317465229936295936000000000*x^9*y^2 - 867407269476658125983216198455842425824234550946156206891628433326167229948\ 5935075259027823494430720000000000000*x^9*y + 132287948592242819730686388197721726586421046648941198415164132202495387061\ 267918873489002706501632000000000000000*x^9 + 142727120530755696*x^8*y^13 + 32988905472599070890328795217808043240900816*x^8*y^12 + 2117324199178304244393290847066787694415213468957410146838208*x^8*y^11 + 2965269806029300518982153645576999878343315273199400249881587616072766840*x\ ^8*y^10 + 11510485988607799847944664306226745280653016997751179971212105953\ 518910829665118960*x^8*y^9 + 7636293775342802395250017527970183420378976311\ 30969295340196615666330614048031692849601680*x^8*y^8 + 215521875334478282185361776613377947372513898932610667740853022425025698790\ 4613455196577522696384*x^8*y^7 + 415431723402642702720731130934926941857797\ 474097020970018619513668017459051573659373309870938643397563*x^8*y^6 + 575755892104844601526655491940234473733350110015297463022510813192038412672\ 2107536788649181513676013568000*x^8*y^5 - 609541439144095479517886966349942582829153845276665356625632792106358406213\ 7305104052711687223009869824000000*x^8*y^4 - 623330217356775601716427499006355649158929417453836923172630139923722104895\ 62891779314959788281383878656000000000*x^8*y^3 + 367699880302507769522184906338576349930282889799687609612600740135262931410\ 546189503475085055061919793152000000000000*x^8*y^2 - 913844005726821508929480521086904504761295550807304466343649705885472617699\ 094229816628221421776732684288000000000000000*x^8*y + 767013621315952423931475176267170123577142608595930709148835175130350223089\ 832292329376203694232005771264000000000000000000*x^8 - 91944131414745883208*x^7*y^13 + 3335518267783421954323715868760230495471290\ 80896*x^7*y^12 - 4818065910052506616682092639469137895837391631762772506333\ 69496316*x^7*y^11 + 3319074015126775003340627498451966608621776985617068464\ 040481273875824853713440*x^7*y^10 - 289718337220047696082183518986029970238\ 73718918496584569542741468721604925350565276800952*x^7*y^9 + 215521875334478282185361776613377947372513898932610667740853022425025698790\ 4613455196577522696384*x^7*y^8 - 353929460696374726747926574659474815670988\ 1306171284362655032102198235369837795589356541679185977279848*x^7*y^7 + 187433051934148497537178792064160144226449743146562769523813325806108271927\ 829978476604969216803944169472000*x^7*y^6 - 370266512714376097999815427881208542616671611455174504512860758453682009932\ 9002243268464660519705479479296000000*x^7*y^5 - 183132205897075543039196288365653711605825416879793969604180531232473994131\ 86658869150749995799620001726464000000000*x^7*y^4 + 303628396849623247388501617704769126069627806954925724909207701265590212162\ 332663163323999037945093480775680000000000000*x^7*y^3 - 226668496996199203777352229716417461096995804909768763297196647245168959821\ 482189931394270493086737753964544000000000000000*x^7*y^2 - 465337020884877935874185748520218965445631193822519111113045800260798180133\ 962179115662432186399226106740736000000000000000000*x^7*y + 668293341501816933957335496054879116332420597931482574352226562547713399336\ 27547003847032182942337299644416000000000000000000000*x^7 + 38373375189621696878784*x^6*y^13 + 1234257162452453722866237618078783279952\ 599399679176*x^6*y^12 + 331575326449921685414791151142774237079206320436392\ 37944990254217082784*x^6*y^11 + 7076023069543359612643877473928307146091249\ 51294341249227988393380722334150416923424*x^6*y^10 + 896870705987792979395381663999962505308565678114644405791268638870640408275\ 3228694260847129920*x^6*y^9 + 415431723402642702720731130934926941857797474\ 097020970018619513668017459051573659373309870938643397563*x^6*y^8 + 187433051934148497537178792064160144226449743146562769523813325806108271927\ 829978476604969216803944169472000*x^6*y^7 + 219195039895025564825329779856591854236856668860882903139307811188547989261\ 06308297736210617657464845238272000000*x^6*y^6 - 141047399911337609692132520692703393244329980827992208054373013771092383615\ 8828899053966820213587545583255552000000000*x^6*y^5 + 177223610503044726201630346912116804030656996825660457881444445704555907254\ 83253301914282961928612252886237184000000000000*x^6*y^4 - 177338063010485010114862175165805653386955604686555592321067088087769914969\ 75958558628543386809658957681917952000000000000000*x^6*y^3 + 175801761541721296614163144760797961999581545737966242399898402245904424096\ 892942484369837626392492960431210496000000000000000000*x^6*y^2 + 342086363139489625052554163828003788905904836985509176805687290711423509605\ 49152337412536609529405160000847872000 ** WARNING: Output too long, hence truncated. Errors: /home/mfd/gomagma: line 2: 10952 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Wed Mar 3 01:50:55 2004 Input: A2:=AffineSpace(RationalField(), 2); X:=ModularCurve(A2, "Classical", 13); Genus(X); X; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Wed Mar 3 2004 01:50:32 on modular [Seed = 3182984687] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 10967 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Wed Mar 3 01:54:08 2004 Input: CanonicalModularPolynomial(2); Output: Magma V2.10-6 Wed Mar 3 2004 01:54:05 on modular [Seed = 2324646893] ------------------------------------- $.1^3 + 48*$.1^2 - $.1*$.2 + 768*$.1 + 4096 Total time: 2.889 seconds, Total memory usage: 2.53MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Wed Mar 3 01:54:53 2004 Input: P:=PolynomialRing(Integers(), 2); P!CanonicalModularPolynomial(2); Output: Magma V2.10-6 Wed Mar 3 2004 01:54:50 on modular [Seed = 2189902802] ------------------------------------- x^3 + 48*x^2 - x*y + 768*x + 4096 Total time: 3.079 seconds, Total memory usage: 2.54MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Wed Mar 3 01:55:43 2004 Input: P:=PolynomialRing(Integers(), 2); P!CanonicalModularPolynomial(2); j; x:=1; j; Output: Magma V2.10-6 Wed Mar 3 2004 01:55:40 on modular [Seed = 2660982680] ------------------------------------- x^3 + 48*x^2 - x*j + 768*x + 4096 j j Total time: 3.039 seconds, Total memory usage: 2.54MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Wed Mar 3 01:56:36 2004 Input: P:=PolynomialRing(Integers(), 2); P!AtkinModularPolynomial(2); P!CanonicalModularPolynomial(2); P!ClassicalModularPolynomial(2); Output: Magma V2.10-6 Wed Mar 3 2004 01:56:32 on modular [Seed = 2526238556] ------------------------------------- x^3 - x^2*j + 744*x^2 - x*j + 184512*x + j^2 + 7256*j + 15252992 x^3 + 48*x^2 - x*j + 768*x + 4096 x^3 - x^2*j^2 + 1488*x^2*j - 162000*x^2 + 1488*x*j^2 + 40773375*x*j + 8748000000*x + j^3 - 162000*j^2 + 8748000000*j - 157464000000000 Total time: 2.979 seconds, Total memory usage: 2.87MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Wed Mar 3 01:57:01 2004 Input: P:=PolynomialRing(Integers(), 2); P!CanonicalModularPolynomial(13); Output: Magma V2.10-6 Wed Mar 3 2004 01:56:58 on modular [Seed = 1869262526] ------------------------------------- x^14 + 26*x^13 + 325*x^12 + 2548*x^11 + 13832*x^10 + 54340*x^9 + 157118*x^8 + 333580*x^7 + 509366*x^6 + 534820*x^5 + 354536*x^4 + 124852*x^3 + 15145*x^2 - x*j + 746*x + 13 Total time: 2.969 seconds, Total memory usage: 2.54MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Wed Mar 3 02:02:12 2004 Input: E:=EllipticCurve([0, 1]); TorsionSubgroupScheme(E); Output: Magma V2.10-6 Wed Mar 3 2004 02:02:09 on modular [Seed = 1296601047] ------------------------------------- >> TorsionSubgroupScheme(E);; ^ Runtime error in 'TorsionSubgroupScheme': Bad argument types Argument types given: CrvEll Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Wed Mar 3 02:02:29 2004 Input: E:=EllipticCurve([0, 1]); TorsionSubgroup(E); Output: Magma V2.10-6 Wed Mar 3 2004 02:02:26 on modular [Seed = 1161856556] ------------------------------------- Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Wed Mar 3 02:02:45 2004 Input: E:=EllipticCurve([0, 8]); TorsionSubgroup(E); Output: Magma V2.10-6 Wed Mar 3 2004 02:02:42 on modular [Seed = 1566088740] ------------------------------------- Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Wed Mar 3 02:05:27 2004 Input: K:=QuadraticField(2); E:=EllipticCurve([K|0, 8]); TorsionSubgroup(E); Output: Magma V2.10-6 Wed Mar 3 2004 02:05:23 on modular [Seed = 674098160] ------------------------------------- Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 to CrvEll: E given by a rule [no inverse] Total time: 3.109 seconds, Total memory usage: 2.29MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Wed Mar 3 02:06:28 2004 Input: K:=QuadraticField(2); E:=EllipticCurve([K|0, 8]); TorsionSubgroup(E); TorsionSubgroupScheme(E, 3); Output: Magma V2.10-6 Wed Mar 3 2004 02:06:25 on modular [Seed = 539354042] ------------------------------------- Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 to CrvEll: E given by a rule [no inverse] Subgroup scheme of E defined by x^4 + 32*x Total time: 3.169 seconds, Total memory usage: 2.29MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Wed Mar 3 02:06:52 2004 Input: K:=QuadraticField(2); E:=EllipticCurve([0, 1]); TorsionSubgroup(E); TorsionSubgroupScheme(E, 3); Output: Magma V2.10-6 Wed Mar 3 2004 02:06:49 on modular [Seed = 943586394] ------------------------------------- Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 Subgroup scheme of E defined by x^4 + 4*x Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Wed Mar 3 02:07:21 2004 Input: K:=QuadraticField(2); E:=EllipticCurve([K|0, 8]); TorsionSubgroup(E); G:=TorsionSubgroupScheme(E, 3); Output: Magma V2.10-6 Wed Mar 3 2004 02:07:17 on modular [Seed = 808842366] ------------------------------------- Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 to CrvEll: E given by a rule [no inverse] Total time: 3.109 seconds, Total memory usage: 2.29MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Wed Mar 3 02:07:53 2004 Input: K:=QuadraticField(2); E:=EllipticCurve([K|0, 8]); TorsionSubgroup(E); G:=TorsionSubgroupScheme(E, 3); IsogenyFromKernel(E, G); Output: Magma V2.10-6 Wed Mar 3 2004 02:07:50 on modular [Seed = 135121957] ------------------------------------- Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 to CrvEll: E given by a rule [no inverse] >> IsogenyFromKernel(E, G);; ^ Runtime error in 'IsogenyFromKernel': Bad argument types Argument types given: CrvEll, SchGrpEll Total time: 3.109 seconds, Total memory usage: 2.29MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Wed Mar 3 02:08:17 2004 Input: K:=QuadraticField(2); E:=EllipticCurve([K|0, 8]); TorsionSubgroup(E); G:=TorsionSubgroupScheme(E, 3); IsogenyFromKernel(G); Output: Magma V2.10-6 Wed Mar 3 2004 02:08:13 on modular [Seed = 377910] ------------------------------------- Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 to CrvEll: E given by a rule [no inverse] Elliptic Curve defined by y^2 = x^3 + 5832 over K Elliptic curve isogeny from: CrvEll: E to Elliptic Curve defined by y^2 = x^3 + 5832 over K taking (x : y : 1) to ((x^9 - 768*x^6 + 3072*x^3 + 32768) / (x^8 + 64*x^5 + 1024*x^2) : (x^12*y + 1760*x^9*y - 113664*x^6*y - 163840*x^3*y - 2097152*y) / (x^12 + 96*x^9 + 3072*x^6 + 32768*x^3) : 1) Total time: 3.179 seconds, Total memory usage: 2.29MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Wed Mar 3 02:09:25 2004 Input: K:=QuadraticField(2); E:=EllipticCurve([K|0, 8]); TorsionSubgroup(E); G:=TorsionSubgroupScheme(E, 3); IsogenyFromKernel(G); Factor(5832); Output: Magma V2.10-6 Wed Mar 3 2004 02:09:22 on modular [Seed = 521853910] ------------------------------------- Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 to CrvEll: E given by a rule [no inverse] Elliptic Curve defined by y^2 = x^3 + 5832 over K Elliptic curve isogeny from: CrvEll: E to Elliptic Curve defined by y^2 = x^3 + 5832 over K taking (x : y : 1) to ((x^9 - 768*x^6 + 3072*x^3 + 32768) / (x^8 + 64*x^5 + 1024*x^2) : (x^12*y + 1760*x^9*y - 113664*x^6*y - 163840*x^3*y - 2097152*y) / (x^12 + 96*x^9 + 3072*x^6 + 32768*x^3) : 1) >> Factor(5832);; ^ Runtime error in 'Factor': Bad argument types Argument types given: RngIntElt Total time: 3.139 seconds, Total memory usage: 2.29MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Wed Mar 3 02:13:16 2004 Input: A2:=AffineSpace(RationalField(), 2); ModularCurve(A2, "Classical", 5); Output: Magma V2.10-6 Wed Mar 3 2004 02:13:13 on modular [Seed = 3907857674] ------------------------------------- Modular Curve over Rational Field defined by x^6 - x^5*y^5 + 3720*x^5*y^4 - 4550940*x^5*y^3 + 2028551200*x^5*y^2 - 246683410950*x^5*y + 1963211489280*x^5 + 3720*x^4*y^5 + 1665999364600*x^4*y^4 + 107878928185336800*x^4*y^3 + 383083609779811215375*x^4*y^2 + 128541798906828816384000*x^4*y + 1284733132841424456253440*x^4 - 4550940*x^3*y^5 + 107878928185336800*x^3*y^4 - 441206965512914835246100*x^3*y^3 + 26898488858380731577417728000*x^3*y^2 - 192457934618928299655108231168000*x^3*y + 280244777828439527804321565297868800*x^3 + 2028551200*x^2*y^5 + 383083609779811215375*x^2*y^4 + 26898488858380731577417728000*x^2*y^3 + 5110941777552418083110765199360000*x^2*y^2 + 36554736583949629295706472332656640000*x^2*y + 6692500042627997708487149415015068467200*x^2 - 246683410950*x*y^5 + 128541798906828816384000*x*y^4 - 192457934618928299655108231168000*x*y^3 + 36554736583949629295706472332656640000*x*y^2 - 264073457076620596259715790247978782949376*x*y + 53274330803424425450420160273356509151232000*x + y^6 + 1963211489280*y^5 + 1284733132841424456253440*y^4 + 280244777828439527804321565297868800*y^3 + 6692500042627997708487149415015068467200*y^2 + 53274330803424425450420160273356509151232000*y + 141359947154721358697753474691071362751004672000 Total time: 3.029 seconds, Total memory usage: 4.70MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Wed Mar 3 02:30:44 2004 Input: e=ellinit([0,0,0,3,0]); P=[1,2]; ellpow(e, P, 2); Output: Magma V2.10-6 Wed Mar 3 2004 02:30:41 on modular [Seed = 3672052496] ------------------------------------- >> e=ellinit([0,0,0,3,0]); ^ User error: Identifier 'ellinit' has not been declared or assigned >> P=[1,2]; ^ User error: Identifier 'P' has not been declared or assigned >> ellpow(e, P, 2);; ^ User error: Identifier 'e' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Wed Mar 3 02:31:42 2004 Input: e=ellinit([0,0,0,3,0]); P=[1,2]; ellpow(e, P, 4) Output: Magma V2.10-6 Wed Mar 3 2004 02:31:39 on modular [Seed = 2846646297] ------------------------------------- >> e=ellinit([0,0,0,3,0]); ^ User error: Identifier 'ellinit' has not been declared or assigned >> P=[1,2]; ^ User error: Identifier 'P' has not been declared or assigned >> ellpow(e, P, 4); ^ User error: Identifier 'e' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Wed Mar 3 02:41:03 2004 Input: e=ellinit([0,0,0,3,0]); P=[1,2]; ellpow(e, P, 6) Output: Magma V2.10-6 Wed Mar 3 2004 02:41:00 on modular [Seed = 2627293435] ------------------------------------- >> e=ellinit([0,0,0,3,0]); ^ User error: Identifier 'ellinit' has not been declared or assigned >> P=[1,2]; ^ User error: Identifier 'P' has not been declared or assigned >> ellpow(e, P, 6); ^ User error: Identifier 'e' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host jcarlos.uab.es. (158.109.9.25) Time: Wed Mar 3 04:18:57 2004 Input: P:=PolynomiaRing(R); Output: Magma V2.10-6 Wed Mar 3 2004 04:18:54 on modular [Seed = 3199949870] ------------------------------------- >> P:=PolynomiaRing(R); ^ User error: Identifier 'R' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host jcarlos.uab.es. (158.109.9.25) Time: Wed Mar 3 04:19:23 2004 Input: P:=PolynomiaRing(3); Output: Magma V2.10-6 Wed Mar 3 2004 04:19:20 on modular [Seed = 3081917633] ------------------------------------- >> P:=PolynomiaRing(3); ^ User error: Identifier 'PolynomiaRing' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host jcarlos.uab.es. (158.109.9.25) Time: Wed Mar 3 04:19:47 2004 Input: P:=PolynomialRing(R); Output: Magma V2.10-6 Wed Mar 3 2004 04:19:43 on modular [Seed = 2357817293] ------------------------------------- >> P:=PolynomialRing(R); ^ User error: Identifier 'R' has not been declared or assigned Total time: 3.649 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host jcarlos.uab.es. (158.109.9.25) Time: Wed Mar 3 04:19:47 2004 Input: P:=PolynomialRing(R); Output: Magma V2.10-6 Wed Mar 3 2004 04:19:44 on modular [Seed = 2341365973] ------------------------------------- >> P:=PolynomialRing(R); ^ User error: Identifier 'R' has not been declared or assigned Total time: 3.649 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host jcarlos.uab.es. (158.109.9.25) Time: Wed Mar 3 04:20:04 2004 Input: P:=PolynomialRing(3); Output: Magma V2.10-6 Wed Mar 3 2004 04:20:00 on modular [Seed = 2509272763] ------------------------------------- >> P:=PolynomialRing(3); ^ Runtime error in 'PolynomialRing': Bad argument types Argument types given: RngIntElt Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host jcarlos.uab.es. (158.109.9.25) Time: Wed Mar 3 04:20:10 2004 Input: P:=PolynomialRing(3); Output: Magma V2.10-6 Wed Mar 3 2004 04:20:07 on modular [Seed = 1684113228] ------------------------------------- >> P:=PolynomialRing(3); ^ Runtime error in 'PolynomialRing': Bad argument types Argument types given: RngIntElt Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host jcarlos.uab.es. (158.109.9.25) Time: Wed Mar 3 04:22:18 2004 Input: R:=RealField(); P:=PolynomialRing(R); Output: Magma V2.10-6 Wed Mar 3 2004 04:22:15 on modular [Seed = 2071894227] ------------------------------------- Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host jcarlos.uab.es. (158.109.9.25) Time: Wed Mar 3 04:23:58 2004 Input: R:=RealField(); P:=PolynomialRing(R); x^3-7*x^2+5; Output: Magma V2.10-6 Wed Mar 3 2004 04:23:55 on modular [Seed = 1903465781] ------------------------------------- x^3 - 7*x^2 + 5 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host jcarlos.uab.es. (158.109.9.25) Time: Wed Mar 3 04:24:20 2004 Input: R:=RealField(); P:=PolynomialRing(R); x^3-7*x^2+5; P; Output: Magma V2.10-6 Wed Mar 3 2004 04:24:17 on modular [Seed = 1213049958] ------------------------------------- x^3 - 7*x^2 + 5 Univariate Polynomial Ring in x over Real Field Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host jcarlos.uab.es. (158.109.9.25) Time: Wed Mar 3 04:24:38 2004 Input: R:=RealField(); P:=PolynomialRing(R); x^3-7*x^2+5; print P; Output: Magma V2.10-6 Wed Mar 3 2004 04:24:35 on modular [Seed = 1599781731] ------------------------------------- x^3 - 7*x^2 + 5 Univariate Polynomial Ring in x over Real Field Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host jcarlos.uab.es. (158.109.9.25) Time: Wed Mar 3 04:27:54 2004 Input: R:=RealField(); P:=PolynomialRing(R); x^3-7*x^2+5; Terms(P); Output: Magma V2.10-6 Wed Mar 3 2004 04:27:51 on modular [Seed = 1381480234] ------------------------------------- x^3 - 7*x^2 + 5 >> Terms(P); ^ Runtime error in 'Terms': Bad argument types Argument types given: RngUPol Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee96.uab.es. (158.109.66.96) Time: Wed Mar 3 05:17:36 2004 Input: a:=5; print a; Output: Magma V2.10-6 Wed Mar 3 2004 05:17:33 on modular [Seed = 4109435942] ------------------------------------- 5 Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee103.uab.es. (158.109.66.103) Time: Wed Mar 3 06:56:27 2004 Input: repetirfrase:=procedure (frase,n) for i in {1..n} do print frase; end for; end procedure; Output: Magma V2.10-6 Wed Mar 3 2004 06:56:24 on modular [Seed = 993967267] ------------------------------------- Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee103.uab.es. (158.109.66.103) Time: Wed Mar 3 06:56:56 2004 Input: repetirfrase:=procedure (frase,n) for i in {1..n} do print frase; end for; end procedure; repetirfrase("No copiare", 3); Output: Magma V2.10-6 Wed Mar 3 2004 06:56:53 on modular [Seed = 674078813] ------------------------------------- No copiare No copiare No copiare Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee103.uab.es. (158.109.66.103) Time: Wed Mar 3 07:06:58 2004 Input: domingos:=procedure (n) for i in {1..n} do if (i % 7) eq 0 then print i; endif end for; end procedure; domingos(366); Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed. ************** MAGMA ***************** Host aula-b-siee103.uab.es. (158.109.66.103) Time: Wed Mar 3 07:08:09 2004 Input: domingos:=procedure (n) for i in {1..n} do if (i / 7) eq 0 then print i; endif end for; end procedure; domingos(366); Output: Magma V2.10-6 Wed Mar 3 2004 07:08:06 on modular [Seed = 4177359406] ------------------------------------- >> end for; ^ User error: bad syntax >> end procedure; ^ User error: bad syntax >> domingos(366);; ^ User error: Identifier 'domingos' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee103.uab.es. (158.109.66.103) Time: Wed Mar 3 07:08:32 2004 Input: domingos:=procedure (n) for i in {1..n} do if (i / 7) eq 0 then print i; endif; end for; end procedure; domingos(366); Output: Magma V2.10-6 Wed Mar 3 2004 07:08:29 on modular [Seed = 3856690984] ------------------------------------- >> end for; ^ User error: bad syntax >> end procedure; ^ User error: bad syntax >> domingos(366);; ^ User error: Identifier 'domingos' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee103.uab.es. (158.109.66.103) Time: Wed Mar 3 07:08:41 2004 Input: domingos:=procedure (n) for i in {1..n} do if (i / 7) eq 0 then print i; endif; end for; end procedure; domingos(366); Output: Magma V2.10-6 Wed Mar 3 2004 07:08:38 on modular [Seed = 4008404056] ------------------------------------- >> end for; ^ User error: bad syntax >> end procedure; ^ User error: bad syntax >> domingos(366);; ^ User error: Identifier 'domingos' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee103.uab.es. (158.109.66.103) Time: Wed Mar 3 07:09:06 2004 Input: domingos:=procedure (n) for i in {1..n} do if (i / 7) eq 0 then print i; end if; end for; end procedure; domingos(366); Output: Magma V2.10-6 Wed Mar 3 2004 07:09:03 on modular [Seed = 3638383223] ------------------------------------- Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee103.uab.es. (158.109.66.103) Time: Wed Mar 3 07:09:30 2004 Input: domingos:=procedure (n) for i in {1..n} do if (i / 7) eq 1 then print i; end if; end for; end procedure; domingos(366); Output: Magma V2.10-6 Wed Mar 3 2004 07:09:27 on modular [Seed = 3250867014] ------------------------------------- 7 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee103.uab.es. (158.109.66.103) Time: Wed Mar 3 07:09:42 2004 Input: domingos:=procedure (n) for i in {1..n} do if (i / 7) eq 2 then print i; end if; end for; end procedure; domingos(366); Output: Magma V2.10-6 Wed Mar 3 2004 07:09:39 on modular [Seed = 3402580409] ------------------------------------- 14 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee103.uab.es. (158.109.66.103) Time: Wed Mar 3 07:10:39 2004 Input: domingos:=procedure (n) for i in {1..n} do if (i / 7) eq 16 then print i; end if; end for; end procedure; domingos(366); Output: Magma V2.10-6 Wed Mar 3 2004 07:10:36 on modular [Seed = 3133092342] ------------------------------------- 112 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee103.uab.es. (158.109.66.103) Time: Wed Mar 3 07:11:06 2004 Input: domingos:=procedure (n) for i in {1..n} do if (i mod 7) eq 16 then print i; end if; end for; end procedure; domingos(366); Output: Magma V2.10-6 Wed Mar 3 2004 07:11:03 on modular [Seed = 2745575556] ------------------------------------- Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee103.uab.es. (158.109.66.103) Time: Wed Mar 3 07:11:17 2004 Input: domingos:=procedure (n) for i in {1..n} do if (i mod 7) eq 0 then print i; end if; end for; end procedure; domingos(366); Output: Magma V2.10-6 Wed Mar 3 2004 07:11:14 on modular [Seed = 2896766910] ------------------------------------- 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112 119 126 133 140 147 154 161 168 175 182 189 196 203 210 217 224 231 238 245 252 259 266 273 280 287 294 301 308 315 322 329 336 343 350 357 364 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee103.uab.es. (158.109.66.103) Time: Wed Mar 3 07:13:03 2004 Input: domingos:=procedure (n) j:=0; for i in {1..n} do if (i mod 7) eq 0 then j:=j+1; print i; end if; end for; print "la j vale : "+i; end procedure; domingos(366); Output: Magma V2.10-6 Wed Mar 3 2004 07:13:00 on modular [Seed = 2509250089] ------------------------------------- >> print "la j vale : "+i; ^ User error: Identifier 'i' has not been declared or assigned >> domingos(366);; ^ User error: Identifier 'domingos' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee103.uab.es. (158.109.66.103) Time: Wed Mar 3 07:13:14 2004 Input: domingos:=procedure (n) j:=0; for i in {1..n} do if (i mod 7) eq 0 then j:=j+1; print i; end if; end for; print "la j vale : "j; end procedure; domingos(366); Output: Magma V2.10-6 Wed Mar 3 2004 07:13:11 on modular [Seed = 2660963641] ------------------------------------- >> print "la j vale : "j; ^ User error: bad syntax >> end procedure; ^ User error: bad syntax >> domingos(366);; ^ User error: Identifier 'domingos' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee103.uab.es. (158.109.66.103) Time: Wed Mar 3 07:13:28 2004 Input: domingos:=procedure (n) j:=0; for i in {1..n} do if (i mod 7) eq 0 then j:=j+1; print i; end if; end for; print "la j vale : ";print j; end procedure; domingos(366); Output: Magma V2.10-6 Wed Mar 3 2004 07:13:25 on modular [Seed = 2273446930] ------------------------------------- 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112 119 126 133 140 147 154 161 168 175 182 189 196 203 210 217 224 231 238 245 252 259 266 273 280 287 294 301 308 315 322 329 336 343 350 357 364 la j vale : 52 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee103.uab.es. (158.109.66.103) Time: Wed Mar 3 07:19:11 2004 Input: t:={(-11)²,(-7)²,(-5)²,(-3)²,3²,5²,7²,11²}; q:={(-11)²,(-7)²,(-5)²,(-3)²,3²,5²,7²,11²}; t,q; Output: Magma V2.10-6 Wed Mar 3 2004 07:19:08 on modular [Seed = 2038232116] ------------------------------------- >> t:={(-11)^ò,(-7)^ò,(-5)^ò,(-3)^ò,3^ò,5^ò,7^ò,11^ò}; ^ User error: Unknown character (ascii value -78) >> q:={(-11)^ò,(-7)^ò,(-5)^ò,(-3)^ò,3^ò,5^ò,7^ò,11^ò}; ^ User error: Unknown character (ascii value -78) >> t,q;; ^ User error: Identifier 't' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee103.uab.es. (158.109.66.103) Time: Wed Mar 3 07:19:29 2004 Input: t:={(-11)²,(-7)²,(-5)²,(-3)²,3²,5²,7²,11²}; q:={(-11)²,(-7)²,(-5)²,(-3)²,3²,5²,7²,11²}; t; Output: Magma V2.10-6 Wed Mar 3 2004 07:19:26 on modular [Seed = 1617292639] ------------------------------------- >> t:={(-11)^ò,(-7)^ò,(-5)^ò,(-3)^ò,3^ò,5^ò,7^ò,11^ò}; ^ User error: Unknown character (ascii value -78) >> q:={(-11)^ò,(-7)^ò,(-5)^ò,(-3)^ò,3^ò,5^ò,7^ò,11^ò}; ^ User error: Unknown character (ascii value -78) >> t; ^ User error: Identifier 't' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee103.uab.es. (158.109.66.103) Time: Wed Mar 3 07:20:05 2004 Input: t:={(-11)²,(-7)²,(-5)²,(-3)²,3²,5²,7²,11²}; q:=[(-11)²,(-7)²,(-5)²,(-3)²,3²,5²,7²,11²]; t,q; Output: Magma V2.10-6 Wed Mar 3 2004 07:20:02 on modular [Seed = 1347804499] ------------------------------------- >> t:={(-11)^ò,(-7)^ò,(-5)^ò,(-3)^ò,3^ò,5^ò,7^ò,11^ò}; ^ User error: Unknown character (ascii value -78) >> q:=[(-11)^ò,(-7)^ò,(-5)^ò,(-3)^ò,3^ò,5^ò,7^ò,11^ò]; ^ User error: Unknown character (ascii value -78) >> t,q; ^ User error: Identifier 't' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee103.uab.es. (158.109.66.103) Time: Wed Mar 3 07:20:19 2004 Input: t:={(-11)²,(-7)²,(-5)²,(-3)²,3²,5²,7²,11²}; q:=[(-11)²,(-7)²,(-5)²,(-3)²,3²,5²,7²,11²]; t,q; Output: Magma V2.10-6 Wed Mar 3 2004 07:20:16 on modular [Seed = 1532941994] ------------------------------------- >> t:={(-11)^ò,(-7)^ò,(-5)^ò,(-3)^ò,3^ò,5^ò,7^ò,11^ò}; ^ User error: Unknown character (ascii value -78) >> q:=[(-11)^ò,(-7)^ò,(-5)^ò,(-3)^ò,3^ò,5^ò,7^ò,11^ò]; ^ User error: Unknown character (ascii value -78) >> t,q; ^ User error: Identifier 't' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee103.uab.es. (158.109.66.103) Time: Wed Mar 3 07:21:09 2004 Input: t:={(-11)²,(-7)²,(-5)²,(-3)²,3²,5²,7²,11²}; q:=[(-11)²,(-7)²,(-5)²,(-3)²,3²,5²,7²,11²]; t; q; Output: Magma V2.10-6 Wed Mar 3 2004 07:21:06 on modular [Seed = 1112002433] ------------------------------------- >> t:={(-11)^ò,(-7)^ò,(-5)^ò,(-3)^ò,3^ò,5^ò,7^ò,11^ò}; ^ User error: Unknown character (ascii value -78) >> q:=[(-11)^ò,(-7)^ò,(-5)^ò,(-3)^ò,3^ò,5^ò,7^ò,11^ò]; ^ User error: Unknown character (ascii value -78) >> t; ^ User error: Identifier 't' has not been declared or assigned >> q; ^ User error: Identifier 'q' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee103.uab.es. (158.109.66.103) Time: Wed Mar 3 07:21:20 2004 Input: t:={(-11)²,(-7)²,(-5)²,(-3)²,3²,5²,7²,11²}; q:=[(-11)²,(-7)²,(-5)²,(-3)²,3²,5²,7²,11²]; t; q; Output: Magma V2.10-6 Wed Mar 3 2004 07:21:17 on modular [Seed = 1296613505] ------------------------------------- >> t:={(-11)^ò,(-7)^ò,(-5)^ò,(-3)^ò,3^ò,5^ò,7^ò,11^ò}; ^ User error: Unknown character (ascii value -78) >> q:=[(-11)^ò,(-7)^ò,(-5)^ò,(-3)^ò,3^ò,5^ò,7^ò,11^ò]; ^ User error: Unknown character (ascii value -78) >> t; ^ User error: Identifier 't' has not been declared or assigned >> q; ^ User error: Identifier 'q' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee108.uab.es. (158.109.66.108) Time: Wed Mar 3 07:21:37 2004 Input: 2+2 Output: Magma V2.10-6 Wed Mar 3 2004 07:21:34 on modular [Seed = 1010413955] ------------------------------------- 4 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee103.uab.es. (158.109.66.103) Time: Wed Mar 3 07:21:41 2004 Input: t:={(-7)²,(-5)²,(-3)²,3²,5²,7²,11²}; q:=[(-7)²,(-5)²,(-3)²,3²,5²,7²,11²]; t; q; Output: Magma V2.10-6 Wed Mar 3 2004 07:21:38 on modular [Seed = 791323276] ------------------------------------- >> t:={(-7)^ò,(-5)^ò,(-3)^ò,3^ò,5^ò,7^ò,11^ò}; ^ User error: Unknown character (ascii value -78) >> q:=[(-7)^ò,(-5)^ò,(-3)^ò,3^ò,5^ò,7^ò,11^ò]; ^ User error: Unknown character (ascii value -78) >> t; ^ User error: Identifier 't' has not been declared or assigned >> q; ^ User error: Identifier 'q' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee103.uab.es. (158.109.66.103) Time: Wed Mar 3 07:22:37 2004 Input: t:={(-11)^2(-7)^2,(-5)^2,(-3)^2,3^2,5^2,7^2,11^2}; q:=[(-11)^2(-7)^2,(-5)^2,(-3)^2,3^2,5^2,7^2,11^2]; t; q; Output: Magma V2.10-6 Wed Mar 3 2004 07:22:34 on modular [Seed = 370382957] ------------------------------------- >> t:={(-11)^2(-7)^2,(-5)^2,(-3)^2,3^2,5^2,7^2,11^2}; ^ Runtime error: Bad argument types Argument types given: RngIntElt, RngIntElt >> q:=[(-11)^2(-7)^2,(-5)^2,(-3)^2,3^2,5^2,7^2,11^2]; ^ Runtime error: Bad argument types Argument types given: RngIntElt, RngIntElt >> t; ^ User error: Identifier 't' has not been declared or assigned >> q; ^ User error: Identifier 'q' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee103.uab.es. (158.109.66.103) Time: Wed Mar 3 07:22:53 2004 Input: t:={(-11)^2,(-7)^2,(-5)^2,(-3)^2,3^2,5^2,7^2,11^2}; q:=[(-11)^2,(-7)^2,(-5)^2,(-3)^2,3^2,5^2,7^2,11^2]; t,q; Output: Magma V2.10-6 Wed Mar 3 2004 07:22:50 on modular [Seed = 17076074] ------------------------------------- { 9, 25, 49, 121 } [ 121, 49, 25, 9, 9, 25, 49, 121 ] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee103.uab.es. (158.109.66.103) Time: Wed Mar 3 07:23:35 2004 Input: t:={(-11)^2,(-7)^2,(-5)^2,(-3)^2,3^2,5^2,7^2,11^2}; q:=[(-11)^2,(-7)^2,(-5)^2,(-3)^2,3^2,5^2,7^2,11^2]; t,q; q[10]:=q[5] -4*q[1]; q[2]:=1000; q; Output: Magma V2.10-6 Wed Mar 3 2004 07:23:32 on modular [Seed = 4093017542] ------------------------------------- { 9, 25, 49, 121 } [ 121, 49, 25, 9, 9, 25, 49, 121 ] [ 121, 1000, 25, 9, 9, 25, 49, 121, undef, -475 ] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee108.uab.es. (158.109.66.108) Time: Wed Mar 3 07:23:40 2004 Input: any:=360; print any; Output: Magma V2.10-6 Wed Mar 3 2004 07:23:37 on modular [Seed = 3856690141] ------------------------------------- 360 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.33.44.proxycache.rima-tde.net. (80.58.33.44) Time: Wed Mar 3 07:26:58 2004 Input: p:=Integers(39); p; Output: Magma V2.10-6 Wed Mar 3 2004 07:26:55 on modular [Seed = 3554041005] ------------------------------------- Residue class ring of integers modulo 39 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.33.44.proxycache.rima-tde.net. (80.58.33.44) Time: Wed Mar 3 07:27:19 2004 Input: p:=Integers(39); print p; Output: Magma V2.10-6 Wed Mar 3 2004 07:27:16 on modular [Seed = 3672069519] ------------------------------------- Residue class ring of integers modulo 39 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.33.44.proxycache.rima-tde.net. (80.58.33.44) Time: Wed Mar 3 07:27:32 2004 Input: p:=Integers(39); print p; Output: Magma V2.10-6 Wed Mar 3 2004 07:27:29 on modular [Seed = 3317713541] ------------------------------------- Residue class ring of integers modulo 39 Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.33.44.proxycache.rima-tde.net. (80.58.33.44) Time: Wed Mar 3 07:27:41 2004 Input: p:=Integers(39); print p; Output: Magma V2.10-6 Wed Mar 3 2004 07:27:38 on modular [Seed = 3435742087] ------------------------------------- Residue class ring of integers modulo 39 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.33.44.proxycache.rima-tde.net. (80.58.33.44) Time: Wed Mar 3 07:31:42 2004 Input: p:=GF(9); print p; Output: Magma V2.10-6 Wed Mar 3 2004 07:31:39 on modular [Seed = 3216650213] ------------------------------------- Finite field of size 3^2 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host askaig.dcs.st-and.ac.uk. (138.251.206.111) Time: Wed Mar 3 07:33:12 2004 Input: 1+1 Output: Magma V2.10-6 Wed Mar 3 2004 07:33:09 on modular [Seed = 2795714130] ------------------------------------- 2 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host andromeda.math.uni-hannover.de. (130.75.46.49) Time: Wed Mar 3 07:43:51 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Wed Mar 3 2004 07:43:48 on modular [Seed = 2256737779] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host andromeda.math.uni-hannover.de. (130.75.46.49) Time: Wed Mar 3 07:44:05 2004 Input: hecke Output: Magma V2.10-6 Wed Mar 3 2004 07:44:02 on modular [Seed = 1937170451] ------------------------------------- >> hecke ^ User error: Identifier 'hecke' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host andromeda.math.uni-hannover.de. (130.75.46.49) Time: Wed Mar 3 07:44:25 2004 Input: >hecke Output: Magma V2.10-6 Wed Mar 3 2004 07:44:22 on modular [Seed = 1617294132] ------------------------------------- >> hecke ^ User error: Identifier 'hecke' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee95.uab.es. (158.109.66.95) Time: Wed Mar 3 08:08:07 2004 Input: M:= GF (4); M22:= MatrixRing (M,2); Output: Magma V2.10-6 Wed Mar 3 2004 08:08:04 on modular [Seed = 3773134886] ------------------------------------- Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee95.uab.es. (158.109.66.95) Time: Wed Mar 3 08:17:23 2004 Input: M:= GF (4); M22:= MatrixRing (M,2); Mt:= { x : x in M22 | Trace (x) eq 0 }; Mt; Output: Magma V2.10-6 Wed Mar 3 2004 08:17:20 on modular [Seed = 3166250542] ------------------------------------- { [ 0 0] [ 0 0], [ 0 0] [M.1^2 0], [ 0 0] [ M.1 0], [ 0 0] [ 1 0], [M.1^2 0] [ 0 M.1^2], [M.1^2 0] [M.1^2 M.1^2], [M.1^2 0] [ M.1 M.1^2], [M.1^2 0] [ 1 M.1^2], [ 1 0] [ 0 1], [ 1 0] [M.1^2 1], [ 1 0] [ M.1 1], [ 1 0] [ 1 1], [ M.1 0] [ 0 M.1], [ M.1 0] [M.1^2 M.1], [ M.1 0] [ M.1 M.1], [ M.1 0] [ 1 M.1], [ 0 M.1^2] [ 0 0], [ 0 M.1^2] [M.1^2 0], [ 0 M.1^2] [ M.1 0], [ 0 M.1^2] [ 1 0], [M.1^2 M.1^2] [ 0 M.1^2], [M.1^2 M.1^2] [M.1^2 M.1^2], [M.1^2 M.1^2] [ M.1 M.1^2], [M.1^2 M.1^2] [ 1 M.1^2], [ 1 M.1^2] [ 0 1], [ 1 M.1^2] [M.1^2 1], [ 1 M.1^2] [ M.1 1], [ 1 M.1^2] [ 1 1], [ M.1 M.1^2] [ 0 M.1], [ M.1 M.1^2] [M.1^2 M.1], [ M.1 M.1^2] [ M.1 M.1], [ M.1 M.1^2] [ 1 M.1], [ 0 M.1] [ 0 0], [ 0 M.1] [M.1^2 0], [ 0 M.1] [ M.1 0], [ 0 M.1] [ 1 0], [M.1^2 M.1] [ 0 M.1^2], [M.1^2 M.1] [M.1^2 M.1^2], [M.1^2 M.1] [ M.1 M.1^2], [M.1^2 M.1] [ 1 M.1^2], [ 1 M.1] [ 0 1], [ 1 M.1] [M.1^2 1], [ 1 M.1] [ M.1 1], [ 1 M.1] [ 1 1], [ M.1 M.1] [ 0 M.1], [ M.1 M.1] [M.1^2 M.1], [ M.1 M.1] [ M.1 M.1], [ M.1 M.1] [ 1 M.1], [ 0 1] [ 0 0], [ 0 1] [M.1^2 0], [ 0 1] [ M.1 0], [ 0 1] [ 1 0], [M.1^2 1] [ 0 M.1^2], [M.1^2 1] [M.1^2 M.1^2], [M.1^2 1] [ M.1 M.1^2], [M.1^2 1] [ 1 M.1^2], [ 1 1] [ 0 1], [ 1 1] [M.1^2 1], [ 1 1] [ M.1 1], [ 1 1] [ 1 1], [ M.1 1] [ 0 M.1], [ M.1 1] [M.1^2 M.1], [ M.1 1] [ M.1 M.1], [ M.1 1] [ 1 M.1] } Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee96.uab.es. (158.109.66.96) Time: Wed Mar 3 08:27:01 2004 Input: polinomi:=function(x,y) llista:=[]; for i:= 0 to b-1 do llista:=Include(llista, x^i); end for; return llista; end function; Output: Magma V2.10-6 Wed Mar 3 2004 08:26:58 on modular [Seed = 2206605011] ------------------------------------- >> for i:= 0 to b-1 do ^ User error: Identifier 'b' has not been declared or assigned Total time: 2.859 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee96.uab.es. (158.109.66.96) Time: Wed Mar 3 08:27:12 2004 Input: polinomi:=function(x,y) llista:=[]; for i:= 0 to y-1 do llista:=Include(llista, x^i); end for; return llista; end function; Output: Magma V2.10-6 Wed Mar 3 2004 08:27:09 on modular [Seed = 2290947543] ------------------------------------- Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee96.uab.es. (158.109.66.96) Time: Wed Mar 3 08:27:33 2004 Input: polinomi:=function(x,y) llista:=[]; for i:= 0 to y-1 do llista:=Include(llista, x^i); end for; return llista; end function; polinomi(7,3); Output: Magma V2.10-6 Wed Mar 3 2004 08:27:30 on modular [Seed = 1886776641] ------------------------------------- [ 1, 7, 49 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee96.uab.es. (158.109.66.96) Time: Wed Mar 3 08:30:30 2004 Input: polinomi:=function(x,y) llista:=[]; for i:= 0 to y-1 do llista:=Include(llista, x^i); end for; return llista; end function; polinomi(7,3); P:=PolinomialRing(R); P!polinomi(7,3); Output: Magma V2.10-6 Wed Mar 3 2004 08:30:27 on modular [Seed = 1852568558] ------------------------------------- [ 1, 7, 49 ] >> P:=PolinomialRing(R); ^ User error: Identifier 'R' has not been declared or assigned >> P!polinomi(7,3);; ^ User error: Identifier 'P' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee95.uab.es. (158.109.66.95) Time: Wed Mar 3 08:33:26 2004 Input: P := PolynomialRing (343); Output: Magma V2.10-6 Wed Mar 3 2004 08:33:23 on modular [Seed = 1414646404] ------------------------------------- >> P := PolynomialRing (343);; ^ Runtime error in 'PolynomialRing': Bad argument types Argument types given: RngIntElt Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee96.uab.es. (158.109.66.96) Time: Wed Mar 3 08:35:54 2004 Input: polinomi:=function(x,y) llista:=[]; for i:= 0 to y-1 do llista:=Include(llista, x^i); end for; return llista; end function; polinomi(7,3); R:=GF(343); P:=PolinomialRing(R); P!polinomi(7,3); Output: Magma V2.10-6 Wed Mar 3 2004 08:35:51 on modular [Seed = 1161878017] ------------------------------------- [ 1, 7, 49 ] >> P:=PolinomialRing(R); ^ User error: Identifier 'PolinomialRing' has not been declared or assigned >> P!polinomi(7,3);; ^ User error: Identifier 'P' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee96.uab.es. (158.109.66.96) Time: Wed Mar 3 08:36:10 2004 Input: polinomi:=function(x,y) llista:=[]; for i:= 0 to y-1 do llista:=Include(llista, x^i); end for; return llista; end function; polinomi(7,3); R:=GF(343); P:=PolynomialRing(R); P!polinomi(7,3); Output: Magma V2.10-6 Wed Mar 3 2004 08:36:07 on modular [Seed = 1279906679] ------------------------------------- [ 1, 7, 49 ] 1 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee96.uab.es. (158.109.66.96) Time: Wed Mar 3 08:36:29 2004 Input: polinomi:=function(x,y) llista:=[]; for i:= 0 to y-1 do llista:=Include(llista, x^i); end for; return llista; end function; polinomi(7,3); R:=GF(343); P:=PolynomialRing(R); P!polinomi(7,3); P; Output: Magma V2.10-6 Wed Mar 3 2004 08:36:26 on modular [Seed = 993960978] ------------------------------------- [ 1, 7, 49 ] 1 Univariate Polynomial Ring in x over GF(7^3) Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee96.uab.es. (158.109.66.96) Time: Wed Mar 3 08:37:14 2004 Input: polinomi:=function(x,y) llista:=[]; for i:= 0 to y-1 do llista:=Include(llista, x^i); end for; return llista; end function; polinomi(7,3); R:=GF(343); P:=PolynomialRing(R); a:= P!polinomi(7,3); a; Output: Magma V2.10-6 Wed Mar 3 2004 08:37:11 on modular [Seed = 556056277] ------------------------------------- [ 1, 7, 49 ] 1 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee96.uab.es. (158.109.66.96) Time: Wed Mar 3 08:37:58 2004 Input: polinomi:=function(x,y) llista:=[]; for i:= 0 to y-1 do llista:=Include(llista, x^i); end for; return llista; end function; polinomi(7,3); R:=GF(343); P:=PolynomialRing(R); a:=P![5,0,-7,1]; /*a:= P!polinomi(7,3);*/ a; Output: Magma V2.10-6 Wed Mar 3 2004 08:37:55 on modular [Seed = 740930540] ------------------------------------- [ 1, 7, 49 ] x^3 + 5 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee95.uab.es. (158.109.66.95) Time: Wed Mar 3 08:38:57 2004 Input: R:= GF (343); P := PolynomialRing (R); Output: Magma V2.10-6 Wed Mar 3 2004 08:38:53 on modular [Seed = 421299847] ------------------------------------- Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee96.uab.es. (158.109.66.96) Time: Wed Mar 3 08:39:13 2004 Input: polinomi:=function(x,y) llista:=[]; for i:= 0 to y-1 do llista:=Include(llista, x^i); end for; return llista; end function; polinomi(7,3); R:=Integers(); P:=PolynomialRing(R); a:=P![5,0,-7,1]; /*a:= P!polinomi(7,3);*/ a; Output: Magma V2.10-6 Wed Mar 3 2004 08:39:10 on modular [Seed = 83925640] ------------------------------------- [ 1, 7, 49 ] x^3 - 7*x^2 + 5 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee96.uab.es. (158.109.66.96) Time: Wed Mar 3 08:40:43 2004 Input: polinomi:=function(x,y) llista:=[]; for i:= 0 to y-1 do llista:=Include(llista, x^i); end for; return llista; end function; polinomi(7,3); R:=GF(343); P:=PolynomialRing(R); /*a:=P![5,0,-7,1];*/ a:= P!polinomi(7,3); a; Output: Magma V2.10-6 Wed Mar 3 2004 08:40:40 on modular [Seed = 4194064850] ------------------------------------- [ 1, 7, 49 ] 1 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee96.uab.es. (158.109.66.96) Time: Wed Mar 3 08:41:00 2004 Input: polinomi:=function(x,y) llista:=[]; for i:= 0 to y-1 do llista:=Include(llista, x^i); end for; return llista; end function; polinomi(7,3); R:=GF(343); P:=PolynomialRing(R); /*a:=P![5,0,-7,1];*/ a:= P!polinomi(7,5); a; Output: Magma V2.10-6 Wed Mar 3 2004 08:40:57 on modular [Seed = 3773120762] ------------------------------------- [ 1, 7, 49 ] 1 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee96.uab.es. (158.109.66.96) Time: Wed Mar 3 08:41:10 2004 Input: polinomi:=function(x,y) llista:=[]; for i:= 0 to y-1 do llista:=Include(llista, x^i); end for; return llista; end function; polinomi(7,3); R:=GF(343); P:=PolynomialRing(R); /*a:=P![5,0,-7,1];*/ a:= P!polinomi(9,5); a; Output: Magma V2.10-6 Wed Mar 3 2004 08:41:07 on modular [Seed = 4025110511] ------------------------------------- [ 1, 7, 49 ] 2*x^4 + x^3 + 4*x^2 + 2*x + 1 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee96.uab.es. (158.109.66.96) Time: Wed Mar 3 08:41:29 2004 Input: polinomi:=function(x,y) llista:=[]; for i:= 0 to y-1 do llista:=Include(llista, x^i); end for; return llista; end function; polinomi(7,3); R:=GF(343); P:=PolynomialRing(R); /*a:=P![5,0,-7,1];*/ a:= P!polinomi(9,3); a; Output: Magma V2.10-6 Wed Mar 3 2004 08:41:26 on modular [Seed = 3587208480] ------------------------------------- [ 1, 7, 49 ] 4*x^2 + 2*x + 1 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee96.uab.es. (158.109.66.96) Time: Wed Mar 3 08:42:07 2004 Input: polinomi:=function(x,y) llista:=[]; for i:= 0 to y-1 do llista:=Include(llista, x^i); end for; return llista; end function; polinomi(7,3); R:=GF(343); P:=PolynomialRing(R); /*a:=P![5,0,-7,1];*/ a:= P!polinomi(7,3); a; Output: Magma V2.10-6 Wed Mar 3 2004 08:42:04 on modular [Seed = 3705240579] ------------------------------------- [ 1, 7, 49 ] 1 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee96.uab.es. (158.109.66.96) Time: Wed Mar 3 08:43:24 2004 Input: polinomi:=function(x,y) llista:=[]; for i:= 0 to y-1 do llista:=Include(llista, x^i); end for; return llista; end function; polinomi(7,3); R:=RealField(); P:=PolynomialRing(R); /*a:=P![5,0,-7,1];*/ a:= P!polinomi(7,3); a; Output: Magma V2.10-6 Wed Mar 3 2004 08:43:21 on modular [Seed = 2981368123] ------------------------------------- [ 1, 7, 49 ] 49*x^2 + 7*x + 1 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee95.uab.es. (158.109.66.95) Time: Wed Mar 3 08:47:38 2004 Input: a:= 3; for i:= 0 to a do a:= a +3; Output: Magma V2.10-6 Wed Mar 3 2004 08:47:35 on modular [Seed = 2778727457] ------------------------------------- User error: syntax error at end of input Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee95.uab.es. (158.109.66.95) Time: Wed Mar 3 08:47:51 2004 Input: a:= 3; for i:= 0 to a do a:= a +3; end for; Output: Magma V2.10-6 Wed Mar 3 2004 08:47:48 on modular [Seed = 2425696999] ------------------------------------- Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee95.uab.es. (158.109.66.95) Time: Wed Mar 3 08:48:00 2004 Input: a:= 3; for i:= 0 to a do a:= a +3; end for; a; Output: Magma V2.10-6 Wed Mar 3 2004 08:47:57 on modular [Seed = 2677685729] ------------------------------------- 15 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee96.uab.es. (158.109.66.96) Time: Wed Mar 3 08:48:58 2004 Input: polinomi:=function(x,y) llista:=[]; for i:= 0 to y-1 do llista:=Include(llista, x^i); end for; return llista; end function; polinomi(7,3); R:=RealField(); P:=PolynomialRing(R); /*a:=P![5,0,-7,1];*/ a:= P!polinomi(7,3); polinomin:=function(x,y) sum:=0; for i=:b-1 to 0 do sum:=sum+x^i; end for; return x^sum; end function; polinomin(7,3); Output: Magma V2.10-6 Wed Mar 3 2004 08:48:55 on modular [Seed = 2239768497] ------------------------------------- [ 1, 7, 49 ] >> for i=:b-1 to 0 do ^ User error: bad syntax >> sum:=sum+x^i; ^ User error: Identifier 'sum' has not been declared or assigned >> end for; ^ User error: bad syntax >> return x^sum; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> polinomin(7,3);; ^ User error: Identifier 'polinomin' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee95.uab.es. (158.109.66.95) Time: Wed Mar 3 08:49:27 2004 Input: polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; polinomi_t; Output: Magma V2.10-6 Wed Mar 3 2004 08:49:24 on modular [Seed = 2357800603] ------------------------------------- function(a, b) ... end function Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee95.uab.es. (158.109.66.95) Time: Wed Mar 3 08:49:40 2004 Input: polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; polinomi_t (7,3); Output: Magma V2.10-6 Wed Mar 3 2004 08:49:37 on modular [Seed = 2088361593] ------------------------------------- [ 49, 7, 1 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee96.uab.es. (158.109.66.96) Time: Wed Mar 3 08:49:47 2004 Input: polinomi:=function(x,y) llista:=[]; for i:= 0 to y-1 do llista:=Include(llista, x^i); end for; return llista; end function; polinomi(7,3); R:=RealField(); P:=PolynomialRing(R); /*a:=P![5,0,-7,1];*/ a:= P!polinomi(7,3); polinomin:=function(x,y) sum:=0; for i:=b-1 to 0 do sum:=sum+x^i; end for; return sum; end function; polinomin(7,3); Output: Magma V2.10-6 Wed Mar 3 2004 08:49:44 on modular [Seed = 1700841321] ------------------------------------- [ 1, 7, 49 ] >> for i:=b-1 to 0 do ^ User error: Identifier 'b' has not been declared or assigned >> polinomin(7,3);; ^ User error: Identifier 'polinomin' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee95.uab.es. (158.109.66.95) Time: Wed Mar 3 08:49:58 2004 Input: polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; polinomi_t (7,3); polinomi_t [1]; Output: Magma V2.10-6 Wed Mar 3 2004 08:49:55 on modular [Seed = 1852558489] ------------------------------------- [ 49, 7, 1 ] >> polinomi_t [1];; ^ Runtime error in '[]': Bad argument types Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee96.uab.es. (158.109.66.96) Time: Wed Mar 3 08:50:04 2004 Input: polinomi:=function(x,y) llista:=[]; for i:= 0 to y-1 do llista:=Include(llista, x^i); end for; return llista; end function; polinomi(7,3); R:=RealField(); P:=PolynomialRing(R); /*a:=P![5,0,-7,1];*/ a:= P!polinomi(7,3); polinomin:=function(x,y) sum:=0; for i:=y-1 to 0 do sum:=sum+x^i; end for; return sum; end function; polinomin(7,3); Output: Magma V2.10-6 Wed Mar 3 2004 08:50:01 on modular [Seed = 1583086755] ------------------------------------- [ 1, 7, 49 ] 0 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee95.uab.es. (158.109.66.95) Time: Wed Mar 3 08:50:15 2004 Input: polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; polinomi_t (7,3); expo [1]; Output: Magma V2.10-6 Wed Mar 3 2004 08:50:12 on modular [Seed = 1195566503] ------------------------------------- [ 49, 7, 1 ] >> expo [1];; ^ User error: Identifier 'expo' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee96.uab.es. (158.109.66.96) Time: Wed Mar 3 08:50:46 2004 Input: polinomi:=function(x,y) llista:=[]; for i:= 0 to y-1 do llista:=Include(llista, x^i); end for; return llista; end function; polinomi(7,3); R:=RealField(); P:=PolynomialRing(R); /*a:=P![5,0,-7,1];*/ a:= P!polinomi(7,3); polinomin:=function(x,y) sum:=0; for i:=y-1 to 0 do sum:=sum+(x^i); end for; return sum; end function; polinomin(7,3); Output: Magma V2.10-6 Wed Mar 3 2004 08:50:43 on modular [Seed = 1213065871] ------------------------------------- [ 1, 7, 49 ] 0 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee95.uab.es. (158.109.66.95) Time: Wed Mar 3 08:50:58 2004 Input: polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; print expo[1]; end function; polinomi_t (7,3); expo [1]; Output: Magma V2.10-6 Wed Mar 3 2004 08:50:55 on modular [Seed = 842502393] ------------------------------------- [ 49, 7, 1 ] >> expo [1];; ^ User error: Identifier 'expo' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee95.uab.es. (158.109.66.95) Time: Wed Mar 3 08:51:08 2004 Input: polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; print expo[1]; end function; polinomi_t (7,3); Output: Magma V2.10-6 Wed Mar 3 2004 08:51:05 on modular [Seed = 993958278] ------------------------------------- [ 49, 7, 1 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee96.uab.es. (158.109.66.96) Time: Wed Mar 3 08:51:34 2004 Input: polinomi:=function(x,y) llista:=[]; for i:= 0 to y-1 do llista:=Include(llista, x^i); end for; return llista; end function; polinomi(7,3); a:= P!polinomi(7,3); polinomin:=function(x,y) sum:=0; for i:=y-1 to 0 do sum:=sum+3; end for; return sum; end function; polinomin(7,3); Output: Magma V2.10-6 Wed Mar 3 2004 08:51:30 on modular [Seed = 740921018] ------------------------------------- [ 1, 7, 49 ] >> a:= P!polinomi(7,3); ^ User error: Identifier 'P' has not been declared or assigned 0 Total time: 3.679 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee95.uab.es. (158.109.66.95) Time: Wed Mar 3 08:51:34 2004 Input: polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; print expo[1]; return expo; end function; polinomi_t (7,3); Output: Magma V2.10-6 Wed Mar 3 2004 08:51:30 on modular [Seed = 791317945] ------------------------------------- 49 [ 49, 7, 1 ] Total time: 3.589 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee96.uab.es. (158.109.66.96) Time: Wed Mar 3 08:51:46 2004 Input: polinomi:=function(x,y) llista:=[]; for i:= 0 to y-1 do llista:=Include(llista, x^i); end for; return llista; end function; polinomi(7,3); polinomin:=function(x,y) sum:=0; for i:=y-1 to 0 do sum:=sum+3; end for; return sum; end function; polinomin(7,3); Output: Magma V2.10-6 Wed Mar 3 2004 08:51:43 on modular [Seed = 505134213] ------------------------------------- [ 1, 7, 49 ] 0 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee19.uab.es. (158.109.66.19) Time: Wed Mar 3 08:58:45 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Wed Mar 3 2004 08:58:42 on modular [Seed = 4277885464] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee19.uab.es. (158.109.66.19) Time: Wed Mar 3 08:58:47 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Wed Mar 3 2004 08:58:44 on modular [Seed = 4194065689] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host iml151.univ-mrs.fr. (139.124.6.151) Time: Wed Mar 3 08:59:47 2004 Input: polroots(X^2-2) Output: Magma V2.10-6 Wed Mar 3 2004 08:59:44 on modular [Seed = 3688791935] ------------------------------------- >> polroots(X^2-2); ^ User error: Identifier 'X' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host iml151.univ-mrs.fr. (139.124.6.151) Time: Wed Mar 3 09:00:04 2004 Input: polroots(X^2-2,X) Output: Magma V2.10-6 Wed Mar 3 2004 09:00:01 on modular [Seed = 3048214816] ------------------------------------- >> polroots(X^2-2,X); ^ User error: Identifier 'X' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host azizu.uab.es. (158.109.12.158) Time: Wed Mar 3 09:00:31 2004 Input: K:=GF(4); Output: Magma V2.10-6 Wed Mar 3 2004 09:00:28 on modular [Seed = 2728855082] ------------------------------------- Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host azizu.uab.es. (158.109.12.158) Time: Wed Mar 3 09:09:59 2004 Input: K:=GF(4); M22 := KMatrixSpace(K, 2, 2); Output: Magma V2.10-6 Wed Mar 3 2004 09:09:56 on modular [Seed = 1414656789] ------------------------------------- Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host azizu.uab.es. (158.109.12.158) Time: Wed Mar 3 09:10:12 2004 Input: K:=GF(4); M22 := KMatrixSpace(K, 2, 2); Output: Magma V2.10-6 Wed Mar 3 2004 09:10:09 on modular [Seed = 1145168752] ------------------------------------- Total time: 2.869 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host azizu.uab.es. (158.109.12.158) Time: Wed Mar 3 09:10:56 2004 Input: K:=GF(4); M22 := KMatrixSpace(K, 2, 2); K; Output: Magma V2.10-6 Wed Mar 3 2004 09:10:53 on modular [Seed = 1330309207] ------------------------------------- Finite field of size 2^2 Total time: 2.869 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host azizu.uab.es. (158.109.12.158) Time: Wed Mar 3 09:15:29 2004 Input: K:=GF(4); M22 := KMatrixSpace(K, 2, 2); K[0]; Output: Magma V2.10-6 Wed Mar 3 2004 09:15:26 on modular [Seed = 1060804404] ------------------------------------- >> K[0];; ^ Runtime error in '[]': Bad argument types Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host azizu.uab.es. (158.109.12.158) Time: Wed Mar 3 09:15:42 2004 Input: K:=GF(4); M22 := KMatrixSpace(K, 2, 2); K.elements; Output: Magma V2.10-6 Wed Mar 3 2004 09:15:39 on modular [Seed = 639864536] ------------------------------------- >> K.elements;; ^ User error: Identifier 'elements' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host azizu.uab.es. (158.109.12.158) Time: Wed Mar 3 09:15:56 2004 Input: K:=GF(4); M22 := KMatrixSpace(K, 2, 2); Elements(K); Output: Magma V2.10-6 Wed Mar 3 2004 09:15:53 on modular [Seed = 724468679] ------------------------------------- >> Elements(K);; ^ Runtime error in 'Elements': Bad argument types Argument types given: FldFin Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host azizu.uab.es. (158.109.12.158) Time: Wed Mar 3 09:17:07 2004 Input: K:=GF(4); M22 := KMatrixSpace(K, 2, 2); K.0; Output: Magma V2.10-6 Wed Mar 3 2004 09:17:04 on modular [Seed = 303544967] ------------------------------------- >> K.0;; ^ Runtime error in '.': Argument 2 (0) should be in the range [1 .. 1] Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host azizu.uab.es. (158.109.12.158) Time: Wed Mar 3 09:17:16 2004 Input: K:=GF(4); M22 := KMatrixSpace(K, 2, 2); K.1; Output: Magma V2.10-6 Wed Mar 3 2004 09:17:13 on modular [Seed = 83930521] ------------------------------------- K.1 Total time: 3.049 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host azizu.uab.es. (158.109.12.158) Time: Wed Mar 3 09:17:32 2004 Input: K:=GF(4); M22 := KMatrixSpace(K, 2, 2); K.6; Output: Magma V2.10-6 Wed Mar 3 2004 09:17:29 on modular [Seed = 201958528] ------------------------------------- >> K.6;; ^ Runtime error in '.': Argument 2 (6) should be in the range [1 .. 1] Total time: 2.889 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host azizu.uab.es. (158.109.12.158) Time: Wed Mar 3 09:17:45 2004 Input: K:=GF(4); M22 := KMatrixSpace(K, 2, 2); K.2; Output: Magma V2.10-6 Wed Mar 3 2004 09:17:42 on modular [Seed = 4143144837] ------------------------------------- >> K.2;; ^ Runtime error in '.': Argument 2 (2) should be in the range [1 .. 1] Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee86.uab.es. (158.109.66.86) Time: Wed Mar 3 09:21:08 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Wed Mar 3 2004 09:21:05 on modular [Seed = 3216643611] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee86.uab.es. (158.109.66.86) Time: Wed Mar 3 09:21:26 2004 Input: quit Output: Magma V2.10-6 Wed Mar 3 2004 09:21:23 on modular [Seed = 2795704112] ------------------------------------- Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host azizu.uab.es. (158.109.12.158) Time: Wed Mar 3 09:26:36 2004 Input: K:=GF(4); M22 := KMatrixSpace(K, 2, 2); Output: Magma V2.10-6 Wed Mar 3 2004 09:26:33 on modular [Seed = 2476095743] ------------------------------------- Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee94.uab.es. (158.109.66.94) Time: Wed Mar 3 09:43:50 2004 Input: bolean := 1; Output: Magma V2.10-6 Wed Mar 3 2004 09:43:47 on modular [Seed = 1684130609] ------------------------------------- Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee94.uab.es. (158.109.66.94) Time: Wed Mar 3 09:44:06 2004 Input: bolean := 1; Output: Magma V2.10-6 Wed Mar 3 2004 09:44:03 on modular [Seed = 1482553117] ------------------------------------- Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee94.uab.es. (158.109.66.94) Time: Wed Mar 3 09:44:33 2004 Input: bolean := 1; assigned := bolean; Output: Magma V2.10-6 Wed Mar 3 2004 09:44:30 on modular [Seed = 1095036537] ------------------------------------- >> assigned := bolean;; ^ User error: bad syntax Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee94.uab.es. (158.109.66.94) Time: Wed Mar 3 09:44:50 2004 Input: bolean := 1; assigned bolean; Output: Magma V2.10-6 Wed Mar 3 2004 09:44:47 on modular [Seed = 909351199] ------------------------------------- true Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee94.uab.es. (158.109.66.94) Time: Wed Mar 3 09:46:20 2004 Input: bolean := 1; assigned bolean; print bolean; Output: Magma V2.10-6 Wed Mar 3 2004 09:46:17 on modular [Seed = 993957108] ------------------------------------- true 1 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee94.uab.es. (158.109.66.94) Time: Wed Mar 3 09:47:01 2004 Input: bolean := 1; assigned bolean; print bolean; print "hello world"; Output: Magma V2.10-6 Wed Mar 3 2004 09:46:58 on modular [Seed = 556043957] ------------------------------------- true 1 hello world Total time: 3.129 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee94.uab.es. (158.109.66.94) Time: Wed Mar 3 09:48:25 2004 Input: bolean := 1; assigned bolean; print bolean; print "hello world"; Floor("3.16"); Output: Magma V2.10-6 Wed Mar 3 2004 09:48:22 on modular [Seed = 370386518] ------------------------------------- true 1 hello world >> Floor("3.16"); ^ Runtime error in 'Floor': Bad argument types Argument types given: MonStgElt Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee94.uab.es. (158.109.66.94) Time: Wed Mar 3 09:48:34 2004 Input: bolean := 1; assigned bolean; print bolean; print "hello world"; Floor(3.16); Output: Magma V2.10-6 Wed Mar 3 2004 09:48:30 on modular [Seed = 521842519] ------------------------------------- true 1 hello world 3 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee94.uab.es. (158.109.66.94) Time: Wed Mar 3 09:49:18 2004 Input: bolean := 1; assigned bolean; print bolean; print "hello world"; Floor(3.16); m,p := Min(2,3,4,1,3,5); Output: Magma V2.10-6 Wed Mar 3 2004 09:49:15 on modular [Seed = 83932440] ------------------------------------- true 1 hello world 3 >> m,p := Min(2,3,4,1,3,5); ^ Runtime error in 'Min': Bad argument types Argument types given: RngIntElt, RngIntElt, RngIntElt, RngIntElt, RngIntElt, RngIntElt Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee94.uab.es. (158.109.66.94) Time: Wed Mar 3 09:49:35 2004 Input: bolean := 1; assigned bolean; print bolean; print "hello world"; Floor(3.16); m,p := Min([2,3,4,1,3,5]); Output: Magma V2.10-6 Wed Mar 3 2004 09:49:32 on modular [Seed = 168802816] ------------------------------------- true 1 hello world 3 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee94.uab.es. (158.109.66.94) Time: Wed Mar 3 09:49:52 2004 Input: bolean := 1; assigned bolean; print bolean; print "hello world"; Floor(3.16); m,p := Min([2,3,4,1,3,5]); print m, p; Output: Magma V2.10-6 Wed Mar 3 2004 09:49:49 on modular [Seed = 4042604555] ------------------------------------- true 1 hello world 3 1 4 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host azizu.uab.es. (158.109.12.158) Time: Wed Mar 3 10:16:03 2004 Input: K:=GF(4); M22 := KMatrixSpace(K, 2, 2); Output: Magma V2.10-6 Wed Mar 3 2004 10:16:00 on modular [Seed = 2476090709] ------------------------------------- Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee95.uab.es. (158.109.66.95) Time: Wed Mar 3 11:16:52 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Wed Mar 3 2004 11:16:49 on modular [Seed = 4059542903] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee94.uab.es. (158.109.66.94) Time: Wed Mar 3 11:16:58 2004 Input: 2+4; Output: Magma V2.10-6 Wed Mar 3 2004 11:16:55 on modular [Seed = 4177443960] ------------------------------------- 6 Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee94.uab.es. (158.109.66.94) Time: Wed Mar 3 11:17:12 2004 Input: 2+4; Count Output: Magma V2.10-6 Wed Mar 3 2004 11:17:09 on modular [Seed = 4008225692] ------------------------------------- 6 >> Count; ^ User error: Identifier 'Count' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee95.uab.es. (158.109.66.95) Time: Wed Mar 3 11:17:23 2004 Input: Count Output: Magma V2.10-6 Wed Mar 3 2004 11:17:19 on modular [Seed = 3587412141] ------------------------------------- >> Count ^ User error: Identifier 'Count' has not been declared or assigned Total time: 3.289 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee94.uab.es. (158.109.66.94) Time: Wed Mar 3 11:17:25 2004 Input: 2+4; Count; Output: Magma V2.10-6 Wed Mar 3 2004 11:17:21 on modular [Seed = 3537147828] ------------------------------------- 6 >> Count;; ^ User error: Identifier 'Count' has not been declared or assigned Total time: 3.279 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee94.uab.es. (158.109.66.94) Time: Wed Mar 3 11:17:50 2004 Input: 2+4; Count(2+3); Output: Magma V2.10-6 Wed Mar 3 2004 11:17:47 on modular [Seed = 3284502175] ------------------------------------- 6 >> Count(2+3); ^ User error: Identifier 'Count' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee94.uab.es. (158.109.66.94) Time: Wed Mar 3 11:18:03 2004 Input: 2+4; c:=Count; Output: Magma V2.10-6 Wed Mar 3 2004 11:18:00 on modular [Seed = 3402403717] ------------------------------------- 6 >> c:=Count; ^ User error: Identifier 'Count' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee94.uab.es. (158.109.66.94) Time: Wed Mar 3 11:18:11 2004 Input: 2+4; c:=Count(); Output: Magma V2.10-6 Wed Mar 3 2004 11:18:08 on modular [Seed = 2981622918] ------------------------------------- 6 >> c:=Count(); ^ User error: Identifier 'Count' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee95.uab.es. (158.109.66.95) Time: Wed Mar 3 11:18:19 2004 Input: Count([1,2,3]); Output: Magma V2.10-6 Wed Mar 3 2004 11:18:16 on modular [Seed = 3099524487] ------------------------------------- >> Count([1,2,3]); ^ User error: Identifier 'Count' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee94.uab.es. (158.109.66.94) Time: Wed Mar 3 11:18:29 2004 Input: l:=2+4; c:=Count(l); Output: Magma V2.10-6 Wed Mar 3 2004 11:18:26 on modular [Seed = 2947148426] ------------------------------------- >> c:=Count(l); ^ User error: Identifier 'Count' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 11:48:48 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2-5); J:= ideal< R |209, (389+y)/2 >; Output: Magma V2.10-6 Wed Mar 3 2004 11:48:45 on modular [Seed = 1785472639] ------------------------------------- >> J:= ideal< R |209, (389+y)/2 >; ^ User error: Identifier 'R' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 11:49:25 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2-5); OK: MaximalOrder(K); J:= ideal< OK |209, (389+y)/2 >; Output: Magma V2.10-6 Wed Mar 3 2004 11:49:22 on modular [Seed = 1700997519] ------------------------------------- >> OK: MaximalOrder(K); ^ User error: bad syntax >> J:= ideal< OK |209, (389+y)/2 >; ^ User error: Identifier 'OK' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 11:49:38 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2-5); OK:= MaximalOrder(K); J:= ideal< OK |209, (389+y)/2 >; Output: Magma V2.10-6 Wed Mar 3 2004 11:49:35 on modular [Seed = 1364663734] ------------------------------------- Total time: 3.079 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 11:49:51 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2-5); OK:= MaximalOrder(K); J:= ideal< OK |209, (389+y)/2 >; J; Output: Magma V2.10-6 Wed Mar 3 2004 11:49:47 on modular [Seed = 1246496409] ------------------------------------- Ideal of OK Two element generators: [209, 0] [194, 1] Total time: 3.160 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 11:50:45 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2-5); OK:= MaximalOrder(K); J:= ideal< OK |209, (389+y)/2 >; J; I:= ideal; I; Output: Magma V2.10-6 Wed Mar 3 2004 11:50:42 on modular [Seed = 977041056] ------------------------------------- Ideal of OK Two element generators: [209, 0] [194, 1] Ideal of OK Two element generators: [5, 0] [1, 2] Total time: 3.099 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 11:53:32 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2-5); OK:= MaximalOrder(K); J:= ideal< OK |209, (389+y)/2 >; J; I:= ideal; I; b:=ChineseRemainderTheorem(I,J, OK!y, OK!(1-y); Output: Magma V2.10-6 Wed Mar 3 2004 11:53:29 on modular [Seed = 875723205] ------------------------------------- Ideal of OK Two element generators: [209, 0] [194, 1] Ideal of OK Two element generators: [5, 0] [1, 2] >> b:=ChineseRemainderTheorem(I,J, OK!y, OK!(1-y); ^ User error: bad syntax Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 11:54:22 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2-5); OK:= MaximalOrder(K); J:= ideal< OK |209, (389+y)/2 >; J; I:= ideal; I; b:=ChineseRemainderTheorem(I, J, OK!y, OK!(1-y)); Output: Magma V2.10-6 Wed Mar 3 2004 11:54:19 on modular [Seed = 774398957] ------------------------------------- Ideal of OK Two element generators: [209, 0] [194, 1] Ideal of OK Two element generators: [5, 0] [1, 2] Total time: 2.989 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 11:55:02 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2-5); OK:= MaximalOrder(K); J:= ideal< OK |209, (389+y)/2 >; J; I:= ideal; I; b:=ChineseRemainderTheorem(I, J, OK!y, OK!(1-y)); b-y in I; b-(1-y) in J; Output: Magma V2.10-6 Wed Mar 3 2004 11:54:59 on modular [Seed = 404641155] ------------------------------------- Ideal of OK Two element generators: [209, 0] [194, 1] Ideal of OK Two element generators: [5, 0] [1, 2] true true Total time: 3.019 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 11:55:19 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2-5); OK:= MaximalOrder(K); J:= ideal< OK |209, (389+y)/2 >; J; I:= ideal; I; b:=ChineseRemainderTheorem(I, J, OK!y, OK!(1-y)); b-y in I; b-(1-y) in J; K!b; Output: Magma V2.10-6 Wed Mar 3 2004 11:55:16 on modular [Seed = 353589401] ------------------------------------- Ideal of OK Two element generators: [209, 0] [194, 1] Ideal of OK Two element generators: [5, 0] [1, 2] true true -28 Total time: 2.979 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 12:09:12 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2-5); OK:= MaximalOrder(K); J:= ideal< OK |209, (389+y)/2 >; J; I:= ideal; I; I':=OK/I; J':=OK/J; M:=DirectSum(I',J'); M; Output: Magma V2.10-6 Wed Mar 3 2004 12:09:09 on modular [Seed = 3890329258] ------------------------------------- Ideal of OK Two element generators: [209, 0] [194, 1] Ideal of OK Two element generators: [5, 0] [1, 2] >> I':=OK/I; ^ User error: Unexpected newline in literal identifier >> J':=OK/J; ^ User error: Unexpected newline in literal identifier >> M:=DirectSum(I',J'); ^ User error: bad syntax >> M; ^ User error: Identifier 'M' has not been declared or assigned Total time: 3.029 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host gate373.ent.ohiou.edu. (132.235.16.203) Time: Wed Mar 3 12:47:57 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Wed Mar 3 2004 12:47:54 on modular [Seed = 2526071972] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host gate373.ent.ohiou.edu. (132.235.16.203) Time: Wed Mar 3 12:48:14 2004 Input: 11100010101 Output: Magma V2.10-6 Wed Mar 3 2004 12:48:10 on modular [Seed = 2408175021] ------------------------------------- 11100010101 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host gate373.ent.ohiou.edu. (132.235.16.203) Time: Wed Mar 3 12:52:28 2004 Input: EuclideanDistance(1011,0101) : ModTupRngElt, ModTupRngElt -> RngIntElt Output: Magma V2.10-6 Wed Mar 3 2004 12:52:25 on modular [Seed = 1937057875] ------------------------------------- >> EuclideanDistance(1011,0101) : ModTupRngElt, ModTupRngElt -> RngIntElt ^ User error: bad syntax Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host gate373.ent.ohiou.edu. (132.235.16.203) Time: Wed Mar 3 13:31:09 2004 Input: EuclideanDistance(1011,0101) : Output: Magma V2.10-6 Wed Mar 3 2004 13:31:06 on modular [Seed = 269906947] ------------------------------------- >> ; ^ User error: bad syntax Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host gate373.ent.ohiou.edu. (132.235.16.203) Time: Wed Mar 3 13:31:25 2004 Input: EuclideanDistance(1011,0101) : Output: Magma V2.10-6 Wed Mar 3 2004 13:31:22 on modular [Seed = 185429768] ------------------------------------- >> ; ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host gate373.ent.ohiou.edu. (132.235.16.203) Time: Wed Mar 3 13:34:38 2004 Input: CodeFld_Coordinates (H107E12) Output: Magma V2.10-6 Wed Mar 3 2004 13:34:35 on modular [Seed = 100688708] ------------------------------------- >> CodeFld_Coordinates (H107E12) ^ User error: Identifier 'H107E12' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host gate373.ent.ohiou.edu. (132.235.16.203) Time: Wed Mar 3 13:42:12 2004 Input: >x:=2 >y:=x+2 >x,y Output: Magma V2.10-6 Wed Mar 3 2004 13:42:09 on modular [Seed = 3991636629] ------------------------------------- >> y:=x+2 ^ User error: bad syntax >> x,y; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host gate373.ent.ohiou.edu. (132.235.16.203) Time: Wed Mar 3 13:42:51 2004 Input: >x :=2; >y :=x+2; >x, y; Output: Magma V2.10-6 Wed Mar 3 2004 13:42:48 on modular [Seed = 3840050101] ------------------------------------- 2 4 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 13:51:51 2004 Input: repetirfrase := procedure (frase,n) for i in {1..n} do print frase; end for; end procedure; repetirfrase("hola Lorena",4); Output: Magma V2.10-6 Wed Mar 3 2004 13:51:48 on modular [Seed = 3469256691] ------------------------------------- hola Lorena hola Lorena hola Lorena hola Lorena Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host gate373.ent.ohiou.edu. (132.235.16.203) Time: Wed Mar 3 13:53:49 2004 Input: >u :=[1 2 0 3]; >v :=[0 3 1 2]; >EuclideanDistance(u,v); Output: Magma V2.10-6 Wed Mar 3 2004 13:53:46 on modular [Seed = 3099513211] ------------------------------------- >> u :=[1 2 0 3]; ^ User error: bad syntax >> v :=[0 3 1 2]; ^ User error: bad syntax >> EuclideanDistance(u,v); ^ User error: Identifier 'u' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host gate373.ent.ohiou.edu. (132.235.16.203) Time: Wed Mar 3 13:54:24 2004 Input: >u :=[1 0 0 1]; >v :=[0 1 1 0]; >EuclideanDistance(u,v); Output: Magma V2.10-6 Wed Mar 3 2004 13:54:21 on modular [Seed = 2998197014] ------------------------------------- >> u :=[1 0 0 1]; ^ User error: bad syntax >> v :=[0 1 1 0]; ^ User error: bad syntax >> EuclideanDistance(u,v); ^ User error: Identifier 'u' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 13:56:15 2004 Input: repetirfrase := procedure (frase,n) for i in {1..n} do print frase; end for; end procedure; repetirfrase("hola Lorena",4); Integers(); Output: Magma V2.10-6 Wed Mar 3 2004 13:56:12 on modular [Seed = 2712128404] ------------------------------------- hola Lorena hola Lorena hola Lorena hola Lorena Integer Ring Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 13:57:32 2004 Input: f := map < Integers() -> Integers() | x:-> 2*x >; f(5); Output: Magma V2.10-6 Wed Mar 3 2004 13:57:29 on modular [Seed = 2610819451] ------------------------------------- 10 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 13:57:46 2004 Input: f := map < Integers() -> Integers() | x:-> 2*x >; f(5); f([1,2,3]); Output: Magma V2.10-6 Wed Mar 3 2004 13:57:43 on modular [Seed = 2459236428] ------------------------------------- 10 [ 2, 4, 6 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 13:58:21 2004 Input: f := map < Integers() -> Integers() | x:-> 2*x >; f(5); f[1,2,3]; Output: Magma V2.10-6 Wed Mar 3 2004 13:58:18 on modular [Seed = 2374756158] ------------------------------------- 10 >> f[1,2,3];; ^ Runtime error in '[]': Bad argument types Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 13:58:57 2004 Input: f := map < Integers() -> Integers() | x:-> 2*x >; f(5); f[1,2,3]; r := [1,2,3]; r(0); r(1); Output: Magma V2.10-6 Wed Mar 3 2004 13:58:54 on modular [Seed = 2273438992] ------------------------------------- 10 >> f[1,2,3]; ^ Runtime error in '[]': Bad argument types >> r(0); ^ Runtime error: Bad argument types Argument types given: RngIntElt, SeqEnum[RngIntElt] >> r(1);; ^ Runtime error: Bad argument types Argument types given: RngIntElt, SeqEnum[RngIntElt] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 13:59:07 2004 Input: r := [1,2,3]; r(0); r(1); Output: Magma V2.10-6 Wed Mar 3 2004 13:59:04 on modular [Seed = 2105219071] ------------------------------------- >> r(0); ^ Runtime error: Bad argument types Argument types given: RngIntElt, SeqEnum[RngIntElt] >> r(1);; ^ Runtime error: Bad argument types Argument types given: RngIntElt, SeqEnum[RngIntElt] Total time: 3.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host gate373.ent.ohiou.edu. (132.235.16.203) Time: Wed Mar 3 13:59:10 2004 Input: >u :=[1 0 0 1]; >v :=[0 1 1 0]; >EuclideanDistance(u,v); >C := ReedMullerCodeZ4(1, 3); >C; Output: Magma V2.10-6 Wed Mar 3 2004 13:59:07 on modular [Seed = 1886788337] ------------------------------------- >> u :=[1 0 0 1]; ^ User error: bad syntax >> v :=[0 1 1 0]; ^ User error: bad syntax >> EuclideanDistance(u,v); ^ User error: Identifier 'u' has not been declared or assigned (8, 256, 4) Linear Code over IntegerRing(4) Generator matrix: [1 0 0 0 3 1 2 1] [0 1 0 0 2 1 1 3] [0 0 1 0 1 1 3 2] [0 0 0 1 3 2 3 3] Total time: 3.059 seconds, Total memory usage: 3.34MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 13:59:17 2004 Input: r := [1,2,3]; r(1); Output: Magma V2.10-6 Wed Mar 3 2004 13:59:14 on modular [Seed = 1667565595] ------------------------------------- >> r(1);; ^ Runtime error: Bad argument types Argument types given: RngIntElt, SeqEnum[RngIntElt] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 13:59:29 2004 Input: r := [1,2,3]; r[1]; Output: Magma V2.10-6 Wed Mar 3 2004 13:59:26 on modular [Seed = 1482568492] ------------------------------------- 1 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 14:01:52 2004 Input: r := [1,2,3]; r[1]; XGCD(2,3); Output: Magma V2.10-6 Wed Mar 3 2004 14:01:49 on modular [Seed = 925981904] ------------------------------------- 1 1 -1 1 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Wed Mar 3 14:02:53 2004 Input: polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; Output: Magma V2.10-6 Wed Mar 3 2004 14:02:50 on modular [Seed = 757810829] ------------------------------------- Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Wed Mar 3 14:03:15 2004 Input: polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; expo; Output: Magma V2.10-6 Wed Mar 3 2004 14:03:12 on modular [Seed = 438071696] ------------------------------------- >> expo;; ^ User error: Identifier 'expo' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Wed Mar 3 14:03:55 2004 Input: polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; polinomi_t (7,3); Output: Magma V2.10-6 Wed Mar 3 2004 14:03:52 on modular [Seed = 320175985] ------------------------------------- [ 49, 7, 1 ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 14:04:03 2004 Input: r := [1,2,3]; r[1]; XGCD(2,3); IsPrimePower(81); Output: Magma V2.10-6 Wed Mar 3 2004 14:04:00 on modular [Seed = 152003923] ------------------------------------- 1 1 -1 1 true 3 4 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 14:04:28 2004 Input: r := [1,2,3]; r[1]; XGCD(2,3); IsPrimePower(16); Output: Magma V2.10-6 Wed Mar 3 2004 14:04:25 on modular [Seed = 100690501] ------------------------------------- 1 1 -1 1 true 2 4 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 14:04:46 2004 Input: r := [1,2,3]; r[1]; XGCD(2,3); IsPrimePower(9); Output: Magma V2.10-6 Wed Mar 3 2004 14:04:43 on modular [Seed = 4294546382] ------------------------------------- 1 1 -1 1 true 3 2 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 14:05:05 2004 Input: r := [1,2,3]; r[1]; XGCD(2,3); IsPrimePower(121); Output: Magma V2.10-6 Wed Mar 3 2004 14:05:02 on modular [Seed = 3907945676] ------------------------------------- 1 1 -1 1 true 11 2 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 14:06:05 2004 Input: r := [1,2,3]; r[1]; XGCD(2,3); IsPrimePower(121); Integers(5); Output: Magma V2.10-6 Wed Mar 3 2004 14:06:02 on modular [Seed = 3873475078] ------------------------------------- 1 1 -1 1 true 11 2 Residue class ring of integers modulo 5 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 14:06:29 2004 Input: r := [1,2,3]; r[1]; XGCD(2,3); IsPrimePower(121); Integers(5); 5! Output: Magma V2.10-6 Wed Mar 3 2004 14:06:26 on modular [Seed = 3755586327] ------------------------------------- 1 1 -1 1 true 11 2 Residue class ring of integers modulo 5 >> 5!; ^ User error: bad syntax Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 14:06:33 2004 Input: r := [1,2,3]; r[1]; XGCD(2,3); IsPrimePower(121); Integers(5); 5!; Output: Magma V2.10-6 Wed Mar 3 2004 14:06:30 on modular [Seed = 3620846363] ------------------------------------- 1 1 -1 1 true 11 2 Residue class ring of integers modulo 5 >> 5!;; ^ User error: bad syntax Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 14:06:45 2004 Input: r := [1,2,3]; r[1]; XGCD(2,3); IsPrimePower(121); Integers(5)!; 5!; Output: Magma V2.10-6 Wed Mar 3 2004 14:06:42 on modular [Seed = 3435831412] ------------------------------------- 1 1 -1 1 true 11 2 >> Integers(5)!; ^ User error: bad syntax >> 5!;; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 14:09:45 2004 Input: r := [1,2,3]; r[1]; XGCD(2,3); IsPrimePower(121); Integers(5)! 3; Output: Magma V2.10-6 Wed Mar 3 2004 14:09:42 on modular [Seed = 3149780663] ------------------------------------- 1 1 -1 1 true 11 2 3 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 14:09:57 2004 Input: r := [1,2,3]; r[1]; XGCD(2,3); IsPrimePower(121); Integers(5)! 5; Output: Magma V2.10-6 Wed Mar 3 2004 14:09:54 on modular [Seed = 2964774216] ------------------------------------- 1 1 -1 1 true 11 2 0 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 14:10:07 2004 Input: r := [1,2,3]; r[1]; XGCD(2,3); IsPrimePower(121); Integers(5)! 6; Output: Magma V2.10-6 Wed Mar 3 2004 14:10:04 on modular [Seed = 2695286102] ------------------------------------- 1 1 -1 1 true 11 2 1 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Wed Mar 3 14:10:48 2004 Input: polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; main := function (a,b) exponent:= polinomi_t (a,b); pol_t := polinomi_t2 (exponent); polt_n := polinomi_n (exponent); return exponent; end function; Output: Magma V2.10-6 Wed Mar 3 2004 14:10:45 on modular [Seed = 2577396822] ------------------------------------- >> pol_t := polinomi_t2 (exponent); ^ User error: Identifier 'polinomi_t2' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Wed Mar 3 14:11:47 2004 Input: polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; R:= Integers (); P := PolynomialRing (R); polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; Output: Magma V2.10-6 Wed Mar 3 2004 14:11:44 on modular [Seed = 2542926365] ------------------------------------- Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 14:11:56 2004 Input: r := [1,2,3]; r[1]; XGCD(2,3); IsPrimePower(121); Integers(5)! 6; PrimitiveRoot(5); Output: Magma V2.10-6 Wed Mar 3 2004 14:11:53 on modular [Seed = 2357911823] ------------------------------------- 1 1 -1 1 true 11 2 1 2 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Wed Mar 3 14:12:01 2004 Input: polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; main := function (a,b) exponent:= polinomi_t (a,b); pol_t := polinomi_t2 (exponent); polt_n := polinomi_n (exponent); return exponent; end function; R:= Integers (); P := PolynomialRing (R); polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; Output: Magma V2.10-6 Wed Mar 3 2004 14:11:58 on modular [Seed = 2240014337] ------------------------------------- >> pol_t := polinomi_t2 (exponent); ^ User error: Identifier 'polinomi_t2' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 14:12:11 2004 Input: PrimitiveRoot(5); Output: Magma V2.10-6 Wed Mar 3 2004 14:12:08 on modular [Seed = 1937054976] ------------------------------------- 2 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 14:12:20 2004 Input: PrimitiveRoot(3); Output: Magma V2.10-6 Wed Mar 3 2004 14:12:17 on modular [Seed = 1785463808] ------------------------------------- 2 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 14:12:30 2004 Input: PrimitiveRoot(1); Output: Magma V2.10-6 Wed Mar 3 2004 14:12:27 on modular [Seed = 1717569542] ------------------------------------- >> PrimitiveRoot(1); ^ Runtime error in 'PrimitiveRoot': Argument 1 (1) should be >= 2 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Wed Mar 3 14:12:34 2004 Input: R:= Integers (); P := PolynomialRing (R); polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; Output: Magma V2.10-6 Wed Mar 3 2004 14:12:31 on modular [Seed = 1582837818] ------------------------------------- Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 14:12:42 2004 Input: PrimitiveRoot(2); Output: Magma V2.10-6 Wed Mar 3 2004 14:12:39 on modular [Seed = 1414674952] ------------------------------------- 1 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Wed Mar 3 14:12:55 2004 Input: R:= Integers (); P := PolynomialRing (R); polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; Output: Magma V2.10-6 Wed Mar 3 2004 14:12:52 on modular [Seed = 1128606988] ------------------------------------- Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host gate373.ent.ohiou.edu. (132.235.16.203) Time: Wed Mar 3 14:13:03 2004 Input: >u :=[1 0 0 1]; >v :=[0 1 1 0]; >EuclideanDistance(u,v); >C := ReedMullerCodeZ4(1, 3); >C; >v :=[0 1 1 0]; >a :=EuclideanWeight(v); >a; Output: Magma V2.10-6 Wed Mar 3 2004 14:13:00 on modular [Seed = 977032317] ------------------------------------- >> u :=[1 0 0 1]; ^ User error: bad syntax >> v :=[0 1 1 0]; ^ User error: bad syntax >> EuclideanDistance(u,v); ^ User error: Identifier 'u' has not been declared or assigned (8, 256, 4) Linear Code over IntegerRing(4) Generator matrix: [1 0 0 0 3 1 2 1] [0 1 0 0 2 1 1 3] [0 0 1 0 1 1 3 2] [0 0 0 1 3 2 3 3] >> v :=[0 1 1 0]; ^ User error: bad syntax >> a :=EuclideanWeight(v); ^ User error: Identifier 'v' has not been declared or assigned >> a; ^ User error: Identifier 'a' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 3.34MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Wed Mar 3 14:13:15 2004 Input: R:= Integers (); P := PolynomialRing (R); polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; main := function (a,b) exponent:= polinomi_t (a,b); pol_t := polinomi_t2 (exponent); polt_n := polinomi_n (exponent); return exponent; end function; Output: Magma V2.10-6 Wed Mar 3 2004 14:13:12 on modular [Seed = 825712386] ------------------------------------- Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Wed Mar 3 14:13:55 2004 Input: R:= Integers (); P := PolynomialRing (R); polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; main := function (a,b) exponent:= polinomi_t (a,b); pol_t := polinomi_t2 (exponent); polt_n := polinomi_n (exponent); return exponent; return pol_t; end function; Output: Magma V2.10-6 Wed Mar 3 2004 14:13:52 on modular [Seed = 791232804] ------------------------------------- Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 14:14:22 2004 Input: PrimitiveRoot(2); PrimitiveElement(1); Output: Magma V2.10-6 Wed Mar 3 2004 14:14:19 on modular [Seed = 639650006] ------------------------------------- 1 >> PrimitiveElement(1); ^ Runtime error in 'PrimitiveElement': Bad argument types Argument types given: RngIntElt Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Wed Mar 3 14:15:11 2004 Input: R:= Integers (); P := PolynomialRing (R); polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; main := function (a,b) exponent:= polinomi_t (a,b); print exponent; pol_t := polinomi_t2 (exponent); print pol_t; pol_n := polinomi_n (exponent); print pol_n; end function; main (7,3); Output: Magma V2.10-6 Wed Mar 3 2004 14:15:08 on modular [Seed = 269909719] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x x^57 >> main (7,3); ^ Runtime error in procedure call: No return statement executed in user-defined function Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Wed Mar 3 14:15:44 2004 Input: R:= Integers (); P := PolynomialRing (R); polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; main := function (a,b) exponent:= polinomi_t (a,b); print exponent; pol_t := polinomi_t2 (exponent); print pol_t; pol_n := polinomi_n (exponent); print pol_n; return 0; end function; main (7,3); Output: Magma V2.10-6 Wed Mar 3 2004 14:15:41 on modular [Seed = 252273065] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x x^57 0 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 14:16:32 2004 Input: PrimitiveRoot(2); PrimitiveElement(1); Order(3,Integers(5)!2); Output: Magma V2.10-6 Wed Mar 3 2004 14:16:29 on modular [Seed = 67267442] ------------------------------------- 1 >> PrimitiveElement(1); ^ Runtime error in 'PrimitiveElement': Bad argument types Argument types given: RngIntElt >> Order(3,Integers(5)!2); ^ Runtime error in 'Order': Bad argument types Argument types given: RngIntElt, RngIntResElt Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Wed Mar 3 14:16:35 2004 Input: R:= Integers (); P := PolynomialRing (R); polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; main := function (a,b) exponent:= polinomi_t (a,b); print exponent; pol_t := polinomi_t2 (exponent); print pol_t; pol_n := polinomi_n (exponent); print pol_n; return 0; end function; main (7,3); PuntsOlav := { (a,b) : a in GF (7,3) , b in GF (7,3) | Evaluate (c,a) eq Evaluate (d,b)}; Output: Magma V2.10-6 Wed Mar 3 2004 14:16:32 on modular [Seed = 4194277010] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x x^57 0 >> PuntsOlav := { (a,b) : a in GF (7,3) , b in GF (7,3) | Evaluate (c,a) ^ User error: Identifier 'c' has not been declared or assigned Total time: 3.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 14:16:44 2004 Input: PrimitiveRoot(2); Order(3,Integers(5)!2); Output: Magma V2.10-6 Wed Mar 3 2004 14:16:41 on modular [Seed = 3941369224] ------------------------------------- 1 >> Order(3,Integers(5)!2); ^ Runtime error in 'Order': Bad argument types Argument types given: RngIntElt, RngIntResElt Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Wed Mar 3 14:17:02 2004 Input: R:= Integers (); P := PolynomialRing (R); polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; main := function (a,b) exponent:= polinomi_t (a,b); print exponent; pol_t := polinomi_t2 (exponent); print pol_t; pol_n := polinomi_n (exponent); print pol_n; return 0; end function; main (7,3); PuntsOlav := { (a,b) : a in GF (7,3) , b in GF (7,3) | Evaluate (pol_t,a) eq Evaluate (pol_n,b)}; Output: Magma V2.10-6 Wed Mar 3 2004 14:16:59 on modular [Seed = 3790048945] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x x^57 0 >> PuntsOlav := { (a,b) : a in GF (7,3) , b in GF (7,3) | Evaluate (pol_t,a) ^ User error: Identifier 'pol_t' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 14:17:07 2004 Input: PrimitiveRoot(2); Order(3,(Integers(5)!2)); Output: Magma V2.10-6 Wed Mar 3 2004 14:17:04 on modular [Seed = 3655317138] ------------------------------------- 1 >> Order(3,(Integers(5)!2)); ^ Runtime error in 'Order': Bad argument types Argument types given: RngIntElt, RngIntResElt Total time: 2.859 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 14:17:20 2004 Input: PrimitiveRoot(2); Order(3,(Integers(5) ! 2)); Output: Magma V2.10-6 Wed Mar 3 2004 14:17:17 on modular [Seed = 3620845713] ------------------------------------- 1 >> Order(3,(Integers(5) ! 2)); ^ Runtime error in 'Order': Bad argument types Argument types given: RngIntElt, RngIntResElt Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 14:18:51 2004 Input: PrimitiveRoot(2); Z5 := Integers(5); Order(3,(Z5 ! 2)); Output: Magma V2.10-6 Wed Mar 3 2004 14:18:48 on modular [Seed = 3452674606] ------------------------------------- 1 >> Order(3,(Z5 ! 2)); ^ Runtime error in 'Order': Bad argument types Argument types given: RngIntElt, RngIntResElt Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 14:19:08 2004 Input: PrimitiveRoot(2); Z5 := Integers(5) !2; Order(3,Z5); Output: Magma V2.10-6 Wed Mar 3 2004 14:19:05 on modular [Seed = 3149780073] ------------------------------------- 1 >> Order(3,Z5); ^ Runtime error in 'Order': Bad argument types Argument types given: RngIntElt, RngIntResElt Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 14:20:24 2004 Input: PrimitiveRoot(2); Z5 := Integers(5) !2; Z5; Output: Magma V2.10-6 Wed Mar 3 2004 14:20:21 on modular [Seed = 2880291877] ------------------------------------- 1 2 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 14:20:44 2004 Input: Z5 := Integers(5) !2; Z5; Output: Magma V2.10-6 Wed Mar 3 2004 14:20:41 on modular [Seed = 2712130003] ------------------------------------- 2 Total time: 3.149 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 14:20:47 2004 Input: Z5 := Integers(5); Z5; Output: Magma V2.10-6 Wed Mar 3 2004 14:20:44 on modular [Seed = 2795558609] ------------------------------------- Residue class ring of integers modulo 5 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 14:21:10 2004 Input: Z5 := Integers(5); [y: y in Z5]; Output: Magma V2.10-6 Wed Mar 3 2004 14:21:07 on modular [Seed = 2425807048] ------------------------------------- [ 0, 1, 2, 3, 4 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee43.uab.es. (158.109.66.43) Time: Wed Mar 3 14:32:43 2004 Input: lexp:=[7^r:r in [2..0 by -1]]; Output: Magma V2.10-6 Wed Mar 3 2004 14:32:40 on modular [Seed = 1634145221] ------------------------------------- Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee43.uab.es. (158.109.66.43) Time: Wed Mar 3 14:32:56 2004 Input: [7^r:r in [2..0 by -1]]; Output: Magma V2.10-6 Wed Mar 3 2004 14:32:52 on modular [Seed = 1515989186] ------------------------------------- [ 49, 7, 1 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Wed Mar 3 14:33:19 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^4-34*x^2+9); E:=EquationOrder(K); OK:=MaximalOrder(K); Index(OK, E); [K!OK.i : i in [1, 2]]; Output: Magma V2.10-6 Wed Mar 3 2004 14:33:16 on modular [Seed = 1398088147] ------------------------------------- 24 [ 1, a ] Total time: 2.979 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Wed Mar 3 14:33:32 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^4-34*x^2+9); E:=EquationOrder(K); OK:=MaximalOrder(K); Index(OK, E); [K!OK.i : i in [1, 2, 3, 4]]; Output: Magma V2.10-6 Wed Mar 3 2004 14:33:29 on modular [Seed = 1145190193] ------------------------------------- 24 [ 1, a, 1/2*(a^2 + 1), 1/12*(a^3 + 3*a^2 + 11*a + 9) ] Total time: 3.019 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Wed Mar 3 14:34:24 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^4-34*x^2+9); E:=EquationOrder(K); OK:=MaximalOrder(K); I;=3*OK; J:=2*OK; Index(OK, E); Factorization(I); Factorization(J); [K!OK.i : i in [1, 2, 3, 4]]; Output: Magma V2.10-6 Wed Mar 3 2004 14:34:20 on modular [Seed = 1043877246] ------------------------------------- >> I;=3*OK; ^ User error: Identifier 'I' has not been declared or assigned >> I;=3*OK; ^ User error: bad syntax 24 >> Factorization(I); ^ User error: Identifier 'I' has not been declared or assigned [ ] [ 1, a, 1/2*(a^2 + 1), 1/12*(a^3 + 3*a^2 + 11*a + 9) ] Total time: 3.349 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host aula-a-siee43.uab.es. (158.109.66.43) Time: Wed Mar 3 14:34:25 2004 Input: lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:= x^r; Output: Magma V2.10-6 Wed Mar 3 2004 14:34:22 on modular [Seed = 960449147] ------------------------------------- >> t:=&+[x^r:r in lexp]; ^ User error: Identifier 'x' has not been declared or assigned >> n:= x^r;; ^ User error: Identifier 'x' has not been declared or assigned Total time: 3.239 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Wed Mar 3 14:34:35 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^4-34*x^2+9); E:=EquationOrder(K); OK:=MaximalOrder(K); I:=3*OK; J:=2*OK; Index(OK, E); Factorization(I); Factorization(J); [K!OK.i : i in [1, 2, 3, 4]]; Output: Magma V2.10-6 Wed Mar 3 2004 14:34:32 on modular [Seed = 674126620] ------------------------------------- 24 [ , , , ] [ ] [ 1, a, 1/2*(a^2 + 1), 1/12*(a^3 + 3*a^2 + 11*a + 9) ] Total time: 3.109 seconds, Total memory usage: 2.05MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 14:34:48 2004 Input: Z5 := Integers(5); [y: y in Z5]; IsInvertible(Z5!1); Output: Magma V2.10-6 Wed Mar 3 2004 14:34:45 on modular [Seed = 556225032] ------------------------------------- [ 0, 1, 2, 3, 4 ] true 1 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee43.uab.es. (158.109.66.43) Time: Wed Mar 3 14:35:56 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:= x^r; Output: Magma V2.10-6 Wed Mar 3 2004 14:35:53 on modular [Seed = 387015922] ------------------------------------- >> n:= x^r;; ^ User error: Identifier 'r' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee43.uab.es. (158.109.66.43) Time: Wed Mar 3 14:36:06 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:= x^sn; Output: Magma V2.10-6 Wed Mar 3 2004 14:36:03 on modular [Seed = 135166935] ------------------------------------- Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Wed Mar 3 14:36:10 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^4-34*x^2+9); E:=EquationOrder(K); OK:=MaximalOrder(K); I:=3*OK; J:=2*OK; Index(OK, E); Factorization(I); Factorization(J); [K!OK.i : i in [1, 2, 3, 4]]; Output: Magma V2.10-6 Wed Mar 3 2004 14:36:07 on modular [Seed = 17265370] ------------------------------------- 24 [ , , , ] [ ] [ 1, a, 1/2*(a^2 + 1), 1/12*(a^3 + 3*a^2 + 11*a + 9) ] Total time: 3.169 seconds, Total memory usage: 2.05MB ************** MAGMA ***************** Host aula-a-siee43.uab.es. (158.109.66.43) Time: Wed Mar 3 14:36:19 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; &+[x^r:r in lexp]; sn:=&+[r:r in lexp]; x^sn; Output: Magma V2.10-6 Wed Mar 3 2004 14:36:16 on modular [Seed = 4210854198] ------------------------------------- x^49 + x^7 + x x^57 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee43.uab.es. (158.109.66.43) Time: Wed Mar 3 14:39:31 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^r:r in [(r-1)..0 by -1]]>; func1(7,3); Output: Magma V2.10-6 Wed Mar 3 2004 14:39:28 on modular [Seed = 3991640545] ------------------------------------- [
:9]( q: 7, r: 3 ) >> func1:= func < q,r | [q^r:r in [(r-1)..0 by -1]]>; ^ Runtime error: Variable 'r' has not been initialized Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee43.uab.es. (158.109.66.43) Time: Wed Mar 3 14:39:54 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; func1(7,3); Output: Magma V2.10-6 Wed Mar 3 2004 14:39:51 on modular [Seed = 3873477149] ------------------------------------- [ 49, 7, 1 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee43.uab.es. (158.109.66.43) Time: Wed Mar 3 14:41:53 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= func :=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; &+[x^e:e in lexp];>; tfunc2(7,3); Output: Magma V2.10-6 Wed Mar 3 2004 14:41:50 on modular [Seed = 3620840277] ------------------------------------- >> s:=GF(7^3); ^ User error: bad syntax >> lexp:=[q^p:p in [(r-1)..0 by -1]]; ^ User error: Identifier 'r' has not been declared or assigned x^49 + x^7 + x >> &+[x^e:e in lexp];>; ^ User error: bad syntax >> tfunc2(7,3);; ^ User error: Identifier 'tfunc2' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee43.uab.es. (158.109.66.43) Time: Wed Mar 3 14:42:10 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= func :=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; &+[x^e:e in lexp];>; tfunc2(7,3); Output: Magma V2.10-6 Wed Mar 3 2004 14:42:07 on modular [Seed = 3368992187] ------------------------------------- >> s:=GF(q^r); ^ User error: bad syntax >> lexp:=[q^p:p in [(r-1)..0 by -1]]; ^ User error: Identifier 'r' has not been declared or assigned x^49 + x^7 + x >> &+[x^e:e in lexp];>; ^ User error: bad syntax >> tfunc2(7,3);; ^ User error: Identifier 'tfunc2' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee43.uab.es. (158.109.66.43) Time: Wed Mar 3 14:43:55 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; tfunc2(7,3); Output: Magma V2.10-6 Wed Mar 3 2004 14:43:52 on modular [Seed = 3251090629] ------------------------------------- x^49 + x^7 + x Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 14:45:35 2004 Input: Z5 := Integers(5); [y: y in Z5]; IsInvertible(Z5!1); Order(2,11); Output: Magma V2.10-6 Wed Mar 3 2004 14:45:31 on modular [Seed = 2896877835] ------------------------------------- [ 0, 1, 2, 3, 4 ] true 1 10 Total time: 3.669 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee43.uab.es. (158.109.66.43) Time: Wed Mar 3 14:45:35 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn;; end function; tfunc2(7,3); nfunc2(7,3); Output: Magma V2.10-6 Wed Mar 3 2004 14:45:31 on modular [Seed = 2998191893] ------------------------------------- x^49 + x^7 + x x^57 Total time: 3.759 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee43.uab.es. (158.109.66.43) Time: Wed Mar 3 14:45:45 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; tfunc2(7,3); nfunc2(7,3); Output: Magma V2.10-6 Wed Mar 3 2004 14:45:42 on modular [Seed = 2745554489] ------------------------------------- x^49 + x^7 + x x^57 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 14:47:08 2004 Input: Z41 := Integers(41); Z41 ! 6; Order(Z41 ! 6); Output: Magma V2.10-6 Wed Mar 3 2004 14:47:05 on modular [Seed = 2492654289] ------------------------------------- 6 40 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 14:47:45 2004 Input: Z41 := Integers(41); Z41 ! 6; Order(Z41 ! 6); Order(6); Output: Magma V2.10-6 Wed Mar 3 2004 14:47:42 on modular [Seed = 2391341228] ------------------------------------- 6 40 >> Order(6);; ^ Runtime error in 'Order': Bad argument types Argument types given: RngIntElt Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee43.uab.es. (158.109.66.43) Time: Wed Mar 3 14:48:46 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; olavfunc3:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; n:= x^sn; t:= &+[x^e:e in lexp]; return {<{a,b}>: a,b in s | Evaluate(t,b) eq Evaluate(n,a)}; end function; olavfunc3(7,3); Output: Magma V2.10-6 Wed Mar 3 2004 14:48:41 on modular [Seed = 2273440098] ------------------------------------- { <{ s.1^246, s.1^306 }>, <{ s.1^323, s.1^118 }>, <{ s.1^29, s.1^63 }>, <{ s.1, s.1^134 }>, <{ s.1^62, s.1^84 }>, <{ s.1^71, s.1^296 }>, <{ s.1^199, s.1^160 }>, <{ s.1^154, s.1^43 }>, <{ s.1^39, s.1^317 }>, <{ s.1^283, s.1^53 }>, <{ s.1^297, s.1^157 }>, <{ s.1^176, s.1^113 }>, <{ 4, s.1^65 }>, <{ s.1^191, s.1^30 }>, <{ s.1^58, s.1^119 }>, <{ s.1^212, s.1^32 }>, <{ s.1^275, s.1^176 }>, <{ s.1^212, s.1^139 }>, <{ s.1^213, s.1^317 }>, <{ s.1^124, s.1^153 }>, <{ s.1^100, s.1^84 }>, <{ s.1^55, s.1^157 }>, <{ s.1^132, s.1^24 }>, <{ s.1^159, s.1^261 }>, <{ s.1^323, s.1^334 }>, <{ s.1^259, s.1^216 }>, <{ s.1^66, s.1^120 }>, <{ s.1^275, 4 }>, <{ s.1^324, s.1^193 }>, <{ s.1^168, s.1^15 }>, <{ s.1^313, s.1^21 }>, <{ s.1^220, s.1^27 }>, <{ s.1^189, s.1^37 }>, <{ s.1^288, s.1^159 }>, <{ s.1^287, s.1^197 }>, <{ 3, s.1^69 }>, <{ s.1^143, s.1^27 }>, <{ s.1^309, s.1^69 }>, <{ s.1^56, s.1^93 }>, <{ s.1^118, s.1^263 }>, <{ s.1^310, s.1^174 }>, <{ s.1^132, s.1^222 }>, <{ s.1^157, s.1^247 }>, <{ s.1^229, s.1^274 }>, <{ s.1^239, s.1^76 }>, <{ s.1^198, s.1^208 }>, <{ s.1^232, s.1^153 }>, <{ s.1^238, s.1^274 }>, <{ s.1^302, s.1^5 }>, <{ s.1^189, s.1^85 }>, <{ s.1^71, s.1^20 }>, <{ s.1^47, s.1^104 }>, <{ s.1^36, s.1^14 }>, <{ s.1^341, s.1^9 }>, <{ s.1^47, s.1^26 }>, <{ 0, s.1^56 }>, <{ s.1^268, s.1^85 }>, <{ s.1^166, s.1^32 }>, <{ s.1^7, s.1^272 }>, <{ s.1^39, s.1^326 }>, <{ s.1^282, s.1^329 }>, <{ s.1^268, s.1^75 }>, <{ 2, s.1^103 }>, <{ s.1^177, s.1^79 }>, <{ s.1^36, s.1^235 }>, <{ s.1^220, s.1^277 }>, <{ s.1^176, s.1^260 }>, <{ s.1^199, s.1^71 }>, <{ s.1^148, s.1^84 }>, <{ s.1^156, s.1^10 }>, <{ s.1^53, s.1^296 }>, <{ 2, s.1^97 }>, <{ s.1^60, s.1^338 }>, <{ s.1^126, s.1^304 }>, <{ s.1^331, s.1^310 }>, <{ s.1^223, s.1^147 }>, <{ s.1^112, s.1^150 }>, <{ s.1^233, s.1^257 }>, <{ s.1^319, s.1^22 }>, <{ s.1^178, s.1^224 }>, <{ s.1^160, s.1^193 }>, <{ s.1^129, s.1^274 }>, <{ s.1^320, s.1^184 }>, <{ s.1^299, s.1^255 }>, <{ s.1^143, s.1^309 }>, <{ s.1^299, s.1^335 }>, <{ s.1^276, s.1 }>, <{ s.1^324, s.1^10 }>, <{ s.1^212, s.1^50 }>, <{ s.1^299, s.1^329 }>, <{ s.1^68, s.1^19 }>, <{ s.1^145, s.1^189 }>, <{ s.1^11, s.1^24 }>, <{ s.1^259, s.1^316 }>, <{ s.1^104, s.1^226 }>, <{ 6, s.1^64 }>, <{ s.1^293, 4 }>, <{ s.1^149, s.1^10 }>, <{ s.1^122, s.1^226 }>, <{ s.1^91, s.1^27 }>, <{ s.1^280, s.1^229 }>, <{ s.1^8, s.1^329 }>, <{ s.1^25, s.1^127 }>, <{ s.1^341, s.1^89 }>, <{ s.1^52, s.1^340 }>, <{ s.1^242, s.1^246 }>, <{ s.1^256, s.1^205 }>, <{ s.1^227, s.1^41 }>, <{ s.1^301, s.1^197 }>, <{ s.1^176, s.1^262 }>, <{ s.1^297, s.1^274 }>, <{ s.1^39, s.1^98 }>, <{ s.1^268, s.1^17 }>, <{ s.1^167, s.1^218 }>, <{ s.1^180, s.1^260 }>, <{ s.1^332, s.1^201 }>, <{ s.1^293, s.1^63 }>, <{ s.1^53, s.1^218 }>, <{ s.1^88, s.1^277 }>, <{ s.1^6, s.1^340 }>, <{ s.1^89, s.1^323 }>, <{ s.1^328, s.1^274 }>, <{ s.1^146, s.1^162 }>, <{ s.1^256, s.1^181 }>, <{ s.1^44, s.1^45 }>, <{ s.1^254, s.1^61 }>, <{ s.1^19, s.1^53 }>, <{ s.1^160, s.1^163 }>, <{ s.1^103, s.1^252 }>, <{ s.1^309, s.1^218 }>, <{ s.1^335, s.1^218 }>, <{ s.1^103, s.1^162 }>, <{ s.1^234, s.1^248 }>, <{ s.1^12, s.1^50 }>, <{ s.1^335, s.1^118 }>, <{ s.1^218, s.1^273 }>, <{ s.1^38, s.1^31 }>, <{ s.1^224, s.1^328 }>, <{ s.1^6, s.1^238 }>, <{ s.1^4, 5 }>, <{ s.1^235, s.1^290 }>, <{ s.1^266, s.1^86 }>, <{ s.1^27, s.1^150 }>, <{ s.1^313, s.1^128 }>, <{ s.1^231, s.1^197 }>, <{ s.1^321, s.1^291 }>, <{ s.1^14, s.1^306 }>, <{ s.1^224, s.1^204 }>, <{ s.1^286, s.1^5 }>, <{ s.1^304, s.1^326 }>, <{ s.1^327, s.1^196 }>, <{ s.1^286, s.1^287 }>, <{ s.1^44, s.1^313 }>, <{ s.1^91, s.1^203 }>, <{ s.1^227, s.1^75 }>, <{ s.1^25, s.1^213 }>, <{ s.1^174, s.1^263 }>, <{ s.1^22, s.1^295 }>, <{ s.1^286, s.1^53 }>, <{ s.1^146, s.1^329 }>, <{ s.1^308, s.1^79 }>, <{ s.1^157, s.1^37 }>, <{ s.1^11, s.1^286 }>, <{ s.1^108, s.1^339 }>, <{ s.1^238, s.1^153 }>, <{ s.1^77, s.1^84 }>, <{ s.1^100, s.1^156 }>, <{ s.1^9, s.1^65 }>, <{ s.1^188, s.1^157 }>, <{ s.1^309, s.1^194 }>, <{ s.1^13, s.1^107 }>, <{ s.1^210, s.1^257 }>, <{ s.1^249, s.1^261 }>, <{ s.1^83, s.1^75 }>, <{ s.1^266, s.1^211 }>, <{ s.1^134, s.1^181 }>, <{ s.1^157, s.1^64 }>, <{ s.1^130, s.1^318 }>, <{ s.1^234, s.1^314 }>, <{ s.1^130, s.1^174 }>, <{ s.1^211, s.1^338 }>, <{ s.1^314, s.1^251 }>, <{ s.1^101, s.1^218 }>, <{ s.1^202, s.1^5 }>, <{ s.1^140, s.1^262 }>, <{ 1, s.1^133 }>, <{ s.1^311, s.1^43 }>, <{ s.1^253, s.1^274 }>, <{ s.1^94, s.1^315 }>, <{ s.1^299, s.1^191 }>, <{ s.1^83, s.1^41 }>, <{ s.1^116, s.1^251 }>, <{ s.1^26, s.1^139 }>, <{ s.1^58, s.1^109 }>, <{ s.1^103, s.1^73 }>, <{ s.1^266, s.1^204 }>, <{ s.1^308, s.1^313 }>, <{ s.1^155, s.1^20 }>, <{ s.1^282, s.1^197 }>, <{ s.1^89, s.1^75 }>, <{ s.1^193, s.1^274 }>, <{ s.1^291, s.1^62 }>, <{ s.1^81, s.1^269 }>, <{ s.1^12, s.1^7 }>, <{ s.1^162, s.1^10 }>, <{ s.1^122, s.1^125 }>, <{ s.1^232, s.1^126 }>, <{ s.1^290, s.1^184 }>, <{ s.1^124, s.1^98 }>, <{ s.1^222, s.1^288 }>, <{ s.1^104, s.1^60 }>, <{ s.1^26, s.1^86 }>, <{ s.1^335, s.1^30 }>, <{ s.1^176, s.1^101 }>, <{ s.1^148, s.1^193 }>, <{ s.1^288, s.1^215 }>, <{ s.1, s.1^82 }>, <{ s.1^293, s.1^142 }>, <{ s.1^12, s.1^215 }>, <{ s.1^144, s.1^312 }>, <{ s.1^176, s.1^109 }>, <{ s.1, s.1^120 }>, <{ s.1^28, s.1^149 }>, <{ s.1^234, s.1^197 }>, <{ s.1^211, s.1^216 }>, <{ s.1^260, s.1^151 }>, <{ s.1^146, s.1^306 }>, <{ s.1^6, s.1^307 }>, <{ s.1^67, s.1^94 }>, <{ s.1^275, s.1^120 }>, <{ s.1^101, s.1^52 }>, <{ s.1^189, s.1^115 }>, <{ s.1^245, s.1^38 }>, <{ s.1^132 }>, <{ s.1^66, s.1^25 }>, <{ s.1^311, s.1^50 }>, <{ s.1^227, s.1^74 }>, <{ s.1^128, s.1^338 }>, <{ s.1^204, 5 }>, <{ s.1^99, s.1^196 }>, <{ s.1^254, 3 }>, <{ s.1^340, s.1^32 }>, <{ s.1^198, s.1^328 }>, <{ s.1^125, s.1^314 }>, <{ s.1^35, s.1^248 }>, <{ s.1^215, s.1^318 }>, <{ s.1^154, s.1^101 }>, <{ s.1^13, s.1^113 }>, <{ s.1^151, s.1^98 }>, <{ s.1^56, s.1^35 }>, <{ s.1^213, s.1^150 }>, <{ s.1^187, 3 }>, <{ s.1^257, s.1^329 }>, <{ s.1^77, s.1^30 }>, <{ s.1^216, s.1^339 }>, <{ s.1^80, s.1^65 }>, <{ s.1^117, s.1^317 }>, <{ s.1^58, s.1^239 }>, <{ s.1^277, s.1^27 }>, <{ s.1^67, s.1^301 }>, <{ s.1^141, s.1^87 }>, <{ s.1^165, s.1^302 }>, <{ s.1^331, s.1^216 }>, <{ s.1^146, s.1^174 }>, <{ s.1^136, s.1^261 }>, <{ s.1^293, s.1^41 }>, <{ s.1^5, s.1^142 }>, <{ s.1^88, s.1^243 }>, <{ s.1^331, s.1^82 }>, <{ s.1^313, s.1^54 }>, <{ s.1^191, s.1^75 }>, <{ s.1^341, s.1^210 }>, <{ s.1^314, s.1^96 }>, <{ s.1^79, s.1^326 }>, <{ s.1^79, s.1^216 }>, <{ s.1^220, s.1^239 }>, <{ s.1^13, s.1^169 }>, <{ s.1^297, s.1^265 }>, <{ s.1^257, s.1^158 }>, <{ s.1^200, s.1^40 }>, <{ s.1^132, 4 }>, <{ s.1^212, s.1^246 }>, <{ s.1^280, s.1^29 }>, <{ s.1^132, s.1^98 }>, <{ s.1^55, s.1^35 }>, <{ s.1^66, s.1^103 }>, <{ s.1^73, s.1^85 }>, <{ s.1^115, s.1^128 }>, <{ s.1^17, s.1^249 }>, <{ s.1^253, s.1^252 }>, <{ s.1^237, s.1^274 }>, <{ s.1^14, s.1^125 }>, <{ s.1^138, s.1^305 }>, <{ 1, 5 }>, <{ s.1^299, s.1^80 }>, <{ s.1^80, s.1^31 }>, <{ s.1^46, s.1^203 }>, <{ s.1^34, s.1^229 }>, <{ s.1^137, s.1^281 }>, <{ s.1^190, s.1^192 }>, <{ s.1^169, s.1^205 }>, <{ s.1^220, s.1^325 }>, <{ s.1^288, s.1^234 }>, <{ s.1^161, s.1^296 }>, <{ s.1^99, s.1^227 }>, <{ s.1^70, s.1^326 }>, <{ s.1^220, s.1^17 }>, <{ s.1^78, s.1^116 }>, <{ s.1^188, s.1^217 }>, <{ s.1^341, s.1^264 }>, <{ s.1^232, s.1^97 }>, <{ s.1^176, s.1^115 }>, <{ s.1^165, s.1^283 }>, <{ s.1^60, s.1^148 }>, <{ s.1^274, s.1^340 }>, <{ s.1^225, s.1^141 }>, <{ s.1^301, s.1^83 }>, <{ s.1^265, s.1^214 }>, <{ s.1^93, s.1^32 }>, <{ s.1^2, s.1^212 }>, <{ s.1^81, s.1^52 }>, <{ s.1^209, s.1^250 }>, <{ s.1^3, s.1^73 }>, <{ s.1^16, s.1^238 }>, <{ 3, s.1^38 }>, <{ s.1^87, s.1^208 }>, <{ s.1^155, s.1^75 }>, <{ s.1^262, s.1^229 }>, <{ s.1^69, s.1^183 }>, <{ s.1^99, s.1^251 }>, <{ s.1^124, s.1^224 }>, <{ s.1^256, s.1^43 }>, <{ s.1^332, s.1^91 }>, <{ s.1^69, s.1^104 }>, <{ s.1^121, s.1^58 }>, <{ s.1^303, s.1^195 }>, <{ s.1^325, s.1^52 }>, <{ s.1^238, s.1^196 }>, <{ s.1^214, s.1^61 }>, <{ s.1^23, s.1^256 }>, <{ s.1^253, s.1^280 }>, <{ s.1^231, s.1^24 }>, <{ s.1^91, s.1^106 }>, <{ s.1^165, s.1^269 }>, <{ s.1^78, s.1^267 }>, <{ s.1^299, s.1^245 }>, <{ 1, s.1^259 }>, <{ s.1^201, s.1^98 }>, <{ s.1^149, s.1^296 }>, <{ s.1^77, s.1^296 }>, <{ s.1^48, s.1^131 }>, <{ s.1^264, s.1^2 }>, <{ s.1^56, s.1^111 }>, <{ s.1^210, s.1^120 }>, <{ s.1^335, s.1^41 }>, <{ s.1^118, s.1^229 }>, <{ s.1^315, s.1^118 }>, <{ s.1^211, s.1^50 }>, <{ s.1^13, s.1^269 }>, <{ s.1^127, s.1^252 }>, <{ s.1^68, s.1^181 }>, <{ s.1^16, s.1^207 }>, <{ s.1^16, s.1^108 }>, <{ s.1^265, s.1^340 }>, <{ s.1^198, s.1^244 }>, <{ s.1^22, s.1^229 }>, ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host aula-a-siee43.uab.es. (158.109.66.43) Time: Wed Mar 3 14:50:11 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; olavfunc3:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; n:= x^sn; t:= &+[x^e:e in lexp]; return {<{a,b}>: a,b in s | Evaluate(t,b) eq Evaluate(n,a)}; end function; j := olavfunc3(7,3); #j; Output: Magma V2.10-6 Wed Mar 3 2004 14:50:07 on modular [Seed = 1903626211] ------------------------------------- 15603 Total time: 4.329 seconds, Total memory usage: 6.90MB ************** MAGMA ***************** Host aula-a-siee43.uab.es. (158.109.66.43) Time: Wed Mar 3 14:50:41 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; olavfunc3:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; n:= x^sn; t:= &+[x^e:e in lexp]; return {<{a,b}>: a,b in s | Evaluate(t,b) eq Evaluate(n,a)}; end function; j := olavfunc3(7,3); #j; 7^((2*r)-1); Output: Magma V2.10-6 Wed Mar 3 2004 14:50:37 on modular [Seed = 1802312731] ------------------------------------- 15603 >> 7^((2*r)-1); ^ User error: Identifier 'r' has not been declared or assigned Total time: 4.369 seconds, Total memory usage: 6.90MB ************** MAGMA ***************** Host aula-a-siee43.uab.es. (158.109.66.43) Time: Wed Mar 3 14:50:53 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; olavfunc3:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; n:= x^sn; t:= &+[x^e:e in lexp]; return {<{a,b}>: a,b in s | Evaluate(t,b) eq Evaluate(n,a)}; end function; j := olavfunc3(7,3); #j; 7^((2*3)-1); Output: Magma V2.10-6 Wed Mar 3 2004 14:50:48 on modular [Seed = 1650726151] ------------------------------------- 15603 16807 Total time: 4.399 seconds, Total memory usage: 6.90MB ************** MAGMA ***************** Host aula-a-siee43.uab.es. (158.109.66.43) Time: Wed Mar 3 14:51:22 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; olavfunc3:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; n:= x^sn; t:= &+[x^e:e in lexp]; return {<{a,b}>: a,b in s | Evaluate(t,b) eq Evaluate(n,a)}; end function; j := {olavfunc3(7,3)}; #j; 7^((2*3)-1); Output: Magma V2.10-6 Wed Mar 3 2004 14:51:18 on modular [Seed = 1431511582] ------------------------------------- 1 16807 Total time: 4.279 seconds, Total memory usage: 6.90MB ************** MAGMA ***************** Host aula-a-siee43.uab.es. (158.109.66.43) Time: Wed Mar 3 14:51:34 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; olavfunc3:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; n:= x^sn; t:= &+[x^e:e in lexp]; return {<{a,b}>: a,b in s | Evaluate(t,b) eq Evaluate(n,a)}; end function; j := olavfunc3(7,3); #j; 7^((2*3)-1); Output: Magma V2.10-6 Wed Mar 3 2004 14:51:30 on modular [Seed = 1279933299] ------------------------------------- 15603 16807 Total time: 4.319 seconds, Total memory usage: 6.90MB ************** MAGMA ***************** Host aula-a-siee43.uab.es. (158.109.66.43) Time: Wed Mar 3 14:51:51 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; olavfunc3:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; n:= x^sn; t:= &+[x^e:e in lexp]; return {<{a,b}>: a,b in s | Evaluate(t,b) eq Evaluate(n,a)}; end function; j := olavfunc3(7,3); #j; 7^(5); Output: Magma V2.10-6 Wed Mar 3 2004 14:51:47 on modular [Seed = 1195454569] ------------------------------------- 15603 16807 Total time: 4.269 seconds, Total memory usage: 6.90MB ************** MAGMA ***************** Host aula-a-siee43.uab.es. (158.109.66.43) Time: Wed Mar 3 14:52:06 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; olavfunc3:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; n:= x^sn; t:= &+[x^e:e in lexp]; return {<{a,b}>: a,b in s | Evaluate(t,b) eq Evaluate(n,a)}; end function; j := olavfunc3(7,3); #j; 7^(4); Output: Magma V2.10-6 Wed Mar 3 2004 14:52:01 on modular [Seed = 1043876130] ------------------------------------- 15603 2401 Total time: 4.359 seconds, Total memory usage: 6.90MB ************** MAGMA ***************** Host aula-a-siee43.uab.es. (158.109.66.43) Time: Wed Mar 3 14:52:16 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; olavfunc3:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; n:= x^sn; t:= &+[x^e:e in lexp]; return {<{a,b}>: a,b in s | Evaluate(t,b) eq Evaluate(n,a)}; end function; j := olavfunc3(7,3); #j; 7^(5); Output: Magma V2.10-6 Wed Mar 3 2004 14:52:12 on modular [Seed = 825706016] ------------------------------------- 15603 16807 Total time: 4.339 seconds, Total memory usage: 6.90MB ************** MAGMA ***************** Host aula-a-siee43.uab.es. (158.109.66.43) Time: Wed Mar 3 14:52:33 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; olavfunc3:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; n:= x^sn; t:= &+[x^e:e in lexp]; return {<(a,b)>: a,b in s | Evaluate(t,b) eq Evaluate(n,a)}; end function; j := olavfunc3(7,3); #j; 7^(5); Output: Magma V2.10-6 Wed Mar 3 2004 14:52:30 on modular [Seed = 674127659] ------------------------------------- [
:23]( q: 7, r: 3 ) >> return {<(a,b)>: a,b in s | Evaluate(t,b) eq Evaluate(n,a)}; ^ Runtime error in elt< ... >: Bad arguments >> #j; ^ User error: Identifier 'j' has not been declared or assigned 16807 Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee43.uab.es. (158.109.66.43) Time: Wed Mar 3 14:53:36 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; olavfunc3:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; n:= x^sn; t:= &+[x^e:e in lexp]; return {a : a,b in s | Evaluate(t,b) eq Evaluate(n,a)}; end function; j := olavfunc3(7,3); #j; 7^(5); Output: Magma V2.10-6 Wed Mar 3 2004 14:53:32 on modular [Seed = 572806627] ------------------------------------- 343 16807 Total time: 4.169 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee43.uab.es. (158.109.66.43) Time: Wed Mar 3 14:54:16 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; olavfunc3:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; n:= x^sn; t:= &+[x^e:e in lexp]; return {a,b : a,b in s | Evaluate(t,b) eq Evaluate(n,a)}; end function; j := olavfunc3(7,3); #j; 7^(5); Output: Magma V2.10-6 Wed Mar 3 2004 14:54:13 on modular [Seed = 336749452] ------------------------------------- >> return {a,b : a,b in s | Evaluate(t,b) eq Evaluate(n,a)}; ^ User error: bad syntax >> end function; ^ User error: bad syntax >> j := olavfunc3(7,3); ^ User error: Identifier 'olavfunc3' has not been declared or assigned >> #j; ^ User error: Identifier 'j' has not been declared or assigned 16807 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee43.uab.es. (158.109.66.43) Time: Wed Mar 3 14:54:35 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; olavfunc3:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; n:= x^sn; t:= &+[x^e:e in lexp]; return {[a,b] : a,b in s | Evaluate(t,b) eq Evaluate(n,a)}; end function; j := olavfunc3(7,3); #j; 7^(5); Output: Magma V2.10-6 Wed Mar 3 2004 14:54:30 on modular [Seed = 185433216] ------------------------------------- 16807 16807 Total time: 4.359 seconds, Total memory usage: 5.38MB ************** MAGMA ***************** Host aula-a-siee43.uab.es. (158.109.66.43) Time: Wed Mar 3 14:54:55 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; olavfunc3:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; n:= x^sn; t:= &+[x^e:e in lexp]; return {[a,b] : a,b in s | Evaluate(t,b) eq Evaluate(n,a)}; end function; j := olavfunc3(7,3); #j; 7^(5); Output: Magma V2.10-6 Wed Mar 3 2004 14:54:51 on modular [Seed = 33847924] ------------------------------------- 16807 16807 Total time: 4.359 seconds, Total memory usage: 5.38MB ************** MAGMA ***************** Host aula-a-siee43.uab.es. (158.109.66.43) Time: Wed Mar 3 14:55:30 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; olavfunc3:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; n:= x^sn; t:= &+[x^e:e in lexp]; return {[a,b] : a,b in s | Evaluate(t,b) eq Evaluate(n,a)}; end function; j := olavfunc3(7,3); #j; 7^(5); jj := olavfunc3(6,2); #jj; 6^(3); Output: Magma V2.10-6 Wed Mar 3 2004 14:55:25 on modular [Seed = 4059531681] ------------------------------------- 16807 16807 [
:23]( q: 6, r: 2 ) >> s:=GF(q^r); ^ Runtime error in 'GF': Argument 1 (36) is not a prime power >> #jj; ^ User error: Identifier 'jj' has not been declared or assigned 216 Total time: 4.429 seconds, Total memory usage: 5.38MB ************** MAGMA ***************** Host aula-a-siee43.uab.es. (158.109.66.43) Time: Wed Mar 3 14:56:01 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; olavfunc3:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; n:= x^sn; t:= &+[x^e:e in lexp]; return {[a,b] : a,b in s | Evaluate(t,b) eq Evaluate(n,a)}; end function; j := olavfunc3(7,3); #j; 7^(5); jj := olavfunc3(5,2); #jj; 5^(3); Output: Magma V2.10-6 Wed Mar 3 2004 14:55:57 on modular [Seed = 3907948760] ------------------------------------- 16807 16807 125 125 Total time: 4.389 seconds, Total memory usage: 5.38MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 15:11:57 2004 Input: Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK:=MaximalOrder(K); Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed. ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 15:12:07 2004 Input: Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK:=MaximalOrder(K); Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed. ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 15:12:27 2004 Input: Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK:=MaximalOrder(K); Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed. ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 15:12:40 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK:=MaximalOrder(K); Output: Magma V2.10-6 Wed Mar 3 2004 15:12:37 on modular [Seed = 2644238805] ------------------------------------- Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 15:14:37 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK:=MaximalOrder(K); J:= .5*(29-a)*OK; Output: Magma V2.10-6 Wed Mar 3 2004 15:14:34 on modular [Seed = 2526079553] ------------------------------------- >> J:= .5*(29-a)*OK;; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 15:15:10 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK:=MaximalOrder(K); J:=a*OK; Output: Magma V2.10-6 Wed Mar 3 2004 15:15:07 on modular [Seed = 2240018739] ------------------------------------- Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 15:15:37 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK:=MaximalOrder(K); J:=(.5*(29-a))*OK; Output: Magma V2.10-6 Wed Mar 3 2004 15:15:34 on modular [Seed = 2138637287] ------------------------------------- >> J:=(.5*(29-a))*OK;; ^ User error: bad syntax Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 15:15:59 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK:=MaximalOrder(K); J:=((29-a)/2)*OK; Output: Magma V2.10-6 Wed Mar 3 2004 15:15:56 on modular [Seed = 1920208624] ------------------------------------- Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 15:16:09 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK:=MaximalOrder(K); J:=((29-a)/2)*OK; J; Output: Magma V2.10-6 Wed Mar 3 2004 15:16:06 on modular [Seed = 1802311187] ------------------------------------- Principal Ideal of OK Generator: [15, -1] Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 15:20:49 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK:=MaximalOrder(K); J:=((29-a)/2)*OK; #quo; Output: Magma V2.10-6 Wed Mar 3 2004 15:20:46 on modular [Seed = 1448093750] ------------------------------------- 209 Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 15:25:20 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK:=MaximalOrder(K); J:=((29-a)/2)*OK; #quo; J1:=ideal> J1:=ideal> J1;; ^ User error: Identifier 'J1' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 15:25:32 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK:=MaximalOrder(K); J:=((29-a)/2)*OK; #quo; J1:=ideal; J1; Output: Magma V2.10-6 Wed Mar 3 2004 15:25:29 on modular [Seed = 977028477] ------------------------------------- 209 >> J1:=ideal; ^ User error: bad syntax >> J1;; ^ User error: Identifier 'J1' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 15:26:17 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK:=MaximalOrder(K); J:=((29-a)/2)*OK; #quo; J1:=ideal; J1; Output: Magma V2.10-6 Wed Mar 3 2004 15:26:14 on modular [Seed = 859130923] ------------------------------------- 209 >> J1:=ideal; ^ User error: bad syntax >> J1;; ^ User error: Identifier 'J1' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 15:28:02 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK:=MaximalOrder(K); J:=((29-a)/2)*OK; #quo; J1:=ideal; J1; Output: Magma V2.10-6 Wed Mar 3 2004 15:27:59 on modular [Seed = 690968216] ------------------------------------- 209 >> J1:=ideal; ^ User error: bad syntax >> J1;; ^ User error: Identifier 'J1' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 15:29:05 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK:=MaximalOrder(K); J:=((29-a)/2)*OK; #quo; J1:=ideal; J1; Output: Magma V2.10-6 Wed Mar 3 2004 15:29:02 on modular [Seed = 521740143] ------------------------------------- 209 Principal Ideal of OK Generator: [209, 0] Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 15:29:40 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK:=MaximalOrder(K); J:=((29-a)/2)*OK; #quo; J1:=ideal; J1; Output: Magma V2.10-6 Wed Mar 3 2004 15:29:37 on modular [Seed = 353572186] ------------------------------------- 209 Ideal of OK Two element generators: [209, 0] [194, 1] Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 15:29:53 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK:=MaximalOrder(K); J:=((29-a)/2)*OK; J; #quo; J1:=ideal; J1; Output: Magma V2.10-6 Wed Mar 3 2004 15:29:50 on modular [Seed = 168561226] ------------------------------------- Principal Ideal of OK Generator: [15, -1] 209 Ideal of OK Two element generators: [209, 0] [194, 1] Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 15:31:44 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK:=MaximalOrder(K); Basis(OK); J:=((29-a)/2)*OK; J; #quo; J1:=ideal; J1; Output: Magma V2.10-6 Wed Mar 3 2004 15:31:41 on modular [Seed = 4210883113] ------------------------------------- [ OK.1, OK.2 ] Principal Ideal of OK Generator: [15, -1] 209 Ideal of OK Two element generators: [209, 0] [194, 1] Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 15:31:56 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK:=MaximalOrder(K); K!Basis(OK); J:=((29-a)/2)*OK; J; #quo; J1:=ideal; J1; Output: Magma V2.10-6 Wed Mar 3 2004 15:31:53 on modular [Seed = 4092982068] ------------------------------------- >> K!Basis(OK); ^ Runtime error in '!': Illegal coercion LHS: FldNum RHS: [FldOrdElt] Principal Ideal of OK Generator: [15, -1] 209 Ideal of OK Two element generators: [209, 0] [194, 1] Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 15:32:27 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK:=MaximalOrder(K); Basis(OK); K!OK.2 J:=((29-a)/2)*OK; J; #quo; J1:=ideal; J1; Output: Magma V2.10-6 Wed Mar 3 2004 15:32:24 on modular [Seed = 3907971150] ------------------------------------- [ OK.1, OK.2 ] >> J:=((29-a)/2)*OK; ^ User error: bad syntax >> J; ^ User error: Identifier 'J' has not been declared or assigned >> #quo; ^ User error: Identifier 'J' has not been declared or assigned Ideal of OK Two element generators: [209, 0] [194, 1] Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 15:32:41 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK:=MaximalOrder(K); Basis(OK); K!OK.2; J:=((29-a)/2)*OK; J; #quo; J1:=ideal; J1; Output: Magma V2.10-6 Wed Mar 3 2004 15:32:38 on modular [Seed = 3738754630] ------------------------------------- [ OK.1, OK.2 ] 1/2*(a + 1) Principal Ideal of OK Generator: [15, -1] 209 Ideal of OK Two element generators: [209, 0] [194, 1] Total time: 3.029 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 15:34:12 2004 Input: Z11 := Integers(11); PrimitiveElement(Z11); Output: Magma V2.10-6 Wed Mar 3 2004 15:34:08 on modular [Seed = 3520581871] ------------------------------------- 2 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 15:34:19 2004 Input: Z11 := Integers(11); PrimitiveElement(Z11); Output: Magma V2.10-6 Wed Mar 3 2004 15:34:16 on modular [Seed = 3385837823] ------------------------------------- 2 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 15:38:20 2004 Input: Z11 := Integers(11); PrimitiveElement(Z11); IsPrimitive(3,11); Output: Magma V2.10-6 Wed Mar 3 2004 15:38:17 on modular [Seed = 3149773308] ------------------------------------- 2 false Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 15:38:35 2004 Input: Z11 := Integers(11); PrimitiveElement(Z11); IsPrimitive(2,11); Output: Magma V2.10-6 Wed Mar 3 2004 15:38:32 on modular [Seed = 2981606279] ------------------------------------- 2 true Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 15:42:01 2004 Input: RationalField(); Output: Magma V2.10-6 Wed Mar 3 2004 15:41:58 on modular [Seed = 2038397456] ------------------------------------- Rational Field Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 159.233.39-62.rev.gaoland.net. (62.39.233.159) Time: Wed Mar 3 15:43:42 2004 Input: 3+3 Output: Magma V2.10-6 Wed Mar 3 2004 15:43:38 on modular [Seed = 1785489775] ------------------------------------- 6 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 159.233.39-62.rev.gaoland.net. (62.39.233.159) Time: Wed Mar 3 15:43:55 2004 Input: 1+1 Output: Magma V2.10-6 Wed Mar 3 2004 15:43:51 on modular [Seed = 1634165401] ------------------------------------- 2 Total time: 3.309 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 15:43:57 2004 Input: RationalField(); Numerator(4/5); Output: Magma V2.10-6 Wed Mar 3 2004 15:43:53 on modular [Seed = 1566269099] ------------------------------------- Rational Field 4 Total time: 3.349 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 15:44:41 2004 Input: RationalField(); Numerator(4/5); RealField(2); Output: Magma V2.10-6 Wed Mar 3 2004 15:44:38 on modular [Seed = 1296780932] ------------------------------------- Rational Field 4 Real Field of precision 4 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 15:45:08 2004 Input: RealField(2)!3; Output: Magma V2.10-6 Wed Mar 3 2004 15:45:05 on modular [Seed = 1078346734] ------------------------------------- 3 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 15:45:34 2004 Input: RationalField(2)!3; Output: Magma V2.10-6 Wed Mar 3 2004 15:45:31 on modular [Seed = 925971619] ------------------------------------- >> RationalField(2)!3; ^ Runtime error in 'RationalField': Bad argument types Argument types given: RngIntElt Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 15:46:22 2004 Input: Ceiling(4.869); Floor(4.869); Root(5.3,2); Output: Magma V2.10-6 Wed Mar 3 2004 15:46:19 on modular [Seed = 774384202] ------------------------------------- 5 4 2.302172886644267644194841586358 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 15:47:44 2004 Input: Ceiling(4.011); Floor(4.869); Root(5.3,2); AbsoluteValue(4.698); Output: Magma V2.10-6 Wed Mar 3 2004 15:47:41 on modular [Seed = 606216246] ------------------------------------- 5 4 2.302172886644267644194841586358 4.69799999999999999999999999991 Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 15:51:01 2004 Input: x := [1..366]; x; Output: Magma V2.10-6 Wed Mar 3 2004 15:50:58 on modular [Seed = 235408195] ------------------------------------- [ 1 .. 366 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 15:51:21 2004 Input: x := [1..366]; x; x[2]; Output: Magma V2.10-6 Wed Mar 3 2004 15:51:18 on modular [Seed = 84082748] ------------------------------------- [ 1 .. 366 ] 2 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 15:55:13 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK:=MaximalOrder(K); J:=((29-a)/2)*OK; Factorization(J); #quo; J1:=ideal; Factorization(J1); Output: Magma V2.10-6 Wed Mar 3 2004 15:55:09 on modular [Seed = 774383616] ------------------------------------- [ , ] 209 [ , ] Total time: 3.039 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 15:55:29 2004 Input: X:=[1..366 by 1]; Y:=[]; for i := 4 to 366 by 7 do Y:=Include(Y,X[i]); end for; Y; Output: Magma V2.10-6 Wed Mar 3 2004 15:55:26 on modular [Seed = 925970697] ------------------------------------- [ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 15:57:32 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK:=MaximalOrder(K); J:=((29-a)/2)*OK; Factorization(J); Output: Magma V2.10-6 Wed Mar 3 2004 15:57:29 on modular [Seed = 1095190520] ------------------------------------- [ , ] Total time: 3.119 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 16:02:11 2004 Input: X:=[1..366 by 1]; Y:=[]; for i := 4 to 366 by 7 do Y:=Include(Y,X[i]); end for; Y; for i:=1 to 366 by 7 do diumenges:=Include(diumenges,i-4); diumenges; Output: Magma V2.10-6 Wed Mar 3 2004 16:02:08 on modular [Seed = 1818913724] ------------------------------------- [ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] User error: syntax error at end of input Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 16:02:35 2004 Input: X:=[1..366 by 1]; Y:=[]; for i := 4 to 366 by 7 do Y:=Include(Y,X[i]); end for; Y; for i:=1 to 366 by 7 do diumenges:=Include(diumenges,i-4); end for; diumenges; Output: Magma V2.10-6 Wed Mar 3 2004 16:02:32 on modular [Seed = 1970500253] ------------------------------------- [ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] >> for i:=1 to 366 by 7 do diumenges:=Include(diumenges,i-4); end for; ^ User error: Identifier 'diumenges' has not been declared or assigned >> diumenges;; ^ User error: Identifier 'diumenges' has not been declared or assigned Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 16:03:02 2004 Input: X:=[1..366 by 1]; Y:=[]; for i := 4 to 366 by 7 do Y:=Include(Y,X[i]); end for; Y; diumenges:=[]; for i:=1 to 366 by 7 do diumenges:=Include(diumenges,i-4); end for; diumenges; Output: Magma V2.10-6 Wed Mar 3 2004 16:02:58 on modular [Seed = 2138666876] ------------------------------------- [ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] [ -3, 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 16:05:03 2004 Input: X:=[1..366 by 1]; Y:=[]; for i := 4 to 366 by 7 do Y:=Include(Y,X[i]); end for; Y; diumenges:=[]; for i:=1 to 366 by 7 do diumenges:=Include(diumenges,i-4); end for; diumenges; t := {n^2: n in [-11..11 by 2]}; t; Output: Magma V2.10-6 Wed Mar 3 2004 16:05:00 on modular [Seed = 2324464374] ------------------------------------- [ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] [ -3, 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] { 1, 9, 25, 49, 81, 121 } Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 16:06:00 2004 Input: X:=[1..366 by 1]; Y:=[]; for i := 4 to 366 by 7 do Y:=Include(Y,X[i]); end for; Y; diumenges:=[]; for i:=1 to 366 by 7 do diumenges:=Include(diumenges,i-4); end for; diumenges; t := {n: n in [4..366 by 7]}; t; Output: Magma V2.10-6 Wed Mar 3 2004 16:05:57 on modular [Seed = 2542903074] ------------------------------------- [ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] [ -3, 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] { 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 } Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 16:06:27 2004 Input: X:=[1..366 by 1]; Y:=[]; for i := 4 to 366 by 7 do Y:=Include(Y,X[i]); end for; Y; /*diumenges:=[]; for i:=1 to 366 by 7 do diumenges:=Include(diumenges,i-4); end for; diumenges;*/ t := {n: n in [4..366 by 7]}; t; Output: Magma V2.10-6 Wed Mar 3 2004 16:06:24 on modular [Seed = 2695276656] ------------------------------------- [ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] { 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 } Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 16:07:27 2004 Input: X:=[1..366 by 1]; Y:=[]; for i := 4 to 366 by 7 do Y:=Include(Y,X[i]); end for; Y; sunday := {n: n in [4..366 by 7]}; sunday; Output: Magma V2.10-6 Wed Mar 3 2004 16:07:24 on modular [Seed = 2863440806] ------------------------------------- [ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] { 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 } Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 16:07:49 2004 Input: X:=[1..366 by 1]; Y:=[]; for i := 4 to 366 by 7 do Y:=Include(Y,X[i]); end for; Y; {n: n in [4..366 by 7]}; Output: Magma V2.10-6 Wed Mar 3 2004 16:07:46 on modular [Seed = 3015031441] ------------------------------------- [ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] { 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 } Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 16:08:07 2004 Input: {n: n in [4..366 by 7]}; Output: Magma V2.10-6 Wed Mar 3 2004 16:08:04 on modular [Seed = 3166352776] ------------------------------------- { 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 } Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 16:16:20 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4+x^3+2x^2+4x+8); OK:= MaximalOrder(K); I:=2*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 16:16:17 on modular [Seed = 3688747258] ------------------------------------- >> K := NumberField(x^4+x^3+2x^2+4x+8); ^ User error: bad syntax >> OK:= MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> I:=2*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I);; ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 16:16:43 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4+x^3+2*x^2+4*x+8); OK:= MaximalOrder(K); I:=2*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 16:16:40 on modular [Seed = 3840077788] ------------------------------------- [ , ] Total time: 2.999 seconds, Total memory usage: 1.91MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 16:16:59 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4+x^3+2*x^2+3*x+8); OK:= MaximalOrder(K); I:=2*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 16:16:56 on modular [Seed = 3991660197] ------------------------------------- [ , ] Total time: 2.969 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 16:17:12 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4+3*x^3+2*x^2+3*x+8); OK:= MaximalOrder(K); I:=2*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 16:17:09 on modular [Seed = 4142988707] ------------------------------------- [ , ] Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 16:17:30 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4+x^3+3*x+8); OK:= MaximalOrder(K); I:=2*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 16:17:27 on modular [Seed = 4294571160] ------------------------------------- [ , ] Total time: 3.249 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 16:17:32 2004 Input: p := PolynomialRing(5); p; Output: Magma V2.10-6 Wed Mar 3 2004 16:17:29 on modular [Seed = 50661483] ------------------------------------- >> p := PolynomialRing(5); ^ Runtime error in 'PolynomialRing': Bad argument types Argument types given: RngIntElt >> p;; ^ User error: Identifier 'p' has not been declared or assigned Total time: 3.239 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 16:18:03 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4+x^3+2*x^2+3*x+8); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 16:18:00 on modular [Seed = 269884313] ------------------------------------- [ , ] Total time: 2.969 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 16:18:15 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4+x^3+2*x^2+3*x+7); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 16:18:12 on modular [Seed = 454889614] ------------------------------------- [ , ] Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 16:18:24 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4+x^3+2*x^2+3*x+7); OK:= MaximalOrder(K); I:=2*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 16:18:21 on modular [Seed = 572795326] ------------------------------------- [ , ] Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 16:18:36 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4+x^3+2*x^2+3*x+1); OK:= MaximalOrder(K); I:=2*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 16:18:33 on modular [Seed = 740960132] ------------------------------------- >> K := NumberField(x^4+x^3+2*x^2+3*x+1); ^ Runtime error in 'NumberField': Argument 1 is not irreducible >> OK:= MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> I:=2*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I);; ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 16:18:50 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4+x^3+2*x^2+3*x+2); OK:= MaximalOrder(K); I:=2*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 16:18:47 on modular [Seed = 925973633] ------------------------------------- [ , ] Total time: 2.929 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 16:19:04 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4+x^3+2*x^2+3*x+2); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 16:19:01 on modular [Seed = 1095191173] ------------------------------------- [ , ] Total time: 2.929 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 16:19:19 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4+2*x^2+3*x+2); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 16:19:16 on modular [Seed = 1213088669] ------------------------------------- [ ] Total time: 2.989 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 16:19:31 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4+5*x^2+3*x+2); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 16:19:28 on modular [Seed = 1398102194] ------------------------------------- [ ] Total time: 2.969 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 16:19:38 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4+6*x^2+3*x+2); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 16:19:35 on modular [Seed = 1515999676] ------------------------------------- [ , , ] Total time: 2.939 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 16:19:56 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4+6*x^2+3*x+2); OK:= MaximalOrder(K); I:=2*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 16:19:53 on modular [Seed = 1701015197] ------------------------------------- [ , , ] Total time: 2.989 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 16:23:34 2004 Input: Z := IntegerRing(); S := PolynomialRing(Z, 2); Output: Magma V2.10-6 Wed Mar 3 2004 16:23:31 on modular [Seed = 2021553322] ------------------------------------- Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 16:26:13 2004 Input: Z := IntegerRing(); S := PolynomialRing(Z, 2); S; Output: Magma V2.10-6 Wed Mar 3 2004 16:26:10 on modular [Seed = 2307884282] ------------------------------------- Polynomial ring of rank 2 over Integer Ring Lexicographical Order Variables: $.1, $.2 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 16:27:41 2004 Input: Z := IntegerRing(); S := PolynomialRing(Integers(2)); S; Output: Magma V2.10-6 Wed Mar 3 2004 16:27:38 on modular [Seed = 2476056152] ------------------------------------- Univariate Polynomial Ring over IntegerRing(2) Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 16:28:12 2004 Input: Z := IntegerRing(); S := PolynomialRing(Integers(2)); S ! [5,0,-7,1]; Output: Magma V2.10-6 Wed Mar 3 2004 16:28:09 on modular [Seed = 2593953650] ------------------------------------- S.1^3 + S.1^2 + 1 Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 16:28:36 2004 Input: Z := IntegerRing(); S := PolynomialRing(Integers(2)); S ! [5,0,-7,1]; Output: Magma V2.10-6 Wed Mar 3 2004 16:28:33 on modular [Seed = 2778966949] ------------------------------------- x^3 + x^2 + 1 Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 16:29:09 2004 Input: Z := IntegerRing(); S := PolynomialRing(Integers(10)); S ! [5,0,-7,1]; Output: Magma V2.10-6 Wed Mar 3 2004 16:29:06 on modular [Seed = 2947129740] ------------------------------------- x^3 + 3*x^2 + 5 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 16:29:52 2004 Input: Z := IntegerRing(); S := PolynomialRing(Integers()); S ! [5,0,-7,1]; Output: Magma V2.10-6 Wed Mar 3 2004 16:29:49 on modular [Seed = 3065035002] ------------------------------------- x^3 - 7*x^2 + 5 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 16:31:07 2004 Input: Z := IntegerRing(); S := PolynomialRing(Integers()); S ! [5,0,-7,1]; elt ; Output: Magma V2.10-6 Wed Mar 3 2004 16:31:04 on modular [Seed = 3907970673] ------------------------------------- x^3 - 7*x^2 + 5 x^3 - 7*x^2 + 5 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 16:32:25 2004 Input: Z := IntegerRing(); S := PolynomialRing(Integers()); hola:=S ! [5,0,-7,1]; Evaluate(hola,2); Degree(hola); Coefficients(hola); Coefficient(hola,2); Terms(hola); Output: Magma V2.10-6 Wed Mar 3 2004 16:32:21 on modular [Seed = 4092984596] ------------------------------------- -15 3 [ 5, 0, -7, 1 ] -7 [ 5, -7*x^2, x^3 ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 16:33:34 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-7, x^2-10); OK:=MaximalOrder(K); Output: Magma V2.10-6 Wed Mar 3 2004 16:33:31 on modular [Seed = 4261147351] ------------------------------------- >> K:=NumberField(x^2-7, x^2-10); ^ Runtime error in 'NumberField': Bad argument types Argument types given: RngUPolElt, RngUPolElt >> OK:=MaximalOrder(K);; ^ User error: Identifier 'K' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 16:34:37 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-7, x^2-10]); OK:=MaximalOrder(K); Output: Magma V2.10-6 Wed Mar 3 2004 16:34:34 on modular [Seed = 67242860] ------------------------------------- Total time: 3.399 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 16:34:49 2004 Input: Z := IntegerRing(); S := PolynomialRing(Integers()); hola:=S ! [5,0,-7,1]; LeadingCoefficient(hola); LeadingTerm(hola); TrailingCoefficient(hola); TrailingTerm(hola); Output: Magma V2.10-6 Wed Mar 3 2004 16:34:45 on modular [Seed = 218825338] ------------------------------------- 1 x^3 5 5 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 16:35:24 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-7, x^2-10]); OK:=MaximalOrder(K); I:=2*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 16:35:20 on modular [Seed = 656484541] ------------------------------------- [ ] Total time: 3.749 seconds, Total memory usage: 2.06MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 16:35:51 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-7, x^2-5]); OK:=MaximalOrder(K); I:=2*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 16:35:48 on modular [Seed = 740959130] ------------------------------------- [ ] Total time: 3.079 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 16:36:09 2004 Input: Z := IntegerRing(); S := PolynomialRing(Integers()); hola:=S ! [5,0,-7,1]; CoefficientRing(S); CoefficientRing(hola); Output: Magma V2.10-6 Wed Mar 3 2004 16:36:06 on modular [Seed = 892549873] ------------------------------------- Integer Ring Integer Ring Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 16:36:38 2004 Input: Z := IntegerRing(); S := PolynomialRing(Integers()); hola:=S ! [5,0,-7,1]; CoefficientRing(S); CoefficientRing(hola); Quotrem(hola,hola); Output: Magma V2.10-6 Wed Mar 3 2004 16:36:35 on modular [Seed = 1128615074] ------------------------------------- Integer Ring Integer Ring 1 0 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 16:37:25 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-7, x^2-5]); OK:=MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 16:37:22 on modular [Seed = 1213093976] ------------------------------------- [ , ] Total time: 3.019 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 16:37:50 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-7, x^2-10]); OK:=MaximalOrder(K); I:=2*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 16:37:45 on modular [Seed = 1364672890] ------------------------------------- [ ] Total time: 3.759 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 16:38:17 2004 Input: Z := IntegerRing(); S := PolynomialRing(Integers()); hola:=S ! [5,0,-7,1]; adios:=S ! [1,2,3,0]; Quotrem(hola,adios); Output: Magma V2.10-6 Wed Mar 3 2004 16:38:14 on modular [Seed = 1582845466] ------------------------------------- -3 x^3 + 2*x^2 + 6*x + 8 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 16:39:00 2004 Input: Z := IntegerRing(); S := PolynomialRing(Integers()); hola:=S ! [5,0,-7,1]; adios:=S ! [1,2,3,0]; Quotrem(x^2+2*x,x); Output: Magma V2.10-6 Wed Mar 3 2004 16:38:57 on modular [Seed = 1734440724] ------------------------------------- x + 2 0 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 16:40:11 2004 Input: Z := IntegerRing(); S := PolynomialRing(Integers()); hola:=S ! [5,0,-7,1]; adios:=S ! [1,2,3,0]; Factorization(x^2+2*x); Output: Magma V2.10-6 Wed Mar 3 2004 16:40:08 on modular [Seed = 1970496975] ------------------------------------- [ , ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 16:52:55 2004 Input: cosfinit:=GF(7); cosfinit; Output: Magma V2.10-6 Wed Mar 3 2004 16:52:52 on modular [Seed = 2577369647] ------------------------------------- Finite field of size 7 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 16:53:37 2004 Input: cosfinit:=GF(7); cosfinit; cosfinit1:=GF(7^4); cosfinit1; Output: Magma V2.10-6 Wed Mar 3 2004 16:53:34 on modular [Seed = 2795550074] ------------------------------------- Finite field of size 7 Finite field of size 7^4 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 16:54:01 2004 Input: cosfinit:=GF(7); cosfinit; cosfinit1:=GF(7,4); cosfinit1; Output: Magma V2.10-6 Wed Mar 3 2004 16:53:58 on modular [Seed = 2947136603] ------------------------------------- Finite field of size 7 Finite field of size 7^4 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 16:59:44 2004 Input: F := GF(27); Output: Magma V2.10-6 Wed Mar 3 2004 16:59:41 on modular [Seed = 3166349811] ------------------------------------- Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 16:59:58 2004 Input: F := GF(27); F; Output: Magma V2.10-6 Wed Mar 3 2004 16:59:55 on modular [Seed = 3317944476] ------------------------------------- Finite field of size 3^3 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 17:00:29 2004 Input: F := GF(27); F; 2*alpha^2+alpha+1; Output: Magma V2.10-6 Wed Mar 3 2004 17:00:26 on modular [Seed = 3671904162] ------------------------------------- Finite field of size 3^3 alpha^20 Total time: 2.839 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 17:02:11 2004 Input: F := GF(27); F; 2*alpha^2+alpha+1; Generator(F); Output: Magma V2.10-6 Wed Mar 3 2004 17:02:08 on modular [Seed = 4294568477] ------------------------------------- Finite field of size 3^3 alpha^20 alpha Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 17:02:53 2004 Input: F := GF(27); F; 2*alpha^2+alpha+1; Generator(F); PrimitiveElement(F); Output: Magma V2.10-6 Wed Mar 3 2004 17:02:50 on modular [Seed = 84087564] ------------------------------------- Finite field of size 3^3 alpha^20 alpha alpha Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 17:18:48 2004 Input: M := Matrix([[1,2,3],[1,4,9]]); M; Trace(M); Output: Magma V2.10-6 Wed Mar 3 2004 17:18:45 on modular [Seed = 791230185] ------------------------------------- [1 2 3] [1 4 9] >> Trace(M);; ^ Runtime error in 'Trace': Argument 1 is not square Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 17:19:12 2004 Input: M := Matrix([[1,2,3],[1,4,9],[1,1,1]]); M; Trace(M); Output: Magma V2.10-6 Wed Mar 3 2004 17:19:09 on modular [Seed = 892546283] ------------------------------------- [1 2 3] [1 4 9] [1 1 1] 6 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 17:23:06 2004 Input: M := Matrix([[1,2,3],[1,4,9],[1,1,1]]); M; Trace(M); M[1] eq M[2]; Output: Magma V2.10-6 Wed Mar 3 2004 17:23:03 on modular [Seed = 1145200256] ------------------------------------- [1 2 3] [1 4 9] [1 1 1] 6 false Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 17:23:22 2004 Input: M := Matrix([[1,2,3],[1,2,3],[1,1,1]]); M; Trace(M); M[1] eq M[2]; Output: Magma V2.10-6 Wed Mar 3 2004 17:23:19 on modular [Seed = 1398098311] ------------------------------------- [1 2 3] [1 2 3] [1 1 1] 4 true Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 17:23:47 2004 Input: M := Matrix([[1,2,3],[1,2,3],[1,1,1]]); M; Trace(M); [1,2,3] eq [1,2,3]; Output: Magma V2.10-6 Wed Mar 3 2004 17:23:44 on modular [Seed = 1515995305] ------------------------------------- [1 2 3] [1 2 3] [1 1 1] 4 true Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 17:27:09 2004 Input: R:= GF(4); M := MatrixRing(R,2); Mt := { A : A in M | Trace(A) eq 0}; Mf := {A: A in M | A[1] eq A[2]}; Mtf := Mt meet Mf; Output: Magma V2.10-6 Wed Mar 3 2004 17:27:06 on modular [Seed = 1802334418] ------------------------------------- Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 17:27:24 2004 Input: R:= GF(4); M := MatrixRing(R,2); Mt := { A : A in M | Trace(A) eq 0}; Mf := {A: A in M | A[1] eq A[2]}; Mtf := Mt meet Mf; Mtf; Output: Magma V2.10-6 Wed Mar 3 2004 17:27:21 on modular [Seed = 1920231864] ------------------------------------- { [ 0 0] [ 0 0], [R.1^2 R.1^2] [R.1^2 R.1^2], [ R.1 R.1] [ R.1 R.1], [ 1 1] [ 1 1] } Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 17:31:05 2004 Input: R:= GF(4); M := MatrixRing(R,2); Mt := { A : A in M | Trace(A) eq 0}; Mf := {A: A in M | A[1] eq A[2]}; Mtf := Mt meet Mf; Mtf; L := Random(M); L; Output: Magma V2.10-6 Wed Mar 3 2004 17:31:02 on modular [Seed = 2273418018] ------------------------------------- { [ 0 0] [ 0 0], [R.1^2 R.1^2] [R.1^2 R.1^2], [ R.1 R.1] [ R.1 R.1], [ 1 1] [ 1 1] } [ 0 R.1] [ 1 1] Total time: 3.029 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 17:35:50 2004 Input: R:= GF(4); M := MatrixRing(R,2); Mt := { A : A in M | Trace(A) eq 0}; Mf := {A: A in M | A[1] eq A[2]}; Mtf := Mt meet Mf; Mtf; seq := {Random(M); L:=[Random(M):n in [1..10]]; L; Output: Magma V2.10-6 Wed Mar 3 2004 17:35:47 on modular [Seed = 2509473877] ------------------------------------- { [ 0 0] [ 0 0], [R.1^2 R.1^2] [R.1^2 R.1^2], [ R.1 R.1] [ R.1 R.1], [ 1 1] [ 1 1] } >> seq := {Random(M); ^ User error: bad syntax [ [R.1^2 R.1^2] [ 0 1], [ 0 R.1] [R.1^2 1], [ R.1 R.1] [ 1 1], [ 1 0] [ 1 0], [ R.1 1] [ 0 0], [R.1^2 R.1^2] [R.1^2 0], [ 1 0] [R.1^2 R.1^2], [ 1 1] [ R.1 0], [ 0 0] [R.1^2 R.1^2], [ 0 0] [ R.1 1] ] Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 17:36:04 2004 Input: [ if (dia mod 7) eq 4 then print dia; end if: dia in [1..366]]; Output: Magma V2.10-6 Wed Mar 3 2004 17:36:01 on modular [Seed = 2627371342] ------------------------------------- >> [ if (dia mod 7) eq 4 then ^ User error: bad syntax >> print dia; ^ User error: Identifier 'dia' has not been declared or assigned >> end if: ^ User error: bad syntax >> dia in [1..366]];; ^ User error: bad syntax Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 17:36:17 2004 Input: R:= GF(4); M := MatrixRing(R,2); Mt := { A : A in M | Trace(A) eq 0}; Mf := {A: A in M | A[1] eq A[2]}; Mtf := Mt meet Mf; Mtf; L:=[Random(M):n in [1..10]]; L; Output: Magma V2.10-6 Wed Mar 3 2004 17:36:14 on modular [Seed = 2880288374] ------------------------------------- { [ 0 0] [ 0 0], [R.1^2 R.1^2] [R.1^2 R.1^2], [ R.1 R.1] [ R.1 R.1], [ 1 1] [ 1 1] } [ [R.1^2 R.1^2] [R.1^2 1], [ R.1 1] [ 0 0], [ 0 1] [ 0 R.1], [ R.1 R.1] [ 0 1], [ 1 1] [R.1^2 0], [ 1 0] [ 1 1], [R.1^2 1] [ R.1 R.1^2], [ R.1 R.1^2] [ 1 R.1^2], [ 1 1] [R.1^2 0], [ R.1 R.1^2] [ 0 R.1] ] Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 17:36:38 2004 Input: [if (dia mod 7) eq 4 then print dia end if: dia in [1..366]]; Output: Magma V2.10-6 Wed Mar 3 2004 17:36:35 on modular [Seed = 2981604417] ------------------------------------- >> [if (dia mod 7) eq 4 then print dia end if: dia in [1..366]];; ^ User error: bad syntax Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 17:36:58 2004 Input: [(if (dia mod 7) eq 4 then print dia end if): dia in [1..366]]; Output: Magma V2.10-6 Wed Mar 3 2004 17:36:55 on modular [Seed = 3099502268] ------------------------------------- >> [(if (dia mod 7) eq 4 then print dia end if): dia in [1..366]];; ^ User error: bad syntax Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 17:37:11 2004 Input: [(if (dia mod 7) eq 4 then print dia; end if;): dia in [1..366]]; Output: Magma V2.10-6 Wed Mar 3 2004 17:37:08 on modular [Seed = 3351370192] ------------------------------------- >> [(if (dia mod 7) eq 4 then print dia; end if;): dia in [1..366]];; ^ User error: bad syntax Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 17:41:00 2004 Input: R:= GF(4); M := MatrixRing(R,2); Mt := { A : A in M | Trace(A) eq 0}; Mf := {A: A in M | A[1] eq A[2]}; Mtf := Mt meet Mf; Mtf; seq:=[Random(M):num in [1..10]]; #([A : A in seq | A in Mt]); #([A : A in seq | A in Mf]); #([A : A in seq | A in Mtf]); seq; Output: Magma V2.10-6 Wed Mar 3 2004 17:40:57 on modular [Seed = 3587427119] ------------------------------------- { [ 0 0] [ 0 0], [R.1^2 R.1^2] [R.1^2 R.1^2], [ R.1 R.1] [ R.1 R.1], [ 1 1] [ 1 1] } 2 1 0 [ [ 0 R.1^2] [ 0 R.1], [ R.1 0] [ 1 1], [ 0 1] [ 0 0], [ 0 R.1] [ 1 0], [ 0 R.1] [ 1 1], [ 1 R.1] [R.1^2 R.1^2], [R.1^2 0] [ 1 0], [ 0 1] [ 0 1], [ 0 R.1^2] [ 1 R.1^2], [ 0 0] [ R.1 1] ] Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 17:42:23 2004 Input: R:= GF(4); M := MatrixRing(R,2); Mt := { A : A in M | Trace(A) eq 0}; Mf := {A: A in M | A[1] eq A[2]}; Mtf := Mt meet Mf; Mtf; /*seq:=[Random(M):num in [1..10]];*/ #([A : A in [Random(M):num in [1..10]] | A in Mt]); /*#([A : A in seq | A in Mf]);*/ /*#([A : A in seq | A in Mtf]);*/ /*seq;*/ Output: Magma V2.10-6 Wed Mar 3 2004 17:42:20 on modular [Seed = 3705324435] ------------------------------------- { [ 0 0] [ 0 0], [R.1^2 R.1^2] [R.1^2 R.1^2], [ R.1 R.1] [ R.1 R.1], [ 1 1] [ 1 1] } 5 Total time: 3.059 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 17:43:19 2004 Input: R:= GF(4); M := MatrixRing(R,2); Mt := { A : A in M | Trace(A) eq 0}; Mf := {A: A in M | A[1] eq A[2]}; Mtf := Mt meet Mf; Mtf; /*seq:=[Random(M):num in [1..10]];*/ #([A : A in [Random(M):num in [1..100000]] | A in Mt]); /*#([A : A in seq | A in Mf]);*/ /*#([A : A in seq | A in Mtf]);*/ /*seq;*/ Output: Magma V2.10-6 Wed Mar 3 2004 17:43:16 on modular [Seed = 4008243561] ------------------------------------- { [ 0 0] [ 0 0], [R.1^2 R.1^2] [R.1^2 R.1^2], [ R.1 R.1] [ R.1 R.1], [ 1 1] [ 1 1] } 24584 Total time: 3.729 seconds, Total memory usage: 7.09MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 17:43:59 2004 Input: R:= GF(4); M := MatrixRing(R,2); Mt := { A : A in M | Trace(A) eq 0}; Mf := {A: A in M | A[1] eq A[2]}; Mtf := Mt meet Mf; Mtf; seq:=[Random(M):num in [1..100000]]; /*#([A : A in [Random(M):num in [1..100000]] | A in Mt]);*/ /*#([A : A in seq | A in Mf]);*/ /*#([A : A in seq | A in Mtf]);*/ /*seq;*/ Output: Magma V2.10-6 Wed Mar 3 2004 17:43:55 on modular [Seed = 4126403165] ------------------------------------- { [ 0 0] [ 0 0], [R.1^2 R.1^2] [R.1^2 R.1^2], [ R.1 R.1] [ R.1 R.1], [ 1 1] [ 1 1] } Total time: 3.449 seconds, Total memory usage: 7.09MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 17:44:55 2004 Input: K:=GF(4); Output: Magma V2.10-6 Wed Mar 3 2004 17:44:52 on modular [Seed = 67247076] ------------------------------------- Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 17:45:01 2004 Input: R:= GF(4); M := MatrixRing(R,2); Mt := { A : A in M | Trace(A) eq 0}; Mf := {A: A in M | A[1] eq A[2]}; Mtf := Mt meet Mf; Mtf; seq:=[Random(M):num in [1..100000]]; #([A : A in [Random(M):num in [1..100000]] | A in Mt]); #([A : A in seq | A in Mf]); #([A : A in seq | A in Mtf]); Output: Magma V2.10-6 Wed Mar 3 2004 17:44:56 on modular [Seed = 218829537] ------------------------------------- { [ 0 0] [ 0 0], [R.1^2 R.1^2] [R.1^2 R.1^2], [ R.1 R.1] [ R.1 R.1], [ 1 1] [ 1 1] } 24993 6242 1529 Total time: 4.659 seconds, Total memory usage: 11.95MB ************** MAGMA ***************** Host 80.58.34.170.proxycache.rima-tde.net. (80.58.34.170) Time: Wed Mar 3 17:45:16 2004 Input: varA:=77 Output: Magma V2.10-6 Wed Mar 3 2004 17:45:13 on modular [Seed = 303304175] ------------------------------------- Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.170.proxycache.rima-tde.net. (80.58.34.170) Time: Wed Mar 3 17:45:42 2004 Input: varA:=77; Output: Magma V2.10-6 Wed Mar 3 2004 17:45:39 on modular [Seed = 606209075] ------------------------------------- Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 17:46:11 2004 Input: K:=GF(4); M22:=MatrixRing(K,2); Output: Magma V2.10-6 Wed Mar 3 2004 17:46:08 on modular [Seed = 757796121] ------------------------------------- Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 17:46:27 2004 Input: R:= GF(4); M := MatrixRing(R,2); Mt := { A : A in M | Trace(A) eq 0}; Mf := {A: A in M | A[1] eq A[2]}; Mtf := Mt meet Mf; Mtf; seq:=[Random(M):num in [1..10]]; #([A : A in seq | A in Mt]); #([A : A in seq | A in Mf]); #([A : A in seq | A in Mtf]); Output: Magma V2.10-6 Wed Mar 3 2004 17:46:24 on modular [Seed = 909121138] ------------------------------------- { [ 0 0] [ 0 0], [R.1^2 R.1^2] [R.1^2 R.1^2], [ R.1 R.1] [ R.1 R.1], [ 1 1] [ 1 1] } 4 1 0 Total time: 3.519 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.34.170.proxycache.rima-tde.net. (80.58.34.170) Time: Wed Mar 3 17:46:28 2004 Input: varA:=77; varA; Output: Magma V2.10-6 Wed Mar 3 2004 17:46:24 on modular [Seed = 825692533] ------------------------------------- 77 Total time: 3.569 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 17:46:43 2004 Input: seq:=[Random(M):num in [1..10]]; #([A : A in seq | A in Mt]); #([A : A in seq | A in Mf]); #([A : A in seq | A in Mtf]); Output: Magma V2.10-6 Wed Mar 3 2004 17:46:40 on modular [Seed = 1078353940] ------------------------------------- >> seq:=[Random(M):num in [1..10]]; ^ User error: Identifier 'M' has not been declared or assigned >> #([A : A in seq | A in Mt]); ^ User error: Identifier 'seq' has not been declared or assigned >> #([A : A in seq | A in Mf]); ^ User error: Identifier 'seq' has not been declared or assigned >> #([A : A in seq | A in Mtf]); ^ User error: Identifier 'seq' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 17:47:28 2004 Input: R:= GF(4); M := MatrixRing(R,2); Mt := { A : A in M | Trace(A) eq 0}; Mf := {A: A in M | A[1] eq A[2]}; Mtf := Mt meet Mf; seq:=[Random(M):num in [1..10]]; #([A : A in seq | A in Mt]); #([A : A in seq | A in Mf]); #([A : A in seq | A in Mtf]); Output: Magma V2.10-6 Wed Mar 3 2004 17:47:25 on modular [Seed = 1229941040] ------------------------------------- 4 0 0 Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 17:47:49 2004 Input: K:=GF(4); M22:=MatrixRing(K,2); m:=M22![5,5,6,8]; Output: Magma V2.10-6 Wed Mar 3 2004 17:47:46 on modular [Seed = 1381266116] ------------------------------------- Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 17:47:59 2004 Input: K:=GF(4); M22:=MatrixRing(K,2); m:=M22![5,5,6,8]; m; Output: Magma V2.10-6 Wed Mar 3 2004 17:47:56 on modular [Seed = 1532853187] ------------------------------------- [ 1 1] [ 0 0] Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 17:48:16 2004 Input: K:=GF(4); M22:=MatrixRing(K,2); m:=M22![K,K,K,K]; m; Output: Magma V2.10-6 Wed Mar 3 2004 17:48:13 on modular [Seed = 1818905797] ------------------------------------- >> m:=M22![K,K,K,K]; ^ Runtime error in '!': Can't coerce sequence element 1 into the coefficient ring >> m;; ^ User error: Identifier 'm' has not been declared or assigned Total time: 3.159 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 17:48:19 2004 Input: R:= GF(4); M := MatrixRing(R,2); Mt := { A : A in M | Trace(A) eq 0}; Mf := {A: A in M | A[1] eq A[2]}; Mtf := Mt meet Mf; seq:=[Random(M):num in [1..10]]; #([A : A in seq | A in Mt]); #([A : A in seq | A in Mf]); #([A : A in seq | A in Mtf]); Output: Magma V2.10-6 Wed Mar 3 2004 17:48:15 on modular [Seed = 1869172676] ------------------------------------- 2 0 0 Total time: 3.159 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 17:48:31 2004 Input: R:= GF(4); M := MatrixRing(R,2); Mt := { A : A in M | Trace(A) eq 0}; Mf := {A: A in M | A[1] eq A[2]}; Mtf := Mt meet Mf; seq:=[Random(M):num in [1..10]]; #([A : A in seq | A in Mt]); #([A : A in seq | A in Mf]); #([A : A in seq | A in Mtf]); Output: Magma V2.10-6 Wed Mar 3 2004 17:48:28 on modular [Seed = 2138660807] ------------------------------------- 2 3 0 Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 17:48:39 2004 Input: K:=GF(4); M22:=MatrixRing(K,2); m:=M22![K.1,K.1,K.1,K.1]; m; Output: Magma V2.10-6 Wed Mar 3 2004 17:48:36 on modular [Seed = 2156306496] ------------------------------------- [ K.1 K.1] [ K.1 K.1] Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 17:48:46 2004 Input: R:= GF(4); M := MatrixRing(R,2); Mt := { A : A in M | Trace(A) eq 0}; Mf := {A: A in M | A[1] eq A[2]}; Mtf := Mt meet Mf; seq:=[Random(M):num in [1..10]]; #([A : A in seq | A in Mt]); #([A : A in seq | A in Mf]); #([A : A in seq | A in Mtf]); Output: Magma V2.10-6 Wed Mar 3 2004 17:48:43 on modular [Seed = 2307893574] ------------------------------------- 2 1 0 Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 17:48:58 2004 Input: K:=GF(4); M22:=MatrixRing(K,2); m:=M22![K.1,K.1,K.1,K.1]; m; m+m; m*m; m*2; Output: Magma V2.10-6 Wed Mar 3 2004 17:48:54 on modular [Seed = 2459218496] ------------------------------------- [ K.1 K.1] [ K.1 K.1] [ 0 0] [ 0 0] [ 0 0] [ 0 0] [ 0 0] [ 0 0] Total time: 3.549 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 17:48:58 2004 Input: R:= GF(4); M := MatrixRing(R,2); Mt := { A : A in M | Trace(A) eq 0}; Mf := {A: A in M | A[1] eq A[2]}; Mtf := Mt meet Mf; seq:=[Random(M):num in [1..10]]; #([A : A in seq | A in Mt]); #([A : A in seq | A in Mf]); #([A : A in seq | A in Mtf]); Output: Magma V2.10-6 Wed Mar 3 2004 17:48:55 on modular [Seed = 2644229454] ------------------------------------- 0 1 0 Total time: 3.509 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 17:49:15 2004 Input: K:=GF(4); M22:=MatrixRing(K,2); m:=M22![K.1,K.1,K.1,K.1]; m; m+m; m*m; m+2; Output: Magma V2.10-6 Wed Mar 3 2004 17:49:12 on modular [Seed = 2913701185] ------------------------------------- [ K.1 K.1] [ K.1 K.1] [ 0 0] [ 0 0] [ 0 0] [ 0 0] [ K.1 K.1] [ K.1 K.1] Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 17:49:23 2004 Input: R:= GF(4); M := MatrixRing(R,2); Mt := { A : A in M | Trace(A) eq 0}; Mf := {A: A in M | A[1] eq A[2]}; Mtf := Mt meet Mf; seq:=[Random(M):num in [1..100000]]; #([A : A in seq | A in Mt]); #([A : A in seq | A in Mf]); #([A : A in seq | A in Mtf]); Output: Magma V2.10-6 Wed Mar 3 2004 17:49:19 on modular [Seed = 3065026141] ------------------------------------- 25128 6223 1613 Total time: 4.069 seconds, Total memory usage: 6.95MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 17:49:29 2004 Input: K:=GF(4); M22:=MatrixRing(K,2); m:=M22![K.1,K.1,K.1,K.1]; m; m+m; m*m; m+3; Output: Magma V2.10-6 Wed Mar 3 2004 17:49:26 on modular [Seed = 3199770188] ------------------------------------- [ K.1 K.1] [ K.1 K.1] [ 0 0] [ 0 0] [ 0 0] [ 0 0] [K.1^2 K.1] [ K.1 K.1^2] Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Wed Mar 3 17:51:04 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-7, x^2-10]); OK:=MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 17:51:00 on modular [Seed = 3486117535] ------------------------------------- [ , , , ] Total time: 3.899 seconds, Total memory usage: 2.06MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Wed Mar 3 18:00:31 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7x^4+3x^2-x+1); OK := RingOfIntegers(K); for m:= 2 to 100 do if isPrime(m) do Factorization(m*OK); end if end for Output: Magma V2.10-6 Wed Mar 3 2004 18:00:27 on modular [Seed = 4092973180] ------------------------------------- >> K := NumberField(x^5+7x^4+3x^2-x+1); ^ User error: bad syntax >> OK := RingOfIntegers(K); ^ User error: Identifier 'K' has not been declared or assigned >> if isPrime(m) do ^ User error: bad syntax >> Factorization(m*OK); ^ User error: Identifier 'm' has not been declared or assigned >> end if ^ User error: bad syntax >> end for ^ User error: bad syntax Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Wed Mar 3 18:00:52 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); OK := RingOfIntegers(K); for m:= 2 to 100 do if isPrime(m) do Factorization(m*OK); end if end for Output: Magma V2.10-6 Wed Mar 3 2004 18:00:48 on modular [Seed = 67250081] ------------------------------------- >> if isPrime(m) do ^ User error: bad syntax >> Factorization(m*OK); ^ User error: Identifier 'm' has not been declared or assigned >> end if ^ User error: bad syntax >> end for ^ User error: bad syntax Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Wed Mar 3 18:01:06 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); OK := RingOfIntegers(K); for m:= 2 to 100 do if isPrime(m) then Factorization(m*OK); end if end for Output: Magma V2.10-6 Wed Mar 3 2004 18:01:02 on modular [Seed = 421477042] ------------------------------------- >> end for ^ User error: bad syntax Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Wed Mar 3 18:01:28 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); OK := RingOfIntegers(K); for m:= 2 to 100 do if isPrime(m) then Factorization(m*OK); end if; end for; Output: Magma V2.10-6 Wed Mar 3 2004 18:01:25 on modular [Seed = 589627619] ------------------------------------- >> if isPrime(m) then ^ User error: Identifier 'isPrime' has not been declared or assigned Total time: 3.099 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 18:03:04 2004 Input: exponents := function (q,r) for i:= r-1 to 0 by -1 do llista := Include(llista,q^i); end for; return llista; end function; t := func < q,r | [q^i: i in [r-1..0]]>; Output: Magma V2.10-6 Wed Mar 3 2004 18:03:01 on modular [Seed = 892539157] ------------------------------------- >> llista := Include(llista,q^i); ^ User error: Identifier 'llista' has not been declared or assigned Total time: 3.649 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Wed Mar 3 18:03:09 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); OK := RingOfIntegers(K); for m:= 2 to 100 do if IsPrime(m) then Factorization(m*OK); end if; end for; Output: Magma V2.10-6 Wed Mar 3 2004 18:03:05 on modular [Seed = 1027283217] ------------------------------------- [ ] [ ] [ , , ] [ , ] [ , , , ] [ , ] [ , , ] [ , , ] [ , ] [ , , ] [ , , ] [ ] [ , ] [ , , , ] [ , ] [ , ] [ , ] [ ] [ , , , ] [ , , , ] [ ] [ , ] [ , , , ] [ , ] [ ] Total time: 3.819 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 18:03:24 2004 Input: exponents := function (q,r) llista := []; for i:= r-1 to 0 by -1 do llista := Include(llista,q^i); end for; return llista; end function; t := func < q,r | [q^i: i in [r-1..0]]>; Output: Magma V2.10-6 Wed Mar 3 2004 18:03:20 on modular [Seed = 1195467642] ------------------------------------- Total time: 3.639 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 18:03:38 2004 Input: K:=GF(4); M22:=MatrixRing(K,2); m:=M22![2,5,1,3]; Output: Magma V2.10-6 Wed Mar 3 2004 18:03:35 on modular [Seed = 1229942027] ------------------------------------- Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 18:03:43 2004 Input: exponents := function (q,r) llista := []; for i:= r-1 to 0 by -1 do llista := Include(llista,q^i); end for; return llista; end function; t := func < q,r | [q^i: i in [r-1..0]]>; t(7,3); Output: Magma V2.10-6 Wed Mar 3 2004 18:03:40 on modular [Seed = 1347843097] ------------------------------------- [] Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 18:03:55 2004 Input: K:=GF(4); M22:=MatrixRing(K,2); m:=M22![2,5,1,3]; Trace(m); Output: Magma V2.10-6 Wed Mar 3 2004 18:03:52 on modular [Seed = 1532854022] ------------------------------------- 1 Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 18:04:01 2004 Input: exponents := function (q,r) llista := []; for i:= r-1 to 0 by -1 do llista := Include(llista,q^i); end for; return llista; end function; exponents(7,3); t := func < q,r | [q^i: i in [r-1..0]]>; t(7,3); Output: Magma V2.10-6 Wed Mar 3 2004 18:03:58 on modular [Seed = 1650738745] ------------------------------------- [ 49, 7, 1 ] [] Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 18:04:34 2004 Input: K:=GF(4); M22:=MatrixRing(K,2); m:=M22![2,5,1,3]; m; Trace(m); Output: Magma V2.10-6 Wed Mar 3 2004 18:04:31 on modular [Seed = 1953648654] ------------------------------------- [ 0 1] [ 1 1] 1 Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 18:04:48 2004 Input: exponents := function (q,r) llista := []; for i:= r-1 to 0 by -1 do llista := Include(llista,q^i); end for; return llista; end function; exponents(7,3); t := func < q,r | ([q^i: i in [r-1..0]]) >; t(7,3); Output: Magma V2.10-6 Wed Mar 3 2004 18:04:45 on modular [Seed = 2138659831] ------------------------------------- [ 49, 7, 1 ] [] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 18:05:10 2004 Input: K:=GF(4); K; M22:=MatrixRing(K,2); m:=M22![2,5,1,3]; m; Trace(m); Output: Magma V2.10-6 Wed Mar 3 2004 18:05:07 on modular [Seed = 2189731364] ------------------------------------- Finite field of size 2^2 [ 0 1] [ 1 1] 1 Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 18:05:21 2004 Input: exponents := function (q,r) llista := []; for i:= r-1 to 0 by -1 do llista := Include(llista,q^i); end for; return llista; end function; exponents(7,3); t := func < q,r | ({q^i: i in [r-1..0]}) >; t(7,3); Output: Magma V2.10-6 Wed Mar 3 2004 18:05:18 on modular [Seed = 2509484350] ------------------------------------- [ 49, 7, 1 ] {} Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 18:05:45 2004 Input: exponents := function (q,r) llista := []; for i:= r-1 to 0 by -1 do llista := Include(llista,q^i); end for; return llista; end function; exponents(7,3); t := func < q,r | ({q^i: i in [r-1..0]}) >; t(7,3); [8..3]; Output: Magma V2.10-6 Wed Mar 3 2004 18:05:42 on modular [Seed = 2627385439] ------------------------------------- [ 49, 7, 1 ] {} [] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 18:05:50 2004 Input: K:=GF(4); K; M22:=MatrixRing(2,K); m:=M22![2,5,1,3]; m; Trace(m); Output: Magma V2.10-6 Wed Mar 3 2004 18:05:47 on modular [Seed = 2762113130] ------------------------------------- Finite field of size 2^2 >> M22:=MatrixRing(2,K); ^ Runtime error in 'MatrixRing': Bad argument types Argument types given: RngIntElt, FldFin >> m:=M22![2,5,1,3]; ^ User error: Identifier 'M22' has not been declared or assigned >> m; ^ User error: Identifier 'm' has not been declared or assigned >> Trace(m);; ^ User error: Identifier 'm' has not been declared or assigned Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 18:06:01 2004 Input: exponents := function (q,r) llista := []; for i:= r-1 to 0 by -1 do llista := Include(llista,q^i); end for; return llista; end function; exponents(7,3); t := func < q,r | ({q^i: i in [r-1..0]}) >; t(7,3); [3..8]; Output: Magma V2.10-6 Wed Mar 3 2004 18:05:58 on modular [Seed = 2930281085] ------------------------------------- [ 49, 7, 1 ] {} [ 3 .. 8 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 18:06:09 2004 Input: K:=GF(8); K; M22:=MatrixRing(K,2); m:=M22![2,5,1,3]; m; Trace(m); Output: Magma V2.10-6 Wed Mar 3 2004 18:06:06 on modular [Seed = 2981598570] ------------------------------------- Finite field of size 2^3 [ 0 1] [ 1 1] 1 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 18:06:19 2004 Input: exponents := function (q,r) llista := []; for i:= r-1 to 0 by -1 do llista := Include(llista,q^i); end for; return llista; end function; exponents(7,3); t := func < q,r | ({q^i: i in [0..r-1]}) >; t(7,3); [3..8]; Output: Magma V2.10-6 Wed Mar 3 2004 18:06:16 on modular [Seed = 3099499605] ------------------------------------- [ 49, 7, 1 ] { 1, 7, 49 } [ 3 .. 8 ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 18:06:36 2004 Input: K:=GF(9); K; M22:=MatrixRing(K,2); m:=M22![2,5,1,3]; m; Trace(m); Output: Magma V2.10-6 Wed Mar 3 2004 18:06:33 on modular [Seed = 3284526911] ------------------------------------- Finite field of size 3^2 [ 2 2] [ 1 0] 2 Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 18:06:39 2004 Input: exponents := function (q,r) llista := []; for i:= r-1 to 0 by -1 do llista := Include(llista,q^i); end for; return llista; end function; exponents(7,3); t := func < q,r | [q^i: i in [0..r-1]] >; t(7,3); [3..8]; Output: Magma V2.10-6 Wed Mar 3 2004 18:06:36 on modular [Seed = 3435849781] ------------------------------------- [ 49, 7, 1 ] [ 1, 7, 49 ] [ 3 .. 8 ] Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 18:07:16 2004 Input: K:=GF(9); K; M22:=MatrixRing(K,2); m:=M22![2,5,2,2]; m; Trace(m); Output: Magma V2.10-6 Wed Mar 3 2004 18:07:13 on modular [Seed = 3722180857] ------------------------------------- Finite field of size 3^2 [ 2 2] [ 2 2] 1 Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 18:07:30 2004 Input: K:=GF(9); K; M22:=MatrixRing(K,2); m:=M22![2,5,2,1]; m; Trace(m); Output: Magma V2.10-6 Wed Mar 3 2004 18:07:26 on modular [Seed = 3840065999] ------------------------------------- Finite field of size 3^2 [ 2 2] [ 2 1] 0 Total time: 3.049 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 18:08:20 2004 Input: exponents := function (q,r) llista := []; for i:= r-1 to 0 by -1 do llista := Include(llista,q^i); end for; return llista; end function; exponents(7,3); t := func < q,r | Reverse([q^i: i in [0..r-1]]) >; t(7,3); [3..8]; Output: Magma V2.10-6 Wed Mar 3 2004 18:08:17 on modular [Seed = 4025076363] ------------------------------------- [ 49, 7, 1 ] [ 49, 7, 1 ] [ 3 .. 8 ] Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 18:08:53 2004 Input: exponents := function (q,r) llista := []; for i:= r-1 to 0 by -1 do llista := Include(llista,q^i); end for; return llista; end function; exponents(7,3); t := func < q,r | Reverse([q^i: i in [0..r-1]]) >; t(7,3); [8..3 by -1]; Output: Magma V2.10-6 Wed Mar 3 2004 18:08:50 on modular [Seed = 4142977905] ------------------------------------- [ 49, 7, 1 ] [ 49, 7, 1 ] [ 8 .. 3 by -1 ] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Wed Mar 3 18:09:25 2004 Input: exponents := function (q,r) llista := []; for i:= r-1 to 0 by -1 do llista := Include(llista,q^i); end for; return llista; end function; exponents(7,3); t := func < q,r | [q^i: i in [r-1..0 by -1]] >; t(7,3); [8..3 by -1]; Output: Magma V2.10-6 Wed Mar 3 2004 18:09:22 on modular [Seed = 4177452383] ------------------------------------- [ 49, 7, 1 ] [ 49, 7, 1 ] [ 8 .. 3 by -1 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 18:09:36 2004 Input: K:=GF(11); K; M22:=MatrixRing(K,2); m:=M22![2,5,2,1]; m; Trace(m); Output: Magma V2.10-6 Wed Mar 3 2004 18:09:33 on modular [Seed = 402859] ------------------------------------- Finite field of size 11 [ 2 5] [ 2 1] 3 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 18:09:58 2004 Input: K:=GF(4); M22:=MatrixRing(K,2); m:=M22![2,5,2,1]; m; Trace(m); Output: Magma V2.10-6 Wed Mar 3 2004 18:09:55 on modular [Seed = 151989452] ------------------------------------- [ 0 1] [ 0 1] 1 Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 18:38:34 2004 Input: K:=GF(4); M22:=MatrixRing(K,2); m:=M22![2,5,2,1]; m; Trace(m); M22; Output: Magma V2.10-6 Wed Mar 3 2004 18:38:31 on modular [Seed = 1178626615] ------------------------------------- [ 0 1] [ 0 1] 1 Full Matrix Algebra of degree 2 over GF(2^2) Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 18:41:45 2004 Input: K:=GF(4); M22:=MatrixRing(K,2); m:=M22![2,5,2,1]; m; Trace(m); {m:=M22! | Trace(m) = 0}; Output: Magma V2.10-6 Wed Mar 3 2004 18:41:42 on modular [Seed = 1464957543] ------------------------------------- [ 0 1] [ 0 1] 1 >> {m:=M22! | Trace(m) = 0};; ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 18:42:32 2004 Input: K:=GF(4); M22:=MatrixRing(K,2); m:=M22![2,5,2,1]; m; Trace(m); {M22! | Trace eq 0}; Output: Magma V2.10-6 Wed Mar 3 2004 18:42:29 on modular [Seed = 1549431103] ------------------------------------- [ 0 1] [ 0 1] 1 >> {M22! | Trace eq 0};; ^ User error: bad syntax Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 18:42:41 2004 Input: K:=GF(4); M22:=MatrixRing(K,2); m:=M22![2,5,2,1]; m; Trace(m); {M22 | Trace eq 0}; Output: Magma V2.10-6 Wed Mar 3 2004 18:42:38 on modular [Seed = 1701005325] ------------------------------------- [ 0 1] [ 0 1] 1 >> {M22 | Trace eq 0};; ^ Runtime error in 'eq': Bad argument types Argument types given: Intrinsic, RngIntElt Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 18:42:58 2004 Input: K:=GF(4); M22:=MatrixRing(K,2); m:=M22![2,5,2,1]; m; Trace(m); {M22 | Trace(M22) eq 0}; Output: Magma V2.10-6 Wed Mar 3 2004 18:42:55 on modular [Seed = 1785480979] ------------------------------------- [ 0 1] [ 0 1] 1 >> {M22 | Trace(M22) eq 0};; ^ Runtime error in 'Trace': Bad argument types Argument types given: AlgMat Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 18:43:08 2004 Input: K:=GF(4); M22:=MatrixRing(K,2); m:=M22![2,5,2,1]; m; Trace(m); {M22 | Trace(m) eq 0}; Output: Magma V2.10-6 Wed Mar 3 2004 18:43:05 on modular [Seed = 1937071868] ------------------------------------- [ 0 1] [ 0 1] 1 >> {M22 | Trace(m) eq 0};; ^ Runtime error in { ... }: Can't coerce argument 1 into the universe Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 18:43:22 2004 Input: K:=GF(4); M22:=MatrixRing(K,2); m:=M22![2,5,2,1]; m; Trace(m); {M22}; Output: Magma V2.10-6 Wed Mar 3 2004 18:43:19 on modular [Seed = 2021545449] ------------------------------------- [ 0 1] [ 0 1] 1 { Full Matrix Algebra of degree 2 over GF(2^2) } Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 18:43:43 2004 Input: K:=GF(4); M22:=MatrixRing(K,2); m:=M22![2,5,2,1]; m; Trace(m); mm:={M22}; mm; Output: Magma V2.10-6 Wed Mar 3 2004 18:43:40 on modular [Seed = 2173152299] ------------------------------------- [ 0 1] [ 0 1] 1 { Full Matrix Algebra of degree 2 over GF(2^2) } Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 18:46:19 2004 Input: K:=GF(4); M22:=MatrixRing(K,2); m:=M22![2,5,2,1]; m; Trace(m); mm:={M22![a,a,a,a] : a in [0..1] | (Trace(M22![a,a,a,a]) eq 0) }; mm; Output: Magma V2.10-6 Wed Mar 3 2004 18:46:16 on modular [Seed = 2425798366] ------------------------------------- [ 0 1] [ 0 1] 1 { [ 0 0] [ 0 0], [ 1 1] [ 1 1] } Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 18:46:48 2004 Input: K:=GF(4); M22:=MatrixRing(K,2); m:=M22![2,5,2,1]; m; Trace(m); mm:={M22![a,b,c,d] : a,b,c,d in [0..1] | (Trace(M22![a,b,c,d]) eq 0) }; mm; Output: Magma V2.10-6 Wed Mar 3 2004 18:46:45 on modular [Seed = 2577381370] ------------------------------------- [ 0 1] [ 0 1] 1 { [ 0 0] [ 0 0], [ 0 1] [ 1 0], [ 1 0] [ 1 1], [ 0 0] [ 1 0], [ 1 1] [ 0 1], [ 0 1] [ 0 0], [ 1 0] [ 0 1], [ 1 1] [ 1 1] } Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 18:51:39 2004 Input: K:=GF(4); M22:=MatrixRing(K,2); Mt:={M22![a,b,c,d] : a,b,c,d in [0..1] | (Trace(M22![a,b,c,d]) eq 0) }; Mt; Mf:={M22![a,b,c,d] : a,b,c,d in [0..1] | ( (M22![a,b,c,d])[1] eq (M22![a,b,c,d])[2]) }; Mf; Output: Magma V2.10-6 Wed Mar 3 2004 18:51:36 on modular [Seed = 3081869369] ------------------------------------- { [ 0 0] [ 0 0], [ 0 1] [ 1 0], [ 1 0] [ 1 1], [ 0 0] [ 1 0], [ 1 1] [ 0 1], [ 0 1] [ 0 0], [ 1 0] [ 0 1], [ 1 1] [ 1 1] } { [ 0 0] [ 0 0], [ 1 0] [ 1 0], [ 0 1] [ 0 1], [ 1 1] [ 1 1] } Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 18:55:14 2004 Input: K:=GF(4); M22:=MatrixRing(K,2); Mt:={M22![a,b,c,d] : a,b,c,d in [0..1] | (Trace(M22![a,b,c,d]) eq 0) }; Mt; Mf:={M22![a,b,c,d] : a,b,c,d in [0..1] | ( (M22![a,b,c,d])[1] eq (M22![a,b,c,d])[2]) }; Mf; Mtf:= Mt meet Mf; Output: Magma V2.10-6 Wed Mar 3 2004 18:55:11 on modular [Seed = 3234263193] ------------------------------------- { [ 0 0] [ 0 0], [ 0 1] [ 1 0], [ 1 0] [ 1 1], [ 0 0] [ 1 0], [ 1 1] [ 0 1], [ 0 1] [ 0 0], [ 1 0] [ 0 1], [ 1 1] [ 1 1] } { [ 0 0] [ 0 0], [ 1 0] [ 1 0], [ 0 1] [ 0 1], [ 1 1] [ 1 1] } Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Wed Mar 3 18:55:29 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-5); E:=EquationOrder(K); OK:=MaximalOrder(K); I:=209*OK; J:=2*OK; Index(OK, E); F := Factorization(I); Factorization(J); [K!OK.i : i in [1, 2, 3, 4]]; Output: Magma V2.10-6 Wed Mar 3 2004 18:55:25 on modular [Seed = 3570590908] ------------------------------------- 2 [ ] >> [K!OK.i : i in [1, 2, 3, 4]];; ^ Runtime error in '.': Value for name index (3) should be in the range [1..2] Total time: 3.719 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 18:55:32 2004 Input: K:=GF(4); M22:=MatrixRing(K,2); Mt:={M22![a,b,c,d] : a,b,c,d in [0..1] | (Trace(M22![a,b,c,d]) eq 0) }; Mt; Mf:={M22![a,b,c,d] : a,b,c,d in [0..1] | ( (M22![a,b,c,d])[1] eq (M22![a,b,c,d])[2]) }; Mf; Mtf:= Mt meet Mf; Mtf; Output: Magma V2.10-6 Wed Mar 3 2004 18:55:27 on modular [Seed = 3755601846] ------------------------------------- { [ 0 0] [ 0 0], [ 0 1] [ 1 0], [ 1 0] [ 1 1], [ 0 0] [ 1 0], [ 1 1] [ 0 1], [ 0 1] [ 0 0], [ 1 0] [ 0 1], [ 1 1] [ 1 1] } { [ 0 0] [ 0 0], [ 1 0] [ 1 0], [ 0 1] [ 0 1], [ 1 1] [ 1 1] } { [ 0 0] [ 0 0], [ 1 1] [ 1 1] } Total time: 3.469 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Wed Mar 3 18:55:50 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-5); E:=EquationOrder(K); OK:=MaximalOrder(K); I:=209*OK; J:=2*OK; Index(OK, E); F := Factorization(I); F; Factorization(J); [K!OK.i : i in [1, 2]]; Output: Magma V2.10-6 Wed Mar 3 2004 18:55:46 on modular [Seed = 4008238698] ------------------------------------- 2 [ , , , ] [ ] [ 1, 1/2*(a + 1) ] Total time: 3.039 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 18:57:40 2004 Input: K:=GF(4); M:=MatrixRing(K,2); Mt:={M![a,b,c,d] : a,b,c,d in [0..1] | (Trace(M22![a,b,c,d]) eq 0) }; Mt; Mf:={M![a,b,c,d] : a,b,c,d in [0..1] | ( (M22![a,b,c,d])[1] eq (M22![a,b,c,d])[2]) }; Mf; Mtf:= Mt meet Mf; Mtf; Random(M); Output: Magma V2.10-6 Wed Mar 3 2004 18:57:37 on modular [Seed = 4159817472] ------------------------------------- >> Mt:={M![a,b,c,d] : a,b,c,d in [0..1] | (Trace(M22![a,b,c,d]) eq 0) }; ^ User error: Identifier 'M22' has not been declared or assigned >> Mt; ^ User error: Identifier 'Mt' has not been declared or assigned >> Mf:={M![a,b,c,d] : a,b,c,d in [0..1] | ( (M22![a,b,c,d])[1] eq (M22![a,b,c, ^ User error: Identifier 'M22' has not been declared or assigned >> Mf; ^ User error: Identifier 'Mf' has not been declared or assigned >> Mtf:= Mt meet Mf; ^ User error: Identifier 'Mt' has not been declared or assigned >> Mtf; ^ User error: Identifier 'Mtf' has not been declared or assigned [ 0 K.1^2] [ 1 0] Total time: 2.889 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 18:57:57 2004 Input: K:=GF(4); M:=MatrixRing(K,2); Mt:={M![a,b,c,d] : a,b,c,d in [0..1] | (Trace(M![a,b,c,d]) eq 0) }; Mt; Mf:={M![a,b,c,d] : a,b,c,d in [0..1] | ( (M![a,b,c,d])[1] eq (M![a,b,c,d])[2]) }; Mf; Mtf:= Mt meet Mf; Mtf; Random(M); Output: Magma V2.10-6 Wed Mar 3 2004 18:57:54 on modular [Seed = 4244295160] ------------------------------------- { [ 0 0] [ 0 0], [ 0 1] [ 1 0], [ 1 0] [ 1 1], [ 0 0] [ 1 0], [ 1 1] [ 0 1], [ 0 1] [ 0 0], [ 1 0] [ 0 1], [ 1 1] [ 1 1] } { [ 0 0] [ 0 0], [ 1 0] [ 1 0], [ 0 1] [ 0 1], [ 1 1] [ 1 1] } { [ 0 0] [ 0 0], [ 1 1] [ 1 1] } [K.1^2 0] [ 0 1] Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 18:58:17 2004 Input: K:=GF(4); M:=MatrixRing(K,2); Mt:={M![a,b,c,d] : a,b,c,d in [0..1] | (Trace(M![a,b,c,d]) eq 0) }; Mt; Mf:={M![a,b,c,d] : a,b,c,d in [0..1] | ( (M![a,b,c,d])[1] eq (M![a,b,c,d])[2]) }; Mf; Mtf:= Mt meet Mf; Mtf; Random(M); Output: Magma V2.10-6 Wed Mar 3 2004 18:58:14 on modular [Seed = 67253525] ------------------------------------- { [ 0 0] [ 0 0], [ 0 1] [ 1 0], [ 1 0] [ 1 1], [ 0 0] [ 1 0], [ 1 1] [ 0 1], [ 0 1] [ 0 0], [ 1 0] [ 0 1], [ 1 1] [ 1 1] } { [ 0 0] [ 0 0], [ 1 0] [ 1 0], [ 0 1] [ 0 1], [ 1 1] [ 1 1] } { [ 0 0] [ 0 0], [ 1 1] [ 1 1] } [ 1 1] [ 0 K.1] Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 19:04:51 2004 Input: K:=GF(4); M:=MatrixRing(K,2); Mt:={M![a,b,c,d] : a,b,c,d in [0..1] | (Trace(M![a,b,c,d]) eq 0) }; Mt; Mf:={M![a,b,c,d] : a,b,c,d in [0..1] | ( (M![a,b,c,d])[1] eq (M![a,b,c,d])[2]) }; Mf; [Random(M): i in [1..100]]; Mtf:= Mt meet Mf; Mtf; Random(M); Output: Magma V2.10-6 Wed Mar 3 2004 19:04:48 on modular [Seed = 740957835] ------------------------------------- { [ 0 0] [ 0 0], [ 0 1] [ 1 0], [ 1 0] [ 1 1], [ 0 0] [ 1 0], [ 1 1] [ 0 1], [ 0 1] [ 0 0], [ 1 0] [ 0 1], [ 1 1] [ 1 1] } { [ 0 0] [ 0 0], [ 1 0] [ 1 0], [ 0 1] [ 0 1], [ 1 1] [ 1 1] } [ [ K.1 K.1^2] [ 1 1], [K.1^2 1] [ 0 K.1^2], [ 0 K.1^2] [K.1^2 K.1], [ 0 K.1] [ 0 K.1], [ 0 0] [ 0 K.1^2], [ 0 1] [ K.1 K.1], [ K.1 K.1] [ 1 K.1], [K.1^2 K.1^2] [ 0 1], [K.1^2 K.1] [K.1^2 0], [ 1 K.1^2] [K.1^2 K.1^2], [ K.1 K.1] [ 0 0], [K.1^2 K.1^2] [ 1 K.1^2], [ 0 0] [ 1 1], [ 0 1] [ K.1 K.1^2], [ 1 0] [ 0 K.1^2], [ 0 K.1^2] [ 0 0], [ 1 K.1^2] [ 1 K.1^2], [ K.1 0] [K.1^2 K.1], [ K.1 1] [ K.1 0], [ K.1 0] [K.1^2 K.1^2], [ K.1 K.1] [ K.1 0], [K.1^2 1] [ 0 K.1], [ 1 K.1^2] [K.1^2 K.1], [ 1 K.1] [ 0 1], [K.1^2 1] [ 0 0], [ K.1 1] [K.1^2 K.1], [ 1 K.1^2] [ 0 K.1^2], [K.1^2 1] [ 0 1], [ 1 0] [ 1 0], [ 1 K.1^2] [ K.1 0], [ 1 K.1^2] [ 1 0], [K.1^2 K.1^2] [K.1^2 K.1], [K.1^2 0] [ K.1 K.1], [K.1^2 1] [ 1 K.1^2], [K.1^2 0] [ 1 K.1], [ 1 K.1] [K.1^2 K.1^2], [ K.1 0] [ 0 K.1^2], [K.1^2 1] [ K.1 K.1], [ K.1 1] [K.1^2 1], [K.1^2 K.1] [ 0 K.1], [ K.1 0] [ 0 0], [K.1^2 K.1^2] [ 1 K.1], [ 0 1] [ 1 1], [ 1 K.1] [ K.1 0], [ K.1 K.1^2] [ 0 K.1], [ K.1 K.1^2] [ K.1 1], [ 1 K.1] [K.1^2 1], [K.1^2 1] [K.1^2 K.1^2], [ K.1 0] [ K.1 K.1], [ 0 1] [ 0 K.1], [ K.1 K.1^2] [K.1^2 0], [ 1 1] [ 1 0], [ 0 K.1] [ K.1 1], [ 1 0] [K.1^2 K.1^2], [ 0 1] [ 0 0], [ K.1 1] [ 0 1], [ 0 K.1^2] [ K.1 0], [ 1 K.1^2] [ 0 K.1], [ K.1 K.1] [K.1^2 K.1^2], [ 0 K.1] [ K.1 0], [ K.1 1] [ 1 K.1], [ 1 0] [ 1 0], [ 0 0] [ 1 K.1], [ K.1 0] [K.1^2 K.1], [ 0 1] [ K.1 1], [ K.1 0] [K.1^2 K.1], [ 0 K.1] [ 0 1], [K.1^2 0] [ 1 K.1^2], [ K.1 1] [ K.1 1], [ 0 K.1^2] [ K.1 K.1], [ 1 K.1^2] [ 1 K.1^2], [K.1^2 K.1^2] [ K.1 K.1], [ K.1 K.1] [ 0 0], [ K.1 K.1] [K.1^2 0], [ 1 K.1] [ 0 0], [ 1 1] [K.1^2 K.1], [ 0 K.1^2] [K.1^2 0], [ 1 1] [ 1 K.1], [K.1^2 1] [ 0 K.1], [ 0 K.1] [ 1 1], [K.1^2 1] [ 1 1], [ 1 K.1] [ K.1 0], [K.1^2 K.1] [ 1 K.1^2], [K.1^2 0] [ 0 K.1^2], [ 1 0] [ K.1 K.1^2], [K.1^2 K.1^2] [ K.1 K.1], [ 0 K.1^2] [ K.1 1], [ 1 K.1^2] [ K.1 0], [ K.1 K.1] [K.1^2 0], [ 1 K.1^2] [K.1^2 K.1], [ K.1 K.1^2] [K.1^2 K.1^2], [ 0 1] [ 0 K.1^2], [ K.1 K.1^2] [K.1^2 K.1], [K.1^2 K.1] [ 0 K.1], [K.1^2 K.1^2] [ 1 0], [K.1^2 K.1] [ K.1 K.1], [ 0 K.1^2] [ K.1 K.1^2], [ 0 K.1^2] [ 0 K.1], [ K.1 0] [ 0 K.1^2], [ 1 0] [ 1 K.1^2] ] { [ 0 0] [ 0 0], [ 1 1] [ 1 1] } [K.1^2 0] [ 0 K.1] Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 19:05:24 2004 Input: K:=GF(4); M:=MatrixRing(K,2); Mt:={M![a,b,c,d] : a,b,c,d in [0..1] | (Trace(M![a,b,c,d]) eq 0) }; Mt; Mf:={M![a,b,c,d] : a,b,c,d in [0..1] | ( (M![a,b,c,d])[1] eq (M![a,b,c,d])[2]) }; Mf; Mtf:= Mt meet Mf; Mtf; [Random(M): i in [1..100000]]; Output: Magma V2.10-6 Wed Mar 3 2004 19:05:16 on modular [Seed = 1060703620] ------------------------------------- { [ 0 0] [ 0 0], [ 0 1] [ 1 0], [ 1 0] [ 1 1], [ 0 0] [ 1 0], [ 1 1] [ 0 1], [ 0 1] [ 0 0], [ 1 0] [ 0 1], [ 1 1] [ 1 1] } { [ 0 0] [ 0 0], [ 1 0] [ 1 0], [ 0 1] [ 0 1], [ 1 1] [ 1 1] } { [ 0 0] [ 0 0], [ 1 1] [ 1 1] } [ [ 1 K.1^2] [K.1^2 K.1^2], [ K.1 K.1] [K.1^2 0], [ K.1 0] [ 1 K.1], [K.1^2 1] [K.1^2 0], [K.1^2 1] [ K.1 1], [ K.1 K.1^2] [K.1^2 1], [ 0 1] [K.1^2 K.1^2], [ 0 K.1] [ 0 K.1], [ 1 K.1^2] [ 0 1], [ K.1 K.1^2] [ 0 K.1], [ 0 0] [ K.1 K.1], [ 0 0] [ 0 1], [K.1^2 K.1] [ 1 K.1^2], [ K.1 0] [ K.1 K.1^2], [K.1^2 K.1^2] [ 1 1], [ 1 K.1^2] [K.1^2 K.1^2], [ 0 0] [ 0 1], [ 0 K.1] [ 1 1], [K.1^2 0] [ 0 K.1], [K.1^2 K.1] [ 1 K.1^2], [ K.1 K.1] [K.1^2 K.1], [ 0 0] [ K.1 K.1], [K.1^2 0] [K.1^2 K.1], [K.1^2 K.1^2] [ K.1 K.1], [ 1 K.1^2] [K.1^2 K.1], [ 1 K.1^2] [ 0 1], [ 1 1] [ 0 0], [ 1 1] [K.1^2 K.1^2], [K.1^2 0] [ K.1 K.1], [ 0 1] [ 1 1], [K.1^2 1] [K.1^2 K.1], [K.1^2 1] [ 1 K.1^2], [ 0 K.1] [ 0 K.1], [K.1^2 K.1] [ 1 0], [ K.1 K.1] [ 1 K.1^2], [ 0 0] [ K.1 K.1], [K.1^2 0] [ 0 0], [ 0 0] [ 1 0], [ 1 1] [ 0 1], [ 1 K.1^2] [K.1^2 0], [ K.1 K.1^2] [K.1^2 0], [ 1 0] [ 0 K.1^2], [ 1 K.1^2] [K.1^2 1], [K.1^2 0] [K.1^2 K.1], [ 0 0] [ 0 K.1], [ 0 1] [K.1^2 1], [K.1^2 0] [ K.1 K.1], [ K.1 K.1^2] [ 1 K.1^2], [ 0 0] [ K.1 K.1], [ 1 K.1^2] [ 0 1], [ 0 K.1] [ 1 K.1^2], [ 1 0] [ 1 K.1], [ 0 K.1] [ 0 K.1^2], [ 1 K.1] [ 1 K.1], [K.1^2 0] [K.1^2 0], [ K.1 0] [K.1^2 0], [ K.1 0] [ 0 K.1], [ K.1 K.1] [ 1 0], [ 0 0] [ K.1 K.1], [ K.1 0] [ 1 0], [ 1 K.1^2] [ 1 0], [ K.1 0] [ K.1 K.1], [K.1^2 0] [ 0 1], [ 0 0] [ 0 K.1], [ K.1 0] [ K.1 0], [ 1 K.1^2] [ 0 K.1^2], [ K.1 K.1] [K.1^2 0], [ 1 0] [ 0 K.1^2], [ 0 K.1] [ 1 K.1^2], [ K.1 K.1^2] [ 0 K.1^2], [K.1^2 K.1] [ 1 K.1^2], [ 1 0] [ K.1 K.1], [ 1 K.1^2] [ K.1 K.1], [ 1 0] [ 0 1], [ K.1 1] [ 1 0], [ 1 1] [ K.1 K.1], [K.1^2 K.1] [ 0 0], [ K.1 1] [ 0 0], [ K.1 K.1] [ 1 1], [K.1^2 K.1^2] [K.1^2 K.1^2], [ K.1 1] [ K.1 K.1^2], [ 1 1] [ 0 K.1], [ 1 0] [K.1^2 1], [ K.1 K.1] [K.1^2 0], [K.1^2 0] [ 0 K.1], [ 0 K.1] [ 0 1], [ 1 0] [ K.1 K.1], [ 0 K.1] [ K.1 K.1], [ K.1 1] [ 0 K.1^2], [ 1 K.1] [ K.1 0], [ 0 1] [ 1 0], [ 1 K.1^2] [K.1^2 K.1], [ 1 K.1] [ K.1 K.1^2], [ 1 1] [ K.1 0], [K.1^2 1] [ 0 K.1], [ 1 0] [ K.1 K.1^2], [ 1 K.1] [ 0 K.1^2], [ K.1 K.1^2] [ 0 K.1^2], [ 0 K.1] [ 1 K.1], [ 1 1] [K.1^2 1], [ K.1 0] [K.1^2 K.1], [K.1^2 K.1^2] [ 0 K.1], [ 0 1] [K.1^2 K.1], [ K.1 K.1] [K.1^2 1], [ 0 K.1^2] [K.1^2 0], [ 0 0] [ 1 K.1^2], [K.1^2 0] [K.1^2 K.1^2], [ 1 0] [ K.1 0], [ 1 0] [ 1 K.1], [ 1 1] [ 1 0], [ 0 K.1^2] [ 0 K.1], [ K.1 K.1] [ 0 0], [ 0 0] [ 0 1], [ 0 K.1^2] [ 0 K.1^2], [K.1^2 K.1] [K.1^2 K.1], [ 0 0] [ K.1 K.1^2], [ 1 0] [ 1 1], [ K.1 K.1^2] [K.1^2 K.1^2], [K.1^2 1] [ K.1 K.1], [ K.1 1] [ K.1 0], [K.1^2 K.1^2] [ 1 1], [K.1^2 K.1^2] [ 1 0], [ K.1 K.1] [ 0 K.1^2], [ 0 K.1^2] [ 0 1], [ 0 0] [K.1^2 K.1^2], [ K.1 K.1^2] [ 0 K.1], [K.1^2 1] [K.1^2 1], [ 0 K.1] [ 1 1], [ 1 K.1^2] [K.1^2 K.1^2], [ 1 0] [ 0 K.1^2], [K.1^2 0] [ K.1 K.1^2], [ 0 K.1] [ 0 K.1^2], [ 1 K.1^2] [ 1 1], [K.1^2 0] [ 1 K.1^2], [ 0 0] [ 0 K.1^2], [ 1 1] [ 1 0], [K.1^2 0] [ 1 K.1], [ K.1 K.1] [K.1^2 0], [ 1 0] [K.1^2 0], [K.1^2 K.1^2] [ K.1 K.1^2], [ K.1 0] [ 0 1], [K.1^2 K.1] [ 0 0], [K.1^2 0] [ K.1 1], [ 0 1] [ K.1 1], [K.1^2 K.1^2] [K.1^2 K.1], [K.1^2 K.1^2] [ 0 1], [ K.1 0] [K.1^2 K.1^2], [ 1 1] [ K.1 1], [ 1 K.1] [K.1^2 1], [ 0 K.1] [K.1^2 K.1], [ 1 0] [ 1 0], [ K.1 0] [ 1 K.1^2], [K.1^2 K.1] [K.1^2 1], [K.1^2 0] [ 1 0], [ 0 0] [ 0 1], [K.1^2 0] [ 1 0], [ 0 1] [ K.1 K.1], [ 1 0] [K.1^2 0], [ 0 K.1^2] [ 0 0], [ 1 K.1^2] [ 1 1], [K.1^2 K.1] [ 1 0], [ 1 1] [ 1 K.1], [ K.1 1] [ 1 0], [ 1 K.1^2] [ 1 1], [ 1 K.1] [ K.1 K.1^2], [K.1^2 1] [ K.1 K.1], [ 1 0] [ K.1 0], [ 0 0] [K.1^2 0], [ K.1 K.1] [ 0 0], [K.1^2 0] [K.1^2 K.1^2], [ K.1 1] [K.1^2 1], [ 0 0] [ K.1 0], [ 0 0] [ 1 K.1], [K.1^2 K.1^2] [K.1^2 K.1], [ 0 0] [ K.1 1], [ K.1 1] [ 1 K.1^2], [ 1 K.1^2] [ 0 0], [K.1^2 K.1] [ K.1 K.1^2], [ 1 K.1^2] [ 0 0], [K.1^2 K.1^2] [K.1^2 K.1], [K.1^2 K.1^2] [K.1^2 K.1^2], [K.1^2 K.1^2] [ 1 K.1^2], [ 1 1] [ K.1 K.1^2], [ K.1 K.1^2] [K.1^2 K.1^2], [ 1 K.1^2] [ K.1 K.1^2], [ 1 K.1^2] [K.1^2 1], [K.1^2 1] [ 1 0], [K.1^2 1] [K.1^2 K.1], [K.1^2 K.1] [ K.1 K.1^2], [ 1 0] [K.1^2 0], [ K.1 K.1^2] [ 1 K.1], [ 1 K.1] [K.1^2 1], [ K.1 K.1^2] [ 1 0], [ K.1 1] [ K.1 0], [ 1 1] [ K.1 K.1^2], [ K.1 1] [ 0 K.1^2], [ 0 K.1] [K.1^2 0], [K.1^2 0] [ 1 K.1], [ K.1 K.1] [K.1^2 0], [ K.1 K.1^2] [K.1^2 K.1^2], [ 1 K.1^2] [ 0 K.1^2], [K.1^2 0] [ 0 1], [ 0 K.1] [K.1^2 K.1], [K.1^2 K.1^2] [ 0 K.1^2], [ K.1 0] [ 1 K.1^2], [K.1^2 K.1^2] [ 1 K.1^2], [ 1 K.1] [ 1 0], [ 1 K.1^2] [ 1 K.1^2], [K.1^2 K.1^2] [ K.1 K.1], [ K.1 0] [ 0 K.1], [K.1^2 0] [ K.1 1], [ K.1 K.1^2] [ 1 K.1^2], [K.1^2 K.1^2] [ 0 1], [ 1 0] [ K.1 K.1^2], [ 0 K.1^2] [K.1^2 K.1], [ 0 0] [ 1 1], [K.1^2 K.1] [ K.1 0], [ K.1 K.1^2] [ K.1 1], [K.1^2 K.1] [K.1^2 0], [ 0 0] [ K.1 0], [ 1 K.1] [ K.1 1], [ 0 K.1] [ 1 1], [ 0 1] [ 1 1], [ K.1 K.1] [K.1^2 1], [K.1^2 1] [K.1^2 K.1], [ 1 K.1] [ K.1 0], [ 0 K.1^2] [K.1^2 0], [ 1 0] [ 1 K.1^2], [ 1 0] [ 1 1], [K.1^2 0] [ 0 K.1], [K.1^2 0] [ 0 K.1^2], [ K.1 K.1^2] [ K.1 K.1], [ 1 K.1^2] [ 1 K.1^2], [ 0 K.1] [K.1^2 K.1], [ 0 1] [ 1 0], [K.1^2 K.1] [ 0 0], [ K.1 K.1] [K.1^2 K.1], [ 0 0] [ K.1 K.1^2], [ 0 K.1] [ K.1 0], [ 1 0] [ 0 K.1^2], [K.1^2 K.1] [ K.1 0], [ 1 K.1] [K.1^2 K.1^2], [ K.1 K.1] [K.1^2 1], [K.1^2 0] [K.1^2 0], [K.1^2 K.1] [ 1 1], [K.1^2 1] [ K.1 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 19:07:36 2004 Input: K:=GF(4); M:=MatrixRing(K,2); Mt:={M![a,b,c,d] : a,b,c,d in [0..1] | (Trace(M![a,b,c,d]) eq 0) }; Mt; Mf:={M![a,b,c,d] : a,b,c,d in [0..1] | ( (M![a,b,c,d])[1] eq (M![a,b,c,d])[2]) }; Mf; Mtf:= Mt meet Mf; Mtf; [Random(M): in [1..100000]]; Output: Magma V2.10-6 Wed Mar 3 2004 19:07:33 on modular [Seed = 1162049031] ------------------------------------- { [ 0 0] [ 0 0], [ 0 1] [ 1 0], [ 1 0] [ 1 1], [ 0 0] [ 1 0], [ 1 1] [ 0 1], [ 0 1] [ 0 0], [ 1 0] [ 0 1], [ 1 1] [ 1 1] } { [ 0 0] [ 0 0], [ 1 0] [ 1 0], [ 0 1] [ 0 1], [ 1 1] [ 1 1] } { [ 0 0] [ 0 0], [ 1 1] [ 1 1] } >> [Random(M): in [1..100000]];; ^ User error: bad syntax Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 19:07:53 2004 Input: K:=GF(4); M:=MatrixRing(K,2); Mt:={M![a,b,c,d] : a,b,c,d in [0..1] | (Trace(M![a,b,c,d]) eq 0) }; Mt; Mf:={M![a,b,c,d] : a,b,c,d in [0..1] | ( (M![a,b,c,d])[1] eq (M![a,b,c,d])[2]) }; Mf; Mtf:= Mt meet Mf; Mtf; [Random(M): i in [1..100000]]; Output: Magma V2.10-6 Wed Mar 3 2004 19:07:46 on modular [Seed = 1279950617] ------------------------------------- { [ 0 0] [ 0 0], [ 0 1] [ 1 0], [ 1 0] [ 1 1], [ 0 0] [ 1 0], [ 1 1] [ 0 1], [ 0 1] [ 0 0], [ 1 0] [ 0 1], [ 1 1] [ 1 1] } { [ 0 0] [ 0 0], [ 1 0] [ 1 0], [ 0 1] [ 0 1], [ 1 1] [ 1 1] } { [ 0 0] [ 0 0], [ 1 1] [ 1 1] } [ [K.1^2 K.1] [ 1 1], [ 1 0] [ 0 1], [ 0 K.1^2] [ 0 K.1], [ 0 K.1^2] [ 0 K.1^2], [ 0 0] [ 1 K.1^2], [K.1^2 0] [K.1^2 K.1], [ 0 K.1^2] [ K.1 0], [ 0 0] [K.1^2 K.1], [K.1^2 1] [ K.1 K.1], [ 1 K.1] [ K.1 K.1^2], [ 0 0] [ 1 K.1], [K.1^2 K.1^2] [K.1^2 K.1^2], [K.1^2 0] [K.1^2 K.1^2], [K.1^2 K.1] [K.1^2 0], [ 1 0] [K.1^2 1], [ 1 K.1] [ K.1 K.1], [ K.1 K.1] [ K.1 0], [K.1^2 K.1^2] [ K.1 1], [ 0 K.1] [ K.1 0], [ 0 1] [ K.1 0], [K.1^2 K.1^2] [K.1^2 1], [ K.1 K.1^2] [ 0 K.1], [K.1^2 0] [ 0 K.1], [ K.1 K.1^2] [K.1^2 1], [ K.1 0] [ 1 0], [ 0 1] [K.1^2 K.1], [ 1 1] [K.1^2 K.1], [ 1 0] [K.1^2 0], [K.1^2 K.1^2] [K.1^2 K.1^2], [ 1 K.1] [ 1 K.1^2], [ 1 1] [ 0 1], [ 0 K.1] [ 0 1], [ 1 K.1^2] [K.1^2 K.1], [ 1 0] [ K.1 K.1], [ 0 K.1] [ 1 K.1], [ K.1 0] [ 1 1], [ 1 K.1] [K.1^2 K.1^2], [ K.1 K.1^2] [ K.1 K.1^2], [ K.1 K.1^2] [ K.1 0], [ 0 0] [ 0 1], [K.1^2 K.1^2] [K.1^2 0], [ 1 1] [K.1^2 1], [K.1^2 K.1] [ K.1 K.1^2], [ 0 1] [ 0 0], [ 0 0] [ K.1 K.1^2], [ 1 0] [ K.1 K.1^2], [K.1^2 0] [ K.1 1], [ 1 1] [K.1^2 K.1^2], [ 1 0] [ 1 1], [ 0 1] [K.1^2 K.1], [ 1 0] [ 0 K.1], [ K.1 1] [ K.1 K.1^2], [ K.1 K.1] [ 1 K.1^2], [ 1 1] [ K.1 K.1^2], [ K.1 K.1] [ 0 0], [K.1^2 0] [K.1^2 0], [ 1 1] [ K.1 0], [ 0 0] [ 0 1], [K.1^2 K.1^2] [ 0 0], [ K.1 K.1^2] [ 1 K.1], [K.1^2 0] [ 0 1], [K.1^2 K.1] [ 1 K.1^2], [ K.1 1] [ 1 K.1^2], [ 0 K.1] [ 1 1], [ 1 1] [K.1^2 K.1], [ K.1 1] [K.1^2 0], [ K.1 K.1] [ 1 0], [ 1 0] [K.1^2 K.1^2], [ 1 1] [K.1^2 0], [ K.1 K.1^2] [ 1 1], [ 1 1] [K.1^2 1], [K.1^2 1] [ K.1 K.1^2], [ 0 0] [ 0 0], [K.1^2 K.1] [ 1 K.1], [K.1^2 K.1^2] [ 0 1], [ K.1 1] [ 1 1], [K.1^2 K.1^2] [K.1^2 K.1^2], [K.1^2 0] [ K.1 K.1^2], [K.1^2 0] [ 1 K.1^2], [ 1 K.1^2] [K.1^2 K.1], [ 1 K.1] [ K.1 K.1^2], [ K.1 K.1^2] [ 1 0], [ K.1 K.1] [K.1^2 K.1^2], [ 0 K.1] [ 0 K.1], [K.1^2 0] [ K.1 1], [ 1 K.1] [ K.1 K.1^2], [ 0 0] [ K.1 0], [ 1 1] [ 0 1], [ 0 K.1] [ K.1 1], [ 0 K.1^2] [ 1 0], [ 0 K.1] [ 1 K.1^2], [K.1^2 K.1^2] [K.1^2 K.1], [K.1^2 K.1^2] [ 1 0], [ 0 K.1^2] [ 1 0], [ K.1 K.1^2] [K.1^2 1], [K.1^2 K.1] [K.1^2 K.1], [ 0 K.1] [ K.1 0], [K.1^2 K.1] [K.1^2 K.1^2], [ 0 K.1^2] [K.1^2 0], [ 0 1] [ 0 0], [ 0 1] [ 0 1], [K.1^2 K.1] [ 1 K.1^2], [ K.1 0] [ 1 1], [ K.1 K.1^2] [ 0 1], [ 0 K.1] [K.1^2 1], [K.1^2 0] [K.1^2 K.1], [ 1 K.1] [K.1^2 K.1], [ K.1 1] [ 0 K.1], [ K.1 K.1^2] [ K.1 1], [ 0 K.1] [ 1 K.1^2], [K.1^2 K.1^2] [ K.1 0], [ 1 0] [ K.1 K.1^2], [ 1 0] [ K.1 K.1], [K.1^2 K.1] [ K.1 0], [ 1 K.1] [K.1^2 K.1], [ 0 K.1] [ K.1 K.1], [ 0 K.1^2] [K.1^2 1], [K.1^2 K.1^2] [ 1 K.1^2], [ K.1 K.1] [K.1^2 1], [K.1^2 1] [K.1^2 K.1^2], [ 1 0] [ 1 0], [K.1^2 K.1] [K.1^2 K.1], [ K.1 K.1] [ K.1 K.1], [ K.1 1] [ 1 1], [K.1^2 0] [K.1^2 K.1], [K.1^2 K.1^2] [K.1^2 K.1^2], [ 0 K.1] [K.1^2 K.1], [ K.1 0] [ 1 1], [ 0 1] [ 0 K.1^2], [ 0 1] [K.1^2 1], [ K.1 1] [ 0 K.1], [K.1^2 K.1] [ 0 1], [ K.1 0] [ 1 K.1^2], [ 0 0] [ 1 K.1^2], [ K.1 K.1] [ K.1 K.1^2], [K.1^2 K.1] [ 0 0], [ 0 1] [ K.1 K.1^2], [K.1^2 0] [K.1^2 K.1^2], [K.1^2 1] [ 1 K.1^2], [ 0 1] [ 1 K.1^2], [ K.1 0] [ K.1 0], [K.1^2 K.1] [ 1 1], [ 1 K.1^2] [ K.1 1], [K.1^2 0] [ 0 K.1^2], [ 1 K.1] [K.1^2 0], [K.1^2 1] [ 1 1], [ 1 1] [ 0 K.1], [ 1 K.1^2] [ 1 K.1^2], [ 1 K.1^2] [ 1 0], [ 1 1] [ K.1 K.1], [ 0 K.1^2] [ K.1 0], [K.1^2 1] [ K.1 K.1^2], [ K.1 0] [ K.1 0], [ K.1 1] [ 1 K.1], [K.1^2 K.1^2] [ K.1 1], [ 0 0] [ 0 0], [K.1^2 K.1^2] [ 0 K.1^2], [ 0 K.1^2] [ 1 1], [ 0 1] [K.1^2 0], [ 1 0] [ K.1 1], [ K.1 1] [ 0 K.1^2], [K.1^2 0] [K.1^2 0], [ 1 1] [ 0 K.1^2], [ 1 K.1^2] [ 1 0], [ K.1 K.1] [K.1^2 1], [ 1 1] [ K.1 1], [ 1 K.1] [ 1 K.1], [K.1^2 0] [ 0 K.1], [ 1 K.1] [ 1 0], [ 0 0] [K.1^2 K.1], [K.1^2 0] [ 0 0], [K.1^2 1] [ 0 1], [ 1 0] [K.1^2 1], [ K.1 K.1] [ 0 K.1^2], [K.1^2 K.1^2] [ K.1 K.1^2], [K.1^2 K.1] [ 0 0], [K.1^2 0] [ K.1 K.1], [ K.1 K.1] [ 1 1], [ 0 K.1] [K.1^2 K.1], [K.1^2 K.1^2] [ K.1 0], [ 0 0] [ 0 K.1], [ 1 K.1^2] [ 1 K.1], [K.1^2 0] [ 0 K.1^2], [K.1^2 0] [ K.1 K.1], [ 0 1] [ 1 0], [ 0 K.1] [K.1^2 K.1^2], [ 1 K.1] [ 0 K.1^2], [ 0 0] [ 0 0], [ 0 1] [ 0 0], [ K.1 1] [ K.1 0], [ 0 K.1] [K.1^2 1], [K.1^2 1] [K.1^2 K.1^2], [ 0 K.1^2] [ 0 0], [ K.1 1] [K.1^2 1], [ 1 K.1^2] [ 0 1], [ K.1 K.1^2] [K.1^2 0], [ 1 K.1^2] [ 0 0], [ K.1 1] [ 1 K.1^2], [ 1 K.1^2] [ 0 K.1], [ K.1 K.1^2] [ 0 0], [ 0 K.1^2] [ 1 K.1], [ 0 1] [ K.1 1], [ 1 K.1^2] [ K.1 1], [ K.1 K.1] [K.1^2 K.1^2], [K.1^2 K.1] [ 1 1], [ 1 1] [ K.1 0], [ 1 0] [ K.1 K.1], [ 0 1] [ 0 K.1^2], [ 0 1] [K.1^2 0], [K.1^2 1] [ 1 1], [ 0 K.1^2] [ 0 0], [ 1 1] [ K.1 1], [ K.1 0] [K.1^2 0], [ K.1 K.1^2] [ 0 1], [ 1 1] [K.1^2 K.1^2], [ K.1 1] [K.1^2 0], [ 0 0] [ K.1 1], [ 1 0] [ 1 K.1], [ K.1 K.1^2] [ K.1 K.1^2], [ K.1 K.1^2] [ 0 K.1], [ 0 1] [ K.1 K.1^2], [K.1^2 0] [ K.1 K.1], [ 0 0] [K.1^2 1], [ 1 K.1^2] [ K.1 1], [ 0 K.1^2] [ 0 K.1], [ K.1 0] [ 1 K.1], [ K.1 K.1^2] [ 0 K.1], [ K.1 0] [ 1 1], [ 1 1] [ 1 K.1], [K.1^2 0] [ 0 K.1^2], [K.1^2 0] [ K.1 K.1^2], [ K.1 1] [ 0 K.1^2], [ 0 1] [K.1^2 K.1^2], [ 1 K.1] [ 1 0], [K.1^2 0] [ K.1 1], [K.1^2 K.1^2] [ 1 1], [ 0 K.1] [ 0 0], [K.1^2 0] [K.1^2 1], [ K.1 K.1^2] [ 1 K.1^2], [ 0 K.1] [ 1 K.1^2], [ 0 K.1^2] [ 0 1], [K.1^2 K.1] [ K.1 K.1^2], [ 0 K.1^2] [ K.1 0], [ 0 K.1^2] [K.1^2 K.1], [ 0 1] [K.1^2 K.1], [K.1^2 K.1^2] [ K.1 K. ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 19:08:30 2004 Input: K:=GF(4); M:=MatrixRing(K,2); Mt:={M![a,b,c,d] : a,b,c,d in K | (Trace(M![a,b,c,d]) eq 0) }; Mt; Mf:={M![a,b,c,d] : a,b,c,d in [0..1] | ( (M![a,b,c,d])[1] eq (M![a,b,c,d])[2]) }; Mf; Mtf:= Mt meet Mf; Mtf; [Random(M): i in [1..100000]]; Output: Magma V2.10-6 Wed Mar 3 2004 19:08:22 on modular [Seed = 1398104098] ------------------------------------- { [ 0 0] [ 0 0], [ 0 0] [K.1^2 0], [ 0 0] [ K.1 0], [ 0 0] [ 1 0], [K.1^2 0] [ 0 K.1^2], [K.1^2 0] [K.1^2 K.1^2], [K.1^2 0] [ K.1 K.1^2], [K.1^2 0] [ 1 K.1^2], [ 1 0] [ 0 1], [ 1 0] [K.1^2 1], [ 1 0] [ K.1 1], [ 1 0] [ 1 1], [ K.1 0] [ 0 K.1], [ K.1 0] [K.1^2 K.1], [ K.1 0] [ K.1 K.1], [ K.1 0] [ 1 K.1], [ 0 K.1^2] [ 0 0], [ 0 K.1^2] [K.1^2 0], [ 0 K.1^2] [ K.1 0], [ 0 K.1^2] [ 1 0], [K.1^2 K.1^2] [ 0 K.1^2], [K.1^2 K.1^2] [K.1^2 K.1^2], [K.1^2 K.1^2] [ K.1 K.1^2], [K.1^2 K.1^2] [ 1 K.1^2], [ 1 K.1^2] [ 0 1], [ 1 K.1^2] [K.1^2 1], [ 1 K.1^2] [ K.1 1], [ 1 K.1^2] [ 1 1], [ K.1 K.1^2] [ 0 K.1], [ K.1 K.1^2] [K.1^2 K.1], [ K.1 K.1^2] [ K.1 K.1], [ K.1 K.1^2] [ 1 K.1], [ 0 K.1] [ 0 0], [ 0 K.1] [K.1^2 0], [ 0 K.1] [ K.1 0], [ 0 K.1] [ 1 0], [K.1^2 K.1] [ 0 K.1^2], [K.1^2 K.1] [K.1^2 K.1^2], [K.1^2 K.1] [ K.1 K.1^2], [K.1^2 K.1] [ 1 K.1^2], [ 1 K.1] [ 0 1], [ 1 K.1] [K.1^2 1], [ 1 K.1] [ K.1 1], [ 1 K.1] [ 1 1], [ K.1 K.1] [ 0 K.1], [ K.1 K.1] [K.1^2 K.1], [ K.1 K.1] [ K.1 K.1], [ K.1 K.1] [ 1 K.1], [ 0 1] [ 0 0], [ 0 1] [K.1^2 0], [ 0 1] [ K.1 0], [ 0 1] [ 1 0], [K.1^2 1] [ 0 K.1^2], [K.1^2 1] [K.1^2 K.1^2], [K.1^2 1] [ K.1 K.1^2], [K.1^2 1] [ 1 K.1^2], [ 1 1] [ 0 1], [ 1 1] [K.1^2 1], [ 1 1] [ K.1 1], [ 1 1] [ 1 1], [ K.1 1] [ 0 K.1], [ K.1 1] [K.1^2 K.1], [ K.1 1] [ K.1 K.1], [ K.1 1] [ 1 K.1] } { [ 0 0] [ 0 0], [ 1 0] [ 1 0], [ 0 1] [ 0 1], [ 1 1] [ 1 1] } { [ 0 0] [ 0 0], [ 1 1] [ 1 1] } [ [ K.1 0] [ 0 1], [ K.1 K.1] [ K.1 K.1], [ 0 0] [ K.1 0], [K.1^2 1] [ 0 0], [K.1^2 1] [ 0 0], [ 0 1] [K.1^2 K.1], [ 1 1] [K.1^2 0], [ 0 1] [K.1^2 K.1^2], [ 0 K.1] [ 0 K.1^2], [ 0 K.1^2] [ K.1 0], [ 0 1] [ K.1 K.1], [ 1 K.1^2] [ 0 1], [K.1^2 K.1] [ K.1 K.1^2], [K.1^2 1] [ 1 1], [ 1 1] [ 0 1], [ 0 K.1] [ 1 1], [ K.1 1] [K.1^2 K.1], [ 1 0] [K.1^2 0], [ 0 K.1] [ K.1 K.1], [ K.1 0] [ 0 0], [ 1 K.1^2] [ 1 K.1^2], [K.1^2 1] [ 1 1], [ 0 1] [ 0 K.1], [ 1 0] [ 1 1], [K.1^2 K.1^2] [ K.1 K.1], [ K.1 1] [K.1^2 1], [K.1^2 1] [ 1 1], [ 1 K.1^2] [ 1 K.1^2], [ 1 0] [ K.1 K.1], [ K.1 0] [ 0 K.1], [ 0 K.1] [ 0 1], [ K.1 K.1] [ 0 0], [K.1^2 K.1] [ K.1 K.1], [K.1^2 0] [ 0 K.1], [ K.1 1] [K.1^2 K.1^2], [K.1^2 K.1] [ K.1 1], [K.1^2 1] [ 1 1], [ 0 K.1^2] [ 1 0], [ 0 K.1^2] [K.1^2 1], [ 1 0] [ 0 1], [ 0 K.1] [ 1 1], [K.1^2 K.1] [ 0 1], [ 1 K.1] [ K.1 0], [K.1^2 0] [ K.1 K.1], [ 0 K.1] [ 0 1], [ 0 K.1^2] [K.1^2 0], [ K.1 K.1^2] [ K.1 K.1^2], [ 1 1] [ 1 1], [ 1 0] [ 0 0], [ 1 1] [ K.1 1], [K.1^2 1] [ 0 K.1^2], [ 0 K.1] [ K.1 K.1], [ K.1 K.1^2] [ 0 0], [K.1^2 0] [ 0 K.1], [K.1^2 K.1] [ 0 K.1], [ 0 K.1] [ 1 1], [ K.1 K.1^2] [K.1^2 K.1], [ 0 1] [ 0 0], [ 1 0] [ K.1 K.1^2], [ K.1 K.1] [ 1 0], [ K.1 1] [ 1 K.1], [ 1 1] [ 0 K.1^2], [K.1^2 K.1^2] [ K.1 K.1^2], [ 0 K.1] [ 0 K.1^2], [ 1 K.1^2] [ K.1 K.1^2], [K.1^2 1] [ 0 0], [K.1^2 K.1^2] [ 1 0], [ 0 K.1] [ 1 K.1], [ 0 0] [ 1 K.1], [ K.1 K.1^2] [ K.1 0], [ 0 0] [K.1^2 0], [K.1^2 K.1] [ 0 K.1], [ K.1 K.1] [ K.1 1], [ 1 1] [K.1^2 0], [ 0 1] [ 1 K.1^2], [K.1^2 K.1] [K.1^2 K.1], [ 0 1] [ K.1 1], [ K.1 1] [ K.1 K.1], [ 0 K.1^2] [ K.1 K.1^2], [ 0 0] [ K.1 K.1^2], [ 1 1] [ 1 1], [ K.1 1] [ 1 K.1], [ K.1 K.1] [ 1 0], [ K.1 1] [K.1^2 K.1], [ K.1 1] [K.1^2 K.1], [ K.1 0] [ 0 1], [ K.1 K.1^2] [K.1^2 K.1], [K.1^2 0] [K.1^2 K.1^2], [ 0 K.1^2] [ 1 K.1^2], [ 1 K.1] [ K.1 1], [ K.1 K.1^2] [ 1 K.1], [ 0 0] [ 0 0], [K.1^2 K.1] [ 0 K.1^2], [K.1^2 K.1^2] [ 1 1], [ 1 0] [ 1 1], [ 0 1] [K.1^2 0], [ K.1 K.1] [ K.1 K.1], [K.1^2 0] [ 1 K.1^2], [ K.1 1] [ 0 K.1^2], [K.1^2 0] [K.1^2 K.1], [K.1^2 1] [ 1 0], [ K.1 K.1^2] [K.1^2 K.1], [ K.1 K.1^2] [ 1 1], [ 0 K.1^2] [K.1^2 1], [K.1^2 0] [K.1^2 0], [ K.1 K.1^2] [K.1^2 0], [K.1^2 1] [ 0 0], [ K.1 K.1^2] [K.1^2 1], [ 0 0] [ 1 K.1], [ K.1 K.1] [K.1^2 0], [ K.1 1] [K.1^2 1], [ 1 1] [K.1^2 0], [K.1^2 0] [ 0 0], [K.1^2 1] [ 0 K.1^2], [ 1 K.1^2] [K.1^2 0], [ K.1 K.1] [ K.1 K.1], [ K.1 K.1^2] [K.1^2 0], [ 0 1] [ K.1 K.1^2], [K.1^2 1] [ 1 K.1^2], [ 1 0] [ K.1 1], [ 1 0] [ K.1 1], [K.1^2 0] [ K.1 K.1], [K.1^2 0] [ K.1 K.1^2], [ K.1 K.1^2] [ 1 0], [ K.1 K.1^2] [ 0 0], [K.1^2 K.1] [ 0 1], [ K.1 0] [ 1 K.1^2], [ 0 0] [ 0 K.1^2], [ 1 K.1^2] [K.1^2 0], [ K.1 1] [K.1^2 1], [ 0 K.1^2] [ K.1 K.1^2], [ 0 K.1^2] [ K.1 K.1], [ 0 K.1] [ 1 K.1], [ 1 K.1^2] [ K.1 K.1^2], [ 1 1] [K.1^2 K.1], [ 0 K.1^2] [ 1 0], [ K.1 K.1^2] [K.1^2 0], [ 0 0] [ 0 1], [ 1 1] [ 1 K.1^2], [ 0 1] [K.1^2 1], [K.1^2 1] [ 0 K.1], [ 1 1] [K.1^2 K.1^2], [ K.1 K.1] [ 0 1], [ 1 1] [ K.1 1], [ K.1 0] [ K.1 K.1], [K.1^2 K.1] [K.1^2 K.1], [K.1^2 K.1^2] [ 1 K.1], [ 0 0] [ 1 K.1], [K.1^2 0] [ K.1 K.1^2], [ 0 K.1] [ 0 K.1^2], [ K.1 K.1] [K.1^2 1], [ 0 K.1] [K.1^2 0], [ K.1 1] [ K.1 K.1^2], [K.1^2 0] [ K.1 1], [K.1^2 0] [ 1 1], [K.1^2 K.1] [ K.1 K.1], [K.1^2 K.1] [K.1^2 K.1], [ K.1 0] [K.1^2 K.1^2], [ 1 1] [ 1 0], [ 1 1] [ K.1 1], [ K.1 K.1] [ 1 1], [K.1^2 1] [ 1 K.1^2], [ K.1 0] [ 0 K.1^2], [ K.1 K.1] [K.1^2 K.1^2], [K.1^2 K.1^2] [ K.1 K.1], [ 1 0] [ 1 1], [ 0 1] [K.1^2 1], [ 1 1] [ K.1 0], [K.1^2 K.1^2] [ K.1 1], [ 0 K.1^2] [ K.1 1], [K.1^2 K.1] [ K.1 K.1], [ 0 K.1^2] [ 1 K.1], [K.1^2 K.1^2] [ 0 1], [ 1 K.1] [ 0 0], [ 1 K.1] [ 0 1], [K.1^2 0] [ 1 K.1^2], [K.1^2 0] [K.1^2 0], [ 0 1] [ 1 1], [K.1^2 K.1] [ 0 1], [K.1^2 1] [ 1 K.1], [ K.1 1] [K.1^2 0], [ 1 1] [ 1 K.1^2], [ 0 K.1^2] [ 1 K.1^2], [ 1 K.1] [ 0 K.1], [ K.1 K.1^2] [ 0 1], [ 0 0] [K.1^2 K.1], [ 1 K.1] [K.1^2 1], [ 0 K.1] [K.1^2 0], [ 0 K.1^2] [ 0 K.1^2], [K.1^2 K.1^2] [K.1^2 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 19:09:04 2004 Input: K:=GF(4); M:=MatrixRing(K,2); Mt:={M![a,b,c,d] : a,b,c,d in K | (Trace(M![a,b,c,d]) eq 0) }; Mt; Mf:={M![a,b,c,d] : a,b,c,d in K | ( (M![a,b,c,d])[1] eq (M![a,b,c,d])[2]) }; Mf; Mtf:= Mt meet Mf; Mtf; [Random(M): i in [1..100000]]; Output: Magma V2.10-6 Wed Mar 3 2004 19:08:56 on modular [Seed = 1516005829] ------------------------------------- { [ 0 0] [ 0 0], [ 0 0] [K.1^2 0], [ 0 0] [ K.1 0], [ 0 0] [ 1 0], [K.1^2 0] [ 0 K.1^2], [K.1^2 0] [K.1^2 K.1^2], [K.1^2 0] [ K.1 K.1^2], [K.1^2 0] [ 1 K.1^2], [ 1 0] [ 0 1], [ 1 0] [K.1^2 1], [ 1 0] [ K.1 1], [ 1 0] [ 1 1], [ K.1 0] [ 0 K.1], [ K.1 0] [K.1^2 K.1], [ K.1 0] [ K.1 K.1], [ K.1 0] [ 1 K.1], [ 0 K.1^2] [ 0 0], [ 0 K.1^2] [K.1^2 0], [ 0 K.1^2] [ K.1 0], [ 0 K.1^2] [ 1 0], [K.1^2 K.1^2] [ 0 K.1^2], [K.1^2 K.1^2] [K.1^2 K.1^2], [K.1^2 K.1^2] [ K.1 K.1^2], [K.1^2 K.1^2] [ 1 K.1^2], [ 1 K.1^2] [ 0 1], [ 1 K.1^2] [K.1^2 1], [ 1 K.1^2] [ K.1 1], [ 1 K.1^2] [ 1 1], [ K.1 K.1^2] [ 0 K.1], [ K.1 K.1^2] [K.1^2 K.1], [ K.1 K.1^2] [ K.1 K.1], [ K.1 K.1^2] [ 1 K.1], [ 0 K.1] [ 0 0], [ 0 K.1] [K.1^2 0], [ 0 K.1] [ K.1 0], [ 0 K.1] [ 1 0], [K.1^2 K.1] [ 0 K.1^2], [K.1^2 K.1] [K.1^2 K.1^2], [K.1^2 K.1] [ K.1 K.1^2], [K.1^2 K.1] [ 1 K.1^2], [ 1 K.1] [ 0 1], [ 1 K.1] [K.1^2 1], [ 1 K.1] [ K.1 1], [ 1 K.1] [ 1 1], [ K.1 K.1] [ 0 K.1], [ K.1 K.1] [K.1^2 K.1], [ K.1 K.1] [ K.1 K.1], [ K.1 K.1] [ 1 K.1], [ 0 1] [ 0 0], [ 0 1] [K.1^2 0], [ 0 1] [ K.1 0], [ 0 1] [ 1 0], [K.1^2 1] [ 0 K.1^2], [K.1^2 1] [K.1^2 K.1^2], [K.1^2 1] [ K.1 K.1^2], [K.1^2 1] [ 1 K.1^2], [ 1 1] [ 0 1], [ 1 1] [K.1^2 1], [ 1 1] [ K.1 1], [ 1 1] [ 1 1], [ K.1 1] [ 0 K.1], [ K.1 1] [K.1^2 K.1], [ K.1 1] [ K.1 K.1], [ K.1 1] [ 1 K.1] } { [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ K.1 0] [ K.1 0], [ 0 K.1^2] [ 0 K.1^2], [ K.1 K.1^2] [ K.1 K.1^2], [ 0 K.1] [ 0 K.1], [ K.1 K.1] [ K.1 K.1], [ 0 1] [ 0 1], [ K.1 1] [ K.1 1], [K.1^2 0] [K.1^2 0], [ 1 0] [ 1 0], [K.1^2 K.1^2] [K.1^2 K.1^2], [ 1 K.1^2] [ 1 K.1^2], [K.1^2 K.1] [K.1^2 K.1], [ 1 K.1] [ 1 K.1], [K.1^2 1] [K.1^2 1] } { [ 0 0] [ 0 0], [K.1^2 K.1^2] [K.1^2 K.1^2], [ K.1 K.1] [ K.1 K.1], [ 1 1] [ 1 1] } [ [ K.1 0] [ K.1 0], [ 0 K.1] [ 1 K.1], [ K.1 K.1^2] [K.1^2 1], [ K.1 1] [ 1 1], [ 1 0] [ K.1 K.1], [ 0 K.1^2] [ 1 1], [K.1^2 K.1^2] [ 1 K.1^2], [ 0 K.1^2] [ 0 K.1], [ 0 K.1] [ 1 K.1], [K.1^2 K.1] [ 0 K.1^2], [ 1 K.1] [ 1 K.1], [ 0 K.1] [K.1^2 1], [ 0 1] [ K.1 K.1], [ K.1 0] [K.1^2 0], [ K.1 0] [ 0 1], [K.1^2 0] [ 1 1], [ 0 1] [ 1 K.1^2], [K.1^2 K.1] [ K.1 K.1^2], [ K.1 K.1^2] [ K.1 0], [K.1^2 K.1^2] [ 1 1], [ K.1 0] [ K.1 1], [K.1^2 0] [ 0 0], [ 1 0] [ K.1 K.1], [ K.1 K.1^2] [ 0 K.1], [ 0 K.1] [ 0 1], [ 0 0] [ 1 K.1], [K.1^2 1] [ 1 0], [K.1^2 1] [ 0 K.1^2], [ 0 0] [ 1 1], [ K.1 K.1^2] [ 0 0], [K.1^2 K.1] [ 0 K.1^2], [ 0 K.1] [ K.1 1], [ 1 1] [ 0 1], [ 0 1] [K.1^2 K.1], [ 0 K.1] [ 1 0], [K.1^2 K.1] [ K.1 K.1^2], [ K.1 0] [ K.1 K.1], [ K.1 1] [ 1 0], [K.1^2 0] [ 0 K.1], [ 0 K.1] [ 0 1], [ K.1 1] [ 1 K.1], [ K.1 K.1] [ K.1 K.1], [ 1 K.1] [ 0 K.1^2], [ 0 1] [ 0 K.1^2], [ 1 K.1^2] [ 0 0], [ K.1 0] [K.1^2 K.1], [K.1^2 0] [ 1 K.1^2], [K.1^2 1] [ 1 K.1^2], [ K.1 K.1^2] [K.1^2 1], [ K.1 0] [K.1^2 0], [ 0 1] [ K.1 K.1], [ 0 K.1^2] [K.1^2 K.1], [ K.1 0] [ 1 1], [ 0 K.1] [ 1 K.1^2], [K.1^2 K.1] [ 0 K.1^2], [ K.1 0] [ K.1 K.1], [K.1^2 1] [ 0 0], [ 0 1] [ 1 0], [ 0 0] [ K.1 K.1^2], [ 1 1] [ 0 0], [ K.1 K.1^2] [ 0 K.1^2], [ K.1 1] [ K.1 1], [ 1 1] [ 0 1], [K.1^2 K.1] [ 0 1], [ 0 K.1^2] [ K.1 0], [ 0 1] [ 0 0], [ 0 0] [ 0 1], [ 0 0] [ 1 K.1^2], [ 0 K.1^2] [ K.1 K.1^2], [K.1^2 K.1] [ K.1 K.1], [ 0 K.1^2] [ 0 K.1], [ K.1 K.1] [ 0 K.1^2], [ 1 K.1] [K.1^2 K.1], [K.1^2 0] [ K.1 0], [ 1 K.1] [K.1^2 0], [ 0 K.1] [K.1^2 0], [ 1 1] [ 0 K.1^2], [ K.1 K.1] [K.1^2 0], [ 1 K.1^2] [ K.1 1], [ K.1 0] [K.1^2 0], [ 1 K.1^2] [K.1^2 K.1], [ 0 K.1^2] [K.1^2 0], [ 1 0] [ 0 1], [ 1 K.1^2] [ 0 K.1^2], [ 0 0] [ 0 K.1], [ 0 K.1^2] [ 1 1], [ K.1 1] [K.1^2 K.1^2], [ K.1 1] [ 1 K.1^2], [K.1^2 K.1^2] [ K.1 1], [ K.1 K.1] [ 1 0], [ 0 0] [K.1^2 K.1^2], [ 1 K.1^2] [ 0 K.1^2], [ K.1 K.1] [K.1^2 1], [ K.1 0] [ 0 0], [ 0 K.1] [ K.1 1], [ 0 K.1] [ 0 0], [ 1 0] [ 0 K.1], [ 1 0] [ 0 K.1], [K.1^2 K.1^2] [ 1 K.1], [ 0 K.1] [ 1 K.1], [ K.1 1] [ K.1 K.1^2], [K.1^2 0] [ 1 K.1], [K.1^2 1] [ 0 K.1^2], [ 0 K.1] [ K.1 1], [K.1^2 0] [ K.1 0], [K.1^2 0] [ 1 0], [ K.1 K.1] [ 1 K.1^2], [ 1 1] [ K.1 0], [K.1^2 K.1] [ 1 1], [ 1 1] [ K.1 K.1], [ 1 K.1] [ K.1 1], [ K.1 K.1] [K.1^2 K.1^2], [ 0 K.1^2] [ 1 K.1], [ 1 0] [ 1 0], [ 1 K.1^2] [ K.1 0], [ K.1 K.1^2] [ 0 0], [ 0 K.1^2] [ 1 1], [ 1 K.1] [ 1 K.1], [ 1 K.1^2] [ 1 1], [ K.1 1] [ K.1 0], [ 1 1] [K.1^2 0], [ K.1 1] [ 0 K.1], [K.1^2 K.1] [ K.1 K.1^2], [ K.1 1] [K.1^2 K.1^2], [ 1 K.1] [ 1 1], [ 1 K.1] [ 1 1], [ K.1 1] [ 0 0], [ K.1 K.1^2] [ 1 0], [ K.1 1] [ 1 0], [ 1 K.1] [ 1 0], [ 0 1] [ 0 1], [ K.1 K.1] [ 0 K.1^2], [K.1^2 K.1] [ K.1 K.1^2], [ 1 K.1^2] [ K.1 K.1], [ 0 1] [ 0 1], [ 0 K.1] [K.1^2 K.1], [ 1 1] [ 1 K.1^2], [ K.1 K.1] [ 1 0], [ K.1 0] [ 1 1], [K.1^2 K.1^2] [ 1 K.1], [K.1^2 1] [ K.1 1], [ 0 K.1^2] [K.1^2 K.1^2], [ 0 1] [ 1 1], [ 0 0] [ K.1 1], [ K.1 K.1^2] [ K.1 K.1^2], [K.1^2 1] [ 0 K.1], [ 0 K.1^2] [ 1 1], [K.1^2 1] [ 0 K.1^2], [ 1 0] [ 0 0], [ K.1 K.1] [ 1 0], [ 0 K.1] [ K.1 K.1], [ 1 K.1^2] [ 0 0], [K.1^2 K.1] [ 1 1], [ 0 0] [ 1 K.1], [K.1^2 1] [K.1^2 K.1], [ 0 K.1] [ K.1 1], [ 1 K.1^2] [ 0 0], [K.1^2 K.1^2] [K.1^2 0], [K.1^2 K.1] [K.1^2 0], [ 1 1] [K.1^2 K.1], [ 0 K.1^2] [ 0 K.1], [ K.1 K.1] [ 1 0], [ K.1 K.1] [ 0 1], [ 1 1] [ 1 K.1], [K.1^2 1] [ K.1 1], [ 1 0] [ 1 0], [ K.1 0] [ 1 0], [K.1^2 K.1] [ 1 K.1^2], [ K.1 0] [ 0 0], [ 0 0] [K.1^2 0], [ 1 0] [ 0 K.1], [ 0 K.1] [ K.1 0], [ K.1 0] [ K.1 1], [ 1 K.1] [ 0 K.1], [K.1^2 1] [ 1 0], [ K.1 K.1^2] [ 1 K.1^ ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 19:26:10 2004 Input: K:=GF(4); M:=MatrixRing(K,2); Mt:={M![a,b,c,d] : a,b,c,d in K | (Trace(M![a,b,c,d]) eq 0) }; Mt; Mf:={M![a,b,c,d] : a,b,c,d in K | ( (M![a,b,c,d])[1] eq (M![a,b,c,d])[2]) }; Mf; Mtf:= Mt meet Mf; Mtf; [Random(M): i in [1..100000]]; quantes := function(seq,Mt,Mf,Mtf) nMtf,nMt,nMf:=0; for i in seq do if i in Mtf then nMtf:=nMtf+1; elif i in Mt then nMt:=nMt+1; elif i in Mf then nMf:=nMf+1; end if; end for; return {nMt,nMf,nMtf}; end function; Output: Magma V2.10-6 Wed Mar 3 2004 19:26:02 on modular [Seed = 2391324947] ------------------------------------- { [ 0 0] [ 0 0], [ 0 0] [K.1^2 0], [ 0 0] [ K.1 0], [ 0 0] [ 1 0], [K.1^2 0] [ 0 K.1^2], [K.1^2 0] [K.1^2 K.1^2], [K.1^2 0] [ K.1 K.1^2], [K.1^2 0] [ 1 K.1^2], [ 1 0] [ 0 1], [ 1 0] [K.1^2 1], [ 1 0] [ K.1 1], [ 1 0] [ 1 1], [ K.1 0] [ 0 K.1], [ K.1 0] [K.1^2 K.1], [ K.1 0] [ K.1 K.1], [ K.1 0] [ 1 K.1], [ 0 K.1^2] [ 0 0], [ 0 K.1^2] [K.1^2 0], [ 0 K.1^2] [ K.1 0], [ 0 K.1^2] [ 1 0], [K.1^2 K.1^2] [ 0 K.1^2], [K.1^2 K.1^2] [K.1^2 K.1^2], [K.1^2 K.1^2] [ K.1 K.1^2], [K.1^2 K.1^2] [ 1 K.1^2], [ 1 K.1^2] [ 0 1], [ 1 K.1^2] [K.1^2 1], [ 1 K.1^2] [ K.1 1], [ 1 K.1^2] [ 1 1], [ K.1 K.1^2] [ 0 K.1], [ K.1 K.1^2] [K.1^2 K.1], [ K.1 K.1^2] [ K.1 K.1], [ K.1 K.1^2] [ 1 K.1], [ 0 K.1] [ 0 0], [ 0 K.1] [K.1^2 0], [ 0 K.1] [ K.1 0], [ 0 K.1] [ 1 0], [K.1^2 K.1] [ 0 K.1^2], [K.1^2 K.1] [K.1^2 K.1^2], [K.1^2 K.1] [ K.1 K.1^2], [K.1^2 K.1] [ 1 K.1^2], [ 1 K.1] [ 0 1], [ 1 K.1] [K.1^2 1], [ 1 K.1] [ K.1 1], [ 1 K.1] [ 1 1], [ K.1 K.1] [ 0 K.1], [ K.1 K.1] [K.1^2 K.1], [ K.1 K.1] [ K.1 K.1], [ K.1 K.1] [ 1 K.1], [ 0 1] [ 0 0], [ 0 1] [K.1^2 0], [ 0 1] [ K.1 0], [ 0 1] [ 1 0], [K.1^2 1] [ 0 K.1^2], [K.1^2 1] [K.1^2 K.1^2], [K.1^2 1] [ K.1 K.1^2], [K.1^2 1] [ 1 K.1^2], [ 1 1] [ 0 1], [ 1 1] [K.1^2 1], [ 1 1] [ K.1 1], [ 1 1] [ 1 1], [ K.1 1] [ 0 K.1], [ K.1 1] [K.1^2 K.1], [ K.1 1] [ K.1 K.1], [ K.1 1] [ 1 K.1] } { [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ K.1 0] [ K.1 0], [ 0 K.1^2] [ 0 K.1^2], [ K.1 K.1^2] [ K.1 K.1^2], [ 0 K.1] [ 0 K.1], [ K.1 K.1] [ K.1 K.1], [ 0 1] [ 0 1], [ K.1 1] [ K.1 1], [K.1^2 0] [K.1^2 0], [ 1 0] [ 1 0], [K.1^2 K.1^2] [K.1^2 K.1^2], [ 1 K.1^2] [ 1 K.1^2], [K.1^2 K.1] [K.1^2 K.1], [ 1 K.1] [ 1 K.1], [K.1^2 1] [K.1^2 1] } { [ 0 0] [ 0 0], [K.1^2 K.1^2] [K.1^2 K.1^2], [ K.1 K.1] [ K.1 K.1], [ 1 1] [ 1 1] } [ [K.1^2 K.1] [ 1 1], [K.1^2 0] [ 1 1], [ 0 K.1^2] [ 1 0], [ K.1 K.1^2] [ K.1 K.1^2], [ K.1 0] [K.1^2 0], [ 1 1] [ 0 1], [ 1 K.1^2] [ K.1 0], [ 0 K.1] [ 1 1], [ K.1 0] [ 0 0], [ 1 0] [ K.1 K.1^2], [ 0 K.1] [ 1 1], [ K.1 1] [ 0 K.1], [K.1^2 K.1] [K.1^2 K.1^2], [K.1^2 0] [ 0 0], [ 1 1] [ K.1 K.1], [ K.1 K.1] [K.1^2 K.1], [ 1 K.1] [ 0 K.1], [K.1^2 0] [K.1^2 K.1], [K.1^2 1] [ K.1 K.1^2], [ 1 1] [ 1 1], [ 0 K.1] [ 0 1], [ K.1 K.1] [K.1^2 0], [K.1^2 1] [K.1^2 K.1^2], [ 0 K.1] [ K.1 K.1], [ K.1 0] [ K.1 1], [K.1^2 K.1^2] [ 0 K.1], [ 0 1] [K.1^2 K.1^2], [K.1^2 0] [K.1^2 1], [ K.1 1] [ 0 1], [ K.1 1] [ K.1 0], [K.1^2 0] [ 1 K.1], [ 1 K.1] [ 0 1], [ 1 0] [K.1^2 K.1^2], [ K.1 0] [ 1 0], [ 1 K.1^2] [ K.1 0], [K.1^2 0] [ 1 K.1], [ 0 K.1^2] [ K.1 K.1], [ 1 0] [ 0 K.1], [ 1 K.1] [ K.1 K.1^2], [ 0 K.1^2] [ 1 1], [ 1 0] [ 1 1], [ 1 K.1] [ K.1 1], [ 0 K.1^2] [ 1 K.1^2], [ 1 K.1^2] [ 1 K.1^2], [ 1 0] [ 1 1], [ K.1 K.1^2] [ 0 K.1], [ K.1 K.1^2] [ K.1 0], [K.1^2 1] [ 1 0], [ K.1 K.1] [ K.1 K.1^2], [K.1^2 K.1^2] [K.1^2 K.1], [ K.1 K.1^2] [ 1 K.1^2], [ 0 K.1^2] [ 1 K.1], [ 0 1] [ K.1 K.1^2], [ 0 0] [ K.1 K.1^2], [ 0 0] [ 1 1], [K.1^2 0] [ 1 0], [ 1 0] [ 0 K.1^2], [ K.1 0] [ 1 1], [K.1^2 K.1^2] [ K.1 0], [K.1^2 K.1] [ 1 K.1], [ 1 K.1^2] [K.1^2 0], [K.1^2 K.1^2] [ K.1 K.1], [ 1 K.1^2] [ 0 K.1], [ 0 K.1] [ 1 1], [ 0 0] [ K.1 K.1^2], [ 1 0] [ 1 1], [ 0 K.1^2] [ K.1 K.1], [ 1 0] [ K.1 1], [ 0 K.1^2] [ 0 1], [K.1^2 0] [ 1 1], [ K.1 1] [ 1 K.1^2], [K.1^2 K.1] [K.1^2 0], [ K.1 0] [ K.1 0], [ K.1 0] [ 1 K.1^2], [K.1^2 0] [ K.1 1], [K.1^2 K.1] [ 1 1], [ 0 K.1^2] [ K.1 K.1^2], [ K.1 K.1] [ 1 0], [K.1^2 1] [K.1^2 K.1^2], [ K.1 K.1] [ 0 0], [ K.1 K.1^2] [K.1^2 K.1^2], [ 1 1] [K.1^2 0], [ 0 K.1] [ 0 K.1], [ 1 K.1^2] [K.1^2 0], [ K.1 1] [ 0 0], [K.1^2 K.1^2] [K.1^2 0], [ K.1 K.1^2] [ K.1 1], [ 1 K.1^2] [ 0 K.1], [ 1 0] [ 0 K.1], [ 0 1] [K.1^2 0], [ 0 1] [ K.1 1], [ K.1 1] [K.1^2 K.1^2], [ K.1 K.1] [ K.1 1], [ 1 1] [ 0 1], [ 0 K.1^2] [ K.1 K.1], [K.1^2 0] [ 0 K.1^2], [ 0 0] [K.1^2 K.1], [K.1^2 0] [ K.1 0], [ K.1 K.1] [ K.1 1], [ 1 0] [ 1 K.1], [ 0 K.1] [ 0 K.1], [K.1^2 K.1^2] [K.1^2 0], [ K.1 K.1^2] [K.1^2 K.1^2], [ 0 K.1^2] [ K.1 K.1^2], [ 0 0] [ K.1 K.1], [ 1 K.1^2] [ 1 K.1], [ 0 0] [ K.1 0], [ K.1 K.1] [ K.1 0], [ 0 0] [K.1^2 0], [ K.1 1] [ 1 1], [ K.1 K.1^2] [ 1 K.1], [ K.1 1] [ K.1 K.1], [K.1^2 K.1^2] [ 0 0], [ 0 K.1] [ 0 0], [ 1 0] [ 1 0], [ 0 1] [ K.1 K.1], [K.1^2 K.1^2] [ 0 K.1], [ K.1 0] [ 1 K.1^2], [K.1^2 0] [K.1^2 1], [ K.1 1] [K.1^2 K.1], [ K.1 K.1] [ 0 1], [ K.1 K.1] [ 1 K.1], [ 1 K.1^2] [K.1^2 K.1], [ 0 1] [ K.1 1], [ 0 1] [ 0 K.1], [ 1 0] [K.1^2 K.1^2], [K.1^2 K.1^2] [ 0 K.1^2], [ 0 K.1^2] [ 0 K.1^2], [ 1 0] [ 1 K.1], [ 1 1] [ 0 K.1], [ K.1 K.1^2] [ K.1 K.1], [K.1^2 K.1] [ 0 1], [ 1 K.1^2] [ K.1 K.1], [ 1 K.1] [ 1 1], [ K.1 K.1^2] [ 1 0], [ 0 1] [ 0 K.1], [ 1 K.1] [K.1^2 K.1], [K.1^2 0] [ 0 K.1], [ K.1 1] [ 0 K.1^2], [ 0 K.1] [ K.1 1], [ 1 K.1^2] [ K.1 1], [ 1 K.1] [ 1 0], [ 1 0] [ 0 K.1], [K.1^2 0] [ 0 K.1^2], [K.1^2 1] [ 0 K.1^2], [ K.1 0] [ 1 K.1], [ 1 K.1^2] [ K.1 0], [K.1^2 1] [ 1 K.1], [ 0 0] [ 1 1], [ K.1 0] [ 1 K.1^2], [ K.1 K.1] [K.1^2 K.1], [ 0 K.1^2] [ K.1 0], [ K.1 0] [ 0 1], [ 0 0] [ K.1 K.1], [ 1 K.1] [ 1 1], [ 0 K.1^2] [K.1^2 K.1], [K.1^2 0] [ K.1 0], [ K.1 K.1^2] [ 0 K.1], [ 0 K.1] [ 0 0], [ 1 K.1^2] [ K.1 K.1], [K.1^2 0] [K.1^2 K.1^2], [ 0 K.1] [ 0 K.1^2], [ 1 K.1] [K.1^2 K.1], [ 1 1] [ 0 0], [ 1 K.1^2] [K.1^2 1], [ 0 K.1] [ K.1 K.1^2], [ 0 K.1] [ K.1 K.1], [K.1^2 K.1] [ 0 K.1], [K.1^2 0] [ 1 K.1], [ 0 1] [K.1^2 0], [K.1^2 1] [ K.1 K.1], [ 0 K.1] [ K.1 0], [K.1^2 0] [K.1^2 1], [K.1^2 0] [ 0 K.1^2], [K.1^2 0] [K.1^2 K.1^2], [ 1 K.1] [ 1 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 19:26:46 2004 Input: K:=GF(4); M:=MatrixRing(K,2); Mt:={M![a,b,c,d] : a,b,c,d in K | (Trace(M![a,b,c,d]) eq 0) }; Mt; Mf:={M![a,b,c,d] : a,b,c,d in K | ( (M![a,b,c,d])[1] eq (M![a,b,c,d])[2]) }; Mf; Mtf:= Mt meet Mf; Mtf; [Random(M): i in [1..100000]]: quantes := function(seq,Mt,Mf,Mtf) nMtf,nMt,nMf:=0; for i in seq do if i in Mtf then nMtf:=nMtf+1; elif i in Mt then nMt:=nMt+1; elif i in Mf then nMf:=nMf+1; end if; end for; return {nMt,nMf,nMtf}; end function; Output: Magma V2.10-6 Wed Mar 3 2004 19:26:43 on modular [Seed = 2509480529] ------------------------------------- { [ 0 0] [ 0 0], [ 0 0] [K.1^2 0], [ 0 0] [ K.1 0], [ 0 0] [ 1 0], [K.1^2 0] [ 0 K.1^2], [K.1^2 0] [K.1^2 K.1^2], [K.1^2 0] [ K.1 K.1^2], [K.1^2 0] [ 1 K.1^2], [ 1 0] [ 0 1], [ 1 0] [K.1^2 1], [ 1 0] [ K.1 1], [ 1 0] [ 1 1], [ K.1 0] [ 0 K.1], [ K.1 0] [K.1^2 K.1], [ K.1 0] [ K.1 K.1], [ K.1 0] [ 1 K.1], [ 0 K.1^2] [ 0 0], [ 0 K.1^2] [K.1^2 0], [ 0 K.1^2] [ K.1 0], [ 0 K.1^2] [ 1 0], [K.1^2 K.1^2] [ 0 K.1^2], [K.1^2 K.1^2] [K.1^2 K.1^2], [K.1^2 K.1^2] [ K.1 K.1^2], [K.1^2 K.1^2] [ 1 K.1^2], [ 1 K.1^2] [ 0 1], [ 1 K.1^2] [K.1^2 1], [ 1 K.1^2] [ K.1 1], [ 1 K.1^2] [ 1 1], [ K.1 K.1^2] [ 0 K.1], [ K.1 K.1^2] [K.1^2 K.1], [ K.1 K.1^2] [ K.1 K.1], [ K.1 K.1^2] [ 1 K.1], [ 0 K.1] [ 0 0], [ 0 K.1] [K.1^2 0], [ 0 K.1] [ K.1 0], [ 0 K.1] [ 1 0], [K.1^2 K.1] [ 0 K.1^2], [K.1^2 K.1] [K.1^2 K.1^2], [K.1^2 K.1] [ K.1 K.1^2], [K.1^2 K.1] [ 1 K.1^2], [ 1 K.1] [ 0 1], [ 1 K.1] [K.1^2 1], [ 1 K.1] [ K.1 1], [ 1 K.1] [ 1 1], [ K.1 K.1] [ 0 K.1], [ K.1 K.1] [K.1^2 K.1], [ K.1 K.1] [ K.1 K.1], [ K.1 K.1] [ 1 K.1], [ 0 1] [ 0 0], [ 0 1] [K.1^2 0], [ 0 1] [ K.1 0], [ 0 1] [ 1 0], [K.1^2 1] [ 0 K.1^2], [K.1^2 1] [K.1^2 K.1^2], [K.1^2 1] [ K.1 K.1^2], [K.1^2 1] [ 1 K.1^2], [ 1 1] [ 0 1], [ 1 1] [K.1^2 1], [ 1 1] [ K.1 1], [ 1 1] [ 1 1], [ K.1 1] [ 0 K.1], [ K.1 1] [K.1^2 K.1], [ K.1 1] [ K.1 K.1], [ K.1 1] [ 1 K.1] } { [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ K.1 0] [ K.1 0], [ 0 K.1^2] [ 0 K.1^2], [ K.1 K.1^2] [ K.1 K.1^2], [ 0 K.1] [ 0 K.1], [ K.1 K.1] [ K.1 K.1], [ 0 1] [ 0 1], [ K.1 1] [ K.1 1], [K.1^2 0] [K.1^2 0], [ 1 0] [ 1 0], [K.1^2 K.1^2] [K.1^2 K.1^2], [ 1 K.1^2] [ 1 K.1^2], [K.1^2 K.1] [K.1^2 K.1], [ 1 K.1] [ 1 K.1], [K.1^2 1] [K.1^2 1] } { [ 0 0] [ 0 0], [K.1^2 K.1^2] [K.1^2 K.1^2], [ K.1 K.1] [ K.1 K.1], [ 1 1] [ 1 1] } >> quantes := function(seq,Mt,Mf,Mtf) ^ User error: bad syntax >> nMtf,nMt,nMf:=0; ^ Runtime error in :=: Expected to assign 3 value(s) but only computed 1 value(s) >> for i in seq do ^ User error: Identifier 'seq' has not been declared or assigned >> return {nMt,nMf,nMtf}; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 19:27:19 2004 Input: K:=GF(4); M:=MatrixRing(K,2); Mt:={M![a,b,c,d] : a,b,c,d in K | (Trace(M![a,b,c,d]) eq 0) }; Mf:={M![a,b,c,d] : a,b,c,d in K | ( (M![a,b,c,d])[1] eq (M![a,b,c,d])[2]) }; Mtf:= Mt meet Mf; [Random(M): i in [1..100000]]: quantes := function(seq,Mt,Mf,Mtf) nMtf,nMt,nMf:=0; for i in seq do if i in Mtf then nMtf:=nMtf+1; elif i in Mt then nMt:=nMt+1; elif i in Mf then nMf:=nMf+1; end if; end for; return {nMt,nMf,nMtf}; end function; Output: Magma V2.10-6 Wed Mar 3 2004 19:27:16 on modular [Seed = 2627382143] ------------------------------------- >> quantes := function(seq,Mt,Mf,Mtf) ^ User error: bad syntax >> nMtf,nMt,nMf:=0; ^ Runtime error in :=: Expected to assign 3 value(s) but only computed 1 value(s) >> for i in seq do ^ User error: Identifier 'seq' has not been declared or assigned >> return {nMt,nMf,nMtf}; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 19:31:03 2004 Input: K:=GF(4); M:=MatrixRing(K,2); Mt:={M![a,b,c,d] : a,b,c,d in K | (Trace(M![a,b,c,d]) eq 0) }; Mf:={M![a,b,c,d] : a,b,c,d in K | ( (M![a,b,c,d])[1] eq (M![a,b,c,d])[2]) }; Mtf:= Mt meet Mf; [Random(M): i in [1..100000]]: quantes:=function(seq, A, B, C) x,y,z:=0; for i in seq do if i in A then x:=x+1; elif i in B then y:=y+1; elif i in C then y:=y+1; end if; end for; return [x,y,z]; end function; Output: Magma V2.10-6 Wed Mar 3 2004 19:31:00 on modular [Seed = 2863436393] ------------------------------------- >> quantes:=function(seq, A, B, C) ^ User error: bad syntax >> x,y,z:=0; ^ Runtime error in :=: Expected to assign 3 value(s) but only computed 1 value(s) >> for i in seq do ^ User error: Identifier 'seq' has not been declared or assigned >> return [x,y,z]; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 19:32:11 2004 Input: K:=GF(4); M:=MatrixRing(K,2); Mt:={M![a,b,c,d] : a,b,c,d in K | (Trace(M![a,b,c,d]) eq 0) }; Mf:={M![a,b,c,d] : a,b,c,d in K | ( (M![a,b,c,d])[1] eq (M![a,b,c,d])[2]) }; Mtf:= Mt meet Mf; [Random(M): i in [1..100000]]: quantes:=function(seq, A, B, C) x:=0; y:=0; z:=0; for i in seq do if i in A then x:=x+1; elif i in B then y:=y+1; elif i in C then y:=y+1; end if; end for; return [x,y,z]; end function; Output: Magma V2.10-6 Wed Mar 3 2004 19:32:08 on modular [Seed = 2964752831] ------------------------------------- >> quantes:=function(seq, A, B, C) ^ User error: bad syntax >> for i in seq do ^ User error: Identifier 'seq' has not been declared or assigned >> return [x,y,z]; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 19:33:58 2004 Input: K:=GF(4); M:=MatrixRing(K,2); Mt:={M![a,b,c,d] : a,b,c,d in K | (Trace(M![a,b,c,d]) eq 0) }; Mf:={M![a,b,c,d] : a,b,c,d in K | ( (M![a,b,c,d])[1] eq (M![a,b,c,d])[2]) }; Mtf:= Mt meet Mf; [Random(M): i in [1..100000]]: quantes := function( seq, A, B, C) x:=0; y:=0; z:=0; for i in seq do if i in A then x:=x+1; elif i in B then y:=y+1; elif i in C then y:=y+1; end if; end for; return {x,y,z}; end function; Output: Magma V2.10-6 Wed Mar 3 2004 19:33:55 on modular [Seed = 3351379635] ------------------------------------- >> quantes := function( seq, A, B, C) ^ User error: bad syntax >> for i in seq do ^ User error: Identifier 'seq' has not been declared or assigned >> return {x,y,z}; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 19:34:24 2004 Input: K:=GF(4); M:=MatrixRing(K,2); Mt:={M![a,b,c,d] : a,b,c,d in K | (Trace(M![a,b,c,d]) eq 0) }; Mf:={M![a,b,c,d] : a,b,c,d in K | ( (M![a,b,c,d])[1] eq (M![a,b,c,d])[2]) }; Mtf:= Mt meet Mf; [Random(M): i in [1..100000]]: quantes := function( seq, A, B, C) x:=0; y:=0; z:=0; for i in [seq] do if i in A then x:=x+1; elif i in B then y:=y+1; elif i in C then y:=y+1; end if; end for; return {x,y,z}; end function; Output: Magma V2.10-6 Wed Mar 3 2004 19:34:21 on modular [Seed = 3435853126] ------------------------------------- >> quantes := function( seq, A, B, C) ^ User error: bad syntax >> for i in [seq] do ^ User error: Identifier 'seq' has not been declared or assigned >> return {x,y,z}; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 19:34:52 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4+6*x^2+3*x+2); OK:= MaximalOrder(K); J:= ideal< OK |209, (389+y)/2 >; Characteristic(J); Output: Magma V2.10-6 Wed Mar 3 2004 19:34:49 on modular [Seed = 3554011773] ------------------------------------- >> Characteristic(J);; ^ Runtime error in 'Characteristic': Bad argument types Argument types given: RngOrdFracIdl Total time: 2.969 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 19:35:41 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4+6*x^2+3*x+2); OK:= MaximalOrder(K); J:= ideal< OK |209, (389+y)/2 >; M:=OK/J; Characteristic(OK/J); Output: Magma V2.10-6 Wed Mar 3 2004 19:35:38 on modular [Seed = 3873496891] ------------------------------------- >> M:=OK/J; ^ Runtime error in '/': Bad argument types Argument types given: RngOrd, RngOrdFracIdl >> Characteristic(OK/J);; ^ Runtime error in '/': Bad argument types Argument types given: RngOrd, RngOrdFracIdl Total time: 2.909 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 19:36:01 2004 Input: quantes := function(A, B, C) x:=0; y:=0; z:=0; return {x,y,z}; end function; Output: Magma V2.10-6 Wed Mar 3 2004 19:35:58 on modular [Seed = 3991655428] ------------------------------------- Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 19:36:25 2004 Input: quantes := function(A, B, C) x:=0; y:=0; z:=0; return {x,y,z}; end function; quantes(5,5,5); Output: Magma V2.10-6 Wed Mar 3 2004 19:36:22 on modular [Seed = 4109553397] ------------------------------------- { 0 } Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 19:36:38 2004 Input: quantes := function(A, B, C) x:=0; y:=0; z:=0; return [x,y,z]; end function; quantes(5,5,5); Output: Magma V2.10-6 Wed Mar 3 2004 19:36:35 on modular [Seed = 4227711471] ------------------------------------- [ 0, 0, 0 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 19:36:56 2004 Input: quantes := function(A, B, C) x:=0; y:=0; z:=0; return [x,y,z]; end function; h:=quantes(5,5,5); Output: Magma V2.10-6 Wed Mar 3 2004 19:36:53 on modular [Seed = 218838816] ------------------------------------- Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 19:37:06 2004 Input: quantes := function(A, B, C) x:=0; y:=0; z:=0; return [x,y,z]; end function; h:=quantes(5,5,5); h; Output: Magma V2.10-6 Wed Mar 3 2004 19:37:03 on modular [Seed = 100678689] ------------------------------------- [ 0, 0, 0 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 19:37:46 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4+6*x^2+3*x+2); OK:= MaximalOrder(K); J:= ideal< OK |209, (389+y)/2 >; J; Output: Magma V2.10-6 Wed Mar 3 2004 19:37:42 on modular [Seed = 269888078] ------------------------------------- Fractional Ideal of OK Two element generators: 209/1*OK.1 389/2*OK.1 + 1/2*OK.2 Total time: 2.999 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 19:37:55 2004 Input: quantes := function(A, B, C,lista) x:=1; y:=2; z:=3; lista[1] := lista[1] + x + y + z; return lista; end function; h:=quantes(5,5,5); h; Output: Magma V2.10-6 Wed Mar 3 2004 19:37:51 on modular [Seed = 690951038] ------------------------------------- >> h:=quantes(5,5,5); ^ Runtime error: Number of arguments (3) does not equal expected number of arguments (4) >> h; ^ User error: Identifier 'h' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 19:38:21 2004 Input: quantes := function(A, B, C,lista) x:=1; y:=2; z:=3; lista[1] := lista[1] + x + y + z; return lista; end function; hm:=[1,2,3,4]; h:=quantes(5,5,5,hm); h; Output: Magma V2.10-6 Wed Mar 3 2004 19:38:18 on modular [Seed = 639638612] ------------------------------------- [ 7, 2, 3, 4 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 19:39:16 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2-5); OK:= MaximalOrder(K); J:= ideal< OK |209, (389+y)/2 >; M:=OK/J; Characteristic(J); Output: Magma V2.10-6 Wed Mar 3 2004 19:39:14 on modular [Seed = 808848010] ------------------------------------- >> M:=OK/J; ^ Runtime error in '/': Bad argument types Argument types given: RngOrd, RngOrdIdl >> Characteristic(J);; ^ Runtime error in 'Characteristic': Bad argument types Argument types given: RngOrdIdl Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 19:39:45 2004 Input: quantes := function(A, B, C,lista) x:=1; y:=2; z:=3; for i in lista do lista[i]:=lista[i]+1; end for; return lista; end function; hm:=[1,2,3,4]; h:=quantes(5,5,5,hm); h; Output: Magma V2.10-6 Wed Mar 3 2004 19:39:42 on modular [Seed = 1229943695] ------------------------------------- [ 2, 3, 4, 5 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 19:40:24 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2-5); OK:= MaximalOrder(K); J:= ideal< OK |209, (389+y)/2 >; M:=OK/J; Characteristic(M); Output: Magma V2.10-6 Wed Mar 3 2004 19:40:21 on modular [Seed = 1516003495] ------------------------------------- >> M:=OK/J; ^ Runtime error in '/': Bad argument types Argument types given: RngOrd, RngOrdIdl >> Characteristic(M);; ^ User error: Identifier 'M' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 19:40:58 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2-5); OK:= MaximalOrder(K); J:= ideal< OK |209, (389+y)/2 >; /; Output: Magma V2.10-6 Wed Mar 3 2004 19:40:55 on modular [Seed = 1414688587] ------------------------------------- >> /;; ^ User error: bad syntax Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 19:41:02 2004 Input: quantes := function(A, B, C,lista) x:=0; y:=0; z:=0; for i in lista do if i in A then x:=x+1; end if; end for; return [x,y,z]; end function; Output: Magma V2.10-6 Wed Mar 3 2004 19:40:59 on modular [Seed = 1852331389] ------------------------------------- Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 19:41:13 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2-5); OK:= MaximalOrder(K); J:= ideal< OK |209, (389+y)/2 >; J; Output: Magma V2.10-6 Wed Mar 3 2004 19:41:10 on modular [Seed = 1734433865] ------------------------------------- Ideal of OK Two element generators: [209, 0] [194, 1] Total time: 3.039 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 19:41:33 2004 Input: quantes := function(A, B, C,lista) x:=0; y:=0; z:=0; for i in lista do if i in A then x:=x+1; end if; if i in B then y:=y+1; end if; if i in C then z:=z+1; end if; end for; return [x,y,z]; end function; Output: Magma V2.10-6 Wed Mar 3 2004 19:41:30 on modular [Seed = 1886800706] ------------------------------------- Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 19:41:44 2004 Input: quantes := function(A, B, C,lista) x:=0; y:=0; z:=0; for i in lista do if i in A then x:=x+1; end if; if i in B then y:=y+1; end if; if i in C then z:=z+1; end if; end for; return [x,y,z]; end function; Output: Magma V2.10-6 Wed Mar 3 2004 19:41:41 on modular [Seed = 2307896004] ------------------------------------- Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 19:41:53 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2-5); OK:= MaximalOrder(K); J:= ideal< OK |209, (389+y)/2 >; J; M:=OK / J; Output: Magma V2.10-6 Wed Mar 3 2004 19:41:50 on modular [Seed = 2189736388] ------------------------------------- Ideal of OK Two element generators: [209, 0] [194, 1] >> M:=OK / J;; ^ Runtime error in '/': Bad argument types Argument types given: RngOrd, RngOrdIdl Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 19:42:01 2004 Input: K:=GF(4); M:=MatrixRing(K,2); Mt:={M![a,b,c,d] : a,b,c,d in K | (Trace(M![a,b,c,d]) eq 0) }; Mf:={M![a,b,c,d] : a,b,c,d in K | ( (M![a,b,c,d])[1] eq (M![a,b,c,d])[2]) }; Mtf:= Mt meet Mf; [Random(M): i in [1..100000]]: quantes := function(A, B, C,lista) x:=0; y:=0; z:=0; for i in lista do if i in A then x:=x+1; end if; if i in B then y:=y+1; end if; if i in C then z:=z+1; end if; end for; return [x,y,z]; end function; Output: Magma V2.10-6 Wed Mar 3 2004 19:41:58 on modular [Seed = 2610798789] ------------------------------------- >> quantes := function(A, B, C,lista) ^ User error: bad syntax >> for i in lista do ^ User error: Identifier 'lista' has not been declared or assigned >> return [x,y,z]; ^ User error: A 'return' can only be used inside a procedure or function >> end function;; ^ User error: bad syntax Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 19:42:35 2004 Input: K:=GF(4); M:=MatrixRing(K,2); Mt:={M![a,b,c,d] : a,b,c,d in K | (Trace(M![a,b,c,d]) eq 0) }; Mf:={M![a,b,c,d] : a,b,c,d in K | ( (M![a,b,c,d])[1] eq (M![a,b,c,d])[2]) }; Mtf:= Mt meet Mf; [Random(M): i in [1..100000]]; quantes := function(A, B, C,lista) x:=0; y:=0; z:=0; for i in lista do if i in A then x:=x+1; end if; if i in B then y:=y+1; end if; if i in C then z:=z+1; end if; end for; return [x,y,z]; end function; Output: Magma V2.10-6 Wed Mar 3 2004 19:42:28 on modular [Seed = 2492641256] ------------------------------------- [ [ 1 0] [K.1^2 0], [K.1^2 K.1^2] [ 0 0], [ 0 1] [K.1^2 0], [ K.1 0] [ 1 K.1], [K.1^2 K.1] [ 1 1], [ 1 K.1] [K.1^2 K.1^2], [ 1 1] [ 0 K.1^2], [ K.1 0] [ 1 0], [ K.1 1] [ K.1 1], [ K.1 K.1] [ 1 K.1], [ 1 1] [ 1 K.1^2], [ K.1 0] [ 1 1], [K.1^2 0] [ K.1 1], [K.1^2 K.1^2] [ 1 0], [ K.1 K.1] [ K.1 K.1], [ K.1 K.1^2] [K.1^2 K.1^2], [ 1 K.1^2] [K.1^2 K.1], [ 1 K.1^2] [ 1 K.1], [ K.1 K.1] [ 1 K.1], [ K.1 0] [K.1^2 K.1^2], [K.1^2 K.1] [ K.1 1], [ 1 K.1] [ K.1 1], [ K.1 K.1^2] [ 0 0], [ 0 K.1^2] [ 0 0], [ K.1 K.1^2] [ K.1 0], [ K.1 0] [K.1^2 K.1^2], [ K.1 1] [ 1 1], [ K.1 1] [ 1 K.1], [ 0 1] [K.1^2 0], [ 0 K.1] [ 1 K.1], [ 0 K.1] [ 1 0], [ K.1 1] [ 0 0], [ 0 K.1^2] [ 1 0], [ K.1 K.1] [K.1^2 1], [K.1^2 1] [ 0 1], [ 1 K.1^2] [ K.1 K.1^2], [ 0 0] [K.1^2 K.1], [ 1 K.1] [K.1^2 K.1^2], [ 1 1] [ 1 1], [K.1^2 K.1^2] [K.1^2 0], [K.1^2 K.1^2] [ 1 K.1], [ 0 1] [ K.1 K.1^2], [ 1 1] [ K.1 K.1^2], [K.1^2 K.1] [ 0 0], [ K.1 K.1^2] [ K.1 K.1^2], [K.1^2 K.1^2] [ K.1 K.1^2], [ 1 K.1] [ 1 0], [ 1 0] [K.1^2 K.1], [ 0 K.1^2] [ K.1 1], [K.1^2 K.1] [ K.1 0], [ 1 0] [K.1^2 K.1^2], [ K.1 K.1^2] [ 1 K.1^2], [K.1^2 K.1^2] [ K.1 K.1], [ K.1 K.1^2] [ 1 K.1], [K.1^2 0] [ 0 0], [ 0 K.1^2] [ 0 0], [ 1 0] [K.1^2 1], [ 0 K.1] [ 1 K.1^2], [ 1 K.1^2] [ 1 K.1], [ 0 K.1] [K.1^2 0], [ 0 1] [ K.1 K.1^2], [ K.1 1] [K.1^2 K.1], [K.1^2 1] [ K.1 0], [ 1 0] [K.1^2 0], [ 1 1] [ 1 K.1], [ 1 1] [ 1 K.1], [ K.1 K.1^2] [ K.1 K.1], [ 1 K.1^2] [ 0 K.1^2], [ 0 K.1] [ 1 0], [K.1^2 1] [ K.1 1], [ K.1 0] [ 0 0], [ 1 0] [K.1^2 K.1], [K.1^2 0] [ 1 K.1^2], [ 1 1] [ 0 0], [ K.1 K.1] [ K.1 K.1^2], [K.1^2 K.1] [K.1^2 K.1^2], [ 0 K.1^2] [ K.1 1], [ K.1 0] [ 1 0], [ 1 0] [K.1^2 K.1], [K.1^2 K.1] [ K.1 K.1^2], [ 1 K.1] [ 0 1], [ 1 K.1^2] [K.1^2 0], [ 0 1] [ 1 0], [ K.1 K.1] [ 0 K.1^2], [ K.1 0] [ K.1 K.1], [ 0 0] [ 1 K.1^2], [ 0 K.1^2] [ K.1 1], [ 0 K.1^2] [ K.1 1], [ K.1 1] [K.1^2 K.1], [ K.1 1] [ 0 K.1^2], [K.1^2 K.1^2] [ K.1 0], [ K.1 K.1] [K.1^2 K.1^2], [ K.1 1] [ 1 K.1^2], [ K.1 K.1^2] [ 1 0], [ 1 K.1] [ 0 0], [ K.1 0] [ 1 K.1], [ 1 1] [ K.1 0], [ 1 K.1] [K.1^2 1], [ 1 1] [ 0 0], [ K.1 K.1] [K.1^2 K.1^2], [K.1^2 0] [ 0 0], [K.1^2 0] [ K.1 1], [ K.1 K.1^2] [K.1^2 1], [ K.1 1] [ K.1 K.1^2], [ 0 1] [ 1 0], [ 1 1] [ 0 1], [ 1 1] [ 1 K.1], [K.1^2 K.1] [ K.1 K.1^2], [ K.1 1] [ 1 0], [ K.1 K.1^2] [K.1^2 0], [ K.1 0] [ 0 1], [ K.1 1] [ 0 1], [ K.1 0] [K.1^2 0], [ K.1 K.1] [ 1 0], [ K.1 K.1^2] [ K.1 1], [K.1^2 0] [ 1 0], [ 1 K.1^2] [K.1^2 K.1^2], [ 0 K.1^2] [ 1 K.1], [ K.1 K.1] [K.1^2 1], [ K.1 0] [ 0 K.1^2], [ 1 0] [ K.1 K.1^2], [ K.1 1] [ 0 1], [ K.1 0] [ K.1 K.1^2], [K.1^2 0] [ K.1 K.1^2], [ 1 K.1] [ 0 0], [ 1 K.1^2] [K.1^2 1], [ 1 K.1^2] [ 1 K.1^2], [K.1^2 K.1^2] [K.1^2 1], [K.1^2 1] [ 1 0], [ 0 1] [K.1^2 K.1], [K.1^2 K.1^2] [K.1^2 1], [ K.1 1] [ K.1 K.1], [K.1^2 0] [K.1^2 K.1^2], [K.1^2 1] [ 0 K.1^2], [ K.1 K.1^2] [ K.1 1], [K.1^2 1] [ 0 0], [ K.1 1] [ 0 K.1^2], [ 1 K.1^2] [ K.1 1], [K.1^2 1] [ 0 K.1^2], [K.1^2 K.1] [ 0 K.1^2], [ 1 K.1^2] [ 0 1], [ 0 K.1^2] [ 0 1], [ K.1 K.1] [ K.1 K.1], [ 1 K.1] [K.1^2 1], [ 0 K.1] [ 0 1], [ K.1 0] [ K.1 0], [ 0 0] [K.1^2 K.1], [K.1^2 1] [ 0 K.1^2], [ K.1 K.1^2] [ 1 1], [ 0 K.1^2] [K.1^2 0], [ 1 0] [ 1 0], [ 0 K.1] [ 1 0], [ 0 K.1^2] [ K.1 K.1^2], [ 1 K.1] [ K.1 K.1], [ 1 1] [ K.1 0], [ K.1 0] [ 0 K.1], [ 1 0] [K.1^2 K.1], [ K.1 0] [K.1^2 0], [K.1^2 0] [K.1^2 0], [ 1 0] [K.1^2 K.1], [ 0 0] [ 0 1], [ 1 1] [ 0 K.1], [K.1^2 K.1] [ K.1 K.1^2], [ 1 K.1^2] [ K.1 1], [ 0 K.1^2] [ 0 1], [ 0 K.1^2] [ 1 K.1^2], [ K.1 K.1] [ K.1 K.1^2], [K.1^2 K.1^2] [ 0 K.1^2], [ K.1 0] [ 0 1], [K.1^2 K.1^2] [ 1 K.1^2], [ 1 1] [ 0 1], [K.1^2 0] [ 1 K.1^2], [ 0 K.1^2] [ 0 K.1], [ 0 0] [ K.1 K.1^2], [ K.1 K.1^2] [ K.1 1], [K.1^2 0] [ 0 0], [ 1 0] [K.1^2 0], [ 0 K.1] [K.1^2 K.1], [ 0 K.1^2] [ 0 K.1^2], [ K.1 K.1] [ 0 0], [ 1 1] [ 0 0], [ 0 K.1^2] [K.1^2 K.1], [ 1 K.1^2] [K.1^2 0], [ 1 K.1^2] [ K.1 1], [K.1^2 K.1^2] [ 0 K.1^2], [ 1 K.1^2] [ 1 1], [ 0 K.1] [ K.1 K.1], [ 1 K.1] [ K.1 1], [ K.1 0] [K.1^2 K.1], [K.1^2 1] [ K.1 K.1], [ K.1 K.1] [ 0 K.1], [K.1^2 K.1] [ K.1 K.1], [K.1^2 K.1^2] [ K.1 0], [ K.1 1] [K.1^2 1], [K.1^2 0] [ 1 1], [ 1 1] [ 1 0], [ K.1 1] [ K.1 0], [ K.1 1] [ K.1 0], [ K.1 K.1^2] [ K.1 K.1^2], [K.1^2 1] [K.1^2 1], [K.1^2 K.1] [K.1^2 1], [ 1 K.1] [ 0 K.1^2], [ 1 K.1^2] [ 0 K.1^2], [ 0 K.1] [K.1^2 0], [ K.1 K.1] [K.1^2 K.1^2], [ K.1 1] [K.1^2 1], [K.1^2 0] [K.1^2 K.1], [K.1^2 K.1] [K.1^2 K.1], [ K.1 1] [ 1 K.1], [ K.1 K.1] [ 1 K.1^2], [ 1 K.1] [ K.1 K.1^2], [K.1^2 0] [K.1^2 K.1], [ 0 K.1] [ 1 0], [ 1 K.1^2] [K.1^2 0], [ 1 1] [ 1 0], [ 0 K.1^2] [ K.1 K.1], [ 1 1] [ 1 K.1], [ 0 K.1] [K.1^2 K.1], [ 0 K.1] [ 1 K.1], [ 0 K.1] [ K.1 K.1^2], [ K.1 K.1] [ 1 K.1], [K.1^2 1] [ K.1 1], [ K.1 0] [K.1^2 K.1], [K.1^2 0] [ 0 K.1], [ K.1 K.1^2] [K.1^2 K.1^2], [ K.1 K.1] [K.1^2 1], [ K.1 0] [K.1^2 1], [ 1 K.1^2] [ 1 K.1], [ K.1 K.1^2] [K.1^2 K.1^2], [ K.1 1] [ 1 1], [ 1 1] [K.1^2 0], [ 1 0] [K.1^2 K.1], [ K.1 0] [ K.1 K.1], [K.1^2 K.1] [ K.1 1], [ 1 0] [ 1 1], [K.1^2 0] [ 0 1], [ 1 K.1] [ 1 K.1^2], [ K.1 K.1] [ 1 K.1], [ 0 0] [ 1 1], [ K.1 K.1^2] [ 0 0], [ K.1 K.1^2] [K.1^2 0], [ 0 K.1] [K.1^2 1], [ 0 1] [ K.1 1], [K.1^2 1] [ 1 K.1^2], [ 1 1] [ K.1 K.1], [ 1 K.1^2] [ K.1 K.1^2], [ 0 K.1] [ 1 K.1], [ 1 1] [ K.1 0], [ 0 K.1^2] [ K.1 0], [ 1 K.1^2] [ 0 K.1], [K.1^2 K.1^2] [ 0 1], [K.1^2 K.1] [K.1^2 0], [ 0 K.1^2] [ K.1 K.1^2], [ K.1 0] [ K.1 K.1], [K.1^2 1] [ 0 1], [ 0 K.1^2] [ 1 1], [ 0 K.1] [ K.1 K.1^2], [ K.1 K.1] [ K.1 0], [ 1 0] [K.1^2 1], [K.1^2 K.1^2] [ 0 K.1], ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 19:43:42 2004 Input: K:=GF(4); M:=MatrixRing(K,2); Mt:={M![a,b,c,d] : a,b,c,d in K | (Trace(M![a,b,c,d]) eq 0) }; Mf:={M![a,b,c,d] : a,b,c,d in K | ( (M![a,b,c,d])[1] eq (M![a,b,c,d])[2]) }; Mtf:= Mt meet Mf; matrius:=[Random(M): i in [1..100000]]; quantes := function(A, B, C,lista) x:=0; y:=0; z:=0; for i in lista do if i in A then x:=x+1; end if; if i in B then y:=y+1; end if; if i in C then z:=z+1; end if; end for; return [x,y,z]; end function; l:=quantes(Mt,Mf,Mtf,matrius); l; Output: Magma V2.10-6 Wed Mar 3 2004 19:43:38 on modular [Seed = 2930283804] ------------------------------------- [ 25318, 6226, 1575 ] Total time: 3.999 seconds, Total memory usage: 7.09MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 19:43:55 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK:=MaximalOrder(K); J:=((29-a)/2)*OK; Factorization(J); #quo; J1:=ideal; Factorization(J1); Output: Magma V2.10-6 Wed Mar 3 2004 19:43:52 on modular [Seed = 2812386407] ------------------------------------- [ , ] 209 [ , ] Total time: 2.939 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 19:45:05 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2-5); OK:= MaximalOrder(K); J:= ideal< OK |209, (389+y)/2 >; J; #quo; Output: Magma V2.10-6 Wed Mar 3 2004 19:45:02 on modular [Seed = 3065023152] ------------------------------------- Ideal of OK Two element generators: [209, 0] [194, 1] 209 Total time: 2.909 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 19:45:23 2004 Input: K:=GF(4); M:=MatrixRing(K,2); Mt:={M![a,b,c,d] : a,b,c,d in K | (Trace(M![a,b,c,d]) eq 0) }; Mf:={M![a,b,c,d] : a,b,c,d in K | ( (M![a,b,c,d])[1] eq (M![a,b,c,d])[2]) }; #(M); #(Mt); #(Mf); #(Mtf); Mtf:= Mt meet Mf; matrius:=[Random(M): i in [1..100000]]; quantes := function(A, B, C,lista) x:=0; y:=0; z:=0; for i in lista do if i in A then x:=x+1; end if; if i in B then y:=y+1; end if; if i in C then z:=z+1; end if; end for; return [x,y,z]; end function; l:=quantes(Mt,Mf,Mtf,matrius); l; Output: Magma V2.10-6 Wed Mar 3 2004 19:45:19 on modular [Seed = 3486118872] ------------------------------------- 256 64 16 >> #(Mtf); ^ User error: Identifier 'Mtf' has not been declared or assigned [ 25058, 6223, 1521 ] Total time: 4.029 seconds, Total memory usage: 7.09MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Wed Mar 3 19:46:05 2004 Input: K:=GF(4); M:=MatrixRing(K,2); Mt:={M![a,b,c,d] : a,b,c,d in K | (Trace(M![a,b,c,d]) eq 0) }; Mf:={M![a,b,c,d] : a,b,c,d in K | ( (M![a,b,c,d])[1] eq (M![a,b,c,d])[2]) }; Mtf:= Mt meet Mf; #(M); #(Mt); #(Mf); #(Mtf); matrius:=[Random(M): i in [1..100000]]; quantes := function(A, B, C,lista) x:=0; y:=0; z:=0; for i in lista do if i in A then x:=x+1; end if; if i in B then y:=y+1; end if; if i in C then z:=z+1; end if; end for; return [x,y,z]; end function; l:=quantes(Mt,Mf,Mtf,matrius); l; Output: Magma V2.10-6 Wed Mar 3 2004 19:46:01 on modular [Seed = 3638486169] ------------------------------------- 256 64 16 4 [ 24925, 6216, 1546 ] Total time: 3.919 seconds, Total memory usage: 6.69MB ************** MAGMA ***************** Host roam240-254.fas.harvard.edu. (140.247.240.254) Time: Wed Mar 3 21:25:53 2004 Input: R := PolynomialRing(RationalField()); Output: Magma V2.10-6 Wed Mar 3 2004 21:25:50 on modular [Seed = 2105257689] ------------------------------------- Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam240-254.fas.harvard.edu. (140.247.240.254) Time: Wed Mar 3 21:29:14 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(X^2 + 1); E := EquationOrder(K); OK := MaximalOrder(K); Index(OK,E); I := 2004*OK; Factorization(I); [K!OK.i: i in [1,2]];; Output: Magma V2.10-6 Wed Mar 3 2004 21:29:11 on modular [Seed = 2374719984] ------------------------------------- >> K := NumberField(X^2 + 1); ^ User error: Identifier 'X' has not been declared or assigned >> E := EquationOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> OK := MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> Index(OK,E); ^ User error: Identifier 'OK' has not been declared or assigned >> I := 2004*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I); ^ User error: Identifier 'I' has not been declared or assigned >> [K!OK.i: i in [1,2]];;; ^ User error: Identifier 'K' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam240-254.fas.harvard.edu. (140.247.240.254) Time: Wed Mar 3 21:29:26 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(X^2 + 1); E := EquationOrder(K); OK := MaximalOrder(K); Index(OK,E); I := 2004*OK; Factorization(I) [K!OK.i: i in [1,2]];; Output: Magma V2.10-6 Wed Mar 3 2004 21:29:23 on modular [Seed = 2239975692] ------------------------------------- >> K := NumberField(X^2 + 1); ^ User error: Identifier 'X' has not been declared or assigned >> E := EquationOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> OK := MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> Index(OK,E); ^ User error: Identifier 'OK' has not been declared or assigned >> I := 2004*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> [K!OK.i: i in [1,2]];;; ^ User error: bad syntax Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam240-254.fas.harvard.edu. (140.247.240.254) Time: Wed Mar 3 21:29:59 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2 + 1); E := EquationOrder(K); OK := MaximalOrder(K); Index(OK,E); I := 2004*OK; Factorization(I) [K!OK.i: i in [1,2]];; Output: Magma V2.10-6 Wed Mar 3 2004 21:29:56 on modular [Seed = 2459190844] ------------------------------------- 1 >> [K!OK.i: i in [1,2]];;; ^ User error: bad syntax Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam240-254.fas.harvard.edu. (140.247.240.254) Time: Wed Mar 3 21:31:54 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2 + 1); E := EquationOrder(K); OK := MaximalOrder(K); Index(OK,E); I := 2004*OK; Factorization(I); [K!OK.i: i in [1,2]];; Output: Magma V2.10-6 Wed Mar 3 2004 21:31:49 on modular [Seed = 2778951866] ------------------------------------- 1 [ , , ] [ 1, a ] Total time: 4.759 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam240-254.fas.harvard.edu. (140.247.240.254) Time: Wed Mar 3 21:34:15 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2 + 1); E := EquationOrder(K); OK := MaximalOrder(K); Index(OK,E); I := 2004*OK; Factorization(I); [K!OK.i: i in [1,2]]; Output: Magma V2.10-6 Wed Mar 3 2004 21:34:12 on modular [Seed = 3469220704] ------------------------------------- 1 [ , , ] [ 1, a ] Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam240-254.fas.harvard.edu. (140.247.240.254) Time: Wed Mar 3 21:39:42 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^6+x^5+x^4+x^3+x^2+x+1); E := EquationOrder(K); OK := MaximalOrder(K); Index(OK,E); I := 7*OK; J := 3*OK; Factorization(I); Factorization(J); [K!OK.i: i in [1,6]]; Output: Magma V2.10-6 Wed Mar 3 2004 21:39:39 on modular [Seed = 3520530224] ------------------------------------- 1 [ ] [ ] [ 1, a^5 ] Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam240-254.fas.harvard.edu. (140.247.240.254) Time: Wed Mar 3 21:40:48 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^6+x^5+x^4+x^3+x^2+x+1); E := EquationOrder(K); OK := MaximalOrder(K); Index(OK,E); I := 7*OK; J := 3*OK; Factorization(I); Factorization(J); [K!OK.i: i in [1,2]]; Output: Magma V2.10-6 Wed Mar 3 2004 21:40:45 on modular [Seed = 3873452481] ------------------------------------- 1 [ ] [ ] [ 1, a ] Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam240-254.fas.harvard.edu. (140.247.240.254) Time: Wed Mar 3 21:41:24 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^6+x^5+x^4+x^3+x^2+x+1); E := EquationOrder(K); OK := MaximalOrder(K); Index(OK,E); I := 7*OK; J := 3*OK; Factorization(I); Factorization(J); [K!OK.i: i in [1,2,3,4,5,6]]; Output: Magma V2.10-6 Wed Mar 3 2004 21:41:21 on modular [Seed = 4294518948] ------------------------------------- 1 [ ] [ ] [ 1, a, a^2, a^3, a^4, a^5 ] Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam240-254.fas.harvard.edu. (140.247.240.254) Time: Wed Mar 3 21:42:02 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^6+x^5+x^4+x^3+x^2+x+1); E := EquationOrder(K); OK := MaximalOrder(K); Index(OK,E); I := 7*OK; J := 3*OK; Factorization(I); Factorization(J); Output: Magma V2.10-6 Wed Mar 3 2004 21:41:59 on modular [Seed = 4109509513] ------------------------------------- 1 [ ] [ ] Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam240-254.fas.harvard.edu. (140.247.240.254) Time: Wed Mar 3 21:44:29 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-2); E := EquationOrder(K); OK := MaximalOrder(K); Index(OK,E); I := (3/8)*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 21:44:26 on modular [Seed = 100720135] ------------------------------------- 1 [ , ] Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam240-254.fas.harvard.edu. (140.247.240.254) Time: Wed Mar 3 22:09:12 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-5); E := EquationOrder(K); OK := MaximalOrder(K); Index(OK,E); I := (3/8)*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 22:09:09 on modular [Seed = 1852355504] ------------------------------------- 2 [ , ] Total time: 2.939 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 22:49:55 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4+6*x^2+3*x+2); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 22:49:52 on modular [Seed = 3048428254] ------------------------------------- [ , , ] Total time: 2.969 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 22:50:08 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4+6*x^3+3*x+2); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 22:50:05 on modular [Seed = 3317899939] ------------------------------------- [ , , ] Total time: 2.919 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 22:50:19 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4+6*x^3+x+2); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 22:50:16 on modular [Seed = 3705289647] ------------------------------------- [ ] Total time: 2.999 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 22:50:35 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4+6*x^3+x^2+5*x+2); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 22:50:32 on modular [Seed = 3958180968] ------------------------------------- [ , ] Total time: 2.909 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 22:50:48 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4+6*x^3+6*x^2+5*x+2); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 22:50:45 on modular [Seed = 3790014079] ------------------------------------- [ ] Total time: 2.939 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 22:50:59 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4+6*x^3+6*x^2+2); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 22:50:56 on modular [Seed = 4177403731] ------------------------------------- [ , , ] Total time: 2.909 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 22:51:09 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4+6*x^3+6*x^2+1); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 22:51:06 on modular [Seed = 4159770710] ------------------------------------- [ , ] Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 22:51:23 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4+6*x^2+1); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 22:51:20 on modular [Seed = 152039101] ------------------------------------- [ , ] Total time: 2.949 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 22:51:31 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4+3*x^2+1); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 22:51:28 on modular [Seed = 33875406] ------------------------------------- [ , ] Total time: 2.999 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 22:51:47 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4+x^2+1); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 22:51:44 on modular [Seed = 454950087] ------------------------------------- >> K := NumberField(x^4+x^2+1); ^ Runtime error in 'NumberField': Argument 1 is not irreducible >> OK:= MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> I:=3*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I); ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 22:51:57 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4+x^3+1); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 22:51:54 on modular [Seed = 741002234] ------------------------------------- [ , ] Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 22:52:08 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4+3*x^3+1); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 22:52:05 on modular [Seed = 623100620] ------------------------------------- [ , ] Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 22:53:21 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-17*x^2+70); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 22:53:18 on modular [Seed = 1043912220] ------------------------------------- >> K := NumberField(x^4-17*x^2+70); ^ Runtime error in 'NumberField': Argument 1 is not irreducible >> OK:= MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> I:=3*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I); ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 22:54:00 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-17*x^3+70); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 22:53:57 on modular [Seed = 808900713] ------------------------------------- [ , ] Total time: 2.989 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 22:54:13 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-17*x^3+79); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 22:54:10 on modular [Seed = 1246536228] ------------------------------------- [ , ] Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 22:54:20 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-17*x^3+13); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 22:54:18 on modular [Seed = 1128639269] ------------------------------------- [ , ] Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 22:54:31 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-11*x^3+13); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 22:54:28 on modular [Seed = 1414708268] ------------------------------------- [ , ] Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 22:54:40 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-8*x^3+13); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 22:54:37 on modular [Seed = 1835762972] ------------------------------------- [ , ] Total time: 2.889 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 22:56:06 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-7*x^3+13); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 22:56:03 on modular [Seed = 1650756285] ------------------------------------- [ , ] Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 22:56:22 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-7*x^3+2*x^2+13); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 22:56:19 on modular [Seed = 2071827348] ------------------------------------- [ , ] Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 22:56:32 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-7*x^3+2*x^2+7); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 22:56:29 on modular [Seed = 2357879917] ------------------------------------- [ , ] Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 22:56:40 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-7*x^3+2*x^2+4); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 22:56:37 on modular [Seed = 2239982972] ------------------------------------- >> K := NumberField(x^4-7*x^3+2*x^2+4); ^ Runtime error in 'NumberField': Argument 1 is not irreducible >> OK:= MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> I:=3*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I); ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 22:56:47 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-7*x^3+2*x^2+3); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 22:56:44 on modular [Seed = 2677634927] ------------------------------------- [ , ] Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 22:56:59 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-7*x^3+5*x^2+3); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 22:56:56 on modular [Seed = 2425780628] ------------------------------------- [ , ] Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 22:57:13 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-7*x^3+1*x^2+3); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 22:57:10 on modular [Seed = 2846834867] ------------------------------------- [ , ] Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 22:57:23 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-2*x^3+1*x^2+3); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 22:57:20 on modular [Seed = 2728676238] ------------------------------------- >> K := NumberField(x^4-2*x^3+1*x^2+3); ^ Runtime error in 'NumberField': Argument 1 is not irreducible >> OK:= MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> I:=3*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I); ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 22:57:31 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-2*x^3+1*x^2+4); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 22:57:28 on modular [Seed = 3149746847] ------------------------------------- [ ] Total time: 2.929 seconds, Total memory usage: 2.10MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 22:57:39 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-2*x^3+1*x^2+5); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 22:57:36 on modular [Seed = 3435800048] ------------------------------------- [ , ] Total time: 2.939 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 22:57:53 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-2*x^3+4*x^2+5); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 22:57:49 on modular [Seed = 3317902580] ------------------------------------- [ , ] Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 22:58:04 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-3*x^3+4*x^2+5); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 22:58:01 on modular [Seed = 3738711963] ------------------------------------- [ ] Total time: 2.979 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 22:58:12 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-3*x^3+4*x^2+3); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 22:58:09 on modular [Seed = 3620814474] ------------------------------------- [ , ] Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 22:58:22 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-3*x^3+4*x^2+1); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 22:58:19 on modular [Seed = 3907912127] ------------------------------------- [ , ] Total time: 3.029 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 22:58:32 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-21*x^3+4*x^2+1); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 22:58:29 on modular [Seed = 3790014600] ------------------------------------- [ , , ] Total time: 3.039 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 22:58:46 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-21*x^3+4*x^2+3); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 22:58:43 on modular [Seed = 4210824069] ------------------------------------- [ , ] Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 22:59:00 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-21*x^3+4*x^2+2); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 22:58:56 on modular [Seed = 4092926590] ------------------------------------- [ ] Total time: 2.999 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 22:59:13 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-21*x^3+6*x^2+1); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 22:59:10 on modular [Seed = 67300743] ------------------------------------- [ , ] Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 22:59:23 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-21*x^3+10*x^2+1); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 22:59:20 on modular [Seed = 521795210] ------------------------------------- [ , ] Total time: 2.939 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 22:59:33 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-21*x^3+11*x^2+1); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 22:59:30 on modular [Seed = 370212793] ------------------------------------- [ ] Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 22:59:43 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-21*x^3+12*x^2+1); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 22:59:40 on modular [Seed = 690995336] ------------------------------------- [ , ] Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 22:59:57 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-21*x^3+21*x^2+1); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 22:59:53 on modular [Seed = 589679255] ------------------------------------- [ , ] Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 23:00:07 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-21*x^3+3*x^2+1); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 23:00:04 on modular [Seed = 859167482] ------------------------------------- [ , ] Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 23:00:18 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-19*x^3+3*x^2+1); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 23:00:15 on modular [Seed = 1246536584] ------------------------------------- [ , ] Total time: 2.969 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 23:00:28 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-13*x^3+3*x^2+1); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 23:00:25 on modular [Seed = 1566291081] ------------------------------------- [ , ] Total time: 2.939 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 23:00:42 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-13*x^3+3*x^2+x+1); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 23:00:39 on modular [Seed = 1414708670] ------------------------------------- [ ] Total time: 2.959 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 23:00:49 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-13*x^3+3*x^2+5x+1); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 23:00:46 on modular [Seed = 1869186700] ------------------------------------- >> K := NumberField(x^4-13*x^3+3*x^2+5x+1); ^ User error: bad syntax >> OK:= MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> I:=3*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I); ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 23:00:56 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-13*x^3+3*x^2+6x+1); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 23:00:53 on modular [Seed = 1717604254] ------------------------------------- >> K := NumberField(x^4-13*x^3+3*x^2+6x+1); ^ User error: bad syntax >> OK:= MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> I:=3*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I); ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 23:01:03 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-13*x^3+3*x^2+6x+3); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 23:01:00 on modular [Seed = 2038403208] ------------------------------------- >> K := NumberField(x^4-13*x^3+3*x^2+6x+3); ^ User error: bad syntax >> OK:= MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> I:=3*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I); ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 23:01:11 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-13*x^3+3*x^2+6x+2); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 23:01:08 on modular [Seed = 2189715595] ------------------------------------- >> K := NumberField(x^4-13*x^3+3*x^2+6x+2); ^ User error: bad syntax >> OK:= MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> I:=3*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I); ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 23:01:23 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-13*x^3+3*x^2+6*x+2); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 23:01:19 on modular [Seed = 2509471639] ------------------------------------- [ ] Total time: 2.899 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 23:01:32 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-13*x^3+6*x+2); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 23:01:29 on modular [Seed = 2896840376] ------------------------------------- [ ] Total time: 2.929 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 23:01:42 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-13*x^3+6*x+1); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 23:01:39 on modular [Seed = 2812366217] ------------------------------------- [ , ] Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 23:01:51 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-9*x^3+6*x+1); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 23:01:48 on modular [Seed = 3199751327] ------------------------------------- [ , ] Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 23:02:01 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-21*x^3+6*x+1); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 23:01:58 on modular [Seed = 2981583754] ------------------------------------- [ , ] Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 23:02:12 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-21*x^3+6*x+21); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 23:02:09 on modular [Seed = 3368952452] ------------------------------------- [ ] Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 23:02:23 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-21*x^3+6*x+70); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 23:02:21 on modular [Seed = 3284478339] ------------------------------------- [ , ] Total time: 2.909 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 23:02:39 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-21*x^3+5*x+70); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 23:02:36 on modular [Seed = 3587391364] ------------------------------------- [ , ] Total time: 3.019 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 23:02:50 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-21*x^3+8*x+70); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 23:02:47 on modular [Seed = 4025025925] ------------------------------------- [ , ] Total time: 2.969 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 3 23:03:08 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4-21*x^3+10*x+70); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 3 2004 23:03:05 on modular [Seed = 4244248200] ------------------------------------- [ , ] Total time: 2.979 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host dhcp-019-141.cns.ohiou.edu. (132.235.19.141) Time: Wed Mar 3 23:06:48 2004 Input: >? Output: Magma V2.10-6 Wed Mar 3 2004 23:06:45 on modular [Seed = 235464021] ------------------------------------- =============================================================================== PATH: / KIND: Overview =============================================================================== You are reading about the Magma online help system. This system gives you information about Magma while you are at the computer. To see this help page at any time, all you have to do is to type ? ---------- The online help system comes in two modes: the single request mode and the Magma Help Browser. To enter the Browser, type ?? The Browser is useful if you intend to read several related help nodes, because you can exploit the tree structure of the online help. Once you are in the Browser, you can type help again to find out how to use the Browser, and for a more detailed explanation of the whole online help system. ---------- Single help requests begin with the ? character. Examples are: ?print ?magma ?ring ?example If your help request is ambiguous, Magma will return a numbered list of matches. To see the contents of one of them, type ? followed by its number. Some help pages suggest other pages that you might like to look at as well. They are prefixed by a code such as +3 or +5 . To read one of them, type ? followed by the code. You can also supply the full pathname of a help node, if you know it. For example: ?/system/quit ?/magma/module/homomorphism ---------- The online help system offers tab completion. If you type a few letters of your help request and then press the tab key, Magma will "complete" the request if there is a unique completion. Otherwise, it will complete the request as far as possible, and then emit a beep. Press the tab key again to see all the possibilities. ALWAYS PRESS TAB BEFORE THE END OF THE LINE, SO AS TO SEE EVERY RELEVANT HELP PAGE. (On a few operating systems, the tab completion feature cannot be made available.) ---------- The content of the online help system comes from two sources: the "Handbook of Magma Functions" (Bosma and Cannon) and specially-written overview nodes. You may also wish to consult the books "An Introduction to Algebraic Programming in Magma" (Cannon and Playoust) and "Solving Problems with Magma" (Bosma, Cannon, Playoust and Steel). ---------- The online help system is also available in an HTML form suitable for Internet browsers. To use this, move to a shell prompt (outside Magma) and type magmahelp ---------- To leave Magma, type quit; or -D. =============================================================================== Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host c-24-30-122-16.we.client2.attbi.com. (24.30.122.16) Time: Wed Mar 3 23:23:41 2004 Input: x^n + x^n Output: Magma V2.10-6 Wed Mar 3 2004 23:23:38 on modular [Seed = 656525411] ------------------------------------- >> x^n + x^n; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (132.235.18.201) Time: Wed Mar 3 23:54:04 2004 Input: .2+4 >2+4; Output: Magma V2.10-6 Wed Mar 3 2004 23:54:01 on modular [Seed = 1667601668] ------------------------------------- >> .2+4 ^ User error: bad syntax 6 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (132.235.18.201) Time: Wed Mar 3 23:55:20 2004 Input: >Factorial(18); Output: Magma V2.10-6 Wed Mar 3 2004 23:55:17 on modular [Seed = 1920238793] ------------------------------------- 6402373705728000 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 00:30:17 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField((x^2_10)*(x^2-7)); OK := MaximalOrder(K) Output: Magma V2.10-6 Thu Mar 4 2004 00:30:14 on modular [Seed = 4008185862] ------------------------------------- >> K:=NumberField((x^2_10)*(x^2-7)); ^ User error: bad syntax >> OK := MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 00:30:21 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField((x^2_10)*(x^2-7)); OK := MaximalOrder(K); Output: Magma V2.10-6 Thu Mar 4 2004 00:30:18 on modular [Seed = 3873445890] ------------------------------------- >> K:=NumberField((x^2_10)*(x^2-7)); ^ User error: bad syntax >> OK := MaximalOrder(K);; ^ User error: Identifier 'K' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 00:30:53 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField((x^2-10)*(x^2-7)); OK := MaximalOrder(K); Output: Magma V2.10-6 Thu Mar 4 2004 00:30:50 on modular [Seed = 4294508795] ------------------------------------- >> K:=NumberField((x^2-10)*(x^2-7)); ^ Runtime error in 'NumberField': Argument 1 is not irreducible >> OK := MaximalOrder(K);; ^ User error: Identifier 'K' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 00:32:49 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField((x^2-10)*(x^2-7) : Abs :=true); OK := MaximalOrder(K); Output: Magma V2.10-6 Thu Mar 4 2004 00:32:46 on modular [Seed = 4076080514] ------------------------------------- >> K:=NumberField((x^2-10)*(x^2-7) : Abs :=true); ^ Runtime error in 'NumberField': Argument 1 is not irreducible >> OK := MaximalOrder(K);; ^ User error: Identifier 'K' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 00:33:35 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField((x^2-10),(x^2-7) : Abs :=true); OK := MaximalOrder(K); Output: Magma V2.10-6 Thu Mar 4 2004 00:33:32 on modular [Seed = 168621481] ------------------------------------- >> K:=NumberField((x^2-10),(x^2-7) : Abs :=true); ^ Runtime error in 'NumberField': Bad argument types Argument types given: RngUPolElt, RngUPolElt >> OK := MaximalOrder(K);; ^ User error: Identifier 'K' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 00:34:55 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-10,x^2-7] : Abs :=true); OK := MaximalOrder(K); Output: Magma V2.10-6 Thu Mar 4 2004 00:34:52 on modular [Seed = 458739] ------------------------------------- Total time: 2.949 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 00:35:29 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-10,x^2-7] : Abs :=true); OK := MaximalOrder(K); Basis(OK); Output: Magma V2.10-6 Thu Mar 4 2004 00:35:26 on modular [Seed = 303337987] ------------------------------------- [ OK.1, OK.2, OK.3, OK.4 ] Total time: 3.039 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 00:35:52 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-10,x^2-7] : Abs :=true); OK := MaximalOrder(K); Basis(OK); Output: Magma V2.10-6 Thu Mar 4 2004 00:35:49 on modular [Seed = 690989331] ------------------------------------- [ OK.1, OK.2, OK.3, OK.4 ] Total time: 2.969 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 00:36:08 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-10,x^2-7] : Abs :=true); OK := MaximalOrder(K); Output: Magma V2.10-6 Thu Mar 4 2004 00:36:05 on modular [Seed = 539402346] ------------------------------------- Total time: 3.009 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Thu Mar 4 00:36:26 2004 Input: R := PolynomialRing(RationalField()); IsPrime(x^4-34*x^2+9); K := NumberField(x^4-34*x^2+9); E:=EquationOrder(K); OK:=MaximalOrder(K); I:=3*OK; J:=2*OK; Index(OK, E); Factorization(I); Factorization(J); [K!OK.i : i in [1, 2, 3, 4]]; Output: Magma V2.10-6 Thu Mar 4 2004 00:36:23 on modular [Seed = 926005103] ------------------------------------- true 24 [ , , , ] [ ] [ 1, a, 1/2*(a^2 + 1), 1/12*(a^3 + 3*a^2 + 11*a + 9) ] Total time: 3.109 seconds, Total memory usage: 2.05MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Thu Mar 4 00:36:42 2004 Input: R := PolynomialRing(RationalField()); IsIrreducible(x^4-34*x^2+9); K := NumberField(x^4-34*x^2+9); E:=EquationOrder(K); OK:=MaximalOrder(K); I:=3*OK; J:=2*OK; Index(OK, E); Factorization(I); Factorization(J); [K!OK.i : i in [1, 2, 3, 4]]; Output: Magma V2.10-6 Thu Mar 4 2004 00:36:39 on modular [Seed = 1313394214] ------------------------------------- true 24 [ , , , ] [ ] [ 1, a, 1/2*(a^2 + 1), 1/12*(a^3 + 3*a^2 + 11*a + 9) ] Total time: 3.159 seconds, Total memory usage: 2.05MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 00:36:51 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-10,x^2-7] : Abs :=true); OK := MaximalOrder(K); B := Basis(OK); B!K; Output: Magma V2.10-6 Thu Mar 4 2004 00:36:48 on modular [Seed = 1162069306] ------------------------------------- >> B!K;; ^ Runtime error in '!': Illegal coercion Total time: 2.989 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 00:37:02 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-10,x^2-7] : Abs :=true); OK := MaximalOrder(K); B := Basis(OK); K!B; Output: Magma V2.10-6 Thu Mar 4 2004 00:36:59 on modular [Seed = 1549458472] ------------------------------------- >> K!B;; ^ Runtime error in '!': Illegal coercion LHS: FldNum RHS: [FldOrdElt] Total time: 3.029 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 00:37:18 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-10,x^2-7] : Abs :=true); OK := MaximalOrder(K); B := Basis(OK); B.1!K; Output: Magma V2.10-6 Thu Mar 4 2004 00:37:15 on modular [Seed = 1398133719] ------------------------------------- >> B.1!K;; ^ Runtime error in '.': Bad argument types Argument types given: SeqEnum[FldOrdElt], RngIntElt Total time: 3.019 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 00:37:30 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-10,x^2-7] : Abs :=true); OK := MaximalOrder(K); B := Basis(OK); B.1; Output: Magma V2.10-6 Thu Mar 4 2004 00:37:26 on modular [Seed = 1785522931] ------------------------------------- >> B.1;; ^ Runtime error in '.': Bad argument types Argument types given: SeqEnum[FldOrdElt], RngIntElt Total time: 2.949 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 00:37:40 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-10,x^2-7] : Abs :=true); OK := MaximalOrder(K); B := Basis(OK); Output: Magma V2.10-6 Thu Mar 4 2004 00:37:36 on modular [Seed = 1634197966] ------------------------------------- Total time: 3.229 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Thu Mar 4 00:37:43 2004 Input: R := PolynomialRing(RationalField()); IsIrreducible(x^4-34*x^2+9); K := NumberField(x^4-34*x^2+9); OK:=MaximalOrder(K); I:=3*OK; Factorization(I); [K!OK.i : i in [1, 2, 3, 4]]; Output: Magma V2.10-6 Thu Mar 4 2004 00:37:38 on modular [Seed = 2121858771] ------------------------------------- true [ , , , ] [ 1, a, 1/2*(a^2 + 1), 1/12*(a^3 + 3*a^2 + 11*a + 9) ] Total time: 3.409 seconds, Total memory usage: 2.05MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 00:37:58 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-10,x^2-7] : Abs :=true); MaximalOrder(K); Output: Magma V2.10-6 Thu Mar 4 2004 00:37:55 on modular [Seed = 2408124211] ------------------------------------- Maximal Order of Equation Order with defining polynomials x^2 - 10, x^2 - 7 over its ground order Total time: 2.969 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 00:38:17 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-10,x^2-7] : Abs :=true); OK := MaximalOrder(K); Basis(OK); Output: Magma V2.10-6 Thu Mar 4 2004 00:38:14 on modular [Seed = 2239956300] ------------------------------------- [ OK.1, OK.2, OK.3, OK.4 ] Total time: 3.039 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 00:41:14 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-10,x^2-7] : Abs :=true); OK := MaximalOrder(K); [K!OK.i : i in [1, 2, 3, 4]] Output: Magma V2.10-6 Thu Mar 4 2004 00:41:11 on modular [Seed = 2947100375] ------------------------------------- [ 1, a, b, 1/2*a*b - 1/2*a ] Total time: 2.969 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 00:41:19 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-10,x^2-7] : Abs :=true); OK := MaximalOrder(K); [K!OK.i : i in [1, 2, 3, 4]]; Output: Magma V2.10-6 Thu Mar 4 2004 00:41:16 on modular [Seed = 2812356308] ------------------------------------- [ 1, a, b, 1/2*a*b - 1/2*a ] Total time: 2.939 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Thu Mar 4 01:05:47 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); OK:=MaximalOrder(K); [K!OK.i : i in [1..5]]; t:=[p*OK: p in [1..100] | IsPrime(p)]; [Factorization( t[i] ) : i in [1..25] ]; Output: Magma V2.10-6 Thu Mar 4 2004 01:05:44 on modular [Seed = 4227693772] ------------------------------------- [ 1, a, a^2, a^3, a^4 ] [ [ ], [ ], [ , , ], [ , ], [ , , , ], [ , ], [ , , ], [ , , ], [ , ], [ , , ], [ , , ], [ ], [ , ], [ , , , ], [ , ], [ , ], [ , ], [ ], [ , , , ], [ , , , ], [ ], [ , ], [ , , , ], [ , ], [ ] ] Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Thu Mar 4 01:20:15 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2+13]); OK:=MaximalOrder(K); I:=ideal; Factorization(I); Output: Magma V2.10-6 Thu Mar 4 2004 01:20:12 on modular [Seed = 892583865] ------------------------------------- [ ] Total time: 3.059 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Thu Mar 4 01:20:59 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2+13]); OK:=MaximalOrder(K); I:=ideal; J:=ideal; Factorization(I); Factorization(J); Output: Magma V2.10-6 Thu Mar 4 2004 01:20:56 on modular [Seed = 1043903718] ------------------------------------- [ ] [ ] Total time: 2.979 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Mar 4 01:31:13 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^4 - 34*x^2 + 9); OK:= MaximalOrder(K); I:=3*OK; Factorization(I); Output: Magma V2.10-6 Thu Mar 4 2004 01:31:10 on modular [Seed = 1599722081] ------------------------------------- [ , , , ] Total time: 3.169 seconds, Total memory usage: 2.05MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 01:54:34 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK := MaximalOrder(K); J := ideal(209*OK.0,(389/2*OK.0+1/2*OK.1); Output: Magma V2.10-6 Thu Mar 4 2004 01:54:31 on modular [Seed = 2560494127] ------------------------------------- >> K:=NumberField(x^2-5); ^ Runtime error in 'AssignNames': Argument 2 must have length 2 >> J := ideal(209*OK.0,(389/2*OK.0+1/2*OK.1); ^ User error: bad syntax Total time: 3.039 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 01:55:13 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK := MaximalOrder(K); J := ideal(209*OK.0,(389/2*OK.0+1/2*OK.1); Output: Magma V2.10-6 Thu Mar 4 2004 01:55:09 on modular [Seed = 2307857236] ------------------------------------- >> J := ideal(209*OK.0,(389/2*OK.0+1/2*OK.1); ^ User error: bad syntax Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 01:55:26 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK := MaximalOrder(K); J := ideal(209*OK.0)+ ideal(389/2*OK.0+1/2*OK.1); Output: Magma V2.10-6 Thu Mar 4 2004 01:55:23 on modular [Seed = 2998149241] ------------------------------------- >> J := ideal(209*OK.0)+ ideal(389/2*OK.0+1/2*OK.1); ^ User error: Identifier 'ideal' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 01:55:39 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK := MaximalOrder(K); J := Ideal(209*OK.0)+ Ideal(389/2*OK.0+1/2*OK.1); Output: Magma V2.10-6 Thu Mar 4 2004 01:55:36 on modular [Seed = 3149736259] ------------------------------------- >> J := Ideal(209*OK.0)+ Ideal(389/2*OK.0+1/2*OK.1); ^ Runtime error in '.': Value for name index (0) should be in the range [1..2] Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 01:55:57 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK := MaximalOrder(K); J := Ideal(209*OK.1, 389/2*OK.1+1/2*OK.2); Output: Magma V2.10-6 Thu Mar 4 2004 01:55:54 on modular [Seed = 2778937167] ------------------------------------- >> J := Ideal(209*OK.1, 389/2*OK.1+1/2*OK.2); ^ Runtime error in 'Ideal': Bad argument types Argument types given: FldOrdElt, FldOrdElt Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 01:56:16 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK := MaximalOrder(K); J := Ideal([209*OK.1, 389/2*OK.1+1/2*OK.2]); Output: Magma V2.10-6 Thu Mar 4 2004 01:56:13 on modular [Seed = 3520545484] ------------------------------------- >> J := Ideal([209*OK.1, 389/2*OK.1+1/2*OK.2]); ^ Runtime error in 'Ideal': Bad argument types Argument types given: SeqEnum[FldOrdElt] Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 01:56:52 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK := MaximalOrder(K); J := Ideal(209*OK.1) + Ideal(389/2*OK.1+1/2*OK.2); Output: Magma V2.10-6 Thu Mar 4 2004 01:56:49 on modular [Seed = 3688712442] ------------------------------------- >> J := Ideal(209*OK.1) + Ideal(389/2*OK.1+1/2*OK.2); ^ Runtime error in 'Ideal': Bad argument types Argument types given: FldOrdElt Total time: 3.049 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Thu Mar 4 01:58:14 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK:=MaximalOrder(K); J:=((29-a)/2)*OK; Factorization(J); I:=((27-a)/2)*OK; Factorization(I); Output: Magma V2.10-6 Thu Mar 4 2004 01:58:10 on modular [Seed = 3301070678] ------------------------------------- [ , ] [ ] Total time: 3.509 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 01:58:15 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK := MaximalOrder(K); J := Ideal(OK | {209*OK.1, 389/2*OK.1+1/2*OK.2}); Output: Magma V2.10-6 Thu Mar 4 2004 01:58:11 on modular [Seed = 3351336020] ------------------------------------- >> J := Ideal(OK | {209*OK.1, 389/2*OK.1+1/2*OK.2}); ^ User error: bad syntax Total time: 3.569 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 01:58:25 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK := MaximalOrder(K); J := Ideal(OK, {209*OK.1, 389/2*OK.1+1/2*OK.2}); Output: Magma V2.10-6 Thu Mar 4 2004 01:58:22 on modular [Seed = 4159792233] ------------------------------------- >> J := Ideal(OK, {209*OK.1, 389/2*OK.1+1/2*OK.2}); ^ Runtime error in 'Ideal': Bad argument types Argument types given: RngOrd, SetEnum[FldOrdElt] Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 01:58:34 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK := MaximalOrder(K); J := Ideal({209*OK.1, 389/2*OK.1+1/2*OK.2}); Output: Magma V2.10-6 Thu Mar 4 2004 01:58:31 on modular [Seed = 3773199207] ------------------------------------- >> J := Ideal({209*OK.1, 389/2*OK.1+1/2*OK.2}); ^ Runtime error in 'Ideal': Bad argument types Argument types given: SetEnum[FldOrdElt] Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 02:01:31 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK := MaximalOrder(K); J := ; Output: Magma V2.10-6 Thu Mar 4 2004 02:01:28 on modular [Seed = 152018256] ------------------------------------- >> J := ; ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 02:01:39 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK := MaximalOrder(K); J := ; Output: Magma V2.10-6 Thu Mar 4 2004 02:01:36 on modular [Seed = 808887409] ------------------------------------- >> J := ; ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 02:01:53 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK := MaximalOrder(K); J := ; Output: Magma V2.10-6 Thu Mar 4 2004 02:01:50 on modular [Seed = 993898356] ------------------------------------- >> J := ; ^ User error: bad syntax Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 02:03:01 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK := MaximalOrder(K); J := ; Output: Magma V2.10-6 Thu Mar 4 2004 02:02:58 on modular [Seed = 623096214] ------------------------------------- >> J := ; ^ User error: bad syntax Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 02:03:12 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK := MaximalOrder(K); J := ; Output: Magma V2.10-6 Thu Mar 4 2004 02:03:09 on modular [Seed = 740997264] ------------------------------------- Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 02:03:23 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK := MaximalOrder(K); ; Output: Magma V2.10-6 Thu Mar 4 2004 02:03:20 on modular [Seed = 1464976382] ------------------------------------- Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 02:04:08 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK := MaximalOrder(K); ; Discriminant(OK); Output: Magma V2.10-6 Thu Mar 4 2004 02:04:04 on modular [Seed = 1582877355] ------------------------------------- 5 Total time: 3.029 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 02:05:04 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK := MaximalOrder(K); J := ; Discriminant(J); Output: Magma V2.10-6 Thu Mar 4 2004 02:05:00 on modular [Seed = 1886840188] ------------------------------------- >> Discriminant(J); ^ Runtime error in 'Discriminant': Bad argument types Argument types given: Tup Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 02:05:31 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK := MaximalOrder(K); J := ; Norm(J); Output: Magma V2.10-6 Thu Mar 4 2004 02:05:28 on modular [Seed = 2055008083] ------------------------------------- >> Norm(J); ^ Runtime error in 'Norm': Bad argument types Argument types given: Tup Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 02:08:45 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK := MaximalOrder(K); J := ; Index(OK, J); Output: Magma V2.10-6 Thu Mar 4 2004 02:08:42 on modular [Seed = 1684205967] ------------------------------------- >> Index(OK, J); ^ Runtime error in 'Index': Bad argument types Argument types given: RngOrd, Tup Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 02:09:20 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK := MaximalOrder(K); J := ideal; Index(OK, J); Output: Magma V2.10-6 Thu Mar 4 2004 02:09:17 on modular [Seed = 1852373090] ------------------------------------- >> J := ideal; ^ User error: bad syntax >> Index(OK, J); ^ User error: Identifier 'J' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 02:10:18 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK := MaximalOrder(K); J := ideal; J; //Index(OK, J); Output: Magma V2.10-6 Thu Mar 4 2004 02:10:15 on modular [Seed = 2660763864] ------------------------------------- >> J := ideal; ^ User error: bad syntax >> J; ^ User error: Identifier 'J' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 02:10:31 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK := MaximalOrder(K); ; //Index(OK, J); Output: Magma V2.10-6 Thu Mar 4 2004 02:10:28 on modular [Seed = 2307858428] ------------------------------------- Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 02:11:07 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK := MaximalOrder(K); ; //Index(OK, J); Output: Magma V2.10-6 Thu Mar 4 2004 02:11:04 on modular [Seed = 2964727337] ------------------------------------- Total time: 3.029 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 02:12:28 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK := MaximalOrder(K); ideal; //Index(OK, J); Output: Magma V2.10-6 Thu Mar 4 2004 02:12:25 on modular [Seed = 3755559191] ------------------------------------- Fractional Ideal of OK Two element generators: 209/1*OK.1 389/2*OK.1 + 1/2*OK.2 Total time: 3.039 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 02:12:52 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK := MaximalOrder(K); J:= ideal; Index(OK, J); Output: Magma V2.10-6 Thu Mar 4 2004 02:12:49 on modular [Seed = 3334492198] ------------------------------------- >> Index(OK, J); ^ Runtime error in 'Index': Bad argument types Argument types given: RngOrd, RngOrdFracIdl Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 02:13:46 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK := MaximalOrder(K); J:= ideal; Norm(J); Output: Magma V2.10-6 Thu Mar 4 2004 02:13:43 on modular [Seed = 4059522759] ------------------------------------- 1/4 Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 02:14:52 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK := MaximalOrder(K); J:= ideal; Index(OK,J); Output: Magma V2.10-6 Thu Mar 4 2004 02:14:49 on modular [Seed = 4210847106] ------------------------------------- >> Index(OK,J); ^ Runtime error in 'Index': Bad argument types Argument types given: RngOrd, RngOrdFracIdl Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 02:15:36 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK := MaximalOrder(K); J:= ideal; Norm(J); Output: Magma V2.10-6 Thu Mar 4 2004 02:15:33 on modular [Seed = 3924786797] ------------------------------------- 209 Total time: 2.979 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 02:16:09 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK := MaximalOrder(K); J:= ideal; Index(OK,J); Output: Magma V2.10-6 Thu Mar 4 2004 02:16:06 on modular [Seed = 286754485] ------------------------------------- 209 Total time: 3.009 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Mar 4 02:22:21 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK := MaximalOrder(K); J:= ideal; I:= ideal; ChineseRemainderTheorem(I,J,a,1-a); Output: Magma V2.10-6 Thu Mar 4 2004 02:22:18 on modular [Seed = 1499447393] ------------------------------------- >> ChineseRemainderTheorem(I,J,a,1-a); ^ Runtime error in 'ChineseRemainderTheorem': Bad argument types Argument types given: RngOrdFracIdl, RngOrdIdl, FldNumElt, FldNumElt Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Mar 4 02:37:14 2004 Input: P:=PolynomialRing(GF(3),2); f:=x^12+x^8-1; Factorization(f); Output: Magma V2.10-6 Thu Mar 4 2004 02:37:10 on modular [Seed = 2105270729] ------------------------------------- [ , , ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Mar 4 02:37:54 2004 Input: P:=PolynomialRing(GF(3),2); f:=x^12-x^8-1; Factorization(f); Output: Magma V2.10-6 Thu Mar 4 2004 02:37:51 on modular [Seed = 1785525943] ------------------------------------- [ , , ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Mar 4 02:38:24 2004 Input: P:=PolynomialRing(GF(3),2); f:=x^12-x^8+1; Factorization(f); Output: Magma V2.10-6 Thu Mar 4 2004 02:38:21 on modular [Seed = 2476019564] ------------------------------------- [ , ] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Mar 4 02:39:08 2004 Input: P:=PolynomialRing(GF(3),2); f:=x^24-x^8+1; Factorization(f); Output: Magma V2.10-6 Thu Mar 4 2004 02:39:05 on modular [Seed = 2577335442] ------------------------------------- [ , ] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Mar 4 02:39:38 2004 Input: P:=PolynomialRing(GF(3),2); f:=x^24-x^8-1; Factorization(f); Output: Magma V2.10-6 Thu Mar 4 2004 02:39:35 on modular [Seed = 2273385122] ------------------------------------- [ , , , , ] Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Mar 4 02:40:27 2004 Input: P:=PolynomialRing(GF(3),2); f:=x^24+x^8-1; Factorization(f); Output: Magma V2.10-6 Thu Mar 4 2004 02:40:24 on modular [Seed = 3081841357] ------------------------------------- [ , , ] Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Thu Mar 4 02:49:49 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); OK:=MaximalOrder(K); I:= Ideal < OK 5, 7 +a>; [K!OK.i : i in [1..5]]; t:=[p*OK: p in [1..100] | IsPrime(p)]; [Factorization( t[i] ) : i in [1..25] ]; Output: Magma V2.10-6 Thu Mar 4 2004 02:49:46 on modular [Seed = 4142950782] ------------------------------------- >> I:= Ideal < OK 5, 7 +a>; ^ User error: bad syntax [ 1, a, a^2, a^3, a^4 ] [ [ ], [ ], [ , , ], [ , ], [ , , , ], [ , ], [ , , ], [ , , ], [ , ], [ , , ], [ , , ], [ ], [ , ], [ , , , ], [ , ], [ , ], [ , ], [ ], [ , , , ], [ , , , ], [ ], [ , ], [ , , , ], [ , ], [ ] ] Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Thu Mar 4 02:50:02 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); OK:=MaximalOrder(K); I:= ideal < OK 5, 7 +a>; [K!OK.i : i in [1..5]]; t:=[p*OK: p in [1..100] | IsPrime(p)]; [Factorization( t[i] ) : i in [1..25] ]; Output: Magma V2.10-6 Thu Mar 4 2004 02:49:58 on modular [Seed = 4294533195] ------------------------------------- >> I:= ideal < OK 5, 7 +a>; ^ User error: bad syntax [ 1, a, a^2, a^3, a^4 ] [ [ ], [ ], [ , , ], [ , ], [ , , , ], [ , ], [ , , ], [ , , ], [ , ], [ , , ], [ , , ], [ ], [ , ], [ , , , ], [ , ], [ , ], [ , ], [ ], [ , , , ], [ , , , ], [ ], [ , ], [ , , , ], [ , ], [ ] ] Total time: 3.219 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Thu Mar 4 02:51:26 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); OK:=MaximalOrder(K); I:= ideal < OK 5, 7 +a>; [K!OK.i : i in [1..5]]; t:=[p*OK: p in [1..100] | IsPrime(p)]; [Factorization( t[i] ) : i in [1..25] ]; Output: Magma V2.10-6 Thu Mar 4 2004 02:51:23 on modular [Seed = 3974787845] ------------------------------------- >> I:= ideal < OK 5, 7 +a>; ^ User error: bad syntax [ 1, a, a^2, a^3, a^4 ] [ [ ], [ ], [ , , ], [ , ], [ , , , ], [ , ], [ , , ], [ , , ], [ , ], [ , , ], [ , , ], [ ], [ , ], [ , , , ], [ , ], [ , ], [ , ], [ ], [ , , , ], [ , , , ], [ ], [ , ], [ , , , ], [ , ], [ ] ] Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Thu Mar 4 02:51:30 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); OK:=MaximalOrder(K); I:= Ideal < OK 5, 7 +a>; [K!OK.i : i in [1..5]]; t:=[p*OK: p in [1..100] | IsPrime(p)]; [Factorization( t[i] ) : i in [1..25] ]; Output: Magma V2.10-6 Thu Mar 4 2004 02:51:26 on modular [Seed = 353602297] ------------------------------------- >> I:= Ideal < OK 5, 7 +a>; ^ User error: bad syntax [ 1, a, a^2, a^3, a^4 ] [ [ ], [ ], [ , , ], [ , ], [ , , , ], [ , ], [ , , ], [ , , ], [ , ], [ , , ], [ , , ], [ ], [ , ], [ , , , ], [ , ], [ , ], [ , ], [ ], [ , , , ], [ , , , ], [ ], [ , ], [ , , , ], [ , ], [ ] ] Total time: 3.309 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Thu Mar 4 02:51:32 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); OK:=MaximalOrder(K); [K!OK.i : i in [1..5]]; t:=[p*OK: p in [1..100] | IsPrime(p)]; [Factorization( t[i] ) : i in [1..25] ]; Output: Magma V2.10-6 Thu Mar 4 2004 02:51:28 on modular [Seed = 438090249] ------------------------------------- [ 1, a, a^2, a^3, a^4 ] [ [ ], [ ], [ , , ], [ , ], [ , , , ], [ , ], [ , , ], [ , , ], [ , ], [ , , ], [ , , ], [ ], [ , ], [ , , , ], [ , ], [ , ], [ , ], [ ], [ , , , ], [ , , , ], [ ], [ , ], [ , , , ], [ , ], [ ] ] Total time: 3.299 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Thu Mar 4 02:51:38 2004 Input: R := PolynomialRing(RationalField()); IsPrime(x^4-34*x^2+9); K := NumberField(x^4-34*x^2+9); E:=EquationOrder(K); OK:=MaximalOrder(K); I:=3*OK; J:=2*OK; Index(OK, E); Factorization(I); Factorization(J); [K!OK.i : i in [1, 2, 3, 4]]; Output: Magma V2.10-6 Thu Mar 4 2004 02:51:34 on modular [Seed = 84124944] ------------------------------------- true 24 [ , , , ] [ ] [ 1, a, 1/2*(a^2 + 1), 1/12*(a^3 + 3*a^2 + 11*a + 9) ] Total time: 3.079 seconds, Total memory usage: 2.05MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Thu Mar 4 02:51:58 2004 Input: R := PolynomialRing(RationalField()); IsIrreducible(x^4-34*x^2+9); K := NumberField(x^4-34*x^2+9); E:=EquationOrder(K); OK:=MaximalOrder(K); I:=3*OK; J:=2*OK; Index(OK, E); Factorization(I); Factorization(J); [K!OK.i : i in [1, 2, 3, 4]]; Output: Magma V2.10-6 Thu Mar 4 2004 02:51:55 on modular [Seed = 202025988] ------------------------------------- true 24 [ , , , ] [ ] [ 1, a, 1/2*(a^2 + 1), 1/12*(a^3 + 3*a^2 + 11*a + 9) ] Total time: 3.179 seconds, Total memory usage: 2.05MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Thu Mar 4 02:52:01 2004 Input: R := PolynomialRing(RationalField()); IsIrreducible(x^4-34*x^2+9); K := NumberField(x^4-34*x^2+9); OK:=MaximalOrder(K); I:=3*OK; Factorization(I); [K!OK.i : i in [1, 2, 3, 4]]; Output: Magma V2.10-6 Thu Mar 4 2004 02:51:58 on modular [Seed = 875729977] ------------------------------------- true [ , , , ] [ 1, a, 1/2*(a^2 + 1), 1/12*(a^3 + 3*a^2 + 11*a + 9) ] Total time: 3.149 seconds, Total memory usage: 2.05MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Thu Mar 4 02:52:20 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); OK:=MaximalOrder(K); I:= Ideal < OK 5, 7 +a>; [K!OK.i : i in [1..5]]; t:=[p*OK: p in [1..100] | IsPrime(p)]; [Factorization( t[i] ) : i in [1..25] ]; Output: Magma V2.10-6 Thu Mar 4 2004 02:52:17 on modular [Seed = 589660929] ------------------------------------- >> I:= Ideal < OK 5, 7 +a>; ^ User error: bad syntax [ 1, a, a^2, a^3, a^4 ] [ [ ], [ ], [ , , ], [ , ], [ , , , ], [ , ], [ , , ], [ , , ], [ , ], [ , , ], [ , , ], [ ], [ , ], [ , , , ], [ , ], [ , ], [ , ], [ ], [ , , , ], [ , , , ], [ ], [ , ], [ , , , ], [ , ], [ ] ] Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Thu Mar 4 02:52:43 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); OK:=MaximalOrder(K); I:= Ideal < OK | {5, 7 +a}>; [K!OK.i : i in [1..5]]; Output: Magma V2.10-6 Thu Mar 4 2004 02:52:40 on modular [Seed = 707562097] ------------------------------------- >> I:= Ideal < OK | {5, 7 +a}>; ^ User error: bad syntax [ 1, a, a^2, a^3, a^4 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Thu Mar 4 02:52:58 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); OK:=MaximalOrder(K); I:= ideal < OK | {5, 7 +a}>; [K!OK.i : i in [1..5]]; Output: Magma V2.10-6 Thu Mar 4 2004 02:52:55 on modular [Seed = 1364717845] ------------------------------------- [ 1, a, a^2, a^3, a^4 ] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Thu Mar 4 02:53:09 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); OK:=MaximalOrder(K); I:= ideal < OK | {5, 7 +a}>; I; [K!OK.i : i in [1..5]]; Output: Magma V2.10-6 Thu Mar 4 2004 02:53:06 on modular [Seed = 1482618921] ------------------------------------- Ideal of OK Two element generators: [5, 0, 0, 0, 0] [7, 1, 0, 0, 0] [ 1, a, a^2, a^3, a^4 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Thu Mar 4 02:54:13 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-5); OK:=MaximalOrder(K); J:= ideal < OK | {209, (389+a)/2}>; J; [K!OK.i : i in [1..5]]; Output: Magma V2.10-6 Thu Mar 4 2004 02:54:10 on modular [Seed = 1178658551] ------------------------------------- Ideal of OK Two element generators: [209, 0] [194, 1] >> [K!OK.i : i in [1..5]]; ^ Runtime error in '.': Value for name index (3) should be in the range [1..2] Total time: 3.089 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Thu Mar 4 02:54:50 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-5); OK:=MaximalOrder(K); J:= ideal < OK | {209, (389+a)/2}>; J; [K!OK.i : i in [1,2]]; 1+a in J; Output: Magma V2.10-6 Thu Mar 4 2004 02:54:47 on modular [Seed = 1279978648] ------------------------------------- Ideal of OK Two element generators: [209, 0] [194, 1] [ 1, 1/2*(a + 1) ] false Total time: 2.949 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Thu Mar 4 02:58:47 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-5); OK:=MaximalOrder(K); J:= ideal < OK | {209, (389+a)/2}>; 1+a in J; Output: Magma V2.10-6 Thu Mar 4 2004 02:58:44 on modular [Seed = 2138693336] ------------------------------------- false Total time: 2.969 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Mar 4 03:39:40 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=-2160+40*y^6-11*y^5-5*y^3-4*y; f3:=-139230+630*y^8-151*y^7-70*y^5-49*y^3-45*y; f4:=4032*L+4100*L^3+5187*L^5+7350*L^7+15619*L^9-9144576; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Mar 4 2004 03:39:37 on modular [Seed = 3655299715] ------------------------------------- >> f4:=4032*L+4100*L^3+5187*L^5+7350*L^7+15619*L^9-9144576; ^ User error: Identifier 'L' has not been declared or assigned >> I:=ideal; ^ User error: Identifier 'f4' has not been declared or assigned >> B:=GroebnerBasis(I:Al:="Direct"); ^ User error: Identifier 'I' has not been declared or assigned >> B; ^ User error: Identifier 'B' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Mar 4 03:41:22 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=-2160+40*y^6-11*y^5-5*y^3-4*y; f3:=-139230+630*y^8-151*y^7-70*y^5-49*y^3-45*y; f4:=4032*y+4100*y^3+5187*y^5+7350*y^7+15619*y^9-9144576; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Mar 4 2004 03:41:19 on modular [Seed = 3385811573] ------------------------------------- [ y^2 + y - 6, 3*y - 6 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Mar 4 03:42:03 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=-2160+40*y^6-11*y^5-5*y^3-4*y; f3:=-139230+630*y^8-151*y^7-70*y^5-49*y^3-45*y; f4:=2086434*y-484000*y^3+42135744*y^5-164236800*y^7+207996928*y^9-180000000*y^8+ 151200000*y^6-35532000*y^4+2324880*y^2-4682042757; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Mar 4 2004 03:42:00 on modular [Seed = 4042677051] ------------------------------------- [ y^2 + y + 45176306169, 3*y + 45176306169, 45176306175 ] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Mar 4 03:42:35 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=-2160+40*y^6-11*y^5-5*y^3-4*y; f3:=-139230+630*y^8-151*y^7-70*y^5-49*y^3-45*y; f4:=2086434*y-484000*y^3+42135744*y^5-164236800*y^7+207996928*y^9-180000000*y^8+ 151200000*y^6-35532000*y^4+2324880*y^2-4682042757; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(45176306175); Output: Magma V2.10-6 Thu Mar 4 2004 03:42:32 on modular [Seed = 4294530068] ------------------------------------- [ y^2 + y + 45176306169, 3*y + 45176306169, 45176306175 ] [ <3, 5>, <5, 2>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1>, <23, 1> ] Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Mar 4 03:42:59 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=-2160+40*y^6-11*y^5-5*y^3-4*y; f3:=-139230+630*y^8-151*y^7-70*y^5-49*y^3-45*y; f4:=2086434*y-484000*y^3+42135744*y^5-164236800*y^7+207996928*y^9-180000000*y^8+ 151200000*y^6-35532000*y^4+2324880*y^2-4682042757; I:=ideal; Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23))); Bn; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(45176306175); Output: Magma V2.10-6 Thu Mar 4 2004 03:42:56 on modular [Seed = 3873458917] ------------------------------------- [ y + 9 ] [ y + 11 ] [ y + 15 ] [ y + 17 ] [ y + 21 ] [ y^2 + y + 45176306169, 3*y + 45176306169, 45176306175 ] [ <3, 5>, <5, 2>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1>, <23, 1> ] Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Mar 4 03:43:31 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=-2160+40*y^6-11*y^5-5*y^3-4*y; f3:=-139230+630*y^8-151*y^7-70*y^5-49*y^3-45*y; f4:=2086434*y-484000*y^3+42135744*y^5-164236800*y^7+207996928*y^9-180000000*y^8+ 151200000*y^6-35532000*y^4+2324880*y^2-4682042757; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(45176306175); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23))); Bn; Output: Magma V2.10-6 Thu Mar 4 2004 03:43:28 on modular [Seed = 3991617998] ------------------------------------- [ y^2 + y + 45176306169, 3*y + 45176306169, 45176306175 ] [ <3, 5>, <5, 2>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1>, <23, 1> ] [ y + 9 ] [ y + 11 ] [ y + 15 ] [ y + 17 ] [ y + 21 ] Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Mar 4 03:43:57 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=-2160+40*y^6-11*y^5-5*y^3-4*y; f3:=-142573095+645120*y^8-2251776*y^7+1075200*y^5-182784*y^3-44280*y+1835008*y^6-1003520*y^4+116032*y^2; f4:=2086434*y-484000*y^3+42135744*y^5-164236800*y^7+207996928*y^9-180000000*y^8+ 151200000*y^6-35532000*y^4+2324880*y^2-4682042757; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Mar 4 2004 03:43:54 on modular [Seed = 320192333] ------------------------------------- [ y^2 + y + 130945809, 3*y + 130945809, 130945815 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Mar 4 03:45:04 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=-2160+40*y^6-11*y^5-5*y^3-4*y; f3:=-142573095+645120*y^8-2251776*y^7+1075200*y^5-182784*y^3-44280*y+1835008*y^6-1003520*y^4+116032*y^2; f4:=2086434*y-484000*y^3+42135744*y^5-164236800*y^7+207996928*y^9-180000000*y^8+ 151200000*y^6-35532000*y^4+2324880*y^2-4682042757; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(130945815); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19))); Bn; Output: Magma V2.10-6 Thu Mar 4 2004 03:45:01 on modular [Seed = 17280408] ------------------------------------- [ y^2 + y + 130945809, 3*y + 130945809, 130945815 ] [ <3, 4>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ y + 9 ] [ y + 11 ] [ y + 15 ] [ y + 17 ] Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Mar 4 03:45:41 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=-2160+40*y^6-11*y^5-5*y^3-4*y; f3:=-142573095+645120*y^8-2251776*y^7+1075200*y^5-182784*y^3-44280*y+1835008*y^6-1003520*y^4+116032*y^2; f4:=212226*y+1415776*y^3-9692480*y^5+20898304*y^7-6715392*y^9+13554432*y^8-27240192 *y^6+12223008*y^4-1394928*y^2-520204923; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Mar 4 2004 03:45:38 on modular [Seed = 168601260] ------------------------------------- [ y^2 + y + 14549529, 3*y + 14549529, 14549535 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Mar 4 03:46:10 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=-2160+40*y^6-11*y^5-5*y^3-4*y; f3:=-142573095+645120*y^8-2251776*y^7+1075200*y^5-182784*y^3-44280*y+1835008*y^6-1003520*y^4+116032*y^2; f4:=212226*y+1415776*y^3-9692480*y^5+20898304*y^7-6715392*y^9+13554432*y^8-27240192 *y^6+12223008*y^4-1394928*y^2-520204923; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(14549535); Output: Magma V2.10-6 Thu Mar 4 2004 03:46:07 on modular [Seed = 859152360] ------------------------------------- [ y^2 + y + 14549529, 3*y + 14549529, 14549535 ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Mar 4 03:46:25 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=-2160+40*y^6-11*y^5-5*y^3-4*y; f3:=-142573095+645120*y^8-2251776*y^7+1075200*y^5-182784*y^3-44280*y+1835008*y^6-1003520*y^4+116032*y^2; f4:=212226*y+1415776*y^3-9692480*y^5+20898304*y^7-6715392*y^9+13554432*y^8-27240192 *y^6+12223008*y^4-1394928*y^2-520204923; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(14549535); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19))); Bn; Output: Magma V2.10-6 Thu Mar 4 2004 03:46:22 on modular [Seed = 606243054] ------------------------------------- [ y^2 + y + 14549529, 3*y + 14549529, 14549535 ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ y + 9 ] [ y + 11 ] [ y + 15 ] [ y + 17 ] Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Mar 4 03:46:56 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=-69105+1280*y^6-2944*y^5+560*y^3-146*y+2160*y^4+600*y^2; f3:=-142573095+645120*y^8-2251776*y^7+1075200*y^5-182784*y^3-44280*y+1835008*y^6-1003520*y^4+116032*y^2; f4:=212226*y+1415776*y^3-9692480*y^5+20898304*y^7-6715392*y^9+13554432*y^8-27240192 *y^6+12223008*y^4-1394928*y^2-520204923; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Mar 4 2004 03:46:53 on modular [Seed = 757825988] ------------------------------------- [ y^2 + y + 24, 3*y + 9, 45 ] Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Mar 4 03:47:33 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=-69105+1280*y^6-2944*y^5+560*y^3-146*y+2160*y^4+600*y^2; f3:=-142560495+645120*y^8-12288*y^7-1102080*y^5+264768*y^3-55080*y-777728*y^6+ 1536640*y^4-406112*y^2; f4:=212226*y+1415776*y^3-9692480*y^5+20898304*y^7-6715392*y^9+13554432*y^8-27240192 *y^6+12223008*y^4-1394928*y^2-520204923; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Mar 4 2004 03:47:30 on modular [Seed = 1448147808] ------------------------------------- [ y^2 + y + 24, 3*y + 9, 45 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Mar 4 03:48:02 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=-69105+1280*y^6-2944*y^5+560*y^3-146*y+2160*y^4+600*y^2; f3:=-142560495+645120*y^8-12288*y^7-1102080*y^5+264768*y^3-55080*y-777728*y^6+ 1536640*y^4-406112*y^2; f4:=69594*y-343520*y^3+1414336*y^5-654080*y^7+840576*y^9-390528*y^8+2007936*y^6-2700432*y^4+697464*y^2-130076037; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Mar 4 2004 03:47:59 on modular [Seed = 1599730292] ------------------------------------- [ y^2 + y + 24, 3*y + 9, 45 ] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Mar 4 03:48:31 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=-69105+1280*y^6-2944*y^5+560*y^3-146*y+2160*y^4+600*y^2; f3:=-142560495+645120*y^8-12288*y^7-1102080*y^5+264768*y^3-55080*y-777728*y^6+ 1536640*y^4-406112*y^2; f4:=69594*y-343520*y^3+1414336*y^5-654080*y^7+840576*y^9-390528*y^8+2007936*y^6-2700432*y^4+697464*y^2-130076037; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Mar 4 2004 03:48:28 on modular [Seed = 1078390024] ------------------------------------- [ y^2 + y + 24, 3*y + 9, 45 ] Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Thu Mar 4 03:48:43 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=-6+2*y^2-y; f1:=-78+6*y^4-2*y^3-y; f2:=-69105+1280*y^6-2944*y^5+560*y^3-146*y+2160*y^4+600*y^2; f3:=-142560495+645120*y^8-12288*y^7-1102080*y^5+264768*y^3-55080*y-777728*y^6+ 1536640*y^4-406112*y^2; f4:=534186*y-70880*y^3-5750976*y^5+68471424*y^6+6113280*y^7-93514752*y^8+6484536*y^ 2-31359888*y^4+57565184*y^9-1170684333; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Mar 4 2004 03:48:40 on modular [Seed = 1229972533] ------------------------------------- [ y^2 + y + 24, 3*y + 9, 45 ] Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 04:23:40 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S' := S sdiff {x^2*y^11, x^8*y^7}; L := [x^2*y^11]; B, V := HomogeneousModuleTest(P, S', L); B; Output: Magma V2.10-6 Thu Mar 4 2004 04:23:35 on modular [Seed = 2391292687] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] >> S' := S sdiff {x^2*y^11, x^8*y^7}; ^ User error: Unexpected newline in literal identifier >> B, V := HomogeneousModuleTest(P, S', L); ^ User error: Unexpected newline in literal identifier >> B;; ^ User error: Identifier 'B' has not been declared or assigned Total time: 3.579 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 04:25:18 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S' := S sdiff {x^2*y^11, x^8*y^7}; L := [x^2*y^11]; HomogeneousModuleTest(P, S', L); Output: Magma V2.10-6 Thu Mar 4 2004 04:25:14 on modular [Seed = 2964718940] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] >> S' := S sdiff {x^2*y^11, x^8*y^7}; ^ User error: Unexpected newline in literal identifier >> HomogeneousModuleTest(P, S', L); ^ User error: Unexpected newline in literal identifier Total time: 3.729 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 04:26:05 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S sdiff {x^2*y^11, x^8*y^7}; L := [x^2*y^11]; HomogeneousModuleTest(P, S', L); Output: Magma V2.10-6 Thu Mar 4 2004 04:26:01 on modular [Seed = 3116306310] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] >> S sdiff {x^2*y^11, x^8*y^7}; ^ Runtime error in 'sdiff': Bad argument types Argument types given: SeqEnum[RngMPolElt], SetEnum[RngMPolElt] >> HomogeneousModuleTest(P, S', L); ^ User error: Unexpected newline in literal identifier Total time: 3.719 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 04:28:27 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; T:={x^2*y^11, x^8*y^7}; S sdiff T; L := [x^2*y^11]; HomogeneousModuleTest(P, S', L); Output: Magma V2.10-6 Thu Mar 4 2004 04:28:24 on modular [Seed = 2930251776] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] >> S sdiff T; ^ Runtime error in 'sdiff': Bad argument types Argument types given: SeqEnum[RngMPolElt], SetEnum[RngMPolElt] >> HomogeneousModuleTest(P, S', L); ^ User error: Unexpected newline in literal identifier Total time: 3.679 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 04:30:03 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; T := { x^2*y^11, x^8*y^7 }; S sdiff T; L := [x^2*y^11]; HomogeneousModuleTest(P, S', L); Output: Magma V2.10-6 Thu Mar 4 2004 04:29:59 on modular [Seed = 3570557909] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] >> S sdiff T; ^ Runtime error in 'sdiff': Bad argument types Argument types given: SeqEnum[RngMPolElt], SetEnum[RngMPolElt] >> HomogeneousModuleTest(P, S', L); ^ User error: Unexpected newline in literal identifier Total time: 3.899 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 04:30:55 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S sdiff { x^2*y^11, x^8*y^7 }; L := [x^2*y^11]; HomogeneousModuleTest(P, S', L); Output: Magma V2.10-6 Thu Mar 4 2004 04:30:51 on modular [Seed = 3301077913] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] >> S sdiff { x^2*y^11, x^8*y^7 }; ^ Runtime error in 'sdiff': Bad argument types Argument types given: SeqEnum[RngMPolElt], SetEnum[RngMPolElt] >> HomogeneousModuleTest(P, S', L); ^ User error: Unexpected newline in literal identifier Total time: 3.579 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 04:32:35 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S sdiff [ x^2*y^11, x^8*y^7 ]; L := [x^2*y^11]; HomogeneousModuleTest(P, S', L); Output: Magma V2.10-6 Thu Mar 4 2004 04:32:32 on modular [Seed = 3452664427] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] >> S sdiff [ x^2*y^11, x^8*y^7 ]; ^ Runtime error in 'sdiff': Bad argument types Argument types given: SeqEnum[RngMPolElt], SeqEnum[RngMPolElt] >> HomogeneousModuleTest(P, S', L); ^ User error: Unexpected newline in literal identifier Total time: 3.639 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 04:40:29 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; T := {R | x^2*y^11, x^8*y^7 }; S sdiff T; L := [x^2*y^11]; HomogeneousModuleTest(P, S', L); Output: Magma V2.10-6 Thu Mar 4 2004 04:40:24 on modular [Seed = 3890306681] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] >> S sdiff T; ^ Runtime error in 'sdiff': Bad argument types Argument types given: SeqEnum[RngMPolElt], SetEnum[RngMPolElt] >> HomogeneousModuleTest(P, S', L); ^ User error: Unexpected newline in literal identifier Total time: 4.869 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 04:41:05 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; T := {R | x^2*y^11, x^8*y^7 }; T; S sdiff T; L := [x^2*y^11]; HomogeneousModuleTest(P, S', L); Output: Magma V2.10-6 Thu Mar 4 2004 04:41:01 on modular [Seed = 3991622742] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] { x^8*y^7, x^2*y^11 } >> S sdiff T; ^ Runtime error in 'sdiff': Bad argument types Argument types given: SeqEnum[RngMPolElt], SetEnum[RngMPolElt] >> HomogeneousModuleTest(P, S', L); ^ User error: Unexpected newline in literal identifier Total time: 3.659 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 04:41:44 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S; T := {R | x^2*y^11, x^8*y^7 }; T; S sdiff T; L := [x^2*y^11]; HomogeneousModuleTest(P, S', L); Output: Magma V2.10-6 Thu Mar 4 2004 04:41:41 on modular [Seed = 320187089] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] [ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, y^11, y^12, y^13, y^14, y^15, y^16, y^17, y^18, y^19, y^20, y^21, y^22, y^23, y^24, y^25, y^26, y^27, y^28, y^29, y^30, y^31, y^32, y^33, y^34, y^35, y^36, y^37, y^38, y^39, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x*y^11, x*y^12, x*y^13, x*y^14, x*y^15, x*y^16, x*y^17, x*y^18, x*y^19, x*y^20, x*y^21, x*y^22, x*y^23, x*y^24, x*y^25, x*y^26, x*y^27, x*y^28, x*y^29, x*y^30, x*y^31, x*y^32, x*y^33, x*y^34, x*y^35, x*y^36, x*y^37, x*y^38, x*y^39, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^2*y^11, x^2*y^12, x^2*y^13, x^2*y^14, x^2*y^15, x^2*y^16, x^2*y^17, x^2*y^18, x^2*y^19, x^2*y^20, x^2*y^21, x^2*y^22, x^2*y^23, x^2*y^24, x^2*y^25, x^2*y^26, x^2*y^27, x^2*y^28, x^2*y^29, x^2*y^30, x^2*y^31, x^2*y^32, x^2*y^33, x^2*y^34, x^2*y^35, x^2*y^36, x^2*y^37, x^2*y^38, x^2*y^39, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^3*y^13, x^3*y^14, x^3*y^15, x^3*y^16, x^3*y^17, x^3*y^18, x^3*y^19, x^3*y^20, x^3*y^21, x^3*y^22, x^3*y^23, x^3*y^24, x^3*y^25, x^3*y^26, x^3*y^27, x^3*y^28, x^3*y^29, x^3*y^30, x^3*y^31, x^3*y^32, x^3*y^33, x^3*y^34, x^3*y^35, x^3*y^36, x^3*y^37, x^3*y^38, x^3*y^39, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^4*y^15, x^4*y^16, x^4*y^17, x^4*y^18, x^4*y^19, x^4*y^20, x^4*y^21, x^4*y^22, x^4*y^23, x^4*y^24, x^4*y^25, x^4*y^26, x^4*y^27, x^4*y^28, x^4*y^29, x^4*y^30, x^4*y^31, x^4*y^32, x^4*y^33, x^4*y^34, x^4*y^35, x^4*y^36, x^4*y^37, x^4*y^38, x^4*y^39, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^5*y^15, x^5*y^16, x^5*y^17, x^5*y^18, x^5*y^19, x^5*y^20, x^5*y^21, x^5*y^22, x^5*y^23, x^5*y^24, x^5*y^25, x^5*y^26, x^5*y^27, x^5*y^28, x^5*y^29, x^5*y^30, x^5*y^31, x^5*y^32, x^5*y^33, x^5*y^34, x^5*y^35, x^5*y^36, x^5*y^37, x^5*y^38, x^5*y^39, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^6*y^15, x^6*y^16, x^6*y^17, x^6*y^18, x^6*y^19, x^6*y^20, x^6*y^21, x^6*y^22, x^6*y^23, x^6*y^24, x^6*y^25, x^6*y^26, x^6*y^27, x^6*y^28, x^6*y^29, x^6*y^30, x^6*y^31, x^6*y^32, x^6*y^33, x^6*y^34, x^6*y^35, x^6*y^36, x^6*y^37, x^6*y^38, x^6*y^39, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^7*y^15, x^7*y^16, x^7*y^17, x^7*y^18, x^7*y^19, x^7*y^20, x^7*y^21, x^7*y^22, x^7*y^23, x^7*y^24, x^7*y^25, x^7*y^26, x^7*y^27, x^7*y^28, x^7*y^29, x^7*y^30, x^7*y^31, x^7*y^32, x^7*y^33, x^7*y^34, x^7*y^35, x^7*y^36, x^7*y^37, x^7*y^38, x^7*y^39, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^8*y^7, x^8*y^8, x^8*y^9, x^8*y^10, x^8*y^11, x^8*y^12, x^8*y^13, x^8*y^14, x^8*y^15, x^8*y^16, x^8*y^17, x^8*y^18, x^8*y^19, x^8*y^20, x^8*y^21, x^8*y^22, x^8*y^23, x^8*y^24, x^8*y^25, x^8*y^26, x^8*y^27, x^8*y^28, x^8*y^29, x^8*y^30, x^8*y^31, x^8*y^32, x^8*y^33, x^8*y^34, x^8*y^35, x^8*y^36, x^8*y^37, x^8*y^38, x^8*y^39, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^9*y^7, x^9*y^8, x^9*y^9, x^9*y^10, x^9*y^11, x^9*y^12, x^9*y^13, x^9*y^14, x^9*y^15, x^9*y^16, x^9*y^17, x^9*y^18, x^9*y^19, x^9*y^20, x^9*y^21, x^9*y^22, x^9*y^23, x^9*y^24, x^9*y^25, x^9*y^26, x^9*y^27, x^9*y^28, x^9*y^29, x^9*y^30, x^9*y^31, x^9*y^32, x^9*y^33, x^9*y^34, x^9*y^35, x^9*y^36, x^9*y^37, x^9*y^38, x^9*y^39, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^10*y^7, x^10*y^8, x^10*y^9, x^10*y^10, x^10*y^11, x^10*y^12, x^10*y^13, x^10*y^14, x^10*y^15, x^10*y^16, x^10*y^17, x^10*y^18, x^10*y^19, x^10*y^20, x^10*y^21, x^10*y^22, x^10*y^23, x^10*y^24, x^10*y^25, x^10*y^26, x^10*y^27, x^10*y^28, x^10*y^29, x^10*y^30, x^10*y^31, x^10*y^32, x^10*y^33, x^10*y^34, x^10*y^35, x^10*y^36, x^10*y^37, x^10*y^38, x^10*y^39, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^11*y^5, x^11*y^6, x^11*y^7, x^11*y^8, x^11*y^9, x^11*y^10, x^11*y^11, x^11*y^12, x^11*y^13, x^11*y^14, x^11*y^15, x^11*y^16, x^11*y^17, x^11*y^18, x^11*y^19, x^11*y^20, x^11*y^21, x^11*y^22, x^11*y^23, x^11*y^24, x^11*y^25, x^11*y^26, x^11*y^27, x^11*y^28, x^11*y^29, x^11*y^30, x^11*y^31, x^11*y^32, x^11*y^33, x^11*y^34, x^11*y^35, x^11*y^36, x^11*y^37, x^11*y^38, x^11*y^39, x^12, x^12*y, x^12*y^2, x^12*y^3, x^12*y^4, x^12*y^5, x^12*y^6, x^12*y^7, x^12*y^8, x^12*y^9, x^12*y^10, x^12*y^11, x^12*y^12, x^12*y^13, x^12*y^14, x^12*y^15, x^12*y^16, x^12*y^17, x^12*y^18, x^12*y^19, x^12*y^20, x^12*y^21, x^12*y^22, x^12*y^23, x^12*y^24, x^12*y^25, x^12*y^26, x^12*y^27, x^12*y^28, x^12*y^29, x^12*y^30, x^12*y^31, x^12*y^32, x^12*y^33, x^12*y^34, x^12*y^35, x^12*y^36, x^12*y^37, x^12*y^38, x^12*y^39, x^13, x^13*y, x^13*y^2, x^13*y^3, x^13*y^4, x^13*y^5, x^13*y^6, x^13*y^7, x^13*y^8, x^13*y^9, x^13*y^10, x^13*y^11, x^13*y^12, x^13*y^13, x^13*y^14, x^13*y^15, x^13*y^16, x^13*y^17, x^13*y^18, x^13*y^19, x^13*y^20, x^13*y^21, x^13*y^22, x^13*y^23, x^13*y^24, x^13*y^25, x^13*y^26, x^13*y^27, x^13*y^28, x^13*y^29, x^13*y^30, x^13*y^31, x^13*y^32, x^13*y^33, x^13*y^34, x^13*y^35, x^13*y^36, x^13*y^37, x^13*y^38, x^13*y^39, x^14, x^14*y, x^14*y^2, x^14*y^3, x^14*y^4, x^14*y^5, x^14*y^6, x^14*y^7, x^14*y^8, x^14*y^9, x^14*y^10, x^14*y^11, x^14*y^12, x^14*y^13, x^14*y^14, x^14*y^15, x^14*y^16, x^14*y^17, x^14*y^18, x^14*y^19, x^14*y^20, x^14*y^21, x^14*y^22, x^14*y^23, x^14*y^24, x^14*y^25, x^14*y^26, x^14*y^27, x^14*y^28, x^14*y^29, x^14*y^30, x^14*y^31, x^14*y^32, x^14*y^33, x^14*y^34, x^14*y^35, x^14*y^36, x^14*y^37, x^14*y^38, x^14*y^39, x^15, x^15*y, x^15*y^2, x^15*y^3, x^15*y^4, x^15*y^5, x^15*y^6, x^15*y^7, x^15*y^8, x^15*y^9, x^15*y^10, x^15*y^11, x^15*y^12, x^15*y^13, x^15*y^14, x^15*y^15, x^15*y^16, x^15*y^17, x^15*y^18, x^15*y^19, x^15*y^20, x^15*y^21, x^15*y^22, x^15*y^23, x^15*y^24, x^15*y^25, x^15*y^26, x^15*y^27, x^15*y^28, x^15*y^29, x^15*y^30, x^15*y^31, x^15*y^32, x^15*y^33, x^15*y^34, x^15*y^35, x^15*y^36, x^15*y^37, x^15*y^38, x^15*y^39, x^16, x^16*y, x^16*y^2, x^16*y^3, x^16*y^4, x^16*y^5, x^16*y^6, x^16*y^7, x^16*y^8, x^16*y^9, x^16*y^10, x^16*y^11, x^16*y^12, x^16*y^13, x^16*y^14, x^16*y^15, x^16*y^16, x^16*y^17, x^16*y^18, x^16*y^19, x^16*y^20, x^16*y^21, x^16*y^22, x^16*y^23, x^16*y^24, x^16*y^25, x^16*y^26, x^16*y^27, x^16*y^28, x^16*y^29, x^16*y^30, x^16*y^31, x^16*y^32, x^16*y^33, x^16*y^34, x^16*y^35, x^16*y^36, x^16*y^37, x^16*y^38, x^16*y^39, x^17, x^17*y, x^17*y^2, x^17*y^3, x^17*y^4, x^17*y^5, x^17*y^6, x^17*y^7, x^17*y^8, x^17*y^9, x^17*y^10, x^17*y^11, x^17*y^12, x^17*y^13, x^17*y^14, x^17*y^15, x^17*y^16, x^17*y^17, x^17*y^18, x^17*y^19, x^17*y^20, x^17*y^21, x^17*y^22, x^17*y^23, x^17*y^24, x^17*y^25, x^17*y^26, x^17*y^27, x^17*y^28, x^17*y^29, x^17*y^30, x^17*y^31 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 04:44:30 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; [IsHomogeneous(f): f in S]; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S; T := {R | x^2*y^11, x^8*y^7 }; T; S sdiff T; L := [x^2*y^11]; HomogeneousModuleTest(P, S', L); Output: Magma V2.10-6 Thu Mar 4 2004 04:44:27 on modular [Seed = 421503861] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 >> [IsHomogeneous(f): f in S]; ^ User error: Identifier 'S' has not been declared or assigned 0 [] [ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, y^11, y^12, y^13, y^14, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x*y^11, x*y^12, x*y^13, x*y^14, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^2*y^11, x^2*y^12, x^2*y^13, x^2*y^14, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^11*y^5, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ] { x^8*y^7, x^2*y^11 } >> S sdiff T; ^ Runtime error in 'sdiff': Bad argument types Argument types given: SeqEnum[RngMPolElt], SetEnum[RngMPolElt] >> HomogeneousModuleTest(P, S', L); ^ User error: Unexpected newline in literal identifier Total time: 2.909 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 04:44:47 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S; T := {R | x^2*y^11, x^8*y^7 }; T; S sdiff T; L := [x^2*y^11]; HomogeneousModuleTest(P, S', L); Output: Magma V2.10-6 Thu Mar 4 2004 04:44:44 on modular [Seed = 440987] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] [ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, y^11, y^12, y^13, y^14, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x*y^11, x*y^12, x*y^13, x*y^14, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^2*y^11, x^2*y^12, x^2*y^13, x^2*y^14, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^11*y^5, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ] { x^8*y^7, x^2*y^11 } >> S sdiff T; ^ Runtime error in 'sdiff': Bad argument types Argument types given: SeqEnum[RngMPolElt], SetEnum[RngMPolElt] >> HomogeneousModuleTest(P, S', L); ^ User error: Unexpected newline in literal identifier Total time: 2.989 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 04:47:13 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; Q := { ! x in S !}; T := {R | x^2*y^11, x^8*y^7 }; T; Q sdiff T; L := [x^2*y^11]; HomogeneousModuleTest(P, S', L); Output: Magma V2.10-6 Thu Mar 4 2004 04:47:10 on modular [Seed = 859146298] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] >> Q := { ! x in S !}; ^ User error: bad syntax { x^8*y^7, x^2*y^11 } >> Q sdiff T; ^ User error: Identifier 'Q' has not been declared or assigned >> HomogeneousModuleTest(P, S', L); ^ User error: Unexpected newline in literal identifier Total time: 2.919 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 04:48:03 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; Q := { ! x in S !} T := {R | x^2*y^11, x^8*y^7 }; T; Q sdiff T; L := [x^2*y^11]; HomogeneousModuleTest(P, S', L); Output: Magma V2.10-6 Thu Mar 4 2004 04:48:00 on modular [Seed = 977043837] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] >> Q := { ! x in S !} ^ User error: bad syntax { x^8*y^7, x^2*y^11 } >> Q sdiff T; ^ User error: Identifier 'Q' has not been declared or assigned >> HomogeneousModuleTest(P, S', L); ^ User error: Unexpected newline in literal identifier Total time: 2.979 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 04:48:34 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; Q := { ! x in S !} T := {R | x^2*y^11, x^8*y^7 }; T; S sdiff T; L := [x^2*y^11]; HomogeneousModuleTest(P, S', L); Output: Magma V2.10-6 Thu Mar 4 2004 04:48:31 on modular [Seed = 556243545] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] >> Q := { ! x in S !} ^ User error: bad syntax { x^8*y^7, x^2*y^11 } >> S sdiff T; ^ Runtime error in 'sdiff': Bad argument types Argument types given: SeqEnum[RngMPolElt], SetEnum[RngMPolElt] >> HomogeneousModuleTest(P, S', L); ^ User error: Unexpected newline in literal identifier Total time: 2.969 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 04:49:27 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; T := {R | x^2*y^11, x^8*y^7 }; T; S SeqEnum[RngMPolElt] T; L := [x^2*y^11]; HomogeneousModuleTest(P, S', L); Output: Magma V2.10-6 Thu Mar 4 2004 04:49:24 on modular [Seed = 1464986852] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] { x^8*y^7, x^2*y^11 } >> S SeqEnum[RngMPolElt] T; ^ User error: bad syntax >> HomogeneousModuleTest(P, S', L); ^ User error: Unexpected newline in literal identifier Total time: 2.909 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 04:50:34 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; T := {R | x^2*y^11, x^8*y^7 }; T; S diff T; L := [x^2*y^11]; HomogeneousModuleTest(P, S', L); Output: Magma V2.10-6 Thu Mar 4 2004 04:50:31 on modular [Seed = 1195506871] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] { x^8*y^7, x^2*y^11 } >> S diff T; ^ Runtime error in 'diff': Bad argument types Argument types given: SeqEnum[RngMPolElt], SetEnum[RngMPolElt] >> HomogeneousModuleTest(P, S', L); ^ User error: Unexpected newline in literal identifier Total time: 2.969 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 04:55:18 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; T := {R | x^2*y^11, x^8*y^7 }; T; S minus T; L := [x^2*y^11]; HomogeneousModuleTest(P, S', L); Output: Magma V2.10-6 Thu Mar 4 2004 04:55:15 on modular [Seed = 1229976669] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] { x^8*y^7, x^2*y^11 } >> S minus T; ^ User error: bad syntax >> HomogeneousModuleTest(P, S', L); ^ User error: Unexpected newline in literal identifier Total time: 2.899 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam240-254.fas.harvard.edu. (140.247.240.254) Time: Thu Mar 4 04:55:26 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-6); E := EquationOrder(K); OK := MaximalOrder(K); Index(OK,E); I := (6)*OK; Factorization(I); Output: Magma V2.10-6 Thu Mar 4 2004 04:55:23 on modular [Seed = 1886834028] ------------------------------------- 1 [ , ] Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 04:56:03 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; T := {R | x^2*y^11, x^8*y^7 }; T; S diff T; L := [x^2*y^11]; HomogeneousModuleTest(P, S', L); Output: Magma V2.10-6 Thu Mar 4 2004 04:56:00 on modular [Seed = 1734466112] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] { x^8*y^7, x^2*y^11 } >> S diff T; ^ Runtime error in 'diff': Bad argument types Argument types given: SeqEnum[RngMPolElt], SetEnum[RngMPolElt] >> HomogeneousModuleTest(P, S', L); ^ User error: Unexpected newline in literal identifier Total time: 2.909 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam240-254.fas.harvard.edu. (140.247.240.254) Time: Thu Mar 4 04:56:55 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-6); E := EquationOrder(K); OK := MaximalOrder(K); Index(OK,E); I := (2)*OK; Factorization(I); Output: Magma V2.10-6 Thu Mar 4 2004 04:56:52 on modular [Seed = 1852363549] ------------------------------------- 1 [ ] Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam240-254.fas.harvard.edu. (140.247.240.254) Time: Thu Mar 4 04:57:17 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-6); E := EquationOrder(K); OK := MaximalOrder(K); Index(OK,E); I := (3)*OK; Factorization(I); Output: Magma V2.10-6 Thu Mar 4 2004 04:57:14 on modular [Seed = 2509449464] ------------------------------------- 1 [ ] Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam240-254.fas.harvard.edu. (140.247.240.254) Time: Thu Mar 4 04:57:53 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-5); E := EquationOrder(K); OK := MaximalOrder(K); Index(OK,E); I := (6)*OK; Factorization(I); Output: Magma V2.10-6 Thu Mar 4 2004 04:57:50 on modular [Seed = 2627346709] ------------------------------------- 2 [ , ] Total time: 2.949 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 04:59:49 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, y^11, y^12, y^13, y^14, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x*y^11, x*y^12, x*y^13, x*y^14, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^2*y^12, x^2*y^13, x^2*y^14, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^8*y^7, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^11*y^5, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; T := {R | x^2*y^11, x^8*y^7 }; T; L := [x^2*y^11]; HomogeneousModuleTest(P, S, L); Output: Magma V2.10-6 Thu Mar 4 2004 04:59:46 on modular [Seed = 2189704327] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] { x^8*y^7, x^2*y^11 } [ false ] [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] ] Total time: 2.869 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host roam240-254.fas.harvard.edu. (140.247.240.254) Time: Thu Mar 4 05:00:44 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+5); E := EquationOrder(K); OK := MaximalOrder(K); Index(OK,E); I := (6)*OK; Factorization(I); Output: Magma V2.10-6 Thu Mar 4 2004 05:00:41 on modular [Seed = 2998144236] ------------------------------------- 1 [ , , ] Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 05:11:19 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, y^11, y^12, y^13, y^14, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x*y^11, x*y^12, x*y^13, x*y^14, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^2*y^12, x^2*y^13, x^2*y^14, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^8*y^7, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^11*y^5, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; T := {R | x^2*y^11, x^8*y^7 }; T; L := [x^2*y^11]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Thu Mar 4 2004 05:11:16 on modular [Seed = 3334571541] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] { x^8*y^7, x^2*y^11 } [ x^2*y^11 ] [ false ] Total time: 2.959 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 05:13:14 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, y^11, y^12, y^13, y^14, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x*y^11, x*y^12, x*y^13, x*y^14, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^2*y^12, x^2*y^13, x^2*y^14, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^8*y^7, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^11*y^5, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; T := {R | x^2*y^11, x^8*y^7 }; T; L := [x^2*y^10]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Thu Mar 4 2004 05:13:11 on modular [Seed = 3452603629] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] { x^8*y^7, x^2*y^11 } [ x^2*y^10 ] [ true ] Total time: 3.009 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 05:15:04 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, y^11, y^12, y^13, y^14, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x*y^11, x*y^12, x*y^13, x*y^14, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^2*y^12, x^2*y^13, x^2*y^14, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^8*y^7, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^11*y^5, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; T := {R | x^2*y^11, x^8*y^7 }; T; L := [y^15]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Thu Mar 4 2004 05:15:01 on modular [Seed = 4294491725] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] { x^8*y^7, x^2*y^11 } [ y^15 ] [ true ] Total time: 2.979 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 05:17:09 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, y^11, y^12, y^13, y^14, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x*y^11, x*y^12, x*y^13, x*y^14, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^2*y^12, x^2*y^13, x^2*y^14, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^8*y^7, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^11*y^5, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; T := {R | x^2*y^11, x^8*y^7 }; T; L := [x^2*y^11]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Thu Mar 4 2004 05:17:05 on modular [Seed = 4008291544] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] { x^8*y^7, x^2*y^11 } [ x^2*y^11 ] [ false ] Total time: 2.999 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 05:20:42 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, y^11, y^12, y^13, y^14, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x*y^11, x*y^12, x*y^13, x*y^14, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^2*y^12, x^2*y^13, x^2*y^14, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^2*y^11, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^8*y^7, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^11*y^5, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; T := {R | x^2*y^11, x^5*y^9 }; T; L := [x^5*y^9]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Thu Mar 4 2004 05:20:39 on modular [Seed = 303386877] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] { x^5*y^9, x^2*y^11 } [ x^5*y^9 ] [ false ] Total time: 2.949 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 05:22:28 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, y^11, y^12, y^13, y^14, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x*y^11, x*y^12, x*y^13, x*y^14, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^2*y^12, x^2*y^13, x^2*y^14, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^2*y^11, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^8*y^7, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^5*y^9, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; T := {R | x^11*y^5, x^5*y^9 }; T; L := [x^11*y^5]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Thu Mar 4 2004 05:22:25 on modular [Seed = 185354354] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] { x^5*y^9, x^11*y^5 } [ x^11*y^5 ] [ false ] Total time: 2.889 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 05:23:30 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, y^11, y^12, y^13, y^14, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x*y^11, x*y^12, x*y^13, x*y^14, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^2*y^12, x^2*y^13, x^2*y^14, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^2*y^11, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^11*y^5, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^5*y^9, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; T := {R | x^11*y^5, x^8*y^7 }; T; L := [x^8*y^7]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Thu Mar 4 2004 05:23:27 on modular [Seed = 100746625] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] { x^8*y^7, x^11*y^5 } [ x^8*y^7 ] [ true ] Total time: 2.939 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 05:56:25 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, y^11, y^12, y^13, y^14, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x*y^11, x*y^12, x*y^13, x*y^14, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^2*y^12, x^2*y^13, x^2*y^14, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^14*y^3, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^11*y^5, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^5*y^9, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; T := {R | x^2*y^11, x^11*y^3 }; T; L := [x^2*y^11]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Thu Mar 4 2004 05:56:22 on modular [Seed = 1263271940] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] { x^11*y^3, x^2*y^11 } [ x^2*y^11 ] [ true ] Total time: 2.939 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 05:59:07 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, x^12*y^3, y^12, y^13, y^14, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x*y^11, x*y^12, x*y^13, x*y^14, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^2*y^12, x^2*y^13, x^2*y^14, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^14*y^3, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^11*y^5, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^5*y^9, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; T := {R | y^11, x^12*y^3 }; T; L := [y^11]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Thu Mar 4 2004 05:59:04 on modular [Seed = 1145245604] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] { x^12*y^3, y^11 } [ y^11 ] [ true ] Total time: 2.969 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 06:01:09 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, x^12*y^3, x^12*y^4, y^13, y^14, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x*y^11, x*y^12, x*y^13, x*y^14, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^2*y^12, x^2*y^13, x^2*y^14, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^14*y^3, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^11*y^5, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^5*y^9, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; T := {R | y^11, x^12*y^3 }; T; L := [y^12]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Thu Mar 4 2004 06:01:06 on modular [Seed = 2610747377] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] { x^12*y^3, y^11 } [ y^12 ] [ true ] Total time: 2.999 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 06:02:21 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, x^12*y^3, x^12*y^4, x^12*y^5, y^14, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x*y^11, x*y^12, x*y^13, x*y^14, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^2*y^12, x^2*y^13, x^2*y^14, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^14*y^3, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^11*y^5, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^5*y^9, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; T := {R | y^11, x^12*y^3 }; T; L := [y^13]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Thu Mar 4 2004 06:02:06 on modular [Seed = 2492717090] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] { x^12*y^3, y^11 } [ y^13 ] [ true ] Total time: 3.099 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 06:03:08 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, x^12*y^3, x^12*y^4, x^12*y^5, x^12*y^6, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x*y^11, x*y^12, x*y^13, x*y^14, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^2*y^12, x^2*y^13, x^2*y^14, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^14*y^3, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^11*y^5, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^5*y^9, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; T := {R | y^11, x^12*y^3 }; T; L := [y^14]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Thu Mar 4 2004 06:03:04 on modular [Seed = 2391392894] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] { x^12*y^3, y^11 } [ y^14 ] [ true ] Total time: 3.299 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 06:06:19 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, x^12*y^3, x^12*y^4, x^12*y^5, x^12*y^6, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x^13*y^3, x*y^12, x*y^13, x*y^14, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^2*y^12, x^2*y^13, x^2*y^14, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^14*y^3, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^11*y^5, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^5*y^9, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; T := {R | y^11, x^12*y^3 }; T; L := [x^13*y^3]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Thu Mar 4 2004 06:06:16 on modular [Seed = 3216568847] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] { x^12*y^3, y^11 } [ x^13*y^3 ] [ true ] Total time: 3.119 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 06:08:09 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, x^12*y^3, x^12*y^4, x^12*y^5, x^12*y^6, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x^13*y^3, x^13*y^4, x*y^13, x*y^14, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^2*y^12, x^2*y^13, x^2*y^14, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^14*y^3, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^11*y^5, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^5*y^9, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; T := {R | y^11, x^12*y^3 }; T; L := [x*y^11]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Thu Mar 4 2004 06:08:06 on modular [Seed = 2830100134] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] { x^12*y^3, y^11 } [ x*y^11 ] [ true ] Total time: 2.919 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 06:08:27 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, x^12*y^3, x^12*y^4, x^12*y^5, x^12*y^6, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x^13*y^3, x^13*y^4, x*y^13, x*y^14, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^2*y^12, x^2*y^13, x^2*y^14, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^14*y^3, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^11*y^5, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^5*y^9, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; T := {R | y^11, x^12*y^3 }; T; L := [x*y^12]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Thu Mar 4 2004 06:08:24 on modular [Seed = 2728782994] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] { x^12*y^3, y^11 } [ x*y^12 ] [ true ] Total time: 3.469 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 06:09:27 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, x^12*y^3, x^12*y^4, x^12*y^5, x^12*y^6, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x^13*y^3, x^13*y^4, x^13*y^5, x*y^14, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^2*y^12, x^2*y^13, x^2*y^14, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^14*y^3, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^11*y^5, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^5*y^9, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; T := {R | y^11, x^12*y^3 }; T; L := [x*y^13]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Thu Mar 4 2004 06:09:24 on modular [Seed = 3520503725] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] { x^12*y^3, y^11 } [ x*y^13 ] [ true ] Total time: 2.919 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 06:10:17 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, x^12*y^3, x^12*y^4, x^12*y^5, x^12*y^6, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x^13*y^3, x^13*y^4, x^13*y^5, x^13*y^6, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^2*y^12, x^2*y^13, x^2*y^14, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^14*y^3, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^11*y^5, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^5*y^9, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; T := {R | y^11, x^12*y^3 }; T; L := [x*y^14]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Thu Mar 4 2004 06:10:14 on modular [Seed = 3251015503] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] { x^12*y^3, y^11 } [ x*y^14 ] [ true ] Total time: 2.939 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 06:13:13 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, x^12*y^3, x^12*y^4, x^12*y^5, x^12*y^6, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x^13*y^3, x^13*y^4, x^13*y^5, x^13*y^6, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^2*y^12, x^14*y^3 x^2*y^13, x^2*y^14, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^11*y^5, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^5*y^9, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; T := {R | y^11, x^12*y^3 }; T; L := [x^2*y^11]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Thu Mar 4 2004 06:13:10 on modular [Seed = 4210931108] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] >> x^2*y^13, ^ User error: bad syntax >> ]; ^ User error: bad syntax { x^12*y^3, y^11 } [ x^2*y^11 ] >> B, V := HomogeneousModuleTest(P, S, L); ^ User error: Identifier 'S' has not been declared or assigned >> B; ^ User error: Identifier 'B' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.92MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 06:14:03 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, x^12*y^3, x^12*y^4, x^12*y^5, x^12*y^6, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x^13*y^3, x^13*y^4, x^13*y^5, x^13*y^6, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^2*y^12, x^14*y^3, x^2*y^13, x^2*y^14, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^11*y^5, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^5*y^9, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; T := {R | y^11, x^12*y^3 }; T; L := [x^2*y^11]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Thu Mar 4 2004 06:14:00 on modular [Seed = 4092902547] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] { x^12*y^3, y^11 } [ x^2*y^11 ] [ true ] Total time: 2.969 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 06:16:04 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, x^12*y^3, x^12*y^4, x^12*y^5, x^12*y^6, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x^13*y^3, x^13*y^4, x^13*y^5, x^13*y^6, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^14*y^6, x^14*y^3, x^14*y^4, x^14*y^5, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^11*y^5, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^5*y^9, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; T := {R | y^11, x^12*y^3 }; T; L := [x^2*y^11, x^2*y^12, x^2*y^13, x^2*y^14]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Thu Mar 4 2004 06:16:01 on modular [Seed = 3823414282] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] { x^12*y^3, y^11 } [ x^2*y^11, x^2*y^12, x^2*y^13, x^2*y^14 ] >> B, V := HomogeneousModuleTest(P, S, L); ^ Runtime error in 'HomogeneousModuleTest': Elements of argument 3 are not all of the same degree >> B; ^ User error: Identifier 'B' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 06:16:43 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, x^12*y^3, x^12*y^4, x^12*y^5, x^12*y^6, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x^13*y^3, x^13*y^4, x^13*y^5, x^13*y^6, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^14*y^6, x^14*y^3, x^14*y^4, x^14*y^5, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^11*y^5, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^5*y^9, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; T := {R | y^11, x^12*y^3 }; T; L := [x^2*y^11]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Thu Mar 4 2004 06:16:40 on modular [Seed = 488262940] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] { x^12*y^3, y^11 } [ x^2*y^11 ] [ true ] Total time: 2.999 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 06:17:14 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, x^12*y^3, x^12*y^4, x^12*y^5, x^12*y^6, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x^13*y^3, x^13*y^4, x^13*y^5, x^13*y^6, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^14*y^6, x^14*y^3, x^14*y^4, x^14*y^5, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^11*y^5, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^5*y^9, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; T := {R | y^11, x^12*y^3 }; T; L := [ x^2*y^12]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Thu Mar 4 2004 06:17:11 on modular [Seed = 336806970] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] { x^12*y^3, y^11 } [ x^2*y^12 ] [ true ] Total time: 2.979 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 06:17:42 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, x^12*y^3, x^12*y^4, x^12*y^5, x^12*y^6, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x^13*y^3, x^13*y^4, x^13*y^5, x^13*y^6, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^14*y^6, x^14*y^3, x^14*y^4, x^14*y^5, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^11*y^5, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^5*y^9, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; T := {R | y^11, x^12*y^3 }; T; L := [ x^2*y^13]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Thu Mar 4 2004 06:17:39 on modular [Seed = 252206917] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] { x^12*y^3, y^11 } [ x^2*y^13 ] [ true ] Total time: 2.929 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 06:18:04 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, x^12*y^3, x^12*y^4, x^12*y^5, x^12*y^6, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x^13*y^3, x^13*y^4, x^13*y^5, x^13*y^6, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^14*y^6, x^14*y^3, x^14*y^4, x^14*y^5, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^11*y^5, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^5*y^9, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; T := {R | y^11, x^12*y^3 }; T; L := [ x^2*y^14]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Thu Mar 4 2004 06:18:01 on modular [Seed = 100750966] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] { x^12*y^3, y^11 } [ x^2*y^14 ] [ true ] Total time: 2.919 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 06:22:13 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, x^12*y^3, x^12*y^4, x^12*y^5, x^12*y^6, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x^13*y^3, x^13*y^4, x^13*y^5, x^13*y^6, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^14*y^6, x^14*y^3, x^14*y^4, x^14*y^5, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^9*y^7, x^9*y^8, x^9*y^9, x^9*y^10, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^11*y^5, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^5*y^9, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; T := {R | y^11, x^12*y^3 }; T; L := [ x^3*y^11]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Thu Mar 4 2004 06:22:10 on modular [Seed = 690911314] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] { x^12*y^3, y^11 } [ x^3*y^11 ] [ false ] Total time: 3.039 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 06:24:51 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, x^12*y^3, x^12*y^4, x^12*y^5, x^12*y^6, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x^13*y^3, x^13*y^4, x^13*y^5, x^13*y^6, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^14*y^6, x^14*y^3, x^14*y^4, x^14*y^5, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^9*y^7, x^3*y^12, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^11*y^5, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^5*y^9, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; T := {R | y^11, x^12*y^3 }; T; L := [ x^3*y^11]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Thu Mar 4 2004 06:24:48 on modular [Seed = 589590842] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] { x^12*y^3, y^11 } [ x^3*y^11 ] [ false ] Total time: 2.929 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 06:26:16 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, x^12*y^3, x^12*y^4, x^12*y^5, x^12*y^6, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x^13*y^3, x^13*y^4, x^13*y^5, x^13*y^6, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^14*y^6, x^14*y^3, x^14*y^4, x^14*y^5, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^9*y^8, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^11*y^5, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^5*y^9, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; T := {R | y^11, x^12*y^3 }; T; L := [ x^3*y^12]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Thu Mar 4 2004 06:26:13 on modular [Seed = 1582894098] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] { x^12*y^3, y^11 } [ x^3*y^12 ] [ false ] Total time: 2.989 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 06:29:19 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, x^12*y^3, x^12*y^4, x^12*y^5, x^12*y^6, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x^13*y^3, x^13*y^4, x^13*y^5, x^13*y^6, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^14*y^6, x^14*y^3, x^14*y^4, x^14*y^5, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^12, x^12*y^5, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^11*y^5, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^5*y^9, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; T := {R | y^11, x^12*y^3 }; T; L := [ x^3*y^11]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Thu Mar 4 2004 06:29:16 on modular [Seed = 1229855324] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] { x^12*y^3, y^11 } [ x^3*y^11 ] [ false ] Total time: 3.079 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 06:30:45 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, x^12*y^3, x^12*y^4, x^12*y^5, x^12*y^6, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x^13*y^3, x^13*y^4, x^13*y^5, x^13*y^6, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^14*y^6, x^14*y^3, x^14*y^4, x^14*y^5, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^12, x^6*y^9, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^11*y^5, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^5*y^9, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; T := {R | y^11, x^12*y^3 }; T; L := [ x^3*y^11]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Thu Mar 4 2004 06:30:42 on modular [Seed = 2021600003] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] { x^12*y^3, y^11 } [ x^3*y^11 ] [ false ] Total time: 2.939 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host cache3.nottingham.ac.uk. (128.243.220.41) Time: Thu Mar 4 07:36:15 2004 Input: Q:=Rationals(); QT:=FunctionField(Q); E:=EllipticCurve([QT|0,0,0,T^2,-1]); E; P2QT:=ProjectivePlane(QT); R:=CoordinateRing(P2QT); F:=R!DefiningPolynomial(E); F; Output: Magma V2.10-6 Thu Mar 4 2004 07:36:12 on modular [Seed = 3351291234] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + T^2*x - 1 over Univariate rational function field over Rational Field -X^3 - T^2*X*Z^2 + Y^2*Z + Z^3 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cache3.nottingham.ac.uk. (128.243.220.41) Time: Thu Mar 4 07:39:07 2004 Input: Q:=Rationals(); QT:=FunctionField(Q); E:=EllipticCurve([QT|0,0,0,T^2,-1]); E; P2QT:=ProjectivePlane(QT); R:=CoordinateRing(P2QT); F:=R!DefiningPolynomial(E); F; B:=PolynomialRing(Q); N:=NumberField([x^2+1]); IsCoercible(E,[0,i,1]); Output: Magma V2.10-6 Thu Mar 4 2004 07:39:04 on modular [Seed = 4277771663] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + T^2*x - 1 over Univariate rational function field over Rational Field -X^3 - T^2*X*Z^2 + Y^2*Z + Z^3 false Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cache3.nottingham.ac.uk. (128.243.220.41) Time: Thu Mar 4 07:39:39 2004 Input: Q:=Rationals(); QT:=FunctionField(Q); E:=EllipticCurve([QT|0,0,0,T^2,-1]); E; P2QT:=ProjectivePlane(QT); R:=CoordinateRing(P2QT); F:=R!DefiningPolynomial(E); F; B:=PolynomialRing(Q); N:=NumberField([x^2+1]); IsCoercible(E,[0,i,0]); Output: Magma V2.10-6 Thu Mar 4 2004 07:39:36 on modular [Seed = 3908012921] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + T^2*x - 1 over Univariate rational function field over Rational Field -X^3 - T^2*X*Z^2 + Y^2*Z + Z^3 false Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cache3.nottingham.ac.uk. (128.243.220.41) Time: Thu Mar 4 07:40:11 2004 Input: Q:=Rationals(); QT:=FunctionField(Q); E:=EllipticCurve([QT|0,0,0,T^2,-1]); E; P2QT:=ProjectivePlane(QT); R:=CoordinateRing(P2QT); F:=R!DefiningPolynomial(E); F; B:=PolynomialRing(Q); N:=NumberField([x^2+1]); IsCoercible(E,[0,1,0]); Output: Magma V2.10-6 Thu Mar 4 2004 07:40:08 on modular [Seed = 454850729] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + T^2*x - 1 over Univariate rational function field over Rational Field -X^3 - T^2*X*Z^2 + Y^2*Z + Z^3 true (0 : 1 : 0) Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee91.uab.es. (158.109.66.91) Time: Thu Mar 4 07:51:54 2004 Input: [x: x in {4..366 by 7}] Output: Magma V2.10-6 Thu Mar 4 2004 07:51:51 on modular [Seed = 218786672] ------------------------------------- [ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee91.uab.es. (158.109.66.91) Time: Thu Mar 4 07:55:35 2004 Input: M22:=MatrixRing(GF(4),2); Output: Magma V2.10-6 Thu Mar 4 2004 07:55:32 on modular [Seed = 1060657249] ------------------------------------- Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee91.uab.es. (158.109.66.91) Time: Thu Mar 4 07:57:33 2004 Input: M22:=MatrixRing(GF(4),2); Mt:= {m: m in M22|Trace(m) eq 0}; Output: Magma V2.10-6 Thu Mar 4 2004 07:57:30 on modular [Seed = 875778964] ------------------------------------- Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee91.uab.es. (158.109.66.91) Time: Thu Mar 4 07:57:45 2004 Input: M22:=MatrixRing(GF(4),2); Mt:= {m: m in M22|Trace(m) eq 0}; Output: Magma V2.10-6 Thu Mar 4 2004 07:57:42 on modular [Seed = 757746417] ------------------------------------- Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee91.uab.es. (158.109.66.91) Time: Thu Mar 4 07:58:03 2004 Input: M22:=MatrixRing(GF(4),2); Mt:= {m: m in M22|Trace(m) eq 0}; print (Mt); Output: Magma V2.10-6 Thu Mar 4 2004 07:58:00 on modular [Seed = 1516060056] ------------------------------------- { [ 0 0] [ 0 0], [ 0 0] [$.1^2 0], [ 0 0] [ $.1 0], [ 0 0] [ 1 0], [$.1^2 0] [ 0 $.1^2], [$.1^2 0] [$.1^2 $.1^2], [$.1^2 0] [ $.1 $.1^2], [$.1^2 0] [ 1 $.1^2], [ 1 0] [ 0 1], [ 1 0] [$.1^2 1], [ 1 0] [ $.1 1], [ 1 0] [ 1 1], [ $.1 0] [ 0 $.1], [ $.1 0] [$.1^2 $.1], [ $.1 0] [ $.1 $.1], [ $.1 0] [ 1 $.1], [ 0 $.1^2] [ 0 0], [ 0 $.1^2] [$.1^2 0], [ 0 $.1^2] [ $.1 0], [ 0 $.1^2] [ 1 0], [$.1^2 $.1^2] [ 0 $.1^2], [$.1^2 $.1^2] [$.1^2 $.1^2], [$.1^2 $.1^2] [ $.1 $.1^2], [$.1^2 $.1^2] [ 1 $.1^2], [ 1 $.1^2] [ 0 1], [ 1 $.1^2] [$.1^2 1], [ 1 $.1^2] [ $.1 1], [ 1 $.1^2] [ 1 1], [ $.1 $.1^2] [ 0 $.1], [ $.1 $.1^2] [$.1^2 $.1], [ $.1 $.1^2] [ $.1 $.1], [ $.1 $.1^2] [ 1 $.1], [ 0 $.1] [ 0 0], [ 0 $.1] [$.1^2 0], [ 0 $.1] [ $.1 0], [ 0 $.1] [ 1 0], [$.1^2 $.1] [ 0 $.1^2], [$.1^2 $.1] [$.1^2 $.1^2], [$.1^2 $.1] [ $.1 $.1^2], [$.1^2 $.1] [ 1 $.1^2], [ 1 $.1] [ 0 1], [ 1 $.1] [$.1^2 1], [ 1 $.1] [ $.1 1], [ 1 $.1] [ 1 1], [ $.1 $.1] [ 0 $.1], [ $.1 $.1] [$.1^2 $.1], [ $.1 $.1] [ $.1 $.1], [ $.1 $.1] [ 1 $.1], [ 0 1] [ 0 0], [ 0 1] [$.1^2 0], [ 0 1] [ $.1 0], [ 0 1] [ 1 0], [$.1^2 1] [ 0 $.1^2], [$.1^2 1] [$.1^2 $.1^2], [$.1^2 1] [ $.1 $.1^2], [$.1^2 1] [ 1 $.1^2], [ 1 1] [ 0 1], [ 1 1] [$.1^2 1], [ 1 1] [ $.1 1], [ 1 1] [ 1 1], [ $.1 1] [ 0 $.1], [ $.1 1] [$.1^2 $.1], [ $.1 1] [ $.1 $.1], [ $.1 1] [ 1 $.1] } Total time: 3.029 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee91.uab.es. (158.109.66.91) Time: Thu Mar 4 07:59:18 2004 Input: M22:=MatrixRing(GF(4),2); Mt:= {m: m in M22|Trace(m) eq 0}; Output: Magma V2.10-6 Thu Mar 4 2004 07:59:15 on modular [Seed = 1398029162] ------------------------------------- Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee91.uab.es. (158.109.66.91) Time: Thu Mar 4 07:59:29 2004 Input: M22:=MatrixRing(GF(4),2); print(Mt):= {m: m in M22|Trace(m) eq 0}; Output: Magma V2.10-6 Thu Mar 4 2004 07:59:26 on modular [Seed = 1279992952] ------------------------------------- >> print(Mt):= {m: m in M22|Trace(m) eq 0}; ^ User error: bad syntax Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee91.uab.es. (158.109.66.91) Time: Thu Mar 4 07:59:47 2004 Input: M22:=MatrixRing(GF(4),2); Mt:= {m: m in M22|Trace(m) eq 0}; print(Mt); Output: Magma V2.10-6 Thu Mar 4 2004 07:59:44 on modular [Seed = 1161964831] ------------------------------------- { [ 0 0] [ 0 0], [ 0 0] [$.1^2 0], [ 0 0] [ $.1 0], [ 0 0] [ 1 0], [$.1^2 0] [ 0 $.1^2], [$.1^2 0] [$.1^2 $.1^2], [$.1^2 0] [ $.1 $.1^2], [$.1^2 0] [ 1 $.1^2], [ 1 0] [ 0 1], [ 1 0] [$.1^2 1], [ 1 0] [ $.1 1], [ 1 0] [ 1 1], [ $.1 0] [ 0 $.1], [ $.1 0] [$.1^2 $.1], [ $.1 0] [ $.1 $.1], [ $.1 0] [ 1 $.1], [ 0 $.1^2] [ 0 0], [ 0 $.1^2] [$.1^2 0], [ 0 $.1^2] [ $.1 0], [ 0 $.1^2] [ 1 0], [$.1^2 $.1^2] [ 0 $.1^2], [$.1^2 $.1^2] [$.1^2 $.1^2], [$.1^2 $.1^2] [ $.1 $.1^2], [$.1^2 $.1^2] [ 1 $.1^2], [ 1 $.1^2] [ 0 1], [ 1 $.1^2] [$.1^2 1], [ 1 $.1^2] [ $.1 1], [ 1 $.1^2] [ 1 1], [ $.1 $.1^2] [ 0 $.1], [ $.1 $.1^2] [$.1^2 $.1], [ $.1 $.1^2] [ $.1 $.1], [ $.1 $.1^2] [ 1 $.1], [ 0 $.1] [ 0 0], [ 0 $.1] [$.1^2 0], [ 0 $.1] [ $.1 0], [ 0 $.1] [ 1 0], [$.1^2 $.1] [ 0 $.1^2], [$.1^2 $.1] [$.1^2 $.1^2], [$.1^2 $.1] [ $.1 $.1^2], [$.1^2 $.1] [ 1 $.1^2], [ 1 $.1] [ 0 1], [ 1 $.1] [$.1^2 1], [ 1 $.1] [ $.1 1], [ 1 $.1] [ 1 1], [ $.1 $.1] [ 0 $.1], [ $.1 $.1] [$.1^2 $.1], [ $.1 $.1] [ $.1 $.1], [ $.1 $.1] [ 1 $.1], [ 0 1] [ 0 0], [ 0 1] [$.1^2 0], [ 0 1] [ $.1 0], [ 0 1] [ 1 0], [$.1^2 1] [ 0 $.1^2], [$.1^2 1] [$.1^2 $.1^2], [$.1^2 1] [ $.1 $.1^2], [$.1^2 1] [ 1 $.1^2], [ 1 1] [ 0 1], [ 1 1] [$.1^2 1], [ 1 1] [ $.1 1], [ 1 1] [ 1 1], [ $.1 1] [ 0 $.1], [ $.1 1] [$.1^2 $.1], [ $.1 1] [ $.1 $.1], [ $.1 1] [ 1 $.1] } Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee91.uab.es. (158.109.66.91) Time: Thu Mar 4 08:01:16 2004 Input: M22:=MatrixRing(GF(4),2); Mf:= {m: m in M22|m[1] eq m[2]}; print(Mf); Output: Magma V2.10-6 Thu Mar 4 2004 08:01:13 on modular [Seed = 2577330458] ------------------------------------- { [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ $.1 0] [ $.1 0], [ 0 $.1^2] [ 0 $.1^2], [ $.1 $.1^2] [ $.1 $.1^2], [ 0 $.1] [ 0 $.1], [ $.1 $.1] [ $.1 $.1], [ 0 1] [ 0 1], [ $.1 1] [ $.1 1], [$.1^2 0] [$.1^2 0], [ 1 0] [ 1 0], [$.1^2 $.1^2] [$.1^2 $.1^2], [ 1 $.1^2] [ 1 $.1^2], [$.1^2 $.1] [$.1^2 $.1], [ 1 $.1] [ 1 $.1], [$.1^2 1] [$.1^2 1] } Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee91.uab.es. (158.109.66.91) Time: Thu Mar 4 08:04:15 2004 Input: M22:=MatrixRing(GF(4),2); Mt:= {m: m in M22|Trace(m) eq 0}; Mtf:= {m: m in Mt|m[1] eq m[2]}; print(Mf); Output: Magma V2.10-6 Thu Mar 4 2004 08:04:12 on modular [Seed = 2526150592] ------------------------------------- >> print(Mf); ^ User error: Identifier 'Mf' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee91.uab.es. (158.109.66.91) Time: Thu Mar 4 08:04:24 2004 Input: M22:=MatrixRing(GF(4),2); Mt:= {m: m in M22|Trace(m) eq 0}; Mtf:= {m: m in Mt|m[1] eq m[2]}; print(Mtf); Output: Magma V2.10-6 Thu Mar 4 2004 08:04:21 on modular [Seed = 2408113856] ------------------------------------- { [ 0 0] [ 0 0], [$.1^2 $.1^2] [$.1^2 $.1^2], [ $.1 $.1] [ $.1 $.1], [ 1 1] [ 1 1] } Total time: 2.889 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee91.uab.es. (158.109.66.91) Time: Thu Mar 4 08:06:46 2004 Input: M22:=MatrixRing(GF(4),2); M:=[i..100000] Output: Magma V2.10-6 Thu Mar 4 2004 08:06:43 on modular [Seed = 3116290112] ------------------------------------- >> M:=[i..100000]; ^ User error: Identifier 'i' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee91.uab.es. (158.109.66.91) Time: Thu Mar 4 08:07:00 2004 Input: M22:=MatrixRing(GF(4),2); M:=[1..100000]; Output: Magma V2.10-6 Thu Mar 4 2004 08:06:57 on modular [Seed = 3065110365] ------------------------------------- Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee91.uab.es. (158.109.66.91) Time: Thu Mar 4 08:08:15 2004 Input: M22:=MatrixRing(GF(4),2); M:=[1..100000]; Mt:={m:m in M|Trace(m) eq 0}; Output: Magma V2.10-6 Thu Mar 4 2004 08:08:12 on modular [Seed = 2947073417] ------------------------------------- Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee91.uab.es. (158.109.66.91) Time: Thu Mar 4 08:08:22 2004 Input: M22:=MatrixRing(GF(4),2); M:=[1..100000]; Mt:={m:m in M|Trace(m) eq 0}; Output: Magma V2.10-6 Thu Mar 4 2004 08:08:19 on modular [Seed = 2762198781] ------------------------------------- Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee91.uab.es. (158.109.66.91) Time: Thu Mar 4 08:08:37 2004 Input: M22:=MatrixRing(GF(4),2); M:=[1..100000]; Mt:={m:m in M|Trace(m) eq 0}; print(Mt); Output: Magma V2.10-6 Thu Mar 4 2004 08:08:34 on modular [Seed = 3722098581] ------------------------------------- {} Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee17.uab.es. (158.109.66.17) Time: Thu Mar 4 08:13:02 2004 Input: SetEchoInput(true); Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed. ************** MAGMA ***************** Host aula-a-siee17.uab.es. (158.109.66.17) Time: Thu Mar 4 08:14:34 2004 Input: SetEchoInput(true); SetLogFile "hola.txt" ; Output: WARNING: MAGMA command contains unsafe command 'file', so it will not be executed. ************** MAGMA ***************** Host aula-a-siee45.uab.es. (158.109.66.45) Time: Thu Mar 4 08:37:30 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; olavfunc3:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; n:= x^sn; t:= &+[x^e:e in lexp]; return {[a,b] : a,b in s | Evaluate(t,b) eq Evaluate(n,a)}; end function; j := olavfunc3(7,3); #j; 7^(5); jj := olavfunc3(5,2); #jj; 5^(3); Output: Magma V2.10-6 Thu Mar 4 2004 08:37:24 on modular [Seed = 1043943217] ------------------------------------- 16807 16807 125 125 Total time: 4.299 seconds, Total memory usage: 5.38MB ************** MAGMA ***************** Host aula-a-siee45.uab.es. (158.109.66.45) Time: Thu Mar 4 08:38:22 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; olavfunc3:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; n:= x^sn; t:= &+[x^e:e in lexp]; return {[a,b] : a,b in s | Evaluate(t,b) eq Evaluate(n,a)}; end function; j := olavfunc3(7,3); #j; 7^(5); j1 := olavfunc3(5,2); #j1; 5^(3); j2 := olavfunc3(11,4); #j2; 5^(3); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 4 2004 08:37:59 on modular [Seed = 892486681] ------------------------------------- 16807 16807 125 125 Errors: /home/mfd/gomagma: line 2: 23342 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host aula-a-siee45.uab.es. (158.109.66.45) Time: Thu Mar 4 08:38:47 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; olavfunc3:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; n:= x^sn; t:= &+[x^e:e in lexp]; return {[a,b] : a,b in s | Evaluate(t,b) eq Evaluate(n,a)}; end function; j := olavfunc3(7,3); #j; 7^(5); j1 := olavfunc3(5,2); #j1; 5^(3); j2 := olavfunc3(1,4); #j2; 1^(7); Output: Magma V2.10-6 Thu Mar 4 2004 08:38:42 on modular [Seed = 741039445] ------------------------------------- 16807 16807 125 125 [
:43]( q: 1, r: 4 ) >> s:=GF(q^r); ^ Runtime error in 'GF': Argument 1 (1) should be >= 2 >> #j2; ^ User error: Identifier 'j2' has not been declared or assigned 1 Total time: 4.299 seconds, Total memory usage: 5.38MB ************** MAGMA ***************** Host aula-a-siee17.uab.es. (158.109.66.17) Time: Thu Mar 4 08:38:48 2004 Input: SetEchoInput(true); SetLogFile "hola.txt" ; print "hola Albertito"; Output: WARNING: MAGMA command contains unsafe command 'file', so it will not be executed. ************** MAGMA ***************** Host aula-a-siee17.uab.es. (158.109.66.17) Time: Thu Mar 4 08:38:56 2004 Input: SetEchoInput(true); SetLogFile "hola.txt" ; print "hola Albertito"; Output: WARNING: MAGMA command contains unsafe command 'file', so it will not be executed. ************** MAGMA ***************** Host aula-a-siee17.uab.es. (158.109.66.17) Time: Thu Mar 4 08:38:58 2004 Input: SetEchoInput(true); SetLogFile "hola.txt" ; print "hola Albertito"; Output: WARNING: MAGMA command contains unsafe command 'file', so it will not be executed. ************** MAGMA ***************** Host aula-a-siee45.uab.es. (158.109.66.45) Time: Thu Mar 4 08:39:08 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; olavfunc3:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; n:= x^sn; t:= &+[x^e:e in lexp]; return {[a,b] : a,b in s | Evaluate(t,b) eq Evaluate(n,a)}; end function; j := olavfunc3(7,3); #j; 7^(5); j1 := olavfunc3(5,2); #j1; 5^(3); j2 := olavfunc3(3,4); #j2; 3^(7); Output: Magma V2.10-6 Thu Mar 4 2004 08:39:04 on modular [Seed = 1313423149] ------------------------------------- 16807 16807 125 125 2187 2187 Total time: 4.429 seconds, Total memory usage: 5.52MB ************** MAGMA ***************** Host aula-a-siee17.uab.es. (158.109.66.17) Time: Thu Mar 4 08:39:13 2004 Input: print "hola Albertito"; Output: Magma V2.10-6 Thu Mar 4 2004 08:39:10 on modular [Seed = 1161966624] ------------------------------------- hola Albertito Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee45.uab.es. (158.109.66.45) Time: Thu Mar 4 08:40:06 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; olavfunc3:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; n:= x^sn; t:= &+[x^e:e in lexp]; return {[a,b] : a,b in s | Evaluate(t,b) eq Evaluate(n,a)}; end function; j := olavfunc3(7,3); #j; 7^(5); j1 := olavfunc3(5,2); #j1; 5^(3); j2 := olavfunc3(3,4); #j2; 3^(7); j3 := olavfunc3(11,2); #j3; 11^(3); Output: Magma V2.10-6 Thu Mar 4 2004 08:40:01 on modular [Seed = 1953695198] ------------------------------------- 16807 16807 125 125 2187 2187 1331 1331 Total time: 4.459 seconds, Total memory usage: 5.82MB ************** MAGMA ***************** Host aula-a-siee45.uab.es. (158.109.66.45) Time: Thu Mar 4 08:41:42 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; olavfunc3:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; n:= x^sn; t:= &+[x^e:e in lexp]; return {[a,b] : a,b in s | Evaluate(t,b) eq Evaluate(n,a)}; end function; j := olavfunc3(11,3); #j; 11^(5); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 4 2004 08:41:19 on modular [Seed = 1667502727] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 23416 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host aula-a-siee17.uab.es. (158.109.66.17) Time: Thu Mar 4 08:42:16 2004 Input: Floor(3.1517); Output: Magma V2.10-6 Thu Mar 4 2004 08:42:13 on modular [Seed = 2594039988] ------------------------------------- 3 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee45.uab.es. (158.109.66.45) Time: Thu Mar 4 08:42:35 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; olavfunc3:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; n:= x^sn; t:= &+[x^e:e in lexp]; return {[a,b] : a,b in s | Evaluate(t,b) eq Evaluate(n,a)}; end function; j := olavfunc3(5,3); #j; 5^(5); Output: Magma V2.10-6 Thu Mar 4 2004 08:42:32 on modular [Seed = 2442585026] ------------------------------------- 3125 3125 Total time: 3.109 seconds, Total memory usage: 2.34MB ************** MAGMA ***************** Host aula-a-siee45.uab.es. (158.109.66.45) Time: Thu Mar 4 08:57:54 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; olavfunc3:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; n:= x^sn; t:= &+[x^e:e in lexp]; return {[a,b] : a,b in s | Evaluate(t,b) eq Evaluate(n,a)}; end function; eolavfunc4:= function(q,olav) s:=GF(q); return {[a,b] : a,b in s }; end function; eolavfunc4(7,olavfunc3(7,3)); Output: Magma V2.10-6 Thu Mar 4 2004 08:57:50 on modular [Seed = 2964833653] ------------------------------------- { [ 0, 0 ], [ 0, 1 ], [ 0, 2 ], [ 0, 3 ], [ 0, 4 ], [ 0, 5 ], [ 0, 6 ], [ 1, 0 ], [ 1, 1 ], [ 1, 2 ], [ 1, 3 ], [ 1, 4 ], [ 1, 5 ], [ 1, 6 ], [ 2, 0 ], [ 2, 1 ], [ 2, 2 ], [ 2, 3 ], [ 2, 4 ], [ 2, 5 ], [ 2, 6 ], [ 3, 0 ], [ 3, 1 ], [ 3, 2 ], [ 3, 3 ], [ 3, 4 ], [ 3, 5 ], [ 3, 6 ], [ 4, 0 ], [ 4, 1 ], [ 4, 2 ], [ 4, 3 ], [ 4, 4 ], [ 4, 5 ], [ 4, 6 ], [ 5, 0 ], [ 5, 1 ], [ 5, 2 ], [ 5, 3 ], [ 5, 4 ], [ 5, 5 ], [ 5, 6 ], [ 6, 0 ], [ 6, 1 ], [ 6, 2 ], [ 6, 3 ], [ 6, 4 ], [ 6, 5 ], [ 6, 6 ] } Total time: 4.319 seconds, Total memory usage: 5.38MB ************** MAGMA ***************** Host aula-a-siee45.uab.es. (158.109.66.45) Time: Thu Mar 4 08:58:50 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; olavfunc3:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; n:= x^sn; t:= &+[x^e:e in lexp]; return {[a,b] : a,b in s | Evaluate(t,b) eq Evaluate(n,a)}; end function; eolavfunc4:= function(q,olav) s:=GF(q); return {[a,b] : (a,b in s)and([a,b] in olav) }; end function; eolavfunc4(7,olavfunc3(7,3)); Output: Magma V2.10-6 Thu Mar 4 2004 08:58:47 on modular [Seed = 2947078563] ------------------------------------- >> return {[a,b] : (a,b in s)and([a,b] in olav) }; ^ User error: bad syntax >> end function; ^ User error: bad syntax >> eolavfunc4(7,olavfunc3(7,3)); ^ User error: Identifier 'eolavfunc4' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee45.uab.es. (158.109.66.45) Time: Thu Mar 4 08:59:36 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; olavfunc3:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; n:= x^sn; t:= &+[x^e:e in lexp]; return {[a,b] : a,b in s | Evaluate(t,b) eq Evaluate(n,a)}; end function; eolavfunc4:= function(q,olav) s:=GF(q); return {[a,b] : (a,b in s)and( in olav) }; end function; eolavfunc4(7,olavfunc3(7,3)); Output: Magma V2.10-6 Thu Mar 4 2004 08:59:33 on modular [Seed = 2778911739] ------------------------------------- >> return {[a,b] : (a,b in s)and( in olav) }; ^ User error: bad syntax >> end function; ^ User error: bad syntax >> eolavfunc4(7,olavfunc3(7,3)); ^ User error: Identifier 'eolavfunc4' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee45.uab.es. (158.109.66.45) Time: Thu Mar 4 09:01:43 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; olavfunc3:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; n:= x^sn; t:= &+[x^e:e in lexp]; return {[a,b] : a,b in s | Evaluate(t,b) eq Evaluate(n,a)}; end function; eolavfunc4:= function(q,olav) s:=GF(q); return {[a,b] : (a,b in s) and (<[a,b]> in olav) }; end function; eolavfunc4(7,olavfunc3(7,3)); Output: Magma V2.10-6 Thu Mar 4 2004 09:01:40 on modular [Seed = 4177497639] ------------------------------------- >> return {[a,b] : (a,b in s) and (<[a,b]> in olav) }; ^ User error: bad syntax >> end function; ^ User error: bad syntax >> eolavfunc4(7,olavfunc3(7,3)); ^ User error: Identifier 'eolavfunc4' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee45.uab.es. (158.109.66.45) Time: Thu Mar 4 09:02:42 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; olavfunc3:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; n:= x^sn; t:= &+[x^e:e in lexp]; return {[a,b] : a,b in s | Evaluate(t,b) eq Evaluate(n,a)}; end function; eolavfunc4:= function(q,olav) s:=GF(q); return {[a,b] : (<[a,b]> in olav) }; end function; eolavfunc4(7,olavfunc3(7,3)); Output: Magma V2.10-6 Thu Mar 4 2004 09:02:39 on modular [Seed = 4143022098] ------------------------------------- >> return {[a,b] : (<[a,b]> in olav) }; ^ User error: bad syntax >> end function; ^ User error: bad syntax >> eolavfunc4(7,olavfunc3(7,3)); ^ User error: Identifier 'eolavfunc4' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee45.uab.es. (158.109.66.45) Time: Thu Mar 4 09:02:58 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; olavfunc3:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; n:= x^sn; t:= &+[x^e:e in lexp]; return {[a,b] : a,b in s | Evaluate(t,b) eq Evaluate(n,a)}; end function; eolavfunc4:= function(q,olav) s:=GF(q); return {[a,b] : <[a,b]> in olav }; end function; eolavfunc4(7,olavfunc3(7,3)); Output: Magma V2.10-6 Thu Mar 4 2004 09:02:55 on modular [Seed = 3991575289] ------------------------------------- >> return {[a,b] : <[a,b]> in olav }; ^ User error: bad syntax >> end function; ^ User error: bad syntax >> eolavfunc4(7,olavfunc3(7,3)); ^ User error: Identifier 'eolavfunc4' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee45.uab.es. (158.109.66.45) Time: Thu Mar 4 09:03:11 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; olavfunc3:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; n:= x^sn; t:= &+[x^e:e in lexp]; return {[a,b] : a,b in s | Evaluate(t,b) eq Evaluate(n,a)}; end function; eolavfunc4:= function(q,olav) s:=GF(q); return {[a,b] : [a,b] in olav }; end function; eolavfunc4(7,olavfunc3(7,3)); Output: Magma V2.10-6 Thu Mar 4 2004 09:03:08 on modular [Seed = 504981790] ------------------------------------- >> return {[a,b] : [a,b] in olav }; ^ User error: bad syntax >> end function; ^ User error: bad syntax >> eolavfunc4(7,olavfunc3(7,3)); ^ User error: Identifier 'eolavfunc4' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee45.uab.es. (158.109.66.45) Time: Thu Mar 4 09:03:51 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; olavfunc3:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; n:= x^sn; t:= &+[x^e:e in lexp]; return {[a,b] : a,b in s | Evaluate(t,b) eq Evaluate(n,a)}; end function; eolavfunc4:= function(q,olav) s:=GF(q); return {[a,b] : a,b in s | [a,b] in olav}; end function; eolavfunc4(7,olavfunc3(7,3)); Output: Magma V2.10-6 Thu Mar 4 2004 09:03:47 on modular [Seed = 386949192] ------------------------------------- { [ 0, 0 ], [ 1, 5 ], [ 3, 2 ], [ 4, 5 ], [ 6, 2 ], [ 5, 2 ], [ 2, 5 ] } Total time: 4.389 seconds, Total memory usage: 5.38MB ************** MAGMA ***************** Host aula-a-siee45.uab.es. (158.109.66.45) Time: Thu Mar 4 09:05:43 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; olavfunc3:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; n:= x^sn; t:= &+[x^e:e in lexp]; return {[a,b] : a,b in s | Evaluate(t,b) eq Evaluate(n,a)}; end function; eolavfunc4:= function(q,olav) s:=GF(q); return {[a,b] : a,b in s | [a,b] in olav}; end function; eolavfunc4(7,olavfunc3(7,3)); s:=GF(7); s; Output: Magma V2.10-6 Thu Mar 4 2004 09:05:39 on modular [Seed = 1549478899] ------------------------------------- { [ 0, 0 ], [ 1, 5 ], [ 3, 2 ], [ 4, 5 ], [ 6, 2 ], [ 5, 2 ], [ 2, 5 ] } Finite field of size 7 Total time: 4.520 seconds, Total memory usage: 5.38MB ************** MAGMA ***************** Host aula-a-siee45.uab.es. (158.109.66.45) Time: Thu Mar 4 09:06:37 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; olavfunc3:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; n:= x^sn; t:= &+[x^e:e in lexp]; return {[a,b] : a,b in s | Evaluate(t,b) eq Evaluate(n,a)}; end function; eolavfunc4:= function(q,olav) s:=GF(q); return {[a,b] : a,b in s | [a,b] in olav}; end function; s:=GF(7); s; Output: Magma V2.10-6 Thu Mar 4 2004 09:06:34 on modular [Seed = 1448157600] ------------------------------------- Finite field of size 7 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee45.uab.es. (158.109.66.45) Time: Thu Mar 4 09:07:28 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; olavfunc3:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; n:= x^sn; t:= &+[x^e:e in lexp]; return {[a,b] : a,b in s | Evaluate(t,b) eq Evaluate(n,a)}; end function; eolavfunc4:= function(q,olav) s:=GF(q); return {[a,b] : a,b in s | [a,b] in olav}; end function; t:=eolavfunc4(7,olavfunc3(7,3)); #t; Output: Magma V2.10-6 Thu Mar 4 2004 09:07:23 on modular [Seed = 1330132808] ------------------------------------- 7 Total time: 4.409 seconds, Total memory usage: 5.38MB ************** MAGMA ***************** Host aula-a-siee45.uab.es. (158.109.66.45) Time: Thu Mar 4 09:08:17 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; olavfunc3:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; n:= x^sn; t:= &+[x^e:e in lexp]; return {[a,b] : a,b in s | Evaluate(t,b) eq Evaluate(n,a)}; end function; eolavfunc4:= function(q,olav) s:=GF(q); return {[a,b] : a,b in s | [a,b] in olav}; end function; t:=eolavfunc4(7,olavfunc3(7,3)); #t; t1:=eolavfunc4(5,olavfunc3(5,6)); #t1; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 4 2004 09:07:54 on modular [Seed = 1095121255] ------------------------------------- 7 Errors: /home/mfd/gomagma: line 2: 23645 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host aula-a-siee45.uab.es. (158.109.66.45) Time: Thu Mar 4 09:08:37 2004 Input: s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; olavfunc3:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; n:= x^sn; t:= &+[x^e:e in lexp]; return {[a,b] : a,b in s | Evaluate(t,b) eq Evaluate(n,a)}; end function; eolavfunc4:= function(q,olav) s:=GF(q); return {[a,b] : a,b in s | [a,b] in olav}; end function; t:=eolavfunc4(7,olavfunc3(7,3)); #t; t1:=eolavfunc4(5,olavfunc3(5,3)); #t1; Output: Magma V2.10-6 Thu Mar 4 2004 09:08:32 on modular [Seed = 2055012870] ------------------------------------- 7 5 Total time: 4.479 seconds, Total memory usage: 5.38MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Thu Mar 4 09:12:08 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^2 -5); O := MaximalOrder(N); Basis(O); I := ideal; Basis(I); J := ideal; Basis(J); b := ChineseRemainderTheorem(I, J, O!w, O!(1 - w)); b; b - w in I; b - (1 - w) in J; Index(O, I); Index(O, J); Output: Magma V2.10-6 Thu Mar 4 2004 09:12:05 on modular [Seed = 1734352462] ------------------------------------- [ O.1, O.2 ] [ [1, 0], [0, 1] ] [ [209, 0], [194, 1] ] [-28, 0] true true 1 209 Total time: 2.979 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host aula-a-siee45.uab.es. (158.109.66.45) Time: Thu Mar 4 09:13:28 2004 Input: [i : i in [4..366]]; Output: Magma V2.10-6 Thu Mar 4 2004 09:13:25 on modular [Seed = 2577326080] ------------------------------------- [ 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366 ] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee45.uab.es. (158.109.66.45) Time: Thu Mar 4 09:13:39 2004 Input: [i : i in [4..366 by 7]]; Output: Magma V2.10-6 Thu Mar 4 2004 09:13:35 on modular [Seed = 2459298561] ------------------------------------- [ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee45.uab.es. (158.109.66.45) Time: Thu Mar 4 09:29:03 2004 Input: /* Respostes a l'exercici 1 */ [i : i in [4..366 by 7]]; /*Respostes a l'exercici 2*/ /*Apartat 1*/ k:=GF(4); p:=MatrixRing(k,2); {n : n in p | Trace(n) eq 0}; /*Apartat 2*/ mf:={n : n in p | Submatrix(n,1,1,1,2) eq Submatrix(n,2,1,1,2)}; /*Apartat 3*/ mtf:={ n : n in p | (n in mf) and (n in mt)}; /*Apartat 4*/ mmt:=[Random(p) : n in [1..100000]]; /*Nombre de les matrius que pertanyen a mf*/ #[n : n in mmt | n in mf]; 6107 /*Nombre de les matrius que pertanyen a mt*/ #[n : n in mmt | n in mt]; 24878 /*Nombre de les matrius que pertanyen a mtf*/ #[n : n in mmt | n in mtf]; 1565 /*Respostes a l'exercici 3*/ /*Apartat 1*/ s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; /*Apartat 2*/ t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; /*Apartat 3*/ {[a,b] : a,b in s | Evaluate(t,b) eq Evaluate(n,a)}; /*Apartat 4*/ func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; /*Apartat 5*/ tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; /*Apartat 6*/ olavfunc3:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; n:= x^sn; t:= &+[x^e:e in lexp]; return {[a,b] : a,b in s | Evaluate(t,b) eq Evaluate(n,a)}; end function; /*Apartat 7*/ j := olavfunc3(7,3); #j; 7^(5); j1 := olavfunc3(5,2); #j1; 5^(3); j2 := olavfunc3(3,4); #j2; 3^(7); j3 := olavfunc3(11,2); #j3; 11^(3); j4 := olavfunc3(11,3); #j4; 11^(5); /*Apartat 8*/ eolavfunc4:= function(q,olav) s:=GF(q); return {[a,b] : a,b in s | [a,b] in olav}; end function; t:=eolavfunc4(7,olavfunc3(7,3)); #t; t1:=eolavfunc4(5,olavfunc3(5,3)); #t1; t2:=eolavfunc4(11,olavfunc3(11,3)); #t2; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 4 2004 09:28:40 on modular [Seed = 3419190991] ------------------------------------- [ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] { [ 0 0] [ 0 0], [ 0 0] [k.1^2 0], [ 0 0] [ k.1 0], [ 0 0] [ 1 0], [k.1^2 0] [ 0 k.1^2], [k.1^2 0] [k.1^2 k.1^2], [k.1^2 0] [ k.1 k.1^2], [k.1^2 0] [ 1 k.1^2], [ 1 0] [ 0 1], [ 1 0] [k.1^2 1], [ 1 0] [ k.1 1], [ 1 0] [ 1 1], [ k.1 0] [ 0 k.1], [ k.1 0] [k.1^2 k.1], [ k.1 0] [ k.1 k.1], [ k.1 0] [ 1 k.1], [ 0 k.1^2] [ 0 0], [ 0 k.1^2] [k.1^2 0], [ 0 k.1^2] [ k.1 0], [ 0 k.1^2] [ 1 0], [k.1^2 k.1^2] [ 0 k.1^2], [k.1^2 k.1^2] [k.1^2 k.1^2], [k.1^2 k.1^2] [ k.1 k.1^2], [k.1^2 k.1^2] [ 1 k.1^2], [ 1 k.1^2] [ 0 1], [ 1 k.1^2] [k.1^2 1], [ 1 k.1^2] [ k.1 1], [ 1 k.1^2] [ 1 1], [ k.1 k.1^2] [ 0 k.1], [ k.1 k.1^2] [k.1^2 k.1], [ k.1 k.1^2] [ k.1 k.1], [ k.1 k.1^2] [ 1 k.1], [ 0 k.1] [ 0 0], [ 0 k.1] [k.1^2 0], [ 0 k.1] [ k.1 0], [ 0 k.1] [ 1 0], [k.1^2 k.1] [ 0 k.1^2], [k.1^2 k.1] [k.1^2 k.1^2], [k.1^2 k.1] [ k.1 k.1^2], [k.1^2 k.1] [ 1 k.1^2], [ 1 k.1] [ 0 1], [ 1 k.1] [k.1^2 1], [ 1 k.1] [ k.1 1], [ 1 k.1] [ 1 1], [ k.1 k.1] [ 0 k.1], [ k.1 k.1] [k.1^2 k.1], [ k.1 k.1] [ k.1 k.1], [ k.1 k.1] [ 1 k.1], [ 0 1] [ 0 0], [ 0 1] [k.1^2 0], [ 0 1] [ k.1 0], [ 0 1] [ 1 0], [k.1^2 1] [ 0 k.1^2], [k.1^2 1] [k.1^2 k.1^2], [k.1^2 1] [ k.1 k.1^2], [k.1^2 1] [ 1 k.1^2], [ 1 1] [ 0 1], [ 1 1] [k.1^2 1], [ 1 1] [ k.1 1], [ 1 1] [ 1 1], [ k.1 1] [ 0 k.1], [ k.1 1] [k.1^2 k.1], [ k.1 1] [ k.1 k.1], [ k.1 1] [ 1 k.1] } >> mtf:={ n : n in p | (n in mf) and (n in mt)}; ^ User error: Identifier 'mt' has not been declared or assigned 6278 >> #[n : n in mmt | n in mt]; ^ User error: bad syntax >> #[n : n in mmt | n in mtf]; ^ User error: bad syntax >> s:=GF(7^3); ^ User error: bad syntax >> p:=PolynomialRing(s); ^ User error: Identifier 's' has not been declared or assigned >> t:=&+[x^r:r in lexp]; ^ User error: Identifier 'x' has not been declared or assigned >> n:=x^sn; ^ User error: Identifier 'x' has not been declared or assigned >> {[a,b] : a,b in s | Evaluate(t,b) eq Evaluate(n,a)}; ^ User error: Identifier 's' has not been declared or assigned 16807 16807 125 125 2187 2187 1331 1331 Errors: /home/mfd/gomagma: line 2: 23767 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host aula-a-siee45.uab.es. (158.109.66.45) Time: Thu Mar 4 09:29:44 2004 Input: /* Respostes a l'exercici 1 */ [i : i in [4..366 by 7]]; Output: Magma V2.10-6 Thu Mar 4 2004 09:29:41 on modular [Seed = 4261052596] ------------------------------------- [ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee45.uab.es. (158.109.66.45) Time: Thu Mar 4 09:30:12 2004 Input: k:=GF(4); p:=MatrixRing(k,2); mt:={n : n in p | Trace(n) eq 0}; Output: Magma V2.10-6 Thu Mar 4 2004 09:30:09 on modular [Seed = 3991572608] ------------------------------------- Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee45.uab.es. (158.109.66.45) Time: Thu Mar 4 09:30:21 2004 Input: k:=GF(4); p:=MatrixRing(k,2); mt:={n : n in p | Trace(n) eq 0}; mt; Output: Magma V2.10-6 Thu Mar 4 2004 09:30:18 on modular [Seed = 3873545088] ------------------------------------- { [ 0 0] [ 0 0], [ 0 0] [k.1^2 0], [ 0 0] [ k.1 0], [ 0 0] [ 1 0], [k.1^2 0] [ 0 k.1^2], [k.1^2 0] [k.1^2 k.1^2], [k.1^2 0] [ k.1 k.1^2], [k.1^2 0] [ 1 k.1^2], [ 1 0] [ 0 1], [ 1 0] [k.1^2 1], [ 1 0] [ k.1 1], [ 1 0] [ 1 1], [ k.1 0] [ 0 k.1], [ k.1 0] [k.1^2 k.1], [ k.1 0] [ k.1 k.1], [ k.1 0] [ 1 k.1], [ 0 k.1^2] [ 0 0], [ 0 k.1^2] [k.1^2 0], [ 0 k.1^2] [ k.1 0], [ 0 k.1^2] [ 1 0], [k.1^2 k.1^2] [ 0 k.1^2], [k.1^2 k.1^2] [k.1^2 k.1^2], [k.1^2 k.1^2] [ k.1 k.1^2], [k.1^2 k.1^2] [ 1 k.1^2], [ 1 k.1^2] [ 0 1], [ 1 k.1^2] [k.1^2 1], [ 1 k.1^2] [ k.1 1], [ 1 k.1^2] [ 1 1], [ k.1 k.1^2] [ 0 k.1], [ k.1 k.1^2] [k.1^2 k.1], [ k.1 k.1^2] [ k.1 k.1], [ k.1 k.1^2] [ 1 k.1], [ 0 k.1] [ 0 0], [ 0 k.1] [k.1^2 0], [ 0 k.1] [ k.1 0], [ 0 k.1] [ 1 0], [k.1^2 k.1] [ 0 k.1^2], [k.1^2 k.1] [k.1^2 k.1^2], [k.1^2 k.1] [ k.1 k.1^2], [k.1^2 k.1] [ 1 k.1^2], [ 1 k.1] [ 0 1], [ 1 k.1] [k.1^2 1], [ 1 k.1] [ k.1 1], [ 1 k.1] [ 1 1], [ k.1 k.1] [ 0 k.1], [ k.1 k.1] [k.1^2 k.1], [ k.1 k.1] [ k.1 k.1], [ k.1 k.1] [ 1 k.1], [ 0 1] [ 0 0], [ 0 1] [k.1^2 0], [ 0 1] [ k.1 0], [ 0 1] [ 1 0], [k.1^2 1] [ 0 k.1^2], [k.1^2 1] [k.1^2 k.1^2], [k.1^2 1] [ k.1 k.1^2], [k.1^2 1] [ 1 k.1^2], [ 1 1] [ 0 1], [ 1 1] [k.1^2 1], [ 1 1] [ k.1 1], [ 1 1] [ 1 1], [ k.1 1] [ 0 k.1], [ k.1 1] [k.1^2 k.1], [ k.1 1] [ k.1 k.1], [ k.1 1] [ 1 k.1] } Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee45.uab.es. (158.109.66.45) Time: Thu Mar 4 09:31:06 2004 Input: k:=GF(4); p:=MatrixRing(k,2); mt:={n : n in p | Trace(n) eq 0}; mf:={n : n in p | Submatrix(n,1,1,1,2) eq Submatrix(n,2,1,1,2)}; mtf:={ n : n in p | (n in mf) and (n in mt)}; Output: Magma V2.10-6 Thu Mar 4 2004 09:31:03 on modular [Seed = 421422243] ------------------------------------- Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee45.uab.es. (158.109.66.45) Time: Thu Mar 4 09:31:45 2004 Input: k:=GF(4); p:=MatrixRing(k,2); mt:={n : n in p | Trace(n) eq 0}; mf:={n : n in p | Submatrix(n,1,1,1,2) eq Submatrix(n,2,1,1,2)}; mtf:={ n : n in p | (n in mf) and (n in mt)}; /*Apartat 4*/ mmt:=[Random(p) : n in [1..100000]]; /*Nombre de les matrius que pertanyen a mf*/ #[n : n in mmt | n in mf]; /*Nombre de les matrius que pertanyen a mt*/ #[n : n in mmt | n in mt]; /*Nombre de les matrius que pertanyen a mtf*/ #[n : n in mmt | n in mtf]; Output: Magma V2.10-6 Thu Mar 4 2004 09:31:41 on modular [Seed = 269970880] ------------------------------------- 6325 25087 1547 Total time: 4.129 seconds, Total memory usage: 7.09MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 09:49:59 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S :=[ x^5*y^9, x^7*y^7, x^10*y^4, x^9*y^2, x^5*y^4, x^12*y^6, x^3*y, x^12*y^3, x^14, x^9*y^3, x^2*y^4, y^8, x*y^2, x^3, x*y^9, x^3*y^10, x^4, x^9*y^4, x*y^6, x^9*y^8, x^6*y^4, x^12*y^10, x^6*y^9, x^7, x^3*y^7, x^10*y^9, y^5, x^6*y, x^7*y^8, x^4*y^7, x^13*y^4, y^9, x^13, x^6, x^13*y^8, x^4*y^2, y^4, x^5*y, x*y^8, y^7, x^2*y, x^9*y^10, x^13*y^3, x^10*y^7, x^7*y^10, x^8*y, x^2*y^8, x^11*y^7, x^3*y^2, x^8*y^10, x^13*y^9, x^12*y^5, y^10, x^9*y^6, x^8*y^4, x^4*y^6, x*y, x^10*y^2, x^3*y^5, x^7*y^3, x^4*y^10, x^12*y^9, x^2*y^7, x^6*y^7, y^6, x^7*y^2, x^10*y^8, x^2*y^3, x^11*y^10, x^12, x*y^10, x^10*y^10, x^11*y^6, x^6*y^6, x^7*y^5, x^12*y^8, x^6*y^3, x^8*y^9, x^12*y^2, x^5*y^2, x^10*y^5, x^6*y^2, x^12*y^7, y, x^8*y^3, x*y^5, x^2*y^9, x^4*y, x^9*y, x^6*y^5, x^5*y^5, x^2*y^2, x^9*y^5, x^13*y^2, x^8*y^7, x^2*y^10, x^5*y^3, x^9*y^7, x^7*y^4, x^2*y^5, x^4*y^9, x*y^4, x^12*y, x^9*y^9, x^11*y^8, x^12*y^4, x^10*y^3, x^4*y^8, x^7*y^9, x^5*y^8, x^5*y^7, x^8*y^8, x^8*y^6, x^10*y^6, x, x^11*y^3, x^5, 1, x^4*y^5, x^3*y^4, x^4*y^4, x^10, x^7*y^6, x^11*y^4, x^2*y^6, x^11*y^2, x^13*y^10, x^5*y^10, x*y^3, x^3*y^6, x^8, x^11, x^6*y^8, x^11*y^5, x^10*y, x^9, x^2, x^3*y^9, y^2, x^5*y^6, x^13*y^6, x^13*y^5, x^8*y^2, x^4*y^3, y^3, x*y^7, x^7*y, x^3*y^8, x^6*y^10, x^3*y^3, x^11*y^9, x^8*y^5, x^13*y^7, x^11*y, x^13*y ] ; L := [ x^3*y^11]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Thu Mar 4 2004 09:49:56 on modular [Seed = 909194303] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] [ x^3*y^11 ] [ false ] Total time: 2.989 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 09:55:48 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; L := [ y^39]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Thu Mar 4 2004 09:55:45 on modular [Seed = 572858702] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] [ y^39 ] [ true ] Total time: 3.609 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 09:56:20 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; L := [ x^5*y^39]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Thu Mar 4 2004 09:56:16 on modular [Seed = 1431459544] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] [ x^5*y^39 ] [ true ] Total time: 3.699 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 09:56:54 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; L := [ x^27*y^39]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Thu Mar 4 2004 09:56:51 on modular [Seed = 1280004066] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] [ x^27*y^39 ] [ true ] Total time: 3.649 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 09:58:06 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; {x^27*y^39} in S; L := [ x^27*y^39]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Thu Mar 4 2004 09:58:02 on modular [Seed = 1195394208] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] >> {x^27*y^39} in S; ^ Runtime error in 'in': Could not lift element into sequence universe [ x^27*y^39 ] [ true ] Total time: 3.639 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 10:00:23 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; x^27*y^39 in S; L := [ x^27*y^39]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Thu Mar 4 2004 10:00:19 on modular [Seed = 1987146472] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] false [ x^27*y^39 ] [ true ] Total time: 3.680 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 10:00:54 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; x^26*y^39 in S; L := [ x^27*y^39]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Thu Mar 4 2004 10:00:50 on modular [Seed = 1768844758] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] true [ x^27*y^39 ] [ true ] Total time: 3.719 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host 3(NXDOMAIN) (196.1.94.254) Time: Thu Mar 4 11:11:56 2004 Input: help; Output: Magma V2.10-6 Thu Mar 4 2004 11:11:53 on modular [Seed = 438112077] ------------------------------------- >> help; ^ User error: Identifier 'help' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (196.1.94.254) Time: Thu Mar 4 11:12:13 2004 Input: ? Output: Magma V2.10-6 Thu Mar 4 2004 11:12:10 on modular [Seed = 320079447] ------------------------------------- =============================================================================== PATH: / KIND: Overview =============================================================================== You are reading about the Magma online help system. This system gives you information about Magma while you are at the computer. To see this help page at any time, all you have to do is to type ? ---------- The online help system comes in two modes: the single request mode and the Magma Help Browser. To enter the Browser, type ?? The Browser is useful if you intend to read several related help nodes, because you can exploit the tree structure of the online help. Once you are in the Browser, you can type help again to find out how to use the Browser, and for a more detailed explanation of the whole online help system. ---------- Single help requests begin with the ? character. Examples are: ?print ?magma ?ring ?example If your help request is ambiguous, Magma will return a numbered list of matches. To see the contents of one of them, type ? followed by its number. Some help pages suggest other pages that you might like to look at as well. They are prefixed by a code such as +3 or +5 . To read one of them, type ? followed by the code. You can also supply the full pathname of a help node, if you know it. For example: ?/system/quit ?/magma/module/homomorphism ---------- The online help system offers tab completion. If you type a few letters of your help request and then press the tab key, Magma will "complete" the request if there is a unique completion. Otherwise, it will complete the request as far as possible, and then emit a beep. Press the tab key again to see all the possibilities. ALWAYS PRESS TAB BEFORE THE END OF THE LINE, SO AS TO SEE EVERY RELEVANT HELP PAGE. (On a few operating systems, the tab completion feature cannot be made available.) ---------- The content of the online help system comes from two sources: the "Handbook of Magma Functions" (Bosma and Cannon) and specially-written overview nodes. You may also wish to consult the books "An Introduction to Algebraic Programming in Magma" (Cannon and Playoust) and "Solving Problems with Magma" (Bosma, Cannon, Playoust and Steel). ---------- The online help system is also available in an HTML form suitable for Internet browsers. To use this, move to a shell prompt (outside Magma) and type magmahelp ---------- To leave Magma, type quit; or -D. =============================================================================== Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (196.1.94.254) Time: Thu Mar 4 11:12:52 2004 Input: ?example Output: Magma V2.10-6 Thu Mar 4 2004 11:12:49 on modular [Seed = 135208343] ------------------------------------- 1320 matches: 1 O /browser/example 2 O /browser/example/example-intrinsic 3 O /browser/example/example-intrinsic-restrict 4 O /browser/example/example-search 5 O /browser/example/example-walk 6 O /example 7 E /language/function-procedure-package/attribute/examples/\ Example-InteractiveUserAttributes 8 E /language/function-procedure-package/attribute/examples/\ Example-PackageUserAttributes 9 E /language/function-procedure-package/attribute/examples/\ Example-SystemAttributes 10 E /language/function-procedure-package/function-procedure/forward/\ Example-forward 11 E /language/function-procedure-package/function-procedure/function/\ Example-Parameters 12 E /language/function-procedure-package/function-procedure/function/\ Example-Recursion 13 E /language/function-procedure-package/function-procedure/function/\ Example-Underscore 14 E /language/function-procedure-package/function-procedure/\ procedure/Example-Procedures 15 E /language/function-procedure-package/package/import/Example-import 16 E /language/function-procedure-package/package/intrinsic/\ Example-intrinsic 17 E /language/function-procedure-package/package/require/\ Example-require 18 E /language/function-procedure-package/package/spec/Example-spec 19 E /language/function-procedure-package/package/startup-spec/\ Example-startup-spec 20 E /language/IO/file/operations/Example-GetTime 21 E /language/IO/file/operations/Example-LineCount 22 E /language/IO/file/reading-file/Example-Read 23 E /language/IO/print/auto-print/Example-auto-print 24 E /language/IO/print/printf/Example-printf 25 E /language/IO/print/printf/Example-printf 26 E /language/IO/print/printf/Example-printf2 27 E /language/IO/print/sprint/Example-Sprintf 28 E /language/IO/string/Boolean/Example-Strings 29 E /language/IO/string/parsing/Example-Regexp 30 E /language/IO/string/parsing/Example-Split 31 E /language/statement-expressions/assignment/generator-assignment/\ Example-GeneratorNaming 32 E /language/statement-expressions/assignment/generator-assignment/\ Example-GeneratorNamingSequence 33 E /language/statement-expressions/assignment/indexed-assignment/\ Example-Indexing 34 E /language/statement-expressions/assignment/mutation/\ Example-MutationAssignment 35 E /language/statement-expressions/assignment/simple-assignment/\ Example-Identifiers 36 E /language/statement-expressions/assignment/simple-assignment/\ Example-MultipleReturns 37 E /language/statement-expressions/boolean/equality-operators/\ Example-Equality 38 E /language/statement-expressions/boolean/iteration/Example-Booleans 39 E /language/statement-expressions/comment-continuation/\ Example-Various 40 E /language/statement-expressions/conditional/case-statement/\ Example-case 41 E /language/statement-expressions/conditional/\ conditional-expression/Example-InLineConditional 42 E /language/statement-expressions/conditional/\ conditional-statement/Example-if 43 E /language/statement-expressions/iteration/continue-break/\ Example-break 44 E /language/statement-expressions/iteration/repeat-statement/\ Example-repeat 45 E /language/statement-expressions/iteration/repeat-statement/\ Example-while 46 E /language/statement-expressions/misc/Example-IsIntrinsic 47 E /language/statement-expressions/random/Example-IsIntrinsic 48 E /language/statement-expressions/timing/Example-Time 49 E /language/statement-expressions/type/Example-TypeStructures 50 E /language/statement-expressions/where-is/Example-where 51 E /magma/aggregate/coproduct/retrieve/Example-cop 52 E /magma/aggregate/record-format/access-modification/\ Example-RecordAccess 53 E /magma/aggregate/record-format/creation-format/\ Example-RecordFormat 54 E /magma/aggregate/record-format/creation-record/Example-Record 55 E /magma/aggregate/sequence/detail/creation/arithmetic-progression/\ Example-Progression 56 E /magma/aggregate/sequence/detail/iteration/Example-NestedIteration 57 E /magma/aggregate/sequence/detail/operation/modification/\ Example-Farey 58 E /magma/aggregate/sequence/detail/operation/other/\ Example-EgyptianFractions 59 E /magma/aggregate/sequence/detail/power-sequence/\ Example-PowerSequence 60 E /magma/aggregate/sequence/detail/recursion-reduction-iteration/\ recursion/Example-Self 61 E /magma/aggregate/set/detail/access-modification/access/\ Example-Miscellaneous 62 E /magma/aggregate/set/detail/access-modification/element/\ Example-ExtractRep 63 E /magma/aggregate/set/detail/access-modification/element/\ Example-Random 64 E /magma/aggregate/set/detail/access-modification/modification/\ Example-Include 65 E /magma/aggregate/set/detail/creation/arithmetic-progression/\ Example-Progression 66 E /magma/aggregate/set/detail/creation/enumerated/\ Example-AlmostFermat 67 E /magma/aggregate/set/detail/creation/enumerated/Example-Universe 68 E /magma/aggregate/set/detail/creation/indexed/\ Example-AlmostFermatIndexed 69 E /magma/aggregate/set/detail/creation/multiset/Example-Multiset 70 E /magma/aggregate/set/detail/operation/binary/Example-Join 71 E /magma/aggregate/set/detail/power-set/Example-PowerSet 72 E /magma/aggregate/set/detail/quantifier/Example-Exists 73 E /magma/aggregate/set/detail/quantifier/Example-NestedExists 74 E /magma/aggregate/set/detail/reduction-iteration/Example-Reduction 75 E /magma/aggregate/tuple-cartesian-product/creation/\ Example-CartesianProduct 76 E /magma/aggregate/tuple-cartesian-product/tuple-access/\ Example-TupleAccess 77 E /magma/aggregate/tuple-cartesian-product/tuple/Example-Tuple 78 E /magma/combinatorial-geometrical-incidence/brandt-modules/\ ModBrdt:brandt-modules/Associated-Structures/\ Example-ModBrdt:Module-Creation 79 E /magma/combinatorial-geometrical-incidence/brandt-modules/\ ModBrdt:brandt-modules/Example-ModBrdt:Constructors 80 E /magma/combinatorial-geometrical-incidence/brandt-modules/\ ModBrdt:brandt-modules/Verbose-Output/\ Example-ModBrdt:Verbose-Output 81 E /magma/combinatorial-geometrical-incidence/brandt-modules/\ ModBrdt:dimension-formulas/Example-ModBrdt:Dimension 82 E /magma/combinatorial-geometrical-incidence/brandt-modules/\ ModBrdt:Subspaces/Example-ModBrdt:Decomposition 83 E /magma/combinatorial-geometrical-incidence/brandt-modules/\ ModBrdt:Subspaces/ModBrdt:Subspaces-Tests/\ Example-ModBrdt:EisensteinSubspace 84 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-change_ring/Example-BaseExtend 85 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/Example-Creation 86 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/Example-CreationFromCurve 87 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/Example-CreationFromCurve2 88 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-model-predicates/Example-Models 89 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/Example-CreationTest 90 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/twists/Example-NonquadraticTwists 91 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/twists/Example-QuadraticTwists 92 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/Example-ecdb1 93 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/Example-ecdb2 94 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ ff_curves/abelian_group/Example-AbelianGroup 95 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ ff_curves/discrete_logs/Example-ECDL 96 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ ff_curves/ff_curves-point_counting/Example-Invariants to Read 97 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ ff_curves/ff_curves-point_counting/Example-Order 98 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ ff_curves/ff_curves-point_counting/Example-SEA 99 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ ff_curves/ff_curves-point_counting/Example-Twists 100 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ function_field/function_field-torsion_polynomials/\ Example-DivisionPolynomial 101 E /magma/combinatorial-geometrical-incidence/ellipti ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 3(NXDOMAIN) (196.1.94.254) Time: Thu Mar 4 11:13:19 2004 Input: ?GF Output: Magma V2.10-6 Thu Mar 4 2004 11:13:16 on modular [Seed = 17175683] ------------------------------------- 4 matches: 1 I /magma/ring-field-algebra/finite-Galois-field/creation/structure/\ FiniteField 2 I /magma/ring-field-algebra/finite-Galois-field/creation/structure/\ FiniteField 3 I /magma/ring-field-algebra/finite-Galois-field/creation/structure/\ FiniteField 4 I /magma/ring-field-algebra/finite-Galois-field/creation/structure/\ FiniteField To view an entry, type ? followed by the number next to it Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (196.1.94.254) Time: Thu Mar 4 11:13:48 2004 Input: ?1 Output: Magma V2.10-6 Thu Mar 4 2004 11:13:45 on modular [Seed = 909190033] ------------------------------------- No numbers are defined Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (196.1.94.254) Time: Thu Mar 4 11:13:58 2004 Input: ?2 Output: Magma V2.10-6 Thu Mar 4 2004 11:13:55 on modular [Seed = 791165682] ------------------------------------- No numbers are defined Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (196.1.94.254) Time: Thu Mar 4 11:14:16 2004 Input: ?GCD Output: Magma V2.10-6 Thu Mar 4 2004 11:14:13 on modular [Seed = 606286319] ------------------------------------- 48 matches: 1 S /magma/ring-field-algebra/distributive-multivariate-polynomial/\ common/gcd-lcm 2 S /magma/ring-field-algebra/integer/gcd-lcm 3 S /magma/ring-field-algebra/univariate-polynomial/common/gcd-lcm 4 I /magma/geometry/algebraic-curve/divisors/divisor-arithmetic/\ divisors-coeff-arith/GCD 5 I /magma/geometry/algebraic-curve/divisors/divisor-arithmetic/\ divisors-coeff-arith/GCD 6 I /magma/geometry/algebraic-curve/divisors/divisor-arithmetic/\ divisors-coeff-arith/GCD 7 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ LeftGCD 8 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ LeftGCD 9 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ LeftGCD 10 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ LeftGCD 11 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ LeftGCD 12 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ LeftGCD 13 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ RightGCD 14 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ RightGCD 15 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ RightGCD 16 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ RightGCD 17 I /magma/ring-field-algebra/algebraic-field/ideal/ideal-arithmetic/\ GCD 18 I /magma/ring-field-algebra/algebraic-field/ideal/ideal-arithmetic/\ GCD 19 I /magma/ring-field-algebra/detail/generic/predicate/HasGCD 20 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ common/gcd-lcm/GCD 21 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ common/gcd-lcm/GCD 22 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ common/gcd-lcm/GreatestCommonDivisor 23 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ common/gcd-lcm/GreatestCommonDivisor 24 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ common/gcd-lcm/GreatestCommonDivisor 25 I /magma/ring-field-algebra/function-field/Divisors/\ operation-element/arithmetic/GCD 26 I /magma/ring-field-algebra/function-field/Divisors/\ operation-element/arithmetic/GCD 27 I /magma/ring-field-algebra/function-field/Divisors/\ operation-element/arithmetic/GCD 28 I /magma/ring-field-algebra/function-field/ideals/\ ideal-ops-further/Gcd 29 I /magma/ring-field-algebra/integer/gcd-lcm/Gcd 30 I /magma/ring-field-algebra/integer/gcd-lcm/Gcd 31 I /magma/ring-field-algebra/integer/gcd-lcm/GreatestCommonDivisor 32 I /magma/ring-field-algebra/integer/gcd-lcm/GreatestCommonDivisor 33 I /magma/ring-field-algebra/integer/residue-class-rings/ideal/\ GreatestCommonDivisor 34 I /magma/ring-field-algebra/integer/residue-class-rings/ideal/\ GreatestCommonDivisor 35 I /magma/ring-field-algebra/integer/residue-class-rings/ideal/\ GreatestCommonDivisor 36 I /magma/ring-field-algebra/integer/residue-class-rings/ideal/\ GreatestCommonDivisor 37 I /magma/ring-field-algebra/local/polynomials/operations/\ GreatestCommonDivisor 38 I /magma/ring-field-algebra/local/polynomials/operations/\ GreatestCommonDivisor 39 I /magma/ring-field-algebra/local/polynomials/operations/\ GreatestCommonDivisor 40 I /magma/ring-field-algebra/quadratic/elements/\ greatest-common-divisor/Gcd 41 I /magma/ring-field-algebra/quadratic/elements/\ greatest-common-divisor/Gcd 42 I /magma/ring-field-algebra/quadratic/elements/\ greatest-common-divisor/Gcd 43 I /magma/ring-field-algebra/univariate-polynomial/common/gcd-lcm/\ GreatestCommonDivisor 44 I /magma/ring-field-algebra/univariate-polynomial/common/gcd-lcm/\ GreatestCommonDivisor 45 I /magma/ring-field-algebra/valuation/element/other/\ GreatestCommonDivisor 46 I /magma/ring-field-algebra/valuation/element/other/\ GreatestCommonDivisor 47 I /magma/ring-field-algebra/valuation/element/other/\ GreatestCommonDivisor 48 E /magma/ring-field-algebra/local/polynomials/operations/Example-gcd To view an entry, type ? followed by the number next to it Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (196.1.94.254) Time: Thu Mar 4 11:14:46 2004 Input: ?GCD ?3 Output: Magma V2.10-6 Thu Mar 4 2004 11:14:43 on modular [Seed = 1516064695] ------------------------------------- 48 matches: 1 S /magma/ring-field-algebra/distributive-multivariate-polynomial/\ common/gcd-lcm 2 S /magma/ring-field-algebra/integer/gcd-lcm 3 S /magma/ring-field-algebra/univariate-polynomial/common/gcd-lcm 4 I /magma/geometry/algebraic-curve/divisors/divisor-arithmetic/\ divisors-coeff-arith/GCD 5 I /magma/geometry/algebraic-curve/divisors/divisor-arithmetic/\ divisors-coeff-arith/GCD 6 I /magma/geometry/algebraic-curve/divisors/divisor-arithmetic/\ divisors-coeff-arith/GCD 7 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ LeftGCD 8 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ LeftGCD 9 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ LeftGCD 10 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ LeftGCD 11 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ LeftGCD 12 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ LeftGCD 13 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ RightGCD 14 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ RightGCD 15 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ RightGCD 16 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ RightGCD 17 I /magma/ring-field-algebra/algebraic-field/ideal/ideal-arithmetic/\ GCD 18 I /magma/ring-field-algebra/algebraic-field/ideal/ideal-arithmetic/\ GCD 19 I /magma/ring-field-algebra/detail/generic/predicate/HasGCD 20 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ common/gcd-lcm/GCD 21 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ common/gcd-lcm/GCD 22 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ common/gcd-lcm/GreatestCommonDivisor 23 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ common/gcd-lcm/GreatestCommonDivisor 24 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ common/gcd-lcm/GreatestCommonDivisor 25 I /magma/ring-field-algebra/function-field/Divisors/\ operation-element/arithmetic/GCD 26 I /magma/ring-field-algebra/function-field/Divisors/\ operation-element/arithmetic/GCD 27 I /magma/ring-field-algebra/function-field/Divisors/\ operation-element/arithmetic/GCD 28 I /magma/ring-field-algebra/function-field/ideals/\ ideal-ops-further/Gcd 29 I /magma/ring-field-algebra/integer/gcd-lcm/Gcd 30 I /magma/ring-field-algebra/integer/gcd-lcm/Gcd 31 I /magma/ring-field-algebra/integer/gcd-lcm/GreatestCommonDivisor 32 I /magma/ring-field-algebra/integer/gcd-lcm/GreatestCommonDivisor 33 I /magma/ring-field-algebra/integer/residue-class-rings/ideal/\ GreatestCommonDivisor 34 I /magma/ring-field-algebra/integer/residue-class-rings/ideal/\ GreatestCommonDivisor 35 I /magma/ring-field-algebra/integer/residue-class-rings/ideal/\ GreatestCommonDivisor 36 I /magma/ring-field-algebra/integer/residue-class-rings/ideal/\ GreatestCommonDivisor 37 I /magma/ring-field-algebra/local/polynomials/operations/\ GreatestCommonDivisor 38 I /magma/ring-field-algebra/local/polynomials/operations/\ GreatestCommonDivisor 39 I /magma/ring-field-algebra/local/polynomials/operations/\ GreatestCommonDivisor 40 I /magma/ring-field-algebra/quadratic/elements/\ greatest-common-divisor/Gcd 41 I /magma/ring-field-algebra/quadratic/elements/\ greatest-common-divisor/Gcd 42 I /magma/ring-field-algebra/quadratic/elements/\ greatest-common-divisor/Gcd 43 I /magma/ring-field-algebra/univariate-polynomial/common/gcd-lcm/\ GreatestCommonDivisor 44 I /magma/ring-field-algebra/univariate-polynomial/common/gcd-lcm/\ GreatestCommonDivisor 45 I /magma/ring-field-algebra/valuation/element/other/\ GreatestCommonDivisor 46 I /magma/ring-field-algebra/valuation/element/other/\ GreatestCommonDivisor 47 I /magma/ring-field-algebra/valuation/element/other/\ GreatestCommonDivisor 48 E /magma/ring-field-algebra/local/polynomials/operations/Example-gcd To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/ring-field-algebra/univariate-polynomial/common/gcd-lcm KIND: Section =============================================================================== Common Divisors and Common Multiples. Intrinsics: [+1] GreatestCommonDivisor [+2] ExtendedGreatestCommonDivisor [+3] LeastCommonMultiple [+4] Normalize =============================================================================== Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (196.1.94.254) Time: Thu Mar 4 11:15:11 2004 Input: ?GCD ?3 +1 Output: Magma V2.10-6 Thu Mar 4 2004 11:15:08 on modular [Seed = 1330141533] ------------------------------------- 48 matches: 1 S /magma/ring-field-algebra/distributive-multivariate-polynomial/\ common/gcd-lcm 2 S /magma/ring-field-algebra/integer/gcd-lcm 3 S /magma/ring-field-algebra/univariate-polynomial/common/gcd-lcm 4 I /magma/geometry/algebraic-curve/divisors/divisor-arithmetic/\ divisors-coeff-arith/GCD 5 I /magma/geometry/algebraic-curve/divisors/divisor-arithmetic/\ divisors-coeff-arith/GCD 6 I /magma/geometry/algebraic-curve/divisors/divisor-arithmetic/\ divisors-coeff-arith/GCD 7 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ LeftGCD 8 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ LeftGCD 9 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ LeftGCD 10 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ LeftGCD 11 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ LeftGCD 12 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ LeftGCD 13 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ RightGCD 14 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ RightGCD 15 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ RightGCD 16 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ RightGCD 17 I /magma/ring-field-algebra/algebraic-field/ideal/ideal-arithmetic/\ GCD 18 I /magma/ring-field-algebra/algebraic-field/ideal/ideal-arithmetic/\ GCD 19 I /magma/ring-field-algebra/detail/generic/predicate/HasGCD 20 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ common/gcd-lcm/GCD 21 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ common/gcd-lcm/GCD 22 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ common/gcd-lcm/GreatestCommonDivisor 23 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ common/gcd-lcm/GreatestCommonDivisor 24 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ common/gcd-lcm/GreatestCommonDivisor 25 I /magma/ring-field-algebra/function-field/Divisors/\ operation-element/arithmetic/GCD 26 I /magma/ring-field-algebra/function-field/Divisors/\ operation-element/arithmetic/GCD 27 I /magma/ring-field-algebra/function-field/Divisors/\ operation-element/arithmetic/GCD 28 I /magma/ring-field-algebra/function-field/ideals/\ ideal-ops-further/Gcd 29 I /magma/ring-field-algebra/integer/gcd-lcm/Gcd 30 I /magma/ring-field-algebra/integer/gcd-lcm/Gcd 31 I /magma/ring-field-algebra/integer/gcd-lcm/GreatestCommonDivisor 32 I /magma/ring-field-algebra/integer/gcd-lcm/GreatestCommonDivisor 33 I /magma/ring-field-algebra/integer/residue-class-rings/ideal/\ GreatestCommonDivisor 34 I /magma/ring-field-algebra/integer/residue-class-rings/ideal/\ GreatestCommonDivisor 35 I /magma/ring-field-algebra/integer/residue-class-rings/ideal/\ GreatestCommonDivisor 36 I /magma/ring-field-algebra/integer/residue-class-rings/ideal/\ GreatestCommonDivisor 37 I /magma/ring-field-algebra/local/polynomials/operations/\ GreatestCommonDivisor 38 I /magma/ring-field-algebra/local/polynomials/operations/\ GreatestCommonDivisor 39 I /magma/ring-field-algebra/local/polynomials/operations/\ GreatestCommonDivisor 40 I /magma/ring-field-algebra/quadratic/elements/\ greatest-common-divisor/Gcd 41 I /magma/ring-field-algebra/quadratic/elements/\ greatest-common-divisor/Gcd 42 I /magma/ring-field-algebra/quadratic/elements/\ greatest-common-divisor/Gcd 43 I /magma/ring-field-algebra/univariate-polynomial/common/gcd-lcm/\ GreatestCommonDivisor 44 I /magma/ring-field-algebra/univariate-polynomial/common/gcd-lcm/\ GreatestCommonDivisor 45 I /magma/ring-field-algebra/valuation/element/other/\ GreatestCommonDivisor 46 I /magma/ring-field-algebra/valuation/element/other/\ GreatestCommonDivisor 47 I /magma/ring-field-algebra/valuation/element/other/\ GreatestCommonDivisor 48 E /magma/ring-field-algebra/local/polynomials/operations/Example-gcd To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/ring-field-algebra/univariate-polynomial/common/gcd-lcm KIND: Section =============================================================================== Common Divisors and Common Multiples. Intrinsics: [+1] GreatestCommonDivisor [+2] ExtendedGreatestCommonDivisor [+3] LeastCommonMultiple [+4] Normalize =============================================================================== 1 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (196.1.94.254) Time: Thu Mar 4 11:15:29 2004 Input: ?GCD ?3 ?+1 Output: Magma V2.10-6 Thu Mar 4 2004 11:15:26 on modular [Seed = 1128551747] ------------------------------------- 48 matches: 1 S /magma/ring-field-algebra/distributive-multivariate-polynomial/\ common/gcd-lcm 2 S /magma/ring-field-algebra/integer/gcd-lcm 3 S /magma/ring-field-algebra/univariate-polynomial/common/gcd-lcm 4 I /magma/geometry/algebraic-curve/divisors/divisor-arithmetic/\ divisors-coeff-arith/GCD 5 I /magma/geometry/algebraic-curve/divisors/divisor-arithmetic/\ divisors-coeff-arith/GCD 6 I /magma/geometry/algebraic-curve/divisors/divisor-arithmetic/\ divisors-coeff-arith/GCD 7 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ LeftGCD 8 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ LeftGCD 9 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ LeftGCD 10 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ LeftGCD 11 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ LeftGCD 12 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ LeftGCD 13 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ RightGCD 14 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ RightGCD 15 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ RightGCD 16 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ RightGCD 17 I /magma/ring-field-algebra/algebraic-field/ideal/ideal-arithmetic/\ GCD 18 I /magma/ring-field-algebra/algebraic-field/ideal/ideal-arithmetic/\ GCD 19 I /magma/ring-field-algebra/detail/generic/predicate/HasGCD 20 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ common/gcd-lcm/GCD 21 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ common/gcd-lcm/GCD 22 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ common/gcd-lcm/GreatestCommonDivisor 23 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ common/gcd-lcm/GreatestCommonDivisor 24 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ common/gcd-lcm/GreatestCommonDivisor 25 I /magma/ring-field-algebra/function-field/Divisors/\ operation-element/arithmetic/GCD 26 I /magma/ring-field-algebra/function-field/Divisors/\ operation-element/arithmetic/GCD 27 I /magma/ring-field-algebra/function-field/Divisors/\ operation-element/arithmetic/GCD 28 I /magma/ring-field-algebra/function-field/ideals/\ ideal-ops-further/Gcd 29 I /magma/ring-field-algebra/integer/gcd-lcm/Gcd 30 I /magma/ring-field-algebra/integer/gcd-lcm/Gcd 31 I /magma/ring-field-algebra/integer/gcd-lcm/GreatestCommonDivisor 32 I /magma/ring-field-algebra/integer/gcd-lcm/GreatestCommonDivisor 33 I /magma/ring-field-algebra/integer/residue-class-rings/ideal/\ GreatestCommonDivisor 34 I /magma/ring-field-algebra/integer/residue-class-rings/ideal/\ GreatestCommonDivisor 35 I /magma/ring-field-algebra/integer/residue-class-rings/ideal/\ GreatestCommonDivisor 36 I /magma/ring-field-algebra/integer/residue-class-rings/ideal/\ GreatestCommonDivisor 37 I /magma/ring-field-algebra/local/polynomials/operations/\ GreatestCommonDivisor 38 I /magma/ring-field-algebra/local/polynomials/operations/\ GreatestCommonDivisor 39 I /magma/ring-field-algebra/local/polynomials/operations/\ GreatestCommonDivisor 40 I /magma/ring-field-algebra/quadratic/elements/\ greatest-common-divisor/Gcd 41 I /magma/ring-field-algebra/quadratic/elements/\ greatest-common-divisor/Gcd 42 I /magma/ring-field-algebra/quadratic/elements/\ greatest-common-divisor/Gcd 43 I /magma/ring-field-algebra/univariate-polynomial/common/gcd-lcm/\ GreatestCommonDivisor 44 I /magma/ring-field-algebra/univariate-polynomial/common/gcd-lcm/\ GreatestCommonDivisor 45 I /magma/ring-field-algebra/valuation/element/other/\ GreatestCommonDivisor 46 I /magma/ring-field-algebra/valuation/element/other/\ GreatestCommonDivisor 47 I /magma/ring-field-algebra/valuation/element/other/\ GreatestCommonDivisor 48 E /magma/ring-field-algebra/local/polynomials/operations/Example-gcd To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/ring-field-algebra/univariate-polynomial/common/gcd-lcm KIND: Section =============================================================================== Common Divisors and Common Multiples. Intrinsics: [+1] GreatestCommonDivisor [+2] ExtendedGreatestCommonDivisor [+3] LeastCommonMultiple [+4] Normalize =============================================================================== =============================================================================== PATH: /magma/ring-field-algebra/univariate-polynomial/common/gcd-lcm/\ GreatestCommonDivisor KIND: Intrinsic =============================================================================== GreatestCommonDivisor(f, g) : RngUPolElt, RngUPolElt -> RngUPolElt Gcd(f, g) : RngUPolElt, RngUPolElt -> RngUPolElt GCD(f, g) : RngUPolElt, RngUPolElt -> RngUPolElt Given univariate polynomials f and g over the ring R, this function returns the greatest common divisor (GCD) of f and g. The valid coefficient rings are those which themselves have a GCD algorithm for their elements (which includes most commutative rings in Magma). If either of the inputs is zero, then the result is the other input (and if the inputs are both zero then the result is zero). The result is normalized (see the function Normalize), so the result is always unique. For polynomials over finite fields, the simple Euclidean algorithm is used, since this is efficient (there is no intermediate coefficient blowup). For polynomials over the integers or rationals, a combination of two algorithms is used: (1) the heuristic evaluation `GCDHEU' algorithm of Char et al. ([CGG89] and [GCL92, section 7.7]), suitable for small to moderate-degree dense polynomials; (2) a modular algorithm similar to that presented in [vzGG99, Algorithm 6.38] or [GCL92, section 7.4] (although lifting all the way up to a bound is not used since it is completely unnecessary for correctness in this algorithm!). For polynomials over an algebraic number field, quadratic field, or cyclotomic field, a fast modular algorithm is used, which maps the field to a residue class polynomial ring modulo a small prime. Since V2.10, for polynomials over an algebraic function field or polynomial quotient ring over a function field, a new fast modular algorithm of Allan Steel (to be published) is used, which evaluates and interpolates for each base transcendental variable. For polynomials over another polynomial ring or function field, the polynomials are first "flattened" to be inside a multivariate polynomial ring over the base coefficient ring, then the appropriate (multivariate) algorithm is used for that base coefficient ring. For polynomials over any other ring, the generic subresultant algorithm [Coh93, section 3.3] is used. =============================================================================== Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Thu Mar 4 11:29:06 2004 Input: polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; R:= Integers (); P := PolynomialRing (R); polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; main := function (a,b) exponent:= polinomi_t (a,b); print exponent; pol_t := polinomi_t2 (exponent); print pol_t; pol_n := polinomi_n (exponent); print pol_n; return 0; end function; Output: Magma V2.10-6 Thu Mar 4 2004 11:29:03 on modular [Seed = 3048385764] ------------------------------------- Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Thu Mar 4 11:29:24 2004 Input: polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; R:= Integers (); P := PolynomialRing (R); polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; main := function (a,b) exponent:= polinomi_t (a,b); print exponent; pol_t := polinomi_t2 (exponent); print pol_t; pol_n := polinomi_n (exponent); print pol_n; return 0; end function; Output: Magma V2.10-6 Thu Mar 4 2004 11:29:21 on modular [Seed = 2863510485] ------------------------------------- Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Thu Mar 4 11:29:45 2004 Input: polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; R:= Integers (); P := PolynomialRing (R); polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; main := function (a,b) exponent:= polinomi_t (a,b); print exponent; pol_t := polinomi_t2 (exponent); print pol_t; pol_n := polinomi_n (exponent); print pol_n; return 0; end function; main (7,3); Output: Magma V2.10-6 Thu Mar 4 2004 11:29:41 on modular [Seed = 2695346635] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x x^57 0 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Thu Mar 4 11:30:09 2004 Input: polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; R:= Integers (); P := PolynomialRing (R); polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; main := function (a,b) exponent:= polinomi_t (a,b); print exponent; pol_t := polinomi_t2 (exponent); print pol_t; pol_n := polinomi_n (exponent); print pol_n; return 0; end function; main (7,3); PuntsOlav := { (a,b) : a in GF (7,3) , b in GF (7,3) | Evaluate (c,a) eq Evaluate (d,b)} Output: Magma V2.10-6 Thu Mar 4 2004 11:30:06 on modular [Seed = 3503802688] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x x^57 0 >> PuntsOlav := { (a,b) : a in GF (7,3) , b in GF (7,3) | Evaluate (c,a) ^ User error: Identifier 'c' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Thu Mar 4 11:30:40 2004 Input: polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; R:= Integers (); P := PolynomialRing (R); polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; main := function (a,b) exponent:= polinomi_t (a,b); print exponent; pol_t := polinomi_t2 (exponent); print pol_t; pol_n := polinomi_n (exponent); print pol_n; return 0; end function; main (7,3); PuntsOlav := { (a,b) : a in GF (7,3) , b in GF (7,3) | Evaluate (pol_t,a) eq Evaluate (pol_n,b)} Output: Magma V2.10-6 Thu Mar 4 2004 11:30:37 on modular [Seed = 3385774202] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x x^57 0 >> PuntsOlav := { (a,b) : a in GF (7,3) , b in GF (7,3) | Evaluate (pol_t,a) ^ User error: Identifier 'pol_t' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Thu Mar 4 11:32:55 2004 Input: polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; R:= Integers (); P := PolynomialRing (R); polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; main := function (a,b) exponent:= polinomi_t (a,b); print exponent; pol_t := polinomi_t2 (exponent); print pol_t; pol_n := polinomi_n (exponent); print pol_n; return 0; end function; main (7,3); PuntsOlav := { (a,b) : a in GF (7,3) , b in GF (7,3) | Evaluate (polinomi_t2(exponent),a) eq Evaluate (polinomi_n(exponent),b)}; Output: Magma V2.10-6 Thu Mar 4 2004 11:32:51 on modular [Seed = 4277789907] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x x^57 0 >> Evaluate (polinomi_t2(exponent),a) eq Evaluate (polinomi_n(exponent),b)}; ^ User error: Identifier 'exponent' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Thu Mar 4 11:37:40 2004 Input: polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; R:= Integers (); P := PolynomialRing (R); polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; main := function (a,b) exponent:= polinomi_t (a,b); print exponent; pol_t := polinomi_t2 (exponent); print pol_t; pol_n := polinomi_n (exponent); print pol_n; return 0; end function; main (7,3); Output: Magma V2.10-6 Thu Mar 4 2004 11:37:37 on modular [Seed = 4042779583] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x x^57 0 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 11:37:50 2004 Input: L:=Lattice("E",8); S:=ShortestVectors(L); #S; Output: Magma V2.10-6 Thu Mar 4 2004 11:37:47 on modular [Seed = 504956250] ------------------------------------- 120 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Thu Mar 4 11:37:54 2004 Input: polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; R:= Integers (); P := PolynomialRing (R); polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; main := function (a,b) exponent:= polinomi_t (a,b); print exponent; pol_t := polinomi_t2 (exponent); print pol_t; pol_n := polinomi_n (exponent); print pol_n; return 0; end function; main (7,3); exponent; Output: Magma V2.10-6 Thu Mar 4 2004 11:37:51 on modular [Seed = 353504853] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x x^57 0 >> exponent; ^ User error: Identifier 'exponent' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 11:38:06 2004 Input: L:=Lattice("G",2); S:=ShortestVectors(L); #S; Output: Magma V2.10-6 Thu Mar 4 2004 11:38:03 on modular [Seed = 202053496] ------------------------------------- 3 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 11:38:29 2004 Input: L:=Lattice("G",2); S:=KissingNumber(L); #S; Output: Magma V2.10-6 Thu Mar 4 2004 11:38:26 on modular [Seed = 50600094] ------------------------------------- >> #S;; ^ Runtime error in '#': Bad argument types Argument types given: RngIntElt Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Thu Mar 4 11:38:32 2004 Input: polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; R:= Integers (); P := PolynomialRing (R); polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; main := function (a,b) exponent:= polinomi_t (a,b); print exponent; pol_t := polinomi_t2 (exponent); print pol_t; pol_n := polinomi_n (exponent); print pol_n; return 0; end function; main (7,3); exponent:= polinomi_t (a,b); Output: Magma V2.10-6 Thu Mar 4 2004 11:38:29 on modular [Seed = 993796257] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x x^57 0 >> exponent:= polinomi_t (a,b);; ^ User error: Identifier 'a' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Thu Mar 4 11:38:50 2004 Input: polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; R:= Integers (); P := PolynomialRing (R); polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; main := function (a,b) exponent:= polinomi_t (a,b); print exponent; pol_t := polinomi_t2 (exponent); print pol_t; pol_n := polinomi_n (exponent); print pol_n; return 0; end function; main (7,3); exponent:= polinomi_t (7,3); Output: Magma V2.10-6 Thu Mar 4 2004 11:38:48 on modular [Seed = 825633462] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x x^57 0 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Thu Mar 4 11:39:06 2004 Input: polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; R:= Integers (); P := PolynomialRing (R); polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; main := function (a,b) exponent:= polinomi_t (a,b); print exponent; pol_t := polinomi_t2 (exponent); print pol_t; pol_n := polinomi_n (exponent); print pol_n; return 0; end function; main (7,3); exponent:= polinomi_t (7,3); exponent; Output: Magma V2.10-6 Thu Mar 4 2004 11:39:03 on modular [Seed = 674182032] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x x^57 0 [ 49, 7, 1 ] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Thu Mar 4 11:39:37 2004 Input: polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; R:= Integers (); P := PolynomialRing (R); polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; main := function (a,b) exponent:= polinomi_t (a,b); print exponent; pol_t := polinomi_t2 (exponent); print pol_t; pol_n := polinomi_n (exponent); print pol_n; return 0; end function; main (7,3); exponent:= polinomi_t (7,3); exponent; PuntsOlav := { (a,b) : a in GF (7,3) , b in GF (7,3) | Evaluate (polinomi_t2(exponent),a) eq Evaluate (polinomi_n(exponent),b)}; Output: Magma V2.10-6 Thu Mar 4 2004 11:39:34 on modular [Seed = 1582908807] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x x^57 0 [ 49, 7, 1 ] >> PuntsOlav := { (a,b) : a in GF (7,3) , b in GF (7,3) | Evaluate (polinomi_ ^ Runtime error in elt< ... >: Bad arguments Total time: 3.109 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 11:39:40 2004 Input: L:=Lattice("G",2); KissingNumber(L); Output: Magma V2.10-6 Thu Mar 4 2004 11:39:36 on modular [Seed = 1532772492] ------------------------------------- 6 Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Thu Mar 4 11:40:21 2004 Input: polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; R:= Integers (); P := PolynomialRing (R); polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; main := function (a,b) exponent:= polinomi_t (a,b); print exponent; pol_t := polinomi_t2 (exponent); print pol_t; pol_n := polinomi_n (exponent); print pol_n; return 0; end function; main (7,3); exponent:= polinomi_t (7,3); exponent; PuntsOlav := { : a in GF (7,3) , b in GF (7,3) | Evaluate (polinomi_t2(exponent),a) eq Evaluate (polinomi_n(exponent),b)}; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 4 2004 11:39:57 on modular [Seed = 1280006030] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x x^57 0 [ 49, 7, 1 ] Errors: /home/mfd/gomagma: line 2: 24403 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Thu Mar 4 11:40:44 2004 Input: polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; R:= Integers (); P := PolynomialRing (R); polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; main := function (a,b) exponent:= polinomi_t (a,b); print exponent; pol_t := polinomi_t2 (exponent); print pol_t; pol_n := polinomi_n (exponent); print pol_n; return 0; end function; main (7,3); exponent:= polinomi_t (7,3); exponent; PuntsOlav := { : a in GF (7,3) , b in GF (7,3) | Evaluate (polinomi_t2(exponent),a) eq Evaluate (polinomi_n(exponent),b)}; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 4 2004 11:40:21 on modular [Seed = 2105173655] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x x^57 0 [ 49, 7, 1 ] Errors: /home/mfd/gomagma: line 2: 24418 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 11:40:56 2004 Input: L:=Lattice("G",2); ThetaSeries(L); Output: Magma V2.10-6 Thu Mar 4 2004 11:40:53 on modular [Seed = 1953720446] ------------------------------------- >> ThetaSeries(L); ^ Runtime error in 'ThetaSeries': Bad argument types Argument types given: Lat Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Thu Mar 4 11:41:51 2004 Input: polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; R:= Integers (); P := PolynomialRing (R); polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; exponent:= polinomi_t (7,3); PuntsOlav := { : a in GF (7,3) , b in GF (7,3) | Evaluate (polinomi_t2(exponent),a) eq Evaluate (polinomi_n(exponent),b)}; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 4 2004 11:41:28 on modular [Seed = 1802270540] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 24436 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Thu Mar 4 11:43:00 2004 Input: polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; R:= Integers (); P := PolynomialRing (R); polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; exponent:= polinomi_t (7,3); PuntsOlav := { : a in GF (7,3) , b in GF (7,3) | Evaluate (polinomi_t2(exponent),a) eq Evaluate (polinomi_n(exponent),b)}; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 4 2004 11:42:37 on modular [Seed = 1650818560] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 24445 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Thu Mar 4 11:46:28 2004 Input: polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; exponent := polinomi_t (7,3); R:= Integers (); P := PolynomialRing (R); polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; pol_t := polinomi_t2 (exponent); polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; pol_n:= polinomi_n (exponent); PuntsOlav := { : a in GF (7,3) , b in GF (7,3) | Evaluate (polinomi_t2(exponent),a) eq Evaluate (polinomi_n(exponent),b)}; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 4 2004 11:46:05 on modular [Seed = 2391380956] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 24465 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Thu Mar 4 11:46:52 2004 Input: polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; exponent := polinomi_t (7,3); R:= Integers (); P := PolynomialRing (R); polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; pol_t := polinomi_t2 (exponent); polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; pol_n:= polinomi_n (exponent); Output: Magma V2.10-6 Thu Mar 4 2004 11:46:49 on modular [Seed = 2239928547] ------------------------------------- Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 11:47:19 2004 Input: L:=Lattice("G",2); Theta(L); Output: Magma V2.10-6 Thu Mar 4 2004 11:47:16 on modular [Seed = 3166413111] ------------------------------------- >> Theta(L); ^ User error: Identifier 'Theta' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Thu Mar 4 11:47:47 2004 Input: polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; exponent := polinomi_t (7,3); R:= Integers (); P := PolynomialRing (R); polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; pol_t := polinomi_t2 (exponent); polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; pol_n:= polinomi_n (exponent); PuntsOlav := { : a in GF (7,3) , b in GF (7,3) | Evaluate (pol_t,a) eq Evaluate (pol_n(exponent),b)}; Output: Magma V2.10-6 Thu Mar 4 2004 11:47:44 on modular [Seed = 3014962716] ------------------------------------- >> Evaluate (pol_t,a) eq Evaluate (pol_n(exponent),b)}; ^ Runtime error: Bad argument types Argument types given: SeqEnum[RngIntElt], RngUPolElt Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 11:48:06 2004 Input: L:=Lattice("G",2); ?theta Output: Magma V2.10-6 Thu Mar 4 2004 11:48:02 on modular [Seed = 2863511414] ------------------------------------- 8 matches: 1 S /magma/module-lattice/lattice/enumeration/minima-theta 2 I /magma/combinatorial-geometrical-incidence/brandt-modules/\ qexpansions/ThetaSeries 3 I /magma/combinatorial-geometrical-incidence/modular-symbol/\ operators/ThetaOperator 4 I /magma/module-lattice/lattice/enumeration/minima-theta/ThetaSeries 5 I /magma/module-lattice/quadratic/invar/ThetaSeries 6 I /magma/ring-field-algebra/real-complex/elliptic-modular/\ jacobi-dedekind/JacobiTheta 7 I /magma/ring-field-algebra/real-complex/elliptic-modular/\ jacobi-dedekind/JacobiTheta 8 I /magma/ring-field-algebra/real-complex/elliptic-modular/\ jacobi-dedekind/JacobiThetaNullK To view an entry, type ? followed by the number next to it Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Thu Mar 4 11:48:14 2004 Input: polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; exponent := polinomi_t (7,3); R:= Integers (); P := PolynomialRing (R); polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; pol_t := polinomi_t2 (exponent); polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; pol_n:= polinomi_n (exponent); PuntsOlav := { : a in GF (7,3) , b in GF (7,3) | Evaluate (pol_t,a) eq Evaluate (pol_n,b)}; Output: Magma V2.10-6 Thu Mar 4 2004 11:48:07 on modular [Seed = 2712059001] ------------------------------------- Total time: 6.869 seconds, Total memory usage: 2.98MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 11:48:39 2004 Input: L:=Lattice("G",2); ?ThetaSeries Output: Magma V2.10-6 Thu Mar 4 2004 11:48:36 on modular [Seed = 3638543651] ------------------------------------- 4 matches: 1 I /magma/combinatorial-geometrical-incidence/brandt-modules/\ qexpansions/ThetaSeries 2 I /magma/module-lattice/lattice/enumeration/minima-theta/ThetaSeries 3 I /magma/module-lattice/quadratic/invar/ThetaSeries 4 E /magma/module-lattice/lattice/enumeration/minima-theta/\ Example-ThetaSeries To view an entry, type ? followed by the number next to it Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Thu Mar 4 11:49:14 2004 Input: polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; exponent := polinomi_t (7,3); R:= Integers (); P := PolynomialRing (R); polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; pol_t := polinomi_t2 (exponent); polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; pol_n:= polinomi_n (exponent); PuntsOlav := { : a in GF (7,3) , b in GF (7,3) | Evaluate (pol_t,a) eq Evaluate (pol_n,b)}; PuntsOlav; Output: Magma V2.10-6 Thu Mar 4 2004 11:49:07 on modular [Seed = 3486044627] ------------------------------------- { <$.1^205, $.1^175>, <$.1^172, 3>, <1, $.1^7>, <$.1^85, $.1^58>, <$.1^23, $.1^112>, <$.1^36, $.1^295>, <$.1^110, $.1^68>, <$.1^301, $.1^95>, <$.1^310, $.1^65>, <$.1^111, $.1^140>, <$.1^88, $.1^177>, <$.1^198, $.1^4>, <$.1^281, $.1^317>, <$.1^131, $.1^174>, <$.1^330, $.1^255>, <$.1^83, $.1^184>, <$.1^145, $.1^214>, <$.1^154, $.1^181>, <$.1^172, $.1^237>, <$.1^264, $.1^23>, <$.1^150, $.1^129>, <$.1^103, $.1^168>, <$.1^83, $.1^256>, <$.1^7, $.1^126>, <$.1^198, $.1^286>, <$.1^66, $.1^180>, <$.1^67, $.1^193>, <$.1^41, $.1^41>, <$.1^193, $.1^208>, <$.1^17, $.1^340>, <$.1^97, $.1^132>, <$.1^195, $.1^282>, <$.1^91, $.1^335>, <$.1^296, $.1^335>, <$.1^80, $.1^119>, <$.1^237, $.1^327>, <$.1^160, $.1^223>, <$.1^96, $.1^99>, <$.1^302, $.1^273>, <$.1^88, 5>, <$.1^139, $.1^62>, <$.1^150, $.1^63>, <$.1^149, $.1^40>, <$.1^316, $.1^169>, <$.1^252, $.1^151>, <$.1^255, $.1^53>, <$.1^42, $.1^112>, <$.1^176, $.1^251>, <$.1^226, $.1^38>, <$.1^124, $.1^182>, <$.1^34, $.1^322>, <$.1^327, $.1^39>, <$.1^161, $.1^340>, <$.1^135, $.1^51>, <$.1^28, $.1^21>, <$.1^332, $.1^73>, <$.1^187, $.1^21>, <$.1^311, $.1^62>, <$.1^102, $.1^131>, <$.1^319, $.1^3>, <$.1^314, $.1^246>, <$.1^44, $.1^69>, <$.1^100, 4>, <$.1^267, $.1^168>, <$.1^224, $.1^280>, <$.1^315, $.1^82>, <$.1^292, $.1^137>, <$.1^200, $.1^280>, <$.1^176, $.1^155>, <$.1^18, $.1^160>, <$.1^121, $.1^230>, <$.1^147, $.1^217>, <$.1^62, $.1^129>, <$.1^318, $.1^88>, <$.1^235, $.1^244>, <$.1^294, $.1^52>, <$.1^270, $.1^92>, <$.1^309, $.1^284>, <$.1^232, $.1^187>, <$.1^67, $.1^103>, <$.1^325, $.1^214>, <$.1^69, $.1^315>, <$.1^24, $.1^303>, <$.1^145, $.1^130>, <$.1^309, $.1^224>, <$.1^46, $.1^83>, <$.1^272, $.1^277>, <$.1^303, $.1^225>, <$.1^311, $.1^2>, <$.1^183, $.1^125>, <$.1^17, $.1^130>, <2, $.1^165>, <$.1^207, $.1^76>, <$.1^318, $.1^208>, <$.1^40, $.1^11>, <$.1^200, $.1^166>, <$.1^119, $.1^244>, <$.1^3, $.1^319>, <3, $.1^38>, <$.1^251, $.1^152>, <$.1^25, $.1^282>, <$.1^174, $.1^16>, <$.1^132, $.1^156>, <$.1^121, $.1^338>, <$.1^88, $.1^303>, <$.1^321, $.1^282>, <$.1^81, $.1^94>, <$.1^149, $.1^262>, <$.1^4, $.1^315>, <$.1^177, $.1^133>, <$.1^136, $.1^3>, <$.1^180, $.1^14>, <$.1^7, $.1^174>, <$.1^121, $.1^26>, <$.1^294, $.1^136>, <$.1^7, $.1^24>, <$.1^308, $.1^189>, <$.1^65, 0>, <$.1^218, $.1^23>, <$.1^132, 2>, <$.1^263, $.1^318>, <$.1^181, $.1^75>, <$.1^35, $.1^32>, <$.1^166, $.1^3>, <$.1^281, $.1^167>, <$.1^220, $.1^303>, <$.1^213, $.1^85>, <$.1, $.1^294>, <1, $.1^175>, <$.1^230, $.1^100>, <$.1^193, $.1^4>, <$.1^267, $.1^60>, <$.1^126, $.1^322>, <$.1^128, $.1^146>, <3, $.1^122>, <$.1^248, $.1^261>, <$.1^92, $.1^213>, <$.1^216, $.1^331>, <2, $.1^129>, <$.1^131, $.1^12>, <$.1^174, $.1^100>, <$.1^20, $.1^323>, <$.1^274, $.1^81>, <$.1^91, $.1^173>, <$.1^197, $.1^216>, <$.1^288, $.1^36>, <$.1^78, $.1^152>, <$.1^150, $.1^339>, <$.1^160, $.1^181>, <$.1^340, $.1^184>, <$.1^239, $.1^112>, <$.1^235, $.1^142>, <$.1^206, $.1^149>, <$.1^232, $.1^19>, <$.1^307, $.1^330>, <$.1, $.1^330>, <$.1^239, $.1^226>, <$.1^116, $.1^266>, <$.1^168, $.1^291>, <$.1^25, $.1^252>, <$.1^244, $.1^226>, <$.1^119, $.1^64>, <$.1^36, $.1^199>, <$.1^127, $.1^31>, <$.1^340, $.1^196>, <$.1^330, $.1^75>, <$.1^288, $.1^60>, <$.1^161, $.1^106>, <$.1^178, $.1^267>, <$.1^298, $.1^40>, <$.1^250, $.1^35>, <$.1^255, $.1^101>, <$.1^194, $.1^25>, <$.1^159, $.1^24>, <$.1^267, $.1^150>, <$.1^16, $.1^150>, <$.1^274, $.1^243>, <$.1^195, $.1^300>, <$.1^30, $.1^245>, <$.1^269, $.1^105>, <$.1^307, $.1^108>, <$.1^181, $.1^21>, <$.1^53, $.1^55>, <$.1^11, $.1^174>, <$.1^225, $.1^34>, <$.1^191, $.1^212>, <$.1^263, $.1^18>, <$.1^6, $.1^304>, <$.1^330, $.1^309>, <$.1^232, $.1^163>, <$.1^292, $.1^5>, <$.1^37, $.1^126>, <$.1^153, $.1^76>, <$.1^156, $.1^282>, <$.1^201, $.1^176>, <$.1^49, $.1^132>, <$.1^290, $.1^169>, <$.1^220, $.1^105>, <$.1^251, $.1^296>, <$.1^231, $.1^77>, <$.1^149, $.1^112>, <$.1^202, $.1^161>, <$.1^273, $.1^284>, <$.1^99, $.1^263>, <$.1^320, $.1^187>, <$.1^34, $.1^172>, <$.1^327, $.1^321>, <$.1^61, $.1^268>, <$.1^93, $.1^296>, <$.1^37, $.1^36>, <$.1^242, $.1^34>, <$.1^320, $.1>, <$.1^22, $.1^79>, <$.1^13, $.1^119>, <$.1^37, $.1^12>, <$.1^24, $.1^69>, <$.1^41, $.1^59>, <$.1^70, $.1^96>, <$.1^200, $.1^10>, <$.1^46, $.1^65>, <$.1^136, $.1^177>, <$.1^193, $.1^160>, <$.1^189, $.1^313>, <$.1^193, $.1^106>, <$.1^107, 0>, <$.1^216, $.1^193>, <$.1^267, $.1^192>, <$.1^249, $.1^257>, <$.1^262, $.1^320>, <$.1^23, $.1^118>, <6, $.1^22>, <$.1^183, $.1^203>, <$.1^207, $.1^10>, <$.1^260, $.1^332>, <$.1^308, $.1^219>, <$.1^145, $.1^124>, <$.1^106, $.1^127>, <$.1^189, $.1^271>, <$.1^138, $.1^245>, <$.1^84, $.1^266>, <$.1^45, $.1^262>, <$.1^235, $.1^304>, <$.1^245, $.1^194>, <$.1^257, $.1^41>, <$.1^24, $.1^249>, <$.1^100, $.1^330>, <$.1^136, $.1^183>, <$.1^62, $.1^99>, <$.1^315, $.1^52>, <$.1^62, $.1^177>, <$.1^242, $.1^82>, <$.1^127, $.1^193>, <$.1^155, $.1^85>, <$.1^158, $.1^167>, <$.1^9, $.1^5>, <$.1^194, $.1^127>, <$.1^42, $.1^268>, <$.1^140, $.1^227>, <$.1^45, $.1^298>, <$.1^196, $.1^213>, <$.1^224, $.1^268>, <$.1^145, $.1^226>, <$.1^3, $.1^259>, <$.1^52, $.1^19>, <$.1^224, $.1^46>, <$.1^23, $.1^196>, <$.1^239, $.1^304>, <$.1^12, $.1^8>, <$.1^325, $.1^22>, <$.1^47, $.1^80>, <$.1^185, $.1^87>, <$.1^169, $.1^7>, <$.1^120, $.1^330>, <$.1, $.1^138>, <$.1^329, $.1^140>, <$.1^55, $.1^23>, <$.1^201, $.1^296>, <$.1^271, $.1^243>, <$.1^58, $.1^103>, <$.1^99, $.1^203>, <$.1^188, $.1^247>, <$.1^144, $.1^85>, <$.1^338, $.1^246>, <$.1^150, $.1^147>, <$.1^58, $.1^97>, <$.1^208, $.1^207>, <$.1^196, $.1^297>, <$.1^315, $.1^106>, <$.1^173, $.1^183>, <$.1^53, $.1^73>, <2, $.1^33>, <$.1^47, $.1^20>, <$.1^185, $.1^213>, <$.1^20, $.1^287>, <$.1^29, $.1^265>, <$.1^259, $.1^330>, <$.1^30, $.1^191>, <$.1^34, $.1^244>, <$.1^144, $.1^13>, <$.1^180, $.1^146>, <$.1^325, $.1^142>, <$.1^150, $.1^249>, <$.1^271, $.1^339>, <$.1^159, 1>, <$.1^264, $.1^83>, <$.1^167, $.1^33>, <$.1^169, $.1^19>, <$.1^140, $.1^173>, <$.1^6, $.1^298>, <$.1^321, $.1^24>, <$.1^173, $.1^237>, <$.1^117, $.1^87>, <4, $.1^107>, <$.1^138, $.1^161>, <$.1^182, $.1^261>, <$.1^206, $.1^227>, <$.1^256, $.1^121>, <$.1^301, $.1^311>, <$.1^310, $.1^179>, <$.1^21, $.1^121>, <$.1^294, $.1^34>, <$.1^155, $.1^163>, <$.1^92, $.1^201>, <$.1^198, $.1^244>, <$.1^88, $.1^141>, <$.1^189, $.1^97>, <$.1^180, $.1^320>, <$.1^241, $.1^201>, <$.1^102, $.1^137>, <$.1^123, $.1^103>, <$.1^220, $.1^153>, <$.1^314, $.1^306>, <$.1^138, $.1^179>, <$.1^68, $.1^199>, <$.1^39, $.1^44>, <$.1^245, $.1^290>, <$.1^89, $.1^83>, <$.1^212, $.1^110>, <$.1^181, $.1^237>, <$.1^53, $.1^217>, <$.1^87, $.1^72>, <$.1^187, $.1^183>, <$.1^309, $.1^92>, <$.1^275, $.1^258>, <$.1^307, $.1^126>, <$.1^231, $.1^221>, <$.1^242, $.1^154>, <$.1^25, $.1^144>, <$.1^80, $.1^161>, <$.1^251, $.1^2>, <$.1^98, $.1^282>, <5, $.1^6>, <$.1^337, $.1^300>, <$.1^45, $.1^244>, <$.1^116, $.1^320>, <$.1^290, $.1^313>, <$.1^123, $.1^7>, <$.1^58, $.1^55>, <$.1^289, $.1^2>, <$.1^284, 0>, <$.1^248, $.1^177>, <$.1^241, $.1^267>, <$.1^218, $.1^263>, <$.1^134, $.1^187>, <$.1^207, $.1^130>, <$.1^20, $.1^263>, <$.1^44, $.1^255>, <6, $.1^322>, <$.1^220, $.1^129>, <6, $.1^82>, <$.1^101, $.1^10>, <$.1^226, $.1^230>, <$.1^145, $.1^136>, <$.1^178, $.1^237>, <$.1^261, $.1^21>, <$.1^241, $.1^273>, <$.1^2, $.1^300>, <$.1^192, $.1^76>, <$.1^260, $.1^98>, <$.1^41, $.1^311>, <$.1^313, $.1^230>, <$.1^339, $.1^270>, <$.1^299, $.1^71>, <$.1^178, $.1^189>, <$.1^156, $.1^60>, <$.1^223, $.1^298>, <$.1^102, $.1^47>, <$.1^308, $.1^99>, <$.1^82, $.1^97>, <$.1^326, $.1^268>, <$.1^21, $.1^241>, <$.1^148, $.1^174>, <$.1^78, $.1^146>, <1, $.1^133>, <$.1^240, $.1^288>, <$.1^229, $.1^196>, <$.1^34, $.1^46>, <$.1^39, $.1^8>, <$.1^177, $.1^139>, <$.1^89, $.1^131>, <$.1^178, $.1^3>, <$.1^80, $.1^71>, <$.1^117, $.1^327>, <$.1^246, $.1^200>, <$.1^137, $.1^216>, <$.1^205, $.1^217>, <$.1^112, $.1^66>, <$.1^317, $.1^159>, <$.1^297, $.1^73>, <$.1^309, $.1^74>, <$.1^86, $.1^50>, <$.1^294, $.1^76>, <$.1^259, $.1^6>, <$.1^302, $.1^333>, <$.1^339, $.1^120>, <$.1^100, $.1^312>, <$.1^86, $.1^200>, <$.1^242, $.1^172>, <$.1^257, $.1^209>, <$.1^337, $.1^324>, <$.1^260, $.1^152>, <$.1^116, $.1^290>, <$.1^43, $.1^95>, <$.1^31, $.1^2>, <$.1^326, $.1^40>, <$.1^93, $.1^326>, <$.1^319, $.1^189>, <$.1^43, $.1^173>, <$.1^261, $.1^33>, <$.1^287, $.1^107>, <$.1^142, $.1^245>, <$.1^43, $.1^185>, <$.1^185, $.1^69>, <$.1^132, $.1^234>, <$.1^326, $.1^304>, <$.1^197, $.1^252>, <$.1^21, $.1^127>, <$.1^9, $.1^281>, <$.1^147, $.1>, <$.1^100, $.1^186>, <$.1^110, $.1^290>, <$.1^290, $.1^43>, <$.1^255, $.1^191>, <$.1^328, $.1^226>, <$.1^253, $.1^124>, <$.1^70, $.1^252>, <$.1^268, $.1^267>, <$.1^71, $.1^157>, <$.1^185, $.1^45>, <$.1^174, $.1^304>, <$.1^16, $.1^270>, <$.1^47, $.1^188>, <$.1^109, $.1^218>, <$.1^258, $.1^243>, <$.1^187, $.1^147>, <$.1^281, $.1^173>, <1, $.1^127>, <$.1^81, $.1^64>, <$.1^314, $.1^222>, <$.1^85, $.1^148>, <$.1^235, $.1^190>, <$.1^143, $.1^279>, <$.1^25, $.1^324>, <$.1^157, $.1^295>, <$.1^202, $.1^89>, <$.1^75, $.1^239>, <$.1^59, $.1^13>, <$.1^151, $.1^128>, <$.1^313, $.1^170>, <$.1^118, $.1^323>, <$.1^22, $.1^85>, <$.1^206, $.1^65>, <$.1^169, $.1^187>, <$.1^296, $.1^41>, <$.1^255, $.1^155>, <$.1^224, $.1^226>, <$.1^339, $.1^264>, <$.1^64, $.1^175>, <$.1^121, $.1^128>, <$.1^24, $.1^147>, <$.1^199, $.1^294>, <$.1^216, $.1^295>, <$.1^177, $.1^127>, <$.1^282, $.1^59>, <$.1^187, $.1^3>, <$.1^309, $.1^152>, <$.1^119, $.1^46>, <$.1^281, $.1^323>, <$.1^148, $.1^216>, <$.1^67, $.1^313>, <$.1^326, $.1^100>, <$.1^334, $.1^125>, <$.1^151, $.1^302>, <$.1^296, $.1^107>, <$.1^117, $.1^105>, <$.1^287, $.1^11>, <$.1^218, $.1^167>, <$.1^286, $.1^125>, <$.1^216, $.1>, <$.1^211, $.1^134>, <$.1^143, $.1^99>, <$.1^338, $.1^48>, <$.1^261, $.1^297>, <$.1^27, $.1^31>, <$.1^39, $.1^320>, <$.1^315, $.1^112>, <$.1^281, $.1^329>, <$.1^254, $.1^217>, <$.1^238, $.1^280>, <$.1^132, $.1^54>, <$.1^25, $.1^186>, <$.1^331, ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 11:49:38 2004 Input: L:=Lattice("G",2); ?ThetaSeries 4 Output: Magma V2.10-6 Thu Mar 4 2004 11:49:34 on modular [Seed = 3317881796] ------------------------------------- 4 matches: 1 I /magma/combinatorial-geometrical-incidence/brandt-modules/\ qexpansions/ThetaSeries 2 I /magma/module-lattice/lattice/enumeration/minima-theta/ThetaSeries 3 I /magma/module-lattice/quadratic/invar/ThetaSeries 4 E /magma/module-lattice/lattice/enumeration/minima-theta/\ Example-ThetaSeries To view an entry, type ? followed by the number next to it Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 11:50:21 2004 Input: L:=Lattice("G",2); ?ThetaSeries; ?4 Output: Magma V2.10-6 Thu Mar 4 2004 11:50:18 on modular [Seed = 4126337952] ------------------------------------- 4 matches: 1 I /magma/combinatorial-geometrical-incidence/brandt-modules/\ qexpansions/ThetaSeries 2 I /magma/module-lattice/lattice/enumeration/minima-theta/ThetaSeries 3 I /magma/module-lattice/quadratic/invar/ThetaSeries 4 E /magma/module-lattice/lattice/enumeration/minima-theta/\ Example-ThetaSeries To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/module-lattice/lattice/enumeration/minima-theta/\ Example-ThetaSeries KIND: Example =============================================================================== We show how a lattice enumeration process can be used to compute the Theta series of a lattice. We write a simple function Theta which takes a lattice L and precision n and returns the Theta series of L up to the term q^n just as in the function ThetaSeries. The function assumes that the lattice L is integral. We simply loop over the non-zero vectors of norm up to n and count the number of vectors for each norm. > function Theta(L, n) > Z := IntegerRing(); > P := ShortVectorsProcess(L, n); > C := [1] cat [0: i in [1 .. n]]; > while not IsEmpty(P) do > v, norm := NextVector(P); > C[Z!norm + 1] +:= 2; > end while; > return PowerSeriesRing(IntegerRing()) ! C; > end function; We now compute the Theta series up to norm 10 of the Gosset lattice E_8 using the function Theta. We compare this Magma-language version with the builtin function ThetaSeries (which is much faster of course because of the lack of interpreter overhead etc.). > L := Lattice("E", 8); > time T := Theta(L, 10); Time: 2.210 > T; 1 + 240*q^2 + 2160*q^4 + 6720*q^6 + 17520*q^8 + 30240*q^10 + O(q^11) > time TT := ThetaSeries(L, 10); Time: 0.039 > TT; 1 + 240*q^2 + 2160*q^4 + 6720*q^6 + 17520*q^8 + 30240*q^10 + O(q^11) To run this example, type: load "H46E10"; (If you are in the Browser at the ??> prompt, type -D first.) =============================================================================== Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 11:52:41 2004 Input: L:=Lattice("G",2); function Theta(L, n) Z := IntegerRing(); P := ShortVectorsProcess(L, n); C := [1] cat [0: i in [1 .. n]]; while not IsEmpty(P) do v, norm := NextVector(P); C[Z!norm + 1] +:= 2; end while; return PowerSeriesRing(IntegerRing()) ! C; end function; L := Lattice("E", 8); T := Theta(L, 10); Output: Magma V2.10-6 Thu Mar 4 2004 11:52:37 on modular [Seed = 3974885926] ------------------------------------- Total time: 3.449 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 11:53:03 2004 Input: L:=Lattice("G",2); function Theta(L, n) Z := IntegerRing(); P := ShortVectorsProcess(L, n); C := [1] cat [0: i in [1 .. n]]; while not IsEmpty(P) do v, norm := NextVector(P); C[Z!norm + 1] +:= 2; end while; return PowerSeriesRing(IntegerRing()) ! C; end function; L := Lattice("E", 8); Theta(L, 10); Output: Magma V2.10-6 Thu Mar 4 2004 11:53:00 on modular [Seed = 3806723089] ------------------------------------- 1 + 240*$.1^2 + 2160*$.1^4 + 6720*$.1^6 + 17520*$.1^8 + 30240*$.1^10 Total time: 3.439 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 11:53:27 2004 Input: L:=Lattice("G",2); function Theta(L, n) Z := IntegerRing(); P := ShortVectorsProcess(L, n); C := [1] cat [0: i in [1 .. n]]; while not IsEmpty(P) do v, norm := NextVector(P); C[Z!norm + 1] +:= 2; end while; return PowerSeriesRing(IntegerRing()) ! C; end function; L := Lattice("G", 2); Theta(L, 10); Output: Magma V2.10-6 Thu Mar 4 2004 11:53:24 on modular [Seed = 639711490] ------------------------------------- 1 + 6*$.1^2 + 6*$.1^6 + 6*$.1^8 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 11:53:47 2004 Input: L:=Lattice("G",2); function Theta(L, n) Z := IntegerRing(); P := ShortVectorsProcess(L, n); C := [1] cat [0: i in [1 .. n]]; while not IsEmpty(P) do v, norm := NextVector(P); C[Z!norm + 1] +:= 2; end while; return PowerSeriesRing(IntegerRing()) ! C; end function; L := Lattice("G", 2); Theta(L, 20); Output: Magma V2.10-6 Thu Mar 4 2004 11:53:44 on modular [Seed = 791162903] ------------------------------------- 1 + 6*$.1^2 + 6*$.1^6 + 6*$.1^8 + 12*$.1^14 + 6*$.1^18 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 11:55:00 2004 Input: L:=Lattice("G",2); function Theta(L, n) Z := IntegerRing(); P := ShortVectorsProcess(L, n); C := [1] cat [0: i in [1 .. n]]; while not IsEmpty(P) do v, norm := NextVector(P); C[Z!norm + 1] +:= 2; end while; return PowerSeriesRing(IntegerRing()) ! C; end function; L := Lattice("D", 16); Theta(L, 20); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 4 2004 11:54:37 on modular [Seed = 960374356] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 24601 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 11:55:22 2004 Input: L:=Lattice("G",2); function Theta(L, n) Z := IntegerRing(); P := ShortVectorsProcess(L, n); C := [1] cat [0: i in [1 .. n]]; while not IsEmpty(P) do v, norm := NextVector(P); C[Z!norm + 1] +:= 2; end while; return PowerSeriesRing(IntegerRing()) ! C; end function; L := Lattice("D", 16); Theta(L, 6); Output: Magma V2.10-6 Thu Mar 4 2004 11:55:15 on modular [Seed = 100735317] ------------------------------------- 1 + 480*$.1^2 + 29152*$.1^4 + 525952*$.1^6 Total time: 7.239 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 11:56:22 2004 Input: L:=Lattice("G",2); function Theta(L, n) Z := IntegerRing(); P := ShortVectorsProcess(L, n); C := [1] cat [0: i in [1 .. n]]; while not IsEmpty(P) do v, norm := NextVector(P); C[Z!norm + 1] +:= 2; end while; return PowerSeriesRing(IntegerRing()) ! C; end function; L := Lattice("D", 4); Theta(L, 6); Output: Magma V2.10-6 Thu Mar 4 2004 11:56:19 on modular [Seed = 252186780] ------------------------------------- 1 + 24*$.1^2 + 24*$.1^4 + 96*$.1^6 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Thu Mar 4 11:56:58 2004 Input: polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; print expo; return expo; end function; polinomi_t (7,3); Output: Magma V2.10-6 Thu Mar 4 2004 11:56:55 on modular [Seed = 404686831] ------------------------------------- [ 49, 7, 1 ] [ 49, 7, 1 ] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 11:57:16 2004 Input: L:=Lattice("G",2); function Theta(L, n) Z := IntegerRing(); P := ShortVectorsProcess(L, n); C := [1] cat [0: i in [1 .. n]]; while not IsEmpty(P) do v, norm := NextVector(P); C[Z!norm + 1] +:= 2; end while; return PowerSeriesRing(IntegerRing()) ! C; end function; L := Lattice("D", 4); Theta(L, 14); Output: Magma V2.10-6 Thu Mar 4 2004 11:57:13 on modular [Seed = 1634107048] ------------------------------------- 1 + 24*$.1^2 + 24*$.1^4 + 96*$.1^6 + 24*$.1^8 + 144*$.1^10 + 96*$.1^12 + 192*$.1^14 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Thu Mar 4 11:57:30 2004 Input: polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; /*print expo;*/ return expo; end function; polinomi_t (7,3); Output: Magma V2.10-6 Thu Mar 4 2004 11:57:27 on modular [Seed = 1785558461] ------------------------------------- [ 49, 7, 1 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 11:57:54 2004 Input: L:=Lattice("G",2); function Theta(L, n) Z := IntegerRing(); P := ShortVectorsProcess(L, n); C := [1] cat [0: i in [1 .. n]]; while not IsEmpty(P) do v, norm := NextVector(P); C[Z!norm + 1] +:= 2; end while; return PowerSeriesRing(IntegerRing()) ! C; end function; L := Lattice("G", 2); Theta(L, 14); Output: Magma V2.10-6 Thu Mar 4 2004 11:57:51 on modular [Seed = 1937003356] ------------------------------------- 1 + 6*$.1^2 + 6*$.1^6 + 6*$.1^8 + 12*$.1^14 Total time: 3.099 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Thu Mar 4 11:59:11 2004 Input: R:= Integers (); P := PolynomialRing (R); polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_t2 (7,3); polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; polinomi_n (7,3); Output: Magma V2.10-6 Thu Mar 4 2004 11:59:08 on modular [Seed = 2088459264] ------------------------------------- >> polinomi_t2 (7,3); ^ Runtime error in procedure call: Number of arguments (2) does not equal expected number of arguments (1) >> polinomi_n (7,3);; ^ Runtime error in procedure call: Number of arguments (2) does not equal expected number of arguments (1) Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 11:59:47 2004 Input: L:=Lattice("G",2); function Theta(L, n) Z := IntegerRing(); P := ShortVectorsProcess(L, n); C := [1] cat [0: i in [1 .. n]]; while not IsEmpty(P) do v, norm := NextVector(P); C[Z!norm + 1] +:= 2; end while; return PowerSeriesRing(IntegerRing()) ! C; end function; L := Lattice("D", 4); Theta(L, 14); Output: Magma V2.10-6 Thu Mar 4 2004 11:59:44 on modular [Seed = 1178691302] ------------------------------------- 1 + 24*$.1^2 + 24*$.1^4 + 96*$.1^6 + 24*$.1^8 + 144*$.1^10 + 96*$.1^12 + 192*$.1^14 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Thu Mar 4 12:00:44 2004 Input: R:= Integers (); P := PolynomialRing (R); polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; polinomi_t (7,3); polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_t2 (7,3); polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; polinomi_n (7,3); Output: Magma V2.10-6 Thu Mar 4 2004 12:00:41 on modular [Seed = 1482651841] ------------------------------------- [ 49, 7, 1 ] >> polinomi_t2 (7,3); ^ Runtime error in procedure call: Number of arguments (2) does not equal expected number of arguments (1) >> polinomi_n (7,3);; ^ Runtime error in procedure call: Number of arguments (2) does not equal expected number of arguments (1) Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Thu Mar 4 12:01:29 2004 Input: R:= Integers (); P := PolynomialRing (R); polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; exponent := polinomi_t (7,3); polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_t2 (exponent); polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; polinomi_n (exponent); Output: Magma V2.10-6 Thu Mar 4 2004 12:01:26 on modular [Seed = 3014955893] ------------------------------------- x^49 + x^7 + x x^57 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Thu Mar 4 12:02:15 2004 Input: R:= Integers (); P := PolynomialRing (R); polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; exponent := polinomi_t (7,3); polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_t2 (exponent); polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; polinomi_n (exponent); Output: Magma V2.10-6 Thu Mar 4 2004 12:02:12 on modular [Seed = 3166412168] ------------------------------------- x^49 + x^7 + x x^57 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 12:04:07 2004 Input: function Theta(L, n) Z := IntegerRing(); P := ShortVectorsProcess(L, n); C := [1] cat [0: i in [1 .. n]]; while not IsEmpty(P) do v, norm := NextVector(P); C[Z!norm + 1] +:= 2; end while; return PowerSeriesRing(IntegerRing()) ! C; end function; L := Lattice("D", 4); Theta(L, 14); Output: Magma V2.10-6 Thu Mar 4 2004 12:04:04 on modular [Seed = 2239931425] ------------------------------------- 1 + 24*$.1^2 + 24*$.1^4 + 96*$.1^6 + 24*$.1^8 + 144*$.1^10 + 96*$.1^12 + 192*$.1^14 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 12:04:56 2004 Input: function Theta(L, n) Z := IntegerRing(); P := ShortVectorsProcess(L, n); C := [1] cat [0: i in [1 .. n]]; while not IsEmpty(P) do v, norm := NextVector(P); C[Z!norm + 1] +:= 2; end while; return PowerSeriesRing(IntegerRing()) ! C; end function; L := Lattice("D", 16); Theta(L, 14); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 4 2004 12:04:33 on modular [Seed = 2408099342] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 24751 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 12:05:13 2004 Input: function Theta(L, n) Z := IntegerRing(); P := ShortVectorsProcess(L, n); C := [1] cat [0: i in [1 .. n]]; while not IsEmpty(P) do v, norm := NextVector(P); C[Z!norm + 1] +:= 2; end while; return PowerSeriesRing(IntegerRing()) ! C; end function; L := Lattice("D", 16); Theta(L, 8); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 4 2004 12:04:50 on modular [Seed = 2459284224] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 24754 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 12:05:22 2004 Input: function Theta(L, n) Z := IntegerRing(); P := ShortVectorsProcess(L, n); C := [1] cat [0: i in [1 .. n]]; while not IsEmpty(P) do v, norm := NextVector(P); C[Z!norm + 1] +:= 2; end while; return PowerSeriesRing(IntegerRing()) ! C; end function; L := Lattice("D", 16); Theta(L, 8); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 4 2004 12:04:58 on modular [Seed = 2594028288] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 24762 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Thu Mar 4 12:06:47 2004 Input: R:= Integers (); P := PolynomialRing (R); polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; main := function (a,b) exponent := polinomi_t (a,b); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); return (pol_t, pol_n); end function; Output: Magma V2.10-6 Thu Mar 4 2004 12:06:44 on modular [Seed = 3974876904] ------------------------------------- Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 12:07:37 2004 Input: function Theta(L, n) Z := IntegerRing(); P := ShortVectorsProcess(L, n); C := [1] cat [0: i in [1 .. n]]; while not IsEmpty(P) do v, norm := NextVector(P); C[Z!norm + 1] +:= 2; end while; return PowerSeriesRing(IntegerRing()) ! C; end function; L := Lattice("D", 16); Theta(L, 6); Output: Magma V2.10-6 Thu Mar 4 2004 12:07:30 on modular [Seed = 4126332807] ------------------------------------- 1 + 480*$.1^2 + 29152*$.1^4 + 525952*$.1^6 Total time: 7.109 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Thu Mar 4 12:08:23 2004 Input: R:= Integers (); P := PolynomialRing (R); polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; main := function (a,b) exponent := polinomi_t (a,b); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); return (pol_t, pol_n); end function; main (7,3); Output: Magma V2.10-6 Thu Mar 4 2004 12:08:20 on modular [Seed = 4277787738] ------------------------------------- [
:31]( a: 7, b: 3 ) >> return (pol_t, pol_n); ^ Runtime error in elt< ... >: Bad arguments Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Thu Mar 4 12:08:56 2004 Input: R:= Integers (); P := PolynomialRing (R); polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; main := function (a,b) exponent := polinomi_t (a,b); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); return ; end function; main (7,3); Output: Magma V2.10-6 Thu Mar 4 2004 12:08:53 on modular [Seed = 3385781068] ------------------------------------- Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Thu Mar 4 12:09:58 2004 Input: R:= Integers (); P := PolynomialRing (R); polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; main := function (a,b) exponent := polinomi_t (a,b); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); return ; end function; main (7,3); Output: Magma V2.10-6 Thu Mar 4 2004 12:09:55 on modular [Seed = 3553947920] ------------------------------------- Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Thu Mar 4 12:10:36 2004 Input: R:= Integers (); P := PolynomialRing (R); polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; main := function (a,b) exponent := polinomi_t (a,b); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); return pol_t; return pol_n; end function; main (7,3); Output: Magma V2.10-6 Thu Mar 4 2004 12:10:33 on modular [Seed = 572850442] ------------------------------------- x^49 + x^7 + x Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Thu Mar 4 12:11:22 2004 Input: R:= Integers (); P := PolynomialRing (R); polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; main := function (a,b) exponent := polinomi_t (a,b); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); return ; end function; main (7,3); Output: Magma V2.10-6 Thu Mar 4 2004 12:11:19 on modular [Seed = 757730875] ------------------------------------- >> return ; ^ User error: bad syntax >> end function; ^ User error: bad syntax >> main (7,3); ^ User error: Identifier 'main' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Thu Mar 4 12:12:55 2004 Input: R:= Integers (); P := PolynomialRing (R); polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; main := function (a,b) exponent := polinomi_t (a,b); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); /*return ;*/ print pol_t; print pol_n; end function; main (7,3); Output: Magma V2.10-6 Thu Mar 4 2004 12:12:52 on modular [Seed = 17179316] ------------------------------------- x^49 + x^7 + x x^57 >> main (7,3); ^ Runtime error in procedure call: No return statement executed in user-defined function Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Thu Mar 4 12:15:11 2004 Input: polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; exponent := polinomi_t (7,3); R:= Integers (); P := PolynomialRing (R); polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; pol_t := polinomi_t2 (exponent); polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; pol_n:= polinomi_n (exponent); PuntsOlav := { : a in GF (7,3) , b in GF (7,3) | Evaluate (pol_t,a) eq Evaluate (pol_n,b)}; PuntsOlav; Output: Magma V2.10-6 Thu Mar 4 2004 12:15:04 on modular [Seed = 1953714253] ------------------------------------- { <$.1^205, $.1^175>, <$.1^172, 3>, <1, $.1^7>, <$.1^85, $.1^58>, <$.1^23, $.1^112>, <$.1^36, $.1^295>, <$.1^110, $.1^68>, <$.1^301, $.1^95>, <$.1^310, $.1^65>, <$.1^111, $.1^140>, <$.1^88, $.1^177>, <$.1^198, $.1^4>, <$.1^281, $.1^317>, <$.1^131, $.1^174>, <$.1^330, $.1^255>, <$.1^83, $.1^184>, <$.1^145, $.1^214>, <$.1^154, $.1^181>, <$.1^172, $.1^237>, <$.1^264, $.1^23>, <$.1^150, $.1^129>, <$.1^103, $.1^168>, <$.1^83, $.1^256>, <$.1^7, $.1^126>, <$.1^198, $.1^286>, <$.1^66, $.1^180>, <$.1^67, $.1^193>, <$.1^41, $.1^41>, <$.1^193, $.1^208>, <$.1^17, $.1^340>, <$.1^97, $.1^132>, <$.1^195, $.1^282>, <$.1^91, $.1^335>, <$.1^296, $.1^335>, <$.1^80, $.1^119>, <$.1^237, $.1^327>, <$.1^160, $.1^223>, <$.1^96, $.1^99>, <$.1^302, $.1^273>, <$.1^88, 5>, <$.1^139, $.1^62>, <$.1^150, $.1^63>, <$.1^149, $.1^40>, <$.1^316, $.1^169>, <$.1^252, $.1^151>, <$.1^255, $.1^53>, <$.1^42, $.1^112>, <$.1^176, $.1^251>, <$.1^226, $.1^38>, <$.1^124, $.1^182>, <$.1^34, $.1^322>, <$.1^327, $.1^39>, <$.1^161, $.1^340>, <$.1^135, $.1^51>, <$.1^28, $.1^21>, <$.1^332, $.1^73>, <$.1^187, $.1^21>, <$.1^311, $.1^62>, <$.1^102, $.1^131>, <$.1^319, $.1^3>, <$.1^314, $.1^246>, <$.1^44, $.1^69>, <$.1^100, 4>, <$.1^267, $.1^168>, <$.1^224, $.1^280>, <$.1^315, $.1^82>, <$.1^292, $.1^137>, <$.1^200, $.1^280>, <$.1^176, $.1^155>, <$.1^18, $.1^160>, <$.1^121, $.1^230>, <$.1^147, $.1^217>, <$.1^62, $.1^129>, <$.1^318, $.1^88>, <$.1^235, $.1^244>, <$.1^294, $.1^52>, <$.1^270, $.1^92>, <$.1^309, $.1^284>, <$.1^232, $.1^187>, <$.1^67, $.1^103>, <$.1^325, $.1^214>, <$.1^69, $.1^315>, <$.1^24, $.1^303>, <$.1^145, $.1^130>, <$.1^309, $.1^224>, <$.1^46, $.1^83>, <$.1^272, $.1^277>, <$.1^303, $.1^225>, <$.1^311, $.1^2>, <$.1^183, $.1^125>, <$.1^17, $.1^130>, <2, $.1^165>, <$.1^207, $.1^76>, <$.1^318, $.1^208>, <$.1^40, $.1^11>, <$.1^200, $.1^166>, <$.1^119, $.1^244>, <$.1^3, $.1^319>, <3, $.1^38>, <$.1^251, $.1^152>, <$.1^25, $.1^282>, <$.1^174, $.1^16>, <$.1^132, $.1^156>, <$.1^121, $.1^338>, <$.1^88, $.1^303>, <$.1^321, $.1^282>, <$.1^81, $.1^94>, <$.1^149, $.1^262>, <$.1^4, $.1^315>, <$.1^177, $.1^133>, <$.1^136, $.1^3>, <$.1^180, $.1^14>, <$.1^7, $.1^174>, <$.1^121, $.1^26>, <$.1^294, $.1^136>, <$.1^7, $.1^24>, <$.1^308, $.1^189>, <$.1^65, 0>, <$.1^218, $.1^23>, <$.1^132, 2>, <$.1^263, $.1^318>, <$.1^181, $.1^75>, <$.1^35, $.1^32>, <$.1^166, $.1^3>, <$.1^281, $.1^167>, <$.1^220, $.1^303>, <$.1^213, $.1^85>, <$.1, $.1^294>, <1, $.1^175>, <$.1^230, $.1^100>, <$.1^193, $.1^4>, <$.1^267, $.1^60>, <$.1^126, $.1^322>, <$.1^128, $.1^146>, <3, $.1^122>, <$.1^248, $.1^261>, <$.1^92, $.1^213>, <$.1^216, $.1^331>, <2, $.1^129>, <$.1^131, $.1^12>, <$.1^174, $.1^100>, <$.1^20, $.1^323>, <$.1^274, $.1^81>, <$.1^91, $.1^173>, <$.1^197, $.1^216>, <$.1^288, $.1^36>, <$.1^78, $.1^152>, <$.1^150, $.1^339>, <$.1^160, $.1^181>, <$.1^340, $.1^184>, <$.1^239, $.1^112>, <$.1^235, $.1^142>, <$.1^206, $.1^149>, <$.1^232, $.1^19>, <$.1^307, $.1^330>, <$.1, $.1^330>, <$.1^239, $.1^226>, <$.1^116, $.1^266>, <$.1^168, $.1^291>, <$.1^25, $.1^252>, <$.1^244, $.1^226>, <$.1^119, $.1^64>, <$.1^36, $.1^199>, <$.1^127, $.1^31>, <$.1^340, $.1^196>, <$.1^330, $.1^75>, <$.1^288, $.1^60>, <$.1^161, $.1^106>, <$.1^178, $.1^267>, <$.1^298, $.1^40>, <$.1^250, $.1^35>, <$.1^255, $.1^101>, <$.1^194, $.1^25>, <$.1^159, $.1^24>, <$.1^267, $.1^150>, <$.1^16, $.1^150>, <$.1^274, $.1^243>, <$.1^195, $.1^300>, <$.1^30, $.1^245>, <$.1^269, $.1^105>, <$.1^307, $.1^108>, <$.1^181, $.1^21>, <$.1^53, $.1^55>, <$.1^11, $.1^174>, <$.1^225, $.1^34>, <$.1^191, $.1^212>, <$.1^263, $.1^18>, <$.1^6, $.1^304>, <$.1^330, $.1^309>, <$.1^232, $.1^163>, <$.1^292, $.1^5>, <$.1^37, $.1^126>, <$.1^153, $.1^76>, <$.1^156, $.1^282>, <$.1^201, $.1^176>, <$.1^49, $.1^132>, <$.1^290, $.1^169>, <$.1^220, $.1^105>, <$.1^251, $.1^296>, <$.1^231, $.1^77>, <$.1^149, $.1^112>, <$.1^202, $.1^161>, <$.1^273, $.1^284>, <$.1^99, $.1^263>, <$.1^320, $.1^187>, <$.1^34, $.1^172>, <$.1^327, $.1^321>, <$.1^61, $.1^268>, <$.1^93, $.1^296>, <$.1^37, $.1^36>, <$.1^242, $.1^34>, <$.1^320, $.1>, <$.1^22, $.1^79>, <$.1^13, $.1^119>, <$.1^37, $.1^12>, <$.1^24, $.1^69>, <$.1^41, $.1^59>, <$.1^70, $.1^96>, <$.1^200, $.1^10>, <$.1^46, $.1^65>, <$.1^136, $.1^177>, <$.1^193, $.1^160>, <$.1^189, $.1^313>, <$.1^193, $.1^106>, <$.1^107, 0>, <$.1^216, $.1^193>, <$.1^267, $.1^192>, <$.1^249, $.1^257>, <$.1^262, $.1^320>, <$.1^23, $.1^118>, <6, $.1^22>, <$.1^183, $.1^203>, <$.1^207, $.1^10>, <$.1^260, $.1^332>, <$.1^308, $.1^219>, <$.1^145, $.1^124>, <$.1^106, $.1^127>, <$.1^189, $.1^271>, <$.1^138, $.1^245>, <$.1^84, $.1^266>, <$.1^45, $.1^262>, <$.1^235, $.1^304>, <$.1^245, $.1^194>, <$.1^257, $.1^41>, <$.1^24, $.1^249>, <$.1^100, $.1^330>, <$.1^136, $.1^183>, <$.1^62, $.1^99>, <$.1^315, $.1^52>, <$.1^62, $.1^177>, <$.1^242, $.1^82>, <$.1^127, $.1^193>, <$.1^155, $.1^85>, <$.1^158, $.1^167>, <$.1^9, $.1^5>, <$.1^194, $.1^127>, <$.1^42, $.1^268>, <$.1^140, $.1^227>, <$.1^45, $.1^298>, <$.1^196, $.1^213>, <$.1^224, $.1^268>, <$.1^145, $.1^226>, <$.1^3, $.1^259>, <$.1^52, $.1^19>, <$.1^224, $.1^46>, <$.1^23, $.1^196>, <$.1^239, $.1^304>, <$.1^12, $.1^8>, <$.1^325, $.1^22>, <$.1^47, $.1^80>, <$.1^185, $.1^87>, <$.1^169, $.1^7>, <$.1^120, $.1^330>, <$.1, $.1^138>, <$.1^329, $.1^140>, <$.1^55, $.1^23>, <$.1^201, $.1^296>, <$.1^271, $.1^243>, <$.1^58, $.1^103>, <$.1^99, $.1^203>, <$.1^188, $.1^247>, <$.1^144, $.1^85>, <$.1^338, $.1^246>, <$.1^150, $.1^147>, <$.1^58, $.1^97>, <$.1^208, $.1^207>, <$.1^196, $.1^297>, <$.1^315, $.1^106>, <$.1^173, $.1^183>, <$.1^53, $.1^73>, <2, $.1^33>, <$.1^47, $.1^20>, <$.1^185, $.1^213>, <$.1^20, $.1^287>, <$.1^29, $.1^265>, <$.1^259, $.1^330>, <$.1^30, $.1^191>, <$.1^34, $.1^244>, <$.1^144, $.1^13>, <$.1^180, $.1^146>, <$.1^325, $.1^142>, <$.1^150, $.1^249>, <$.1^271, $.1^339>, <$.1^159, 1>, <$.1^264, $.1^83>, <$.1^167, $.1^33>, <$.1^169, $.1^19>, <$.1^140, $.1^173>, <$.1^6, $.1^298>, <$.1^321, $.1^24>, <$.1^173, $.1^237>, <$.1^117, $.1^87>, <4, $.1^107>, <$.1^138, $.1^161>, <$.1^182, $.1^261>, <$.1^206, $.1^227>, <$.1^256, $.1^121>, <$.1^301, $.1^311>, <$.1^310, $.1^179>, <$.1^21, $.1^121>, <$.1^294, $.1^34>, <$.1^155, $.1^163>, <$.1^92, $.1^201>, <$.1^198, $.1^244>, <$.1^88, $.1^141>, <$.1^189, $.1^97>, <$.1^180, $.1^320>, <$.1^241, $.1^201>, <$.1^102, $.1^137>, <$.1^123, $.1^103>, <$.1^220, $.1^153>, <$.1^314, $.1^306>, <$.1^138, $.1^179>, <$.1^68, $.1^199>, <$.1^39, $.1^44>, <$.1^245, $.1^290>, <$.1^89, $.1^83>, <$.1^212, $.1^110>, <$.1^181, $.1^237>, <$.1^53, $.1^217>, <$.1^87, $.1^72>, <$.1^187, $.1^183>, <$.1^309, $.1^92>, <$.1^275, $.1^258>, <$.1^307, $.1^126>, <$.1^231, $.1^221>, <$.1^242, $.1^154>, <$.1^25, $.1^144>, <$.1^80, $.1^161>, <$.1^251, $.1^2>, <$.1^98, $.1^282>, <5, $.1^6>, <$.1^337, $.1^300>, <$.1^45, $.1^244>, <$.1^116, $.1^320>, <$.1^290, $.1^313>, <$.1^123, $.1^7>, <$.1^58, $.1^55>, <$.1^289, $.1^2>, <$.1^284, 0>, <$.1^248, $.1^177>, <$.1^241, $.1^267>, <$.1^218, $.1^263>, <$.1^134, $.1^187>, <$.1^207, $.1^130>, <$.1^20, $.1^263>, <$.1^44, $.1^255>, <6, $.1^322>, <$.1^220, $.1^129>, <6, $.1^82>, <$.1^101, $.1^10>, <$.1^226, $.1^230>, <$.1^145, $.1^136>, <$.1^178, $.1^237>, <$.1^261, $.1^21>, <$.1^241, $.1^273>, <$.1^2, $.1^300>, <$.1^192, $.1^76>, <$.1^260, $.1^98>, <$.1^41, $.1^311>, <$.1^313, $.1^230>, <$.1^339, $.1^270>, <$.1^299, $.1^71>, <$.1^178, $.1^189>, <$.1^156, $.1^60>, <$.1^223, $.1^298>, <$.1^102, $.1^47>, <$.1^308, $.1^99>, <$.1^82, $.1^97>, <$.1^326, $.1^268>, <$.1^21, $.1^241>, <$.1^148, $.1^174>, <$.1^78, $.1^146>, <1, $.1^133>, <$.1^240, $.1^288>, <$.1^229, $.1^196>, <$.1^34, $.1^46>, <$.1^39, $.1^8>, <$.1^177, $.1^139>, <$.1^89, $.1^131>, <$.1^178, $.1^3>, <$.1^80, $.1^71>, <$.1^117, $.1^327>, <$.1^246, $.1^200>, <$.1^137, $.1^216>, <$.1^205, $.1^217>, <$.1^112, $.1^66>, <$.1^317, $.1^159>, <$.1^297, $.1^73>, <$.1^309, $.1^74>, <$.1^86, $.1^50>, <$.1^294, $.1^76>, <$.1^259, $.1^6>, <$.1^302, $.1^333>, <$.1^339, $.1^120>, <$.1^100, $.1^312>, <$.1^86, $.1^200>, <$.1^242, $.1^172>, <$.1^257, $.1^209>, <$.1^337, $.1^324>, <$.1^260, $.1^152>, <$.1^116, $.1^290>, <$.1^43, $.1^95>, <$.1^31, $.1^2>, <$.1^326, $.1^40>, <$.1^93, $.1^326>, <$.1^319, $.1^189>, <$.1^43, $.1^173>, <$.1^261, $.1^33>, <$.1^287, $.1^107>, <$.1^142, $.1^245>, <$.1^43, $.1^185>, <$.1^185, $.1^69>, <$.1^132, $.1^234>, <$.1^326, $.1^304>, <$.1^197, $.1^252>, <$.1^21, $.1^127>, <$.1^9, $.1^281>, <$.1^147, $.1>, <$.1^100, $.1^186>, <$.1^110, $.1^290>, <$.1^290, $.1^43>, <$.1^255, $.1^191>, <$.1^328, $.1^226>, <$.1^253, $.1^124>, <$.1^70, $.1^252>, <$.1^268, $.1^267>, <$.1^71, $.1^157>, <$.1^185, $.1^45>, <$.1^174, $.1^304>, <$.1^16, $.1^270>, <$.1^47, $.1^188>, <$.1^109, $.1^218>, <$.1^258, $.1^243>, <$.1^187, $.1^147>, <$.1^281, $.1^173>, <1, $.1^127>, <$.1^81, $.1^64>, <$.1^314, $.1^222>, <$.1^85, $.1^148>, <$.1^235, $.1^190>, <$.1^143, $.1^279>, <$.1^25, $.1^324>, <$.1^157, $.1^295>, <$.1^202, $.1^89>, <$.1^75, $.1^239>, <$.1^59, $.1^13>, <$.1^151, $.1^128>, <$.1^313, $.1^170>, <$.1^118, $.1^323>, <$.1^22, $.1^85>, <$.1^206, $.1^65>, <$.1^169, $.1^187>, <$.1^296, $.1^41>, <$.1^255, $.1^155>, <$.1^224, $.1^226>, <$.1^339, $.1^264>, <$.1^64, $.1^175>, <$.1^121, $.1^128>, <$.1^24, $.1^147>, <$.1^199, $.1^294>, <$.1^216, $.1^295>, <$.1^177, $.1^127>, <$.1^282, $.1^59>, <$.1^187, $.1^3>, <$.1^309, $.1^152>, <$.1^119, $.1^46>, <$.1^281, $.1^323>, <$.1^148, $.1^216>, <$.1^67, $.1^313>, <$.1^326, $.1^100>, <$.1^334, $.1^125>, <$.1^151, $.1^302>, <$.1^296, $.1^107>, <$.1^117, $.1^105>, <$.1^287, $.1^11>, <$.1^218, $.1^167>, <$.1^286, $.1^125>, <$.1^216, $.1>, <$.1^211, $.1^134>, <$.1^143, $.1^99>, <$.1^338, $.1^48>, <$.1^261, $.1^297>, <$.1^27, $.1^31>, <$.1^39, $.1^320>, <$.1^315, $.1^112>, <$.1^281, $.1^329>, <$.1^254, $.1^217>, <$.1^238, $.1^280>, <$.1^132, $.1^54>, <$.1^25, $.1^186>, <$.1^331, ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 12:16:35 2004 Input: L := Lattice("D", 16); ?Theta Output: Magma V2.10-6 Thu Mar 4 2004 12:16:32 on modular [Seed = 4025011134] ------------------------------------- 8 matches: 1 S /magma/module-lattice/lattice/enumeration/minima-theta 2 I /magma/combinatorial-geometrical-incidence/brandt-modules/\ qexpansions/ThetaSeries 3 I /magma/combinatorial-geometrical-incidence/modular-symbol/\ operators/ThetaOperator 4 I /magma/module-lattice/lattice/enumeration/minima-theta/ThetaSeries 5 I /magma/module-lattice/quadratic/invar/ThetaSeries 6 I /magma/ring-field-algebra/real-complex/elliptic-modular/\ jacobi-dedekind/JacobiTheta 7 I /magma/ring-field-algebra/real-complex/elliptic-modular/\ jacobi-dedekind/JacobiTheta 8 I /magma/ring-field-algebra/real-complex/elliptic-modular/\ jacobi-dedekind/JacobiThetaNullK To view an entry, type ? followed by the number next to it Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 12:17:08 2004 Input: L := Lattice("D", 16); ?Theta; ?5 Output: Magma V2.10-6 Thu Mar 4 2004 12:17:05 on modular [Seed = 4143043142] ------------------------------------- 8 matches: 1 S /magma/module-lattice/lattice/enumeration/minima-theta 2 I /magma/combinatorial-geometrical-incidence/brandt-modules/\ qexpansions/ThetaSeries 3 I /magma/combinatorial-geometrical-incidence/modular-symbol/\ operators/ThetaOperator 4 I /magma/module-lattice/lattice/enumeration/minima-theta/ThetaSeries 5 I /magma/module-lattice/quadratic/invar/ThetaSeries 6 I /magma/ring-field-algebra/real-complex/elliptic-modular/\ jacobi-dedekind/JacobiTheta 7 I /magma/ring-field-algebra/real-complex/elliptic-modular/\ jacobi-dedekind/JacobiTheta 8 I /magma/ring-field-algebra/real-complex/elliptic-modular/\ jacobi-dedekind/JacobiThetaNullK To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/module-lattice/quadratic/invar/ThetaSeries KIND: Intrinsic =============================================================================== ThetaSeries(f, n) : QuadBinElt, RngIntElt -> RngSerElt The integral theta series of the binary quadratic form f to precision n. =============================================================================== Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 12:17:39 2004 Input: L := Lattice("D", 16); ?Theta; ?1 Output: Magma V2.10-6 Thu Mar 4 2004 12:17:36 on modular [Seed = 3251037520] ------------------------------------- 8 matches: 1 S /magma/module-lattice/lattice/enumeration/minima-theta 2 I /magma/combinatorial-geometrical-incidence/brandt-modules/\ qexpansions/ThetaSeries 3 I /magma/combinatorial-geometrical-incidence/modular-symbol/\ operators/ThetaOperator 4 I /magma/module-lattice/lattice/enumeration/minima-theta/ThetaSeries 5 I /magma/module-lattice/quadratic/invar/ThetaSeries 6 I /magma/ring-field-algebra/real-complex/elliptic-modular/\ jacobi-dedekind/JacobiTheta 7 I /magma/ring-field-algebra/real-complex/elliptic-modular/\ jacobi-dedekind/JacobiTheta 8 I /magma/ring-field-algebra/real-complex/elliptic-modular/\ jacobi-dedekind/JacobiThetaNullK To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/module-lattice/lattice/enumeration/minima-theta KIND: Section =============================================================================== Successive Minima and Theta Series. Intrinsics: [+1] SuccessiveMinima [+2] ThetaSeries Examples: [+3] Example-ThetaSeries =============================================================================== Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 12:18:47 2004 Input: L := Lattice("D", 16); ?ThetaSeries; Output: Magma V2.10-6 Thu Mar 4 2004 12:18:44 on modular [Seed = 3369069597] ------------------------------------- 4 matches: 1 I /magma/combinatorial-geometrical-incidence/brandt-modules/\ qexpansions/ThetaSeries 2 I /magma/module-lattice/lattice/enumeration/minima-theta/ThetaSeries 3 I /magma/module-lattice/quadratic/invar/ThetaSeries 4 E /magma/module-lattice/lattice/enumeration/minima-theta/\ Example-ThetaSeries To view an entry, type ? followed by the number next to it Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 12:19:01 2004 Input: L := Lattice("D", 16); ?ThetaSeries; ?4? Output: Magma V2.10-6 Thu Mar 4 2004 12:18:58 on modular [Seed = 3553949424] ------------------------------------- 4 matches: 1 I /magma/combinatorial-geometrical-incidence/brandt-modules/\ qexpansions/ThetaSeries 2 I /magma/module-lattice/lattice/enumeration/minima-theta/ThetaSeries 3 I /magma/module-lattice/quadratic/invar/ThetaSeries 4 E /magma/module-lattice/lattice/enumeration/minima-theta/\ Example-ThetaSeries To view an entry, type ? followed by the number next to it No references for word "4?" Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 12:19:07 2004 Input: L := Lattice("D", 16); ?ThetaSeries; ?4? Output: Magma V2.10-6 Thu Mar 4 2004 12:19:03 on modular [Seed = 3671982076] ------------------------------------- 4 matches: 1 I /magma/combinatorial-geometrical-incidence/brandt-modules/\ qexpansions/ThetaSeries 2 I /magma/module-lattice/lattice/enumeration/minima-theta/ThetaSeries 3 I /magma/module-lattice/quadratic/invar/ThetaSeries 4 E /magma/module-lattice/lattice/enumeration/minima-theta/\ Example-ThetaSeries To view an entry, type ? followed by the number next to it No references for word "4?" Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 12:19:19 2004 Input: L := Lattice("D", 16); ?ThetaSeries; ?4; Output: Magma V2.10-6 Thu Mar 4 2004 12:19:16 on modular [Seed = 639697680] ------------------------------------- 4 matches: 1 I /magma/combinatorial-geometrical-incidence/brandt-modules/\ qexpansions/ThetaSeries 2 I /magma/module-lattice/lattice/enumeration/minima-theta/ThetaSeries 3 I /magma/module-lattice/quadratic/invar/ThetaSeries 4 E /magma/module-lattice/lattice/enumeration/minima-theta/\ Example-ThetaSeries To view an entry, type ? followed by the number next to it No references for word "4;" Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 12:19:32 2004 Input: L := Lattice("D", 16); ?ThetaSeries; ?4 Output: Magma V2.10-6 Thu Mar 4 2004 12:19:29 on modular [Seed = 791153196] ------------------------------------- 4 matches: 1 I /magma/combinatorial-geometrical-incidence/brandt-modules/\ qexpansions/ThetaSeries 2 I /magma/module-lattice/lattice/enumeration/minima-theta/ThetaSeries 3 I /magma/module-lattice/quadratic/invar/ThetaSeries 4 E /magma/module-lattice/lattice/enumeration/minima-theta/\ Example-ThetaSeries To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/module-lattice/lattice/enumeration/minima-theta/\ Example-ThetaSeries KIND: Example =============================================================================== We show how a lattice enumeration process can be used to compute the Theta series of a lattice. We write a simple function Theta which takes a lattice L and precision n and returns the Theta series of L up to the term q^n just as in the function ThetaSeries. The function assumes that the lattice L is integral. We simply loop over the non-zero vectors of norm up to n and count the number of vectors for each norm. > function Theta(L, n) > Z := IntegerRing(); > P := ShortVectorsProcess(L, n); > C := [1] cat [0: i in [1 .. n]]; > while not IsEmpty(P) do > v, norm := NextVector(P); > C[Z!norm + 1] +:= 2; > end while; > return PowerSeriesRing(IntegerRing()) ! C; > end function; We now compute the Theta series up to norm 10 of the Gosset lattice E_8 using the function Theta. We compare this Magma-language version with the builtin function ThetaSeries (which is much faster of course because of the lack of interpreter overhead etc.). > L := Lattice("E", 8); > time T := Theta(L, 10); Time: 2.210 > T; 1 + 240*q^2 + 2160*q^4 + 6720*q^6 + 17520*q^8 + 30240*q^10 + O(q^11) > time TT := ThetaSeries(L, 10); Time: 0.039 > TT; 1 + 240*q^2 + 2160*q^4 + 6720*q^6 + 17520*q^8 + 30240*q^10 + O(q^11) To run this example, type: load "H46E10"; (If you are in the Browser at the ??> prompt, type -D first.) =============================================================================== Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Thu Mar 4 12:20:40 2004 Input: R:= Integers (); P := PolynomialRing (R); polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; main := function (a,b) exponent := polinomi_t (a,b); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); PuntsOlav := { : a in GF (a,b) , b in GF (a,b) | Evaluate (pol_t,c) eq Evaluate (pol_n,d)}; return (PuntsOlav); end function; Output: Magma V2.10-6 Thu Mar 4 2004 12:20:37 on modular [Seed = 1010506107] ------------------------------------- >> PuntsOlav := { : a in GF (a,b) , b in GF (a,b) | Evaluate (pol_t,c) ^ User error: Identifier 'c' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 12:22:21 2004 Input: function Theta(L, n) Z := IntegerRing(); P := ShortVectorsProcess(L, n); C := [1] cat [0: i in [1 .. n]]; while not IsEmpty(P) do v, norm := NextVector(P); C[Z!norm + 1] +:= 2; end while; return PowerSeriesRing(IntegerRing()) ! C; end function; L := Lattice("E", 8); time T := Theta(L, 10); T; Output: Magma V2.10-6 Thu Mar 4 2004 12:22:18 on modular [Seed = 168636386] ------------------------------------- Time: 0.520 1 + 240*q^2 + 2160*q^4 + 6720*q^6 + 17520*q^8 + 30240*q^10 Total time: 3.499 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 12:22:54 2004 Input: function Theta(L, n) Z := IntegerRing(); P := ShortVectorsProcess(L, n); C := [1] cat [0: i in [1 .. n]]; while not IsEmpty(P) do v, norm := NextVector(P); C[Z!norm + 1] +:= 2; end while; return PowerSeriesRing(IntegerRing()) ! C; end function; L := Lattice("E", 8); T := Theta(L, 10); T; Output: Magma V2.10-6 Thu Mar 4 2004 12:22:51 on modular [Seed = 471546325] ------------------------------------- 1 + 240*q^2 + 2160*q^4 + 6720*q^6 + 17520*q^8 + 30240*q^10 Total time: 3.439 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 12:23:34 2004 Input: function Theta(L, n) Z := IntegerRing(); P := ShortVectorsProcess(L, n); C := [1] cat [0: i in [1 .. n]]; while not IsEmpty(P) do v, norm := NextVector(P); C[Z!norm + 1] +:= 2; end while; return PowerSeriesRing(IntegerRing()) ! C; end function; L := Lattice("D", 16); T := Theta(L, 10); T; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 4 2004 12:23:11 on modular [Seed = 1700937912] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 25159 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 12:24:02 2004 Input: function Theta(L, n) Z := IntegerRing(); P := ShortVectorsProcess(L, n); C := [1] cat [0: i in [1 .. n]]; while not IsEmpty(P) do v, norm := NextVector(P); C[Z!norm + 1] +:= 2; end while; return PowerSeriesRing(IntegerRing()) ! C; end function; L := Lattice("D", 16); T := Theta(L, 10); T; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 4 2004 12:23:39 on modular [Seed = 1920291915] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 25168 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 12:24:15 2004 Input: function Theta(L, n) Z := IntegerRing(); P := ShortVectorsProcess(L, n); C := [1] cat [0: i in [1 .. n]]; while not IsEmpty(P) do v, norm := NextVector(P); C[Z!norm + 1] +:= 2; end while; return PowerSeriesRing(IntegerRing()) ! C; end function; L := Lattice("D", 4); T := Theta(L, 10); T; Output: Magma V2.10-6 Thu Mar 4 2004 12:24:12 on modular [Seed = 2071747941] ------------------------------------- 1 + 24*q^2 + 24*q^4 + 96*q^6 + 24*q^8 + 144*q^10 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Thu Mar 4 12:24:22 2004 Input: R:= Integers (); P := PolynomialRing (R); polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; main := function (a,b) exponent := polinomi_t (a,b); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); PuntsOlav := { : c in GF (a,b) , d in GF (a,b) | Evaluate (pol_t,c) eq Evaluate (pol_n,d)}; return (PuntsOlav); end function; Output: Magma V2.10-6 Thu Mar 4 2004 12:24:19 on modular [Seed = 1078421025] ------------------------------------- Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 12:24:37 2004 Input: function Theta(L, n) Z := IntegerRing(); P := ShortVectorsProcess(L, n); C := [1] cat [0: i in [1 .. n]]; while not IsEmpty(P) do v, norm := NextVector(P); C[Z!norm + 1] +:= 2; end while; return PowerSeriesRing(IntegerRing()) ! C; end function; L := Lattice("G", 2); T := Theta(L, 10); T; Output: Magma V2.10-6 Thu Mar 4 2004 12:24:34 on modular [Seed = 1330145599] ------------------------------------- 1 + 6*q^2 + 6*q^6 + 6*q^8 Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Thu Mar 4 12:24:47 2004 Input: R:= Integers (); P := PolynomialRing (R); polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; main := function (a,b) exponent := polinomi_t (a,b); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); PuntsOlav := { : c in GF (a,b) , d in GF (a,b) | Evaluate (pol_t,c) eq Evaluate (pol_n,d)}; return (PuntsOlav); end function; main (7,3); Output: Magma V2.10-6 Thu Mar 4 2004 12:24:40 on modular [Seed = 1414754862] ------------------------------------- { <$.1^205, $.1^175>, <$.1^172, 3>, <1, $.1^7>, <$.1^85, $.1^58>, <$.1^23, $.1^112>, <$.1^36, $.1^295>, <$.1^110, $.1^68>, <$.1^301, $.1^95>, <$.1^310, $.1^65>, <$.1^111, $.1^140>, <$.1^88, $.1^177>, <$.1^198, $.1^4>, <$.1^281, $.1^317>, <$.1^131, $.1^174>, <$.1^330, $.1^255>, <$.1^83, $.1^184>, <$.1^145, $.1^214>, <$.1^154, $.1^181>, <$.1^172, $.1^237>, <$.1^264, $.1^23>, <$.1^150, $.1^129>, <$.1^103, $.1^168>, <$.1^83, $.1^256>, <$.1^7, $.1^126>, <$.1^198, $.1^286>, <$.1^66, $.1^180>, <$.1^67, $.1^193>, <$.1^41, $.1^41>, <$.1^193, $.1^208>, <$.1^17, $.1^340>, <$.1^97, $.1^132>, <$.1^195, $.1^282>, <$.1^91, $.1^335>, <$.1^296, $.1^335>, <$.1^80, $.1^119>, <$.1^237, $.1^327>, <$.1^160, $.1^223>, <$.1^96, $.1^99>, <$.1^302, $.1^273>, <$.1^88, 5>, <$.1^139, $.1^62>, <$.1^150, $.1^63>, <$.1^149, $.1^40>, <$.1^316, $.1^169>, <$.1^252, $.1^151>, <$.1^255, $.1^53>, <$.1^42, $.1^112>, <$.1^176, $.1^251>, <$.1^226, $.1^38>, <$.1^124, $.1^182>, <$.1^34, $.1^322>, <$.1^327, $.1^39>, <$.1^161, $.1^340>, <$.1^135, $.1^51>, <$.1^28, $.1^21>, <$.1^332, $.1^73>, <$.1^187, $.1^21>, <$.1^311, $.1^62>, <$.1^102, $.1^131>, <$.1^319, $.1^3>, <$.1^314, $.1^246>, <$.1^44, $.1^69>, <$.1^100, 4>, <$.1^267, $.1^168>, <$.1^224, $.1^280>, <$.1^315, $.1^82>, <$.1^292, $.1^137>, <$.1^200, $.1^280>, <$.1^176, $.1^155>, <$.1^18, $.1^160>, <$.1^121, $.1^230>, <$.1^147, $.1^217>, <$.1^62, $.1^129>, <$.1^318, $.1^88>, <$.1^235, $.1^244>, <$.1^294, $.1^52>, <$.1^270, $.1^92>, <$.1^309, $.1^284>, <$.1^232, $.1^187>, <$.1^67, $.1^103>, <$.1^325, $.1^214>, <$.1^69, $.1^315>, <$.1^24, $.1^303>, <$.1^145, $.1^130>, <$.1^309, $.1^224>, <$.1^46, $.1^83>, <$.1^272, $.1^277>, <$.1^303, $.1^225>, <$.1^311, $.1^2>, <$.1^183, $.1^125>, <$.1^17, $.1^130>, <2, $.1^165>, <$.1^207, $.1^76>, <$.1^318, $.1^208>, <$.1^40, $.1^11>, <$.1^200, $.1^166>, <$.1^119, $.1^244>, <$.1^3, $.1^319>, <3, $.1^38>, <$.1^251, $.1^152>, <$.1^25, $.1^282>, <$.1^174, $.1^16>, <$.1^132, $.1^156>, <$.1^121, $.1^338>, <$.1^88, $.1^303>, <$.1^321, $.1^282>, <$.1^81, $.1^94>, <$.1^149, $.1^262>, <$.1^4, $.1^315>, <$.1^177, $.1^133>, <$.1^136, $.1^3>, <$.1^180, $.1^14>, <$.1^7, $.1^174>, <$.1^121, $.1^26>, <$.1^294, $.1^136>, <$.1^7, $.1^24>, <$.1^308, $.1^189>, <$.1^65, 0>, <$.1^218, $.1^23>, <$.1^132, 2>, <$.1^263, $.1^318>, <$.1^181, $.1^75>, <$.1^35, $.1^32>, <$.1^166, $.1^3>, <$.1^281, $.1^167>, <$.1^220, $.1^303>, <$.1^213, $.1^85>, <$.1, $.1^294>, <1, $.1^175>, <$.1^230, $.1^100>, <$.1^193, $.1^4>, <$.1^267, $.1^60>, <$.1^126, $.1^322>, <$.1^128, $.1^146>, <3, $.1^122>, <$.1^248, $.1^261>, <$.1^92, $.1^213>, <$.1^216, $.1^331>, <2, $.1^129>, <$.1^131, $.1^12>, <$.1^174, $.1^100>, <$.1^20, $.1^323>, <$.1^274, $.1^81>, <$.1^91, $.1^173>, <$.1^197, $.1^216>, <$.1^288, $.1^36>, <$.1^78, $.1^152>, <$.1^150, $.1^339>, <$.1^160, $.1^181>, <$.1^340, $.1^184>, <$.1^239, $.1^112>, <$.1^235, $.1^142>, <$.1^206, $.1^149>, <$.1^232, $.1^19>, <$.1^307, $.1^330>, <$.1, $.1^330>, <$.1^239, $.1^226>, <$.1^116, $.1^266>, <$.1^168, $.1^291>, <$.1^25, $.1^252>, <$.1^244, $.1^226>, <$.1^119, $.1^64>, <$.1^36, $.1^199>, <$.1^127, $.1^31>, <$.1^340, $.1^196>, <$.1^330, $.1^75>, <$.1^288, $.1^60>, <$.1^161, $.1^106>, <$.1^178, $.1^267>, <$.1^298, $.1^40>, <$.1^250, $.1^35>, <$.1^255, $.1^101>, <$.1^194, $.1^25>, <$.1^159, $.1^24>, <$.1^267, $.1^150>, <$.1^16, $.1^150>, <$.1^274, $.1^243>, <$.1^195, $.1^300>, <$.1^30, $.1^245>, <$.1^269, $.1^105>, <$.1^307, $.1^108>, <$.1^181, $.1^21>, <$.1^53, $.1^55>, <$.1^11, $.1^174>, <$.1^225, $.1^34>, <$.1^191, $.1^212>, <$.1^263, $.1^18>, <$.1^6, $.1^304>, <$.1^330, $.1^309>, <$.1^232, $.1^163>, <$.1^292, $.1^5>, <$.1^37, $.1^126>, <$.1^153, $.1^76>, <$.1^156, $.1^282>, <$.1^201, $.1^176>, <$.1^49, $.1^132>, <$.1^290, $.1^169>, <$.1^220, $.1^105>, <$.1^251, $.1^296>, <$.1^231, $.1^77>, <$.1^149, $.1^112>, <$.1^202, $.1^161>, <$.1^273, $.1^284>, <$.1^99, $.1^263>, <$.1^320, $.1^187>, <$.1^34, $.1^172>, <$.1^327, $.1^321>, <$.1^61, $.1^268>, <$.1^93, $.1^296>, <$.1^37, $.1^36>, <$.1^242, $.1^34>, <$.1^320, $.1>, <$.1^22, $.1^79>, <$.1^13, $.1^119>, <$.1^37, $.1^12>, <$.1^24, $.1^69>, <$.1^41, $.1^59>, <$.1^70, $.1^96>, <$.1^200, $.1^10>, <$.1^46, $.1^65>, <$.1^136, $.1^177>, <$.1^193, $.1^160>, <$.1^189, $.1^313>, <$.1^193, $.1^106>, <$.1^107, 0>, <$.1^216, $.1^193>, <$.1^267, $.1^192>, <$.1^249, $.1^257>, <$.1^262, $.1^320>, <$.1^23, $.1^118>, <6, $.1^22>, <$.1^183, $.1^203>, <$.1^207, $.1^10>, <$.1^260, $.1^332>, <$.1^308, $.1^219>, <$.1^145, $.1^124>, <$.1^106, $.1^127>, <$.1^189, $.1^271>, <$.1^138, $.1^245>, <$.1^84, $.1^266>, <$.1^45, $.1^262>, <$.1^235, $.1^304>, <$.1^245, $.1^194>, <$.1^257, $.1^41>, <$.1^24, $.1^249>, <$.1^100, $.1^330>, <$.1^136, $.1^183>, <$.1^62, $.1^99>, <$.1^315, $.1^52>, <$.1^62, $.1^177>, <$.1^242, $.1^82>, <$.1^127, $.1^193>, <$.1^155, $.1^85>, <$.1^158, $.1^167>, <$.1^9, $.1^5>, <$.1^194, $.1^127>, <$.1^42, $.1^268>, <$.1^140, $.1^227>, <$.1^45, $.1^298>, <$.1^196, $.1^213>, <$.1^224, $.1^268>, <$.1^145, $.1^226>, <$.1^3, $.1^259>, <$.1^52, $.1^19>, <$.1^224, $.1^46>, <$.1^23, $.1^196>, <$.1^239, $.1^304>, <$.1^12, $.1^8>, <$.1^325, $.1^22>, <$.1^47, $.1^80>, <$.1^185, $.1^87>, <$.1^169, $.1^7>, <$.1^120, $.1^330>, <$.1, $.1^138>, <$.1^329, $.1^140>, <$.1^55, $.1^23>, <$.1^201, $.1^296>, <$.1^271, $.1^243>, <$.1^58, $.1^103>, <$.1^99, $.1^203>, <$.1^188, $.1^247>, <$.1^144, $.1^85>, <$.1^338, $.1^246>, <$.1^150, $.1^147>, <$.1^58, $.1^97>, <$.1^208, $.1^207>, <$.1^196, $.1^297>, <$.1^315, $.1^106>, <$.1^173, $.1^183>, <$.1^53, $.1^73>, <2, $.1^33>, <$.1^47, $.1^20>, <$.1^185, $.1^213>, <$.1^20, $.1^287>, <$.1^29, $.1^265>, <$.1^259, $.1^330>, <$.1^30, $.1^191>, <$.1^34, $.1^244>, <$.1^144, $.1^13>, <$.1^180, $.1^146>, <$.1^325, $.1^142>, <$.1^150, $.1^249>, <$.1^271, $.1^339>, <$.1^159, 1>, <$.1^264, $.1^83>, <$.1^167, $.1^33>, <$.1^169, $.1^19>, <$.1^140, $.1^173>, <$.1^6, $.1^298>, <$.1^321, $.1^24>, <$.1^173, $.1^237>, <$.1^117, $.1^87>, <4, $.1^107>, <$.1^138, $.1^161>, <$.1^182, $.1^261>, <$.1^206, $.1^227>, <$.1^256, $.1^121>, <$.1^301, $.1^311>, <$.1^310, $.1^179>, <$.1^21, $.1^121>, <$.1^294, $.1^34>, <$.1^155, $.1^163>, <$.1^92, $.1^201>, <$.1^198, $.1^244>, <$.1^88, $.1^141>, <$.1^189, $.1^97>, <$.1^180, $.1^320>, <$.1^241, $.1^201>, <$.1^102, $.1^137>, <$.1^123, $.1^103>, <$.1^220, $.1^153>, <$.1^314, $.1^306>, <$.1^138, $.1^179>, <$.1^68, $.1^199>, <$.1^39, $.1^44>, <$.1^245, $.1^290>, <$.1^89, $.1^83>, <$.1^212, $.1^110>, <$.1^181, $.1^237>, <$.1^53, $.1^217>, <$.1^87, $.1^72>, <$.1^187, $.1^183>, <$.1^309, $.1^92>, <$.1^275, $.1^258>, <$.1^307, $.1^126>, <$.1^231, $.1^221>, <$.1^242, $.1^154>, <$.1^25, $.1^144>, <$.1^80, $.1^161>, <$.1^251, $.1^2>, <$.1^98, $.1^282>, <5, $.1^6>, <$.1^337, $.1^300>, <$.1^45, $.1^244>, <$.1^116, $.1^320>, <$.1^290, $.1^313>, <$.1^123, $.1^7>, <$.1^58, $.1^55>, <$.1^289, $.1^2>, <$.1^284, 0>, <$.1^248, $.1^177>, <$.1^241, $.1^267>, <$.1^218, $.1^263>, <$.1^134, $.1^187>, <$.1^207, $.1^130>, <$.1^20, $.1^263>, <$.1^44, $.1^255>, <6, $.1^322>, <$.1^220, $.1^129>, <6, $.1^82>, <$.1^101, $.1^10>, <$.1^226, $.1^230>, <$.1^145, $.1^136>, <$.1^178, $.1^237>, <$.1^261, $.1^21>, <$.1^241, $.1^273>, <$.1^2, $.1^300>, <$.1^192, $.1^76>, <$.1^260, $.1^98>, <$.1^41, $.1^311>, <$.1^313, $.1^230>, <$.1^339, $.1^270>, <$.1^299, $.1^71>, <$.1^178, $.1^189>, <$.1^156, $.1^60>, <$.1^223, $.1^298>, <$.1^102, $.1^47>, <$.1^308, $.1^99>, <$.1^82, $.1^97>, <$.1^326, $.1^268>, <$.1^21, $.1^241>, <$.1^148, $.1^174>, <$.1^78, $.1^146>, <1, $.1^133>, <$.1^240, $.1^288>, <$.1^229, $.1^196>, <$.1^34, $.1^46>, <$.1^39, $.1^8>, <$.1^177, $.1^139>, <$.1^89, $.1^131>, <$.1^178, $.1^3>, <$.1^80, $.1^71>, <$.1^117, $.1^327>, <$.1^246, $.1^200>, <$.1^137, $.1^216>, <$.1^205, $.1^217>, <$.1^112, $.1^66>, <$.1^317, $.1^159>, <$.1^297, $.1^73>, <$.1^309, $.1^74>, <$.1^86, $.1^50>, <$.1^294, $.1^76>, <$.1^259, $.1^6>, <$.1^302, $.1^333>, <$.1^339, $.1^120>, <$.1^100, $.1^312>, <$.1^86, $.1^200>, <$.1^242, $.1^172>, <$.1^257, $.1^209>, <$.1^337, $.1^324>, <$.1^260, $.1^152>, <$.1^116, $.1^290>, <$.1^43, $.1^95>, <$.1^31, $.1^2>, <$.1^326, $.1^40>, <$.1^93, $.1^326>, <$.1^319, $.1^189>, <$.1^43, $.1^173>, <$.1^261, $.1^33>, <$.1^287, $.1^107>, <$.1^142, $.1^245>, <$.1^43, $.1^185>, <$.1^185, $.1^69>, <$.1^132, $.1^234>, <$.1^326, $.1^304>, <$.1^197, $.1^252>, <$.1^21, $.1^127>, <$.1^9, $.1^281>, <$.1^147, $.1>, <$.1^100, $.1^186>, <$.1^110, $.1^290>, <$.1^290, $.1^43>, <$.1^255, $.1^191>, <$.1^328, $.1^226>, <$.1^253, $.1^124>, <$.1^70, $.1^252>, <$.1^268, $.1^267>, <$.1^71, $.1^157>, <$.1^185, $.1^45>, <$.1^174, $.1^304>, <$.1^16, $.1^270>, <$.1^47, $.1^188>, <$.1^109, $.1^218>, <$.1^258, $.1^243>, <$.1^187, $.1^147>, <$.1^281, $.1^173>, <1, $.1^127>, <$.1^81, $.1^64>, <$.1^314, $.1^222>, <$.1^85, $.1^148>, <$.1^235, $.1^190>, <$.1^143, $.1^279>, <$.1^25, $.1^324>, <$.1^157, $.1^295>, <$.1^202, $.1^89>, <$.1^75, $.1^239>, <$.1^59, $.1^13>, <$.1^151, $.1^128>, <$.1^313, $.1^170>, <$.1^118, $.1^323>, <$.1^22, $.1^85>, <$.1^206, $.1^65>, <$.1^169, $.1^187>, <$.1^296, $.1^41>, <$.1^255, $.1^155>, <$.1^224, $.1^226>, <$.1^339, $.1^264>, <$.1^64, $.1^175>, <$.1^121, $.1^128>, <$.1^24, $.1^147>, <$.1^199, $.1^294>, <$.1^216, $.1^295>, <$.1^177, $.1^127>, <$.1^282, $.1^59>, <$.1^187, $.1^3>, <$.1^309, $.1^152>, <$.1^119, $.1^46>, <$.1^281, $.1^323>, <$.1^148, $.1^216>, <$.1^67, $.1^313>, <$.1^326, $.1^100>, <$.1^334, $.1^125>, <$.1^151, $.1^302>, <$.1^296, $.1^107>, <$.1^117, $.1^105>, <$.1^287, $.1^11>, <$.1^218, $.1^167>, <$.1^286, $.1^125>, <$.1^216, $.1>, <$.1^211, $.1^134>, <$.1^143, $.1^99>, <$.1^338, $.1^48>, <$.1^261, $.1^297>, <$.1^27, $.1^31>, <$.1^39, $.1^320>, <$.1^315, $.1^112>, <$.1^281, $.1^329>, <$.1^254, $.1^217>, <$.1^238, $.1^280>, <$.1^132, $.1^54>, <$.1^25, $.1^186>, <$.1^331, ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 12:25:07 2004 Input: function Theta(L, n) Z := Ring(); P := ShortVectorsProcess(L, n); C := [1] cat [0: i in [1 .. n]]; while not IsEmpty(P) do v, norm := NextVector(P); C[Z!norm + 1] +:= 2; end while; return PowerSeriesRing(Ring()) ! C; end function; L := Lattice("G", 2); T := Theta(L, 10); T; Output: Magma V2.10-6 Thu Mar 4 2004 12:25:04 on modular [Seed = 2712045555] ------------------------------------- Theta( L: Lattice of rank 2 and degree 3, n: 10 ) >> Z := Ring(); ^ Runtime error in 'Ring': Bad argument types Argument types given: >> T;; ^ User error: Identifier 'T' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 12:25:32 2004 Input: function Theta(L, n) Z := ModularRing(); P := ShortVectorsProcess(L, n); C := [1] cat [0: i in [1 .. n]]; while not IsEmpty(P) do v, norm := NextVector(P); C[Z!norm + 1] +:= 2; end while; return PowerSeriesRing(ModularRing()) ! C; end function; L := Lattice("G", 2); T := Theta(L, 10); T; Output: Magma V2.10-6 Thu Mar 4 2004 12:25:29 on modular [Seed = 2930345989] ------------------------------------- >> Z := ModularRing(); ^ User error: Identifier 'ModularRing' has not been declared or assigned >> T := Theta(L, 10); ^ User error: Identifier 'Theta' has not been declared or assigned >> T;; ^ User error: Identifier 'T' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 12:26:09 2004 Input: function Theta(L, n) Z := IntegerRing(); P := ShortVectorsProcess(L, n); C := [1] cat [0: i in [1 .. n]]; while not IsEmpty(P) do v, norm := NextVector(P); C[Z!norm + 1] +:= 2; end while; return PowerSeriesRing(IntegerRing()) ! C; end function; L := Lattice("G", 2); T := Theta(L, 10); T; Output: Magma V2.10-6 Thu Mar 4 2004 12:26:06 on modular [Seed = 3081802043] ------------------------------------- 1 + 6*q^2 + 6*q^6 + 6*q^8 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 12:26:26 2004 Input: function Theta(L, n) Z := IntegerRing(); P := ShortVectorsProcess(L, n); C := [1] cat [0: i in [1 .. n]]; while not IsEmpty(P) do v, norm := NextVector(P); C[Z!norm + 1] +:= 2; end while; return PowerSeriesRing(IntegerRing()) ! C; end function; L := Lattice("G", 2); T := Theta(L, 10); T; ?ring Output: Magma V2.10-6 Thu Mar 4 2004 12:26:22 on modular [Seed = 3166411296] ------------------------------------- 1 + 6*q^2 + 6*q^6 + 6*q^8 174 matches: 1 O /magma/ring-field-algebra 2 S /magma/group/character/creation/creation-class-function-ring 3 S /magma/group/character/ring 4 S /magma/group/matrix/creation-general-linear-group/change-ring 5 S /magma/module-lattice/general/homomorphisms/endomorphism-ring 6 S /magma/module-lattice/general/K[G]-module/polynomial-ring-action 7 S /magma/module-lattice/general/operation/changing-ring 8 S /magma/module-lattice/general/operation/changing-ring 9 S /magma/module-lattice/general/operation/changing-ring 10 S /magma/module-lattice/general/operation/\ modification-coefficient-ring 11 S /magma/module-lattice/lattice/lattice-properties/base-ring 12 S /magma/module-lattice/mat/change-ring 13 S /magma/module-lattice/smat/change-ring 14 S /magma/ring-field-algebra/algebraic-field/ideal/quotient-ring 15 S /magma/ring-field-algebra/distributive-multivariate-polynomial/\ operation/change-ring 16 S /magma/ring-field-algebra/finitely-presented/creation/ring-monoid 17 S /magma/ring-field-algebra/galois-ring 18 S /magma/ring-field-algebra/grp_alg/ops/change-ring 19 S /magma/ring-field-algebra/ideal-groebner/change-ring 20 S /magma/ring-field-algebra/invariant-ring 21 S /magma/ring-field-algebra/invariant-ring/invariant-ring 22 S /magma/ring-field-algebra/lie_alg/operation/change-ring 23 S /magma/ring-field-algebra/matrix/change-ring 24 S /magma/ring-field-algebra/univariate-polynomial/operation/\ change-ring 25 I /magma/combinatorial-geometrical-incidence/brandt-modules/\ ModBrdt:brandt-modules/Elementary-Invariants/BaseRing 26 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-change_ring/ChangeRing 27 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ operations_curve/operations_curve-category/BaseRing 28 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ pointset/pointset-category/Ring 29 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ subgroup_schemes/subgroup_schemes-category/BaseRing 30 I /magma/combinatorial-geometrical-incidence/hyperelliptic-curve/\ creation/base_change_curve/ChangeRing 31 I /magma/combinatorial-geometrical-incidence/hyperelliptic-curve/\ jacobian/base_ring_jacobian/BaseField 32 I /magma/combinatorial-geometrical-incidence/hyperelliptic-curve/\ kummer-surfaces/base_ring_kummer/BaseField 33 I /magma/combinatorial-geometrical-incidence/hyperelliptic-curve/\ structure_operations/base_ring_curve/BaseField 34 I /magma/combinatorial-geometrical-incidence/modular-symbol/\ hecke-algebra/HeckeEigenvalueRing 35 I /magma/geometry/algebraic-curve/ambients/CoordinateRing 36 I /magma/geometry/algebraic-curve/curves/curves-attributes/BaseRing 37 I /magma/geometry/algebraic-curve/curves/curves-attributes/\ CoordinateRing 38 I /magma/geometry/modular-forms/predicates/IsRingOfAllModularForms 39 I /magma/geometry/schemes/schemes-ambient/\ schemes-ambient-functions/CoordinateRing 40 I /magma/geometry/schemes/schemes-basic/equations/CoordinateRing 41 I /magma/geometry/schemes/schemes-basic/schemes-basic-ambient/\ BaseRing 42 I /magma/geometry/schemes/schemes-basic/schemes-basic-ambient/\ CoefficientRing 43 I /magma/geometry/schemes/schemes-points/Ring 44 I /magma/geometry/schemes/schemes-points/RingMap 45 I /magma/geometry/supersingular-divisors-on-module-curves/\ properties/BaseRing 46 I /magma/group/character/creation/creation-class-function-ring/\ ClassFunctionSpace 47 I /magma/group/cohomology/structure-invar/Ring 48 I /magma/group/groups-lie-type/operations/BaseRing 49 I /magma/group/GrpPSL2/Congruence-subgroups/predicates-GrpPsl2/\ BaseRing 50 I /magma/group/matrix/creation-general-linear-group/change-ring/\ ChangeRing 51 I /magma/group/matrix/creation-general-linear-group/change-ring/\ ChangeRing 52 I /magma/group/matrix/properties/access/CoefficientRing 53 I /magma/group/root-data/operators-root-dtm/BaseRing 54 I /magma/lie-theory/root-systems/operators-root-sys/BaseField 55 I /magma/module-lattice/dedekind-modules/elementary-functions/\ BaseRing 56 I /magma/module-lattice/general/access/access-vector-space/\ CoefficientRing 57 I /magma/module-lattice/general/access/CoefficientRing 58 I /magma/module-lattice/general/operation/changing-ring/ChangeRing 59 I /magma/module-lattice/general/operation/changing-ring/ChangeRing 60 I /magma/module-lattice/general/operation/changing-ring/ChangeRing 61 I /magma/module-lattice/general/operation/changing-ring/ChangeRing 62 I /magma/module-lattice/general/operation/\ modification-coefficient-ring/ChangeRing 63 I /magma/module-lattice/general/operation/\ modification-coefficient-ring/ChangeRing 64 I /magma/module-lattice/lattice/G-lattices/endo-hom/\ CentreOfEndomorphismRing 65 I /magma/module-lattice/lattice/G-lattices/endo-hom/\ DimensionOfCentreOfEndomorphismRing 66 I /magma/module-lattice/lattice/G-lattices/endo-hom/\ DimensionOfEndomorphismRing 67 I /magma/module-lattice/lattice/G-lattices/endo-hom/EndomorphismRing 68 I /magma/module-lattice/lattice/lattice-properties/base-ring/\ BaseRing 69 I /magma/module-lattice/lattice/lattice-properties/base-ring/\ ChangeRing 70 I /magma/module-lattice/lattice/lattice-properties/base-ring/\ CoordinateRing 71 I /magma/module-lattice/mat/access/BaseRing 72 I /magma/module-lattice/mat/change-ring/ChangeRing 73 I /magma/module-lattice/modules-affine-algebras/access/\ CoefficientRing 74 I /magma/module-lattice/smat/access/invariants/BaseRing 75 I /magma/module-lattice/smat/change-ring/ChangeRing 76 I /magma/ring-field-algebra/abelian-extension/creation/\ ray-class-group/RayResidueRing 77 I /magma/ring-field-algebra/abelian-extension/invariants/BaseRing 78 I /magma/ring-field-algebra/abelian-extension/invariants/BaseRing 79 I /magma/ring-field-algebra/affine-algebra/operations/\ CoefficientRing 80 I /magma/ring-field-algebra/affine-algebra/operations/OriginalRing 81 I /magma/ring-field-algebra/affine-algebra/operations/PreimageRing 82 I /magma/ring-field-algebra/alg_quat/algebra-attributes/BaseField 83 I /magma/ring-field-algebra/alg_quat/order-attributes/BaseRing 84 I /magma/ring-field-algebra/algebraic-field/creation/homomorphism/\ IsRingHomomorphism 85 I /magma/ring-field-algebra/algebraic-field/creation/order/\ MaximalOrder 86 I /magma/ring-field-algebra/algebraic-field/creation/orders_ideals/\ MultiplicatorRing 87 I /magma/ring-field-algebra/algebraic-field/operation/Boolean/\ IsPrincipalIdealRing 88 I /magma/ring-field-algebra/algebraic-field/operation/Boolean/\ IsPrincipalIdealRing 89 I /magma/ring-field-algebra/algebraic-field/operation/related/\ BaseRing 90 I /magma/ring-field-algebra/algebraic-field/operation/related/\ LocalRing 91 I /magma/ring-field-algebra/algebraically-closed-field/absolute/\ AbsoluteAffineAlgebra 92 I /magma/ring-field-algebra/algebraically-closed-field/property/\ AffineAlgebra 93 I /magma/ring-field-algebra/basic/algebras/access/BaseRing 94 I /magma/ring-field-algebra/basic/cohomology/\ CohomologyRingGenerators 95 I /magma/ring-field-algebra/detail/generic/predicate/IsDivisionRing 96 I /magma/ring-field-algebra/detail/generic/predicate/IsEuclideanRing 97 I /magma/ring-field-algebra/detail/generic/predicate/\ IsMagmaEuclideanRing 98 I /magma/ring-field-algebra/detail/generic/predicate/IsPIR 99 I /magma/ring-field-algebra/detail/generic/related/PrimeRing 100 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ operation/change-ring/ChangeRing 101 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ operation/generic/BaseRing 102 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ rings/creation/PolynomialRing 103 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ rings/creation/PolynomialRing 104 I /magma/ring-field-algebra/finitely-presented/creation/\ ring-monoid/CoefficientRing 105 I /magma/ring-field-algebra/function-field/class-fields/structures/\ RayResidueRing 106 I /magma/ring-field-algebra/function-field/class-fields/witt-rings/\ BaseRing 107 I /magma/ring-field-algebra/function-field/class-fields/witt-rings/\ LocalRing 108 I /magma/ring-field-algebra/function-field/class-fields/witt-rings/\ WittRing 109 I /magma/ring-field-algebra/function-field/creation/orders_ideals/\ MultiplicatorRing 110 I /magma/ring-field-algebra/function-field/hom/IsRingHomomorphism ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 12:26:49 2004 Input: function Theta(L, n) Z := IntegerRing(); P := ShortVectorsProcess(L, n); C := [1] cat [0: i in [1 .. n]]; while not IsEmpty(P) do v, norm := NextVector(P); C[Z!norm + 1] +:= 2; end while; return PowerSeriesRing(IntegerRing()) ! C; end function; L := Lattice("G", 2); T := Theta(L, 10); T; ?lattice Output: Magma V2.10-6 Thu Mar 4 2004 12:26:46 on modular [Seed = 2239931249] ------------------------------------- 1 + 6*q^2 + 6*q^6 + 6*q^8 72 matches: 1 O /magma/module-lattice 2 S /magma/group/braid/braid-groups-elements/braid-groups-lattice 3 S /magma/group/braid/braid-groups-introduction/\ braid-groups-introduction-lattice 4 S /magma/module-lattice/general/submodule-lattice 5 S /magma/module-lattice/general/submodule-lattice/lattice-element 6 S /magma/module-lattice/general/submodule-lattice/lattice-element 7 S /magma/module-lattice/lattice 8 S /magma/module-lattice/lattice/lattice-properties 9 S /magma/module-lattice/lattice/lattice-properties/\ lattice-attributes 10 S /magma/module-lattice/lattice/lattice-properties/\ lattice-predicates 11 S /magma/ring-field-algebra/algebraic-field/subfields/\ subfield-lattice 12 I /magma/combinatorial-geometrical-incidence/graph/\ group-code-design/constr-misc/SquareLatticeGraph 13 I /magma/combinatorial-geometrical-incidence/modular-symbol/\ l-series/winding/WindingLattice 14 I /magma/combinatorial-geometrical-incidence/modular-symbol/\ underlying-representation/Lattice 15 I /magma/combinatorial-geometrical-incidence/tableaux-chap/words/\ ordered-monoid/IsReverseLatticeWord 16 I /magma/group/databases-overview/quatgps/Lattice 17 I /magma/group/databases-overview/quatgps/Lattice 18 I /magma/group/databases-overview/ratgps/Lattice 19 I /magma/group/databases-overview/ratgps/Lattice 20 I /magma/group/fiurg/action/weights/WeightLattice 21 I /magma/group/fiurg/action/weights/WeightLattice 22 I /magma/group/group-overview/\ characteristic-subgroup-normal-structure/subgroup-series/\ NormalLattice 23 I /magma/group/group-overview/subgroup/subgroup-poset/creation/\ SubgroupLattice 24 I /magma/group/groups-lie-type/operations/WeightLattice 25 I /magma/group/groups-lie-type/operations/WeightLattice 26 I /magma/group/permutation/\ characteristic-subgroup-normal-structure/normal-subgroups/\ NormalLattice 27 I /magma/group/root-data/roots-coroots-weights/weights/\ CoweightLattice 28 I /magma/group/root-data/roots-coroots-weights/weights/WeightLattice 29 I /magma/group/soluble/normal-series/normals/NormalLattice 30 I /magma/group/soluble/subgroups/subgroup-classes/SubgroupLattice 31 I /magma/lie-theory/finite-coxeter-groups/root-data-roots/weights/\ WeightLattice 32 I /magma/lie-theory/finite-coxeter-groups/root-data-roots/weights/\ WeightLattice 33 I /magma/module-lattice/general/submodule-lattice/create/\ SubmoduleLattice 34 I /magma/module-lattice/general/submodule-lattice/create/\ SubmoduleLatticeAbort 35 I /magma/module-lattice/lattice/creation/anf/MinkowskiLattice 36 I /magma/module-lattice/lattice/creation/anf/MinkowskiLattice 37 I /magma/module-lattice/lattice/creation/anf/MinkowskiLattice 38 I /magma/module-lattice/lattice/creation/code/Lattice 39 I /magma/module-lattice/lattice/creation/code/Lattice 40 I /magma/module-lattice/lattice/creation/creation/CoordinateLattice 41 I /magma/module-lattice/lattice/creation/creation/Lattice 42 I /magma/module-lattice/lattice/creation/creation/Lattice 43 I /magma/module-lattice/lattice/creation/creation/LatticeWithBasis 44 I /magma/module-lattice/lattice/creation/creation/LatticeWithBasis 45 I /magma/module-lattice/lattice/creation/creation/LatticeWithBasis 46 I /magma/module-lattice/lattice/creation/creation/LatticeWithBasis 47 I /magma/module-lattice/lattice/creation/creation/LatticeWithBasis 48 I /magma/module-lattice/lattice/creation/creation/LatticeWithGram 49 I /magma/module-lattice/lattice/creation/creation/LatticeWithGram 50 I /magma/module-lattice/lattice/creation/creation/ScaledLattice 51 I /magma/module-lattice/lattice/creation/creation/ScaledLattice 52 I /magma/module-lattice/lattice/creation/creation/StandardLattice 53 I /magma/module-lattice/lattice/creation/special-lattices/Lattice 54 I /magma/module-lattice/lattice/G-lattices/create/Lattice 55 I /magma/module-lattice/lattice/G-lattices/create/LatticeWithBasis 56 I /magma/module-lattice/lattice/G-lattices/create/LatticeWithBasis 57 I /magma/module-lattice/lattice/G-lattices/create/LatticeWithGram 58 I /magma/module-lattice/lattice/latdb/access/Lattice 59 I /magma/module-lattice/lattice/latdb/access/LatticeData 60 I /magma/module-lattice/lattice/latdb/access/LatticeData 61 I /magma/module-lattice/lattice/latdb/access/LatticeData 62 I /magma/module-lattice/lattice/latdb/creation/LatticeDatabase 63 I /magma/module-lattice/lattice/latdb/information/LatticeName 64 I /magma/module-lattice/lattice/latdb/information/LatticeName 65 I /magma/module-lattice/lattice/latdb/information/LatticeName 66 I /magma/module-lattice/lattice/new-construction/construction/\ DualBasisLattice 67 I /magma/module-lattice/lattice/new-construction/construction/\ PureLattice 68 I /magma/module-lattice/quadratic/invar/Lattice 69 I /magma/ring-field-algebra/algebraic-field/ideal/ideal-other/\ Lattice 70 I /magma/ring-field-algebra/algebraic-field/ideal/ideal-other/\ Lattice 71 I /magma/ring-field-algebra/algebraic-field/operation/related/\ Lattice 72 I /magma/ring-field-algebra/algebraic-field/subfields/\ subfield-lattice/SubfieldLattice To view an entry, type ? followed by the number next to it Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 12:36:27 2004 Input: L := Lattice("G", 2); T := ThetaSeries(L, 10); T; Output: Magma V2.10-6 Thu Mar 4 2004 12:36:24 on modular [Seed = 4294497989] ------------------------------------- 1 + 6*q^2 + 6*q^6 + 6*q^8 + O(q^11) Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 12:36:52 2004 Input: L := Lattice("D", 16); T := ThetaSeries(L, 6); T; Output: Magma V2.10-6 Thu Mar 4 2004 12:36:48 on modular [Seed = 3301174742] ------------------------------------- 1 + 480*q^2 + 29152*q^4 + 525952*q^6 + O(q^7) Total time: 3.179 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (128.197.227.252) Time: Thu Mar 4 12:39:14 2004 Input: xyu Output: Magma V2.10-6 Thu Mar 4 2004 12:39:11 on modular [Seed = 3553950286] ------------------------------------- >> xyu; ^ User error: Identifier 'xyu' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 12:48:38 2004 Input: K := GF(3); R := PolynomialRing(K, [3^4 -3^3, 3^4 -3^2, 3^4 -3, 3^4 -1, 3^5 -3^4]); R; P := [ u, x*u-x^(3+1)+y^3, z^3 +y*u -y*x^3, w^3 +z*u -z*x^3, u*w -w*x^3 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S; Output: Magma V2.10-6 Thu Mar 4 2004 12:48:35 on modular [Seed = 875765732] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 54 72 78 80 162 0 [] [ 1, w, w^2, w^3, z, z*w, z*w^2, z*w^3, z^2, z^2*w, z^2*w^2, z^2*w^3, z^3, z^4, z^5, z^6, y, y*w, y*w^2, y*z, y*z*w, y*z*w^2, y*z^2, y*z^2*w, y*z^2*w^2, y*z^3, y*z^4, y*z^5, y*z^6, y^2, y^2*w, y^2*w^2, y^2*z, y^2*z*w, y^2*z*w^2, y^2*z^2, y^2*z^2*w, y^2*z^2*w^2, y^2*z^3, y^3, y^3*z, y^3*z^2, y^3*z^3, y^4, y^4*z, y^4*z^2, y^4*z^3, y^5, y^5*z, y^5*z^2, y^5*z^3, y^6, y^7, y^8, y^9, x, x*w, x*w^2, x*z, x*z*w, x*z*w^2, x*z^2, x*z^2*w, x*z^2*w^2, x*y, x*y*w, x*y*w^2, x*y*z, x*y*z*w, x*y*z*w^2, x*y*z^2, x*y*z^2*w, x*y*z^2*w^2, x*y^2, x*y^2*w, x*y^2*w^2, x*y^2*z, x*y^2*z*w, x*y^2*z*w^2, x*y^2*z^2, x*y^2*z^2*w, x*y^2*z^2*w^2, x*y^3, x*y^3*z, x*y^3*z^2, x*y^4, x*y^4*z, x*y^4*z^2, x*y^5, x*y^5*z, x*y^5*z^2, x*y^6, x^2, x^2*w, x^2*w^2, x^2*z, x^2*z*w, x^2*z*w^2, x^2*z^2, x^2*z^2*w, x^2*z^2*w^2, x^2*y, x^2*y*w, x^2*y*w^2, x^2*y*z, x^2*y*z*w, x^2*y*z*w^2, x^2*y*z^2, x^2*y*z^2*w, x^2*y*z^2*w^2, x^2*y^2, x^2*y^2*w, x^2*y^2*w^2, x^2*y^2*z, x^2*y^2*z*w, x^2*y^2*z*w^2, x^2*y^2*z^2, x^2*y^2*z^2*w, x^2*y^2*z^2*w^2, x^2*y^3, x^3 ] Total time: 3.049 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (132.235.18.125) Time: Thu Mar 4 13:17:30 2004 Input: >Z4 := IntegerRing(4); >K8 :=LinearCode[0,2,3,1,1,0,3,2]>; >EW :=EuclideanWeight(K8); Output: Magma V2.10-6 Thu Mar 4 2004 13:17:27 on modular [Seed = 1347904196] ------------------------------------- >> EW :=EuclideanWeight(K8); ^ Runtime error in 'EuclideanWeight': Bad argument types Argument types given: Code Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (132.235.18.125) Time: Thu Mar 4 13:17:59 2004 Input: >Z4 := IntegerRing(4); >K8 :=LinearCode[0,2,3,1,1,0,3,2]>; >EW :=EuclideanWeight(K8.1); Output: Magma V2.10-6 Thu Mar 4 2004 13:17:56 on modular [Seed = 1599630760] ------------------------------------- Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (132.235.18.125) Time: Thu Mar 4 13:18:15 2004 Input: >Z4 := IntegerRing(4); >K8 :=LinearCode[0,2,3,1,1,0,3,2]>; >EW :=EuclideanWeight(K8.1); Output: Magma V2.10-6 Thu Mar 4 2004 13:18:12 on modular [Seed = 2795607137] ------------------------------------- Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (132.235.18.125) Time: Thu Mar 4 13:18:27 2004 Input: >Z4 := IntegerRing(4); >K8 :=LinearCode[0,2,3,1,1,0,3,2]>; >EW :=EuclideanWeight(K8.1); Output: Magma V2.10-6 Thu Mar 4 2004 13:18:24 on modular [Seed = 2913640318] ------------------------------------- Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (132.235.18.125) Time: Thu Mar 4 13:19:33 2004 Input: >Z4 := IntegerRing(4); >K8 :=LinearCode [0,2,3,1,1,0,3,2]>; >EW :=EuclideanWeight(K8.1); Output: Magma V2.10-6 Thu Mar 4 2004 13:19:30 on modular [Seed = 2627448717] ------------------------------------- Total time: 2.889 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (132.235.18.125) Time: Thu Mar 4 13:20:09 2004 Input: >Z4 := IntegerRing(4); >K8 :=LinearCode [0,2,3,1,1,0,3,2]>; >EW :=EuclideanWeight(K8.1); >EW; Output: Magma V2.10-6 Thu Mar 4 2004 13:20:06 on modular [Seed = 4076192135] ------------------------------------- 12 Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.111.111) Time: Thu Mar 4 13:21:50 2004 Input: [i : i in [1..100]]; Output: Magma V2.10-6 Thu Mar 4 2004 13:21:47 on modular [Seed = 3469344086] ------------------------------------- [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.111.111) Time: Thu Mar 4 13:22:24 2004 Input: [i : i in [1..10]]; Output: Magma V2.10-6 Thu Mar 4 2004 13:22:21 on modular [Seed = 3587368491] ------------------------------------- [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Thu Mar 4 13:32:48 2004 Input: K := GF(3); R := PolynomialRing(K, [3^4 -3^3, 3^4 -3^2, 3^4 -3, 3^4 -1, 3^5 -3^4]); R; P := [ u, x*u-x^(3+1)+y^3, z^3 +y*u -y*x^3, w^3 +z*u -z*x^3, u*w -w*x^3 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, w, w^2, w^3, z, z*w, z*w^2, z*w^3, z^2, z^2*w, z^2*w^2, z^2*w^3, z^3, z^4, z^5, w*z^2*y^3*x^3, y, y*w, y*w^2, y*z, y*z*w, y*z*w^2, y*z^2, y*z^2*w, y*z^2*w^2, y*z^3, y*z^4, y*z^5, y*z^6, y^2, y^2*w, y^2*w^2, y^2*z, y^2*z*w, y^2*z*w^2, y^2*z^2, y^2*z^2*w, y^2*z^2*w^2, y^2*z^3, y^3, y^3*z, y^3*z^2, y^3*z^3, y^4, y^4*z, y^4*z^2, y^4*z^3, y^5, y^5*z, y^5*z^2, y^5*z^3, y^6, y^7, y^8, y^9, x, x*w, x*w^2, x*z, x*z*w, x*z*w^2, x*z^2, x*z^2*w, x*z^2*w^2, x*y, x*y*w, x*y*w^2, x*y*z, x*y*z*w, x*y*z*w^2, x*y*z^2, x*y*z^2*w, x*y*z^2*w^2, x*y^2, x*y^2*w, x*y^2*w^2, x*y^2*z, x*y^2*z*w, x*y^2*z*w^2, x*y^2*z^2, x*y^2*z^2*w, x*y^2*z^2*w^2, x*y^3, x*y^3*z, x*y^3*z^2, x*y^4, x*y^4*z, x*y^4*z^2, x*y^5, x*y^5*z, x*y^5*z^2, x*y^6, x^2, x^2*w, x^2*w^2, x^2*z, x^2*z*w, x^2*z*w^2, x^2*z^2, x^2*z^2*w, x^2*z^2*w^2, x^2*y, x^2*y*w, x^2*y*w^2, x^2*y*z, x^2*y*z*w, x^2*y*z*w^2, x^2*y*z^2, x^2*y*z^2*w, x^2*y*z^2*w^2, x^2*y^2, x^2*y^2*w, x^2*y^2*w^2, x^2*y^2*z, x^2*y^2*z*w, x^2*y^2*z*w^2, x^2*y^2*z^2, x^2*y^2*z^2*w, x^2*y^2*z^2*w^2, x^2*y^3, x^3 ]; L := [z^6]; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Thu Mar 4 2004 13:32:45 on modular [Seed = 269952633] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 54 72 78 80 162 0 [] [ false ] Total time: 2.919 seconds, Total memory usage: 2.11MB ************** MAGMA ***************** Host 3(NXDOMAIN) (66.144.41.233) Time: Thu Mar 4 14:58:55 2004 Input: (x+y+z)^2 Output: Magma V2.10-6 Thu Mar 4 2004 14:58:52 on modular [Seed = 1532793090] ------------------------------------- >> (x+y+z)^2; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 14:59:39 2004 Input: function Theta(L, n) Z := IntegerRing(); P := ShortVectorsProcess(L, n); C := [1] cat [0: i in [1 .. n]]; while not IsEmpty(P) do v, norm := NextVector(P); C[Z!norm + 1] +:= 0.5; end while; return PowerSeriesRing(IntegerRing()) ! C; end function; L := Lattice("G", 2); T := Theta(L, 10); T; ?lattice Output: Magma V2.10-6 Thu Mar 4 2004 14:59:36 on modular [Seed = 2913625888] ------------------------------------- Theta( L: Lattice of rank 2 and degree 3, n: 10 ) >> C[Z!norm + 1] +:= 0.5; ^ Runtime error in :=: Sequence mutation failed >> T; ^ User error: Identifier 'T' has not been declared or assigned 72 matches: 1 O /magma/module-lattice 2 S /magma/group/braid/braid-groups-elements/braid-groups-lattice 3 S /magma/group/braid/braid-groups-introduction/\ braid-groups-introduction-lattice 4 S /magma/module-lattice/general/submodule-lattice 5 S /magma/module-lattice/general/submodule-lattice/lattice-element 6 S /magma/module-lattice/general/submodule-lattice/lattice-element 7 S /magma/module-lattice/lattice 8 S /magma/module-lattice/lattice/lattice-properties 9 S /magma/module-lattice/lattice/lattice-properties/\ lattice-attributes 10 S /magma/module-lattice/lattice/lattice-properties/\ lattice-predicates 11 S /magma/ring-field-algebra/algebraic-field/subfields/\ subfield-lattice 12 I /magma/combinatorial-geometrical-incidence/graph/\ group-code-design/constr-misc/SquareLatticeGraph 13 I /magma/combinatorial-geometrical-incidence/modular-symbol/\ l-series/winding/WindingLattice 14 I /magma/combinatorial-geometrical-incidence/modular-symbol/\ underlying-representation/Lattice 15 I /magma/combinatorial-geometrical-incidence/tableaux-chap/words/\ ordered-monoid/IsReverseLatticeWord 16 I /magma/group/databases-overview/quatgps/Lattice 17 I /magma/group/databases-overview/quatgps/Lattice 18 I /magma/group/databases-overview/ratgps/Lattice 19 I /magma/group/databases-overview/ratgps/Lattice 20 I /magma/group/fiurg/action/weights/WeightLattice 21 I /magma/group/fiurg/action/weights/WeightLattice 22 I /magma/group/group-overview/\ characteristic-subgroup-normal-structure/subgroup-series/\ NormalLattice 23 I /magma/group/group-overview/subgroup/subgroup-poset/creation/\ SubgroupLattice 24 I /magma/group/groups-lie-type/operations/WeightLattice 25 I /magma/group/groups-lie-type/operations/WeightLattice 26 I /magma/group/permutation/\ characteristic-subgroup-normal-structure/normal-subgroups/\ NormalLattice 27 I /magma/group/root-data/roots-coroots-weights/weights/\ CoweightLattice 28 I /magma/group/root-data/roots-coroots-weights/weights/WeightLattice 29 I /magma/group/soluble/normal-series/normals/NormalLattice 30 I /magma/group/soluble/subgroups/subgroup-classes/SubgroupLattice 31 I /magma/lie-theory/finite-coxeter-groups/root-data-roots/weights/\ WeightLattice 32 I /magma/lie-theory/finite-coxeter-groups/root-data-roots/weights/\ WeightLattice 33 I /magma/module-lattice/general/submodule-lattice/create/\ SubmoduleLattice 34 I /magma/module-lattice/general/submodule-lattice/create/\ SubmoduleLatticeAbort 35 I /magma/module-lattice/lattice/creation/anf/MinkowskiLattice 36 I /magma/module-lattice/lattice/creation/anf/MinkowskiLattice 37 I /magma/module-lattice/lattice/creation/anf/MinkowskiLattice 38 I /magma/module-lattice/lattice/creation/code/Lattice 39 I /magma/module-lattice/lattice/creation/code/Lattice 40 I /magma/module-lattice/lattice/creation/creation/CoordinateLattice 41 I /magma/module-lattice/lattice/creation/creation/Lattice 42 I /magma/module-lattice/lattice/creation/creation/Lattice 43 I /magma/module-lattice/lattice/creation/creation/LatticeWithBasis 44 I /magma/module-lattice/lattice/creation/creation/LatticeWithBasis 45 I /magma/module-lattice/lattice/creation/creation/LatticeWithBasis 46 I /magma/module-lattice/lattice/creation/creation/LatticeWithBasis 47 I /magma/module-lattice/lattice/creation/creation/LatticeWithBasis 48 I /magma/module-lattice/lattice/creation/creation/LatticeWithGram 49 I /magma/module-lattice/lattice/creation/creation/LatticeWithGram 50 I /magma/module-lattice/lattice/creation/creation/ScaledLattice 51 I /magma/module-lattice/lattice/creation/creation/ScaledLattice 52 I /magma/module-lattice/lattice/creation/creation/StandardLattice 53 I /magma/module-lattice/lattice/creation/special-lattices/Lattice 54 I /magma/module-lattice/lattice/G-lattices/create/Lattice 55 I /magma/module-lattice/lattice/G-lattices/create/LatticeWithBasis 56 I /magma/module-lattice/lattice/G-lattices/create/LatticeWithBasis 57 I /magma/module-lattice/lattice/G-lattices/create/LatticeWithGram 58 I /magma/module-lattice/lattice/latdb/access/Lattice 59 I /magma/module-lattice/lattice/latdb/access/LatticeData 60 I /magma/module-lattice/lattice/latdb/access/LatticeData 61 I /magma/module-lattice/lattice/latdb/access/LatticeData 62 I /magma/module-lattice/lattice/latdb/creation/LatticeDatabase 63 I /magma/module-lattice/lattice/latdb/information/LatticeName 64 I /magma/module-lattice/lattice/latdb/information/LatticeName 65 I /magma/module-lattice/lattice/latdb/information/LatticeName 66 I /magma/module-lattice/lattice/new-construction/construction/\ DualBasisLattice 67 I /magma/module-lattice/lattice/new-construction/construction/\ PureLattice 68 I /magma/module-lattice/quadratic/invar/Lattice 69 I /magma/ring-field-algebra/algebraic-field/ideal/ideal-other/\ Lattice 70 I /magma/ring-field-algebra/algebraic-field/ideal/ideal-other/\ Lattice 71 I /magma/ring-field-algebra/algebraic-field/operation/related/\ Lattice 72 I /magma/ring-field-algebra/algebraic-field/subfields/\ subfield-lattice/SubfieldLattice To view an entry, type ? followed by the number next to it Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (66.144.41.233) Time: Thu Mar 4 15:11:42 2004 Input: 5 Output: Magma V2.10-6 Thu Mar 4 2004 15:11:39 on modular [Seed = 1717676859] ------------------------------------- 5 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (66.144.41.233) Time: Thu Mar 4 15:11:50 2004 Input: 5+5 Output: Magma V2.10-6 Thu Mar 4 2004 15:11:47 on modular [Seed = 1869128394] ------------------------------------- 10 Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (66.144.41.233) Time: Thu Mar 4 15:12:10 2004 Input: (x+y+z)^2 Output: Magma V2.10-6 Thu Mar 4 2004 15:12:07 on modular [Seed = 1953741253] ------------------------------------- >> (x+y+z)^2; ^ User error: Identifier 'x' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 15:36:20 2004 Input: function Theta(L, n) Z := IntegerRing(); P := ShortVectorsProcess(L, n); C := [1] cat [0: i in [1 .. n]]; while not IsEmpty(P) do v, norm := NextVector(P); C[Z!norm + 1] +:= 2; end while; return PowerSeriesRing(IntegerRing()) ! C; end function; L := Lattice("G", 2); T := Theta(L, 10); T; ?lattice Output: Magma V2.10-6 Thu Mar 4 2004 15:36:17 on modular [Seed = 2795599297] ------------------------------------- 1 + 6*q^2 + 6*q^6 + 6*q^8 72 matches: 1 O /magma/module-lattice 2 S /magma/group/braid/braid-groups-elements/braid-groups-lattice 3 S /magma/group/braid/braid-groups-introduction/\ braid-groups-introduction-lattice 4 S /magma/module-lattice/general/submodule-lattice 5 S /magma/module-lattice/general/submodule-lattice/lattice-element 6 S /magma/module-lattice/general/submodule-lattice/lattice-element 7 S /magma/module-lattice/lattice 8 S /magma/module-lattice/lattice/lattice-properties 9 S /magma/module-lattice/lattice/lattice-properties/\ lattice-attributes 10 S /magma/module-lattice/lattice/lattice-properties/\ lattice-predicates 11 S /magma/ring-field-algebra/algebraic-field/subfields/\ subfield-lattice 12 I /magma/combinatorial-geometrical-incidence/graph/\ group-code-design/constr-misc/SquareLatticeGraph 13 I /magma/combinatorial-geometrical-incidence/modular-symbol/\ l-series/winding/WindingLattice 14 I /magma/combinatorial-geometrical-incidence/modular-symbol/\ underlying-representation/Lattice 15 I /magma/combinatorial-geometrical-incidence/tableaux-chap/words/\ ordered-monoid/IsReverseLatticeWord 16 I /magma/group/databases-overview/quatgps/Lattice 17 I /magma/group/databases-overview/quatgps/Lattice 18 I /magma/group/databases-overview/ratgps/Lattice 19 I /magma/group/databases-overview/ratgps/Lattice 20 I /magma/group/fiurg/action/weights/WeightLattice 21 I /magma/group/fiurg/action/weights/WeightLattice 22 I /magma/group/group-overview/\ characteristic-subgroup-normal-structure/subgroup-series/\ NormalLattice 23 I /magma/group/group-overview/subgroup/subgroup-poset/creation/\ SubgroupLattice 24 I /magma/group/groups-lie-type/operations/WeightLattice 25 I /magma/group/groups-lie-type/operations/WeightLattice 26 I /magma/group/permutation/\ characteristic-subgroup-normal-structure/normal-subgroups/\ NormalLattice 27 I /magma/group/root-data/roots-coroots-weights/weights/\ CoweightLattice 28 I /magma/group/root-data/roots-coroots-weights/weights/WeightLattice 29 I /magma/group/soluble/normal-series/normals/NormalLattice 30 I /magma/group/soluble/subgroups/subgroup-classes/SubgroupLattice 31 I /magma/lie-theory/finite-coxeter-groups/root-data-roots/weights/\ WeightLattice 32 I /magma/lie-theory/finite-coxeter-groups/root-data-roots/weights/\ WeightLattice 33 I /magma/module-lattice/general/submodule-lattice/create/\ SubmoduleLattice 34 I /magma/module-lattice/general/submodule-lattice/create/\ SubmoduleLatticeAbort 35 I /magma/module-lattice/lattice/creation/anf/MinkowskiLattice 36 I /magma/module-lattice/lattice/creation/anf/MinkowskiLattice 37 I /magma/module-lattice/lattice/creation/anf/MinkowskiLattice 38 I /magma/module-lattice/lattice/creation/code/Lattice 39 I /magma/module-lattice/lattice/creation/code/Lattice 40 I /magma/module-lattice/lattice/creation/creation/CoordinateLattice 41 I /magma/module-lattice/lattice/creation/creation/Lattice 42 I /magma/module-lattice/lattice/creation/creation/Lattice 43 I /magma/module-lattice/lattice/creation/creation/LatticeWithBasis 44 I /magma/module-lattice/lattice/creation/creation/LatticeWithBasis 45 I /magma/module-lattice/lattice/creation/creation/LatticeWithBasis 46 I /magma/module-lattice/lattice/creation/creation/LatticeWithBasis 47 I /magma/module-lattice/lattice/creation/creation/LatticeWithBasis 48 I /magma/module-lattice/lattice/creation/creation/LatticeWithGram 49 I /magma/module-lattice/lattice/creation/creation/LatticeWithGram 50 I /magma/module-lattice/lattice/creation/creation/ScaledLattice 51 I /magma/module-lattice/lattice/creation/creation/ScaledLattice 52 I /magma/module-lattice/lattice/creation/creation/StandardLattice 53 I /magma/module-lattice/lattice/creation/special-lattices/Lattice 54 I /magma/module-lattice/lattice/G-lattices/create/Lattice 55 I /magma/module-lattice/lattice/G-lattices/create/LatticeWithBasis 56 I /magma/module-lattice/lattice/G-lattices/create/LatticeWithBasis 57 I /magma/module-lattice/lattice/G-lattices/create/LatticeWithGram 58 I /magma/module-lattice/lattice/latdb/access/Lattice 59 I /magma/module-lattice/lattice/latdb/access/LatticeData 60 I /magma/module-lattice/lattice/latdb/access/LatticeData 61 I /magma/module-lattice/lattice/latdb/access/LatticeData 62 I /magma/module-lattice/lattice/latdb/creation/LatticeDatabase 63 I /magma/module-lattice/lattice/latdb/information/LatticeName 64 I /magma/module-lattice/lattice/latdb/information/LatticeName 65 I /magma/module-lattice/lattice/latdb/information/LatticeName 66 I /magma/module-lattice/lattice/new-construction/construction/\ DualBasisLattice 67 I /magma/module-lattice/lattice/new-construction/construction/\ PureLattice 68 I /magma/module-lattice/quadratic/invar/Lattice 69 I /magma/ring-field-algebra/algebraic-field/ideal/ideal-other/\ Lattice 70 I /magma/ring-field-algebra/algebraic-field/ideal/ideal-other/\ Lattice 71 I /magma/ring-field-algebra/algebraic-field/operation/related/\ Lattice 72 I /magma/ring-field-algebra/algebraic-field/subfields/\ subfield-lattice/SubfieldLattice To view an entry, type ? followed by the number next to it Total time: 2.859 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 15:36:37 2004 Input: function Theta(L, n) Z := IntegerRing(); P := ShortVectorsProcess(L, n); C := [1] cat [0: i in [1 .. n]]; while not IsEmpty(P) do v, norm := NextVector(P); C[Z!norm + 1] +:= 2; end while; return PowerSeriesRing(IntegerRing()) ! C; end function; L := Lattice("A", 1); T := Theta(L, 10); T; ?lattice Output: Magma V2.10-6 Thu Mar 4 2004 15:36:34 on modular [Seed = 2947054811] ------------------------------------- 1 + 2*q^2 + 2*q^8 72 matches: 1 O /magma/module-lattice 2 S /magma/group/braid/braid-groups-elements/braid-groups-lattice 3 S /magma/group/braid/braid-groups-introduction/\ braid-groups-introduction-lattice 4 S /magma/module-lattice/general/submodule-lattice 5 S /magma/module-lattice/general/submodule-lattice/lattice-element 6 S /magma/module-lattice/general/submodule-lattice/lattice-element 7 S /magma/module-lattice/lattice 8 S /magma/module-lattice/lattice/lattice-properties 9 S /magma/module-lattice/lattice/lattice-properties/\ lattice-attributes 10 S /magma/module-lattice/lattice/lattice-properties/\ lattice-predicates 11 S /magma/ring-field-algebra/algebraic-field/subfields/\ subfield-lattice 12 I /magma/combinatorial-geometrical-incidence/graph/\ group-code-design/constr-misc/SquareLatticeGraph 13 I /magma/combinatorial-geometrical-incidence/modular-symbol/\ l-series/winding/WindingLattice 14 I /magma/combinatorial-geometrical-incidence/modular-symbol/\ underlying-representation/Lattice 15 I /magma/combinatorial-geometrical-incidence/tableaux-chap/words/\ ordered-monoid/IsReverseLatticeWord 16 I /magma/group/databases-overview/quatgps/Lattice 17 I /magma/group/databases-overview/quatgps/Lattice 18 I /magma/group/databases-overview/ratgps/Lattice 19 I /magma/group/databases-overview/ratgps/Lattice 20 I /magma/group/fiurg/action/weights/WeightLattice 21 I /magma/group/fiurg/action/weights/WeightLattice 22 I /magma/group/group-overview/\ characteristic-subgroup-normal-structure/subgroup-series/\ NormalLattice 23 I /magma/group/group-overview/subgroup/subgroup-poset/creation/\ SubgroupLattice 24 I /magma/group/groups-lie-type/operations/WeightLattice 25 I /magma/group/groups-lie-type/operations/WeightLattice 26 I /magma/group/permutation/\ characteristic-subgroup-normal-structure/normal-subgroups/\ NormalLattice 27 I /magma/group/root-data/roots-coroots-weights/weights/\ CoweightLattice 28 I /magma/group/root-data/roots-coroots-weights/weights/WeightLattice 29 I /magma/group/soluble/normal-series/normals/NormalLattice 30 I /magma/group/soluble/subgroups/subgroup-classes/SubgroupLattice 31 I /magma/lie-theory/finite-coxeter-groups/root-data-roots/weights/\ WeightLattice 32 I /magma/lie-theory/finite-coxeter-groups/root-data-roots/weights/\ WeightLattice 33 I /magma/module-lattice/general/submodule-lattice/create/\ SubmoduleLattice 34 I /magma/module-lattice/general/submodule-lattice/create/\ SubmoduleLatticeAbort 35 I /magma/module-lattice/lattice/creation/anf/MinkowskiLattice 36 I /magma/module-lattice/lattice/creation/anf/MinkowskiLattice 37 I /magma/module-lattice/lattice/creation/anf/MinkowskiLattice 38 I /magma/module-lattice/lattice/creation/code/Lattice 39 I /magma/module-lattice/lattice/creation/code/Lattice 40 I /magma/module-lattice/lattice/creation/creation/CoordinateLattice 41 I /magma/module-lattice/lattice/creation/creation/Lattice 42 I /magma/module-lattice/lattice/creation/creation/Lattice 43 I /magma/module-lattice/lattice/creation/creation/LatticeWithBasis 44 I /magma/module-lattice/lattice/creation/creation/LatticeWithBasis 45 I /magma/module-lattice/lattice/creation/creation/LatticeWithBasis 46 I /magma/module-lattice/lattice/creation/creation/LatticeWithBasis 47 I /magma/module-lattice/lattice/creation/creation/LatticeWithBasis 48 I /magma/module-lattice/lattice/creation/creation/LatticeWithGram 49 I /magma/module-lattice/lattice/creation/creation/LatticeWithGram 50 I /magma/module-lattice/lattice/creation/creation/ScaledLattice 51 I /magma/module-lattice/lattice/creation/creation/ScaledLattice 52 I /magma/module-lattice/lattice/creation/creation/StandardLattice 53 I /magma/module-lattice/lattice/creation/special-lattices/Lattice 54 I /magma/module-lattice/lattice/G-lattices/create/Lattice 55 I /magma/module-lattice/lattice/G-lattices/create/LatticeWithBasis 56 I /magma/module-lattice/lattice/G-lattices/create/LatticeWithBasis 57 I /magma/module-lattice/lattice/G-lattices/create/LatticeWithGram 58 I /magma/module-lattice/lattice/latdb/access/Lattice 59 I /magma/module-lattice/lattice/latdb/access/LatticeData 60 I /magma/module-lattice/lattice/latdb/access/LatticeData 61 I /magma/module-lattice/lattice/latdb/access/LatticeData 62 I /magma/module-lattice/lattice/latdb/creation/LatticeDatabase 63 I /magma/module-lattice/lattice/latdb/information/LatticeName 64 I /magma/module-lattice/lattice/latdb/information/LatticeName 65 I /magma/module-lattice/lattice/latdb/information/LatticeName 66 I /magma/module-lattice/lattice/new-construction/construction/\ DualBasisLattice 67 I /magma/module-lattice/lattice/new-construction/construction/\ PureLattice 68 I /magma/module-lattice/quadratic/invar/Lattice 69 I /magma/ring-field-algebra/algebraic-field/ideal/ideal-other/\ Lattice 70 I /magma/ring-field-algebra/algebraic-field/ideal/ideal-other/\ Lattice 71 I /magma/ring-field-algebra/algebraic-field/operation/related/\ Lattice 72 I /magma/ring-field-algebra/algebraic-field/subfields/\ subfield-lattice/SubfieldLattice To view an entry, type ? followed by the number next to it Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 15:41:22 2004 Input: function Theta(L, n) Z := IntegerRing(); P := ShortVectorsProcess(L, n); C := [1] cat [0: i in [1 .. n]]; while not IsEmpty(P) do v, norm := NextVector(P); C[Z!norm + 1] +:= 2; end while; return PowerSeriesRing(IntegerRing()) ! C; end function; L := Lattice("E", 6); T := Theta(L, 10); T; ?lattice Output: Magma V2.10-6 Thu Mar 4 2004 15:41:19 on modular [Seed = 3183110644] ------------------------------------- 1 + 72*q^2 + 270*q^4 + 720*q^6 + 936*q^8 + 2160*q^10 72 matches: 1 O /magma/module-lattice 2 S /magma/group/braid/braid-groups-elements/braid-groups-lattice 3 S /magma/group/braid/braid-groups-introduction/\ braid-groups-introduction-lattice 4 S /magma/module-lattice/general/submodule-lattice 5 S /magma/module-lattice/general/submodule-lattice/lattice-element 6 S /magma/module-lattice/general/submodule-lattice/lattice-element 7 S /magma/module-lattice/lattice 8 S /magma/module-lattice/lattice/lattice-properties 9 S /magma/module-lattice/lattice/lattice-properties/\ lattice-attributes 10 S /magma/module-lattice/lattice/lattice-properties/\ lattice-predicates 11 S /magma/ring-field-algebra/algebraic-field/subfields/\ subfield-lattice 12 I /magma/combinatorial-geometrical-incidence/graph/\ group-code-design/constr-misc/SquareLatticeGraph 13 I /magma/combinatorial-geometrical-incidence/modular-symbol/\ l-series/winding/WindingLattice 14 I /magma/combinatorial-geometrical-incidence/modular-symbol/\ underlying-representation/Lattice 15 I /magma/combinatorial-geometrical-incidence/tableaux-chap/words/\ ordered-monoid/IsReverseLatticeWord 16 I /magma/group/databases-overview/quatgps/Lattice 17 I /magma/group/databases-overview/quatgps/Lattice 18 I /magma/group/databases-overview/ratgps/Lattice 19 I /magma/group/databases-overview/ratgps/Lattice 20 I /magma/group/fiurg/action/weights/WeightLattice 21 I /magma/group/fiurg/action/weights/WeightLattice 22 I /magma/group/group-overview/\ characteristic-subgroup-normal-structure/subgroup-series/\ NormalLattice 23 I /magma/group/group-overview/subgroup/subgroup-poset/creation/\ SubgroupLattice 24 I /magma/group/groups-lie-type/operations/WeightLattice 25 I /magma/group/groups-lie-type/operations/WeightLattice 26 I /magma/group/permutation/\ characteristic-subgroup-normal-structure/normal-subgroups/\ NormalLattice 27 I /magma/group/root-data/roots-coroots-weights/weights/\ CoweightLattice 28 I /magma/group/root-data/roots-coroots-weights/weights/WeightLattice 29 I /magma/group/soluble/normal-series/normals/NormalLattice 30 I /magma/group/soluble/subgroups/subgroup-classes/SubgroupLattice 31 I /magma/lie-theory/finite-coxeter-groups/root-data-roots/weights/\ WeightLattice 32 I /magma/lie-theory/finite-coxeter-groups/root-data-roots/weights/\ WeightLattice 33 I /magma/module-lattice/general/submodule-lattice/create/\ SubmoduleLattice 34 I /magma/module-lattice/general/submodule-lattice/create/\ SubmoduleLatticeAbort 35 I /magma/module-lattice/lattice/creation/anf/MinkowskiLattice 36 I /magma/module-lattice/lattice/creation/anf/MinkowskiLattice 37 I /magma/module-lattice/lattice/creation/anf/MinkowskiLattice 38 I /magma/module-lattice/lattice/creation/code/Lattice 39 I /magma/module-lattice/lattice/creation/code/Lattice 40 I /magma/module-lattice/lattice/creation/creation/CoordinateLattice 41 I /magma/module-lattice/lattice/creation/creation/Lattice 42 I /magma/module-lattice/lattice/creation/creation/Lattice 43 I /magma/module-lattice/lattice/creation/creation/LatticeWithBasis 44 I /magma/module-lattice/lattice/creation/creation/LatticeWithBasis 45 I /magma/module-lattice/lattice/creation/creation/LatticeWithBasis 46 I /magma/module-lattice/lattice/creation/creation/LatticeWithBasis 47 I /magma/module-lattice/lattice/creation/creation/LatticeWithBasis 48 I /magma/module-lattice/lattice/creation/creation/LatticeWithGram 49 I /magma/module-lattice/lattice/creation/creation/LatticeWithGram 50 I /magma/module-lattice/lattice/creation/creation/ScaledLattice 51 I /magma/module-lattice/lattice/creation/creation/ScaledLattice 52 I /magma/module-lattice/lattice/creation/creation/StandardLattice 53 I /magma/module-lattice/lattice/creation/special-lattices/Lattice 54 I /magma/module-lattice/lattice/G-lattices/create/Lattice 55 I /magma/module-lattice/lattice/G-lattices/create/LatticeWithBasis 56 I /magma/module-lattice/lattice/G-lattices/create/LatticeWithBasis 57 I /magma/module-lattice/lattice/G-lattices/create/LatticeWithGram 58 I /magma/module-lattice/lattice/latdb/access/Lattice 59 I /magma/module-lattice/lattice/latdb/access/LatticeData 60 I /magma/module-lattice/lattice/latdb/access/LatticeData 61 I /magma/module-lattice/lattice/latdb/access/LatticeData 62 I /magma/module-lattice/lattice/latdb/creation/LatticeDatabase 63 I /magma/module-lattice/lattice/latdb/information/LatticeName 64 I /magma/module-lattice/lattice/latdb/information/LatticeName 65 I /magma/module-lattice/lattice/latdb/information/LatticeName 66 I /magma/module-lattice/lattice/new-construction/construction/\ DualBasisLattice 67 I /magma/module-lattice/lattice/new-construction/construction/\ PureLattice 68 I /magma/module-lattice/quadratic/invar/Lattice 69 I /magma/ring-field-algebra/algebraic-field/ideal/ideal-other/\ Lattice 70 I /magma/ring-field-algebra/algebraic-field/ideal/ideal-other/\ Lattice 71 I /magma/ring-field-algebra/algebraic-field/operation/related/\ Lattice 72 I /magma/ring-field-algebra/algebraic-field/subfields/\ subfield-lattice/SubfieldLattice To view an entry, type ? followed by the number next to it Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 15:42:01 2004 Input: function Theta(L, n) Z := IntegerRing(); P := ShortVectorsProcess(L, n); C := [1] cat [0: i in [1 .. n]]; while not IsEmpty(P) do v, norm := NextVector(P); C[Z!norm + 1] +:= 2; end while; return PowerSeriesRing(IntegerRing()) ! C; end function; L := Lattice("A", 1); T := Theta(L, 10); T; ?lattice Output: Magma V2.10-6 Thu Mar 4 2004 15:41:58 on modular [Seed = 2189776434] ------------------------------------- 1 + 2*q^2 + 2*q^8 72 matches: 1 O /magma/module-lattice 2 S /magma/group/braid/braid-groups-elements/braid-groups-lattice 3 S /magma/group/braid/braid-groups-introduction/\ braid-groups-introduction-lattice 4 S /magma/module-lattice/general/submodule-lattice 5 S /magma/module-lattice/general/submodule-lattice/lattice-element 6 S /magma/module-lattice/general/submodule-lattice/lattice-element 7 S /magma/module-lattice/lattice 8 S /magma/module-lattice/lattice/lattice-properties 9 S /magma/module-lattice/lattice/lattice-properties/\ lattice-attributes 10 S /magma/module-lattice/lattice/lattice-properties/\ lattice-predicates 11 S /magma/ring-field-algebra/algebraic-field/subfields/\ subfield-lattice 12 I /magma/combinatorial-geometrical-incidence/graph/\ group-code-design/constr-misc/SquareLatticeGraph 13 I /magma/combinatorial-geometrical-incidence/modular-symbol/\ l-series/winding/WindingLattice 14 I /magma/combinatorial-geometrical-incidence/modular-symbol/\ underlying-representation/Lattice 15 I /magma/combinatorial-geometrical-incidence/tableaux-chap/words/\ ordered-monoid/IsReverseLatticeWord 16 I /magma/group/databases-overview/quatgps/Lattice 17 I /magma/group/databases-overview/quatgps/Lattice 18 I /magma/group/databases-overview/ratgps/Lattice 19 I /magma/group/databases-overview/ratgps/Lattice 20 I /magma/group/fiurg/action/weights/WeightLattice 21 I /magma/group/fiurg/action/weights/WeightLattice 22 I /magma/group/group-overview/\ characteristic-subgroup-normal-structure/subgroup-series/\ NormalLattice 23 I /magma/group/group-overview/subgroup/subgroup-poset/creation/\ SubgroupLattice 24 I /magma/group/groups-lie-type/operations/WeightLattice 25 I /magma/group/groups-lie-type/operations/WeightLattice 26 I /magma/group/permutation/\ characteristic-subgroup-normal-structure/normal-subgroups/\ NormalLattice 27 I /magma/group/root-data/roots-coroots-weights/weights/\ CoweightLattice 28 I /magma/group/root-data/roots-coroots-weights/weights/WeightLattice 29 I /magma/group/soluble/normal-series/normals/NormalLattice 30 I /magma/group/soluble/subgroups/subgroup-classes/SubgroupLattice 31 I /magma/lie-theory/finite-coxeter-groups/root-data-roots/weights/\ WeightLattice 32 I /magma/lie-theory/finite-coxeter-groups/root-data-roots/weights/\ WeightLattice 33 I /magma/module-lattice/general/submodule-lattice/create/\ SubmoduleLattice 34 I /magma/module-lattice/general/submodule-lattice/create/\ SubmoduleLatticeAbort 35 I /magma/module-lattice/lattice/creation/anf/MinkowskiLattice 36 I /magma/module-lattice/lattice/creation/anf/MinkowskiLattice 37 I /magma/module-lattice/lattice/creation/anf/MinkowskiLattice 38 I /magma/module-lattice/lattice/creation/code/Lattice 39 I /magma/module-lattice/lattice/creation/code/Lattice 40 I /magma/module-lattice/lattice/creation/creation/CoordinateLattice 41 I /magma/module-lattice/lattice/creation/creation/Lattice 42 I /magma/module-lattice/lattice/creation/creation/Lattice 43 I /magma/module-lattice/lattice/creation/creation/LatticeWithBasis 44 I /magma/module-lattice/lattice/creation/creation/LatticeWithBasis 45 I /magma/module-lattice/lattice/creation/creation/LatticeWithBasis 46 I /magma/module-lattice/lattice/creation/creation/LatticeWithBasis 47 I /magma/module-lattice/lattice/creation/creation/LatticeWithBasis 48 I /magma/module-lattice/lattice/creation/creation/LatticeWithGram 49 I /magma/module-lattice/lattice/creation/creation/LatticeWithGram 50 I /magma/module-lattice/lattice/creation/creation/ScaledLattice 51 I /magma/module-lattice/lattice/creation/creation/ScaledLattice 52 I /magma/module-lattice/lattice/creation/creation/StandardLattice 53 I /magma/module-lattice/lattice/creation/special-lattices/Lattice 54 I /magma/module-lattice/lattice/G-lattices/create/Lattice 55 I /magma/module-lattice/lattice/G-lattices/create/LatticeWithBasis 56 I /magma/module-lattice/lattice/G-lattices/create/LatticeWithBasis 57 I /magma/module-lattice/lattice/G-lattices/create/LatticeWithGram 58 I /magma/module-lattice/lattice/latdb/access/Lattice 59 I /magma/module-lattice/lattice/latdb/access/LatticeData 60 I /magma/module-lattice/lattice/latdb/access/LatticeData 61 I /magma/module-lattice/lattice/latdb/access/LatticeData 62 I /magma/module-lattice/lattice/latdb/creation/LatticeDatabase 63 I /magma/module-lattice/lattice/latdb/information/LatticeName 64 I /magma/module-lattice/lattice/latdb/information/LatticeName 65 I /magma/module-lattice/lattice/latdb/information/LatticeName 66 I /magma/module-lattice/lattice/new-construction/construction/\ DualBasisLattice 67 I /magma/module-lattice/lattice/new-construction/construction/\ PureLattice 68 I /magma/module-lattice/quadratic/invar/Lattice 69 I /magma/ring-field-algebra/algebraic-field/ideal/ideal-other/\ Lattice 70 I /magma/ring-field-algebra/algebraic-field/ideal/ideal-other/\ Lattice 71 I /magma/ring-field-algebra/algebraic-field/operation/related/\ Lattice 72 I /magma/ring-field-algebra/algebraic-field/subfields/\ subfield-lattice/SubfieldLattice To view an entry, type ? followed by the number next to it Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 18:55:08 2004 Input: L := Lattice("D", 16); T := ThetaSeries(L, 10); T; Output: Magma V2.10-6 Thu Mar 4 2004 18:54:58 on modular [Seed = 17203451] ------------------------------------- 1 + 480*q^2 + 29152*q^4 + 525952*q^6 + 3994080*q^8 + 18626112*q^10 + O(q^11) Total time: 10.449 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 18:56:13 2004 Input: L := Lattice("E", 8); T := ThetaSeries(L, 10); T; Output: Magma V2.10-6 Thu Mar 4 2004 18:56:10 on modular [Seed = 504994860] ------------------------------------- 1 + 240*q^2 + 2160*q^4 + 6720*q^6 + 17520*q^8 + 30240*q^10 + O(q^11) Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 18:56:42 2004 Input: L := Lattice("G", 2); T := ThetaSeries(L, 10); T; Output: Magma V2.10-6 Thu Mar 4 2004 18:56:39 on modular [Seed = 386962696] ------------------------------------- 1 + 6*q^2 + 6*q^6 + 6*q^8 + O(q^11) Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A117171.N1.Vanderbilt.Edu. (129.59.117.171) Time: Thu Mar 4 18:58:04 2004 Input: L := Lattice("G", 2); T := ThetaSeries(L, 20); T; Output: Magma V2.10-6 Thu Mar 4 2004 18:58:01 on modular [Seed = 1617420993] ------------------------------------- 1 + 6*q^2 + 6*q^6 + 6*q^8 + 12*q^14 + 6*q^18 + O(q^21) Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (63.139.104.190) Time: Thu Mar 4 23:44:55 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Thu Mar 4 2004 23:44:52 on modular [Seed = 2947017280] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Fri Mar 5 02:40:17 2004 Input: K := GF(3); R := PolynomialRing(K, [3^4 -3^3, 3^4 -3^2, 3^4 -3, 3^4 -1, 3^5 -3^4]); R; P := [ u, x*u-x^(3+1)+y^3, z^3 +y*u -y*x^3, w^3 +z*u -z*x^3, u*w -w*x^3 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S; [ 1, w, w^2, w^3, z, z*w, z*w^2, z*w^3, z^2, z^2*w, z^2*w^2, z^2*w^3, z^3, z^4, z^5, z^3*y*x^3, y, y*w, y*w^2, y*z, y*z*w, y*z*w^2, y*z^2, y*z^2*w, y*z^2*w^2, y*z^3, y*z^4, y*z^5, y*z^6, y^2, y^2*w, y^2*w^2, y^2*z, y^2*z*w, y^2*z*w^2, y^2*z^2, y^2*z^2*w, y^2*z^2*w^2, y^2*z^3, y^3, y^3*z, y^3*z^2, y^3*z^3, y^4, y^4*z, y^4*z^2, y^4*z^3, y^5, y^5*z, y^5*z^2, y^5*z^3, y^6, y^7, y^8, y^9, x, x*w, x*w^2, x*z, x*z*w, x*z*w^2, x*z^2, x*z^2*w, x*z^2*w^2, x*y, x*y*w, x*y*w^2, x*y*z, x*y*z*w, x*y*z*w^2, x*y*z^2, x*y*z^2*w, x*y*z^2*w^2, x*y^2, x*y^2*w, x*y^2*w^2, x*y^2*z, x*y^2*z*w, x*y^2*z*w^2, x*y^2*z^2, x*y^2*z^2*w, x*y^2*z^2*w^2, x*y^3, x*y^3*z, x*y^3*z^2, x*y^4, x*y^4*z, x*y^4*z^2, x*y^5, x*y^5*z, x*y^5*z^2, x*y^6, x^2, x^2*w, x^2*w^2, x^2*z, x^2*z*w, x^2*z*w^2, x^2*z^2, x^2*z^2*w, x^2*z^2*w^2, x^2*y, x^2*y*w, x^2*y*w^2, x^2*y*z, x^2*y*z*w, x^2*y*z*w^2, x^2*y*z^2, x^2*y*z^2*w, x^2*y*z^2*w^2, x^2*y^2, x^2*y^2*w, x^2*y^2*w^2, x^2*y^2*z, x^2*y^2*z*w, x^2*y^2*z*w^2, x^2*y^2*z^2, x^2*y^2*z^2*w, x^2*y^2*z^2*w^2, x^2*y^3, x^3 ] L := [z^6]; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Fri Mar 5 2004 02:40:13 on modular [Seed = 2610165096] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 54 72 78 80 162 0 [] [ 1, w, w^2, w^3, z, z*w, z*w^2, z*w^3, z^2, z^2*w, z^2*w^2, z^2*w^3, z^3, z^4, z^5, z^6, y, y*w, y*w^2, y*z, y*z*w, y*z*w^2, y*z^2, y*z^2*w, y*z^2*w^2, y*z^3, y*z^4, y*z^5, y*z^6, y^2, y^2*w, y^2*w^2, y^2*z, y^2*z*w, y^2*z*w^2, y^2*z^2, y^2*z^2*w, y^2*z^2*w^2, y^2*z^3, y^3, y^3*z, y^3*z^2, y^3*z^3, y^4, y^4*z, y^4*z^2, y^4*z^3, y^5, y^5*z, y^5*z^2, y^5*z^3, y^6, y^7, y^8, y^9, x, x*w, x*w^2, x*z, x*z*w, x*z*w^2, x*z^2, x*z^2*w, x*z^2*w^2, x*y, x*y*w, x*y*w^2, x*y*z, x*y*z*w, x*y*z*w^2, x*y*z^2, x*y*z^2*w, x*y*z^2*w^2, x*y^2, x*y^2*w, x*y^2*w^2, x*y^2*z, x*y^2*z*w, x*y^2*z*w^2, x*y^2*z^2, x*y^2*z^2*w, x*y^2*z^2*w^2, x*y^3, x*y^3*z, x*y^3*z^2, x*y^4, x*y^4*z, x*y^4*z^2, x*y^5, x*y^5*z, x*y^5*z^2, x*y^6, x^2, x^2*w, x^2*w^2, x^2*z, x^2*z*w, x^2*z*w^2, x^2*z^2, x^2*z^2*w, x^2*z^2*w^2, x^2*y, x^2*y*w, x^2*y*w^2, x^2*y*z, x^2*y*z*w, x^2*y*z*w^2, x^2*y*z^2, x^2*y*z^2*w, x^2*y*z^2*w^2, x^2*y^2, x^2*y^2*w, x^2*y^2*w^2, x^2*y^2*z, x^2*y^2*z*w, x^2*y^2*z*w^2, x^2*y^2*z^2, x^2*y^2*z^2*w, x^2*y^2*z^2*w^2, x^2*y^3, x^3 ] >> L := [z^6]; ^ User error: bad syntax >> B, V := HomogeneousModuleTest(P, S, L); ^ User error: Identifier 'L' has not been declared or assigned >> B; ^ User error: Identifier 'B' has not been declared or assigned Total time: 3.039 seconds, Total memory usage: 2.12MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Fri Mar 5 02:40:56 2004 Input: K := GF(3); R := PolynomialRing(K, [3^4 -3^3, 3^4 -3^2, 3^4 -3, 3^4 -1, 3^5 -3^4]); R; P := [ u, x*u-x^(3+1)+y^3, z^3 +y*u -y*x^3, w^3 +z*u -z*x^3, u*w -w*x^3 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, w, w^2, w^3, z, z*w, z*w^2, z*w^3, z^2, z^2*w, z^2*w^2, z^2*w^3, z^3, z^4, z^5, z^3*y*x^3, y, y*w, y*w^2, y*z, y*z*w, y*z*w^2, y*z^2, y*z^2*w, y*z^2*w^2, y*z^3, y*z^4, y*z^5, y*z^6, y^2, y^2*w, y^2*w^2, y^2*z, y^2*z*w, y^2*z*w^2, y^2*z^2, y^2*z^2*w, y^2*z^2*w^2, y^2*z^3, y^3, y^3*z, y^3*z^2, y^3*z^3, y^4, y^4*z, y^4*z^2, y^4*z^3, y^5, y^5*z, y^5*z^2, y^5*z^3, y^6, y^7, y^8, y^9, x, x*w, x*w^2, x*z, x*z*w, x*z*w^2, x*z^2, x*z^2*w, x*z^2*w^2, x*y, x*y*w, x*y*w^2, x*y*z, x*y*z*w, x*y*z*w^2, x*y*z^2, x*y*z^2*w, x*y*z^2*w^2, x*y^2, x*y^2*w, x*y^2*w^2, x*y^2*z, x*y^2*z*w, x*y^2*z*w^2, x*y^2*z^2, x*y^2*z^2*w, x*y^2*z^2*w^2, x*y^3, x*y^3*z, x*y^3*z^2, x*y^4, x*y^4*z, x*y^4*z^2, x*y^5, x*y^5*z, x*y^5*z^2, x*y^6, x^2, x^2*w, x^2*w^2, x^2*z, x^2*z*w, x^2*z*w^2, x^2*z^2, x^2*z^2*w, x^2*z^2*w^2, x^2*y, x^2*y*w, x^2*y*w^2, x^2*y*z, x^2*y*z*w, x^2*y*z*w^2, x^2*y*z^2, x^2*y*z^2*w, x^2*y*z^2*w^2, x^2*y^2, x^2*y^2*w, x^2*y^2*w^2, x^2*y^2*z, x^2*y^2*z*w, x^2*y^2*z*w^2, x^2*y^2*z^2, x^2*y^2*z^2*w, x^2*y^2*z^2*w^2, x^2*y^3, x^3 ] L := [z^6]; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Fri Mar 5 2004 02:40:53 on modular [Seed = 2459631034] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 54 72 78 80 162 0 [] >> L := [z^6]; ^ User error: bad syntax >> B, V := HomogeneousModuleTest(P, S, L); ^ User error: Identifier 'S' has not been declared or assigned >> B; ^ User error: Identifier 'B' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Fri Mar 5 02:43:29 2004 Input: K := GF(3); R := PolynomialRing(K, [3^4 -3^3, 3^4 -3^2, 3^4 -3, 3^4 -1, 3^5 -3^4]); R; P := [ u, x*u-x^(3+1)+y^3, z^3 +y*u -y*x^3, w^3 +z*u -z*x^3, u*w -w*x^3 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, w, w^2, w^3, z, z*w, z*w^2, z*w^3, z^2, z^2*w, z^2*w^2, z^2*w^3, z^3, z^4, z^5, z^3*y*x^3, y, y*w, y*w^2, y*z, y*z*w, y*z*w^2, y*z^2, y*z^2*w, y*z^2*w^2, y*z^3, y*z^4, y*z^5, y*z^6, y^2, y^2*w, y^2*w^2, y^2*z, y^2*z*w, y^2*z*w^2, y^2*z^2, y^2*z^2*w, y^2*z^2*w^2, y^2*z^3, y^3, y^3*z, y^3*z^2, y^3*z^3, y^4, y^4*z, y^4*z^2, y^4*z^3, y^5, y^5*z, y^5*z^2, y^5*z^3, y^6, y^7, y^8, y^9, x, x*w, x*w^2, x*z, x*z*w, x*z*w^2, x*z^2, x*z^2*w, x*z^2*w^2, x*y, x*y*w, x*y*w^2, x*y*z, x*y*z*w, x*y*z*w^2, x*y*z^2, x*y*z^2*w, x*y*z^2*w^2, x*y^2, x*y^2*w, x*y^2*w^2, x*y^2*z, x*y^2*z*w, x*y^2*z*w^2, x*y^2*z^2, x*y^2*z^2*w, x*y^2*z^2*w^2, x*y^3, x*y^3*z, x*y^3*z^2, x*y^4, x*y^4*z, x*y^4*z^2, x*y^5, x*y^5*z, x*y^5*z^2, x*y^6, x^2, x^2*w, x^2*w^2, x^2*z, x^2*z*w, x^2*z*w^2, x^2*z^2, x^2*z^2*w, x^2*z^2*w^2, x^2*y, x^2*y*w, x^2*y*w^2, x^2*y*z, x^2*y*z*w, x^2*y*z*w^2, x^2*y*z^2, x^2*y*z^2*w, x^2*y*z^2*w^2, x^2*y^2, x^2*y^2*w, x^2*y^2*w^2, x^2*y^2*z, x^2*y^2*z*w, x^2*y^2*z*w^2, x^2*y^2*z^2, x^2*y^2*z^2*w, x^2*y^2*z^2*w^2, x^2*y^3, x^3 ]; L := [z^6]; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Fri Mar 5 2004 02:43:26 on modular [Seed = 3857549910] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 54 72 78 80 162 0 [] [ true ] Total time: 2.969 seconds, Total memory usage: 2.11MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Fri Mar 5 02:48:50 2004 Input: K := GF(3); R := PolynomialRing(K, [3^4 -3^3, 3^4 -3^2, 3^4 -3, 3^4 -1, 3^5 -3^4]); R; P := [ u, x*u-x^(3+1)+y^3, z^3 +y*u -y*x^3, w^3 +z*u -z*x^3, u*w -w*x^3 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, w, w^2, w^3, z, z*w, z*w^2, z*w^3, z^2, z^2*w, z^2*w^2, z^2*w^3, z^3, z^4, w^3*z*y, z^3*y*x^3, y, y*w, y*w^2, y*z, y*z*w, y*z*w^2, y*z^2, y*z^2*w, y*z^2*w^2, y*z^3, y*z^4, y*z^5, y*z^6, y^2, y^2*w, y^2*w^2, y^2*z, y^2*z*w, y^2*z*w^2, y^2*z^2, y^2*z^2*w, y^2*z^2*w^2, y^2*z^3, y^3, y^3*z, y^3*z^2, y^3*z^3, y^4, y^4*z, y^4*z^2, y^4*z^3, y^5, y^5*z, y^5*z^2, y^5*z^3, y^6, y^7, y^8, y^9, x, x*w, x*w^2, x*z, x*z*w, x*z*w^2, x*z^2, x*z^2*w, x*z^2*w^2, x*y, x*y*w, x*y*w^2, x*y*z, x*y*z*w, x*y*z*w^2, x*y*z^2, x*y*z^2*w, x*y*z^2*w^2, x*y^2, x*y^2*w, x*y^2*w^2, x*y^2*z, x*y^2*z*w, x*y^2*z*w^2, x*y^2*z^2, x*y^2*z^2*w, x*y^2*z^2*w^2, x*y^3, x*y^3*z, x*y^3*z^2, x*y^4, x*y^4*z, x*y^4*z^2, x*y^5, x*y^5*z, x*y^5*z^2, x*y^6, x^2, x^2*w, x^2*w^2, x^2*z, x^2*z*w, x^2*z*w^2, x^2*z^2, x^2*z^2*w, x^2*z^2*w^2, x^2*y, x^2*y*w, x^2*y*w^2, x^2*y*z, x^2*y*z*w, x^2*y*z*w^2, x^2*y*z^2, x^2*y*z^2*w, x^2*y*z^2*w^2, x^2*y^2, x^2*y^2*w, x^2*y^2*w^2, x^2*y^2*z, x^2*y^2*z*w, x^2*y^2*z*w^2, x^2*y^2*z^2, x^2*y^2*z^2*w, x^2*y^2*z^2*w^2, x^2*y^3, x^3 ]; L := [z^5]; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Fri Mar 5 2004 02:48:47 on modular [Seed = 4227042057] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 54 72 78 80 162 0 [] [ true ] Total time: 2.939 seconds, Total memory usage: 2.11MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Fri Mar 5 02:56:00 2004 Input: K := GF(3); R := PolynomialRing(K, [3^4 -3^3, 3^4 -3^2, 3^4 -3, 3^4 -1, 3^5 -3^4]); R; P := [ u, x*u-x^(3+1)+y^3, z^3 +y*u -y*x^3, w^3 +z*u -z*x^3, u*w -w*x^3 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, w, w^2, w^3, z, z*w, z*w^2, z*w^3, z^2, z^2*w, z^2*w^2, z^2*w^3, z^3, z^4, w^3*z*y, z^3*y*x^3, y, y*w, y*w^2, y*z, y*z*w, y*z*w^2, y*z^2, y*z^2*w, y*z^2*w^2, y*z^3, y*z^4, y*z^5, y*z^6, y^2, y^2*w, y^2*w^2, y^2*z, y^2*z*w, y^2*z*w^2, y^2*z^2, y^2*z^2*w, y^2*z^2*w^2, y^2*z^3, y^3, y^3*z, y^3*z^2, y^3*z^3, z^3*x, y^4*z, y^4*z^2, y^4*z^3, y^5, y^5*z, y^5*z^2, y^5*z^3, y^6, y^7, y^8, y^9, x, x*w, x*w^2, x*z, x*z*w, x*z*w^2, x*z^2, x*z^2*w, x*z^2*w^2, x*y, x*y*w, x*y*w^2, x*y*z, x*y*z*w, x*y*z*w^2, x*y*z^2, x*y*z^2*w, x*y*z^2*w^2, x*y^2, x*y^2*w, x*y^2*w^2, x*y^2*z, x*y^2*z*w, x*y^2*z*w^2, x*y^2*z^2, x*y^2*z^2*w, x*y^2*z^2*w^2, x*y^3, x*y^3*z, x*y^3*z^2, x*y^4, x*y^4*z, x*y^4*z^2, x*y^5, x*y^5*z, x*y^5*z^2, x*y^6, x^2, x^2*w, x^2*w^2, x^2*z, x^2*z*w, x^2*z*w^2, x^2*z^2, x^2*z^2*w, x^2*z^2*w^2, x^2*y, x^2*y*w, x^2*y*w^2, x^2*y*z, x^2*y*z*w, x^2*y*z*w^2, x^2*y*z^2, x^2*y*z^2*w, x^2*y*z^2*w^2, x^2*y^2, x^2*y^2*w, x^2*y^2*w^2, x^2*y^2*z, x^2*y^2*z*w, x^2*y^2*z*w^2, x^2*y^2*z^2, x^2*y^2*z^2*w, x^2*y^2*z^2*w^2, x^2*y^3, x^3 ]; L := [y^4]; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Fri Mar 5 2004 02:55:57 on modular [Seed = 3251221345] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 54 72 78 80 162 0 [] [ true ] Total time: 2.919 seconds, Total memory usage: 2.11MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Fri Mar 5 03:10:36 2004 Input: K := GF(3); R := PolynomialRing(K, [3^4 -3^3, 3^4 -3^2, 3^4 -3, 3^4 -1, 3^5 -3^4]); R; P := [ u, x*u-x^(3+1)+y^3, z^3 +y*u -y*x^3, w^3 +z*u -z*x^3, u*w -w*x^3 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, w, w^2, w^3, z, z*w, z*w^2, z*w^3, z^2, z^2*w, z^2*w^2, z^2*w^3, z^3, z^4, w^3*z*y, z^3*y*x^3, y, y*w, y*w^2, y*z, y*z*w, y*z*w^2, y*z^2, y*z^2*w, y*z^2*w^2, y*z^3, y*z^4, y*z^5, y*z^6, y^2, y^2*w, y^2*w^2, y^2*z, y^2*z*w, y^2*z*w^2, y^2*z^2, y^2*z^2*w, y^2*z^2*w^2, y^2*z^3, y^3, y^3*z, y^3*z^2, y^3*z^3, z^3*x, y^4*z, y^4*z^2, y^4*z^3, y^5, y^5*z, y^5*z^2, y^5*z^3, y^6, y^7, w^3*z^2*y*x^2, y^9, x, x*w, x*w^2, x*z, x*z*w, x*z*w^2, x*z^2, x*z^2*w, x*z^2*w^2, x*y, x*y*w, x*y*w^2, x*y*z, x*y*z*w, x*y*z*w^2, x*y*z^2, x*y*z^2*w, x*y*z^2*w^2, x*y^2, x*y^2*w, x*y^2*w^2, x*y^2*z, x*y^2*z*w, x*y^2*z*w^2, x*y^2*z^2, x*y^2*z^2*w, x*y^2*z^2*w^2, x*y^3, x*y^3*z, x*y^3*z^2, x*y^4, x*y^4*z, x*y^4*z^2, x*y^5, x*y^5*z, x*y^5*z^2, x*y^6, x^2, x^2*w, x^2*w^2, x^2*z, x^2*z*w, x^2*z*w^2, x^2*z^2, x^2*z^2*w, x^2*z^2*w^2, x^2*y, x^2*y*w, x^2*y*w^2, x^2*y*z, x^2*y*z*w, x^2*y*z*w^2, x^2*y*z^2, x^2*y*z^2*w, x^2*y*z^2*w^2, x^2*y^2, x^2*y^2*w, x^2*y^2*w^2, x^2*y^2*z, x^2*y^2*z*w, x^2*y^2*z*w^2, x^2*y^2*z^2, x^2*y^2*z^2*w, x^2*y^2*z^2*w^2, x^2*y^3, x^3 ]; L := [y^8]; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Fri Mar 5 2004 03:10:33 on modular [Seed = 842680293] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 54 72 78 80 162 0 [] [ true ] Total time: 2.989 seconds, Total memory usage: 2.11MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Fri Mar 5 04:00:44 2004 Input: s1 := {x^i : i in [0 .. 3]}; s2 := {x^i *y^j : i in [0 .. 2], j in [1 .. 3]}; s3 := {x^i *y^j *z^l : i in [0 .. 2], j in [0 .. 2], l in [1 .. 3]}; s4 := {x^i *y^j *z^l *w^k : i in [0 .. 2], j in [0 .. 2], l in [1 .. 2], k in [1 .. 3]}; S' := s1 join s2 join s3 join s4; Output: Magma V2.10-6 Fri Mar 5 2004 04:00:41 on modular [Seed = 1481660879] ------------------------------------- >> s1 := {x^i : i in [0 .. 3]}; ^ User error: Identifier 'x' has not been declared or assigned >> s2 := {x^i *y^j : i in [0 .. 2], j in [1 .. 3]}; ^ User error: Identifier 'x' has not been declared or assigned >> s3 := {x^i *y^j *z^l : i in [0 .. 2], j in [0 .. 2], l in [1 .. 3]}; ^ User error: Identifier 'x' has not been declared or assigned >> s4 := {x^i *y^j *z^l *w^k : i in [0 .. 2], j in [0 .. 2], l in [1 .. 2], k ^ User error: Identifier 'x' has not been declared or assigned >> S' := s1 join s2 join s3 join s4; ; ^ User error: Unexpected newline in literal identifier Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Fri Mar 5 04:01:42 2004 Input: K := GF(3); R := PolynomialRing(K, [3^4 -3^3, 3^4 -3^2, 3^4 -3, 3^4 -1, 3^5 -3^4]); R; P := [ u, x*u-x^(3+1)+y^3, z^3 +y*u -y*x^3, w^3 +z*u -z*x^3, u*w -w*x^3 ] ; s1 := {x^i : i in [0 .. 3]}; s2 := {x^i *y^j : i in [0 .. 2], j in [1 .. 3]}; s3 := {x^i *y^j *z^l : i in [0 .. 2], j in [0 .. 2], l in [1 .. 3]}; s4 := {x^i *y^j *z^l *w^k : i in [0 .. 2], j in [0 .. 2], l in [1 .. 2], k in [1 .. 3]}; S' := s1 join s2 join s3 join s4; Output: Magma V2.10-6 Fri Mar 5 2004 04:01:39 on modular [Seed = 3216490082] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 54 72 78 80 162 >> S' := s1 join s2 join s3 join s4; ; ^ User error: Unexpected newline in literal identifier Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Fri Mar 5 04:02:57 2004 Input: K := GF(3); R := PolynomialRing(K, [3^4 -3^3, 3^4 -3^2, 3^4 -3, 3^4 -1, 3^5 -3^4]); R; P := [ u, x*u-x^(3+1)+y^3, z^3 +y*u -y*x^3, w^3 +z*u -z*x^3, u*w -w*x^3 ] ; s1 := {x^i : i in [0 .. 3]}; s1; s2 := {x^i *y^j : i in [0 .. 2], j in [1 .. 3]}; s3 := {x^i *y^j *z^l : i in [0 .. 2], j in [0 .. 2], l in [1 .. 3]}; s4 := {x^i *y^j *z^l *w^k : i in [0 .. 2], j in [0 .. 2], l in [1 .. 2], k in [1 .. 3]}; S' := s1 join s2 join s3 join s4 ; S'; Output: Magma V2.10-6 Fri Mar 5 2004 04:02:54 on modular [Seed = 3182804908] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 54 72 78 80 162 { x, x^3, 1, x^2 } >> S' := s1 join s2 join s3 join s4 ; ^ User error: Unexpected newline in literal identifier >> S';; ^ User error: Unexpected newline in literal identifier Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Fri Mar 5 04:04:02 2004 Input: K := GF(3); R := PolynomialRing(K, [3^4 -3^3, 3^4 -3^2, 3^4 -3, 3^4 -1, 3^5 -3^4]); R; P := [ u, x*u-x^(3+1)+y^3, z^3 +y*u -y*x^3, w^3 +z*u -z*x^3, u*w -w*x^3 ] ; s1 := {x^i : i in [0 .. 3]}; s1; s2 := {x^i *y^j : i in [0 .. 2], j in [1 .. 3]}; s2; s1 join s2; s3 := {x^i *y^j *z^l : i in [0 .. 2], j in [0 .. 2], l in [1 .. 3]}; s4 := {x^i *y^j *z^l *w^k : i in [0 .. 2], j in [0 .. 2], l in [1 .. 2], k in [1 .. 3]}; S' := s1 join s2 join s3 join s4 ; S'; Output: Magma V2.10-6 Fri Mar 5 2004 04:03:59 on modular [Seed = 3032266468] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 54 72 78 80 162 { x, x^3, 1, x^2 } { y, x^2*y, x*y, y^2, x^2*y^2, x*y^2, y^3, x^2*y^3, x*y^3 } { x, y, x^3, x^2*y, x*y, y^2, x^2*y^2, x*y^2, y^3, x^2*y^3, x*y^3, 1, x^2 } >> S' := s1 join s2 join s3 join s4 ; ^ User error: Unexpected newline in literal identifier >> S';; ^ User error: Unexpected newline in literal identifier Total time: 3.079 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Fri Mar 5 04:04:42 2004 Input: K := GF(3); R := PolynomialRing(K, [3^4 -3^3, 3^4 -3^2, 3^4 -3, 3^4 -1, 3^5 -3^4]); R; P := [ u, x*u-x^(3+1)+y^3, z^3 +y*u -y*x^3, w^3 +z*u -z*x^3, u*w -w*x^3 ] ; s1 := {x^i : i in [0 .. 3]}; s1; s2 := {x^i *y^j : i in [0 .. 2], j in [1 .. 3]}; s2; s1 join s2; s3 := {x^i *y^j *z^l : i in [0 .. 2], j in [0 .. 2], l in [1 .. 3]}; s4 := {x^i *y^j *z^l *w^k : i in [0 .. 2], j in [0 .. 2], l in [1 .. 2], k in [1 .. 3]}; s1 join s2 join s3 join s4 ; S'; Output: Magma V2.10-6 Fri Mar 5 2004 04:04:39 on modular [Seed = 2340653315] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 54 72 78 80 162 { x, x^3, 1, x^2 } { y, x^2*y, x*y, y^2, x^2*y^2, x*y^2, y^3, x^2*y^3, x*y^3 } { x, y, x^3, x^2*y, x*y, y^2, x^2*y^2, x*y^2, y^3, x^2*y^3, x*y^3, 1, x^2 } { z*w^2, x^2*z*w^2, y*z*w^2, x^2*y*z*w^2, y^2*z*w^2, x^2*y^2*z*w^2, z^2*w^2, x*z*w^2, x^2*z^2*w^2, y*z^2*w^2, x*y*z*w^2, x^2*y*z^2*w^2, x*y^2*z*w^2, y^2*z^2*w^2, x^2*y^2*z^2*w^2, x*z^2*w^2, x*y*z^2*w^2, x*y^2*z^2*w^2, z*w^3, x^2*z*w^3, y*z*w^3, x^2*y*z*w^3, y^2*z*w^3, x^2*y^2*z*w^3, z^2*w^3, x*z*w^3, x^2*z^2*w^3, x*y*z*w^3, y*z^2*w^3, x^2*y*z^2*w^3, x*y^2*z*w^3, y^2*z^2*w^3, x^2*y^2*z^2*w^3, x*z^2*w^3, x*y*z^2*w^3, x*y^2*z^2*w^3, 1, x^2, y, x^2*y, y^2, x^2*y^2, y^3, x^2*y^3, z, x, x^2*z, x^3, y*z, x*y, x^2*y*z, x*y^2, y^2*z, x^2*y^2*z, x*y^3, x*z, z^2, x^2*z^2, y*z^2, x*y*z, x^2*y*z^2, y^2*z^2, x*y^2*z, x^2*y^2*z^2, x*z^2, z^3, x^2*z^3, x*y*z^2, y*z^3, x^2*y*z^3, y^2*z^3, x*y^2*z^2, x^2*y^2*z^3, x*z^3, x*y*z^3, x*y^2*z^3, z*w, x^2*z*w, y*z*w, x^2*y*z*w, y^2*z*w, x^2*y^2*z*w, z^2*w, x*z*w, x^2*z^2*w, y*z^2*w, x*y*z*w, x^2*y*z^2*w, y^2*z^2*w, x*y^2*z*w, x^2*y^2*z^2*w, x*z^2*w, x*y*z^2*w, x*y^2*z^2*w } >> S';; ^ User error: Unexpected newline in literal identifier Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Fri Mar 5 04:08:37 2004 Input: K := GF(3); R := PolynomialRing(K, [3^4 -3^3, 3^4 -3^2, 3^4 -3, 3^4 -1, 3^5 -3^4]); R; P := [ u, x*u-x^(3+1)+y^3, z^3 +y*u -y*x^3, w^3 +z*u -z*x^3, u*w -w*x^3 ] ; { z*w^2, x^2*z*w^2, y*z*w^2, x^2*y*z*w^2, y^2*z*w^2, x^2*y^2*z*w^2, z^2*w^2, x*z*w^2, x^2*z^2*w^2, y*z^2*w^2, x*y*z*w^2, x^2*y*z^2*w^2, x*y^2*z*w^2, y^2*z^2*w^2, x^2*y^2*z^2*w^2, x*z^2*w^2, x*y*z^2*w^2, x*y^2*z^2*w^2, z*w^3, x^2*z*w^3, y*z*w^3, x^2*y*z*w^3, y^2*z*w^3, x^2*y^2*z*w^3, z^2*w^3, x*z*w^3, x^2*z^2*w^3, x*y*z*w^3, y*z^2*w^3, x^2*y*z^2*w^3, x*y^2*z*w^3, y^2*z^2*w^3, x^2*y^2*z^2*w^3, x*z^2*w^3, x*y*z^2*w^3, x*y^2*z^2*w^3, 1, x^2, y, x^2*y, y^2, x^2*y^2, y^3, x^2*y^3, z, x, x^2*z, x^3, y*z, x*y, x^2*y*z, x*y^2, y^2*z, x^2*y^2*z, x*y^3, x*z, z^2, x^2*z^2, y*z^2, x*y*z, x^2*y*z^2, y^2*z^2, x*y^2*z, x^2*y^2*z^2, x*z^2, z^3, x^2*z^3, x*y*z^2, y*z^3, x^2*y*z^3, y^2*z^3, x*y^2*z^2, x^2*y^2*z^3, x*z^3, x*y*z^3, x*y^2*z^3, z*w, x^2*z*w, y*z*w, x^2*y*z*w, y^2*z*w, x^2*y^2*z*w, z^2*w, x*z*w, x^2*z^2*w, y*z^2*w, x*y*z*w, x^2*y*z^2*w, y^2*z^2*w, x*y^2*z*w, x^2*y^2*z^2*w, x*z^2*w, x*y*z^2*w, x*y^2*z^2*w } diff { 1, w, w^2, w^3, z, z*w, z*w^2, z*w^3, z^2, z^2*w, z^2*w^2, z^2*w^3, z^3, w^3*y, w^3*z*y, z^3*y*x^3, y, y*w, y*w^2, y*z, y*z*w, y*z*w^2, y*z^2, y*z^2*w, y*z^2*w^2, y*z^3, w^3*y^2, w^3*z*y^2, z^3*y^2*x^3, y^2, y^2*w, y^2*w^2, y^2*z, y^2*z*w, y^2*z*w^2, y^2*z^2, y^2*z^2*w, y^2*z^2*w^2, y^2*z^3, y^3, y^3*z, y^3*z^2, y^3*z^3, z^3*x, w^3*y*x, w^3*z*y*x, w^3*z^2*y*x, z^3*y*x, w^3*y^2*x, w^3*z*y^2*x, w^3*z^2*y^2*x, z^3*y^2*x, z^3*y^3*x, w^3*z^2*y*x^2, w^3*z^2*y^2*x^2, x, x*w, x*w^2, x*z, x*z*w, x*z*w^2, x*z^2, x*z^2*w, x*z^2*w^2, x*y, x*y*w, x*y*w^2, x*y*z, x*y*z*w, x*y*z*w^2, x*y*z^2, x*y*z^2*w, x*y*z^2*w^2, x*y^2, x*y^2*w, x*y^2*w^2, x*y^2*z, x*y^2*z*w, x*y^2*z*w^2, x*y^2*z^2, x*y^2*z^2*w, x*y^2*z^2*w^2, x*y^3, x*y^3*z, x*y^3*z^2, z^3*x^2, w^3*y*x^2, w^3*z*y*x^2, z^3*y*x^2, w^3*y^2*x^2, w^3*z*y^2*x^2, z^3*y^2*x^2, x^2, x^2*w, x^2*w^2, x^2*z, x^2*z*w, x^2*z*w^2, x^2*z^2, x^2*z^2*w, x^2*z^2*w^2, x^2*y, x^2*y*w, x^2*y*w^2, x^2*y*z, x^2*y*z*w, x^2*y*z*w^2, x^2*y*z^2, x^2*y*z^2*w, x^2*y*z^2*w^2, x^2*y^2, x^2*y^2*w, x^2*y^2*w^2, x^2*y^2*z, x^2*y^2*z*w, x^2*y^2*z*w^2, x^2*y^2*z^2, x^2*y^2*z^2*w, x^2*y^2*z^2*w^2, x^2*y^3, x^3 } ; s1 := {x^i : i in [0 .. 3]}; s1; s2 := {x^i *y^j : i in [0 .. 2], j in [1 .. 3]}; s2; s1 join s2; s3 := {x^i *y^j *z^l : i in [0 .. 2], j in [0 .. 2], l in [1 .. 3]}; s4 := {x^i *y^j *z^l *w^k : i in [0 .. 2], j in [0 .. 2], l in [1 .. 2], k in [1 .. 3]}; s1 join s2 join s3 join s4 ; S'; Output: Magma V2.10-6 Fri Mar 5 2004 04:08:34 on modular [Seed = 2964894482] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 54 72 78 80 162 { x^2*z*w^3, x*z*w^3, y^2*z^2*w^3, x^2*z^2*w^3, x*z^2*w^3, y*z^2*w^3 } { x, x^3, 1, x^2 } { y, x^2*y, x*y, y^2, x^2*y^2, x*y^2, y^3, x^2*y^3, x*y^3 } { x, y, x^3, x^2*y, x*y, y^2, x^2*y^2, x*y^2, y^3, x^2*y^3, x*y^3, 1, x^2 } { z*w^2, x^2*z*w^2, y*z*w^2, x^2*y*z*w^2, y^2*z*w^2, x^2*y^2*z*w^2, z^2*w^2, x*z*w^2, x^2*z^2*w^2, y*z^2*w^2, x*y*z*w^2, x^2*y*z^2*w^2, x*y^2*z*w^2, y^2*z^2*w^2, x^2*y^2*z^2*w^2, x*z^2*w^2, x*y*z^2*w^2, x*y^2*z^2*w^2, z*w^3, x^2*z*w^3, y*z*w^3, x^2*y*z*w^3, y^2*z*w^3, x^2*y^2*z*w^3, z^2*w^3, x*z*w^3, x^2*z^2*w^3, x*y*z*w^3, y*z^2*w^3, x^2*y*z^2*w^3, x*y^2*z*w^3, y^2*z^2*w^3, x^2*y^2*z^2*w^3, x*z^2*w^3, x*y*z^2*w^3, x*y^2*z^2*w^3, 1, x^2, y, x^2*y, y^2, x^2*y^2, y^3, x^2*y^3, z, x, x^2*z, x^3, y*z, x*y, x^2*y*z, x*y^2, y^2*z, x^2*y^2*z, x*y^3, x*z, z^2, x^2*z^2, y*z^2, x*y*z, x^2*y*z^2, y^2*z^2, x*y^2*z, x^2*y^2*z^2, x*z^2, z^3, x^2*z^3, x*y*z^2, y*z^3, x^2*y*z^3, y^2*z^3, x*y^2*z^2, x^2*y^2*z^3, x*z^3, x*y*z^3, x*y^2*z^3, z*w, x^2*z*w, y*z*w, x^2*y*z*w, y^2*z*w, x^2*y^2*z*w, z^2*w, x*z*w, x^2*z^2*w, y*z^2*w, x*y*z*w, x^2*y*z^2*w, y^2*z^2*w, x*y^2*z*w, x^2*y^2*z^2*w, x*z^2*w, x*y*z^2*w, x*y^2*z^2*w } >> S';; ^ User error: Unexpected newline in literal identifier Total time: 3.419 seconds, Total memory usage: 2.20MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Fri Mar 5 04:12:12 2004 Input: K := GF(3); R := PolynomialRing(K, [3^4 -3^3, 3^4 -3^2, 3^4 -3, 3^4 -1, 3^5 -3^4]); R; P := [ u, x*u-x^(3+1)+y^3, z^3 +y*u -y*x^3, w^3 +z*u -z*x^3, u*w -w*x^3 ] ; { 1, w, w^2, w^3, z, z*w, z*w^2, z*w^3, z^2, z^2*w, z^2*w^2, z^2*w^3, z^3, w^3*y, w^3*z*y, z^3*y*x^3, y, y*w, y*w^2, y*z, y*z*w, y*z*w^2, y*z^2, y*z^2*w, y*z^2*w^2, y*z^3, w^3*y^2, w^3*z*y^2, z^3*y^2*x^3, y^2, y^2*w, y^2*w^2, y^2*z, y^2*z*w, y^2*z*w^2, y^2*z^2, y^2*z^2*w, y^2*z^2*w^2, y^2*z^3, y^3, y^3*z, y^3*z^2, y^3*z^3, z^3*x, w^3*y*x, w^3*z*y*x, w^3*z^2*y*x, z^3*y*x, w^3*y^2*x, w^3*z*y^2*x, w^3*z^2*y^2*x, z^3*y^2*x, z^3*y^3*x, w^3*z^2*y*x^2, w^3*z^2*y^2*x^2, x, x*w, x*w^2, x*z, x*z*w, x*z*w^2, x*z^2, x*z^2*w, x*z^2*w^2, x*y, x*y*w, x*y*w^2, x*y*z, x*y*z*w, x*y*z*w^2, x*y*z^2, x*y*z^2*w, x*y*z^2*w^2, x*y^2, x*y^2*w, x*y^2*w^2, x*y^2*z, x*y^2*z*w, x*y^2*z*w^2, x*y^2*z^2, x*y^2*z^2*w, x*y^2*z^2*w^2, x*y^3, x*y^3*z, x*y^3*z^2, z^3*x^2, w^3*y*x^2, w^3*z*y*x^2, z^3*y*x^2, w^3*y^2*x^2, w^3*z*y^2*x^2, z^3*y^2*x^2, x^2, x^2*w, x^2*w^2, x^2*z, x^2*z*w, x^2*z*w^2, x^2*z^2, x^2*z^2*w, x^2*z^2*w^2, x^2*y, x^2*y*w, x^2*y*w^2, x^2*y*z, x^2*y*z*w, x^2*y*z*w^2, x^2*y*z^2, x^2*y*z^2*w, x^2*y*z^2*w^2, x^2*y^2, x^2*y^2*w, x^2*y^2*w^2, x^2*y^2*z, x^2*y^2*z*w, x^2*y^2*z*w^2, x^2*y^2*z^2, x^2*y^2*z^2*w, x^2*y^2*z^2*w^2, x^2*y^3, x^3 } diff { z*w^2, x^2*z*w^2, y*z*w^2, x^2*y*z*w^2, y^2*z*w^2, x^2*y^2*z*w^2, z^2*w^2, x*z*w^2, x^2*z^2*w^2, y*z^2*w^2, x*y*z*w^2, x^2*y*z^2*w^2, x*y^2*z*w^2, y^2*z^2*w^2, x^2*y^2*z^2*w^2, x*z^2*w^2, x*y*z^2*w^2, x*y^2*z^2*w^2, z*w^3, x^2*z*w^3, y*z*w^3, x^2*y*z*w^3, y^2*z*w^3, x^2*y^2*z*w^3, z^2*w^3, x*z*w^3, x^2*z^2*w^3, x*y*z*w^3, y*z^2*w^3, x^2*y*z^2*w^3, x*y^2*z*w^3, y^2*z^2*w^3, x^2*y^2*z^2*w^3, x*z^2*w^3, x*y*z^2*w^3, x*y^2*z^2*w^3, 1, x^2, y, x^2*y, y^2, x^2*y^2, y^3, x^2*y^3, z, x, x^2*z, x^3, y*z, x*y, x^2*y*z, x*y^2, y^2*z, x^2*y^2*z, x*y^3, x*z, z^2, x^2*z^2, y*z^2, x*y*z, x^2*y*z^2, y^2*z^2, x*y^2*z, x^2*y^2*z^2, x*z^2, z^3, x^2*z^3, x*y*z^2, y*z^3, x^2*y*z^3, y^2*z^3, x*y^2*z^2, x^2*y^2*z^3, x*z^3, x*y*z^3, x*y^2*z^3, z*w, x^2*z*w, y*z*w, x^2*y*z*w, y^2*z*w, x^2*y^2*z*w, z^2*w, x*z*w, x^2*z^2*w, y*z^2*w, x*y*z*w, x^2*y*z^2*w, y^2*z^2*w, x*y^2*z*w, x^2*y^2*z^2*w, x*z^2*w, x*y*z^2*w, x*y^2*z^2*w } ; s1 := {x^i : i in [0 .. 3]}; s1; s2 := {x^i *y^j : i in [0 .. 2], j in [1 .. 3]}; s2; s1 join s2; s3 := {x^i *y^j *z^l : i in [0 .. 2], j in [0 .. 2], l in [1 .. 3]}; s4 := {x^i *y^j *z^l *w^k : i in [0 .. 2], j in [0 .. 2], l in [1 .. 2], k in [1 .. 3]}; s1 join s2 join s3 join s4 ; S'; Output: Magma V2.10-6 Fri Mar 5 2004 04:12:09 on modular [Seed = 2712249848] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 54 72 78 80 162 { x*y^2*w^2, y^3*z^2, x*y*w^3, x*y^3*z^3, y^2*w^3, x^2*y^2*w^3, x*y^2*w, x*y*w^2, x^3*y^2*z^3, y^2*w^2, x^2*y^2*w^2, y*w^3, x^2*y*w^3, y^3*z^3, x*y*w, x*w^2, x^3*y*z^3, y^2*w, x^2*y^2*w, y*w^2, w^3, x^2*y*w^2, x*y^3*z, x*w, y*w, w^2, x^2*y*w, x^2*w^2, y^3*z, x*y^3*z^2, w, x^2*w, x*y^2*w^3 } { x, x^3, 1, x^2 } { y, x^2*y, x*y, y^2, x^2*y^2, x*y^2, y^3, x^2*y^3, x*y^3 } { x, y, x^3, x^2*y, x*y, y^2, x^2*y^2, x*y^2, y^3, x^2*y^3, x*y^3, 1, x^2 } { z*w^2, x^2*z*w^2, y*z*w^2, x^2*y*z*w^2, y^2*z*w^2, x^2*y^2*z*w^2, z^2*w^2, x*z*w^2, x^2*z^2*w^2, y*z^2*w^2, x*y*z*w^2, x^2*y*z^2*w^2, x*y^2*z*w^2, y^2*z^2*w^2, x^2*y^2*z^2*w^2, x*z^2*w^2, x*y*z^2*w^2, x*y^2*z^2*w^2, z*w^3, x^2*z*w^3, y*z*w^3, x^2*y*z*w^3, y^2*z*w^3, x^2*y^2*z*w^3, z^2*w^3, x*z*w^3, x^2*z^2*w^3, x*y*z*w^3, y*z^2*w^3, x^2*y*z^2*w^3, x*y^2*z*w^3, y^2*z^2*w^3, x^2*y^2*z^2*w^3, x*z^2*w^3, x*y*z^2*w^3, x*y^2*z^2*w^3, 1, x^2, y, x^2*y, y^2, x^2*y^2, y^3, x^2*y^3, z, x, x^2*z, x^3, y*z, x*y, x^2*y*z, x*y^2, y^2*z, x^2*y^2*z, x*y^3, x*z, z^2, x^2*z^2, y*z^2, x*y*z, x^2*y*z^2, y^2*z^2, x*y^2*z, x^2*y^2*z^2, x*z^2, z^3, x^2*z^3, x*y*z^2, y*z^3, x^2*y*z^3, y^2*z^3, x*y^2*z^2, x^2*y^2*z^3, x*z^3, x*y*z^3, x*y^2*z^3, z*w, x^2*z*w, y*z*w, x^2*y*z*w, y^2*z*w, x^2*y^2*z*w, z^2*w, x*z*w, x^2*z^2*w, y*z^2*w, x*y*z*w, x^2*y*z^2*w, y^2*z^2*w, x*y^2*z*w, x^2*y^2*z^2*w, x*z^2*w, x*y*z^2*w, x*y^2*z^2*w } >> S';; ^ User error: Unexpected newline in literal identifier Total time: 3.069 seconds, Total memory usage: 2.20MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Fri Mar 5 04:17:56 2004 Input: K := GF(3); R := PolynomialRing(K, [3^4 -3^3, 3^4 -3^2, 3^4 -3, 3^4 -1, 3^5 -3^4]); R; P := [ u, x*u-x^(3+1)+y^3, z^3 +y*u -y*x^3, w^3 +z*u -z*x^3, u*w -w*x^3 ] ; s1 := {x^i : i in [0 .. 3]}; s2 := {x^i *y^j : i in [0 .. 2], j in [1 .. 3]}; s3 := {x^i *y^j *z^l : i in [0 .. 2], j in [0 .. 2], l in [1 .. 3]}; s4 := {x^i *y^j *z^l *w^k : i in [0 .. 2], j in [0 .. 2], l in [1 .. 2], k in [1 .. 3]}; s1 join s2 join s3 join s4; Output: Magma V2.10-6 Fri Mar 5 2004 04:17:52 on modular [Seed = 3807045395] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 54 72 78 80 162 { z*w^2, x^2*z*w^2, y*z*w^2, x^2*y*z*w^2, y^2*z*w^2, x^2*y^2*z*w^2, z^2*w^2, x*z*w^2, x^2*z^2*w^2, y*z^2*w^2, x*y*z*w^2, x^2*y*z^2*w^2, x*y^2*z*w^2, y^2*z^2*w^2, x^2*y^2*z^2*w^2, x*z^2*w^2, x*y*z^2*w^2, x*y^2*z^2*w^2, z*w^3, x^2*z*w^3, y*z*w^3, x^2*y*z*w^3, y^2*z*w^3, x^2*y^2*z*w^3, z^2*w^3, x*z*w^3, x^2*z^2*w^3, x*y*z*w^3, y*z^2*w^3, x^2*y*z^2*w^3, x*y^2*z*w^3, y^2*z^2*w^3, x^2*y^2*z^2*w^3, x*z^2*w^3, x*y*z^2*w^3, x*y^2*z^2*w^3, 1, x^2, y, x^2*y, y^2, x^2*y^2, y^3, x^2*y^3, z, x, x^2*z, x^3, y*z, x*y, x^2*y*z, x*y^2, y^2*z, x^2*y^2*z, x*y^3, x*z, z^2, x^2*z^2, y*z^2, x*y*z, x^2*y*z^2, y^2*z^2, x*y^2*z, x^2*y^2*z^2, x*z^2, z^3, x^2*z^3, x*y*z^2, y*z^3, x^2*y*z^3, y^2*z^3, x*y^2*z^2, x^2*y^2*z^3, x*z^3, x*y*z^3, x*y^2*z^3, z*w, x^2*z*w, y*z*w, x^2*y*z*w, y^2*z*w, x^2*y^2*z*w, z^2*w, x*z*w, x^2*z^2*w, y*z^2*w, x*y*z*w, x^2*y*z^2*w, y^2*z^2*w, x*y^2*z*w, x^2*y^2*z^2*w, x*z^2*w, x*y*z^2*w, x*y^2*z^2*w } Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Fri Mar 5 04:18:35 2004 Input: K := GF(3); R := PolynomialRing(K, [3^4 -3^3, 3^4 -3^2, 3^4 -3, 3^4 -1, 3^5 -3^4]); R; P := [ u, x*u-x^(3+1)+y^3, z^3 +y*u -y*x^3, w^3 +z*u -z*x^3, u*w -w*x^3 ] ; #{ z*w^2, x^2*z*w^2, y*z*w^2, x^2*y*z*w^2, y^2*z*w^2, x^2*y^2*z*w^2, z^2*w^2, x*z*w^2, x^2*z^2*w^2, y*z^2*w^2, x*y*z*w^2, x^2*y*z^2*w^2, x*y^2*z*w^2, y^2*z^2*w^2, x^2*y^2*z^2*w^2, x*z^2*w^2, x*y*z^2*w^2, x*y^2*z^2*w^2, z*w^3, x^2*z*w^3, y*z*w^3, x^2*y*z*w^3, y^2*z*w^3, x^2*y^2*z*w^3, z^2*w^3, x*z*w^3, x^2*z^2*w^3, x*y*z*w^3, y*z^2*w^3, x^2*y*z^2*w^3, x*y^2*z*w^3, y^2*z^2*w^3, x^2*y^2*z^2*w^3, x*z^2*w^3, x*y*z^2*w^3, x*y^2*z^2*w^3, 1, x^2, y, x^2*y, y^2, x^2*y^2, y^3, x^2*y^3, z, x, x^2*z, x^3, y*z, x*y, x^2*y*z, x*y^2, y^2*z, x^2*y^2*z, x*y^3, x*z, z^2, x^2*z^2, y*z^2, x*y*z, x^2*y*z^2, y^2*z^2, x*y^2*z, x^2*y^2*z^2, x*z^2, z^3, x^2*z^3, x*y*z^2, y*z^3, x^2*y*z^3, y^2*z^3, x*y^2*z^2, x^2*y^2*z^3, x*z^3, x*y*z^3, x*y^2*z^3, z*w, x^2*z*w, y*z*w, x^2*y*z*w, y^2*z*w, x^2*y^2*z*w, z^2*w, x*z*w, x^2*z^2*w, y*z^2*w, x*y*z*w, x^2*y*z^2*w, y^2*z^2*w, x*y^2*z*w, x^2*y^2*z^2*w, x*z^2*w, x*y*z^2*w, x*y^2*z^2*w }; Output: Magma V2.10-6 Fri Mar 5 2004 04:18:32 on modular [Seed = 3957583411] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 54 72 78 80 162 94 Total time: 2.909 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Fri Mar 5 04:21:52 2004 Input: K := GF(3); R := PolynomialRing(K, [3^4 -3^3, 3^4 -3^2, 3^4 -3, 3^4 -1, 3^5 -3^4]); R; P := [ u, x*u-x^(3+1)+y^3, z^3 +y*u -y*x^3, w^3 +z*u -z*x^3, u*w -w*x^3 ] ; s1 := {x^i : i in [0 .. 3]}; s2 := {x^i *y^j : i in [0 .. 2], j in [1 .. 3]}; s3 := {x^i *y^j *z^l : i in [0 .. 2], j in [0 .. 2], l in [1 .. 3]}; s4 := {x^i *y^j *z^l *w^k : i in [0 .. 2], j in [0 .. 2], l in [0 .. 2], k in [1 .. 3]}; s1 join s2 join s3 join s4; Output: Magma V2.10-6 Fri Mar 5 2004 04:21:49 on modular [Seed = 3704937025] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 54 72 78 80 162 { y^3, x^2*y^3, w^3, x^2*w^3, x*w, y*z^2*w^2, x^2*y*z^2*w^2, y^2*z*w^3, x^2*y^2*z*w^3, x*y*z^2, x*y^2*z*w, y^2, x^2*y^2, z^2*w^2, x^2*z^2*w^2, y*z*w^3, x^2*y*z*w^3, x*z^2, x*y*z*w, y, x^2*y, x*y^2*w^2, x*y^2*z^3, z*w^3, x^2*z*w^3, x*z*w, 1, x^2, x*y*w^2, y^2*z^2*w^3, x^2*y^2*z^2*w^3, x*y*z^3, x*y^2*z^2*w, y^2*z, x^2*y^2*z, x*w^2, y*z^2*w^3, x^2*y*z^2*w^3, x*z^3, x*y*z^2*w, y*z, x^2*y*z, x*y^2*z*w^2, y^2*w, x^2*y^2*w, z^2*w^3, x^2*z^2*w^3, z, x*z^2*w, x^2*z, y*w, x*y*z*w^2, x^2*y*w, x*y^2*w^3, y^2*z^2, x^2*y^2*z^2, x*z*w^2, w, x^2*w, x*y*w^3, y*z^2, x^2*y*z^2, x*y^2*z^2*w^2, y^2*z*w, x^2*y^2*z*w, x*y^3, x*w^3, z^2, x^2*z^2, x*y*z^2*w^2, y*z*w, x^2*y*z*w, x*y^2*z*w^3, y^2*w^2, x^2*y^2*w^2, x*y^2, y^2*z^3, x^2*y^2*z^3, z*w, x*z^2*w^2, x^2*z*w, y*w^2, x*y*z*w^3, x^2*y*w^2, x*y, y*z^3, x^2*y*z^3, y^2*z^2*w, x^2*y^2*z^2*w, x*z*w^3, w^2, x^2*w^2, x, x^3, z^3, x^2*z^3, y*z^2*w, x^2*y*z^2*w, x*y^2*z^2*w^3, y^2*z*w^2, x^2*y^2*z*w^2, x*y^2*z, z^2*w, x^2*z^2*w, x*y*z^2*w^3, y*z*w^2, x^2*y*z*w^2, y^2*w^3, x^2*y^2*w^3, x*y*z, x*y^2*w, z*w^2, x*z^2*w^3, x^2*z*w^2, y*w^3, x^2*y*w^3, x*z, x*y*w, y^2*z^2*w^2, x^2*y^2*z^2*w^2, x*y^2*z^2 } Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Fri Mar 5 04:23:35 2004 Input: K := GF(3); R := PolynomialRing(K, [3^4 -3^3, 3^4 -3^2, 3^4 -3, 3^4 -1, 3^5 -3^4]); R; P := [ u, x*u-x^(3+1)+y^3, z^3 +y*u -y*x^3, w^3 +z*u -z*x^3, u*w -w*x^3 ] ; #{ y^3, x^2*y^3, w^3, x^2*w^3, x*w, y*z^2*w^2, x^2*y*z^2*w^2, y^2*z*w^3, x^2*y^2*z*w^3, x*y*z^2, x*y^2*z*w, y^2, x^2*y^2, z^2*w^2, x^2*z^2*w^2, y*z*w^3, x^2*y*z*w^3, x*z^2, x*y*z*w, y, x^2*y, x*y^2*w^2, x*y^2*z^3, z*w^3, x^2*z*w^3, x*z*w, 1, x^2, x*y*w^2, y^2*z^2*w^3, x^2*y^2*z^2*w^3, x*y*z^3, x*y^2*z^2*w, y^2*z, x^2*y^2*z, x*w^2, y*z^2*w^3, x^2*y*z^2*w^3, x*z^3, x*y*z^2*w, y*z, x^2*y*z, x*y^2*z*w^2, y^2*w, x^2*y^2*w, z^2*w^3, x^2*z^2*w^3, z, x*z^2*w, x^2*z, y*w, x*y*z*w^2, x^2*y*w, x*y^2*w^3, y^2*z^2, x^2*y^2*z^2, x*z*w^2, w, x^2*w, x*y*w^3, y*z^2, x^2*y*z^2, x*y^2*z^2*w^2, y^2*z*w, x^2*y^2*z*w, x*y^3, x*w^3, z^2, x^2*z^2, x*y*z^2*w^2, y*z*w, x^2*y*z*w, x*y^2*z*w^3, y^2*w^2, x^2*y^2*w^2, x*y^2, y^2*z^3, x^2*y^2*z^3, z*w, x*z^2*w^2, x^2*z*w, y*w^2, x*y*z*w^3, x^2*y*w^2, x*y, y*z^3, x^2*y*z^3, y^2*z^2*w, x^2*y^2*z^2*w, x*z*w^3, w^2, x^2*w^2, x, x^3, z^3, x^2*z^3, y*z^2*w, x^2*y*z^2*w, x*y^2*z^2*w^3, y^2*z*w^2, x^2*y^2*z*w^2, x*y^2*z, z^2*w, x^2*z^2*w, x*y*z^2*w^3, y*z*w^2, x^2*y*z*w^2, y^2*w^3, x^2*y^2*w^3, x*y*z, x*y^2*w, z*w^2, x*z^2*w^3, x^2*z*w^2, y*w^3, x^2*y*w^3, x*z, x*y*w, y^2*z^2*w^2, x^2*y^2*z^2*w^2, x*y^2*z^2 }; Output: Magma V2.10-6 Fri Mar 5 2004 04:23:32 on modular [Seed = 3318596321] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 54 72 78 80 162 121 Total time: 2.929 seconds, Total memory usage: 2.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Fri Mar 5 04:24:59 2004 Input: K := GF(3); R := PolynomialRing(K, [3^4 -3^3, 3^4 -3^2, 3^4 -3, 3^4 -1, 3^5 -3^4]); R; P := [ u, x*u-x^(3+1)+y^3, z^3 +y*u -y*x^3, w^3 +z*u -z*x^3, u*w -w*x^3 ] ; { y^3, x^2*y^3, w^3, x^2*w^3, x*w, y*z^2*w^2, x^2*y*z^2*w^2, y^2*z*w^3, x^2*y^2*z*w^3, x*y*z^2, x*y^2*z*w, y^2, x^2*y^2, z^2*w^2, x^2*z^2*w^2, y*z*w^3, x^2*y*z*w^3, x*z^2, x*y*z*w, y, x^2*y, x*y^2*w^2, x*y^2*z^3, z*w^3, x^2*z*w^3, x*z*w, 1, x^2, x*y*w^2, y^2*z^2*w^3, x^2*y^2*z^2*w^3, x*y*z^3, x*y^2*z^2*w, y^2*z, x^2*y^2*z, x*w^2, y*z^2*w^3, x^2*y*z^2*w^3, x*z^3, x*y*z^2*w, y*z, x^2*y*z, x*y^2*z*w^2, y^2*w, x^2*y^2*w, z^2*w^3, x^2*z^2*w^3, z, x*z^2*w, x^2*z, y*w, x*y*z*w^2, x^2*y*w, x*y^2*w^3, y^2*z^2, x^2*y^2*z^2, x*z*w^2, w, x^2*w, x*y*w^3, y*z^2, x^2*y*z^2, x*y^2*z^2*w^2, y^2*z*w, x^2*y^2*z*w, x*y^3, x*w^3, z^2, x^2*z^2, x*y*z^2*w^2, y*z*w, x^2*y*z*w, x*y^2*z*w^3, y^2*w^2, x^2*y^2*w^2, x*y^2, y^2*z^3, x^2*y^2*z^3, z*w, x*z^2*w^2, x^2*z*w, y*w^2, x*y*z*w^3, x^2*y*w^2, x*y, y*z^3, x^2*y*z^3, y^2*z^2*w, x^2*y^2*z^2*w, x*z*w^3, w^2, x^2*w^2, x, x^3, z^3, x^2*z^3, y*z^2*w, x^2*y*z^2*w, x*y^2*z^2*w^3, y^2*z*w^2, x^2*y^2*z*w^2, x*y^2*z, z^2*w, x^2*z^2*w, x*y*z^2*w^3, y*z*w^2, x^2*y*z*w^2, y^2*w^3, x^2*y^2*w^3, x*y*z, x*y^2*w, z*w^2, x*z^2*w^3, x^2*z*w^2, y*w^3, x^2*y*w^3, x*z, x*y*w, y^2*z^2*w^2, x^2*y^2*z^2*w^2, x*y^2*z^2 } diff { 1, w, w^2, w^3, z, z*w, z*w^2, z*w^3, z^2, z^2*w, z^2*w^2, z^2*w^3, z^3, w^3*y, w^3*z*y, z^3*y*x^3, y, y*w, y*w^2, y*z, y*z*w, y*z*w^2, y*z^2, y*z^2*w, y*z^2*w^2, y*z^3, w^3*y^2, w^3*z*y^2, z^3*y^2*x^3, y^2, y^2*w, y^2*w^2, y^2*z, y^2*z*w, y^2*z*w^2, y^2*z^2, y^2*z^2*w, y^2*z^2*w^2, y^2*z^3, y^3, y^3*z, y^3*z^2, y^3*z^3, z^3*x, w^3*y*x, w^3*z*y*x, w^3*z^2*y*x, z^3*y*x, w^3*y^2*x, w^3*z*y^2*x, w^3*z^2*y^2*x, z^3*y^2*x, z^3*y^3*x, w^3*z^2*y*x^2, w^3*z^2*y^2*x^2, x, x*w, x*w^2, x*z, x*z*w, x*z*w^2, x*z^2, x*z^2*w, x*z^2*w^2, x*y, x*y*w, x*y*w^2, x*y*z, x*y*z*w, x*y*z*w^2, x*y*z^2, x*y*z^2*w, x*y*z^2*w^2, x*y^2, x*y^2*w, x*y^2*w^2, x*y^2*z, x*y^2*z*w, x*y^2*z*w^2, x*y^2*z^2, x*y^2*z^2*w, x*y^2*z^2*w^2, x*y^3, x*y^3*z, x*y^3*z^2, z^3*x^2, w^3*y*x^2, w^3*z*y*x^2, z^3*y*x^2, w^3*y^2*x^2, w^3*z*y^2*x^2, z^3*y^2*x^2, x^2, x^2*w, x^2*w^2, x^2*z, x^2*z*w, x^2*z*w^2, x^2*z^2, x^2*z^2*w, x^2*z^2*w^2, x^2*y, x^2*y*w, x^2*y*w^2, x^2*y*z, x^2*y*z*w, x^2*y*z*w^2, x^2*y*z^2, x^2*y*z^2*w, x^2*y*z^2*w^2, x^2*y^2, x^2*y^2*w, x^2*y^2*w^2, x^2*y^2*z, x^2*y^2*z*w, x^2*y^2*z*w^2, x^2*y^2*z^2, x^2*y^2*z^2*w, x^2*y^2*z^2*w^2, x^2*y^3, x^3 }; Output: Magma V2.10-6 Fri Mar 5 2004 04:24:56 on modular [Seed = 3469134230] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 54 72 78 80 162 { x^2*z*w^3, x*z*w^3, y^2*z^2*w^3, x^2*w^3, x*w^3, x^2*z^2*w^3, x*z^2*w^3, y*z^2*w^3 } Total time: 2.949 seconds, Total memory usage: 2.30MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Fri Mar 5 04:26:22 2004 Input: K := GF(3); R := PolynomialRing(K, [3^4 -3^3, 3^4 -3^2, 3^4 -3, 3^4 -1, 3^5 -3^4]); R; P := [ u, x*u-x^(3+1)+y^3, z^3 +y*u -y*x^3, w^3 +z*u -z*x^3, u*w -w*x^3 ] ; { 1, w, w^2, w^3, z, z*w, z*w^2, z*w^3, z^2, z^2*w, z^2*w^2, z^2*w^3, z^3, w^3*y, w^3*z*y, z^3*y*x^3, y, y*w, y*w^2, y*z, y*z*w, y*z*w^2, y*z^2, y*z^2*w, y*z^2*w^2, y*z^3, w^3*y^2, w^3*z*y^2, z^3*y^2*x^3, y^2, y^2*w, y^2*w^2, y^2*z, y^2*z*w, y^2*z*w^2, y^2*z^2, y^2*z^2*w, y^2*z^2*w^2, y^2*z^3, y^3, y^3*z, y^3*z^2, y^3*z^3, z^3*x, w^3*y*x, w^3*z*y*x, w^3*z^2*y*x, z^3*y*x, w^3*y^2*x, w^3*z*y^2*x, w^3*z^2*y^2*x, z^3*y^2*x, z^3*y^3*x, w^3*z^2*y*x^2, w^3*z^2*y^2*x^2, x, x*w, x*w^2, x*z, x*z*w, x*z*w^2, x*z^2, x*z^2*w, x*z^2*w^2, x*y, x*y*w, x*y*w^2, x*y*z, x*y*z*w, x*y*z*w^2, x*y*z^2, x*y*z^2*w, x*y*z^2*w^2, x*y^2, x*y^2*w, x*y^2*w^2, x*y^2*z, x*y^2*z*w, x*y^2*z*w^2, x*y^2*z^2, x*y^2*z^2*w, x*y^2*z^2*w^2, x*y^3, x*y^3*z, x*y^3*z^2, z^3*x^2, w^3*y*x^2, w^3*z*y*x^2, z^3*y*x^2, w^3*y^2*x^2, w^3*z*y^2*x^2, z^3*y^2*x^2, x^2, x^2*w, x^2*w^2, x^2*z, x^2*z*w, x^2*z*w^2, x^2*z^2, x^2*z^2*w, x^2*z^2*w^2, x^2*y, x^2*y*w, x^2*y*w^2, x^2*y*z, x^2*y*z*w, x^2*y*z*w^2, x^2*y*z^2, x^2*y*z^2*w, x^2*y*z^2*w^2, x^2*y^2, x^2*y^2*w, x^2*y^2*w^2, x^2*y^2*z, x^2*y^2*z*w, x^2*y^2*z*w^2, x^2*y^2*z^2, x^2*y^2*z^2*w, x^2*y^2*z^2*w^2, x^2*y^3, x^3 } diff { y^3, x^2*y^3, w^3, x^2*w^3, x*w, y*z^2*w^2, x^2*y*z^2*w^2, y^2*z*w^3, x^2*y^2*z*w^3, x*y*z^2, x*y^2*z*w, y^2, x^2*y^2, z^2*w^2, x^2*z^2*w^2, y*z*w^3, x^2*y*z*w^3, x*z^2, x*y*z*w, y, x^2*y, x*y^2*w^2, x*y^2*z^3, z*w^3, x^2*z*w^3, x*z*w, 1, x^2, x*y*w^2, y^2*z^2*w^3, x^2*y^2*z^2*w^3, x*y*z^3, x*y^2*z^2*w, y^2*z, x^2*y^2*z, x*w^2, y*z^2*w^3, x^2*y*z^2*w^3, x*z^3, x*y*z^2*w, y*z, x^2*y*z, x*y^2*z*w^2, y^2*w, x^2*y^2*w, z^2*w^3, x^2*z^2*w^3, z, x*z^2*w, x^2*z, y*w, x*y*z*w^2, x^2*y*w, x*y^2*w^3, y^2*z^2, x^2*y^2*z^2, x*z*w^2, w, x^2*w, x*y*w^3, y*z^2, x^2*y*z^2, x*y^2*z^2*w^2, y^2*z*w, x^2*y^2*z*w, x*y^3, x*w^3, z^2, x^2*z^2, x*y*z^2*w^2, y*z*w, x^2*y*z*w, x*y^2*z*w^3, y^2*w^2, x^2*y^2*w^2, x*y^2, y^2*z^3, x^2*y^2*z^3, z*w, x*z^2*w^2, x^2*z*w, y*w^2, x*y*z*w^3, x^2*y*w^2, x*y, y*z^3, x^2*y*z^3, y^2*z^2*w, x^2*y^2*z^2*w, x*z*w^3, w^2, x^2*w^2, x, x^3, z^3, x^2*z^3, y*z^2*w, x^2*y*z^2*w, x*y^2*z^2*w^3, y^2*z*w^2, x^2*y^2*z*w^2, x*y^2*z, z^2*w, x^2*z^2*w, x*y*z^2*w^3, y*z*w^2, x^2*y*z*w^2, y^2*w^3, x^2*y^2*w^3, x*y*z, x*y^2*w, z*w^2, x*z^2*w^3, x^2*z*w^2, y*w^3, x^2*y*w^3, x*z, x*y*w, y^2*z^2*w^2, x^2*y^2*z^2*w^2, x*y^2*z^2 }; Output: Magma V2.10-6 Fri Mar 5 2004 04:26:19 on modular [Seed = 1026898615] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 54 72 78 80 162 { x*y^3*z^2, y^3*z, x^3*y*z^3, x*y^3*z, y^3*z^3, x^3*y^2*z^3, x*y^3*z^3, y^3*z^2 } Total time: 2.929 seconds, Total memory usage: 2.30MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Fri Mar 5 04:34:40 2004 Input: K := GF(3); R := PolynomialRing(K, [3^4 -3^3, 3^4 -3^2, 3^4 -3, 3^4 -1, 3^5 -3^4]); R; P := [ u, x*u-x^(3+1)+y^3, z^3 +y*u -y*x^3, w^3 +z*u -z*x^3, u*w -w*x^3 ] ; S :=[ y^3, x^2*y^3, w^3, x^2*w^3, x*w, y*z^2*w^2, x^2*y*z^2*w^2, y^2*z*w^3, x^2*y^2*z*w^3, x*y*z^2, x*y^2*z*w, y^2, x^2*y^2, z^2*w^2, x^2*z^2*w^2, y*z*w^3, x^2*y*z*w^3, x*z^2, x*y*z*w, y, x^2*y, x*y^2*w^2, x*y^2*z^3, z*w^3, x^2*z*w^3, x*z*w, 1, x^2, x*y*w^2, y^2*z^2*w^3, x^2*y^2*z^2*w^3, x*y*z^3, x*y^2*z^2*w, y^2*z, x^2*y^2*z, x*w^2, y*z^2*w^3, x^2*y*z^2*w^3, x*z^3, x*y*z^2*w, y*z, x^2*y*z, x*y^2*z*w^2, y^2*w, x^2*y^2*w, z^2*w^3, x^2*z^2*w^3, z, x*z^2*w, x^2*z, y*w, x*y*z*w^2, x^2*y*w, x*y^2*w^3, y^2*z^2, x^2*y^2*z^2, x*z*w^2, w, x^2*w, x*y*w^3, y*z^2, x^2*y*z^2, x*y^2*z^2*w^2, y^2*z*w, x^2*y^2*z*w, x*y^3, x*w^3, z^2, x^2*z^2, x*y*z^2*w^2, y*z*w, x^2*y*z*w, x*y^2*z*w^3, y^2*w^2, x^2*y^2*w^2, x*y^2, y^2*z^3, x^2*y^2*z^3, z*w, x*z^2*w^2, x^2*z*w, y*w^2, x*y*z*w^3, x^2*y*w^2, x*y, y*z^3, x^2*y*z^3, y^2*z^2*w, x^2*y^2*z^2*w, x*z*w^3, w^2, x^2*w^2, x, x^3, z^3, x^2*z^3, y*z^2*w, x^2*y*z^2*w, x*y^2*z^2*w^3, y^2*z*w^2, x^2*y^2*z*w^2, x*y^2*z, z^2*w, x^2*z^2*w, x*y*z^2*w^3, y*z*w^2, x^2*y*z*w^2, y^2*w^3, x^2*y^2*w^3, x*y*z, x*y^2*w, z*w^2, x*z^2*w^3, x^2*z*w^2, y*w^3, x^2*y*w^3, x*z, x*y*w, y^2*z^2*w^2, x^2*y^2*z^2*w^2, x*y^2*z^2 ]; L := [x*y^3*z^2]; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Fri Mar 5 2004 04:34:37 on modular [Seed = 740566448] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 54 72 78 80 162 [ true ] Total time: 3.019 seconds, Total memory usage: 2.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Fri Mar 5 04:35:17 2004 Input: K := GF(3); R := PolynomialRing(K, [3^4 -3^3, 3^4 -3^2, 3^4 -3, 3^4 -1, 3^5 -3^4]); R; P := [ u, x*u-x^(3+1)+y^3, z^3 +y*u -y*x^3, w^3 +z*u -z*x^3, u*w -w*x^3 ] ; S :=[ y^3, x^2*y^3, w^3, x^2*w^3, x*w, y*z^2*w^2, x^2*y*z^2*w^2, y^2*z*w^3, x^2*y^2*z*w^3, x*y*z^2, x*y^2*z*w, y^2, x^2*y^2, z^2*w^2, x^2*z^2*w^2, y*z*w^3, x^2*y*z*w^3, x*z^2, x*y*z*w, y, x^2*y, x*y^2*w^2, x*y^2*z^3, z*w^3, x^2*z*w^3, x*z*w, 1, x^2, x*y*w^2, y^2*z^2*w^3, x^2*y^2*z^2*w^3, x*y*z^3, x*y^2*z^2*w, y^2*z, x^2*y^2*z, x*w^2, y*z^2*w^3, x^2*y*z^2*w^3, x*z^3, x*y*z^2*w, y*z, x^2*y*z, x*y^2*z*w^2, y^2*w, x^2*y^2*w, z^2*w^3, x^2*z^2*w^3, z, x*z^2*w, x^2*z, y*w, x*y*z*w^2, x^2*y*w, x*y^2*w^3, y^2*z^2, x^2*y^2*z^2, x*z*w^2, w, x^2*w, x*y*w^3, y*z^2, x^2*y*z^2, x*y^2*z^2*w^2, y^2*z*w, x^2*y^2*z*w, x*y^3, x*w^3, z^2, x^2*z^2, x*y*z^2*w^2, y*z*w, x^2*y*z*w, x*y^2*z*w^3, y^2*w^2, x^2*y^2*w^2, x*y^2, y^2*z^3, x^2*y^2*z^3, z*w, x*z^2*w^2, x^2*z*w, y*w^2, x*y*z*w^3, x^2*y*w^2, x*y, y*z^3, x^2*y*z^3, y^2*z^2*w, x^2*y^2*z^2*w, x*z*w^3, w^2, x^2*w^2, x, x^3, z^3, x^2*z^3, y*z^2*w, x^2*y*z^2*w, x*y^2*z^2*w^3, y^2*z*w^2, x^2*y^2*z*w^2, x*y^2*z, z^2*w, x^2*z^2*w, x*y*z^2*w^3, y*z*w^2, x^2*y*z*w^2, y^2*w^3, x^2*y^2*w^3, x*y*z, x*y^2*w, z*w^2, x*z^2*w^3, x^2*z*w^2, y*w^3, x^2*y*w^3, x*z, x*y*w, y^2*z^2*w^2, x^2*y^2*z^2*w^2, x*y^2*z^2 ]; L := [y^3*z]; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Fri Mar 5 2004 04:35:14 on modular [Seed = 437392377] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 54 72 78 80 162 [ true ] Total time: 2.999 seconds, Total memory usage: 2.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Fri Mar 5 04:35:43 2004 Input: K := GF(3); R := PolynomialRing(K, [3^4 -3^3, 3^4 -3^2, 3^4 -3, 3^4 -1, 3^5 -3^4]); R; P := [ u, x*u-x^(3+1)+y^3, z^3 +y*u -y*x^3, w^3 +z*u -z*x^3, u*w -w*x^3 ] ; S :=[ y^3, x^2*y^3, w^3, x^2*w^3, x*w, y*z^2*w^2, x^2*y*z^2*w^2, y^2*z*w^3, x^2*y^2*z*w^3, x*y*z^2, x*y^2*z*w, y^2, x^2*y^2, z^2*w^2, x^2*z^2*w^2, y*z*w^3, x^2*y*z*w^3, x*z^2, x*y*z*w, y, x^2*y, x*y^2*w^2, x*y^2*z^3, z*w^3, x^2*z*w^3, x*z*w, 1, x^2, x*y*w^2, y^2*z^2*w^3, x^2*y^2*z^2*w^3, x*y*z^3, x*y^2*z^2*w, y^2*z, x^2*y^2*z, x*w^2, y*z^2*w^3, x^2*y*z^2*w^3, x*z^3, x*y*z^2*w, y*z, x^2*y*z, x*y^2*z*w^2, y^2*w, x^2*y^2*w, z^2*w^3, x^2*z^2*w^3, z, x*z^2*w, x^2*z, y*w, x*y*z*w^2, x^2*y*w, x*y^2*w^3, y^2*z^2, x^2*y^2*z^2, x*z*w^2, w, x^2*w, x*y*w^3, y*z^2, x^2*y*z^2, x*y^2*z^2*w^2, y^2*z*w, x^2*y^2*z*w, x*y^3, x*w^3, z^2, x^2*z^2, x*y*z^2*w^2, y*z*w, x^2*y*z*w, x*y^2*z*w^3, y^2*w^2, x^2*y^2*w^2, x*y^2, y^2*z^3, x^2*y^2*z^3, z*w, x*z^2*w^2, x^2*z*w, y*w^2, x*y*z*w^3, x^2*y*w^2, x*y, y*z^3, x^2*y*z^3, y^2*z^2*w, x^2*y^2*z^2*w, x*z*w^3, w^2, x^2*w^2, x, x^3, z^3, x^2*z^3, y*z^2*w, x^2*y*z^2*w, x*y^2*z^2*w^3, y^2*z*w^2, x^2*y^2*z*w^2, x*y^2*z, z^2*w, x^2*z^2*w, x*y*z^2*w^3, y*z*w^2, x^2*y*z*w^2, y^2*w^3, x^2*y^2*w^3, x*y*z, x*y^2*w, z*w^2, x*z^2*w^3, x^2*z*w^2, y*w^3, x^2*y*w^3, x*z, x*y*w, y^2*z^2*w^2, x^2*y^2*z^2*w^2, x*y^2*z^2 ]; L := [x^3*y*z^3]; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Fri Mar 5 2004 04:35:40 on modular [Seed = 84741336] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 54 72 78 80 162 [ true ] Total time: 3.009 seconds, Total memory usage: 2.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Fri Mar 5 04:36:13 2004 Input: K := GF(3); R := PolynomialRing(K, [3^4 -3^3, 3^4 -3^2, 3^4 -3, 3^4 -1, 3^5 -3^4]); R; P := [ u, x*u-x^(3+1)+y^3, z^3 +y*u -y*x^3, w^3 +z*u -z*x^3, u*w -w*x^3 ] ; S :=[ y^3, x^2*y^3, w^3, x^2*w^3, x*w, y*z^2*w^2, x^2*y*z^2*w^2, y^2*z*w^3, x^2*y^2*z*w^3, x*y*z^2, x*y^2*z*w, y^2, x^2*y^2, z^2*w^2, x^2*z^2*w^2, y*z*w^3, x^2*y*z*w^3, x*z^2, x*y*z*w, y, x^2*y, x*y^2*w^2, x*y^2*z^3, z*w^3, x^2*z*w^3, x*z*w, 1, x^2, x*y*w^2, y^2*z^2*w^3, x^2*y^2*z^2*w^3, x*y*z^3, x*y^2*z^2*w, y^2*z, x^2*y^2*z, x*w^2, y*z^2*w^3, x^2*y*z^2*w^3, x*z^3, x*y*z^2*w, y*z, x^2*y*z, x*y^2*z*w^2, y^2*w, x^2*y^2*w, z^2*w^3, x^2*z^2*w^3, z, x*z^2*w, x^2*z, y*w, x*y*z*w^2, x^2*y*w, x*y^2*w^3, y^2*z^2, x^2*y^2*z^2, x*z*w^2, w, x^2*w, x*y*w^3, y*z^2, x^2*y*z^2, x*y^2*z^2*w^2, y^2*z*w, x^2*y^2*z*w, x*y^3, x*w^3, z^2, x^2*z^2, x*y*z^2*w^2, y*z*w, x^2*y*z*w, x*y^2*z*w^3, y^2*w^2, x^2*y^2*w^2, x*y^2, y^2*z^3, x^2*y^2*z^3, z*w, x*z^2*w^2, x^2*z*w, y*w^2, x*y*z*w^3, x^2*y*w^2, x*y, y*z^3, x^2*y*z^3, y^2*z^2*w, x^2*y^2*z^2*w, x*z*w^3, w^2, x^2*w^2, x, x^3, z^3, x^2*z^3, y*z^2*w, x^2*y*z^2*w, x*y^2*z^2*w^3, y^2*z*w^2, x^2*y^2*z*w^2, x*y^2*z, z^2*w, x^2*z^2*w, x*y*z^2*w^3, y*z*w^2, x^2*y*z*w^2, y^2*w^3, x^2*y^2*w^3, x*y*z, x*y^2*w, z*w^2, x*z^2*w^3, x^2*z*w^2, y*w^3, x^2*y*w^3, x*z, x*y*w, y^2*z^2*w^2, x^2*y^2*z^2*w^2, x*y^2*z^2 ]; L := [x*y^3*z]; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Fri Mar 5 2004 04:36:10 on modular [Seed = 201590327] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 54 72 78 80 162 [ true ] Total time: 2.949 seconds, Total memory usage: 2.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Fri Mar 5 04:36:49 2004 Input: K := GF(3); R := PolynomialRing(K, [3^4 -3^3, 3^4 -3^2, 3^4 -3, 3^4 -1, 3^5 -3^4]); R; P := [ u, x*u-x^(3+1)+y^3, z^3 +y*u -y*x^3, w^3 +z*u -z*x^3, u*w -w*x^3 ] ; S :=[ y^3, x^2*y^3, w^3, x^2*w^3, x*w, y*z^2*w^2, x^2*y*z^2*w^2, y^2*z*w^3, x^2*y^2*z*w^3, x*y*z^2, x*y^2*z*w, y^2, x^2*y^2, z^2*w^2, x^2*z^2*w^2, y*z*w^3, x^2*y*z*w^3, x*z^2, x*y*z*w, y, x^2*y, x*y^2*w^2, x*y^2*z^3, z*w^3, x^2*z*w^3, x*z*w, 1, x^2, x*y*w^2, y^2*z^2*w^3, x^2*y^2*z^2*w^3, x*y*z^3, x*y^2*z^2*w, y^2*z, x^2*y^2*z, x*w^2, y*z^2*w^3, x^2*y*z^2*w^3, x*z^3, x*y*z^2*w, y*z, x^2*y*z, x*y^2*z*w^2, y^2*w, x^2*y^2*w, z^2*w^3, x^2*z^2*w^3, z, x*z^2*w, x^2*z, y*w, x*y*z*w^2, x^2*y*w, x*y^2*w^3, y^2*z^2, x^2*y^2*z^2, x*z*w^2, w, x^2*w, x*y*w^3, y*z^2, x^2*y*z^2, x*y^2*z^2*w^2, y^2*z*w, x^2*y^2*z*w, x*y^3, x*w^3, z^2, x^2*z^2, x*y*z^2*w^2, y*z*w, x^2*y*z*w, x*y^2*z*w^3, y^2*w^2, x^2*y^2*w^2, x*y^2, y^2*z^3, x^2*y^2*z^3, z*w, x*z^2*w^2, x^2*z*w, y*w^2, x*y*z*w^3, x^2*y*w^2, x*y, y*z^3, x^2*y*z^3, y^2*z^2*w, x^2*y^2*z^2*w, x*z*w^3, w^2, x^2*w^2, x, x^3, z^3, x^2*z^3, y*z^2*w, x^2*y*z^2*w, x*y^2*z^2*w^3, y^2*z*w^2, x^2*y^2*z*w^2, x*y^2*z, z^2*w, x^2*z^2*w, x*y*z^2*w^3, y*z*w^2, x^2*y*z*w^2, y^2*w^3, x^2*y^2*w^3, x*y*z, x*y^2*w, z*w^2, x*z^2*w^3, x^2*z*w^2, y*w^3, x^2*y*w^3, x*z, x*y*w, y^2*z^2*w^2, x^2*y^2*z^2*w^2, x*y^2*z^2 ]; L := [y^3*z^3]; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Fri Mar 5 2004 04:36:46 on modular [Seed = 2004843880] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 54 72 78 80 162 [ true ] Total time: 2.939 seconds, Total memory usage: 2.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Fri Mar 5 04:37:18 2004 Input: K := GF(3); R := PolynomialRing(K, [3^4 -3^3, 3^4 -3^2, 3^4 -3, 3^4 -1, 3^5 -3^4]); R; P := [ u, x*u-x^(3+1)+y^3, z^3 +y*u -y*x^3, w^3 +z*u -z*x^3, u*w -w*x^3 ] ; S :=[ y^3, x^2*y^3, w^3, x^2*w^3, x*w, y*z^2*w^2, x^2*y*z^2*w^2, y^2*z*w^3, x^2*y^2*z*w^3, x*y*z^2, x*y^2*z*w, y^2, x^2*y^2, z^2*w^2, x^2*z^2*w^2, y*z*w^3, x^2*y*z*w^3, x*z^2, x*y*z*w, y, x^2*y, x*y^2*w^2, x*y^2*z^3, z*w^3, x^2*z*w^3, x*z*w, 1, x^2, x*y*w^2, y^2*z^2*w^3, x^2*y^2*z^2*w^3, x*y*z^3, x*y^2*z^2*w, y^2*z, x^2*y^2*z, x*w^2, y*z^2*w^3, x^2*y*z^2*w^3, x*z^3, x*y*z^2*w, y*z, x^2*y*z, x*y^2*z*w^2, y^2*w, x^2*y^2*w, z^2*w^3, x^2*z^2*w^3, z, x*z^2*w, x^2*z, y*w, x*y*z*w^2, x^2*y*w, x*y^2*w^3, y^2*z^2, x^2*y^2*z^2, x*z*w^2, w, x^2*w, x*y*w^3, y*z^2, x^2*y*z^2, x*y^2*z^2*w^2, y^2*z*w, x^2*y^2*z*w, x*y^3, x*w^3, z^2, x^2*z^2, x*y*z^2*w^2, y*z*w, x^2*y*z*w, x*y^2*z*w^3, y^2*w^2, x^2*y^2*w^2, x*y^2, y^2*z^3, x^2*y^2*z^3, z*w, x*z^2*w^2, x^2*z*w, y*w^2, x*y*z*w^3, x^2*y*w^2, x*y, y*z^3, x^2*y*z^3, y^2*z^2*w, x^2*y^2*z^2*w, x*z*w^3, w^2, x^2*w^2, x, x^3, z^3, x^2*z^3, y*z^2*w, x^2*y*z^2*w, x*y^2*z^2*w^3, y^2*z*w^2, x^2*y^2*z*w^2, x*y^2*z, z^2*w, x^2*z^2*w, x*y*z^2*w^3, y*z*w^2, x^2*y*z*w^2, y^2*w^3, x^2*y^2*w^3, x*y*z, x*y^2*w, z*w^2, x*z^2*w^3, x^2*z*w^2, y*w^3, x^2*y*w^3, x*z, x*y*w, y^2*z^2*w^2, x^2*y^2*z^2*w^2, x*y^2*z^2 ]; L := [x^3*y^2*z^3]; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Fri Mar 5 2004 04:37:15 on modular [Seed = 2121692164] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 54 72 78 80 162 [ true ] Total time: 2.929 seconds, Total memory usage: 2.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Fri Mar 5 04:37:48 2004 Input: K := GF(3); R := PolynomialRing(K, [3^4 -3^3, 3^4 -3^2, 3^4 -3, 3^4 -1, 3^5 -3^4]); R; P := [ u, x*u-x^(3+1)+y^3, z^3 +y*u -y*x^3, w^3 +z*u -z*x^3, u*w -w*x^3 ] ; S :=[ y^3, x^2*y^3, w^3, x^2*w^3, x*w, y*z^2*w^2, x^2*y*z^2*w^2, y^2*z*w^3, x^2*y^2*z*w^3, x*y*z^2, x*y^2*z*w, y^2, x^2*y^2, z^2*w^2, x^2*z^2*w^2, y*z*w^3, x^2*y*z*w^3, x*z^2, x*y*z*w, y, x^2*y, x*y^2*w^2, x*y^2*z^3, z*w^3, x^2*z*w^3, x*z*w, 1, x^2, x*y*w^2, y^2*z^2*w^3, x^2*y^2*z^2*w^3, x*y*z^3, x*y^2*z^2*w, y^2*z, x^2*y^2*z, x*w^2, y*z^2*w^3, x^2*y*z^2*w^3, x*z^3, x*y*z^2*w, y*z, x^2*y*z, x*y^2*z*w^2, y^2*w, x^2*y^2*w, z^2*w^3, x^2*z^2*w^3, z, x*z^2*w, x^2*z, y*w, x*y*z*w^2, x^2*y*w, x*y^2*w^3, y^2*z^2, x^2*y^2*z^2, x*z*w^2, w, x^2*w, x*y*w^3, y*z^2, x^2*y*z^2, x*y^2*z^2*w^2, y^2*z*w, x^2*y^2*z*w, x*y^3, x*w^3, z^2, x^2*z^2, x*y*z^2*w^2, y*z*w, x^2*y*z*w, x*y^2*z*w^3, y^2*w^2, x^2*y^2*w^2, x*y^2, y^2*z^3, x^2*y^2*z^3, z*w, x*z^2*w^2, x^2*z*w, y*w^2, x*y*z*w^3, x^2*y*w^2, x*y, y*z^3, x^2*y*z^3, y^2*z^2*w, x^2*y^2*z^2*w, x*z*w^3, w^2, x^2*w^2, x, x^3, z^3, x^2*z^3, y*z^2*w, x^2*y*z^2*w, x*y^2*z^2*w^3, y^2*z*w^2, x^2*y^2*z*w^2, x*y^2*z, z^2*w, x^2*z^2*w, x*y*z^2*w^3, y*z*w^2, x^2*y*z*w^2, y^2*w^3, x^2*y^2*w^3, x*y*z, x*y^2*w, z*w^2, x*z^2*w^3, x^2*z*w^2, y*w^3, x^2*y*w^3, x*z, x*y*w, y^2*z^2*w^2, x^2*y^2*z^2*w^2, x*y^2*z^2 ]; L := [x*y^3*z^3]; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Fri Mar 5 2004 04:37:45 on modular [Seed = 1767990065] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 54 72 78 80 162 [ true ] Total time: 3.079 seconds, Total memory usage: 2.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Fri Mar 5 04:38:26 2004 Input: K := GF(3); R := PolynomialRing(K, [3^4 -3^3, 3^4 -3^2, 3^4 -3, 3^4 -1, 3^5 -3^4]); R; P := [ u, x*u-x^(3+1)+y^3, z^3 +y*u -y*x^3, w^3 +z*u -z*x^3, u*w -w*x^3 ] ; S :=[ y^3, x^2*y^3, w^3, x^2*w^3, x*w, y*z^2*w^2, x^2*y*z^2*w^2, y^2*z*w^3, x^2*y^2*z*w^3, x*y*z^2, x*y^2*z*w, y^2, x^2*y^2, z^2*w^2, x^2*z^2*w^2, y*z*w^3, x^2*y*z*w^3, x*z^2, x*y*z*w, y, x^2*y, x*y^2*w^2, x*y^2*z^3, z*w^3, x^2*z*w^3, x*z*w, 1, x^2, x*y*w^2, y^2*z^2*w^3, x^2*y^2*z^2*w^3, x*y*z^3, x*y^2*z^2*w, y^2*z, x^2*y^2*z, x*w^2, y*z^2*w^3, x^2*y*z^2*w^3, x*z^3, x*y*z^2*w, y*z, x^2*y*z, x*y^2*z*w^2, y^2*w, x^2*y^2*w, z^2*w^3, x^2*z^2*w^3, z, x*z^2*w, x^2*z, y*w, x*y*z*w^2, x^2*y*w, x*y^2*w^3, y^2*z^2, x^2*y^2*z^2, x*z*w^2, w, x^2*w, x*y*w^3, y*z^2, x^2*y*z^2, x*y^2*z^2*w^2, y^2*z*w, x^2*y^2*z*w, x*y^3, x*w^3, z^2, x^2*z^2, x*y*z^2*w^2, y*z*w, x^2*y*z*w, x*y^2*z*w^3, y^2*w^2, x^2*y^2*w^2, x*y^2, y^2*z^3, x^2*y^2*z^3, z*w, x*z^2*w^2, x^2*z*w, y*w^2, x*y*z*w^3, x^2*y*w^2, x*y, y*z^3, x^2*y*z^3, y^2*z^2*w, x^2*y^2*z^2*w, x*z*w^3, w^2, x^2*w^2, x, x^3, z^3, x^2*z^3, y*z^2*w, x^2*y*z^2*w, x*y^2*z^2*w^3, y^2*z*w^2, x^2*y^2*z*w^2, x*y^2*z, z^2*w, x^2*z^2*w, x*y*z^2*w^3, y*z*w^2, x^2*y*z*w^2, y^2*w^3, x^2*y^2*w^3, x*y*z, x*y^2*w, z*w^2, x*z^2*w^3, x^2*z*w^2, y*w^3, x^2*y*w^3, x*z, x*y*w, y^2*z^2*w^2, x^2*y^2*z^2*w^2, x*y^2*z^2 ]; L := [y^3*z^2]; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Fri Mar 5 2004 04:38:23 on modular [Seed = 1347967726] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 54 72 78 80 162 [ true ] Total time: 2.909 seconds, Total memory usage: 2.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Fri Mar 5 05:16:56 2004 Input: K := GF(5); R := PolynomialRing(K, [5^2 -5, 5^2 -1, 5^3 -5^2 ]); R; P := [ z, z*y -x^5 *y, y^5 +x*z -x^(5+1) ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S; Output: Magma V2.10-6 Fri Mar 5 2004 05:16:53 on modular [Seed = 2408029227] ------------------------------------- Graded Polynomial ring of rank 3 over GF(5) Lexicographical Order Variables: x, y, z Variable weights: 20 24 100 0 [] [ 1, y, y^2, y^3, y^4, y^5, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^5 ] Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Fri Mar 5 06:17:50 2004 Input: K := GF(3); R := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]); R; P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y*(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S; Output: Magma V2.10-6 Fri Mar 5 2004 06:17:45 on modular [Seed = 51061480] ------------------------------------- Graded Polynomial ring of rank 4 over GF(3) Lexicographical Order Variables: x, y, z, w Variable weights: 6 8 54 72 0 [] [ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^8*y^7, x^8*y^8, x^8*y^9, x^8*y^10, x^9, x^9*y, x^10, x^10*y, x^11, x^11*y, x^12 ] Total time: 3.099 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Fri Mar 5 06:35:03 2004 Input: K := GF(3); R := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]); R; P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y*(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S; Output: Magma V2.10-6 Fri Mar 5 2004 06:35:00 on modular [Seed = 1718502320] ------------------------------------- Graded Polynomial ring of rank 4 over GF(3) Lexicographical Order Variables: x, y, z, w Variable weights: 6 8 54 72 0 [] [ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^8*y^7, x^8*y^8, x^8*y^9, x^8*y^10, x^9, x^9*y, x^10, x^10*y, x^11, x^11*y, x^12 ] Total time: 2.929 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Fri Mar 5 06:48:33 2004 Input: K := GF(3); R := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]); R; P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y*(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ; I:=ideal; Dimension(I); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^8*y^7, x^8*y^8, x^8*y^9, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^9*y^7, x^9*y^8, x^9*y^9, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^10*y^7, x^10*y^8, x^10*y^9, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^11*y^5, x^11*y^6, x^11*y^7, x^11*y^8, x^11*y^9, x^12, x^12*y, x^12*y^2, x^12*y^3, x^12*y^4, x^12*y^5, x^12*y^6, x^12*y^7, x^12*y^8, x^12*y^9, x^12 ]; L := [y^10]; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Fri Mar 5 2004 06:48:30 on modular [Seed = 1481666916] ------------------------------------- Graded Polynomial ring of rank 4 over GF(3) Lexicographical Order Variables: x, y, z, w Variable weights: 6 8 54 72 0 [] >> B, V := HomogeneousModuleTest(P, S, L); ^ Runtime error in 'HomogeneousModuleTest': Elements of argument 1 are not homogeneous >> B; ^ User error: Identifier 'B' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 2.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Fri Mar 5 06:49:48 2004 Input: K := GF(3); R := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]); R; P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y*(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ; I:=ideal; Dimension(I); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^8*y^7, x^8*y^8, x^8*y^9, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^9*y^7, x^9*y^8, x^9*y^9, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^10*y^7, x^10*y^8, x^10*y^9, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^11*y^5, x^11*y^6, x^11*y^7, x^11*y^8, x^11*y^9, x^12, x^12*y, x^12*y^2, x^12*y^3, x^12*y^4, x^12*y^5, x^12*y^6, x^12*y^7, x^12*y^8, x^12*y^9 ]; L := [y^10]; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Fri Mar 5 2004 06:49:45 on modular [Seed = 1095329834] ------------------------------------- Graded Polynomial ring of rank 4 over GF(3) Lexicographical Order Variables: x, y, z, w Variable weights: 6 8 54 72 0 [] >> B, V := HomogeneousModuleTest(P, S, L); ^ Runtime error in 'HomogeneousModuleTest': Elements of argument 1 are not homogeneous >> B; ^ User error: Identifier 'B' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 2.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Fri Mar 5 06:54:02 2004 Input: K := GF(3); R := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]); R; P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y*(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^8*y^7, x^8*y^8, x^8*y^9, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^9*y^7, x^9*y^8, x^9*y^9, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^10*y^7, x^10*y^8, x^10*y^9, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^11*y^5, x^11*y^6, x^11*y^7, x^11*y^8, x^11*y^9, x^12, x^12*y, x^12*y^2, x^12*y^3, x^12*y^4, x^12*y^5, x^12*y^6, x^12*y^7, x^12*y^8, x^12*y^9 ]; L := [y^10]; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Fri Mar 5 2004 06:53:59 on modular [Seed = 3065945299] ------------------------------------- Graded Polynomial ring of rank 4 over GF(3) Lexicographical Order Variables: x, y, z, w Variable weights: 6 8 54 72 0 [] >> B, V := HomogeneousModuleTest(P, S, L); ^ Runtime error in 'HomogeneousModuleTest': Elements of argument 1 are not homogeneous >> B; ^ User error: Identifier 'B' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 2.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Fri Mar 5 06:56:40 2004 Input: K := GF(3); R := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]); R; P := [ z, w, y^3 *(w-y^9 -x^3 *(z-x^9)), y*(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^8*y^7, x^8*y^8, x^8*y^9, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^9*y^7, x^9*y^8, x^9*y^9, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^10*y^7, x^10*y^8, x^10*y^9, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^11*y^5, x^11*y^6, x^11*y^7, x^11*y^8, x^11*y^9, x^12, x^12*y, x^12*y^2, x^12*y^3, x^12*y^4, x^12*y^5, x^12*y^6, x^12*y^7, x^12*y^8, x^12*y^9 ]; L := [y^10]; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Fri Mar 5 2004 06:56:37 on modular [Seed = 2695400039] ------------------------------------- Graded Polynomial ring of rank 4 over GF(3) Lexicographical Order Variables: x, y, z, w Variable weights: 6 8 54 72 0 [] >> B, V := HomogeneousModuleTest(P, S, L); ^ Runtime error in 'HomogeneousModuleTest': Elements of argument 1 are not homogeneous >> B; ^ User error: Identifier 'B' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 2.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Fri Mar 5 06:57:34 2004 Input: K := GF(3); R := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]); R; P := [ z, w, y *(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^8*y^7, x^8*y^8, x^8*y^9, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^9*y^7, x^9*y^8, x^9*y^9, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^10*y^7, x^10*y^8, x^10*y^9, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^11*y^5, x^11*y^6, x^11*y^7, x^11*y^8, x^11*y^9, x^12, x^12*y, x^12*y^2, x^12*y^3, x^12*y^4, x^12*y^5, x^12*y^6, x^12*y^7, x^12*y^8, x^12*y^9 ]; L := [y^10]; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Fri Mar 5 2004 06:57:31 on modular [Seed = 2845934256] ------------------------------------- Graded Polynomial ring of rank 4 over GF(3) Lexicographical Order Variables: x, y, z, w Variable weights: 6 8 54 72 0 [] [ true ] Total time: 2.989 seconds, Total memory usage: 2.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Fri Mar 5 06:58:51 2004 Input: K := GF(3); R := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]); R; P := [ z, w, y *(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S; Output: Magma V2.10-6 Fri Mar 5 2004 06:58:48 on modular [Seed = 2526985692] ------------------------------------- Graded Polynomial ring of rank 4 over GF(3) Lexicographical Order Variables: x, y, z, w Variable weights: 6 8 54 72 0 [] [ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, y^11, y^12, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x*y^11, x*y^12, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^2*y^11, x^2*y^12, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^8*y^7, x^8*y^8, x^8*y^9, x^8*y^10, x^8*y^11, x^8*y^12, x^9, x^9*y, x^9*y^2, x^9*y^3, x^10, x^10*y, x^10*y^2, x^10*y^3, x^11, x^11*y, x^11*y^2, x^11*y^3, x^12 ] Total time: 2.959 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Fri Mar 5 07:02:05 2004 Input: K := GF(3); R := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]); R; P := [ z, w, y *(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^8*y^7, x^8*y^8, x^8*y^9, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^9*y^7, x^9*y^8, x^9*y^9, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^10*y^7, x^10*y^8, x^10*y^9, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^11*y^5, x^11*y^6, x^11*y^7, x^11*y^8, x^11*y^9, x^12, x^12*y, x^12*y^2, x^12*y^3, x^12*y^4, x^12*y^5, x^12*y^6, x^12*y^7, x^12*y^8, x^12*y^9, x^12 ]; L := [y^11]; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Fri Mar 5 2004 07:02:02 on modular [Seed = 4277588726] ------------------------------------- Graded Polynomial ring of rank 4 over GF(3) Lexicographical Order Variables: x, y, z, w Variable weights: 6 8 54 72 0 [] [ true ] Total time: 2.909 seconds, Total memory usage: 2.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Fri Mar 5 07:02:20 2004 Input: K := GF(3); R := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]); R; P := [ z, w, y *(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^8*y^7, x^8*y^8, x^8*y^9, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^9*y^7, x^9*y^8, x^9*y^9, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^10*y^7, x^10*y^8, x^10*y^9, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^11*y^5, x^11*y^6, x^11*y^7, x^11*y^8, x^11*y^9, x^12, x^12*y, x^12*y^2, x^12*y^3, x^12*y^4, x^12*y^5, x^12*y^6, x^12*y^7, x^12*y^8, x^12*y^9, x^12 ]; L := [y^12]; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Fri Mar 5 2004 07:02:17 on modular [Seed = 3891252124] ------------------------------------- Graded Polynomial ring of rank 4 over GF(3) Lexicographical Order Variables: x, y, z, w Variable weights: 6 8 54 72 0 [] [ true ] Total time: 2.929 seconds, Total memory usage: 2.10MB ************** MAGMA ***************** Host 3(NXDOMAIN) (217.21.41.62) Time: Fri Mar 5 08:31:31 2004 Input: 2+2 Output: Magma V2.10-6 Fri Mar 5 2004 08:31:20 on modular [Seed = 1279561047] ------------------------------------- 4 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (217.21.41.62) Time: Fri Mar 5 08:31:59 2004 Input: sin(5) Output: Magma V2.10-6 Fri Mar 5 2004 08:31:56 on modular [Seed = 3149101764] ------------------------------------- >> sin(5); ^ User error: Identifier 'sin' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (217.21.41.62) Time: Fri Mar 5 08:32:23 2004 Input: Sin[5] Output: Magma V2.10-6 Fri Mar 5 2004 08:32:20 on modular [Seed = 2712232182] ------------------------------------- >> Sin[5] ^ Runtime error in '[]': Bad argument types Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam23-109.fas.harvard.edu. (140.247.23.109) Time: Fri Mar 5 13:25:15 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^4-34x^2+9); OK:=MaximalOrder(K); [K!x : x in Basis(OK)]; Output: Magma V2.10-6 Fri Mar 5 2004 13:25:12 on modular [Seed = 2576424871] ------------------------------------- >> K:=NumberField(x^4-34x^2+9); ^ User error: bad syntax >> OK:=MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> [K!x : x in Basis(OK)];; ^ User error: Identifier 'OK' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam23-109.fas.harvard.edu. (140.247.23.109) Time: Fri Mar 5 13:25:46 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^4-34*x^2+9); OK:=MaximalOrder(K); [K!x : x in Basis(OK)]; Output: Magma V2.10-6 Fri Mar 5 2004 13:25:43 on modular [Seed = 2391148703] ------------------------------------- [ 1, a, 1/2*(a^2 + 1), 1/12*(a^3 + 3*a^2 + 11*a + 9) ] Total time: 2.999 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam23-109.fas.harvard.edu. (140.247.23.109) Time: Fri Mar 5 13:30:19 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^4-34*x^2+9); OK:=MaximalOrder(K); Factorization(3*OK); Output: Magma V2.10-6 Fri Mar 5 2004 13:30:16 on modular [Seed = 4008077792] ------------------------------------- [ , , , ] Total time: 3.059 seconds, Total memory usage: 2.05MB ************** MAGMA ***************** Host roam23-109.fas.harvard.edu. (140.247.23.109) Time: Fri Mar 5 14:21:00 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^4-34*x^2+9); OK:=MaximalOrder(K); [K!x : x in Basis(OK)]; FActorization(2*OK); Output: Magma V2.10-6 Fri Mar 5 2004 14:20:57 on modular [Seed = 2054351188] ------------------------------------- [ 1, a, 1/2*(a^2 + 1), 1/12*(a^3 + 3*a^2 + 11*a + 9) ] >> FActorization(2*OK);; ^ User error: Identifier 'FActorization' has not been declared or assigned Total time: 3.039 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam23-109.fas.harvard.edu. (140.247.23.109) Time: Fri Mar 5 14:21:14 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^4-34*x^2+9); OK:=MaximalOrder(K); [K!x : x in Basis(OK)]; Factorization(2*OK); Output: Magma V2.10-6 Fri Mar 5 2004 14:21:11 on modular [Seed = 1634333297] ------------------------------------- [ 1, a, 1/2*(a^2 + 1), 1/12*(a^3 + 3*a^2 + 11*a + 9) ] [ ] Total time: 2.969 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam23-109.fas.harvard.edu. (140.247.23.109) Time: Fri Mar 5 14:26:41 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^5+7*x^4+3*x^2-x+1); OK:=MaximalOrder(K); [K!x : x in Basis(OK)]; Factorization(2*OK); Factorization(3*OK); Factorization(5*OK); Factorization(7*OK); Factorization(11*OK); Factorization(13*OK); Factorization(17*OK); Factorization(19*OK); Factorization(23*OK); Factorization(29*OK); Factorization(31*OK); Factorization(37*OK); Factorization(41*OK); Factorization(43*OK); Factorization(47*OK); Factorization(53*OK); Factorization(59*OK); Factorization(61*OK); Factorization(67*OK); Factorization(71*OK); Factorization(73*OK); Factorization(79*OK); Factorization(83*OK); Factorization(89*OK); Factorization(97*OK); Output: Magma V2.10-6 Fri Mar 5 2004 14:26:38 on modular [Seed = 1481690113] ------------------------------------- [ 1, a, a^2, a^3, a^4 ] [ ] [ ] [ , , ] [ , ] [ , , , ] [ , ] [ , , ] [ , , ] [ , ] [ , , ] [ , , ] [ ] [ , ] [ , , , ] [ , ] [ , ] [ , ] [ ] [ , , , ] [ , , , ] [ ] [ , ] [ , , , ] [ , ] [ ] Total time: 3.059 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam23-109.fas.harvard.edu. (140.247.23.109) Time: Fri Mar 5 14:54:49 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^5+7*x^4+3*x^2-x+1); OK:=MaximalOrder(K); [K!x : x in Basis(OK)]; Factorization(2*OK); Factorization(3*OK); Factorization(5*OK); Factorization(7*OK); Output: Magma V2.10-6 Fri Mar 5 2004 14:54:46 on modular [Seed = 2677474478] ------------------------------------- [ 1, a, a^2, a^3, a^4 ] [ ] [ ] [ , , ] [ , ] Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host modemcable035.141-200-24.mc.videotron.ca. (24.200.141.35) Time: Fri Mar 5 16:22:44 2004 Input: 2+2 Output: Magma V2.10-6 Fri Mar 5 2004 16:22:41 on modular [Seed = 1095364312] ------------------------------------- 4 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Sat Mar 6 04:24:25 2004 Input: /*Respostes a l'exercici 2*/ /*Apartat 1*/ k:=GF(4); p:=MatrixRing(k,2); mt:={n : n in p | Trace(n) eq 0}; /*Apartat 2*/ mf:={n : n in p | Submatrix(n,1,1,1,2) eq Submatrix(n,2,1,1,2)}; /*Apartat 3*/ mtf:={ n : n in p | (n in mf) and (n in mt)}; /*Apartat 4*/ mmt:=[Random(p) : n in [1..100000]]; /*Nombre de les matrius que pertanyen a mf*/ #[n : n in mmt | n in mf]; /*Nombre de les matrius que pertanyen a mt*/ #[n : n in mmt | n in mt]; /*Nombre de les matrius que pertanyen a mtf*/ #[n : n in mmt | n in mtf]; #mt; #mf; #mtf; Output: Magma V2.10-6 Sat Mar 6 2004 04:24:21 on modular [Seed = 3755345749] ------------------------------------- 6258 24913 1599 64 16 4 Total time: 4.119 seconds, Total memory usage: 7.09MB ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Sat Mar 6 04:26:12 2004 Input: /*Respostes a l'exercici 2*/ /*Apartat 1*/ k:=GF(4); p:=MatrixRing(k,2); mt:={n : n in p | Trace(n) eq 0}; /*Apartat 2*/ mf:={n : n in p | Submatrix(n,1,1,1,2) eq Submatrix(n,2,1,1,2)}; /*Apartat 3*/ mtf:={ n : n in p | (n in mf) and (n in mt)}; /*Apartat 4*/ mmt:=[Random(p) : n in [1..100000]]; /*Nombre de les matrius que pertanyen a mf*/ print "mf"; #[n : n in mmt | n in mf]; /*Nombre de les matrius que pertanyen a mt*/ print "mt"; #[n : n in mmt | n in mt]; /*Nombre de les matrius que pertanyen a mtf*/ print "mtf"; #[n : n in mmt | n in mtf]; print "mt"; #mt; print "mf"; #mf; print "mtf"; #mtf; Output: Magma V2.10-6 Sat Mar 6 2004 04:26:07 on modular [Seed = 3520596145] ------------------------------------- mf 6216 mt 24998 mtf 1546 mt 64 mf 16 mtf 4 Total time: 4.149 seconds, Total memory usage: 7.09MB ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Sat Mar 6 04:43:15 2004 Input: /*Respostes a l'exercici 2*/ /*Apartat 1*/ k:=GF(4); p:=MatrixRing(k,2); mt:={n : n in p | Trace(n) eq 0}; /*Apartat 2*/ mf:={n : n in p | Submatrix(n,1,1,1,2) eq Submatrix(n,2,1,1,2)}; /*Apartat 3*/ mtf:={ n : n in p | (n in mf) and (n in mt)}; /*Apartat 4*/ mmt:=[Random(p) : n in [1..100000]]; /*Nombre de les matrius que pertanyen a mf*/ print "mf"; #[n : n in mmt | n in mf]; /*Nombre de les matrius que pertanyen a mt*/ print "mt"; #[n : n in mmt | n in mt]; /*Nombre de les matrius que pertanyen a mtf*/ print "mtf"; #[n : n in mmt | n in mtf]; print "mt"; #mt; print "mf"; #mf; print "mtf"; #mtf; #p; Output: Magma V2.10-6 Sat Mar 6 2004 04:43:11 on modular [Seed = 4093259411] ------------------------------------- mf 6305 mt 24891 mtf 1570 mt 64 mf 16 mtf 4 256 Total time: 4.119 seconds, Total memory usage: 7.09MB ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Sat Mar 6 04:43:52 2004 Input: /*Respostes a l'exercici 2*/ /*Apartat 1*/ k:=GF(4); p:=MatrixRing(k,2); mt:={n : n in p | Trace(n) eq 0}; /*Apartat 2*/ mf:={n : n in p | Submatrix(n,1,1,1,2) eq Submatrix(n,2,1,1,2)}; /*Apartat 3*/ mtf:={ n : n in p | (n in mf) and (n in mt)}; /*Apartat 4*/ mmt:=[Random(p) : n in [1..100000]]; /*Nombre de les matrius que pertanyen a mf*/ print "mf"; #[n : n in mmt | n in mf]; /*Nombre de les matrius que pertanyen a mt*/ print "mt"; #[n : n in mmt | n in mt]; /*Nombre de les matrius que pertanyen a mtf*/ print "mtf"; #[n : n in mmt | n in mtf]; print "mt"; #mt; print "mf"; #mf; print "mtf"; #mtf; 4/256; Output: Magma V2.10-6 Sat Mar 6 2004 04:43:48 on modular [Seed = 2323863441] ------------------------------------- mf 6287 mt 25300 mtf 1575 mt 64 mf 16 mtf 4 1/64 Total time: 4.000 seconds, Total memory usage: 7.09MB ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Sat Mar 6 04:45:49 2004 Input: /*Respostes a l'exercici 3*/ /*Apartat 1*/ s:=GF(7^3); p:=PolynomialRing(s); lexp:=[7^r:r in [2..0 by -1]]; /*Apartat 2*/ t:=&+[x^r:r in lexp]; sn:=&+[r:r in lexp]; n:=x^sn; /*Apartat 3*/ {[a,b] : a,b in s | Evaluate(t,b) eq Evaluate(n,a)}; /*Apartat 4*/ func1:= func < q,r | [q^p: p in [(r-1)..0 by -1]]>; /*Apartat 5*/ tfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; return &+[x^e:e in lexp]; end function; nfunc2:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; return x^sn; end function; /*Apartat 6*/ olavfunc3:= function(q,r) s:=GF(q^r); p:=PolynomialRing(s); lexp:=[q^p:p in [(r-1)..0 by -1]]; sn:=&+[w:w in lexp]; n:= x^sn; t:= &+[x^e:e in lexp]; return {[a,b] : a,b in s | Evaluate(t,b) eq Evaluate(n,a)}; end function; /*Apartat 7*/ j := olavfunc3(7,3); #j; 7^(5); j1 := olavfunc3(5,2); #j1; 5^(3); j2 := olavfunc3(3,4); #j2; 3^(7); j3 := olavfunc3(11,2); #j3; 11^(3); j4 := olavfunc3(11,3); #j4; 11^(5); /*Apartat 8*/ eolavfunc4:= function(q,olav) s:=GF(q); return {[a,b] : a,b in s | [a,b] in olav}; end function; t:=eolavfunc4(7,olavfunc3(7,3)); #t; t1:=eolavfunc4(5,olavfunc3(5,3)); #t1; t2:=eolavfunc4(11,olavfunc3(11,3)); #t2; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Mar 6 2004 04:45:26 on modular [Seed = 2643738724] ------------------------------------- { [ s.1^3, s.1^24 ], [ s.1^35, s.1^280 ], [ s.1^30, s.1^240 ], [ s.1^28, s.1^224 ], [ s.1^4, s.1^32 ], [ s.1^5, s.1^40 ], [ s.1^21, s.1^168 ], [ s.1^36, s.1^288 ], [ 1, s.1 ], [ s.1^35, s.1^281 ], [ s.1^28, s.1^225 ], [ s.1^12, s.1^97 ], [ s.1^11, s.1^89 ], [ s.1^6, s.1^49 ], [ s.1^5, s.1^41 ], [ s.1^10, s.1^81 ], [ s.1^37, s.1^297 ], [ s.1^42, s.1^337 ], [ 1, s.1^2 ], [ s.1^13, s.1^106 ], [ s.1^12, s.1^98 ], [ s.1^7, s.1^58 ], [ s.1^3, s.1^26 ], [ s.1^4, s.1^34 ], [ s.1^17, s.1^138 ], [ s.1^18, s.1^146 ], [ s.1^19, s.1^154 ], [ s.1^35, s.1^282 ], [ s.1^42, s.1^338 ], [ s.1^5, s.1^43 ], [ s.1^26, s.1^211 ], [ s.1^25, s.1^203 ], [ s.1^24, s.1^195 ], [ s.1^14, s.1^115 ], [ s.1^11, s.1^91 ], [ s.1^7, s.1^59 ], [ s.1^10, s.1^83 ], [ s.1^19, s.1^155 ], [ s.1^20, s.1^163 ], [ s.1^42, s.1^339 ], [ s.1^3, s.1^28 ], [ s.1^33, s.1^268 ], [ s.1^32, s.1^260 ], [ s.1^31, s.1^252 ], [ s.1^27, s.1^220 ], [ s.1^26, s.1^212 ], [ s.1^14, s.1^116 ], [ s.1^12, s.1^100 ], [ s.1^17, s.1^140 ], [ s.1^18, s.1^148 ], [ s.1^21, s.1^172 ], [ s.1^10, s.1^85 ], [ s.1^34, s.1^277 ], [ s.1^33, s.1^269 ], [ s.1^28, s.1^229 ], [ s.1^25, s.1^205 ], [ s.1^24, s.1^197 ], [ s.1^19, s.1^157 ], [ s.1^21, s.1^173 ], [ s.1^38, s.1^309 ], [ s.1^39, s.1^317 ], [ s.1^40, s.1^325 ], [ s.1^5, s.1^46 ], [ s.1^32, s.1^262 ], [ s.1^31, s.1^254 ], [ s.1^28, s.1^230 ], [ s.1^26, s.1^214 ], [ s.1^17, s.1^142 ], [ s.1^35, s.1^286 ], [ s.1^40, s.1^326 ], [ s.1^41, s.1^334 ], [ 1, s.1^7 ], [ s.1^33, s.1^271 ], [ s.1^24, s.1^199 ], [ s.1^12, s.1^103 ], [ s.1^35, s.1^287 ], [ s.1^38, s.1^311 ], [ s.1^39, s.1^319 ], [ s.1, 1 ], [ s.1^27, s.1^208 ], [ s.1^23, s.1^176 ], [ s.1^11, s.1^80 ], [ s.1^19, s.1^144 ], [ s.1^40, s.1^328 ], [ s.1^5, s.1^33 ], [ s.1^26, s.1^217 ], [ s.1^14, s.1^121 ], [ s.1^38, s.1^313 ], [ 1, s.1^10 ], [ s.1^33, s.1^258 ], [ s.1^25, s.1^194 ], [ s.1^4, s.1^42 ], [ s.1^15, 2 ], [ s.1^37, s.1^290 ], [ s.1^41, s.1^322 ], [ 1, s.1^11 ], [ s.1^28, s.1^235 ], [ s.1, s.1^3 ], [ s.1^19, s.1^147 ], [ s.1^40, s.1^331 ], [ s.1^7, s.1^52 ], [ s.1^29, 4 ], [ s.1^14, s.1^124 ], [ s.1^18, s.1^156 ], [ s.1^39, s.1^308 ], [ s.1^4, s.1^45 ], [ s.1^33, s.1^261 ], [ s.1^14, s.1^125 ], [ s.1^7, s.1^53 ], [ s.1^9, s.1^69 ], [ s.1^15, s.1^117 ], [ 1, s.1^14 ], [ s.1^32, s.1^270 ], [ s.1^28, s.1^238 ], [ s.1^7, s.1^54 ], [ s.1^8, s.1^78 ], [ s.1^21, s.1^166 ], [ s.1^2, s.1^31 ], [ s.1^29, s.1^231 ], [ s.1^28, s.1^239 ], [ s.1^23, s.1^183 ], [ s.1^8, s.1^79 ], [ s.1^18, s.1^159 ], [ s.1^21, s.1^167 ], [ 1, s.1^16 ], [ s.1^35, s.1^264 ], [ s.1^31, s.1^232 ], [ s.1^25, s.1^216 ], [ s.1^12, s.1^112 ], [ s.1^9, s.1^88 ], [ s.1^15, s.1^104 ], [ s.1^16, s.1^145 ], [ s.1^32, s.1^273 ], [ s.1^29, s.1^249 ], [ s.1^21, s.1^185 ], [ s.1^22, s.1^161 ], [ s.1^38, s.1^289 ], [ s.1^42, s.1^321 ], [ s.1^11, s.1^74 ], [ s.1^29, s.1^250 ], [ s.1^28, s.1^242 ], [ s.1^36, s.1^306 ], [ s.1, s.1^27 ], [ s.1^33, s.1^283 ], [ s.1^13, s.1^123 ], [ s.1^11, s.1^75 ], [ s.1^18, s.1^131 ], [ s.1^21, s.1^187 ], [ s.1^36, s.1^307 ], [ s.1^8, s.1^84 ], [ s.1^28, s.1^244 ], [ s.1^9, s.1^92 ], [ s.1^18, s.1^132 ], [ s.1^20, s.1^180 ], [ s.1^37, s.1^316 ], [ s.1^40, s.1^340 ], [ s.1^43, s.1^332 ], [ s.1, s.1^29 ], [ s.1^6, s.1^37 ], [ s.1^2, s.1^5 ], [ s.1^16, s.1^149 ], [ s.1^8, s.1^86 ], [ s.1^17, s.1^158 ], [ s.1^39, s.1^302 ], [ s.1^5, s.1^63 ], [ s.1^29, s.1^255 ], [ s.1^24, s.1^215 ], [ s.1^13, s.1^127 ], [ s.1^39, s.1^303 ], [ s.1^12, s.1^120 ], [ s.1^15, s.1^96 ], [ s.1^20, s.1^184 ], [ s.1^36, s.1^312 ], [ s.1^43, s.1^320 ], [ 1, s.1^25 ], [ s.1^35, s.1^257 ], [ s.1^34, s.1^265 ], [ s.1^30, s.1^233 ], [ s.1^26, s.1^201 ], [ s.1^16, s.1^153 ], [ s.1^18, s.1^137 ], [ s.1^21, s.1^178 ], [ s.1^33, s.1^274 ], [ s.1^36, s.1^314 ], [ s.1^22, 6 ], [ s.1^39, s.1^291 ], [ s.1^2, s.1^12 ], [ s.1^27, s.1^196 ], [ s.1^26, s.1^204 ], [ s.1^7, s.1^36 ], [ s.1^3, s.1^4 ], [ s.1^43, s.1^324 ], [ s.1, s.1^21 ], [ s.1^28, s.1^253 ], [ s.1^25, s.1^213 ], [ s.1^14, s.1^109 ], [ s.1^4, s.1^61 ], [ s.1^8, s.1^93 ], [ s.1^21, s.1^181 ], [ s.1, s.1^22 ], [ s.1^14, s.1^110 ], [ s.1^19, s.1^134 ], [ s.1^21, s.1^182 ], [ s.1^22, s.1^174 ], [ s.1^5, s.1^55 ], [ s.1^14, s.1^111 ], [ s.1^20, s.1^191 ], [ s.1^6, s.1^16 ], [ s.1^31, s.1^216 ], [ s.1^28, s.1^192 ], [ s.1^27, s.1^248 ], [ s.1^25, s.1^232 ], [ s.1^9, s.1^104 ], [ s.1^15, s.1^88 ], [ s.1^20, s.1^128 ], [ s.1^21, s.1^136 ], [ s.1^5, s.1^9 ], [ s.1^34, s.1^305 ], [ s.1^32, s.1^289 ], [ s.1^28, s.1^193 ], [ s.1^13, s.1^73 ], [ s.1^16, s.1^161 ], [ s.1^22, s.1^145 ], [ s.1^38, s.1^273 ], [ s.1^12, s.1^66 ], [ s.1^29, s.1^202 ], [ s.1^20, s.1^130 ], [ s.1^45, s.1^330 ], [ s.1^7, s.1^27 ], [ s.1^36, s.1^259 ], [ s.1^39, s.1^283 ], [ s.1^14, s.1^84 ], [ s.1^15, s.1^92 ], [ s.1^19, s.1^188 ], [ s.1^46, s.1^340 ], [ 1, s.1^37 ], [ s.1^26, s.1^245 ], [ s.1^7, s.1^29 ], [ s.1^5, s.1^13 ], [ s.1^19, s.1^189 ], [ s.1^21, s.1^141 ], [ s.1^22, s.1^149 ], [ s.1^3, s.1^62 ], [ s.1^33, s.1^302 ], [ s.1^29, s.1^206 ], [ s.1^28, s.1^198 ], [ s.1^26, s.1^246 ], [ s.1^23, s.1^158 ], [ s.1^14, s.1^86 ], [ s.1^12, s.1^70 ], [ s.1^4, s.1^6 ], [ s.1^10, s.1^119 ], [ s.1^33, s.1^303 ], [ s.1^30, s.1^215 ], [ s.1^21, s.1^143 ], [ s.1^36, s.1^263 ], [ s.1^9, s.1^96 ], [ s.1^28, s.1^200 ], [ s.1^13, s.1^64 ], [ s.1^37, s.1^256 ], [ s.1^2, 3 ], [ s.1^27, s.1^241 ], [ s.1^24, s.1^233 ], [ s.1^6, s.1^25 ], [ s.1^19, s.1^177 ], [ s.1^22, s.1^153 ], [ s.1^44, s.1^329 ], [ s.1^39, s.1^274 ], [ s.1^13, s.1^67 ], [ s.1^34, s.1^315 ], [ s.1^33, s.1^291 ], [ s.1^26, s.1^251 ], [ s.1^16, 6 ], [ s.1^20, s.1^139 ], [ s.1^36, s.1^267 ], [ s.1, s.1^36 ], [ s.1^13, s.1^68 ], [ s.1^2, s.1^60 ], [ s.1^7, s.1^21 ], [ s.1^31, s.1^213 ], [ s.1^14, s.1^93 ], [ s.1^12, s.1^77 ], [ s.1^8, s.1^109 ], [ s.1^7, s.1^22 ], [ s.1^34, s.1^318 ], [ s.1^11, s.1^118 ], [ s.1^8, s.1^110 ], [ s.1^10, s.1^126 ], [ s.1^16, s.1^174 ], [ s.1^35, s.1^310 ], [ s.1^8, s.1^111 ], [ s.1^28, s.1^207 ], [ s.1^13, s.1^71 ], [ s.1^21, s.1^135 ], [ s.1^45, s.1^327 ], [ s.1^24, s.1^240 ], [ s.1^35, s.1^296 ], [ 1, s.1^49 ], [ s.1^6, s.1 ], [ s.1^4, s.1^17 ], [ s.1^19, s.1^169 ], [ s.1, s.1^58 ], [ s.1^29, s.1^218 ], [ s.1^26, s.1^226 ], [ s.1^23, s.1^138 ], [ s.1^6, s.1^2 ], [ s.1^4, s.1^18 ], [ s.1, s.1^59 ], [ s.1^31, s.1^203 ], [ s.1^30, s.1^195 ], [ s.1^2, s.1^35 ], [ s.1^8, s.1^115 ], [ s.1^35, s.1^299 ], [ s.1^36, s.1^275 ], [ s.1^3, s.1^44 ], [ s.1^25, s.1^252 ], [ s.1^23, s.1^140 ], [ s.1^8, s.1^116 ], [ s.1^38, s.1^260 ], [ s.1^39, s.1^268 ], [ s.1^10, s.1^101 ], [ s.1^33, s.1^317 ], [ s.1^32, s.1^309 ], [ s.1^31, s.1^205 ], [ s.1^30, s.1^197 ], [ s.1^27, s.1^237 ], [ s.1^35, s.1^301 ], [ s.1^39, s.1^269 ], [ s.1^46, s.1^325 ], [ s.1^5, s.1^30 ], [ s.1^34, s.1^294 ], [ s.1^25, s.1^254 ], [ s.1^23, s.1^142 ], [ s.1^13, s.1^94 ], [ s.1^38, s.1^262 ], [ s.1^46, s.1^326 ], [ s.1^47, s.1^334 ], [ s.1^2, s.1^39 ], [ s.1^33, s.1^319 ], [ s.1^32, s.1^311 ], [ s.1^30, s.1^199 ], [ s.1^12, s.1^87 ], [ s.1^6, s.1^7 ], [ s.1^4, s.1^23 ], [ s.1^20, s.1^151 ], [ s.1^39, s.1^271 ], [ s.1^7, 1 ], [ s.1^17, s.1^176 ], [ s.1^19, s.1^160 ], [ s.1^37, s.1^272 ], [ s.1^46, s.1^328 ], [ s.1^8, s.1^121 ], [ s.1^32, s.1^313 ], [ s.1^6, s.1^10 ], [ s.1^34, s.1^298 ], [ s.1^31, s.1^194 ], [ s.1^29, s.1^210 ], [ s.1^26, s.1^234 ], [ s.1^13, s.1^82 ], [ s.1^12, s.1^90 ], [ s.1^9, 2 ], [ s.1^39, s.1^258 ], [ s.1^47, s.1^322 ], [ s.1^6, s.1^11 ], [ s.1^11, s.1^99 ], [ s.1^7, s.1^3 ], [ s.1^46, s.1^331 ], [ s.1, s.1^52 ], [ s.1^33, s.1^308 ], [ s.1^5, s.1^20 ], [ s.1^8, s.1^124 ], [ s.1^35, s.1^292 ], [ s.1, s.1^53 ], [ s.1^8, s.1^125 ], [ s.1^9, s.1^117 ], [ s.1^15, s.1^69 ], [ s.1^36, 5 ], [ s.1^39, s.1^261 ], [ s.1, s.1^54 ], [ s.1^14, s.1^78 ], [ s.1^11, s.1^102 ], [ s.1^6, s.1^14 ], [ s.1^21, s.1^150 ], [ s.1^38, s.1^270 ], [ s.1^2, s.1^47 ], [ s.1^28, s.1^223 ], [ s.1^14, s.1^79 ], [ s.1^17, s.1^183 ], [ s.1^18, s.1^175 ], [ s.1^35, s.1^295 ], [ s.1^3, s.1^88 ], [ s.1^6, s.1^112 ], [ s.1^16, s.1^192 ], [ s.1^19, s.1^216 ], [ s.1^41, s.1^264 ], [ s.1, s.1^73 ], [ s.1^28, s.1^161 ], [ s.1^23, s.1^249 ], [ s.1^10, s.1^17 ], [ s.1^16, s.1^193 ], [ s.1^44, s.1^289 ], [ s.1^46, s.1^305 ], [ 1, s.1^66 ], [ s.1^33, s.1^330 ], [ s.1^23, s.1^250 ], [ s.1^10, s.1^18 ], [ s.1^17, s.1^202 ], [ s.1^20, s.1^226 ], [ s.1^22, s.1^242 ], [ s.1^7, s.1^12 ** WARNING: Output too long, hence truncated. Errors: /home/mfd/gomagma: line 2: 4050 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 04:57:04 2004 Input: diumenges:={i: i in [4..366 by 7]}; print diumenges; Output: Magma V2.10-6 Sat Mar 6 2004 04:57:01 on modular [Seed = 2796504708] ------------------------------------- { 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 } Total time: 3.139 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 05:14:04 2004 Input: [7^i : i in [0..2]]; Output: Magma V2.10-6 Sat Mar 6 2004 05:14:01 on modular [Seed = 1245949555] ------------------------------------- [ 1, 7, 49 ] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 05:16:21 2004 Input: [i : x^i i in [0..2]]; Output: Magma V2.10-6 Sat Mar 6 2004 05:16:18 on modular [Seed = 2054397656] ------------------------------------- >> [i : x^i i in [0..2]];; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 05:17:17 2004 Input: x^&+[i : i i in [0..2]]; Output: Magma V2.10-6 Sat Mar 6 2004 05:17:14 on modular [Seed = 1667925529] ------------------------------------- >> x^&+[i : i i in [0..2]];; ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 05:17:32 2004 Input: x^&+[i : i in [0..2]]; Output: Magma V2.10-6 Sat Mar 6 2004 05:17:29 on modular [Seed = 1818593541] ------------------------------------- >> x^&+[i : i in [0..2]];; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 05:18:05 2004 Input: [x: x^&+[i : i in [0..2]]]; Output: Magma V2.10-6 Sat Mar 6 2004 05:18:02 on modular [Seed = 354218015] ------------------------------------- >> [x: x^&+[i : i in [0..2]]];; ^ User error: bad syntax Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 05:18:23 2004 Input: [x: x^(&+[i : i in [0..2]])]; Output: Magma V2.10-6 Sat Mar 6 2004 05:18:20 on modular [Seed = 504888098] ------------------------------------- >> [x: x^(&+[i : i in [0..2]])];; ^ User error: bad syntax Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 05:19:01 2004 Input: &+[x^i : i in [0..2]])]; Output: Magma V2.10-6 Sat Mar 6 2004 05:18:58 on modular [Seed = 118416069] ------------------------------------- >> &+[x^i : i in [0..2]])];; ^ User error: bad syntax Total time: 2.839 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 05:19:08 2004 Input: &+[x^i : i in [0..2]]; Output: Magma V2.10-6 Sat Mar 6 2004 05:19:05 on modular [Seed = 252111558] ------------------------------------- >> &+[x^i : i in [0..2]];; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 05:19:42 2004 Input: &+[x,i : x^i | i in [0..2]]; Output: Magma V2.10-6 Sat Mar 6 2004 05:19:39 on modular [Seed = 942792147] ------------------------------------- >> &+[x,i : x^i | i in [0..2]];; ^ User error: bad syntax Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 05:20:08 2004 Input: &+[x^i | i in [0..2]]; Output: Magma V2.10-6 Sat Mar 6 2004 05:20:05 on modular [Seed = 673303981] ------------------------------------- >> &+[x^i | i in [0..2]];; ^ User error: Identifier 'i' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 05:21:16 2004 Input: &+[x,i | [x^i : i in [0..2]]; Output: Magma V2.10-6 Sat Mar 6 2004 05:21:13 on modular [Seed = 3537581211] ------------------------------------- >> &+[x,i | [x^i : i in [0..2]];; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 05:21:41 2004 Input: &+[x | [x^i : i in [0..2]]; Output: Magma V2.10-6 Sat Mar 6 2004 05:21:38 on modular [Seed = 3687988665] ------------------------------------- >> &+[x | [x^i : i in [0..2]];; ^ User error: bad syntax Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 05:22:03 2004 Input: &+[x | [x^i : i in [0..2]]]; Output: Magma V2.10-6 Sat Mar 6 2004 05:22:00 on modular [Seed = 3301778140] ------------------------------------- >> &+[x | [x^i : i in [0..2]]];; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 05:23:58 2004 Input: &+[x^i : i in [7^j : j in [0..2]]]; Output: Magma V2.10-6 Sat Mar 6 2004 05:23:55 on modular [Seed = 3452185382] ------------------------------------- >> &+[x^i : i in [7^j : j in [0..2]]];; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 05:24:18 2004 Input: ny:=&+[x^i : i in [7^j : j in [0..2]]]; Output: Magma V2.10-6 Sat Mar 6 2004 05:24:15 on modular [Seed = 4143911017] ------------------------------------- >> ny:=&+[x^i : i in [7^j : j in [0..2]]];; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 05:24:50 2004 Input: p:=PolynomialRing(GF(7^3)); ny:=&+[x^i : i in [7^j : j in [0..2]]]; Output: Magma V2.10-6 Sat Mar 6 2004 05:24:47 on modular [Seed = 4294318400] ------------------------------------- Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 05:25:07 2004 Input: p:=PolynomialRing(GF(7^3)); ny:=&+[x^i : i in [7^j : j in [0..2]]]; ny; Output: Magma V2.10-6 Sat Mar 6 2004 05:25:04 on modular [Seed = 3974433724] ------------------------------------- x^49 + x^7 + x Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 05:25:58 2004 Input: P:=PolynomialRing(GF(7^3)); n:=&+[x^i : i in [7^j : j in [0..2]]]; n; Output: Magma V2.10-6 Sat Mar 6 2004 05:25:55 on modular [Seed = 2527031797] ------------------------------------- x^49 + x^7 + x Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 05:29:18 2004 Input: P:=PolynomialRing(GF(7^3)); n:=&+[x^i : i eq &+[7^j : j in [0..2]]]; n; Output: Magma V2.10-6 Sat Mar 6 2004 05:29:15 on modular [Seed = 2677438516] ------------------------------------- >> n:=&+[x^i : i eq &+[7^j : j in [0..2]]]; ^ User error: bad syntax >> n;; ^ User error: Identifier 'n' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 05:29:37 2004 Input: P:=PolynomialRing(GF(7^3)); n:=&+[x^i | i eq &+[7^j : j in [0..2]]]; n; Output: Magma V2.10-6 Sat Mar 6 2004 05:29:34 on modular [Seed = 2290180310] ------------------------------------- >> n:=&+[x^i | i eq &+[7^j : j in [0..2]]]; ^ User error: Identifier 'i' has not been declared or assigned >> n;; ^ User error: Identifier 'n' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 05:30:28 2004 Input: P:=PolynomialRing(GF(7^3)); n:=&+[x^i : i is &+[7^j : j in [0..2]]]; n; Output: Magma V2.10-6 Sat Mar 6 2004 05:30:25 on modular [Seed = 3098628265] ------------------------------------- >> n:=&+[x^i : i is &+[7^j : j in [0..2]]]; ^ User error: bad syntax >> n;; ^ User error: Identifier 'n' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 05:30:44 2004 Input: P:=PolynomialRing(GF(7^3)); n:=&+[x^i : i in &+[7^j : j in [0..2]]]; n; Output: Magma V2.10-6 Sat Mar 6 2004 05:30:41 on modular [Seed = 2729134755] ------------------------------------- >> n:=&+[x^i : i in &+[7^j : j in [0..2]]]; ^ Runtime error in for: Iteration is not possible over this object >> n;; ^ User error: Identifier 'n' has not been declared or assigned Total time: 2.869 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 05:32:17 2004 Input: P:=PolynomialRing(GF(7^3)); n:=&+[x^(&+[i] : i in [7^j : j in [0..2]]]; n; Output: Magma V2.10-6 Sat Mar 6 2004 05:32:14 on modular [Seed = 2879538005] ------------------------------------- >> n:=&+[x^(&+[i] : i in [7^j : j in [0..2]]]; ^ User error: bad syntax >> n;; ^ User error: Identifier 'n' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 05:32:27 2004 Input: P:=PolynomialRing(GF(7^3)); n:=&+[x^(&+[i]) : i in [7^j : j in [0..2]]]; n; Output: Magma V2.10-6 Sat Mar 6 2004 05:32:24 on modular [Seed = 1381743291] ------------------------------------- x^49 + x^7 + x Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 05:32:57 2004 Input: P:=PolynomialRing(GF(7^3)); n:=[x^(&+[i]) : i in [7^j : j in [0..2]]]; n; Output: Magma V2.10-6 Sat Mar 6 2004 05:32:53 on modular [Seed = 1565832665] ------------------------------------- [ x, x^7, x^49 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 05:33:35 2004 Input: P:=PolynomialRing(GF(7^3)); n:=[x^(&+[i: i in 7^j : j in [0..2]])]; n; Output: Magma V2.10-6 Sat Mar 6 2004 05:33:32 on modular [Seed = 1145941225] ------------------------------------- >> n:=[x^(&+[i: i in 7^j : j in [0..2]])]; ^ User error: bad syntax >> n;; ^ User error: Identifier 'n' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 05:34:09 2004 Input: P:=PolynomialRing(GF(7^3)); n:=[x^(&+[i: i in [0..2 by 7])]; n; Output: Magma V2.10-6 Sat Mar 6 2004 05:34:06 on modular [Seed = 1330030080] ------------------------------------- >> n:=[x^(&+[i: i in [0..2 by 7])]; ^ User error: bad syntax >> n;; ^ User error: Identifier 'n' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 05:34:28 2004 Input: P:=PolynomialRing(GF(7^3)); n:=[x^(&+[i: i in [0..2 by 7]])]; n; Output: Magma V2.10-6 Sat Mar 6 2004 05:34:25 on modular [Seed = 1988075286] ------------------------------------- [ 1 ] Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 05:36:41 2004 Input: P:=PolynomialRing(GF(7^3)); n:=[x^(&+[i: i in [ 7^j : j in [0..2 ]]))]; n; Output: Magma V2.10-6 Sat Mar 6 2004 05:36:38 on modular [Seed = 1684901251] ------------------------------------- >> n:=[x^(&+[i: i in [ 7^j : j in [0..2 ]]))]; ^ User error: bad syntax >> n;; ^ User error: Identifier 'n' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 05:37:01 2004 Input: P:=PolynomialRing(GF(7^3)); n:=[x^(&+[i: i in [ 7^j : j in [0..2 ]]])]; n; Output: Magma V2.10-6 Sat Mar 6 2004 05:36:58 on modular [Seed = 1868990196] ------------------------------------- [ x^57 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 05:39:23 2004 Input: P:=PolynomialRing(GF(7^3)); t:=&+[x^i : i in [7^j : j in [0..2]]]; t; Output: Magma V2.10-6 Sat Mar 6 2004 05:39:20 on modular [Seed = 371194911] ------------------------------------- x^49 + x^7 + x Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 05:39:30 2004 Input: P:=PolynomialRing(GF(7^3)); t:=&+[x^i : i in [7^j : j in [0..2]]]; t; Output: Magma V2.10-6 Sat Mar 6 2004 05:39:27 on modular [Seed = 504886288] ------------------------------------- x^49 + x^7 + x Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 05:42:54 2004 Input: P:=PolynomialRing(GF(7^3)); n:=x^(&+[i: i in [ 7^j : j in [0..2]]]); t:=&+[x^i : i in [7^j : j in [0..2]]]; { : a,b in P | Evaluate(n,a) eq Evaluate(t,b)}; Output: Magma V2.10-6 Sat Mar 6 2004 05:42:52 on modular [Seed = 825809484] ------------------------------------- >> { : a,b in P | Evaluate(n,a) eq Evaluate(t,b)}; ^ Runtime error in for: Iteration is not possible over this object Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 05:43:25 2004 Input: P:=PolynomialRing(GF(7^3)); n:=x^(&+[i: i in [ 7^j : j in [0..2]]]); t:=&+[x^i : i in [7^j : j in [0..2]]]; {[a,b] : a,b in P | Evaluate(n,a) eq Evaluate(t,b)}; Output: Magma V2.10-6 Sat Mar 6 2004 05:43:22 on modular [Seed = 942789411] ------------------------------------- >> {[a,b] : a,b in P | Evaluate(n,a) eq Evaluate(t,b)}; ^ Runtime error in for: Iteration is not possible over this object Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 05:49:00 2004 Input: exponents:=[7^i : i in [0..2]]; n:=x^(&+[i: i in exponents]); n; Output: Magma V2.10-6 Sat Mar 6 2004 05:48:57 on modular [Seed = 640666350] ------------------------------------- >> n:=x^(&+[i: i in exponents]); ^ User error: Identifier 'x' has not been declared or assigned >> n;; ^ User error: Identifier 'n' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 05:49:19 2004 Input: P:=PolynomialRing(GF(7^3)); exponents:=[7^i : i in [0..2]]; n:=x^(&+[i: i in exponents]); n; Output: Magma V2.10-6 Sat Mar 6 2004 05:49:16 on modular [Seed = 3520609580] ------------------------------------- x^57 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 05:49:46 2004 Input: P:=PolynomialRing(GF(7^3)); exponents:=[7^i : i in [0..2]]; t:=&+[x^i : i in exponents];t; Output: Magma V2.10-6 Sat Mar 6 2004 05:49:43 on modular [Seed = 3637589070] ------------------------------------- x^49 + x^7 + x Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 05:53:27 2004 Input: P:=PolynomialRing(GF(7^3)); exponents:=[7^i : i in [0..2]]; t:=&+[x^i : i in exponents]; n:=x^(&+[i: i in exponents]); {[a,b] : a,b in P | Evaluate(n,a) eq Evaluate(t,b)}; Output: Magma V2.10-6 Sat Mar 6 2004 05:53:24 on modular [Seed = 3418498622] ------------------------------------- >> {[a,b] : a,b in P | Evaluate(n,a) eq Evaluate(t,b)};; ^ Runtime error in for: Iteration is not possible over this object Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 05:54:19 2004 Input: P:=PolynomialRing(GF(7^3)); exponents:=[7^i : i in [0..2]]; t:=&+[x^i : i in exponents]; n:=x^(&+[i: i in exponents]); {[a,b] : a,b in GF(7^3) | Evaluate(n,a) eq Evaluate(t,b)}; Output: Magma V2.10-6 Sat Mar 6 2004 05:54:15 on modular [Seed = 4076543860] ------------------------------------- { [ $.1^3, $.1^24 ], [ $.1^35, $.1^280 ], [ $.1^30, $.1^240 ], [ $.1^28, $.1^224 ], [ $.1^4, $.1^32 ], [ $.1^5, $.1^40 ], [ $.1^21, $.1^168 ], [ $.1^36, $.1^288 ], [ 1, $.1 ], [ $.1^35, $.1^281 ], [ $.1^28, $.1^225 ], [ $.1^12, $.1^97 ], [ $.1^11, $.1^89 ], [ $.1^6, $.1^49 ], [ $.1^5, $.1^41 ], [ $.1^10, $.1^81 ], [ $.1^37, $.1^297 ], [ $.1^42, $.1^337 ], [ 1, $.1^2 ], [ $.1^13, $.1^106 ], [ $.1^12, $.1^98 ], [ $.1^7, $.1^58 ], [ $.1^3, $.1^26 ], [ $.1^4, $.1^34 ], [ $.1^17, $.1^138 ], [ $.1^18, $.1^146 ], [ $.1^19, $.1^154 ], [ $.1^35, $.1^282 ], [ $.1^42, $.1^338 ], [ $.1^5, $.1^43 ], [ $.1^26, $.1^211 ], [ $.1^25, $.1^203 ], [ $.1^24, $.1^195 ], [ $.1^14, $.1^115 ], [ $.1^11, $.1^91 ], [ $.1^7, $.1^59 ], [ $.1^10, $.1^83 ], [ $.1^19, $.1^155 ], [ $.1^20, $.1^163 ], [ $.1^42, $.1^339 ], [ $.1^3, $.1^28 ], [ $.1^33, $.1^268 ], [ $.1^32, $.1^260 ], [ $.1^31, $.1^252 ], [ $.1^27, $.1^220 ], [ $.1^26, $.1^212 ], [ $.1^14, $.1^116 ], [ $.1^12, $.1^100 ], [ $.1^17, $.1^140 ], [ $.1^18, $.1^148 ], [ $.1^21, $.1^172 ], [ $.1^10, $.1^85 ], [ $.1^34, $.1^277 ], [ $.1^33, $.1^269 ], [ $.1^28, $.1^229 ], [ $.1^25, $.1^205 ], [ $.1^24, $.1^197 ], [ $.1^19, $.1^157 ], [ $.1^21, $.1^173 ], [ $.1^38, $.1^309 ], [ $.1^39, $.1^317 ], [ $.1^40, $.1^325 ], [ $.1^5, $.1^46 ], [ $.1^32, $.1^262 ], [ $.1^31, $.1^254 ], [ $.1^28, $.1^230 ], [ $.1^26, $.1^214 ], [ $.1^17, $.1^142 ], [ $.1^35, $.1^286 ], [ $.1^40, $.1^326 ], [ $.1^41, $.1^334 ], [ 1, $.1^7 ], [ $.1^33, $.1^271 ], [ $.1^24, $.1^199 ], [ $.1^12, $.1^103 ], [ $.1^35, $.1^287 ], [ $.1^38, $.1^311 ], [ $.1^39, $.1^319 ], [ $.1, 1 ], [ $.1^27, $.1^208 ], [ $.1^23, $.1^176 ], [ $.1^11, $.1^80 ], [ $.1^19, $.1^144 ], [ $.1^40, $.1^328 ], [ $.1^5, $.1^33 ], [ $.1^26, $.1^217 ], [ $.1^14, $.1^121 ], [ $.1^38, $.1^313 ], [ 1, $.1^10 ], [ $.1^33, $.1^258 ], [ $.1^25, $.1^194 ], [ $.1^4, $.1^42 ], [ $.1^15, 2 ], [ $.1^37, $.1^290 ], [ $.1^41, $.1^322 ], [ 1, $.1^11 ], [ $.1^28, $.1^235 ], [ $.1, $.1^3 ], [ $.1^19, $.1^147 ], [ $.1^40, $.1^331 ], [ $.1^7, $.1^52 ], [ $.1^29, 4 ], [ $.1^14, $.1^124 ], [ $.1^18, $.1^156 ], [ $.1^39, $.1^308 ], [ $.1^4, $.1^45 ], [ $.1^33, $.1^261 ], [ $.1^14, $.1^125 ], [ $.1^7, $.1^53 ], [ $.1^9, $.1^69 ], [ $.1^15, $.1^117 ], [ 1, $.1^14 ], [ $.1^32, $.1^270 ], [ $.1^28, $.1^238 ], [ $.1^7, $.1^54 ], [ $.1^8, $.1^78 ], [ $.1^21, $.1^166 ], [ $.1^2, $.1^31 ], [ $.1^29, $.1^231 ], [ $.1^28, $.1^239 ], [ $.1^23, $.1^183 ], [ $.1^8, $.1^79 ], [ $.1^18, $.1^159 ], [ $.1^21, $.1^167 ], [ 1, $.1^16 ], [ $.1^35, $.1^264 ], [ $.1^31, $.1^232 ], [ $.1^25, $.1^216 ], [ $.1^12, $.1^112 ], [ $.1^9, $.1^88 ], [ $.1^15, $.1^104 ], [ $.1^16, $.1^145 ], [ $.1^32, $.1^273 ], [ $.1^29, $.1^249 ], [ $.1^21, $.1^185 ], [ $.1^22, $.1^161 ], [ $.1^38, $.1^289 ], [ $.1^42, $.1^321 ], [ $.1^11, $.1^74 ], [ $.1^29, $.1^250 ], [ $.1^28, $.1^242 ], [ $.1^36, $.1^306 ], [ $.1, $.1^27 ], [ $.1^33, $.1^283 ], [ $.1^13, $.1^123 ], [ $.1^11, $.1^75 ], [ $.1^18, $.1^131 ], [ $.1^21, $.1^187 ], [ $.1^36, $.1^307 ], [ $.1^8, $.1^84 ], [ $.1^28, $.1^244 ], [ $.1^9, $.1^92 ], [ $.1^18, $.1^132 ], [ $.1^20, $.1^180 ], [ $.1^37, $.1^316 ], [ $.1^40, $.1^340 ], [ $.1^43, $.1^332 ], [ $.1, $.1^29 ], [ $.1^6, $.1^37 ], [ $.1^2, $.1^5 ], [ $.1^16, $.1^149 ], [ $.1^8, $.1^86 ], [ $.1^17, $.1^158 ], [ $.1^39, $.1^302 ], [ $.1^5, $.1^63 ], [ $.1^29, $.1^255 ], [ $.1^24, $.1^215 ], [ $.1^13, $.1^127 ], [ $.1^39, $.1^303 ], [ $.1^12, $.1^120 ], [ $.1^15, $.1^96 ], [ $.1^20, $.1^184 ], [ $.1^36, $.1^312 ], [ $.1^43, $.1^320 ], [ 1, $.1^25 ], [ $.1^35, $.1^257 ], [ $.1^34, $.1^265 ], [ $.1^30, $.1^233 ], [ $.1^26, $.1^201 ], [ $.1^16, $.1^153 ], [ $.1^18, $.1^137 ], [ $.1^21, $.1^178 ], [ $.1^33, $.1^274 ], [ $.1^36, $.1^314 ], [ $.1^22, 6 ], [ $.1^39, $.1^291 ], [ $.1^2, $.1^12 ], [ $.1^27, $.1^196 ], [ $.1^26, $.1^204 ], [ $.1^7, $.1^36 ], [ $.1^3, $.1^4 ], [ $.1^43, $.1^324 ], [ $.1, $.1^21 ], [ $.1^28, $.1^253 ], [ $.1^25, $.1^213 ], [ $.1^14, $.1^109 ], [ $.1^4, $.1^61 ], [ $.1^8, $.1^93 ], [ $.1^21, $.1^181 ], [ $.1, $.1^22 ], [ $.1^14, $.1^110 ], [ $.1^19, $.1^134 ], [ $.1^21, $.1^182 ], [ $.1^22, $.1^174 ], [ $.1^5, $.1^55 ], [ $.1^14, $.1^111 ], [ $.1^20, $.1^191 ], [ $.1^6, $.1^16 ], [ $.1^31, $.1^216 ], [ $.1^28, $.1^192 ], [ $.1^27, $.1^248 ], [ $.1^25, $.1^232 ], [ $.1^9, $.1^104 ], [ $.1^15, $.1^88 ], [ $.1^20, $.1^128 ], [ $.1^21, $.1^136 ], [ $.1^5, $.1^9 ], [ $.1^34, $.1^305 ], [ $.1^32, $.1^289 ], [ $.1^28, $.1^193 ], [ $.1^13, $.1^73 ], [ $.1^16, $.1^161 ], [ $.1^22, $.1^145 ], [ $.1^38, $.1^273 ], [ $.1^12, $.1^66 ], [ $.1^29, $.1^202 ], [ $.1^20, $.1^130 ], [ $.1^45, $.1^330 ], [ $.1^7, $.1^27 ], [ $.1^36, $.1^259 ], [ $.1^39, $.1^283 ], [ $.1^14, $.1^84 ], [ $.1^15, $.1^92 ], [ $.1^19, $.1^188 ], [ $.1^46, $.1^340 ], [ 1, $.1^37 ], [ $.1^26, $.1^245 ], [ $.1^7, $.1^29 ], [ $.1^5, $.1^13 ], [ $.1^19, $.1^189 ], [ $.1^21, $.1^141 ], [ $.1^22, $.1^149 ], [ $.1^3, $.1^62 ], [ $.1^33, $.1^302 ], [ $.1^29, $.1^206 ], [ $.1^28, $.1^198 ], [ $.1^26, $.1^246 ], [ $.1^23, $.1^158 ], [ $.1^14, $.1^86 ], [ $.1^12, $.1^70 ], [ $.1^4, $.1^6 ], [ $.1^10, $.1^119 ], [ $.1^33, $.1^303 ], [ $.1^30, $.1^215 ], [ $.1^21, $.1^143 ], [ $.1^36, $.1^263 ], [ $.1^9, $.1^96 ], [ $.1^28, $.1^200 ], [ $.1^13, $.1^64 ], [ $.1^37, $.1^256 ], [ $.1^2, 3 ], [ $.1^27, $.1^241 ], [ $.1^24, $.1^233 ], [ $.1^6, $.1^25 ], [ $.1^19, $.1^177 ], [ $.1^22, $.1^153 ], [ $.1^44, $.1^329 ], [ $.1^39, $.1^274 ], [ $.1^13, $.1^67 ], [ $.1^34, $.1^315 ], [ $.1^33, $.1^291 ], [ $.1^26, $.1^251 ], [ $.1^16, 6 ], [ $.1^20, $.1^139 ], [ $.1^36, $.1^267 ], [ $.1, $.1^36 ], [ $.1^13, $.1^68 ], [ $.1^2, $.1^60 ], [ $.1^7, $.1^21 ], [ $.1^31, $.1^213 ], [ $.1^14, $.1^93 ], [ $.1^12, $.1^77 ], [ $.1^8, $.1^109 ], [ $.1^7, $.1^22 ], [ $.1^34, $.1^318 ], [ $.1^11, $.1^118 ], [ $.1^8, $.1^110 ], [ $.1^10, $.1^126 ], [ $.1^16, $.1^174 ], [ $.1^35, $.1^310 ], [ $.1^8, $.1^111 ], [ $.1^28, $.1^207 ], [ $.1^13, $.1^71 ], [ $.1^21, $.1^135 ], [ $.1^45, $.1^327 ], [ $.1^24, $.1^240 ], [ $.1^35, $.1^296 ], [ 1, $.1^49 ], [ $.1^6, $.1 ], [ $.1^4, $.1^17 ], [ $.1^19, $.1^169 ], [ $.1, $.1^58 ], [ $.1^29, $.1^218 ], [ $.1^26, $.1^226 ], [ $.1^23, $.1^138 ], [ $.1^6, $.1^2 ], [ $.1^4, $.1^18 ], [ $.1, $.1^59 ], [ $.1^31, $.1^203 ], [ $.1^30, $.1^195 ], [ $.1^2, $.1^35 ], [ $.1^8, $.1^115 ], [ $.1^35, $.1^299 ], [ $.1^36, $.1^275 ], [ $.1^3, $.1^44 ], [ $.1^25, $.1^252 ], [ $.1^23, $.1^140 ], [ $.1^8, $.1^116 ], [ $.1^38, $.1^260 ], [ $.1^39, $.1^268 ], [ $.1^10, $.1^101 ], [ $.1^33, $.1^317 ], [ $.1^32, $.1^309 ], [ $.1^31, $.1^205 ], [ $.1^30, $.1^197 ], [ $.1^27, $.1^237 ], [ $.1^35, $.1^301 ], [ $.1^39, $.1^269 ], [ $.1^46, $.1^325 ], [ $.1^5, $.1^30 ], [ $.1^34, $.1^294 ], [ $.1^25, $.1^254 ], [ $.1^23, $.1^142 ], [ $.1^13, $.1^94 ], [ $.1^38, $.1^262 ], [ $.1^46, $.1^326 ], [ $.1^47, $.1^334 ], [ $.1^2, $.1^39 ], [ $.1^33, $.1^319 ], [ $.1^32, $.1^311 ], [ $.1^30, $.1^199 ], [ $.1^12, $.1^87 ], [ $.1^6, $.1^7 ], [ $.1^4, $.1^23 ], [ $.1^20, $.1^151 ], [ $.1^39, $.1^271 ], [ $.1^7, 1 ], [ $.1^17, $.1^176 ], [ $.1^19, $.1^160 ], [ $.1^37, $.1^272 ], [ $.1^46, $.1^328 ], [ $.1^8, $.1^121 ], [ $.1^32, $.1^313 ], [ $.1^6, $.1^10 ], [ $.1^34, $.1^298 ], [ $.1^31, $.1^194 ], [ $.1^29, $.1^210 ], [ $.1^26, $.1^234 ], [ $.1^13, $.1^82 ], [ $.1^12, $.1^90 ], [ $.1^9, 2 ], [ $.1^39, $.1^258 ], [ $.1^47, $.1^322 ], [ $.1^6, $.1^11 ], [ $.1^11, $.1^99 ], [ $.1^7, $.1^3 ], [ $.1^46, $.1^331 ], [ $.1, $.1^52 ], [ $.1^33, $.1^308 ], [ $.1^5, $.1^20 ], [ $.1^8, $.1^124 ], [ $.1^35, $.1^292 ], [ $.1, $.1^53 ], [ $.1^8, $.1^125 ], [ $.1^9, $.1^117 ], [ $.1^15, $.1^69 ], [ $.1^36, 5 ], [ $.1^39, $.1^261 ], [ $.1, $.1^54 ], [ $.1^14, $.1^78 ], [ $.1^11, $.1^102 ], [ $.1^6, $.1^14 ], [ $.1^21, $.1^150 ], [ $.1^38, $.1^270 ], [ $.1^2, $.1^47 ], [ $.1^28, $.1^223 ], [ $.1^14, $.1^79 ], [ $.1^17, $.1^183 ], [ $.1^18, $.1^175 ], [ $.1^35, $.1^295 ], [ $.1^3, $.1^88 ], [ $.1^6, $.1^112 ], [ $.1^16, $.1^192 ], [ $.1^19, $.1^216 ], [ $.1^41, $.1^264 ], [ $.1, $.1^73 ], [ $.1^28, $.1^161 ], [ $.1^23, $.1^249 ], [ $.1^10, $.1^17 ], [ $.1^16, $.1^193 ], [ $.1^44, $.1^289 ], [ $.1^46, $.1^305 ], [ 1, $.1^66 ], [ $.1^33, $.1^330 ], [ $.1^23, $.1^250 ], [ $.1^10, $.1^18 ], [ $.1^17, $.1^202 ], [ $.1^20, $.1^226 ], [ $.1^22, $.1^242 ], [ $.1^7, $.1^12 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 05:55:11 2004 Input: P:=PolynomialRing(GF(7^3)); exponents:=[7^i : i in [0..2]]; t:=&+[x^i : i in exponents]; n:=x^(&+[i: i in exponents]); { : a,b in GF(7^3) | Evaluate(n,a) eq Evaluate(t,b)}; Output: Magma V2.10-6 Sat Mar 6 2004 05:55:07 on modular [Seed = 3790081979] ------------------------------------- { <$.1^189, $.1^104>, <$.1^268, $.1^223>, <$.1^266, $.1^125>, <$.1^340, $.1^294>, <$.1^245, $.1^281>, <$.1^173, $.1^218>, <1, $.1^7>, <$.1^85, $.1^58>, <$.1^167, $.1^140>, <$.1^108, $.1^100>, <$.1^330, $.1^66>, <$.1^10, $.1^326>, <$.1^303, $.1^319>, <$.1^87, $.1^261>, <$.1^214, $.1^244>, <$.1^20, $.1^201>, <$.1^116, $.1^270>, <$.1^222, $.1^156>, <$.1^338, $.1^201>, <4, $.1^10>, <$.1^19, $.1^188>, <$.1^204, $.1^70>, <$.1^301, $.1^147>, <$.1^56, $.1^311>, <$.1^101, $.1^210>, <$.1^311, $.1^210>, <$.1^238, $.1^229>, <$.1^41, $.1^41>, <$.1^63, $.1^261>, <4, $.1^195>, <$.1^219, $.1^303>, <$.1^144, $.1^339>, <$.1^329, $.1^43>, <$.1^319, $.1^154>, <3, $.1^150>, <$.1^56, $.1^78>, <$.1^237, $.1^327>, <$.1^134, $.1^262>, <$.1^147, $.1^167>, <$.1^160, $.1^223>, <$.1^284, $.1^329>, <$.1^302, $.1^273>, <$.1^239, $.1^140>, <$.1^196, $.1^42>, <$.1^8, $.1^262>, <$.1^250, $.1^318>, <$.1^294, $.1^11>, <$.1^149, $.1^40>, <$.1^22, $.1^119>, <$.1^339, $.1^308>, <$.1^238, $.1^126>, <$.1^48, $.1^197>, <$.1^328, $.1^32>, <$.1^32, $.1^273>, <$.1^97, $.1^205>, <$.1^184, $.1^174>, <$.1^42, $.1^112>, <$.1^176, $.1^251>, <$.1^133, $.1^82>, <$.1^53, $.1^202>, <$.1^135, $.1^167>, <$.1^218, $.1^86>, <$.1^311, $.1^89>, <$.1^87, $.1^28>, <$.1^187, $.1^21>, <$.1^98, $.1^111>, <$.1^104, $.1^214>, <$.1^102, $.1^131>, <$.1^319, $.1^3>, <$.1^314, $.1^246>, <$.1^42, $.1^275>, <$.1^27, $.1^196>, <$.1^267, $.1^168>, <$.1^249, $.1^168>, <$.1^81, $.1^117>, <$.1^291, $.1^271>, <$.1^72, $.1^197>, <$.1^293, $.1^43>, <$.1^297, $.1^135>, <$.1^26, $.1^151>, <$.1^289, $.1^52>, <$.1^239, $.1^295>, <$.1^268, $.1^277>, <$.1^319, $.1^232>, <$.1^122, $.1^226>, <$.1^93, $.1^178>, <$.1^212, $.1^204>, <$.1^82, $.1^244>, <$.1^217, $.1^64>, <$.1^327, $.1^92>, <$.1^272, $.1^214>, <$.1^72, $.1^148>, <$.1^49, $.1^123>, <$.1^200, $.1^211>, <$.1^146, $.1^311>, <$.1^106, $.1^18>, <$.1^46, $.1^83>, <$.1^223, $.1^155>, <$.1^159, $.1^69>, <$.1^37, $.1^59>, <$.1^147, 2>, <$.1^240, $.1^49>, <$.1^294, $.1^338>, <$.1^294, $.1^215>, <$.1^3, $.1^319>, <$.1^177, $.1^172>, <$.1^277, 1>, <$.1^152, $.1^234>, <$.1^116, $.1^214>, <$.1^174, $.1^16>, <$.1^132, $.1^156>, <$.1^72, $.1^195>, <$.1^45, $.1^330>, <$.1^4, $.1^315>, <$.1^34, $.1^6>, <$.1^303, $.1^92>, <$.1^180, $.1^14>, <$.1^307, $.1^82>, <$.1^83, $.1^20>, <0, $.1^300>, <$.1^273, $.1^319>, <$.1^241, $.1^256>, <$.1^29, $.1^9>, <$.1^331, $.1^147>, <$.1^72, $.1^199>, <$.1^180, $.1^77>, <$.1^293, $.1^63>, <$.1^19, $.1^73>, <1, $.1^175>, <$.1^20, $.1^184>, <$.1^303, $.1^28>, <$.1^31, $.1^216>, <$.1^198, $.1^25>, <$.1^209, $.1^334>, <$.1^47, $.1^334>, <$.1^277, $.1^188>, <$.1^85, $.1^332>, <$.1^281, $.1^292>, <$.1^276, $.1^215>, <$.1^212, $.1^245>, <$.1^187, $.1^22>, <$.1^264, $.1^159>, <$.1^184, $.1^101>, <$.1^91, $.1^256>, <$.1^304, $.1^83>, <$.1^183, $.1^117>, <$.1^14, $.1^311>, <$.1^98, $.1^212>, <$.1^222, $.1^146>, <$.1^174, $.1^100>, <$.1^12, $.1^37>, <$.1^274, $.1^81>, <$.1^80, $.1^93>, <$.1^81, $.1^62>, <$.1^313, $.1^59>, <$.1^200, $.1^309>, <$.1^150, $.1^339>, <$.1^277, $.1^71>, <$.1^64, $.1^6>, <$.1^31, $.1^21>, <$.1^150, $.1^314>, <$.1^262, $.1^294>, <$.1^25, $.1^252>, <$.1^339, $.1^248>, <$.1^8, $.1^12>, <$.1^36, $.1^199>, <$.1^222, $.1^233>, <$.1^108, $.1^120>, <$.1^289, $.1^216>, <$.1^194, $.1^60>, <$.1^133, $.1^68>, <$.1^274, $.1^224>, <$.1^101, $.1^41>, <$.1^141, $.1^88>, <$.1^21, $.1^96>, <$.1^8, $.1^5>, <$.1^109, $.1^169>, <$.1^247, $.1^71>, <$.1^126, $.1^321>, <$.1^159, $.1^24>, <$.1^279, $.1^135>, <$.1^104, $.1^191>, <$.1^284, $.1^262>, <$.1^267, $.1^150>, <$.1^204, $.1^233>, <$.1^300, $.1^199>, <$.1^294, $.1^240>, <$.1^131, $.1^33>, <$.1^181, $.1^21>, <$.1^53, $.1^55>, <$.1^91, $.1^254>, <$.1^221, $.1^99>, <$.1^117, $.1^62>, <$.1^32, $.1^79>, <$.1^258, $.1^137>, <$.1^96, $.1>, <$.1^270, $.1^288>, <$.1^202, $.1^85>, <$.1^270, $.1^132>, <$.1^10, $.1^149>, <$.1^229, $.1^127>, <$.1^108, $.1^288>, <$.1^72, $.1^338>, <$.1^170, $.1^130>, <$.1^284, $.1^163>, <$.1^251, $.1^296>, <$.1^259, $.1^320>, <$.1^109, $.1^189>, <$.1^80, $.1^151>, <$.1^135, $.1^178>, <$.1^275, $.1^13>, <$.1^319, $.1^256>, <$.1^323, $.1^138>, <$.1^276, $.1^148>, <$.1^230, $.1^251>, <$.1^33, $.1^24>, <$.1^202, $.1^161>, <$.1^175, $.1^232>, <$.1^248, $.1^78>, <$.1^78, $.1^148>, <$.1^311, $.1^75>, <$.1^29, $.1^75>, <$.1^225, $.1^241>, <$.1^239, $.1^33>, <$.1^37, $.1^36>, <$.1^28, $.1^242>, <$.1^23, $.1^287>, <$.1^238, $.1^225>, <$.1^259, $.1^64>, <$.1^317, $.1^206>, <$.1^64, $.1^298>, <$.1^193, $.1^160>, <$.1^255, $.1^291>, <$.1^275, $.1^142>, <$.1^125, $.1^75>, <$.1^104, $.1^204>, <$.1^92, $.1^84>, <$.1^193, $.1^106>, <$.1^78, $.1^337>, <$.1^112, $.1^235>, <$.1^169, $.1^123>, <$.1^277, $.1^67>, <$.1^9, 2>, <$.1^173, $.1^334>, <$.1^110, $.1^245>, <$.1^18, $.1^2>, <$.1^23, $.1^118>, <$.1^103, $.1^232>, <$.1^106, $.1^32>, <$.1^53, $.1^210>, <$.1^71, $.1^9>, <$.1^189, $.1^271>, <$.1^151, $.1^324>, <$.1^304, $.1^253>, <$.1^257, $.1^41>, <$.1^174, $.1^321>, <$.1^330, $.1^100>, <$.1^104, $.1^262>, <$.1^51, $.1^327>, <$.1^186, $.1^240>, <$.1^208, $.1^239>, <$.1^249, $.1^308>, <$.1^253, $.1^169>, <$.1^147, $.1^248>, <$.1^8, $.1^124>, <$.1^181, $.1^82>, <$.1^20, $.1^124>, <$.1^73, $.1^59>, <$.1^88, $.1^198>, <$.1^150, $.1^70>, <$.1^289, $.1^213>, <$.1^325, $.1^169>, <$.1^209, $.1^264>, <$.1^295, $.1^134>, <$.1^11, $.1^41>, <$.1^209, $.1^158>, <$.1^99, $.1^104>, <$.1^277, $.1^54>, <$.1^204, $.1^25>, <$.1^12, $.1^7>, <$.1^203, $.1^299>, <$.1^172, $.1^223>, <$.1^325, $.1^22>, <$.1^47, $.1^80>, <$.1^203, $.1^250>, <$.1^275, $.1^218>, <$.1^46, $.1^229>, <$.1^9, $.1^24>, <$.1^292, $.1^81>, <$.1^329, $.1^140>, <$.1^115, $.1^67>, <$.1^224, $.1^12>, <2, $.1^120>, <6, 2>, <$.1^317, $.1^250>, <$.1^338, $.1^246>, <$.1^132, $.1>, <$.1^326, $.1^151>, <$.1^247, $.1^254>, <$.1^208, $.1^207>, <$.1^221, $.1^310>, <$.1^173, $.1^183>, <$.1^206, $.1^128>, <$.1^238, $.1^230>, <$.1^36, $.1^2>, <$.1^50, $.1^116>, <$.1^47, $.1^20>, <$.1^50, $.1^329>, <$.1^58, $.1^305>, <$.1^2, $.1^273>, <$.1^39, $.1^28>, <6, $.1^187>, <$.1^306, $.1^159>, <$.1^333, $.1^24>, <$.1^323, $.1^301>, <$.1^157, $.1^177>, <$.1^34, $.1^244>, <$.1^50, $.1^79>, <$.1^212, $.1^184>, <$.1^132, $.1^137>, <$.1^310, $.1^207>, <$.1^180, $.1^146>, <$.1^336, $.1^137>, <$.1^239, $.1^299>, <$.1^338, $.1^110>, <$.1^18, $.1^131>, <$.1^147, $.1^291>, <2, $.1^14>, <$.1^214, $.1^235>, <$.1^53, $.1^287>, <$.1^167, $.1^33>, <$.1^321, $.1^24>, <$.1^206, $.1^84>, <$.1^162, $.1^267>, <$.1^161, $.1^299>, <$.1^34, $.1^230>, <$.1^92, $.1^201>, <$.1^312, $.1^263>, <$.1^239, $.1^218>, <$.1^155, $.1^206>, <$.1^220, $.1^153>, <$.1^102, $.1^137>, <$.1^128, $.1^246>, <$.1^271, $.1^320>, <$.1^288, $.1^49>, <$.1^179, $.1^264>, <$.1^39, $.1^44>, <$.1^217, $.1^232>, <$.1^202, $.1^81>, <$.1^146, $.1^273>, <$.1^297, 2>, <$.1^164, $.1^251>, <$.1^212, $.1^110>, <$.1^268, $.1^224>, <$.1^182, $.1^204>, <$.1^309, $.1^92>, <$.1^134, $.1^184>, <$.1^184, $.1^328>, <$.1^74, $.1^115>, <$.1^25, $.1^144>, <$.1^220, $.1^331>, <$.1^248, $.1^214>, <$.1^75, $.1^178>, <$.1^58, $.1^340>, <$.1^216, $.1^314>, <$.1^47, $.1^30>, <$.1^38, $.1^204>, <$.1^32, $.1^245>, <$.1^290, $.1^313>, <$.1^216, $.1^11>, <$.1^81, $.1^150>, <$.1^219, $.1^261>, <$.1^291, $.1^274>, <$.1^230, $.1^245>, <$.1^84, $.1^87>, <$.1^154, $.1^18>, <$.1^226, $.1^230>, <$.1^190, $.1^223>, <$.1^25, $.1^213>, <2, $.1^10>, <$.1^12, $.1^159>, <$.1^280, $.1^294>, <$.1^101, $.1^91>, <$.1^47, $.1^255>, <$.1^28, $.1^305>, <$.1^58, $.1^101>, <$.1^220, $.1^253>, <$.1^196, $.1^23>, <$.1^43, $.1^290>, <$.1^21, $.1^241>, <$.1^182, $.1^191>, <$.1^324, $.1^159>, <$.1^47, $.1^287>, <$.1^226, $.1^253>, <$.1^174, $.1^77>, <$.1^148, $.1^174>, <6, $.1^283>, <$.1^78, $.1^146>, <$.1^339, $.1^268>, <$.1^240, $.1^288>, <4, $.1^312>, <$.1^84, $.1^195>, <$.1^117, $.1^327>, <$.1^158, $.1^111>, <$.1^28, $.1^277>, <$.1^16, $.1^225>, <$.1^322, $.1^253>, <5, $.1^135>, <$.1^320, $.1^47>, <$.1^191, $.1^250>, <$.1^282, $.1^156>, <$.1, $.1^189>, <$.1^140, $.1^270>, <$.1^161, $.1^287>, <$.1^100, $.1^326>, <$.1^139, $.1^82>, <$.1^337, $.1^324>, <$.1^13, $.1^73>, <$.1^254, $.1^128>, <$.1^170, $.1^212>, <$.1^319, $.1^189>, <$.1^338, $.1^115>, <$.1^336, $.1^49>, <$.1^73, $.1^3>, <$.1^130, $.1^45>, <$.1^289, $.1^160>, <$.1^260, $.1^12>, <$.1^59, $.1^249>, <$.1^317, $.1^91>, <$.1^173, $.1^287>, <$.1^320, $.1^60>, <$.1^18, $.1^337>, <$.1^251, $.1^255>, <$.1^289, $.1^22>, <$.1^123, $.1^291>, <$.1^258, $.1^146>, <$.1^187, $.1^147>, <$.1^87, $.1^269>, <$.1^73, $.1^290>, <$.1^184, $.1^145>, <$.1^96, $.1^240>, <$.1^25, $.1^324>, <$.1^48, $.1^37>, <$.1^272, $.1^226>, <$.1^321, $.1^44>, <$.1^102, $.1^132>, <$.1^331, $.1^205>, <$.1^198, $.1^307>, <$.1^45, $.1^24>, <$.1^51, $.1^269>, <$.1^59, $.1^13>, <$.1^9, $.1^258>, <$.1^110, $.1^329>, <$.1^186, 5>, <$.1^22, $.1^85>, <$.1^126, $.1>, <$.1^198, $.1^14>, <$.1^224, $.1^226>, <$.1^299, $.1^250>, <$.1^27, $.1^117>, <$.1^253, $.1^36>, <$.1^235, $.1^27>, <$.1^124, $.1^225>, <$.1^160, $.1^81>, <$.1^277, $.1^123>, <$.1^49, $.1^21>, <$.1^293, $.1^80>, <$.1^52, $.1^200>, <$.1^277, $.1^194>, <$.1^84, $.1^90>, <$.1^303, $.1^302>, <$.1^187, $.1^3>, <$.1^186, $.1^132>, <$.1^151, $.1^316>, <$.1^119, $.1^46>, <$.1^238, $.1^326>, <$.1^142, $.1^326>, <$.1^157, $.1^320>, <$.1^279, $.1^308>, <$.1^270, $.1>, <$.1^290, $.1^47>, <$.1^74, $.1^110>, <$.1^9, $.1^268>, <$.1^111, $.1^319>, <$.1^218, $.1^139>, <$.1^275, $.1^41>, <$.1^78, $.1^156>, <$.1^240, $.1^337>, <$.1^216, $.1>, <$.1^273, $.1^4>, <$.1^211, $.1^134>, <$.1^143, $.1^99>, <$.1^61, $.1^123>, <$.1^276, $.1^16>, <$.1^129, $.1^241>, <$.1^7, $.1^68>, <$.1^256, $.1^174>, <$.1^31, $.1^203>, <$.1^254, $.1^217>, <$.1^39, 2>, <$.1^212, $.1^151>, <$.1^19, $.1^106>, <$.1^164, $.1^93>, <$.1^339, $.1^258>, <$.1^156, $.1^131>, <$.1^13, $.1^68>, <$.1^204, $.1^10>, <$.1^288, $.1^337>, <$.1^266, $.1^78>, <$.1^332, $.1^163>, <$.1^335, $.1^287>, <$.1^195, $ ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 05:58:38 2004 Input: P:=PolynomialRing(GF(7^3)); exp:= func ; t_qr:= function (q,r) pol:=0; e:=exp(q,r); for i in [0..r-1] do pol:=pol+x^e[i]; end for; return pol; end function; t_qr(7,3); Output: Magma V2.10-6 Sat Mar 6 2004 05:58:35 on modular [Seed = 3957458273] ------------------------------------- [
:5]( q: 7, r: 3 ) >> pol:=pol+x^e[i]; ^ Runtime error in '[]': Sequence element 0 not defined Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 05:59:25 2004 Input: P:=PolynomialRing(GF(7^3)); exp:= func ; t_qr:= function (q,r) pol:=x; e:=exp(q,r); for i in [1..r-1] do pol:=pol+x^e[i]; end for; return pol; end function; t_qr(7,3); Output: Magma V2.10-6 Sat Mar 6 2004 05:59:22 on modular [Seed = 2459663817] ------------------------------------- x^49 + x^7 + x Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 06:07:57 2004 Input: P:=PolynomialRing(GF(7^3)); exp:= func ; t_qr:= function (q,r) pol:=0; e:=exp(q,r); for i in [0..r-1] do pol:=pol+x^e[i]; end for; return pol; end function; t_qr(7,3); Output: Magma V2.10-6 Sat Mar 6 2004 06:07:53 on modular [Seed = 2729137146] ------------------------------------- [
:5]( q: 7, r: 3 ) >> pol:=pol+x^e[i]; ^ Runtime error in '[]': Sequence element 0 not defined Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 06:10:36 2004 Input: n_qr:= function (q,r) exp:= func ; sum:=0; e:=exp(q,r); for i in [0..r-1] do sum:=sum+e[i]; end for; return (x^sum); end function; n_qr(7,3); Output: Magma V2.10-6 Sat Mar 6 2004 06:10:33 on modular [Seed = 1449109421] ------------------------------------- >> return (x^sum); ^ User error: Identifier 'x' has not been declared or assigned >> n_qr(7,3);; ^ User error: Identifier 'n_qr' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 06:10:59 2004 Input: P:=PolynomialRing(GF(7^3)); n_qr:= function (q,r) exp:= func ; sum:=0; e:=exp(q,r); for i in [0..r-1] do sum:=sum+e[i]; end for; return (x^sum); end function; n_qr(7,3); Output: Magma V2.10-6 Sat Mar 6 2004 06:10:56 on modular [Seed = 1599516365] ------------------------------------- [
:4]( q: 7, r: 3 ) >> sum:=sum+e[i]; ^ Runtime error in '[]': Sequence element 0 not defined Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 06:11:18 2004 Input: P:=PolynomialRing(GF(7^3)); n_qr:= function (q,r) exp:= func ; sum:=1; e:=exp(q,r); for i in [1..r-1] do sum:=sum+e[i]; end for; return (x^sum); end function; n_qr(7,3); Output: Magma V2.10-6 Sat Mar 6 2004 06:11:15 on modular [Seed = 1145943493] ------------------------------------- x^57 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 06:13:08 2004 Input: P:=PolynomialRing(GF(7^3)); n_qr:= function (q,r) exp:= func ; return (x^(&+[i : i in exp])); end function; n_qr(7,3); Output: Magma V2.10-6 Sat Mar 6 2004 06:13:05 on modular [Seed = 1296351070] ------------------------------------- [
:4]( q: 7, r: 3 ) >> return (x^(&+[i : i in exp])); ^ Runtime error in for: Iteration is not possible over this object Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 06:14:01 2004 Input: P:=PolynomialRing(GF(7^3)); n_qr:= function (q,r) exp:= func ; return (x^(&+[i : i in exp])); end function; n_qr(7,3); Output: Magma V2.10-6 Sat Mar 6 2004 06:13:58 on modular [Seed = 2054391902] ------------------------------------- [
:4]( q: 7, r: 3 ) >> return (x^(&+[i : i in exp])); ^ Runtime error in for: Iteration is not possible over this object Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 06:14:59 2004 Input: P:=PolynomialRing(GF(7^3)); exp:= func ; exp(7,3); Output: Magma V2.10-6 Sat Mar 6 2004 06:14:56 on modular [Seed = 1667928449] ------------------------------------- [ 1, 7, 49 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 06:15:32 2004 Input: P:=PolynomialRing(GF(7^3)); n_qr:= function (q,r) exp:= func ; return (x^(&+[j : j in exp])); end function; n_qr(7,3); Output: Magma V2.10-6 Sat Mar 6 2004 06:15:29 on modular [Seed = 1818599151] ------------------------------------- [
:4]( q: 7, r: 3 ) >> return (x^(&+[j : j in exp])); ^ Runtime error in for: Iteration is not possible over this object Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 06:16:35 2004 Input: P:=PolynomialRing(GF(7^3)); n_qr:= function (q,r) exp:= func ; return (x^(&+[j : j in exp(q,r)])); end function; n_qr(7,3); Output: Magma V2.10-6 Sat Mar 6 2004 06:16:32 on modular [Seed = 403827546] ------------------------------------- x^57 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 06:18:28 2004 Input: P:=PolynomialRing(GF(7^3)); t_qr:= function (q,r) exp:= func ; return ( &+[x^i : i in exp(q,r) ); end function;t_qr(7,3); Output: Magma V2.10-6 Sat Mar 6 2004 06:18:25 on modular [Seed = 17363666] ------------------------------------- >> return ( &+[x^i : i in exp(q,r) ); ^ User error: bad syntax >> end function;t_qr(7,3);; ^ User error: bad syntax Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 06:18:46 2004 Input: P:=PolynomialRing(GF(7^3)); t_qr:= function (q,r) exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function;t_qr(7,3); Output: Magma V2.10-6 Sat Mar 6 2004 06:18:43 on modular [Seed = 235404751] ------------------------------------- x^49 + x^7 + x Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 06:20:28 2004 Input: M:=MatrixRing(F,2); Output: Magma V2.10-6 Sat Mar 6 2004 06:20:25 on modular [Seed = 1043844501] ------------------------------------- >> M:=MatrixRing(F,2);; ^ User error: Identifier 'F' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 06:20:59 2004 Input: F:=GF(4); M:=MatrixRing(F,2); F; M; Output: Magma V2.10-6 Sat Mar 6 2004 06:20:56 on modular [Seed = 606982254] ------------------------------------- Finite field of size 2^2 Full Matrix Algebra of degree 2 over GF(2^2) Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 06:21:51 2004 Input: F:=GF(4); M:=MatrixRing(F,2); M22:=[j: j in M]; Mt:={i : i in M22 | Trace(i) eq 0}; Output: Magma V2.10-6 Sat Mar 6 2004 06:21:47 on modular [Seed = 757389619] ------------------------------------- Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 06:22:08 2004 Input: F:=GF(4); M:=MatrixRing(F,2); M22:=[j: j in M]; Mt:={i : i in M22 | Trace(i) eq 0}; Mt; Output: Magma V2.10-6 Sat Mar 6 2004 06:22:05 on modular [Seed = 3671273173] ------------------------------------- { [ 0 0] [ 0 0], [ 0 0] [F.1^2 0], [ 0 0] [ F.1 0], [ 0 0] [ 1 0], [F.1^2 0] [ 0 F.1^2], [F.1^2 0] [F.1^2 F.1^2], [F.1^2 0] [ F.1 F.1^2], [F.1^2 0] [ 1 F.1^2], [ 1 0] [ 0 1], [ 1 0] [F.1^2 1], [ 1 0] [ F.1 1], [ 1 0] [ 1 1], [ F.1 0] [ 0 F.1], [ F.1 0] [F.1^2 F.1], [ F.1 0] [ F.1 F.1], [ F.1 0] [ 1 F.1], [ 0 F.1^2] [ 0 0], [ 0 F.1^2] [F.1^2 0], [ 0 F.1^2] [ F.1 0], [ 0 F.1^2] [ 1 0], [F.1^2 F.1^2] [ 0 F.1^2], [F.1^2 F.1^2] [F.1^2 F.1^2], [F.1^2 F.1^2] [ F.1 F.1^2], [F.1^2 F.1^2] [ 1 F.1^2], [ 1 F.1^2] [ 0 1], [ 1 F.1^2] [F.1^2 1], [ 1 F.1^2] [ F.1 1], [ 1 F.1^2] [ 1 1], [ F.1 F.1^2] [ 0 F.1], [ F.1 F.1^2] [F.1^2 F.1], [ F.1 F.1^2] [ F.1 F.1], [ F.1 F.1^2] [ 1 F.1], [ 0 F.1] [ 0 0], [ 0 F.1] [F.1^2 0], [ 0 F.1] [ F.1 0], [ 0 F.1] [ 1 0], [F.1^2 F.1] [ 0 F.1^2], [F.1^2 F.1] [F.1^2 F.1^2], [F.1^2 F.1] [ F.1 F.1^2], [F.1^2 F.1] [ 1 F.1^2], [ 1 F.1] [ 0 1], [ 1 F.1] [F.1^2 1], [ 1 F.1] [ F.1 1], [ 1 F.1] [ 1 1], [ F.1 F.1] [ 0 F.1], [ F.1 F.1] [F.1^2 F.1], [ F.1 F.1] [ F.1 F.1], [ F.1 F.1] [ 1 F.1], [ 0 1] [ 0 0], [ 0 1] [F.1^2 0], [ 0 1] [ F.1 0], [ 0 1] [ 1 0], [F.1^2 1] [ 0 F.1^2], [F.1^2 1] [F.1^2 F.1^2], [F.1^2 1] [ F.1 F.1^2], [F.1^2 1] [ 1 F.1^2], [ 1 1] [ 0 1], [ 1 1] [F.1^2 1], [ 1 1] [ F.1 1], [ 1 1] [ 1 1], [ F.1 1] [ 0 F.1], [ F.1 1] [F.1^2 F.1], [ F.1 1] [ F.1 F.1], [ F.1 1] [ 1 F.1] } Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 06:22:52 2004 Input: F:=GF(4); M:=MatrixRing(F,2); M22:=[j: j in M]; Mf:={ i : i in M22 | i[1] eq i[2]};Mf; Output: Magma V2.10-6 Sat Mar 6 2004 06:22:48 on modular [Seed = 3284809497] ------------------------------------- { [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ F.1 0] [ F.1 0], [ 0 F.1^2] [ 0 F.1^2], [ F.1 F.1^2] [ F.1 F.1^2], [ 0 F.1] [ 0 F.1], [ F.1 F.1] [ F.1 F.1], [ 0 1] [ 0 1], [ F.1 1] [ F.1 1], [F.1^2 0] [F.1^2 0], [ 1 0] [ 1 0], [F.1^2 F.1^2] [F.1^2 F.1^2], [ 1 F.1^2] [ 1 F.1^2], [F.1^2 F.1] [F.1^2 F.1], [ 1 F.1] [ 1 F.1], [F.1^2 1] [F.1^2 1] } Total time: 3.039 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 06:23:35 2004 Input: F:=GF(4); M:=MatrixRing(F,2); M22:=[j: j in M]; Mf:={ i : i in M22 | i[1] eq i[2]}; Mtf:= Mt meet Mf; print Mtf; Output: Magma V2.10-6 Sat Mar 6 2004 06:23:32 on modular [Seed = 3368107054] ------------------------------------- >> Mtf:= Mt meet Mf; ^ User error: Identifier 'Mt' has not been declared or assigned >> print Mtf;; ^ User error: Identifier 'Mtf' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 06:24:00 2004 Input: F:=GF(4); M:=MatrixRing(F,2); M22:=[j: j in M]; Mt:={i : i in M22 | Trace(i) eq 0}; Mf:={ i : i in M22 | i[1] eq i[2]}; Mtf:= Mt meet Mf; print Mtf; Output: Magma V2.10-6 Sat Mar 6 2004 06:23:57 on modular [Seed = 4059563374] ------------------------------------- { [ 0 0] [ 0 0], [F.1^2 F.1^2] [F.1^2 F.1^2], [ F.1 F.1] [ F.1 F.1], [ 1 1] [ 1 1] } Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 06:25:12 2004 Input: t_qr:= function (q,r) exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; t_qr(12,3); Output: Magma V2.10-6 Sat Mar 6 2004 06:25:09 on modular [Seed = 3807057829] ------------------------------------- >> return ( &+[x^i : i in exp(q,r)] ); ^ User error: Identifier 'x' has not been declared or assigned >> t_qr(12,3);; ^ User error: Identifier 't_qr' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 06:25:36 2004 Input: P:=PolynomialRing(GF(7^3)); t_qr:= function (q,r) exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; t_qr(12,3); Output: Magma V2.10-6 Sat Mar 6 2004 06:25:33 on modular [Seed = 3907067287] ------------------------------------- x^144 + x^12 + x Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 06:32:58 2004 Input: P:=PolynomialRing(GF(7^3)); olav_qr:= function (q,r) exp:= func ; return ( { : a,b in GF(7^3) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ) end function; olav_qr(7,3); Output: Magma V2.10-6 Sat Mar 6 2004 06:32:55 on modular [Seed = 2576379692] ------------------------------------- >> end function; ^ User error: bad syntax >> olav_qr(7,3);; ^ User error: Identifier 'olav_qr' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 06:33:37 2004 Input: P:=PolynomialRing(GF(7^3)); olav_qr:= function (q,r) exp:= func ; return ( { : a,b in GF(7^3) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ); end function; olav_qr(7,3); Output: Magma V2.10-6 Sat Mar 6 2004 06:33:34 on modular [Seed = 2257547738] ------------------------------------- >> return ( { : a,b in GF(7^3) | Evaluate(n_qr(q,r),a) eq Evaluat ^ User error: Identifier 'n_qr' has not been declared or assigned >> olav_qr(7,3);; ^ User error: Identifier 'olav_qr' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 06:34:19 2004 Input: P:=PolynomialRing(GF(7^3)); n_qr:= function (q,r) exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; t_qr:= function (q,r) exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; olav_qr:= function (q,r) exp:= func ; return ( { : a,b in GF(7^3) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ); end function; olav_qr(7,3); Output: Magma V2.10-6 Sat Mar 6 2004 06:34:04 on modular [Seed = 2407954673] ------------------------------------- { <$.1^189, $.1^104>, <$.1^268, $.1^223>, <$.1^266, $.1^125>, <$.1^340, $.1^294>, <$.1^245, $.1^281>, <$.1^173, $.1^218>, <1, $.1^7>, <$.1^85, $.1^58>, <$.1^167, $.1^140>, <$.1^108, $.1^100>, <$.1^330, $.1^66>, <$.1^10, $.1^326>, <$.1^303, $.1^319>, <$.1^87, $.1^261>, <$.1^214, $.1^244>, <$.1^20, $.1^201>, <$.1^116, $.1^270>, <$.1^222, $.1^156>, <$.1^338, $.1^201>, <4, $.1^10>, <$.1^19, $.1^188>, <$.1^204, $.1^70>, <$.1^301, $.1^147>, <$.1^56, $.1^311>, <$.1^101, $.1^210>, <$.1^311, $.1^210>, <$.1^238, $.1^229>, <$.1^41, $.1^41>, <$.1^63, $.1^261>, <4, $.1^195>, <$.1^219, $.1^303>, <$.1^144, $.1^339>, <$.1^329, $.1^43>, <$.1^319, $.1^154>, <3, $.1^150>, <$.1^56, $.1^78>, <$.1^237, $.1^327>, <$.1^134, $.1^262>, <$.1^147, $.1^167>, <$.1^160, $.1^223>, <$.1^284, $.1^329>, <$.1^302, $.1^273>, <$.1^239, $.1^140>, <$.1^196, $.1^42>, <$.1^8, $.1^262>, <$.1^250, $.1^318>, <$.1^294, $.1^11>, <$.1^149, $.1^40>, <$.1^22, $.1^119>, <$.1^339, $.1^308>, <$.1^238, $.1^126>, <$.1^48, $.1^197>, <$.1^328, $.1^32>, <$.1^32, $.1^273>, <$.1^97, $.1^205>, <$.1^184, $.1^174>, <$.1^42, $.1^112>, <$.1^176, $.1^251>, <$.1^133, $.1^82>, <$.1^53, $.1^202>, <$.1^135, $.1^167>, <$.1^218, $.1^86>, <$.1^311, $.1^89>, <$.1^87, $.1^28>, <$.1^187, $.1^21>, <$.1^98, $.1^111>, <$.1^104, $.1^214>, <$.1^102, $.1^131>, <$.1^319, $.1^3>, <$.1^314, $.1^246>, <$.1^42, $.1^275>, <$.1^27, $.1^196>, <$.1^267, $.1^168>, <$.1^249, $.1^168>, <$.1^81, $.1^117>, <$.1^291, $.1^271>, <$.1^72, $.1^197>, <$.1^293, $.1^43>, <$.1^297, $.1^135>, <$.1^26, $.1^151>, <$.1^289, $.1^52>, <$.1^239, $.1^295>, <$.1^268, $.1^277>, <$.1^319, $.1^232>, <$.1^122, $.1^226>, <$.1^93, $.1^178>, <$.1^212, $.1^204>, <$.1^82, $.1^244>, <$.1^217, $.1^64>, <$.1^327, $.1^92>, <$.1^272, $.1^214>, <$.1^72, $.1^148>, <$.1^49, $.1^123>, <$.1^200, $.1^211>, <$.1^146, $.1^311>, <$.1^106, $.1^18>, <$.1^46, $.1^83>, <$.1^223, $.1^155>, <$.1^159, $.1^69>, <$.1^37, $.1^59>, <$.1^147, 2>, <$.1^240, $.1^49>, <$.1^294, $.1^338>, <$.1^294, $.1^215>, <$.1^3, $.1^319>, <$.1^177, $.1^172>, <$.1^277, 1>, <$.1^152, $.1^234>, <$.1^116, $.1^214>, <$.1^174, $.1^16>, <$.1^132, $.1^156>, <$.1^72, $.1^195>, <$.1^45, $.1^330>, <$.1^4, $.1^315>, <$.1^34, $.1^6>, <$.1^303, $.1^92>, <$.1^180, $.1^14>, <$.1^307, $.1^82>, <$.1^83, $.1^20>, <0, $.1^300>, <$.1^273, $.1^319>, <$.1^241, $.1^256>, <$.1^29, $.1^9>, <$.1^331, $.1^147>, <$.1^72, $.1^199>, <$.1^180, $.1^77>, <$.1^293, $.1^63>, <$.1^19, $.1^73>, <1, $.1^175>, <$.1^20, $.1^184>, <$.1^303, $.1^28>, <$.1^31, $.1^216>, <$.1^198, $.1^25>, <$.1^209, $.1^334>, <$.1^47, $.1^334>, <$.1^277, $.1^188>, <$.1^85, $.1^332>, <$.1^281, $.1^292>, <$.1^276, $.1^215>, <$.1^212, $.1^245>, <$.1^187, $.1^22>, <$.1^264, $.1^159>, <$.1^184, $.1^101>, <$.1^91, $.1^256>, <$.1^304, $.1^83>, <$.1^183, $.1^117>, <$.1^14, $.1^311>, <$.1^98, $.1^212>, <$.1^222, $.1^146>, <$.1^174, $.1^100>, <$.1^12, $.1^37>, <$.1^274, $.1^81>, <$.1^80, $.1^93>, <$.1^81, $.1^62>, <$.1^313, $.1^59>, <$.1^200, $.1^309>, <$.1^150, $.1^339>, <$.1^277, $.1^71>, <$.1^64, $.1^6>, <$.1^31, $.1^21>, <$.1^150, $.1^314>, <$.1^262, $.1^294>, <$.1^25, $.1^252>, <$.1^339, $.1^248>, <$.1^8, $.1^12>, <$.1^36, $.1^199>, <$.1^222, $.1^233>, <$.1^108, $.1^120>, <$.1^289, $.1^216>, <$.1^194, $.1^60>, <$.1^133, $.1^68>, <$.1^274, $.1^224>, <$.1^101, $.1^41>, <$.1^141, $.1^88>, <$.1^21, $.1^96>, <$.1^8, $.1^5>, <$.1^109, $.1^169>, <$.1^247, $.1^71>, <$.1^126, $.1^321>, <$.1^159, $.1^24>, <$.1^279, $.1^135>, <$.1^104, $.1^191>, <$.1^284, $.1^262>, <$.1^267, $.1^150>, <$.1^204, $.1^233>, <$.1^300, $.1^199>, <$.1^294, $.1^240>, <$.1^131, $.1^33>, <$.1^181, $.1^21>, <$.1^53, $.1^55>, <$.1^91, $.1^254>, <$.1^221, $.1^99>, <$.1^117, $.1^62>, <$.1^32, $.1^79>, <$.1^258, $.1^137>, <$.1^96, $.1>, <$.1^270, $.1^288>, <$.1^202, $.1^85>, <$.1^270, $.1^132>, <$.1^10, $.1^149>, <$.1^229, $.1^127>, <$.1^108, $.1^288>, <$.1^72, $.1^338>, <$.1^170, $.1^130>, <$.1^284, $.1^163>, <$.1^251, $.1^296>, <$.1^259, $.1^320>, <$.1^109, $.1^189>, <$.1^80, $.1^151>, <$.1^135, $.1^178>, <$.1^275, $.1^13>, <$.1^319, $.1^256>, <$.1^323, $.1^138>, <$.1^276, $.1^148>, <$.1^230, $.1^251>, <$.1^33, $.1^24>, <$.1^202, $.1^161>, <$.1^175, $.1^232>, <$.1^248, $.1^78>, <$.1^78, $.1^148>, <$.1^311, $.1^75>, <$.1^29, $.1^75>, <$.1^225, $.1^241>, <$.1^239, $.1^33>, <$.1^37, $.1^36>, <$.1^28, $.1^242>, <$.1^23, $.1^287>, <$.1^238, $.1^225>, <$.1^259, $.1^64>, <$.1^317, $.1^206>, <$.1^64, $.1^298>, <$.1^193, $.1^160>, <$.1^255, $.1^291>, <$.1^275, $.1^142>, <$.1^125, $.1^75>, <$.1^104, $.1^204>, <$.1^92, $.1^84>, <$.1^193, $.1^106>, <$.1^78, $.1^337>, <$.1^112, $.1^235>, <$.1^169, $.1^123>, <$.1^277, $.1^67>, <$.1^9, 2>, <$.1^173, $.1^334>, <$.1^110, $.1^245>, <$.1^18, $.1^2>, <$.1^23, $.1^118>, <$.1^103, $.1^232>, <$.1^106, $.1^32>, <$.1^53, $.1^210>, <$.1^71, $.1^9>, <$.1^189, $.1^271>, <$.1^151, $.1^324>, <$.1^304, $.1^253>, <$.1^257, $.1^41>, <$.1^174, $.1^321>, <$.1^330, $.1^100>, <$.1^104, $.1^262>, <$.1^51, $.1^327>, <$.1^186, $.1^240>, <$.1^208, $.1^239>, <$.1^249, $.1^308>, <$.1^253, $.1^169>, <$.1^147, $.1^248>, <$.1^8, $.1^124>, <$.1^181, $.1^82>, <$.1^20, $.1^124>, <$.1^73, $.1^59>, <$.1^88, $.1^198>, <$.1^150, $.1^70>, <$.1^289, $.1^213>, <$.1^325, $.1^169>, <$.1^209, $.1^264>, <$.1^295, $.1^134>, <$.1^11, $.1^41>, <$.1^209, $.1^158>, <$.1^99, $.1^104>, <$.1^277, $.1^54>, <$.1^204, $.1^25>, <$.1^12, $.1^7>, <$.1^203, $.1^299>, <$.1^172, $.1^223>, <$.1^325, $.1^22>, <$.1^47, $.1^80>, <$.1^203, $.1^250>, <$.1^275, $.1^218>, <$.1^46, $.1^229>, <$.1^9, $.1^24>, <$.1^292, $.1^81>, <$.1^329, $.1^140>, <$.1^115, $.1^67>, <$.1^224, $.1^12>, <2, $.1^120>, <6, 2>, <$.1^317, $.1^250>, <$.1^338, $.1^246>, <$.1^132, $.1>, <$.1^326, $.1^151>, <$.1^247, $.1^254>, <$.1^208, $.1^207>, <$.1^221, $.1^310>, <$.1^173, $.1^183>, <$.1^206, $.1^128>, <$.1^238, $.1^230>, <$.1^36, $.1^2>, <$.1^50, $.1^116>, <$.1^47, $.1^20>, <$.1^50, $.1^329>, <$.1^58, $.1^305>, <$.1^2, $.1^273>, <$.1^39, $.1^28>, <6, $.1^187>, <$.1^306, $.1^159>, <$.1^333, $.1^24>, <$.1^323, $.1^301>, <$.1^157, $.1^177>, <$.1^34, $.1^244>, <$.1^50, $.1^79>, <$.1^212, $.1^184>, <$.1^132, $.1^137>, <$.1^310, $.1^207>, <$.1^180, $.1^146>, <$.1^336, $.1^137>, <$.1^239, $.1^299>, <$.1^338, $.1^110>, <$.1^18, $.1^131>, <$.1^147, $.1^291>, <2, $.1^14>, <$.1^214, $.1^235>, <$.1^53, $.1^287>, <$.1^167, $.1^33>, <$.1^321, $.1^24>, <$.1^206, $.1^84>, <$.1^162, $.1^267>, <$.1^161, $.1^299>, <$.1^34, $.1^230>, <$.1^92, $.1^201>, <$.1^312, $.1^263>, <$.1^239, $.1^218>, <$.1^155, $.1^206>, <$.1^220, $.1^153>, <$.1^102, $.1^137>, <$.1^128, $.1^246>, <$.1^271, $.1^320>, <$.1^288, $.1^49>, <$.1^179, $.1^264>, <$.1^39, $.1^44>, <$.1^217, $.1^232>, <$.1^202, $.1^81>, <$.1^146, $.1^273>, <$.1^297, 2>, <$.1^164, $.1^251>, <$.1^212, $.1^110>, <$.1^268, $.1^224>, <$.1^182, $.1^204>, <$.1^309, $.1^92>, <$.1^134, $.1^184>, <$.1^184, $.1^328>, <$.1^74, $.1^115>, <$.1^25, $.1^144>, <$.1^220, $.1^331>, <$.1^248, $.1^214>, <$.1^75, $.1^178>, <$.1^58, $.1^340>, <$.1^216, $.1^314>, <$.1^47, $.1^30>, <$.1^38, $.1^204>, <$.1^32, $.1^245>, <$.1^290, $.1^313>, <$.1^216, $.1^11>, <$.1^81, $.1^150>, <$.1^219, $.1^261>, <$.1^291, $.1^274>, <$.1^230, $.1^245>, <$.1^84, $.1^87>, <$.1^154, $.1^18>, <$.1^226, $.1^230>, <$.1^190, $.1^223>, <$.1^25, $.1^213>, <2, $.1^10>, <$.1^12, $.1^159>, <$.1^280, $.1^294>, <$.1^101, $.1^91>, <$.1^47, $.1^255>, <$.1^28, $.1^305>, <$.1^58, $.1^101>, <$.1^220, $.1^253>, <$.1^196, $.1^23>, <$.1^43, $.1^290>, <$.1^21, $.1^241>, <$.1^182, $.1^191>, <$.1^324, $.1^159>, <$.1^47, $.1^287>, <$.1^226, $.1^253>, <$.1^174, $.1^77>, <$.1^148, $.1^174>, <6, $.1^283>, <$.1^78, $.1^146>, <$.1^339, $.1^268>, <$.1^240, $.1^288>, <4, $.1^312>, <$.1^84, $.1^195>, <$.1^117, $.1^327>, <$.1^158, $.1^111>, <$.1^28, $.1^277>, <$.1^16, $.1^225>, <$.1^322, $.1^253>, <5, $.1^135>, <$.1^320, $.1^47>, <$.1^191, $.1^250>, <$.1^282, $.1^156>, <$.1, $.1^189>, <$.1^140, $.1^270>, <$.1^161, $.1^287>, <$.1^100, $.1^326>, <$.1^139, $.1^82>, <$.1^337, $.1^324>, <$.1^13, $.1^73>, <$.1^254, $.1^128>, <$.1^170, $.1^212>, <$.1^319, $.1^189>, <$.1^338, $.1^115>, <$.1^336, $.1^49>, <$.1^73, $.1^3>, <$.1^130, $.1^45>, <$.1^289, $.1^160>, <$.1^260, $.1^12>, <$.1^59, $.1^249>, <$.1^317, $.1^91>, <$.1^173, $.1^287>, <$.1^320, $.1^60>, <$.1^18, $.1^337>, <$.1^251, $.1^255>, <$.1^289, $.1^22>, <$.1^123, $.1^291>, <$.1^258, $.1^146>, <$.1^187, $.1^147>, <$.1^87, $.1^269>, <$.1^73, $.1^290>, <$.1^184, $.1^145>, <$.1^96, $.1^240>, <$.1^25, $.1^324>, <$.1^48, $.1^37>, <$.1^272, $.1^226>, <$.1^321, $.1^44>, <$.1^102, $.1^132>, <$.1^331, $.1^205>, <$.1^198, $.1^307>, <$.1^45, $.1^24>, <$.1^51, $.1^269>, <$.1^59, $.1^13>, <$.1^9, $.1^258>, <$.1^110, $.1^329>, <$.1^186, 5>, <$.1^22, $.1^85>, <$.1^126, $.1>, <$.1^198, $.1^14>, <$.1^224, $.1^226>, <$.1^299, $.1^250>, <$.1^27, $.1^117>, <$.1^253, $.1^36>, <$.1^235, $.1^27>, <$.1^124, $.1^225>, <$.1^160, $.1^81>, <$.1^277, $.1^123>, <$.1^49, $.1^21>, <$.1^293, $.1^80>, <$.1^52, $.1^200>, <$.1^277, $.1^194>, <$.1^84, $.1^90>, <$.1^303, $.1^302>, <$.1^187, $.1^3>, <$.1^186, $.1^132>, <$.1^151, $.1^316>, <$.1^119, $.1^46>, <$.1^238, $.1^326>, <$.1^142, $.1^326>, <$.1^157, $.1^320>, <$.1^279, $.1^308>, <$.1^270, $.1>, <$.1^290, $.1^47>, <$.1^74, $.1^110>, <$.1^9, $.1^268>, <$.1^111, $.1^319>, <$.1^218, $.1^139>, <$.1^275, $.1^41>, <$.1^78, $.1^156>, <$.1^240, $.1^337>, <$.1^216, $.1>, <$.1^273, $.1^4>, <$.1^211, $.1^134>, <$.1^143, $.1^99>, <$.1^61, $.1^123>, <$.1^276, $.1^16>, <$.1^129, $.1^241>, <$.1^7, $.1^68>, <$.1^256, $.1^174>, <$.1^31, $.1^203>, <$.1^254, $.1^217>, <$.1^39, 2>, <$.1^212, $.1^151>, <$.1^19, $.1^106>, <$.1^164, $.1^93>, <$.1^339, $.1^258>, <$.1^156, $.1^131>, <$.1^13, $.1^68>, <$.1^204, $.1^10>, <$.1^288, $.1^337>, <$.1^266, $.1^78>, <$.1^332, $.1^163>, <$.1^335, $.1^287>, <$.1^195, $ ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 06:39:47 2004 Input: P:=PolynomialRing(GF(7^3)); n_qr:= function (q,r) exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; t_qr:= function (q,r) exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; olav_qr:= function (q,r) exp:= func ; return ( { : a,b in GF(7^3) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ); end function; #olav_qr(7,3); #olav_qr(9,2); #olav_qr(12,3); #olav_qr(8,5); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Mar 6 2004 06:39:24 on modular [Seed = 3115336071] ------------------------------------- 16807 Errors: /home/mfd/gomagma: line 2: 4843 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 06:40:43 2004 Input: P:=PolynomialRing(GF(7^3)); n_qr:= function (q,r) exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; t_qr:= function (q,r) exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; olav_qr:= function (q,r) exp:= func ; return ( { : a,b in GF(7^3) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ); end function; #olav_qr(5,3); #olav_qr(5,2); #olav_qr(4,3); #olav_qr(4,2); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Mar 6 2004 06:40:20 on modular [Seed = 2845856095] ------------------------------------- 343 Errors: /home/mfd/gomagma: line 2: 4859 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 06:41:13 2004 Input: P:=PolynomialRing(GF(7^3)); n_qr:= function (q,r) exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; t_qr:= {function (q,r) exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function}; olav_qr:= function (q,r) exp:= func ; return ( { : a,b in GF(7^3) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ); end function; #olav_qr(5,3); #olav_qr(5,2); #olav_qr(4,3); #olav_qr(4,2); Output: Magma V2.10-6 Sat Mar 6 2004 06:41:10 on modular [Seed = 1449111251] ------------------------------------- >> t_qr:= {function (q,r) ^ Runtime error in { ... }: Invalid set universe (no hashing algorithm) >> r(q,r),a) eq Evaluate(t_qr(q,r),b)} ); ^ User error: Identifier 't_qr' has not been declared or assigned >> #olav_qr(5,3); ^ User error: Identifier 'olav_qr' has not been declared or assigned >> #olav_qr(5,2); ^ User error: Identifier 'olav_qr' has not been declared or assigned >> #olav_qr(4,3); ^ User error: Identifier 'olav_qr' has not been declared or assigned >> #olav_qr(4,2);; ^ User error: Identifier 'olav_qr' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 06:43:26 2004 Input: P:=PolynomialRing(GF(7^3)); n_qr:= function (q,r) exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; t_qr:= function (q,r) exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; olav_qr:= function (q,r) exp:= func ; return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ); end function; #olav_qr(5,3); #olav_qr(5,2); #olav_qr(4,3); #olav_qr(4,2); Output: Magma V2.10-6 Sat Mar 6 2004 06:43:23 on modular [Seed = 1565828181] ------------------------------------- [
:12]( q: 5, r: 3 ) >> return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluat ^ Runtime error in 'Evaluate': Incompatible rings [
:12]( q: 5, r: 2 ) >> return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluat ^ Runtime error in 'Evaluate': Incompatible rings [
:12]( q: 4, r: 3 ) >> return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluat ^ Runtime error in 'Evaluate': Incompatible rings [
:12]( q: 4, r: 2 ) >> return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluat ^ Runtime error in 'Evaluate': Incompatible rings Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 06:45:27 2004 Input: P:=PolynomialRing(GF(7^3)); n_qr:= function (q,r) exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; t_qr:= function (q,r) exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; olav_qr:= function (q,r) exp:= func ; return ( { | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ); end function; #olav_qr(5,3); #olav_qr(5,2); #olav_qr(4,3); #olav_qr(4,2); Output: Magma V2.10-6 Sat Mar 6 2004 06:45:24 on modular [Seed = 1212264911] ------------------------------------- >> return ( { | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ) ^ User error: Identifier 'a' has not been declared or assigned >> #olav_qr(5,3); ^ User error: Identifier 'olav_qr' has not been declared or assigned >> #olav_qr(5,2); ^ User error: Identifier 'olav_qr' has not been declared or assigned >> #olav_qr(4,3); ^ User error: Identifier 'olav_qr' has not been declared or assigned >> #olav_qr(4,2);; ^ User error: Identifier 'olav_qr' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 06:45:53 2004 Input: P:=PolynomialRing(GF(7^3)); n_qr:= function (q,r) exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; t_qr:= function (q,r) exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; olav_qr:= function (q,r) exp:= func ; return ( { a,b : | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ); end function; #olav_qr(5,3); #olav_qr(5,2); #olav_qr(4,3); #olav_qr(4,2); Output: Magma V2.10-6 Sat Mar 6 2004 06:45:50 on modular [Seed = 1988071371] ------------------------------------- >> return ( { a,b : | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r ^ User error: bad syntax >> end function; ^ User error: bad syntax >> #olav_qr(5,3); ^ User error: Identifier 'olav_qr' has not been declared or assigned >> #olav_qr(5,2); ^ User error: Identifier 'olav_qr' has not been declared or assigned >> #olav_qr(4,3); ^ User error: Identifier 'olav_qr' has not been declared or assigned >> #olav_qr(4,2);; ^ User error: Identifier 'olav_qr' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 06:49:44 2004 Input: P:=PolynomialRing(GF(7^3)); n_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; t_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; olav_qr:= function (q,r) exp:= func ; return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ); end function; #olav_qr(5,3); #olav_qr(5,2); #olav_qr(4,3); #olav_qr(4,2); Output: Magma V2.10-6 Sat Mar 6 2004 06:49:38 on modular [Seed = 2104788988] ------------------------------------- 3125 125 1024 64 Total time: 6.639 seconds, Total memory usage: 2.14MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 06:52:37 2004 Input: P:=PolynomialRing(GF(7^3)); n_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; t_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; olav_qr:= function (q,r) exp:= func ; return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ); end function; #olav_qr(5,3) eq 5^(2*3-1); #olav_qr(5,2) eq 5^(2*2-1); #olav_qr(4,3) eq 4^(2*3-1); #olav_qr(4,2) eq 4^(2*2-1); #olav_qr(7,2) eq 7^(2*2-1); Output: Magma V2.10-6 Sat Mar 6 2004 06:52:30 on modular [Seed = 1818597185] ------------------------------------- true true true true true Total time: 6.899 seconds, Total memory usage: 2.14MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 06:55:21 2004 Input: P:=PolynomialRing(GF(7^3)); n_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; t_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; olav_qr:= function (q,r) exp:= func ; return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ); end function; #olav_qr(4,1); #olav_qr(4,3) eq 4^(2*3-1); Output: Magma V2.10-6 Sat Mar 6 2004 06:55:18 on modular [Seed = 521593706] ------------------------------------- 4 true Total time: 3.629 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 07:12:13 2004 Input: P:=PolynomialRing(GF(7^3)); n_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; t_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; olav_qr:= function (q,r) exp:= func ; return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ); end function; olav_q:= function (q,func_olav) return ( { : a,b in GF(q) | in func_olav } end function; #olav_qr(4,1); #olav_qr(4,3) eq 4^(2*3-1); Output: Magma V2.10-6 Sat Mar 6 2004 07:12:09 on modular [Seed = 3621672861] ------------------------------------- >> end function; ^ User error: bad syntax 4 true Total time: 3.709 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 07:13:35 2004 Input: P:=PolynomialRing(GF(7^3)); n_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; t_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; olav_qr:= function (q,r) exp:= func ; return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ); end function; olav_q:= function (q,r) return ( { : a,b in GF(q) | in olav_qr(q,r) }); end function; olav_q(4,1); #olav_qr(4,1); #olav_qr(4,3) eq 4^(2*3-1); Output: Magma V2.10-6 Sat Mar 6 2004 07:13:31 on modular [Seed = 3738656486] ------------------------------------- { <0, 0>, <$.1, $.1>, <1, 1>, <$.1^2, $.1^2> } 4 true Total time: 3.729 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 07:14:41 2004 Input: P:=PolynomialRing(GF(7^3)); n_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; t_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; olav_qr:= function (q,r) exp:= func ; return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ); end function; olav_q:= function (q,r) return ( { : a,b in GF(q) | in olav_qr(q,r) }); end function; olav_q(4,3); #olav_qr(4,3); #olav_qr(4,3) eq 4^(2*3-1); Output: Magma V2.10-6 Sat Mar 6 2004 07:14:24 on modular [Seed = 3318498614] ------------------------------------- { <$.1^2, 1>, <$.1, 1>, <0, 0>, <1, 1> } 1024 true Total time: 17.139 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 07:15:24 2004 Input: P:=PolynomialRing(GF(7^3)); n_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; t_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; olav_qr:= function (q,r) exp:= func ; return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ); end function; olav_q:= function (q,r) return ( { : a,b in GF(q) | in olav_qr(q,r) }); end function; #olav_q(4,3); #olav_qr(4,3); #olav_qr(4,3) eq 4^(2*3-1); Output: Magma V2.10-6 Sat Mar 6 2004 07:15:07 on modular [Seed = 4042879080] ------------------------------------- 4 1024 true Total time: 17.340 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 07:21:52 2004 Input: P:=PolynomialRing(GF(7^3)); n_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; t_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; olav_qr:= function (q,r) exp:= func ; return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ); end function; olav_q:= function (q,r) return ( { : a,b in GF(q) | in olav_qr(q,r) }); end function; #olav_q(4,3); #olav_qr(4,3); #olav_q(5,3); #olav_qr(5,3); #olav_qr(4,3) eq 4^(2*3-1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Mar 6 2004 07:21:29 on modular [Seed = 3840763646] ------------------------------------- 4 1024 Errors: /home/mfd/gomagma: line 2: 5047 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 07:22:43 2004 Input: P:=PolynomialRing(GF(7^3)); n_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; t_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; olav_qr:= function (q,r) exp:= func ; return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ); end function; olav_q:= function (q,r) return ( { : a,b in GF(q) | in olav_qr(q,r) }); end function; #olav_q(4,3); #olav_qr(4,3); #olav_q(5,2); #olav_qr(5,2); #olav_qr(4,3) eq 4^(2*3-1); Output: Magma V2.10-6 Sat Mar 6 2004 07:22:24 on modular [Seed = 2476347712] ------------------------------------- 4 1024 5 125 true Total time: 19.449 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 07:25:59 2004 Input: P:=PolynomialRing(GF(7^3)); n_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; t_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; olav_qr:= function (q,r) exp:= func ; return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ); end function; olav_q:= function (q,r) return ( { : a,b in GF(q) | in olav_qr(q,r) }); end function; #olav_q(4,3); #olav_qr(4,3); olav_q(5,2); #olav_qr(5,2); #olav_qr(4,3) eq 4^(2*3-1); Output: Magma V2.10-6 Sat Mar 6 2004 07:25:40 on modular [Seed = 2643730058] ------------------------------------- 4 1024 { <3, 2>, <1, 3>, <0, 0>, <2, 2>, <4, 3> } 125 true Total time: 19.369 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 80.58.52.170.proxycache.rima-tde.net. (80.58.52.170) Time: Sat Mar 6 07:37:46 2004 Input: P:=PolynomialRing(GF(7^3)); n_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; t_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; olav_qr:= function (q,r) exp:= func ; return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ); end function; olav_q:= function (q,r) return ( { : a,b in GF(q) | in olav_qr(q,r) }); end function; #olav_q(4,3); #olav_qr(4,3); olav_q(5,2); t_qr(3,2); n_qr(3,2); #olav_qr(5,2); #olav_qr(4,3) eq 4^(2*3-1); Output: Magma V2.10-6 Sat Mar 6 2004 07:37:27 on modular [Seed = 3082695139] ------------------------------------- 4 1024 { <3, 2>, <1, 3>, <0, 0>, <2, 2>, <4, 3> } x^3 + x x^4 125 true Total time: 19.430 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Sat Mar 6 10:55:42 2004 Input: K := GF(3); R := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]); R; P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S; Output: Magma V2.10-6 Sat Mar 6 2004 10:55:39 on modular [Seed = 487893299] ------------------------------------- Graded Polynomial ring of rank 4 over GF(3) Lexicographical Order Variables: x, y, z, w Variable weights: 6 8 54 72 0 [] [ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^8*y^7, x^8*y^8, x^8*y^9, x^8*y^10, x^9, x^9*y, x^10, x^10*y, x^11, x^11*y, x^12 ] Total time: 2.929 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host c211-28-150-222.thoms1.vic.optusnet.com.au. (211.28.150.222) Time: Sat Mar 6 21:45:21 2004 Input: 1+1 Output: Magma V2.10-6 Sat Mar 6 2004 21:45:17 on modular [Seed = 4193465672] ------------------------------------- 2 Total time: 4.000 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Sun Mar 7 00:57:38 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2-23); ClassNumber(K); Output: Magma V2.10-6 Sun Mar 7 2004 00:57:34 on modular [Seed = 1937345182] ------------------------------------- 1 Total time: 3.139 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Sun Mar 7 01:53:29 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^3-x+2); MinimalPolynomial(a+b*y+c*y^2); Output: Magma V2.10-6 Sun Mar 7 2004 01:53:26 on modular [Seed = 3687931157] ------------------------------------- >> MinimalPolynomial(a+b*y+c*y^2);; ^ User error: Identifier 'a' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Sun Mar 7 01:54:27 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^3-x+2); MinimalPolynomial(3+5*y+2*y^2); Output: Magma V2.10-6 Sun Mar 7 2004 01:54:24 on modular [Seed = 3571340252] ------------------------------------- x^3 - 13*x^2 + 90*x - 2 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Sun Mar 7 02:08:24 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^3-x+2); (x-a-b*y-c*y^2)(x-a+b*y-c*y^2); Output: Magma V2.10-6 Sun Mar 7 2004 02:08:21 on modular [Seed = 1381554205] ------------------------------------- >> (x-a-b*y-c*y^2)(x-a+b*y-c*y^2);; ^ User error: Identifier 'a' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.66.195) Time: Sun Mar 7 05:54:17 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Sun Mar 7 2004 05:54:14 on modular [Seed = 2677350579] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.869 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 06:05:50 2004 Input: /* PRACTICA 1. TEORIA DE LA CODIFICACIÓ */ print "EXERCICI 1:"; {n: n in [4..366 by 7]}; /* Com que l'any va començar en dijous (quart dia de la setmana), els diumenges de tot l'any són els que apareixen al conjunt donat, que va de 7 en 7 dies. */ Output: Magma V2.10-6 Sun Mar 7 2004 06:05:45 on modular [Seed = 1531975977] ------------------------------------- EXERCICI 1: { 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 } Total time: 2.960 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 06:09:39 2004 Input: print "EXERCICI 2:"; R:= GF(4); M := MatrixRing(R,2); Output: Magma V2.10-6 Sun Mar 7 2004 06:09:36 on modular [Seed = 1348145883] ------------------------------------- EXERCICI 2: Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 06:10:01 2004 Input: print "EXERCICI 2:"; R:= GF(4); M := MatrixRing(R,2); print "apartat (i)"; Mt := { A : A in M | Trace(A) eq 0}; Output: Magma V2.10-6 Sun Mar 7 2004 06:09:58 on modular [Seed = 1329859634] ------------------------------------- EXERCICI 2: apartat (i) Total time: 3.069 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 06:10:44 2004 Input: print "EXERCICI 2:"; R:= GF(4); M := MatrixRing(R,2); print "apartat (i)"; Mt := { A : A in M | Trace(A) eq 0}; print "apartat (ii)"; Mf := {A: A in M | A[1] eq A[2]}; print "apartat (iii)"; Mtf := Mt meet Mf; Output: Magma V2.10-6 Sun Mar 7 2004 06:10:41 on modular [Seed = 1060404341] ------------------------------------- EXERCICI 2: apartat (i) apartat (ii) apartat (iii) Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 06:13:04 2004 Input: print "EXERCICI 2:"; R:= GF(4); M := MatrixRing(R,2); print "apartat (i)"; Mt := { A : A in M | Trace(A) eq 0}; print "apartat (ii)"; Mf := {A: A in M | A[1] eq A[2]}; print "apartat (iii)"; Mtf := Mt meet Mf; /* S'utilitza 'meet' degut a que ens demanen la intersecció de dos conjunts. */ print "apartat (iv)"; seq:=[Random(M):num in [1..100000]]; print "Matrius que pertanyen a Mt:"; #([A : A in seq | A in Mt]); print "Matrius que pertanyen a Mf:"; #([A : A in seq | A in Mf]); print "Matrius que pertanyen a Mtf:"; #([A : A in seq | A in Mtf]); Output: Magma V2.10-6 Sun Mar 7 2004 06:13:00 on modular [Seed = 893286130] ------------------------------------- EXERCICI 2: apartat (i) apartat (ii) apartat (iii) apartat (iv) Matrius que pertanyen a Mt: 25082 Matrius que pertanyen a Mf: 6287 Matrius que pertanyen a Mtf: 1608 Total time: 4.099 seconds, Total memory usage: 7.09MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 06:26:07 2004 Input: exponents73 := [7^i: i in [3-1..0]]; Output: Magma V2.10-6 Sun Mar 7 2004 06:26:04 on modular [Seed = 235227321] ------------------------------------- Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 06:26:19 2004 Input: exponents73 := [7^i: i in [3-1..0]]; exponents73; Output: Magma V2.10-6 Sun Mar 7 2004 06:26:16 on modular [Seed = 84820902] ------------------------------------- [] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 06:26:39 2004 Input: exponents73 := [7^i: i in [2..0 by -1]]; exponents73; Output: Magma V2.10-6 Sun Mar 7 2004 06:26:36 on modular [Seed = 4244093547] ------------------------------------- [ 49, 7, 1 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 06:30:39 2004 Input: exponents73 := [7^i: i in [2..0 by -1]]; exp := func < q,r | [q^i: i in [r-1..0 by -1]] >; exp(7,3); Output: Magma V2.10-6 Sun Mar 7 2004 06:30:36 on modular [Seed = 3823674436] ------------------------------------- [ 49, 7, 1 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 06:32:26 2004 Input: print "EXERCICI 3:"; print "apartat (i)"; exponents73 := [7^i: i in [2..0 by -1]]; exp := func < q,r | [q^i: i in [r-1..0 by -1]] >; exp(7,3); /* Resultat: [ 49, 7, 1 ] */ print "apartat (ii)"; P := PolynomialRing (Integers()); t := &+[x^i : i in exp(7,3) ]; t; n := x^ &+(exp(7,3)); n; print "apartat (iii)"; Output: Magma V2.10-6 Sun Mar 7 2004 06:32:23 on modular [Seed = 3671167718] ------------------------------------- EXERCICI 3: apartat (i) [ 49, 7, 1 ] apartat (ii) x^49 + x^7 + x x^57 apartat (iii) Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 06:35:30 2004 Input: print "EXERCICI 3:"; print "apartat (i)"; exponents73 := [7^i: i in [2..0 by -1]]; exp := func < q,r | [q^i: i in [r-1..0 by -1]] >; exp(7,3); /* Resultat: [ 49, 7, 1 ] */ print "apartat (ii)"; P := PolynomialRing (Integers()); t := &+[x^i : i in exp(7,3) ]; t; n := x^ &+(exp(7,3)); n; print "apartat (iii)"; puntsOlav := [ : a,b in GF(7^3) | Evaluate(n,a) eq Evaluate(t,b) ]; puntsOlav; Output: Magma V2.10-6 Sun Mar 7 2004 06:35:22 on modular [Seed = 2829312041] ------------------------------------- EXERCICI 3: apartat (i) [ 49, 7, 1 ] apartat (ii) x^49 + x^7 + x x^57 apartat (iii) [ <1, $.1>, <1, $.1^2>, <1, $.1^7>, <1, $.1^10>, <1, $.1^11>, <1, $.1^14>, <1, $.1^16>, <1, $.1^25>, <1, $.1^37>, <1, $.1^49>, <1, $.1^66>, <1, $.1^70>, <1, $.1^77>, <1, $.1^87>, <1, $.1^90>, <1, $.1^97>, <1, $.1^98>, <1, $.1^100>, <1, $.1^103>, <1, $.1^112>, <1, $.1^120>, <1, $.1^131>, <1, $.1^132>, <1, $.1^137>, <1, $.1^146>, <1, $.1^148>, <1, $.1^156>, <1, $.1^159>, <1, $.1^175>, <1, $.1^195>, <1, $.1^197>, <1, $.1^199>, <1, $.1^215>, <1, $.1^233>, <1, $.1^240>, <1, $.1^259>, <1, $.1^263>, <1, $.1^267>, <1, $.1^275>, <1, 5>, <1, $.1^288>, <1, $.1^306>, <1, $.1^307>, <1, $.1^312>, <1, $.1^314>, <1, $.1^321>, <1, $.1^337>, <1, $.1^338>, <1, $.1^339>, <$.1, 1>, <$.1, $.1^3>, <$.1, $.1^21>, <$.1, $.1^22>, <$.1, $.1^27>, <$.1, $.1^29>, <$.1, $.1^36>, <$.1, $.1^52>, <$.1, $.1^53>, <$.1, $.1^54>, <$.1, $.1^58>, <$.1, $.1^59>, <$.1, $.1^64>, <$.1, $.1^67>, <$.1, $.1^68>, <$.1, $.1^71>, <$.1, $.1^73>, <$.1, $.1^82>, <$.1, $.1^94>, <$.1, $.1^106>, <$.1, $.1^123>, <$.1, $.1^127>, <$.1, $.1^134>, <$.1, $.1^144>, <$.1, $.1^147>, <$.1, $.1^154>, <$.1, $.1^155>, <$.1, $.1^157>, <$.1, $.1^160>, <$.1, $.1^169>, <$.1, $.1^177>, <$.1, $.1^188>, <$.1, $.1^189>, <$.1, $.1^194>, <$.1, $.1^203>, <$.1, $.1^205>, <$.1, $.1^213>, <$.1, $.1^216>, <$.1, $.1^232>, <$.1, $.1^252>, <$.1, $.1^254>, <$.1, $.1^256>, <$.1, $.1^272>, <$.1, $.1^290>, <$.1, $.1^297>, <$.1, $.1^316>, <$.1, $.1^320>, <$.1, $.1^324>, <$.1, $.1^332>, <$.1^2, $.1^5>, <$.1^2, $.1^12>, <$.1^2, $.1^31>, <$.1^2, $.1^35>, <$.1^2, $.1^39>, <$.1^2, $.1^47>, <$.1^2, 3>, <$.1^2, $.1^60>, <$.1^2, $.1^78>, <$.1^2, $.1^79>, <$.1^2, $.1^84>, <$.1^2, $.1^86>, <$.1^2, $.1^93>, <$.1^2, $.1^109>, <$.1^2, $.1^110>, <$.1^2, $.1^111>, <$.1^2, $.1^115>, <$.1^2, $.1^116>, <$.1^2, $.1^121>, <$.1^2, $.1^124>, <$.1^2, $.1^125>, <$.1^2, $.1^128>, <$.1^2, $.1^130>, <$.1^2, $.1^139>, <$.1^2, $.1^151>, <$.1^2, $.1^163>, <$.1^2, $.1^180>, <$.1^2, $.1^184>, <$.1^2, $.1^191>, <$.1^2, $.1^201>, <$.1^2, $.1^204>, <$.1^2, $.1^211>, <$.1^2, $.1^212>, <$.1^2, $.1^214>, <$.1^2, $.1^217>, <$.1^2, $.1^226>, <$.1^2, $.1^234>, <$.1^2, $.1^245>, <$.1^2, $.1^246>, <$.1^2, $.1^251>, <$.1^2, $.1^260>, <$.1^2, $.1^262>, <$.1^2, $.1^270>, <$.1^2, $.1^273>, <$.1^2, $.1^289>, <$.1^2, $.1^309>, <$.1^2, $.1^311>, <$.1^2, $.1^313>, <$.1^2, $.1^329>, <$.1^3, $.1^4>, <$.1^3, $.1^24>, <$.1^3, $.1^26>, <$.1^3, $.1^28>, <$.1^3, $.1^44>, <$.1^3, $.1^62>, <$.1^3, $.1^69>, <$.1^3, $.1^88>, <$.1^3, $.1^92>, <$.1^3, $.1^96>, <$.1^3, $.1^104>, <$.1^3, 2>, <$.1^3, $.1^117>, <$.1^3, $.1^135>, <$.1^3, $.1^136>, <$.1^3, $.1^141>, <$.1^3, $.1^143>, <$.1^3, $.1^150>, <$.1^3, $.1^166>, <$.1^3, $.1^167>, <$.1^3, $.1^168>, <$.1^3, $.1^172>, <$.1^3, $.1^173>, <$.1^3, $.1^178>, <$.1^3, $.1^181>, <$.1^3, $.1^182>, <$.1^3, $.1^185>, <$.1^3, $.1^187>, <$.1^3, $.1^196>, <$.1^3, $.1^208>, <$.1^3, $.1^220>, <$.1^3, $.1^237>, <$.1^3, $.1^241>, <$.1^3, $.1^248>, <$.1^3, $.1^258>, <$.1^3, $.1^261>, <$.1^3, $.1^268>, <$.1^3, $.1^269>, <$.1^3, $.1^271>, <$.1^3, $.1^274>, <$.1^3, $.1^283>, <$.1^3, $.1^291>, <$.1^3, $.1^302>, <$.1^3, $.1^303>, <$.1^3, $.1^308>, <$.1^3, $.1^317>, <$.1^3, $.1^319>, <$.1^3, $.1^327>, <$.1^3, $.1^330>, <$.1^4, $.1^6>, <$.1^4, $.1^17>, <$.1^4, $.1^18>, <$.1^4, $.1^23>, <$.1^4, $.1^32>, <$.1^4, $.1^34>, <$.1^4, $.1^42>, <$.1^4, $.1^45>, <$.1^4, $.1^61>, <$.1^4, $.1^81>, <$.1^4, $.1^83>, <$.1^4, $.1^85>, <$.1^4, $.1^101>, <$.1^4, $.1^119>, <$.1^4, $.1^126>, <$.1^4, $.1^145>, <$.1^4, $.1^149>, <$.1^4, $.1^153>, <$.1^4, $.1^161>, <$.1^4, 6>, <$.1^4, $.1^174>, <$.1^4, $.1^192>, <$.1^4, $.1^193>, <$.1^4, $.1^198>, <$.1^4, $.1^200>, <$.1^4, $.1^207>, <$.1^4, $.1^223>, <$.1^4, $.1^224>, <$.1^4, $.1^225>, <$.1^4, $.1^229>, <$.1^4, $.1^230>, <$.1^4, $.1^235>, <$.1^4, $.1^238>, <$.1^4, $.1^239>, <$.1^4, $.1^242>, <$.1^4, $.1^244>, <$.1^4, $.1^253>, <$.1^4, $.1^265>, <$.1^4, $.1^277>, <$.1^4, $.1^294>, <$.1^4, $.1^298>, <$.1^4, $.1^305>, <$.1^4, $.1^315>, <$.1^4, $.1^318>, <$.1^4, $.1^325>, <$.1^4, $.1^326>, <$.1^4, $.1^328>, <$.1^4, $.1^331>, <$.1^4, $.1^340>, <$.1^5, $.1^9>, <$.1^5, $.1^13>, <$.1^5, $.1^20>, <$.1^5, $.1^30>, <$.1^5, $.1^33>, <$.1^5, $.1^40>, <$.1^5, $.1^41>, <$.1^5, $.1^43>, <$.1^5, $.1^46>, <$.1^5, $.1^55>, <$.1^5, $.1^63>, <$.1^5, $.1^74>, <$.1^5, $.1^75>, <$.1^5, $.1^80>, <$.1^5, $.1^89>, <$.1^5, $.1^91>, <$.1^5, $.1^99>, <$.1^5, $.1^102>, <$.1^5, $.1^118>, <$.1^5, $.1^138>, <$.1^5, $.1^140>, <$.1^5, $.1^142>, <$.1^5, $.1^158>, <$.1^5, $.1^176>, <$.1^5, $.1^183>, <$.1^5, $.1^202>, <$.1^5, $.1^206>, <$.1^5, $.1^210>, <$.1^5, $.1^218>, <$.1^5, 4>, <$.1^5, $.1^231>, <$.1^5, $.1^249>, <$.1^5, $.1^250>, <$.1^5, $.1^255>, <$.1^5, $.1^257>, <$.1^5, $.1^264>, <$.1^5, $.1^280>, <$.1^5, $.1^281>, <$.1^5, $.1^282>, <$.1^5, $.1^286>, <$.1^5, $.1^287>, <$.1^5, $.1^292>, <$.1^5, $.1^295>, <$.1^5, $.1^296>, <$.1^5, $.1^299>, <$.1^5, $.1^301>, <$.1^5, $.1^310>, <$.1^5, $.1^322>, <$.1^5, $.1^334>, <$.1^6, $.1>, <$.1^6, $.1^2>, <$.1^6, $.1^7>, <$.1^6, $.1^10>, <$.1^6, $.1^11>, <$.1^6, $.1^14>, <$.1^6, $.1^16>, <$.1^6, $.1^25>, <$.1^6, $.1^37>, <$.1^6, $.1^49>, <$.1^6, $.1^66>, <$.1^6, $.1^70>, <$.1^6, $.1^77>, <$.1^6, $.1^87>, <$.1^6, $.1^90>, <$.1^6, $.1^97>, <$.1^6, $.1^98>, <$.1^6, $.1^100>, <$.1^6, $.1^103>, <$.1^6, $.1^112>, <$.1^6, $.1^120>, <$.1^6, $.1^131>, <$.1^6, $.1^132>, <$.1^6, $.1^137>, <$.1^6, $.1^146>, <$.1^6, $.1^148>, <$.1^6, $.1^156>, <$.1^6, $.1^159>, <$.1^6, $.1^175>, <$.1^6, $.1^195>, <$.1^6, $.1^197>, <$.1^6, $.1^199>, <$.1^6, $.1^215>, <$.1^6, $.1^233>, <$.1^6, $.1^240>, <$.1^6, $.1^259>, <$.1^6, $.1^263>, <$.1^6, $.1^267>, <$.1^6, $.1^275>, <$.1^6, 5>, <$.1^6, $.1^288>, <$.1^6, $.1^306>, <$.1^6, $.1^307>, <$.1^6, $.1^312>, <$.1^6, $.1^314>, <$.1^6, $.1^321>, <$.1^6, $.1^337>, <$.1^6, $.1^338>, <$.1^6, $.1^339>, <$.1^7, 1>, <$.1^7, $.1^3>, <$.1^7, $.1^21>, <$.1^7, $.1^22>, <$.1^7, $.1^27>, <$.1^7, $.1^29>, <$.1^7, $.1^36>, <$.1^7, $.1^52>, <$.1^7, $.1^53>, <$.1^7, $.1^54>, <$.1^7, $.1^58>, <$.1^7, $.1^59>, <$.1^7, $.1^64>, <$.1^7, $.1^67>, <$.1^7, $.1^68>, <$.1^7, $.1^71>, <$.1^7, $.1^73>, <$.1^7, $.1^82>, <$.1^7, $.1^94>, <$.1^7, $.1^106>, <$.1^7, $.1^123>, <$.1^7, $.1^127>, <$.1^7, $.1^134>, <$.1^7, $.1^144>, <$.1^7, $.1^147>, <$.1^7, $.1^154>, <$.1^7, $.1^155>, <$.1^7, $.1^157>, <$.1^7, $.1^160>, <$.1^7, $.1^169>, <$.1^7, $.1^177>, <$.1^7, $.1^188>, <$.1^7, $.1^189>, <$.1^7, $.1^194>, <$.1^7, $.1^203>, <$.1^7, $.1^205>, <$.1^7, $.1^213>, <$.1^7, $.1^216>, <$.1^7, $.1^232>, <$.1^7, $.1^252>, <$.1^7, $.1^254>, <$.1^7, $.1^256>, <$.1^7, $.1^272>, <$.1^7, $.1^290>, <$.1^7, $.1^297>, <$.1^7, $.1^316>, <$.1^7, $.1^320>, <$.1^7, $.1^324>, <$.1^7, $.1^332>, <$.1^8, $.1^5>, <$.1^8, $.1^12>, <$.1^8, $.1^31>, <$.1^8, $.1^35>, <$.1^8, $.1^39>, <$.1^8, $.1^47>, <$.1^8, 3>, <$.1^8, $.1^60>, <$.1^8, $.1^78>, <$.1^8, $.1^79>, <$.1^8, $.1^84>, <$.1^8, $.1^86>, <$.1^8, $.1^93>, <$.1^8, $.1^109>, <$.1^8, $.1^110>, <$.1^8, $.1^111>, <$.1^8, $.1^115>, <$.1^8, $.1^116>, <$.1^8, $.1^121>, <$.1^8, $.1^124>, <$.1^8, $.1^125>, <$.1^8, $.1^128>, <$.1^8, $.1^130>, <$.1^8, $.1^139>, <$.1^8, $.1^151>, <$.1^8, $.1^163>, <$.1^8, $.1^180>, <$.1^8, $.1^184>, <$.1^8, $.1^191>, <$.1^8, $.1^201>, <$.1^8, $.1^204>, <$.1^8, $.1^211>, <$.1^8, $.1^212>, <$.1^8, $.1^214>, <$.1^8, $.1^217>, <$.1^8, $.1^226>, <$.1^8, $.1^234>, <$.1^8, $.1^245>, <$.1^8, $.1^246>, <$.1^8, $.1^251>, <$.1^8, $.1^260>, <$.1^8, $.1^262>, <$.1^8, $.1^270>, <$.1^8, $.1^273>, <$.1^8, $.1^289>, <$.1^8, $.1^309>, <$.1^8, $.1^311>, <$.1^8, $.1^313>, <$.1^8, $.1^329>, <$.1^9, $.1^4>, <$.1^9, $.1^24>, <$.1^9, $.1^26>, <$.1^9, $.1^28>, <$.1^9, $.1^44>, <$.1^9, $.1^62>, <$.1^9, $.1^69>, <$.1^9, $.1^88>, <$.1^9, $.1^92>, <$.1^9, $.1^96>, <$.1^9, $.1^104>, <$.1^9, 2>, <$.1^9, $.1^117>, <$.1^9, $.1^135>, <$.1^9, $.1^136>, <$.1^9, $.1^141>, <$.1^9, $.1^143>, <$.1^9, $.1^150>, <$.1^9, $.1^166>, <$.1^9, $.1^167>, <$.1^9, $.1^168>, <$.1^9, $.1^172>, <$.1^9, $.1^173>, <$.1^9, $.1^178>, <$.1^9, $.1^181>, <$.1^9, $.1^182>, <$.1^9, $.1^185>, <$.1^9, $.1^187>, <$.1^9, $.1^196>, <$.1^9, $.1^208>, <$.1^9, $.1^220>, <$.1^9, $.1^237>, <$.1^9, $.1^241>, <$.1^9, $.1^248>, <$.1^9, $.1^258>, <$.1^9, $.1^261>, <$.1^9, $.1^268>, <$.1^9, $.1^269>, <$.1^9, $.1^271>, <$.1^9, $.1^274>, <$.1^9, $.1^283>, <$.1^9, $.1^291>, <$.1^9, $.1^302>, <$.1^9, $.1^303>, <$.1^9, $.1^308>, <$.1^9, $.1^317>, <$.1^9, $.1^319>, <$.1^9, $.1^327>, <$.1^9, $.1^330>, <$.1^10, $.1^6>, <$.1^10, $.1^17>, <$.1^10, $.1^18>, <$.1^10, $.1^23>, <$.1^10, $.1^32>, <$.1^10, $.1^34>, <$.1^10, $.1^42>, <$.1^10, $.1^45>, <$.1^10, $.1^61>, <$.1^10, $.1^81>, <$.1^10, $.1^83>, <$.1^10, $.1^85>, <$.1^10, $.1^101>, <$.1^10, $.1^119>, <$.1^10, $.1^126>, <$.1^10, $.1^145>, <$.1^10, $.1^149>, <$.1^10, $.1^153>, <$.1^10, $.1^161>, <$.1^10, 6>, <$.1^10, $.1^174>, <$.1^10, $.1^192>, <$.1^10, $.1^193>, <$.1^10, $.1^198>, <$.1^10, $.1^200>, <$.1^10, $.1^207>, <$.1^10, $.1^223>, <$.1^10, $.1^224>, <$.1^10, $.1^225>, <$.1^10, $.1^229>, <$.1^10, $.1^230>, <$.1^10, $.1^235>, <$.1^10, $.1^238>, <$.1^10, $.1^239>, <$.1^10, $.1^242>, <$.1^10, $.1^244>, <$.1^10, $.1^253>, <$.1^10, $.1^265>, <$.1^10, $.1^277>, <$.1^10, $.1^294>, <$.1^10, $.1^298>, <$.1^10, $.1^305>, <$.1^10, $.1^315>, <$.1^10, $.1^318>, <$.1^10, $.1^325>, <$.1^10, $.1^326>, <$.1^10, $.1^328>, <$.1^10, $.1^331>, <$.1^10, $.1^340>, <$.1^11, $.1^9>, <$.1^11, $.1^13>, <$.1^11, $.1^20>, <$.1^11, $.1^30>, <$.1^11, $.1^33>, <$.1^11, $.1^40>, <$.1^11, $.1^41>, <$.1^11, $.1^43>, <$.1^11, $.1^46>, <$.1^11, $.1^55>, <$.1^11, $.1^63>, <$.1^11, $.1^74>, <$.1^11, $.1^75>, <$.1^11, $.1^80>, <$.1^11, $.1^89>, <$.1^11, $.1^91>, <$.1^11, $.1^99>, <$.1^11, $.1^102>, <$.1^11, $.1^118>, <$.1^11, $.1^138>, <$.1^11, $.1^140>, <$.1^11, $.1^142>, <$.1^11, $.1^158>, <$.1^11, $.1^176>, <$.1^11, $.1^183>, <$. ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 06:36:19 2004 Input: print "EXERCICI 3:"; print "apartat (i)"; exponents73 := [7^i: i in [2..0 by -1]]; exp := func < q,r | [q^i: i in [r-1..0 by -1]] >; exp(7,3); /* Resultat: [ 49, 7, 1 ] */ print "apartat (ii)"; P := PolynomialRing (Integers()); t := &+[x^i : i in exp(7,3) ]; t; n := x^ &+(exp(7,3)); n; print "apartat (iii)"; puntsOlav := [ : a,b in GF(7^3) | Evaluate(n,a) eq Evaluate(t,b) ]; #puntsOlav; Output: Magma V2.10-6 Sun Mar 7 2004 06:36:11 on modular [Seed = 2323760090] ------------------------------------- EXERCICI 3: apartat (i) [ 49, 7, 1 ] apartat (ii) x^49 + x^7 + x x^57 apartat (iii) 16807 Total time: 7.219 seconds, Total memory usage: 2.73MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 06:50:37 2004 Input: print "EXERCICI 3:"; print "apartat (i)"; exponents73 := [7^i: i in [2..0 by -1]]; exp := func < q,r | [q^i: i in [r-1..0 by -1]] >; exp(7,3); /* Resultat: [ 49, 7, 1 ] */ print "apartat (ii)"; P := PolynomialRing (Integers()); t := &+[x^i : i in exp(7,3) ]; t; n := x^ &+(exp(7,3)); n; print "apartat (iii)"; puntsOlav73 := [ : a,b in GF(7^3) | Evaluate(n,a) eq Evaluate(t,b) ]; #puntsOlav73; print "- apartat (v)"; polt := func < q,r | &+[x^i: i in exp(q,r)] >; poln := func < q,r | x^(&+(exp(q,r))) >; print "- apartat (vi)"; puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(n,a) eq Evaluate(t,b)] >; print "- apartat (vii)"; print "-- Exemple 1:"; #puntsOlav(7,3) eq 7^(2*3-1); print "-- Exemple 2:"; #puntsOlav(9,1) eq 9^(2*1-1); print "-- Exemple 3:"; #puntsOlav(5,100) eq 5^(2*100-1); print "-- Exemple 4:"; #puntsOlav(0,3) eq 0^(2*3-1); print "-- Exemple 5:"; #puntsOlav(9,0) eq 9^(2*0-1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Mar 7 2004 06:50:14 on modular [Seed = 3401680577] ------------------------------------- EXERCICI 3: apartat (i) [ 49, 7, 1 ] apartat (ii) x^49 + x^7 + x x^57 apartat (iii) 16807 - apartat (v) - apartat (vi) - apartat (vii) -- Exemple 1: true -- Exemple 2: true -- Exemple 3: Errors: /home/mfd/gomagma: line 2: 15799 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 06:52:13 2004 Input: /*print "EXERCICI 3:"; print "apartat (i)"; exp := func < q,r | [q^i: i in [r-1..0 by -1]] >; exp(7,3); print "apartat (ii)"; P := PolynomialRing (Integers()); t := &+[x^i : i in exp(7,3) ]; t; n := x^ &+(exp(7,3)); n; print "apartat (iii)"; puntsOlav73 := [ : a,b in GF(7^3) | Evaluate(n,a) eq Evaluate(t,b) ]; #puntsOlav73; print "- apartat (v)"; polt := func < q,r | &+[x^i: i in exp(q,r)] >; poln := func < q,r | x^(&+(exp(q,r))) >; print "- apartat (vi)"; */ puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(n,a) eq Evaluate(t,b)] >; print "- apartat (vii)"; print "-- Exemple 1:"; #puntsOlav(7,3) eq 7^(2*3-1); print "-- Exemple 2:"; #puntsOlav(9,1) eq 9^(2*1-1); print "-- Exemple 3:"; #puntsOlav(5,100) eq 5^(2*100-1); print "-- Exemple 4:"; #puntsOlav(0,3) eq 0^(2*3-1); print "-- Exemple 5:"; #puntsOlav(9,0) eq 9^(2*0-1); Output: Magma V2.10-6 Sun Mar 7 2004 06:52:10 on modular [Seed = 2156645399] ------------------------------------- >> puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(n,a) eq Evaluat ^ User error: Identifier 'n' has not been declared or assigned - apartat (vii) -- Exemple 1: >> #puntsOlav(7,3) eq 7^(2*3-1); ^ User error: Identifier 'puntsOlav' has not been declared or assigned -- Exemple 2: >> #puntsOlav(9,1) eq 9^(2*1-1); ^ User error: Identifier 'puntsOlav' has not been declared or assigned -- Exemple 3: >> #puntsOlav(5,100) eq 5^(2*100-1); ^ User error: Identifier 'puntsOlav' has not been declared or assigned -- Exemple 4: >> #puntsOlav(0,3) eq 0^(2*3-1); ^ User error: Identifier 'puntsOlav' has not been declared or assigned -- Exemple 5: >> #puntsOlav(9,0) eq 9^(2*0-1);; ^ User error: Identifier 'puntsOlav' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 06:55:17 2004 Input: exp := func < q,r | [q^i: i in [r-1..0 by -1]] >; P := PolynomialRing (Integers()); t := &+[x^i : i in exp(7,3) ]; n := x^ &+(exp(7,3)); polt := func < q,r | &+[x^i: i in exp(q,r)] >; poln := func < q,r | x^(&+(exp(q,r))) >; puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)] >; print "-- Exemple 1:"; #puntsOlav(7,3) eq 7^(2*3-1); print "-- Exemple 2:"; #puntsOlav(9,1) eq 9^(2*1-1); print "-- Exemple 3:"; #puntsOlav(5,100) eq 5^(2*100-1); print "-- Exemple 4:"; #puntsOlav(0,3) eq 0^(2*3-1); print "-- Exemple 5:"; #puntsOlav(9,0) eq 9^(2*0-1); Output: Magma V2.10-6 Sun Mar 7 2004 06:54:59 on modular [Seed = 942896597] ------------------------------------- -- Exemple 1: true -- Exemple 2: true -- Exemple 3: [
:9]( q: 5, r: 100 ) [
:8]( q: 5, r: 100 ) >> poln := func < q,r | x^(&+(exp(q,r))) >; ^ Runtime error in '^': Argument 1 (197215226305252951352932141320696557418301608\ 7772557511925697326660156) is too large -- Exemple 4: [
:9]( q: 0, r: 3 ) >> puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(poln(q,r),a) eq ^ Runtime error in 'GF': Argument 1 (0) should be >= 2 -- Exemple 5: [
:9]( q: 9, r: 0 ) >> puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(poln(q,r),a) eq ^ Runtime error in 'GF': Argument 1 (1) should be >= 2 Total time: 17.709 seconds, Total memory usage: 2.73MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 06:57:23 2004 Input: exp := func < q,r | [q^i: i in [r-1..0 by -1]] >; P := PolynomialRing (Integers()); t := &+[x^i : i in exp(7,3) ]; n := x^ &+(exp(7,3)); polt := func < q,r | &+[x^i: i in exp(q,r)] >; poln := func < q,r | x^(&+(exp(q,r))) >; puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)] >; print "-- Exemple 1:"; #puntsOlav(7,3) eq 7^(2*3-1); print "-- Exemple 2:"; #puntsOlav(9,1) eq 9^(2*1-1); /* print "-- Exemple 3:"; #puntsOlav(5,100) eq 5^(2*100-1); print "-- Exemple 4:"; #puntsOlav(0,3) eq 0^(2*3-1); print "-- Exemple 5:"; #puntsOlav(9,0) eq 9^(2*0-1); */ Output: Magma V2.10-6 Sun Mar 7 2004 06:57:06 on modular [Seed = 4160534939] ------------------------------------- -- Exemple 1: true -- Exemple 2: true Total time: 17.149 seconds, Total memory usage: 2.73MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 06:57:46 2004 Input: exp := func < q,r | [q^i: i in [r-1..0 by -1]] >; P := PolynomialRing (Integers()); t := &+[x^i : i in exp(7,3) ]; n := x^ &+(exp(7,3)); polt := func < q,r | &+[x^i: i in exp(q,r)] >; poln := func < q,r | x^(&+(exp(q,r))) >; puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)] >; print "-- Exemple 3:"; #puntsOlav(5,100) eq 5^(2*100-1); /* print "-- Exemple 4:"; #puntsOlav(0,3) eq 0^(2*3-1); print "-- Exemple 5:"; #puntsOlav(9,0) eq 9^(2*0-1); */ Output: Magma V2.10-6 Sun Mar 7 2004 06:57:42 on modular [Seed = 3773542056] ------------------------------------- -- Exemple 3: [
:9]( q: 5, r: 100 ) [
:8]( q: 5, r: 100 ) >> poln := func < q,r | x^(&+(exp(q,r))) >; ^ Runtime error in '^': Argument 1 (197215226305252951352932141320696557418301608\ 7772557511925697326660156) is too large Total time: 3.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 06:58:46 2004 Input: exp := func < q,r | [q^i: i in [r-1..0 by -1]] >; P := PolynomialRing (Integers()); t := &+[x^i : i in exp(7,3) ]; n := x^ &+(exp(7,3)); polt := func < q,r | &+[x^i: i in exp(q,r)] >; poln := func < q,r | x^(&+(exp(q,r))) >; puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)] >; print "-- Exemple 3:"; #puntsOlav(5,50) eq 5^(2*50-1); /* print "-- Exemple 4:"; #puntsOlav(0,3) eq 0^(2*3-1); print "-- Exemple 5:"; #puntsOlav(9,0) eq 9^(2*0-1); */ Output: Magma V2.10-6 Sun Mar 7 2004 06:58:42 on modular [Seed = 3352070603] ------------------------------------- -- Exemple 3: [
:9]( q: 5, r: 50 ) [
:8]( q: 5, r: 50 ) >> poln := func < q,r | x^(&+(exp(q,r))) >; ^ Runtime error in '^': Argument 1 (22204460492503130808472633361816406) is too large Total time: 3.369 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 06:59:57 2004 Input: exp := func < q,r | [q^i: i in [r-1..0 by -1]] >; P := PolynomialRing (Integers()); t := &+[x^i : i in exp(7,3) ]; n := x^ &+(exp(7,3)); polt := func < q,r | &+[x^i: i in exp(q,r)] >; poln := func < q,r | x^(&+(exp(q,r))) >; puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)] >; poln(5,50); polt(5,50); /* print "-- Exemple 3:"; #puntsOlav(5,50) eq 5^(2*50-1); print "-- Exemple 4:"; #puntsOlav(0,3) eq 0^(2*3-1); print "-- Exemple 5:"; #puntsOlav(9,0) eq 9^(2*0-1); */ Output: Magma V2.10-6 Sun Mar 7 2004 06:59:54 on modular [Seed = 2677330267] ------------------------------------- [
:8]( q: 5, r: 50 ) >> poln := func < q,r | x^(&+(exp(q,r))) >; ^ Runtime error in '^': Argument 1 (22204460492503130808472633361816406) is too large [
:7]( q: 5, r: 50 ) >> polt := func < q,r | &+[x^i: i in exp(q,r)] >; ^ Runtime error in '^': Argument 1 (17763568394002504646778106689453125) is too large Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 07:00:33 2004 Input: exp := func < q,r | [q^i: i in [r-1..0 by -1]] >; P := PolynomialRing (Integers()); t := &+[x^i : i in exp(7,3) ]; n := x^ &+(exp(7,3)); polt := func < q,r | &+[x^i: i in exp(q,r)] >; poln := func < q,r | x^(&+(exp(q,r))) >; puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)] >; poln(5,25); polt(5,25); /* print "-- Exemple 3:"; #puntsOlav(5,50) eq 5^(2*50-1); print "-- Exemple 4:"; #puntsOlav(0,3) eq 0^(2*3-1); print "-- Exemple 5:"; #puntsOlav(9,0) eq 9^(2*0-1); */ Output: Magma V2.10-6 Sun Mar 7 2004 07:00:30 on modular [Seed = 2357707308] ------------------------------------- [
:8]( q: 5, r: 25 ) >> poln := func < q,r | x^(&+(exp(q,r))) >; ^ Runtime error in '^': Argument 1 (74505805969238281) is too large [
:7]( q: 5, r: 25 ) >> polt := func < q,r | &+[x^i: i in exp(q,r)] >; ^ Runtime error in '^': Argument 1 (59604644775390625) is too large Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 07:01:14 2004 Input: exp := func < q,r | [q^i: i in [r-1..0 by -1]] >; P := PolynomialRing (Integers()); t := &+[x^i : i in exp(7,3) ]; n := x^ &+(exp(7,3)); polt := func < q,r | &+[x^i: i in exp(q,r)] >; poln := func < q,r | x^(&+(exp(q,r))) >; puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)] >; poln(5,25); polt(5,25); exp(5,25); /* print "-- Exemple 3:"; #puntsOlav(5,50) eq 5^(2*50-1); print "-- Exemple 4:"; #puntsOlav(0,3) eq 0^(2*3-1); print "-- Exemple 5:"; #puntsOlav(9,0) eq 9^(2*0-1); */ Output: Magma V2.10-6 Sun Mar 7 2004 07:01:11 on modular [Seed = 1920548106] ------------------------------------- [
:8]( q: 5, r: 25 ) >> poln := func < q,r | x^(&+(exp(q,r))) >; ^ Runtime error in '^': Argument 1 (74505805969238281) is too large [
:7]( q: 5, r: 25 ) >> polt := func < q,r | &+[x^i: i in exp(q,r)] >; ^ Runtime error in '^': Argument 1 (59604644775390625) is too large [ 59604644775390625, 11920928955078125, 2384185791015625, 476837158203125, 95367431640625, 19073486328125, 3814697265625, 762939453125, 152587890625, 30517578125, 6103515625, 1220703125, 244140625, 48828125, 9765625, 1953125, 390625, 78125, 15625, 3125, 625, 125, 25, 5, 1 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 07:01:48 2004 Input: exp := func < q,r | [q^i: i in [r-1..0 by -1]] >; P := PolynomialRing (Integers()); t := &+[x^i : i in exp(7,3) ]; n := x^ &+(exp(7,3)); polt := func < q,r | &+[x^i: i in exp(q,r)] >; poln := func < q,r | x^(&+(exp(q,r))) >; puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)] >; poln(5,15); polt(5,15); exp(5,15); /* print "-- Exemple 3:"; #puntsOlav(5,50) eq 5^(2*50-1); print "-- Exemple 4:"; #puntsOlav(0,3) eq 0^(2*3-1); print "-- Exemple 5:"; #puntsOlav(9,0) eq 9^(2*0-1); */ Output: Magma V2.10-6 Sun Mar 7 2004 07:01:45 on modular [Seed = 1768039999] ------------------------------------- [
:8]( q: 5, r: 15 ) >> poln := func < q,r | x^(&+(exp(q,r))) >; ^ Runtime error in '^': Argument 1 (7629394531) is too large [
:7]( q: 5, r: 15 ) >> polt := func < q,r | &+[x^i: i in exp(q,r)] >; ^ Runtime error in '^': Argument 1 (6103515625) is too large [ 6103515625, 1220703125, 244140625, 48828125, 9765625, 1953125, 390625, 78125, 15625, 3125, 625, 125, 25, 5, 1 ] Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 07:02:33 2004 Input: exp := func < q,r | [q^i: i in [r-1..0 by -1]] >; P := PolynomialRing (Integers()); t := &+[x^i : i in exp(7,3) ]; n := x^ &+(exp(7,3)); polt := func < q,r | &+[x^i: i in exp(q,r)] >; poln := func < q,r | x^(&+(exp(q,r))) >; puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)] >; poln(5,10); polt(5,10); exp(5,10); /* print "-- Exemple 3:"; #puntsOlav(5,50) eq 5^(2*50-1); print "-- Exemple 4:"; #puntsOlav(0,3) eq 0^(2*3-1); print "-- Exemple 5:"; #puntsOlav(9,0) eq 9^(2*0-1); */ Output: Magma V2.10-6 Sun Mar 7 2004 07:02:28 on modular [Seed = 1617637195] ------------------------------------- x^2441406 x^1953125 + x^390625 + x^78125 + x^15625 + x^3125 + x^625 + x^125 + x^25 + x^5 + x [ 1953125, 390625, 78125, 15625, 3125, 625, 125, 25, 5, 1 ] Total time: 4.539 seconds, Total memory usage: 36.85MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 07:03:22 2004 Input: exp := func < q,r | [q^i: i in [r-1..0 by -1]] >; P := PolynomialRing (Integers()); t := &+[x^i : i in exp(7,3) ]; n := x^ &+(exp(7,3)); polt := func < q,r | &+[x^i: i in exp(q,r)] >; poln := func < q,r | x^(&+(exp(q,r))) >; puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)] >; poln(5,10); polt(5,10); exp(5,10); print "-- Exemple 3:"; #puntsOlav(5,10) eq 5^(2*10-1); /* print "-- Exemple 4:"; #puntsOlav(0,3) eq 0^(2*3-1); print "-- Exemple 5:"; #puntsOlav(9,0) eq 9^(2*0-1); */ Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Mar 7 2004 07:02:59 on modular [Seed = 1465653339] ------------------------------------- x^2441406 x^1953125 + x^390625 + x^78125 + x^15625 + x^3125 + x^625 + x^125 + x^25 + x^5 + x [ 1953125, 390625, 78125, 15625, 3125, 625, 125, 25, 5, 1 ] -- Exemple 3: Errors: /home/mfd/gomagma: line 2: 16168 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 07:04:05 2004 Input: exp := func < q,r | [q^i: i in [r-1..0 by -1]] >; P := PolynomialRing (Integers()); t := &+[x^i : i in exp(7,3) ]; n := x^ &+(exp(7,3)); polt := func < q,r | &+[x^i: i in exp(q,r)] >; poln := func < q,r | x^(&+(exp(q,r))) >; puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)] >; print "-- Exemple 3:"; #puntsOlav(5,10) eq 5^(2*10-1); /* print "-- Exemple 4:"; #puntsOlav(0,3) eq 0^(2*3-1); print "-- Exemple 5:"; #puntsOlav(9,0) eq 9^(2*0-1); */ Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Mar 7 2004 07:03:42 on modular [Seed = 1313145263] ------------------------------------- -- Exemple 3: Errors: /home/mfd/gomagma: line 2: 16177 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 07:05:00 2004 Input: exp := func < q,r | [q^i: i in [r-1..0 by -1]] >; P := PolynomialRing (Integers()); t := &+[x^i : i in exp(7,3) ]; n := x^ &+(exp(7,3)); polt := func < q,r | &+[x^i: i in exp(q,r)] >; poln := func < q,r | x^(&+(exp(q,r))) >; puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)] >; #puntsOlav(5,10) eq 5^(2*10-1); /* print "-- Exemple 4:"; #puntsOlav(0,3) eq 0^(2*3-1); print "-- Exemple 5:"; #puntsOlav(9,0) eq 9^(2*0-1); */ Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Mar 7 2004 07:04:37 on modular [Seed = 1146031086] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 16187 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 07:05:37 2004 Input: exp := func < q,r | [q^i: i in [r-1..0 by -1]] >; P := PolynomialRing (Integers()); t := &+[x^i : i in exp(7,3) ]; n := x^ &+(exp(7,3)); polt := func < q,r | &+[x^i: i in exp(q,r)] >; poln := func < q,r | x^(&+(exp(q,r))) >; puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)] >; #puntsOlav(5,10) eq 5^(2*10-1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Mar 7 2004 07:05:14 on modular [Seed = 926709938] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 16200 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 07:06:11 2004 Input: exp := func < q,r | [q^i: i in [r-1..0 by -1]] >; P := PolynomialRing (Integers()); t := &+[x^i : i in exp(7,3) ]; n := x^ &+(exp(7,3)); polt := func < q,r | &+[x^i: i in exp(q,r)] >; poln := func < q,r | x^(&+(exp(q,r))) >; puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)] >; #puntsOlav(5,10) eq 5^(2*10-1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Mar 7 2004 07:05:48 on modular [Seed = 774209101] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 16209 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 07:06:45 2004 Input: exp := func < q,r | [q^i: i in [r-1..0 by -1]] >; P := PolynomialRing (Integers()); polt := func < q,r | &+[x^i: i in exp(q,r)] >; poln := func < q,r | x^(&+(exp(q,r))) >; puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)] >; #puntsOlav(5,10) eq 5^(2*10-1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Mar 7 2004 07:06:22 on modular [Seed = 623801700] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 16218 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 07:08:42 2004 Input: exp := func < q,r | [q^i: i in [r-1..0 by -1]] >; P := PolynomialRing (Integers()); polt := func < q,r | &+[x^i: i in exp(q,r)] >; poln := func < q,r | x^(&+(exp(q,r))) >; puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)] >; #puntsOlav(5,10) eq 5^(2*10-1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Mar 7 2004 07:08:19 on modular [Seed = 471289040] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 16227 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 07:14:50 2004 Input: exp := func < q,r | [q^i: i in [r-1..0 by -1]] >; P := PolynomialRing (Integers()); polt := func < q,r | &+[x^i: i in exp(q,r)] >; poln := func < q,r | x^(&+(exp(q,r))) >; puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)] >; #puntsOlav(5,10) eq 5^(2*10-1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Mar 7 2004 07:14:27 on modular [Seed = 167860310] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 16245 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 07:26:10 2004 Input: exp := func < q,r | [q^i: i in [r-1..0 by -1]] >; P := PolynomialRing (Integers()); polt := func < q,r | &+[x^i: i in exp(q,r)] >; poln := func < q,r | x^(&+(exp(q,r))) >; puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)] >; #puntsOlav(5,10) eq 5^(2*10-1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Mar 7 2004 07:25:47 on modular [Seed = 3452344702] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 16306 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 07:27:28 2004 Input: /* PRACTICA 1. TEORIA DE LA CODIFICACIÓ */ print "EXERCICI 1:"; {n: n in [4..366 by 7]}; /* Resultat: { 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 } */ Output: Magma V2.10-6 Sun Mar 7 2004 07:27:25 on modular [Seed = 3148934889] ------------------------------------- EXERCICI 1: { 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 } Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 07:27:50 2004 Input: print "EXERCICI 2:"; R:= GF(4); M := MatrixRing(R,2); print "- APARTAT (i)"; Mt := { A : A in M | Trace(A) eq 0}; print "- APARTAT (ii)"; Mf := {A: A in M | A[1] eq A[2]}; print "- APARTAT (iii)"; Mtf := Mt meet Mf; print "- APARTAT (iv)"; seq:=[Random(M):num in [1..100000]]; print "Matrius que pertanyen a Mt:"; #([A : A in seq | A in Mt]); print "Matrius que pertanyen a Mf:"; #([A : A in seq | A in Mf]); print "Matrius que pertanyen a Mtf:"; #([A : A in seq | A in Mtf]); /* Resultat: Matrius que pertanyen a Mt: 25082 Matrius que pertanyen a Mf: 6287 Matrius que pertanyen a Mtf: 1608 */ /* Resposta a la pregunta 'Ho trobeu raonable?': Sí, es raonable, donat que el nombre de matrius pertanyents a Mt, Mf i Mtf mantenen una proporcio respecte el conjunt de matrius M. Donat un nombre qualsevol de matrius M, un 25% d'elles són Mt, un 6.25% són Mf i un 1.56% són Mtf. Per tant, donades 100 000 matrius M, el 25% són matrius Mf (aproximadament 25000), el 6.25% són Mt (aproximadament 6250) i el 1.56% són Mtf (aproximadament 1560). */ Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed. ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 07:28:56 2004 Input: print "EXERCICI 2:"; R:= GF(4); M := MatrixRing(R,2); print "- APARTAT (i)"; Mt := { A : A in M | Trace(A) eq 0}; print "- APARTAT (ii)"; Mf := {A: A in M | A[1] eq A[2]}; print "- APARTAT (iii)"; Mtf := Mt meet Mf; print "- APARTAT (iv)"; seq:=[Random(M):num in [1..100000]]; print "Matrius que pertanyen a Mt:"; #([A : A in seq | A in Mt]); print "Matrius que pertanyen a Mf:"; #([A : A in seq | A in Mf]); print "Matrius que pertanyen a Mtf:"; #([A : A in seq | A in Mtf]); /* Resultat: Matrius que pertanyen a Mt: 25082 Matrius que pertanyen a Mf: 6287 Matrius que pertanyen a Mtf: 1608 */ /* Resposta a la pregunta 'Ho trobeu raonable?': Sí, es raonable, donat que el nombre de matrius pertanyents a Mt, Mf i Mtf mantenen una proporcio respecte el conjunt de matrius M. Donat un nombre qualsevol de matrius M, un 25 per cent d'elles són Mt, un 6.25 per cent són Mf i un 1.56 per cent són Mtf. Per tant, donades 100 000 matrius M, el 25 per cent són matrius Mf (aproximadament 25000), el 6.25 per cent són Mt (aproximadament 6250) i el 1.56 per cent són Mtf (aproximadament 1560). */ Output: Magma V2.10-6 Sun Mar 7 2004 07:28:52 on modular [Seed = 2526921581] ------------------------------------- EXERCICI 2: - APARTAT (i) - APARTAT (ii) - APARTAT (iii) - APARTAT (iv) Matrius que pertanyen a Mt: 24775 Matrius que pertanyen a Mf: 6139 Matrius que pertanyen a Mtf: 1504 Total time: 4.089 seconds, Total memory usage: 6.89MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 07:29:42 2004 Input: print "EXERCICI 3:"; print "- APARTAT (i)"; exp := func < q,r | [q^i: i in [r-1..0 by -1]] >; exp(7,3); /* Resultat: [ 49, 7, 1 ] */ Output: Magma V2.10-6 Sun Mar 7 2004 07:29:39 on modular [Seed = 2257441610] ------------------------------------- EXERCICI 3: - APARTAT (i) [ 49, 7, 1 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 07:30:06 2004 Input: print "EXERCICI 3:"; print "- APARTAT (i)"; exp := func < q,r | [q^i: i in [r-1..0 by -1]] >; exp(7,3); /* Resultat: [ 49, 7, 1 ] */ print "- APARTAT (ii)"; P := PolynomialRing (Integers()); t := &+[x^i : i in exp(7,3) ]; t; n := x^ &+(exp(7,3)); n; /* Resultat: x^49 + x^7 + x x^57 */ Output: Magma V2.10-6 Sun Mar 7 2004 07:30:03 on modular [Seed = 251943620] ------------------------------------- EXERCICI 3: - APARTAT (i) [ 49, 7, 1 ] - APARTAT (ii) x^49 + x^7 + x x^57 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 07:30:33 2004 Input: print "EXERCICI 3:"; print "- APARTAT (i)"; exp := func < q,r | [q^i: i in [r-1..0 by -1]] >; exp(7,3); /* Resultat: [ 49, 7, 1 ] */ print "- APARTAT (ii)"; P := PolynomialRing (Integers()); t := &+[x^i : i in exp(7,3) ]; t; n := x^ &+(exp(7,3)); n; /* Resultat: x^49 + x^7 + x x^57 */ print "- APARTAT (iii)"; puntsOlav73 := [ : a,b in GF(7^3) | Evaluate(n,a) eq Evaluate(t,b) ]; # puntsOlav73; /* Resultat: 16807 */ Output: Magma V2.10-6 Sun Mar 7 2004 07:30:27 on modular [Seed = 403918331] ------------------------------------- EXERCICI 3: - APARTAT (i) [ 49, 7, 1 ] - APARTAT (ii) x^49 + x^7 + x x^57 - APARTAT (iii) 16807 Total time: 6.779 seconds, Total memory usage: 2.73MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 07:32:28 2004 Input: exp := func < q,r | [q^i: i in [r-1..0 by -1]] >; P := PolynomialRing (Integers()); polt := func < q,r | &+[x^i: i in exp(q,r)] >; poln := func < q,r | x^(&+(exp(q,r))) >; puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(n,a) eq Evaluate(t,b)] >; #puntsOlav(7,3) eq 7^(2*3-1); #puntsOlav(9,1) eq 9^(2*1-1); #puntsOlav(5,10) eq 5^(2*10-1); Output: Magma V2.10-6 Sun Mar 7 2004 07:32:24 on modular [Seed = 909992046] ------------------------------------- >> puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(n,a) eq Evaluat ^ User error: Identifier 'n' has not been declared or assigned >> #puntsOlav(7,3) eq 7^(2*3-1); ^ User error: Identifier 'puntsOlav' has not been declared or assigned >> #puntsOlav(9,1) eq 9^(2*1-1); ^ User error: Identifier 'puntsOlav' has not been declared or assigned >> #puntsOlav(5,10) eq 5^(2*10-1);; ^ User error: Identifier 'puntsOlav' has not been declared or assigned Total time: 3.449 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 07:33:32 2004 Input: exp := func < q,r | [q^i: i in [r-1..0 by -1]] >; P := PolynomialRing (Integers()); polt := func < q,r | &+[x^i: i in exp(q,r)] >; poln := func < q,r | x^(&+(exp(q,r))) >; puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)] >; #puntsOlav(7,3) eq 7^(2*3-1); #puntsOlav(9,1) eq 9^(2*1-1); #puntsOlav(5,10) eq 5^(2*10-1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Mar 7 2004 07:33:08 on modular [Seed = 1465647571] ------------------------------------- true true Errors: /home/mfd/gomagma: line 2: 16471 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 07:34:13 2004 Input: exp := func < q,r | [q^i: i in [r-1..0 by -1]] >; P := PolynomialRing (Integers()); polt := func < q,r | &+[x^i: i in exp(q,r)] >; poln := func < q,r | x^(&+(exp(q,r))) >; puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)] >; #puntsOlav(5,10) eq 5^(2*10-1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Mar 7 2004 07:33:50 on modular [Seed = 2088184530] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 16508 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 07:35:06 2004 Input: exp := func < q,r | [q^i: i in [r-1..0 by -1]] >; P := PolynomialRing (Integers()); polt := func < q,r | &+[x^i: i in exp(q,r)] >; poln := func < q,r | x^(&+(exp(q,r))) >; puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)] >; #puntsOlav(5,5) eq 5^(2*5-1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Mar 7 2004 07:34:43 on modular [Seed = 2829319755] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 16552 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 07:35:33 2004 Input: exp := func < q,r | [q^i: i in [r-1..0 by -1]] >; P := PolynomialRing (Integers()); polt := func < q,r | &+[x^i: i in exp(q,r)] >; poln := func < q,r | x^(&+(exp(q,r))) >; puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)] >; #puntsOlav(5,5) eq 5^(2*5-1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Mar 7 2004 07:35:09 on modular [Seed = 3401686071] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 16586 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 07:35:35 2004 Input: exp := func < q,r | [q^i: i in [r-1..0 by -1]] >; P := PolynomialRing (Integers()); polt := func < q,r | &+[x^i: i in exp(q,r)] >; poln := func < q,r | x^(&+(exp(q,r))) >; puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)] >; #puntsOlav(2,2) eq 2^(2*2-1); Output: Magma V2.10-6 Sun Mar 7 2004 07:35:32 on modular [Seed = 3654454989] ------------------------------------- true Total time: 3.269 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 07:36:21 2004 Input: exp := func < q,r | [q^i: i in [r-1..0 by -1]] >; P := PolynomialRing (Integers()); polt := func < q,r | &+[x^i: i in exp(q,r)] >; poln := func < q,r | x^(&+(exp(q,r))) >; puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)] >; #puntsOlav(2,2) eq 2^(2*2-1); #puntsOlav(0,3) eq 0^(2*3-1); #puntsOlav(9,0) eq 9^(2*0-1); Output: Magma V2.10-6 Sun Mar 7 2004 07:36:18 on modular [Seed = 118247492] ------------------------------------- true [
:7]( q: 0, r: 3 ) >> puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(poln(q,r),a) eq ^ Runtime error in 'GF': Argument 1 (0) should be >= 2 [
:7]( q: 9, r: 0 ) >> puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(poln(q,r),a) eq ^ Runtime error in 'GF': Argument 1 (1) should be >= 2 Total time: 3.219 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 07:36:34 2004 Input: exp := func < q,r | [q^i: i in [r-1..0 by -1]] >; P := PolynomialRing (Integers()); polt := func < q,r | &+[x^i: i in exp(q,r)] >; poln := func < q,r | x^(&+(exp(q,r))) >; puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)] >; #puntsOlav(0,3) eq 0^(2*3-1); #puntsOlav(9,0) eq 9^(2*0-1); Output: Magma V2.10-6 Sun Mar 7 2004 07:36:31 on modular [Seed = 337593178] ------------------------------------- [
:7]( q: 0, r: 3 ) >> puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(poln(q,r),a) eq ^ Runtime error in 'GF': Argument 1 (0) should be >= 2 [
:7]( q: 9, r: 0 ) >> puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(poln(q,r),a) eq ^ Runtime error in 'GF': Argument 1 (1) should be >= 2 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 07:37:38 2004 Input: exp := func < q,r | [q^i: i in [r-1..0 by -1]] >; P := PolynomialRing (Integers()); polt := func < q,r | &+[x^i: i in exp(q,r)] >; poln := func < q,r | x^(&+(exp(q,r))) >; puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)] >; #puntsOlav(9,4) eq 0^(2*3-1); #puntsOlav(4,9) eq 9^(2*0-1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Mar 7 2004 07:37:15 on modular [Seed = 1010264902] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 16701 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 07:38:36 2004 Input: exp := func < q,r | [q^i: i in [r-1..0 by -1]] >; P := PolynomialRing (Integers()); polt := func < q,r | &+[x^i: i in exp(q,r)] >; poln := func < q,r | x^(&+(exp(q,r))) >; puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)] >; #puntsOlav(3,5) eq 3^(2*5-1); #puntsOlav(4,9) eq 9^(2*0-1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Mar 7 2004 07:38:13 on modular [Seed = 1617639380] ------------------------------------- true Errors: /home/mfd/gomagma: line 2: 16737 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 07:39:22 2004 Input: exp := func < q,r | [q^i: i in [r-1..0 by -1]] >; P := PolynomialRing (Integers()); polt := func < q,r | &+[x^i: i in exp(q,r)] >; poln := func < q,r | x^(&+(exp(q,r))) >; puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)] >; #puntsOlav(9,1) eq 9^(2*1-1); Output: Magma V2.10-6 Sun Mar 7 2004 07:39:19 on modular [Seed = 2224018290] ------------------------------------- true Total time: 3.209 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 07:40:35 2004 Input: exp := func < q,r | [q^i: i in [r-1..0 by -1]] >; P := PolynomialRing (Integers()); polt := func < q,r | &+[x^i: i in exp(q,r)] >; poln := func < q,r | x^(&+(exp(q,r))) >; puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)] >; sel := [punt: punt in puntsOlav(7,3) | punt[1] in GF(7) and punt[2] in GF(7)]; #sel; sel2 := [punt: punt in puntsOlav(5,10) | punt[1] in GF(5) and punt[2] in GF(5)]; #sel2; sel3 := [punt: punt in puntsOlav(9,0) | punt[1] in GF(9) and punt[2] in GF(9)]; #sel3; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Mar 7 2004 07:40:12 on modular [Seed = 2913400192] ------------------------------------- 7 Errors: /home/mfd/gomagma: line 2: 16812 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 07:41:27 2004 Input: exp := func < q,r | [q^i: i in [r-1..0 by -1]] >; P := PolynomialRing (Integers()); polt := func < q,r | &+[x^i: i in exp(q,r)] >; poln := func < q,r | x^(&+(exp(q,r))) >; puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)] >; sel2 := [punt: punt in puntsOlav(2,1) | punt[1] in GF(2) and punt[2] in GF(2)]; #sel2; sel3 := [punt: punt in puntsOlav(9,0) | punt[1] in GF(9) and punt[2] in GF(9)]; #sel3; Output: Magma V2.10-6 Sun Mar 7 2004 07:41:23 on modular [Seed = 3721823663] ------------------------------------- 2 [
:7]( q: 9, r: 0 ) >> puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(poln(q,r),a) eq ^ Runtime error in 'GF': Argument 1 (1) should be >= 2 >> #sel3;; ^ User error: Identifier 'sel3' has not been declared or assigned Total time: 4.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 07:42:05 2004 Input: exp := func < q,r | [q^i: i in [r-1..0 by -1]] >; P := PolynomialRing (Integers()); polt := func < q,r | &+[x^i: i in exp(q,r)] >; poln := func < q,r | x^(&+(exp(q,r))) >; puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)] >; sel3 := [punt: punt in puntsOlav(9,0) | punt[1] in GF(9) and punt[2] in GF(9)]; #sel3; Output: Magma V2.10-6 Sun Mar 7 2004 07:42:01 on modular [Seed = 4043024488] ------------------------------------- [
:7]( q: 9, r: 0 ) >> puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(poln(q,r),a) eq ^ Runtime error in 'GF': Argument 1 (1) should be >= 2 >> #sel3;; ^ User error: Identifier 'sel3' has not been declared or assigned Total time: 3.739 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 7 07:42:17 2004 Input: exp := func < q,r | [q^i: i in [r-1..0 by -1]] >; P := PolynomialRing (Integers()); polt := func < q,r | &+[x^i: i in exp(q,r)] >; poln := func < q,r | x^(&+(exp(q,r))) >; puntsOlav := func < q,r | [: a,b in GF(q^r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)] >; sel3 := [punt: punt in puntsOlav(9,1) | punt[1] in GF(9) and punt[2] in GF(9)]; #sel3; Output: Magma V2.10-6 Sun Mar 7 2004 07:42:13 on modular [Seed = 34167461] ------------------------------------- 9 Total time: 3.769 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sun Mar 7 15:49:45 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3+x^2-2*x+8); E:=EquationOrder(K); OK:=MaximalOrder(K); J:=2*OK; Index(OK, E); Factorization(J); [K!OK.i : i in [1, 2, 3]]; Output: Magma V2.10-6 Sun Mar 7 2004 15:49:42 on modular [Seed = 3721795328] ------------------------------------- 2 [ , , ] [ 1, a, 1/2*(a^2 + a) ] Total time: 3.179 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Sun Mar 7 16:13:53 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^3-x+2); OK:=MaximalOrder(K); MinkowskiBound(K); Output: Magma V2.10-6 Sun Mar 7 2004 16:13:49 on modular [Seed = 2510177574] ------------------------------------- 2 Total time: 4.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sun Mar 7 19:41:28 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3+x^2-2*x+8); E:=EquationOrder(K); OK:=MaximalOrder(K); J:=2*OK; Index(OK, E); Factorization(J); [K!OK.i : i in [1, 2, 3]]; m:=2*a; f:=MinimalPolynomial(m); Output: Magma V2.10-6 Sun Mar 7 2004 19:41:24 on modular [Seed = 640526150] ------------------------------------- 2 [ , , ] [ 1, a, 1/2*(a^2 + a) ] Total time: 4.209 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sun Mar 7 19:41:42 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3+x^2-2*x+8); E:=EquationOrder(K); OK:=MaximalOrder(K); J:=2*OK; Index(OK, E); Factorization(J); [K!OK.i : i in [1, 2, 3]]; m:=2*a; f:=MinimalPolynomial(m); f; Output: Magma V2.10-6 Sun Mar 7 2004 19:41:39 on modular [Seed = 706849597] ------------------------------------- 2 [ , , ] [ 1, a, 1/2*(a^2 + a) ] x^3 + 2*x^2 - 8*x + 64 Total time: 3.219 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sun Mar 7 19:41:53 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3+x^2-2*x+8); E:=EquationOrder(K); OK:=MaximalOrder(K); J:=2*OK; Index(OK, E); Factorization(J); [K!OK.i : i in [1, 2, 3]]; m:=2*a; f:=MinimalPolynomial(m); f; Output: Magma V2.10-6 Sun Mar 7 2004 19:41:49 on modular [Seed = 3301918173] ------------------------------------- 2 [ , , ] [ 1, a, 1/2*(a^2 + a) ] x^3 + 2*x^2 - 8*x + 64 Total time: 3.119 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sun Mar 7 19:42:11 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3+x^2-2*x+8); E:=EquationOrder(K); OK:=MaximalOrder(K); J:=2*OK; Index(OK, E); Factorization(J); [K!OK.i : i in [1, 2, 3]]; m:=c*a; f:=MinimalPolynomial(m); f; Output: Magma V2.10-6 Sun Mar 7 2004 19:42:07 on modular [Seed = 4143806461] ------------------------------------- 2 [ , , ] [ 1, a, 1/2*(a^2 + a) ] >> m:=c*a; ^ User error: Identifier 'c' has not been declared or assigned >> f:=MinimalPolynomial(m); ^ User error: Identifier 'm' has not been declared or assigned >> f;; ^ User error: Identifier 'f' has not been declared or assigned Total time: 3.349 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sun Mar 7 20:09:26 2004 Input: R := PolynomialRing(RationalField(), 4); R; Output: Magma V2.10-6 Sun Mar 7 2004 20:09:22 on modular [Seed = 993049761] ------------------------------------- Polynomial ring of rank 4 over Rational Field Lexicographical Order Variables: x, $.2, $.3, $.4 Total time: 4.099 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sun Mar 7 20:11:19 2004 Input: R := PolynomialRing(RationalField(), 4); R; K := NumberField(x^3-x+2); K; E:=EquationOrder(K); OK:=MaximalOrder(K); I:=3*OK; J:=2*OK; Index(OK, E); Factorization(I); Factorization(J); [K!OK.i : i in [1, 2, 3]]; Output: Magma V2.10-6 Sun Mar 7 2004 20:11:16 on modular [Seed = 4093148063] ------------------------------------- Polynomial ring of rank 4 over Rational Field Lexicographical Order Variables: x, a, b, c >> K := NumberField(x^3-x+2); ^ Runtime error in 'NumberField': Bad argument types Argument types given: RngMPolElt >> K; ^ User error: Identifier 'K' has not been declared or assigned >> E:=EquationOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> OK:=MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> I:=3*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> J:=2*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Index(OK, E); ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I); ^ User error: Identifier 'I' has not been declared or assigned >> Factorization(J); ^ User error: Identifier 'J' has not been declared or assigned >> [K!OK.i : i in [1, 2, 3]];; ^ User error: Identifier 'K' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sun Mar 7 20:12:07 2004 Input: R := PolynomialRing(RationalField(), 4); R; K := NumberField(x^3-x+2); NumberField; Output: Magma V2.10-6 Sun Mar 7 2004 20:12:03 on modular [Seed = 2677282724] ------------------------------------- Polynomial ring of rank 4 over Rational Field Lexicographical Order Variables: x, a, b, c >> K := NumberField(x^3-x+2); ^ Runtime error in 'NumberField': Bad argument types Argument types given: RngMPolElt Intrinsic 'NumberField' Signatures: ( f) -> FldNum [ Abs: BoolElt, DoLinearExtension: BoolElt, Check: BoolElt, Global: BoolElt ] Create the number field obtained by adjoining a root of f to the number field containing the coefficients of f. ( S) -> FldNum [ Abs: BoolElt, DoLinearExtension: BoolElt, Check: BoolElt, Global: BoolElt ] Create the number field obtained by adjoining a root of each polynomial. ( e) -> FldNum Return the subfield lattice element e as a number field. ( F) -> FldNum The unique number field associated with F and its order. ( O) -> FldNum The unique number field associated with O and its field of fractions. ( P) -> FldNum ( P) -> FldNum The unique number field associated with P. ( F) -> FldNum The NumberField corresponding to F. Total time: 4.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sun Mar 7 20:13:06 2004 Input: R := PolynomialRing(RationalField(), 4); R; K := NumberField(x^3-x+2); NumberField; RngMPolElt; Output: Magma V2.10-6 Sun Mar 7 2004 20:13:03 on modular [Seed = 2896634987] ------------------------------------- Polynomial ring of rank 4 over Rational Field Lexicographical Order Variables: x, a, b, c >> K := NumberField(x^3-x+2); ^ Runtime error in 'NumberField': Bad argument types Argument types given: RngMPolElt Intrinsic 'NumberField' Signatures: ( f) -> FldNum [ Abs: BoolElt, DoLinearExtension: BoolElt, Check: BoolElt, Global: BoolElt ] Create the number field obtained by adjoining a root of f to the number field containing the coefficients of f. ( S) -> FldNum [ Abs: BoolElt, DoLinearExtension: BoolElt, Check: BoolElt, Global: BoolElt ] Create the number field obtained by adjoining a root of each polynomial. ( e) -> FldNum Return the subfield lattice element e as a number field. ( F) -> FldNum The unique number field associated with F and its order. ( O) -> FldNum The unique number field associated with O and its field of fractions. ( P) -> FldNum ( P) -> FldNum The unique number field associated with P. ( F) -> FldNum The NumberField corresponding to F. RngMPolElt Total time: 3.199 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sun Mar 7 20:13:25 2004 Input: R := PolynomialRing(RationalField(), 4); R; K := NumberField(x^3-x+2); NumberField; RngMPolElt? Output: Magma V2.10-6 Sun Mar 7 2004 20:13:22 on modular [Seed = 1245823649] ------------------------------------- Polynomial ring of rank 4 over Rational Field Lexicographical Order Variables: x, a, b, c >> K := NumberField(x^3-x+2); ^ Runtime error in 'NumberField': Bad argument types Argument types given: RngMPolElt Intrinsic 'NumberField' Signatures: ( f) -> FldNum [ Abs: BoolElt, DoLinearExtension: BoolElt, Check: BoolElt, Global: BoolElt ] Create the number field obtained by adjoining a root of f to the number field containing the coefficients of f. ( S) -> FldNum [ Abs: BoolElt, DoLinearExtension: BoolElt, Check: BoolElt, Global: BoolElt ] Create the number field obtained by adjoining a root of each polynomial. ( e) -> FldNum Return the subfield lattice element e as a number field. ( F) -> FldNum The unique number field associated with F and its order. ( O) -> FldNum The unique number field associated with O and its field of fractions. ( P) -> FldNum ( P) -> FldNum The unique number field associated with P. ( F) -> FldNum The NumberField corresponding to F. >> RngMPolElt?; ^ User error: bad syntax Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam240-23.fas.harvard.edu. (140.247.240.23) Time: Sun Mar 7 20:23:01 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-5); OK := MaximalOrder(K); I := (5*OK) + ((2+a)*OK); Factorizion(I); Output: Magma V2.10-6 Sun Mar 7 2004 20:22:57 on modular [Seed = 1971257310] ------------------------------------- >> Factorizion(I);; ^ User error: Identifier 'Factorizion' has not been declared or assigned Total time: 3.509 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam240-23.fas.harvard.edu. (140.247.240.23) Time: Sun Mar 7 20:23:29 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-5); OK := MaximalOrder(K); I := (5*OK) + ((2+a)*OK); Factorization(I); Output: Magma V2.10-6 Sun Mar 7 2004 20:23:26 on modular [Seed = 488019529] ------------------------------------- [] Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam240-23.fas.harvard.edu. (140.247.240.23) Time: Sun Mar 7 20:23:41 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-5); OK := MaximalOrder(K); I := (5*OK) + ((2+a)*OK); Factorization(I) Output: Magma V2.10-6 Sun Mar 7 2004 20:23:36 on modular [Seed = 201819982] ------------------------------------- [] Total time: 4.139 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam240-23.fas.harvard.edu. (140.247.240.23) Time: Sun Mar 7 20:23:46 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-5); OK := MaximalOrder(K); I := (5*OK) + ((2+a)*OK); Factorization(I) Output: Magma V2.10-6 Sun Mar 7 2004 20:23:43 on modular [Seed = 942912381] ------------------------------------- [] Total time: 2.879 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam240-23.fas.harvard.edu. (140.247.240.23) Time: Sun Mar 7 20:24:02 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-5); OK := MaximalOrder(K); I := (5*OK) + ((2+a)*OK); I; Output: Magma V2.10-6 Sun Mar 7 2004 20:23:59 on modular [Seed = 723558494] ------------------------------------- Principal Ideal of OK Generator: [1, 0] Total time: 3.029 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam240-23.fas.harvard.edu. (140.247.240.23) Time: Sun Mar 7 20:31:46 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-5); OK := MaximalOrder(K); I := 5*OK J := (2+a)*OK I; J; Output: Magma V2.10-6 Sun Mar 7 2004 20:31:43 on modular [Seed = 3485746027] ------------------------------------- >> J := (2+a)*OK ^ User error: bad syntax >> I; ^ User error: Identifier 'I' has not been declared or assigned >> J;; ^ User error: Identifier 'J' has not been declared or assigned Total time: 3.109 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam240-23.fas.harvard.edu. (140.247.240.23) Time: Sun Mar 7 20:32:03 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-5); OK := MaximalOrder(K); I := 5*OK; J := (2+a)*OK; I; J; Output: Magma V2.10-6 Sun Mar 7 2004 20:32:00 on modular [Seed = 4160518844] ------------------------------------- Principal Ideal of OK Generator: [5, 0] Principal Ideal of OK Generator: [1, 2] Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam240-23.fas.harvard.edu. (140.247.240.23) Time: Sun Mar 7 20:32:39 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-5); OK := MaximalOrder(K); I := 5*OK; J := (2+a)*OK; K := I+J; I; J; K; Output: Magma V2.10-6 Sun Mar 7 2004 20:32:36 on modular [Seed = 2526878713] ------------------------------------- Principal Ideal of OK Generator: [5, 0] Principal Ideal of OK Generator: [1, 2] Principal Ideal of OK Generator: [1, 0] Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Sun Mar 7 20:48:43 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-23); OK:=MaximalOrder(K); Discriminant(OK); Output: Magma V2.10-6 Sun Mar 7 2004 20:48:40 on modular [Seed = 2223969313] ------------------------------------- 92 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-154-147-143.wma.east.verizon.net. (141.154.147.143) Time: Sun Mar 7 20:58:50 2004 Input: log2 4-logx 16 Output: Magma V2.10-6 Sun Mar 7 2004 20:58:47 on modular [Seed = 1868889191] ------------------------------------- >> log2 4-logx 16; ^ User error: bad syntax Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam240-23.fas.harvard.edu. (140.247.240.23) Time: Sun Mar 7 22:36:25 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7x^4+3x^2-x+1); OK := MaximalOrder(K); I := (2)*OK; I; Output: Magma V2.10-6 Sun Mar 7 2004 22:36:22 on modular [Seed = 2290295510] ------------------------------------- >> K := NumberField(x^5+7x^4+3x^2-x+1); ^ User error: bad syntax >> OK := MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> I := (2)*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> I;; ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam240-23.fas.harvard.edu. (140.247.240.23) Time: Sun Mar 7 22:36:54 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); OK := MaximalOrder(K); I := (2)*OK; I; Output: Magma V2.10-6 Sun Mar 7 2004 22:36:50 on modular [Seed = 2274110909] ------------------------------------- Principal Ideal of OK Generator: [2, 0, 0, 0, 0] Total time: 3.129 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam240-23.fas.harvard.edu. (140.247.240.23) Time: Sun Mar 7 22:37:37 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); OK := MaximalOrder(K); I := (2)*OK; Factorization(I); Output: Magma V2.10-6 Sun Mar 7 2004 22:37:33 on modular [Seed = 1651099766] ------------------------------------- [ ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam240-23.fas.harvard.edu. (140.247.240.23) Time: Sun Mar 7 22:37:58 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); OK := MaximalOrder(K); I := (3)*OK; Factorization(I); Output: Magma V2.10-6 Sun Mar 7 2004 22:37:54 on modular [Seed = 2004671884] ------------------------------------- [ ] Total time: 3.799 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam240-23.fas.harvard.edu. (140.247.240.23) Time: Sun Mar 7 22:38:10 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); OK := MaximalOrder(K); I := (5)*OK; Factorization(I); Output: Magma V2.10-6 Sun Mar 7 2004 22:38:06 on modular [Seed = 1146089139] ------------------------------------- [ , , ] Total time: 4.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam240-23.fas.harvard.edu. (140.247.240.23) Time: Sun Mar 7 22:39:03 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); OK := MaximalOrder(K); Factorization((5)*OK); Output: Magma V2.10-6 Sun Mar 7 2004 22:38:59 on modular [Seed = 657231261] ------------------------------------- [ , , ] Total time: 4.049 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam240-23.fas.harvard.edu. (140.247.240.23) Time: Sun Mar 7 22:42:54 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); OK := MaximalOrder(K); p =: 5 Factorization((p)*OK); Output: Magma V2.10-6 Sun Mar 7 2004 22:42:50 on modular [Seed = 2695564147] ------------------------------------- >> p =: 5 ^ User error: bad syntax >> Factorization((p)*OK);; ^ User error: Identifier 'p' has not been declared or assigned Total time: 3.519 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam240-23.fas.harvard.edu. (140.247.240.23) Time: Sun Mar 7 22:43:10 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); OK := MaximalOrder(K); p := 5 Factorization((p)*OK); Output: Magma V2.10-6 Sun Mar 7 2004 22:43:06 on modular [Seed = 2998475025] ------------------------------------- >> Factorization((p)*OK);; ^ User error: bad syntax Total time: 4.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam240-23.fas.harvard.edu. (140.247.240.23) Time: Sun Mar 7 22:43:25 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); OK := MaximalOrder(K); p := 5; Factorization((p)*OK); Output: Magma V2.10-6 Sun Mar 7 2004 22:43:21 on modular [Seed = 2391090494] ------------------------------------- [ , , ] Total time: 3.719 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam240-23.fas.harvard.edu. (140.247.240.23) Time: Sun Mar 7 22:43:27 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); OK := MaximalOrder(K); p := 5; Factorization((p)*OK); Output: Magma V2.10-6 Sun Mar 7 2004 22:43:21 on modular [Seed = 2206738483] ------------------------------------- [ , , ] Total time: 3.849 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam240-23.fas.harvard.edu. (140.247.240.23) Time: Sun Mar 7 22:46:20 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); OK := MaximalOrder(K); procedure fz(p) Factorization((p)*OK); end procedure fz(2); fz(3); fz(5); fz(7); fz(11); Output: Magma V2.10-6 Sun Mar 7 2004 22:46:17 on modular [Seed = 1095429538] ------------------------------------- >> fz(2); ^ User error: bad syntax >> fz(3); ^ User error: Identifier 'fz' has not been declared or assigned >> fz(5); ^ User error: Identifier 'fz' has not been declared or assigned >> fz(7); ^ User error: Identifier 'fz' has not been declared or assigned >> fz(11);; ^ User error: Identifier 'fz' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam240-23.fas.harvard.edu. (140.247.240.23) Time: Sun Mar 7 22:46:50 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); OK := MaximalOrder(K); procedure fz(p) Factorization((p)*OK); end procedure; fz(2); fz(3); fz(5); fz(7); fz(11); Output: Magma V2.10-6 Sun Mar 7 2004 22:46:47 on modular [Seed = 1599402898] ------------------------------------- [ ] [ ] [ , , ] [ , ] [ , , , ] Total time: 3.049 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam240-23.fas.harvard.edu. (140.247.240.23) Time: Sun Mar 7 22:48:01 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); OK := MaximalOrder(K); procedure fz(p) p; Factorization((p)*OK); end procedure; fz(2); fz(3); fz(5); fz(7); fz(11); Output: Magma V2.10-6 Sun Mar 7 2004 22:47:58 on modular [Seed = 556436901] ------------------------------------- 2 [ ] 3 [ ] 5 [ , , ] 7 [ , ] 11 [ , , , ] Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam240-23.fas.harvard.edu. (140.247.240.23) Time: Sun Mar 7 22:56:00 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x^4+3*x^2-x+1); OK := MaximalOrder(K); procedure fz(p) p; Factorization((p)*OK); end procedure; fz(2); fz(3); fz(5); fz(7); fz(11); fz(13); fz(17); fz(19); fz(23); fz(29); fz(31); fz(37); fz(41); fz(43); fz(47); fz(53); fz(59); fz(61); fz(67); fz(71); fz(73); fz(79); fz(83); fz(89); fz(97); Output: Magma V2.10-6 Sun Mar 7 2004 22:55:57 on modular [Seed = 1565979643] ------------------------------------- 2 [ ] 3 [ ] 5 [ , , ] 7 [ , ] 11 [ , , , ] 13 [ , ] 17 [ , , ] 19 [ , , ] 23 [ , ] 29 [ , , ] 31 [ , , ] 37 [ ] 41 [ , ] 43 [ , , , ] 47 [ , ] 53 [ , ] 59 [ , ] 61 [ ] 67 [ , , , ] 71 [ , , , ] 73 [ ] 79 [ , ] 83 [ , , , ] 89 [ , ] 97 [ ] Total time: 3.319 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host n137.ryd.student.liu.se. (130.236.215.137) Time: Mon Mar 8 01:05:45 2004 Input: Factor(23409); Output: Magma V2.10-6 Mon Mar 8 2004 01:05:42 on modular [Seed = 2037724212] ------------------------------------- >> Factor(23409);; ^ Runtime error in 'Factor': Bad argument types Argument types given: RngIntElt Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-65-64-201-176.dsl.rcsntx.swbell.net. (65.64.201.176) Time: Mon Mar 8 01:50:41 2004 Input: 700 Output: Magma V2.10-6 Mon Mar 8 2004 01:50:37 on modular [Seed = 3721497184] ------------------------------------- 700 Total time: 3.819 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-65-64-201-176.dsl.rcsntx.swbell.net. (65.64.201.176) Time: Mon Mar 8 01:55:15 2004 Input: sevsn zero zero Output: Magma V2.10-6 Mon Mar 8 2004 01:55:12 on modular [Seed = 2054562475] ------------------------------------- >> sevsn zero zero; ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-65-64-201-176.dsl.rcsntx.swbell.net. (65.64.201.176) Time: Mon Mar 8 01:56:07 2004 Input: seven zero zero Output: Magma V2.10-6 Mon Mar 8 2004 01:56:04 on modular [Seed = 2998856631] ------------------------------------- >> seven zero zero; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-65-64-201-176.dsl.rcsntx.swbell.net. (65.64.201.176) Time: Mon Mar 8 01:56:36 2004 Input: nine one one Output: Magma V2.10-6 Mon Mar 8 2004 01:56:33 on modular [Seed = 3504114160] ------------------------------------- >> nine one one; ^ User error: bad syntax Total time: 3.539 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (196.12.46.41) Time: Mon Mar 8 02:33:43 2004 Input: help Output: Magma V2.10-6 Mon Mar 8 2004 02:33:35 on modular [Seed = 2290411841] ------------------------------------- >> help ^ User error: Identifier 'help' has not been declared or assigned Total time: 3.509 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host c-24-126-214-191.we.client2.attbi.com. (24.126.214.191) Time: Mon Mar 8 04:30:07 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Mon Mar 8 2004 04:30:03 on modular [Seed = 2796215210] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.659 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host n137.ryd.student.liu.se. (130.236.215.137) Time: Mon Mar 8 04:39:29 2004 Input: Factorize(27749); Output: Magma V2.10-6 Mon Mar 8 2004 04:39:26 on modular [Seed = 3368335262] ------------------------------------- >> Factorize(27749);; ^ User error: Identifier 'Factorize' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-66-137-204-37.dsl.stlsmo.swbell.net. (66.137.204.37) Time: Mon Mar 8 08:36:01 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Mon Mar 8 2004 08:35:56 on modular [Seed = 3165686325] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.170 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (134.147.19.204) Time: Mon Mar 8 09:02:37 2004 Input: 2+3= Output: Magma V2.10-6 Mon Mar 8 2004 09:02:32 on modular [Seed = 2998832755] ------------------------------------- >> ; ^ User error: bad syntax Total time: 4.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (134.147.19.204) Time: Mon Mar 8 09:02:39 2004 Input: 2+3= Output: Magma V2.10-6 Mon Mar 8 2004 09:02:34 on modular [Seed = 3082521460] ------------------------------------- >> ; ^ User error: bad syntax Total time: 3.769 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (134.147.19.204) Time: Mon Mar 8 09:02:40 2004 Input: 2+3= Output: Magma V2.10-6 Mon Mar 8 2004 09:02:35 on modular [Seed = 2829358186] ------------------------------------- >> ; ^ User error: bad syntax Total time: 3.689 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (134.147.19.204) Time: Mon Mar 8 09:03:00 2004 Input: 2+3; Output: Magma V2.10-6 Mon Mar 8 2004 09:02:55 on modular [Seed = 2340927165] ------------------------------------- 5 Total time: 4.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (134.147.19.204) Time: Mon Mar 8 09:03:02 2004 Input: 2+3; Output: Magma V2.10-6 Mon Mar 8 2004 09:02:58 on modular [Seed = 2173549738] ------------------------------------- 5 Total time: 3.259 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host r6c37.ad.uni-heidelberg.de. (129.206.111.137) Time: Mon Mar 8 11:15:06 2004 Input: F:=FiniteField(2); V:=VectorSpace(F,4); Output: Magma V2.10-6 Mon Mar 8 2004 11:15:03 on modular [Seed = 2020910132] ------------------------------------- Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host r6c37.ad.uni-heidelberg.de. (129.206.111.137) Time: Mon Mar 8 11:15:18 2004 Input: F:=FiniteField(2); V:=VectorSpace(F,4); V; Output: Magma V2.10-6 Mon Mar 8 2004 11:15:14 on modular [Seed = 218222932] ------------------------------------- Full Vector space of degree 4 over GF(2) Total time: 3.839 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host r6c37.ad.uni-heidelberg.de. (129.206.111.137) Time: Mon Mar 8 11:15:33 2004 Input: V; Output: Magma V2.10-6 Mon Mar 8 2004 11:15:30 on modular [Seed = 270322809] ------------------------------------- >> V;; ^ User error: Identifier 'V' has not been declared or assigned Total time: 3.809 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathdhcp41.ces.clemson.edu. (130.127.112.170) Time: Mon Mar 8 13:54:42 2004 Input: ? NullSpace; Output: Magma V2.10-6 Mon Mar 8 2004 13:54:38 on modular [Seed = 1229310073] ------------------------------------- 10 matches: 1 I /magma/module-lattice/general/homomorphisms/operation-element/\ Kernel 2 I /magma/module-lattice/mat/solution-equation/Nullspace 3 I /magma/module-lattice/mat/solution-equation/NullspaceMatrix 4 I /magma/module-lattice/mat/solution-equation/NullspaceOfTranspose 5 I /magma/module-lattice/smat/non-trivial/solution-equation/Nullspace 6 I /magma/module-lattice/smat/non-trivial/solution-equation/\ NullspaceMatrix 7 I /magma/module-lattice/smat/non-trivial/solution-equation/\ NullspaceOfTranspose 8 I /magma/module-lattice/vector-space-linear-transformation/\ linear-transformation/Kernel 9 I /magma/ring-field-algebra/matrix/homomorphism-element/Kernel 10 E /magma/module-lattice/mat/solution-equation/Example-Nullspace To view an entry, type ? followed by the number next to it Total time: 4.109 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host faema.Math.Berkeley.EDU. (169.229.58.25) Time: Mon Mar 8 13:55:29 2004 Input: ClassicalModularPolynomial(5); Output: Magma V2.10-6 Mon Mar 8 2004 13:55:25 on modular [Seed = 1684596135] ------------------------------------- $.1^6 - $.1^5*$.2^5 + 3720*$.1^5*$.2^4 - 4550940*$.1^5*$.2^3 + 2028551200*$.1^5*$.2^2 - 246683410950*$.1^5*$.2 + 1963211489280*$.1^5 + 3720*$.1^4*$.2^5 + 1665999364600*$.1^4*$.2^4 + 107878928185336800*$.1^4*$.2^3 + 383083609779811215375*$.1^4*$.2^2 + 128541798906828816384000*$.1^4*$.2 + 1284733132841424456253440*$.1^4 - 4550940*$.1^3*$.2^5 + 107878928185336800*$.1^3*$.2^4 - 441206965512914835246100*$.1^3*$.2^3 + 26898488858380731577417728000*$.1^3*$.2^2 - 192457934618928299655108231168000*$.1^3*$.2 + 280244777828439527804321565297868800*$.1^3 + 2028551200*$.1^2*$.2^5 + 383083609779811215375*$.1^2*$.2^4 + 26898488858380731577417728000*$.1^2*$.2\ ^3 + 5110941777552418083110765199360000*$.1^2*$.2^2 + 36554736583949629295706472332656640000*$.1^2*$.2 + 6692500042627997708487149415015068467200*$.1^2 - 246683410950*$.1*$.2^5 + 128541798906828816384000*$.1*$.2^4 - 192457934618928299655108231168000*$.1*\ $.2^3 + 36554736583949629295706472332656640000*$.1*$.2^2 - 264073457076620596259715790247978782949376*$.1*$.2 + 53274330803424425450420160273356509151232000*$.1 + $.2^6 + 1963211489280*$.2^5 + 1284733132841424456253440*$.2^4 + 280244777828439527804321565297868800*$.2^3 + 6692500042627997708487149415015068467200*$.2^2 + 53274330803424425450420160273356509151232000*$.2 + 141359947154721358697753474691071362751004672000 Total time: 3.019 seconds, Total memory usage: 2.78MB ************** MAGMA ***************** Host faema.Math.Berkeley.EDU. (169.229.58.25) Time: Mon Mar 8 13:56:58 2004 Input: ClassicalModularPolynomial(5) mod 144169; Output: Magma V2.10-6 Mon Mar 8 2004 13:56:55 on modular [Seed = 859812506] ------------------------------------- >> ClassicalModularPolynomial(5) mod 144169; ^ Runtime error in 'mod': Bad argument types Argument types given: RngMPolElt, RngMPolElt Total time: 3.059 seconds, Total memory usage: 2.78MB ************** MAGMA ***************** Host faema.Math.Berkeley.EDU. (169.229.58.25) Time: Mon Mar 8 13:57:21 2004 Input: ClassicalModularPolynomial(2); Output: Magma V2.10-6 Mon Mar 8 2004 13:57:17 on modular [Seed = 3721486222] ------------------------------------- $.1^3 - $.1^2*$.2^2 + 1488*$.1^2*$.2 - 162000*$.1^2 + 1488*$.1*$.2^2 + 40773375*$.1*$.2 + 8748000000*$.1 + $.2^3 - 162000*$.2^2 + 8748000000*$.2 - 157464000000000 Total time: 3.669 seconds, Total memory usage: 2.78MB ************** MAGMA ***************** Host 3(NXDOMAIN) (210.204.33.2) Time: Mon Mar 8 14:49:46 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Mon Mar 8 2004 14:49:39 on modular [Seed = 690333471] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (210.204.33.2) Time: Mon Mar 8 14:49:46 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Mon Mar 8 2004 14:49:40 on modular [Seed = 707175451] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.799 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (210.204.33.2) Time: Mon Mar 8 14:49:46 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Mon Mar 8 2004 14:49:37 on modular [Seed = 740336152] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.809 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Mon Mar 8 17:32:06 2004 Input: /*****************/ /*** APARTAT 2 ***/ /*****************/ /*Conjunt de matrius M2x2 sobre GF(4)*/ K:=GF(4); {i:i in K}; M:=MatrixRing(K,2); /*i*/ Mt:={m : m in M | (Trace(m) eq 0)}; /*ii*/ Mf:={m : m in M | m[1] eq m[2] }; /*iii*/ Mtf:= Mt meet Mf; /*iv*/ matrius:=[Random(M): i in [1..100000]]; #[m :m in matrius | m in Mt]; #[m :m in matrius | m in Mf]; #[m :m in matrius | m in Mtf]; Output: Magma V2.10-6 Mon Mar 8 2004 17:32:01 on modular [Seed = 3924123123] ------------------------------------- { 1, a, a^2, 0 } 24931 6304 1572 Total time: 4.419 seconds, Total memory usage: 6.95MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Mon Mar 8 17:36:43 2004 Input: K:=GF(4); {i:i in K}; M:=MatrixRing(K,2); Output: Magma V2.10-6 Mon Mar 8 2004 17:36:40 on modular [Seed = 1718276962] ------------------------------------- { 1, a, a^2, 0 } Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Mon Mar 8 17:38:41 2004 Input: P:=PolynomialRing(Integers()); [7^(3-i) : i in [1..3]]; x^(&+ e73); &+ [x^i:i in e73]; C:=GF(7^3); [ [a,b] : a,b in C|Evaluate(n73,a) eq Evaluate(t73,b)]; Output: Magma V2.10-6 Mon Mar 8 2004 17:38:38 on modular [Seed = 640324532] ------------------------------------- [ 49, 7, 1 ] >> x^(&+ e73); ^ User error: Identifier 'e73' has not been declared or assigned >> &+ [x^i:i in e73]; ^ User error: Identifier 'e73' has not been declared or assigned >> [ [a,b] : a,b in C|Evaluate(n73,a) eq Evaluate(t73,b)];; ^ User error: Identifier 'n73' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Mon Mar 8 17:40:52 2004 Input: P:=PolynomialRing(Integers()); e73:=[7^(3-i) : i in [1..3]]; x^(&+ e73); &+ [x^i:i in e73]; C:=GF(7^3); [ [a,b] : a,b in C|Evaluate(n73,a) eq Evaluate(t73,b)]; Output: Magma V2.10-6 Mon Mar 8 2004 17:40:49 on modular [Seed = 3671485655] ------------------------------------- x^57 x^49 + x^7 + x >> [ [a,b] : a,b in C|Evaluate(n73,a) eq Evaluate(t73,b)];; ^ User error: Identifier 'n73' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 134-236-ADSL.red.retevision.es. (80.224.236.134) Time: Mon Mar 8 17:42:04 2004 Input: P:=PolynomialRing(Integers()); e73:=[7^(3-i) : i in [1..3]]; n73:= x^(&+ e73); t73:= &+ [x^i:i in e73]; C:=GF(7^3); [ [a,b] : a,b in C|Evaluate(n73,a) eq Evaluate(t73,b)]; Output: Magma V2.10-6 Mon Mar 8 2004 17:41:57 on modular [Seed = 2946701670] ------------------------------------- [ [ 1, C.1 ], [ 1, C.1^2 ], [ 1, C.1^7 ], [ 1, C.1^10 ], [ 1, C.1^11 ], [ 1, C.1^14 ], [ 1, C.1^16 ], [ 1, C.1^25 ], [ 1, C.1^37 ], [ 1, C.1^49 ], [ 1, C.1^66 ], [ 1, C.1^70 ], [ 1, C.1^77 ], [ 1, C.1^87 ], [ 1, C.1^90 ], [ 1, C.1^97 ], [ 1, C.1^98 ], [ 1, C.1^100 ], [ 1, C.1^103 ], [ 1, C.1^112 ], [ 1, C.1^120 ], [ 1, C.1^131 ], [ 1, C.1^132 ], [ 1, C.1^137 ], [ 1, C.1^146 ], [ 1, C.1^148 ], [ 1, C.1^156 ], [ 1, C.1^159 ], [ 1, C.1^175 ], [ 1, C.1^195 ], [ 1, C.1^197 ], [ 1, C.1^199 ], [ 1, C.1^215 ], [ 1, C.1^233 ], [ 1, C.1^240 ], [ 1, C.1^259 ], [ 1, C.1^263 ], [ 1, C.1^267 ], [ 1, C.1^275 ], [ 1, 5 ], [ 1, C.1^288 ], [ 1, C.1^306 ], [ 1, C.1^307 ], [ 1, C.1^312 ], [ 1, C.1^314 ], [ 1, C.1^321 ], [ 1, C.1^337 ], [ 1, C.1^338 ], [ 1, C.1^339 ], [ C.1, 1 ], [ C.1, C.1^3 ], [ C.1, C.1^21 ], [ C.1, C.1^22 ], [ C.1, C.1^27 ], [ C.1, C.1^29 ], [ C.1, C.1^36 ], [ C.1, C.1^52 ], [ C.1, C.1^53 ], [ C.1, C.1^54 ], [ C.1, C.1^58 ], [ C.1, C.1^59 ], [ C.1, C.1^64 ], [ C.1, C.1^67 ], [ C.1, C.1^68 ], [ C.1, C.1^71 ], [ C.1, C.1^73 ], [ C.1, C.1^82 ], [ C.1, C.1^94 ], [ C.1, C.1^106 ], [ C.1, C.1^123 ], [ C.1, C.1^127 ], [ C.1, C.1^134 ], [ C.1, C.1^144 ], [ C.1, C.1^147 ], [ C.1, C.1^154 ], [ C.1, C.1^155 ], [ C.1, C.1^157 ], [ C.1, C.1^160 ], [ C.1, C.1^169 ], [ C.1, C.1^177 ], [ C.1, C.1^188 ], [ C.1, C.1^189 ], [ C.1, C.1^194 ], [ C.1, C.1^203 ], [ C.1, C.1^205 ], [ C.1, C.1^213 ], [ C.1, C.1^216 ], [ C.1, C.1^232 ], [ C.1, C.1^252 ], [ C.1, C.1^254 ], [ C.1, C.1^256 ], [ C.1, C.1^272 ], [ C.1, C.1^290 ], [ C.1, C.1^297 ], [ C.1, C.1^316 ], [ C.1, C.1^320 ], [ C.1, C.1^324 ], [ C.1, C.1^332 ], [ C.1^2, C.1^5 ], [ C.1^2, C.1^12 ], [ C.1^2, C.1^31 ], [ C.1^2, C.1^35 ], [ C.1^2, C.1^39 ], [ C.1^2, C.1^47 ], [ C.1^2, 3 ], [ C.1^2, C.1^60 ], [ C.1^2, C.1^78 ], [ C.1^2, C.1^79 ], [ C.1^2, C.1^84 ], [ C.1^2, C.1^86 ], [ C.1^2, C.1^93 ], [ C.1^2, C.1^109 ], [ C.1^2, C.1^110 ], [ C.1^2, C.1^111 ], [ C.1^2, C.1^115 ], [ C.1^2, C.1^116 ], [ C.1^2, C.1^121 ], [ C.1^2, C.1^124 ], [ C.1^2, C.1^125 ], [ C.1^2, C.1^128 ], [ C.1^2, C.1^130 ], [ C.1^2, C.1^139 ], [ C.1^2, C.1^151 ], [ C.1^2, C.1^163 ], [ C.1^2, C.1^180 ], [ C.1^2, C.1^184 ], [ C.1^2, C.1^191 ], [ C.1^2, C.1^201 ], [ C.1^2, C.1^204 ], [ C.1^2, C.1^211 ], [ C.1^2, C.1^212 ], [ C.1^2, C.1^214 ], [ C.1^2, C.1^217 ], [ C.1^2, C.1^226 ], [ C.1^2, C.1^234 ], [ C.1^2, C.1^245 ], [ C.1^2, C.1^246 ], [ C.1^2, C.1^251 ], [ C.1^2, C.1^260 ], [ C.1^2, C.1^262 ], [ C.1^2, C.1^270 ], [ C.1^2, C.1^273 ], [ C.1^2, C.1^289 ], [ C.1^2, C.1^309 ], [ C.1^2, C.1^311 ], [ C.1^2, C.1^313 ], [ C.1^2, C.1^329 ], [ C.1^3, C.1^4 ], [ C.1^3, C.1^24 ], [ C.1^3, C.1^26 ], [ C.1^3, C.1^28 ], [ C.1^3, C.1^44 ], [ C.1^3, C.1^62 ], [ C.1^3, C.1^69 ], [ C.1^3, C.1^88 ], [ C.1^3, C.1^92 ], [ C.1^3, C.1^96 ], [ C.1^3, C.1^104 ], [ C.1^3, 2 ], [ C.1^3, C.1^117 ], [ C.1^3, C.1^135 ], [ C.1^3, C.1^136 ], [ C.1^3, C.1^141 ], [ C.1^3, C.1^143 ], [ C.1^3, C.1^150 ], [ C.1^3, C.1^166 ], [ C.1^3, C.1^167 ], [ C.1^3, C.1^168 ], [ C.1^3, C.1^172 ], [ C.1^3, C.1^173 ], [ C.1^3, C.1^178 ], [ C.1^3, C.1^181 ], [ C.1^3, C.1^182 ], [ C.1^3, C.1^185 ], [ C.1^3, C.1^187 ], [ C.1^3, C.1^196 ], [ C.1^3, C.1^208 ], [ C.1^3, C.1^220 ], [ C.1^3, C.1^237 ], [ C.1^3, C.1^241 ], [ C.1^3, C.1^248 ], [ C.1^3, C.1^258 ], [ C.1^3, C.1^261 ], [ C.1^3, C.1^268 ], [ C.1^3, C.1^269 ], [ C.1^3, C.1^271 ], [ C.1^3, C.1^274 ], [ C.1^3, C.1^283 ], [ C.1^3, C.1^291 ], [ C.1^3, C.1^302 ], [ C.1^3, C.1^303 ], [ C.1^3, C.1^308 ], [ C.1^3, C.1^317 ], [ C.1^3, C.1^319 ], [ C.1^3, C.1^327 ], [ C.1^3, C.1^330 ], [ C.1^4, C.1^6 ], [ C.1^4, C.1^17 ], [ C.1^4, C.1^18 ], [ C.1^4, C.1^23 ], [ C.1^4, C.1^32 ], [ C.1^4, C.1^34 ], [ C.1^4, C.1^42 ], [ C.1^4, C.1^45 ], [ C.1^4, C.1^61 ], [ C.1^4, C.1^81 ], [ C.1^4, C.1^83 ], [ C.1^4, C.1^85 ], [ C.1^4, C.1^101 ], [ C.1^4, C.1^119 ], [ C.1^4, C.1^126 ], [ C.1^4, C.1^145 ], [ C.1^4, C.1^149 ], [ C.1^4, C.1^153 ], [ C.1^4, C.1^161 ], [ C.1^4, 6 ], [ C.1^4, C.1^174 ], [ C.1^4, C.1^192 ], [ C.1^4, C.1^193 ], [ C.1^4, C.1^198 ], [ C.1^4, C.1^200 ], [ C.1^4, C.1^207 ], [ C.1^4, C.1^223 ], [ C.1^4, C.1^224 ], [ C.1^4, C.1^225 ], [ C.1^4, C.1^229 ], [ C.1^4, C.1^230 ], [ C.1^4, C.1^235 ], [ C.1^4, C.1^238 ], [ C.1^4, C.1^239 ], [ C.1^4, C.1^242 ], [ C.1^4, C.1^244 ], [ C.1^4, C.1^253 ], [ C.1^4, C.1^265 ], [ C.1^4, C.1^277 ], [ C.1^4, C.1^294 ], [ C.1^4, C.1^298 ], [ C.1^4, C.1^305 ], [ C.1^4, C.1^315 ], [ C.1^4, C.1^318 ], [ C.1^4, C.1^325 ], [ C.1^4, C.1^326 ], [ C.1^4, C.1^328 ], [ C.1^4, C.1^331 ], [ C.1^4, C.1^340 ], [ C.1^5, C.1^9 ], [ C.1^5, C.1^13 ], [ C.1^5, C.1^20 ], [ C.1^5, C.1^30 ], [ C.1^5, C.1^33 ], [ C.1^5, C.1^40 ], [ C.1^5, C.1^41 ], [ C.1^5, C.1^43 ], [ C.1^5, C.1^46 ], [ C.1^5, C.1^55 ], [ C.1^5, C.1^63 ], [ C.1^5, C.1^74 ], [ C.1^5, C.1^75 ], [ C.1^5, C.1^80 ], [ C.1^5, C.1^89 ], [ C.1^5, C.1^91 ], [ C.1^5, C.1^99 ], [ C.1^5, C.1^102 ], [ C.1^5, C.1^118 ], [ C.1^5, C.1^138 ], [ C.1^5, C.1^140 ], [ C.1^5, C.1^142 ], [ C.1^5, C.1^158 ], [ C.1^5, C.1^176 ], [ C.1^5, C.1^183 ], [ C.1^5, C.1^202 ], [ C.1^5, C.1^206 ], [ C.1^5, C.1^210 ], [ C.1^5, C.1^218 ], [ C.1^5, 4 ], [ C.1^5, C.1^231 ], [ C.1^5, C.1^249 ], [ C.1^5, C.1^250 ], [ C.1^5, C.1^255 ], [ C.1^5, C.1^257 ], [ C.1^5, C.1^264 ], [ C.1^5, C.1^280 ], [ C.1^5, C.1^281 ], [ C.1^5, C.1^282 ], [ C.1^5, C.1^286 ], [ C.1^5, C.1^287 ], [ C.1^5, C.1^292 ], [ C.1^5, C.1^295 ], [ C.1^5, C.1^296 ], [ C.1^5, C.1^299 ], [ C.1^5, C.1^301 ], [ C.1^5, C.1^310 ], [ C.1^5, C.1^322 ], [ C.1^5, C.1^334 ], [ C.1^6, C.1 ], [ C.1^6, C.1^2 ], [ C.1^6, C.1^7 ], [ C.1^6, C.1^10 ], [ C.1^6, C.1^11 ], [ C.1^6, C.1^14 ], [ C.1^6, C.1^16 ], [ C.1^6, C.1^25 ], [ C.1^6, C.1^37 ], [ C.1^6, C.1^49 ], [ C.1^6, C.1^66 ], [ C.1^6, C.1^70 ], [ C.1^6, C.1^77 ], [ C.1^6, C.1^87 ], [ C.1^6, C.1^90 ], [ C.1^6, C.1^97 ], [ C.1^6, C.1^98 ], [ C.1^6, C.1^100 ], [ C.1^6, C.1^103 ], [ C.1^6, C.1^112 ], [ C.1^6, C.1^120 ], [ C.1^6, C.1^131 ], [ C.1^6, C.1^132 ], [ C.1^6, C.1^137 ], [ C.1^6, C.1^146 ], [ C.1^6, C.1^148 ], [ C.1^6, C.1^156 ], [ C.1^6, C.1^159 ], [ C.1^6, C.1^175 ], [ C.1^6, C.1^195 ], [ C.1^6, C.1^197 ], [ C.1^6, C.1^199 ], [ C.1^6, C.1^215 ], [ C.1^6, C.1^233 ], [ C.1^6, C.1^240 ], [ C.1^6, C.1^259 ], [ C.1^6, C.1^263 ], [ C.1^6, C.1^267 ], [ C.1^6, C.1^275 ], [ C.1^6, 5 ], [ C.1^6, C.1^288 ], [ C.1^6, C.1^306 ], [ C.1^6, C.1^307 ], [ C.1^6, C.1^312 ], [ C.1^6, C.1^314 ], [ C.1^6, C.1^321 ], [ C.1^6, C.1^337 ], [ C.1^6, C.1^338 ], [ C.1^6, C.1^339 ], [ C.1^7, 1 ], [ C.1^7, C.1^3 ], [ C.1^7, C.1^21 ], [ C.1^7, C.1^22 ], [ C.1^7, C.1^27 ], [ C.1^7, C.1^29 ], [ C.1^7, C.1^36 ], [ C.1^7, C.1^52 ], [ C.1^7, C.1^53 ], [ C.1^7, C.1^54 ], [ C.1^7, C.1^58 ], [ C.1^7, C.1^59 ], [ C.1^7, C.1^64 ], [ C.1^7, C.1^67 ], [ C.1^7, C.1^68 ], [ C.1^7, C.1^71 ], [ C.1^7, C.1^73 ], [ C.1^7, C.1^82 ], [ C.1^7, C.1^94 ], [ C.1^7, C.1^106 ], [ C.1^7, C.1^123 ], [ C.1^7, C.1^127 ], [ C.1^7, C.1^134 ], [ C.1^7, C.1^144 ], [ C.1^7, C.1^147 ], [ C.1^7, C.1^154 ], [ C.1^7, C.1^155 ], [ C.1^7, C.1^157 ], [ C.1^7, C.1^160 ], [ C.1^7, C.1^169 ], [ C.1^7, C.1^177 ], [ C.1^7, C.1^188 ], [ C.1^7, C.1^189 ], [ C.1^7, C.1^194 ], [ C.1^7, C.1^203 ], [ C.1^7, C.1^205 ], [ C.1^7, C.1^213 ], [ C.1^7, C.1^216 ], [ C.1^7, C.1^232 ], [ C.1^7, C.1^252 ], [ C.1^7, C.1^254 ], [ C.1^7, C.1^256 ], [ C.1^7, C.1^272 ], [ C.1^7, C.1^290 ], [ C.1^7, C.1^297 ], [ C.1^7, C.1^316 ], [ C.1^7, C.1^320 ], [ C.1^7, C.1^324 ], [ C.1^7, C.1^332 ], [ C.1^8, C.1^5 ], [ C.1^8, C.1^12 ], [ C.1^8, C.1^31 ], [ C.1^8, C.1^35 ], [ C.1^8, C.1^39 ], [ C.1^8, C.1^47 ], [ C.1^8, 3 ], [ C.1^8, C.1^60 ], [ C.1^8, C.1^78 ], [ C.1^8, C.1^79 ], [ C.1^8, C.1^84 ], [ C.1^8, C.1^86 ], [ C.1^8, C.1^93 ], [ C.1^8, C.1^109 ], [ C.1^8, C.1^110 ], [ C.1^8, C.1^111 ], [ C.1^8, C.1^115 ], [ C.1^8, C.1^116 ], [ C.1^8, C.1^121 ], [ C.1^8, C.1^124 ], [ C.1^8, C.1^125 ], [ C.1^8, C.1^128 ], [ C.1^8, C.1^130 ], [ C.1^8, C.1^139 ], [ C.1^8, C.1^151 ], [ C.1^8, C.1^163 ], [ C.1^8, C.1^180 ], [ C.1^8, C.1^184 ], [ C.1^8, C.1^191 ], [ C.1^8, C.1^201 ], [ C.1^8, C.1^204 ], [ C.1^8, C.1^211 ], [ C.1^8, C.1^212 ], [ C.1^8, C.1^214 ], [ C.1^8, C.1^217 ], [ C.1^8, C.1^226 ], [ C.1^8, C.1^234 ], [ C.1^8, C.1^245 ], [ C.1^8, C.1^246 ], [ C.1^8, C.1^251 ], [ C.1^8 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Mar 8 18:09:49 2004 Input: P := PolynomialRing(RationalField()); P := PolynomialRing(P); F := FunctionField(y^3 - x^4); Output: Magma V2.10-6 Mon Mar 8 2004 18:09:46 on modular [Seed = 3115648131] ------------------------------------- Total time: 3.199 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Mar 8 18:10:06 2004 Input: P := PolynomialRing(RationalField()); P := PolynomialRing(P); F := FunctionField(x^3 - x^4); Output: Magma V2.10-6 Mon Mar 8 2004 18:10:02 on modular [Seed = 3587795103] ------------------------------------- >> F := FunctionField(x^3 - x^4);; ^ Runtime error in 'FunctionField': Bad coefficient ring for polynomial Total time: 4.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Mar 8 18:10:23 2004 Input: P := PolynomialRing(RationalField()); P := PolynomialRing(P); F := FunctionField(x^3 - x^4, y); Output: Magma V2.10-6 Mon Mar 8 2004 18:10:20 on modular [Seed = 3890961083] ------------------------------------- >> F := FunctionField(x^3 - x^4, y);; ^ Runtime error in 'FunctionField': Bad argument types Argument types given: RngUPolElt, RngUPolElt Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Mar 8 18:10:34 2004 Input: P := PolynomialRing(RationalField()); P := PolynomialRing(P); F := FunctionField(x^3 - y^4); Output: Magma V2.10-6 Mon Mar 8 2004 18:10:31 on modular [Seed = 4143598494] ------------------------------------- Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Mar 8 18:10:44 2004 Input: P := PolynomialRing(RationalField()); P := PolynomialRing(P); F := FunctionField(x^3 - y^4); F; Output: Magma V2.10-6 Mon Mar 8 2004 18:10:41 on modular [Seed = 34520946] ------------------------------------- Algebraic function field defined over Univariate rational function field over Rational Field by -y^4 + x^3 Total time: 3.659 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Mar 8 18:13:08 2004 Input: P := PolynomialRing(RationalField()); K := NumberField(x^3 -x+2); Output: Magma V2.10-6 Mon Mar 8 2004 18:13:05 on modular [Seed = 1617747552] ------------------------------------- Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Mar 8 18:13:48 2004 Input: P := PolynomialRing(RationalField()); K := NumberField(x^3 -x+2); Q := PolynomialRing(K); Q; Output: Magma V2.10-6 Mon Mar 8 2004 18:13:44 on modular [Seed = 2138292566] ------------------------------------- Univariate Polynomial Ring in y over K Total time: 3.509 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Mar 8 18:14:02 2004 Input: P := PolynomialRing(RationalField()); K := NumberField(x^3 -x+2); Q := PolynomialRing(K, 2); Q; Output: Magma V2.10-6 Mon Mar 8 2004 18:13:59 on modular [Seed = 2426154662] ------------------------------------- Polynomial ring of rank 2 over K Lexicographical Order Variables: y, a Total time: 3.479 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Mar 8 18:14:18 2004 Input: P := PolynomialRing(RationalField()); K := NumberField(x^3 -x+2); Q := PolynomialRing(K, 4); Q; Output: Magma V2.10-6 Mon Mar 8 2004 18:14:14 on modular [Seed = 2779323362] ------------------------------------- Polynomial ring of rank 4 over K Lexicographical Order Variables: y, a, b, c Total time: 4.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Mar 8 18:15:19 2004 Input: P := PolynomialRing(RationalField()); K := NumberField(x^3 -x+2); Q := PolynomialRing(K, 4); k:=(1/2)* (a +b*d + c*d^2); Output: Magma V2.10-6 Mon Mar 8 2004 18:15:16 on modular [Seed = 3637798493] ------------------------------------- Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Mar 8 18:15:42 2004 Input: P := PolynomialRing(RationalField()); K := NumberField(x^3 -x+2); Q := PolynomialRing(K, 4); k:=(1/2)* (a +b*d + c*d^2); MinimalPolynomial(k); Output: Magma V2.10-6 Mon Mar 8 2004 18:15:39 on modular [Seed = 4024652149] ------------------------------------- >> MinimalPolynomial(k);; ^ Runtime error in 'MinimalPolynomial': Bad argument types Argument types given: RngMPolElt Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Mar 8 18:19:16 2004 Input: P := PolynomialRing(RationalField()); K := NumberField(x^3 -x+2); Q := PolynomialRing(K); elt; Output: Magma V2.10-6 Mon Mar 8 2004 18:19:13 on modular [Seed = 2340893944] ------------------------------------- >> elt;; ^ User error: Identifier 'a' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Mar 8 18:20:11 2004 Input: P := PolynomialRing(RationalField()); K := NumberField(x^3 -x+2); Q := PolynomialRing(K); a; elt; Output: Magma V2.10-6 Mon Mar 8 2004 18:20:07 on modular [Seed = 3015642134] ------------------------------------- >> a; ^ User error: Identifier 'a' has not been declared or assigned >> elt;; ^ User error: Identifier 'a' has not been declared or assigned Total time: 3.539 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Mar 8 18:20:22 2004 Input: P := PolynomialRing(RationalField()); K := NumberField(x^3 -x+2); Q := PolynomialRing(K); a := a; elt; Output: Magma V2.10-6 Mon Mar 8 2004 18:20:18 on modular [Seed = 3268312434] ------------------------------------- >> a := a; ^ User error: Identifier 'a' has not been declared or assigned >> elt;; ^ User error: Identifier 'a' has not been declared or assigned Total time: 3.859 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Mar 8 18:37:46 2004 Input: P := PolynomialRing(RationalField()); K := NumberField(x^3 -x+2); Q := PolynomialRing(K, 4); Q; Output: Magma V2.10-6 Mon Mar 8 2004 18:37:43 on modular [Seed = 1634476707] ------------------------------------- Polynomial ring of rank 4 over K Lexicographical Order Variables: y, a, b, c Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Mar 8 18:38:29 2004 Input: P := PolynomialRing(RationalField()); K := NumberField(x^3 -x+2); Q := PolynomialRing(K, 4); Q; CharacteristicPolynomial(a); Output: Magma V2.10-6 Mon Mar 8 2004 18:38:25 on modular [Seed = 2190459254] ------------------------------------- Polynomial ring of rank 4 over K Lexicographical Order Variables: y, a, b, c >> CharacteristicPolynomial(a);; ^ Runtime error in 'CharacteristicPolynomial': Bad argument types Argument types given: RngMPolElt Total time: 3.539 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Mar 8 18:41:04 2004 Input: P := PolynomialRing(RationalField()); K := NumberField(x^3 -x+2); Q := PolynomialRing(K, 4); Q; $.1; Output: Magma V2.10-6 Mon Mar 8 2004 18:41:01 on modular [Seed = 3485633351] ------------------------------------- Polynomial ring of rank 4 over K Lexicographical Order Variables: y, a, b, c >> $.1;; ^ Runtime error: Bad dollar structure Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Mar 8 18:53:05 2004 Input: k=MOD(x, x^2-2) k^2 Output: Magma V2.10-6 Mon Mar 8 2004 18:53:01 on modular [Seed = 1364989451] ------------------------------------- >> k^2; ^ User error: bad syntax Total time: 3.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Mar 8 19:37:20 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3-x+2); OK:=MaximalOrder(K); MinimalPolynomial(1/2); MinimalPolynomial(a/2); Output: Magma V2.10-6 Mon Mar 8 2004 19:37:17 on modular [Seed = 2476655139] ------------------------------------- x - 1/2 x^3 - 1/4*x + 1/4 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Mar 8 19:38:56 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3-x+2); OK:=MaximalOrder(K); MinimalPolynomial(1/2); MinimalPolynomial(a/2); MinimalPolynomial(a^2/2); MinimalPolynomial((1+a)/2); MinimalPolynomial((1+a^2)/2); MinimalPolynomial((a+a^2)/2); MinimalPolynomial((1+a+a^2)/2); Output: Magma V2.10-6 Mon Mar 8 2004 19:38:51 on modular [Seed = 3268382932] ------------------------------------- x - 1/2 x^3 - 1/4*x + 1/4 x^3 - x^2 + 1/4*x - 1/2 x^3 - 3/2*x^2 + 1/2*x + 1/4 x^3 - 5/2*x^2 + 2*x - 1 x^3 - x^2 + 3/2*x - 1/2 x^3 - 5/2*x^2 + 13/4*x - 13/8 Total time: 4.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Mon Mar 8 20:07:43 2004 Input: P := PolynomailRing(RationalField()); N := Numberfield(x^3 - x + 2); O := MaximalOrder(N); Discrimant(0); Output: Magma V2.10-6 Mon Mar 8 2004 20:07:40 on modular [Seed = 1313019523] ------------------------------------- >> P := PolynomailRing(RationalField()); ^ User error: Identifier 'PolynomailRing' has not been declared or assigned >> N := Numberfield(x^3 - x + 2); ^ User error: Identifier 'x' has not been declared or assigned >> O := MaximalOrder(N); ^ User error: Identifier 'N' has not been declared or assigned >> Discrimant(0);; ^ User error: Identifier 'Discrimant' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Mon Mar 8 20:07:55 2004 Input: P := PolynomialRing(RationalField()); N := Numberfield(x^3 - x + 2); O := MaximalOrder(N); Discrimant(0); Output: Magma V2.10-6 Mon Mar 8 2004 20:07:52 on modular [Seed = 2138187654] ------------------------------------- >> N := Numberfield(x^3 - x + 2); ^ User error: Identifier 'Numberfield' has not been declared or assigned >> O := MaximalOrder(N); ^ User error: Identifier 'N' has not been declared or assigned >> Discrimant(0);; ^ User error: Identifier 'Discrimant' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Mon Mar 8 20:08:08 2004 Input: P := PolynomialRing(RationalField()); N := NumberField(x^3 - x + 2); O := MaximalOrder(N); Discrimant(0); Output: Magma V2.10-6 Mon Mar 8 2004 20:08:04 on modular [Seed = 1818309769] ------------------------------------- >> Discrimant(0);; ^ User error: Identifier 'Discrimant' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Mon Mar 8 20:08:18 2004 Input: P := PolynomialRing(RationalField()); N := NumberField(x^3 - x + 2); O := MaximalOrder(N); Disc(0); Output: Magma V2.10-6 Mon Mar 8 2004 20:08:15 on modular [Seed = 2626798706] ------------------------------------- >> Disc(0);; ^ User error: Identifier 'Disc' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Mon Mar 8 20:08:57 2004 Input: P := PolynomialRing(RationalField()); N := NumberField(x^3 - x + 2); O := MaximalOrder(N); Discriminant(0); Output: Magma V2.10-6 Mon Mar 8 2004 20:08:55 on modular [Seed = 3115638927] ------------------------------------- >> Discriminant(0);; ^ Runtime error in 'Discriminant': Bad argument types Argument types given: FldPrElt Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Mon Mar 8 20:09:55 2004 Input: P := PolynomialRing(RationalField()); N := NumberField(x^3 - x + 2); O := MaximalOrder(N); Discriminant(N); Output: Magma V2.10-6 Mon Mar 8 2004 20:09:52 on modular [Seed = 2796290007] ------------------------------------- -104 Total time: 2.859 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Mon Mar 8 20:13:25 2004 Input: P := PolynomialRing(RationalField()); N := NumberField(x^3 - x + 2); O := MaximalOrder(N); Discriminant(N); Discriminant(x^3 - x + 2); Output: Magma V2.10-6 Mon Mar 8 2004 20:13:22 on modular [Seed = 3351944676] ------------------------------------- -104 -104 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Mon Mar 8 20:18:44 2004 Input: P := PolynomialRing(RationalField()); N := NumberField(x^3 - x + 2); O := MaximalOrder(N); Discriminant(N); Discriminant(x^3 - x + 2); P := PolynomialRing(P); Output: Magma V2.10-6 Mon Mar 8 2004 20:18:41 on modular [Seed = 4193559193] ------------------------------------- -104 -104 >> P := PolynomialRing(P);; ^ User error: bad syntax Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Mar 8 20:44:36 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^3-x+2); OK:=MaximalOrder(K); I:=ideal< OK |2, y>; IsPrinciple(I); Output: Magma V2.10-6 Mon Mar 8 2004 20:44:33 on modular [Seed = 2846148666] ------------------------------------- >> IsPrinciple(I);; ^ User error: Identifier 'IsPrinciple' has not been declared or assigned Total time: 3.259 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Mar 8 20:44:50 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^3-x+2); OK:=MaximalOrder(K); I:=ideal< OK |2, y>; IsPrincipal(I); Output: Magma V2.10-6 Mon Mar 8 2004 20:44:47 on modular [Seed = 3587748936] ------------------------------------- true Total time: 3.289 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Mar 8 20:45:04 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^3-x+2); OK:=MaximalOrder(K); I:=ideal< OK |2, 1+y>; IsPrincipal(I); Output: Magma V2.10-6 Mon Mar 8 2004 20:45:01 on modular [Seed = 3402083141] ------------------------------------- true Total time: 3.259 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Mar 8 20:45:56 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^3-x+2); OK:=MaximalOrder(K); I:=ideal< OK |2, 1+y>; Generators(I); Output: Magma V2.10-6 Mon Mar 8 2004 20:45:53 on modular [Seed = 4126708790] ------------------------------------- [ [2, 0, 0], [1, 1, 0] ] Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Mar 8 20:46:22 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^3-x+2); OK:=MaximalOrder(K); I:=ideal< OK |2, 1+y>; Norm(I); Output: Magma V2.10-6 Mon Mar 8 2004 20:46:19 on modular [Seed = 3957754386] ------------------------------------- 2 Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Mon Mar 8 21:06:58 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-5,x^2+3] : Abs :=true); OK := MaximalOrder(K); O := sub< OK | a,b>; I := ideal< O | 2, 1+a, 1+b>; Basis(I); Output: Magma V2.10-6 Mon Mar 8 2004 21:06:54 on modular [Seed = 3301548655] ------------------------------------- [ [2, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1] ] Total time: 4.069 seconds, Total memory usage: 1.96MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Mon Mar 8 21:07:14 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-5,x^2+3] : Abs :=true); OK := MaximalOrder(K); O := sub< OK | a,b>; I := ideal< O | 2, 1+a, 1+b> Basis(I) Output: Magma V2.10-6 Mon Mar 8 2004 21:07:11 on modular [Seed = 4076835880] ------------------------------------- >> Basis(I); ^ User error: bad syntax Total time: 2.989 seconds, Total memory usage: 1.96MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Mon Mar 8 21:07:26 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-5,x^2+3] : Abs :=true); OK := MaximalOrder(K); O := sub< OK | a,b>; I := ideal< O | 2, 1+a, 1+b> Output: Magma V2.10-6 Mon Mar 8 2004 21:07:21 on modular [Seed = 3874193450] ------------------------------------- Total time: 4.089 seconds, Total memory usage: 1.96MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Mon Mar 8 21:07:50 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-5,x^2+3] : Abs :=true); OK := MaximalOrder(K); O := sub< OK | a,b>; I := ideal< O | 2, 1+a, 1+b>; isPrincipal(I); Output: Magma V2.10-6 Mon Mar 8 2004 21:07:46 on modular [Seed = 521304571] ------------------------------------- >> isPrincipal(I); ^ User error: Identifier 'isPrincipal' has not been declared or assigned Total time: 3.529 seconds, Total memory usage: 1.96MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Mon Mar 8 21:07:59 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-5,x^2+3] : Abs :=true); OK := MaximalOrder(K); O := sub< OK | a,b>; I := ideal< O | 2, 1+a, 1+b>; IsPrincipal(I); Output: Magma V2.10-6 Mon Mar 8 2004 21:07:56 on modular [Seed = 235104484] ------------------------------------- false Total time: 3.059 seconds, Total memory usage: 1.96MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Mon Mar 8 21:08:14 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-5,x^2+3] : Abs :=true); OK := MaximalOrder(K); O := sub< OK | a,b>; I := ideal< O | 2, 1+a, 1+b>; Basis(I); Output: Magma V2.10-6 Mon Mar 8 2004 21:08:10 on modular [Seed = 1026578977] ------------------------------------- [ [2, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1] ] Total time: 3.359 seconds, Total memory usage: 1.96MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Mon Mar 8 21:08:34 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-5,x^2+3] : Abs :=true); OK := MaximalOrder(K); O := sub< OK | a,b>; I := ideal< O | 2, 1+a, 1+b>; Basis(I); 0 Output: Magma V2.10-6 Mon Mar 8 2004 21:08:31 on modular [Seed = 1398682714] ------------------------------------- [ [2, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1] ] 0 Total time: 2.959 seconds, Total memory usage: 1.96MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Mon Mar 8 21:08:45 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-5,x^2+3] : Abs :=true); OK := MaximalOrder(K); O := sub< OK | a,b>; I := ideal< O | 2, 1+a, 1+b>; Basis(I); O; Output: Magma V2.10-6 Mon Mar 8 2004 21:08:41 on modular [Seed = 1196040312] ------------------------------------- [ [2, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1] ] Transformation of OK Transformation Matrix: [1 0 0 0] [0 2 0 0] [0 0 2 0] [0 0 0 4] Total time: 3.179 seconds, Total memory usage: 1.96MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Mon Mar 8 21:09:30 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-5,x^2+3] : Abs :=true); OK := MaximalOrder(K); O := sub< OK | a,b>; I := ideal< O | 2, 1+a, 1+b>; Basis(I); Basis(O); Output: Magma V2.10-6 Mon Mar 8 2004 21:09:26 on modular [Seed = 1684603684] ------------------------------------- [ [2, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1] ] [ O.1, O.2, O.3, O.4 ] Total time: 4.139 seconds, Total memory usage: 1.96MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Mon Mar 8 21:10:59 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-5,x^2+3] : Abs :=true); OK := MaximalOrder(K); O := sub< OK | 1,a,b>; I := ideal< O | 2, 1+a, 1+b>; Basis(I); Basis(O); Output: Magma V2.10-6 Mon Mar 8 2004 21:10:56 on modular [Seed = 3098926878] ------------------------------------- [ [2, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1] ] [ O.1, O.2, O.3, O.4 ] Total time: 3.279 seconds, Total memory usage: 1.96MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Mon Mar 8 21:11:59 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-5,x^2+3] : Abs :=true); OK := MaximalOrder(K); O := sub< OK | 1,a,b>; I := ideal< O | 2, 1+a, 1+b>; Basis(I); Basis(O); O.4!K Output: Magma V2.10-6 Mon Mar 8 2004 21:11:56 on modular [Seed = 3418795057] ------------------------------------- [ [2, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1] ] [ O.1, O.2, O.3, O.4 ] >> O.4!K ^ Runtime error in '!': Illegal coercion Total time: 3.089 seconds, Total memory usage: 1.96MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Mon Mar 8 21:12:14 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-5,x^2+3] : Abs :=true); OK := MaximalOrder(K); O := sub< OK | 1,a,b>; I := ideal< O | 2, 1+a, 1+b>; Basis(I); Basis(O); K!O.4 Output: Magma V2.10-6 Mon Mar 8 2004 21:12:11 on modular [Seed = 3857220104] ------------------------------------- [ [2, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1] ] [ O.1, O.2, O.3, O.4 ] a*b - a - b - 3 Total time: 2.999 seconds, Total memory usage: 1.96MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Mon Mar 8 21:12:40 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-5,x^2+3] : Abs :=true); OK := MaximalOrder(K); O := sub< OK | 1,a,b>; I := ideal< O | 2, 1+a, 1+b>; Basis(I); Basis(O); K!O.3 Output: Magma V2.10-6 Mon Mar 8 2004 21:12:37 on modular [Seed = 521303837] ------------------------------------- [ [2, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1] ] [ O.1, O.2, O.3, O.4 ] b - 1 Total time: 2.989 seconds, Total memory usage: 1.96MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Mon Mar 8 21:13:09 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-5,x^2+3] : Abs :=true); OK := MaximalOrder(K); O := sub< OK | 1,a,b>; I := ideal< O | 2, 1+a, 1+b>; Basis(I); Basis(O); [K!b : b in Basis(O)]; Output: Magma V2.10-6 Mon Mar 8 2004 21:13:06 on modular [Seed = 876174353] ------------------------------------- [ [2, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1] ] [ O.1, O.2, O.3, O.4 ] [ 1, a - 1, b - 1, a*b - a - b - 3 ] Total time: 3.209 seconds, Total memory usage: 1.96MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Mon Mar 8 21:13:46 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-5,x^2+3] : Abs :=true); OK := MaximalOrder(K); O := sub< OK | 1,a,b>; I := ideal< O | 2, 1+a, 1+b>; Basis(I); Basis(O); [K!y : y in Basis(O)]; Output: Magma V2.10-6 Mon Mar 8 2004 21:13:43 on modular [Seed = 1381972498] ------------------------------------- [ [2, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1] ] [ O.1, O.2, O.3, O.4 ] [ 1, a - 1, b - 1, a*b - a - b - 3 ] Total time: 2.949 seconds, Total memory usage: 1.96MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Mon Mar 8 21:18:04 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-5,x^2+3] : Abs :=true); OK := MaximalOrder(K); O := sub< OK | 1,a,b>; I := ideal< O | 2, 1+a, 1+b>; [K!y : y in Basis(I)]; [K!y : y in Basis(O)]; Output: Magma V2.10-6 Mon Mar 8 2004 21:18:01 on modular [Seed = 3537877916] ------------------------------------- [ 2, a - 1, b - 1, a*b - a - b - 3 ] [ 1, a - 1, b - 1, a*b - a - b - 3 ] Total time: 3.029 seconds, Total memory usage: 1.96MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Mon Mar 8 21:20:45 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-5,x^2+3] : Abs :=true); OK := MaximalOrder(K); O := sub< OK | 1,a,b>; I := ideal< O | 2, 1+a, 1+b>; [K!y : y in MinimalBasis(I)]; [K!y : y in Basis(O)]; Output: Magma V2.10-6 Mon Mar 8 2004 21:20:41 on modular [Seed = 1868695182] ------------------------------------- >> [K!y : y in MinimalBasis(I)]; ^ Runtime error in 'MinimalBasis': Bad argument types Argument types given: RngOrdIdl [ 1, a - 1, b - 1, a*b - a - b - 3 ] Total time: 3.879 seconds, Total memory usage: 1.96MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Mon Mar 8 21:22:20 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-5,x^2+3] : Abs :=true); OK := MaximalOrder(K); O := sub< OK | 1,a,b>; I := ideal< O | 2, 1+a, 1+b>; [K!y : y in MinimalBasis(Module(I))]; [K!y : y in Basis(O)]; Output: Magma V2.10-6 Mon Mar 8 2004 21:22:16 on modular [Seed = 3065765110] ------------------------------------- >> [K!y : y in MinimalBasis(Module(I))]; ^ Runtime error in 'Module': The ideal must be of a relative order [ 1, a - 1, b - 1, a*b - a - b - 3 ] Total time: 4.049 seconds, Total memory usage: 1.96MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Mon Mar 8 21:23:17 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-5,x^2+3] : Abs :=true); OK := MaximalOrder(K); O := sub< OK | 1,a,b>; I := module< O | 2, 1+a, 1+b>; [K!y : y in MinimalBasis(I)]; [K!y : y in Basis(O)]; Output: Magma V2.10-6 Mon Mar 8 2004 21:23:13 on modular [Seed = 3318263628] ------------------------------------- >> I := module< O | 2, 1+a, 1+b>; ^ User error: bad syntax >> [K!y : y in MinimalBasis(I)]; ^ User error: Identifier 'I' has not been declared or assigned [ 1, a - 1, b - 1, a*b - a - b - 3 ] Total time: 3.609 seconds, Total memory usage: 1.96MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Mon Mar 8 21:26:40 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-5,x^2+3] : Abs :=true); OK := MaximalOrder(K); O := sub< OK | 1,a,b>; I := ideal< O | 2, 1+a, 1+b>; Norm(I); [K!y : y in Basis(I)]; Norm(O); [K!y : y in Basis(O)]; Norm(OK); Output: Magma V2.10-6 Mon Mar 8 2004 21:26:36 on modular [Seed = 1701318176] ------------------------------------- 2 [ 2, a - 1, b - 1, a*b - a - b - 3 ] >> Norm(O); ^ Runtime error in 'Norm': Bad argument types Argument types given: RngOrd [ 1, a - 1, b - 1, a*b - a - b - 3 ] >> Norm(OK); ^ Runtime error in 'Norm': Bad argument types Argument types given: RngOrd Total time: 3.509 seconds, Total memory usage: 1.96MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Mon Mar 8 21:28:06 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-5,x^2+3] : Abs :=true); OK := MaximalOrder(K); O := sub< OK | 1,a,b>; I := ideal< O | 2, 1+a, 1+b>; Index(O,I); Norm(I); [K!y : y in Basis(I)]; Discriminant(O); [K!y : y in Basis(O)]; Discriminant(OK); Output: Magma V2.10-6 Mon Mar 8 2004 21:28:03 on modular [Seed = 3065765148] ------------------------------------- 2 2 [ 2, a - 1, b - 1, a*b - a - b - 3 ] 57600 [ 1, a - 1, b - 1, a*b - a - b - 3 ] 225 Total time: 3.009 seconds, Total memory usage: 1.96MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Mon Mar 8 21:32:51 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-5,x^2+3] : Abs :=true); OK := MaximalOrder(K); O := sub< OK | 1,a,b>; I := ideal< O | 2, 1+a, 1+b>; Index(O,I); Norm(I); [K!y : y in Basis(I)]; Discriminant(O); [K!y : y in Basis(O)]; Discriminant(OK); Module(I); Output: Magma V2.10-6 Mon Mar 8 2004 21:32:48 on modular [Seed = 1599222677] ------------------------------------- 2 2 [ 2, a - 1, b - 1, a*b - a - b - 3 ] 57600 [ 1, a - 1, b - 1, a*b - a - b - 3 ] 225 >> Module(I); ^ Runtime error in 'Module': The ideal must be of a relative order Total time: 3.039 seconds, Total memory usage: 1.96MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Mon Mar 8 21:33:19 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-5,x^2+3] : Abs :=true); OK := MaximalOrder(K); O := sub< OK | 1,a,b>; I := ideal< O | 2, 1+a, 1+b>; Index(O,I); Norm(I); [K!y : y in Basis(I)]; Discriminant(O); [K!y : y in Basis(O)]; Discriminant(OK); Describe(I); Module(I); Output: Magma V2.10-6 Mon Mar 8 2004 21:33:16 on modular [Seed = 2054624908] ------------------------------------- 2 2 [ 2, a - 1, b - 1, a*b - a - b - 3 ] 57600 [ 1, a - 1, b - 1, a*b - a - b - 3 ] 225 >> Describe(I); ^ User error: Identifier 'Describe' has not been declared or assigned >> Module(I); ^ Runtime error in 'Module': The ideal must be of a relative order Total time: 3.389 seconds, Total memory usage: 1.96MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Mon Mar 8 21:35:41 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-5,x^2+3] : Abs :=true); OK := MaximalOrder(K); O := sub< OK | 1,a,b>; I := ideal< O | 2, 1+a, 1+b>; Index(O,I); Norm(I); [K!y : y in Basis(I)]; Discriminant(O); [K!y : y in Basis(O)]; Discriminant(OK); I; Module(I); Output: Magma V2.10-6 Mon Mar 8 2004 21:35:37 on modular [Seed = 2695744963] ------------------------------------- 2 2 [ 2, a - 1, b - 1, a*b - a - b - 3 ] 57600 [ 1, a - 1, b - 1, a*b - a - b - 3 ] 225 Ideal of O Basis: [2 0 0 0] [0 1 0 0] [0 0 1 0] [0 0 0 1] >> Module(I); ^ Runtime error in 'Module': The ideal must be of a relative order Total time: 3.389 seconds, Total memory usage: 1.96MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Mon Mar 8 21:42:56 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-5,x^2+3] : Abs :=true); OK := MaximalOrder(K); O := sub< OK | 1,a,b>; I := ideal< O | 2, 1+a, 1+b>; Index(O,I); Norm(I); [K!y : y in Basis(I)]; Discriminant(O); [K!y : y in Basis(O)]; Discriminant(OK); I; M := module; Output: Magma V2.10-6 Mon Mar 8 2004 21:42:53 on modular [Seed = 2290476990] ------------------------------------- 2 2 [ 2, a - 1, b - 1, a*b - a - b - 3 ] 57600 [ 1, a - 1, b - 1, a*b - a - b - 3 ] 225 Ideal of O Basis: [2 0 0 0] [0 1 0 0] [0 0 1 0] [0 0 0 1] >> M := module; ^ User error: bad syntax Total time: 3.049 seconds, Total memory usage: 1.96MB ************** MAGMA ***************** Host n137.ryd.student.liu.se. (130.236.215.137) Time: Mon Mar 8 21:43:01 2004 Input: Factorization(120987); Output: Magma V2.10-6 Mon Mar 8 2004 21:42:57 on modular [Seed = 3149321361] ------------------------------------- [ <3, 3>, <4481, 1> ] Total time: 4.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Mon Mar 8 21:44:57 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-5,x^2+3] : Abs :=true); OK := MaximalOrder(K); O := sub< OK | 1,a,b>; I := ideal< O | 2, 1+a, 1+b>; Index(O,I); Norm(I); [K!y : y in Basis(I)]; Discriminant(O); [K!y : y in Basis(O)]; Discriminant(OK); I; M := sub; Output: Magma V2.10-6 Mon Mar 8 2004 21:44:54 on modular [Seed = 3335235963] ------------------------------------- 2 2 [ 2, a - 1, b - 1, a*b - a - b - 3 ] 57600 [ 1, a - 1, b - 1, a*b - a - b - 3 ] 225 Ideal of O Basis: [2 0 0 0] [0 1 0 0] [0 0 1 0] [0 0 0 1] >> M := sub; ^ Runtime error in 'Module': Order must be over a maximal order Total time: 3.149 seconds, Total memory usage: 1.96MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Mon Mar 8 21:45:12 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-5,x^2+3] : Abs :=true); OK := MaximalOrder(K); O := sub< OK | 1,a,b>; I := ideal< O | 2, 1+a, 1+b>; Index(O,I); Norm(I); [K!y : y in Basis(I)]; Discriminant(O); [K!y : y in Basis(O)]; Discriminant(OK); I; M := sub; Output: Magma V2.10-6 Mon Mar 8 2004 21:45:09 on modular [Seed = 3907356486] ------------------------------------- 2 2 [ 2, a - 1, b - 1, a*b - a - b - 3 ] 57600 [ 1, a - 1, b - 1, a*b - a - b - 3 ] 225 Ideal of O Basis: [2 0 0 0] [0 1 0 0] [0 0 1 0] [0 0 0 1] >> M := sub; ^ Runtime error in 'Module': Order must be over a maximal order Total time: 3.029 seconds, Total memory usage: 1.96MB ************** MAGMA ***************** Host n137.ryd.student.liu.se. (130.236.215.137) Time: Mon Mar 8 21:52:35 2004 Input: A:=183644927970493652379520199612371016129808623765435978928547447812355498393276408815934661940916727725; B:=142414307082626392761681182176265269658295385675644646459146500411279307831593316369809671305509521267; p:=54013058863727113968017564276782484149501; E:=ChangeRing(EllipticCurve([A,B]),GF(p)); print(E); go:=Order(E); Factorization(go); Output: Magma V2.10-6 Mon Mar 8 2004 21:52:22 on modular [Seed = 3721440423] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 14511341764480564502293333972121876454443\ *x + 11518630941026512440284437665874699584349 over GF(54013058863727113968017564276782484149501) [ <2, 4>, <3, 3>, <13, 2>, <19, 1>, <37, 1>, <193, 1>, <223, 1>, <431, 1>, <1619, 1>, <3259, 1>, <101111, 1>, <410411, 1>, <259110461, 1> ] Total time: 12.239 seconds, Total memory usage: 3.48MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Mon Mar 8 22:22:17 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+23); OK := MaximalOrder(K); I:=ideal; quot; Output: Magma V2.10-6 Mon Mar 8 2004 22:22:13 on modular [Seed = 84442432] ------------------------------------- >> quot;; ^ User error: bad syntax Total time: 3.439 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Mon Mar 8 22:22:33 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+23); OK := MaximalOrder(K); I:=ideal; I; Output: Magma V2.10-6 Mon Mar 8 2004 22:22:29 on modular [Seed = 1920928295] ------------------------------------- Ideal of OK Two element generators: [2, 0] [0, 2] Total time: 3.629 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Mon Mar 8 22:23:36 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+23); OK := MaximalOrder(K); I:=ideal; I; Output: Magma V2.10-6 Mon Mar 8 2004 22:23:33 on modular [Seed = 2746145590] ------------------------------------- Ideal of OK Two element generators: [2, 0] [0, 1] Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Mon Mar 8 22:30:58 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+23); OK := MaximalOrder(K); I:=ideal; quo; Output: Magma V2.10-6 Mon Mar 8 2004 22:30:55 on modular [Seed = 2391012544] ------------------------------------- >> quo;; ^ Runtime error: No constructor provided for this type of object Total time: 3.189 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Mon Mar 8 22:31:12 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+23); OK := MaximalOrder(K); I:=ideal; quo; Output: Magma V2.10-6 Mon Mar 8 2004 22:31:08 on modular [Seed = 3857227704] ------------------------------------- Quotient Ring of Ideal of OK Two element generators: [2, 0] [0, 1] Mapping from: RngOrd: OK to Quotient Ring of I Total time: 4.159 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Mon Mar 8 22:31:58 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+23); OK := MaximalOrder(K); I:=ideal; Factorization(I); Output: Magma V2.10-6 Mon Mar 8 2004 22:31:54 on modular [Seed = 3268393033] ------------------------------------- [ ] Total time: 3.239 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Mon Mar 8 22:32:49 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+23); OK := MaximalOrder(K); I:=ideal; #quo; Output: Magma V2.10-6 Mon Mar 8 2004 22:32:46 on modular [Seed = 673534676] ------------------------------------- 2 Total time: 2.989 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Mon Mar 8 22:38:45 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+23); OK := MaximalOrder(K); I:=ideal; J:=2*I #quo; Output: Magma V2.10-6 Mon Mar 8 2004 22:38:41 on modular [Seed = 3807354497] ------------------------------------- >> #quo;; ^ User error: bad syntax Total time: 3.889 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Mon Mar 8 22:38:55 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+23); OK := MaximalOrder(K); I:=ideal; J:=2*I; #quo; Output: Magma V2.10-6 Mon Mar 8 2004 22:38:51 on modular [Seed = 4007891591] ------------------------------------- 8 Total time: 3.549 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Mon Mar 8 22:39:54 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+23); OK := MaximalOrder(K); I:=ideal; J:=ideal; #quo; Output: Magma V2.10-6 Mon Mar 8 2004 22:39:49 on modular [Seed = 3554586484] ------------------------------------- 3 Total time: 4.039 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Mon Mar 8 22:42:40 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+23); OK := MaximalOrder(K); I:=ideal; J:=ideal; #quo; Output: Magma V2.10-6 Mon Mar 8 2004 22:42:37 on modular [Seed = 2746146477] ------------------------------------- 1 Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Mon Mar 8 22:43:00 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+23); OK := MaximalOrder(K); J:=ideal; #quo; Output: Magma V2.10-6 Mon Mar 8 2004 22:42:57 on modular [Seed = 2240346343] ------------------------------------- 1 Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Mon Mar 8 22:43:14 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+23); OK := MaximalOrder(K); J:=ideal; #quo; Output: Magma V2.10-6 Mon Mar 8 2004 22:43:11 on modular [Seed = 3790380173] ------------------------------------- 3 Total time: 3.079 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Mon Mar 8 22:44:47 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+23); OK := MaximalOrder(K); J:=ideal; #quo; Output: Magma V2.10-6 Mon Mar 8 2004 22:44:44 on modular [Seed = 168261506] ------------------------------------- 8 Total time: 3.439 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Mon Mar 8 22:44:58 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+23); OK := MaximalOrder(K); J:=ideal; #quo; Output: Magma V2.10-6 Mon Mar 8 2004 22:44:55 on modular [Seed = 420766858] ------------------------------------- 2 Total time: 2.969 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Mon Mar 8 22:45:31 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+23); OK := MaximalOrder(K); J:=ideal; #quo; Output: Magma V2.10-6 Mon Mar 8 2004 22:45:27 on modular [Seed = 2037646474] ------------------------------------- 4 Total time: 4.069 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Mon Mar 8 23:04:30 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+23); OK := MaximalOrder(K); I:2*OK; Factorization(I); Output: Magma V2.10-6 Mon Mar 8 2004 23:04:26 on modular [Seed = 3048781785] ------------------------------------- >> I:2*OK; ^ User error: bad syntax >> Factorization(I);; ^ User error: Identifier 'I' has not been declared or assigned Total time: 4.169 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Mon Mar 8 23:04:41 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+23); OK := MaximalOrder(K); I:=2*OK; Factorization(I); Output: Magma V2.10-6 Mon Mar 8 2004 23:04:38 on modular [Seed = 2274002423] ------------------------------------- [ , ] Total time: 2.959 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Mon Mar 8 23:07:16 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+23); OK := MaximalOrder(K); for p in [1..8] do if IsPrime(p) then p; I := p * OK; Factorization(I); end if; end for; Output: Magma V2.10-6 Mon Mar 8 2004 23:07:12 on modular [Seed = 707209469] ------------------------------------- 2 [ , ] 3 [ , ] 5 [ ] 7 [ ] Total time: 4.129 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Mon Mar 8 23:13:24 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+23); OK := MaximalOrder(K); I:=ideal; Output: Magma V2.10-6 Mon Mar 8 2004 23:13:20 on modular [Seed = 4093573045] ------------------------------------- Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Mon Mar 8 23:14:18 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+23); OK := MaximalOrder(K); I:=ideal; #quo; Output: Magma V2.10-6 Mon Mar 8 2004 23:14:15 on modular [Seed = 690236822] ------------------------------------- 2 Total time: 2.899 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Mon Mar 8 23:16:41 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+23); OK := MaximalOrder(K); I:=ideal; #quo; Output: Magma V2.10-6 Mon Mar 8 2004 23:16:38 on modular [Seed = 1868720737] ------------------------------------- 3 Total time: 3.559 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Mon Mar 8 23:19:58 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+23); OK := MaximalOrder(K); I:=ideal; #quo; Output: Magma V2.10-6 Mon Mar 8 2004 23:19:54 on modular [Seed = 4007914284] ------------------------------------- 3 Total time: 4.169 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Mon Mar 8 23:20:38 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+23); OK := MaximalOrder(K); I:=ideal; #quo; Output: Magma V2.10-6 Mon Mar 8 2004 23:20:35 on modular [Seed = 3451964406] ------------------------------------- 2 Total time: 2.959 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam159-81.student.harvard.edu. (140.247.159.81) Time: Mon Mar 8 23:21:20 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+23); OK := MaximalOrder(K); I:=ideal; #quo; Output: Magma V2.10-6 Mon Mar 8 2004 23:21:16 on modular [Seed = 707210303] ------------------------------------- 2 Total time: 3.769 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 9 01:27:34 2004 Input: R:=PolynomialRing(RationalField()); K:= NumberField(x^3+x^2-2*x+8); OK:=MaximalOrder(K); E:=EquationOrder(K); Index[OK : E]; Output: Magma V2.10-6 Tue Mar 9 2004 01:27:30 on modular [Seed = 3318277678] ------------------------------------- >> Index[OK : E];; ^ User error: bad syntax Total time: 3.499 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 9 01:27:46 2004 Input: R:=PolynomialRing(RationalField()); K:= NumberField(x^3+x^2-2*x+8); OK:=MaximalOrder(K); E:=EquationOrder(K); Index(OK : E); Output: Magma V2.10-6 Tue Mar 9 2004 01:27:42 on modular [Seed = 826020565] ------------------------------------- >> Index(OK : E);; ^ Runtime error in 'Index': Bad argument types Argument types given: RngOrd Total time: 3.419 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 9 01:27:56 2004 Input: R:=PolynomialRing(RationalField()); K:= NumberField(x^3+x^2-2*x+8); OK:=MaximalOrder(K); E:=EquationOrder(K); Index(OK, E); Output: Magma V2.10-6 Tue Mar 9 2004 01:27:53 on modular [Seed = 539821043] ------------------------------------- 2 Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 9 01:29:41 2004 Input: R:=PolynomialRing(RationalField()); K:= NumberField(x^4-34*x^2+9); OK:=MaximalOrder(K); E:=EquationOrder(K); Index(OK, E); Output: Magma V2.10-6 Tue Mar 9 2004 01:29:37 on modular [Seed = 2004505372] ------------------------------------- 24 Total time: 3.889 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 9 01:33:36 2004 Input: R:=PolynomialRing(RationalField()); K:= NumberField(x^4-34*x^2+9); OK:=MaximalOrder(K); E:=EquationOrder(K); Index(OK, E); [K!OK.i : i in [1, 2, 3, 4]]; [K!E.i : i in [1, 2, 3, 4]]; Output: Magma V2.10-6 Tue Mar 9 2004 01:33:32 on modular [Seed = 4143698928] ------------------------------------- 24 [ 1, a, 1/2*(a^2 + 1), 1/12*(a^3 + 3*a^2 + 11*a + 9) ] [ 1, a, a^2, a^3 ] Total time: 3.939 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 9 01:35:03 2004 Input: R:=PolynomialRing(RationalField()); K:= NumberField(x^4-34*x^2+9); OK:=MaximalOrder(K); E:=EquationOrder(K); O:=sub; Index(OK,O); Index(OK, E); [K!OK.i : i in [1, 2, 3, 4]]; [K!E.i : i in [1, 2, 3, 4]]; Output: Magma V2.10-6 Tue Mar 9 2004 01:34:59 on modular [Seed = 3335250799] ------------------------------------- 6 24 [ 1, a, 1/2*(a^2 + 1), 1/12*(a^3 + 3*a^2 + 11*a + 9) ] [ 1, a, a^2, a^3 ] Total time: 3.049 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 9 01:35:23 2004 Input: R:=PolynomialRing(RationalField()); K:= NumberField(x^4-34*x^2+9); OK:=MaximalOrder(K); E:=EquationOrder(K); O:=sub; Index(OK,O); Index(OK, E); [K!OK.i : i in [1, 2, 3, 4]]; [K!E.i : i in [1, 2, 3, 4]]; [K!O.i : i in [1, 2, 3, 4]]; Output: Magma V2.10-6 Tue Mar 9 2004 01:35:20 on modular [Seed = 757074110] ------------------------------------- 6 24 [ 1, a, 1/2*(a^2 + 1), 1/12*(a^3 + 3*a^2 + 11*a + 9) ] [ 1, a, a^2, a^3 ] [ 1, a, 1/2*(a^2 + 1), 1/2*(a^3 + 3*a^2 + 11*a + 9) ] Total time: 3.529 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 9 01:38:32 2004 Input: R:=PolynomialRing(RationalField()); K:= NumberField(x^2+1); OK:=MaximalOrder(K); I:=2*OK Factorization(I); Output: Magma V2.10-6 Tue Mar 9 2004 01:38:27 on modular [Seed = 1112499226] ------------------------------------- >> Factorization(I);; ^ User error: bad syntax Total time: 3.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 9 01:38:46 2004 Input: R:=PolynomialRing(RationalField()); K:= NumberField(x^2+1); OK:=MaximalOrder(K); I:=2*OK; Factorization(I); Output: Magma V2.10-6 Tue Mar 9 2004 01:38:41 on modular [Seed = 3015611897] ------------------------------------- [ ] Total time: 4.119 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 9 01:39:12 2004 Input: R:=PolynomialRing(RationalField()); K:= NumberField(x^2+1); OK:=MaximalOrder(K); I:=2*OK; g:=Factorization(I); g[1][1]; Output: Magma V2.10-6 Tue Mar 9 2004 01:39:08 on modular [Seed = 2593635373] ------------------------------------- Prime Ideal of OK Two element generators: [2, 0] [3, 1] Total time: 4.119 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 9 01:40:01 2004 Input: R:=PolynomialRing(RationalField()); K:= NumberField(x^2+1); OK:=MaximalOrder(K); I:=2*OK; g:=Factorization(I); OptimizedRepresentation(g[1][1]); Output: Magma V2.10-6 Tue Mar 9 2004 01:39:56 on modular [Seed = 2223612419] ------------------------------------- >> OptimizedRepresentation(g[1][1]);; ^ Runtime error in 'OptimizedRepresentation': Bad argument types Argument types given: RngOrdIdl Total time: 3.819 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 9 01:40:13 2004 Input: R:=PolynomialRing(RationalField()); K:= NumberField(x^2+1); OK:=MaximalOrder(K); I:=2*OK; g:=Factorization(I); OptimizedRepresentation; Output: Magma V2.10-6 Tue Mar 9 2004 01:40:10 on modular [Seed = 3990932252] ------------------------------------- Intrinsic 'OptimizedRepresentation' Signatures: ( K) -> FldAlg, Map ( K, d) -> FldAlg, Map An algebraic field whose defining polynomial is better, if possible. ( O) -> BoolElt, RngOrd, Map ( O, d) -> BoolElt, RngOrd, Map A maximal order whose defining polynomial is better, if possible. Total time: 3.579 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 9 01:42:44 2004 Input: R:=PolynomialRing(RationalField()); K:= NumberField(x^2+1); OK:=MaximalOrder(K); I:=2*OK; g:=Factorization(I); IsPrincipal(I); Output: Magma V2.10-6 Tue Mar 9 2004 01:42:41 on modular [Seed = 67707737] ------------------------------------- true Total time: 3.039 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam240-85.fas.harvard.edu. (140.247.240.85) Time: Tue Mar 9 02:09:15 2004 Input: K := NumberField(x^4-34*x^2+9); OK := MaximalOrder(K); Factorization(3*OK); Output: Magma V2.10-6 Tue Mar 9 2004 02:09:12 on modular [Seed = 842997739] ------------------------------------- >> K := NumberField(x^4-34*x^2+9); ^ User error: Identifier 'x' has not been declared or assigned >> OK := MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> Factorization(3*OK);; ^ User error: Identifier 'OK' has not been declared or assigned Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam240-85.fas.harvard.edu. (140.247.240.85) Time: Tue Mar 9 02:10:04 2004 Input: R :+ PolynomialRing(RationalField()); K := NumberField(x^4-34*x^2+9); OK := MaximalOrder(K); Factorization(3*OK); Output: Magma V2.10-6 Tue Mar 9 2004 02:10:00 on modular [Seed = 3504209241] ------------------------------------- >> R :+ PolynomialRing(RationalField()); ^ User error: bad syntax >> K := NumberField(x^4-34*x^2+9); ^ User error: Identifier 'x' has not been declared or assigned >> OK := MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> Factorization(3*OK);; ^ User error: Identifier 'OK' has not been declared or assigned Total time: 3.799 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam240-85.fas.harvard.edu. (140.247.240.85) Time: Tue Mar 9 02:10:16 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^4-34*x^2+9); OK := MaximalOrder(K); Factorization(3*OK); Output: Magma V2.10-6 Tue Mar 9 2004 02:10:13 on modular [Seed = 3874212722] ------------------------------------- [ , , , ] Total time: 3.059 seconds, Total memory usage: 2.05MB ************** MAGMA ***************** Host roam240-85.fas.harvard.edu. (140.247.240.85) Time: Tue Mar 9 02:33:25 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2 + 13); OK := MaximalOrder(K); Factorization(2*OK); Output: Magma V2.10-6 Tue Mar 9 2004 02:33:22 on modular [Seed = 943000382] ------------------------------------- [ ] Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee83.uab.es. (158.109.66.83) Time: Tue Mar 9 03:15:52 2004 Input: dsaf Output: Magma V2.10-6 Tue Mar 9 2004 03:15:47 on modular [Seed = 3285122742] ------------------------------------- >> dsaf; ^ User error: Identifier 'dsaf' has not been declared or assigned Total time: 4.149 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cache1-2.ruh.isu.net.sa. (212.138.47.11) Time: Tue Mar 9 04:01:17 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Tue Mar 9 2004 04:01:12 on modular [Seed = 3165748008] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 4.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cache10-5.ruh.isu.net.sa. (212.138.47.20) Time: Tue Mar 9 04:02:08 2004 Input: a:=(1,2); b:=(1,2,3); g:=Group(a,b); Output: Magma V2.10-6 Tue Mar 9 2004 04:02:03 on modular [Seed = 4176818366] ------------------------------------- >> a:=(1,2); ^ Runtime error in elt< ... >: No permutation group context in which to create cycle >> b:=(1,2,3); ^ Runtime error in elt< ... >: No permutation group context in which to create cycle >> g:=Group(a,b); ^ User error: Identifier 'a' has not been declared or assigned Total time: 4.269 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cache1-2.ruh.isu.net.sa. (212.138.47.11) Time: Tue Mar 9 04:03:11 2004 Input: help Output: Magma V2.10-6 Tue Mar 9 2004 04:03:08 on modular [Seed = 1887287410] ------------------------------------- >> help ; ^ User error: Identifier 'help' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 9 04:54:04 2004 Input: Diumenges := []; dies := [1..366 by 1]; for i:=4 to 366 by 7 do Diumenges := Include (Diumenges,dies[i]); end for; print Diumenges; Output: Magma V2.10-6 Tue Mar 9 2004 04:53:59 on modular [Seed = 3773641857] ------------------------------------- [ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] Total time: 4.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 9 04:54:30 2004 Input: /*Exercici 1*/ Diumenges := []; dies := [1..366 by 1]; for i:=4 to 366 by 7 do Diumenges := Include (Diumenges,dies[i]); end for; print Diumenges; /*resposta*/ [ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] Output: Magma V2.10-6 Tue Mar 9 2004 04:54:25 on modular [Seed = 2576633246] ------------------------------------- [ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] [ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] Total time: 4.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 9 04:54:56 2004 Input: /*Exercici 1*/ Diumenges := []; dies := [1..366 by 1]; for i:=4 to 366 by 7 do Diumenges := Include (Diumenges,dies[i]); end for; print Diumenges; /*resposta*/ /*[ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ]*/ Output: Magma V2.10-6 Tue Mar 9 2004 04:54:52 on modular [Seed = 3082445709] ------------------------------------- [ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 9 04:57:43 2004 Input: M:= GF (4); /*creem cos finit */ M22:= MatrixRing (M,2); /*creem matrius 2x2*/ /*matrius de traça 0*/ Mt:= { x : x in M22 | Trace (x) eq 0 }; /*resposta*/ /*Matrius on la primer fila = Segona fila*/ Mf:= { y : y in M22 | Submatrix (y,1,1,1,2) eq Submatrix (y,2,1,1,2); /*resposta*/ /*Matrius que cumpleixen les dues funciones anterios*/ Mtf := Mt meet Mf; /*resposta*/ Output: Magma V2.10-6 Tue Mar 9 2004 04:57:39 on modular [Seed = 404082012] ------------------------------------- >> Mf:= { y : y in M22 | Submatrix (y,1,1,1,2) eq Submatrix (y,2,1,1,2); ^ User error: bad syntax >> Mtf := Mt meet Mf; ^ User error: Identifier 'Mf' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 9 04:58:13 2004 Input: M:= GF (4); /*creem cos finit */ M22:= MatrixRing (M,2); /*creem matrius 2x2*/ /*matrius de traça 0*/ Mt:= { x : x in M22 | Trace (x) eq 0 }; /*resposta*/ /*Matrius on la primer fila = Segona fila*/ Mf:= { y : y in M22 | Submatrix (y,1,1,1,2) eq Submatrix (y,2,1,1,2)}; /*resposta*/ /*Matrius que cumpleixen les dues funciones anterios*/ Mtf := Mt meet Mf; /*resposta*/ Output: Magma V2.10-6 Tue Mar 9 2004 04:58:09 on modular [Seed = 134602094] ------------------------------------- Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 9 04:58:53 2004 Input: M:= GF (4); /*creem cos finit */ M22:= MatrixRing (M,2); /*creem matrius 2x2*/ /*matrius de traça 0*/ Mt:= { x : x in M22 | Trace (x) eq 0 }; /*resposta*/ print Mt; /*Matrius on la primer fila = Segona fila*/ Mf:= { y : y in M22 | Submatrix (y,1,1,1,2) eq Submatrix (y,2,1,1,2)}; /*resposta*/ print Mf; /*Matrius que cumpleixen les dues funciones anterios*/ Mtf := Mt meet Mf; /*resposta*/ print Mtf; Output: Magma V2.10-6 Tue Mar 9 2004 04:58:49 on modular [Seed = 959769655] ------------------------------------- { [ 0 0] [ 0 0], [ 0 0] [M.1^2 0], [ 0 0] [ M.1 0], [ 0 0] [ 1 0], [M.1^2 0] [ 0 M.1^2], [M.1^2 0] [M.1^2 M.1^2], [M.1^2 0] [ M.1 M.1^2], [M.1^2 0] [ 1 M.1^2], [ 1 0] [ 0 1], [ 1 0] [M.1^2 1], [ 1 0] [ M.1 1], [ 1 0] [ 1 1], [ M.1 0] [ 0 M.1], [ M.1 0] [M.1^2 M.1], [ M.1 0] [ M.1 M.1], [ M.1 0] [ 1 M.1], [ 0 M.1^2] [ 0 0], [ 0 M.1^2] [M.1^2 0], [ 0 M.1^2] [ M.1 0], [ 0 M.1^2] [ 1 0], [M.1^2 M.1^2] [ 0 M.1^2], [M.1^2 M.1^2] [M.1^2 M.1^2], [M.1^2 M.1^2] [ M.1 M.1^2], [M.1^2 M.1^2] [ 1 M.1^2], [ 1 M.1^2] [ 0 1], [ 1 M.1^2] [M.1^2 1], [ 1 M.1^2] [ M.1 1], [ 1 M.1^2] [ 1 1], [ M.1 M.1^2] [ 0 M.1], [ M.1 M.1^2] [M.1^2 M.1], [ M.1 M.1^2] [ M.1 M.1], [ M.1 M.1^2] [ 1 M.1], [ 0 M.1] [ 0 0], [ 0 M.1] [M.1^2 0], [ 0 M.1] [ M.1 0], [ 0 M.1] [ 1 0], [M.1^2 M.1] [ 0 M.1^2], [M.1^2 M.1] [M.1^2 M.1^2], [M.1^2 M.1] [ M.1 M.1^2], [M.1^2 M.1] [ 1 M.1^2], [ 1 M.1] [ 0 1], [ 1 M.1] [M.1^2 1], [ 1 M.1] [ M.1 1], [ 1 M.1] [ 1 1], [ M.1 M.1] [ 0 M.1], [ M.1 M.1] [M.1^2 M.1], [ M.1 M.1] [ M.1 M.1], [ M.1 M.1] [ 1 M.1], [ 0 1] [ 0 0], [ 0 1] [M.1^2 0], [ 0 1] [ M.1 0], [ 0 1] [ 1 0], [M.1^2 1] [ 0 M.1^2], [M.1^2 1] [M.1^2 M.1^2], [M.1^2 1] [ M.1 M.1^2], [M.1^2 1] [ 1 M.1^2], [ 1 1] [ 0 1], [ 1 1] [M.1^2 1], [ 1 1] [ M.1 1], [ 1 1] [ 1 1], [ M.1 1] [ 0 M.1], [ M.1 1] [M.1^2 M.1], [ M.1 1] [ M.1 M.1], [ M.1 1] [ 1 M.1] } { [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ M.1 0] [ M.1 0], [ 0 M.1^2] [ 0 M.1^2], [ M.1 M.1^2] [ M.1 M.1^2], [ 0 M.1] [ 0 M.1], [ M.1 M.1] [ M.1 M.1], [ 0 1] [ 0 1], [ M.1 1] [ M.1 1], [M.1^2 0] [M.1^2 0], [ 1 0] [ 1 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ 1 M.1^2] [ 1 M.1^2], [M.1^2 M.1] [M.1^2 M.1], [ 1 M.1] [ 1 M.1], [M.1^2 1] [M.1^2 1] } { [ 0 0] [ 0 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ M.1 M.1] [ M.1 M.1], [ 1 1] [ 1 1] } Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 9 05:02:31 2004 Input: Aleatori := [Random(M22): n in [1..10]]; #([a : a in Aleatori | a in Mt]); #([a : a in Aleatori | a in Mf]); #([a : a in Aleatori | a in Mtf]); print Aleatori; Output: Magma V2.10-6 Tue Mar 9 2004 05:02:27 on modular [Seed = 2746119623] ------------------------------------- >> Aleatori := [Random(M22): n in [1..10]]; ^ User error: Identifier 'M22' has not been declared or assigned >> #([a : a in Aleatori | a in Mt]); ^ User error: Identifier 'Aleatori' has not been declared or assigned >> #([a : a in Aleatori | a in Mf]); ^ User error: Identifier 'Aleatori' has not been declared or assigned >> #([a : a in Aleatori | a in Mtf]); ^ User error: Identifier 'Aleatori' has not been declared or assigned >> print Aleatori;; ^ User error: Identifier 'Aleatori' has not been declared or assigned Total time: 3.189 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 9 05:03:14 2004 Input: M:= GF (4); /*creem cos finit */ M22:= MatrixRing (M,2); /*creem matrius 2x2*/ Aleatori := [Random(M22): n in [1..10]]; #([a : a in Aleatori | a in Mt]); #([a : a in Aleatori | a in Mf]); #([a : a in Aleatori | a in Mtf]); print Aleatori; Output: Magma V2.10-6 Tue Mar 9 2004 05:03:09 on modular [Seed = 1212522061] ------------------------------------- >> #([a : a in Aleatori | a in Mt]); ^ User error: Identifier 'Mt' has not been declared or assigned >> #([a : a in Aleatori | a in Mf]); ^ User error: Identifier 'Mf' has not been declared or assigned >> #([a : a in Aleatori | a in Mtf]); ^ User error: Identifier 'Mtf' has not been declared or assigned [ [ 1 0] [ M.1 0], [ 0 0] [ 0 1], [ 0 M.1^2] [ 0 M.1], [M.1^2 1] [ 1 M.1^2], [ 0 0] [ M.1 0], [ 1 0] [ 0 1], [ M.1 0] [ M.1 1], [ M.1 0] [M.1^2 0], [ M.1 M.1^2] [M.1^2 M.1], [ 1 M.1] [M.1^2 0] ] Total time: 3.749 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 9 05:04:11 2004 Input: M:= GF (4); /*creem cos finit */ M22:= MatrixRing (M,2); /*creem matrius 2x2*/ /*matrius de traça 0*/ Mt:= { x : x in M22 | Trace (x) eq 0 }; /*resposta*/ print Mt; /* [ 0 0] [ 0 0], [ 0 0] [M.1^2 0], [ 0 0] [ M.1 0], [ 0 0] [ 1 0], [M.1^2 0] [ 0 M.1^2], [M.1^2 0] [M.1^2 M.1^2], [M.1^2 0] [ M.1 M.1^2], [M.1^2 0] [ 1 M.1^2], [ 1 0] [ 0 1], [ 1 0] [M.1^2 1], [ 1 0] [ M.1 1], [ 1 0] [ 1 1], [ M.1 0] [ 0 M.1], [ M.1 0] [M.1^2 M.1], [ M.1 0] [ M.1 M.1], [ M.1 0] [ 1 M.1], [ 0 M.1^2] [ 0 0], [ 0 M.1^2] [M.1^2 0], [ 0 M.1^2] [ M.1 0], [ 0 M.1^2] [ 1 0], [M.1^2 M.1^2] [ 0 M.1^2], [M.1^2 M.1^2] [M.1^2 M.1^2], [M.1^2 M.1^2] [ M.1 M.1^2], [M.1^2 M.1^2] [ 1 M.1^2], [ 1 M.1^2] [ 0 1], [ 1 M.1^2] [M.1^2 1], [ 1 M.1^2] [ M.1 1], [ 1 M.1^2] [ 1 1], [ M.1 M.1^2] [ 0 M.1], [ M.1 M.1^2] [M.1^2 M.1], [ M.1 M.1^2] [ M.1 M.1], [ M.1 M.1^2] [ 1 M.1], [ 0 M.1] [ 0 0], [ 0 M.1] [M.1^2 0], [ 0 M.1] [ M.1 0], [ 0 M.1] [ 1 0], [M.1^2 M.1] [ 0 M.1^2], [M.1^2 M.1] [M.1^2 M.1^2], [M.1^2 M.1] [ M.1 M.1^2], [M.1^2 M.1] [ 1 M.1^2], [ 1 M.1] [ 0 1], [ 1 M.1] [M.1^2 1], [ 1 M.1] [ M.1 1], [ 1 M.1] [ 1 1], [ M.1 M.1] [ 0 M.1], [ M.1 M.1] [M.1^2 M.1], [ M.1 M.1] [ M.1 M.1], [ M.1 M.1] [ 1 M.1], [ 0 1] [ 0 0], [ 0 1] [M.1^2 0], [ 0 1] [ M.1 0], [ 0 1] [ 1 0], [M.1^2 1] [ 0 M.1^2], [M.1^2 1] [M.1^2 M.1^2], [M.1^2 1] [ M.1 M.1^2], [M.1^2 1] [ 1 M.1^2], [ 1 1] [ 0 1], [ 1 1] [M.1^2 1], [ 1 1] [ M.1 1], [ 1 1] [ 1 1], [ M.1 1] [ 0 M.1], [ M.1 1] [M.1^2 M.1], [ M.1 1] [ M.1 M.1], [ M.1 1] [ 1 M.1] } */ /*Matrius on la primer fila = Segona fila*/ Mf:= { y : y in M22 | Submatrix (y,1,1,1,2) eq Submatrix (y,2,1,1,2)}; /*resposta*/ print Mf; /*{ [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ M.1 0] [ M.1 0], [ 0 M.1^2] [ 0 M.1^2], [ M.1 M.1^2] [ M.1 M.1^2], [ 0 M.1] [ 0 M.1], [ M.1 M.1] [ M.1 M.1], [ 0 1] [ 0 1], [ M.1 1] [ M.1 1], [M.1^2 0] [M.1^2 0], [ 1 0] [ 1 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ 1 M.1^2] [ 1 M.1^2], [M.1^2 M.1] [M.1^2 M.1], [ 1 M.1] [ 1 M.1], [M.1^2 1] [M.1^2 1] } */ /*Matrius que cumpleixen les dues funciones anterios*/ Mtf := Mt meet Mf; /*resposta*/ print Mtf; /* { [ 0 0] [ 0 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ M.1 M.1] [ M.1 M.1], [ 1 1] [ 1 1] } */ Exercici 2d Aleatori := [Random(M22): n in [1..10]]; #([a : a in Aleatori | a in Mt]); #([a : a in Aleatori | a in Mf]); #([a : a in Aleatori | a in Mtf]); print; Output: Magma V2.10-6 Tue Mar 9 2004 05:04:06 on modular [Seed = 1617802926] ------------------------------------- { [ 0 0] [ 0 0], [ 0 0] [M.1^2 0], [ 0 0] [ M.1 0], [ 0 0] [ 1 0], [M.1^2 0] [ 0 M.1^2], [M.1^2 0] [M.1^2 M.1^2], [M.1^2 0] [ M.1 M.1^2], [M.1^2 0] [ 1 M.1^2], [ 1 0] [ 0 1], [ 1 0] [M.1^2 1], [ 1 0] [ M.1 1], [ 1 0] [ 1 1], [ M.1 0] [ 0 M.1], [ M.1 0] [M.1^2 M.1], [ M.1 0] [ M.1 M.1], [ M.1 0] [ 1 M.1], [ 0 M.1^2] [ 0 0], [ 0 M.1^2] [M.1^2 0], [ 0 M.1^2] [ M.1 0], [ 0 M.1^2] [ 1 0], [M.1^2 M.1^2] [ 0 M.1^2], [M.1^2 M.1^2] [M.1^2 M.1^2], [M.1^2 M.1^2] [ M.1 M.1^2], [M.1^2 M.1^2] [ 1 M.1^2], [ 1 M.1^2] [ 0 1], [ 1 M.1^2] [M.1^2 1], [ 1 M.1^2] [ M.1 1], [ 1 M.1^2] [ 1 1], [ M.1 M.1^2] [ 0 M.1], [ M.1 M.1^2] [M.1^2 M.1], [ M.1 M.1^2] [ M.1 M.1], [ M.1 M.1^2] [ 1 M.1], [ 0 M.1] [ 0 0], [ 0 M.1] [M.1^2 0], [ 0 M.1] [ M.1 0], [ 0 M.1] [ 1 0], [M.1^2 M.1] [ 0 M.1^2], [M.1^2 M.1] [M.1^2 M.1^2], [M.1^2 M.1] [ M.1 M.1^2], [M.1^2 M.1] [ 1 M.1^2], [ 1 M.1] [ 0 1], [ 1 M.1] [M.1^2 1], [ 1 M.1] [ M.1 1], [ 1 M.1] [ 1 1], [ M.1 M.1] [ 0 M.1], [ M.1 M.1] [M.1^2 M.1], [ M.1 M.1] [ M.1 M.1], [ M.1 M.1] [ 1 M.1], [ 0 1] [ 0 0], [ 0 1] [M.1^2 0], [ 0 1] [ M.1 0], [ 0 1] [ 1 0], [M.1^2 1] [ 0 M.1^2], [M.1^2 1] [M.1^2 M.1^2], [M.1^2 1] [ M.1 M.1^2], [M.1^2 1] [ 1 M.1^2], [ 1 1] [ 0 1], [ 1 1] [M.1^2 1], [ 1 1] [ M.1 1], [ 1 1] [ 1 1], [ M.1 1] [ 0 M.1], [ M.1 1] [M.1^2 M.1], [ M.1 1] [ M.1 M.1], [ M.1 1] [ 1 M.1] } { [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ M.1 0] [ M.1 0], [ 0 M.1^2] [ 0 M.1^2], [ M.1 M.1^2] [ M.1 M.1^2], [ 0 M.1] [ 0 M.1], [ M.1 M.1] [ M.1 M.1], [ 0 1] [ 0 1], [ M.1 1] [ M.1 1], [M.1^2 0] [M.1^2 0], [ 1 0] [ 1 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ 1 M.1^2] [ 1 M.1^2], [M.1^2 M.1] [M.1^2 M.1], [ 1 M.1] [ 1 M.1], [M.1^2 1] [M.1^2 1] } { [ 0 0] [ 0 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ M.1 M.1] [ M.1 M.1], [ 1 1] [ 1 1] } >> Exercici 2d ^ User error: bad syntax 1 2 1 >> print; ^ User error: bad syntax Total time: 4.099 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 9 05:04:48 2004 Input: M:= GF (4); /*creem cos finit */ M22:= MatrixRing (M,2); /*creem matrius 2x2*/ /*matrius de traça 0*/ Mt:= { x : x in M22 | Trace (x) eq 0 }; /*resposta*/ print Mt; /* [ 0 0] [ 0 0], [ 0 0] [M.1^2 0], [ 0 0] [ M.1 0], [ 0 0] [ 1 0], [M.1^2 0] [ 0 M.1^2], [M.1^2 0] [M.1^2 M.1^2], [M.1^2 0] [ M.1 M.1^2], [M.1^2 0] [ 1 M.1^2], [ 1 0] [ 0 1], [ 1 0] [M.1^2 1], [ 1 0] [ M.1 1], [ 1 0] [ 1 1], [ M.1 0] [ 0 M.1], [ M.1 0] [M.1^2 M.1], [ M.1 0] [ M.1 M.1], [ M.1 0] [ 1 M.1], [ 0 M.1^2] [ 0 0], [ 0 M.1^2] [M.1^2 0], [ 0 M.1^2] [ M.1 0], [ 0 M.1^2] [ 1 0], [M.1^2 M.1^2] [ 0 M.1^2], [M.1^2 M.1^2] [M.1^2 M.1^2], [M.1^2 M.1^2] [ M.1 M.1^2], [M.1^2 M.1^2] [ 1 M.1^2], [ 1 M.1^2] [ 0 1], [ 1 M.1^2] [M.1^2 1], [ 1 M.1^2] [ M.1 1], [ 1 M.1^2] [ 1 1], [ M.1 M.1^2] [ 0 M.1], [ M.1 M.1^2] [M.1^2 M.1], [ M.1 M.1^2] [ M.1 M.1], [ M.1 M.1^2] [ 1 M.1], [ 0 M.1] [ 0 0], [ 0 M.1] [M.1^2 0], [ 0 M.1] [ M.1 0], [ 0 M.1] [ 1 0], [M.1^2 M.1] [ 0 M.1^2], [M.1^2 M.1] [M.1^2 M.1^2], [M.1^2 M.1] [ M.1 M.1^2], [M.1^2 M.1] [ 1 M.1^2], [ 1 M.1] [ 0 1], [ 1 M.1] [M.1^2 1], [ 1 M.1] [ M.1 1], [ 1 M.1] [ 1 1], [ M.1 M.1] [ 0 M.1], [ M.1 M.1] [M.1^2 M.1], [ M.1 M.1] [ M.1 M.1], [ M.1 M.1] [ 1 M.1], [ 0 1] [ 0 0], [ 0 1] [M.1^2 0], [ 0 1] [ M.1 0], [ 0 1] [ 1 0], [M.1^2 1] [ 0 M.1^2], [M.1^2 1] [M.1^2 M.1^2], [M.1^2 1] [ M.1 M.1^2], [M.1^2 1] [ 1 M.1^2], [ 1 1] [ 0 1], [ 1 1] [M.1^2 1], [ 1 1] [ M.1 1], [ 1 1] [ 1 1], [ M.1 1] [ 0 M.1], [ M.1 1] [M.1^2 M.1], [ M.1 1] [ M.1 M.1], [ M.1 1] [ 1 M.1] } */ /*Matrius on la primer fila = Segona fila*/ Mf:= { y : y in M22 | Submatrix (y,1,1,1,2) eq Submatrix (y,2,1,1,2)}; /*resposta*/ print Mf; /*{ [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ M.1 0] [ M.1 0], [ 0 M.1^2] [ 0 M.1^2], [ M.1 M.1^2] [ M.1 M.1^2], [ 0 M.1] [ 0 M.1], [ M.1 M.1] [ M.1 M.1], [ 0 1] [ 0 1], [ M.1 1] [ M.1 1], [M.1^2 0] [M.1^2 0], [ 1 0] [ 1 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ 1 M.1^2] [ 1 M.1^2], [M.1^2 M.1] [M.1^2 M.1], [ 1 M.1] [ 1 M.1], [M.1^2 1] [M.1^2 1] } */ /*Matrius que cumpleixen les dues funciones anterios*/ Mtf := Mt meet Mf; /*resposta*/ print Mtf; /* { [ 0 0] [ 0 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ M.1 M.1] [ M.1 M.1], [ 1 1] [ 1 1] } */ Exercici 2d Aleatori := [Random(M22): n in [1..10]]; #([a : a in Aleatori | a in Mt]); #([a : a in Aleatori | a in Mf]); #([a : a in Aleatori | a in Mtf]); print Aleatori; Output: Magma V2.10-6 Tue Mar 9 2004 05:04:43 on modular [Seed = 251845100] ------------------------------------- { [ 0 0] [ 0 0], [ 0 0] [M.1^2 0], [ 0 0] [ M.1 0], [ 0 0] [ 1 0], [M.1^2 0] [ 0 M.1^2], [M.1^2 0] [M.1^2 M.1^2], [M.1^2 0] [ M.1 M.1^2], [M.1^2 0] [ 1 M.1^2], [ 1 0] [ 0 1], [ 1 0] [M.1^2 1], [ 1 0] [ M.1 1], [ 1 0] [ 1 1], [ M.1 0] [ 0 M.1], [ M.1 0] [M.1^2 M.1], [ M.1 0] [ M.1 M.1], [ M.1 0] [ 1 M.1], [ 0 M.1^2] [ 0 0], [ 0 M.1^2] [M.1^2 0], [ 0 M.1^2] [ M.1 0], [ 0 M.1^2] [ 1 0], [M.1^2 M.1^2] [ 0 M.1^2], [M.1^2 M.1^2] [M.1^2 M.1^2], [M.1^2 M.1^2] [ M.1 M.1^2], [M.1^2 M.1^2] [ 1 M.1^2], [ 1 M.1^2] [ 0 1], [ 1 M.1^2] [M.1^2 1], [ 1 M.1^2] [ M.1 1], [ 1 M.1^2] [ 1 1], [ M.1 M.1^2] [ 0 M.1], [ M.1 M.1^2] [M.1^2 M.1], [ M.1 M.1^2] [ M.1 M.1], [ M.1 M.1^2] [ 1 M.1], [ 0 M.1] [ 0 0], [ 0 M.1] [M.1^2 0], [ 0 M.1] [ M.1 0], [ 0 M.1] [ 1 0], [M.1^2 M.1] [ 0 M.1^2], [M.1^2 M.1] [M.1^2 M.1^2], [M.1^2 M.1] [ M.1 M.1^2], [M.1^2 M.1] [ 1 M.1^2], [ 1 M.1] [ 0 1], [ 1 M.1] [M.1^2 1], [ 1 M.1] [ M.1 1], [ 1 M.1] [ 1 1], [ M.1 M.1] [ 0 M.1], [ M.1 M.1] [M.1^2 M.1], [ M.1 M.1] [ M.1 M.1], [ M.1 M.1] [ 1 M.1], [ 0 1] [ 0 0], [ 0 1] [M.1^2 0], [ 0 1] [ M.1 0], [ 0 1] [ 1 0], [M.1^2 1] [ 0 M.1^2], [M.1^2 1] [M.1^2 M.1^2], [M.1^2 1] [ M.1 M.1^2], [M.1^2 1] [ 1 M.1^2], [ 1 1] [ 0 1], [ 1 1] [M.1^2 1], [ 1 1] [ M.1 1], [ 1 1] [ 1 1], [ M.1 1] [ 0 M.1], [ M.1 1] [M.1^2 M.1], [ M.1 1] [ M.1 M.1], [ M.1 1] [ 1 M.1] } { [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ M.1 0] [ M.1 0], [ 0 M.1^2] [ 0 M.1^2], [ M.1 M.1^2] [ M.1 M.1^2], [ 0 M.1] [ 0 M.1], [ M.1 M.1] [ M.1 M.1], [ 0 1] [ 0 1], [ M.1 1] [ M.1 1], [M.1^2 0] [M.1^2 0], [ 1 0] [ 1 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ 1 M.1^2] [ 1 M.1^2], [M.1^2 M.1] [M.1^2 M.1], [ 1 M.1] [ 1 M.1], [M.1^2 1] [M.1^2 1] } { [ 0 0] [ 0 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ M.1 M.1] [ M.1 M.1], [ 1 1] [ 1 1] } >> Exercici 2d ^ User error: bad syntax 3 1 0 [ [M.1^2 1] [M.1^2 M.1^2], [ 1 1] [ M.1 1], [ M.1 0] [ 0 M.1^2], [ M.1 M.1^2] [M.1^2 M.1], [M.1^2 M.1] [ M.1 M.1], [M.1^2 1] [ M.1 1], [ 0 M.1^2] [ 1 1], [M.1^2 M.1^2] [M.1^2 1], [ 1 1] [ 1 0], [ M.1 0] [ M.1 0] ] Total time: 4.109 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 9 05:05:32 2004 Input: M:= GF (4); /*creem cos finit */ M22:= MatrixRing (M,2); /*creem matrius 2x2*/ /*matrius de traça 0*/ Mt:= { x : x in M22 | Trace (x) eq 0 }; /*resposta*/ print Mt; /* [ 0 0] [ 0 0], [ 0 0] [M.1^2 0], [ 0 0] [ M.1 0], [ 0 0] [ 1 0], [M.1^2 0] [ 0 M.1^2], [M.1^2 0] [M.1^2 M.1^2], [M.1^2 0] [ M.1 M.1^2], [M.1^2 0] [ 1 M.1^2], [ 1 0] [ 0 1], [ 1 0] [M.1^2 1], [ 1 0] [ M.1 1], [ 1 0] [ 1 1], [ M.1 0] [ 0 M.1], [ M.1 0] [M.1^2 M.1], [ M.1 0] [ M.1 M.1], [ M.1 0] [ 1 M.1], [ 0 M.1^2] [ 0 0], [ 0 M.1^2] [M.1^2 0], [ 0 M.1^2] [ M.1 0], [ 0 M.1^2] [ 1 0], [M.1^2 M.1^2] [ 0 M.1^2], [M.1^2 M.1^2] [M.1^2 M.1^2], [M.1^2 M.1^2] [ M.1 M.1^2], [M.1^2 M.1^2] [ 1 M.1^2], [ 1 M.1^2] [ 0 1], [ 1 M.1^2] [M.1^2 1], [ 1 M.1^2] [ M.1 1], [ 1 M.1^2] [ 1 1], [ M.1 M.1^2] [ 0 M.1], [ M.1 M.1^2] [M.1^2 M.1], [ M.1 M.1^2] [ M.1 M.1], [ M.1 M.1^2] [ 1 M.1], [ 0 M.1] [ 0 0], [ 0 M.1] [M.1^2 0], [ 0 M.1] [ M.1 0], [ 0 M.1] [ 1 0], [M.1^2 M.1] [ 0 M.1^2], [M.1^2 M.1] [M.1^2 M.1^2], [M.1^2 M.1] [ M.1 M.1^2], [M.1^2 M.1] [ 1 M.1^2], [ 1 M.1] [ 0 1], [ 1 M.1] [M.1^2 1], [ 1 M.1] [ M.1 1], [ 1 M.1] [ 1 1], [ M.1 M.1] [ 0 M.1], [ M.1 M.1] [M.1^2 M.1], [ M.1 M.1] [ M.1 M.1], [ M.1 M.1] [ 1 M.1], [ 0 1] [ 0 0], [ 0 1] [M.1^2 0], [ 0 1] [ M.1 0], [ 0 1] [ 1 0], [M.1^2 1] [ 0 M.1^2], [M.1^2 1] [M.1^2 M.1^2], [M.1^2 1] [ M.1 M.1^2], [M.1^2 1] [ 1 M.1^2], [ 1 1] [ 0 1], [ 1 1] [M.1^2 1], [ 1 1] [ M.1 1], [ 1 1] [ 1 1], [ M.1 1] [ 0 M.1], [ M.1 1] [M.1^2 M.1], [ M.1 1] [ M.1 M.1], [ M.1 1] [ 1 M.1] } */ /*Matrius on la primer fila = Segona fila*/ Mf:= { y : y in M22 | Submatrix (y,1,1,1,2) eq Submatrix (y,2,1,1,2)}; /*resposta*/ print Mf; /*{ [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ M.1 0] [ M.1 0], [ 0 M.1^2] [ 0 M.1^2], [ M.1 M.1^2] [ M.1 M.1^2], [ 0 M.1] [ 0 M.1], [ M.1 M.1] [ M.1 M.1], [ 0 1] [ 0 1], [ M.1 1] [ M.1 1], [M.1^2 0] [M.1^2 0], [ 1 0] [ 1 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ 1 M.1^2] [ 1 M.1^2], [M.1^2 M.1] [M.1^2 M.1], [ 1 M.1] [ 1 M.1], [M.1^2 1] [M.1^2 1] } */ /*Matrius que cumpleixen les dues funciones anterios*/ Mtf := Mt meet Mf; /*resposta*/ print Mtf; /* { [ 0 0] [ 0 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ M.1 M.1] [ M.1 M.1], [ 1 1] [ 1 1] } */ /*Exercici 2d*/ Aleatori := [Random(M22): n in [1..10]]; #([a : a in Aleatori | a in Mt]); #([a : a in Aleatori | a in Mf]); #([a : a in Aleatori | a in Mtf]); print Aleatori; Output: Magma V2.10-6 Tue Mar 9 2004 05:05:27 on modular [Seed = 790821264] ------------------------------------- { [ 0 0] [ 0 0], [ 0 0] [M.1^2 0], [ 0 0] [ M.1 0], [ 0 0] [ 1 0], [M.1^2 0] [ 0 M.1^2], [M.1^2 0] [M.1^2 M.1^2], [M.1^2 0] [ M.1 M.1^2], [M.1^2 0] [ 1 M.1^2], [ 1 0] [ 0 1], [ 1 0] [M.1^2 1], [ 1 0] [ M.1 1], [ 1 0] [ 1 1], [ M.1 0] [ 0 M.1], [ M.1 0] [M.1^2 M.1], [ M.1 0] [ M.1 M.1], [ M.1 0] [ 1 M.1], [ 0 M.1^2] [ 0 0], [ 0 M.1^2] [M.1^2 0], [ 0 M.1^2] [ M.1 0], [ 0 M.1^2] [ 1 0], [M.1^2 M.1^2] [ 0 M.1^2], [M.1^2 M.1^2] [M.1^2 M.1^2], [M.1^2 M.1^2] [ M.1 M.1^2], [M.1^2 M.1^2] [ 1 M.1^2], [ 1 M.1^2] [ 0 1], [ 1 M.1^2] [M.1^2 1], [ 1 M.1^2] [ M.1 1], [ 1 M.1^2] [ 1 1], [ M.1 M.1^2] [ 0 M.1], [ M.1 M.1^2] [M.1^2 M.1], [ M.1 M.1^2] [ M.1 M.1], [ M.1 M.1^2] [ 1 M.1], [ 0 M.1] [ 0 0], [ 0 M.1] [M.1^2 0], [ 0 M.1] [ M.1 0], [ 0 M.1] [ 1 0], [M.1^2 M.1] [ 0 M.1^2], [M.1^2 M.1] [M.1^2 M.1^2], [M.1^2 M.1] [ M.1 M.1^2], [M.1^2 M.1] [ 1 M.1^2], [ 1 M.1] [ 0 1], [ 1 M.1] [M.1^2 1], [ 1 M.1] [ M.1 1], [ 1 M.1] [ 1 1], [ M.1 M.1] [ 0 M.1], [ M.1 M.1] [M.1^2 M.1], [ M.1 M.1] [ M.1 M.1], [ M.1 M.1] [ 1 M.1], [ 0 1] [ 0 0], [ 0 1] [M.1^2 0], [ 0 1] [ M.1 0], [ 0 1] [ 1 0], [M.1^2 1] [ 0 M.1^2], [M.1^2 1] [M.1^2 M.1^2], [M.1^2 1] [ M.1 M.1^2], [M.1^2 1] [ 1 M.1^2], [ 1 1] [ 0 1], [ 1 1] [M.1^2 1], [ 1 1] [ M.1 1], [ 1 1] [ 1 1], [ M.1 1] [ 0 M.1], [ M.1 1] [M.1^2 M.1], [ M.1 1] [ M.1 M.1], [ M.1 1] [ 1 M.1] } { [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ M.1 0] [ M.1 0], [ 0 M.1^2] [ 0 M.1^2], [ M.1 M.1^2] [ M.1 M.1^2], [ 0 M.1] [ 0 M.1], [ M.1 M.1] [ M.1 M.1], [ 0 1] [ 0 1], [ M.1 1] [ M.1 1], [M.1^2 0] [M.1^2 0], [ 1 0] [ 1 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ 1 M.1^2] [ 1 M.1^2], [M.1^2 M.1] [M.1^2 M.1], [ 1 M.1] [ 1 M.1], [M.1^2 1] [M.1^2 1] } { [ 0 0] [ 0 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ M.1 M.1] [ M.1 M.1], [ 1 1] [ 1 1] } 0 0 0 [ [ M.1 M.1^2] [ 0 0], [M.1^2 1] [ 0 1], [ M.1 1] [ 0 1], [M.1^2 M.1] [M.1^2 1], [M.1^2 M.1^2] [ 0 1], [ 1 M.1] [M.1^2 M.1^2], [ M.1 0] [M.1^2 1], [ 0 0] [ M.1 1], [ 1 0] [ M.1 M.1], [ 1 M.1] [ 0 M.1^2] ] Total time: 4.069 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 9 05:08:38 2004 Input: R:= Integers (); P := PolynomialRing (R); polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; main := function (a,b) exponent := polinomi_t (a,b); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); PuntsOlav := { : c in GF (a,b) , d in GF (a,b) | Evaluate (pol_t,c) eq Evaluate (pol_n,d)}; return (PuntsOlav); end function; Output: Magma V2.10-6 Tue Mar 9 2004 05:08:33 on modular [Seed = 2223592317] ------------------------------------- Total time: 3.679 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 9 05:09:09 2004 Input: R:= Integers (); P := PolynomialRing (R); polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; main := function (a,b) exponent := polinomi_t (a,b); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); PuntsOlav := { : c in GF (a,b) , d in GF (a,b) | Evaluate (pol_t,c) eq Evaluate (pol_n,d)}; return (PuntsOlav); end function; main (7,3); Output: Magma V2.10-6 Tue Mar 9 2004 05:09:00 on modular [Seed = 2846129741] ------------------------------------- { <$.1^205, $.1^175>, <$.1^172, 3>, <1, $.1^7>, <$.1^85, $.1^58>, <$.1^23, $.1^112>, <$.1^36, $.1^295>, <$.1^110, $.1^68>, <$.1^301, $.1^95>, <$.1^310, $.1^65>, <$.1^111, $.1^140>, <$.1^88, $.1^177>, <$.1^198, $.1^4>, <$.1^281, $.1^317>, <$.1^131, $.1^174>, <$.1^330, $.1^255>, <$.1^83, $.1^184>, <$.1^145, $.1^214>, <$.1^154, $.1^181>, <$.1^172, $.1^237>, <$.1^264, $.1^23>, <$.1^150, $.1^129>, <$.1^103, $.1^168>, <$.1^83, $.1^256>, <$.1^7, $.1^126>, <$.1^198, $.1^286>, <$.1^66, $.1^180>, <$.1^67, $.1^193>, <$.1^41, $.1^41>, <$.1^193, $.1^208>, <$.1^17, $.1^340>, <$.1^97, $.1^132>, <$.1^195, $.1^282>, <$.1^91, $.1^335>, <$.1^296, $.1^335>, <$.1^80, $.1^119>, <$.1^237, $.1^327>, <$.1^160, $.1^223>, <$.1^96, $.1^99>, <$.1^302, $.1^273>, <$.1^88, 5>, <$.1^139, $.1^62>, <$.1^150, $.1^63>, <$.1^149, $.1^40>, <$.1^316, $.1^169>, <$.1^252, $.1^151>, <$.1^255, $.1^53>, <$.1^42, $.1^112>, <$.1^176, $.1^251>, <$.1^226, $.1^38>, <$.1^124, $.1^182>, <$.1^34, $.1^322>, <$.1^327, $.1^39>, <$.1^161, $.1^340>, <$.1^135, $.1^51>, <$.1^28, $.1^21>, <$.1^332, $.1^73>, <$.1^187, $.1^21>, <$.1^311, $.1^62>, <$.1^102, $.1^131>, <$.1^319, $.1^3>, <$.1^314, $.1^246>, <$.1^44, $.1^69>, <$.1^100, 4>, <$.1^267, $.1^168>, <$.1^224, $.1^280>, <$.1^315, $.1^82>, <$.1^292, $.1^137>, <$.1^200, $.1^280>, <$.1^176, $.1^155>, <$.1^18, $.1^160>, <$.1^121, $.1^230>, <$.1^147, $.1^217>, <$.1^62, $.1^129>, <$.1^318, $.1^88>, <$.1^235, $.1^244>, <$.1^294, $.1^52>, <$.1^270, $.1^92>, <$.1^309, $.1^284>, <$.1^232, $.1^187>, <$.1^67, $.1^103>, <$.1^325, $.1^214>, <$.1^69, $.1^315>, <$.1^24, $.1^303>, <$.1^145, $.1^130>, <$.1^309, $.1^224>, <$.1^46, $.1^83>, <$.1^272, $.1^277>, <$.1^303, $.1^225>, <$.1^311, $.1^2>, <$.1^183, $.1^125>, <$.1^17, $.1^130>, <2, $.1^165>, <$.1^207, $.1^76>, <$.1^318, $.1^208>, <$.1^40, $.1^11>, <$.1^200, $.1^166>, <$.1^119, $.1^244>, <$.1^3, $.1^319>, <3, $.1^38>, <$.1^251, $.1^152>, <$.1^25, $.1^282>, <$.1^174, $.1^16>, <$.1^132, $.1^156>, <$.1^121, $.1^338>, <$.1^88, $.1^303>, <$.1^321, $.1^282>, <$.1^81, $.1^94>, <$.1^149, $.1^262>, <$.1^4, $.1^315>, <$.1^177, $.1^133>, <$.1^136, $.1^3>, <$.1^180, $.1^14>, <$.1^7, $.1^174>, <$.1^121, $.1^26>, <$.1^294, $.1^136>, <$.1^7, $.1^24>, <$.1^308, $.1^189>, <$.1^65, 0>, <$.1^218, $.1^23>, <$.1^132, 2>, <$.1^263, $.1^318>, <$.1^181, $.1^75>, <$.1^35, $.1^32>, <$.1^166, $.1^3>, <$.1^281, $.1^167>, <$.1^220, $.1^303>, <$.1^213, $.1^85>, <$.1, $.1^294>, <1, $.1^175>, <$.1^230, $.1^100>, <$.1^193, $.1^4>, <$.1^267, $.1^60>, <$.1^126, $.1^322>, <$.1^128, $.1^146>, <3, $.1^122>, <$.1^248, $.1^261>, <$.1^92, $.1^213>, <$.1^216, $.1^331>, <2, $.1^129>, <$.1^131, $.1^12>, <$.1^174, $.1^100>, <$.1^20, $.1^323>, <$.1^274, $.1^81>, <$.1^91, $.1^173>, <$.1^197, $.1^216>, <$.1^288, $.1^36>, <$.1^78, $.1^152>, <$.1^150, $.1^339>, <$.1^160, $.1^181>, <$.1^340, $.1^184>, <$.1^239, $.1^112>, <$.1^235, $.1^142>, <$.1^206, $.1^149>, <$.1^232, $.1^19>, <$.1^307, $.1^330>, <$.1, $.1^330>, <$.1^239, $.1^226>, <$.1^116, $.1^266>, <$.1^168, $.1^291>, <$.1^25, $.1^252>, <$.1^244, $.1^226>, <$.1^119, $.1^64>, <$.1^36, $.1^199>, <$.1^127, $.1^31>, <$.1^340, $.1^196>, <$.1^330, $.1^75>, <$.1^288, $.1^60>, <$.1^161, $.1^106>, <$.1^178, $.1^267>, <$.1^298, $.1^40>, <$.1^250, $.1^35>, <$.1^255, $.1^101>, <$.1^194, $.1^25>, <$.1^159, $.1^24>, <$.1^267, $.1^150>, <$.1^16, $.1^150>, <$.1^274, $.1^243>, <$.1^195, $.1^300>, <$.1^30, $.1^245>, <$.1^269, $.1^105>, <$.1^307, $.1^108>, <$.1^181, $.1^21>, <$.1^53, $.1^55>, <$.1^11, $.1^174>, <$.1^225, $.1^34>, <$.1^191, $.1^212>, <$.1^263, $.1^18>, <$.1^6, $.1^304>, <$.1^330, $.1^309>, <$.1^232, $.1^163>, <$.1^292, $.1^5>, <$.1^37, $.1^126>, <$.1^153, $.1^76>, <$.1^156, $.1^282>, <$.1^201, $.1^176>, <$.1^49, $.1^132>, <$.1^290, $.1^169>, <$.1^220, $.1^105>, <$.1^251, $.1^296>, <$.1^231, $.1^77>, <$.1^149, $.1^112>, <$.1^202, $.1^161>, <$.1^273, $.1^284>, <$.1^99, $.1^263>, <$.1^320, $.1^187>, <$.1^34, $.1^172>, <$.1^327, $.1^321>, <$.1^61, $.1^268>, <$.1^93, $.1^296>, <$.1^37, $.1^36>, <$.1^242, $.1^34>, <$.1^320, $.1>, <$.1^22, $.1^79>, <$.1^13, $.1^119>, <$.1^37, $.1^12>, <$.1^24, $.1^69>, <$.1^41, $.1^59>, <$.1^70, $.1^96>, <$.1^200, $.1^10>, <$.1^46, $.1^65>, <$.1^136, $.1^177>, <$.1^193, $.1^160>, <$.1^189, $.1^313>, <$.1^193, $.1^106>, <$.1^107, 0>, <$.1^216, $.1^193>, <$.1^267, $.1^192>, <$.1^249, $.1^257>, <$.1^262, $.1^320>, <$.1^23, $.1^118>, <6, $.1^22>, <$.1^183, $.1^203>, <$.1^207, $.1^10>, <$.1^260, $.1^332>, <$.1^308, $.1^219>, <$.1^145, $.1^124>, <$.1^106, $.1^127>, <$.1^189, $.1^271>, <$.1^138, $.1^245>, <$.1^84, $.1^266>, <$.1^45, $.1^262>, <$.1^235, $.1^304>, <$.1^245, $.1^194>, <$.1^257, $.1^41>, <$.1^24, $.1^249>, <$.1^100, $.1^330>, <$.1^136, $.1^183>, <$.1^62, $.1^99>, <$.1^315, $.1^52>, <$.1^62, $.1^177>, <$.1^242, $.1^82>, <$.1^127, $.1^193>, <$.1^155, $.1^85>, <$.1^158, $.1^167>, <$.1^9, $.1^5>, <$.1^194, $.1^127>, <$.1^42, $.1^268>, <$.1^140, $.1^227>, <$.1^45, $.1^298>, <$.1^196, $.1^213>, <$.1^224, $.1^268>, <$.1^145, $.1^226>, <$.1^3, $.1^259>, <$.1^52, $.1^19>, <$.1^224, $.1^46>, <$.1^23, $.1^196>, <$.1^239, $.1^304>, <$.1^12, $.1^8>, <$.1^325, $.1^22>, <$.1^47, $.1^80>, <$.1^185, $.1^87>, <$.1^169, $.1^7>, <$.1^120, $.1^330>, <$.1, $.1^138>, <$.1^329, $.1^140>, <$.1^55, $.1^23>, <$.1^201, $.1^296>, <$.1^271, $.1^243>, <$.1^58, $.1^103>, <$.1^99, $.1^203>, <$.1^188, $.1^247>, <$.1^144, $.1^85>, <$.1^338, $.1^246>, <$.1^150, $.1^147>, <$.1^58, $.1^97>, <$.1^208, $.1^207>, <$.1^196, $.1^297>, <$.1^315, $.1^106>, <$.1^173, $.1^183>, <$.1^53, $.1^73>, <2, $.1^33>, <$.1^47, $.1^20>, <$.1^185, $.1^213>, <$.1^20, $.1^287>, <$.1^29, $.1^265>, <$.1^259, $.1^330>, <$.1^30, $.1^191>, <$.1^34, $.1^244>, <$.1^144, $.1^13>, <$.1^180, $.1^146>, <$.1^325, $.1^142>, <$.1^150, $.1^249>, <$.1^271, $.1^339>, <$.1^159, 1>, <$.1^264, $.1^83>, <$.1^167, $.1^33>, <$.1^169, $.1^19>, <$.1^140, $.1^173>, <$.1^6, $.1^298>, <$.1^321, $.1^24>, <$.1^173, $.1^237>, <$.1^117, $.1^87>, <4, $.1^107>, <$.1^138, $.1^161>, <$.1^182, $.1^261>, <$.1^206, $.1^227>, <$.1^256, $.1^121>, <$.1^301, $.1^311>, <$.1^310, $.1^179>, <$.1^21, $.1^121>, <$.1^294, $.1^34>, <$.1^155, $.1^163>, <$.1^92, $.1^201>, <$.1^198, $.1^244>, <$.1^88, $.1^141>, <$.1^189, $.1^97>, <$.1^180, $.1^320>, <$.1^241, $.1^201>, <$.1^102, $.1^137>, <$.1^123, $.1^103>, <$.1^220, $.1^153>, <$.1^314, $.1^306>, <$.1^138, $.1^179>, <$.1^68, $.1^199>, <$.1^39, $.1^44>, <$.1^245, $.1^290>, <$.1^89, $.1^83>, <$.1^212, $.1^110>, <$.1^181, $.1^237>, <$.1^53, $.1^217>, <$.1^87, $.1^72>, <$.1^187, $.1^183>, <$.1^309, $.1^92>, <$.1^275, $.1^258>, <$.1^307, $.1^126>, <$.1^231, $.1^221>, <$.1^242, $.1^154>, <$.1^25, $.1^144>, <$.1^80, $.1^161>, <$.1^251, $.1^2>, <$.1^98, $.1^282>, <5, $.1^6>, <$.1^337, $.1^300>, <$.1^45, $.1^244>, <$.1^116, $.1^320>, <$.1^290, $.1^313>, <$.1^123, $.1^7>, <$.1^58, $.1^55>, <$.1^289, $.1^2>, <$.1^284, 0>, <$.1^248, $.1^177>, <$.1^241, $.1^267>, <$.1^218, $.1^263>, <$.1^134, $.1^187>, <$.1^207, $.1^130>, <$.1^20, $.1^263>, <$.1^44, $.1^255>, <6, $.1^322>, <$.1^220, $.1^129>, <6, $.1^82>, <$.1^101, $.1^10>, <$.1^226, $.1^230>, <$.1^145, $.1^136>, <$.1^178, $.1^237>, <$.1^261, $.1^21>, <$.1^241, $.1^273>, <$.1^2, $.1^300>, <$.1^192, $.1^76>, <$.1^260, $.1^98>, <$.1^41, $.1^311>, <$.1^313, $.1^230>, <$.1^339, $.1^270>, <$.1^299, $.1^71>, <$.1^178, $.1^189>, <$.1^156, $.1^60>, <$.1^223, $.1^298>, <$.1^102, $.1^47>, <$.1^308, $.1^99>, <$.1^82, $.1^97>, <$.1^326, $.1^268>, <$.1^21, $.1^241>, <$.1^148, $.1^174>, <$.1^78, $.1^146>, <1, $.1^133>, <$.1^240, $.1^288>, <$.1^229, $.1^196>, <$.1^34, $.1^46>, <$.1^39, $.1^8>, <$.1^177, $.1^139>, <$.1^89, $.1^131>, <$.1^178, $.1^3>, <$.1^80, $.1^71>, <$.1^117, $.1^327>, <$.1^246, $.1^200>, <$.1^137, $.1^216>, <$.1^205, $.1^217>, <$.1^112, $.1^66>, <$.1^317, $.1^159>, <$.1^297, $.1^73>, <$.1^309, $.1^74>, <$.1^86, $.1^50>, <$.1^294, $.1^76>, <$.1^259, $.1^6>, <$.1^302, $.1^333>, <$.1^339, $.1^120>, <$.1^100, $.1^312>, <$.1^86, $.1^200>, <$.1^242, $.1^172>, <$.1^257, $.1^209>, <$.1^337, $.1^324>, <$.1^260, $.1^152>, <$.1^116, $.1^290>, <$.1^43, $.1^95>, <$.1^31, $.1^2>, <$.1^326, $.1^40>, <$.1^93, $.1^326>, <$.1^319, $.1^189>, <$.1^43, $.1^173>, <$.1^261, $.1^33>, <$.1^287, $.1^107>, <$.1^142, $.1^245>, <$.1^43, $.1^185>, <$.1^185, $.1^69>, <$.1^132, $.1^234>, <$.1^326, $.1^304>, <$.1^197, $.1^252>, <$.1^21, $.1^127>, <$.1^9, $.1^281>, <$.1^147, $.1>, <$.1^100, $.1^186>, <$.1^110, $.1^290>, <$.1^290, $.1^43>, <$.1^255, $.1^191>, <$.1^328, $.1^226>, <$.1^253, $.1^124>, <$.1^70, $.1^252>, <$.1^268, $.1^267>, <$.1^71, $.1^157>, <$.1^185, $.1^45>, <$.1^174, $.1^304>, <$.1^16, $.1^270>, <$.1^47, $.1^188>, <$.1^109, $.1^218>, <$.1^258, $.1^243>, <$.1^187, $.1^147>, <$.1^281, $.1^173>, <1, $.1^127>, <$.1^81, $.1^64>, <$.1^314, $.1^222>, <$.1^85, $.1^148>, <$.1^235, $.1^190>, <$.1^143, $.1^279>, <$.1^25, $.1^324>, <$.1^157, $.1^295>, <$.1^202, $.1^89>, <$.1^75, $.1^239>, <$.1^59, $.1^13>, <$.1^151, $.1^128>, <$.1^313, $.1^170>, <$.1^118, $.1^323>, <$.1^22, $.1^85>, <$.1^206, $.1^65>, <$.1^169, $.1^187>, <$.1^296, $.1^41>, <$.1^255, $.1^155>, <$.1^224, $.1^226>, <$.1^339, $.1^264>, <$.1^64, $.1^175>, <$.1^121, $.1^128>, <$.1^24, $.1^147>, <$.1^199, $.1^294>, <$.1^216, $.1^295>, <$.1^177, $.1^127>, <$.1^282, $.1^59>, <$.1^187, $.1^3>, <$.1^309, $.1^152>, <$.1^119, $.1^46>, <$.1^281, $.1^323>, <$.1^148, $.1^216>, <$.1^67, $.1^313>, <$.1^326, $.1^100>, <$.1^334, $.1^125>, <$.1^151, $.1^302>, <$.1^296, $.1^107>, <$.1^117, $.1^105>, <$.1^287, $.1^11>, <$.1^218, $.1^167>, <$.1^286, $.1^125>, <$.1^216, $.1>, <$.1^211, $.1^134>, <$.1^143, $.1^99>, <$.1^338, $.1^48>, <$.1^261, $.1^297>, <$.1^27, $.1^31>, <$.1^39, $.1^320>, <$.1^315, $.1^112>, <$.1^281, $.1^329>, <$.1^254, $.1^217>, <$.1^238, $.1^280>, <$.1^132, $.1^54>, <$.1^25, $.1^186>, <$.1^331, ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 9 05:10:47 2004 Input: R:= Integers (); P := PolynomialRing (R); polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; main := function (a,b) exponent := polinomi_t (a,b); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); PuntsOlav := { : c in GF (a,b) , d in GF (a,b) | Evaluate (pol_t,c) eq Evaluate (pol_n,d)}; return (PuntsOlav); end function; list := main (7,3); #list; Output: Magma V2.10-6 Tue Mar 9 2004 05:10:39 on modular [Seed = 1801892653] ------------------------------------- 16807 Total time: 7.079 seconds, Total memory usage: 2.98MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 9 05:11:28 2004 Input: R:= Integers (); P := PolynomialRing (R); polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; main := function (a,b) exponent := polinomi_t (a,b); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); PuntsOlav := { : c in GF (a,b) , d in GF (a,b) | Evaluate (pol_t,c) eq Evaluate (pol_n,d)}; return (PuntsOlav); end function; list := main (8,4); #list; Output: Magma V2.10-6 Tue Mar 9 2004 05:11:24 on modular [Seed = 337234945] ------------------------------------- [
:31]( a: 8, b: 4 ) >> PuntsOlav := { : c in GF (a,b) , d in GF (a,b) | Evaluate (pol_t,c) ^ Runtime error in 'GF': Argument 1 (8) should be prime >> #list; ^ User error: Identifier 'list' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 9 05:12:24 2004 Input: R:= Integers (); P := PolynomialRing (R); polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; main := function (a,b) exponent := polinomi_t (a,b); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); PuntsOlav := { : c in GF (a,b) , d in GF (a,b) | Evaluate (pol_t,c) eq Evaluate (pol_n,d)}; return (PuntsOlav); end function; list := main (11,4); #list; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Mar 9 2004 05:11:59 on modular [Seed = 993452813] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 6498 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 9 05:13:00 2004 Input: R:= Integers (); P := PolynomialRing (R); polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; main := function (a,b) exponent := polinomi_t (a,b); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); PuntsOlav := { : c in GF (a,b) , d in GF (a,b) | Evaluate (pol_t,c) eq Evaluate (pol_n,d)}; return (PuntsOlav); end function; list := main (3,1); #list; Output: Magma V2.10-6 Tue Mar 9 2004 05:12:55 on modular [Seed = 3451917619] ------------------------------------- 3 Total time: 3.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 9 05:13:54 2004 Input: R:= Integers (); P := PolynomialRing (R); polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; main := function (a,b) exponent := polinomi_t (a,b); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); PuntsOlav := { : c in GF (a,b) , d in GF (a,b) | Evaluate (pol_t,c) eq Evaluate (pol_n,d)}; return (PuntsOlav); end function; list := main (5,7); #list; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Mar 9 2004 05:13:30 on modular [Seed = 3907334267] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 6577 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 9 05:14:30 2004 Input: R:= Integers (); P := PolynomialRing (R); polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; main := function (a,b) exponent := polinomi_t (a,b); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); PuntsOlav := { : c in GF (a,b) , d in GF (a,b) | Evaluate (pol_t,c) eq Evaluate (pol_n,d)}; return (PuntsOlav); end function; list := main (7,5); #list; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Mar 9 2004 05:14:06 on modular [Seed = 2543472416] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 6606 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 9 05:14:50 2004 Input: R:= Integers (); P := PolynomialRing (R); polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; main := function (a,b) exponent := polinomi_t (a,b); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); PuntsOlav := { : c in GF (a,b) , d in GF (a,b) | Evaluate (pol_t,c) eq Evaluate (pol_n,d)}; return (PuntsOlav); end function; list := main (7,3); #list; Output: Magma V2.10-6 Tue Mar 9 2004 05:14:42 on modular [Seed = 3032051199] ------------------------------------- 16807 Total time: 6.859 seconds, Total memory usage: 2.98MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 9 05:15:26 2004 Input: R:= Integers (); P := PolynomialRing (R); polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; main := function (a,b) exponent := polinomi_t (a,b); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); PuntsOlav := { : c in GF (a,b) , d in GF (a,b) | Evaluate (pol_t,c) eq Evaluate (pol_n,d)}; return (PuntsOlav); end function; list := main (11,3); #list; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Mar 9 2004 05:15:01 on modular [Seed = 1498710054] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 6659 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 9 05:15:46 2004 Input: R:= Integers (); P := PolynomialRing (R); polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; main := function (a,b) exponent := polinomi_t (a,b); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); PuntsOlav := { : c in GF (a,b) , d in GF (a,b) | Evaluate (pol_t,c) eq Evaluate (pol_n,d)}; return (PuntsOlav); end function; list := main (5,3); #list; Output: Magma V2.10-6 Tue Mar 9 2004 05:15:42 on modular [Seed = 1095538773] ------------------------------------- 3125 Total time: 3.649 seconds, Total memory usage: 2.13MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 9 05:16:48 2004 Input: R:= Integers (); P := PolynomialRing (R); polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; main := function (a,b) exponent := polinomi_t (a,b); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); PuntsOlav := { : c in GF (a,b) , d in GF (a,b) | Evaluate (pol_t,c) eq Evaluate (pol_n,d)}; return (PuntsOlav); end function; list := main (13,3); #list; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Mar 9 2004 05:16:23 on modular [Seed = 1868740162] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 6709 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 9 05:17:41 2004 Input: R:= Integers (); P := PolynomialRing (R); polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; main := function (a,b) exponent := polinomi_t (a,b); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); PuntsOlav := { : c in GF (a,b) , d in GF (a,b) | Evaluate (pol_t,c) eq Evaluate (pol_n,d)}; return (PuntsOlav); end function; list := main (3,3); #list; Output: Magma V2.10-6 Tue Mar 9 2004 05:17:36 on modular [Seed = 1026614439] ------------------------------------- 243 Total time: 3.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 9 05:18:30 2004 Input: R:= Integers (); P := PolynomialRing (R); polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; main := function (a,b) exponent := polinomi_t (a,b); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); PuntsOlav := { : c in GF (a,b) , d in GF (a,b) | Evaluate (pol_t,c) eq Evaluate (pol_n,d)}; return (PuntsOlav); end function; list := main (11,1); #list; Output: Magma V2.10-6 Tue Mar 9 2004 05:18:26 on modular [Seed = 3554544251] ------------------------------------- 11 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 9 05:18:48 2004 Input: R:= Integers (); P := PolynomialRing (R); polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; main := function (a,b) exponent := polinomi_t (a,b); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); PuntsOlav := { : c in GF (a,b) , d in GF (a,b) | Evaluate (pol_t,c) eq Evaluate (pol_n,d)}; return (PuntsOlav); end function; list := main (11,2); #list; Output: Magma V2.10-6 Tue Mar 9 2004 05:18:43 on modular [Seed = 3251379096] ------------------------------------- 1331 Total time: 4.249 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 9 05:22:42 2004 Input: R:= Integers (); P := PolynomialRing (R); polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; main := function (a,b) exponent := polinomi_t (a,b); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); PuntsOlav := { : c in GF (a,b) , d in GF (a,b) | Evaluate (pol_t,c) eq Evaluate (pol_n,d)}; return (PuntsOlav); end function; list := main (7,1); #list; Output: Magma V2.10-6 Tue Mar 9 2004 05:22:38 on modular [Seed = 2087823049] ------------------------------------- 7 Total time: 3.349 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 9 05:24:28 2004 Input: R:= Integers (); P := PolynomialRing (R); polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; main := function (a) exponent := polinomi_t (a,1); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); PuntsOlav := { : c in GF (a,1) , d in GF (a,1) | Evaluate (pol_t,c) eq Evaluate (pol_n,d)}; return (PuntsOlav); end function; list := main (7); #list; Output: Magma V2.10-6 Tue Mar 9 2004 05:24:23 on modular [Seed = 1060299827] ------------------------------------- 7 Total time: 3.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 9 05:24:42 2004 Input: R:= Integers (); P := PolynomialRing (R); polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; main := function (a) exponent := polinomi_t (a,1); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); PuntsOlav := { : c in GF (a,1) , d in GF (a,1) | Evaluate (pol_t,c) eq Evaluate (pol_n,d)}; return (PuntsOlav); end function; list := main (11); #list; Output: Magma V2.10-6 Tue Mar 9 2004 05:24:37 on modular [Seed = 707260692] ------------------------------------- 11 Total time: 4.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 9 05:30:06 2004 Input: /*Exercici 1*/ Diumenges := []; dies := [1..366 by 1]; for i:=4 to 366 by 7 do Diumenges := Include (Diumenges,dies[i]); end for; print Diumenges; /*resposta*/ /*[ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ]*/ /*Exercici 2*/ M:= GF (4); /*creem cos finit */ M22:= MatrixRing (M,2); /*creem matrius 2x2*/ /*matrius de traça 0*/ Mt:= { x : x in M22 | Trace (x) eq 0 }; /*resposta*/ print Mt; /* [ 0 0] [ 0 0], [ 0 0] [M.1^2 0], [ 0 0] [ M.1 0], [ 0 0] [ 1 0], [M.1^2 0] [ 0 M.1^2], [M.1^2 0] [M.1^2 M.1^2], [M.1^2 0] [ M.1 M.1^2], [M.1^2 0] [ 1 M.1^2], [ 1 0] [ 0 1], [ 1 0] [M.1^2 1], [ 1 0] [ M.1 1], [ 1 0] [ 1 1], [ M.1 0] [ 0 M.1], [ M.1 0] [M.1^2 M.1], [ M.1 0] [ M.1 M.1], [ M.1 0] [ 1 M.1], [ 0 M.1^2] [ 0 0], [ 0 M.1^2] [M.1^2 0], [ 0 M.1^2] [ M.1 0], [ 0 M.1^2] [ 1 0], [M.1^2 M.1^2] [ 0 M.1^2], [M.1^2 M.1^2] [M.1^2 M.1^2], [M.1^2 M.1^2] [ M.1 M.1^2], [M.1^2 M.1^2] [ 1 M.1^2], [ 1 M.1^2] [ 0 1], [ 1 M.1^2] [M.1^2 1], [ 1 M.1^2] [ M.1 1], [ 1 M.1^2] [ 1 1], [ M.1 M.1^2] [ 0 M.1], [ M.1 M.1^2] [M.1^2 M.1], [ M.1 M.1^2] [ M.1 M.1], [ M.1 M.1^2] [ 1 M.1], [ 0 M.1] [ 0 0], [ 0 M.1] [M.1^2 0], [ 0 M.1] [ M.1 0], [ 0 M.1] [ 1 0], [M.1^2 M.1] [ 0 M.1^2], [M.1^2 M.1] [M.1^2 M.1^2], [M.1^2 M.1] [ M.1 M.1^2], [M.1^2 M.1] [ 1 M.1^2], [ 1 M.1] [ 0 1], [ 1 M.1] [M.1^2 1], [ 1 M.1] [ M.1 1], [ 1 M.1] [ 1 1], [ M.1 M.1] [ 0 M.1], [ M.1 M.1] [M.1^2 M.1], [ M.1 M.1] [ M.1 M.1], [ M.1 M.1] [ 1 M.1], [ 0 1] [ 0 0], [ 0 1] [M.1^2 0], [ 0 1] [ M.1 0], [ 0 1] [ 1 0], [M.1^2 1] [ 0 M.1^2], [M.1^2 1] [M.1^2 M.1^2], [M.1^2 1] [ M.1 M.1^2], [M.1^2 1] [ 1 M.1^2], [ 1 1] [ 0 1], [ 1 1] [M.1^2 1], [ 1 1] [ M.1 1], [ 1 1] [ 1 1], [ M.1 1] [ 0 M.1], [ M.1 1] [M.1^2 M.1], [ M.1 1] [ M.1 M.1], [ M.1 1] [ 1 M.1] } */ /*Matrius on la primer fila = Segona fila*/ Mf:= { y : y in M22 | Submatrix (y,1,1,1,2) eq Submatrix (y,2,1,1,2)}; /*resposta*/ print Mf; /*{ [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ M.1 0] [ M.1 0], [ 0 M.1^2] [ 0 M.1^2], [ M.1 M.1^2] [ M.1 M.1^2], [ 0 M.1] [ 0 M.1], [ M.1 M.1] [ M.1 M.1], [ 0 1] [ 0 1], [ M.1 1] [ M.1 1], [M.1^2 0] [M.1^2 0], [ 1 0] [ 1 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ 1 M.1^2] [ 1 M.1^2], [M.1^2 M.1] [M.1^2 M.1], [ 1 M.1] [ 1 M.1], [M.1^2 1] [M.1^2 1] } */ /*Matrius que cumpleixen les dues funciones anterios*/ Mtf := Mt meet Mf; /*resposta*/ print Mtf; /* { [ 0 0] [ 0 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ M.1 M.1] [ M.1 M.1], [ 1 1] [ 1 1] } */ /*Exercici 2d*/ Aleatori := [Random(M22): n in [1..10]]; #([a : a in Aleatori | a in Mt]); #([a : a in Aleatori | a in Mf]); #([a : a in Aleatori | a in Mtf]); print Aleatori; Output: Magma V2.10-6 Tue Mar 9 2004 05:30:02 on modular [Seed = 1145673906] ------------------------------------- [ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] { [ 0 0] [ 0 0], [ 0 0] [M.1^2 0], [ 0 0] [ M.1 0], [ 0 0] [ 1 0], [M.1^2 0] [ 0 M.1^2], [M.1^2 0] [M.1^2 M.1^2], [M.1^2 0] [ M.1 M.1^2], [M.1^2 0] [ 1 M.1^2], [ 1 0] [ 0 1], [ 1 0] [M.1^2 1], [ 1 0] [ M.1 1], [ 1 0] [ 1 1], [ M.1 0] [ 0 M.1], [ M.1 0] [M.1^2 M.1], [ M.1 0] [ M.1 M.1], [ M.1 0] [ 1 M.1], [ 0 M.1^2] [ 0 0], [ 0 M.1^2] [M.1^2 0], [ 0 M.1^2] [ M.1 0], [ 0 M.1^2] [ 1 0], [M.1^2 M.1^2] [ 0 M.1^2], [M.1^2 M.1^2] [M.1^2 M.1^2], [M.1^2 M.1^2] [ M.1 M.1^2], [M.1^2 M.1^2] [ 1 M.1^2], [ 1 M.1^2] [ 0 1], [ 1 M.1^2] [M.1^2 1], [ 1 M.1^2] [ M.1 1], [ 1 M.1^2] [ 1 1], [ M.1 M.1^2] [ 0 M.1], [ M.1 M.1^2] [M.1^2 M.1], [ M.1 M.1^2] [ M.1 M.1], [ M.1 M.1^2] [ 1 M.1], [ 0 M.1] [ 0 0], [ 0 M.1] [M.1^2 0], [ 0 M.1] [ M.1 0], [ 0 M.1] [ 1 0], [M.1^2 M.1] [ 0 M.1^2], [M.1^2 M.1] [M.1^2 M.1^2], [M.1^2 M.1] [ M.1 M.1^2], [M.1^2 M.1] [ 1 M.1^2], [ 1 M.1] [ 0 1], [ 1 M.1] [M.1^2 1], [ 1 M.1] [ M.1 1], [ 1 M.1] [ 1 1], [ M.1 M.1] [ 0 M.1], [ M.1 M.1] [M.1^2 M.1], [ M.1 M.1] [ M.1 M.1], [ M.1 M.1] [ 1 M.1], [ 0 1] [ 0 0], [ 0 1] [M.1^2 0], [ 0 1] [ M.1 0], [ 0 1] [ 1 0], [M.1^2 1] [ 0 M.1^2], [M.1^2 1] [M.1^2 M.1^2], [M.1^2 1] [ M.1 M.1^2], [M.1^2 1] [ 1 M.1^2], [ 1 1] [ 0 1], [ 1 1] [M.1^2 1], [ 1 1] [ M.1 1], [ 1 1] [ 1 1], [ M.1 1] [ 0 M.1], [ M.1 1] [M.1^2 M.1], [ M.1 1] [ M.1 M.1], [ M.1 1] [ 1 M.1] } { [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ M.1 0] [ M.1 0], [ 0 M.1^2] [ 0 M.1^2], [ M.1 M.1^2] [ M.1 M.1^2], [ 0 M.1] [ 0 M.1], [ M.1 M.1] [ M.1 M.1], [ 0 1] [ 0 1], [ M.1 1] [ M.1 1], [M.1^2 0] [M.1^2 0], [ 1 0] [ 1 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ 1 M.1^2] [ 1 M.1^2], [M.1^2 M.1] [M.1^2 M.1], [ 1 M.1] [ 1 M.1], [M.1^2 1] [M.1^2 1] } { [ 0 0] [ 0 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ M.1 M.1] [ M.1 M.1], [ 1 1] [ 1 1] } 2 0 0 [ [ 0 M.1] [M.1^2 M.1], [ 1 0] [ M.1 1], [ 1 M.1] [M.1^2 M.1], [ 1 M.1^2] [ 1 M.1], [ M.1 M.1] [ 1 M.1], [M.1^2 M.1^2] [ M.1 0], [ 1 M.1] [M.1^2 0], [ 1 1] [M.1^2 M.1], [ 1 M.1] [ M.1 M.1], [M.1^2 0] [ 1 1] ] Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 9 05:31:58 2004 Input: /*Exercici 1*/ Diumenges := []; dies := [1..366 by 1]; for i:=4 to 366 by 7 do Diumenges := Include (Diumenges,dies[i]); end for; print Diumenges; /*resposta*/ /*[ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ]*/ /*Exercici 2*/ M:= GF (4); /*creem cos finit */ M22:= MatrixRing (M,2); /*creem matrius 2x2*/ /*matrius de traça 0*/ Mt:= { x : x in M22 | Trace (x) eq 0 }; /*resposta*/ print Mt; /* [ 0 0] [ 0 0], [ 0 0] [M.1^2 0], [ 0 0] [ M.1 0], [ 0 0] [ 1 0], [M.1^2 0] [ 0 M.1^2], [M.1^2 0] [M.1^2 M.1^2], [M.1^2 0] [ M.1 M.1^2], [M.1^2 0] [ 1 M.1^2], [ 1 0] [ 0 1], [ 1 0] [M.1^2 1], [ 1 0] [ M.1 1], [ 1 0] [ 1 1], [ M.1 0] [ 0 M.1], [ M.1 0] [M.1^2 M.1], [ M.1 0] [ M.1 M.1], [ M.1 0] [ 1 M.1], [ 0 M.1^2] [ 0 0], [ 0 M.1^2] [M.1^2 0], [ 0 M.1^2] [ M.1 0], [ 0 M.1^2] [ 1 0], [M.1^2 M.1^2] [ 0 M.1^2], [M.1^2 M.1^2] [M.1^2 M.1^2], [M.1^2 M.1^2] [ M.1 M.1^2], [M.1^2 M.1^2] [ 1 M.1^2], [ 1 M.1^2] [ 0 1], [ 1 M.1^2] [M.1^2 1], [ 1 M.1^2] [ M.1 1], [ 1 M.1^2] [ 1 1], [ M.1 M.1^2] [ 0 M.1], [ M.1 M.1^2] [M.1^2 M.1], [ M.1 M.1^2] [ M.1 M.1], [ M.1 M.1^2] [ 1 M.1], [ 0 M.1] [ 0 0], [ 0 M.1] [M.1^2 0], [ 0 M.1] [ M.1 0], [ 0 M.1] [ 1 0], [M.1^2 M.1] [ 0 M.1^2], [M.1^2 M.1] [M.1^2 M.1^2], [M.1^2 M.1] [ M.1 M.1^2], [M.1^2 M.1] [ 1 M.1^2], [ 1 M.1] [ 0 1], [ 1 M.1] [M.1^2 1], [ 1 M.1] [ M.1 1], [ 1 M.1] [ 1 1], [ M.1 M.1] [ 0 M.1], [ M.1 M.1] [M.1^2 M.1], [ M.1 M.1] [ M.1 M.1], [ M.1 M.1] [ 1 M.1], [ 0 1] [ 0 0], [ 0 1] [M.1^2 0], [ 0 1] [ M.1 0], [ 0 1] [ 1 0], [M.1^2 1] [ 0 M.1^2], [M.1^2 1] [M.1^2 M.1^2], [M.1^2 1] [ M.1 M.1^2], [M.1^2 1] [ 1 M.1^2], [ 1 1] [ 0 1], [ 1 1] [M.1^2 1], [ 1 1] [ M.1 1], [ 1 1] [ 1 1], [ M.1 1] [ 0 M.1], [ M.1 1] [M.1^2 M.1], [ M.1 1] [ M.1 M.1], [ M.1 1] [ 1 M.1] } */ /*Matrius on la primer fila = Segona fila*/ Mf:= { y : y in M22 | Submatrix (y,1,1,1,2) eq Submatrix (y,2,1,1,2)}; /*resposta*/ print Mf; /*{ [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ M.1 0] [ M.1 0], [ 0 M.1^2] [ 0 M.1^2], [ M.1 M.1^2] [ M.1 M.1^2], [ 0 M.1] [ 0 M.1], [ M.1 M.1] [ M.1 M.1], [ 0 1] [ 0 1], [ M.1 1] [ M.1 1], [M.1^2 0] [M.1^2 0], [ 1 0] [ 1 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ 1 M.1^2] [ 1 M.1^2], [M.1^2 M.1] [M.1^2 M.1], [ 1 M.1] [ 1 M.1], [M.1^2 1] [M.1^2 1] } */ /*Matrius que cumpleixen les dues funciones anterios*/ Mtf := Mt meet Mf; /*resposta*/ print Mtf; /* { [ 0 0] [ 0 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ M.1 M.1] [ M.1 M.1], [ 1 1] [ 1 1] } */ /*Exercici 2d*/ Aleatori := [Random(M22): n in [1..100000]]; #([a : a in Aleatori | a in Mt]); #([a : a in Aleatori | a in Mf]); #([a : a in Aleatori | a in Mtf]); print Aleatori; Output: Magma V2.10-6 Tue Mar 9 2004 05:31:48 on modular [Seed = 908616] ------------------------------------- [ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] { [ 0 0] [ 0 0], [ 0 0] [M.1^2 0], [ 0 0] [ M.1 0], [ 0 0] [ 1 0], [M.1^2 0] [ 0 M.1^2], [M.1^2 0] [M.1^2 M.1^2], [M.1^2 0] [ M.1 M.1^2], [M.1^2 0] [ 1 M.1^2], [ 1 0] [ 0 1], [ 1 0] [M.1^2 1], [ 1 0] [ M.1 1], [ 1 0] [ 1 1], [ M.1 0] [ 0 M.1], [ M.1 0] [M.1^2 M.1], [ M.1 0] [ M.1 M.1], [ M.1 0] [ 1 M.1], [ 0 M.1^2] [ 0 0], [ 0 M.1^2] [M.1^2 0], [ 0 M.1^2] [ M.1 0], [ 0 M.1^2] [ 1 0], [M.1^2 M.1^2] [ 0 M.1^2], [M.1^2 M.1^2] [M.1^2 M.1^2], [M.1^2 M.1^2] [ M.1 M.1^2], [M.1^2 M.1^2] [ 1 M.1^2], [ 1 M.1^2] [ 0 1], [ 1 M.1^2] [M.1^2 1], [ 1 M.1^2] [ M.1 1], [ 1 M.1^2] [ 1 1], [ M.1 M.1^2] [ 0 M.1], [ M.1 M.1^2] [M.1^2 M.1], [ M.1 M.1^2] [ M.1 M.1], [ M.1 M.1^2] [ 1 M.1], [ 0 M.1] [ 0 0], [ 0 M.1] [M.1^2 0], [ 0 M.1] [ M.1 0], [ 0 M.1] [ 1 0], [M.1^2 M.1] [ 0 M.1^2], [M.1^2 M.1] [M.1^2 M.1^2], [M.1^2 M.1] [ M.1 M.1^2], [M.1^2 M.1] [ 1 M.1^2], [ 1 M.1] [ 0 1], [ 1 M.1] [M.1^2 1], [ 1 M.1] [ M.1 1], [ 1 M.1] [ 1 1], [ M.1 M.1] [ 0 M.1], [ M.1 M.1] [M.1^2 M.1], [ M.1 M.1] [ M.1 M.1], [ M.1 M.1] [ 1 M.1], [ 0 1] [ 0 0], [ 0 1] [M.1^2 0], [ 0 1] [ M.1 0], [ 0 1] [ 1 0], [M.1^2 1] [ 0 M.1^2], [M.1^2 1] [M.1^2 M.1^2], [M.1^2 1] [ M.1 M.1^2], [M.1^2 1] [ 1 M.1^2], [ 1 1] [ 0 1], [ 1 1] [M.1^2 1], [ 1 1] [ M.1 1], [ 1 1] [ 1 1], [ M.1 1] [ 0 M.1], [ M.1 1] [M.1^2 M.1], [ M.1 1] [ M.1 M.1], [ M.1 1] [ 1 M.1] } { [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ M.1 0] [ M.1 0], [ 0 M.1^2] [ 0 M.1^2], [ M.1 M.1^2] [ M.1 M.1^2], [ 0 M.1] [ 0 M.1], [ M.1 M.1] [ M.1 M.1], [ 0 1] [ 0 1], [ M.1 1] [ M.1 1], [M.1^2 0] [M.1^2 0], [ 1 0] [ 1 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ 1 M.1^2] [ 1 M.1^2], [M.1^2 M.1] [M.1^2 M.1], [ 1 M.1] [ 1 M.1], [M.1^2 1] [M.1^2 1] } { [ 0 0] [ 0 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ M.1 M.1] [ M.1 M.1], [ 1 1] [ 1 1] } 24830 6187 1539 [ [ 0 1] [ M.1 0], [ M.1 1] [ 1 M.1^2], [ 1 0] [ 1 0], [ 1 M.1^2] [M.1^2 1], [M.1^2 1] [M.1^2 M.1], [M.1^2 M.1] [ 1 M.1], [ 1 1] [ M.1 0], [ M.1 M.1] [ 0 1], [M.1^2 1] [ 0 0], [ M.1 M.1] [ M.1 1], [M.1^2 M.1] [M.1^2 M.1^2], [ M.1 0] [ M.1 1], [M.1^2 0] [M.1^2 0], [ M.1 M.1] [ 0 1], [M.1^2 M.1] [ M.1 1], [M.1^2 0] [ 0 1], [ M.1 M.1] [M.1^2 M.1], [ 1 0] [ M.1 M.1^2], [ 0 M.1^2] [ 0 0], [ M.1 M.1] [ 1 0], [ 1 1] [ 0 1], [ 1 M.1^2] [ 1 M.1], [ 1 M.1^2] [ 1 M.1^2], [M.1^2 0] [ M.1 1], [ 1 1] [M.1^2 0], [ 1 0] [ 1 0], [ 0 0] [ 1 1], [ M.1 0] [ 1 0], [ 0 1] [M.1^2 1], [ 1 M.1^2] [ M.1 1], [ 0 0] [ 0 1], [M.1^2 0] [ 0 M.1^2], [ 0 0] [ 1 M.1], [ M.1 0] [M.1^2 M.1], [ 0 0] [ M.1 0], [M.1^2 M.1^2] [ 0 0], [ 1 M.1^2] [M.1^2 1], [ 1 M.1^2] [ M.1 M.1^2], [ M.1 0] [ M.1 0], [ M.1 1] [M.1^2 M.1^2], [M.1^2 0] [ 0 M.1^2], [ M.1 0] [ 1 1], [ 1 0] [ 1 M.1^2], [M.1^2 1] [ M.1 0], [ M.1 M.1] [ 0 M.1], [ M.1 1] [ 0 0], [M.1^2 M.1] [M.1^2 1], [ 1 0] [M.1^2 1], [ M.1 M.1^2] [M.1^2 M.1^2], [ 1 0] [ M.1 0], [ M.1 1] [ 1 M.1], [ 0 1] [M.1^2 M.1^2], [ M.1 1] [M.1^2 M.1^2], [ M.1 1] [ M.1 M.1^2], [M.1^2 0] [ M.1 M.1], [M.1^2 M.1] [M.1^2 M.1], [ M.1 1] [ 1 M.1^2], [ M.1 M.1] [ 0 M.1^2], [ 0 1] [ M.1 M.1^2], [M.1^2 1] [ 1 1], [ M.1 0] [ 0 1], [ M.1 M.1^2] [M.1^2 M.1^2], [M.1^2 0] [ 0 1], [ 0 0] [M.1^2 1], [ M.1 M.1^2] [ 1 M.1], [M.1^2 M.1] [ 0 0], [M.1^2 0] [ 0 M.1^2], [ 1 1] [ M.1 M.1], [ M.1 1] [M.1^2 M.1], [ 1 M.1] [ 0 0], [M.1^2 M.1] [ 0 M.1], [ 1 1] [ 1 0], [ 0 M.1] [M.1^2 0], [ 0 0] [ 1 1], [ M.1 0] [ M.1 0], [M.1^2 1] [ 1 0], [ 1 0] [ M.1 M.1^2], [ 0 0] [M.1^2 M.1^2], [ 0 M.1^2] [ M.1 M.1^2], [ 1 0] [ 1 0], [ 0 1] [ 1 M.1], [M.1^2 0] [M.1^2 M.1^2], [M.1^2 M.1^2] [ 1 M.1], [ 1 1] [M.1^2 M.1], [ 0 M.1] [ 0 M.1], [ M.1 1] [M.1^2 0], [M.1^2 1] [ 1 M.1], [ 1 M.1^2] [ 0 M.1], [ M.1 M.1^2] [ 0 M.1^2], [M.1^2 M.1] [ 1 0], [M.1^2 M.1] [ 0 M.1], [M.1^2 M.1^2] [ 0 M.1], [ M.1 1] [ M.1 1], [ 1 0] [M.1^2 0], [ M.1 0] [ M.1 M.1^2], [M.1^2 0] [ 1 M.1^2], [ 0 0] [M.1^2 1], [ 0 1] [ 1 M.1], [ M.1 1] [M.1^2 M.1^2], [M.1^2 0] [ 1 M.1^2], [ 0 1] [ 0 0], [ M.1 M.1^2] [ M.1 1], [ 0 M.1^2] [M.1^2 M.1^2], [ M.1 0] [ 1 0], [ M.1 M.1] [M.1^2 M.1], [ 1 0] [M.1^2 0], [M.1^2 M.1^2] [ 0 1], [ 1 0] [ M.1 M.1], [ M.1 0] [ M.1 1], [ 1 1] [ 1 M.1^2], [ 1 1] [ 1 1], [ 0 M.1^2] [M.1^2 M.1], [ M.1 M.1] [ 1 M.1^2], [ 1 1] [ 1 M.1^2], [ M.1 1] [M.1^2 0], [ M.1 1] [ M.1 M.1], [ 0 M.1^2] [ 1 M.1^2], [ M.1 M.1] [ 0 M.1^2], [M.1^2 0] [M.1^2 1], [ M.1 M.1] [ M.1 0], [ M.1 0] [M.1^2 M.1^2], [M.1^2 M.1] [ M.1 1], [ 1 M.1^2] [M.1^2 1], [M.1^2 1] [ M.1 1], [ 0 1] [ M.1 0], [ 0 1] [ 0 1], [ 1 M.1] [M.1^2 1], [ 1 1] [ 1 1], [M.1^2 0] [M.1^2 M.1^2], [ 1 M.1] [ 1 1], [ M.1 1] [ 0 M.1^2], [ M.1 0] [M.1^2 1], [M.1^2 1] [ 1 M.1], [ M.1 M.1^2] [ 1 1], [ 1 M.1] [ 0 0], [ 1 0] [ 0 1], [ 1 M.1] [ M.1 M.1^2], [ 1 1] [ M.1 M.1], [ 1 M.1] [ 1 0], [ 0 1] [ M.1 M.1^2], [ 1 0] [ 0 M.1], [M.1^2 M.1^2] [M.1^2 M.1^2], [M.1^2 1] [ 0 M.1^2], [ 0 0] [ 0 M.1^2], [ 0 M.1^2] [ M.1 M.1^2], [ M.1 0] [M.1^2 M.1^2], [ 1 M.1] [M.1^2 0], [ M.1 M.1] [ 0 M.1^2], [ 1 1] [M.1^2 0], [ 0 M.1] [M.1^2 M.1^2], [M.1^2 1] [M.1^2 M.1^2], [ 1 0] [ 0 M.1], [ 1 0] [ 0 M.1], [ M.1 M.1^2] [ 0 M.1], [ M.1 M.1^2] [M.1^2 1], [ 1 1] [M.1^2 M.1^2], [ 1 M.1] [ 1 M.1], [ 1 0] [M.1^2 1], [ M.1 1] [ 0 1], [M.1^2 M.1^2] [ M.1 M.1^2], [ 1 1] [ 0 1], [ 1 M.1] [M.1^2 M.1^2], [ 0 M.1^2] [M.1^2 M.1], [M.1^2 0] [M.1^2 M.1^2], [ M.1 M.1^2] [ 1 M.1], [ 0 M.1] [ M.1 M.1], [M.1^2 1] [M.1^2 M.1^2], [ M.1 0] [M.1^2 M.1^2], [ M.1 1] [M.1^2 M.1], ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 9 05:32:25 2004 Input: /*Exercici 1*/ Diumenges := []; dies := [1..366 by 1]; for i:=4 to 366 by 7 do Diumenges := Include (Diumenges,dies[i]); end for; print Diumenges; /*resposta*/ /*[ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ]*/ /*Exercici 2*/ M:= GF (4); /*creem cos finit */ M22:= MatrixRing (M,2); /*creem matrius 2x2*/ /*matrius de traça 0*/ Mt:= { x : x in M22 | Trace (x) eq 0 }; /*resposta*/ print Mt; /* [ 0 0] [ 0 0], [ 0 0] [M.1^2 0], [ 0 0] [ M.1 0], [ 0 0] [ 1 0], [M.1^2 0] [ 0 M.1^2], [M.1^2 0] [M.1^2 M.1^2], [M.1^2 0] [ M.1 M.1^2], [M.1^2 0] [ 1 M.1^2], [ 1 0] [ 0 1], [ 1 0] [M.1^2 1], [ 1 0] [ M.1 1], [ 1 0] [ 1 1], [ M.1 0] [ 0 M.1], [ M.1 0] [M.1^2 M.1], [ M.1 0] [ M.1 M.1], [ M.1 0] [ 1 M.1], [ 0 M.1^2] [ 0 0], [ 0 M.1^2] [M.1^2 0], [ 0 M.1^2] [ M.1 0], [ 0 M.1^2] [ 1 0], [M.1^2 M.1^2] [ 0 M.1^2], [M.1^2 M.1^2] [M.1^2 M.1^2], [M.1^2 M.1^2] [ M.1 M.1^2], [M.1^2 M.1^2] [ 1 M.1^2], [ 1 M.1^2] [ 0 1], [ 1 M.1^2] [M.1^2 1], [ 1 M.1^2] [ M.1 1], [ 1 M.1^2] [ 1 1], [ M.1 M.1^2] [ 0 M.1], [ M.1 M.1^2] [M.1^2 M.1], [ M.1 M.1^2] [ M.1 M.1], [ M.1 M.1^2] [ 1 M.1], [ 0 M.1] [ 0 0], [ 0 M.1] [M.1^2 0], [ 0 M.1] [ M.1 0], [ 0 M.1] [ 1 0], [M.1^2 M.1] [ 0 M.1^2], [M.1^2 M.1] [M.1^2 M.1^2], [M.1^2 M.1] [ M.1 M.1^2], [M.1^2 M.1] [ 1 M.1^2], [ 1 M.1] [ 0 1], [ 1 M.1] [M.1^2 1], [ 1 M.1] [ M.1 1], [ 1 M.1] [ 1 1], [ M.1 M.1] [ 0 M.1], [ M.1 M.1] [M.1^2 M.1], [ M.1 M.1] [ M.1 M.1], [ M.1 M.1] [ 1 M.1], [ 0 1] [ 0 0], [ 0 1] [M.1^2 0], [ 0 1] [ M.1 0], [ 0 1] [ 1 0], [M.1^2 1] [ 0 M.1^2], [M.1^2 1] [M.1^2 M.1^2], [M.1^2 1] [ M.1 M.1^2], [M.1^2 1] [ 1 M.1^2], [ 1 1] [ 0 1], [ 1 1] [M.1^2 1], [ 1 1] [ M.1 1], [ 1 1] [ 1 1], [ M.1 1] [ 0 M.1], [ M.1 1] [M.1^2 M.1], [ M.1 1] [ M.1 M.1], [ M.1 1] [ 1 M.1] } */ /*Matrius on la primer fila = Segona fila*/ Mf:= { y : y in M22 | Submatrix (y,1,1,1,2) eq Submatrix (y,2,1,1,2)}; /*resposta*/ print Mf; /*{ [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ M.1 0] [ M.1 0], [ 0 M.1^2] [ 0 M.1^2], [ M.1 M.1^2] [ M.1 M.1^2], [ 0 M.1] [ 0 M.1], [ M.1 M.1] [ M.1 M.1], [ 0 1] [ 0 1], [ M.1 1] [ M.1 1], [M.1^2 0] [M.1^2 0], [ 1 0] [ 1 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ 1 M.1^2] [ 1 M.1^2], [M.1^2 M.1] [M.1^2 M.1], [ 1 M.1] [ 1 M.1], [M.1^2 1] [M.1^2 1] } */ /*Matrius que cumpleixen les dues funciones anterios*/ Mtf := Mt meet Mf; /*resposta*/ print Mtf; /* { [ 0 0] [ 0 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ M.1 M.1] [ M.1 M.1], [ 1 1] [ 1 1] } */ /*Exercici 2d*/ Aleatori := [Random(M22): n in [1..10000]]; #([a : a in Aleatori | a in Mt]); #([a : a in Aleatori | a in Mf]); #([a : a in Aleatori | a in Mtf]); Output: Magma V2.10-6 Tue Mar 9 2004 05:32:20 on modular [Seed = 707262274] ------------------------------------- [ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] { [ 0 0] [ 0 0], [ 0 0] [M.1^2 0], [ 0 0] [ M.1 0], [ 0 0] [ 1 0], [M.1^2 0] [ 0 M.1^2], [M.1^2 0] [M.1^2 M.1^2], [M.1^2 0] [ M.1 M.1^2], [M.1^2 0] [ 1 M.1^2], [ 1 0] [ 0 1], [ 1 0] [M.1^2 1], [ 1 0] [ M.1 1], [ 1 0] [ 1 1], [ M.1 0] [ 0 M.1], [ M.1 0] [M.1^2 M.1], [ M.1 0] [ M.1 M.1], [ M.1 0] [ 1 M.1], [ 0 M.1^2] [ 0 0], [ 0 M.1^2] [M.1^2 0], [ 0 M.1^2] [ M.1 0], [ 0 M.1^2] [ 1 0], [M.1^2 M.1^2] [ 0 M.1^2], [M.1^2 M.1^2] [M.1^2 M.1^2], [M.1^2 M.1^2] [ M.1 M.1^2], [M.1^2 M.1^2] [ 1 M.1^2], [ 1 M.1^2] [ 0 1], [ 1 M.1^2] [M.1^2 1], [ 1 M.1^2] [ M.1 1], [ 1 M.1^2] [ 1 1], [ M.1 M.1^2] [ 0 M.1], [ M.1 M.1^2] [M.1^2 M.1], [ M.1 M.1^2] [ M.1 M.1], [ M.1 M.1^2] [ 1 M.1], [ 0 M.1] [ 0 0], [ 0 M.1] [M.1^2 0], [ 0 M.1] [ M.1 0], [ 0 M.1] [ 1 0], [M.1^2 M.1] [ 0 M.1^2], [M.1^2 M.1] [M.1^2 M.1^2], [M.1^2 M.1] [ M.1 M.1^2], [M.1^2 M.1] [ 1 M.1^2], [ 1 M.1] [ 0 1], [ 1 M.1] [M.1^2 1], [ 1 M.1] [ M.1 1], [ 1 M.1] [ 1 1], [ M.1 M.1] [ 0 M.1], [ M.1 M.1] [M.1^2 M.1], [ M.1 M.1] [ M.1 M.1], [ M.1 M.1] [ 1 M.1], [ 0 1] [ 0 0], [ 0 1] [M.1^2 0], [ 0 1] [ M.1 0], [ 0 1] [ 1 0], [M.1^2 1] [ 0 M.1^2], [M.1^2 1] [M.1^2 M.1^2], [M.1^2 1] [ M.1 M.1^2], [M.1^2 1] [ 1 M.1^2], [ 1 1] [ 0 1], [ 1 1] [M.1^2 1], [ 1 1] [ M.1 1], [ 1 1] [ 1 1], [ M.1 1] [ 0 M.1], [ M.1 1] [M.1^2 M.1], [ M.1 1] [ M.1 M.1], [ M.1 1] [ 1 M.1] } { [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ M.1 0] [ M.1 0], [ 0 M.1^2] [ 0 M.1^2], [ M.1 M.1^2] [ M.1 M.1^2], [ 0 M.1] [ 0 M.1], [ M.1 M.1] [ M.1 M.1], [ 0 1] [ 0 1], [ M.1 1] [ M.1 1], [M.1^2 0] [M.1^2 0], [ 1 0] [ 1 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ 1 M.1^2] [ 1 M.1^2], [M.1^2 M.1] [M.1^2 M.1], [ 1 M.1] [ 1 M.1], [M.1^2 1] [M.1^2 1] } { [ 0 0] [ 0 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ M.1 M.1] [ M.1 M.1], [ 1 1] [ 1 1] } 2531 637 160 Total time: 4.269 seconds, Total memory usage: 2.44MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 9 05:50:56 2004 Input: /*Exercici 1*/ Diumenges := []; dies := [1..366 by 1]; for i:=4 to 366 by 7 do Diumenges := Include (Diumenges,dies[i]); end for; print Diumenges; /*resposta*/ /*[ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ]*/ /*Exercici 2*/ M:= GF (4); /*creem cos finit */ M22:= MatrixRing (M,2); /*creem matrius 2x2*/ /*matrius de traça 0*/ Mt:= { x : x in M22 | Trace (x) eq 0 }; /*resposta*/ print Mt; /* [ 0 0] [ 0 0], [ 0 0] [M.1^2 0], [ 0 0] [ M.1 0], [ 0 0] [ 1 0], [M.1^2 0] [ 0 M.1^2], [M.1^2 0] [M.1^2 M.1^2], [M.1^2 0] [ M.1 M.1^2], [M.1^2 0] [ 1 M.1^2], [ 1 0] [ 0 1], [ 1 0] [M.1^2 1], [ 1 0] [ M.1 1], [ 1 0] [ 1 1], [ M.1 0] [ 0 M.1], [ M.1 0] [M.1^2 M.1], [ M.1 0] [ M.1 M.1], [ M.1 0] [ 1 M.1], [ 0 M.1^2] [ 0 0], [ 0 M.1^2] [M.1^2 0], [ 0 M.1^2] [ M.1 0], [ 0 M.1^2] [ 1 0], [M.1^2 M.1^2] [ 0 M.1^2], [M.1^2 M.1^2] [M.1^2 M.1^2], [M.1^2 M.1^2] [ M.1 M.1^2], [M.1^2 M.1^2] [ 1 M.1^2], [ 1 M.1^2] [ 0 1], [ 1 M.1^2] [M.1^2 1], [ 1 M.1^2] [ M.1 1], [ 1 M.1^2] [ 1 1], [ M.1 M.1^2] [ 0 M.1], [ M.1 M.1^2] [M.1^2 M.1], [ M.1 M.1^2] [ M.1 M.1], [ M.1 M.1^2] [ 1 M.1], [ 0 M.1] [ 0 0], [ 0 M.1] [M.1^2 0], [ 0 M.1] [ M.1 0], [ 0 M.1] [ 1 0], [M.1^2 M.1] [ 0 M.1^2], [M.1^2 M.1] [M.1^2 M.1^2], [M.1^2 M.1] [ M.1 M.1^2], [M.1^2 M.1] [ 1 M.1^2], [ 1 M.1] [ 0 1], [ 1 M.1] [M.1^2 1], [ 1 M.1] [ M.1 1], [ 1 M.1] [ 1 1], [ M.1 M.1] [ 0 M.1], [ M.1 M.1] [M.1^2 M.1], [ M.1 M.1] [ M.1 M.1], [ M.1 M.1] [ 1 M.1], [ 0 1] [ 0 0], [ 0 1] [M.1^2 0], [ 0 1] [ M.1 0], [ 0 1] [ 1 0], [M.1^2 1] [ 0 M.1^2], [M.1^2 1] [M.1^2 M.1^2], [M.1^2 1] [ M.1 M.1^2], [M.1^2 1] [ 1 M.1^2], [ 1 1] [ 0 1], [ 1 1] [M.1^2 1], [ 1 1] [ M.1 1], [ 1 1] [ 1 1], [ M.1 1] [ 0 M.1], [ M.1 1] [M.1^2 M.1], [ M.1 1] [ M.1 M.1], [ M.1 1] [ 1 M.1] } */ /*Matrius on la primer fila = Segona fila*/ Mf:= { y : y in M22 | Submatrix (y,1,1,1,2) eq Submatrix (y,2,1,1,2)}; /*resposta*/ print Mf; /*{ [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ M.1 0] [ M.1 0], [ 0 M.1^2] [ 0 M.1^2], [ M.1 M.1^2] [ M.1 M.1^2], [ 0 M.1] [ 0 M.1], [ M.1 M.1] [ M.1 M.1], [ 0 1] [ 0 1], [ M.1 1] [ M.1 1], [M.1^2 0] [M.1^2 0], [ 1 0] [ 1 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ 1 M.1^2] [ 1 M.1^2], [M.1^2 M.1] [M.1^2 M.1], [ 1 M.1] [ 1 M.1], [M.1^2 1] [M.1^2 1] } */ /*Matrius que cumpleixen les dues funciones anterios*/ Mtf := Mt meet Mf; /*resposta*/ print Mtf; /* { [ 0 0] [ 0 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ M.1 M.1] [ M.1 M.1], [ 1 1] [ 1 1] } */ /*Exercici 2d*/ Aleatori := [Random(M22): n in [1..10000]]; #([a : a in Aleatori | a in Mt]); #([a : a in Aleatori | a in Mf]); #([a : a in Aleatori | a in Mtf]); #Aleatori; Output: Magma V2.10-6 Tue Mar 9 2004 05:50:51 on modular [Seed = 134605276] ------------------------------------- [ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] { [ 0 0] [ 0 0], [ 0 0] [M.1^2 0], [ 0 0] [ M.1 0], [ 0 0] [ 1 0], [M.1^2 0] [ 0 M.1^2], [M.1^2 0] [M.1^2 M.1^2], [M.1^2 0] [ M.1 M.1^2], [M.1^2 0] [ 1 M.1^2], [ 1 0] [ 0 1], [ 1 0] [M.1^2 1], [ 1 0] [ M.1 1], [ 1 0] [ 1 1], [ M.1 0] [ 0 M.1], [ M.1 0] [M.1^2 M.1], [ M.1 0] [ M.1 M.1], [ M.1 0] [ 1 M.1], [ 0 M.1^2] [ 0 0], [ 0 M.1^2] [M.1^2 0], [ 0 M.1^2] [ M.1 0], [ 0 M.1^2] [ 1 0], [M.1^2 M.1^2] [ 0 M.1^2], [M.1^2 M.1^2] [M.1^2 M.1^2], [M.1^2 M.1^2] [ M.1 M.1^2], [M.1^2 M.1^2] [ 1 M.1^2], [ 1 M.1^2] [ 0 1], [ 1 M.1^2] [M.1^2 1], [ 1 M.1^2] [ M.1 1], [ 1 M.1^2] [ 1 1], [ M.1 M.1^2] [ 0 M.1], [ M.1 M.1^2] [M.1^2 M.1], [ M.1 M.1^2] [ M.1 M.1], [ M.1 M.1^2] [ 1 M.1], [ 0 M.1] [ 0 0], [ 0 M.1] [M.1^2 0], [ 0 M.1] [ M.1 0], [ 0 M.1] [ 1 0], [M.1^2 M.1] [ 0 M.1^2], [M.1^2 M.1] [M.1^2 M.1^2], [M.1^2 M.1] [ M.1 M.1^2], [M.1^2 M.1] [ 1 M.1^2], [ 1 M.1] [ 0 1], [ 1 M.1] [M.1^2 1], [ 1 M.1] [ M.1 1], [ 1 M.1] [ 1 1], [ M.1 M.1] [ 0 M.1], [ M.1 M.1] [M.1^2 M.1], [ M.1 M.1] [ M.1 M.1], [ M.1 M.1] [ 1 M.1], [ 0 1] [ 0 0], [ 0 1] [M.1^2 0], [ 0 1] [ M.1 0], [ 0 1] [ 1 0], [M.1^2 1] [ 0 M.1^2], [M.1^2 1] [M.1^2 M.1^2], [M.1^2 1] [ M.1 M.1^2], [M.1^2 1] [ 1 M.1^2], [ 1 1] [ 0 1], [ 1 1] [M.1^2 1], [ 1 1] [ M.1 1], [ 1 1] [ 1 1], [ M.1 1] [ 0 M.1], [ M.1 1] [M.1^2 M.1], [ M.1 1] [ M.1 M.1], [ M.1 1] [ 1 M.1] } { [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ M.1 0] [ M.1 0], [ 0 M.1^2] [ 0 M.1^2], [ M.1 M.1^2] [ M.1 M.1^2], [ 0 M.1] [ 0 M.1], [ M.1 M.1] [ M.1 M.1], [ 0 1] [ 0 1], [ M.1 1] [ M.1 1], [M.1^2 0] [M.1^2 0], [ 1 0] [ 1 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ 1 M.1^2] [ 1 M.1^2], [M.1^2 M.1] [M.1^2 M.1], [ 1 M.1] [ 1 M.1], [M.1^2 1] [M.1^2 1] } { [ 0 0] [ 0 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ M.1 M.1] [ M.1 M.1], [ 1 1] [ 1 1] } 2518 650 161 10000 Total time: 3.179 seconds, Total memory usage: 2.44MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 9 05:55:04 2004 Input: /*Exercici 1*/ Diumenges := []; dies := [1..366 by 1]; for i:=4 to 366 by 7 do Diumenges := Include (Diumenges,dies[i]); end for; print Diumenges; /*resposta*/ /*[ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ]*/ /*Exercici 2*/ M:= GF (4); /*creem cos finit */ M22:= MatrixRing (M,2); /*creem matrius 2x2*/ /*matrius de traça 0*/ Mt:= { x : x in M22 | Trace (x) eq 0 }; /*resposta*/ print Mt; /* [ 0 0] [ 0 0], [ 0 0] [M.1^2 0], [ 0 0] [ M.1 0], [ 0 0] [ 1 0], [M.1^2 0] [ 0 M.1^2], [M.1^2 0] [M.1^2 M.1^2], [M.1^2 0] [ M.1 M.1^2], [M.1^2 0] [ 1 M.1^2], [ 1 0] [ 0 1], [ 1 0] [M.1^2 1], [ 1 0] [ M.1 1], [ 1 0] [ 1 1], [ M.1 0] [ 0 M.1], [ M.1 0] [M.1^2 M.1], [ M.1 0] [ M.1 M.1], [ M.1 0] [ 1 M.1], [ 0 M.1^2] [ 0 0], [ 0 M.1^2] [M.1^2 0], [ 0 M.1^2] [ M.1 0], [ 0 M.1^2] [ 1 0], [M.1^2 M.1^2] [ 0 M.1^2], [M.1^2 M.1^2] [M.1^2 M.1^2], [M.1^2 M.1^2] [ M.1 M.1^2], [M.1^2 M.1^2] [ 1 M.1^2], [ 1 M.1^2] [ 0 1], [ 1 M.1^2] [M.1^2 1], [ 1 M.1^2] [ M.1 1], [ 1 M.1^2] [ 1 1], [ M.1 M.1^2] [ 0 M.1], [ M.1 M.1^2] [M.1^2 M.1], [ M.1 M.1^2] [ M.1 M.1], [ M.1 M.1^2] [ 1 M.1], [ 0 M.1] [ 0 0], [ 0 M.1] [M.1^2 0], [ 0 M.1] [ M.1 0], [ 0 M.1] [ 1 0], [M.1^2 M.1] [ 0 M.1^2], [M.1^2 M.1] [M.1^2 M.1^2], [M.1^2 M.1] [ M.1 M.1^2], [M.1^2 M.1] [ 1 M.1^2], [ 1 M.1] [ 0 1], [ 1 M.1] [M.1^2 1], [ 1 M.1] [ M.1 1], [ 1 M.1] [ 1 1], [ M.1 M.1] [ 0 M.1], [ M.1 M.1] [M.1^2 M.1], [ M.1 M.1] [ M.1 M.1], [ M.1 M.1] [ 1 M.1], [ 0 1] [ 0 0], [ 0 1] [M.1^2 0], [ 0 1] [ M.1 0], [ 0 1] [ 1 0], [M.1^2 1] [ 0 M.1^2], [M.1^2 1] [M.1^2 M.1^2], [M.1^2 1] [ M.1 M.1^2], [M.1^2 1] [ 1 M.1^2], [ 1 1] [ 0 1], [ 1 1] [M.1^2 1], [ 1 1] [ M.1 1], [ 1 1] [ 1 1], [ M.1 1] [ 0 M.1], [ M.1 1] [M.1^2 M.1], [ M.1 1] [ M.1 M.1], [ M.1 1] [ 1 M.1] } */ /*Matrius on la primer fila = Segona fila*/ Mf:= { y : y in M22 | Submatrix (y,1,1,1,2) eq Submatrix (y,2,1,1,2)}; /*resposta*/ print Mf; /*{ [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ M.1 0] [ M.1 0], [ 0 M.1^2] [ 0 M.1^2], [ M.1 M.1^2] [ M.1 M.1^2], [ 0 M.1] [ 0 M.1], [ M.1 M.1] [ M.1 M.1], [ 0 1] [ 0 1], [ M.1 1] [ M.1 1], [M.1^2 0] [M.1^2 0], [ 1 0] [ 1 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ 1 M.1^2] [ 1 M.1^2], [M.1^2 M.1] [M.1^2 M.1], [ 1 M.1] [ 1 M.1], [M.1^2 1] [M.1^2 1] } */ /*Matrius que cumpleixen les dues funciones anterios*/ Mtf := Mt meet Mf; /*resposta*/ print Mtf; /* { [ 0 0] [ 0 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ M.1 M.1] [ M.1 M.1], [ 1 1] [ 1 1] } */ /*Exercici 2d*/ Aleatori := [Random(M22): n in [1..10000]]; /*hem posat 10.000 perquè donava error de truncament*/ #([a : a in Aleatori | a in Mt]); #([a : a in Aleatori | a in Mf]); #([a : a in Aleatori | a in Mtf]); /*resposta*/ /*Mt : 2531 Mf : 637 Mtf : 160*/ /*Hi ha més Matrius de traça 0 al cos finit GF(4) perquè la probabilitat que la primera*/ /* i la segona fila siguin iguals (els números han de coincidir dos a dos) és menor que */ /*la probabilitat que la diagonal sigui zero (és a dir, que els dos números siguin iguals*/ /*i a més zero)*/ /*Exercici 3a */ polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; polinomi_t (7,3); /*resposta*/ /*[49,7,1]*/ /*Exercici 3b*/ R:= Integers (); P := PolynomialRing (R); exponent := polinomi_t (7,3); polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_t2 (exponent); polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; polinomi_n (exponent); /*resposta*/ /*exercici 3c*/ pol_t := polinomi_t2 (exponent); pol_n:= polinomi_n (exponent); PuntsOlav := { : a in GF (7,3) , b in GF (7,3) | Evaluate (pol_t,a) eq Evaluate (pol_n,b)}; PuntsOlav; /*resposta*/ /*Exercici 3d*/ polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; /*Exercici 3e*/ main := function (a,b) exponent := polinomi_t (a,b); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); return ; end function; /*Exercici 3f*/ main := function (a,b) exponent := polinomi_t (a,b); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); PuntsOlav := { : c in GF (a,b) , d in GF (a,b) | Evaluate (pol_t,c) eq Evaluate (pol_n,d)}; return (PuntsOlav); end function; /*Exercici 3g*/ /*exemples*/ list := main (7,3); #list; /*Resposta 16807*/ list := main (3,1); #list; /*Resposta 3*/ list := main (5,3); #list; /*Resposta 3125*/ list := main (3,3); #list; /*Resposta 243*/ list := main (11,2); #list; /*Resposta 1331*/ /*hem comprovat que es compleix que q^(2r-1) és igual a la resposta de la funció main*/ /*Exercici 3h*/ main := function (a) exponent := polinomi_t (a,1); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); PuntsOlav := { : c in GF (a,1) , d in GF (a,1) | Evaluate (pol_t,c) eq Evaluate (pol_n,d)}; return (PuntsOlav); end function; /*En el cas que q=3 , sempre hi hauran 3 punts Olav.*/ /*Podem deduir que sempre hi hauran "q" punts Olav.*/ /*exemples*/ main := function (7); /*resposta*/ /*7 punts Olav*/ main := function (11); /*resposta*/ /*11 punts Olav*/ Output: Magma V2.10-6 Tue Mar 9 2004 05:54:50 on modular [Seed = 2257282211] ------------------------------------- [ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] { [ 0 0] [ 0 0], [ 0 0] [M.1^2 0], [ 0 0] [ M.1 0], [ 0 0] [ 1 0], [M.1^2 0] [ 0 M.1^2], [M.1^2 0] [M.1^2 M.1^2], [M.1^2 0] [ M.1 M.1^2], [M.1^2 0] [ 1 M.1^2], [ 1 0] [ 0 1], [ 1 0] [M.1^2 1], [ 1 0] [ M.1 1], [ 1 0] [ 1 1], [ M.1 0] [ 0 M.1], [ M.1 0] [M.1^2 M.1], [ M.1 0] [ M.1 M.1], [ M.1 0] [ 1 M.1], [ 0 M.1^2] [ 0 0], [ 0 M.1^2] [M.1^2 0], [ 0 M.1^2] [ M.1 0], [ 0 M.1^2] [ 1 0], [M.1^2 M.1^2] [ 0 M.1^2], [M.1^2 M.1^2] [M.1^2 M.1^2], [M.1^2 M.1^2] [ M.1 M.1^2], [M.1^2 M.1^2] [ 1 M.1^2], [ 1 M.1^2] [ 0 1], [ 1 M.1^2] [M.1^2 1], [ 1 M.1^2] [ M.1 1], [ 1 M.1^2] [ 1 1], [ M.1 M.1^2] [ 0 M.1], [ M.1 M.1^2] [M.1^2 M.1], [ M.1 M.1^2] [ M.1 M.1], [ M.1 M.1^2] [ 1 M.1], [ 0 M.1] [ 0 0], [ 0 M.1] [M.1^2 0], [ 0 M.1] [ M.1 0], [ 0 M.1] [ 1 0], [M.1^2 M.1] [ 0 M.1^2], [M.1^2 M.1] [M.1^2 M.1^2], [M.1^2 M.1] [ M.1 M.1^2], [M.1^2 M.1] [ 1 M.1^2], [ 1 M.1] [ 0 1], [ 1 M.1] [M.1^2 1], [ 1 M.1] [ M.1 1], [ 1 M.1] [ 1 1], [ M.1 M.1] [ 0 M.1], [ M.1 M.1] [M.1^2 M.1], [ M.1 M.1] [ M.1 M.1], [ M.1 M.1] [ 1 M.1], [ 0 1] [ 0 0], [ 0 1] [M.1^2 0], [ 0 1] [ M.1 0], [ 0 1] [ 1 0], [M.1^2 1] [ 0 M.1^2], [M.1^2 1] [M.1^2 M.1^2], [M.1^2 1] [ M.1 M.1^2], [M.1^2 1] [ 1 M.1^2], [ 1 1] [ 0 1], [ 1 1] [M.1^2 1], [ 1 1] [ M.1 1], [ 1 1] [ 1 1], [ M.1 1] [ 0 M.1], [ M.1 1] [M.1^2 M.1], [ M.1 1] [ M.1 M.1], [ M.1 1] [ 1 M.1] } { [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ M.1 0] [ M.1 0], [ 0 M.1^2] [ 0 M.1^2], [ M.1 M.1^2] [ M.1 M.1^2], [ 0 M.1] [ 0 M.1], [ M.1 M.1] [ M.1 M.1], [ 0 1] [ 0 1], [ M.1 1] [ M.1 1], [M.1^2 0] [M.1^2 0], [ 1 0] [ 1 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ 1 M.1^2] [ 1 M.1^2], [M.1^2 M.1] [M.1^2 M.1], [ 1 M.1] [ 1 M.1], [M.1^2 1] [M.1^2 1] } { [ 0 0] [ 0 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ M.1 M.1] [ M.1 M.1], [ 1 1] [ 1 1] } 2532 661 154 [ 49, 7, 1 ] x^49 + x^7 + x x^57 { <$.1^205, $.1^175>, <$.1^172, 3>, <1, $.1^7>, <$.1^85, $.1^58>, <$.1^23, $.1^112>, <$.1^36, $.1^295>, <$.1^110, $.1^68>, <$.1^301, $.1^95>, <$.1^310, $.1^65>, <$.1^111, $.1^140>, <$.1^88, $.1^177>, <$.1^198, $.1^4>, <$.1^281, $.1^317>, <$.1^131, $.1^174>, <$.1^330, $.1^255>, <$.1^83, $.1^184>, <$.1^145, $.1^214>, <$.1^154, $.1^181>, <$.1^172, $.1^237>, <$.1^264, $.1^23>, <$.1^150, $.1^129>, <$.1^103, $.1^168>, <$.1^83, $.1^256>, <$.1^7, $.1^126>, <$.1^198, $.1^286>, <$.1^66, $.1^180>, <$.1^67, $.1^193>, <$.1^41, $.1^41>, <$.1^193, $.1^208>, <$.1^17, $.1^340>, <$.1^97, $.1^132>, <$.1^195, $.1^282>, <$.1^91, $.1^335>, <$.1^296, $.1^335>, <$.1^80, $.1^119>, <$.1^237, $.1^327>, <$.1^160, $.1^223>, <$.1^96, $.1^99>, <$.1^302, $.1^273>, <$.1^88, 5>, <$.1^139, $.1^62>, <$.1^150, $.1^63>, <$.1^149, $.1^40>, <$.1^316, $.1^169>, <$.1^252, $.1^151>, <$.1^255, $.1^53>, <$.1^42, $.1^112>, <$.1^176, $.1^251>, <$.1^226, $.1^38>, <$.1^124, $.1^182>, <$.1^34, $.1^322>, <$.1^327, $.1^39>, <$.1^161, $.1^340>, <$.1^135, $.1^51>, <$.1^28, $.1^21>, <$.1^332, $.1^73>, <$.1^187, $.1^21>, <$.1^311, $.1^62>, <$.1^102, $.1^131>, <$.1^319, $.1^3>, <$.1^314, $.1^246>, <$.1^44, $.1^69>, <$.1^100, 4>, <$.1^267, $.1^168>, <$.1^224, $.1^280>, <$.1^315, $.1^82>, <$.1^292, $.1^137>, <$.1^200, $.1^280>, <$.1^176, $.1^155>, <$.1^18, $.1^160>, <$.1^121, $.1^230>, <$.1^147, $.1^217>, <$.1^62, $.1^129>, <$.1^318, $.1^88>, <$.1^235, $.1^244>, <$.1^294, $.1^52>, <$.1^270, $.1^92>, <$.1^309, $.1^284>, <$.1^232, $.1^187>, <$.1^67, $.1^103>, <$.1^325, $.1^214>, <$.1^69, $.1^315>, <$.1^24, $.1^303>, <$.1^145, $.1^130>, <$.1^309, $.1^224>, <$.1^46, $.1^83>, <$.1^272, $.1^277>, <$.1^303, $.1^225>, <$.1^311, $.1^2>, <$.1^183, $.1^125>, <$.1^17, $.1^130>, <2, $.1^165>, <$.1^207, $.1^76>, <$.1^318, $.1^208>, <$.1^40, $.1^11>, <$.1^200, $.1^166>, <$.1^119, $.1^244>, <$.1^3, $.1^319>, <3, $.1^38>, <$.1^251, $.1^152>, <$.1^25, $.1^282>, <$.1^174, $.1^16>, <$.1^132, $.1^156>, <$.1^121, $.1^338>, <$.1^88, $.1^303>, <$.1^321, $.1^282>, <$.1^81, $.1^94>, <$.1^149, $.1^262>, <$.1^4, $.1^315>, <$.1^177, $.1^133>, <$.1^136, $.1^3>, <$.1^180, $.1^14>, <$.1^7, $.1^174>, <$.1^121, $.1^26>, <$.1^294, $.1^136>, <$.1^7, $.1^24>, <$.1^308, $.1^189>, <$.1^65, 0>, <$.1^218, $.1^23>, <$.1^132, 2>, <$.1^263, $.1^318>, <$.1^181, $.1^75>, <$.1^35, $.1^32>, <$.1^166, $.1^3>, <$.1^281, $.1^167>, <$.1^220, $.1^303>, <$.1^213, $.1^85>, <$.1, $.1^294>, <1, $.1^175>, <$.1^230, $.1^100>, <$.1^193, $.1^4>, <$.1^267, $.1^60>, <$.1^126, $.1^322>, <$.1^128, $.1^146>, <3, $.1^122>, <$.1^248, $.1^261>, <$.1^92, $.1^213>, <$.1^216, $.1^331>, <2, $.1^129>, <$.1^131, $.1^12>, <$.1^174, $.1^100>, <$.1^20, $.1^323>, <$.1^274, $.1^81>, <$.1^91, $.1^173>, <$.1^197, $.1^216>, <$.1^288, $.1^36>, <$.1^78, $.1^152>, <$.1^150, $.1^339>, <$.1^160, $.1^181>, <$.1^340, $.1^184>, <$.1^239, $.1^112>, <$.1^235, $.1^142>, <$.1^206, $.1^149>, <$.1^232, $.1^19>, <$.1^307, $.1^330>, <$.1, $.1^330>, <$.1^239, $.1^226>, <$.1^116, $.1^266>, <$.1^168, $.1^291>, <$.1^25, $.1^252>, <$.1^244, $.1^226>, <$.1^119, $.1^64>, <$.1^36, $.1^199>, <$.1^127, $.1^31>, <$.1^340, $.1^196>, <$.1^330, $.1^75>, <$.1^288, $.1^60>, <$.1^161, $.1^106>, <$.1^178, $.1^267>, <$.1^298, $.1^40>, <$.1^250, $.1^35>, <$.1^255, $.1^101>, <$.1^194, $.1^25>, <$.1^159, $.1^24>, <$.1^267, $.1^150>, <$.1^16, $.1^150>, <$.1^274, $.1^243>, <$.1^195, $.1^300>, <$.1^30, $.1^245>, <$.1^269, $.1^105>, <$.1^307, $.1^108>, <$.1^181, $.1^21>, <$.1^53, $.1^55>, <$.1^11, $.1^174>, <$.1^225, $.1^34>, <$.1^191, $.1^212>, <$.1^263, $.1^18>, <$.1^6, $.1^304>, <$.1^330, $.1^309>, <$.1^232, $.1^163>, <$.1^292, $.1^5>, <$.1^37, $.1^126>, <$.1^153, $.1^76>, <$.1^156, $.1^282>, <$.1^201, $.1^176>, <$.1^49, $.1^132>, <$.1^290, $.1^169>, <$.1^220, $.1^105>, <$.1^251, $.1^296>, <$.1^231, $.1^77>, <$.1^149, $.1^112>, <$.1^202, $.1^161>, <$.1^273, $.1^284>, <$.1^99, $.1^263>, <$.1^320, $.1^187>, <$.1^34, $.1^172>, <$.1^327, $.1^321>, <$.1^61, $.1^268>, <$.1^93, $.1^296>, <$.1^37, $.1^36>, <$.1^242, $.1^34>, <$.1^320, $.1>, <$.1^22, $.1^79>, <$.1^13, $.1^119>, <$.1^37, $.1^12>, <$.1^24, $.1^69>, <$.1^41, $.1^59>, <$.1^70, $.1^96>, <$.1^200, $.1^10>, <$.1^46, $.1^65>, <$.1^136, $.1^177>, <$.1^193, $.1^160>, <$.1^189, $.1^313>, <$.1^193, $.1^106>, <$.1^107, 0>, <$.1^216, $.1^193>, <$.1^267, $.1^192>, <$.1^249, $.1^257>, <$.1^262, $.1^320>, <$.1^23, $.1^118>, <6, $.1^22>, <$.1^183, $.1^203>, <$.1^207, $.1^10>, <$.1^260, $.1^332>, <$.1^308, $.1^219>, <$.1^145, $.1^124>, <$.1^106, $.1^127>, <$.1^189, $.1^271>, <$.1^138, $.1^245>, <$.1^84, $.1^266>, <$.1^45, $.1^262>, <$.1^235, $.1^304>, <$.1^245, $.1^194>, <$.1^257, $.1^41>, <$.1^24, $.1^249>, <$.1^100, $.1^330>, <$.1^136, $.1^183>, <$.1^62, $.1^99>, <$.1^315, $.1^52>, <$.1^62, $.1^177>, <$.1^242, $.1^82>, <$.1^127, $.1^193>, <$.1^155, $.1^85>, <$.1^158, $.1^167>, <$.1^9, $.1^5>, <$.1^194, $.1^127>, <$.1^42, $.1^268>, <$.1^140, $.1^227>, <$.1^45, $.1^298>, <$.1^196, $.1^213>, <$.1^224, $.1^268>, <$.1^145, $.1^226>, <$.1^3, $.1^259>, <$.1^52, $.1^19>, <$.1^224, $.1^46>, <$.1^23, $.1^196>, <$.1^239, $.1^304>, <$.1^12, $.1^8>, <$.1^325, $.1^22>, <$.1^47, $.1^80>, <$.1^185, $.1^87>, <$.1^169, $.1^7>, <$.1^120, $.1^330>, <$.1, $.1^138>, <$.1^329, $.1^140>, <$.1^55, $.1^23>, <$.1^201, $.1^296>, <$.1^271, $.1^243>, <$.1^58, $.1^103>, <$.1^99, $.1^203>, <$.1^188, $.1^247>, <$.1^144, $.1^85>, <$.1^338, $.1^246>, <$.1^150, $.1^147>, <$.1^58, $.1^97>, <$.1^208, $.1^207>, <$.1^196, $.1^297>, <$.1^315, $.1^106>, <$.1^173, $.1^183>, <$.1^53, $.1^73>, <2, $.1^33>, <$.1^47, $.1^20>, <$.1^185, $.1^213>, <$.1^20, $.1^287>, <$.1^29, $.1^265>, <$.1^259, $.1^330>, <$.1^30, $.1^191>, <$.1^34, $.1^244>, <$.1^144, $.1^13>, <$.1^180, $.1^146>, <$.1^325, $.1^142>, <$.1^150, $.1^249>, <$.1^271, $.1^339>, <$.1^159, 1>, <$.1^264, $.1^83>, <$.1^167, $.1^33>, <$.1^169, $.1^19>, <$.1^140, $.1^173>, <$.1^6, $.1^298>, <$.1^321, $.1^24>, <$.1^173, $.1^237>, <$.1^117, $.1^87>, <4, $.1^107>, <$.1^138, $.1^161>, <$.1^182, $.1^261>, <$.1^206, $.1^227>, <$.1^256, $.1^121>, <$.1^301, $.1^311>, <$.1^310, $.1^179>, <$.1^21, $.1^121>, <$.1^294, $.1^34>, <$.1^155, $.1^163>, <$.1^92, $.1^201>, <$.1^198, $.1^244>, <$.1^88, $.1^141>, <$.1^189, $.1^97>, <$.1^180, $.1^320>, <$.1^241, $.1^201>, <$.1^102, $.1^137>, <$.1^123, $.1^103>, <$.1^220, $.1^153>, <$.1^314, ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 9 05:56:30 2004 Input: /*Exercici 1*/ Diumenges := []; dies := [1..366 by 1]; for i:=4 to 366 by 7 do Diumenges := Include (Diumenges,dies[i]); end for; print Diumenges; /*resposta*/ /*[ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ]*/ /*Exercici 2*/ M:= GF (4); /*creem cos finit */ M22:= MatrixRing (M,2); /*creem matrius 2x2*/ /*matrius de traça 0*/ Mt:= { x : x in M22 | Trace (x) eq 0 }; /*resposta*/ print Mt; /* [ 0 0] [ 0 0], [ 0 0] [M.1^2 0], [ 0 0] [ M.1 0], [ 0 0] [ 1 0], [M.1^2 0] [ 0 M.1^2], [M.1^2 0] [M.1^2 M.1^2], [M.1^2 0] [ M.1 M.1^2], [M.1^2 0] [ 1 M.1^2], [ 1 0] [ 0 1], [ 1 0] [M.1^2 1], [ 1 0] [ M.1 1], [ 1 0] [ 1 1], [ M.1 0] [ 0 M.1], [ M.1 0] [M.1^2 M.1], [ M.1 0] [ M.1 M.1], [ M.1 0] [ 1 M.1], [ 0 M.1^2] [ 0 0], [ 0 M.1^2] [M.1^2 0], [ 0 M.1^2] [ M.1 0], [ 0 M.1^2] [ 1 0], [M.1^2 M.1^2] [ 0 M.1^2], [M.1^2 M.1^2] [M.1^2 M.1^2], [M.1^2 M.1^2] [ M.1 M.1^2], [M.1^2 M.1^2] [ 1 M.1^2], [ 1 M.1^2] [ 0 1], [ 1 M.1^2] [M.1^2 1], [ 1 M.1^2] [ M.1 1], [ 1 M.1^2] [ 1 1], [ M.1 M.1^2] [ 0 M.1], [ M.1 M.1^2] [M.1^2 M.1], [ M.1 M.1^2] [ M.1 M.1], [ M.1 M.1^2] [ 1 M.1], [ 0 M.1] [ 0 0], [ 0 M.1] [M.1^2 0], [ 0 M.1] [ M.1 0], [ 0 M.1] [ 1 0], [M.1^2 M.1] [ 0 M.1^2], [M.1^2 M.1] [M.1^2 M.1^2], [M.1^2 M.1] [ M.1 M.1^2], [M.1^2 M.1] [ 1 M.1^2], [ 1 M.1] [ 0 1], [ 1 M.1] [M.1^2 1], [ 1 M.1] [ M.1 1], [ 1 M.1] [ 1 1], [ M.1 M.1] [ 0 M.1], [ M.1 M.1] [M.1^2 M.1], [ M.1 M.1] [ M.1 M.1], [ M.1 M.1] [ 1 M.1], [ 0 1] [ 0 0], [ 0 1] [M.1^2 0], [ 0 1] [ M.1 0], [ 0 1] [ 1 0], [M.1^2 1] [ 0 M.1^2], [M.1^2 1] [M.1^2 M.1^2], [M.1^2 1] [ M.1 M.1^2], [M.1^2 1] [ 1 M.1^2], [ 1 1] [ 0 1], [ 1 1] [M.1^2 1], [ 1 1] [ M.1 1], [ 1 1] [ 1 1], [ M.1 1] [ 0 M.1], [ M.1 1] [M.1^2 M.1], [ M.1 1] [ M.1 M.1], [ M.1 1] [ 1 M.1] } */ /*Matrius on la primer fila = Segona fila*/ Mf:= { y : y in M22 | Submatrix (y,1,1,1,2) eq Submatrix (y,2,1,1,2)}; /*resposta*/ print Mf; /*{ [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ M.1 0] [ M.1 0], [ 0 M.1^2] [ 0 M.1^2], [ M.1 M.1^2] [ M.1 M.1^2], [ 0 M.1] [ 0 M.1], [ M.1 M.1] [ M.1 M.1], [ 0 1] [ 0 1], [ M.1 1] [ M.1 1], [M.1^2 0] [M.1^2 0], [ 1 0] [ 1 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ 1 M.1^2] [ 1 M.1^2], [M.1^2 M.1] [M.1^2 M.1], [ 1 M.1] [ 1 M.1], [M.1^2 1] [M.1^2 1] } */ /*Matrius que cumpleixen les dues funciones anterios*/ Mtf := Mt meet Mf; /*resposta*/ print Mtf; /* { [ 0 0] [ 0 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ M.1 M.1] [ M.1 M.1], [ 1 1] [ 1 1] } */ /*Exercici 2d*/ Aleatori := [Random(M22): n in [1..10000]]; /*hem posat 10.000 perquè donava error de truncament*/ #([a : a in Aleatori | a in Mt]); #([a : a in Aleatori | a in Mf]); #([a : a in Aleatori | a in Mtf]); /*resposta*/ /*Mt : 2531 Mf : 637 Mtf : 160*/ /*Hi ha més Matrius de traça 0 al cos finit GF(4) perquè la probabilitat que la primera*/ /* i la segona fila siguin iguals (els números han de coincidir dos a dos) és menor que */ /*la probabilitat que la diagonal sigui zero (és a dir, que els dos números siguin iguals*/ /*i a més zero)*/ /*Exercici 3a */ polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; polinomi_t (7,3); /*resposta*/ /*[49,7,1]*/ /*Exercici 3b*/ R:= Integers (); P := PolynomialRing (R); exponent := polinomi_t (7,3); polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_t2 (exponent); polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; polinomi_n (exponent); /*resposta*/ /*exercici 3c*/ pol_t := polinomi_t2 (exponent); pol_n:= polinomi_n (exponent); PuntsOlav := { : a in GF (7,3) , b in GF (7,3) | Evaluate (pol_t,a) eq Evaluate (pol_n,b)}; /*PuntsOlav*/ /*resposta*/ /*Exercici 3d*/ polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; /*Exercici 3e*/ main := function (a,b) exponent := polinomi_t (a,b); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); return ; end function; /*Exercici 3f*/ main := function (a,b) exponent := polinomi_t (a,b); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); PuntsOlav := { : c in GF (a,b) , d in GF (a,b) | Evaluate (pol_t,c) eq Evaluate (pol_n,d)}; return (PuntsOlav); end function; /*Exercici 3g*/ /*exemples*/ list := main (7,3); #list; /*Resposta 16807*/ list := main (3,1); #list; /*Resposta 3*/ list := main (5,3); #list; /*Resposta 3125*/ list := main (3,3); #list; /*Resposta 243*/ list := main (11,2); #list; /*Resposta 1331*/ /*hem comprovat que es compleix que q^(2r-1) és igual a la resposta de la funció main*/ /*Exercici 3h*/ main := function (a) exponent := polinomi_t (a,1); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); PuntsOlav := { : c in GF (a,1) , d in GF (a,1) | Evaluate (pol_t,c) eq Evaluate (pol_n,d)}; return (PuntsOlav); end function; /*En el cas que q=3 , sempre hi hauran 3 punts Olav.*/ /*Podem deduir que sempre hi hauran "q" punts Olav.*/ /*exemples*/ main := function (7); /*resposta*/ /*7 punts Olav*/ main := function (11); /*resposta*/ /*11 punts Olav*/ Output: Magma V2.10-6 Tue Mar 9 2004 05:56:17 on modular [Seed = 1835044828] ------------------------------------- [ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] { [ 0 0] [ 0 0], [ 0 0] [M.1^2 0], [ 0 0] [ M.1 0], [ 0 0] [ 1 0], [M.1^2 0] [ 0 M.1^2], [M.1^2 0] [M.1^2 M.1^2], [M.1^2 0] [ M.1 M.1^2], [M.1^2 0] [ 1 M.1^2], [ 1 0] [ 0 1], [ 1 0] [M.1^2 1], [ 1 0] [ M.1 1], [ 1 0] [ 1 1], [ M.1 0] [ 0 M.1], [ M.1 0] [M.1^2 M.1], [ M.1 0] [ M.1 M.1], [ M.1 0] [ 1 M.1], [ 0 M.1^2] [ 0 0], [ 0 M.1^2] [M.1^2 0], [ 0 M.1^2] [ M.1 0], [ 0 M.1^2] [ 1 0], [M.1^2 M.1^2] [ 0 M.1^2], [M.1^2 M.1^2] [M.1^2 M.1^2], [M.1^2 M.1^2] [ M.1 M.1^2], [M.1^2 M.1^2] [ 1 M.1^2], [ 1 M.1^2] [ 0 1], [ 1 M.1^2] [M.1^2 1], [ 1 M.1^2] [ M.1 1], [ 1 M.1^2] [ 1 1], [ M.1 M.1^2] [ 0 M.1], [ M.1 M.1^2] [M.1^2 M.1], [ M.1 M.1^2] [ M.1 M.1], [ M.1 M.1^2] [ 1 M.1], [ 0 M.1] [ 0 0], [ 0 M.1] [M.1^2 0], [ 0 M.1] [ M.1 0], [ 0 M.1] [ 1 0], [M.1^2 M.1] [ 0 M.1^2], [M.1^2 M.1] [M.1^2 M.1^2], [M.1^2 M.1] [ M.1 M.1^2], [M.1^2 M.1] [ 1 M.1^2], [ 1 M.1] [ 0 1], [ 1 M.1] [M.1^2 1], [ 1 M.1] [ M.1 1], [ 1 M.1] [ 1 1], [ M.1 M.1] [ 0 M.1], [ M.1 M.1] [M.1^2 M.1], [ M.1 M.1] [ M.1 M.1], [ M.1 M.1] [ 1 M.1], [ 0 1] [ 0 0], [ 0 1] [M.1^2 0], [ 0 1] [ M.1 0], [ 0 1] [ 1 0], [M.1^2 1] [ 0 M.1^2], [M.1^2 1] [M.1^2 M.1^2], [M.1^2 1] [ M.1 M.1^2], [M.1^2 1] [ 1 M.1^2], [ 1 1] [ 0 1], [ 1 1] [M.1^2 1], [ 1 1] [ M.1 1], [ 1 1] [ 1 1], [ M.1 1] [ 0 M.1], [ M.1 1] [M.1^2 M.1], [ M.1 1] [ M.1 M.1], [ M.1 1] [ 1 M.1] } { [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ M.1 0] [ M.1 0], [ 0 M.1^2] [ 0 M.1^2], [ M.1 M.1^2] [ M.1 M.1^2], [ 0 M.1] [ 0 M.1], [ M.1 M.1] [ M.1 M.1], [ 0 1] [ 0 1], [ M.1 1] [ M.1 1], [M.1^2 0] [M.1^2 0], [ 1 0] [ 1 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ 1 M.1^2] [ 1 M.1^2], [M.1^2 M.1] [M.1^2 M.1], [ 1 M.1] [ 1 M.1], [M.1^2 1] [M.1^2 1] } { [ 0 0] [ 0 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ M.1 M.1] [ M.1 M.1], [ 1 1] [ 1 1] } 2504 648 172 [ 49, 7, 1 ] x^49 + x^7 + x x^57 16807 3 3125 243 1331 >> main := function (7); ^ User error: bad syntax >> main := function (11); ^ User error: bad syntax Total time: 11.819 seconds, Total memory usage: 5.11MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 9 05:59:47 2004 Input: /*Exercici 1*/ Diumenges := []; dies := [1..366 by 1]; for i:=4 to 366 by 7 do Diumenges := Include (Diumenges,dies[i]); end for; print Diumenges; /*resposta*/ /*[ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ]*/ /*Exercici 2*/ M:= GF (4); /*creem cos finit */ M22:= MatrixRing (M,2); /*creem matrius 2x2*/ /*matrius de traça 0*/ Mt:= { x : x in M22 | Trace (x) eq 0 }; /*resposta*/ print Mt; /* [ 0 0] [ 0 0], [ 0 0] [M.1^2 0], [ 0 0] [ M.1 0], [ 0 0] [ 1 0], [M.1^2 0] [ 0 M.1^2], [M.1^2 0] [M.1^2 M.1^2], [M.1^2 0] [ M.1 M.1^2], [M.1^2 0] [ 1 M.1^2], [ 1 0] [ 0 1], [ 1 0] [M.1^2 1], [ 1 0] [ M.1 1], [ 1 0] [ 1 1], [ M.1 0] [ 0 M.1], [ M.1 0] [M.1^2 M.1], [ M.1 0] [ M.1 M.1], [ M.1 0] [ 1 M.1], [ 0 M.1^2] [ 0 0], [ 0 M.1^2] [M.1^2 0], [ 0 M.1^2] [ M.1 0], [ 0 M.1^2] [ 1 0], [M.1^2 M.1^2] [ 0 M.1^2], [M.1^2 M.1^2] [M.1^2 M.1^2], [M.1^2 M.1^2] [ M.1 M.1^2], [M.1^2 M.1^2] [ 1 M.1^2], [ 1 M.1^2] [ 0 1], [ 1 M.1^2] [M.1^2 1], [ 1 M.1^2] [ M.1 1], [ 1 M.1^2] [ 1 1], [ M.1 M.1^2] [ 0 M.1], [ M.1 M.1^2] [M.1^2 M.1], [ M.1 M.1^2] [ M.1 M.1], [ M.1 M.1^2] [ 1 M.1], [ 0 M.1] [ 0 0], [ 0 M.1] [M.1^2 0], [ 0 M.1] [ M.1 0], [ 0 M.1] [ 1 0], [M.1^2 M.1] [ 0 M.1^2], [M.1^2 M.1] [M.1^2 M.1^2], [M.1^2 M.1] [ M.1 M.1^2], [M.1^2 M.1] [ 1 M.1^2], [ 1 M.1] [ 0 1], [ 1 M.1] [M.1^2 1], [ 1 M.1] [ M.1 1], [ 1 M.1] [ 1 1], [ M.1 M.1] [ 0 M.1], [ M.1 M.1] [M.1^2 M.1], [ M.1 M.1] [ M.1 M.1], [ M.1 M.1] [ 1 M.1], [ 0 1] [ 0 0], [ 0 1] [M.1^2 0], [ 0 1] [ M.1 0], [ 0 1] [ 1 0], [M.1^2 1] [ 0 M.1^2], [M.1^2 1] [M.1^2 M.1^2], [M.1^2 1] [ M.1 M.1^2], [M.1^2 1] [ 1 M.1^2], [ 1 1] [ 0 1], [ 1 1] [M.1^2 1], [ 1 1] [ M.1 1], [ 1 1] [ 1 1], [ M.1 1] [ 0 M.1], [ M.1 1] [M.1^2 M.1], [ M.1 1] [ M.1 M.1], [ M.1 1] [ 1 M.1] } */ /*Matrius on la primer fila = Segona fila*/ Mf:= { y : y in M22 | Submatrix (y,1,1,1,2) eq Submatrix (y,2,1,1,2)}; /*resposta*/ print Mf; /*{ [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ M.1 0] [ M.1 0], [ 0 M.1^2] [ 0 M.1^2], [ M.1 M.1^2] [ M.1 M.1^2], [ 0 M.1] [ 0 M.1], [ M.1 M.1] [ M.1 M.1], [ 0 1] [ 0 1], [ M.1 1] [ M.1 1], [M.1^2 0] [M.1^2 0], [ 1 0] [ 1 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ 1 M.1^2] [ 1 M.1^2], [M.1^2 M.1] [M.1^2 M.1], [ 1 M.1] [ 1 M.1], [M.1^2 1] [M.1^2 1] } */ /*Matrius que cumpleixen les dues funciones anterios*/ Mtf := Mt meet Mf; /*resposta*/ print Mtf; /* { [ 0 0] [ 0 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ M.1 M.1] [ M.1 M.1], [ 1 1] [ 1 1] } */ /*Exercici 2d*/ Aleatori := [Random(M22): n in [1..10000]]; /*hem posat 10.000 perquè donava error de truncament*/ #([a : a in Aleatori | a in Mt]); #([a : a in Aleatori | a in Mf]); #([a : a in Aleatori | a in Mtf]); /*resposta*/ /*Mt : 2531 Mf : 637 Mtf : 160*/ /*Hi ha més Matrius de traça 0 al cos finit GF(4) perquè la probabilitat que la primera*/ /* i la segona fila siguin iguals (els números han de coincidir dos a dos) és menor que */ /*la probabilitat que la diagonal sigui zero (és a dir, que els dos números siguin iguals*/ /*i a més zero)*/ /*Exercici 3a */ polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; polinomi_t (7,3); /*resposta*/ /*[49,7,1]*/ /*Exercici 3b*/ R:= Integers (); P := PolynomialRing (R); exponent := polinomi_t (7,3); polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_t2 (exponent); polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; polinomi_n (exponent); /*resposta*/ /*[ 49, 7, 1 ] x^49 + x^7 + x x^57*/ /*exercici 3c*/ pol_t := polinomi_t2 (exponent); pol_n:= polinomi_n (exponent); PuntsOlav := { : a in GF (7,3) , b in GF (7,3) | Evaluate (pol_t,a) eq Evaluate (pol_n,b)}; /*PuntsOlav*/ /*resposta*/ /*Exercici 3d*/ polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; /*Exercici 3e*/ main := function (a,b) exponent := polinomi_t (a,b); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); return ; end function; /*Exercici 3f*/ main := function (a,b) exponent := polinomi_t (a,b); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); PuntsOlav := { : c in GF (a,b) , d in GF (a,b) | Evaluate (pol_t,c) eq Evaluate (pol_n,d)}; return (PuntsOlav); end function; /*Exercici 3g*/ /*exemples*/ list := main (7,3); #list; /*Resposta 16807*/ list := main (3,1); #list; /*Resposta 3*/ list := main (5,3); #list; /*Resposta 3125*/ list := main (3,3); #list; /*Resposta 243*/ list := main (11,2); #list; /*Resposta 1331*/ /*hem comprovat que es compleix que q^(2r-1) és igual a la resposta de la funció main*/ /*Exercici 3h*/ main1 := function (a) exponent := polinomi_t (a,1); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); PuntsOlav := { : c in GF (a,1) , d in GF (a,1) | Evaluate (pol_t,c) eq Evaluate (pol_n,d)}; return (PuntsOlav); end function; /*En el cas que q=3 , sempre hi hauran 3 punts Olav.*/ /*Podem deduir que sempre hi hauran "q" punts Olav.*/ /*exemples*/ main1 (7); /*resposta*/ /*7 punts Olav*/ main1 (11); /*resposta*/ /*11 punts Olav*/ Output: Magma V2.10-6 Tue Mar 9 2004 05:59:35 on modular [Seed = 3840476947] ------------------------------------- [ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] { [ 0 0] [ 0 0], [ 0 0] [M.1^2 0], [ 0 0] [ M.1 0], [ 0 0] [ 1 0], [M.1^2 0] [ 0 M.1^2], [M.1^2 0] [M.1^2 M.1^2], [M.1^2 0] [ M.1 M.1^2], [M.1^2 0] [ 1 M.1^2], [ 1 0] [ 0 1], [ 1 0] [M.1^2 1], [ 1 0] [ M.1 1], [ 1 0] [ 1 1], [ M.1 0] [ 0 M.1], [ M.1 0] [M.1^2 M.1], [ M.1 0] [ M.1 M.1], [ M.1 0] [ 1 M.1], [ 0 M.1^2] [ 0 0], [ 0 M.1^2] [M.1^2 0], [ 0 M.1^2] [ M.1 0], [ 0 M.1^2] [ 1 0], [M.1^2 M.1^2] [ 0 M.1^2], [M.1^2 M.1^2] [M.1^2 M.1^2], [M.1^2 M.1^2] [ M.1 M.1^2], [M.1^2 M.1^2] [ 1 M.1^2], [ 1 M.1^2] [ 0 1], [ 1 M.1^2] [M.1^2 1], [ 1 M.1^2] [ M.1 1], [ 1 M.1^2] [ 1 1], [ M.1 M.1^2] [ 0 M.1], [ M.1 M.1^2] [M.1^2 M.1], [ M.1 M.1^2] [ M.1 M.1], [ M.1 M.1^2] [ 1 M.1], [ 0 M.1] [ 0 0], [ 0 M.1] [M.1^2 0], [ 0 M.1] [ M.1 0], [ 0 M.1] [ 1 0], [M.1^2 M.1] [ 0 M.1^2], [M.1^2 M.1] [M.1^2 M.1^2], [M.1^2 M.1] [ M.1 M.1^2], [M.1^2 M.1] [ 1 M.1^2], [ 1 M.1] [ 0 1], [ 1 M.1] [M.1^2 1], [ 1 M.1] [ M.1 1], [ 1 M.1] [ 1 1], [ M.1 M.1] [ 0 M.1], [ M.1 M.1] [M.1^2 M.1], [ M.1 M.1] [ M.1 M.1], [ M.1 M.1] [ 1 M.1], [ 0 1] [ 0 0], [ 0 1] [M.1^2 0], [ 0 1] [ M.1 0], [ 0 1] [ 1 0], [M.1^2 1] [ 0 M.1^2], [M.1^2 1] [M.1^2 M.1^2], [M.1^2 1] [ M.1 M.1^2], [M.1^2 1] [ 1 M.1^2], [ 1 1] [ 0 1], [ 1 1] [M.1^2 1], [ 1 1] [ M.1 1], [ 1 1] [ 1 1], [ M.1 1] [ 0 M.1], [ M.1 1] [M.1^2 M.1], [ M.1 1] [ M.1 M.1], [ M.1 1] [ 1 M.1] } { [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ M.1 0] [ M.1 0], [ 0 M.1^2] [ 0 M.1^2], [ M.1 M.1^2] [ M.1 M.1^2], [ 0 M.1] [ 0 M.1], [ M.1 M.1] [ M.1 M.1], [ 0 1] [ 0 1], [ M.1 1] [ M.1 1], [M.1^2 0] [M.1^2 0], [ 1 0] [ 1 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ 1 M.1^2] [ 1 M.1^2], [M.1^2 M.1] [M.1^2 M.1], [ 1 M.1] [ 1 M.1], [M.1^2 1] [M.1^2 1] } { [ 0 0] [ 0 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ M.1 M.1] [ M.1 M.1], [ 1 1] [ 1 1] } 2473 606 162 [ 49, 7, 1 ] x^49 + x^7 + x x^57 16807 3 3125 243 1331 { <5, 5>, <6, 6>, <3, 3>, <1, 1>, <4, 4>, <0, 0>, <2, 2> } { <5, 5>, <3, 3>, <2, 2>, <7, 7>, <8, 8>, <1, 1>, <0, 0>, <4, 4>, <9, 9>, <6, 6>, <10, 10> } Total time: 11.629 seconds, Total memory usage: 5.11MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 9 06:01:04 2004 Input: /*Exercici 1*/ Diumenges := []; dies := [1..366 by 1]; for i:=4 to 366 by 7 do Diumenges := Include (Diumenges,dies[i]); end for; print Diumenges; /*resposta*/ /*[ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ]*/ /*Exercici 2*/ M:= GF (4); /*creem cos finit */ M22:= MatrixRing (M,2); /*creem matrius 2x2*/ /*matrius de traça 0*/ Mt:= { x : x in M22 | Trace (x) eq 0 }; /*resposta*/ print Mt; /* [ 0 0] [ 0 0], [ 0 0] [M.1^2 0], [ 0 0] [ M.1 0], [ 0 0] [ 1 0], [M.1^2 0] [ 0 M.1^2], [M.1^2 0] [M.1^2 M.1^2], [M.1^2 0] [ M.1 M.1^2], [M.1^2 0] [ 1 M.1^2], [ 1 0] [ 0 1], [ 1 0] [M.1^2 1], [ 1 0] [ M.1 1], [ 1 0] [ 1 1], [ M.1 0] [ 0 M.1], [ M.1 0] [M.1^2 M.1], [ M.1 0] [ M.1 M.1], [ M.1 0] [ 1 M.1], [ 0 M.1^2] [ 0 0], [ 0 M.1^2] [M.1^2 0], [ 0 M.1^2] [ M.1 0], [ 0 M.1^2] [ 1 0], [M.1^2 M.1^2] [ 0 M.1^2], [M.1^2 M.1^2] [M.1^2 M.1^2], [M.1^2 M.1^2] [ M.1 M.1^2], [M.1^2 M.1^2] [ 1 M.1^2], [ 1 M.1^2] [ 0 1], [ 1 M.1^2] [M.1^2 1], [ 1 M.1^2] [ M.1 1], [ 1 M.1^2] [ 1 1], [ M.1 M.1^2] [ 0 M.1], [ M.1 M.1^2] [M.1^2 M.1], [ M.1 M.1^2] [ M.1 M.1], [ M.1 M.1^2] [ 1 M.1], [ 0 M.1] [ 0 0], [ 0 M.1] [M.1^2 0], [ 0 M.1] [ M.1 0], [ 0 M.1] [ 1 0], [M.1^2 M.1] [ 0 M.1^2], [M.1^2 M.1] [M.1^2 M.1^2], [M.1^2 M.1] [ M.1 M.1^2], [M.1^2 M.1] [ 1 M.1^2], [ 1 M.1] [ 0 1], [ 1 M.1] [M.1^2 1], [ 1 M.1] [ M.1 1], [ 1 M.1] [ 1 1], [ M.1 M.1] [ 0 M.1], [ M.1 M.1] [M.1^2 M.1], [ M.1 M.1] [ M.1 M.1], [ M.1 M.1] [ 1 M.1], [ 0 1] [ 0 0], [ 0 1] [M.1^2 0], [ 0 1] [ M.1 0], [ 0 1] [ 1 0], [M.1^2 1] [ 0 M.1^2], [M.1^2 1] [M.1^2 M.1^2], [M.1^2 1] [ M.1 M.1^2], [M.1^2 1] [ 1 M.1^2], [ 1 1] [ 0 1], [ 1 1] [M.1^2 1], [ 1 1] [ M.1 1], [ 1 1] [ 1 1], [ M.1 1] [ 0 M.1], [ M.1 1] [M.1^2 M.1], [ M.1 1] [ M.1 M.1], [ M.1 1] [ 1 M.1] } */ /*Matrius on la primer fila = Segona fila*/ Mf:= { y : y in M22 | Submatrix (y,1,1,1,2) eq Submatrix (y,2,1,1,2)}; /*resposta*/ print Mf; /*{ [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ M.1 0] [ M.1 0], [ 0 M.1^2] [ 0 M.1^2], [ M.1 M.1^2] [ M.1 M.1^2], [ 0 M.1] [ 0 M.1], [ M.1 M.1] [ M.1 M.1], [ 0 1] [ 0 1], [ M.1 1] [ M.1 1], [M.1^2 0] [M.1^2 0], [ 1 0] [ 1 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ 1 M.1^2] [ 1 M.1^2], [M.1^2 M.1] [M.1^2 M.1], [ 1 M.1] [ 1 M.1], [M.1^2 1] [M.1^2 1] } */ /*Matrius que cumpleixen les dues funciones anterios*/ Mtf := Mt meet Mf; /*resposta*/ print Mtf; /* { [ 0 0] [ 0 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ M.1 M.1] [ M.1 M.1], [ 1 1] [ 1 1] } */ /*Exercici 2d*/ Aleatori := [Random(M22): n in [1..10000]]; /*hem posat 10.000 perquè donava error de truncament*/ #([a : a in Aleatori | a in Mt]); #([a : a in Aleatori | a in Mf]); #([a : a in Aleatori | a in Mtf]); /*resposta*/ /*Mt : 2531 Mf : 637 Mtf : 160*/ /*Hi ha més Matrius de traça 0 al cos finit GF(4) perquè la probabilitat que la primera*/ /* i la segona fila siguin iguals (els números han de coincidir dos a dos) és menor que */ /*la probabilitat que la diagonal sigui zero (és a dir, que els dos números siguin iguals*/ /*i a més zero)*/ /*Exercici 3a */ polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; polinomi_t (7,3); /*resposta*/ /*[49,7,1]*/ /*Exercici 3b*/ R:= Integers (); P := PolynomialRing (R); exponent := polinomi_t (7,3); polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_t2 (exponent); polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; polinomi_n (exponent); /*resposta*/ /*[ 49, 7, 1 ] x^49 + x^7 + x x^57*/ /*exercici 3c*/ pol_t := polinomi_t2 (exponent); pol_n:= polinomi_n (exponent); PuntsOlav := { : a in GF (7,3) , b in GF (7,3) | Evaluate (pol_t,a) eq Evaluate (pol_n,b)}; /*PuntsOlav*/ /*resposta*/ /*Exercici 3d*/ polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; /*Exercici 3e*/ main := function (a,b) exponent := polinomi_t (a,b); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); return ; end function; /*Exercici 3f*/ main := function (a,b) exponent := polinomi_t (a,b); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); PuntsOlav := { : c in GF (a,b) , d in GF (a,b) | Evaluate (pol_t,c) eq Evaluate (pol_n,d)}; return (PuntsOlav); end function; /*Exercici 3g*/ /*exemples*/ list := main (7,3); #list; /*Resposta 16807*/ list := main (3,1); #list; /*Resposta 3*/ list := main (5,3); #list; /*Resposta 3125*/ list := main (3,3); #list; /*Resposta 243*/ list := main (11,2); #list; /*Resposta 1331*/ /*hem comprovat que es compleix que q^(2r-1) és igual a la resposta de la funció main*/ /*Exercici 3h*/ main1 := function (a) exponent := polinomi_t (a,1); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); PuntsOlav := { : c in GF (a,1) , d in GF (a,1) | Evaluate (pol_t,c) eq Evaluate (pol_n,d)}; return (PuntsOlav); end function; /*En el cas que q=3 , sempre hi hauran 3 punts Olav.*/ /*Podem deduir que sempre hi hauran "q" punts Olav.*/ /*exemples*/ main1 (7); /*resposta*/ /*7 punts Olav { <5, 5>, <6, 6>, <3, 3>, <1, 1>, <4, 4>, <0, 0>, <2, 2> }*/ main1 (11); /*resposta*/ /*11 punts Olav { <5, 5>, <3, 3>, <2, 2>, <7, 7>, <8, 8>, <1, 1>, <0, 0>, <4, 4>, <9, 9>, <6, 6>, <10, 10> }*/ Output: Magma V2.10-6 Tue Mar 9 2004 06:00:35 on modular [Seed = 3637853035] ------------------------------------- [ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] { [ 0 0] [ 0 0], [ 0 0] [M.1^2 0], [ 0 0] [ M.1 0], [ 0 0] [ 1 0], [M.1^2 0] [ 0 M.1^2], [M.1^2 0] [M.1^2 M.1^2], [M.1^2 0] [ M.1 M.1^2], [M.1^2 0] [ 1 M.1^2], [ 1 0] [ 0 1], [ 1 0] [M.1^2 1], [ 1 0] [ M.1 1], [ 1 0] [ 1 1], [ M.1 0] [ 0 M.1], [ M.1 0] [M.1^2 M.1], [ M.1 0] [ M.1 M.1], [ M.1 0] [ 1 M.1], [ 0 M.1^2] [ 0 0], [ 0 M.1^2] [M.1^2 0], [ 0 M.1^2] [ M.1 0], [ 0 M.1^2] [ 1 0], [M.1^2 M.1^2] [ 0 M.1^2], [M.1^2 M.1^2] [M.1^2 M.1^2], [M.1^2 M.1^2] [ M.1 M.1^2], [M.1^2 M.1^2] [ 1 M.1^2], [ 1 M.1^2] [ 0 1], [ 1 M.1^2] [M.1^2 1], [ 1 M.1^2] [ M.1 1], [ 1 M.1^2] [ 1 1], [ M.1 M.1^2] [ 0 M.1], [ M.1 M.1^2] [M.1^2 M.1], [ M.1 M.1^2] [ M.1 M.1], [ M.1 M.1^2] [ 1 M.1], [ 0 M.1] [ 0 0], [ 0 M.1] [M.1^2 0], [ 0 M.1] [ M.1 0], [ 0 M.1] [ 1 0], [M.1^2 M.1] [ 0 M.1^2], [M.1^2 M.1] [M.1^2 M.1^2], [M.1^2 M.1] [ M.1 M.1^2], [M.1^2 M.1] [ 1 M.1^2], [ 1 M.1] [ 0 1], [ 1 M.1] [M.1^2 1], [ 1 M.1] [ M.1 1], [ 1 M.1] [ 1 1], [ M.1 M.1] [ 0 M.1], [ M.1 M.1] [M.1^2 M.1], [ M.1 M.1] [ M.1 M.1], [ M.1 M.1] [ 1 M.1], [ 0 1] [ 0 0], [ 0 1] [M.1^2 0], [ 0 1] [ M.1 0], [ 0 1] [ 1 0], [M.1^2 1] [ 0 M.1^2], [M.1^2 1] [M.1^2 M.1^2], [M.1^2 1] [ M.1 M.1^2], [M.1^2 1] [ 1 M.1^2], [ 1 1] [ 0 1], [ 1 1] [M.1^2 1], [ 1 1] [ M.1 1], [ 1 1] [ 1 1], [ M.1 1] [ 0 M.1], [ M.1 1] [M.1^2 M.1], [ M.1 1] [ M.1 M.1], [ M.1 1] [ 1 M.1] } { [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ M.1 0] [ M.1 0], [ 0 M.1^2] [ 0 M.1^2], [ M.1 M.1^2] [ M.1 M.1^2], [ 0 M.1] [ 0 M.1], [ M.1 M.1] [ M.1 M.1], [ 0 1] [ 0 1], [ M.1 1] [ M.1 1], [M.1^2 0] [M.1^2 0], [ 1 0] [ 1 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ 1 M.1^2] [ 1 M.1^2], [M.1^2 M.1] [M.1^2 M.1], [ 1 M.1] [ 1 M.1], [M.1^2 1] [M.1^2 1] } { [ 0 0] [ 0 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ M.1 M.1] [ M.1 M.1], [ 1 1] [ 1 1] } 2481 611 140 [ 49, 7, 1 ] x^49 + x^7 + x x^57 16807 3 3125 243 1331 { <5, 5>, <6, 6>, <3, 3>, <1, 1>, <4, 4>, <0, 0>, <2, 2> } { <5, 5>, <3, 3>, <2, 2>, <7, 7>, <8, 8>, <1, 1>, <0, 0>, <4, 4>, <9, 9>, <6, 6>, <10, 10> } Total time: 12.339 seconds, Total memory usage: 5.11MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 9 06:02:20 2004 Input: /*Exercici 1*/ Diumenges := []; dies := [1..366 by 1]; for i:=4 to 366 by 7 do Diumenges := Include (Diumenges,dies[i]); end for; print Diumenges; /*resposta*/ /*[ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ]*/ /*Exercici 2*/ M:= GF (4); /*creem cos finit */ M22:= MatrixRing (M,2); /*creem matrius 2x2*/ /*matrius de traça 0*/ Mt:= { x : x in M22 | Trace (x) eq 0 }; /*resposta*/ print Mt; /* [ 0 0] [ 0 0], [ 0 0] [M.1^2 0], [ 0 0] [ M.1 0], [ 0 0] [ 1 0], [M.1^2 0] [ 0 M.1^2], [M.1^2 0] [M.1^2 M.1^2], [M.1^2 0] [ M.1 M.1^2], [M.1^2 0] [ 1 M.1^2], [ 1 0] [ 0 1], [ 1 0] [M.1^2 1], [ 1 0] [ M.1 1], [ 1 0] [ 1 1], [ M.1 0] [ 0 M.1], [ M.1 0] [M.1^2 M.1], [ M.1 0] [ M.1 M.1], [ M.1 0] [ 1 M.1], [ 0 M.1^2] [ 0 0], [ 0 M.1^2] [M.1^2 0], [ 0 M.1^2] [ M.1 0], [ 0 M.1^2] [ 1 0], [M.1^2 M.1^2] [ 0 M.1^2], [M.1^2 M.1^2] [M.1^2 M.1^2], [M.1^2 M.1^2] [ M.1 M.1^2], [M.1^2 M.1^2] [ 1 M.1^2], [ 1 M.1^2] [ 0 1], [ 1 M.1^2] [M.1^2 1], [ 1 M.1^2] [ M.1 1], [ 1 M.1^2] [ 1 1], [ M.1 M.1^2] [ 0 M.1], [ M.1 M.1^2] [M.1^2 M.1], [ M.1 M.1^2] [ M.1 M.1], [ M.1 M.1^2] [ 1 M.1], [ 0 M.1] [ 0 0], [ 0 M.1] [M.1^2 0], [ 0 M.1] [ M.1 0], [ 0 M.1] [ 1 0], [M.1^2 M.1] [ 0 M.1^2], [M.1^2 M.1] [M.1^2 M.1^2], [M.1^2 M.1] [ M.1 M.1^2], [M.1^2 M.1] [ 1 M.1^2], [ 1 M.1] [ 0 1], [ 1 M.1] [M.1^2 1], [ 1 M.1] [ M.1 1], [ 1 M.1] [ 1 1], [ M.1 M.1] [ 0 M.1], [ M.1 M.1] [M.1^2 M.1], [ M.1 M.1] [ M.1 M.1], [ M.1 M.1] [ 1 M.1], [ 0 1] [ 0 0], [ 0 1] [M.1^2 0], [ 0 1] [ M.1 0], [ 0 1] [ 1 0], [M.1^2 1] [ 0 M.1^2], [M.1^2 1] [M.1^2 M.1^2], [M.1^2 1] [ M.1 M.1^2], [M.1^2 1] [ 1 M.1^2], [ 1 1] [ 0 1], [ 1 1] [M.1^2 1], [ 1 1] [ M.1 1], [ 1 1] [ 1 1], [ M.1 1] [ 0 M.1], [ M.1 1] [M.1^2 M.1], [ M.1 1] [ M.1 M.1], [ M.1 1] [ 1 M.1] } */ /*Matrius on la primer fila = Segona fila*/ Mf:= { y : y in M22 | Submatrix (y,1,1,1,2) eq Submatrix (y,2,1,1,2)}; /*resposta*/ print Mf; /*{ [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ M.1 0] [ M.1 0], [ 0 M.1^2] [ 0 M.1^2], [ M.1 M.1^2] [ M.1 M.1^2], [ 0 M.1] [ 0 M.1], [ M.1 M.1] [ M.1 M.1], [ 0 1] [ 0 1], [ M.1 1] [ M.1 1], [M.1^2 0] [M.1^2 0], [ 1 0] [ 1 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ 1 M.1^2] [ 1 M.1^2], [M.1^2 M.1] [M.1^2 M.1], [ 1 M.1] [ 1 M.1], [M.1^2 1] [M.1^2 1] } */ /*Matrius que cumpleixen les dues funciones anterios*/ Mtf := Mt meet Mf; /*resposta*/ print Mtf; /* { [ 0 0] [ 0 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ M.1 M.1] [ M.1 M.1], [ 1 1] [ 1 1] } */ /*Exercici 2d*/ Aleatori := [Random(M22): n in [1..10000]]; /*hem posat 10.000 perquè donava error de truncament*/ #([a : a in Aleatori | a in Mt]); #([a : a in Aleatori | a in Mf]); #([a : a in Aleatori | a in Mtf]); /*resposta*/ /*Mt : 2531 Mf : 637 Mtf : 160*/ /*Hi ha més Matrius de traça 0 al cos finit GF(4) perquè la probabilitat que la primera*/ /* i la segona fila siguin iguals (els números han de coincidir dos a dos) és menor que */ /*la probabilitat que la diagonal sigui zero (és a dir, que els dos números siguin iguals*/ /*i a més zero)*/ /*Exercici 3a */ polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; polinomi_t (7,3); /*resposta*/ /*[49,7,1]*/ /*Exercici 3b*/ R:= Integers (); P := PolynomialRing (R); exponent := polinomi_t (7,3); polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_t2 (exponent); polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; polinomi_n (exponent); /*resposta*/ /*[ 49, 7, 1 ] x^49 + x^7 + x x^57*/ /*exercici 3c*/ pol_t := polinomi_t2 (exponent); pol_n:= polinomi_n (exponent); PuntsOlav := { : a in GF (7,3) , b in GF (7,3) | Evaluate (pol_t,a) eq Evaluate (pol_n,b)}; /*PuntsOlav*/ /*resposta*/ /*Exercici 3d*/ polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; /*Exercici 3e*/ main := function (a,b) exponent := polinomi_t (a,b); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); return ; end function; /*Exercici 3f*/ main := function (a,b) exponent := polinomi_t (a,b); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); PuntsOlav := { : c in GF (a,b) , d in GF (a,b) | Evaluate (pol_t,c) eq Evaluate (pol_n,d)}; return (PuntsOlav); end function; /*Exercici 3g*/ /*exemples*/ list := main (7,3); #list; /*Resposta 16807*/ list := main (3,1); #list; /*Resposta 3*/ list := main (5,3); #list; /*Resposta 3125*/ list := main (3,3); #list; /*Resposta 243*/ list := main (11,2); #list; /*Resposta 1331*/ /*hem comprovat que es compleix que q^(2r-1) és igual a la resposta de la funció main*/ /*Exercici 3h*/ main1 := function (a) exponent := polinomi_t (a,1); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); PuntsOlav := { : c in GF (a,1) , d in GF (a,1) | Evaluate (pol_t,c) eq Evaluate (pol_n,d)}; return (PuntsOlav); end function; /*En el cas que q=3 , sempre hi hauran 3 punts Olav.*/ /*Podem deduir que sempre hi hauran "q" punts Olav.*/ /*exemples*/ main1 (7); /*resposta*/ /*7 punts Olav { <5, 5>, <6, 6>, <3, 3>, <1, 1>, <4, 4>, <0, 0>, <2, 2> }*/ main1 (11); /*resposta*/ /*11 punts Olav { <5, 5>, <3, 3>, <2, 2>, <7, 7>, <8, 8>, <1, 1>, <0, 0>, <4, 4>, <9, 9>, <6, 6>, <10, 10> }*/ Output: Magma V2.10-6 Tue Mar 9 2004 06:02:05 on modular [Seed = 2257281739] ------------------------------------- [ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] { [ 0 0] [ 0 0], [ 0 0] [M.1^2 0], [ 0 0] [ M.1 0], [ 0 0] [ 1 0], [M.1^2 0] [ 0 M.1^2], [M.1^2 0] [M.1^2 M.1^2], [M.1^2 0] [ M.1 M.1^2], [M.1^2 0] [ 1 M.1^2], [ 1 0] [ 0 1], [ 1 0] [M.1^2 1], [ 1 0] [ M.1 1], [ 1 0] [ 1 1], [ M.1 0] [ 0 M.1], [ M.1 0] [M.1^2 M.1], [ M.1 0] [ M.1 M.1], [ M.1 0] [ 1 M.1], [ 0 M.1^2] [ 0 0], [ 0 M.1^2] [M.1^2 0], [ 0 M.1^2] [ M.1 0], [ 0 M.1^2] [ 1 0], [M.1^2 M.1^2] [ 0 M.1^2], [M.1^2 M.1^2] [M.1^2 M.1^2], [M.1^2 M.1^2] [ M.1 M.1^2], [M.1^2 M.1^2] [ 1 M.1^2], [ 1 M.1^2] [ 0 1], [ 1 M.1^2] [M.1^2 1], [ 1 M.1^2] [ M.1 1], [ 1 M.1^2] [ 1 1], [ M.1 M.1^2] [ 0 M.1], [ M.1 M.1^2] [M.1^2 M.1], [ M.1 M.1^2] [ M.1 M.1], [ M.1 M.1^2] [ 1 M.1], [ 0 M.1] [ 0 0], [ 0 M.1] [M.1^2 0], [ 0 M.1] [ M.1 0], [ 0 M.1] [ 1 0], [M.1^2 M.1] [ 0 M.1^2], [M.1^2 M.1] [M.1^2 M.1^2], [M.1^2 M.1] [ M.1 M.1^2], [M.1^2 M.1] [ 1 M.1^2], [ 1 M.1] [ 0 1], [ 1 M.1] [M.1^2 1], [ 1 M.1] [ M.1 1], [ 1 M.1] [ 1 1], [ M.1 M.1] [ 0 M.1], [ M.1 M.1] [M.1^2 M.1], [ M.1 M.1] [ M.1 M.1], [ M.1 M.1] [ 1 M.1], [ 0 1] [ 0 0], [ 0 1] [M.1^2 0], [ 0 1] [ M.1 0], [ 0 1] [ 1 0], [M.1^2 1] [ 0 M.1^2], [M.1^2 1] [M.1^2 M.1^2], [M.1^2 1] [ M.1 M.1^2], [M.1^2 1] [ 1 M.1^2], [ 1 1] [ 0 1], [ 1 1] [M.1^2 1], [ 1 1] [ M.1 1], [ 1 1] [ 1 1], [ M.1 1] [ 0 M.1], [ M.1 1] [M.1^2 M.1], [ M.1 1] [ M.1 M.1], [ M.1 1] [ 1 M.1] } { [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ M.1 0] [ M.1 0], [ 0 M.1^2] [ 0 M.1^2], [ M.1 M.1^2] [ M.1 M.1^2], [ 0 M.1] [ 0 M.1], [ M.1 M.1] [ M.1 M.1], [ 0 1] [ 0 1], [ M.1 1] [ M.1 1], [M.1^2 0] [M.1^2 0], [ 1 0] [ 1 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ 1 M.1^2] [ 1 M.1^2], [M.1^2 M.1] [M.1^2 M.1], [ 1 M.1] [ 1 M.1], [M.1^2 1] [M.1^2 1] } { [ 0 0] [ 0 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ M.1 M.1] [ M.1 M.1], [ 1 1] [ 1 1] } 2532 644 156 [ 49, 7, 1 ] x^49 + x^7 + x x^57 16807 3 3125 243 1331 { <5, 5>, <6, 6>, <3, 3>, <1, 1>, <4, 4>, <0, 0>, <2, 2> } { <5, 5>, <3, 3>, <2, 2>, <7, 7>, <8, 8>, <1, 1>, <0, 0>, <4, 4>, <9, 9>, <6, 6>, <10, 10> } Total time: 12.349 seconds, Total memory usage: 5.11MB ************** MAGMA ***************** Host aula-a-siee30.uab.es. (158.109.66.30) Time: Tue Mar 9 06:08:07 2004 Input: /*Exercici 1*/ Diumenges := []; dies := [1..366 by 1]; for i:=4 to 366 by 7 do Diumenges := Include (Diumenges,dies[i]); end for; print Diumenges; /*resposta*/ /*[ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ]*/ /*Exercici 2*/ M:= GF (4); /*creem cos finit */ M22:= MatrixRing (M,2); /*creem matrius 2x2*/ /*matrius de traça 0*/ Mt:= { x : x in M22 | Trace (x) eq 0 }; /*resposta*/ print Mt; /* [ 0 0] [ 0 0], [ 0 0] [M.1^2 0], [ 0 0] [ M.1 0], [ 0 0] [ 1 0], [M.1^2 0] [ 0 M.1^2], [M.1^2 0] [M.1^2 M.1^2], [M.1^2 0] [ M.1 M.1^2], [M.1^2 0] [ 1 M.1^2], [ 1 0] [ 0 1], [ 1 0] [M.1^2 1], [ 1 0] [ M.1 1], [ 1 0] [ 1 1], [ M.1 0] [ 0 M.1], [ M.1 0] [M.1^2 M.1], [ M.1 0] [ M.1 M.1], [ M.1 0] [ 1 M.1], [ 0 M.1^2] [ 0 0], [ 0 M.1^2] [M.1^2 0], [ 0 M.1^2] [ M.1 0], [ 0 M.1^2] [ 1 0], [M.1^2 M.1^2] [ 0 M.1^2], [M.1^2 M.1^2] [M.1^2 M.1^2], [M.1^2 M.1^2] [ M.1 M.1^2], [M.1^2 M.1^2] [ 1 M.1^2], [ 1 M.1^2] [ 0 1], [ 1 M.1^2] [M.1^2 1], [ 1 M.1^2] [ M.1 1], [ 1 M.1^2] [ 1 1], [ M.1 M.1^2] [ 0 M.1], [ M.1 M.1^2] [M.1^2 M.1], [ M.1 M.1^2] [ M.1 M.1], [ M.1 M.1^2] [ 1 M.1], [ 0 M.1] [ 0 0], [ 0 M.1] [M.1^2 0], [ 0 M.1] [ M.1 0], [ 0 M.1] [ 1 0], [M.1^2 M.1] [ 0 M.1^2], [M.1^2 M.1] [M.1^2 M.1^2], [M.1^2 M.1] [ M.1 M.1^2], [M.1^2 M.1] [ 1 M.1^2], [ 1 M.1] [ 0 1], [ 1 M.1] [M.1^2 1], [ 1 M.1] [ M.1 1], [ 1 M.1] [ 1 1], [ M.1 M.1] [ 0 M.1], [ M.1 M.1] [M.1^2 M.1], [ M.1 M.1] [ M.1 M.1], [ M.1 M.1] [ 1 M.1], [ 0 1] [ 0 0], [ 0 1] [M.1^2 0], [ 0 1] [ M.1 0], [ 0 1] [ 1 0], [M.1^2 1] [ 0 M.1^2], [M.1^2 1] [M.1^2 M.1^2], [M.1^2 1] [ M.1 M.1^2], [M.1^2 1] [ 1 M.1^2], [ 1 1] [ 0 1], [ 1 1] [M.1^2 1], [ 1 1] [ M.1 1], [ 1 1] [ 1 1], [ M.1 1] [ 0 M.1], [ M.1 1] [M.1^2 M.1], [ M.1 1] [ M.1 M.1], [ M.1 1] [ 1 M.1] } */ /*Matrius on la primer fila = Segona fila*/ Mf:= { y : y in M22 | Submatrix (y,1,1,1,2) eq Submatrix (y,2,1,1,2)}; /*resposta*/ print Mf; /*{ [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ M.1 0] [ M.1 0], [ 0 M.1^2] [ 0 M.1^2], [ M.1 M.1^2] [ M.1 M.1^2], [ 0 M.1] [ 0 M.1], [ M.1 M.1] [ M.1 M.1], [ 0 1] [ 0 1], [ M.1 1] [ M.1 1], [M.1^2 0] [M.1^2 0], [ 1 0] [ 1 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ 1 M.1^2] [ 1 M.1^2], [M.1^2 M.1] [M.1^2 M.1], [ 1 M.1] [ 1 M.1], [M.1^2 1] [M.1^2 1] } */ /*Matrius que cumpleixen les dues funciones anterios*/ Mtf := Mt meet Mf; /*resposta*/ print Mtf; /* { [ 0 0] [ 0 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ M.1 M.1] [ M.1 M.1], [ 1 1] [ 1 1] } */ /*Exercici 2d*/ Aleatori := [Random(M22): n in [1..10000]]; /*hem posat 10.000 perquè donava error de truncament*/ #([a : a in Aleatori | a in Mt]); #([a : a in Aleatori | a in Mf]); #([a : a in Aleatori | a in Mtf]); /*resposta*/ /*Mt : 2531 Mf : 637 Mtf : 160*/ /*Hi ha més Matrius de traça 0 al cos finit GF(4) perquè la probabilitat que la primera*/ /* i la segona fila siguin iguals (els números han de coincidir dos a dos) és menor que */ /*la probabilitat que la diagonal sigui zero (és a dir, que els dos números siguin iguals*/ /*i a més zero)*/ /*Exercici 3a */ polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; polinomi_t (7,3); /*resposta*/ /*[49,7,1]*/ /*Exercici 3b*/ R:= Integers (); P := PolynomialRing (R); exponent := polinomi_t (7,3); polinomi_t2 := function (expo) llista := [0*i: i in [1..expo[1]+1]]; for i:= 1 to #expo do llista[expo[i]+1]:=1; end for; pol_t:= P!llista; return pol_t; end function; polinomi_t2 (exponent); polinomi_n := function (expo) b:= 1; for i:= 1 to #expo do b := b + expo[i]; end for; llista1 := [0*i: i in [1..b+1]]; llista1 [b] := 1; pol_n:= P!llista1; return pol_n; end function; polinomi_n (exponent); /*resposta*/ /*exercici 3c*/ pol_t := polinomi_t2 (exponent); pol_n:= polinomi_n (exponent); PuntsOlav := { : a in GF (7,3) , b in GF (7,3) | Evaluate (pol_t,a) eq Evaluate (pol_n,b)}; /*PuntsOlav;*/ /*resposta*/ /*Exercici 3d*/ polinomi_t := function (a,b) expo := []; while b ne 0 do expo := Include (expo, a^(b-1)); b:= b-1; end while; return expo; end function; /*Exercici 3e*/ main := function (a,b) exponent := polinomi_t (a,b); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); return ; end function; /*Exercici 3f*/ main := function (a,b) exponent := polinomi_t (a,b); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); PuntsOlav := { : c in GF (a,b) , d in GF (a,b) | Evaluate (pol_t,c) eq Evaluate (pol_n,d)}; return (PuntsOlav); end function; /*Exercici 3g*/ /*exemples*/ list := main (7,3); #list; /*Resposta 16807*/ list := main (3,1); #list; /*Resposta 3*/ list := main (5,3); #list; /*Resposta 3125*/ list := main (3,3); #list; /*Resposta 243*/ list := main (11,2); #list; /*Resposta 1331*/ /*hem comprovat que es compleix que q^(2r-1) és igual a la resposta de la funció main*/ /*Exercici 3h*/ main1 := function (a) exponent := polinomi_t (a,1); pol_t := polinomi_t2 (exponent); pol_n := polinomi_n (exponent); PuntsOlav := { : c in GF (a,1) , d in GF (a,1) | Evaluate (pol_t,c) eq Evaluate (pol_n,d)}; return (PuntsOlav); end function; /*En el cas que q=3 , sempre hi hauran 3 punts Olav.*/ /*Podem deduir que sempre hi hauran "q" punts Olav.*/ /*exemples*/ main1 (7); /*resposta*/ /*7 punts Olav */ main1 (11); /*resposta*/ /*11 punts Olav { <5, 5>, <3, 3>, <2, 2>, <7, 7>, <8, 8>, <1, 1>, <0, 0>, <4, 4>, <9, 9>, <6, 6>, <10, 10> }*/ Output: Magma V2.10-6 Tue Mar 9 2004 06:07:53 on modular [Seed = 876204508] ------------------------------------- [ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] { [ 0 0] [ 0 0], [ 0 0] [M.1^2 0], [ 0 0] [ M.1 0], [ 0 0] [ 1 0], [M.1^2 0] [ 0 M.1^2], [M.1^2 0] [M.1^2 M.1^2], [M.1^2 0] [ M.1 M.1^2], [M.1^2 0] [ 1 M.1^2], [ 1 0] [ 0 1], [ 1 0] [M.1^2 1], [ 1 0] [ M.1 1], [ 1 0] [ 1 1], [ M.1 0] [ 0 M.1], [ M.1 0] [M.1^2 M.1], [ M.1 0] [ M.1 M.1], [ M.1 0] [ 1 M.1], [ 0 M.1^2] [ 0 0], [ 0 M.1^2] [M.1^2 0], [ 0 M.1^2] [ M.1 0], [ 0 M.1^2] [ 1 0], [M.1^2 M.1^2] [ 0 M.1^2], [M.1^2 M.1^2] [M.1^2 M.1^2], [M.1^2 M.1^2] [ M.1 M.1^2], [M.1^2 M.1^2] [ 1 M.1^2], [ 1 M.1^2] [ 0 1], [ 1 M.1^2] [M.1^2 1], [ 1 M.1^2] [ M.1 1], [ 1 M.1^2] [ 1 1], [ M.1 M.1^2] [ 0 M.1], [ M.1 M.1^2] [M.1^2 M.1], [ M.1 M.1^2] [ M.1 M.1], [ M.1 M.1^2] [ 1 M.1], [ 0 M.1] [ 0 0], [ 0 M.1] [M.1^2 0], [ 0 M.1] [ M.1 0], [ 0 M.1] [ 1 0], [M.1^2 M.1] [ 0 M.1^2], [M.1^2 M.1] [M.1^2 M.1^2], [M.1^2 M.1] [ M.1 M.1^2], [M.1^2 M.1] [ 1 M.1^2], [ 1 M.1] [ 0 1], [ 1 M.1] [M.1^2 1], [ 1 M.1] [ M.1 1], [ 1 M.1] [ 1 1], [ M.1 M.1] [ 0 M.1], [ M.1 M.1] [M.1^2 M.1], [ M.1 M.1] [ M.1 M.1], [ M.1 M.1] [ 1 M.1], [ 0 1] [ 0 0], [ 0 1] [M.1^2 0], [ 0 1] [ M.1 0], [ 0 1] [ 1 0], [M.1^2 1] [ 0 M.1^2], [M.1^2 1] [M.1^2 M.1^2], [M.1^2 1] [ M.1 M.1^2], [M.1^2 1] [ 1 M.1^2], [ 1 1] [ 0 1], [ 1 1] [M.1^2 1], [ 1 1] [ M.1 1], [ 1 1] [ 1 1], [ M.1 1] [ 0 M.1], [ M.1 1] [M.1^2 M.1], [ M.1 1] [ M.1 M.1], [ M.1 1] [ 1 M.1] } { [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ M.1 0] [ M.1 0], [ 0 M.1^2] [ 0 M.1^2], [ M.1 M.1^2] [ M.1 M.1^2], [ 0 M.1] [ 0 M.1], [ M.1 M.1] [ M.1 M.1], [ 0 1] [ 0 1], [ M.1 1] [ M.1 1], [M.1^2 0] [M.1^2 0], [ 1 0] [ 1 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ 1 M.1^2] [ 1 M.1^2], [M.1^2 M.1] [M.1^2 M.1], [ 1 M.1] [ 1 M.1], [M.1^2 1] [M.1^2 1] } { [ 0 0] [ 0 0], [M.1^2 M.1^2] [M.1^2 M.1^2], [ M.1 M.1] [ M.1 M.1], [ 1 1] [ 1 1] } 2514 562 141 [ 49, 7, 1 ] x^49 + x^7 + x x^57 16807 3 3125 243 1331 { <5, 5>, <6, 6>, <3, 3>, <1, 1>, <4, 4>, <0, 0>, <2, 2> } { <5, 5>, <3, 3>, <2, 2>, <7, 7>, <8, 8>, <1, 1>, <0, 0>, <4, 4>, <9, 9>, <6, 6>, <10, 10> } Total time: 12.559 seconds, Total memory usage: 5.11MB ************** MAGMA ***************** Host 3(NXDOMAIN) (61.100.215.239) Time: Tue Mar 9 07:26:41 2004 Input: 1+1 Output: Magma V2.10-6 Tue Mar 9 2004 07:26:37 on modular [Seed = 3824030834] ------------------------------------- 2 Total time: 3.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dpc6682009024.direcpc.com. (66.82.9.24) Time: Tue Mar 9 10:57:42 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Tue Mar 9 2004 10:57:38 on modular [Seed = 3637866915] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-64-172-59-148.dsl.snfc21.pacbell.net. (64.172.59.148) Time: Tue Mar 9 12:27:10 2004 Input: ClassicalModularPolynomial(3); Output: Magma V2.10-6 Tue Mar 9 2004 12:27:07 on modular [Seed = 2020984325] ------------------------------------- $.1^4 - $.1^3*$.2^3 + 2232*$.1^3*$.2^2 - 1069956*$.1^3*$.2 + 36864000*$.1^3 + 2232*$.1^2*$.2^3 + 2587918086*$.1^2*$.2^2 + 8900222976000*$.1^2*$.2 + 452984832000000*$.1^2 - 1069956*$.1*$.2^3 + 8900222976000*$.1*$.2^2 - 770845966336000000*$.1*$.2 + 1855425871872000000000*$.1 + $.2^4 + 36864000*$.2^3 + 452984832000000*$.2^2 + 1855425871872000000000*$.2 Total time: 2.909 seconds, Total memory usage: 2.78MB ************** MAGMA ***************** Host adsl-64-172-59-148.dsl.snfc21.pacbell.net. (64.172.59.148) Time: Tue Mar 9 12:28:21 2004 Input: P2 := PolynomialRing(Integers(),2); P2!ClassicalModularPolynomial(3); Output: Magma V2.10-6 Tue Mar 9 2004 12:28:17 on modular [Seed = 2324116525] ------------------------------------- x^4 - x^3*j^3 + 2232*x^3*j^2 - 1069956*x^3*j + 36864000*x^3 + 2232*x^2*j^3 + 2587918086*x^2*j^2 + 8900222976000*x^2*j + 452984832000000*x^2 - 1069956*x*j^3 + 8900222976000*x*j^2 - 770845966336000000*x*j + 1855425871872000000000*x + j^4 + 36864000*j^3 + 452984832000000*j^2 + 1855425871872000000000*j Total time: 3.719 seconds, Total memory usage: 2.78MB ************** MAGMA ***************** Host adsl-64-172-59-148.dsl.snfc21.pacbell.net. (64.172.59.148) Time: Tue Mar 9 12:28:40 2004 Input: P2 := PolynomialRing(Integers(),2); P2!ClassicalModularPolynomial(5); Output: Magma V2.10-6 Tue Mar 9 2004 12:28:37 on modular [Seed = 3098871403] ------------------------------------- x^6 - x^5*j^5 + 3720*x^5*j^4 - 4550940*x^5*j^3 + 2028551200*x^5*j^2 - 246683410950*x^5*j + 1963211489280*x^5 + 3720*x^4*j^5 + 1665999364600*x^4*j^4 + 107878928185336800*x^4*j^3 + 383083609779811215375*x^4*j^2 + 128541798906828816384000*x^4*j + 1284733132841424456253440*x^4 - 4550940*x^3*j^5 + 107878928185336800*x^3*j^4 - 441206965512914835246100*x^3*j^3 + 26898488858380731577417728000*x^3*j^2 - 192457934618928299655108231168000*x^3*j + 280244777828439527804321565297868800*x^3 + 2028551200*x^2*j^5 + 383083609779811215375*x^2*j^4 + 26898488858380731577417728000*x^2*j^3 + 5110941777552418083110765199360000*x^2*j^2 + 36554736583949629295706472332656640000*x^2*j + 6692500042627997708487149415015068467200*x^2 - 246683410950*x*j^5 + 128541798906828816384000*x*j^4 - 192457934618928299655108231168000*x*j^3 + 36554736583949629295706472332656640000*x*j^2 - 264073457076620596259715790247978782949376*x*j + 53274330803424425450420160273356509151232000*x + j^6 + 1963211489280*j^5 + 1284733132841424456253440*j^4 + 280244777828439527804321565297868800*j^3 + 6692500042627997708487149415015068467200*j^2 + 53274330803424425450420160273356509151232000*j + 141359947154721358697753474691071362751004672000 Total time: 3.389 seconds, Total memory usage: 2.78MB ************** MAGMA ***************** Host adsl-64-172-59-148.dsl.snfc21.pacbell.net. (64.172.59.148) Time: Tue Mar 9 12:37:00 2004 Input: P2 := PolynomialRing(Integers(),2); P2!ClassicalModularPolynomial(7); Output: Magma V2.10-6 Tue Mar 9 2004 12:36:56 on modular [Seed = 3571094651] ------------------------------------- x^8 - x^7*j^7 + 5208*x^7*j^6 - 10246068*x^7*j^5 + 9437674400*x^7*j^4 - 4079701128594*x^7*j^3 + 720168419610864*x^7*j^2 - 34993297342013192*x^7*j + 104545516658688000*x^7 + 5208*x^6*j^7 + 312598931380281*x^6*j^6 + 177089350028475373552*x^6*j^5 + 4460942463213898353207432*x^6*j^4 + 16125487429368412743622133040*x^6*j^3 + 10685207605419433304631062899228*x^6*j^2 + 1038063543615451121419229773824000*x^6*j + 3643255017844740441130401792000000*x^6 - 10246068*x^5*j^7 + 177089350028475373552*x^5*j^6 - 18300817137706889881369818348*x^5*j^5 + 14066810691825882583305340438456800*x^5*j^4 - 901645312135695263877115693740562092344*x^5*j^3 + 11269804827778129625111322263056523132928000*x^5*j^2 - 40689839325168186578698294668599003971584000000*x^5*j + 42320664241971721884753245384947305283584000000000*x^5 + 9437674400*x^4*j^7 + 4460942463213898353207432*x^4*j^6 + 14066810691825882583305340438456800*x\ ^4*j^5 + 88037255060655710247136461896264828390470*x^4*j^4 + 17972351380696034759035751584170427941396480000*x^4*j^3 + 308718989330868920558541707287296140145328128000000*x^4*j^2 + 553293497305121712634517214392820316998991872000000000*x^4*j + 41375720005635744770247248526572116368162816000000000000*x^4 - 4079701128594*x^3*j^7 + 16125487429368412743622133040*x^3*j^6 - 901645312135695263877115693740562092344*x^3*j^5 + 17972351380696034759035751584170427941396480000*x^3*j^4 - 5397554444336630396660447092290576395211374592000000*x^3*j^3 + 72269669689202948469186346100000679630099972096000000000*x^3*j^2 - 129686683986501811181602978946723823397619367936000000000000*x^3*j + 13483958224762213714698012883865296529472356352000000000000000*x^3 + 720168419610864*x^2*j^7 + 10685207605419433304631062899228*x^2*j^6 + 11269804827778129625111322263056523132928000*x^2*j^5 + 308718989330868920558541707287296140145328128000000*x^2*j^4 + 72269669689202948469186346100000679630099972096000000000*x^2*j^3 - 46666007311089950798495647194817495401448341504000000000000*x^2*j^2 - 838538082798149465723818021032241603179964268544000000000000000*x^2*j + 1464765079488386840337633731737402825128271675392000000000000000000*x^2 - 34993297342013192*x*j^7 + 1038063543615451121419229773824000*x*j^6 - 40689839325168186578698294668599003971584000000*x*j^5 + 553293497305121712634517214392820316998991872000000000*x*j^4 - 129686683986501811181602978946723823397619367936000000000000*x*j^3 - 838538082798149465723818021032241603179964268544000000000000000*x*j^2 + 1221349308261453750252370983314569119494710493184000000000000000000*x*j + j^8 + 104545516658688000*j^7 + 3643255017844740441130401792000000*j^6 + 42320664241971721884753245384947305283584000000000*j^5 + 41375720005635744770247248526572116368162816000000000000*j^4 + 13483958224762213714698012883865296529472356352000000000000000*j^3 + 1464765079488386840337633731737402825128271675392000000000000000000*j^2 Total time: 3.459 seconds, Total memory usage: 2.78MB ************** MAGMA ***************** Host bln2-t2-2.mcbone.net. (62.104.208.83) Time: Tue Mar 9 12:42:31 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Tue Mar 9 2004 12:42:27 on modular [Seed = 3216113060] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-64-172-59-148.dsl.snfc21.pacbell.net. (64.172.59.148) Time: Tue Mar 9 13:21:35 2004 Input: P2 := PolynomialRing(Integers(),2); P2!ClassicalModularPolynomial(11); Output: Magma V2.10-6 Tue Mar 9 2004 13:21:31 on modular [Seed = 2257112499] ------------------------------------- x^12 - x^11*j^11 + 8184*x^11*j^10 - 28278756*x^11*j^9 + 53686822816*x^11*j^8 - 61058988656490*x^11*j^7 + 42570393135641712*x^11*j^6 - 17899526272883039048*x^11*j^5 + 4297837238774928467520*x^11*j^4 - 529134841844639613861795*x^11*j^3 + 27209811658056645815522600*x^11*j^2 - 374642006356701393515817612*x^11*j + 296470902355240575283200000*x^11 + 8184*x^10*j^11 + 1608331026427734378*x^10*j^10 + 30134971854812981978547264*x^10*j^9 + 12407796387712093514736413264496*x^10\ *j^8 + 645470833566425875717489618904152240*x^10*j^7 + 7848482999227584325448694633580010490867*x^10*j^6 + 28890545335855949285086003898461917345026160*x^10*j^5 + 35372414460361796790312007060191890803134127320*x^10*j^4 + 14131378888778142661582693947549844785863493325800*x^10*j^3 + 1587728122949690904187089204116332301200302760915266*x^10*j^2 + 33446467926379842030532687838341039552110187929600000*x^10*j + 29298331981110197366602526090413106879319244800000000*x^10 - 28278756*x^9*j^11 + 30134971854812981978547264*x^9*j^10 - 573388748843683532691009051194955437*x^9*j^9 + 24228593349948582884094197811518266845689352*x^9*j^8 - 51135193038502008150804190472844550800569441050500*x^9*j^7 + 14690460927260804690751501000083244161647396386205851440*x^9*j^6 - 994774826102691960922410649494629085486856242714439003812180*x^9*j^5 + 22148485195925584385790489089697473918894904664093860668378292000*x^9*j^4 - 199188452917764242987050083089364860927274115441197382331866126825820*x^9*j\ ^3 + 8044364183079957387401325981668933650994688420897059005250506278912000\ 00*x^9*j^2 - 14581782545972952078399807867686230186502343069323313930136349\ 52069120000000*x^9*j + 9651225466603492984067240639408842527438736331761292\ 90337528305418240000000000*x^9 + 53686822816*x^8*j^11 + 12407796387712093514736413264496*x^8*j^10 + 24228593349948582884094197811518266845689352*x^8*j^9 + 29211180544704743418963619709378403797452606969172658*x^8*j^8 + 636861023141767565580039581191818069063579259290464688398880*x^8*j^7 + 987807801334019988631500819088661487281712947788833523552559299560*x^8*j^6 + 208334210762751500564946204497082337222910461284651050215872586641463200*x^\ 8*j^5 + 8498500708725193890718329655230574962816784139443636591086906768989\ 729050095*x^8*j^4 + 7951324712505790649284198939520744230013378175092486044\ 9090230806481243648000000*x^8*j^3 + 171790435018380416903247878610824648919\ 543398246401012395341432490921925017600000000*x^8*j^2 + 668063044679983105817933911947911151848051275284130912352843152941437367091\ 20000000000*x^8*j + 1338586400912357073420399795635643400599836918986297982\ 928179335149920452608000000000000*x^8 - 61058988656490*x^7*j^11 + 645470833566425875717489618904152240*x^7*j^10 - 51135193038502008150804190472844550800569441050500*x^7*j^9 + 636861023141767565580039581191818069063579259290464688398880*x^7*j^8 - 64999046469909490143435875140651300541119093852394968074094803537810*x^7*j^\ 7 + 24790023356193929438861279985747642436485625176909488028808653790427939\ 6400*x^7*j^6 - 759485852012679734036275336311389950898826472843074845794136\ 91458563029509971992*x^7*j^5 + 29731196727162122194564718811128885698355755\ 78534065127175856819648732682854604800000*x^7*j^4 - 220932496966279334196552268236040576388972225626826358002699091783257109851\ 17040640000000*x^7*j^3 + 44681231489418997440503069818655052635806384532381\ 152777755381649015689662976491520000000000*x^7*j^2 - 241559572537644189753077428231295861870612436207563395156025710750612369922\ 94518784000000000000*x^7*j + 6188407231077618898963630168852515740786353884\ 43306832549992828319945330157158400000000000000000*x^7 + 42570393135641712*x^6*j^11 + 7848482999227584325448694633580010490867*x^6*j\ ^10 + 14690460927260804690751501000083244161647396386205851440*x^6*j^9 + 987807801334019988631500819088661487281712947788833523552559299560*x^6*j^8 + 247900233561939294388612799857476424364856251769094880288086537904279396400\ *x^6*j^7 + 1168150167526575837857761510359647773943258089269992605255478096\ 499695783789300124*x^6*j^6 + 2240803998866274951497716546923691770940596499\ 40825305182078225594292057242702643200000*x^6*j^5 + 193873837382174012147044636866579741283308287387546853037164291333930267899\ 9680942080000000*x^6*j^4 - 721191229974600751053515948619991969748296038927\ 8446632552985263875183091897870581760000000000*x^6*j^3 + 304940442465503101178718956284212733791730506305683970723911106883665585358\ 04457582592000000000000*x^6*j^2 - 95333447356443287210404497374050404132491\ 763274506548619337189691919811046970438451200000000000000000*x^6*j + 953562665947317950794933099657566747110587348311644892128115531290587730803\ 52804044800000000000000000000*x^6 - 17899526272883039048*x^5*j^11 + 28890545335855949285086003898461917345026160*x^5*j^10 - 994774826102691960922410649494629085486856242714439003812180*x^5*j^9 + 208334210762751500564946204497082337222910461284651050215872586641463200*x^\ 5*j^8 - 7594858520126797340362753363113899508988264728430748457941369145856\ 3029509971992*x^5*j^7 + 224080399886627495149771654692369177094059649940825\ 305182078225594292057242702643200000*x^5*j^6 - 150572973117089225265805144105638484783346937586249997741086009686674872608\ 27388477440000000*x^5*j^5 - 17799464186707526269518498092046260860406035746\ 6681128822395417442867019643767352197120000000000*x^5*j^4 - 132899390746510815213576388699982507144408409988109860756557471614019142636\ 9978927939584000000000000*x^5*j^3 + 971814871813934664738444920164383351748\ 8848029697396574289278515913329360524510494720000000000000000000*x^5*j^2 - 784037924821419672964306279649326942508185993010014130404793290934602248317\ 1510017064960000000000000000000*x^5*j - 311135714890286591241798839183635025168280538591757187756842266421807890101\ 0004935966720000000000000000000000*x^5 + 4297837238774928467520*x^4*j^11 + 35372414460361796790312007060191890803134127320*x^4*j^10 + 22148485195925584385790489089697473918894904664093860668378292000*x^4*j^9 + 849850070872519389071832965523057496281678413944363659108690676898972905009\ 5*x^4*j^8 + 297311967271621221945647188111288856983557557853406512717585681\ 9648732682854604800000*x^4*j^7 + 193873837382174012147044636866579741283308\ 2873875468530371642913339302678999680942080000000*x^4*j^6 - 177994641867075262695184980920462608604060357466681128822395417442867019643\ 767352197120000000000*x^4*j^5 + 1504342316556396664561828460973036017600526\ 5392518745580151910727157028699006028388237312000000000000*x^4*j^4 - 510387788704673753171746274142812030167891533922654498803534638710043488164\ 11677478092800000000000000000*x^4*j^3 + 378494977797549959360178068152933818044335078157093771639955480261351930169\ 113765048483840000000000000000000*x^4*j^2 + 596596095770309616375411102891120210780911047671877878225490788693942054393\ 02452893450240000000000000000000000*x^4*j + 437146826371712360213676049668333053099237469748508946653253316043623031097\ 15777067941888000000000000000000000000*x^4 - 529134841844639613861795*x^3*j^11 + 141313788887781426615826939475498447858\ 63493325800*x^3*j^10 - 1991884529177642429870500830893648609272741154411973\ 82331866126825820*x^3*j^9 + 79513247125057906492841989395207442300133781750\ 924860449090230806481243648000000*x^3*j^8 - 220932496966279334196552268236040576388972225626826358002699091783257109851\ 17040640000000*x^3*j^7 - 72119122997460075105351594861999196974829603892784\ 46632552985263875183091897870581760000000000*x^3*j^6 - 132899390746510815213576388699982507144408409988109860756557471614019142636\ 9978927939584000000000000*x^3*j^5 - 510387788704673753171746274142812030167\ 89153392265449880353463871004348816411677478092800000000000000000*x^3*j^4 - 925461466455522523607980072366478440235575959511945288268604770825451300845\ 059605937520640000000000000000000*x^3*j^3 + 103867720178991499136209046596137730276914706598548722228567268915891817571\ 6097236444119040000000000000000000000*x^3*j^2 + 493751729222149651035457063068642305508233453469401395944974296438196687728\ 770695603159040000000000000000000000000*x^3*j - 337500037290942764495395868386562971754016116785390841072048221617443316658\ 082155384012800000000000000000000000000000*x^3 + 27209811658056645815522600*x^2*j^11 + 1587728122949690904187089204116332301\ 200302760915266*x^2*j^10 + 804436418307995738740132598166893365099468842089\ 705900525050627891200000*x^2*j^9 + 1717904350183804169032478786108246489195\ 43398246401012395341432490921925017600000000*x^2*j^8 + 446812314894189974405030698186550526358063845323811527777553816490156896629\ 76491520000000000*x^2*j^7 + 30494044246550310117871895628421273379173050630\ 568397072391110688366558535804457582592000000000000*x^2*j^6 + 971814871813934664738444920164383351748884802969739657428927851591332936052\ 4510494720000000000000000000*x^2*j^5 + 378494977797549959360178068152933818044335078157093771639955480261351930169\ 113765048483840000000000000000000*x^2*j^4 + 103867720178991499136209046596137730276914706598548722228567268915891817571\ 6097236444119040000000000000000000000*x^2*j^3 - 301851634381591833346238394387907563828793379391119445614595161272769455527\ 698270716428288000000000000000000000000*x^2*j^2 - 417519094737708994161145213538320499717294846522136843211955441884544692965\ 5566146994176000000000000000000000000000000*x^2*j + 1509 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host faema.Math.Berkeley.EDU. (169.229.58.25) Time: Tue Mar 9 13:59:49 2004 Input: ClassicalModularPolynomial(3) Output: Magma V2.10-6 Tue Mar 9 2004 13:59:45 on modular [Seed = 1195971394] ------------------------------------- $.1^4 - $.1^3*$.2^3 + 2232*$.1^3*$.2^2 - 1069956*$.1^3*$.2 + 36864000*$.1^3 + 2232*$.1^2*$.2^3 + 2587918086*$.1^2*$.2^2 + 8900222976000*$.1^2*$.2 + 452984832000000*$.1^2 - 1069956*$.1*$.2^3 + 8900222976000*$.1*$.2^2 - 770845966336000000*$.1*$.2 + 1855425871872000000000*$.1 + $.2^4 + 36864000*$.2^3 + 452984832000000*$.2^2 + 1855425871872000000000*$.2 Total time: 3.799 seconds, Total memory usage: 2.78MB ************** MAGMA ***************** Host faema.Math.Berkeley.EDU. (169.229.58.25) Time: Tue Mar 9 14:00:30 2004 Input: integersMod5; Output: Magma V2.10-6 Tue Mar 9 2004 14:00:26 on modular [Seed = 2896361666] ------------------------------------- >> integersMod5; ^ User error: Identifier 'integersMod5' has not been declared or assigned Total time: 4.139 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 14:07:16 2004 Input: nqr:= func; Output: Magma V2.10-6 Tue Mar 9 2004 14:07:12 on modular [Seed = 2240532544] ------------------------------------- >> nqr:= func;; ^ User error: bad syntax Total time: 3.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 14:07:24 2004 Input: nqr:= func; nqr(7,3); Output: Magma V2.10-6 Tue Mar 9 2004 14:07:21 on modular [Seed = 2323963718] ------------------------------------- >> nqr:= func; ^ User error: bad syntax >> nqr(7,3);; ^ User error: Identifier 'nqr' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 14:08:14 2004 Input: exponents:= func; exponents(7,3); Output: Magma V2.10-6 Tue Mar 9 2004 14:08:10 on modular [Seed = 4126909386] ------------------------------------- [ 49, 7, 1 ] Total time: 3.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 14:09:30 2004 Input: nqr:= func; nqr(7,3); Output: Magma V2.10-6 Tue Mar 9 2004 14:09:27 on modular [Seed = 657027430] ------------------------------------- >> nqr:= func; ^ User error: bad syntax >> nqr(7,3);; ^ User error: Identifier 'nqr' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 14:11:29 2004 Input: nqr:= func; nqr(7,3); Output: Magma V2.10-6 Tue Mar 9 2004 14:11:25 on modular [Seed = 1801797008] ------------------------------------- [ 1, 7, 49 ] Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 14:18:36 2004 Input: nqr:= func; nqr(7,3); Output: Magma V2.10-6 Tue Mar 9 2004 14:18:33 on modular [Seed = 3149259541] ------------------------------------- >> nqr:= func; ^ User error: bad syntax >> nqr(7,3);; ^ User error: Identifier 'nqr' has not been declared or assigned Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 14:27:55 2004 Input: g:=map<[0,1,2,3] -> [0,2,3,4] | x:->2*x>; Output: Magma V2.10-6 Tue Mar 9 2004 14:27:52 on modular [Seed = 4110069348] ------------------------------------- Total time: 3.119 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 14:28:34 2004 Input: g:=map<[0,1,2,3] -> [0,2,3,4] | x:->2*x>; g(2); g(4); g(0); Output: Magma V2.10-6 Tue Mar 9 2004 14:28:30 on modular [Seed = 3755050281] ------------------------------------- 4 >> g(4); ^ Runtime error in map application: Element is not in the domain of the map 0 Total time: 3.489 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 14:38:49 2004 Input: exponents:= map Integer() | 7^i>; exponent(3); Output: Magma V2.10-6 Tue Mar 9 2004 14:38:46 on modular [Seed = 2965302748] ------------------------------------- >> exponents:= map Integer() | 7^i>; ^ User error: Identifier 'Integer' has not been declared or assigned >> exponent(3);; ^ User error: Identifier 'exponent' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 14:39:49 2004 Input: exponents:= map < Integers() -> Integers() |i:-> 7^i>; exponent(3); Output: Magma V2.10-6 Tue Mar 9 2004 14:39:45 on modular [Seed = 2493172031] ------------------------------------- >> exponent(3);; ^ User error: Identifier 'exponent' has not been declared or assigned Total time: 3.659 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 14:41:30 2004 Input: exponents:= map < Integers() -> Integers() |i:-> 7^i>; exponents(3); Output: Magma V2.10-6 Tue Mar 9 2004 14:41:27 on modular [Seed = 3285032462] ------------------------------------- 343 Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Tue Mar 9 15:22:55 2004 Input: K:=QuadraticField(17); E=EllipticCurve([-1048*s-4323, 55208*s+227630]); TorsionSubgroup(E); Output: Magma V2.10-6 Tue Mar 9 2004 15:22:52 on modular [Seed = 1415197667] ------------------------------------- >> E=EllipticCurve([-1048*s-4323, 55208*s+227630]); ^ User error: Identifier 'E' has not been declared or assigned >> TorsionSubgroup(E);; ^ User error: Identifier 'E' has not been declared or assigned Total time: 2.869 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Tue Mar 9 15:23:15 2004 Input: K:=QuadraticField(17); E:=EllipticCurve([-1048*s-4323, 55208*s+227630]); TorsionSubgroup(E); Output: Magma V2.10-6 Tue Mar 9 2004 15:23:02 on modular [Seed = 2746074158] ------------------------------------- Abelian Group isomorphic to Z/13 Defined on 1 generator Relations: 13*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/13 Defined on 1 generator Relations: 13*$.1 = 0 to CrvEll: E given by a rule [no inverse] Total time: 12.939 seconds, Total memory usage: 5.05MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Tue Mar 9 15:23:49 2004 Input: K:=QuadraticField(17); E:=EllipticCurve([-1048*s-4323, 55208*s+227630]); TorsionSubgroup(E); AbelianGroup(E); Output: Magma V2.10-6 Tue Mar 9 2004 15:23:36 on modular [Seed = 2982139474] ------------------------------------- Abelian Group isomorphic to Z/13 Defined on 1 generator Relations: 13*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/13 Defined on 1 generator Relations: 13*$.1 = 0 to CrvEll: E given by a rule [no inverse] >> AbelianGroup(E);; ^ Runtime error in 'AbelianGroup': Curve must be defined over a (FldFin) finite field or the rationals Total time: 12.659 seconds, Total memory usage: 5.05MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 15:43:47 2004 Input: exponents:= func Integers() |i:-> 7^i) in [0..r-1]>; exponents(3); Output: Magma V2.10-6 Tue Mar 9 2004 15:43:43 on modular [Seed = 2626875598] ------------------------------------- >> exponents:= func Integers() |i:-> 7^i) in [0..r-1] ^ User error: bad syntax >> exponents(3);; ^ User error: Identifier 'exponents' has not been declared or assigned Total time: 3.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 15:44:43 2004 Input: exponents:= func Integers() |i:-> 7^i)> in [0..r-1]>; exponents(3); Output: Magma V2.10-6 Tue Mar 9 2004 15:44:40 on modular [Seed = 3823996790] ------------------------------------- >> exponents:= func Integers() |i:-> 7^i)> in [0..r-1 ^ User error: bad syntax >> exponents(3);; ^ User error: Identifier 'exponents' has not been declared or assigned Total time: 3.179 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 15:58:42 2004 Input: mu1 := &+[ S1[k] : k in [1..n] ]/n; mu1(4); Output: Magma V2.10-6 Tue Mar 9 2004 15:58:38 on modular [Seed = 337279941] ------------------------------------- >> mu1 := &+[ S1[k] : k in [1..n] ]/n; ^ User error: Identifier 'n' has not been declared or assigned >> mu1(4);; ^ User error: Identifier 'mu1' has not been declared or assigned Total time: 3.689 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 9 16:22:43 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+23); OK:=MaximalOrder(K); I:=3*OK; F:=Factorization(I); IsPrincipal(F[1][1]); Output: Magma V2.10-6 Tue Mar 9 2004 16:22:40 on modular [Seed = 3285038674] ------------------------------------- false Total time: 3.239 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 16:30:20 2004 Input: nqr:=func> nqr:=func> nqr[1,2,3]; ; ^ User error: Identifier 'nqr' has not been declared or assigned Total time: 3.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 16:31:50 2004 Input: nqr:=func> nqr:=func> nqr[1,2,3]; ; ^ User error: Identifier 'nqr' has not been declared or assigned Total time: 3.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 16:32:08 2004 Input: nqr:=func> nqr:=func> nqr[1,2,3]; ; ^ User error: Identifier 'nqr' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 16:33:07 2004 Input: nqr:=func; nqr([1,2,3]); Output: Magma V2.10-6 Tue Mar 9 2004 16:33:03 on modular [Seed = 1329674099] ------------------------------------- >> nqr:=func; ^ User error: bad syntax >> nqr([1,2,3]); ; ^ User error: Identifier 'nqr' has not been declared or assigned Total time: 4.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 16:35:14 2004 Input: nqr:=func ; nqr([1,2,3]); Output: Magma V2.10-6 Tue Mar 9 2004 16:35:10 on modular [Seed = 4193747268] ------------------------------------- >> nqr:=func ; ^ User error: bad syntax >> nqr([1,2,3]); ; ^ User error: Identifier 'nqr' has not been declared or assigned Total time: 3.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 16:36:00 2004 Input: nqr:=func ; nqr([1,2,3]); Output: Magma V2.10-6 Tue Mar 9 2004 16:35:57 on modular [Seed = 3688211285] ------------------------------------- >> nqr:=func ; ^ User error: bad syntax >> nqr([1,2,3]); ; ^ User error: Identifier 'nqr' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 16:37:55 2004 Input: nqr:= x=x+n[i : i in [0..#n-1]] ; nqr([1,2,3]); Output: Magma V2.10-6 Tue Mar 9 2004 16:37:51 on modular [Seed = 134639891] ------------------------------------- >> nqr:= x=x+n[i : i in [0..#n-1]] ; ^ User error: bad syntax >> nqr([1,2,3]); ^ User error: Identifier 'nqr' has not been declared or assigned Total time: 3.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 16:38:38 2004 Input: nqr:= x=x+n[i] : i in [0..#n-1] ; nqr([1,2,3]); Output: Magma V2.10-6 Tue Mar 9 2004 16:38:34 on modular [Seed = 1634670607] ------------------------------------- >> nqr:= x=x+n[i] : i in [0..#n-1] ; ^ User error: bad syntax >> nqr([1,2,3]); ^ User error: Identifier 'nqr' has not been declared or assigned Total time: 4.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 9 16:41:17 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+23); OK:=MaximalOrder(K); I:=ideal; IsPrincipal(I); Output: Magma V2.10-6 Tue Mar 9 2004 16:41:13 on modular [Seed = 2643715152] ------------------------------------- false Total time: 3.199 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 16:44:00 2004 Input: nqr:= func < q,r |x=q^i : i in [0..r-1]]>; nqr(7,3) Output: Magma V2.10-6 Tue Mar 9 2004 16:43:57 on modular [Seed = 3268196459] ------------------------------------- >> nqr:= func < q,r |x=q^i : i in [0..r-1]]>; ^ User error: bad syntax >> nqr(7,3); ^ User error: Identifier 'nqr' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 16:45:45 2004 Input: nqr:= func < q,r |x=q^i : i in [0..r-1]>; nqr(7,3) Output: Magma V2.10-6 Tue Mar 9 2004 16:45:42 on modular [Seed = 67796791] ------------------------------------- >> nqr:= func < q,r |x=q^i : i in [0..r-1]>; ^ User error: bad syntax >> nqr(7,3); ^ User error: Identifier 'nqr' has not been declared or assigned Total time: 3.249 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 16:46:38 2004 Input: nqr:= func < q,r |x=q^i : i in [0..r-1]>; nqr(7,3) exponents:= func; exponents(7,3); Output: Magma V2.10-6 Tue Mar 9 2004 16:46:34 on modular [Seed = 2054422901] ------------------------------------- >> nqr:= func < q,r |x=q^i : i in [0..r-1]>; ^ User error: bad syntax >> exponents:= func; ^ User error: bad syntax >> exponents(7,3);; ^ User error: Identifier 'exponents' has not been declared or assigned Total time: 3.649 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 16:47:12 2004 Input: nqr:= func < q,r |x=q^i : i in [0..r-1]>; nqr(7,3) exponents:= func; exponents(7,3); Output: Magma V2.10-6 Tue Mar 9 2004 16:47:09 on modular [Seed = 1381771578] ------------------------------------- >> nqr:= func < q,r |x=q^i : i in [0..r-1]>; ^ User error: bad syntax >> exponents:= func; ^ User error: bad syntax >> exponents(7,3);; ^ User error: Identifier 'exponents' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 16:47:22 2004 Input: nqr:= func < q,r |x=q^i : i in [0..r-1]>; nqr(7,3); exponents:= func; exponents(7,3); Output: Magma V2.10-6 Tue Mar 9 2004 16:47:19 on modular [Seed = 1515462920] ------------------------------------- >> nqr:= func < q,r |x=q^i : i in [0..r-1]>; ^ User error: bad syntax >> nqr(7,3); ^ User error: Identifier 'nqr' has not been declared or assigned [ 49, 7, 1 ] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 16:47:27 2004 Input: nqr:= func < q,r |x=q^i : i in [0..r-1]>; nqr(7,3); exponents:= func; exponents(7,3); Output: Magma V2.10-6 Tue Mar 9 2004 16:47:23 on modular [Seed = 1296250387] ------------------------------------- >> nqr:= func < q,r |x=q^i : i in [0..r-1]>; ^ User error: bad syntax >> nqr(7,3); ^ User error: Identifier 'nqr' has not been declared or assigned [ 49, 7, 1 ] Total time: 3.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 16:48:18 2004 Input: nqr:= func < q,r |x=q^(i : i in [0..r-1])>; nqr(7,3); exponents:= func; exponents(7,3); Output: Magma V2.10-6 Tue Mar 9 2004 16:48:16 on modular [Seed = 2812927026] ------------------------------------- >> nqr:= func < q,r |x=q^(i : i in [0..r-1])>; ^ User error: bad syntax >> nqr(7,3); ^ User error: Identifier 'nqr' has not been declared or assigned [ 49, 7, 1 ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 16:49:08 2004 Input: nqr:= func < q,r |q^i : i in [0..r-1]>; nqr(7,3); exponents:= func; exponents(7,3); Output: Magma V2.10-6 Tue Mar 9 2004 16:49:04 on modular [Seed = 2173696612] ------------------------------------- >> nqr:= func < q,r |q^i : i in [0..r-1]>; ^ User error: bad syntax >> nqr(7,3); ^ User error: Identifier 'nqr' has not been declared or assigned [ 49, 7, 1 ] Total time: 3.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 16:49:38 2004 Input: nqr:= func < q,r|[q^i : i in [0..r-1]]>; nqr(7,3); exponents:= func; exponents(7,3); Output: Magma V2.10-6 Tue Mar 9 2004 16:49:34 on modular [Seed = 4243752743] ------------------------------------- [ 1, 7, 49 ] [ 49, 7, 1 ] Total time: 3.849 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 16:51:40 2004 Input: nqr:= func < q,r|for j:=0 to (r-1) do [q^i : i in [0..r-1]]end for>; nqr(7,3); exponents:= func; exponents(7,3); Output: Magma V2.10-6 Tue Mar 9 2004 16:51:36 on modular [Seed = 976504420] ------------------------------------- >> nqr:= func < q,r|for j:=0 to (r-1) do [q^i : i in [0..r-1]]end for>; ^ User error: bad syntax >> nqr(7,3); ^ User error: Identifier 'nqr' has not been declared or assigned [ 49, 7, 1 ] Total time: 4.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 16:56:16 2004 Input: nqr:= func < q,r|for y in [0..r-1] do [q^i : i in [0..r-1]]end for>; nqr(7,3); exponents:= func; exponents(7,3); Output: Magma V2.10-6 Tue Mar 9 2004 16:56:12 on modular [Seed = 1498883091] ------------------------------------- >> nqr:= func < q,r|for y in [0..r-1] do [q^i : i in [0..r-1]]end for>; ^ User error: bad syntax >> nqr(7,3); ^ User error: Identifier 'nqr' has not been declared or assigned [ 49, 7, 1 ] Total time: 4.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 16:57:45 2004 Input: nqr:= func < q,r|for y in [0..r-1] do [q^i : i in [0..r-1]]end for>; nqr(7,3); exponents:= func; exponents(7,3); Output: Magma V2.10-6 Tue Mar 9 2004 16:57:42 on modular [Seed = 2493180276] ------------------------------------- >> nqr:= func < q,r|for y in [0..r-1] do [q^i : i in [0..r-1]]end for>; ^ User error: bad syntax >> nqr(7,3); ^ User error: Identifier 'nqr' has not been declared or assigned [ 49, 7, 1 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 9 17:05:29 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+23); OK:=MaximalOrder(K); I:=3*OK; F:=Factorization(I); IsPrincipal(F[1][1]); IsPrincipal(F[1][1]^2); Output: Magma V2.10-6 Tue Mar 9 2004 17:05:25 on modular [Seed = 2796083508] ------------------------------------- false false Total time: 4.119 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 9 17:05:49 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+23); OK:=MaximalOrder(K); I:=3*OK; F:=Factorization(I); IsPrincipal(F[1][1]); IsPrincipal(F[1][1]^2); IsPrincipal(F[1][1]^3); Output: Magma V2.10-6 Tue Mar 9 2004 17:05:45 on modular [Seed = 2426335006] ------------------------------------- false false true Total time: 4.099 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 17:22:07 2004 Input: f := map< R -> R | x :-> x^2 >; f(3); Output: Magma V2.10-6 Tue Mar 9 2004 17:22:02 on modular [Seed = 3587954278] ------------------------------------- >> f := map< R -> R | x :-> x^2 >; ^ User error: Identifier 'R' has not been declared or assigned >> f(3);; ^ User error: Identifier 'f' has not been declared or assigned Total time: 3.709 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 9 17:22:08 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+23); OK:=MaximalOrder(K); I:=2*OK; J=3*OK; F:=Factorization(I); G:=Factorization(J); T:=F[1][1]*G[1][1]; IsPrincipal(T); Output: Magma V2.10-6 Tue Mar 9 2004 17:22:03 on modular [Seed = 3604534628] ------------------------------------- >> J=3*OK; ^ User error: Identifier 'J' has not been declared or assigned >> G:=Factorization(J); ^ User error: Identifier 'J' has not been declared or assigned >> T:=F[1][1]*G[1][1]; ^ User error: Identifier 'G' has not been declared or assigned >> IsPrincipal(T);; ^ User error: Identifier 'T' has not been declared or assigned Total time: 3.999 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 9 17:22:19 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+23); OK:=MaximalOrder(K); I:=2*OK; J:=3*OK; F:=Factorization(I); G:=Factorization(J); T:=F[1][1]*G[1][1]; IsPrincipal(T); Output: Magma V2.10-6 Tue Mar 9 2004 17:22:16 on modular [Seed = 993343641] ------------------------------------- true Total time: 3.279 seconds, Total memory usage: 2.10MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 17:22:23 2004 Input: R := RealField(); f := map< R -> R | x :-> x^2 >; f(3); Output: Magma V2.10-6 Tue Mar 9 2004 17:22:20 on modular [Seed = 859648149] ------------------------------------- 9 Total time: 3.279 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 9 17:22:30 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+23); OK:=MaximalOrder(K); I:=2*OK; J:=3*OK; F:=Factorization(I); G:=Factorization(J); T:=F[1][1]*G[1][2]; IsPrincipal(T); Output: Magma V2.10-6 Tue Mar 9 2004 17:22:27 on modular [Seed = 740437941] ------------------------------------- false Total time: 3.759 seconds, Total memory usage: 2.10MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 9 17:22:46 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+23); OK:=MaximalOrder(K); I:=2*OK; J:=3*OK; F:=Factorization(I); G:=Factorization(J); T:=F[1][1]*G[1][1]; T; IsPrincipal(T); Output: Magma V2.10-6 Tue Mar 9 2004 17:22:42 on modular [Seed = 303829402] ------------------------------------- Ideal of OK Basis: [3 1] [0 2] false Total time: 4.349 seconds, Total memory usage: 2.10MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 17:22:57 2004 Input: R := RealField(); f := map< R -> R | x :-> x^2 >; f([1,2,3]); Output: Magma V2.10-6 Tue Mar 9 2004 17:22:54 on modular [Seed = 234884491] ------------------------------------- [ 1, 4, 9 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 9 17:23:18 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+23); OK:=MaximalOrder(K); I:=2*OK; J:=3*OK; F:=Factorization(I); G:=Factorization(J); F[1][1]; G[1][1]; T:=F[1][1]*G[1][1]; T; IsPrincipal(T); Output: Magma V2.10-6 Tue Mar 9 2004 17:23:13 on modular [Seed = 2087878551] ------------------------------------- Prime Ideal of OK Two element generators: [2, 0] [5, 3] Prime Ideal of OK Two element generators: [3, 0] [3, 2] Ideal of OK Basis: [3 1] [0 2] false Total time: 4.339 seconds, Total memory usage: 2.10MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 9 17:23:38 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+23); OK:=MaximalOrder(K); I:=2*OK; J:=3*OK; F:=Factorization(I); G:=Factorization(J); F[1][1]; G[1][2]; T:=F[1][1]*G[1][1]; T; IsPrincipal(T); Output: Magma V2.10-6 Tue Mar 9 2004 17:23:34 on modular [Seed = 1868655795] ------------------------------------- Prime Ideal of OK Two element generators: [2, 0] [0, 3] 1 Ideal of OK Basis: [6 0] [0 1] true Total time: 3.459 seconds, Total memory usage: 2.10MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 9 17:24:05 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+23); OK:=MaximalOrder(K); I:=2*OK; J:=3*OK; F:=Factorization(I); G:=Factorization(J); F[1][1]; G[1][2]; T:=F[1][1]*G[1][1]; T; IsPrincipal(T); 1 in T; Output: Magma V2.10-6 Tue Mar 9 2004 17:24:01 on modular [Seed = 1381783145] ------------------------------------- Prime Ideal of OK Two element generators: [2, 0] [4, 1] 1 Ideal of OK Basis: [6 0] [0 1] true >> 1 in T;; ^ Runtime error in 'in': Bad argument types Argument types given: RngIntElt, RngOrdIdl Total time: 3.809 seconds, Total memory usage: 2.10MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 17:24:15 2004 Input: exponents:= func; exponets(7,3); Output: Magma V2.10-6 Tue Mar 9 2004 17:24:12 on modular [Seed = 1296255355] ------------------------------------- >> exponets(7,3); ^ User error: Identifier 'exponets' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 17:24:45 2004 Input: exponents:= func; exponents(7,3); Output: Magma V2.10-6 Tue Mar 9 2004 17:24:42 on modular [Seed = 3082400679] ------------------------------------- [ 1, 7, 49 ] Total time: 3.119 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 17:26:41 2004 Input: x:=0; exponents:= func; exponents(7,3); sumlist:= func; Output: Magma V2.10-6 Tue Mar 9 2004 17:26:37 on modular [Seed = 4024560456] ------------------------------------- [ 1, 7, 49 ] >> sumlist:= func;; ^ User error: bad syntax Total time: 3.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 17:27:16 2004 Input: x:=0; exponents:= func; exponents(7,3); sumlist:= func<[1,2,3]|x+exponets[i] : i in [0..r-1]>; Output: Magma V2.10-6 Tue Mar 9 2004 17:27:13 on modular [Seed = 3621376812] ------------------------------------- [ 1, 7, 49 ] >> sumlist:= func<[1,2,3]|x+exponets[i] : i in [0..r-1]>;; ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 17:27:51 2004 Input: x:=0; exponents:= func; li:=exponents(7,3); sumlist:= func; Output: Magma V2.10-6 Tue Mar 9 2004 17:27:48 on modular [Seed = 993345508] ------------------------------------- >> sumlist:= func;; ^ User error: bad syntax Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 17:28:33 2004 Input: x:=0; exponents:= func; li:=exponents(7,3); sumlist:= func; Output: Magma V2.10-6 Tue Mar 9 2004 17:28:30 on modular [Seed = 470948137] ------------------------------------- >> sumlist:= func;; ^ User error: bad syntax Total time: 3.409 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 17:30:40 2004 Input: x:=0; exponents:= func; li:=exponents(7,3); sumlist:= for y in [0..r-1] do x:=x+li[y] end for; /* func; */ Output: Magma V2.10-6 Tue Mar 9 2004 17:30:37 on modular [Seed = 1432047843] ------------------------------------- >> sumlist:= for y in [0..r-1] do ^ User error: bad syntax >> end for; ^ User error: bad syntax Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 17:30:58 2004 Input: x:=0; exponents:= func; li:=exponents(7,3); for y in [0..r-1] do x:=x+li[y] end for; /* func; */ Output: Magma V2.10-6 Tue Mar 9 2004 17:30:54 on modular [Seed = 1179141091] ------------------------------------- >> end for; ^ User error: bad syntax Total time: 3.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 17:31:15 2004 Input: x:=0; exponents:= func; li:=exponents(7,3); for y in [0..r-1] do x:=x+li[y]; end for; /* func; */ Output: Magma V2.10-6 Tue Mar 9 2004 17:31:10 on modular [Seed = 2829495613] ------------------------------------- >> for y in [0..r-1] do ^ User error: Identifier 'r' has not been declared or assigned Total time: 3.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 17:32:03 2004 Input: x:=0; exponents:= func; li:=exponents(7,3); r:=3; for y in [0..r-1] do x:=x+li[y]; end for; /* func; */ Output: Magma V2.10-6 Tue Mar 9 2004 17:31:59 on modular [Seed = 2323943278] ------------------------------------- >> x:=x+li[y]; ^ Runtime error in '[]': Sequence element 0 not defined Total time: 3.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 17:32:28 2004 Input: x:=0; exponents:= func; li:=exponents(7,3); r:=3; for y in [1..r-1] do x:=x+li[y]; end for; /* func; */ Output: Magma V2.10-6 Tue Mar 9 2004 17:32:24 on modular [Seed = 4176936251] ------------------------------------- Total time: 4.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 17:32:49 2004 Input: x:=0; exponents:= func; li:=exponents(7,3); r:=3; for y in [1..r-1] do x:=x+li[y]; end for; x; /* func; */ Output: Magma V2.10-6 Tue Mar 9 2004 17:32:45 on modular [Seed = 4007717080] ------------------------------------- 8 Total time: 3.329 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 17:33:02 2004 Input: x:=0; exponents:= func; li:=exponents(7,3); r:=3; for y in [1..r] do x:=x+li[y]; end for; x; /* func; */ Output: Magma V2.10-6 Tue Mar 9 2004 17:32:57 on modular [Seed = 3755071997] ------------------------------------- 57 Total time: 4.129 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 17:38:11 2004 Input: nqr:= func(q,r); x:=0 li:=[q^i : i in [0..r-1]] for y in [1..r] do x:=x+li[y]; end for; x; end function; func(7,3); /* func; */ Output: Magma V2.10-6 Tue Mar 9 2004 17:38:07 on modular [Seed = 1279413055] ------------------------------------- >> nqr:= func(q,r); ^ User error: Identifier 'q' has not been declared or assigned >> li:=[q^i : i in [0..r-1]] ^ User error: bad syntax >> for y in [1..r] do ^ User error: Identifier 'r' has not been declared or assigned >> x; ^ User error: Identifier 'x' has not been declared or assigned >> end function; ^ User error: bad syntax >> func(7,3); ^ User error: Identifier 'func' has not been declared or assigned Total time: 3.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 17:38:27 2004 Input: nqr:= function(q,r); x:=0 li:=[q^i : i in [0..r-1]] for y in [1..r] do x:=x+li[y]; end for; x; end function; func(7,3); /* func; */ Output: Magma V2.10-6 Tue Mar 9 2004 17:38:23 on modular [Seed = 3199252957] ------------------------------------- >> li:=[q^i : i in [0..r-1]] ^ User error: bad syntax >> for y in [1..r] do ^ User error: Identifier 'r' has not been declared or assigned >> x; ^ User error: Identifier 'x' has not been declared or assigned >> end function; ^ User error: bad syntax >> func(7,3); ^ User error: Identifier 'func' has not been declared or assigned Total time: 4.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 17:38:33 2004 Input: nqr:= function(q,r); x:=0 li:=[q^i : i in [0..r-1]] for y in [1..r] do x:=x+li[y]; end for; x; end function; nqr(7,3); /* func; */ Output: Magma V2.10-6 Tue Mar 9 2004 17:38:30 on modular [Seed = 2982131435] ------------------------------------- >> li:=[q^i : i in [0..r-1]] ^ User error: bad syntax >> for y in [1..r] do ^ User error: Identifier 'r' has not been declared or assigned >> x; ^ User error: Identifier 'x' has not been declared or assigned >> end function; ^ User error: bad syntax >> nqr(7,3); ^ User error: Identifier 'nqr' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 17:39:07 2004 Input: nqr:= function(q,r); x:=0; li:=[q^i : i in [0..r-1]] for y in [1..r] do x:=x+li[y]; end for; x; end function; nqr(7,3); /* func; */ Output: Magma V2.10-6 Tue Mar 9 2004 17:39:04 on modular [Seed = 2459735334] ------------------------------------- >> for y in [1..r] do ^ User error: bad syntax >> x:=x+li[y]; ^ User error: Identifier 'x' has not been declared or assigned >> end for; ^ User error: bad syntax >> x; ^ User error: Identifier 'x' has not been declared or assigned >> end function; ^ User error: bad syntax >> nqr(7,3); ^ User error: Identifier 'nqr' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 17:39:33 2004 Input: nqr:= function(q,r); x:=0; li:=[q^i : i in [0..r-1]] for y in [1..r] do x:=x+li[y]; end for; x; end function; nqr(7,3); /* func; */ Output: Magma V2.10-6 Tue Mar 9 2004 17:39:29 on modular [Seed = 4110087017] ------------------------------------- >> for y in [1..r] do ^ User error: bad syntax >> x:=x+li[y]; ^ User error: Identifier 'x' has not been declared or assigned >> end for; ^ User error: bad syntax >> x; ^ User error: Identifier 'x' has not been declared or assigned >> end function; ^ User error: bad syntax >> nqr(7,3); ^ User error: Identifier 'nqr' has not been declared or assigned Total time: 3.559 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 17:39:58 2004 Input: nqr:= function(q,r); x:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do x:=x+li[y]; end for; x; end function; nqr(7,3); /* func; */ Output: Magma V2.10-6 Tue Mar 9 2004 17:39:54 on modular [Seed = 3521107543] ------------------------------------- 57 >> nqr(7,3); ^ Runtime error in procedure call: No return statement executed in user-defined function Total time: 4.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 17:40:36 2004 Input: nqr:= function(q,r); x:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do x:=x+li[y]; end for; end function; nqr(7,3); /* func; */ Output: Magma V2.10-6 Tue Mar 9 2004 17:40:33 on modular [Seed = 859649263] ------------------------------------- >> nqr(7,3); ^ Runtime error in procedure call: No return statement executed in user-defined function Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 17:41:03 2004 Input: nqr:= function(q,r); x:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do x:=x+li[y]; end for; return(x); end function; nqr(7,3); /* func; */ Output: Magma V2.10-6 Tue Mar 9 2004 17:41:00 on modular [Seed = 370676183] ------------------------------------- 57 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 17:44:08 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()) n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); Output: Magma V2.10-6 Tue Mar 9 2004 17:44:04 on modular [Seed = 2998712891] ------------------------------------- >> n:=0; ^ User error: bad syntax >> li:=[q^i : i in [0..r-1]]; ^ User error: Identifier 'r' has not been declared or assigned >> for y in [1..r] do ^ User error: Identifier 'r' has not been declared or assigned >> return x^(n); ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> nqr(7,3); ^ User error: Identifier 'nqr' has not been declared or assigned Total time: 3.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 17:44:25 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); Output: Magma V2.10-6 Tue Mar 9 2004 17:44:21 on modular [Seed = 2746067803] ------------------------------------- x^57 Total time: 3.469 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 17:46:44 2004 Input: tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; nqr(7,3); Output: Magma V2.10-6 Tue Mar 9 2004 17:46:41 on modular [Seed = 3874025354] ------------------------------------- >> nqr(7,3); ^ User error: Identifier 'nqr' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 9 17:47:05 2004 Input: tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); Output: Magma V2.10-6 Tue Mar 9 2004 17:47:02 on modular [Seed = 3621379724] ------------------------------------- x^49 + x^7 + x Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 9 18:27:38 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2+23); OK:=MaximalOrder(K); MinimalPolynomial((1+y)/2); Output: Magma V2.10-6 Tue Mar 9 2004 18:27:35 on modular [Seed = 4160349523] ------------------------------------- x^2 - x + 6 Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 9 18:28:59 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2+23); OK:=MaximalOrder(K); MinimalPolynomial(y); Output: Magma V2.10-6 Tue Mar 9 2004 18:28:56 on modular [Seed = 3115821762] ------------------------------------- x^2 + 23 Total time: 3.599 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 9 18:29:26 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2+23); OK:=MaximalOrder(K); MinimalPolynomial((1+y)/2); Output: Magma V2.10-6 Tue Mar 9 2004 18:29:23 on modular [Seed = 1415202627] ------------------------------------- x^2 - x + 6 Total time: 3.029 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 9 18:31:35 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2-5); OK:=MaximalOrder(K); MinimalPolynomial((1+y)/2); Output: Magma V2.10-6 Tue Mar 9 2004 18:31:32 on modular [Seed = 590164147] ------------------------------------- x^2 - x - 1 Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 9 18:33:07 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2+23); OK:=MaximalOrder(K); MinimalPolynomial((1+y)/2); Output: Magma V2.10-6 Tue Mar 9 2004 18:33:02 on modular [Seed = 3721644471] ------------------------------------- x^2 - x + 6 Total time: 4.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 9 19:46:12 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2+23); OK:=MaximalOrder(K); I:=ideal; IsPrincipal(I); Output: Magma V2.10-6 Tue Mar 9 2004 19:46:09 on modular [Seed = 4093499115] ------------------------------------- false Total time: 3.159 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 9 19:52:05 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2+23); OK:=MaximalOrder(K); I:=ideal; IsPrincipal(I); J:=ideal; IsPrincipal(J); Output: Magma V2.10-6 Tue Mar 9 2004 19:52:01 on modular [Seed = 723848656] ------------------------------------- false false Total time: 4.449 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 9 19:52:26 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2+23); OK:=MaximalOrder(K); ClassNumber(OK); I:=ideal; IsPrincipal(I); J:=ideal; IsPrincipal(J); Output: Magma V2.10-6 Tue Mar 9 2004 19:52:23 on modular [Seed = 1009916593] ------------------------------------- 3 false false Total time: 3.109 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 9 19:53:35 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2+23); OK:=MaximalOrder(K); ClassNumber(OK); I:=ideal; IsPrincipal(I); J:=I*I; IsPrincipal(J); M:=J*I; IsPrincipal(M); Output: Magma V2.10-6 Tue Mar 9 2004 19:53:32 on modular [Seed = 3721656987] ------------------------------------- 3 false false true Total time: 3.249 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 9 19:55:57 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2+23); OK:=MaximalOrder(K); ClassNumber(OK); I:=ideal; IsPrincipal(I); I2:=I*I; IsPrincipal(J); I3:=I2*I; IsPrincipal(I3); Output: Magma V2.10-6 Tue Mar 9 2004 19:55:52 on modular [Seed = 2896333694] ------------------------------------- 3 false >> IsPrincipal(J); ^ User error: Identifier 'J' has not been declared or assigned true Total time: 4.449 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 9 19:56:06 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2+23); OK:=MaximalOrder(K); ClassNumber(OK); I:=ideal; IsPrincipal(I); I2:=I*I; IsPrincipal(I2); I3:=I2*I; IsPrincipal(I3); Output: Magma V2.10-6 Tue Mar 9 2004 19:56:03 on modular [Seed = 3098976081] ------------------------------------- 3 false false true Total time: 3.149 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 9 19:57:00 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2+23); OK:=MaximalOrder(K); ClassNumber(OK); I:=ideal; IsPrincipal(I); I2:=I*I; IsPrincipal(I2); I3:=I2*I; IsPrincipal(I3); J:=ideal; IsPrincipal(J); J2:=J*J; IsPrincipal(J2); J3:=J2*J; IsPrincipal(J3); Output: Magma V2.10-6 Tue Mar 9 2004 19:56:56 on modular [Seed = 1532329160] ------------------------------------- 3 false false true false false true Total time: 3.349 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 9 19:58:20 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2+23); OK:=MaximalOrder(K); ClassNumber(OK); I:=ideal; IsPrincipal(I); I2:=I*I; IsPrincipal(I2); I3:=I2*I; IsPrincipal(I3); J:=ideal; IsPrincipal(J); J2:=J*J; IsPrincipal(J2); J3:=J2*J; IsPrincipal(J3); M:=ideal IsPrincipal(M*M); Output: Magma V2.10-6 Tue Mar 9 2004 19:58:16 on modular [Seed = 2138134300] ------------------------------------- 3 false false true false false true >> IsPrincipal(M*M);; ^ User error: bad syntax Total time: 4.389 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 9 19:58:50 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2+23); OK:=MaximalOrder(K); ClassNumber(OK); I:=ideal; IsPrincipal(I); I2:=I*I; IsPrincipal(I2); I3:=I2*I; IsPrincipal(I3); J:=ideal; IsPrincipal(J); J2:=J*J; IsPrincipal(J2); J3:=J2*J; IsPrincipal(J3); M:=ideal M2:=M*M IsPrincipal(M2); Output: Magma V2.10-6 Tue Mar 9 2004 19:58:45 on modular [Seed = 17770767] ------------------------------------- 3 false false true false false true >> M2:=M*M ^ User error: bad syntax >> IsPrincipal(M2);; ^ User error: Identifier 'M2' has not been declared or assigned Total time: 4.459 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 9 19:59:09 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2+23); OK:=MaximalOrder(K); ClassNumber(OK); I:=ideal; IsPrincipal(I); I2:=I*I; IsPrincipal(I2); I3:=I2*I; IsPrincipal(I3); J:=ideal; IsPrincipal(J); J2:=J*J; IsPrincipal(J2); J3:=J2*J; IsPrincipal(J3); M:=ideal; M2:=M*M IsPrincipal(M2); Output: Magma V2.10-6 Tue Mar 9 2004 19:59:06 on modular [Seed = 387530502] ------------------------------------- 3 false false true false false true >> IsPrincipal(M2);; ^ User error: bad syntax Total time: 3.249 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 9 19:59:37 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2+23); OK:=MaximalOrder(K); ClassNumber(OK); I:=ideal; IsPrincipal(I); I2:=I*I; IsPrincipal(I2); I3:=I2*I; IsPrincipal(I3); J:=ideal; IsPrincipal(J); J2:=J*J; IsPrincipal(J2); J3:=J2*J; IsPrincipal(J3); M:=ideal; M2:=M*M M2=OK; Output: Magma V2.10-6 Tue Mar 9 2004 19:59:33 on modular [Seed = 623578395] ------------------------------------- 3 false false true false false true >> M2=OK;; ^ User error: bad syntax Total time: 3.839 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 9 20:01:02 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2+23); OK:=MaximalOrder(K); ClassNumber(OK); I:=ideal; IsPrincipal(I); I2:=I*I; IsPrincipal(I2); I3:=I2*I; IsPrincipal(I3); J:=ideal; IsPrincipal(J); J2:=J*J; IsPrincipal(J2); J3:=J2*J; IsPrincipal(J3); M:=ideal; M2:=M*M; IsPrincipal(M2); Output: Magma V2.10-6 Tue Mar 9 2004 20:00:59 on modular [Seed = 3957703531] ------------------------------------- 3 false false true false false true true Total time: 3.389 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 9 20:02:30 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2+23); OK:=MaximalOrder(K); ClassNumber(OK); I:=ideal; IsPrincipal(I); I2:=I*I; IsPrincipal(I2); I3:=I2*I; IsPrincipal(I3); J:=ideal; IsPrincipal(J); J2:=J*J; IsPrincipal(J2); J3:=J2*J; IsPrincipal(J3); M:=ideal; M2:=M*M; IsPrincipal(M2); M1:=ideal IsPrincipal(M1); Output: Magma V2.10-6 Tue Mar 9 2004 20:02:26 on modular [Seed = 2543435518] ------------------------------------- 3 false false true false false true true >> IsPrincipal(M1);; ^ User error: bad syntax Total time: 3.629 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 9 20:02:57 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2+23); OK:=MaximalOrder(K); ClassNumber(OK); I:=ideal; IsPrincipal(I); I2:=I*I; IsPrincipal(I2); I3:=I2*I; IsPrincipal(I3); J:=ideal; IsPrincipal(J); J2:=J*J; IsPrincipal(J2); J3:=J2*J; IsPrincipal(J3); M:=ideal; M2:=M*M; IsPrincipal(M2); M1:=ideal; IsPrincipal(M1); Output: Magma V2.10-6 Tue Mar 9 2004 20:02:54 on modular [Seed = 1279419710] ------------------------------------- 3 false false true false false true true true Total time: 3.579 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 9 20:10:19 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2+23); OK:=MaximalOrder(K); ClassNumber(OK); P3:=ideal; IsPrincipal(P3); P33:=P3*P3; IsPrincipal(P3P3); P333:=P33*P3; IsPrincipal(P333); P4:=ideal; IsPrincipal(P4); P44:=P4*P4; IsPrincipal(P44); P444:=P44*P4; IsPrincipal(P444); P2:=ideal; P22:=P2*P2; IsPrincipal(P22); P1:=ideal; IsPrincipal(P2*P1); Output: Magma V2.10-6 Tue Mar 9 2004 20:10:15 on modular [Seed = 1365212139] ------------------------------------- 3 false >> IsPrincipal(P3P3); ^ User error: Identifier 'P3P3' has not been declared or assigned true false false true true true Total time: 3.809 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 9 20:10:34 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2+23); OK:=MaximalOrder(K); ClassNumber(OK); P3:=ideal; IsPrincipal(P3); P33:=P3*P3; IsPrincipal(P33); P333:=P33*P3; IsPrincipal(P333); P4:=ideal; IsPrincipal(P4); P44:=P4*P4; IsPrincipal(P44); P444:=P44*P4; IsPrincipal(P444); P2:=ideal; P22:=P2*P2; IsPrincipal(P22); P1:=ideal; IsPrincipal(P2*P1); Output: Magma V2.10-6 Tue Mar 9 2004 20:10:31 on modular [Seed = 1718111532] ------------------------------------- 3 false false true false false true true true Total time: 3.639 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 9 20:15:42 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2+23); OK:=MaximalOrder(K); ClassNumber(OK); P3:=ideal; IsPrincipal(P3); P33:=P3*P3; IsPrincipal(P33); P333:=P33*P3; IsPrincipal(P333); P4:=ideal; IsPrincipal(P4); P44:=P4*P4; IsPrincipal(P44); P444:=P44*P4; IsPrincipal(P444); P2:=ideal; P22:=P2*P2; IsPrincipal(P22); P1:=ideal; IsPrincipal(P2*P1); Output: Magma V2.10-6 Tue Mar 9 2004 20:15:39 on modular [Seed = 2374214139] ------------------------------------- 3 true true true false false true true true Total time: 3.249 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 9 20:21:23 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2+23); OK:=MaximalOrder(K); ClassNumber(OK); P3:=ideal; IsPrincipal(P3); P33:=P3*P3; IsPrincipal(P33); P333:=P33*P3; IsPrincipal(P333); P4:=ideal; IsPrincipal(P4); P44:=P4*P4; IsPrincipal(P44); P444:=P44*P4; IsPrincipal(P444); P2:=ideal; IsPrincipal(P2); P22:=P2*P2; IsPrincipal(P22); P1:=ideal; IsPrincipal(P2*P1); Output: Magma V2.10-6 Tue Mar 9 2004 20:21:19 on modular [Seed = 4277195583] ------------------------------------- 3 true true true false false true true true true Total time: 3.399 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 9 20:22:23 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2+23); OK:=MaximalOrder(K); ClassNumber(OK); P3:=ideal; IsPrincipal(P3); P4:=ideal; IsPrincipal(P4); P44:=P4*P4; IsPrincipal(P44); P444:=P44*P4; IsPrincipal(P444); P2:=ideal; IsPrincipal(P2); P1:=ideal; IsPrincipal(P1); Output: Magma V2.10-6 Tue Mar 9 2004 20:22:19 on modular [Seed = 2593437471] ------------------------------------- 3 true false false true true true Total time: 3.379 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 9 21:29:18 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2+23); OK:=MaximalOrder(K); ClassNumber(OK); P3:=ideal; IsPrincipal(P3); P4:=ideal; IsPrincipal(P4); P44:=P4*P4; IsPrincipal(P44); P444:=P44*P4; IsPrincipal(P444); P2:=ideal; IsPrincipal(P2); P1:=ideal; IsPrincipal(P1); Output: Magma V2.10-6 Tue Mar 9 2004 21:29:14 on modular [Seed = 790696451] ------------------------------------- 3 false false false true false false Total time: 3.949 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 9 21:36:17 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2+23); OK:=MaximalOrder(K); ClassNumber(OK); P3:=ideal; IsPrincipal(P3); P33:=P3*P3; IsPrincipal(P33); P333:=P33*P3; IsPrincipal(P333); P4:=ideal; IsPrincipal(P4); P44:=P4*P4; IsPrincipal(P44); P444:=P44*P4; IsPrincipal(P444); P2:=ideal; IsPrincipal(P2); P222:=P2*P2*P2; IsPrincipal(P222); P1:=ideal; IsPrincipal(P1); Output: Magma V2.10-6 Tue Mar 9 2004 21:36:13 on modular [Seed = 3401905536] ------------------------------------- 3 false false true false false true false true false Total time: 3.459 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 9 21:37:49 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2+23); OK:=MaximalOrder(K); ClassNumber(OK); P3:=ideal; IsPrincipal(P3); P33:=P3*P3; IsPrincipal(P33); P333:=P33*P3; IsPrincipal(P333); P4:=ideal; IsPrincipal(P4); P44:=P4*P4; IsPrincipal(P44); P444:=P44*P4; IsPrincipal(P444); P2:=ideal; IsPrincipal(P2); P22:=P2*P2; IsPrincipal(P22); P222:=P22*P2; IsPrincipal(P222); P1:=ideal; IsPrincipal(P1); P11:=P1*P1; IsPrincipal(P11); P111:=P11*P1; IsPrincipal(P111); Output: Magma V2.10-6 Tue Mar 9 2004 21:37:44 on modular [Seed = 2643698354] ------------------------------------- 3 false false true false false true false false true false false true Total time: 4.289 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 9 21:48:24 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2+23); OK:=MaximalOrder(K); ClassNumber(OK); P3:=ideal; IsPrincipal(P3); P33:=P3*P3; IsPrincipal(P33); P333:=P33*P3; IsPrincipal(P333); P4:=ideal; IsPrincipal(P4); P44:=P4*P4; IsPrincipal(P44); P444:=P44*P4; IsPrincipal(P444); P2:=ideal; IsPrincipal(P2); P22:=P2*P2; IsPrincipal(P22); P222:=P22*P2; IsPrincipal(P222); P1:=ideal; IsPrincipal(P1); P11:=P1*P1; IsPrincipal(P11); P111:=P11*P1; IsPrincipal(P111); IsPrincipal(P1*P2); Output: Magma V2.10-6 Tue Mar 9 2004 21:48:21 on modular [Seed = 2695782669] ------------------------------------- 3 false false true false false true false false true false false true true Total time: 3.459 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 9 21:49:00 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2+23); OK:=MaximalOrder(K); ClassNumber(OK); P3:=ideal; IsPrincipal(P3); P33:=P3*P3; IsPrincipal(P33); P333:=P33*P3; IsPrincipal(P333); P4:=ideal; IsPrincipal(P4); P44:=P4*P4; IsPrincipal(P44); P444:=P44*P4; IsPrincipal(P444); P2:=ideal; IsPrincipal(P2); P22:=P2*P2; IsPrincipal(P22); P222:=P22*P2; IsPrincipal(P222); P1:=ideal; IsPrincipal(P1); P11:=P1*P1; IsPrincipal(P11); P111:=P11*P1; IsPrincipal(P111); IsPrincipal(P1*P2); IsPrincipal(P2*P3); IsPrincipal(P3*P4); Output: Magma V2.10-6 Tue Mar 9 2004 21:48:55 on modular [Seed = 1229425415] ------------------------------------- 3 false false true false false true false false true false false true true false true Total time: 4.589 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 9 21:53:58 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2+23); OK:=MaximalOrder(K); ClassNumber(OK); P3:=ideal; IsPrincipal(P3); P33:=P3*P3; IsPrincipal(P33); P333:=P33*P3; IsPrincipal(P333); P4:=ideal; IsPrincipal(P4); P44:=P4*P4; IsPrincipal(P44); P444:=P44*P4; IsPrincipal(P444); P2:=ideal; IsPrincipal(P2); P22:=P2*P2; IsPrincipal(P22); P222:=P22*P2; IsPrincipal(P222); P1:=ideal; IsPrincipal(P1); P11:=P1*P1; IsPrincipal(P11); P111:=P11*P1; IsPrincipal(P111); IsPrincipal(P1*P2); IsPrincipal(P2*P3*P1); IsPrincipal(P3*P4); Output: Magma V2.10-6 Tue Mar 9 2004 21:53:55 on modular [Seed = 3840550910] ------------------------------------- 3 false false true false false true false false true false false true true false true Total time: 3.519 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host cache6.syd.ops.aspac.uu.net. (203.166.96.240) Time: Tue Mar 9 22:07:50 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Tue Mar 9 2004 22:07:45 on modular [Seed = 2087893670] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cache6.syd.ops.aspac.uu.net. (203.166.96.240) Time: Tue Mar 9 22:08:30 2004 Input: x+y=65 Output: Magma V2.10-6 Tue Mar 9 2004 22:08:27 on modular [Seed = 504420590] ------------------------------------- >> x+y=65; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam241-142.fas.harvard.edu. (140.247.241.142) Time: Tue Mar 9 23:29:18 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+23); OK := MaximalOrder(K); Factorization(2*OK); Factorization(3*OK); Output: Magma V2.10-6 Tue Mar 9 2004 23:29:15 on modular [Seed = 790755024] ------------------------------------- [ , ] [ , ] Total time: 3.019 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 200-147-20-199.tlf.dialuol.com.br. (200.147.20.199) Time: Tue Mar 9 23:35:23 2004 Input: sin(x+y); Output: Magma V2.10-6 Tue Mar 9 2004 23:35:18 on modular [Seed = 2576827131] ------------------------------------- >> sin(x+y); ^ User error: Identifier 'x' has not been declared or assigned Total time: 4.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host GLORFINDEL.MIT.EDU. (18.243.1.196) Time: Wed Mar 10 04:40:26 2004 Input: ClassGroup(QuadraticField(-15)); Output: Magma V2.10-6 Wed Mar 10 2004 04:40:21 on modular [Seed = 2223646215] ------------------------------------- Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 to Set of ideals of Maximal Order of Quadratic Field with defining polynomial $.1^2 + 15 over the Rational Field Total time: 4.129 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host GLORFINDEL.MIT.EDU. (18.243.1.196) Time: Wed Mar 10 04:40:46 2004 Input: ClassGroup(QuadraticField(62)); Output: Magma V2.10-6 Wed Mar 10 2004 04:40:42 on modular [Seed = 2459709454] ------------------------------------- Abelian Group of order 1 Mapping from: Abelian Group of order 1 to Set of ideals of Maximal Equation Order of Quadratic Field with defining polynomial $.1^2 - 62 over the Rational Field Total time: 3.759 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host GLORFINDEL.MIT.EDU. (18.243.1.196) Time: Wed Mar 10 04:40:58 2004 Input: ClassGroup(QuadraticField(67)); Output: Magma V2.10-6 Wed Mar 10 2004 04:40:54 on modular [Seed = 2729181186] ------------------------------------- Abelian Group of order 1 Mapping from: Abelian Group of order 1 to Set of ideals of Maximal Equation Order of Quadratic Field with defining polynomial $.1^2 - 67 over the Rational Field Total time: 4.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host GLORFINDEL.MIT.EDU. (18.243.1.196) Time: Wed Mar 10 04:41:10 2004 Input: ClassGroup(QuadraticField(71)); Output: Magma V2.10-6 Wed Mar 10 2004 04:41:05 on modular [Seed = 2982089478] ------------------------------------- Abelian Group of order 1 Mapping from: Abelian Group of order 1 to Set of ideals of Maximal Equation Order of Quadratic Field with defining polynomial $.1^2 - 71 over the Rational Field Total time: 5.249 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host GLORFINDEL.MIT.EDU. (18.243.1.196) Time: Wed Mar 10 04:41:21 2004 Input: ClassGroup(QuadraticField(-87)); Output: Magma V2.10-6 Wed Mar 10 2004 04:41:17 on modular [Seed = 3318441854] ------------------------------------- Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 to Set of ideals of Maximal Order of Quadratic Field with defining polynomial $.1^2 + 87 over the Rational Field Total time: 3.219 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host GLORFINDEL.MIT.EDU. (18.243.1.196) Time: Wed Mar 10 04:42:04 2004 Input: ClassGroup(QuadraticField(-39)); Output: Magma V2.10-6 Wed Mar 10 2004 04:42:00 on modular [Seed = 3654777655] ------------------------------------- Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 to Set of ideals of Maximal Order of Quadratic Field with defining polynomial $.1^2 + 39 over the Rational Field Total time: 4.229 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host GLORFINDEL.MIT.EDU. (18.243.1.196) Time: Wed Mar 10 04:42:22 2004 Input: ClassGroup(QuadraticField(-55)); Output: Magma V2.10-6 Wed Mar 10 2004 04:42:19 on modular [Seed = 4243742214] ------------------------------------- Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 to Set of ideals of Maximal Order of Quadratic Field with defining polynomial $.1^2 + 55 over the Rational Field Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host GLORFINDEL.MIT.EDU. (18.243.1.196) Time: Wed Mar 10 04:42:31 2004 Input: ClassGroup(QuadraticField(-56)); Output: Magma V2.10-6 Wed Mar 10 2004 04:42:27 on modular [Seed = 67806976] ------------------------------------- Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 to Set of ideals of Maximal Equation Order of Quadratic Field with defining polynomial $.1^2 + 14 over the Rational Field Total time: 3.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host GLORFINDEL.MIT.EDU. (18.243.1.196) Time: Wed Mar 10 04:42:47 2004 Input: ClassGroup(QuadraticField(-68)); Output: Magma V2.10-6 Wed Mar 10 2004 04:42:42 on modular [Seed = 303870215] ------------------------------------- Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 to Set of ideals of Maximal Equation Order of Quadratic Field with defining polynomial $.1^2 + 17 over the Rational Field Total time: 4.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host GLORFINDEL.MIT.EDU. (18.243.1.196) Time: Wed Mar 10 04:42:54 2004 Input: ClassGroup(QuadraticField(-84)); Output: Magma V2.10-6 Wed Mar 10 2004 04:42:51 on modular [Seed = 640189754] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Mapping from: Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 to Set of ideals of Maximal Equation Order of Quadratic Field with defining polynomial $.1^2 + 21 over the Rational Field Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host GLORFINDEL.MIT.EDU. (18.243.1.196) Time: Wed Mar 10 04:43:13 2004 Input: ClassGroup(QuadraticField(-21)); Output: Magma V2.10-6 Wed Mar 10 2004 04:43:10 on modular [Seed = 926520350] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Mapping from: Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 to Set of ideals of Maximal Equation Order of Quadratic Field with defining polynomial $.1^2 + 21 over the Rational Field Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host GLORFINDEL.MIT.EDU. (18.243.1.196) Time: Wed Mar 10 04:51:23 2004 Input: ClassGroup(QuadraticField(567)); Output: Magma V2.10-6 Wed Mar 10 2004 04:51:18 on modular [Seed = 1498938439] ------------------------------------- Abelian Group of order 1 Mapping from: Abelian Group of order 1 to Set of ideals of Maximal Equation Order of Quadratic Field with defining polynomial $.1^2 - 7 over the Rational Field Total time: 4.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host GLORFINDEL.MIT.EDU. (18.243.1.196) Time: Wed Mar 10 04:51:53 2004 Input: ClassGroup(QuadraticField(354)); Output: Magma V2.10-6 Wed Mar 10 2004 04:51:49 on modular [Seed = 1684717913] ------------------------------------- Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 to Set of ideals of Maximal Equation Order of Quadratic Field with defining polynomial $.1^2 - 354 over the Rational Field Total time: 4.329 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host GLORFINDEL.MIT.EDU. (18.243.1.196) Time: Wed Mar 10 04:52:16 2004 Input: ClassGroup(QuadraticField(973)); Output: Magma V2.10-6 Wed Mar 10 2004 04:52:11 on modular [Seed = 1937626672] ------------------------------------- Abelian Group of order 1 Mapping from: Abelian Group of order 1 to Set of ideals of Maximal Order of Quadratic Field with defining polynomial $.1^2 - 973 over the Rational Field Total time: 4.179 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host GLORFINDEL.MIT.EDU. (18.243.1.196) Time: Wed Mar 10 05:05:40 2004 Input: ClassGroup(QuadraticField(74)); Output: Magma V2.10-6 Wed Mar 10 2004 05:05:36 on modular [Seed = 809408586] ------------------------------------- Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 to Set of ideals of Maximal Equation Order of Quadratic Field with defining polynomial $.1^2 - 74 over the Rational Field Total time: 3.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host GLORFINDEL.MIT.EDU. (18.243.1.196) Time: Wed Mar 10 05:26:01 2004 Input: ClassGroup(QuadraticField(26)); Output: Magma V2.10-6 Wed Mar 10 2004 05:25:57 on modular [Seed = 437565218] ------------------------------------- Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 to Set of ideals of Maximal Equation Order of Quadratic Field with defining polynomial $.1^2 - 26 over the Rational Field Total time: 3.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host GLORFINDEL.MIT.EDU. (18.243.1.196) Time: Wed Mar 10 05:29:17 2004 Input: ClassGroup(QuadraticField(19)); Output: Magma V2.10-6 Wed Mar 10 2004 05:29:12 on modular [Seed = 2156801397] ------------------------------------- Abelian Group of order 1 Mapping from: Abelian Group of order 1 to Set of ideals of Maximal Equation Order of Quadratic Field with defining polynomial $.1^2 - 19 over the Rational Field Total time: 5.159 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cache2.nottingham.ac.uk. (128.243.220.22) Time: Wed Mar 10 09:19:23 2004 Input: log(x) Output: Magma V2.10-6 Wed Mar 10 2004 09:19:19 on modular [Seed = 1329605772] ------------------------------------- >> log(x) ^ User error: Identifier 'x' has not been declared or assigned Total time: 4.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cache2.nottingham.ac.uk. (128.243.220.22) Time: Wed Mar 10 09:19:48 2004 Input: log(x+1) Output: Magma V2.10-6 Wed Mar 10 2004 09:19:45 on modular [Seed = 2896414857] ------------------------------------- >> log(x+1) ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 09:59:05 2004 Input: [i : i in [1..366]|((i+3) mod 7) eq 0] Output: Magma V2.10-6 Wed Mar 10 2004 09:59:00 on modular [Seed = 1010973] ------------------------------------- [ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] Total time: 3.609 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 09:59:47 2004 Input: [i : i in [4..366 by 7]]; Output: Magma V2.10-6 Wed Mar 10 2004 09:59:42 on modular [Seed = 1835139098] ------------------------------------- [ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] Total time: 3.749 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:00:09 2004 Input: M22:=MatrixRing(F,2); F:=GF(4); Mt:={i:i in M22|Trace(i) eq 0}; Output: Magma V2.10-6 Wed Mar 10 2004 10:00:05 on modular [Seed = 1954224424] ------------------------------------- >> M22:=MatrixRing(F,2); ^ User error: Identifier 'F' has not been declared or assigned >> Mt:={i:i in M22|Trace(i) eq 0}; ^ User error: Identifier 'M22' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:01:44 2004 Input: F=GF(4); M22:=MatrixRing(F,2); F:=GF(4); Mt:={i:i in M22|Trace(i) eq 0}; Output: Magma V2.10-6 Wed Mar 10 2004 10:01:39 on modular [Seed = 3048921167] ------------------------------------- >> F=GF(4); ^ User error: Identifier 'F' has not been declared or assigned >> M22:=MatrixRing(F,2); ^ User error: Identifier 'F' has not been declared or assigned >> Mt:={i:i in M22|Trace(i) eq 0}; ^ User error: Identifier 'M22' has not been declared or assigned Total time: 3.829 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:02:07 2004 Input: M22:=MatrixRing(F,2); F:=GF(4); Mt:={i:i in M22|Trace(i) eq 0}; Output: Magma V2.10-6 Wed Mar 10 2004 10:02:03 on modular [Seed = 2257185604] ------------------------------------- >> M22:=MatrixRing(F,2); ^ User error: Identifier 'F' has not been declared or assigned >> Mt:={i:i in M22|Trace(i) eq 0}; ^ User error: Identifier 'M22' has not been declared or assigned Total time: 3.119 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:06:06 2004 Input: F=GF(4); M22:=MatrixRing(F,2); F:=GF(4); Mt:={i:i in M22|Trace(i) eq 0}; Output: Magma V2.10-6 Wed Mar 10 2004 10:06:01 on modular [Seed = 1785005209] ------------------------------------- >> F=GF(4); ^ User error: Identifier 'F' has not been declared or assigned >> M22:=MatrixRing(F,2); ^ User error: Identifier 'F' has not been declared or assigned >> Mt:={i:i in M22|Trace(i) eq 0};; ^ User error: Identifier 'M22' has not been declared or assigned Total time: 3.659 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:06:27 2004 Input: F:=GF(4); M22:=MatrixRing(F,2); F:=GF(4); Mt:={i:i in M22|Trace(i) eq 0}; Output: Magma V2.10-6 Wed Mar 10 2004 10:06:23 on modular [Seed = 2121339067] ------------------------------------- Total time: 2.889 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:06:54 2004 Input: F:=GF(4); M22:=MatrixRing(F,2); F:=GF(4); Mt:={i:i in M22|Trace(i) eq 0}; print(Mt); Output: Magma V2.10-6 Wed Mar 10 2004 10:06:49 on modular [Seed = 1482110843] ------------------------------------- { [ 0 0] [ 0 0], [ 0 0] [alfa^2 0], [ 0 0] [ alfa 0], [ 0 0] [ 1 0], [alfa^2 0] [ 0 alfa^2], [alfa^2 0] [alfa^2 alfa^2], [alfa^2 0] [ alfa alfa^2], [alfa^2 0] [ 1 alfa^2], [ 1 0] [ 0 1], [ 1 0] [alfa^2 1], [ 1 0] [ alfa 1], [ 1 0] [ 1 1], [ alfa 0] [ 0 alfa], [ alfa 0] [alfa^2 alfa], [ alfa 0] [ alfa alfa], [ alfa 0] [ 1 alfa], [ 0 alfa^2] [ 0 0], [ 0 alfa^2] [alfa^2 0], [ 0 alfa^2] [ alfa 0], [ 0 alfa^2] [ 1 0], [alfa^2 alfa^2] [ 0 alfa^2], [alfa^2 alfa^2] [alfa^2 alfa^2], [alfa^2 alfa^2] [ alfa alfa^2], [alfa^2 alfa^2] [ 1 alfa^2], [ 1 alfa^2] [ 0 1], [ 1 alfa^2] [alfa^2 1], [ 1 alfa^2] [ alfa 1], [ 1 alfa^2] [ 1 1], [ alfa alfa^2] [ 0 alfa], [ alfa alfa^2] [alfa^2 alfa], [ alfa alfa^2] [ alfa alfa], [ alfa alfa^2] [ 1 alfa], [ 0 alfa] [ 0 0], [ 0 alfa] [alfa^2 0], [ 0 alfa] [ alfa 0], [ 0 alfa] [ 1 0], [alfa^2 alfa] [ 0 alfa^2], [alfa^2 alfa] [alfa^2 alfa^2], [alfa^2 alfa] [ alfa alfa^2], [alfa^2 alfa] [ 1 alfa^2], [ 1 alfa] [ 0 1], [ 1 alfa] [alfa^2 1], [ 1 alfa] [ alfa 1], [ 1 alfa] [ 1 1], [ alfa alfa] [ 0 alfa], [ alfa alfa] [alfa^2 alfa], [ alfa alfa] [ alfa alfa], [ alfa alfa] [ 1 alfa], [ 0 1] [ 0 0], [ 0 1] [alfa^2 0], [ 0 1] [ alfa 0], [ 0 1] [ 1 0], [alfa^2 1] [ 0 alfa^2], [alfa^2 1] [alfa^2 alfa^2], [alfa^2 1] [ alfa alfa^2], [alfa^2 1] [ 1 alfa^2], [ 1 1] [ 0 1], [ 1 1] [alfa^2 1], [ 1 1] [ alfa 1], [ 1 1] [ 1 1], [ alfa 1] [ 0 alfa], [ alfa 1] [alfa^2 alfa], [ alfa 1] [ alfa alfa], [ alfa 1] [ 1 alfa] } Total time: 4.099 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:07:25 2004 Input: F:=GF(4); M22:=MatrixRing(F,2); F:=GF(4); Mt:={i:i in M22|Trace(i) eq 0}; print(Mt); print(#(Mt)); Output: Magma V2.10-6 Wed Mar 10 2004 10:07:20 on modular [Seed = 3149190329] ------------------------------------- { [ 0 0] [ 0 0], [ 0 0] [alfa^2 0], [ 0 0] [ alfa 0], [ 0 0] [ 1 0], [alfa^2 0] [ 0 alfa^2], [alfa^2 0] [alfa^2 alfa^2], [alfa^2 0] [ alfa alfa^2], [alfa^2 0] [ 1 alfa^2], [ 1 0] [ 0 1], [ 1 0] [alfa^2 1], [ 1 0] [ alfa 1], [ 1 0] [ 1 1], [ alfa 0] [ 0 alfa], [ alfa 0] [alfa^2 alfa], [ alfa 0] [ alfa alfa], [ alfa 0] [ 1 alfa], [ 0 alfa^2] [ 0 0], [ 0 alfa^2] [alfa^2 0], [ 0 alfa^2] [ alfa 0], [ 0 alfa^2] [ 1 0], [alfa^2 alfa^2] [ 0 alfa^2], [alfa^2 alfa^2] [alfa^2 alfa^2], [alfa^2 alfa^2] [ alfa alfa^2], [alfa^2 alfa^2] [ 1 alfa^2], [ 1 alfa^2] [ 0 1], [ 1 alfa^2] [alfa^2 1], [ 1 alfa^2] [ alfa 1], [ 1 alfa^2] [ 1 1], [ alfa alfa^2] [ 0 alfa], [ alfa alfa^2] [alfa^2 alfa], [ alfa alfa^2] [ alfa alfa], [ alfa alfa^2] [ 1 alfa], [ 0 alfa] [ 0 0], [ 0 alfa] [alfa^2 0], [ 0 alfa] [ alfa 0], [ 0 alfa] [ 1 0], [alfa^2 alfa] [ 0 alfa^2], [alfa^2 alfa] [alfa^2 alfa^2], [alfa^2 alfa] [ alfa alfa^2], [alfa^2 alfa] [ 1 alfa^2], [ 1 alfa] [ 0 1], [ 1 alfa] [alfa^2 1], [ 1 alfa] [ alfa 1], [ 1 alfa] [ 1 1], [ alfa alfa] [ 0 alfa], [ alfa alfa] [alfa^2 alfa], [ alfa alfa] [ alfa alfa], [ alfa alfa] [ 1 alfa], [ 0 1] [ 0 0], [ 0 1] [alfa^2 0], [ 0 1] [ alfa 0], [ 0 1] [ 1 0], [alfa^2 1] [ 0 alfa^2], [alfa^2 1] [alfa^2 alfa^2], [alfa^2 1] [ alfa alfa^2], [alfa^2 1] [ 1 alfa^2], [ 1 1] [ 0 1], [ 1 1] [alfa^2 1], [ 1 1] [ alfa 1], [ 1 1] [ 1 1], [ alfa 1] [ 0 alfa], [ alfa 1] [alfa^2 alfa], [ alfa 1] [ alfa alfa], [ alfa 1] [ 1 alfa] } 64 Total time: 4.119 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:08:06 2004 Input: Mf:={i:i in M22| i[1] eq i[2]}; Output: Magma V2.10-6 Wed Mar 10 2004 10:08:02 on modular [Seed = 2207051003] ------------------------------------- >> Mf:={i:i in M22| i[1] eq i[2]}; ^ User error: Identifier 'M22' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:09:37 2004 Input: F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; print(Mt); print(#(Mt)); Output: Magma V2.10-6 Wed Mar 10 2004 10:09:32 on modular [Seed = 4043284342] ------------------------------------- { [ 0 0] [ 0 0], [ 0 0] [alpha^2 0], [ 0 0] [ alpha 0], [ 0 0] [ 1 0], [alpha^2 0] [ 0 alpha^2], [alpha^2 0] [alpha^2 alpha^2], [alpha^2 0] [ alpha alpha^2], [alpha^2 0] [ 1 alpha^2], [ 1 0] [ 0 1], [ 1 0] [alpha^2 1], [ 1 0] [ alpha 1], [ 1 0] [ 1 1], [ alpha 0] [ 0 alpha], [ alpha 0] [alpha^2 alpha], [ alpha 0] [ alpha alpha], [ alpha 0] [ 1 alpha], [ 0 alpha^2] [ 0 0], [ 0 alpha^2] [alpha^2 0], [ 0 alpha^2] [ alpha 0], [ 0 alpha^2] [ 1 0], [alpha^2 alpha^2] [ 0 alpha^2], [alpha^2 alpha^2] [alpha^2 alpha^2], [alpha^2 alpha^2] [ alpha alpha^2], [alpha^2 alpha^2] [ 1 alpha^2], [ 1 alpha^2] [ 0 1], [ 1 alpha^2] [alpha^2 1], [ 1 alpha^2] [ alpha 1], [ 1 alpha^2] [ 1 1], [ alpha alpha^2] [ 0 alpha], [ alpha alpha^2] [alpha^2 alpha], [ alpha alpha^2] [ alpha alpha], [ alpha alpha^2] [ 1 alpha], [ 0 alpha] [ 0 0], [ 0 alpha] [alpha^2 0], [ 0 alpha] [ alpha 0], [ 0 alpha] [ 1 0], [alpha^2 alpha] [ 0 alpha^2], [alpha^2 alpha] [alpha^2 alpha^2], [alpha^2 alpha] [ alpha alpha^2], [alpha^2 alpha] [ 1 alpha^2], [ 1 alpha] [ 0 1], [ 1 alpha] [alpha^2 1], [ 1 alpha] [ alpha 1], [ 1 alpha] [ 1 1], [ alpha alpha] [ 0 alpha], [ alpha alpha] [alpha^2 alpha], [ alpha alpha] [ alpha alpha], [ alpha alpha] [ 1 alpha], [ 0 1] [ 0 0], [ 0 1] [alpha^2 0], [ 0 1] [ alpha 0], [ 0 1] [ 1 0], [alpha^2 1] [ 0 alpha^2], [alpha^2 1] [alpha^2 alpha^2], [alpha^2 1] [ alpha alpha^2], [alpha^2 1] [ 1 alpha^2], [ 1 1] [ 0 1], [ 1 1] [alpha^2 1], [ 1 1] [ alpha 1], [ 1 1] [ 1 1], [ alpha 1] [ 0 alpha], [ alpha 1] [alpha^2 alpha], [ alpha 1] [ alpha alpha], [ alpha 1] [ 1 alpha] } 64 Total time: 4.129 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:09:54 2004 Input: F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; print(Mt); print(#(Mt)); Output: Magma V2.10-6 Wed Mar 10 2004 10:09:49 on modular [Seed = 3284970580] ------------------------------------- { [ 0 0] [ 0 0], [ 0 0] [pringao^2 0], [ 0 0] [ pringao 0], [ 0 0] [ 1 0], [pringao^2 0] [ 0 pringao^2], [pringao^2 0] [pringao^2 pringao^2], [pringao^2 0] [ pringao pringao^2], [pringao^2 0] [ 1 pringao^2], [ 1 0] [ 0 1], [ 1 0] [pringao^2 1], [ 1 0] [ pringao 1], [ 1 0] [ 1 1], [ pringao 0] [ 0 pringao], [ pringao 0] [pringao^2 pringao], [ pringao 0] [ pringao pringao], [ pringao 0] [ 1 pringao], [ 0 pringao^2] [ 0 0], [ 0 pringao^2] [pringao^2 0], [ 0 pringao^2] [ pringao 0], [ 0 pringao^2] [ 1 0], [pringao^2 pringao^2] [ 0 pringao^2], [pringao^2 pringao^2] [pringao^2 pringao^2], [pringao^2 pringao^2] [ pringao pringao^2], [pringao^2 pringao^2] [ 1 pringao^2], [ 1 pringao^2] [ 0 1], [ 1 pringao^2] [pringao^2 1], [ 1 pringao^2] [ pringao 1], [ 1 pringao^2] [ 1 1], [ pringao pringao^2] [ 0 pringao], [ pringao pringao^2] [pringao^2 pringao], [ pringao pringao^2] [ pringao pringao], [ pringao pringao^2] [ 1 pringao], [ 0 pringao] [ 0 0], [ 0 pringao] [pringao^2 0], [ 0 pringao] [ pringao 0], [ 0 pringao] [ 1 0], [pringao^2 pringao] [ 0 pringao^2], [pringao^2 pringao] [pringao^2 pringao^2], [pringao^2 pringao] [ pringao pringao^2], [pringao^2 pringao] [ 1 pringao^2], [ 1 pringao] [ 0 1], [ 1 pringao] [pringao^2 1], [ 1 pringao] [ pringao 1], [ 1 pringao] [ 1 1], [ pringao pringao] [ 0 pringao], [ pringao pringao] [pringao^2 pringao], [ pringao pringao] [ pringao pringao], [ pringao pringao] [ 1 pringao], [ 0 1] [ 0 0], [ 0 1] [pringao^2 0], [ 0 1] [ pringao 0], [ 0 1] [ 1 0], [pringao^2 1] [ 0 pringao^2], [pringao^2 1] [pringao^2 pringao^2], [pringao^2 1] [ pringao pringao^2], [pringao^2 1] [ 1 pringao^2], [ 1 1] [ 0 1], [ 1 1] [pringao^2 1], [ 1 1] [ pringao 1], [ 1 1] [ 1 1], [ pringao 1] [ 0 pringao], [ pringao 1] [pringao^2 pringao], [ pringao 1] [ pringao pringao], [ pringao 1] [ 1 pringao] } 64 Total time: 4.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee130.uab.es. (158.109.66.130) Time: Wed Mar 10 10:10:24 2004 Input: F:=GF(4); M22:=MatrixRing(a,2); Mt:={i:i in M22|Trace(i) eq 0}; Output: Magma V2.10-6 Wed Mar 10 2004 10:10:19 on modular [Seed = 573394386] ------------------------------------- >> M22:=MatrixRing(a,2); ^ Runtime error in 'MatrixRing': Bad argument types Argument types given: FldFinElt, RngIntElt >> Mt:={i:i in M22|Trace(i) eq 0}; ^ User error: Identifier 'M22' has not been declared or assigned Total time: 3.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:10:32 2004 Input: F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Output: Magma V2.10-6 Wed Mar 10 2004 10:10:28 on modular [Seed = 1043419633] ------------------------------------- Total time: 3.039 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:10:55 2004 Input: F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; print(Mf); Output: Magma V2.10-6 Wed Mar 10 2004 10:10:50 on modular [Seed = 251683038] ------------------------------------- { [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ a 0] [ a 0], [ 0 a^2] [ 0 a^2], [ a a^2] [ a a^2], [ 0 a] [ 0 a], [ a a] [ a a], [ 0 1] [ 0 1], [ a 1] [ a 1], [a^2 0] [a^2 0], [ 1 0] [ 1 0], [a^2 a^2] [a^2 a^2], [ 1 a^2] [ 1 a^2], [a^2 a] [a^2 a], [ 1 a] [ 1 a], [a^2 1] [a^2 1] } Total time: 3.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:11:28 2004 Input: F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; print(Mf); print(#(Mf)); Output: Magma V2.10-6 Wed Mar 10 2004 10:11:24 on modular [Seed = 303915557] ------------------------------------- { [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ a 0] [ a 0], [ 0 a^2] [ 0 a^2], [ a a^2] [ a a^2], [ 0 a] [ 0 a], [ a a] [ a a], [ 0 1] [ 0 1], [ a 1] [ a 1], [a^2 0] [a^2 0], [ 1 0] [ 1 0], [a^2 a^2] [a^2 a^2], [ 1 a^2] [ 1 a^2], [a^2 a] [a^2 a], [ 1 a] [ 1 a], [a^2 1] [a^2 1] } 16 Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:15:53 2004 Input: F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; print(Mt); print(#(Mt)); /*(ii)*/ Mf:={i:i in M22| i[1] eq i[2]}; /*(iii)*/ Mtf:={i:i in M22| (Trace(i) eq 0) and (i[1] eq i[2] )}; /*(iv)*/ Mtf:={Random(M22):i in [1..100000]}; for i in Mtfv do if Mt subset i then a+1; print(a); Output: Magma V2.10-6 Wed Mar 10 2004 10:15:48 on modular [Seed = 2610227860] ------------------------------------- { [ 0 0] [ 0 0], [ 0 0] [a^2 0], [ 0 0] [ a 0], [ 0 0] [ 1 0], [a^2 0] [ 0 a^2], [a^2 0] [a^2 a^2], [a^2 0] [ a a^2], [a^2 0] [ 1 a^2], [ 1 0] [ 0 1], [ 1 0] [a^2 1], [ 1 0] [ a 1], [ 1 0] [ 1 1], [ a 0] [ 0 a], [ a 0] [a^2 a], [ a 0] [ a a], [ a 0] [ 1 a], [ 0 a^2] [ 0 0], [ 0 a^2] [a^2 0], [ 0 a^2] [ a 0], [ 0 a^2] [ 1 0], [a^2 a^2] [ 0 a^2], [a^2 a^2] [a^2 a^2], [a^2 a^2] [ a a^2], [a^2 a^2] [ 1 a^2], [ 1 a^2] [ 0 1], [ 1 a^2] [a^2 1], [ 1 a^2] [ a 1], [ 1 a^2] [ 1 1], [ a a^2] [ 0 a], [ a a^2] [a^2 a], [ a a^2] [ a a], [ a a^2] [ 1 a], [ 0 a] [ 0 0], [ 0 a] [a^2 0], [ 0 a] [ a 0], [ 0 a] [ 1 0], [a^2 a] [ 0 a^2], [a^2 a] [a^2 a^2], [a^2 a] [ a a^2], [a^2 a] [ 1 a^2], [ 1 a] [ 0 1], [ 1 a] [a^2 1], [ 1 a] [ a 1], [ 1 a] [ 1 1], [ a a] [ 0 a], [ a a] [a^2 a], [ a a] [ a a], [ a a] [ 1 a], [ 0 1] [ 0 0], [ 0 1] [a^2 0], [ 0 1] [ a 0], [ 0 1] [ 1 0], [a^2 1] [ 0 a^2], [a^2 1] [a^2 a^2], [a^2 1] [ a a^2], [a^2 1] [ 1 a^2], [ 1 1] [ 0 1], [ 1 1] [a^2 1], [ 1 1] [ a 1], [ 1 1] [ 1 1], [ a 1] [ 0 a], [ a 1] [a^2 a], [ a 1] [ a a], [ a 1] [ 1 a] } 64 User error: syntax error at end of input Total time: 4.439 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:16:44 2004 Input: F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={i:i in M22| (Trace(i) eq 0) and (i[1] eq i[2] )}; Mtf:={Random(M22):i in [1..100000]}; for i in Mtfv do if Mt subset i then a+1; print(a); Output: Magma V2.10-6 Wed Mar 10 2004 10:16:39 on modular [Seed = 3773796764] ------------------------------------- User error: syntax error at end of input Total time: 3.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:17:10 2004 Input: F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={i:i in M22| (Trace(i) eq 0) and (i[1] eq i[2] )}; Mtf:={Random(M22):i in [1..100000]}; for i in Mtfv do if Mt subset i then a+1; end for; print(a); Output: Magma V2.10-6 Wed Mar 10 2004 10:17:04 on modular [Seed = 3418667664] ------------------------------------- >> for i in Mtfv do if Mt subset i then a+1; end for; ^ User error: bad syntax a Total time: 4.469 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:17:26 2004 Input: F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={i:i in M22| (Trace(i) eq 0) and (i[1] eq i[2] )}; Mtf:={Random(M22):i in [1..100000]}; for i in Mtfv do if Mt subset i then a+1 end for; print(a); Output: Magma V2.10-6 Wed Mar 10 2004 10:17:20 on modular [Seed = 3688147568] ------------------------------------- >> for i in Mtfv do if Mt subset i then a+1 end for; ^ User error: bad syntax a Total time: 4.439 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:17:42 2004 Input: F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={i:i in M22| (Trace(i) eq 0) and (i[1] eq i[2] )}; Mtf:={Random(M22):i in [1..100000]}; for i in Mtfv do if Mt subset i then a+1 end if; end for; print(a); Output: Magma V2.10-6 Wed Mar 10 2004 10:17:37 on modular [Seed = 3571164526] ------------------------------------- >> for i in Mtfv do if Mt subset i then a+1 end if; end for; ^ User error: bad syntax a Total time: 3.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:18:03 2004 Input: F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={i:i in M22| (Trace(i) eq 0) and (i[1] eq i[2] )}; Mtf:={Random(M22):i in [1..100000]}; for i in Mtfv do if Mt subset i then a+1; end if; end for; print(a); Output: Magma V2.10-6 Wed Mar 10 2004 10:17:59 on modular [Seed = 1026706614] ------------------------------------- >> for i in Mtfv do if Mt subset i then a+1; end if; end for; ^ User error: Identifier 'Mtfv' has not been declared or assigned a Total time: 3.389 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:19:32 2004 Input: F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={Random(M22):i in [1..10]}; Output: Magma V2.10-6 Wed Mar 10 2004 10:19:27 on modular [Seed = 1851858877] ------------------------------------- Total time: 3.889 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:19:52 2004 Input: F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={Random(M22):i in [1..10]}; print(Mtf); Output: Magma V2.10-6 Wed Mar 10 2004 10:19:48 on modular [Seed = 2021067328] ------------------------------------- { [ a 1] [ 1 a^2], [ 0 0] [ 0 a^2], [ 1 0] [ a 1], [ a a] [ a a], [ 0 a] [ a a], [ 0 0] [ 0 a], [ 0 a^2] [ 0 1], [a^2 a] [ 0 a], [ 1 1] [ 0 1], [ a a] [ 0 a^2] } Total time: 3.219 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:26:17 2004 Input: F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={Random(M22):i in [1..10]}; mtcont:=0; mfcont:=0; mtfcont:=0; for i in Mtf do if i subset Mt then mtcont+1 end if if i subset Mf then mfcont+1 end if if i subset Mtf then mtfcont+1 end if end for; print)() print(Mtf); Output: Magma V2.10-6 Wed Mar 10 2004 10:26:12 on modular [Seed = 723802258] ------------------------------------- >> if i subset Mt then mtcont+1 end if ^ User error: bad syntax >> if i subset Mf then mfcont+1 end if ^ User error: bad syntax >> if i subset Mtf then mtfcont+1 end if ^ User error: bad syntax >> end for; ^ User error: bad syntax >> print)() ^ User error: bad syntax { [ 1 a] [a^2 0], [a^2 a^2] [ a 1], [ a 0] [a^2 a^2], [ a a^2] [ a a], [ 1 1] [ 1 a^2], [ a a^2] [ 0 1], [ 0 1] [ 0 0], [ a 0] [ a 1], [ 0 a] [ a 0], [ 1 1] [ a 1] } Total time: 3.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:26:32 2004 Input: F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={Random(M22):i in [1..10]}; mtcont:=0; mfcont:=0; mtfcont:=0; for i in Mtf do if i subset Mt then mtcont+1 end if; if i subset Mf then mfcont+1 end if if i subset Mtf then mtfcont+1 end if end for; print)() print(Mtf); Output: Magma V2.10-6 Wed Mar 10 2004 10:26:28 on modular [Seed = 1060129974] ------------------------------------- >> if i subset Mt then mtcont+1 end if; ^ User error: bad syntax >> if i subset Mf then mfcont+1 end if ^ User error: bad syntax >> if i subset Mtf then mtfcont+1 end if ^ User error: bad syntax >> end for; ^ User error: bad syntax >> print)() ^ User error: bad syntax { [ 0 0] [ 0 0], [ a a^2] [a^2 a], [ 0 a^2] [ 1 1], [a^2 a^2] [ 0 1], [ 0 0] [ 0 a^2], [ 1 a] [ a a], [ 0 a^2] [ 1 a^2], [ a a^2] [ a 1], [ a 0] [ a 0], [a^2 a] [a^2 a] } Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:26:43 2004 Input: F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={Random(M22):i in [1..10]}; mtcont:=0; mfcont:=0; mtfcont:=0; for i in Mtf do if i subset Mt then mtcont+1; end if; if i subset Mf then mfcont+1 end if if i subset Mtf then mtfcont+1 end if end for; print)() print(Mtf); Output: Magma V2.10-6 Wed Mar 10 2004 10:26:39 on modular [Seed = 859586737] ------------------------------------- >> if i subset Mf then mfcont+1 end if ^ User error: bad syntax >> if i subset Mtf then mtfcont+1 end if ^ User error: bad syntax >> end for; ^ User error: bad syntax >> print)() ^ User error: bad syntax { [a^2 a] [ 0 1], [a^2 a^2] [ 1 a], [ a a^2] [a^2 a^2], [ 1 a] [ a 0], [ 0 a^2] [ 1 a^2], [ a a] [a^2 1], [ 1 a^2] [ 0 a^2], [a^2 a] [ a a^2], [ a 0] [ 1 a], [ 1 a^2] [ 0 a] } Total time: 3.059 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:26:56 2004 Input: F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={Random(M22):i in [1..10]}; mtcont:=0; mfcont:=0; mtfcont:=0; for i in Mtf do if i subset Mt then mtcont+1; end if; if i subset Mf then mfcont+1; end if; if i subset Mtf then mtfcont+1 end if end for; print)() print(Mtf); Output: Magma V2.10-6 Wed Mar 10 2004 10:26:51 on modular [Seed = 1012630] ------------------------------------- >> if i subset Mtf then mtfcont+1 end if ^ User error: bad syntax >> end for; ^ User error: bad syntax >> print)() ^ User error: bad syntax { [ a 1] [ 1 a^2], [ a 1] [ 0 a], [ 1 0] [ 1 a], [a^2 a] [ 1 0], [ 0 1] [a^2 1], [ a a^2] [ 1 a], [ a 1] [ 1 1], [ a 1] [ 0 0], [ 0 a^2] [ a 1], [ a 1] [ 1 0] } Total time: 3.599 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:27:09 2004 Input: F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={Random(M22):i in [1..10]}; mtcont:=0; mfcont:=0; mtfcont:=0; for i in Mtf do if i subset Mt then mtcont+1; end if; if i subset Mf then mfcont+1; end if; if i subset Mtf then mtfcont+1; end if; end for; print)() print(Mtf); Output: Magma V2.10-6 Wed Mar 10 2004 10:27:04 on modular [Seed = 287204084] ------------------------------------- >> if i subset Mt then mtcont+1; end if; ^ Runtime error in 'subset': Bad argument types Argument types given: AlgMatElt, SetEnum[AlgMatElt] >> print)() ^ User error: bad syntax { [ 1 0] [a^2 a], [a^2 a] [ 1 0], [ a 0] [a^2 a], [ a 1] [ 1 1], [ 1 a^2] [ 1 0], [ 1 a^2] [a^2 a^2], [a^2 a^2] [ a a^2], [ 1 a] [a^2 a], [ a 0] [ 1 1], [a^2 a^2] [ 0 a] } Total time: 3.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:27:46 2004 Input: F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={Random(M22):i in [1..10]}; mtcont:=0; mfcont:=0; mtfcont:=0; for i in Mtf do if i subset Mt then mtcont+1; end if; if i subset Mf then mfcont+1; end if; if i subset Mtf then mtfcont+1; end if; end for; print(mtcont); print(mfcont); print(mtfcont); Output: Magma V2.10-6 Wed Mar 10 2004 10:27:42 on modular [Seed = 2021067707] ------------------------------------- >> if i subset Mt then mtcont+1; end if; ^ Runtime error in 'subset': Bad argument types Argument types given: AlgMatElt, SetEnum[AlgMatElt] 0 0 0 Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:28:16 2004 Input: F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={Random(M22):i in [1..10]}; mtcont:=0; mfcont:=0; mtfcont:=0; for i in Mtf do if Mt subset i then mtcont+1; end if; if i subset Mf then mfcont+1; end if; if i subset Mtf then mtfcont+1; end if; end for; print(mtcont); print(mfcont); print(mtfcont); Output: Magma V2.10-6 Wed Mar 10 2004 10:28:12 on modular [Seed = 1599089534] ------------------------------------- >> if Mt subset i then mtcont+1; end if; ^ Runtime error in 'subset': Bad argument types Argument types given: SetEnum[AlgMatElt], AlgMatElt 0 0 0 Total time: 3.519 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:28:27 2004 Input: F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={Random(M22):i in [1..10]}; mtcont:=0; mfcont:=0; mtfcont:=0; for i in Mtf do if Mt subset i then mtcont+1; end if; if i subset Mf then mfcont+1; end if; if i subset Mtf then mtfcont+1; end if; end for; print(mtcont); print(mfcont); print(mtfcont); Output: Magma V2.10-6 Wed Mar 10 2004 10:28:23 on modular [Seed = 2829573266] ------------------------------------- >> if Mt subset i then mtcont+1; end if; ^ Runtime error in 'subset': Bad argument types Argument types given: SetEnum[AlgMatElt], AlgMatElt 0 0 0 Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:31:57 2004 Input: F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={Random(M22):i in [1..10]}; mtcont:=0; mfcont:=0; mtfcont:=0; for i in Mtf do if Mt in i then mtcont+1; end if; if i subset Mf then mfcont+1; end if; if i subset Mtf then mtfcont+1; end if; end for; print(mtcont); print(mfcont); print(mtfcont); Output: Magma V2.10-6 Wed Mar 10 2004 10:31:53 on modular [Seed = 3268261382] ------------------------------------- >> if Mt in i then mtcont+1; end if; ^ Runtime error in 'in': Bad argument types Argument types given: SetEnum[AlgMatElt], AlgMatElt 0 0 0 Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:35:12 2004 Input: F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={i:i in M22| (Trace(i) eq 0) and (i[1] eq i[2] )}; Mran:={Random(M22):i in [1..100]}; mtcont:=0; mfcont:=0; mtfcont:=0; for i in Mran do if Mran[i] subset Mt then mtcont+1; end if; if i subset Mf then mfcont+1; end if; if i subset Mtf then mtfcont+1; end if; end for; print(mtcont); print(mfcont); print(mtfcont); Output: Magma V2.10-6 Wed Mar 10 2004 10:35:08 on modular [Seed = 3082338869] ------------------------------------- >> if Mran[i] subset Mt then mtcont+1; end if; ^ Runtime error in '[]': Bad argument types 0 0 0 Total time: 3.069 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:35:36 2004 Input: F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={i:i in M22| (Trace(i) eq 0) and (i[1] eq i[2] )}; Mran:={Random(M22):i in [1..100]}; mtcont:=0; mfcont:=0; mtfcont:=0; for i in Mran do if Mran{i} subset Mt then mtcont+1; end if; if i subset Mf then mfcont+1; end if; if i subset Mtf then mtfcont+1; end if; end for; print(mtcont); print(mfcont); print(mtfcont); Output: Magma V2.10-6 Wed Mar 10 2004 10:35:31 on modular [Seed = 2240475240] ------------------------------------- >> if Mran{i} subset Mt then mtcont+1; end if; ^ User error: bad syntax >> if i subset Mf then mfcont+1; end if; ^ User error: Identifier 'i' has not been declared or assigned >> if i subset Mtf then mtfcont+1; end if; ^ User error: Identifier 'i' has not been declared or assigned >> end for; ^ User error: bad syntax 0 0 0 Total time: 3.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host fw.su.lt. (193.219.168.126) Time: Wed Mar 10 10:35:41 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Wed Mar 10 2004 10:35:38 on modular [Seed = 2576804989] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:36:49 2004 Input: F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={i:i in M22| (Trace(i) eq 0) and (i[1] eq i[2] )}; Mran:={Random(M22):i in [1..100]}; mtcont:=0; mfcont:=0; mtfcont:=0; for i in #(Mran) do if Mran[i] subset Mt then mtcont+1; end if; if i subset Mf then mfcont+1; end if; if i subset Mtf then mtfcont+1; end if; end for; print(mtcont); print(mfcont); print(mtfcont); Output: Magma V2.10-6 Wed Mar 10 2004 10:36:44 on modular [Seed = 3554452977] ------------------------------------- >> for i in #(Mran) do ^ Runtime error in for: Iteration is not possible over this object 0 0 0 Total time: 3.869 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:37:09 2004 Input: F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={i:i in M22| (Trace(i) eq 0) and (i[1] eq i[2] )}; Mran:={Random(M22):i in [1..100]}; mtcont:=0; mfcont:=0; mtfcont:=0; for i in #Mran do if Mran[i] subset Mt then mtcont+1; end if; if i subset Mf then mfcont+1; end if; if i subset Mtf then mtfcont+1; end if; end for; print(mtcont); print(mfcont); print(mtfcont); Output: Magma V2.10-6 Wed Mar 10 2004 10:37:05 on modular [Seed = 640241704] ------------------------------------- >> for i in #Mran do ^ Runtime error in for: Iteration is not possible over this object 0 0 0 Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:37:42 2004 Input: F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={i:i in M22| (Trace(i) eq 0) and (i[1] eq i[2] )}; Mran:={Random(M22):i in [1..100]}; mtcont:=0; mfcont:=0; mtfcont:=0; for i in Mran do if i subset Mt then mtcont+1; end if; if i subset Mf then mfcont+1; end if; if i subset Mtf then mtfcont+1; end if; end for; print(mtcont); print(mfcont); print(mtfcont); Output: Magma V2.10-6 Wed Mar 10 2004 10:37:37 on modular [Seed = 1801723141] ------------------------------------- >> if i subset Mt then mtcont+1; end if; ^ Runtime error in 'subset': Bad argument types Argument types given: AlgMatElt, SetEnum[AlgMatElt] 0 0 0 Total time: 4.069 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:39:34 2004 Input: F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={i:i in M22| (Trace(i) eq 0) and (i[1] eq i[2] )}; Mran:={Random(M22):i in [1..100]}; mtcont:=0; mfcont:=0; mtfcont:=0; for i in Mran do if Mran[i] subset Mt then mtcont+1; end if; if i subset Mf then mfcont+1; end if; if i subset Mtf then mtfcont+1; end if; end for; print(mtcont); print(mfcont); print(mtfcont); Output: Magma V2.10-6 Wed Mar 10 2004 10:39:30 on modular [Seed = 1448681675] ------------------------------------- >> if Mran[i] subset Mt then mtcont+1; end if; ^ Runtime error in '[]': Bad argument types 0 0 0 Total time: 3.129 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:40:02 2004 Input: F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={i:i in M22| (Trace(i) eq 0) and (i[1] eq i[2] )}; Mran:={Random(M22):i in [1..100]}; print(Mran) mtcont:=0; mfcont:=0; mtfcont:=0; for i in Mran do if Mran[i] subset Mt then mtcont+1; end if; if i subset Mf then mfcont+1; end if; if i subset Mtf then mtfcont+1; end if; end for; print(mtcont); print(mfcont); print(mtfcont); Output: Magma V2.10-6 Wed Mar 10 2004 10:39:57 on modular [Seed = 2695878210] ------------------------------------- >> mtcont:=0; ^ User error: bad syntax >> if Mran[i] subset Mt then mtcont+1; end if; ^ User error: Identifier 'mtcont' has not been declared or assigned >> print(mtcont); ^ User error: Identifier 'mtcont' has not been declared or assigned 0 0 Total time: 3.049 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:40:16 2004 Input: F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={i:i in M22| (Trace(i) eq 0) and (i[1] eq i[2] )}; Mran:={Random(M22):i in [1..100]}; print(Mran); mtcont:=0; mfcont:=0; mtfcont:=0; for i in Mran do if Mran[i] subset Mt then mtcont+1; end if; if i subset Mf then mfcont+1; end if; if i subset Mtf then mtfcont+1; end if; end for; print(mtcont); print(mfcont); print(mtfcont); Output: Magma V2.10-6 Wed Mar 10 2004 10:40:11 on modular [Seed = 2324036734] ------------------------------------- { [a^2 0] [ 0 a], [ 0 0] [ a a^2], [a^2 0] [ 1 1], [a^2 0] [ 0 0], [ 0 0] [a^2 a], [ 0 0] [ 1 a], [a^2 0] [ 1 0], [a^2 0] [ 0 a^2], [ 0 0] [ 1 1], [ 1 0] [ 0 a], [ 1 0] [a^2 a], [ a 0] [ a 0], [ 1 0] [ a a], [ a 0] [a^2 a^2], [ a 0] [ a a^2], [ 1 0] [ a 1], [ a 0] [ 1 a^2], [ a 0] [a^2 a], [ 1 0] [a^2 a^2], [a^2 a^2] [ 0 a], [ 0 a^2] [a^2 0], [a^2 a^2] [ a 1], [a^2 a^2] [ 0 0], [ 0 a^2] [ a a], [ 0 a^2] [a^2 1], [a^2 a^2] [ a a^2], [ 1 a^2] [ 0 a], [ a a^2] [ 0 0], [ 1 a^2] [ 1 a], [ 1 a^2] [ 1 1], [ a a^2] [ 0 a], [ 1 a^2] [ 1 0], [ a a^2] [ 0 1], [ 1 a^2] [ 0 a^2], [ a a^2] [a^2 1], [ a a^2] [ a 1], [ 1 a^2] [ a a^2], [a^2 a] [ 0 a], [ 0 a] [a^2 0], [a^2 a] [ 1 a], [ 0 a] [ 0 a^2], [ 0 a] [a^2 a^2], [a^2 a] [a^2 1], [a^2 a] [ a 1], [ 0 a] [a^2 a], [ 0 a] [ 1 a], [ 1 a] [ 0 a], [ 1 a] [ 1 a], [ a a] [ 0 a^2], [ 1 a] [a^2 1], [ a a] [ 0 a], [ 1 a] [ a 0], [ 1 a] [ 1 0], [ a a] [ 1 a], [ 1 a] [ 1 a^2], [ 0 1] [ 0 0], [ 0 1] [a^2 0], [a^2 1] [ a a], [ 0 1] [ a 0], [a^2 1] [ 0 1], [ 0 1] [a^2 a^2], [a^2 1] [ 1 1], [ 0 1] [ 0 a], [a^2 1] [a^2 0], [ 0 1] [a^2 a], [a^2 1] [ a 0], [a^2 1] [ 1 0], [a^2 1] [ 0 a^2], [ 0 1] [a^2 1], [a^2 1] [a^2 a^2], [ 1 1] [a^2 a], [ 1 1] [ a a], [ a 1] [ 1 0], [ a 1] [ 0 a^2], [ a 1] [ 1 a^2], [ a 1] [ 0 a], [ 1 1] [ a 0], [ a 1] [ 1 a] } >> if Mran[i] subset Mt then mtcont+1; end if; ^ Runtime error in '[]': Bad argument types 0 0 0 Total time: 3.159 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:40:44 2004 Input: F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={i:i in M22| (Trace(i) eq 0) and (i[1] eq i[2] )}; Mran:={Random(M22):i in [1..100]}; print(Mran); print(#(Mran)); mtcont:=0; mfcont:=0; mtfcont:=0; for i in Mran do if Mran[i] subset Mt then mtcont+1; end if; if i subset Mf then mfcont+1; end if; if i subset Mtf then mtfcont+1; end if; end for; print(mtcont); print(mfcont); print(mtfcont); Output: Magma V2.10-6 Wed Mar 10 2004 10:40:40 on modular [Seed = 2509955906] ------------------------------------- { [ 0 0] [ 0 0], [a^2 0] [a^2 a], [a^2 0] [ a a], [a^2 0] [ a 1], [a^2 0] [ 1 1], [ 0 0] [a^2 a], [ 0 0] [ a a], [a^2 0] [ 1 0], [a^2 0] [ 0 a^2], [ 0 0] [ 1 1], [ 1 0] [a^2 a], [ a 0] [ a 0], [ a 0] [ 0 a^2], [ a 0] [a^2 a^2], [ a 0] [ a a^2], [ 1 0] [ a 1], [ 1 0] [ 1 1], [ a 0] [a^2 a], [ 1 0] [a^2 0], [ 1 0] [ 1 0], [ a 0] [a^2 1], [ 0 a^2] [ a 0], [a^2 a^2] [ 0 1], [a^2 a^2] [a^2 1], [a^2 a^2] [ a 1], [a^2 a^2] [ 1 1], [ 0 a^2] [ 0 a], [a^2 a^2] [a^2 0], [a^2 a^2] [ a 0], [ 0 a^2] [ 0 1], [ 0 a^2] [ 1 1], [ a a^2] [ 0 0], [ 1 a^2] [ 1 a], [ a a^2] [ 0 a^2], [ 1 a^2] [a^2 1], [ a a^2] [ a a^2], [ 1 a^2] [ 1 1], [ 1 a^2] [ 0 0], [ a a^2] [a^2 a], [ a a^2] [ a a], [ 1 a^2] [ 0 a^2], [ a a^2] [ 0 1], [ 1 a^2] [a^2 a^2], [ a a^2] [ 1 1], [ 0 a] [a^2 0], [a^2 a] [ a a], [ 0 a] [ a 0], [ 0 a] [a^2 a^2], [a^2 a] [ a 1], [ 0 a] [ 1 a^2], [ 0 a] [a^2 a], [ 0 a] [ a a], [a^2 a] [ 1 0], [ a a] [a^2 0], [ a a] [ 0 a^2], [ 1 a] [ a 1], [ a a] [ a a^2], [ a a] [ 1 a^2], [ 1 a] [ 0 0], [ a a] [ 0 a], [ 1 a] [ 1 0], [ 1 a] [ 0 a^2], [ 1 a] [a^2 a^2], [ 1 a] [ 1 a^2], [ 0 1] [ a 0], [a^2 1] [ 1 a], [ 0 1] [ 0 a^2], [ 0 1] [a^2 a^2], [a^2 1] [ a 1], [ 0 1] [ 0 a], [a^2 1] [ a 0], [a^2 1] [a^2 a^2], [ 0 1] [ 1 1], [ a 1] [ 0 0], [ a 1] [a^2 0], [ 1 1] [ 1 a], [ a 1] [ a a^2], [ 1 1] [ a 1], [ 1 1] [a^2 0], [ a 1] [a^2 a], [ a 1] [ a a], [ 1 1] [ a 0], [ a 1] [ 0 1], [ 1 1] [a^2 a^2], [ 1 1] [ a a^2] } 85 >> if Mran[i] subset Mt then mtcont+1; end if; ^ Runtime error in '[]': Bad argument types 0 0 0 Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:41:10 2004 Input: F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={i:i in M22| (Trace(i) eq 0) and (i[1] eq i[2] )}; Mran:={Random(M22):i in [1..17]}; print(Mran); print(#(Mran)); mtcont:=0; mfcont:=0; mtfcont:=0; for i in Mran do if Mran[i] subset Mt then mtcont+1; end if; if i subset Mf then mfcont+1; end if; if i subset Mtf then mtfcont+1; end if; end for; print(mtcont); print(mfcont); print(mtfcont); Output: Magma V2.10-6 Wed Mar 10 2004 10:41:05 on modular [Seed = 4260530883] ------------------------------------- { [a^2 a^2] [ a a], [a^2 0] [ a a], [ 0 a^2] [ 0 a^2], [ a a] [ 0 a], [a^2 1] [a^2 0], [ 0 a^2] [a^2 a^2], [ a 1] [ 1 a], [a^2 0] [ 0 1], [ 1 a^2] [ 0 0], [a^2 0] [ 0 0], [a^2 a] [a^2 a^2], [ 0 a] [a^2 1], [ a a] [ 1 1], [a^2 a] [ 1 a^2], [a^2 a^2] [ a a^2], [ 0 a] [ 0 0], [ a 0] [ 1 1] } 17 >> if Mran[i] subset Mt then mtcont+1; end if; ^ Runtime error in '[]': Bad argument types 0 0 0 Total time: 3.329 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:41:26 2004 Input: F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={i:i in M22| (Trace(i) eq 0) and (i[1] eq i[2] )}; Mran:={Random(M22):i in [1..56]}; print(Mran); print(#(Mran)); mtcont:=0; mfcont:=0; mtfcont:=0; for i in Mran do if Mran[i] subset Mt then mtcont+1; end if; if i subset Mf then mfcont+1; end if; if i subset Mtf then mtfcont+1; end if; end for; print(mtcont); print(mfcont); print(mtfcont); Output: Magma V2.10-6 Wed Mar 10 2004 10:41:21 on modular [Seed = 3401956804] ------------------------------------- { [a^2 0] [ 0 a], [ 1 1] [ 1 a^2], [ a 1] [ 1 1], [ 0 0] [ a 0], [ 0 0] [ 1 0], [a^2 0] [ 0 1], [a^2 0] [ 1 1], [a^2 0] [ 0 0], [a^2 0] [a^2 0], [a^2 0] [a^2 a^2], [ 1 0] [a^2 a], [ a 0] [ a a^2], [ 1 0] [ a 1], [ a 0] [ 1 a^2], [ a 0] [a^2 a], [ 1 0] [ 0 a^2], [ 1 0] [a^2 a^2], [ 0 a^2] [ a 0], [a^2 a^2] [ 0 1], [ 0 a^2] [a^2 a^2], [ 0 a^2] [ 1 a^2], [a^2 a^2] [a^2 a^2], [ 1 a^2] [ 0 a], [ 1 a^2] [a^2 a], [ 1 a^2] [ a a], [ a a^2] [ a 0], [ a a^2] [ 0 a], [ a a^2] [ 1 a], [ a a^2] [ a 1], [a^2 a] [ a a], [ 0 a] [ 0 a^2], [ 0 a] [ 1 a^2], [a^2 a] [ 1 1], [ 0 a] [ 0 a], [a^2 a] [ a 0], [ a a] [ 0 0], [ a a] [a^2 0], [ 1 a] [ 0 0], [ a a] [ 0 a], [ a a] [ a a], [ 1 a] [ a 0], [ 1 a] [ a a^2], [a^2 1] [ 0 1], [ 0 1] [a^2 a^2], [a^2 1] [ a 0], [ 1 1] [ 0 a], [ a 1] [ 0 a], [ a 1] [a^2 a], [ 1 1] [ a 0], [ 1 1] [ 0 a^2], [ 1 1] [ a a^2] } 51 >> if Mran[i] subset Mt then mtcont+1; end if; ^ Runtime error in '[]': Bad argument types 0 0 0 Total time: 4.079 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:42:04 2004 Input: F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={i:i in M22| (Trace(i) eq 0) and (i[1] eq i[2] )}; Mran:=[Random(M22):i in [1..56]]; print(Mran); print(#(Mran)); mtcont:=0; mfcont:=0; mtfcont:=0; for i in Mran do if Mran[i] subset Mt then mtcont+1; end if; if i subset Mf then mfcont+1; end if; if i subset Mtf then mtfcont+1; end if; end for; print(mtcont); print(mfcont); print(mtfcont); Output: Magma V2.10-6 Wed Mar 10 2004 10:42:00 on modular [Seed = 826164809] ------------------------------------- [ [a^2 a] [a^2 a], [ 1 1] [ 1 1], [a^2 0] [ 1 1], [a^2 0] [ 0 a], [ 0 1] [ 0 1], [ a a] [a^2 a], [a^2 0] [ 1 a], [ a a^2] [ 1 a], [ 0 a^2] [ 0 0], [a^2 a] [a^2 a], [ 0 a] [a^2 a], [ 1 a] [ 1 a^2], [a^2 0] [ 1 a^2], [ 1 0] [ 0 1], [ 0 a] [ a 1], [ a a] [ 0 0], [ a 0] [a^2 a], [ 0 0] [ a a^2], [ 1 a] [a^2 a], [a^2 1] [ 1 0], [a^2 0] [ a a], [ a a] [a^2 a], [ 1 a] [a^2 a^2], [ 0 0] [ 0 0], [a^2 a] [ 0 a], [a^2 0] [a^2 a], [ 0 a^2] [ 1 a^2], [ 1 1] [ a a], [a^2 0] [ a 0], [ 1 0] [ 0 a], [a^2 a^2] [ 0 a^2], [ 0 0] [ a a^2], [ 1 0] [ a a^2], [a^2 0] [ a 0], [ 1 a^2] [ 1 1], [a^2 0] [ 1 1], [ 0 1] [ 1 1], [a^2 0] [ a 0], [ 1 0] [ a 0], [ 1 a^2] [a^2 a], [ 0 1] [a^2 a^2], [a^2 0] [ a a^2], [a^2 0] [ 1 a^2], [ 1 0] [ 1 1], [a^2 a] [a^2 a^2], [ 1 0] [a^2 1], [ a 0] [ 1 a^2], [ a a] [ 1 a], [ a a^2] [ 0 a^2], [ a a] [a^2 1], [ a a] [a^2 0], [ a 0] [ 0 a], [a^2 0] [ a 0], [a^2 a^2] [ 0 a^2], [ 0 a] [ a 1], [a^2 a^2] [ a a] ] 56 >> if Mran[i] subset Mt then mtcont+1; end if; ^ Runtime error in '[]': Bad argument types 0 0 0 Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:42:18 2004 Input: F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={i:i in M22| (Trace(i) eq 0) and (i[1] eq i[2] )}; Mran:=[Random(M22):i in [1..1200]]; print(Mran); print(#(Mran)); mtcont:=0; mfcont:=0; mtfcont:=0; for i in Mran do if Mran[i] subset Mt then mtcont+1; end if; if i subset Mf then mfcont+1; end if; if i subset Mtf then mtfcont+1; end if; end for; print(mtcont); print(mfcont); print(mtfcont); Output: Magma V2.10-6 Wed Mar 10 2004 10:42:14 on modular [Seed = 606819138] ------------------------------------- [ [ a 0] [a^2 a], [ 0 1] [a^2 a], [ 1 a^2] [ 1 a], [ a 1] [ a 1], [ 1 a^2] [ 1 1], [ 1 0] [ a a^2], [ 1 0] [ 1 a], [ 0 0] [a^2 0], [a^2 0] [ 1 a], [ 0 a^2] [ 0 0], [a^2 1] [a^2 a^2], [a^2 a] [ a a], [ 1 1] [ 1 1], [ 0 a^2] [a^2 1], [ a a^2] [a^2 0], [ 1 0] [ 0 1], [ 0 0] [ a a], [a^2 a^2] [a^2 1], [ 0 1] [ 1 0], [ a 1] [a^2 0], [a^2 a] [a^2 1], [ 0 a^2] [ a 0], [ a 0] [ a 1], [ a a] [ 0 a^2], [ 0 0] [ 0 a], [a^2 0] [a^2 0], [ 0 0] [ 0 a], [ 0 1] [ 1 a], [ 0 0] [a^2 a^2], [ a a^2] [ a 1], [ a 1] [ 0 a^2], [ a 0] [a^2 1], [a^2 1] [ 0 1], [ 1 1] [ a 1], [ a a^2] [ 1 a], [a^2 a] [ 0 a^2], [a^2 0] [ 1 0], [ 0 a] [ 0 a], [ a a^2] [ 1 1], [ 1 1] [ a 0], [ a 0] [ 1 a^2], [ 1 a] [ 0 1], [ 0 0] [ 1 0], [ 0 1] [ 0 0], [a^2 a] [ 0 a^2], [a^2 0] [ 0 a], [ 0 0] [ 1 a], [a^2 1] [a^2 1], [ a 0] [a^2 1], [ 1 a] [ 0 1], [ 0 0] [ 0 a], [ 0 0] [ a a], [ 0 1] [ 0 0], [ 1 a] [a^2 1], [a^2 0] [ a 1], [ a 1] [ 0 a^2], [ 0 0] [ 1 1], [ a 0] [a^2 a], [ 1 1] [ 1 1], [ a 0] [a^2 1], [ 1 1] [ a a^2], [ a 1] [a^2 a], [a^2 1] [ a 0], [a^2 a^2] [ 0 0], [ a a] [ 0 0], [ a a^2] [a^2 0], [a^2 0] [ a 1], [ 1 a^2] [ 1 0], [ a a^2] [ a a^2], [ 1 1] [ 0 1], [ a 0] [ a 1], [ a 1] [ a 0], [ a 1] [ 1 a^2], [ 1 a] [ 0 0], [ 0 0] [ a a], [ 1 1] [ 1 a^2], [a^2 a] [ 0 1], [ 0 a] [a^2 1], [ 1 0] [ 0 0], [a^2 a^2] [ a a], [a^2 a^2] [ 0 a^2], [ a a] [a^2 0], [ 1 0] [ 1 1], [ 0 0] [ 0 a^2], [ 0 a] [a^2 1], [ a 1] [ 1 0], [a^2 a] [ a a^2], [ 1 a^2] [ a 1], [ a 1] [ a 1], [a^2 1] [a^2 1], [ a 0] [ 0 a], [a^2 a] [ 1 0], [ 0 0] [a^2 0], [a^2 0] [ 0 1], [a^2 a] [ a 0], [ 0 0] [a^2 1], [ 0 0] [ 0 0], [ a 0] [ 0 a^2], [ 0 a] [ 1 1], [ a 1] [a^2 a^2], [a^2 0] [a^2 1], [a^2 a^2] [a^2 a^2], [a^2 1] [ 0 a^2], [a^2 0] [ a a], [ 1 a^2] [a^2 1], [ a a^2] [ 0 a], [ a a] [ 0 1], [a^2 1] [ 0 a], [a^2 a^2] [ 0 1], [a^2 a^2] [ 0 0], [ 0 a] [ 0 a], [ 1 a^2] [a^2 a], [a^2 0] [ 0 0], [ 1 a] [ 1 a], [ a 1] [ 1 a], [ a 1] [ a a^2], [a^2 a^2] [ 1 0], [a^2 a] [a^2 0], [a^2 1] [ 0 0], [ 0 a] [ 1 a], [a^2 a] [ a 0], [a^2 0] [ 1 a^2], [ a 0] [a^2 1], [ 0 0] [ 1 a^2], [ 0 a] [ a a^2], [ a a] [ a a], [ 1 a] [ 1 0], [a^2 0] [ 1 a^2], [ a a] [ a 0], [ a a^2] [ a a^2], [a^2 a] [a^2 0], [ 1 1] [ 1 0], [a^2 1] [ a 1], [ 1 a^2] [ 0 0], [a^2 a^2] [ 0 a], [ 0 a^2] [a^2 a^2], [ 0 1] [ a a^2], [ a a^2] [ a a^2], [ 1 1] [ 0 a^2], [ 1 a] [a^2 a^2], [ 0 1] [ 0 a], [ a 0] [a^2 0], [ 1 1] [ 0 a], [ 1 0] [ 1 a^2], [a^2 1] [ 0 a^2], [ 0 a^2] [ a a], [ 1 0] [ a a^2], [ 1 1] [a^2 0], [ 0 1] [ 1 1], [a^2 a^2] [ 1 0], [ a a] [ a 1], [ 0 0] [a^2 a^2], [ 1 1] [ 1 a^2], [a^2 0] [ a 1], [ 1 a] [a^2 a^2], [ a a] [a^2 a], [ 1 0] [ 0 a], [ a a^2] [ a a^2], [a^2 a^2] [a^2 a^2], [ a a^2] [a^2 0], [a^2 a] [ 0 1], [ a 0] [ a a^2], [ 1 0] [ 0 0], [ a a^2] [ a a], [ a 1] [ a a], [a^2 0] [ 1 0], [a^2 a] [a^2 1], [a^2 a^2] [a^2 0], [ 1 a^2] [a^2 0], [ 0 0] [ a a], [a^2 a^2] [ 1 a^2], [ 1 a] [a^2 0], [ 1 a] [a^2 a], [ a a^2] [a^2 0], [a^2 a] [a^2 0], [ 1 1] [a^2 1], [ a a] [a^2 a], [ a a] [ 0 a], [a^2 a] [ 1 a], [a^2 0] [ a a^2], [ 1 a] [ 0 0], [ a 0] [ a 1], [ a 1] [ a a], [a^2 a^2] [ a 0], [ 1 a^2] [ 1 a^2], [ 1 a^2] [ a 0], [ a a^2] [a^2 a^2], [ a a^2] [ a a^2], [ 0 a^2] [ a a^2], [ a a^2] [ 1 1], [ 1 a^2] [ 0 0], [ a 1] [ 1 0], [ 1 0] [ a 1], [a^2 1] [a^2 a], [ 0 1] [a^2 0], [ 0 a] [a^2 a], [a^2 a] [a^2 a], [ a 1] [a^2 a^2], [ 0 a^2] [ 1 a], [a^2 0] [ 1 0], [ a a^2] [a^2 a], [ 0 1] [ 0 a^2], [a^2 1] [ 1 0], [a^2 a^2] [a^2 a^2], [ a a^2] [a^2 a^2], [ 1 a^2] [a^2 0], [a^2 a^2] [ 1 a^2], [ 0 a] [ 0 a], [ a 1] [ 1 1], [ a a^2] [ a 1], [ 1 a] [ 1 a], [ 0 1] [ 0 a^2], [ 0 a^2] [ 0 0], [ a a] [ 1 1], [ 1 a^2] [ 0 1], [ a a] [ 0 1], [ 1 a^2] [ 1 1], [ 1 a] [ 1 a^2], [a^2 a^2] [a^2 a], [a^2 0] [a^2 a^2], [ 1 1] [ a 1], [ 0 a] [ 1 a^2], [ 1 a] [ a a^2], [ a 1] [a^2 a^2], [a^2 a^2] [ 1 a^2], [ a a^2] [ 1 1], [ 1 a] [ a 1], [ 1 1] [ 0 a^2], [ a 0] [ a a^2], [ a 0] [ 0 1], [a^2 0] [ a 0], [a^2 a] [ a 0], [ 1 1] [ 1 0], [ 0 a] [ 0 a], [ a 1] [ a a], [a^2 1] [ 1 0], [ 1 a] [ 1 0], [ 1 a] [a^2 0], [a^2 a] [ 1 a], [a^2 a] [a^2 0], [ 0 a^2] [a^2 1], [a^2 1] [ 0 a^2], [ 1 a] [ a 1], [ 1 a] [ 1 a], [ 0 a] [a^2 0], [ a 1] [ 1 1], [ 0 0] [ 0 a], [ 0 a^2] [a^2 a^2], [ 1 1] [ 1 0], [a^2 1] [ 1 a^2], [ 0 a^2] [ 0 a], [a^2 a] [a^2 0], [a^2 a] [ 0 a^2], [ 0 0] [a^2 1], [a^2 a^2] [ a 1], [ 0 a] [ 0 0], [ 1 a^2] [a^2 a^2], [a^2 1] [a^2 a], [ a a] [a^2 a], [ 0 0] [a^2 a], [ a 1] [a^2 1], [ 1 1] [ a 1], [ 1 a^2] [ 1 a], [ 0 a^2] [ a a^2], [ 0 a] [ 1 a], [ 0 0] [ 1 0], [ a 0] [ 0 a^2], [ 0 0] [ 0 a^2], [ a a^2] [a^2 a^2], [a^2 0] [ 1 a], [ 1 0] [ 1 a], [a^2 0] [ 0 a^2], [ a a^2] [ a a^2], [ 0 0] [a^2 a^2], [a^2 1] [a^2 a^2], [ 1 0] [ 0 1], [a^2 1] [ a a^2], [ a 1] [a^2 0], [ 0 a^2] [ a 1], [a^2 1] [a^2 a], [ 0 a^2] [ 1 1], [ 0 0] [ 0 a], [ a a^2] [ 1 0], [a^2 a^2] [ a a], [ 0 0] [ a a], [ a a^2] [ a a^2], [ a 0] [ 1 a], [ a 1] [ a 1], [ 1 a] [ 1 a^2], [a^2 0] [ 0 a], [a^2 0] [ a 1], [ 0 a^2] [ 1 0], [ 0 1] [ 1 0], [ 0 a] [ 0 0], [ a a] [a^2 1], [ 1 a^2] [ 1 a], [ a 0] [ 0 1], [ 0 a] [ 0 a^2], [ 1 0] [a^2 a], [a^2 a^2] [a^2 a], [ a 1] [ 0 1], [ 0 a^2] [ 0 0], [ 0 0] [ 0 a^2], [ 1 0] [ a a], [ 1 a^2] [ 0 1], [ a 0] [ 0 0], [ 1 a^2] [ a 0], [ 1 a] [ a a^2], [ 0 a] [ 1 1], [ a 0] [ a a], [a^2 a^2] [ 0 a], [ 0 1] [a^2 a^2], [ 1 0] [ 0 0], [ 0 a] [ 0 0], [ 1 a^2] [ 1 1], [ 1 a] [ a a], [a^2 a^2] [a^2 a^2], [ 0 0] [ a a^2], [a^2 0] [a^2 a^2], [a^2 a^2] [a^2 a], [ 0 a^2] [ 0 0], [ 0 a^2] [a^2 0], [ 1 0] [a^2 1], [a^2 a] [a^2 a], [ 1 0] [a^2 a], [ a 1] [ 0 a], [ 0 0] [ 0 a^2], [ a a] [a^2 1], [ a a] [a^2 0], [a^2 1 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:42:34 2004 Input: F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={i:i in M22| (Trace(i) eq 0) and (i[1] eq i[2] )}; Mran:=[Random(M22):i in [1..160]]; print(Mran); print(#(Mran)); mtcont:=0; mfcont:=0; mtfcont:=0; for i in Mran do if Mran[i] subset Mt then mtcont+1; end if; if i subset Mf then mfcont+1; end if; if i subset Mtf then mtfcont+1; end if; end for; print(mtcont); print(mfcont); print(mtfcont); Output: Magma V2.10-6 Wed Mar 10 2004 10:42:30 on modular [Seed = 387473473] ------------------------------------- [ [a^2 0] [ 1 1], [ a 1] [a^2 a^2], [a^2 1] [ 1 0], [ 0 a^2] [ a a^2], [ a a] [ 1 a], [ a a] [ 1 a], [ 1 a] [ 0 a], [ 1 a] [ a a], [a^2 a] [ 0 0], [a^2 1] [ 0 1], [a^2 0] [ 0 1], [ a a^2] [ 0 a], [ 1 1] [ 1 0], [a^2 1] [ 1 0], [ 1 a] [ 0 a^2], [ 1 0] [ 0 a], [ 0 1] [a^2 1], [ a a^2] [ a 0], [ 1 0] [ a 0], [a^2 a^2] [ 1 1], [a^2 a] [a^2 a], [ 1 a^2] [ a 1], [a^2 a^2] [ a a^2], [ 1 1] [ a 1], [ a 1] [ a a], [a^2 1] [ a 1], [ 0 a^2] [ a a^2], [ a a] [ a a], [ 1 1] [ 0 1], [ 1 0] [ a a^2], [ 1 a] [ a a^2], [ a a] [ 1 1], [ 0 a] [a^2 1], [ a 0] [ 1 0], [a^2 a^2] [a^2 a^2], [ 0 0] [a^2 a^2], [ a 1] [ a 1], [ a 0] [ a 0], [ 1 1] [ a 1], [ 1 a^2] [ a 1], [ 0 a^2] [ a 0], [ 1 a^2] [ a 1], [ a a^2] [ a a], [a^2 a^2] [ 0 a], [ 1 a^2] [ a a^2], [ a a] [ a a], [a^2 a] [ a a^2], [ 0 a] [ a 0], [ 1 a^2] [ 0 a^2], [ 1 a] [ 0 1], [a^2 a^2] [ 1 1], [a^2 a^2] [ 0 1], [ 1 0] [ a 1], [a^2 a] [ 0 1], [ 1 a^2] [ 0 0], [ 0 1] [ 0 0], [ 0 a^2] [ 1 0], [ 1 a^2] [a^2 0], [ 0 a] [ a a], [ 0 1] [ 1 a^2], [ 0 a^2] [ 0 a], [ a a^2] [ 1 a^2], [ 1 1] [a^2 1], [a^2 a^2] [ 1 1], [ a a] [ a a^2], [a^2 a^2] [ 0 a^2], [ 1 0] [ 1 a], [ 0 1] [ 1 a], [ 1 a^2] [a^2 a^2], [ 1 0] [ 1 0], [a^2 1] [ 1 a^2], [ a 0] [ 1 a^2], [ 0 a^2] [ 0 1], [ 0 1] [ 1 0], [ 0 1] [ 1 0], [ 1 1] [a^2 1], [ 0 a] [ a 1], [ 1 1] [ 1 a^2], [ a 1] [a^2 1], [ a a] [a^2 a], [ a a] [ 1 0], [ a a] [a^2 0], [ a a] [a^2 1], [ 1 1] [ 1 0], [ 0 0] [a^2 0], [ 0 a^2] [a^2 a^2], [ a a] [ 0 0], [ 0 1] [ 1 1], [a^2 a] [ a a^2], [a^2 a] [ 1 1], [ 1 a] [ 0 a^2], [ 1 a] [a^2 0], [ 0 0] [ a a], [ a 1] [ 0 a], [ 0 a^2] [a^2 0], [ 1 0] [ 1 a], [a^2 a] [a^2 1], [ a a^2] [ 0 a^2], [ 0 0] [ a 0], [ 0 1] [a^2 1], [a^2 a] [ 1 0], [a^2 a^2] [ 0 0], [a^2 0] [a^2 0], [a^2 a] [ a a^2], [ 1 a^2] [ 0 0], [ 1 a] [ 0 1], [ a 0] [ 1 0], [ 1 a] [ 0 a^2], [ 0 a^2] [ a 0], [a^2 1] [ 1 a], [ a a^2] [a^2 a], [ 1 a] [ a 1], [ 0 0] [a^2 1], [ 0 0] [ 1 a], [ a 1] [ 1 1], [a^2 a] [ 1 a^2], [ 0 a] [ 0 1], [ 0 a] [ 1 a], [ a 1] [a^2 1], [ 1 a^2] [ 0 1], [a^2 a] [ 1 0], [ 1 a^2] [ 1 1], [ 0 1] [a^2 0], [ 0 1] [ 1 a^2], [a^2 1] [ 0 1], [ 0 a^2] [ 1 0], [ 1 0] [ a 1], [a^2 a^2] [ 1 a], [a^2 a^2] [a^2 a^2], [ 0 1] [a^2 a], [ a 0] [a^2 0], [ 0 1] [ 0 a^2], [ a a^2] [ 0 1], [ a a] [ a a], [ 1 0] [ a a], [a^2 1] [ a a^2], [ 0 a] [a^2 0], [ 1 a^2] [ 0 0], [ a a] [a^2 a], [a^2 a] [ 1 1], [ a 0] [ 0 0], [ a a^2] [ 1 a^2], [ 1 a] [ a a], [ 0 0] [ a 1], [ 1 0] [ 1 a], [ 0 0] [ 1 a], [ 1 a] [ 1 1], [ 0 a^2] [ a 1], [a^2 1] [ 1 a^2], [a^2 a^2] [ 0 a], [a^2 1] [ 0 a], [ 0 a^2] [ 1 a], [a^2 1] [ 0 a^2], [ 0 a] [ 1 a^2], [ 0 a^2] [a^2 0], [a^2 1] [ 1 1], [ 1 1] [a^2 a], [ 1 0] [ a a], [ 1 a] [ a 1], [a^2 1] [a^2 a] ] 160 >> if Mran[i] subset Mt then mtcont+1; end if; ^ Runtime error in '[]': Bad argument types 0 0 0 Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:43:24 2004 Input: mtcont:=0; mfcont:=0; mtfcont:=0; F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={i:i in M22| (Trace(i) eq 0) and (i[1] eq i[2] )}; Mran:=[Random(M22):i in [1..160]]; for i in Mran do if i subset Mt then mtcont+1; end if; if i subset Mf then mfcont+1; end if; if i subset Mtf then mtfcont+1; end if; end for; print(mtcont); print(mfcont); print(mtfcont); Output: Magma V2.10-6 Wed Mar 10 2004 10:43:20 on modular [Seed = 2021068752] ------------------------------------- >> if i subset Mt then mtcont+1; end if; ^ Runtime error in 'subset': Bad argument types Argument types given: AlgMatElt, SetEnum[AlgMatElt] 0 0 0 Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:43:43 2004 Input: mtcont:=0; mfcont:=0; mtfcont:=0; F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={i:i in M22| (Trace(i) eq 0) and (i[1] eq i[2] )}; Mran:=[Random(M22):i in [1..10]]; for i in Mran do if i subset Mt[i] then mtcont+1; end if; if i subset Mf then mfcont+1; end if; if i subset Mtf then mtfcont+1; end if; end for; print(mtcont); print(mfcont); print(mtfcont); Output: Magma V2.10-6 Wed Mar 10 2004 10:43:39 on modular [Seed = 1734873340] ------------------------------------- >> if i subset Mt[i] then mtcont+1; end if; ^ Runtime error in '[]': Bad argument types 0 0 0 Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:43:51 2004 Input: mtcont:=0; mfcont:=0; mtfcont:=0; F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={i:i in M22| (Trace(i) eq 0) and (i[1] eq i[2] )}; Mran:=[Random(M22):i in [1..10]]; for i in Mran do if i subset Mt[i] then mtcont+1; end if; if i subset Mf then mfcont+1; end if; if i subset Mtf then mtfcont+1; end if; end for; print(mtcont); print(mfcont); print(mtfcont); Output: Magma V2.10-6 Wed Mar 10 2004 10:43:46 on modular [Seed = 1398547665] ------------------------------------- >> if i subset Mt[i] then mtcont+1; end if; ^ Runtime error in '[]': Bad argument types 0 0 0 Total time: 3.779 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:44:24 2004 Input: mtcont:=0; mfcont:=0; mtfcont:=0; F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={i:i in M22| (Trace(i) eq 0) and (i[1] eq i[2] )}; Mran:=[Random(M22):i in [1..10]]; for i in Mran do print(i); /* if i subset Mti then mtcont+1; end if; if i subset Mf then mfcont+1; end if; if i subset Mtf then mtfcont+1; end if; end for; print(mtcont); print(mfcont); print(mtfcont); Output: Magma V2.10-6 Wed Mar 10 2004 10:44:20 on modular [Seed = 1162490529] ------------------------------------- >> /* ^ User error: Unterminated /* comment Total time: 3.059 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:44:36 2004 Input: mtcont:=0; mfcont:=0; mtfcont:=0; F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={i:i in M22| (Trace(i) eq 0) and (i[1] eq i[2] )}; Mran:=[Random(M22):i in [1..10]]; for i in Mran do print(i); /* if i subset Mti then mtcont+1; end if; if i subset Mf then mfcont+1; end if; if i subset Mtf then mtfcont+1; end if;*/ end for; print(mtcont); print(mfcont); print(mtfcont); Output: Magma V2.10-6 Wed Mar 10 2004 10:44:32 on modular [Seed = 3082338407] ------------------------------------- [ 1 1] [ 1 a^2] [ 0 1] [ 0 a] [ 0 a] [ 0 0] [ 0 a] [a^2 1] [ a a^2] [a^2 a] [a^2 a^2] [ a 1] [ 0 a^2] [ 0 a^2] [ 0 1] [ 0 1] [a^2 a] [ a 1] [ 0 0] [ a a] 0 0 0 Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:45:11 2004 Input: mtcont:=0; mfcont:=0; mtfcont:=0; F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={i:i in M22| (Trace(i) eq 0) and (i[1] eq i[2] )}; Mran:=[Random(M22):i in [1..10]]; for i in Mran do print(i); /* if i subset Mti then mtcont+1; end if; if i subset Mf then mfcont+1; end if; if i subset Mtf then mtfcont+1; end if;*/ end for; print(#i) print(mtcont); print(mfcont); print(mtfcont); Output: Magma V2.10-6 Wed Mar 10 2004 10:45:06 on modular [Seed = 2526670500] ------------------------------------- [ 1 1] [ 0 1] [a^2 a^2] [a^2 0] [ 1 0] [ 0 0] [a^2 1] [ a a] [ 0 0] [a^2 a] [ 1 a^2] [ 0 a^2] [a^2 0] [ 0 a^2] [ a a] [ a a] [ 1 0] [ 0 a] [ a a^2] [ 1 0] >> print(mtcont); ^ User error: bad syntax 0 0 Total time: 3.859 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:45:27 2004 Input: mtcont:=0; mfcont:=0; mtfcont:=0; F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={i:i in M22| (Trace(i) eq 0) and (i[1] eq i[2] )}; Mran:=[Random(M22):i in [1..10]]; for i in Mran do print(i); /* if i subset Mti then mtcont+1; end if; if i subset Mf then mfcont+1; end if; if i subset Mtf then mtfcont+1; end if;*/ end for; print(#i); print(mtcont); print(mfcont); print(mtfcont); Output: Magma V2.10-6 Wed Mar 10 2004 10:45:22 on modular [Seed = 2240478631] ------------------------------------- [ 1 0] [ 1 a] [ 1 1] [ 0 1] [ a 0] [ 1 1] [a^2 a] [a^2 a] [ 0 0] [ 1 0] [ a 1] [ a a^2] [ a 1] [ 1 a] [ 1 1] [ 0 0] [ a a^2] [ 0 a] [ a a^2] [ 1 a] >> print(#i); ^ User error: Identifier 'i' has not been declared or assigned 0 0 0 Total time: 3.669 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:46:35 2004 Input: mtcont:=0; mfcont:=0; mtfcont:=0; F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={i:i in M22| (Trace(i) eq 0) and (i[1] eq i[2] )}; Mran:=[Random(M22):i in [1..10]]; for i in Mran do if i in Mt then mtcont+1; end if; if i subset Mf then mfcont+1; end if; if i subset Mtf then mtfcont+1; end if; end for; print(#i); print(mtcont); print(mfcont); print(mtfcont); Output: Magma V2.10-6 Wed Mar 10 2004 10:46:31 on modular [Seed = 3991049610] ------------------------------------- 1 >> if i subset Mf then mfcont+1; end if; ^ Runtime error in 'subset': Bad argument types Argument types given: AlgMatElt, SetEnum[AlgMatElt] >> print(#i); ^ User error: Identifier 'i' has not been declared or assigned 0 0 0 Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:46:56 2004 Input: mtcont:=0; mfcont:=0; mtfcont:=0; F:=GF(4); M22:=MatrixRing(F,2); Mt:=[i:i in M22|Trace(i) eq 0]; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={i:i in M22| (Trace(i) eq 0) and (i[1] eq i[2] )}; Mran:=[Random(M22):i in [1..10]]; for i in Mran do if i in Mt then mtcont+1; end if; if i subset Mf then mfcont+1; end if; if i subset Mtf then mtfcont+1; end if; end for; print(#i); print(mtcont); print(mfcont); print(mtfcont); Output: Magma V2.10-6 Wed Mar 10 2004 10:46:51 on modular [Seed = 3754993540] ------------------------------------- >> if i subset Mf then mfcont+1; end if; ^ Runtime error in 'subset': Bad argument types Argument types given: AlgMatElt, SetEnum[AlgMatElt] >> print(#i); ^ User error: Identifier 'i' has not been declared or assigned 0 0 0 Total time: 4.059 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:47:16 2004 Input: mtcont:=0; mfcont:=0; mtfcont:=0; F:=GF(4); M22:=MatrixRing(F,2); Mt:=[i:i in M22|Trace(i) eq 0]; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={i:i in M22| (Trace(i) eq 0) and (i[1] eq i[2] )}; Mran:=[Random(M22):i in [1..10]]; for i in Mran do if i in Mt then mtcont+1; end if; if i in Mf then mfcont+1; end if; if i subset Mtf then mtfcont+1; end if; end for; print(#i); print(mtcont); print(mfcont); print(mtfcont); Output: Magma V2.10-6 Wed Mar 10 2004 10:47:11 on modular [Seed = 809453694] ------------------------------------- 1 >> if i subset Mtf then mtfcont+1; end if; ^ Runtime error in 'subset': Bad argument types Argument types given: AlgMatElt, SetEnum[AlgMatElt] >> print(#i); ^ User error: Identifier 'i' has not been declared or assigned 0 0 0 Total time: 3.609 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:47:38 2004 Input: mtcont:=0; mfcont:=0; mtfcont:=0; F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={i:i in M22| (Trace(i) eq 0) and (i[1] eq i[2] )}; Mran:=[Random(M22):i in [1..10]]; for i in Mran do if i in Mt then mtcont+1; end if; if i in Mf then mfcont+1; end if; if i in Mtf then mtfcont+1; end if; end for; print(#i); print(mtcont); print(mfcont); print(mtfcont); Output: Magma V2.10-6 Wed Mar 10 2004 10:47:34 on modular [Seed = 623533442] ------------------------------------- 1 1 1 1 1 >> print(#i); ^ User error: Identifier 'i' has not been declared or assigned 0 0 0 Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:48:04 2004 Input: mtcont:=0; mfcont:=0; mtfcont:=0; F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={i:i in M22| (Trace(i) eq 0) and (i[1] eq i[2] )}; Mran:=[Random(M22):i in [1..10]]; for i in Mran do if i in Mt then mtcont+1; end if; if i in Mf then mfcont+1; end if; if i in Mtf then mtfcont+1; end if; end for; print(mtcont); print(mfcont); print(mtfcont); Output: Magma V2.10-6 Wed Mar 10 2004 10:48:00 on modular [Seed = 387477398] ------------------------------------- 1 1 1 1 0 0 0 Total time: 3.439 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:48:44 2004 Input: mtcont:=0; mfcont:=0; mtfcont:=0; F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={i:i in M22| (Trace(i) eq 0) and (i[1] eq i[2] )}; Mran:=[Random(M22):i in [1..10]]; for i in Mran do if i in Mt then mtcont:=mtcont+1; end if; if i in Mf then mfcont:=mfcont+1; end if; if i in Mtf then mtfcont:=mtfcont+1; end if; end for; print(mtcont); print(mfcont); print(mtfcont); Output: Magma V2.10-6 Wed Mar 10 2004 10:48:39 on modular [Seed = 1904085400] ------------------------------------- 2 0 0 Total time: 3.459 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:49:05 2004 Input: mtcont:=0; mfcont:=0; mtfcont:=0; F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={i:i in M22| (Trace(i) eq 0) and (i[1] eq i[2] )}; Mran:=[Random(M22):i in [1..100000]]; for i in Mran do if i in Mt then mtcont:=mtcont+1; end if; if i in Mf then mfcont:=mfcont+1; end if; if i in Mtf then mtfcont:=mtfcont+1; end if; end for; print(mtcont); print(mfcont); print(mtfcont); Output: Magma V2.10-6 Wed Mar 10 2004 10:48:59 on modular [Seed = 1718165180] ------------------------------------- 24815 6159 1491 Total time: 5.009 seconds, Total memory usage: 7.09MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:49:24 2004 Input: mtcont:=0; mfcont:=0; mtfcont:=0; F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={i:i in M22| (Trace(i) eq 0) and (i[1] eq i[2] )}; Mran:=[Random(M22):i in [1..100000]]; for i in Mran do if i subset Mt then mtcont:=mtcont+1; end if; if i in Mf then mfcont:=mfcont+1; end if; if i in Mtf then mtfcont:=mtfcont+1; end if; end for; print(mtcont); print(mfcont); print(mtfcont); Output: Magma V2.10-6 Wed Mar 10 2004 10:49:20 on modular [Seed = 1482105193] ------------------------------------- >> if i subset Mt then mtcont:=mtcont+1; end if; ^ Runtime error in 'subset': Bad argument types Argument types given: AlgMatElt, SetEnum[AlgMatElt] 0 0 0 Total time: 3.399 seconds, Total memory usage: 7.09MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 10:49:37 2004 Input: mtcont:=0; mfcont:=0; mtfcont:=0; F:=GF(4); M22:=MatrixRing(F,2); Mt:={i:i in M22|Trace(i) eq 0}; Mf:={i:i in M22| i[1] eq i[2]}; Mtf:={i:i in M22| (Trace(i) eq 0) and (i[1] eq i[2] )}; Mran:=[Random(M22):i in [1..100000]]; for i in Mran do if i in Mt then mtcont:=mtcont+1; end if; if i in Mf then mfcont:=mfcont+1; end if; if i in Mtf then mtfcont:=mtfcont+1; end if; end for; print(mtcont); print(mfcont); print(mtfcont); Output: Magma V2.10-6 Wed Mar 10 2004 10:49:32 on modular [Seed = 1229336692] ------------------------------------- 25056 6422 1620 Total time: 3.949 seconds, Total memory usage: 7.09MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 11:08:05 2004 Input: t(7,3)(x); Output: Magma V2.10-6 Wed Mar 10 2004 11:08:01 on modular [Seed = 2138047021] ------------------------------------- >> t(7,3)(x); ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 11:13:54 2004 Input: polav:=function (q,r); KQR:=GF(q,r); punts:=[: a,b in KQR | Evaluate(n73,a) eq Evaluate(t73,b)]; return{punts}; end function; Output: Magma V2.10-6 Wed Mar 10 2004 11:13:50 on modular [Seed = 1851855075] ------------------------------------- >> punts:=[: a,b in KQR | Evaluate(n73,a) eq Evaluate(t73,b)]; ^ User error: bad syntax >> return{punts}; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 11:14:12 2004 Input: polav:=function (q,r); KQR:=GF(q,r); punts:=[ a,b in KQR | Evaluate(n73,a) eq Evaluate(t73,b)]; return{punts}; end function; Output: Magma V2.10-6 Wed Mar 10 2004 11:14:08 on modular [Seed = 1431972790] ------------------------------------- >> punts:=[ a,b in KQR | Evaluate(n73,a) eq Evaluate(t73,b)]; ^ User error: bad syntax >> return{punts}; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 11:49:53 2004 Input: f:=GF(7*7*7); n := n^(7*2+7*1+7*0); Output: Magma V2.10-6 Wed Mar 10 2004 11:49:49 on modular [Seed = 454302720] ------------------------------------- >> n := n^(7*2+7*1+7*0); ^ User error: Identifier 'n' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 11:51:04 2004 Input: F:=GF(7*7*7); n := alpha^(7*2+7*1+7*0); Output: Magma V2.10-6 Wed Mar 10 2004 11:51:00 on modular [Seed = 1801743401] ------------------------------------- Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 11:51:11 2004 Input: F:=GF(7*7*7); n := alpha^(7*2+7*1+7*0); Output: Magma V2.10-6 Wed Mar 10 2004 11:51:06 on modular [Seed = 1482120980] ------------------------------------- Total time: 3.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 11:51:31 2004 Input: F:=GF(7*7*7); n := alpha^(7*2+7*1+7*0); print(n); Output: Magma V2.10-6 Wed Mar 10 2004 11:51:27 on modular [Seed = 3149184002] ------------------------------------- alpha^21 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 11:51:59 2004 Input: F:=GF(7*7*7); n := alpha^(7^2+7^1+7^0); print(n); Output: Magma V2.10-6 Wed Mar 10 2004 11:51:55 on modular [Seed = 2493223689] ------------------------------------- 3 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 11:52:25 2004 Input: F:=GF(7*7*7); n := alpha^(7*7+7+7*0); print(n); Output: Magma V2.10-6 Wed Mar 10 2004 11:52:21 on modular [Seed = 2190312817] ------------------------------------- alpha^56 Total time: 3.379 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 11:53:51 2004 Input: F:=GF(7*7*7); n := alpha^(7*7+7+7*0); t := alpha^(7^2)+alpha^(7)+alpha print(n); Output: Magma V2.10-6 Wed Mar 10 2004 11:53:46 on modular [Seed = 3587890681] ------------------------------------- >> print(n); ^ User error: bad syntax Total time: 3.579 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 11:54:01 2004 Input: F:=GF(7*7*7); n := alpha^(7*7+7+7*0); t := alpha^(7^2)+alpha^(7)+alpha; print(n); Output: Magma V2.10-6 Wed Mar 10 2004 11:53:56 on modular [Seed = 3654734283] ------------------------------------- alpha^56 Total time: 3.409 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 11:54:15 2004 Input: F:=GF(7*7*7); n := alpha^(7*7+7+7*0); t := alpha^(7^2)+alpha^(7)+alpha; print(n); print(t); Output: Magma V2.10-6 Wed Mar 10 2004 11:54:11 on modular [Seed = 3368534221] ------------------------------------- alpha^56 1 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 11:54:37 2004 Input: F:=GF(7*7*7); n := alpha^(7*7+7+7*0); t := (alpha^(7^2))+(alpha^(7))+(alpha); print(n); print(t); Output: Magma V2.10-6 Wed Mar 10 2004 11:54:32 on modular [Seed = 606809179] ------------------------------------- alpha^56 1 Total time: 4.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 11:55:37 2004 Input: F:=GF(7*7*7); n := alpha^(7*7+7+7*0); t := alpha^49+alpha^7+alpha; print(n); print(t); Output: Magma V2.10-6 Wed Mar 10 2004 11:55:32 on modular [Seed = 251660220] ------------------------------------- alpha^56 1 Total time: 3.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 11:55:55 2004 Input: /*F:=GF(7*7*7);*/ n := alpha^(7*7+7+7*0); t := alpha^49+alpha^7+alpha; print(n); print(t); Output: Magma V2.10-6 Wed Mar 10 2004 11:55:49 on modular [Seed = 1920826064] ------------------------------------- >> n := alpha^(7*7+7+7*0); ^ User error: Identifier 'alpha' has not been declared or assigned >> t := alpha^49+alpha^7+alpha; ^ User error: Identifier 'alpha' has not been declared or assigned >> print(n); ^ User error: Identifier 'n' has not been declared or assigned >> print(t); ^ User error: Identifier 't' has not been declared or assigned Total time: 3.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 11:56:21 2004 Input: F:=GF(49*7); n := alpha^(7*7+7+7*0); t := alpha^49+alpha^7+alpha; print(n); print(t); Output: Magma V2.10-6 Wed Mar 10 2004 11:56:16 on modular [Seed = 1851877097] ------------------------------------- alpha^56 1 Total time: 3.569 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 11:56:31 2004 Input: F:=GF(49*7); n := alpha^(7*7+7+7*0); t := alpha^49; print(n); print(t); Output: Magma V2.10-6 Wed Mar 10 2004 11:56:27 on modular [Seed = 1599100883] ------------------------------------- alpha^56 alpha^49 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 11:56:48 2004 Input: F:=GF(49*7); n := alpha^(7*7+7+7*0); t := alpha^49+ alpha^7; print(n); print(t); Output: Magma V2.10-6 Wed Mar 10 2004 11:56:43 on modular [Seed = 1279476912] ------------------------------------- alpha^56 alpha^226 Total time: 3.099 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 11:57:02 2004 Input: F:=GF(49*7); n := alpha^(7*7+7+7*0); t := alpha^49 + alpha^7; print(n); print(t); Output: Magma V2.10-6 Wed Mar 10 2004 11:56:58 on modular [Seed = 3115757908] ------------------------------------- alpha^56 alpha^226 Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 11:57:28 2004 Input: F:=GF(49*7); n := alpha^(7*7+7+7*0); t := alpha^49; t += alpha^7; print(n); print(t); Output: Magma V2.10-6 Wed Mar 10 2004 11:57:24 on modular [Seed = 2626917471] ------------------------------------- >> t += alpha^7; ^ User error: bad syntax alpha^56 alpha^49 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 11:57:46 2004 Input: F:=GF(49*7); n := alpha^(7*7+7+7*0); t := alpha^49; t := t + alpha^7; print(n); print(t); Output: Magma V2.10-6 Wed Mar 10 2004 11:57:41 on modular [Seed = 2324005816] ------------------------------------- alpha^56 alpha^226 Total time: 3.299 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 11:58:12 2004 Input: F:=GF(49*7); n := alpha^(7*7+7+7*0); t := alpha^49; t := t + alpha^7; t := t + alpha; print(n); print(t); Output: Magma V2.10-6 Wed Mar 10 2004 11:58:08 on modular [Seed = 4210422765] ------------------------------------- alpha^56 1 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 11:58:45 2004 Input: F:=GF(49*7); n := x^(7*7+7+7*0); t := x^49; t := t + x^7; t := t + x; print(n); print(t); Output: Magma V2.10-6 Wed Mar 10 2004 11:58:40 on modular [Seed = 3504331175] ------------------------------------- x^56 1 Total time: 4.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 11:59:07 2004 Input: F:=GF(49*7); n := x^(7*7+7+1); t := x^49; t := t + x^7; t := t + x; print(n); print(t); Output: Magma V2.10-6 Wed Mar 10 2004 11:59:03 on modular [Seed = 3468806062] ------------------------------------- 3 1 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 11:59:29 2004 Input: F:=GF(49*7); n := x^(7*7); t := x^49; t := t + x^7; t := t + x; print(n); print(t); Output: Magma V2.10-6 Wed Mar 10 2004 11:59:24 on modular [Seed = 859585127] ------------------------------------- x^49 1 Total time: 3.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 11:59:52 2004 Input: F:=GF(49*7); n := x^(7*7); n := x^7; t := x^49; t := t + x^7; t := t + x; print(n); print(t); Output: Magma V2.10-6 Wed Mar 10 2004 11:59:48 on modular [Seed = 656944795] ------------------------------------- x^7 1 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 12:00:05 2004 Input: F:=GF(49*7); n := x^(7*7); n := n * x^7; t := x^49; t := t + x^7; t := t + x; print(n); print(t); Output: Magma V2.10-6 Wed Mar 10 2004 12:00:01 on modular [Seed = 251659942] ------------------------------------- x^56 1 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 12:00:38 2004 Input: F:=GF(49*7); n := x^(7*7); n := n * x^7; n := n * n; t := x^49; t := t + x^7; t := t + x; print(n); print(t); Output: Magma V2.10-6 Wed Mar 10 2004 12:00:34 on modular [Seed = 1954250238] ------------------------------------- x^112 1 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 12:01:00 2004 Input: F:=GF(49*7); n := x^(7*7); n := n * x^7; n := n * x; t := x^49; t := t + x^7; t := t + x; print(n); print(t); Output: Magma V2.10-6 Wed Mar 10 2004 12:00:56 on modular [Seed = 1668049555] ------------------------------------- 3 1 Total time: 3.379 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 12:01:23 2004 Input: F:=GF(7*7*7); n := x^(7*7); n := n * x^7; n := n * x; t := x^49; t := t + x^7; t := t + x; print(n); print(t); Output: Magma V2.10-6 Wed Mar 10 2004 12:01:19 on modular [Seed = 1195921056] ------------------------------------- 3 1 Total time: 3.489 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 10 12:03:48 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2-33); K := NumberField(x^2-21); MinimalPolynomial(a,b); Output: Magma V2.10-6 Wed Mar 10 2004 12:03:46 on modular [Seed = 4260558775] ------------------------------------- >> MinimalPolynomial(a,b); ^ Runtime error in 'MinimalPolynomial': Bad argument types Argument types given: FldNumElt, FldNumElt Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 10 12:04:03 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2-33); K := NumberField(x^2-21); MinimalPolynomial(a+b); Output: Magma V2.10-6 Wed Mar 10 2004 12:03:59 on modular [Seed = 3924222894] ------------------------------------- >> MinimalPolynomial(a+b); ^ Runtime error in '+': Arguments are not compatible Argument types given: FldNumElt, FldNumElt Total time: 3.279 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 12:10:00 2004 Input: F:=GF(7*7*7); n := x^(7*7); n := n * x^7; n := n * x; t := x^49; t := t + x^7; t := t + x; print(n); print(t); Output: Magma V2.10-6 Wed Mar 10 2004 12:09:55 on modular [Seed = 3048914543] ------------------------------------- 3 1 Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 12:10:17 2004 Input: F:=GF(7*7*7); n := x^(7*7); n := n * x^7; n := n +x; t := x^49; t := t + x^7; t := t + x; print(n); print(t); Output: Magma V2.10-6 Wed Mar 10 2004 12:10:13 on modular [Seed = 2459801950] ------------------------------------- x^2 1 Total time: 3.439 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 12:10:34 2004 Input: F:=GF(7*7*7); n := x^(7*7); n := n * x^7; n := n * x; t := x^49; t := t + x^7; t := t + x; print(n); print(t); Output: Magma V2.10-6 Wed Mar 10 2004 12:10:29 on modular [Seed = 2223737016] ------------------------------------- 3 1 Total time: 3.749 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 12:10:45 2004 Input: F:=GF(7*7*7*7); n := x^(7*7); n := n * x^7; n := n * x; t := x^49; t := t + x^7; t := t + x; print(n); print(t); Output: Magma V2.10-6 Wed Mar 10 2004 12:10:41 on modular [Seed = 3924223425] ------------------------------------- x^57 x^1543 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 12:11:16 2004 Input: F:=GF(7*7*7); n := x^(7*7); n := n * x^7; n := n * x; t := x^49; t := t + x^7; t := t + x; print(n); print(t); Output: Magma V2.10-6 Wed Mar 10 2004 12:11:11 on modular [Seed = 3452092891] ------------------------------------- 3 1 Total time: 3.449 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 12:11:30 2004 Input: F:=GF(7*7*7); n := x^(7*7); n := n * x^7; t := x^49; t := t + x^7; print(n); print(t); Output: Magma V2.10-6 Wed Mar 10 2004 12:11:26 on modular [Seed = 1009987640] ------------------------------------- x^56 x^226 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 12:11:52 2004 Input: n := x^(7*7); n := n * x^7; t := x^49; t := t + x^7; print(n); print(t); Output: Magma V2.10-6 Wed Mar 10 2004 12:11:47 on modular [Seed = 573386315] ------------------------------------- >> n := x^(7*7); ^ User error: Identifier 'x' has not been declared or assigned >> n := n * x^7; ^ User error: Identifier 'n' has not been declared or assigned >> t := x^49; ^ User error: Identifier 'x' has not been declared or assigned >> t := t + x^7; ^ User error: Identifier 't' has not been declared or assigned >> print(n); ^ User error: Identifier 'n' has not been declared or assigned >> print(t); ^ User error: Identifier 't' has not been declared or assigned Total time: 3.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 12:12:26 2004 Input: F := GF(7*7*7); n := x^(7*7); n := n * x^7; t := x^49; t := t + x^7; print(n); print(t); Output: Magma V2.10-6 Wed Mar 10 2004 12:12:21 on modular [Seed = 387455832] ------------------------------------- x^56 x^226 Total time: 3.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 12:14:11 2004 Input: P := PolinomialRing(GF(7*7*7); Output: Magma V2.10-6 Wed Mar 10 2004 12:14:07 on modular [Seed = 2965355605] ------------------------------------- >> P := PolinomialRing(GF(7*7*7); ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 12:14:22 2004 Input: P := PolinomialRing(GF(7*7*7)); Output: Magma V2.10-6 Wed Mar 10 2004 12:14:17 on modular [Seed = 2896404607] ------------------------------------- >> P := PolinomialRing(GF(7*7*7)); ^ User error: Identifier 'PolinomialRing' has not been declared or assigned Total time: 3.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 12:14:49 2004 Input: P := PolynomialRing(GF(7*7*7)); Output: Magma V2.10-6 Wed Mar 10 2004 12:14:45 on modular [Seed = 2459803565] ------------------------------------- Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 12:15:37 2004 Input: P := PolynomialRing(GF(7*7*7)); n := x^(7*7 + 7 + 1); print(n); Output: Magma V2.10-6 Wed Mar 10 2004 12:15:33 on modular [Seed = 4260557042] ------------------------------------- x^57 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 12:16:32 2004 Input: P := PolynomialRing(GF(7*7*7)); n := x^(7*7 + 7 + 1); t:= x^(7*7) + x^(7) + x; print(n); print(t); Output: Magma V2.10-6 Wed Mar 10 2004 12:16:26 on modular [Seed = 1043411823] ------------------------------------- x^57 x^49 + x^7 + x Total time: 4.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 12:18:08 2004 Input: [i : i in [1..100 by 7]]; P := PolynomialRing(GF(7*7*7)); n := x^(7*7 + 7 + 1); t:= x^(7*7) + x^(7) + x; print(n); print(t); Output: Magma V2.10-6 Wed Mar 10 2004 12:18:03 on modular [Seed = 1734896279] ------------------------------------- [ 1, 8, 15, 22, 29, 36, 43, 50, 57, 64, 71, 78, 85, 92, 99 ] x^57 x^49 + x^7 + x Total time: 4.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee128.uab.es. (158.109.66.128) Time: Wed Mar 10 12:18:27 2004 Input: [i : i in [1..100 by 7*i]]; P := PolynomialRing(GF(7*7*7)); n := x^(7*7 + 7 + 1); t:= x^(7*7) + x^(7) + x; print(n); print(t); Output: Magma V2.10-6 Wed Mar 10 2004 12:18:22 on modular [Seed = 1415272881] ------------------------------------- >> [i : i in [1..100 by 7*i]]; ^ Runtime error: Variable 'i' has not been initialized x^57 x^49 + x^7 + x Total time: 4.109 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 10 13:04:20 2004 Input: polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); //aparta v) polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; //apartat vi) puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(x^sum,b)}>; #(puntsOlav(7,3)); Output: Magma V2.10-6 Wed Mar 10 2004 13:04:16 on modular [Seed = 3132465755] ------------------------------------- [ 49, 7, 1 ] >> return x^sum; ^ User error: Identifier 'x' has not been declared or assigned >> pol:=pol+x^newlist[i]; ^ User error: Identifier 'x' has not been declared or assigned >> puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq E ^ User error: Identifier 'pol' has not been declared or assigned >> #(puntsOlav(7,3));; ^ User error: Identifier 'puntsOlav' has not been declared or assigned Total time: 3.859 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 10 13:04:55 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); //aparta v) polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; //apartat vi) puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(x^sum,b)}>; #(puntsOlav(7,3)); Output: Magma V2.10-6 Wed Mar 10 2004 13:04:52 on modular [Seed = 1365133783] ------------------------------------- [ 49, 7, 1 ] >> puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq E ^ User error: Identifier 'pol' has not been declared or assigned >> #(puntsOlav(7,3));; ^ User error: Identifier 'puntsOlav' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 10 13:05:45 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); //aparta v) polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; //apartat vi) puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(x^sum,b)}>; Output: Magma V2.10-6 Wed Mar 10 2004 13:05:42 on modular [Seed = 1887398084] ------------------------------------- [ 49, 7, 1 ] >> puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq E ^ User error: Identifier 'pol' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 10 13:06:22 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); //aparta v) polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; //apartat vi) /*puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(x^sum,b)}>;*/ Output: Magma V2.10-6 Wed Mar 10 2004 13:06:18 on modular [Seed = 84548701] ------------------------------------- [ 49, 7, 1 ] Total time: 3.759 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 10 13:08:48 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); //aparta v) polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; pol:=polinomit(7,3); print pol; //apartat vi) puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(x^sum,b)}>; Output: Magma V2.10-6 Wed Mar 10 2004 13:08:43 on modular [Seed = 1009984981] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x >> Evaluate(pol,a) eq Evaluate(x^sum,b)}>; ^ User error: Identifier 'sum' has not been declared or assigned Total time: 4.179 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 10 13:10:35 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); //aparta v) polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; xsum:=polinomin(7,3); print xsum; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; pol:=polinomit(7,3); print pol; //apartat vi) puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; Output: Magma V2.10-6 Wed Mar 10 2004 13:10:32 on modular [Seed = 2290586322] ------------------------------------- [ 49, 7, 1 ] x^57 x^49 + x^7 + x Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 10 13:11:36 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); //aparta v) polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; xsum:=polinomin(7,3); print xsum; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; pol:=polinomit(7,3); print pol; //apartat vi) puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; #(puntsOlav(7,3)); Output: Magma V2.10-6 Wed Mar 10 2004 13:11:29 on modular [Seed = 2812853684] ------------------------------------- [ 49, 7, 1 ] x^57 x^49 + x^7 + x 16807 Total time: 7.399 seconds, Total memory usage: 2.98MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 10 13:19:58 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); //aparta v) polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; xsum:=polinomin(7,3); print xsum; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; pol:=polinomit(7,3); print pol; //apartat vi) puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; #(puntsOlav(7,3)); exemples:=function(q,r) pol:=polinomit(q,r); xsum:=polinomin(q,r); #(puntsOlav(q,r)); print (q^(2*r-1)); end function; exemples(7,3); Output: Magma V2.10-6 Wed Mar 10 2004 13:19:47 on modular [Seed = 2946544559] ------------------------------------- [ 49, 7, 1 ] x^57 x^49 + x^7 + x 16807 16807 16807 >> exemples(7,3);; ^ Runtime error in procedure call: No return statement executed in user-defined function Total time: 10.679 seconds, Total memory usage: 2.98MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 10 13:20:43 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); //aparta v) polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; xsum:=polinomin(7,3); print xsum; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; pol:=polinomit(7,3); print pol; //apartat vi) puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; #(puntsOlav(7,3)); exemples:=function(q,r) pol:=polinomit(q,r); xsum:=polinomin(q,r); #(puntsOlav(q,r)); print (q^(2*r-1)); end function; exemples(7,3); print ("hola k tal"); Output: Magma V2.10-6 Wed Mar 10 2004 13:20:31 on modular [Seed = 1279479911] ------------------------------------- [ 49, 7, 1 ] x^57 x^49 + x^7 + x 16807 16807 16807 >> exemples(7,3); ^ Runtime error in procedure call: No return statement executed in user-defined function hola k tal Total time: 11.210 seconds, Total memory usage: 2.98MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 10 13:22:11 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); //aparta v) polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; xsum:=polinomin(7,3); print xsum; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; pol:=polinomit(7,3); print pol; //apartat vi) puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; #(puntsOlav(7,3)); exemples:=function(q,r) pol:=polinomit(q,r); xsum:=polinomin(q,r); print (q^(2*r-1)); return #(puntsOlav(q,r)); end function; exemples(7,3); print ("hola k tal"); Output: Magma V2.10-6 Wed Mar 10 2004 13:22:00 on modular [Seed = 234951298] ------------------------------------- [ 49, 7, 1 ] x^57 x^49 + x^7 + x 16807 16807 16807 hola k tal Total time: 11.130 seconds, Total memory usage: 2.98MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 10 13:29:56 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); //aparta v) polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; xsum:=polinomin(7,3); print xsum; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; pol:=polinomit(7,3); print pol; //apartat vi) puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; #(puntsOlav(7,3)); exemples:=function(q,r) pol:=polinomit(q,r); xsum:=polinomin(q,r); print ("hola k tal %d", q^(2*r-1)); return #(puntsOlav(q,r)); end function; exemples(7,3); print ("hola k tal",exemples(); Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed. ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 10 13:31:04 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); //aparta v) polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; xsum:=polinomin(7,3); print xsum; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; pol:=polinomit(7,3); print pol; //apartat vi) puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; #(puntsOlav(7,3)); exemples:=function(q,r) pol:=polinomit(q,r); xsum:=polinomin(q,r); print q^(2*r-1); return #(puntsOlav(q,r)); end function; exemples(7,3); print ("hola k tal",exemples(); Output: Magma V2.10-6 Wed Mar 10 2004 13:30:52 on modular [Seed = 3435385429] ------------------------------------- [ 49, 7, 1 ] x^57 x^49 + x^7 + x 16807 16807 16807 >> print ("hola k tal",exemples();; ^ User error: bad syntax Total time: 11.889 seconds, Total memory usage: 2.98MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 10 13:32:02 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); //aparta v) polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; xsum:=polinomin(7,3); print xsum; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; pol:=polinomit(7,3); print pol; //apartat vi) puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; #(puntsOlav(7,3)); exemples:=function(q,r) pol:=polinomit(q,r); xsum:=polinomin(q,r); print("q^(2*r-1) és igual a:"); print q^(2*r-1); return #(puntsOlav(q,r)); end function; exemples(7,3); print ("hola k tal",exemples(); Output: Magma V2.10-6 Wed Mar 10 2004 13:31:50 on modular [Seed = 3940939193] ------------------------------------- [ 49, 7, 1 ] x^57 x^49 + x^7 + x 16807 q^(2*r-1) és igual a: 16807 16807 >> print ("hola k tal",exemples();; ^ User error: bad syntax Total time: 11.559 seconds, Total memory usage: 2.98MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 10 13:33:11 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); //aparta v) polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; xsum:=polinomin(7,3); print xsum; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; pol:=polinomit(7,3); print pol; //apartat vi) puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; #(puntsOlav(7,3)); exemples:=function(q,r) pol:=polinomit(q,r); xsum:=polinomin(q,r); print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r)); end function; exemples(7,3); print ("hola k tal",exemples(); Output: Magma V2.10-6 Wed Mar 10 2004 13:32:59 on modular [Seed = 2660336000] ------------------------------------- [ 49, 7, 1 ] x^57 x^49 + x^7 + x 16807 q^(2*r-1) és igual a: 16807 El cardinal dels punts Olav en aquest exemple és: 16807 >> print ("hola k tal",exemples();; ^ User error: bad syntax Total time: 11.949 seconds, Total memory usage: 2.98MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 10 13:34:29 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); //aparta v) polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; xsum:=polinomin(7,3); print xsum; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; pol:=polinomit(7,3); print pol; //apartat vi) puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; #(puntsOlav(7,3)); exemples:=function(q,r) pol:=polinomit(q,r); xsum:=polinomin(q,r); print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r)); end function; exemples(7,3); exemples(5,4); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Wed Mar 10 2004 13:34:05 on modular [Seed = 3099043680] ------------------------------------- [ 49, 7, 1 ] x^57 x^49 + x^7 + x 16807 q^(2*r-1) és igual a: 16807 El cardinal dels punts Olav en aquest exemple és: 16807 q^(2*r-1) és igual a: 78125 El cardinal dels punts Olav en aquest exemple és: Errors: /home/mfd/gomagma: line 2: 1533 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 10 13:35:14 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); //aparta v) polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; xsum:=polinomin(7,3); print xsum; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; pol:=polinomit(7,3); print pol; //apartat vi) puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; #(puntsOlav(7,3)); exemples:=function(q,r) pol:=polinomit(q,r); xsum:=polinomin(q,r); print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r)); end function; exemples(5,3); Output: Magma V2.10-6 Wed Mar 10 2004 13:35:06 on modular [Seed = 1701477113] ------------------------------------- [ 49, 7, 1 ] x^57 x^49 + x^7 + x 16807 q^(2*r-1) és igual a: 3125 El cardinal dels punts Olav en aquest exemple és: 125 Total time: 7.839 seconds, Total memory usage: 2.98MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 10 13:37:40 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); //aparta v) polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; //apartat vi) puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; #(puntsOlav(7,3)); exemples:=function(q,r) pol:=polinomit(q,r); xsum:=polinomin(q,r); print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r)); end function; exemples(5,3); Output: Magma V2.10-6 Wed Mar 10 2004 13:37:37 on modular [Seed = 926422784] ------------------------------------- [ 49, 7, 1 ] >> puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq E ^ User error: Identifier 'pol' has not been declared or assigned >> #(puntsOlav(7,3)); ^ User error: Identifier 'puntsOlav' has not been declared or assigned >> return #(puntsOlav(q,r)); ^ User error: Identifier 'puntsOlav' has not been declared or assigned >> exemples(5,3); ^ User error: Identifier 'exemples' has not been declared or assigned Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 10 13:39:13 2004 Input: R:=Integers(); P:=PolynomialRing(R); pol:=0; xsum:=0; polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); //aparta v) polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; //apartat vi) puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; #(puntsOlav(7,3)); exemples:=function(q,r) pol:=polinomit(q,r); xsum:=polinomin(q,r); print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r)); end function; exemples(5,3); Output: Magma V2.10-6 Wed Mar 10 2004 13:39:09 on modular [Seed = 4007775845] ------------------------------------- [ 49, 7, 1 ] [
:32]( q: 7, r: 3 ) >> puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq E ^ Runtime error in 'Evaluate': Bad argument types Argument types given: RngIntElt, FldFinElt q^(2*r-1) és igual a: 3125 El cardinal dels punts Olav en aquest exemple és: [
:34]( q: 5, r: 3 ) [
:32]( q: 5, r: 3 ) >> puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq E ^ Runtime error in 'Evaluate': Bad argument types Argument types given: RngIntElt, FldFinElt Total time: 4.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 10 13:40:23 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); //aparta v) polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; //apartat vi) pol:=0; xsum:=0; puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; #(puntsOlav(7,3)); exemples:=function(q,r) pol:=polinomit(q,r); xsum:=polinomin(q,r); print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r)); end function; exemples(5,3); Output: Magma V2.10-6 Wed Mar 10 2004 13:40:20 on modular [Seed = 2443096259] ------------------------------------- [ 49, 7, 1 ] [
:32]( q: 7, r: 3 ) >> puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq E ^ Runtime error in 'Evaluate': Bad argument types Argument types given: RngIntElt, FldFinElt q^(2*r-1) és igual a: 3125 El cardinal dels punts Olav en aquest exemple és: [
:34]( q: 5, r: 3 ) [
:32]( q: 5, r: 3 ) >> puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq E ^ Runtime error in 'Evaluate': Bad argument types Argument types given: RngIntElt, FldFinElt Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 10 13:41:07 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); //aparta v) polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; //apartat vi) pol:=polinomit(5,3); xsum:=polinomin(5,3); puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; #(puntsOlav(7,3)); exemples:=function(q,r) pol:=polinomit(q,r); xsum:=polinomin(q,r); print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r)); end function; exemples(5,3); Output: Magma V2.10-6 Wed Mar 10 2004 13:41:00 on modular [Seed = 3199311812] ------------------------------------- [ 49, 7, 1 ] 343 q^(2*r-1) és igual a: 3125 El cardinal dels punts Olav en aquest exemple és: 3125 Total time: 6.369 seconds, Total memory usage: 2.13MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 10 13:42:31 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); //aparta v) polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; //apartat vi) pol:=polinomit(5,3); xsum:=polinomin(5,3); puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; #(puntsOlav(7,3)); exemples:=function(q,r) pol:=polinomit(q,r); xsum:=polinomin(q,r); print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r)); end function; exemples(4,3); Output: Magma V2.10-6 Wed Mar 10 2004 13:42:24 on modular [Seed = 1887392167] ------------------------------------- [ 49, 7, 1 ] 343 q^(2*r-1) és igual a: 1024 El cardinal dels punts Olav en aquest exemple és: [
:34]( q: 4, r: 3 ) [
:32]( q: 4, r: 3 ) >> puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq E ^ Runtime error in 'GF': Argument 1 (4) should be prime Total time: 6.379 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 10 13:43:05 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); //aparta v) polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; //apartat vi) pol:=polinomit(4,3); xsum:=polinomin(4,3); puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; #(puntsOlav(7,3)); exemples:=function(q,r) pol:=polinomit(q,r); xsum:=polinomin(q,r); print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r)); end function; exemples(4,3); Output: Magma V2.10-6 Wed Mar 10 2004 13:43:00 on modular [Seed = 134687227] ------------------------------------- [ 49, 7, 1 ] 295 q^(2*r-1) és igual a: 1024 El cardinal dels punts Olav en aquest exemple és: [
:34]( q: 4, r: 3 ) [
:32]( q: 4, r: 3 ) >> puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq E ^ Runtime error in 'GF': Argument 1 (4) should be prime Total time: 4.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 10 13:44:21 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; //aparta v) polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; //apartat vi) pol:=polinomit(4,3); xsum:=polinomin(4,3); puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; #(puntsOlav(7,3)); exemples:=function(q,r) pol:=polinomit(q,r); xsum:=polinomin(q,r); print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r)); end function; exemples(4,3); Output: Magma V2.10-6 Wed Mar 10 2004 13:44:15 on modular [Seed = 976558978] ------------------------------------- 295 q^(2*r-1) és igual a: 1024 El cardinal dels punts Olav en aquest exemple és: [
:33]( q: 4, r: 3 ) [
:31]( q: 4, r: 3 ) >> puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq E ^ Runtime error in 'GF': Argument 1 (4) should be prime Total time: 5.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 10 13:45:21 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; //aparta v) polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; //apartat vi) pol:=polinomit(4,3); xsum:=polinomin(4,3); puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; exemples:=function(q,r) pol:=polinomit(q,r); xsum:=polinomin(q,r); print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r)); end function; exemples(4,3); Output: Magma V2.10-6 Wed Mar 10 2004 13:45:18 on modular [Seed = 3807232155] ------------------------------------- q^(2*r-1) és igual a: 1024 El cardinal dels punts Olav en aquest exemple és: [
:32]( q: 4, r: 3 ) [
:31]( q: 4, r: 3 ) >> puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq E ^ Runtime error in 'GF': Argument 1 (4) should be prime Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 10 13:46:38 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; //aparta v) polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; //apartat vi) pol:=polinomit(4,3); xsum:=polinomin(4,3); puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; #puntsOlav(4,3); print(q^(2*r-1); /*exemples:=function(q,r) pol:=polinomit(q,r); xsum:=polinomin(q,r); print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r)); end function; exemples(4,3); */ Output: Magma V2.10-6 Wed Mar 10 2004 13:46:34 on modular [Seed = 2643640144] ------------------------------------- [
:31]( q: 4, r: 3 ) >> puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq E ^ Runtime error in 'GF': Argument 1 (4) should be prime >> print(q^(2*r-1); ^ User error: bad syntax Total time: 3.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 10 13:47:55 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; //aparta v) polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; //apartat vi) pol:=polinomit(11,3); xsum:=polinomin(11,3); puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; #puntsOlav(11,3); print(q^(2*r-1); /*exemples:=function(q,r) pol:=polinomit(q,r); xsum:=polinomin(q,r); print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r)); end function; exemples(4,3); */ Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Wed Mar 10 2004 13:47:31 on modular [Seed = 3165888056] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 2043 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 10 13:48:27 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; //aparta v) polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; //apartat vi) pol:=polinomit(1,3); xsum:=polinomin(1,3); puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; #puntsOlav(1,3); print(q^(2*r-1); /*exemples:=function(q,r) pol:=polinomit(q,r); xsum:=polinomin(q,r); print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r)); end function; exemples(4,3); */ Output: Magma V2.10-6 Wed Mar 10 2004 13:48:23 on modular [Seed = 1734886872] ------------------------------------- [
:31]( q: 1, r: 3 ) >> puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq E ^ Runtime error in 'GF': Argument 1 (1) should be >= 2 >> print(q^(2*r-1); ^ User error: bad syntax Total time: 3.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 10 13:49:00 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; //aparta v) polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; //apartat vi) pol:=polinomit(2,3); xsum:=polinomin(2,3); puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; #puntsOlav(1,3); print(q^(2*r-1); /*exemples:=function(q,r) pol:=polinomit(q,r); xsum:=polinomin(q,r); print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r)); end function; exemples(4,3); */ Output: Magma V2.10-6 Wed Mar 10 2004 13:48:56 on modular [Seed = 218246749] ------------------------------------- [
:31]( q: 1, r: 3 ) >> puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq E ^ Runtime error in 'GF': Argument 1 (1) should be >= 2 >> print(q^(2*r-1); ^ User error: bad syntax Total time: 3.219 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 10 13:49:22 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; //aparta v) polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; //apartat vi) pol:=polinomit(2,3); xsum:=polinomin(2,3); puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; #puntsOlav(2,3); print(q^(2*r-1); /*exemples:=function(q,r) pol:=polinomit(q,r); xsum:=polinomin(q,r); print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r)); end function; exemples(4,3); */ Output: Magma V2.10-6 Wed Mar 10 2004 13:49:18 on modular [Seed = 287191671] ------------------------------------- 32 >> print(q^(2*r-1); ^ User error: bad syntax Total time: 3.479 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 10 13:49:45 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; //aparta v) polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; //apartat vi) pol:=polinomit(2,3); xsum:=polinomin(2,3); puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; #puntsOlav(2,3); print(q^(2*r-1)); /*exemples:=function(q,r) pol:=polinomit(q,r); xsum:=polinomin(q,r); print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r)); end function; exemples(4,3); */ Output: Magma V2.10-6 Wed Mar 10 2004 13:49:41 on modular [Seed = 993269814] ------------------------------------- 32 >> print(q^(2*r-1)); ^ User error: Identifier 'q' has not been declared or assigned Total time: 3.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 10 13:50:32 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; //aparta v) polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; //apartat vi) pol:=polinomit(2,3); xsum:=polinomin(2,3); puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; #puntsOlav(2,3); print(2^(2*3-1)); /*exemples:=function(q,r) pol:=polinomit(q,r); xsum:=polinomin(q,r); print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r)); end function; exemples(4,3); */ Output: Magma V2.10-6 Wed Mar 10 2004 13:50:28 on modular [Seed = 3890791643] ------------------------------------- 32 32 Total time: 4.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 10 13:56:49 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; //aparta v) polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; //apartat vi) pol:=polinomit(2,3); xsum:=polinomin(2,3); puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; #puntsOlav(2,3); print(q^(2*r-1)); exemples:=function(q,r) pol:=polinomit(q,r); xsum:=polinomin(q,r); print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r,pol,xsum)); end function; exemples(2,3); Output: Magma V2.10-6 Wed Mar 10 2004 13:56:46 on modular [Seed = 51128228] ------------------------------------- >> #puntsOlav(2,3); ^ Runtime error: Number of arguments (2) does not equal expected number of arguments (4) >> print(q^(2*r-1)); ^ User error: Identifier 'q' has not been declared or assigned q^(2*r-1) és igual a: 32 El cardinal dels punts Olav en aquest exemple és: 32 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 10 13:57:19 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; //aparta v) polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; //apartat vi) pol:=polinomit(2,3); xsum:=polinomin(2,3); puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; //#puntsOlav(2,3); print(q^(2*r-1)); exemples:=function(q,r) pol:=polinomit(q,r); xsum:=polinomin(q,r); print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r,pol,xsum)); end function; exemples(2,3); Output: Magma V2.10-6 Wed Mar 10 2004 13:57:16 on modular [Seed = 270480725] ------------------------------------- >> print(q^(2*r-1)); ^ User error: Identifier 'q' has not been declared or assigned q^(2*r-1) és igual a: 32 El cardinal dels punts Olav en aquest exemple és: 32 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 10 13:58:05 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; //aparta v) polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; //apartat vi) pol:=polinomit(2,3); xsum:=polinomin(2,3); puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; //#puntsOlav(2,3); //print(q^(2*r-1)); exemples:=function(q,r) pol:=polinomit(q,r); xsum:=polinomin(q,r); print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r,pol,xsum)); end function; exemples(2,3); Output: Magma V2.10-6 Wed Mar 10 2004 13:58:01 on modular [Seed = 573376338] ------------------------------------- q^(2*r-1) és igual a: 32 El cardinal dels punts Olav en aquest exemple és: 32 Total time: 4.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 10 14:00:44 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; //aparta v) polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; //apartat vi) pol:=polinomit(2,3); xsum:=polinomin(2,3); puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; //#puntsOlav(2,3); //print(q^(2*r-1)); exemples:=function(q,r) pol:=polinomit(q,r); xsum:=polinomin(q,r); print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r,pol,xsum)); end function; exemples(2,3); exemples(3,3); exemples(5,3); exemples(3,4); exemples(2,4); Output: Magma V2.10-6 Wed Mar 10 2004 14:00:39 on modular [Seed = 2390862608] ------------------------------------- q^(2*r-1) és igual a: 32 El cardinal dels punts Olav en aquest exemple és: 32 q^(2*r-1) és igual a: 243 El cardinal dels punts Olav en aquest exemple és: 243 q^(2*r-1) és igual a: 3125 El cardinal dels punts Olav en aquest exemple és: 3125 q^(2*r-1) és igual a: 2187 El cardinal dels punts Olav en aquest exemple és: 2187 q^(2*r-1) és igual a: 128 El cardinal dels punts Olav en aquest exemple és: 128 Total time: 4.579 seconds, Total memory usage: 2.13MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 10 14:04:50 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; //aparta v) polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; //apartat vi) pol:=polinomit(2,3); xsum:=polinomin(2,3); puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; //#puntsOlav(2,3); //print(q^(2*r-1)); exemples:=function(q,r) pol:=polinomit(q,r); xsum:=polinomin(q,r); print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r,pol,xsum)); end function; exemples(2,3); puntsOlav(2,3,polinomit(2,3),polinomin(2,3)); Output: Magma V2.10-6 Wed Mar 10 2004 14:04:47 on modular [Seed = 471022233] ------------------------------------- q^(2*r-1) és igual a: 32 El cardinal dels punts Olav en aquest exemple és: 32 { <1, $.1^4>, <$.1^3, $.1^3>, <$.1^3, $.1^6>, <$.1^6, 1>, <$.1^6, $.1^2>, <1, $.1>, <$.1^5, 1>, <$.1^6, $.1^3>, <$.1^3, $.1^2>, <1, $.1^3>, <1, $.1^2>, <$.1^3, $.1^5>, <$.1, 0>, <0, 0>, <$.1^6, $.1^4>, <$.1^5, $.1^5>, <$.1^3, 1>, <1, $.1^5>, <$.1^5, $.1>, <$.1^5, $.1^4>, <$.1^6, $.1>, <$.1^3, $.1^4>, <1, 1>, <$.1^5, $.1^2>, <$.1^6, $.1^5>, <$.1^5, $.1^6>, <$.1^3, $.1>, <1, $.1^6>, <$.1^5, $.1^3>, <$.1^6, $.1^6>, <$.1^2, 0>, <$.1^4, 0> } Total time: 3.159 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 10 14:06:53 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; //aparta v) polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; //apartat vi) pol:=polinomit(2,3); xsum:=polinomin(2,3); puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; //#puntsOlav(2,3); //print(q^(2*r-1)); exemples:=function(q,r) pol:=polinomit(q,r); xsum:=polinomin(q,r); print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r,pol,xsum)); end function; exemples(2,3); puntsOlav2:=func: a in GF(q,r), b in GF(q,r), a in GF(q), b in GF(q)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; #(puntsOlav2(2,3,polinomit(2,3),polinomin(2,3)))); Output: Magma V2.10-6 Wed Mar 10 2004 14:06:51 on modular [Seed = 3704880093] ------------------------------------- q^(2*r-1) és igual a: 32 El cardinal dels punts Olav en aquest exemple és: 32 >> #(puntsOlav2(2,3,polinomit(2,3),polinomin(2,3)))); ^ User error: bad syntax Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 10 14:07:20 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; //aparta v) polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; //apartat vi) pol:=polinomit(2,3); xsum:=polinomin(2,3); puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; //#puntsOlav(2,3); //print(q^(2*r-1)); exemples:=function(q,r) pol:=polinomit(q,r); xsum:=polinomin(q,r); print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r,pol,xsum)); end function; exemples(2,3); puntsOlav2:=func: a in GF(q,r), b in GF(q,r), a in GF(q), b in GF(q)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; #(puntsOlav2(2,3,polinomit(2,3),polinomin(2,3))); Output: Magma V2.10-6 Wed Mar 10 2004 14:07:16 on modular [Seed = 3807233484] ------------------------------------- q^(2*r-1) és igual a: 32 El cardinal dels punts Olav en aquest exemple és: 32 32 Total time: 3.549 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 10 14:08:04 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; //aparta v) polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; //apartat vi) pol:=polinomit(2,3); xsum:=polinomin(2,3); puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; //#puntsOlav(2,3); //print(q^(2*r-1)); exemples:=function(q,r) pol:=polinomit(q,r); xsum:=polinomin(q,r); print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r,pol,xsum)); end function; exemples(5,3); puntsOlav2:=func: a in GF(q,r), b in GF(q,r), a in GF(q), b in GF(q)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; #(puntsOlav2(5,3,polinomit(5,3),polinomin(5,3))); Output: Magma V2.10-6 Wed Mar 10 2004 14:07:52 on modular [Seed = 2324016456] ------------------------------------- q^(2*r-1) és igual a: 3125 El cardinal dels punts Olav en aquest exemple és: 3125 3125 Total time: 11.949 seconds, Total memory usage: 2.13MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Wed Mar 10 14:16:25 2004 Input: A2:=AffinePlane(Rationals()); P2:=ProjectivePlane(Rationals()); f13:=CanonicalModularPolynomial(13); f13; C13:=Curve(A2,f13); C,f:=Conic(ProjectiveClosure(C13)); CoordinateRing(P2)!DefiningPolynomial(C); Output: Magma V2.10-6 Wed Mar 10 2004 14:16:21 on modular [Seed = 3554474526] ------------------------------------- $.1^14 + 26*$.1^13 + 325*$.1^12 + 2548*$.1^11 + 13832*$.1^10 + 54340*$.1^9 + 157118*$.1^8 + 333580*$.1^7 + 509366*$.1^6 + 534820*$.1^5 + 354536*$.1^4 + 124852*$.1^3 + 15145*$.1^2 - $.1*$.2 + 746*$.1 + 13 -X*Z + Y^2 Total time: 2.949 seconds, Total memory usage: 2.54MB ************** MAGMA ***************** Host B56-46.DAS.McGill.CA. (198.168.182.198) Time: Wed Mar 10 14:25:33 2004 Input: p := NextPrime(10); Output: Magma V2.10-6 Wed Mar 10 2004 14:25:30 on modular [Seed = 3907502862] ------------------------------------- Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host B56-46.DAS.McGill.CA. (198.168.182.198) Time: Wed Mar 10 14:27:34 2004 Input: for k in [1..4] do printf "Found curve"; end for; Output: Magma V2.10-6 Wed Mar 10 2004 14:27:31 on modular [Seed = 2476523516] ------------------------------------- Found curveFound curveFound curveFound curve Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host B56-31.DAS.McGill.CA. (198.168.182.183) Time: Wed Mar 10 15:54:38 2004 Input: 2+2 Output: Magma V2.10-6 Wed Mar 10 2004 15:54:34 on modular [Seed = 1498847627] ------------------------------------- 4 Total time: 3.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host B56-31.DAS.McGill.CA. (198.168.182.183) Time: Wed Mar 10 15:55:44 2004 Input: 1 eq 3 Output: Magma V2.10-6 Wed Mar 10 2004 15:55:40 on modular [Seed = 1701488113] ------------------------------------- false Total time: 4.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host B56-31.DAS.McGill.CA. (198.168.182.183) Time: Wed Mar 10 15:56:20 2004 Input: 1 eq 3 Output: Magma V2.10-6 Wed Mar 10 2004 15:56:17 on modular [Seed = 234999463] ------------------------------------- false Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host TORQUE-WRENCH.MIT.EDU. (18.54.0.43) Time: Wed Mar 10 19:04:08 2004 Input: ClassGroup(QuadraticField(9699690)); Output: Magma V2.10-6 Wed Mar 10 2004 19:03:54 on modular [Seed = 2390843914] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 Defined on 6 generators Relations: 2*$.1 = 0 2*$.2 = 0 2*$.3 = 0 2*$.4 = 0 2*$.5 = 0 2*$.6 = 0 Mapping from: Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 Defined on 6 generators Relations: 2*$.1 = 0 2*$.2 = 0 2*$.3 = 0 2*$.4 = 0 2*$.5 = 0 2*$.6 = 0 to Set of ideals of Maximal Equation Order of Quadratic Field with defining polynomial $.1^2 - 9699690 over the Rational Field Total time: 13.549 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host n137.ryd.student.liu.se. (130.236.215.137) Time: Wed Mar 10 19:18:43 2004 Input: A:=253137311381033656585177539690984821119631218749378041980953813630048326765616065486601771316; B:=940698877581438960056503716535395648160090395543493255756019150339533797393313982650950218415; p:=2264235845763803646877911845142004517489; E:=ChangeRing(EllipticCurve([A,B]),GF(p)); print(E); go:=Order(E); Factorization(go); Output: Magma V2.10-6 Wed Mar 10 2004 19:18:33 on modular [Seed = 1868603206] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 23739840206235062827123765248367137923*x + 599530237426612075286906583731523238660 over GF(2264235845763803646877911845142004517489) [ <2, 5>, <3, 2>, <11, 1>, <23, 1>, <89, 1>, <457, 1>, <1823, 1>, <4231, 1>, <7621, 1>, <66569, 1>, <346867, 1>, <562892903, 1> ] Total time: 9.449 seconds, Total memory usage: 3.11MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Wed Mar 10 20:36:59 2004 Input: Q := QuadraticField(-23); // arbitrary choice Q := QuadraticForms(Discriminant(Q)); C, m := ClassGroup(Q); C; Output: Magma V2.10-6 Wed Mar 10 2004 20:36:56 on modular [Seed = 773958895] ------------------------------------- Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*C.1 = 0 Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (133.71.38.72) Time: Wed Mar 10 21:47:30 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Wed Mar 10 2004 21:47:25 on modular [Seed = 3015450865] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 4.099 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Wed Mar 10 21:49:31 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^4-34*x^2+9); OK := MaximalOrder(K); Output: Magma V2.10-6 Wed Mar 10 2004 21:49:28 on modular [Seed = 287212201] ------------------------------------- Total time: 3.039 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Wed Mar 10 21:49:51 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3-x+2); OK := MaximalOrder(K); OK; Output: Magma V2.10-6 Wed Mar 10 2004 21:49:48 on modular [Seed = 656979179] ------------------------------------- Maximal Equation Order with defining polynomial x^3 - x + 2 over its ground order Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Wed Mar 10 21:52:19 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3-x+2); OK := MaximalOrder(K); Discriminant(OK); Output: Magma V2.10-6 Wed Mar 10 2004 21:52:16 on modular [Seed = 1887429648] ------------------------------------- -104 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam189-147.student.harvard.edu. (140.247.189.147) Time: Wed Mar 10 23:57:29 2004 Input: P:=PolynomialRing(RationalField()); N:=NumberField(x^2-x+2); MinimalPolynomial(1/2+1/2*w); MinimalPolynomial(1/2+1/2*w+1/2*w^2); MinimalPolynomial(1/2+1/2*w^2); MinimalPolynomial(1/2*w); MinimalPolynomial(1/2*w+1/2*w^2); MinimalPolynomial(1/2*w^2); Output: Magma V2.10-6 Wed Mar 10 2004 23:57:25 on modular [Seed = 1920844759] ------------------------------------- >> MinimalPolynomial(1/2+1/2*w); ^ User error: Identifier 'w' has not been declared or assigned >> MinimalPolynomial(1/2+1/2*w+1/2*w^2); ^ User error: Identifier 'w' has not been declared or assigned >> MinimalPolynomial(1/2+1/2*w^2); ^ User error: Identifier 'w' has not been declared or assigned >> MinimalPolynomial(1/2*w); ^ User error: Identifier 'w' has not been declared or assigned >> MinimalPolynomial(1/2*w+1/2*w^2); ^ User error: Identifier 'w' has not been declared or assigned >> MinimalPolynomial(1/2*w^2);; ^ User error: Identifier 'w' has not been declared or assigned Total time: 3.769 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam189-147.student.harvard.edu. (140.247.189.147) Time: Wed Mar 10 23:57:41 2004 Input: P:=PolynomialRing(RationalField()); N:=NumberField(x^2-x+2); MinimalPolynomial(1/2+1/2*w); MinimalPolynomial(1/2+1/2*w+1/2*w^2); MinimalPolynomial(1/2+1/2*w^2); MinimalPolynomial(1/2*w); MinimalPolynomial(1/2*w+1/2*w^2); MinimalPolynomial(1/2*w^2); Output: Magma V2.10-6 Wed Mar 10 2004 23:57:38 on modular [Seed = 1634652339] ------------------------------------- x^2 - 3/2*x + 1 x^2 + 7/4 x^2 + 1/2*x + 1/2 x^2 - 1/2*x + 1/2 x^2 + x + 2 x^2 + 3/2*x + 1 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam189-147.student.harvard.edu. (140.247.189.147) Time: Wed Mar 10 23:58:35 2004 Input: P:=PolynomialRing(RationalField()); N:=NumberField(x^2-x+2); MinimalPolynomial(1/2+1/2*w); MinimalPolynomial(1/2+1/2*w+1/2*w^2); MinimalPolynomial(1/2+1/2*w^2); MinimalPolynomial(1/2*w); MinimalPolynomial(1/2*w+1/2*w^2); MinimalPolynomial(1/2*w^2); Output: Magma V2.10-6 Wed Mar 10 2004 23:58:31 on modular [Seed = 2493195635] ------------------------------------- x^2 - 3/2*x + 1 x^2 + 7/4 x^2 + 1/2*x + 1/2 x^2 - 1/2*x + 1/2 x^2 + x + 2 x^2 + 3/2*x + 1 Total time: 3.779 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam189-147.student.harvard.edu. (140.247.189.147) Time: Wed Mar 10 23:58:57 2004 Input: P:=PolynomialRing(RationalField()); N:=NumberField(x^3-x+2); MinimalPolynomial(1/2+1/2*w); MinimalPolynomial(1/2+1/2*w+1/2*w^2); MinimalPolynomial(1/2+1/2*w^2); MinimalPolynomial(1/2*w); MinimalPolynomial(1/2*w+1/2*w^2); MinimalPolynomial(1/2*w^2); Output: Magma V2.10-6 Wed Mar 10 2004 23:58:54 on modular [Seed = 2257138840] ------------------------------------- x^3 - 3/2*x^2 + 1/2*x + 1/4 x^3 - 5/2*x^2 + 13/4*x - 13/8 x^3 - 5/2*x^2 + 2*x - 1 x^3 - 1/4*x + 1/4 x^3 - x^2 + 3/2*x - 1/2 x^3 - x^2 + 1/4*x - 1/2 Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host gb1000.math.kyushu-u.ac.jp. (133.5.165.4) Time: Thu Mar 11 01:34:58 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Thu Mar 11 2004 01:34:54 on modular [Seed = 3807554165] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Thu Mar 11 01:58:40 2004 Input: E:=EllipticCurveWithjInvariant(903792); Output: Magma V2.10-6 Thu Mar 11 2004 01:58:36 on modular [Seed = 1163201349] ------------------------------------- Total time: 3.679 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Thu Mar 11 01:58:56 2004 Input: E:=EllipticCurveWithjInvariant(903792); E; Output: Magma V2.10-6 Thu Mar 11 2004 01:58:53 on modular [Seed = 1952725573] ------------------------------------- Elliptic Curve defined by y^2 + x*y = x^3 - 3/75172*x - 1/902064 over Rational Field Total time: 3.669 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.31) Time: Thu Mar 11 02:23:57 2004 Input: dias := { x : x in {4..366 by 7}}; dias; Output: Magma V2.10-6 Thu Mar 11 2004 02:23:54 on modular [Seed = 3942301438] ------------------------------------- { 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 } Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.31) Time: Thu Mar 11 02:28:13 2004 Input: M := MatrixRing(GF(4),2); Mt := {A : A in M | Trace(A) eq 0}; Mt; Output: Magma V2.10-6 Thu Mar 11 2004 02:28:09 on modular [Seed = 2104305771] ------------------------------------- { [ 0 0] [ 0 0], [ 0 0] [$.1^2 0], [ 0 0] [ $.1 0], [ 0 0] [ 1 0], [$.1^2 0] [ 0 $.1^2], [$.1^2 0] [$.1^2 $.1^2], [$.1^2 0] [ $.1 $.1^2], [$.1^2 0] [ 1 $.1^2], [ 1 0] [ 0 1], [ 1 0] [$.1^2 1], [ 1 0] [ $.1 1], [ 1 0] [ 1 1], [ $.1 0] [ 0 $.1], [ $.1 0] [$.1^2 $.1], [ $.1 0] [ $.1 $.1], [ $.1 0] [ 1 $.1], [ 0 $.1^2] [ 0 0], [ 0 $.1^2] [$.1^2 0], [ 0 $.1^2] [ $.1 0], [ 0 $.1^2] [ 1 0], [$.1^2 $.1^2] [ 0 $.1^2], [$.1^2 $.1^2] [$.1^2 $.1^2], [$.1^2 $.1^2] [ $.1 $.1^2], [$.1^2 $.1^2] [ 1 $.1^2], [ 1 $.1^2] [ 0 1], [ 1 $.1^2] [$.1^2 1], [ 1 $.1^2] [ $.1 1], [ 1 $.1^2] [ 1 1], [ $.1 $.1^2] [ 0 $.1], [ $.1 $.1^2] [$.1^2 $.1], [ $.1 $.1^2] [ $.1 $.1], [ $.1 $.1^2] [ 1 $.1], [ 0 $.1] [ 0 0], [ 0 $.1] [$.1^2 0], [ 0 $.1] [ $.1 0], [ 0 $.1] [ 1 0], [$.1^2 $.1] [ 0 $.1^2], [$.1^2 $.1] [$.1^2 $.1^2], [$.1^2 $.1] [ $.1 $.1^2], [$.1^2 $.1] [ 1 $.1^2], [ 1 $.1] [ 0 1], [ 1 $.1] [$.1^2 1], [ 1 $.1] [ $.1 1], [ 1 $.1] [ 1 1], [ $.1 $.1] [ 0 $.1], [ $.1 $.1] [$.1^2 $.1], [ $.1 $.1] [ $.1 $.1], [ $.1 $.1] [ 1 $.1], [ 0 1] [ 0 0], [ 0 1] [$.1^2 0], [ 0 1] [ $.1 0], [ 0 1] [ 1 0], [$.1^2 1] [ 0 $.1^2], [$.1^2 1] [$.1^2 $.1^2], [$.1^2 1] [ $.1 $.1^2], [$.1^2 1] [ 1 $.1^2], [ 1 1] [ 0 1], [ 1 1] [$.1^2 1], [ 1 1] [ $.1 1], [ 1 1] [ 1 1], [ $.1 1] [ 0 $.1], [ $.1 1] [$.1^2 $.1], [ $.1 1] [ $.1 $.1], [ $.1 1] [ 1 $.1] } Total time: 3.059 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.31) Time: Thu Mar 11 02:29:49 2004 Input: M := MatrixRing(GF(4),2); Mt := {A : A in M | Trace(A) eq 0}; Mf := {A : A in M | A[1] eq A[2]}; Mtf := Mt meet Mf; Mtf; Output: Magma V2.10-6 Thu Mar 11 2004 02:29:46 on modular [Seed = 3470695355] ------------------------------------- { [ 0 0] [ 0 0], [$.1^2 $.1^2] [$.1^2 $.1^2], [ $.1 $.1] [ $.1 $.1], [ 1 1] [ 1 1] } Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.31) Time: Thu Mar 11 02:31:49 2004 Input: M := MatrixRing(GF(4),2); Mt := {A : A in M | Trace(A) eq 0}; Mf := {A : A in M | A[1] eq A[2]}; Mtf := Mt meet Mf; Seq := {Random(M) : x in {1..100000}}; #Seq; Output: Magma V2.10-6 Thu Mar 11 2004 02:31:46 on modular [Seed = 925328117] ------------------------------------- 256 Total time: 3.769 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.31) Time: Thu Mar 11 02:32:40 2004 Input: M := MatrixRing(GF(4),2); Mt := {A : A in M | Trace(A) eq 0}; Mf := {A : A in M | A[1] eq A[2]}; Mtf := Mt meet Mf; Seq := {Random(M) : x in {1..100001}}; #Seq; Output: Magma V2.10-6 Thu Mar 11 2004 02:32:35 on modular [Seed = 504252461] ------------------------------------- 256 Total time: 4.529 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.31) Time: Thu Mar 11 02:35:52 2004 Input: M := MatrixRing(GF(4),2); Mt := {A : A in M | Trace(A) eq 0}; Mf := {A : A in M | A[1] eq A[2]}; Mtf := Mt meet Mf; Seq := {Random(M) : x in {1..100000}}; SeqMf := Seq meet Mf; #SeqMf; SeqMtf := Seq meet Mtf; #SeqMtf; Output: Magma V2.10-6 Thu Mar 11 2004 02:35:48 on modular [Seed = 2156975732] ------------------------------------- 16 4 Total time: 3.399 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.31) Time: Thu Mar 11 02:37:10 2004 Input: M := MatrixRing(GF(4),2); Mt := {A : A in M | Trace(A) eq 0}; Mf := {A : A in M | A[1] eq A[2]}; Mtf := Mt meet Mf; Seq := {Random(M) : x in {1..100000}}; SeqMf := Seq meet Mf; #(SeqMf); SeqMtf := Seq meet Mtf; #(SeqMtf); Output: Magma V2.10-6 Thu Mar 11 2004 02:37:07 on modular [Seed = 3841242087] ------------------------------------- 16 4 Total time: 3.429 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.31) Time: Thu Mar 11 02:38:45 2004 Input: M := MatrixRing(GF(4),2); Mt := {A : A in M | Trace(A) eq 0}; Mf := {A : A in M | A[1] eq A[2]}; Mtf := Mt meet Mf; Seq := {x : x in {1..100000}}; #(Seq); Output: Magma V2.10-6 Thu Mar 11 2004 02:38:42 on modular [Seed = 775846285] ------------------------------------- 100000 Total time: 3.189 seconds, Total memory usage: 4.27MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.31) Time: Thu Mar 11 02:39:17 2004 Input: M := MatrixRing(GF(4),2); Mt := {A : A in M | Trace(A) eq 0}; Mf := {A : A in M | A[1] eq A[2]}; Mtf := Mt meet Mf; Seq := {x : x in {1..100000}}; #M; Output: Magma V2.10-6 Thu Mar 11 2004 02:39:13 on modular [Seed = 2036936441] ------------------------------------- 256 Total time: 3.769 seconds, Total memory usage: 4.27MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.31) Time: Thu Mar 11 02:40:05 2004 Input: M := MatrixRing(GF(4),2); Mt := {A : A in M | Trace(A) eq 0}; Mf := {A : A in M | A[1] eq A[2]}; Mtf := Mt meet Mf; Seq := [Random(M) : x in {1..100000}]; #Seq; Output: Magma V2.10-6 Thu Mar 11 2004 02:40:02 on modular [Seed = 1497960106] ------------------------------------- 100000 Total time: 3.519 seconds, Total memory usage: 6.95MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.31) Time: Thu Mar 11 02:40:21 2004 Input: M := MatrixRing(GF(4),2); Mt := {A : A in M | Trace(A) eq 0}; Mf := {A : A in M | A[1] eq A[2]}; Mtf := Mt meet Mf; Seq := {Random(M) : x in {1..100000}}; SeqMf := Seq meet Mf; #(SeqMf); SeqMtf := Seq meet Mtf; #(SeqMtf); Output: Magma V2.10-6 Thu Mar 11 2004 02:40:17 on modular [Seed = 2797007206] ------------------------------------- 16 4 Total time: 3.439 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.31) Time: Thu Mar 11 02:40:32 2004 Input: M := MatrixRing(GF(4),2); Mt := {A : A in M | Trace(A) eq 0}; Mf := {A : A in M | A[1] eq A[2]}; Mtf := Mt meet Mf; Seq := [Random(M) : x in {1..100000}]; SeqMf := Seq meet Mf; #(SeqMf); SeqMtf := Seq meet Mtf; #(SeqMtf); Output: Magma V2.10-6 Thu Mar 11 2004 02:40:29 on modular [Seed = 3081232507] ------------------------------------- >> SeqMf := Seq meet Mf; ^ Runtime error in 'meet': Bad argument types Argument types given: SeqEnum[AlgMatElt], SetEnum[AlgMatElt] >> #(SeqMf); ^ User error: Identifier 'SeqMf' has not been declared or assigned >> SeqMtf := Seq meet Mtf; ^ Runtime error in 'meet': Bad argument types Argument types given: SeqEnum[AlgMatElt], SetEnum[AlgMatElt] >> #(SeqMtf);; ^ User error: Identifier 'SeqMtf' has not been declared or assigned Total time: 3.479 seconds, Total memory usage: 6.95MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.31) Time: Thu Mar 11 02:41:19 2004 Input: M := MatrixRing(GF(4),2); Mt := [A : A in M | Trace(A) eq 0]; Mf := [A : A in M | A[1] eq A[2]]; Mtf := Mt meet Mf; Seq := [Random(M) : x in {1..100000}]; SeqMf := Seq meet Mf; #(SeqMf); SeqMtf := Seq meet Mtf; #(SeqMtf); Output: Magma V2.10-6 Thu Mar 11 2004 02:41:16 on modular [Seed = 2508574120] ------------------------------------- >> Mtf := Mt meet Mf; ^ Runtime error in 'meet': Bad argument types Argument types given: SeqEnum[AlgMatElt], SeqEnum[AlgMatElt] >> SeqMf := Seq meet Mf; ^ Runtime error in 'meet': Bad argument types Argument types given: SeqEnum[AlgMatElt], SeqEnum[AlgMatElt] >> #(SeqMf); ^ User error: Identifier 'SeqMf' has not been declared or assigned >> SeqMtf := Seq meet Mtf; ^ User error: Identifier 'Mtf' has not been declared or assigned >> #(SeqMtf);; ^ User error: Identifier 'SeqMtf' has not been declared or assigned Total time: 3.489 seconds, Total memory usage: 7.09MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.31) Time: Thu Mar 11 02:43:35 2004 Input: M := MatrixRing(GF(4),2); Mt := {A : A in M | Trace(A) eq 0}; Mf := {A : A in M | A[1] eq A[2]}; Mtf := Mt meet Mf; Seq := [Random(M) : x in {1..100000}]; SeqMf := {m : m in Seq | m in Mt} #(SeqMt); Output: Magma V2.10-6 Thu Mar 11 2004 02:43:31 on modular [Seed = 3535964752] ------------------------------------- >> #(SeqMt); ^ User error: bad syntax Total time: 4.599 seconds, Total memory usage: 6.95MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.31) Time: Thu Mar 11 02:43:46 2004 Input: M := MatrixRing(GF(4),2); Mt := {A : A in M | Trace(A) eq 0}; Mf := {A : A in M | A[1] eq A[2]}; Mtf := Mt meet Mf; Seq := [Random(M) : x in {1..100000}]; SeqMt := {m : m in Seq | m in Mt} #(SeqMt); Output: Magma V2.10-6 Thu Mar 11 2004 02:43:42 on modular [Seed = 3738076753] ------------------------------------- >> #(SeqMt); ^ User error: bad syntax Total time: 3.859 seconds, Total memory usage: 6.95MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.31) Time: Thu Mar 11 02:44:00 2004 Input: M := MatrixRing(GF(4),2); Mt := {A : A in M | Trace(A) eq 0}; Mf := {A : A in M | A[1] eq A[2]}; Mtf := Mt meet Mf; Seq := [Random(M) : x in {1..100000}]; SeqMt := {m : m in Seq | m in Mt}; #(SeqMt); Output: Magma V2.10-6 Thu Mar 11 2004 02:43:56 on modular [Seed = 742159538] ------------------------------------- 64 Total time: 3.679 seconds, Total memory usage: 6.95MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.31) Time: Thu Mar 11 02:44:19 2004 Input: M := MatrixRing(GF(4),2); Mt := {A : A in M | Trace(A) eq 0}; Mf := {A : A in M | A[1] eq A[2]}; Mtf := Mt meet Mf; Seq := [Random(M) : x in {1..100000}]; SeqMt := [m : m in Seq | m in Mt]; #(SeqMt); Output: Magma V2.10-6 Thu Mar 11 2004 02:44:15 on modular [Seed = 1060071378] ------------------------------------- 25154 Total time: 3.609 seconds, Total memory usage: 6.95MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.31) Time: Thu Mar 11 02:44:54 2004 Input: M := MatrixRing(GF(4),2); Mt := {A : A in M | Trace(A) eq 0}; Mf := {A : A in M | A[1] eq A[2]}; Mtf := Mt meet Mf; Seq := [Random(M) : x in {1..100000}]; SeqMt := [m : m in Seq | m in Mt]; #(SeqMt); SeqMf := [m : m in Seq | m in Mf]; #(SeqMf); SeqMtf := [m : m in Seq | m in Mtf]; #(SeqMtf); Output: Magma V2.10-6 Thu Mar 11 2004 02:44:49 on modular [Seed = 302140097] ------------------------------------- 24799 6361 1593 Total time: 4.219 seconds, Total memory usage: 6.95MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.31) Time: Thu Mar 11 03:09:15 2004 Input: P:=PolynomialRing(R); t73 := x^(7^2)+x^7+x; Output: Magma V2.10-6 Thu Mar 11 2004 03:09:12 on modular [Seed = 4209681526] ------------------------------------- >> P:=PolynomialRing(R); ^ User error: Identifier 'R' has not been declared or assigned >> t73 := x^(7^2)+x^7+x; ^ User error: Identifier 'x' has not been declared or assigned Total time: 3.269 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.31) Time: Thu Mar 11 03:09:50 2004 Input: P:=PolynomialRing(Realfield()); t73 := x^(7^2)+x^7+x; Output: Magma V2.10-6 Thu Mar 11 2004 03:09:47 on modular [Seed = 3670705205] ------------------------------------- >> P:=PolynomialRing(Realfield()); ^ User error: Identifier 'Realfield' has not been declared or assigned >> t73 := x^(7^2)+x^7+x; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.31) Time: Thu Mar 11 03:10:30 2004 Input: P:=PolynomialRing(RealField()); t73 := x^(7^2)+x^7+x; Output: Magma V2.10-6 Thu Mar 11 2004 03:10:26 on modular [Seed = 1043226857] ------------------------------------- Total time: 3.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.31) Time: Thu Mar 11 03:10:48 2004 Input: P:=PolynomialRing(RealField()); t73 := x^(7^2)+x^7+x; t73; Output: Magma V2.10-6 Thu Mar 11 2004 03:10:44 on modular [Seed = 135812905] ------------------------------------- x^49 + x^7 + x Total time: 4.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.31) Time: Thu Mar 11 03:19:53 2004 Input: P:=PolynomialRing(RealField()); seqt := [7^(r-1) : r in {2..3}]; seqt; Output: Magma V2.10-6 Thu Mar 11 2004 03:19:49 on modular [Seed = 102131461] ------------------------------------- [ 7, 49 ] Total time: 3.699 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.31) Time: Thu Mar 11 03:23:06 2004 Input: P:=PolynomialRing(RealField()); seqt := [7^(r-1) : r in {3..2}]; seqt; Output: Magma V2.10-6 Thu Mar 11 2004 03:23:02 on modular [Seed = 2190664514] ------------------------------------- [] Total time: 3.769 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.31) Time: Thu Mar 11 03:23:20 2004 Input: P:=PolynomialRing(RealField()); seqt := [7^(r-1) : r in {3..2 by (-1)}]; seqt; Output: Magma V2.10-6 Thu Mar 11 2004 03:23:17 on modular [Seed = 2508584006] ------------------------------------- [ 7, 49 ] Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.31) Time: Thu Mar 11 03:25:52 2004 Input: P:=PolynomialRing(RealField()); seqt := [7^(r-1) : r in {2..3}]; seqt; t73 := x^(seqt[1]); t73; Output: Magma V2.10-6 Thu Mar 11 2004 03:25:48 on modular [Seed = 624248718] ------------------------------------- [ 7, 49 ] x^7 Total time: 4.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.31) Time: Thu Mar 11 03:26:45 2004 Input: P:=PolynomialRing(RealField()); seqt := [7^(r-1) : r in {2..3}]; seqt; t73 := x^(seqt[1]); t73 := t73 + x^(seqt[2]); t73; Output: Magma V2.10-6 Thu Mar 11 2004 03:26:42 on modular [Seed = 51601894] ------------------------------------- [ 7, 49 ] x^49 + x^7 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.31) Time: Thu Mar 11 03:28:37 2004 Input: seqt := [7^(r-1) : r in {2..3}]; seqt; P:=PolynomialRing(RealField()); t73 := x^(seqt[1]) + x^(seqt[2]); t73; n73 := x^(seqt[1] + seqt[2]); n73; Output: Magma V2.10-6 Thu Mar 11 2004 03:28:34 on modular [Seed = 2830683069] ------------------------------------- [ 7, 49 ] x^49 + x^7 x^56 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.31) Time: Thu Mar 11 03:29:51 2004 Input: seqt := [7^(r-1) : r in {1..3}]; seqt; P:=PolynomialRing(RealField()); t73 := x^(seqt[1]) + x^(seqt[2]) + x^(seqt[3]); t73; n73 := x^(seqt[1] + seqt[2] + + seqt[3]); n73; Output: Magma V2.10-6 Thu Mar 11 2004 03:29:48 on modular [Seed = 2441212618] ------------------------------------- [ 1, 7, 49 ] x^49 + x^7 + x x^57 Total time: 3.169 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.31) Time: Thu Mar 11 03:34:03 2004 Input: seqt := [7^(r-1) : r in {1..3}]; seqt; P:=PolynomialRing(RealField()); t73 := x^(seqt[1]) + x^(seqt[2]) + x^(seqt[3]); t73; n73 := x^(seqt[1] + seqt[2] + + seqt[3]); n73; Olav := [(a,b) : a,b in GF(7,3) | Evaluate(n73,a) eq Evaluate(t73,b)]; Olav; Output: Magma V2.10-6 Thu Mar 11 2004 03:34:00 on modular [Seed = 1820067900] ------------------------------------- [ 1, 7, 49 ] x^49 + x^7 + x x^57 >> Olav := [(a,b) : a,b in GF(7,3) | Evaluate(n73,a) eq Evaluate(t73,b)]; ^ Runtime error in 'Evaluate': Incompatible rings >> Olav;; ^ User error: Identifier 'Olav' has not been declared or assigned Total time: 3.169 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.31) Time: Thu Mar 11 03:37:22 2004 Input: seqt := [7^(r-1) : r in {1..3}]; seqt; P:=PolynomialRing(RealField()); t73 := x^(seqt[1]) + x^(seqt[2]) + x^(seqt[3]); t73; n73 := x^(seqt[1] + seqt[2] + + seqt[3]); n73; Evaluate(n73,2); Olav := [(a,b) : a,b in GF(7,3) | Evaluate(n73,a) eq Evaluate(t73,b)]; Olav; Output: Magma V2.10-6 Thu Mar 11 2004 03:37:19 on modular [Seed = 2508583042] ------------------------------------- [ 1, 7, 49 ] x^49 + x^7 + x x^57 144115188075855872 >> Olav := [(a,b) : a,b in GF(7,3) | Evaluate(n73,a) eq Evaluate(t73,b)]; ^ Runtime error in 'Evaluate': Incompatible rings >> Olav;; ^ User error: Identifier 'Olav' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.31) Time: Thu Mar 11 03:37:41 2004 Input: seqt := [7^(r-1) : r in {1..3}]; seqt; P:=PolynomialRing(RealField()); t73 := x^(seqt[1]) + x^(seqt[2]) + x^(seqt[3]); t73; n73 := x^(seqt[1] + seqt[2] + + seqt[3]); n73; Evaluate(n73,1); Olav := [(a,b) : a,b in GF(7,3) | Evaluate(n73,a) eq Evaluate(t73,b)]; Olav; Output: Magma V2.10-6 Thu Mar 11 2004 03:37:36 on modular [Seed = 3891757727] ------------------------------------- [ 1, 7, 49 ] x^49 + x^7 + x x^57 1 >> Olav := [(a,b) : a,b in GF(7,3) | Evaluate(n73,a) eq Evaluate(t73,b)]; ^ Runtime error in 'Evaluate': Incompatible rings >> Olav;; ^ User error: Identifier 'Olav' has not been declared or assigned Total time: 3.769 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.31) Time: Thu Mar 11 03:38:21 2004 Input: seqt := [7^(r-1) : r in {1..3}]; seqt; P:=PolynomialRing(RealField()); t73 := x^(seqt[1]) + x^(seqt[2]) + x^(seqt[3]); t73; n73 := x^(seqt[1] + seqt[2] + + seqt[3]); n73; Evaluate(n73,2); Olav := [(a,b) : a,b in GF(7,3) | Evaluate(n73,a) eq Evaluate(t73,b)]; Olav; Output: Magma V2.10-6 Thu Mar 11 2004 03:38:17 on modular [Seed = 3268585363] ------------------------------------- [ 1, 7, 49 ] x^49 + x^7 + x x^57 144115188075855872 >> Olav := [(a,b) : a,b in GF(7,3) | Evaluate(n73,a) eq Evaluate(t73,b)]; ^ Runtime error in 'Evaluate': Incompatible rings >> Olav;; ^ User error: Identifier 'Olav' has not been declared or assigned Total time: 4.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.31) Time: Thu Mar 11 03:39:10 2004 Input: seqt := [7^(r-1) : r in {1..3}]; seqt; P:=PolynomialRing(RealField()); t73 := x^(seqt[1]) + x^(seqt[2]) + x^(seqt[3]); t73; n73 := x^(seqt[1] + seqt[2] + + seqt[3]); n73; Evaluate(n73,2); Olav := [ : a,b in GF(7,3) | Evaluate(n73,a) eq Evaluate(t73,b)]; Olav; Output: Magma V2.10-6 Thu Mar 11 2004 03:39:07 on modular [Seed = 556876963] ------------------------------------- [ 1, 7, 49 ] x^49 + x^7 + x x^57 144115188075855872 >> Olav := [ : a,b in GF(7,3) | Evaluate(n73,a) eq Evaluate(t73,b)]; ^ User error: bad syntax >> Olav;; ^ User error: Identifier 'Olav' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.31) Time: Thu Mar 11 03:39:56 2004 Input: seqt := [7^(r-1) : r in {1..3}]; seqt; P:=PolynomialRing(RealField()); t73 := x^(seqt[1]) + x^(seqt[2]) + x^(seqt[3]); t73; n73 := x^(seqt[1] + seqt[2] + + seqt[3]); n73; Evaluate(n73,2); Olav := [Evaluate(n73,a) : a in GF(7,3)]; Olav; Output: Magma V2.10-6 Thu Mar 11 2004 03:39:53 on modular [Seed = 169504762] ------------------------------------- [ 1, 7, 49 ] x^49 + x^7 + x x^57 144115188075855872 >> Olav := [Evaluate(n73,a) : a in GF(7,3)]; ^ Runtime error in 'Evaluate': Incompatible rings >> Olav;; ^ User error: Identifier 'Olav' has not been declared or assigned Total time: 3.099 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.31) Time: Thu Mar 11 03:40:53 2004 Input: seqt := [7^(r-1) : r in {1..3}]; seqt; P:=PolynomialRing(GF(7,3)); t73 := x^(seqt[1]) + x^(seqt[2]) + x^(seqt[3]); t73; n73 := x^(seqt[1] + seqt[2] + + seqt[3]); n73; Evaluate(n73,2); Olav := [Evaluate(n73,a) : a in GF(7,3)]; Olav; Output: Magma V2.10-6 Thu Mar 11 2004 03:40:49 on modular [Seed = 1702167389] ------------------------------------- [ 1, 7, 49 ] x^49 + x^7 + x x^57 1 [ 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 0 ] Total time: 4.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.31) Time: Thu Mar 11 03:43:10 2004 Input: seqt := [7^(r-1) : r in {1..3}]; seqt; P:=PolynomialRing(GF(7,3)); t73 := x^(seqt[1]) + x^(seqt[2]) + x^(seqt[3]); t73; n73 := x^(seqt[1] + seqt[2] + + seqt[3]); n73; Evaluate(n73,2); Olav := [(a,b): a,b in GF(7,3) | Evaluate(n73,a) eq Evaluate(t73,b)]; Olav; Output: Magma V2.10-6 Thu Mar 11 2004 03:43:06 on modular [Seed = 2729624593] ------------------------------------- [ 1, 7, 49 ] x^49 + x^7 + x x^57 1 >> Olav := [(a,b): a,b in GF(7,3) | Evaluate(n73,a) eq Evaluate(t73,b)]; ^ Runtime error in elt< ... >: Bad arguments >> Olav;; ^ User error: Identifier 'Olav' has not been declared or assigned Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.31) Time: Thu Mar 11 03:43:40 2004 Input: seqt := [7^(r-1) : r in {1..3}]; seqt; P:=PolynomialRing(GF(7,3)); t73 := x^(seqt[1]) + x^(seqt[2]) + x^(seqt[3]); t73; n73 := x^(seqt[1] + seqt[2] + + seqt[3]); n73; Evaluate(n73,2); Olav := [[a,b]: a,b in GF(7,3) | Evaluate(n73,a) eq Evaluate(t73,b)]; Olav; Output: Magma V2.10-6 Thu Mar 11 2004 03:43:34 on modular [Seed = 2308566806] ------------------------------------- [ 1, 7, 49 ] x^49 + x^7 + x x^57 1 [ [ 1, $.1 ], [ 1, $.1^2 ], [ 1, $.1^7 ], [ 1, $.1^10 ], [ 1, $.1^11 ], [ 1, $.1^14 ], [ 1, $.1^16 ], [ 1, $.1^25 ], [ 1, $.1^37 ], [ 1, $.1^49 ], [ 1, $.1^66 ], [ 1, $.1^70 ], [ 1, $.1^77 ], [ 1, $.1^87 ], [ 1, $.1^90 ], [ 1, $.1^97 ], [ 1, $.1^98 ], [ 1, $.1^100 ], [ 1, $.1^103 ], [ 1, $.1^112 ], [ 1, $.1^120 ], [ 1, $.1^131 ], [ 1, $.1^132 ], [ 1, $.1^137 ], [ 1, $.1^146 ], [ 1, $.1^148 ], [ 1, $.1^156 ], [ 1, $.1^159 ], [ 1, $.1^175 ], [ 1, $.1^195 ], [ 1, $.1^197 ], [ 1, $.1^199 ], [ 1, $.1^215 ], [ 1, $.1^233 ], [ 1, $.1^240 ], [ 1, $.1^259 ], [ 1, $.1^263 ], [ 1, $.1^267 ], [ 1, $.1^275 ], [ 1, 5 ], [ 1, $.1^288 ], [ 1, $.1^306 ], [ 1, $.1^307 ], [ 1, $.1^312 ], [ 1, $.1^314 ], [ 1, $.1^321 ], [ 1, $.1^337 ], [ 1, $.1^338 ], [ 1, $.1^339 ], [ $.1, 1 ], [ $.1, $.1^3 ], [ $.1, $.1^21 ], [ $.1, $.1^22 ], [ $.1, $.1^27 ], [ $.1, $.1^29 ], [ $.1, $.1^36 ], [ $.1, $.1^52 ], [ $.1, $.1^53 ], [ $.1, $.1^54 ], [ $.1, $.1^58 ], [ $.1, $.1^59 ], [ $.1, $.1^64 ], [ $.1, $.1^67 ], [ $.1, $.1^68 ], [ $.1, $.1^71 ], [ $.1, $.1^73 ], [ $.1, $.1^82 ], [ $.1, $.1^94 ], [ $.1, $.1^106 ], [ $.1, $.1^123 ], [ $.1, $.1^127 ], [ $.1, $.1^134 ], [ $.1, $.1^144 ], [ $.1, $.1^147 ], [ $.1, $.1^154 ], [ $.1, $.1^155 ], [ $.1, $.1^157 ], [ $.1, $.1^160 ], [ $.1, $.1^169 ], [ $.1, $.1^177 ], [ $.1, $.1^188 ], [ $.1, $.1^189 ], [ $.1, $.1^194 ], [ $.1, $.1^203 ], [ $.1, $.1^205 ], [ $.1, $.1^213 ], [ $.1, $.1^216 ], [ $.1, $.1^232 ], [ $.1, $.1^252 ], [ $.1, $.1^254 ], [ $.1, $.1^256 ], [ $.1, $.1^272 ], [ $.1, $.1^290 ], [ $.1, $.1^297 ], [ $.1, $.1^316 ], [ $.1, $.1^320 ], [ $.1, $.1^324 ], [ $.1, $.1^332 ], [ $.1^2, $.1^5 ], [ $.1^2, $.1^12 ], [ $.1^2, $.1^31 ], [ $.1^2, $.1^35 ], [ $.1^2, $.1^39 ], [ $.1^2, $.1^47 ], [ $.1^2, 3 ], [ $.1^2, $.1^60 ], [ $.1^2, $.1^78 ], [ $.1^2, $.1^79 ], [ $.1^2, $.1^84 ], [ $.1^2, $.1^86 ], [ $.1^2, $.1^93 ], [ $.1^2, $.1^109 ], [ $.1^2, $.1^110 ], [ $.1^2, $.1^111 ], [ $.1^2, $.1^115 ], [ $.1^2, $.1^116 ], [ $.1^2, $.1^121 ], [ $.1^2, $.1^124 ], [ $.1^2, $.1^125 ], [ $.1^2, $.1^128 ], [ $.1^2, $.1^130 ], [ $.1^2, $.1^139 ], [ $.1^2, $.1^151 ], [ $.1^2, $.1^163 ], [ $.1^2, $.1^180 ], [ $.1^2, $.1^184 ], [ $.1^2, $.1^191 ], [ $.1^2, $.1^201 ], [ $.1^2, $.1^204 ], [ $.1^2, $.1^211 ], [ $.1^2, $.1^212 ], [ $.1^2, $.1^214 ], [ $.1^2, $.1^217 ], [ $.1^2, $.1^226 ], [ $.1^2, $.1^234 ], [ $.1^2, $.1^245 ], [ $.1^2, $.1^246 ], [ $.1^2, $.1^251 ], [ $.1^2, $.1^260 ], [ $.1^2, $.1^262 ], [ $.1^2, $.1^270 ], [ $.1^2, $.1^273 ], [ $.1^2, $.1^289 ], [ $.1^2, $.1^309 ], [ $.1^2, $.1^311 ], [ $.1^2, $.1^313 ], [ $.1^2, $.1^329 ], [ $.1^3, $.1^4 ], [ $.1^3, $.1^24 ], [ $.1^3, $.1^26 ], [ $.1^3, $.1^28 ], [ $.1^3, $.1^44 ], [ $.1^3, $.1^62 ], [ $.1^3, $.1^69 ], [ $.1^3, $.1^88 ], [ $.1^3, $.1^92 ], [ $.1^3, $.1^96 ], [ $.1^3, $.1^104 ], [ $.1^3, 2 ], [ $.1^3, $.1^117 ], [ $.1^3, $.1^135 ], [ $.1^3, $.1^136 ], [ $.1^3, $.1^141 ], [ $.1^3, $.1^143 ], [ $.1^3, $.1^150 ], [ $.1^3, $.1^166 ], [ $.1^3, $.1^167 ], [ $.1^3, $.1^168 ], [ $.1^3, $.1^172 ], [ $.1^3, $.1^173 ], [ $.1^3, $.1^178 ], [ $.1^3, $.1^181 ], [ $.1^3, $.1^182 ], [ $.1^3, $.1^185 ], [ $.1^3, $.1^187 ], [ $.1^3, $.1^196 ], [ $.1^3, $.1^208 ], [ $.1^3, $.1^220 ], [ $.1^3, $.1^237 ], [ $.1^3, $.1^241 ], [ $.1^3, $.1^248 ], [ $.1^3, $.1^258 ], [ $.1^3, $.1^261 ], [ $.1^3, $.1^268 ], [ $.1^3, $.1^269 ], [ $.1^3, $.1^271 ], [ $.1^3, $.1^274 ], [ $.1^3, $.1^283 ], [ $.1^3, $.1^291 ], [ $.1^3, $.1^302 ], [ $.1^3, $.1^303 ], [ $.1^3, $.1^308 ], [ $.1^3, $.1^317 ], [ $.1^3, $.1^319 ], [ $.1^3, $.1^327 ], [ $.1^3, $.1^330 ], [ $.1^4, $.1^6 ], [ $.1^4, $.1^17 ], [ $.1^4, $.1^18 ], [ $.1^4, $.1^23 ], [ $.1^4, $.1^32 ], [ $.1^4, $.1^34 ], [ $.1^4, $.1^42 ], [ $.1^4, $.1^45 ], [ $.1^4, $.1^61 ], [ $.1^4, $.1^81 ], [ $.1^4, $.1^83 ], [ $.1^4, $.1^85 ], [ $.1^4, $.1^101 ], [ $.1^4, $.1^119 ], [ $.1^4, $.1^126 ], [ $.1^4, $.1^145 ], [ $.1^4, $.1^149 ], [ $.1^4, $.1^153 ], [ $.1^4, $.1^161 ], [ $.1^4, 6 ], [ $.1^4, $.1^174 ], [ $.1^4, $.1^192 ], [ $.1^4, $.1^193 ], [ $.1^4, $.1^198 ], [ $.1^4, $.1^200 ], [ $.1^4, $.1^207 ], [ $.1^4, $.1^223 ], [ $.1^4, $.1^224 ], [ $.1^4, $.1^225 ], [ $.1^4, $.1^229 ], [ $.1^4, $.1^230 ], [ $.1^4, $.1^235 ], [ $.1^4, $.1^238 ], [ $.1^4, $.1^239 ], [ $.1^4, $.1^242 ], [ $.1^4, $.1^244 ], [ $.1^4, $.1^253 ], [ $.1^4, $.1^265 ], [ $.1^4, $.1^277 ], [ $.1^4, $.1^294 ], [ $.1^4, $.1^298 ], [ $.1^4, $.1^305 ], [ $.1^4, $.1^315 ], [ $.1^4, $.1^318 ], [ $.1^4, $.1^325 ], [ $.1^4, $.1^326 ], [ $.1^4, $.1^328 ], [ $.1^4, $.1^331 ], [ $.1^4, $.1^340 ], [ $.1^5, $.1^9 ], [ $.1^5, $.1^13 ], [ $.1^5, $.1^20 ], [ $.1^5, $.1^30 ], [ $.1^5, $.1^33 ], [ $.1^5, $.1^40 ], [ $.1^5, $.1^41 ], [ $.1^5, $.1^43 ], [ $.1^5, $.1^46 ], [ $.1^5, $.1^55 ], [ $.1^5, $.1^63 ], [ $.1^5, $.1^74 ], [ $.1^5, $.1^75 ], [ $.1^5, $.1^80 ], [ $.1^5, $.1^89 ], [ $.1^5, $.1^91 ], [ $.1^5, $.1^99 ], [ $.1^5, $.1^102 ], [ $.1^5, $.1^118 ], [ $.1^5, $.1^138 ], [ $.1^5, $.1^140 ], [ $.1^5, $.1^142 ], [ $.1^5, $.1^158 ], [ $.1^5, $.1^176 ], [ $.1^5, $.1^183 ], [ $.1^5, $.1^202 ], [ $.1^5, $.1^206 ], [ $.1^5, $.1^210 ], [ $.1^5, $.1^218 ], [ $.1^5, 4 ], [ $.1^5, $.1^231 ], [ $.1^5, $.1^249 ], [ $.1^5, $.1^250 ], [ $.1^5, $.1^255 ], [ $.1^5, $.1^257 ], [ $.1^5, $.1^264 ], [ $.1^5, $.1^280 ], [ $.1^5, $.1^281 ], [ $.1^5, $.1^282 ], [ $.1^5, $.1^286 ], [ $.1^5, $.1^287 ], [ $.1^5, $.1^292 ], [ $.1^5, $.1^295 ], [ $.1^5, $.1^296 ], [ $.1^5, $.1^299 ], [ $.1^5, $.1^301 ], [ $.1^5, $.1^310 ], [ $.1^5, $.1^322 ], [ $.1^5, $.1^334 ], [ $.1^6, $.1 ], [ $.1^6, $.1^2 ], [ $.1^6, $.1^7 ], [ $.1^6, $.1^10 ], [ $.1^6, $.1^11 ], [ $.1^6, $.1^14 ], [ $.1^6, $.1^16 ], [ $.1^6, $.1^25 ], [ $.1^6, $.1^37 ], [ $.1^6, $.1^49 ], [ $.1^6, $.1^66 ], [ $.1^6, $.1^70 ], [ $.1^6, $.1^77 ], [ $.1^6, $.1^87 ], [ $.1^6, $.1^90 ], [ $.1^6, $.1^97 ], [ $.1^6, $.1^98 ], [ $.1^6, $.1^100 ], [ $.1^6, $.1^103 ], [ $.1^6, $.1^112 ], [ $.1^6, $.1^120 ], [ $.1^6, $.1^131 ], [ $.1^6, $.1^132 ], [ $.1^6, $.1^137 ], [ $.1^6, $.1^146 ], [ $.1^6, $.1^148 ], [ $.1^6, $.1^156 ], [ $.1^6, $.1^159 ], [ $.1^6, $.1^175 ], [ $.1^6, $.1^195 ], [ $.1^6, $.1^197 ], [ $.1^6, $.1^199 ], [ $.1^6, $.1^215 ], [ $.1^6, $.1^233 ], [ $.1^6, $.1^240 ], [ $.1^6, $.1^259 ], [ $.1^6, $.1^263 ], [ $.1^6, $.1^267 ], [ $.1^6, $.1^275 ], [ $.1^6, 5 ], [ $.1^6, $.1^288 ], [ $.1^6, $.1^306 ], [ $.1^6, $.1^307 ], [ $.1^6, $.1^312 ], [ $.1^6, $.1^314 ], [ $.1^6, $.1^321 ], [ $.1^6, $.1^337 ], [ $.1^6, $.1^338 ], [ $.1^6, $.1^339 ], [ $.1^7, 1 ], [ $.1^7, $.1^3 ], [ $.1^7, $.1^21 ], [ $.1^7, $.1^22 ], [ $.1^7, $.1^27 ], [ $.1^7, $.1^29 ], [ $.1^7, $.1^36 ], [ $.1^7, $.1^52 ], [ $.1^7, $.1^53 ], [ $.1^7, $.1^54 ], [ $.1^7, $.1^58 ], [ $.1^7, $.1^59 ], [ $.1^7, $.1^64 ], [ $.1^7, $.1^67 ], [ $.1^7, $.1^68 ], [ $.1^7, $.1^71 ], [ $.1^7, $.1^73 ], [ $.1^7, $.1^82 ], [ $.1^7, $.1^94 ], [ $.1^7, $.1^106 ], [ $.1^7, $.1^123 ], [ $.1^7, $.1^127 ], [ $.1^7, $.1^134 ], [ $.1^7, $.1^144 ], [ $.1^7, $.1^147 ], [ $.1^7, $.1^154 ], [ $.1^7, $.1^155 ], [ $.1^7, $.1^157 ], [ $.1^7, $.1^160 ], [ $.1^7, $.1^169 ], [ $.1^7, $.1^177 ], [ $.1^7, $.1^188 ], [ $.1^7, $.1^189 ], [ $.1^7, $.1^194 ], [ $.1^7, $.1^203 ], [ $.1^7, $.1^205 ], [ $.1^7, $.1^213 ], [ $.1^7, $.1^216 ], [ $.1^7, $.1^232 ], [ $.1^7, $.1^252 ], [ $.1^7, $.1^254 ], [ $.1^7, $.1^256 ], [ $.1^7, $.1^272 ], [ $.1^7, $.1^290 ], [ $.1^7, $.1^297 ], [ $.1^7, $.1^316 ], [ $.1^7, $.1^320 ], [ $.1^7, $.1^324 ], [ $.1^7, $.1^332 ], [ $.1^8, $.1^5 ], [ $.1^8, $.1^12 ], [ $.1^8, $.1^31 ], [ $.1^8, $.1^35 ], [ $.1^8, $.1^39 ], [ $.1^8, $.1^47 ], [ $.1^8, 3 ], [ $.1^8, $.1^60 ], [ $.1^8, $.1^78 ], [ $.1^8, $.1^79 ], [ $.1^8, $.1^84 ], [ $.1^8, $.1^86 ], [ $.1^8, $.1^93 ], [ $.1^8, $.1^109 ], [ $.1^8, $.1^110 ], [ $.1^8, $.1^111 ], [ $.1^8, $.1^115 ], [ $.1^8, $.1^116 ], [ $.1^8, $.1^121 ], [ $.1^8, $.1^124 ], [ $.1^8, $.1^125 ], [ $.1^8, $.1^128 ], [ $.1^8, $.1^130 ], [ $.1^8, $.1^139 ], [ $.1^8, $.1^151 ], [ $.1^8, $.1^163 ], [ $.1^8, $.1^180 ], [ $.1^8, $.1^184 ], [ $.1^8, $.1^191 ], [ $.1^8, $.1^201 ], [ $.1^8, $.1^204 ], [ $.1^8, $.1^211 ], [ $.1^8, $.1^212 ], [ $.1^8, $.1^214 ], [ $.1^8, $.1^217 ], [ $.1^8, $.1^226 ], [ $.1^8, $.1^234 ], [ $.1^8, $.1^245 ], [ $.1^8, $.1^246 ], ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.31) Time: Thu Mar 11 03:44:18 2004 Input: seqt := [7^(r-1) : r in {1..3}]; seqt; P:=PolynomialRing(GF(7,3)); t73 := x^(seqt[1]) + x^(seqt[2]) + x^(seqt[3]); t73; n73 := x^(seqt[1] + seqt[2] + + seqt[3]); n73; Evaluate(n73,2); Olav := {[a,b]: a,b in GF(7,3) | Evaluate(n73,a) eq Evaluate(t73,b)}; Olav; Output: Magma V2.10-6 Thu Mar 11 2004 03:44:14 on modular [Seed = 2441213798] ------------------------------------- [ 1, 7, 49 ] x^49 + x^7 + x x^57 1 { [ $.1^3, $.1^24 ], [ $.1^35, $.1^280 ], [ $.1^30, $.1^240 ], [ $.1^28, $.1^224 ], [ $.1^4, $.1^32 ], [ $.1^5, $.1^40 ], [ $.1^21, $.1^168 ], [ $.1^36, $.1^288 ], [ 1, $.1 ], [ $.1^35, $.1^281 ], [ $.1^28, $.1^225 ], [ $.1^12, $.1^97 ], [ $.1^11, $.1^89 ], [ $.1^6, $.1^49 ], [ $.1^5, $.1^41 ], [ $.1^10, $.1^81 ], [ $.1^37, $.1^297 ], [ $.1^42, $.1^337 ], [ 1, $.1^2 ], [ $.1^13, $.1^106 ], [ $.1^12, $.1^98 ], [ $.1^7, $.1^58 ], [ $.1^3, $.1^26 ], [ $.1^4, $.1^34 ], [ $.1^17, $.1^138 ], [ $.1^18, $.1^146 ], [ $.1^19, $.1^154 ], [ $.1^35, $.1^282 ], [ $.1^42, $.1^338 ], [ $.1^5, $.1^43 ], [ $.1^26, $.1^211 ], [ $.1^25, $.1^203 ], [ $.1^24, $.1^195 ], [ $.1^14, $.1^115 ], [ $.1^11, $.1^91 ], [ $.1^7, $.1^59 ], [ $.1^10, $.1^83 ], [ $.1^19, $.1^155 ], [ $.1^20, $.1^163 ], [ $.1^42, $.1^339 ], [ $.1^3, $.1^28 ], [ $.1^33, $.1^268 ], [ $.1^32, $.1^260 ], [ $.1^31, $.1^252 ], [ $.1^27, $.1^220 ], [ $.1^26, $.1^212 ], [ $.1^14, $.1^116 ], [ $.1^12, $.1^100 ], [ $.1^17, $.1^140 ], [ $.1^18, $.1^148 ], [ $.1^21, $.1^172 ], [ $.1^10, $.1^85 ], [ $.1^34, $.1^277 ], [ $.1^33, $.1^269 ], [ $.1^28, $.1^229 ], [ $.1^25, $.1^205 ], [ $.1^24, $.1^197 ], [ $.1^19, $.1^157 ], [ $.1^21, $.1^173 ], [ $.1^38, $.1^309 ], [ $.1^39, $.1^317 ], [ $.1^40, $.1^325 ], [ $.1^5, $.1^46 ], [ $.1^32, $.1^262 ], [ $.1^31, $.1^254 ], [ $.1^28, $.1^230 ], [ $.1^26, $.1^214 ], [ $.1^17, $.1^142 ], [ $.1^35, $.1^286 ], [ $.1^40, $.1^326 ], [ $.1^41, $.1^334 ], [ 1, $.1^7 ], [ $.1^33, $.1^271 ], [ $.1^24, $.1^199 ], [ $.1^12, $.1^103 ], [ $.1^35, $.1^287 ], [ $.1^38, $.1^311 ], [ $.1^39, $.1^319 ], [ $.1, 1 ], [ $.1^27, $.1^208 ], [ $.1^23, $.1^176 ], [ $.1^11, $.1^80 ], [ $.1^19, $.1^144 ], [ $.1^40, $.1^328 ], [ $.1^5, $.1^33 ], [ $.1^26, $.1^217 ], [ $.1^14, $.1^121 ], [ $.1^38, $.1^313 ], [ 1, $.1^10 ], [ $.1^33, $.1^258 ], [ $.1^25, $.1^194 ], [ $.1^4, $.1^42 ], [ $.1^15, 2 ], [ $.1^37, $.1^290 ], [ $.1^41, $.1^322 ], [ 1, $.1^11 ], [ $.1^28, $.1^235 ], [ $.1, $.1^3 ], [ $.1^19, $.1^147 ], [ $.1^40, $.1^331 ], [ $.1^7, $.1^52 ], [ $.1^29, 4 ], [ $.1^14, $.1^124 ], [ $.1^18, $.1^156 ], [ $.1^39, $.1^308 ], [ $.1^4, $.1^45 ], [ $.1^33, $.1^261 ], [ $.1^14, $.1^125 ], [ $.1^7, $.1^53 ], [ $.1^9, $.1^69 ], [ $.1^15, $.1^117 ], [ 1, $.1^14 ], [ $.1^32, $.1^270 ], [ $.1^28, $.1^238 ], [ $.1^7, $.1^54 ], [ $.1^8, $.1^78 ], [ $.1^21, $.1^166 ], [ $.1^2, $.1^31 ], [ $.1^29, $.1^231 ], [ $.1^28, $.1^239 ], [ $.1^23, $.1^183 ], [ $.1^8, $.1^79 ], [ $.1^18, $.1^159 ], [ $.1^21, $.1^167 ], [ 1, $.1^16 ], [ $.1^35, $.1^264 ], [ $.1^31, $.1^232 ], [ $.1^25, $.1^216 ], [ $.1^12, $.1^112 ], [ $.1^9, $.1^88 ], [ $.1^15, $.1^104 ], [ $.1^16, $.1^145 ], [ $.1^32, $.1^273 ], [ $.1^29, $.1^249 ], [ $.1^21, $.1^185 ], [ $.1^22, $.1^161 ], [ $.1^38, $.1^289 ], [ $.1^42, $.1^321 ], [ $.1^11, $.1^74 ], [ $.1^29, $.1^250 ], [ $.1^28, $.1^242 ], [ $.1^36, $.1^306 ], [ $.1, $.1^27 ], [ $.1^33, $.1^283 ], [ $.1^13, $.1^123 ], [ $.1^11, $.1^75 ], [ $.1^18, $.1^131 ], [ $.1^21, $.1^187 ], [ $.1^36, $.1^307 ], [ $.1^8, $.1^84 ], [ $.1^28, $.1^244 ], [ $.1^9, $.1^92 ], [ $.1^18, $.1^132 ], [ $.1^20, $.1^180 ], [ $.1^37, $.1^316 ], [ $.1^40, $.1^340 ], [ $.1^43, $.1^332 ], [ $.1, $.1^29 ], [ $.1^6, $.1^37 ], [ $.1^2, $.1^5 ], [ $.1^16, $.1^149 ], [ $.1^8, $.1^86 ], [ $.1^17, $.1^158 ], [ $.1^39, $.1^302 ], [ $.1^5, $.1^63 ], [ $.1^29, $.1^255 ], [ $.1^24, $.1^215 ], [ $.1^13, $.1^127 ], [ $.1^39, $.1^303 ], [ $.1^12, $.1^120 ], [ $.1^15, $.1^96 ], [ $.1^20, $.1^184 ], [ $.1^36, $.1^312 ], [ $.1^43, $.1^320 ], [ 1, $.1^25 ], [ $.1^35, $.1^257 ], [ $.1^34, $.1^265 ], [ $.1^30, $.1^233 ], [ $.1^26, $.1^201 ], [ $.1^16, $.1^153 ], [ $.1^18, $.1^137 ], [ $.1^21, $.1^178 ], [ $.1^33, $.1^274 ], [ $.1^36, $.1^314 ], [ $.1^22, 6 ], [ $.1^39, $.1^291 ], [ $.1^2, $.1^12 ], [ $.1^27, $.1^196 ], [ $.1^26, $.1^204 ], [ $.1^7, $.1^36 ], [ $.1^3, $.1^4 ], [ $.1^43, $.1^324 ], [ $.1, $.1^21 ], [ $.1^28, $.1^253 ], [ $.1^25, $.1^213 ], [ $.1^14, $.1^109 ], [ $.1^4, $.1^61 ], [ $.1^8, $.1^93 ], [ $.1^21, $.1^181 ], [ $.1, $.1^22 ], [ $.1^14, $.1^110 ], [ $.1^19, $.1^134 ], [ $.1^21, $.1^182 ], [ $.1^22, $.1^174 ], [ $.1^5, $.1^55 ], [ $.1^14, $.1^111 ], [ $.1^20, $.1^191 ], [ $.1^6, $.1^16 ], [ $.1^31, $.1^216 ], [ $.1^28, $.1^192 ], [ $.1^27, $.1^248 ], [ $.1^25, $.1^232 ], [ $.1^9, $.1^104 ], [ $.1^15, $.1^88 ], [ $.1^20, $.1^128 ], [ $.1^21, $.1^136 ], [ $.1^5, $.1^9 ], [ $.1^34, $.1^305 ], [ $.1^32, $.1^289 ], [ $.1^28, $.1^193 ], [ $.1^13, $.1^73 ], [ $.1^16, $.1^161 ], [ $.1^22, $.1^145 ], [ $.1^38, $.1^273 ], [ $.1^12, $.1^66 ], [ $.1^29, $.1^202 ], [ $.1^20, $.1^130 ], [ $.1^45, $.1^330 ], [ $.1^7, $.1^27 ], [ $.1^36, $.1^259 ], [ $.1^39, $.1^283 ], [ $.1^14, $.1^84 ], [ $.1^15, $.1^92 ], [ $.1^19, $.1^188 ], [ $.1^46, $.1^340 ], [ 1, $.1^37 ], [ $.1^26, $.1^245 ], [ $.1^7, $.1^29 ], [ $.1^5, $.1^13 ], [ $.1^19, $.1^189 ], [ $.1^21, $.1^141 ], [ $.1^22, $.1^149 ], [ $.1^3, $.1^62 ], [ $.1^33, $.1^302 ], [ $.1^29, $.1^206 ], [ $.1^28, $.1^198 ], [ $.1^26, $.1^246 ], [ $.1^23, $.1^158 ], [ $.1^14, $.1^86 ], [ $.1^12, $.1^70 ], [ $.1^4, $.1^6 ], [ $.1^10, $.1^119 ], [ $.1^33, $.1^303 ], [ $.1^30, $.1^215 ], [ $.1^21, $.1^143 ], [ $.1^36, $.1^263 ], [ $.1^9, $.1^96 ], [ $.1^28, $.1^200 ], [ $.1^13, $.1^64 ], [ $.1^37, $.1^256 ], [ $.1^2, 3 ], [ $.1^27, $.1^241 ], [ $.1^24, $.1^233 ], [ $.1^6, $.1^25 ], [ $.1^19, $.1^177 ], [ $.1^22, $.1^153 ], [ $.1^44, $.1^329 ], [ $.1^39, $.1^274 ], [ $.1^13, $.1^67 ], [ $.1^34, $.1^315 ], [ $.1^33, $.1^291 ], [ $.1^26, $.1^251 ], [ $.1^16, 6 ], [ $.1^20, $.1^139 ], [ $.1^36, $.1^267 ], [ $.1, $.1^36 ], [ $.1^13, $.1^68 ], [ $.1^2, $.1^60 ], [ $.1^7, $.1^21 ], [ $.1^31, $.1^213 ], [ $.1^14, $.1^93 ], [ $.1^12, $.1^77 ], [ $.1^8, $.1^109 ], [ $.1^7, $.1^22 ], [ $.1^34, $.1^318 ], [ $.1^11, $.1^118 ], [ $.1^8, $.1^110 ], [ $.1^10, $.1^126 ], [ $.1^16, $.1^174 ], [ $.1^35, $.1^310 ], [ $.1^8, $.1^111 ], [ $.1^28, $.1^207 ], [ $.1^13, $.1^71 ], [ $.1^21, $.1^135 ], [ $.1^45, $.1^327 ], [ $.1^24, $.1^240 ], [ $.1^35, $.1^296 ], [ 1, $.1^49 ], [ $.1^6, $.1 ], [ $.1^4, $.1^17 ], [ $.1^19, $.1^169 ], [ $.1, $.1^58 ], [ $.1^29, $.1^218 ], [ $.1^26, $.1^226 ], [ $.1^23, $.1^138 ], [ $.1^6, $.1^2 ], [ $.1^4, $.1^18 ], [ $.1, $.1^59 ], [ $.1^31, $.1^203 ], [ $.1^30, $.1^195 ], [ $.1^2, $.1^35 ], [ $.1^8, $.1^115 ], [ $.1^35, $.1^299 ], [ $.1^36, $.1^275 ], [ $.1^3, $.1^44 ], [ $.1^25, $.1^252 ], [ $.1^23, $.1^140 ], [ $.1^8, $.1^116 ], [ $.1^38, $.1^260 ], [ $.1^39, $.1^268 ], [ $.1^10, $.1^101 ], [ $.1^33, $.1^317 ], [ $.1^32, $.1^309 ], [ $.1^31, $.1^205 ], [ $.1^30, $.1^197 ], [ $.1^27, $.1^237 ], [ $.1^35, $.1^301 ], [ $.1^39, $.1^269 ], [ $.1^46, $.1^325 ], [ $.1^5, $.1^30 ], [ $.1^34, $.1^294 ], [ $.1^25, $.1^254 ], [ $.1^23, $.1^142 ], [ $.1^13, $.1^94 ], [ $.1^38, $.1^262 ], [ $.1^46, $.1^326 ], [ $.1^47, $.1^334 ], [ $.1^2, $.1^39 ], [ $.1^33, $.1^319 ], [ $.1^32, $.1^311 ], [ $.1^30, $.1^199 ], [ $.1^12, $.1^87 ], [ $.1^6, $.1^7 ], [ $.1^4, $.1^23 ], [ $.1^20, $.1^151 ], [ $.1^39, $.1^271 ], [ $.1^7, 1 ], [ $.1^17, $.1^176 ], [ $.1^19, $.1^160 ], [ $.1^37, $.1^272 ], [ $.1^46, $.1^328 ], [ $.1^8, $.1^121 ], [ $.1^32, $.1^313 ], [ $.1^6, $.1^10 ], [ $.1^34, $.1^298 ], [ $.1^31, $.1^194 ], [ $.1^29, $.1^210 ], [ $.1^26, $.1^234 ], [ $.1^13, $.1^82 ], [ $.1^12, $.1^90 ], [ $.1^9, 2 ], [ $.1^39, $.1^258 ], [ $.1^47, $.1^322 ], [ $.1^6, $.1^11 ], [ $.1^11, $.1^99 ], [ $.1^7, $.1^3 ], [ $.1^46, $.1^331 ], [ $.1, $.1^52 ], [ $.1^33, $.1^308 ], [ $.1^5, $.1^20 ], [ $.1^8, $.1^124 ], [ $.1^35, $.1^292 ], [ $.1, $.1^53 ], [ $.1^8, $.1^125 ], [ $.1^9, $.1^117 ], [ $.1^15, $.1^69 ], [ $.1^36, 5 ], [ $.1^39, $.1^261 ], [ $.1, $.1^54 ], [ $.1^14, $.1^78 ], [ $.1^11, $.1^102 ], [ $.1^6, $.1^14 ], [ $.1^21, $.1^150 ], [ $.1^38, $.1^270 ], [ $.1^2, $.1^47 ], [ $.1^28, $.1^223 ], [ $.1^14, $.1^79 ], [ $.1^17, $.1^183 ], [ $.1^18, $.1^175 ], [ $.1^35, $.1^295 ], [ $.1^3, $.1^88 ], [ $.1^6, $.1^112 ], [ $.1^16, $.1^192 ], [ $.1^19, $.1^216 ], [ $.1^41, $.1^264 ], [ $.1, $.1^73 ], [ $.1^28, $.1^161 ], [ $.1^23, $.1^249 ], [ $.1^10, $.1^17 ], [ $.1^16, $.1^193 ], [ $.1^44, $.1^289 ], [ $.1^46, $.1^305 ], [ 1, $.1^66 ], [ $.1^33, $.1^330 ], [ $.1^23, $.1^250 ], [ $.1^10, $.1^18 ], [ $.1^17, $.1^202 ], [ $.1^20, $.1^226 ], [ $.1 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.31) Time: Thu Mar 11 03:44:45 2004 Input: seqt := [7^(r-1) : r in {1..3}]; seqt; P:=PolynomialRing(GF(7,3)); t73 := x^(seqt[1]) + x^(seqt[2]) + x^(seqt[3]); t73; n73 := x^(seqt[1] + seqt[2] + + seqt[3]); n73; Evaluate(n73,2); Olav := {[a,b]: a,b in GF(7,3) | Evaluate(n73,a) eq Evaluate(t73,b)}; #Olav; Output: Magma V2.10-6 Thu Mar 11 2004 03:44:41 on modular [Seed = 3841229364] ------------------------------------- [ 1, 7, 49 ] x^49 + x^7 + x x^57 1 16807 Total time: 4.289 seconds, Total memory usage: 5.38MB ************** MAGMA ***************** Host mnprox15.epo.nl. (145.64.134.235) Time: Thu Mar 11 04:18:39 2004 Input: 5+6 Output: Magma V2.10-6 Thu Mar 11 2004 04:18:36 on modular [Seed = 2291721803] ------------------------------------- 11 Total time: 3.289 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee93.uab.es. (158.109.66.93) Time: Thu Mar 11 04:31:22 2004 Input: exp:=fun; Output: Magma V2.10-6 Thu Mar 11 2004 04:31:14 on modular [Seed = 674781691] ------------------------------------- >> exp:=fun;; ^ User error: bad syntax Total time: 3.299 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee93.uab.es. (158.109.66.93) Time: Thu Mar 11 04:31:34 2004 Input: exp:=func; Output: Magma V2.10-6 Thu Mar 11 2004 04:31:29 on modular [Seed = 420047065] ------------------------------------- >> exp:=func;; ^ User error: Identifier 'qri' has not been declared or assigned Total time: 3.369 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Thu Mar 11 05:55:22 2004 Input: Random(100); Output: Magma V2.10-6 Thu Mar 11 2004 05:55:16 on modular [Seed = 3874939721] ------------------------------------- 35 Total time: 4.249 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee109.uab.es. (158.109.66.109) Time: Thu Mar 11 06:26:22 2004 Input: poli:=GF(343); Output: Magma V2.10-6 Thu Mar 11 2004 06:26:16 on modular [Seed = 470552827] ------------------------------------- Total time: 3.249 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee109.uab.es. (158.109.66.109) Time: Thu Mar 11 06:26:31 2004 Input: poli:=GF(343); Output: Magma V2.10-6 Thu Mar 11 2004 06:26:25 on modular [Seed = 203161810] ------------------------------------- Total time: 4.269 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee109.uab.es. (158.109.66.109) Time: Thu Mar 11 06:27:29 2004 Input: poli:=GF(343); 7^3 Output: Magma V2.10-6 Thu Mar 11 2004 06:27:25 on modular [Seed = 1836933199] ------------------------------------- 343 Total time: 3.209 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee109.uab.es. (158.109.66.109) Time: Thu Mar 11 06:39:57 2004 Input: poli:=GF(343); P:=PolynomialRing(poli); Output: Magma V2.10-6 Thu Mar 11 2004 06:39:52 on modular [Seed = 1565347095] ------------------------------------- Total time: 3.719 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee109.uab.es. (158.109.66.109) Time: Thu Mar 11 06:40:10 2004 Input: poli:=GF(343); P:=PolynomialRing(poli); P; Output: Magma V2.10-6 Thu Mar 11 2004 06:40:06 on modular [Seed = 2003265315] ------------------------------------- Univariate Polynomial Ring over GF(7^3) Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 06:48:30 2004 Input: K := GF(16); R := PolynomialRing(K); a := w^5; p1 := DicksonFirst(3, a); p1; #{ Evaluate(p1, x) : x in K }; IsProbablyPermutationPolynomial(p1); Output: Magma V2.10-6 Thu Mar 11 2004 06:48:26 on modular [Seed = 1752726049] ------------------------------------- x^3 + w^5*x 11 false Total time: 4.069 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 06:49:03 2004 Input: K := GF(16); R := PolynomialRing(K); a := w^5; p1 := DicksonFirst(3, a); IsProbablyPermutationPolynomial(p1); Output: Magma V2.10-6 Thu Mar 11 2004 06:48:59 on modular [Seed = 135797344] ------------------------------------- false Total time: 4.069 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 06:49:23 2004 Input: K := GF(16); R := PolynomialRing(K); a := w^5; p1 := DicksonFirst(4, a); IsProbablyPermutationPolynomial(p1); Output: Magma V2.10-6 Thu Mar 11 2004 06:49:19 on modular [Seed = 487395169] ------------------------------------- true Total time: 4.099 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 06:49:43 2004 Input: K := GF(64); R := PolynomialRing(K); a := w^5; p1 := DicksonFirst(4, a); IsProbablyPermutationPolynomial(p1); Output: Magma V2.10-6 Thu Mar 11 2004 06:49:40 on modular [Seed = 925312288] ------------------------------------- true Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 06:50:17 2004 Input: K := GF(64); R := PolynomialRing(K); p1 := x^7+x; IsProbablyPermutationPolynomial(p1); Output: Magma V2.10-6 Thu Mar 11 2004 06:50:14 on modular [Seed = 3535978727] ------------------------------------- false Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 06:50:30 2004 Input: K := GF(1024); R := PolynomialRing(K); p1 := x^7+x; IsProbablyPermutationPolynomial(p1); Output: Magma V2.10-6 Thu Mar 11 2004 06:50:27 on modular [Seed = 3807572002] ------------------------------------- false Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 06:50:56 2004 Input: K := GF(1024); p1 := x^7+x; IsProbablyPermutationPolynomial(p1); Output: Magma V2.10-6 Thu Mar 11 2004 06:50:52 on modular [Seed = 4041269807] ------------------------------------- >> p1 := x^7+x; ^ User error: Identifier 'x' has not been declared or assigned >> IsProbablyPermutationPolynomial(p1);; ^ User error: Identifier 'p1' has not been declared or assigned Total time: 4.139 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 06:51:05 2004 Input: K := GF(1024); R := PolynomialRing(K); p1 := x^7+x; IsProbablyPermutationPolynomial(p1); Output: Magma V2.10-6 Thu Mar 11 2004 06:51:01 on modular [Seed = 2207486309] ------------------------------------- false Total time: 3.149 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 06:51:26 2004 Input: K := GF(7^4); R := PolynomialRing(K); p1 := x^8+x; IsProbablyPermutationPolynomial(p1); Output: Magma V2.10-6 Thu Mar 11 2004 06:51:22 on modular [Seed = 2424341097] ------------------------------------- false Total time: 4.139 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee109.uab.es. (158.109.66.109) Time: Thu Mar 11 06:53:26 2004 Input: r:=RationalField(); P:=PolynomialRing(r); P; Output: Magma V2.10-6 Thu Mar 11 2004 06:53:22 on modular [Seed = 1331649593] ------------------------------------- Univariate Polynomial Ring over Rational Field Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee109.uab.es. (158.109.66.109) Time: Thu Mar 11 06:53:41 2004 Input: r:=RationalField(); P:=PolynomialRing(r); P; Output: Magma V2.10-6 Thu Mar 11 2004 06:53:37 on modular [Seed = 1685354337] ------------------------------------- Univariate Polynomial Ring over Rational Field Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee109.uab.es. (158.109.66.109) Time: Thu Mar 11 06:54:05 2004 Input: r:=RationalField(); P:=PolynomialRing(r); P; print(P); Output: Magma V2.10-6 Thu Mar 11 2004 06:53:59 on modular [Seed = 1986422117] ------------------------------------- Univariate Polynomial Ring over Rational Field Univariate Polynomial Ring over Rational Field Total time: 4.169 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Thu Mar 11 07:03:48 2004 Input: function> C:={}; function> for i in {1..r} do Include(C,q^(r-i)); end for;return {C}; end function; > tqr(7,3); Output: Magma V2.10-6 Thu Mar 11 2004 07:03:42 on modular [Seed = 453709505] ------------------------------------- >> function> C:={}; ^ User error: bad syntax >> function> for i in {1..r} do Include(C,q^(r-i)); end for;return {C}; end fu ^ User error: bad syntax >> tqr(7,3);; ^ User error: Identifier 'tqr' has not been declared or assigned Total time: 3.709 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee109.uab.es. (158.109.66.109) Time: Thu Mar 11 07:03:50 2004 Input: poli:=GF(343); exponentes:=[7^r:r in [2,1,0]]; Output: Magma V2.10-6 Thu Mar 11 2004 07:03:44 on modular [Seed = 775830475] ------------------------------------- Total time: 3.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee109.uab.es. (158.109.66.109) Time: Thu Mar 11 07:04:19 2004 Input: poli:=GF(343); exponentes:=[7^r:r in [2,1,0]]; exponentes; Output: Magma V2.10-6 Thu Mar 11 2004 07:04:15 on modular [Seed = 3487554101] ------------------------------------- [ 49, 7, 1 ] Total time: 3.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Thu Mar 11 07:05:30 2004 Input: SetEchoInput(true); Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed. ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 07:15:27 2004 Input: K := GF(11,11); #K; Output: Magma V2.10-6 Thu Mar 11 2004 07:15:24 on modular [Seed = 1196908380] ------------------------------------- 285311670611 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 07:15:43 2004 Input: K := GF(11,11); #K; Output: Magma V2.10-6 Thu Mar 11 2004 07:15:40 on modular [Seed = 1497973106] ------------------------------------- 285311670611 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 07:16:45 2004 Input: // comment K := GF(11,11); #K; Output: Magma V2.10-6 Thu Mar 11 2004 07:16:42 on modular [Seed = 2036949396] ------------------------------------- 285311670611 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 07:17:02 2004 Input: // comment K := GF(11,21); #K; Output: Magma V2.10-6 Thu Mar 11 2004 07:16:58 on modular [Seed = 1054973] ------------------------------------- 7400249944258160101211 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 07:35:20 2004 Input: // test si x^[(q+n-1)/n]+bx est un poly de permut. sur Fq test_poly := function(n,b,K) if ((-b)^n eq 1) then return false; end if; z:=RootOfUnity(n,K); k:=(q-1)/n; W[0]:=1; B[0]:=(b+1)^k; for j:=1 to (n-1) do W[j]:=W[j-1]*z; B[j]:=(b+W[j])^k; for i:=0 to j-1 do if ( (B[i]/B[j]) eq W[j-i] ) then return false; end for; end for; return true; end function; K:=GF(26); R := PolynomialRing(K); test_poly(2,1,K); Output: Magma V2.10-6 Thu Mar 11 2004 07:35:17 on modular [Seed = 3470709635] ------------------------------------- >> end for; ^ User error: bad syntax >> end for; ^ User error: bad syntax >> return true; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> K:=GF(26); ^ Runtime error in 'GF': Argument 1 (26) is not a prime power >> R := PolynomialRing(K); ^ User error: Identifier 'K' has not been declared or assigned >> test_poly(2,1,K);; ^ User error: Identifier 'K' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 07:35:35 2004 Input: test_poly := function(n,b,K) if ((-b)^n eq 1) then return false; end if; z:=RootOfUnity(n,K); k:=(q-1)/n; W[0]:=1; B[0]:=(b+1)^k; for j:=1 to (n-1) do W[j]:=W[j-1]*z; B[j]:=(b+W[j])^k; for i:=0 to j-1 do if ( (B[i]/B[j]) eq W[j-i] ) then return false; end for; end for; return true; end function; K:=GF(26); R := PolynomialRing(K); test_poly(2,1,K); Output: Magma V2.10-6 Thu Mar 11 2004 07:35:32 on modular [Seed = 3352812187] ------------------------------------- >> end for; ^ User error: bad syntax >> end for; ^ User error: bad syntax >> return true; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> K:=GF(26); ^ Runtime error in 'GF': Argument 1 (26) is not a prime power >> R := PolynomialRing(K); ^ User error: Identifier 'K' has not been declared or assigned >> test_poly(2,1,K);; ^ User error: Identifier 'K' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 07:36:44 2004 Input: test_poly := function(n,b,K) if ((-b)^n eq 1) then return false; end if; z:=RootOfUnity(n,K); k:=(q-1)/n; W[0]:=1; B[0]:=(b+1)^k; for j in [1..(n-1)] do W[j]:=W[j-1]*z; B[j]:=(b+W[j])^k; for i in [0..(j-1)] do if ( (B[i]/B[j]) eq W[j-i] ) then return false; end if; end for; end for; return true; end function; K:=GF(26); R := PolynomialRing(K); test_poly(2,1,K); Output: Magma V2.10-6 Thu Mar 11 2004 07:36:41 on modular [Seed = 3519139008] ------------------------------------- >> k:=(q-1)/n; ^ User error: Identifier 'q' has not been declared or assigned >> K:=GF(26); ^ Runtime error in 'GF': Argument 1 (26) is not a prime power >> R := PolynomialRing(K); ^ User error: Identifier 'K' has not been declared or assigned >> test_poly(2,1,K);; ^ User error: Identifier 'K' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 07:37:18 2004 Input: test_poly := function(n,b,K) if ((-b)^n eq 1) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1)/n; W[0]:=1; B[0]:=(b+1)^k; for j in [1..(n-1)] do W[j]:=W[j-1]*z; B[j]:=(b+W[j])^k; for i in [0..(j-1)] do if ( (B[i]/B[j]) eq W[j-i] ) then return false; end if; end for; end for; return true; end function; K:=GF(26); R := PolynomialRing(K); test_poly(2,1,K); Output: Magma V2.10-6 Thu Mar 11 2004 07:37:15 on modular [Seed = 3942315993] ------------------------------------- >> W[0]:=1; ^ User error: Identifier 'W' has not been declared or assigned >> K:=GF(26); ^ Runtime error in 'GF': Argument 1 (26) is not a prime power >> R := PolynomialRing(K); ^ User error: Identifier 'K' has not been declared or assigned >> test_poly(2,1,K);; ^ User error: Identifier 'K' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 07:42:26 2004 Input: test_poly := function(n,b,K) if ((-b)^n eq 1) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1)/n; W:=[]; W[0]:=1; B[0]:=(b+1)^k; for j in [1..(n-1)] do W[j]:=W[j-1]*z; B[j]:=(b+W[j])^k; for i in [0..(j-1)] do if ( (B[i]/B[j]) eq W[j-i] ) then return false; end if; end for; end for; return true; end function; K:=GF(26); R := PolynomialRing(K); test_poly(2,1,K); Output: Magma V2.10-6 Thu Mar 11 2004 07:42:23 on modular [Seed = 4260225818] ------------------------------------- >> B[0]:=(b+1)^k; ^ User error: Identifier 'B' has not been declared or assigned >> K:=GF(26); ^ Runtime error in 'GF': Argument 1 (26) is not a prime power >> R := PolynomialRing(K); ^ User error: Identifier 'K' has not been declared or assigned >> test_poly(2,1,K);; ^ User error: Identifier 'K' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 07:42:41 2004 Input: test_poly := function(n,b,K) if ((-b)^n eq 1) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1)/n; W:=[]; B:=[]; W[0]:=1; B[0]:=(b+1)^k; for j in [1..(n-1)] do W[j]:=W[j-1]*z; B[j]:=(b+W[j])^k; for i in [0..(j-1)] do if ( (B[i]/B[j]) eq W[j-i] ) then return false; end if; end for; end for; return true; end function; K:=GF(26); R := PolynomialRing(K); test_poly(2,1,K); Output: Magma V2.10-6 Thu Mar 11 2004 07:42:38 on modular [Seed = 4142327808] ------------------------------------- >> K:=GF(26); ^ Runtime error in 'GF': Argument 1 (26) is not a prime power >> R := PolynomialRing(K); ^ User error: Identifier 'K' has not been declared or assigned >> test_poly(2,1,K);; ^ User error: Identifier 'K' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 07:43:02 2004 Input: test_poly := function(n,b,K) if ((-b)^n eq 1) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1)/n; W:=[]; B:=[]; W[0]:=1; B[0]:=(b+1)^k; for j in [1..(n-1)] do W[j]:=W[j-1]*z; B[j]:=(b+W[j])^k; for i in [0..(j-1)] do if ( (B[i]/B[j]) eq W[j-i] ) then return false; end if; end for; end for; return true; end function; K:=GF(49); R := PolynomialRing(K); test_poly(2,1,K); Output: Magma V2.10-6 Thu Mar 11 2004 07:42:59 on modular [Seed = 2156961307] ------------------------------------- false Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 07:43:22 2004 Input: test_poly := function(n,b,K) if ((-b)^n eq 1) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1)/n; W:=[]; B:=[]; W[0]:=1; B[0]:=(b+1)^k; for j in [1..(n-1)] do W[j]:=W[j-1]*z; B[j]:=(b+W[j])^k; for i in [0..(j-1)] do if ( (B[i]/B[j]) eq W[j-i] ) then return false; end if; end for; end for; return true; end function; K:=GF(49); R := PolynomialRing(K); test_poly(2,w,K); Output: Magma V2.10-6 Thu Mar 11 2004 07:43:19 on modular [Seed = 2575927094] ------------------------------------- [
:3]( n: 2, b: w, K: GF(7^2) ) >> W[0]:=1; ^ Runtime error in :=: Bad sequence index Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 07:44:36 2004 Input: test_poly := function(n,b,K) if ((-b)^n eq 1) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1)/n; W:=[]; B:=[]; W[1]:=1; B[1]:=(b+1)^k; for j in [2..n] do W[j]:=W[j-1]*z; B[j]:=(b+W[j])^k; for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i] ) then return false; end if; end for; end for; return true; end function; K:=GF(49); R := PolynomialRing(K); test_poly(2,w,K); Output: Magma V2.10-6 Thu Mar 11 2004 07:44:33 on modular [Seed = 2474872042] ------------------------------------- [
:3]( n: 2, b: w, K: GF(7^2) ) >> B[1]:=(b+1)^k; ^ Runtime error in '^': Bad argument types Argument types given: FldFinElt, FldFinElt Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 07:45:14 2004 Input: test_poly := function(n,b,K) if ((-b)^n eq 1) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1)/n; W:=[]; B:=[]; W[1]:=1; B[1]:=(b+1)^3; for j in [2..n] do W[j]:=W[j-1]*z; B[j]:=(b+W[j])^k; for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i] ) then return false; end if; end for; end for; return true; end function; K:=GF(49); R := PolynomialRing(K); test_poly(2,w,K); Output: Magma V2.10-6 Thu Mar 11 2004 07:45:11 on modular [Seed = 2813835448] ------------------------------------- [
:3]( n: 2, b: w, K: GF(7^2) ) >> B[j]:=(b+W[j])^k; ^ Runtime error in '^': Bad argument types Argument types given: FldFinElt, FldFinElt Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 07:45:37 2004 Input: test_poly := function(n,b,K) if ((-b)^n eq 1) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1)/n; W:=[]; B:=[]; W[1]:=1; B[1]:=(b+1)^k; for j in [2..n] do W[j]:=W[j-1]*z; B[j]:=(b+W[j])^k; for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i] ) then return false; end if; end for; end for; return true; end function; K:=GF(49); R := PolynomialRing(K); test_poly(2,w,K); Output: Magma V2.10-6 Thu Mar 11 2004 07:45:34 on modular [Seed = 2963320726] ------------------------------------- [
:3]( n: 2, b: w, K: GF(7^2) ) >> B[1]:=(b+1)^k; ^ Runtime error in '^': Bad argument types Argument types given: FldFinElt, FldFinElt Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 07:49:23 2004 Input: test_poly := function(n,b,K) if ((-b)^n eq 1) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1)/n; W:=[]; B:=[]; W[1]:=1; B[1]:=(b+1)^k; for j in [2..n] do W[j]:=W[j-1]*z; B[j]:=(b+W[j])^k; for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i] ) then return false; end if; end for; end for; return true; end function; K:=GF(49); Type(#K); R := PolynomialRing(K); test_poly(2,w,K); Output: Magma V2.10-6 Thu Mar 11 2004 07:49:20 on modular [Seed = 1919046251] ------------------------------------- RngIntElt [
:3]( n: 2, b: w, K: GF(7^2) ) >> B[1]:=(b+1)^k; ^ Runtime error in '^': Bad argument types Argument types given: FldFinElt, FldFinElt Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 07:50:07 2004 Input: test_poly := function(n,b,K) if (((-b)^n) eq 1) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1)/n; W:=[]; B:=[]; W[1]:=1; B[1]:=(b+1)^k; for j in [2..n] do W[j]:=W[j-1]*z; B[j]:=(b+W[j])^k; for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i] ) then return false; end if; end for; end for; return true; end function; K:=GF(49); Type(#K); R := PolynomialRing(K); test_poly(2,w,K); Output: Magma V2.10-6 Thu Mar 11 2004 07:50:03 on modular [Seed = 470563886] ------------------------------------- RngIntElt [
:3]( n: 2, b: w, K: GF(7^2) ) >> B[1]:=(b+1)^k; ^ Runtime error in '^': Bad argument types Argument types given: FldFinElt, FldFinElt Total time: 4.099 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 07:51:03 2004 Input: test_poly := function(n,b,K) if ( ((-b)^n) eq 1) then return false; end if; z:=RootOfUnity(n,K); print Type(n); k:=(#K-1)/n; W:=[]; B:=[]; W[1]:=1; B[1]:=(b+1)^k; for j in [2..n] do W[j]:=W[j-1]*z; B[j]:=(b+W[j])^k; for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i] ) then return false; end if; end for; end for; return true; end function; K:=GF(49); Type(#K); R := PolynomialRing(K); test_poly(2,w,K); Output: Magma V2.10-6 Thu Mar 11 2004 07:51:00 on modular [Seed = 590545886] ------------------------------------- RngIntElt RngIntElt [
:3]( n: 2, b: w, K: GF(7^2) ) >> B[1]:=(b+1)^k; ^ Runtime error in '^': Bad argument types Argument types given: FldFinElt, FldFinElt Total time: 3.219 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 07:51:21 2004 Input: test_poly := function(n,b,K) if ( ((-b)^n) eq 1) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1)/n; print Type(k); W:=[]; B:=[]; W[1]:=1; B[1]:=(b+1)^k; for j in [2..n] do W[j]:=W[j-1]*z; B[j]:=(b+W[j])^k; for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i] ) then return false; end if; end for; end for; return true; end function; K:=GF(49); Type(#K); R := PolynomialRing(K); test_poly(2,w,K); Output: Magma V2.10-6 Thu Mar 11 2004 07:51:18 on modular [Seed = 1043209905] ------------------------------------- RngIntElt FldRatElt [
:3]( n: 2, b: w, K: GF(7^2) ) >> B[1]:=(b+1)^k; ^ Runtime error in '^': Bad argument types Argument types given: FldFinElt, FldFinElt Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 07:51:48 2004 Input: test_poly := function(n,b,K) if ( ((-b)^n) eq 1) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1)/n; print k; W:=[]; B:=[]; W[1]:=1; B[1]:=(b+1)^k; for j in [2..n] do W[j]:=W[j-1]*z; B[j]:=(b+W[j])^k; for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i] ) then return false; end if; end for; end for; return true; end function; K:=GF(49); Type(#K); R := PolynomialRing(K); test_poly(2,w,K); Output: Magma V2.10-6 Thu Mar 11 2004 07:51:44 on modular [Seed = 3470716519] ------------------------------------- RngIntElt 24 [
:3]( n: 2, b: w, K: GF(7^2) ) >> B[1]:=(b+1)^k; ^ Runtime error in '^': Bad argument types Argument types given: FldFinElt, FldFinElt Total time: 3.599 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 07:52:11 2004 Input: test_poly := function(n,b,K) if ( ((-b)^n) eq 1) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1)/n; print k; W:=[]; B:=[]; W[1]:=1; B[1]:=((b+1)^k); for j in [2..n] do W[j]:=W[j-1]*z; B[j]:=(b+W[j])^k; for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i] ) then return false; end if; end for; end for; return true; end function; K:=GF(49); Type(#K); R := PolynomialRing(K); test_poly(2,w,K); Output: Magma V2.10-6 Thu Mar 11 2004 07:52:08 on modular [Seed = 3754950510] ------------------------------------- RngIntElt 24 [
:3]( n: 2, b: w, K: GF(7^2) ) >> B[1]:=((b+1)^k); ^ Runtime error in '^': Bad argument types Argument types given: FldFinElt, FldFinElt Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 07:53:52 2004 Input: test_poly := function(n,b,K) if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1)/n; print k; W:=[]; B:=[]; W[1]:=1; B[1]:=((b+1)^k); for j in [2..n] do W[j]:=W[j-1]*z; B[j]:=(b+W[j])^k; for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i] ) then return false; end if; end for; end for; return true; end function; K:=GF(49); R := PolynomialRing(K); test_poly(2,w,K); Output: Magma V2.10-6 Thu Mar 11 2004 07:53:49 on modular [Seed = 4041265636] ------------------------------------- 24 [
:3]( n: 2, b: w, K: GF(7^2) ) >> B[1]:=((b+1)^k); ^ Runtime error in '^': Bad argument types Argument types given: FldFinElt, FldFinElt Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 07:57:04 2004 Input: test_poly := function(n,b,K) if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; print k; W:=[]; B:=[]; W[1]:=1; B[1]:=((b+1)^k); for j in [2..n] do W[j]:=W[j-1]*z; B[j]:=(b+W[j])^k; for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i] ) then return false; end if; end for; end for; return true; end function; K:=GF(49); R := PolynomialRing(K); test_poly(2,w,K); Output: Magma V2.10-6 Thu Mar 11 2004 07:57:01 on modular [Seed = 3047528417] ------------------------------------- 24 false Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 07:59:10 2004 Input: test_poly := function(n,b,K) if (#K mod n neq 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; print k; W:=[]; B:=[]; W[1]:=1; B[1]:=((b+1)^k); for j in [2..n] do W[j]:=W[j-1]*z; B[j]:=(b+W[j])^k; for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i] ) then return false; end if; end for; end for; return true; end function; K:=GF(49); R := PolynomialRing(K); test_poly(2,w,K); Output: Magma V2.10-6 Thu Mar 11 2004 07:59:06 on modular [Seed = 1752713912] ------------------------------------- >> if (#K mod n neq 1) then ^ User error: bad syntax erreur, il faut #K = 1 mod n >> return false; ^ User error: A 'return' can only be used inside a procedure or function >> end if; ^ User error: bad syntax >> if IsOne((-b)^n) then ^ User error: Identifier 'b' has not been declared or assigned >> z:=RootOfUnity(n,K); ^ User error: Identifier 'n' has not been declared or assigned >> k:=(#K-1) div n; ^ User error: Identifier 'K' has not been declared or assigned >> print k; ^ User error: Identifier 'k' has not been declared or assigned >> B[1]:=((b+1)^k); ^ User error: Identifier 'b' has not been declared or assigned >> for j in [2..n] do ^ User error: Identifier 'n' has not been declared or assigned >> return true; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> test_poly(2,w,K);; ^ User error: Identifier 'test_poly' has not been declared or assigned Total time: 4.099 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 07:59:27 2004 Input: test_poly := function(n,b,K) if ((#K mod n) neq 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; print k; W:=[]; B:=[]; W[1]:=1; B[1]:=((b+1)^k); for j in [2..n] do W[j]:=W[j-1]*z; B[j]:=(b+W[j])^k; for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i] ) then return false; end if; end for; end for; return true; end function; K:=GF(49); R := PolynomialRing(K); test_poly(2,w,K); Output: Magma V2.10-6 Thu Mar 11 2004 07:59:24 on modular [Seed = 1685341826] ------------------------------------- >> if ((#K mod n) neq 1) then ^ User error: bad syntax erreur, il faut #K = 1 mod n >> return false; ^ User error: A 'return' can only be used inside a procedure or function >> end if; ^ User error: bad syntax >> if IsOne((-b)^n) then ^ User error: Identifier 'b' has not been declared or assigned >> z:=RootOfUnity(n,K); ^ User error: Identifier 'n' has not been declared or assigned >> k:=(#K-1) div n; ^ User error: Identifier 'K' has not been declared or assigned >> print k; ^ User error: Identifier 'k' has not been declared or assigned >> B[1]:=((b+1)^k); ^ User error: Identifier 'b' has not been declared or assigned >> for j in [2..n] do ^ User error: Identifier 'n' has not been declared or assigned >> return true; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> test_poly(2,w,K);; ^ User error: Identifier 'test_poly' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 07:59:54 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; print k; W:=[]; B:=[]; W[1]:=1; B[1]:=((b+1)^k); for j in [2..n] do W[j]:=W[j-1]*z; B[j]:=(b+W[j])^k; for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i] ) then return false; end if; end for; end for; return true; end function; K:=GF(49); R := PolynomialRing(K); test_poly(2,w,K); Output: Magma V2.10-6 Thu Mar 11 2004 07:59:51 on modular [Seed = 2003260922] ------------------------------------- 24 false Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:00:12 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; print k; W:=[]; B:=[]; W[1]:=1; B[1]:=((b+1)^k); for j in [2..n] do W[j]:=W[j-1]*z; B[j]:=(b+W[j])^k; for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i] ) then return false; end if; end for; end for; return true; end function; K:=GF(49); R := PolynomialRing(K); test_poly(5,w,K); Output: Magma V2.10-6 Thu Mar 11 2004 08:00:09 on modular [Seed = 521092492] ------------------------------------- erreur, il faut #K = 1 mod n false Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:00:37 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; print k; W:=[]; B:=[]; W[1]:=1; B[1]:=((b+1)^k); for j in [2..n] do W[j]:=W[j-1]*z; B[j]:=(b+W[j])^k; for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i] ) then return false; end if; end for; end for; return true; end function; K:=GF(49); R := PolynomialRing(K); test_poly(4,w,K); Output: Magma V2.10-6 Thu Mar 11 2004 08:00:34 on modular [Seed = 556860313] ------------------------------------- 12 [
:3]( n: 4, b: w, K: GF(7^2) ) >> W[j]:=W[j-1]*z; ^ Runtime error in :=: Sequence mutation failed Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:01:16 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; print k; W:=[]; B:=[]; W[1]:=1; B[1]:=(b+1)^k; for j in [2..n] do W[j]:=W[j-1]*z; B[j]:=(b+W[j])^k; for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i] ) then return false; end if; end for; end for; return true; end function; K:=GF(49); R := PolynomialRing(K); test_poly(4,w,K); Output: Magma V2.10-6 Thu Mar 11 2004 08:01:13 on modular [Seed = 3653892746] ------------------------------------- 12 [
:3]( n: 4, b: w, K: GF(7^2) ) >> W[j]:=W[j-1]*z; ^ Runtime error in :=: Sequence mutation failed Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:02:13 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; print k; W:=[]; B:=[]; W[1]:=1; B[1]:=(b+1)^k; print W; for j in [2..n] do W[j]:=W[j-1]*z; B[j]:=(b+W[j])^k; for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i] ) then return false; end if; end for; end for; return true; end function; K:=GF(49); R := PolynomialRing(K); test_poly(4,w,K); Output: Magma V2.10-6 Thu Mar 11 2004 08:02:10 on modular [Seed = 2375921301] ------------------------------------- 12 [ 1 ] [
:3]( n: 4, b: w, K: GF(7^2) ) >> W[j]:=W[j-1]*z; ^ Runtime error in :=: Sequence mutation failed Total time: 3.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:07:47 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; print k; W:=[]; B:=[]; Append(~W,1); B[1]:=(b+1)^k; print W; for j in [2..n] do W[j]:=W[j-1]*z; B[j]:=(b+W[j])^k; for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i] ) then return false; end if; end for; end for; return true; end function; K:=GF(49); R := PolynomialRing(K); test_poly(4,w,K); Output: Magma V2.10-6 Thu Mar 11 2004 08:07:43 on modular [Seed = 590546935] ------------------------------------- 12 [ 1 ] [
:3]( n: 4, b: w, K: GF(7^2) ) >> W[j]:=W[j-1]*z; ^ Runtime error in :=: Sequence mutation failed Total time: 4.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:08:25 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; print k; W:=[]; B:=[]; Append(~W,1); Append(~B,(b+1)^k); print W; for j in [2..n] do Append(~W,W[j-1]*z); B[j]:=(b+W[j])^k; for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i] ) then return false; end if; end for; end for; return true; end function; K:=GF(49); R := PolynomialRing(K); test_poly(4,w,K); Output: Magma V2.10-6 Thu Mar 11 2004 08:08:21 on modular [Seed = 3470715456] ------------------------------------- 12 [ 1 ] [
:3]( n: 4, b: w, K: GF(7^2) ) >> Append(~W,W[j-1]*z); ^ Runtime error in 'Append': Could not lift element into sequence Total time: 3.789 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:09:12 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; print k; W:=[]; B:=[]; Append(~W,1); Append(~B,(b+1)^k); print W; for j in [2..n] do print(W[j-1]*z; Append(~W,W[j-1]*z); B[j]:=(b+W[j])^k; for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i] ) then return false; end if; end for; end for; return true; end function; K:=GF(49); R := PolynomialRing(K); test_poly(4,w,K); Output: Magma V2.10-6 Thu Mar 11 2004 08:09:09 on modular [Seed = 3959148373] ------------------------------------- >> print(W[j-1]*z; ^ User error: bad syntax >> Append(~W,W[j-1]*z); ^ User error: Identifier 'j' has not been declared or assigned >> B[j]:=(b+W[j])^k; ^ User error: Identifier 'b' has not been declared or assigned >> for i in [1..j] do ^ User error: Identifier 'j' has not been declared or assigned >> end for; ^ User error: bad syntax >> return true; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> test_poly(4,w,K);; ^ User error: Identifier 'test_poly' has not been declared or assigned Total time: 3.119 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:09:26 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; print k; W:=[]; B:=[]; Append(~W,1); Append(~B,(b+1)^k); print W; for j in [2..n] do print(W[j-1]*z); Append(~W,W[j-1]*z); B[j]:=(b+W[j])^k; for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i] ) then return false; end if; end for; end for; return true; end function; K:=GF(49); R := PolynomialRing(K); test_poly(4,w,K); Output: Magma V2.10-6 Thu Mar 11 2004 08:09:22 on modular [Seed = 4226539186] ------------------------------------- 12 [ 1 ] w^12 [
:3]( n: 4, b: w, K: GF(7^2) ) >> Append(~W,W[j-1]*z); ^ Runtime error in 'Append': Could not lift element into sequence Total time: 4.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:10:11 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; print k; W:=[]; B:=[]; Append(~W,1); Append(~B,(b+1)^k); print z; for j in [2..n] do print(W[j-1]*z); Append(~W,W[j-1]*z); B[j]:=(b+W[j])^k; for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i] ) then return false; end if; end for; end for; return true; end function; K:=GF(49); R := PolynomialRing(K); test_poly(4,w,K); Output: Magma V2.10-6 Thu Mar 11 2004 08:10:08 on modular [Seed = 2575940834] ------------------------------------- 12 w^12 w^12 [
:3]( n: 4, b: w, K: GF(7^2) ) >> Append(~W,W[j-1]*z); ^ Runtime error in 'Append': Could not lift element into sequence Total time: 3.529 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:11:00 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; print k; W:=[]; B:=[]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do print Type(W[j-1]*z); Append(~W,W[j-1]*z); B[j]:=(b+W[j])^k; for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i] ) then return false; end if; end for; end for; return true; end function; K:=GF(49); R := PolynomialRing(K); test_poly(4,w,K); Output: Magma V2.10-6 Thu Mar 11 2004 08:10:57 on modular [Seed = 2780135567] ------------------------------------- 12 FldFinElt [
:3]( n: 4, b: w, K: GF(7^2) ) >> Append(~W,W[j-1]*z); ^ Runtime error in 'Append': Could not lift element into sequence Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:11:43 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; print k; W:=[]; B:=[]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i] ) then return false; end if; end for; end for; return true; end function; K:=GF(49); R := PolynomialRing(K); test_poly(4,w,K); Output: Magma V2.10-6 Thu Mar 11 2004 08:11:39 on modular [Seed = 1112696709] ------------------------------------- 12 [
:3]( n: 4, b: w, K: GF(7^2) ) >> Append(~W,W[j-1]*z); ^ Runtime error in 'Append': Could not lift element into sequence Total time: 4.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:12:27 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; print k; W:=[]; B:=[]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do print Type(W); print Type(W[j-1]*z); Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i] ) then return false; end if; end for; end for; return true; end function; K:=GF(49); R := PolynomialRing(K); test_poly(4,w,K); Output: Magma V2.10-6 Thu Mar 11 2004 08:12:23 on modular [Seed = 1719026589] ------------------------------------- 12 SeqEnum FldFinElt [
:3]( n: 4, b: w, K: GF(7^2) ) >> Append(~W,W[j-1]*z); ^ Runtime error in 'Append': Could not lift element into sequence Total time: 4.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:12:58 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; print k; W:=[]; B:=[]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do print Type(W); print Type(W[j-1]*z); Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i] ) then return false; end if; end for; end for; return true; end function; K:=GF(7,2); R := PolynomialRing(K); test_poly(4,w,K); Output: Magma V2.10-6 Thu Mar 11 2004 08:12:54 on modular [Seed = 203172246] ------------------------------------- 12 SeqEnum FldFinElt [
:3]( n: 4, b: w, K: GF(7^2) ) >> Append(~W,W[j-1]*z); ^ Runtime error in 'Append': Could not lift element into sequence Total time: 4.099 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:19:51 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; print k; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do print Type(W); print Type(W[j-1]*z); Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i] ) then return false; end if; end for; end for; return true; end function; K:=GF(7,2); R := PolynomialRing(K); test_poly(4,w,K); Output: Magma V2.10-6 Thu Mar 11 2004 08:19:47 on modular [Seed = 3148586116] ------------------------------------- 12 SeqEnum FldFinElt [
:3]( n: 4, b: w, K: GF(7^2) ) >> if ( (B[i]/B[j]) eq W[j-i] ) then ^ Runtime error in '[]': Sequence element 0 not defined Total time: 3.599 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:20:18 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; print k; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do print Type(W); print Type(W[j-1]*z); Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i+1] ) then return false; end if; end for; end for; return true; end function; K:=GF(7,2); R := PolynomialRing(K); test_poly(4,w,K); Output: Magma V2.10-6 Thu Mar 11 2004 08:20:15 on modular [Seed = 1565358751] ------------------------------------- 12 SeqEnum FldFinElt false Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:23:31 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; print k; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do print Type(W); print Type(W[j-1]*z); Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i+1] ) then return false; end if; end for; end for; return true; end function; K:=GF(7,2); R := PolynomialRing(K); time test_poly(4,w,K); time IsProbablyPermutationPolynomial(x^((49+4-1)/4)+w*x); Output: Magma V2.10-6 Thu Mar 11 2004 08:23:27 on modular [Seed = 1043207740] ------------------------------------- 12 SeqEnum FldFinElt false Time: 0.000 >> time IsProbablyPermutationPolynomial(x^((49+4-1)/4)+w*x);; ^ Runtime error in '^': Bad argument types Argument types given: RngUPolElt, RngUPolElt Total time: 3.819 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:23:54 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; print k; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do print Type(W); print Type(W[j-1]*z); Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i+1] ) then return false; end if; end for; end for; return true; end function; K:=GF(7,2); R := PolynomialRing(K); time test_poly(4,w,K); time IsProbablyPermutationPolynomial(x^((49+4-1) div 4)+w*x); Output: Magma V2.10-6 Thu Mar 11 2004 08:23:50 on modular [Seed = 3420185569] ------------------------------------- 12 SeqEnum FldFinElt false Time: 0.000 false Time: 0.000 Total time: 3.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:25:11 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; print k; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do print Type(W); print Type(W[j-1]*z); Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i+1] ) then return false; end if; end for; end for; return true; end function; K:=GF(2,10); R := PolynomialRing(K); time test_poly(3,w,K); time IsProbablyPermutationPolynomial(x^342+w*x); Output: Magma V2.10-6 Thu Mar 11 2004 08:25:07 on modular [Seed = 4192850183] ------------------------------------- 341 SeqEnum FldFinElt false Time: 0.010 false Time: 0.000 Total time: 4.129 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:25:37 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i+1] ) then return false; end if; end for; end for; return true; end function; K:=GF(2,10); R := PolynomialRing(K); time test_poly(3,w,K); time IsProbablyPermutationPolynomial(x^342+w*x); Output: Magma V2.10-6 Thu Mar 11 2004 08:25:33 on modular [Seed = 2592780826] ------------------------------------- false Time: 0.000 false Time: 0.000 Total time: 3.599 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:26:43 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i+1] ) then return false; end if; end for; end for; return true; end function; K:=GF(2,10); R := PolynomialRing(K); time test_poly(94,w,K); time IsProbablyPermutationPolynomial(x^94+w*x); Output: Magma V2.10-6 Thu Mar 11 2004 08:26:40 on modular [Seed = 1314809616] ------------------------------------- erreur, il faut #K = 1 mod n false Time: 0.000 false Time: 0.010 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:26:54 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i+1] ) then return false; end if; end for; end for; return true; end function; K:=GF(2,10); R := PolynomialRing(K); time test_poly(94,w,K); time IsProbablyPermutationPolynomial(x^94+w*x); Output: Magma V2.10-6 Thu Mar 11 2004 08:26:50 on modular [Seed = 1196912147] ------------------------------------- erreur, il faut #K = 1 mod n false Time: 0.000 false Time: 0.000 Total time: 3.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:27:38 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i+1] ) then return false; end if; end for; end for; return true; end function; K:=GF(2,10); R := PolynomialRing(K); time test_poly(32,w,K); time IsProbablyPermutationPolynomial(x^32+w*x); Output: Magma V2.10-6 Thu Mar 11 2004 08:27:35 on modular [Seed = 1969577084] ------------------------------------- erreur, il faut #K = 1 mod n false Time: 0.000 true Time: 0.050 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:27:53 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i+1] ) then return false; end if; end for; end for; return true; end function; K:=GF(2,10); R := PolynomialRing(K); time test_poly(32,w,K); time IsProbablyPermutationPolynomial(x^32+w*x); Output: Magma V2.10-6 Thu Mar 11 2004 08:27:50 on modular [Seed = 68431132] ------------------------------------- erreur, il faut #K = 1 mod n false Time: 0.000 true Time: 0.050 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:28:32 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i+1] ) then return false; end if; end for; end for; return true; end function; K:=GF(2,10); R := PolynomialRing(K); time test_poly(33,w,K); time IsProbablyPermutationPolynomial(x^32+w*x); Output: Magma V2.10-6 Thu Mar 11 2004 08:28:29 on modular [Seed = 657919508] ------------------------------------- false Time: 0.000 true Time: 0.040 Total time: 3.689 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:28:43 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i+1] ) then return false; end if; end for; end for; return true; end function; K:=GF(2,10); R := PolynomialRing(K); time test_poly(33,w,K); time IsProbablyPermutationPolynomial(x^32+w*x); Output: Magma V2.10-6 Thu Mar 11 2004 08:28:39 on modular [Seed = 3487557126] ------------------------------------- false Time: 0.000 true Time: 0.050 Total time: 3.689 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:31:18 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i+1] ) then return false; end if; end for; end for; return true; end function; q:=2^10; K=GF(q); R := PolynomialRing(K); n:=33; a:=w; p:=x^((q-1+n) div n)+a*x; time test_poly(n,a,K); time IsProbablyPermutationPolynomial(p); Output: Magma V2.10-6 Thu Mar 11 2004 08:31:14 on modular [Seed = 2881192391] ------------------------------------- >> K=GF(q); ^ User error: bad syntax >> R := PolynomialRing(K); ^ User error: Identifier 'K' has not been declared or assigned >> a:=w; ^ User error: Identifier 'w' has not been declared or assigned >> p:=x^((q-1+n) div n)+a*x; ^ User error: Identifier 'x' has not been declared or assigned >> time test_poly(n,a,K); ^ User error: Identifier 'a' has not been declared or assigned >> time IsProbablyPermutationPolynomial(p);; ^ User error: Identifier 'p' has not been declared or assigned Total time: 3.679 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:31:41 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i+1] ) then return false; end if; end for; end for; return true; end function; q := 2^10; K := GF(q); R := PolynomialRing(K); n := 33; a := w; p := x^((q-1+n) div n)+a*x; time test_poly(n,a,K); time IsProbablyPermutationPolynomial(p); Output: Magma V2.10-6 Thu Mar 11 2004 08:31:37 on modular [Seed = 3114898382] ------------------------------------- false Time: 0.000 true Time: 0.050 Total time: 3.519 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:32:16 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i+1] ) then return false; end if; end for; end for; return true; end function; q := 2^10; K := GF(q); R := PolynomialRing(K); n := 33; a := w; p := x^((q-1+n) div n)+a*x; time test_poly(n,a,K); time IsProbablyPermutationPolynomial(p); #{p(x)|x in K} Output: Magma V2.10-6 Thu Mar 11 2004 08:32:13 on modular [Seed = 1599042893] ------------------------------------- false Time: 0.000 true Time: 0.050 >> #{p(x)|x in K}; ^ Runtime error: Bad argument types Argument types given: RngUPolElt, RngUPolElt Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:32:30 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i+1] ) then return false; end if; end for; end for; return true; end function; q := 2^10; K := GF(q); R := PolynomialRing(K); n := 33; a := w; p := x^((q-1+n) div n)+a*x; time test_poly(n,a,K); time IsProbablyPermutationPolynomial(p); #{p(x)|x in K}; Output: Magma V2.10-6 Thu Mar 11 2004 08:32:27 on modular [Seed = 1346402932] ------------------------------------- false Time: 0.000 true Time: 0.050 >> #{p(x)|x in K};; ^ Runtime error: Bad argument types Argument types given: RngUPolElt, RngUPolElt Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:32:49 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i+1] ) then return false; end if; end for; end for; return true; end function; q := 2^10; K := GF(q); R := PolynomialRing(K); n := 33; a := w; p := x^((q-1+n) div n)+a*x; time test_poly(n,a,K); time IsProbablyPermutationPolynomial(p); #{x^((q-1+n) div n)+a*x|x in K}; Output: Magma V2.10-6 Thu Mar 11 2004 08:32:46 on modular [Seed = 1719028823] ------------------------------------- false Time: 0.000 true Time: 0.050 >> #{x^((q-1+n) div n)+a*x|x in K};; ^ Runtime error in { ... }: Invalid set universe (no hashing algorithm) Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:33:09 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i+1] ) then return false; end if; end for; end for; return true; end function; q := 2^10; K := GF(q); R := PolynomialRing(K); n := 33; a := w; p := x^((q-1+n) div n)+a*x; time test_poly(n,a,K); time IsProbablyPermutationPolynomial(p); #{K:x^((q-1+n) div n)+a*x|x in K}; Output: Magma V2.10-6 Thu Mar 11 2004 08:33:06 on modular [Seed = 2003262890] ------------------------------------- false Time: 0.000 true Time: 0.050 >> #{K:x^((q-1+n) div n)+a*x|x in K};; ^ User error: bad syntax Total time: 3.269 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:33:40 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i+1] ) then return false; end if; end for; end for; return true; end function; q := 2^10; K := GF(q); R := PolynomialRing(K); n := 33; a := w; p := x^((q-1+n) div n)+a*x; time test_poly(n,a,K); time IsProbablyPermutationPolynomial(p); #{Evaluate(p,x|x in K}; Output: Magma V2.10-6 Thu Mar 11 2004 08:33:37 on modular [Seed = 17902591] ------------------------------------- false Time: 0.000 true Time: 0.050 >> #{Evaluate(p,x|x in K};; ^ User error: bad syntax Total time: 3.549 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:33:51 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i+1] ) then return false; end if; end for; end for; return true; end function; q := 2^10; K := GF(q); R := PolynomialRing(K); n := 33; a := w; p := x^((q-1+n) div n)+a*x; time test_poly(n,a,K); time IsProbablyPermutationPolynomial(p); #{Evaluate(p,x)|x in K}; Output: Magma V2.10-6 Thu Mar 11 2004 08:33:48 on modular [Seed = 302135521] ------------------------------------- false Time: 0.000 true Time: 0.050 >> #{Evaluate(p,x)|x in K};; ^ Runtime error in { ... }: Invalid set universe (no hashing algorithm) Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:34:27 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i+1] ) then return false; end if; end for; end for; return true; end function; q := 2^10; K := GF(q); R := PolynomialRing(K); n := 33; a := w; p := x^((q-1+n) div n)+a*x; time test_poly(n,a,K); time IsProbablyPermutationPolynomial(p); p; #{Evaluate(p,x)|x in K}; Output: Magma V2.10-6 Thu Mar 11 2004 08:34:23 on modular [Seed = 1026365357] ------------------------------------- false Time: 0.000 true Time: 0.050 x^32 + w*x >> #{Evaluate(p,x)|x in K};; ^ Runtime error in { ... }: Invalid set universe (no hashing algorithm) Total time: 3.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:34:51 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i+1] ) then return false; end if; end for; end for; return true; end function; q := 2^10; K := GF(q); R := PolynomialRing(K); n := 33; a := w; p := x^((q-1+n) div n)+a*x; time test_poly(n,a,K); time IsProbablyPermutationPolynomial(p); p; #{ Evaluate(p,x) | x in K}; Output: Magma V2.10-6 Thu Mar 11 2004 08:34:48 on modular [Seed = 3369656959] ------------------------------------- false Time: 0.000 true Time: 0.050 x^32 + w*x >> #{ Evaluate(p,x) | x in K};; ^ Runtime error in { ... }: Invalid set universe (no hashing algorithm) Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:35:05 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i+1] ) then return false; end if; end for; end for; return true; end function; q := 2^10; K := GF(q); R := PolynomialRing(K); n := 33; a := w; p := x^((q-1+n) div n)+a*x; time test_poly(n,a,K); time IsProbablyPermutationPolynomial(p); p; #{ Evaluate(p,x) : x in K}; Output: Magma V2.10-6 Thu Mar 11 2004 08:35:02 on modular [Seed = 3637048209] ------------------------------------- false Time: 0.000 true Time: 0.040 x^32 + w*x 1024 Total time: 3.429 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:37:15 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do Append(~W,W[j-1]*z); print (j,W[j]); Append(~B,(b+W[j])^k); for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i+1] ) then return false; end if; end for; end for; return true; end function; q := 2^10; K := GF(q); R := PolynomialRing(K); n := 33; a := w; p := x^((q-1+n) div n)+a*x; time test_poly(n,a,K); time IsProbablyPermutationPolynomial(p); p; #{ Evaluate(p,x) : x in K}; Output: Magma V2.10-6 Thu Mar 11 2004 08:37:11 on modular [Seed = 2224336716] ------------------------------------- [
:3]( n: 33, b: w, K: GF(2^10) ) >> print (j,W[j]); ^ Runtime error in elt< ... >: Bad arguments true Time: 0.050 x^32 + w*x 1024 Total time: 3.649 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:37:37 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do Append(~W,W[j-1]*z); print W[j]; Append(~B,(b+W[j])^k); for i in [1..j] do if ( (B[i]/B[j]) eq W[j-i+1] ) then return false; end if; end for; end for; return true; end function; q := 2^10; K := GF(q); R := PolynomialRing(K); n := 33; a := w; p := x^((q-1+n) div n)+a*x; time test_poly(n,a,K); time IsProbablyPermutationPolynomial(p); p; #{ Evaluate(p,x) : x in K}; Output: Magma V2.10-6 Thu Mar 11 2004 08:37:34 on modular [Seed = 2948564094] ------------------------------------- w^31 false Time: 0.000 true Time: 0.050 x^32 + w*x 1024 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:38:16 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do Append(~W,W[j-1]*z); print W[j]; Append(~B,(b+W[j])^k); for i in [1..(j-1)] do if ( (B[i]/B[j]) eq W[j-i] ) then return false; end if; end for; end for; return true; end function; q := 2^10; K := GF(q); R := PolynomialRing(K); n := 33; a := w; p := x^((q-1+n) div n)+a*x; time test_poly(n,a,K); time IsProbablyPermutationPolynomial(p); p; #{ Evaluate(p,x) : x in K}; Output: Magma V2.10-6 Thu Mar 11 2004 08:38:12 on modular [Seed = 3030687551] ------------------------------------- w^31 w^62 false Time: 0.000 true Time: 0.050 x^32 + w*x 1024 Total time: 4.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:38:57 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); print z; for j in [2..n] do Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..(j-1)] do if ( (B[i]/B[j]) eq W[j-i] ) then return false; end if; end for; end for; return true; end function; q := 2^10; K := GF(q); R := PolynomialRing(K); n := 33; a := w; p := x^((q-1+n) div n)+a*x; time test_poly(n,a,K); time IsProbablyPermutationPolynomial(p); p; #{ Evaluate(p,x) : x in K}; Output: Magma V2.10-6 Thu Mar 11 2004 08:38:54 on modular [Seed = 1986420168] ------------------------------------- w^31 false Time: 0.000 true Time: 0.050 x^32 + w*x 1024 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:47:42 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..(j-1)] do if ( (B[i]/B[j]) eq W[j-i] ) then return false; end if; end for; end for; return true; end function; q := 2^10; K := GF(q); R := PolynomialRing(K); n := 33; a := w; p := x^((q-1+n) div n)+a*x; time test_poly(n,a,K); time IsProbablyPermutationPolynomial(p); p; #{ Evaluate(p,x) : x in K}; Output: Magma V2.10-6 Thu Mar 11 2004 08:47:39 on modular [Seed = 1820082630] ------------------------------------- false Time: 0.000 true Time: 0.050 x^32 + w*x 1024 Total time: 3.519 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:48:44 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..(j-1)] do if ( (B[i]/B[j]) eq W[j-i] ) then print i; print j; print B[i]/B[j]; return false; end if; end for; end for; return true; end function; q := 2^10; K := GF(q); R := PolynomialRing(K); n := 33; a := w; p := x^((q-1+n) div n)+a*x; time test_poly(n,a,K); time IsProbablyPermutationPolynomial(p); p; #{ Evaluate(p,x) : x in K}; Output: Magma V2.10-6 Thu Mar 11 2004 08:48:41 on modular [Seed = 908466270] ------------------------------------- 1 3 w^31 false Time: 0.000 true Time: 0.050 x^32 + w*x 1024 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:49:40 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..(j-1)] do if ( (B[i]/B[j]) eq W[j-i+1] ) then print i; print j; print B[i]/B[j]; return false; end if; end for; end for; return true; end function; q := 2^10; K := GF(q); R := PolynomialRing(K); n := 33; a := w; p := x^((q-1+n) div n)+a*x; time test_poly(n,a,K); time IsProbablyPermutationPolynomial(p); p; #{ Evaluate(p,x) : x in K}; Output: Magma V2.10-6 Thu Mar 11 2004 08:49:37 on modular [Seed = 3653892089] ------------------------------------- true Time: 0.000 true Time: 0.050 x^32 + w*x 1024 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:49:54 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..(j-1)] do if ( (B[i]/B[j]) eq W[j-i+1] ) then print i; print j; print B[i]/B[j]; return false; end if; end for; end for; return true; end function; q := 2^10; K := GF(q); R := PolynomialRing(K); n := 33; a := w; p := x^((q-1+n) div n)+a*x; time test_poly(n,a,K); time IsProbablyPermutationPolynomial(p); p; #{ Evaluate(p,x) : x in K}; Output: Magma V2.10-6 Thu Mar 11 2004 08:49:51 on modular [Seed = 3319131115] ------------------------------------- true Time: 0.010 true Time: 0.050 x^32 + w*x 1024 Total time: 3.289 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:50:00 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..(j-1)] do if ( (B[i]/B[j]) eq W[j-i+1] ) then print i; print j; print B[i]/B[j]; return false; end if; end for; end for; return true; end function; q := 2^10; K := GF(q); R := PolynomialRing(K); n := 33; a := w; p := x^((q-1+n) div n)+a*x; time test_poly(n,a,K); time IsProbablyPermutationPolynomial(p); p; #{ Evaluate(p,x) : x in K}; Output: Magma V2.10-6 Thu Mar 11 2004 08:49:57 on modular [Seed = 4058111781] ------------------------------------- true Time: 0.000 true Time: 0.050 x^32 + w*x 1024 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:58:07 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..(j-1)] do if ( (B[i]/B[j]) eq W[j-i+1] ) then print i; print j; print B[i]/B[j]; return false; end if; end for; end for; return true; end function; q := 2^10; K := GF(q); R := PolynomialRing(K); n := 93; a := w; p := x^((q-1+n) div n)+a*x; time test_poly(n,a,K); time IsProbablyPermutationPolynomial(p); p; #{ Evaluate(p,x) : x in K}; Output: Magma V2.10-6 Thu Mar 11 2004 08:58:04 on modular [Seed = 3637045478] ------------------------------------- 8 11 w^33 false Time: 0.000 false Time: 0.000 x^12 + w*x 639 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 08:58:36 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..(j-1)] do if ( (B[i]/B[j]) eq W[j-i+1] ) then print i; print j; print B[i]/B[j]; return false; end if; end for; end for; return true; end function; q := 2^10; K := GF(q); R := PolynomialRing(K); n := 341; a := w; p := x^((q-1+n) div n)+a*x; time test_poly(n,a,K); time IsProbablyPermutationPolynomial(p); p; #{ Evaluate(p,x) : x in K}; Output: Magma V2.10-6 Thu Mar 11 2004 08:58:32 on modular [Seed = 4091790121] ------------------------------------- true Time: 0.220 true Time: 0.030 x^4 + w*x 1024 Total time: 4.269 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 09:00:17 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..(j-1)] do if ( (B[i]/B[j]) eq W[j-i+1] ) then print i; print j; print B[i]/B[j]; return false; end if; end for; end for; return true; end function; q := 2^10; K := GF(q); R := PolynomialRing(K); n := 93; a := w; p := x^((q-1+n) div n)+a*x; time test_poly(n,a,K); time IsProbablyPermutationPolynomial(p); p; #{ Evaluate(p,x) : x in K}; Output: Magma V2.10-6 Thu Mar 11 2004 09:00:14 on modular [Seed = 2375925041] ------------------------------------- 8 11 w^33 false Time: 0.000 false Time: 0.000 x^12 + w*x 639 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 09:00:32 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..(j-1)] do if ( (B[i]/B[j]) eq W[j-i+1] ) then print i; print j; print B[i]/B[j]; return false; end if; end for; end for; return true; end function; q := 2^10; K := GF(q); R := PolynomialRing(K); n := 341; a := w; p := x^((q-1+n) div n)+a*x; time test_poly(n,a,K); time IsProbablyPermutationPolynomial(p); p; #{ Evaluate(p,x) : x in K}; Output: Magma V2.10-6 Thu Mar 11 2004 09:00:29 on modular [Seed = 3165424659] ------------------------------------- true Time: 0.220 true Time: 0.030 x^4 + w*x 1024 Total time: 3.159 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 09:10:49 2004 Input: // teste si x^((q-1+n)/n)+b*x est un polynome de permutation sur K test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..(j-1)] do if ( (B[i]/B[j]) eq W[j-i+1] ) then return false; end if; end for; end for; return true; end function; q := 2^10; K := GF(q); R := PolynomialRing(K); n := 33; #{x: x in K, test(n,x,K)} Output: Magma V2.10-6 Thu Mar 11 2004 09:10:45 on modular [Seed = 857931778] ------------------------------------- >> #{x: x in K, test(n,x,K)}; ^ User error: bad syntax Total time: 4.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 09:11:08 2004 Input: // teste si x^((q-1+n)/n)+b*x est un polynome de permutation sur K test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..(j-1)] do if ( (B[i]/B[j]) eq W[j-i+1] ) then return false; end if; end for; end for; return true; end function; q := 2^10; K := GF(q); R := PolynomialRing(K); n := 33; #{x: x in K, test_poly(n,x,K)} Output: Magma V2.10-6 Thu Mar 11 2004 09:11:05 on modular [Seed = 573706511] ------------------------------------- >> #{x: x in K, test_poly(n,x,K)}; ^ User error: bad syntax Total time: 3.679 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 09:11:43 2004 Input: // teste si x^((q-1+n)/n)+b*x est un polynome de permutation sur K test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..(j-1)] do if ( (B[i]/B[j]) eq W[j-i+1] ) then return false; end if; end for; end for; return true; end function; q := 2^10; K := GF(q); R := PolynomialRing(K); n := 33; #{x: x in K | test_poly(n,x,K)} Output: Magma V2.10-6 Thu Mar 11 2004 09:11:37 on modular [Seed = 3637046037] ------------------------------------- 991 Total time: 6.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 09:12:35 2004 Input: // teste si x^((q-1+n)/n)+b*x est un polynome de permutation sur K test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..(j-1)] do if ( (B[i]/B[j]) eq W[j-i+1] ) then return false; end if; end for; end for; return true; end function; q := 3^7; K := GF(q); R := PolynomialRing(K); n := 2; #{x: x in K | test_poly(n,x,K)}; Output: Magma V2.10-6 Thu Mar 11 2004 09:12:31 on modular [Seed = 4277063013] ------------------------------------- 1092 Total time: 3.659 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 09:13:08 2004 Input: // teste si x^((q-1+n)/n)+b*x est un polynome de permutation sur K test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..(j-1)] do if ( (B[i]/B[j]) eq W[j-i+1] ) then return false; end if; end for; end for; return true; end function; q := 3^7; K := GF(q); R := PolynomialRing(K); n := 2; #{x: x in K | test_poly(n,x,K)}; (3^7-9)/4; Output: Magma V2.10-6 Thu Mar 11 2004 09:13:04 on modular [Seed = 3959150671] ------------------------------------- 1092 1089/2 Total time: 4.079 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 09:13:20 2004 Input: // teste si x^((q-1+n)/n)+b*x est un polynome de permutation sur K test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..(j-1)] do if ( (B[i]/B[j]) eq W[j-i+1] ) then return false; end if; end for; end for; return true; end function; q := 3^7; K := GF(q); R := PolynomialRing(K); n := 2; #{x: x in K | test_poly(n,x,K)}; (3^7-3)/4; Output: Magma V2.10-6 Thu Mar 11 2004 09:13:17 on modular [Seed = 2592778547] ------------------------------------- 1092 546 Total time: 3.109 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 09:13:51 2004 Input: // teste si x^((q-1+n)/n)+b*x est un polynome de permutation sur K test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..(j-1)] do if ( (B[i]/B[j]) eq W[j-i+1] ) then return false; end if; end for; end for; return true; end function; q := 3^7; K := GF(q); R := PolynomialRing(K); n := 2; #{x: x in K | test_poly(n,x,K)}; (3^7-3)/2; Output: Magma V2.10-6 Thu Mar 11 2004 09:13:48 on modular [Seed = 2963309816] ------------------------------------- 1092 1092 Total time: 3.089 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 09:14:40 2004 Input: // teste si x^((q-1+n)/n)+b*x est un polynome de permutation sur K test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..(j-1)] do if ( (B[i]/B[j]) eq W[j-i+1] ) then return false; end if; end for; end for; return true; end function; q := 5^7; K := GF(q); R := PolynomialRing(K); n := 2; #{x: x in K | test_poly(n,x,K)}; Output: Magma V2.10-6 Thu Mar 11 2004 09:14:31 on modular [Seed = 2830671035] ------------------------------------- 39061 Total time: 8.969 seconds, Total memory usage: 4.05MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 09:15:21 2004 Input: // teste si x^((q-1+n)/n)+b*x est un polynome de permutation sur K test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..(j-1)] do if ( (B[i]/B[j]) eq W[j-i+1] ) then return false; end if; end for; end for; return true; end function; q := 5^7; K := GF(q); R := PolynomialRing(K); n := 2; #{x: x in K | test_poly(n,x,K)}; q/2-3q^(1/2)/2; Output: Magma V2.10-6 Thu Mar 11 2004 09:15:14 on modular [Seed = 1281128555] ------------------------------------- 39061 >> q/2-3q^(1/2)/2;; ^ User error: bad syntax Total time: 7.679 seconds, Total memory usage: 4.05MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 09:15:44 2004 Input: // teste si x^((q-1+n)/n)+b*x est un polynome de permutation sur K test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..(j-1)] do if ( (B[i]/B[j]) eq W[j-i+1] ) then return false; end if; end for; end for; return true; end function; q := 5^7; K := GF(q); R := PolynomialRing(K); n := 2; #{x: x in K | test_poly(n,x,K)}; q/2-3/2*q^(1/2); Output: Magma V2.10-6 Thu Mar 11 2004 09:15:35 on modular [Seed = 2121157292] ------------------------------------- 39061 38643.23725421878943192328 Total time: 8.779 seconds, Total memory usage: 4.05MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Thu Mar 11 09:24:26 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^2 -23); O := MaximalOrder(N); A := ideal; B := ideal; D := ideal; C := ideal; IsPrinciple(A*C); IsPrinciple(A*D); IsPrinciple(B*C); IsPrinciple(B*D); Output: Magma V2.10-6 Thu Mar 11 2004 09:24:23 on modular [Seed = 1668502957] ------------------------------------- >> IsPrinciple(A*C); ^ User error: Identifier 'IsPrinciple' has not been declared or assigned >> IsPrinciple(A*D); ^ User error: Identifier 'IsPrinciple' has not been declared or assigned >> IsPrinciple(B*C); ^ User error: Identifier 'IsPrinciple' has not been declared or assigned >> IsPrinciple(B*D);; ^ User error: Identifier 'IsPrinciple' has not been declared or assigned Total time: 3.109 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Thu Mar 11 09:24:49 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^2 -23); O := MaximalOrder(N); A := ideal; B := ideal; D := ideal; C := ideal; IsPrincipal(A*C); IsPrincipal(A*D); IsPrincipal(B*C); IsPrincipal(B*D); Output: Magma V2.10-6 Thu Mar 11 2004 09:24:46 on modular [Seed = 691609566] ------------------------------------- true true true true Total time: 3.269 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host aula-etse013.uab.es. (158.109.66.132) Time: Thu Mar 11 09:28:55 2004 Input: conj:= { n : n in [1..366 by 1] | (n mod 7) eq 4}; Output: Magma V2.10-6 Thu Mar 11 2004 09:28:51 on modular [Seed = 1531669667] ------------------------------------- Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Thu Mar 11 09:29:16 2004 Input: F := PolynomialRing(RationalField()); F := PolynomialRing(RationalField()); N := NumberField(x^2 -23); O := MaximalOrder(N); A := ideal; B := ideal; D := ideal; C := ideal; IsPrincipal(A*A); IsPrincipal(A*C); IsPrincipal(A*D); IsPrincipal(B*C); IsPrincipal(B*D); Output: Magma V2.10-6 Thu Mar 11 2004 09:29:13 on modular [Seed = 68432870] ------------------------------------- true true true true true Total time: 3.189 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host aula-etse013.uab.es. (158.109.66.132) Time: Thu Mar 11 09:29:23 2004 Input: conj:= { n : n in [1..366 by 1] | (n mod 7) eq 4}; conj; Output: Magma V2.10-6 Thu Mar 11 2004 09:29:19 on modular [Seed = 3653889597] ------------------------------------- { 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 } Total time: 3.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Thu Mar 11 09:31:23 2004 Input: F := PolynomialRing(RationalField()); F := PolynomialRing(RationalField()); N := NumberField(x^2 -23); O := MaximalOrder(N); A := ideal; B := ideal; D := ideal; C := ideal; A B C D IsPrincipal(A*A); IsPrincipal(A*C); IsPrincipal(A*D); IsPrincipal(B*C); IsPrincipal(B*D); Output: Magma V2.10-6 Thu Mar 11 2004 09:31:19 on modular [Seed = 4108635295] ------------------------------------- >> B ^ User error: bad syntax >> D ^ User error: bad syntax true true true true true Total time: 3.159 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Thu Mar 11 09:31:38 2004 Input: F := PolynomialRing(RationalField()); F := PolynomialRing(RationalField()); N := NumberField(x^2 -23); O := MaximalOrder(N); A := ideal; B := ideal; D := ideal; C := ideal; A; B; C; D; IsPrincipal(A*A); IsPrincipal(A*C); IsPrincipal(A*D); IsPrincipal(B*C); IsPrincipal(B*D); Output: Magma V2.10-6 Thu Mar 11 2004 09:31:34 on modular [Seed = 2575933827] ------------------------------------- Fractional Ideal of O Two element generators: 2/1*O.1 3/2*O.1 + 1/2*O.2 Fractional Ideal of O Two element generators: 2/1*O.1 1/2*O.1 + 1/2*O.2 Fractional Ideal of O Two element generators: 3/1*O.1 1/2*O.1 + 1/2*O.2 Fractional Ideal of O Two element generators: 3/1*O.1 5/2*O.1 + 1/2*O.2 true true true true true Total time: 3.149 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Thu Mar 11 09:33:20 2004 Input: F := PolynomialRing(RationalField()); F := PolynomialRing(RationalField()); N := NumberField(x^2 -23); O := MaximalOrder(N); A := ideal; B := ideal; D := ideal; C := ideal; A*B; C*D; IsPrincipal(A*A); IsPrincipal(A*C); IsPrincipal(A*D); IsPrincipal(B*C); IsPrincipal(B*D); Output: Magma V2.10-6 Thu Mar 11 2004 09:33:16 on modular [Seed = 3369660473] ------------------------------------- Fractional Principal Ideal of O Generator: 1/2*O.1 Fractional Principal Ideal of O Generator: 1/2*O.1 true true true true true Total time: 3.119 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host aula-etse013.uab.es. (158.109.66.132) Time: Thu Mar 11 09:34:18 2004 Input: MT:= { k : k in M | Trace(k) eq 0}; > MT; Output: Magma V2.10-6 Thu Mar 11 2004 09:34:14 on modular [Seed = 17906105] ------------------------------------- >> MT:= { k : k in M | Trace(k) eq 0}; ^ User error: Identifier 'M' has not been declared or assigned >> MT; ^ User error: Identifier 'MT' has not been declared or assigned Total time: 3.099 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse013.uab.es. (158.109.66.132) Time: Thu Mar 11 09:34:58 2004 Input: M:=KMatrixSpace(GF(4),2,2); MT:= { k : k in M | Trace(k) eq 0}; > MT; Output: Magma V2.10-6 Thu Mar 11 2004 09:34:54 on modular [Seed = 2458037186] ------------------------------------- { [ 0 0] [ 0 0], [ 0 0] [$.1^2 0], [ 0 0] [ $.1 0], [ 0 0] [ 1 0], [$.1^2 0] [ 0 $.1^2], [$.1^2 0] [$.1^2 $.1^2], [$.1^2 0] [ $.1 $.1^2], [$.1^2 0] [ 1 $.1^2], [ 1 0] [ 0 1], [ 1 0] [$.1^2 1], [ 1 0] [ $.1 1], [ 1 0] [ 1 1], [ $.1 0] [ 0 $.1], [ $.1 0] [$.1^2 $.1], [ $.1 0] [ $.1 $.1], [ $.1 0] [ 1 $.1], [ 0 $.1^2] [ 0 0], [ 0 $.1^2] [$.1^2 0], [ 0 $.1^2] [ $.1 0], [ 0 $.1^2] [ 1 0], [$.1^2 $.1^2] [ 0 $.1^2], [$.1^2 $.1^2] [$.1^2 $.1^2], [$.1^2 $.1^2] [ $.1 $.1^2], [$.1^2 $.1^2] [ 1 $.1^2], [ 1 $.1^2] [ 0 1], [ 1 $.1^2] [$.1^2 1], [ 1 $.1^2] [ $.1 1], [ 1 $.1^2] [ 1 1], [ $.1 $.1^2] [ 0 $.1], [ $.1 $.1^2] [$.1^2 $.1], [ $.1 $.1^2] [ $.1 $.1], [ $.1 $.1^2] [ 1 $.1], [ 0 $.1] [ 0 0], [ 0 $.1] [$.1^2 0], [ 0 $.1] [ $.1 0], [ 0 $.1] [ 1 0], [$.1^2 $.1] [ 0 $.1^2], [$.1^2 $.1] [$.1^2 $.1^2], [$.1^2 $.1] [ $.1 $.1^2], [$.1^2 $.1] [ 1 $.1^2], [ 1 $.1] [ 0 1], [ 1 $.1] [$.1^2 1], [ 1 $.1] [ $.1 1], [ 1 $.1] [ 1 1], [ $.1 $.1] [ 0 $.1], [ $.1 $.1] [$.1^2 $.1], [ $.1 $.1] [ $.1 $.1], [ $.1 $.1] [ 1 $.1], [ 0 1] [ 0 0], [ 0 1] [$.1^2 0], [ 0 1] [ $.1 0], [ 0 1] [ 1 0], [$.1^2 1] [ 0 $.1^2], [$.1^2 1] [$.1^2 $.1^2], [$.1^2 1] [ $.1 $.1^2], [$.1^2 1] [ 1 $.1^2], [ 1 1] [ 0 1], [ 1 1] [$.1^2 1], [ 1 1] [ $.1 1], [ 1 1] [ 1 1], [ $.1 1] [ 0 $.1], [ $.1 1] [$.1^2 $.1], [ $.1 1] [ $.1 $.1], [ $.1 1] [ 1 $.1] } Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-etse013.uab.es. (158.109.66.132) Time: Thu Mar 11 09:36:08 2004 Input: M:=KMatrixSpace(GF(4),2,2); MT:= { k : k in M | Trace(k) eq 0}; > MT; Output: Magma V2.10-6 Thu Mar 11 2004 09:36:04 on modular [Seed = 2003259004] ------------------------------------- { [ 0 0] [ 0 0], [ 0 0] [$.1^2 0], [ 0 0] [ $.1 0], [ 0 0] [ 1 0], [$.1^2 0] [ 0 $.1^2], [$.1^2 0] [$.1^2 $.1^2], [$.1^2 0] [ $.1 $.1^2], [$.1^2 0] [ 1 $.1^2], [ 1 0] [ 0 1], [ 1 0] [$.1^2 1], [ 1 0] [ $.1 1], [ 1 0] [ 1 1], [ $.1 0] [ 0 $.1], [ $.1 0] [$.1^2 $.1], [ $.1 0] [ $.1 $.1], [ $.1 0] [ 1 $.1], [ 0 $.1^2] [ 0 0], [ 0 $.1^2] [$.1^2 0], [ 0 $.1^2] [ $.1 0], [ 0 $.1^2] [ 1 0], [$.1^2 $.1^2] [ 0 $.1^2], [$.1^2 $.1^2] [$.1^2 $.1^2], [$.1^2 $.1^2] [ $.1 $.1^2], [$.1^2 $.1^2] [ 1 $.1^2], [ 1 $.1^2] [ 0 1], [ 1 $.1^2] [$.1^2 1], [ 1 $.1^2] [ $.1 1], [ 1 $.1^2] [ 1 1], [ $.1 $.1^2] [ 0 $.1], [ $.1 $.1^2] [$.1^2 $.1], [ $.1 $.1^2] [ $.1 $.1], [ $.1 $.1^2] [ 1 $.1], [ 0 $.1] [ 0 0], [ 0 $.1] [$.1^2 0], [ 0 $.1] [ $.1 0], [ 0 $.1] [ 1 0], [$.1^2 $.1] [ 0 $.1^2], [$.1^2 $.1] [$.1^2 $.1^2], [$.1^2 $.1] [ $.1 $.1^2], [$.1^2 $.1] [ 1 $.1^2], [ 1 $.1] [ 0 1], [ 1 $.1] [$.1^2 1], [ 1 $.1] [ $.1 1], [ 1 $.1] [ 1 1], [ $.1 $.1] [ 0 $.1], [ $.1 $.1] [$.1^2 $.1], [ $.1 $.1] [ $.1 $.1], [ $.1 $.1] [ 1 $.1], [ 0 1] [ 0 0], [ 0 1] [$.1^2 0], [ 0 1] [ $.1 0], [ 0 1] [ 1 0], [$.1^2 1] [ 0 $.1^2], [$.1^2 1] [$.1^2 $.1^2], [$.1^2 1] [ $.1 $.1^2], [$.1^2 1] [ 1 $.1^2], [ 1 1] [ 0 1], [ 1 1] [$.1^2 1], [ 1 1] [ $.1 1], [ 1 1] [ 1 1], [ $.1 1] [ 0 $.1], [ $.1 1] [$.1^2 $.1], [ $.1 1] [ $.1 $.1], [ $.1 1] [ 1 $.1] } Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Thu Mar 11 09:36:44 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^2 -23); O := MaximalOrder(N); A := ideal; B := ideal; D := ideal; C := ideal; A*B; C*D; IsPrincipal(A*A); IsPrincipal(A*C); IsPrincipal(A*D); IsPrincipal(B*C); IsPrincipal(B*D); Output: Magma V2.10-6 Thu Mar 11 2004 09:36:41 on modular [Seed = 4108635602] ------------------------------------- Fractional Principal Ideal of O Generator: 1/2*O.1 Fractional Principal Ideal of O Generator: 1/2*O.1 true true true true true Total time: 2.959 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host aula-etse013.uab.es. (158.109.66.132) Time: Thu Mar 11 09:37:51 2004 Input: M:=KMatrixSpace(GF(4),2,2); M; Output: Magma V2.10-6 Thu Mar 11 2004 09:37:47 on modular [Seed = 1769558194] ------------------------------------- Full KMatrixSpace of 2 by 2 matrices over GF(2^2) Total time: 3.099 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-etse013.uab.es. (158.109.66.132) Time: Thu Mar 11 09:38:18 2004 Input: M:=KMatrixSpace(GF(4),2,2); M; MT:= { k : k in M | Trace(k) eq 0}; > MT; Output: Magma V2.10-6 Thu Mar 11 2004 09:38:14 on modular [Seed = 1565353195] ------------------------------------- Full KMatrixSpace of 2 by 2 matrices over GF(2^2) { [ 0 0] [ 0 0], [ 0 0] [$.1^2 0], [ 0 0] [ $.1 0], [ 0 0] [ 1 0], [$.1^2 0] [ 0 $.1^2], [$.1^2 0] [$.1^2 $.1^2], [$.1^2 0] [ $.1 $.1^2], [$.1^2 0] [ 1 $.1^2], [ 1 0] [ 0 1], [ 1 0] [$.1^2 1], [ 1 0] [ $.1 1], [ 1 0] [ 1 1], [ $.1 0] [ 0 $.1], [ $.1 0] [$.1^2 $.1], [ $.1 0] [ $.1 $.1], [ $.1 0] [ 1 $.1], [ 0 $.1^2] [ 0 0], [ 0 $.1^2] [$.1^2 0], [ 0 $.1^2] [ $.1 0], [ 0 $.1^2] [ 1 0], [$.1^2 $.1^2] [ 0 $.1^2], [$.1^2 $.1^2] [$.1^2 $.1^2], [$.1^2 $.1^2] [ $.1 $.1^2], [$.1^2 $.1^2] [ 1 $.1^2], [ 1 $.1^2] [ 0 1], [ 1 $.1^2] [$.1^2 1], [ 1 $.1^2] [ $.1 1], [ 1 $.1^2] [ 1 1], [ $.1 $.1^2] [ 0 $.1], [ $.1 $.1^2] [$.1^2 $.1], [ $.1 $.1^2] [ $.1 $.1], [ $.1 $.1^2] [ 1 $.1], [ 0 $.1] [ 0 0], [ 0 $.1] [$.1^2 0], [ 0 $.1] [ $.1 0], [ 0 $.1] [ 1 0], [$.1^2 $.1] [ 0 $.1^2], [$.1^2 $.1] [$.1^2 $.1^2], [$.1^2 $.1] [ $.1 $.1^2], [$.1^2 $.1] [ 1 $.1^2], [ 1 $.1] [ 0 1], [ 1 $.1] [$.1^2 1], [ 1 $.1] [ $.1 1], [ 1 $.1] [ 1 1], [ $.1 $.1] [ 0 $.1], [ $.1 $.1] [$.1^2 $.1], [ $.1 $.1] [ $.1 $.1], [ $.1 $.1] [ 1 $.1], [ 0 1] [ 0 0], [ 0 1] [$.1^2 0], [ 0 1] [ $.1 0], [ 0 1] [ 1 0], [$.1^2 1] [ 0 $.1^2], [$.1^2 1] [$.1^2 $.1^2], [$.1^2 1] [ $.1 $.1^2], [$.1^2 1] [ 1 $.1^2], [ 1 1] [ 0 1], [ 1 1] [$.1^2 1], [ 1 1] [ $.1 1], [ 1 1] [ 1 1], [ $.1 1] [ 0 $.1], [ $.1 1] [$.1^2 $.1], [ $.1 1] [ $.1 $.1], [ $.1 1] [ 1 $.1] } Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-etse013.uab.es. (158.109.66.132) Time: Thu Mar 11 09:40:38 2004 Input: Mf:= { k: k in M| (k[1][1] eq k[2][1]) and (k[1][2] eq k[2][2])}; > Mf; Output: Magma V2.10-6 Thu Mar 11 2004 09:40:34 on modular [Seed = 4293903868] ------------------------------------- >> Mf:= { k: k in M| (k[1][1] eq k[2][1]) and (k[1][2] eq k[2][2])}; ^ User error: Identifier 'M' has not been declared or assigned >> Mf;; ^ User error: Identifier 'Mf' has not been declared or assigned Total time: 3.119 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse013.uab.es. (158.109.66.132) Time: Thu Mar 11 09:41:19 2004 Input: M:=KMatrixSpace(GF(4),2,2); Mf:= { k: k in M| (k[1][1] eq k[2][1]) and (k[1][2] eq k[2][2])}; > Mf; Output: Magma V2.10-6 Thu Mar 11 2004 09:41:15 on modular [Seed = 1112701099] ------------------------------------- { [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ $.1 0] [ $.1 0], [ 0 $.1^2] [ 0 $.1^2], [ $.1 $.1^2] [ $.1 $.1^2], [ 0 $.1] [ 0 $.1], [ $.1 $.1] [ $.1 $.1], [ 0 1] [ 0 1], [ $.1 1] [ $.1 1], [$.1^2 0] [$.1^2 0], [ 1 0] [ 1 0], [$.1^2 $.1^2] [$.1^2 $.1^2], [ 1 $.1^2] [ 1 $.1^2], [$.1^2 $.1] [$.1^2 $.1], [ 1 $.1] [ 1 $.1], [$.1^2 1] [$.1^2 1] } Total time: 3.059 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Thu Mar 11 09:42:46 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^2 -23); O := MaximalOrder(N); ClassNumber(N); A := ideal; B := ideal; D := ideal; C := ideal; A*B; C*D; IsPrincipal(A*A); IsPrincipal(A*C); IsPrincipal(A*D); IsPrincipal(B*C); IsPrincipal(B*D); Output: Magma V2.10-6 Thu Mar 11 2004 09:42:42 on modular [Seed = 2003258870] ------------------------------------- 1 Fractional Principal Ideal of O Generator: 1/2*O.1 Fractional Principal Ideal of O Generator: 1/2*O.1 true true true true true Total time: 3.349 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host aula-etse013.uab.es. (158.109.66.132) Time: Thu Mar 11 09:42:51 2004 Input: M:=KMatrixSpace(GF(4),2,2); MT:= { k : k in M | Trace(k) eq 0}; > MT; Output: Magma V2.10-6 Thu Mar 11 2004 09:42:46 on modular [Seed = 1247441103] ------------------------------------- { [ 0 0] [ 0 0], [ 0 0] [$.1^2 0], [ 0 0] [ $.1 0], [ 0 0] [ 1 0], [$.1^2 0] [ 0 $.1^2], [$.1^2 0] [$.1^2 $.1^2], [$.1^2 0] [ $.1 $.1^2], [$.1^2 0] [ 1 $.1^2], [ 1 0] [ 0 1], [ 1 0] [$.1^2 1], [ 1 0] [ $.1 1], [ 1 0] [ 1 1], [ $.1 0] [ 0 $.1], [ $.1 0] [$.1^2 $.1], [ $.1 0] [ $.1 $.1], [ $.1 0] [ 1 $.1], [ 0 $.1^2] [ 0 0], [ 0 $.1^2] [$.1^2 0], [ 0 $.1^2] [ $.1 0], [ 0 $.1^2] [ 1 0], [$.1^2 $.1^2] [ 0 $.1^2], [$.1^2 $.1^2] [$.1^2 $.1^2], [$.1^2 $.1^2] [ $.1 $.1^2], [$.1^2 $.1^2] [ 1 $.1^2], [ 1 $.1^2] [ 0 1], [ 1 $.1^2] [$.1^2 1], [ 1 $.1^2] [ $.1 1], [ 1 $.1^2] [ 1 1], [ $.1 $.1^2] [ 0 $.1], [ $.1 $.1^2] [$.1^2 $.1], [ $.1 $.1^2] [ $.1 $.1], [ $.1 $.1^2] [ 1 $.1], [ 0 $.1] [ 0 0], [ 0 $.1] [$.1^2 0], [ 0 $.1] [ $.1 0], [ 0 $.1] [ 1 0], [$.1^2 $.1] [ 0 $.1^2], [$.1^2 $.1] [$.1^2 $.1^2], [$.1^2 $.1] [ $.1 $.1^2], [$.1^2 $.1] [ 1 $.1^2], [ 1 $.1] [ 0 1], [ 1 $.1] [$.1^2 1], [ 1 $.1] [ $.1 1], [ 1 $.1] [ 1 1], [ $.1 $.1] [ 0 $.1], [ $.1 $.1] [$.1^2 $.1], [ $.1 $.1] [ $.1 $.1], [ $.1 $.1] [ 1 $.1], [ 0 1] [ 0 0], [ 0 1] [$.1^2 0], [ 0 1] [ $.1 0], [ 0 1] [ 1 0], [$.1^2 1] [ 0 $.1^2], [$.1^2 1] [$.1^2 $.1^2], [$.1^2 1] [ $.1 $.1^2], [$.1^2 1] [ 1 $.1^2], [ 1 1] [ 0 1], [ 1 1] [$.1^2 1], [ 1 1] [ $.1 1], [ 1 1] [ 1 1], [ $.1 1] [ 0 $.1], [ $.1 1] [$.1^2 $.1], [ $.1 1] [ $.1 $.1], [ $.1 1] [ 1 $.1] } Total time: 3.189 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Thu Mar 11 09:43:06 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^2+23); O := MaximalOrder(N); ClassNumber(N); A := ideal; B := ideal; D := ideal; C := ideal; A*B; C*D; IsPrincipal(A*A); IsPrincipal(A*C); IsPrincipal(A*D); IsPrincipal(B*C); IsPrincipal(B*D); Output: Magma V2.10-6 Thu Mar 11 2004 09:43:03 on modular [Seed = 792663483] ------------------------------------- 3 Principal Ideal of O Generator: [2, 0] Principal Ideal of O Generator: [3, 0] false false true true false Total time: 3.249 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Mar 11 09:43:28 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^2+23); OK:=MaximalOrder(K); ClassNumber(OK); P3:=ideal; IsPrincipal(P3); P33:=P3*P3; IsPrincipal(P33); P333:=P33*P3; IsPrincipal(P333); P4:=ideal; IsPrincipal(P4); P44:=P4*P4; IsPrincipal(P44); P444:=P44*P4; IsPrincipal(P444); P2:=ideal; IsPrincipal(P2); P22:=P2*P2; IsPrincipal(P22); P222:=P22*P2; IsPrincipal(P222); P1:=ideal; IsPrincipal(P1); P11:=P1*P1; IsPrincipal(P11); P111:=P11*P1; IsPrincipal(P111); IsPrincipal(P1*P2); IsPrincipal(P3*P4); IsPrincipal(P2*P4); IsPrincipal(P1*P3); Output: Magma V2.10-6 Thu Mar 11 2004 09:43:24 on modular [Seed = 4091791516] ------------------------------------- 3 false false true false false true false false true false false true true true true true Total time: 3.749 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Thu Mar 11 09:43:31 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^2+23); O := MaximalOrder(N); ClassNumber(N); A := ideal; B := ideal; D := ideal; C := ideal; IsPrincipal(A*A); IsPrincipal(A*C); IsPrincipal(A*D); IsPrincipal(B*C); IsPrincipal(B*D); Output: Magma V2.10-6 Thu Mar 11 2004 09:43:27 on modular [Seed = 4192846485] ------------------------------------- 3 false false true true false Total time: 3.619 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host aula-etse013.uab.es. (158.109.66.132) Time: Thu Mar 11 09:46:02 2004 Input: > M:=KMatrixSpace(GF(4),2,2); > Mf:= { k: k in M| (k[1][1] eq k[2][1]) and (k[1][2] eq k[2][2])}; > Mt:= { k : k in M | Trace(k) eq 0}; > Mtf:= {k : k in M | (k in Mt) and (k in Mf) }; > Mtf; Output: Magma V2.10-6 Thu Mar 11 2004 09:45:58 on modular [Seed = 3891780644] ------------------------------------- { [ 0 0] [ 0 0], [$.1^2 $.1^2] [$.1^2 $.1^2], [ $.1 $.1] [ $.1 $.1], [ 1 1] [ 1 1] } Total time: 3.109 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-etse013.uab.es. (158.109.66.132) Time: Thu Mar 11 09:47:25 2004 Input: > M:=KMatrixSpace(GF(4),2,2); > MT:= { k : k in M | Trace(k) eq 0}; > MT; Output: Magma V2.10-6 Thu Mar 11 2004 09:47:21 on modular [Seed = 1247441365] ------------------------------------- { [ 0 0] [ 0 0], [ 0 0] [$.1^2 0], [ 0 0] [ $.1 0], [ 0 0] [ 1 0], [$.1^2 0] [ 0 $.1^2], [$.1^2 0] [$.1^2 $.1^2], [$.1^2 0] [ $.1 $.1^2], [$.1^2 0] [ 1 $.1^2], [ 1 0] [ 0 1], [ 1 0] [$.1^2 1], [ 1 0] [ $.1 1], [ 1 0] [ 1 1], [ $.1 0] [ 0 $.1], [ $.1 0] [$.1^2 $.1], [ $.1 0] [ $.1 $.1], [ $.1 0] [ 1 $.1], [ 0 $.1^2] [ 0 0], [ 0 $.1^2] [$.1^2 0], [ 0 $.1^2] [ $.1 0], [ 0 $.1^2] [ 1 0], [$.1^2 $.1^2] [ 0 $.1^2], [$.1^2 $.1^2] [$.1^2 $.1^2], [$.1^2 $.1^2] [ $.1 $.1^2], [$.1^2 $.1^2] [ 1 $.1^2], [ 1 $.1^2] [ 0 1], [ 1 $.1^2] [$.1^2 1], [ 1 $.1^2] [ $.1 1], [ 1 $.1^2] [ 1 1], [ $.1 $.1^2] [ 0 $.1], [ $.1 $.1^2] [$.1^2 $.1], [ $.1 $.1^2] [ $.1 $.1], [ $.1 $.1^2] [ 1 $.1], [ 0 $.1] [ 0 0], [ 0 $.1] [$.1^2 0], [ 0 $.1] [ $.1 0], [ 0 $.1] [ 1 0], [$.1^2 $.1] [ 0 $.1^2], [$.1^2 $.1] [$.1^2 $.1^2], [$.1^2 $.1] [ $.1 $.1^2], [$.1^2 $.1] [ 1 $.1^2], [ 1 $.1] [ 0 1], [ 1 $.1] [$.1^2 1], [ 1 $.1] [ $.1 1], [ 1 $.1] [ 1 1], [ $.1 $.1] [ 0 $.1], [ $.1 $.1] [$.1^2 $.1], [ $.1 $.1] [ $.1 $.1], [ $.1 $.1] [ 1 $.1], [ 0 1] [ 0 0], [ 0 1] [$.1^2 0], [ 0 1] [ $.1 0], [ 0 1] [ 1 0], [$.1^2 1] [ 0 $.1^2], [$.1^2 1] [$.1^2 $.1^2], [$.1^2 1] [ $.1 $.1^2], [$.1^2 1] [ 1 $.1^2], [ 1 1] [ 0 1], [ 1 1] [$.1^2 1], [ 1 1] [ $.1 1], [ 1 1] [ 1 1], [ $.1 1] [ 0 $.1], [ $.1 1] [$.1^2 $.1], [ $.1 1] [ $.1 $.1], [ $.1 1] [ 1 $.1] } Total time: 3.129 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.68) Time: Thu Mar 11 09:48:44 2004 Input: seqt := [7^(r-1) : r in {1..3}]; seqt; P:=PolynomialRing(RealField()); t73 := x^(seqt[1]) + x^(seqt[2]) + x^(seqt[3]); t73; n73 := x^(seqt[1] + seqt[2] + + seqt[3]); n73; Evaluate(n73,2); Olav := {[a,b]: a,b in {1..343) | Evaluate(n73,a) eq Evaluate(t73,b)}; #Olav; Output: Magma V2.10-6 Thu Mar 11 2004 09:48:40 on modular [Seed = 2241182123] ------------------------------------- [ 1, 7, 49 ] x^49 + x^7 + x x^57 144115188075855872 >> Olav := {[a,b]: a,b in {1..343) | Evaluate(n73,a) eq Evaluate(t73,b)}; ^ User error: bad syntax >> #Olav;; ^ User error: Identifier 'Olav' has not been declared or assigned Total time: 3.619 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.68) Time: Thu Mar 11 09:49:09 2004 Input: seqt := [7^(r-1) : r in {1..3}]; seqt; P:=PolynomialRing(RealField()); t73 := x^(seqt[1]) + x^(seqt[2]) + x^(seqt[3]); t73; n73 := x^(seqt[1] + seqt[2] + + seqt[3]); n73; Evaluate(n73,2); Olav := {[a,b]: a,b in {1..343} | Evaluate(n73,a) eq Evaluate(t73,b)}; #Olav; Output: Magma V2.10-6 Thu Mar 11 2004 09:48:51 on modular [Seed = 2491721889] ------------------------------------- [ 1, 7, 49 ] x^49 + x^7 + x x^57 144115188075855872 0 Total time: 18.199 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.68) Time: Thu Mar 11 09:50:07 2004 Input: seqt := [7^(r-1) : r in {1..3}]; seqt; P:=PolynomialRing(RealField()); t73 := x^(seqt[1]) + x^(seqt[2]) + x^(seqt[3]); t73; n73 := x^(seqt[1] + seqt[2] + + seqt[3]); n73; Evaluate(n73,2); Olav := {[a,b]: a,b in {1..49} | Evaluate(n73,a) eq Evaluate(t73,b)}; #Olav; Output: Magma V2.10-6 Thu Mar 11 2004 09:50:03 on modular [Seed = 3470717490] ------------------------------------- [ 1, 7, 49 ] x^49 + x^7 + x x^57 144115188075855872 0 Total time: 3.429 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse013.uab.es. (158.109.66.132) Time: Thu Mar 11 09:51:18 2004 Input: > lista:= function () function> C:={}; function> for i in {1..100000} do Include(C,Random(M)); end for; return {C}; end function; > lista(); Output: Magma V2.10-6 Thu Mar 11 2004 09:51:14 on modular [Seed = 318975897] ------------------------------------- >> function> C:={}; ^ User error: bad syntax >> function> for i in {1..100000} do Include(C,Random(M)); end for; return {C} ^ User error: bad syntax >> lista();; ^ User error: Identifier 'lista' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse013.uab.es. (158.109.66.132) Time: Thu Mar 11 09:53:36 2004 Input: > lista:= function () C:={}; for i in {1..100000} do Include(C,Random(M)); end for; return {C}; end function; > lista(); Output: Magma V2.10-6 Thu Mar 11 2004 09:53:31 on modular [Seed = 2409607821] ------------------------------------- >> for i in {1..100000} do Include(C,Random(M)); end for; return {C}; end func ^ User error: Identifier 'M' has not been declared or assigned >> lista();; ^ User error: Identifier 'lista' has not been declared or assigned Total time: 3.139 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse013.uab.es. (158.109.66.132) Time: Thu Mar 11 09:55:17 2004 Input: > lista:= function () M:=KMatrixSpace(GF(4),2,2); C:={}; for i in {1..100000} do Include(C,Random(M)); end for; return {C}; end function; > lista(); Output: Magma V2.10-6 Thu Mar 11 2004 09:55:06 on modular [Seed = 3670730618] ------------------------------------- { [ 1 1] [ 0 $.1^2] } { [$.1^2 $.1] [ 1 1] } { [ 1 1] [ 1 1] } { [ $.1 $.1^2] [ $.1 $.1^2] } { [ 0 $.1^2] [ 1 $.1^2] } { [ 1 $.1] [ 0 $.1] } { [ 1 1] [ $.1 1] } { [$.1^2 0] [$.1^2 1] } { [$.1^2 1] [ 0 $.1] } { [$.1^2 0] [ $.1 1] } { [ 1 1] [$.1^2 1] } { [ 1 1] [ 1 $.1^2] } { [ 0 0] [ 0 $.1] } { [ $.1 $.1] [$.1^2 $.1] } { [ $.1 $.1^2] [$.1^2 $.1^2] } { [ 0 $.1] [ 0 1] } { [ 0 0] [ 1 $.1] } { [ 0 $.1] [ 0 1] } { [ 0 $.1] [$.1^2 0] } { [ 1 0] [ $.1 0] } { [$.1^2 $.1^2] [ $.1 $.1^2] } { [$.1^2 $.1] [$.1^2 $.1^2] } { [ 0 $.1^2] [$.1^2 $.1^2] } { [ 1 $.1] [ 1 $.1] } { [$.1^2 $.1] [ 0 1] } { [$.1^2 1] [$.1^2 $.1] } { [ 1 $.1^2] [ 0 $.1^2] } { [ $.1 0] [ $.1 0] } { [ $.1 $.1^2] [ 0 $.1^2] } { [ 1 $.1^2] [ $.1 1] } { [ 0 1] [ $.1 1] } { [$.1^2 $.1^2] [ $.1 0] } { [ $.1 $.1^2] [ $.1 $.1] } { [ 0 0] [ 0 1] } { [ $.1 $.1] [ 1 $.1] } { [ 1 1] [ 0 $.1] } { [ 0 0] [ $.1 $.1^2] } { [$.1^2 0] [ $.1 1] } { [ $.1 1] [$.1^2 $.1] } { [ 0 1] [ 1 $.1^2] } { [$.1^2 0] [ 0 $.1^2] } { [ $.1 0] [ $.1 1] } { [ 0 0] [ $.1 $.1] } { [ 0 $.1] [ $.1 1] } { [$.1^2 $.1^2] [$.1^2 $.1^2] } { [$.1^2 0] [ 1 1] } { [ $.1 $.1^2] [ 0 0] } { [ 1 0] [ $.1 $.1^2] } { [ $.1 1] [ $.1 0] } { [ 0 $.1] [ 1 $.1] } { [$.1^2 0] [ $.1 $.1^2] } { [ 0 1] [ 0 $.1^2] } { [$.1^2 $.1^2] [$.1^2 $.1^2] } { [ $.1 1] [$.1^2 $.1^2] } { [$.1^2 $.1] [ 1 0] } { [ $.1 1] [ $.1 $.1] } { [$.1^2 $.1] [ $.1 $.1^2] } { [ 0 $.1^2] [ $.1 $.1^2] } { [$.1^2 1] [ 0 1] } { [ 0 $.1] [ $.1 $.1^2] } { [ 0 1] [$.1^2 0] } { [ 0 1] [ $.1 1] } { [ 0 1] [ 0 1] } { [ $.1 $.1^2] [ $.1 $.1] } { [ 1 1] [$.1^2 0] } { [ 0 $.1] [ 1 0] } { [ 0 0] [ 0 $.1] } { [$.1^2 0] [ 0 $.1] } { [ 0 1] [$.1^2 1] } { [ 1 1] [$.1^2 $.1^2] } { [$.1^2 $.1] [ $.1 0] } { [ 0 0] [ $.1 0] } { [ 0 $.1^2] [ 1 0] } { [ $.1 $.1^2] [ 0 1] } { [ $.1 $.1^2] [ $.1 0] } { [ 1 $.1] [$.1^2 0] } { [$.1^2 $.1^2] [ $.1 $.1] } { [ $.1 1] [ 0 1] } { [$.1^2 $.1^2] [ $.1 $.1^2] } { [ 1 $.1] [ 1 0] } { [$.1^2 $.1^2] [ 1 1] } { [ 0 $.1] [ $.1 0] } { [ 1 $.1^2] [ $.1 $.1] } { [ 0 $.1^2] [$.1^2 1] } { [ $.1 $.1^2] [$.1^2 1] } { [$.1^2 0] [ 0 0] } { [ 1 $.1] [ $.1 $.1] } { [$.1^2 0] [ $.1 $.1^2] } { [$.1^2 $.1^2] [ 0 0] } { [ 0 $.1^2] [ $.1 $.1^2] } { [ 1 $.1] [ 1 $.1^2] } { [ 0 $.1^2] [ $.1 $.1] } { [$.1^2 $.1] [ 0 $.1] } { [ 1 $.1^2] [ 0 $.1^2] } { [ $.1 0] [$.1^2 1] } { [$.1^2 $.1^2] [ 0 0] } { [ $.1 1] [$.1^2 $.1] } { [ 1 1] [ 0 $.1] } { [ 1 0] [$.1^2 $.1] } { [$.1^2 1] [ $.1 $.1^2] } { [$.1^2 $.1] [$.1^2 1] } { [$.1^2 1] [ 0 1] } { [$.1^2 $.1] [ $.1 $.1] } { [ $.1 0] [ $.1 0] } { [ $.1 $.1^2] [ 1 $.1] } { [ 0 1] [$.1^2 0] } { [ $.1 $.1^2] [ $.1 $.1^2] } { [ 0 $.1^2] [$.1^2 $.1^2] } { [ 0 1] [ $.1 $.1] } { [ 0 $.1] [ 1 0] } { [$.1^2 0] [ $.1 0] } { [ 0 1] [$.1^2 0] } { [$.1^2 $.1] [ 1 0] } { [$.1^2 1] [$.1^2 $.1^2] } { [ 1 $.1] [ 1 1] } { [$.1^2 $.1] [$.1^2 1] } { [ 0 0] [ $.1 $.1] } { [ 1 1] [ 0 $.1^2] } { [ $.1 $.1^2] [ 0 $.1^2] } { [ $.1 0] [$.1^2 0] } { [ 0 $.1] [ 0 1] } { [$.1^2 $.1] [ 1 0] } { [$.1^2 $.1] [ 0 $.1^2] } { [$.1^2 1] [ $.1 $.1^2] } { [ $.1 1] [ $.1 $.1] } { [ 1 $.1] [ $.1 1] } { [ $.1 $.1] [ $.1 $.1^2] } { [ 1 $.1^2] [ 0 $.1^2] } { [ 1 $.1] [ 0 1] } { [ 1 1] [$.1^2 1] } { [$.1^2 $.1] [$.1^2 0] } { [ $.1 $.1] [$.1^2 $.1^2] } { [ 1 0] [ 1 $.1^2] } { [ 1 0] [ 0 $.1] } { [ $.1 $.1^2] [ 0 $.1^2] } { [ $.1 $.1] [ 0 0] } { [ 0 1] [ 1 $.1] } { [ 1 0] [ $.1 $.1^2] } { [ 0 1] [$.1^2 1] } { [ 0 $.1^2] [ 1 $.1] } { [$.1^2 0] [ 1 $.1] } { [ $.1 $.1^2] [ $.1 0] } { [$.1^2 1] [ 1 0] } { [ 0 1] [ 1 0] } { [ $.1 0] [ 0 $.1] } { [ 1 1] [ 0 $.1^2] } { [ 1 $.1^2] [ $.1 $.1] } { [ 1 1] [$.1^2 1] } { [ 1 0] [$.1^2 $.1] } { [ 0 $.1^2] [ $.1 $.1] } { [$.1^2 $.1^2] [$.1^2 0] } { [ 0 1] [ 1 $.1^2] } { [ 1 $.1] [ 1 $.1] } { [ $.1 0] [ 0 $.1] } { [ $.1 $.1^2] [ 0 1] } { [$.1^2 0] [$.1^2 0] } { [ 1 $.1] [ 0 $.1^2] } { [ $.1 0] [ 0 0] } { [ 0 0] [ 0 $.1] } { [ 0 1] [ 1 1] } { [ 1 1] [ $.1 1] } { [ 1 $.1^2] [$.1^2 1] } { [ $.1 1] [ 1 $.1^2] } { [ $.1 $.1^2] [ 0 1] } { [ $.1 0] [ 0 1] } { [ $.1 $.1] [ 1 0] } { [$.1^2 1] [ 0 0] } { [ 1 $.1] [$.1^2 1] } { [ $.1 $.1^2] [$.1^2 $.1] } { [ $.1 0] [$.1^2 1] } { [ $.1 1] [$.1^2 1] } { [$.1^2 0] [$.1^2 $.1] } { [ $.1 1] [ 1 1] } { [ 1 0] [ $.1 0] } { [ 1 0] [ $.1 1] } { [$.1^2 $.1] [ $.1 1] } { [ $.1 $.1^2] [ $.1 $.1^2] } { [$.1^2 1] [ 1 $.1^2] } { [ $.1 1] [ 1 $.1^2] } { [ 0 1] [ $.1 1] } { [ $.1 $.1^2] [ 0 0] } { [$.1^2 0] [$.1^2 1] } { [$.1^2 $.1^2] [ 1 $.1] } { [ 1 0] [ 1 0] } { [ 0 0] [$.1^2 $.1^2] } { [ 1 $.1] [ 1 0] } { [ $.1 $.1^2] [ $.1 $.1^2] } { [ 0 $.1^2] [ $.1 0] } { [ $.1 $.1] [ $.1 1] } { [ 0 1] [ 0 1] } { [ $.1 0] [ 0 $.1] } { [ 0 $.1^2] [$.1^2 $.1] } { [ $.1 $.1] [$.1^2 $.1] } { [$.1^2 1] [ 0 0] } { [ 0 0] [$.1^2 $.1^2] } { [ 1 1] [$.1^2 $.1] } { [ $.1 $.1] [ 1 0] } { [ $.1 $.1] [$.1^2 $.1] } { [ $.1 1] [ 0 1] } { [ 0 $.1] [ $.1 1] } { [$.1^2 $.1] [ $.1 1] } { [ 1 0] [$.1^2 $.1] } { [$.1^2 $.1] [ $.1 1] } { [ 0 $.1] [$.1^2 $.1] } { [ $.1 1] [ $.1 $.1] } { [$.1^2 1] [ 0 1] } { [ $.1 $.1] [$.1^2 1] } { [ 1 $.1] [ 1 1] } { [ $.1 $.1^2] [$.1^2 $.1] } { [ 1 0] [ 1 $.1] } { [ $.1 1] [ $.1 0] } { [ 0 $.1] [ 0 1] } { [$.1^2 1] [$.1^2 $.1^2] } { [ $.1 $.1^2] [ $.1 0] } { [ 1 1] [ 1 0] } { [$.1^2 1] [ 1 $.1] } { [$.1^2 0] [ 1 $.1] } { [$.1^2 0] [ $.1 $.1] } { [$.1^2 1] [ 1 1] } { [ 0 1] [ 0 $.1] } { [ $.1 1] [ 0 $.1^2] } { [$.1^2 $.1] [$.1^2 $.1^2] } { [ 1 $.1^2] [ $.1 $.1] } { [ 0 0] [ 0 0] } { [ $.1 0] [ 0 0] } { [ $.1 $.1^2] [$.1^2 $.1^2] } { [ 1 $.1^2] [ 0 0] } { [ $.1 0] [ 0 $.1] } { [ 0 $.1^2] [ 1 $.1] } { [ 0 0] [ 0 0] } { [ 0 1] [ $.1 $.1] } { [ 0 $.1^2] [ 0 1] } { [$.1^2 $.1^2] [ 1 1] } { [ 1 1] [ 1 $.1^2] } { [$.1^2 $.1] [ 1 $.1] } { [ 0 0] [ 0 1] } { [ 1 1] [$.1^2 $.1] } { [ 0 $.1] [ 1 $.1] } { [$.1^2 $.1] [ $.1 0] } { [ $.1 1] [$.1^2 0] } { [ $.1 $.1^2] [ $.1 0] } { [ 1 $.1^2] [$.1^2 1] } { [ 1 $.1^2] [ 0 $.1^2] } { [ 1 $.1] [ 1 1] } { [ $.1 1] [$.1^2 0] } { [ 1 $.1] [ 1 $.1^2] } { [ 1 1] [ 1 1] } { ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host aula-etse013.uab.es. (158.109.66.132) Time: Thu Mar 11 09:55:41 2004 Input: > lista:= function () M:=KMatrixSpace(GF(4),2,2); C:={}; for i in {1..100} do Include(C,Random(M)); end for; return {C}; end function; > lista(); Output: Magma V2.10-6 Thu Mar 11 2004 09:55:37 on modular [Seed = 2137998077] ------------------------------------- { [$.1^2 1] [$.1^2 0] } { [ 0 0] [ 0 $.1^2] } { [ $.1 $.1] [$.1^2 1] } { [$.1^2 $.1^2] [$.1^2 $.1^2] } { [ 0 $.1] [$.1^2 1] } { [ $.1 1] [ 0 1] } { [ 0 $.1] [ 1 $.1^2] } { [ 1 $.1^2] [$.1^2 $.1] } { [ 1 1] [ 1 $.1^2] } { [ 0 1] [ $.1 0] } { [ 1 0] [$.1^2 1] } { [$.1^2 $.1] [$.1^2 1] } { [ $.1 $.1] [ 1 0] } { [$.1^2 1] [ 0 1] } { [ 1 0] [ $.1 $.1^2] } { [ 0 1] [ $.1 $.1] } { [ $.1 1] [ 1 1] } { [ 1 1] [ 0 $.1] } { [$.1^2 $.1] [ 0 $.1] } { [$.1^2 1] [ 0 $.1^2] } { [ 0 $.1^2] [ $.1 $.1^2] } { [ 1 0] [$.1^2 $.1] } { [ 1 0] [ 1 0] } { [$.1^2 $.1^2] [$.1^2 0] } { [ $.1 $.1] [ 1 1] } { [ 0 0] [ 1 1] } { [$.1^2 $.1] [$.1^2 $.1^2] } { [$.1^2 $.1^2] [ 1 1] } { [ 1 $.1] [ $.1 1] } { [ $.1 0] [$.1^2 0] } { [ 1 1] [ 1 1] } { [ 1 $.1^2] [ $.1 1] } { [ 0 $.1] [ 0 0] } { [ $.1 $.1] [$.1^2 $.1] } { [ $.1 1] [ 0 0] } { [ 1 0] [ 0 1] } { [ $.1 0] [ $.1 0] } { [ 0 0] [$.1^2 1] } { [ $.1 1] [ 0 0] } { [ 1 0] [ $.1 $.1^2] } { [$.1^2 $.1^2] [ 1 1] } { [$.1^2 $.1^2] [ $.1 1] } { [ 0 $.1^2] [ $.1 $.1] } { [ 0 1] [ 1 1] } { [ 1 $.1^2] [ 1 0] } { [ 0 0] [ $.1 1] } { [$.1^2 $.1^2] [ 1 $.1] } { [ $.1 1] [ 0 $.1] } { [ 0 0] [$.1^2 $.1] } { [$.1^2 0] [$.1^2 1] } { [ $.1 $.1^2] [$.1^2 0] } { [ 0 $.1^2] [ 1 $.1] } { [ 1 $.1] [ 1 1] } { [ 1 $.1] [ 0 $.1] } { [ 1 1] [ $.1 $.1^2] } { [$.1^2 0] [ $.1 1] } { [ 1 $.1] [ $.1 1] } { [ $.1 $.1^2] [ 1 0] } { [ 1 $.1^2] [ 0 $.1] } { [ $.1 $.1^2] [ 1 1] } { [ 0 1] [ 1 $.1^2] } { [ 1 $.1] [ $.1 $.1^2] } { [ 1 1] [ $.1 1] } { [ 1 $.1^2] [ 0 $.1] } { [ 1 $.1] [ 1 $.1] } { [ 0 $.1] [$.1^2 1] } { [ $.1 $.1^2] [ 1 $.1] } { [ 1 1] [ 1 1] } { [$.1^2 0] [ $.1 1] } { [ 1 $.1^2] [ 0 $.1] } { [ 1 1] [ 1 1] } { [ 0 $.1] [ 0 $.1] } { [$.1^2 $.1] [$.1^2 1] } { [ 0 $.1] [ 0 1] } { [ $.1 $.1] [ 1 $.1^2] } { [$.1^2 0] [ 1 $.1] } { [ 0 $.1^2] [ 1 $.1] } { [ 1 $.1^2] [$.1^2 0] } { [ 0 0] [ 0 1] } { [ 1 1] [$.1^2 $.1^2] } { [ 1 0] [ $.1 1] } { [ 0 0] [ 0 $.1] } { [ 0 $.1] [ 1 $.1] } { [$.1^2 $.1^2] [$.1^2 0] } { [ 0 1] [$.1^2 $.1^2] } { [$.1^2 $.1] [ 1 $.1^2] } { [ 0 1] [ $.1 $.1^2] } { [ 1 $.1^2] [$.1^2 1] } { [ 1 $.1^2] [ 0 $.1^2] } { [ $.1 $.1] [ 0 0] } { [ $.1 $.1] [$.1^2 1] } { [$.1^2 0] [ 0 1] } { [ 1 $.1^2] [$.1^2 0] } { [ 0 1] [$.1^2 $.1^2] } { [$.1^2 $.1^2] [$.1^2 1] } { [ 0 $.1^2] [ 0 1] } { [$.1^2 $.1^2] [$.1^2 $.1] } { [ $.1 $.1^2] [ 1 $.1] } { [$.1^2 0] [ 1 0] } { [ $.1 $.1] [ $.1 $.1] } { {} } Total time: 3.209 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-etse013.uab.es. (158.109.66.132) Time: Thu Mar 11 09:57:32 2004 Input: > lista:= function () M:=KMatrixSpace(GF(4),2,2); C:={}; for i in {1..100} do Include(C,Random(M)); end for; return {C}; end function; > lista(); nmt:= [#[k : k in lista| k in Mt],#[k: k in lista| k in Mf],#[k:k in lista| k in Mtf]]; > nmt; Output: Magma V2.10-6 Thu Mar 11 2004 09:57:28 on modular [Seed = 1836929881] ------------------------------------- { [ 0 1] [ 0 0] } { [$.1^2 1] [ 0 0] } { [ 0 $.1] [$.1^2 $.1] } { [ 1 0] [ 0 1] } { [ $.1 $.1] [$.1^2 $.1^2] } { [$.1^2 1] [$.1^2 $.1] } { [ 1 $.1] [ 1 $.1] } { [ $.1 $.1^2] [$.1^2 1] } { [ 1 $.1^2] [ 0 0] } { [$.1^2 $.1] [$.1^2 1] } { [ $.1 0] [$.1^2 $.1] } { [ 0 1] [ 1 $.1] } { [ $.1 $.1] [ 1 0] } { [ 1 1] [ 1 $.1^2] } { [$.1^2 $.1] [ $.1 $.1] } { [ 1 $.1^2] [ 0 1] } { [ $.1 0] [ 1 1] } { [$.1^2 0] [$.1^2 $.1^2] } { [$.1^2 $.1] [ 0 $.1^2] } { [ $.1 0] [ $.1 $.1^2] } { [$.1^2 $.1^2] [ 1 $.1^2] } { [ $.1 $.1^2] [ $.1 $.1^2] } { [ $.1 $.1^2] [ 0 1] } { [ 1 0] [ 1 $.1^2] } { [ 1 1] [ $.1 0] } { [$.1^2 1] [ 0 $.1] } { [ $.1 0] [$.1^2 0] } { [$.1^2 $.1^2] [ $.1 $.1] } { [ 0 1] [ $.1 $.1^2] } { [ $.1 1] [ 0 $.1^2] } { [ $.1 1] [ $.1 $.1^2] } { [$.1^2 $.1] [ 0 0] } { [ $.1 $.1^2] [$.1^2 $.1] } { [ 0 $.1^2] [$.1^2 $.1^2] } { [ $.1 0] [$.1^2 $.1] } { [$.1^2 $.1] [ 0 0] } { [$.1^2 1] [ 0 0] } { [ 0 1] [ 0 0] } { [ $.1 $.1] [$.1^2 1] } { [$.1^2 1] [ 0 0] } { [$.1^2 $.1] [$.1^2 1] } { [ 1 $.1] [ 0 1] } { [ 0 $.1^2] [$.1^2 $.1] } { [ 0 $.1^2] [ 1 0] } { [ 1 0] [ $.1 $.1] } { [ $.1 0] [$.1^2 $.1^2] } { [$.1^2 0] [ 1 0] } { [$.1^2 $.1^2] [ 0 1] } { [ 1 $.1] [ 1 $.1^2] } { [$.1^2 $.1] [ 1 1] } { [ $.1 0] [ 0 $.1] } { [ 0 1] [ 0 1] } { [ 0 $.1] [ 0 0] } { [$.1^2 0] [ 1 0] } { [ $.1 $.1] [ 0 $.1^2] } { [ $.1 $.1] [ $.1 $.1^2] } { [ $.1 1] [$.1^2 1] } { [ 1 $.1] [ 0 $.1^2] } { [ $.1 0] [ $.1 0] } { [ 0 $.1] [ $.1 0] } { [ $.1 $.1] [ $.1 1] } { [$.1^2 $.1^2] [ 1 1] } { [$.1^2 $.1] [ 0 1] } { [ 1 $.1] [$.1^2 $.1^2] } { [ 0 $.1^2] [ 1 $.1] } { [$.1^2 0] [ $.1 $.1] } { [ $.1 1] [ 1 $.1] } { [$.1^2 $.1] [$.1^2 $.1] } { [ $.1 0] [ 0 $.1] } { [ 0 1] [ 0 0] } { [ 1 $.1^2] [$.1^2 0] } { [ 0 $.1] [$.1^2 $.1^2] } { [ 1 $.1] [ 1 1] } { [ 0 $.1] [ $.1 $.1^2] } { [$.1^2 $.1] [ 1 1] } { [$.1^2 $.1] [ $.1 0] } { [$.1^2 1] [$.1^2 $.1^2] } { [ $.1 1] [ 1 1] } { [ 0 0] [ $.1 $.1] } { [ 1 1] [$.1^2 $.1] } { [ $.1 $.1^2] [ $.1 0] } { [ 1 $.1] [ 1 $.1] } { [$.1^2 1] [ 0 1] } { [ 0 $.1] [ 1 $.1] } { [ 1 $.1] [$.1^2 0] } { [ $.1 0] [$.1^2 $.1^2] } { [ 1 1] [$.1^2 1] } { [$.1^2 $.1^2] [ 0 $.1] } { [ $.1 $.1^2] [ 1 $.1] } { [ $.1 1] [ 1 $.1] } { [$.1^2 0] [ 1 0] } { [ 1 $.1] [$.1^2 1] } { [ 1 1] [ 1 $.1^2] } { [ 1 $.1] [ 1 0] } { [ 0 $.1^2] [ 0 $.1^2] } { [ $.1 0] [ $.1 0] } { [ $.1 $.1^2] [$.1^2 $.1] } { [$.1^2 $.1^2] [$.1^2 $.1] } { [$.1^2 $.1] [ $.1 $.1^2] } { [ $.1 $.1^2] [$.1^2 $.1] } { {} } >> nmt:= [#[k : k in lista| k in Mt],#[k: k in lista| k in Mf],#[k:k in lista| ^ User error: Identifier 'Mt' has not been declared or assigned >> nmt; ^ User error: Identifier 'nmt' has not been declared or assigned Total time: 3.259 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-etse013.uab.es. (158.109.66.132) Time: Thu Mar 11 09:59:21 2004 Input: > lista:= function () > M:=KMatrixSpace(GF(4),2,2); > C:={}; for i in {1..100} do Include(C,Random(M)); end for; return {C}; end function; > lista(); > Mf:= { k: k in M| (k[1][1] eq k[2][1]) and (k[1][2] eq k[2][2])}; > Mt:= { k : k in M | Trace(k) eq 0}; > Mtf:= {k : k in M | (k in Mt) and (k in Mf) }; > nmt:= [#[k : k in lista| k in Mt],#[k: k in lista| k in Mf],#[k:k in lista| k in Mtf]]; > nmt; Output: Magma V2.10-6 Thu Mar 11 2004 09:59:17 on modular [Seed = 2676990262] ------------------------------------- { [$.1^2 $.1^2] [ 1 $.1^2] } { [ 1 0] [ $.1 1] } { [ 1 $.1] [ 1 $.1^2] } { [$.1^2 1] [ 0 0] } { [ $.1 $.1^2] [ 0 $.1^2] } { [ $.1 $.1^2] [ 1 $.1] } { [$.1^2 $.1] [ 1 0] } { [ $.1 0] [ $.1 1] } { [ $.1 1] [ 0 1] } { [ 0 1] [$.1^2 1] } { [$.1^2 0] [ 1 $.1] } { [ $.1 $.1^2] [ 1 1] } { [ 1 0] [$.1^2 1] } { [ 1 0] [ 0 $.1] } { [ 0 0] [ 0 $.1^2] } { [$.1^2 $.1^2] [ $.1 0] } { [$.1^2 $.1] [ 0 1] } { [ $.1 $.1] [ $.1 0] } { [ 0 $.1^2] [ 1 0] } { [ 1 1] [ 1 $.1^2] } { [ $.1 $.1] [ 1 0] } { [ 1 $.1] [ 1 $.1] } { [ 0 0] [$.1^2 1] } { [ 1 0] [$.1^2 1] } { [$.1^2 1] [ 1 0] } { [ 1 $.1] [$.1^2 0] } { [ 0 $.1^2] [ 0 0] } { [ 1 $.1] [ 0 0] } { [ 0 0] [ 1 0] } { [ $.1 $.1^2] [ $.1 1] } { [$.1^2 1] [ $.1 $.1^2] } { [$.1^2 $.1^2] [ 1 0] } { [ $.1 1] [ 0 $.1^2] } { [ 0 $.1] [ $.1 $.1] } { [ 0 $.1^2] [ $.1 $.1^2] } { [ 0 $.1^2] [ $.1 0] } { [ 1 1] [ 1 $.1] } { [ $.1 $.1^2] [ 0 $.1^2] } { [$.1^2 $.1] [ $.1 $.1^2] } { [ 1 0] [ $.1 $.1^2] } { [ 0 $.1] [$.1^2 $.1] } { [ $.1 $.1] [ 0 $.1^2] } { [ $.1 $.1] [$.1^2 $.1] } { [ $.1 $.1] [$.1^2 0] } { [ 1 1] [ 0 $.1] } { [$.1^2 1] [$.1^2 $.1] } { [$.1^2 $.1^2] [ 1 1] } { [ 1 $.1] [ $.1 $.1] } { [$.1^2 $.1^2] [ $.1 $.1^2] } { [$.1^2 0] [ 1 1] } { [ 1 $.1^2] [$.1^2 0] } { [ $.1 0] [ 0 $.1^2] } { [ $.1 $.1] [ $.1 1] } { [ $.1 1] [$.1^2 0] } { [$.1^2 $.1] [$.1^2 $.1] } { [$.1^2 0] [ 0 1] } { [ 1 0] [$.1^2 $.1^2] } { [$.1^2 $.1^2] [$.1^2 1] } { [ 1 $.1^2] [$.1^2 0] } { [ 1 $.1] [ 1 $.1] } { [ $.1 $.1^2] [ $.1 1] } { [ $.1 $.1] [ 0 1] } { [$.1^2 $.1^2] [$.1^2 $.1] } { [ $.1 $.1^2] [$.1^2 0] } { [ 1 0] [ $.1 $.1^2] } { [$.1^2 1] [ $.1 $.1^2] } { [ 1 $.1^2] [ 1 $.1] } { [ 0 1] [$.1^2 1] } { [$.1^2 $.1] [$.1^2 $.1] } { [ $.1 1] [$.1^2 1] } { [ 0 1] [ 0 $.1] } { [ 0 $.1] [$.1^2 0] } { [$.1^2 1] [$.1^2 $.1] } { [ 0 $.1^2] [ 0 $.1^2] } { [$.1^2 $.1^2] [ 1 $.1^2] } { [ 1 $.1^2] [ 1 $.1] } { [ $.1 $.1] [ 1 $.1^2] } { [$.1^2 $.1] [$.1^2 $.1] } { [$.1^2 $.1] [ 1 1] } { [ $.1 $.1] [ 1 0] } { [ $.1 $.1] [ 0 1] } { [ 0 $.1] [ $.1 0] } { [ $.1 $.1^2] [ 1 1] } { [ 0 0] [ 1 $.1^2] } { [ 0 $.1^2] [ 1 $.1] } { [ 0 1] [ 1 $.1] } { [$.1^2 $.1] [ 0 $.1] } { [$.1^2 1] [ 1 $.1] } { [ 0 0] [ 0 $.1] } { [$.1^2 $.1^2] [ $.1 $.1] } { [ 0 1] [$.1^2 $.1] } { [$.1^2 $.1] [ 0 $.1] } { [ 1 $.1^2] [ 0 1] } { [ $.1 $.1] [ $.1 1] } { [ 1 $.1^2] [ 1 $.1] } { [ 1 1] [$.1^2 1] } { [ $.1 $.1^2] [$.1^2 $.1] } { [$.1^2 $.1^2] [ 0 0] } { [ $.1 0] [ 1 0] } { [ $.1 0] [ 0 $.1^2] } { {} } >> Mf:= { k: k in M| (k[1][1] eq k[2][1]) and (k[1][2] eq k[2][2])}; ^ User error: Identifier 'M' has not been declared or assigned >> Mt:= { k : k in M | Trace(k) eq 0}; ^ User error: Identifier 'M' has not been declared or assigned >> Mtf:= {k : k in M | (k in Mt) and (k in Mf) }; ^ User error: Identifier 'M' has not been declared or assigned >> nmt:= [#[k : k in lista| k in Mt],#[k: k in lista| k in Mf],#[k:k in list ^ User error: Identifier 'Mt' has not been declared or assigned >> nmt; ^ User error: Identifier 'nmt' has not been declared or assigned Total time: 3.079 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-etse013.uab.es. (158.109.66.132) Time: Thu Mar 11 10:00:26 2004 Input: > lista:= function () > M:=KMatrixSpace(GF(4),2,2); > C:={}; for i in {1..100} do Include(C,Random(M)); end for; return {C}; end function; > lista(); > M:=KMatrixSpace(GF(4),2,2); > Mf:= { k: k in M| (k[1][1] eq k[2][1]) and (k[1][2] eq k[2][2])}; > Mt:= { k : k in M | Trace(k) eq 0}; > Mtf:= {k : k in M | (k in Mt) and (k in Mf) }; > nmt:= [#[k : k in lista| k in Mt],#[k: k in lista| k in Mf],#[k:k in lista| k in Mtf]]; > nmt; Output: Magma V2.10-6 Thu Mar 11 2004 10:00:22 on modular [Seed = 4026519684] ------------------------------------- { [ 1 0] [ 0 0] } { [ $.1 $.1^2] [$.1^2 0] } { [$.1^2 0] [ 1 0] } { [ 0 1] [ 0 1] } { [$.1^2 $.1] [ 1 0] } { [$.1^2 $.1^2] [ 0 1] } { [ 1 $.1^2] [ 1 1] } { [$.1^2 $.1] [ $.1 1] } { [ $.1 $.1^2] [ 0 $.1^2] } { [ 1 0] [ $.1 0] } { [ 1 $.1^2] [ 1 $.1] } { [ 1 $.1^2] [ $.1 0] } { [ 0 $.1] [$.1^2 0] } { [ 0 $.1^2] [ 0 $.1^2] } { [ $.1 $.1^2] [$.1^2 1] } { [ 1 0] [$.1^2 0] } { [ $.1 1] [ 0 $.1^2] } { [ $.1 0] [$.1^2 $.1] } { [ 1 $.1] [$.1^2 $.1] } { [ $.1 1] [ $.1 0] } { [ $.1 $.1^2] [ $.1 0] } { [ 0 $.1] [ 1 1] } { [ 0 $.1^2] [ 0 0] } { [$.1^2 0] [$.1^2 1] } { [ 0 0] [ $.1 0] } { [$.1^2 1] [ $.1 $.1^2] } { [$.1^2 0] [ 1 0] } { [ 0 1] [ 0 0] } { [ 1 $.1^2] [ 1 1] } { [ $.1 $.1^2] [ 0 0] } { [ 0 0] [ $.1 0] } { [ 1 $.1^2] [ 0 $.1] } { [ 0 $.1^2] [$.1^2 $.1] } { [$.1^2 $.1^2] [ $.1 1] } { [$.1^2 1] [ $.1 $.1] } { [$.1^2 $.1] [ 0 $.1] } { [ 0 $.1^2] [$.1^2 $.1^2] } { [ 0 $.1] [ $.1 $.1] } { [ 0 $.1] [ 0 $.1^2] } { [ 1 $.1^2] [ $.1 1] } { [ $.1 1] [ $.1 0] } { [ 0 0] [ 1 1] } { [ 0 1] [ 0 $.1] } { [ 0 0] [ 0 $.1^2] } { [$.1^2 $.1^2] [ 1 $.1] } { [$.1^2 $.1] [ 0 $.1^2] } { [ $.1 1] [ 0 $.1] } { [$.1^2 $.1] [$.1^2 0] } { [$.1^2 0] [ 1 $.1] } { [ 1 1] [ 0 1] } { [ $.1 1] [ 0 $.1] } { [ 1 $.1] [ $.1 0] } { [ 1 $.1] [ 0 0] } { [$.1^2 1] [ 0 0] } { [ 0 $.1^2] [$.1^2 1] } { [ 0 1] [ 0 0] } { [ 1 $.1^2] [ 1 0] } { [ 0 $.1^2] [ 0 $.1] } { [ 0 $.1] [ 0 $.1^2] } { [ $.1 $.1^2] [$.1^2 1] } { [ 0 $.1^2] [ 0 $.1^2] } { [ 1 $.1^2] [ $.1 $.1] } { [$.1^2 0] [ 1 1] } { [ 0 $.1] [$.1^2 0] } { [$.1^2 1] [ 0 0] } { [ 0 $.1] [ 1 $.1^2] } { [ 0 1] [ 1 $.1^2] } { [ 0 $.1^2] [ 1 0] } { [ 1 1] [ $.1 1] } { [ $.1 0] [ 1 0] } { [ $.1 1] [ $.1 0] } { [ 0 $.1^2] [ 1 $.1^2] } { [$.1^2 0] [ 1 0] } { [ 0 $.1] [ $.1 $.1] } { [ 0 $.1^2] [ 1 $.1^2] } { [ $.1 1] [ $.1 1] } { [ 0 1] [$.1^2 $.1^2] } { [ $.1 $.1] [ 1 $.1] } { [ 1 $.1^2] [ $.1 1] } { [$.1^2 $.1] [ 1 1] } { [$.1^2 1] [$.1^2 1] } { [ 0 0] [ 1 1] } { [$.1^2 $.1^2] [ 0 $.1^2] } { [ 1 $.1] [ $.1 0] } { [ 0 0] [$.1^2 0] } { [ 0 1] [$.1^2 0] } { [$.1^2 0] [ 0 $.1] } { [ $.1 0] [$.1^2 0] } { [$.1^2 1] [ 1 $.1] } { [ $.1 1] [ 1 0] } { [ 0 $.1] [$.1^2 $.1^2] } { [ 0 1] [ 0 $.1^2] } { [ $.1 $.1^2] [ 0 $.1] } { [$.1^2 $.1^2] [$.1^2 0] } { [ 1 0] [ 1 0] } { [ 0 $.1] [ 1 $.1^2] } { [ $.1 0] [ $.1 0] } { [$.1^2 0] [ 1 1] } { [ $.1 $.1] [$.1^2 $.1] } { [$.1^2 1] [ $.1 $.1^2] } { {} } >> nmt:= [#[k : k in lista| k in Mt],#[k: k in lista| k in Mf],#[k:k in list ^ Runtime error in for: Iteration is not possible over this object >> nmt; ^ User error: Identifier 'nmt' has not been declared or assigned Total time: 3.159 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-etse013.uab.es. (158.109.66.132) Time: Thu Mar 11 10:03:51 2004 Input: > lista:= [Random(M): i in [1..100]]; > M:=KMatrixSpace(GF(4),2,2); > Mf:= { k: k in M| (k[1][1] eq k[2][1]) and (k[1][2] eq k[2][2])}; > Mt:= { k : k in M | Trace(k) eq 0}; > Mtf:= {k : k in M | (k in Mt) and (k in Mf) }; > nmt:= [#[k : k in lista| k in Mt],#[k: k in lista| k in Mf],#[k:k in lista| k in Mtf]]; > nmt; Output: Magma V2.10-6 Thu Mar 11 2004 10:03:47 on modular [Seed = 3925464660] ------------------------------------- >> lista:= [Random(M): i in [1..100]]; ^ User error: Identifier 'M' has not been declared or assigned >> nmt:= [#[k : k in lista| k in Mt],#[k: k in lista| k in Mf],#[k:k in list ^ User error: Identifier 'lista' has not been declared or assigned >> nmt; ^ User error: Identifier 'nmt' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-etse013.uab.es. (158.109.66.132) Time: Thu Mar 11 10:04:13 2004 Input: > M:=KMatrixSpace(GF(4),2,2); >lista:= [Random(M): i in [1..100]]; > Mf:= { k: k in M| (k[1][1] eq k[2][1]) and (k[1][2] eq k[2][2])}; > Mt:= { k : k in M | Trace(k) eq 0}; > Mtf:= {k : k in M | (k in Mt) and (k in Mf) }; > nmt:= [#[k : k in lista| k in Mt],#[k: k in lista| k in Mf],#[k:k in lista| k in Mtf]]; > nmt; Output: Magma V2.10-6 Thu Mar 11 2004 10:04:09 on modular [Seed = 4293902456] ------------------------------------- [ 29, 7, 1 ] Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-etse013.uab.es. (158.109.66.132) Time: Thu Mar 11 10:04:33 2004 Input: > M:=KMatrixSpace(GF(4),2,2); >lista:= [Random(M): i in [1..100000]]; > Mf:= { k: k in M| (k[1][1] eq k[2][1]) and (k[1][2] eq k[2][2])}; > Mt:= { k : k in M | Trace(k) eq 0}; > Mtf:= {k : k in M | (k in Mt) and (k in Mf) }; > nmt:= [#[k : k in lista| k in Mt],#[k: k in lista| k in Mf],#[k:k in lista| k in Mtf]]; > nmt; Output: Magma V2.10-6 Thu Mar 11 2004 10:04:28 on modular [Seed = 4108634982] ------------------------------------- [ 24962, 6260, 1542 ] Total time: 4.199 seconds, Total memory usage: 7.09MB ************** MAGMA ***************** Host aula-etse013.uab.es. (158.109.66.132) Time: Thu Mar 11 10:05:04 2004 Input: > M:=KMatrixSpace(GF(4),2,2); >lista:= [Random(M): i in [1..100000]]; > Mf:= { k: k in M| (k[1][1] eq k[2][1]) and (k[1][2] eq k[2][2])}; > Mt:= { k : k in M | Trace(k) eq 0}; > Mtf:= {k : k in M | (k in Mt) and (k in Mf) }; > nmt:= [#[k : k in lista| k in Mt],#[k: k in lista| k in Mf],#[k:k in lista| k in Mtf]]; > nmt; Output: Magma V2.10-6 Thu Mar 11 2004 10:04:59 on modular [Seed = 3453816248] ------------------------------------- [ 24814, 6220, 1577 ] Total time: 4.229 seconds, Total memory usage: 7.09MB ************** MAGMA ***************** Host aula-etse013.uab.es. (158.109.66.132) Time: Thu Mar 11 10:05:13 2004 Input: > M:=KMatrixSpace(GF(4),2,2); >lista:= [Random(M): i in [1..100000]]; > Mf:= { k: k in M| (k[1][1] eq k[2][1]) and (k[1][2] eq k[2][2])}; > Mt:= { k : k in M | Trace(k) eq 0}; > Mtf:= {k : k in M | (k in Mt) and (k in Mf) }; > nmt:= [#[k : k in lista| k in Mt],#[k: k in lista| k in Mf],#[k:k in lista| k in Mtf]]; > nmt; Output: Magma V2.10-6 Thu Mar 11 2004 10:05:08 on modular [Seed = 3738050196] ------------------------------------- [ 25264, 6298, 1558 ] Total time: 4.089 seconds, Total memory usage: 7.09MB ************** MAGMA ***************** Host aula-etse013.uab.es. (158.109.66.132) Time: Thu Mar 11 10:05:35 2004 Input: > M:=KMatrixSpace(GF(4),2,2); >lista:= [Random(M): i in [1..100000]]; > Mf:= { k: k in M| (k[1][1] eq k[2][1]) and (k[1][2] eq k[2][2])}; > Mt:= { k : k in M | Trace(k) eq 0}; > Mtf:= {k : k in M | (k in Mt) and (k in Mf) }; > nmt:= [#[k : k in lista| k in Mt],#[k: k in lista| k in Mf],#[k:k in lista| k in Mtf]]; > nmt; Output: Magma V2.10-6 Thu Mar 11 2004 10:05:30 on modular [Seed = 3620149123] ------------------------------------- [ 25071, 6491, 1597 ] Total time: 4.099 seconds, Total memory usage: 7.09MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 10:13:29 2004 Input: comp:=function(x,y) return (x[1] lt y[1]); end function; mini_car:=function(k) p:=[car]; next:=2; while (next); next:=NextPrime(next); end while; Sort(~p,comp); return p; emd function; mini_car(12); Output: Magma V2.10-6 Thu Mar 11 2004 10:13:26 on modular [Seed = 2763286236] ------------------------------------- >> while (next> Append(~p,); ^ User error: Identifier 'k' has not been declared or assigned >> next:=NextPrime(next); ^ User error: Identifier 'next' has not been declared or assigned >> end while; ^ User error: bad syntax >> Sort(~p,comp); ^ Runtime error in 'Sort': Argument 1 has not been initialized Argument types given: *nothing ~, UserProgram >> return p; ^ User error: A 'return' can only be used inside a procedure or function >> emd function; ^ User error: bad syntax >> mini_car(12);; ^ User error: Identifier 'mini_car' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 10:13:42 2004 Input: comp:=function(x,y) return (x[1] lt y[1]); end function; mini_car:=function(k) p:=[car]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p,comp); return p; emd function; mini_car(12); Output: Magma V2.10-6 Thu Mar 11 2004 10:13:39 on modular [Seed = 3182264304] ------------------------------------- >> emd function; ^ User error: bad syntax >> mini_car(12);; ^ User error: Identifier 'mini_car' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 10:13:58 2004 Input: comp:=function(x,y) return (x[1] lt y[1]); end function; mini_car:=function(k) p:=[car]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p,comp); return p; end function; mini_car(12); Output: Magma V2.10-6 Thu Mar 11 2004 10:13:55 on modular [Seed = 2996990191] ------------------------------------- [
:6]( k: 12 ) >> Append(~p,); ^ Runtime error in 'Ilog': Bad argument types Argument types given: SeqEnum[SetCart], RngIntElt Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 10:14:24 2004 Input: comp:=function(x,y) return (x[1] lt y[1]); end function; mini_car:=function(k) p:=[car]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p,comp); return p; end function; mini_car(12); Output: Magma V2.10-6 Thu Mar 11 2004 10:14:21 on modular [Seed = 2291681963] ------------------------------------- [
:6]( k: 12 ) >> Append(~p,); ^ Runtime error in '^': Bad argument types Argument types given: SeqEnum[SetCart], RngIntElt Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 10:14:33 2004 Input: comp:=function(x,y) return (x[1] lt y[1]); end function; mini_car:=function(k) p:=[car]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p,comp); return p; end function; mini_car(12); Output: Magma V2.10-6 Thu Mar 11 2004 10:14:29 on modular [Seed = 2173780922] ------------------------------------- [
:6]( k: 12 ) >> Append(~p,); ^ Runtime error in 'Append': Could not lift element into sequence Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 10:15:04 2004 Input: comp:=function(x,y) return (x[1] lt y[1]); end function; mini_car:=function(k) p:=[car]; next:=2; while (next lt k*(k-1)) do print Type(); Append(~p,); next:=NextPrime(next); end while; Sort(~p,comp); return p; end function; mini_car(12); Output: Magma V2.10-6 Thu Mar 11 2004 10:15:01 on modular [Seed = 2458013833] ------------------------------------- Tup [
:6]( k: 12 ) >> Append(~p,); ^ Runtime error in 'Append': Could not lift element into sequence Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 10:15:35 2004 Input: comp:=function(x,y) return (x[1] lt y[1]); end function; mini_car:=function(k) p:=[car]; next:=2; while (next lt k*(k-1)) do print Type(); print Type(p); Append(~p,); next:=NextPrime(next); end while; Sort(~p,comp); return p; end function; mini_car(12); Output: Magma V2.10-6 Thu Mar 11 2004 10:15:32 on modular [Seed = 1786423441] ------------------------------------- Tup SeqEnum [
:6]( k: 12 ) >> Append(~p,); ^ Runtime error in 'Append': Could not lift element into sequence Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 10:17:20 2004 Input: comp:=function(x,y) return (x[1] lt y[1]); end function; mini_car:=function(k) ZZ:=car; p:=[ZZ]; next:=2; while (next lt k*(k-1)) do print Type(); print Type(p); Append(~p,); next:=NextPrime(next); end while; Sort(~p,comp); return p; end function; mini_car(12); Output: Magma V2.10-6 Thu Mar 11 2004 10:17:17 on modular [Seed = 2138029549] ------------------------------------- >> print Type(); ^ User error: bad syntax >> print Type(p); ^ User error: Identifier 'p' has not been declared or assigned >> Append(~p,); ^ User error: Identifier 'next' has not been declared or assigned >> next:=NextPrime(next); ^ User error: Identifier 'next' has not been declared or assigned >> end while; ^ User error: bad syntax >> Sort(~p,comp); ^ Runtime error in 'Sort': Argument 1 has not been initialized Argument types given: *nothing ~, UserProgram >> return p; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> mini_car(12);; ^ User error: Identifier 'mini_car' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 10:17:49 2004 Input: comp:=function(x,y) return (x[1] lt y[1]); end function; mini_car:=function(k) ZZ:=car; p:=[ZZ]; next:=2; while (next lt k*(k-1)) do print Type(ZZ!); print Type(p); Append(~p,); next:=NextPrime(next); end while; Sort(~p,comp); return p; end function; mini_car(12); Output: Magma V2.10-6 Thu Mar 11 2004 10:17:46 on modular [Seed = 1986442499] ------------------------------------- Tup SeqEnum [
:6]( k: 12 ) >> Append(~p,); ^ Runtime error in 'Append': Could not lift element into sequence Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 10:18:15 2004 Input: comp:=function(x,y) return (x[1] lt y[1]); end function; mini_car:=function(k) ZZ:=car; p:=[ZZ]; next:=2; while (next lt k*(k-1)) do print Type(ZZ!); print Type(p); Append(~p,ZZ!); next:=NextPrime(next); end while; Sort(~p,comp); return p; end function; mini_car(12); Output: Magma V2.10-6 Thu Mar 11 2004 10:18:12 on modular [Seed = 1297976854] ------------------------------------- Tup SeqEnum [
:6]( k: 12 ) >> Append(~p,ZZ!); ^ Runtime error in 'Append': Could not lift element into sequence Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 10:21:31 2004 Input: comp:=function(x,y) return (x[1] lt y[1]); end function; mini_car:=function(k) ZZ:=car; p:=[ZZ]; next:=2; while (next lt k*(k-1)) do print Type(next^Ilog(next,(k-2)^4+4*k-4)); Append(~p,ZZ!); next:=NextPrime(next); end while; Sort(~p,comp); return p; end function; mini_car(12); Output: Magma V2.10-6 Thu Mar 11 2004 10:21:28 on modular [Seed = 1548525515] ------------------------------------- RngIntElt [
:6]( k: 12 ) >> Append(~p,ZZ!); ^ Runtime error in 'Append': Could not lift element into sequence Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 10:23:03 2004 Input: comp:=function(x,y) return (x[1] lt y[1]); end function; mini_car:=function(k) ZZ:=car; p:=[ZZ]; next:=2; while (next lt k*(k-1)) do print Type(next^Ilog(next,(k-2)^4+4*k-4)); Append(~p,ZZ!); next:=NextPrime(next); end while; Sort(~p,comp); return p; end function; mini_car(12); Output: Magma V2.10-6 Thu Mar 11 2004 10:23:00 on modular [Seed = 1396938600] ------------------------------------- [
:6]( k: 12 ) >> ZZ:=car; ^ Runtime error in car< ... >: Argument 1 is not a structure Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 10:26:30 2004 Input: comp:=function(x,y) return (x[1] lt y[1]); end function; mini_car:=function(k) ZZ:=car; p:=[ZZ]; next:=2; while (next lt k*(k-1)) do print ( in ZZ); Append(~p,ZZ!); next:=NextPrime(next); end while; Sort(~p,comp); return p; end function; mini_car(12); Output: Magma V2.10-6 Thu Mar 11 2004 10:26:27 on modular [Seed = 624287849] ------------------------------------- true [
:6]( k: 12 ) >> Append(~p,ZZ!); ^ Runtime error in 'Append': Could not lift element into sequence Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 10:26:40 2004 Input: comp:=function(x,y) return (x[1] lt y[1]); end function; mini_car:=function(k) ZZ:=car; p:=[ZZ]; next:=2; while (next lt k*(k-1)) do print ( in ZZ); Append(~p,); next:=NextPrime(next); end while; Sort(~p,comp); return p; end function; mini_car(12); Output: Magma V2.10-6 Thu Mar 11 2004 10:26:37 on modular [Seed = 1009580414] ------------------------------------- true [
:6]( k: 12 ) >> Append(~p,); ^ Runtime error in 'Append': Could not lift element into sequence Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 10:26:48 2004 Input: comp:=function(x,y) return (x[1] lt y[1]); end function; mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do print ( in ZZ); Append(~p,); next:=NextPrime(next); end while; Sort(~p,comp); return p; end function; mini_car(12); Output: Magma V2.10-6 Thu Mar 11 2004 10:26:45 on modular [Seed = 857994857] ------------------------------------- true true true true true true true true true true true true true true true true true true true true true true true true true true true true true true true true [
:6]( k: 12 ) Sort( Q: [ <8192, 2>, <6561, 3>, <3125, 5>, <2401, 7>, <1331, 11>, <2..., compare: function(x, y) ... end function ) Sort( Q: [ <8192, 2>, <6561, 3>, <3125, 5>, <2401, 7>, <1331, 11>, <2..., compare: function(x, y) ... end function, permut: ) In file "/usr/local/magma/package/Aggregate/SeqEnum/sort.m", line 47, column 33: >> while compare(k, Q[i]) lt 0 do ^ Runtime error in 'lt': Bad argument types Argument types given: BoolElt, RngIntElt Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 10:26:56 2004 Input: comp:=function(x,y) return (x[1] lt y[1]); end function; mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p,comp); return p; end function; mini_car(12); Output: Magma V2.10-6 Thu Mar 11 2004 10:26:53 on modular [Seed = 169529176] ------------------------------------- [
:6]( k: 12 ) Sort( Q: [ <8192, 2>, <6561, 3>, <3125, 5>, <2401, 7>, <1331, 11>, <2..., compare: function(x, y) ... end function ) Sort( Q: [ <8192, 2>, <6561, 3>, <3125, 5>, <2401, 7>, <1331, 11>, <2..., compare: function(x, y) ... end function, permut: ) In file "/usr/local/magma/package/Aggregate/SeqEnum/sort.m", line 47, column 33: >> while compare(k, Q[i]) lt 0 do ^ Runtime error in 'lt': Bad argument types Argument types given: BoolElt, RngIntElt Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 10:29:28 2004 Input: comp:=function(x,y) return (x[1] - y[1]); end function; mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p,comp); return p; end function; mini_car(12); Output: Magma V2.10-6 Thu Mar 11 2004 10:29:25 on modular [Seed = 1099194] ------------------------------------- [ <101, 101>, <103, 103>, <107, 107>, <109, 109>, <113, 113>, <127, 127>, <131, 131>, <529, 23>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5>, <3481, 59>, <3721, 61>, <4489, 67>, <4913, 17>, <5041, 71>, <5329, 73>, <6241, 79>, <6561, 3>, <6859, 19>, <6889, 83>, <7921, 89>, <8192, 2>, <9409, 97> ] Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 10:30:12 2004 Input: comp:=function(x,y) return (x[1] - y[1]); end function; mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); return p; end function; mini_car(12); Output: Magma V2.10-6 Thu Mar 11 2004 10:30:09 on modular [Seed = 268490366] ------------------------------------- [ <101, 101>, <103, 103>, <107, 107>, <109, 109>, <113, 113>, <127, 127>, <131, 131>, <529, 23>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5>, <3481, 59>, <3721, 61>, <4489, 67>, <4913, 17>, <5041, 71>, <5329, 73>, <6241, 79>, <6561, 3>, <6859, 19>, <6889, 83>, <7921, 89>, <8192, 2>, <9409, 97> ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 10:30:28 2004 Input: comp:=function(x,y) return (x[1] - y[1]); end function; mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); return p; end function; mini_car(15); Output: Magma V2.10-6 Thu Mar 11 2004 10:30:25 on modular [Seed = 3891732889] ------------------------------------- [ <173, 173>, <179, 179>, <181, 181>, <191, 191>, <193, 193>, <197, 197>, <199, 199>, <961, 31>, <1369, 37>, <1681, 41>, <1849, 43>, <2209, 47>, <2809, 53>, <3481, 59>, <3721, 61>, <4489, 67>, <4913, 17>, <5041, 71>, <5329, 73>, <6241, 79>, <6859, 19>, <6889, 83>, <7921, 89>, <9409, 97>, <10201, 101>, <10609, 103>, <11449, 107>, <11881, 109>, <12167, 23>, <12769, 113>, <14641, 11>, <15625, 5>, <16129, 127>, <16384, 2>, <16807, 7>, <17161, 131>, <18769, 137>, <19321, 139>, <19683, 3>, <22201, 149>, <22801, 151>, <24389, 29>, <24649, 157>, <26569, 163>, <27889, 167>, <28561, 13> ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 10:31:14 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); return p; end function; mini_car(15); Output: Magma V2.10-6 Thu Mar 11 2004 10:31:11 on modular [Seed = 4277024942] ------------------------------------- [ <173, 173>, <179, 179>, <181, 181>, <191, 191>, <193, 193>, <197, 197>, <199, 199>, <961, 31>, <1369, 37>, <1681, 41>, <1849, 43>, <2209, 47>, <2809, 53>, <3481, 59>, <3721, 61>, <4489, 67>, <4913, 17>, <5041, 71>, <5329, 73>, <6241, 79>, <6859, 19>, <6889, 83>, <7921, 89>, <9409, 97>, <10201, 101>, <10609, 103>, <11449, 107>, <11881, 109>, <12167, 23>, <12769, 113>, <14641, 11>, <15625, 5>, <16129, 127>, <16384, 2>, <16807, 7>, <17161, 131>, <18769, 137>, <19321, 139>, <19683, 3>, <22201, 149>, <22801, 151>, <24389, 29>, <24649, 157>, <26569, 163>, <27889, 167>, <28561, 13> ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 10:31:24 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); return p; end function; mini_car(17); Output: Magma V2.10-6 Thu Mar 11 2004 10:31:21 on modular [Seed = 4125438931] ------------------------------------- [ <227, 227>, <229, 229>, <233, 233>, <239, 239>, <241, 241>, <251, 251>, <257, 257>, <263, 263>, <269, 269>, <271, 271>, <1681, 41>, <1849, 43>, <2209, 47>, <2809, 53>, <3481, 59>, <3721, 61>, <4489, 67>, <4913, 17>, <5041, 71>, <5329, 73>, <6241, 79>, <6859, 19>, <6889, 83>, <7921, 89>, <9409, 97>, <10201, 101>, <10609, 103>, <11449, 107>, <11881, 109>, <12167, 23>, <12769, 113>, <14641, 11>, <15625, 5>, <16129, 127>, <16807, 7>, <17161, 131>, <18769, 137>, <19321, 139>, <19683, 3>, <22201, 149>, <22801, 151>, <24389, 29>, <24649, 157>, <26569, 163>, <27889, 167>, <28561, 13>, <29791, 31>, <29929, 173>, <32041, 179>, <32761, 181>, <32768, 2>, <36481, 191>, <37249, 193>, <38809, 197>, <39601, 199>, <44521, 211>, <49729, 223>, <50653, 37> ] Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 10:32:13 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); return p; end function; mini_car(18); Output: Magma V2.10-6 Thu Mar 11 2004 10:32:10 on modular [Seed = 3436972761] ------------------------------------- [ <257, 257>, <263, 263>, <269, 269>, <271, 271>, <277, 277>, <281, 281>, <283, 283>, <293, 293>, <1681, 41>, <1849, 43>, <2209, 47>, <2809, 53>, <3481, 59>, <3721, 61>, <4489, 67>, <4913, 17>, <5041, 71>, <5329, 73>, <6241, 79>, <6859, 19>, <6889, 83>, <7921, 89>, <9409, 97>, <10201, 101>, <10609, 103>, <11449, 107>, <11881, 109>, <12167, 23>, <12769, 113>, <14641, 11>, <15625, 5>, <16129, 127>, <16807, 7>, <17161, 131>, <18769, 137>, <19321, 139>, <22201, 149>, <22801, 151>, <24389, 29>, <24649, 157>, <26569, 163>, <27889, 167>, <28561, 13>, <29791, 31>, <29929, 173>, <32041, 179>, <32761, 181>, <36481, 191>, <37249, 193>, <38809, 197>, <39601, 199>, <44521, 211>, <49729, 223>, <50653, 37>, <51529, 227>, <52441, 229>, <54289, 233>, <57121, 239>, <58081, 241>, <59049, 3>, <63001, 251>, <65536, 2> ] Total time: 3.109 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 10:33:24 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); return p; end function; mini_car(18); 18*17; 16^4+4*18-4; Output: Magma V2.10-6 Thu Mar 11 2004 10:33:21 on modular [Seed = 3285386605] ------------------------------------- [ <257, 257>, <263, 263>, <269, 269>, <271, 271>, <277, 277>, <281, 281>, <283, 283>, <293, 293>, <1681, 41>, <1849, 43>, <2209, 47>, <2809, 53>, <3481, 59>, <3721, 61>, <4489, 67>, <4913, 17>, <5041, 71>, <5329, 73>, <6241, 79>, <6859, 19>, <6889, 83>, <7921, 89>, <9409, 97>, <10201, 101>, <10609, 103>, <11449, 107>, <11881, 109>, <12167, 23>, <12769, 113>, <14641, 11>, <15625, 5>, <16129, 127>, <16807, 7>, <17161, 131>, <18769, 137>, <19321, 139>, <22201, 149>, <22801, 151>, <24389, 29>, <24649, 157>, <26569, 163>, <27889, 167>, <28561, 13>, <29791, 31>, <29929, 173>, <32041, 179>, <32761, 181>, <36481, 191>, <37249, 193>, <38809, 197>, <39601, 199>, <44521, 211>, <49729, 223>, <50653, 37>, <51529, 227>, <52441, 229>, <54289, 233>, <57121, 239>, <58081, 241>, <59049, 3>, <63001, 251>, <65536, 2> ] 306 65604 Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 10:38:48 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); Reverse(~p); return p; end function; mini_car(18); 18*17; 16^4+4*18-4; Output: Magma V2.10-6 Thu Mar 11 2004 10:38:45 on modular [Seed = 3586465215] ------------------------------------- [ <65536, 2>, <63001, 251>, <59049, 3>, <58081, 241>, <57121, 239>, <54289, 233>, <52441, 229>, <51529, 227>, <50653, 37>, <49729, 223>, <44521, 211>, <39601, 199>, <38809, 197>, <37249, 193>, <36481, 191>, <32761, 181>, <32041, 179>, <29929, 173>, <29791, 31>, <28561, 13>, <27889, 167>, <26569, 163>, <24649, 157>, <24389, 29>, <22801, 151>, <22201, 149>, <19321, 139>, <18769, 137>, <17161, 131>, <16807, 7>, <16129, 127>, <15625, 5>, <14641, 11>, <12769, 113>, <12167, 23>, <11881, 109>, <11449, 107>, <10609, 103>, <10201, 101>, <9409, 97>, <7921, 89>, <6889, 83>, <6859, 19>, <6241, 79>, <5329, 73>, <5041, 71>, <4913, 17>, <4489, 67>, <3721, 61>, <3481, 59>, <2809, 53>, <2209, 47>, <1849, 43>, <1681, 41>, <293, 293>, <283, 283>, <281, 281>, <277, 277>, <271, 271>, <269, 269>, <263, 263>, <257, 257> ] 306 65604 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 10:39:13 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); return p; end function; mini_car(18); 18*17; 16^4+4*18-4; Output: Magma V2.10-6 Thu Mar 11 2004 10:39:10 on modular [Seed = 2881184730] ------------------------------------- [ <257, 257>, <263, 263>, <269, 269>, <271, 271>, <277, 277>, <281, 281>, <283, 283>, <293, 293>, <1681, 41>, <1849, 43>, <2209, 47>, <2809, 53>, <3481, 59>, <3721, 61>, <4489, 67>, <4913, 17>, <5041, 71>, <5329, 73>, <6241, 79>, <6859, 19>, <6889, 83>, <7921, 89>, <9409, 97>, <10201, 101>, <10609, 103>, <11449, 107>, <11881, 109>, <12167, 23>, <12769, 113>, <14641, 11>, <15625, 5>, <16129, 127>, <16807, 7>, <17161, 131>, <18769, 137>, <19321, 139>, <22201, 149>, <22801, 151>, <24389, 29>, <24649, 157>, <26569, 163>, <27889, 167>, <28561, 13>, <29791, 31>, <29929, 173>, <32041, 179>, <32761, 181>, <36481, 191>, <37249, 193>, <38809, 197>, <39601, 199>, <44521, 211>, <49729, 223>, <50653, 37>, <51529, 227>, <52441, 229>, <54289, 233>, <57121, 239>, <58081, 241>, <59049, 3>, <63001, 251>, <65536, 2> ] 306 65604 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 10:41:40 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); return p; end function; mini_car(34); Output: Magma V2.10-6 Thu Mar 11 2004 10:41:37 on modular [Seed = 3148575589] ------------------------------------- [ <1031, 1031>, <1033, 1033>, <1039, 1039>, <1049, 1049>, <1051, 1051>, <1061, 1061>, <1063, 1063>, <1069, 1069>, <1087, 1087>, <1091, 1091>, <1093, 1093>, <1097, 1097>, <1103, 1103>, <1109, 1109>, <1117, 1117>, <10609, 103>, <11449, 107>, <11881, 109>, <12769, 113>, <16129, 127>, <17161, 131>, <18769, 137>, <19321, 139>, <22201, 149>, <22801, 151>, <24649, 157>, <26569, 163>, <27889, 167>, <29929, 173>, <32041, 179>, <32761, 181>, <36481, 191>, <37249, 193>, <38809, 197>, <39601, 199>, <44521, 211>, <49729, 223>, <50653, 37>, <51529, 227>, <52441, 229>, <54289, 233>, <57121, 239>, <58081, 241>, <63001, 251>, <66049, 257>, <68921, 41>, <69169, 263>, <72361, 269>, <73441, 271>, <76729, 277>, <78961, 281>, <79507, 43>, <80089, 283>, <83521, 17>, <85849, 293>, <94249, 307>, <96721, 311>, <97969, 313>, <100489, 317>, <103823, 47>, <109561, 331>, <113569, 337>, <120409, 347>, <121801, 349>, <124609, 353>, <128881, 359>, <130321, 19>, <134689, 367>, <139129, 373>, <143641, 379>, <146689, 383>, <148877, 53>, <151321, 389>, <157609, 397>, <160801, 401>, <161051, 11>, <167281, 409>, <175561, 419>, <177241, 421>, <185761, 431>, <187489, 433>, <192721, 439>, <196249, 443>, <201601, 449>, <205379, 59>, <208849, 457>, <212521, 461>, <214369, 463>, <218089, 467>, <226981, 61>, <229441, 479>, <237169, 487>, <241081, 491>, <249001, 499>, <253009, 503>, <259081, 509>, <271441, 521>, <273529, 523>, <279841, 23>, <292681, 541>, <299209, 547>, <300763, 67>, <310249, 557>, <316969, 563>, <323761, 569>, <326041, 571>, <332929, 577>, <344569, 587>, <351649, 593>, <357911, 71>, <358801, 599>, <361201, 601>, <368449, 607>, <371293, 13>, <375769, 613>, <380689, 617>, <383161, 619>, <389017, 73>, <390625, 5>, <398161, 631>, <410881, 641>, <413449, 643>, <418609, 647>, <426409, 653>, <434281, 659>, <436921, 661>, <452929, 673>, <458329, 677>, <466489, 683>, <477481, 691>, <491401, 701>, <493039, 79>, <502681, 709>, <516961, 719>, <528529, 727>, <531441, 3>, <537289, 733>, <546121, 739>, <552049, 743>, <564001, 751>, <571787, 83>, <573049, 757>, <579121, 761>, <591361, 769>, <597529, 773>, <619369, 787>, <635209, 797>, <654481, 809>, <657721, 811>, <674041, 821>, <677329, 823>, <683929, 827>, <687241, 829>, <703921, 839>, <704969, 89>, <707281, 29>, <727609, 853>, <734449, 857>, <737881, 859>, <744769, 863>, <769129, 877>, <776161, 881>, <779689, 883>, <786769, 887>, <822649, 907>, <823543, 7>, <829921, 911>, <844561, 919>, <863041, 929>, <877969, 937>, <885481, 941>, <896809, 947>, <908209, 953>, <912673, 97>, <923521, 31>, <935089, 967>, <942841, 971>, <954529, 977>, <966289, 983>, <982081, 991>, <994009, 997>, <1018081, 1009>, <1026169, 1013>, <1030301, 101>, <1038361, 1019>, <1042441, 1021>, <1048576, 2> ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 10:42:07 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); return p; end function; mini_car(74); Output: Magma V2.10-6 Thu Mar 11 2004 10:42:04 on modular [Seed = 2996992529] ------------------------------------- [ <5189, 5189>, <5197, 5197>, <5209, 5209>, <5227, 5227>, <5231, 5231>, <5233, 5233>, <5237, 5237>, <5261, 5261>, <5273, 5273>, <5279, 5279>, <5281, 5281>, <5297, 5297>, <5303, 5303>, <5309, 5309>, <5323, 5323>, <5333, 5333>, <5347, 5347>, <5351, 5351>, <5381, 5381>, <5387, 5387>, <5393, 5393>, <5399, 5399>, <94249, 307>, <96721, 311>, <97969, 313>, <100489, 317>, <109561, 331>, <113569, 337>, <120409, 347>, <121801, 349>, <124609, 353>, <128881, 359>, <134689, 367>, <139129, 373>, <143641, 379>, <146689, 383>, <151321, 389>, <157609, 397>, <160801, 401>, <167281, 409>, <175561, 419>, <177241, 421>, <185761, 431>, <187489, 433>, <192721, 439>, <196249, 443>, <201601, 449>, <208849, 457>, <212521, 461>, <214369, 463>, <218089, 467>, <229441, 479>, <237169, 487>, <241081, 491>, <249001, 499>, <253009, 503>, <259081, 509>, <271441, 521>, <273529, 523>, <292681, 541>, <299209, 547>, <310249, 557>, <316969, 563>, <323761, 569>, <326041, 571>, <332929, 577>, <344569, 587>, <351649, 593>, <358801, 599>, <361201, 601>, <368449, 607>, <375769, 613>, <380689, 617>, <383161, 619>, <389017, 73>, <398161, 631>, <410881, 641>, <413449, 643>, <418609, 647>, <426409, 653>, <434281, 659>, <436921, 661>, <452929, 673>, <458329, 677>, <466489, 683>, <477481, 691>, <491401, 701>, <493039, 79>, <502681, 709>, <516961, 719>, <528529, 727>, <537289, 733>, <546121, 739>, <552049, 743>, <564001, 751>, <571787, 83>, <573049, 757>, <579121, 761>, <591361, 769>, <597529, 773>, <619369, 787>, <635209, 797>, <654481, 809>, <657721, 811>, <674041, 821>, <677329, 823>, <683929, 827>, <687241, 829>, <703921, 839>, <704969, 89>, <727609, 853>, <734449, 857>, <737881, 859>, <744769, 863>, <769129, 877>, <776161, 881>, <779689, 883>, <786769, 887>, <822649, 907>, <829921, 911>, <844561, 919>, <863041, 929>, <877969, 937>, <885481, 941>, <896809, 947>, <908209, 953>, <912673, 97>, <923521, 31>, <935089, 967>, <942841, 971>, <954529, 977>, <966289, 983>, <982081, 991>, <994009, 997>, <1018081, 1009>, <1026169, 1013>, <1030301, 101>, <1038361, 1019>, <1042441, 1021>, <1062961, 1031>, <1067089, 1033>, <1079521, 1039>, <1092727, 103>, <1100401, 1049>, <1104601, 1051>, <1125721, 1061>, <1129969, 1063>, <1142761, 1069>, <1181569, 1087>, <1190281, 1091>, <1194649, 1093>, <1203409, 1097>, <1216609, 1103>, <1225043, 107>, <1229881, 1109>, <1247689, 1117>, <1261129, 1123>, <1274641, 1129>, <1295029, 109>, <1324801, 1151>, <1329409, 1153>, <1352569, 1163>, <1371241, 1171>, <1394761, 1181>, <1408969, 1187>, <1423249, 1193>, <1442401, 1201>, <1442897, 113>, <1471369, 1213>, <1481089, 1217>, <1495729, 1223>, <1510441, 1229>, <1515361, 1231>, <1530169, 1237>, <1560001, 1249>, <1585081, 1259>, <1630729, 1277>, <1635841, 1279>, <1646089, 1283>, <1661521, 1289>, <1666681, 1291>, <1682209, 1297>, <1692601, 1301>, <1697809, 1303>, <1708249, 1307>, <1739761, 1319>, <1745041, 1321>, <1760929, 1327>, <1852321, 1361>, <1868689, 1367>, <1874161, 37>, <1885129, 1373>, <1907161, 1381>, <1957201, 1399>, <1985281, 1409>, <2024929, 1423>, <2036329, 1427>, <2042041, 1429>, <2048383, 127>, <2053489, 1433>, <2070721, 1439>, <2093809, 1447>, <2105401, 1451>, <2111209, 1453>, <2128681, 1459>, <2163841, 1471>, <2193361, 1481>, <2199289, 1483>, <2211169, 1487>, <2217121, 1489>, <2229049, 1493>, <2247001, 1499>, <2248091, 131>, <2283121, 1511>, <2319529, 1523>, <2343961, 1531>, <2380849, 1543>, <2399401, 1549>, <2411809, 1553>, <2430481, 1559>, <2455489, 1567>, <2468041, 1571>, <2476099, 19>, <2493241, 1579>, <2505889, 1583>, <2550409, 1597>, <2563201, 1601>, <2571353, 137>, <2582449, 1607>, <2588881, 1609>, <2601769, 1613>, <2621161, 1619>, <2627641, 1621>, <2647129, 1627>, <2679769, 1637>, <2685619, 139>, <2745649, 1657>, <2765569, 1663>, <2778889, 1667>, <2785561, 1669>, <2825761, 41>, <2866249, 1693>, <2879809, 1697>, <2886601, 1699>, <2920681, 1709>, <2961841, 1721>, <2968729, 1723>, <3003289, 1733>, <3031081, 1741>, <3052009, 1747>, <3073009, 1753>, <3094081, 1759>, <3157729, 1777>, <3179089, 1783>, <3193369, 1787>, <3200521, 1789>, <3243601, 1801>, <3279721, 1811>, <3307949, 149>, <3323329, 1823>, <3352561, 1831>, <3411409, 1847>, <3418801, 43>, <3442951, 151>, <3463321, 1861>, <3485689, 1867>, <3500641, 1871>, <3508129, 1873>, <3523129, 1877>, <3530641, 1879>, <3568321, 1889>, <3613801, 1901>, <3636649, 1907>, <3659569, 1913>, <3728761, 1931>, <3736489, 1933>, <3798601, 1949>, <3806401, 1951>, <3869893, 157>, <3892729, 1973>, <3916441, 1979>, <3948169, 1987>, <3972049, 1993>, <3988009, 1997>, <3996001, 1999>, <4012009, 2003>, <4044121, 2011>, <4068289, 2017>, <4108729, 2027>, <4116841, 2029>, <4157521, 2039>, <4214809, 2053>, <4255969, 2063>, <4280761, 2069>, <4330561, 2081>, <4330747, 163>, <4338889, 2083>, <4355569, 2087>, <4363921, 2089>, <4405801, 2099>, <4456321, 2111>, <4464769, 2113>, <4532641, 2129>, <4541161, 2131>, <4566769, 2137>, <4583881, 2141>, <4592449, 2143>, <4635409, 2153>, <4657463, 167>, <4669921, 2161>, <4748041, 2179>, <4826809, 13>, <4853209, 2203>, <4870849, 2207>, <4879681, 47>, <4897369, 2213>, <4932841, 2221>, <5004169, 2237>, <5013121, 2239>, <5031049, 2243>, <5067001, 2251>, <5139289, 2267>, <5148361, 2269>, <5166529, 2273>, <5177717, 173>, <5202961, 2281>, <5230369, 2287>, <5257849, 2293>, <5276209, 2297>, <5331481, 2309>, <5340721, 2311>, <5442889, 2333>, <5470921, 2339>, <5480281, 2341>, <5508409, 2347>, <5527201, 2351>, <5555449, 2357>, <5621641, 2371>, <5650129, 2377>, <5669161, 2381>, <5678689, 2383>, <5707321, 2389>, <5726449, 2393>, <5735339, 179>, <5755201, 2399>, <5764801, 7>, <5812921, 2411>, <5841889, 2417>, <5870929, 2423>, <5929741, 181>, <5938969, 2437>, <5958481, 2441>, <5987809, 2447>, <6046681, 2459>, <6086089, 2467>, <6115729, 2473>, <6135529, 2477>, <6265009, 2503>, <6355441, 2521>, <6405961, 2531>, <6436343, 23>, <6446521, 2539>, <6466849, 2543>, <6497401, 2549>, <6507601, 2551>, <6538249, 2557>, <6651241, 2579>, <6713281, 2591>, <6723649, 2593>, <6806881, 2609>, <6848689, 2617>, <6869641, 2621>, <6932689, 2633>, <6967871, 191>, <7006609, 2647>, <7059649, 2657>, <7070281, 2659>, <7091569, 2663>, <7134241, 2671>, <7166329, 2677>, <7189057, 193>, <7198489, 2683>, <7219969, 2687>, <7230721, 2689>, <7252249, 2693>, <7284601, 2699>, <7327849, 2707>, <7349521, 2711>, <7360369, 2713>, <7392961, 2719>, <7447441, 2729>, <7458361, 2731>, <7513081, 2741>, <7557001, 2749>, <7579009, 2753>, <7645373, 197>, <7656289, 2767>, <7711729, 2777>, <7778521, 2789>, <7789681, 2791>, <7823209, 2797>, <7845601, 2801>, <7856809, 2803>, <7880599, 199>, <7890481, 53>, <7946761, 2819>, <8025889, 2833>, <8048569, 2837>, <8082649, 2843>, <8128201, 2851>, <8162449, 2857>, <8185321, 2861>, <8288641, 2879>, <8334769, 2887>, <8392609, 2897>, <8427409, 2903>, <8462281, 2909>, <8508889, 2917>, <8567329, 2927>, <8637721, 2939>, <8720209, 2953>, <8743849, 2957>, <8779369, 2963>, <8814961, 2969>, <8826841, 2971>, <8994001, 2999>, <9006001, 3001>, <9066121, 3011>, <9114361, 3019>, <9138529, 3023>, <9223369, 3037>, <9247681, 3041>, <9296401, 3049>, <9369721, 3061>, <9393931, 211>, <9406489, 3067>, <9480241, 3079>, <9504889, 3083>, <9541921, 3089>, <9665881, 3109>, <9728161, 3119>, <9740641, 3121>, <9765625, 5>, <9840769, 3137>, <10004569, 3163>, <10029889, 3167>, <10042561, 3169>, <10118761, 3181>, <10156969, 3187>, <10182481, 3191>, <10259209, 3203>, <10297681, 3209>, <10349089, 3217>, <10374841, 3221>, <10426441, 3229>, <10569001, 3251>, <10582009, 3253>, <10608049, 3257>, <10621081, 3259>, <10699441, 3271>, <10883401, 3299>, <10896601, 3301>, <10936249, 3307>, <10975969, 3313>, <11015761, 3319>, <11042329, 3323>, <11082241, 3329>, <11089567, 223>, <11095561, 3331>, <11175649, 3343>, <11202409, 3347>, <11282881, 3359>, <11296321, 3361>, <11363641, 3371>, <11377129, 3373>, <11485321, 3389>, <11498881, 3391>, <11607649, 3407>, <11648569, 3413>, <11697083, 227>, <11785489, 3433>, <11895601, 3449>, <11950849, 3457>, <11978521, 3461>, <11992369, 3463>, <12008989, 229>, <12020089, 3467>, <12033961, 3469>, <12117361, 59>, <12187081, 3491>, <12243001, 3499>, <12327121, 3511>, <12369289, 3517>, <12439729, 3527>, <12453841, 3529>, <12482089, 3533>, <12524521, 3539>, <12538681, 3541>, <12581209, 3547>, <12649337, 233>, <12652249, 3557>, <12666481, 3559>, <12752041, 3571>, <12823561, 3581>, <12837889, 3583>, <12909649, 3593>, <13010449, 3607>, <13053769, 3613>, <13082689, 3617>, <13126129, 3623>, <13184161, 3631>, <13227769, 3637>, <13271449, 3643>, <13388281, 3659>, <13476241, 3671>, <13490929, 3673>, <13520329, 3677>, <13623481, 3691>, <13651919, 239>, <13667809, 3697>, <13697401, 3701>, <13756681, 3709>, <13830961, 3719>, <13845841, 61>, <13890529, 3727>, <13935289, 3733>, <13980121, 3739>, <13997521, 241>, <14145121, 3761>, <14190289, 3767>, <14205361, 3769>, <14280841, 3779>, <14348907, 3>, <14386849, 3793>, <14417209, 3797>, <14462809, 3803>, <14600041, 3821>, <14615329, 3823>, <14691889, 3833>, <14799409, 3847>, <14830201, 3851>, <14845609, 3853>, <14922769, 3863>, <15031129, 3877>, <15062161, 3881>, <15124321, 3889>, <15264649, 3907>, <15295921, 3911>, <15342889, 3917>, <15358561, 3919>, <15389929, 3923>, <15437041, 3929>, <15452761, 3931>, <15547249, 3943>, <15578809, 3947>, <15737089, 3967>, <15813251, 251>, <15912121, 3989>, <16008001, 4001>, <16024009, 4003>, <16056049, 4007>, <16104169, 4013>, <16152361, 4019>, <16168441, 4021>, <16216729, 4027>, <16394401, 4049>, <16410601, 4051>, <16459249, 4057>, <16589329, 4073>, <16638241, 4079>, <16736281, 4091>, <16752649, 4093>, <16777216, 2>, <16801801, 4099>, <16900321, 4111>, <16974593, 257>, <17032129, 4127>, <17048641, 4129>, <17081689, 4133>, <17131321, 4139>, <17247409, 4153>, <17280649, 4157>, <17297281, 4159>, <17447329, 4177>, <17648401, 4201>, <17732521, 4211>, <17783089, 42 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 10:42:45 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); return p; end function; mini_car(60); Output: Magma V2.10-6 Thu Mar 11 2004 10:42:42 on modular [Seed = 2308522260] ------------------------------------- [ <3371, 3371>, <3373, 3373>, <3389, 3389>, <3391, 3391>, <3407, 3407>, <3413, 3413>, <3433, 3433>, <3449, 3449>, <3457, 3457>, <3461, 3461>, <3463, 3463>, <3467, 3467>, <3469, 3469>, <3491, 3491>, <3499, 3499>, <3511, 3511>, <3517, 3517>, <3527, 3527>, <3529, 3529>, <3533, 3533>, <3539, 3539>, <51529, 227>, <52441, 229>, <54289, 233>, <57121, 239>, <58081, 241>, <63001, 251>, <66049, 257>, <69169, 263>, <72361, 269>, <73441, 271>, <76729, 277>, <78961, 281>, <80089, 283>, <85849, 293>, <94249, 307>, <96721, 311>, <97969, 313>, <100489, 317>, <109561, 331>, <113569, 337>, <120409, 347>, <121801, 349>, <124609, 353>, <128881, 359>, <134689, 367>, <139129, 373>, <143641, 379>, <146689, 383>, <151321, 389>, <157609, 397>, <160801, 401>, <167281, 409>, <175561, 419>, <177241, 421>, <185761, 431>, <187489, 433>, <192721, 439>, <196249, 443>, <201601, 449>, <205379, 59>, <208849, 457>, <212521, 461>, <214369, 463>, <218089, 467>, <226981, 61>, <229441, 479>, <237169, 487>, <241081, 491>, <249001, 499>, <253009, 503>, <259081, 509>, <271441, 521>, <273529, 523>, <292681, 541>, <299209, 547>, <300763, 67>, <310249, 557>, <316969, 563>, <323761, 569>, <326041, 571>, <332929, 577>, <344569, 587>, <351649, 593>, <357911, 71>, <358801, 599>, <361201, 601>, <368449, 607>, <375769, 613>, <380689, 617>, <383161, 619>, <389017, 73>, <398161, 631>, <410881, 641>, <413449, 643>, <418609, 647>, <426409, 653>, <434281, 659>, <436921, 661>, <452929, 673>, <458329, 677>, <466489, 683>, <477481, 691>, <491401, 701>, <493039, 79>, <502681, 709>, <516961, 719>, <528529, 727>, <537289, 733>, <546121, 739>, <552049, 743>, <564001, 751>, <571787, 83>, <573049, 757>, <579121, 761>, <591361, 769>, <597529, 773>, <619369, 787>, <635209, 797>, <654481, 809>, <657721, 811>, <674041, 821>, <677329, 823>, <683929, 827>, <687241, 829>, <703921, 839>, <704969, 89>, <707281, 29>, <727609, 853>, <734449, 857>, <737881, 859>, <744769, 863>, <769129, 877>, <776161, 881>, <779689, 883>, <786769, 887>, <822649, 907>, <829921, 911>, <844561, 919>, <863041, 929>, <877969, 937>, <885481, 941>, <896809, 947>, <908209, 953>, <912673, 97>, <923521, 31>, <935089, 967>, <942841, 971>, <954529, 977>, <966289, 983>, <982081, 991>, <994009, 997>, <1018081, 1009>, <1026169, 1013>, <1030301, 101>, <1038361, 1019>, <1042441, 1021>, <1062961, 1031>, <1067089, 1033>, <1079521, 1039>, <1092727, 103>, <1100401, 1049>, <1104601, 1051>, <1125721, 1061>, <1129969, 1063>, <1142761, 1069>, <1181569, 1087>, <1190281, 1091>, <1194649, 1093>, <1203409, 1097>, <1216609, 1103>, <1225043, 107>, <1229881, 1109>, <1247689, 1117>, <1261129, 1123>, <1274641, 1129>, <1295029, 109>, <1324801, 1151>, <1329409, 1153>, <1352569, 1163>, <1371241, 1171>, <1394761, 1181>, <1408969, 1187>, <1419857, 17>, <1423249, 1193>, <1442401, 1201>, <1442897, 113>, <1471369, 1213>, <1481089, 1217>, <1495729, 1223>, <1510441, 1229>, <1515361, 1231>, <1530169, 1237>, <1560001, 1249>, <1585081, 1259>, <1630729, 1277>, <1635841, 1279>, <1646089, 1283>, <1661521, 1289>, <1666681, 1291>, <1682209, 1297>, <1692601, 1301>, <1697809, 1303>, <1708249, 1307>, <1739761, 1319>, <1745041, 1321>, <1760929, 1327>, <1771561, 11>, <1852321, 1361>, <1868689, 1367>, <1874161, 37>, <1885129, 1373>, <1907161, 1381>, <1957201, 1399>, <1985281, 1409>, <2024929, 1423>, <2036329, 1427>, <2042041, 1429>, <2048383, 127>, <2053489, 1433>, <2070721, 1439>, <2093809, 1447>, <2105401, 1451>, <2111209, 1453>, <2128681, 1459>, <2163841, 1471>, <2193361, 1481>, <2199289, 1483>, <2211169, 1487>, <2217121, 1489>, <2229049, 1493>, <2247001, 1499>, <2248091, 131>, <2283121, 1511>, <2319529, 1523>, <2343961, 1531>, <2380849, 1543>, <2399401, 1549>, <2411809, 1553>, <2430481, 1559>, <2455489, 1567>, <2468041, 1571>, <2476099, 19>, <2493241, 1579>, <2505889, 1583>, <2550409, 1597>, <2563201, 1601>, <2571353, 137>, <2582449, 1607>, <2588881, 1609>, <2601769, 1613>, <2621161, 1619>, <2627641, 1621>, <2647129, 1627>, <2679769, 1637>, <2685619, 139>, <2745649, 1657>, <2765569, 1663>, <2778889, 1667>, <2785561, 1669>, <2825761, 41>, <2866249, 1693>, <2879809, 1697>, <2886601, 1699>, <2920681, 1709>, <2961841, 1721>, <2968729, 1723>, <3003289, 1733>, <3031081, 1741>, <3052009, 1747>, <3073009, 1753>, <3094081, 1759>, <3157729, 1777>, <3179089, 1783>, <3193369, 1787>, <3200521, 1789>, <3243601, 1801>, <3279721, 1811>, <3307949, 149>, <3323329, 1823>, <3352561, 1831>, <3411409, 1847>, <3418801, 43>, <3442951, 151>, <3463321, 1861>, <3485689, 1867>, <3500641, 1871>, <3508129, 1873>, <3523129, 1877>, <3530641, 1879>, <3568321, 1889>, <3613801, 1901>, <3636649, 1907>, <3659569, 1913>, <3728761, 1931>, <3736489, 1933>, <3798601, 1949>, <3806401, 1951>, <3869893, 157>, <3892729, 1973>, <3916441, 1979>, <3948169, 1987>, <3972049, 1993>, <3988009, 1997>, <3996001, 1999>, <4012009, 2003>, <4044121, 2011>, <4068289, 2017>, <4108729, 2027>, <4116841, 2029>, <4157521, 2039>, <4214809, 2053>, <4255969, 2063>, <4280761, 2069>, <4330561, 2081>, <4330747, 163>, <4338889, 2083>, <4355569, 2087>, <4363921, 2089>, <4405801, 2099>, <4456321, 2111>, <4464769, 2113>, <4532641, 2129>, <4541161, 2131>, <4566769, 2137>, <4583881, 2141>, <4592449, 2143>, <4635409, 2153>, <4657463, 167>, <4669921, 2161>, <4748041, 2179>, <4782969, 3>, <4826809, 13>, <4853209, 2203>, <4870849, 2207>, <4879681, 47>, <4897369, 2213>, <4932841, 2221>, <5004169, 2237>, <5013121, 2239>, <5031049, 2243>, <5067001, 2251>, <5139289, 2267>, <5148361, 2269>, <5166529, 2273>, <5177717, 173>, <5202961, 2281>, <5230369, 2287>, <5257849, 2293>, <5276209, 2297>, <5331481, 2309>, <5340721, 2311>, <5442889, 2333>, <5470921, 2339>, <5480281, 2341>, <5508409, 2347>, <5527201, 2351>, <5555449, 2357>, <5621641, 2371>, <5650129, 2377>, <5669161, 2381>, <5678689, 2383>, <5707321, 2389>, <5726449, 2393>, <5735339, 179>, <5755201, 2399>, <5764801, 7>, <5812921, 2411>, <5841889, 2417>, <5870929, 2423>, <5929741, 181>, <5938969, 2437>, <5958481, 2441>, <5987809, 2447>, <6046681, 2459>, <6086089, 2467>, <6115729, 2473>, <6135529, 2477>, <6265009, 2503>, <6355441, 2521>, <6405961, 2531>, <6436343, 23>, <6446521, 2539>, <6466849, 2543>, <6497401, 2549>, <6507601, 2551>, <6538249, 2557>, <6651241, 2579>, <6713281, 2591>, <6723649, 2593>, <6806881, 2609>, <6848689, 2617>, <6869641, 2621>, <6932689, 2633>, <6967871, 191>, <7006609, 2647>, <7059649, 2657>, <7070281, 2659>, <7091569, 2663>, <7134241, 2671>, <7166329, 2677>, <7189057, 193>, <7198489, 2683>, <7219969, 2687>, <7230721, 2689>, <7252249, 2693>, <7284601, 2699>, <7327849, 2707>, <7349521, 2711>, <7360369, 2713>, <7392961, 2719>, <7447441, 2729>, <7458361, 2731>, <7513081, 2741>, <7557001, 2749>, <7579009, 2753>, <7645373, 197>, <7656289, 2767>, <7711729, 2777>, <7778521, 2789>, <7789681, 2791>, <7823209, 2797>, <7845601, 2801>, <7856809, 2803>, <7880599, 199>, <7890481, 53>, <7946761, 2819>, <8025889, 2833>, <8048569, 2837>, <8082649, 2843>, <8128201, 2851>, <8162449, 2857>, <8185321, 2861>, <8288641, 2879>, <8334769, 2887>, <8388608, 2>, <8392609, 2897>, <8427409, 2903>, <8462281, 2909>, <8508889, 2917>, <8567329, 2927>, <8637721, 2939>, <8720209, 2953>, <8743849, 2957>, <8779369, 2963>, <8814961, 2969>, <8826841, 2971>, <8994001, 2999>, <9006001, 3001>, <9066121, 3011>, <9114361, 3019>, <9138529, 3023>, <9223369, 3037>, <9247681, 3041>, <9296401, 3049>, <9369721, 3061>, <9393931, 211>, <9406489, 3067>, <9480241, 3079>, <9504889, 3083>, <9541921, 3089>, <9665881, 3109>, <9728161, 3119>, <9740641, 3121>, <9765625, 5>, <9840769, 3137>, <10004569, 3163>, <10029889, 3167>, <10042561, 3169>, <10118761, 3181>, <10156969, 3187>, <10182481, 3191>, <10259209, 3203>, <10297681, 3209>, <10349089, 3217>, <10374841, 3221>, <10426441, 3229>, <10569001, 3251>, <10582009, 3253>, <10608049, 3257>, <10621081, 3259>, <10699441, 3271>, <10883401, 3299>, <10896601, 3301>, <10936249, 3307>, <10975969, 3313>, <11015761, 3319>, <11042329, 3323>, <11082241, 3329>, <11089567, 223>, <11095561, 3331>, <11175649, 3343>, <11202409, 3347>, <11282881, 3359>, <11296321, 3361> ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 10:52:16 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); q:=p[#p][1]; while (q gt 1) do K:=GF(next); R := PolynomialRing(K); for a in {x: x in K|x ne 0} do if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q endif; end for; p[#p][1]/:=p[#p][2]; Sort(~p); end while; return 0; end function; mini_car(10); Output: Magma V2.10-6 Thu Mar 11 2004 10:52:13 on modular [Seed = 1885387565] ------------------------------------- >> if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q endif; ^ User error: bad syntax >> end for; ^ User error: bad syntax >> p[#p][1]/:=p[#p][2]; ^ User error: Identifier 'p' has not been declared or assigned >> Sort(~p); ^ Runtime error in 'Sort': Argument 1 has not been initialized Argument types given: *nothing ~ >> end while; ^ User error: bad syntax >> return 0; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> mini_car(10);; ^ User error: Identifier 'mini_car' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 10:52:30 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); q:=p[#p][1]; while (q gt 1) do K:=GF(next); R := PolynomialRing(K); for a in {x: x in K|x ne 0} do if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q end if; end for; p[#p][1]/:=p[#p][2]; Sort(~p); end while; return 0; end function; mini_car(10); Output: Magma V2.10-6 Thu Mar 11 2004 10:52:27 on modular [Seed = 2036970034] ------------------------------------- >> if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q end if; ^ User error: bad syntax >> end for; ^ User error: bad syntax >> p[#p][1]/:=p[#p][2]; ^ User error: Identifier 'p' has not been declared or assigned >> Sort(~p); ^ Runtime error in 'Sort': Argument 1 has not been initialized Argument types given: *nothing ~ >> end while; ^ User error: bad syntax >> return 0; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> mini_car(10);; ^ User error: Identifier 'mini_car' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 10:52:49 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); q:=p[#p][1]; while (q gt 1) do K:=GF(next); R := PolynomialRing(K); for a in {x: x in K|x ne 0} do if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end for; p[#p][1]/:=p[#p][2]; Sort(~p); end while; return 0; end function; mini_car(10); Output: Magma V2.10-6 Thu Mar 11 2004 10:52:44 on modular [Seed = 1651681630] ------------------------------------- [
:3]( k: 10 ) >> p[#p][1]/:=p[#p][2]; ^ Runtime error in :=: New component not in cartesian product Total time: 4.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 10:53:26 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); q:=p[#p][1]; while (q gt 1) do K:=GF(next); R := PolynomialRing(K); for a in {x: x in K|x ne 0} do if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end for; (p[#p])[1]/:=(p[#p])[2]; Sort(~p); end while; return 0; end function; mini_car(10); Output: Magma V2.10-6 Thu Mar 11 2004 10:53:21 on modular [Seed = 1803264106] ------------------------------------- [
:3]( k: 10 ) >> (p[#p])[1]/:=(p[#p])[2]; ^ Runtime error in :=: New component not in cartesian product Total time: 4.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 10:54:34 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); q:=p[#p][1]; while (q gt 1) do K:=GF(next); R := PolynomialRing(K); for a in {x: x in K|x ne 0} do if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end for; p[#p]:=; Sort(~p); end while; return 0; end function; mini_car(10); Output: Magma V2.10-6 Thu Mar 11 2004 10:54:31 on modular [Seed = 1430625938] ------------------------------------- [
:3]( k: 10 ) >> p[#p]:=; ^ Runtime error in :=: Sequence mutation failed Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 10:55:12 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); q:=p[#p][1]; while (q gt 1) do K:=GF(next); R := PolynomialRing(K); for a in {x: x in K|x ne 0} do if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end for; print Type(); p[#p]:=; Sort(~p); end while; return 0; end function; mini_car(10); Output: Magma V2.10-6 Thu Mar 11 2004 10:55:09 on modular [Seed = 1112705519] ------------------------------------- Tup Tup [
:3]( k: 10 ) >> p[#p]:=; ^ Runtime error in :=: Sequence mutation failed Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 10:57:52 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); q:=p[#p]; while (q[1] gt 1) do K:=GF(next); R := PolynomialRing(K); for a in {x: x in K|x ne 0} do if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q[1]; end if; end for; Prune(~p); Append(~p,; Sort(~p); end while; return 0; end function; mini_car(10); Output: Magma V2.10-6 Thu Mar 11 2004 10:57:49 on modular [Seed = 1281130561] ------------------------------------- >> Append(~p,; ^ User error: bad syntax >> Sort(~p); ^ Runtime error in 'Sort': Argument 1 has not been initialized Argument types given: *nothing ~ >> end while; ^ User error: bad syntax >> return 0; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> mini_car(10);; ^ User error: Identifier 'mini_car' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 10:58:27 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); q:=p[#p]; while (q[1] gt 1) do K:=GF(next); R := PolynomialRing(K); for a in {x: x in K|x ne 0} do if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q[1]; end if; end for; Prune(~p); Append(~p,); Sort(~p); end while; return 0; end function; mini_car(10); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 11 2004 10:58:04 on modular [Seed = 891681225] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 12357 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 10:59:06 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); q:=p[#p]; while (q[1] gt 1) do K:=GF(next); R := PolynomialRing(K); for a in {x: x in K|x ne 0} do if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q[1]; end if; end for; Prune(~p); Append(~p,); Sort(~p); end while; return 0; end function; mini_car(6); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 11 2004 10:58:43 on modular [Seed = 1060107260] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 12367 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 10:59:46 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); q:=p[#p]; while (q[1] gt 1) do K:=GF(next); R := PolynomialRing(K); for a in {x: x in K|x ne 0} do if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q[1]; end if; end for; Prune(~p); Append(~p,); print p; Sort(~p); end while; return 0; end function; mini_car(6); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 11 2004 10:59:23 on modular [Seed = 691660162] ------------------------------------- [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <169, 13>, <243, 3>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <169, 13>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <128, 2>, <128, 2> ] [ ** WARNING: Output too long, hence truncated. Errors: /home/mfd/gomagma: line 2: 12377 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 11:00:58 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); q:=p[#p]; while (q[1] gt 1) do K:=GF(next); R := PolynomialRing(K); for a in {x: x in K|x ne 0} do if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q[1]; end if; end for; Prune(~p); Append(~p,); print p; Sort(~p); q:=p[#p]; end while; return 0; end function; mini_car(6); Output: Magma V2.10-6 Thu Mar 11 2004 11:00:54 on modular [Seed = 420074591] ------------------------------------- [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <169, 13>, <243, 3>, <128, 2> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <128, 2>, <169, 13>, <81, 3> ] [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <81, 3>, <121, 11>, <125, 5>, <128, 2>, <13, 13> ] [ <13, 13>, <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <81, 3>, <121, 11>, <125, 5>, <64, 2> ] [ <13, 13>, <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <64, 2>, <81, 3>, <121, 11>, <25, 5> ] [ <13, 13>, <17, 17>, <19, 19>, <23, 23>, <25, 5>, <29, 29>, <49, 7>, <64, 2>, <81, 3>, <11, 11> ] [ <11, 11>, <13, 13>, <17, 17>, <19, 19>, <23, 23>, <25, 5>, <29, 29>, <49, 7>, <64, 2>, <27, 3> ] [ <11, 11>, <13, 13>, <17, 17>, <19, 19>, <23, 23>, <25, 5>, <27, 3>, <29, 29>, <49, 7>, <32, 2> ] [ <11, 11>, <13, 13>, <17, 17>, <19, 19>, <23, 23>, <25, 5>, <27, 3>, <29, 29>, <32, 2>, <7, 7> ] [ <7, 7>, <11, 11>, <13, 13>, <17, 17>, <19, 19>, <23, 23>, <25, 5>, <27, 3>, <29, 29>, <16, 2> ] [ <7, 7>, <11, 11>, <13, 13>, <16, 2>, <17, 17>, <19, 19>, <23, 23>, <25, 5>, <27, 3>, <1, 29> ] [ <1, 29>, <7, 7>, <11, 11>, <13, 13>, <16, 2>, <17, 17>, <19, 19>, <23, 23>, <25, 5>, <9, 3> ] [ <1, 29>, <7, 7>, <9, 3>, <11, 11>, <13, 13>, <16, 2>, <17, 17>, <19, 19>, <23, 23>, <5, 5> ] [ <1, 29>, <5, 5>, <7, 7>, <9, 3>, <11, 11>, <13, 13>, <16, 2>, <17, 17>, <19, 19>, <1, 23> ] [ <1, 23>, <1, 29>, <5, 5>, <7, 7>, <9, 3>, <11, 11>, <13, 13>, <16, 2>, <17, 17>, <1, 19> ] [ <1, 19>, <1, 23>, <1, 29>, <5, 5>, <7, 7>, <9, 3>, <11, 11>, <13, 13>, <16, 2>, <1, 17> ] [ <1, 17>, <1, 19>, <1, 23>, <1, 29>, <5, 5>, <7, 7>, <9, 3>, <11, 11>, <13, 13>, <8, 2> ] [ <1, 17>, <1, 19>, <1, 23>, <1, 29>, <5, 5>, <7, 7>, <8, 2>, <9, 3>, <11, 11>, <1, 13> ] [ <1, 13>, <1, 17>, <1, 19>, <1, 23>, <1, 29>, <5, 5>, <7, 7>, <8, 2>, <9, 3>, <1, 11> ] [ <1, 11>, <1, 13>, <1, 17>, <1, 19>, <1, 23>, <1, 29>, <5, 5>, <7, 7>, <8, 2>, <3, 3> ] [ <1, 11>, <1, 13>, <1, 17>, <1, 19>, <1, 23>, <1, 29>, <3, 3>, <5, 5>, <7, 7>, <4, 2> ] [ <1, 11>, <1, 13>, <1, 17>, <1, 19>, <1, 23>, <1, 29>, <3, 3>, <4, 2>, <5, 5>, <1, 7> ] [ <1, 7>, <1, 11>, <1, 13>, <1, 17>, <1, 19>, <1, 23>, <1, 29>, <3, 3>, <4, 2>, <1, 5> ] [ <1, 5>, <1, 7>, <1, 11>, <1, 13>, <1, 17>, <1, 19>, <1, 23>, <1, 29>, <3, 3>, <2, 2> ] [ <1, 5>, <1, 7>, <1, 11>, <1, 13>, <1, 17>, <1, 19>, <1, 23>, <1, 29>, <2, 2>, <1, 3> ] [ <1, 3>, <1, 5>, <1, 7>, <1, 11>, <1, 13>, <1, 17>, <1, 19>, <1, 23>, <1, 29>, <1, 2> ] 0 Total time: 3.289 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 11:01:48 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); q:=p[#p]; while (q[1] gt 1) do K:=GF(next); R := PolynomialRing(K); for a in {x: x in K|x ne 0} do if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q[1]; end if; end for; Prune(~p); Append(~p,); Sort(~p); q:=p[#p]; end while; return 0; end function; mini_car(6); Output: Magma V2.10-6 Thu Mar 11 2004 11:01:45 on modular [Seed = 4125440236] ------------------------------------- 0 Total time: 3.249 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 11:02:02 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); q:=p[#p]; while (q[1] gt 1) do K:=GF(next); R := PolynomialRing(K); for a in {x: x in K|x ne 0} do if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q[1]; end if; end for; Prune(~p); Append(~p,); Sort(~p); q:=p[#p]; end while; return 0; end function; mini_car(10); Output: Magma V2.10-6 Thu Mar 11 2004 11:01:58 on modular [Seed = 4277023736] ------------------------------------- 0 Total time: 4.829 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 11:02:19 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); q:=p[#p]; while (q[1] gt 1) do K:=GF(next); R := PolynomialRing(K); for a in {x: x in K|x ne 0} do if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q[1]; end if; end for; Prune(~p); Append(~p,); Sort(~p); q:=p[#p]; end while; return 0; end function; mini_car(12); Output: Magma V2.10-6 Thu Mar 11 2004 11:02:11 on modular [Seed = 3891735060] ------------------------------------- 0 Total time: 7.500 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 11:02:37 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); q:=p[#p]; while (q[1] gt 1) do K:=GF(next); R := PolynomialRing(K); for a in {x: x in K|x ne 0} do if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q[1]; end if; end for; Prune(~p); Append(~p,); Sort(~p); q:=p[#p]; end while; return 0; end function; mini_car(14); Output: Magma V2.10-6 Thu Mar 11 2004 11:02:27 on modular [Seed = 3502251315] ------------------------------------- 0 Total time: 10.510 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 11:04:13 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); q:=p[#p]; while (q[1] gt 1) do K:=GF(next); R := PolynomialRing(K); for a in {x: x in K|x ne 0} do if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q[1]; end if; end for; Prune(~p); Append(~p,); Sort(~p); q:=p[#p]; end while; return 0; end function; mini_car(15); Output: Magma V2.10-6 Thu Mar 11 2004 11:03:59 on modular [Seed = 3653833798] ------------------------------------- 0 Total time: 14.219 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 11:04:48 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); q:=p[#p]; while (q[1] gt 1) do K:=GF(next); R := PolynomialRing(K); for a in {x: x in K|x ne 0} do if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q[1]; end if; end for; Prune(~p); Append(~p,); Sort(~p); q:=p[#p]; end while; return 0; end function; mini_car(18); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 11 2004 11:04:25 on modular [Seed = 3285388730] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 12467 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 11:06:45 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); q:=p[#p]; while (q[1] gt 1) do K:=GF(next); R := PolynomialRing(K); for a in {x: x in K|x ne 0} do if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q[1]; end if; end for; Prune(~p); Append(~p,); Sort(~p); q:=p[#p]; end while; return 0; end function; mini_car(14); Output: Magma V2.10-6 Thu Mar 11 2004 11:06:34 on modular [Seed = 2980151115] ------------------------------------- 0 Total time: 10.309 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 11:08:09 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); q:=p[#p]; while (q[1] gt 1) do K:=GF(q[1]); R := PolynomialRing(K); for a in {x: x in K|x ne 0} do if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q[1]; end if; end for; Prune(~p); Append(~p,); Sort(~p); q:=p[#p]; end while; return 0; end function; mini_car(14); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 11 2004 11:07:46 on modular [Seed = 3131733016] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 12490 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 11:08:34 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); q:=p[#p]; while (q[1] gt 1) do K:=GF(q[1]); R := PolynomialRing(K); for a in {x: x in K|x ne 0} do if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q[1]; end if; end for; Prune(~p); Append(~p,); Sort(~p); q:=p[#p]; end while; return 0; end function; mini_car(10); Output: Magma V2.10-6 Thu Mar 11 2004 11:08:16 on modular [Seed = 2746445091] ------------------------------------- 343 Total time: 17.219 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 11:09:16 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); q:=p[#p]; print p; while (q[1] gt 1) do K:=GF(q[1]); R := PolynomialRing(K); for a in {x: x in K|x ne 0} do if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q[1]; end if; end for; Prune(~p); Append(~p,); Sort(~p); q:=p[#p]; end while; return 0; end function; mini_car(10); Output: Magma V2.10-6 Thu Mar 11 2004 11:08:58 on modular [Seed = 2914869959] ------------------------------------- [ <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5>, <3481, 59>, <3721, 61>, <4096, 2> ] 343 Total time: 17.170 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 11:09:51 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); q:=p[#p]; print p; while (q[1] gt 1) do K:=GF(q[1]); R := PolynomialRing(K); for a in {x: x in K|x ne 0} do if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end for; Prune(~p); Append(~p,); Sort(~p); q:=p[#p]; end while; return 0; end function; mini_car(10); Output: Magma V2.10-6 Thu Mar 11 2004 11:09:33 on modular [Seed = 2542229722] ------------------------------------- [ <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5>, <3481, 59>, <3721, 61>, <4096, 2> ] <343, 7> Total time: 17.280 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 11:11:15 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); q:=p[#p]; print p; while (q[1] gt 1) do K:=GF(q[1]); R := PolynomialRing(K); for a in {x: x in K|x ne 0} do if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end for; Prune(~p); Append(~p,); Sort(~p); q:=p[#p]; end while; return 0; end function; mini_car(6); Output: Magma V2.10-6 Thu Mar 11 2004 11:11:12 on modular [Seed = 2274838615] ------------------------------------- [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <169, 13>, <243, 3>, <256, 2> ] <11, 11> Total time: 3.309 seconds, Total memory usage: 2.39MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 11:12:19 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); q:=p[#p]; print p; while (q[1] gt 1) do K:=GF(q[1]); R := PolynomialRing(K); for a in {x: x in K|x ne 0} do if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end for; Prune(~p); Append(~p,); Sort(~p); q:=p[#p]; end while; return 0; end function; mini_car(12); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 11 2004 11:11:56 on modular [Seed = 1902231244] ------------------------------------- [ <101, 101>, <103, 103>, <107, 107>, <109, 109>, <113, 113>, <127, 127>, <131, 131>, <529, 23>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5>, <3481, 59>, <3721, 61>, <4489, 67>, <4913, 17>, <5041, 71>, <5329, 73>, <6241, 79>, <6561, 3>, <6859, 19>, <6889, 83>, <7921, 89>, <8192, 2>, <9409, 97> ] Errors: /home/mfd/gomagma: line 2: 12544 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 11:18:50 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); q:=p[#p]; print p; while (q[1] gt 1) do K:=GF(q[1]); R := PolynomialRing(K); for a in {x: x in K|x ne 0} do if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end for; Prune(~p); Append(~p,); Sort(~p); q:=p[#p]; end while; return 0; end function; mini_car(12); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 11 2004 11:18:26 on modular [Seed = 1651684161] ------------------------------------- [ <101, 101>, <103, 103>, <107, 107>, <109, 109>, <113, 113>, <127, 127>, <131, 131>, <529, 23>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5>, <3481, 59>, <3721, 61>, <4489, 67>, <4913, 17>, <5041, 71>, <5329, 73>, <6241, 79>, <6561, 3>, <6859, 19>, <6889, 83>, <7921, 89>, <8192, 2>, <9409, 97> ] Errors: /home/mfd/gomagma: line 2: 12563 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 11:20:16 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); q:=p[#p]; print p; while (q[1] gt 1) do K:=GF(q[1]); R := PolynomialRing(K); for a in {x: x in K|x ne 0} do if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end for; Prune(~p); Append(~p,); Sort(~p); q:=p[#p]; end while; return 0; end function; mini_car(6); Output: Magma V2.10-6 Thu Mar 11 2004 11:20:13 on modular [Seed = 1430619289] ------------------------------------- [ <17, 17>, <19, 19>, <23, 23>, <29, 29>, <49, 7>, <121, 11>, <125, 5>, <169, 13>, <243, 3>, <256, 2> ] <11, 11> Total time: 3.379 seconds, Total memory usage: 2.39MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 11:20:42 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); q:=p[#p]; print p; while (q[1] gt 1) do K:=GF(q[1]); R := PolynomialRing(K); for a in {x: x in K|x ne 0} do if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end for; Prune(~p); Append(~p,); Sort(~p); q:=p[#p]; end while; return 0; end function; mini_car(10); Output: Magma V2.10-6 Thu Mar 11 2004 11:20:25 on modular [Seed = 1548520932] ------------------------------------- [ <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5>, <3481, 59>, <3721, 61>, <4096, 2> ] <343, 7> Total time: 17.059 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 11:21:11 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); q:=p[#p]; print p; while (q[1] gt 1) do K:=GF(q[1]); R := PolynomialRing(K); for a in {x: x in (K diff {0})} do if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end for; Prune(~p); Append(~p,); Sort(~p); q:=p[#p]; end while; return 0; end function; mini_car(10); Output: Magma V2.10-6 Thu Mar 11 2004 11:21:08 on modular [Seed = 1180080067] ------------------------------------- [ <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5>, <3481, 59>, <3721, 61>, <4096, 2> ] [
:3]( k: 10 ) >> for a in {x: x in (K diff {0})} do ^ Runtime error in 'diff': Bad argument types Argument types given: FldFin, SetEnum[RngIntElt] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 11:25:24 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); q:=p[#p]; print p; while (q[1] gt 1) do K:=GF(q[1]); R := PolynomialRing(K); for a in x in K do if x ne 0 then if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end if; end for; Prune(~p); Append(~p,); Sort(~p); q:=p[#p]; end while; return 0; end function; mini_car(10); Output: Magma V2.10-6 Thu Mar 11 2004 11:25:21 on modular [Seed = 925361591] ------------------------------------- [ <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5>, <3481, 59>, <3721, 61>, <4096, 2> ] [
:3]( k: 10 ) >> for a in x in K do ^ Runtime error in for: Iteration is not possible over this object Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 11:26:04 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); q:=p[#p]; print p; while (q[1] gt 1) do K:=GF(q[1]); R := PolynomialRing(K); for a in K do if a ne 0 then if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end if; end for; Prune(~p); Append(~p,); Sort(~p); q:=p[#p]; end while; return 0; end function; mini_car(10); Output: Magma V2.10-6 Thu Mar 11 2004 11:25:46 on modular [Seed = 1043262789] ------------------------------------- [ <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5>, <3481, 59>, <3721, 61>, <4096, 2> ] <343, 7> Total time: 17.559 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host serv.math.metu.edu.tr. (144.122.136.16) Time: Thu Mar 11 11:31:58 2004 Input: 2 + 3 ; Output: Magma V2.10-6 Thu Mar 11 2004 11:31:53 on modular [Seed = 268485656] ------------------------------------- 5 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 11:35:26 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); q:=p[#p]; print p; while (q[1] gt 1) do K:=GF(q[1]); R := PolynomialRing(K); for a in K do if a ne 0 then if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end if; end for; Prune(~p); q[1]/:=q[2]; Append(~p,q); Sort(~p); q:=p[#p]; end while; return 0; end function; mini_car(10); Output: Magma V2.10-6 Thu Mar 11 2004 11:35:09 on modular [Seed = 236903234] ------------------------------------- [ <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5>, <3481, 59>, <3721, 61>, <4096, 2> ] <343, 7> Total time: 17.469 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 11:35:55 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); l=#p; q:=p[l]; print p; while (q[1] gt 1) do K:=GF(q[1]); R := PolynomialRing(K); for a in K do if a ne 0 then if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end if; end for; Prune(~p); q[1]/:=q[2]; Append(~p,q); Sort(~p); q:=p[l]; end while; return 0; end function; mini_car(10); Output: Magma V2.10-6 Thu Mar 11 2004 11:35:52 on modular [Seed = 4192808160] ------------------------------------- >> l=#p; ^ User error: Identifier 'l' has not been declared or assigned >> mini_car(10);; ^ User error: Identifier 'mini_car' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 11:36:25 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); l:=#p; q:=p[l]; print p; while (q[1] gt 1) do K:=GF(q[1]); R := PolynomialRing(K); for a in K do if a ne 0 then if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end if; end for; Prune(~p); q[1]/:=q[2]; Append(~p,q); Sort(~p); q:=p[l]; end while; return 0; end function; mini_car(10); Output: Magma V2.10-6 Thu Mar 11 2004 11:36:08 on modular [Seed = 3773838825] ------------------------------------- [ <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5>, <3481, 59>, <3721, 61>, <4096, 2> ] <343, 7> Total time: 17.250 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 11:37:13 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); next:=#p; q:=p[next]; print p; while (q[1] gt 1) do K:=GF(q[1]); R := PolynomialRing(K); for a in K do if a ne 0 then if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end if; end for; Prune(~p); q[1]/:=q[2]; Append(~p,q); Sort(~p); q:=p[next]; end while; return 0; end function; mini_car(10); Output: Magma V2.10-6 Thu Mar 11 2004 11:36:56 on modular [Seed = 3959111218] ------------------------------------- [ <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5>, <3481, 59>, <3721, 61>, <4096, 2> ] <343, 7> Total time: 17.199 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 11:40:42 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); next:=#p; q:=p[next]; print p; while (q[1] gt 1) do K:=GF(q[1]); R := PolynomialRing(K); for a in K do if a ne 0 then if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end if; end for; Prune(~p); q[1]/:=q[2]; Append(~p,q); Sort(~p); for i in [1..next] do if p[i] ge q then Insert(~p,i,q); break; end if; end for; q:=p[next]; end while; return 0; end function; mini_car(10); Output: Magma V2.10-6 Thu Mar 11 2004 11:40:38 on modular [Seed = 3704359467] ------------------------------------- [ <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5>, <3481, 59>, <3721, 61>, <4096, 2> ] [
:3]( k: 10 ) >> if p[i] ge q then ^ Runtime error in 'ge': Bad argument types Argument types given: Tup, Tup Total time: 4.129 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (207.193.176.61) Time: Thu Mar 11 11:41:06 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Thu Mar 11 2004 11:41:03 on modular [Seed = 3352760617] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 11:41:18 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); next:=#p; q:=p[next]; print p; while (q[1] gt 1) do K:=GF(q[1]); R := PolynomialRing(K); for a in K do if a ne 0 then if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end if; end for; Prune(~p); q[1]/:=q[2]; Append(~p,q); Sort(~p); for i in [1..next] do if p[i][1] ge q[1] then Insert(~p,i,q); break; end if; end for; q:=p[next]; end while; return 0; end function; mini_car(10); Output: Magma V2.10-6 Thu Mar 11 2004 11:41:07 on modular [Seed = 3470661660] ------------------------------------- [ <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5>, <3481, 59>, <3721, 61>, <4096, 2> ] <64, 2> Total time: 11.069 seconds, Total memory usage: 2.39MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 11:42:23 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); next:=#p; q:=p[next]; while (q[1] gt 1) do print p; K:=GF(q[1]); R := PolynomialRing(K); for a in K do if a ne 0 then if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end if; end for; Prune(~p); q[1]/:=q[2]; Append(~p,q); Sort(~p); for i in [1..next] do if p[i][1] ge q[1] then Insert(~p,i,q); break; end if; end for; q:=p[next]; end while; return 0; end function; mini_car(10); Output: Magma V2.10-6 Thu Mar 11 2004 11:42:11 on modular [Seed = 1935910373] ------------------------------------- [ <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5>, <3481, 59>, <3721, 61>, <4096, 2> ] [ <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2048, 2>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5>, <3481, 59>, <3721, 61> ] [ <59, 59>, <59, 59>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2048, 2>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5>, <3481, 59> ] [ <53, 53>, <53, 53>, <59, 59>, <59, 59>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2048, 2>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5> ] [ <47, 47>, <47, 47>, <53, 53>, <53, 53>, <59, 59>, <59, 59>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2048, 2>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53> ] [ <47, 47>, <47, 47>, <53, 53>, <53, 53>, <59, 59>, <59, 59>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <729, 3>, <729, 3>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2048, 2>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7> ] [ <47, 47>, <47, 47>, <53, 53>, <53, 53>, <59, 59>, <59, 59>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <729, 3>, <729, 3>, <841, 29>, <961, 31>, <1024, 2>, <1024, 2>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2048, 2>, <2187, 3>, <2197, 13>, <2209, 47> ] [ <41, 41>, <41, 41>, <47, 47>, <47, 47>, <53, 53>, <53, 53>, <59, 59>, <59, 59>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <729, 3>, <729, 3>, <841, 29>, <961, 31>, <1024, 2>, <1024, 2>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2048, 2>, <2187, 3>, <2197, 13> ] [ <41, 41>, <41, 41>, <47, 47>, <47, 47>, <53, 53>, <53, 53>, <59, 59>, <59, 59>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <121, 11>, <289, 17>, <361, 19>, <529, 23>, <729, 3>, <729, 3>, <841, 29>, <961, 31>, <1024, 2>, <1024, 2>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2048, 2>, <2187, 3> ] [ <41, 41>, <41, 41>, <47, 47>, <47, 47>, <53, 53>, <53, 53>, <59, 59>, <59, 59>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <121, 11>, <289, 17>, <361, 19>, <512, 2>, <512, 2>, <529, 23>, <729, 3>, <729, 3>, <841, 29>, <961, 31>, <1024, 2>, <1024, 2>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2048, 2> ] [ <29, 29>, <29, 29>, <41, 41>, <41, 41>, <47, 47>, <47, 47>, <53, 53>, <53, 53>, <59, 59>, <59, 59>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <121, 11>, <289, 17>, <361, 19>, <512, 2>, <512, 2>, <529, 23>, <729, 3>, <729, 3>, <841, 29>, <961, 31>, <1024, 2>, <1024, 2>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2> ] [ <29, 29>, <29, 29>, <41, 41>, <41, 41>, <47, 47>, <47, 47>, <53, 53>, <53, 53>, <59, 59>, <59, 59>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <121, 11>, <243, 3>, <243, 3>, <289, 17>, <361, 19>, <512, 2>, <512, 2>, <529, 23>, <729, 3>, <729, 3>, <841, 29>, <961, 31>, <1024, 2>, <1024, 2>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43> ] [ <29, 29>, <29, 29>, <41, 41>, <41, 41>, <47, 47>, <47, 47>, <53, 53>, <53, 53>, <59, 59>, <59, 59>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <121, 11>, <243, 3>, <243, 3>, <256, 2>, <256, 2>, <289, 17>, <361, 19>, <512, 2>, <512, 2>, <529, 23>, <729, 3>, <729, 3>, <841, 29>, <961, 31>, <1024, 2>, <1024, 2>, <1331, 11>, <1369, 37>, <1681, 41> ] [ <19, 19>, <19, 19>, <29, 29>, <29, 29>, <41, 41>, <41, 41>, <47, 47>, <47, 47>, <53, 53>, <53, 53>, <59, 59>, <59, 59>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <121, 11>, <243, 3>, <243, 3>, <256, 2>, <256, 2>, <289, 17>, <361, 19>, <512, 2>, <512, 2>, <529, 23>, <729, 3>, <729, 3>, <841, 29>, <961, 31>, <1024, 2>, <1024, 2>, <1331, 11>, <1369, 37> ] [ <19, 19>, <19, 19>, <29, 29>, <29, 29>, <41, 41>, <41, 41>, <47, 47>, <47, 47>, <53, 53>, <53, 53>, <59, 59>, <59, 59>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <121, 11>, <128, 2>, <128, 2>, <243, 3>, <243, 3>, <256, 2>, <256, 2>, <289, 17>, <361, 19>, <512, 2>, <512, 2>, <529, 23>, <729, 3>, <729, 3>, <841, 29>, <961, 31>, <1024, 2>, <1024, 2>, <1331, 11> ] [ <19, 19>, <19, 19>, <29, 29>, <29, 29>, <41, 41>, <41, 41>, <47, 47>, <47, 47>, <53, 53>, <53, 53>, <59, 59>, <59, 59>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <81, 3>, <81, 3>, <83, 83>, <89, 89>, <121, 11>, <121, 11>, <128, 2>, <128, 2>, <243, 3>, <243, 3>, <256, 2>, <256, 2>, <289, 17>, <361, 19>, <512, 2>, <512, 2>, <529, 23>, <729, 3>, <729, 3>, <841, 29>, <961, 31>, <1024, 2>, <1024, 2> ] [ <19, 19>, <19, 19>, <29, 29>, <29, 29>, <41, 41>, <41, 41>, <47, 47>, <47, 47>, <53, 53>, <53, 53>, <59, 59>, <59, 59>, <64, 2>, <64, 2>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <81, 3>, <81, 3>, <83, 83>, <89, 89>, <121, 11>, <121, 11>, <128, 2>, <128, 2>, <243, 3>, <243, 3>, <256, 2>, <256, 2>, <289, 17>, <361, 19>, <512, 2>, <512, 2>, <529, 23>, <729, 3>, <729, 3>, <841, 29>, <961, 31>, <1024, 2> ] [ <11, 11>, <11, 11>, <19, 19>, <19, 19>, <29, 29>, <29, 29>, <41, 41>, <41, 41>, <47, 47>, <47, 47>, <53, 53>, <53, 53>, <59, 59>, <59, 59>, <64, 2>, <64, 2>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <81, 3>, <81, 3>, <83, 83>, <89, 89>, <121, 11>, <121, 11>, <128, 2>, <128, 2>, <243, 3>, <243, 3>, <256, 2>, <256, 2>, <289, 17>, <361, 19>, <512, 2>, <512, 2>, <529, 23>, <729, 3>, <729, 3>, <841, 29>, <961, 31> ] [ <1, 89>, <1, 89>, <11, 11>, <11, 11>, <19, 19>, <19, 19>, <29, 29>, <29, 29>, <41, 41>, <41, 41>, <47, 47>, <47, 47>, <53, 53>, <53, 53>, <59, 59>, <59, 59>, <64, 2>, <64, 2>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <81, 3>, <81, 3>, <83, 83>, <89, 89>, <121, 11>, <121, 11>, <128, 2>, <128, 2>, <243, 3>, <243, 3>, <256, 2>, <256, 2>, <289, 17>, <361, 19>, <512, 2>, <512, 2>, <529, 23>, <729, 3>, <729, 3>, <841, 29> ] [ <1, 89>, <1, 89>, <11, 11>, <11, 11>, <19, 19>, <19, 19>, <27, 3>, <27, 3>, <29, 29>, <29, 29>, <41, 41>, <41, 41>, <47, 47>, <47, 47>, <53, 53>, <53, 53>, <59, 59>, <59, 59>, <64, 2>, <64, 2>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <81, 3>, <81, 3>, <83, 83>, <89, 89>, <121, 11>, <121, 11>, <128, 2>, <128, 2>, <243, 3>, <243, 3>, <256, 2>, <256, 2>, <289, 17>, <361, 19>, <512, 2>, <512, 2>, <529, 23>, <729, 3>, <729, 3> ] [ <1, 79>, <1, 79>, <1, 89>, <1, 89>, <11, 11>, <11, 11>, <19, 19>, <19, 19>, <27, 3>, <27, 3>, <29, 29>, <29, 29>, <41, 41>, <41, 41>, <47, 47>, <47, 47>, <53, 53>, <53, 53>, <59, 59>, <59, 59>, <64, 2>, <64, 2>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <81, 3>, <81, 3>, <83, 83>, <89, 89>, <121, 11>, <121, 11>, <128, 2>, <128, 2>, <243, 3>, <243, 3>, <256, 2>, <256, 2>, <289, 17>, <361, 19>, <512, 2>, <512, 2>, <529, 23>, <729, 3> ] [ <1, 71>, <1, 71>, <1, 79>, <1, 79>, <1, 89>, <1, 89>, <11, 11>, <11, 11>, <19, 19>, <19, 19>, <27, 3>, <27, 3>, <29, 29>, <29, 29>, <41, 41>, <41, 41>, <47, 47>, <47, 47>, <53, 53>, <53, 53>, <59, 59>, <59, 59>, <64, 2>, <64, 2>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <81, 3>, <81, 3>, <83, 83>, <89, 89>, <121, 11>, <121, 11>, <128, 2>, <128, 2>, <243, 3>, <243, 3>, <256, 2>, <256, 2>, <289, 17>, <361, 19>, <512, 2>, <512, 2>, <529, 23> ] <64, 2> Total time: 11.149 seconds, Total memory usage: 2.39MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 11:44:26 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); next:=#p; q:=p[next]; while (q[1] gt 1) do print p; K:=GF(q[1]); R := PolynomialRing(K); for a in K do if a ne 0 then if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end if; end for; Prune(~p); q[1]/:=q[2]; //Append(~p,q); //Sort(~p); for i in [1..next] do if p[i][1] ge q[1] then Insert(~p,i,q); break; end if; end for; q:=p[next]; end while; return 0; end function; mini_car(10); Output: Magma V2.10-6 Thu Mar 11 2004 11:44:08 on modular [Seed = 1870641221] ------------------------------------- [ <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5>, <3481, 59>, <3721, 61>, <4096, 2> ] [ <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5>, <3481, 59>, <3721, 61> ] [ <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5>, <3481, 59> ] [ <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5> ] [ <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <625, 5>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53> ] [ <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <625, 5>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7> ] [ <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2187, 3>, <2197, 13>, <2209, 47> ] [ <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2187, 3>, <2197, 13> ] [ <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2187, 3> ] [ <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <729, 3>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2> ] [ <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <729, 3>, <841, 29>, <961, 31>, <1024, 2>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43> ] [ <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <729, 3>, <841, 29>, <961, 31>, <1024, 2>, <1331, 11>, <1369, 37>, <1681, 41> ] [ <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <729, 3>, <841, 29>, <961, 31>, <1024, 2>, <1331, 11>, <1369, 37> ] [ <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <729, 3>, <841, 29>, <961, 31>, <1024, 2>, <1331, 11> ] [ <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <729, 3>, <841, 29>, <961, 31>, <1024, 2> ] [ <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <512, 2>, <529, 23>, <625, 5>, <729, 3>, <841, 29>, <961, 31> ] [ <31, 31>, <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <512, 2>, <529, 23>, <625, 5>, <729, 3>, <841, 29> ] [ <29, 29>, <31, 31>, <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <512, 2>, <529, 23>, <625, 5>, <729, 3> ] [ <29, 29>, <31, 31>, <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <169, 13>, <243, 3>, <289, 17>, <343, 7>, <361, 19>, <512, 2>, <529, 23>, <625, 5> ] [ <29, 29>, <31, 31>, <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <125, 5>, <169, 13>, <243, 3>, <289, 17>, <343, 7>, <361, 19>, <512, 2>, <529, 23> ] [ <23, 23>, <29, 29>, <31, 31>, <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <125, 5>, <169, 13>, <243, 3>, <289, 17>, <343, 7>, <361, 19>, <512, 2> ] [ <23, 23>, <29, 29>, <31, 31>, <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <125, 5>, <169, 13>, <243, 3>, <256, 2>, <289, 17>, <343, 7>, <361, 19> ] [ <19, 19>, <23, 23>, <29, 29>, <31, 31>, <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <125, 5>, <169, 13>, <243, 3>, <256, 2>, <289, 17>, <343, 7> ] <343, 7> Total time: 17.439 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 11:45:12 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); next:=#p; q:=p[next]; while (q[1] gt 1) do print p; K:=GF(q[1]); R := PolynomialRing(K); for a in K do if a ne 0 then if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end if; end for; Prune(~p); q[1]/:=q[2]; Append(~p,q); Sort(~p); /*for i in [1..next] do if p[i][1] ge q[1] then Insert(~p,i,q); break; end if; end for;*/ q:=p[next]; end while; return 0; end function; mini_car(10); Output: Magma V2.10-6 Thu Mar 11 2004 11:44:54 on modular [Seed = 1413776288] ------------------------------------- [ <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5>, <3481, 59>, <3721, 61>, <4096, 2> ] [ <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5>, <3481, 59>, <3721, 61> ] [ <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5>, <3481, 59> ] [ <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5> ] [ <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <625, 5>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53> ] [ <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <625, 5>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7> ] [ <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2187, 3>, <2197, 13>, <2209, 47> ] [ <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2187, 3>, <2197, 13> ] [ <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2187, 3> ] [ <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <729, 3>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2> ] [ <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <729, 3>, <841, 29>, <961, 31>, <1024, 2>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43> ] [ <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <729, 3>, <841, 29>, <961, 31>, <1024, 2>, <1331, 11>, <1369, 37>, <1681, 41> ] [ <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <729, 3>, <841, 29>, <961, 31>, <1024, 2>, <1331, 11>, <1369, 37> ] [ <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <729, 3>, <841, 29>, <961, 31>, <1024, 2>, <1331, 11> ] [ <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <729, 3>, <841, 29>, <961, 31>, <1024, 2> ] [ <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <512, 2>, <529, 23>, <625, 5>, <729, 3>, <841, 29>, <961, 31> ] [ <31, 31>, <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <512, 2>, <529, 23>, <625, 5>, <729, 3>, <841, 29> ] [ <29, 29>, <31, 31>, <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <512, 2>, <529, 23>, <625, 5>, <729, 3> ] [ <29, 29>, <31, 31>, <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <169, 13>, <243, 3>, <289, 17>, <343, 7>, <361, 19>, <512, 2>, <529, 23>, <625, 5> ] [ <29, 29>, <31, 31>, <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <125, 5>, <169, 13>, <243, 3>, <289, 17>, <343, 7>, <361, 19>, <512, 2>, <529, 23> ] [ <23, 23>, <29, 29>, <31, 31>, <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <125, 5>, <169, 13>, <243, 3>, <289, 17>, <343, 7>, <361, 19>, <512, 2> ] [ <23, 23>, <29, 29>, <31, 31>, <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <125, 5>, <169, 13>, <243, 3>, <256, 2>, <289, 17>, <343, 7>, <361, 19> ] [ <19, 19>, <23, 23>, <29, 29>, <31, 31>, <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <125, 5>, <169, 13>, <243, 3>, <256, 2>, <289, 17>, <343, 7> ] <343, 7> Total time: 17.340 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 11:48:00 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); next:=#p; q:=p[next]; while (q[1] gt 1) do print p; K:=GF(q[1]); R := PolynomialRing(K); for a in K do if a ne 0 then if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end if; end for; Prune(~p); q[1]/:=q[2]; Append(~p,q); Sort(~p); q:=p[next]; end while; return 0; end function; mini_car(10); Output: Magma V2.10-6 Thu Mar 11 2004 11:47:39 on modular [Seed = 1196924702] ------------------------------------- [ <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5>, <3481, 59>, <3721, 61>, <4096, 2> ] [ <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5>, <3481, 59>, <3721, 61> ] [ <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5>, <3481, 59> ] [ <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5> ] [ <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <625, 5>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53> ] [ <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <625, 5>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7> ] [ <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2187, 3>, <2197, 13>, <2209, 47> ] [ <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2187, 3>, <2197, 13> ] [ <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2187, 3> ] [ <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <729, 3>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2> ] [ <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <729, 3>, <841, 29>, <961, 31>, <1024, 2>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43> ] [ <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <729, 3>, <841, 29>, <961, 31>, <1024, 2>, <1331, 11>, <1369, 37>, <1681, 41> ] [ <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <729, 3>, <841, 29>, <961, 31>, <1024, 2>, <1331, 11>, <1369, 37> ] [ <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <729, 3>, <841, 29>, <961, 31>, <1024, 2>, <1331, 11> ] [ <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <729, 3>, <841, 29>, <961, 31>, <1024, 2> ] [ <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <512, 2>, <529, 23>, <625, 5>, <729, 3>, <841, 29>, <961, 31> ] [ <31, 31>, <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <512, 2>, <529, 23>, <625, 5>, <729, 3>, <841, 29> ] [ <29, 29>, <31, 31>, <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <512, 2>, <529, 23>, <625, 5>, <729, 3> ] [ <29, 29>, <31, 31>, <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <169, 13>, <243, 3>, <289, 17>, <343, 7>, <361, 19>, <512, 2>, <529, 23>, <625, 5> ] [ <29, 29>, <31, 31>, <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <125, 5>, <169, 13>, <243, 3>, <289, 17>, <343, 7>, <361, 19>, <512, 2>, <529, 23> ] [ <23, 23>, <29, 29>, <31, 31>, <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <125, 5>, <169, 13>, <243, 3>, <289, 17>, <343, 7>, <361, 19>, <512, 2> ] [ <23, 23>, <29, 29>, <31, 31>, <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <125, 5>, <169, 13>, <243, 3>, <256, 2>, <289, 17>, <343, 7>, <361, 19> ] [ <19, 19>, <23, 23>, <29, 29>, <31, 31>, <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <125, 5>, <169, 13>, <243, 3>, <256, 2>, <289, 17>, <343, 7> ] <343, 7> Total time: 18.629 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 11:48:33 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); next:=#p; q:=p[next]; while (q[1] gt 1) do print p; K:=GF(q[1]); R := PolynomialRing(K); for a in K do if a ne 0 then if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end if; end for; Prune(~p); q[1]/:=q[2]; Append(~p,q); Sort(~p); q:=p[next]; end while; return 0; end function; mini_car(10); Output: Magma V2.10-6 Thu Mar 11 2004 11:48:14 on modular [Seed = 1297978737] ------------------------------------- [ <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5>, <3481, 59>, <3721, 61>, <4096, 2> ] [ <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5>, <3481, 59>, <3721, 61> ] [ <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5>, <3481, 59> ] [ <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5> ] [ <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <625, 5>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53> ] [ <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <625, 5>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7> ] [ <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2187, 3>, <2197, 13>, <2209, 47> ] [ <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2187, 3>, <2197, 13> ] [ <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2187, 3> ] [ <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <729, 3>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2> ] [ <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <729, 3>, <841, 29>, <961, 31>, <1024, 2>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43> ] [ <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <729, 3>, <841, 29>, <961, 31>, <1024, 2>, <1331, 11>, <1369, 37>, <1681, 41> ] [ <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <729, 3>, <841, 29>, <961, 31>, <1024, 2>, <1331, 11>, <1369, 37> ] [ <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <729, 3>, <841, 29>, <961, 31>, <1024, 2>, <1331, 11> ] [ <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <729, 3>, <841, 29>, <961, 31>, <1024, 2> ] [ <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <512, 2>, <529, 23>, <625, 5>, <729, 3>, <841, 29>, <961, 31> ] [ <31, 31>, <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <512, 2>, <529, 23>, <625, 5>, <729, 3>, <841, 29> ] [ <29, 29>, <31, 31>, <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <512, 2>, <529, 23>, <625, 5>, <729, 3> ] [ <29, 29>, <31, 31>, <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <169, 13>, <243, 3>, <289, 17>, <343, 7>, <361, 19>, <512, 2>, <529, 23>, <625, 5> ] [ <29, 29>, <31, 31>, <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <125, 5>, <169, 13>, <243, 3>, <289, 17>, <343, 7>, <361, 19>, <512, 2>, <529, 23> ] [ <23, 23>, <29, 29>, <31, 31>, <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <125, 5>, <169, 13>, <243, 3>, <289, 17>, <343, 7>, <361, 19>, <512, 2> ] [ <23, 23>, <29, 29>, <31, 31>, <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <125, 5>, <169, 13>, <243, 3>, <256, 2>, <289, 17>, <343, 7>, <361, 19> ] [ <19, 19>, <23, 23>, <29, 29>, <31, 31>, <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <125, 5>, <169, 13>, <243, 3>, <256, 2>, <289, 17>, <343, 7> ] <343, 7> Total time: 17.510 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 11:51:28 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do if (k mod p eq 0) then Append(~p,); end if; next:=NextPrime(next); end while; Sort(~p); next:=#p; q:=p[next]; while (q[1] gt 1) do print p; K:=GF(q[1]); R := PolynomialRing(K); for a in K do if a ne 0 then if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end if; end for; Prune(~p); q[1]/:=q[2]; Append(~p,q); Sort(~p); q:=p[next]; end while; return 0; end function; mini_car(10); Output: Magma V2.10-6 Thu Mar 11 2004 11:51:25 on modular [Seed = 556922974] ------------------------------------- [
:3]( k: 10 ) >> if (k mod p eq 0) then ^ Runtime error in 'mod': Bad argument types Argument types given: RngIntElt, SeqEnum[Tup] Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 11:51:46 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do if (k mod next eq 0) then Append(~p,); end if; next:=NextPrime(next); end while; Sort(~p); next:=#p; q:=p[next]; while (q[1] gt 1) do print p; K:=GF(q[1]); R := PolynomialRing(K); for a in K do if a ne 0 then if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end if; end for; Prune(~p); q[1]/:=q[2]; Append(~p,q); Sort(~p); q:=p[next]; end while; return 0; end function; mini_car(10); Output: Magma V2.10-6 Thu Mar 11 2004 11:51:40 on modular [Seed = 775878464] ------------------------------------- [ <3125, 5>, <4096, 2> ] [ <2048, 2>, <3125, 5> ] [ <625, 5>, <2048, 2> ] [ <625, 5>, <1024, 2> ] [ <512, 2>, <625, 5> ] [ <125, 5>, <512, 2> ] [ <125, 5>, <256, 2> ] [ <125, 5>, <128, 2> ] [ <64, 2>, <125, 5> ] [ <25, 5>, <64, 2> ] <64, 2> Total time: 6.389 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host facultypc-210.faculty.iu-bremen.de. (212.201.48.210) Time: Thu Mar 11 11:53:00 2004 Input: G:=Group( a,t | a^11=t^2=1,a^t=a^-1 ); Output: Magma V2.10-6 Thu Mar 11 2004 11:52:57 on modular [Seed = 386387468] ------------------------------------- >> G:=Group( a,t | a^11=t^2=1,a^t=a^-1 ); ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host facultypc-210.faculty.iu-bremen.de. (212.201.48.210) Time: Thu Mar 11 11:53:03 2004 Input: G:=Group( a,t | a^11=t^2=1,a^t=a^-1 ); Output: Magma V2.10-6 Thu Mar 11 2004 11:53:00 on modular [Seed = 403226886] ------------------------------------- >> G:=Group( a,t | a^11=t^2=1,a^t=a^-1 ); ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host facultypc-210.faculty.iu-bremen.de. (212.201.48.210) Time: Thu Mar 11 11:54:02 2004 Input: G:=Group< a,t | a^11=t^2=1,a^t=a^-1 >; Output: Magma V2.10-6 Thu Mar 11 2004 11:53:58 on modular [Seed = 85318864] ------------------------------------- Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host facultypc-210.faculty.iu-bremen.de. (212.201.48.210) Time: Thu Mar 11 11:54:12 2004 Input: G:=Group< a,t | a^11=t^2=1,a^t=a^-1 >; G; Output: Magma V2.10-6 Thu Mar 11 2004 11:54:09 on modular [Seed = 4091750960] ------------------------------------- Finitely presented group G on 2 generators Relations a^11 = Id(G) t^2 = Id(G) a^t = a^-1 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 11:54:30 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; b,c:=IsPrimePower(k); while (next lt k*(k-1)) do if (next ne c) then Append(~p,); end if; next:=NextPrime(next); end while; Sort(~p); next:=#p; q:=p[next]; print p; while (q[1] gt 1) do K:=GF(q[1]); R := PolynomialRing(K); for a in K do if a ne 0 then if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end if; end for; Prune(~p); q[1]/:=q[2]; Append(~p,q); Sort(~p); q:=p[next]; end while; return 0; end function; mini_car(10); Output: Magma V2.10-6 Thu Mar 11 2004 11:54:27 on modular [Seed = 4192804936] ------------------------------------- [
:3]( k: 10 ) >> if (next ne c) then ^ Runtime error: Variable 'c' has not been initialized Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host facultypc-210.faculty.iu-bremen.de. (212.201.48.210) Time: Thu Mar 11 11:54:37 2004 Input: G:=Group< a,t | a^11=t^2=1,a^t=a^-1 >; a^-1; Output: Magma V2.10-6 Thu Mar 11 2004 11:54:33 on modular [Seed = 3874897758] ------------------------------------- a^-1 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host facultypc-210.faculty.iu-bremen.de. (212.201.48.210) Time: Thu Mar 11 11:54:45 2004 Input: G:=Group< a,t | a^11=t^2=1,a^t=a^-1 >; a^10; Output: Magma V2.10-6 Thu Mar 11 2004 11:54:42 on modular [Seed = 4026480207] ------------------------------------- a^10 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host facultypc-210.faculty.iu-bremen.de. (212.201.48.210) Time: Thu Mar 11 11:54:57 2004 Input: G:=Group< a,t | a^11=t^2=1,a^t=a^-1 >; a^10*a; Output: Magma V2.10-6 Thu Mar 11 2004 11:54:54 on modular [Seed = 3569618296] ------------------------------------- a^11 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.211.77) Time: Thu Mar 11 11:55:10 2004 Input: olav_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ) end function; olav_qr(7,3); Output: Magma V2.10-6 Thu Mar 11 2004 11:55:07 on modular [Seed = 3251705944] ------------------------------------- >> end function; ^ User error: bad syntax >> olav_qr(7,3);; ^ User error: Identifier 'olav_qr' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 11:55:24 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; b,c:=IsPrimePower(k); while (next lt k*(k-1)) do if (b & (next ne c)) then Append(~p,); end if; next:=NextPrime(next); end while; Sort(~p); next:=#p; q:=p[next]; print p; while (q[1] gt 1) do K:=GF(q[1]); R := PolynomialRing(K); for a in K do if a ne 0 then if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end if; end for; Prune(~p); q[1]/:=q[2]; Append(~p,q); Sort(~p); q:=p[next]; end while; return 0; end function; mini_car(10); Output: Magma V2.10-6 Thu Mar 11 2004 11:55:21 on modular [Seed = 3470661445] ------------------------------------- >> if (b & (next ne c)) then ^ User error: Bad reduction operator >> Append(~p,); ^ User error: Identifier 'next' has not been declared or assigned >> end if; ^ User error: bad syntax >> next:=NextPrime(next); ^ User error: Identifier 'next' has not been declared or assigned >> end while; ^ User error: bad syntax >> Sort(~p); ^ Runtime error in 'Sort': Argument 1 has not been initialized Argument types given: *nothing ~ >> next:=#p; ^ User error: Identifier 'p' has not been declared or assigned >> q:=p[next]; ^ User error: Identifier 'p' has not been declared or assigned >> print p; ^ User error: Identifier 'p' has not been declared or assigned >> while (q[1] gt 1) do ^ User error: Identifier 'q' has not been declared or assigned >> return 0; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> mini_car(10);; ^ User error: Identifier 'mini_car' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 11:55:35 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; b,c:=IsPrimePower(k); while (next lt k*(k-1)) do if (b and (next ne c)) then Append(~p,); end if; next:=NextPrime(next); end while; Sort(~p); next:=#p; q:=p[next]; print p; while (q[1] gt 1) do K:=GF(q[1]); R := PolynomialRing(K); for a in K do if a ne 0 then if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end if; end for; Prune(~p); q[1]/:=q[2]; Append(~p,q); Sort(~p); q:=p[next]; end while; return 0; end function; mini_car(10); Output: Magma V2.10-6 Thu Mar 11 2004 11:55:32 on modular [Seed = 3081203137] ------------------------------------- [
:3]( k: 10 ) >> q:=p[next]; ^ Runtime error in '[]': Sequence element 0 not defined Total time: 3.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host facultypc-210.faculty.iu-bremen.de. (212.201.48.210) Time: Thu Mar 11 11:55:38 2004 Input: G:=Group< a,t | a^11=t^2=1,a^t=a^-1 >; Order(G); Output: Magma V2.10-6 Thu Mar 11 2004 11:55:35 on modular [Seed = 3131728079] ------------------------------------- 22 Total time: 3.139 seconds, Total memory usage: 17.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.211.77) Time: Thu Mar 11 11:56:42 2004 Input: t_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; n_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; olav_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ) end function; olav_qr(7,3); Output: Magma V2.10-6 Thu Mar 11 2004 11:56:39 on modular [Seed = 2864345247] ------------------------------------- >> end function; ^ User error: bad syntax >> olav_qr(7,3);; ^ User error: Identifier 'olav_qr' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.211.77) Time: Thu Mar 11 11:57:24 2004 Input: t_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; n_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; n_qr(7,3); t_qr(7,3); Output: Magma V2.10-6 Thu Mar 11 2004 11:57:21 on modular [Seed = 2474854800] ------------------------------------- x^57 x^49 + x^7 + x Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 11:57:45 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; b,c:=IsPrimePower(k); while (next lt k*(k-1)) do if (not (b and next ne c)) then Append(~p,); end if; next:=NextPrime(next); end while; Sort(~p); next:=#p; q:=p[next]; print p; while (q[1] gt 1) do K:=GF(q[1]); R := PolynomialRing(K); for a in K do if a ne 0 then if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end if; end for; Prune(~p); q[1]/:=q[2]; Append(~p,q); Sort(~p); q:=p[next]; end while; return 0; end function; mini_car(10); Output: Magma V2.10-6 Thu Mar 11 2004 11:57:28 on modular [Seed = 2559066770] ------------------------------------- [ <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5>, <3481, 59>, <3721, 61>, <4096, 2> ] <343, 7> Total time: 17.129 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.211.77) Time: Thu Mar 11 11:57:51 2004 Input: t_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; n_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; olav_qr:= function (q,r) exp:= func ; return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ) end function; n_qr(7,3); t_qr(7,3); Output: Magma V2.10-6 Thu Mar 11 2004 11:57:49 on modular [Seed = 2173787006] ------------------------------------- >> end function; ^ User error: bad syntax x^57 x^49 + x^7 + x Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host facultypc-210.faculty.iu-bremen.de. (212.201.48.210) Time: Thu Mar 11 11:58:09 2004 Input: G:=Group< a,t | a^10=t^2=1,a^t=a^-1 >; S:=sub< G | a^2,t >; S; Output: Magma V2.10-6 Thu Mar 11 2004 11:58:06 on modular [Seed = 2375898977] ------------------------------------- Finitely presented group S on 2 generators Generators as words in group G S.1 = a^2 S.2 = t Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 11:58:13 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; b,c:=IsPrimePower(k); while (next lt k*(k-1)) do if (not (b and next eq c)) then Append(~p,); end if; next:=NextPrime(next); end while; Sort(~p); next:=#p; q:=p[next]; print p; while (q[1] gt 1) do K:=GF(q[1]); R := PolynomialRing(K); for a in K do if a ne 0 then if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end if; end for; Prune(~p); q[1]/:=q[2]; Append(~p,q); Sort(~p); q:=p[next]; end while; return 0; end function; mini_car(10); Output: Magma V2.10-6 Thu Mar 11 2004 11:57:56 on modular [Seed = 2392740968] ------------------------------------- [ <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5>, <3481, 59>, <3721, 61>, <4096, 2> ] <343, 7> Total time: 17.059 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.211.77) Time: Thu Mar 11 11:59:13 2004 Input: t_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; n_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; exp:= func ; olav_qr:= function (q,r) exp:= func ; return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ) end function; n_qr(7,3); t_qr(7,3); Output: Magma V2.10-6 Thu Mar 11 2004 11:59:10 on modular [Seed = 1634843596] ------------------------------------- >> end function; ^ User error: bad syntax x^57 x^49 + x^7 + x Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 11:59:14 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; b,c:=IsPrimePower(k); borne:=(k-2)^4+4*k-4; while (next lt k*(k-1)) do if (not (b and next eq c)) then Append(~p,); end if; next:=NextPrime(next); end while; Sort(~p); next:=#p; q:=p[next]; print p; while (q[1] gt 1) do K:=GF(q[1]); R := PolynomialRing(K); for a in K do if a ne 0 then if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end if; end for; Prune(~p); q[1]/:=q[2]; Append(~p,q); Sort(~p); q:=p[next]; end while; return 0; end function; mini_car(10); Output: Magma V2.10-6 Thu Mar 11 2004 11:58:57 on modular [Seed = 2104338399] ------------------------------------- [ <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5>, <3481, 59>, <3721, 61>, <4096, 2> ] <343, 7> Total time: 17.209 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 11:59:49 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; b,c:=IsPrimePower(k); borne:=(k-2)^4+4*k-4; while (next lt k*(k-1)) do if (not (b and next eq c)) then Append(~p,); end if; next:=NextPrime(next); end while; Sort(~p); next:=#p; q:=p[next]; print p; while (q[1] gt 1) do K:=GF(q[1]); R := PolynomialRing(K); for a in K do if a ne 0 then if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end if; end for; Prune(~p); q[1]/:=q[2]; Append(~p,q); Sort(~p); q:=p[next]; end while; return 0; end function; mini_car(10); Output: Magma V2.10-6 Thu Mar 11 2004 11:59:31 on modular [Seed = 1380092117] ------------------------------------- [ <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5>, <3481, 59>, <3721, 61>, <4096, 2> ] <343, 7> Total time: 17.159 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 12:00:02 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; b,c:=IsPrimePower(k); borne:=(k-2)^4+4*k-4; while (next lt k*(k-1)) do if (not (b and next eq c)) then Append(~p,); end if; next:=NextPrime(next); end while; Sort(~p); next:=#p; q:=p[next]; print p; while (q[1] gt 1) do K:=GF(q[1]); R := PolynomialRing(K); for a in K do if a ne 0 then if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end if; end for; Prune(~p); q[1]/:=q[2]; Append(~p,q); Sort(~p); q:=p[next]; end while; return 0; end function; mini_car(2); Output: Magma V2.10-6 Thu Mar 11 2004 11:59:59 on modular [Seed = 1481147172] ------------------------------------- [
:3]( k: 2 ) >> q:=p[next]; ^ Runtime error in '[]': Sequence element 0 not defined Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host facultypc-210.faculty.iu-bremen.de. (212.201.48.210) Time: Thu Mar 11 12:00:14 2004 Input: G:=Group< a,t | a^10=t^2=1,a^t=a^-1 >; S:=sub< G | a^2,t >; IsTrivial(S) Output: Magma V2.10-6 Thu Mar 11 2004 12:00:10 on modular [Seed = 857991258] ------------------------------------- >> S:=sub< G | a^2,t >; IsTrivial(S) ^ Runtime error in 'IsTrivial': Bad argument types Argument types given: GrpFP Total time: 3.779 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 12:00:14 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; b,c:=IsPrimePower(k); borne:=(k-2)^4+4*k-4; while (next lt k*(k-1)) do if (not (b and next eq c)) then Append(~p,); end if; next:=NextPrime(next); end while; Sort(~p); next:=#p; q:=p[next]; print p; while (q[1] gt 1) do K:=GF(q[1]); R := PolynomialRing(K); for a in K do if a ne 0 then if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end if; end for; Prune(~p); q[1]/:=q[2]; Append(~p,q); Sort(~p); q:=p[next]; end while; return 0; end function; mini_car(3); Output: Magma V2.10-6 Thu Mar 11 2004 12:00:10 on modular [Seed = 1297978916] ------------------------------------- [ <5, 5>, <8, 2> ] 0 Total time: 3.869 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host facultypc-210.faculty.iu-bremen.de. (212.201.48.210) Time: Thu Mar 11 12:00:21 2004 Input: G:=Group< a,t | a^10=t^2=1,a^t=a^-1 >; S:=sub< G | a^2,t >; IsTrivial(S); Output: Magma V2.10-6 Thu Mar 11 2004 12:00:18 on modular [Seed = 1009575789] ------------------------------------- >> S:=sub< G | a^2,t >; IsTrivial(S); ^ Runtime error in 'IsTrivial': Bad argument types Argument types given: GrpFP Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 12:00:26 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; b,c:=IsPrimePower(k); borne:=(k-2)^4+4*k-4; while (next lt k*(k-1)) do if (not (b and next eq c)) then Append(~p,); end if; next:=NextPrime(next); end while; Sort(~p); next:=#p; q:=p[next]; print p; while (q[1] gt 1) do K:=GF(q[1]); R := PolynomialRing(K); for a in K do if a ne 0 then if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end if; end for; Prune(~p); q[1]/:=q[2]; Append(~p,q); Sort(~p); q:=p[next]; end while; return 0; end function; mini_car(4); Output: Magma V2.10-6 Thu Mar 11 2004 12:00:22 on modular [Seed = 725348478] ------------------------------------- [ <7, 7>, <11, 11>, <25, 5>, <27, 3> ] <7, 7> Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.211.77) Time: Thu Mar 11 12:00:30 2004 Input: t_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; n_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; exp:= func ; olav_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ); end function; n_qr(7,3); t_qr(7,3); olav(7,3); Output: Magma V2.10-6 Thu Mar 11 2004 12:00:27 on modular [Seed = 302172490] ------------------------------------- x^57 x^49 + x^7 + x >> olav(7,3); ^ User error: Identifier 'olav' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 12:00:46 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; b,c:=IsPrimePower(k); borne:=(k-2)^4+4*k-4; while (next lt k*(k-1)) do if (not (b and next eq c)) then Append(~p,); end if; next:=NextPrime(next); end while; Sort(~p); next:=#p; q:=p[next]; print p; while (q[1] gt 1) do K:=GF(q[1]); R := PolynomialRing(K); for a in K do if a ne 0 then if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end if; end for; Prune(~p); q[1]/:=q[2]; Append(~p,q); Sort(~p); q:=p[next]; end while; return 0; end function; mini_car(5); Output: Magma V2.10-6 Thu Mar 11 2004 12:00:42 on modular [Seed = 420069968] ------------------------------------- [ <11, 11>, <13, 13>, <17, 17>, <19, 19>, <49, 7>, <64, 2>, <81, 3> ] <9, 3> Total time: 3.619 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host facultypc-210.faculty.iu-bremen.de. (212.201.48.210) Time: Thu Mar 11 12:00:48 2004 Input: G:=Group< a,t | a^10=t^2=1,a^t=a^-1 >; S:=sub< G | a^2,t >; Type(S); Type(G); Output: Magma V2.10-6 Thu Mar 11 2004 12:00:43 on modular [Seed = 51632203] ------------------------------------- GrpFP GrpFP Total time: 3.649 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host facultypc-210.faculty.iu-bremen.de. (212.201.48.210) Time: Thu Mar 11 12:01:03 2004 Input: G:=Group< a,t | a^10=t^2=1,a^t=a^-1 >; S:=sub< G | a^2,t >; IsTrivial(S); Output: Magma V2.10-6 Thu Mar 11 2004 12:01:00 on modular [Seed = 203216691] ------------------------------------- >> S:=sub< G | a^2,t >; IsTrivial(S); ^ Runtime error in 'IsTrivial': Bad argument types Argument types given: GrpFP Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.211.77) Time: Thu Mar 11 12:01:08 2004 Input: t_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; n_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; exp:= func ; olav_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ); end function; n_qr(7,3); t_qr(7,3); olav_qr(7,3); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 11 2004 12:00:43 on modular [Seed = 504284502] ------------------------------------- x^57 x^49 + x^7 + x Errors: /home/mfd/gomagma: line 2: 13165 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 12:01:10 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; b,c:=IsPrimePower(k); borne:=(k-2)^4+4*k-4; while (next lt k*(k-1)) do if (not (b and next eq c)) then Append(~p,); end if; next:=NextPrime(next); end while; Sort(~p); next:=#p; q:=p[next]; print p; while (q[1] gt 1) do K:=GF(q[1]); R := PolynomialRing(K); for a in K do if a ne 0 then if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end if; end for; Prune(~p); q[1]/:=q[2]; Append(~p,q); Sort(~p); q:=p[next]; end while; return 0; end function; mini_car(7); Output: Magma V2.10-6 Thu Mar 11 2004 12:01:06 on modular [Seed = 3925422792] ------------------------------------- [ <29, 29>, <31, 31>, <37, 37>, <41, 41>, <121, 11>, <169, 13>, <243, 3>, <289, 17>, <361, 19>, <512, 2>, <529, 23>, <625, 5> ] <25, 5> Total time: 3.979 seconds, Total memory usage: 2.39MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 12:01:39 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; b,c:=IsPrimePower(k); borne:=(k-2)^4+4*k-4; while (next lt k*(k-1)) do if (not (b and next eq c)) then Append(~p,); end if; next:=NextPrime(next); end while; Sort(~p); next:=#p; q:=p[next]; print p; while (q[1] gt 1) do K:=GF(q[1]); R := PolynomialRing(K); for a in K do if a ne 0 then if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end if; end for; Prune(~p); q[1]/:=q[2]; Append(~p,q); Sort(~p); q:=p[next]; end while; return 0; end function; mini_car(8); Output: Magma V2.10-6 Thu Mar 11 2004 12:01:34 on modular [Seed = 3754886338] ------------------------------------- [ <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <121, 11>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <729, 3>, <841, 29>, <961, 31> ] <29, 29> Total time: 4.699 seconds, Total memory usage: 2.39MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.211.77) Time: Thu Mar 11 12:01:48 2004 Input: t_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; n_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; exp:= func ; olav_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ); end function; n_qr(7,3); t_qr(7,3); #olav_qr(7,3); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 11 2004 12:01:25 on modular [Seed = 3670671820] ------------------------------------- x^57 x^49 + x^7 + x Errors: /home/mfd/gomagma: line 2: 13225 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 12:02:05 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; b,c:=IsPrimePower(k); borne:=(k-2)^4+4*k-4; while (next lt k*(k-1)) do if (not (b and next eq c)) then Append(~p,); end if; next:=NextPrime(next); end while; Sort(~p); next:=#p; q:=p[next]; print p; while (q[1] gt 1) do K:=GF(q[1]); R := PolynomialRing(K); for a in K do if a ne 0 then if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end if; end for; Prune(~p); q[1]/:=q[2]; Append(~p,q); Sort(~p); q:=p[next]; end while; return 0; end function; mini_car(9); Output: Magma V2.10-6 Thu Mar 11 2004 12:01:55 on modular [Seed = 3369603896] ------------------------------------- [ <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <289, 17>, <361, 19>, <529, 23>, <625, 5>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2197, 13>, <2209, 47>, <2401, 7> ] <25, 5> Total time: 10.170 seconds, Total memory usage: 2.29MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.211.77) Time: Thu Mar 11 12:02:17 2004 Input: t_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; n_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; exp:= func ; olav_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ); end function; n_qr(7,3); t_qr(7,3); #olav_qr(4,3); Output: Magma V2.10-6 Thu Mar 11 2004 12:02:13 on modular [Seed = 3081202769] ------------------------------------- x^57 x^49 + x^7 + x 1024 Total time: 3.619 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 12:02:45 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; b,c:=IsPrimePower(k); borne:=(k-2)^4+4*k-4; while (next lt k*(k-1)) do if (not (b and next eq c)) then Append(~p,); end if; next:=NextPrime(next); end while; Sort(~p); next:=#p; q:=p[next]; print p; while (q[1] gt 1) do K:=GF(q[1]); R := PolynomialRing(K); for a in K do if a ne 0 then if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end if; end for; Prune(~p); q[1]/:=q[2]; Append(~p,q); Sort(~p); q:=p[next]; end while; return 0; end function; mini_car(11); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 11 2004 12:02:22 on modular [Seed = 3182257744] ------------------------------------- [ <83, 83>, <89, 89>, <97, 97>, <101, 101>, <103, 103>, <107, 107>, <109, 109>, <361, 19>, <529, 23>, <841, 29>, <961, 31>, <1369, 37>, <1681, 41>, <1849, 43>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5>, <3481, 59>, <3721, 61>, <4096, 2>, <4489, 67>, <4913, 17>, <5041, 71>, <5329, 73>, <6241, 79>, <6561, 3> ] Errors: /home/mfd/gomagma: line 2: 13262 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.211.77) Time: Thu Mar 11 12:03:03 2004 Input: t_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; n_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; exp:= func ; olav_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ); end function; n_qr(7,3); t_qr(7,3); #olav_qr(4,3); #olav_qr(4,1); Output: Magma V2.10-6 Thu Mar 11 2004 12:02:59 on modular [Seed = 2847502873] ------------------------------------- x^57 x^49 + x^7 + x 1024 4 Total time: 3.689 seconds, Total memory usage: 1.91MB ************** MAGMA ***************** Host www-rocqbis.inria.fr. (192.93.2.12) Time: Thu Mar 11 12:03:16 2004 Input: mini_car:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; b,c:=IsPrimePower(k); borne:=(k-2)^4+4*k-4; while (next lt k*(k-1)) do if (not (b and next eq c)) then Append(~p,); end if; next:=NextPrime(next); end while; Sort(~p); next:=#p; q:=p[next]; print p; while (q[1] gt 1) do K:=GF(q[1]); R := PolynomialRing(K); for a in K do if a ne 0 then if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end if; end for; Prune(~p); q[1]/:=q[2]; Append(~p,q); Sort(~p); q:=p[next]; end while; return 0; end function; mini_car(11); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 11 2004 12:02:53 on modular [Seed = 2763292522] ------------------------------------- [ <83, 83>, <89, 89>, <97, 97>, <101, 101>, <103, 103>, <107, 107>, <109, 109>, <361, 19>, <529, 23>, <841, 29>, <961, 31>, <1369, 37>, <1681, 41>, <1849, 43>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5>, <3481, 59>, <3721, 61>, <4096, 2>, <4489, 67>, <4913, 17>, <5041, 71>, <5329, 73>, <6241, 79>, <6561, 3> ] Errors: /home/mfd/gomagma: line 2: 13271 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.211.77) Time: Thu Mar 11 12:06:51 2004 Input: t_qr:= function (q,r) P:=PolynomialRing(Integers()); exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; n_qr:= function (q,r) P:=PolynomialRing(Integers()); exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; exp:= func ; olav_qr:= function (q,r) P:=PolynomialRing(Integers()); exp:= func ; return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ); end function; n_qr(7,3); t_qr(7,3); #olav_qr(4,3); #olav_qr(4,1); Output: Magma V2.10-6 Thu Mar 11 2004 12:06:47 on modular [Seed = 2626437192] ------------------------------------- x^57 x^49 + x^7 + x 1024 4 Total time: 3.629 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.211.77) Time: Thu Mar 11 12:09:58 2004 Input: t_qr:= function (q,r) P:=PolynomialRing(Integers()); exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; n_qr:= function (q,r) P:=PolynomialRing(Integers()); exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; exp:= func ; olav_qr:= function (q,r) P:=PolynomialRing(Integers()); exp:= func ; return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ); end function; n_qr(7,3); t_qr(7,3); #olav_qr(4,3); #olav_qr(4,1); #olav_qr(5,3) eq 5^(2*3-1); Output: Magma V2.10-6 Thu Mar 11 2004 12:09:53 on modular [Seed = 2308527259] ------------------------------------- x^57 x^49 + x^7 + x 1024 4 true Total time: 5.799 seconds, Total memory usage: 2.13MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.211.77) Time: Thu Mar 11 12:19:58 2004 Input: t_qr:= function (q,r) P:=PolynomialRing(Integers()); exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; n_qr:= function (q,r) P:=PolynomialRing(Integers()); exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; exp:= func ; olav_qr:= function (q,r) P:=PolynomialRing(Integers()); exp:= func ; return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ); end function; olav_q:= function (q,r) return ( { : a,b in GF(q) | in olav_qr(q,r) }); end function; n_qr(7,3); t_qr(7,3); #olav_qr(4,3); #olav_qr(4,1); #olav_qr(5,3) eq 5^(2*3-1); #olav_q(7,3); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 11 2004 12:19:35 on modular [Seed = 1651686833] ------------------------------------- x^57 x^49 + x^7 + x 1024 4 true Errors: /home/mfd/gomagma: line 2: 13334 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.211.77) Time: Thu Mar 11 12:20:18 2004 Input: t_qr:= function (q,r) P:=PolynomialRing(Integers()); exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; n_qr:= function (q,r) P:=PolynomialRing(Integers()); exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; exp:= func ; olav_qr:= function (q,r) P:=PolynomialRing(Integers()); exp:= func ; return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ); end function; olav_q:= function (q,r) return ( { : a,b in GF(q) | in olav_qr(q,r) }); end function; n_qr(7,3); t_qr(7,3); #olav_qr(4,3); #olav_qr(4,1); #olav_qr(5,3) eq 5^(2*3-1); #olav_q(6,3); Output: Magma V2.10-6 Thu Mar 11 2004 12:20:12 on modular [Seed = 1380093418] ------------------------------------- x^57 x^49 + x^7 + x 1024 4 true [
:19]( q: 6, r: 3 ) >> return ( { : a,b in GF(q) | in olav_qr(q,r) }); ^ Runtime error in 'GF': Argument 1 (6) is not a prime power Total time: 5.770 seconds, Total memory usage: 2.13MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.211.77) Time: Thu Mar 11 12:21:25 2004 Input: t_qr:= function (q,r) P:=PolynomialRing(Integers()); exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; n_qr:= function (q,r) P:=PolynomialRing(Integers()); exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; exp:= func ; olav_qr:= function (q,r) P:=PolynomialRing(Integers()); exp:= func ; return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ); end function; olav_q:= function (q,r) return ( { : a,b in GF(q) | in olav_qr(q,r) }); end function; n_qr(7,3); t_qr(7,3); #olav_qr(4,3); #olav_qr(4,1); #olav_qr(5,3) eq 5^(2*3-1); #olav_q(7,2); Output: Magma V2.10-6 Thu Mar 11 2004 12:21:06 on modular [Seed = 1146397746] ------------------------------------- x^57 x^49 + x^7 + x 1024 4 true 7 Total time: 19.229 seconds, Total memory usage: 2.13MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.211.77) Time: Thu Mar 11 12:22:10 2004 Input: t_qr:= function (q,r) P:=PolynomialRing(Integers()); exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; n_qr:= function (q,r) P:=PolynomialRing(Integers()); exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; exp:= func ; olav_qr:= function (q,r) P:=PolynomialRing(Integers()); exp:= func ; return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ); end function; olav_q:= function (q,r) return ( { : a,b in GF(q) | in olav_qr(q,r) }); end function; n_qr(7,3); t_qr(7,3); #olav_qr(4,3); #olav_qr(4,1); #olav_qr(5,3) eq 5^(2*3-1); #olav_q(12,2); Output: Magma V2.10-6 Thu Mar 11 2004 12:22:05 on modular [Seed = 1297984772] ------------------------------------- x^57 x^49 + x^7 + x 1024 4 true [
:19]( q: 12, r: 2 ) >> return ( { : a,b in GF(q) | in olav_qr(q,r) }); ^ Runtime error in 'GF': Argument 1 (12) is not a prime power Total time: 5.799 seconds, Total memory usage: 2.13MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.211.77) Time: Thu Mar 11 12:23:51 2004 Input: t_qr:= function (q,r) P:=PolynomialRing(Integers()); exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; n_qr:= function (q,r) P:=PolynomialRing(Integers()); exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; exp:= func ; olav_qr:= function (q,r) P:=PolynomialRing(Integers()); exp:= func ; return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ); end function; olav_q:= function (q,r) return ( { : a,b in GF(q) | in olav_qr(q,r) }); end function; n_qr(7,3); t_qr(7,3); #olav_qr(4,3); #olav_qr(4,1); #olav_qr(5,3) eq 5^(2*3-1); #olav_q(10,2); Output: Magma V2.10-6 Thu Mar 11 2004 12:23:46 on modular [Seed = 925358049] ------------------------------------- x^57 x^49 + x^7 + x 1024 4 true [
:19]( q: 10, r: 2 ) >> return ( { : a,b in GF(q) | in olav_qr(q,r) }); ^ Runtime error in 'GF': Argument 1 (10) is not a prime power Total time: 5.750 seconds, Total memory usage: 2.13MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.211.77) Time: Thu Mar 11 12:24:28 2004 Input: t_qr:= function (q,r) P:=PolynomialRing(Integers()); exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; n_qr:= function (q,r) P:=PolynomialRing(Integers()); exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; exp:= func ; olav_qr:= function (q,r) P:=PolynomialRing(Integers()); exp:= func ; return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ); end function; olav_q:= function (q,r) return ( { : a,b in GF(q) | in olav_qr(q,r) }); end function; n_qr(7,3); t_qr(7,3); #olav_qr(4,3); #olav_qr(4,1); #olav_qr(5,3) eq 5^(2*3-1); #olav_q(9,2); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 11 2004 12:24:05 on modular [Seed = 959044088] ------------------------------------- x^57 x^49 + x^7 + x 1024 4 true Errors: /home/mfd/gomagma: line 2: 13389 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.211.77) Time: Thu Mar 11 12:24:48 2004 Input: t_qr:= function (q,r) P:=PolynomialRing(Integers()); exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; n_qr:= function (q,r) P:=PolynomialRing(Integers()); exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; exp:= func ; olav_qr:= function (q,r) P:=PolynomialRing(Integers()); exp:= func ; return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ); end function; olav_q:= function (q,r) return ( { : a,b in GF(q) | in olav_qr(q,r) }); end function; n_qr(7,3); t_qr(7,3); #olav_qr(4,3); #olav_qr(4,1); #olav_qr(5,3) eq 5^(2*3-1); #olav_q(9,1); Output: Magma V2.10-6 Thu Mar 11 2004 12:24:41 on modular [Seed = 573751951] ------------------------------------- x^57 x^49 + x^7 + x 1024 4 true 9 Total time: 6.579 seconds, Total memory usage: 2.13MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.211.77) Time: Thu Mar 11 12:27:02 2004 Input: t_qr:= function (q,r) P:=PolynomialRing(Integers()); exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; n_qr:= function (q,r) P:=PolynomialRing(Integers()); exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; exp:= func ; olav_qr:= function (q,r) P:=PolynomialRing(Integers()); exp:= func ; return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ); end function; olav_q:= function (q,r) return ( { : a,b in GF(q) | in olav_qr(q,r) }); end function; n_qr(7,3); t_qr(7,3); #olav_qr(4,3); #olav_qr(4,3) eq 4^(2*3-1); #olav_qr(4,1); #olav_qr(6,3) eq 4^(6*3-1); #olav_qr(5,3) eq 5^(2*3-1); #olav_q(9,1); Output: Magma V2.10-6 Thu Mar 11 2004 12:26:54 on modular [Seed = 268497210] ------------------------------------- x^57 x^49 + x^7 + x 1024 true 4 [
:14]( q: 6, r: 3 ) >> return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluat ^ Runtime error in 'GF': Argument 1 (216) is not a prime power true 9 Total time: 7.109 seconds, Total memory usage: 2.13MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.211.77) Time: Thu Mar 11 12:27:49 2004 Input: t_qr:= function (q,r) P:=PolynomialRing(Integers()); exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; n_qr:= function (q,r) P:=PolynomialRing(Integers()); exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; exp:= func ; olav_qr:= function (q,r) P:=PolynomialRing(GF(7^3)); exp:= func ; return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ); end function; olav_q:= function (q,r) return ( { : a,b in GF(q) | in olav_qr(q,r) }); end function; n_qr(7,3); t_qr(7,3); #olav_qr(4,3); #olav_qr(4,3) eq 4^(2*3-1); #olav_qr(4,1); #olav_qr(6,3) eq 4^(6*3-1); #olav_qr(5,3) eq 5^(2*3-1); #olav_q(9,1); Output: Magma V2.10-6 Thu Mar 11 2004 12:27:42 on modular [Seed = 420083939] ------------------------------------- x^57 x^49 + x^7 + x 1024 true 4 [
:14]( q: 6, r: 3 ) >> return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluat ^ Runtime error in 'GF': Argument 1 (216) is not a prime power true 9 Total time: 7.079 seconds, Total memory usage: 2.14MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.211.77) Time: Thu Mar 11 12:28:41 2004 Input: t_qr:= function (q,r) P:=PolynomialRing(GF(7^3));); exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; n_qr:= function (q,r) P:=PolynomialRing(GF(7^3));); exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; exp:= func ; olav_qr:= function (q,r) P:=PolynomialRing(GF(7^3)); exp:= func ; return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ); end function; olav_q:= function (q,r) return ( { : a,b in GF(q) | in olav_qr(q,r) }); end function; n_qr(7,3); t_qr(7,3); #olav_qr(4,3); #olav_qr(4,3) eq 4^(2*3-1); #olav_qr(4,1); #olav_qr(6,3) eq 4^(6*3-1); #olav_qr(5,3) eq 5^(2*3-1); #olav_q(9,1); Output: Magma V2.10-6 Thu Mar 11 2004 12:28:38 on modular [Seed = 152692923] ------------------------------------- >> P:=PolynomialRing(GF(7^3));); ^ User error: bad syntax >> return ( &+[x^i : i in exp(q,r)] ); ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> P:=PolynomialRing(GF(7^3));); ^ User error: bad syntax >> return ( x^(&+[j : j in exp(q,r)]) ); ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluat ^ User error: Identifier 'n_qr' has not been declared or assigned >> return ( { : a,b in GF(q) | in olav_qr(q,r) }); ^ User error: Identifier 'olav_qr' has not been declared or assigned >> n_qr(7,3); ^ User error: Identifier 'n_qr' has not been declared or assigned >> t_qr(7,3); ^ User error: Identifier 't_qr' has not been declared or assigned >> #olav_qr(4,3); ^ User error: Identifier 'olav_qr' has not been declared or assigned >> #olav_qr(4,3) eq 4^(2*3-1); ^ User error: Identifier 'olav_qr' has not been declared or assigned >> #olav_qr(4,1); ^ User error: Identifier 'olav_qr' has not been declared or assigned >> #olav_qr(6,3) eq 4^(6*3-1); ^ User error: Identifier 'olav_qr' has not been declared or assigned >> #olav_qr(5,3) eq 5^(2*3-1); ^ User error: Identifier 'olav_qr' has not been declared or assigned >> #olav_q(9,1); ^ User error: Identifier 'olav_q' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.211.77) Time: Thu Mar 11 12:28:53 2004 Input: t_qr:= function (q,r) P:=PolynomialRing(GF(7^3)); exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; n_qr:= function (q,r) P:=PolynomialRing(GF(7^3));); exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; exp:= func ; olav_qr:= function (q,r) P:=PolynomialRing(GF(7^3)); exp:= func ; return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ); end function; olav_q:= function (q,r) return ( { : a,b in GF(q) | in olav_qr(q,r) }); end function; n_qr(7,3); t_qr(7,3); #olav_qr(4,3); #olav_qr(4,3) eq 4^(2*3-1); #olav_qr(4,1); #olav_qr(6,3) eq 4^(6*3-1); #olav_qr(5,3) eq 5^(2*3-1); #olav_q(9,1); Output: Magma V2.10-6 Thu Mar 11 2004 12:28:50 on modular [Seed = 4074902356] ------------------------------------- >> P:=PolynomialRing(GF(7^3));); ^ User error: bad syntax >> return ( x^(&+[j : j in exp(q,r)]) ); ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluat ^ User error: Identifier 'n_qr' has not been declared or assigned >> return ( { : a,b in GF(q) | in olav_qr(q,r) }); ^ User error: Identifier 'olav_qr' has not been declared or assigned >> n_qr(7,3); ^ User error: Identifier 'n_qr' has not been declared or assigned x^49 + x^7 + x >> #olav_qr(4,3); ^ User error: Identifier 'olav_qr' has not been declared or assigned >> #olav_qr(4,3) eq 4^(2*3-1); ^ User error: Identifier 'olav_qr' has not been declared or assigned >> #olav_qr(4,1); ^ User error: Identifier 'olav_qr' has not been declared or assigned >> #olav_qr(6,3) eq 4^(6*3-1); ^ User error: Identifier 'olav_qr' has not been declared or assigned >> #olav_qr(5,3) eq 5^(2*3-1); ^ User error: Identifier 'olav_qr' has not been declared or assigned >> #olav_q(9,1); ^ User error: Identifier 'olav_q' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.211.77) Time: Thu Mar 11 12:29:04 2004 Input: t_qr:= function (q,r) P:=PolynomialRing(GF(7^3)); exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; n_qr:= function (q,r) P:=PolynomialRing(GF(7^3)); exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; exp:= func ; olav_qr:= function (q,r) P:=PolynomialRing(GF(7^3)); exp:= func ; return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ); end function; olav_q:= function (q,r) return ( { : a,b in GF(q) | in olav_qr(q,r) }); end function; n_qr(7,3); t_qr(7,3); #olav_qr(4,3); #olav_qr(4,3) eq 4^(2*3-1); #olav_qr(4,1); #olav_qr(6,3) eq 4^(6*3-1); #olav_qr(5,3) eq 5^(2*3-1); #olav_q(9,1); Output: Magma V2.10-6 Thu Mar 11 2004 12:29:01 on modular [Seed = 4226488914] ------------------------------------- x^57 x^49 + x^7 + x [
:14]( q: 4, r: 3 ) >> return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluat ^ Runtime error in 'Evaluate': Incompatible rings [
:14]( q: 4, r: 3 ) >> return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluat ^ Runtime error in 'Evaluate': Incompatible rings [
:14]( q: 4, r: 1 ) >> return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluat ^ Runtime error in 'Evaluate': Incompatible rings [
:14]( q: 6, r: 3 ) >> return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluat ^ Runtime error in 'GF': Argument 1 (216) is not a prime power [
:14]( q: 5, r: 3 ) >> return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluat ^ Runtime error in 'Evaluate': Incompatible rings [
:19]( q: 9, r: 1 ) [
:14]( q: 9, r: 1 ) >> return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluat ^ Runtime error in 'Evaluate': Incompatible rings Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.211.77) Time: Thu Mar 11 12:30:09 2004 Input: t_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; n_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; exp:= func ; olav_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ); end function; olav_q:= function (q,r) return ( { : a,b in GF(q) | in olav_qr(q,r) }); end function; n_qr(7,3); t_qr(7,3); #olav_qr(4,3); #olav_qr(4,3) eq 4^(2*3-1); #olav_qr(4,1); #olav_qr(6,3) eq 4^(6*3-1); #olav_qr(5,3) eq 5^(2*3-1); #olav_q(9,1); Output: Magma V2.10-6 Thu Mar 11 2004 12:30:01 on modular [Seed = 3603313851] ------------------------------------- x^57 x^49 + x^7 + x 1024 true 4 [
:14]( q: 6, r: 3 ) >> P:=PolynomialRing(GF(q^r)); ^ Runtime error in 'GF': Argument 1 (216) is not a prime power true 9 Total time: 8.099 seconds, Total memory usage: 2.13MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.211.77) Time: Thu Mar 11 12:49:06 2004 Input: t_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; n_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; exp:= func ; olav_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ); end function; olav_q:= function (q,r) return ( { : a,b in GF(q) | in olav_qr(q,r) }); end function; n_qr(7,3); t_qr(7,3); #olav_qr(4,3); #olav_qr(4,3) eq 4^(2*3-1); #olav_qr(4,1); #olav_qr(4,4) eq 4^(2*4-1); #olav_qr(5,3) eq 5^(2*3-1); #olav_q(9,1); Output: Magma V2.10-6 Thu Mar 11 2004 12:48:45 on modular [Seed = 2592767122] ------------------------------------- x^57 x^49 + x^7 + x 1024 true 4 true true 9 Total time: 20.850 seconds, Total memory usage: 3.24MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.211.77) Time: Thu Mar 11 12:50:47 2004 Input: t_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; n_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; exp:= func ; olav_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ); end function; olav_q:= function (q,r) return ( { : a,b in GF(q) | in olav_qr(q,r) }); end function; n_qr(7,3); t_qr(7,3); #olav_qr(4,3); #olav_qr(4,3) eq 4^(2*3-1); #olav_qr(4,4); #olav_qr(4,4) eq 4^(2*4-1); #olav_qr(5,3) eq 5^(2*3-1); #olav_q(9,1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 11 2004 12:50:24 on modular [Seed = 1836944379] ------------------------------------- x^57 x^49 + x^7 + x 1024 true 16384 Errors: /home/mfd/gomagma: line 2: 13851 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.211.77) Time: Thu Mar 11 12:54:18 2004 Input: t_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; n_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; exp:= func ; olav_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ); end function; olav_q:= function (q,r) return ( { : a,b in GF(q) | in olav_qr(q,r) }); end function; n_qr(7,3); t_qr(7,3); #olav_qr(4,3); #olav_qr(4,3) eq 4^(2*3-1); #olav_qr(5,1); #olav_qr(4,4) eq 4^(2*4-1); #olav_qr(5,3) eq 5^(2*3-1); #olav_q(9,1); Output: Magma V2.10-6 Thu Mar 11 2004 12:53:57 on modular [Seed = 319026384] ------------------------------------- x^57 x^49 + x^7 + x 1024 true 5 true true 9 Total time: 21.159 seconds, Total memory usage: 3.24MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.211.77) Time: Thu Mar 11 12:55:59 2004 Input: t_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; n_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; exp:= func ; olav_qr:= function (q,r) P:=PolynomialRing(GF(q^r)); exp:= func ; return ( { : a,b in GF(q^r) | Evaluate(n_qr(q,r),a) eq Evaluate(t_qr(q,r),b)} ); end function; olav_q:= function (q,r) return ( { : a,b in GF(q) | in olav_qr(q,r) }); end function; #olav_qr(6,3); #olav_qr(6,3) eq 6^(2*3-1); #olav_qr(5,1); #olav_qr(4,4) eq 4^(2*4-1); #olav_qr(5,3) eq 5^(2*3-1); #olav_q(9,1); Output: Magma V2.10-6 Thu Mar 11 2004 12:55:39 on modular [Seed = 3891728266] ------------------------------------- [
:14]( q: 6, r: 3 ) >> P:=PolynomialRing(GF(q^r)); ^ Runtime error in 'GF': Argument 1 (216) is not a prime power [
:14]( q: 6, r: 3 ) >> P:=PolynomialRing(GF(q^r)); ^ Runtime error in 'GF': Argument 1 (216) is not a prime power 5 true true 9 Total time: 19.180 seconds, Total memory usage: 3.24MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.211.77) Time: Thu Mar 11 13:00:45 2004 Input: F:=GF(4); M:=MatrixRing(F,2); RM:=[Random(M) : i in [1..100000]]; M22:=[j: j in M]; Output: Magma V2.10-6 Thu Mar 11 2004 13:00:42 on modular [Seed = 2342216375] ------------------------------------- Total time: 3.389 seconds, Total memory usage: 7.09MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.211.77) Time: Thu Mar 11 13:01:47 2004 Input: F:=GF(4); M:=MatrixRing(F,2); RM:=[Random(M) : i in [1..100000]]; M22:=[j: j in M]; Mt:={i : i in M22 | Trace(i) eq 0}; Mf:={ i : i in M22 | i[1] eq i[2]}; Mtf:= Mt meet Mf; #[ i : i in RM | i in Mt]; #[ i : i in RM | i in Mf]; #[i : i in RM | i in Mtf]; Output: Magma V2.10-6 Thu Mar 11 2004 13:01:43 on modular [Seed = 1565373613] ------------------------------------- 25022 6108 1553 Total time: 4.129 seconds, Total memory usage: 7.09MB ************** MAGMA ***************** Host 80.58.50.170.proxycache.rima-tde.net. (80.58.50.170) Time: Thu Mar 11 13:44:46 2004 Input: F:=GF(4); M:=MatrixRing(F,2); Output: Magma V2.10-6 Thu Mar 11 2004 13:44:43 on modular [Seed = 1331674286] ------------------------------------- Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.170.proxycache.rima-tde.net. (80.58.50.170) Time: Thu Mar 11 13:44:57 2004 Input: F:=GF(4); M:=MatrixRing(F,2); Output: Magma V2.10-6 Thu Mar 11 2004 13:44:54 on modular [Seed = 1146402712] ------------------------------------- Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.170.proxycache.rima-tde.net. (80.58.50.170) Time: Thu Mar 11 13:49:52 2004 Input: F:=GF(4); M:=MatrixRing(F,2); M22:=[j: j in M]; Output: Magma V2.10-6 Thu Mar 11 2004 13:49:49 on modular [Seed = 674815135] ------------------------------------- Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.170.proxycache.rima-tde.net. (80.58.50.170) Time: Thu Mar 11 13:50:11 2004 Input: F:=GF(4); M:=MatrixRing(F,2); M22:=[j: j in M]; #Mt:={i : i in M22 | Trace(i) eq 0}; Output: Magma V2.10-6 Thu Mar 11 2004 13:50:08 on modular [Seed = 403238018] ------------------------------------- >> #Mt:={i : i in M22 | Trace(i) eq 0}; ^ User error: Illegal left hand side of an assignment statement Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.170.proxycache.rima-tde.net. (80.58.50.170) Time: Thu Mar 11 13:50:50 2004 Input: F:=GF(4); M:=MatrixRing(F,2); M22:=[j: j in M]; Mt:={i : i in M22 | Trace(i) eq 0}; #[ i : i in RM | i in Mt]; Output: Magma V2.10-6 Thu Mar 11 2004 13:50:47 on modular [Seed = 285336684] ------------------------------------- >> #[ i : i in RM | i in Mt];; ^ User error: Identifier 'RM' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.170.proxycache.rima-tde.net. (80.58.50.170) Time: Thu Mar 11 13:51:03 2004 Input: F:=GF(4); M:=MatrixRing(F,2); M22:=[j: j in M]; Mt:={i : i in M22 | Trace(i) eq 0}; #[ i : i in Mt]; Output: Magma V2.10-6 Thu Mar 11 2004 13:50:59 on modular [Seed = 236911463] ------------------------------------- 64 Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Thu Mar 11 14:26:21 2004 Input: EllipticCurveWithjInvartiant(9938375/21952); Output: Magma V2.10-6 Thu Mar 11 2004 14:26:18 on modular [Seed = 2931708814] ------------------------------------- >> EllipticCurveWithjInvartiant(9938375/21952);; ^ User error: Identifier 'EllipticCurveWithjInvartiant' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Thu Mar 11 14:26:42 2004 Input: EllipticCurveWithjInvariant(9938375/21952); Output: Magma V2.10-6 Thu Mar 11 2004 14:26:39 on modular [Seed = 2813811378] ------------------------------------- Elliptic Curve defined by y^2 + x*y = x^3 + 790272/27994681*x + 21952/27994681 over Rational Field Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Thu Mar 11 14:35:38 2004 Input: EllipticCurveWithjInvariant(406749952); Output: Magma V2.10-6 Thu Mar 11 2004 14:35:35 on modular [Seed = 2359063409] ------------------------------------- Elliptic Curve defined by y^2 + x*y = x^3 - 9/101687056*x - 1/406748224 over Rational Field Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Thu Mar 11 15:17:17 2004 Input: test_poly := function(n,b,K) if ((#K mod n) ne 1) then print "erreur, il faut #K = 1 mod n"; return false; end if; if IsOne((-b)^n) then return false; end if; z:=RootOfUnity(n,K); k:=(#K-1) div n; W:=[K|]; B:=[K|]; Append(~W,1); Append(~B,(b+1)^k); for j in [2..n] do Append(~W,W[j-1]*z); Append(~B,(b+W[j])^k); for i in [1..(j-1)] do if ( (B[i]/B[j]) eq W[j-i+1] ) then return false; end if; end for; end for; return true; end function; q := 2^10; K := GF(q); R := PolynomialRing(K); n := 33; a := w; p := x^((q-1+n) div n)+a*x; time test_poly(n,a,K); time IsProbablyPermutationPolynomial(p); Output: Magma V2.10-6 Thu Mar 11 2004 15:17:14 on modular [Seed = 3285404402] ------------------------------------- true Time: 0.000 true Time: 0.050 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Thu Mar 11 15:18:25 2004 Input: maxi_card:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); next:=#p; q:=p[next]; while (q[1] gt 1) do print p; K:=GF(q[1]); R := PolynomialRing(K); for a in K do if a ne 0 then if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end if; end for; Prune(~p); q[1]/:=q[2]; Append(~p,q); Sort(~p); q:=p[next]; end while; return 0; end function; maxi_card(10); Output: Magma V2.10-6 Thu Mar 11 2004 15:18:08 on modular [Seed = 3215930948] ------------------------------------- [ <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5>, <3481, 59>, <3721, 61>, <4096, 2> ] [ <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5>, <3481, 59>, <3721, 61> ] [ <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5>, <3481, 59> ] [ <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53>, <3125, 5> ] [ <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <625, 5>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7>, <2809, 53> ] [ <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <361, 19>, <529, 23>, <625, 5>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2187, 3>, <2197, 13>, <2209, 47>, <2401, 7> ] [ <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2187, 3>, <2197, 13>, <2209, 47> ] [ <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2187, 3>, <2197, 13> ] [ <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2>, <2187, 3> ] [ <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <729, 3>, <841, 29>, <961, 31>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43>, <2048, 2> ] [ <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <729, 3>, <841, 29>, <961, 31>, <1024, 2>, <1331, 11>, <1369, 37>, <1681, 41>, <1849, 43> ] [ <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <729, 3>, <841, 29>, <961, 31>, <1024, 2>, <1331, 11>, <1369, 37>, <1681, 41> ] [ <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <729, 3>, <841, 29>, <961, 31>, <1024, 2>, <1331, 11>, <1369, 37> ] [ <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <729, 3>, <841, 29>, <961, 31>, <1024, 2>, <1331, 11> ] [ <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <529, 23>, <625, 5>, <729, 3>, <841, 29>, <961, 31>, <1024, 2> ] [ <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <512, 2>, <529, 23>, <625, 5>, <729, 3>, <841, 29>, <961, 31> ] [ <31, 31>, <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <512, 2>, <529, 23>, <625, 5>, <729, 3>, <841, 29> ] [ <29, 29>, <31, 31>, <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <169, 13>, <289, 17>, <343, 7>, <361, 19>, <512, 2>, <529, 23>, <625, 5>, <729, 3> ] [ <29, 29>, <31, 31>, <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <169, 13>, <243, 3>, <289, 17>, <343, 7>, <361, 19>, <512, 2>, <529, 23>, <625, 5> ] [ <29, 29>, <31, 31>, <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <125, 5>, <169, 13>, <243, 3>, <289, 17>, <343, 7>, <361, 19>, <512, 2>, <529, 23> ] [ <23, 23>, <29, 29>, <31, 31>, <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <125, 5>, <169, 13>, <243, 3>, <289, 17>, <343, 7>, <361, 19>, <512, 2> ] [ <23, 23>, <29, 29>, <31, 31>, <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <125, 5>, <169, 13>, <243, 3>, <256, 2>, <289, 17>, <343, 7>, <361, 19> ] [ <19, 19>, <23, 23>, <29, 29>, <31, 31>, <37, 37>, <41, 41>, <43, 43>, <47, 47>, <53, 53>, <59, 59>, <61, 61>, <67, 67>, <71, 71>, <73, 73>, <79, 79>, <83, 83>, <89, 89>, <121, 11>, <125, 5>, <169, 13>, <243, 3>, <256, 2>, <289, 17>, <343, 7> ] <343, 7> Total time: 17.059 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Thu Mar 11 15:19:04 2004 Input: maxi_card:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); next:=#p; q:=p[next]; while (q[1] gt 1) do K:=GF(q[1]); R := PolynomialRing(K); for a in K do if a ne 0 then if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end if; end for; Prune(~p); q[1]/:=q[2]; Append(~p,q); Sort(~p); q:=p[next]; end while; return 0; end function; maxi_card(10); Output: Magma V2.10-6 Thu Mar 11 2004 15:18:47 on modular [Seed = 3081191019] ------------------------------------- <343, 7> Total time: 17.090 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Thu Mar 11 15:20:37 2004 Input: maxi_card:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); next:=#p; q:=p[next]; while (q[1] gt 1) do K:=GF(q[1]); R := PolynomialRing(K); for a in K do if a ne 0 then if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end if; end for; Prune(~p); q[1]/:=q[2]; Append(~p,q); Sort(~p); q:=p[next]; end while; return 0; end function; maxi_card(11); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 11 2004 15:20:14 on modular [Seed = 2609582622] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 15328 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Thu Mar 11 15:21:12 2004 Input: maxi_card:=function(k) ZZ:=car; p:=[ZZ|]; next:=2; while (next lt k*(k-1)) do Append(~p,); next:=NextPrime(next); end while; Sort(~p); next:=#p; q:=p[next]; while (q[1] gt 1) do K:=GF(q[1]); R := PolynomialRing(K); for a in K do if a ne 0 then if (IsProbablyPermutationPolynomial(x^k+a*x)) then return q; end if; end if; end for; Prune(~p); q[1]/:=q[2]; Append(~p,q); Sort(~p); q:=p[next]; end while; return 0; end function; maxi_card(10); Output: Magma V2.10-6 Thu Mar 11 2004 15:20:55 on modular [Seed = 2474842575] ------------------------------------- <343, 7> Total time: 17.189 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Thu Mar 11 15:25:48 2004 Input: Factorize(2^16-1) Output: Magma V2.10-6 Thu Mar 11 2004 15:25:45 on modular [Seed = 2359035838] ------------------------------------- >> Factorize(2^16-1); ^ User error: Identifier 'Factorize' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Thu Mar 11 15:26:00 2004 Input: Factorise(2^16-1) Output: Magma V2.10-6 Thu Mar 11 2004 15:25:58 on modular [Seed = 2224295849] ------------------------------------- >> Factorise(2^16-1); ^ User error: Identifier 'Factorise' has not been declared or assigned Total time: 2.859 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Thu Mar 11 15:26:09 2004 Input: Factor(2^16-1) Output: Magma V2.10-6 Thu Mar 11 2004 15:26:06 on modular [Seed = 2070671449] ------------------------------------- >> Factor(2^16-1); ^ Runtime error in 'Factor': Bad argument types Argument types given: RngIntElt Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Thu Mar 11 15:29:04 2004 Input: Factorization(2^16-1) Output: Magma V2.10-6 Thu Mar 11 2004 15:29:01 on modular [Seed = 1820123165] ------------------------------------- [ <3, 1>, <5, 1>, <17, 1>, <257, 1> ] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Thu Mar 11 15:29:32 2004 Input: Factorization(2^32-1) Output: Magma V2.10-6 Thu Mar 11 2004 15:29:29 on modular [Seed = 1702226224] ------------------------------------- [ <3, 1>, <5, 1>, <17, 1>, <257, 1>, <65537, 1> ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Thu Mar 11 15:30:27 2004 Input: Factorization(2^32+1) Output: Magma V2.10-6 Thu Mar 11 2004 15:30:24 on modular [Seed = 1413797960] ------------------------------------- [ <641, 1>, <6700417, 1> ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Thu Mar 11 15:30:53 2004 Input: Factorization(2^(2^6)+1) Output: Magma V2.10-6 Thu Mar 11 2004 15:30:50 on modular [Seed = 1281146954] ------------------------------------- [ <274177, 1>, <67280421310721, 1> ] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Thu Mar 11 15:31:15 2004 Input: Factorization(2^(2^9)+1) Output: Magma V2.10-6 Thu Mar 11 2004 15:31:10 on modular [Seed = 1146407094] ------------------------------------- [ <2424833, 1>, <7455602825647884208337395736200454918783366342657, 1>, <741640062627530801524787141901937474059940781097519023905821316144415759504705\ 008092818711693940737, 1> ] Total time: 4.759 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Thu Mar 11 15:31:59 2004 Input: Factorization(2^(2^11)+1) Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 11 2004 15:31:36 on modular [Seed = 1026404841] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 15425 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Thu Mar 11 15:32:28 2004 Input: Factorization(2^(2^10)+1) Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 11 2004 15:32:05 on modular [Seed = 891664780] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 15433 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Thu Mar 11 15:33:06 2004 Input: Factorization(3^(3^7)+1) Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 11 2004 15:32:43 on modular [Seed = 759013818] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 15441 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Thu Mar 11 15:33:37 2004 Input: Factorization(3^(3^6)+1) Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 11 2004 15:33:15 on modular [Seed = 624273490] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 15449 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Thu Mar 11 15:33:53 2004 Input: Factorization(3^(3^5)+1) Output: Magma V2.10-6 Thu Mar 11 2004 15:33:50 on modular [Seed = 487428175] ------------------------------------- [ <2, 2>, <7, 1>, <19, 1>, <37, 1>, <163, 1>, <487, 1>, <1297, 1>, <19441, 1>, <19927, 1>, <59779, 1>, <208657, 1>, <224209, 1>, <572023, 1>, <2051893, 1>, <5062663, 1>, <859270843, 1>, <1319934691, 1>, <5879415781, 1>, <8638915776957163, 1>, <116004991998176173, 1> ] Total time: 3.349 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Thu Mar 11 15:34:29 2004 Input: Factorization(3^(2^7)+1) Output: Magma V2.10-6 Thu Mar 11 2004 15:34:26 on modular [Seed = 386374201] ------------------------------------- [ <2, 1>, <257, 1>, <275201, 1>, <138424618868737, 1>, <3913786281514524929, 1>, <153849834853910661121, 1> ] Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Thu Mar 11 15:34:45 2004 Input: Factorization(3^(2^7)) Output: Magma V2.10-6 Thu Mar 11 2004 15:34:42 on modular [Seed = 253723153] ------------------------------------- [ <3, 128> ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Thu Mar 11 15:35:04 2004 Input: Factorization(3^(2^7)+2) Output: Magma V2.10-6 Thu Mar 11 2004 15:34:52 on modular [Seed = 118983191] ------------------------------------- [ <10243, 1>, <17321, 1>, <56435857, 1>, <11191072115939882443, 1>, <105218874264995750588770171, 1> ] Total time: 11.129 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Thu Mar 11 15:35:18 2004 Input: 2+2 Output: Magma V2.10-6 Thu Mar 11 2004 15:35:15 on modular [Seed = 4125456394] ------------------------------------- 4 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dhip-159.ams.residences.colby.edu. (137.146.134.223) Time: Thu Mar 11 17:05:14 2004 Input: gcd(121,375) Output: Magma V2.10-6 Thu Mar 11 2004 17:05:11 on modular [Seed = 2898005574] ------------------------------------- >> gcd(121,375); ^ User error: Identifier 'gcd' has not been declared or assigned Total time: 3.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Thu Mar 11 17:28:49 2004 Input: l:= Output: Magma V2.10-6 Thu Mar 11 2004 17:28:46 on modular [Seed = 1769586953] ------------------------------------- >> l:=; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-67-122-208-92.dsl.pltn13.pacbell.net. (67.122.208.92) Time: Thu Mar 11 19:56:38 2004 Input: P2:=ProjectiveSpace(Rationals(),2); C:=Curve(P2,v^2*w^2+u^4-6*u^2*w^2+w^4); E:=Curve(P2,-v^2*w+u^3-u*w^2); phi:=mapP2|[w*(u-w)*(2*u+v),(u+w)*(u^2-4*u*w-v*w+w^2),(u-w)^3]>; phiC:=Restriction(phi,C,E); Output: Magma V2.10-6 Thu Mar 11 2004 19:56:35 on modular [Seed = 386293163] ------------------------------------- Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-67-122-208-92.dsl.pltn13.pacbell.net. (67.122.208.92) Time: Thu Mar 11 19:56:56 2004 Input: P2:=ProjectiveSpace(Rationals(),2); C:=Curve(P2,v^2*w^2+u^4-6*u^2*w^2+w^4); E:=Curve(P2,-v^2*w+u^3-u*w^2); phi:=mapP2|[w*(u-w)*(2*u+v),(u+w)*(u^2-4*u*w-v*w+w^2),(u-w)^3]>; phiC:=Restriction(phi,C,E); Degree(phiC); Output: Magma V2.10-6 Thu Mar 11 2004 19:56:53 on modular [Seed = 236930212] ------------------------------------- Degree( phi: (u : v : w) -> (2*u^2*w + u*v*w - 2*u*w^2 - v*w^2 : u^3 - 3*... ) In file "/usr/local/magma/package/Geometry/Crv/pushpull.m", line 87, column 18: >> d:=Integers()!(Degree(PBD)/Degree(D)); ^ Runtime error in '!': Rational argument is not a whole integer LHS: RngInt RHS: FldRatElt Total time: 3.049 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host csarami.resnet.mtu.edu. (141.219.83.104) Time: Thu Mar 11 20:45:13 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Thu Mar 11 2004 20:45:10 on modular [Seed = 2173753304] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host csarami.resnet.mtu.edu. (141.219.83.104) Time: Thu Mar 11 20:45:40 2004 Input: M := KMatrixSpace(FiniteField(3), 2, 4); Output: Magma V2.10-6 Thu Mar 11 2004 20:45:37 on modular [Seed = 118903110] ------------------------------------- Total time: 3.099 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host csarami.resnet.mtu.edu. (141.219.83.104) Time: Thu Mar 11 20:45:43 2004 Input: M := KMatrixSpace(FiniteField(3), 2, 4); Output: Magma V2.10-6 Thu Mar 11 2004 20:45:39 on modular [Seed = 169565257] ------------------------------------- Total time: 3.149 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host csarami.resnet.mtu.edu. (141.219.83.104) Time: Thu Mar 11 20:45:58 2004 Input: M := KMatrixSpace(FiniteField(3), 2, 4);G1:=M! [1,2,0,0, 1,0,1,0]; Output: Magma V2.10-6 Thu Mar 11 2004 20:45:55 on modular [Seed = 403263051] ------------------------------------- Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host csarami.resnet.mtu.edu. (141.219.83.104) Time: Thu Mar 11 20:46:32 2004 Input: M := KMatrixSpace(FiniteField(3), 2, 4);G1:=M! [1,2,0,0, 1,0,1,0];G2:=M! [1,0,2,0,0,1,2,0]; C1:= LinearCode(G1);C1; Output: Magma V2.10-6 Thu Mar 11 2004 20:46:29 on modular [Seed = 657879378] ------------------------------------- [4, 2, 2] Linear Code over GF(3) Generator matrix: [1 0 1 0] [0 1 1 0] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host csarami.resnet.mtu.edu. (141.219.83.104) Time: Thu Mar 11 20:52:16 2004 Input: P:=PolynomialRing(GF(2)); f::=(1 + x + x^2 + x^5 + x^6 + x^11 + x^14 + x^15 + x^16 + x^22 + x^23 + x^24 + x^25 + x^26 + x^28 + x^31 + x^32 + x^33 + x^35 + x^36); C:=LinearCode(63,f); #AutomorphismGroup(C); Output: Magma V2.10-6 Thu Mar 11 2004 20:52:13 on modular [Seed = 992636150] ------------------------------------- >> f::=(1 + x + x^2 + x^5 + x^6 + x^11 + x^14 + x^15 + x^16 + x^22 + ^ User error: bad syntax >> x^36); ^ User error: bad syntax >> C:=LinearCode(63,f); #AutomorphismGroup(C);; ^ User error: Identifier 'f' has not been declared or assigned >> C:=LinearCode(63,f); #AutomorphismGroup(C);; ^ User error: Identifier 'C' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host csarami.resnet.mtu.edu. (141.219.83.104) Time: Thu Mar 11 20:52:36 2004 Input: P:=PolynomialRing(GF(2)); f:=(1 + x + x^2 + x^5 + x^6 + x^11 + x^14 + x^15 + x^16 + x^22 + x^23 + x^24 + x^25 + x^26 + x^28 + x^31 + x^32 + x^33 + x^35 + x^36); C:=LinearCode(63,f); #AutomorphismGroup(C); Output: Magma V2.10-6 Thu Mar 11 2004 20:52:33 on modular [Seed = 1163137700] ------------------------------------- >> C:=LinearCode(63,f); #AutomorphismGroup(C);; ^ Runtime error in 'LinearCode': Bad argument types Argument types given: RngIntElt, RngUPolElt >> C:=LinearCode(63,f); #AutomorphismGroup(C);; ^ User error: Identifier 'C' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host csarami.resnet.mtu.edu. (141.219.83.104) Time: Thu Mar 11 20:53:20 2004 Input: P:=PolynomialRing(GF(2)); f:=(1 + x + x^2 + x^5 + x^6 + x^11 + x^14 + x^15 + x^16 + x^22 + x^23 + x^24 + x^25 + x^26 + x^28 + x^31 + x^32 + x^33 + x^35 + x^36); C:=CyclicCode(63,f); #AutomorphismGroup(C); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 11 2004 20:52:57 on modular [Seed = 1314855351] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 16462 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Thu Mar 11 21:58:57 2004 Input: > F := EllipticCurve([-1, 1]); > F; > MW; > a := f(MW.1); > a; > intpts := [ pt : i, j in [-60..60] | > IsIntegral(pt) where pt is i*a] ; > intpts; > #intpts; Output: Magma V2.10-6 Thu Mar 11 2004 21:58:54 on modular [Seed = 34825581] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - x + 1 over Rational Field >> MW; ^ User error: Identifier 'MW' has not been declared or assigned >> a := f(MW.1); ^ User error: Identifier 'MW' has not been declared or assigned >> a; ^ User error: Identifier 'a' has not been declared or assigned >> IsIntegral(pt) where pt is i*a] ; ^ User error: Identifier 'a' has not been declared or assigned >> intpts; ^ User error: Identifier 'intpts' has not been declared or assigned >> #intpts;; ^ User error: Identifier 'intpts' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Thu Mar 11 22:00:59 2004 Input: > F := EllipticCurve([-1, 1]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i, j in [-60..60] | > IsIntegral(pt) where pt is i*a] ; > intpts; > #intpts; Output: Magma V2.10-6 Thu Mar 11 2004 22:00:53 on modular [Seed = 335901680] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - x + 1 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (1 : 1 : 1) [ (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (56 : 419 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (5 : -11 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (3 : 5 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (0 : 1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (-1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : -1 : 1), (1 : ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Thu Mar 11 22:01:39 2004 Input: > F := EllipticCurve([-1, 1]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i in [-60..60] | > IsIntegral(pt) where pt is i*a] ; > intpts; > #intpts; Output: Magma V2.10-6 Thu Mar 11 2004 22:01:35 on modular [Seed = 824203583] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - x + 1 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (1 : 1 : 1) [ (56 : 419 : 1), (5 : -11 : 1), (3 : 5 : 1), (0 : 1 : 1), (-1 : -1 : 1), (1 : -1 : 1), (1 : 1 : 1), (-1 : 1 : 1), (0 : -1 : 1), (3 : -5 : 1), (5 : 11 : 1), (56 : -419 : 1) ] 12 Total time: 3.239 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Thu Mar 11 22:06:59 2004 Input: > F := EllipticCurve([-16, 64]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i in [-60..60] | > IsIntegral(pt) where pt is i*a] ; > intpts; > #intpts; Output: Magma V2.10-6 Thu Mar 11 2004 22:06:56 on modular [Seed = 1095772176] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 16*x + 64 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (4 : 8 : 1) [ (224 : 3352 : 1), (1 : -7 : 1), (20 : -88 : 1), (12 : 40 : 1), (0 : 8 : 1), (-4 : -8 : 1), (4 : -8 : 1), (4 : 8 : 1), (-4 : 8 : 1), (0 : -8 : 1), (12 : -40 : 1), (20 : 88 : 1), (1 : 7 : 1), (224 : -3352 : 1) ] 14 Total time: 3.259 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Thu Mar 11 22:07:51 2004 Input: > F := EllipticCurve([-16, 64]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i in [-160..160] | > IsIntegral(pt) where pt is i*a] ; > intpts; > #intpts; Output: Magma V2.10-6 Thu Mar 11 2004 22:07:47 on modular [Seed = 1213800906] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 16*x + 64 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (4 : 8 : 1) [ (224 : 3352 : 1), (1 : -7 : 1), (20 : -88 : 1), (12 : 40 : 1), (0 : 8 : 1), (-4 : -8 : 1), (4 : -8 : 1), (4 : 8 : 1), (-4 : 8 : 1), (0 : -8 : 1), (12 : -40 : 1), (20 : 88 : 1), (1 : 7 : 1), (224 : -3352 : 1) ] 14 Total time: 3.599 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Thu Mar 11 22:10:03 2004 Input: > F := EllipticCurve([-1296, 46656]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i in [-160..160] | > IsIntegral(pt) where pt is i*a] ; > intpts; > #intpts; Output: Magma V2.10-6 Thu Mar 11 2004 22:09:59 on modular [Seed = 1430536019] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 1296*x + 46656 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (36 : 216 : 1) [ (2016 : 90504 : 1), (-44 : 136 : 1), (9 : -189 : 1), (180 : -2376 : 1), (108 : 1080 : 1), (0 : 216 : 1), (-36 : -216 : 1), (36 : -216 : 1), (36 : 216 : 1), (-36 : 216 : 1), (0 : -216 : 1), (108 : -1080 : 1), (180 : 2376 : 1), (9 : 189 : 1), (-44 : -136 : 1), (2016 : -90504 : 1) ] 16 Total time: 3.749 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Thu Mar 11 22:11:06 2004 Input: > F := EllipticCurve([-1296, 46656]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i in [-1600..1600] | > IsIntegral(pt) where pt is i*a] ; > intpts; > #intpts; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 11 2004 22:10:43 on modular [Seed = 1702104919] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 1296*x + 46656 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (36 : 216 : 1) Errors: /home/mfd/gomagma: line 2: 16740 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Thu Mar 11 22:11:38 2004 Input: > F := EllipticCurve([-1296, 46656]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i in [-200..200] | > IsIntegral(pt) where pt is i*a] ; > intpts; > #intpts; Output: Magma V2.10-6 Thu Mar 11 2004 22:11:34 on modular [Seed = 1820132875] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 1296*x + 46656 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (36 : 216 : 1) [ (2016 : 90504 : 1), (-44 : 136 : 1), (9 : -189 : 1), (180 : -2376 : 1), (108 : 1080 : 1), (0 : 216 : 1), (-36 : -216 : 1), (36 : -216 : 1), (36 : 216 : 1), (-36 : 216 : 1), (0 : -216 : 1), (108 : -1080 : 1), (180 : 2376 : 1), (9 : 189 : 1), (-44 : -136 : 1), (2016 : -90504 : 1) ] 16 Total time: 4.279 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Thu Mar 11 22:13:52 2004 Input: > F := EllipticCurve([-810000, 719000000]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i in [-200..200] | > IsIntegral(pt) where pt is i*a] ; > intpts; > #intpts; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 11 2004 22:13:29 on modular [Seed = 1986469038] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 810000*x + 719000000 over Rational Field Abelian Group isomorphic to Z + Z Defined on 2 generators (free) (-1000 : -23000 : 1) Errors: /home/mfd/gomagma: line 2: 16759 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Thu Mar 11 22:14:39 2004 Input: > F := EllipticCurve([-810000, 719000000]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i in [-200..20] | > IsIntegral(pt) where pt is i*a] ; > intpts; > #intpts; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 11 2004 22:14:16 on modular [Seed = 2173758088] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 810000*x + 719000000 over Rational Field Abelian Group isomorphic to Z + Z Defined on 2 generators (free) (-1000 : -23000 : 1) Errors: /home/mfd/gomagma: line 2: 16768 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Thu Mar 11 22:16:06 2004 Input: > F := EllipticCurve([-810000, 729000000]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i in [-200..20] | > IsIntegral(pt) where pt is i*a] ; > intpts; > #intpts; Output: Magma V2.10-6 Thu Mar 11 2004 22:16:02 on modular [Seed = 2424437731] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 810000*x + 729000000 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (900 : 27000 : 1) [ (50400 : 11313000 : 1), (684 : 22248 : 1), (-1100 : 17000 : 1), (225 : -23625 : 1), (4500 : -297000 : 1), (2700 : 135000 : 1), (0 : 27000 : 1), (-900 : -27000 : 1), (900 : -27000 : 1), (900 : 27000 : 1), (-900 : 27000 : 1), (0 : -27000 : 1), (2700 : -135000 : 1), (4500 : 297000 : 1), (225 : 23625 : 1), (-1100 : -17000 : 1), (684 : -22248 : 1), (50400 : -11313000 : 1) ] 18 Total time: 3.769 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Thu Mar 11 22:16:38 2004 Input: > F := EllipticCurve([-810000, 729000000]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i in [-200..200] | > IsIntegral(pt) where pt is i*a] ; > intpts; > #intpts; Output: Magma V2.10-6 Thu Mar 11 2004 22:16:34 on modular [Seed = 2609573896] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 810000*x + 729000000 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (900 : 27000 : 1) [ (50400 : 11313000 : 1), (684 : 22248 : 1), (-1100 : 17000 : 1), (225 : -23625 : 1), (4500 : -297000 : 1), (2700 : 135000 : 1), (0 : 27000 : 1), (-900 : -27000 : 1), (900 : -27000 : 1), (900 : 27000 : 1), (-900 : 27000 : 1), (0 : -27000 : 1), (2700 : -135000 : 1), (4500 : 297000 : 1), (225 : 23625 : 1), (-1100 : -17000 : 1), (684 : -22248 : 1), (50400 : -11313000 : 1) ] 18 Total time: 4.209 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Thu Mar 11 22:17:59 2004 Input: > F := EllipticCurve([-256, 4096]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i in [-200..200] | > IsIntegral(pt) where pt is i*a] ; > intpts; > #intpts; Output: Magma V2.10-6 Thu Mar 11 2004 22:17:55 on modular [Seed = 2729691456] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 256*x + 4096 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (16 : 64 : 1) [ (896 : 26816 : 1), (4 : -56 : 1), (80 : -704 : 1), (48 : 320 : 1), (0 : 64 : 1), (-16 : -64 : 1), (16 : -64 : 1), (16 : 64 : 1), (-16 : 64 : 1), (0 : -64 : 1), (48 : -320 : 1), (80 : 704 : 1), (4 : 56 : 1), (896 : -26816 : 1) ] 14 Total time: 4.249 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Thu Mar 11 22:19:51 2004 Input: > F := EllipticCurve([-81,729]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i in [-200..200] | > IsIntegral(pt) where pt is i*a] ; > intpts; > #intpts; Output: Magma V2.10-6 Thu Mar 11 2004 22:19:47 on modular [Seed = 2948514813] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 81*x + 729 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (9 : 27 : 1) [ (504 : 11313 : 1), (-11 : 17 : 1), (45 : -297 : 1), (27 : 135 : 1), (0 : 27 : 1), (-9 : -27 : 1), (9 : -27 : 1), (9 : 27 : 1), (-9 : 27 : 1), (0 : -27 : 1), (27 : -135 : 1), (45 : 297 : 1), (-11 : -17 : 1), (504 : -11313 : 1) ] 14 Total time: 4.159 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host gw1.btc.transwitch.com. (63.149.68.2) Time: Fri Mar 12 00:18:41 2004 Input: R := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^15-2*x^14-163*x^13+572*x^12+8741*x^11-43566*x^10-158357*x^9+1218850*x^8-268843*x^7-10964358*x^6+22615039*x^5-6993034*x^4-9237443*x^3-232532*x^2+291180*x-14600)); Output: Magma V2.10-6 Fri Mar 12 2004 00:18:36 on modular [Seed = 4041341150] ------------------------------------- 9 15 Total time: 5.169 seconds, Total memory usage: 2.39MB ************** MAGMA ***************** Host gw1.btc.transwitch.com. (63.149.68.2) Time: Fri Mar 12 00:55:52 2004 Input: R := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^15-325*x^13-210*x^12+39230*x^11+59078*x^10-2164525*x^9-5469310*x^8+52187410*x^7+197632325*x^6-366037518*x^5-2448970425*x^4-1850397340*x^3+5590040885*x^2+9036863220*x+2686354033)); Output: Magma V2.10-6 Fri Mar 12 2004 00:55:47 on modular [Seed = 942221528] ------------------------------------- 25 15 Total time: 4.750 seconds, Total memory usage: 3.30MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Fri Mar 12 02:06:02 2004 Input: > P := PolynomialRing(IntegerRing(), 2); > S := [x^2 - y, x^3 + y^2, x*y^3 - 1]; > I := Ideal(S); > 1 in I; Output: Magma V2.10-6 Fri Mar 12 2004 02:05:59 on modular [Seed = 3891709619] ------------------------------------- false Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Fri Mar 12 02:06:35 2004 Input: > P := PolynomialRing(IntegerRing(), 2); > S := [x^2 - y, x^3 + y^2, x*y^3 - 1]; > I := Ideal(S); > GroebnerBasis(I); Output: Magma V2.10-6 Fri Mar 12 2004 02:06:32 on modular [Seed = 3992767638] ------------------------------------- [ x + 1, y + 1, 2 ] Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Fri Mar 12 02:07:25 2004 Input: > P := PolynomialRing(IntegerRing(), 2); > S := [(1-x)^2, (1-y)^2, (1-z)^2,(1-x*y)^2]; > I := Ideal(S); > GroebnerBasis(I); Output: Magma V2.10-6 Fri Mar 12 2004 02:07:22 on modular [Seed = 4108703069] ------------------------------------- >> P := PolynomialRing(IntegerRing(), 2); ^ Runtime error in 'AssignNames': Argument 2 should have length at most 2 >> S := [(1-x)^2, (1-y)^2, (1-z)^2,(1-x*y)^2]; ^ User error: Identifier 'x' has not been declared or assigned >> I := Ideal(S); ^ User error: Identifier 'S' has not been declared or assigned >> GroebnerBasis(I); ^ User error: Identifier 'I' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Fri Mar 12 02:08:07 2004 Input: > P := PolynomialRing(IntegerRing(), 2); > S := [1-2x+x^2, (1-y)^2, (1-z)^2,(1-x*y)^2]; > I := Ideal(S); > GroebnerBasis(I); Output: Magma V2.10-6 Fri Mar 12 2004 02:08:04 on modular [Seed = 68494804] ------------------------------------- >> P := PolynomialRing(IntegerRing(), 2); ^ Runtime error in 'AssignNames': Argument 2 should have length at most 2 >> S := [1-2x+x^2, (1-y)^2, (1-z)^2,(1-x*y)^2]; ^ User error: bad syntax >> I := Ideal(S); ^ User error: Identifier 'S' has not been declared or assigned >> GroebnerBasis(I); ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Fri Mar 12 02:08:38 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > S := [1-2x+x^2, (1-y)^2, (1-z)^2,(1-x*y)^2]; > I := Ideal(S); > GroebnerBasis(I); Output: Magma V2.10-6 Fri Mar 12 2004 02:08:35 on modular [Seed = 219950330] ------------------------------------- >> S := [1-2x+x^2, (1-y)^2, (1-z)^2,(1-x*y)^2]; ^ User error: bad syntax >> I := Ideal(S); ^ User error: Identifier 'S' has not been declared or assigned >> GroebnerBasis(I); ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Fri Mar 12 02:08:49 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > S := [1-2*x+x^2, (1-y)^2, (1-z)^2,(1-x*y)^2]; > I := Ideal(S); > GroebnerBasis(I); Output: Magma V2.10-6 Fri Mar 12 2004 02:08:46 on modular [Seed = 369571820] ------------------------------------- [ x^2 - 2*x + 1, 2*x*y - 2*x - 2*y + 2, y^2 - 2*y + 1, z^2 - 2*z + 1 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Fri Mar 12 02:09:43 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > S := [1-2*x+x^2, (1-y)^2, (1-z)^2,(1-x*y)^2]; > I := Ideal(S); > GroebnerBasis(I); > (1-x)(1-y)(1-z)(1-x*y) in I; Output: Magma V2.10-6 Fri Mar 12 2004 02:09:40 on modular [Seed = 419969833] ------------------------------------- [ x^2 - 2*x + 1, 2*x*y - 2*x - 2*y + 2, y^2 - 2*y + 1, z^2 - 2*z + 1 ] >> (1-x)(1-y)(1-z)(1-x*y) in I; ^ Runtime error: Bad argument types Argument types given: RngMPolElt, RngMPolElt Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Fri Mar 12 02:10:03 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > S := [1-2*x+x^2, (1-y)^2, (1-z)^2,(1-x*y)^2]; > I := Ideal(S); > GroebnerBasis(I); > (1-x)*(1-y)*(1-z)*(1-x*y) in I; Output: Magma V2.10-6 Fri Mar 12 2004 02:10:00 on modular [Seed = 573767790] ------------------------------------- [ x^2 - 2*x + 1, 2*x*y - 2*x - 2*y + 2, y^2 - 2*y + 1, z^2 - 2*z + 1 ] true Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Fri Mar 12 02:11:06 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > S := [(1-x)^2, (2-y)^2, (3-z)^2,(5-x*y)^2]; > I := Ideal(S); > GroebnerBasis(I); > (1-x)*(1-y)*(1-z)*(1-x*y) in I; Output: Magma V2.10-6 Fri Mar 12 2004 02:11:03 on modular [Seed = 841158833] ------------------------------------- [ x^2 + 7*x + 9*y + 1, x*y + 4*x + 2*y + 26, 9*x + 9*y, y^2 + 23*y + 4, z^2 + 21*z + 9, 27 ] false Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Fri Mar 12 02:11:25 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > S := [(1-x)^2, (2-y)^2, (3-z)^2,(5-x*y)^2]; > I := Ideal(S); > GroebnerBasis(I); > (1-x)*(2-y)*(3-z)*(5-x*y) in I; Output: Magma V2.10-6 Fri Mar 12 2004 02:11:22 on modular [Seed = 992614821] ------------------------------------- [ x^2 + 7*x + 9*y + 1, x*y + 4*x + 2*y + 26, 9*x + 9*y, y^2 + 23*y + 4, z^2 + 21*z + 9, 27 ] false Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Fri Mar 12 02:15:27 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > S := [(1-x)^2, (2-y)^2, (3-z)^2,(5-x*y)^2,(7-x*z)^2]; > I := Ideal(S); > GroebnerBasis(I); > (1-x)*(2-y)*(3-z)*(5-x*y)(7-x*z) in I; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Mar 12 2004 02:15:04 on modular [Seed = 1247504694] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 17486 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Fri Mar 12 02:15:47 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > S := [(1-x)^2, (2-y)^2, (3-z)^2,(5-x*y)^2]; > I := Ideal(S); > GroebnerBasis(I); > (1-x)*(2-y)*(3-z)*(5-x*y)(7-x*z) in I; Output: Magma V2.10-6 Fri Mar 12 2004 02:15:44 on modular [Seed = 1548582904] ------------------------------------- [ x^2 + 7*x + 9*y + 1, x*y + 4*x + 2*y + 26, 9*x + 9*y, y^2 + 23*y + 4, z^2 + 21*z + 9, 27 ] >> (1-x)*(2-y)*(3-z)*(5-x*y)(7-x*z) in I; ^ Runtime error: Bad argument types Argument types given: RngMPolElt, RngMPolElt Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Fri Mar 12 02:16:00 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > S := [(1-x)^2, (2-y)^2, (3-z)^2,(5-x*y)^2]; > I := Ideal(S); > GroebnerBasis(I); > (1-x)*(2-y)*(3-z)*(5-x*y)*(7-x*z) in I; Output: Magma V2.10-6 Fri Mar 12 2004 02:15:57 on modular [Seed = 1735804110] ------------------------------------- [ x^2 + 7*x + 9*y + 1, x*y + 4*x + 2*y + 26, 9*x + 9*y, y^2 + 23*y + 4, z^2 + 21*z + 9, 27 ] false Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Fri Mar 12 02:17:04 2004 Input: > P := PolynomialRing(IntegerRing(), 2); > S := [(1-x-y^2)^2,(1-2x-y)^3]; > I := Ideal(S); > GroebnerBasis(I); > (1-x)*(2-y)*(3-z)*(5-x*y)*(7-x*z) in I; Output: Magma V2.10-6 Fri Mar 12 2004 02:17:01 on modular [Seed = 1752779649] ------------------------------------- >> S := [(1-x-y^2)^2,(1-2x-y)^3]; ^ User error: bad syntax >> I := Ideal(S); ^ User error: Identifier 'S' has not been declared or assigned >> GroebnerBasis(I); ^ User error: Identifier 'I' has not been declared or assigned >> (1-x)*(2-y)*(3-z)*(5-x*y)*(7-x*z) in I; ^ User error: Identifier 'z' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Fri Mar 12 02:17:17 2004 Input: > P := PolynomialRing(IntegerRing(), 2); > S := [(1-x-y^2)^2,(1-2x-y^3)^2]; > I := Ideal(S); > GroebnerBasis(I); > (1-x)*(2-y)*(3-z)*(5-x*y)*(7-x*z) in I; Output: Magma V2.10-6 Fri Mar 12 2004 02:17:14 on modular [Seed = 1902137999] ------------------------------------- >> S := [(1-x-y^2)^2,(1-2x-y^3)^2]; ^ User error: bad syntax >> I := Ideal(S); ^ User error: Identifier 'S' has not been declared or assigned >> GroebnerBasis(I); ^ User error: Identifier 'I' has not been declared or assigned >> (1-x)*(2-y)*(3-z)*(5-x*y)*(7-x*z) in I; ^ User error: Identifier 'z' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Fri Mar 12 02:17:25 2004 Input: > P := PolynomialRing(IntegerRing(), 2); > S := [(1-x-y^2)^2,(1-2*x-y^3)^2]; > I := Ideal(S); > GroebnerBasis(I); > (1-x)*(2-y)*(3-z)*(5-x*y)*(7-x*z) in I; Output: Magma V2.10-6 Fri Mar 12 2004 02:17:22 on modular [Seed = 2053856892] ------------------------------------- [ x^2 + 2*x*y^2 - 2*x + y^4 - 2*y^2 + 1, x*y^6 + 2*x*y^3 - 16*x*y^2 + 4*x*y + 9*x + 2*y^8 - 3*y^7 + y^6 - 10*y^4 + 2*y^3 + 18*y^2 - 3*y - 7, 4*x*y^3 - 8*x*y^2 + 4*x + y^6 - 4*y^4 - 2*y^3 + 8*y^2 - 3, y^9 - 6*y^8 + 12*y^7 - 5*y^6 - 12*y^5 + 12*y^4 + 3*y^3 - 6*y^2 + 1 ] >> (1-x)*(2-y)*(3-z)*(5-x*y)*(7-x*z) in I; ^ User error: Identifier 'z' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Fri Mar 12 02:17:50 2004 Input: > P := PolynomialRing(IntegerRing(), 2); > S := [(1-x-y^2)^2,(1-2*x-y^3)^2]; > I := Ideal(S); > GroebnerBasis(I); > (1-x-y^2)(1-2*x-y^3) in I; Output: Magma V2.10-6 Fri Mar 12 2004 02:17:47 on modular [Seed = 2359142547] ------------------------------------- [ x^2 + 2*x*y^2 - 2*x + y^4 - 2*y^2 + 1, x*y^6 + 2*x*y^3 - 16*x*y^2 + 4*x*y + 9*x + 2*y^8 - 3*y^7 + y^6 - 10*y^4 + 2*y^3 + 18*y^2 - 3*y - 7, 4*x*y^3 - 8*x*y^2 + 4*x + y^6 - 4*y^4 - 2*y^3 + 8*y^2 - 3, y^9 - 6*y^8 + 12*y^7 - 5*y^6 - 12*y^5 + 12*y^4 + 3*y^3 - 6*y^2 + 1 ] >> (1-x-y^2)(1-2*x-y^3) in I; ^ Runtime error: Bad argument types Argument types given: RngMPolElt, RngMPolElt Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Fri Mar 12 02:18:03 2004 Input: > P := PolynomialRing(IntegerRing(), 2); > S := [(1-x-y^2)^2,(1-2*x-y^3)^2]; > I := Ideal(S); > GroebnerBasis(I); > (1-x-y^2)*(1-2*x-y^3) in I; Output: Magma V2.10-6 Fri Mar 12 2004 02:18:00 on modular [Seed = 2508501433] ------------------------------------- [ x^2 + 2*x*y^2 - 2*x + y^4 - 2*y^2 + 1, x*y^6 + 2*x*y^3 - 16*x*y^2 + 4*x*y + 9*x + 2*y^8 - 3*y^7 + y^6 - 10*y^4 + 2*y^3 + 18*y^2 - 3*y - 7, 4*x*y^3 - 8*x*y^2 + 4*x + y^6 - 4*y^4 - 2*y^3 + 8*y^2 - 3, y^9 - 6*y^8 + 12*y^7 - 5*y^6 - 12*y^5 + 12*y^4 + 3*y^3 - 6*y^2 + 1 ] false Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Fri Mar 12 02:18:56 2004 Input: > P := PolynomialRing(IntegerRing(), 2); > S := [(1-x-y^2)^2,(1-2*x-y^3)^2, (1-5*x-y^4)^2]; > I := Ideal(S); > GroebnerBasis(I); > (1-x-y^2)*(1-2*x-y^3)*(1-5*x-y^4) in I; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Mar 12 2004 02:18:33 on modular [Seed = 2676931538] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 17563 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Fri Mar 12 02:19:34 2004 Input: > P := PolynomialRing(IntegerRing(), 2); > S := [(1-x-y^2)^2,(1-2*x-y^3)^2, (1-x-y^4)^2]; > I := Ideal(S); > GroebnerBasis(I); > (1-x-y^2)*(1-2*x-y^3)*(1-x-y^4) in I; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Mar 12 2004 02:19:11 on modular [Seed = 2695988427] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 17572 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Fri Mar 12 02:20:04 2004 Input: > P := PolynomialRing(IntegerRing(), 2); > S := [(1-x-y^2)^2,(1-2*x-y^3)^2, (1-x-y^4)^2]; > I := Ideal(S); > (1-x-y^2)*(1-2*x-y^3)*(1-x-y^4) in I; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Mar 12 2004 02:19:41 on modular [Seed = 2864418339] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 17582 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Fri Mar 12 02:20:15 2004 Input: > P := PolynomialRing(IntegerRing(), 2); > S := [(1-x-y^2)^2,(1-x-y^3)^2, (1-x-y^4)^2]; > I := Ideal(S); > (1-x-y^2)*(1-x-y^3)*(1-x-y^4) in I; Output: Magma V2.10-6 Fri Mar 12 2004 02:20:12 on modular [Seed = 3131809298] ------------------------------------- true Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Fri Mar 12 02:29:39 2004 Input: > P := PolynomialRing(IntegerRing(), 2); > S := [(1-x-2*y^2)^2,(1-x-3*y^3)^2, (1-x-4*y^4)^2]; > I := Ideal(S); > (1-x-2*y^2)*(1-x-3*y^3)*(1-x-4*y^4) in I; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Mar 12 2004 02:29:16 on modular [Seed = 3420122371] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 17615 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Fri Mar 12 02:30:14 2004 Input: > P := PolynomialRing(IntegerRing(), 2); > S := [(1-x-1*y^2)^2,(1-x-1*y^3)^2, (1-x-1*y^4)^2]; > I := Ideal(S); > (1-x-y^2)*(1-x-y^2)*(1-x-y^4) in I; Output: Magma V2.10-6 Fri Mar 12 2004 02:30:11 on modular [Seed = 3841311715] ------------------------------------- true Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee91.uab.es. (158.109.66.91) Time: Fri Mar 12 03:58:43 2004 Input: Alumnes: Sergio López Cantero David López Giró Practica TC -Sessió 1- -EXERCICI 1- conj:= { n : n in [1..366 by 1] | (n mod 7) eq 4}; > conj; Output: Magma V2.10-6 Fri Mar 12 2004 03:58:40 on modular [Seed = 2626529113] ------------------------------------- >> Alumnes: Sergio L^3pez Cantero ^ User error: bad syntax >> David L^3pez Gir^3 ^ User error: bad syntax >> Practica TC -Sessi^3 1- ^ User error: bad syntax >> -EXERCICI 1- ^ User error: bad syntax { 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 } Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee91.uab.es. (158.109.66.91) Time: Fri Mar 12 04:05:06 2004 Input: t73:= [7^(3-k) : k in {1..3}]; Output: Magma V2.10-6 Fri Mar 12 2004 04:05:03 on modular [Seed = 3182198916] ------------------------------------- Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee91.uab.es. (158.109.66.91) Time: Fri Mar 12 04:05:21 2004 Input: t73:= [7^(3-k) : k in {1..3}]; t73; Output: Magma V2.10-6 Fri Mar 12 2004 04:05:18 on modular [Seed = 3268673418] ------------------------------------- [ 49, 7, 1 ] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-26-13.go.retevision.es. (81.61.13.26) Time: Fri Mar 12 04:08:12 2004 Input: P:=PolynomialRing(RealField()); t73 := x^(seqt[1]) + x^(seqt[2]) + x^(seqt[3]); t73; n73 := x^(seqt[1] + seqt[2] + seqt[3]); n73; Olav := {[a,b]: a,b in GF(7,3) | Evaluate(n73,a) eq Evaluate(t73,b)}; #Olav; Output: Magma V2.10-6 Fri Mar 12 2004 04:08:08 on modular [Seed = 2458103661] ------------------------------------- >> t73 := x^(seqt[1]) + x^(seqt[2]) + x^(seqt[3]); ^ User error: Identifier 'seqt' has not been declared or assigned >> t73; ^ User error: Identifier 't73' has not been declared or assigned >> n73 := x^(seqt[1] + seqt[2] + seqt[3]); ^ User error: Identifier 'seqt' has not been declared or assigned >> n73; ^ User error: Identifier 'n73' has not been declared or assigned >> Olav := {[a,b]: a,b in GF(7,3) | Evaluate(n73,a) eq Evaluate(t73,b)}; ^ User error: Identifier 'n73' has not been declared or assigned >> #Olav;; ^ User error: Identifier 'Olav' has not been declared or assigned Total time: 3.099 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-26-13.go.retevision.es. (81.61.13.26) Time: Fri Mar 12 04:08:33 2004 Input: seqt := [7^(r-1) : r in {1..3}]; seqt; P:=PolynomialRing(RealField()); t73 := x^(seqt[1]) + x^(seqt[2]) + x^(seqt[3]); t73; n73 := x^(seqt[1] + seqt[2] + seqt[3]); n73; Olav := {[a,b]: a,b in GF(7,3) | Evaluate(n73,a) eq Evaluate(t73,b)}; #Olav; Output: Magma V2.10-6 Fri Mar 12 2004 04:08:30 on modular [Seed = 2575869840] ------------------------------------- [ 1, 7, 49 ] x^49 + x^7 + x x^57 >> Olav := {[a,b]: a,b in GF(7,3) | Evaluate(n73,a) eq Evaluate(t73,b)}; ^ Runtime error in 'Evaluate': Incompatible rings >> #Olav;; ^ User error: Identifier 'Olav' has not been declared or assigned Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee91.uab.es. (158.109.66.91) Time: Fri Mar 12 04:12:08 2004 Input: pt73:=function () C:=0; for i in {1..3} do C=C+x^(7^(3-i)); end for; return C; end function; Output: Magma V2.10-6 Fri Mar 12 2004 04:12:05 on modular [Seed = 3081144661] ------------------------------------- >> C=C+x^(7^(3-i)); ^ User error: Identifier 'x' has not been declared or assigned Total time: 3.229 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-26-13.go.retevision.es. (81.61.13.26) Time: Fri Mar 12 04:13:01 2004 Input: seqt := [7^(r-1) : r in {1..3}]; seqt; P:=PolynomialRing(RealField()); t73 := x^(seqt[1]) + x^(seqt[2]) + x^(seqt[3]); t73; n73 := x^(seqt[1] + seqt[2] + seqt[3]); n73; Olav := {[a,b]: a,b in {300..600} | Evaluate(n73,a) eq Evaluate(t73,b)}; #Olav; Output: Magma V2.10-6 Fri Mar 12 2004 04:12:45 on modular [Seed = 3199173044] ------------------------------------- [ 1, 7, 49 ] x^49 + x^7 + x x^57 0 Total time: 15.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee91.uab.es. (158.109.66.91) Time: Fri Mar 12 04:13:31 2004 Input: pt73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C=C+x^(7^(3-i)); end for; return C; end function; Output: Magma V2.10-6 Fri Mar 12 2004 04:13:28 on modular [Seed = 4108700619] ------------------------------------- Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee91.uab.es. (158.109.66.91) Time: Fri Mar 12 04:13:48 2004 Input: pt73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C=C+x^(7^(3-i)); end for; return C; end function; pt73; Output: Magma V2.10-6 Fri Mar 12 2004 04:13:45 on modular [Seed = 4209755572] ------------------------------------- function() ... end function Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-26-13.go.retevision.es. (81.61.13.26) Time: Fri Mar 12 04:14:24 2004 Input: seqt := [7^(r-1) : r in {1..3}]; seqt; P:=PolynomialRing(GF(7,3)); t73 := x^(seqt[1]) + x^(seqt[2]) + x^(seqt[3]); t73; n73 := x^(seqt[1] + seqt[2] + seqt[3]); n73; Olav := {[a,b]: a,b in GF(7,3) | Evaluate(n73,a) eq Evaluate(t73,b)}; #Olav; Output: Magma V2.10-6 Fri Mar 12 2004 04:14:19 on modular [Seed = 236925293] ------------------------------------- [ 1, 7, 49 ] x^49 + x^7 + x x^57 16807 Total time: 4.369 seconds, Total memory usage: 5.38MB ************** MAGMA ***************** Host aula-b-siee91.uab.es. (158.109.66.91) Time: Fri Mar 12 04:14:46 2004 Input: pt73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C=C+x^(7^(3-i)); end for; return {C}; end function; pt73; Output: Magma V2.10-6 Fri Mar 12 2004 04:14:43 on modular [Seed = 403253140] ------------------------------------- function() ... end function Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee91.uab.es. (158.109.66.91) Time: Fri Mar 12 04:15:15 2004 Input: pt73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C=C+x^(7^(3-i)); end for; return C; end function; w:=pt73; w; Output: Magma V2.10-6 Fri Mar 12 2004 04:15:12 on modular [Seed = 352594621] ------------------------------------- function() ... end function Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee91.uab.es. (158.109.66.91) Time: Fri Mar 12 04:16:02 2004 Input: pt73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C=C+x^(7^(3-i)); end for; return C; end function; w:=pt73(); w; Output: Magma V2.10-6 Fri Mar 12 2004 04:15:59 on modular [Seed = 540090343] ------------------------------------- x^49 = 0 x^7 = 0 x = 0 0 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee91.uab.es. (158.109.66.91) Time: Fri Mar 12 04:16:50 2004 Input: pt73:=function () P:=PolynomialRing(GF(7^3)); for i in {1..3} do C=C+x^(7^(3-i)); end for; return C; end function; w:=pt73(); w; Output: Magma V2.10-6 Fri Mar 12 2004 04:16:47 on modular [Seed = 958924494] ------------------------------------- >> C=C+x^(7^(3-i)); ^ User error: Identifier 'C' has not been declared or assigned >> w:=pt73(); ^ User error: Identifier 'pt73' has not been declared or assigned >> w;; ^ User error: Identifier 'w' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee91.uab.es. (158.109.66.91) Time: Fri Mar 12 04:17:06 2004 Input: pt73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C=C+x^(7^(3-i)); end for; return C; end function; w:=pt73(); w; Output: Magma V2.10-6 Fri Mar 12 2004 04:17:02 on modular [Seed = 841216565] ------------------------------------- x^49 = 0 x^7 = 0 x = 0 0 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee91.uab.es. (158.109.66.91) Time: Fri Mar 12 04:17:30 2004 Input: pt73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+x^(7^(3-i)); end for; return C; end function; w:=pt73(); w; Output: Magma V2.10-6 Fri Mar 12 2004 04:17:27 on modular [Seed = 1281199203] ------------------------------------- x^49 + x^7 + x Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee91.uab.es. (158.109.66.91) Time: Fri Mar 12 04:19:00 2004 Input: pq73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+(7^(3-i)); end for; return x^C; end function; w:=pt73(); w; Output: Magma V2.10-6 Fri Mar 12 2004 04:18:57 on modular [Seed = 1163167180] ------------------------------------- >> w:=pt73(); ^ User error: Identifier 'pt73' has not been declared or assigned >> w;; ^ User error: Identifier 'w' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee91.uab.es. (158.109.66.91) Time: Fri Mar 12 04:19:10 2004 Input: pq73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+(7^(3-i)); end for; return x^C; end function; w:=qt73(); w; Output: Magma V2.10-6 Fri Mar 12 2004 04:19:07 on modular [Seed = 1582276317] ------------------------------------- >> w:=qt73(); ^ User error: Identifier 'qt73' has not been declared or assigned >> w;; ^ User error: Identifier 'w' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee91.uab.es. (158.109.66.91) Time: Fri Mar 12 04:19:18 2004 Input: pq73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+(7^(3-i)); end for; return x^C; end function; w:=pqt73(); w; Output: Magma V2.10-6 Fri Mar 12 2004 04:19:16 on modular [Seed = 1464244171] ------------------------------------- >> w:=pqt73(); ^ User error: Identifier 'pqt73' has not been declared or assigned >> w;; ^ User error: Identifier 'w' has not been declared or assigned Total time: 2.859 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee91.uab.es. (158.109.66.91) Time: Fri Mar 12 04:19:22 2004 Input: pq73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+(7^(3-i)); end for; return x^C; end function; w:=pqt73(); w; Output: Magma V2.10-6 Fri Mar 12 2004 04:19:19 on modular [Seed = 1634771454] ------------------------------------- >> w:=pqt73(); ^ User error: Identifier 'pqt73' has not been declared or assigned >> w;; ^ User error: Identifier 'w' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee91.uab.es. (158.109.66.91) Time: Fri Mar 12 04:19:28 2004 Input: pq73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+(7^(3-i)); end for; return x^C; end function; w:=pq73(); w; Output: Magma V2.10-6 Fri Mar 12 2004 04:19:25 on modular [Seed = 2053880559] ------------------------------------- x^57 Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee91.uab.es. (158.109.66.91) Time: Fri Mar 12 04:19:43 2004 Input: pn73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+(7^(3-i)); end for; return x^C; end function; w:=pn73(); w; Output: Magma V2.10-6 Fri Mar 12 2004 04:19:40 on modular [Seed = 1969534417] ------------------------------------- x^57 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host l2-372b.kn.vutbr.cz. (147.229.201.96) Time: Fri Mar 12 07:11:55 2004 Input: P:=PolynomialAlgebra(GF(2)); function PolynomialOrder(p); //------------------------------------------------------------------- // PolynomialOrder calculates the order of a polynomial over a finite // field //------------------------------------------------------------------- Fqm:=SplittingField(p); // Create extension field GF(q^m) if IsIrreducible(p) then // Order of p is order of root of p order:=Order(Representative(Roots(p,Fqm))[1]); else // Order of prime factors of p must P:=Parent(p); // divide order of p x:=P.1; allorders:={Order(a[1]):a in Roots(p,Fqm)}; orders:=[order:order in allorders]; step:=Lcm(orders); order:=0; repeat order:=order+step; until Gcd(x^order-1,p) eq p; end if; return order; end function; function SecPoly(s); return &+[x^i:i in s]; end function; function PrintLaTeXFactor(n); a:=Factorization(n); c:=""; for b in a do c:=c*IntegerToString(b[1])*"^{"*IntegerToString(b[2])*"}"; end for; return c; end function; function PrintIrreduciblePolynomialOrder(m,w); //------------------------------------------------------------------- // PrintIrreduciblePolynomialOrder(m,w) prints all irreducible // polynomials over GF(2) of degree m and weight w and their orders. // // Created by Mikael Olofsson 970627. //------------------------------------------------------------------- if m lt 0 then powers:=[]; elif m eq 0 then if w eq 1 then powers:=[[0]]; else powers:=[]; end if; elif (m ge w-1) and (w ge 2) then //P:=PolynomialAlgebra(GF(2)); powers:=[[0]]; if w ge 3 then for i in [2..w-1] do newpowers:=[]; for a in powers do for j in [a[i-1]+1..m-w+i] do Append(~newpowers,Append(a,j)); end for; end for; powers:=newpowers; end for; end if; powers:=[Append(a,m):a in powers]; else powers:=[]; end if; polynomials:=[SecPoly(a):a in powers]; irrpolynomials:=[p:p in polynomials|IsIrreducible(p)]; M:=#irrpolynomials; print "A search of irreducible polynomials using MAGMA gave the following result."; print " "; print "Found", M, "irreducible polynomials"; print "of degree", m, "and weight "*IntegerToString(w)*"."; print " "; print "begin{tabular}{|l|l|}"; print " Polynomial & Order "; maxorder:=0; for p in irrpolynomials do order:=PolynomialOrder(p); maxorder:=Max({maxorder,order}); print "$", p, "$ & $"*IntegerToString(order)*"="*PrintLaTeXFactor(order)*"$ "; end for; print "end{tabular}"; return irrpolynomials,M,maxorder; end function; print "Use DoItNow(m1,m2,step) to generate irreducible polynomials of"; print "weight 5"; procedure DoItNow(m1,m2,step); //------------------------------------------------------------------- // DoItNow(m1,m2,step) is a procedure that generates tables of // irreducible polynomials of weight five using the function // PrintIrreduciblePolynomialOrder(m,w). For each degree two separate // files are created for the polynomials, one in MAGMA form and one // in LaTeX form. Additionally, for each degree interval of length // step a file containing a table of degrees and the number of // irreducible polynomials of that degree and weight three is produced. // // Created by Mikael Olofsson 970706. //------------------------------------------------------------------- mm1:=IntegerToString(m1); mm2:=IntegerToString(m2); print "Searching for irreducible polynomials in the interval ]"*mm1*","*mm2*"]."; print " "; for i in [m1..m2 by step] do i1:=IntegerToString(i+1); i2:=IntegerToString(i+step); print "Treatíng degrees "*i1*" - "*i2; filename1:="WeightFivePoly"*i1*"-"*i2*".tex"; filename2:="WeightFivePoly"*i1*"-"*i2*".def"; print "Initiating "*filename1*"."; SetOutputFile(filename1); print "The number $N_m$ of irreducible polynomials of weight $5$"; print "and the maximum order $r$ of these polynomials for degrees $min["*i1*","*i2*"]$."; print " "; print "begin{tabular}{|l|l|}hline"; print " $m$ & $N_m$ & $r$ hlinehline"; UnsetOutputFile(); print "Initiating "*filename2*"."; SetOutputFile(filename2); print "// Definition of IrrPolyWeightFiveNumberAndOrder, containing"; print "// [m,Nm,r], the number Nm of irreducible polynomials of weight 5"; print "// and the maximum order r of these polynomials for degrees"; print "// m ranging from "*i1*" to "*i2*"."; print " "; print "IrrPolyWeightFiveNumberAndOrder:=[]"; UnsetOutputFile(); for j in [1..step] do ij1:=IntegerToString(i+j); filename3:="WeightFivePoly"*ij1*".tex"; filename4:="WeightFivePoly"*ij1*".def"; print "Writing in "*filename3*"."; SetOutputFile(filename3); irrpolys, Nm, maxorder := PrintIrreduciblePolynomialOrder(i+j,5); UnsetOutputFile(); print "Writing in "*filename4*"."; SetOutputFile(filename4); print "// Definition of irrpolys"*ij1*"weight5, all irreducible polynomials"; print "// of degree "*ij1*" and weight 5 over GF(2), and definition of "; print "// N"*ij1*"weight5, the number of these polynomials. Also definition of "; print "// maxorder"*ij1*"weight5, the maximum order among these polynomials."; print " "; print "irrpolys"*ij1*"weight5:=",irrpolys,";"; print "N"*ij1*"weight5:=",Nm,";"; print "maxorder"*ij1*"weight5:=",maxorder,";"; UnsetOutputFile(); print "Writing in "*filename1*"."; SetOutputFile(filename1); NNm:=IntegerToString(Nm); MO:=IntegerToString(maxorder); print " "*ij1*" & "*NNm*" & "*MO*" "; UnsetOutputFile(); print "Writing in "*filename2*"."; SetOutputFile(filename2); print "Append(~IrrPolyWeightFiveNumberAndOrder,["*ij1*","*NNm*","*MO*"]);"; UnsetOutputFile(); end for; print "Terminating "*filename1*"."; SetOutputFile(filename1); print "hline"; print "end{tabular}"; UnsetOutputFile(); print "Terminating "*filename2*"."; SetOutputFile(filename2); print "// Ready!"; UnsetOutputFile(); print "Subinterval ready."; print " "; end for; print "The search is terminated."; end procedure; Output: WARNING: MAGMA command contains unsafe command 'file', so it will not be executed. ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Fri Mar 12 07:25:41 2004 Input: 2+3 Output: Magma V2.10-6 Fri Mar 12 2004 07:25:38 on modular [Seed = 1213834240] ------------------------------------- 5 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Fri Mar 12 07:26:15 2004 Input: x^2+1/(x+1) Output: Magma V2.10-6 Fri Mar 12 2004 07:26:12 on modular [Seed = 1095806255] ------------------------------------- >> x^2+1/(x+1) ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cisco-cache-1.kuleuven.ac.be. (134.58.253.113) Time: Fri Mar 12 09:14:58 2004 Input: 1+2 Output: Magma V2.10-6 Fri Mar 12 2004 09:14:55 on modular [Seed = 1163182225] ------------------------------------- 3 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 09:54:57 2004 Input: i:i in [i..366] by 7 Output: Magma V2.10-6 Fri Mar 12 2004 09:54:54 on modular [Seed = 2441092772] ------------------------------------- >> i:i in [i..366] by 7 ^ User error: bad syntax Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 09:55:31 2004 Input: i:i + 7 in [i..366] by 7 Output: Magma V2.10-6 Fri Mar 12 2004 09:55:28 on modular [Seed = 2898076615] ------------------------------------- >> i:i + 7 in [i..366] by 7 ^ User error: bad syntax Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 10:01:41 2004 Input: i:= i + 7 in [i..366] by 7 Output: Magma V2.10-6 Fri Mar 12 2004 10:01:38 on modular [Seed = 3352712990] ------------------------------------- >> i:= i + 7 in [i..366] by 7 ^ User error: bad syntax Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 10:04:16 2004 Input: i:= i + 7 in [i..366]; Output: Magma V2.10-6 Fri Mar 12 2004 10:04:13 on modular [Seed = 3721153720] ------------------------------------- >> i:= i + 7 in [i..366]; ^ User error: Identifier 'i' has not been declared or assigned Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 10:04:47 2004 Input: i: i + 7 in [i..366]; Output: Magma V2.10-6 Fri Mar 12 2004 10:04:44 on modular [Seed = 3959061100] ------------------------------------- >> i: i + 7 in [i..366]; ^ User error: bad syntax Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 10:05:33 2004 Input: i:= i in [i..366]; Output: Magma V2.10-6 Fri Mar 12 2004 10:05:30 on modular [Seed = 3858003028] ------------------------------------- >> i:= i in [i..366]; ^ User error: Identifier 'i' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 10:07:38 2004 Input: i:= {i : i in [i..366 by 7]}; Output: Magma V2.10-6 Fri Mar 12 2004 10:07:34 on modular [Seed = 4243418816] ------------------------------------- >> i:= {i : i in [i..366 by 7]}; ^ Runtime error: Variable 'i' has not been initialized Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 10:07:56 2004 Input: i:= {i : i in [1..366 by 7]}; Output: Magma V2.10-6 Fri Mar 12 2004 10:07:53 on modular [Seed = 219979592] ------------------------------------- Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 10:08:09 2004 Input: i:= {i : i in [1..366 by 7]}; i; Output: Magma V2.10-6 Fri Mar 12 2004 10:08:06 on modular [Seed = 102208604] ------------------------------------- { 1, 8, 15, 22, 29, 36, 43, 50, 57, 64, 71, 78, 85, 92, 99, 106, 113, 120, 127, 134, 141, 148, 155, 162, 169, 176, 183, 190, 197, 204, 211, 218, 225, 232, 239, 246, 253, 260, 267, 274, 281, 288, 295, 302, 309, 316, 323, 330, 337, 344, 351, 358, 365 } Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 10:51:16 2004 Input: i:= [i : i in [1..366 by 7]]; i; Output: Magma V2.10-6 Fri Mar 12 2004 10:51:13 on modular [Seed = 1702164760] ------------------------------------- [ 1, 8, 15, 22, 29, 36, 43, 50, 57, 64, 71, 78, 85, 92, 99, 106, 113, 120, 127, 134, 141, 148, 155, 162, 169, 176, 183, 190, 197, 204, 211, 218, 225, 232, 239, 246, 253, 260, 267, 274, 281, 288, 295, 302, 309, 316, 323, 330, 337, 344, 351, 358, 365 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 10:52:39 2004 Input: i:= [i : i in [4..366 by 7]]; i; Output: Magma V2.10-6 Fri Mar 12 2004 10:52:36 on modular [Seed = 2121261750] ------------------------------------- [ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 200-BAR2-X4.libre.retevision.es. (62.82.186.200) Time: Fri Mar 12 10:54:30 2004 Input: polav73:=function() c:=[]; for i in GF(7^3) do for j in GF(7^3) do if (pq73(i) eq pt73(j) ) then Include(C, (i,j)); end if; end for; end for; return C; end function; Output: Magma V2.10-6 Fri Mar 12 2004 10:54:27 on modular [Seed = 1885465935] ------------------------------------- >> if (pq73(i) eq pt73(j) ) then Include(C, (i,j)); ^ User error: Identifier 'pq73' has not been declared or assigned Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 10:54:50 2004 Input: pt73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+x^(7^(3-i)); end for; return C; end function; pn73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+(7^(3-i)); end for; return x^C; end function; polav73:=function() c:=[]; for i in GF(7^3) do for j in GF(7^3) do if (pq73(i) eq pt73(j) ) then Include(C, (i,j)); end if; end for; end for; return C; end function; Output: Magma V2.10-6 Fri Mar 12 2004 10:54:47 on modular [Seed = 2325419969] ------------------------------------- >> if (pq73(i) eq pt73(j) ) then Include(C, (i,j)); ^ User error: Identifier 'pq73' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 10:55:10 2004 Input: pt73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+x^(7^(3-i)); end for; return C; end function; pn73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+(7^(3-i)); end for; return x^C; end function; polav73:=function() c:=[]; for i in GF(7^3) do for j in GF(7^3) do if (pn73(i) eq pt73(j) ) then Include(C, (i,j)); end if; end for; end for; return C; end function; Output: Magma V2.10-6 Fri Mar 12 2004 10:55:07 on modular [Seed = 2676884168] ------------------------------------- >> if (pn73(i) eq pt73(j) ) then Include(C, (i,j)); ^ User error: Identifier 'C' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 10:55:36 2004 Input: pt73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+x^(7^(3-i)); end for; return C; end function; pn73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+(7^(3-i)); end for; return x^C; end function; polav73:=function() C:=[]; for i in GF(7^3) do for j in GF(7^3) do if (pn73(i) eq pt73(j) ) then Include(C, (i,j)); end if; end for; end for; return C; end function; Output: Magma V2.10-6 Fri Mar 12 2004 10:55:33 on modular [Seed = 2424376809] ------------------------------------- Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 10:55:53 2004 Input: pt73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+x^(7^(3-i)); end for; return C; end function; pn73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+(7^(3-i)); end for; return x^C; end function; polav73:=function() C:=[]; for i in GF(7^3) do for j in GF(7^3) do if (pn73(i) eq pt73(j) ) then Include(C, (i,j)); end if; end for; end for; return C; end function; polav73(); Output: Magma V2.10-6 Fri Mar 12 2004 10:55:50 on modular [Seed = 2847421475] ------------------------------------- [
:19]( ) >> if (pn73(i) eq pt73(j) ) then Include(C, (i,j)); ^ Runtime error: Number of arguments (1) does not equal expected number of arguments (0) Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 10:56:23 2004 Input: pt73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+x^(7^(3-i)); end for; return C; end function; pn73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+(7^(3-i)); end for; return x^C; end function; polav73:=function() C:=[]; for i in GF(7^3) do for j in GF(7^3) do if (pn73[i] eq pt73[j] ) then Include(C, (i,j)); end if; end for; end for; return C; end function; polav73(); Output: Magma V2.10-6 Fri Mar 12 2004 10:56:20 on modular [Seed = 2729656074] ------------------------------------- [
:19]( ) >> if (pn73[i] eq pt73[j] ) then Include(C, (i,j)); ^ Runtime error in '[]': Bad argument types Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 200-BAR2-X4.libre.retevision.es. (62.82.186.200) Time: Fri Mar 12 10:56:28 2004 Input: pn73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+(7^(3-i)); end for; return x^C; end function; pt73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+x^(7^(3-i)); end for; return C; end function; polav73:=function() c:=[]; for i in GF(7^3) do for j in GF(7^3) do if (pq73(i) eq pt73(j) ) then Include(C, (i,j)); end if; end for; end for; return C; end function; polav73; Output: Magma V2.10-6 Fri Mar 12 2004 10:56:25 on modular [Seed = 3148490270] ------------------------------------- >> if (pq73(i) eq pt73(j) ) then Include(C, (i,j)); ^ User error: Identifier 'pq73' has not been declared or assigned >> polav73;; ^ User error: Identifier 'polav73' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 10:56:48 2004 Input: pt73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+x^(7^(3-i)); end for; return C; end function; pn73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+(7^(3-i)); end for; return x^C; end function; polav73:=function() C:=[]; for i in GF(7^3) do for j in GF(7^3) do if (pn73()=i eq pt73()=j ) then Include(C, (i,j)); end if; end for; end for; return C; end function; polav73(); Output: Magma V2.10-6 Fri Mar 12 2004 10:56:45 on modular [Seed = 3437056381] ------------------------------------- >> if (pn73()=i eq pt73()=j ) then Include(C, (i,j)); ^ User error: relation chains can only be used inside a constructor >> polav73();; ^ User error: Identifier 'polav73' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 200-BAR2-X4.libre.retevision.es. (62.82.186.200) Time: Fri Mar 12 10:57:05 2004 Input: pn73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+(7^(3-i)); end for; return x^C; end function; pt73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+x^(7^(3-i)); end for; return C; end function; polav73:=function() c:=[]; for i in GF(7^3) do for j in GF(7^3) do if (pn73(i) eq pt73(j) ) then Include(C, (i,j)); end if; end for; end for; return C; end function; polav73; Output: Magma V2.10-6 Fri Mar 12 2004 10:57:02 on modular [Seed = 3336002308] ------------------------------------- >> if (pn73(i) eq pt73(j) ) then Include(C, (i,j)); ^ User error: Identifier 'C' has not been declared or assigned >> polav73;; ^ User error: Identifier 'polav73' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 200-BAR2-X4.libre.retevision.es. (62.82.186.200) Time: Fri Mar 12 10:57:32 2004 Input: pn73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+(7^(3-i)); end for; return x^C; end function; pt73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+x^(7^(3-i)); end for; return C; end function; polav73:=function() C:=[]; for i in GF(7^3) do for j in GF(7^3) do if (pn73(i) eq pt73(j) ) then Include(C, (i,j)); end if; end for; end for; return C; end function; polav73; Output: Magma V2.10-6 Fri Mar 12 2004 10:57:29 on modular [Seed = 3754836538] ------------------------------------- function() ... end function Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 200-BAR2-X4.libre.retevision.es. (62.82.186.200) Time: Fri Mar 12 10:58:39 2004 Input: pn73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+(7^(3-i)); end for; return x^C; end function; pt73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+x^(7^(3-i)); end for; return C; end function; polav73:=function() C:=[]; for i in GF(7^3) do for j in GF(7^3) do if (pn73(i) eq pt73(j) ) then Include(C, (i,j)); end if; end for; end for; return C; end function; polav73(); Output: Magma V2.10-6 Fri Mar 12 2004 10:58:36 on modular [Seed = 3502329584] ------------------------------------- [
:19]( ) >> if (pn73(i) eq pt73(j) ) then Include(C, (i,j)); ^ Runtime error: Number of arguments (1) does not equal expected number of arguments (0) Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 11:00:27 2004 Input: pt73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+x^(7^(3-i)); end for; return C; end function; pn73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+(7^(3-i)); end for; return x^C; end function; polav73:=function() C:=[]; for i in GF(7^3) do for j in GF(7^3) do if (Evaluate(pn73(),i) eq Evaluate(pt73(),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; polav73(); Output: Magma V2.10-6 Fri Mar 12 2004 11:00:05 on modular [Seed = 3807607915] ------------------------------------- [ [ 1, $.1 ] ] [ [ 1, $.1^2 ] ] [ [ 1, $.1^7 ] ] [ [ 1, $.1^10 ] ] [ [ 1, $.1^11 ] ] [ [ 1, $.1^14 ] ] [ [ 1, $.1^16 ] ] [ [ 1, $.1^25 ] ] [ [ 1, $.1^37 ] ] [ [ 1, $.1^49 ] ] [ [ 1, $.1^66 ] ] [ [ 1, $.1^70 ] ] [ [ 1, $.1^77 ] ] [ [ 1, $.1^87 ] ] [ [ 1, $.1^90 ] ] [ [ 1, $.1^97 ] ] [ [ 1, $.1^98 ] ] [ [ 1, $.1^100 ] ] [ [ 1, $.1^103 ] ] [ [ 1, $.1^112 ] ] [ [ 1, $.1^120 ] ] [ [ 1, $.1^131 ] ] [ [ 1, $.1^132 ] ] [ [ 1, $.1^137 ] ] [ [ 1, $.1^146 ] ] [ [ 1, $.1^148 ] ] [ [ 1, $.1^156 ] ] [ [ 1, $.1^159 ] ] [ [ 1, $.1^175 ] ] [ [ 1, $.1^195 ] ] [ [ 1, $.1^197 ] ] [ [ 1, $.1^199 ] ] [ [ 1, $.1^215 ] ] [ [ 1, $.1^233 ] ] [ [ 1, $.1^240 ] ] [ [ 1, $.1^259 ] ] [ [ 1, $.1^263 ] ] [ [ 1, $.1^267 ] ] [ [ 1, $.1^275 ] ] [ [ 1, 5 ] ] [ [ 1, $.1^288 ] ] [ [ 1, $.1^306 ] ] [ [ 1, $.1^307 ] ] [ [ 1, $.1^312 ] ] [ [ 1, $.1^314 ] ] [ [ 1, $.1^321 ] ] [ [ 1, $.1^337 ] ] [ [ 1, $.1^338 ] ] [ [ 1, $.1^339 ] ] [ [ $.1, 1 ] ] [ [ $.1, $.1^3 ] ] [ [ $.1, $.1^21 ] ] [ [ $.1, $.1^22 ] ] [ [ $.1, $.1^27 ] ] [ [ $.1, $.1^29 ] ] [ [ $.1, $.1^36 ] ] [ [ $.1, $.1^52 ] ] [ [ $.1, $.1^53 ] ] [ [ $.1, $.1^54 ] ] [ [ $.1, $.1^58 ] ] [ [ $.1, $.1^59 ] ] [ [ $.1, $.1^64 ] ] [ [ $.1, $.1^67 ] ] [ [ $.1, $.1^68 ] ] [ [ $.1, $.1^71 ] ] [ [ $.1, $.1^73 ] ] [ [ $.1, $.1^82 ] ] [ [ $.1, $.1^94 ] ] [ [ $.1, $.1^106 ] ] [ [ $.1, $.1^123 ] ] [ [ $.1, $.1^127 ] ] [ [ $.1, $.1^134 ] ] [ [ $.1, $.1^144 ] ] [ [ $.1, $.1^147 ] ] [ [ $.1, $.1^154 ] ] [ [ $.1, $.1^155 ] ] [ [ $.1, $.1^157 ] ] [ [ $.1, $.1^160 ] ] [ [ $.1, $.1^169 ] ] [ [ $.1, $.1^177 ] ] [ [ $.1, $.1^188 ] ] [ [ $.1, $.1^189 ] ] [ [ $.1, $.1^194 ] ] [ [ $.1, $.1^203 ] ] [ [ $.1, $.1^205 ] ] [ [ $.1, $.1^213 ] ] [ [ $.1, $.1^216 ] ] [ [ $.1, $.1^232 ] ] [ [ $.1, $.1^252 ] ] [ [ $.1, $.1^254 ] ] [ [ $.1, $.1^256 ] ] [ [ $.1, $.1^272 ] ] [ [ $.1, $.1^290 ] ] [ [ $.1, $.1^297 ] ] [ [ $.1, $.1^316 ] ] [ [ $.1, $.1^320 ] ] [ [ $.1, $.1^324 ] ] [ [ $.1, $.1^332 ] ] [ [ $.1^2, $.1^5 ] ] [ [ $.1^2, $.1^12 ] ] [ [ $.1^2, $.1^31 ] ] [ [ $.1^2, $.1^35 ] ] [ [ $.1^2, $.1^39 ] ] [ [ $.1^2, $.1^47 ] ] [ [ $.1^2, 3 ] ] [ [ $.1^2, $.1^60 ] ] [ [ $.1^2, $.1^78 ] ] [ [ $.1^2, $.1^79 ] ] [ [ $.1^2, $.1^84 ] ] [ [ $.1^2, $.1^86 ] ] [ [ $.1^2, $.1^93 ] ] [ [ $.1^2, $.1^109 ] ] [ [ $.1^2, $.1^110 ] ] [ [ $.1^2, $.1^111 ] ] [ [ $.1^2, $.1^115 ] ] [ [ $.1^2, $.1^116 ] ] [ [ $.1^2, $.1^121 ] ] [ [ $.1^2, $.1^124 ] ] [ [ $.1^2, $.1^125 ] ] [ [ $.1^2, $.1^128 ] ] [ [ $.1^2, $.1^130 ] ] [ [ $.1^2, $.1^139 ] ] [ [ $.1^2, $.1^151 ] ] [ [ $.1^2, $.1^163 ] ] [ [ $.1^2, $.1^180 ] ] [ [ $.1^2, $.1^184 ] ] [ [ $.1^2, $.1^191 ] ] [ [ $.1^2, $.1^201 ] ] [ [ $.1^2, $.1^204 ] ] [ [ $.1^2, $.1^211 ] ] [ [ $.1^2, $.1^212 ] ] [ [ $.1^2, $.1^214 ] ] [ [ $.1^2, $.1^217 ] ] [ [ $.1^2, $.1^226 ] ] [ [ $.1^2, $.1^234 ] ] [ [ $.1^2, $.1^245 ] ] [ [ $.1^2, $.1^246 ] ] [ [ $.1^2, $.1^251 ] ] [ [ $.1^2, $.1^260 ] ] [ [ $.1^2, $.1^262 ] ] [ [ $.1^2, $.1^270 ] ] [ [ $.1^2, $.1^273 ] ] [ [ $.1^2, $.1^289 ] ] [ [ $.1^2, $.1^309 ] ] [ [ $.1^2, $.1^311 ] ] [ [ $.1^2, $.1^313 ] ] [ [ $.1^2, $.1^329 ] ] [ [ $.1^3, $.1^4 ] ] [ [ $.1^3, $.1^24 ] ] [ [ $.1^3, $.1^26 ] ] [ [ $.1^3, $.1^28 ] ] [ [ $.1^3, $.1^44 ] ] [ [ $.1^3, $.1^62 ] ] [ [ $.1^3, $.1^69 ] ] [ [ $.1^3, $.1^88 ] ] [ [ $.1^3, $.1^92 ] ] [ [ $.1^3, $.1^96 ] ] [ [ $.1^3, $.1^104 ] ] [ [ $.1^3, 2 ] ] [ [ $.1^3, $.1^117 ] ] [ [ $.1^3, $.1^135 ] ] [ [ $.1^3, $.1^136 ] ] [ [ $.1^3, $.1^141 ] ] [ [ $.1^3, $.1^143 ] ] [ [ $.1^3, $.1^150 ] ] [ [ $.1^3, $.1^166 ] ] [ [ $.1^3, $.1^167 ] ] [ [ $.1^3, $.1^168 ] ] [ [ $.1^3, $.1^172 ] ] [ [ $.1^3, $.1^173 ] ] [ [ $.1^3, $.1^178 ] ] [ [ $.1^3, $.1^181 ] ] [ [ $.1^3, $.1^182 ] ] [ [ $.1^3, $.1^185 ] ] [ [ $.1^3, $.1^187 ] ] [ [ $.1^3, $.1^196 ] ] [ [ $.1^3, $.1^208 ] ] [ [ $.1^3, $.1^220 ] ] [ [ $.1^3, $.1^237 ] ] [ [ $.1^3, $.1^241 ] ] [ [ $.1^3, $.1^248 ] ] [ [ $.1^3, $.1^258 ] ] [ [ $.1^3, $.1^261 ] ] [ [ $.1^3, $.1^268 ] ] [ [ $.1^3, $.1^269 ] ] [ [ $.1^3, $.1^271 ] ] [ [ $.1^3, $.1^274 ] ] [ [ $.1^3, $.1^283 ] ] [ [ $.1^3, $.1^291 ] ] [ [ $.1^3, $.1^302 ] ] [ [ $.1^3, $.1^303 ] ] [ [ $.1^3, $.1^308 ] ] [ [ $.1^3, $.1^317 ] ] [ [ $.1^3, $.1^319 ] ] [ [ $.1^3, $.1^327 ] ] [ [ $.1^3, $.1^330 ] ] [ [ $.1^4, $.1^6 ] ] [ [ $.1^4, $.1^17 ] ] [ [ $.1^4, $.1^18 ] ] [ [ $.1^4, $.1^23 ] ] [ [ $.1^4, $.1^32 ] ] [ [ $.1^4, $.1^34 ] ] [ [ $.1^4, $.1^42 ] ] [ [ $.1^4, $.1^45 ] ] [ [ $.1^4, $.1^61 ] ] [ [ $.1^4, $.1^81 ] ] [ [ $.1^4, $.1^83 ] ] [ [ $.1^4, $.1^85 ] ] [ [ $.1^4, $.1^101 ] ] [ [ $.1^4, $.1^119 ] ] [ [ $.1^4, $.1^126 ] ] [ [ $.1^4, $.1^145 ] ] [ [ $.1^4, $.1^149 ] ] [ [ $.1^4, $.1^153 ] ] [ [ $.1^4, $.1^161 ] ] [ [ $.1^4, 6 ] ] [ [ $.1^4, $.1^174 ] ] [ [ $.1^4, $.1^192 ] ] [ [ $.1^4, $.1^193 ] ] [ [ $.1^4, $.1^198 ] ] [ [ $.1^4, $.1^200 ] ] [ [ $.1^4, $.1^207 ] ] [ [ $.1^4, $.1^223 ] ] [ [ $.1^4, $.1^224 ] ] [ [ $.1^4, $.1^225 ] ] [ [ $.1^4, $.1^229 ] ] [ [ $.1^4, $.1^230 ] ] [ [ $.1^4, $.1^235 ] ] [ [ $.1^4, $.1^238 ] ] [ [ $.1^4, $.1^239 ] ] [ [ $.1^4, $.1^242 ] ] [ [ $.1^4, $.1^244 ] ] [ [ $.1^4, $.1^253 ] ] [ [ $.1^4, $.1^265 ] ] [ [ $.1^4, $.1^277 ] ] [ [ $.1^4, $.1^294 ] ] [ [ $.1^4, $.1^298 ] ] [ [ $.1^4, $.1^305 ] ] [ [ $.1^4, $.1^315 ] ] [ [ $.1^4, $.1^318 ] ] [ [ $.1^4, $.1^325 ] ] [ [ $.1^4, $.1^326 ] ] [ [ $.1^4, $.1^328 ] ] [ [ $.1^4, $.1^331 ] ] [ [ $.1^4, $.1^340 ] ] [ [ $.1^5, $.1^9 ] ] [ [ $.1^5, $.1^13 ] ] [ [ $.1^5, $.1^20 ] ] [ [ $.1^5, $.1^30 ] ] [ [ $.1^5, $.1^33 ] ] [ [ $.1^5, $.1^40 ] ] [ [ $.1^5, $.1^41 ] ] [ [ $.1^5, $.1^43 ] ] [ [ $.1^5, $.1^46 ] ] [ [ $.1^5, $.1^55 ] ] [ [ $.1^5, $.1^63 ] ] [ [ $.1^5, $.1^74 ] ] [ [ $.1^5, $.1^75 ] ] [ [ $.1^5, $.1^80 ] ] [ [ $.1^5, $.1^89 ] ] [ [ $.1^5, $.1^91 ] ] [ [ $.1^5, $.1^99 ] ] [ [ $.1^5, $.1^102 ] ] [ [ $.1^5, $.1^118 ] ] [ [ $.1^5, $.1^138 ] ] [ [ $.1^5, $.1^140 ] ] [ [ $.1^5, $.1^142 ] ] [ [ $.1^5, $.1^158 ] ] [ [ $.1^5, $.1^176 ] ] [ [ $.1^5, $.1^183 ] ] [ [ $.1^5, $.1^202 ] ] [ [ $.1^5, $.1^206 ] ] [ [ $.1^5, $.1^210 ] ] [ [ $.1^5, $.1^218 ] ] [ [ $.1^5, 4 ] ] [ [ $.1^5, $.1^231 ] ] [ [ $.1^5, $.1^249 ] ] [ [ $.1^5, $.1^250 ] ] [ [ $.1^5, $.1^255 ] ] [ [ $.1^5, $.1^257 ] ] [ [ $.1^5, $.1^264 ] ] [ [ $.1^5, $.1^280 ] ] [ [ $.1^5, $.1^281 ] ] [ [ $.1^5, $.1^282 ] ] [ [ $.1^5, $.1^286 ] ] [ [ $.1^5, $.1^287 ] ] [ [ $.1^5, $.1^292 ] ] [ [ $.1^5, $.1^295 ] ] [ [ $.1^5, $.1^296 ] ] [ [ $.1^5, $.1^299 ] ] [ [ $.1^5, $.1^301 ] ] [ [ $.1^5, $.1^310 ] ] [ [ $.1^5, $.1^322 ] ] [ [ $.1^5, $.1^334 ] ] [ [ $.1^6, $.1 ] ] [ [ $.1^6, $.1^2 ] ] [ [ $.1^6, $.1^7 ] ] [ [ $.1^6, $.1^10 ] ] [ [ $.1^6, $.1^11 ] ] [ [ $.1^6, $.1^14 ] ] [ [ $.1^6, $.1^16 ] ] [ [ $.1^6, $.1^25 ] ] [ [ $.1^6, $.1^37 ] ] [ [ $.1^6, $.1^49 ] ] [ [ $.1^6, $.1^66 ] ] [ [ $.1^6, $.1^70 ] ] [ [ $.1^6, $.1^77 ] ] [ [ $.1^6, $.1^87 ] ] [ [ $.1^6, $.1^90 ] ] [ [ $.1^6, $.1^97 ] ] [ [ $.1^6, $.1^98 ] ] [ [ $.1^6, $.1^100 ] ] [ [ $.1^6, $.1^103 ] ] [ [ $.1^6, $.1^112 ] ] [ [ $.1^6, $.1^120 ] ] [ [ $.1^6, $.1^131 ] ] [ [ $.1^6, $.1^132 ] ] [ [ $.1^6, $.1^137 ] ] [ [ $.1^6, $.1^146 ] ] [ [ $.1^6, $.1^148 ] ] [ [ $.1^6, $.1^156 ] ] [ [ $.1^6, $.1^159 ] ] [ [ $.1^6, $.1^175 ] ] [ [ $.1^6, $.1^195 ] ] [ [ $.1^6, $.1^197 ] ] [ [ $.1^6, $.1^199 ] ] [ [ $.1^6, $.1^215 ] ] [ [ $.1^6, $.1^233 ] ] [ [ $.1^6, $.1^240 ] ] [ [ $.1^6, $.1^259 ] ] [ [ $.1^6, $.1^263 ] ] [ [ $.1^6, $.1^267 ] ] [ [ $.1^6, $.1^275 ] ] [ [ $.1^6, 5 ] ] [ [ $.1^6, $.1^288 ] ] [ [ $.1^6, $.1^306 ] ] [ [ $.1^6, $.1^307 ] ] [ [ $.1^6, $.1^312 ] ] [ [ $.1^6, $.1^314 ] ] [ [ $.1^6, $.1^321 ] ] [ [ $.1^6, $.1^337 ] ] [ [ $.1^6, $.1^338 ] ] [ [ $.1^6, $.1^339 ] ] [ [ $.1^7, 1 ] ] [ [ $.1^7, $.1^3 ] ] [ [ $.1^7, $.1^21 ] ] [ [ $.1^7, $.1^22 ] ] [ [ $.1^7, $.1^27 ] ] [ [ $.1^7, $.1^29 ] ] [ [ $.1^7, $.1^36 ] ] [ [ $.1^7, $.1^52 ] ] [ [ $.1^7, $.1^53 ] ] [ [ $.1^7, $.1^54 ] ] [ [ $.1^7, $.1^58 ] ] [ [ $.1^7, $.1^59 ] ] [ [ $.1^7, $.1^64 ] ] [ [ $.1^7, $.1^67 ] ] [ [ $.1^7, $.1^68 ] ] [ [ $.1^7, $.1^71 ] ] [ [ $.1^7, $.1^73 ] ] [ [ $.1^7, $.1^82 ] ] [ [ $.1^7, $.1^94 ] ] [ [ $.1^7, $.1^106 ] ] [ [ $.1^7, $.1^123 ] ] [ [ $.1^7, $.1^127 ] ] [ [ $.1^7, $.1^134 ] ] [ [ $.1^7, $.1^144 ] ] [ [ $.1^7, $.1^147 ] ] [ [ $.1^7, $.1^154 ] ] [ [ $.1^7, $.1^155 ] ] [ [ $.1^7, $.1^157 ] ] [ [ $.1^7, $.1^160 ] ] [ [ $.1^7, $.1^169 ] ] [ [ $.1^7, $.1^177 ] ] [ [ $.1^7, $.1^188 ] ] [ [ $.1^7, $.1^189 ] ] [ [ $.1^7, $.1^194 ] ] [ [ $.1^7, $.1^203 ] ] [ [ $.1^7, $.1^205 ] ] [ [ $.1^7, $.1^213 ] ] [ [ $.1^7, $.1^216 ] ] [ [ $.1^7, $.1^232 ] ] [ [ $.1^7, $.1^252 ] ] [ [ $.1^7, $.1^25 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 11:00:32 2004 Input: R := GF(4); M := MatrixRing(R,2); Mt := {A : A in M | Trace(A) eq 0}; Output: Magma V2.10-6 Fri Mar 12 2004 11:00:29 on modular [Seed = 4125387620] ------------------------------------- Total time: 3.029 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 11:00:42 2004 Input: pt73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+x^(7^(3-i)); end for; return C; end function; pn73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+(7^(3-i)); end for; return x^C; end function; polav73:=function() C:=[]; for i in GF(7^3) do for j in GF(7^3) do if (Evaluate(pn73(),i) eq Evaluate(pt73(),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; polav73(); Output: Magma V2.10-6 Fri Mar 12 2004 11:00:20 on modular [Seed = 4260127589] ------------------------------------- [ [ 1, $.1 ] ] [ [ 1, $.1^2 ] ] [ [ 1, $.1^7 ] ] [ [ 1, $.1^10 ] ] [ [ 1, $.1^11 ] ] [ [ 1, $.1^14 ] ] [ [ 1, $.1^16 ] ] [ [ 1, $.1^25 ] ] [ [ 1, $.1^37 ] ] [ [ 1, $.1^49 ] ] [ [ 1, $.1^66 ] ] [ [ 1, $.1^70 ] ] [ [ 1, $.1^77 ] ] [ [ 1, $.1^87 ] ] [ [ 1, $.1^90 ] ] [ [ 1, $.1^97 ] ] [ [ 1, $.1^98 ] ] [ [ 1, $.1^100 ] ] [ [ 1, $.1^103 ] ] [ [ 1, $.1^112 ] ] [ [ 1, $.1^120 ] ] [ [ 1, $.1^131 ] ] [ [ 1, $.1^132 ] ] [ [ 1, $.1^137 ] ] [ [ 1, $.1^146 ] ] [ [ 1, $.1^148 ] ] [ [ 1, $.1^156 ] ] [ [ 1, $.1^159 ] ] [ [ 1, $.1^175 ] ] [ [ 1, $.1^195 ] ] [ [ 1, $.1^197 ] ] [ [ 1, $.1^199 ] ] [ [ 1, $.1^215 ] ] [ [ 1, $.1^233 ] ] [ [ 1, $.1^240 ] ] [ [ 1, $.1^259 ] ] [ [ 1, $.1^263 ] ] [ [ 1, $.1^267 ] ] [ [ 1, $.1^275 ] ] [ [ 1, 5 ] ] [ [ 1, $.1^288 ] ] [ [ 1, $.1^306 ] ] [ [ 1, $.1^307 ] ] [ [ 1, $.1^312 ] ] [ [ 1, $.1^314 ] ] [ [ 1, $.1^321 ] ] [ [ 1, $.1^337 ] ] [ [ 1, $.1^338 ] ] [ [ 1, $.1^339 ] ] [ [ $.1, 1 ] ] [ [ $.1, $.1^3 ] ] [ [ $.1, $.1^21 ] ] [ [ $.1, $.1^22 ] ] [ [ $.1, $.1^27 ] ] [ [ $.1, $.1^29 ] ] [ [ $.1, $.1^36 ] ] [ [ $.1, $.1^52 ] ] [ [ $.1, $.1^53 ] ] [ [ $.1, $.1^54 ] ] [ [ $.1, $.1^58 ] ] [ [ $.1, $.1^59 ] ] [ [ $.1, $.1^64 ] ] [ [ $.1, $.1^67 ] ] [ [ $.1, $.1^68 ] ] [ [ $.1, $.1^71 ] ] [ [ $.1, $.1^73 ] ] [ [ $.1, $.1^82 ] ] [ [ $.1, $.1^94 ] ] [ [ $.1, $.1^106 ] ] [ [ $.1, $.1^123 ] ] [ [ $.1, $.1^127 ] ] [ [ $.1, $.1^134 ] ] [ [ $.1, $.1^144 ] ] [ [ $.1, $.1^147 ] ] [ [ $.1, $.1^154 ] ] [ [ $.1, $.1^155 ] ] [ [ $.1, $.1^157 ] ] [ [ $.1, $.1^160 ] ] [ [ $.1, $.1^169 ] ] [ [ $.1, $.1^177 ] ] [ [ $.1, $.1^188 ] ] [ [ $.1, $.1^189 ] ] [ [ $.1, $.1^194 ] ] [ [ $.1, $.1^203 ] ] [ [ $.1, $.1^205 ] ] [ [ $.1, $.1^213 ] ] [ [ $.1, $.1^216 ] ] [ [ $.1, $.1^232 ] ] [ [ $.1, $.1^252 ] ] [ [ $.1, $.1^254 ] ] [ [ $.1, $.1^256 ] ] [ [ $.1, $.1^272 ] ] [ [ $.1, $.1^290 ] ] [ [ $.1, $.1^297 ] ] [ [ $.1, $.1^316 ] ] [ [ $.1, $.1^320 ] ] [ [ $.1, $.1^324 ] ] [ [ $.1, $.1^332 ] ] [ [ $.1^2, $.1^5 ] ] [ [ $.1^2, $.1^12 ] ] [ [ $.1^2, $.1^31 ] ] [ [ $.1^2, $.1^35 ] ] [ [ $.1^2, $.1^39 ] ] [ [ $.1^2, $.1^47 ] ] [ [ $.1^2, 3 ] ] [ [ $.1^2, $.1^60 ] ] [ [ $.1^2, $.1^78 ] ] [ [ $.1^2, $.1^79 ] ] [ [ $.1^2, $.1^84 ] ] [ [ $.1^2, $.1^86 ] ] [ [ $.1^2, $.1^93 ] ] [ [ $.1^2, $.1^109 ] ] [ [ $.1^2, $.1^110 ] ] [ [ $.1^2, $.1^111 ] ] [ [ $.1^2, $.1^115 ] ] [ [ $.1^2, $.1^116 ] ] [ [ $.1^2, $.1^121 ] ] [ [ $.1^2, $.1^124 ] ] [ [ $.1^2, $.1^125 ] ] [ [ $.1^2, $.1^128 ] ] [ [ $.1^2, $.1^130 ] ] [ [ $.1^2, $.1^139 ] ] [ [ $.1^2, $.1^151 ] ] [ [ $.1^2, $.1^163 ] ] [ [ $.1^2, $.1^180 ] ] [ [ $.1^2, $.1^184 ] ] [ [ $.1^2, $.1^191 ] ] [ [ $.1^2, $.1^201 ] ] [ [ $.1^2, $.1^204 ] ] [ [ $.1^2, $.1^211 ] ] [ [ $.1^2, $.1^212 ] ] [ [ $.1^2, $.1^214 ] ] [ [ $.1^2, $.1^217 ] ] [ [ $.1^2, $.1^226 ] ] [ [ $.1^2, $.1^234 ] ] [ [ $.1^2, $.1^245 ] ] [ [ $.1^2, $.1^246 ] ] [ [ $.1^2, $.1^251 ] ] [ [ $.1^2, $.1^260 ] ] [ [ $.1^2, $.1^262 ] ] [ [ $.1^2, $.1^270 ] ] [ [ $.1^2, $.1^273 ] ] [ [ $.1^2, $.1^289 ] ] [ [ $.1^2, $.1^309 ] ] [ [ $.1^2, $.1^311 ] ] [ [ $.1^2, $.1^313 ] ] [ [ $.1^2, $.1^329 ] ] [ [ $.1^3, $.1^4 ] ] [ [ $.1^3, $.1^24 ] ] [ [ $.1^3, $.1^26 ] ] [ [ $.1^3, $.1^28 ] ] [ [ $.1^3, $.1^44 ] ] [ [ $.1^3, $.1^62 ] ] [ [ $.1^3, $.1^69 ] ] [ [ $.1^3, $.1^88 ] ] [ [ $.1^3, $.1^92 ] ] [ [ $.1^3, $.1^96 ] ] [ [ $.1^3, $.1^104 ] ] [ [ $.1^3, 2 ] ] [ [ $.1^3, $.1^117 ] ] [ [ $.1^3, $.1^135 ] ] [ [ $.1^3, $.1^136 ] ] [ [ $.1^3, $.1^141 ] ] [ [ $.1^3, $.1^143 ] ] [ [ $.1^3, $.1^150 ] ] [ [ $.1^3, $.1^166 ] ] [ [ $.1^3, $.1^167 ] ] [ [ $.1^3, $.1^168 ] ] [ [ $.1^3, $.1^172 ] ] [ [ $.1^3, $.1^173 ] ] [ [ $.1^3, $.1^178 ] ] [ [ $.1^3, $.1^181 ] ] [ [ $.1^3, $.1^182 ] ] [ [ $.1^3, $.1^185 ] ] [ [ $.1^3, $.1^187 ] ] [ [ $.1^3, $.1^196 ] ] [ [ $.1^3, $.1^208 ] ] [ [ $.1^3, $.1^220 ] ] [ [ $.1^3, $.1^237 ] ] [ [ $.1^3, $.1^241 ] ] [ [ $.1^3, $.1^248 ] ] [ [ $.1^3, $.1^258 ] ] [ [ $.1^3, $.1^261 ] ] [ [ $.1^3, $.1^268 ] ] [ [ $.1^3, $.1^269 ] ] [ [ $.1^3, $.1^271 ] ] [ [ $.1^3, $.1^274 ] ] [ [ $.1^3, $.1^283 ] ] [ [ $.1^3, $.1^291 ] ] [ [ $.1^3, $.1^302 ] ] [ [ $.1^3, $.1^303 ] ] [ [ $.1^3, $.1^308 ] ] [ [ $.1^3, $.1^317 ] ] [ [ $.1^3, $.1^319 ] ] [ [ $.1^3, $.1^327 ] ] [ [ $.1^3, $.1^330 ] ] [ [ $.1^4, $.1^6 ] ] [ [ $.1^4, $.1^17 ] ] [ [ $.1^4, $.1^18 ] ] [ [ $.1^4, $.1^23 ] ] [ [ $.1^4, $.1^32 ] ] [ [ $.1^4, $.1^34 ] ] [ [ $.1^4, $.1^42 ] ] [ [ $.1^4, $.1^45 ] ] [ [ $.1^4, $.1^61 ] ] [ [ $.1^4, $.1^81 ] ] [ [ $.1^4, $.1^83 ] ] [ [ $.1^4, $.1^85 ] ] [ [ $.1^4, $.1^101 ] ] [ [ $.1^4, $.1^119 ] ] [ [ $.1^4, $.1^126 ] ] [ [ $.1^4, $.1^145 ] ] [ [ $.1^4, $.1^149 ] ] [ [ $.1^4, $.1^153 ] ] [ [ $.1^4, $.1^161 ] ] [ [ $.1^4, 6 ] ] [ [ $.1^4, $.1^174 ] ] [ [ $.1^4, $.1^192 ] ] [ [ $.1^4, $.1^193 ] ] [ [ $.1^4, $.1^198 ] ] [ [ $.1^4, $.1^200 ] ] [ [ $.1^4, $.1^207 ] ] [ [ $.1^4, $.1^223 ] ] [ [ $.1^4, $.1^224 ] ] [ [ $.1^4, $.1^225 ] ] [ [ $.1^4, $.1^229 ] ] [ [ $.1^4, $.1^230 ] ] [ [ $.1^4, $.1^235 ] ] [ [ $.1^4, $.1^238 ] ] [ [ $.1^4, $.1^239 ] ] [ [ $.1^4, $.1^242 ] ] [ [ $.1^4, $.1^244 ] ] [ [ $.1^4, $.1^253 ] ] [ [ $.1^4, $.1^265 ] ] [ [ $.1^4, $.1^277 ] ] [ [ $.1^4, $.1^294 ] ] [ [ $.1^4, $.1^298 ] ] [ [ $.1^4, $.1^305 ] ] [ [ $.1^4, $.1^315 ] ] [ [ $.1^4, $.1^318 ] ] [ [ $.1^4, $.1^325 ] ] [ [ $.1^4, $.1^326 ] ] [ [ $.1^4, $.1^328 ] ] [ [ $.1^4, $.1^331 ] ] [ [ $.1^4, $.1^340 ] ] [ [ $.1^5, $.1^9 ] ] [ [ $.1^5, $.1^13 ] ] [ [ $.1^5, $.1^20 ] ] [ [ $.1^5, $.1^30 ] ] [ [ $.1^5, $.1^33 ] ] [ [ $.1^5, $.1^40 ] ] [ [ $.1^5, $.1^41 ] ] [ [ $.1^5, $.1^43 ] ] [ [ $.1^5, $.1^46 ] ] [ [ $.1^5, $.1^55 ] ] [ [ $.1^5, $.1^63 ] ] [ [ $.1^5, $.1^74 ] ] [ [ $.1^5, $.1^75 ] ] [ [ $.1^5, $.1^80 ] ] [ [ $.1^5, $.1^89 ] ] [ [ $.1^5, $.1^91 ] ] [ [ $.1^5, $.1^99 ] ] [ [ $.1^5, $.1^102 ] ] [ [ $.1^5, $.1^118 ] ] [ [ $.1^5, $.1^138 ] ] [ [ $.1^5, $.1^140 ] ] [ [ $.1^5, $.1^142 ] ] [ [ $.1^5, $.1^158 ] ] [ [ $.1^5, $.1^176 ] ] [ [ $.1^5, $.1^183 ] ] [ [ $.1^5, $.1^202 ] ] [ [ $.1^5, $.1^206 ] ] [ [ $.1^5, $.1^210 ] ] [ [ $.1^5, $.1^218 ] ] [ [ $.1^5, 4 ] ] [ [ $.1^5, $.1^231 ] ] [ [ $.1^5, $.1^249 ] ] [ [ $.1^5, $.1^250 ] ] [ [ $.1^5, $.1^255 ] ] [ [ $.1^5, $.1^257 ] ] [ [ $.1^5, $.1^264 ] ] [ [ $.1^5, $.1^280 ] ] [ [ $.1^5, $.1^281 ] ] [ [ $.1^5, $.1^282 ] ] [ [ $.1^5, $.1^286 ] ] [ [ $.1^5, $.1^287 ] ] [ [ $.1^5, $.1^292 ] ] [ [ $.1^5, $.1^295 ] ] [ [ $.1^5, $.1^296 ] ] [ [ $.1^5, $.1^299 ] ] [ [ $.1^5, $.1^301 ] ] [ [ $.1^5, $.1^310 ] ] [ [ $.1^5, $.1^322 ] ] [ [ $.1^5, $.1^334 ] ] [ [ $.1^6, $.1 ] ] [ [ $.1^6, $.1^2 ] ] [ [ $.1^6, $.1^7 ] ] [ [ $.1^6, $.1^10 ] ] [ [ $.1^6, $.1^11 ] ] [ [ $.1^6, $.1^14 ] ] [ [ $.1^6, $.1^16 ] ] [ [ $.1^6, $.1^25 ] ] [ [ $.1^6, $.1^37 ] ] [ [ $.1^6, $.1^49 ] ] [ [ $.1^6, $.1^66 ] ] [ [ $.1^6, $.1^70 ] ] [ [ $.1^6, $.1^77 ] ] [ [ $.1^6, $.1^87 ] ] [ [ $.1^6, $.1^90 ] ] [ [ $.1^6, $.1^97 ] ] [ [ $.1^6, $.1^98 ] ] [ [ $.1^6, $.1^100 ] ] [ [ $.1^6, $.1^103 ] ] [ [ $.1^6, $.1^112 ] ] [ [ $.1^6, $.1^120 ] ] [ [ $.1^6, $.1^131 ] ] [ [ $.1^6, $.1^132 ] ] [ [ $.1^6, $.1^137 ] ] [ [ $.1^6, $.1^146 ] ] [ [ $.1^6, $.1^148 ] ] [ [ $.1^6, $.1^156 ] ] [ [ $.1^6, $.1^159 ] ] [ [ $.1^6, $.1^175 ] ] [ [ $.1^6, $.1^195 ] ] [ [ $.1^6, $.1^197 ] ] [ [ $.1^6, $.1^199 ] ] [ [ $.1^6, $.1^215 ] ] [ [ $.1^6, $.1^233 ] ] [ [ $.1^6, $.1^240 ] ] [ [ $.1^6, $.1^259 ] ] [ [ $.1^6, $.1^263 ] ] [ [ $.1^6, $.1^267 ] ] [ [ $.1^6, $.1^275 ] ] [ [ $.1^6, 5 ] ] [ [ $.1^6, $.1^288 ] ] [ [ $.1^6, $.1^306 ] ] [ [ $.1^6, $.1^307 ] ] [ [ $.1^6, $.1^312 ] ] [ [ $.1^6, $.1^314 ] ] [ [ $.1^6, $.1^321 ] ] [ [ $.1^6, $.1^337 ] ] [ [ $.1^6, $.1^338 ] ] [ [ $.1^6, $.1^339 ] ] [ [ $.1^7, 1 ] ] [ [ $.1^7, $.1^3 ] ] [ [ $.1^7, $.1^21 ] ] [ [ $.1^7, $.1^22 ] ] [ [ $.1^7, $.1^27 ] ] [ [ $.1^7, $.1^29 ] ] [ [ $.1^7, $.1^36 ] ] [ [ $.1^7, $.1^52 ] ] [ [ $.1^7, $.1^53 ] ] [ [ $.1^7, $.1^54 ] ] [ [ $.1^7, $.1^58 ] ] [ [ $.1^7, $.1^59 ] ] [ [ $.1^7, $.1^64 ] ] [ [ $.1^7, $.1^67 ] ] [ [ $.1^7, $.1^68 ] ] [ [ $.1^7, $.1^71 ] ] [ [ $.1^7, $.1^73 ] ] [ [ $.1^7, $.1^82 ] ] [ [ $.1^7, $.1^94 ] ] [ [ $.1^7, $.1^106 ] ] [ [ $.1^7, $.1^123 ] ] [ [ $.1^7, $.1^127 ] ] [ [ $.1^7, $.1^134 ] ] [ [ $.1^7, $.1^144 ] ] [ [ $.1^7, $.1^147 ] ] [ [ $.1^7, $.1^154 ] ] [ [ $.1^7, $.1^155 ] ] [ [ $.1^7, $.1^157 ] ] [ [ $.1^7, $.1^160 ] ] [ [ $.1^7, $.1^169 ] ] [ [ $.1^7, $.1^177 ] ] [ [ $.1^7, $.1^188 ] ] [ [ $.1^7, $.1^189 ] ] [ [ $.1^7, $.1^194 ] ] [ [ $.1^7, $.1^203 ] ] [ [ $.1^7, $.1^205 ] ] [ [ $.1^7, $.1^213 ] ] [ [ $.1^7, $.1^216 ] ] [ [ $.1^7, $.1^232 ] ] [ [ $.1^7, $.1^252 ] ] [ [ $.1^7, $.1^25 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 11:00:45 2004 Input: R := GF(4); M := MatrixRing(R,2); Mt := {A : A in M | Trace(A) eq 0} Output: Magma V2.10-6 Fri Mar 12 2004 11:00:42 on modular [Seed = 253661608] ------------------------------------- Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 11:00:58 2004 Input: R := GF(4); M := MatrixRing(R,2); Mt := {A : A in M | Trace(A) eq 0}; Mt; Output: Magma V2.10-6 Fri Mar 12 2004 11:00:55 on modular [Seed = 470647462] ------------------------------------- { [ 0 0] [ 0 0], [ 0 0] [R.1^2 0], [ 0 0] [ R.1 0], [ 0 0] [ 1 0], [R.1^2 0] [ 0 R.1^2], [R.1^2 0] [R.1^2 R.1^2], [R.1^2 0] [ R.1 R.1^2], [R.1^2 0] [ 1 R.1^2], [ 1 0] [ 0 1], [ 1 0] [R.1^2 1], [ 1 0] [ R.1 1], [ 1 0] [ 1 1], [ R.1 0] [ 0 R.1], [ R.1 0] [R.1^2 R.1], [ R.1 0] [ R.1 R.1], [ R.1 0] [ 1 R.1], [ 0 R.1^2] [ 0 0], [ 0 R.1^2] [R.1^2 0], [ 0 R.1^2] [ R.1 0], [ 0 R.1^2] [ 1 0], [R.1^2 R.1^2] [ 0 R.1^2], [R.1^2 R.1^2] [R.1^2 R.1^2], [R.1^2 R.1^2] [ R.1 R.1^2], [R.1^2 R.1^2] [ 1 R.1^2], [ 1 R.1^2] [ 0 1], [ 1 R.1^2] [R.1^2 1], [ 1 R.1^2] [ R.1 1], [ 1 R.1^2] [ 1 1], [ R.1 R.1^2] [ 0 R.1], [ R.1 R.1^2] [R.1^2 R.1], [ R.1 R.1^2] [ R.1 R.1], [ R.1 R.1^2] [ 1 R.1], [ 0 R.1] [ 0 0], [ 0 R.1] [R.1^2 0], [ 0 R.1] [ R.1 0], [ 0 R.1] [ 1 0], [R.1^2 R.1] [ 0 R.1^2], [R.1^2 R.1] [R.1^2 R.1^2], [R.1^2 R.1] [ R.1 R.1^2], [R.1^2 R.1] [ 1 R.1^2], [ 1 R.1] [ 0 1], [ 1 R.1] [R.1^2 1], [ 1 R.1] [ R.1 1], [ 1 R.1] [ 1 1], [ R.1 R.1] [ 0 R.1], [ R.1 R.1] [R.1^2 R.1], [ R.1 R.1] [ R.1 R.1], [ R.1 R.1] [ 1 R.1], [ 0 1] [ 0 0], [ 0 1] [R.1^2 0], [ 0 1] [ R.1 0], [ 0 1] [ 1 0], [R.1^2 1] [ 0 R.1^2], [R.1^2 1] [R.1^2 R.1^2], [R.1^2 1] [ R.1 R.1^2], [R.1^2 1] [ 1 R.1^2], [ 1 1] [ 0 1], [ 1 1] [R.1^2 1], [ 1 1] [ R.1 1], [ 1 1] [ 1 1], [ R.1 1] [ 0 R.1], [ R.1 1] [R.1^2 R.1], [ R.1 1] [ R.1 R.1], [ R.1 1] [ 1 R.1] } Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 200-BAR2-X4.libre.retevision.es. (62.82.186.200) Time: Fri Mar 12 11:02:11 2004 Input: pt73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+x^(7^(3-i)); end for; return C; end function; pn73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+(7^(3-i)); end for; return x^C; end function; polav73:=function() c:=[]; for i in GF(7^3) do for j in GF(7^3) do if (Evaluate(pn73,i) eq Evaluate(pt73,j) then Include(C, (i,j)); end if; end for; end for; return C; end function; Output: Magma V2.10-6 Fri Mar 12 2004 11:02:08 on modular [Seed = 556842540] ------------------------------------- >> if (Evaluate(pn73,i) eq Evaluate(pt73,j) then Include(C, (i,j)); ^ User error: bad syntax >> end if; ^ User error: bad syntax >> end for; ^ User error: bad syntax >> end for; ^ User error: bad syntax >> return C; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 200-BAR2-X4.libre.retevision.es. (62.82.186.200) Time: Fri Mar 12 11:02:44 2004 Input: pt73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+x^(7^(3-i)); end for; return C; end function; pn73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+(7^(3-i)); end for; return x^C; end function; polav73:=function() c:=[]; for i in GF(7^3) do for j in GF(7^3) do if (Evaluate(pn73,i) eq Evaluate(pt73,j)) then Include(C, (i,j)); end if; end for; end for; return C; end function; Output: Magma V2.10-6 Fri Mar 12 2004 11:02:41 on modular [Seed = 992650263] ------------------------------------- >> if (Evaluate(pn73,i) eq Evaluate(pt73,j)) then Include(C, (i,j)); ^ User error: Identifier 'C' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 200-BAR2-X4.libre.retevision.es. (62.82.186.200) Time: Fri Mar 12 11:03:02 2004 Input: pt73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+x^(7^(3-i)); end for; return C; end function; pn73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+(7^(3-i)); end for; return x^C; end function; polav73:=function() c:=[]; for i in GF(7^3) do for j in GF(7^3) do if (Evaluate(pn73,i) eq Evaluate(pt73,j)) then Include(c, (i,j)); end if; end for; end for; return C; end function; Output: Magma V2.10-6 Fri Mar 12 2004 11:02:59 on modular [Seed = 841198860] ------------------------------------- >> return C; ^ User error: Identifier 'C' has not been declared or assigned Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 200-BAR2-X4.libre.retevision.es. (62.82.186.200) Time: Fri Mar 12 11:03:20 2004 Input: pt73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+x^(7^(3-i)); end for; return c; end function; pn73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+(7^(3-i)); end for; return x^C; end function; polav73:=function() c:=[]; for i in GF(7^3) do for j in GF(7^3) do if (Evaluate(pn73,i) eq Evaluate(pt73,j)) then Include(c, (i,j)); end if; end for; end for; return C; end function; Output: Magma V2.10-6 Fri Mar 12 2004 11:03:17 on modular [Seed = 1163188749] ------------------------------------- >> return c; ^ User error: Identifier 'c' has not been declared or assigned >> if (Evaluate(pn73,i) eq Evaluate(pt73,j)) then Include(c, (i,j)); ^ User error: Identifier 'pt73' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 200-BAR2-X4.libre.retevision.es. (62.82.186.200) Time: Fri Mar 12 11:03:49 2004 Input: pt73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+x^(7^(3-i)); end for; return C; end function; pn73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+(7^(3-i)); end for; return x^C; end function; polav73:=function() c:=[]; for i in GF(7^3) do for j in GF(7^3) do if (Evaluate(pn73,i) eq Evaluate(pt73,j)) then Include(c, (i,j)); end if; end for; end for; return c; end function; Output: Magma V2.10-6 Fri Mar 12 2004 11:03:46 on modular [Seed = 1548600115] ------------------------------------- Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 200-BAR2-X4.libre.retevision.es. (62.82.186.200) Time: Fri Mar 12 11:04:13 2004 Input: pt73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+x^(7^(3-i)); end for; return C; end function; pn73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+(7^(3-i)); end for; return x^C; end function; polav73:=function() c:=[]; for i in GF(7^3) do for j in GF(7^3) do if (Evaluate(pn73,i) eq Evaluate(pt73,j)) then Include(c, (i,j)); end if; end for; end for; return c; end function; polav73(); Output: Magma V2.10-6 Fri Mar 12 2004 11:04:10 on modular [Seed = 1464256544] ------------------------------------- [
:19]( ) >> if (Evaluate(pn73,i) eq Evaluate(pt73,j)) then Include(c, (i,j)); ^ Runtime error in 'Evaluate': Bad argument types Argument types given: UserProgram, FldFinElt Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 11:04:20 2004 Input: R := GF(4); M := MatrixRing(R,2); Mf := {A : A in M | A[1] eq A[2]}; Mf; Output: Magma V2.10-6 Fri Mar 12 2004 11:04:17 on modular [Seed = 1853878754] ------------------------------------- { [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ R.1 0] [ R.1 0], [ 0 R.1^2] [ 0 R.1^2], [ R.1 R.1^2] [ R.1 R.1^2], [ 0 R.1] [ 0 R.1], [ R.1 R.1] [ R.1 R.1], [ 0 1] [ 0 1], [ R.1 1] [ R.1 1], [R.1^2 0] [R.1^2 0], [ 1 0] [ 1 0], [R.1^2 R.1^2] [R.1^2 R.1^2], [ 1 R.1^2] [ 1 R.1^2], [R.1^2 R.1] [R.1^2 R.1], [ 1 R.1] [ 1 R.1], [R.1^2 1] [R.1^2 1] } Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 11:04:57 2004 Input: ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; ptqr(7,3); Output: Magma V2.10-6 Fri Mar 12 2004 11:04:54 on modular [Seed = 1618083787] ------------------------------------- x^49 + x^7 + x Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 200-BAR2-X4.libre.retevision.es. (62.82.186.200) Time: Fri Mar 12 11:05:11 2004 Input: pt73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+x^(7^(3-i)); end for; return C; end function; pn73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+(7^(3-i)); end for; return x^C; end function; olav73:=function() C:=[]; for i in GF(7^3) do for j in GF(7^3) do if (Evaluate(pn73(),i) eq Evaluate(pt73(),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; polav73(); Output: Magma V2.10-6 Fri Mar 12 2004 11:05:08 on modular [Seed = 2003232974] ------------------------------------- >> polav73();; ^ User error: Identifier 'polav73' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 11:05:15 2004 Input: pnqr:=function () P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; pnqr(7,3); Output: Magma V2.10-6 Fri Mar 12 2004 11:05:12 on modular [Seed = 2409500730] ------------------------------------- >> P:=PolynomialRing(GF(q^r)); ^ User error: Identifier 'q' has not been declared or assigned >> pnqr(7,3);; ^ User error: Identifier 'pnqr' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 11:05:36 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; pnqr(7,3); Output: Magma V2.10-6 Fri Mar 12 2004 11:05:33 on modular [Seed = 2173705793] ------------------------------------- x^57 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 200-BAR2-X4.libre.retevision.es. (62.82.186.200) Time: Fri Mar 12 11:06:00 2004 Input: pt73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+x^(7^(3-i)); end for; return C; end function; pn73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+(7^(3-i)); end for; return x^C; end function; polav73:=function() C:=[]; for i in GF(7^3) do for j in GF(7^3) do if (Evaluate(pn73(),i) eq Evaluate(pt73(),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; polav73(); Output: Magma V2.10-6 Fri Mar 12 2004 11:05:38 on modular [Seed = 2559117127] ------------------------------------- [ [ 1, $.1 ] ] [ [ 1, $.1^2 ] ] [ [ 1, $.1^7 ] ] [ [ 1, $.1^10 ] ] [ [ 1, $.1^11 ] ] [ [ 1, $.1^14 ] ] [ [ 1, $.1^16 ] ] [ [ 1, $.1^25 ] ] [ [ 1, $.1^37 ] ] [ [ 1, $.1^49 ] ] [ [ 1, $.1^66 ] ] [ [ 1, $.1^70 ] ] [ [ 1, $.1^77 ] ] [ [ 1, $.1^87 ] ] [ [ 1, $.1^90 ] ] [ [ 1, $.1^97 ] ] [ [ 1, $.1^98 ] ] [ [ 1, $.1^100 ] ] [ [ 1, $.1^103 ] ] [ [ 1, $.1^112 ] ] [ [ 1, $.1^120 ] ] [ [ 1, $.1^131 ] ] [ [ 1, $.1^132 ] ] [ [ 1, $.1^137 ] ] [ [ 1, $.1^146 ] ] [ [ 1, $.1^148 ] ] [ [ 1, $.1^156 ] ] [ [ 1, $.1^159 ] ] [ [ 1, $.1^175 ] ] [ [ 1, $.1^195 ] ] [ [ 1, $.1^197 ] ] [ [ 1, $.1^199 ] ] [ [ 1, $.1^215 ] ] [ [ 1, $.1^233 ] ] [ [ 1, $.1^240 ] ] [ [ 1, $.1^259 ] ] [ [ 1, $.1^263 ] ] [ [ 1, $.1^267 ] ] [ [ 1, $.1^275 ] ] [ [ 1, 5 ] ] [ [ 1, $.1^288 ] ] [ [ 1, $.1^306 ] ] [ [ 1, $.1^307 ] ] [ [ 1, $.1^312 ] ] [ [ 1, $.1^314 ] ] [ [ 1, $.1^321 ] ] [ [ 1, $.1^337 ] ] [ [ 1, $.1^338 ] ] [ [ 1, $.1^339 ] ] [ [ $.1, 1 ] ] [ [ $.1, $.1^3 ] ] [ [ $.1, $.1^21 ] ] [ [ $.1, $.1^22 ] ] [ [ $.1, $.1^27 ] ] [ [ $.1, $.1^29 ] ] [ [ $.1, $.1^36 ] ] [ [ $.1, $.1^52 ] ] [ [ $.1, $.1^53 ] ] [ [ $.1, $.1^54 ] ] [ [ $.1, $.1^58 ] ] [ [ $.1, $.1^59 ] ] [ [ $.1, $.1^64 ] ] [ [ $.1, $.1^67 ] ] [ [ $.1, $.1^68 ] ] [ [ $.1, $.1^71 ] ] [ [ $.1, $.1^73 ] ] [ [ $.1, $.1^82 ] ] [ [ $.1, $.1^94 ] ] [ [ $.1, $.1^106 ] ] [ [ $.1, $.1^123 ] ] [ [ $.1, $.1^127 ] ] [ [ $.1, $.1^134 ] ] [ [ $.1, $.1^144 ] ] [ [ $.1, $.1^147 ] ] [ [ $.1, $.1^154 ] ] [ [ $.1, $.1^155 ] ] [ [ $.1, $.1^157 ] ] [ [ $.1, $.1^160 ] ] [ [ $.1, $.1^169 ] ] [ [ $.1, $.1^177 ] ] [ [ $.1, $.1^188 ] ] [ [ $.1, $.1^189 ] ] [ [ $.1, $.1^194 ] ] [ [ $.1, $.1^203 ] ] [ [ $.1, $.1^205 ] ] [ [ $.1, $.1^213 ] ] [ [ $.1, $.1^216 ] ] [ [ $.1, $.1^232 ] ] [ [ $.1, $.1^252 ] ] [ [ $.1, $.1^254 ] ] [ [ $.1, $.1^256 ] ] [ [ $.1, $.1^272 ] ] [ [ $.1, $.1^290 ] ] [ [ $.1, $.1^297 ] ] [ [ $.1, $.1^316 ] ] [ [ $.1, $.1^320 ] ] [ [ $.1, $.1^324 ] ] [ [ $.1, $.1^332 ] ] [ [ $.1^2, $.1^5 ] ] [ [ $.1^2, $.1^12 ] ] [ [ $.1^2, $.1^31 ] ] [ [ $.1^2, $.1^35 ] ] [ [ $.1^2, $.1^39 ] ] [ [ $.1^2, $.1^47 ] ] [ [ $.1^2, 3 ] ] [ [ $.1^2, $.1^60 ] ] [ [ $.1^2, $.1^78 ] ] [ [ $.1^2, $.1^79 ] ] [ [ $.1^2, $.1^84 ] ] [ [ $.1^2, $.1^86 ] ] [ [ $.1^2, $.1^93 ] ] [ [ $.1^2, $.1^109 ] ] [ [ $.1^2, $.1^110 ] ] [ [ $.1^2, $.1^111 ] ] [ [ $.1^2, $.1^115 ] ] [ [ $.1^2, $.1^116 ] ] [ [ $.1^2, $.1^121 ] ] [ [ $.1^2, $.1^124 ] ] [ [ $.1^2, $.1^125 ] ] [ [ $.1^2, $.1^128 ] ] [ [ $.1^2, $.1^130 ] ] [ [ $.1^2, $.1^139 ] ] [ [ $.1^2, $.1^151 ] ] [ [ $.1^2, $.1^163 ] ] [ [ $.1^2, $.1^180 ] ] [ [ $.1^2, $.1^184 ] ] [ [ $.1^2, $.1^191 ] ] [ [ $.1^2, $.1^201 ] ] [ [ $.1^2, $.1^204 ] ] [ [ $.1^2, $.1^211 ] ] [ [ $.1^2, $.1^212 ] ] [ [ $.1^2, $.1^214 ] ] [ [ $.1^2, $.1^217 ] ] [ [ $.1^2, $.1^226 ] ] [ [ $.1^2, $.1^234 ] ] [ [ $.1^2, $.1^245 ] ] [ [ $.1^2, $.1^246 ] ] [ [ $.1^2, $.1^251 ] ] [ [ $.1^2, $.1^260 ] ] [ [ $.1^2, $.1^262 ] ] [ [ $.1^2, $.1^270 ] ] [ [ $.1^2, $.1^273 ] ] [ [ $.1^2, $.1^289 ] ] [ [ $.1^2, $.1^309 ] ] [ [ $.1^2, $.1^311 ] ] [ [ $.1^2, $.1^313 ] ] [ [ $.1^2, $.1^329 ] ] [ [ $.1^3, $.1^4 ] ] [ [ $.1^3, $.1^24 ] ] [ [ $.1^3, $.1^26 ] ] [ [ $.1^3, $.1^28 ] ] [ [ $.1^3, $.1^44 ] ] [ [ $.1^3, $.1^62 ] ] [ [ $.1^3, $.1^69 ] ] [ [ $.1^3, $.1^88 ] ] [ [ $.1^3, $.1^92 ] ] [ [ $.1^3, $.1^96 ] ] [ [ $.1^3, $.1^104 ] ] [ [ $.1^3, 2 ] ] [ [ $.1^3, $.1^117 ] ] [ [ $.1^3, $.1^135 ] ] [ [ $.1^3, $.1^136 ] ] [ [ $.1^3, $.1^141 ] ] [ [ $.1^3, $.1^143 ] ] [ [ $.1^3, $.1^150 ] ] [ [ $.1^3, $.1^166 ] ] [ [ $.1^3, $.1^167 ] ] [ [ $.1^3, $.1^168 ] ] [ [ $.1^3, $.1^172 ] ] [ [ $.1^3, $.1^173 ] ] [ [ $.1^3, $.1^178 ] ] [ [ $.1^3, $.1^181 ] ] [ [ $.1^3, $.1^182 ] ] [ [ $.1^3, $.1^185 ] ] [ [ $.1^3, $.1^187 ] ] [ [ $.1^3, $.1^196 ] ] [ [ $.1^3, $.1^208 ] ] [ [ $.1^3, $.1^220 ] ] [ [ $.1^3, $.1^237 ] ] [ [ $.1^3, $.1^241 ] ] [ [ $.1^3, $.1^248 ] ] [ [ $.1^3, $.1^258 ] ] [ [ $.1^3, $.1^261 ] ] [ [ $.1^3, $.1^268 ] ] [ [ $.1^3, $.1^269 ] ] [ [ $.1^3, $.1^271 ] ] [ [ $.1^3, $.1^274 ] ] [ [ $.1^3, $.1^283 ] ] [ [ $.1^3, $.1^291 ] ] [ [ $.1^3, $.1^302 ] ] [ [ $.1^3, $.1^303 ] ] [ [ $.1^3, $.1^308 ] ] [ [ $.1^3, $.1^317 ] ] [ [ $.1^3, $.1^319 ] ] [ [ $.1^3, $.1^327 ] ] [ [ $.1^3, $.1^330 ] ] [ [ $.1^4, $.1^6 ] ] [ [ $.1^4, $.1^17 ] ] [ [ $.1^4, $.1^18 ] ] [ [ $.1^4, $.1^23 ] ] [ [ $.1^4, $.1^32 ] ] [ [ $.1^4, $.1^34 ] ] [ [ $.1^4, $.1^42 ] ] [ [ $.1^4, $.1^45 ] ] [ [ $.1^4, $.1^61 ] ] [ [ $.1^4, $.1^81 ] ] [ [ $.1^4, $.1^83 ] ] [ [ $.1^4, $.1^85 ] ] [ [ $.1^4, $.1^101 ] ] [ [ $.1^4, $.1^119 ] ] [ [ $.1^4, $.1^126 ] ] [ [ $.1^4, $.1^145 ] ] [ [ $.1^4, $.1^149 ] ] [ [ $.1^4, $.1^153 ] ] [ [ $.1^4, $.1^161 ] ] [ [ $.1^4, 6 ] ] [ [ $.1^4, $.1^174 ] ] [ [ $.1^4, $.1^192 ] ] [ [ $.1^4, $.1^193 ] ] [ [ $.1^4, $.1^198 ] ] [ [ $.1^4, $.1^200 ] ] [ [ $.1^4, $.1^207 ] ] [ [ $.1^4, $.1^223 ] ] [ [ $.1^4, $.1^224 ] ] [ [ $.1^4, $.1^225 ] ] [ [ $.1^4, $.1^229 ] ] [ [ $.1^4, $.1^230 ] ] [ [ $.1^4, $.1^235 ] ] [ [ $.1^4, $.1^238 ] ] [ [ $.1^4, $.1^239 ] ] [ [ $.1^4, $.1^242 ] ] [ [ $.1^4, $.1^244 ] ] [ [ $.1^4, $.1^253 ] ] [ [ $.1^4, $.1^265 ] ] [ [ $.1^4, $.1^277 ] ] [ [ $.1^4, $.1^294 ] ] [ [ $.1^4, $.1^298 ] ] [ [ $.1^4, $.1^305 ] ] [ [ $.1^4, $.1^315 ] ] [ [ $.1^4, $.1^318 ] ] [ [ $.1^4, $.1^325 ] ] [ [ $.1^4, $.1^326 ] ] [ [ $.1^4, $.1^328 ] ] [ [ $.1^4, $.1^331 ] ] [ [ $.1^4, $.1^340 ] ] [ [ $.1^5, $.1^9 ] ] [ [ $.1^5, $.1^13 ] ] [ [ $.1^5, $.1^20 ] ] [ [ $.1^5, $.1^30 ] ] [ [ $.1^5, $.1^33 ] ] [ [ $.1^5, $.1^40 ] ] [ [ $.1^5, $.1^41 ] ] [ [ $.1^5, $.1^43 ] ] [ [ $.1^5, $.1^46 ] ] [ [ $.1^5, $.1^55 ] ] [ [ $.1^5, $.1^63 ] ] [ [ $.1^5, $.1^74 ] ] [ [ $.1^5, $.1^75 ] ] [ [ $.1^5, $.1^80 ] ] [ [ $.1^5, $.1^89 ] ] [ [ $.1^5, $.1^91 ] ] [ [ $.1^5, $.1^99 ] ] [ [ $.1^5, $.1^102 ] ] [ [ $.1^5, $.1^118 ] ] [ [ $.1^5, $.1^138 ] ] [ [ $.1^5, $.1^140 ] ] [ [ $.1^5, $.1^142 ] ] [ [ $.1^5, $.1^158 ] ] [ [ $.1^5, $.1^176 ] ] [ [ $.1^5, $.1^183 ] ] [ [ $.1^5, $.1^202 ] ] [ [ $.1^5, $.1^206 ] ] [ [ $.1^5, $.1^210 ] ] [ [ $.1^5, $.1^218 ] ] [ [ $.1^5, 4 ] ] [ [ $.1^5, $.1^231 ] ] [ [ $.1^5, $.1^249 ] ] [ [ $.1^5, $.1^250 ] ] [ [ $.1^5, $.1^255 ] ] [ [ $.1^5, $.1^257 ] ] [ [ $.1^5, $.1^264 ] ] [ [ $.1^5, $.1^280 ] ] [ [ $.1^5, $.1^281 ] ] [ [ $.1^5, $.1^282 ] ] [ [ $.1^5, $.1^286 ] ] [ [ $.1^5, $.1^287 ] ] [ [ $.1^5, $.1^292 ] ] [ [ $.1^5, $.1^295 ] ] [ [ $.1^5, $.1^296 ] ] [ [ $.1^5, $.1^299 ] ] [ [ $.1^5, $.1^301 ] ] [ [ $.1^5, $.1^310 ] ] [ [ $.1^5, $.1^322 ] ] [ [ $.1^5, $.1^334 ] ] [ [ $.1^6, $.1 ] ] [ [ $.1^6, $.1^2 ] ] [ [ $.1^6, $.1^7 ] ] [ [ $.1^6, $.1^10 ] ] [ [ $.1^6, $.1^11 ] ] [ [ $.1^6, $.1^14 ] ] [ [ $.1^6, $.1^16 ] ] [ [ $.1^6, $.1^25 ] ] [ [ $.1^6, $.1^37 ] ] [ [ $.1^6, $.1^49 ] ] [ [ $.1^6, $.1^66 ] ] [ [ $.1^6, $.1^70 ] ] [ [ $.1^6, $.1^77 ] ] [ [ $.1^6, $.1^87 ] ] [ [ $.1^6, $.1^90 ] ] [ [ $.1^6, $.1^97 ] ] [ [ $.1^6, $.1^98 ] ] [ [ $.1^6, $.1^100 ] ] [ [ $.1^6, $.1^103 ] ] [ [ $.1^6, $.1^112 ] ] [ [ $.1^6, $.1^120 ] ] [ [ $.1^6, $.1^131 ] ] [ [ $.1^6, $.1^132 ] ] [ [ $.1^6, $.1^137 ] ] [ [ $.1^6, $.1^146 ] ] [ [ $.1^6, $.1^148 ] ] [ [ $.1^6, $.1^156 ] ] [ [ $.1^6, $.1^159 ] ] [ [ $.1^6, $.1^175 ] ] [ [ $.1^6, $.1^195 ] ] [ [ $.1^6, $.1^197 ] ] [ [ $.1^6, $.1^199 ] ] [ [ $.1^6, $.1^215 ] ] [ [ $.1^6, $.1^233 ] ] [ [ $.1^6, $.1^240 ] ] [ [ $.1^6, $.1^259 ] ] [ [ $.1^6, $.1^263 ] ] [ [ $.1^6, $.1^267 ] ] [ [ $.1^6, $.1^275 ] ] [ [ $.1^6, 5 ] ] [ [ $.1^6, $.1^288 ] ] [ [ $.1^6, $.1^306 ] ] [ [ $.1^6, $.1^307 ] ] [ [ $.1^6, $.1^312 ] ] [ [ $.1^6, $.1^314 ] ] [ [ $.1^6, $.1^321 ] ] [ [ $.1^6, $.1^337 ] ] [ [ $.1^6, $.1^338 ] ] [ [ $.1^6, $.1^339 ] ] [ [ $.1^7, 1 ] ] [ [ $.1^7, $.1^3 ] ] [ [ $.1^7, $.1^21 ] ] [ [ $.1^7, $.1^22 ] ] [ [ $.1^7, $.1^27 ] ] [ [ $.1^7, $.1^29 ] ] [ [ $.1^7, $.1^36 ] ] [ [ $.1^7, $.1^52 ] ] [ [ $.1^7, $.1^53 ] ] [ [ $.1^7, $.1^54 ] ] [ [ $.1^7, $.1^58 ] ] [ [ $.1^7, $.1^59 ] ] [ [ $.1^7, $.1^64 ] ] [ [ $.1^7, $.1^67 ] ] [ [ $.1^7, $.1^68 ] ] [ [ $.1^7, $.1^71 ] ] [ [ $.1^7, $.1^73 ] ] [ [ $.1^7, $.1^82 ] ] [ [ $.1^7, $.1^94 ] ] [ [ $.1^7, $.1^106 ] ] [ [ $.1^7, $.1^123 ] ] [ [ $.1^7, $.1^127 ] ] [ [ $.1^7, $.1^134 ] ] [ [ $.1^7, $.1^144 ] ] [ [ $.1^7, $.1^147 ] ] [ [ $.1^7, $.1^154 ] ] [ [ $.1^7, $.1^155 ] ] [ [ $.1^7, $.1^157 ] ] [ [ $.1^7, $.1^160 ] ] [ [ $.1^7, $.1^169 ] ] [ [ $.1^7, $.1^177 ] ] [ [ $.1^7, $.1^188 ] ] [ [ $.1^7, $.1^189 ] ] [ [ $.1^7, $.1^194 ] ] [ [ $.1^7, $.1^203 ] ] [ [ $.1^7, $.1^205 ] ] [ [ $.1^7, $.1^213 ] ] [ [ $.1^7, $.1^216 ] ] [ [ $.1^7, $.1^232 ] ] [ [ $.1^7, $.1^252 ] ] [ [ $.1^7, $.1^25 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 11:07:32 2004 Input: R := GF(4); M := MatrixRing(R,2); Mt := {A : A in M | Trace(A) eq 0}; Mf := {A : A in M | A[1] eq A[2]}; Mtf := Mt meet Mf; Mtf; Output: Magma V2.10-6 Fri Mar 12 2004 11:07:29 on modular [Seed = 2458071774] ------------------------------------- { [ 0 0] [ 0 0], [R.1^2 R.1^2] [R.1^2 R.1^2], [ R.1 R.1] [ R.1 R.1], [ 1 1] [ 1 1] } Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 200-BAR2-X4.libre.retevision.es. (62.82.186.200) Time: Fri Mar 12 11:08:05 2004 Input: pt73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+x^(7^(3-i)); end for; return C; end function; pn73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+(7^(3-i)); end for; return x^C; end function; tqr:= function (q,r) function> C:=[]; function> for i in {1..r} do Include(C,q^(r-i)); end for;return C; end function; tqr(7,3); Output: Magma V2.10-6 Fri Mar 12 2004 11:08:03 on modular [Seed = 2780038603] ------------------------------------- >> function> C:=[]; ^ User error: bad syntax >> function> for i in {1..r} do Include(C,q^(r-i)); end for;return C; end func ^ User error: bad syntax >> tqr(7,3);; ^ User error: Identifier 'tqr' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 200-BAR2-X4.libre.retevision.es. (62.82.186.200) Time: Fri Mar 12 11:08:50 2004 Input: pt73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+x^(7^(3-i)); end for; return C; end function; pn73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+(7^(3-i)); end for; return x^C; end function; tqr:= function (q,r) C:=[]; for i in {1..r} do Include(C,q^(r-i)); end for;return C; end function; tqr(7,3); Output: Magma V2.10-6 Fri Mar 12 2004 11:08:47 on modular [Seed = 3215859517] ------------------------------------- [ 49 ] [ 7 ] [ 1 ] [] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 200-BAR2-X4.libre.retevision.es. (62.82.186.200) Time: Fri Mar 12 11:09:42 2004 Input: pt73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+x^(7^(3-i)); end for; return C; end function; pn73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+(7^(3-i)); end for; return x^C; end function; pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; pnqr(4,5); Output: Magma V2.10-6 Fri Mar 12 2004 11:09:39 on modular [Seed = 3064403576] ------------------------------------- x^341 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 11:10:03 2004 Input: R := GF(4); M := MatrixRing(R,2); Mf := {A : A in M | A[1] eq A[2]}; Mf; Output: Magma V2.10-6 Fri Mar 12 2004 11:10:00 on modular [Seed = 3251659028] ------------------------------------- { [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ R.1 0] [ R.1 0], [ 0 R.1^2] [ 0 R.1^2], [ R.1 R.1^2] [ R.1 R.1^2], [ 0 R.1] [ 0 R.1], [ R.1 R.1] [ R.1 R.1], [ 0 1] [ 0 1], [ R.1 1] [ R.1 1], [R.1^2 0] [R.1^2 0], [ 1 0] [ 1 0], [R.1^2 R.1^2] [R.1^2 R.1^2], [ 1 R.1^2] [ 1 R.1^2], [R.1^2 R.1] [R.1^2 R.1], [ 1 R.1] [ 1 R.1], [R.1^2 1] [R.1^2 1] } Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 11:11:21 2004 Input: R := GF(4); M := MatrixRing(R,2); Mt := {A : A in M | Trace(A) eq 0}; Mt; Output: Magma V2.10-6 Fri Mar 12 2004 11:11:18 on modular [Seed = 3637082611] ------------------------------------- { [ 0 0] [ 0 0], [ 0 0] [R.1^2 0], [ 0 0] [ R.1 0], [ 0 0] [ 1 0], [R.1^2 0] [ 0 R.1^2], [R.1^2 0] [R.1^2 R.1^2], [R.1^2 0] [ R.1 R.1^2], [R.1^2 0] [ 1 R.1^2], [ 1 0] [ 0 1], [ 1 0] [R.1^2 1], [ 1 0] [ R.1 1], [ 1 0] [ 1 1], [ R.1 0] [ 0 R.1], [ R.1 0] [R.1^2 R.1], [ R.1 0] [ R.1 R.1], [ R.1 0] [ 1 R.1], [ 0 R.1^2] [ 0 0], [ 0 R.1^2] [R.1^2 0], [ 0 R.1^2] [ R.1 0], [ 0 R.1^2] [ 1 0], [R.1^2 R.1^2] [ 0 R.1^2], [R.1^2 R.1^2] [R.1^2 R.1^2], [R.1^2 R.1^2] [ R.1 R.1^2], [R.1^2 R.1^2] [ 1 R.1^2], [ 1 R.1^2] [ 0 1], [ 1 R.1^2] [R.1^2 1], [ 1 R.1^2] [ R.1 1], [ 1 R.1^2] [ 1 1], [ R.1 R.1^2] [ 0 R.1], [ R.1 R.1^2] [R.1^2 R.1], [ R.1 R.1^2] [ R.1 R.1], [ R.1 R.1^2] [ 1 R.1], [ 0 R.1] [ 0 0], [ 0 R.1] [R.1^2 0], [ 0 R.1] [ R.1 0], [ 0 R.1] [ 1 0], [R.1^2 R.1] [ 0 R.1^2], [R.1^2 R.1] [R.1^2 R.1^2], [R.1^2 R.1] [ R.1 R.1^2], [R.1^2 R.1] [ 1 R.1^2], [ 1 R.1] [ 0 1], [ 1 R.1] [R.1^2 1], [ 1 R.1] [ R.1 1], [ 1 R.1] [ 1 1], [ R.1 R.1] [ 0 R.1], [ R.1 R.1] [R.1^2 R.1], [ R.1 R.1] [ R.1 R.1], [ R.1 R.1] [ 1 R.1], [ 0 1] [ 0 0], [ 0 1] [R.1^2 0], [ 0 1] [ R.1 0], [ 0 1] [ 1 0], [R.1^2 1] [ 0 R.1^2], [R.1^2 1] [R.1^2 R.1^2], [R.1^2 1] [ R.1 R.1^2], [R.1^2 1] [ 1 R.1^2], [ 1 1] [ 0 1], [ 1 1] [R.1^2 1], [ 1 1] [ R.1 1], [ 1 1] [ 1 1], [ R.1 1] [ 0 R.1], [ R.1 1] [R.1^2 R.1], [ R.1 1] [ R.1 R.1], [ R.1 1] [ 1 R.1] } Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 200-BAR2-X4.libre.retevision.es. (62.82.186.200) Time: Fri Mar 12 11:13:29 2004 Input: pt73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+x^(7^(3-i)); end for; return C; end function; pn73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+(7^(3-i)); end for; return x^C; end function; pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) c:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr73(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; polav(4,7); Output: Magma V2.10-6 Fri Mar 12 2004 11:13:26 on modular [Seed = 3536024441] ------------------------------------- >> if (Evaluate(pnqr73(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j ^ User error: Identifier 'pnqr73' has not been declared or assigned >> polav(4,7);; ^ User error: Identifier 'polav' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 200-BAR2-X4.libre.retevision.es. (62.82.186.200) Time: Fri Mar 12 11:13:49 2004 Input: pt73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+x^(7^(3-i)); end for; return C; end function; pn73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+(7^(3-i)); end for; return x^C; end function; pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) c:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; polav(4,7); Output: Magma V2.10-6 Fri Mar 12 2004 11:13:46 on modular [Seed = 3857990738] ------------------------------------- >> if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]) ^ User error: Identifier 'C' has not been declared or assigned >> polav(4,7);; ^ User error: Identifier 'polav' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 200-BAR2-X4.libre.retevision.es. (62.82.186.200) Time: Fri Mar 12 11:14:15 2004 Input: pt73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+x^(7^(3-i)); end for; return C; end function; pn73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+(7^(3-i)); end for; return x^C; end function; pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; polav(4,7); Output: Magma V2.10-6 Fri Mar 12 2004 11:14:12 on modular [Seed = 4243414309] ------------------------------------- >> polav(4,7);; ^ User error: Identifier 'polav' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 200-BAR2-X4.libre.retevision.es. (62.82.186.200) Time: Fri Mar 12 11:14:57 2004 Input: pt73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+x^(7^(3-i)); end for; return C; end function; pn73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+(7^(3-i)); end for; return x^C; end function; pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; polavqr(4,7); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Mar 12 2004 11:14:34 on modular [Seed = 4142356241] ------------------------------------- [ [ 1, 1 ] ] [ [ 1, $.1^3 ] ] [ [ 1, $.1^5 ] ] [ [ 1, $.1^6 ] ] [ [ 1, $.1^10 ] ] [ [ 1, $.1^12 ] ] [ [ 1, $.1^15 ] ] [ [ 1, $.1^17 ] ] [ [ 1, $.1^19 ] ] [ [ 1, $.1^20 ] ] [ [ 1, $.1^21 ] ] [ [ 1, $.1^23 ] ] [ [ 1, $.1^24 ] ] [ [ 1, $.1^30 ] ] [ [ 1, $.1^34 ] ] [ [ 1, $.1^38 ] ] [ [ 1, $.1^39 ] ] [ [ 1, $.1^40 ] ] [ [ 1, $.1^42 ] ] [ [ 1, $.1^46 ] ] [ [ 1, $.1^47 ] ] [ [ 1, $.1^48 ] ] [ [ 1, $.1^51 ] ] [ [ 1, $.1^57 ] ] [ [ 1, $.1^60 ] ] [ [ 1, $.1^68 ] ] [ [ 1, $.1^76 ] ] [ [ 1, $.1^78 ] ] [ [ 1, $.1^80 ] ] [ [ 1, $.1^84 ] ] [ [ 1, $.1^85 ] ] [ [ 1, $.1^91 ] ] [ [ 1, $.1^92 ] ] [ [ 1, $.1^94 ] ] [ [ 1, $.1^96 ] ] [ [ 1, $.1^102 ] ] [ [ 1, $.1^103 ] ] [ [ 1, $.1^107 ] ] [ [ 1, $.1^111 ] ] [ [ 1, $.1^114 ] ] [ [ 1, $.1^117 ] ] [ [ 1, $.1^120 ] ] [ [ 1, $.1^136 ] ] [ [ 1, $.1^139 ] ] [ [ 1, $.1^149 ] ] [ [ 1, $.1^151 ] ] [ [ 1, $.1^152 ] ] [ [ 1, $.1^156 ] ] [ [ 1, $.1^160 ] ] [ [ 1, $.1^168 ] ] [ [ 1, $.1^169 ] ] [ [ 1, $.1^170 ] ] [ [ 1, $.1^171 ] ] [ [ 1, $.1^177 ] ] [ [ 1, $.1^182 ] ] [ [ 1, $.1^184 ] ] [ [ 1, $.1^185 ] ] [ [ 1, $.1^187 ] ] [ [ 1, $.1^188 ] ] [ [ 1, $.1^191 ] ] [ [ 1, $.1^192 ] ] [ [ 1, $.1^197 ] ] [ [ 1, $.1^204 ] ] [ [ 1, $.1^206 ] ] [ [ 1, $.1^213 ] ] [ [ 1, $.1^214 ] ] [ [ 1, $.1^222 ] ] [ [ 1, $.1^223 ] ] [ [ 1, $.1^225 ] ] [ [ 1, $.1^227 ] ] [ [ 1, $.1^228 ] ] [ [ 1, $.1^234 ] ] [ [ 1, $.1^240 ] ] [ [ 1, $.1^249 ] ] [ [ 1, $.1^251 ] ] [ [ 1, $.1^255 ] ] [ [ 1, $.1^271 ] ] [ [ 1, $.1^272 ] ] [ [ 1, $.1^278 ] ] [ [ 1, $.1^285 ] ] [ [ 1, $.1^289 ] ] [ [ 1, $.1^291 ] ] [ [ 1, $.1^298 ] ] [ [ 1, $.1^302 ] ] [ [ 1, $.1^304 ] ] [ [ 1, $.1^305 ] ] [ [ 1, $.1^311 ] ] [ [ 1, $.1^312 ] ] [ [ 1, $.1^319 ] ] [ [ 1, $.1^320 ] ] [ [ 1, $.1^323 ] ] [ [ 1, $.1^325 ] ] [ [ 1, $.1^329 ] ] [ [ 1, $.1^331 ] ] [ [ 1, $.1^335 ] ] [ [ 1, $.1^336 ] ] [ [ 1, $.1^338 ] ] [ [ 1, $.1^340 ] ] [ [ 1, $.1^341 ] ] [ [ 1, $.1^342 ] ] [ [ 1, $.1^343 ] ] [ [ 1, $.1^351 ] ] [ [ 1, $.1^354 ] ] [ [ 1, $.1^359 ] ] [ [ 1, $.1^364 ] ] [ [ 1, $.1^368 ] ] [ [ 1, $.1^369 ] ] [ [ 1, $.1^370 ] ] [ [ 1, $.1^371 ] ] [ [ 1, $.1^374 ] ] [ [ 1, $.1^375 ] ] [ [ 1, $.1^376 ] ] [ [ 1, $.1^377 ] ] [ [ 1, $.1^382 ] ] [ [ 1, $.1^383 ] ] [ [ 1, $.1^384 ] ] [ [ 1, $.1^389 ] ] [ [ 1, $.1^394 ] ] [ [ 1, $.1^395 ] ] [ [ 1, $.1^397 ] ] [ [ 1, $.1^401 ] ] [ [ 1, $.1^408 ] ] [ [ 1, $.1^411 ] ] [ [ 1, $.1^412 ] ] [ [ 1, $.1^426 ] ] [ [ 1, $.1^428 ] ] [ [ 1, $.1^439 ] ] [ [ 1, $.1^444 ] ] [ [ 1, $.1^446 ] ] [ [ 1, $.1^450 ] ] [ [ 1, $.1^451 ] ] [ [ 1, $.1^454 ] ] [ [ 1, $.1^456 ] ] [ [ 1, $.1^457 ] ] [ [ 1, $.1^468 ] ] [ [ 1, $.1^469 ] ] [ [ 1, $.1^477 ] ] [ [ 1, $.1^479 ] ] [ [ 1, $.1^480 ] ] [ [ 1, $.1^487 ] ] [ [ 1, $.1^493 ] ] [ [ 1, $.1^497 ] ] [ [ 1, $.1^498 ] ] [ [ 1, $.1^499 ] ] [ [ 1, $.1^502 ] ] [ [ 1, $.1^503 ] ] [ [ 1, $.1^510 ] ] [ [ 1, $.1^519 ] ] [ [ 1, $.1^521 ] ] [ [ 1, $.1^529 ] ] [ [ 1, $.1^542 ] ] [ [ 1, $.1^544 ] ] [ [ 1, $.1^545 ] ] [ [ 1, $.1^549 ] ] [ [ 1, $.1^556 ] ] [ [ 1, $.1^557 ] ] [ [ 1, $.1^565 ] ] [ [ 1, $.1^569 ] ] [ [ 1, $.1^570 ] ] [ [ 1, $.1^575 ] ] [ [ 1, $.1^578 ] ] [ [ 1, $.1^582 ] ] [ [ 1, $.1^589 ] ] [ [ 1, $.1^591 ] ] [ [ 1, $.1^596 ] ] [ [ 1, $.1^599 ] ] [ [ 1, $.1^601 ] ] [ [ 1, $.1^604 ] ] [ [ 1, $.1^607 ] ] [ [ 1, $.1^608 ] ] [ [ 1, $.1^610 ] ] [ [ 1, $.1^613 ] ] [ [ 1, $.1^619 ] ] [ [ 1, $.1^622 ] ] [ [ 1, $.1^624 ] ] [ [ 1, $.1^629 ] ] [ [ 1, $.1^631 ] ] [ [ 1, $.1^635 ] ] [ [ 1, $.1^638 ] ] [ [ 1, $.1^640 ] ] [ [ 1, $.1^643 ] ] [ [ 1, $.1^646 ] ] [ [ 1, $.1^650 ] ] [ [ 1, $.1^658 ] ] [ [ 1, $.1^659 ] ] [ [ 1, $.1^662 ] ] [ [ 1, $.1^663 ] ] [ [ 1, $.1^670 ] ] [ [ 1, $.1^672 ] ] [ [ 1, $.1^675 ] ] [ [ 1, $.1^676 ] ] [ [ 1, $.1^677 ] ] [ [ 1, $.1^680 ] ] [ [ 1, $.1^682 ] ] [ [ 1, $.1^684 ] ] [ [ 1, $.1^686 ] ] [ [ 1, $.1^693 ] ] [ [ 1, $.1^699 ] ] [ [ 1, $.1^701 ] ] [ [ 1, $.1^702 ] ] [ [ 1, $.1^703 ] ] [ [ 1, $.1^707 ] ] [ [ 1, $.1^708 ] ] [ [ 1, $.1^717 ] ] [ [ 1, $.1^718 ] ] [ [ 1, $.1^725 ] ] [ [ 1, $.1^727 ] ] [ [ 1, $.1^728 ] ] [ [ 1, $.1^736 ] ] [ [ 1, $.1^738 ] ] [ [ 1, $.1^740 ] ] [ [ 1, $.1^741 ] ] [ [ 1, $.1^742 ] ] [ [ 1, $.1^747 ] ] [ [ 1, $.1^748 ] ] [ [ 1, $.1^749 ] ] [ [ 1, $.1^750 ] ] [ [ 1, $.1^752 ] ] [ [ 1, $.1^754 ] ] [ [ 1, $.1^764 ] ] [ [ 1, $.1^766 ] ] [ [ 1, $.1^768 ] ] [ [ 1, $.1^773 ] ] [ [ 1, $.1^775 ] ] [ [ 1, $.1^778 ] ] [ [ 1, $.1^779 ] ] [ [ 1, $.1^785 ] ] [ [ 1, $.1^788 ] ] [ [ 1, $.1^789 ] ] [ [ 1, $.1^790 ] ] [ [ 1, $.1^794 ] ] [ [ 1, $.1^802 ] ] [ [ 1, $.1^803 ] ] [ [ 1, $.1^805 ] ] [ [ 1, $.1^807 ] ] [ [ 1, $.1^811 ] ] [ [ 1, $.1^816 ] ] [ [ 1, $.1^822 ] ] [ [ 1, $.1^824 ] ] [ [ 1, $.1^839 ] ] [ [ 1, $.1^847 ] ] [ [ 1, $.1^852 ] ] [ [ 1, $.1^853 ] ] [ [ 1, $.1^856 ] ] [ [ 1, $.1^857 ] ] [ [ 1, $.1^875 ] ] [ [ 1, $.1^877 ] ] [ [ 1, $.1^878 ] ] [ [ 1, $.1^887 ] ] [ [ 1, $.1^888 ] ] [ [ 1, $.1^892 ] ] [ [ 1, $.1^900 ] ] [ [ 1, $.1^902 ] ] [ [ 1, $.1^903 ] ] [ [ 1, $.1^908 ] ] [ [ 1, $.1^912 ] ] [ [ 1, $.1^914 ] ] [ [ 1, $.1^915 ] ] [ [ 1, $.1^921 ] ] [ [ 1, $.1^933 ] ] [ [ 1, $.1^936 ] ] [ [ 1, $.1^938 ] ] [ [ 1, $.1^939 ] ] [ [ 1, $.1^947 ] ] [ [ 1, $.1^954 ] ] [ [ 1, $.1^957 ] ] [ [ 1, $.1^958 ] ] [ [ 1, $.1^960 ] ] [ [ 1, $.1^961 ] ] [ [ 1, $.1^973 ] ] [ [ 1, $.1^974 ] ] [ [ 1, $.1^983 ] ] [ [ 1, $.1^986 ] ] [ [ 1, $.1^994 ] ] [ [ 1, $.1^996 ] ] [ [ 1, $.1^998 ] ] [ [ 1, $.1^1003 ] ] [ [ 1, $.1^1004 ] ] [ [ 1, $.1^1006 ] ] [ [ 1, $.1^1015 ] ] [ [ 1, $.1^1017 ] ] [ [ 1, $.1^1020 ] ] [ [ 1, $.1^1025 ] ] [ [ 1, $.1^1035 ] ] [ [ 1, $.1^1038 ] ] [ [ 1, $.1^1042 ] ] [ [ 1, $.1^1043 ] ] [ [ 1, $.1^1047 ] ] [ [ 1, $.1^1049 ] ] [ [ 1, $.1^1055 ] ] [ [ 1, $.1^1057 ] ] [ [ 1, $.1^1058 ] ] [ [ 1, $.1^1073 ] ] [ [ 1, $.1^1084 ] ] [ [ 1, $.1^1088 ] ] [ [ 1, $.1^1090 ] ] [ [ 1, $.1^1091 ] ] [ [ 1, $.1^1098 ] ] [ [ 1, $.1^1112 ] ] [ [ 1, $.1^1113 ] ] [ [ 1, $.1^1114 ] ] [ [ 1, $.1^1119 ] ] [ [ 1, $.1^1127 ] ] [ [ 1, $.1^1130 ] ] [ [ 1, $.1^1138 ] ] [ [ 1, $.1^1140 ] ] [ [ 1, $.1^1141 ] ] [ [ 1, $.1^1149 ] ] [ [ 1, $.1^1150 ] ] [ [ 1, $.1^1156 ] ] [ [ 1, $.1^1163 ] ] [ [ 1, $.1^1164 ] ] [ [ 1, $.1^1165 ] ] [ [ 1, $.1^1171 ] ] [ [ 1, $.1^1178 ] ] [ [ 1, $.1^1182 ] ] [ [ 1, $.1^1185 ] ] [ [ 1, $.1^1192 ] ] [ [ 1, $.1^1197 ] ] [ [ 1, $.1^1198 ] ] [ [ 1, $.1^1202 ] ] [ [ 1, $.1^1203 ] ] [ [ 1, $.1^1205 ] ] [ [ 1, $.1^1208 ] ] [ [ 1, $.1^1214 ] ] [ [ 1, $.1^1215 ] ] [ [ 1, $.1^1216 ] ] [ [ 1, $.1^1220 ] ] [ [ 1, $.1^1223 ] ] [ [ 1, $.1^1226 ] ] [ [ 1, $.1^1235 ] ] [ [ 1, $.1^1238 ] ] [ [ 1, $.1^1244 ] ] [ [ 1, $.1^1245 ] ] [ [ 1, $.1^1248 ] ] [ [ 1, $.1^1258 ] ] [ [ 1, $.1^1261 ] ] [ [ 1, $.1^1262 ] ] [ [ 1, $.1^1270 ] ] [ [ 1, $.1^1276 ] ] [ [ 1, $.1^1280 ] ] [ [ 1, $.1^1283 ] ] [ [ 1, $.1^1285 ] ] [ [ 1, $.1^1286 ] ] [ [ 1, $.1^1292 ] ] [ [ 1, $.1^1300 ] ] [ [ 1, $.1^1316 ] ] [ [ 1, $.1^1317 ] ] [ [ 1, $.1^1318 ] ] [ [ 1, $.1^1319 ] ] [ [ 1, $.1^1324 ] ] [ [ 1, $.1^1326 ] ] [ [ 1, $.1^1340 ] ] [ [ 1, $.1^1343 ] ] [ [ 1, $.1^1344 ] ] [ [ 1, $.1^1347 ] ] [ [ 1, $.1^1350 ] ] [ [ 1, $.1^1352 ] ] [ [ 1, $.1^1353 ] ] [ [ 1, $.1^1354 ] ] [ [ 1, $.1^1360 ] ] [ [ 1, $.1^1364 ] ] [ [ 1, $.1^1368 ] ] [ [ 1, $.1^1372 ] ] [ [ 1, $.1^1373 ] ] [ [ 1, $.1^1386 ] ] [ [ 1, $.1^1398 ] ] [ [ 1, $.1^1401 ] ] [ [ 1, $.1^1402 ] ] [ [ 1, $.1^1404 ] ] [ [ 1, $.1^1406 ] ] [ [ 1, $.1^1407 ] ] [ [ 1, $.1^1409 ] ] [ [ 1, $.1^1411 ] ] [ [ 1, $.1^1414 ] ] [ [ 1, $.1^1416 ] ] [ [ 1, $.1^1417 ] ] [ [ 1, $.1^1425 ] ] [ [ 1, $.1^1434 ] ] [ [ 1, $.1^1436 ] ] [ [ 1, $.1^1437 ] ] [ [ 1, $.1^1441 ] ] [ [ 1, $.1^1447 ] ] [ [ 1, $.1^1450 ] ] [ [ 1, $.1^1454 ] ] [ [ 1, $.1^1456 ] ] [ [ 1, $.1^1463 ] ] [ [ 1, $.1^1467 ] ] [ [ 1, $.1^1471 ] ] [ [ 1, $.1^1472 ] ] [ [ 1, $.1^1476 ] ] [ [ 1, $.1^1480 ] ] [ [ 1, $.1^1482 ] ] [ [ 1, $.1^1484 ] ] [ [ 1, $.1^1494 ] ] [ [ 1, $.1^1496 ] ] [ [ 1, $.1^1497 ] ] [ [ 1, $.1^1498 ] ] [ [ 1, $.1^1500 ] ] [ [ 1, $.1^1501 ] ] [ [ 1, $.1^1504 ] ] [ [ 1, $.1^1507 ] ] [ [ 1, $.1^1508 ] ] [ [ 1, $.1^1511 ] ] [ [ 1, $.1^1519 ] ] [ [ 1, $.1^1521 ] ] [ [ 1, $.1^1525 ] ] [ [ 1, $.1^1528 ] ] [ [ 1, $.1^1532 ] ] [ [ 1, $.1^1533 ] ] [ [ 1, $.1^1536 ] ] [ [ 1, $.1^1543 ] ] [ [ 1, $.1^1545 ] ] [ [ 1, $.1^1546 ] ] [ [ 1, $.1^1550 ] ] [ [ 1, $.1^1556 ] ] [ [ 1, $.1^1557 ] ] [ [ 1, $.1^1558 ] ] [ [ 1, $.1^1561 ] ] [ [ 1, $.1^1570 ] ] [ [ 1, $.1^1576 ] ] [ [ 1, $.1^1578 ] ] [ [ 1, $.1^1580 ] ] [ [ 1, $.1^1583 ] ] [ [ 1, $.1^1588 ] ] [ ** WARNING: Output too long, hence truncated. Errors: /home/mfd/gomagma: line 2: 19963 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 11:15:32 2004 Input: R := GF(4); M := MatrixRing(R,2); rand := [Random(M) num in [1..100000]]; rand; Output: Magma V2.10-6 Fri Mar 12 2004 11:15:29 on modular [Seed = 118924587] ------------------------------------- >> rand := [Random(M) num in [1..100000]]; ^ User error: bad syntax >> rand;; ^ User error: Identifier 'rand' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 11:16:02 2004 Input: R := GF(4); M := MatrixRing(R,2); rand := [Random(M): num in [1..100000]]; rand; Output: Magma V2.10-6 Fri Mar 12 2004 11:15:54 on modular [Seed = 436975662] ------------------------------------- [ [ 0 R.1^2] [ 1 0], [ 1 0] [ 1 0], [ 0 R.1^2] [R.1^2 0], [ R.1 R.1^2] [R.1^2 R.1], [R.1^2 1] [ R.1 R.1^2], [R.1^2 R.1^2] [R.1^2 1], [ R.1 R.1] [ 0 R.1^2], [R.1^2 1] [ 0 R.1^2], [ 1 R.1^2] [ 1 1], [ R.1 1] [R.1^2 1], [ 1 1] [R.1^2 R.1^2], [ 0 R.1^2] [ R.1 R.1^2], [ R.1 R.1^2] [ 0 R.1^2], [ 1 R.1^2] [R.1^2 1], [ 1 R.1^2] [R.1^2 1], [ 1 0] [ 0 0], [ 0 0] [ R.1 R.1], [ R.1 R.1^2] [R.1^2 0], [ 1 R.1] [ 0 1], [ R.1 R.1^2] [ 1 R.1^2], [R.1^2 R.1] [ 1 1], [ R.1 R.1] [ R.1 1], [R.1^2 R.1^2] [ 0 R.1^2], [ 0 1] [R.1^2 R.1], [R.1^2 R.1] [ R.1 R.1^2], [ 0 0] [ 0 0], [ 1 0] [ R.1 0], [ 1 R.1] [ R.1 R.1^2], [ 1 R.1^2] [ 0 1], [ R.1 R.1^2] [R.1^2 0], [ 0 0] [ 1 R.1], [ R.1 1] [ 1 1], [ 1 R.1] [R.1^2 0], [R.1^2 0] [ R.1 R.1], [ R.1 R.1] [ 0 R.1^2], [ 0 R.1] [ R.1 R.1^2], [ 1 R.1] [ R.1 R.1^2], [ 1 R.1] [R.1^2 0], [ R.1 0] [R.1^2 R.1^2], [ 1 1] [ 1 R.1^2], [ 1 1] [R.1^2 1], [ 0 R.1] [ 0 R.1], [ 1 R.1] [ R.1 R.1^2], [ 1 R.1^2] [ 0 0], [R.1^2 1] [ R.1 1], [ R.1 1] [R.1^2 0], [R.1^2 1] [ 0 R.1], [ 0 R.1] [R.1^2 R.1^2], [R.1^2 0] [ 0 1], [ 0 R.1] [ R.1 R.1^2], [R.1^2 1] [ R.1 R.1], [ 0 R.1^2] [R.1^2 R.1^2], [R.1^2 1] [ 1 R.1], [R.1^2 R.1^2] [ R.1 R.1^2], [ 1 0] [ R.1 R.1^2], [R.1^2 R.1^2] [ 0 R.1], [ 0 1] [R.1^2 1], [ 1 R.1] [ R.1 1], [ R.1 0] [ 0 1], [ R.1 0] [ 0 0], [R.1^2 R.1^2] [R.1^2 0], [ 1 R.1] [ 1 R.1^2], [ 0 R.1^2] [ R.1 1], [ R.1 1] [ R.1 1], [ 0 R.1] [ 1 1], [R.1^2 R.1] [ 0 1], [ 1 1] [R.1^2 R.1^2], [ 0 R.1^2] [ R.1 R.1^2], [R.1^2 0] [ R.1 0], [ 1 1] [R.1^2 R.1], [ R.1 R.1^2] [ R.1 1], [ 0 1] [ 1 1], [ 0 0] [ R.1 0], [ 0 1] [ R.1 1], [ 0 R.1] [ 1 0], [R.1^2 1] [R.1^2 R.1], [ R.1 R.1] [ R.1 R.1^2], [R.1^2 R.1^2] [ 1 1], [ 0 R.1] [ 1 R.1^2], [ 0 0] [R.1^2 1], [ R.1 0] [ R.1 0], [ 1 1] [ R.1 0], [R.1^2 0] [R.1^2 1], [ 1 R.1^2] [R.1^2 R.1^2], [ R.1 R.1] [ 1 1], [ 1 1] [ 1 R.1], [R.1^2 1] [ R.1 R.1^2], [ 1 0] [ 0 0], [ R.1 R.1] [R.1^2 1], [ R.1 1] [ R.1 R.1^2], [ R.1 0] [ 0 1], [ 0 0] [R.1^2 0], [ 1 R.1^2] [ R.1 R.1^2], [ R.1 0] [ 0 1], [ 1 0] [R.1^2 1], [R.1^2 R.1] [ R.1 0], [ 0 R.1] [ R.1 R.1], [R.1^2 0] [ R.1 1], [ R.1 R.1] [ 1 R.1], [ R.1 R.1^2] [ 0 R.1^2], [R.1^2 R.1^2] [R.1^2 1], [ R.1 R.1^2] [ 1 1], [ R.1 1] [ 1 0], [ 0 0] [ 1 R.1^2], [ 0 1] [ 1 0], [ 0 R.1^2] [R.1^2 1], [R.1^2 1] [ R.1 R.1], [ 1 R.1] [ R.1 R.1], [R.1^2 R.1] [ R.1 R.1], [R.1^2 R.1^2] [ R.1 R.1^2], [ 1 1] [ 1 1], [ 0 0] [R.1^2 R.1^2], [ 1 0] [ R.1 1], [ R.1 0] [ R.1 R.1], [ 0 R.1^2] [ R.1 1], [ 0 0] [ 1 R.1^2], [ R.1 0] [ R.1 R.1], [ 1 R.1^2] [ 0 0], [ 1 0] [R.1^2 R.1^2], [ R.1 1] [ 1 1], [ 1 0] [ 0 R.1^2], [R.1^2 0] [ 0 R.1], [ R.1 0] [ R.1 1], [ 0 R.1] [ R.1 1], [ 1 R.1] [ 0 0], [ 1 R.1^2] [R.1^2 R.1^2], [ 0 1] [ R.1 R.1], [R.1^2 R.1^2] [ 1 R.1^2], [ 1 R.1^2] [ 0 1], [ 1 R.1] [ 1 R.1], [ R.1 1] [ 0 R.1^2], [ 0 R.1] [R.1^2 1], [ R.1 0] [R.1^2 R.1^2], [ 1 1] [ 0 1], [ R.1 R.1] [ 1 0], [ 1 1] [ R.1 R.1], [ R.1 R.1] [ 1 R.1^2], [ R.1 0] [ 1 1], [ R.1 R.1^2] [ R.1 1], [ 0 1] [R.1^2 R.1], [R.1^2 R.1] [ 1 R.1^2], [ 1 R.1] [ 0 R.1^2], [ 1 R.1^2] [ R.1 R.1], [ 1 R.1] [ 1 0], [R.1^2 1] [R.1^2 1], [ R.1 0] [ 0 0], [R.1^2 R.1] [R.1^2 R.1], [R.1^2 0] [R.1^2 R.1], [R.1^2 0] [R.1^2 R.1^2], [R.1^2 R.1] [ 0 R.1], [R.1^2 R.1^2] [R.1^2 1], [R.1^2 0] [ 0 0], [R.1^2 1] [ R.1 R.1], [ 0 R.1^2] [R.1^2 R.1^2], [ 0 R.1] [R.1^2 1], [ 0 1] [ R.1 0], [ R.1 R.1] [R.1^2 0], [ R.1 R.1^2] [ 0 R.1^2], [ 1 1] [ 0 0], [R.1^2 1] [ R.1 R.1], [ 0 R.1] [R.1^2 0], [ R.1 1] [ 0 1], [ 1 1] [ 1 1], [R.1^2 0] [ 1 R.1^2], [ 0 R.1] [ 1 0], [ R.1 R.1^2] [R.1^2 0], [ 1 0] [R.1^2 1], [ R.1 R.1] [R.1^2 R.1^2], [ 0 R.1] [ 1 R.1], [ 1 R.1] [R.1^2 0], [ R.1 0] [ R.1 1], [ 0 R.1] [ 0 0], [ R.1 0] [ 0 R.1^2], [ 1 R.1^2] [ 0 1], [ R.1 1] [ 1 1], [ 1 R.1^2] [R.1^2 0], [R.1^2 0] [ 0 1], [ R.1 R.1^2] [ 1 0], [R.1^2 R.1^2] [ 0 0], [ 0 1] [R.1^2 0], [ 0 R.1^2] [R.1^2 R.1], [ R.1 R.1] [ 0 R.1^2], [ 1 0] [ 1 0], [ 1 R.1] [R.1^2 R.1^2], [ 0 R.1] [ 0 0], [ 0 0] [ R.1 1], [ 1 0] [R.1^2 R.1^2], [R.1^2 0] [R.1^2 R.1], [ 0 1] [ 1 R.1^2], [R.1^2 1] [ 1 1], [R.1^2 R.1^2] [ 0 1], [ 0 R.1^2] [ 1 0], [R.1^2 R.1] [ R.1 R.1^2], [R.1^2 R.1^2] [ R.1 R.1], [R.1^2 R.1^2] [ R.1 1], [ R.1 R.1] [ 0 R.1^2], [ R.1 R.1] [ R.1 R.1], [ 0 0] [R.1^2 1], [ 1 R.1] [ 1 0], [ 0 1] [ 1 1], [R.1^2 R.1] [ R.1 1], [R.1^2 R.1^2] [R.1^2 R.1^2], [ 1 R.1^2] [ R.1 0], [ 1 1] [ 1 1], [ 0 1] [ 0 R.1], [ R.1 0] [R.1^2 R.1^2], [ R.1 R.1] [ 1 1], [R.1^2 1] [ 0 R.1^2], [ 0 1] [R.1^2 R.1^2], [R.1^2 0] [R.1^2 0], [ 0 R.1] [ 0 R.1^2], [ 1 0] [ 1 R.1^2], [R.1^2 R.1^2] [ R.1 1], [ R.1 1] [ 0 1], [R.1^2 1] [ R.1 1], [ R.1 R.1] [R.1^2 1], [ R.1 R.1] [ 0 R.1], [R.1^2 R.1^2] [ 0 1], [ 1 R.1^2] [R.1^2 R.1^2], [R.1^2 0] [ R.1 R.1^2], [ 1 R.1] [ 0 1], [R.1^2 R.1] [R.1^2 R.1^2], [ R.1 0] [ 1 1], [ R.1 R.1^2] [R.1^2 R.1], [ R.1 R.1] [R.1^2 1], [ R.1 0] [ 0 0], [R.1^2 R.1^2] [ 1 0], [ 0 1] [ 1 1], [ R.1 R.1] [ 0 0], [ R.1 0] [ 0 R.1^2], [ 0 R.1] [ R.1 R.1], [ R.1 R.1^2] [ R.1 1], [ R.1 0] [ 1 R.1^2], [ R.1 1] [ R.1 0], [R.1^2 R.1] [ 1 1], [ 1 1] [R.1^2 R.1], [R.1^2 1] [ 0 R.1^2], [ 0 1] [ 0 1], [ R.1 1] [ 1 0], [ 1 R.1^2] [ 1 1], [ R.1 1] [ 1 R.1], [ R.1 1] [ R.1 1], [ R.1 1] [ R.1 1], [R.1^2 R.1^2] [ R.1 1], [ 1 R.1^2] [ 1 R.1^2], [ 1 1] [ 0 0], [ 0 R.1^2] [ 1 0], [ 0 0] [ 0 1], [ R.1 R.1] [ 1 R.1], [ 0 R.1] [ R.1 1], [ 0 1] [ 1 0], [R.1^2 0] [ R.1 R.1], [ 1 R.1^2] [ 1 0], [ 1 0] [ R.1 0], [R.1^2 0] [R.1^2 R.1], [ 1 R.1^2] [ 1 1], [ 1 1] [R.1^2 R.1^2], [ 1 R.1^2] [ 1 R.1], [ 1 R.1^2] [R.1^2 1], [ 1 0] [R.1^2 1], ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 200-BAR2-X4.libre.retevision.es. (62.82.186.200) Time: Fri Mar 12 11:16:44 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; spolav:= [k : k in polavqr(7,3) | k[1] in GF(7) and k[2] in GF(7) ]; #spolav; Output: Magma V2.10-6 Fri Mar 12 2004 11:16:21 on modular [Seed = 318943560] ------------------------------------- [ [ 1, $.1 ] ] [ [ 1, $.1^2 ] ] [ [ 1, $.1^7 ] ] [ [ 1, $.1^10 ] ] [ [ 1, $.1^11 ] ] [ [ 1, $.1^14 ] ] [ [ 1, $.1^16 ] ] [ [ 1, $.1^25 ] ] [ [ 1, $.1^37 ] ] [ [ 1, $.1^49 ] ] [ [ 1, $.1^66 ] ] [ [ 1, $.1^70 ] ] [ [ 1, $.1^77 ] ] [ [ 1, $.1^87 ] ] [ [ 1, $.1^90 ] ] [ [ 1, $.1^97 ] ] [ [ 1, $.1^98 ] ] [ [ 1, $.1^100 ] ] [ [ 1, $.1^103 ] ] [ [ 1, $.1^112 ] ] [ [ 1, $.1^120 ] ] [ [ 1, $.1^131 ] ] [ [ 1, $.1^132 ] ] [ [ 1, $.1^137 ] ] [ [ 1, $.1^146 ] ] [ [ 1, $.1^148 ] ] [ [ 1, $.1^156 ] ] [ [ 1, $.1^159 ] ] [ [ 1, $.1^175 ] ] [ [ 1, $.1^195 ] ] [ [ 1, $.1^197 ] ] [ [ 1, $.1^199 ] ] [ [ 1, $.1^215 ] ] [ [ 1, $.1^233 ] ] [ [ 1, $.1^240 ] ] [ [ 1, $.1^259 ] ] [ [ 1, $.1^263 ] ] [ [ 1, $.1^267 ] ] [ [ 1, $.1^275 ] ] [ [ 1, 5 ] ] [ [ 1, $.1^288 ] ] [ [ 1, $.1^306 ] ] [ [ 1, $.1^307 ] ] [ [ 1, $.1^312 ] ] [ [ 1, $.1^314 ] ] [ [ 1, $.1^321 ] ] [ [ 1, $.1^337 ] ] [ [ 1, $.1^338 ] ] [ [ 1, $.1^339 ] ] [ [ $.1, 1 ] ] [ [ $.1, $.1^3 ] ] [ [ $.1, $.1^21 ] ] [ [ $.1, $.1^22 ] ] [ [ $.1, $.1^27 ] ] [ [ $.1, $.1^29 ] ] [ [ $.1, $.1^36 ] ] [ [ $.1, $.1^52 ] ] [ [ $.1, $.1^53 ] ] [ [ $.1, $.1^54 ] ] [ [ $.1, $.1^58 ] ] [ [ $.1, $.1^59 ] ] [ [ $.1, $.1^64 ] ] [ [ $.1, $.1^67 ] ] [ [ $.1, $.1^68 ] ] [ [ $.1, $.1^71 ] ] [ [ $.1, $.1^73 ] ] [ [ $.1, $.1^82 ] ] [ [ $.1, $.1^94 ] ] [ [ $.1, $.1^106 ] ] [ [ $.1, $.1^123 ] ] [ [ $.1, $.1^127 ] ] [ [ $.1, $.1^134 ] ] [ [ $.1, $.1^144 ] ] [ [ $.1, $.1^147 ] ] [ [ $.1, $.1^154 ] ] [ [ $.1, $.1^155 ] ] [ [ $.1, $.1^157 ] ] [ [ $.1, $.1^160 ] ] [ [ $.1, $.1^169 ] ] [ [ $.1, $.1^177 ] ] [ [ $.1, $.1^188 ] ] [ [ $.1, $.1^189 ] ] [ [ $.1, $.1^194 ] ] [ [ $.1, $.1^203 ] ] [ [ $.1, $.1^205 ] ] [ [ $.1, $.1^213 ] ] [ [ $.1, $.1^216 ] ] [ [ $.1, $.1^232 ] ] [ [ $.1, $.1^252 ] ] [ [ $.1, $.1^254 ] ] [ [ $.1, $.1^256 ] ] [ [ $.1, $.1^272 ] ] [ [ $.1, $.1^290 ] ] [ [ $.1, $.1^297 ] ] [ [ $.1, $.1^316 ] ] [ [ $.1, $.1^320 ] ] [ [ $.1, $.1^324 ] ] [ [ $.1, $.1^332 ] ] [ [ $.1^2, $.1^5 ] ] [ [ $.1^2, $.1^12 ] ] [ [ $.1^2, $.1^31 ] ] [ [ $.1^2, $.1^35 ] ] [ [ $.1^2, $.1^39 ] ] [ [ $.1^2, $.1^47 ] ] [ [ $.1^2, 3 ] ] [ [ $.1^2, $.1^60 ] ] [ [ $.1^2, $.1^78 ] ] [ [ $.1^2, $.1^79 ] ] [ [ $.1^2, $.1^84 ] ] [ [ $.1^2, $.1^86 ] ] [ [ $.1^2, $.1^93 ] ] [ [ $.1^2, $.1^109 ] ] [ [ $.1^2, $.1^110 ] ] [ [ $.1^2, $.1^111 ] ] [ [ $.1^2, $.1^115 ] ] [ [ $.1^2, $.1^116 ] ] [ [ $.1^2, $.1^121 ] ] [ [ $.1^2, $.1^124 ] ] [ [ $.1^2, $.1^125 ] ] [ [ $.1^2, $.1^128 ] ] [ [ $.1^2, $.1^130 ] ] [ [ $.1^2, $.1^139 ] ] [ [ $.1^2, $.1^151 ] ] [ [ $.1^2, $.1^163 ] ] [ [ $.1^2, $.1^180 ] ] [ [ $.1^2, $.1^184 ] ] [ [ $.1^2, $.1^191 ] ] [ [ $.1^2, $.1^201 ] ] [ [ $.1^2, $.1^204 ] ] [ [ $.1^2, $.1^211 ] ] [ [ $.1^2, $.1^212 ] ] [ [ $.1^2, $.1^214 ] ] [ [ $.1^2, $.1^217 ] ] [ [ $.1^2, $.1^226 ] ] [ [ $.1^2, $.1^234 ] ] [ [ $.1^2, $.1^245 ] ] [ [ $.1^2, $.1^246 ] ] [ [ $.1^2, $.1^251 ] ] [ [ $.1^2, $.1^260 ] ] [ [ $.1^2, $.1^262 ] ] [ [ $.1^2, $.1^270 ] ] [ [ $.1^2, $.1^273 ] ] [ [ $.1^2, $.1^289 ] ] [ [ $.1^2, $.1^309 ] ] [ [ $.1^2, $.1^311 ] ] [ [ $.1^2, $.1^313 ] ] [ [ $.1^2, $.1^329 ] ] [ [ $.1^3, $.1^4 ] ] [ [ $.1^3, $.1^24 ] ] [ [ $.1^3, $.1^26 ] ] [ [ $.1^3, $.1^28 ] ] [ [ $.1^3, $.1^44 ] ] [ [ $.1^3, $.1^62 ] ] [ [ $.1^3, $.1^69 ] ] [ [ $.1^3, $.1^88 ] ] [ [ $.1^3, $.1^92 ] ] [ [ $.1^3, $.1^96 ] ] [ [ $.1^3, $.1^104 ] ] [ [ $.1^3, 2 ] ] [ [ $.1^3, $.1^117 ] ] [ [ $.1^3, $.1^135 ] ] [ [ $.1^3, $.1^136 ] ] [ [ $.1^3, $.1^141 ] ] [ [ $.1^3, $.1^143 ] ] [ [ $.1^3, $.1^150 ] ] [ [ $.1^3, $.1^166 ] ] [ [ $.1^3, $.1^167 ] ] [ [ $.1^3, $.1^168 ] ] [ [ $.1^3, $.1^172 ] ] [ [ $.1^3, $.1^173 ] ] [ [ $.1^3, $.1^178 ] ] [ [ $.1^3, $.1^181 ] ] [ [ $.1^3, $.1^182 ] ] [ [ $.1^3, $.1^185 ] ] [ [ $.1^3, $.1^187 ] ] [ [ $.1^3, $.1^196 ] ] [ [ $.1^3, $.1^208 ] ] [ [ $.1^3, $.1^220 ] ] [ [ $.1^3, $.1^237 ] ] [ [ $.1^3, $.1^241 ] ] [ [ $.1^3, $.1^248 ] ] [ [ $.1^3, $.1^258 ] ] [ [ $.1^3, $.1^261 ] ] [ [ $.1^3, $.1^268 ] ] [ [ $.1^3, $.1^269 ] ] [ [ $.1^3, $.1^271 ] ] [ [ $.1^3, $.1^274 ] ] [ [ $.1^3, $.1^283 ] ] [ [ $.1^3, $.1^291 ] ] [ [ $.1^3, $.1^302 ] ] [ [ $.1^3, $.1^303 ] ] [ [ $.1^3, $.1^308 ] ] [ [ $.1^3, $.1^317 ] ] [ [ $.1^3, $.1^319 ] ] [ [ $.1^3, $.1^327 ] ] [ [ $.1^3, $.1^330 ] ] [ [ $.1^4, $.1^6 ] ] [ [ $.1^4, $.1^17 ] ] [ [ $.1^4, $.1^18 ] ] [ [ $.1^4, $.1^23 ] ] [ [ $.1^4, $.1^32 ] ] [ [ $.1^4, $.1^34 ] ] [ [ $.1^4, $.1^42 ] ] [ [ $.1^4, $.1^45 ] ] [ [ $.1^4, $.1^61 ] ] [ [ $.1^4, $.1^81 ] ] [ [ $.1^4, $.1^83 ] ] [ [ $.1^4, $.1^85 ] ] [ [ $.1^4, $.1^101 ] ] [ [ $.1^4, $.1^119 ] ] [ [ $.1^4, $.1^126 ] ] [ [ $.1^4, $.1^145 ] ] [ [ $.1^4, $.1^149 ] ] [ [ $.1^4, $.1^153 ] ] [ [ $.1^4, $.1^161 ] ] [ [ $.1^4, 6 ] ] [ [ $.1^4, $.1^174 ] ] [ [ $.1^4, $.1^192 ] ] [ [ $.1^4, $.1^193 ] ] [ [ $.1^4, $.1^198 ] ] [ [ $.1^4, $.1^200 ] ] [ [ $.1^4, $.1^207 ] ] [ [ $.1^4, $.1^223 ] ] [ [ $.1^4, $.1^224 ] ] [ [ $.1^4, $.1^225 ] ] [ [ $.1^4, $.1^229 ] ] [ [ $.1^4, $.1^230 ] ] [ [ $.1^4, $.1^235 ] ] [ [ $.1^4, $.1^238 ] ] [ [ $.1^4, $.1^239 ] ] [ [ $.1^4, $.1^242 ] ] [ [ $.1^4, $.1^244 ] ] [ [ $.1^4, $.1^253 ] ] [ [ $.1^4, $.1^265 ] ] [ [ $.1^4, $.1^277 ] ] [ [ $.1^4, $.1^294 ] ] [ [ $.1^4, $.1^298 ] ] [ [ $.1^4, $.1^305 ] ] [ [ $.1^4, $.1^315 ] ] [ [ $.1^4, $.1^318 ] ] [ [ $.1^4, $.1^325 ] ] [ [ $.1^4, $.1^326 ] ] [ [ $.1^4, $.1^328 ] ] [ [ $.1^4, $.1^331 ] ] [ [ $.1^4, $.1^340 ] ] [ [ $.1^5, $.1^9 ] ] [ [ $.1^5, $.1^13 ] ] [ [ $.1^5, $.1^20 ] ] [ [ $.1^5, $.1^30 ] ] [ [ $.1^5, $.1^33 ] ] [ [ $.1^5, $.1^40 ] ] [ [ $.1^5, $.1^41 ] ] [ [ $.1^5, $.1^43 ] ] [ [ $.1^5, $.1^46 ] ] [ [ $.1^5, $.1^55 ] ] [ [ $.1^5, $.1^63 ] ] [ [ $.1^5, $.1^74 ] ] [ [ $.1^5, $.1^75 ] ] [ [ $.1^5, $.1^80 ] ] [ [ $.1^5, $.1^89 ] ] [ [ $.1^5, $.1^91 ] ] [ [ $.1^5, $.1^99 ] ] [ [ $.1^5, $.1^102 ] ] [ [ $.1^5, $.1^118 ] ] [ [ $.1^5, $.1^138 ] ] [ [ $.1^5, $.1^140 ] ] [ [ $.1^5, $.1^142 ] ] [ [ $.1^5, $.1^158 ] ] [ [ $.1^5, $.1^176 ] ] [ [ $.1^5, $.1^183 ] ] [ [ $.1^5, $.1^202 ] ] [ [ $.1^5, $.1^206 ] ] [ [ $.1^5, $.1^210 ] ] [ [ $.1^5, $.1^218 ] ] [ [ $.1^5, 4 ] ] [ [ $.1^5, $.1^231 ] ] [ [ $.1^5, $.1^249 ] ] [ [ $.1^5, $.1^250 ] ] [ [ $.1^5, $.1^255 ] ] [ [ $.1^5, $.1^257 ] ] [ [ $.1^5, $.1^264 ] ] [ [ $.1^5, $.1^280 ] ] [ [ $.1^5, $.1^281 ] ] [ [ $.1^5, $.1^282 ] ] [ [ $.1^5, $.1^286 ] ] [ [ $.1^5, $.1^287 ] ] [ [ $.1^5, $.1^292 ] ] [ [ $.1^5, $.1^295 ] ] [ [ $.1^5, $.1^296 ] ] [ [ $.1^5, $.1^299 ] ] [ [ $.1^5, $.1^301 ] ] [ [ $.1^5, $.1^310 ] ] [ [ $.1^5, $.1^322 ] ] [ [ $.1^5, $.1^334 ] ] [ [ $.1^6, $.1 ] ] [ [ $.1^6, $.1^2 ] ] [ [ $.1^6, $.1^7 ] ] [ [ $.1^6, $.1^10 ] ] [ [ $.1^6, $.1^11 ] ] [ [ $.1^6, $.1^14 ] ] [ [ $.1^6, $.1^16 ] ] [ [ $.1^6, $.1^25 ] ] [ [ $.1^6, $.1^37 ] ] [ [ $.1^6, $.1^49 ] ] [ [ $.1^6, $.1^66 ] ] [ [ $.1^6, $.1^70 ] ] [ [ $.1^6, $.1^77 ] ] [ [ $.1^6, $.1^87 ] ] [ [ $.1^6, $.1^90 ] ] [ [ $.1^6, $.1^97 ] ] [ [ $.1^6, $.1^98 ] ] [ [ $.1^6, $.1^100 ] ] [ [ $.1^6, $.1^103 ] ] [ [ $.1^6, $.1^112 ] ] [ [ $.1^6, $.1^120 ] ] [ [ $.1^6, $.1^131 ] ] [ [ $.1^6, $.1^132 ] ] [ [ $.1^6, $.1^137 ] ] [ [ $.1^6, $.1^146 ] ] [ [ $.1^6, $.1^148 ] ] [ [ $.1^6, $.1^156 ] ] [ [ $.1^6, $.1^159 ] ] [ [ $.1^6, $.1^175 ] ] [ [ $.1^6, $.1^195 ] ] [ [ $.1^6, $.1^197 ] ] [ [ $.1^6, $.1^199 ] ] [ [ $.1^6, $.1^215 ] ] [ [ $.1^6, $.1^233 ] ] [ [ $.1^6, $.1^240 ] ] [ [ $.1^6, $.1^259 ] ] [ [ $.1^6, $.1^263 ] ] [ [ $.1^6, $.1^267 ] ] [ [ $.1^6, $.1^275 ] ] [ [ $.1^6, 5 ] ] [ [ $.1^6, $.1^288 ] ] [ [ $.1^6, $.1^306 ] ] [ [ $.1^6, $.1^307 ] ] [ [ $.1^6, $.1^312 ] ] [ [ $.1^6, $.1^314 ] ] [ [ $.1^6, $.1^321 ] ] [ [ $.1^6, $.1^337 ] ] [ [ $.1^6, $.1^338 ] ] [ [ $.1^6, $.1^339 ] ] [ [ $.1^7, 1 ] ] [ [ $.1^7, $.1^3 ] ] [ [ $.1^7, $.1^21 ] ] [ [ $.1^7, $.1^22 ] ] [ [ $.1^7, $.1^27 ] ] [ [ $.1^7, $.1^29 ] ] [ [ $.1^7, $.1^36 ] ] [ [ $.1^7, $.1^52 ] ] [ [ $.1^7, $.1^53 ] ] [ [ $.1^7, $.1^54 ] ] [ [ $.1^7, $.1^58 ] ] [ [ $.1^7, $.1^59 ] ] [ [ $.1^7, $.1^64 ] ] [ [ $.1^7, $.1^67 ] ] [ [ $.1^7, $.1^68 ] ] [ [ $.1^7, $.1^71 ] ] [ [ $.1^7, $.1^73 ] ] [ [ $.1^7, $.1^82 ] ] [ [ $.1^7, $.1^94 ] ] [ [ $.1^7, $.1^106 ] ] [ [ $.1^7, $.1^123 ] ] [ [ $.1^7, $.1^127 ] ] [ [ $.1^7, $.1^134 ] ] [ [ $.1^7, $.1^144 ] ] [ [ $.1^7, $.1^147 ] ] [ [ $.1^7, $.1^154 ] ] [ [ $.1^7, $.1^155 ] ] [ [ $.1^7, $.1^157 ] ] [ [ $.1^7, $.1^160 ] ] [ [ $.1^7, $.1^169 ] ] [ [ $.1^7, $.1^177 ] ] [ [ $.1^7, $.1^188 ] ] [ [ $.1^7, $.1^189 ] ] [ [ $.1^7, $.1^194 ] ] [ [ $.1^7, $.1^203 ] ] [ [ $.1^7, $.1^205 ] ] [ [ $.1^7, $.1^213 ] ] [ [ $.1^7, $.1^216 ] ] [ [ $.1^7, $.1^232 ] ] [ [ $.1^7, $.1^252 ] ] [ [ $.1^7, $.1^254 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 200-BAR2-X4.libre.retevision.es. (62.82.186.200) Time: Fri Mar 12 11:17:22 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; spolav:= [k : k in polavqr(2,3) | k[1] in GF(7) and k[2] in GF(7) ]; #spolav; Output: Magma V2.10-6 Fri Mar 12 2004 11:17:19 on modular [Seed = 674859689] ------------------------------------- [ [ 1, 1 ] ] [ [ 1, $.1^3 ] ] [ [ 1, $.1^5 ] ] [ [ 1, $.1^6 ] ] [ [ $.1, 1 ] ] [ [ $.1, $.1^3 ] ] [ [ $.1, $.1^5 ] ] [ [ $.1, $.1^6 ] ] [ [ $.1^2, 1 ] ] [ [ $.1^2, $.1^3 ] ] [ [ $.1^2, $.1^5 ] ] [ [ $.1^2, $.1^6 ] ] [ [ $.1^3, 1 ] ] [ [ $.1^3, $.1^3 ] ] [ [ $.1^3, $.1^5 ] ] [ [ $.1^3, $.1^6 ] ] [ [ $.1^4, 1 ] ] [ [ $.1^4, $.1^3 ] ] [ [ $.1^4, $.1^5 ] ] [ [ $.1^4, $.1^6 ] ] [ [ $.1^5, 1 ] ] [ [ $.1^5, $.1^3 ] ] [ [ $.1^5, $.1^5 ] ] [ [ $.1^5, $.1^6 ] ] [ [ $.1^6, 1 ] ] [ [ $.1^6, $.1^3 ] ] [ [ $.1^6, $.1^5 ] ] [ [ $.1^6, $.1^6 ] ] [ [ 0, $.1 ] ] [ [ 0, $.1^2 ] ] [ [ 0, $.1^4 ] ] [ [ 0, 0 ] ] 0 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 200-BAR2-X4.libre.retevision.es. (62.82.186.200) Time: Fri Mar 12 11:17:47 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; spolav:= [k : k in polavqr(2,2) | k[1] in GF(7) and k[2] in GF(7) ]; #spolav; Output: Magma V2.10-6 Fri Mar 12 2004 11:17:44 on modular [Seed = 556827527] ------------------------------------- [ [ 1, $.1 ] ] [ [ 1, $.1^2 ] ] [ [ $.1, $.1 ] ] [ [ $.1, $.1^2 ] ] [ [ $.1^2, $.1 ] ] [ [ $.1^2, $.1^2 ] ] [ [ 0, 1 ] ] [ [ 0, 0 ] ] 0 Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 200-BAR2-X4.libre.retevision.es. (62.82.186.200) Time: Fri Mar 12 11:18:52 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; spolav:= [k : k in polavqr(3,1) | k[1] in GF(7) and k[2] in GF(7) ]; #spolav; Output: Magma V2.10-6 Fri Mar 12 2004 11:18:49 on modular [Seed = 925275600] ------------------------------------- [ [ 0, 0 ] ] [ [ 1, 1 ] ] [ [ 2, 2 ] ] 0 Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 200-BAR2-X4.libre.retevision.es. (62.82.186.200) Time: Fri Mar 12 11:19:48 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; spolav:= [k : k in polavqr(3,1) | k[1] in GF(7) and k[2] in GF(7) ]; #(spolav); Output: Magma V2.10-6 Fri Mar 12 2004 11:19:45 on modular [Seed = 1297935970] ------------------------------------- [ [ 0, 0 ] ] [ [ 1, 1 ] ] [ [ 2, 2 ] ] 0 Total time: 3.039 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 11:22:56 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; spolav:= [k : k in polavqr(3,1) | k[1] in GF(7) and k[2] in GF(7) ]; #spolav; Output: Magma V2.10-6 Fri Mar 12 2004 11:22:53 on modular [Seed = 1531639944] ------------------------------------- [ [ 0, 0 ] ] [ [ 1, 1 ] ] [ [ 2, 2 ] ] 0 Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 11:24:31 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; spolav:= [k : k in polavqr(7,3) | k[1] in GF(7) and k[2] in GF(7) ]; #spolav; Output: Magma V2.10-6 Fri Mar 12 2004 11:24:08 on modular [Seed = 1346499702] ------------------------------------- [ [ 1, $.1 ] ] [ [ 1, $.1^2 ] ] [ [ 1, $.1^7 ] ] [ [ 1, $.1^10 ] ] [ [ 1, $.1^11 ] ] [ [ 1, $.1^14 ] ] [ [ 1, $.1^16 ] ] [ [ 1, $.1^25 ] ] [ [ 1, $.1^37 ] ] [ [ 1, $.1^49 ] ] [ [ 1, $.1^66 ] ] [ [ 1, $.1^70 ] ] [ [ 1, $.1^77 ] ] [ [ 1, $.1^87 ] ] [ [ 1, $.1^90 ] ] [ [ 1, $.1^97 ] ] [ [ 1, $.1^98 ] ] [ [ 1, $.1^100 ] ] [ [ 1, $.1^103 ] ] [ [ 1, $.1^112 ] ] [ [ 1, $.1^120 ] ] [ [ 1, $.1^131 ] ] [ [ 1, $.1^132 ] ] [ [ 1, $.1^137 ] ] [ [ 1, $.1^146 ] ] [ [ 1, $.1^148 ] ] [ [ 1, $.1^156 ] ] [ [ 1, $.1^159 ] ] [ [ 1, $.1^175 ] ] [ [ 1, $.1^195 ] ] [ [ 1, $.1^197 ] ] [ [ 1, $.1^199 ] ] [ [ 1, $.1^215 ] ] [ [ 1, $.1^233 ] ] [ [ 1, $.1^240 ] ] [ [ 1, $.1^259 ] ] [ [ 1, $.1^263 ] ] [ [ 1, $.1^267 ] ] [ [ 1, $.1^275 ] ] [ [ 1, 5 ] ] [ [ 1, $.1^288 ] ] [ [ 1, $.1^306 ] ] [ [ 1, $.1^307 ] ] [ [ 1, $.1^312 ] ] [ [ 1, $.1^314 ] ] [ [ 1, $.1^321 ] ] [ [ 1, $.1^337 ] ] [ [ 1, $.1^338 ] ] [ [ 1, $.1^339 ] ] [ [ $.1, 1 ] ] [ [ $.1, $.1^3 ] ] [ [ $.1, $.1^21 ] ] [ [ $.1, $.1^22 ] ] [ [ $.1, $.1^27 ] ] [ [ $.1, $.1^29 ] ] [ [ $.1, $.1^36 ] ] [ [ $.1, $.1^52 ] ] [ [ $.1, $.1^53 ] ] [ [ $.1, $.1^54 ] ] [ [ $.1, $.1^58 ] ] [ [ $.1, $.1^59 ] ] [ [ $.1, $.1^64 ] ] [ [ $.1, $.1^67 ] ] [ [ $.1, $.1^68 ] ] [ [ $.1, $.1^71 ] ] [ [ $.1, $.1^73 ] ] [ [ $.1, $.1^82 ] ] [ [ $.1, $.1^94 ] ] [ [ $.1, $.1^106 ] ] [ [ $.1, $.1^123 ] ] [ [ $.1, $.1^127 ] ] [ [ $.1, $.1^134 ] ] [ [ $.1, $.1^144 ] ] [ [ $.1, $.1^147 ] ] [ [ $.1, $.1^154 ] ] [ [ $.1, $.1^155 ] ] [ [ $.1, $.1^157 ] ] [ [ $.1, $.1^160 ] ] [ [ $.1, $.1^169 ] ] [ [ $.1, $.1^177 ] ] [ [ $.1, $.1^188 ] ] [ [ $.1, $.1^189 ] ] [ [ $.1, $.1^194 ] ] [ [ $.1, $.1^203 ] ] [ [ $.1, $.1^205 ] ] [ [ $.1, $.1^213 ] ] [ [ $.1, $.1^216 ] ] [ [ $.1, $.1^232 ] ] [ [ $.1, $.1^252 ] ] [ [ $.1, $.1^254 ] ] [ [ $.1, $.1^256 ] ] [ [ $.1, $.1^272 ] ] [ [ $.1, $.1^290 ] ] [ [ $.1, $.1^297 ] ] [ [ $.1, $.1^316 ] ] [ [ $.1, $.1^320 ] ] [ [ $.1, $.1^324 ] ] [ [ $.1, $.1^332 ] ] [ [ $.1^2, $.1^5 ] ] [ [ $.1^2, $.1^12 ] ] [ [ $.1^2, $.1^31 ] ] [ [ $.1^2, $.1^35 ] ] [ [ $.1^2, $.1^39 ] ] [ [ $.1^2, $.1^47 ] ] [ [ $.1^2, 3 ] ] [ [ $.1^2, $.1^60 ] ] [ [ $.1^2, $.1^78 ] ] [ [ $.1^2, $.1^79 ] ] [ [ $.1^2, $.1^84 ] ] [ [ $.1^2, $.1^86 ] ] [ [ $.1^2, $.1^93 ] ] [ [ $.1^2, $.1^109 ] ] [ [ $.1^2, $.1^110 ] ] [ [ $.1^2, $.1^111 ] ] [ [ $.1^2, $.1^115 ] ] [ [ $.1^2, $.1^116 ] ] [ [ $.1^2, $.1^121 ] ] [ [ $.1^2, $.1^124 ] ] [ [ $.1^2, $.1^125 ] ] [ [ $.1^2, $.1^128 ] ] [ [ $.1^2, $.1^130 ] ] [ [ $.1^2, $.1^139 ] ] [ [ $.1^2, $.1^151 ] ] [ [ $.1^2, $.1^163 ] ] [ [ $.1^2, $.1^180 ] ] [ [ $.1^2, $.1^184 ] ] [ [ $.1^2, $.1^191 ] ] [ [ $.1^2, $.1^201 ] ] [ [ $.1^2, $.1^204 ] ] [ [ $.1^2, $.1^211 ] ] [ [ $.1^2, $.1^212 ] ] [ [ $.1^2, $.1^214 ] ] [ [ $.1^2, $.1^217 ] ] [ [ $.1^2, $.1^226 ] ] [ [ $.1^2, $.1^234 ] ] [ [ $.1^2, $.1^245 ] ] [ [ $.1^2, $.1^246 ] ] [ [ $.1^2, $.1^251 ] ] [ [ $.1^2, $.1^260 ] ] [ [ $.1^2, $.1^262 ] ] [ [ $.1^2, $.1^270 ] ] [ [ $.1^2, $.1^273 ] ] [ [ $.1^2, $.1^289 ] ] [ [ $.1^2, $.1^309 ] ] [ [ $.1^2, $.1^311 ] ] [ [ $.1^2, $.1^313 ] ] [ [ $.1^2, $.1^329 ] ] [ [ $.1^3, $.1^4 ] ] [ [ $.1^3, $.1^24 ] ] [ [ $.1^3, $.1^26 ] ] [ [ $.1^3, $.1^28 ] ] [ [ $.1^3, $.1^44 ] ] [ [ $.1^3, $.1^62 ] ] [ [ $.1^3, $.1^69 ] ] [ [ $.1^3, $.1^88 ] ] [ [ $.1^3, $.1^92 ] ] [ [ $.1^3, $.1^96 ] ] [ [ $.1^3, $.1^104 ] ] [ [ $.1^3, 2 ] ] [ [ $.1^3, $.1^117 ] ] [ [ $.1^3, $.1^135 ] ] [ [ $.1^3, $.1^136 ] ] [ [ $.1^3, $.1^141 ] ] [ [ $.1^3, $.1^143 ] ] [ [ $.1^3, $.1^150 ] ] [ [ $.1^3, $.1^166 ] ] [ [ $.1^3, $.1^167 ] ] [ [ $.1^3, $.1^168 ] ] [ [ $.1^3, $.1^172 ] ] [ [ $.1^3, $.1^173 ] ] [ [ $.1^3, $.1^178 ] ] [ [ $.1^3, $.1^181 ] ] [ [ $.1^3, $.1^182 ] ] [ [ $.1^3, $.1^185 ] ] [ [ $.1^3, $.1^187 ] ] [ [ $.1^3, $.1^196 ] ] [ [ $.1^3, $.1^208 ] ] [ [ $.1^3, $.1^220 ] ] [ [ $.1^3, $.1^237 ] ] [ [ $.1^3, $.1^241 ] ] [ [ $.1^3, $.1^248 ] ] [ [ $.1^3, $.1^258 ] ] [ [ $.1^3, $.1^261 ] ] [ [ $.1^3, $.1^268 ] ] [ [ $.1^3, $.1^269 ] ] [ [ $.1^3, $.1^271 ] ] [ [ $.1^3, $.1^274 ] ] [ [ $.1^3, $.1^283 ] ] [ [ $.1^3, $.1^291 ] ] [ [ $.1^3, $.1^302 ] ] [ [ $.1^3, $.1^303 ] ] [ [ $.1^3, $.1^308 ] ] [ [ $.1^3, $.1^317 ] ] [ [ $.1^3, $.1^319 ] ] [ [ $.1^3, $.1^327 ] ] [ [ $.1^3, $.1^330 ] ] [ [ $.1^4, $.1^6 ] ] [ [ $.1^4, $.1^17 ] ] [ [ $.1^4, $.1^18 ] ] [ [ $.1^4, $.1^23 ] ] [ [ $.1^4, $.1^32 ] ] [ [ $.1^4, $.1^34 ] ] [ [ $.1^4, $.1^42 ] ] [ [ $.1^4, $.1^45 ] ] [ [ $.1^4, $.1^61 ] ] [ [ $.1^4, $.1^81 ] ] [ [ $.1^4, $.1^83 ] ] [ [ $.1^4, $.1^85 ] ] [ [ $.1^4, $.1^101 ] ] [ [ $.1^4, $.1^119 ] ] [ [ $.1^4, $.1^126 ] ] [ [ $.1^4, $.1^145 ] ] [ [ $.1^4, $.1^149 ] ] [ [ $.1^4, $.1^153 ] ] [ [ $.1^4, $.1^161 ] ] [ [ $.1^4, 6 ] ] [ [ $.1^4, $.1^174 ] ] [ [ $.1^4, $.1^192 ] ] [ [ $.1^4, $.1^193 ] ] [ [ $.1^4, $.1^198 ] ] [ [ $.1^4, $.1^200 ] ] [ [ $.1^4, $.1^207 ] ] [ [ $.1^4, $.1^223 ] ] [ [ $.1^4, $.1^224 ] ] [ [ $.1^4, $.1^225 ] ] [ [ $.1^4, $.1^229 ] ] [ [ $.1^4, $.1^230 ] ] [ [ $.1^4, $.1^235 ] ] [ [ $.1^4, $.1^238 ] ] [ [ $.1^4, $.1^239 ] ] [ [ $.1^4, $.1^242 ] ] [ [ $.1^4, $.1^244 ] ] [ [ $.1^4, $.1^253 ] ] [ [ $.1^4, $.1^265 ] ] [ [ $.1^4, $.1^277 ] ] [ [ $.1^4, $.1^294 ] ] [ [ $.1^4, $.1^298 ] ] [ [ $.1^4, $.1^305 ] ] [ [ $.1^4, $.1^315 ] ] [ [ $.1^4, $.1^318 ] ] [ [ $.1^4, $.1^325 ] ] [ [ $.1^4, $.1^326 ] ] [ [ $.1^4, $.1^328 ] ] [ [ $.1^4, $.1^331 ] ] [ [ $.1^4, $.1^340 ] ] [ [ $.1^5, $.1^9 ] ] [ [ $.1^5, $.1^13 ] ] [ [ $.1^5, $.1^20 ] ] [ [ $.1^5, $.1^30 ] ] [ [ $.1^5, $.1^33 ] ] [ [ $.1^5, $.1^40 ] ] [ [ $.1^5, $.1^41 ] ] [ [ $.1^5, $.1^43 ] ] [ [ $.1^5, $.1^46 ] ] [ [ $.1^5, $.1^55 ] ] [ [ $.1^5, $.1^63 ] ] [ [ $.1^5, $.1^74 ] ] [ [ $.1^5, $.1^75 ] ] [ [ $.1^5, $.1^80 ] ] [ [ $.1^5, $.1^89 ] ] [ [ $.1^5, $.1^91 ] ] [ [ $.1^5, $.1^99 ] ] [ [ $.1^5, $.1^102 ] ] [ [ $.1^5, $.1^118 ] ] [ [ $.1^5, $.1^138 ] ] [ [ $.1^5, $.1^140 ] ] [ [ $.1^5, $.1^142 ] ] [ [ $.1^5, $.1^158 ] ] [ [ $.1^5, $.1^176 ] ] [ [ $.1^5, $.1^183 ] ] [ [ $.1^5, $.1^202 ] ] [ [ $.1^5, $.1^206 ] ] [ [ $.1^5, $.1^210 ] ] [ [ $.1^5, $.1^218 ] ] [ [ $.1^5, 4 ] ] [ [ $.1^5, $.1^231 ] ] [ [ $.1^5, $.1^249 ] ] [ [ $.1^5, $.1^250 ] ] [ [ $.1^5, $.1^255 ] ] [ [ $.1^5, $.1^257 ] ] [ [ $.1^5, $.1^264 ] ] [ [ $.1^5, $.1^280 ] ] [ [ $.1^5, $.1^281 ] ] [ [ $.1^5, $.1^282 ] ] [ [ $.1^5, $.1^286 ] ] [ [ $.1^5, $.1^287 ] ] [ [ $.1^5, $.1^292 ] ] [ [ $.1^5, $.1^295 ] ] [ [ $.1^5, $.1^296 ] ] [ [ $.1^5, $.1^299 ] ] [ [ $.1^5, $.1^301 ] ] [ [ $.1^5, $.1^310 ] ] [ [ $.1^5, $.1^322 ] ] [ [ $.1^5, $.1^334 ] ] [ [ $.1^6, $.1 ] ] [ [ $.1^6, $.1^2 ] ] [ [ $.1^6, $.1^7 ] ] [ [ $.1^6, $.1^10 ] ] [ [ $.1^6, $.1^11 ] ] [ [ $.1^6, $.1^14 ] ] [ [ $.1^6, $.1^16 ] ] [ [ $.1^6, $.1^25 ] ] [ [ $.1^6, $.1^37 ] ] [ [ $.1^6, $.1^49 ] ] [ [ $.1^6, $.1^66 ] ] [ [ $.1^6, $.1^70 ] ] [ [ $.1^6, $.1^77 ] ] [ [ $.1^6, $.1^87 ] ] [ [ $.1^6, $.1^90 ] ] [ [ $.1^6, $.1^97 ] ] [ [ $.1^6, $.1^98 ] ] [ [ $.1^6, $.1^100 ] ] [ [ $.1^6, $.1^103 ] ] [ [ $.1^6, $.1^112 ] ] [ [ $.1^6, $.1^120 ] ] [ [ $.1^6, $.1^131 ] ] [ [ $.1^6, $.1^132 ] ] [ [ $.1^6, $.1^137 ] ] [ [ $.1^6, $.1^146 ] ] [ [ $.1^6, $.1^148 ] ] [ [ $.1^6, $.1^156 ] ] [ [ $.1^6, $.1^159 ] ] [ [ $.1^6, $.1^175 ] ] [ [ $.1^6, $.1^195 ] ] [ [ $.1^6, $.1^197 ] ] [ [ $.1^6, $.1^199 ] ] [ [ $.1^6, $.1^215 ] ] [ [ $.1^6, $.1^233 ] ] [ [ $.1^6, $.1^240 ] ] [ [ $.1^6, $.1^259 ] ] [ [ $.1^6, $.1^263 ] ] [ [ $.1^6, $.1^267 ] ] [ [ $.1^6, $.1^275 ] ] [ [ $.1^6, 5 ] ] [ [ $.1^6, $.1^288 ] ] [ [ $.1^6, $.1^306 ] ] [ [ $.1^6, $.1^307 ] ] [ [ $.1^6, $.1^312 ] ] [ [ $.1^6, $.1^314 ] ] [ [ $.1^6, $.1^321 ] ] [ [ $.1^6, $.1^337 ] ] [ [ $.1^6, $.1^338 ] ] [ [ $.1^6, $.1^339 ] ] [ [ $.1^7, 1 ] ] [ [ $.1^7, $.1^3 ] ] [ [ $.1^7, $.1^21 ] ] [ [ $.1^7, $.1^22 ] ] [ [ $.1^7, $.1^27 ] ] [ [ $.1^7, $.1^29 ] ] [ [ $.1^7, $.1^36 ] ] [ [ $.1^7, $.1^52 ] ] [ [ $.1^7, $.1^53 ] ] [ [ $.1^7, $.1^54 ] ] [ [ $.1^7, $.1^58 ] ] [ [ $.1^7, $.1^59 ] ] [ [ $.1^7, $.1^64 ] ] [ [ $.1^7, $.1^67 ] ] [ [ $.1^7, $.1^68 ] ] [ [ $.1^7, $.1^71 ] ] [ [ $.1^7, $.1^73 ] ] [ [ $.1^7, $.1^82 ] ] [ [ $.1^7, $.1^94 ] ] [ [ $.1^7, $.1^106 ] ] [ [ $.1^7, $.1^123 ] ] [ [ $.1^7, $.1^127 ] ] [ [ $.1^7, $.1^134 ] ] [ [ $.1^7, $.1^144 ] ] [ [ $.1^7, $.1^147 ] ] [ [ $.1^7, $.1^154 ] ] [ [ $.1^7, $.1^155 ] ] [ [ $.1^7, $.1^157 ] ] [ [ $.1^7, $.1^160 ] ] [ [ $.1^7, $.1^169 ] ] [ [ $.1^7, $.1^177 ] ] [ [ $.1^7, $.1^188 ] ] [ [ $.1^7, $.1^189 ] ] [ [ $.1^7, $.1^194 ] ] [ [ $.1^7, $.1^203 ] ] [ [ $.1^7, $.1^205 ] ] [ [ $.1^7, $.1^213 ] ] [ [ $.1^7, $.1^216 ] ] [ [ $.1^7, $.1^232 ] ] [ [ $.1^7, $.1^252 ] ] [ [ $.1^7, $.1^25 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 11:24:48 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; spolav:= [k : k in polavqr(7,3) | k[1] in GF(7) and k[2] in GF(7) ]; #spolav; Output: Magma V2.10-6 Fri Mar 12 2004 11:24:26 on modular [Seed = 1870580571] ------------------------------------- [ [ 1, $.1 ] ] [ [ 1, $.1^2 ] ] [ [ 1, $.1^7 ] ] [ [ 1, $.1^10 ] ] [ [ 1, $.1^11 ] ] [ [ 1, $.1^14 ] ] [ [ 1, $.1^16 ] ] [ [ 1, $.1^25 ] ] [ [ 1, $.1^37 ] ] [ [ 1, $.1^49 ] ] [ [ 1, $.1^66 ] ] [ [ 1, $.1^70 ] ] [ [ 1, $.1^77 ] ] [ [ 1, $.1^87 ] ] [ [ 1, $.1^90 ] ] [ [ 1, $.1^97 ] ] [ [ 1, $.1^98 ] ] [ [ 1, $.1^100 ] ] [ [ 1, $.1^103 ] ] [ [ 1, $.1^112 ] ] [ [ 1, $.1^120 ] ] [ [ 1, $.1^131 ] ] [ [ 1, $.1^132 ] ] [ [ 1, $.1^137 ] ] [ [ 1, $.1^146 ] ] [ [ 1, $.1^148 ] ] [ [ 1, $.1^156 ] ] [ [ 1, $.1^159 ] ] [ [ 1, $.1^175 ] ] [ [ 1, $.1^195 ] ] [ [ 1, $.1^197 ] ] [ [ 1, $.1^199 ] ] [ [ 1, $.1^215 ] ] [ [ 1, $.1^233 ] ] [ [ 1, $.1^240 ] ] [ [ 1, $.1^259 ] ] [ [ 1, $.1^263 ] ] [ [ 1, $.1^267 ] ] [ [ 1, $.1^275 ] ] [ [ 1, 5 ] ] [ [ 1, $.1^288 ] ] [ [ 1, $.1^306 ] ] [ [ 1, $.1^307 ] ] [ [ 1, $.1^312 ] ] [ [ 1, $.1^314 ] ] [ [ 1, $.1^321 ] ] [ [ 1, $.1^337 ] ] [ [ 1, $.1^338 ] ] [ [ 1, $.1^339 ] ] [ [ $.1, 1 ] ] [ [ $.1, $.1^3 ] ] [ [ $.1, $.1^21 ] ] [ [ $.1, $.1^22 ] ] [ [ $.1, $.1^27 ] ] [ [ $.1, $.1^29 ] ] [ [ $.1, $.1^36 ] ] [ [ $.1, $.1^52 ] ] [ [ $.1, $.1^53 ] ] [ [ $.1, $.1^54 ] ] [ [ $.1, $.1^58 ] ] [ [ $.1, $.1^59 ] ] [ [ $.1, $.1^64 ] ] [ [ $.1, $.1^67 ] ] [ [ $.1, $.1^68 ] ] [ [ $.1, $.1^71 ] ] [ [ $.1, $.1^73 ] ] [ [ $.1, $.1^82 ] ] [ [ $.1, $.1^94 ] ] [ [ $.1, $.1^106 ] ] [ [ $.1, $.1^123 ] ] [ [ $.1, $.1^127 ] ] [ [ $.1, $.1^134 ] ] [ [ $.1, $.1^144 ] ] [ [ $.1, $.1^147 ] ] [ [ $.1, $.1^154 ] ] [ [ $.1, $.1^155 ] ] [ [ $.1, $.1^157 ] ] [ [ $.1, $.1^160 ] ] [ [ $.1, $.1^169 ] ] [ [ $.1, $.1^177 ] ] [ [ $.1, $.1^188 ] ] [ [ $.1, $.1^189 ] ] [ [ $.1, $.1^194 ] ] [ [ $.1, $.1^203 ] ] [ [ $.1, $.1^205 ] ] [ [ $.1, $.1^213 ] ] [ [ $.1, $.1^216 ] ] [ [ $.1, $.1^232 ] ] [ [ $.1, $.1^252 ] ] [ [ $.1, $.1^254 ] ] [ [ $.1, $.1^256 ] ] [ [ $.1, $.1^272 ] ] [ [ $.1, $.1^290 ] ] [ [ $.1, $.1^297 ] ] [ [ $.1, $.1^316 ] ] [ [ $.1, $.1^320 ] ] [ [ $.1, $.1^324 ] ] [ [ $.1, $.1^332 ] ] [ [ $.1^2, $.1^5 ] ] [ [ $.1^2, $.1^12 ] ] [ [ $.1^2, $.1^31 ] ] [ [ $.1^2, $.1^35 ] ] [ [ $.1^2, $.1^39 ] ] [ [ $.1^2, $.1^47 ] ] [ [ $.1^2, 3 ] ] [ [ $.1^2, $.1^60 ] ] [ [ $.1^2, $.1^78 ] ] [ [ $.1^2, $.1^79 ] ] [ [ $.1^2, $.1^84 ] ] [ [ $.1^2, $.1^86 ] ] [ [ $.1^2, $.1^93 ] ] [ [ $.1^2, $.1^109 ] ] [ [ $.1^2, $.1^110 ] ] [ [ $.1^2, $.1^111 ] ] [ [ $.1^2, $.1^115 ] ] [ [ $.1^2, $.1^116 ] ] [ [ $.1^2, $.1^121 ] ] [ [ $.1^2, $.1^124 ] ] [ [ $.1^2, $.1^125 ] ] [ [ $.1^2, $.1^128 ] ] [ [ $.1^2, $.1^130 ] ] [ [ $.1^2, $.1^139 ] ] [ [ $.1^2, $.1^151 ] ] [ [ $.1^2, $.1^163 ] ] [ [ $.1^2, $.1^180 ] ] [ [ $.1^2, $.1^184 ] ] [ [ $.1^2, $.1^191 ] ] [ [ $.1^2, $.1^201 ] ] [ [ $.1^2, $.1^204 ] ] [ [ $.1^2, $.1^211 ] ] [ [ $.1^2, $.1^212 ] ] [ [ $.1^2, $.1^214 ] ] [ [ $.1^2, $.1^217 ] ] [ [ $.1^2, $.1^226 ] ] [ [ $.1^2, $.1^234 ] ] [ [ $.1^2, $.1^245 ] ] [ [ $.1^2, $.1^246 ] ] [ [ $.1^2, $.1^251 ] ] [ [ $.1^2, $.1^260 ] ] [ [ $.1^2, $.1^262 ] ] [ [ $.1^2, $.1^270 ] ] [ [ $.1^2, $.1^273 ] ] [ [ $.1^2, $.1^289 ] ] [ [ $.1^2, $.1^309 ] ] [ [ $.1^2, $.1^311 ] ] [ [ $.1^2, $.1^313 ] ] [ [ $.1^2, $.1^329 ] ] [ [ $.1^3, $.1^4 ] ] [ [ $.1^3, $.1^24 ] ] [ [ $.1^3, $.1^26 ] ] [ [ $.1^3, $.1^28 ] ] [ [ $.1^3, $.1^44 ] ] [ [ $.1^3, $.1^62 ] ] [ [ $.1^3, $.1^69 ] ] [ [ $.1^3, $.1^88 ] ] [ [ $.1^3, $.1^92 ] ] [ [ $.1^3, $.1^96 ] ] [ [ $.1^3, $.1^104 ] ] [ [ $.1^3, 2 ] ] [ [ $.1^3, $.1^117 ] ] [ [ $.1^3, $.1^135 ] ] [ [ $.1^3, $.1^136 ] ] [ [ $.1^3, $.1^141 ] ] [ [ $.1^3, $.1^143 ] ] [ [ $.1^3, $.1^150 ] ] [ [ $.1^3, $.1^166 ] ] [ [ $.1^3, $.1^167 ] ] [ [ $.1^3, $.1^168 ] ] [ [ $.1^3, $.1^172 ] ] [ [ $.1^3, $.1^173 ] ] [ [ $.1^3, $.1^178 ] ] [ [ $.1^3, $.1^181 ] ] [ [ $.1^3, $.1^182 ] ] [ [ $.1^3, $.1^185 ] ] [ [ $.1^3, $.1^187 ] ] [ [ $.1^3, $.1^196 ] ] [ [ $.1^3, $.1^208 ] ] [ [ $.1^3, $.1^220 ] ] [ [ $.1^3, $.1^237 ] ] [ [ $.1^3, $.1^241 ] ] [ [ $.1^3, $.1^248 ] ] [ [ $.1^3, $.1^258 ] ] [ [ $.1^3, $.1^261 ] ] [ [ $.1^3, $.1^268 ] ] [ [ $.1^3, $.1^269 ] ] [ [ $.1^3, $.1^271 ] ] [ [ $.1^3, $.1^274 ] ] [ [ $.1^3, $.1^283 ] ] [ [ $.1^3, $.1^291 ] ] [ [ $.1^3, $.1^302 ] ] [ [ $.1^3, $.1^303 ] ] [ [ $.1^3, $.1^308 ] ] [ [ $.1^3, $.1^317 ] ] [ [ $.1^3, $.1^319 ] ] [ [ $.1^3, $.1^327 ] ] [ [ $.1^3, $.1^330 ] ] [ [ $.1^4, $.1^6 ] ] [ [ $.1^4, $.1^17 ] ] [ [ $.1^4, $.1^18 ] ] [ [ $.1^4, $.1^23 ] ] [ [ $.1^4, $.1^32 ] ] [ [ $.1^4, $.1^34 ] ] [ [ $.1^4, $.1^42 ] ] [ [ $.1^4, $.1^45 ] ] [ [ $.1^4, $.1^61 ] ] [ [ $.1^4, $.1^81 ] ] [ [ $.1^4, $.1^83 ] ] [ [ $.1^4, $.1^85 ] ] [ [ $.1^4, $.1^101 ] ] [ [ $.1^4, $.1^119 ] ] [ [ $.1^4, $.1^126 ] ] [ [ $.1^4, $.1^145 ] ] [ [ $.1^4, $.1^149 ] ] [ [ $.1^4, $.1^153 ] ] [ [ $.1^4, $.1^161 ] ] [ [ $.1^4, 6 ] ] [ [ $.1^4, $.1^174 ] ] [ [ $.1^4, $.1^192 ] ] [ [ $.1^4, $.1^193 ] ] [ [ $.1^4, $.1^198 ] ] [ [ $.1^4, $.1^200 ] ] [ [ $.1^4, $.1^207 ] ] [ [ $.1^4, $.1^223 ] ] [ [ $.1^4, $.1^224 ] ] [ [ $.1^4, $.1^225 ] ] [ [ $.1^4, $.1^229 ] ] [ [ $.1^4, $.1^230 ] ] [ [ $.1^4, $.1^235 ] ] [ [ $.1^4, $.1^238 ] ] [ [ $.1^4, $.1^239 ] ] [ [ $.1^4, $.1^242 ] ] [ [ $.1^4, $.1^244 ] ] [ [ $.1^4, $.1^253 ] ] [ [ $.1^4, $.1^265 ] ] [ [ $.1^4, $.1^277 ] ] [ [ $.1^4, $.1^294 ] ] [ [ $.1^4, $.1^298 ] ] [ [ $.1^4, $.1^305 ] ] [ [ $.1^4, $.1^315 ] ] [ [ $.1^4, $.1^318 ] ] [ [ $.1^4, $.1^325 ] ] [ [ $.1^4, $.1^326 ] ] [ [ $.1^4, $.1^328 ] ] [ [ $.1^4, $.1^331 ] ] [ [ $.1^4, $.1^340 ] ] [ [ $.1^5, $.1^9 ] ] [ [ $.1^5, $.1^13 ] ] [ [ $.1^5, $.1^20 ] ] [ [ $.1^5, $.1^30 ] ] [ [ $.1^5, $.1^33 ] ] [ [ $.1^5, $.1^40 ] ] [ [ $.1^5, $.1^41 ] ] [ [ $.1^5, $.1^43 ] ] [ [ $.1^5, $.1^46 ] ] [ [ $.1^5, $.1^55 ] ] [ [ $.1^5, $.1^63 ] ] [ [ $.1^5, $.1^74 ] ] [ [ $.1^5, $.1^75 ] ] [ [ $.1^5, $.1^80 ] ] [ [ $.1^5, $.1^89 ] ] [ [ $.1^5, $.1^91 ] ] [ [ $.1^5, $.1^99 ] ] [ [ $.1^5, $.1^102 ] ] [ [ $.1^5, $.1^118 ] ] [ [ $.1^5, $.1^138 ] ] [ [ $.1^5, $.1^140 ] ] [ [ $.1^5, $.1^142 ] ] [ [ $.1^5, $.1^158 ] ] [ [ $.1^5, $.1^176 ] ] [ [ $.1^5, $.1^183 ] ] [ [ $.1^5, $.1^202 ] ] [ [ $.1^5, $.1^206 ] ] [ [ $.1^5, $.1^210 ] ] [ [ $.1^5, $.1^218 ] ] [ [ $.1^5, 4 ] ] [ [ $.1^5, $.1^231 ] ] [ [ $.1^5, $.1^249 ] ] [ [ $.1^5, $.1^250 ] ] [ [ $.1^5, $.1^255 ] ] [ [ $.1^5, $.1^257 ] ] [ [ $.1^5, $.1^264 ] ] [ [ $.1^5, $.1^280 ] ] [ [ $.1^5, $.1^281 ] ] [ [ $.1^5, $.1^282 ] ] [ [ $.1^5, $.1^286 ] ] [ [ $.1^5, $.1^287 ] ] [ [ $.1^5, $.1^292 ] ] [ [ $.1^5, $.1^295 ] ] [ [ $.1^5, $.1^296 ] ] [ [ $.1^5, $.1^299 ] ] [ [ $.1^5, $.1^301 ] ] [ [ $.1^5, $.1^310 ] ] [ [ $.1^5, $.1^322 ] ] [ [ $.1^5, $.1^334 ] ] [ [ $.1^6, $.1 ] ] [ [ $.1^6, $.1^2 ] ] [ [ $.1^6, $.1^7 ] ] [ [ $.1^6, $.1^10 ] ] [ [ $.1^6, $.1^11 ] ] [ [ $.1^6, $.1^14 ] ] [ [ $.1^6, $.1^16 ] ] [ [ $.1^6, $.1^25 ] ] [ [ $.1^6, $.1^37 ] ] [ [ $.1^6, $.1^49 ] ] [ [ $.1^6, $.1^66 ] ] [ [ $.1^6, $.1^70 ] ] [ [ $.1^6, $.1^77 ] ] [ [ $.1^6, $.1^87 ] ] [ [ $.1^6, $.1^90 ] ] [ [ $.1^6, $.1^97 ] ] [ [ $.1^6, $.1^98 ] ] [ [ $.1^6, $.1^100 ] ] [ [ $.1^6, $.1^103 ] ] [ [ $.1^6, $.1^112 ] ] [ [ $.1^6, $.1^120 ] ] [ [ $.1^6, $.1^131 ] ] [ [ $.1^6, $.1^132 ] ] [ [ $.1^6, $.1^137 ] ] [ [ $.1^6, $.1^146 ] ] [ [ $.1^6, $.1^148 ] ] [ [ $.1^6, $.1^156 ] ] [ [ $.1^6, $.1^159 ] ] [ [ $.1^6, $.1^175 ] ] [ [ $.1^6, $.1^195 ] ] [ [ $.1^6, $.1^197 ] ] [ [ $.1^6, $.1^199 ] ] [ [ $.1^6, $.1^215 ] ] [ [ $.1^6, $.1^233 ] ] [ [ $.1^6, $.1^240 ] ] [ [ $.1^6, $.1^259 ] ] [ [ $.1^6, $.1^263 ] ] [ [ $.1^6, $.1^267 ] ] [ [ $.1^6, $.1^275 ] ] [ [ $.1^6, 5 ] ] [ [ $.1^6, $.1^288 ] ] [ [ $.1^6, $.1^306 ] ] [ [ $.1^6, $.1^307 ] ] [ [ $.1^6, $.1^312 ] ] [ [ $.1^6, $.1^314 ] ] [ [ $.1^6, $.1^321 ] ] [ [ $.1^6, $.1^337 ] ] [ [ $.1^6, $.1^338 ] ] [ [ $.1^6, $.1^339 ] ] [ [ $.1^7, 1 ] ] [ [ $.1^7, $.1^3 ] ] [ [ $.1^7, $.1^21 ] ] [ [ $.1^7, $.1^22 ] ] [ [ $.1^7, $.1^27 ] ] [ [ $.1^7, $.1^29 ] ] [ [ $.1^7, $.1^36 ] ] [ [ $.1^7, $.1^52 ] ] [ [ $.1^7, $.1^53 ] ] [ [ $.1^7, $.1^54 ] ] [ [ $.1^7, $.1^58 ] ] [ [ $.1^7, $.1^59 ] ] [ [ $.1^7, $.1^64 ] ] [ [ $.1^7, $.1^67 ] ] [ [ $.1^7, $.1^68 ] ] [ [ $.1^7, $.1^71 ] ] [ [ $.1^7, $.1^73 ] ] [ [ $.1^7, $.1^82 ] ] [ [ $.1^7, $.1^94 ] ] [ [ $.1^7, $.1^106 ] ] [ [ $.1^7, $.1^123 ] ] [ [ $.1^7, $.1^127 ] ] [ [ $.1^7, $.1^134 ] ] [ [ $.1^7, $.1^144 ] ] [ [ $.1^7, $.1^147 ] ] [ [ $.1^7, $.1^154 ] ] [ [ $.1^7, $.1^155 ] ] [ [ $.1^7, $.1^157 ] ] [ [ $.1^7, $.1^160 ] ] [ [ $.1^7, $.1^169 ] ] [ [ $.1^7, $.1^177 ] ] [ [ $.1^7, $.1^188 ] ] [ [ $.1^7, $.1^189 ] ] [ [ $.1^7, $.1^194 ] ] [ [ $.1^7, $.1^203 ] ] [ [ $.1^7, $.1^205 ] ] [ [ $.1^7, $.1^213 ] ] [ [ $.1^7, $.1^216 ] ] [ [ $.1^7, $.1^232 ] ] [ [ $.1^7, $.1^252 ] ] [ [ $.1^7, $.1^25 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 11:25:08 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; spolav:= [k : k in polavqr(3,1) | k[1] in GF(3) and k[2] in GF(3) ]; #spolav; Output: Magma V2.10-6 Fri Mar 12 2004 11:25:05 on modular [Seed = 2070601492] ------------------------------------- [ [ 0, 0 ] ] [ [ 1, 1 ] ] [ [ 2, 2 ] ] 0 Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 11:26:06 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; spolav:= [k : k in polavqr(3,1) ]; #spolav; Output: Magma V2.10-6 Fri Mar 12 2004 11:26:03 on modular [Seed = 1885459685] ------------------------------------- [ [ 0, 0 ] ] [ [ 1, 1 ] ] [ [ 2, 2 ] ] 0 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 200-BAR2-X4.libre.retevision.es. (62.82.186.200) Time: Fri Mar 12 11:26:16 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; spolav:= [k : k in polavqr(3,1) | k[1] in GF(3) and k[2] in GF(3) ]; #spolav; Output: Magma V2.10-6 Fri Mar 12 2004 11:26:13 on modular [Seed = 2308451618] ------------------------------------- [ [ 0, 0 ] ] [ [ 1, 1 ] ] [ [ 2, 2 ] ] 0 Total time: 3.049 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 11:26:22 2004 Input: R := GF(4); M := MatrixRing(R,2); Mt := {A : A in M | Trace(A) eq 0}; Mf := {A : A in M | A[1] eq A[2]}; Mtf := Mt meet Mf; rand := [Random(M): num in [1..100000]]; #([A: A in rand | A in Mt]); Output: Magma V2.10-6 Fri Mar 12 2004 11:26:18 on modular [Seed = 2660186682] ------------------------------------- 24759 Total time: 3.709 seconds, Total memory usage: 6.95MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 11:27:34 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; spolav:= {k : k in polavqr(3,1)| k[1] in GF(3) and k[2] in GF(3) }; #spolav; Output: Magma V2.10-6 Fri Mar 12 2004 11:27:31 on modular [Seed = 2542154602] ------------------------------------- [ [ 0, 0 ] ] [ [ 1, 1 ] ] [ [ 2, 2 ] ] 0 Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 11:27:52 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; spolav:= {k : k in polavqr(3,1)| k[1] in GF(3) and k[2] in GF(3) }; #spolav; Output: Magma V2.10-6 Fri Mar 12 2004 11:27:49 on modular [Seed = 2914781350] ------------------------------------- [ [ 0, 0 ] ] [ [ 1, 1 ] ] [ [ 2, 2 ] ] 0 Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 11:28:15 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; spolav:= [k : k in polavqr(3,1)| k[1] in GF(3) and k[2] in GF(3)]; spolav; Output: Magma V2.10-6 Fri Mar 12 2004 11:28:12 on modular [Seed = 2729641904] ------------------------------------- [ [ 0, 0 ] ] [ [ 1, 1 ] ] [ [ 2, 2 ] ] [] Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 11:29:49 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; spolav:= [k : k in polavqr(3,1)| k[1] in GF(3) and k[2] in GF(3)]; spolav; l:=[1,2,3]; l[1]; Output: Magma V2.10-6 Fri Mar 12 2004 11:29:46 on modular [Seed = 3098090956] ------------------------------------- [ [ 0, 0 ] ] [ [ 1, 1 ] ] [ [ 2, 2 ] ] [] 1 Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 11:30:14 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; spolav:= [k : k in polavqr(4,2)| k[1] in GF(4) and k[2] in GF(4)]; spolav; l:=[1,2,3]; l[1]; Output: Magma V2.10-6 Fri Mar 12 2004 11:30:11 on modular [Seed = 3369692501] ------------------------------------- [ [ 1, $.1 ] ] [ [ 1, $.1^2 ] ] [ [ 1, $.1^4 ] ] [ [ 1, $.1^8 ] ] [ [ $.1, $.1^6 ] ] [ [ $.1, $.1^7 ] ] [ [ $.1, $.1^9 ] ] [ [ $.1, $.1^13 ] ] [ [ $.1^2, $.1^3 ] ] [ [ $.1^2, $.1^11 ] ] [ [ $.1^2, $.1^12 ] ] [ [ $.1^2, $.1^14 ] ] [ [ $.1^3, $.1 ] ] [ [ $.1^3, $.1^2 ] ] [ [ $.1^3, $.1^4 ] ] [ [ $.1^3, $.1^8 ] ] [ [ $.1^4, $.1^6 ] ] [ [ $.1^4, $.1^7 ] ] [ [ $.1^4, $.1^9 ] ] [ [ $.1^4, $.1^13 ] ] [ [ $.1^5, $.1^3 ] ] [ [ $.1^5, $.1^11 ] ] [ [ $.1^5, $.1^12 ] ] [ [ $.1^5, $.1^14 ] ] [ [ $.1^6, $.1 ] ] [ [ $.1^6, $.1^2 ] ] [ [ $.1^6, $.1^4 ] ] [ [ $.1^6, $.1^8 ] ] [ [ $.1^7, $.1^6 ] ] [ [ $.1^7, $.1^7 ] ] [ [ $.1^7, $.1^9 ] ] [ [ $.1^7, $.1^13 ] ] [ [ $.1^8, $.1^3 ] ] [ [ $.1^8, $.1^11 ] ] [ [ $.1^8, $.1^12 ] ] [ [ $.1^8, $.1^14 ] ] [ [ $.1^9, $.1 ] ] [ [ $.1^9, $.1^2 ] ] [ [ $.1^9, $.1^4 ] ] [ [ $.1^9, $.1^8 ] ] [ [ $.1^10, $.1^6 ] ] [ [ $.1^10, $.1^7 ] ] [ [ $.1^10, $.1^9 ] ] [ [ $.1^10, $.1^13 ] ] [ [ $.1^11, $.1^3 ] ] [ [ $.1^11, $.1^11 ] ] [ [ $.1^11, $.1^12 ] ] [ [ $.1^11, $.1^14 ] ] [ [ $.1^12, $.1 ] ] [ [ $.1^12, $.1^2 ] ] [ [ $.1^12, $.1^4 ] ] [ [ $.1^12, $.1^8 ] ] [ [ $.1^13, $.1^6 ] ] [ [ $.1^13, $.1^7 ] ] [ [ $.1^13, $.1^9 ] ] [ [ $.1^13, $.1^13 ] ] [ [ $.1^14, $.1^3 ] ] [ [ $.1^14, $.1^11 ] ] [ [ $.1^14, $.1^12 ] ] [ [ $.1^14, $.1^14 ] ] [ [ 0, 1 ] ] [ [ 0, $.1^5 ] ] [ [ 0, $.1^10 ] ] [ [ 0, 0 ] ] [] 1 Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 11:31:06 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; spolav:= [k : k in polavqr(4,2)| k[1] in GF(4) and k[2] in GF(4)]; #spolav; Output: Magma V2.10-6 Fri Mar 12 2004 11:31:03 on modular [Seed = 3738139415] ------------------------------------- [ [ 1, $.1 ] ] [ [ 1, $.1^2 ] ] [ [ 1, $.1^4 ] ] [ [ 1, $.1^8 ] ] [ [ $.1, $.1^6 ] ] [ [ $.1, $.1^7 ] ] [ [ $.1, $.1^9 ] ] [ [ $.1, $.1^13 ] ] [ [ $.1^2, $.1^3 ] ] [ [ $.1^2, $.1^11 ] ] [ [ $.1^2, $.1^12 ] ] [ [ $.1^2, $.1^14 ] ] [ [ $.1^3, $.1 ] ] [ [ $.1^3, $.1^2 ] ] [ [ $.1^3, $.1^4 ] ] [ [ $.1^3, $.1^8 ] ] [ [ $.1^4, $.1^6 ] ] [ [ $.1^4, $.1^7 ] ] [ [ $.1^4, $.1^9 ] ] [ [ $.1^4, $.1^13 ] ] [ [ $.1^5, $.1^3 ] ] [ [ $.1^5, $.1^11 ] ] [ [ $.1^5, $.1^12 ] ] [ [ $.1^5, $.1^14 ] ] [ [ $.1^6, $.1 ] ] [ [ $.1^6, $.1^2 ] ] [ [ $.1^6, $.1^4 ] ] [ [ $.1^6, $.1^8 ] ] [ [ $.1^7, $.1^6 ] ] [ [ $.1^7, $.1^7 ] ] [ [ $.1^7, $.1^9 ] ] [ [ $.1^7, $.1^13 ] ] [ [ $.1^8, $.1^3 ] ] [ [ $.1^8, $.1^11 ] ] [ [ $.1^8, $.1^12 ] ] [ [ $.1^8, $.1^14 ] ] [ [ $.1^9, $.1 ] ] [ [ $.1^9, $.1^2 ] ] [ [ $.1^9, $.1^4 ] ] [ [ $.1^9, $.1^8 ] ] [ [ $.1^10, $.1^6 ] ] [ [ $.1^10, $.1^7 ] ] [ [ $.1^10, $.1^9 ] ] [ [ $.1^10, $.1^13 ] ] [ [ $.1^11, $.1^3 ] ] [ [ $.1^11, $.1^11 ] ] [ [ $.1^11, $.1^12 ] ] [ [ $.1^11, $.1^14 ] ] [ [ $.1^12, $.1 ] ] [ [ $.1^12, $.1^2 ] ] [ [ $.1^12, $.1^4 ] ] [ [ $.1^12, $.1^8 ] ] [ [ $.1^13, $.1^6 ] ] [ [ $.1^13, $.1^7 ] ] [ [ $.1^13, $.1^9 ] ] [ [ $.1^13, $.1^13 ] ] [ [ $.1^14, $.1^3 ] ] [ [ $.1^14, $.1^11 ] ] [ [ $.1^14, $.1^12 ] ] [ [ $.1^14, $.1^14 ] ] [ [ 0, 1 ] ] [ [ 0, $.1^5 ] ] [ [ 0, $.1^10 ] ] [ [ 0, 0 ] ] 0 Total time: 3.069 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 11:31:20 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; spolav:= [k : k in polavqr(4,3)| k[1] in GF(4) and k[2] in GF(4)]; #spolav; Output: Magma V2.10-6 Fri Mar 12 2004 11:31:16 on modular [Seed = 3620106765] ------------------------------------- [ [ 1, 1 ] ] [ [ 1, $.1 ] ] [ [ 1, $.1^2 ] ] [ [ 1, $.1^4 ] ] [ [ 1, $.1^5 ] ] [ [ 1, $.1^8 ] ] [ [ 1, $.1^10 ] ] [ [ 1, $.1^16 ] ] [ [ 1, $.1^17 ] ] [ [ 1, $.1^20 ] ] [ [ 1, $.1^27 ] ] [ [ 1, $.1^32 ] ] [ [ 1, $.1^34 ] ] [ [ 1, $.1^40 ] ] [ [ 1, $.1^45 ] ] [ [ 1, $.1^54 ] ] [ [ $.1, $.1^3 ] ] [ [ $.1, $.1^12 ] ] [ [ $.1, $.1^21 ] ] [ [ $.1, $.1^22 ] ] [ [ $.1, $.1^23 ] ] [ [ $.1, $.1^25 ] ] [ [ $.1, $.1^26 ] ] [ [ $.1, $.1^29 ] ] [ [ $.1, $.1^31 ] ] [ [ $.1, $.1^37 ] ] [ [ $.1, $.1^38 ] ] [ [ $.1, $.1^41 ] ] [ [ $.1, $.1^48 ] ] [ [ $.1, $.1^53 ] ] [ [ $.1, $.1^55 ] ] [ [ $.1, $.1^61 ] ] [ [ $.1^2, $.1^6 ] ] [ [ $.1^2, $.1^11 ] ] [ [ $.1^2, $.1^13 ] ] [ [ $.1^2, $.1^19 ] ] [ [ $.1^2, $.1^24 ] ] [ [ $.1^2, $.1^33 ] ] [ [ $.1^2, $.1^42 ] ] [ [ $.1^2, $.1^43 ] ] [ [ $.1^2, $.1^44 ] ] [ [ $.1^2, $.1^46 ] ] [ [ $.1^2, $.1^47 ] ] [ [ $.1^2, $.1^50 ] ] [ [ $.1^2, $.1^52 ] ] [ [ $.1^2, $.1^58 ] ] [ [ $.1^2, $.1^59 ] ] [ [ $.1^2, $.1^62 ] ] [ [ $.1^3, 1 ] ] [ [ $.1^3, $.1 ] ] [ [ $.1^3, $.1^2 ] ] [ [ $.1^3, $.1^4 ] ] [ [ $.1^3, $.1^5 ] ] [ [ $.1^3, $.1^8 ] ] [ [ $.1^3, $.1^10 ] ] [ [ $.1^3, $.1^16 ] ] [ [ $.1^3, $.1^17 ] ] [ [ $.1^3, $.1^20 ] ] [ [ $.1^3, $.1^27 ] ] [ [ $.1^3, $.1^32 ] ] [ [ $.1^3, $.1^34 ] ] [ [ $.1^3, $.1^40 ] ] [ [ $.1^3, $.1^45 ] ] [ [ $.1^3, $.1^54 ] ] [ [ $.1^4, $.1^3 ] ] [ [ $.1^4, $.1^12 ] ] [ [ $.1^4, $.1^21 ] ] [ [ $.1^4, $.1^22 ] ] [ [ $.1^4, $.1^23 ] ] [ [ $.1^4, $.1^25 ] ] [ [ $.1^4, $.1^26 ] ] [ [ $.1^4, $.1^29 ] ] [ [ $.1^4, $.1^31 ] ] [ [ $.1^4, $.1^37 ] ] [ [ $.1^4, $.1^38 ] ] [ [ $.1^4, $.1^41 ] ] [ [ $.1^4, $.1^48 ] ] [ [ $.1^4, $.1^53 ] ] [ [ $.1^4, $.1^55 ] ] [ [ $.1^4, $.1^61 ] ] [ [ $.1^5, $.1^6 ] ] [ [ $.1^5, $.1^11 ] ] [ [ $.1^5, $.1^13 ] ] [ [ $.1^5, $.1^19 ] ] [ [ $.1^5, $.1^24 ] ] [ [ $.1^5, $.1^33 ] ] [ [ $.1^5, $.1^42 ] ] [ [ $.1^5, $.1^43 ] ] [ [ $.1^5, $.1^44 ] ] [ [ $.1^5, $.1^46 ] ] [ [ $.1^5, $.1^47 ] ] [ [ $.1^5, $.1^50 ] ] [ [ $.1^5, $.1^52 ] ] [ [ $.1^5, $.1^58 ] ] [ [ $.1^5, $.1^59 ] ] [ [ $.1^5, $.1^62 ] ] [ [ $.1^6, 1 ] ] [ [ $.1^6, $.1 ] ] [ [ $.1^6, $.1^2 ] ] [ [ $.1^6, $.1^4 ] ] [ [ $.1^6, $.1^5 ] ] [ [ $.1^6, $.1^8 ] ] [ [ $.1^6, $.1^10 ] ] [ [ $.1^6, $.1^16 ] ] [ [ $.1^6, $.1^17 ] ] [ [ $.1^6, $.1^20 ] ] [ [ $.1^6, $.1^27 ] ] [ [ $.1^6, $.1^32 ] ] [ [ $.1^6, $.1^34 ] ] [ [ $.1^6, $.1^40 ] ] [ [ $.1^6, $.1^45 ] ] [ [ $.1^6, $.1^54 ] ] [ [ $.1^7, $.1^3 ] ] [ [ $.1^7, $.1^12 ] ] [ [ $.1^7, $.1^21 ] ] [ [ $.1^7, $.1^22 ] ] [ [ $.1^7, $.1^23 ] ] [ [ $.1^7, $.1^25 ] ] [ [ $.1^7, $.1^26 ] ] [ [ $.1^7, $.1^29 ] ] [ [ $.1^7, $.1^31 ] ] [ [ $.1^7, $.1^37 ] ] [ [ $.1^7, $.1^38 ] ] [ [ $.1^7, $.1^41 ] ] [ [ $.1^7, $.1^48 ] ] [ [ $.1^7, $.1^53 ] ] [ [ $.1^7, $.1^55 ] ] [ [ $.1^7, $.1^61 ] ] [ [ $.1^8, $.1^6 ] ] [ [ $.1^8, $.1^11 ] ] [ [ $.1^8, $.1^13 ] ] [ [ $.1^8, $.1^19 ] ] [ [ $.1^8, $.1^24 ] ] [ [ $.1^8, $.1^33 ] ] [ [ $.1^8, $.1^42 ] ] [ [ $.1^8, $.1^43 ] ] [ [ $.1^8, $.1^44 ] ] [ [ $.1^8, $.1^46 ] ] [ [ $.1^8, $.1^47 ] ] [ [ $.1^8, $.1^50 ] ] [ [ $.1^8, $.1^52 ] ] [ [ $.1^8, $.1^58 ] ] [ [ $.1^8, $.1^59 ] ] [ [ $.1^8, $.1^62 ] ] [ [ $.1^9, 1 ] ] [ [ $.1^9, $.1 ] ] [ [ $.1^9, $.1^2 ] ] [ [ $.1^9, $.1^4 ] ] [ [ $.1^9, $.1^5 ] ] [ [ $.1^9, $.1^8 ] ] [ [ $.1^9, $.1^10 ] ] [ [ $.1^9, $.1^16 ] ] [ [ $.1^9, $.1^17 ] ] [ [ $.1^9, $.1^20 ] ] [ [ $.1^9, $.1^27 ] ] [ [ $.1^9, $.1^32 ] ] [ [ $.1^9, $.1^34 ] ] [ [ $.1^9, $.1^40 ] ] [ [ $.1^9, $.1^45 ] ] [ [ $.1^9, $.1^54 ] ] [ [ $.1^10, $.1^3 ] ] [ [ $.1^10, $.1^12 ] ] [ [ $.1^10, $.1^21 ] ] [ [ $.1^10, $.1^22 ] ] [ [ $.1^10, $.1^23 ] ] [ [ $.1^10, $.1^25 ] ] [ [ $.1^10, $.1^26 ] ] [ [ $.1^10, $.1^29 ] ] [ [ $.1^10, $.1^31 ] ] [ [ $.1^10, $.1^37 ] ] [ [ $.1^10, $.1^38 ] ] [ [ $.1^10, $.1^41 ] ] [ [ $.1^10, $.1^48 ] ] [ [ $.1^10, $.1^53 ] ] [ [ $.1^10, $.1^55 ] ] [ [ $.1^10, $.1^61 ] ] [ [ $.1^11, $.1^6 ] ] [ [ $.1^11, $.1^11 ] ] [ [ $.1^11, $.1^13 ] ] [ [ $.1^11, $.1^19 ] ] [ [ $.1^11, $.1^24 ] ] [ [ $.1^11, $.1^33 ] ] [ [ $.1^11, $.1^42 ] ] [ [ $.1^11, $.1^43 ] ] [ [ $.1^11, $.1^44 ] ] [ [ $.1^11, $.1^46 ] ] [ [ $.1^11, $.1^47 ] ] [ [ $.1^11, $.1^50 ] ] [ [ $.1^11, $.1^52 ] ] [ [ $.1^11, $.1^58 ] ] [ [ $.1^11, $.1^59 ] ] [ [ $.1^11, $.1^62 ] ] [ [ $.1^12, 1 ] ] [ [ $.1^12, $.1 ] ] [ [ $.1^12, $.1^2 ] ] [ [ $.1^12, $.1^4 ] ] [ [ $.1^12, $.1^5 ] ] [ [ $.1^12, $.1^8 ] ] [ [ $.1^12, $.1^10 ] ] [ [ $.1^12, $.1^16 ] ] [ [ $.1^12, $.1^17 ] ] [ [ $.1^12, $.1^20 ] ] [ [ $.1^12, $.1^27 ] ] [ [ $.1^12, $.1^32 ] ] [ [ $.1^12, $.1^34 ] ] [ [ $.1^12, $.1^40 ] ] [ [ $.1^12, $.1^45 ] ] [ [ $.1^12, $.1^54 ] ] [ [ $.1^13, $.1^3 ] ] [ [ $.1^13, $.1^12 ] ] [ [ $.1^13, $.1^21 ] ] [ [ $.1^13, $.1^22 ] ] [ [ $.1^13, $.1^23 ] ] [ [ $.1^13, $.1^25 ] ] [ [ $.1^13, $.1^26 ] ] [ [ $.1^13, $.1^29 ] ] [ [ $.1^13, $.1^31 ] ] [ [ $.1^13, $.1^37 ] ] [ [ $.1^13, $.1^38 ] ] [ [ $.1^13, $.1^41 ] ] [ [ $.1^13, $.1^48 ] ] [ [ $.1^13, $.1^53 ] ] [ [ $.1^13, $.1^55 ] ] [ [ $.1^13, $.1^61 ] ] [ [ $.1^14, $.1^6 ] ] [ [ $.1^14, $.1^11 ] ] [ [ $.1^14, $.1^13 ] ] [ [ $.1^14, $.1^19 ] ] [ [ $.1^14, $.1^24 ] ] [ [ $.1^14, $.1^33 ] ] [ [ $.1^14, $.1^42 ] ] [ [ $.1^14, $.1^43 ] ] [ [ $.1^14, $.1^44 ] ] [ [ $.1^14, $.1^46 ] ] [ [ $.1^14, $.1^47 ] ] [ [ $.1^14, $.1^50 ] ] [ [ $.1^14, $.1^52 ] ] [ [ $.1^14, $.1^58 ] ] [ [ $.1^14, $.1^59 ] ] [ [ $.1^14, $.1^62 ] ] [ [ $.1^15, 1 ] ] [ [ $.1^15, $.1 ] ] [ [ $.1^15, $.1^2 ] ] [ [ $.1^15, $.1^4 ] ] [ [ $.1^15, $.1^5 ] ] [ [ $.1^15, $.1^8 ] ] [ [ $.1^15, $.1^10 ] ] [ [ $.1^15, $.1^16 ] ] [ [ $.1^15, $.1^17 ] ] [ [ $.1^15, $.1^20 ] ] [ [ $.1^15, $.1^27 ] ] [ [ $.1^15, $.1^32 ] ] [ [ $.1^15, $.1^34 ] ] [ [ $.1^15, $.1^40 ] ] [ [ $.1^15, $.1^45 ] ] [ [ $.1^15, $.1^54 ] ] [ [ $.1^16, $.1^3 ] ] [ [ $.1^16, $.1^12 ] ] [ [ $.1^16, $.1^21 ] ] [ [ $.1^16, $.1^22 ] ] [ [ $.1^16, $.1^23 ] ] [ [ $.1^16, $.1^25 ] ] [ [ $.1^16, $.1^26 ] ] [ [ $.1^16, $.1^29 ] ] [ [ $.1^16, $.1^31 ] ] [ [ $.1^16, $.1^37 ] ] [ [ $.1^16, $.1^38 ] ] [ [ $.1^16, $.1^41 ] ] [ [ $.1^16, $.1^48 ] ] [ [ $.1^16, $.1^53 ] ] [ [ $.1^16, $.1^55 ] ] [ [ $.1^16, $.1^61 ] ] [ [ $.1^17, $.1^6 ] ] [ [ $.1^17, $.1^11 ] ] [ [ $.1^17, $.1^13 ] ] [ [ $.1^17, $.1^19 ] ] [ [ $.1^17, $.1^24 ] ] [ [ $.1^17, $.1^33 ] ] [ [ $.1^17, $.1^42 ] ] [ [ $.1^17, $.1^43 ] ] [ [ $.1^17, $.1^44 ] ] [ [ $.1^17, $.1^46 ] ] [ [ $.1^17, $.1^47 ] ] [ [ $.1^17, $.1^50 ] ] [ [ $.1^17, $.1^52 ] ] [ [ $.1^17, $.1^58 ] ] [ [ $.1^17, $.1^59 ] ] [ [ $.1^17, $.1^62 ] ] [ [ $.1^18, 1 ] ] [ [ $.1^18, $.1 ] ] [ [ $.1^18, $.1^2 ] ] [ [ $.1^18, $.1^4 ] ] [ [ $.1^18, $.1^5 ] ] [ [ $.1^18, $.1^8 ] ] [ [ $.1^18, $.1^10 ] ] [ [ $.1^18, $.1^16 ] ] [ [ $.1^18, $.1^17 ] ] [ [ $.1^18, $.1^20 ] ] [ [ $.1^18, $.1^27 ] ] [ [ $.1^18, $.1^32 ] ] [ [ $.1^18, $.1^34 ] ] [ [ $.1^18, $.1^40 ] ] [ [ $.1^18, $.1^45 ] ] [ [ $.1^18, $.1^54 ] ] [ [ $.1^19, $.1^3 ] ] [ [ $.1^19, $.1^12 ] ] [ [ $.1^19, $.1^21 ] ] [ [ $.1^19, $.1^22 ] ] [ [ $.1^19, $.1^23 ] ] [ [ $.1^19, $.1^25 ] ] [ [ $.1^19, $.1^26 ] ] [ [ $.1^19, $.1^29 ] ] [ [ $.1^19, $.1^31 ] ] [ [ $.1^19, $.1^37 ] ] [ [ $.1^19, $.1^38 ] ] [ [ $.1^19, $.1^41 ] ] [ [ $.1^19, $.1^48 ] ] [ [ $.1^19, $.1^53 ] ] [ [ $.1^19, $.1^55 ] ] [ [ $.1^19, $.1^61 ] ] [ [ $.1^20, $.1^6 ] ] [ [ $.1^20, $.1^11 ] ] [ [ $.1^20, $.1^13 ] ] [ [ $.1^20, $.1^19 ] ] [ [ $.1^20, $.1^24 ] ] [ [ $.1^20, $.1^33 ] ] [ [ $.1^20, $.1^42 ] ] [ [ $.1^20, $.1^43 ] ] [ [ $.1^20, $.1^44 ] ] [ [ $.1^20, $.1^46 ] ] [ [ $.1^20, $.1^47 ] ] [ [ $.1^20, $.1^50 ] ] [ [ $.1^20, $.1^52 ] ] [ [ $.1^20, $.1^58 ] ] [ [ $.1^20, $.1^59 ] ] [ [ $.1^20, $.1^62 ] ] [ [ $.1^21, 1 ] ] [ [ $.1^21, $.1 ] ] [ [ $.1^21, $.1^2 ] ] [ [ $.1^21, $.1^4 ] ] [ [ $.1^21, $.1^5 ] ] [ [ $.1^21, $.1^8 ] ] [ [ $.1^21, $.1^10 ] ] [ [ $.1^21, $.1^16 ] ] [ [ $.1^21, $.1^17 ] ] [ [ $.1^21, $.1^20 ] ] [ [ $.1^21, $.1^27 ] ] [ [ $.1^21, $.1^32 ] ] [ [ $.1^21, $.1^34 ] ] [ [ $.1^21, $.1^40 ] ] [ [ $.1^21, $.1^45 ] ] [ [ $.1^21, $.1^54 ] ] [ [ $.1^22, $.1^3 ] ] [ [ $.1^22, $.1^12 ] ] [ [ $.1^22, $.1^21 ] ] [ [ $.1^22, $.1^22 ] ] [ [ $.1^22, $.1^23 ] ] [ [ $.1^22, $.1^25 ] ] [ [ $.1^22, $.1^26 ] ] [ [ $.1^22, $.1^29 ] ] [ [ $.1^22, $.1^31 ] ] [ [ $.1^22, $.1^37 ] ] [ [ $.1^22, $.1^38 ] ] [ [ $.1^22, $.1^41 ] ] [ [ $.1^22, $.1^48 ] ] [ [ $.1^22, $.1^53 ] ] [ [ $.1^22, $.1^55 ] ] [ [ $.1^22, $.1^61 ] ] [ [ $.1^23, $.1^6 ] ] [ [ $.1^23, $.1^11 ] ] [ [ $.1^23, $.1^13 ] ] [ [ $.1^23, $.1^19 ] ] [ [ $.1^23, $.1^24 ] ] [ [ $.1^23, $.1^33 ] ] [ [ $.1^23, $.1^42 ] ] [ [ $.1^23, $.1^43 ] ] [ [ $.1^23, $.1^44 ] ] [ [ $.1^23, $.1^46 ] ] [ [ $.1^23, $.1^47 ] ] [ [ $.1^23, $. ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 11:31:34 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; spolav:= [k : k in polavqr(4,1)| k[1] in GF(4) and k[2] in GF(4)]; #spolav; Output: Magma V2.10-6 Fri Mar 12 2004 11:31:31 on modular [Seed = 3976022273] ------------------------------------- [ [ 1, 1 ] ] [ [ $.1, $.1 ] ] [ [ $.1^2, $.1^2 ] ] [ [ 0, 0 ] ] 0 Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 11:32:11 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; spolav:= [k : k in polavqr(4,1)| (k[1] in GF(4)) and (k[2] in GF(4))]; #spolav; Output: Magma V2.10-6 Fri Mar 12 2004 11:32:08 on modular [Seed = 3857990627] ------------------------------------- [ [ 1, 1 ] ] [ [ $.1, $.1 ] ] [ [ $.1^2, $.1^2 ] ] [ [ 0, 0 ] ] 0 Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 200-BAR2-X4.libre.retevision.es. (62.82.186.200) Time: Fri Mar 12 11:32:18 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; spolav:= {k : k in polavqr(3,1) | k[1] in GF(3) and k[2] in GF(3) }; #spolav; Output: Magma V2.10-6 Fri Mar 12 2004 11:32:15 on modular [Seed = 4209728763] ------------------------------------- [ [ 0, 0 ] ] [ [ 1, 1 ] ] [ [ 2, 2 ] ] 0 Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 11:34:03 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; spolav:= [k : k in polavqr(4,1)]; #spolav; Output: Magma V2.10-6 Fri Mar 12 2004 11:34:00 on modular [Seed = 4041299590] ------------------------------------- [ [ 1, 1 ] ] [ [ $.1, $.1 ] ] [ [ $.1^2, $.1^2 ] ] [ [ 0, 0 ] ] 0 Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 11:34:45 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:={}; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; spolav:= [k : k in polavqr(4,1)]| k[1] in GF(4)) and (k[2] in GF(4)); #spolav; Output: Magma V2.10-6 Fri Mar 12 2004 11:34:42 on modular [Seed = 118923690] ------------------------------------- >> spolav:= [k : k in polavqr(4,1)]| k[1] in GF(4)) and (k[2] in GF(4)); ^ User error: bad syntax >> #spolav; ^ User error: Identifier 'spolav' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 200-BAR2-X4.libre.retevision.es. (62.82.186.200) Time: Fri Mar 12 11:34:58 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; spolav:= [k : k in polavqr(3,3) | k[1] in GF(3) and k[2] in GF(3)]; #spolav; Output: Magma V2.10-6 Fri Mar 12 2004 11:34:55 on modular [Seed = 504346814] ------------------------------------- [ [ 1, $.1^5 ] ] [ [ 1, $.1^8 ] ] [ [ 1, $.1^15 ] ] [ [ 1, $.1^17 ] ] [ [ 1, $.1^19 ] ] [ [ 1, $.1^20 ] ] [ [ 1, $.1^23 ] ] [ [ 1, $.1^24 ] ] [ [ 1, $.1^25 ] ] [ [ $.1, $.1^2 ] ] [ [ $.1, $.1^4 ] ] [ [ $.1, $.1^6 ] ] [ [ $.1, $.1^7 ] ] [ [ $.1, $.1^10 ] ] [ [ $.1, $.1^11 ] ] [ [ $.1, $.1^12 ] ] [ [ $.1, $.1^18 ] ] [ [ $.1, $.1^21 ] ] [ [ $.1^2, $.1^5 ] ] [ [ $.1^2, $.1^8 ] ] [ [ $.1^2, $.1^15 ] ] [ [ $.1^2, $.1^17 ] ] [ [ $.1^2, $.1^19 ] ] [ [ $.1^2, $.1^20 ] ] [ [ $.1^2, $.1^23 ] ] [ [ $.1^2, $.1^24 ] ] [ [ $.1^2, $.1^25 ] ] [ [ $.1^3, $.1^2 ] ] [ [ $.1^3, $.1^4 ] ] [ [ $.1^3, $.1^6 ] ] [ [ $.1^3, $.1^7 ] ] [ [ $.1^3, $.1^10 ] ] [ [ $.1^3, $.1^11 ] ] [ [ $.1^3, $.1^12 ] ] [ [ $.1^3, $.1^18 ] ] [ [ $.1^3, $.1^21 ] ] [ [ $.1^4, $.1^5 ] ] [ [ $.1^4, $.1^8 ] ] [ [ $.1^4, $.1^15 ] ] [ [ $.1^4, $.1^17 ] ] [ [ $.1^4, $.1^19 ] ] [ [ $.1^4, $.1^20 ] ] [ [ $.1^4, $.1^23 ] ] [ [ $.1^4, $.1^24 ] ] [ [ $.1^4, $.1^25 ] ] [ [ $.1^5, $.1^2 ] ] [ [ $.1^5, $.1^4 ] ] [ [ $.1^5, $.1^6 ] ] [ [ $.1^5, $.1^7 ] ] [ [ $.1^5, $.1^10 ] ] [ [ $.1^5, $.1^11 ] ] [ [ $.1^5, $.1^12 ] ] [ [ $.1^5, $.1^18 ] ] [ [ $.1^5, $.1^21 ] ] [ [ $.1^6, $.1^5 ] ] [ [ $.1^6, $.1^8 ] ] [ [ $.1^6, $.1^15 ] ] [ [ $.1^6, $.1^17 ] ] [ [ $.1^6, $.1^19 ] ] [ [ $.1^6, $.1^20 ] ] [ [ $.1^6, $.1^23 ] ] [ [ $.1^6, $.1^24 ] ] [ [ $.1^6, $.1^25 ] ] [ [ $.1^7, $.1^2 ] ] [ [ $.1^7, $.1^4 ] ] [ [ $.1^7, $.1^6 ] ] [ [ $.1^7, $.1^7 ] ] [ [ $.1^7, $.1^10 ] ] [ [ $.1^7, $.1^11 ] ] [ [ $.1^7, $.1^12 ] ] [ [ $.1^7, $.1^18 ] ] [ [ $.1^7, $.1^21 ] ] [ [ $.1^8, $.1^5 ] ] [ [ $.1^8, $.1^8 ] ] [ [ $.1^8, $.1^15 ] ] [ [ $.1^8, $.1^17 ] ] [ [ $.1^8, $.1^19 ] ] [ [ $.1^8, $.1^20 ] ] [ [ $.1^8, $.1^23 ] ] [ [ $.1^8, $.1^24 ] ] [ [ $.1^8, $.1^25 ] ] [ [ $.1^9, $.1^2 ] ] [ [ $.1^9, $.1^4 ] ] [ [ $.1^9, $.1^6 ] ] [ [ $.1^9, $.1^7 ] ] [ [ $.1^9, $.1^10 ] ] [ [ $.1^9, $.1^11 ] ] [ [ $.1^9, $.1^12 ] ] [ [ $.1^9, $.1^18 ] ] [ [ $.1^9, $.1^21 ] ] [ [ $.1^10, $.1^5 ] ] [ [ $.1^10, $.1^8 ] ] [ [ $.1^10, $.1^15 ] ] [ [ $.1^10, $.1^17 ] ] [ [ $.1^10, $.1^19 ] ] [ [ $.1^10, $.1^20 ] ] [ [ $.1^10, $.1^23 ] ] [ [ $.1^10, $.1^24 ] ] [ [ $.1^10, $.1^25 ] ] [ [ $.1^11, $.1^2 ] ] [ [ $.1^11, $.1^4 ] ] [ [ $.1^11, $.1^6 ] ] [ [ $.1^11, $.1^7 ] ] [ [ $.1^11, $.1^10 ] ] [ [ $.1^11, $.1^11 ] ] [ [ $.1^11, $.1^12 ] ] [ [ $.1^11, $.1^18 ] ] [ [ $.1^11, $.1^21 ] ] [ [ $.1^12, $.1^5 ] ] [ [ $.1^12, $.1^8 ] ] [ [ $.1^12, $.1^15 ] ] [ [ $.1^12, $.1^17 ] ] [ [ $.1^12, $.1^19 ] ] [ [ $.1^12, $.1^20 ] ] [ [ $.1^12, $.1^23 ] ] [ [ $.1^12, $.1^24 ] ] [ [ $.1^12, $.1^25 ] ] [ [ 2, $.1^2 ] ] [ [ 2, $.1^4 ] ] [ [ 2, $.1^6 ] ] [ [ 2, $.1^7 ] ] [ [ 2, $.1^10 ] ] [ [ 2, $.1^11 ] ] [ [ 2, $.1^12 ] ] [ [ 2, $.1^18 ] ] [ [ 2, $.1^21 ] ] [ [ $.1^14, $.1^5 ] ] [ [ $.1^14, $.1^8 ] ] [ [ $.1^14, $.1^15 ] ] [ [ $.1^14, $.1^17 ] ] [ [ $.1^14, $.1^19 ] ] [ [ $.1^14, $.1^20 ] ] [ [ $.1^14, $.1^23 ] ] [ [ $.1^14, $.1^24 ] ] [ [ $.1^14, $.1^25 ] ] [ [ $.1^15, $.1^2 ] ] [ [ $.1^15, $.1^4 ] ] [ [ $.1^15, $.1^6 ] ] [ [ $.1^15, $.1^7 ] ] [ [ $.1^15, $.1^10 ] ] [ [ $.1^15, $.1^11 ] ] [ [ $.1^15, $.1^12 ] ] [ [ $.1^15, $.1^18 ] ] [ [ $.1^15, $.1^21 ] ] [ [ $.1^16, $.1^5 ] ] [ [ $.1^16, $.1^8 ] ] [ [ $.1^16, $.1^15 ] ] [ [ $.1^16, $.1^17 ] ] [ [ $.1^16, $.1^19 ] ] [ [ $.1^16, $.1^20 ] ] [ [ $.1^16, $.1^23 ] ] [ [ $.1^16, $.1^24 ] ] [ [ $.1^16, $.1^25 ] ] [ [ $.1^17, $.1^2 ] ] [ [ $.1^17, $.1^4 ] ] [ [ $.1^17, $.1^6 ] ] [ [ $.1^17, $.1^7 ] ] [ [ $.1^17, $.1^10 ] ] [ [ $.1^17, $.1^11 ] ] [ [ $.1^17, $.1^12 ] ] [ [ $.1^17, $.1^18 ] ] [ [ $.1^17, $.1^21 ] ] [ [ $.1^18, $.1^5 ] ] [ [ $.1^18, $.1^8 ] ] [ [ $.1^18, $.1^15 ] ] [ [ $.1^18, $.1^17 ] ] [ [ $.1^18, $.1^19 ] ] [ [ $.1^18, $.1^20 ] ] [ [ $.1^18, $.1^23 ] ] [ [ $.1^18, $.1^24 ] ] [ [ $.1^18, $.1^25 ] ] [ [ $.1^19, $.1^2 ] ] [ [ $.1^19, $.1^4 ] ] [ [ $.1^19, $.1^6 ] ] [ [ $.1^19, $.1^7 ] ] [ [ $.1^19, $.1^10 ] ] [ [ $.1^19, $.1^11 ] ] [ [ $.1^19, $.1^12 ] ] [ [ $.1^19, $.1^18 ] ] [ [ $.1^19, $.1^21 ] ] [ [ $.1^20, $.1^5 ] ] [ [ $.1^20, $.1^8 ] ] [ [ $.1^20, $.1^15 ] ] [ [ $.1^20, $.1^17 ] ] [ [ $.1^20, $.1^19 ] ] [ [ $.1^20, $.1^20 ] ] [ [ $.1^20, $.1^23 ] ] [ [ $.1^20, $.1^24 ] ] [ [ $.1^20, $.1^25 ] ] [ [ $.1^21, $.1^2 ] ] [ [ $.1^21, $.1^4 ] ] [ [ $.1^21, $.1^6 ] ] [ [ $.1^21, $.1^7 ] ] [ [ $.1^21, $.1^10 ] ] [ [ $.1^21, $.1^11 ] ] [ [ $.1^21, $.1^12 ] ] [ [ $.1^21, $.1^18 ] ] [ [ $.1^21, $.1^21 ] ] [ [ $.1^22, $.1^5 ] ] [ [ $.1^22, $.1^8 ] ] [ [ $.1^22, $.1^15 ] ] [ [ $.1^22, $.1^17 ] ] [ [ $.1^22, $.1^19 ] ] [ [ $.1^22, $.1^20 ] ] [ [ $.1^22, $.1^23 ] ] [ [ $.1^22, $.1^24 ] ] [ [ $.1^22, $.1^25 ] ] [ [ $.1^23, $.1^2 ] ] [ [ $.1^23, $.1^4 ] ] [ [ $.1^23, $.1^6 ] ] [ [ $.1^23, $.1^7 ] ] [ [ $.1^23, $.1^10 ] ] [ [ $.1^23, $.1^11 ] ] [ [ $.1^23, $.1^12 ] ] [ [ $.1^23, $.1^18 ] ] [ [ $.1^23, $.1^21 ] ] [ [ $.1^24, $.1^5 ] ] [ [ $.1^24, $.1^8 ] ] [ [ $.1^24, $.1^15 ] ] [ [ $.1^24, $.1^17 ] ] [ [ $.1^24, $.1^19 ] ] [ [ $.1^24, $.1^20 ] ] [ [ $.1^24, $.1^23 ] ] [ [ $.1^24, $.1^24 ] ] [ [ $.1^24, $.1^25 ] ] [ [ $.1^25, $.1^2 ] ] [ [ $.1^25, $.1^4 ] ] [ [ $.1^25, $.1^6 ] ] [ [ $.1^25, $.1^7 ] ] [ [ $.1^25, $.1^10 ] ] [ [ $.1^25, $.1^11 ] ] [ [ $.1^25, $.1^12 ] ] [ [ $.1^25, $.1^18 ] ] [ [ $.1^25, $.1^21 ] ] [ [ 0, 1 ] ] [ [ 0, $.1 ] ] [ [ 0, $.1^3 ] ] [ [ 0, $.1^9 ] ] [ [ 0, 2 ] ] [ [ 0, $.1^14 ] ] [ [ 0, $.1^16 ] ] [ [ 0, $.1^22 ] ] [ [ 0, 0 ] ] 0 Total time: 3.039 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 11:35:05 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:={}; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; spolav:= [k : k in polavqr(4,1) | k[1] in GF(4)) and (k[2] in GF(4))]; #spolav; Output: Magma V2.10-6 Fri Mar 12 2004 11:35:02 on modular [Seed = 285259688] ------------------------------------- >> spolav:= [k : k in polavqr(4,1) | k[1] in GF(4)) and (k[2] in GF(4))]; ^ User error: bad syntax >> #spolav; ^ User error: Identifier 'spolav' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 11:35:21 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:={}; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; spolav:= [k : k in polavqr(4,1) | k[1] in GF(4) and k[2] in GF(4)]; #spolav; Output: Magma V2.10-6 Fri Mar 12 2004 11:35:18 on modular [Seed = 674860769] ------------------------------------- { [ 1, 1 ] } { [ $.1, $.1 ] } { [ $.1^2, $.1^2 ] } { [ 0, 0 ] } 0 Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 200-BAR2-X4.libre.retevision.es. (62.82.186.200) Time: Fri Mar 12 11:35:41 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; #polav(1,2); 1^(2*2-1); spolav:= [k : k in polavqr(3,3) | k[1] in GF(3) and k[2] in GF(3)]; #spolav; Output: Magma V2.10-6 Fri Mar 12 2004 11:35:38 on modular [Seed = 1060018666] ------------------------------------- >> #polav(1,2); ^ User error: Identifier 'polav' has not been declared or assigned 1 [ [ 1, $.1^5 ] ] [ [ 1, $.1^8 ] ] [ [ 1, $.1^15 ] ] [ [ 1, $.1^17 ] ] [ [ 1, $.1^19 ] ] [ [ 1, $.1^20 ] ] [ [ 1, $.1^23 ] ] [ [ 1, $.1^24 ] ] [ [ 1, $.1^25 ] ] [ [ $.1, $.1^2 ] ] [ [ $.1, $.1^4 ] ] [ [ $.1, $.1^6 ] ] [ [ $.1, $.1^7 ] ] [ [ $.1, $.1^10 ] ] [ [ $.1, $.1^11 ] ] [ [ $.1, $.1^12 ] ] [ [ $.1, $.1^18 ] ] [ [ $.1, $.1^21 ] ] [ [ $.1^2, $.1^5 ] ] [ [ $.1^2, $.1^8 ] ] [ [ $.1^2, $.1^15 ] ] [ [ $.1^2, $.1^17 ] ] [ [ $.1^2, $.1^19 ] ] [ [ $.1^2, $.1^20 ] ] [ [ $.1^2, $.1^23 ] ] [ [ $.1^2, $.1^24 ] ] [ [ $.1^2, $.1^25 ] ] [ [ $.1^3, $.1^2 ] ] [ [ $.1^3, $.1^4 ] ] [ [ $.1^3, $.1^6 ] ] [ [ $.1^3, $.1^7 ] ] [ [ $.1^3, $.1^10 ] ] [ [ $.1^3, $.1^11 ] ] [ [ $.1^3, $.1^12 ] ] [ [ $.1^3, $.1^18 ] ] [ [ $.1^3, $.1^21 ] ] [ [ $.1^4, $.1^5 ] ] [ [ $.1^4, $.1^8 ] ] [ [ $.1^4, $.1^15 ] ] [ [ $.1^4, $.1^17 ] ] [ [ $.1^4, $.1^19 ] ] [ [ $.1^4, $.1^20 ] ] [ [ $.1^4, $.1^23 ] ] [ [ $.1^4, $.1^24 ] ] [ [ $.1^4, $.1^25 ] ] [ [ $.1^5, $.1^2 ] ] [ [ $.1^5, $.1^4 ] ] [ [ $.1^5, $.1^6 ] ] [ [ $.1^5, $.1^7 ] ] [ [ $.1^5, $.1^10 ] ] [ [ $.1^5, $.1^11 ] ] [ [ $.1^5, $.1^12 ] ] [ [ $.1^5, $.1^18 ] ] [ [ $.1^5, $.1^21 ] ] [ [ $.1^6, $.1^5 ] ] [ [ $.1^6, $.1^8 ] ] [ [ $.1^6, $.1^15 ] ] [ [ $.1^6, $.1^17 ] ] [ [ $.1^6, $.1^19 ] ] [ [ $.1^6, $.1^20 ] ] [ [ $.1^6, $.1^23 ] ] [ [ $.1^6, $.1^24 ] ] [ [ $.1^6, $.1^25 ] ] [ [ $.1^7, $.1^2 ] ] [ [ $.1^7, $.1^4 ] ] [ [ $.1^7, $.1^6 ] ] [ [ $.1^7, $.1^7 ] ] [ [ $.1^7, $.1^10 ] ] [ [ $.1^7, $.1^11 ] ] [ [ $.1^7, $.1^12 ] ] [ [ $.1^7, $.1^18 ] ] [ [ $.1^7, $.1^21 ] ] [ [ $.1^8, $.1^5 ] ] [ [ $.1^8, $.1^8 ] ] [ [ $.1^8, $.1^15 ] ] [ [ $.1^8, $.1^17 ] ] [ [ $.1^8, $.1^19 ] ] [ [ $.1^8, $.1^20 ] ] [ [ $.1^8, $.1^23 ] ] [ [ $.1^8, $.1^24 ] ] [ [ $.1^8, $.1^25 ] ] [ [ $.1^9, $.1^2 ] ] [ [ $.1^9, $.1^4 ] ] [ [ $.1^9, $.1^6 ] ] [ [ $.1^9, $.1^7 ] ] [ [ $.1^9, $.1^10 ] ] [ [ $.1^9, $.1^11 ] ] [ [ $.1^9, $.1^12 ] ] [ [ $.1^9, $.1^18 ] ] [ [ $.1^9, $.1^21 ] ] [ [ $.1^10, $.1^5 ] ] [ [ $.1^10, $.1^8 ] ] [ [ $.1^10, $.1^15 ] ] [ [ $.1^10, $.1^17 ] ] [ [ $.1^10, $.1^19 ] ] [ [ $.1^10, $.1^20 ] ] [ [ $.1^10, $.1^23 ] ] [ [ $.1^10, $.1^24 ] ] [ [ $.1^10, $.1^25 ] ] [ [ $.1^11, $.1^2 ] ] [ [ $.1^11, $.1^4 ] ] [ [ $.1^11, $.1^6 ] ] [ [ $.1^11, $.1^7 ] ] [ [ $.1^11, $.1^10 ] ] [ [ $.1^11, $.1^11 ] ] [ [ $.1^11, $.1^12 ] ] [ [ $.1^11, $.1^18 ] ] [ [ $.1^11, $.1^21 ] ] [ [ $.1^12, $.1^5 ] ] [ [ $.1^12, $.1^8 ] ] [ [ $.1^12, $.1^15 ] ] [ [ $.1^12, $.1^17 ] ] [ [ $.1^12, $.1^19 ] ] [ [ $.1^12, $.1^20 ] ] [ [ $.1^12, $.1^23 ] ] [ [ $.1^12, $.1^24 ] ] [ [ $.1^12, $.1^25 ] ] [ [ 2, $.1^2 ] ] [ [ 2, $.1^4 ] ] [ [ 2, $.1^6 ] ] [ [ 2, $.1^7 ] ] [ [ 2, $.1^10 ] ] [ [ 2, $.1^11 ] ] [ [ 2, $.1^12 ] ] [ [ 2, $.1^18 ] ] [ [ 2, $.1^21 ] ] [ [ $.1^14, $.1^5 ] ] [ [ $.1^14, $.1^8 ] ] [ [ $.1^14, $.1^15 ] ] [ [ $.1^14, $.1^17 ] ] [ [ $.1^14, $.1^19 ] ] [ [ $.1^14, $.1^20 ] ] [ [ $.1^14, $.1^23 ] ] [ [ $.1^14, $.1^24 ] ] [ [ $.1^14, $.1^25 ] ] [ [ $.1^15, $.1^2 ] ] [ [ $.1^15, $.1^4 ] ] [ [ $.1^15, $.1^6 ] ] [ [ $.1^15, $.1^7 ] ] [ [ $.1^15, $.1^10 ] ] [ [ $.1^15, $.1^11 ] ] [ [ $.1^15, $.1^12 ] ] [ [ $.1^15, $.1^18 ] ] [ [ $.1^15, $.1^21 ] ] [ [ $.1^16, $.1^5 ] ] [ [ $.1^16, $.1^8 ] ] [ [ $.1^16, $.1^15 ] ] [ [ $.1^16, $.1^17 ] ] [ [ $.1^16, $.1^19 ] ] [ [ $.1^16, $.1^20 ] ] [ [ $.1^16, $.1^23 ] ] [ [ $.1^16, $.1^24 ] ] [ [ $.1^16, $.1^25 ] ] [ [ $.1^17, $.1^2 ] ] [ [ $.1^17, $.1^4 ] ] [ [ $.1^17, $.1^6 ] ] [ [ $.1^17, $.1^7 ] ] [ [ $.1^17, $.1^10 ] ] [ [ $.1^17, $.1^11 ] ] [ [ $.1^17, $.1^12 ] ] [ [ $.1^17, $.1^18 ] ] [ [ $.1^17, $.1^21 ] ] [ [ $.1^18, $.1^5 ] ] [ [ $.1^18, $.1^8 ] ] [ [ $.1^18, $.1^15 ] ] [ [ $.1^18, $.1^17 ] ] [ [ $.1^18, $.1^19 ] ] [ [ $.1^18, $.1^20 ] ] [ [ $.1^18, $.1^23 ] ] [ [ $.1^18, $.1^24 ] ] [ [ $.1^18, $.1^25 ] ] [ [ $.1^19, $.1^2 ] ] [ [ $.1^19, $.1^4 ] ] [ [ $.1^19, $.1^6 ] ] [ [ $.1^19, $.1^7 ] ] [ [ $.1^19, $.1^10 ] ] [ [ $.1^19, $.1^11 ] ] [ [ $.1^19, $.1^12 ] ] [ [ $.1^19, $.1^18 ] ] [ [ $.1^19, $.1^21 ] ] [ [ $.1^20, $.1^5 ] ] [ [ $.1^20, $.1^8 ] ] [ [ $.1^20, $.1^15 ] ] [ [ $.1^20, $.1^17 ] ] [ [ $.1^20, $.1^19 ] ] [ [ $.1^20, $.1^20 ] ] [ [ $.1^20, $.1^23 ] ] [ [ $.1^20, $.1^24 ] ] [ [ $.1^20, $.1^25 ] ] [ [ $.1^21, $.1^2 ] ] [ [ $.1^21, $.1^4 ] ] [ [ $.1^21, $.1^6 ] ] [ [ $.1^21, $.1^7 ] ] [ [ $.1^21, $.1^10 ] ] [ [ $.1^21, $.1^11 ] ] [ [ $.1^21, $.1^12 ] ] [ [ $.1^21, $.1^18 ] ] [ [ $.1^21, $.1^21 ] ] [ [ $.1^22, $.1^5 ] ] [ [ $.1^22, $.1^8 ] ] [ [ $.1^22, $.1^15 ] ] [ [ $.1^22, $.1^17 ] ] [ [ $.1^22, $.1^19 ] ] [ [ $.1^22, $.1^20 ] ] [ [ $.1^22, $.1^23 ] ] [ [ $.1^22, $.1^24 ] ] [ [ $.1^22, $.1^25 ] ] [ [ $.1^23, $.1^2 ] ] [ [ $.1^23, $.1^4 ] ] [ [ $.1^23, $.1^6 ] ] [ [ $.1^23, $.1^7 ] ] [ [ $.1^23, $.1^10 ] ] [ [ $.1^23, $.1^11 ] ] [ [ $.1^23, $.1^12 ] ] [ [ $.1^23, $.1^18 ] ] [ [ $.1^23, $.1^21 ] ] [ [ $.1^24, $.1^5 ] ] [ [ $.1^24, $.1^8 ] ] [ [ $.1^24, $.1^15 ] ] [ [ $.1^24, $.1^17 ] ] [ [ $.1^24, $.1^19 ] ] [ [ $.1^24, $.1^20 ] ] [ [ $.1^24, $.1^23 ] ] [ [ $.1^24, $.1^24 ] ] [ [ $.1^24, $.1^25 ] ] [ [ $.1^25, $.1^2 ] ] [ [ $.1^25, $.1^4 ] ] [ [ $.1^25, $.1^6 ] ] [ [ $.1^25, $.1^7 ] ] [ [ $.1^25, $.1^10 ] ] [ [ $.1^25, $.1^11 ] ] [ [ $.1^25, $.1^12 ] ] [ [ $.1^25, $.1^18 ] ] [ [ $.1^25, $.1^21 ] ] [ [ 0, 1 ] ] [ [ 0, $.1 ] ] [ [ 0, $.1^3 ] ] [ [ 0, $.1^9 ] ] [ [ 0, 2 ] ] [ [ 0, $.1^14 ] ] [ [ 0, $.1^16 ] ] [ [ 0, $.1^22 ] ] [ [ 0, 0 ] ] 0 Total time: 3.089 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 11:35:50 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:={}; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; spolav:= [k : k in polavqr(4,1)]; #spolav; Output: Magma V2.10-6 Fri Mar 12 2004 11:35:47 on modular [Seed = 908562650] ------------------------------------- { [ 1, 1 ] } { [ $.1, $.1 ] } { [ $.1^2, $.1^2 ] } { [ 0, 0 ] } 0 Total time: 3.089 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 200-BAR2-X4.libre.retevision.es. (62.82.186.200) Time: Fri Mar 12 11:36:32 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; #polavqr(1,2); 1^(2*2-1); spolav:= [k : k in polavqr(3,3) | k[1] in GF(3) and k[2] in GF(3)]; #spolav; Output: Magma V2.10-6 Fri Mar 12 2004 11:36:29 on modular [Seed = 1297934927] ------------------------------------- [
:19]( q: 1, r: 2 ) >> for i in GF(q^r) do ^ Runtime error in 'GF': Argument 1 (1) should be >= 2 1 [ [ 1, $.1^5 ] ] [ [ 1, $.1^8 ] ] [ [ 1, $.1^15 ] ] [ [ 1, $.1^17 ] ] [ [ 1, $.1^19 ] ] [ [ 1, $.1^20 ] ] [ [ 1, $.1^23 ] ] [ [ 1, $.1^24 ] ] [ [ 1, $.1^25 ] ] [ [ $.1, $.1^2 ] ] [ [ $.1, $.1^4 ] ] [ [ $.1, $.1^6 ] ] [ [ $.1, $.1^7 ] ] [ [ $.1, $.1^10 ] ] [ [ $.1, $.1^11 ] ] [ [ $.1, $.1^12 ] ] [ [ $.1, $.1^18 ] ] [ [ $.1, $.1^21 ] ] [ [ $.1^2, $.1^5 ] ] [ [ $.1^2, $.1^8 ] ] [ [ $.1^2, $.1^15 ] ] [ [ $.1^2, $.1^17 ] ] [ [ $.1^2, $.1^19 ] ] [ [ $.1^2, $.1^20 ] ] [ [ $.1^2, $.1^23 ] ] [ [ $.1^2, $.1^24 ] ] [ [ $.1^2, $.1^25 ] ] [ [ $.1^3, $.1^2 ] ] [ [ $.1^3, $.1^4 ] ] [ [ $.1^3, $.1^6 ] ] [ [ $.1^3, $.1^7 ] ] [ [ $.1^3, $.1^10 ] ] [ [ $.1^3, $.1^11 ] ] [ [ $.1^3, $.1^12 ] ] [ [ $.1^3, $.1^18 ] ] [ [ $.1^3, $.1^21 ] ] [ [ $.1^4, $.1^5 ] ] [ [ $.1^4, $.1^8 ] ] [ [ $.1^4, $.1^15 ] ] [ [ $.1^4, $.1^17 ] ] [ [ $.1^4, $.1^19 ] ] [ [ $.1^4, $.1^20 ] ] [ [ $.1^4, $.1^23 ] ] [ [ $.1^4, $.1^24 ] ] [ [ $.1^4, $.1^25 ] ] [ [ $.1^5, $.1^2 ] ] [ [ $.1^5, $.1^4 ] ] [ [ $.1^5, $.1^6 ] ] [ [ $.1^5, $.1^7 ] ] [ [ $.1^5, $.1^10 ] ] [ [ $.1^5, $.1^11 ] ] [ [ $.1^5, $.1^12 ] ] [ [ $.1^5, $.1^18 ] ] [ [ $.1^5, $.1^21 ] ] [ [ $.1^6, $.1^5 ] ] [ [ $.1^6, $.1^8 ] ] [ [ $.1^6, $.1^15 ] ] [ [ $.1^6, $.1^17 ] ] [ [ $.1^6, $.1^19 ] ] [ [ $.1^6, $.1^20 ] ] [ [ $.1^6, $.1^23 ] ] [ [ $.1^6, $.1^24 ] ] [ [ $.1^6, $.1^25 ] ] [ [ $.1^7, $.1^2 ] ] [ [ $.1^7, $.1^4 ] ] [ [ $.1^7, $.1^6 ] ] [ [ $.1^7, $.1^7 ] ] [ [ $.1^7, $.1^10 ] ] [ [ $.1^7, $.1^11 ] ] [ [ $.1^7, $.1^12 ] ] [ [ $.1^7, $.1^18 ] ] [ [ $.1^7, $.1^21 ] ] [ [ $.1^8, $.1^5 ] ] [ [ $.1^8, $.1^8 ] ] [ [ $.1^8, $.1^15 ] ] [ [ $.1^8, $.1^17 ] ] [ [ $.1^8, $.1^19 ] ] [ [ $.1^8, $.1^20 ] ] [ [ $.1^8, $.1^23 ] ] [ [ $.1^8, $.1^24 ] ] [ [ $.1^8, $.1^25 ] ] [ [ $.1^9, $.1^2 ] ] [ [ $.1^9, $.1^4 ] ] [ [ $.1^9, $.1^6 ] ] [ [ $.1^9, $.1^7 ] ] [ [ $.1^9, $.1^10 ] ] [ [ $.1^9, $.1^11 ] ] [ [ $.1^9, $.1^12 ] ] [ [ $.1^9, $.1^18 ] ] [ [ $.1^9, $.1^21 ] ] [ [ $.1^10, $.1^5 ] ] [ [ $.1^10, $.1^8 ] ] [ [ $.1^10, $.1^15 ] ] [ [ $.1^10, $.1^17 ] ] [ [ $.1^10, $.1^19 ] ] [ [ $.1^10, $.1^20 ] ] [ [ $.1^10, $.1^23 ] ] [ [ $.1^10, $.1^24 ] ] [ [ $.1^10, $.1^25 ] ] [ [ $.1^11, $.1^2 ] ] [ [ $.1^11, $.1^4 ] ] [ [ $.1^11, $.1^6 ] ] [ [ $.1^11, $.1^7 ] ] [ [ $.1^11, $.1^10 ] ] [ [ $.1^11, $.1^11 ] ] [ [ $.1^11, $.1^12 ] ] [ [ $.1^11, $.1^18 ] ] [ [ $.1^11, $.1^21 ] ] [ [ $.1^12, $.1^5 ] ] [ [ $.1^12, $.1^8 ] ] [ [ $.1^12, $.1^15 ] ] [ [ $.1^12, $.1^17 ] ] [ [ $.1^12, $.1^19 ] ] [ [ $.1^12, $.1^20 ] ] [ [ $.1^12, $.1^23 ] ] [ [ $.1^12, $.1^24 ] ] [ [ $.1^12, $.1^25 ] ] [ [ 2, $.1^2 ] ] [ [ 2, $.1^4 ] ] [ [ 2, $.1^6 ] ] [ [ 2, $.1^7 ] ] [ [ 2, $.1^10 ] ] [ [ 2, $.1^11 ] ] [ [ 2, $.1^12 ] ] [ [ 2, $.1^18 ] ] [ [ 2, $.1^21 ] ] [ [ $.1^14, $.1^5 ] ] [ [ $.1^14, $.1^8 ] ] [ [ $.1^14, $.1^15 ] ] [ [ $.1^14, $.1^17 ] ] [ [ $.1^14, $.1^19 ] ] [ [ $.1^14, $.1^20 ] ] [ [ $.1^14, $.1^23 ] ] [ [ $.1^14, $.1^24 ] ] [ [ $.1^14, $.1^25 ] ] [ [ $.1^15, $.1^2 ] ] [ [ $.1^15, $.1^4 ] ] [ [ $.1^15, $.1^6 ] ] [ [ $.1^15, $.1^7 ] ] [ [ $.1^15, $.1^10 ] ] [ [ $.1^15, $.1^11 ] ] [ [ $.1^15, $.1^12 ] ] [ [ $.1^15, $.1^18 ] ] [ [ $.1^15, $.1^21 ] ] [ [ $.1^16, $.1^5 ] ] [ [ $.1^16, $.1^8 ] ] [ [ $.1^16, $.1^15 ] ] [ [ $.1^16, $.1^17 ] ] [ [ $.1^16, $.1^19 ] ] [ [ $.1^16, $.1^20 ] ] [ [ $.1^16, $.1^23 ] ] [ [ $.1^16, $.1^24 ] ] [ [ $.1^16, $.1^25 ] ] [ [ $.1^17, $.1^2 ] ] [ [ $.1^17, $.1^4 ] ] [ [ $.1^17, $.1^6 ] ] [ [ $.1^17, $.1^7 ] ] [ [ $.1^17, $.1^10 ] ] [ [ $.1^17, $.1^11 ] ] [ [ $.1^17, $.1^12 ] ] [ [ $.1^17, $.1^18 ] ] [ [ $.1^17, $.1^21 ] ] [ [ $.1^18, $.1^5 ] ] [ [ $.1^18, $.1^8 ] ] [ [ $.1^18, $.1^15 ] ] [ [ $.1^18, $.1^17 ] ] [ [ $.1^18, $.1^19 ] ] [ [ $.1^18, $.1^20 ] ] [ [ $.1^18, $.1^23 ] ] [ [ $.1^18, $.1^24 ] ] [ [ $.1^18, $.1^25 ] ] [ [ $.1^19, $.1^2 ] ] [ [ $.1^19, $.1^4 ] ] [ [ $.1^19, $.1^6 ] ] [ [ $.1^19, $.1^7 ] ] [ [ $.1^19, $.1^10 ] ] [ [ $.1^19, $.1^11 ] ] [ [ $.1^19, $.1^12 ] ] [ [ $.1^19, $.1^18 ] ] [ [ $.1^19, $.1^21 ] ] [ [ $.1^20, $.1^5 ] ] [ [ $.1^20, $.1^8 ] ] [ [ $.1^20, $.1^15 ] ] [ [ $.1^20, $.1^17 ] ] [ [ $.1^20, $.1^19 ] ] [ [ $.1^20, $.1^20 ] ] [ [ $.1^20, $.1^23 ] ] [ [ $.1^20, $.1^24 ] ] [ [ $.1^20, $.1^25 ] ] [ [ $.1^21, $.1^2 ] ] [ [ $.1^21, $.1^4 ] ] [ [ $.1^21, $.1^6 ] ] [ [ $.1^21, $.1^7 ] ] [ [ $.1^21, $.1^10 ] ] [ [ $.1^21, $.1^11 ] ] [ [ $.1^21, $.1^12 ] ] [ [ $.1^21, $.1^18 ] ] [ [ $.1^21, $.1^21 ] ] [ [ $.1^22, $.1^5 ] ] [ [ $.1^22, $.1^8 ] ] [ [ $.1^22, $.1^15 ] ] [ [ $.1^22, $.1^17 ] ] [ [ $.1^22, $.1^19 ] ] [ [ $.1^22, $.1^20 ] ] [ [ $.1^22, $.1^23 ] ] [ [ $.1^22, $.1^24 ] ] [ [ $.1^22, $.1^25 ] ] [ [ $.1^23, $.1^2 ] ] [ [ $.1^23, $.1^4 ] ] [ [ $.1^23, $.1^6 ] ] [ [ $.1^23, $.1^7 ] ] [ [ $.1^23, $.1^10 ] ] [ [ $.1^23, $.1^11 ] ] [ [ $.1^23, $.1^12 ] ] [ [ $.1^23, $.1^18 ] ] [ [ $.1^23, $.1^21 ] ] [ [ $.1^24, $.1^5 ] ] [ [ $.1^24, $.1^8 ] ] [ [ $.1^24, $.1^15 ] ] [ [ $.1^24, $.1^17 ] ] [ [ $.1^24, $.1^19 ] ] [ [ $.1^24, $.1^20 ] ] [ [ $.1^24, $.1^23 ] ] [ [ $.1^24, $.1^24 ] ] [ [ $.1^24, $.1^25 ] ] [ [ $.1^25, $.1^2 ] ] [ [ $.1^25, $.1^4 ] ] [ [ $.1^25, $.1^6 ] ] [ [ $.1^25, $.1^7 ] ] [ [ $.1^25, $.1^10 ] ] [ [ $.1^25, $.1^11 ] ] [ [ $.1^25, $.1^12 ] ] [ [ $.1^25, $.1^18 ] ] [ [ $.1^25, $.1^21 ] ] [ [ 0, 1 ] ] [ [ 0, $.1 ] ] [ [ 0, $.1^3 ] ] [ [ 0, $.1^9 ] ] [ [ 0, 2 ] ] [ [ 0, $.1^14 ] ] [ [ 0, $.1^16 ] ] [ [ 0, $.1^22 ] ] [ [ 0, 0 ] ] 0 Total time: 3.029 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 11:37:03 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; spolav:= [k : k in polavqr(4,1) | k[1] in GF(4) and k[2] in GF(4)]; #spolav; Output: Magma V2.10-6 Fri Mar 12 2004 11:37:00 on modular [Seed = 1129505888] ------------------------------------- [ [ 1, 1 ] ] [ [ $.1, $.1 ] ] [ [ $.1^2, $.1^2 ] ] [ [ 0, 0 ] ] 0 Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 11:37:51 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return [C]; end function; spolav:= [k : k in polavqr(4,1) | k[1] in GF(4) and k[2] in GF(4)]; #spolav; Output: Magma V2.10-6 Fri Mar 12 2004 11:37:48 on modular [Seed = 1514929417] ------------------------------------- [ [ 1, 1 ] ] [ [ $.1, $.1 ] ] [ [ $.1^2, $.1^2 ] ] [ [ 0, 0 ] ] >> spolav:= [k : k in polavqr(4,1) | k[1] in GF(4) and k[2] in GF(4)]; ^ Runtime error in '[]': Sequence element 1 not defined >> #spolav; ^ User error: Identifier 'spolav' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 200-BAR2-X4.libre.retevision.es. (62.82.186.200) Time: Fri Mar 12 11:38:05 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q,r) do for j in GF(q,r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; #polavqr(1,2); 1^(2*2-1); spolav:= [k : k in polavqr(3,3) | k[1] in GF(3) and k[2] in GF(3)]; #spolav; Output: Magma V2.10-6 Fri Mar 12 2004 11:38:02 on modular [Seed = 1363211828] ------------------------------------- [
:19]( q: 1, r: 2 ) >> for i in GF(q,r) do ^ Runtime error in 'GF': Argument 1 (1) should be >= 2 1 [ [ 1, $.1^5 ] ] [ [ 1, $.1^8 ] ] [ [ 1, $.1^15 ] ] [ [ 1, $.1^17 ] ] [ [ 1, $.1^19 ] ] [ [ 1, $.1^20 ] ] [ [ 1, $.1^23 ] ] [ [ 1, $.1^24 ] ] [ [ 1, $.1^25 ] ] [ [ $.1, $.1^2 ] ] [ [ $.1, $.1^4 ] ] [ [ $.1, $.1^6 ] ] [ [ $.1, $.1^7 ] ] [ [ $.1, $.1^10 ] ] [ [ $.1, $.1^11 ] ] [ [ $.1, $.1^12 ] ] [ [ $.1, $.1^18 ] ] [ [ $.1, $.1^21 ] ] [ [ $.1^2, $.1^5 ] ] [ [ $.1^2, $.1^8 ] ] [ [ $.1^2, $.1^15 ] ] [ [ $.1^2, $.1^17 ] ] [ [ $.1^2, $.1^19 ] ] [ [ $.1^2, $.1^20 ] ] [ [ $.1^2, $.1^23 ] ] [ [ $.1^2, $.1^24 ] ] [ [ $.1^2, $.1^25 ] ] [ [ $.1^3, $.1^2 ] ] [ [ $.1^3, $.1^4 ] ] [ [ $.1^3, $.1^6 ] ] [ [ $.1^3, $.1^7 ] ] [ [ $.1^3, $.1^10 ] ] [ [ $.1^3, $.1^11 ] ] [ [ $.1^3, $.1^12 ] ] [ [ $.1^3, $.1^18 ] ] [ [ $.1^3, $.1^21 ] ] [ [ $.1^4, $.1^5 ] ] [ [ $.1^4, $.1^8 ] ] [ [ $.1^4, $.1^15 ] ] [ [ $.1^4, $.1^17 ] ] [ [ $.1^4, $.1^19 ] ] [ [ $.1^4, $.1^20 ] ] [ [ $.1^4, $.1^23 ] ] [ [ $.1^4, $.1^24 ] ] [ [ $.1^4, $.1^25 ] ] [ [ $.1^5, $.1^2 ] ] [ [ $.1^5, $.1^4 ] ] [ [ $.1^5, $.1^6 ] ] [ [ $.1^5, $.1^7 ] ] [ [ $.1^5, $.1^10 ] ] [ [ $.1^5, $.1^11 ] ] [ [ $.1^5, $.1^12 ] ] [ [ $.1^5, $.1^18 ] ] [ [ $.1^5, $.1^21 ] ] [ [ $.1^6, $.1^5 ] ] [ [ $.1^6, $.1^8 ] ] [ [ $.1^6, $.1^15 ] ] [ [ $.1^6, $.1^17 ] ] [ [ $.1^6, $.1^19 ] ] [ [ $.1^6, $.1^20 ] ] [ [ $.1^6, $.1^23 ] ] [ [ $.1^6, $.1^24 ] ] [ [ $.1^6, $.1^25 ] ] [ [ $.1^7, $.1^2 ] ] [ [ $.1^7, $.1^4 ] ] [ [ $.1^7, $.1^6 ] ] [ [ $.1^7, $.1^7 ] ] [ [ $.1^7, $.1^10 ] ] [ [ $.1^7, $.1^11 ] ] [ [ $.1^7, $.1^12 ] ] [ [ $.1^7, $.1^18 ] ] [ [ $.1^7, $.1^21 ] ] [ [ $.1^8, $.1^5 ] ] [ [ $.1^8, $.1^8 ] ] [ [ $.1^8, $.1^15 ] ] [ [ $.1^8, $.1^17 ] ] [ [ $.1^8, $.1^19 ] ] [ [ $.1^8, $.1^20 ] ] [ [ $.1^8, $.1^23 ] ] [ [ $.1^8, $.1^24 ] ] [ [ $.1^8, $.1^25 ] ] [ [ $.1^9, $.1^2 ] ] [ [ $.1^9, $.1^4 ] ] [ [ $.1^9, $.1^6 ] ] [ [ $.1^9, $.1^7 ] ] [ [ $.1^9, $.1^10 ] ] [ [ $.1^9, $.1^11 ] ] [ [ $.1^9, $.1^12 ] ] [ [ $.1^9, $.1^18 ] ] [ [ $.1^9, $.1^21 ] ] [ [ $.1^10, $.1^5 ] ] [ [ $.1^10, $.1^8 ] ] [ [ $.1^10, $.1^15 ] ] [ [ $.1^10, $.1^17 ] ] [ [ $.1^10, $.1^19 ] ] [ [ $.1^10, $.1^20 ] ] [ [ $.1^10, $.1^23 ] ] [ [ $.1^10, $.1^24 ] ] [ [ $.1^10, $.1^25 ] ] [ [ $.1^11, $.1^2 ] ] [ [ $.1^11, $.1^4 ] ] [ [ $.1^11, $.1^6 ] ] [ [ $.1^11, $.1^7 ] ] [ [ $.1^11, $.1^10 ] ] [ [ $.1^11, $.1^11 ] ] [ [ $.1^11, $.1^12 ] ] [ [ $.1^11, $.1^18 ] ] [ [ $.1^11, $.1^21 ] ] [ [ $.1^12, $.1^5 ] ] [ [ $.1^12, $.1^8 ] ] [ [ $.1^12, $.1^15 ] ] [ [ $.1^12, $.1^17 ] ] [ [ $.1^12, $.1^19 ] ] [ [ $.1^12, $.1^20 ] ] [ [ $.1^12, $.1^23 ] ] [ [ $.1^12, $.1^24 ] ] [ [ $.1^12, $.1^25 ] ] [ [ 2, $.1^2 ] ] [ [ 2, $.1^4 ] ] [ [ 2, $.1^6 ] ] [ [ 2, $.1^7 ] ] [ [ 2, $.1^10 ] ] [ [ 2, $.1^11 ] ] [ [ 2, $.1^12 ] ] [ [ 2, $.1^18 ] ] [ [ 2, $.1^21 ] ] [ [ $.1^14, $.1^5 ] ] [ [ $.1^14, $.1^8 ] ] [ [ $.1^14, $.1^15 ] ] [ [ $.1^14, $.1^17 ] ] [ [ $.1^14, $.1^19 ] ] [ [ $.1^14, $.1^20 ] ] [ [ $.1^14, $.1^23 ] ] [ [ $.1^14, $.1^24 ] ] [ [ $.1^14, $.1^25 ] ] [ [ $.1^15, $.1^2 ] ] [ [ $.1^15, $.1^4 ] ] [ [ $.1^15, $.1^6 ] ] [ [ $.1^15, $.1^7 ] ] [ [ $.1^15, $.1^10 ] ] [ [ $.1^15, $.1^11 ] ] [ [ $.1^15, $.1^12 ] ] [ [ $.1^15, $.1^18 ] ] [ [ $.1^15, $.1^21 ] ] [ [ $.1^16, $.1^5 ] ] [ [ $.1^16, $.1^8 ] ] [ [ $.1^16, $.1^15 ] ] [ [ $.1^16, $.1^17 ] ] [ [ $.1^16, $.1^19 ] ] [ [ $.1^16, $.1^20 ] ] [ [ $.1^16, $.1^23 ] ] [ [ $.1^16, $.1^24 ] ] [ [ $.1^16, $.1^25 ] ] [ [ $.1^17, $.1^2 ] ] [ [ $.1^17, $.1^4 ] ] [ [ $.1^17, $.1^6 ] ] [ [ $.1^17, $.1^7 ] ] [ [ $.1^17, $.1^10 ] ] [ [ $.1^17, $.1^11 ] ] [ [ $.1^17, $.1^12 ] ] [ [ $.1^17, $.1^18 ] ] [ [ $.1^17, $.1^21 ] ] [ [ $.1^18, $.1^5 ] ] [ [ $.1^18, $.1^8 ] ] [ [ $.1^18, $.1^15 ] ] [ [ $.1^18, $.1^17 ] ] [ [ $.1^18, $.1^19 ] ] [ [ $.1^18, $.1^20 ] ] [ [ $.1^18, $.1^23 ] ] [ [ $.1^18, $.1^24 ] ] [ [ $.1^18, $.1^25 ] ] [ [ $.1^19, $.1^2 ] ] [ [ $.1^19, $.1^4 ] ] [ [ $.1^19, $.1^6 ] ] [ [ $.1^19, $.1^7 ] ] [ [ $.1^19, $.1^10 ] ] [ [ $.1^19, $.1^11 ] ] [ [ $.1^19, $.1^12 ] ] [ [ $.1^19, $.1^18 ] ] [ [ $.1^19, $.1^21 ] ] [ [ $.1^20, $.1^5 ] ] [ [ $.1^20, $.1^8 ] ] [ [ $.1^20, $.1^15 ] ] [ [ $.1^20, $.1^17 ] ] [ [ $.1^20, $.1^19 ] ] [ [ $.1^20, $.1^20 ] ] [ [ $.1^20, $.1^23 ] ] [ [ $.1^20, $.1^24 ] ] [ [ $.1^20, $.1^25 ] ] [ [ $.1^21, $.1^2 ] ] [ [ $.1^21, $.1^4 ] ] [ [ $.1^21, $.1^6 ] ] [ [ $.1^21, $.1^7 ] ] [ [ $.1^21, $.1^10 ] ] [ [ $.1^21, $.1^11 ] ] [ [ $.1^21, $.1^12 ] ] [ [ $.1^21, $.1^18 ] ] [ [ $.1^21, $.1^21 ] ] [ [ $.1^22, $.1^5 ] ] [ [ $.1^22, $.1^8 ] ] [ [ $.1^22, $.1^15 ] ] [ [ $.1^22, $.1^17 ] ] [ [ $.1^22, $.1^19 ] ] [ [ $.1^22, $.1^20 ] ] [ [ $.1^22, $.1^23 ] ] [ [ $.1^22, $.1^24 ] ] [ [ $.1^22, $.1^25 ] ] [ [ $.1^23, $.1^2 ] ] [ [ $.1^23, $.1^4 ] ] [ [ $.1^23, $.1^6 ] ] [ [ $.1^23, $.1^7 ] ] [ [ $.1^23, $.1^10 ] ] [ [ $.1^23, $.1^11 ] ] [ [ $.1^23, $.1^12 ] ] [ [ $.1^23, $.1^18 ] ] [ [ $.1^23, $.1^21 ] ] [ [ $.1^24, $.1^5 ] ] [ [ $.1^24, $.1^8 ] ] [ [ $.1^24, $.1^15 ] ] [ [ $.1^24, $.1^17 ] ] [ [ $.1^24, $.1^19 ] ] [ [ $.1^24, $.1^20 ] ] [ [ $.1^24, $.1^23 ] ] [ [ $.1^24, $.1^24 ] ] [ [ $.1^24, $.1^25 ] ] [ [ $.1^25, $.1^2 ] ] [ [ $.1^25, $.1^4 ] ] [ [ $.1^25, $.1^6 ] ] [ [ $.1^25, $.1^7 ] ] [ [ $.1^25, $.1^10 ] ] [ [ $.1^25, $.1^11 ] ] [ [ $.1^25, $.1^12 ] ] [ [ $.1^25, $.1^18 ] ] [ [ $.1^25, $.1^21 ] ] [ [ 0, 1 ] ] [ [ 0, $.1 ] ] [ [ 0, $.1^3 ] ] [ [ 0, $.1^9 ] ] [ [ 0, 2 ] ] [ [ 0, $.1^14 ] ] [ [ 0, $.1^16 ] ] [ [ 0, $.1^22 ] ] [ [ 0, 0 ] ] 0 Total time: 3.059 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 11:38:41 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, (i,j)); end if; end for; end for; return C; end function; spolav:= [k : k in polavqr(4,1) | k[1] in GF(4) and k[2] in GF(4)]; #spolav; Output: Magma V2.10-6 Fri Mar 12 2004 11:38:38 on modular [Seed = 1752813545] ------------------------------------- [
:19]( q: 4, r: 1 ) >> if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, (i,j)) ^ Runtime error in elt< ... >: Bad arguments >> #spolav; ^ User error: Identifier 'spolav' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 11:39:01 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, {i,j}); end if; end for; end for; return C; end function; spolav:= [k : k in polavqr(4,1) | k[1] in GF(4) and k[2] in GF(4)]; #spolav; Output: Magma V2.10-6 Fri Mar 12 2004 11:38:58 on modular [Seed = 2121259475] ------------------------------------- [ { 1 } ] [ { $.1 } ] [ { $.1^2 } ] [ { 0 } ] 0 Total time: 3.079 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 200-BAR2-X4.libre.retevision.es. (62.82.186.200) Time: Fri Mar 12 11:39:04 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; #(polavqr(1,2)); 1^(2*2-1); spolav:= [k : k in polavqr(3,1) | k[1] in GF(3) and k[2] in GF(3)]; #spolav; Output: Magma V2.10-6 Fri Mar 12 2004 11:39:00 on modular [Seed = 2087574487] ------------------------------------- [
:19]( q: 1, r: 2 ) >> for i in GF(q^r) do ^ Runtime error in 'GF': Argument 1 (1) should be >= 2 1 [ [ 0, 0 ] ] [ [ 1, 1 ] ] [ [ 2, 2 ] ] 0 Total time: 3.209 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 11:39:29 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; spolav:= [k : k in polavqr(4,1) | k[1] in GF(4) and k[2] in GF(4)]; #spolav; Output: Magma V2.10-6 Fri Mar 12 2004 11:39:26 on modular [Seed = 2375821884] ------------------------------------- [ [ 1, 1 ] ] [ [ $.1, $.1 ] ] [ [ $.1^2, $.1^2 ] ] [ [ 0, 0 ] ] 0 Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 11:39:56 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; #polavqr(4,1); spolav:= [k : k in polavqr(4,1) | k[1] in GF(4) and k[2] in GF(4)]; #spolav; Output: Magma V2.10-6 Fri Mar 12 2004 11:39:53 on modular [Seed = 2207392853] ------------------------------------- [ [ 1, 1 ] ] [ [ $.1, $.1 ] ] [ [ $.1^2, $.1^2 ] ] [ [ 0, 0 ] ] 0 [ [ 1, 1 ] ] [ [ $.1, $.1 ] ] [ [ $.1^2, $.1^2 ] ] [ [ 0, 0 ] ] 0 Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host lupetti2.cs.uit.no. (129.242.18.56) Time: Fri Mar 12 11:40:02 2004 Input: F7 := FiniteField(7); Output: Magma V2.10-6 Fri Mar 12 2004 11:39:58 on modular [Seed = 2592816459] ------------------------------------- Total time: 3.179 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host lupetti2.cs.uit.no. (129.242.18.56) Time: Fri Mar 12 11:40:23 2004 Input: F7 := FiniteField(7);F49 := ext< F7 | 2 >; Output: Magma V2.10-6 Fri Mar 12 2004 11:40:20 on modular [Seed = 2695956315] ------------------------------------- Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 11:40:33 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; #polavqr(4,1); spolav:= [k : k in polavqr(4,1) | k[1] in GF(4) and k[2] in GF(4)]; #spolav; Output: Magma V2.10-6 Fri Mar 12 2004 11:40:30 on modular [Seed = 3081113670] ------------------------------------- >> C; ^ User error: Identifier 'C' has not been declared or assigned >> #polavqr(4,1); ^ User error: Identifier 'polavqr' has not been declared or assigned >> spolav:= [k : k in polavqr(4,1) | k[1] in GF(4) and k[2] in GF(4)]; ^ User error: Identifier 'polavqr' has not been declared or assigned >> #spolav; ^ User error: Identifier 'spolav' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 11:41:19 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=0; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; #polavqr(4,1); spolav:= [k : k in polavqr(4,1) | k[1] in GF(4) and k[2] in GF(4)]; #spolav; Output: Magma V2.10-6 Fri Mar 12 2004 11:41:16 on modular [Seed = 3437061359] ------------------------------------- [
:19]( q: 4, r: 1 ) >> if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]) ^ Runtime error in 'Include': Bad argument types Argument types given: RngIntElt, SeqEnum[FldFinElt] [
:19]( q: 4, r: 1 ) >> if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]) ^ Runtime error in 'Include': Bad argument types Argument types given: RngIntElt, SeqEnum[FldFinElt] >> #spolav; ^ User error: Identifier 'spolav' has not been declared or assigned Total time: 3.049 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 200-BAR2-X4.libre.retevision.es. (62.82.186.200) Time: Fri Mar 12 11:41:29 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; polavqr(1,2); 1^(2*2-1); spolav:= [k : k in polavqr(3,1) | k[1] in GF(3) and k[2] in GF(3)]; #spolav; Output: Magma V2.10-6 Fri Mar 12 2004 11:41:26 on modular [Seed = 3285347322] ------------------------------------- [
:19]( q: 1, r: 2 ) >> for i in GF(q^r) do ^ Runtime error in 'GF': Argument 1 (1) should be >= 2 1 [ [ 0, 0 ] ] [ [ 1, 1 ] ] [ [ 2, 2 ] ] 0 Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 11:41:34 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; #polavqr(4,1); spolav:= [k : k in polavqr(4,1) | k[1] in GF(4) and k[2] in GF(4)]; #spolav; Output: Magma V2.10-6 Fri Mar 12 2004 11:41:31 on modular [Seed = 3670766318] ------------------------------------- [ [ 1, 1 ] ] [ [ $.1, $.1 ] ] [ [ $.1^2, $.1^2 ] ] [ [ 0, 0 ] ] 0 [ [ 1, 1 ] ] [ [ $.1, $.1 ] ] [ [ $.1^2, $.1^2 ] ] [ [ 0, 0 ] ] 0 Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 200-BAR2-X4.libre.retevision.es. (62.82.186.200) Time: Fri Mar 12 11:42:31 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; #polavqr(9,5); 9^(5*2-1); spolav:= [k : k in polavqr(3,1) | k[1] in GF(3) and k[2] in GF(3)]; #spolav; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Mar 12 2004 11:42:08 on modular [Seed = 3519052222] ------------------------------------- [ [ 1, $.1^11 ] ] [ [ 1, $.1^17 ] ] [ [ 1, $.1^33 ] ] [ [ 1, $.1^38 ] ] [ [ 1, $.1^40 ] ] [ [ 1, $.1^51 ] ] [ [ 1, $.1^79 ] ] [ [ 1, $.1^88 ] ] [ [ 1, $.1^99 ] ] [ [ 1, $.1^110 ] ] [ [ 1, $.1^112 ] ] [ [ 1, $.1^113 ] ] [ [ 1, $.1^114 ] ] [ [ 1, $.1^120 ] ] [ [ 1, $.1^131 ] ] [ [ 1, $.1^136 ] ] [ [ 1, $.1^153 ] ] [ [ 1, $.1^161 ] ] [ [ 1, $.1^178 ] ] [ [ 1, $.1^190 ] ] [ [ 1, $.1^199 ] ] [ [ 1, $.1^212 ] ] [ [ 1, $.1^220 ] ] [ [ 1, $.1^230 ] ] [ [ 1, $.1^237 ] ] [ [ 1, $.1^239 ] ] [ [ 1, $.1^264 ] ] [ [ 1, $.1^271 ] ] [ [ 1, $.1^297 ] ] [ [ 1, $.1^323 ] ] [ [ 1, $.1^330 ] ] [ [ 1, $.1^336 ] ] [ [ 1, $.1^339 ] ] [ [ 1, $.1^342 ] ] [ [ 1, $.1^349 ] ] [ [ 1, $.1^355 ] ] [ [ 1, $.1^356 ] ] [ [ 1, $.1^360 ] ] [ [ 1, $.1^371 ] ] [ [ 1, $.1^373 ] ] [ [ 1, $.1^385 ] ] [ [ 1, $.1^393 ] ] [ [ 1, $.1^408 ] ] [ [ 1, $.1^412 ] ] [ [ 1, $.1^419 ] ] [ [ 1, $.1^459 ] ] [ [ 1, $.1^475 ] ] [ [ 1, $.1^483 ] ] [ [ 1, $.1^523 ] ] [ [ 1, $.1^530 ] ] [ [ 1, $.1^532 ] ] [ [ 1, $.1^534 ] ] [ [ 1, $.1^554 ] ] [ [ 1, $.1^556 ] ] [ [ 1, $.1^569 ] ] [ [ 1, $.1^570 ] ] [ [ 1, $.1^574 ] ] [ [ 1, $.1^589 ] ] [ [ 1, $.1^597 ] ] [ [ 1, $.1^604 ] ] [ [ 1, $.1^608 ] ] [ [ 1, $.1^611 ] ] [ [ 1, $.1^617 ] ] [ [ 1, $.1^632 ] ] [ [ 1, $.1^636 ] ] [ [ 1, $.1^660 ] ] [ [ 1, $.1^668 ] ] [ [ 1, $.1^685 ] ] [ [ 1, $.1^690 ] ] [ [ 1, $.1^711 ] ] [ [ 1, $.1^713 ] ] [ [ 1, $.1^717 ] ] [ [ 1, $.1^740 ] ] [ [ 1, $.1^754 ] ] [ [ 1, $.1^760 ] ] [ [ 1, $.1^775 ] ] [ [ 1, $.1^779 ] ] [ [ 1, $.1^791 ] ] [ [ 1, $.1^792 ] ] [ [ 1, $.1^813 ] ] [ [ 1, $.1^857 ] ] [ [ 1, $.1^877 ] ] [ [ 1, $.1^883 ] ] [ [ 1, $.1^889 ] ] [ [ 1, $.1^891 ] ] [ [ 1, $.1^892 ] ] [ [ 1, $.1^911 ] ] [ [ 1, $.1^913 ] ] [ [ 1, $.1^916 ] ] [ [ 1, $.1^925 ] ] [ [ 1, $.1^926 ] ] [ [ 1, $.1^950 ] ] [ [ 1, $.1^964 ] ] [ [ 1, $.1^967 ] ] [ [ 1, $.1^969 ] ] [ [ 1, $.1^976 ] ] [ [ 1, $.1^990 ] ] [ [ 1, $.1^1008 ] ] [ [ 1, $.1^1017 ] ] [ [ 1, $.1^1021 ] ] [ [ 1, $.1^1026 ] ] [ [ 1, $.1^1039 ] ] [ [ 1, $.1^1045 ] ] [ [ 1, $.1^1047 ] ] [ [ 1, $.1^1065 ] ] [ [ 1, $.1^1068 ] ] [ [ 1, $.1^1080 ] ] [ [ 1, $.1^1087 ] ] [ [ 1, $.1^1096 ] ] [ [ 1, $.1^1105 ] ] [ [ 1, $.1^1113 ] ] [ [ 1, $.1^1119 ] ] [ [ 1, $.1^1127 ] ] [ [ 1, $.1^1130 ] ] [ [ 1, $.1^1150 ] ] [ [ 1, $.1^1155 ] ] [ [ 1, $.1^1160 ] ] [ [ 1, $.1^1165 ] ] [ [ 1, $.1^1178 ] ] [ [ 1, $.1^1179 ] ] [ [ 1, $.1^1184 ] ] [ [ 1, $.1^1208 ] ] [ [ 1, $.1^1210 ] ] [ [ 1, $.1^1220 ] ] [ [ 1, $.1^1224 ] ] [ [ 1, $.1^1231 ] ] [ [ 1, $.1^1236 ] ] [ [ 1, $.1^1240 ] ] [ [ 1, $.1^1255 ] ] [ [ 1, $.1^1257 ] ] [ [ 1, $.1^1265 ] ] [ [ 1, $.1^1274 ] ] [ [ 1, $.1^1294 ] ] [ [ 1, $.1^1306 ] ] [ [ 1, $.1^1309 ] ] [ [ 1, $.1^1316 ] ] [ [ 1, $.1^1318 ] ] [ [ 1, $.1^1330 ] ] [ [ 1, $.1^1373 ] ] [ [ 1, $.1^1377 ] ] [ [ 1, $.1^1384 ] ] [ [ 1, $.1^1385 ] ] [ [ 1, $.1^1391 ] ] [ [ 1, $.1^1393 ] ] [ [ 1, $.1^1408 ] ] [ [ 1, $.1^1415 ] ] [ [ 1, $.1^1425 ] ] [ [ 1, $.1^1449 ] ] [ [ 1, $.1^1465 ] ] [ [ 1, $.1^1501 ] ] [ [ 1, $.1^1502 ] ] [ [ 1, $.1^1522 ] ] [ [ 1, $.1^1537 ] ] [ [ 1, $.1^1564 ] ] [ [ 1, $.1^1569 ] ] [ [ 1, $.1^1585 ] ] [ [ 1, $.1^1590 ] ] [ [ 1, $.1^1596 ] ] [ [ 1, $.1^1602 ] ] [ [ 1, $.1^1613 ] ] [ [ 1, $.1^1639 ] ] [ [ 1, $.1^1643 ] ] [ [ 1, $.1^1651 ] ] [ [ 1, $.1^1662 ] ] [ [ 1, $.1^1663 ] ] [ [ 1, $.1^1668 ] ] [ [ 1, $.1^1678 ] ] [ [ 1, $.1^1687 ] ] [ [ 1, $.1^1694 ] ] [ [ 1, $.1^1699 ] ] [ [ 1, $.1^1707 ] ] [ [ 1, $.1^1710 ] ] [ [ 1, $.1^1715 ] ] [ [ 1, $.1^1717 ] ] [ [ 1, $.1^1722 ] ] [ [ 1, $.1^1726 ] ] [ [ 1, $.1^1744 ] ] [ [ 1, $.1^1751 ] ] [ [ 1, $.1^1767 ] ] [ [ 1, $.1^1791 ] ] [ [ 1, $.1^1812 ] ] [ [ 1, $.1^1819 ] ] [ [ 1, $.1^1823 ] ] [ [ 1, $.1^1824 ] ] [ [ 1, $.1^1833 ] ] [ [ 1, $.1^1851 ] ] [ [ 1, $.1^1852 ] ] [ [ 1, $.1^1870 ] ] [ [ 1, $.1^1874 ] ] [ [ 1, $.1^1879 ] ] [ [ 1, $.1^1896 ] ] [ [ 1, $.1^1898 ] ] [ [ 1, $.1^1908 ] ] [ [ 1, $.1^1924 ] ] [ [ 1, $.1^1930 ] ] [ [ 1, $.1^1936 ] ] [ [ 1, $.1^1952 ] ] [ [ 1, $.1^1954 ] ] [ [ 1, $.1^1955 ] ] [ [ 1, $.1^1958 ] ] [ [ 1, $.1^1961 ] ] [ [ 1, $.1^1975 ] ] [ [ 1, $.1^1980 ] ] [ [ 1, $.1^1990 ] ] [ [ 1, $.1^1991 ] ] [ [ 1, $.1^2003 ] ] [ [ 1, $.1^2004 ] ] [ [ 1, $.1^2009 ] ] [ [ 1, $.1^2011 ] ] [ [ 1, $.1^2014 ] ] [ [ 1, $.1^2026 ] ] [ [ 1, $.1^2035 ] ] [ [ 1, $.1^2055 ] ] [ [ 1, $.1^2059 ] ] [ [ 1, $.1^2070 ] ] [ [ 1, $.1^2080 ] ] [ [ 1, $.1^2084 ] ] [ [ 1, $.1^2133 ] ] [ [ 1, $.1^2138 ] ] [ [ 1, $.1^2139 ] ] [ [ 1, $.1^2150 ] ] [ [ 1, $.1^2151 ] ] [ [ 1, $.1^2158 ] ] [ [ 1, $.1^2173 ] ] [ [ 1, $.1^2180 ] ] [ [ 1, $.1^2192 ] ] [ [ 1, $.1^2194 ] ] [ [ 1, $.1^2197 ] ] [ [ 1, $.1^2220 ] ] [ [ 1, $.1^2262 ] ] [ [ 1, $.1^2264 ] ] [ [ 1, $.1^2273 ] ] [ [ 1, $.1^2275 ] ] [ [ 1, $.1^2280 ] ] [ [ 1, $.1^2287 ] ] [ [ 1, $.1^2294 ] ] [ [ 1, $.1^2314 ] ] [ [ 1, $.1^2323 ] ] [ [ 1, $.1^2325 ] ] [ [ 1, $.1^2329 ] ] [ [ 1, $.1^2337 ] ] [ [ 1, $.1^2342 ] ] [ [ 1, $.1^2345 ] ] [ [ 1, $.1^2354 ] ] [ [ 1, $.1^2360 ] ] [ [ 1, $.1^2362 ] ] [ [ 1, $.1^2371 ] ] [ [ 1, $.1^2373 ] ] [ [ 1, $.1^2376 ] ] [ [ 1, $.1^2377 ] ] [ [ 1, $.1^2399 ] ] [ [ 1, $.1^2401 ] ] [ [ 1, $.1^2425 ] ] [ [ 1, $.1^2438 ] ] [ [ 1, $.1^2439 ] ] [ [ 1, $.1^2462 ] ] [ [ 1, $.1^2486 ] ] [ [ 1, $.1^2492 ] ] [ [ 1, $.1^2495 ] ] [ [ 1, $.1^2512 ] ] [ [ 1, $.1^2522 ] ] [ [ 1, $.1^2527 ] ] [ [ 1, $.1^2567 ] ] [ [ 1, $.1^2569 ] ] [ [ 1, $.1^2571 ] ] [ [ 1, $.1^2581 ] ] [ [ 1, $.1^2603 ] ] [ [ 1, $.1^2631 ] ] [ [ 1, $.1^2633 ] ] [ [ 1, $.1^2635 ] ] [ [ 1, $.1^2649 ] ] [ [ 1, $.1^2657 ] ] [ [ 1, $.1^2667 ] ] [ [ 1, $.1^2673 ] ] [ [ 1, $.1^2676 ] ] [ [ 1, $.1^2681 ] ] [ [ 1, $.1^2701 ] ] [ [ 1, $.1^2713 ] ] [ [ 1, $.1^2716 ] ] [ [ 1, $.1^2723 ] ] [ [ 1, $.1^2725 ] ] [ [ 1, $.1^2732 ] ] [ [ 1, $.1^2733 ] ] [ [ 1, $.1^2735 ] ] [ [ 1, $.1^2739 ] ] [ [ 1, $.1^2744 ] ] [ [ 1, $.1^2748 ] ] [ [ 1, $.1^2773 ] ] [ [ 1, $.1^2775 ] ] [ [ 1, $.1^2778 ] ] [ [ 1, $.1^2800 ] ] [ [ 1, $.1^2818 ] ] [ [ 1, $.1^2825 ] ] [ [ 1, $.1^2843 ] ] [ [ 1, $.1^2850 ] ] [ [ 1, $.1^2872 ] ] [ [ 1, $.1^2876 ] ] [ [ 1, $.1^2890 ] ] [ [ 1, $.1^2892 ] ] [ [ 1, $.1^2897 ] ] [ [ 1, $.1^2900 ] ] [ [ 1, $.1^2901 ] ] [ [ 1, $.1^2907 ] ] [ [ 1, $.1^2914 ] ] [ [ 1, $.1^2928 ] ] [ [ 1, $.1^2966 ] ] [ [ 1, $.1^2970 ] ] [ [ 1, $.1^3024 ] ] [ [ 1, $.1^3034 ] ] [ [ 1, $.1^3037 ] ] [ [ 1, $.1^3043 ] ] [ [ 1, $.1^3051 ] ] [ [ 1, $.1^3061 ] ] [ [ 1, $.1^3063 ] ] [ [ 1, $.1^3077 ] ] [ [ 1, $.1^3078 ] ] [ [ 1, $.1^3091 ] ] [ [ 1, $.1^3116 ] ] [ [ 1, $.1^3117 ] ] [ [ 1, $.1^3118 ] ] [ [ 1, $.1^3135 ] ] [ [ 1, $.1^3137 ] ] [ [ 1, $.1^3141 ] ] [ [ 1, $.1^3152 ] ] [ [ 1, $.1^3181 ] ] [ [ 1, $.1^3182 ] ] [ [ 1, $.1^3185 ] ] [ [ 1, $.1^3190 ] ] [ [ 1, $.1^3193 ] ] [ [ 1, $.1^3195 ] ] [ [ 1, $.1^3202 ] ] [ [ 1, $.1^3204 ] ] [ [ 1, $.1^3206 ] ] [ [ 1, $.1^3212 ] ] [ [ 1, $.1^3217 ] ] [ [ 1, $.1^3240 ] ] [ [ 1, $.1^3257 ] ] [ [ 1, $.1^3261 ] ] [ [ 1, $.1^3288 ] ] [ [ 1, $.1^3305 ] ] [ [ 1, $.1^3315 ] ] [ [ 1, $.1^3326 ] ] [ [ 1, $.1^3339 ] ] [ [ 1, $.1^3343 ] ] [ [ 1, $.1^3352 ] ] [ [ 1, $.1^3357 ] ] [ [ 1, $.1^3359 ] ] [ [ 1, $.1^3365 ] ] [ [ 1, $.1^3374 ] ] [ [ 1, $.1^3377 ] ] [ [ 1, $.1^3379 ] ] [ [ 1, $.1^3381 ] ] [ [ 1, $.1^3382 ] ] [ [ 1, $.1^3390 ] ] [ [ 1, $.1^3392 ] ] [ [ 1, $.1^3394 ] ] [ [ 1, $.1^3409 ] ] [ [ 1, $.1^3410 ] ] [ [ 1, $.1^3425 ] ] [ [ 1, $.1^3430 ] ] [ [ 1, $.1^3445 ] ] [ [ 1, $.1^3450 ] ] [ [ 1, $.1^3451 ] ] [ [ 1, $.1^3460 ] ] [ [ 1, $.1^3465 ] ] [ [ 1, $.1^3470 ] ] [ [ 1, $.1^3480 ] ] [ [ 1, $.1^3485 ] ] [ [ 1, $.1^3495 ] ] [ [ 1, $.1^3500 ] ] [ [ 1, $.1^3515 ] ] [ [ 1, $.1^3517 ] ] [ [ 1, $.1^3527 ] ] [ [ 1, $.1^3530 ] ] [ [ 1, $.1^3534 ] ] [ [ 1, $.1^3536 ] ] [ [ 1, $.1^3537 ] ] [ [ 1, $.1^3539 ] ] [ [ 1, $.1^3552 ] ] [ [ 1, $.1^3559 ] ] [ [ 1, $.1^3566 ] ] [ [ 1, $.1^3574 ] ] [ [ 1, $.1^3575 ] ] [ [ 1, $.1^3614 ] ] [ [ 1, $.1^3620 ] ] [ [ 1, $.1^3624 ] ] [ [ 1, $.1^3630 ] ] [ [ 1, $.1^3643 ] ] [ [ 1, $.1^3660 ] ] [ [ 1, $.1^3672 ] ] [ [ 1, $.1^3673 ] ] [ [ 1, $.1^3674 ] ] [ [ 1, $.1^3686 ] ] [ [ 1, $.1^3693 ] ] [ [ 1, $.1^3694 ] ] [ [ 1, $.1^3708 ] ] [ [ 1, $.1^3709 ] ] [ [ 1, $.1^3719 ] ] [ [ 1, $.1^3720 ] ] [ [ 1, $.1^3727 ] ] [ [ 1, $.1^3752 ] ] [ [ 1, $.1^3765 ] ] [ [ 1, $.1^3770 ] ] [ [ 1, $.1^3771 ] ] [ [ 1, $.1^3795 ] ] [ [ 1, $.1^3803 ] ] [ [ 1, $.1^3822 ] ] [ [ 1, $.1^3827 ] ] [ [ 1, $.1^3835 ] ] [ [ 1, $.1^3854 ] ] [ [ 1, $.1^3866 ] ] [ [ 1, $.1^3871 ] ] [ [ 1, $.1^3882 ] ] [ [ 1, $.1^3893 ] ] [ [ 1, $.1^3895 ] ] [ [ 1, $.1^3904 ] ] [ ** WARNING: Output too long, hence truncated. Errors: /home/mfd/gomagma: line 2: 20446 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 11:43:07 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, i); end if; end for; end for; return C; end function; spolav:= [k : k in polavqr(4,1) | k[1] in GF(4) and k[2] in GF(4)]; #spolav; Output: Magma V2.10-6 Fri Mar 12 2004 11:43:04 on modular [Seed = 3908649087] ------------------------------------- [ 1 ] [ $.1 ] [ $.1^2 ] [ 0 ] 0 Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 200-BAR2-X4.libre.retevision.es. (62.82.186.200) Time: Fri Mar 12 11:43:14 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; #polavqr(3,2); 3^(2*2-1); spolav:= [k : k in polavqr(3,1) | k[1] in GF(3) and k[2] in GF(3)]; #spolav; Output: Magma V2.10-6 Fri Mar 12 2004 11:43:11 on modular [Seed = 4277098094] ------------------------------------- [ [ 1, $.1 ] ] [ [ 1, $.1^3 ] ] [ [ 1, 2 ] ] [ [ $.1, 1 ] ] [ [ $.1, $.1^5 ] ] [ [ $.1, $.1^7 ] ] [ [ $.1^2, $.1 ] ] [ [ $.1^2, $.1^3 ] ] [ [ $.1^2, 2 ] ] [ [ $.1^3, 1 ] ] [ [ $.1^3, $.1^5 ] ] [ [ $.1^3, $.1^7 ] ] [ [ 2, $.1 ] ] [ [ 2, $.1^3 ] ] [ [ 2, 2 ] ] [ [ $.1^5, 1 ] ] [ [ $.1^5, $.1^5 ] ] [ [ $.1^5, $.1^7 ] ] [ [ $.1^6, $.1 ] ] [ [ $.1^6, $.1^3 ] ] [ [ $.1^6, 2 ] ] [ [ $.1^7, 1 ] ] [ [ $.1^7, $.1^5 ] ] [ [ $.1^7, $.1^7 ] ] [ [ 0, $.1^2 ] ] [ [ 0, $.1^6 ] ] [ [ 0, 0 ] ] 0 27 [ [ 0, 0 ] ] [ [ 1, 1 ] ] [ [ 2, 2 ] ] 0 Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 11:43:27 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, i); end if; end for; end for; return C; end function; spolav:= [k : k in polavqr(4,1) | k[1] in GF(4) and k[2] in GF(4)]; #spolav; Output: Magma V2.10-6 Fri Mar 12 2004 11:43:24 on modular [Seed = 4125384022] ------------------------------------- [ 1 ] [ $.1 ] [ $.1^2 ] [ 0 ] 0 Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host lupetti2.cs.uit.no. (129.242.18.56) Time: Fri Mar 12 11:48:28 2004 Input: F := FiniteField(37, 9); Output: Magma V2.10-6 Fri Mar 12 2004 11:48:25 on modular [Seed = 419999952] ------------------------------------- Total time: 2.979 seconds, Total memory usage: 2.40MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 11:53:18 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return [C]; end function; spolav:= [k : k in polavqr(4,1) | k[1] in GF(4) and k[2] in GF(4)]; #spolav; Output: Magma V2.10-6 Fri Mar 12 2004 11:53:15 on modular [Seed = 203269863] ------------------------------------- [ [ 1, 1 ] ] [ [ $.1, $.1 ] ] [ [ $.1^2, $.1^2 ] ] [ [ 0, 0 ] ] >> spolav:= [k : k in polavqr(4,1) | k[1] in GF(4) and k[2] in GF(4)]; ^ Runtime error in '[]': Sequence element 1 not defined >> #spolav; ^ User error: Identifier 'spolav' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 11:53:39 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; spolav:= [k : k in polavqr(4,1) | k[1] in GF(4) and k[2] in GF(4)]; #spolav; Output: Magma V2.10-6 Fri Mar 12 2004 11:53:36 on modular [Seed = 891592245] ------------------------------------- [ [ 1, 1 ] ] [ [ $.1, $.1 ] ] [ [ $.1^2, $.1^2 ] ] [ [ 0, 0 ] ] 0 Total time: 3.039 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 11:53:50 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; spolav:= [k : k in polavqr(4,1) | k[1] in GF(4) and k[2] in GF(4)]; #spolav; Output: Magma V2.10-6 Fri Mar 12 2004 11:53:47 on modular [Seed = 1043305781] ------------------------------------- [ [ 1, 1 ] ] [ [ $.1, $.1 ] ] [ [ $.1^2, $.1^2 ] ] [ [ 0, 0 ] ] 0 Total time: 3.119 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 11:57:29 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; spolav:= [k : k in polavqr(4,1) | k[1] in GF(4) and k[2] in GF(4)]; #spolav; l:=[]; Insert(l,3); l; Output: Magma V2.10-6 Fri Mar 12 2004 11:57:26 on modular [Seed = 1885461398] ------------------------------------- [ [ 1, 1 ] ] [ [ $.1, $.1 ] ] [ [ $.1^2, $.1^2 ] ] [ [ 0, 0 ] ] 0 >> Insert(l,3); ^ Runtime error in 'Insert': Bad argument types Argument types given: SeqEnum[], RngIntElt [] Total time: 3.089 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 11:57:50 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; spolav:= [k : k in polavqr(4,1) | k[1] in GF(4) and k[2] in GF(4)]; #spolav; l:=[]; Insert(l,3); l; Output: Magma V2.10-6 Fri Mar 12 2004 11:57:47 on modular [Seed = 2104283494] ------------------------------------- [ [ 1, 1 ] ] [ [ $.1, $.1 ] ] [ [ $.1^2, $.1^2 ] ] [ [ 0, 0 ] ] 0 >> Insert(l,3); ^ Runtime error in 'Insert': Bad argument types Argument types given: SeqEnum[], RngIntElt [] Total time: 3.039 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 11:58:08 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; spolav:= [k : k in polavqr(4,1) | k[1] in GF(4) and k[2] in GF(4)]; #spolav; L:=[]; Insert(L,3); L; Output: Magma V2.10-6 Fri Mar 12 2004 11:58:05 on modular [Seed = 1719126635] ------------------------------------- [ [ 1, 1 ] ] [ [ $.1, $.1 ] ] [ [ $.1^2, $.1^2 ] ] [ [ 0, 0 ] ] 0 >> Insert(L,3); ^ Runtime error in 'Insert': Bad argument types Argument types given: SeqEnum[], RngIntElt [] Total time: 3.099 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 11:58:53 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; spolav:= [k : k in polavqr(4,1) | k[1] in GF(4) and k[2] in GF(4)]; #spolav; L:=[]; Include(L,3); L; Output: Magma V2.10-6 Fri Mar 12 2004 11:58:50 on modular [Seed = 1870578485] ------------------------------------- [ [ 1, 1 ] ] [ [ $.1, $.1 ] ] [ [ $.1^2, $.1^2 ] ] [ [ 0, 0 ] ] 0 [ 3 ] [] Total time: 3.069 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 11:59:29 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; spolav:= [k : k in polavqr(4,1) | k[1] in GF(4) and k[2] in GF(4)]; #spolav; L:=[]; L:=L+3; L; Include(L,3); L; Output: Magma V2.10-6 Fri Mar 12 2004 11:59:26 on modular [Seed = 2559128806] ------------------------------------- [ [ 1, 1 ] ] [ [ $.1, $.1 ] ] [ [ $.1^2, $.1^2 ] ] [ [ 0, 0 ] ] 0 >> L:=L+3; ^ Runtime error in '+': Bad argument types Argument types given: SeqEnum[], RngIntElt [] [ 3 ] [] Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Fri Mar 12 11:59:43 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; spolav:= [k : k in polavqr(4,1) | k[1] in GF(4) and k[2] in GF(4)]; #spolav; L:=[]; L:=L&3; L; Include(L,3); L; Output: Magma V2.10-6 Fri Mar 12 2004 11:59:40 on modular [Seed = 2190683886] ------------------------------------- [ [ 1, 1 ] ] [ [ $.1, $.1 ] ] [ [ $.1^2, $.1^2 ] ] [ [ 0, 0 ] ] 0 >> L:=L&3; ^ User error: Bad reduction operator [] [ 3 ] [] Total time: 3.059 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 12:02:18 2004 Input: R := GF(4); M := MatrixRing(R,2); Mt := {A : A in M | Trace(A) eq 0}; Mf := {A : A in M | A[1] eq A[2]}; Mtf := Mt meet Mf; rand := [Random(M): num in [1..100000]]; #([A: A in rand | A in Mt]); Output: Magma V2.10-6 Fri Mar 12 2004 12:02:14 on modular [Seed = 2813725345] ------------------------------------- 25053 Total time: 3.689 seconds, Total memory usage: 6.95MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 12:04:13 2004 Input: R := GF(4); M := MatrixRing(R,2); Mt := {A : A in M | Trace(A) eq 0}; Mf := {A : A in M | A[1] eq A[2]}; Mtf := Mt meet Mf; rand := [Random(M): num in [1..100000]]; #([A: A in rand | A in Mf]); Output: Magma V2.10-6 Fri Mar 12 2004 12:04:10 on modular [Seed = 3519052875] ------------------------------------- 6312 Total time: 3.659 seconds, Total memory usage: 6.95MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 12:04:59 2004 Input: R := GF(4); M := MatrixRing(R,2); Mt := {A : A in M | Trace(A) eq 0}; Mf := {A : A in M | A[1] eq A[2]}; Mtf := Mt meet Mf; rand := [Random(M): num in [1..100000]]; #([A: A in rand | A in Mtf]); Output: Magma V2.10-6 Fri Mar 12 2004 12:04:55 on modular [Seed = 3687478908] ------------------------------------- 1581 Total time: 3.669 seconds, Total memory usage: 6.95MB ************** MAGMA ***************** Host 200-BAR2-X4.libre.retevision.es. (62.82.186.200) Time: Fri Mar 12 12:07:15 2004 Input: polav73:=function() C:=[]; for i in GF(7^3) do for j in GF(7^3) do if (Evaluate(pn73(),i) eq Evaluate(pt73(),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; polav73(); Output: Magma V2.10-6 Fri Mar 12 2004 12:07:12 on modular [Seed = 3386402713] ------------------------------------- >> if (Evaluate(pn73(),i) eq Evaluate(pt73(),j) ) then Include(C, [i,j]); ^ User error: Identifier 'pn73' has not been declared or assigned >> polav73();; ^ User error: Identifier 'polav73' has not been declared or assigned Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 200-BAR2-X4.libre.retevision.es. (62.82.186.200) Time: Fri Mar 12 12:08:28 2004 Input: pt73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+x^(7^(3-i)); end for; return C; end function; pn73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+(7^(3-i)); end for; return x^C; end function; polav73:=function() C:=[]; for i in GF(7^3) do for j in GF(7^3) do if (Evaluate(pn73(),i) eq Evaluate(pt73(),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; polav73(); Output: Magma V2.10-6 Fri Mar 12 2004 12:08:06 on modular [Seed = 302234741] ------------------------------------- [ [ 1, $.1 ] ] [ [ 1, $.1^2 ] ] [ [ 1, $.1^7 ] ] [ [ 1, $.1^10 ] ] [ [ 1, $.1^11 ] ] [ [ 1, $.1^14 ] ] [ [ 1, $.1^16 ] ] [ [ 1, $.1^25 ] ] [ [ 1, $.1^37 ] ] [ [ 1, $.1^49 ] ] [ [ 1, $.1^66 ] ] [ [ 1, $.1^70 ] ] [ [ 1, $.1^77 ] ] [ [ 1, $.1^87 ] ] [ [ 1, $.1^90 ] ] [ [ 1, $.1^97 ] ] [ [ 1, $.1^98 ] ] [ [ 1, $.1^100 ] ] [ [ 1, $.1^103 ] ] [ [ 1, $.1^112 ] ] [ [ 1, $.1^120 ] ] [ [ 1, $.1^131 ] ] [ [ 1, $.1^132 ] ] [ [ 1, $.1^137 ] ] [ [ 1, $.1^146 ] ] [ [ 1, $.1^148 ] ] [ [ 1, $.1^156 ] ] [ [ 1, $.1^159 ] ] [ [ 1, $.1^175 ] ] [ [ 1, $.1^195 ] ] [ [ 1, $.1^197 ] ] [ [ 1, $.1^199 ] ] [ [ 1, $.1^215 ] ] [ [ 1, $.1^233 ] ] [ [ 1, $.1^240 ] ] [ [ 1, $.1^259 ] ] [ [ 1, $.1^263 ] ] [ [ 1, $.1^267 ] ] [ [ 1, $.1^275 ] ] [ [ 1, 5 ] ] [ [ 1, $.1^288 ] ] [ [ 1, $.1^306 ] ] [ [ 1, $.1^307 ] ] [ [ 1, $.1^312 ] ] [ [ 1, $.1^314 ] ] [ [ 1, $.1^321 ] ] [ [ 1, $.1^337 ] ] [ [ 1, $.1^338 ] ] [ [ 1, $.1^339 ] ] [ [ $.1, 1 ] ] [ [ $.1, $.1^3 ] ] [ [ $.1, $.1^21 ] ] [ [ $.1, $.1^22 ] ] [ [ $.1, $.1^27 ] ] [ [ $.1, $.1^29 ] ] [ [ $.1, $.1^36 ] ] [ [ $.1, $.1^52 ] ] [ [ $.1, $.1^53 ] ] [ [ $.1, $.1^54 ] ] [ [ $.1, $.1^58 ] ] [ [ $.1, $.1^59 ] ] [ [ $.1, $.1^64 ] ] [ [ $.1, $.1^67 ] ] [ [ $.1, $.1^68 ] ] [ [ $.1, $.1^71 ] ] [ [ $.1, $.1^73 ] ] [ [ $.1, $.1^82 ] ] [ [ $.1, $.1^94 ] ] [ [ $.1, $.1^106 ] ] [ [ $.1, $.1^123 ] ] [ [ $.1, $.1^127 ] ] [ [ $.1, $.1^134 ] ] [ [ $.1, $.1^144 ] ] [ [ $.1, $.1^147 ] ] [ [ $.1, $.1^154 ] ] [ [ $.1, $.1^155 ] ] [ [ $.1, $.1^157 ] ] [ [ $.1, $.1^160 ] ] [ [ $.1, $.1^169 ] ] [ [ $.1, $.1^177 ] ] [ [ $.1, $.1^188 ] ] [ [ $.1, $.1^189 ] ] [ [ $.1, $.1^194 ] ] [ [ $.1, $.1^203 ] ] [ [ $.1, $.1^205 ] ] [ [ $.1, $.1^213 ] ] [ [ $.1, $.1^216 ] ] [ [ $.1, $.1^232 ] ] [ [ $.1, $.1^252 ] ] [ [ $.1, $.1^254 ] ] [ [ $.1, $.1^256 ] ] [ [ $.1, $.1^272 ] ] [ [ $.1, $.1^290 ] ] [ [ $.1, $.1^297 ] ] [ [ $.1, $.1^316 ] ] [ [ $.1, $.1^320 ] ] [ [ $.1, $.1^324 ] ] [ [ $.1, $.1^332 ] ] [ [ $.1^2, $.1^5 ] ] [ [ $.1^2, $.1^12 ] ] [ [ $.1^2, $.1^31 ] ] [ [ $.1^2, $.1^35 ] ] [ [ $.1^2, $.1^39 ] ] [ [ $.1^2, $.1^47 ] ] [ [ $.1^2, 3 ] ] [ [ $.1^2, $.1^60 ] ] [ [ $.1^2, $.1^78 ] ] [ [ $.1^2, $.1^79 ] ] [ [ $.1^2, $.1^84 ] ] [ [ $.1^2, $.1^86 ] ] [ [ $.1^2, $.1^93 ] ] [ [ $.1^2, $.1^109 ] ] [ [ $.1^2, $.1^110 ] ] [ [ $.1^2, $.1^111 ] ] [ [ $.1^2, $.1^115 ] ] [ [ $.1^2, $.1^116 ] ] [ [ $.1^2, $.1^121 ] ] [ [ $.1^2, $.1^124 ] ] [ [ $.1^2, $.1^125 ] ] [ [ $.1^2, $.1^128 ] ] [ [ $.1^2, $.1^130 ] ] [ [ $.1^2, $.1^139 ] ] [ [ $.1^2, $.1^151 ] ] [ [ $.1^2, $.1^163 ] ] [ [ $.1^2, $.1^180 ] ] [ [ $.1^2, $.1^184 ] ] [ [ $.1^2, $.1^191 ] ] [ [ $.1^2, $.1^201 ] ] [ [ $.1^2, $.1^204 ] ] [ [ $.1^2, $.1^211 ] ] [ [ $.1^2, $.1^212 ] ] [ [ $.1^2, $.1^214 ] ] [ [ $.1^2, $.1^217 ] ] [ [ $.1^2, $.1^226 ] ] [ [ $.1^2, $.1^234 ] ] [ [ $.1^2, $.1^245 ] ] [ [ $.1^2, $.1^246 ] ] [ [ $.1^2, $.1^251 ] ] [ [ $.1^2, $.1^260 ] ] [ [ $.1^2, $.1^262 ] ] [ [ $.1^2, $.1^270 ] ] [ [ $.1^2, $.1^273 ] ] [ [ $.1^2, $.1^289 ] ] [ [ $.1^2, $.1^309 ] ] [ [ $.1^2, $.1^311 ] ] [ [ $.1^2, $.1^313 ] ] [ [ $.1^2, $.1^329 ] ] [ [ $.1^3, $.1^4 ] ] [ [ $.1^3, $.1^24 ] ] [ [ $.1^3, $.1^26 ] ] [ [ $.1^3, $.1^28 ] ] [ [ $.1^3, $.1^44 ] ] [ [ $.1^3, $.1^62 ] ] [ [ $.1^3, $.1^69 ] ] [ [ $.1^3, $.1^88 ] ] [ [ $.1^3, $.1^92 ] ] [ [ $.1^3, $.1^96 ] ] [ [ $.1^3, $.1^104 ] ] [ [ $.1^3, 2 ] ] [ [ $.1^3, $.1^117 ] ] [ [ $.1^3, $.1^135 ] ] [ [ $.1^3, $.1^136 ] ] [ [ $.1^3, $.1^141 ] ] [ [ $.1^3, $.1^143 ] ] [ [ $.1^3, $.1^150 ] ] [ [ $.1^3, $.1^166 ] ] [ [ $.1^3, $.1^167 ] ] [ [ $.1^3, $.1^168 ] ] [ [ $.1^3, $.1^172 ] ] [ [ $.1^3, $.1^173 ] ] [ [ $.1^3, $.1^178 ] ] [ [ $.1^3, $.1^181 ] ] [ [ $.1^3, $.1^182 ] ] [ [ $.1^3, $.1^185 ] ] [ [ $.1^3, $.1^187 ] ] [ [ $.1^3, $.1^196 ] ] [ [ $.1^3, $.1^208 ] ] [ [ $.1^3, $.1^220 ] ] [ [ $.1^3, $.1^237 ] ] [ [ $.1^3, $.1^241 ] ] [ [ $.1^3, $.1^248 ] ] [ [ $.1^3, $.1^258 ] ] [ [ $.1^3, $.1^261 ] ] [ [ $.1^3, $.1^268 ] ] [ [ $.1^3, $.1^269 ] ] [ [ $.1^3, $.1^271 ] ] [ [ $.1^3, $.1^274 ] ] [ [ $.1^3, $.1^283 ] ] [ [ $.1^3, $.1^291 ] ] [ [ $.1^3, $.1^302 ] ] [ [ $.1^3, $.1^303 ] ] [ [ $.1^3, $.1^308 ] ] [ [ $.1^3, $.1^317 ] ] [ [ $.1^3, $.1^319 ] ] [ [ $.1^3, $.1^327 ] ] [ [ $.1^3, $.1^330 ] ] [ [ $.1^4, $.1^6 ] ] [ [ $.1^4, $.1^17 ] ] [ [ $.1^4, $.1^18 ] ] [ [ $.1^4, $.1^23 ] ] [ [ $.1^4, $.1^32 ] ] [ [ $.1^4, $.1^34 ] ] [ [ $.1^4, $.1^42 ] ] [ [ $.1^4, $.1^45 ] ] [ [ $.1^4, $.1^61 ] ] [ [ $.1^4, $.1^81 ] ] [ [ $.1^4, $.1^83 ] ] [ [ $.1^4, $.1^85 ] ] [ [ $.1^4, $.1^101 ] ] [ [ $.1^4, $.1^119 ] ] [ [ $.1^4, $.1^126 ] ] [ [ $.1^4, $.1^145 ] ] [ [ $.1^4, $.1^149 ] ] [ [ $.1^4, $.1^153 ] ] [ [ $.1^4, $.1^161 ] ] [ [ $.1^4, 6 ] ] [ [ $.1^4, $.1^174 ] ] [ [ $.1^4, $.1^192 ] ] [ [ $.1^4, $.1^193 ] ] [ [ $.1^4, $.1^198 ] ] [ [ $.1^4, $.1^200 ] ] [ [ $.1^4, $.1^207 ] ] [ [ $.1^4, $.1^223 ] ] [ [ $.1^4, $.1^224 ] ] [ [ $.1^4, $.1^225 ] ] [ [ $.1^4, $.1^229 ] ] [ [ $.1^4, $.1^230 ] ] [ [ $.1^4, $.1^235 ] ] [ [ $.1^4, $.1^238 ] ] [ [ $.1^4, $.1^239 ] ] [ [ $.1^4, $.1^242 ] ] [ [ $.1^4, $.1^244 ] ] [ [ $.1^4, $.1^253 ] ] [ [ $.1^4, $.1^265 ] ] [ [ $.1^4, $.1^277 ] ] [ [ $.1^4, $.1^294 ] ] [ [ $.1^4, $.1^298 ] ] [ [ $.1^4, $.1^305 ] ] [ [ $.1^4, $.1^315 ] ] [ [ $.1^4, $.1^318 ] ] [ [ $.1^4, $.1^325 ] ] [ [ $.1^4, $.1^326 ] ] [ [ $.1^4, $.1^328 ] ] [ [ $.1^4, $.1^331 ] ] [ [ $.1^4, $.1^340 ] ] [ [ $.1^5, $.1^9 ] ] [ [ $.1^5, $.1^13 ] ] [ [ $.1^5, $.1^20 ] ] [ [ $.1^5, $.1^30 ] ] [ [ $.1^5, $.1^33 ] ] [ [ $.1^5, $.1^40 ] ] [ [ $.1^5, $.1^41 ] ] [ [ $.1^5, $.1^43 ] ] [ [ $.1^5, $.1^46 ] ] [ [ $.1^5, $.1^55 ] ] [ [ $.1^5, $.1^63 ] ] [ [ $.1^5, $.1^74 ] ] [ [ $.1^5, $.1^75 ] ] [ [ $.1^5, $.1^80 ] ] [ [ $.1^5, $.1^89 ] ] [ [ $.1^5, $.1^91 ] ] [ [ $.1^5, $.1^99 ] ] [ [ $.1^5, $.1^102 ] ] [ [ $.1^5, $.1^118 ] ] [ [ $.1^5, $.1^138 ] ] [ [ $.1^5, $.1^140 ] ] [ [ $.1^5, $.1^142 ] ] [ [ $.1^5, $.1^158 ] ] [ [ $.1^5, $.1^176 ] ] [ [ $.1^5, $.1^183 ] ] [ [ $.1^5, $.1^202 ] ] [ [ $.1^5, $.1^206 ] ] [ [ $.1^5, $.1^210 ] ] [ [ $.1^5, $.1^218 ] ] [ [ $.1^5, 4 ] ] [ [ $.1^5, $.1^231 ] ] [ [ $.1^5, $.1^249 ] ] [ [ $.1^5, $.1^250 ] ] [ [ $.1^5, $.1^255 ] ] [ [ $.1^5, $.1^257 ] ] [ [ $.1^5, $.1^264 ] ] [ [ $.1^5, $.1^280 ] ] [ [ $.1^5, $.1^281 ] ] [ [ $.1^5, $.1^282 ] ] [ [ $.1^5, $.1^286 ] ] [ [ $.1^5, $.1^287 ] ] [ [ $.1^5, $.1^292 ] ] [ [ $.1^5, $.1^295 ] ] [ [ $.1^5, $.1^296 ] ] [ [ $.1^5, $.1^299 ] ] [ [ $.1^5, $.1^301 ] ] [ [ $.1^5, $.1^310 ] ] [ [ $.1^5, $.1^322 ] ] [ [ $.1^5, $.1^334 ] ] [ [ $.1^6, $.1 ] ] [ [ $.1^6, $.1^2 ] ] [ [ $.1^6, $.1^7 ] ] [ [ $.1^6, $.1^10 ] ] [ [ $.1^6, $.1^11 ] ] [ [ $.1^6, $.1^14 ] ] [ [ $.1^6, $.1^16 ] ] [ [ $.1^6, $.1^25 ] ] [ [ $.1^6, $.1^37 ] ] [ [ $.1^6, $.1^49 ] ] [ [ $.1^6, $.1^66 ] ] [ [ $.1^6, $.1^70 ] ] [ [ $.1^6, $.1^77 ] ] [ [ $.1^6, $.1^87 ] ] [ [ $.1^6, $.1^90 ] ] [ [ $.1^6, $.1^97 ] ] [ [ $.1^6, $.1^98 ] ] [ [ $.1^6, $.1^100 ] ] [ [ $.1^6, $.1^103 ] ] [ [ $.1^6, $.1^112 ] ] [ [ $.1^6, $.1^120 ] ] [ [ $.1^6, $.1^131 ] ] [ [ $.1^6, $.1^132 ] ] [ [ $.1^6, $.1^137 ] ] [ [ $.1^6, $.1^146 ] ] [ [ $.1^6, $.1^148 ] ] [ [ $.1^6, $.1^156 ] ] [ [ $.1^6, $.1^159 ] ] [ [ $.1^6, $.1^175 ] ] [ [ $.1^6, $.1^195 ] ] [ [ $.1^6, $.1^197 ] ] [ [ $.1^6, $.1^199 ] ] [ [ $.1^6, $.1^215 ] ] [ [ $.1^6, $.1^233 ] ] [ [ $.1^6, $.1^240 ] ] [ [ $.1^6, $.1^259 ] ] [ [ $.1^6, $.1^263 ] ] [ [ $.1^6, $.1^267 ] ] [ [ $.1^6, $.1^275 ] ] [ [ $.1^6, 5 ] ] [ [ $.1^6, $.1^288 ] ] [ [ $.1^6, $.1^306 ] ] [ [ $.1^6, $.1^307 ] ] [ [ $.1^6, $.1^312 ] ] [ [ $.1^6, $.1^314 ] ] [ [ $.1^6, $.1^321 ] ] [ [ $.1^6, $.1^337 ] ] [ [ $.1^6, $.1^338 ] ] [ [ $.1^6, $.1^339 ] ] [ [ $.1^7, 1 ] ] [ [ $.1^7, $.1^3 ] ] [ [ $.1^7, $.1^21 ] ] [ [ $.1^7, $.1^22 ] ] [ [ $.1^7, $.1^27 ] ] [ [ $.1^7, $.1^29 ] ] [ [ $.1^7, $.1^36 ] ] [ [ $.1^7, $.1^52 ] ] [ [ $.1^7, $.1^53 ] ] [ [ $.1^7, $.1^54 ] ] [ [ $.1^7, $.1^58 ] ] [ [ $.1^7, $.1^59 ] ] [ [ $.1^7, $.1^64 ] ] [ [ $.1^7, $.1^67 ] ] [ [ $.1^7, $.1^68 ] ] [ [ $.1^7, $.1^71 ] ] [ [ $.1^7, $.1^73 ] ] [ [ $.1^7, $.1^82 ] ] [ [ $.1^7, $.1^94 ] ] [ [ $.1^7, $.1^106 ] ] [ [ $.1^7, $.1^123 ] ] [ [ $.1^7, $.1^127 ] ] [ [ $.1^7, $.1^134 ] ] [ [ $.1^7, $.1^144 ] ] [ [ $.1^7, $.1^147 ] ] [ [ $.1^7, $.1^154 ] ] [ [ $.1^7, $.1^155 ] ] [ [ $.1^7, $.1^157 ] ] [ [ $.1^7, $.1^160 ] ] [ [ $.1^7, $.1^169 ] ] [ [ $.1^7, $.1^177 ] ] [ [ $.1^7, $.1^188 ] ] [ [ $.1^7, $.1^189 ] ] [ [ $.1^7, $.1^194 ] ] [ [ $.1^7, $.1^203 ] ] [ [ $.1^7, $.1^205 ] ] [ [ $.1^7, $.1^213 ] ] [ [ $.1^7, $.1^216 ] ] [ [ $.1^7, $.1^232 ] ] [ [ $.1^7, $.1^252 ] ] [ [ $.1^7, $.1^254 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 200-BAR2-X4.libre.retevision.es. (62.82.186.200) Time: Fri Mar 12 12:11:07 2004 Input: tqr:= function (q,r) function> C:=[]; function> for i in {1..r} do Include(C,q^(r-i)); end for;return C; end function; tqr(3,4); Output: Magma V2.10-6 Fri Mar 12 2004 12:11:04 on modular [Seed = 68528957] ------------------------------------- >> function> C:=[]; ^ User error: bad syntax >> function> for i in {1..r} do Include(C,q^(r-i)); end for;return C; end func ^ User error: bad syntax >> tqr(3,4);; ^ User error: Identifier 'tqr' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 200-BAR2-X4.libre.retevision.es. (62.82.186.200) Time: Fri Mar 12 12:11:34 2004 Input: tqr:= function (q,r) C:=[]; for i in {1..r} do Include(C,q^(r-i)); end for;return C; end function; tqr(3,4); Output: Magma V2.10-6 Fri Mar 12 2004 12:11:31 on modular [Seed = 253665373] ------------------------------------- [ 27 ] [ 9 ] [ 3 ] [ 1 ] [] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host Donnelly.iuhb02.iu-bremen.de. (212.201.48.249) Time: Fri Mar 12 12:22:51 2004 Input: 1+1; Output: Magma V2.10-6 Fri Mar 12 2004 12:22:48 on modular [Seed = 742235605] ------------------------------------- 2 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host Donnelly.iuhb02.iu-bremen.de. (212.201.48.249) Time: Fri Mar 12 12:23:14 2004 Input: 1+1; Output: Magma V2.10-6 Fri Mar 12 2004 12:23:08 on modular [Seed = 1464264379] ------------------------------------- 2 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host Donnelly.iuhb02.iu-bremen.de. (212.201.48.249) Time: Fri Mar 12 12:23:24 2004 Input: 1+1+1; Output: Magma V2.10-6 Fri Mar 12 2004 12:23:21 on modular [Seed = 1095824217] ------------------------------------- 3 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host Donnelly.iuhb02.iu-bremen.de. (212.201.48.249) Time: Fri Mar 12 12:23:34 2004 Input: 1+1+1+1; Output: Magma V2.10-6 Fri Mar 12 2004 12:23:31 on modular [Seed = 1213856330] ------------------------------------- 4 Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 13:05:34 2004 Input: n73 := func ; Output: Magma V2.10-6 Fri Mar 12 2004 13:05:31 on modular [Seed = 4277093636] ------------------------------------- Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 13:06:30 2004 Input: t73 := [q^i : i in [2..0 by -1]]>; t73; Output: Magma V2.10-6 Fri Mar 12 2004 13:06:27 on modular [Seed = 3908654298] ------------------------------------- >> t73 := [q^i : i in [2..0 by -1]]>; ^ User error: bad syntax >> t73; ^ User error: Identifier 't73' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 13:06:42 2004 Input: t73 := [q^i : i in [2..0 by -1]]; t73; Output: Magma V2.10-6 Fri Mar 12 2004 13:06:38 on modular [Seed = 268545069] ------------------------------------- >> t73 := [q^i : i in [2..0 by -1]]; ^ User error: Identifier 'q' has not been declared or assigned >> t73; ^ User error: Identifier 't73' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 13:06:53 2004 Input: t73 := [i : i in [2..0 by -1]]; t73; Output: Magma V2.10-6 Fri Mar 12 2004 13:06:50 on modular [Seed = 419996977] ------------------------------------- [ 2, 1, 0 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 13:07:20 2004 Input: t73 := [7^i : i in [2..0 by -1]]; t73; Output: Magma V2.10-6 Fri Mar 12 2004 13:07:15 on modular [Seed = 102218311] ------------------------------------- [ 49, 7, 1 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 13:09:29 2004 Input: p(x):=PolynomialRing(R); Output: Magma V2.10-6 Fri Mar 12 2004 13:09:26 on modular [Seed = 203272392] ------------------------------------- >> p(x):=PolynomialRing(R);; ^ User error: Identifier 'R' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 13:14:12 2004 Input: n73 := x^&+(exp(7,3)); Output: Magma V2.10-6 Fri Mar 12 2004 13:14:09 on modular [Seed = 573808577] ------------------------------------- >> n73 := x^&+(exp(7,3));; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 13:15:47 2004 Input: p(x) := PolynomialRing(7^3); n73 := x^&+(exp(7,3)); Output: Magma V2.10-6 Fri Mar 12 2004 13:15:44 on modular [Seed = 758944623] ------------------------------------- >> p(x) := PolynomialRing(7^3); ^ User error: Illegal left hand side of an assignment statement >> n73 := x^&+(exp(7,3));; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 13:16:07 2004 Input: p(x) := PolynomialRing(GF(7^3)); n73 := x^&+(exp(7,3)); Output: Magma V2.10-6 Fri Mar 12 2004 13:16:04 on modular [Seed = 1481238062] ------------------------------------- >> p(x) := PolynomialRing(GF(7^3)); ^ User error: Illegal left hand side of an assignment statement >> n73 := x^&+(exp(7,3));; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 13:20:05 2004 Input: p := PolinomilaRing(R); n73 := x^&+(exp(7,3)); Output: Magma V2.10-6 Fri Mar 12 2004 13:20:01 on modular [Seed = 2474781904] ------------------------------------- >> p := PolinomilaRing(R); ^ User error: Identifier 'R' has not been declared or assigned >> n73 := x^&+(exp(7,3));; ^ User error: Identifier 'x' has not been declared or assigned Total time: 3.759 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 13:22:19 2004 Input: R := GF(7^3); p := PolinomilaRing(R); n73 := x^&+(exp(7,3)); Output: Magma V2.10-6 Fri Mar 12 2004 13:22:15 on modular [Seed = 2575836764] ------------------------------------- >> p := PolinomilaRing(R); ^ User error: Identifier 'PolinomilaRing' has not been declared or assigned >> n73 := x^&+(exp(7,3));; ^ User error: Identifier 'x' has not been declared or assigned Total time: 3.869 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 13:22:53 2004 Input: R := GF(7^3); p := PolynomilaRing(R); n73 := x^&+(exp(7,3)); Output: Magma V2.10-6 Fri Mar 12 2004 13:22:49 on modular [Seed = 2258057581] ------------------------------------- >> p := PolynomilaRing(R); ^ User error: Identifier 'PolynomilaRing' has not been declared or assigned >> n73 := x^&+(exp(7,3));; ^ User error: Identifier 'x' has not been declared or assigned Total time: 3.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 13:23:17 2004 Input: R := GF(7^3); p := PolynomialRing(R); n73 := x^&+(exp(7,3)); Output: Magma V2.10-6 Fri Mar 12 2004 13:23:13 on modular [Seed = 2409484172] ------------------------------------- >> n73 := x^&+(exp(7,3));; ^ User error: Identifier 'exp' has not been declared or assigned Total time: 3.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 13:24:41 2004 Input: R := GF(7^3); p := PolynomialRing(R); exp := [7^i : i in [2..0 by -1]]; n73 := x^&+(exp); Output: Magma V2.10-6 Fri Mar 12 2004 13:24:38 on modular [Seed = 3148479439] ------------------------------------- Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 13:24:54 2004 Input: R := GF(7^3); p := PolynomialRing(R); exp := [7^i : i in [2..0 by -1]]; n73 := x^&+(exp); n73; Output: Magma V2.10-6 Fri Mar 12 2004 13:24:51 on modular [Seed = 2712920512] ------------------------------------- x^57 Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 13:27:53 2004 Input: R := GF(7^3); p := PolynomialRing(R); exp := [7^i : i in [2..0 by -1]]; t73 := &+[x^i : i..in exp]; n73; Output: Magma V2.10-6 Fri Mar 12 2004 13:27:50 on modular [Seed = 3502412260] ------------------------------------- >> t73 := &+[x^i : i..in exp]; ^ User error: bad syntax >> n73;; ^ User error: Identifier 'n73' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 13:28:10 2004 Input: R := GF(7^3); p := PolynomialRing(R); exp := [7^i : i in [2..0 by -1]]; t73 := &+[x^i : i in exp]; t73; Output: Magma V2.10-6 Fri Mar 12 2004 13:28:07 on modular [Seed = 3653998844] ------------------------------------- x^49 + x^7 + x Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 13:32:02 2004 Input: R := GF(7^3); p := PolynomialRing(R); exp := [7^i : i in [2..0 by -1]]; n73 := x^&+(exp); t73 := &+[x^i : i in exp]; Olav := [(a,b) : a,b in GF(7^3) | Evaluate(n73,a) eq Evaluate (t73,b)]; Olav; Output: Magma V2.10-6 Fri Mar 12 2004 13:31:59 on modular [Seed = 3487403458] ------------------------------------- >> Olav := [(a,b) : a,b in GF(7^3) | Evaluate(n73,a) eq Evaluate (t73,b)]; ^ Runtime error in elt< ... >: Bad arguments >> Olav;; ^ User error: Identifier 'Olav' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 13:33:55 2004 Input: R := GF(7^3); p := PolynomialRing(R); exp := [7^i : i in [2..0 by -1]]; n73 := x^&+(exp); t73 := &+[x^i : i in exp]; Olav := [(a,b) : a,b in GF(7^3) | Evaluate(n73,a) eq Evaluate(t73,b)]; Olav; Output: Magma V2.10-6 Fri Mar 12 2004 13:33:52 on modular [Seed = 4125603703] ------------------------------------- >> Olav := [(a,b) : a,b in GF(7^3) | Evaluate(n73,a) eq Evaluate(t73,b)]; ^ Runtime error in elt< ... >: Bad arguments >> Olav;; ^ User error: Identifier 'Olav' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 13:36:04 2004 Input: R := GF(7^3); p := PolynomialRing(R); exp := [7^i : i in [2..0 by -1]]; n73 := x^&+(exp); t73 := &+[x^i : i in exp]; Olav := [a,b : a,b in GF(7^3) | Evaluate(n73,a) eq Evaluate(t73,b)]; Olav; Output: Magma V2.10-6 Fri Mar 12 2004 13:36:01 on modular [Seed = 3891635428] ------------------------------------- >> Olav := [a,b : a,b in GF(7^3) | Evaluate(n73,a) eq Evaluate(t73,b)]; ^ User error: bad syntax >> Olav;; ^ User error: Identifier 'Olav' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 13:39:49 2004 Input: R := GF(7^3); p := PolynomialRing(R); exp := [7^i : i in [2..0 by -1]]; n73 := x^&+(exp); t73 := &+[x^i : i in exp]; Olav := [(a,b) : a,b in GF(7^3) | Evaluate(n73,a) eq Evaluate(t73,b)]; Output: Magma V2.10-6 Fri Mar 12 2004 13:39:46 on modular [Seed = 318853362] ------------------------------------- >> Olav := [(a,b) : a,b in GF(7^3) | Evaluate(n73,a) eq Evaluate(t73,b)];; ^ Runtime error in elt< ... >: Bad arguments Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 13:40:08 2004 Input: R := GF(7^3); p := PolynomialRing(R); exp := [7^i : i in [2..0 by -1]]; n73 := x^&+(exp); t73 := &+[x^i : i in exp]; Olav := [(a,b) : a,b in GF(7^3) | Evaluate(n73,a) eq Evaluate(t73,b)] Output: Magma V2.10-6 Fri Mar 12 2004 13:40:05 on modular [Seed = 51463957] ------------------------------------- >> Olav := [(a,b) : a,b in GF(7^3) | Evaluate(n73,a) eq Evaluate(t73,b)]; ^ Runtime error in elt< ... >: Bad arguments Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 13:40:34 2004 Input: R := GF(7^3); p := PolynomialRing(R); exp := [7^i : i in [2..0 by -1]]; n73 := x^&+(exp); t73 := &+[x^i : i in exp] Olav := [ (a,b) : a,b in GF(7^3) | Evaluate(n73,a) eq Evaluate(t73,b)] Output: Magma V2.10-6 Fri Mar 12 2004 13:40:31 on modular [Seed = 152784133] ------------------------------------- >> Olav := [ (a,b) : a,b in GF(7^3) | Evaluate(n73,a) eq Evaluate(t73,b)]; ^ User error: bad syntax Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 13:41:05 2004 Input: R := GF(7^3); p := PolynomialRing(R); exp := [7^i : i in [2..0 by -1]]; n73 := x^&+(exp); t73 := &+[x^i : i in exp]; Olav := [ (a,b) : a,b in GF(7^3) | Evaluate(n73,a) eq Evaluate(t73,b)] Output: Magma V2.10-6 Fri Mar 12 2004 13:41:02 on modular [Seed = 807564317] ------------------------------------- >> Olav := [ (a,b) : a,b in GF(7^3) | Evaluate(n73,a) eq Evaluate(t73,b)]; ^ Runtime error in elt< ... >: Bad arguments Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 13:41:47 2004 Input: R := GF(7^3); p := PolynomialRing(R); exp := [7^i : i in [2..0 by -1]]; n73 := x^&+(exp); t73 := &+[x^i : i in exp]; PuntsOlav := [ (a,b) : a,b in GF(7^3) | Evaluate(n73,a) eq Evaluate(t73,b)] Output: Magma V2.10-6 Fri Mar 12 2004 13:41:44 on modular [Seed = 1059945284] ------------------------------------- >> PuntsOlav := [ (a,b) : a,b in GF(7^3) | Evaluate(n73,a) eq Evaluate(t73,b)] ^ Runtime error in elt< ... >: Bad arguments Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 13:42:58 2004 Input: R := GF(7^3); p := PolynomialRing(R); exp := [7^i : i in [2..0 by -1]]; n73 := x^&+(exp); t73 := &+[x^i : i in exp]; PuntsOlav := {(a,b):a,b in GF(7^3) | Evaluate(n73,a) eq Evaluate(t73,b)} Output: Magma V2.10-6 Fri Mar 12 2004 13:42:55 on modular [Seed = 640967322] ------------------------------------- >> PuntsOlav := {(a,b):a,b in GF(7^3) | Evaluate(n73,a) eq Evaluate(t73,b)}; ^ Runtime error in elt< ... >: Bad arguments Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 13:43:40 2004 Input: R := GF(7^3); p := PolynomialRing(R); exp := [7^i : i in [2..0 by -1]]; n73 := x^&+(exp); t73 := &+[x^i : i in exp]; PuntsOlav := [a:a in GF(7^3) | Evaluate(n73,a) eq Evaluate(t73,a)] Output: Magma V2.10-6 Fri Mar 12 2004 13:43:37 on modular [Seed = 742287590] ------------------------------------- Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 13:43:54 2004 Input: R := GF(7^3); p := PolynomialRing(R); exp := [7^i : i in [2..0 by -1]]; n73 := x^&+(exp); t73 := &+[x^i : i in exp]; PuntsOlav := [a,b:a in GF(7^3) | Evaluate(n73,a) eq Evaluate(t73,a)] Output: Magma V2.10-6 Fri Mar 12 2004 13:43:51 on modular [Seed = 1531518895] ------------------------------------- >> PuntsOlav := [a,b:a in GF(7^3) | Evaluate(n73,a) eq Evaluate(t73,a)]; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 13:44:09 2004 Input: R := GF(7^3); p := PolynomialRing(R); exp := [7^i : i in [2..0 by -1]]; n73 := x^&+(exp); t73 := &+[x^i : i in exp]; PuntsOlav := [(a,b) :a in GF(7^3) | Evaluate(n73,a) eq Evaluate(t73,a)] Output: Magma V2.10-6 Fri Mar 12 2004 13:44:07 on modular [Seed = 1112540838] ------------------------------------- >> PuntsOlav := [(a,b) :a in GF(7^3) | Evaluate(n73,a) eq Evaluate(t73,a)]; ^ User error: Identifier 'b' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 13:44:35 2004 Input: R := GF(7^3); p := PolynomialRing(R); exp := [7^i : i in [2..0 by -1]]; n73 := x^&+(exp); t73 := &+[x^i : i in exp]; PuntsOlav := [(a,b) : a in GF(7^3) b in GF(7^3) | Evaluate(n73,a) eq Evaluate(t73,a)] Output: Magma V2.10-6 Fri Mar 12 2004 13:44:32 on modular [Seed = 1230703690] ------------------------------------- >> PuntsOlav := [(a,b) : a in GF(7^3) b in GF(7^3) | Evaluate(n73,a) eq Evalua ^ User error: bad syntax Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 13:44:46 2004 Input: R := GF(7^3); p := PolynomialRing(R); exp := [7^i : i in [2..0 by -1]]; n73 := x^&+(exp); t73 := &+[x^i : i in exp]; PuntsOlav := [(a,b) : a in GF(7^3),b in GF(7^3) | Evaluate(n73,a) eq Evaluate(t73,a)] Output: Magma V2.10-6 Fri Mar 12 2004 13:44:43 on modular [Seed = 2003120767] ------------------------------------- >> PuntsOlav := [(a,b) : a in GF(7^3),b in GF(7^3) | Evaluate(n73,a) eq Evalua ^ Runtime error in elt< ... >: Bad arguments Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 13:54:12 2004 Input: R := GF(7^3); p := PolynomialRing(R); exp := [7^i : i in [2..0 by -1]]; n73 := x^&+(exp); t73 := &+[x^i : i in exp]; PuntsOlav := [ : a,b in GF(7^3) | Evaluate(n73,a) eq Evaluate(t73,a)]; Output: Magma V2.10-6 Fri Mar 12 2004 13:54:08 on modular [Seed = 1870473260] ------------------------------------- Total time: 4.129 seconds, Total memory usage: 2.63MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 13:55:00 2004 Input: R := GF(7^3); p := PolynomialRing(R); exp := [7^i : i in [2..0 by -1]]; n73 := x^&+(exp); t73 := &+[x^i : i in exp]; PuntsOlav := [ : a,b in GF(7^3) | Evaluate(n73,a) eq Evaluate(t73,a)]; PuntsOlav; Output: Magma V2.10-6 Fri Mar 12 2004 13:54:55 on modular [Seed = 2592660982] ------------------------------------- [ , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , := PolynomialRing(R); exp := [7^i : i in [2..0 by -1]]; n73 := x^&+(exp); t73 := &+[x^i : i in exp]; PuntsOlav := [ : a,b in GF(7^3) | Evaluate(n73,a) eq Evaluate(t73,a)]; #(PuntsOlav); Output: Magma V2.10-6 Fri Mar 12 2004 13:58:07 on modular [Seed = 2224475304] ------------------------------------- 14749 Total time: 4.129 seconds, Total memory usage: 2.63MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Fri Mar 12 13:58:56 2004 Input: R := GF(7^3); p := PolynomialRing(R); exp := [7^i : i in [2..0 by -1]]; n73 := x^&+(exp); t73 := &+[x^i : i in exp]; PuntsOlav := [ : a,b in GF(7^3) | Evaluate(n73,a) eq Evaluate(t73,b)]; PuntsOlav; Output: Magma V2.10-6 Fri Mar 12 2004 13:58:52 on modular [Seed = 3013737420] ------------------------------------- [ <1, R.1>, <1, R.1^2>, <1, R.1^7>, <1, R.1^10>, <1, R.1^11>, <1, R.1^14>, <1, R.1^16>, <1, R.1^25>, <1, R.1^37>, <1, R.1^49>, <1, R.1^66>, <1, R.1^70>, <1, R.1^77>, <1, R.1^87>, <1, R.1^90>, <1, R.1^97>, <1, R.1^98>, <1, R.1^100>, <1, R.1^103>, <1, R.1^112>, <1, R.1^120>, <1, R.1^131>, <1, R.1^132>, <1, R.1^137>, <1, R.1^146>, <1, R.1^148>, <1, R.1^156>, <1, R.1^159>, <1, R.1^175>, <1, R.1^195>, <1, R.1^197>, <1, R.1^199>, <1, R.1^215>, <1, R.1^233>, <1, R.1^240>, <1, R.1^259>, <1, R.1^263>, <1, R.1^267>, <1, R.1^275>, <1, 5>, <1, R.1^288>, <1, R.1^306>, <1, R.1^307>, <1, R.1^312>, <1, R.1^314>, <1, R.1^321>, <1, R.1^337>, <1, R.1^338>, <1, R.1^339>, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , := PolynomialRing(R); exp := [7^i : i in [2..0 by -1]]; n73 := x^&+(exp); t73 := &+[x^i : i in exp]; PuntsOlav := [ : a,b in GF(7^3) | Evaluate(n73,a) eq Evaluate(t73,b)]; #(PuntsOlav); Output: Magma V2.10-6 Fri Mar 12 2004 13:59:43 on modular [Seed = 3098210356] ------------------------------------- 16807 Total time: 4.269 seconds, Total memory usage: 2.73MB ************** MAGMA ***************** Host pD9E186FE.dip.t-dialin.net. (217.225.134.254) Time: Fri Mar 12 16:30:55 2004 Input: M:= FreeMonoid(3); F := FreeAlgebra(Integers(), M); (1+a-a^2+a^3)*(1+b+b^2+b^3) - (1+b+b^2+b^3)*(1+a-a^2+a^3); Output: Magma V2.10-6 Fri Mar 12 2004 16:30:51 on modular [Seed = 487551235] ------------------------------------- a * b - b * a - a^2 * b + a * b^2 + b * a^2 - b^2 * a + a^3 * b - a^2 * b^2 + a * b^3 - b * a^3 + b^2 * a^2 - b^3 * a + a^3 * b^2 - a^2 * b^3 - b^2 * a^3 + b^3 * a^2 + a^3 * b^3 - b^3 * a^3 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sc1-27648.fas.harvard.edu. (140.247.38.205) Time: Fri Mar 12 16:33:07 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3-x+2); OK := MaximalOrder(K); OK Output: Magma V2.10-6 Fri Mar 12 2004 16:33:04 on modular [Seed = 118844290] ------------------------------------- Maximal Equation Order with defining polynomial x^3 - x + 2 over its ground order Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sc1-27648.fas.harvard.edu. (140.247.38.205) Time: Fri Mar 12 16:33:09 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3-x+2); OK := MaximalOrder(K); OK; Output: Magma V2.10-6 Fri Mar 12 2004 16:33:06 on modular [Seed = 1207431] ------------------------------------- Maximal Equation Order with defining polynomial x^3 - x + 2 over its ground order Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sc1-27648.fas.harvard.edu. (140.247.38.205) Time: Fri Mar 12 16:33:45 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3-x+2); MinimalPolynomial(a); Output: Magma V2.10-6 Fri Mar 12 2004 16:33:42 on modular [Seed = 908352149] ------------------------------------- x^3 - x + 2 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sc1-27648.fas.harvard.edu. (140.247.38.205) Time: Fri Mar 12 16:33:52 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3-x+2); MinimalPolynomial(1); Output: Magma V2.10-6 Fri Mar 12 2004 16:33:49 on modular [Seed = 959141265] ------------------------------------- $.1 - 1 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sc1-27648.fas.harvard.edu. (140.247.38.205) Time: Fri Mar 12 16:34:01 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3-x+2); MinimalPolynomial(1/2); Output: Magma V2.10-6 Fri Mar 12 2004 16:33:58 on modular [Seed = 540167411] ------------------------------------- x - 1/2 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sc1-27648.fas.harvard.edu. (140.247.38.205) Time: Fri Mar 12 16:34:14 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3-x+2); MinimalPolynomial(1/2*a); Output: Magma V2.10-6 Fri Mar 12 2004 16:34:11 on modular [Seed = 708331244] ------------------------------------- x^3 - 1/4*x + 1/4 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sc1-27648.fas.harvard.edu. (140.247.38.205) Time: Fri Mar 12 16:34:33 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3-x+2); MinimalPolynomial(1/2*a^2); Output: Magma V2.10-6 Fri Mar 12 2004 16:34:30 on modular [Seed = 1565471150] ------------------------------------- x^3 - x^2 + 1/4*x - 1/2 Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sc1-27648.fas.harvard.edu. (140.247.38.205) Time: Fri Mar 12 16:34:51 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3-x+2); MinimalPolynomial(1/2*(1+a); Output: Magma V2.10-6 Fri Mar 12 2004 16:34:48 on modular [Seed = 1196764074] ------------------------------------- >> MinimalPolynomial(1/2*(1+a);; ^ User error: bad syntax Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sc1-27648.fas.harvard.edu. (140.247.38.205) Time: Fri Mar 12 16:34:55 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3-x+2); MinimalPolynomial(1/2*(1+a); Output: Magma V2.10-6 Fri Mar 12 2004 16:34:52 on modular [Seed = 1314661031] ------------------------------------- >> MinimalPolynomial(1/2*(1+a);; ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sc1-27648.fas.harvard.edu. (140.247.38.205) Time: Fri Mar 12 16:35:03 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3-x+2); MinimalPolynomial(1/2*(1+a)); Output: Magma V2.10-6 Fri Mar 12 2004 16:34:59 on modular [Seed = 1902320743] ------------------------------------- x^3 - 3/2*x^2 + 1/2*x + 1/4 Total time: 3.109 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sc1-27648.fas.harvard.edu. (140.247.38.205) Time: Fri Mar 12 16:35:21 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3-x+2); MinimalPolynomial(1/2*(1+a^2)); Output: Magma V2.10-6 Fri Mar 12 2004 16:35:18 on modular [Seed = 1685457255] ------------------------------------- x^3 - 5/2*x^2 + 2*x - 1 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sc1-27648.fas.harvard.edu. (140.247.38.205) Time: Fri Mar 12 16:35:35 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3-x+2); MinimalPolynomial(1/2*(a+a^2)); Output: Magma V2.10-6 Fri Mar 12 2004 16:35:32 on modular [Seed = 1870463582] ------------------------------------- x^3 - x^2 + 3/2*x - 1/2 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sc1-27648.fas.harvard.edu. (140.247.38.205) Time: Fri Mar 12 16:35:57 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3-x+2); MinimalPolynomial(1/2*(1+a+a^2)); Output: Magma V2.10-6 Fri Mar 12 2004 16:35:54 on modular [Seed = 2525297593] ------------------------------------- x^3 - 5/2*x^2 + 13/4*x - 13/8 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host Donnelly.iuhb02.iu-bremen.de. (212.201.48.249) Time: Fri Mar 12 17:57:33 2004 Input: M:= FreeMonoid(2); F := FreeAlgebra(Integers(), M); A:= quo< F | a-b >; Parent(aA-bA); IsZero(aA-bA); Output: Magma V2.10-6 Fri Mar 12 2004 17:57:30 on modular [Seed = 691743077] ------------------------------------- Finitely presented algebra Coefficient ring:Integer Ring Monoid: Free finitely presented monoid of rank 2 Relations: aA - bA = 0 false Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 02:47:45 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; Output: Magma V2.10-6 Sat Mar 13 2004 02:47:41 on modular [Seed = 2980269366] ------------------------------------- Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 02:48:12 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-6 Sat Mar 13 2004 02:48:09 on modular [Seed = 2931577357] ------------------------------------- [ x^2 - 1, x*z - 2*y, 2*x - y*z, y^2 - 1, z^2 - 4 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 02:49:00 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-6 Sat Mar 13 2004 02:48:57 on modular [Seed = 2813680468] ------------------------------------- [ 1 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 02:49:16 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-6 Sat Mar 13 2004 02:49:13 on modular [Seed = 3586599222] ------------------------------------- [ 1 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 02:49:39 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-6 Sat Mar 13 2004 02:49:36 on modular [Seed = 3285270217] ------------------------------------- >> I := ideal; ^ User error: bad syntax >> GroebnerBasis(I); ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 02:49:50 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-6 Sat Mar 13 2004 02:49:47 on modular [Seed = 4192929016] ------------------------------------- [ 1 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 02:50:11 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-6 Sat Mar 13 2004 02:50:08 on modular [Seed = 4009497540] ------------------------------------- [ x^2, 2*x ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 02:50:46 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-6 Sat Mar 13 2004 02:50:43 on modular [Seed = 3891600046] ------------------------------------- [ x^2 + 2*x*y - 2*x + y^2 - 2*y + 1, x*y^4 + 2*x*y^3 - 7*x*y^2 + 4*x*y + 2*y^4 - 8*y^3 + 10*y^2 - 4*y, 4*x*y^3 - 8*x*y^2 + 4*x*y + 3*y^4 - 10*y^3 + 11*y^2 - 4*y, y^5 - 2*y^4 + y^3 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 02:51:06 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > (1-y-x)(1-y-x^2) in I Output: Magma V2.10-6 Sat Mar 13 2004 02:51:03 on modular [Seed = 487579745] ------------------------------------- >> (1-y-x)(1-y-x^2) in I ^ Runtime error: Bad argument types Argument types given: RngMPolElt, RngMPolElt Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 02:51:19 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > (1-y-x)*(1-y-x^2) in I; Output: Magma V2.10-6 Sat Mar 13 2004 02:51:16 on modular [Seed = 335997307] ------------------------------------- false Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 02:51:33 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > (1-y-x)*(1-y-x^2) in I; Output: Magma V2.10-6 Sat Mar 13 2004 02:51:30 on modular [Seed = 51510938] ------------------------------------- true Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 02:51:41 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > (1-y-x)*(1-y-x^2) in I; Output: Magma V2.10-6 Sat Mar 13 2004 02:51:38 on modular [Seed = 975751083] ------------------------------------- false Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 02:51:54 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > (1-y-x)*(1-y-x^2)(1-y-x^3) in I; Output: Magma V2.10-6 Sat Mar 13 2004 02:51:51 on modular [Seed = 824429757] ------------------------------------- >> (1-y-x)*(1-y-x^2)(1-y-x^3) in I; ^ Runtime error: Bad argument types Argument types given: RngMPolElt, RngMPolElt Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 02:52:04 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > (1-y-x)*(1-y-x^2)*(1-y-x^3) in I; Output: Magma V2.10-6 Sat Mar 13 2004 02:52:01 on modular [Seed = 674944402] ------------------------------------- true Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 02:52:24 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > (1-y-x)*(1-y-x^2)*(1-y^2-x^3) in I; Output: Magma V2.10-6 Sat Mar 13 2004 02:52:21 on modular [Seed = 657840777] ------------------------------------- true Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 02:53:01 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > (1-y*x)*(1-y)*(1-x) in I; Output: Magma V2.10-6 Sat Mar 13 2004 02:52:58 on modular [Seed = 1565499548] ------------------------------------- true Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 02:53:20 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > (1-y*x)*(2-y)*(1-x) in I; Output: Magma V2.10-6 Sat Mar 13 2004 02:53:17 on modular [Seed = 1413917090] ------------------------------------- true Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 02:53:32 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > (3-y*x)*(2-y)*(1-x) in I; Output: Magma V2.10-6 Sat Mar 13 2004 02:53:29 on modular [Seed = 1129430689] ------------------------------------- true Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 02:53:59 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > (3-y+x)*(2-y)*(1-x) in I; Output: Magma V2.10-6 Sat Mar 13 2004 02:53:56 on modular [Seed = 2053670005] ------------------------------------- false Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 02:54:29 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > (3-y+x)*(2-y)*(1-x)*(5-x+2*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 02:54:26 on modular [Seed = 1902350168] ------------------------------------- true Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 02:54:45 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > (3-y+x)*(2-y)*(1-x)*(5-x^2+2*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 02:54:42 on modular [Seed = 1870500151] ------------------------------------- true Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 02:54:57 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > (3-y+x)*(2-y)*(1-x)*(5-x^2+2*y^3) in I; Output: Magma V2.10-6 Sat Mar 13 2004 02:54:54 on modular [Seed = 1718917171] ------------------------------------- true Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 02:55:11 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > (3-y+x)*(2-y)*(1-x^3)*(5-x^2+2*y^3) in I; Output: Magma V2.10-6 Sat Mar 13 2004 02:55:08 on modular [Seed = 2441310166] ------------------------------------- true Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 02:55:42 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > (3-y+x)*(2-y*x)*(1-x^3)*(5-x^2+2*y^3) in I; Output: Magma V2.10-6 Sat Mar 13 2004 02:55:39 on modular [Seed = 2291824360] ------------------------------------- true Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 02:55:52 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > (3-y+x)*(2-y*x)*(1-x^3)*(15-x^2+2*y^3) in I; Output: Magma V2.10-6 Sat Mar 13 2004 02:55:49 on modular [Seed = 2274720025] ------------------------------------- true Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 02:56:08 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroeBnerBasis(I); > (3-y+x)*(2-y*x)*(1-x^3)*(15-x^2+2*y^3) in I; Output: Magma V2.10-6 Sat Mar 13 2004 02:56:05 on modular [Seed = 3198959664] ------------------------------------- >> GroeBnerBasis(I); ^ User error: Identifier 'GroeBnerBasis' has not been declared or assigned true Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 02:56:22 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (3-y+x)*(2-y*x)*(1-x^3)*(15-x^2+2*y^3) in I; Output: Magma V2.10-6 Sat Mar 13 2004 02:56:19 on modular [Seed = 3047639821] ------------------------------------- [ x^2 + 2*x + 1, 2*x*y + 2*y, y^2, 4 ] true Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 02:57:00 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (3-y+x)*(2-y*x)*(1-x^3+y^2)*(15-x^2+2*y^3) in I; Output: Magma V2.10-6 Sat Mar 13 2004 02:56:57 on modular [Seed = 2746310001] ------------------------------------- [ x^2 + 2*x + 1, 2*x*y + 2*y, y^2, 4 ] true Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 02:57:28 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (3-y+x)*(2-y*x)*(7-3*x^3+y^2)*(15-x^2+2*y^3) in I; Output: Magma V2.10-6 Sat Mar 13 2004 02:57:25 on modular [Seed = 3670549540] ------------------------------------- [ x^2 + 2*x + 1, 2*x*y + 2*y, y^2, 4 ] true Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 02:57:47 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (3-2*y+x)*(2-y*x)*(7-3*x^3+y^2)*(15-x^2+2*y^3) in I; Output: Magma V2.10-6 Sat Mar 13 2004 02:57:44 on modular [Seed = 3519229746] ------------------------------------- [ x^2 + 2*x + 1, y^2, 4 ] true Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 02:58:00 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (3-2*y+x^2)*(2-y*x)*(7-3*x^3+y^2)*(15-x^2+2*y^3) in I; Output: Magma V2.10-6 Sat Mar 13 2004 02:57:57 on modular [Seed = 3369744342] ------------------------------------- [ x^2 + 2*x + 1, y^2, 4 ] true Total time: 3.069 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 02:58:58 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (3-2*y+x^2)*(2-y*x)*(7-3*x^3+y^2)*(15-x^2+2*y^3) in I; Output: Magma V2.10-6 Sat Mar 13 2004 02:58:55 on modular [Seed = 3352639715] ------------------------------------- [ x^2 + 2*x*y^2 + 2*x + y^4 + 2*y^2 + 1, x*y^6 + x*y^4 - 2*x*y^2 + y^7 + 4*y^6 - 3*y^5 - 2*y^2, 2*x*y^3 - 2*x*y^2 + y^6 - y^4 + 2*y^3 - 2*y^2, y^8 + y^7 - 5*y^6 + 3*y^5, 2*y^7 - 4*y^6 + 2*y^5 ] false Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 02:59:19 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1+x+y^2) in I; Output: Magma V2.10-6 Sat Mar 13 2004 02:59:16 on modular [Seed = 4276879793] ------------------------------------- [ x^2 + 2*x*y^2 + 2*x + y^4 + 2*y^2 + 1, x*y^6 + x*y^4 - 2*x*y^2 + y^7 + 4*y^6 - 3*y^5 - 2*y^2, 2*x*y^3 - 2*x*y^2 + y^6 - y^4 + 2*y^3 - 2*y^2, y^8 + y^7 - 5*y^6 + 3*y^5, 2*y^7 - 4*y^6 + 2*y^5 ] false Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 02:59:34 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1+x+y^2)*(1+x+y^3) in I; Output: Magma V2.10-6 Sat Mar 13 2004 02:59:31 on modular [Seed = 4125559437] ------------------------------------- [ x^2 + 2*x*y^2 + 2*x + y^4 + 2*y^2 + 1, x*y^6 + x*y^4 - 2*x*y^2 + y^7 + 4*y^6 - 3*y^5 - 2*y^2, 2*x*y^3 - 2*x*y^2 + y^6 - y^4 + 2*y^3 - 2*y^2, y^8 + y^7 - 5*y^6 + 3*y^5, 2*y^7 - 4*y^6 + 2*y^5 ] false Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 02:59:48 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1+x+y^2)*(1+x+y^3)*(1+x+y^4) in I; Output: Magma V2.10-6 Sat Mar 13 2004 02:59:45 on modular [Seed = 3807387016] ------------------------------------- [ x^2 + 2*x*y^2 + 2*x + y^4 + 2*y^2 + 1, x*y^6 + x*y^4 - 2*x*y^2 + y^7 + 4*y^6 - 3*y^5 - 2*y^2, 2*x*y^3 - 2*x*y^2 + y^6 - y^4 + 2*y^3 - 2*y^2, y^8 + y^7 - 5*y^6 + 3*y^5, 2*y^7 - 4*y^6 + 2*y^5 ] true Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:00:01 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1+x+y^2)*(1+x+y^3)*(1+x+y^5) in I; Output: Magma V2.10-6 Sat Mar 13 2004 02:59:58 on modular [Seed = 504160636] ------------------------------------- [ x^2 + 2*x*y^2 + 2*x + y^4 + 2*y^2 + 1, x*y^6 + x*y^4 - 2*x*y^2 + y^7 + 4*y^6 - 3*y^5 - 2*y^2, 2*x*y^3 - 2*x*y^2 + y^6 - y^4 + 2*y^3 - 2*y^2, y^8 + y^7 - 5*y^6 + 3*y^5, 2*y^7 - 4*y^6 + 2*y^5 ] true Total time: 2.819 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:00:17 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1+x+y^2)*(1+x+y^3)*(1+x+y^5) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:00:14 on modular [Seed = 236777884] ------------------------------------- [ x^2 + 2*x + 1, x*y^4 + y^4, 2*x*y^2 + y^4 + 2*y^2, y^6, 2*y^5 ] true Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:00:43 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1+x+y^2)*(1+x+2*y^3)*(1+x+4*y^5) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:00:40 on modular [Seed = 118880435] ------------------------------------- [ x^2 + 2*x + 1, x*y^4 + y^4, 2*x*y^2 + y^4 + 2*y^2, y^6, 2*y^5 ] true Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:01:03 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1+x+y^2)*(1+x+2*y^3)*(1+x+4*y^5) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:01:00 on modular [Seed = 942327704] ------------------------------------- [ 1 ] true Total time: 3.039 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:01:18 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1+x+y^2)*(1+x+2*y^3)*(1+x+4*y^5) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:01:15 on modular [Seed = 590470388] ------------------------------------- [ x^2 + 2*x + 1, x*y^4 + 4*x + 3*y^4 + 24*y^2 + 28, 2*x*y^2 + 4*x + 3*y^4 + 6*y^2, 8*x + 16*y^2 + 24, y^6 + 2*y^4 + 12*y^2 + 24, 2*y^5 + 8*y^3 + 16*y^2 + 24*y, 4*y^4 + 16, 16*y^3, 32 ] false Total time: 2.989 seconds, Total memory usage: 1.92MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:01:34 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1+3*x+y^2)*(1+x+2*y^3)*(1+x+4*y^5) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:01:31 on modular [Seed = 1413917587] ------------------------------------- [ x^2 + 2*x + 1, x*y^4 + 4*x + 3*y^4 + 24*y^2 + 28, 2*x*y^2 + 4*x + 3*y^4 + 6*y^2, 8*x + 16*y^2 + 24, y^6 + 2*y^4 + 12*y^2 + 24, 2*y^5 + 8*y^3 + 16*y^2 + 24*y, 4*y^4 + 16, 16*y^3, 32 ] false Total time: 2.969 seconds, Total memory usage: 1.92MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:01:52 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1+3*x+y^2)*(1+x+2*y^3)*(1+x+3*y^4)*(1+x+4*y^5) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:01:49 on modular [Seed = 1298117308] ------------------------------------- [ x^2 + 2*x + 1, x*y^4 + 4*x + 3*y^4 + 24*y^2 + 28, 2*x*y^2 + 4*x + 3*y^4 + 6*y^2, 8*x + 16*y^2 + 24, y^6 + 2*y^4 + 12*y^2 + 24, 2*y^5 + 8*y^3 + 16*y^2 + 24*y, 4*y^4 + 16, 16*y^3, 32 ] true Total time: 2.929 seconds, Total memory usage: 1.92MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:02:12 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1+3*x+y^2)*(1+x+2*y^3)*(1+7*x+3*y^4)*(1+x+4*y^5) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:02:09 on modular [Seed = 1179960923] ------------------------------------- [ x^2 + 2*x + 1, x*y^4 + y^4, 2*x*y^2 + y^4 + 2*y^2, y^6, 2*y^4, 4 ] true Total time: 2.909 seconds, Total memory usage: 1.92MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:02:33 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1+3*x+y^2)*(1+x+2*y^3)*(1+7*x+3*y^4)*(1+x+4*y^5) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:02:30 on modular [Seed = 2137915253] ------------------------------------- [ 1 ] true Total time: 2.959 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:02:49 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1+3*x+y^2)*(1+x+2*y^3)*(1+7*x+3*y^4)*(1+x+4*y^5) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:02:45 on modular [Seed = 1902375240] ------------------------------------- [ 1 ] true Total time: 2.949 seconds, Total memory usage: 2.04MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:04:02 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)*(1+y)(1-x*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:03:59 on modular [Seed = 1786309145] ------------------------------------- [ x^2 - 1, y^2 - 1 ] >> (1-x)*(1+y)(1-x*y) in I; ^ Runtime error: Bad argument types Argument types given: RngMPolElt, RngMPolElt Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:04:16 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)*(1+y)*(1-x*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:04:12 on modular [Seed = 1668408066] ------------------------------------- [ x^2 - 1, y^2 - 1 ] false Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:04:38 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)*(1-y)*(1-x*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:04:35 on modular [Seed = 2491814939] ------------------------------------- [ x^2 - 1, y^2 - 1 ] true Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:04:49 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)*(1+y)*(1+x*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:04:46 on modular [Seed = 2392591884] ------------------------------------- [ x^2 - 1, y^2 - 1 ] true Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:04:59 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)*(1+y)*(1-x*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:04:57 on modular [Seed = 2157051957] ------------------------------------- [ x^2 - 1, y^2 - 1 ] false Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:05:25 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)*(1+y)*(1-x*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:05:22 on modular [Seed = 3047634283] ------------------------------------- [ x^2 + 2, y^2 + 2, 3 ] false Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:05:36 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)*(1+y)*(2-x*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:05:33 on modular [Seed = 2931568255] ------------------------------------- [ x^2 + 2, y^2 + 2, 3 ] true Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:05:46 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)*(1+y)*(2+x*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:05:43 on modular [Seed = 2813667180] ------------------------------------- [ x^2 + 2, y^2 + 2, 3 ] false Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:05:55 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1+x)*(1+y)*(2+x*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:05:52 on modular [Seed = 3637139492] ------------------------------------- [ x^2 + 2, y^2 + 2, 3 ] true Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:06:04 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1+x)*(1-y)*(2+x*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:06:00 on modular [Seed = 3519238436] ------------------------------------- [ x^2 + 2, y^2 + 2, 3 ] false Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:06:55 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1+x)*(1-y)*(2+x*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:06:52 on modular [Seed = 3403172810] ------------------------------------- >> I := ideal; ^ Runtime error: Bad argument types Argument types given: RngMPolElt, RngMPolElt >> GroebnerBasis(I); ^ User error: Identifier 'I' has not been declared or assigned >> (1+x)*(1-y)*(2+x*y) in I; ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:07:04 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1+x)*(1-y)*(2+x*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:07:01 on modular [Seed = 3285271290] ------------------------------------- >> I := ideal; ^ User error: bad syntax >> GroebnerBasis(I); ^ User error: Identifier 'I' has not been declared or assigned >> (1+x)*(1-y)*(2+x*y) in I; ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:07:14 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1+x)*(1-y)*(2+x*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:07:11 on modular [Seed = 4108744135] ------------------------------------- [ x^2 - 2*x + y^4 - 2*y^2 + 2, x*y - x - y + 1, y^5 - y^4 - 2*y^3 + 2*y^2 + y - 1 ] false Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:07:31 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1+x)*(2-x-y^2) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:07:28 on modular [Seed = 3992939697] ------------------------------------- [ x^2 - 2*x + y^4 - 2*y^2 + 2, x*y - x - y + 1, y^5 - y^4 - 2*y^3 + 2*y^2 + y - 1 ] false Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:07:38 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)*(2-x-y^2) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:07:35 on modular [Seed = 3874777021] ------------------------------------- [ x^2 - 2*x + y^4 - 2*y^2 + 2, x*y - x - y + 1, y^5 - y^4 - 2*y^3 + 2*y^2 + y - 1 ] false Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:07:49 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-y)*(2-x-y^2) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:07:46 on modular [Seed = 504143697] ------------------------------------- [ x^2 - 2*x + y^4 - 2*y^2 + 2, x*y - x - y + 1, y^5 - y^4 - 2*y^3 + 2*y^2 + y - 1 ] false Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:08:21 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-y)*(2-x-y^2) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:08:18 on modular [Seed = 268603775] ------------------------------------- [ x^2 + x + y^2 + 37*y + 2084, x*y + 2*x + 29*y + 553, 3*x + 30*y + 552, y^3 + 42*y + 3143, 3*y^2 + 66*y + 363, 135*y + 810, 3375 ] false Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:08:37 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-y)*(2-x-y^2)*(5-x-y^3) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:08:34 on modular [Seed = 186223252] ------------------------------------- [ x^2 + x + y^2 + 37*y + 2084, x*y + 2*x + 29*y + 553, 3*x + 30*y + 552, y^3 + 42*y + 3143, 3*y^2 + 66*y + 363, 135*y + 810, 3375 ] false Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:08:55 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-y)*(2-x-y^2)*(5-x^3-y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:08:52 on modular [Seed = 34636683] ------------------------------------- [ x^2 + x + y^2 + 37*y + 2084, x*y + 2*x + 29*y + 553, 3*x + 30*y + 552, y^3 + 42*y + 3143, 3*y^2 + 66*y + 363, 135*y + 810, 3375 ] false Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:11:26 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-y)*(2-x-y^2)*(5-x^3-y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:11:23 on modular [Seed = 759148315] ------------------------------------- >> I := ideal; ^ Runtime error: Bad argument types Argument types given: RngMPolElt, RngIntElt >> GroebnerBasis(I); ^ User error: Identifier 'I' has not been declared or assigned >> (1-y)*(2-x-y^2)*(5-x^3-y) in I; ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:11:34 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-y)*(2-x-y^2)*(5-x^3-y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:11:32 on modular [Seed = 607561229] ------------------------------------- [ 1 ] true Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:12:04 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-y)*(2-x-y^2)*(5-x^3-y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:12:01 on modular [Seed = 1582095378] ------------------------------------- >> I := ideal; ^ Runtime error: Bad argument types Argument types given: RngMPolElt, RngIntElt >> GroebnerBasis(I); ^ User error: Identifier 'I' has not been declared or assigned >> (1-y)*(2-x-y^2)*(5-x^3-y) in I; ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:12:14 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-y)*(2-x-y^2)*(5-x^3-y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:12:11 on modular [Seed = 1363399447] ------------------------------------- [ 2*x^2*y^2 + 2*x^2*y + 5*x^2 + 4*x*y^5 + 4*x*y^4 + x*y^3 - 4*x*y^2 - 4*x*y - 4*x + 12*y^7 + 3*y^5 + y^4 - 5*y^3 + 2*y + 1, 9*x^2 + 8*x*y^5 + 8*x*y^4 + 2*x*y^3 - 4*x*y^2 - 4*x*y - 7*x + 8*y^7 + 14*y^5 + 6*y^4 - 11*y^3 - 3*y^2 + 3*y + 2, 16*y^4 - 8*y^2 + 1 ] false Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:12:52 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-2*x)(1+2*y)(1-3*x)(1-2*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:12:49 on modular [Seed = 1213909716] ------------------------------------- [ 2*x^2*y^2 + 2*x^2*y + 5*x^2 + 4*x*y^5 + 4*x*y^4 + x*y^3 - 4*x*y^2 - 4*x*y - 4*x + 12*y^7 + 3*y^5 + y^4 - 5*y^3 + 2*y + 1, 9*x^2 + 8*x*y^5 + 8*x*y^4 + 2*x*y^3 - 4*x*y^2 - 4*x*y - 7*x + 8*y^7 + 14*y^5 + 6*y^4 - 11*y^3 - 3*y^2 + 3*y + 2, 16*y^4 - 8*y^2 + 1 ] >> (1-2*x)(1+2*y)(1-3*x)(1-2*y) in I; ^ Runtime error: Bad argument types Argument types given: RngMPolElt, RngMPolElt Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:13:10 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-2*x)*(1+2*y)*(1-3*x)*(1-2*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:13:07 on modular [Seed = 1129431501] ------------------------------------- [ 2*x^2*y^2 + 2*x^2*y + 5*x^2 + 4*x*y^5 + 4*x*y^4 + x*y^3 - 4*x*y^2 - 4*x*y - 4*x + 12*y^7 + 3*y^5 + y^4 - 5*y^3 + 2*y + 1, 9*x^2 + 8*x*y^5 + 8*x*y^4 + 2*x*y^3 - 4*x*y^2 - 4*x*y - 7*x + 8*y^7 + 14*y^5 + 6*y^4 - 11*y^3 - 3*y^2 + 3*y + 2, 16*y^4 - 8*y^2 + 1 ] false Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:14:28 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-2*x)*(1+2*y)*(1-3*x)*(1+3*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:14:25 on modular [Seed = 2053699718] ------------------------------------- [ x^2*y^2 + 10*x^2*y + 25*x^2 + 3024*x*y^3 + 3770*x*y^2 + 1496*x*y + 170*x - 1260*y^3 - 1571*y^2 - 625*y - 75, 36*x^2 + 5184*x*y^3 + 6480*x*y^2 + 2592*x*y + 300*x - 2160*y^3 - 2700*y^2 - 1080*y - 131, 36*y^4 + 60*y^3 + 37*y^2 + 10*y + 1 ] false Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:14:50 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-2*x)*(1+2*y)*(1-3*x)*(1+3*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:14:47 on modular [Seed = 1870523781] ------------------------------------- [ 1 ] true Total time: 2.979 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:15:08 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-2*x)*(1+2*y)*(1-3*x)*(1+3*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:15:05 on modular [Seed = 1651564918] ------------------------------------- [ x^2 + 35*x*y^3 + 71*x*y^2 + 72*x*y + 903473*x + 49*y^3 + 593103*y^2 + 341903*y + 22847, x*y^4 + 38*x*y^3 + 107*x*y^2 + 79*x*y + 404714*x + y^8 + y^7 + y^6 + 2*y^5 + y^4 + 148*y^3 + 164304*y^2 + 23520*y + 969217, 109*x*y + 160448*x + 1134581*y + 810851, 3*y^4 + 223*y^3 + 1076478*y^2 + 573686*y + 1078873, 327*y^3 + 481562*y^2 + 1184285*y + 485159, 1295029 ] false Total time: 3.019 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:15:36 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-2*x)*(1+2*y)*(1-3*x)*(1+3*y)*(1-111*x)*(1+111*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:15:33 on modular [Seed = 2508658350] ------------------------------------- [ x^2 + 35*x*y^3 + 71*x*y^2 + 72*x*y + 903473*x + 49*y^3 + 593103*y^2 + 341903*y + 22847, x*y^4 + 38*x*y^3 + 107*x*y^2 + 79*x*y + 404714*x + y^8 + y^7 + y^6 + 2*y^5 + y^4 + 148*y^3 + 164304*y^2 + 23520*y + 969217, 109*x*y + 160448*x + 1134581*y + 810851, 3*y^4 + 223*y^3 + 1076478*y^2 + 573686*y + 1078873, 327*y^3 + 481562*y^2 + 1184285*y + 485159, 1295029 ] false Total time: 2.919 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:40:40 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-2*x)*(1+2*y)*(1-3*x)*(1+3*y)*(1-21*x)*(1+21*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:40:37 on modular [Seed = 3586612429] ------------------------------------- [ x^2 + 11*x*y^3 + 9*x*y^2 + 15*x*y + 2187*x + 2*y^5 + 3*y^3 + 5797*y^2 + 733*y + 2781, x*y^4 + 8*x*y^3 + 10*x*y^2 + 14*x*y + 2555*x + 2*y^6 + 2*y^4 + 7*y^3 + 2680*y^2 + 1909*y + 2643, 19*x*y + 5966*x + 893*y + 6042, 3*y^4 + 5*y^3 + 2861*y^2 + 1144*y + 2858, 19*y^3 + 1406*y^2 + 931*y + 1425, 6859 ] false Total time: 2.959 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:41:05 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-2*x)*(1+2*y)*(1-3*x)*(1+3*y)*(1-21*x)*(1+21*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:41:02 on modular [Seed = 3437118927] ------------------------------------- [ 1 ] true Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:41:24 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-2*x)*(1+2*y)*(1-3*x)*(1+3*y)*(1-21*x)*(1+21*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:41:21 on modular [Seed = 3352645355] ------------------------------------- [ 1 ] true Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:41:35 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-2*x)*(1+2*y)*(1-3*x)*(1+3*y)*(1-21*x)*(1+21*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:41:32 on modular [Seed = 4276910047] ------------------------------------- [ 1 ] true Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:41:48 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-2*x)*(1+2*y)*(1-3*x)*(1+3*y)*(1-21*x)*(1+21*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:41:45 on modular [Seed = 4058216613] ------------------------------------- [ 1 ] true Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:42:04 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-2*x)*(1+2*y)*(1-3*x)*(1+3*y)*(1-21*x)*(1+21*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:42:01 on modular [Seed = 3958989487] ------------------------------------- [ 1 ] true Total time: 2.919 seconds, Total memory usage: 1.92MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:42:20 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-2*x)*(1+2*y)*(1-3*x)*(1+3*y)*(1-21*x)*(1+21*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:42:17 on modular [Seed = 3807406998] ------------------------------------- [ x^2 + 10*x + 1114, x*y + 4*x + 71*y + 889, 11*x + 781, y^2 + 41*y + 753, 121*y + 484, 1331 ] false Total time: 2.959 seconds, Total memory usage: 1.92MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:42:37 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-2*x)*(1+2*y)*(1-3*x)*(1+3*y)*(1-211*x)*(1+21*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:42:34 on modular [Seed = 369401714] ------------------------------------- [ x^2 + 10*x + 1114, x*y + 4*x + 71*y + 889, 11*x + 781, y^2 + 41*y + 753, 121*y + 484, 1331 ] true Total time: 2.969 seconds, Total memory usage: 1.92MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:43:07 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-2*x)*(1+2*y)*(1-3*x)*(1+3*y)*(1-211*x)*(1+21*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:43:04 on modular [Seed = 253593225] ------------------------------------- [ x^2 + 10*x + 1114, x*y + 4*x + 71*y + 889, 11*x + 781, y^2 + 41*y + 753, 121*y + 484, 1331 ] true Total time: 2.919 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:43:29 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-2*x)*(1+2*y)*(1-3*x)*(1+3*y)*(1-211*x)*(1+21*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:43:26 on modular [Seed = 68586932] ------------------------------------- [ x^2 + 4572*x + 6097, 3*x*y^2 + 22*x*y + 4252*x + 29*y^3 + 23*y^2 + 44*y + 6563, 36*y^2 + 36*y + 9, 57*y + 4180, 6859 ] false Total time: 2.909 seconds, Total memory usage: 1.92MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:43:47 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-2*x)*(1+2*y)*(1-3*x)*(1+3*y)*(1-211*x)*(1+21*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:43:44 on modular [Seed = 1026536675] ------------------------------------- [ x^2 + 11*x*y^3 + 9*x*y^2 + 15*x*y + 2187*x + 2*y^5 + 3*y^3 + 5797*y^2 + 733*y + 2781, x*y^4 + 8*x*y^3 + 10*x*y^2 + 14*x*y + 2555*x + 2*y^6 + 2*y^4 + 7*y^3 + 2680*y^2 + 1909*y + 2643, 19*x*y + 5966*x + 893*y + 6042, 3*y^4 + 5*y^3 + 2861*y^2 + 1144*y + 2858, 19*y^3 + 1406*y^2 + 931*y + 1425, 6859 ] false Total time: 2.979 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:44:11 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-2*x)*(1+2*y)*(1-3*x)*(1+3*y)*(1-211*x)*(1+21*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:44:08 on modular [Seed = 841006068] ------------------------------------- >> 2, (1-21*x)^2*(1+21*y)^2, (1-31*x)^2(1-31*y)^2>; ^ Runtime error: Bad argument types Argument types given: RngMPolElt, RngIntElt >> GroebnerBasis(I); ^ User error: Identifier 'I' has not been declared or assigned >> (1-2*x)*(1+2*y)*(1-3*x)*(1+3*y)*(1-211*x)*(1+21*y) in I; ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:44:19 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-2*x)*(1+2*y)*(1-3*x)*(1+3*y)*(1-211*x)*(1+21*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:44:16 on modular [Seed = 725197525] ------------------------------------- [ 1 ] true Total time: 2.969 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:44:29 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-2*x)*(1+2*y)*(1-3*x)*(1+3*y)*(1-211*x)*(1+21*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:44:26 on modular [Seed = 540191188] ------------------------------------- [ 1 ] true Total time: 2.989 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:45:00 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-2*x)*(1+2*y)*(1-3*x)*(1+3*y)*(1-21*x)*(1+21*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:44:57 on modular [Seed = 1447353409] ------------------------------------- >> 2, (1-21*x)^2*(1+21*y)^2, (1-x-y)^2(1-x+y)^2>; ^ Runtime error: Bad argument types Argument types given: RngMPolElt, RngIntElt >> GroebnerBasis(I); ^ User error: Identifier 'I' has not been declared or assigned >> (1-2*x)*(1+2*y)*(1-3*x)*(1+3*y)*(1-21*x)*(1+21*y) in I; ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:45:11 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-2*x)*(1+2*y)*(1-3*x)*(1+3*y)*(1-21*x)*(1+21*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:45:08 on modular [Seed = 1264173377] ------------------------------------- [ 1 ] true Total time: 2.979 seconds, Total memory usage: 1.92MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:45:23 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-2*x)*(1+2*y)*(1-3*x)*(1+3*y)*(1-21*x)*(1+21*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:45:20 on modular [Seed = 1079167614] ------------------------------------- [ 1 ] true Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:45:35 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-2*x)*(1+2*y)*(1-3*x)*(1+3*y)*(1-21*x)*(1+21*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:45:32 on modular [Seed = 2037117771] ------------------------------------- [ 1 ] true Total time: 2.959 seconds, Total memory usage: 1.92MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:45:44 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-2*x)*(1+2*y)*(1-3*x)*(1+3*y)*(1-21*x)*(1+21*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:45:41 on modular [Seed = 1870521668] ------------------------------------- [ 1 ] true Total time: 2.929 seconds, Total memory usage: 1.92MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:45:53 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-2*x)*(1+2*y)*(1-3*x)*(1+3*y)*(1-21*x)*(1+21*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:45:50 on modular [Seed = 1685515844] ------------------------------------- [ 1 ] true Total time: 2.999 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:46:18 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-2*x)*(1+2*y)*(1-3*x)*(1+3*y)*(1-21*x)*(1+21*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:46:15 on modular [Seed = 2643400660] ------------------------------------- [ x^2 + 240*x + 682, x*y + 200*x + 6*y + 6615, 361*x + 2166, y^2 + y + 1715, 19*y + 5966, 6859 ] true Total time: 2.989 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:47:12 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-2*x)*(1+2*y)*(1-3*x)*(1+3*y)*(1-21*x)*(1+21*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:47:09 on modular [Seed = 2457868289] ------------------------------------- >> I := ideal; ^ User error: bad syntax >> GroebnerBasis(I); ^ User error: Identifier 'I' has not been declared or assigned >> (1-2*x)*(1+2*y)*(1-3*x)*(1+3*y)*(1-21*x)*(1+21*y) in I; ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:47:23 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-2*x)*(1+2*y)*(1-3*x)*(1+3*y)*(1-21*x)*(1+21*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:47:20 on modular [Seed = 2342060301] ------------------------------------- [ 121*x^4 + 1892*x^3 + 1826*x^2*y + 3194*x^2 + 135*x*y^5 + 642*x*y^4 + 235783211*x*y^3 + 20952576*x*y^2 + 130990656*x*y - 52398948*x + 313014375*y^8 - 128941875*y^7 + 466080075*y^6 - 529478490*y^5 + 351884616*y^4 - 382096029*y^3 + 180705165*y^2 - 100592782*y + 24011841, 968*x^3*y + 968*x^3 + 616*x^2*y + 2552*x^2 + 225*x*y^5 + 650*x*y^4 + 255002941*x*y^3 + 22660732*x*y^2 + 141668852*x*y - 56669208*x + 338529375*y^8 - 139451625*y^7 + 504071100*y^6 - 572637425*y^5 + 380565506*y^4 - 413241466*y^3 + 195433719*y^2 - 108791636*y + 25968788, 1936*x^3 + 1232*x^2 + 90*x*y^5 + 233*x*y^4 + 116830780*x*y^3 + 10381457*x*y^2 + 64904140*x*y - 25962972*x + 155094750*y^8 - 63890775*y^7 + 230936670*y^6 - 262353152*y^5 + 174355965*y^4 - 189324603*y^3 + 89537573*y^2 - 49842640*y + 11897604, x^2*y^2 + 646*x^2*y + 3657*x^2 + 164875920*x*y^3 + 14648598*x*y^2 + 91599884*x*y - 36641714*x + 218882250*y^8 - 90165150*y^7 + 325917945*y^6 - 370249147*y^5 + 246064865*y^4 - 267190551*y^3 + 126363153*y^2 - 70342030*y + 16790857, 1936*x^2*y + 1936*x^2 + 45*x*y^5 + 409*x*y^4 + 118952431*x*y^3 + 10571119*x*y^2 + 66086496*x*y - 26435972*x + 157919625*y^8 - 65051100*y^7 + 235143405*y^6 - 267125338*y^5 + 177528651*y^4 - 192771426*y^3 + 91167567*y^2 - 50750132*y + 12114236, 3872*x^2 + 135*x*y^5 + 147*x*y^4 + 235783797*x*y^3 + 20950677*x*y^2 + 130992856*x*y - 52398844*x + 313014375*y^8 - 128941875*y^7 + 466080075*y^6 - 529479165*y^5 + 351884556*y^4 - 382097304*y^3 + 180705410*y^2 - 100592656*y + 24011672, 45*x*y^6 + 184*x*y^5 + 626*x*y^4 + 193843492*x*y^3 + 17230805*x*y^2 + 107690620*x*y - 43076300*x + 257337000*y^8 - 106005375*y^7 + 383172825*y^6 - 435297134*y^5 + 289285590*y^4 - 314128387*y^3 + 148558885*y^2 - 82698320*y + 19740100, 360*x*y^5 + 32*x*y^4 + 187940000*x*y^3 + 16705680*x*y^2 + 104411000*x*y - 41764400*x + 249500250*y^8 - 102776850*y^7 + 371504205*y^6 - 422040268*y^5 + 280475708*y^4 - 304561750*y^3 + 144034545*y^2 - 80179700*y + 19138900, 720*x*y^4 + 272300464*x*y^3 + 24204880*x*y^2 + 151277840*x*y - 60511200*x + 361492875*y^8 - 148910400*y^7 + 538260120*y^6 - 611481332*y^5 + 406372487*y^4 - 441270204*y^3 + 208687350*y^2 - 116170040*y + 27729800, 285753600*x*y^3 + 25400320*x*y^2 + 158752000*x*y - 63500800*x + 379353375*y^8 - 156267225*y^7 + 564854580*y^6 - 641692318*y^5 + 426450175*y^4 - 463071805*y^3 + 218997830*y^2 - 121909500*y + 29099800, 91125*y^9 + 24300*y^8 + 154035*y^7 - 33686*y^6 + 74775*y^5 - 60480*y^4 + 23125*y^3 - 17550*y^2 + 7500*y - 1000 ] false Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:47:57 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y-3*x*y)*(1-2*x-5*y+11*x^2) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:47:54 on modular [Seed = 2157054500] ------------------------------------- [ 121*x^4 + 1892*x^3 + 1826*x^2*y + 3194*x^2 + 135*x*y^5 + 642*x*y^4 + 235783211*x*y^3 + 20952576*x*y^2 + 130990656*x*y - 52398948*x + 313014375*y^8 - 128941875*y^7 + 466080075*y^6 - 529478490*y^5 + 351884616*y^4 - 382096029*y^3 + 180705165*y^2 - 100592782*y + 24011841, 968*x^3*y + 968*x^3 + 616*x^2*y + 2552*x^2 + 225*x*y^5 + 650*x*y^4 + 255002941*x*y^3 + 22660732*x*y^2 + 141668852*x*y - 56669208*x + 338529375*y^8 - 139451625*y^7 + 504071100*y^6 - 572637425*y^5 + 380565506*y^4 - 413241466*y^3 + 195433719*y^2 - 108791636*y + 25968788, 1936*x^3 + 1232*x^2 + 90*x*y^5 + 233*x*y^4 + 116830780*x*y^3 + 10381457*x*y^2 + 64904140*x*y - 25962972*x + 155094750*y^8 - 63890775*y^7 + 230936670*y^6 - 262353152*y^5 + 174355965*y^4 - 189324603*y^3 + 89537573*y^2 - 49842640*y + 11897604, x^2*y^2 + 646*x^2*y + 3657*x^2 + 164875920*x*y^3 + 14648598*x*y^2 + 91599884*x*y - 36641714*x + 218882250*y^8 - 90165150*y^7 + 325917945*y^6 - 370249147*y^5 + 246064865*y^4 - 267190551*y^3 + 126363153*y^2 - 70342030*y + 16790857, 1936*x^2*y + 1936*x^2 + 45*x*y^5 + 409*x*y^4 + 118952431*x*y^3 + 10571119*x*y^2 + 66086496*x*y - 26435972*x + 157919625*y^8 - 65051100*y^7 + 235143405*y^6 - 267125338*y^5 + 177528651*y^4 - 192771426*y^3 + 91167567*y^2 - 50750132*y + 12114236, 3872*x^2 + 135*x*y^5 + 147*x*y^4 + 235783797*x*y^3 + 20950677*x*y^2 + 130992856*x*y - 52398844*x + 313014375*y^8 - 128941875*y^7 + 466080075*y^6 - 529479165*y^5 + 351884556*y^4 - 382097304*y^3 + 180705410*y^2 - 100592656*y + 24011672, 45*x*y^6 + 184*x*y^5 + 626*x*y^4 + 193843492*x*y^3 + 17230805*x*y^2 + 107690620*x*y - 43076300*x + 257337000*y^8 - 106005375*y^7 + 383172825*y^6 - 435297134*y^5 + 289285590*y^4 - 314128387*y^3 + 148558885*y^2 - 82698320*y + 19740100, 360*x*y^5 + 32*x*y^4 + 187940000*x*y^3 + 16705680*x*y^2 + 104411000*x*y - 41764400*x + 249500250*y^8 - 102776850*y^7 + 371504205*y^6 - 422040268*y^5 + 280475708*y^4 - 304561750*y^3 + 144034545*y^2 - 80179700*y + 19138900, 720*x*y^4 + 272300464*x*y^3 + 24204880*x*y^2 + 151277840*x*y - 60511200*x + 361492875*y^8 - 148910400*y^7 + 538260120*y^6 - 611481332*y^5 + 406372487*y^4 - 441270204*y^3 + 208687350*y^2 - 116170040*y + 27729800, 285753600*x*y^3 + 25400320*x*y^2 + 158752000*x*y - 63500800*x + 379353375*y^8 - 156267225*y^7 + 564854580*y^6 - 641692318*y^5 + 426450175*y^4 - 463071805*y^3 + 218997830*y^2 - 121909500*y + 29099800, 91125*y^9 + 24300*y^8 + 154035*y^7 - 33686*y^6 + 74775*y^5 - 60480*y^4 + 23125*y^3 - 17550*y^2 + 7500*y - 1000 ] false Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:48:44 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y-3*x*y)*(1-2*x-5*y+11*x^2) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:48:41 on modular [Seed = 3064216641] ------------------------------------- [ x^2 + 6*x*y + 7714*x + y^4 + 10*y^3 + 614*y^2 + 24259226*y + 47977847013, x*y^4 + x*y^2 + 14*x*y + 784*x + 2*y^4 + 10*y^3 + 410*y^2 + 35890782*y + 106318125868, 2*x*y^3 + 2*x*y + 4140*x + y^4 + 741*y^2 + 26490146*y + 250303646680, 4*x*y^2 + 4*x*y + 8296*x + 13*y^4 + 6*y^3 + 609*y^2 + 29379872*y + 42015775420, 16*x*y + 6624*x + 4*y^4 + 8*y^3 + 740*y^2 + 26133504*y + 21023281648, 13312*x + 3*y^4 + 14*y^3 + 39*y^2 + 18415900*y + 272783209612, 5*y^5 + 8*y^4 + 13*y^3 + 162*y^2 + 35475020*y + 259097714520, 16*y^3 + 112*y^2 + 18862464*y + 48664386240, 832*y^2 + 25608960*y + 169416289536, 35995648*y + 51761741824, 294876348416 ] false Total time: 2.999 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 03:49:04 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y-3*x*y)*(1-2*x-5*y+11*x^2)*(1-3*x-5*y+4*x^2) in I; Output: Magma V2.10-6 Sat Mar 13 2004 03:49:00 on modular [Seed = 2948408653] ------------------------------------- [ x^2 + 6*x*y + 7714*x + y^4 + 10*y^3 + 614*y^2 + 24259226*y + 47977847013, x*y^4 + x*y^2 + 14*x*y + 784*x + 2*y^4 + 10*y^3 + 410*y^2 + 35890782*y + 106318125868, 2*x*y^3 + 2*x*y + 4140*x + y^4 + 741*y^2 + 26490146*y + 250303646680, 4*x*y^2 + 4*x*y + 8296*x + 13*y^4 + 6*y^3 + 609*y^2 + 29379872*y + 42015775420, 16*x*y + 6624*x + 4*y^4 + 8*y^3 + 740*y^2 + 26133504*y + 21023281648, 13312*x + 3*y^4 + 14*y^3 + 39*y^2 + 18415900*y + 272783209612, 5*y^5 + 8*y^4 + 13*y^3 + 162*y^2 + 35475020*y + 259097714520, 16*y^3 + 112*y^2 + 18862464*y + 48664386240, 832*y^2 + 25608960*y + 169416289536, 35995648*y + 51761741824, 294876348416 ] false Total time: 2.919 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 04:58:14 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y-3*x*y)*(1-2*x-5*y+11*x^2)*(1-3*x-5*y+4*x^2) in I; Output: Magma V2.10-6 Sat Mar 13 2004 04:58:11 on modular [Seed = 1803153529] ------------------------------------- [ x^2 + 2, 3 ] false Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 04:58:30 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y-3*x*y)*(1-2*x-5*y+11*x^2)*(1-3*x-5*y+4*x^2) in I; Output: Magma V2.10-6 Sat Mar 13 2004 04:58:27 on modular [Seed = 1969745431] ------------------------------------- [ 1 ] true Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 04:59:24 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y-3*x*y)*(1-2*x-5*y+11*x^2)*(1-3*x-5*y+4*x^2) in I; Output: Magma V2.10-6 Sat Mar 13 2004 04:59:21 on modular [Seed = 2087642916] ------------------------------------- [ x^2, y^2 ] false Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 04:59:56 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y-3*x*y)*(1-2*x-5*y+11*x^2)*(1-3*x-5*y+4*x^2) in I; Output: Magma V2.10-6 Sat Mar 13 2004 04:59:53 on modular [Seed = 1179966974] ------------------------------------- [ x^2 + 2, 3 ] false Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 05:00:14 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y-3*x*y)*(1-2*x-5*y+11*x^2)*(1-3*x-5*y+4*x^2) in I; Output: Magma V2.10-6 Sat Mar 13 2004 05:00:11 on modular [Seed = 1447349724] ------------------------------------- [ 1 ] true Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 05:00:22 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y-3*x*y)*(1-2*x-5*y+11*x^2)*(1-3*x-5*y+4*x^2) in I; Output: Magma V2.10-6 Sat Mar 13 2004 05:00:19 on modular [Seed = 2712877619] ------------------------------------- [ x^2 + 2, 3 ] false Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 05:00:37 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y-3*x*y)*(1-2*x-5*y+11*x^2)*(1-3*x-5*y+4*x^2) in I; Output: Magma V2.10-6 Sat Mar 13 2004 05:00:34 on modular [Seed = 2830775115] ------------------------------------- [ 1 ] true Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 05:00:46 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y-3*x*y)*(1-2*x-5*y+11*x^2)*(1-3*x-5*y+4*x^2) in I; Output: Magma V2.10-6 Sat Mar 13 2004 05:00:43 on modular [Seed = 3013683289] ------------------------------------- [ x^2 + 2, 3 ] false Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 05:01:04 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y-3*x*y)*(1-2*x-5*y+11*x^2)*(1-3*x-5*y+4*x^2) in I; Output: Magma V2.10-6 Sat Mar 13 2004 05:01:01 on modular [Seed = 2291798900] ------------------------------------- [ x^2 + 2, 3 ] false Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 05:01:14 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y-3*x*y)*(1-2*x-5*y+11*x^2)*(1-3*x-5*y+4*x^2) in I; Output: Magma V2.10-6 Sat Mar 13 2004 05:01:11 on modular [Seed = 2542079057] ------------------------------------- [ x^2 + 2, 3 ] false Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 05:02:18 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y-3*x*y)*(1-2*x-5*y+11*x^2)*(1-3*x-5*y+4*x^2) in I; Output: Magma V2.10-6 Sat Mar 13 2004 05:02:15 on modular [Seed = 3790831079] ------------------------------------- [ x^4 + 4, 5 ] false Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 05:02:47 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y-3*x*y)*(1-2*x-5*y+11*x^2)*(1-3*x-5*y+4*x^2) in I; Output: Magma V2.10-6 Sat Mar 13 2004 05:02:44 on modular [Seed = 3908727949] ------------------------------------- [ x^4 + 4, 5 ] false Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 05:03:13 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y-3*x*y)*(1-2*x-5*y+11*x^2)*(1-3*x-5*y+4*x^2) in I; Output: Magma V2.10-6 Sat Mar 13 2004 05:03:10 on modular [Seed = 4091637644] ------------------------------------- [ x^4 + 4, 5 ] false Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 05:03:27 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y-3*x*y)*(1-2*x-5*y+11*x^2)*(1-3*x-5*y+4*x^2) in I; Output: Magma V2.10-6 Sat Mar 13 2004 05:03:24 on modular [Seed = 4209534647] ------------------------------------- [ x^4 + 14, 15 ] false Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 05:04:14 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y-3*x*y)*(1-2*x-5*y+11*x^2)*(1-3*x-5*y+4*x^2) in I; Output: Magma V2.10-6 Sat Mar 13 2004 05:04:11 on modular [Seed = 3319224703] ------------------------------------- [ x^4 + 14, 15 ] false Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 05:27:05 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y-3*x*y)*(1-2*x-5*y+11*x^2)*(1-3*x-5*y+4*x^2) in I; > (1-x^4)(1+x+2x)+(2^4-x^4)(3+4x^4) Output: Magma V2.10-6 Sat Mar 13 2004 05:27:02 on modular [Seed = 874943968] ------------------------------------- [ x^4 + 14, 15 ] false >> (1-x^4)(1+x+2x)+(2^4-x^4)(3+4x^4) ^ User error: bad syntax Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 05:27:23 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y-3*x*y)*(1-2*x-5*y+11*x^2)*(1-3*x-5*y+4*x^2) in I; > (1-x^4)*(1+x+2x)+(2^4-x^4)*(3+4x^4) in I Output: Magma V2.10-6 Sat Mar 13 2004 05:27:20 on modular [Seed = 1026531095] ------------------------------------- [ x^4 + 14, 15 ] false >> (1-x^4)*(1+x+2x)+(2^4-x^4)*(3+4x^4) in I ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 05:27:41 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y-3*x*y)*(1-2*x-5*y+11*x^2)*(1-3*x-5*y+4*x^2) in I; > (1-x^4)*(1+x+2*x^2)+(2^4-x^4)*(3+4*x^4) in I Output: Magma V2.10-6 Sat Mar 13 2004 05:27:38 on modular [Seed = 169388082] ------------------------------------- [ x^4 + 14, 15 ] false true Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 05:37:18 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y-3*x*y)*(1-2*x-5*y+11*x^2)*(1-3*x-5*y+4*x^2) in I; > (1-x^4)*(1+x+2*x^2)+(2^4-x^4)*(3+4*x^4) in I Output: Magma V2.10-6 Sat Mar 13 2004 05:37:15 on modular [Seed = 1668400922] ------------------------------------- [ x^2 + 5, 9 ] false false Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 05:37:27 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y-3*x*y)*(1-2*x-5*y+11*x^2)*(1-3*x-5*y+4*x^2) in I; > (1-x^4)*(1+x+2*x^2)+(2^4-x^4)*(3+4*x^4) in I Output: Magma V2.10-6 Sat Mar 13 2004 05:37:24 on modular [Seed = 1752878126] ------------------------------------- [ x^4 + x^2 + 7, 3*x^2 + 6, 27 ] false false Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 05:37:50 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y-3*x*y)*(1-2*x-5*y+11*x^2)*(1-3*x-5*y+4*x^2) in I; > (1-x^4)*(1+x+2*x^2)+(2^4-x^4)*(3+4*x^4) in I Output: Magma V2.10-6 Sat Mar 13 2004 05:37:47 on modular [Seed = 1902368040] ------------------------------------- [ x^4 + x^2 + 7, 3*x^2 + 6, 9 ] false false Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 05:38:06 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y-3*x*y)*(1-2*x-5*y+11*x^2)*(1-3*x-5*y+4*x^2) in I; > (1-x^4)*(1+x+2*x^2)+(2^4-x^4)*(3+4*x^4) in I Output: Magma V2.10-6 Sat Mar 13 2004 05:38:03 on modular [Seed = 2121063127] ------------------------------------- [ x^4 + x^2 + 7, 3*x^2 + 6, 9 ] false false Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 05:38:37 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y-3*x*y)*(1-2*x-5*y+11*x^2)*(1-3*x-5*y+4*x^2) in I; > (1-x^4)*(1+x+2*x^2)+(2^4-x^4)*(3+4*x^4) in I Output: Magma V2.10-6 Sat Mar 13 2004 05:38:34 on modular [Seed = 1196811215] ------------------------------------- [ x^4 + x^2 + 7, 3*x^2 + 6, 9 ] false false Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 05:40:06 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y-3*x*y)*(1-2*x-5*y+11*x^2)*(1-3*x-5*y+4*x^2) in I; > (1-x^4)*(1+x+2*x^2)+(2^4-x^4)*(3+4*x^4) in I Output: Magma V2.10-6 Sat Mar 13 2004 05:40:03 on modular [Seed = 1413935477] ------------------------------------- [ 1 ] true true Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 05:40:16 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y-3*x*y)*(1-2*x-5*y+11*x^2)*(1-3*x-5*y+4*x^2) in I; > (1-x^4)*(1+x+2*x^2)+(2^4-x^4)*(3+4*x^4) in I Output: Magma V2.10-6 Sat Mar 13 2004 05:40:13 on modular [Seed = 2729445261] ------------------------------------- [ x^4 + 14*x^2 + 49, 16*x^2 + 48, 128 ] false false Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 05:40:30 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y-3*x*y)*(1-2*x-5*y+11*x^2)*(1-3*x-5*y+4*x^2) in I; > (1-x^4)*(1+x+2*x^2)+(2^4-x^4)*(3+4*x^4) in I Output: Magma V2.10-6 Sat Mar 13 2004 05:40:27 on modular [Seed = 2881031826] ------------------------------------- [ x^4 + 14*x^2 + 49, 16*x^2 + 48, 128 ] false false Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 06:04:46 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y-3*x*y)*(1-2*x-5*y+11*x^2)*(1-3*x-5*y+4*x^2) in I; > (1-x^4)*(1+x+2*x^2)+(2^4-x^4)*(3+4*x^4) in I Output: Magma V2.10-6 Sat Mar 13 2004 06:04:43 on modular [Seed = 3908715009] ------------------------------------- [ x^4 + 14*x^2 + 49, 16*x^2 + 48, 128 ] false false Total time: 3.209 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 06:04:59 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y-3*x*y)*(1-2*x-5*y+11*x^2)*(1-3*x-5*y+4*x^2) in I; > (1-x^4)*(1+x+2*x^2)+(2^4-x^4)*(3+4*x^4) in I Output: Magma V2.10-6 Sat Mar 13 2004 06:04:56 on modular [Seed = 4125581071] ------------------------------------- [ x^4 + 14*x^2 + 49, 16*x^2 + 48, 128 ] false false Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 06:05:07 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y-3*x*y)*(1-2*x-5*y+11*x^2)*(1-3*x-5*y+4*x^2) in I; > (1-x^4)*(1+x+2*x^2)+(2^4-x^4)*(3+4*x^4) in I Output: Magma V2.10-6 Sat Mar 13 2004 06:05:04 on modular [Seed = 3335810052] ------------------------------------- [ x^4 + 14*x^2 + 49, 16*x^2 + 48, 128 ] false false Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 06:06:05 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y-3*x*y)*(1-2*x-5*y+11*x^2)*(1-3*x-5*y+4*x^2) in I; > (1-x^4)*(1+x+2*x^2)+(2^4-x^4)*(3+4*x^4) in I Output: Magma V2.10-6 Sat Mar 13 2004 06:06:02 on modular [Seed = 3437127668] ------------------------------------- [ x^4 + 14*x^2 + 49, 16*x^2 + 48, 128 ] false false Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 06:06:21 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y-3*x*y)*(1-2*x-5*y+11*x^2)*(1-3*x-5*y+4*x^2) in I; > (1-x^4)*(1+x+2*x^2)+(2^4-x^4)*(3+4*x^4) in I Output: Magma V2.10-6 Sat Mar 13 2004 06:06:18 on modular [Seed = 3586621149] ------------------------------------- [ x^4 + 14*x^2 + 49, 16*x^2 + 48, 128 ] false false Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 06:07:21 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y-3*x*y)*(1-2*x-5*y+11*x^2)*(1-3*x-5*y+4*x^2) in I; > (1-x^4)*(1+x+2*x^2)+(2^4-x^4)*(3+4*x^4) in I Output: Magma V2.10-6 Sat Mar 13 2004 06:07:18 on modular [Seed = 590448742] ------------------------------------- >> I := ideal> GroebnerBasis(I); ^ User error: Identifier 'I' has not been declared or assigned >> (1-x-y-3*x*y)*(1-2*x-5*y+11*x^2)*(1-3*x-5*y+4*x^2) in I; ^ User error: Identifier 'I' has not been declared or assigned >> (1-x^4)*(1+x+2*x^2)+(2^4-x^4)*(3+4*x^4) in I ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 06:07:43 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y-3*x*y)*(1-2*x-5*y+11*x^2)*(1-3*x-5*y+4*x^2) in I; > (1-x^4)*(1+x+2*x^2)+(2^4-x^4)*(3+4*x^4) in I Output: Magma V2.10-6 Sat Mar 13 2004 06:07:40 on modular [Seed = 708346229] ------------------------------------- [ x^4 + x^2 + 7, 3*x^2 + 6, 9 ] false false Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 06:09:00 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal GroebnerBasis(I); > (1-x-y-3*x*y)*(1-2*x-5*y+11*x^2)*(1-3*x-5*y+4*x^2) in I; Output: Magma V2.10-6 Sat Mar 13 2004 06:08:57 on modular [Seed = 807574490] ------------------------------------- >> I := ideal> GroebnerBasis(I); ^ User error: Identifier 'I' has not been declared or assigned >> (1-x-y-3*x*y)*(1-2*x-5*y+11*x^2)*(1-3*x-5*y+4*x^2) in I; ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 06:09:11 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y-3*x*y)*(1-2*x-5*y+11*x^2)*(1-3*x-5*y+4*x^2) in I; Output: Magma V2.10-6 Sat Mar 13 2004 06:09:08 on modular [Seed = 1059951816] ------------------------------------- [ x^2 + 2*x*y - 2*x + y^2 - 2*y + 1, 2*x*y^2 - 2*x*y + x + 4*y^7 - 16*y^5 + 32*y^4 - 29*y^3 + 14*y^2 - 3*y, 8*y^6 - 24*y^5 + 36*y^4 - 32*y^3 + 18*y^2 - 6*y + 1 ] false Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 06:09:29 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y-3*x*y)*(1-2*x-5*y+11*x^2)*(1-3*x-5*y+4*x^2) in I; Output: Magma V2.10-6 Sat Mar 13 2004 06:09:26 on modular [Seed = 102018499] ------------------------------------- [ x^2 + x + 3*y^2 + y + 367, x*y + x + y^2 + 20*y + 369, 5*x + 4*y^2 + 18*y + 79, y^3 + 3*y^2 + 3*y + 501, 5*y^2 + 10*y + 380, 25*y + 400, 625 ] false Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 06:09:57 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y)*(1-2*x*y)*(1-3*x) in I; Output: Magma V2.10-6 Sat Mar 13 2004 06:09:54 on modular [Seed = 203333677] ------------------------------------- [ x^2 + x + 3*y^2 + y + 367, x*y + x + y^2 + 20*y + 369, 5*x + 4*y^2 + 18*y + 79, y^3 + 3*y^2 + 3*y + 501, 5*y^2 + 10*y + 380, 25*y + 400, 625 ] false Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (217.66.208.249) Time: Sat Mar 13 06:25:09 2004 Input: 2^20996011 Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Mar 13 2004 06:24:46 on modular [Seed = 1885527853] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 25427 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 13 06:36:52 2004 Input: SetLogFile("sessio2 grup232.log"); Output: WARNING: MAGMA command contains unsafe command 'file', so it will not be executed. ************** MAGMA ***************** Host n137.ryd.student.liu.se. (130.236.215.137) Time: Sat Mar 13 07:02:06 2004 Input: A:=7552303358170263902914554564327725358469929639968983087695649031517406364061712339739824578084287764058083180164336917777906990457445737600839992985802080816552100186198412600277410646809961854489987509913987112597074464; B:=9371950671503412372533636878668990806999190400211385974213287958233912073374497530149151638460143053668897319415688199297577720758321107020761694959578963725010908020113314284964390803755062864619173007709615879679092575; p:=195303555153105689394605664018778179073; E:=ChangeRing(EllipticCurve([A,B]),GF(p)); print(E); go:=Order(E); Factorization(go); Output: Magma V2.10-6 Sat Mar 13 2004 07:02:00 on modular [Seed = 2491821199] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 96969244432163517629402382751585239602*x + 106598328600354781932225432498148599643 over GF(195303555153105689394605664018778179073) [ <2, 5>, <3, 2>, <7, 1>, <157, 1>, <239, 1>, <641, 1>, <673, 1>, <797, 1>, <30497, 1>, <37181, 1>, <249859, 1>, <26504369, 1> ] Total time: 5.929 seconds, Total memory usage: 3.12MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sat Mar 13 09:44:05 2004 Input: tqr:=func; tqr(7,3); Output: Magma V2.10-6 Sat Mar 13 2004 09:44:02 on modular [Seed = 540245559] ------------------------------------- [ 49, 7, 1 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sat Mar 13 09:58:21 2004 Input: polt:=function(q,r) R := GF(q^r); p := PolynomialRing(R); exp := [q^i : i in [r-1..0 by -1]]; pol := &+ [x^i: i in exp]); return(pol); end function; Output: Magma V2.10-6 Sat Mar 13 2004 09:58:18 on modular [Seed = 17981614] ------------------------------------- >> pol := &+ [x^i: i in exp]); ^ User error: bad syntax >> return(pol); ^ User error: A 'return' can only be used inside a procedure or function >> end function;; ^ User error: bad syntax Total time: 3.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sat Mar 13 09:58:37 2004 Input: polt:=function(q,r) R := GF(q^r); p := PolynomialRing(R); exp := [q^i : i in [r-1..0 by -1]]; pol := &+ [x^i: i in exp]; return(pol); end function; Output: Magma V2.10-6 Sat Mar 13 2004 09:58:34 on modular [Seed = 136014263] ------------------------------------- Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sat Mar 13 09:58:52 2004 Input: polt:=function(q,r) R := GF(q^r); p := PolynomialRing(R); exp := [q^i : i in [r-1..0 by -1]]; pol := &+ [x^i: i in exp]; return(pol); end function; polt(7,3); Output: Magma V2.10-6 Sat Mar 13 2004 09:58:49 on modular [Seed = 318796447] ------------------------------------- x^49 + x^7 + x Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sat Mar 13 10:03:24 2004 Input: poln:=function(q,r) R := GF(q^r); p := PolynomialRing(R); exp := [q^i : i in [r-1..0 by -1]]; pol := x^&+(exp); return(pol); end function; polt(7,3); Output: Magma V2.10-6 Sat Mar 13 2004 10:03:21 on modular [Seed = 2137791971] ------------------------------------- >> polt(7,3);; ^ User error: Identifier 'polt' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sat Mar 13 10:03:33 2004 Input: poln:=function(q,r) R := GF(q^r); p := PolynomialRing(R); exp := [q^i : i in [r-1..0 by -1]]; pol := x^&+(exp); return(pol); end function; poln(7,3); Output: Magma V2.10-6 Sat Mar 13 2004 10:03:30 on modular [Seed = 1179985057] ------------------------------------- x^57 Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sat Mar 13 10:09:40 2004 Input: poln:=function(q,r) R := GF(q^r); p := PolynomialRing(R); exp := [q^i : i in [r-1..0 by -1]]; pol := x^&+(exp); return(pol); end function; polt:=function(q,r) R := GF(q^r); p := PolynomialRing(R); exp := [q^i : i in [r-1..0 by -1]]; pol := &+ [x^i: i in exp]; return(pol); end function; PuntsOlav := func : a, b in GF(q^r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)]>; Output: Magma V2.10-6 Sat Mar 13 2004 10:09:37 on modular [Seed = 1464087363] ------------------------------------- Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sat Mar 13 10:10:29 2004 Input: poln:=function(q,r) R := GF(q^r); p := PolynomialRing(R); exp := [q^i : i in [r-1..0 by -1]]; pol := x^&+(exp); return(pol); end function; polt:=function(q,r) R := GF(q^r); p := PolynomialRing(R); exp := [q^i : i in [r-1..0 by -1]]; pol := &+ [x^i: i in exp]; return(pol); end function; PuntsOlav := func : a, b in GF(q^r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)]>; PuntsOlav(7,3); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Mar 13 2004 10:10:06 on modular [Seed = 2712847818] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 25988 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sat Mar 13 10:13:02 2004 Input: poln:=function(q,r) R := GF(q^r); p := PolynomialRing(R); exp := [q^i : i in [r-1..0 by -1]]; pol := x^&+(exp); return(pol); end function; polt:=function(q,r) R := GF(q^r); p := PolynomialRing(R); exp := [q^i : i in [r-1..0 by -1]]; pol := &+ [x^i: i in exp]; return(pol); end function; PuntsOlav := func : a, b in GF(q^r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)]>; PuntsOlav(7,3); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Mar 13 2004 10:12:38 on modular [Seed = 2881015657] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 25998 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host knox.pace.edu. (198.105.45.18) Time: Sat Mar 13 15:51:02 2004 Input: 25*5 Output: Magma V2.10-6 Sat Mar 13 2004 15:50:59 on modular [Seed = 3774076154] ------------------------------------- 125 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host knox.pace.edu. (198.105.45.18) Time: Sat Mar 13 15:51:33 2004 Input: factor(x^2-25) Output: Magma V2.10-6 Sat Mar 13 2004 15:51:30 on modular [Seed = 4226338688] ------------------------------------- >> factor(x^2-25); ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host knox.pace.edu. (198.105.45.18) Time: Sat Mar 13 15:52:03 2004 Input: polroots(x^2-25) Output: Magma V2.10-6 Sat Mar 13 2004 15:52:01 on modular [Seed = 3453942165] ------------------------------------- >> polroots(x^2-25); ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host knox.pace.edu. (198.105.45.18) Time: Sat Mar 13 15:54:48 2004 Input: factor((44*x+3*17)*(44*y+3)-17*713) Output: Magma V2.10-6 Sat Mar 13 2004 15:54:46 on modular [Seed = 824312845] ------------------------------------- >> factor((44*x+3*17)*(44*y+3)-17*713); ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 16:47:59 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y)*(1-2*x*y)*(1-3*x) in I; Output: Magma V2.10-6 Sat Mar 13 2004 16:47:56 on modular [Seed = 2359250218] ------------------------------------- [ 1 ] true Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 16:48:17 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y)*(1-2*x*y)*(1-3*x) in I; Output: Magma V2.10-6 Sat Mar 13 2004 16:48:14 on modular [Seed = 2241217585] ------------------------------------- [ 1 ] true Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 16:48:35 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y)*(1-2*x*y)*(1-3*x) in I; Output: Magma V2.10-6 Sat Mar 13 2004 16:48:32 on modular [Seed = 2457948936] ------------------------------------- [ 1 ] true Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 16:48:47 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y)*(1-2*x*y)*(1-3*x) in I; Output: Magma V2.10-6 Sat Mar 13 2004 16:48:44 on modular [Seed = 3958909565] ------------------------------------- [ 1 ] true Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 16:49:24 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y)*(1-2*x*y)*(1-3*x) in I; Output: Magma V2.10-6 Sat Mar 13 2004 16:49:21 on modular [Seed = 3790741546] ------------------------------------- [ x^2 + 2, 3 ] false Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 16:49:44 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y)*(1-2*x*y)*(1-3*x) in I; Output: Magma V2.10-6 Sat Mar 13 2004 16:49:41 on modular [Seed = 4276961057] ------------------------------------- >> I := ideal; ^ Runtime error in elt< ... >: Rhs arity (2) should be 1 >> GroebnerBasis(I); ^ User error: Identifier 'I' has not been declared or assigned >> (1-x-y)*(1-2*x*y)*(1-3*x) in I; ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 16:49:57 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y)*(1-2*x*y)*(1-3*x) in I; Output: Magma V2.10-6 Sat Mar 13 2004 16:49:54 on modular [Seed = 4108793564] ------------------------------------- [ x^2 + 2, 3 ] false Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 16:50:08 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y)*(1-2*x*y)*(1-3*x) in I; Output: Magma V2.10-6 Sat Mar 13 2004 16:50:05 on modular [Seed = 3302426339] ------------------------------------- [ x^2 + 2, 3 ] false Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 16:50:32 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y)*(1-2*x*y)*(1-3*x) in I; Output: Magma V2.10-6 Sat Mar 13 2004 16:50:29 on modular [Seed = 3721273298] ------------------------------------- [ x^2 + 8, 12 ] false Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 16:50:45 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y)*(1-2*x*y)*(1-3*x) in I; Output: Magma V2.10-6 Sat Mar 13 2004 16:50:41 on modular [Seed = 725150002] ------------------------------------- [ x^4 + 8, 12 ] false Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 16:51:13 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y)*(1-2*x*y)*(1-3*x) in I; Output: Magma V2.10-6 Sat Mar 13 2004 16:51:10 on modular [Seed = 573694023] ------------------------------------- [ x^4 + 16*x^2 + 64, 24*x^2 + 48, 288 ] false Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 16:51:28 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y)*(1-2*x*y)*(1-3*x) in I; Output: Magma V2.10-6 Sat Mar 13 2004 16:51:25 on modular [Seed = 959118159] ------------------------------------- [ x^4 + 16*x^2 + 64, 24*x^2 + 48, 288 ] false Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 16:51:40 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y)*(1-2*x*y)*(1-3*x) in I; Output: Magma V2.10-6 Sat Mar 13 2004 16:51:37 on modular [Seed = 807662194] ------------------------------------- [ x^4 + 16*x^2 + 64, 48*x^2 + 96, 144 ] false Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 16:52:01 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y)*(1-2*x*y)*(1-3*x) in I; Output: Magma V2.10-6 Sat Mar 13 2004 16:51:58 on modular [Seed = 253545818] ------------------------------------- [ x^4 + 16*x^2 + 64, 48*x^2 + 96, 144 ] false Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 16:53:32 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-y)*(1-2*x*y)*(1-3*x) in I; Output: Magma V2.10-6 Sat Mar 13 2004 16:53:29 on modular [Seed = 85379063] ------------------------------------- [ x^2 + 3*x + 284, 7*x + 182, 343 ] false Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 16:53:57 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-4*x)(1-11*x) in I; Output: Magma V2.10-6 Sat Mar 13 2004 16:53:54 on modular [Seed = 470802117] ------------------------------------- [ x^2 + 3*x + 284, 7*x + 182, 343 ] >> (1-4*x)(1-11*x) in I; ^ Runtime error: Bad argument types Argument types given: RngMPolElt, RngMPolElt Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 16:54:07 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-4*x)*(1-11*x) in I; Output: Magma V2.10-6 Sat Mar 13 2004 16:54:04 on modular [Seed = 1803069884] ------------------------------------- [ x^2 + 3*x + 284, 7*x + 182, 343 ] false Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sat Mar 13 16:59:35 2004 Input: f:=CyclotomicPolynomial(2); Output: Magma V2.10-6 Sat Mar 13 2004 16:59:32 on modular [Seed = 2053750293] ------------------------------------- Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sat Mar 13 16:59:47 2004 Input: f:=CyclotomicPolynomial(2); f; Output: Magma V2.10-6 Sat Mar 13 2004 16:59:44 on modular [Seed = 1902294282] ------------------------------------- $.1 + 1 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sat Mar 13 17:00:14 2004 Input: R:=PolynomialRing(Rationals()); f:=CyclotomicPolynomial(2); f; Output: Magma V2.10-6 Sat Mar 13 2004 17:00:11 on modular [Seed = 1079215104] ------------------------------------- $.1 + 1 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 17:01:13 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-4*x)*(1-11*x) in I; Output: Magma V2.10-6 Sat Mar 13 2004 17:01:10 on modular [Seed = 2914937120] ------------------------------------- [ 1 ] true Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 17:01:23 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-4*x)*(1-11*x) in I; Output: Magma V2.10-6 Sat Mar 13 2004 17:01:19 on modular [Seed = 2763481151] ------------------------------------- [ 1 ] true Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 17:01:34 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-4*x)*(1-11*x) in I; Output: Magma V2.10-6 Sat Mar 13 2004 17:01:31 on modular [Seed = 3013637923] ------------------------------------- [ 1 ] true Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 17:01:41 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-4*x)*(1-11*x) in I; Output: Magma V2.10-6 Sat Mar 13 2004 17:01:38 on modular [Seed = 2325302883] ------------------------------------- [ 1 ] true Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 17:01:48 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-4*x)*(1-11*x) in I; Output: Magma V2.10-6 Sat Mar 13 2004 17:01:45 on modular [Seed = 2173846883] ------------------------------------- [ x^2 + x + 7, 3*x + 6, 9 ] false Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 17:02:03 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-4*x)*(11-131*x) in I; Output: Magma V2.10-6 Sat Mar 13 2004 17:02:00 on modular [Seed = 2559269995] ------------------------------------- [ x^2 + x + 7, 3*x + 6, 9 ] true Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 17:02:16 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (3-117*x)*(11-131*x) in I; Output: Magma V2.10-6 Sat Mar 13 2004 17:02:14 on modular [Seed = 2542031706] ------------------------------------- [ x^2 + x + 7, 3*x + 6, 9 ] true Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 17:02:42 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (3-117*x)*(11-131*x) in I; Output: Magma V2.10-6 Sat Mar 13 2004 17:02:39 on modular [Seed = 3992856889] ------------------------------------- [ x^2 + x + 7, 3*x + 6, 9 ] true Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 17:03:00 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (3-117*x)*(11-131*x) in I; Output: Magma V2.10-6 Sat Mar 13 2004 17:02:57 on modular [Seed = 3841401310] ------------------------------------- [ x^2 + 4*x + 4, 9 ] false Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 17:03:19 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (3-117*x)*(11-x^2+131*x) in I; Output: Magma V2.10-6 Sat Mar 13 2004 17:03:16 on modular [Seed = 4091557628] ------------------------------------- [ x^2 + 4*x + 4, 9 ] true Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 17:03:33 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (3-117*x)*(11-x^2+131*x) in I; Output: Magma V2.10-6 Sat Mar 13 2004 17:03:30 on modular [Seed = 3403222995] ------------------------------------- [ 1 ] true Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 17:03:43 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (3-117*x)*(11-x^2+131*x) in I; Output: Magma V2.10-6 Sat Mar 13 2004 17:03:40 on modular [Seed = 3251766486] ------------------------------------- [ x^2 + 7*x + 1, 9 ] true Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sat Mar 13 17:04:58 2004 Input: R:=PolynomialRing(Rationals()); f:=CyclotomicPolynomial(2); f; Output: Magma V2.10-6 Sat Mar 13 2004 17:04:54 on modular [Seed = 3754695282] ------------------------------------- $.1 + 1 Total time: 3.529 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Sat Mar 13 17:04:59 2004 Input: f:=CyclotomicPolynomial(2); f; Output: Magma V2.10-6 Sat Mar 13 2004 17:04:56 on modular [Seed = 3704559999] ------------------------------------- $.1 + 1 Total time: 3.419 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 17:05:20 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (3-x-y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 17:05:17 on modular [Seed = 624353428] ------------------------------------- [ x^2 + 2*x*y - 6*x + y^2 - 6*y + 9, x*y^2 + 2*x*y - 15*x - 14*y^2 - 76*y - 30, 4*x*y + 20*x + 3*y^2 - 2*y - 85, y^3 + 15*y^2 + 75*y + 125 ] false Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 17:05:32 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (3-x-y)*(11-2*x-y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 17:05:29 on modular [Seed = 1059912378] ------------------------------------- [ x^2 + 2*x*y - 6*x + y^2 - 6*y + 9, x*y^2 + 2*x*y - 15*x - 14*y^2 - 76*y - 30, 4*x*y + 20*x + 3*y^2 - 2*y - 85, y^3 + 15*y^2 + 75*y + 125 ] false Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 17:05:48 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (3-x-y)*(11-2*x-y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 17:05:45 on modular [Seed = 807663013] ------------------------------------- [ x^2 + 2*x*y + 34*x + 6*y^2 + 564*y + 2014, x*y^2 + 2*x*y + 25*x + y^2 + 994*y + 4225, 4*x*y + 20*x + 3*y^2 + 1998*y + 5915, 40*x + 5*y^2 + 570*y + 2005, y^3 + 5*y^2 + 1575*y + 3875, 10*y^2 + 500*y + 2250, 2000*y + 6000, 8000 ] false Total time: 2.859 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 17:06:04 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (3-x-y)*(11-2*x-y)*(13-x-3*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 17:06:01 on modular [Seed = 152751340] ------------------------------------- [ x^2 + 2*x*y + 34*x + 6*y^2 + 564*y + 2014, x*y^2 + 2*x*y + 25*x + y^2 + 994*y + 4225, 4*x*y + 20*x + 3*y^2 + 1998*y + 5915, 40*x + 5*y^2 + 570*y + 2005, y^3 + 5*y^2 + 1575*y + 3875, 10*y^2 + 500*y + 2250, 2000*y + 6000, 8000 ] false Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 17:13:04 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (3-x-y)*(11-2*x-y)*(13-x-3*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 17:13:01 on modular [Seed = 352768596] ------------------------------------- [ x^2 + 2*x*y + 3413*y^2, x*y^2, 4*x*y + 3412*y^2, y^3, 6165*y^2 ] false Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 17:13:31 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (x-y)*(11*y-2*x)*(13*x-3*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 17:13:28 on modular [Seed = 1853729226] ------------------------------------- [ x^2 + 2*x*y + 3413*y^2, x*y^2, 4*x*y + 3412*y^2, y^3, 6165*y^2 ] true Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 17:13:55 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (111*x-y)*(11*y-2*x)*(13*x-3*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 17:13:52 on modular [Seed = 1735696619] ------------------------------------- [ x^2 + 2*x*y + 19894073*y^2, x*y^2, 4*x*y + 10232087*y^2, y^3, 26720480*y^2 ] true Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 17:20:21 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (111*x-y)*(11*y-2*x)*(13*x-3*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 17:20:18 on modular [Seed = 1230667847] ------------------------------------- [ x^2 + 3646*x*y + 25754978053490*y^2, x*y^2 + 4556*x*y + 824*y^5 + 350*y^4 + 400840877*y^3 + 2062745112373*y^2, 4876*x*y + 7869576617093*y^2, y^6 + 259*y^5 + 12*y^4 + 1064310058*y^3 + 11812963885120*y^2, 1219*y^4 + 1152325576*y^3 + 21657590331520*y^2, 1811386459*y^3, 39705591181280*y^2 ] false Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sat Mar 13 17:20:42 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (111*x-y)*(11*y-2*x)*(13*x-3*y+x*y) in I; Output: Magma V2.10-6 Sat Mar 13 2004 17:20:38 on modular [Seed = 1129351769] ------------------------------------- [ x^2 + 3646*x*y + 25754978053490*y^2, x*y^2 + 4556*x*y + 824*y^5 + 350*y^4 + 400840877*y^3 + 2062745112373*y^2, 4876*x*y + 7869576617093*y^2, y^6 + 259*y^5 + 12*y^4 + 1064310058*y^3 + 11812963885120*y^2, 1219*y^4 + 1152325576*y^3 + 21657590331520*y^2, 1811386459*y^3, 39705591181280*y^2 ] false Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (24.81.108.53) Time: Sun Mar 14 00:52:29 2004 Input: K:=QuadraticField(3); E:=EllipticCurve([178726274280*s-309562987707, -100613589603711624*s+174267849125512314]); TorsionSubgroup(E); Output: Magma V2.10-6 Sun Mar 14 2004 00:52:24 on modular [Seed = 253541441] ------------------------------------- Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 to CrvEll: E given by a rule [no inverse] Total time: 3.659 seconds, Total memory usage: 2.49MB ************** MAGMA ***************** Host dynamic.ucsd.edu. (132.239.95.48) Time: Sun Mar 14 04:02:31 2004 Input: L := LatticeWithGram(6, [4, 1,4, 2,2,4, 2,2,1,4, 2,2,1,1,4, 2,2,2,2,2,4]); L; Output: Magma V2.10-6 Sun Mar 14 2004 04:02:26 on modular [Seed = 1498220194] ------------------------------------- Standard Lattice of rank 6 and degree 6 Inner Product Matrix: [4 1 2 2 2 2] [1 4 2 2 2 2] [2 2 4 1 1 2] [2 2 1 4 1 2] [2 2 1 1 4 2] [2 2 2 2 2 4] Total time: 3.309 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dynamic.ucsd.edu. (132.239.95.48) Time: Sun Mar 14 04:03:24 2004 Input: L := LatticeWithGram(6, [4, 1,4, 2,2,4, 2,2,1,4, 2,2,1,1,4, 2,2,2,2,2,4]); L; time V, E, P := VoronoiCell(L); #Holes(L), #DeepHoles(L), CoveringRadius(L); Output: Magma V2.10-6 Sun Mar 14 2004 04:03:15 on modular [Seed = 1297683143] ------------------------------------- Standard Lattice of rank 6 and degree 6 Inner Product Matrix: [4 1 2 2 2 2] [1 4 2 2 2 2] [2 2 4 1 1 2] [2 2 1 4 1 2] [2 2 1 1 4 2] [2 2 2 2 2 4] Time: 5.650 782 28 5/2 Total time: 8.799 seconds, Total memory usage: 4.78MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:19:08 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (111*x-y)*(11*y-2*x)*(13*x-3*y+x*y) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:19:04 on modular [Seed = 925062373] ------------------------------------- [ x^2 + 2*x*y, 4*x*y, y^2 ] true Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:19:25 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (111*x-y)*(11*y-2*x)*(13*x-3*y+x*y) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:19:22 on modular [Seed = 741887980] ------------------------------------- [ x^2 + 2*x*y, 4*x*y, y^2 ] true Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:20:56 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (111*x-y)*(11*y-2*x)*(13*x-3*y+x*y) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:20:53 on modular [Seed = 3553079420] ------------------------------------- [ x^4 + x^2 + 7, 3*x^2 + 6, 27 ] false Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:21:19 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (111*x-y)*(11*y-2*x)*(13*x-3*y+x*y) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:21:16 on modular [Seed = 3369905310] ------------------------------------- [ 1 ] true Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:21:32 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (111*x-y)*(11*y-2*x)*(13*x-3*y+x*y) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:21:29 on modular [Seed = 3252004226] ------------------------------------- [ x^4 + x^2 + 7, 3*x^2 + 6, 9 ] false Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:21:56 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-6 Sun Mar 14 2004 04:21:53 on modular [Seed = 4276787861] ------------------------------------- [ x^4 + x^2 + 7, 3*x^2 + 6, 9 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:23:11 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-6 Sun Mar 14 2004 04:23:07 on modular [Seed = 3637296351] ------------------------------------- >> I := ideal; ^ User error: bad syntax >> GroebnerBasis(I); ^ User error: Identifier 'I' has not been declared or assigned Total time: 4.329 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:23:27 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-6 Sun Mar 14 2004 04:23:23 on modular [Seed = 1464021976] ------------------------------------- [ x^4 + x^2 + 16, 3*x^2 + 15, 27 ] Total time: 4.369 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:25:18 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-6 Sun Mar 14 2004 04:25:15 on modular [Seed = 1214000290] ------------------------------------- [ x^4 + 2*x^2 + 1, 5*x^2 + 5, 25 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:25:33 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-6 Sun Mar 14 2004 04:25:30 on modular [Seed = 1936135784] ------------------------------------- [ x^4 + 5*x^2 + 97, 11*x^2 + 88, 121 ] Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:30:33 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-6 Sun Mar 14 2004 04:30:30 on modular [Seed = 1685062211] ------------------------------------- [ 1 ] Total time: 3.159 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:30:46 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-6 Sun Mar 14 2004 04:30:42 on modular [Seed = 1870334268] ------------------------------------- [ 1 ] Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:31:00 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-6 Sun Mar 14 2004 04:30:57 on modular [Seed = 2525163734] ------------------------------------- [ x^4 + 5*x^2 + 97, 11*x^2 + 88, 121 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:31:25 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-4*x^2)(2^2-16*x^2) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:31:22 on modular [Seed = 2174085114] ------------------------------------- [ x^4 + 5*x^2 + 97, 11*x^2 + 88, 121 ] >> (1-4*x^2)(2^2-16*x^2) in I; ^ Runtime error: Bad argument types Argument types given: RngMPolElt, RngMPolElt Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:31:35 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-4*x^2)*(2^2-16*x^2) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:31:32 on modular [Seed = 2291986157] ------------------------------------- [ x^4 + 5*x^2 + 97, 11*x^2 + 88, 121 ] true Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:32:13 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-4*x^2)*(4^2-9*x^2) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:32:10 on modular [Seed = 3014120760] ------------------------------------- [ x^4 + 5*x^2 + 97, 11*x^2 + 88, 121 ] true Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:32:43 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (8^2-25*x^2)*(4^2-9*x^2) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:32:40 on modular [Seed = 3132021779] ------------------------------------- [ x^4 + 5*x^2 + 97, 11*x^2 + 88, 121 ] true Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:33:14 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (8^2-25*x^2)*(4^2-9*x^2) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:33:11 on modular [Seed = 2763047522] ------------------------------------- [ x^4 + 5*x^2 + 97, 11*x^2 + 88, 121 ] true Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:33:31 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (8^2-25*x^2)*(4^2-9*x^2) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:33:28 on modular [Seed = 2948319574] ------------------------------------- [ 1 ] true Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:34:04 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (8^2-25*x^2)*(4^2-9*x^2) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:34:01 on modular [Seed = 3603083726] ------------------------------------- [ x^2 + 2*x + 5, 2*x*y + 2*x + 2*y + 6, 4*x + 4, y^2 + 2*y + 1, 4*y + 4, 8 ] false Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:34:39 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)*(3-y)*(5-x*y) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:34:36 on modular [Seed = 3252004604] ------------------------------------- [ x^2 + 2*x + 5, 2*x*y + 2*x + 2*y + 6, 4*x + 4, y^2 + 2*y + 1, 4*y + 4, 8 ] false Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:35:01 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)*(3-y)*(5-x*y) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:34:58 on modular [Seed = 3420433560] ------------------------------------- [ 1 ] true Total time: 3.109 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:35:09 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)*(3-y)*(5-x*y) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:35:06 on modular [Seed = 4142043565] ------------------------------------- [ x^2 + 2*x + 1, 2*x*y + 2*x + 2*y + 2, y^2 + 2*y + 1, 4 ] true Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:35:35 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)*(3-y)*(5-x*y) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:35:32 on modular [Seed = 3790964372] ------------------------------------- [ x^2 + 2*x + 5, 2*x*y + 2*x + 2*y + 6, 4*x + 4, y^2 + 2*y + 1, 4*y + 4, 8 ] false Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:35:53 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)*(3-y)*(5-x*y)*(11-2*x-7*y) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:35:50 on modular [Seed = 3959393420] ------------------------------------- [ x^2 + 2*x + 5, 2*x*y + 2*x + 2*y + 6, 4*x + 4, y^2 + 2*y + 1, 4*y + 4, 8 ] true Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:36:14 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)*(3-y)*(5-x*y)*(11-21*x-7*y) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:36:11 on modular [Seed = 285570696] ------------------------------------- [ 1 ] true Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:36:25 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)*(3-y)*(5-x*y)*(113-21*x-7*y) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:36:22 on modular [Seed = 504002970] ------------------------------------- [ 1 ] true Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:36:48 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)*(3-y)*(5-x*y)*(7-z) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:36:45 on modular [Seed = 118710456] ------------------------------------- [ x^2 + 2*x + 5, 2*x*y + 2*x + 2*y + 6, 4*x + 4, y^2 + 2*y + 1, 4*y + 4, z^2 + 2*z + 1, 8 ] false Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:37:04 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)*(3-y)*(5-x*y)*(7-z) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:37:01 on modular [Seed = 202927011] ------------------------------------- >> I := ideal; ^ User error: Real literal has no digits after decimal point >> GroebnerBasis(I); ^ User error: Identifier 'I' has not been declared or assigned >> (1-x)*(3-y)*(5-x*y)*(7-z) in I; ^ User error: Identifier 'I' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:37:14 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)*(3-y)*(5-x*y)*(7-z) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:37:11 on modular [Seed = 891376352] ------------------------------------- [ x^2 + 2*x + 5, 2*x*y + 2*x + 2*y + 6, 2*x*z + 2*x + 2*z + 2, 4*x + 4, y^2 + 2*y + 1, 4*y + 4, z^2 + 2*z + 1, 4*z + 4, 8 ] true Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:37:27 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)*(3-y)*(5-x*y)*(7-z) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:37:24 on modular [Seed = 573982180] ------------------------------------- [ x^2 + 2*x + 5, 2*x*y + 2*x + 2*y + 6, 2*x*z + 2*x + 2*z + 6, 4*x + 4, y^2 + 2*y + 1, 4*y + 4, z^2 + 2*z + 1, 4*z + 4, 8 ] true Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:37:39 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)*(3-y)*(5-x*y)*(7-z) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:37:36 on modular [Seed = 725568729] ------------------------------------- [ 1 ] true Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:37:49 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)*(3-y)*(5-x*y)*(7-z) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:37:46 on modular [Seed = 1346647976] ------------------------------------- [ x^2 + 2*x + 5, 2*x*y + 2*x + 2*y + 6, 2*x*z + 2*x + 2*z + 2, 4*x + 4, y^2 + 2*y + 1, 4*y + 4, z^2 + 2*z + 1, 4*z + 4, 8 ] true Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:38:03 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)*(3-y)*(5-x*y)*(7-z) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:38:00 on modular [Seed = 1498234547] ------------------------------------- [ 1 ] true Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:38:15 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)*(3-y)*(5-x*y)*(7-z) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:38:12 on modular [Seed = 1179790928] ------------------------------------- [ 1 ] true Total time: 2.969 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:38:23 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)*(3-y)*(5-x*y)*(7-z) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:38:20 on modular [Seed = 1331373905] ------------------------------------- [ 1 ] true Total time: 2.929 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:38:51 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)*(3-y)*(5-x*y)*(7-z) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:38:48 on modular [Seed = 1969298767] ------------------------------------- [ x^2 - 2*x - 2*y^2 + 4*y - 1, x*y^2 - x + 2*y^2 - 6*y + 4, 2*x*y - 2*x + 3*y^2 - 8*y + 5, y^3 - 3*y^2 + 3*y - 1 ] false Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:39:09 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x*y)(1-x*y^2) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:39:06 on modular [Seed = 1651903050] ------------------------------------- [ x^2 - 2*x - 2*y^2 + 4*y - 1, x*y^2 - x + 2*y^2 - 6*y + 4, 2*x*y - 2*x + 3*y^2 - 8*y + 5, y^3 - 3*y^2 + 3*y - 1 ] >> (1-x*y)(1-x*y^2) in I; ^ Runtime error: Bad argument types Argument types given: RngMPolElt, RngMPolElt Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:39:25 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x*y)*(1-x*y^2) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:39:22 on modular [Seed = 1803486003] ------------------------------------- [ x^2 - 2*x - 2*y^2 + 4*y - 1, x*y^2 - x + 2*y^2 - 6*y + 4, 2*x*y - 2*x + 3*y^2 - 8*y + 5, y^3 - 3*y^2 + 3*y - 1 ] false Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:39:43 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x*y)*(1-x*y^2) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:39:40 on modular [Seed = 2424633566] ------------------------------------- [ x^2 - 2*x + y^2 - 2*y + 2, x*y^2 - x + 2*y^2 - 6*y + 4, 2*x*y - 2*x - 2*y + 2, y^3 - 3*y + 2, 3*y^2 - 6*y + 3 ] false Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:39:57 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x*y)*(1-x*y^2)*(1-x^2*y) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:39:54 on modular [Seed = 2576216545] ------------------------------------- [ x^2 - 2*x + y^2 - 2*y + 2, x*y^2 - x + 2*y^2 - 6*y + 4, 2*x*y - 2*x - 2*y + 2, y^3 - 3*y + 2, 3*y^2 - 6*y + 3 ] true Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:40:11 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x*y)*(1-x*y^2)*(3-x^2*y) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:40:08 on modular [Seed = 2392516324] ------------------------------------- [ x^2 + 2*x + 5, 2*x*y + 2*x + 2*y + 6, 4*x + 4, y^2 + 2*y + 1, 4*y + 4, 8 ] false Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:40:34 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x*y)*(1-x*y^2)*(3-x^2*y) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:40:31 on modular [Seed = 3080970026] ------------------------------------- [ x^2 + 2*x + 1, 2*x*y + 2*x + 2*y + 2, y^2 + 2*y + 1, 4 ] true Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:40:45 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x*y)*(1-x*y^2)*(3-x^2*y) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:40:42 on modular [Seed = 3165180980] ------------------------------------- [ 1 ] true Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:40:53 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x*y)*(1-x*y^2)*(3-x^2*y) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:40:50 on modular [Seed = 2779893013] ------------------------------------- [ x^2 + 2*x + 5, 2*x*y + 2*x + 2*y + 6, 4*x + 4, y^2 + 2*y + 1, 4*y + 4, 8 ] false Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:41:08 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x*y)*(1-x*y^2)*(3-x^2*y)*(7-11*x*y^3) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:41:05 on modular [Seed = 3536239217] ------------------------------------- [ x^2 + 2*x + 5, 2*x*y + 2*x + 2*y + 6, 4*x + 4, y^2 + 2*y + 1, 4*y + 4, 8 ] true Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:41:29 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x*y)*(1-x*y^2)*(3-x^2*y)*(7-x-11*x*y^3) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:41:26 on modular [Seed = 3687822095] ------------------------------------- [ 1 ] true Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:41:41 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x*y)*(1-x*y^2)*(3-x^2*y)*(7-3*x-11*x*y^3) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:41:38 on modular [Seed = 3235162112] ------------------------------------- [ 1 ] true Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:41:58 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x*y)*(1-x*y^2)*(3-x^2*y)*(7*y-3*x-11*x*y^3) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:41:55 on modular [Seed = 3470435903] ------------------------------------- [ 1 ] true Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:42:14 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x*y)*(1-x*y^2)*(3-x^2*y)*(7*y^3-3*x-11*x*y^3) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:42:11 on modular [Seed = 4158889750] ------------------------------------- [ 1 ] true Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:42:47 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x*y)*(1-x*y^2)*(3-x^2*y)*(7*y^3-3*x-11*x*y^3) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:42:44 on modular [Seed = 4243101178] ------------------------------------- >> I := ideal; ^ Runtime error: Bad argument types Argument types given: RngMPolElt, RngMPolElt >> GroebnerBasis(I); ^ User error: Identifier 'I' has not been declared or assigned >> (1-x*y)*(1-x*y^2)*(3-x^2*y)*(7*y^3-3*x-11*x*y^3) in I; ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:42:56 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x*y)*(1-x*y^2)*(3-x^2*y)*(7*y^3-3*x-11*x*y^3) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:42:53 on modular [Seed = 3857812714] ------------------------------------- [ x*y - x - y + 1 ] false Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:43:17 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)(1-y^2) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:43:14 on modular [Seed = 319257138] ------------------------------------- [ x*y - x - y + 1 ] >> (1-x)(1-y^2) in I; ^ Runtime error: Bad argument types Argument types given: RngMPolElt, RngMPolElt Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:43:27 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)*(1-y^2) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:43:24 on modular [Seed = 437154613] ------------------------------------- [ x*y - x - y + 1 ] true Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:43:42 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)*(1-y^2) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:43:39 on modular [Seed = 18180185] ------------------------------------- [ 6*x^2 - 6, x*y - 3*x - y + 3 ] false Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:43:54 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)*(3-y^2) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:43:51 on modular [Seed = 136077644] ------------------------------------- [ 6*x^2 - 6, x*y - 3*x - y + 3 ] false Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:44:12 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)*(3-y^2) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:44:09 on modular [Seed = 925064781] ------------------------------------- >> I := ideal; ^ Runtime error: Bad argument types Argument types given: RngMPolElt, RngMPolElt >> GroebnerBasis(I); ^ User error: Identifier 'I' has not been declared or assigned >> (1-x)*(3-y^2) in I; ^ User error: Identifier 'I' has not been declared or assigned Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:44:20 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)*(3-y^2) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:44:17 on modular [Seed = 1042962268] ------------------------------------- [ 2*x^3 + 18*x - 20, 6*x^2 - 6, x*y + 57*x - y - 57, 60*x - 60 ] false Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:44:35 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)*(3-y^2)*(7-y^3) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:44:32 on modular [Seed = 623987894] ------------------------------------- [ 2*x^3 + 18*x - 20, 6*x^2 - 6, x*y + 57*x - y - 57, 60*x - 60 ] true Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:44:45 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)*(3-y^2)*(1-x^3) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:44:42 on modular [Seed = 741885365] ------------------------------------- [ 2*x^3 + 18*x - 20, 6*x^2 - 6, x*y + 57*x - y - 57, 60*x - 60 ] false Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:44:57 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)*(1-x^2)*(1-x^3) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:44:54 on modular [Seed = 1515074527] ------------------------------------- [ 2*x^3 + 18*x - 20, 6*x^2 - 6, x*y + 57*x - y - 57, 60*x - 60 ] false Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:46:22 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)*(1-x^2)*(1-x^3) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:46:18 on modular [Seed = 1146105277] ------------------------------------- [ x^4 + 2*x^3 - x^2 - 2*x + 1 ] false Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:46:33 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)*(1-x^2)*(1-x^3) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:46:30 on modular [Seed = 1936136854] ------------------------------------- [ 1 ] true Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:46:45 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)*(1-x^2)*(1-x^3) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:46:42 on modular [Seed = 2054033515] ------------------------------------- [ 1 ] true Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:46:59 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)*(1-x^2)*(1-x^3) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:46:56 on modular [Seed = 1635060578] ------------------------------------- [ 1 ] true Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:47:11 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)*(1-x^2)*(1-x^3) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:47:07 on modular [Seed = 1752957536] ------------------------------------- [ x^4 + 2*x^3 + 2*x^2 + 10*x + 7, 3*x^2 + 12*x + 6, 27 ] false Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:47:33 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-x^2)*(1-x-x^2-3*x^3) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:47:30 on modular [Seed = 2542009782] ------------------------------------- [ x^4 + 2*x^3 + 2*x^2 + 10*x + 7, 3*x^2 + 12*x + 6, 27 ] false Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:48:07 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-x^2)*(1-x-x^2-3*x^3) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:48:04 on modular [Seed = 2643064794] ------------------------------------- [ 1 ] true Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:48:16 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-x^2)*(1-x-x^2-3*x^3) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:48:13 on modular [Seed = 2224090826] ------------------------------------- [ 1 ] true Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:48:23 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-x^2)*(1-x-x^2-3*x^3) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:48:20 on modular [Seed = 3014121924] ------------------------------------- [ 1 ] true Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:48:35 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-x^2)*(1-x-x^2-3*x^3) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:48:32 on modular [Seed = 3132018905] ------------------------------------- [ 1 ] true Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:48:53 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-x^2)*(1-x-x^2-3*x^3) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:48:50 on modular [Seed = 2713045808] ------------------------------------- [ 1 ] true Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:49:01 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-x^2)*(1-x-x^2-3*x^3) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:48:58 on modular [Seed = 2830942769] ------------------------------------- [ 1 ] true Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:49:15 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-x^2)*(1-x-x^2-3*x^3) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:49:12 on modular [Seed = 3619929436] ------------------------------------- [ 1 ] true Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:49:23 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-x^2)*(1-x-x^2-3*x^3) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:49:20 on modular [Seed = 3737826413] ------------------------------------- [ 1 ] true Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:49:34 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-x^2)*(1-x-x^2-3*x^3) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:49:31 on modular [Seed = 3318853501] ------------------------------------- [ 1 ] true Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:50:00 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x-x^2)*(1-x-x^2-3*x^3) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:49:57 on modular [Seed = 4092041509] ------------------------------------- [ x^2 + 2*x + 1, 4 ] true Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:50:16 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-3*x)(1-5*x) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:50:13 on modular [Seed = 3824650533] ------------------------------------- [ x^2 + 2*x + 1, 4 ] >> (1-3*x)(1-5*x) in I; ^ Runtime error: Bad argument types Argument types given: RngMPolElt, RngMPolElt Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:50:26 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-3*x)*(1-5*x) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:50:23 on modular [Seed = 3942547494] ------------------------------------- [ x^2 + 2*x + 1, 4 ] false Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:53:04 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-3*x)*(1-5*x) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:53:01 on modular [Seed = 386104446] ------------------------------------- [ x^2 + 2*x + 1, 4 ] false Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:53:18 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-3*x)*(1-5*x)*(3-7*x) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:53:15 on modular [Seed = 403469191] ------------------------------------- [ x^2 + 2*x + 1, 4 ] true Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:53:26 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-3*x)*(1-5*x)*(3-7*x) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:53:23 on modular [Seed = 202925963] ------------------------------------- [ x^2 + 6*x + 9, 8*x + 8, 32 ] true Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:53:52 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > 131 in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:53:49 on modular [Seed = 807689097] ------------------------------------- [ x^2 + 6*x + 9, 8*x + 8, 32 ] false Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:54:11 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:54:08 on modular [Seed = 959271661] ------------------------------------- [ x^2 + 38*x + 17701, 68*x + 3604, 19652 ] >> in I; ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:54:32 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (11-3*x)*(211-5*x) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:54:29 on modular [Seed = 590825698] ------------------------------------- [ x^2 + 38*x + 17701, 68*x + 3604, 19652 ] false Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:54:44 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (11-3*x)*(211-5*x)*(3-7*x) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:54:41 on modular [Seed = 1413496737] ------------------------------------- [ x^2 + 38*x + 17701, 68*x + 3604, 19652 ] true Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:54:55 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (11-3*x)*(211-5*x)*(3-7*x) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:54:52 on modular [Seed = 1565079205] ------------------------------------- [ x^2 + 2*x + 1, 4 ] true Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:55:09 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (11-3*x)*(211-5*x)*(3-7*x) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:55:06 on modular [Seed = 1280845730] ------------------------------------- [ x^2 + 2*x + 1, 4 ] true Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:55:36 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (11-3*x)*(211-5*x)*(3-7*x) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:55:33 on modular [Seed = 1969297780] ------------------------------------- [ x^2 + 2*x + 1, 4 ] true Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:55:48 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (11-3*x)*(211-5*x)*(3-7*x) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:55:45 on modular [Seed = 2120880715] ------------------------------------- [ 1 ] true Total time: 3.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:56:02 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (11-3*x)*(211-5*x)*(3-7*x) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:55:59 on modular [Seed = 1735592796] ------------------------------------- [ 1 ] true Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:56:27 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (11-3*x)*(211-5*x)*(3-7*x) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:56:24 on modular [Seed = 1752958004] ------------------------------------- [ x^2 + 2*x + 1, 4 ] true Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:56:38 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (11-3*x)*(211-5*x)*(21-3*x) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:56:35 on modular [Seed = 2441477590] ------------------------------------- [ x^2 + 2*x + 1, 4 ] true Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:56:48 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (11-3*x)*(211-5*x)*(21-3*x) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:56:45 on modular [Seed = 2593060563] ------------------------------------- [ x^2 + 2*x + 1, 9 ] false Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:57:04 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (112312401-312414*x)*(211-5*x)*(21-3*x) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:57:01 on modular [Seed = 2358829301] ------------------------------------- [ x^2 + 2*x + 1, 9 ] true Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:57:17 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (112312401-312414*x)*(211-5*x)*(21-3*x) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:57:14 on modular [Seed = 3047283163] ------------------------------------- [ x^2 + 2*x + 1, 9 ] true Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:57:35 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (112312401-312414*x)*(211-5*x)*(21-3*x) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:57:32 on modular [Seed = 3198865958] ------------------------------------- [ 1 ] true Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:57:50 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (112312401-312414*x)*(211-5*x)*(21-3*x) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:57:47 on modular [Seed = 2813578024] ------------------------------------- [ x^2 + 2*x + 1, 15*x + 15, 225 ] false Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:58:19 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (112312401-312414*x)*(234532511-52345234*x)*(21-3*x) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:58:16 on modular [Seed = 2830943236] ------------------------------------- [ x^2 + 2*x + 1, 15*x + 15, 225 ] true Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:58:52 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (112312401-312414*x)*(234532511-52345234*x)*(21-3*x) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:58:49 on modular [Seed = 3519397148] ------------------------------------- [ x^2 + 2*x + 1, 5*x + 5, 25 ] true Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:59:10 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (112312401-312414*x)*(24234223+2123423*x)*(21-3*x) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:59:07 on modular [Seed = 3670980133] ------------------------------------- [ x^2 + 2*x + 1, 5*x + 5, 25 ] true Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:59:33 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (112312401-312414*x)*(24234223+2123423*x)*(21-3*x) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:59:30 on modular [Seed = 3285692117] ------------------------------------- [ 1 ] true Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 04:59:45 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (112312401-312414*x)*(24234223+2123423*x)*(21-3*x) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:59:42 on modular [Seed = 4108360174] ------------------------------------- [ 1 ] true Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 05:00:00 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (112312401-312414*x)*(24234223+2123423*x)*(21-3*x) in I; Output: Magma V2.10-6 Sun Mar 14 2004 04:59:57 on modular [Seed = 4293628662] ------------------------------------- [ 1 ] true Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 05:00:18 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (112312401-312414*x)*(24234223+2123423*x)*(21-3*x) in I; Output: Magma V2.10-6 Sun Mar 14 2004 05:00:15 on modular [Seed = 4026237652] ------------------------------------- [ x^3 + 2*x - 1 ] false Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 05:00:38 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (112312401-312414*x)*(24234223+2123423*x)*(21-3*x) in I; Output: Magma V2.10-6 Sun Mar 14 2004 05:00:35 on modular [Seed = 285572167] ------------------------------------- [ x^4 + 2*x^3 + 3*x^2 + 46*x + 925, 4*x^2 + 16*x + 1368, 52*x + 4836, 8788 ] false Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 05:01:04 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-2*x-x^3)*(1-3*x-x^5) in I; Output: Magma V2.10-6 Sun Mar 14 2004 05:01:01 on modular [Seed = 1338696] ------------------------------------- [ x^4 + 2*x^3 + 3*x^2 + 46*x + 925, 4*x^2 + 16*x + 1368, 52*x + 4836, 8788 ] false Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 05:01:19 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-2*x-x^3)*(1-3*x-x^5) in I; Output: Magma V2.10-6 Sun Mar 14 2004 05:01:16 on modular [Seed = 1026117700] ------------------------------------- [ 1 ] true Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 05:01:27 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-2*x-x^3)*(1-3*x-x^5) in I; Output: Magma V2.10-6 Sun Mar 14 2004 05:01:24 on modular [Seed = 607144261] ------------------------------------- [ 1 ] true Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 05:01:41 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-2*x-x^3)*(1-3*x-x^5) in I; Output: Magma V2.10-6 Sun Mar 14 2004 05:01:38 on modular [Seed = 792412856] ------------------------------------- [ x^2 + 2*x + 1, 4 ] false Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 146-BARC-X25.libre.retevision.es. (62.82.3.146) Time: Sun Mar 14 05:14:30 2004 Input: Mf := {x: x in M | x[1] eq x[2]}; Mtf := Mt meet Mf; Mr := [Random(M) : n in [1..100000]]; numMt:= #({x: x in Mr | x in Mt}); numMf:= #({x: x in Mr | x in Mf}); numMtf:= #({x: x in Mr | x in Mtf}); coef:=function(q,r) exp:=[1]; for i:=1 to r-1 do exp:= Include(exp,q^i); end for; return Reverse(exp); end function; Nqr:=function(q,r) sum:=function(C) S:=0; for i:=1 to #(C) do S:=C[i]+S; end for; return S; end function; P:=PolynomialRing(GF(q^r)); C:=coef(q,r); nqr:=x^(sum(C)); return nqr; end function; Tqr:=function(q,r) P:=PolynomialRing(GF(q^r)); C:=coef(q,r); tqr:=0; for i:=1 to #(C) do tqr:=x^C[i]+tqr; end for; return tqr; end function; Output: Magma V2.10-6 Sun Mar 14 2004 05:14:26 on modular [Seed = 1096102358] ------------------------------------- >> Mf := {x: x in M | x[1] eq x[2]}; ^ User error: Identifier 'M' has not been declared or assigned >> Mtf := Mt meet Mf; ^ User error: Identifier 'Mt' has not been declared or assigned >> Mr := [Random(M) : n in [1..100000]]; ^ User error: Identifier 'M' has not been declared or assigned >> numMt:= #({x: x in Mr | x in Mt}); ^ User error: Identifier 'Mr' has not been declared or assigned >> numMf:= #({x: x in Mr | x in Mf}); ^ User error: Identifier 'Mr' has not been declared or assigned >> numMtf:= #({x: x in Mr | x in Mtf}); ^ User error: Identifier 'Mr' has not been declared or assigned Total time: 3.159 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 09:10:24 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); KQR:=GF(q,r); punts:=[a,b in KQR | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b)]; return (punts); end function; punts_olav(7,3); Output: Magma V2.10-6 Sun Mar 14 2004 09:10:21 on modular [Seed = 1214017426] ------------------------------------- x^57 x^49 + x^7 + x >> punts:=[a,b in KQR | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b)]; ^ User error: bad syntax >> return (punts); ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> punts_olav(7,3);; ^ User error: Identifier 'punts_olav' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 09:10:53 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); KQR:=GF(q,r); punts:=[:a,b in KQR | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b)]; return (punts); end function; punts_olav(7,3); Output: Magma V2.10-6 Sun Mar 14 2004 09:10:50 on modular [Seed = 2120898947] ------------------------------------- x^57 x^49 + x^7 + x >> punts:=[:a,b in KQR | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b)]; ^ User error: bad syntax >> return (punts); ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> punts_olav(7,3);; ^ User error: Identifier 'punts_olav' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 09:11:12 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); KQR:=GF(q,r); punts:=[a,b in KQR | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b)]; return (punts); end function; punts_olav(7,3); Output: Magma V2.10-6 Sun Mar 14 2004 09:11:09 on modular [Seed = 1701921423] ------------------------------------- x^57 x^49 + x^7 + x >> punts:=[a,b in KQR | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b)]; ^ User error: bad syntax >> return (punts); ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> punts_olav(7,3);; ^ User error: Identifier 'punts_olav' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 09:12:14 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); KQR:=GF(q,r); punts:=; return (punts); end function; punts_olav(7,3); Output: Magma V2.10-6 Sun Mar 14 2004 09:12:11 on modular [Seed = 1819821120] ------------------------------------- x^57 x^49 + x^7 + x >> punts:=; ^ User error: bad syntax >> return (punts); ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> punts_olav(7,3);; ^ User error: Identifier 'punts_olav' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 09:12:40 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); KQR:=GF(q,r); punts:=; return (punts); end function; punts_olav(7,3); Output: Magma V2.10-6 Sun Mar 14 2004 09:12:37 on modular [Seed = 2475146193] ------------------------------------- x^57 x^49 + x^7 + x >> punts:=; ^ User error: bad syntax >> return (punts); ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> punts_olav(7,3);; ^ User error: Identifier 'punts_olav' has not been declared or assigned Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 09:12:58 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); KQR:=GF(q,r); punts:=; return (punts); end function; punts_olav(7,3); Output: Magma V2.10-6 Sun Mar 14 2004 09:12:55 on modular [Seed = 2593043178] ------------------------------------- x^57 x^49 + x^7 + x >> punts:=; ^ User error: bad syntax >> return (punts); ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> punts_olav(7,3);; ^ User error: Identifier 'punts_olav' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 09:15:18 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); KQR:=GF(q,r); punts_olav:=function (q,r); KQR:=GF(q,r); punts:=[a,b in KQR | Evaluate(x^57,a) eq Evaluate(x^49 + x^7 + x,b)]; return (punts); end function; punts_olav(7,3); Output: Magma V2.10-6 Sun Mar 14 2004 09:15:15 on modular [Seed = 2342495087] ------------------------------------- x^57 x^49 + x^7 + x >> punts:=[a,b in KQR | Evaluate(x^57,a) eq Evaluate(x^49 + x^7 + x,b)]; ^ User error: bad syntax >> return (punts); ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> punts_olav(7,3);; ^ User error: Identifier 'punts_olav' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 09:15:37 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); KQR:=GF(q,r); punts_olav:=function (q,r); KQR:=GF(q,r); punts:=; return (punts); end function; punts_olav(7,3); Output: Magma V2.10-6 Sun Mar 14 2004 09:15:34 on modular [Seed = 2997263267] ------------------------------------- x^57 x^49 + x^7 + x >> punts:=; ^ User error: bad syntax >> return (punts); ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> punts_olav(7,3);; ^ User error: Identifier 'punts_olav' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 09:15:57 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); KQR:=GF(q,r); punts_olav:=function (q,r); KQR:=GF(q,r); punts:=func; return (punts); end function; punts_olav(7,3); Output: Magma V2.10-6 Sun Mar 14 2004 09:15:54 on modular [Seed = 2813562538] ------------------------------------- x^57 x^49 + x^7 + x >> punts:=func; ^ User error: bad syntax >> return (punts); ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> punts_olav(7,3);; ^ User error: Identifier 'punts_olav' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 09:16:45 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); KQR:=GF(q,r); punts_olav:=function (q,r); KQR:=GF(q,r); punts:=func; return (punts); end function; punts_olav(7,3); Output: Magma V2.10-6 Sun Mar 14 2004 09:16:42 on modular [Seed = 2914616560] ------------------------------------- x^57 x^49 + x^7 + x >> punts:=func; ^ User error: bad syntax >> return (punts); ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> punts_olav(7,3);; ^ User error: Identifier 'punts_olav' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 09:17:02 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); KQR:=GF(q,r); punts_olav:=function (q,r); KQR:=GF(q,r); punts:=func[a,b in KQR | Evaluate(x^57,a) eq Evaluate(x^49 + x^7 + x,b)]; return (punts); end function; punts_olav(7,3); Output: Magma V2.10-6 Sun Mar 14 2004 09:16:59 on modular [Seed = 3569417624] ------------------------------------- x^57 x^49 + x^7 + x >> punts:=func[a,b in KQR | Evaluate(x^57,a) eq Evaluate(x^49 + x^7 + x,b)]; ^ User error: bad syntax >> return (punts); ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> punts_olav(7,3);; ^ User error: Identifier 'punts_olav' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 09:17:23 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); KQR:=GF(q,r); punts_olav:=function (q,r); KQR:=GF(q,r); punts:=func; return (punts); end function; punts_olav(7,3); Output: Magma V2.10-6 Sun Mar 14 2004 09:17:20 on modular [Seed = 3687838396] ------------------------------------- x^57 x^49 + x^7 + x >> punts:=func; ^ User error: bad syntax >> return (punts); ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> punts_olav(7,3);; ^ User error: Identifier 'punts_olav' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 09:19:44 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); KQR:=GF(q,r); punts_olav:=function (q,r); KQR:=GF(q,r); punts:=func; return (punts); end function; punts_olav(7,3); Output: Magma V2.10-6 Sun Mar 14 2004 09:19:41 on modular [Seed = 3252021291] ------------------------------------- x^57 x^49 + x^7 + x >> punts:=func; ^ User error: bad syntax >> return (punts); ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> punts_olav(7,3);; ^ User error: Identifier 'punts_olav' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 09:20:05 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); KQR:=GF(q,r); punts_olav:=function (q,r); KQR:=GF(q,r); punts:=func<:a,b in KQR | Evaluate(x^57,a) eq Evaluate(x^49 + x^7 + x,b)>; return (punts); end function; punts_olav(7,3); Output: Magma V2.10-6 Sun Mar 14 2004 09:20:02 on modular [Seed = 4041530101] ------------------------------------- x^57 x^49 + x^7 + x >> punts:=func<:a,b in KQR | Evaluate(x^57,a) eq Evaluate(x^49 + x^7 + x,b)>; ^ User error: bad syntax >> return (punts); ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> punts_olav(7,3);; ^ User error: Identifier 'punts_olav' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 09:22:26 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); KQR:=GF(q,r); punts:=[[a, b] : a, b in KQR | Evaluate(x^57,a) eq Evaluate(x^49 + x^7 + x,b)]; return (punts); end function; punts_olav(7,3); Output: Magma V2.10-6 Sun Mar 14 2004 09:22:23 on modular [Seed = 3891514735] ------------------------------------- x^57 x^49 + x^7 + x >> punts:=[[a, b] : a, b in KQR | Evaluate(x^57,a) eq Evaluate(x^49 + x^7 + x, ^ User error: Identifier 'x' has not been declared or assigned >> end function; punts_olav(7,3);; ^ User error: Identifier 'punts_olav' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 09:23:21 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); KQR:=GF(q,r); punts:=[[a, b] : a, b in KQR | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),,b)]; return (punts); end function; punts_olav(7,3); Output: Magma V2.10-6 Sun Mar 14 2004 09:23:18 on modular [Seed = 3992569644] ------------------------------------- x^57 x^49 + x^7 + x >> punts:=[[a, b] : a, b in KQR | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),,b ^ User error: bad syntax >> return (punts); ^ User error: A 'return' can only be used inside a procedure or function >> end function; punts_olav(7,3);; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 09:23:57 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); KQR:=GF(q,r); punts:=[[a, b] : a, b in KQR | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b)]; return (punts); end function; punts_olav(7,3); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Mar 14 2004 09:23:34 on modular [Seed = 453980645] ------------------------------------- x^57 x^49 + x^7 + x [ [ 1, $.1 ], [ 1, $.1^2 ], [ 1, $.1^7 ], [ 1, $.1^10 ], [ 1, $.1^11 ], [ 1, $.1^14 ], [ 1, $.1^16 ], [ 1, $.1^25 ], [ 1, $.1^37 ], [ 1, $.1^49 ], [ 1, $.1^66 ], [ 1, $.1^70 ], [ 1, $.1^77 ], [ 1, $.1^87 ], [ 1, $.1^90 ], [ 1, $.1^97 ], [ 1, $.1^98 ], [ 1, $.1^100 ], [ 1, $.1^103 ], [ 1, $.1^112 ], [ 1, $.1^120 ], [ 1, $.1^131 ], [ 1, $.1^132 ], [ 1, $.1^137 ], [ 1, $.1^146 ], [ 1, $.1^148 ], [ 1, $.1^156 ], [ 1, $.1^159 ], [ 1, $.1^175 ], [ 1, $.1^195 ], [ 1, $.1^197 ], [ 1, $.1^199 ], [ 1, $.1^215 ], [ 1, $.1^233 ], [ 1, $.1^240 ], [ 1, $.1^259 ], [ 1, $.1^263 ], [ 1, $.1^267 ], [ 1, $.1^275 ], [ 1, 5 ], [ 1, $.1^288 ], [ 1, $.1^306 ], [ 1, $.1^307 ], [ 1, $.1^312 ], [ 1, $.1^314 ], [ 1, $.1^321 ], [ 1, $.1^337 ], [ 1, $.1^338 ], [ 1, $.1^339 ], [ $.1, 1 ], [ $.1, $.1^3 ], [ $.1, $.1^21 ], [ $.1, $.1^22 ], [ $.1, $.1^27 ], [ $.1, $.1^29 ], [ $.1, $.1^36 ], [ $.1, $.1^52 ], [ $.1, $.1^53 ], [ $.1, $.1^54 ], [ $.1, $.1^58 ], [ $.1, $.1^59 ], [ $.1, $.1^64 ], [ $.1, $.1^67 ], [ $.1, $.1^68 ], [ $.1, $.1^71 ], [ $.1, $.1^73 ], [ $.1, $.1^82 ], [ $.1, $.1^94 ], [ $.1, $.1^106 ], [ $.1, $.1^123 ], [ $.1, $.1^127 ], [ $.1, $.1^134 ], [ $.1, $.1^144 ], [ $.1, $.1^147 ], [ $.1, $.1^154 ], [ $.1, $.1^155 ], [ $.1, $.1^157 ], [ $.1, $.1^160 ], [ $.1, $.1^169 ], [ $.1, $.1^177 ], [ $.1, $.1^188 ], [ $.1, $.1^189 ], [ $.1, $.1^194 ], [ $.1, $.1^203 ], [ $.1, $.1^205 ], [ $.1, $.1^213 ], [ $.1, $.1^216 ], [ $.1, $.1^232 ], [ $.1, $.1^252 ], [ $.1, $.1^254 ], [ $.1, $.1^256 ], [ $.1, $.1^272 ], [ $.1, $.1^290 ], [ $.1, $.1^297 ], [ $.1, $.1^316 ], [ $.1, $.1^320 ], [ $.1, $.1^324 ], [ $.1, $.1^332 ], [ $.1^2, $.1^5 ], [ $.1^2, $.1^12 ], [ $.1^2, $.1^31 ], [ $.1^2, $.1^35 ], [ $.1^2, $.1^39 ], [ $.1^2, $.1^47 ], [ $.1^2, 3 ], [ $.1^2, $.1^60 ], [ $.1^2, $.1^78 ], [ $.1^2, $.1^79 ], [ $.1^2, $.1^84 ], [ $.1^2, $.1^86 ], [ $.1^2, $.1^93 ], [ $.1^2, $.1^109 ], [ $.1^2, $.1^110 ], [ $.1^2, $.1^111 ], [ $.1^2, $.1^115 ], [ $.1^2, $.1^116 ], [ $.1^2, $.1^121 ], [ $.1^2, $.1^124 ], [ $.1^2, $.1^125 ], [ $.1^2, $.1^128 ], [ $.1^2, $.1^130 ], [ $.1^2, $.1^139 ], [ $.1^2, $.1^151 ], [ $.1^2, $.1^163 ], [ $.1^2, $.1^180 ], [ $.1^2, $.1^184 ], [ $.1^2, $.1^191 ], [ $.1^2, $.1^201 ], [ $.1^2, $.1^204 ], [ $.1^2, $.1^211 ], [ $.1^2, $.1^212 ], [ $.1^2, $.1^214 ], [ $.1^2, $.1^217 ], [ $.1^2, $.1^226 ], [ $.1^2, $.1^234 ], [ $.1^2, $.1^245 ], [ $.1^2, $.1^246 ], [ $.1^2, $.1^251 ], [ $.1^2, $.1^260 ], [ $.1^2, $.1^262 ], [ $.1^2, $.1^270 ], [ $.1^2, $.1^273 ], [ $.1^2, $.1^289 ], [ $.1^2, $.1^309 ], [ $.1^2, $.1^311 ], [ $.1^2, $.1^313 ], [ $.1^2, $.1^329 ], [ $.1^3, $.1^4 ], [ $.1^3, $.1^24 ], [ $.1^3, $.1^26 ], [ $.1^3, $.1^28 ], [ $.1^3, $.1^44 ], [ $.1^3, $.1^62 ], [ $.1^3, $.1^69 ], [ $.1^3, $.1^88 ], [ $.1^3, $.1^92 ], [ $.1^3, $.1^96 ], [ $.1^3, $.1^104 ], [ $.1^3, 2 ], [ $.1^3, $.1^117 ], [ $.1^3, $.1^135 ], [ $.1^3, $.1^136 ], [ $.1^3, $.1^141 ], [ $.1^3, $.1^143 ], [ $.1^3, $.1^150 ], [ $.1^3, $.1^166 ], [ $.1^3, $.1^167 ], [ $.1^3, $.1^168 ], [ $.1^3, $.1^172 ], [ $.1^3, $.1^173 ], [ $.1^3, $.1^178 ], [ $.1^3, $.1^181 ], [ $.1^3, $.1^182 ], [ $.1^3, $.1^185 ], [ $.1^3, $.1^187 ], [ $.1^3, $.1^196 ], [ $.1^3, $.1^208 ], [ $.1^3, $.1^220 ], [ $.1^3, $.1^237 ], [ $.1^3, $.1^241 ], [ $.1^3, $.1^248 ], [ $.1^3, $.1^258 ], [ $.1^3, $.1^261 ], [ $.1^3, $.1^268 ], [ $.1^3, $.1^269 ], [ $.1^3, $.1^271 ], [ $.1^3, $.1^274 ], [ $.1^3, $.1^283 ], [ $.1^3, $.1^291 ], [ $.1^3, $.1^302 ], [ $.1^3, $.1^303 ], [ $.1^3, $.1^308 ], [ $.1^3, $.1^317 ], [ $.1^3, $.1^319 ], [ $.1^3, $.1^327 ], [ $.1^3, $.1^330 ], [ $.1^4, $.1^6 ], [ $.1^4, $.1^17 ], [ $.1^4, $.1^18 ], [ $.1^4, $.1^23 ], [ $.1^4, $.1^32 ], [ $.1^4, $.1^34 ], [ $.1^4, $.1^42 ], [ $.1^4, $.1^45 ], [ $.1^4, $.1^61 ], [ $.1^4, $.1^81 ], [ $.1^4, $.1^83 ], [ $.1^4, $.1^85 ], [ $.1^4, $.1^101 ], [ $.1^4, $.1^119 ], [ $.1^4, $.1^126 ], [ $.1^4, $.1^145 ], [ $.1^4, $.1^149 ], [ $.1^4, $.1^153 ], [ $.1^4, $.1^161 ], [ $.1^4, 6 ], [ $.1^4, $.1^174 ], [ $.1^4, $.1^192 ], [ $.1^4, $.1^193 ], [ $.1^4, $.1^198 ], [ $.1^4, $.1^200 ], [ $.1^4, $.1^207 ], [ $.1^4, $.1^223 ], [ $.1^4, $.1^224 ], [ $.1^4, $.1^225 ], [ $.1^4, $.1^229 ], [ $.1^4, $.1^230 ], [ $.1^4, $.1^235 ], [ $.1^4, $.1^238 ], [ $.1^4, $.1^239 ], [ $.1^4, $.1^242 ], [ $.1^4, $.1^244 ], [ $.1^4, $.1^253 ], [ $.1^4, $.1^265 ], [ $.1^4, $.1^277 ], [ $.1^4, $.1^294 ], [ $.1^4, $.1^298 ], [ $.1^4, $.1^305 ], [ $.1^4, $.1^315 ], [ $.1^4, $.1^318 ], [ $.1^4, $.1^325 ], [ $.1^4, $.1^326 ], [ $.1^4, $.1^328 ], [ $.1^4, $.1^331 ], [ $.1^4, $.1^340 ], [ $.1^5, $.1^9 ], [ $.1^5, $.1^13 ], [ $.1^5, $.1^20 ], [ $.1^5, $.1^30 ], [ $.1^5, $.1^33 ], [ $.1^5, $.1^40 ], [ $.1^5, $.1^41 ], [ $.1^5, $.1^43 ], [ $.1^5, $.1^46 ], [ $.1^5, $.1^55 ], [ $.1^5, $.1^63 ], [ $.1^5, $.1^74 ], [ $.1^5, $.1^75 ], [ $.1^5, $.1^80 ], [ $.1^5, $.1^89 ], [ $.1^5, $.1^91 ], [ $.1^5, $.1^99 ], [ $.1^5, $.1^102 ], [ $.1^5, $.1^118 ], [ $.1^5, $.1^138 ], [ $.1^5, $.1^140 ], [ $.1^5, $.1^142 ], [ $.1^5, $.1^158 ], [ $.1^5, $.1^176 ], [ $.1^5, $.1^183 ], [ $.1^5, $.1^202 ], [ $.1^5, $.1^206 ], [ $.1^5, $.1^210 ], [ $.1^5, $.1^218 ], [ $.1^5, 4 ], [ $.1^5, $.1^231 ], [ $.1^5, $.1^249 ], [ $.1^5, $.1^250 ], [ $.1^5, $.1^255 ], [ $.1^5, $.1^257 ], [ $.1^5, $.1^264 ], [ $.1^5, $.1^280 ], [ $.1^5, $.1^281 ], [ $.1^5, $.1^282 ], [ $.1^5, $.1^286 ], [ $.1^5, $.1^287 ], [ $.1^5, $.1^292 ], [ $.1^5, $.1^295 ], [ $.1^5, $.1^296 ], [ $.1^5, $.1^299 ], [ $.1^5, $.1^301 ], [ $.1^5, $.1^310 ], [ $.1^5, $.1^322 ], [ $.1^5, $.1^334 ], [ $.1^6, $.1 ], [ $.1^6, $.1^2 ], [ $.1^6, $.1^7 ], [ $.1^6, $.1^10 ], [ $.1^6, $.1^11 ], [ $.1^6, $.1^14 ], [ $.1^6, $.1^16 ], [ $.1^6, $.1^25 ], [ $.1^6, $.1^37 ], [ $.1^6, $.1^49 ], [ $.1^6, $.1^66 ], [ $.1^6, $.1^70 ], [ $.1^6, $.1^77 ], [ $.1^6, $.1^87 ], [ $.1^6, $.1^90 ], [ $.1^6, $.1^97 ], [ $.1^6, $.1^98 ], [ $.1^6, $.1^100 ], [ $.1^6, $.1^103 ], [ $.1^6, $.1^112 ], [ $.1^6, $.1^120 ], [ $.1^6, $.1^131 ], [ $.1^6, $.1^132 ], [ $.1^6, $.1^137 ], [ $.1^6, $.1^146 ], [ $.1^6, $.1^148 ], [ $.1^6, $.1^156 ], [ $.1^6, $.1^159 ], [ $.1^6, $.1^175 ], [ $.1^6, $.1^195 ], [ $.1^6, $.1^197 ], [ $.1^6, $.1^199 ], [ $.1^6, $.1^215 ], [ $.1^6, $.1^233 ], [ $.1^6, $.1^240 ], [ $.1^6, $.1^259 ], [ $.1^6, $.1^263 ], [ $.1^6, $.1^267 ], [ $.1^6, $.1^275 ], [ $.1^6, 5 ], [ $.1^6, $.1^288 ], [ $.1^6, $.1^306 ], [ $.1^6, $.1^307 ], [ $.1^6, $.1^312 ], [ $.1^6, $.1^314 ], [ $.1^6, $.1^321 ], [ $.1^6, $.1^337 ], [ $.1^6, $.1^338 ], [ $.1^6, $.1^339 ], [ $.1^7, 1 ], [ $.1^7, $.1^3 ], [ $.1^7, $.1^21 ], [ $.1^7, $.1^22 ], [ $.1^7, $.1^27 ], [ $.1^7, $.1^29 ], [ $.1^7, $.1^36 ], [ $.1^7, $.1^52 ], [ $.1^7, $.1^53 ], [ $.1^7, $.1^54 ], [ $.1^7, $.1^58 ], [ $.1^7, $.1^59 ], [ $.1^7, $.1^64 ], [ $.1^7, $.1^67 ], [ $.1^7, $.1^68 ], [ $.1^7, $.1^71 ], [ $.1^7, $.1^73 ], [ $.1^7, $.1^82 ], [ $.1^7, $.1^94 ], [ $.1^7, $.1^106 ], [ $.1^7, $.1^123 ], [ $.1^7, $.1^127 ], [ $.1^7, $.1^134 ], [ $.1^7, $.1^144 ], [ $.1^7, $.1^147 ], [ $.1^7, $.1^154 ], [ $.1^7, $.1^155 ], [ $.1^7, $.1^157 ], [ $.1^7, $.1^160 ], [ $.1^7, $.1^169 ], [ $.1^7, $.1^177 ], [ $.1^7, $.1^188 ], [ $.1^7, $.1^189 ], [ $.1^7, $.1^194 ], [ $.1^7, $.1^203 ], [ $.1^7, $.1^205 ], [ $.1^7, $.1^213 ], [ $.1^7, $.1^216 ], [ $.1^7, $.1^232 ], [ $.1^7, $.1^252 ], [ $.1^7, $.1^254 ], [ $.1^7, $.1^256 ], [ $.1^7, $.1^272 ], [ $.1^7, $.1^290 ], [ $.1^7, $.1^297 ], [ $.1^7, $.1^316 ], [ $.1^7, $.1^320 ], [ $.1^7, $.1^324 ], [ $.1^7, $.1^332 ], [ $.1^8, $.1^5 ], [ $.1^8, $.1^12 ], [ $.1^8, $.1^31 ], [ $.1^8, $.1^35 ], [ $.1^8, $.1^39 ], [ $.1^8, $.1^47 ], [ $.1^8, 3 ], [ $.1^8, $.1^60 ], [ $.1^8, $.1^78 ], [ $.1^8, $.1^79 ], [ $.1^8, $.1^84 ], [ $.1^8, $.1^86 ], [ $.1^8, $.1^93 ], [ $.1^8, $.1^109 ], [ $.1^8, $.1^110 ], [ $.1^8, $.1^111 ], [ $.1^8, $.1^115 ], [ $.1^8, $.1^116 ], [ $.1^8, $.1^121 ], [ $.1^8, $.1^124 ], [ $.1^8, $.1^125 ], [ $.1^8, $.1^128 ], [ $.1^8, $.1^130 ], [ $.1^8, $.1^139 ], [ $.1^8, $.1^151 ], [ $.1^8, $.1^163 ], [ $.1^8, $.1^180 ], [ $.1^8, $.1^184 ], [ $.1^8, $.1^191 ], [ $.1^8, $.1^201 ], [ $.1^8, $.1^204 ], [ $.1^8, $.1^211 ], [ $.1^8, $.1^212 ], [ $.1^8, $.1^214 ], [ $.1^8, $.1^217 ], [ $.1^8, $.1^226 ], [ $.1^8, $.1^234 ], [ $.1^8, $.1^245 ], [ $.1^8, $.1^246 ], [ $.1^8, $.1 ** WARNING: Output too long, hence truncated. Errors: /home/mfd/gomagma: line 2: 22531 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 09:26:34 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); KQR:=GF(q,r); punts:=[[a, b] : a, b in KQR | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b)]; return [punts]; end function; punts_olav(7,3); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Mar 14 2004 09:26:11 on modular [Seed = 169746833] ------------------------------------- x^57 x^49 + x^7 + x [ [ [ 1, $.1 ], [ 1, $.1^2 ], [ 1, $.1^7 ], [ 1, $.1^10 ], [ 1, $.1^11 ], [ 1, $.1^14 ], [ 1, $.1^16 ], [ 1, $.1^25 ], [ 1, $.1^37 ], [ 1, $.1^49 ], [ 1, $.1^66 ], [ 1, $.1^70 ], [ 1, $.1^77 ], [ 1, $.1^87 ], [ 1, $.1^90 ], [ 1, $.1^97 ], [ 1, $.1^98 ], [ 1, $.1^100 ], [ 1, $.1^103 ], [ 1, $.1^112 ], [ 1, $.1^120 ], [ 1, $.1^131 ], [ 1, $.1^132 ], [ 1, $.1^137 ], [ 1, $.1^146 ], [ 1, $.1^148 ], [ 1, $.1^156 ], [ 1, $.1^159 ], [ 1, $.1^175 ], [ 1, $.1^195 ], [ 1, $.1^197 ], [ 1, $.1^199 ], [ 1, $.1^215 ], [ 1, $.1^233 ], [ 1, $.1^240 ], [ 1, $.1^259 ], [ 1, $.1^263 ], [ 1, $.1^267 ], [ 1, $.1^275 ], [ 1, 5 ], [ 1, $.1^288 ], [ 1, $.1^306 ], [ 1, $.1^307 ], [ 1, $.1^312 ], [ 1, $.1^314 ], [ 1, $.1^321 ], [ 1, $.1^337 ], [ 1, $.1^338 ], [ 1, $.1^339 ], [ $.1, 1 ], [ $.1, $.1^3 ], [ $.1, $.1^21 ], [ $.1, $.1^22 ], [ $.1, $.1^27 ], [ $.1, $.1^29 ], [ $.1, $.1^36 ], [ $.1, $.1^52 ], [ $.1, $.1^53 ], [ $.1, $.1^54 ], [ $.1, $.1^58 ], [ $.1, $.1^59 ], [ $.1, $.1^64 ], [ $.1, $.1^67 ], [ $.1, $.1^68 ], [ $.1, $.1^71 ], [ $.1, $.1^73 ], [ $.1, $.1^82 ], [ $.1, $.1^94 ], [ $.1, $.1^106 ], [ $.1, $.1^123 ], [ $.1, $.1^127 ], [ $.1, $.1^134 ], [ $.1, $.1^144 ], [ $.1, $.1^147 ], [ $.1, $.1^154 ], [ $.1, $.1^155 ], [ $.1, $.1^157 ], [ $.1, $.1^160 ], [ $.1, $.1^169 ], [ $.1, $.1^177 ], [ $.1, $.1^188 ], [ $.1, $.1^189 ], [ $.1, $.1^194 ], [ $.1, $.1^203 ], [ $.1, $.1^205 ], [ $.1, $.1^213 ], [ $.1, $.1^216 ], [ $.1, $.1^232 ], [ $.1, $.1^252 ], [ $.1, $.1^254 ], [ $.1, $.1^256 ], [ $.1, $.1^272 ], [ $.1, $.1^290 ], [ $.1, $.1^297 ], [ $.1, $.1^316 ], [ $.1, $.1^320 ], [ $.1, $.1^324 ], [ $.1, $.1^332 ], [ $.1^2, $.1^5 ], [ $.1^2, $.1^12 ], [ $.1^2, $.1^31 ], [ $.1^2, $.1^35 ], [ $.1^2, $.1^39 ], [ $.1^2, $.1^47 ], [ $.1^2, 3 ], [ $.1^2, $.1^60 ], [ $.1^2, $.1^78 ], [ $.1^2, $.1^79 ], [ $.1^2, $.1^84 ], [ $.1^2, $.1^86 ], [ $.1^2, $.1^93 ], [ $.1^2, $.1^109 ], [ $.1^2, $.1^110 ], [ $.1^2, $.1^111 ], [ $.1^2, $.1^115 ], [ $.1^2, $.1^116 ], [ $.1^2, $.1^121 ], [ $.1^2, $.1^124 ], [ $.1^2, $.1^125 ], [ $.1^2, $.1^128 ], [ $.1^2, $.1^130 ], [ $.1^2, $.1^139 ], [ $.1^2, $.1^151 ], [ $.1^2, $.1^163 ], [ $.1^2, $.1^180 ], [ $.1^2, $.1^184 ], [ $.1^2, $.1^191 ], [ $.1^2, $.1^201 ], [ $.1^2, $.1^204 ], [ $.1^2, $.1^211 ], [ $.1^2, $.1^212 ], [ $.1^2, $.1^214 ], [ $.1^2, $.1^217 ], [ $.1^2, $.1^226 ], [ $.1^2, $.1^234 ], [ $.1^2, $.1^245 ], [ $.1^2, $.1^246 ], [ $.1^2, $.1^251 ], [ $.1^2, $.1^260 ], [ $.1^2, $.1^262 ], [ $.1^2, $.1^270 ], [ $.1^2, $.1^273 ], [ $.1^2, $.1^289 ], [ $.1^2, $.1^309 ], [ $.1^2, $.1^311 ], [ $.1^2, $.1^313 ], [ $.1^2, $.1^329 ], [ $.1^3, $.1^4 ], [ $.1^3, $.1^24 ], [ $.1^3, $.1^26 ], [ $.1^3, $.1^28 ], [ $.1^3, $.1^44 ], [ $.1^3, $.1^62 ], [ $.1^3, $.1^69 ], [ $.1^3, $.1^88 ], [ $.1^3, $.1^92 ], [ $.1^3, $.1^96 ], [ $.1^3, $.1^104 ], [ $.1^3, 2 ], [ $.1^3, $.1^117 ], [ $.1^3, $.1^135 ], [ $.1^3, $.1^136 ], [ $.1^3, $.1^141 ], [ $.1^3, $.1^143 ], [ $.1^3, $.1^150 ], [ $.1^3, $.1^166 ], [ $.1^3, $.1^167 ], [ $.1^3, $.1^168 ], [ $.1^3, $.1^172 ], [ $.1^3, $.1^173 ], [ $.1^3, $.1^178 ], [ $.1^3, $.1^181 ], [ $.1^3, $.1^182 ], [ $.1^3, $.1^185 ], [ $.1^3, $.1^187 ], [ $.1^3, $.1^196 ], [ $.1^3, $.1^208 ], [ $.1^3, $.1^220 ], [ $.1^3, $.1^237 ], [ $.1^3, $.1^241 ], [ $.1^3, $.1^248 ], [ $.1^3, $.1^258 ], [ $.1^3, $.1^261 ], [ $.1^3, $.1^268 ], [ $.1^3, $.1^269 ], [ $.1^3, $.1^271 ], [ $.1^3, $.1^274 ], [ $.1^3, $.1^283 ], [ $.1^3, $.1^291 ], [ $.1^3, $.1^302 ], [ $.1^3, $.1^303 ], [ $.1^3, $.1^308 ], [ $.1^3, $.1^317 ], [ $.1^3, $.1^319 ], [ $.1^3, $.1^327 ], [ $.1^3, $.1^330 ], [ $.1^4, $.1^6 ], [ $.1^4, $.1^17 ], [ $.1^4, $.1^18 ], [ $.1^4, $.1^23 ], [ $.1^4, $.1^32 ], [ $.1^4, $.1^34 ], [ $.1^4, $.1^42 ], [ $.1^4, $.1^45 ], [ $.1^4, $.1^61 ], [ $.1^4, $.1^81 ], [ $.1^4, $.1^83 ], [ $.1^4, $.1^85 ], [ $.1^4, $.1^101 ], [ $.1^4, $.1^119 ], [ $.1^4, $.1^126 ], [ $.1^4, $.1^145 ], [ $.1^4, $.1^149 ], [ $.1^4, $.1^153 ], [ $.1^4, $.1^161 ], [ $.1^4, 6 ], [ $.1^4, $.1^174 ], [ $.1^4, $.1^192 ], [ $.1^4, $.1^193 ], [ $.1^4, $.1^198 ], [ $.1^4, $.1^200 ], [ $.1^4, $.1^207 ], [ $.1^4, $.1^223 ], [ $.1^4, $.1^224 ], [ $.1^4, $.1^225 ], [ $.1^4, $.1^229 ], [ $.1^4, $.1^230 ], [ $.1^4, $.1^235 ], [ $.1^4, $.1^238 ], [ $.1^4, $.1^239 ], [ $.1^4, $.1^242 ], [ $.1^4, $.1^244 ], [ $.1^4, $.1^253 ], [ $.1^4, $.1^265 ], [ $.1^4, $.1^277 ], [ $.1^4, $.1^294 ], [ $.1^4, $.1^298 ], [ $.1^4, $.1^305 ], [ $.1^4, $.1^315 ], [ $.1^4, $.1^318 ], [ $.1^4, $.1^325 ], [ $.1^4, $.1^326 ], [ $.1^4, $.1^328 ], [ $.1^4, $.1^331 ], [ $.1^4, $.1^340 ], [ $.1^5, $.1^9 ], [ $.1^5, $.1^13 ], [ $.1^5, $.1^20 ], [ $.1^5, $.1^30 ], [ $.1^5, $.1^33 ], [ $.1^5, $.1^40 ], [ $.1^5, $.1^41 ], [ $.1^5, $.1^43 ], [ $.1^5, $.1^46 ], [ $.1^5, $.1^55 ], [ $.1^5, $.1^63 ], [ $.1^5, $.1^74 ], [ $.1^5, $.1^75 ], [ $.1^5, $.1^80 ], [ $.1^5, $.1^89 ], [ $.1^5, $.1^91 ], [ $.1^5, $.1^99 ], [ $.1^5, $.1^102 ], [ $.1^5, $.1^118 ], [ $.1^5, $.1^138 ], [ $.1^5, $.1^140 ], [ $.1^5, $.1^142 ], [ $.1^5, $.1^158 ], [ $.1^5, $.1^176 ], [ $.1^5, $.1^183 ], [ $.1^5, $.1^202 ], [ $.1^5, $.1^206 ], [ $.1^5, $.1^210 ], [ $.1^5, $.1^218 ], [ $.1^5, 4 ], [ $.1^5, $.1^231 ], [ $.1^5, $.1^249 ], [ $.1^5, $.1^250 ], [ $.1^5, $.1^255 ], [ $.1^5, $.1^257 ], [ $.1^5, $.1^264 ], [ $.1^5, $.1^280 ], [ $.1^5, $.1^281 ], [ $.1^5, $.1^282 ], [ $.1^5, $.1^286 ], [ $.1^5, $.1^287 ], [ $.1^5, $.1^292 ], [ $.1^5, $.1^295 ], [ $.1^5, $.1^296 ], [ $.1^5, $.1^299 ], [ $.1^5, $.1^301 ], [ $.1^5, $.1^310 ], [ $.1^5, $.1^322 ], [ $.1^5, $.1^334 ], [ $.1^6, $.1 ], [ $.1^6, $.1^2 ], [ $.1^6, $.1^7 ], [ $.1^6, $.1^10 ], [ $.1^6, $.1^11 ], [ $.1^6, $.1^14 ], [ $.1^6, $.1^16 ], [ $.1^6, $.1^25 ], [ $.1^6, $.1^37 ], [ $.1^6, $.1^49 ], [ $.1^6, $.1^66 ], [ $.1^6, $.1^70 ], [ $.1^6, $.1^77 ], [ $.1^6, $.1^87 ], [ $.1^6, $.1^90 ], [ $.1^6, $.1^97 ], [ $.1^6, $.1^98 ], [ $.1^6, $.1^100 ], [ $.1^6, $.1^103 ], [ $.1^6, $.1^112 ], [ $.1^6, $.1^120 ], [ $.1^6, $.1^131 ], [ $.1^6, $.1^132 ], [ $.1^6, $.1^137 ], [ $.1^6, $.1^146 ], [ $.1^6, $.1^148 ], [ $.1^6, $.1^156 ], [ $.1^6, $.1^159 ], [ $.1^6, $.1^175 ], [ $.1^6, $.1^195 ], [ $.1^6, $.1^197 ], [ $.1^6, $.1^199 ], [ $.1^6, $.1^215 ], [ $.1^6, $.1^233 ], [ $.1^6, $.1^240 ], [ $.1^6, $.1^259 ], [ $.1^6, $.1^263 ], [ $.1^6, $.1^267 ], [ $.1^6, $.1^275 ], [ $.1^6, 5 ], [ $.1^6, $.1^288 ], [ $.1^6, $.1^306 ], [ $.1^6, $.1^307 ], [ $.1^6, $.1^312 ], [ $.1^6, $.1^314 ], [ $.1^6, $.1^321 ], [ $.1^6, $.1^337 ], [ $.1^6, $.1^338 ], [ $.1^6, $.1^339 ], [ $.1^7, 1 ], [ $.1^7, $.1^3 ], [ $.1^7, $.1^21 ], [ $.1^7, $.1^22 ], [ $.1^7, $.1^27 ], [ $.1^7, $.1^29 ], [ $.1^7, $.1^36 ], [ $.1^7, $.1^52 ], [ $.1^7, $.1^53 ], [ $.1^7, $.1^54 ], [ $.1^7, $.1^58 ], [ $.1^7, $.1^59 ], [ $.1^7, $.1^64 ], [ $.1^7, $.1^67 ], [ $.1^7, $.1^68 ], [ $.1^7, $.1^71 ], [ $.1^7, $.1^73 ], [ $.1^7, $.1^82 ], [ $.1^7, $.1^94 ], [ $.1^7, $.1^106 ], [ $.1^7, $.1^123 ], [ $.1^7, $.1^127 ], [ $.1^7, $.1^134 ], [ $.1^7, $.1^144 ], [ $.1^7, $.1^147 ], [ $.1^7, $.1^154 ], ** WARNING: Output too long, hence truncated. Errors: /home/mfd/gomagma: line 2: 22546 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 09:27:54 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); KQR:=GF(q,r); punts:=[[a, b] : a, b in KQR | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b)]; return [punts]; end function; #punts_olav(7,3); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Mar 14 2004 09:27:31 on modular [Seed = 85012174] ------------------------------------- x^57 x^49 + x^7 + x Errors: /home/mfd/gomagma: line 2: 22557 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host YahooBB218117016036.bbtec.net. (218.117.16.36) Time: Sun Mar 14 09:28:50 2004 Input: SmallGroupDatabase(); Output: Magma V2.10-6 Sun Mar 14 2004 09:28:46 on modular [Seed = 841358900] ------------------------------------- Small group database (handles layers 1 to 7) Total time: 2.999 seconds, Total memory usage: 2.11MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 09:28:53 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); KQR:=GF(q,r); punts:=[[a, b] : a, b in KQR | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b)]; return [punts]; end function; #(punts_olav(7,3)); Output: Magma V2.10-6 Sun Mar 14 2004 09:28:30 on modular [Seed = 1042944552] ------------------------------------- x^57 x^49 + x^7 + x 1 Total time: 22.939 seconds, Total memory usage: 4.09MB ************** MAGMA ***************** Host YahooBB218117016036.bbtec.net. (218.117.16.36) Time: Sun Mar 14 09:29:15 2004 Input: OpenSmallGroupDatabase(); Output: WARNING: MAGMA command contains unsafe command 'open', so it will not be executed. ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 09:29:37 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); KQR:=GF(q,r); punts:={[a, b] : a, b in KQR | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b}; return [punts]; end function; #(punts_olav(7,3)); Output: Magma V2.10-6 Sun Mar 14 2004 09:29:34 on modular [Seed = 1481405454] ------------------------------------- x^57 x^49 + x^7 + x >> punts:={[a, b] : a, b in KQR | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b} ^ User error: bad syntax >> return [punts]; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> #(punts_olav(7,3)); ^ User error: Identifier 'punts_olav' has not been declared or assigned Total time: 3.449 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 09:29:39 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); KQR:=GF(q,r); punts:={[a, b] : a, b in KQR | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b}; return [punts]; end function; (punts_olav(7,3)); Output: Magma V2.10-6 Sun Mar 14 2004 09:29:35 on modular [Seed = 1531934476] ------------------------------------- x^57 x^49 + x^7 + x >> punts:={[a, b] : a, b in KQR | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b} ^ User error: bad syntax >> return [punts]; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> (punts_olav(7,3)); ^ User error: Identifier 'punts_olav' has not been declared or assigned Total time: 3.499 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 09:30:26 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); KQR:=GF(q,r); punts:={[a, b] : a, b in KQR | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b)}; return [punts]; end function; punts_olav(7,3); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Mar 14 2004 09:30:03 on modular [Seed = 1096117554] ------------------------------------- x^57 x^49 + x^7 + x Errors: /home/mfd/gomagma: line 2: 22617 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 09:31:32 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); KQR:=GF(q,r); punts:={{a, b} : a, b in KQR | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b)}; return [punts]; end function; punts_olav(7,3); Output: Magma V2.10-6 Sun Mar 14 2004 09:31:10 on modular [Seed = 2054051532] ------------------------------------- x^57 x^49 + x^7 + x [ { { $.1^212, $.1^152 }, { $.1^55, $.1^160 }, { $.1^199, $.1^138 }, { $.1^59, $.1^183 }, { $.1^36, $.1^127 }, { $.1^77, $.1^294 }, { $.1^194, $.1^329 }, { $.1^71, $.1^20 }, { $.1^231, 2 }, { $.1^170, $.1^270 }, { $.1^160, $.1^153 }, { $.1^112, $.1^312 }, { $.1^319, $.1^194 }, { $.1^47, $.1^314 }, { $.1^94, $.1^241 }, { $.1^66, 5 }, { $.1^282, $.1^175 }, { $.1^200, $.1^151 }, { $.1^333, $.1^283 }, { $.1^46, $.1^281 }, { $.1^13, $.1^281 }, { $.1, $.1^168 }, { $.1^157, $.1^316 }, { $.1^34, $.1^136 }, { $.1^42, $.1^240 }, { $.1^231, $.1^155 }, { $.1^112, $.1^270 }, { $.1^203, $.1^73 }, { $.1^314, $.1^30 }, { $.1^99, $.1^161 }, { $.1^325, $.1^262 }, { $.1^157, $.1^295 }, { $.1^146, $.1^260 }, { $.1^178, $.1^153 }, { $.1^61, $.1^118 }, { $.1^306, $.1^318 }, { $.1^272, $.1^130 }, { $.1^232, $.1^307 }, { $.1^105, $.1^261 }, { $.1^33, $.1^220 }, { $.1^40, $.1^317 }, { $.1^67, $.1^216 }, { $.1^242, $.1^232 }, { $.1^78, $.1^70 }, { $.1^310, $.1^315 }, { $.1^82, $.1^283 }, { $.1^189, $.1^223 }, { $.1^319, $.1^141 }, { $.1^90, $.1^294 }, { $.1^103, $.1^108 }, { $.1^302, $.1^39 }, { $.1^277, $.1^3 }, { $.1^89, $.1^203 }, { $.1^258, $.1^207 }, { $.1^55, $.1^41 }, { $.1^223, $.1^250 }, { $.1^160, $.1^6 }, { $.1^188, $.1^270 }, { $.1^11, $.1^75 }, { $.1^89, $.1^292 }, { $.1^154, $.1^109 }, { $.1^271, $.1^216 }, { $.1^106, $.1^294 }, { $.1^341, $.1^292 }, { $.1^81, $.1^226 }, { $.1^239, $.1^296 }, { $.1^260, $.1^272 }, { $.1^210, $.1^83 }, { 1, $.1^148 }, { $.1^198, $.1^339 }, { $.1^158, $.1^151 }, { $.1^145, $.1^238 }, { $.1^291, $.1^104 }, { $.1^210, $.1^159 }, { $.1^99, $.1^47 }, { $.1^112, $.1^328 }, { $.1^67, $.1^325 }, { $.1^253, $.1^112 }, { $.1^319, $.1^256 }, { $.1^72, $.1^263 }, { $.1^269, $.1^140 }, { $.1^143, $.1^310 }, { $.1^194, $.1^109 }, { 3, $.1^338 }, { $.1^105, $.1^274 }, { $.1^242, $.1^274 }, { $.1^47, $.1^30 }, { $.1^215, $.1^292 }, { $.1^178, $.1^318 }, { $.1^239, $.1^140 }, { $.1^326, $.1^184 }, { $.1^308, $.1^267 }, { $.1^145, $.1^328 }, { $.1^145, $.1^118 }, { $.1^222, $.1^137 }, { $.1^76, $.1^32 }, { $.1^81, $.1^94 }, { $.1^275, $.1^18 }, { $.1^178, $.1^225 }, { $.1^308, $.1^86 }, { $.1^135, $.1^159 }, { $.1^151, $.1^296 }, { $.1^302, $.1^117 }, { $.1^341, $.1^287 }, { $.1^264, $.1^299 }, { $.1^90, $.1^102 }, { $.1^165, $.1^172 }, { 3, $.1^4 }, { $.1^309, $.1^212 }, { $.1^334, $.1^207 }, { $.1^176, $.1^201 }, { $.1^148, 6 }, { 1, $.1^109 }, { $.1^17, $.1^118 }, { $.1^55, $.1^173 }, { $.1^204, $.1^307 }, { $.1^167, $.1^129 }, { $.1^116, $.1^270 }, { $.1^323, $.1^75 }, { $.1^35, $.1^86 }, { $.1^105, $.1^62 }, { $.1^138, $.1^120 }, { $.1^320, $.1^19 }, { $.1^83, $.1^75 }, { $.1^6, $.1^314 }, { $.1^34, $.1^340 }, { $.1^210, $.1^314 }, { $.1^25, $.1^94 }, { $.1^35, $.1^281 }, { $.1^44, $.1^163 }, { $.1^56, $.1^234 }, { $.1^187, $.1^68 }, { $.1^306, $.1^186 }, { $.1^70, $.1^174 }, { $.1^187, $.1^94 }, { $.1^123, $.1^247 }, { $.1^156, $.1^336 }, { $.1^190, $.1^153 }, { $.1^34, $.1^239 }, { $.1^207, $.1^142 }, { $.1^137, $.1^54 }, { $.1^277, $.1^130 }, { $.1^299, $.1^9 }, { $.1^11, $.1^295 }, { $.1^203, $.1^140 }, { $.1^298, $.1^64 }, { $.1^101, 4 }, { $.1^101, $.1^292 }, { $.1^245, $.1^63 }, { $.1^133, $.1^290 }, { $.1^44, $.1^63 }, { $.1^232, $.1^193 }, { $.1^288, $.1^267 }, { $.1^22, $.1^315 }, { $.1^81, $.1^16 }, { 1, $.1 }, { $.1^155, $.1^301 }, { $.1^255, $.1^185 }, { $.1^91, $.1^64 }, { $.1^115, $.1^98 }, { $.1^25, $.1^72 }, { $.1^245, $.1^116 }, { $.1^288, $.1^294 }, { $.1^160, $.1^97 }, { $.1^94, $.1^307 }, { $.1^110, $.1^309 }, { $.1^292, $.1^305 }, { $.1^24, $.1^51 }, { $.1^62, $.1^184 }, { $.1^93, $.1^116 }, { $.1^78, $.1^195 }, { $.1^281, $.1^140 }, { $.1^101, $.1^28 }, { $.1^62, $.1^86 }, { $.1^204, $.1^20 }, { $.1^258, $.1^120 }, { $.1^104, $.1^115 }, { $.1^136, $.1^340 }, { $.1^234, $.1^16 }, { $.1^143, $.1^206 }, { $.1^308, $.1^117 }, { $.1^105, $.1^241 }, { $.1^227, $.1^249 }, { $.1^24, $.1^146 }, { $.1^298, $.1^207 }, { $.1^91, $.1^329 }, { $.1^318, $.1^131 }, { $.1^242, $.1^311 }, { $.1^248, $.1^262 }, { $.1^53, $.1^296 }, { $.1^99, $.1^311 }, { $.1^55, $.1^299 }, { $.1^122, $.1^311 }, { $.1^67, $.1^97 }, { $.1^310, $.1^317 }, { $.1^332, $.1^37 }, { $.1^322, $.1^293 }, { $.1^97, $.1^120 }, { $.1^140, $.1^86 }, { $.1^255, $.1^47 }, { $.1^330, $.1^7 }, { $.1^117, $.1^273 }, { $.1^220, $.1^85 }, { $.1^5, $.1^164 }, { $.1^210, $.1^29 }, { $.1^286, $.1^242 }, { $.1^2, $.1^31 }, { $.1^255, $.1^83 }, { $.1^305, $.1^340 }, { $.1^223, $.1^70 }, { $.1^202, $.1^335 }, { $.1^177, $.1^235 }, { $.1^137, 4 }, { $.1^289, $.1^314 }, { $.1^15, $.1^136 }, { $.1^137, $.1^292 }, { $.1^258, $.1^97 }, { $.1^16, $.1^306 }, { $.1^173, $.1^142 }, { $.1^81, $.1^40 }, { $.1^210, $.1^199 }, { $.1^7, $.1^186 }, { $.1^135, $.1^291 }, { $.1^168, $.1^93 }, { $.1^188, $.1^307 }, { $.1^68, $.1^246 }, { $.1^165, $.1^308 }, { $.1^3, $.1^196 }, { $.1^290, $.1^43 }, { $.1^324, $.1^259 }, { $.1^325, $.1^40 }, { $.1^199, $.1^6 }, { $.1^170, $.1^163 }, { $.1^255, $.1^237 }, { $.1^266, $.1^246 }, { $.1^100, $.1^224 }, { $.1^277, $.1^172 }, { $.1^240, $.1^10 }, { $.1^332, $.1^295 }, { $.1^178, $.1^229 }, { $.1^265, $.1^147 }, { $.1^73, $.1^163 }, { $.1^25, $.1^60 }, { $.1^254, $.1^289 }, { $.1^79, $.1^38 }, { $.1^205, $.1^283 }, { 1, $.1^97 }, { $.1^291, $.1^150 }, { $.1^2, $.1^125 }, { $.1^79, $.1^71 }, { $.1^91, $.1^324 }, { $.1^189, $.1^7 }, { $.1^220, 6 }, { $.1^5, $.1^152 }, { $.1^12, $.1^32 }, { $.1^15, $.1^261 }, { $.1^3, $.1^4 }, { $.1^198, $.1^166 }, { $.1^266, $.1^245 }, { $.1^66, $.1^267 }, { $.1^155, $.1^25 }, { $.1^135, $.1^237 }, { $.1^265, $.1^124 }, { $.1^222, $.1^267 }, { $.1^242, $.1^270 }, { $.1^88, $.1^145 }, { $.1^180, $.1^104 }, { $.1^166, 5 }, { $.1^253, $.1^202 }, { $.1^286, $.1^81 }, { $.1^220, $.1^207 }, { $.1^270, $.1^307 }, { $.1^123, $.1^172 }, { $.1^6, $.1^76 }, { $.1^246, $.1^137 }, { $.1^224, $.1^106 }, { $.1^37, $.1^18 }, { $.1^334, $.1^126 }, { $.1^232, $.1^247 }, { $.1^326, $.1^328 }, { $.1^231, $.1^241 }, { $.1^203, $.1^175 }, { $.1^242, $.1^130 }, { $.1^189, $.1^289 }, { $.1, $.1^120 }, { $.1^94, $.1^239 }, { $.1^264, $.1^53 }, { $.1^45, $.1^268 }, { $.1^189, $.1^135 }, { $.1^270, $.1^197 }, { $.1^13, $.1^65 }, { $.1^78, $.1^306 }, { $.1^224, $.1^280 }, { $.1^290, $.1^184 }, { $.1^96, $.1^141 }, { $.1^255, $.1^135 }, { $.1^194, $.1^295 }, { $.1^247, $.1^73 }, { $.1^14, $.1^192 }, { $.1^56, $.1^260 }, { $.1^277, $.1^4 }, { $.1^33, $.1^248 }, { $.1^176, $.1^299 }, { $.1^281, $.1^282 }, { $.1^248, $.1^9 }, { $.1^235, $.1^205 }, { $.1^187, $.1^82 }, { $.1^69, $.1^27 }, { $.1^281, $.1^305 }, { $.1^322, $.1^269 }, { $.1^315, $.1^52 }, { $.1^133, $.1^73 }, { $.1^192, $.1^262 }, { $.1^319, $.1^67 }, { $.1^89, $.1^95 }, { $.1^5, $.1^314 }, { $.1^7, $.1^30 }, { $.1^100, $.1^315 }, { $.1^316, $.1^32 }, { $.1^277, $.1^190 }, { $.1^7, $.1^318 }, { 1, $.1^2 }, { $.1^204, $.1^260 }, { $.1^218, $.1^163 }, { $.1^226, $.1^239 }, { $.1^217, $.1^230 }, { $.1^239, $.1^328 }, { $.1^18, $.1^98 }, { $.1^44, $.1^321 }, { $.1^36, $.1^229 }, { $.1^286, $.1^323 }, { $.1^77, $.1^41 }, { $.1^89, $.1^210 }, { $.1^110, $.1^180 }, { $.1^195, $.1^306 }, { $.1^200, $.1^260 }, { $.1^37, $.1^318 }, { $.1^289, $.1^316 }, { $.1^341, $.1 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.64.62) Time: Sun Mar 14 11:43:04 2004 Input: ex1:={i in 1..366 | i mod 7 eq 6}; Output: Magma V2.10-6 Sun Mar 14 2004 11:43:01 on modular [Seed = 1635101421] ------------------------------------- >> ex1:={i in 1..366 | i mod 7 eq 6}; ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.64.62) Time: Sun Mar 14 11:44:12 2004 Input: ex1:={i in 1..366 | (i mod 7) eq 6}; Output: Magma V2.10-6 Sun Mar 14 2004 11:44:09 on modular [Seed = 2609860699] ------------------------------------- >> ex1:={i in 1..366 | (i mod 7) eq 6}; ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.64.62) Time: Sun Mar 14 11:44:25 2004 Input: ex1:={i in [1..366] | (i mod 7) eq 6}; Output: Magma V2.10-6 Sun Mar 14 2004 11:44:22 on modular [Seed = 2458278253] ------------------------------------- >> ex1:={i in [1..366] | (i mod 7) eq 6}; ^ User error: Identifier 'i' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.64.62) Time: Sun Mar 14 11:45:52 2004 Input: i:=0; ex1:={i in [1..366] | (i mod 7) eq 6}; Output: Magma V2.10-6 Sun Mar 14 2004 11:45:49 on modular [Seed = 2207731623] ------------------------------------- >> ex1:={i in [1..366] | (i mod 7) eq 6}; ^ Runtime error in { ... }: Invalid set universe (no hashing algorithm) Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.64.62) Time: Sun Mar 14 11:46:18 2004 Input: i in [1..366]; Output: Magma V2.10-6 Sun Mar 14 2004 11:46:15 on modular [Seed = 3131995892] ------------------------------------- >> i in [1..366]; ^ User error: Identifier 'i' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.64.62) Time: Sun Mar 14 11:48:22 2004 Input: i:=0; Output: Magma V2.10-6 Sun Mar 14 2004 11:48:19 on modular [Seed = 3030415486] ------------------------------------- Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.64.62) Time: Sun Mar 14 11:49:10 2004 Input: {i: i in 1..36} Output: Magma V2.10-6 Sun Mar 14 2004 11:49:07 on modular [Seed = 2948293301] ------------------------------------- >> {i: i in 1..36} ^ User error: bad syntax Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.64.62) Time: Sun Mar 14 11:49:24 2004 Input: {i: i in [1..36]} Output: Magma V2.10-6 Sun Mar 14 2004 11:49:21 on modular [Seed = 2796710830] ------------------------------------- { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36 } Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.64.62) Time: Sun Mar 14 11:49:49 2004 Input: {i: i in [1..36]| (i mod 7) eq 6} Output: Magma V2.10-6 Sun Mar 14 2004 11:49:46 on modular [Seed = 3519356130] ------------------------------------- { 6, 13, 20, 27, 34 } Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.64.62) Time: Sun Mar 14 11:49:59 2004 Input: {i: i in [1..366]| (i mod 7) eq 6} Output: Magma V2.10-6 Sun Mar 14 2004 11:49:56 on modular [Seed = 3369862629] ------------------------------------- { 6, 13, 20, 27, 34, 41, 48, 55, 62, 69, 76, 83, 90, 97, 104, 111, 118, 125, 132, 139, 146, 153, 160, 167, 174, 181, 188, 195, 202, 209, 216, 223, 230, 237, 244, 251, 258, 265, 272, 279, 286, 293, 300, 307, 314, 321, 328, 335, 342, 349, 356, 363 } Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.64.62) Time: Sun Mar 14 11:50:19 2004 Input: ex1:={i: i in [1..366]| (i mod 7) eq 6}; Output: Magma V2.10-6 Sun Mar 14 2004 11:50:16 on modular [Seed = 4226758314] ------------------------------------- Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.64.62) Time: Sun Mar 14 11:50:45 2004 Input: ex1:={i: i in [1..366]| (i mod 7) eq 6}; print ex1; Output: Magma V2.10-6 Sun Mar 14 2004 11:50:41 on modular [Seed = 4125177997] ------------------------------------- { 6, 13, 20, 27, 34, 41, 48, 55, 62, 69, 76, 83, 90, 97, 104, 111, 118, 125, 132, 139, 146, 153, 160, 167, 174, 181, 188, 195, 202, 209, 216, 223, 230, 237, 244, 251, 258, 265, 272, 279, 286, 293, 300, 307, 314, 321, 328, 335, 342, 349, 356, 363 } Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.64.62) Time: Sun Mar 14 11:51:45 2004 Input: ex1:={i: i in [1..366]| (i mod 7) eq 6}-2; print ex1; Output: Magma V2.10-6 Sun Mar 14 2004 11:51:42 on modular [Seed = 3790941286] ------------------------------------- >> ex1:={i: i in [1..366]| (i mod 7) eq 6}-2; ^ Runtime error in '-': Bad argument types Argument types given: SetEnum[RngIntElt], RngIntElt >> print ex1; ^ User error: Identifier 'ex1' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.64.62) Time: Sun Mar 14 11:51:59 2004 Input: ex1:={i-2: i in [1..366]| (i mod 7) eq 6}; print ex1; Output: Magma V2.10-6 Sun Mar 14 2004 11:51:56 on modular [Seed = 454022829] ------------------------------------- { 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 } Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.64.62) Time: Sun Mar 14 11:52:39 2004 Input: print "Solució Exercici nº 1n"; ex1:={i-2: i in [1..366]| (i mod 7) eq 6}; print ex1; Output: Magma V2.10-6 Sun Mar 14 2004 11:52:36 on modular [Seed = 268754399] ------------------------------------- Solució Exercici nº 1n { 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 } Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.64.62) Time: Sun Mar 14 11:53:15 2004 Input: print "Solució Exercici nº 1"; print "---------------------"; ex1:={i-2: i in [1..366]| (i mod 7) eq 6}; print ex1; print " ---oo0oo---" Output: Magma V2.10-6 Sun Mar 14 2004 11:53:12 on modular [Seed = 152945899] ------------------------------------- Solució Exercici nº 1 --------------------- { 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 } ---oo0oo--- Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.64.62) Time: Sun Mar 14 12:00:19 2004 Input: m:=MatrixRing(GF(4),2); Output: Magma V2.10-6 Sun Mar 14 2004 12:00:16 on modular [Seed = 874576782] ------------------------------------- Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.64.62) Time: Sun Mar 14 12:00:45 2004 Input: m:=MatrixRing(GF(4),2); Random(m); Output: Magma V2.10-6 Sun Mar 14 2004 12:00:42 on modular [Seed = 758768269] ------------------------------------- [$.1^2 $.1^2] [ 0 $.1^2] Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.64.62) Time: Sun Mar 14 12:02:03 2004 Input: print "Solució exercici nº2"; print "--------------------"; m:=MatrixRing(GF(4),2); mt:={mi in m | trace(mi) eq 0}; Output: Magma V2.10-6 Sun Mar 14 2004 12:02:00 on modular [Seed = 1331404637] ------------------------------------- Solució exercici nº2 -------------------- >> mt:={mi in m | trace(mi) eq 0}; ^ User error: Identifier 'mi' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.64.62) Time: Sun Mar 14 12:02:37 2004 Input: print "Solució exercici nº2"; print "--------------------"; m:=MatrixRing(GF(4),2); c:=random(m); Output: Magma V2.10-6 Sun Mar 14 2004 12:02:35 on modular [Seed = 1162974580] ------------------------------------- Solució exercici nº2 -------------------- >> c:=random(m); ^ User error: bad syntax Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.64.62) Time: Sun Mar 14 12:02:59 2004 Input: print "Solució exercici nº2"; print "--------------------"; m:=MatrixRing(GF(4),2); c:=random(m); trace(c); Output: Magma V2.10-6 Sun Mar 14 2004 12:02:56 on modular [Seed = 1936171817] ------------------------------------- Solució exercici nº2 -------------------- >> c:=random(m); ^ User error: bad syntax >> trace(c); ^ User error: Identifier 'c' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.64.62) Time: Sun Mar 14 12:03:09 2004 Input: print "Solució exercici nº2"; print "--------------------"; m:=MatrixRing(GF(4),2); c:=Random(m); trace(c); Output: Magma V2.10-6 Sun Mar 14 2004 12:03:06 on modular [Seed = 1753004088] ------------------------------------- Solució exercici nº2 -------------------- >> trace(c); ^ User error: Identifier 'trace' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.64.62) Time: Sun Mar 14 12:03:19 2004 Input: print "Solució exercici nº2"; print "--------------------"; m:=MatrixRing(GF(4),2); c:=Random(m); Trace(c); Output: Magma V2.10-6 Sun Mar 14 2004 12:03:16 on modular [Seed = 1635103023] ------------------------------------- Solució exercici nº2 -------------------- 1 Total time: 3.059 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.64.62) Time: Sun Mar 14 12:03:52 2004 Input: print "Solució exercici nº2"; print "--------------------"; m:=MatrixRing(GF(4),2); mt:={mi in m | Trace(mi) eq 0}; Output: Magma V2.10-6 Sun Mar 14 2004 12:03:49 on modular [Seed = 2659864305] ------------------------------------- Solució exercici nº2 -------------------- >> mt:={mi in m | Trace(mi) eq 0}; ^ User error: Identifier 'mi' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.64.62) Time: Sun Mar 14 12:04:20 2004 Input: print "Solució exercici nº2"; print "--------------------"; m:=MatrixRing(GF(4),2); mt:={i in m | Trace(i) eq 0}; Output: Magma V2.10-6 Sun Mar 14 2004 12:04:17 on modular [Seed = 2541963036] ------------------------------------- Solució exercici nº2 -------------------- >> mt:={i in m | Trace(i) eq 0}; ^ User error: Identifier 'i' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.64.62) Time: Sun Mar 14 12:04:35 2004 Input: print "Solució exercici nº2"; print "--------------------"; m:=MatrixRing(GF(4),2); mt:={i:i in m | Trace(i) eq 0}; Output: Magma V2.10-6 Sun Mar 14 2004 12:04:32 on modular [Seed = 2358795318] ------------------------------------- Solució exercici nº2 -------------------- Total time: 3.039 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.64.62) Time: Sun Mar 14 12:05:09 2004 Input: print "Solució exercici nº2"; print "--------------------"; m:=MatrixRing(GF(4),2); mt:={i:i in m | Trace(i) eq 0}; mf:={i:i in m | i[1] eq i[2]}; Output: Magma V2.10-6 Sun Mar 14 2004 12:05:06 on modular [Seed = 3198840422] ------------------------------------- Solució exercici nº2 -------------------- Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.64.62) Time: Sun Mar 14 12:05:31 2004 Input: print "Solució exercici nº2"; print "--------------------"; m:=MatrixRing(GF(4),2); mt:={i:i in m | Trace(i) eq 0}; mf:={i:i in m | i[1] eq i[2]}; c:=Random(m); c[1]; Output: Magma V2.10-6 Sun Mar 14 2004 12:05:28 on modular [Seed = 3080939381] ------------------------------------- Solució exercici nº2 -------------------- ( $.1 0) Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.64.62) Time: Sun Mar 14 12:05:54 2004 Input: print "Solució exercici nº2"; print "--------------------"; m:=MatrixRing(GF(4),2); mt:={i:i in m | Trace(i) eq 0}; mf:={i:i in m | i[1] eq i[2]}; mtf:= mf meet mt; Output: Magma V2.10-6 Sun Mar 14 2004 12:05:51 on modular [Seed = 2914614616] ------------------------------------- Solució exercici nº2 -------------------- Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.64.62) Time: Sun Mar 14 12:06:20 2004 Input: print "Solució exercici nº2"; print "--------------------"; m:=MatrixRing(GF(4),2); mt:={i:i in m | Trace(i) eq 0}; mf:={i:i in m | i[1] eq i[2]}; mtf:= mf meet mt; printf "Elementos mt:";#(mt); Output: Magma V2.10-6 Sun Mar 14 2004 12:06:17 on modular [Seed = 3670936521] ------------------------------------- Solució exercici nº2 -------------------- Elementos mt:64 Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.64.62) Time: Sun Mar 14 12:06:48 2004 Input: print "Solució exercici nº2"; print "--------------------"; m:=MatrixRing(GF(4),2); mt:={i:i in m | Trace(i) eq 0}; mf:={i:i in m | i[1] eq i[2]}; mtf:= mf meet mt; printf "Elementos mt : ";#(mt); printf "Elementos mf : ";#(mf); printf "Elementos mtf: ";#(mtf); Output: Magma V2.10-6 Sun Mar 14 2004 12:06:45 on modular [Seed = 3553034988] ------------------------------------- Solució exercici nº2 -------------------- Elementos mt : 64 Elementos mf : 16 Elementos mtf: 4 Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.64.62) Time: Sun Mar 14 12:09:05 2004 Input: print "Solució exercici nº2"; print "--------------------"; m:=MatrixRing(GF(4),2); mt:={i:i in m | Trace(i) eq 0}; mf:={i:i in m | i[1] eq i[2]}; mtf:= mf meet mt; printf "Elementos mt : ";#(mt); printf "Elementos mf : ";#(mf); printf "Elementos mtf: ";#(mtf); for i:=1 to 100000 do ex2:=Random(m) join ex2; end for; Output: Magma V2.10-6 Sun Mar 14 2004 12:09:02 on modular [Seed = 3470401402] ------------------------------------- Solució exercici nº2 -------------------- Elementos mt : 64 Elementos mf : 16 Elementos mtf: 4 >> ex2:=Random(m) join ex2; ^ User error: Identifier 'ex2' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.64.62) Time: Sun Mar 14 12:10:00 2004 Input: print "Solució exercici nº2"; print "--------------------"; m:=MatrixRing(GF(4),2); mt:={i:i in m | Trace(i) eq 0}; mf:={i:i in m | i[1] eq i[2]}; mtf:= mf meet mt; printf "Elementos mt : ";#(mt); printf "Elementos mf : ";#(mf); printf "Elementos mtf: ";#(mtf); ex2:=null; for i:=1 to 100000 do ex2:=Random(m) join ex2; end for; Output: Magma V2.10-6 Sun Mar 14 2004 12:09:57 on modular [Seed = 3352499768] ------------------------------------- Solució exercici nº2 -------------------- Elementos mt : 64 Elementos mf : 16 Elementos mtf: 4 >> ex2:=null; ^ User error: Identifier 'null' has not been declared or assigned >> ex2:=Random(m) join ex2; ^ User error: Identifier 'ex2' has not been declared or assigned Total time: 3.109 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.64.62) Time: Sun Mar 14 12:10:11 2004 Input: print "Solució exercici nº2"; print "--------------------"; m:=MatrixRing(GF(4),2); mt:={i:i in m | Trace(i) eq 0}; mf:={i:i in m | i[1] eq i[2]}; mtf:= mf meet mt; printf "Elementos mt : ";#(mt); printf "Elementos mf : ";#(mf); printf "Elementos mtf: ";#(mtf); ex2:=Null; for i:=1 to 100000 do ex2:=Random(m) join ex2; end for; Output: Magma V2.10-6 Sun Mar 14 2004 12:10:08 on modular [Seed = 4108330270] ------------------------------------- Solució exercici nº2 -------------------- Elementos mt : 64 Elementos mf : 16 Elementos mtf: 4 >> ex2:=Null; ^ User error: Identifier 'Null' has not been declared or assigned >> ex2:=Random(m) join ex2; ^ User error: Identifier 'ex2' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.64.62) Time: Sun Mar 14 12:10:45 2004 Input: print "Solució exercici nº2"; print "--------------------"; m:=MatrixRing(GF(4),2); mt:={i:i in m | Trace(i) eq 0}; mf:={i:i in m | i[1] eq i[2]}; mtf:= mf meet mt; printf "Elementos mt : ";#(mt); printf "Elementos mf : ";#(mf); printf "Elementos mtf: ";#(mtf); ex2:=[]; for i:=1 to 100000 do ex2:=Random(m) join ex2; end for; Output: Magma V2.10-6 Sun Mar 14 2004 12:10:42 on modular [Seed = 3992535013] ------------------------------------- Solució exercici nº2 -------------------- Elementos mt : 64 Elementos mf : 16 Elementos mtf: 4 >> ex2:=Random(m) join ex2; ^ Runtime error in 'join': Bad argument types Argument types given: AlgMatElt, SeqEnum[] Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.64.62) Time: Sun Mar 14 12:11:00 2004 Input: print "Solució exercici nº2"; print "--------------------"; m:=MatrixRing(GF(4),2); mt:={i:i in m | Trace(i) eq 0}; mf:={i:i in m | i[1] eq i[2]}; mtf:= mf meet mt; printf "Elementos mt : ";#(mt); printf "Elementos mf : ";#(mf); printf "Elementos mtf: ";#(mtf); ex2:={}; for i:=1 to 100000 do ex2:=Random(m) join ex2; end for; Output: Magma V2.10-6 Sun Mar 14 2004 12:10:57 on modular [Seed = 454019361] ------------------------------------- Solució exercici nº2 -------------------- Elementos mt : 64 Elementos mf : 16 Elementos mtf: 4 >> ex2:=Random(m) join ex2; ^ Runtime error in 'join': Bad argument types Argument types given: AlgMatElt, SetEnum[] Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.64.62) Time: Sun Mar 14 12:14:14 2004 Input: print "Solució exercici nº2"; print "--------------------"; m:=MatrixRing(GF(4),2); mt:={i:i in m | Trace(i) eq 0}; mf:={i:i in m | i[1] eq i[2]}; mtf:= mf meet mt; printf "Elementos mt : ";#(mt); printf "Elementos mf : ";#(mf); printf "Elementos mtf: ";#(mtf); for i:=1 to 100000 do Append(ex2,Random(m)); end for; Output: Magma V2.10-6 Sun Mar 14 2004 12:14:11 on modular [Seed = 285590505] ------------------------------------- Solució exercici nº2 -------------------- Elementos mt : 64 Elementos mf : 16 Elementos mtf: 4 >> Append(ex2,Random(m)); ^ User error: Identifier 'ex2' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.64.62) Time: Sun Mar 14 12:14:55 2004 Input: print "Solució exercici nº2"; print "--------------------"; m:=MatrixRing(GF(4),2); mt:={i:i in m | Trace(i) eq 0}; mf:={i:i in m | i[1] eq i[2]}; mtf:= mf meet mt; printf "Elementos mt : ";#(mt); printf "Elementos mf : ";#(mf); printf "Elementos mtf: ";#(mtf); ex2:=[]; for i:=1 to 100000 do Append(ex2,Random(m)); end for; Output: Magma V2.10-6 Sun Mar 14 2004 12:14:47 on modular [Seed = 253484051] ------------------------------------- Solució exercici nº2 -------------------- Elementos mt : 64 Elementos mf : 16 Elementos mtf: 4 [ [ 1 $.1^2] [ $.1 $.1] ] [ [ 1 1] [$.1^2 1] ] [ [ $.1 $.1] [ 1 $.1^2] ] [ [ $.1 1] [ 1 $.1^2] ] [ [ 1 0] [ 1 $.1] ] [ [ 1 $.1] [ $.1 $.1] ] [ [ 0 0] [ $.1 $.1^2] ] [ [ 0 $.1^2] [ 0 $.1] ] [ [ 0 0] [ $.1 $.1^2] ] [ [ $.1 $.1] [ $.1 $.1^2] ] [ [ $.1 0] [ 0 $.1] ] [ [ 1 $.1] [ 1 $.1^2] ] [ [ $.1 0] [ 1 1] ] [ [ 1 $.1^2] [ 0 1] ] [ [ 1 $.1^2] [ $.1 1] ] [ [$.1^2 $.1] [ 1 $.1] ] [ [ 1 1] [$.1^2 $.1^2] ] [ [ 1 $.1] [$.1^2 $.1^2] ] [ [$.1^2 $.1^2] [ 0 0] ] [ [ $.1 $.1] [ $.1 0] ] [ [ $.1 1] [ 1 $.1] ] [ [ $.1 0] [ 1 0] ] [ [ $.1 $.1] [ $.1 $.1^2] ] [ [ 0 1] [ $.1 $.1] ] [ [$.1^2 $.1] [ 1 $.1] ] [ [ 0 1] [ $.1 1] ] [ [ $.1 $.1] [$.1^2 0] ] [ [ 1 $.1] [ 1 1] ] [ [ 0 0] [ 0 1] ] [ [ 1 0] [ 0 0] ] [ [ $.1 $.1] [$.1^2 $.1^2] ] [ [ 1 $.1] [ 0 0] ] [ [ 0 $.1] [ 1 0] ] [ [ $.1 1] [ $.1 $.1] ] [ [$.1^2 $.1^2] [ 1 1] ] [ [ 0 0] [ 1 0] ] [ [ $.1 1] [ 1 $.1] ] [ [ 0 1] [ 0 $.1] ] [ [$.1^2 $.1^2] [ 0 $.1] ] [ [ 1 1] [ 1 $.1] ] [ [ 1 1] [ 1 $.1^2] ] [ [ 0 0] [ 0 1] ] [ [ $.1 $.1^2] [ 0 $.1] ] [ [$.1^2 $.1] [ 0 1] ] [ [$.1^2 $.1^2] [ 0 $.1^2] ] [ [ 1 0] [ 0 1] ] [ [ 0 $.1] [ 0 1] ] [ [ $.1 1] [ 1 $.1] ] [ [ 0 0] [ 1 $.1] ] [ [ 0 0] [ 0 $.1] ] [ [ $.1 $.1^2] [ 1 0] ] [ [ 0 $.1] [ 1 0] ] [ [ $.1 0] [ 1 $.1^2] ] [ [ $.1 $.1] [ 1 1] ] [ [ $.1 1] [ $.1 0] ] [ [ 0 $.1^2] [ $.1 0] ] [ [ $.1 $.1] [ 0 $.1^2] ] [ [ 1 $.1] [ $.1 1] ] [ [ 0 0] [ 1 0] ] [ [ 1 $.1] [ 1 0] ] [ [ $.1 $.1^2] [$.1^2 $.1] ] [ [ 0 0] [ $.1 $.1^2] ] [ [ 1 1] [ 0 1] ] [ [ 1 $.1^2] [ 0 $.1] ] [ [ $.1 1] [ 0 1] ] [ [ $.1 1] [$.1^2 0] ] [ [ 0 $.1] [ 1 0] ] [ [ $.1 0] [ $.1 $.1] ] [ [ $.1 $.1^2] [ 0 0] ] [ [ 1 0] [ 0 1] ] [ [ 0 $.1^2] [ 1 $.1^2] ] [ [ 0 $.1] [$.1^2 0] ] [ [ 0 0] [ $.1 $.1] ] [ [ 1 1] [ $.1 1] ] [ [ 0 $.1^2] [ 1 $.1^2] ] [ [ $.1 0] [ 1 $.1] ] [ [ $.1 $.1] [ 0 0] ] [ [$.1^2 0] [$.1^2 1] ] [ [ 0 $.1] [ 0 1] ] [ [ 0 $.1^2] [ 0 $.1] ] [ [ 1 1] [ 0 1] ] [ [ 1 0] [ 1 $.1^2] ] [ [$.1^2 $.1^2] [ $.1 1] ] [ [$.1^2 1] [ 0 0] ] [ [ 0 $.1^2] [ 0 0] ] [ [ 0 0] [ $.1 0] ] [ [$.1^2 $.1] [$.1^2 1] ] [ [ $.1 1] [ $.1 0] ] [ [ 1 0] [$.1^2 0] ] [ [$.1^2 $.1] [ $.1 $.1^2] ] [ [ $.1 $.1^2] [ $.1 0] ] [ [ 1 1] [ $.1 $.1] ] [ [ 1 $.1^2] [ $.1 0] ] [ [$.1^2 $.1^2] [$.1^2 $.1^2] ] [ [$.1^2 1] [$.1^2 $.1^2] ] [ [ 0 $.1^2] [ 0 1] ] [ [$.1^2 1] [$.1^2 1] ] [ [$.1^2 1] [ 1 $.1] ] [ [ $.1 $.1^2] [ 0 $.1^2] ] [ [ 0 0] [ 1 $.1^2] ] [ [ $.1 1] [ 0 $.1^2] ] [ [$.1^2 $.1] [$.1^2 1] ] [ [ 1 $.1] [$.1^2 $.1] ] [ [ 0 1] [ $.1 1] ] [ [$.1^2 $.1^2] [ 1 $.1^2] ] [ [$.1^2 0] [ $.1 $.1] ] [ [$.1^2 1] [ 0 $.1] ] [ [ 0 $.1^2] [ 1 $.1^2] ] [ [ 0 $.1] [ 0 0] ] [ [ 0 0] [ $.1 $.1] ] [ [ 1 $.1^2] [ 1 1] ] [ [ 0 $.1] [ 1 $.1] ] [ [ 0 $.1^2] [ 1 1] ] [ [ $.1 0] [ 1 0] ] [ [ $.1 1] [$.1^2 1] ] [ [$.1^2 0] [ 1 $.1^2] ] [ [ $.1 $.1^2] [$.1^2 $.1^2] ] [ [ 1 0] [$.1^2 $.1] ] [ [ $.1 1] [$.1^2 0] ] [ [ 1 1] [ 1 $.1] ] [ [$.1^2 $.1] [$.1^2 $.1^2] ] [ [ 0 $.1^2] [$.1^2 1] ] [ [ 0 0] [ $.1 $.1^2] ] [ [ 0 $.1] [ 1 $.1^2] ] [ [ $.1 1] [ 0 $.1^2] ] [ [ $.1 0] [$.1^2 0] ] [ [ 0 0] [ 0 $.1^2] ] [ [ 1 $.1^2] [ 0 $.1^2] ] [ [ 1 0] [ 0 0] ] [ [ 0 0] [$.1^2 0] ] [ [$.1^2 1] [ 1 $.1] ] [ [ 0 1] [ $.1 $.1] ] [ [$.1^2 1] [ 1 1] ] [ [$.1^2 $.1] [ $.1 1] ] [ [$.1^2 0] [ 1 1] ] [ [ $.1 0] [$.1^2 1] ] [ [ 0 $.1] [ 0 $.1] ] [ [ 1 0] [ 1 1] ] [ [ 0 $.1^2] [ 0 0] ] [ [ $.1 1] [ 0 1] ] [ [$.1^2 $.1^2] [ 0 1] ] [ [ 1 $.1] [ 0 1] ] [ [ 1 0] [ 0 1] ] [ [$.1^2 1] [ 1 0] ] [ [ 0 1] [ $.1 0] ] [ [ 1 0] [$.1^2 0] ] [ [ 1 $.1^2] [ 0 $.1] ] [ [ 1 1] [$.1^2 0] ] [ [ 1 $.1] [$.1^2 0] ] [ [ $.1 1] [$.1^2 1] ] [ [ 0 $.1] [ $.1 0] ] [ [ 0 $.1^2] [$.1^2 1] ] [ [$.1^2 1] [ $.1 1] ] [ [$.1^2 0] [$.1^2 $.1^2] ] [ [ 1 $.1^2] [ 1 0] ] [ [ 1 0] [$.1^2 $.1^2] ] [ [$.1^2 $.1^2] [ 0 1] ] [ [ 1 0] [$.1^2 1] ] [ [$.1^2 $.1] [ 1 $.1] ] [ [$.1^2 1] [$.1^2 $.1] ] [ [$.1^2 0] [ 1 1] ] [ [ $.1 1] [ $.1 $.1^2] ] [ [ $.1 $.1^2] [ 1 0] ] [ [$.1^2 0] [$.1^2 $.1^2] ] [ [ 1 $.1^2] [ $.1 $.1^2] ] [ [ $.1 1] [$.1^2 1] ] [ [$.1^2 $.1^2] [ 0 1] ] [ [ 1 1] [ $.1 $.1^2] ] [ [ 1 1] [$.1^2 0] ] [ [$.1^2 $.1^2] [ $.1 $.1^2] ] [ [$.1^2 1] [ 0 $.1] ] [ [ 0 $.1^2] [ 1 0] ] [ [ 0 1] [$.1^2 $.1^2] ] [ [ 0 1] [ $.1 0] ] [ [ 1 1] [$.1^2 $.1] ] [ [$.1^2 $.1] [ 1 0] ] [ [ $.1 $.1] [ $.1 1] ] [ [ $.1 $.1^2] [$.1^2 0] ] [ [ 1 $.1] [ $.1 $.1^2] ] [ [ 0 1] [ 1 0] ] [ [ 0 0] [$.1^2 $.1] ] [ [ 0 $.1] [ $.1 $.1^2] ] [ [$.1^2 0] [ 1 0] ] [ [ 1 $.1] [ 1 1] ] [ [ 1 1] [ 1 $.1] ] [ [$.1^2 $.1^2] [ $.1 1] ] [ [ 1 0] [$.1^2 $.1] ] [ [ 1 1] [ 0 $.1] ] [ [ 0 $.1] [ 1 1] ] [ [ 0 0] [ 1 $.1] ] [ [$.1^2 $.1] [$.1^2 1] ] [ [ $.1 $.1] [$.1^2 $.1] ] [ [ 0 $.1] [ 0 1] ] [ [$.1^2 0] [ 1 0] ] [ [$.1^2 0] [$.1^2 $.1^2] ] [ [ 1 $.1] [$.1^2 $.1] ] [ [ 0 0] [ 1 $.1^2] ] [ [ 1 $.1] [ 1 $.1^2] ] [ [ 1 $.1^2] [ $.1 $.1] ] [ [ 1 0] [ 0 0] ] [ [ $.1 1] [$.1^2 $.1^2] ] [ [$.1^2 $.1^2] [ 1 1] ] [ [ $.1 1] [ 1 $.1^2] ] [ [ $.1 $.1^2] [ 0 $.1^2] ] [ [ 0 1] [$.1^2 $.1] ] [ [$.1^2 $.1] [ 1 $.1^2] ] [ [$.1^2 0] [ 1 1] ] [ [ 1 0] [$.1^2 $.1^2] ] [ [ 0 $.1^2] [ 0 $.1] ] [ [ 1 $.1^2] [$.1^2 0] ] [ [ 0 1] [ $.1 $.1] ] [ [ 1 0] [$.1^2 1] ] [ [ $.1 1] [$.1^2 0] ] [ [ 0 1] [ $.1 0] ] [ [ 0 $.1^2] [$.1^2 $.1^2] ] [ [ 1 $.1^2] [ 0 1] ] [ [$.1^2 $.1^2] [ $.1 0] ] [ [ 0 $.1^2] [$.1^2 $.1^2] ] [ [ $.1 1] [ $.1 0] ] [ [$.1^2 $.1^2] [ 1 1] ] [ [ 1 0] [ 0 $.1^2] ] [ [$.1^2 $.1] [ 1 1] ] [ [ 1 0] [ 1 $.1^2] ] [ [ 1 $.1^2] [ 1 1] ] [ [ $.1 1] [ 1 0] ] [ [ $.1 $.1^2] [ 0 $.1^2] ] [ [$.1^2 $.1] [$.1^2 1] ] [ [ 0 0] [ 1 $.1^2] ] [ [$.1^2 0] [$.1^2 $.1] ] [ [ $.1 $.1] [ $.1 1] ] [ [ 0 1] [ 1 1] ] [ [ 1 $.1^2] [ $.1 0] ] [ [ $.1 $.1] [ $.1 1] ] [ [ $.1 $.1] [$.1^2 1] ] [ [ 1 $.1] [ 1 $.1] ] [ [ $.1 1] [$.1^2 0] ] [ [ $.1 1] [$.1^2 0] ] [ [$.1^2 0] [ $.1 0] ] [ [ 1 0] [$.1^2 1] ] [ [ 0 $.1] [ 0 $.1^2] ] [ [ 0 $.1] [ $.1 $.1^2] ] [ [ 1 1] [ 0 0] ] [ [ 1 $.1^2] [ $.1 1] ] [ [$.1^2 $.1] [ 1 $.1^2] ] [ [ $.1 1] [ $. ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host p2027-adsao02yokonib2-acca.kanagawa.ocn.ne.jp. (219.96.164.27) Time: Sun Mar 14 12:15:11 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Sun Mar 14 2004 12:15:08 on modular [Seed = 959310398] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.64.62) Time: Sun Mar 14 12:17:37 2004 Input: print "Solució exercici nº2"; print "--------------------"; m:=MatrixRing(GF(4),2); mt:={i:i in m | Trace(i) eq 0}; mf:={i:i in m | i[1] eq i[2]}; mtf:= mf meet mt; printf "Elementos mt : ";#(mt); printf "Elementos mf : ";#(mf); printf "Elementos mtf: ";#(mtf); ex2:=[]; for i:=1 to 100000 do ex2:=Append(ex2,Random(m)); end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Mar 14 2004 12:17:14 on modular [Seed = 2104078076] ------------------------------------- Solució exercici nº2 -------------------- Elementos mt : 64 Elementos mf : 16 Elementos mtf: 4 Errors: /home/mfd/gomagma: line 2: 23398 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.64.62) Time: Sun Mar 14 12:22:03 2004 Input: print "Solució exercici nº2"; print "--------------------"; m:=MatrixRing(GF(4),2); mt:={i:i in m | Trace(i) eq 0}; mf:={i:i in m | i[1] eq i[2]}; mtf:= mf meet mt; printf "Elementos mt : ";#(mt); printf "Elementos mf : ";#(mf); printf "Elementos mtf: ";#(mtf); ex2:=[]; for i:=1 to 100000 do Append(~ex2,Random(m)); end for; Output: Magma V2.10-6 Sun Mar 14 2004 12:21:59 on modular [Seed = 1618261196] ------------------------------------- Solució exercici nº2 -------------------- Elementos mt : 64 Elementos mf : 16 Elementos mtf: 4 Total time: 3.539 seconds, Total memory usage: 7.09MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.28.64.62) Time: Sun Mar 14 12:22:21 2004 Input: print "Solució exercici nº2"; print "--------------------"; m:=MatrixRing(GF(4),2); mt:={i:i in m | Trace(i) eq 0}; mf:={i:i in m | i[1] eq i[2]}; mtf:= mf meet mt; printf "Elementos mt : ";#(mt); printf "Elementos mf : ";#(mf); printf "Elementos mtf: ";#(mtf); ex2:=[]; for i:=1 to 100000 do Append(~ex2,Random(m)); end for; #(ex2); Output: Magma V2.10-6 Sun Mar 14 2004 12:22:18 on modular [Seed = 2676706126] ------------------------------------- Solució exercici nº2 -------------------- Elementos mt : 64 Elementos mf : 16 Elementos mtf: 4 100000 Total time: 3.509 seconds, Total memory usage: 7.09MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 12:23:31 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); KQR:=GF(q,r); punts:={{a, b} : a, b in KQR | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b)}; return [punts]; end function; #punts_olav(7,3); Output: Magma V2.10-6 Sun Mar 14 2004 12:23:10 on modular [Seed = 2525119091] ------------------------------------- x^57 x^49 + x^7 + x 1 Total time: 21.109 seconds, Total memory usage: 6.12MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 12:24:20 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); KQR:=GF(q,r); punts:=[[a, b] : a, b in KQR | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b)]; return [punts]; end function; #punts_olav(7,3); Output: Magma V2.10-6 Sun Mar 14 2004 12:23:57 on modular [Seed = 2358794681] ------------------------------------- x^57 x^49 + x^7 + x 1 Total time: 22.709 seconds, Total memory usage: 4.09MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 12:25:43 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); KQR:=GF(q,r); punts:=[[a, b] : a, b in KQR | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b)]; return (punts); end function; #punts_olav(7,3); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Mar 14 2004 12:25:20 on modular [Seed = 3198839589] ------------------------------------- x^57 x^49 + x^7 + x Errors: /home/mfd/gomagma: line 2: 23461 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.125.37) Time: Sun Mar 14 12:26:53 2004 Input: exp:= func ; exp(7,3); Output: Magma V2.10-6 Sun Mar 14 2004 12:26:50 on modular [Seed = 3030409589] ------------------------------------- [ 7, 49 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 12:29:40 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); K:=GF(q,r); punts:=[[a, b] : a, b in R | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b)]; return (punts); end function; #punts_olav(7,3); Output: Magma V2.10-6 Sun Mar 14 2004 12:29:37 on modular [Seed = 2729866296] ------------------------------------- x^57 x^49 + x^7 + x >> punts:=[[a, b] : a, b in R | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b)]; ^ User error: Identifier 'R' has not been declared or assigned >> #punts_olav(7,3); ^ User error: Identifier 'punts_olav' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 12:30:35 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); K:=GF(q,r); punts:=[[a, b] : a, b in K | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b)]; return (punts); end function; #(punts_olav(7,3)); Output: Magma V2.10-6 Sun Mar 14 2004 12:30:13 on modular [Seed = 3519350639] ------------------------------------- x^57 x^49 + x^7 + x 16807 Total time: 22.719 seconds, Total memory usage: 4.01MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.125.37) Time: Sun Mar 14 12:30:41 2004 Input: exp:= func ; exp(7,3); crea_t:= func Output: Magma V2.10-6 Sun Mar 14 2004 12:30:38 on modular [Seed = 3386711916] ------------------------------------- [ 7, 49 ] >> crea_t:= func ; ^ User error: bad syntax Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 12:31:40 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); K:=GF(q,r); punts:=[[a, b] : a, b in K | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b)]; return (punts); end function; #(punts_olav(7,3)); #(punts_olav(5,2)); Output: Magma V2.10-6 Sun Mar 14 2004 12:31:17 on modular [Seed = 3352498489] ------------------------------------- x^57 x^49 + x^7 + x 16807 125 Total time: 22.789 seconds, Total memory usage: 4.01MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 12:33:41 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); K:=GF(q,r); punts:=[[a, b] : a, b in K | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b)]; return (punts); end function; #(punts_olav(7,3)); #(punts_olav(5,2)); #(punts_olav(9,2)); #(punts_olav(5,4)); #(punts_olav(8,3)); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Mar 14 2004 12:33:18 on modular [Seed = 4058326708] ------------------------------------- x^57 x^49 + x^7 + x 16807 125 [
:23]( q: 9, r: 2 ) >> K:=GF(q,r); ^ Runtime error in 'GF': Argument 1 (9) should be prime Errors: /home/mfd/gomagma: line 2: 23530 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 12:34:54 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); K:=GF(q,r); punts:=[[a, b] : a, b in K | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b)]; return (punts); end function; #(punts_olav(7,3)); #(punts_olav(5,2)); #(punts_olav(11,2)); #(punts_olav(5,4)); #(punts_olav(7,6)); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Mar 14 2004 12:34:31 on modular [Seed = 3908845396] ------------------------------------- x^57 x^49 + x^7 + x 16807 125 Errors: /home/mfd/gomagma: line 2: 23539 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 12:36:00 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); K:=GF(q,r); punts:=[[a, b] : a, b in K | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b)]; return (punts); end function; #(punts_olav(11,2)); #(punts_olav(5,4)); #(punts_olav(7,6)); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Mar 14 2004 12:35:37 on modular [Seed = 504023531] ------------------------------------- x^57 x^49 + x^7 + x 1331 Errors: /home/mfd/gomagma: line 2: 23554 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 12:36:55 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); K:=GF(q,r); punts:=[[a, b] : a, b in K | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b)]; return (punts); end function; #(punts_olav(5,4)); #(punts_olav(7,6)); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Mar 14 2004 12:36:32 on modular [Seed = 386125611] ------------------------------------- x^57 x^49 + x^7 + x Errors: /home/mfd/gomagma: line 2: 23563 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 12:39:51 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); K:=GF(q,r); punts:=[[a, b] : a, b in K | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b)]; return (punts); end function; #(punts_olav(7,4)); #(punts_olav(7,6)); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Mar 14 2004 12:39:28 on modular [Seed = 152949189] ------------------------------------- x^57 x^49 + x^7 + x Errors: /home/mfd/gomagma: line 2: 23573 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.125.37) Time: Sun Mar 14 12:39:52 2004 Input: P:=PolynomialRing(Integer); exp:= func ; P!exp(7,3); Output: Magma V2.10-6 Sun Mar 14 2004 12:39:49 on modular [Seed = 68214013] ------------------------------------- >> P:=PolynomialRing(Integer); ^ User error: Identifier 'Integer' has not been declared or assigned >> P!exp(7,3); ^ User error: Identifier 'P' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 12:40:33 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); K:=GF(q,r); punts:=[[a, b] : a, b in K | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b)]; return (punts); end function; #(punts_olav(7,3)); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Mar 14 2004 12:40:10 on modular [Seed = 858254293] ------------------------------------- x^57 x^49 + x^7 + x Errors: /home/mfd/gomagma: line 2: 23599 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.125.37) Time: Sun Mar 14 12:41:07 2004 Input: P:=PolynomialRing(Integers()); exp:= func ; P!exp(7,3); Output: Magma V2.10-6 Sun Mar 14 2004 12:41:04 on modular [Seed = 607190280] ------------------------------------- 49*x + 7 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 12:41:33 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); K:=GF(q,r); punts:=[[a, b] : a, b in K | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b)]; return (punts); end function; #(punts_olav(7,3)); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Mar 14 2004 12:41:10 on modular [Seed = 1548256630] ------------------------------------- x^57 x^49 + x^7 + x Errors: /home/mfd/gomagma: line 2: 23616 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 12:41:54 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); K:=GF(q,r); punts:=[[a, b] : a, b in K | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b)]; return (punts); end function; #(punts_olav(5,1)); Output: Magma V2.10-6 Sun Mar 14 2004 12:41:51 on modular [Seed = 1464045076] ------------------------------------- x^57 x^49 + x^7 + x 5 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.125.37) Time: Sun Mar 14 12:42:01 2004 Input: P:=PolynomialRing(Integers()); exp:= func ; P!exp(7,3); Output: Magma V2.10-6 Sun Mar 14 2004 12:41:58 on modular [Seed = 1214026034] ------------------------------------- 49*x^2 + 7*x + 1 Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 12:43:02 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); K:=GF(q,r); punts:=[[a, b] : a, b in K | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b)]; return (punts); end function; #(punts_olav(5,3)); Output: Magma V2.10-6 Sun Mar 14 2004 12:42:57 on modular [Seed = 1096128764] ------------------------------------- x^57 x^49 + x^7 + x 3125 Total time: 5.439 seconds, Total memory usage: 2.30MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.125.37) Time: Sun Mar 14 12:44:16 2004 Input: P:=PolynomialRing(Integers()); exp:= func ; exp(7,3); Output: Magma V2.10-6 Sun Mar 14 2004 12:44:13 on modular [Seed = 2054071179] ------------------------------------- [ 1, 7, 49 ] Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.125.37) Time: Sun Mar 14 12:45:27 2004 Input: P:=PolynomialRing(Integers()); exp:= func ; exp(7,3); Output: Magma V2.10-6 Sun Mar 14 2004 12:45:24 on modular [Seed = 1769845569] ------------------------------------- [ x, x^7, x^49 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 12:49:44 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); K:=GF(q,r); k1:=GF(q); punts:=[[a, b] : a, b in K |[a,b]:a,b in K1| Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b)]; return (punts); end function; #(punts_olav(5,3)); Output: Magma V2.10-6 Sun Mar 14 2004 12:49:41 on modular [Seed = 1668790346] ------------------------------------- x^57 x^49 + x^7 + x >> punts:=[[a, b] : a, b in K |[a,b]:a,b in K1| Evaluate(nqr(q,r),a) eq Evalua ^ User error: bad syntax >> return (punts); ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> #(punts_olav(5,3));; ^ User error: Identifier 'punts_olav' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 12:50:09 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); K:=GF(q,r); k1:=GF(q); punts:=[[a, b] : a, b in K |[a,b] : a,b in K1| Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b)]; return (punts); end function; #(punts_olav(5,3)); Output: Magma V2.10-6 Sun Mar 14 2004 12:50:06 on modular [Seed = 2358794206] ------------------------------------- x^57 x^49 + x^7 + x >> punts:=[[a, b] : a, b in K |[a,b] : a,b in K1| Evaluate(nqr(q,r),a) eq Eval ^ User error: bad syntax >> return (punts); ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> #(punts_olav(5,3));; ^ User error: Identifier 'punts_olav' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 12:51:00 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); K:=GF(q,r); K1:=GF(q); punts:=[[a, b] : a, b in K |[a,b] : a,b in K1| Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b)]; return (punts); end function; #(punts_olav(5,3)); Output: Magma V2.10-6 Sun Mar 14 2004 12:50:57 on modular [Seed = 2257739035] ------------------------------------- x^57 x^49 + x^7 + x >> punts:=[[a, b] : a, b in K |[a,b] : a,b in K1| Evaluate(nqr(q,r),a) eq Eval ^ User error: bad syntax >> return (punts); ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> #(punts_olav(5,3));; ^ User error: Identifier 'punts_olav' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 12:51:24 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); K:=GF(q,r); punts:=[[a, b] : a, b in K | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b)]; return (punts); end function; #punts_olav(5,3)); Output: Magma V2.10-6 Sun Mar 14 2004 12:51:21 on modular [Seed = 3215680570] ------------------------------------- x^57 x^49 + x^7 + x >> #punts_olav(5,3));; ^ User error: bad syntax Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 12:51:54 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); K:=GF(q,r); punts:=[[a, b] : a, b in K | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b)]; return (punts); end function; punts_olav(5,3); Output: Magma V2.10-6 Sun Mar 14 2004 12:51:48 on modular [Seed = 2963565336] ------------------------------------- x^57 x^49 + x^7 + x [ [ 1, $.1^3 ], [ 1, $.1^7 ], [ 1, $.1^8 ], [ 1, $.1^15 ], [ 1, $.1^16 ], [ 1, $.1^28 ], [ 1, 2 ], [ 1, $.1^35 ], [ 1, $.1^37 ], [ 1, $.1^40 ], [ 1, $.1^42 ], [ 1, $.1^51 ], [ 1, $.1^57 ], [ 1, $.1^58 ], [ 1, $.1^61 ], [ 1, $.1^64 ], [ 1, $.1^72 ], [ 1, $.1^74 ], [ 1, $.1^75 ], [ 1, $.1^76 ], [ 1, $.1^80 ], [ 1, $.1^86 ], [ 1, $.1^112 ], [ 1, $.1^114 ], [ 1, $.1^122 ], [ $.1, $.1^19 ], [ $.1, $.1^21 ], [ $.1, $.1^29 ], [ $.1, $.1^34 ], [ $.1, $.1^38 ], [ $.1, $.1^39 ], [ $.1, $.1^46 ], [ $.1, $.1^47 ], [ $.1, $.1^59 ], [ $.1, 4 ], [ $.1, $.1^66 ], [ $.1, $.1^68 ], [ $.1, $.1^71 ], [ $.1, $.1^73 ], [ $.1, $.1^82 ], [ $.1, $.1^88 ], [ $.1, $.1^89 ], [ $.1, $.1^92 ], [ $.1, $.1^95 ], [ $.1, $.1^103 ], [ $.1, $.1^105 ], [ $.1, $.1^106 ], [ $.1, $.1^107 ], [ $.1, $.1^111 ], [ $.1, $.1^117 ], [ $.1^2, $.1^2 ], [ $.1^2, $.1^10 ], [ $.1^2, $.1^12 ], [ $.1^2, $.1^13 ], [ $.1^2, $.1^14 ], [ $.1^2, $.1^18 ], [ $.1^2, $.1^24 ], [ $.1^2, $.1^50 ], [ $.1^2, $.1^52 ], [ $.1^2, $.1^60 ], [ $.1^2, $.1^65 ], [ $.1^2, $.1^69 ], [ $.1^2, $.1^70 ], [ $.1^2, $.1^77 ], [ $.1^2, $.1^78 ], [ $.1^2, $.1^90 ], [ $.1^2, 3 ], [ $.1^2, $.1^97 ], [ $.1^2, $.1^99 ], [ $.1^2, $.1^102 ], [ $.1^2, $.1^104 ], [ $.1^2, $.1^113 ], [ $.1^2, $.1^119 ], [ $.1^2, $.1^120 ], [ $.1^2, $.1^123 ], [ $.1^3, 1 ], [ $.1^3, $.1^4 ], [ $.1^3, $.1^6 ], [ $.1^3, $.1^9 ], [ $.1^3, $.1^11 ], [ $.1^3, $.1^20 ], [ $.1^3, $.1^26 ], [ $.1^3, $.1^27 ], [ $.1^3, $.1^30 ], [ $.1^3, $.1^33 ], [ $.1^3, $.1^41 ], [ $.1^3, $.1^43 ], [ $.1^3, $.1^44 ], [ $.1^3, $.1^45 ], [ $.1^3, $.1^49 ], [ $.1^3, $.1^55 ], [ $.1^3, $.1^81 ], [ $.1^3, $.1^83 ], [ $.1^3, $.1^91 ], [ $.1^3, $.1^96 ], [ $.1^3, $.1^100 ], [ $.1^3, $.1^101 ], [ $.1^3, $.1^108 ], [ $.1^3, $.1^109 ], [ $.1^3, $.1^121 ], [ $.1^4, $.1^3 ], [ $.1^4, $.1^7 ], [ $.1^4, $.1^8 ], [ $.1^4, $.1^15 ], [ $.1^4, $.1^16 ], [ $.1^4, $.1^28 ], [ $.1^4, 2 ], [ $.1^4, $.1^35 ], [ $.1^4, $.1^37 ], [ $.1^4, $.1^40 ], [ $.1^4, $.1^42 ], [ $.1^4, $.1^51 ], [ $.1^4, $.1^57 ], [ $.1^4, $.1^58 ], [ $.1^4, $.1^61 ], [ $.1^4, $.1^64 ], [ $.1^4, $.1^72 ], [ $.1^4, $.1^74 ], [ $.1^4, $.1^75 ], [ $.1^4, $.1^76 ], [ $.1^4, $.1^80 ], [ $.1^4, $.1^86 ], [ $.1^4, $.1^112 ], [ $.1^4, $.1^114 ], [ $.1^4, $.1^122 ], [ $.1^5, $.1^19 ], [ $.1^5, $.1^21 ], [ $.1^5, $.1^29 ], [ $.1^5, $.1^34 ], [ $.1^5, $.1^38 ], [ $.1^5, $.1^39 ], [ $.1^5, $.1^46 ], [ $.1^5, $.1^47 ], [ $.1^5, $.1^59 ], [ $.1^5, 4 ], [ $.1^5, $.1^66 ], [ $.1^5, $.1^68 ], [ $.1^5, $.1^71 ], [ $.1^5, $.1^73 ], [ $.1^5, $.1^82 ], [ $.1^5, $.1^88 ], [ $.1^5, $.1^89 ], [ $.1^5, $.1^92 ], [ $.1^5, $.1^95 ], [ $.1^5, $.1^103 ], [ $.1^5, $.1^105 ], [ $.1^5, $.1^106 ], [ $.1^5, $.1^107 ], [ $.1^5, $.1^111 ], [ $.1^5, $.1^117 ], [ $.1^6, $.1^2 ], [ $.1^6, $.1^10 ], [ $.1^6, $.1^12 ], [ $.1^6, $.1^13 ], [ $.1^6, $.1^14 ], [ $.1^6, $.1^18 ], [ $.1^6, $.1^24 ], [ $.1^6, $.1^50 ], [ $.1^6, $.1^52 ], [ $.1^6, $.1^60 ], [ $.1^6, $.1^65 ], [ $.1^6, $.1^69 ], [ $.1^6, $.1^70 ], [ $.1^6, $.1^77 ], [ $.1^6, $.1^78 ], [ $.1^6, $.1^90 ], [ $.1^6, 3 ], [ $.1^6, $.1^97 ], [ $.1^6, $.1^99 ], [ $.1^6, $.1^102 ], [ $.1^6, $.1^104 ], [ $.1^6, $.1^113 ], [ $.1^6, $.1^119 ], [ $.1^6, $.1^120 ], [ $.1^6, $.1^123 ], [ $.1^7, 1 ], [ $.1^7, $.1^4 ], [ $.1^7, $.1^6 ], [ $.1^7, $.1^9 ], [ $.1^7, $.1^11 ], [ $.1^7, $.1^20 ], [ $.1^7, $.1^26 ], [ $.1^7, $.1^27 ], [ $.1^7, $.1^30 ], [ $.1^7, $.1^33 ], [ $.1^7, $.1^41 ], [ $.1^7, $.1^43 ], [ $.1^7, $.1^44 ], [ $.1^7, $.1^45 ], [ $.1^7, $.1^49 ], [ $.1^7, $.1^55 ], [ $.1^7, $.1^81 ], [ $.1^7, $.1^83 ], [ $.1^7, $.1^91 ], [ $.1^7, $.1^96 ], [ $.1^7, $.1^100 ], [ $.1^7, $.1^101 ], [ $.1^7, $.1^108 ], [ $.1^7, $.1^109 ], [ $.1^7, $.1^121 ], [ $.1^8, $.1^3 ], [ $.1^8, $.1^7 ], [ $.1^8, $.1^8 ], [ $.1^8, $.1^15 ], [ $.1^8, $.1^16 ], [ $.1^8, $.1^28 ], [ $.1^8, 2 ], [ $.1^8, $.1^35 ], [ $.1^8, $.1^37 ], [ $.1^8, $.1^40 ], [ $.1^8, $.1^42 ], [ $.1^8, $.1^51 ], [ $.1^8, $.1^57 ], [ $.1^8, $.1^58 ], [ $.1^8, $.1^61 ], [ $.1^8, $.1^64 ], [ $.1^8, $.1^72 ], [ $.1^8, $.1^74 ], [ $.1^8, $.1^75 ], [ $.1^8, $.1^76 ], [ $.1^8, $.1^80 ], [ $.1^8, $.1^86 ], [ $.1^8, $.1^112 ], [ $.1^8, $.1^114 ], [ $.1^8, $.1^122 ], [ $.1^9, $.1^19 ], [ $.1^9, $.1^21 ], [ $.1^9, $.1^29 ], [ $.1^9, $.1^34 ], [ $.1^9, $.1^38 ], [ $.1^9, $.1^39 ], [ $.1^9, $.1^46 ], [ $.1^9, $.1^47 ], [ $.1^9, $.1^59 ], [ $.1^9, 4 ], [ $.1^9, $.1^66 ], [ $.1^9, $.1^68 ], [ $.1^9, $.1^71 ], [ $.1^9, $.1^73 ], [ $.1^9, $.1^82 ], [ $.1^9, $.1^88 ], [ $.1^9, $.1^89 ], [ $.1^9, $.1^92 ], [ $.1^9, $.1^95 ], [ $.1^9, $.1^103 ], [ $.1^9, $.1^105 ], [ $.1^9, $.1^106 ], [ $.1^9, $.1^107 ], [ $.1^9, $.1^111 ], [ $.1^9, $.1^117 ], [ $.1^10, $.1^2 ], [ $.1^10, $.1^10 ], [ $.1^10, $.1^12 ], [ $.1^10, $.1^13 ], [ $.1^10, $.1^14 ], [ $.1^10, $.1^18 ], [ $.1^10, $.1^24 ], [ $.1^10, $.1^50 ], [ $.1^10, $.1^52 ], [ $.1^10, $.1^60 ], [ $.1^10, $.1^65 ], [ $.1^10, $.1^69 ], [ $.1^10, $.1^70 ], [ $.1^10, $.1^77 ], [ $.1^10, $.1^78 ], [ $.1^10, $.1^90 ], [ $.1^10, 3 ], [ $.1^10, $.1^97 ], [ $.1^10, $.1^99 ], [ $.1^10, $.1^102 ], [ $.1^10, $.1^104 ], [ $.1^10, $.1^113 ], [ $.1^10, $.1^119 ], [ $.1^10, $.1^120 ], [ $.1^10, $.1^123 ], [ $.1^11, 1 ], [ $.1^11, $.1^4 ], [ $.1^11, $.1^6 ], [ $.1^11, $.1^9 ], [ $.1^11, $.1^11 ], [ $.1^11, $.1^20 ], [ $.1^11, $.1^26 ], [ $.1^11, $.1^27 ], [ $.1^11, $.1^30 ], [ $.1^11, $.1^33 ], [ $.1^11, $.1^41 ], [ $.1^11, $.1^43 ], [ $.1^11, $.1^44 ], [ $.1^11, $.1^45 ], [ $.1^11, $.1^49 ], [ $.1^11, $.1^55 ], [ $.1^11, $.1^81 ], [ $.1^11, $.1^83 ], [ $.1^11, $.1^91 ], [ $.1^11, $.1^96 ], [ $.1^11, $.1^100 ], [ $.1^11, $.1^101 ], [ $.1^11, $.1^108 ], [ $.1^11, $.1^109 ], [ $.1^11, $.1^121 ], [ $.1^12, $.1^3 ], [ $.1^12, $.1^7 ], [ $.1^12, $.1^8 ], [ $.1^12, $.1^15 ], [ $.1^12, $.1^16 ], [ $.1^12, $.1^28 ], [ $.1^12, 2 ], [ $.1^12, $.1^35 ], [ $.1^12, $.1^37 ], [ $.1^12, $.1^40 ], [ $.1^12, $.1^42 ], [ $.1^12, $.1^51 ], [ $.1^12, $.1^57 ], [ $.1^12, $.1^58 ], [ $.1^12, $.1^61 ], [ $.1^12, $.1^64 ], [ $.1^12, $.1^72 ], [ $.1^12, $.1^74 ], [ $.1^12, $.1^75 ], [ $.1^12, $.1^76 ], [ $.1^12, $.1^80 ], [ $.1^12, $.1^86 ], [ $.1^12, $.1^112 ], [ $.1^12, $.1^114 ], [ $.1^12, $.1^122 ], [ $.1^13, $.1^19 ], [ $.1^13, $.1^21 ], [ $.1^13, $.1^29 ], [ $.1^13, $.1^34 ], [ $.1^13, $.1^38 ], [ $.1^13, $.1^39 ], [ $.1^13, $.1^46 ], [ $.1^13, $.1^47 ], [ $.1^13, $.1^59 ], [ $.1^13, 4 ], [ $.1^13, $.1^66 ], [ $.1^13, $.1^68 ], [ $.1^13, $.1^71 ], [ $.1^13, $.1^73 ], [ $.1^13, $.1^82 ], [ $.1^13, $.1^88 ], [ $.1^13, $.1^89 ], [ $.1^13, $.1^92 ], [ $.1^13, $.1^95 ], [ $.1^13, $.1^103 ], [ $.1^13, $.1^105 ], [ $.1^13, $.1^106 ], [ $.1^13, $.1^107 ], [ $.1^13, $.1^111 ], [ $.1^13, $.1^117 ], [ $.1^14, $.1^2 ], [ $.1^14, $.1^10 ], [ $.1^14, $.1^12 ], [ $.1^14, $.1^13 ], [ $.1^14, $.1^14 ], [ $.1^14, $.1^18 ], [ $.1^14, $.1^24 ], [ $.1^14, $.1^50 ], [ $.1^14, $.1^52 ], [ $.1^14, $.1^60 ], [ $.1^14, $.1^65 ], [ $.1^14, $.1^69 ], [ $.1^14, $.1^70 ], [ $.1^14, $.1^77 ], [ $.1^14, $.1^78 ], [ $.1^14, $.1^90 ], [ $.1^14, 3 ], [ $.1^14, $.1^97 ], [ $.1^14, $.1^99 ], [ $.1^14, $.1^102 ], [ $.1^14, $.1^104 ], [ $.1^14, $.1^113 ], [ $.1^14, $.1^119 ], [ $.1^14, $.1^120 ], [ $.1^14, $.1^123 ], [ $.1^15, 1 ], [ $.1^15, $.1^4 ], [ $.1^15, $.1^6 ], [ $.1^15, $.1^9 ], [ $.1^15, $.1^11 ], [ $.1^15, $.1^20 ], [ $.1^15, $.1^26 ], [ $.1^15, $.1^27 ], [ $.1^15, $.1^30 ], [ $.1^15, $.1^33 ], [ $.1^15, $.1^41 ], [ $.1^15, $.1^43 ], [ $.1^15, $.1^44 ], [ $.1^15, $.1^45 ], [ $.1^15, $.1^49 ], [ $.1^15, $.1^55 ], [ $.1^15, $.1^81 ], [ $.1^15, $.1^83 ], [ $.1^15, $.1^91 ], [ $.1^15, $.1^96 ], [ $.1^15, $.1^100 ], [ $.1^15, $.1^101 ], [ $.1^15, $.1^108 ], [ $.1^15, $.1^109 ], [ $.1^15, $.1^121 ], [ $.1^16, $.1^3 ], [ $.1^16, $.1^7 ], [ $.1^16, $.1^8 ], [ $.1^16, $.1^15 ], [ $.1^16, $.1^16 ], [ $.1^16, $.1^28 ], [ $.1^16, 2 ], [ $.1^16, $.1^35 ], [ $.1^16, $.1^37 ], [ $.1^16, $.1^40 ], [ $.1^16, $.1^42 ], [ $.1^16, $.1^51 ], [ $.1^16, $.1^57 ], [ $.1^16, $.1^58 ], [ $.1^16, $.1^61 ], [ $.1^16, $.1^64 ], [ $.1^16, $.1^72 ], [ $.1^16, $.1^74 ], [ $.1^16, $.1^75 ], [ $.1^16, $.1^76 ], [ $.1^16, $.1^80 ], [ $.1^16, $.1^86 ], [ $.1^16, $.1^112 ], [ $.1^16, $.1^114 ], [ $.1^16, $.1^122 ], [ $.1^17, $.1^19 ], [ $.1^17, $.1^21 ], [ $.1^17, $.1^29 ], [ $.1^17, $.1^34 ] ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 12:54:58 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); K:=GF(q,r); punts:=[[a, b] : a, b in K | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b)]; return (punts); end function; punts_olav(5,1); Output: Magma V2.10-6 Sun Mar 14 2004 12:54:55 on modular [Seed = 2864608985] ------------------------------------- x^57 x^49 + x^7 + x [ [ 0, 0 ], [ 1, 1 ], [ 2, 2 ], [ 3, 3 ], [ 4, 4 ] ] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host n137.ryd.student.liu.se. (130.236.215.137) Time: Sun Mar 14 12:55:46 2004 Input: A:=383652543938472915822611587153678018703223876280881548837256346963054598912743440824929710651875507216458563824146064655931783363804907196579127582; B:=277344227772537008614840520507086703845369524308102117047838647330800082563554488447648920746347701628029763520248726284064162556190504931479350237; p:=2750801028499115405998700637559537964310409; E:=ChangeRing(EllipticCurve([A,B]),GF(p)); print(E); go:=Order(E); Factorization(go); Output: Magma V2.10-6 Sun Mar 14 2004 12:55:36 on modular [Seed = 3637249116] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 12720317259914333457209859836260518307910\ 10*x + 1428841998493343107851003761120822132525846 over GF(2750801028499115405998700637559537964310409) [ <2, 2>, <3, 2>, <23, 1>, <61, 1>, <4027, 1>, <140527, 1>, <176431, 1>, <402947, 1>, <547301, 1>, <689257, 1>, <3588619, 1> ] Total time: 9.479 seconds, Total memory usage: 3.48MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 12:55:51 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); K:=GF(q,r); punts:=[[a, b] : a, b in K | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b)]; return (punts); end function; nqr(5,1); tqr(5,1); punts_olav(5,1); Output: Magma V2.10-6 Sun Mar 14 2004 12:55:48 on modular [Seed = 3519352169] ------------------------------------- x^57 x^49 + x^7 + x x x [ [ 0, 0 ], [ 1, 1 ], [ 2, 2 ], [ 3, 3 ], [ 4, 4 ] ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 12:56:18 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); K:=GF(q,r); punts:=[[a, b] : a, b in K | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b)]; return (punts); end function; nqr(5,2); tqr(5,2); punts_olav(5,2); Output: Magma V2.10-6 Sun Mar 14 2004 12:56:15 on modular [Seed = 3335658085] ------------------------------------- x^57 x^49 + x^7 + x x^6 x^5 + x [ [ 1, $.1 ], [ 1, $.1^4 ], [ 1, $.1^5 ], [ 1, 3 ], [ 1, $.1^20 ], [ $.1, 1 ], [ $.1, $.1^2 ], [ $.1, $.1^7 ], [ $.1, $.1^10 ], [ $.1, $.1^11 ], [ $.1^2, 2 ], [ $.1^2, $.1^8 ], [ $.1^2, $.1^13 ], [ $.1^2, $.1^16 ], [ $.1^2, $.1^17 ], [ $.1^3, 4 ], [ $.1^3, $.1^14 ], [ $.1^3, $.1^19 ], [ $.1^3, $.1^22 ], [ $.1^3, $.1^23 ], [ $.1^4, $.1 ], [ $.1^4, $.1^4 ], [ $.1^4, $.1^5 ], [ $.1^4, 3 ], [ $.1^4, $.1^20 ], [ $.1^5, 1 ], [ $.1^5, $.1^2 ], [ $.1^5, $.1^7 ], [ $.1^5, $.1^10 ], [ $.1^5, $.1^11 ], [ 2, 2 ], [ 2, $.1^8 ], [ 2, $.1^13 ], [ 2, $.1^16 ], [ 2, $.1^17 ], [ $.1^7, 4 ], [ $.1^7, $.1^14 ], [ $.1^7, $.1^19 ], [ $.1^7, $.1^22 ], [ $.1^7, $.1^23 ], [ $.1^8, $.1 ], [ $.1^8, $.1^4 ], [ $.1^8, $.1^5 ], [ $.1^8, 3 ], [ $.1^8, $.1^20 ], [ $.1^9, 1 ], [ $.1^9, $.1^2 ], [ $.1^9, $.1^7 ], [ $.1^9, $.1^10 ], [ $.1^9, $.1^11 ], [ $.1^10, 2 ], [ $.1^10, $.1^8 ], [ $.1^10, $.1^13 ], [ $.1^10, $.1^16 ], [ $.1^10, $.1^17 ], [ $.1^11, 4 ], [ $.1^11, $.1^14 ], [ $.1^11, $.1^19 ], [ $.1^11, $.1^22 ], [ $.1^11, $.1^23 ], [ 4, $.1 ], [ 4, $.1^4 ], [ 4, $.1^5 ], [ 4, 3 ], [ 4, $.1^20 ], [ $.1^13, 1 ], [ $.1^13, $.1^2 ], [ $.1^13, $.1^7 ], [ $.1^13, $.1^10 ], [ $.1^13, $.1^11 ], [ $.1^14, 2 ], [ $.1^14, $.1^8 ], [ $.1^14, $.1^13 ], [ $.1^14, $.1^16 ], [ $.1^14, $.1^17 ], [ $.1^15, 4 ], [ $.1^15, $.1^14 ], [ $.1^15, $.1^19 ], [ $.1^15, $.1^22 ], [ $.1^15, $.1^23 ], [ $.1^16, $.1 ], [ $.1^16, $.1^4 ], [ $.1^16, $.1^5 ], [ $.1^16, 3 ], [ $.1^16, $.1^20 ], [ $.1^17, 1 ], [ $.1^17, $.1^2 ], [ $.1^17, $.1^7 ], [ $.1^17, $.1^10 ], [ $.1^17, $.1^11 ], [ 3, 2 ], [ 3, $.1^8 ], [ 3, $.1^13 ], [ 3, $.1^16 ], [ 3, $.1^17 ], [ $.1^19, 4 ], [ $.1^19, $.1^14 ], [ $.1^19, $.1^19 ], [ $.1^19, $.1^22 ], [ $.1^19, $.1^23 ], [ $.1^20, $.1 ], [ $.1^20, $.1^4 ], [ $.1^20, $.1^5 ], [ $.1^20, 3 ], [ $.1^20, $.1^20 ], [ $.1^21, 1 ], [ $.1^21, $.1^2 ], [ $.1^21, $.1^7 ], [ $.1^21, $.1^10 ], [ $.1^21, $.1^11 ], [ $.1^22, 2 ], [ $.1^22, $.1^8 ], [ $.1^22, $.1^13 ], [ $.1^22, $.1^16 ], [ $.1^22, $.1^17 ], [ $.1^23, 4 ], [ $.1^23, $.1^14 ], [ $.1^23, $.1^19 ], [ $.1^23, $.1^22 ], [ $.1^23, $.1^23 ], [ 0, $.1^3 ], [ 0, $.1^9 ], [ 0, $.1^15 ], [ 0, $.1^21 ], [ 0, 0 ] ] Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.33.44.proxycache.rima-tde.net. (80.58.33.44) Time: Sun Mar 14 13:00:08 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Sun Mar 14 2004 13:00:05 on modular [Seed = 3992531028] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 13:06:29 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); K:=GF(q); punts:=[[a, b] : a, b in K | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b)]; return (punts); end function; nqr(5,2); tqr(5,2); punts_olav(5,2); Output: Magma V2.10-6 Sun Mar 14 2004 13:06:26 on modular [Seed = 236638513] ------------------------------------- x^57 x^49 + x^7 + x x^6 x^5 + x [ [ 0, 0 ], [ 1, 3 ], [ 2, 2 ], [ 3, 2 ], [ 4, 3 ] ] Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 13:07:23 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); K:=GF(q); punts:=[[a, b] : a, b in K | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b)]; return (punts); end function; nqr(7,3); tqr(5,2); punts_olav(5,2); Output: Magma V2.10-6 Sun Mar 14 2004 13:07:20 on modular [Seed = 18210372] ------------------------------------- x^57 x^49 + x^7 + x x^57 x^5 + x [ [ 0, 0 ], [ 1, 3 ], [ 2, 2 ], [ 3, 2 ], [ 4, 3 ] ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 13:08:02 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); K:=GF(q); punts:=[[a, b] : a, b in K | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b)]; return (punts); end function; nqr(7,3); tqr(7,3); punts_olav(7,3); Output: Magma V2.10-6 Sun Mar 14 2004 13:07:59 on modular [Seed = 942466906] ------------------------------------- x^57 x^49 + x^7 + x x^57 x^49 + x^7 + x [ [ 0, 0 ], [ 1, 5 ], [ 2, 5 ], [ 3, 2 ], [ 4, 5 ], [ 5, 2 ], [ 6, 2 ] ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 13:08:31 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); K:=GF(q); punts:=[[a, b] : a, b in K | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b)]; return (punts); end function; nqr(7,3); tqr(7,3); punts_olav(5,2); Output: Magma V2.10-6 Sun Mar 14 2004 13:08:28 on modular [Seed = 858254514] ------------------------------------- x^57 x^49 + x^7 + x x^57 x^49 + x^7 + x [ [ 0, 0 ], [ 1, 3 ], [ 2, 2 ], [ 3, 2 ], [ 4, 3 ] ] Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 13:11:06 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); K:=GF(q); punts:=[[a, b] : a, b in K | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b)]; return (punts); end function; nqr(7,3); tqr(7,3); #(punts_olav(7,5)); Output: Magma V2.10-6 Sun Mar 14 2004 13:11:03 on modular [Seed = 1565113719] ------------------------------------- x^57 x^49 + x^7 + x x^57 x^49 + x^7 + x 7 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Sun Mar 14 13:11:47 2004 Input: nqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+li[y]; end for; return x^(n); end function; nqr(7,3); tqr:= function(q,r); P:=PolynomialRing(Integers()); n:=0; li:=[q^i : i in [0..r-1]]; for y in [1..r] do n:=n+x^li[y]; end for; return (n); end function; tqr(7,3); punts_olav:=function (q,r); K:=GF(q); punts:=[[a, b] : a, b in K | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b)]; return (punts); end function; nqr(7,3); tqr(7,3); #(punts_olav(11,5)); Output: Magma V2.10-6 Sun Mar 14 2004 13:11:43 on modular [Seed = 1464055573] ------------------------------------- x^57 x^49 + x^7 + x x^57 x^49 + x^7 + x 11 Total time: 4.019 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host io.yourlibrary.ca. (208.181.90.67) Time: Sun Mar 14 14:20:27 2004 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(441,2,+1))))); E:=EllipticCurve([0,0,1,-840,362]);Conductor(E); for i in [1..#A] do CongruenceGroupAnemic(A[i],Parent(Newform(E)),200); end for; Output: Magma V2.10-6 Sun Mar 14 2004 14:20:17 on modular [Seed = 420342134] ------------------------------------- 13671 Abelian Group of order 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Total time: 9.139 seconds, Total memory usage: 4.96MB ************** MAGMA ***************** Host net-29067.fas.harvard.edu. (140.247.28.233) Time: Sun Mar 14 14:24:49 2004 Input: K:=CyclotomicField(11); G, phi := UnitGroup(K); G; Output: Magma V2.10-6 Sun Mar 14 2004 14:24:44 on modular [Seed = 590860865] ------------------------------------- Abelian Group isomorphic to Z/22 + Z + Z + Z + Z Defined on 5 generators Relations: 22*G.1 = 0 Total time: 4.269 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host net-29067.fas.harvard.edu. (140.247.28.233) Time: Sun Mar 14 14:25:27 2004 Input: K:=CyclotomicField(11); G:= UnitGroup(K); G; Output: Magma V2.10-6 Sun Mar 14 2004 14:25:23 on modular [Seed = 1430365416] ------------------------------------- Abelian Group isomorphic to Z/22 + Z + Z + Z + Z Defined on 5 generators Relations: 22*G.1 = 0 Total time: 4.239 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host net-29067.fas.harvard.edu. (140.247.28.233) Time: Sun Mar 14 14:25:44 2004 Input: K:=CyclotomicField(8); G:= UnitGroup(K); G; Output: Magma V2.10-6 Sun Mar 14 2004 14:25:41 on modular [Seed = 1247722465] ------------------------------------- Abelian Group isomorphic to Z/8 + Z Defined on 2 generators Relations: 8*G.1 = 0 Total time: 3.029 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host net-29067.fas.harvard.edu. (140.247.28.233) Time: Sun Mar 14 14:25:57 2004 Input: K:=CyclotomicField(2); G:= UnitGroup(K); G; Output: Magma V2.10-6 Sun Mar 14 2004 14:25:54 on modular [Seed = 1129820831] ------------------------------------- Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*G.1 = 0 Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host net-29067.fas.harvard.edu. (140.247.28.233) Time: Sun Mar 14 14:26:20 2004 Input: K:=CyclotomicField(4); G:= UnitGroup(K); G; Output: Magma V2.10-6 Sun Mar 14 2004 14:26:17 on modular [Seed = 2020379071] ------------------------------------- Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*G.1 = 0 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host net-29067.fas.harvard.edu. (140.247.28.233) Time: Sun Mar 14 14:26:34 2004 Input: K:=CyclotomicField(8); G:= UnitGroup(K); G; Output: Magma V2.10-6 Sun Mar 14 2004 14:26:31 on modular [Seed = 1853530007] ------------------------------------- Abelian Group isomorphic to Z/8 + Z Defined on 2 generators Relations: 8*G.1 = 0 Total time: 3.009 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host net-29067.fas.harvard.edu. (140.247.28.233) Time: Sun Mar 14 14:27:07 2004 Input: K:=CyclotomicField(16); G:= UnitGroup(K); G; Output: Magma V2.10-6 Sun Mar 14 2004 14:27:03 on modular [Seed = 1735628158] ------------------------------------- Abelian Group isomorphic to Z/16 + Z + Z + Z Defined on 4 generators Relations: 16*G.1 = 0 Total time: 3.739 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host net-29067.fas.harvard.edu. (140.247.28.233) Time: Sun Mar 14 14:27:41 2004 Input: K:=CyclotomicField(32); G:= UnitGroup(K); G; Output: Magma V2.10-6 Sun Mar 14 2004 14:27:29 on modular [Seed = 2626186915] ------------------------------------- Abelian Group isomorphic to Z/32 + Z (7 copies) Defined on 8 generators Relations: 32*G.1 = 0 Total time: 11.599 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host net-29067.fas.harvard.edu. (140.247.28.233) Time: Sun Mar 14 14:28:22 2004 Input: K:=CyclotomicField(6); G:= UnitGroup(K); G; Output: Magma V2.10-6 Sun Mar 14 2004 14:28:19 on modular [Seed = 2508285912] ------------------------------------- Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*G.1 = 0 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host net-29067.fas.harvard.edu. (140.247.28.233) Time: Sun Mar 14 14:28:38 2004 Input: K:=CyclotomicField(15); G:= UnitGroup(K); G; Output: Magma V2.10-6 Sun Mar 14 2004 14:28:34 on modular [Seed = 2325641462] ------------------------------------- Abelian Group isomorphic to Z/30 + Z + Z + Z Defined on 4 generators Relations: 30*G.1 = 0 Total time: 3.899 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host net-29067.fas.harvard.edu. (140.247.28.233) Time: Sun Mar 14 14:29:33 2004 Input: K:=CyclotomicField(35); G:= UnitGroup(K); G; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Mar 14 2004 14:29:10 on modular [Seed = 2207740187] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 24221 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 14:51:37 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-6 Sun Mar 14 2004 14:51:34 on modular [Seed = 403500993] ------------------------------------- [ x^4 + x^2 + 7, 3*x^2 + 6, 27 ] Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 14:51:51 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-6 Sun Mar 14 2004 14:51:48 on modular [Seed = 253491396] ------------------------------------- [ x^4 + x^2 + 7, 3*x^2 + 6, 9 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 14:52:08 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-6 Sun Mar 14 2004 14:52:05 on modular [Seed = 101904892] ------------------------------------- [ x^4 + x^2 + 7, 3*x^2 + 6, 9 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 14:52:17 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-6 Sun Mar 14 2004 14:52:14 on modular [Seed = 1026149068] ------------------------------------- [ x^4 + x^2 + 7, 3*x^2 + 6, 9 ] Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 14:52:34 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-6 Sun Mar 14 2004 14:52:31 on modular [Seed = 874562516] ------------------------------------- [ x^4 + x^2 + 7, 3*x^2 + 6, 9 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 14:52:43 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-6 Sun Mar 14 2004 14:52:40 on modular [Seed = 725603132] ------------------------------------- [ x^4 + x^2 + 7, 3*x^2 + 6, 9 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 14 15:39:30 2004 Input: G2 := GF(2); G2; Output: Magma V2.10-6 Sun Mar 14 2004 15:39:27 on modular [Seed = 3098294872] ------------------------------------- Finite field of size 2 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 14 15:40:20 2004 Input: G2 := GF(2); G2!2; Output: Magma V2.10-6 Sun Mar 14 2004 15:40:17 on modular [Seed = 2813535369] ------------------------------------- 0 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 14 15:40:30 2004 Input: G2 := GF(2); G2!1; Output: Magma V2.10-6 Sun Mar 14 2004 15:40:27 on modular [Seed = 3737804282] ------------------------------------- 1 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 14 15:42:56 2004 Input: G2 := GF(2); print "G2"; G2!0; G2!1; G3 := GF(3); print "G3"; G3!0; G3!1; G3!2; G3!3; G5 := GF(5); print "G5"; G5!0; G5!1; G5!2; G5!3; G5!4; G5!5; Output: Magma V2.10-6 Sun Mar 14 2004 15:42:53 on modular [Seed = 3553054721] ------------------------------------- G2 0 1 G3 0 1 2 0 G5 0 1 2 3 4 0 Total time: 3.119 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 15:44:52 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x^10)*(2^2-x^4) in I Output: Magma V2.10-6 Sun Mar 14 2004 15:44:49 on modular [Seed = 3386723735] ------------------------------------- [ x^4 + x^2 + 7, 3*x^2 + 6, 9 ] true Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 15:45:08 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x^10)*(4^2-x^6) in I Output: Magma V2.10-6 Sun Mar 14 2004 15:45:05 on modular [Seed = 4243093682] ------------------------------------- [ x^4 + x^2 + 7, 3*x^2 + 6, 9 ] true Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host net-29067.fas.harvard.edu. (140.247.28.233) Time: Sun Mar 14 15:45:14 2004 Input: K:=CyclotomicField(5); G, phi:= UnitGroup(K); G; Output: Magma V2.10-6 Sun Mar 14 2004 15:45:11 on modular [Seed = 4075189946] ------------------------------------- Abelian Group isomorphic to Z/10 + Z Defined on 2 generators Relations: 10*G.1 = 0 Total time: 3.049 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 15:45:40 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x^10)*(4^2-x^6) in I Output: Magma V2.10-6 Sun Mar 14 2004 15:45:37 on modular [Seed = 3925699975] ------------------------------------- [ 1 ] true Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 15:45:48 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x^10)*(4^2-x^6) in I Output: Magma V2.10-6 Sun Mar 14 2004 15:45:45 on modular [Seed = 3774112902] ------------------------------------- [ x^2 + 7*x + 154, 9*x + 153, 729 ] false Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 15:46:06 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)*(11-2*x) in I Output: Magma V2.10-6 Sun Mar 14 2004 15:46:02 on modular [Seed = 675064962] ------------------------------------- [ x^2 + 7*x + 154, 9*x + 153, 729 ] false Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 14 15:46:25 2004 Input: G2 := GF(2); print "G2"; G2!0; G2!1; G2!2; G3 := GF(3); print "G3"; G3!0; G3!1; G3!2; G3!3; G5 := GF(5); print "G5"; G5!0; G5!1; G5!2; G5!3; G5!4; G5!5; Output: Magma V2.10-6 Sun Mar 14 2004 15:46:22 on modular [Seed = 824554895] ------------------------------------- G2 0 1 0 G3 0 1 2 0 G5 0 1 2 3 4 0 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 15:46:30 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)*(11-2*x)*(1-y)*(11-2*y) in I Output: Magma V2.10-6 Sun Mar 14 2004 15:46:27 on modular [Seed = 976142009] ------------------------------------- [ x^2 + 7*x + 154, 9*x + 153, y^2 + 7*y + 154, 9*y + 153, 729 ] true Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host net-29067.fas.harvard.edu. (140.247.28.233) Time: Sun Mar 14 15:47:03 2004 Input: K:=CyclotomicField(5); G, phi:= UnitGroup(K); G; K!phi(G.1); K!phi(G.2); Output: Magma V2.10-6 Sun Mar 14 2004 15:47:00 on modular [Seed = 51873767] ------------------------------------- Abelian Group isomorphic to Z/10 + Z Defined on 2 generators Relations: 10*G.1 = 0 -zeta_5^2 zeta_5^3 + zeta_5 + 1 Total time: 3.009 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 15:47:16 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)*(11-2*x)*(3-y)*(13-2*y) in I Output: Magma V2.10-6 Sun Mar 14 2004 15:47:13 on modular [Seed = 219777532] ------------------------------------- [ 1 ] true Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 15:47:32 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)*(11-2*x)*(3-y)*(13-2*y) in I Output: Magma V2.10-6 Sun Mar 14 2004 15:47:29 on modular [Seed = 369267415] ------------------------------------- [ x^2 + 7*x + 154, 9*x + 153, y^2 + 5*y + 148, 9*y + 144, 729 ] true Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 15:47:44 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x)*(11-2*x)*(2-y)*(13-2*y) in I Output: Magma V2.10-6 Sun Mar 14 2004 15:47:41 on modular [Seed = 520854482] ------------------------------------- [ x^2 + 7*x + 154, 9*x + 153, y^2 + 5*y + 148, 9*y + 144, 729 ] true Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 15:50:35 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x^2-y^3)*(11-2*x) in I Output: Magma V2.10-6 Sun Mar 14 2004 15:50:32 on modular [Seed = 1902507209] ------------------------------------- [ x^2 - 11*x + 48*y^9 + 4212*y^6 + 123201*y^3 + 1201240, 8*x*y^6 + 6*x*y^3 - 6669*x + 48*y^12 + 24*y^9 - 244361*y^6 - 9549339*y^3 - 104786838, 44*x*y^3 + 1287*x + 32*y^12 + 48*y^9 - 160054*y^6 - 6283376*y^3 - 69074928, 64*y^9 + 5616*y^6 + 164268*y^3 + 1601613 ] false Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 15:51:08 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x^2-y^3)*(11-2*x) in I Output: Magma V2.10-6 Sun Mar 14 2004 15:51:05 on modular [Seed = 2054094819] ------------------------------------- [ x^4 + 2*x^2*y^3 + 2*x^2 - 4964*x*y^3 - 44*x + 1540082*y^6 + 27300*y^3 + 122, x^2*y^6 + 2*x^2*y^3 + x^2 + 9239245*x*y^9 + 42410911921*x*y^6 + 751952067*x*y^3 + 3221935*x + 2510775826537337453*y^15 + 111294877820076119*y^12 + 1933868476027275*y^9 + 16444623097844*y^6 + 68327077618*y^3 + 110760859, 4*x^2 - 4964*x*y^3 - 44*x + 1540081*y^6 + 27302*y^3 + 121, 1540081*x*y^12 + 3107468*x*y^9 + 23133611430*x*y^6 + 410163660*x*y^3 + 1757457*x + 1027269359274948149*y^18 + 1424181173508723541*y^15 + 61910372205053505*y^12 + 1068885208501342*y^9 + 9061350613155*y^6 + 37585377333*y^3 + 60866559, 12320648*x*y^9 + 15413349096*x*y^6 + 273279384*x*y^3 + 1170936*x + 912474215974882310*y^15 + 40447137826881607*y^12 + 702812545345360*y^9 + 5976355645530*y^6 + 24831632034*y^3 + 40253031, 61701805184*x*y^6 + 1093987584*x*y^3 + 4687488*x + 3652840329112351441*y^15 + 161919048899059787*y^12 + 2813518132482778*y^9 + 23924711929990*y^6 + 99406693413*y^3 + 161142111, 3652840329112351441*y^18 + 194297166240103998*y^15 + 4277453833188459*y^12 + 49881358322388*y^9 + 324958296663*y^6 + 1121375502*y^3 + 1601613 ] false Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 15:51:29 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x^2-y^3)*(11-2*x+1241*y^3) in I Output: Magma V2.10-6 Sun Mar 14 2004 15:51:26 on modular [Seed = 1129825965] ------------------------------------- [ x^4 + 2*x^2*y^3 + 2*x^2 - 4964*x*y^3 - 44*x + 1540082*y^6 + 27300*y^3 + 122, x^2*y^6 + 2*x^2*y^3 + x^2 + 9239245*x*y^9 + 42410911921*x*y^6 + 751952067*x*y^3 + 3221935*x + 2510775826537337453*y^15 + 111294877820076119*y^12 + 1933868476027275*y^9 + 16444623097844*y^6 + 68327077618*y^3 + 110760859, 4*x^2 - 4964*x*y^3 - 44*x + 1540081*y^6 + 27302*y^3 + 121, 1540081*x*y^12 + 3107468*x*y^9 + 23133611430*x*y^6 + 410163660*x*y^3 + 1757457*x + 1027269359274948149*y^18 + 1424181173508723541*y^15 + 61910372205053505*y^12 + 1068885208501342*y^9 + 9061350613155*y^6 + 37585377333*y^3 + 60866559, 12320648*x*y^9 + 15413349096*x*y^6 + 273279384*x*y^3 + 1170936*x + 912474215974882310*y^15 + 40447137826881607*y^12 + 702812545345360*y^9 + 5976355645530*y^6 + 24831632034*y^3 + 40253031, 61701805184*x*y^6 + 1093987584*x*y^3 + 4687488*x + 3652840329112351441*y^15 + 161919048899059787*y^12 + 2813518132482778*y^9 + 23924711929990*y^6 + 99406693413*y^3 + 161142111, 3652840329112351441*y^18 + 194297166240103998*y^15 + 4277453833188459*y^12 + 49881358322388*y^9 + 324958296663*y^6 + 1121375502*y^3 + 1601613 ] false Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 15:51:50 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x^2-y^3)*(11-2*x+1241*y^3) in I Output: Magma V2.10-6 Sun Mar 14 2004 15:51:47 on modular [Seed = 1280887183] ------------------------------------- [ x^2 + 950385687624527497111*x + 797467652307976218506*y^2 + 1087319206591119357647845601650792558327827134*y + 16563501451880566591569484958965962647477394358523406873294179602432546\ 60652823374486940, x*y^2 + 2517965891967612549645*x + 499721664193469039551*y^2 + 1483249265686797666280067020216019760900797223*y + 13732430336861711462067661787959268972939946187387333403724988724166281\ 87010784016653687, 13*x*y + 1758105071853004337723*x + 769854866669304769065*y^2 + 1004441797196137650592156221431360768029838795*y + 23471448643622473048052204828528957497161300502081182968428328804615872\ 1036157236004334, 13866522203068301815217*x + 779671539866993013489*y^2 + 1065076321552346468897235619629032828657129059*y + 93578506377097633678648370581647318581527381142353983561431830353667686\ 9135954927728749, y^3 + 405716555043001001013*y^2 + 13414669184140978955774992075591236848246\ 33622*y + 5071816814967690491777540387528126467140990970933563470642273\ 45750484745087614029346601, 1066655554082177062709*y^2 + 28732358320905373465229499676622836342816503*y + 137544215869859947795388760785384543345248789492102444111060436789969\ 9234165889482736400, 2499645694106420476284565724632831183765842157*y + 81526243273273591197277269801957705866079441684726234417351376693554408\ 0858016562961529, 284398206466307173719053845345904697991662239203516659541843268588954502594\ 3412686134917 ] false Total time: 3.019 seconds, Total memory usage: 2.14MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 15:52:10 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x^2-y^3)*(11-2*x+1241*y^3)*(13-24*x*y) in I Output: Magma V2.10-6 Sun Mar 14 2004 15:52:07 on modular [Seed = 1430376578] ------------------------------------- [ x^2 + 950385687624527497111*x + 797467652307976218506*y^2 + 1087319206591119357647845601650792558327827134*y + 16563501451880566591569484958965962647477394358523406873294179602432546\ 60652823374486940, x*y^2 + 2517965891967612549645*x + 499721664193469039551*y^2 + 1483249265686797666280067020216019760900797223*y + 13732430336861711462067661787959268972939946187387333403724988724166281\ 87010784016653687, 13*x*y + 1758105071853004337723*x + 769854866669304769065*y^2 + 1004441797196137650592156221431360768029838795*y + 23471448643622473048052204828528957497161300502081182968428328804615872\ 1036157236004334, 13866522203068301815217*x + 779671539866993013489*y^2 + 1065076321552346468897235619629032828657129059*y + 93578506377097633678648370581647318581527381142353983561431830353667686\ 9135954927728749, y^3 + 405716555043001001013*y^2 + 13414669184140978955774992075591236848246\ 33622*y + 5071816814967690491777540387528126467140990970933563470642273\ 45750484745087614029346601, 1066655554082177062709*y^2 + 28732358320905373465229499676622836342816503*y + 137544215869859947795388760785384543345248789492102444111060436789969\ 9234165889482736400, 2499645694106420476284565724632831183765842157*y + 81526243273273591197277269801957705866079441684726234417351376693554408\ 0858016562961529, 284398206466307173719053845345904697991662239203516659541843268588954502594\ 3412686134917 ] false Total time: 3.169 seconds, Total memory usage: 2.14MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 15:52:41 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x^2-y^3)*(11-2*x+1241*y^3)*(13-24*x*y) in I Output: Magma V2.10-6 Sun Mar 14 2004 15:52:38 on modular [Seed = 1581963368] ------------------------------------- [ 1 ] true Total time: 2.999 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 15:53:20 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x^2-y^3)*(11-2*x+1241*y^3)*(13-24*x*y) in I Output: Magma V2.10-6 Sun Mar 14 2004 15:53:17 on modular [Seed = 2830905013] ------------------------------------- [ 1 ] true Total time: 2.959 seconds, Total memory usage: 1.94MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 16:01:30 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x^2-y^3)*(11-2*x+1241*y^3)*(13-24*x*y) in I Output: Magma V2.10-6 Sun Mar 14 2004 16:01:27 on modular [Seed = 2458262165] ------------------------------------- [ x^2 - 2*x + 1, 2*x*y - 2*x - 2*y + 2, y^2 - 2*y + 1 ] false Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 16:01:50 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x*y)*(1-x)*(1-y) in I Output: Magma V2.10-6 Sun Mar 14 2004 16:01:47 on modular [Seed = 2609845120] ------------------------------------- [ x^2 - 2*x + 1, 2*x*y - 2*x - 2*y + 2, y^2 - 2*y + 1 ] true Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 16:02:02 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x*y)*(1-x)*(1-y) in I Output: Magma V2.10-6 Sun Mar 14 2004 16:01:59 on modular [Seed = 3840961667] ------------------------------------- [ x^2 + 19*x + 59, x*y + 8*x + 12*y + 521, 25*x + 50, y^2 + 21*y + 454, 25*y + 450, 625 ] false Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 16:02:13 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x*y)*(3-x)*(2-y) in I Output: Magma V2.10-6 Sun Mar 14 2004 16:02:09 on modular [Seed = 3992544668] ------------------------------------- [ x^2 + 19*x + 59, x*y + 8*x + 12*y + 521, 25*x + 50, y^2 + 21*y + 454, 25*y + 450, 625 ] false Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 16:02:48 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x*y)*(3-x)*(2-y)*(11-z*y)*(5-z) in I Output: Magma V2.10-6 Sun Mar 14 2004 16:02:46 on modular [Seed = 4158881697] ------------------------------------- [ 1 ] true Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 16:02:58 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x*y)*(3-x)*(2-y)*(11-z*y)*(5-z) in I Output: Magma V2.10-6 Sun Mar 14 2004 16:02:55 on modular [Seed = 3235137695] ------------------------------------- [ 1 ] true Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 16:03:14 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x*y)*(3-x)*(2-y)*(11-z*y)*(5-z) in I Output: Magma V2.10-6 Sun Mar 14 2004 16:03:11 on modular [Seed = 3386720614] ------------------------------------- [ 1 ] true Total time: 2.939 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 16:03:43 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x*y)*(3-x)*(2-y)*(11-z*y)*(5-z) in I Output: Magma V2.10-6 Sun Mar 14 2004 16:03:40 on modular [Seed = 3536214622] ------------------------------------- [ 1 ] true Total time: 2.999 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 16:03:57 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x*y)*(3-x)*(2-y)*(11-z*y)*(5-z) in I Output: Magma V2.10-6 Sun Mar 14 2004 16:03:54 on modular [Seed = 3687797569] ------------------------------------- [ x^2 + x + 94, x*y + 2*x + 8*y + 91, 5*x*z + 15*z, 25*x + 75, y^2 + 19*y + 59, y*z + 5*y + 12*z + 110, 25*y + 50, z^2 + 15*z + 25, 25*z, 125 ] false Total time: 2.979 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 16:04:47 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > (1-x*y)*(3-x)*(2-y)*(11-z*y)*(5-z) in I Output: Magma V2.10-6 Sun Mar 14 2004 16:04:44 on modular [Seed = 607169769] ------------------------------------- [ x^2 + 2*x + 1, 4 ] false Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 16:05:42 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > in I Output: Magma V2.10-6 Sun Mar 14 2004 16:05:39 on modular [Seed = 1042986812] ------------------------------------- [ x^2 + 2*x + 1, 4 ] >> in I ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 16:06:00 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > in I Output: Magma V2.10-6 Sun Mar 14 2004 16:05:57 on modular [Seed = 319265287] ------------------------------------- >> I := ideal; ^ Runtime error: Bad argument types Argument types given: RngMPolElt, RngIntElt >> GroebnerBasis(I); ^ User error: Identifier 'I' has not been declared or assigned >> in I ^ User error: bad syntax Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 16:06:08 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > in I Output: Magma V2.10-6 Sun Mar 14 2004 16:06:05 on modular [Seed = 437162758] ------------------------------------- [ 2*x^2 + 2, 4 ] >> in I ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 16:07:07 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > in I Output: Magma V2.10-6 Sun Mar 14 2004 16:07:04 on modular [Seed = 1819862325] ------------------------------------- [ 2*x^2 + 2, 2*y^2 + 2, 4 ] >> in I ^ User error: bad syntax Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 16:07:33 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-6 Sun Mar 14 2004 16:07:30 on modular [Seed = 2120939469] ------------------------------------- [ 2*x^2 + 2, 2*y^2 + 2, 4 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 14 16:23:50 2004 Input: G2 := GF(2); IsField(G2); print "G2"; G2!0; G2!1; G2!2; G3 := GF(3); print "G3"; G3!0; G3!1; G3!2; G3!3; G5 := GF(5); print "G5"; G5!0; G5!1; G5!2; G5!3; G5!4; G5!5; Output: Magma V2.10-6 Sun Mar 14 2004 16:23:46 on modular [Seed = 3453567118] ------------------------------------- true G2 0 1 0 G3 0 1 2 0 G5 0 1 2 3 4 0 Total time: 3.449 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 14 16:25:03 2004 Input: G2 := GF(2); IsField(G2); print "G2"; [G2!i: i in [0..2]]; G3 := GF(3); print "G3"; G3!0; G3!1; G3!2; G3!3; G5 := GF(5); print "G5"; G5!0; G5!1; G5!2; G5!3; G5!4; G5!5; Output: Magma V2.10-6 Sun Mar 14 2004 16:24:59 on modular [Seed = 590851754] ------------------------------------- true G2 [ 0, 1, 0 ] G3 0 1 2 0 G5 0 1 2 3 4 0 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 14 16:25:38 2004 Input: G2 := GF(2); IsField(G2); print "G2"; [G2!i: i in [0..2]]; G3 := GF(3); print "G3"; [G3!i: i in [0..3]]; G5 := GF(5); print "G5"; G5!0; G5!1; G5!2; G5!3; G5!4; G5!5; Output: Magma V2.10-6 Sun Mar 14 2004 16:25:35 on modular [Seed = 976140247] ------------------------------------- true G2 [ 0, 1, 0 ] G3 [ 0, 1, 2, 0 ] G5 0 1 2 3 4 0 Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 14 16:27:59 2004 Input: G2 := GF(2); IsField(G2); print "G2"; [G2!i: i in [0..1]]; G3 := GF(3); print "G3"; [G3!i: i in [0..2]]; G5 := GF(5); print "G5"; [G5!i: i in [0..4]]; Output: Magma V2.10-6 Sun Mar 14 2004 16:27:56 on modular [Seed = 470323810] ------------------------------------- true G2 [ 0, 1 ] G3 [ 0, 1, 2 ] G5 [ 0, 1, 2, 3, 4 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Sun Mar 14 16:29:40 2004 Input: P:=PolynomialRing(Integers()); exp:= func ; exp(7,3); Output: Magma V2.10-6 Sun Mar 14 2004 16:29:37 on modular [Seed = 1853546637] ------------------------------------- [ 1, 7, 49 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 14 16:34:30 2004 Input: G2 := GF(2); print "G2"; [G2!i: i in [0..1]]; G3 := GF(3); print "G3"; [G3!i: i in [0..2]]; G5 := GF(5); print "G5"; [G5!i: i in [0..4]]; Z9 := GF(9); IsField(Z9); Output: Magma V2.10-6 Sun Mar 14 2004 16:34:27 on modular [Seed = 1179830663] ------------------------------------- G2 [ 0, 1 ] G3 [ 0, 1, 2 ] G5 [ 0, 1, 2, 3, 4 ] true Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 14 16:35:04 2004 Input: G2 := GF(2); print "G2"; [G2!i: i in [0..1]]; G3 := GF(3); print "G3"; [G3!i: i in [0..2]]; G5 := GF(5); print "G5"; [G5!i: i in [0..4]]; Z9 := Integers(9); IsField(Z9); Output: Magma V2.10-6 Sun Mar 14 2004 16:35:01 on modular [Seed = 1397212020] ------------------------------------- G2 [ 0, 1 ] G3 [ 0, 1, 2 ] G5 [ 0, 1, 2, 3, 4 ] false Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 14 16:42:53 2004 Input: G2 := GF(2); print "G2"; [G2!i: i in [0..1]]; G3 := GF(3); print "G3"; [G3!i: i in [0..2]]; G5 := GF(5); print "G5"; [G5!i: i in [0..4]]; Z9 := Integers(9); IsField(Z9); PrimitiveElement(Z9); Output: Magma V2.10-6 Sun Mar 14 2004 16:42:50 on modular [Seed = 2763011420] ------------------------------------- G2 [ 0, 1 ] G3 [ 0, 1, 2 ] G5 [ 0, 1, 2, 3, 4 ] false 2 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 14 16:45:51 2004 Input: G2 := GF(2); print "G2"; [G2!i: i in [0..1]]; G3 := GF(3); print "G3"; [G3!i: i in [0..2]]; G5 := GF(5); print "G5"; [G5!i: i in [0..4]]; Z9 := Integers(9); IsField(Z9); PrimitiveElement(Z9); Order(2,9); Output: Magma V2.10-6 Sun Mar 14 2004 16:45:48 on modular [Seed = 3080922393] ------------------------------------- G2 [ 0, 1 ] G3 [ 0, 1, 2 ] G5 [ 0, 1, 2, 3, 4 ] false 2 6 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 14 16:46:48 2004 Input: G2 := GF(2); print "G2"; [G2!i: i in [0..1]]; G3 := GF(3); print "G3"; [G3!i: i in [0..2]]; G5 := GF(5); print "G5"; [G5!i: i in [0..4]]; Z9 := Integers(9); IsField(Z9); PrimitiveElement(Z9); Order(3,9); Output: Magma V2.10-6 Sun Mar 14 2004 16:46:45 on modular [Seed = 3165138523] ------------------------------------- G2 [ 0, 1 ] G3 [ 0, 1, 2 ] G5 [ 0, 1, 2, 3, 4 ] false 2 0 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 14 16:47:40 2004 Input: G2 := GF(2); print "G2"; [G2!i: i in [0..1]]; G3 := GF(3); print "G3"; [G3!i: i in [0..2]]; G5 := GF(5); print "G5"; [G5!i: i in [0..4]]; Z9 := Integers(9); IsField(Z9); PrimitiveElement(Z9); Order(4,9); Output: Magma V2.10-6 Sun Mar 14 2004 16:47:37 on modular [Seed = 2325616721] ------------------------------------- G2 [ 0, 1 ] G3 [ 0, 1, 2 ] G5 [ 0, 1, 2, 3, 4 ] false 2 3 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 14 16:47:58 2004 Input: Z9 := Integers(9); IsField(Z9); PrimitiveElement(Z9); Order(5,9); Output: Magma V2.10-6 Sun Mar 14 2004 16:47:55 on modular [Seed = 2475098298] ------------------------------------- false 2 6 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 14 16:48:05 2004 Input: Z9 := Integers(9); IsField(Z9); PrimitiveElement(Z9); Order(6,9); Output: Magma V2.10-6 Sun Mar 14 2004 16:48:02 on modular [Seed = 2559314856] ------------------------------------- false 2 0 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 14 17:12:04 2004 Input: Z9 := Integers(9); IsField(Z9); PrimitiveElement(Z9); Order(6,9); IsInvertible(Z9!3); Output: Magma V2.10-6 Sun Mar 14 2004 17:12:01 on modular [Seed = 607173814] ------------------------------------- false 2 0 false Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 14 17:18:53 2004 Input: P3 := PolynomialRing(Integers(3)); elt < P3 | 2, 2, 1>; Output: Magma V2.10-6 Sun Mar 14 2004 17:18:50 on modular [Seed = 18193256] ------------------------------------- x^2 + 2*x + 2 Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.33.44.proxycache.rima-tde.net. (80.58.33.44) Time: Sun Mar 14 17:26:26 2004 Input: ser:={1,23.4}; Output: Magma V2.10-6 Sun Mar 14 2004 17:26:23 on modular [Seed = 403473460] ------------------------------------- Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 14 17:26:31 2004 Input: P3 := PolynomialRing(Integers(3)); elt < P3 | 2, 2, 1>; P2 := PolynomialRing(Integers(2)); elt < P2 | 1, 1, 0, 0, 1>; Output: Magma V2.10-6 Sun Mar 14 2004 17:26:28 on modular [Seed = 1735654224] ------------------------------------- x^2 + 2*x + 2 x^4 + x + 1 Total time: 2.979 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 80.58.33.44.proxycache.rima-tde.net. (80.58.33.44) Time: Sun Mar 14 17:26:55 2004 Input: ser:={1,23.4}; print ser; Output: Magma V2.10-6 Sun Mar 14 2004 17:26:52 on modular [Seed = 1853551201] ------------------------------------- { 23.399999999999999999999999999919, 1 } Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 14 17:28:30 2004 Input: P3 := PolynomialRing(Integers(3)); elt < P3 | 2, 2, 1>; P2 := PolynomialRing(Integers(2)); elt < P2 | 1, 1, 0, 0, 1>; P5 := PolynomialRing(Integers(5)); elt < P5 | 3, 2, 1>; elt < P3 | 1, 2, 1>; Output: Magma V2.10-6 Sun Mar 14 2004 17:28:27 on modular [Seed = 1969351133] ------------------------------------- x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 Total time: 2.989 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 14 17:29:39 2004 Input: P3 := PolynomialRing(Integers(3)); elt < P3 | 2, 2, 1>; P2 := PolynomialRing(Integers(2)); elt < P2 | 1, 1, 0, 0, 1>; P5 := PolynomialRing(Integers(5)); elt < P5 | 3, 2, 1>; elt < P3 | 1, 2, 1>; elt < P3 | 4, 4, 4>; Output: Magma V2.10-6 Sun Mar 14 2004 17:29:36 on modular [Seed = 1129832368] ------------------------------------- x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 x^2 + x + 1 Total time: 2.939 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 14 17:33:10 2004 Input: P3 := PolynomialRing(Integers(3)); elt < P3 | 2, 2, 1>; P2 := PolynomialRing(Integers(2)); elt < P2 | 1, 1, 0, 0, 1>; P5 := PolynomialRing(Integers(5)); elt < P5 | 3, 2, 1>; elt < P3 | 1, 2, 1>; elt < P3 | 4, 4, 4>; Output: Magma V2.10-6 Sun Mar 14 2004 17:33:07 on modular [Seed = 1363528913] ------------------------------------- x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 x^2 + x + 1 Total time: 2.969 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 14 17:33:39 2004 Input: P3 := PolynomialRing(Integers(3)); elt < P3 | 2, 2, 1>; P2 := PolynomialRing(Integers(2)); elt < P2 | 1, 1, 0, 0, 1>; P5 := PolynomialRing(Integers(5)); elt < P5 | 3, 2, 1>; elt < P3 | 1, 2, 1>; elt < P3 | 5, 5, 5>; Output: Magma V2.10-6 Sun Mar 14 2004 17:33:36 on modular [Seed = 1481426363] ------------------------------------- x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 2*x^2 + 2*x + 2 Total time: 2.929 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 14 17:45:16 2004 Input: P3 := PolynomialRing(Integers(3)); f := P3 ! [ 2, 2, 1]; P2 := PolynomialRing(Integers(2)); g := P2 ! [ 1, 1, 0, 0, 1]; P5 := PolynomialRing(Integers(5)); h := P5 ! [ 3, 2, 1]; i := P3 ! [ 1, 2, 1]; Output: Magma V2.10-6 Sun Mar 14 2004 17:45:13 on modular [Seed = 3115129315] ------------------------------------- Total time: 2.949 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 14 17:45:48 2004 Input: P3 := PolynomialRing(Integers(3)); f := P3 ! [ 2, 2, 1]; P2 := PolynomialRing(Integers(2)); g := P2 ! [ 1, 1, 0, 0, 1]; P5 := PolynomialRing(Integers(5)); h := P5 ! [ 3, 2, 1]; i := P3 ! [ 1, 2, 1]; IsIrreductible(f); IsIrreductible(g); IsIrreductible(h); IsIrreductible(i); Output: Magma V2.10-6 Sun Mar 14 2004 17:45:45 on modular [Seed = 2157191226] ------------------------------------- >> IsIrreductible(f); ^ User error: Identifier 'IsIrreductible' has not been declared or assigned >> IsIrreductible(g); ^ User error: Identifier 'IsIrreductible' has not been declared or assigned >> IsIrreductible(h); ^ User error: Identifier 'IsIrreductible' has not been declared or assigned >> IsIrreductible(i);; ^ User error: Identifier 'IsIrreductible' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 14 17:46:10 2004 Input: P3 := PolynomialRing(Integers(3)); f := P3 ! [ 2, 2, 1]; P2 := PolynomialRing(Integers(2)); g := P2 ! [ 1, 1, 0, 0, 1]; P5 := PolynomialRing(Integers(5)); h := P5 ! [ 3, 2, 1]; i := P3 ! [ 1, 2, 1]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); Output: Magma V2.10-6 Sun Mar 14 2004 17:46:07 on modular [Seed = 2409312003] ------------------------------------- true true true false Total time: 2.919 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 14 17:52:17 2004 Input: P3 := PolynomialRing(Integers(3)); f := P3 ! [ 2, 2, 1]; P2 := PolynomialRing(Integers(2)); g := P2 ! [ 1, 1, 0, 0, 1]; P5 := PolynomialRing(Integers(5)); h := P5 ! [ 3, 2, 1]; i := P3 ! [ 1, 2, 1]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); G9 := ext ; Output: Magma V2.10-6 Sun Mar 14 2004 17:52:14 on modular [Seed = 2626174625] ------------------------------------- true true true false >> G9 := ext ;; ^ Runtime error: No constructor provided for this type of object Total time: 2.959 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 14 17:54:22 2004 Input: P3 := PolynomialRing(Integers(3)); f := P3 ! [ 2, 2, 1]; P2 := PolynomialRing(Integers(2)); g := P2 ! [ 1, 1, 0, 0, 1]; P5 := PolynomialRing(Integers(5)); h := P5 ! [ 3, 2, 1]; i := P3 ! [ 1, 2, 1]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); G9 := ext < GF(9) | f>; Output: Magma V2.10-6 Sun Mar 14 2004 17:54:19 on modular [Seed = 3942533202] ------------------------------------- true true true false >> G9 := ext < GF(9) | f>;; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 3.009 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 14 18:03:08 2004 Input: P3 := PolynomialRing(Integers(3)); f := P3 ! [ 2, 2, 1]; P2 := PolynomialRing(Integers(2)); g := P2 ! [ 1, 1, 0, 0, 1]; P5 := PolynomialRing(Integers(5)); h := P5 ! [ 3, 2, 1]; i := P3 ! [ 1, 2, 1]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); K := GF(9); G9 := ext < K | f>; Output: Magma V2.10-6 Sun Mar 14 2004 18:03:05 on modular [Seed = 3619910493] ------------------------------------- true true true false >> G9 := ext < K | f>;; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 2.979 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 101-223-ADSL.red.retevision.es. (80.224.223.101) Time: Sun Mar 14 18:05:21 2004 Input: P3 := PolynomialRing(Integers(3)); f := P3 ! [ 2, 2, 1]; P2 := PolynomialRing(Integers(2)); g := P2 ! [ 1, 1, 0, 0, 1]; P5 := PolynomialRing(Integers(5)); h := P5 ! [ 3, 2, 1]; i := P3 ! [ 1, 2, 1]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); K := GF(9); G9 := ext< K | f>; Output: Magma V2.10-6 Sun Mar 14 2004 18:05:17 on modular [Seed = 590841386] ------------------------------------- true true true false >> G9 := ext< K | f>;; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 3.139 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Sun Mar 14 18:05:23 2004 Input: F:=GF(4); M:=MatrixRing(F,2); [i : i in M]; Output: Magma V2.10-6 Sun Mar 14 2004 18:05:20 on modular [Seed = 775588666] ------------------------------------- [ [ 1 1] [ 1 1], [ F.1 1] [ 1 1], [F.1^2 1] [ 1 1], [ 0 1] [ 1 1], [ 1 F.1] [ 1 1], [ F.1 F.1] [ 1 1], [F.1^2 F.1] [ 1 1], [ 0 F.1] [ 1 1], [ 1 F.1^2] [ 1 1], [ F.1 F.1^2] [ 1 1], [F.1^2 F.1^2] [ 1 1], [ 0 F.1^2] [ 1 1], [ 1 0] [ 1 1], [ F.1 0] [ 1 1], [F.1^2 0] [ 1 1], [ 0 0] [ 1 1], [ 1 1] [ F.1 1], [ F.1 1] [ F.1 1], [F.1^2 1] [ F.1 1], [ 0 1] [ F.1 1], [ 1 F.1] [ F.1 1], [ F.1 F.1] [ F.1 1], [F.1^2 F.1] [ F.1 1], [ 0 F.1] [ F.1 1], [ 1 F.1^2] [ F.1 1], [ F.1 F.1^2] [ F.1 1], [F.1^2 F.1^2] [ F.1 1], [ 0 F.1^2] [ F.1 1], [ 1 0] [ F.1 1], [ F.1 0] [ F.1 1], [F.1^2 0] [ F.1 1], [ 0 0] [ F.1 1], [ 1 1] [F.1^2 1], [ F.1 1] [F.1^2 1], [F.1^2 1] [F.1^2 1], [ 0 1] [F.1^2 1], [ 1 F.1] [F.1^2 1], [ F.1 F.1] [F.1^2 1], [F.1^2 F.1] [F.1^2 1], [ 0 F.1] [F.1^2 1], [ 1 F.1^2] [F.1^2 1], [ F.1 F.1^2] [F.1^2 1], [F.1^2 F.1^2] [F.1^2 1], [ 0 F.1^2] [F.1^2 1], [ 1 0] [F.1^2 1], [ F.1 0] [F.1^2 1], [F.1^2 0] [F.1^2 1], [ 0 0] [F.1^2 1], [ 1 1] [ 0 1], [ F.1 1] [ 0 1], [F.1^2 1] [ 0 1], [ 0 1] [ 0 1], [ 1 F.1] [ 0 1], [ F.1 F.1] [ 0 1], [F.1^2 F.1] [ 0 1], [ 0 F.1] [ 0 1], [ 1 F.1^2] [ 0 1], [ F.1 F.1^2] [ 0 1], [F.1^2 F.1^2] [ 0 1], [ 0 F.1^2] [ 0 1], [ 1 0] [ 0 1], [ F.1 0] [ 0 1], [F.1^2 0] [ 0 1], [ 0 0] [ 0 1], [ 1 1] [ 1 F.1], [ F.1 1] [ 1 F.1], [F.1^2 1] [ 1 F.1], [ 0 1] [ 1 F.1], [ 1 F.1] [ 1 F.1], [ F.1 F.1] [ 1 F.1], [F.1^2 F.1] [ 1 F.1], [ 0 F.1] [ 1 F.1], [ 1 F.1^2] [ 1 F.1], [ F.1 F.1^2] [ 1 F.1], [F.1^2 F.1^2] [ 1 F.1], [ 0 F.1^2] [ 1 F.1], [ 1 0] [ 1 F.1], [ F.1 0] [ 1 F.1], [F.1^2 0] [ 1 F.1], [ 0 0] [ 1 F.1], [ 1 1] [ F.1 F.1], [ F.1 1] [ F.1 F.1], [F.1^2 1] [ F.1 F.1], [ 0 1] [ F.1 F.1], [ 1 F.1] [ F.1 F.1], [ F.1 F.1] [ F.1 F.1], [F.1^2 F.1] [ F.1 F.1], [ 0 F.1] [ F.1 F.1], [ 1 F.1^2] [ F.1 F.1], [ F.1 F.1^2] [ F.1 F.1], [F.1^2 F.1^2] [ F.1 F.1], [ 0 F.1^2] [ F.1 F.1], [ 1 0] [ F.1 F.1], [ F.1 0] [ F.1 F.1], [F.1^2 0] [ F.1 F.1], [ 0 0] [ F.1 F.1], [ 1 1] [F.1^2 F.1], [ F.1 1] [F.1^2 F.1], [F.1^2 1] [F.1^2 F.1], [ 0 1] [F.1^2 F.1], [ 1 F.1] [F.1^2 F.1], [ F.1 F.1] [F.1^2 F.1], [F.1^2 F.1] [F.1^2 F.1], [ 0 F.1] [F.1^2 F.1], [ 1 F.1^2] [F.1^2 F.1], [ F.1 F.1^2] [F.1^2 F.1], [F.1^2 F.1^2] [F.1^2 F.1], [ 0 F.1^2] [F.1^2 F.1], [ 1 0] [F.1^2 F.1], [ F.1 0] [F.1^2 F.1], [F.1^2 0] [F.1^2 F.1], [ 0 0] [F.1^2 F.1], [ 1 1] [ 0 F.1], [ F.1 1] [ 0 F.1], [F.1^2 1] [ 0 F.1], [ 0 1] [ 0 F.1], [ 1 F.1] [ 0 F.1], [ F.1 F.1] [ 0 F.1], [F.1^2 F.1] [ 0 F.1], [ 0 F.1] [ 0 F.1], [ 1 F.1^2] [ 0 F.1], [ F.1 F.1^2] [ 0 F.1], [F.1^2 F.1^2] [ 0 F.1], [ 0 F.1^2] [ 0 F.1], [ 1 0] [ 0 F.1], [ F.1 0] [ 0 F.1], [F.1^2 0] [ 0 F.1], [ 0 0] [ 0 F.1], [ 1 1] [ 1 F.1^2], [ F.1 1] [ 1 F.1^2], [F.1^2 1] [ 1 F.1^2], [ 0 1] [ 1 F.1^2], [ 1 F.1] [ 1 F.1^2], [ F.1 F.1] [ 1 F.1^2], [F.1^2 F.1] [ 1 F.1^2], [ 0 F.1] [ 1 F.1^2], [ 1 F.1^2] [ 1 F.1^2], [ F.1 F.1^2] [ 1 F.1^2], [F.1^2 F.1^2] [ 1 F.1^2], [ 0 F.1^2] [ 1 F.1^2], [ 1 0] [ 1 F.1^2], [ F.1 0] [ 1 F.1^2], [F.1^2 0] [ 1 F.1^2], [ 0 0] [ 1 F.1^2], [ 1 1] [ F.1 F.1^2], [ F.1 1] [ F.1 F.1^2], [F.1^2 1] [ F.1 F.1^2], [ 0 1] [ F.1 F.1^2], [ 1 F.1] [ F.1 F.1^2], [ F.1 F.1] [ F.1 F.1^2], [F.1^2 F.1] [ F.1 F.1^2], [ 0 F.1] [ F.1 F.1^2], [ 1 F.1^2] [ F.1 F.1^2], [ F.1 F.1^2] [ F.1 F.1^2], [F.1^2 F.1^2] [ F.1 F.1^2], [ 0 F.1^2] [ F.1 F.1^2], [ 1 0] [ F.1 F.1^2], [ F.1 0] [ F.1 F.1^2], [F.1^2 0] [ F.1 F.1^2], [ 0 0] [ F.1 F.1^2], [ 1 1] [F.1^2 F.1^2], [ F.1 1] [F.1^2 F.1^2], [F.1^2 1] [F.1^2 F.1^2], [ 0 1] [F.1^2 F.1^2], [ 1 F.1] [F.1^2 F.1^2], [ F.1 F.1] [F.1^2 F.1^2], [F.1^2 F.1] [F.1^2 F.1^2], [ 0 F.1] [F.1^2 F.1^2], [ 1 F.1^2] [F.1^2 F.1^2], [ F.1 F.1^2] [F.1^2 F.1^2], [F.1^2 F.1^2] [F.1^2 F.1^2], [ 0 F.1^2] [F.1^2 F.1^2], [ 1 0] [F.1^2 F.1^2], [ F.1 0] [F.1^2 F.1^2], [F.1^2 0] [F.1^2 F.1^2], [ 0 0] [F.1^2 F.1^2], [ 1 1] [ 0 F.1^2], [ F.1 1] [ 0 F.1^2], [F.1^2 1] [ 0 F.1^2], [ 0 1] [ 0 F.1^2], [ 1 F.1] [ 0 F.1^2], [ F.1 F.1] [ 0 F.1^2], [F.1^2 F.1] [ 0 F.1^2], [ 0 F.1] [ 0 F.1^2], [ 1 F.1^2] [ 0 F.1^2], [ F.1 F.1^2] [ 0 F.1^2], [F.1^2 F.1^2] [ 0 F.1^2], [ 0 F.1^2] [ 0 F.1^2], [ 1 0] [ 0 F.1^2], [ F.1 0] [ 0 F.1^2], [F.1^2 0] [ 0 F.1^2], [ 0 0] [ 0 F.1^2], [ 1 1] [ 1 0], [ F.1 1] [ 1 0], [F.1^2 1] [ 1 0], [ 0 1] [ 1 0], [ 1 F.1] [ 1 0], [ F.1 F.1] [ 1 0], [F.1^2 F.1] [ 1 0], [ 0 F.1] [ 1 0], [ 1 F.1^2] [ 1 0], [ F.1 F.1^2] [ 1 0], [F.1^2 F.1^2] [ 1 0], [ 0 F.1^2] [ 1 0], [ 1 0] [ 1 0], [ F.1 0] [ 1 0], [F.1^2 0] [ 1 0], [ 0 0] [ 1 0], [ 1 1] [ F.1 0], [ F.1 1] [ F.1 0], [F.1^2 1] [ F.1 0], [ 0 1] [ F.1 0], [ 1 F.1] [ F.1 0], [ F.1 F.1] [ F.1 0], [F.1^2 F.1] [ F.1 0], [ 0 F.1] [ F.1 0], [ 1 F.1^2] [ F.1 0], [ F.1 F.1^2] [ F.1 0], [F.1^2 F.1^2] [ F.1 0], [ 0 F.1^2] [ F.1 0], [ 1 0] [ F.1 0], [ F.1 0] [ F.1 0], [F.1^2 0] [ F.1 0], [ 0 0] [ F.1 0], [ 1 1] [F.1^2 0], [ F.1 1] [F.1^2 0], [F.1^2 1] [F.1^2 0], [ 0 1] [F.1^2 0], [ 1 F.1] [F.1^2 0], [ F.1 F.1] [F.1^2 0], [F.1^2 F.1] [F.1^2 0], [ 0 F.1] [F.1^2 0], [ 1 F.1^2] [F.1^2 0], [ F.1 F.1^2] [F.1^2 0], [F.1^2 F.1^2] [F.1^2 0], [ 0 F.1^2] [F.1^2 0], [ 1 0] [F.1^2 0], [ F.1 0] [F.1^2 0], [F.1^2 0] [F.1^2 0], [ 0 0] [F.1^2 0], [ 1 1] [ 0 0], [ F.1 1] [ 0 0], [F.1^2 1] [ 0 0], [ 0 1] [ 0 0], [ 1 F.1] [ 0 0], [ F.1 F.1] [ 0 0], [F.1^2 F.1] [ 0 0], [ 0 F.1] [ 0 0], [ 1 F.1^2] [ 0 0], [ F.1 F.1^2] [ 0 0], [F.1^2 F.1^2] [ 0 0], [ 0 F.1^2] [ 0 0], [ 1 0] [ 0 0], [ F.1 0] [ 0 0], [F.1^2 0] [ 0 0], [ 0 0] [ 0 0] ] Total time: 3.089 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 19:19:57 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-6 Sun Mar 14 2004 19:19:54 on modular [Seed = 3235149390] ------------------------------------- [ x^2 + 2*x*y - 4*x + y^2 - 4*y + 4, x*y^2 + 2*x*y - 3*x + 2*y^2 - 8*y + 6, 4*x*y - 4*x + 3*y^2 - 10*y + 7, y^3 - 3*y^2 + 3*y - 1 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 19:20:11 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-6 Sun Mar 14 2004 19:20:08 on modular [Seed = 3502532172] ------------------------------------- [ x^2 + x + 2*y - 4, x*y + 2*x + y - 4, 3*x + 2*y - 5, y^2 - 2*y + 1 ] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 19:20:18 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-6 Sun Mar 14 2004 19:20:15 on modular [Seed = 3670961217] ------------------------------------- [ x^2 - 2*x + 1, 2*x*y - 2*x - 2*y + 2, y^2 - 2*y + 1 ] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 19:20:43 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal, (131-x^5)^2; > GroebnerBasis(I); Output: Magma V2.10-6 Sun Mar 14 2004 19:20:40 on modular [Seed = 574002399] ------------------------------------- >> I := ideal, (131-x^5)^2; ^ User error: bad syntax >> GroebnerBasis(I); ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 19:20:53 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal, (131-x^5)^2> ; > GroebnerBasis(I); Output: Magma V2.10-6 Sun Mar 14 2004 19:20:50 on modular [Seed = 891388914] ------------------------------------- >> I := ideal, (131-x^5)^2> ; ^ User error: bad syntax >> GroebnerBasis(I); ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 19:21:03 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal ; > GroebnerBasis(I); Output: Magma V2.10-6 Sun Mar 14 2004 19:21:00 on modular [Seed = 1009289973] ------------------------------------- [ x^2 + 1298*x + 201501, 2*x*y + 1298*x + 16898*y + 184602, 1300*x + 201500, y^2 + 16898*y + 202801, 16900*y + 202800, 219700 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Sun Mar 14 19:30:05 2004 Input: ? GF Output: Magma V2.10-6 Sun Mar 14 2004 19:30:02 on modular [Seed = 268740927] ------------------------------------- 4 matches: 1 I /magma/ring-field-algebra/finite-Galois-field/creation/structure/\ FiniteField 2 I /magma/ring-field-algebra/finite-Galois-field/creation/structure/\ FiniteField 3 I /magma/ring-field-algebra/finite-Galois-field/creation/structure/\ FiniteField 4 I /magma/ring-field-algebra/finite-Galois-field/creation/structure/\ FiniteField To view an entry, type ? followed by the number next to it Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Sun Mar 14 19:32:13 2004 Input: > exp:= func ; > exp(7,3); > P:=PolynomialRing(Integers()); > crea_t:= function (q,r) function> pol:=0; e:=exp(q,r); for i in [1..r-1] do pol:=pol+x^e[i]; end for; return pol; end function; > crea_t(7,3); > crea_n:= function (q,r) function> sum:=0; e:=exp(q,r); for i in [1..r-1] do sum:=sum+e[i]; end for; ret urn (x^sum); end function; > crea_n(7,3); Output: Magma V2.10-6 Sun Mar 14 2004 19:32:09 on modular [Seed = 437167030] ------------------------------------- [ 1, 7, 49 ] >> function> pol:=0; e:=exp(q,r); for i in [1..r-1] do pol:=pol+x^e[i]; end fo ^ User error: bad syntax >> return pol; end function; ^ User error: A 'return' can only be used inside a procedure or function >> return pol; end function; ^ User error: bad syntax >> crea_t(7,3); ^ User error: Identifier 'crea_t' has not been declared or assigned >> function> sum:=0; e:=exp(q,r); for i in [1..r-1] do sum:=sum+e[i]; end for; ^ User error: bad syntax >> urn (x^sum); end function; ^ User error: Identifier 'sum' has not been declared or assigned >> urn (x^sum); end function; ^ User error: bad syntax >> crea_n(7,3); ; ^ User error: Identifier 'crea_n' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 19:33:41 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal ; > GroebnerBasis(I); > (1-x*y)*(1-x^2*y)*(1-x^3*y^2) in I; Output: Magma V2.10-6 Sun Mar 14 2004 19:33:38 on modular [Seed = 1819858347] ------------------------------------- [ x^2 + 1298*x + 201501, 2*x*y + 1298*x + 16898*y + 184602, 1300*x + 201500, y^2 + 16898*y + 202801, 16900*y + 202800, 219700 ] true Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 19:33:59 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal ; > GroebnerBasis(I); > (1-x*y)*(1-x^2*y)*(131-x^5) in I; Output: Magma V2.10-6 Sun Mar 14 2004 19:33:56 on modular [Seed = 2003029670] ------------------------------------- [ x^2 + 1298*x + 201501, 2*x*y + 1298*x + 16898*y + 184602, 1300*x + 201500, y^2 + 16898*y + 202801, 16900*y + 202800, 219700 ] true Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 19:34:11 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal ; > GroebnerBasis(I); > (1-x*y)*(1-x^2*y) in I; Output: Magma V2.10-6 Sun Mar 14 2004 19:34:08 on modular [Seed = 2120926299] ------------------------------------- [ x^2 + 1298*x + 201501, 2*x*y + 1298*x + 16898*y + 184602, 1300*x + 201500, y^2 + 16898*y + 202801, 16900*y + 202800, 219700 ] false Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 19:34:42 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal ; > GroebnerBasis(I); > (14123-x*y)*(1-x^2*y) in I; Output: Magma V2.10-6 Sun Mar 14 2004 19:34:39 on modular [Seed = 1079310970] ------------------------------------- [ x^2 + 2*x + 1, 2*x*y + 2*x + 2*y + 2, y^2 + 2*y + 1, 4 ] false Total time: 2.989 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Sun Mar 14 19:34:54 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal ; > GroebnerBasis(I); > (14123-x*y)*(1-x^2*y) in I; Output: Magma V2.10-6 Sun Mar 14 2004 19:34:51 on modular [Seed = 1264578885] ------------------------------------- [ x^2 + 18*x + y^2 + 18*y + 62, x*y^2 + 19*x + 4*y^2 + 10*y + 66, 2*x*y + 18*x + 18*y + 62, 20*x + 3*y^2 + 14*y + 63, y^3 + 2*y^2 + 93*y + 4, 5*y^2 + 90*y + 5, 100 ] false Total time: 2.919 seconds, Total memory usage: 1.92MB ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Sun Mar 14 19:35:49 2004 Input: > exp:= func ; > exp(7,3); > P:=PolynomialRing(Integers()); > crea_t:= function (q,r) pol:=0; e:=exp(q,r); for i in [1..r-1] do pol:=pol+x^e[i]; end for; return pol; end function; > crea_t(7,3); > crea_n:= function (q,r) sum:=0; e:=exp(q,r); for i in [1..r-1] do sum:=sum+e[i]; end for; return (x^sum); end function; > crea_n(7,3); Output: Magma V2.10-6 Sun Mar 14 2004 19:35:46 on modular [Seed = 1498276638] ------------------------------------- [ 1, 7, 49 ] x^7 + x x^8 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Sun Mar 14 19:38:29 2004 Input: > exp:= func ; > exp(7,3); > P:=PolynomialRing(Integers()); > crea_t:= function (q,r) pol:=0; e:=exp(q,r); for i in [0..r-1] do pol:=pol+x^e[i]; end for; return pol; end function; > crea_t(7,3); > crea_n:= function (q,r) sum:=0; e:=exp(q,r); for i in [0..r-1] do sum:=sum+e[i]; end for; return (x^sum); end function; > crea_n(7,3); Output: Magma V2.10-6 Sun Mar 14 2004 19:38:26 on modular [Seed = 2746685572] ------------------------------------- [ 1, 7, 49 ] [
:6]( q: 7, r: 3 ) >> pol:=pol+x^e[i]; ^ Runtime error in '[]': Sequence element 0 not defined [
:15]( q: 7, r: 3 ) >> sum:=sum+e[i]; ^ Runtime error in '[]': Sequence element 0 not defined Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Sun Mar 14 19:39:38 2004 Input: > exp:= func ; > exp(7,3); > P:=PolynomialRing(Integers()); > crea_t:= function (q,r) pol:=0; e:=exp(q,r); for i in [1..r] do pol:=pol+x^e[i]; end for; return pol; end function; > crea_t(7,3); > crea_n:= function (q,r) sum:=0; e:=exp(q,r); for i in [1..r] do sum:=sum+e[i]; end for; return (x^sum); end function; > crea_n(7,3); Output: Magma V2.10-6 Sun Mar 14 2004 19:39:35 on modular [Seed = 2864583112] ------------------------------------- [ 1, 7, 49 ] x^49 + x^7 + x x^57 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Sun Mar 14 19:43:50 2004 Input: [7^i : i in [0..2]]; Output: Magma V2.10-6 Sun Mar 14 2004 19:43:47 on modular [Seed = 2274573281] ------------------------------------- [ 1, 7, 49 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Sun Mar 14 19:47:26 2004 Input: > P:=PolynomialRing(Integers()); >n73:= x^49 + x^7 + x; >t73:= x^57; Output: Magma V2.10-6 Sun Mar 14 2004 19:47:23 on modular [Seed = 2491427242] ------------------------------------- Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Sun Mar 14 19:47:47 2004 Input: > P:=PolynomialRing(Integers()); >n73:= x^49 + x^7 + x; >t73:= x^57; n73; t73; Output: Magma V2.10-6 Sun Mar 14 2004 19:47:44 on modular [Seed = 2676695690] ------------------------------------- x^49 + x^7 + x x^57 Total time: 2.849 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Sun Mar 14 19:51:57 2004 Input: > P:=PolynomialRing(Integers()); >n73:= x^49 + x^7 + x; >t73:= x^57; n73; t73; [a,b: a,b in car | n73(a) equ t73(b)]; Output: Magma V2.10-6 Sun Mar 14 2004 19:51:54 on modular [Seed = 3925694438] ------------------------------------- x^49 + x^7 + x x^57 >> [a,b: a,b in car | n73(a) equ t73(b)];; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Sun Mar 14 19:55:33 2004 Input: > P:=PolynomialRing(Integers()); >n73:= x^49 + x^7 + x; >t73:= x^57; >n73; >t73; >[: a,b in car | n73(a) eq t73(b)]; Output: Magma V2.10-6 Sun Mar 14 2004 19:55:30 on modular [Seed = 4193076958] ------------------------------------- x^49 + x^7 + x x^57 >> [: a,b in car | n73(a) eq t73(b)]; ^ Runtime error: Bad argument types Argument types given: Tup, RngUPolElt Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Sun Mar 14 19:56:27 2004 Input: > P:=PolynomialRing(Integers()); >n73:= x^49 + x^7 + x; >t73:= x^57; >n73; >t73; >[{a,b}: a,b in car | n73(a) eq t73(b)]; Output: Magma V2.10-6 Sun Mar 14 2004 19:56:24 on modular [Seed = 3235151837] ------------------------------------- x^49 + x^7 + x x^57 >> [{a,b}: a,b in car | n73(a) eq t73(b)]; ^ Runtime error: Bad argument types Argument types given: Tup, RngUPolElt Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Sun Mar 14 20:14:39 2004 Input: > P:=PolynomialRing(Integers()); >n73:= x^49 + x^7 + x; >t73:= x^57; >n73; >t73; >n73(4); >[{a,b}: a,b in car | n73(a) eq t73(b)]; Output: Magma V2.10-6 Sun Mar 14 2004 20:14:36 on modular [Seed = 386028621] ------------------------------------- x^49 + x^7 + x x^57 >> n73(4); ^ Runtime error: Bad argument types Argument types given: RngIntElt, RngUPolElt >> [{a,b}: a,b in car | n73(a) eq t73(b)]; ^ Runtime error: Bad argument types Argument types given: Tup, RngUPolElt Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Sun Mar 14 20:15:45 2004 Input: > P:=PolynomialRing(Integers()); >n73:= x^49 + x^7 + x; >t73:= x^57; >n73; >t73; >evaluate(n73,4); >[{a,b}: a,b in car | n73(a) eq t73(b)]; Output: Magma V2.10-6 Sun Mar 14 2004 20:15:42 on modular [Seed = 420240001] ------------------------------------- x^49 + x^7 + x x^57 >> evaluate(n73,4); ^ User error: Identifier 'evaluate' has not been declared or assigned >> [{a,b}: a,b in car | n73(a) eq t73(b)]; ^ Runtime error: Bad argument types Argument types given: Tup, RngUPolElt Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Sun Mar 14 20:16:42 2004 Input: > P:=PolynomialRing(Integers()); >n73:= x^49 + x^7 + x; >t73:= x^57; >n73; >t73; >Evaluate(n73,4); >[{a,b}: a,b in car | n73(a) eq t73(b)]; Output: Magma V2.10-6 Sun Mar 14 2004 20:16:39 on modular [Seed = 1836592828] ------------------------------------- x^49 + x^7 + x x^57 316912650057057350374175817732 >> [{a,b}: a,b in car | n73(a) eq t73(b)]; ^ Runtime error: Bad argument types Argument types given: Tup, RngUPolElt Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Sun Mar 14 20:17:11 2004 Input: > P:=PolynomialRing(Integers()); >n73:= x^49 + x^7 + x; >t73:= x^57; >n73; >t73; >[{a,b}: a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)]; Output: Magma V2.10-6 Sun Mar 14 2004 20:17:08 on modular [Seed = 1919366720] ------------------------------------- x^49 + x^7 + x x^57 >> [{a,b}: a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)]; ^ Runtime error in 'Evaluate': Bad argument types Argument types given: RngUPolElt, Tup Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Sun Mar 14 20:17:47 2004 Input: > P:=PolynomialRing(Integers()); >n73:= x^49 + x^7 + x; >t73:= x^57; >n73; >t73; >[{}: a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)]; Output: Magma V2.10-6 Sun Mar 14 2004 20:17:44 on modular [Seed = 2070822757] ------------------------------------- x^49 + x^7 + x x^57 >> [{}: a,b in car | Evaluate(n73,a) eq Evaluate(t73,b) ^ Runtime error in 'Evaluate': Bad argument types Argument types given: RngUPolElt, Tup Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Sun Mar 14 20:19:37 2004 Input: > P:=PolynomialRing(Integers()); >n73:= x^49 + x^7 + x; >t73:= x^57; >n73; >t73; >[: a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)]; Output: Magma V2.10-6 Sun Mar 14 2004 20:19:34 on modular [Seed = 1096025537] ------------------------------------- x^49 + x^7 + x x^57 >> [: a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)]; ^ Runtime error in 'Evaluate': Bad argument types Argument types given: RngUPolElt, Tup Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Sun Mar 14 20:21:49 2004 Input: > P:=PolynomialRing(Integers()); >n73:= x^49 + x^7 + x; >t73:= x^57; >n73; >t73; >[: a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)]; >? RngUPolElt Output: Magma V2.10-6 Sun Mar 14 2004 20:21:46 on modular [Seed = 1581980498] ------------------------------------- x^49 + x^7 + x x^57 >> [: a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)]; ^ Runtime error in 'Evaluate': Bad argument types Argument types given: RngUPolElt, Tup No references for word "RngUPolElt" Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Sun Mar 14 20:25:24 2004 Input: > P:=PolynomialRing(Integers()); >n73:= x^49 + x^7 + x; >t73:= x^57; >n73; >t73; >{: a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)}; Output: Magma V2.10-6 Sun Mar 14 2004 20:25:21 on modular [Seed = 2931550345] ------------------------------------- x^49 + x^7 + x x^57 >> {: a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)}; ^ Runtime error in 'Evaluate': Bad argument types Argument types given: RngUPolElt, Tup Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Sun Mar 14 20:26:18 2004 Input: > P:=PolynomialRing(Integers()); >n73:= x^49 + x^7 + x; >t73:= x^57; >n73; >t73; >[: a,b in car]; >[: a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)}]; Output: ** WARNING: Computation used more memory than allowed. ** Magma V2.10-6 Sun Mar 14 2004 20:26:09 on modular [Seed = 3080909216] ------------------------------------- x^49 + x^7 + x x^57 Current total memory usage: 87.4MB, failed memory request: 8.3MB System Error: User memory limit has been reached Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Wed Apr 23 11:13:24 EST 2003 Initial seed: 3080909216 Time to this point: 8.96 Segmentation fault Errors: Magma: Fatal Error: Magma: Irrecoverable error; exiting ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Sun Mar 14 20:27:06 2004 Input: > P:=PolynomialRing(Integers()); >n73:= x^49 + x^7 + x; >t73:= x^57; >n73; >t73; >car; >[: a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)}]; Output: Magma V2.10-6 Sun Mar 14 2004 20:27:03 on modular [Seed = 3165256445] ------------------------------------- x^49 + x^7 + x x^57 Cartesian Product >> [: a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)}] ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Sun Mar 14 20:27:52 2004 Input: > P:=PolynomialRing(Integers()); >n73:= x^49 + x^7 + x; >t73:= x^57; >n73; >t73; >[: Evaluate(n73,a) eq Evaluate(t73,b)}]; >[: a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)}]; Output: Magma V2.10-6 Sun Mar 14 2004 20:27:49 on modular [Seed = 2240856886] ------------------------------------- x^49 + x^7 + x x^57 >> [: Evaluate(n73,a) eq Evaluate(t73,b)}]; ^ User error: bad syntax >> [: a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)}] ^ User error: bad syntax Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Sun Mar 14 20:28:30 2004 Input: > P:=PolynomialRing(Integers()); >n73:= x^49 + x^7 + x; >t73:= x^57; >n73; >t73; >[a: Evaluate(n73,a)]; >[: a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)}]; Output: Magma V2.10-6 Sun Mar 14 2004 20:28:27 on modular [Seed = 2342440214] ------------------------------------- x^49 + x^7 + x x^57 >> [a: Evaluate(n73,a)]; ^ User error: bad syntax >> [: a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)}] ^ User error: bad syntax Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Sun Mar 14 20:28:58 2004 Input: > P:=PolynomialRing(Integers()); >n73:= x^49 + x^7 + x; >t73:= x^57; >n73; >t73; >[a: a in [0..10] | Evaluate(n73,a)]; >[: a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)}]; Output: Magma V2.10-6 Sun Mar 14 2004 20:28:55 on modular [Seed = 2424690273] ------------------------------------- x^49 + x^7 + x x^57 >> [a: a in [0..10] | Evaluate(n73,a)]; ^ Runtime error in sequence construction: Logical expected >> [: a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)}] ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Sun Mar 14 20:29:39 2004 Input: > P:=PolynomialRing(Integers()); >n73:= x^49 + x^7 + x; >t73:= x^57; >n73; >t73; >[a : a in [0..10] | Evaluate(n73,a)]; >[ : a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)}]; Output: Magma V2.10-6 Sun Mar 14 2004 20:29:36 on modular [Seed = 2576146111] ------------------------------------- x^49 + x^7 + x x^57 >> [a : a in [0..10] | Evaluate(n73,a)]; ^ Runtime error in sequence construction: Logical expected >> [ : a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)} ^ User error: bad syntax Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Sun Mar 14 20:30:01 2004 Input: > P:=PolynomialRing(Integers()); >n73:= x^49 + x^7 + x; >t73:= x^57; >n73; >t73; >[ a : a in [0..10] | Evaluate(n73,a)]; >[ : a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)}]; Output: Magma V2.10-6 Sun Mar 14 2004 20:29:57 on modular [Seed = 4009470429] ------------------------------------- x^49 + x^7 + x x^57 >> [ a : a in [0..10] | Evaluate(n73,a)]; ^ Runtime error in sequence construction: Logical expected >> [ : a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)} ^ User error: bad syntax Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Sun Mar 14 20:30:26 2004 Input: > P:=PolynomialRing(Integers()); >n73:= x^49 + x^7 + x; >t73:= x^57; >n73; >t73; >[ a : a in [0..10] | Evaluate(n73,a)]; >[7^i : i in [0..2]]; >[ : a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)}]; Output: Magma V2.10-6 Sun Mar 14 2004 20:30:23 on modular [Seed = 4293572854] ------------------------------------- x^49 + x^7 + x x^57 >> [ a : a in [0..10] | Evaluate(n73,a)]; ^ Runtime error in sequence construction: Logical expected [ 1, 7, 49 ] >> [ : a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)} ^ User error: bad syntax Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Sun Mar 14 20:30:47 2004 Input: > P:=PolynomialRing(Integers()); >n73:= x^49 + x^7 + x; >t73:= x^57; >n73; >t73; >[ a : a in [0..10] | Evaluate(n73,a)]; >[i : i in [0..10]]; >[ : a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)}]; Output: Magma V2.10-6 Sun Mar 14 2004 20:30:44 on modular [Seed = 3302065062] ------------------------------------- x^49 + x^7 + x x^57 >> [ a : a in [0..10] | Evaluate(n73,a)]; ^ Runtime error in sequence construction: Logical expected [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ] >> [ : a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)} ^ User error: bad syntax Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Sun Mar 14 20:31:40 2004 Input: > P:=PolynomialRing(Integers()); >n73:= x^49 + x^7 + x; >t73:= x^57; >n73; >t73; >[ a : a in [0..10] | Evaluate(n73,a)]; >[i : i in [0..10] | Evaluate(n73,i)]; >[ : a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)}]; Output: Magma V2.10-6 Sun Mar 14 2004 20:31:37 on modular [Seed = 3403648405] ------------------------------------- x^49 + x^7 + x x^57 >> [ a : a in [0..10] | Evaluate(n73,a)]; ^ Runtime error in sequence construction: Logical expected >> [i : i in [0..10] | Evaluate(n73,i)]; ^ Runtime error in sequence construction: Logical expected >> [ : a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)} ^ User error: bad syntax Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Sun Mar 14 20:32:09 2004 Input: > P:=PolynomialRing(Integers()); >n73:= x^49 + x^7 + x; >t73:= x^57; >n73; >t73; >[ a : a in [0..10] | Evaluate(n73,a)]; >Evaluate(n73,5); >[ : a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)}]; Output: Magma V2.10-6 Sun Mar 14 2004 20:32:06 on modular [Seed = 3553006691] ------------------------------------- x^49 + x^7 + x x^57 >> [ a : a in [0..10] | Evaluate(n73,a)]; ^ Runtime error in sequence construction: Logical expected 17763568394002504646778106689531255 >> [ : a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)} ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Sun Mar 14 20:33:11 2004 Input: > P:=PolynomialRing(Integers()); >n73:= x^49 + x^7 + x; >t73:= x^57; >n73; >t73; >[a: a in [0..10] | Evaluate(n73,a) eq Evaluate(n73,5)]; >Evaluate(n73,5); >[: a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)}]; Output: Magma V2.10-6 Sun Mar 14 2004 20:33:08 on modular [Seed = 3637354282] ------------------------------------- x^49 + x^7 + x x^57 [ 5 ] 17763568394002504646778106689531255 >> [: a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)}] ^ User error: bad syntax Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Sun Mar 14 20:33:36 2004 Input: > P:=PolynomialRing(Integers()); >n73:= x^49 + x^7 + x; >t73:= x^57; >n73; >t73; >[a: a in car | Evaluate(n73,a) eq Evaluate(n73,5)]; >Evaluate(n73,5); >[: a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)}]; Output: Magma V2.10-6 Sun Mar 14 2004 20:33:33 on modular [Seed = 540370922] ------------------------------------- x^49 + x^7 + x x^57 >> [a: a in car | Evaluate(n73,a) eq Evaluate(n73,5)]; ^ Runtime error in 'Evaluate': Bad argument types Argument types given: RngUPolElt, Tup 17763568394002504646778106689531255 >> [: a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)}] ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Sun Mar 14 20:34:18 2004 Input: > P:=PolynomialRing(Integers()); >n73:= x^49 + x^7 + x; >t73:= x^57; >n73; >t73; >[a: a in GF(7,3) | Evaluate(n73,a) eq Evaluate(n73,5)]; >Evaluate(n73,5); >[: a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)}]; Output: Magma V2.10-6 Sun Mar 14 2004 20:34:15 on modular [Seed = 908295686] ------------------------------------- x^49 + x^7 + x x^57 [ $.1, $.1^2, $.1^7, $.1^10, $.1^11, $.1^14, $.1^16, $.1^25, $.1^37, $.1^49, $.1^66, $.1^70, $.1^77, $.1^87, $.1^90, $.1^97, $.1^98, $.1^100, $.1^103, $.1^112, $.1^120, $.1^131, $.1^132, $.1^137, $.1^146, $.1^148, $.1^156, $.1^159, $.1^175, $.1^195, $.1^197, $.1^199, $.1^215, $.1^233, $.1^240, $.1^259, $.1^263, $.1^267, $.1^275, 5, $.1^288, $.1^306, $.1^307, $.1^312, $.1^314, $.1^321, $.1^337, $.1^338, $.1^339 ] 17763568394002504646778106689531255 >> [: a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)}] ^ User error: bad syntax Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Sun Mar 14 20:38:30 2004 Input: > P:=PolynomialRing(Integers()); >n73:= x^49 + x^7 + x; >t73:= x^57; >n73; >t73; >Ov:=GF(7,3)*GF(7,3); >[a: a in GF(7,3) | Evaluate(n73,a) eq Evaluate(n73,5)]; >Evaluate(n73,5); >[: a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)}]; Output: Magma V2.10-6 Sun Mar 14 2004 20:38:27 on modular [Seed = 118640179] ------------------------------------- x^49 + x^7 + x x^57 >> Ov:=GF(7,3)*GF(7,3); ^ Runtime error in '*': Bad argument types Argument types given: FldFin, FldFin [ $.1, $.1^2, $.1^7, $.1^10, $.1^11, $.1^14, $.1^16, $.1^25, $.1^37, $.1^49, $.1^66, $.1^70, $.1^77, $.1^87, $.1^90, $.1^97, $.1^98, $.1^100, $.1^103, $.1^112, $.1^120, $.1^131, $.1^132, $.1^137, $.1^146, $.1^148, $.1^156, $.1^159, $.1^175, $.1^195, $.1^197, $.1^199, $.1^215, $.1^233, $.1^240, $.1^259, $.1^263, $.1^267, $.1^275, 5, $.1^288, $.1^306, $.1^307, $.1^312, $.1^314, $.1^321, $.1^337, $.1^338, $.1^339 ] 17763568394002504646778106689531255 >> [: a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)}] ^ User error: bad syntax Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Sun Mar 14 20:38:58 2004 Input: > P:=PolynomialRing(Integers()); >n73:= x^49 + x^7 + x; >t73:= x^57; >n73; >t73; >Ov:=GF(7,3); >Ov2:=Ov*Ov; >[a: a in GF(7,3) | Evaluate(n73,a) eq Evaluate(n73,5)]; >Evaluate(n73,5); >[: a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)}]; Output: Magma V2.10-6 Sun Mar 14 2004 20:38:55 on modular [Seed = 236668678] ------------------------------------- x^49 + x^7 + x x^57 >> Ov2:=Ov*Ov; ^ Runtime error in '*': Bad argument types Argument types given: FldFin, FldFin [ Ov.1, Ov.1^2, Ov.1^7, Ov.1^10, Ov.1^11, Ov.1^14, Ov.1^16, Ov.1^25, Ov.1^37, Ov.1^49, Ov.1^66, Ov.1^70, Ov.1^77, Ov.1^87, Ov.1^90, Ov.1^97, Ov.1^98, Ov.1^100, Ov.1^103, Ov.1^112, Ov.1^120, Ov.1^131, Ov.1^132, Ov.1^137, Ov.1^146, Ov.1^148, Ov.1^156, Ov.1^159, Ov.1^175, Ov.1^195, Ov.1^197, Ov.1^199, Ov.1^215, Ov.1^233, Ov.1^240, Ov.1^259, Ov.1^263, Ov.1^267, Ov.1^275, 5, Ov.1^288, Ov.1^306, Ov.1^307, Ov.1^312, Ov.1^314, Ov.1^321, Ov.1^337, Ov.1^338, Ov.1^339 ] 17763568394002504646778106689531255 >> [: a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)}] ^ User error: bad syntax Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Sun Mar 14 20:48:45 2004 Input: > P:=PolynomialRing(Integers()); >n73:= x^49 + x^7 + x; >t73:= x^57; >n73; >t73; >Ov:=GF(7,3); >Ov2:=Ov*Ov; >[: a in GF(7,3) | Evaluate(n73,a) eq Evaluate(n73,b)]; >[: a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)}]; Output: Magma V2.10-6 Sun Mar 14 2004 20:48:42 on modular [Seed = 1701850680] ------------------------------------- x^49 + x^7 + x x^57 >> Ov2:=Ov*Ov; ^ Runtime error in '*': Bad argument types Argument types given: FldFin, FldFin >> [: a in GF(7,3) | Evaluate(n73,a) eq Evaluate(n73,b)]; ^ User error: Identifier 'b' has not been declared or assigned >> [: a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)}] ^ User error: bad syntax Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Sun Mar 14 20:49:22 2004 Input: > P:=PolynomialRing(Integers()); >n73:= x^49 + x^7 + x; >t73:= x^57; >n73; >t73; >[{a,b}: a in GF(7,3) | Evaluate(n73,a) eq Evaluate(n73,b)]; >[: a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)}]; Output: Magma V2.10-6 Sun Mar 14 2004 20:49:19 on modular [Seed = 1803428051] ------------------------------------- x^49 + x^7 + x x^57 >> [{a,b}: a in GF(7,3) | Evaluate(n73,a) eq Evaluate(n73,b)]; ^ User error: Identifier 'b' has not been declared or assigned >> [: a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)}] ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Sun Mar 14 20:49:46 2004 Input: > P:=PolynomialRing(Integers()); >n73:= x^49 + x^7 + x; >t73:= x^57; >n73; >t73; >[: a,b in GF(7,3) | Evaluate(n73,a) eq Evaluate(n73,b)]; >[: a,b in car | Evaluate(n73,a) eq Evaluate(t73,b)}]; Output: Magma V2.10-6 Sun Mar 14 2004 20:49:40 on modular [Seed = 1919367649] ------------------------------------- x^49 + x^7 + x x^57 [ <1, 1>, <1, $.1^3>, <1, $.1^21>, <1, $.1^22>, <1, $.1^27>, <1, $.1^29>, <1, $.1^36>, <1, $.1^52>, <1, $.1^53>, <1, $.1^54>, <1, $.1^58>, <1, $.1^59>, <1, $.1^64>, <1, $.1^67>, <1, $.1^68>, <1, $.1^71>, <1, $.1^73>, <1, $.1^82>, <1, $.1^94>, <1, $.1^106>, <1, $.1^123>, <1, $.1^127>, <1, $.1^134>, <1, $.1^144>, <1, $.1^147>, <1, $.1^154>, <1, $.1^155>, <1, $.1^157>, <1, $.1^160>, <1, $.1^169>, <1, $.1^177>, <1, $.1^188>, <1, $.1^189>, <1, $.1^194>, <1, $.1^203>, <1, $.1^205>, <1, $.1^213>, <1, $.1^216>, <1, $.1^232>, <1, $.1^252>, <1, $.1^254>, <1, $.1^256>, <1, $.1^272>, <1, $.1^290>, <1, $.1^297>, <1, $.1^316>, <1, $.1^320>, <1, $.1^324>, <1, $.1^332>, <$.1, $.1>, <$.1, $.1^2>, <$.1, $.1^7>, <$.1, $.1^10>, <$.1, $.1^11>, <$.1, $.1^14>, <$.1, $.1^16>, <$.1, $.1^25>, <$.1, $.1^37>, <$.1, $.1^49>, <$.1, $.1^66>, <$.1, $.1^70>, <$.1, $.1^77>, <$.1, $.1^87>, <$.1, $.1^90>, <$.1, $.1^97>, <$.1, $.1^98>, <$.1, $.1^100>, <$.1, $.1^103>, <$.1, $.1^112>, <$.1, $.1^120>, <$.1, $.1^131>, <$.1, $.1^132>, <$.1, $.1^137>, <$.1, $.1^146>, <$.1, $.1^148>, <$.1, $.1^156>, <$.1, $.1^159>, <$.1, $.1^175>, <$.1, $.1^195>, <$.1, $.1^197>, <$.1, $.1^199>, <$.1, $.1^215>, <$.1, $.1^233>, <$.1, $.1^240>, <$.1, $.1^259>, <$.1, $.1^263>, <$.1, $.1^267>, <$.1, $.1^275>, <$.1, 5>, <$.1, $.1^288>, <$.1, $.1^306>, <$.1, $.1^307>, <$.1, $.1^312>, <$.1, $.1^314>, <$.1, $.1^321>, <$.1, $.1^337>, <$.1, $.1^338>, <$.1, $.1^339>, <$.1^2, $.1>, <$.1^2, $.1^2>, <$.1^2, $.1^7>, <$.1^2, $.1^10>, <$.1^2, $.1^11>, <$.1^2, $.1^14>, <$.1^2, $.1^16>, <$.1^2, $.1^25>, <$.1^2, $.1^37>, <$.1^2, $.1^49>, <$.1^2, $.1^66>, <$.1^2, $.1^70>, <$.1^2, $.1^77>, <$.1^2, $.1^87>, <$.1^2, $.1^90>, <$.1^2, $.1^97>, <$.1^2, $.1^98>, <$.1^2, $.1^100>, <$.1^2, $.1^103>, <$.1^2, $.1^112>, <$.1^2, $.1^120>, <$.1^2, $.1^131>, <$.1^2, $.1^132>, <$.1^2, $.1^137>, <$.1^2, $.1^146>, <$.1^2, $.1^148>, <$.1^2, $.1^156>, <$.1^2, $.1^159>, <$.1^2, $.1^175>, <$.1^2, $.1^195>, <$.1^2, $.1^197>, <$.1^2, $.1^199>, <$.1^2, $.1^215>, <$.1^2, $.1^233>, <$.1^2, $.1^240>, <$.1^2, $.1^259>, <$.1^2, $.1^263>, <$.1^2, $.1^267>, <$.1^2, $.1^275>, <$.1^2, 5>, <$.1^2, $.1^288>, <$.1^2, $.1^306>, <$.1^2, $.1^307>, <$.1^2, $.1^312>, <$.1^2, $.1^314>, <$.1^2, $.1^321>, <$.1^2, $.1^337>, <$.1^2, $.1^338>, <$.1^2, $.1^339>, <$.1^3, 1>, <$.1^3, $.1^3>, <$.1^3, $.1^21>, <$.1^3, $.1^22>, <$.1^3, $.1^27>, <$.1^3, $.1^29>, <$.1^3, $.1^36>, <$.1^3, $.1^52>, <$.1^3, $.1^53>, <$.1^3, $.1^54>, <$.1^3, $.1^58>, <$.1^3, $.1^59>, <$.1^3, $.1^64>, <$.1^3, $.1^67>, <$.1^3, $.1^68>, <$.1^3, $.1^71>, <$.1^3, $.1^73>, <$.1^3, $.1^82>, <$.1^3, $.1^94>, <$.1^3, $.1^106>, <$.1^3, $.1^123>, <$.1^3, $.1^127>, <$.1^3, $.1^134>, <$.1^3, $.1^144>, <$.1^3, $.1^147>, <$.1^3, $.1^154>, <$.1^3, $.1^155>, <$.1^3, $.1^157>, <$.1^3, $.1^160>, <$.1^3, $.1^169>, <$.1^3, $.1^177>, <$.1^3, $.1^188>, <$.1^3, $.1^189>, <$.1^3, $.1^194>, <$.1^3, $.1^203>, <$.1^3, $.1^205>, <$.1^3, $.1^213>, <$.1^3, $.1^216>, <$.1^3, $.1^232>, <$.1^3, $.1^252>, <$.1^3, $.1^254>, <$.1^3, $.1^256>, <$.1^3, $.1^272>, <$.1^3, $.1^290>, <$.1^3, $.1^297>, <$.1^3, $.1^316>, <$.1^3, $.1^320>, <$.1^3, $.1^324>, <$.1^3, $.1^332>, <$.1^4, $.1^4>, <$.1^4, $.1^24>, <$.1^4, $.1^26>, <$.1^4, $.1^28>, <$.1^4, $.1^44>, <$.1^4, $.1^62>, <$.1^4, $.1^69>, <$.1^4, $.1^88>, <$.1^4, $.1^92>, <$.1^4, $.1^96>, <$.1^4, $.1^104>, <$.1^4, 2>, <$.1^4, $.1^117>, <$.1^4, $.1^135>, <$.1^4, $.1^136>, <$.1^4, $.1^141>, <$.1^4, $.1^143>, <$.1^4, $.1^150>, <$.1^4, $.1^166>, <$.1^4, $.1^167>, <$.1^4, $.1^168>, <$.1^4, $.1^172>, <$.1^4, $.1^173>, <$.1^4, $.1^178>, <$.1^4, $.1^181>, <$.1^4, $.1^182>, <$.1^4, $.1^185>, <$.1^4, $.1^187>, <$.1^4, $.1^196>, <$.1^4, $.1^208>, <$.1^4, $.1^220>, <$.1^4, $.1^237>, <$.1^4, $.1^241>, <$.1^4, $.1^248>, <$.1^4, $.1^258>, <$.1^4, $.1^261>, <$.1^4, $.1^268>, <$.1^4, $.1^269>, <$.1^4, $.1^271>, <$.1^4, $.1^274>, <$.1^4, $.1^283>, <$.1^4, $.1^291>, <$.1^4, $.1^302>, <$.1^4, $.1^303>, <$.1^4, $.1^308>, <$.1^4, $.1^317>, <$.1^4, $.1^319>, <$.1^4, $.1^327>, <$.1^4, $.1^330>, <$.1^5, $.1^5>, <$.1^5, $.1^12>, <$.1^5, $.1^31>, <$.1^5, $.1^35>, <$.1^5, $.1^39>, <$.1^5, $.1^47>, <$.1^5, 3>, <$.1^5, $.1^60>, <$.1^5, $.1^78>, <$.1^5, $.1^79>, <$.1^5, $.1^84>, <$.1^5, $.1^86>, <$.1^5, $.1^93>, <$.1^5, $.1^109>, <$.1^5, $.1^110>, <$.1^5, $.1^111>, <$.1^5, $.1^115>, <$.1^5, $.1^116>, <$.1^5, $.1^121>, <$.1^5, $.1^124>, <$.1^5, $.1^125>, <$.1^5, $.1^128>, <$.1^5, $.1^130>, <$.1^5, $.1^139>, <$.1^5, $.1^151>, <$.1^5, $.1^163>, <$.1^5, $.1^180>, <$.1^5, $.1^184>, <$.1^5, $.1^191>, <$.1^5, $.1^201>, <$.1^5, $.1^204>, <$.1^5, $.1^211>, <$.1^5, $.1^212>, <$.1^5, $.1^214>, <$.1^5, $.1^217>, <$.1^5, $.1^226>, <$.1^5, $.1^234>, <$.1^5, $.1^245>, <$.1^5, $.1^246>, <$.1^5, $.1^251>, <$.1^5, $.1^260>, <$.1^5, $.1^262>, <$.1^5, $.1^270>, <$.1^5, $.1^273>, <$.1^5, $.1^289>, <$.1^5, $.1^309>, <$.1^5, $.1^311>, <$.1^5, $.1^313>, <$.1^5, $.1^329>, <$.1^6, $.1^6>, <$.1^6, $.1^17>, <$.1^6, $.1^18>, <$.1^6, $.1^23>, <$.1^6, $.1^32>, <$.1^6, $.1^34>, <$.1^6, $.1^42>, <$.1^6, $.1^45>, <$.1^6, $.1^61>, <$.1^6, $.1^81>, <$.1^6, $.1^83>, <$.1^6, $.1^85>, <$.1^6, $.1^101>, <$.1^6, $.1^119>, <$.1^6, $.1^126>, <$.1^6, $.1^145>, <$.1^6, $.1^149>, <$.1^6, $.1^153>, <$.1^6, $.1^161>, <$.1^6, 6>, <$.1^6, $.1^174>, <$.1^6, $.1^192>, <$.1^6, $.1^193>, <$.1^6, $.1^198>, <$.1^6, $.1^200>, <$.1^6, $.1^207>, <$.1^6, $.1^223>, <$.1^6, $.1^224>, <$.1^6, $.1^225>, <$.1^6, $.1^229>, <$.1^6, $.1^230>, <$.1^6, $.1^235>, <$.1^6, $.1^238>, <$.1^6, $.1^239>, <$.1^6, $.1^242>, <$.1^6, $.1^244>, <$.1^6, $.1^253>, <$.1^6, $.1^265>, <$.1^6, $.1^277>, <$.1^6, $.1^294>, <$.1^6, $.1^298>, <$.1^6, $.1^305>, <$.1^6, $.1^315>, <$.1^6, $.1^318>, <$.1^6, $.1^325>, <$.1^6, $.1^326>, <$.1^6, $.1^328>, <$.1^6, $.1^331>, <$.1^6, $.1^340>, <$.1^7, $.1>, <$.1^7, $.1^2>, <$.1^7, $.1^7>, <$.1^7, $.1^10>, <$.1^7, $.1^11>, <$.1^7, $.1^14>, <$.1^7, $.1^16>, <$.1^7, $.1^25>, <$.1^7, $.1^37>, <$.1^7, $.1^49>, <$.1^7, $.1^66>, <$.1^7, $.1^70>, <$.1^7, $.1^77>, <$.1^7, $.1^87>, <$.1^7, $.1^90>, <$.1^7, $.1^97>, <$.1^7, $.1^98>, <$.1^7, $.1^100>, <$.1^7, $.1^103>, <$.1^7, $.1^112>, <$.1^7, $.1^120>, <$.1^7, $.1^131>, <$.1^7, $.1^132>, <$.1^7, $.1^137>, <$.1^7, $.1^146>, <$.1^7, $.1^148>, <$.1^7, $.1^156>, <$.1^7, $.1^159>, <$.1^7, $.1^175>, <$.1^7, $.1^195>, <$.1^7, $.1^197>, <$.1^7, $.1^199>, <$.1^7, $.1^215>, <$.1^7, $.1^233>, <$.1^7, $.1^240>, <$.1^7, $.1^259>, <$.1^7, $.1^263>, <$.1^7, $.1^267>, <$.1^7, $.1^275>, <$.1^7, 5>, <$.1^7, $.1^288>, <$.1^7, $.1^306>, <$.1^7, $.1^307>, <$.1^7, $.1^312>, <$.1^7, $.1^314>, <$.1^7, $.1^321>, <$.1^7, $.1^337>, <$.1^7, $.1^338>, <$.1^7, $.1^339>, <$.1^8, $.1^8>, <$.1^8, $.1^15>, <$.1^8, $.1^19>, <$.1^8, $.1^38>, <$.1^8, $.1^48>, <$.1^8, $.1^50>, <$.1^8, $.1^51>, <$.1^8, $.1^56>, <$.1^8, $.1^65>, <$.1^8, $.1^72>, <$.1^8, $.1^76>, <$.1^8, $.1^95>, <$.1^8, $.1^105>, <$.1^8, $.1^107>, <$.1^8, $.1^108>, <$.1^8, $.1^113>, <$.1^8, $.1^122>, <$.1^8, $.1^129>, <$.1^8, $.1^133>, <$.1^8, $.1^152>, <$.1^8, $.1^162>, <$.1^8, $.1^164>, <$.1^8, $.1^165>, <$.1^8, $.1^170>, <$.1^8, $.1^179>, <$.1^8, $.1^186>, <$.1^8, $.1^190>, <$.1^8, $.1^209>, <$.1^8, $.1^219>, <$.1^8, $.1^221>, <$.1^8, $.1^222>, <$.1^8, $.1^227>, <$.1^8, $.1^236>, <$.1^8, $.1^243>, <$.1^8, $.1^247>, <$.1^8, $.1^266>, <$.1^8, $.1^276>, <$.1^8, $.1^278>, <$.1^8, $.1^279>, <$.1^8, $.1^284>, <$.1^8, $.1^293>, <$.1^8, $.1^300>, <$.1^8, $.1^304>, <$.1^8, $.1^323>, <$.1^8, $.1^333>, <$.1^8, $.1^335>, <$.1^8, $.1^336>, <$.1^8, $.1^341>, <$.1^8, 0>, <$.1^9, $.1^9>, <$.1^9, $.1^13>, <$.1^9, $.1^20>, <$.1^9, $.1^30>, <$.1^9, $.1^33>, <$.1^9, $.1^40>, <$.1^9, $.1^41>, <$.1^9, $.1^43>, <$.1^9, $.1^46>, <$.1^9, $.1^55>, <$.1^9, $.1^63>, <$.1^9, $.1^74>, <$.1^9, $.1^75>, <$.1^9, $.1^80>, <$.1^9, $.1^89>, <$.1^9, $.1^91>, <$.1^9, $.1^99>, <$.1^9, $.1^102>, <$.1^9, $.1^118>, <$.1^9, $.1^138>, <$.1^9, $.1^140>, <$.1^9, $.1^142>, <$.1^9, $.1^158>, <$.1^9, $.1^176>, <$.1^9, $.1^183>, <$.1^9, $.1^202>, <$.1^9, $.1^206>, <$.1^9, $.1^210>, <$.1^9, $.1^218>, <$.1^9, 4>, <$.1^9, $.1^231>, <$.1^9, $.1^249>, <$.1^9, $.1^250>, <$.1^9, $.1^255>, <$.1^9, $.1^257>, <$.1^9, $.1^264>, <$.1^9, $.1^280>, <$.1^9, $.1^281>, <$.1^9, $.1^282>, <$.1^9, $.1^286>, <$.1^9, $.1^287>, <$.1^9, $.1^292>, <$.1^9, $.1^295>, <$.1^9, $.1^296>, <$.1^9, $.1^299>, <$.1^9, $.1^301>, <$.1^9, $.1^310>, <$.1^9, $.1^322>, <$.1^9, $.1^334>, <$.1^10, $.1>, <$.1^10, $.1^2>, <$.1^10, $.1^7>, <$.1^10, $.1^10>, <$.1^10, $.1^11>, <$.1^10, $.1^14>, <$.1^10, $.1^16>, <$.1^10, $.1^25>, <$.1^10, $.1^37>, <$.1^10, $.1^49>, <$.1^10, $.1^66>, <$.1^10, $.1^70>, <$.1^10, $.1^77>, <$.1^10, $.1^87>, <$.1^10, $.1^90>, <$.1^10, $.1^97>, <$.1^10, $.1^98>, <$.1^10, $.1^100>, <$.1^10, $.1^103>, <$.1^10, $.1^112>, <$.1^10, $.1^120>, <$.1^10, $.1^131>, <$.1^10, $.1^132>, <$.1^10, $.1^137>, <$.1^10, $.1^146>, <$.1^10, $.1^148>, <$.1^10, $.1^156>, <$.1^10, $.1^159>, <$.1^10, $.1^175>, <$.1^10, $.1^195>, <$.1^10, $.1^197>, <$.1^10, $.1^199>, <$.1^10, $.1^215>, <$.1^10, $.1^233>, <$.1^10, $.1^240>, <$.1^10, $.1^259>, <$.1^10, $.1^263>, <$.1^10, $.1^267>, <$.1^10, $.1^275>, <$.1^10, 5>, <$.1^10, $.1^288>, <$.1^10, $.1^306>, <$.1^10, $.1^307>, <$.1^10, $.1^312>, <$.1^10, $.1^314>, <$.1^10, $.1^321>, <$.1^10, $.1^337>, <$.1^10, $.1^338>, <$.1^10, $.1^339>, <$.1^11, $.1>, <$.1^11, $.1^2>, <$.1^11, $.1^7>, <$.1^11, $.1^10>, <$.1^11, $.1^11>, <$.1^11, $.1^14>, <$.1^11, $.1^16>, <$.1^11, $.1^25>, <$.1^11, $.1^37>, <$.1^11, $.1^49>, <$.1^11, $.1^66>, <$.1^11, $.1^70>, <$.1^11, $.1^77>, <$.1^11, $.1^87>, <$.1^11, $.1^90>, <$.1^11, $.1^97>, <$.1^11, $.1^98>, <$.1^11, $.1^100>, <$.1^11, $.1^103>, <$.1^11, $.1^112>, <$.1^11, $.1^120>, <$.1^11, $.1^131>, <$.1^11, $.1^132>, <$.1^11, $.1^137>, <$.1^11, $.1^146>, <$.1^11, $.1^148>, <$.1^11, $.1^156>, <$.1^11, $.1^159>, <$.1^11, $.1^175>, <$.1^11, $.1^ ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Sun Mar 14 20:52:15 2004 Input: > P:=PolynomialRing(Integers()); >n73:= x^49 + x^7 + x; >t73:= x^57; >n73; >t73; >Ov:=car; >[: a,b in Ov | Evaluate(n73,a) eq Evaluate(n73,b)]; Output: Magma V2.10-6 Sun Mar 14 2004 20:52:12 on modular [Seed = 1096027434] ------------------------------------- x^49 + x^7 + x x^57 >> [: a,b in Ov | Evaluate(n73,a) eq Evaluate(n73,b)];; ^ Runtime error in 'Evaluate': Bad argument types Argument types given: RngUPolElt, Tup Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Sun Mar 14 20:53:45 2004 Input: > P:=PolynomialRing(Integers()); >n73:= x^49 + x^7 + x; >t73:= x^57; >n73; >t73; >Ov:=car; >[: a,b in Ov | Evaluate(n73,a) eq Evaluate(n73,b)]; Output: Magma V2.10-6 Sun Mar 14 2004 20:53:42 on modular [Seed = 1463950294] ------------------------------------- x^49 + x^7 + x x^57 >> [: a,b in Ov | Evaluate(n73,a) eq Evaluate(n73,b)];; ^ Runtime error in 'Evaluate': Bad argument types Argument types given: RngUPolElt, Tup Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Sun Mar 14 20:54:00 2004 Input: > P:=PolynomialRing(Integers()); >n73:= x^49 + x^7 + x; >t73:= x^57; >n73; >t73; >car; >[: a,b in Ov | Evaluate(n73,a) eq Evaluate(n73,b)]; Output: Magma V2.10-6 Sun Mar 14 2004 20:53:57 on modular [Seed = 1581978316] ------------------------------------- x^49 + x^7 + x x^57 Cartesian Product >> [: a,b in Ov | Evaluate(n73,a) eq Evaluate(n73,b)];; ^ User error: Identifier 'Ov' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 02:52:52 2004 Input: res := {i:i in [4..366 by 7]}; res; Output: Magma V2.10-6 Mon Mar 15 2004 02:52:48 on modular [Seed = 557056475] ------------------------------------- { 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 } Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 02:53:06 2004 Input: res := {i:i in [4..366 by 7]}; Output: Magma V2.10-6 Mon Mar 15 2004 02:53:03 on modular [Seed = 1043013323] ------------------------------------- Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:11:09 2004 Input: t7_3:=PolynomialRing(R); t7_3; Output: Magma V2.10-6 Mon Mar 15 2004 03:11:06 on modular [Seed = 1668695635] ------------------------------------- >> t7_3:=PolynomialRing(R); ^ User error: Identifier 'R' has not been declared or assigned >> t7_3;; ^ User error: Identifier 't7_3' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:11:30 2004 Input: t7_3:=PolynomialRing(Z); t7_3; Output: Magma V2.10-6 Mon Mar 15 2004 03:11:27 on modular [Seed = 2120964987] ------------------------------------- >> t7_3:=PolynomialRing(Z); ^ User error: Identifier 'Z' has not been declared or assigned >> t7_3;; ^ User error: Identifier 't7_3' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:12:44 2004 Input: t7_3:=PolynomialRing(integers()); t7_3; Output: Magma V2.10-6 Mon Mar 15 2004 03:12:41 on modular [Seed = 2002932260] ------------------------------------- >> t7_3:=PolynomialRing(integers()); ^ User error: Identifier 'integers' has not been declared or assigned >> t7_3;; ^ User error: Identifier 't7_3' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:13:05 2004 Input: Z:=integers(); t7_3:=PolynomialRing(Z); t7_3; Output: Magma V2.10-6 Mon Mar 15 2004 03:13:02 on modular [Seed = 1280928232] ------------------------------------- >> Z:=integers(); ^ User error: Identifier 'integers' has not been declared or assigned >> t7_3:=PolynomialRing(Z); ^ User error: Identifier 'Z' has not been declared or assigned >> t7_3;; ^ User error: Identifier 't7_3' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:13:25 2004 Input: Z:=Integers(); t7_3:=PolynomialRing(Z); t7_3; Output: Magma V2.10-6 Mon Mar 15 2004 03:13:22 on modular [Seed = 1162895565] ------------------------------------- Univariate Polynomial Ring over Integer Ring Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:15:05 2004 Input: Z:=Integers(); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; t7_3; Output: Magma V2.10-6 Mon Mar 15 2004 03:15:02 on modular [Seed = 1447260282] ------------------------------------- >> t7_3:=x^49+x^7+x; ^ User error: Identifier 'x' has not been declared or assigned Univariate Polynomial Ring over Integer Ring Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:15:26 2004 Input: Z:=Integers(); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; t7_3; Output: Magma V2.10-6 Mon Mar 15 2004 03:15:23 on modular [Seed = 2897840797] ------------------------------------- x^49 + x^7 + x Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:16:00 2004 Input: Z:=Integers(); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; Coefficients(t7_3); Output: Magma V2.10-6 Mon Mar 15 2004 03:15:57 on modular [Seed = 3148783020] ------------------------------------- [ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:16:41 2004 Input: Z:=Integers(); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; Terms(t7_3); Output: Magma V2.10-6 Mon Mar 15 2004 03:16:38 on modular [Seed = 2963642108] ------------------------------------- [ x, x^7, x^49 ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:17:15 2004 Input: Z:=Integers(); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; LeadingCoefficient(t7_3); Output: Magma V2.10-6 Mon Mar 15 2004 03:17:13 on modular [Seed = 2308747050] ------------------------------------- 1 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:20:03 2004 Input: Z:=Integers(); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; coefficientRing(t7_3); Output: Magma V2.10-6 Mon Mar 15 2004 03:20:00 on modular [Seed = 2576137859] ------------------------------------- >> coefficientRing(t7_3);; ^ User error: Identifier 'coefficientRing' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:20:19 2004 Input: Z:=Integers(); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; CoefficientRing(t7_3); Output: Magma V2.10-6 Mon Mar 15 2004 03:20:16 on modular [Seed = 2541924605] ------------------------------------- Integer Ring Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:20:38 2004 Input: Z:=Integers(); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; Coefficients(t7_3); Output: Magma V2.10-6 Mon Mar 15 2004 03:20:35 on modular [Seed = 3975793557] ------------------------------------- [ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:22:51 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; Output: Magma V2.10-6 Mon Mar 15 2004 03:22:48 on modular [Seed = 3857760791] ------------------------------------- Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:23:08 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Output: Magma V2.10-6 Mon Mar 15 2004 03:23:05 on modular [Seed = 4075279665] ------------------------------------- x^57 x^49 + x^7 + x Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 03:27:29 2004 Input: m:=MatrixRing(GF(4),2); mt:={i:i in m | Trace(i) eq 0}; mf:={i:i in m | i[1] eq i[2]}; mtf:= mf meet mt; ex2:=[]; for i:=1 to 100000 do Append(~ex2,Random(m)); end for; Output: Magma V2.10-6 Mon Mar 15 2004 03:27:25 on modular [Seed = 3268930053] ------------------------------------- Total time: 3.549 seconds, Total memory usage: 7.09MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:28:02 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Olav:=[(i,j): n7_3(i)=t7_3(j) | (i,j) in GF(343)xGF(343)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:27:59 on modular [Seed = 3687772926] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i,j): n7_3(i)=t7_3(j) | (i,j) in GF(343)xGF(343)];; ^ User error: bad syntax Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:28:19 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Olav:=[(i,j): n7_3=t7_3 | (i,j) in GF(343)xGF(343)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:28:15 on modular [Seed = 3502635493] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i,j): n7_3=t7_3 | (i,j) in GF(343)xGF(343)];; ^ User error: bad syntax Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 03:28:31 2004 Input: m:=MatrixRing(GF(4),2); mt:={i:i in m | Trace(i) eq 0}; mf:={i:i in m | i[1] eq i[2]}; mtf:= mf meet mt; ex2:=[]; for i:=1 to 100000 do Append(~ex2,Random(m)); end for; nmtf:=0; nmt:=0; nmf:=0; for i:=1 to 100000 do if ex2[i] in mf nmf:=nmf+1; end if; end for; Output: Magma V2.10-6 Mon Mar 15 2004 03:28:28 on modular [Seed = 675086639] ------------------------------------- >> nmf:=nmf+1; ^ User error: bad syntax >> end if; ^ User error: bad syntax >> end for; ^ User error: bad syntax Total time: 3.619 seconds, Total memory usage: 7.09MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:28:34 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Olav:=[(i,j): n7_3[i]=t7_3[j] | (i,j) in GF(343)xGF(343)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:28:31 on modular [Seed = 758645801] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i,j): n7_3[i]=t7_3[j] | (i,j) in GF(343)xGF(343)];; ^ User error: bad syntax Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 03:28:47 2004 Input: m:=MatrixRing(GF(4),2); mt:={i:i in m | Trace(i) eq 0}; mf:={i:i in m | i[1] eq i[2]}; mtf:= mf meet mt; ex2:=[]; for i:=1 to 100000 do Append(~ex2,Random(m)); end for; nmtf:=0; nmt:=0; nmf:=0; for i:=1 to 100000 do if ex2[i] in mf then nmf:=nmf+1; end if; end for; Output: Magma V2.10-6 Mon Mar 15 2004 03:28:44 on modular [Seed = 1043011369] ------------------------------------- Total time: 3.739 seconds, Total memory usage: 7.09MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:28:53 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; n7_3(2); Output: Magma V2.10-6 Mon Mar 15 2004 03:28:50 on modular [Seed = 891296860] ------------------------------------- x^57 x^49 + x^7 + x >> n7_3(2); ^ Runtime error: Bad argument types Argument types given: RngIntElt, RngUPolElt Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:29:26 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Olav:=[(i,j): Evaluate(n7_3,i)=Evaluate(t7_3,j) | (i,j) in GF(343)xGF(343)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:29:23 on modular [Seed = 202974532] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i,j): Evaluate(n7_3,i)=Evaluate(t7_3,j) | (i,j) in GF(343)xGF(343)] ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:29:57 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Evaluate(n7_3,2); Output: Magma V2.10-6 Mon Mar 15 2004 03:29:54 on modular [Seed = 453915314] ------------------------------------- x^57 x^49 + x^7 + x 144115188075855872 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:30:30 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Olav:=[i,j: Evaluate(n7_3,i)=Evaluate(t7_3,j) | i,j in GF(343)xGF(343)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:30:27 on modular [Seed = 1786725346] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[i,j: Evaluate(n7_3,i)=Evaluate(t7_3,j) | i,j in GF(343)xGF(343)];; ^ User error: bad syntax Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:30:43 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Olav:=[(i,j): Evaluate(n7_3,i)=Evaluate(t7_3,j) | (i,j) in GF(343)xGF(343)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:30:40 on modular [Seed = 1635010810] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i,j): Evaluate(n7_3,i)=Evaluate(t7_3,j) | (i,j) in GF(343)xGF(343)] ^ User error: bad syntax Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 03:31:01 2004 Input: m:=MatrixRing(GF(4),2); mt:={i:i in m | Trace(i) eq 0}; mf:={i:i in m | i[1] eq i[2]}; mtf:= mf meet mt; printf "Resultados muestra aleatoria"; ex2:=[]; for i:=1 to 100000 do Append(~ex2,Random(m)); end for; nmtf:=0; nmt:=0; nmf:=0; for i:=1 to 100000 do if ex2[i] in mf then nmf:=nmf+1; end if; if ex2[i] in mt then nmt:=nmt+1; end if; if ex2[i] in mtf then nmtf:=nmtf+1; end if; end for; printf "Elementos mt : ";nmt; printf "Elementos mf : ";nmf; printf "Elementos mtf: ";nmtf; printf " ---oo0oo---"; Output: Magma V2.10-6 Mon Mar 15 2004 03:30:56 on modular [Seed = 2020430227] ------------------------------------- Resultados muestra aleatoriaElementos mt : 25358 Elementos mf : 6274 Elementos mtf: 1537 ---oo0oo--- Total time: 4.189 seconds, Total memory usage: 7.09MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:31:04 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Olav:=[(i,j): Evaluate(n7_3,i) equ Evaluate(t7_3,j) | (i,j) in GF(343)xGF(343)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:31:01 on modular [Seed = 2103989395] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i,j): Evaluate(n7_3,i) equ Evaluate(t7_3,j) | (i,j) in GF(343)xGF(3 ^ User error: bad syntax Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:31:17 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Olav:=[(i,j): Evaluate(n7_3,i) eq Evaluate(t7_3,j) | (i,j) in GF(343)xGF(343)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:31:14 on modular [Seed = 1314613175] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i,j): Evaluate(n7_3,i) eq Evaluate(t7_3,j) | (i,j) in GF(343)xGF(34 ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 03:31:35 2004 Input: m:=MatrixRing(GF(4),2); mt:={i:i in m | Trace(i) eq 0}; mf:={i:i in m | i[1] eq i[2]}; mtf:= mf meet mt; printf "Resultados muestra aleatorian"; ex2:=[]; for i:=1 to 100000 do Append(~ex2,Random(m)); end for; nmtf:=0; nmt:=0; nmf:=0; for i:=1 to 100000 do if ex2[i] in mf then nmf:=nmf+1; end if; if ex2[i] in mt then nmt:=nmt+1; end if; if ex2[i] in mtf then nmtf:=nmtf+1; end if; end for; printf "Elementos mt : ";nmt; printf "Elementos mf : ";nmf; printf "Elementos mtf: ";nmtf; printf " ---oo0oo---"; Output: Magma V2.10-6 Mon Mar 15 2004 03:31:31 on modular [Seed = 1162898573] ------------------------------------- Resultados muestra aleatorianElementos mt : 25179 Elementos mf : 6301 Elementos mtf: 1609 ---oo0oo--- Total time: 4.169 seconds, Total memory usage: 7.09MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:31:47 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Olav:=[(i,j): (i,j) in GF(343)xGF(343) | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:31:44 on modular [Seed = 1548318087] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i,j): (i,j) in GF(343)xGF(343) | Evaluate(n7_3,i) eq Evaluate(t7_3, ^ User error: bad syntax Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:32:22 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Olav:=[(i,j): i in GF(343) AND j in GF(343) | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:32:19 on modular [Seed = 2881388947] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i,j): i in GF(343) AND j in GF(343) | Evaluate(n7_3,i) eq Evaluate( ^ User error: bad syntax Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:32:35 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Olav:=[(i,j): i in GF(343) and j in GF(343) | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:32:32 on modular [Seed = 2729937065] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i,j): i in GF(343) and j in GF(343) | Evaluate(n7_3,i) eq Evaluate( ^ User error: Identifier 'j' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 03:32:59 2004 Input: m:=MatrixRing(GF(4),2); mt:={i:i in m | Trace(i) eq 0}; mf:={i:i in m | i[1] eq i[2]}; mtf:= mf meet mt; printf "Resultados muestra aleatorian"; ex2:=[]; for i:=1 to 100000 do Append(~ex2,Random(m)); end for; nmtf:=0; nmt:=0; nmf:=0; for i:=1 to 100000 do if ex2[i] in mf then nmf:=nmf+1; end if; if ex2[i] in mt then nmt:=nmt+1; end if; if ex2[i] in mtf then nmtf:=nmtf+1; end if; end for; printf "Elementos mt : ";nmt; printf "Elementos mf : ";nmf; printf "Elementos mtf: ";nmtf; printf " ---oo0oo---"; Output: Magma V2.10-6 Mon Mar 15 2004 03:32:55 on modular [Seed = 3115094949] ------------------------------------- Resultados muestra aleatorianElementos mt : 25285 Elementos mf : 6208 Elementos mtf: 1595 ---oo0oo--- Total time: 4.229 seconds, Total memory usage: 7.09MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 03:33:08 2004 Input: m:=MatrixRing(GF(4),2); mt:={i:i in m | Trace(i) eq 0}; mf:={i:i in m | i[1] eq i[2]}; mtf:= mf meet mt; printf "Resultados muestra aleatoria/n"; ex2:=[]; for i:=1 to 100000 do Append(~ex2,Random(m)); end for; nmtf:=0; nmt:=0; nmf:=0; for i:=1 to 100000 do if ex2[i] in mf then nmf:=nmf+1; end if; if ex2[i] in mt then nmt:=nmt+1; end if; if ex2[i] in mtf then nmtf:=nmtf+1; end if; end for; printf "Elementos mt : ";nmt; printf "Elementos mf : ";nmf; printf "Elementos mtf: ";nmtf; printf " ---oo0oo---"; Output: Magma V2.10-6 Mon Mar 15 2004 03:33:04 on modular [Seed = 2963643099] ------------------------------------- Resultados muestra aleatoria/nElementos mt : 24911 Elementos mf : 6296 Elementos mtf: 1623 ---oo0oo--- Total time: 4.149 seconds, Total memory usage: 7.09MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:34:56 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=Integers(7^3); Olav:=[(i,j): i in Z7_3 and j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:34:53 on modular [Seed = 2409276681] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i,j): i in Z7_3 and j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j ^ User error: Identifier 'j' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:35:41 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[(i,j): i in Z7_3 and j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:35:38 on modular [Seed = 2576135016] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i,j): i in Z7_3 and j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j ^ User error: Identifier 'j' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 03:36:28 2004 Input: print "Solució exercici nº2"; print "--------------------"; m:=MatrixRing(GF(4),2); mt:={i:i in m | Trace(i) eq 0}; mf:={i:i in m | i[1] eq i[2]}; mtf:= mf meet mt; ex2:=[]; for i:=1 to 100000 do Append(~ex2,Random(m)); end for; nmtf:=0; nmt:=0; nmf:=0; for i:=1 to 100000 do if ex2[i] in mf then nmf:=nmf+1; end if; if ex2[i] in mt then nmt:=nmt+1; end if; if ex2[i] in mtf then nmtf:=nmtf+1; end if; end for; printf "Mostra mt : ";nmt; printf "Elements mt : ";#(mt); printf "Mostra mf : ";nmf; printf "Elements mf : ";#(mf); printf "Mostra mtf: ";nmtf; printf "Elements mtf: ";#(mtf); printf " ---oo0oo---"; Output: Magma V2.10-6 Mon Mar 15 2004 03:36:24 on modular [Seed = 2424683443] ------------------------------------- Solució exercici nº2 -------------------- Mostra mt : 25092 Elements mt : 64 Mostra mf : 6224 Elements mf : 16 Mostra mtf: 1561 Elements mtf: 4 ---oo0oo--- Total time: 4.219 seconds, Total memory usage: 7.09MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:36:45 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[(i,j): i in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:36:42 on modular [Seed = 4026189022] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i,j): i in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)];; ^ User error: Identifier 'j' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 03:36:59 2004 Input: print "Solució exercici nº2"; print "--------------------"; m:=MatrixRing(GF(4),2); mt:={i:i in m | Trace(i) eq 0}; mf:={i:i in m | i[1] eq i[2]}; mtf:= mf meet mt; ex2:=[]; for i:=1 to 100000 do Append(~ex2,Random(m)); end for; nmtf:=0; nmt:=0; nmf:=0; for i:=1 to 100000 do if ex2[i] in mf then nmf:=nmf+1; end if; if ex2[i] in mt then nmt:=nmt+1; end if; if ex2[i] in mtf then nmtf:=nmtf+1; end if; end for; printf "Mostra mt : ";nmt; printf "Mostra mf : ";nmf; printf "Mostra mtf: ";nmtf; printf " ---oo0oo---"; Output: Magma V2.10-6 Mon Mar 15 2004 03:36:55 on modular [Seed = 3874737642] ------------------------------------- Solució exercici nº2 -------------------- Mostra mt : 24986 Mostra mf : 6256 Mostra mtf: 1525 ---oo0oo--- Total time: 4.159 seconds, Total memory usage: 7.09MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:37:07 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[i,j: i in Z7_3 and j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:37:04 on modular [Seed = 4259895014] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[i,j: i in Z7_3 and j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)] ^ User error: bad syntax Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:37:42 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[(i,j): (i,j) in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:37:39 on modular [Seed = 4108443532] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i,j): (i,j) in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)];; ^ User error: bad syntax Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:37:53 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[(i,j): i,j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:37:51 on modular [Seed = 3285641399] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i,j): i,j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)];; ^ Runtime error in elt< ... >: Bad arguments Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 03:38:48 2004 Input: print "Solució Exercici nº1"; print "--------------------"; ex1:={i-2:i in [1..366] | (i mod 7) eq 6}; print ex1; print " ---oo0oo---"; Output: Magma V2.10-6 Mon Mar 15 2004 03:38:45 on modular [Seed = 3671060836] ------------------------------------- Solució Exercici nº1 -------------------- { 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 } ---oo0oo--- Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:40:40 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[i, j: i in Z7_3 and j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:40:37 on modular [Seed = 775619079] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[i, j: i in Z7_3 and j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j) ^ User error: bad syntax Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:40:49 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[i, j : i in Z7_3 and j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:40:46 on modular [Seed = 657591045] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[i, j : i in Z7_3 and j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j ^ User error: bad syntax Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:40:59 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[[i, j] : i in Z7_3 and j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:40:55 on modular [Seed = 942478348] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[[i, j] : i in Z7_3 and j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3 ^ User error: Identifier 'j' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:42:48 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[(i, j): (i,j) in ZxZ and i<3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:42:45 on modular [Seed = 824450456] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i, j): (i,j) in ZxZ and i<3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)] ^ User error: bad syntax Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:43:00 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[(i, j): in ZxZ and i<3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:42:56 on modular [Seed = 169813687] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i, j): in ZxZ and i<3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)] ^ User error: bad syntax Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:43:11 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[(i, j): [i,j] in ZxZ and i<3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:43:08 on modular [Seed = 51785651] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i, j): [i,j] in ZxZ and i<3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)] ^ User error: bad syntax Total time: 2.869 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:43:32 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[(i, j): i in Z and j in Z and i<3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:43:29 on modular [Seed = 335624329] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i, j): i in Z and j in Z and i<3 | Evaluate(n7_3,i) eq Evaluate(t7_ ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:43:44 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[(i, j): i in Z and j in Z | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:43:41 on modular [Seed = 1836597756] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i, j): i in Z and j in Z | Evaluate(n7_3,i) eq Evaluate(t7_3,j)];; ^ User error: Identifier 'j' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:44:16 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[i: i in Z | j: j in Z | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:44:13 on modular [Seed = 1718831767] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[i: i in Z | j: j in Z | Evaluate(n7_3,i) eq Evaluate(t7_3,j)];; ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:44:37 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[(i,j): i in Z | j in Z | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:44:34 on modular [Seed = 2137674657] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i,j): i in Z | j in Z | Evaluate(n7_3,i) eq Evaluate(t7_3,j)];; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:44:47 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[(i,j): i in Z | j in Z and Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:44:44 on modular [Seed = 1885691040] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i,j): i in Z | j in Z and Evaluate(n7_3,i) eq Evaluate(t7_3,j)];; ^ User error: Identifier 'j' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:45:01 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[(i,j): i in Z and j in Z | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:44:57 on modular [Seed = 1230791791] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i,j): i in Z and j in Z | Evaluate(n7_3,i) eq Evaluate(t7_3,j)];; ^ User error: Identifier 'j' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:51:00 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[(i,j): (i,j) in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:50:57 on modular [Seed = 1463974154] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i,j): (i,j) in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)];; ^ User error: bad syntax Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:51:12 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[(i,j): i,j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:51:09 on modular [Seed = 2830993145] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i,j): i,j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)];; ^ Runtime error in elt< ... >: Bad arguments Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:51:28 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[(i x j): i x j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:51:25 on modular [Seed = 2712964864] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i x j): i x j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)];; ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:51:39 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[(i, j): i x j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:51:36 on modular [Seed = 3132068878] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i, j): i x j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)];; ^ User error: bad syntax Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:51:50 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[(i, j): i and j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:51:47 on modular [Seed = 3014040892] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i, j): i and j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)];; ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:52:01 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[(i, j): (i and j) in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:51:58 on modular [Seed = 2224138758] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i, j): (i and j) in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)];; ^ User error: bad syntax Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:52:12 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[(i, j): (i,j) in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:52:09 on modular [Seed = 2642981640] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i, j): (i,j) in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)];; ^ User error: bad syntax Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 03:52:15 2004 Input: print "Solució Exercici nº 3"; print "---------------------"; q:=7; r:=3; expt:={q^(r-n): n in 1..r}; Output: Magma V2.10-6 Mon Mar 15 2004 03:52:12 on modular [Seed = 2559424008] ------------------------------------- Solució Exercici nº 3 --------------------- >> expt:={q^(r-n): n in 1..r};; ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:52:35 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[(i, j): i in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:52:32 on modular [Seed = 3908945428] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i, j): i in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)];; ^ User error: Identifier 'j' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 03:52:43 2004 Input: print "Solució Exercici nº 3"; print "---------------------"; q:=7; r:=3; expt:={q^(r-n): n in [1..r]}; Output: Magma V2.10-6 Mon Mar 15 2004 03:52:40 on modular [Seed = 3790917397] ------------------------------------- Solució Exercici nº 3 --------------------- Total time: 2.869 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:52:53 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[(i, j): i in Z7_3,j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:52:50 on modular [Seed = 4210021428] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i, j): i in Z7_3,j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; ^ Runtime error in elt< ... >: Bad arguments Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 03:52:57 2004 Input: print "Solució Exercici nº 3"; print "---------------------"; q:=7; r:=3; expt:={q^(r-n): n in [1..r]}; print expt; Output: Magma V2.10-6 Mon Mar 15 2004 03:52:54 on modular [Seed = 4091993401] ------------------------------------- Solució Exercici nº 3 --------------------- { 1, 7, 49 } Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:53:04 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[(i, j): (i in Z7_3,j in Z7_3) | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:53:01 on modular [Seed = 3302091269] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i, j): (i in Z7_3,j in Z7_3) | Evaluate(n7_3,i) eq Evaluate(t7_3,j) ^ User error: bad syntax Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:53:19 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[(i, j): | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:53:16 on modular [Seed = 3720934157] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i, j): | Evaluate(n7_3,i) eq Evaluate(t7_3,j) ^ User error: bad syntax Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:53:38 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[(i, j): i in Z7_3, j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:53:35 on modular [Seed = 3603167733] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i, j): i in Z7_3, j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)] ^ Runtime error in elt< ... >: Bad arguments Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 03:53:48 2004 Input: print "Solució Exercici nº 3"; print "---------------------"; q:=7; r:=3; expt:={q^(r-n): n in [r..1]}; print expt; Output: Magma V2.10-6 Mon Mar 15 2004 03:53:45 on modular [Seed = 775618842] ------------------------------------- Solució Exercici nº 3 --------------------- {} Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:53:51 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[(i, j): elt | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:53:48 on modular [Seed = 725484570] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i, j): elt | Evaluate(n7_3,i) eq Evaluate(t7_ ^ User error: bad syntax Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 03:54:00 2004 Input: print "Solució Exercici nº 3"; print "---------------------"; q:=7; r:=3; expt:={q^(r-n): n in [1..r]}; print expt; Output: Magma V2.10-6 Mon Mar 15 2004 03:53:57 on modular [Seed = 942479152] ------------------------------------- Solució Exercici nº 3 --------------------- { 1, 7, 49 } Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:54:08 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[elt: i in Z7_3, j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:54:05 on modular [Seed = 858135603] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[elt: i in Z7_3, j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3, ^ User error: bad syntax Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:54:45 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[(i, j): i in Z7_3 | j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:54:41 on modular [Seed = 169813366] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i, j): i in Z7_3 | j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j) ^ User error: bad syntax Total time: 3.219 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 03:54:46 2004 Input: print "Solució Exercici nº 3"; print "---------------------"; q:=7; r:=3; expt:=reverse({q^(r-n): n in [1..r]}); print expt; Output: Magma V2.10-6 Mon Mar 15 2004 03:54:43 on modular [Seed = 118630521] ------------------------------------- Solució Exercici nº 3 --------------------- >> expt:=reverse({q^(r-n): n in [1..r]}); ^ User error: Identifier 'reverse' has not been declared or assigned >> print expt; ^ User error: Identifier 'expt' has not been declared or assigned Total time: 3.209 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:54:54 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[(i, j): i in Z7_3 | (j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j))]; Output: Magma V2.10-6 Mon Mar 15 2004 03:54:50 on modular [Seed = 335625058] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i, j): i in Z7_3 | (j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j ^ User error: bad syntax Total time: 3.129 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 03:54:56 2004 Input: print "Solució Exercici nº 3"; print "---------------------"; q:=7; r:=3; expt:=Reverse({q^(r-n): n in [1..r]}); print expt; Output: Magma V2.10-6 Mon Mar 15 2004 03:54:53 on modular [Seed = 285490785] ------------------------------------- Solució Exercici nº 3 --------------------- >> expt:=Reverse({q^(r-n): n in [1..r]}); ^ Runtime error in 'Reverse': Bad argument types Argument types given: SetEnum[RngIntElt] >> print expt; ^ User error: Identifier 'expt' has not been declared or assigned Total time: 3.159 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:55:13 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[(i, j): i in Z7_3, j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:55:10 on modular [Seed = 1651985697] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i, j): i in Z7_3, j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)] ^ Runtime error in elt< ... >: Bad arguments Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 03:55:39 2004 Input: print "Solució Exercici nº 3"; print "---------------------"; q:=7; r:=3; expt:={q^(r-n): n in [1..r]}; expt:=Reverse(expt); print expt; Output: Magma V2.10-6 Mon Mar 15 2004 03:55:36 on modular [Seed = 1952537553] ------------------------------------- Solució Exercici nº 3 --------------------- >> expt:=Reverse(expt); ^ Runtime error in 'Reverse': Bad argument types Argument types given: SetEnum[RngIntElt] { 1, 7, 49 } Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 03:56:55 2004 Input: print "Solució Exercici nº 3"; print "---------------------"; q:=7; r:=3; expt:={q^(r-n): n in Reverse([1..r])}; print expt; Output: Magma V2.10-6 Mon Mar 15 2004 03:56:52 on modular [Seed = 1331323062] ------------------------------------- Solució Exercici nº 3 --------------------- { 1, 7, 49 } Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:57:37 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[(i * j): i in Z7_3, j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Output: Magma V2.10-6 Mon Mar 15 2004 03:57:31 on modular [Seed = 1179871632] ------------------------------------- x^57 x^49 + x^7 + x Total time: 6.639 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:57:55 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[(i * j): i in Z7_3, j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Olav; Output: Magma V2.10-6 Mon Mar 15 2004 03:57:48 on modular [Seed = 1498179960] ------------------------------------- x^57 x^49 + x^7 + x [ Z7_3.1, Z7_3.1^7, Z7_3.1^13, Z7_3.1^19, Z7_3.1^25, Z7_3.1^31, Z7_3.1^37, Z7_3.1^43, Z7_3.1^49, Z7_3.1^55, Z7_3.1^61, Z7_3.1^67, Z7_3.1^73, Z7_3.1^79, Z7_3.1^85, Z7_3.1^91, Z7_3.1^97, Z7_3.1^103, Z7_3.1^109, Z7_3.1^115, Z7_3.1^121, Z7_3.1^127, Z7_3.1^133, Z7_3.1^139, Z7_3.1^145, Z7_3.1^151, Z7_3.1^157, Z7_3.1^163, Z7_3.1^169, Z7_3.1^175, Z7_3.1^181, Z7_3.1^187, Z7_3.1^193, Z7_3.1^199, Z7_3.1^205, Z7_3.1^211, Z7_3.1^217, Z7_3.1^223, Z7_3.1^229, Z7_3.1^235, Z7_3.1^241, Z7_3.1^247, Z7_3.1^253, Z7_3.1^259, Z7_3.1^265, Z7_3.1^271, Z7_3.1^277, Z7_3.1^283, Z7_3.1^289, Z7_3.1^295, Z7_3.1^301, Z7_3.1^307, Z7_3.1^313, Z7_3.1^319, Z7_3.1^325, Z7_3.1^331, Z7_3.1^337, Z7_3.1, Z7_3.1^7, Z7_3.1^13, Z7_3.1^19, Z7_3.1^25, Z7_3.1^31, Z7_3.1^37, Z7_3.1^43, Z7_3.1^49, Z7_3.1^55, Z7_3.1^61, Z7_3.1^67, Z7_3.1^73, Z7_3.1^79, Z7_3.1^85, Z7_3.1^91, Z7_3.1^97, Z7_3.1^103, Z7_3.1^109, Z7_3.1^115, Z7_3.1^121, Z7_3.1^127, Z7_3.1^133, Z7_3.1^139, Z7_3.1^145, Z7_3.1^151, Z7_3.1^157, Z7_3.1^163, Z7_3.1^169, Z7_3.1^175, Z7_3.1^181, Z7_3.1^187, Z7_3.1^193, Z7_3.1^199, Z7_3.1^205, Z7_3.1^211, Z7_3.1^217, Z7_3.1^223, Z7_3.1^229, Z7_3.1^235, Z7_3.1^241, Z7_3.1^247, Z7_3.1^253, Z7_3.1^259, Z7_3.1^265, Z7_3.1^271, Z7_3.1^277, Z7_3.1^283, Z7_3.1^289, Z7_3.1^295, Z7_3.1^301, Z7_3.1^307, Z7_3.1^313, Z7_3.1^319, Z7_3.1^325, Z7_3.1^331, Z7_3.1^337, Z7_3.1^2, Z7_3.1^8, Z7_3.1^14, Z7_3.1^20, Z7_3.1^26, Z7_3.1^32, Z7_3.1^38, Z7_3.1^44, Z7_3.1^50, Z7_3.1^56, Z7_3.1^62, Z7_3.1^68, Z7_3.1^74, Z7_3.1^80, Z7_3.1^86, Z7_3.1^92, Z7_3.1^98, Z7_3.1^104, Z7_3.1^110, Z7_3.1^116, Z7_3.1^122, Z7_3.1^128, Z7_3.1^134, Z7_3.1^140, Z7_3.1^146, Z7_3.1^152, Z7_3.1^158, Z7_3.1^164, Z7_3.1^170, Z7_3.1^176, Z7_3.1^182, Z7_3.1^188, Z7_3.1^194, Z7_3.1^200, Z7_3.1^206, Z7_3.1^212, Z7_3.1^218, Z7_3.1^224, Z7_3.1^230, Z7_3.1^236, Z7_3.1^242, Z7_3.1^248, Z7_3.1^254, Z7_3.1^260, Z7_3.1^266, Z7_3.1^272, Z7_3.1^278, Z7_3.1^284, Z7_3.1^290, Z7_3.1^296, Z7_3.1^302, Z7_3.1^308, Z7_3.1^314, Z7_3.1^320, Z7_3.1^326, Z7_3.1^332, Z7_3.1^338, Z7_3.1^4, Z7_3.1^10, Z7_3.1^16, Z7_3.1^22, Z7_3.1^28, Z7_3.1^34, Z7_3.1^40, Z7_3.1^46, Z7_3.1^52, Z7_3.1^58, Z7_3.1^64, Z7_3.1^70, Z7_3.1^76, Z7_3.1^82, Z7_3.1^88, Z7_3.1^94, Z7_3.1^100, Z7_3.1^106, Z7_3.1^112, Z7_3.1^118, Z7_3.1^124, Z7_3.1^130, Z7_3.1^136, Z7_3.1^142, Z7_3.1^148, Z7_3.1^154, Z7_3.1^160, Z7_3.1^166, Z7_3.1^172, Z7_3.1^178, Z7_3.1^184, Z7_3.1^190, Z7_3.1^196, Z7_3.1^202, Z7_3.1^208, Z7_3.1^214, Z7_3.1^220, Z7_3.1^226, Z7_3.1^232, Z7_3.1^238, Z7_3.1^244, Z7_3.1^250, Z7_3.1^256, Z7_3.1^262, Z7_3.1^268, Z7_3.1^274, Z7_3.1^280, Z7_3.1^286, Z7_3.1^292, Z7_3.1^298, Z7_3.1^304, Z7_3.1^310, Z7_3.1^316, Z7_3.1^322, Z7_3.1^328, Z7_3.1^334, Z7_3.1^340, Z7_3.1^7, Z7_3.1^13, Z7_3.1^19, Z7_3.1^25, Z7_3.1^31, Z7_3.1^37, Z7_3.1^43, Z7_3.1^49, Z7_3.1^55, Z7_3.1^61, Z7_3.1^67, Z7_3.1^73, Z7_3.1^79, Z7_3.1^85, Z7_3.1^91, Z7_3.1^97, Z7_3.1^103, Z7_3.1^109, Z7_3.1^115, Z7_3.1^121, Z7_3.1^127, Z7_3.1^133, Z7_3.1^139, Z7_3.1^145, Z7_3.1^151, Z7_3.1^157, Z7_3.1^163, Z7_3.1^169, Z7_3.1^175, Z7_3.1^181, Z7_3.1^187, Z7_3.1^193, Z7_3.1^199, Z7_3.1^205, Z7_3.1^211, Z7_3.1^217, Z7_3.1^223, Z7_3.1^229, Z7_3.1^235, Z7_3.1^241, Z7_3.1^247, Z7_3.1^253, Z7_3.1^259, Z7_3.1^265, Z7_3.1^271, Z7_3.1^277, Z7_3.1^283, Z7_3.1^289, Z7_3.1^295, Z7_3.1^301, Z7_3.1^307, Z7_3.1^313, Z7_3.1^319, Z7_3.1^325, Z7_3.1^331, Z7_3.1^337, Z7_3.1, Z7_3.1^7, Z7_3.1^13, Z7_3.1^19, Z7_3.1^25, Z7_3.1^31, Z7_3.1^37, Z7_3.1^43, Z7_3.1^49, Z7_3.1^55, Z7_3.1^61, Z7_3.1^67, Z7_3.1^73, Z7_3.1^79, Z7_3.1^85, Z7_3.1^91, Z7_3.1^97, Z7_3.1^103, Z7_3.1^109, Z7_3.1^115, Z7_3.1^121, Z7_3.1^127, Z7_3.1^133, Z7_3.1^139, Z7_3.1^145, Z7_3.1^151, Z7_3.1^157, Z7_3.1^163, Z7_3.1^169, Z7_3.1^175, Z7_3.1^181, Z7_3.1^187, Z7_3.1^193, Z7_3.1^199, Z7_3.1^205, Z7_3.1^211, Z7_3.1^217, Z7_3.1^223, Z7_3.1^229, Z7_3.1^235, Z7_3.1^241, Z7_3.1^247, Z7_3.1^253, Z7_3.1^259, Z7_3.1^265, Z7_3.1^271, Z7_3.1^277, Z7_3.1^283, Z7_3.1^289, Z7_3.1^295, Z7_3.1^301, Z7_3.1^307, Z7_3.1^313, Z7_3.1^319, Z7_3.1^325, Z7_3.1^331, Z7_3.1^337, Z7_3.1, Z7_3.1^10, Z7_3.1^16, Z7_3.1^22, Z7_3.1^28, Z7_3.1^34, Z7_3.1^40, Z7_3.1^46, Z7_3.1^52, Z7_3.1^58, Z7_3.1^64, Z7_3.1^70, Z7_3.1^76, Z7_3.1^82, Z7_3.1^88, Z7_3.1^94, Z7_3.1^100, Z7_3.1^106, Z7_3.1^112, Z7_3.1^118, Z7_3.1^124, Z7_3.1^130, Z7_3.1^136, Z7_3.1^142, Z7_3.1^148, Z7_3.1^154, Z7_3.1^160, Z7_3.1^166, Z7_3.1^172, Z7_3.1^178, Z7_3.1^184, Z7_3.1^190, Z7_3.1^196, Z7_3.1^202, Z7_3.1^208, Z7_3.1^214, Z7_3.1^220, Z7_3.1^226, Z7_3.1^232, Z7_3.1^238, Z7_3.1^244, Z7_3.1^250, Z7_3.1^256, Z7_3.1^262, Z7_3.1^268, Z7_3.1^274, Z7_3.1^280, Z7_3.1^286, Z7_3.1^292, Z7_3.1^298, Z7_3.1^304, Z7_3.1^310, Z7_3.1^316, Z7_3.1^322, Z7_3.1^328, Z7_3.1^334, Z7_3.1^340, Z7_3.1^4, Z7_3.1^7, Z7_3.1^13, Z7_3.1^19, Z7_3.1^25, Z7_3.1^31, Z7_3.1^37, Z7_3.1^43, Z7_3.1^49, Z7_3.1^55, Z7_3.1^61, Z7_3.1^67, Z7_3.1^73, Z7_3.1^79, Z7_3.1^85, Z7_3.1^91, Z7_3.1^97, Z7_3.1^103, Z7_3.1^109, Z7_3.1^115, Z7_3.1^121, Z7_3.1^127, Z7_3.1^133, Z7_3.1^139, Z7_3.1^145, Z7_3.1^151, Z7_3.1^157, Z7_3.1^163, Z7_3.1^169, Z7_3.1^175, Z7_3.1^181, Z7_3.1^187, Z7_3.1^193, Z7_3.1^199, Z7_3.1^205, Z7_3.1^211, Z7_3.1^217, Z7_3.1^223, Z7_3.1^229, Z7_3.1^235, Z7_3.1^241, Z7_3.1^247, Z7_3.1^253, Z7_3.1^259, Z7_3.1^265, Z7_3.1^271, Z7_3.1^277, Z7_3.1^283, Z7_3.1^289, Z7_3.1^295, Z7_3.1^301, Z7_3.1^307, Z7_3.1^313, Z7_3.1^319, Z7_3.1^325, Z7_3.1^331, Z7_3.1^337, Z7_3.1, 0, Z7_3.1^14, Z7_3.1^20, Z7_3.1^26, Z7_3.1^32, Z7_3.1^38, Z7_3.1^44, Z7_3.1^50, Z7_3.1^56, Z7_3.1^62, Z7_3.1^68, Z7_3.1^74, Z7_3.1^80, Z7_3.1^86, Z7_3.1^92, Z7_3.1^98, Z7_3.1^104, Z7_3.1^110, Z7_3.1^116, Z7_3.1^122, Z7_3.1^128, Z7_3.1^134, Z7_3.1^140, Z7_3.1^146, Z7_3.1^152, Z7_3.1^158, Z7_3.1^164, Z7_3.1^170, Z7_3.1^176, Z7_3.1^182, Z7_3.1^188, Z7_3.1^194, Z7_3.1^200, Z7_3.1^206, Z7_3.1^212, Z7_3.1^218, Z7_3.1^224, Z7_3.1^230, Z7_3.1^236, Z7_3.1^242, Z7_3.1^248, Z7_3.1^254, Z7_3.1^260, Z7_3.1^266, Z7_3.1^272, Z7_3.1^278, Z7_3.1^284, Z7_3.1^290, Z7_3.1^296, Z7_3.1^302, Z7_3.1^308, Z7_3.1^314, Z7_3.1^320, Z7_3.1^326, Z7_3.1^332, Z7_3.1^338, Z7_3.1^2, Z7_3.1^8, Z7_3.1^10, Z7_3.1^16, Z7_3.1^22, Z7_3.1^28, Z7_3.1^34, Z7_3.1^40, Z7_3.1^46, Z7_3.1^52, Z7_3.1^58, Z7_3.1^64, Z7_3.1^70, Z7_3.1^76, Z7_3.1^82, Z7_3.1^88, Z7_3.1^94, Z7_3.1^100, Z7_3.1^106, Z7_3.1^112, Z7_3.1^118, Z7_3.1^124, Z7_3.1^130, Z7_3.1^136, Z7_3.1^142, Z7_3.1^148, Z7_3.1^154, Z7_3.1^160, Z7_3.1^166, Z7_3.1^172, Z7_3.1^178, Z7_3.1^184, Z7_3.1^190, Z7_3.1^196, Z7_3.1^202, Z7_3.1^208, Z7_3.1^214, Z7_3.1^220, Z7_3.1^226, Z7_3.1^232, Z7_3.1^238, Z7_3.1^244, Z7_3.1^250, Z7_3.1^256, Z7_3.1^262, Z7_3.1^268, Z7_3.1^274, Z7_3.1^280, Z7_3.1^286, Z7_3.1^292, Z7_3.1^298, Z7_3.1^304, Z7_3.1^310, Z7_3.1^316, Z7_3.1^322, Z7_3.1^328, Z7_3.1^334, Z7_3.1^340, Z7_3.1^4, Z7_3.1^11, Z7_3.1^17, Z7_3.1^23, Z7_3.1^29, Z7_3.1^35, Z7_3.1^41, Z7_3.1^47, Z7_3.1^53, Z7_3.1^59, Z7_3.1^65, Z7_3.1^71, Z7_3.1^77, Z7_3.1^83, Z7_3.1^89, Z7_3.1^95, Z7_3.1^101, Z7_3.1^107, Z7_3.1^113, Z7_3.1^119, Z7_3.1^125, Z7_3.1^131, Z7_3.1^137, Z7_3.1^143, Z7_3.1^149, Z7_3.1^155, Z7_3.1^161, Z7_3.1^167, Z7_3.1^173, Z7_3.1^179, Z7_3.1^185, Z7_3.1^191, Z7_3.1^197, Z7_3.1^203, Z7_3.1^209, Z7_3.1^215, Z7_3.1^221, Z7_3.1^227, Z7_3.1^233, Z7_3.1^239, Z7_3.1^245, Z7_3.1^251, Z7_3.1^257, Z7_3.1^263, Z7_3.1^269, Z7_3.1^275, Z7_3.1^281, Z7_3.1^287, Z7_3.1^293, Z7_3.1^299, Z7_3.1^305, Z7_3.1^311, Z7_3.1^317, Z7_3.1^323, Z7_3.1^329, Z7_3.1^335, Z7_3.1^341, Z7_3.1^5, Z7_3.1^14, Z7_3.1^20, Z7_3.1^26, Z7_3.1^32, Z7_3.1^38, Z7_3.1^44, Z7_3.1^50, Z7_3.1^56, Z7_3.1^62, Z7_3.1^68, Z7_3.1^74, Z7_3.1^80, Z7_3.1^86, Z7_3.1^92, Z7_3.1^98, Z7_3.1^104, Z7_3.1^110, Z7_3.1^116, Z7_3.1^122, Z7_3.1^128, Z7_3.1^134, Z7_3.1^140, Z7_3.1^146, Z7_3.1^152, Z7_3.1^158, Z7_3.1^164, Z7_3.1^170, Z7_3.1^176, Z7_3.1^182, Z7_3.1^188, Z7_3.1^194, Z7_3.1^200, Z7_3.1^206, Z7_3.1^212, Z7_3.1^218, Z7_3.1^224, Z7_3.1^230, Z7_3.1^236, Z7_3.1^242, Z7_3.1^248, Z7_3.1^254, Z7_3.1^260, Z7_3.1^266, Z7_3.1^272, Z7_3.1^278, Z7_3.1^284, Z7_3.1^290, Z7_3.1^296, Z7_3.1^302, Z7_3.1^308, Z7_3.1^314, Z7_3.1^320, Z7_3.1^326, Z7_3.1^332, Z7_3.1^338, Z7_3.1^2, Z7_3.1^8, Z7_3.1^18, Z7_3.1^24, Z7_3.1^30, Z7_3.1^36, Z7_3.1^42, Z7_3.1^48, Z7_3.1^54, Z7_3.1^60, Z7_3.1^66, Z7_3.1^72, Z7_3.1^78, Z7_3.1^84, Z7_3.1^90, Z7_3.1^96, Z7_3.1^102, Z7_3.1^108, 2, Z7_3.1^120, Z7_3.1^126, Z7_3.1^132, Z7_3.1^138, Z7_3.1^144, Z7_3.1^150, Z7_3.1^156, Z7_3.1^162, Z7_3.1^168, Z7_3.1^174, Z7_3.1^180, Z7_3.1^186, Z7_3.1^192, Z7_3.1^198, Z7_3.1^204, Z7_3.1^210, Z7_3.1^216, Z7_3.1^222, 4, Z7_3.1^234, Z7_3.1^240, Z7_3.1^246, Z7_3.1^252, Z7_3.1^258, Z7_3.1^264, Z7_3.1^270, Z7_3.1^276, Z7_3.1^282, Z7_3.1^288, Z7_3.1^294, Z7_3.1^300, Z7_3.1^306, Z7_3.1^312, Z7_3.1^318, Z7_3.1^324, Z7_3.1^330, Z7_3.1^336, 1, Z7_3.1^6, Z7_3.1^12, Z7_3.1^14, Z7_3.1^20, Z7_3.1^26, Z7_3.1^32, Z7_3.1^38, Z7_3.1^44, Z7_3.1^50, Z7_3.1^56, Z7_3.1^62, Z7_3.1^68, Z7_3.1^74, Z7_3.1^80, Z7_3.1^86, Z7_3.1^92, Z7_3.1^98, Z7_3.1^104, Z7_3.1^110, Z7_3.1^116, Z7_3.1^122, Z7_3.1^128, Z7_3.1^134, Z7_3.1^140, Z7_3.1^146, Z7_3.1^152, Z7_3.1^158, Z7_3.1^164, Z7_3.1^170, Z7_3.1^176, Z7_3.1^182, Z7_3.1^188, Z7_3.1^194, Z7_3.1^200, Z7_3.1^206, Z7_3.1^212, Z7_3.1^218, Z7_3.1^224, Z7_3.1^230, Z7_3.1^236, Z7_3.1^242, Z7_3.1^248, Z7_3.1^254, Z7_3.1^260, Z7_3.1^266, Z7_3.1^272, Z7_3.1^278, Z7_3.1^284, Z7_3.1^290, Z7_3.1^296, Z7_3.1^302, Z7_3.1^308, Z7_3.1^314, Z7_3.1^320, Z7_3.1^326, Z7_3.1^332, Z7_3.1^338, Z7_3.1^2, Z7_3.1^8, 0, Z7_3.1^16, Z7_3.1^22, Z7_3.1^28, Z7_3.1^34, Z7_3.1^40, Z7_3.1^46, Z7_3.1^52, Z7_3.1^58, Z7_3.1^64, Z7_3.1^70, Z7_3.1^76, Z7_3.1^82, Z7_3.1^88, Z7_3.1^94, Z7_3.1^100, Z7_3.1^106, Z7_3.1^112, Z7_3.1^118, Z7_3.1^124, Z7_3.1^130, Z7_3.1^136, Z7_3.1^142, Z7_3.1^148, Z7_3.1^154, Z7_3.1^160, Z7_3.1^166, Z7_3.1^172, Z7_3.1^178, Z7_3.1^184, Z7_3.1^190, Z7_3.1^196, Z7_3.1^202, Z7_3.1^208, Z7_3.1^214, Z7_3.1^220, Z7_3.1^226, Z7_3.1^232, Z7_3.1^238, Z7_ ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 03:58:11 2004 Input: print "Solució Exercici nº 3"; print "---------------------"; q:=7; r:=3; expt:={q^(r-n): n in [1..r]}; print "Exponents del polinomi t 7,3(x): ";expt; Output: Magma V2.10-6 Mon Mar 15 2004 03:58:08 on modular [Seed = 1346723933] ------------------------------------- Solució Exercici nº 3 --------------------- Exponents del polinomi t 7,3(x): { 1, 7, 49 } Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 03:58:25 2004 Input: print "Solució Exercici nº 3"; print "---------------------"; q:=7; r:=3; expt:={q^(r-n): n in [1..r]}; print "Exponents del polinomi t: ";expt; Output: Magma V2.10-6 Mon Mar 15 2004 03:58:22 on modular [Seed = 2881395624] ------------------------------------- Solució Exercici nº 3 --------------------- Exponents del polinomi t: { 1, 7, 49 } Total time: 2.869 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 03:58:39 2004 Input: print "Solució Exercici nº 3"; print "---------------------"; q:=7; r:=3; expt:={q^(r-n): n in [1..r]}; print "Exponents: ";expt; Output: Magma V2.10-6 Mon Mar 15 2004 03:58:36 on modular [Seed = 2729939635] ------------------------------------- Solució Exercici nº 3 --------------------- Exponents: { 1, 7, 49 } Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:59:06 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[(i * j): i in Z7_3 * j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Olav; Output: Magma V2.10-6 Mon Mar 15 2004 03:59:03 on modular [Seed = 3047196111] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i * j): i in Z7_3 * j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j ^ User error: Identifier 'j' has not been declared or assigned >> Olav; ^ User error: Identifier 'Olav' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 03:59:15 2004 Input: print "Solució Exercici nº 3"; print "---------------------"; q:=7; r:=3; expt:={q^(r-n): n in [1..r]}; print "Exponents: ";expt; t:=P!expt; print "Polinomi t:"; Output: Magma V2.10-6 Mon Mar 15 2004 03:59:12 on modular [Seed = 2358885569] ------------------------------------- Solució Exercici nº 3 --------------------- Exponents: { 1, 7, 49 } >> t:=P!expt; ^ User error: Identifier 'P' has not been declared or assigned Polinomi t: Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:59:24 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[(i * j): (i * j) in Z7_3*Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Olav; Output: Magma V2.10-6 Mon Mar 15 2004 03:59:21 on modular [Seed = 2274539459] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i * j): (i * j) in Z7_3*Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j) ^ User error: bad syntax >> Olav; ^ User error: Identifier 'Olav' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 03:59:37 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[(i * j): i * j in Z7_3*Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Olav; Output: Magma V2.10-6 Mon Mar 15 2004 03:59:34 on modular [Seed = 2659954373] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i * j): i * j in Z7_3*Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; ^ User error: bad syntax >> Olav; ^ User error: Identifier 'Olav' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 03:59:48 2004 Input: print "Solució Exercici nº 3"; print "---------------------"; q:=7; r:=3; expt:=[q^(r-n): n in [1..r]]; print "Exponents: ";expt; t:=P!expt; print "Polinomi t:"; Output: Magma V2.10-6 Mon Mar 15 2004 03:59:45 on modular [Seed = 2441388349] ------------------------------------- Solució Exercici nº 3 --------------------- Exponents: [ 49, 7, 1 ] >> t:=P!expt; ^ User error: Identifier 'P' has not been declared or assigned Polinomi t: Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 04:00:02 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[(i * j): i in Z7_3, j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Olav; Output: Magma V2.10-6 Mon Mar 15 2004 03:59:55 on modular [Seed = 3908950094] ------------------------------------- x^57 x^49 + x^7 + x [ Z7_3.1, Z7_3.1^7, Z7_3.1^13, Z7_3.1^19, Z7_3.1^25, Z7_3.1^31, Z7_3.1^37, Z7_3.1^43, Z7_3.1^49, Z7_3.1^55, Z7_3.1^61, Z7_3.1^67, Z7_3.1^73, Z7_3.1^79, Z7_3.1^85, Z7_3.1^91, Z7_3.1^97, Z7_3.1^103, Z7_3.1^109, Z7_3.1^115, Z7_3.1^121, Z7_3.1^127, Z7_3.1^133, Z7_3.1^139, Z7_3.1^145, Z7_3.1^151, Z7_3.1^157, Z7_3.1^163, Z7_3.1^169, Z7_3.1^175, Z7_3.1^181, Z7_3.1^187, Z7_3.1^193, Z7_3.1^199, Z7_3.1^205, Z7_3.1^211, Z7_3.1^217, Z7_3.1^223, Z7_3.1^229, Z7_3.1^235, Z7_3.1^241, Z7_3.1^247, Z7_3.1^253, Z7_3.1^259, Z7_3.1^265, Z7_3.1^271, Z7_3.1^277, Z7_3.1^283, Z7_3.1^289, Z7_3.1^295, Z7_3.1^301, Z7_3.1^307, Z7_3.1^313, Z7_3.1^319, Z7_3.1^325, Z7_3.1^331, Z7_3.1^337, Z7_3.1, Z7_3.1^7, Z7_3.1^13, Z7_3.1^19, Z7_3.1^25, Z7_3.1^31, Z7_3.1^37, Z7_3.1^43, Z7_3.1^49, Z7_3.1^55, Z7_3.1^61, Z7_3.1^67, Z7_3.1^73, Z7_3.1^79, Z7_3.1^85, Z7_3.1^91, Z7_3.1^97, Z7_3.1^103, Z7_3.1^109, Z7_3.1^115, Z7_3.1^121, Z7_3.1^127, Z7_3.1^133, Z7_3.1^139, Z7_3.1^145, Z7_3.1^151, Z7_3.1^157, Z7_3.1^163, Z7_3.1^169, Z7_3.1^175, Z7_3.1^181, Z7_3.1^187, Z7_3.1^193, Z7_3.1^199, Z7_3.1^205, Z7_3.1^211, Z7_3.1^217, Z7_3.1^223, Z7_3.1^229, Z7_3.1^235, Z7_3.1^241, Z7_3.1^247, Z7_3.1^253, Z7_3.1^259, Z7_3.1^265, Z7_3.1^271, Z7_3.1^277, Z7_3.1^283, Z7_3.1^289, Z7_3.1^295, Z7_3.1^301, Z7_3.1^307, Z7_3.1^313, Z7_3.1^319, Z7_3.1^325, Z7_3.1^331, Z7_3.1^337, Z7_3.1^2, Z7_3.1^8, Z7_3.1^14, Z7_3.1^20, Z7_3.1^26, Z7_3.1^32, Z7_3.1^38, Z7_3.1^44, Z7_3.1^50, Z7_3.1^56, Z7_3.1^62, Z7_3.1^68, Z7_3.1^74, Z7_3.1^80, Z7_3.1^86, Z7_3.1^92, Z7_3.1^98, Z7_3.1^104, Z7_3.1^110, Z7_3.1^116, Z7_3.1^122, Z7_3.1^128, Z7_3.1^134, Z7_3.1^140, Z7_3.1^146, Z7_3.1^152, Z7_3.1^158, Z7_3.1^164, Z7_3.1^170, Z7_3.1^176, Z7_3.1^182, Z7_3.1^188, Z7_3.1^194, Z7_3.1^200, Z7_3.1^206, Z7_3.1^212, Z7_3.1^218, Z7_3.1^224, Z7_3.1^230, Z7_3.1^236, Z7_3.1^242, Z7_3.1^248, Z7_3.1^254, Z7_3.1^260, Z7_3.1^266, Z7_3.1^272, Z7_3.1^278, Z7_3.1^284, Z7_3.1^290, Z7_3.1^296, Z7_3.1^302, Z7_3.1^308, Z7_3.1^314, Z7_3.1^320, Z7_3.1^326, Z7_3.1^332, Z7_3.1^338, Z7_3.1^4, Z7_3.1^10, Z7_3.1^16, Z7_3.1^22, Z7_3.1^28, Z7_3.1^34, Z7_3.1^40, Z7_3.1^46, Z7_3.1^52, Z7_3.1^58, Z7_3.1^64, Z7_3.1^70, Z7_3.1^76, Z7_3.1^82, Z7_3.1^88, Z7_3.1^94, Z7_3.1^100, Z7_3.1^106, Z7_3.1^112, Z7_3.1^118, Z7_3.1^124, Z7_3.1^130, Z7_3.1^136, Z7_3.1^142, Z7_3.1^148, Z7_3.1^154, Z7_3.1^160, Z7_3.1^166, Z7_3.1^172, Z7_3.1^178, Z7_3.1^184, Z7_3.1^190, Z7_3.1^196, Z7_3.1^202, Z7_3.1^208, Z7_3.1^214, Z7_3.1^220, Z7_3.1^226, Z7_3.1^232, Z7_3.1^238, Z7_3.1^244, Z7_3.1^250, Z7_3.1^256, Z7_3.1^262, Z7_3.1^268, Z7_3.1^274, Z7_3.1^280, Z7_3.1^286, Z7_3.1^292, Z7_3.1^298, Z7_3.1^304, Z7_3.1^310, Z7_3.1^316, Z7_3.1^322, Z7_3.1^328, Z7_3.1^334, Z7_3.1^340, Z7_3.1^7, Z7_3.1^13, Z7_3.1^19, Z7_3.1^25, Z7_3.1^31, Z7_3.1^37, Z7_3.1^43, Z7_3.1^49, Z7_3.1^55, Z7_3.1^61, Z7_3.1^67, Z7_3.1^73, Z7_3.1^79, Z7_3.1^85, Z7_3.1^91, Z7_3.1^97, Z7_3.1^103, Z7_3.1^109, Z7_3.1^115, Z7_3.1^121, Z7_3.1^127, Z7_3.1^133, Z7_3.1^139, Z7_3.1^145, Z7_3.1^151, Z7_3.1^157, Z7_3.1^163, Z7_3.1^169, Z7_3.1^175, Z7_3.1^181, Z7_3.1^187, Z7_3.1^193, Z7_3.1^199, Z7_3.1^205, Z7_3.1^211, Z7_3.1^217, Z7_3.1^223, Z7_3.1^229, Z7_3.1^235, Z7_3.1^241, Z7_3.1^247, Z7_3.1^253, Z7_3.1^259, Z7_3.1^265, Z7_3.1^271, Z7_3.1^277, Z7_3.1^283, Z7_3.1^289, Z7_3.1^295, Z7_3.1^301, Z7_3.1^307, Z7_3.1^313, Z7_3.1^319, Z7_3.1^325, Z7_3.1^331, Z7_3.1^337, Z7_3.1, Z7_3.1^7, Z7_3.1^13, Z7_3.1^19, Z7_3.1^25, Z7_3.1^31, Z7_3.1^37, Z7_3.1^43, Z7_3.1^49, Z7_3.1^55, Z7_3.1^61, Z7_3.1^67, Z7_3.1^73, Z7_3.1^79, Z7_3.1^85, Z7_3.1^91, Z7_3.1^97, Z7_3.1^103, Z7_3.1^109, Z7_3.1^115, Z7_3.1^121, Z7_3.1^127, Z7_3.1^133, Z7_3.1^139, Z7_3.1^145, Z7_3.1^151, Z7_3.1^157, Z7_3.1^163, Z7_3.1^169, Z7_3.1^175, Z7_3.1^181, Z7_3.1^187, Z7_3.1^193, Z7_3.1^199, Z7_3.1^205, Z7_3.1^211, Z7_3.1^217, Z7_3.1^223, Z7_3.1^229, Z7_3.1^235, Z7_3.1^241, Z7_3.1^247, Z7_3.1^253, Z7_3.1^259, Z7_3.1^265, Z7_3.1^271, Z7_3.1^277, Z7_3.1^283, Z7_3.1^289, Z7_3.1^295, Z7_3.1^301, Z7_3.1^307, Z7_3.1^313, Z7_3.1^319, Z7_3.1^325, Z7_3.1^331, Z7_3.1^337, Z7_3.1, Z7_3.1^10, Z7_3.1^16, Z7_3.1^22, Z7_3.1^28, Z7_3.1^34, Z7_3.1^40, Z7_3.1^46, Z7_3.1^52, Z7_3.1^58, Z7_3.1^64, Z7_3.1^70, Z7_3.1^76, Z7_3.1^82, Z7_3.1^88, Z7_3.1^94, Z7_3.1^100, Z7_3.1^106, Z7_3.1^112, Z7_3.1^118, Z7_3.1^124, Z7_3.1^130, Z7_3.1^136, Z7_3.1^142, Z7_3.1^148, Z7_3.1^154, Z7_3.1^160, Z7_3.1^166, Z7_3.1^172, Z7_3.1^178, Z7_3.1^184, Z7_3.1^190, Z7_3.1^196, Z7_3.1^202, Z7_3.1^208, Z7_3.1^214, Z7_3.1^220, Z7_3.1^226, Z7_3.1^232, Z7_3.1^238, Z7_3.1^244, Z7_3.1^250, Z7_3.1^256, Z7_3.1^262, Z7_3.1^268, Z7_3.1^274, Z7_3.1^280, Z7_3.1^286, Z7_3.1^292, Z7_3.1^298, Z7_3.1^304, Z7_3.1^310, Z7_3.1^316, Z7_3.1^322, Z7_3.1^328, Z7_3.1^334, Z7_3.1^340, Z7_3.1^4, Z7_3.1^7, Z7_3.1^13, Z7_3.1^19, Z7_3.1^25, Z7_3.1^31, Z7_3.1^37, Z7_3.1^43, Z7_3.1^49, Z7_3.1^55, Z7_3.1^61, Z7_3.1^67, Z7_3.1^73, Z7_3.1^79, Z7_3.1^85, Z7_3.1^91, Z7_3.1^97, Z7_3.1^103, Z7_3.1^109, Z7_3.1^115, Z7_3.1^121, Z7_3.1^127, Z7_3.1^133, Z7_3.1^139, Z7_3.1^145, Z7_3.1^151, Z7_3.1^157, Z7_3.1^163, Z7_3.1^169, Z7_3.1^175, Z7_3.1^181, Z7_3.1^187, Z7_3.1^193, Z7_3.1^199, Z7_3.1^205, Z7_3.1^211, Z7_3.1^217, Z7_3.1^223, Z7_3.1^229, Z7_3.1^235, Z7_3.1^241, Z7_3.1^247, Z7_3.1^253, Z7_3.1^259, Z7_3.1^265, Z7_3.1^271, Z7_3.1^277, Z7_3.1^283, Z7_3.1^289, Z7_3.1^295, Z7_3.1^301, Z7_3.1^307, Z7_3.1^313, Z7_3.1^319, Z7_3.1^325, Z7_3.1^331, Z7_3.1^337, Z7_3.1, 0, Z7_3.1^14, Z7_3.1^20, Z7_3.1^26, Z7_3.1^32, Z7_3.1^38, Z7_3.1^44, Z7_3.1^50, Z7_3.1^56, Z7_3.1^62, Z7_3.1^68, Z7_3.1^74, Z7_3.1^80, Z7_3.1^86, Z7_3.1^92, Z7_3.1^98, Z7_3.1^104, Z7_3.1^110, Z7_3.1^116, Z7_3.1^122, Z7_3.1^128, Z7_3.1^134, Z7_3.1^140, Z7_3.1^146, Z7_3.1^152, Z7_3.1^158, Z7_3.1^164, Z7_3.1^170, Z7_3.1^176, Z7_3.1^182, Z7_3.1^188, Z7_3.1^194, Z7_3.1^200, Z7_3.1^206, Z7_3.1^212, Z7_3.1^218, Z7_3.1^224, Z7_3.1^230, Z7_3.1^236, Z7_3.1^242, Z7_3.1^248, Z7_3.1^254, Z7_3.1^260, Z7_3.1^266, Z7_3.1^272, Z7_3.1^278, Z7_3.1^284, Z7_3.1^290, Z7_3.1^296, Z7_3.1^302, Z7_3.1^308, Z7_3.1^314, Z7_3.1^320, Z7_3.1^326, Z7_3.1^332, Z7_3.1^338, Z7_3.1^2, Z7_3.1^8, Z7_3.1^10, Z7_3.1^16, Z7_3.1^22, Z7_3.1^28, Z7_3.1^34, Z7_3.1^40, Z7_3.1^46, Z7_3.1^52, Z7_3.1^58, Z7_3.1^64, Z7_3.1^70, Z7_3.1^76, Z7_3.1^82, Z7_3.1^88, Z7_3.1^94, Z7_3.1^100, Z7_3.1^106, Z7_3.1^112, Z7_3.1^118, Z7_3.1^124, Z7_3.1^130, Z7_3.1^136, Z7_3.1^142, Z7_3.1^148, Z7_3.1^154, Z7_3.1^160, Z7_3.1^166, Z7_3.1^172, Z7_3.1^178, Z7_3.1^184, Z7_3.1^190, Z7_3.1^196, Z7_3.1^202, Z7_3.1^208, Z7_3.1^214, Z7_3.1^220, Z7_3.1^226, Z7_3.1^232, Z7_3.1^238, Z7_3.1^244, Z7_3.1^250, Z7_3.1^256, Z7_3.1^262, Z7_3.1^268, Z7_3.1^274, Z7_3.1^280, Z7_3.1^286, Z7_3.1^292, Z7_3.1^298, Z7_3.1^304, Z7_3.1^310, Z7_3.1^316, Z7_3.1^322, Z7_3.1^328, Z7_3.1^334, Z7_3.1^340, Z7_3.1^4, Z7_3.1^11, Z7_3.1^17, Z7_3.1^23, Z7_3.1^29, Z7_3.1^35, Z7_3.1^41, Z7_3.1^47, Z7_3.1^53, Z7_3.1^59, Z7_3.1^65, Z7_3.1^71, Z7_3.1^77, Z7_3.1^83, Z7_3.1^89, Z7_3.1^95, Z7_3.1^101, Z7_3.1^107, Z7_3.1^113, Z7_3.1^119, Z7_3.1^125, Z7_3.1^131, Z7_3.1^137, Z7_3.1^143, Z7_3.1^149, Z7_3.1^155, Z7_3.1^161, Z7_3.1^167, Z7_3.1^173, Z7_3.1^179, Z7_3.1^185, Z7_3.1^191, Z7_3.1^197, Z7_3.1^203, Z7_3.1^209, Z7_3.1^215, Z7_3.1^221, Z7_3.1^227, Z7_3.1^233, Z7_3.1^239, Z7_3.1^245, Z7_3.1^251, Z7_3.1^257, Z7_3.1^263, Z7_3.1^269, Z7_3.1^275, Z7_3.1^281, Z7_3.1^287, Z7_3.1^293, Z7_3.1^299, Z7_3.1^305, Z7_3.1^311, Z7_3.1^317, Z7_3.1^323, Z7_3.1^329, Z7_3.1^335, Z7_3.1^341, Z7_3.1^5, Z7_3.1^14, Z7_3.1^20, Z7_3.1^26, Z7_3.1^32, Z7_3.1^38, Z7_3.1^44, Z7_3.1^50, Z7_3.1^56, Z7_3.1^62, Z7_3.1^68, Z7_3.1^74, Z7_3.1^80, Z7_3.1^86, Z7_3.1^92, Z7_3.1^98, Z7_3.1^104, Z7_3.1^110, Z7_3.1^116, Z7_3.1^122, Z7_3.1^128, Z7_3.1^134, Z7_3.1^140, Z7_3.1^146, Z7_3.1^152, Z7_3.1^158, Z7_3.1^164, Z7_3.1^170, Z7_3.1^176, Z7_3.1^182, Z7_3.1^188, Z7_3.1^194, Z7_3.1^200, Z7_3.1^206, Z7_3.1^212, Z7_3.1^218, Z7_3.1^224, Z7_3.1^230, Z7_3.1^236, Z7_3.1^242, Z7_3.1^248, Z7_3.1^254, Z7_3.1^260, Z7_3.1^266, Z7_3.1^272, Z7_3.1^278, Z7_3.1^284, Z7_3.1^290, Z7_3.1^296, Z7_3.1^302, Z7_3.1^308, Z7_3.1^314, Z7_3.1^320, Z7_3.1^326, Z7_3.1^332, Z7_3.1^338, Z7_3.1^2, Z7_3.1^8, Z7_3.1^18, Z7_3.1^24, Z7_3.1^30, Z7_3.1^36, Z7_3.1^42, Z7_3.1^48, Z7_3.1^54, Z7_3.1^60, Z7_3.1^66, Z7_3.1^72, Z7_3.1^78, Z7_3.1^84, Z7_3.1^90, Z7_3.1^96, Z7_3.1^102, Z7_3.1^108, 2, Z7_3.1^120, Z7_3.1^126, Z7_3.1^132, Z7_3.1^138, Z7_3.1^144, Z7_3.1^150, Z7_3.1^156, Z7_3.1^162, Z7_3.1^168, Z7_3.1^174, Z7_3.1^180, Z7_3.1^186, Z7_3.1^192, Z7_3.1^198, Z7_3.1^204, Z7_3.1^210, Z7_3.1^216, Z7_3.1^222, 4, Z7_3.1^234, Z7_3.1^240, Z7_3.1^246, Z7_3.1^252, Z7_3.1^258, Z7_3.1^264, Z7_3.1^270, Z7_3.1^276, Z7_3.1^282, Z7_3.1^288, Z7_3.1^294, Z7_3.1^300, Z7_3.1^306, Z7_3.1^312, Z7_3.1^318, Z7_3.1^324, Z7_3.1^330, Z7_3.1^336, 1, Z7_3.1^6, Z7_3.1^12, Z7_3.1^14, Z7_3.1^20, Z7_3.1^26, Z7_3.1^32, Z7_3.1^38, Z7_3.1^44, Z7_3.1^50, Z7_3.1^56, Z7_3.1^62, Z7_3.1^68, Z7_3.1^74, Z7_3.1^80, Z7_3.1^86, Z7_3.1^92, Z7_3.1^98, Z7_3.1^104, Z7_3.1^110, Z7_3.1^116, Z7_3.1^122, Z7_3.1^128, Z7_3.1^134, Z7_3.1^140, Z7_3.1^146, Z7_3.1^152, Z7_3.1^158, Z7_3.1^164, Z7_3.1^170, Z7_3.1^176, Z7_3.1^182, Z7_3.1^188, Z7_3.1^194, Z7_3.1^200, Z7_3.1^206, Z7_3.1^212, Z7_3.1^218, Z7_3.1^224, Z7_3.1^230, Z7_3.1^236, Z7_3.1^242, Z7_3.1^248, Z7_3.1^254, Z7_3.1^260, Z7_3.1^266, Z7_3.1^272, Z7_3.1^278, Z7_3.1^284, Z7_3.1^290, Z7_3.1^296, Z7_3.1^302, Z7_3.1^308, Z7_3.1^314, Z7_3.1^320, Z7_3.1^326, Z7_3.1^332, Z7_3.1^338, Z7_3.1^2, Z7_3.1^8, 0, Z7_3.1^16, Z7_3.1^22, Z7_3.1^28, Z7_3.1^34, Z7_3.1^40, Z7_3.1^46, Z7_3.1^52, Z7_3.1^58, Z7_3.1^64, Z7_3.1^70, Z7_3.1^76, Z7_3.1^82, Z7_3.1^88, Z7_3.1^94, Z7_3.1^100, Z7_3.1^106, Z7_3.1^112, Z7_3.1^118, Z7_3.1^124, Z7_3.1^130, Z7_3.1^136, Z7_3.1^142, Z7_3.1^148, Z7_3.1^154, Z7_3.1^160, Z7_3.1^166, Z7_3.1^172, Z7_3.1^178, Z7_3.1^184, Z7_3.1^190, Z7_3.1^196, Z7_3.1^202, Z7_3.1^208, Z7_3.1^214, Z7_3.1^220, Z7_3.1^226, Z7_3.1^232, Z7_3.1^238, Z7_ ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 04:00:36 2004 Input: print "Solució Exercici nº 3"; print "---------------------"; q:=7; r:=3; expt:=[q^(r-n): n in [1..r]]; print "Exponents: ";expt; P!expt; Output: Magma V2.10-6 Mon Mar 15 2004 04:00:33 on modular [Seed = 4226730855] ------------------------------------- Solució Exercici nº 3 --------------------- Exponents: [ 49, 7, 1 ] >> P!expt; ^ User error: Identifier 'P' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 04:01:09 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Z7_3; Olav:=[(i * j): i in Z7_3, j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Olav; Output: Magma V2.10-6 Mon Mar 15 2004 04:01:02 on modular [Seed = 3704220735] ------------------------------------- x^57 x^49 + x^7 + x Finite field of size 7^3 [ Z7_3.1, Z7_3.1^7, Z7_3.1^13, Z7_3.1^19, Z7_3.1^25, Z7_3.1^31, Z7_3.1^37, Z7_3.1^43, Z7_3.1^49, Z7_3.1^55, Z7_3.1^61, Z7_3.1^67, Z7_3.1^73, Z7_3.1^79, Z7_3.1^85, Z7_3.1^91, Z7_3.1^97, Z7_3.1^103, Z7_3.1^109, Z7_3.1^115, Z7_3.1^121, Z7_3.1^127, Z7_3.1^133, Z7_3.1^139, Z7_3.1^145, Z7_3.1^151, Z7_3.1^157, Z7_3.1^163, Z7_3.1^169, Z7_3.1^175, Z7_3.1^181, Z7_3.1^187, Z7_3.1^193, Z7_3.1^199, Z7_3.1^205, Z7_3.1^211, Z7_3.1^217, Z7_3.1^223, Z7_3.1^229, Z7_3.1^235, Z7_3.1^241, Z7_3.1^247, Z7_3.1^253, Z7_3.1^259, Z7_3.1^265, Z7_3.1^271, Z7_3.1^277, Z7_3.1^283, Z7_3.1^289, Z7_3.1^295, Z7_3.1^301, Z7_3.1^307, Z7_3.1^313, Z7_3.1^319, Z7_3.1^325, Z7_3.1^331, Z7_3.1^337, Z7_3.1, Z7_3.1^7, Z7_3.1^13, Z7_3.1^19, Z7_3.1^25, Z7_3.1^31, Z7_3.1^37, Z7_3.1^43, Z7_3.1^49, Z7_3.1^55, Z7_3.1^61, Z7_3.1^67, Z7_3.1^73, Z7_3.1^79, Z7_3.1^85, Z7_3.1^91, Z7_3.1^97, Z7_3.1^103, Z7_3.1^109, Z7_3.1^115, Z7_3.1^121, Z7_3.1^127, Z7_3.1^133, Z7_3.1^139, Z7_3.1^145, Z7_3.1^151, Z7_3.1^157, Z7_3.1^163, Z7_3.1^169, Z7_3.1^175, Z7_3.1^181, Z7_3.1^187, Z7_3.1^193, Z7_3.1^199, Z7_3.1^205, Z7_3.1^211, Z7_3.1^217, Z7_3.1^223, Z7_3.1^229, Z7_3.1^235, Z7_3.1^241, Z7_3.1^247, Z7_3.1^253, Z7_3.1^259, Z7_3.1^265, Z7_3.1^271, Z7_3.1^277, Z7_3.1^283, Z7_3.1^289, Z7_3.1^295, Z7_3.1^301, Z7_3.1^307, Z7_3.1^313, Z7_3.1^319, Z7_3.1^325, Z7_3.1^331, Z7_3.1^337, Z7_3.1^2, Z7_3.1^8, Z7_3.1^14, Z7_3.1^20, Z7_3.1^26, Z7_3.1^32, Z7_3.1^38, Z7_3.1^44, Z7_3.1^50, Z7_3.1^56, Z7_3.1^62, Z7_3.1^68, Z7_3.1^74, Z7_3.1^80, Z7_3.1^86, Z7_3.1^92, Z7_3.1^98, Z7_3.1^104, Z7_3.1^110, Z7_3.1^116, Z7_3.1^122, Z7_3.1^128, Z7_3.1^134, Z7_3.1^140, Z7_3.1^146, Z7_3.1^152, Z7_3.1^158, Z7_3.1^164, Z7_3.1^170, Z7_3.1^176, Z7_3.1^182, Z7_3.1^188, Z7_3.1^194, Z7_3.1^200, Z7_3.1^206, Z7_3.1^212, Z7_3.1^218, Z7_3.1^224, Z7_3.1^230, Z7_3.1^236, Z7_3.1^242, Z7_3.1^248, Z7_3.1^254, Z7_3.1^260, Z7_3.1^266, Z7_3.1^272, Z7_3.1^278, Z7_3.1^284, Z7_3.1^290, Z7_3.1^296, Z7_3.1^302, Z7_3.1^308, Z7_3.1^314, Z7_3.1^320, Z7_3.1^326, Z7_3.1^332, Z7_3.1^338, Z7_3.1^4, Z7_3.1^10, Z7_3.1^16, Z7_3.1^22, Z7_3.1^28, Z7_3.1^34, Z7_3.1^40, Z7_3.1^46, Z7_3.1^52, Z7_3.1^58, Z7_3.1^64, Z7_3.1^70, Z7_3.1^76, Z7_3.1^82, Z7_3.1^88, Z7_3.1^94, Z7_3.1^100, Z7_3.1^106, Z7_3.1^112, Z7_3.1^118, Z7_3.1^124, Z7_3.1^130, Z7_3.1^136, Z7_3.1^142, Z7_3.1^148, Z7_3.1^154, Z7_3.1^160, Z7_3.1^166, Z7_3.1^172, Z7_3.1^178, Z7_3.1^184, Z7_3.1^190, Z7_3.1^196, Z7_3.1^202, Z7_3.1^208, Z7_3.1^214, Z7_3.1^220, Z7_3.1^226, Z7_3.1^232, Z7_3.1^238, Z7_3.1^244, Z7_3.1^250, Z7_3.1^256, Z7_3.1^262, Z7_3.1^268, Z7_3.1^274, Z7_3.1^280, Z7_3.1^286, Z7_3.1^292, Z7_3.1^298, Z7_3.1^304, Z7_3.1^310, Z7_3.1^316, Z7_3.1^322, Z7_3.1^328, Z7_3.1^334, Z7_3.1^340, Z7_3.1^7, Z7_3.1^13, Z7_3.1^19, Z7_3.1^25, Z7_3.1^31, Z7_3.1^37, Z7_3.1^43, Z7_3.1^49, Z7_3.1^55, Z7_3.1^61, Z7_3.1^67, Z7_3.1^73, Z7_3.1^79, Z7_3.1^85, Z7_3.1^91, Z7_3.1^97, Z7_3.1^103, Z7_3.1^109, Z7_3.1^115, Z7_3.1^121, Z7_3.1^127, Z7_3.1^133, Z7_3.1^139, Z7_3.1^145, Z7_3.1^151, Z7_3.1^157, Z7_3.1^163, Z7_3.1^169, Z7_3.1^175, Z7_3.1^181, Z7_3.1^187, Z7_3.1^193, Z7_3.1^199, Z7_3.1^205, Z7_3.1^211, Z7_3.1^217, Z7_3.1^223, Z7_3.1^229, Z7_3.1^235, Z7_3.1^241, Z7_3.1^247, Z7_3.1^253, Z7_3.1^259, Z7_3.1^265, Z7_3.1^271, Z7_3.1^277, Z7_3.1^283, Z7_3.1^289, Z7_3.1^295, Z7_3.1^301, Z7_3.1^307, Z7_3.1^313, Z7_3.1^319, Z7_3.1^325, Z7_3.1^331, Z7_3.1^337, Z7_3.1, Z7_3.1^7, Z7_3.1^13, Z7_3.1^19, Z7_3.1^25, Z7_3.1^31, Z7_3.1^37, Z7_3.1^43, Z7_3.1^49, Z7_3.1^55, Z7_3.1^61, Z7_3.1^67, Z7_3.1^73, Z7_3.1^79, Z7_3.1^85, Z7_3.1^91, Z7_3.1^97, Z7_3.1^103, Z7_3.1^109, Z7_3.1^115, Z7_3.1^121, Z7_3.1^127, Z7_3.1^133, Z7_3.1^139, Z7_3.1^145, Z7_3.1^151, Z7_3.1^157, Z7_3.1^163, Z7_3.1^169, Z7_3.1^175, Z7_3.1^181, Z7_3.1^187, Z7_3.1^193, Z7_3.1^199, Z7_3.1^205, Z7_3.1^211, Z7_3.1^217, Z7_3.1^223, Z7_3.1^229, Z7_3.1^235, Z7_3.1^241, Z7_3.1^247, Z7_3.1^253, Z7_3.1^259, Z7_3.1^265, Z7_3.1^271, Z7_3.1^277, Z7_3.1^283, Z7_3.1^289, Z7_3.1^295, Z7_3.1^301, Z7_3.1^307, Z7_3.1^313, Z7_3.1^319, Z7_3.1^325, Z7_3.1^331, Z7_3.1^337, Z7_3.1, Z7_3.1^10, Z7_3.1^16, Z7_3.1^22, Z7_3.1^28, Z7_3.1^34, Z7_3.1^40, Z7_3.1^46, Z7_3.1^52, Z7_3.1^58, Z7_3.1^64, Z7_3.1^70, Z7_3.1^76, Z7_3.1^82, Z7_3.1^88, Z7_3.1^94, Z7_3.1^100, Z7_3.1^106, Z7_3.1^112, Z7_3.1^118, Z7_3.1^124, Z7_3.1^130, Z7_3.1^136, Z7_3.1^142, Z7_3.1^148, Z7_3.1^154, Z7_3.1^160, Z7_3.1^166, Z7_3.1^172, Z7_3.1^178, Z7_3.1^184, Z7_3.1^190, Z7_3.1^196, Z7_3.1^202, Z7_3.1^208, Z7_3.1^214, Z7_3.1^220, Z7_3.1^226, Z7_3.1^232, Z7_3.1^238, Z7_3.1^244, Z7_3.1^250, Z7_3.1^256, Z7_3.1^262, Z7_3.1^268, Z7_3.1^274, Z7_3.1^280, Z7_3.1^286, Z7_3.1^292, Z7_3.1^298, Z7_3.1^304, Z7_3.1^310, Z7_3.1^316, Z7_3.1^322, Z7_3.1^328, Z7_3.1^334, Z7_3.1^340, Z7_3.1^4, Z7_3.1^7, Z7_3.1^13, Z7_3.1^19, Z7_3.1^25, Z7_3.1^31, Z7_3.1^37, Z7_3.1^43, Z7_3.1^49, Z7_3.1^55, Z7_3.1^61, Z7_3.1^67, Z7_3.1^73, Z7_3.1^79, Z7_3.1^85, Z7_3.1^91, Z7_3.1^97, Z7_3.1^103, Z7_3.1^109, Z7_3.1^115, Z7_3.1^121, Z7_3.1^127, Z7_3.1^133, Z7_3.1^139, Z7_3.1^145, Z7_3.1^151, Z7_3.1^157, Z7_3.1^163, Z7_3.1^169, Z7_3.1^175, Z7_3.1^181, Z7_3.1^187, Z7_3.1^193, Z7_3.1^199, Z7_3.1^205, Z7_3.1^211, Z7_3.1^217, Z7_3.1^223, Z7_3.1^229, Z7_3.1^235, Z7_3.1^241, Z7_3.1^247, Z7_3.1^253, Z7_3.1^259, Z7_3.1^265, Z7_3.1^271, Z7_3.1^277, Z7_3.1^283, Z7_3.1^289, Z7_3.1^295, Z7_3.1^301, Z7_3.1^307, Z7_3.1^313, Z7_3.1^319, Z7_3.1^325, Z7_3.1^331, Z7_3.1^337, Z7_3.1, 0, Z7_3.1^14, Z7_3.1^20, Z7_3.1^26, Z7_3.1^32, Z7_3.1^38, Z7_3.1^44, Z7_3.1^50, Z7_3.1^56, Z7_3.1^62, Z7_3.1^68, Z7_3.1^74, Z7_3.1^80, Z7_3.1^86, Z7_3.1^92, Z7_3.1^98, Z7_3.1^104, Z7_3.1^110, Z7_3.1^116, Z7_3.1^122, Z7_3.1^128, Z7_3.1^134, Z7_3.1^140, Z7_3.1^146, Z7_3.1^152, Z7_3.1^158, Z7_3.1^164, Z7_3.1^170, Z7_3.1^176, Z7_3.1^182, Z7_3.1^188, Z7_3.1^194, Z7_3.1^200, Z7_3.1^206, Z7_3.1^212, Z7_3.1^218, Z7_3.1^224, Z7_3.1^230, Z7_3.1^236, Z7_3.1^242, Z7_3.1^248, Z7_3.1^254, Z7_3.1^260, Z7_3.1^266, Z7_3.1^272, Z7_3.1^278, Z7_3.1^284, Z7_3.1^290, Z7_3.1^296, Z7_3.1^302, Z7_3.1^308, Z7_3.1^314, Z7_3.1^320, Z7_3.1^326, Z7_3.1^332, Z7_3.1^338, Z7_3.1^2, Z7_3.1^8, Z7_3.1^10, Z7_3.1^16, Z7_3.1^22, Z7_3.1^28, Z7_3.1^34, Z7_3.1^40, Z7_3.1^46, Z7_3.1^52, Z7_3.1^58, Z7_3.1^64, Z7_3.1^70, Z7_3.1^76, Z7_3.1^82, Z7_3.1^88, Z7_3.1^94, Z7_3.1^100, Z7_3.1^106, Z7_3.1^112, Z7_3.1^118, Z7_3.1^124, Z7_3.1^130, Z7_3.1^136, Z7_3.1^142, Z7_3.1^148, Z7_3.1^154, Z7_3.1^160, Z7_3.1^166, Z7_3.1^172, Z7_3.1^178, Z7_3.1^184, Z7_3.1^190, Z7_3.1^196, Z7_3.1^202, Z7_3.1^208, Z7_3.1^214, Z7_3.1^220, Z7_3.1^226, Z7_3.1^232, Z7_3.1^238, Z7_3.1^244, Z7_3.1^250, Z7_3.1^256, Z7_3.1^262, Z7_3.1^268, Z7_3.1^274, Z7_3.1^280, Z7_3.1^286, Z7_3.1^292, Z7_3.1^298, Z7_3.1^304, Z7_3.1^310, Z7_3.1^316, Z7_3.1^322, Z7_3.1^328, Z7_3.1^334, Z7_3.1^340, Z7_3.1^4, Z7_3.1^11, Z7_3.1^17, Z7_3.1^23, Z7_3.1^29, Z7_3.1^35, Z7_3.1^41, Z7_3.1^47, Z7_3.1^53, Z7_3.1^59, Z7_3.1^65, Z7_3.1^71, Z7_3.1^77, Z7_3.1^83, Z7_3.1^89, Z7_3.1^95, Z7_3.1^101, Z7_3.1^107, Z7_3.1^113, Z7_3.1^119, Z7_3.1^125, Z7_3.1^131, Z7_3.1^137, Z7_3.1^143, Z7_3.1^149, Z7_3.1^155, Z7_3.1^161, Z7_3.1^167, Z7_3.1^173, Z7_3.1^179, Z7_3.1^185, Z7_3.1^191, Z7_3.1^197, Z7_3.1^203, Z7_3.1^209, Z7_3.1^215, Z7_3.1^221, Z7_3.1^227, Z7_3.1^233, Z7_3.1^239, Z7_3.1^245, Z7_3.1^251, Z7_3.1^257, Z7_3.1^263, Z7_3.1^269, Z7_3.1^275, Z7_3.1^281, Z7_3.1^287, Z7_3.1^293, Z7_3.1^299, Z7_3.1^305, Z7_3.1^311, Z7_3.1^317, Z7_3.1^323, Z7_3.1^329, Z7_3.1^335, Z7_3.1^341, Z7_3.1^5, Z7_3.1^14, Z7_3.1^20, Z7_3.1^26, Z7_3.1^32, Z7_3.1^38, Z7_3.1^44, Z7_3.1^50, Z7_3.1^56, Z7_3.1^62, Z7_3.1^68, Z7_3.1^74, Z7_3.1^80, Z7_3.1^86, Z7_3.1^92, Z7_3.1^98, Z7_3.1^104, Z7_3.1^110, Z7_3.1^116, Z7_3.1^122, Z7_3.1^128, Z7_3.1^134, Z7_3.1^140, Z7_3.1^146, Z7_3.1^152, Z7_3.1^158, Z7_3.1^164, Z7_3.1^170, Z7_3.1^176, Z7_3.1^182, Z7_3.1^188, Z7_3.1^194, Z7_3.1^200, Z7_3.1^206, Z7_3.1^212, Z7_3.1^218, Z7_3.1^224, Z7_3.1^230, Z7_3.1^236, Z7_3.1^242, Z7_3.1^248, Z7_3.1^254, Z7_3.1^260, Z7_3.1^266, Z7_3.1^272, Z7_3.1^278, Z7_3.1^284, Z7_3.1^290, Z7_3.1^296, Z7_3.1^302, Z7_3.1^308, Z7_3.1^314, Z7_3.1^320, Z7_3.1^326, Z7_3.1^332, Z7_3.1^338, Z7_3.1^2, Z7_3.1^8, Z7_3.1^18, Z7_3.1^24, Z7_3.1^30, Z7_3.1^36, Z7_3.1^42, Z7_3.1^48, Z7_3.1^54, Z7_3.1^60, Z7_3.1^66, Z7_3.1^72, Z7_3.1^78, Z7_3.1^84, Z7_3.1^90, Z7_3.1^96, Z7_3.1^102, Z7_3.1^108, 2, Z7_3.1^120, Z7_3.1^126, Z7_3.1^132, Z7_3.1^138, Z7_3.1^144, Z7_3.1^150, Z7_3.1^156, Z7_3.1^162, Z7_3.1^168, Z7_3.1^174, Z7_3.1^180, Z7_3.1^186, Z7_3.1^192, Z7_3.1^198, Z7_3.1^204, Z7_3.1^210, Z7_3.1^216, Z7_3.1^222, 4, Z7_3.1^234, Z7_3.1^240, Z7_3.1^246, Z7_3.1^252, Z7_3.1^258, Z7_3.1^264, Z7_3.1^270, Z7_3.1^276, Z7_3.1^282, Z7_3.1^288, Z7_3.1^294, Z7_3.1^300, Z7_3.1^306, Z7_3.1^312, Z7_3.1^318, Z7_3.1^324, Z7_3.1^330, Z7_3.1^336, 1, Z7_3.1^6, Z7_3.1^12, Z7_3.1^14, Z7_3.1^20, Z7_3.1^26, Z7_3.1^32, Z7_3.1^38, Z7_3.1^44, Z7_3.1^50, Z7_3.1^56, Z7_3.1^62, Z7_3.1^68, Z7_3.1^74, Z7_3.1^80, Z7_3.1^86, Z7_3.1^92, Z7_3.1^98, Z7_3.1^104, Z7_3.1^110, Z7_3.1^116, Z7_3.1^122, Z7_3.1^128, Z7_3.1^134, Z7_3.1^140, Z7_3.1^146, Z7_3.1^152, Z7_3.1^158, Z7_3.1^164, Z7_3.1^170, Z7_3.1^176, Z7_3.1^182, Z7_3.1^188, Z7_3.1^194, Z7_3.1^200, Z7_3.1^206, Z7_3.1^212, Z7_3.1^218, Z7_3.1^224, Z7_3.1^230, Z7_3.1^236, Z7_3.1^242, Z7_3.1^248, Z7_3.1^254, Z7_3.1^260, Z7_3.1^266, Z7_3.1^272, Z7_3.1^278, Z7_3.1^284, Z7_3.1^290, Z7_3.1^296, Z7_3.1^302, Z7_3.1^308, Z7_3.1^314, Z7_3.1^320, Z7_3.1^326, Z7_3.1^332, Z7_3.1^338, Z7_3.1^2, Z7_3.1^8, 0, Z7_3.1^16, Z7_3.1^22, Z7_3.1^28, Z7_3.1^34, Z7_3.1^40, Z7_3.1^46, Z7_3.1^52, Z7_3.1^58, Z7_3.1^64, Z7_3.1^70, Z7_3.1^76, Z7_3.1^82, Z7_3.1^88, Z7_3.1^94, Z7_3.1^100, Z7_3.1^106, Z7_3.1^112, Z7_3.1^118, Z7_3.1^124, Z7_3.1^130, Z7_3.1^136, Z7_3.1^142, Z7_3.1^148, Z7_3.1^154, Z7_3.1^160, Z7_3.1^166, Z7_3.1^172, Z7_3.1^178, Z7_3.1^184, Z7_3.1^190, Z7_3.1^196, Z7_3.1^202, Z7_3.1^208, Z7_3.1^214, Z7_3.1^220, Z7_3.1^226, Z7_ ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 04:03:25 2004 Input: print "Solució Exercici nº 3"; print "---------------------"; q:=7; r:=3; expt:=[q^(r-n): n in [1..r]]; print "Exponents: ";expt; Z:=Integers(x); P:=PolynomialRing(Z); P!expt; Output: Magma V2.10-6 Mon Mar 15 2004 04:03:22 on modular [Seed = 3704221096] ------------------------------------- Solució Exercici nº 3 --------------------- Exponents: [ 49, 7, 1 ] >> Z:=Integers(x); ^ User error: Identifier 'x' has not been declared or assigned >> P:=PolynomialRing(Z); ^ User error: Identifier 'Z' has not been declared or assigned >> P!expt; ^ User error: Identifier 'P' has not been declared or assigned Total time: 3.319 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 04:03:58 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[(i * j): i in Z, j in Z, i<3 , j<3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Olav; Output: Magma V2.10-6 Mon Mar 15 2004 04:03:55 on modular [Seed = 3992509625] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i * j): i in Z, j in Z, i<3 , j<3 | Evaluate(n7_3,i) eq Evaluate(t7 ^ User error: bad syntax >> Olav; ^ User error: Identifier 'Olav' has not been declared or assigned Total time: 3.519 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 04:04:24 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[(i * j): i in Z, j in Z, i lt 3 , j lt 3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Olav; Output: Magma V2.10-6 Mon Mar 15 2004 04:04:21 on modular [Seed = 3774206298] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i * j): i in Z, j in Z, i lt 3 , j lt 3 | Evaluate(n7_3,i) eq Evalu ^ User error: bad syntax >> Olav; ^ User error: Identifier 'Olav' has not been declared or assigned Total time: 3.199 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 04:04:57 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[(i * j): i in Z, j in Z, lt(i,3) , j lt 3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Olav; Output: Magma V2.10-6 Mon Mar 15 2004 04:04:53 on modular [Seed = 4058300523] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i * j): i in Z, j in Z, lt(i,3) , j lt 3 | Evaluate(n7_3,i) eq Eval ^ User error: bad syntax >> Olav; ^ User error: Identifier 'Olav' has not been declared or assigned Total time: 3.359 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 04:05:24 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[(i * j): i in Z, j in Z | (i lt 3) and j( lt 3) and Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Olav; Output: Magma V2.10-6 Mon Mar 15 2004 04:05:21 on modular [Seed = 3285643837] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i * j): i in Z, j in Z | (i lt 3) and j( lt 3) and Evaluate(n7_3,i) ^ User error: bad syntax >> Olav; ^ User error: Identifier 'Olav' has not been declared or assigned Total time: 3.199 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 04:05:38 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(7,3); Olav:=[(i * j): i in Z, j in Z | (i lt 3) and (j lt 3) and Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Olav; Output: Magma V2.10-6 Mon Mar 15 2004 04:05:35 on modular [Seed = 3671059242] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i * j): i in Z, j in Z | (i lt 3) and (j lt 3) and Evaluate(n7_3,i) ^ Runtime error in for: Iteration is not possible over this object >> Olav; ^ User error: Identifier 'Olav' has not been declared or assigned Total time: 3.399 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 04:05:42 2004 Input: print "Solució Exercici nº 3"; print "---------------------"; q:=7; r:=3; print "Exponents de t7,3(x): ";expt; expt:=[q^(r-n): n in [1..r]]; P:=PolynomialRing(GF(q^r)); P!expt; Output: Magma V2.10-6 Mon Mar 15 2004 04:05:39 on modular [Seed = 3536315166] ------------------------------------- Solució Exercici nº 3 --------------------- Exponents de t7,3(x): >> print "Exponents de t7,3(x): ";expt; ^ User error: Identifier 'expt' has not been declared or assigned x^2 Total time: 3.319 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 04:05:57 2004 Input: print "Solució Exercici nº 3"; print "---------------------"; q:=7; r:=3; expt:=[q^(r-n): n in [1..r]]; print "Exponents de t7,3(x): ";expt; P:=PolynomialRing(GF(q^r)); P!expt; Output: Magma V2.10-6 Mon Mar 15 2004 04:05:54 on modular [Seed = 924976885] ------------------------------------- Solució Exercici nº 3 --------------------- Exponents de t7,3(x): [ 49, 7, 1 ] x^2 Total time: 3.539 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 04:06:17 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(2,1); Olav:=[(i * j): i in Z7_3, j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Olav; Output: Magma V2.10-6 Mon Mar 15 2004 04:06:13 on modular [Seed = 540348949] ------------------------------------- x^57 x^49 + x^7 + x [ 0, 1 ] Total time: 3.229 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 04:06:29 2004 Input: print "Solució Exercici nº 3"; print "---------------------"; q:=7; r:=3; expt:=[q^(r-n): n in [1..r]]; print "Exponents de t7,3(x): ";expt; P:=PolynomialRing(GF(q^r)); P![3,2,1]; Output: Magma V2.10-6 Mon Mar 15 2004 04:06:26 on modular [Seed = 691804939] ------------------------------------- Solució Exercici nº 3 --------------------- Exponents de t7,3(x): [ 49, 7, 1 ] x^2 + 2*x + 3 Total time: 3.309 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 04:06:57 2004 Input: print "Solució Exercici nº 3"; print "---------------------"; q:=7; r:=3; expt:=[q^(r-n): n in [1..r]]; print "Exponents de t7,3(x): ";expt; P:=PolynomialRing(GF(q^r)); P!expt; Output: Magma V2.10-6 Mon Mar 15 2004 04:06:54 on modular [Seed = 302456844] ------------------------------------- Solució Exercici nº 3 --------------------- Exponents de t7,3(x): [ 49, 7, 1 ] x^2 Total time: 3.449 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Mon Mar 15 04:07:01 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal ; > GroebnerBasis(I); > (14123-x*y)*(1-x^2*y) in I; Output: Magma V2.10-6 Mon Mar 15 2004 04:06:57 on modular [Seed = 352331540] ------------------------------------- [ x*y^2 + 2*x + 10*y^3 + 3*y, 3*x + 5*y, 25*y^2 - 1 ] false Total time: 3.849 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 04:07:02 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(2,1); Olav:=[(i * j): i in Z7_3 * j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Olav; Output: Magma V2.10-6 Mon Mar 15 2004 04:06:58 on modular [Seed = 504048668] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i * j): i in Z7_3 * j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j ^ User error: Identifier 'j' has not been declared or assigned >> Olav; ^ User error: Identifier 'Olav' has not been declared or assigned Total time: 3.699 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 04:07:35 2004 Input: print "Solució Exercici nº 3"; print "---------------------"; q:=7; r:=3; expt:=[q^(r-n): n in [1..r]]; print "Exponents de t7,3(x): ";expt; P:=PolynomialRing(GF(q^r)); expt:=[3,2,1]; P!expt; Output: Magma V2.10-6 Mon Mar 15 2004 04:07:14 on modular [Seed = 219692927] ------------------------------------- Solució Exercici nº 3 --------------------- Exponents de t7,3(x): [ 49, 7, 1 ] x^2 + 2*x + 3 Total time: 3.499 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 04:07:38 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(2,1); Olav:=[(i * j): i in Z7_3 , j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Olav; Output: Magma V2.10-6 Mon Mar 15 2004 04:07:17 on modular [Seed = 1885684229] ------------------------------------- x^57 x^49 + x^7 + x [ 0, 1 ] Total time: 3.669 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Mon Mar 15 04:07:42 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal ; > GroebnerBasis(I); > (14123-x*y)*(1-x^2*y) in I; Output: Magma V2.10-6 Mon Mar 15 2004 04:07:39 on modular [Seed = 2137672980] ------------------------------------- >> I := ideal ; ^ User error: bad syntax >> GroebnerBasis(I); ^ User error: Identifier 'I' has not been declared or assigned >> (14123-x*y)*(1-x^2*y) in I; ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 04:07:51 2004 Input: print "Solució Exercici nº 3"; print "---------------------"; q:=7; r:=3; expt:=[q^(r-n): n in [1..r]]; print "Exponents de t7,3(x): ";expt; P:=PolynomialRing(GF(q^r)); expt:=[49,7,1]; P!expt; Output: Magma V2.10-6 Mon Mar 15 2004 04:07:48 on modular [Seed = 1753045564] ------------------------------------- Solució Exercici nº 3 --------------------- Exponents de t7,3(x): [ 49, 7, 1 ] x^2 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Mon Mar 15 04:07:55 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal ; > GroebnerBasis(I); > (14123-x*y)*(1-x^2*y) in I; Output: Magma V2.10-6 Mon Mar 15 2004 04:07:52 on modular [Seed = 1363436297] ------------------------------------- [ x + 1, y + 1, 2 ] true Total time: 3.159 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 04:08:05 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(2,1); Olav:=[(i * j): i in Z7_3 , j in Z7_3 | i eq j]; Olav; Output: Magma V2.10-6 Mon Mar 15 2004 04:08:02 on modular [Seed = 1515153432] ------------------------------------- x^57 x^49 + x^7 + x [ 0, 1 ] Total time: 3.129 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Mon Mar 15 04:08:08 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal ; > GroebnerBasis(I); > (14123-x*y)*(1-x^2*y) in I; Output: Magma V2.10-6 Mon Mar 15 2004 04:08:05 on modular [Seed = 1565028120] ------------------------------------- [ x + 1, y + 1, 2 ] true Total time: 3.139 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 04:08:30 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(2,1); Olav:=[(i * j): i in Z7_3 , j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Olav; Output: Magma V2.10-6 Mon Mar 15 2004 04:08:27 on modular [Seed = 1280933623] ------------------------------------- x^57 x^49 + x^7 + x [ 0, 1 ] Total time: 3.149 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Mon Mar 15 04:09:04 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal ; > GroebnerBasis(I); > (14123-x*y)*(1-x^2*y) in I; Output: Magma V2.10-6 Mon Mar 15 2004 04:08:43 on modular [Seed = 3047196446] ------------------------------------- [ x + 1, y + 1, 2 ] true Total time: 3.139 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 04:09:28 2004 Input: print "Solució Exercici nº 3"; print "---------------------"; q:=7; r:=3; expt:=[q^(r-n): n in [1..r]]; print "Exponents de t7,3(x): ";expt; P:=PolynomialRing(GF(q^r)); t:=P!expt; &+(expt); Output: Magma V2.10-6 Mon Mar 15 2004 04:09:25 on modular [Seed = 3198913611] ------------------------------------- Solució Exercici nº 3 --------------------- Exponents de t7,3(x): [ 49, 7, 1 ] 57 Total time: 3.139 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 04:09:49 2004 Input: print "Solució Exercici nº 3"; print "---------------------"; q:=7; r:=3; expt:=[q^(r-n): n in [1..r]]; print "Exponents de t7,3(x): ";expt; P:=PolynomialRing(GF(q^r)); t:=P!expt; n:=P!&+(expt); Output: Magma V2.10-6 Mon Mar 15 2004 04:09:46 on modular [Seed = 2813498701] ------------------------------------- Solució Exercici nº 3 --------------------- Exponents de t7,3(x): [ 49, 7, 1 ] Total time: 3.139 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 04:10:35 2004 Input: print "Solució Exercici nº 3"; print "---------------------"; q:=7; r:=3; expt:=[q^(r-n): n in [1..r]]; print "Exponents de t7,3(x): ";expt; P:=PolynomialRing(GF(q^r)); t:=P!expt; print "Polinomio t: ";t; n:=P!&+(expt); print "Polinomio n: ";n; Output: Magma V2.10-6 Mon Mar 15 2004 04:10:32 on modular [Seed = 2559421344] ------------------------------------- Solució Exercici nº 3 --------------------- Exponents de t7,3(x): [ 49, 7, 1 ] Polinomio t: x^2 Polinomio n: 1 Total time: 3.149 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Mon Mar 15 04:10:40 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal ; > GroebnerBasis(I); > (14123-x*y)*(1-x^2*y) in I; Output: Magma V2.10-6 Mon Mar 15 2004 04:10:37 on modular [Seed = 2174005948] ------------------------------------- [ x + 1, y + 1, 2 ] true Total time: 3.099 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-142-104.pitt.east.verizon.net. (141.151.142.104) Time: Mon Mar 15 04:11:01 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal ; > GroebnerBasis(I); > (14123-x*y)*(1-x^2*y) in I; Output: Magma V2.10-6 Mon Mar 15 2004 04:10:58 on modular [Seed = 2325723544] ------------------------------------- [ x + 1, y^2 + 1, 2 ] true Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 04:11:20 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(2,1); Olav:=[[i * j]: i in Z7_3 , j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Olav; Output: Magma V2.10-6 Mon Mar 15 2004 04:11:17 on modular [Seed = 4091986166] ------------------------------------- x^57 x^49 + x^7 + x [ [ 0 ], [ 1 ] ] Total time: 3.159 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 04:11:37 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(2,1); Olav:=[i * j: i in Z7_3 , j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Olav; Output: Magma V2.10-6 Mon Mar 15 2004 04:11:34 on modular [Seed = 4243181450] ------------------------------------- x^57 x^49 + x^7 + x [ 0, 1 ] Total time: 3.339 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 04:12:00 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(2,1); Olav:=[i * j: (i in Z7_3 , j in Z7_3) | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Olav; Output: Magma V2.10-6 Mon Mar 15 2004 04:11:57 on modular [Seed = 3857766024] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[i * j: (i in Z7_3 , j in Z7_3) | Evaluate(n7_3,i) eq Evaluate(t7_3,j ^ User error: bad syntax >> Olav; ^ User error: Identifier 'Olav' has not been declared or assigned Total time: 3.649 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 04:12:24 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(2,1); Olav:=[(i,j): i in Z7_3 * j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Olav; Output: Magma V2.10-6 Mon Mar 15 2004 04:12:20 on modular [Seed = 4009483690] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i,j): i in Z7_3 * j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)] ^ User error: Identifier 'j' has not been declared or assigned >> Olav; ^ User error: Identifier 'Olav' has not been declared or assigned Total time: 3.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 04:12:42 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(2,1); Olav:=[(i and j): i in Z7_3 * j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Olav; Output: Magma V2.10-6 Mon Mar 15 2004 04:12:38 on modular [Seed = 3619873889] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[(i and j): i in Z7_3 * j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3 ^ User error: Identifier 'j' has not been declared or assigned >> Olav; ^ User error: Identifier 'Olav' has not been declared or assigned Total time: 3.829 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 04:12:54 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(2,1); Olav:=[(i * j): i in Z7_3 , j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Olav; Output: Magma V2.10-6 Mon Mar 15 2004 04:12:51 on modular [Seed = 268772274] ------------------------------------- x^57 x^49 + x^7 + x [ 0, 1 ] Total time: 3.119 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Mon Mar 15 04:14:34 2004 Input: pn73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+(7^(3-i)); end for; return x^C; end function; pt73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+x^(7^(3-i)); end for; return C; end function; polav73:=function() c:=[]; for i in GF(7^3) do for j in GF(7^3) do if (pn73(i) eq pt73(j) ) then Include(C, (i,j)); end if; end for; end for; return C; end function; polav73(); Output: Magma V2.10-6 Mon Mar 15 2004 04:14:31 on modular [Seed = 453912797] ------------------------------------- >> if (pn73(i) eq pt73(j) ) then Include(C, (i,j)); ^ User error: Identifier 'C' has not been declared or assigned >> polav73();; ^ User error: Identifier 'polav73' has not been declared or assigned Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Mon Mar 15 04:14:51 2004 Input: pn73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+(7^(3-i)); end for; return x^C; end function; pt73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+x^(7^(3-i)); end for; return C; end function; polav73:=function() C:=[]; for i in GF(7^3) do for j in GF(7^3) do if (pn73(i) eq pt73(j) ) then Include(C, (i,j)); end if; end for; end for; return C; end function; polav73(); Output: Magma V2.10-6 Mon Mar 15 2004 04:14:48 on modular [Seed = 35075643] ------------------------------------- [
:19]( ) >> if (pn73(i) eq pt73(j) ) then Include(C, (i,j)); ^ Runtime error: Number of arguments (1) does not equal expected number of arguments (0) Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 04:22:47 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(2,1); Olav:=[: in Z7_3*Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Olav; Output: Magma V2.10-6 Mon Mar 15 2004 04:22:44 on modular [Seed = 2054115247] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[: in Z7_3*Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; ^ User error: bad syntax >> Olav; ^ User error: Identifier 'Olav' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 04:23:05 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(2,1); Olav:=[: i in Z7_3, j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Olav; Output: Magma V2.10-6 Mon Mar 15 2004 04:23:02 on modular [Seed = 1769757870] ------------------------------------- x^57 x^49 + x^7 + x [ <0, 0>, <1, 1> ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 04:24:23 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(2,1); Olav:=[: i in Z7_3, j in Z7_3 | i ne j]; Olav; Output: Magma V2.10-6 Mon Mar 15 2004 04:24:20 on modular [Seed = 1346725413] ------------------------------------- x^57 x^49 + x^7 + x [ <1, 0>, <0, 1> ] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 04:24:59 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(2,1); Evaluate(n7_3,0); Evaluate(n7_3,1); Evaluate(t7_3,0); Evaluate(t7_3,1); Olav:=[: i in Z7_3, j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Olav; Output: Magma V2.10-6 Mon Mar 15 2004 04:24:56 on modular [Seed = 1531866370] ------------------------------------- x^57 x^49 + x^7 + x 0 1 0 3 [ <0, 0>, <1, 1> ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 04:25:26 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(2,1); Evaluate(n7_3,0); Evaluate(n7_3,1) eq Evaluate(t7_3,1); Evaluate(t7_3,0); Olav:=[: i in Z7_3, j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(t7_3,j)]; Olav; Output: Magma V2.10-6 Mon Mar 15 2004 04:25:23 on modular [Seed = 1230798843] ------------------------------------- x^57 x^49 + x^7 + x 0 false 0 [ <0, 0>, <1, 1> ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 04:25:58 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(2,1); Evaluate(n7_3,0); Evaluate(n7_3,1) eq Evaluate(t7_3,1); Evaluate(t7_3,0); Olav:=[: i in Z7_3, j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(n7_3,j)]; Olav; Output: Magma V2.10-6 Mon Mar 15 2004 04:25:55 on modular [Seed = 2963637794] ------------------------------------- x^57 x^49 + x^7 + x 0 false 0 [ <0, 0>, <1, 1> ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 04:26:44 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(2,1); Olav:=[: i in Z7_3, j in Z7_3 | (Evaluate(n7_3,i) eq Evaluate(n7_3,j)) eq true]; Olav; Output: Magma V2.10-6 Mon Mar 15 2004 04:26:41 on modular [Seed = 3148778843] ------------------------------------- x^57 x^49 + x^7 + x [ <0, 0>, <1, 1> ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 04:28:04 2004 Input: print "Solució Exercici nº 3"; print "---------------------"; q:=7; r:=3; expt:=[q^(r-n): n in [1..r]]; print "Exponents de t7,3(x): ";expt; P:=PolynomialRing(Integers()); t:=P!expt; print "Polinomio t: ";t; n:=P!&+(expt); print "Polinomio n: ";n; Output: Magma V2.10-6 Mon Mar 15 2004 04:28:01 on modular [Seed = 2796786102] ------------------------------------- Solució Exercici nº 3 --------------------- Exponents de t7,3(x): [ 49, 7, 1 ] Polinomio t: x^2 + 7*x + 49 Polinomio n: 57 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 04:28:36 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(2,1); Olav:=[: in Z7_3 | Evaluate(n7_3,i) eq Evaluate(n7_3,j)]; Olav; Output: Magma V2.10-6 Mon Mar 15 2004 04:28:33 on modular [Seed = 2441389793] ------------------------------------- x^57 x^49 + x^7 + x >> Olav:=[: in Z7_3 | Evaluate(n7_3,i) eq Evaluate(n7_3,j)]; ^ User error: bad syntax >> Olav; ^ User error: Identifier 'Olav' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 04:29:16 2004 Input: print "Solució Exercici nº 3"; print "---------------------"; q:=7; r:=3; expt:=[q^(r-n): n in [1..r]]; print "Exponents de t7,3(x): ";expt; P:=PolynomialRing(Integers()); t:=P!expt; print "Polinomio t: ";t; n:=x^&+(expt); print "Polinomio n: ";n; Output: Magma V2.10-6 Mon Mar 15 2004 04:29:13 on modular [Seed = 2559422400] ------------------------------------- Solució Exercici nº 3 --------------------- Exponents de t7,3(x): [ 49, 7, 1 ] Polinomio t: x^2 + 7*x + 49 Polinomio n: x^57 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Mon Mar 15 04:30:29 2004 Input: Z:=Integers(); n7_3:=PolynomialRing(Z); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Z); t7_3:=x^49+x^7+x; n7_3; t7_3; Z7_3:=GF(2,1); Olav:=[: i in Z7_3, j in Z7_3 | Evaluate(n7_3,i) eq Evaluate(n7_3,j)]; Olav; Output: Magma V2.10-6 Mon Mar 15 2004 04:30:26 on modular [Seed = 2342435848] ------------------------------------- x^57 x^49 + x^7 + x [ <0, 0>, <1, 1> ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 04:31:34 2004 Input: print "Solució Exercici nº 3"; print "---------------------"; q:=7; r:=3; expt:=[q^(r-n): n in [1..r]]; print "Exponents de t7,3(x): ";expt; P:=PolynomialRing(Integers()); t:=0; for i in expt do t:=t + x^i; print "Polinomio t: ";t; n:=x^&+(expt); print "Polinomio n: ";n; Output: Magma V2.10-6 Mon Mar 15 2004 04:31:31 on modular [Seed = 4075275568] ------------------------------------- Solució Exercici nº 3 --------------------- Exponents de t7,3(x): [ 49, 7, 1 ] User error: syntax error at end of input Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 04:32:05 2004 Input: print "Solució Exercici nº 3"; print "---------------------"; q:=7; r:=3; expt:=[q^(r-n): n in [1..r]]; print "Exponents de t7,3(x): ";expt; t:=0; for i in expt do t:=t + i; print "Polinomio t: ";t; n:=x^&+(expt); print "Polinomio n: ";n; Output: Magma V2.10-6 Mon Mar 15 2004 04:32:03 on modular [Seed = 4259890655] ------------------------------------- Solució Exercici nº 3 --------------------- Exponents de t7,3(x): [ 49, 7, 1 ] User error: syntax error at end of input Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 04:33:05 2004 Input: print "Solució Exercici nº 3"; print "---------------------"; q:=7; r:=3; expt:=[q^(r-n): n in [1..r]]; print "Exponents de t7,3(x): ";expt; n:=x^&+(expt); print "Polinomio n: ";n; Output: Magma V2.10-6 Mon Mar 15 2004 04:33:02 on modular [Seed = 3841055899] ------------------------------------- Solució Exercici nº 3 --------------------- Exponents de t7,3(x): [ 49, 7, 1 ] >> n:=x^&+(expt); ^ User error: Identifier 'x' has not been declared or assigned Polinomio n: >> print "Polinomio n: ";n; ^ User error: Identifier 'n' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 04:34:35 2004 Input: print "Solució Exercici nº 3"; print "---------------------"; q:=7; r:=3; expt:=[q^(r-n): n in [1..r]]; print "Exponents de t7,3(x): ";expt; P:=PolynomialRing(Integers()); n:=x^&+(expt); print "Polinomio n: ";n; Output: Magma V2.10-6 Mon Mar 15 2004 04:34:32 on modular [Seed = 4026193782] ------------------------------------- Solució Exercici nº 3 --------------------- Exponents de t7,3(x): [ 49, 7, 1 ] Polinomio n: x^57 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 04:35:09 2004 Input: print "Solució Exercici nº 3"; print "---------------------"; q:=7; r:=3; expt:=[q^(r-n): n in [1..r]]; print "Exponents de t7,3(x): ";expt; P:=PolynomialRing(Integers()); t:=0; for i in expt do t:=t + i; end for; print "Polinomio t: ";t n:=x^&+(expt); print "Polinomio n: ";n; Output: Magma V2.10-6 Mon Mar 15 2004 04:35:06 on modular [Seed = 3671056929] ------------------------------------- Solució Exercici nº 3 --------------------- Exponents de t7,3(x): [ 49, 7, 1 ] Polinomio t: >> n:=x^&+(expt); ^ User error: bad syntax Polinomio n: >> print "Polinomio n: ";n; ^ User error: Identifier 'n' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 04:35:28 2004 Input: print "Solució Exercici nº 3"; print "---------------------"; q:=7; r:=3; expt:=[q^(r-n): n in [1..r]]; print "Exponents de t7,3(x): ";expt; P:=PolynomialRing(Integers()); t:=0; for i in expt do t:=t + i; end for; print "Polinomio t: ";t; n:=x^&+(expt); print "Polinomio n: ";n; Output: Magma V2.10-6 Mon Mar 15 2004 04:35:25 on modular [Seed = 3302095912] ------------------------------------- Solució Exercici nº 3 --------------------- Exponents de t7,3(x): [ 49, 7, 1 ] Polinomio t: 57 Polinomio n: x^57 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 04:35:45 2004 Input: print "Solució Exercici nº 3"; print "---------------------"; q:=7; r:=3; expt:=[q^(r-n): n in [1..r]]; print "Exponents de t7,3(x): ";expt; P:=PolynomialRing(Integers()); t:=0; for i in expt do t:=t + x^i; end for; print "Polinomio t: ";t; n:=x^&+(expt); print "Polinomio n: ";n; Output: Magma V2.10-6 Mon Mar 15 2004 04:35:41 on modular [Seed = 3487233808] ------------------------------------- Solució Exercici nº 3 --------------------- Exponents de t7,3(x): [ 49, 7, 1 ] Polinomio t: x^49 + x^7 + x Polinomio n: x^57 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 04:39:46 2004 Input: print "Solució Exercici nº 3"; print "---------------------"; q:=7; r:=3; expt:=[q^(r-n): n in [1..r]]; print "Exponents de t7,3(x): ";expt; P:=PolynomialRing(Integers()); t:=0; for i in expt do t:=t + x^i; end for; print "Polinomio t: ";t; n:=x^&+(expt); print "Polinomio n: ";n; olav:={: a,b in GF(q^r) | n(a) eq t(b)} Output: Magma V2.10-6 Mon Mar 15 2004 04:39:43 on modular [Seed = 891292888] ------------------------------------- Solució Exercici nº 3 --------------------- Exponents de t7,3(x): [ 49, 7, 1 ] Polinomio t: x^49 + x^7 + x Polinomio n: x^57 >> olav:={: a,b in GF(q^r) | n(a) eq t(b)} ^ Runtime error: Bad argument types Argument types given: FldFinElt, RngUPolElt Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 04:40:15 2004 Input: print "Solució Exercici nº 3"; print "---------------------"; q:=7; r:=3; expt:=[q^(r-n): n in [1..r]]; print "Exponents de t7,3(x): ";expt; P:=PolynomialRing(Integers()); t:=0; for i in expt do t:=t + x^i; end for; print "Polinomio t: ";t; n:=x^&+(expt); print "Polinomio n: ";n; olav:={: a,b in GF(q^r) | n eq t} Output: Magma V2.10-6 Mon Mar 15 2004 04:40:12 on modular [Seed = 623910123] ------------------------------------- Solució Exercici nº 3 --------------------- Exponents de t7,3(x): [ 49, 7, 1 ] Polinomio t: x^49 + x^7 + x Polinomio n: x^57 >> olav:={: a,b in GF(q^r) | n eq t} ^ User error: bad syntax Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 04:41:18 2004 Input: print "Solució Exercici nº 3"; print "---------------------"; q:=7; r:=3; expt:=[q^(r-n): n in [1..r]]; print "Exponents de t7,3(x): ";expt; P:=PolynomialRing(Integers()); t:=0; for i in expt do t:=t + x^i; end for; print "Polinomio t: ";t; n:=x^&+(expt); print "Polinomio n: ";n; olav:={: a,b in GF(q^r) | Evaluate(n,a) eq Evaluate(t,b)} Output: Magma V2.10-6 Mon Mar 15 2004 04:41:11 on modular [Seed = 319170838] ------------------------------------- Solució Exercici nº 3 --------------------- Exponents de t7,3(x): [ 49, 7, 1 ] Polinomio t: x^49 + x^7 + x Polinomio n: x^57 Total time: 6.809 seconds, Total memory usage: 2.98MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 04:41:45 2004 Input: print "Solució Exercici nº 3"; print "---------------------"; q:=7; r:=3; expt:=[q^(r-n): n in [1..r]]; print "Exponents de t7,3(x): ";expt; P:=PolynomialRing(Integers()); t:=0; for i in expt do t:=t + x^i; end for; print "Polinomio t: ";t; n:=x^&+(expt); print "Polinomio n: ";n; olav:={: a,b in GF(q^r) | Evaluate(n,a) eq Evaluate(t,b)} print "Punts d'Olav: ";olav; Output: Magma V2.10-6 Mon Mar 15 2004 04:41:42 on modular [Seed = 403513980] ------------------------------------- Solució Exercici nº 3 --------------------- Exponents de t7,3(x): [ 49, 7, 1 ] Polinomio t: x^49 + x^7 + x Polinomio n: x^57 >> print "Punts d'Olav: ";olav;; ^ User error: bad syntax Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee84.uab.es. (158.109.66.84) Time: Mon Mar 15 04:42:09 2004 Input: print "Solució Exercici nº 3"; print "---------------------"; q:=7; r:=3; expt:=[q^(r-n): n in [1..r]]; print "Exponents de t7,3(x): ";expt; P:=PolynomialRing(Integers()); t:=0; for i in expt do t:=t + x^i; end for; print "Polinomio t: ";t; n:=x^&+(expt); print "Polinomio n: ";n; olav:={: a,b in GF(q^r) | Evaluate(n,a) eq Evaluate(t,b)}; print "Punts d'Olav: ";olav; Output: Magma V2.10-6 Mon Mar 15 2004 04:42:02 on modular [Seed = 18103129] ------------------------------------- Solució Exercici nº 3 --------------------- Exponents de t7,3(x): [ 49, 7, 1 ] Polinomio t: x^49 + x^7 + x Polinomio n: x^57 Punts d'Olav: { <$.1^189, $.1^104>, <$.1^268, $.1^223>, <$.1^266, $.1^125>, <$.1^340, $.1^294>, <$.1^245, $.1^281>, <$.1^173, $.1^218>, <1, $.1^7>, <$.1^85, $.1^58>, <$.1^167, $.1^140>, <$.1^108, $.1^100>, <$.1^330, $.1^66>, <$.1^10, $.1^326>, <$.1^303, $.1^319>, <$.1^87, $.1^261>, <$.1^214, $.1^244>, <$.1^20, $.1^201>, <$.1^116, $.1^270>, <$.1^222, $.1^156>, <$.1^338, $.1^201>, <4, $.1^10>, <$.1^19, $.1^188>, <$.1^204, $.1^70>, <$.1^301, $.1^147>, <$.1^56, $.1^311>, <$.1^101, $.1^210>, <$.1^311, $.1^210>, <$.1^238, $.1^229>, <$.1^41, $.1^41>, <$.1^63, $.1^261>, <4, $.1^195>, <$.1^219, $.1^303>, <$.1^144, $.1^339>, <$.1^329, $.1^43>, <$.1^319, $.1^154>, <3, $.1^150>, <$.1^56, $.1^78>, <$.1^237, $.1^327>, <$.1^134, $.1^262>, <$.1^147, $.1^167>, <$.1^160, $.1^223>, <$.1^284, $.1^329>, <$.1^302, $.1^273>, <$.1^239, $.1^140>, <$.1^196, $.1^42>, <$.1^8, $.1^262>, <$.1^250, $.1^318>, <$.1^294, $.1^11>, <$.1^149, $.1^40>, <$.1^22, $.1^119>, <$.1^339, $.1^308>, <$.1^238, $.1^126>, <$.1^48, $.1^197>, <$.1^328, $.1^32>, <$.1^32, $.1^273>, <$.1^97, $.1^205>, <$.1^184, $.1^174>, <$.1^42, $.1^112>, <$.1^176, $.1^251>, <$.1^133, $.1^82>, <$.1^53, $.1^202>, <$.1^135, $.1^167>, <$.1^218, $.1^86>, <$.1^311, $.1^89>, <$.1^87, $.1^28>, <$.1^187, $.1^21>, <$.1^98, $.1^111>, <$.1^104, $.1^214>, <$.1^102, $.1^131>, <$.1^319, $.1^3>, <$.1^314, $.1^246>, <$.1^42, $.1^275>, <$.1^27, $.1^196>, <$.1^267, $.1^168>, <$.1^249, $.1^168>, <$.1^81, $.1^117>, <$.1^291, $.1^271>, <$.1^72, $.1^197>, <$.1^293, $.1^43>, <$.1^297, $.1^135>, <$.1^26, $.1^151>, <$.1^289, $.1^52>, <$.1^239, $.1^295>, <$.1^268, $.1^277>, <$.1^319, $.1^232>, <$.1^122, $.1^226>, <$.1^93, $.1^178>, <$.1^212, $.1^204>, <$.1^82, $.1^244>, <$.1^217, $.1^64>, <$.1^327, $.1^92>, <$.1^272, $.1^214>, <$.1^72, $.1^148>, <$.1^49, $.1^123>, <$.1^200, $.1^211>, <$.1^146, $.1^311>, <$.1^106, $.1^18>, <$.1^46, $.1^83>, <$.1^223, $.1^155>, <$.1^159, $.1^69>, <$.1^37, $.1^59>, <$.1^147, 2>, <$.1^240, $.1^49>, <$.1^294, $.1^338>, <$.1^294, $.1^215>, <$.1^3, $.1^319>, <$.1^177, $.1^172>, <$.1^277, 1>, <$.1^152, $.1^234>, <$.1^116, $.1^214>, <$.1^174, $.1^16>, <$.1^132, $.1^156>, <$.1^72, $.1^195>, <$.1^45, $.1^330>, <$.1^4, $.1^315>, <$.1^34, $.1^6>, <$.1^303, $.1^92>, <$.1^180, $.1^14>, <$.1^307, $.1^82>, <$.1^83, $.1^20>, <0, $.1^300>, <$.1^273, $.1^319>, <$.1^241, $.1^256>, <$.1^29, $.1^9>, <$.1^331, $.1^147>, <$.1^72, $.1^199>, <$.1^180, $.1^77>, <$.1^293, $.1^63>, <$.1^19, $.1^73>, <1, $.1^175>, <$.1^20, $.1^184>, <$.1^303, $.1^28>, <$.1^31, $.1^216>, <$.1^198, $.1^25>, <$.1^209, $.1^334>, <$.1^47, $.1^334>, <$.1^277, $.1^188>, <$.1^85, $.1^332>, <$.1^281, $.1^292>, <$.1^276, $.1^215>, <$.1^212, $.1^245>, <$.1^187, $.1^22>, <$.1^264, $.1^159>, <$.1^184, $.1^101>, <$.1^91, $.1^256>, <$.1^304, $.1^83>, <$.1^183, $.1^117>, <$.1^14, $.1^311>, <$.1^98, $.1^212>, <$.1^222, $.1^146>, <$.1^174, $.1^100>, <$.1^12, $.1^37>, <$.1^274, $.1^81>, <$.1^80, $.1^93>, <$.1^81, $.1^62>, <$.1^313, $.1^59>, <$.1^200, $.1^309>, <$.1^150, $.1^339>, <$.1^277, $.1^71>, <$.1^64, $.1^6>, <$.1^31, $.1^21>, <$.1^150, $.1^314>, <$.1^262, $.1^294>, <$.1^25, $.1^252>, <$.1^339, $.1^248>, <$.1^8, $.1^12>, <$.1^36, $.1^199>, <$.1^222, $.1^233>, <$.1^108, $.1^120>, <$.1^289, $.1^216>, <$.1^194, $.1^60>, <$.1^133, $.1^68>, <$.1^274, $.1^224>, <$.1^101, $.1^41>, <$.1^141, $.1^88>, <$.1^21, $.1^96>, <$.1^8, $.1^5>, <$.1^109, $.1^169>, <$.1^247, $.1^71>, <$.1^126, $.1^321>, <$.1^159, $.1^24>, <$.1^279, $.1^135>, <$.1^104, $.1^191>, <$.1^284, $.1^262>, <$.1^267, $.1^150>, <$.1^204, $.1^233>, <$.1^300, $.1^199>, <$.1^294, $.1^240>, <$.1^131, $.1^33>, <$.1^181, $.1^21>, <$.1^53, $.1^55>, <$.1^91, $.1^254>, <$.1^221, $.1^99>, <$.1^117, $.1^62>, <$.1^32, $.1^79>, <$.1^258, $.1^137>, <$.1^96, $.1>, <$.1^270, $.1^288>, <$.1^202, $.1^85>, <$.1^270, $.1^132>, <$.1^10, $.1^149>, <$.1^229, $.1^127>, <$.1^108, $.1^288>, <$.1^72, $.1^338>, <$.1^170, $.1^130>, <$.1^284, $.1^163>, <$.1^251, $.1^296>, <$.1^259, $.1^320>, <$.1^109, $.1^189>, <$.1^80, $.1^151>, <$.1^135, $.1^178>, <$.1^275, $.1^13>, <$.1^319, $.1^256>, <$.1^323, $.1^138>, <$.1^276, $.1^148>, <$.1^230, $.1^251>, <$.1^33, $.1^24>, <$.1^202, $.1^161>, <$.1^175, $.1^232>, <$.1^248, $.1^78>, <$.1^78, $.1^148>, <$.1^311, $.1^75>, <$.1^29, $.1^75>, <$.1^225, $.1^241>, <$.1^239, $.1^33>, <$.1^37, $.1^36>, <$.1^28, $.1^242>, <$.1^23, $.1^287>, <$.1^238, $.1^225>, <$.1^259, $.1^64>, <$.1^317, $.1^206>, <$.1^64, $.1^298>, <$.1^193, $.1^160>, <$.1^255, $.1^291>, <$.1^275, $.1^142>, <$.1^125, $.1^75>, <$.1^104, $.1^204>, <$.1^92, $.1^84>, <$.1^193, $.1^106>, <$.1^78, $.1^337>, <$.1^112, $.1^235>, <$.1^169, $.1^123>, <$.1^277, $.1^67>, <$.1^9, 2>, <$.1^173, $.1^334>, <$.1^110, $.1^245>, <$.1^18, $.1^2>, <$.1^23, $.1^118>, <$.1^103, $.1^232>, <$.1^106, $.1^32>, <$.1^53, $.1^210>, <$.1^71, $.1^9>, <$.1^189, $.1^271>, <$.1^151, $.1^324>, <$.1^304, $.1^253>, <$.1^257, $.1^41>, <$.1^174, $.1^321>, <$.1^330, $.1^100>, <$.1^104, $.1^262>, <$.1^51, $.1^327>, <$.1^186, $.1^240>, <$.1^208, $.1^239>, <$.1^249, $.1^308>, <$.1^253, $.1^169>, <$.1^147, $.1^248>, <$.1^8, $.1^124>, <$.1^181, $.1^82>, <$.1^20, $.1^124>, <$.1^73, $.1^59>, <$.1^88, $.1^198>, <$.1^150, $.1^70>, <$.1^289, $.1^213>, <$.1^325, $.1^169>, <$.1^209, $.1^264>, <$.1^295, $.1^134>, <$.1^11, $.1^41>, <$.1^209, $.1^158>, <$.1^99, $.1^104>, <$.1^277, $.1^54>, <$.1^204, $.1^25>, <$.1^12, $.1^7>, <$.1^203, $.1^299>, <$.1^172, $.1^223>, <$.1^325, $.1^22>, <$.1^47, $.1^80>, <$.1^203, $.1^250>, <$.1^275, $.1^218>, <$.1^46, $.1^229>, <$.1^9, $.1^24>, <$.1^292, $.1^81>, <$.1^329, $.1^140>, <$.1^115, $.1^67>, <$.1^224, $.1^12>, <2, $.1^120>, <6, 2>, <$.1^317, $.1^250>, <$.1^338, $.1^246>, <$.1^132, $.1>, <$.1^326, $.1^151>, <$.1^247, $.1^254>, <$.1^208, $.1^207>, <$.1^221, $.1^310>, <$.1^173, $.1^183>, <$.1^206, $.1^128>, <$.1^238, $.1^230>, <$.1^36, $.1^2>, <$.1^50, $.1^116>, <$.1^47, $.1^20>, <$.1^50, $.1^329>, <$.1^58, $.1^305>, <$.1^2, $.1^273>, <$.1^39, $.1^28>, <6, $.1^187>, <$.1^306, $.1^159>, <$.1^333, $.1^24>, <$.1^323, $.1^301>, <$.1^157, $.1^177>, <$.1^34, $.1^244>, <$.1^50, $.1^79>, <$.1^212, $.1^184>, <$.1^132, $.1^137>, <$.1^310, $.1^207>, <$.1^180, $.1^146>, <$.1^336, $.1^137>, <$.1^239, $.1^299>, <$.1^338, $.1^110>, <$.1^18, $.1^131>, <$.1^147, $.1^291>, <2, $.1^14>, <$.1^214, $.1^235>, <$.1^53, $.1^287>, <$.1^167, $.1^33>, <$.1^321, $.1^24>, <$.1^206, $.1^84>, <$.1^162, $.1^267>, <$.1^161, $.1^299>, <$.1^34, $.1^230>, <$.1^92, $.1^201>, <$.1^312, $.1^263>, <$.1^239, $.1^218>, <$.1^155, $.1^206>, <$.1^220, $.1^153>, <$.1^102, $.1^137>, <$.1^128, $.1^246>, <$.1^271, $.1^320>, <$.1^288, $.1^49>, <$.1^179, $.1^264>, <$.1^39, $.1^44>, <$.1^217, $.1^232>, <$.1^202, $.1^81>, <$.1^146, $.1^273>, <$.1^297, 2>, <$.1^164, $.1^251>, <$.1^212, $.1^110>, <$.1^268, $.1^224>, <$.1^182, $.1^204>, <$.1^309, $.1^92>, <$.1^134, $.1^184>, <$.1^184, $.1^328>, <$.1^74, $.1^115>, <$.1^25, $.1^144>, <$.1^220, $.1^331>, <$.1^248, $.1^214>, <$.1^75, $.1^178>, <$.1^58, $.1^340>, <$.1^216, $.1^314>, <$.1^47, $.1^30>, <$.1^38, $.1^204>, <$.1^32, $.1^245>, <$.1^290, $.1^313>, <$.1^216, $.1^11>, <$.1^81, $.1^150>, <$.1^219, $.1^261>, <$.1^291, $.1^274>, <$.1^230, $.1^245>, <$.1^84, $.1^87>, <$.1^154, $.1^18>, <$.1^226, $.1^230>, <$.1^190, $.1^223>, <$.1^25, $.1^213>, <2, $.1^10>, <$.1^12, $.1^159>, <$.1^280, $.1^294>, <$.1^101, $.1^91>, <$.1^47, $.1^255>, <$.1^28, $.1^305>, <$.1^58, $.1^101>, <$.1^220, $.1^253>, <$.1^196, $.1^23>, <$.1^43, $.1^290>, <$.1^21, $.1^241>, <$.1^182, $.1^191>, <$.1^324, $.1^159>, <$.1^47, $.1^287>, <$.1^226, $.1^253>, <$.1^174, $.1^77>, <$.1^148, $.1^174>, <6, $.1^283>, <$.1^78, $.1^146>, <$.1^339, $.1^268>, <$.1^240, $.1^288>, <4, $.1^312>, <$.1^84, $.1^195>, <$.1^117, $.1^327>, <$.1^158, $.1^111>, <$.1^28, $.1^277>, <$.1^16, $.1^225>, <$.1^322, $.1^253>, <5, $.1^135>, <$.1^320, $.1^47>, <$.1^191, $.1^250>, <$.1^282, $.1^156>, <$.1, $.1^189>, <$.1^140, $.1^270>, <$.1^161, $.1^287>, <$.1^100, $.1^326>, <$.1^139, $.1^82>, <$.1^337, $.1^324>, <$.1^13, $.1^73>, <$.1^254, $.1^128>, <$.1^170, $.1^212>, <$.1^319, $.1^189>, <$.1^338, $.1^115>, <$.1^336, $.1^49>, <$.1^73, $.1^3>, <$.1^130, $.1^45>, <$.1^289, $.1^160>, <$.1^260, $.1^12>, <$.1^59, $.1^249>, <$.1^317, $.1^91>, <$.1^173, $.1^287>, <$.1^320, $.1^60>, <$.1^18, $.1^337>, <$.1^251, $.1^255>, <$.1^289, $.1^22>, <$.1^123, $.1^291>, <$.1^258, $.1^146>, <$.1^187, $.1^147>, <$.1^87, $.1^269>, <$.1^73, $.1^290>, <$.1^184, $.1^145>, <$.1^96, $.1^240>, <$.1^25, $.1^324>, <$.1^48, $.1^37>, <$.1^272, $.1^226>, <$.1^321, $.1^44>, <$.1^102, $.1^132>, <$.1^331, $.1^205>, <$.1^198, $.1^307>, <$.1^45, $.1^24>, <$.1^51, $.1^269>, <$.1^59, $.1^13>, <$.1^9, $.1^258>, <$.1^110, $.1^329>, <$.1^186, 5>, <$.1^22, $.1^85>, <$.1^126, $.1>, <$.1^198, $.1^14>, <$.1^224, $.1^226>, <$.1^299, $.1^250>, <$.1^27, $.1^117>, <$.1^253, $.1^36>, <$.1^235, $.1^27>, <$.1^124, $.1^225>, <$.1^160, $.1^81>, <$.1^277, $.1^123>, <$.1^49, $.1^21>, <$.1^293, $.1^80>, <$.1^52, $.1^200>, <$.1^277, $.1^194>, <$.1^84, $.1^90>, <$.1^303, $.1^302>, <$.1^187, $.1^3>, <$.1^186, $.1^132>, <$.1^151, $.1^316>, <$.1^119, $.1^46>, <$.1^238, $.1^326>, <$.1^142, $.1^326>, <$.1^157, $.1^320>, <$.1^279, $.1^308>, <$.1^270, $.1>, <$.1^290, $.1^47>, <$.1^74, $.1^110>, <$.1^9, $.1^268>, <$.1^111, $.1^319>, <$.1^218, $.1^139>, <$.1^275, $.1^41>, <$.1^78, $.1^156>, <$.1^240, $.1^337>, <$.1^216, $.1>, <$.1^273, $.1^4>, <$.1^211, $.1^134>, <$.1^143, $.1^99>, <$.1^61, $.1^123>, <$.1^276, $.1^16>, <$.1^129, $.1^241>, <$.1^7, $.1^68>, <$.1^256, $.1^174>, <$.1^31, $.1^203>, <$.1^254, $.1^217>, <$.1^39, 2>, <$.1^212, $.1^151>, <$.1^19, $.1^106>, <$.1^164, $.1^93>, <$.1^339, $.1^258>, <$.1^156 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host aula-b-siee93.uab.es. (158.109.66.93) Time: Mon Mar 15 06:07:37 2004 Input: expf:=function(q,r) expt:=[q^(r-n): n in [1..r]]; return expt; end function; Output: Magma V2.10-6 Mon Mar 15 2004 06:07:24 on modular [Seed = 3369928342] ------------------------------------- Total time: 6.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee93.uab.es. (158.109.66.93) Time: Mon Mar 15 06:07:49 2004 Input: expf:=function(q,r) expt:=[q^(r-n): n in [1..r]]; return expt; end function; Output: Magma V2.10-6 Mon Mar 15 2004 06:07:40 on modular [Seed = 807796351] ------------------------------------- Total time: 5.509 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee93.uab.es. (158.109.66.93) Time: Mon Mar 15 06:07:53 2004 Input: expf:=function(q,r) expt:=[q^(r-n): n in [1..r]]; return expt; end function; expf(7,3); Output: Magma V2.10-6 Mon Mar 15 2004 06:07:49 on modular [Seed = 942536334] ------------------------------------- [ 49, 7, 1 ] Total time: 3.649 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee93.uab.es. (158.109.66.93) Time: Mon Mar 15 06:10:44 2004 Input: tf:=function(q,r) expt:=[q^(r-n): n in [1..r]]; P:=PolynomialRing(Integers()); t:=0; for i in expt do t:=t + x^i; end for; return t; end function; tf:=function(q,r) expt:=[q^(r-n): n in [1..r]]; P:=PolynomialRing(Integers()); n:=x^&+(expt); return n; end function; nf(7,3); tf(7,3); Output: Magma V2.10-6 Mon Mar 15 2004 06:10:41 on modular [Seed = 487117343] ------------------------------------- >> nf(7,3); ^ User error: Identifier 'nf' has not been declared or assigned x^57 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee93.uab.es. (158.109.66.93) Time: Mon Mar 15 06:11:05 2004 Input: tf:=function(q,r) expt:=[q^(r-n): n in [1..r]]; P:=PolynomialRing(Integers()); t:=0; for i in expt do t:=t + x^i; end for; return t; end function; nf:=function(q,r) expt:=[q^(r-n): n in [1..r]]; P:=PolynomialRing(Integers()); n:=x^&+(expt); return n; end function; nf(7,3); tf(7,3); Output: Magma V2.10-6 Mon Mar 15 2004 06:11:02 on modular [Seed = 68275057] ------------------------------------- x^57 x^49 + x^7 + x Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee93.uab.es. (158.109.66.93) Time: Mon Mar 15 06:12:30 2004 Input: olav:=function(q,r) expt:=[q^(r-n): n in [1..r]]; P:=PolynomialRing(Integers()); t:=0; for i in expt do t:=t + x^i; end for; n:=x^&+(expt); olav:={: a,b in GF(q^r) | Evaluate(n,a) eq Evaluate(t,b)}; return olav; end function; nf(7,3); tf(7,3); Output: Magma V2.10-6 Mon Mar 15 2004 06:12:27 on modular [Seed = 1936112859] ------------------------------------- >> nf(7,3); ^ User error: Identifier 'nf' has not been declared or assigned >> tf(7,3); ^ User error: Identifier 'tf' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee93.uab.es. (158.109.66.93) Time: Mon Mar 15 06:12:46 2004 Input: olav:=function(q,r) expt:=[q^(r-n): n in [1..r]]; P:=PolynomialRing(Integers()); t:=0; for i in expt do t:=t + x^i; end for; n:=x^&+(expt); olav:={: a,b in GF(q^r) | Evaluate(n,a) eq Evaluate(t,b)}; return olav; end function; olav(7,3); Output: Magma V2.10-6 Mon Mar 15 2004 06:12:38 on modular [Seed = 2054141422] ------------------------------------- { <$.1^189, $.1^104>, <$.1^268, $.1^223>, <$.1^266, $.1^125>, <$.1^340, $.1^294>, <$.1^245, $.1^281>, <$.1^173, $.1^218>, <1, $.1^7>, <$.1^85, $.1^58>, <$.1^167, $.1^140>, <$.1^108, $.1^100>, <$.1^330, $.1^66>, <$.1^10, $.1^326>, <$.1^303, $.1^319>, <$.1^87, $.1^261>, <$.1^214, $.1^244>, <$.1^20, $.1^201>, <$.1^116, $.1^270>, <$.1^222, $.1^156>, <$.1^338, $.1^201>, <4, $.1^10>, <$.1^19, $.1^188>, <$.1^204, $.1^70>, <$.1^301, $.1^147>, <$.1^56, $.1^311>, <$.1^101, $.1^210>, <$.1^311, $.1^210>, <$.1^238, $.1^229>, <$.1^41, $.1^41>, <$.1^63, $.1^261>, <4, $.1^195>, <$.1^219, $.1^303>, <$.1^144, $.1^339>, <$.1^329, $.1^43>, <$.1^319, $.1^154>, <3, $.1^150>, <$.1^56, $.1^78>, <$.1^237, $.1^327>, <$.1^134, $.1^262>, <$.1^147, $.1^167>, <$.1^160, $.1^223>, <$.1^284, $.1^329>, <$.1^302, $.1^273>, <$.1^239, $.1^140>, <$.1^196, $.1^42>, <$.1^8, $.1^262>, <$.1^250, $.1^318>, <$.1^294, $.1^11>, <$.1^149, $.1^40>, <$.1^22, $.1^119>, <$.1^339, $.1^308>, <$.1^238, $.1^126>, <$.1^48, $.1^197>, <$.1^328, $.1^32>, <$.1^32, $.1^273>, <$.1^97, $.1^205>, <$.1^184, $.1^174>, <$.1^42, $.1^112>, <$.1^176, $.1^251>, <$.1^133, $.1^82>, <$.1^53, $.1^202>, <$.1^135, $.1^167>, <$.1^218, $.1^86>, <$.1^311, $.1^89>, <$.1^87, $.1^28>, <$.1^187, $.1^21>, <$.1^98, $.1^111>, <$.1^104, $.1^214>, <$.1^102, $.1^131>, <$.1^319, $.1^3>, <$.1^314, $.1^246>, <$.1^42, $.1^275>, <$.1^27, $.1^196>, <$.1^267, $.1^168>, <$.1^249, $.1^168>, <$.1^81, $.1^117>, <$.1^291, $.1^271>, <$.1^72, $.1^197>, <$.1^293, $.1^43>, <$.1^297, $.1^135>, <$.1^26, $.1^151>, <$.1^289, $.1^52>, <$.1^239, $.1^295>, <$.1^268, $.1^277>, <$.1^319, $.1^232>, <$.1^122, $.1^226>, <$.1^93, $.1^178>, <$.1^212, $.1^204>, <$.1^82, $.1^244>, <$.1^217, $.1^64>, <$.1^327, $.1^92>, <$.1^272, $.1^214>, <$.1^72, $.1^148>, <$.1^49, $.1^123>, <$.1^200, $.1^211>, <$.1^146, $.1^311>, <$.1^106, $.1^18>, <$.1^46, $.1^83>, <$.1^223, $.1^155>, <$.1^159, $.1^69>, <$.1^37, $.1^59>, <$.1^147, 2>, <$.1^240, $.1^49>, <$.1^294, $.1^338>, <$.1^294, $.1^215>, <$.1^3, $.1^319>, <$.1^177, $.1^172>, <$.1^277, 1>, <$.1^152, $.1^234>, <$.1^116, $.1^214>, <$.1^174, $.1^16>, <$.1^132, $.1^156>, <$.1^72, $.1^195>, <$.1^45, $.1^330>, <$.1^4, $.1^315>, <$.1^34, $.1^6>, <$.1^303, $.1^92>, <$.1^180, $.1^14>, <$.1^307, $.1^82>, <$.1^83, $.1^20>, <0, $.1^300>, <$.1^273, $.1^319>, <$.1^241, $.1^256>, <$.1^29, $.1^9>, <$.1^331, $.1^147>, <$.1^72, $.1^199>, <$.1^180, $.1^77>, <$.1^293, $.1^63>, <$.1^19, $.1^73>, <1, $.1^175>, <$.1^20, $.1^184>, <$.1^303, $.1^28>, <$.1^31, $.1^216>, <$.1^198, $.1^25>, <$.1^209, $.1^334>, <$.1^47, $.1^334>, <$.1^277, $.1^188>, <$.1^85, $.1^332>, <$.1^281, $.1^292>, <$.1^276, $.1^215>, <$.1^212, $.1^245>, <$.1^187, $.1^22>, <$.1^264, $.1^159>, <$.1^184, $.1^101>, <$.1^91, $.1^256>, <$.1^304, $.1^83>, <$.1^183, $.1^117>, <$.1^14, $.1^311>, <$.1^98, $.1^212>, <$.1^222, $.1^146>, <$.1^174, $.1^100>, <$.1^12, $.1^37>, <$.1^274, $.1^81>, <$.1^80, $.1^93>, <$.1^81, $.1^62>, <$.1^313, $.1^59>, <$.1^200, $.1^309>, <$.1^150, $.1^339>, <$.1^277, $.1^71>, <$.1^64, $.1^6>, <$.1^31, $.1^21>, <$.1^150, $.1^314>, <$.1^262, $.1^294>, <$.1^25, $.1^252>, <$.1^339, $.1^248>, <$.1^8, $.1^12>, <$.1^36, $.1^199>, <$.1^222, $.1^233>, <$.1^108, $.1^120>, <$.1^289, $.1^216>, <$.1^194, $.1^60>, <$.1^133, $.1^68>, <$.1^274, $.1^224>, <$.1^101, $.1^41>, <$.1^141, $.1^88>, <$.1^21, $.1^96>, <$.1^8, $.1^5>, <$.1^109, $.1^169>, <$.1^247, $.1^71>, <$.1^126, $.1^321>, <$.1^159, $.1^24>, <$.1^279, $.1^135>, <$.1^104, $.1^191>, <$.1^284, $.1^262>, <$.1^267, $.1^150>, <$.1^204, $.1^233>, <$.1^300, $.1^199>, <$.1^294, $.1^240>, <$.1^131, $.1^33>, <$.1^181, $.1^21>, <$.1^53, $.1^55>, <$.1^91, $.1^254>, <$.1^221, $.1^99>, <$.1^117, $.1^62>, <$.1^32, $.1^79>, <$.1^258, $.1^137>, <$.1^96, $.1>, <$.1^270, $.1^288>, <$.1^202, $.1^85>, <$.1^270, $.1^132>, <$.1^10, $.1^149>, <$.1^229, $.1^127>, <$.1^108, $.1^288>, <$.1^72, $.1^338>, <$.1^170, $.1^130>, <$.1^284, $.1^163>, <$.1^251, $.1^296>, <$.1^259, $.1^320>, <$.1^109, $.1^189>, <$.1^80, $.1^151>, <$.1^135, $.1^178>, <$.1^275, $.1^13>, <$.1^319, $.1^256>, <$.1^323, $.1^138>, <$.1^276, $.1^148>, <$.1^230, $.1^251>, <$.1^33, $.1^24>, <$.1^202, $.1^161>, <$.1^175, $.1^232>, <$.1^248, $.1^78>, <$.1^78, $.1^148>, <$.1^311, $.1^75>, <$.1^29, $.1^75>, <$.1^225, $.1^241>, <$.1^239, $.1^33>, <$.1^37, $.1^36>, <$.1^28, $.1^242>, <$.1^23, $.1^287>, <$.1^238, $.1^225>, <$.1^259, $.1^64>, <$.1^317, $.1^206>, <$.1^64, $.1^298>, <$.1^193, $.1^160>, <$.1^255, $.1^291>, <$.1^275, $.1^142>, <$.1^125, $.1^75>, <$.1^104, $.1^204>, <$.1^92, $.1^84>, <$.1^193, $.1^106>, <$.1^78, $.1^337>, <$.1^112, $.1^235>, <$.1^169, $.1^123>, <$.1^277, $.1^67>, <$.1^9, 2>, <$.1^173, $.1^334>, <$.1^110, $.1^245>, <$.1^18, $.1^2>, <$.1^23, $.1^118>, <$.1^103, $.1^232>, <$.1^106, $.1^32>, <$.1^53, $.1^210>, <$.1^71, $.1^9>, <$.1^189, $.1^271>, <$.1^151, $.1^324>, <$.1^304, $.1^253>, <$.1^257, $.1^41>, <$.1^174, $.1^321>, <$.1^330, $.1^100>, <$.1^104, $.1^262>, <$.1^51, $.1^327>, <$.1^186, $.1^240>, <$.1^208, $.1^239>, <$.1^249, $.1^308>, <$.1^253, $.1^169>, <$.1^147, $.1^248>, <$.1^8, $.1^124>, <$.1^181, $.1^82>, <$.1^20, $.1^124>, <$.1^73, $.1^59>, <$.1^88, $.1^198>, <$.1^150, $.1^70>, <$.1^289, $.1^213>, <$.1^325, $.1^169>, <$.1^209, $.1^264>, <$.1^295, $.1^134>, <$.1^11, $.1^41>, <$.1^209, $.1^158>, <$.1^99, $.1^104>, <$.1^277, $.1^54>, <$.1^204, $.1^25>, <$.1^12, $.1^7>, <$.1^203, $.1^299>, <$.1^172, $.1^223>, <$.1^325, $.1^22>, <$.1^47, $.1^80>, <$.1^203, $.1^250>, <$.1^275, $.1^218>, <$.1^46, $.1^229>, <$.1^9, $.1^24>, <$.1^292, $.1^81>, <$.1^329, $.1^140>, <$.1^115, $.1^67>, <$.1^224, $.1^12>, <2, $.1^120>, <6, 2>, <$.1^317, $.1^250>, <$.1^338, $.1^246>, <$.1^132, $.1>, <$.1^326, $.1^151>, <$.1^247, $.1^254>, <$.1^208, $.1^207>, <$.1^221, $.1^310>, <$.1^173, $.1^183>, <$.1^206, $.1^128>, <$.1^238, $.1^230>, <$.1^36, $.1^2>, <$.1^50, $.1^116>, <$.1^47, $.1^20>, <$.1^50, $.1^329>, <$.1^58, $.1^305>, <$.1^2, $.1^273>, <$.1^39, $.1^28>, <6, $.1^187>, <$.1^306, $.1^159>, <$.1^333, $.1^24>, <$.1^323, $.1^301>, <$.1^157, $.1^177>, <$.1^34, $.1^244>, <$.1^50, $.1^79>, <$.1^212, $.1^184>, <$.1^132, $.1^137>, <$.1^310, $.1^207>, <$.1^180, $.1^146>, <$.1^336, $.1^137>, <$.1^239, $.1^299>, <$.1^338, $.1^110>, <$.1^18, $.1^131>, <$.1^147, $.1^291>, <2, $.1^14>, <$.1^214, $.1^235>, <$.1^53, $.1^287>, <$.1^167, $.1^33>, <$.1^321, $.1^24>, <$.1^206, $.1^84>, <$.1^162, $.1^267>, <$.1^161, $.1^299>, <$.1^34, $.1^230>, <$.1^92, $.1^201>, <$.1^312, $.1^263>, <$.1^239, $.1^218>, <$.1^155, $.1^206>, <$.1^220, $.1^153>, <$.1^102, $.1^137>, <$.1^128, $.1^246>, <$.1^271, $.1^320>, <$.1^288, $.1^49>, <$.1^179, $.1^264>, <$.1^39, $.1^44>, <$.1^217, $.1^232>, <$.1^202, $.1^81>, <$.1^146, $.1^273>, <$.1^297, 2>, <$.1^164, $.1^251>, <$.1^212, $.1^110>, <$.1^268, $.1^224>, <$.1^182, $.1^204>, <$.1^309, $.1^92>, <$.1^134, $.1^184>, <$.1^184, $.1^328>, <$.1^74, $.1^115>, <$.1^25, $.1^144>, <$.1^220, $.1^331>, <$.1^248, $.1^214>, <$.1^75, $.1^178>, <$.1^58, $.1^340>, <$.1^216, $.1^314>, <$.1^47, $.1^30>, <$.1^38, $.1^204>, <$.1^32, $.1^245>, <$.1^290, $.1^313>, <$.1^216, $.1^11>, <$.1^81, $.1^150>, <$.1^219, $.1^261>, <$.1^291, $.1^274>, <$.1^230, $.1^245>, <$.1^84, $.1^87>, <$.1^154, $.1^18>, <$.1^226, $.1^230>, <$.1^190, $.1^223>, <$.1^25, $.1^213>, <2, $.1^10>, <$.1^12, $.1^159>, <$.1^280, $.1^294>, <$.1^101, $.1^91>, <$.1^47, $.1^255>, <$.1^28, $.1^305>, <$.1^58, $.1^101>, <$.1^220, $.1^253>, <$.1^196, $.1^23>, <$.1^43, $.1^290>, <$.1^21, $.1^241>, <$.1^182, $.1^191>, <$.1^324, $.1^159>, <$.1^47, $.1^287>, <$.1^226, $.1^253>, <$.1^174, $.1^77>, <$.1^148, $.1^174>, <6, $.1^283>, <$.1^78, $.1^146>, <$.1^339, $.1^268>, <$.1^240, $.1^288>, <4, $.1^312>, <$.1^84, $.1^195>, <$.1^117, $.1^327>, <$.1^158, $.1^111>, <$.1^28, $.1^277>, <$.1^16, $.1^225>, <$.1^322, $.1^253>, <5, $.1^135>, <$.1^320, $.1^47>, <$.1^191, $.1^250>, <$.1^282, $.1^156>, <$.1, $.1^189>, <$.1^140, $.1^270>, <$.1^161, $.1^287>, <$.1^100, $.1^326>, <$.1^139, $.1^82>, <$.1^337, $.1^324>, <$.1^13, $.1^73>, <$.1^254, $.1^128>, <$.1^170, $.1^212>, <$.1^319, $.1^189>, <$.1^338, $.1^115>, <$.1^336, $.1^49>, <$.1^73, $.1^3>, <$.1^130, $.1^45>, <$.1^289, $.1^160>, <$.1^260, $.1^12>, <$.1^59, $.1^249>, <$.1^317, $.1^91>, <$.1^173, $.1^287>, <$.1^320, $.1^60>, <$.1^18, $.1^337>, <$.1^251, $.1^255>, <$.1^289, $.1^22>, <$.1^123, $.1^291>, <$.1^258, $.1^146>, <$.1^187, $.1^147>, <$.1^87, $.1^269>, <$.1^73, $.1^290>, <$.1^184, $.1^145>, <$.1^96, $.1^240>, <$.1^25, $.1^324>, <$.1^48, $.1^37>, <$.1^272, $.1^226>, <$.1^321, $.1^44>, <$.1^102, $.1^132>, <$.1^331, $.1^205>, <$.1^198, $.1^307>, <$.1^45, $.1^24>, <$.1^51, $.1^269>, <$.1^59, $.1^13>, <$.1^9, $.1^258>, <$.1^110, $.1^329>, <$.1^186, 5>, <$.1^22, $.1^85>, <$.1^126, $.1>, <$.1^198, $.1^14>, <$.1^224, $.1^226>, <$.1^299, $.1^250>, <$.1^27, $.1^117>, <$.1^253, $.1^36>, <$.1^235, $.1^27>, <$.1^124, $.1^225>, <$.1^160, $.1^81>, <$.1^277, $.1^123>, <$.1^49, $.1^21>, <$.1^293, $.1^80>, <$.1^52, $.1^200>, <$.1^277, $.1^194>, <$.1^84, $.1^90>, <$.1^303, $.1^302>, <$.1^187, $.1^3>, <$.1^186, $.1^132>, <$.1^151, $.1^316>, <$.1^119, $.1^46>, <$.1^238, $.1^326>, <$.1^142, $.1^326>, <$.1^157, $.1^320>, <$.1^279, $.1^308>, <$.1^270, $.1>, <$.1^290, $.1^47>, <$.1^74, $.1^110>, <$.1^9, $.1^268>, <$.1^111, $.1^319>, <$.1^218, $.1^139>, <$.1^275, $.1^41>, <$.1^78, $.1^156>, <$.1^240, $.1^337>, <$.1^216, $.1>, <$.1^273, $.1^4>, <$.1^211, $.1^134>, <$.1^143, $.1^99>, <$.1^61, $.1^123>, <$.1^276, $.1^16>, <$.1^129, $.1^241>, <$.1^7, $.1^68>, <$.1^256, $.1^174>, <$.1^31, $.1^203>, <$.1^254, $.1^217>, <$.1^39, 2>, <$.1^212, $.1^151>, <$.1^19, $.1^106>, <$.1^164, $.1^93>, <$.1^339, $.1^258>, <$.1^156, $.1^131>, <$.1^13, $.1^68>, <$.1^204, $.1^10>, <$.1^288, $.1^337>, <$.1^266, $.1^78>, <$.1^332, $.1^163>, <$.1^335, $.1^287>, <$.1^195, $ ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host aula-b-siee93.uab.es. (158.109.66.93) Time: Mon Mar 15 06:14:42 2004 Input: olav:=function(q,r) expt:=[q^(r-n): n in [1..r]]; P:=PolynomialRing(Integers()); t:=0; for i in expt do t:=t + x^i; end for; n:=x^&+(expt); olav:={: a,b in GF(q^r) | Evaluate(n,a) eq Evaluate(t,b)}; return olav; end function; q:=7; r:=3; #(olav(q,r)); q^(2*r-1); Output: Magma V2.10-6 Mon Mar 15 2004 06:14:35 on modular [Seed = 1635037513] ------------------------------------- 16807 16807 Total time: 6.879 seconds, Total memory usage: 2.98MB ************** MAGMA ***************** Host aula-b-siee93.uab.es. (158.109.66.93) Time: Mon Mar 15 06:14:53 2004 Input: olav:=function(q,r) expt:=[q^(r-n): n in [1..r]]; P:=PolynomialRing(Integers()); t:=0; for i in expt do t:=t + x^i; end for; n:=x^&+(expt); olav:={: a,b in GF(q^r) | Evaluate(n,a) eq Evaluate(t,b)}; return olav; end function; q:=5; r:=2; #(olav(q,r)); q^(2*r-1); Output: Magma V2.10-6 Mon Mar 15 2004 06:14:50 on modular [Seed = 1753069681] ------------------------------------- 125 125 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee93.uab.es. (158.109.66.93) Time: Mon Mar 15 06:15:58 2004 Input: olav:=function(q,r) expt:=[q^(r-n): n in [1..r]]; P:=PolynomialRing(Integers()); t:=0; for i in expt do t:=t + x^i; end for; n:=x^&+(expt); olav:={: a,b in GF(q^r) | Evaluate(n,a) eq Evaluate(t,b)}; return olav; end function; q:=4; r:=3; #(olav(q,r)); q^(2*r-1); Output: Magma V2.10-6 Mon Mar 15 2004 06:15:55 on modular [Seed = 1481476096] ------------------------------------- 1024 1024 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee93.uab.es. (158.109.66.93) Time: Mon Mar 15 06:17:36 2004 Input: olav:=function(q,r) expt:=[q^(r-n): n in [1..r]]; P:=PolynomialRing(Integers()); t:=0; for i in expt do t:=t + x^i; end for; n:=x^&+(expt); olav:={: a,b in GF(q^r) | Evaluate(n,a) eq Evaluate(t,b)}; return olav; end function; q:=4; r:=3; olis:=olav(q,r); olis[1]; Output: Magma V2.10-6 Mon Mar 15 2004 06:17:33 on modular [Seed = 1196595129] ------------------------------------- >> olis[1]; ^ Runtime error in '[]': Bad argument types Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee93.uab.es. (158.109.66.93) Time: Mon Mar 15 06:17:52 2004 Input: olav:=function(q,r) expt:=[q^(r-n): n in [1..r]]; P:=PolynomialRing(Integers()); t:=0; for i in expt do t:=t + x^i; end for; n:=x^&+(expt); olav:={: a,b in GF(q^r) | Evaluate(n,a) eq Evaluate(t,b)}; return olav; end function; q:=4; r:=3; olis:=olav(q,r); olis(1); Output: Magma V2.10-6 Mon Mar 15 2004 06:17:49 on modular [Seed = 1314627232] ------------------------------------- >> olis(1); ^ Runtime error: Bad argument types Argument types given: RngIntElt, SetEnum[Tup] Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee93.uab.es. (158.109.66.93) Time: Mon Mar 15 06:18:04 2004 Input: olav:=function(q,r) expt:=[q^(r-n): n in [1..r]]; P:=PolynomialRing(Integers()); t:=0; for i in expt do t:=t + x^i; end for; n:=x^&+(expt); olav:={: a,b in GF(q^r) | Evaluate(n,a) eq Evaluate(t,b)}; return olav; end function; q:=4; r:=3; olis:=olav(q,r); olis; Output: Magma V2.10-6 Mon Mar 15 2004 06:18:01 on modular [Seed = 3047187823] ------------------------------------- { <$.1^13, $.1^48>, <$.1^21, $.1^4>, <$.1^17, $.1^58>, <$.1^37, $.1^21>, <$.1^3, $.1^16>, <$.1^25, $.1^22>, <$.1^52, $.1^41>, <$.1^24, $.1>, <$.1^59, $.1^52>, <$.1^38, $.1^58>, <$.1^10, $.1^53>, <$.1^11, $.1^42>, <$.1^48, 1>, <$.1^43, $.1^61>, <$.1^52, $.1^22>, <$.1^61, $.1^22>, <$.1^18, 1>, <$.1^56, $.1^58>, <$.1^53, $.1^44>, <$.1^10, $.1^22>, <$.1^4, $.1^22>, <$.1^40, $.1^48>, <$.1^49, $.1^22>, <$.1^28, $.1^25>, <$.1^60, $.1^10>, <$.1^29, $.1^43>, <$.1^11, $.1^47>, <$.1^10, $.1^48>, <$.1^3, $.1^45>, <$.1^46, $.1^38>, <$.1^10, $.1^3>, <$.1, $.1^25>, <$.1^20, $.1^59>, <$.1^38, $.1^44>, <$.1^36, $.1^8>, <$.1^61, $.1^3>, <$.1^2, $.1^44>, <$.1^14, $.1^46>, <$.1^12, $.1^32>, <$.1^14, $.1^11>, <$.1^2, $.1^11>, <$.1^19, $.1^21>, <$.1^52, $.1^55>, <$.1^34, $.1^41>, <$.1^42, $.1>, <$.1^33, $.1^4>, <$.1^35, $.1^33>, <$.1^33, $.1^32>, <$.1^51, $.1^32>, <$.1^9, $.1^40>, <$.1^12, $.1^10>, <$.1^5, $.1^59>, <$.1^58, $.1^3>, <0, $.1^7>, <$.1^59, $.1^43>, <$.1^49, $.1^31>, <$.1^19, $.1^53>, <1, $.1^2>, <$.1^58, $.1^31>, <$.1^45, $.1^10>, <$.1^24, $.1^2>, <$.1^50, $.1^19>, <$.1^8, $.1^42>, <$.1^50, $.1^43>, <$.1^10, $.1^38>, <$.1^54, $.1^45>, <$.1^30, $.1^20>, <$.1^55, $.1^29>, <$.1^47, $.1^47>, <$.1^44, $.1^33>, <$.1^3, $.1^17>, <$.1^41, $.1^44>, <$.1^3, $.1>, <$.1^13, $.1^22>, <$.1^34, $.1^53>, <$.1^62, $.1^13>, <$.1^42, 1>, <$.1^24, $.1^54>, <$.1^24, $.1^40>, <$.1^8, $.1^59>, <$.1^44, $.1^43>, <$.1^29, $.1^46>, <$.1^31, $.1^61>, <$.1^49, $.1^29>, <$.1^58, $.1^23>, <$.1^15, $.1^2>, <$.1^22, $.1^21>, <$.1^23, $.1^52>, <$.1^39, $.1^4>, <$.1^32, $.1^44>, <$.1^54, $.1^16>, <$.1^19, $.1^26>, <$.1^52, $.1^31>, <$.1^9, $.1^32>, <$.1^8, $.1^58>, <$.1^47, $.1^59>, <$.1^2, $.1^62>, <$.1^26, $.1^43>, <$.1^61, $.1^12>, <1, $.1^40>, <$.1^28, $.1^26>, <$.1^4, $.1^41>, <$.1^36, $.1^10>, <$.1, $.1^21>, <$.1^22, $.1^26>, <$.1^28, $.1^3>, <$.1^26, $.1^19>, <$.1^7, $.1^22>, <$.1^29, $.1^62>, <$.1^42, $.1^4>, <$.1^29, $.1^19>, <$.1^52, $.1^12>, <$.1^7, $.1^12>, <$.1^11, $.1^44>, <$.1^49, $.1^3>, <$.1^54, $.1^34>, <$.1^47, $.1^50>, <$.1^39, 1>, <$.1^13, $.1^25>, <$.1^40, $.1^26>, <$.1^20, $.1^62>, <$.1^10, $.1^29>, <$.1^4, $.1^25>, <$.1^4, $.1^3>, <$.1^58, $.1^12>, <$.1^58, $.1^55>, <$.1^61, $.1^26>, <$.1^41, $.1^6>, <$.1^55, $.1^38>, <$.1^16, $.1^21>, <$.1^36, $.1^34>, <$.1^4, $.1^37>, <$.1^32, $.1^46>, <$.1, $.1^37>, <$.1^42, $.1^32>, <1, $.1^10>, <$.1^58, $.1^61>, <$.1^60, $.1^27>, <$.1^12, $.1^2>, <$.1^49, $.1^25>, <$.1^45, $.1^8>, <$.1^43, $.1^29>, <$.1^62, $.1^33>, <$.1^32, $.1^19>, <$.1^17, $.1^50>, <$.1^44, $.1^6>, <$.1^40, $.1^22>, <$.1^8, $.1^50>, <$.1^44, $.1^46>, <$.1^41, $.1^13>, <$.1^31, $.1^3>, <$.1^13, $.1^41>, <$.1^27, 1>, <$.1^37, $.1^12>, <$.1^62, $.1^46>, <$.1^11, $.1^50>, <$.1^29, $.1^6>, <$.1^50, $.1^59>, <$.1^21, $.1^16>, <$.1^39, $.1^40>, <$.1^14, $.1^33>, <$.1^32, $.1^42>, <$.1^36, $.1^17>, <$.1^43, $.1^21>, <$.1^46, $.1^25>, <$.1^56, $.1^46>, <$.1^11, $.1^24>, <$.1^5, $.1^24>, <$.1^37, $.1^3>, <$.1^40, $.1^61>, <$.1^27, $.1^2>, <$.1^62, $.1^50>, <$.1^24, $.1^17>, <1, $.1^8>, <$.1^47, $.1^42>, <$.1^10, $.1^23>, <$.1^4, $.1^23>, <$.1^38, $.1^52>, <$.1^35, $.1^59>, <$.1^56, $.1^47>, <$.1^27, $.1^8>, <$.1^45, $.1^27>, <$.1^58, $.1^21>, <$.1^13, $.1^61>, <$.1^23, $.1^13>, <$.1^20, $.1^46>, <$.1^19, $.1^48>, <$.1^42, $.1^5>, <$.1^6, $.1^4>, <$.1^2, $.1^19>, <$.1^43, $.1^23>, <$.1^61, $.1^53>, <$.1^35, $.1^50>, <$.1^50, $.1^44>, <$.1^3, $.1^8>, <$.1^21, 1>, <$.1^27, $.1^40>, <$.1^16, $.1^25>, <$.1^3, $.1^4>, <$.1^9, $.1^2>, <0, $.1^35>, <$.1^27, $.1>, <$.1^43, $.1^26>, <$.1^9, $.1>, <$.1^46, $.1^3>, <$.1^46, $.1^26>, <$.1^53, $.1^62>, <$.1^51, $.1^8>, <$.1^39, $.1^17>, <$.1^46, $.1^55>, <$.1^47, $.1^6>, <$.1^62, $.1^11>, <$.1^16, $.1^26>, <$.1^46, $.1^22>, <$.1^59, $.1^19>, <$.1^8, $.1^62>, <$.1^5, $.1^19>, <$.1^29, $.1^50>, <$.1^20, $.1^43>, <$.1^55, $.1^61>, <$.1^24, $.1^27>, <$.1^3, $.1^2>, <$.1^8, $.1^13>, <$.1^49, $.1^26>, <$.1^45, $.1>, <$.1^42, $.1^16>, <$.1^9, 1>, <$.1^25, $.1^38>, <$.1^22, $.1^12>, <$.1^54, $.1^5>, <$.1^56, $.1^44>, <$.1^59, $.1^24>, <$.1^42, $.1^2>, <$.1^43, $.1^22>, <$.1^55, $.1^53>, <$.1^25, $.1^3>, <$.1^31, $.1^31>, <$.1^25, $.1^31>, <$.1^13, $.1^12>, <$.1^58, $.1^48>, <$.1^8, $.1^24>, <$.1^45, $.1^16>, <$.1^50, $.1^11>, <$.1^23, $.1^62>, <$.1^40, $.1^53>, <$.1^16, $.1^37>, <$.1^28, $.1^38>, <$.1^28, $.1^61>, <$.1^24, $.1^34>, <$.1^42, $.1^54>, <$.1^25, $.1^12>, <$.1^18, $.1^10>, <$.1^15, $.1^45>, <$.1^32, $.1^11>, <$.1^59, $.1^42>, <$.1^22, $.1^37>, <$.1^18, $.1^2>, <$.1^60, $.1^5>, <$.1^43, $.1^53>, <$.1^7, $.1^29>, <$.1^46, $.1^29>, <$.1^25, $.1^61>, <$.1^46, $.1^41>, <$.1^50, $.1^46>, <$.1^20, $.1^19>, <$.1^60, $.1>, <$.1^49, $.1^21>, <$.1^51, $.1^54>, <$.1^25, $.1^26>, <$.1^46, $.1^61>, <$.1^43, $.1^48>, <$.1^19, $.1^12>, <$.1^51, $.1^5>, <$.1^50, $.1^50>, <$.1^9, $.1^16>, <$.1^32, $.1^24>, <$.1^15, $.1^16>, <$.1^7, $.1^37>, <$.1^24, $.1^4>, <$.1^21, $.1^5>, <$.1, $.1^48>, <$.1^36, $.1^20>, <$.1^46, $.1^23>, <$.1^23, $.1^46>, <$.1^14, $.1^59>, <$.1^2, $.1^59>, <$.1^44, $.1^52>, <$.1^7, $.1^61>, <$.1, $.1^31>, <$.1^20, $.1^52>, <$.1^42, $.1^10>, <$.1^6, $.1^34>, <$.1^21, $.1^20>, <$.1^7, $.1^25>, <$.1^57, $.1^34>, <$.1^44, $.1^47>, <$.1^41, $.1^47>, <$.1^56, $.1^43>, <$.1^26, $.1^42>, <$.1^29, $.1^11>, <$.1^37, $.1^22>, <$.1^13, $.1^38>, <$.1^35, $.1^43>, <$.1^39, $.1^34>, <$.1^13, $.1^3>, <$.1^30, $.1^54>, <$.1^30, $.1^27>, <$.1^7, $.1^48>, <$.1^61, $.1^21>, <$.1^16, $.1^38>, <$.1^38, $.1^19>, <$.1^51, $.1>, <$.1^61, $.1^25>, <$.1, $.1^38>, <$.1^45, $.1^54>, <$.1^13, $.1^53>, <$.1^39, $.1^5>, <$.1^40, $.1^55>, <0, $.1^14>, <$.1^53, $.1^11>, <$.1^27, $.1^54>, <$.1^55, $.1^21>, <$.1^4, $.1^31>, <$.1^10, $.1^31>, <$.1^25, $.1^37>, <$.1^61, $.1^55>, <$.1^17, $.1^33>, <$.1^48, $.1^2>, <$.1^38, $.1^50>, <$.1, $.1^23>, <$.1^19, $.1^3>, <$.1^54, $.1^20>, <$.1^5, $.1^13>, <$.1^36, $.1^45>, <$.1^33, $.1^2>, <$.1^22, $.1^3>, <$.1^3, $.1^40>, <$.1^52, $.1^29>, <$.1^34, $.1^3>, <$.1^60, $.1^8>, <$.1^40, $.1^25>, <$.1^33, $.1^17>, <$.1^9, $.1^20>, <$.1^41, $.1^52>, <$.1^27, $.1^17>, <$.1^33, $.1^16>, <$.1^26, $.1^58>, <$.1^56, $.1^59>, <$.1^24, $.1^45>, <$.1^11, $.1^11>, <$.1^29, $.1^13>, <$.1^35, $.1^44>, <$.1^40, $.1^3>, <1, $.1^5>, <$.1^55, $.1^23>, <$.1^5, $.1^33>, <$.1^51, $.1^10>, <$.1^21, $.1>, <$.1^39, $.1^10>, <$.1^54, $.1^17>, <$.1^58, $.1^37>, <1, $.1>, <$.1^55, $.1^37>, <$.1^56, $.1^50>, <1, $.1^16>, <$.1^15, $.1^5>, <$.1^3, $.1^32>, <$.1^52, $.1^21>, <$.1^60, $.1^32>, <$.1^51, $.1^2>, <$.1^33, $.1^5>, <$.1^3, $.1^54>, <$.1^62, $.1^19>, <$.1^20, $.1^13>, <$.1^36, $.1^54>, <$.1^10, $.1^61>, <$.1^35, $.1^52>, <$.1^9, $.1^34>, <$.1^37, $.1^55>, <$.1^6, $.1^27>, <$.1^23, $.1^50>, <$.1^22, $.1^23>, <$.1^57, $.1^17>, <$.1^30, $.1^4>, <$.1^46, $.1^12>, <$.1^9, $.1^54>, <$.1^17, $.1^6>, <$.1^49, $.1^38>, <$.1, $.1^3>, <$.1^16, $.1^12>, <$.1^61, $.1^61>, <$.1^3, $.1^10>, <$.1^55, $.1^26>, <$.1^16, $.1^48>, <$.1^27, $.1^32>, <$.1^8, $.1^47>, <$.1^50, $.1^58>, <$.1^29, $.1^42>, <$.1^51, $.1^27>, <$.1^56, $.1^42>, <$.1^51, $.1^40>, <$.1^18, $.1^5>, <$.1^41, $.1^33>, <$.1^9, $.1^8>, <$.1^48, $.1^45>, <$.1^59, $.1^58>, <$.1^54, $.1^32>, <$.1^22, $.1^55>, <$.1^13, $.1^23>, <$.1^18, $.1^34>, <$.1^23, $.1^33>, <$.1^54, $.1>, <$.1^52, $.1^53>, <$.1^54, $.1^54>, <$.1^19, $.1^25>, <$.1^17, $.1^43>, <$.1^34, $.1^25>, <$.1^16, $.1^29>, <$.1^24, $.1^5>, <$.1^26, $.1^62>, <$.1^10, $.1^37>, <$.1^11, $.1^58>, <$.1^12, $.1^4>, <$.1^57, $.1^45>, <$.1^19, $.1^31>, <$.1^22, $.1^53>, <$.1^35, $.1^58>, <$.1^34, $.1^61>, <$.1^30, $.1^8>, <$.1^41, $.1^58>, <$.1^12, $.1^34>, <$.1^16, $.1^55>, <$.1^16, $.1^53>, <$.1^55, $.1^48>, <0, 0>, <$.1^40, $.1^31>, <$.1^3, 1>, <$.1^38, $.1^24>, <$.1^23, $.1^19>, <$.1^35, $.1^13>, <$.1^47, $.1^46>, <$.1^44, $.1^59>, <$.1^50, $.1^6>, <$.1^2, $.1^24>, <$.1^30, $.1^5>, <$.1^21, $.1^40>, <$.1^39, $.1>, <$.1^55, $.1^41>, <$.1^18, $.1>, <$.1^43, $.1^25>, <$.1^12, $.1^54>, <$.1^45, $.1^5>, <$.1^11, $.1^52>, <$.1^15, $.1>, <$.1^39, $.1^45>, <$.1^37, $.1^53>, <$.1^3, $.1^34>, <$.1^14, $.1^62>, <$.1^45, $.1^45>, <$.1^57, $.1^4>, <$.1^35, $.1^46>, <$.1^39, $.1^16>, <$.1^57, $.1^40>, <$.1^51, $.1^16>, <$.1^27, $.1^4>, <$.1^39, $.1^54>, <$.1^5, $.1^46>, <$.1^41, $.1^19>, <0, $.1^15>, <$.1^7, $.1^38>, <$.1^17, $.1^19>, <$.1^54, $.1^27>, <$.1^12, 1>, <$.1^34, $.1^26>, <$.1^15, $.1^34>, <$.1^56, $.1^33>, <$.1^3, $.1^20>, <$.1^62, $.1^58>, <$.1^9, $.1^5>, <$.1^46, $.1^31>, <$.1^16, $.1^22>, <0, $.1^57>, <$.1^28, $.1^41>, <1, $.1^27>, <$.1^33, 1>, <$.1^57, $.1^5>, <$.1^38, $.1^42>, <$.1^5, $.1^58>, <$.1^34, $.1^48>, <$.1, $.1^55>, <$.1^60, $.1^45>, <$.1^43, $.1^37>, <$.1^48, $.1^16>, <$.1^26, $.1^50>, <$.1^37, $.1^26>, <$.1^18, $.1^32>, <$.1^9, $.1^45>, <$.1^45, 1>, <$.1^59, $.1^50>, <$.1^40, $.1^21>, <$.1^51, $.1^34>, <1, $.1^45>, <$.1^28, $.1^12>, <$.1^56, $.1^62>, <$.1^8, $.1^43>, <$.1^36, $.1^2>, <$.1^55, $.1^25>, <$.1^51, $.1^4>, <$.1^16, $.1^61>, <$.1^12, $.1^20>, <$.1^6, $.1^2>, <$.1^32, $.1^50>, <$.1^22, $.1^41>, <$.1^62, $.1^43>, <$.1^48, $.1^5>, <$.1^59, $.1^13>, <$.1^46, $.1^21>, <$.1^37, $.1^25>, <$.1^57, $.1^10>, <$.1^39, $.1^8>, <$.1^34, $.1^37>, <$.1^60, $.1^54>, <$.1^57, $.1^27>, <$.1^52, $.1^37>, <$.1^59, $.1^62>, <$.1^54, $.1^4>, <$.1^28, $.1^21>, <$.1^53, $.1^13>, <$.1^26, $.1^11>, <$.1^46, $.1^37>, <$.1^18, $.1^20>, <$.1^30, $.1^17>, <$.1^31, $.1^41>, <$.1^7, $.1^3>, <$.1^35, $.1^6>, <$.1^25, $.1^23>, <$.1^34, $.1^31>, <$.1^19, $.1^23>, <$.1^59, $.1^44>, <$.1^32, $.1^58>, <$.1^58, $.1^53>, <$.1^24, $.1^10>, <$.1^11, $.1^19>, <$.1^10, $.1^12>, <$.1^49, $.1^41>, <$.1^4, $.1^55>, <$.1^13, $.1^26>, <$.1^26, $.1^44>, <1, $.1^34>, <$.1^30, $.1^2>, <$.1^23, $.1^6>, <$.1^56, $.1^6>, <$.1^38, $.1^6>, <$.1^41, $.1^46>, <$.1^20, $.1^47>, <$.1^25, $.1^21>, <$.1^19, $.1^29>, <$.1^55, $.1^31>, <$.1^15, $.1^27>, <$.1^18, $.1^27>, <$.1^14, $.1^19>, <$.1^6, $.1^20>, <$.1^60, $.1^17>, <$.1^50 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host aula-b-siee93.uab.es. (158.109.66.93) Time: Mon Mar 15 06:18:23 2004 Input: olav:=function(q,r) expt:=[q^(r-n): n in [1..r]]; P:=PolynomialRing(Integers()); t:=0; for i in expt do t:=t + x^i; end for; n:=x^&+(expt); olav:={: a,b in GF(q^r) | Evaluate(n,a) eq Evaluate(t,b)}; return olav; end function; q:=4; r:=3; olis:=olav(q,r); olis{1}; Output: Magma V2.10-6 Mon Mar 15 2004 06:18:20 on modular [Seed = 3165219955] ------------------------------------- >> olis{1}; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee93.uab.es. (158.109.66.93) Time: Mon Mar 15 06:21:25 2004 Input: olav:=function(q,r) expt:=[q^(r-n): n in [1..r]]; P:=PolynomialRing(Integers()); t:=0; for i in expt do t:=t + x^i; end for; n:=x^&+(expt); olav:=[: a,b in GF(q^r) | Evaluate(n,a) eq Evaluate(t,b)]; return olav; end function; q:=4; r:=3; olis:=olav(q,r); olis[1]; Output: Magma V2.10-6 Mon Mar 15 2004 06:21:22 on modular [Seed = 2475049490] ------------------------------------- <1, 1> Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee93.uab.es. (158.109.66.93) Time: Mon Mar 15 06:22:59 2004 Input: olav:=function(q,r) expt:=[q^(r-n): n in [1..r]]; P:=PolynomialRing(Integers()); t:=0; for i in expt do t:=t + x^i; end for; n:=x^&+(expt); olav:=[: a,b in GF(q^r) | Evaluate(n,a) eq Evaluate(t,b)]; return olav; end function; q:=4; r:=3; olis:=olav(q,r); olisgf:={:a,b in GF(q) | in olis} Output: Magma V2.10-6 Mon Mar 15 2004 06:22:56 on modular [Seed = 2593081529] ------------------------------------- Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee93.uab.es. (158.109.66.93) Time: Mon Mar 15 06:23:14 2004 Input: olav:=function(q,r) expt:=[q^(r-n): n in [1..r]]; P:=PolynomialRing(Integers()); t:=0; for i in expt do t:=t + x^i; end for; n:=x^&+(expt); olav:=[: a,b in GF(q^r) | Evaluate(n,a) eq Evaluate(t,b)]; return olav; end function; q:=4; r:=3; olis:=olav(q,r); olisgf:={:a,b in GF(q) | in olis}; olisgf; Output: Magma V2.10-6 Mon Mar 15 2004 06:23:11 on modular [Seed = 2173981613] ------------------------------------- { <$.1^2, 1>, <$.1, 1>, <0, 0>, <1, 1> } Total time: 3.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee93.uab.es. (158.109.66.93) Time: Mon Mar 15 06:24:18 2004 Input: olav:=function(q,r) expt:=[q^(r-n): n in [1..r]]; P:=PolynomialRing(Integers()); t:=0; for i in expt do t:=t + x^i; end for; n:=x^&+(expt); olav:=[: a,b in GF(q^r) | Evaluate(n,a) eq Evaluate(t,b)]; return olav; end function; q:=5; r:=2; olis:=olav(q,r); olisgf:={:a,b in GF(q) | in olis} Output: Magma V2.10-6 Mon Mar 15 2004 06:24:15 on modular [Seed = 2292013796] ------------------------------------- Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee93.uab.es. (158.109.66.93) Time: Mon Mar 15 06:25:08 2004 Input: olav:=function(q,r) expt:=[q^(r-n): n in [1..r]]; P:=PolynomialRing(Integers()); t:=0; for i in expt do t:=t + x^i; end for; n:=x^&+(expt); olav:=[: a,b in GF(q^r) | Evaluate(n,a) eq Evaluate(t,b)]; return olav; end function; q:=5; r:=2; olis:=olav(q,r); olisgf:={:a,b in GF(q) | in olis}; print "Punts olav: ";olis; print "Punts olav en GF(q): ";olisgf; Output: Magma V2.10-6 Mon Mar 15 2004 06:25:05 on modular [Seed = 4226689369] ------------------------------------- Punts olav: [ <1, $.1>, <1, $.1^4>, <1, $.1^5>, <1, 3>, <1, $.1^20>, <$.1, 1>, <$.1, $.1^2>, <$.1, $.1^7>, <$.1, $.1^10>, <$.1, $.1^11>, <$.1^2, 2>, <$.1^2, $.1^8>, <$.1^2, $.1^13>, <$.1^2, $.1^16>, <$.1^2, $.1^17>, <$.1^3, 4>, <$.1^3, $.1^14>, <$.1^3, $.1^19>, <$.1^3, $.1^22>, <$.1^3, $.1^23>, <$.1^4, $.1>, <$.1^4, $.1^4>, <$.1^4, $.1^5>, <$.1^4, 3>, <$.1^4, $.1^20>, <$.1^5, 1>, <$.1^5, $.1^2>, <$.1^5, $.1^7>, <$.1^5, $.1^10>, <$.1^5, $.1^11>, <2, 2>, <2, $.1^8>, <2, $.1^13>, <2, $.1^16>, <2, $.1^17>, <$.1^7, 4>, <$.1^7, $.1^14>, <$.1^7, $.1^19>, <$.1^7, $.1^22>, <$.1^7, $.1^23>, <$.1^8, $.1>, <$.1^8, $.1^4>, <$.1^8, $.1^5>, <$.1^8, 3>, <$.1^8, $.1^20>, <$.1^9, 1>, <$.1^9, $.1^2>, <$.1^9, $.1^7>, <$.1^9, $.1^10>, <$.1^9, $.1^11>, <$.1^10, 2>, <$.1^10, $.1^8>, <$.1^10, $.1^13>, <$.1^10, $.1^16>, <$.1^10, $.1^17>, <$.1^11, 4>, <$.1^11, $.1^14>, <$.1^11, $.1^19>, <$.1^11, $.1^22>, <$.1^11, $.1^23>, <4, $.1>, <4, $.1^4>, <4, $.1^5>, <4, 3>, <4, $.1^20>, <$.1^13, 1>, <$.1^13, $.1^2>, <$.1^13, $.1^7>, <$.1^13, $.1^10>, <$.1^13, $.1^11>, <$.1^14, 2>, <$.1^14, $.1^8>, <$.1^14, $.1^13>, <$.1^14, $.1^16>, <$.1^14, $.1^17>, <$.1^15, 4>, <$.1^15, $.1^14>, <$.1^15, $.1^19>, <$.1^15, $.1^22>, <$.1^15, $.1^23>, <$.1^16, $.1>, <$.1^16, $.1^4>, <$.1^16, $.1^5>, <$.1^16, 3>, <$.1^16, $.1^20>, <$.1^17, 1>, <$.1^17, $.1^2>, <$.1^17, $.1^7>, <$.1^17, $.1^10>, <$.1^17, $.1^11>, <3, 2>, <3, $.1^8>, <3, $.1^13>, <3, $.1^16>, <3, $.1^17>, <$.1^19, 4>, <$.1^19, $.1^14>, <$.1^19, $.1^19>, <$.1^19, $.1^22>, <$.1^19, $.1^23>, <$.1^20, $.1>, <$.1^20, $.1^4>, <$.1^20, $.1^5>, <$.1^20, 3>, <$.1^20, $.1^20>, <$.1^21, 1>, <$.1^21, $.1^2>, <$.1^21, $.1^7>, <$.1^21, $.1^10>, <$.1^21, $.1^11>, <$.1^22, 2>, <$.1^22, $.1^8>, <$.1^22, $.1^13>, <$.1^22, $.1^16>, <$.1^22, $.1^17>, <$.1^23, 4>, <$.1^23, $.1^14>, <$.1^23, $.1^19>, <$.1^23, $.1^22>, <$.1^23, $.1^23>, <0, $.1^3>, <0, $.1^9>, <0, $.1^15>, <0, $.1^21>, <0, 0> ] Punts olav en GF(q): { <3, 2>, <1, 3>, <0, 0>, <2, 2>, <4, 3> } Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee93.uab.es. (158.109.66.93) Time: Mon Mar 15 06:25:31 2004 Input: olav:=function(q,r) expt:=[q^(r-n): n in [1..r]]; P:=PolynomialRing(Integers()); t:=0; for i in expt do t:=t + x^i; end for; n:=x^&+(expt); olav:=[: a,b in GF(q^r) | Evaluate(n,a) eq Evaluate(t,b)]; return olav; end function; q:=5; r:=2; olis:=olav(q,r); olisgf:={:a,b in GF(q) | in olis}; print "Punts olav: ";#(olis); print "Punts olav en GF(q): ";#(olisgf); Output: Magma V2.10-6 Mon Mar 15 2004 06:25:28 on modular [Seed = 3790877562] ------------------------------------- Punts olav: 125 Punts olav en GF(q): 5 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee93.uab.es. (158.109.66.93) Time: Mon Mar 15 06:25:50 2004 Input: olav:=function(q,r) expt:=[q^(r-n): n in [1..r]]; P:=PolynomialRing(Integers()); t:=0; for i in expt do t:=t + x^i; end for; n:=x^&+(expt); olav:=[: a,b in GF(q^r) | Evaluate(n,a) eq Evaluate(t,b)]; return olav; end function; q:=5; r:=3; olis:=olav(q,r); olisgf:={:a,b in GF(q) | in olis}; print "Punts olav: ";#(olis); print "Punts olav en GF(q): ";#(olisgf); Output: Magma V2.10-6 Mon Mar 15 2004 06:25:47 on modular [Seed = 3908909664] ------------------------------------- Punts olav: 3125 Punts olav en GF(q): 5 Total time: 3.269 seconds, Total memory usage: 2.12MB ************** MAGMA ***************** Host aula-b-siee93.uab.es. (158.109.66.93) Time: Mon Mar 15 06:26:01 2004 Input: olav:=function(q,r) expt:=[q^(r-n): n in [1..r]]; P:=PolynomialRing(Integers()); t:=0; for i in expt do t:=t + x^i; end for; n:=x^&+(expt); olav:=[: a,b in GF(q^r) | Evaluate(n,a) eq Evaluate(t,b)]; return olav; end function; q:=6; r:=3; olis:=olav(q,r); olisgf:={:a,b in GF(q) | in olis}; print "Punts olav: ";#(olis); print "Punts olav en GF(q): ";#(olisgf); Output: Magma V2.10-6 Mon Mar 15 2004 06:25:58 on modular [Seed = 3619816738] ------------------------------------- [
:3]( q: 6, r: 3 ) >> olav:=[: a,b in GF(q^r) | Evaluate(n,a) eq Evaluate(t,b)]; ^ Runtime error in 'GF': Argument 1 (216) is not a prime power >> olisgf:={:a,b in GF(q) | in olis}; ^ User error: Identifier 'olis' has not been declared or assigned Punts olav: >> print "Punts olav: ";#(olis); ^ User error: Identifier 'olis' has not been declared or assigned Punts olav en GF(q): >> print "Punts olav en GF(q): ";#(olisgf); ^ User error: Identifier 'olisgf' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee93.uab.es. (158.109.66.93) Time: Mon Mar 15 06:26:59 2004 Input: olav:=function(q,r) expt:=[q^(r-n): n in [1..r]]; P:=PolynomialRing(Integers()); t:=0; for i in expt do t:=t + x^i; end for; n:=x^&+(expt); olav:=[: a,b in GF(q^r) | Evaluate(n,a) eq Evaluate(t,b)]; return olav; end function; // Polla q:=6; r:=3; olis:=olav(q,r); olisgf:={:a,b in GF(q) | in olis}; print "Punts olav: ";#(olis); print "Punts olav en GF(q): ";#(olisgf); Output: Magma V2.10-6 Mon Mar 15 2004 06:26:56 on modular [Seed = 3737849325] ------------------------------------- [
:3]( q: 6, r: 3 ) >> olav:=[: a,b in GF(q^r) | Evaluate(n,a) eq Evaluate(t,b)]; ^ Runtime error in 'GF': Argument 1 (216) is not a prime power >> olisgf:={:a,b in GF(q) | in olis}; ^ User error: Identifier 'olis' has not been declared or assigned Punts olav: >> print "Punts olav: ";#(olis); ^ User error: Identifier 'olis' has not been declared or assigned Punts olav en GF(q): >> print "Punts olav en GF(q): ";#(olisgf); ^ User error: Identifier 'olisgf' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee93.uab.es. (158.109.66.93) Time: Mon Mar 15 06:27:13 2004 Input: olav:=function(q,r) expt:=[q^(r-n): n in [1..r]]; P:=PolynomialRing(Integers()); t:=0; for i in expt do t:=t + x^i; end for; n:=x^&+(expt); olav:=[: a,b in GF(q^r) | Evaluate(n,a) eq Evaluate(t,b)]; return olav; end function; /* Polla */ q:=6; r:=3; olis:=olav(q,r); olisgf:={:a,b in GF(q) | in olis}; print "Punts olav: ";#(olis); print "Punts olav en GF(q): ";#(olisgf); Output: Magma V2.10-6 Mon Mar 15 2004 06:27:10 on modular [Seed = 3318748920] ------------------------------------- [
:3]( q: 6, r: 3 ) >> olav:=[: a,b in GF(q^r) | Evaluate(n,a) eq Evaluate(t,b)]; ^ Runtime error in 'GF': Argument 1 (216) is not a prime power >> olisgf:={:a,b in GF(q) | in olis}; ^ User error: Identifier 'olis' has not been declared or assigned Punts olav: >> print "Punts olav: ";#(olis); ^ User error: Identifier 'olis' has not been declared or assigned Punts olav en GF(q): >> print "Punts olav en GF(q): ";#(olisgf); ^ User error: Identifier 'olisgf' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217) Time: Mon Mar 15 08:13:39 2004 Input: 2+2 Output: Magma V2.10-6 Mon Mar 15 2004 08:13:36 on modular [Seed = 2070845262] ------------------------------------- 4 Total time: 3.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Mon Mar 15 08:20:22 2004 Input: >P:=PolynomialRing(Integers()); >n73:= x^49 + x^7 + x; >t73:= x^57; >[: a,b in GF(7,3) | Evaluate(n73,a) eq Evaluate(n73,b)]; Output: Magma V2.10-6 Mon Mar 15 2004 08:20:15 on modular [Seed = 1247782896] ------------------------------------- [ <1, 1>, <1, $.1^3>, <1, $.1^21>, <1, $.1^22>, <1, $.1^27>, <1, $.1^29>, <1, $.1^36>, <1, $.1^52>, <1, $.1^53>, <1, $.1^54>, <1, $.1^58>, <1, $.1^59>, <1, $.1^64>, <1, $.1^67>, <1, $.1^68>, <1, $.1^71>, <1, $.1^73>, <1, $.1^82>, <1, $.1^94>, <1, $.1^106>, <1, $.1^123>, <1, $.1^127>, <1, $.1^134>, <1, $.1^144>, <1, $.1^147>, <1, $.1^154>, <1, $.1^155>, <1, $.1^157>, <1, $.1^160>, <1, $.1^169>, <1, $.1^177>, <1, $.1^188>, <1, $.1^189>, <1, $.1^194>, <1, $.1^203>, <1, $.1^205>, <1, $.1^213>, <1, $.1^216>, <1, $.1^232>, <1, $.1^252>, <1, $.1^254>, <1, $.1^256>, <1, $.1^272>, <1, $.1^290>, <1, $.1^297>, <1, $.1^316>, <1, $.1^320>, <1, $.1^324>, <1, $.1^332>, <$.1, $.1>, <$.1, $.1^2>, <$.1, $.1^7>, <$.1, $.1^10>, <$.1, $.1^11>, <$.1, $.1^14>, <$.1, $.1^16>, <$.1, $.1^25>, <$.1, $.1^37>, <$.1, $.1^49>, <$.1, $.1^66>, <$.1, $.1^70>, <$.1, $.1^77>, <$.1, $.1^87>, <$.1, $.1^90>, <$.1, $.1^97>, <$.1, $.1^98>, <$.1, $.1^100>, <$.1, $.1^103>, <$.1, $.1^112>, <$.1, $.1^120>, <$.1, $.1^131>, <$.1, $.1^132>, <$.1, $.1^137>, <$.1, $.1^146>, <$.1, $.1^148>, <$.1, $.1^156>, <$.1, $.1^159>, <$.1, $.1^175>, <$.1, $.1^195>, <$.1, $.1^197>, <$.1, $.1^199>, <$.1, $.1^215>, <$.1, $.1^233>, <$.1, $.1^240>, <$.1, $.1^259>, <$.1, $.1^263>, <$.1, $.1^267>, <$.1, $.1^275>, <$.1, 5>, <$.1, $.1^288>, <$.1, $.1^306>, <$.1, $.1^307>, <$.1, $.1^312>, <$.1, $.1^314>, <$.1, $.1^321>, <$.1, $.1^337>, <$.1, $.1^338>, <$.1, $.1^339>, <$.1^2, $.1>, <$.1^2, $.1^2>, <$.1^2, $.1^7>, <$.1^2, $.1^10>, <$.1^2, $.1^11>, <$.1^2, $.1^14>, <$.1^2, $.1^16>, <$.1^2, $.1^25>, <$.1^2, $.1^37>, <$.1^2, $.1^49>, <$.1^2, $.1^66>, <$.1^2, $.1^70>, <$.1^2, $.1^77>, <$.1^2, $.1^87>, <$.1^2, $.1^90>, <$.1^2, $.1^97>, <$.1^2, $.1^98>, <$.1^2, $.1^100>, <$.1^2, $.1^103>, <$.1^2, $.1^112>, <$.1^2, $.1^120>, <$.1^2, $.1^131>, <$.1^2, $.1^132>, <$.1^2, $.1^137>, <$.1^2, $.1^146>, <$.1^2, $.1^148>, <$.1^2, $.1^156>, <$.1^2, $.1^159>, <$.1^2, $.1^175>, <$.1^2, $.1^195>, <$.1^2, $.1^197>, <$.1^2, $.1^199>, <$.1^2, $.1^215>, <$.1^2, $.1^233>, <$.1^2, $.1^240>, <$.1^2, $.1^259>, <$.1^2, $.1^263>, <$.1^2, $.1^267>, <$.1^2, $.1^275>, <$.1^2, 5>, <$.1^2, $.1^288>, <$.1^2, $.1^306>, <$.1^2, $.1^307>, <$.1^2, $.1^312>, <$.1^2, $.1^314>, <$.1^2, $.1^321>, <$.1^2, $.1^337>, <$.1^2, $.1^338>, <$.1^2, $.1^339>, <$.1^3, 1>, <$.1^3, $.1^3>, <$.1^3, $.1^21>, <$.1^3, $.1^22>, <$.1^3, $.1^27>, <$.1^3, $.1^29>, <$.1^3, $.1^36>, <$.1^3, $.1^52>, <$.1^3, $.1^53>, <$.1^3, $.1^54>, <$.1^3, $.1^58>, <$.1^3, $.1^59>, <$.1^3, $.1^64>, <$.1^3, $.1^67>, <$.1^3, $.1^68>, <$.1^3, $.1^71>, <$.1^3, $.1^73>, <$.1^3, $.1^82>, <$.1^3, $.1^94>, <$.1^3, $.1^106>, <$.1^3, $.1^123>, <$.1^3, $.1^127>, <$.1^3, $.1^134>, <$.1^3, $.1^144>, <$.1^3, $.1^147>, <$.1^3, $.1^154>, <$.1^3, $.1^155>, <$.1^3, $.1^157>, <$.1^3, $.1^160>, <$.1^3, $.1^169>, <$.1^3, $.1^177>, <$.1^3, $.1^188>, <$.1^3, $.1^189>, <$.1^3, $.1^194>, <$.1^3, $.1^203>, <$.1^3, $.1^205>, <$.1^3, $.1^213>, <$.1^3, $.1^216>, <$.1^3, $.1^232>, <$.1^3, $.1^252>, <$.1^3, $.1^254>, <$.1^3, $.1^256>, <$.1^3, $.1^272>, <$.1^3, $.1^290>, <$.1^3, $.1^297>, <$.1^3, $.1^316>, <$.1^3, $.1^320>, <$.1^3, $.1^324>, <$.1^3, $.1^332>, <$.1^4, $.1^4>, <$.1^4, $.1^24>, <$.1^4, $.1^26>, <$.1^4, $.1^28>, <$.1^4, $.1^44>, <$.1^4, $.1^62>, <$.1^4, $.1^69>, <$.1^4, $.1^88>, <$.1^4, $.1^92>, <$.1^4, $.1^96>, <$.1^4, $.1^104>, <$.1^4, 2>, <$.1^4, $.1^117>, <$.1^4, $.1^135>, <$.1^4, $.1^136>, <$.1^4, $.1^141>, <$.1^4, $.1^143>, <$.1^4, $.1^150>, <$.1^4, $.1^166>, <$.1^4, $.1^167>, <$.1^4, $.1^168>, <$.1^4, $.1^172>, <$.1^4, $.1^173>, <$.1^4, $.1^178>, <$.1^4, $.1^181>, <$.1^4, $.1^182>, <$.1^4, $.1^185>, <$.1^4, $.1^187>, <$.1^4, $.1^196>, <$.1^4, $.1^208>, <$.1^4, $.1^220>, <$.1^4, $.1^237>, <$.1^4, $.1^241>, <$.1^4, $.1^248>, <$.1^4, $.1^258>, <$.1^4, $.1^261>, <$.1^4, $.1^268>, <$.1^4, $.1^269>, <$.1^4, $.1^271>, <$.1^4, $.1^274>, <$.1^4, $.1^283>, <$.1^4, $.1^291>, <$.1^4, $.1^302>, <$.1^4, $.1^303>, <$.1^4, $.1^308>, <$.1^4, $.1^317>, <$.1^4, $.1^319>, <$.1^4, $.1^327>, <$.1^4, $.1^330>, <$.1^5, $.1^5>, <$.1^5, $.1^12>, <$.1^5, $.1^31>, <$.1^5, $.1^35>, <$.1^5, $.1^39>, <$.1^5, $.1^47>, <$.1^5, 3>, <$.1^5, $.1^60>, <$.1^5, $.1^78>, <$.1^5, $.1^79>, <$.1^5, $.1^84>, <$.1^5, $.1^86>, <$.1^5, $.1^93>, <$.1^5, $.1^109>, <$.1^5, $.1^110>, <$.1^5, $.1^111>, <$.1^5, $.1^115>, <$.1^5, $.1^116>, <$.1^5, $.1^121>, <$.1^5, $.1^124>, <$.1^5, $.1^125>, <$.1^5, $.1^128>, <$.1^5, $.1^130>, <$.1^5, $.1^139>, <$.1^5, $.1^151>, <$.1^5, $.1^163>, <$.1^5, $.1^180>, <$.1^5, $.1^184>, <$.1^5, $.1^191>, <$.1^5, $.1^201>, <$.1^5, $.1^204>, <$.1^5, $.1^211>, <$.1^5, $.1^212>, <$.1^5, $.1^214>, <$.1^5, $.1^217>, <$.1^5, $.1^226>, <$.1^5, $.1^234>, <$.1^5, $.1^245>, <$.1^5, $.1^246>, <$.1^5, $.1^251>, <$.1^5, $.1^260>, <$.1^5, $.1^262>, <$.1^5, $.1^270>, <$.1^5, $.1^273>, <$.1^5, $.1^289>, <$.1^5, $.1^309>, <$.1^5, $.1^311>, <$.1^5, $.1^313>, <$.1^5, $.1^329>, <$.1^6, $.1^6>, <$.1^6, $.1^17>, <$.1^6, $.1^18>, <$.1^6, $.1^23>, <$.1^6, $.1^32>, <$.1^6, $.1^34>, <$.1^6, $.1^42>, <$.1^6, $.1^45>, <$.1^6, $.1^61>, <$.1^6, $.1^81>, <$.1^6, $.1^83>, <$.1^6, $.1^85>, <$.1^6, $.1^101>, <$.1^6, $.1^119>, <$.1^6, $.1^126>, <$.1^6, $.1^145>, <$.1^6, $.1^149>, <$.1^6, $.1^153>, <$.1^6, $.1^161>, <$.1^6, 6>, <$.1^6, $.1^174>, <$.1^6, $.1^192>, <$.1^6, $.1^193>, <$.1^6, $.1^198>, <$.1^6, $.1^200>, <$.1^6, $.1^207>, <$.1^6, $.1^223>, <$.1^6, $.1^224>, <$.1^6, $.1^225>, <$.1^6, $.1^229>, <$.1^6, $.1^230>, <$.1^6, $.1^235>, <$.1^6, $.1^238>, <$.1^6, $.1^239>, <$.1^6, $.1^242>, <$.1^6, $.1^244>, <$.1^6, $.1^253>, <$.1^6, $.1^265>, <$.1^6, $.1^277>, <$.1^6, $.1^294>, <$.1^6, $.1^298>, <$.1^6, $.1^305>, <$.1^6, $.1^315>, <$.1^6, $.1^318>, <$.1^6, $.1^325>, <$.1^6, $.1^326>, <$.1^6, $.1^328>, <$.1^6, $.1^331>, <$.1^6, $.1^340>, <$.1^7, $.1>, <$.1^7, $.1^2>, <$.1^7, $.1^7>, <$.1^7, $.1^10>, <$.1^7, $.1^11>, <$.1^7, $.1^14>, <$.1^7, $.1^16>, <$.1^7, $.1^25>, <$.1^7, $.1^37>, <$.1^7, $.1^49>, <$.1^7, $.1^66>, <$.1^7, $.1^70>, <$.1^7, $.1^77>, <$.1^7, $.1^87>, <$.1^7, $.1^90>, <$.1^7, $.1^97>, <$.1^7, $.1^98>, <$.1^7, $.1^100>, <$.1^7, $.1^103>, <$.1^7, $.1^112>, <$.1^7, $.1^120>, <$.1^7, $.1^131>, <$.1^7, $.1^132>, <$.1^7, $.1^137>, <$.1^7, $.1^146>, <$.1^7, $.1^148>, <$.1^7, $.1^156>, <$.1^7, $.1^159>, <$.1^7, $.1^175>, <$.1^7, $.1^195>, <$.1^7, $.1^197>, <$.1^7, $.1^199>, <$.1^7, $.1^215>, <$.1^7, $.1^233>, <$.1^7, $.1^240>, <$.1^7, $.1^259>, <$.1^7, $.1^263>, <$.1^7, $.1^267>, <$.1^7, $.1^275>, <$.1^7, 5>, <$.1^7, $.1^288>, <$.1^7, $.1^306>, <$.1^7, $.1^307>, <$.1^7, $.1^312>, <$.1^7, $.1^314>, <$.1^7, $.1^321>, <$.1^7, $.1^337>, <$.1^7, $.1^338>, <$.1^7, $.1^339>, <$.1^8, $.1^8>, <$.1^8, $.1^15>, <$.1^8, $.1^19>, <$.1^8, $.1^38>, <$.1^8, $.1^48>, <$.1^8, $.1^50>, <$.1^8, $.1^51>, <$.1^8, $.1^56>, <$.1^8, $.1^65>, <$.1^8, $.1^72>, <$.1^8, $.1^76>, <$.1^8, $.1^95>, <$.1^8, $.1^105>, <$.1^8, $.1^107>, <$.1^8, $.1^108>, <$.1^8, $.1^113>, <$.1^8, $.1^122>, <$.1^8, $.1^129>, <$.1^8, $.1^133>, <$.1^8, $.1^152>, <$.1^8, $.1^162>, <$.1^8, $.1^164>, <$.1^8, $.1^165>, <$.1^8, $.1^170>, <$.1^8, $.1^179>, <$.1^8, $.1^186>, <$.1^8, $.1^190>, <$.1^8, $.1^209>, <$.1^8, $.1^219>, <$.1^8, $.1^221>, <$.1^8, $.1^222>, <$.1^8, $.1^227>, <$.1^8, $.1^236>, <$.1^8, $.1^243>, <$.1^8, $.1^247>, <$.1^8, $.1^266>, <$.1^8, $.1^276>, <$.1^8, $.1^278>, <$.1^8, $.1^279>, <$.1^8, $.1^284>, <$.1^8, $.1^293>, <$.1^8, $.1^300>, <$.1^8, $.1^304>, <$.1^8, $.1^323>, <$.1^8, $.1^333>, <$.1^8, $.1^335>, <$.1^8, $.1^336>, <$.1^8, $.1^341>, <$.1^8, 0>, <$.1^9, $.1^9>, <$.1^9, $.1^13>, <$.1^9, $.1^20>, <$.1^9, $.1^30>, <$.1^9, $.1^33>, <$.1^9, $.1^40>, <$.1^9, $.1^41>, <$.1^9, $.1^43>, <$.1^9, $.1^46>, <$.1^9, $.1^55>, <$.1^9, $.1^63>, <$.1^9, $.1^74>, <$.1^9, $.1^75>, <$.1^9, $.1^80>, <$.1^9, $.1^89>, <$.1^9, $.1^91>, <$.1^9, $.1^99>, <$.1^9, $.1^102>, <$.1^9, $.1^118>, <$.1^9, $.1^138>, <$.1^9, $.1^140>, <$.1^9, $.1^142>, <$.1^9, $.1^158>, <$.1^9, $.1^176>, <$.1^9, $.1^183>, <$.1^9, $.1^202>, <$.1^9, $.1^206>, <$.1^9, $.1^210>, <$.1^9, $.1^218>, <$.1^9, 4>, <$.1^9, $.1^231>, <$.1^9, $.1^249>, <$.1^9, $.1^250>, <$.1^9, $.1^255>, <$.1^9, $.1^257>, <$.1^9, $.1^264>, <$.1^9, $.1^280>, <$.1^9, $.1^281>, <$.1^9, $.1^282>, <$.1^9, $.1^286>, <$.1^9, $.1^287>, <$.1^9, $.1^292>, <$.1^9, $.1^295>, <$.1^9, $.1^296>, <$.1^9, $.1^299>, <$.1^9, $.1^301>, <$.1^9, $.1^310>, <$.1^9, $.1^322>, <$.1^9, $.1^334>, <$.1^10, $.1>, <$.1^10, $.1^2>, <$.1^10, $.1^7>, <$.1^10, $.1^10>, <$.1^10, $.1^11>, <$.1^10, $.1^14>, <$.1^10, $.1^16>, <$.1^10, $.1^25>, <$.1^10, $.1^37>, <$.1^10, $.1^49>, <$.1^10, $.1^66>, <$.1^10, $.1^70>, <$.1^10, $.1^77>, <$.1^10, $.1^87>, <$.1^10, $.1^90>, <$.1^10, $.1^97>, <$.1^10, $.1^98>, <$.1^10, $.1^100>, <$.1^10, $.1^103>, <$.1^10, $.1^112>, <$.1^10, $.1^120>, <$.1^10, $.1^131>, <$.1^10, $.1^132>, <$.1^10, $.1^137>, <$.1^10, $.1^146>, <$.1^10, $.1^148>, <$.1^10, $.1^156>, <$.1^10, $.1^159>, <$.1^10, $.1^175>, <$.1^10, $.1^195>, <$.1^10, $.1^197>, <$.1^10, $.1^199>, <$.1^10, $.1^215>, <$.1^10, $.1^233>, <$.1^10, $.1^240>, <$.1^10, $.1^259>, <$.1^10, $.1^263>, <$.1^10, $.1^267>, <$.1^10, $.1^275>, <$.1^10, 5>, <$.1^10, $.1^288>, <$.1^10, $.1^306>, <$.1^10, $.1^307>, <$.1^10, $.1^312>, <$.1^10, $.1^314>, <$.1^10, $.1^321>, <$.1^10, $.1^337>, <$.1^10, $.1^338>, <$.1^10, $.1^339>, <$.1^11, $.1>, <$.1^11, $.1^2>, <$.1^11, $.1^7>, <$.1^11, $.1^10>, <$.1^11, $.1^11>, <$.1^11, $.1^14>, <$.1^11, $.1^16>, <$.1^11, $.1^25>, <$.1^11, $.1^37>, <$.1^11, $.1^49>, <$.1^11, $.1^66>, <$.1^11, $.1^70>, <$.1^11, $.1^77>, <$.1^11, $.1^87>, <$.1^11, $.1^90>, <$.1^11, $.1^97>, <$.1^11, $.1^98>, <$.1^11, $.1^100>, <$.1^11, $.1^103>, <$.1^11, $.1^112>, <$.1^11, $.1^120>, <$.1^11, $.1^131>, <$.1^11, $.1^132>, <$.1^11, $.1^137>, <$.1^11, $.1^146>, <$.1^11, $.1^148>, <$.1^11, $.1^156>, <$.1^11, $.1^159>, <$.1^11, $.1^175>, <$.1^11, $.1^195>, <$.1^11, $.1^1 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Mon Mar 15 08:21:36 2004 Input: >P:=PolynomialRing(Integers()); >n73:= x^49 + x^7 + x; >t73:= x^57; >#[: a,b in GF(7,3) | Evaluate(n73,a) eq Evaluate(n73,b)]; Output: Magma V2.10-6 Mon Mar 15 2004 08:21:30 on modular [Seed = 2541910648] ------------------------------------- 16807 Total time: 6.619 seconds, Total memory usage: 2.73MB ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Mon Mar 15 08:34:56 2004 Input: >P:=PolynomialRing(Integers()); >n73:= x^49 + x^7 + x; >t73:= x^57; >[: a,b in GF(7,3) | Evaluate(n73,a) eq Evaluate(t73,b)]; >#[: a,b in GF(7,3) | Evaluate(n73,a) eq Evaluate(t73,b)]; Output: Magma V2.10-6 Mon Mar 15 2004 08:34:46 on modular [Seed = 3992460590] ------------------------------------- [ <1, $.1>, <1, $.1^7>, <1, $.1^13>, <1, $.1^19>, <1, $.1^25>, <1, $.1^31>, <1, $.1^37>, <1, $.1^43>, <1, $.1^49>, <1, $.1^55>, <1, $.1^61>, <1, $.1^67>, <1, $.1^73>, <1, $.1^79>, <1, $.1^85>, <1, $.1^91>, <1, $.1^97>, <1, $.1^103>, <1, $.1^109>, <1, $.1^115>, <1, $.1^121>, <1, $.1^127>, <1, $.1^133>, <1, $.1^139>, <1, $.1^145>, <1, $.1^151>, <1, $.1^157>, <1, $.1^163>, <1, $.1^169>, <1, $.1^175>, <1, $.1^181>, <1, $.1^187>, <1, $.1^193>, <1, $.1^199>, <1, $.1^205>, <1, $.1^211>, <1, $.1^217>, <1, $.1^223>, <1, $.1^229>, <1, $.1^235>, <1, $.1^241>, <1, $.1^247>, <1, $.1^253>, <1, $.1^259>, <1, $.1^265>, <1, $.1^271>, <1, $.1^277>, <1, $.1^283>, <1, $.1^289>, <1, $.1^295>, <1, $.1^301>, <1, $.1^307>, <1, $.1^313>, <1, $.1^319>, <1, $.1^325>, <1, $.1^331>, <1, $.1^337>, <$.1, 1>, <$.1, $.1^6>, <$.1, $.1^12>, <$.1, $.1^18>, <$.1, $.1^24>, <$.1, $.1^30>, <$.1, $.1^36>, <$.1, $.1^42>, <$.1, $.1^48>, <$.1, $.1^54>, <$.1, $.1^60>, <$.1, $.1^66>, <$.1, $.1^72>, <$.1, $.1^78>, <$.1, $.1^84>, <$.1, $.1^90>, <$.1, $.1^96>, <$.1, $.1^102>, <$.1, $.1^108>, <$.1, 2>, <$.1, $.1^120>, <$.1, $.1^126>, <$.1, $.1^132>, <$.1, $.1^138>, <$.1, $.1^144>, <$.1, $.1^150>, <$.1, $.1^156>, <$.1, $.1^162>, <$.1, $.1^168>, <$.1, $.1^174>, <$.1, $.1^180>, <$.1, $.1^186>, <$.1, $.1^192>, <$.1, $.1^198>, <$.1, $.1^204>, <$.1, $.1^210>, <$.1, $.1^216>, <$.1, $.1^222>, <$.1, 4>, <$.1, $.1^234>, <$.1, $.1^240>, <$.1, $.1^246>, <$.1, $.1^252>, <$.1, $.1^258>, <$.1, $.1^264>, <$.1, $.1^270>, <$.1, $.1^276>, <$.1, $.1^282>, <$.1, $.1^288>, <$.1, $.1^294>, <$.1, $.1^300>, <$.1, $.1^306>, <$.1, $.1^312>, <$.1, $.1^318>, <$.1, $.1^324>, <$.1, $.1^330>, <$.1, $.1^336>, <$.1^2, 1>, <$.1^2, $.1^6>, <$.1^2, $.1^12>, <$.1^2, $.1^18>, <$.1^2, $.1^24>, <$.1^2, $.1^30>, <$.1^2, $.1^36>, <$.1^2, $.1^42>, <$.1^2, $.1^48>, <$.1^2, $.1^54>, <$.1^2, $.1^60>, <$.1^2, $.1^66>, <$.1^2, $.1^72>, <$.1^2, $.1^78>, <$.1^2, $.1^84>, <$.1^2, $.1^90>, <$.1^2, $.1^96>, <$.1^2, $.1^102>, <$.1^2, $.1^108>, <$.1^2, 2>, <$.1^2, $.1^120>, <$.1^2, $.1^126>, <$.1^2, $.1^132>, <$.1^2, $.1^138>, <$.1^2, $.1^144>, <$.1^2, $.1^150>, <$.1^2, $.1^156>, <$.1^2, $.1^162>, <$.1^2, $.1^168>, <$.1^2, $.1^174>, <$.1^2, $.1^180>, <$.1^2, $.1^186>, <$.1^2, $.1^192>, <$.1^2, $.1^198>, <$.1^2, $.1^204>, <$.1^2, $.1^210>, <$.1^2, $.1^216>, <$.1^2, $.1^222>, <$.1^2, 4>, <$.1^2, $.1^234>, <$.1^2, $.1^240>, <$.1^2, $.1^246>, <$.1^2, $.1^252>, <$.1^2, $.1^258>, <$.1^2, $.1^264>, <$.1^2, $.1^270>, <$.1^2, $.1^276>, <$.1^2, $.1^282>, <$.1^2, $.1^288>, <$.1^2, $.1^294>, <$.1^2, $.1^300>, <$.1^2, $.1^306>, <$.1^2, $.1^312>, <$.1^2, $.1^318>, <$.1^2, $.1^324>, <$.1^2, $.1^330>, <$.1^2, $.1^336>, <$.1^3, $.1>, <$.1^3, $.1^7>, <$.1^3, $.1^13>, <$.1^3, $.1^19>, <$.1^3, $.1^25>, <$.1^3, $.1^31>, <$.1^3, $.1^37>, <$.1^3, $.1^43>, <$.1^3, $.1^49>, <$.1^3, $.1^55>, <$.1^3, $.1^61>, <$.1^3, $.1^67>, <$.1^3, $.1^73>, <$.1^3, $.1^79>, <$.1^3, $.1^85>, <$.1^3, $.1^91>, <$.1^3, $.1^97>, <$.1^3, $.1^103>, <$.1^3, $.1^109>, <$.1^3, $.1^115>, <$.1^3, $.1^121>, <$.1^3, $.1^127>, <$.1^3, $.1^133>, <$.1^3, $.1^139>, <$.1^3, $.1^145>, <$.1^3, $.1^151>, <$.1^3, $.1^157>, <$.1^3, $.1^163>, <$.1^3, $.1^169>, <$.1^3, $.1^175>, <$.1^3, $.1^181>, <$.1^3, $.1^187>, <$.1^3, $.1^193>, <$.1^3, $.1^199>, <$.1^3, $.1^205>, <$.1^3, $.1^211>, <$.1^3, $.1^217>, <$.1^3, $.1^223>, <$.1^3, $.1^229>, <$.1^3, $.1^235>, <$.1^3, $.1^241>, <$.1^3, $.1^247>, <$.1^3, $.1^253>, <$.1^3, $.1^259>, <$.1^3, $.1^265>, <$.1^3, $.1^271>, <$.1^3, $.1^277>, <$.1^3, $.1^283>, <$.1^3, $.1^289>, <$.1^3, $.1^295>, <$.1^3, $.1^301>, <$.1^3, $.1^307>, <$.1^3, $.1^313>, <$.1^3, $.1^319>, <$.1^3, $.1^325>, <$.1^3, $.1^331>, <$.1^3, $.1^337>, <$.1^4, $.1^3>, <$.1^4, $.1^9>, <$.1^4, $.1^15>, <$.1^4, $.1^21>, <$.1^4, $.1^27>, <$.1^4, $.1^33>, <$.1^4, $.1^39>, <$.1^4, $.1^45>, <$.1^4, $.1^51>, <$.1^4, 3>, <$.1^4, $.1^63>, <$.1^4, $.1^69>, <$.1^4, $.1^75>, <$.1^4, $.1^81>, <$.1^4, $.1^87>, <$.1^4, $.1^93>, <$.1^4, $.1^99>, <$.1^4, $.1^105>, <$.1^4, $.1^111>, <$.1^4, $.1^117>, <$.1^4, $.1^123>, <$.1^4, $.1^129>, <$.1^4, $.1^135>, <$.1^4, $.1^141>, <$.1^4, $.1^147>, <$.1^4, $.1^153>, <$.1^4, $.1^159>, <$.1^4, $.1^165>, <$.1^4, 6>, <$.1^4, $.1^177>, <$.1^4, $.1^183>, <$.1^4, $.1^189>, <$.1^4, $.1^195>, <$.1^4, $.1^201>, <$.1^4, $.1^207>, <$.1^4, $.1^213>, <$.1^4, $.1^219>, <$.1^4, $.1^225>, <$.1^4, $.1^231>, <$.1^4, $.1^237>, <$.1^4, $.1^243>, <$.1^4, $.1^249>, <$.1^4, $.1^255>, <$.1^4, $.1^261>, <$.1^4, $.1^267>, <$.1^4, $.1^273>, <$.1^4, $.1^279>, <$.1^4, 5>, <$.1^4, $.1^291>, <$.1^4, $.1^297>, <$.1^4, $.1^303>, <$.1^4, $.1^309>, <$.1^4, $.1^315>, <$.1^4, $.1^321>, <$.1^4, $.1^327>, <$.1^4, $.1^333>, <$.1^4, $.1^339>, <$.1^5, $.1^2>, <$.1^5, $.1^8>, <$.1^5, $.1^14>, <$.1^5, $.1^20>, <$.1^5, $.1^26>, <$.1^5, $.1^32>, <$.1^5, $.1^38>, <$.1^5, $.1^44>, <$.1^5, $.1^50>, <$.1^5, $.1^56>, <$.1^5, $.1^62>, <$.1^5, $.1^68>, <$.1^5, $.1^74>, <$.1^5, $.1^80>, <$.1^5, $.1^86>, <$.1^5, $.1^92>, <$.1^5, $.1^98>, <$.1^5, $.1^104>, <$.1^5, $.1^110>, <$.1^5, $.1^116>, <$.1^5, $.1^122>, <$.1^5, $.1^128>, <$.1^5, $.1^134>, <$.1^5, $.1^140>, <$.1^5, $.1^146>, <$.1^5, $.1^152>, <$.1^5, $.1^158>, <$.1^5, $.1^164>, <$.1^5, $.1^170>, <$.1^5, $.1^176>, <$.1^5, $.1^182>, <$.1^5, $.1^188>, <$.1^5, $.1^194>, <$.1^5, $.1^200>, <$.1^5, $.1^206>, <$.1^5, $.1^212>, <$.1^5, $.1^218>, <$.1^5, $.1^224>, <$.1^5, $.1^230>, <$.1^5, $.1^236>, <$.1^5, $.1^242>, <$.1^5, $.1^248>, <$.1^5, $.1^254>, <$.1^5, $.1^260>, <$.1^5, $.1^266>, <$.1^5, $.1^272>, <$.1^5, $.1^278>, <$.1^5, $.1^284>, <$.1^5, $.1^290>, <$.1^5, $.1^296>, <$.1^5, $.1^302>, <$.1^5, $.1^308>, <$.1^5, $.1^314>, <$.1^5, $.1^320>, <$.1^5, $.1^326>, <$.1^5, $.1^332>, <$.1^5, $.1^338>, <$.1^6, $.1^4>, <$.1^6, $.1^10>, <$.1^6, $.1^16>, <$.1^6, $.1^22>, <$.1^6, $.1^28>, <$.1^6, $.1^34>, <$.1^6, $.1^40>, <$.1^6, $.1^46>, <$.1^6, $.1^52>, <$.1^6, $.1^58>, <$.1^6, $.1^64>, <$.1^6, $.1^70>, <$.1^6, $.1^76>, <$.1^6, $.1^82>, <$.1^6, $.1^88>, <$.1^6, $.1^94>, <$.1^6, $.1^100>, <$.1^6, $.1^106>, <$.1^6, $.1^112>, <$.1^6, $.1^118>, <$.1^6, $.1^124>, <$.1^6, $.1^130>, <$.1^6, $.1^136>, <$.1^6, $.1^142>, <$.1^6, $.1^148>, <$.1^6, $.1^154>, <$.1^6, $.1^160>, <$.1^6, $.1^166>, <$.1^6, $.1^172>, <$.1^6, $.1^178>, <$.1^6, $.1^184>, <$.1^6, $.1^190>, <$.1^6, $.1^196>, <$.1^6, $.1^202>, <$.1^6, $.1^208>, <$.1^6, $.1^214>, <$.1^6, $.1^220>, <$.1^6, $.1^226>, <$.1^6, $.1^232>, <$.1^6, $.1^238>, <$.1^6, $.1^244>, <$.1^6, $.1^250>, <$.1^6, $.1^256>, <$.1^6, $.1^262>, <$.1^6, $.1^268>, <$.1^6, $.1^274>, <$.1^6, $.1^280>, <$.1^6, $.1^286>, <$.1^6, $.1^292>, <$.1^6, $.1^298>, <$.1^6, $.1^304>, <$.1^6, $.1^310>, <$.1^6, $.1^316>, <$.1^6, $.1^322>, <$.1^6, $.1^328>, <$.1^6, $.1^334>, <$.1^6, $.1^340>, <$.1^7, 1>, <$.1^7, $.1^6>, <$.1^7, $.1^12>, <$.1^7, $.1^18>, <$.1^7, $.1^24>, <$.1^7, $.1^30>, <$.1^7, $.1^36>, <$.1^7, $.1^42>, <$.1^7, $.1^48>, <$.1^7, $.1^54>, <$.1^7, $.1^60>, <$.1^7, $.1^66>, <$.1^7, $.1^72>, <$.1^7, $.1^78>, <$.1^7, $.1^84>, <$.1^7, $.1^90>, <$.1^7, $.1^96>, <$.1^7, $.1^102>, <$.1^7, $.1^108>, <$.1^7, 2>, <$.1^7, $.1^120>, <$.1^7, $.1^126>, <$.1^7, $.1^132>, <$.1^7, $.1^138>, <$.1^7, $.1^144>, <$.1^7, $.1^150>, <$.1^7, $.1^156>, <$.1^7, $.1^162>, <$.1^7, $.1^168>, <$.1^7, $.1^174>, <$.1^7, $.1^180>, <$.1^7, $.1^186>, <$.1^7, $.1^192>, <$.1^7, $.1^198>, <$.1^7, $.1^204>, <$.1^7, $.1^210>, <$.1^7, $.1^216>, <$.1^7, $.1^222>, <$.1^7, 4>, <$.1^7, $.1^234>, <$.1^7, $.1^240>, <$.1^7, $.1^246>, <$.1^7, $.1^252>, <$.1^7, $.1^258>, <$.1^7, $.1^264>, <$.1^7, $.1^270>, <$.1^7, $.1^276>, <$.1^7, $.1^282>, <$.1^7, $.1^288>, <$.1^7, $.1^294>, <$.1^7, $.1^300>, <$.1^7, $.1^306>, <$.1^7, $.1^312>, <$.1^7, $.1^318>, <$.1^7, $.1^324>, <$.1^7, $.1^330>, <$.1^7, $.1^336>, <$.1^8, 0>, <$.1^9, $.1^5>, <$.1^9, $.1^11>, <$.1^9, $.1^17>, <$.1^9, $.1^23>, <$.1^9, $.1^29>, <$.1^9, $.1^35>, <$.1^9, $.1^41>, <$.1^9, $.1^47>, <$.1^9, $.1^53>, <$.1^9, $.1^59>, <$.1^9, $.1^65>, <$.1^9, $.1^71>, <$.1^9, $.1^77>, <$.1^9, $.1^83>, <$.1^9, $.1^89>, <$.1^9, $.1^95>, <$.1^9, $.1^101>, <$.1^9, $.1^107>, <$.1^9, $.1^113>, <$.1^9, $.1^119>, <$.1^9, $.1^125>, <$.1^9, $.1^131>, <$.1^9, $.1^137>, <$.1^9, $.1^143>, <$.1^9, $.1^149>, <$.1^9, $.1^155>, <$.1^9, $.1^161>, <$.1^9, $.1^167>, <$.1^9, $.1^173>, <$.1^9, $.1^179>, <$.1^9, $.1^185>, <$.1^9, $.1^191>, <$.1^9, $.1^197>, <$.1^9, $.1^203>, <$.1^9, $.1^209>, <$.1^9, $.1^215>, <$.1^9, $.1^221>, <$.1^9, $.1^227>, <$.1^9, $.1^233>, <$.1^9, $.1^239>, <$.1^9, $.1^245>, <$.1^9, $.1^251>, <$.1^9, $.1^257>, <$.1^9, $.1^263>, <$.1^9, $.1^269>, <$.1^9, $.1^275>, <$.1^9, $.1^281>, <$.1^9, $.1^287>, <$.1^9, $.1^293>, <$.1^9, $.1^299>, <$.1^9, $.1^305>, <$.1^9, $.1^311>, <$.1^9, $.1^317>, <$.1^9, $.1^323>, <$.1^9, $.1^329>, <$.1^9, $.1^335>, <$.1^9, $.1^341>, <$.1^10, 1>, <$.1^10, $.1^6>, <$.1^10, $.1^12>, <$.1^10, $.1^18>, <$.1^10, $.1^24>, <$.1^10, $.1^30>, <$.1^10, $.1^36>, <$.1^10, $.1^42>, <$.1^10, $.1^48>, <$.1^10, $.1^54>, <$.1^10, $.1^60>, <$.1^10, $.1^66>, <$.1^10, $.1^72>, <$.1^10, $.1^78>, <$.1^10, $.1^84>, <$.1^10, $.1^90>, <$.1^10, $.1^96>, <$.1^10, $.1^102>, <$.1^10, $.1^108>, <$.1^10, 2>, <$.1^10, $.1^120>, <$.1^10, $.1^126>, <$.1^10, $.1^132>, <$.1^10, $.1^138>, <$.1^10, $.1^144>, <$.1^10, $.1^150>, <$.1^10, $.1^156>, <$.1^10, $.1^162>, <$.1^10, $.1^168>, <$.1^10, $.1^174>, <$.1^10, $.1^180>, <$.1^10, $.1^186>, <$.1^10, $.1^192>, <$.1^10, $.1^198>, <$.1^10, $.1^204>, <$.1^10, $.1^210>, <$.1^10, $.1^216>, <$.1^10, $.1^222>, <$.1^10, 4>, <$.1^10, $.1^234>, <$.1^10, $.1^240>, <$.1^10, $.1^246>, <$.1^10, $.1^252>, <$.1^10, $.1^258>, <$.1^10, $.1^264>, <$.1^10, $.1^270>, <$.1^10, $.1^276>, <$.1^10, $.1^282>, <$.1^10, $.1^288>, <$.1^10, $.1^294>, <$.1^10, $.1^300>, <$.1^10, $.1^306>, <$.1^10, $.1^312>, <$.1^10, $.1^318>, <$.1^10, $.1^324>, <$.1^10, $.1^330>, <$.1^10, $.1^336>, <$.1^11, 1>, <$.1^11, $.1^6>, <$.1^11, $ ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Mon Mar 15 08:35:56 2004 Input: >P:=PolynomialRing(Integers()); >n73:= x^49 + x^7 + x; >t73:= x^57; >#[: a,b in GF(7,3) | Evaluate(n73,a) eq Evaluate(t73,b)]; Output: Magma V2.10-6 Mon Mar 15 2004 08:35:49 on modular [Seed = 3552977619] ------------------------------------- 16807 Total time: 6.809 seconds, Total memory usage: 2.73MB ************** MAGMA ***************** Host mordor.uab.es. (158.109.31.189) Time: Mon Mar 15 08:37:58 2004 Input: >P:=PolynomialRing(Integers()); >n73:= x^49 + x^7 + x; >t73:= x^57; >#[: a,b in GF(7,3) | Evaluate(n73,a) eq Evaluate(t73,b)]; > exp:= func ; > crea_t:= function (q,r) pol:=0; e:=exp(q,r); for i in [1..r] do pol:=pol+x^e[i]; end for; return pol; end function; > crea_n:= function (q,r) sum:=0; e:=exp(q,r); for i in [1..r] do sum:=sum+e[i]; end for; return (x^sum); end function; > olav:= func : a,b in GF(q,r) | Evaluate(crea_n(q,r),a) eq Evaluate(crea_t(q,r),b)]>; >#olav(7,3); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Mar 15 2004 08:37:35 on modular [Seed = 3318756463] ------------------------------------- 16807 Errors: /home/mfd/gomagma: line 2: 30192 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.169) Time: Mon Mar 15 08:50:40 2004 Input: seqt := [7^(r-1) : r in {1..3}]; seqt; P:=PolynomialRing(Integers()); t73 := x^(seqt[1]) + x^(seqt[2]) + x^(seqt[3]); t73; n73 := x^(seqt[1] + seqt[2] + seqt[3]); n73; Olav := {[a,b]: a,b in GF(7,3) | Evaluate(n73,a) eq Evaluate(t73,b)}; #Olav; Output: Magma V2.10-6 Mon Mar 15 2004 08:50:33 on modular [Seed = 607244475] ------------------------------------- [ 1, 7, 49 ] x^49 + x^7 + x x^57 16807 Total time: 7.039 seconds, Total memory usage: 5.38MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.169) Time: Mon Mar 15 08:51:12 2004 Input: seqt := [7^(r-1) : r in {1..3}]; seqt; P:=PolynomialRing(Integers()); t73 := x^(seqt[1]) + x^(seqt[2]) + x^(seqt[3]); t73; n73 := x^(seqt[1] + seqt[2] + seqt[3]); n73; Olav := {[a,b]: a,b in GF(7,3) | Evaluate(n73,a) eq Evaluate(t73,b)}; Olav; Output: Magma V2.10-6 Mon Mar 15 2004 08:51:04 on modular [Seed = 758700499] ------------------------------------- [ 1, 7, 49 ] x^49 + x^7 + x x^57 { [ $.1^3, $.1^24 ], [ $.1^35, $.1^280 ], [ $.1^30, $.1^240 ], [ $.1^28, $.1^224 ], [ $.1^4, $.1^32 ], [ $.1^5, $.1^40 ], [ $.1^21, $.1^168 ], [ $.1^36, $.1^288 ], [ 1, $.1 ], [ $.1^35, $.1^281 ], [ $.1^28, $.1^225 ], [ $.1^12, $.1^97 ], [ $.1^11, $.1^89 ], [ $.1^6, $.1^49 ], [ $.1^5, $.1^41 ], [ $.1^10, $.1^81 ], [ $.1^37, $.1^297 ], [ $.1^42, $.1^337 ], [ 1, $.1^2 ], [ $.1^13, $.1^106 ], [ $.1^12, $.1^98 ], [ $.1^7, $.1^58 ], [ $.1^3, $.1^26 ], [ $.1^4, $.1^34 ], [ $.1^17, $.1^138 ], [ $.1^18, $.1^146 ], [ $.1^19, $.1^154 ], [ $.1^35, $.1^282 ], [ $.1^42, $.1^338 ], [ $.1^5, $.1^43 ], [ $.1^26, $.1^211 ], [ $.1^25, $.1^203 ], [ $.1^24, $.1^195 ], [ $.1^14, $.1^115 ], [ $.1^11, $.1^91 ], [ $.1^7, $.1^59 ], [ $.1^10, $.1^83 ], [ $.1^19, $.1^155 ], [ $.1^20, $.1^163 ], [ $.1^42, $.1^339 ], [ $.1^3, $.1^28 ], [ $.1^33, $.1^268 ], [ $.1^32, $.1^260 ], [ $.1^31, $.1^252 ], [ $.1^27, $.1^220 ], [ $.1^26, $.1^212 ], [ $.1^14, $.1^116 ], [ $.1^12, $.1^100 ], [ $.1^17, $.1^140 ], [ $.1^18, $.1^148 ], [ $.1^21, $.1^172 ], [ $.1^10, $.1^85 ], [ $.1^34, $.1^277 ], [ $.1^33, $.1^269 ], [ $.1^28, $.1^229 ], [ $.1^25, $.1^205 ], [ $.1^24, $.1^197 ], [ $.1^19, $.1^157 ], [ $.1^21, $.1^173 ], [ $.1^38, $.1^309 ], [ $.1^39, $.1^317 ], [ $.1^40, $.1^325 ], [ $.1^5, $.1^46 ], [ $.1^32, $.1^262 ], [ $.1^31, $.1^254 ], [ $.1^28, $.1^230 ], [ $.1^26, $.1^214 ], [ $.1^17, $.1^142 ], [ $.1^35, $.1^286 ], [ $.1^40, $.1^326 ], [ $.1^41, $.1^334 ], [ 1, $.1^7 ], [ $.1^33, $.1^271 ], [ $.1^24, $.1^199 ], [ $.1^12, $.1^103 ], [ $.1^35, $.1^287 ], [ $.1^38, $.1^311 ], [ $.1^39, $.1^319 ], [ $.1, 1 ], [ $.1^27, $.1^208 ], [ $.1^23, $.1^176 ], [ $.1^11, $.1^80 ], [ $.1^19, $.1^144 ], [ $.1^40, $.1^328 ], [ $.1^5, $.1^33 ], [ $.1^26, $.1^217 ], [ $.1^14, $.1^121 ], [ $.1^38, $.1^313 ], [ 1, $.1^10 ], [ $.1^33, $.1^258 ], [ $.1^25, $.1^194 ], [ $.1^4, $.1^42 ], [ $.1^15, 2 ], [ $.1^37, $.1^290 ], [ $.1^41, $.1^322 ], [ 1, $.1^11 ], [ $.1^28, $.1^235 ], [ $.1, $.1^3 ], [ $.1^19, $.1^147 ], [ $.1^40, $.1^331 ], [ $.1^7, $.1^52 ], [ $.1^29, 4 ], [ $.1^14, $.1^124 ], [ $.1^18, $.1^156 ], [ $.1^39, $.1^308 ], [ $.1^4, $.1^45 ], [ $.1^33, $.1^261 ], [ $.1^14, $.1^125 ], [ $.1^7, $.1^53 ], [ $.1^9, $.1^69 ], [ $.1^15, $.1^117 ], [ 1, $.1^14 ], [ $.1^32, $.1^270 ], [ $.1^28, $.1^238 ], [ $.1^7, $.1^54 ], [ $.1^8, $.1^78 ], [ $.1^21, $.1^166 ], [ $.1^2, $.1^31 ], [ $.1^29, $.1^231 ], [ $.1^28, $.1^239 ], [ $.1^23, $.1^183 ], [ $.1^8, $.1^79 ], [ $.1^18, $.1^159 ], [ $.1^21, $.1^167 ], [ 1, $.1^16 ], [ $.1^35, $.1^264 ], [ $.1^31, $.1^232 ], [ $.1^25, $.1^216 ], [ $.1^12, $.1^112 ], [ $.1^9, $.1^88 ], [ $.1^15, $.1^104 ], [ $.1^16, $.1^145 ], [ $.1^32, $.1^273 ], [ $.1^29, $.1^249 ], [ $.1^21, $.1^185 ], [ $.1^22, $.1^161 ], [ $.1^38, $.1^289 ], [ $.1^42, $.1^321 ], [ $.1^11, $.1^74 ], [ $.1^29, $.1^250 ], [ $.1^28, $.1^242 ], [ $.1^36, $.1^306 ], [ $.1, $.1^27 ], [ $.1^33, $.1^283 ], [ $.1^13, $.1^123 ], [ $.1^11, $.1^75 ], [ $.1^18, $.1^131 ], [ $.1^21, $.1^187 ], [ $.1^36, $.1^307 ], [ $.1^8, $.1^84 ], [ $.1^28, $.1^244 ], [ $.1^9, $.1^92 ], [ $.1^18, $.1^132 ], [ $.1^20, $.1^180 ], [ $.1^37, $.1^316 ], [ $.1^40, $.1^340 ], [ $.1^43, $.1^332 ], [ $.1, $.1^29 ], [ $.1^6, $.1^37 ], [ $.1^2, $.1^5 ], [ $.1^16, $.1^149 ], [ $.1^8, $.1^86 ], [ $.1^17, $.1^158 ], [ $.1^39, $.1^302 ], [ $.1^5, $.1^63 ], [ $.1^29, $.1^255 ], [ $.1^24, $.1^215 ], [ $.1^13, $.1^127 ], [ $.1^39, $.1^303 ], [ $.1^12, $.1^120 ], [ $.1^15, $.1^96 ], [ $.1^20, $.1^184 ], [ $.1^36, $.1^312 ], [ $.1^43, $.1^320 ], [ 1, $.1^25 ], [ $.1^35, $.1^257 ], [ $.1^34, $.1^265 ], [ $.1^30, $.1^233 ], [ $.1^26, $.1^201 ], [ $.1^16, $.1^153 ], [ $.1^18, $.1^137 ], [ $.1^21, $.1^178 ], [ $.1^33, $.1^274 ], [ $.1^36, $.1^314 ], [ $.1^22, 6 ], [ $.1^39, $.1^291 ], [ $.1^2, $.1^12 ], [ $.1^27, $.1^196 ], [ $.1^26, $.1^204 ], [ $.1^7, $.1^36 ], [ $.1^3, $.1^4 ], [ $.1^43, $.1^324 ], [ $.1, $.1^21 ], [ $.1^28, $.1^253 ], [ $.1^25, $.1^213 ], [ $.1^14, $.1^109 ], [ $.1^4, $.1^61 ], [ $.1^8, $.1^93 ], [ $.1^21, $.1^181 ], [ $.1, $.1^22 ], [ $.1^14, $.1^110 ], [ $.1^19, $.1^134 ], [ $.1^21, $.1^182 ], [ $.1^22, $.1^174 ], [ $.1^5, $.1^55 ], [ $.1^14, $.1^111 ], [ $.1^20, $.1^191 ], [ $.1^6, $.1^16 ], [ $.1^31, $.1^216 ], [ $.1^28, $.1^192 ], [ $.1^27, $.1^248 ], [ $.1^25, $.1^232 ], [ $.1^9, $.1^104 ], [ $.1^15, $.1^88 ], [ $.1^20, $.1^128 ], [ $.1^21, $.1^136 ], [ $.1^5, $.1^9 ], [ $.1^34, $.1^305 ], [ $.1^32, $.1^289 ], [ $.1^28, $.1^193 ], [ $.1^13, $.1^73 ], [ $.1^16, $.1^161 ], [ $.1^22, $.1^145 ], [ $.1^38, $.1^273 ], [ $.1^12, $.1^66 ], [ $.1^29, $.1^202 ], [ $.1^20, $.1^130 ], [ $.1^45, $.1^330 ], [ $.1^7, $.1^27 ], [ $.1^36, $.1^259 ], [ $.1^39, $.1^283 ], [ $.1^14, $.1^84 ], [ $.1^15, $.1^92 ], [ $.1^19, $.1^188 ], [ $.1^46, $.1^340 ], [ 1, $.1^37 ], [ $.1^26, $.1^245 ], [ $.1^7, $.1^29 ], [ $.1^5, $.1^13 ], [ $.1^19, $.1^189 ], [ $.1^21, $.1^141 ], [ $.1^22, $.1^149 ], [ $.1^3, $.1^62 ], [ $.1^33, $.1^302 ], [ $.1^29, $.1^206 ], [ $.1^28, $.1^198 ], [ $.1^26, $.1^246 ], [ $.1^23, $.1^158 ], [ $.1^14, $.1^86 ], [ $.1^12, $.1^70 ], [ $.1^4, $.1^6 ], [ $.1^10, $.1^119 ], [ $.1^33, $.1^303 ], [ $.1^30, $.1^215 ], [ $.1^21, $.1^143 ], [ $.1^36, $.1^263 ], [ $.1^9, $.1^96 ], [ $.1^28, $.1^200 ], [ $.1^13, $.1^64 ], [ $.1^37, $.1^256 ], [ $.1^2, 3 ], [ $.1^27, $.1^241 ], [ $.1^24, $.1^233 ], [ $.1^6, $.1^25 ], [ $.1^19, $.1^177 ], [ $.1^22, $.1^153 ], [ $.1^44, $.1^329 ], [ $.1^39, $.1^274 ], [ $.1^13, $.1^67 ], [ $.1^34, $.1^315 ], [ $.1^33, $.1^291 ], [ $.1^26, $.1^251 ], [ $.1^16, 6 ], [ $.1^20, $.1^139 ], [ $.1^36, $.1^267 ], [ $.1, $.1^36 ], [ $.1^13, $.1^68 ], [ $.1^2, $.1^60 ], [ $.1^7, $.1^21 ], [ $.1^31, $.1^213 ], [ $.1^14, $.1^93 ], [ $.1^12, $.1^77 ], [ $.1^8, $.1^109 ], [ $.1^7, $.1^22 ], [ $.1^34, $.1^318 ], [ $.1^11, $.1^118 ], [ $.1^8, $.1^110 ], [ $.1^10, $.1^126 ], [ $.1^16, $.1^174 ], [ $.1^35, $.1^310 ], [ $.1^8, $.1^111 ], [ $.1^28, $.1^207 ], [ $.1^13, $.1^71 ], [ $.1^21, $.1^135 ], [ $.1^45, $.1^327 ], [ $.1^24, $.1^240 ], [ $.1^35, $.1^296 ], [ 1, $.1^49 ], [ $.1^6, $.1 ], [ $.1^4, $.1^17 ], [ $.1^19, $.1^169 ], [ $.1, $.1^58 ], [ $.1^29, $.1^218 ], [ $.1^26, $.1^226 ], [ $.1^23, $.1^138 ], [ $.1^6, $.1^2 ], [ $.1^4, $.1^18 ], [ $.1, $.1^59 ], [ $.1^31, $.1^203 ], [ $.1^30, $.1^195 ], [ $.1^2, $.1^35 ], [ $.1^8, $.1^115 ], [ $.1^35, $.1^299 ], [ $.1^36, $.1^275 ], [ $.1^3, $.1^44 ], [ $.1^25, $.1^252 ], [ $.1^23, $.1^140 ], [ $.1^8, $.1^116 ], [ $.1^38, $.1^260 ], [ $.1^39, $.1^268 ], [ $.1^10, $.1^101 ], [ $.1^33, $.1^317 ], [ $.1^32, $.1^309 ], [ $.1^31, $.1^205 ], [ $.1^30, $.1^197 ], [ $.1^27, $.1^237 ], [ $.1^35, $.1^301 ], [ $.1^39, $.1^269 ], [ $.1^46, $.1^325 ], [ $.1^5, $.1^30 ], [ $.1^34, $.1^294 ], [ $.1^25, $.1^254 ], [ $.1^23, $.1^142 ], [ $.1^13, $.1^94 ], [ $.1^38, $.1^262 ], [ $.1^46, $.1^326 ], [ $.1^47, $.1^334 ], [ $.1^2, $.1^39 ], [ $.1^33, $.1^319 ], [ $.1^32, $.1^311 ], [ $.1^30, $.1^199 ], [ $.1^12, $.1^87 ], [ $.1^6, $.1^7 ], [ $.1^4, $.1^23 ], [ $.1^20, $.1^151 ], [ $.1^39, $.1^271 ], [ $.1^7, 1 ], [ $.1^17, $.1^176 ], [ $.1^19, $.1^160 ], [ $.1^37, $.1^272 ], [ $.1^46, $.1^328 ], [ $.1^8, $.1^121 ], [ $.1^32, $.1^313 ], [ $.1^6, $.1^10 ], [ $.1^34, $.1^298 ], [ $.1^31, $.1^194 ], [ $.1^29, $.1^210 ], [ $.1^26, $.1^234 ], [ $.1^13, $.1^82 ], [ $.1^12, $.1^90 ], [ $.1^9, 2 ], [ $.1^39, $.1^258 ], [ $.1^47, $.1^322 ], [ $.1^6, $.1^11 ], [ $.1^11, $.1^99 ], [ $.1^7, $.1^3 ], [ $.1^46, $.1^331 ], [ $.1, $.1^52 ], [ $.1^33, $.1^308 ], [ $.1^5, $.1^20 ], [ $.1^8, $.1^124 ], [ $.1^35, $.1^292 ], [ $.1, $.1^53 ], [ $.1^8, $.1^125 ], [ $.1^9, $.1^117 ], [ $.1^15, $.1^69 ], [ $.1^36, 5 ], [ $.1^39, $.1^261 ], [ $.1, $.1^54 ], [ $.1^14, $.1^78 ], [ $.1^11, $.1^102 ], [ $.1^6, $.1^14 ], [ $.1^21, $.1^150 ], [ $.1^38, $.1^270 ], [ $.1^2, $.1^47 ], [ $.1^28, $.1^223 ], [ $.1^14, $.1^79 ], [ $.1^17, $.1^183 ], [ $.1^18, $.1^175 ], [ $.1^35, $.1^295 ], [ $.1^3, $.1^88 ], [ $.1^6, $.1^112 ], [ $.1^16, $.1^192 ], [ $.1^19, $.1^216 ], [ $.1^41, $.1^264 ], [ $.1, $.1^73 ], [ $.1^28, $.1^161 ], [ $.1^23, $.1^249 ], [ $.1^10, $.1^17 ], [ $.1^16, $.1^193 ], [ $.1^44, $.1^289 ], [ $.1^46, $.1^305 ], [ 1, $.1^66 ], [ $.1^33, $.1^330 ], [ $.1^23, $.1^250 ], [ $.1^10, $.1^18 ], [ $.1^17, $.1^202 ], [ $.1^20, $.1^226 ], [ $.1^22 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.169) Time: Mon Mar 15 08:52:56 2004 Input: seqt := [7^(r-1) : r in {1..3}]; seqt; P:=PolynomialRing(Integers()); t73 := x^(seqt[1]) + x^(seqt[2]) + x^(seqt[3]); t73; n73 := x^(seqt[1] + seqt[2] + seqt[3]); n73; Olav := {[a,b]: a,b in GF(7,3) | Evaluate(n73,a) eq Evaluate(t73,b)}; #Olav; Output: Magma V2.10-6 Mon Mar 15 2004 08:52:49 on modular [Seed = 302507797] ------------------------------------- [ 1, 7, 49 ] x^49 + x^7 + x x^57 16807 Total time: 7.039 seconds, Total memory usage: 5.38MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.169) Time: Mon Mar 15 09:02:33 2004 Input: P:=PolynomialRing(Integers()); seqt := func < q,r | [q^(a-1) : a in {1..r}]>; seqt(7,5); Output: Magma V2.10-6 Mon Mar 15 2004 09:02:30 on modular [Seed = 1735561255] ------------------------------------- [ 1, 7, 49, 343, 2401 ] Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.169) Time: Mon Mar 15 09:13:52 2004 Input: P:=PolynomialRing(Integers()); seqt := func < q,r | [q^(a-1) : a in {1..r}]>; polt := funtion(q,r) tmp := seqt(q,r); pol := 0; for i in {1..r} do pol := pol + tmp[i]; end for; return pol; end function; Output: Magma V2.10-6 Mon Mar 15 2004 09:13:49 on modular [Seed = 1146207855] ------------------------------------- >> tmp := seqt(q,r); ^ User error: bad syntax >> for i in {1..r} do ^ User error: Identifier 'r' has not been declared or assigned >> return pol; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.169) Time: Mon Mar 15 09:14:21 2004 Input: P:=PolynomialRing(Integers()); seqt := func < q,r | [q^(a-1) : a in {1..r}]>; polt := function(q,r) tmp := seqt(q,r); pol := 0; for i in {1..r} do pol := pol + tmp[i]; end for; return pol; end function; Output: Magma V2.10-6 Mon Mar 15 2004 09:14:17 on modular [Seed = 1297659714] ------------------------------------- Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.169) Time: Mon Mar 15 09:14:46 2004 Input: P:=PolynomialRing(Integers()); seqt := func < q,r | [q^(a-1) : a in {1..r}]>; polt := function(q,r) tmp := seqt(q,r); pol := 0; for i in {1..r} do pol := pol + tmp[i]; end for; return pol; end function; polt(7,3); Output: Magma V2.10-6 Mon Mar 15 2004 09:14:42 on modular [Seed = 2997307606] ------------------------------------- 57 Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.169) Time: Mon Mar 15 09:15:21 2004 Input: P:=PolynomialRing(Integers()); seqt := func < q,r | [q^(a-1) : a in {1..r}]>; polt := function(q,r) tmp := seqt(q,r); pol := 0; for i in {1..r} do pol := pol + x^tmp[i]; end for; return pol; end function; polt(7,3); Output: Magma V2.10-6 Mon Mar 15 2004 09:15:18 on modular [Seed = 2779799525] ------------------------------------- x^49 + x^7 + x Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.169) Time: Mon Mar 15 09:19:15 2004 Input: P:=PolynomialRing(Integers()); seq := func < q,r | [q^(a-1) : a in {1..r}]>; poln := function(q,r) tmp := seq(q,r); exp := 0; for i in {1..r} do exp := exp + seq[i]; end for; return (x^exp); end function; poln(7,3); Output: Magma V2.10-6 Mon Mar 15 2004 09:19:12 on modular [Seed = 2847691519] ------------------------------------- [
:5]( q: 7, r: 3 ) >> exp := exp + seq[i]; ^ Runtime error in '[]': Bad argument types Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.169) Time: Mon Mar 15 09:19:41 2004 Input: P:=PolynomialRing(Integers()); seq := func < q,r | [q^(a-1) : a in {1..r}]>; poln := function(q,r) tmp := seq(q,r); exp := 0; for i in {1..r} do exp := exp + tmp[i]; end for; return (x^exp); end function; poln(7,3); Output: Magma V2.10-6 Mon Mar 15 2004 09:19:38 on modular [Seed = 2659935698] ------------------------------------- x^57 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.169) Time: Mon Mar 15 09:24:27 2004 Input: P:=PolynomialRing(Integers()); seq := func < q,r | [q^(a-1) : a in {1..r}]>; POlav := function(q,r) Olav := {[a,b]: a,b in GF(q,r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)}; return Olav; end function; #POlav(7,3); Output: Magma V2.10-6 Mon Mar 15 2004 09:24:24 on modular [Seed = 2375577891] ------------------------------------- >> Olav := {[a,b]: a,b in GF(q,r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r ^ User error: Identifier 'poln' has not been declared or assigned >> #POlav(7,3); ^ User error: Identifier 'POlav' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.169) Time: Mon Mar 15 09:25:08 2004 Input: P:=PolynomialRing(Integers()); seq := func < q,r | [q^(a-1) : a in {1..r}]>; polt := function(q,r) tmp := seq(q,r); pol := 0; for i in {1..r} do pol := pol + x^tmp[i]; end for; return pol; end function; poln := function(q,r) tmp := seq(q,r); exp := 0; for i in {1..r} do exp := exp + tmp[i]; end for; return (x^exp); end function; POlav := function(q,r) Olav := {[a,b]: a,b in GF(q,r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)}; return Olav; end function; #POlav(7,3); Output: Magma V2.10-6 Mon Mar 15 2004 09:24:47 on modular [Seed = 4075228779] ------------------------------------- 16807 Total time: 21.770 seconds, Total memory usage: 5.38MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.169) Time: Mon Mar 15 09:29:13 2004 Input: P:=PolynomialRing(Integers()); seq := func < q,r | [q^(a-1) : a in {1..r}]>; polt := function(q,r) tmp := seq(q,r); pol := 0; for i in {1..r} do pol := pol + x^tmp[i]; end for; return pol; end function; poln := function(q,r) tmp := seq(q,r); exp := 0; for i in {1..r} do exp := exp + tmp[i]; end for; return (x^exp); end function; POlav := function(q,r) Olav := {[a,b]: a,b in GF(q,r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)}; return Olav; end function; #POlav(7,3); 7^(3-1); Output: Magma V2.10-6 Mon Mar 15 2004 09:28:51 on modular [Seed = 4009431931] ------------------------------------- 16807 49 Total time: 21.869 seconds, Total memory usage: 5.38MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.169) Time: Mon Mar 15 09:29:54 2004 Input: P:=PolynomialRing(Integers()); seq := func < q,r | [q^(a-1) : a in {1..r}]>; polt := function(q,r) tmp := seq(q,r); pol := 0; for i in {1..r} do pol := pol + x^tmp[i]; end for; return pol; end function; poln := function(q,r) tmp := seq(q,r); exp := 0; for i in {1..r} do exp := exp + tmp[i]; end for; return (x^exp); end function; POlav := function(q,r) Olav := {[a,b]: a,b in GF(q,r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)}; return Olav; end function; #POlav(7,3); 7^(2*3-1); Output: Magma V2.10-6 Mon Mar 15 2004 09:29:32 on modular [Seed = 3619826221] ------------------------------------- 16807 16807 Total time: 21.969 seconds, Total memory usage: 5.38MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.169) Time: Mon Mar 15 09:31:01 2004 Input: P:=PolynomialRing(Integers()); seq := func < q,r | [q^(a-1) : a in {1..r}]>; polt := function(q,r) tmp := seq(q,r); pol := 0; for i in {1..r} do pol := pol + x^tmp[i]; end for; return pol; end function; poln := function(q,r) tmp := seq(q,r); exp := 0; for i in {1..r} do exp := exp + tmp[i]; end for; return (x^exp); end function; POlav := function(q,r) Olav := {[a,b]: a,b in GF(q,r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)}; return Olav; end function; #POlav(2,5); 2^(2*5-1); Output: Magma V2.10-6 Mon Mar 15 2004 09:30:57 on modular [Seed = 3251912662] ------------------------------------- 512 512 Total time: 3.139 seconds, Total memory usage: 1.91MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.169) Time: Mon Mar 15 09:31:58 2004 Input: P:=PolynomialRing(Integers()); seq := func < q,r | [q^(a-1) : a in {1..r}]>; polt := function(q,r) tmp := seq(q,r); pol := 0; for i in {1..r} do pol := pol + x^tmp[i]; end for; return pol; end function; poln := function(q,r) tmp := seq(q,r); exp := 0; for i in {1..r} do exp := exp + tmp[i]; end for; return (x^exp); end function; POlav := function(q,r) Olav := {[a,b]: a,b in GF(q,r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)}; return Olav; end function; #POlav(6,4); 6^(2*4-1); Output: Magma V2.10-6 Mon Mar 15 2004 09:31:55 on modular [Seed = 925026651] ------------------------------------- [
:21]( q: 6, r: 4 ) >> Olav := {[a,b]: a,b in GF(q,r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r ^ Runtime error in 'GF': Argument 1 (6) should be prime 279936 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.169) Time: Mon Mar 15 09:33:02 2004 Input: P:=PolynomialRing(Integers()); seq := func < q,r | [q^(a-1) : a in {1..r}]>; polt := function(q,r) tmp := seq(q,r); pol := 0; for i in {1..r} do pol := pol + x^tmp[i]; end for; return pol; end function; poln := function(q,r) tmp := seq(q,r); exp := 0; for i in {1..r} do exp := exp + tmp[i]; end for; return (x^exp); end function; POlav := function(q,r) Olav := {[a,b]: a,b in GF(q,r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)}; return Olav; end function; #POlav(11,4); 11^(2*4-1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Mar 15 2004 09:32:39 on modular [Seed = 1043054734] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 30473 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.169) Time: Mon Mar 15 09:33:40 2004 Input: P:=PolynomialRing(Integers()); seq := func < q,r | [q^(a-1) : a in {1..r}]>; polt := function(q,r) tmp := seq(q,r); pol := 0; for i in {1..r} do pol := pol + x^tmp[i]; end for; return pol; end function; poln := function(q,r) tmp := seq(q,r); exp := 0; for i in {1..r} do exp := exp + tmp[i]; end for; return (x^exp); end function; POlav := function(q,r) Olav := {[a,b]: a,b in GF(q,r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)}; return Olav; end function; #POlav(5,4); 5^(2*4-1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Mar 15 2004 09:33:17 on modular [Seed = 623958975] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 30482 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.169) Time: Mon Mar 15 09:34:19 2004 Input: P:=PolynomialRing(Integers()); seq := func < q,r | [q^(a-1) : a in {1..r}]>; polt := function(q,r) tmp := seq(q,r); pol := 0; for i in {1..r} do pol := pol + x^tmp[i]; end for; return pol; end function; poln := function(q,r) tmp := seq(q,r); exp := 0; for i in {1..r} do exp := exp + tmp[i]; end for; return (x^exp); end function; POlav := function(q,r) Olav := {[a,b]: a,b in GF(q,r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)}; return Olav; end function; #POlav(5,4); 5^(2*4-1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Mar 15 2004 09:33:56 on modular [Seed = 708826313] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 30493 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.169) Time: Mon Mar 15 09:34:35 2004 Input: P:=PolynomialRing(Integers()); seq := func < q,r | [q^(a-1) : a in {1..r}]>; polt := function(q,r) tmp := seq(q,r); pol := 0; for i in {1..r} do pol := pol + x^tmp[i]; end for; return pol; end function; poln := function(q,r) tmp := seq(q,r); exp := 0; for i in {1..r} do exp := exp + tmp[i]; end for; return (x^exp); end function; POlav := function(q,r) Olav := {[a,b]: a,b in GF(q,r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)}; return Olav; end function; #POlav(5,2); 5^(2*2-1); Output: Magma V2.10-6 Mon Mar 15 2004 09:34:32 on modular [Seed = 285536222] ------------------------------------- 125 125 Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.169) Time: Mon Mar 15 09:35:18 2004 Input: P:=PolynomialRing(Integers()); seq := func < q,r | [q^(a-1) : a in {1..r}]>; polt := function(q,r) tmp := seq(q,r); pol := 0; for i in {1..r} do pol := pol + x^tmp[i]; end for; return pol; end function; poln := function(q,r) tmp := seq(q,r); exp := 0; for i in {1..r} do exp := exp + tmp[i]; end for; return (x^exp); end function; POlav := function(q,r) Olav := {[a,b]: a,b in GF(q,r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)}; return Olav; end function; #POlav(3,4); 3^(2*4-1); Output: Magma V2.10-6 Mon Mar 15 2004 09:35:14 on modular [Seed = 68287249] ------------------------------------- 2187 2187 Total time: 4.119 seconds, Total memory usage: 2.29MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.169) Time: Mon Mar 15 09:36:37 2004 Input: P:=PolynomialRing(Integers()); seq := func < q,r | [q^(a-1) : a in {1..r}]>; polt := function(q,r) tmp := seq(q,r); pol := 0; for i in {1..r} do pol := pol + x^tmp[i]; end for; return pol; end function; poln := function(q,r) tmp := seq(q,r); exp := 0; for i in {1..r} do exp := exp + tmp[i]; end for; return (x^exp); end function; POlav := function(q,r) Olav := {[a,b]: a,b in GF(q,r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)}; return Olav; end function; #POlav(11,3); 11^(2*3-1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Mar 15 2004 09:36:14 on modular [Seed = 169866595] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 30525 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.169) Time: Mon Mar 15 09:36:49 2004 Input: P:=PolynomialRing(Integers()); seq := func < q,r | [q^(a-1) : a in {1..r}]>; polt := function(q,r) tmp := seq(q,r); pol := 0; for i in {1..r} do pol := pol + x^tmp[i]; end for; return pol; end function; poln := function(q,r) tmp := seq(q,r); exp := 0; for i in {1..r} do exp := exp + tmp[i]; end for; return (x^exp); end function; POlav := function(q,r) Olav := {[a,b]: a,b in GF(q,r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)}; return Olav; end function; 11^(2*3-1); Output: Magma V2.10-6 Mon Mar 15 2004 09:36:46 on modular [Seed = 1885703993] ------------------------------------- 161051 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.169) Time: Mon Mar 15 09:38:30 2004 Input: P:=PolynomialRing(Integers()); seq := func < q,r | [q^(a-1) : a in {1..r}]>; polt := function(q,r) tmp := seq(q,r); pol := 0; for i in {1..r} do pol := pol + x^tmp[i]; end for; return pol; end function; poln := function(q,r) tmp := seq(q,r); exp := 0; for i in {1..r} do exp := exp + tmp[i]; end for; return (x^exp); end function; POlav := function(q,r) Olav := {[a,b]: a,b in GF(q,r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)}; return Olav; end function; POlav(5,2) in GF(5); Output: Magma V2.10-6 Mon Mar 15 2004 09:38:27 on modular [Seed = 1735563443] ------------------------------------- >> POlav(5,2) in GF(5); ^ Runtime error in 'in': Bad argument types Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mahler.is.nottingham.ac.uk. (128.243.40.94) Time: Mon Mar 15 09:38:52 2004 Input: Q:=Rationals(); QT:=FunctionField(Q); EC:=EllipticCurve([QT|0,0,T,2,-1]); EC; P2QT:=ProjectivePlane(QT); F:=CoordinateRing(P2QT)!DefiningPolynomial(EC); F; d:=1; L1:=AffineSpace(QT,3*(d+1)); L1; fx1:=&+[L1.(i+1)*T^i:i in [0..d]]; fy1:=&+[L1.(d+i+2)*T^i:i in [0..d]]; fz1:=&+[L1.(2*d+i+3)*T^i:i in [0..d]]; [fx1,fy1,fz1]; FT:=Evaluate(F,[fx1,fy1,fz1]); A:=PolynomialRing(CoordinateRing(L1)); Tt:=homA|t>; eqns:=Coefficients(homA|Tt,[L1.i:i in [1..3*(d+1)]]>(FT)); eqns1:=eqns; eqns1; P1:=ProjectiveSpace(Q,3*d+2); eqns1:=[CoordinateRing(P1)!eqn:eqn in eqns]; V1:=Scheme(P1,eqns1); I1:=Ideal(V1); Output: Magma V2.10-6 Mon Mar 15 2004 09:38:49 on modular [Seed = 1853591968] ------------------------------------- Elliptic Curve defined by y^2 + T*y = x^3 + 2*x - 1 over Univariate rational function field over Rational Field -X^3 - 2*X*Z^2 + Y^2*Z + T*Y*Z^2 + Z^3 Affine Space of dimension 6 Variables : $.1, $.2, $.3, $.4, $.5, $.6 [ $.1 + T*$.2, $.3 + T*$.4, $.5 + T*$.6 ] [ -$.1^3 - 2*$.1*$.5^2 + $.3^2*$.5 + $.5^3, -3*$.1^2*$.2 - 4*$.1*$.5*$.6 - 2*$.2*$.5^2 + $.3^2*$.6 + 2*$.3*$.4*$.5 + $.3*$.5^2 + 3*$.5^2*$.6, -3*$.1*$.2^2 - 2*$.1*$.6^2 - 4*$.2*$.5*$.6 + 2*$.3*$.4*$.6 + 2*$.3*$.5*$.6 + $.4^2*$.5 + $.4*$.5^2 + 3*$.5*$.6^2, -$.2^3 - 2*$.2*$.6^2 + $.3*$.6^2 + $.4^2*$.6 + 2*$.4*$.5*$.6 + $.6^3, $.4*$.6^2 ] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.169) Time: Mon Mar 15 09:39:11 2004 Input: P:=PolynomialRing(Integers()); seq := func < q,r | [q^(a-1) : a in {1..r}]>; polt := function(q,r) tmp := seq(q,r); pol := 0; for i in {1..r} do pol := pol + x^tmp[i]; end for; return pol; end function; poln := function(q,r) tmp := seq(q,r); exp := 0; for i in {1..r} do exp := exp + tmp[i]; end for; return (x^exp); end function; POlav := function(q,r) Olav := {[a,b]: a,b in GF(q,r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)}; return Olav; end function; POlav(5,2) meet GF(5); Output: Magma V2.10-6 Mon Mar 15 2004 09:39:08 on modular [Seed = 1430312302] ------------------------------------- >> POlav(5,2) meet GF(5); ^ Runtime error in 'meet': Bad argument types Argument types given: SetEnum[SeqEnum], FldFin Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mahler.is.nottingham.ac.uk. (128.243.40.94) Time: Mon Mar 15 09:40:03 2004 Input: Q:=Rationals(); QT:=FunctionField(Q); EC:=EllipticCurve([QT|0,0,T,2,-1]); EC; P2QT:=ProjectivePlane(QT); F:=CoordinateRing(P2QT)!DefiningPolynomial(EC); F; d:=1; L1:=AffineSpace(QT,3*(d+1)); L1; fx1:=&+[L1.(i+1)*T^i:i in [0..d]]; fy1:=&+[L1.(d+i+2)*T^i:i in [0..d]]; fz1:=&+[L1.(2*d+i+3)*T^i:i in [0..d]]; [fx1,fy1,fz1]; FT:=Evaluate(F,[fx1,fy1,fz1]); A:=PolynomialRing(CoordinateRing(L1)); Tt:=homA|t>; eqns:=Coefficients(homA|Tt,[L1.i:i in [1..3*(d+1)]]>(FT)); eqns1:=eqns; eqns1; P1:=ProjectiveSpace(Q,3*d+2); eqns1:=[CoordinateRing(P1)!eqn:eqn in eqns]; V1:=Scheme(P1,eqns1); I1:=Ideal(V1); rad1:=Radical(I1); Output: Magma V2.10-6 Mon Mar 15 2004 09:40:00 on modular [Seed = 1146209331] ------------------------------------- Elliptic Curve defined by y^2 + T*y = x^3 + 2*x - 1 over Univariate rational function field over Rational Field -X^3 - 2*X*Z^2 + Y^2*Z + T*Y*Z^2 + Z^3 Affine Space of dimension 6 Variables : $.1, $.2, $.3, $.4, $.5, $.6 [ $.1 + T*$.2, $.3 + T*$.4, $.5 + T*$.6 ] [ -$.1^3 - 2*$.1*$.5^2 + $.3^2*$.5 + $.5^3, -3*$.1^2*$.2 - 4*$.1*$.5*$.6 - 2*$.2*$.5^2 + $.3^2*$.6 + 2*$.3*$.4*$.5 + $.3*$.5^2 + 3*$.5^2*$.6, -3*$.1*$.2^2 - 2*$.1*$.6^2 - 4*$.2*$.5*$.6 + 2*$.3*$.4*$.6 + 2*$.3*$.5*$.6 + $.4^2*$.5 + $.4*$.5^2 + 3*$.5*$.6^2, -$.2^3 - 2*$.2*$.6^2 + $.3*$.6^2 + $.4^2*$.6 + 2*$.4*$.5*$.6 + $.6^3, $.4*$.6^2 ] Total time: 3.209 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host mahler.is.nottingham.ac.uk. (128.243.40.94) Time: Mon Mar 15 09:40:35 2004 Input: Q:=Rationals(); QT:=FunctionField(Q); EC:=EllipticCurve([QT|0,0,T,2,-1]); EC; P2QT:=ProjectivePlane(QT); F:=CoordinateRing(P2QT)!DefiningPolynomial(EC); F; d:=1; L1:=AffineSpace(QT,3*(d+1)); L1; fx1:=&+[L1.(i+1)*T^i:i in [0..d]]; fy1:=&+[L1.(d+i+2)*T^i:i in [0..d]]; fz1:=&+[L1.(2*d+i+3)*T^i:i in [0..d]]; [fx1,fy1,fz1]; FT:=Evaluate(F,[fx1,fy1,fz1]); A:=PolynomialRing(CoordinateRing(L1)); Tt:=homA|t>; eqns:=Coefficients(homA|Tt,[L1.i:i in [1..3*(d+1)]]>(FT)); eqns1:=eqns; eqns1; P1:=ProjectiveSpace(Q,3*d+2); eqns1:=[CoordinateRing(P1)!eqn:eqn in eqns]; V1:=Scheme(P1,eqns1); I1:=Ideal(V1); rad1:=Radical(I1); rad1; H1:=PrimaryDecomposition(rad1); H1; Output: Magma V2.10-6 Mon Mar 15 2004 09:40:32 on modular [Seed = 1247791645] ------------------------------------- Elliptic Curve defined by y^2 + T*y = x^3 + 2*x - 1 over Univariate rational function field over Rational Field -X^3 - 2*X*Z^2 + Y^2*Z + T*Y*Z^2 + Z^3 Affine Space of dimension 6 Variables : $.1, $.2, $.3, $.4, $.5, $.6 [ $.1 + T*$.2, $.3 + T*$.4, $.5 + T*$.6 ] [ -$.1^3 - 2*$.1*$.5^2 + $.3^2*$.5 + $.5^3, -3*$.1^2*$.2 - 4*$.1*$.5*$.6 - 2*$.2*$.5^2 + $.3^2*$.6 + 2*$.3*$.4*$.5 + $.3*$.5^2 + 3*$.5^2*$.6, -3*$.1*$.2^2 - 2*$.1*$.6^2 - 4*$.2*$.5*$.6 + 2*$.3*$.4*$.6 + 2*$.3*$.5*$.6 + $.4^2*$.5 + $.4*$.5^2 + 3*$.5*$.6^2, -$.2^3 - 2*$.2*$.6^2 + $.3*$.6^2 + $.4^2*$.6 + 2*$.4*$.5*$.6 + $.6^3, $.4*$.6^2 ] Ideal of Polynomial ring of rank 6 over Rational Field Lexicographical Order Variables: y1, y2, y3, y4, y5, y6 Radical Groebner basis: [ y1^3 + 2*y1*y5^2 - y5^3, y1^2*y2 + 2*y2*y5^2 - y5^2*y6, y1*y2^2 + 2*y2*y5*y6 - y5*y6^2, y1*y3, y1*y4^2 + y1*y4*y5, y1*y6 - y2*y5, y2^3 + 2*y2*y6^2 - y6^3, y2*y3, y2*y4, y3*y5, y3*y6, y4^2*y5 + y4*y5^2, y4*y6 ] [ Ideal of Polynomial ring of rank 6 over Rational Field Lexicographical Order Variables: y1, y2, y3, y4, y5, y6 Dimension 2, Radical, Prime Groebner basis: [ y1^3 + 2*y1*y5^2 - y5^3, y1^2*y2 + 2*y2*y5^2 - y5^2*y6, y1*y2^2 + 2*y2*y5*y6 - y5*y6^2, y1*y6 - y2*y5, y2^3 + 2*y2*y6^2 - y6^3, y3, y4 ], Ideal of Polynomial ring of rank 6 over Rational Field Lexicographical Order Variables: y1, y2, y3, y4, y5, y6 Dimension 2, Radical, Prime Groebner basis: [ y1, y2, y5, y6 ], Ideal of Polynomial ring of rank 6 over Rational Field Lexicographical Order Variables: y1, y2, y3, y4, y5, y6 Dimension 1, Radical, Prime Groebner basis: [ y1^3 + 2*y1*y5^2 - y5^3, y2, y3, y4 + y5, y6 ] ] Total time: 3.329 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.169) Time: Mon Mar 15 09:40:43 2004 Input: P:=PolynomialRing(Integers()); seq := func < q,r | [q^(a-1) : a in {1..r}]>; polt := function(q,r) tmp := seq(q,r); pol := 0; for i in {1..r} do pol := pol + x^tmp[i]; end for; return pol; end function; poln := function(q,r) tmp := seq(q,r); exp := 0; for i in {1..r} do exp := exp + tmp[i]; end for; return (x^exp); end function; POlav := function(q,r) Olav := {[a,b]: a,b in GF(q,r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)}; return Olav; end function; POlav(5,2); Output: Magma V2.10-6 Mon Mar 15 2004 09:40:40 on modular [Seed = 2980327918] ------------------------------------- { [ $.1^2, $.1^16 ], [ 1, $.1 ], [ $.1^2, $.1^17 ], [ $.1, $.1^10 ], [ 0, $.1^21 ], [ $.1, $.1^11 ], [ 1, $.1^4 ], [ 1, $.1^5 ], [ 0, 0 ], [ $.1, 1 ], [ $.1, $.1^2 ], [ $.1^3, $.1^19 ], [ $.1^3, $.1^22 ], [ $.1, $.1^7 ], [ $.1^3, $.1^23 ], [ 1, 3 ], [ 1, $.1^20 ], [ $.1^3, 4 ], [ $.1^2, 2 ], [ $.1^3, $.1^14 ], [ $.1^2, $.1^8 ], [ $.1^2, $.1^13 ], [ 2, $.1^16 ], [ $.1^4, $.1 ], [ 2, $.1^17 ], [ $.1^5, $.1^10 ], [ $.1^5, $.1^11 ], [ $.1^4, $.1^4 ], [ $.1^4, $.1^5 ], [ $.1^5, 1 ], [ $.1^5, $.1^2 ], [ $.1^7, $.1^19 ], [ $.1^7, $.1^22 ], [ $.1^5, $.1^7 ], [ $.1^7, $.1^23 ], [ $.1^4, 3 ], [ $.1^4, $.1^20 ], [ $.1^7, 4 ], [ 2, 2 ], [ $.1^7, $.1^14 ], [ 2, $.1^8 ], [ 2, $.1^13 ], [ $.1^10, $.1^16 ], [ $.1^8, $.1 ], [ $.1^10, $.1^17 ], [ $.1^9, $.1^10 ], [ $.1^9, $.1^11 ], [ $.1^8, $.1^4 ], [ $.1^8, $.1^5 ], [ $.1^9, 1 ], [ $.1^9, $.1^2 ], [ $.1^11, $.1^19 ], [ $.1^11, $.1^22 ], [ $.1^9, $.1^7 ], [ $.1^11, $.1^23 ], [ $.1^8, 3 ], [ $.1^8, $.1^20 ], [ $.1^11, 4 ], [ $.1^10, 2 ], [ $.1^11, $.1^14 ], [ $.1^10, $.1^8 ], [ $.1^10, $.1^13 ], [ $.1^14, $.1^16 ], [ 4, $.1 ], [ $.1^14, $.1^17 ], [ $.1^13, $.1^10 ], [ $.1^13, $.1^11 ], [ 4, $.1^4 ], [ 4, $.1^5 ], [ $.1^13, 1 ], [ $.1^13, $.1^2 ], [ $.1^15, $.1^19 ], [ $.1^15, $.1^22 ], [ $.1^13, $.1^7 ], [ $.1^15, $.1^23 ], [ 4, 3 ], [ 4, $.1^20 ], [ $.1^15, 4 ], [ $.1^14, 2 ], [ $.1^15, $.1^14 ], [ $.1^14, $.1^8 ], [ $.1^14, $.1^13 ], [ 3, $.1^16 ], [ $.1^16, $.1 ], [ 3, $.1^17 ], [ $.1^17, $.1^10 ], [ $.1^17, $.1^11 ], [ $.1^16, $.1^4 ], [ $.1^16, $.1^5 ], [ $.1^17, 1 ], [ $.1^17, $.1^2 ], [ $.1^19, $.1^19 ], [ $.1^19, $.1^22 ], [ $.1^17, $.1^7 ], [ $.1^19, $.1^23 ], [ $.1^16, 3 ], [ $.1^16, $.1^20 ], [ $.1^19, 4 ], [ 3, 2 ], [ $.1^19, $.1^14 ], [ 3, $.1^8 ], [ 3, $.1^13 ], [ $.1^22, $.1^16 ], [ $.1^20, $.1 ], [ $.1^22, $.1^17 ], [ $.1^21, $.1^10 ], [ $.1^21, $.1^11 ], [ $.1^20, $.1^4 ], [ $.1^20, $.1^5 ], [ $.1^21, 1 ], [ $.1^21, $.1^2 ], [ $.1^23, $.1^19 ], [ $.1^23, $.1^22 ], [ $.1^21, $.1^7 ], [ $.1^23, $.1^23 ], [ $.1^20, 3 ], [ $.1^20, $.1^20 ], [ $.1^23, 4 ], [ $.1^22, 2 ], [ $.1^23, $.1^14 ], [ $.1^22, $.1^8 ], [ $.1^22, $.1^13 ], [ 0, $.1^3 ], [ 0, $.1^9 ], [ 0, $.1^15 ] } Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.169) Time: Mon Mar 15 09:41:37 2004 Input: P:=PolynomialRing(Integers()); seq := func < q,r | [q^(a-1) : a in {1..r}]>; polt := function(q,r) tmp := seq(q,r); pol := 0; for i in {1..r} do pol := pol + x^tmp[i]; end for; return pol; end function; poln := function(q,r) tmp := seq(q,r); exp := 0; for i in {1..r} do exp := exp + tmp[i]; end for; return (x^exp); end function; POlav := function(q,r) Olav := [[a,b]: a,b in GF(q,r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)]; return Olav; end function; POlav(5,2) meet GF(5); Output: Magma V2.10-6 Mon Mar 15 2004 09:41:34 on modular [Seed = 2779784460] ------------------------------------- >> POlav(5,2) meet GF(5); ^ Runtime error in 'meet': Bad argument types Argument types given: SeqEnum[SeqEnum], FldFin Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mahler.is.nottingham.ac.uk. (128.243.40.94) Time: Mon Mar 15 09:41:42 2004 Input: Q:=Rationals(); QT:=FunctionField(Q); EC:=EllipticCurve([QT|0,0,T,2,-1]); EC; P2QT:=ProjectivePlane(QT); F:=CoordinateRing(P2QT)!DefiningPolynomial(EC); F; d:=1; L1:=AffineSpace(QT,3*(d+1)); L1; fx1:=&+[L1.(i+1)*T^i:i in [0..d]]; fy1:=&+[L1.(d+i+2)*T^i:i in [0..d]]; fz1:=&+[L1.(2*d+i+3)*T^i:i in [0..d]]; [fx1,fy1,fz1]; FT:=Evaluate(F,[fx1,fy1,fz1]); A:=PolynomialRing(CoordinateRing(L1)); Tt:=homA|t>; eqns:=Coefficients(homA|Tt,[L1.i:i in [1..3*(d+1)]]>(FT)); eqns1:=eqns; eqns1; P1:=ProjectiveSpace(Q,3*d+2); eqns1:=[CoordinateRing(P1)!eqn:eqn in eqns]; V1:=Scheme(P1,eqns1); I1:=Ideal(V1); rad1:=Radical(I1); rad1; H1:=PrimaryDecomposition(rad1); H1; J1:=PrimaryDecomposition(I1); J1; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Mar 15 2004 09:41:19 on modular [Seed = 3098359808] ------------------------------------- Elliptic Curve defined by y^2 + T*y = x^3 + 2*x - 1 over Univariate rational function field over Rational Field -X^3 - 2*X*Z^2 + Y^2*Z + T*Y*Z^2 + Z^3 Affine Space of dimension 6 Variables : $.1, $.2, $.3, $.4, $.5, $.6 [ $.1 + T*$.2, $.3 + T*$.4, $.5 + T*$.6 ] [ -$.1^3 - 2*$.1*$.5^2 + $.3^2*$.5 + $.5^3, -3*$.1^2*$.2 - 4*$.1*$.5*$.6 - 2*$.2*$.5^2 + $.3^2*$.6 + 2*$.3*$.4*$.5 + $.3*$.5^2 + 3*$.5^2*$.6, -3*$.1*$.2^2 - 2*$.1*$.6^2 - 4*$.2*$.5*$.6 + 2*$.3*$.4*$.6 + 2*$.3*$.5*$.6 + $.4^2*$.5 + $.4*$.5^2 + 3*$.5*$.6^2, -$.2^3 - 2*$.2*$.6^2 + $.3*$.6^2 + $.4^2*$.6 + 2*$.4*$.5*$.6 + $.6^3, $.4*$.6^2 ] Ideal of Polynomial ring of rank 6 over Rational Field Lexicographical Order Variables: y1, y2, y3, y4, y5, y6 Radical Groebner basis: [ y1^3 + 2*y1*y5^2 - y5^3, y1^2*y2 + 2*y2*y5^2 - y5^2*y6, y1*y2^2 + 2*y2*y5*y6 - y5*y6^2, y1*y3, y1*y4^2 + y1*y4*y5, y1*y6 - y2*y5, y2^3 + 2*y2*y6^2 - y6^3, y2*y3, y2*y4, y3*y5, y3*y6, y4^2*y5 + y4*y5^2, y4*y6 ] [ Ideal of Polynomial ring of rank 6 over Rational Field Lexicographical Order Variables: y1, y2, y3, y4, y5, y6 Dimension 2, Radical, Prime Groebner basis: [ y1^3 + 2*y1*y5^2 - y5^3, y1^2*y2 + 2*y2*y5^2 - y5^2*y6, y1*y2^2 + 2*y2*y5*y6 - y5*y6^2, y1*y6 - y2*y5, y2^3 + 2*y2*y6^2 - y6^3, y3, y4 ], Ideal of Polynomial ring of rank 6 over Rational Field Lexicographical Order Variables: y1, y2, y3, y4, y5, y6 Dimension 2, Radical, Prime Groebner basis: [ y1, y2, y5, y6 ], Ideal of Polynomial ring of rank 6 over Rational Field Lexicographical Order Variables: y1, y2, y3, y4, y5, y6 Dimension 1, Radical, Prime Groebner basis: [ y1^3 + 2*y1*y5^2 - y5^3, y2, y3, y4 + y5, y6 ] ] Errors: /home/mfd/gomagma: line 2: 30607 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.169) Time: Mon Mar 15 09:41:52 2004 Input: P:=PolynomialRing(Integers()); seq := func < q,r | [q^(a-1) : a in {1..r}]>; polt := function(q,r) tmp := seq(q,r); pol := 0; for i in {1..r} do pol := pol + x^tmp[i]; end for; return pol; end function; poln := function(q,r) tmp := seq(q,r); exp := 0; for i in {1..r} do exp := exp + tmp[i]; end for; return (x^exp); end function; POlav := function(q,r) Olav := [[a,b]: a,b in GF(q,r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)]; return Olav; end function; POlav(5,2) in GF(5); Output: Magma V2.10-6 Mon Mar 15 2004 09:41:49 on modular [Seed = 2525173260] ------------------------------------- >> POlav(5,2) in GF(5); ^ Runtime error in 'in': Bad argument types Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.169) Time: Mon Mar 15 09:43:01 2004 Input: P:=PolynomialRing(Integers()); seq := func < q,r | [q^(a-1) : a in {1..r}]>; polt := function(q,r) tmp := seq(q,r); pol := 0; for i in {1..r} do pol := pol + x^tmp[i]; end for; return pol; end function; poln := function(q,r) tmp := seq(q,r); exp := 0; for i in {1..r} do exp := exp + tmp[i]; end for; return (x^exp); end function; POlav := function(q,r) Olav := [[a,b]: a,b in GF(q,r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)]; return Olav; end function; sol := POlav(5,2) in GF(5); sol; Output: Magma V2.10-6 Mon Mar 15 2004 09:42:58 on modular [Seed = 2626231385] ------------------------------------- >> sol := POlav(5,2) in GF(5); ^ Runtime error in 'in': Bad argument types >> sol; ^ User error: Identifier 'sol' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.169) Time: Mon Mar 15 09:43:40 2004 Input: P:=PolynomialRing(Integers()); seq := func < q,r | [q^(a-1) : a in {1..r}]>; polt := function(q,r) tmp := seq(q,r); pol := 0; for i in {1..r} do pol := pol + x^tmp[i]; end for; return pol; end function; poln := function(q,r) tmp := seq(q,r); exp := 0; for i in {1..r} do exp := exp + tmp[i]; end for; return (x^exp); end function; POlav := function(q,r) Olav := {[a,b]: a,b in GF(q,r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)}; return Olav; end function; sol := POlav(5,2) meet GF(5); sol; Output: Magma V2.10-6 Mon Mar 15 2004 09:43:37 on modular [Seed = 2207646381] ------------------------------------- >> sol := POlav(5,2) meet GF(5); ^ Runtime error in 'meet': Bad argument types Argument types given: SetEnum[SeqEnum], FldFin >> sol; ^ User error: Identifier 'sol' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.169) Time: Mon Mar 15 09:44:55 2004 Input: P:=PolynomialRing(Integers()); seq := func < q,r | [q^(a-1) : a in {1..r}]>; polt := function(q,r) tmp := seq(q,r); pol := 0; for i in {1..r} do pol := pol + x^tmp[i]; end for; return pol; end function; poln := function(q,r) tmp := seq(q,r); exp := 0; for i in {1..r} do exp := exp + tmp[i]; end for; return (x^exp); end function; POlav := function(q,r) Olav := {[a,b]: a,b in GF(q,r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)}; return Olav; end function; sol := {a : a in POlav(5,2) | a in GF(5)}; sol; Output: Magma V2.10-6 Mon Mar 15 2004 09:44:52 on modular [Seed = 2325679065] ------------------------------------- >> sol := {a : a in POlav(5,2) | a in GF(5)}; ^ Runtime error in 'in': Bad argument types >> sol; ^ User error: Identifier 'sol' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.169) Time: Mon Mar 15 09:45:42 2004 Input: P:=PolynomialRing(Integers()); seq := func < q,r | [q^(a-1) : a in {1..r}]>; polt := function(q,r) tmp := seq(q,r); pol := 0; for i in {1..r} do pol := pol + x^tmp[i]; end for; return pol; end function; poln := function(q,r) tmp := seq(q,r); exp := 0; for i in {1..r} do exp := exp + tmp[i]; end for; return (x^exp); end function; POlav := function(q,r) Olav := {[a,b]: a,b in GF(q,r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)}; return Olav; end function; sol := {a : a in GF(5) | a in POlav(5,2)}; sol; Output: Magma V2.10-6 Mon Mar 15 2004 09:45:39 on modular [Seed = 4243160408] ------------------------------------- >> sol := {a : a in GF(5) | a in POlav(5,2)}; ^ Runtime error in 'in': Illegal coercion >> sol; ^ User error: Identifier 'sol' has not been declared or assigned Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.169) Time: Mon Mar 15 09:45:57 2004 Input: P:=PolynomialRing(Integers()); seq := func < q,r | [q^(a-1) : a in {1..r}]>; polt := function(q,r) tmp := seq(q,r); pol := 0; for i in {1..r} do pol := pol + x^tmp[i]; end for; return pol; end function; poln := function(q,r) tmp := seq(q,r); exp := 0; for i in {1..r} do exp := exp + tmp[i]; end for; return (x^exp); end function; POlav := function(q,r) Olav := {[a,b]: a,b in GF(q,r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)}; return Olav; end function; sol := {a : a in GF(5) | a meet POlav(5,2)}; sol; Output: Magma V2.10-6 Mon Mar 15 2004 09:45:54 on modular [Seed = 3807863671] ------------------------------------- >> sol := {a : a in GF(5) | a meet POlav(5,2)}; ^ Runtime error in 'meet': Bad argument types Argument types given: FldFinElt, SetEnum[SeqEnum] >> sol; ^ User error: Identifier 'sol' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.169) Time: Mon Mar 15 09:48:47 2004 Input: P:=PolynomialRing(Integers()); seq := func < q,r | [q^(a-1) : a in {1..r}]>; polt := function(q,r) tmp := seq(q,r); pol := 0; for i in {1..r} do pol := pol + x^tmp[i]; end for; return pol; end function; poln := function(q,r) tmp := seq(q,r); exp := 0; for i in {1..r} do exp := exp + tmp[i]; end for; return (x^exp); end function; POlav := function(q,r) Olav := {[a,b]: a,b in GF(q,r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)}; return Olav; end function; sol := {a : a in {GF(5)} | a meet POlav(5,2)}; sol; Output: Magma V2.10-6 Mon Mar 15 2004 09:48:44 on modular [Seed = 3925633938] ------------------------------------- >> sol := {a : a in {GF(5)} | a meet POlav(5,2)}; ^ Runtime error in 'meet': Bad argument types Argument types given: FldFin, SetEnum[SeqEnum] >> sol; ^ User error: Identifier 'sol' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.169) Time: Mon Mar 15 09:49:14 2004 Input: P:=PolynomialRing(Integers()); seq := func < q,r | [q^(a-1) : a in {1..r}]>; polt := function(q,r) tmp := seq(q,r); pol := 0; for i in {1..r} do pol := pol + x^tmp[i]; end for; return pol; end function; poln := function(q,r) tmp := seq(q,r); exp := 0; for i in {1..r} do exp := exp + tmp[i]; end for; return (x^exp); end function; POlav := function(q,r) Olav := {[a,b]: a,b in GF(q,r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)}; return Olav; end function; sol := {a : a in GF(5) | a meet POlav(5,2)}; sol; Output: Magma V2.10-6 Mon Mar 15 2004 09:49:10 on modular [Seed = 3720896396] ------------------------------------- >> sol := {a : a in GF(5) | a meet POlav(5,2)}; ^ Runtime error in 'meet': Bad argument types Argument types given: FldFinElt, SetEnum[SeqEnum] >> sol; ^ User error: Identifier 'sol' has not been declared or assigned Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.169) Time: Mon Mar 15 09:49:53 2004 Input: P:=PolynomialRing(Integers()); seq := func < q,r | [q^(a-1) : a in {1..r}]>; polt := function(q,r) tmp := seq(q,r); pol := 0; for i in {1..r} do pol := pol + x^tmp[i]; end for; return pol; end function; poln := function(q,r) tmp := seq(q,r); exp := 0; for i in {1..r} do exp := exp + tmp[i]; end for; return (x^exp); end function; POlav := function(q,r) Olav := {[a,b]: a,b in GF(q,r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)}; return Olav; end function; GF(5) meet POlav(5,2)}; Output: Magma V2.10-6 Mon Mar 15 2004 09:49:50 on modular [Seed = 3268886651] ------------------------------------- >> GF(5) meet POlav(5,2)}; ^ User error: bad syntax Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.169) Time: Mon Mar 15 09:50:04 2004 Input: P:=PolynomialRing(Integers()); seq := func < q,r | [q^(a-1) : a in {1..r}]>; polt := function(q,r) tmp := seq(q,r); pol := 0; for i in {1..r} do pol := pol + x^tmp[i]; end for; return pol; end function; poln := function(q,r) tmp := seq(q,r); exp := 0; for i in {1..r} do exp := exp + tmp[i]; end for; return (x^exp); end function; POlav := function(q,r) Olav := {[a,b]: a,b in GF(q,r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)}; return Olav; end function; GF(5) meet POlav(5,2); Output: Magma V2.10-6 Mon Mar 15 2004 09:50:01 on modular [Seed = 1026080668] ------------------------------------- >> GF(5) meet POlav(5,2); ^ Runtime error in 'meet': Bad argument types Argument types given: FldFin, SetEnum[SeqEnum] Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.169) Time: Mon Mar 15 09:51:53 2004 Input: P:=PolynomialRing(Integers()); seq := func < q,r | [q^(a-1) : a in {1..r}]>; polt := function(q,r) tmp := seq(q,r); pol := 0; for i in {1..r} do pol := pol + x^tmp[i]; end for; return pol; end function; poln := function(q,r) tmp := seq(q,r); exp := 0; for i in {1..r} do exp := exp + tmp[i]; end for; return (x^exp); end function; POlav := function(q,r) Olav := {[a,b]: a,b in GF(q,r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)}; return Olav; end function; sol := {[a,b] : a,b in GF(5) | [a,b] in POlav(5,2); Output: Magma V2.10-6 Mon Mar 15 2004 09:51:50 on modular [Seed = 675130134] ------------------------------------- >> sol := {[a,b] : a,b in GF(5) | [a,b] in POlav(5,2); ^ User error: bad syntax Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.169) Time: Mon Mar 15 09:52:09 2004 Input: P:=PolynomialRing(Integers()); seq := func < q,r | [q^(a-1) : a in {1..r}]>; polt := function(q,r) tmp := seq(q,r); pol := 0; for i in {1..r} do pol := pol + x^tmp[i]; end for; return pol; end function; poln := function(q,r) tmp := seq(q,r); exp := 0; for i in {1..r} do exp := exp + tmp[i]; end for; return (x^exp); end function; POlav := function(q,r) Olav := {[a,b]: a,b in GF(q,r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)}; return Olav; end function; sol := {[a,b] : a,b in GF(5) | [a,b] in POlav(5,2)}; sol; Output: Magma V2.10-6 Mon Mar 15 2004 09:52:04 on modular [Seed = 590782479] ------------------------------------- { [ 0, 0 ], [ 1, 3 ], [ 4, 3 ], [ 3, 2 ], [ 2, 2 ] } Total time: 4.750 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.169) Time: Mon Mar 15 09:53:48 2004 Input: P:=PolynomialRing(Integers()); seq := func < q,r | [q^(a-1) : a in {1..r}]>; polt := function(q,r) tmp := seq(q,r); pol := 0; for i in {1..r} do pol := pol + x^tmp[i]; end for; return pol; end function; poln := function(q,r) tmp := seq(q,r); exp := 0; for i in {1..r} do exp := exp + tmp[i]; end for; return (x^exp); end function; POlav := function(q,r) Olav := {[a,b]: a,b in GF(q,r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)}; return Olav; end function; sol := {[a,b] : a,b in GF(7) | [a,b] in POlav(7,3)}; sol; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Mar 15 2004 09:53:25 on modular [Seed = 470392641] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 30756 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.169) Time: Mon Mar 15 09:54:34 2004 Input: P:=PolynomialRing(Integers()); seq := func < q,r | [q^(a-1) : a in {1..r}]>; polt := function(q,r) tmp := seq(q,r); pol := 0; for i in {1..r} do pol := pol + x^tmp[i]; end for; return pol; end function; poln := function(q,r) tmp := seq(q,r); exp := 0; for i in {1..r} do exp := exp + tmp[i]; end for; return (x^exp); end function; POlav := function(q,r) Olav := {[a,b]: a,b in GF(q,r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)}; return Olav; end function; sol := {[a,b] : a,b in GF(7) | [a,b] in POlav(7,3)}; sol; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Mar 15 2004 09:54:11 on modular [Seed = 352360126] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 30765 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.169) Time: Mon Mar 15 09:55:05 2004 Input: P:=PolynomialRing(Integers()); seq := func < q,r | [q^(a-1) : a in {1..r}]>; polt := function(q,r) tmp := seq(q,r); pol := 0; for i in {1..r} do pol := pol + x^tmp[i]; end for; return pol; end function; poln := function(q,r) tmp := seq(q,r); exp := 0; for i in {1..r} do exp := exp + tmp[i]; end for; return (x^exp); end function; POlav := function(q,r) Olav := {[a,b]: a,b in GF(q,r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)}; return Olav; end function; sol := {[a,b] : a,b in GF(3) | [a,b] in POlav(3,4)}; sol; Output: Magma V2.10-6 Mon Mar 15 2004 09:54:52 on modular [Seed = 236686730] ------------------------------------- { [ 0, 0 ], [ 2, 1 ], [ 1, 1 ] } Total time: 13.090 seconds, Total memory usage: 2.29MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.14.169) Time: Mon Mar 15 09:55:27 2004 Input: P:=PolynomialRing(Integers()); seq := func < q,r | [q^(a-1) : a in {1..r}]>; polt := function(q,r) tmp := seq(q,r); pol := 0; for i in {1..r} do pol := pol + x^tmp[i]; end for; return pol; end function; poln := function(q,r) tmp := seq(q,r); exp := 0; for i in {1..r} do exp := exp + tmp[i]; end for; return (x^exp); end function; POlav := function(q,r) Olav := {[a,b]: a,b in GF(q,r) | Evaluate(poln(q,r),a) eq Evaluate(polt(q,r),b)}; return Olav; end function; sol := {[a,b] : a,b in GF(2) | [a,b] in POlav(2,5)}; sol; Output: Magma V2.10-6 Mon Mar 15 2004 09:55:23 on modular [Seed = 2104032926] ------------------------------------- { [ 0, 0 ], [ 1, 1 ] } Total time: 3.559 seconds, Total memory usage: 1.91MB ************** MAGMA ***************** Host aula-b-siee115.uab.es. (158.109.66.115) Time: Mon Mar 15 10:02:46 2004 Input: 4 mod 2; Output: Magma V2.10-6 Mon Mar 15 2004 10:02:43 on modular [Seed = 1380440057] ------------------------------------- 0 Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee115.uab.es. (158.109.66.115) Time: Mon Mar 15 10:04:48 2004 Input: for i:= 1 to 366 do if (i mod 7)-4 = 0 then i end if; end for; Output: Magma V2.10-6 Mon Mar 15 2004 10:04:45 on modular [Seed = 1280952953] ------------------------------------- >> if (i mod 7)-4 = 0 then i end if; ^ User error: bad syntax >> end for;; ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee115.uab.es. (158.109.66.115) Time: Mon Mar 15 10:05:02 2004 Input: for i:= 1 to 366 do if (i mod 7)-4 = 0 then i end if; end for;; Output: Magma V2.10-6 Mon Mar 15 2004 10:04:59 on modular [Seed = 1162920806] ------------------------------------- >> if (i mod 7)-4 = 0 then i end if; ^ User error: bad syntax >> end for;;; ^ User error: bad syntax Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee115.uab.es. (158.109.66.115) Time: Mon Mar 15 10:05:16 2004 Input: for i:= 1 to 366 do if (i mod 7)-4 = 0 then i end if; end for; Output: Magma V2.10-6 Mon Mar 15 2004 10:05:13 on modular [Seed = 2997302435] ------------------------------------- >> if (i mod 7)-4 = 0 then i end if; ^ User error: bad syntax >> end for; ^ User error: bad syntax Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee115.uab.es. (158.109.66.115) Time: Mon Mar 15 10:05:30 2004 Input: for i:= 1 to 366 do if ((i mod 7)-4 )= 0 then i end if; end for; Output: Magma V2.10-6 Mon Mar 15 2004 10:05:27 on modular [Seed = 2897816227] ------------------------------------- >> if ((i mod 7)-4 )= 0 then i end if; ^ User error: bad syntax >> end for; ^ User error: bad syntax Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee115.uab.es. (158.109.66.115) Time: Mon Mar 15 10:05:46 2004 Input: for i:= 1 to 366 do if (i mod 7)= 0 then i end if; end for; Output: Magma V2.10-6 Mon Mar 15 2004 10:05:43 on modular [Seed = 2779784154] ------------------------------------- >> if (i mod 7)= 0 then i end if; ^ User error: bad syntax >> end for; ^ User error: bad syntax Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee115.uab.es. (158.109.66.115) Time: Mon Mar 15 10:06:42 2004 Input: i:=1; while i < 367 do if (i mod 7)= 0 then i end if; end while; Output: Magma V2.10-6 Mon Mar 15 2004 10:06:39 on modular [Seed = 2659915993] ------------------------------------- >> while i < 367 do ^ User error: bad syntax >> if (i mod 7)= 0 then i end if; ^ User error: bad syntax >> end while; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee115.uab.es. (158.109.66.115) Time: Mon Mar 15 10:07:02 2004 Input: i:=1; while i < 367 do if (i mod 7)= 0 then i end if; i:=i+1; end while; Output: Magma V2.10-6 Mon Mar 15 2004 10:06:59 on modular [Seed = 2541883708] ------------------------------------- >> while i < 367 do ^ User error: bad syntax >> if (i mod 7)= 0 then i end if; ^ User error: bad syntax >> end while; ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee115.uab.es. (158.109.66.115) Time: Mon Mar 15 10:07:25 2004 Input: i:=1; while i < 367 do if (i mod 7) eq 0 then i end if; i:=i+1; end while; Output: Magma V2.10-6 Mon Mar 15 2004 10:07:22 on modular [Seed = 2173962003] ------------------------------------- >> while i < 367 do ^ User error: bad syntax >> if (i mod 7) eq 0 then i end if; ^ User error: bad syntax >> end while; ^ User error: bad syntax Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee115.uab.es. (158.109.66.115) Time: Mon Mar 15 10:07:39 2004 Input: i:=1; while i lt 367 do if (i mod 7) eq 0 then i end if; i:=i+1; end while; Output: Magma V2.10-6 Mon Mar 15 2004 10:07:36 on modular [Seed = 4209998970] ------------------------------------- >> if (i mod 7) eq 0 then i end if; ^ User error: bad syntax >> end while; ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee115.uab.es. (158.109.66.115) Time: Mon Mar 15 10:08:02 2004 Input: i:=1; while i lt 367 do if i mod 7 eq 0 then i end if; i:=i+1; end while; Output: Magma V2.10-6 Mon Mar 15 2004 10:07:59 on modular [Seed = 4091966724] ------------------------------------- >> if i mod 7 eq 0 then i end if; ^ User error: bad syntax >> end while; ^ User error: bad syntax Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee115.uab.es. (158.109.66.115) Time: Mon Mar 15 10:08:53 2004 Input: i:=1; while i lt 367 do modul:=i mod 7; if modul eq 0 then i end if; i:=i+1; end while; Output: Magma V2.10-6 Mon Mar 15 2004 10:08:50 on modular [Seed = 3975769046] ------------------------------------- >> if modul eq 0 then i end if; ^ User error: bad syntax >> end while; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee115.uab.es. (158.109.66.115) Time: Mon Mar 15 10:09:26 2004 Input: i:=1; while i lt 367 do modul:=i mod 7; if modul eq 0 then i else 0 end if; i:=i+1; end while; Output: Magma V2.10-6 Mon Mar 15 2004 10:09:23 on modular [Seed = 3857736446] ------------------------------------- >> if modul eq 0 then i else 0 end if; ^ User error: bad syntax >> end while; ^ User error: bad syntax Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee115.uab.es. (158.109.66.115) Time: Mon Mar 15 10:09:49 2004 Input: i:=1; while i lt 367 do modul:=i mod 7; if modul eq 0 then i else 0 end if; i:=i+1; end while; Output: Magma V2.10-6 Mon Mar 15 2004 10:09:46 on modular [Seed = 3737868764] ------------------------------------- >> if modul eq 0 then i else 0 end if; ^ User error: bad syntax >> end while; ^ User error: bad syntax Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee115.uab.es. (158.109.66.115) Time: Mon Mar 15 10:10:59 2004 Input: i:=1; while i lt 367 do modul:=i mod 7; if modul eq 0 then i elif end if; i:=i+1; end while; Output: Magma V2.10-6 Mon Mar 15 2004 10:10:55 on modular [Seed = 3235202936] ------------------------------------- >> if modul eq 0 then i elif end if; ^ User error: bad syntax >> end while; ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 93-BAR2-X4.libre.retevision.es. (62.82.186.93) Time: Mon Mar 15 10:15:08 2004 Input: ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; ptqr(3,4); Output: Magma V2.10-6 Mon Mar 15 2004 10:15:05 on modular [Seed = 1059764095] ------------------------------------- x^27 + x^9 + x^3 + x Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 93-BAR2-X4.libre.retevision.es. (62.82.186.93) Time: Mon Mar 15 10:17:20 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; pnqr(3,4); Output: Magma V2.10-6 Mon Mar 15 2004 10:17:17 on modular [Seed = 708813550] ------------------------------------- x^40 Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 93-BAR2-X4.libre.retevision.es. (62.82.186.93) Time: Mon Mar 15 10:17:44 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; pnqr(4,4); Output: Magma V2.10-6 Mon Mar 15 2004 10:17:41 on modular [Seed = 623946761] ------------------------------------- x^85 Total time: 2.969 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 93-BAR2-X4.libre.retevision.es. (62.82.186.93) Time: Mon Mar 15 10:17:56 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; pnqr(3,4); Output: Magma V2.10-6 Mon Mar 15 2004 10:17:53 on modular [Seed = 470390020] ------------------------------------- x^40 Total time: 3.049 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 93-BAR2-X4.libre.retevision.es. (62.82.186.93) Time: Mon Mar 15 10:20:16 2004 Input: ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; polavqr(3,4); Output: Magma V2.10-6 Mon Mar 15 2004 10:20:12 on modular [Seed = 253396634] ------------------------------------- [ [ 1, 1 ] ] [ [ 1, $.1 ] ] [ [ 1, $.1^2 ] ] [ [ 1, $.1^3 ] ] [ [ 1, $.1^6 ] ] [ [ 1, $.1^8 ] ] [ [ 1, $.1^9 ] ] [ [ 1, $.1^11 ] ] [ [ 1, $.1^18 ] ] [ [ 1, $.1^19 ] ] [ [ 1, $.1^23 ] ] [ [ 1, $.1^24 ] ] [ [ 1, $.1^27 ] ] [ [ 1, $.1^33 ] ] [ [ 1, $.1^44 ] ] [ [ 1, $.1^47 ] ] [ [ 1, $.1^50 ] ] [ [ 1, $.1^52 ] ] [ [ 1, $.1^54 ] ] [ [ 1, $.1^56 ] ] [ [ 1, $.1^57 ] ] [ [ 1, $.1^61 ] ] [ [ 1, $.1^68 ] ] [ [ 1, $.1^69 ] ] [ [ 1, $.1^70 ] ] [ [ 1, $.1^72 ] ] [ [ 1, $.1^76 ] ] [ [ $.1, $.1^4 ] ] [ [ $.1, $.1^7 ] ] [ [ $.1, $.1^10 ] ] [ [ $.1, $.1^12 ] ] [ [ $.1, $.1^14 ] ] [ [ $.1, $.1^16 ] ] [ [ $.1, $.1^17 ] ] [ [ $.1, $.1^21 ] ] [ [ $.1, $.1^28 ] ] [ [ $.1, $.1^29 ] ] [ [ $.1, $.1^30 ] ] [ [ $.1, $.1^32 ] ] [ [ $.1, $.1^36 ] ] [ [ $.1, 2 ] ] [ [ $.1, $.1^41 ] ] [ [ $.1, $.1^42 ] ] [ [ $.1, $.1^43 ] ] [ [ $.1, $.1^46 ] ] [ [ $.1, $.1^48 ] ] [ [ $.1, $.1^49 ] ] [ [ $.1, $.1^51 ] ] [ [ $.1, $.1^58 ] ] [ [ $.1, $.1^59 ] ] [ [ $.1, $.1^63 ] ] [ [ $.1, $.1^64 ] ] [ [ $.1, $.1^67 ] ] [ [ $.1, $.1^73 ] ] [ [ $.1^2, 1 ] ] [ [ $.1^2, $.1 ] ] [ [ $.1^2, $.1^2 ] ] [ [ $.1^2, $.1^3 ] ] [ [ $.1^2, $.1^6 ] ] [ [ $.1^2, $.1^8 ] ] [ [ $.1^2, $.1^9 ] ] [ [ $.1^2, $.1^11 ] ] [ [ $.1^2, $.1^18 ] ] [ [ $.1^2, $.1^19 ] ] [ [ $.1^2, $.1^23 ] ] [ [ $.1^2, $.1^24 ] ] [ [ $.1^2, $.1^27 ] ] [ [ $.1^2, $.1^33 ] ] [ [ $.1^2, $.1^44 ] ] [ [ $.1^2, $.1^47 ] ] [ [ $.1^2, $.1^50 ] ] [ [ $.1^2, $.1^52 ] ] [ [ $.1^2, $.1^54 ] ] [ [ $.1^2, $.1^56 ] ] [ [ $.1^2, $.1^57 ] ] [ [ $.1^2, $.1^61 ] ] [ [ $.1^2, $.1^68 ] ] [ [ $.1^2, $.1^69 ] ] [ [ $.1^2, $.1^70 ] ] [ [ $.1^2, $.1^72 ] ] [ [ $.1^2, $.1^76 ] ] [ [ $.1^3, $.1^4 ] ] [ [ $.1^3, $.1^7 ] ] [ [ $.1^3, $.1^10 ] ] [ [ $.1^3, $.1^12 ] ] [ [ $.1^3, $.1^14 ] ] [ [ $.1^3, $.1^16 ] ] [ [ $.1^3, $.1^17 ] ] [ [ $.1^3, $.1^21 ] ] [ [ $.1^3, $.1^28 ] ] [ [ $.1^3, $.1^29 ] ] [ [ $.1^3, $.1^30 ] ] [ [ $.1^3, $.1^32 ] ] [ [ $.1^3, $.1^36 ] ] [ [ $.1^3, 2 ] ] [ [ $.1^3, $.1^41 ] ] [ [ $.1^3, $.1^42 ] ] [ [ $.1^3, $.1^43 ] ] [ [ $.1^3, $.1^46 ] ] [ [ $.1^3, $.1^48 ] ] [ [ $.1^3, $.1^49 ] ] [ [ $.1^3, $.1^51 ] ] [ [ $.1^3, $.1^58 ] ] [ [ $.1^3, $.1^59 ] ] [ [ $.1^3, $.1^63 ] ] [ [ $.1^3, $.1^64 ] ] [ [ $.1^3, $.1^67 ] ] [ [ $.1^3, $.1^73 ] ] [ [ $.1^4, 1 ] ] [ [ $.1^4, $.1 ] ] [ [ $.1^4, $.1^2 ] ] [ [ $.1^4, $.1^3 ] ] [ [ $.1^4, $.1^6 ] ] [ [ $.1^4, $.1^8 ] ] [ [ $.1^4, $.1^9 ] ] [ [ $.1^4, $.1^11 ] ] [ [ $.1^4, $.1^18 ] ] [ [ $.1^4, $.1^19 ] ] [ [ $.1^4, $.1^23 ] ] [ [ $.1^4, $.1^24 ] ] [ [ $.1^4, $.1^27 ] ] [ [ $.1^4, $.1^33 ] ] [ [ $.1^4, $.1^44 ] ] [ [ $.1^4, $.1^47 ] ] [ [ $.1^4, $.1^50 ] ] [ [ $.1^4, $.1^52 ] ] [ [ $.1^4, $.1^54 ] ] [ [ $.1^4, $.1^56 ] ] [ [ $.1^4, $.1^57 ] ] [ [ $.1^4, $.1^61 ] ] [ [ $.1^4, $.1^68 ] ] [ [ $.1^4, $.1^69 ] ] [ [ $.1^4, $.1^70 ] ] [ [ $.1^4, $.1^72 ] ] [ [ $.1^4, $.1^76 ] ] [ [ $.1^5, $.1^4 ] ] [ [ $.1^5, $.1^7 ] ] [ [ $.1^5, $.1^10 ] ] [ [ $.1^5, $.1^12 ] ] [ [ $.1^5, $.1^14 ] ] [ [ $.1^5, $.1^16 ] ] [ [ $.1^5, $.1^17 ] ] [ [ $.1^5, $.1^21 ] ] [ [ $.1^5, $.1^28 ] ] [ [ $.1^5, $.1^29 ] ] [ [ $.1^5, $.1^30 ] ] [ [ $.1^5, $.1^32 ] ] [ [ $.1^5, $.1^36 ] ] [ [ $.1^5, 2 ] ] [ [ $.1^5, $.1^41 ] ] [ [ $.1^5, $.1^42 ] ] [ [ $.1^5, $.1^43 ] ] [ [ $.1^5, $.1^46 ] ] [ [ $.1^5, $.1^48 ] ] [ [ $.1^5, $.1^49 ] ] [ [ $.1^5, $.1^51 ] ] [ [ $.1^5, $.1^58 ] ] [ [ $.1^5, $.1^59 ] ] [ [ $.1^5, $.1^63 ] ] [ [ $.1^5, $.1^64 ] ] [ [ $.1^5, $.1^67 ] ] [ [ $.1^5, $.1^73 ] ] [ [ $.1^6, 1 ] ] [ [ $.1^6, $.1 ] ] [ [ $.1^6, $.1^2 ] ] [ [ $.1^6, $.1^3 ] ] [ [ $.1^6, $.1^6 ] ] [ [ $.1^6, $.1^8 ] ] [ [ $.1^6, $.1^9 ] ] [ [ $.1^6, $.1^11 ] ] [ [ $.1^6, $.1^18 ] ] [ [ $.1^6, $.1^19 ] ] [ [ $.1^6, $.1^23 ] ] [ [ $.1^6, $.1^24 ] ] [ [ $.1^6, $.1^27 ] ] [ [ $.1^6, $.1^33 ] ] [ [ $.1^6, $.1^44 ] ] [ [ $.1^6, $.1^47 ] ] [ [ $.1^6, $.1^50 ] ] [ [ $.1^6, $.1^52 ] ] [ [ $.1^6, $.1^54 ] ] [ [ $.1^6, $.1^56 ] ] [ [ $.1^6, $.1^57 ] ] [ [ $.1^6, $.1^61 ] ] [ [ $.1^6, $.1^68 ] ] [ [ $.1^6, $.1^69 ] ] [ [ $.1^6, $.1^70 ] ] [ [ $.1^6, $.1^72 ] ] [ [ $.1^6, $.1^76 ] ] [ [ $.1^7, $.1^4 ] ] [ [ $.1^7, $.1^7 ] ] [ [ $.1^7, $.1^10 ] ] [ [ $.1^7, $.1^12 ] ] [ [ $.1^7, $.1^14 ] ] [ [ $.1^7, $.1^16 ] ] [ [ $.1^7, $.1^17 ] ] [ [ $.1^7, $.1^21 ] ] [ [ $.1^7, $.1^28 ] ] [ [ $.1^7, $.1^29 ] ] [ [ $.1^7, $.1^30 ] ] [ [ $.1^7, $.1^32 ] ] [ [ $.1^7, $.1^36 ] ] [ [ $.1^7, 2 ] ] [ [ $.1^7, $.1^41 ] ] [ [ $.1^7, $.1^42 ] ] [ [ $.1^7, $.1^43 ] ] [ [ $.1^7, $.1^46 ] ] [ [ $.1^7, $.1^48 ] ] [ [ $.1^7, $.1^49 ] ] [ [ $.1^7, $.1^51 ] ] [ [ $.1^7, $.1^58 ] ] [ [ $.1^7, $.1^59 ] ] [ [ $.1^7, $.1^63 ] ] [ [ $.1^7, $.1^64 ] ] [ [ $.1^7, $.1^67 ] ] [ [ $.1^7, $.1^73 ] ] [ [ $.1^8, 1 ] ] [ [ $.1^8, $.1 ] ] [ [ $.1^8, $.1^2 ] ] [ [ $.1^8, $.1^3 ] ] [ [ $.1^8, $.1^6 ] ] [ [ $.1^8, $.1^8 ] ] [ [ $.1^8, $.1^9 ] ] [ [ $.1^8, $.1^11 ] ] [ [ $.1^8, $.1^18 ] ] [ [ $.1^8, $.1^19 ] ] [ [ $.1^8, $.1^23 ] ] [ [ $.1^8, $.1^24 ] ] [ [ $.1^8, $.1^27 ] ] [ [ $.1^8, $.1^33 ] ] [ [ $.1^8, $.1^44 ] ] [ [ $.1^8, $.1^47 ] ] [ [ $.1^8, $.1^50 ] ] [ [ $.1^8, $.1^52 ] ] [ [ $.1^8, $.1^54 ] ] [ [ $.1^8, $.1^56 ] ] [ [ $.1^8, $.1^57 ] ] [ [ $.1^8, $.1^61 ] ] [ [ $.1^8, $.1^68 ] ] [ [ $.1^8, $.1^69 ] ] [ [ $.1^8, $.1^70 ] ] [ [ $.1^8, $.1^72 ] ] [ [ $.1^8, $.1^76 ] ] [ [ $.1^9, $.1^4 ] ] [ [ $.1^9, $.1^7 ] ] [ [ $.1^9, $.1^10 ] ] [ [ $.1^9, $.1^12 ] ] [ [ $.1^9, $.1^14 ] ] [ [ $.1^9, $.1^16 ] ] [ [ $.1^9, $.1^17 ] ] [ [ $.1^9, $.1^21 ] ] [ [ $.1^9, $.1^28 ] ] [ [ $.1^9, $.1^29 ] ] [ [ $.1^9, $.1^30 ] ] [ [ $.1^9, $.1^32 ] ] [ [ $.1^9, $.1^36 ] ] [ [ $.1^9, 2 ] ] [ [ $.1^9, $.1^41 ] ] [ [ $.1^9, $.1^42 ] ] [ [ $.1^9, $.1^43 ] ] [ [ $.1^9, $.1^46 ] ] [ [ $.1^9, $.1^48 ] ] [ [ $.1^9, $.1^49 ] ] [ [ $.1^9, $.1^51 ] ] [ [ $.1^9, $.1^58 ] ] [ [ $.1^9, $.1^59 ] ] [ [ $.1^9, $.1^63 ] ] [ [ $.1^9, $.1^64 ] ] [ [ $.1^9, $.1^67 ] ] [ [ $.1^9, $.1^73 ] ] [ [ $.1^10, 1 ] ] [ [ $.1^10, $.1 ] ] [ [ $.1^10, $.1^2 ] ] [ [ $.1^10, $.1^3 ] ] [ [ $.1^10, $.1^6 ] ] [ [ $.1^10, $.1^8 ] ] [ [ $.1^10, $.1^9 ] ] [ [ $.1^10, $.1^11 ] ] [ [ $.1^10, $.1^18 ] ] [ [ $.1^10, $.1^19 ] ] [ [ $.1^10, $.1^23 ] ] [ [ $.1^10, $.1^24 ] ] [ [ $.1^10, $.1^27 ] ] [ [ $.1^10, $.1^33 ] ] [ [ $.1^10, $.1^44 ] ] [ [ $.1^10, $.1^47 ] ] [ [ $.1^10, $.1^50 ] ] [ [ $.1^10, $.1^52 ] ] [ [ $.1^10, $.1^54 ] ] [ [ $.1^10, $.1^56 ] ] [ [ $.1^10, $.1^57 ] ] [ [ $.1^10, $.1^61 ] ] [ [ $.1^10, $.1^68 ] ] [ [ $.1^10, $.1^69 ] ] [ [ $.1^10, $.1^70 ] ] [ [ $.1^10, $.1^72 ] ] [ [ $.1^10, $.1^76 ] ] [ [ $.1^11, $.1^4 ] ] [ [ $.1^11, $.1^7 ] ] [ [ $.1^11, $.1^10 ] ] [ [ $.1^11, $.1^12 ] ] [ [ $.1^11, $.1^14 ] ] [ [ $.1^11, $.1^16 ] ] [ [ $.1^11, $.1^17 ] ] [ [ $.1^11, $.1^21 ] ] [ [ $.1^11, $.1^28 ] ] [ [ $.1^11, $.1^29 ] ] [ [ $.1^11, $.1^30 ] ] [ [ $.1^11, $.1^32 ] ] [ [ $.1^11, $.1^36 ] ] [ [ $.1^11, 2 ] ] [ [ $.1^11, $.1^41 ] ] [ [ $.1^11, $.1^42 ] ] [ [ $.1^11, $.1^43 ] ] [ [ $.1^11, $.1^46 ] ] [ [ $.1^11, $.1^48 ] ] [ [ $.1^11, $.1^49 ] ] [ [ $.1^11, $.1^51 ] ] [ [ $.1^11, $.1^58 ] ] [ [ $.1^11, $.1^59 ] ] [ [ $.1^11, $.1^63 ] ] [ [ $.1^11, $.1^64 ] ] [ [ $.1^11, $.1^67 ] ] [ [ $.1^11, $.1^73 ] ] [ [ $.1^12, 1 ] ] [ [ $.1^12, $.1 ] ] [ [ $.1^12, $.1^2 ] ] [ [ $.1^12, $.1^3 ] ] [ [ $.1^12, $.1^6 ] ] [ [ $.1^12, $.1^8 ] ] [ [ $.1^12, $.1^9 ] ] [ [ $.1^12, $.1^11 ] ] [ [ $.1^12, $.1^18 ] ] [ [ $.1^12, $.1^19 ] ] [ [ $.1^12, $.1^23 ] ] [ [ $.1^12, $.1^24 ] ] [ [ $.1^12, $.1^27 ] ] [ [ $.1^12, $.1^33 ] ] [ [ $.1^12, $.1^44 ] ] [ [ $.1^12, $.1^47 ] ] [ [ $.1^12, $.1^50 ] ] [ [ $.1^12, $.1^52 ] ] [ [ $.1^12, $.1^54 ] ] [ [ $.1^12, $.1^56 ] ] [ [ $.1^12, $.1^57 ] ] [ [ $.1^12, $.1^61 ] ] [ [ $.1^12, $.1^68 ] ] [ [ $.1^12, $.1^69 ] ] [ [ $.1^12, $.1^70 ] ] [ [ $.1^12, $.1^72 ] ] [ [ $.1^12, $.1^76 ] ] [ [ $.1^13, $.1^4 ] ] [ [ $.1^13, $.1^7 ] ] [ [ $.1^13, $.1^10 ] ] [ [ $.1^13, $.1^12 ] ] [ [ $.1^13, $.1^14 ] ] [ [ $.1^13, $.1^16 ] ] [ [ $.1^13, $.1^17 ] ] [ [ $.1^13, $.1^21 ] ] [ [ $.1^13, $.1^28 ] ] [ [ $.1^13, $.1^29 ] ] [ [ $.1^13, $.1^30 ] ] [ [ $.1^13, $.1^32 ] ] [ [ $.1^13, $.1^36 ] ] [ [ $.1^13, 2 ] ] [ [ $.1^13, $.1^41 ] ] [ [ $.1^13, $.1^42 ] ] [ [ $.1^13, $.1^43 ] ] [ [ $.1^13, $.1^46 ] ] [ [ $.1^13, $.1^48 ] ] [ [ $.1^13, $.1^49 ] ] [ [ $.1^13, $.1^51 ] ] [ [ $.1^13, $.1^58 ] ] [ [ $.1^13, $.1^59 ] ] [ [ $.1^13, $.1^63 ] ] [ [ $.1^13, $.1^64 ] ] [ [ $.1^13, $.1^67 ] ] [ [ $.1^13, $.1^73 ] ] [ [ $.1^14, 1 ] ] [ [ $.1^14, $.1 ] ] [ [ $.1^14, $.1^2 ] ] [ [ $.1^14, $.1^3 ] ] [ [ $.1^14, $.1^6 ] ] [ [ $.1^14, $.1^8 ] ] [ [ $.1^14, $.1^9 ] ] [ [ $.1^14, $.1^11 ] ] [ [ $.1^14, $.1^18 ] ] [ [ $.1^14, $.1^ ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 93-BAR2-X4.libre.retevision.es. (62.82.186.93) Time: Mon Mar 15 10:22:52 2004 Input: ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; polavqr(1,2); Output: Magma V2.10-6 Mon Mar 15 2004 10:22:49 on modular [Seed = 2020471304] ------------------------------------- [
:19]( q: 1, r: 2 ) >> for i in GF(q^r) do ^ Runtime error in 'GF': Argument 1 (1) should be >= 2 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 93-BAR2-X4.libre.retevision.es. (62.82.186.93) Time: Mon Mar 15 10:23:25 2004 Input: ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; polavqr(2,2); Output: Magma V2.10-6 Mon Mar 15 2004 10:23:22 on modular [Seed = 1936128288] ------------------------------------- [ [ 1, $.1 ] ] [ [ 1, $.1^2 ] ] [ [ $.1, $.1 ] ] [ [ $.1, $.1^2 ] ] [ [ $.1^2, $.1 ] ] [ [ $.1^2, $.1^2 ] ] [ [ 0, 1 ] ] [ [ 0, 0 ] ] [] Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 93-BAR2-X4.libre.retevision.es. (62.82.186.93) Time: Mon Mar 15 10:25:29 2004 Input: ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; #polavqr(1,2); 1^(2*2-1); Output: Magma V2.10-6 Mon Mar 15 2004 10:25:25 on modular [Seed = 1618340543] ------------------------------------- [
:19]( q: 1, r: 2 ) >> for i in GF(q^r) do ^ Runtime error in 'GF': Argument 1 (1) should be >= 2 1 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 93-BAR2-X4.libre.retevision.es. (62.82.186.93) Time: Mon Mar 15 10:26:15 2004 Input: ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; #polavqr(2,2); 2^(2*2-1); Output: Magma V2.10-6 Mon Mar 15 2004 10:26:12 on modular [Seed = 1531891830] ------------------------------------- [ [ 1, $.1 ] ] [ [ 1, $.1^2 ] ] [ [ $.1, $.1 ] ] [ [ $.1, $.1^2 ] ] [ [ $.1^2, $.1 ] ] [ [ $.1^2, $.1^2 ] ] [ [ 0, 1 ] ] [ [ 0, 0 ] ] 0 8 Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 93-BAR2-X4.libre.retevision.es. (62.82.186.93) Time: Mon Mar 15 10:26:52 2004 Input: ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); end if; end for; end for; return C; end function; #(polavqr(2,2)); 2^(2*2-1); Output: Magma V2.10-6 Mon Mar 15 2004 10:26:49 on modular [Seed = 1380440402] ------------------------------------- [ [ 1, $.1 ] ] [ [ 1, $.1^2 ] ] [ [ $.1, $.1 ] ] [ [ $.1, $.1^2 ] ] [ [ $.1^2, $.1 ] ] [ [ $.1^2, $.1^2 ] ] [ [ 0, 1 ] ] [ [ 0, 0 ] ] 0 8 Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host LLN-DHCP-87.grenoble.cnrs.fr. (147.173.65.87) Time: Mon Mar 15 10:43:42 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Mon Mar 15 2004 10:43:39 on modular [Seed = 3064150436] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Mon Mar 15 10:56:22 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, x^12*y^3, x^12*y^4, x^12*y^5, x^12*y^6, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x^13*y^3, x^13*y^4, x^13*y^5, x^13*y^6, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^14*y^6, x^14*y^3, x^14*y^4, x^14*y^5, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^12, x^12*y^5, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^11*y^5, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^5*y^9, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; L := [ x^3*y^11]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Mon Mar 15 2004 10:56:18 on modular [Seed = 4176308963] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] [ x^3*y^11 ] [ false ] Total time: 3.499 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host 93-BAR2-X4.libre.retevision.es. (62.82.186.93) Time: Mon Mar 15 10:56:22 2004 Input: ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; polavqr:=function(q,r) C:=[]; p:=0; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); p:=p+1; end if; end for; end for; return C,p; end function; polavqr(2,2); 2^(2*2-1); Output: Magma V2.10-6 Mon Mar 15 2004 10:56:19 on modular [Seed = 4209993952] ------------------------------------- [ [ 1, $.1 ] ] [ [ 1, $.1^2 ] ] [ [ $.1, $.1 ] ] [ [ $.1, $.1^2 ] ] [ [ $.1^2, $.1 ] ] [ [ $.1^2, $.1^2 ] ] [ [ 0, 1 ] ] [ [ 0, 0 ] ] [] 8 8 Total time: 3.519 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 93-BAR2-X4.libre.retevision.es. (62.82.186.93) Time: Mon Mar 15 10:57:24 2004 Input: ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; polavqr:=function(q,r) C:=[]; p:=0; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); p:=p+1; end if; end for; end for; return C,p; end function; #polavqr(14,2); 14^(2*2-1); Output: Magma V2.10-6 Mon Mar 15 2004 10:57:21 on modular [Seed = 4026170807] ------------------------------------- [
:19]( q: 14, r: 2 ) >> for i in GF(q^r) do ^ Runtime error in 'GF': Argument 1 (196) is not a prime power 2744 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 93-BAR2-X4.libre.retevision.es. (62.82.186.93) Time: Mon Mar 15 10:57:52 2004 Input: ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; polavqr:=function(q,r) C:=[]; p:=0; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); p:=p+1; end if; end for; end for; return C,p; end function; #polavqr(13,2); 13^(2*2-1); Output: Magma V2.10-6 Mon Mar 15 2004 10:57:45 on modular [Seed = 3874714790] ------------------------------------- [ [ 1, $.1 ] ] [ [ 1, $.1^4 ] ] [ [ 1, $.1^13 ] ] [ [ 1, $.1^30 ] ] [ [ 1, $.1^52 ] ] [ [ 1, $.1^54 ] ] [ [ 1, $.1^62 ] ] [ [ 1, $.1^75 ] ] [ [ 1, $.1^129 ] ] [ [ 1, $.1^134 ] ] [ [ 1, $.1^135 ] ] [ [ 1, 7 ] ] [ [ 1, $.1^165 ] ] [ [ $.1, 1 ] ] [ [ $.1, $.1^11 ] ] [ [ $.1, $.1^15 ] ] [ [ $.1, $.1^18 ] ] [ [ $.1, $.1^27 ] ] [ [ $.1, $.1^44 ] ] [ [ $.1, $.1^66 ] ] [ [ $.1, $.1^68 ] ] [ [ $.1, $.1^76 ] ] [ [ $.1, $.1^89 ] ] [ [ $.1, $.1^143 ] ] [ [ $.1, $.1^148 ] ] [ [ $.1, $.1^149 ] ] [ [ $.1^2, 2 ] ] [ [ $.1^2, $.1^25 ] ] [ [ $.1^2, $.1^29 ] ] [ [ $.1^2, $.1^32 ] ] [ [ $.1^2, $.1^41 ] ] [ [ $.1^2, $.1^58 ] ] [ [ $.1^2, $.1^80 ] ] [ [ $.1^2, $.1^82 ] ] [ [ $.1^2, $.1^90 ] ] [ [ $.1^2, $.1^103 ] ] [ [ $.1^2, $.1^157 ] ] [ [ $.1^2, $.1^162 ] ] [ [ $.1^2, $.1^163 ] ] [ [ $.1^3, $.1^3 ] ] [ [ $.1^3, $.1^8 ] ] [ [ $.1^3, $.1^9 ] ] [ [ $.1^3, 4 ] ] [ [ $.1^3, $.1^39 ] ] [ [ $.1^3, $.1^43 ] ] [ [ $.1^3, $.1^46 ] ] [ [ $.1^3, $.1^55 ] ] [ [ $.1^3, $.1^72 ] ] [ [ $.1^3, $.1^94 ] ] [ [ $.1^3, $.1^96 ] ] [ [ $.1^3, $.1^104 ] ] [ [ $.1^3, $.1^117 ] ] [ [ $.1^4, $.1^17 ] ] [ [ $.1^4, $.1^22 ] ] [ [ $.1^4, $.1^23 ] ] [ [ $.1^4, 8 ] ] [ [ $.1^4, $.1^53 ] ] [ [ $.1^4, $.1^57 ] ] [ [ $.1^4, $.1^60 ] ] [ [ $.1^4, $.1^69 ] ] [ [ $.1^4, $.1^86 ] ] [ [ $.1^4, $.1^108 ] ] [ [ $.1^4, $.1^110 ] ] [ [ $.1^4, $.1^118 ] ] [ [ $.1^4, $.1^131 ] ] [ [ $.1^5, $.1^31 ] ] [ [ $.1^5, $.1^36 ] ] [ [ $.1^5, $.1^37 ] ] [ [ $.1^5, 3 ] ] [ [ $.1^5, $.1^67 ] ] [ [ $.1^5, $.1^71 ] ] [ [ $.1^5, $.1^74 ] ] [ [ $.1^5, $.1^83 ] ] [ [ $.1^5, $.1^100 ] ] [ [ $.1^5, $.1^122 ] ] [ [ $.1^5, $.1^124 ] ] [ [ $.1^5, $.1^132 ] ] [ [ $.1^5, $.1^145 ] ] [ [ $.1^6, $.1^45 ] ] [ [ $.1^6, $.1^50 ] ] [ [ $.1^6, $.1^51 ] ] [ [ $.1^6, 6 ] ] [ [ $.1^6, $.1^81 ] ] [ [ $.1^6, $.1^85 ] ] [ [ $.1^6, $.1^88 ] ] [ [ $.1^6, $.1^97 ] ] [ [ $.1^6, $.1^114 ] ] [ [ $.1^6, $.1^136 ] ] [ [ $.1^6, $.1^138 ] ] [ [ $.1^6, $.1^146 ] ] [ [ $.1^6, $.1^159 ] ] [ [ $.1^7, $.1^5 ] ] [ [ $.1^7, $.1^59 ] ] [ [ $.1^7, $.1^64 ] ] [ [ $.1^7, $.1^65 ] ] [ [ $.1^7, 12 ] ] [ [ $.1^7, $.1^95 ] ] [ [ $.1^7, $.1^99 ] ] [ [ $.1^7, $.1^102 ] ] [ [ $.1^7, $.1^111 ] ] [ [ $.1^7, $.1^128 ] ] [ [ $.1^7, $.1^150 ] ] [ [ $.1^7, $.1^152 ] ] [ [ $.1^7, $.1^160 ] ] [ [ $.1^8, $.1^6 ] ] [ [ $.1^8, $.1^19 ] ] [ [ $.1^8, $.1^73 ] ] [ [ $.1^8, $.1^78 ] ] [ [ $.1^8, $.1^79 ] ] [ [ $.1^8, 11 ] ] [ [ $.1^8, $.1^109 ] ] [ [ $.1^8, $.1^113 ] ] [ [ $.1^8, $.1^116 ] ] [ [ $.1^8, $.1^125 ] ] [ [ $.1^8, $.1^142 ] ] [ [ $.1^8, $.1^164 ] ] [ [ $.1^8, $.1^166 ] ] [ [ $.1^9, $.1^10 ] ] [ [ $.1^9, $.1^12 ] ] [ [ $.1^9, $.1^20 ] ] [ [ $.1^9, $.1^33 ] ] [ [ $.1^9, $.1^87 ] ] [ [ $.1^9, $.1^92 ] ] [ [ $.1^9, $.1^93 ] ] [ [ $.1^9, 9 ] ] [ [ $.1^9, $.1^123 ] ] [ [ $.1^9, $.1^127 ] ] [ [ $.1^9, $.1^130 ] ] [ [ $.1^9, $.1^139 ] ] [ [ $.1^9, $.1^156 ] ] [ [ $.1^10, $.1^2 ] ] [ [ $.1^10, $.1^24 ] ] [ [ $.1^10, $.1^26 ] ] [ [ $.1^10, $.1^34 ] ] [ [ $.1^10, $.1^47 ] ] [ [ $.1^10, $.1^101 ] ] [ [ $.1^10, $.1^106 ] ] [ [ $.1^10, $.1^107 ] ] [ [ $.1^10, 5 ] ] [ [ $.1^10, $.1^137 ] ] [ [ $.1^10, $.1^141 ] ] [ [ $.1^10, $.1^144 ] ] [ [ $.1^10, $.1^153 ] ] [ [ $.1^11, $.1^16 ] ] [ [ $.1^11, $.1^38 ] ] [ [ $.1^11, $.1^40 ] ] [ [ $.1^11, $.1^48 ] ] [ [ $.1^11, $.1^61 ] ] [ [ $.1^11, $.1^115 ] ] [ [ $.1^11, $.1^120 ] ] [ [ $.1^11, $.1^121 ] ] [ [ $.1^11, 10 ] ] [ [ $.1^11, $.1^151 ] ] [ [ $.1^11, $.1^155 ] ] [ [ $.1^11, $.1^158 ] ] [ [ $.1^11, $.1^167 ] ] [ [ $.1^12, $.1 ] ] [ [ $.1^12, $.1^4 ] ] [ [ $.1^12, $.1^13 ] ] [ [ $.1^12, $.1^30 ] ] [ [ $.1^12, $.1^52 ] ] [ [ $.1^12, $.1^54 ] ] [ [ $.1^12, $.1^62 ] ] [ [ $.1^12, $.1^75 ] ] [ [ $.1^12, $.1^129 ] ] [ [ $.1^12, $.1^134 ] ] [ [ $.1^12, $.1^135 ] ] [ [ $.1^12, 7 ] ] [ [ $.1^12, $.1^165 ] ] [ [ $.1^13, 1 ] ] [ [ $.1^13, $.1^11 ] ] [ [ $.1^13, $.1^15 ] ] [ [ $.1^13, $.1^18 ] ] [ [ $.1^13, $.1^27 ] ] [ [ $.1^13, $.1^44 ] ] [ [ $.1^13, $.1^66 ] ] [ [ $.1^13, $.1^68 ] ] [ [ $.1^13, $.1^76 ] ] [ [ $.1^13, $.1^89 ] ] [ [ $.1^13, $.1^143 ] ] [ [ $.1^13, $.1^148 ] ] [ [ $.1^13, $.1^149 ] ] [ [ 2, 2 ] ] [ [ 2, $.1^25 ] ] [ [ 2, $.1^29 ] ] [ [ 2, $.1^32 ] ] [ [ 2, $.1^41 ] ] [ [ 2, $.1^58 ] ] [ [ 2, $.1^80 ] ] [ [ 2, $.1^82 ] ] [ [ 2, $.1^90 ] ] [ [ 2, $.1^103 ] ] [ [ 2, $.1^157 ] ] [ [ 2, $.1^162 ] ] [ [ 2, $.1^163 ] ] [ [ $.1^15, $.1^3 ] ] [ [ $.1^15, $.1^8 ] ] [ [ $.1^15, $.1^9 ] ] [ [ $.1^15, 4 ] ] [ [ $.1^15, $.1^39 ] ] [ [ $.1^15, $.1^43 ] ] [ [ $.1^15, $.1^46 ] ] [ [ $.1^15, $.1^55 ] ] [ [ $.1^15, $.1^72 ] ] [ [ $.1^15, $.1^94 ] ] [ [ $.1^15, $.1^96 ] ] [ [ $.1^15, $.1^104 ] ] [ [ $.1^15, $.1^117 ] ] [ [ $.1^16, $.1^17 ] ] [ [ $.1^16, $.1^22 ] ] [ [ $.1^16, $.1^23 ] ] [ [ $.1^16, 8 ] ] [ [ $.1^16, $.1^53 ] ] [ [ $.1^16, $.1^57 ] ] [ [ $.1^16, $.1^60 ] ] [ [ $.1^16, $.1^69 ] ] [ [ $.1^16, $.1^86 ] ] [ [ $.1^16, $.1^108 ] ] [ [ $.1^16, $.1^110 ] ] [ [ $.1^16, $.1^118 ] ] [ [ $.1^16, $.1^131 ] ] [ [ $.1^17, $.1^31 ] ] [ [ $.1^17, $.1^36 ] ] [ [ $.1^17, $.1^37 ] ] [ [ $.1^17, 3 ] ] [ [ $.1^17, $.1^67 ] ] [ [ $.1^17, $.1^71 ] ] [ [ $.1^17, $.1^74 ] ] [ [ $.1^17, $.1^83 ] ] [ [ $.1^17, $.1^100 ] ] [ [ $.1^17, $.1^122 ] ] [ [ $.1^17, $.1^124 ] ] [ [ $.1^17, $.1^132 ] ] [ [ $.1^17, $.1^145 ] ] [ [ $.1^18, $.1^45 ] ] [ [ $.1^18, $.1^50 ] ] [ [ $.1^18, $.1^51 ] ] [ [ $.1^18, 6 ] ] [ [ $.1^18, $.1^81 ] ] [ [ $.1^18, $.1^85 ] ] [ [ $.1^18, $.1^88 ] ] [ [ $.1^18, $.1^97 ] ] [ [ $.1^18, $.1^114 ] ] [ [ $.1^18, $.1^136 ] ] [ [ $.1^18, $.1^138 ] ] [ [ $.1^18, $.1^146 ] ] [ [ $.1^18, $.1^159 ] ] [ [ $.1^19, $.1^5 ] ] [ [ $.1^19, $.1^59 ] ] [ [ $.1^19, $.1^64 ] ] [ [ $.1^19, $.1^65 ] ] [ [ $.1^19, 12 ] ] [ [ $.1^19, $.1^95 ] ] [ [ $.1^19, $.1^99 ] ] [ [ $.1^19, $.1^102 ] ] [ [ $.1^19, $.1^111 ] ] [ [ $.1^19, $.1^128 ] ] [ [ $.1^19, $.1^150 ] ] [ [ $.1^19, $.1^152 ] ] [ [ $.1^19, $.1^160 ] ] [ [ $.1^20, $.1^6 ] ] [ [ $.1^20, $.1^19 ] ] [ [ $.1^20, $.1^73 ] ] [ [ $.1^20, $.1^78 ] ] [ [ $.1^20, $.1^79 ] ] [ [ $.1^20, 11 ] ] [ [ $.1^20, $.1^109 ] ] [ [ $.1^20, $.1^113 ] ] [ [ $.1^20, $.1^116 ] ] [ [ $.1^20, $.1^125 ] ] [ [ $.1^20, $.1^142 ] ] [ [ $.1^20, $.1^164 ] ] [ [ $.1^20, $.1^166 ] ] [ [ $.1^21, $.1^10 ] ] [ [ $.1^21, $.1^12 ] ] [ [ $.1^21, $.1^20 ] ] [ [ $.1^21, $.1^33 ] ] [ [ $.1^21, $.1^87 ] ] [ [ $.1^21, $.1^92 ] ] [ [ $.1^21, $.1^93 ] ] [ [ $.1^21, 9 ] ] [ [ $.1^21, $.1^123 ] ] [ [ $.1^21, $.1^127 ] ] [ [ $.1^21, $.1^130 ] ] [ [ $.1^21, $.1^139 ] ] [ [ $.1^21, $.1^156 ] ] [ [ $.1^22, $.1^2 ] ] [ [ $.1^22, $.1^24 ] ] [ [ $.1^22, $.1^26 ] ] [ [ $.1^22, $.1^34 ] ] [ [ $.1^22, $.1^47 ] ] [ [ $.1^22, $.1^101 ] ] [ [ $.1^22, $.1^106 ] ] [ [ $.1^22, $.1^107 ] ] [ [ $.1^22, 5 ] ] [ [ $.1^22, $.1^137 ] ] [ [ $.1^22, $.1^141 ] ] [ [ $.1^22, $.1^144 ] ] [ [ $.1^22, $.1^153 ] ] [ [ $.1^23, $.1^16 ] ] [ [ $.1^23, $.1^38 ] ] [ [ $.1^23, $.1^40 ] ] [ [ $.1^23, $.1^48 ] ] [ [ $.1^23, $.1^61 ] ] [ [ $.1^23, $.1^115 ] ] [ [ $.1^23, $.1^120 ] ] [ [ $.1^23, $.1^121 ] ] [ [ $.1^23, 10 ] ] [ [ $.1^23, $.1^151 ] ] [ [ $.1^23, $.1^155 ] ] [ [ $.1^23, $.1^158 ] ] [ [ $.1^23, $.1^167 ] ] [ [ $.1^24, $.1 ] ] [ [ $.1^24, $.1^4 ] ] [ [ $.1^24, $.1^13 ] ] [ [ $.1^24, $.1^30 ] ] [ [ $.1^24, $.1^52 ] ] [ [ $.1^24, $.1^54 ] ] [ [ $.1^24, $.1^62 ] ] [ [ $.1^24, $.1^75 ] ] [ [ $.1^24, $.1^129 ] ] [ [ $.1^24, $.1^134 ] ] [ [ $.1^24, $.1^135 ] ] [ [ $.1^24, 7 ] ] [ [ $.1^24, $.1^165 ] ] [ [ $.1^25, 1 ] ] [ [ $.1^25, $.1^11 ] ] [ [ $.1^25, $.1^15 ] ] [ [ $.1^25, $.1^18 ] ] [ [ $.1^25, $.1^27 ] ] [ [ $.1^25, $.1^44 ] ] [ [ $.1^25, $.1^66 ] ] [ [ $.1^25, $.1^68 ] ] [ [ $.1^25, $.1^76 ] ] [ [ $.1^25, $.1^89 ] ] [ [ $.1^25, $.1^143 ] ] [ [ $.1^25, $.1^148 ] ] [ [ $.1^25, $.1^149 ] ] [ [ $.1^26, 2 ] ] [ [ $.1^26, $.1^25 ] ] [ [ $.1^26, $.1^29 ] ] [ [ $.1^26, $.1^32 ] ] [ [ $.1^26, $.1^41 ] ] [ [ $.1^26, $.1^58 ] ] [ [ $.1^26, $.1^80 ] ] [ [ $.1^26, $.1^82 ] ] [ [ $.1^26, $.1^90 ] ] [ [ $.1^26, $.1^103 ] ] [ [ $.1^26, $.1^157 ] ] [ [ $.1^26, $.1^162 ] ] [ [ $.1^26, $.1^163 ] ] [ [ $.1^27, $.1^3 ] ] [ [ $.1^27, $.1^8 ] ] [ [ $.1^27, $.1^9 ] ] [ [ $.1^27, 4 ] ] [ [ $.1^27, $.1^39 ] ] [ [ $.1^27, $.1^43 ] ] [ [ $.1^27, $.1^46 ] ] [ [ $.1^27, $.1^55 ] ] [ [ $.1^27, $.1^72 ] ] [ [ $.1^27, $.1^94 ] ] [ [ $.1^27, $.1^96 ] ] [ [ $.1^27, $.1^104 ] ] [ [ $.1^27, $.1^117 ] ] [ [ 4, $.1^17 ] ] [ [ 4, $.1^22 ] ] [ [ 4, $.1^23 ] ] [ [ 4, 8 ] ] [ [ 4, $.1^53 ] ] [ [ 4, $.1^57 ] ] [ [ 4, $.1^60 ] ] [ [ 4, $.1^69 ] ] [ [ 4, $.1^86 ] ] [ [ 4, $.1^108 ] ] [ [ 4, $.1^110 ] ] [ [ 4, $.1^118 ] ] [ [ 4, $.1^131 ] ] [ [ $.1^29, $.1^31 ] ] [ [ $.1^29, $.1^36 ] ] [ [ $.1^29, $.1 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Mon Mar 15 10:57:59 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, x^12*y^3, x^12*y^4, x^12*y^5, x^12*y^6, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x^13*y^3, x^13*y^4, x^13*y^5, x^13*y^6, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^14*y^6, x^14*y^3, x^14*y^4, x^14*y^5, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^12*y^6, x^3*y^11, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^11*y^5, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^5*y^9, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; L := [ x^3*y^12]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Mon Mar 15 2004 10:57:56 on modular [Seed = 3519300460] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] [ x^3*y^12 ] [ false ] Total time: 2.979 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host 93-BAR2-X4.libre.retevision.es. (62.82.186.93) Time: Mon Mar 15 10:58:26 2004 Input: ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; polavqr:=function(q,r) C:=[]; p:=0; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); p:=p+1; end if; end for; end for; return C,p; end function; #polavqr(3,2); 3^(2*2-1); Output: Magma V2.10-6 Mon Mar 15 2004 10:58:23 on modular [Seed = 3369949806] ------------------------------------- [ [ 1, $.1 ] ] [ [ 1, $.1^3 ] ] [ [ 1, 2 ] ] [ [ $.1, 1 ] ] [ [ $.1, $.1^5 ] ] [ [ $.1, $.1^7 ] ] [ [ $.1^2, $.1 ] ] [ [ $.1^2, $.1^3 ] ] [ [ $.1^2, 2 ] ] [ [ $.1^3, 1 ] ] [ [ $.1^3, $.1^5 ] ] [ [ $.1^3, $.1^7 ] ] [ [ 2, $.1 ] ] [ [ 2, $.1^3 ] ] [ [ 2, 2 ] ] [ [ $.1^5, 1 ] ] [ [ $.1^5, $.1^5 ] ] [ [ $.1^5, $.1^7 ] ] [ [ $.1^6, $.1 ] ] [ [ $.1^6, $.1^3 ] ] [ [ $.1^6, 2 ] ] [ [ $.1^7, 1 ] ] [ [ $.1^7, $.1^5 ] ] [ [ $.1^7, $.1^7 ] ] [ [ 0, $.1^2 ] ] [ [ 0, $.1^6 ] ] [ [ 0, 0 ] ] 0 27 Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 93-BAR2-X4.libre.retevision.es. (62.82.186.93) Time: Mon Mar 15 10:58:52 2004 Input: ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; polavqr:=function(q,r) C:=[]; p:=0; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); p:=p+1; end if; end for; end for; return C,p; end function; polavqr(3,2); 3^(2*2-1); Output: Magma V2.10-6 Mon Mar 15 2004 10:58:49 on modular [Seed = 3268890690] ------------------------------------- [ [ 1, $.1 ] ] [ [ 1, $.1^3 ] ] [ [ 1, 2 ] ] [ [ $.1, 1 ] ] [ [ $.1, $.1^5 ] ] [ [ $.1, $.1^7 ] ] [ [ $.1^2, $.1 ] ] [ [ $.1^2, $.1^3 ] ] [ [ $.1^2, 2 ] ] [ [ $.1^3, 1 ] ] [ [ $.1^3, $.1^5 ] ] [ [ $.1^3, $.1^7 ] ] [ [ 2, $.1 ] ] [ [ 2, $.1^3 ] ] [ [ 2, 2 ] ] [ [ $.1^5, 1 ] ] [ [ $.1^5, $.1^5 ] ] [ [ $.1^5, $.1^7 ] ] [ [ $.1^6, $.1 ] ] [ [ $.1^6, $.1^3 ] ] [ [ $.1^6, 2 ] ] [ [ $.1^7, 1 ] ] [ [ $.1^7, $.1^5 ] ] [ [ $.1^7, $.1^7 ] ] [ [ 0, $.1^2 ] ] [ [ 0, $.1^6 ] ] [ [ 0, 0 ] ] [] 27 27 Total time: 2.889 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Mon Mar 15 10:59:40 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, x^12*y^3, x^12*y^4, x^12*y^5, x^12*y^6, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x^13*y^3, x^13*y^4, x^13*y^5, x^13*y^6, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^14*y^6, x^14*y^3, x^14*y^4, x^14*y^5, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^9*y^8, x^3*y^11, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^11*y^5, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^5*y^9, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; L := [ x^3*y^12]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Mon Mar 15 2004 10:59:38 on modular [Seed = 1043049710] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] [ x^3*y^12 ] [ false ] Total time: 2.929 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host 93-BAR2-X4.libre.retevision.es. (62.82.186.93) Time: Mon Mar 15 11:00:48 2004 Input: ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; polavqr:=function(q,r) C:=[]; p:=0; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(C, [i,j]); p:=p+1; end if; end for; end for; return C,p; end function; spolav:= [k : k in polavqr(3,2) | k[1] in GF(3) and k[2] in GF(3) ]; #spolav; Output: Magma V2.10-6 Mon Mar 15 2004 11:00:45 on modular [Seed = 574075189] ------------------------------------- [ [ 1, $.1 ] ] [ [ 1, $.1^3 ] ] [ [ 1, 2 ] ] [ [ $.1, 1 ] ] [ [ $.1, $.1^5 ] ] [ [ $.1, $.1^7 ] ] [ [ $.1^2, $.1 ] ] [ [ $.1^2, $.1^3 ] ] [ [ $.1^2, 2 ] ] [ [ $.1^3, 1 ] ] [ [ $.1^3, $.1^5 ] ] [ [ $.1^3, $.1^7 ] ] [ [ 2, $.1 ] ] [ [ 2, $.1^3 ] ] [ [ 2, 2 ] ] [ [ $.1^5, 1 ] ] [ [ $.1^5, $.1^5 ] ] [ [ $.1^5, $.1^7 ] ] [ [ $.1^6, $.1 ] ] [ [ $.1^6, $.1^3 ] ] [ [ $.1^6, 2 ] ] [ [ $.1^7, 1 ] ] [ [ $.1^7, $.1^5 ] ] [ [ $.1^7, $.1^7 ] ] [ [ 0, $.1^2 ] ] [ [ 0, $.1^6 ] ] [ [ 0, 0 ] ] 0 Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Mon Mar 15 11:55:10 2004 Input: t73 := [7^i : i in [2..0 by -1]]; print(t73); Output: Magma V2.10-6 Mon Mar 15 2004 11:55:06 on modular [Seed = 2864657786] ------------------------------------- [ 49, 7, 1 ] Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Mon Mar 15 11:55:45 2004 Input: t73 := [7^i : i in [0..2]]; print(t73); Output: Magma V2.10-6 Mon Mar 15 2004 11:55:42 on modular [Seed = 2696216724] ------------------------------------- [ 1, 7, 49 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Mon Mar 15 11:58:00 2004 Input: R := GF(7^3); Output: Magma V2.10-6 Mon Mar 15 2004 11:57:57 on modular [Seed = 2659925553] ------------------------------------- Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 11:58:58 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Mon Mar 15 2004 11:58:55 on modular [Seed = 2541893474] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:00:52 2004 Input: q:=7; r:=3; exp_t := { q^i : i in [r-1..0 by -1] }; Output: Magma V2.10-6 Mon Mar 15 2004 12:00:49 on modular [Seed = 4226701952] ------------------------------------- Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:01:06 2004 Input: q:=7; r:=3; exp_t := { q^i : i in [r-1..0 by -1] }; print exp_t; Output: Magma V2.10-6 Mon Mar 15 2004 12:01:03 on modular [Seed = 3874703251] ------------------------------------- { 1, 7, 49 } Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee13.uab.es. (158.109.66.13) Time: Mon Mar 15 12:02:17 2004 Input: exemples:=function(q,r) pol:=polinomit(q,r); xsum:=polinomin(q,r); print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r,pol,xsum)); end function; exemples(2,3); exemples(3,3); exemples(5,3); exemples(3,4); exemples(2,4); Output: Magma V2.10-6 Mon Mar 15 2004 12:02:14 on modular [Seed = 3754589811] ------------------------------------- >> pol:=polinomit(q,r); ^ User error: Identifier 'polinomit' has not been declared or assigned >> exemples(2,3); ^ User error: Identifier 'exemples' has not been declared or assigned >> exemples(3,3); ^ User error: Identifier 'exemples' has not been declared or assigned >> exemples(5,3); ^ User error: Identifier 'exemples' has not been declared or assigned >> exemples(3,4); ^ User error: Identifier 'exemples' has not been declared or assigned >> exemples(2,4); ^ User error: Identifier 'exemples' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:02:30 2004 Input: q:=7; r:=3; exp_t := [ q^i : i in [r-1..0 by -1] ]; print exp_t; Output: Magma V2.10-6 Mon Mar 15 2004 12:02:27 on modular [Seed = 3569448269] ------------------------------------- [ 49, 7, 1 ] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Mon Mar 15 12:02:56 2004 Input: R := GF(7^3); p := PolynomialRing(R); exp := [7^i : i in [2..0 by -1]]; n73 := x^&+(exp); print(n73); Output: Magma V2.10-6 Mon Mar 15 2004 12:02:53 on modular [Seed = 3268895557] ------------------------------------- x^57 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:03:09 2004 Input: q:=7; r:=3; exp_t := [ q^i : i in [0..r-1 by 1] ]; print exp_t; Output: Magma V2.10-6 Mon Mar 15 2004 12:03:06 on modular [Seed = 976198603] ------------------------------------- [ 1, 7, 49 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:03:30 2004 Input: q:=7; r:=3; exp_t := [ q^i : i in [r-1..0 by -1] ]; print exp_t; Output: Magma V2.10-6 Mon Mar 15 2004 12:03:27 on modular [Seed = 824479957] ------------------------------------- [ 49, 7, 1 ] Total time: 2.849 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Mon Mar 15 12:03:53 2004 Input: R := GF(7^3); p := PolynomialRing(R); exp := [7^i : i in [2..0 by -1]]; print(exp); Output: Magma V2.10-6 Mon Mar 15 2004 12:03:50 on modular [Seed = 675121637] ------------------------------------- [ 49, 7, 1 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:04:49 2004 Input: exp_n := &+(exp_t); print exp_n; Output: Magma V2.10-6 Mon Mar 15 2004 12:04:46 on modular [Seed = 657622322] ------------------------------------- >> exp_n := &+(exp_t); ^ User error: Identifier 'exp_t' has not been declared or assigned >> print exp_n;; ^ User error: Identifier 'exp_n' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:05:12 2004 Input: q:=7; r:=3; exp_t := [ q^i : i in [r-1..0 by -1] ]; exp_n := &+(exp_t); print exp_n; Output: Magma V2.10-6 Mon Mar 15 2004 12:05:09 on modular [Seed = 302493804] ------------------------------------- 57 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:06:24 2004 Input: q:=7; r:=3; exp_t := [ q^i : i in [r-1..0 by -1] ]; exp_n := &+(exp_t); print exp_n; polinomi_t := &+{ x^i | i in exp_t }; polinomi_n := x^exp_n; Output: Magma V2.10-6 Mon Mar 15 2004 12:06:21 on modular [Seed = 253406649] ------------------------------------- 57 >> polinomi_t := &+{ x^i | i in exp_t }; ^ User error: Identifier 'i' has not been declared or assigned >> polinomi_n := x^exp_n; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.869 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:06:59 2004 Input: q:=7; r:=3; exp_t := [ q^i : i in [r-1..0 by -1] ]; exp_n := &+(exp_t); print exp_n; polinomi_t := &+{ x^i : i in exp_t }; polinomi_n := x^exp_n; Output: Magma V2.10-6 Mon Mar 15 2004 12:06:56 on modular [Seed = 101950605] ------------------------------------- 57 >> polinomi_t := &+{ x^i : i in exp_t }; ^ User error: Identifier 'x' has not been declared or assigned >> polinomi_n := x^exp_n; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:07:26 2004 Input: q:=7; r:=3; exp_t := [ q^i : i in [r-1..0 by -1] ]; exp_n := &+(exp_t); print exp_n; polinomi_n := x^exp_n; print polinomi_n; Output: Magma V2.10-6 Mon Mar 15 2004 12:07:23 on modular [Seed = 2104024973] ------------------------------------- 57 >> polinomi_n := x^exp_n; ^ User error: Identifier 'x' has not been declared or assigned >> print polinomi_n; ^ User error: Identifier 'polinomi_n' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee13.uab.es. (158.109.66.13) Time: Mon Mar 15 12:08:17 2004 Input: R:=Integers(); P:=PolynomialRing(R); sum:=0; for i:= 2 to 0 by -1 do sum:=sum+7^i; end for; x^sum; pol:=0; for i:=1 to #(llista) do pol:=pol+x^llista[i]; end for; pol; polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; exemples:=function(q,r) pol:=polinomit(q,r); xsum:=polinomin(q,r); print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r,pol,xsum)); end function; exemples(2,3); exemples(3,3); exemples(5,3); exemples(3,4); exemples(2,4); Output: Magma V2.10-6 Mon Mar 15 2004 12:08:14 on modular [Seed = 1952569009] ------------------------------------- x^57 >> for i:=1 to #(llista) do ^ User error: Identifier 'llista' has not been declared or assigned 0 [ 49, 7, 1 ] >> return #(puntsOlav(q,r,pol,xsum)); ^ User error: Identifier 'puntsOlav' has not been declared or assigned >> exemples(2,3); ^ User error: Identifier 'exemples' has not been declared or assigned >> exemples(3,3); ^ User error: Identifier 'exemples' has not been declared or assigned >> exemples(5,3); ^ User error: Identifier 'exemples' has not been declared or assigned >> exemples(3,4); ^ User error: Identifier 'exemples' has not been declared or assigned >> exemples(2,4); ^ User error: Identifier 'exemples' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee13.uab.es. (158.109.66.13) Time: Mon Mar 15 12:08:51 2004 Input: R:=Integers(); P:=PolynomialRing(R); sum:=0; for i:= 2 to 0 by -1 do sum:=sum+7^i; end for; x^sum; pol:=0; for i:=1 to #(llista) do pol:=pol+x^llista[i]; end for; pol; polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; exemples:=function(q,r) pol:=polinomit(q,r); xsum:=polinomin(q,r); print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r,pol,xsum)); end function; exemples(2,3); exemples(3,3); exemples(5,3); exemples(3,4); exemples(2,4); Output: Magma V2.10-6 Mon Mar 15 2004 12:08:48 on modular [Seed = 1652015481] ------------------------------------- x^57 >> for i:=1 to #(llista) do ^ User error: Identifier 'llista' has not been declared or assigned 0 [ 49, 7, 1 ] q^(2*r-1) és igual a: 32 El cardinal dels punts Olav en aquest exemple és: 32 q^(2*r-1) és igual a: 243 El cardinal dels punts Olav en aquest exemple és: 243 q^(2*r-1) és igual a: 3125 El cardinal dels punts Olav en aquest exemple és: 3125 q^(2*r-1) és igual a: 2187 El cardinal dels punts Olav en aquest exemple és: 2187 q^(2*r-1) és igual a: 128 El cardinal dels punts Olav en aquest exemple és: 128 Total time: 3.449 seconds, Total memory usage: 2.13MB ************** MAGMA ***************** Host aula-a-siee13.uab.es. (158.109.66.13) Time: Mon Mar 15 12:09:43 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; exemples:=function(q,r) pol:=polinomit(q,r); xsum:=polinomin(q,r); print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r,pol,xsum)); end function; exemples(2,3); exemples(3,3); exemples(5,3); exemples(3,4); exemples(2,4); Output: Magma V2.10-6 Mon Mar 15 2004 12:09:40 on modular [Seed = 1498217014] ------------------------------------- [ 49, 7, 1 ] q^(2*r-1) és igual a: 32 El cardinal dels punts Olav en aquest exemple és: 32 q^(2*r-1) és igual a: 243 El cardinal dels punts Olav en aquest exemple és: 243 q^(2*r-1) és igual a: 3125 El cardinal dels punts Olav en aquest exemple és: 3125 q^(2*r-1) és igual a: 2187 El cardinal dels punts Olav en aquest exemple és: 2187 q^(2*r-1) és igual a: 128 El cardinal dels punts Olav en aquest exemple és: 128 Total time: 3.449 seconds, Total memory usage: 2.13MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:09:50 2004 Input: q:=7; r:=3; exp_t := [ q^i : i in [r-1..0 by -1] ]; exp_n := &+(exp_t); print exp_n; polinomi_n := PolynomialRing(7); polinomi_n := x^exp_n; print polinomi_n; Output: Magma V2.10-6 Mon Mar 15 2004 12:09:47 on modular [Seed = 1346761520] ------------------------------------- 57 >> polinomi_n := PolynomialRing(7); ^ Runtime error in 'PolynomialRing': Bad argument types Argument types given: RngIntElt >> polinomi_n := x^exp_n; ^ User error: Identifier 'x' has not been declared or assigned >> print polinomi_n; ^ User error: Identifier 'polinomi_n' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:10:02 2004 Input: q:=7; r:=3; exp_t := [ q^i : i in [r-1..0 by -1] ]; exp_n := &+(exp_t); print exp_n; polinomi_n := PolynomialRing(R); polinomi_n := x^exp_n; print polinomi_n; Output: Magma V2.10-6 Mon Mar 15 2004 12:09:59 on modular [Seed = 1331358739] ------------------------------------- 57 >> polinomi_n := PolynomialRing(R); ^ User error: Identifier 'R' has not been declared or assigned >> polinomi_n := x^exp_n; ^ User error: Identifier 'x' has not been declared or assigned >> print polinomi_n; ^ User error: Identifier 'polinomi_n' has not been declared or assigned Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:10:33 2004 Input: elt; Output: Magma V2.10-6 Mon Mar 15 2004 12:10:30 on modular [Seed = 3198885123] ------------------------------------- >> elt; ^ User error: Identifier 'P' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee13.uab.es. (158.109.66.13) Time: Mon Mar 15 12:11:01 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; exemples:=function(q,r) pol:=polinomit(q,r); xsum:=polinomin(q,r); print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r,pol,xsum)); end function; exemples(2,3); exemples(3,3); exemples(5,3); exemples(3,4); exemples(2,4); puntsOlav2:=func: a in GF(q,r), b in GF(q,r), a in GF(q), b in GF(q)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; Output: Magma V2.10-6 Mon Mar 15 2004 12:10:57 on modular [Seed = 3047167535] ------------------------------------- [ 49, 7, 1 ] q^(2*r-1) és igual a: 32 El cardinal dels punts Olav en aquest exemple és: 32 q^(2*r-1) és igual a: 243 El cardinal dels punts Olav en aquest exemple és: 243 q^(2*r-1) és igual a: 3125 El cardinal dels punts Olav en aquest exemple és: 3125 q^(2*r-1) és igual a: 2187 El cardinal dels punts Olav en aquest exemple és: 2187 q^(2*r-1) és igual a: 128 El cardinal dels punts Olav en aquest exemple és: 128 Total time: 3.469 seconds, Total memory usage: 2.13MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:11:28 2004 Input: R := GF(4); Output: Magma V2.10-6 Mon Mar 15 2004 12:11:25 on modular [Seed = 2897809194] ------------------------------------- Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:12:08 2004 Input: R := GF(4); P := PolynomialRing(R); elt < P | 5, 0, -7 ,1 >; Output: Magma V2.10-6 Mon Mar 15 2004 12:12:05 on modular [Seed = 2609788997] ------------------------------------- x^3 + x^2 + 1 Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee13.uab.es. (158.109.66.13) Time: Mon Mar 15 12:12:26 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; exemples:=function(q,r) pol:=polinomit(q,r); xsum:=polinomin(q,r); print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r,pol,xsum)); end function; exemples(2,3); exemples(3,3); exemples(5,3); exemples(3,4); exemples(2,4); puntsOlav2:=func: a in GF(q,r), b in GF(q,r), a in GF(q), b in GF(q)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; puntsOlav2(5,3,pol,xsum); Output: Magma V2.10-6 Mon Mar 15 2004 12:12:22 on modular [Seed = 2458333535] ------------------------------------- [ 49, 7, 1 ] q^(2*r-1) és igual a: 32 El cardinal dels punts Olav en aquest exemple és: 32 q^(2*r-1) és igual a: 243 El cardinal dels punts Olav en aquest exemple és: 243 q^(2*r-1) és igual a: 3125 El cardinal dels punts Olav en aquest exemple és: 3125 q^(2*r-1) és igual a: 2187 El cardinal dels punts Olav en aquest exemple és: 2187 q^(2*r-1) és igual a: 128 El cardinal dels punts Olav en aquest exemple és: 128 >> puntsOlav2(5,3,pol,xsum); ^ User error: Identifier 'pol' has not been declared or assigned Total time: 3.539 seconds, Total memory usage: 2.13MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:12:45 2004 Input: R := GF(9); P := PolynomialRing(R); elt < P | 5, 0, -7 ,1 >; Output: Magma V2.10-6 Mon Mar 15 2004 12:12:42 on modular [Seed = 2292001977] ------------------------------------- x^3 + 2*x^2 + 2 Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Mon Mar 15 12:13:15 2004 Input: i = [i | i in {0..2}]; print(i); Output: Magma V2.10-6 Mon Mar 15 2004 12:13:12 on modular [Seed = 2274501524] ------------------------------------- >> i = [i | i in {0..2}]; ^ User error: Identifier 'i' has not been declared or assigned >> print(i);; ^ User error: Identifier 'i' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Mon Mar 15 12:13:41 2004 Input: i = [i : i in {0..2}]; print(i); Output: Magma V2.10-6 Mon Mar 15 2004 12:13:38 on modular [Seed = 4276836999] ------------------------------------- >> i = [i : i in {0..2}]; ^ User error: Identifier 'i' has not been declared or assigned >> print(i);; ^ User error: Identifier 'i' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Mon Mar 15 12:13:55 2004 Input: x = [i : i in {0..2}]; print(i); Output: Magma V2.10-6 Mon Mar 15 2004 12:13:52 on modular [Seed = 4125118878] ------------------------------------- >> x = [i : i in {0..2}]; ^ User error: Identifier 'x' has not been declared or assigned >> print(i);; ^ User error: Identifier 'i' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:13:59 2004 Input: R := GF(7,3); P := PolynomialRing(R); elt < P | 5, 0, -7 ,1 >; Output: Magma V2.10-6 Mon Mar 15 2004 12:13:56 on modular [Seed = 3992471938] ------------------------------------- x^3 + 5 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Mon Mar 15 12:14:12 2004 Input: x = [i : i in {0..2}]; print(x); Output: Magma V2.10-6 Mon Mar 15 2004 12:14:09 on modular [Seed = 3687743361] ------------------------------------- >> x = [i : i in {0..2}]; ^ User error: Identifier 'x' has not been declared or assigned >> print(x);; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Mon Mar 15 12:14:30 2004 Input: x := [i : i in {0..2}]; print(x); Output: Magma V2.10-6 Mon Mar 15 2004 12:14:27 on modular [Seed = 3536287386] ------------------------------------- [ 0, 1, 2 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Mon Mar 15 12:14:49 2004 Input: x := [i : i in {0..2}]; x1 := &+x; print(x1); Output: Magma V2.10-6 Mon Mar 15 2004 12:14:46 on modular [Seed = 3386666356] ------------------------------------- 3 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Mon Mar 15 12:15:04 2004 Input: x := [i : i in {0..2}]; x1 := &*x; print(x1); Output: Magma V2.10-6 Mon Mar 15 2004 12:15:01 on modular [Seed = 3302056042] ------------------------------------- 0 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:15:23 2004 Input: q:=7; r:=3; exp_t := [ q^i : i in [r-1..0 by -1] ]; print exp_t; exp_n := &+(exp_t); print exp_n; R := GF(7,3); polinomi_n := PolynomialRing(R); polinomi_n := x^exp_n; Output: Magma V2.10-6 Mon Mar 15 2004 12:15:20 on modular [Seed = 891326881] ------------------------------------- [ 49, 7, 1 ] 57 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:15:44 2004 Input: q:=7; r:=3; exp_t := [ q^i : i in [r-1..0 by -1] ]; print exp_t; exp_n := &+(exp_t); print exp_n; R := GF(7,3); polinomi_n := PolynomialRing(R); polinomi_n := x^exp_n; print polinomi_n; Output: Magma V2.10-6 Mon Mar 15 2004 12:15:41 on modular [Seed = 775654063] ------------------------------------- [ 49, 7, 1 ] 57 x^57 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:17:22 2004 Input: q:=7; r:=3; exp_t := [ q^i : i in [r-1..0 by -1] ]; print exp_t; exp_n := &+(exp_t); print exp_n; R := GF(7,3); polinomi_t:= GF(R); polinomi_t := &+{ x^i | i in exp_t }; print polinomi_t; Output: Magma V2.10-6 Mon Mar 15 2004 12:17:19 on modular [Seed = 574064385] ------------------------------------- [ 49, 7, 1 ] 57 >> polinomi_t:= GF(R); ^ Runtime error in 'GF': Bad argument types Argument types given: FldFin >> polinomi_t := &+{ x^i | i in exp_t }; ^ User error: Identifier 'i' has not been declared or assigned >> print polinomi_t; ^ User error: Identifier 'polinomi_t' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:17:53 2004 Input: q:=7; r:=3; exp_t := [ q^i : i in [r-1..0 by -1] ]; print exp_t; exp_n := &+(exp_t); print exp_n; R := GF(7,3); polinomi_t:= PolynomialRing(R); polinomi_t := &+{ x^i | i in exp_t }; print polinomi_t; Output: Magma V2.10-6 Mon Mar 15 2004 12:17:50 on modular [Seed = 453951001] ------------------------------------- [ 49, 7, 1 ] 57 >> polinomi_t := &+{ x^i | i in exp_t }; ^ User error: Identifier 'i' has not been declared or assigned Univariate Polynomial Ring in x over GF(7^3) Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:19:06 2004 Input: q:=7; r:=3; exp_t := [ q^i : i in [r-1..0 by -1] ]; print exp_t; exp_n := &+(exp_t); print exp_n; R := GF(7,3); polinomi_t:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exp_t }; print polinomi_t; Output: Magma V2.10-6 Mon Mar 15 2004 12:19:03 on modular [Seed = 203008439] ------------------------------------- [ 49, 7, 1 ] 57 x^49 + x^7 + x Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:20:24 2004 Input: q:=7; r:=3; exp_t := [ q^i : i in [r-1..0 by -1] ]; exp_n := &+(exp_t); R := GF(7,3); polinomi_t:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exp_t }; puntsolav := { a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) }; Output: Magma V2.10-6 Mon Mar 15 2004 12:20:21 on modular [Seed = 2104023188] ------------------------------------- >> puntsolav := { a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee13.uab.es. (158.109.66.13) Time: Mon Mar 15 12:22:03 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; exemples:=function(q,r) pol:=polinomit(q,r); xsum:=polinomin(q,r); print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r,pol,xsum)); end function; exemples(2,3); exemples(3,3); exemples(5,3); exemples(3,4); exemples(2,4); puntsOlav2:=func: a in GF(q,r), b in GF(q,r), a in GF(q), b in GF(q)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; pol:=polinomit(5,3); xsum:=polinomin(5,3); puntsOlav2(5,3,pol,xsum); Output: Magma V2.10-6 Mon Mar 15 2004 12:21:51 on modular [Seed = 2002964836] ------------------------------------- [ 49, 7, 1 ] q^(2*r-1) és igual a: 32 El cardinal dels punts Olav en aquest exemple és: 32 q^(2*r-1) és igual a: 243 El cardinal dels punts Olav en aquest exemple és: 243 q^(2*r-1) és igual a: 3125 El cardinal dels punts Olav en aquest exemple és: 3125 q^(2*r-1) és igual a: 2187 El cardinal dels punts Olav en aquest exemple és: 2187 q^(2*r-1) és igual a: 128 El cardinal dels punts Olav en aquest exemple és: 128 { <$.1^96, $.1^99>, <$.1^26, $.1^63>, <$.1^35, $.1^8>, <1, $.1^7>, <$.1^37, $.1^120>, <$.1^26, $.1^59>, <$.1^11, $.1^55>, <$.1^99, $.1^30>, <$.1^121, $.1^7>, <$.1^106, 3>, <$.1^86, $.1^116>, <$.1^96, $.1^51>, <$.1^88, $.1^77>, <$.1^89, $.1^113>, <$.1^50, $.1^46>, <$.1^112, $.1^16>, <$.1^61, $.1^80>, <$.1^96, $.1^23>, <$.1^20, $.1^123>, <$.1^71, $.1^73>, <$.1^37, $.1^80>, <$.1^45, $.1^3>, <$.1^70, $.1^66>, <$.1^65, $.1^42>, <$.1^9, $.1^59>, <$.1^12, $.1^22>, <$.1^101, 2>, <$.1^24, $.1^86>, <$.1^7, $.1^16>, <$.1^88, $.1^117>, <$.1^10, $.1^122>, <2, $.1^8>, <$.1^49, $.1^83>, <$.1^117, 3>, <$.1^12, $.1^30>, <$.1^18, $.1^6>, <$.1^7, $.1^72>, <$.1^27, $.1^63>, <$.1^75, $.1^72>, <$.1^18, 4>, <$.1^66, $.1^41>, <$.1^97, $.1^22>, <$.1^15, $.1^32>, <$.1^51, $.1^96>, <$.1^80, $.1^88>, <$.1^38, $.1^73>, <$.1^107, $.1^109>, <$.1^34, $.1^101>, <$.1^44, $.1^59>, <$.1^24, $.1^18>, <$.1^8, $.1^56>, <$.1^45, $.1^19>, <$.1^71, $.1^49>, <$.1^39, $.1^9>, <$.1^16, $.1^28>, <$.1^64, $.1^52>, <$.1^27, $.1^111>, <$.1^74, $.1^12>, <$.1^30, $.1^123>, <$.1^64, $.1^4>, <$.1^122, $.1^88>, <3, 4>, <$.1^58, $.1^80>, <$.1^95, $.1^9>, <$.1^60, 4>, <$.1^90, $.1^54>, <$.1^104, $.1^6>, <$.1^80, $.1^100>, <$.1^58, $.1^8>, <$.1^105, $.1^33>, <$.1^72, $.1^24>, <$.1^90, $.1^34>, <$.1^33, $.1^15>, <$.1^43, $.1^79>, <$.1^55, $.1^83>, <$.1^122, $.1^68>, <$.1^101, $.1^87>, <$.1^59, $.1^85>, <$.1^55, $.1^27>, <$.1^57, $.1^92>, <$.1^113, $.1^14>, <$.1^3, $.1^40>, <$.1^26, $.1^83>, <$.1^122, $.1^92>, <$.1^117, $.1^61>, <$.1^58, $.1^56>, <$.1^39, $.1^49>, <$.1^99, $.1^10>, <$.1^11, $.1^35>, <$.1^105, $.1^121>, <$.1^100, $.1^83>, <$.1^86, $.1^4>, <$.1^90, $.1^30>, <$.1^96, $.1^63>, <$.1^83, 2>, <$.1^109, $.1^119>, <$.1^51, $.1^92>, <$.1^95, $.1^65>, <$.1^69, $.1^102>, <$.1^114, $.1^68>, <$.1^74, $.1^64>, <$.1^121, $.1^87>, <$.1^105, $.1^41>, <$.1^8, $.1^4>, <$.1^107, $.1^49>, <$.1^59, $.1^69>, <$.1^80, $.1^96>, <$.1^76, $.1^40>, <$.1^47, $.1^97>, <$.1^104, $.1^90>, <$.1^82, $.1^13>, <1, $.1^59>, <$.1^77, $.1^30>, <$.1^123, $.1^58>, <$.1^97, $.1^2>, <$.1^29, $.1^89>, <$.1^107, $.1^113>, <$.1^2, $.1^98>, <$.1^24, $.1^122>, <$.1^111, 3>, <$.1^10, $.1^86>, <$.1^99, $.1^54>, <$.1^43, $.1^63>, <$.1^82, $.1^37>, <$.1^86, $.1^80>, <$.1^107, $.1^81>, <$.1^117, $.1^81>, <$.1^95, $.1^45>, <$.1^89, $.1^21>, <$.1^50, $.1^86>, <$.1^47, $.1^41>, <$.1^96, $.1^71>, <$.1^6, $.1^75>, <$.1^68, $.1^33>, <$.1^90, $.1^114>, <$.1^51, $.1^4>, <$.1^121, $.1^71>, <$.1^76, $.1^32>, <$.1^29, $.1^85>, <$.1^123, $.1^34>, <$.1^26, $.1^39>, <$.1^19, $.1>, <$.1^77, $.1^86>, <$.1^66, $.1^73>, <$.1^45, $.1^91>, <$.1^75, $.1^24>, <$.1^34, $.1^105>, <$.1^66, $.1^53>, <$.1^95, $.1^77>, <$.1^58, $.1^72>, <$.1^92, $.1^33>, <$.1^121, $.1^27>, <$.1^80, $.1^44>, <$.1^68, $.1^121>, <$.1^88, 3>, <$.1^73, $.1^45>, <$.1^121, $.1^111>, <$.1^15, $.1^112>, <3, $.1^118>, <$.1^10, $.1^90>, <2, $.1^44>, <$.1^11, $.1^3>, <$.1^51, $.1^84>, <$.1^92, $.1^77>, <$.1^4, $.1^19>, <$.1^117, $.1^57>, <$.1^40, $.1^80>, <$.1^4, $.1^27>, <$.1^112, $.1^88>, <$.1^78, $.1^10>, <$.1^7, $.1^60>, <$.1^101, $.1^91>, <$.1^21, $.1^85>, <$.1^44, $.1^107>, <$.1^24, $.1^98>, <$.1^40, $.1^92>, <$.1^73, $.1^41>, <$.1^28, $.1^120>, <$.1^92, $.1^73>, <$.1^38, $.1^17>, <$.1^5, 0>, <$.1^100, $.1^91>, <$.1^102, $.1^94>, <$.1^45, $.1^123>, <$.1^59, $.1^13>, <$.1^107, $.1^101>, <$.1^46, $.1^13>, <$.1^16, $.1^24>, <3, $.1^6>, <$.1^42, $.1^116>, <$.1^59, $.1^41>, <$.1^45, $.1^79>, <$.1^69, $.1^98>, <$.1^29, $.1^105>, <$.1^83, $.1^3>, <$.1^95, $.1^17>, <$.1^105, $.1^53>, <$.1^30, $.1^27>, <$.1^46, $.1^97>, <$.1^30, $.1^39>, <$.1^42, $.1^12>, <$.1^103, $.1>, <$.1^6, $.1^123>, <$.1^71, $.1^105>, <$.1^122, $.1^116>, <$.1^38, $.1^45>, <$.1^97, $.1^14>, <$.1^46, $.1^45>, <$.1^66, $.1^77>, <$.1^122, $.1^44>, <$.1^24, $.1^74>, <$.1^119, $.1^2>, <$.1^110, 0>, <$.1^86, $.1^32>, <$.1^70, $.1^2>, <$.1^69, $.1^70>, <$.1^96, $.1^115>, <$.1^55, $.1^99>, <$.1^91, $.1^87>, <$.1^58, $.1^4>, <$.1^97, $.1^34>, <$.1^55, $.1^103>, <$.1^89, $.1>, <$.1^50, $.1^34>, <$.1^119, $.1^6>, <$.1^32, 0>, <$.1^42, $.1^96>, <$.1^50, 4>, <$.1^65, $.1^2>, <$.1^60, $.1^14>, <2, $.1^24>, <$.1^49, $.1^119>, <$.1^3, $.1^56>, <$.1^34, $.1^25>, <$.1^78, $.1^122>, <$.1^111, $.1^57>, <$.1^34, $.1^73>, <$.1^38, $.1^105>, <$.1^28, $.1^80>, <$.1^37, $.1^8>, <$.1^59, $.1^45>, <$.1^81, 2>, <$.1^47, $.1^121>, <$.1^14, $.1^18>, <$.1^119, $.1^46>, <$.1^21, $.1^29>, <$.1^81, $.1^39>, <$.1^83, $.1^23>, <$.1^8, $.1^72>, <$.1^100, $.1^55>, <$.1^74, $.1^88>, <$.1^15, $.1^28>, <$.1^14, $.1^22>, <$.1^114, $.1^96>, <$.1^49, $.1^115>, <$.1^86, $.1^28>, <$.1^75, $.1^64>, <$.1^19, $.1^49>, <$.1^92, $.1^17>, <$.1^122, $.1^16>, <$.1^104, $.1^82>, <$.1^50, $.1^42>, <$.1^60, $.1^58>, <$.1^15, $.1^56>, <$.1^33, $.1^107>, <$.1^19, $.1^89>, <$.1^9, $.1^27>, <$.1^46, $.1^109>, <$.1^72, $.1^72>, <$.1^30, $.1^87>, <$.1^26, $.1^99>, <$.1^86, $.1^72>, <$.1^119, $.1^102>, <$.1^38, $.1>, <$.1^3, $.1^44>, <$.1^14, 4>, <$.1^96, 2>, <$.1^42, 1>, <$.1^20, $.1^95>, <$.1^121, $.1^67>, <$.1^46, $.1^49>, <$.1^20, $.1^111>, <$.1^101, $.1^123>, <$.1^95, $.1^117>, <$.1^7, $.1^4>, <$.1^51, $.1^8>, <$.1^55, 2>, <$.1^69, $.1^90>, <$.1^105, $.1^109>, <$.1^46, $.1^41>, <$.1^59, $.1^113>, <$.1^97, $.1^38>, <$.1^41, $.1^43>, <$.1^95, $.1^101>, <$.1^43, $.1^87>, <$.1^27, $.1^99>, <$.1^7, $.1^84>, <$.1^90, $.1^10>, <$.1^51, $.1^64>, <$.1^16, $.1^100>, <$.1^111, $.1^41>, <$.1^80, $.1^52>, <$.1^45, $.1^59>, <$.1^18, $.1^30>, <$.1^55, $.1^23>, <$.1^49, $.1^39>, <$.1^114, $.1^80>, <$.1^99, $.1^90>, <$.1^60, $.1^34>, <$.1^6, $.1^95>, <$.1^43, $.1^27>, <$.1^18, $.1^38>, <$.1^71, $.1^65>, <$.1^52, $.1^94>, <$.1^72, $.1^8>, <$.1^37, $.1^16>, <$.1^72, $.1^60>, <$.1^101, $.1^7>, <$.1^33, $.1^19>, <$.1^103, $.1^17>, <$.1^40, 1>, <$.1^3, $.1^20>, <$.1^75, 1>, <$.1^11, $.1^103>, <$.1^112, $.1^40>, <$.1^43, $.1^55>, <2, $.1^28>, <$.1^33, $.1^67>, <$.1^15, $.1^120>, <$.1^33, $.1^83>, <$.1^10, $.1^102>, <$.1^55, $.1^123>, <$.1^111, $.1^85>, <$.1^58, $.1^12>, <$.1^2, $.1^78>, <$.1^59, $.1^109>, <$.1^29, $.1^65>, <4, $.1^57>, <$.1^57, $.1^60>, <1, $.1^91>, <$.1^13, $.1^2>, <$.1^50, $.1^30>, <$.1^89, $.1^97>, <$.1^16, $.1^40>, <$.1^106, $.1^21>, <$.1^2, $.1^94>, <$.1^72, $.1^40>, <$.1^27, $.1^19>, <$.1^108, $.1^123>, <$.1^26, $.1^23>, <$.1^44, $.1^123>, <$.1^76, $.1^16>, <$.1^16, $.1^16>, <$.1^6, $.1^83>, <$.1^78, $.1^118>, <$.1^21, $.1^73>, <$.1^82, $.1^5>, <$.1^27, $.1^15>, <$.1^44, $.1^111>, <$.1^7, $.1^80>, <$.1^68, $.1^13>, <$.1^75, $.1^32>, <$.1^35, $.1^120>, <$.1^19, $.1^61>, <$.1^21, $.1^69>, <2, $.1^56>, <$.1^100, $.1^111>, <$.1^117, $.1^89>, <$.1^96, $.1^55>, <$.1^3, $.1^68>, <$.1^80, $.1^28>, <$.1^108, $.1^11>, <$.1^68, 3>, <$.1^75, $.1^116>, <$.1^41, $.1^27>, <$.1^55, $.1^11>, <$.1^66, $.1^45>, <$.1^57, $.1^76>, <$.1^15, $.1^88>, <$.1^68, $.1^77>, <$.1^2, $.1^14>, <$.1^82, $.1^45>, <$.1^99, $.1^34>, <$.1^15, $.1^20>, <$.1^37, $.1^88>, <$.1^103, $.1^101>, <$.1^92, $.1^85>, <$.1^119, $.1^26>, <$.1^21, $.1^81>, <$.1^12, $.1^46>, <$.1^56, 0>, <$.1^60, $.1^18>, <$.1^120, $.1^42>, <$.1^27, $.1^39>, <$.1^3, $.1^84>, <$.1^111, $.1^113>, <$.1^8, $.1^40>, <$.1^89, $.1^41>, <$.1^73, $.1^21>, <$.1^7, $.1^104>, <$.1^44, $.1^103>, <$.1^106, $.1^45>, <$.1^106, $.1^53>, <$.1^16, $.1^88>, <$.1^109, $.1^95>, <$.1^14, $.1^78>, <$.1^13, $.1^78>, <$.1^104, $.1^106>, <$.1^8, $.1^20>, <$.1^6, $.1^115>, <$.1^8, $.1^100>, <$.1^28, $.1^112>, <$.1^14, $.1^10>, <$.1^121, $.1^75>, <$.1^20, $.1^51>, <$.1^117, $.1^21>, <$.1^38, 3>, <$.1^10, $.1^78>, <3, $.1^18>, <$.1^69, $.1^122>, <$.1^19, $.1^109>, <$.1^26, $.1^67>, <$.1^34, $.1^29>, <$.1^6, $.1^23>, <$.1^111, $.1^45>, <$.1^50, $.1^78>, <$.1^52, $.1^78>, <$.1^60, $.1^98>, <$.1^16, $.1^60>, <$.1^104, $.1^118>, <$.1^61, $.1^24>, <$.1^39, $.1^85>, <$.1^43, $.1^3>, <$.1^60, $.1^46>, <$.1^117, $.1^49>, <2, $.1^4>, <$.1^86, $.1^52>, <$.1^34, $.1^9>, <$.1^103, $.1^21>, <$.1^100, $.1^51>, <$.1^97, $.1^6>, <4, $.1^41>, <$.1^26, $.1^55>, <$.1^107, $.1^5>, <$.1^107, $.1^61>, <$.1^39, $.1^89>, <$.1^74, $.1^120>, <$.1^39, $.1^97>, <$.1^70, $.1^38>, <$.1^60, $.1^90>, <$.1^104, $.1^114>, <$.1^30, $.1^103>, <$.1^102, $.1^6>, <$.1^9, $.1^83>, <$.1^3, $.1^24>, <$.1^80, $.1^120>, <$.1^49, $.1^79>, <$.1^53, 0>, <$.1^102, $.1^54>, <$.1^97, $.1^98>, <$.1^61, $.1^72>, <$.1^20, $.1^87>, <$.1^16, $.1^48>, <$.1^95, $.1^49>, <$.1^20, $.1^119>, <$.1^85, 0>, <$.1^37, $.1^48>, <$.1^91, $.1^59>, <$.1^64, $.1^24>, <$.1^64, $.1^16>, <3, $.1^34>, <$.1^40, $.1^36>, <$.1^122, $.1^84>, <$.1^100, $.1^43>, <$.1^95, $.1^69>, <$.1^114, $.1^32>, <$.1^95, $.1^89>, <$.1^12, $.1^70>, <$.1^90, $.1^38>, <$.1^99, $.1^14>, <$.1^20, $.1^23>, <$.1^33, $.1^71>, <$.1^47, $.1^117>, <3, $.1^38>, <$.1^21, $.1^37>, <$.1^47, $.1^69>, <$.1^65, $.1^18>, <$.1^52, $.1^90>, <$.1^7, $.1^20>, <$.1^105, $.1^89>, <$.1^35, $.1^72>, <$.1^105, 3>, <$.1^66, $.1^85>, <$.1^9, $.1^107>, <4, $.1^77>, <$.1^14, $.1^106>, <$.1^40, $.1^16>, <$.1^24, $.1^58>, <$.1^77, $.1^114>, <$.1^111, $.1^121>, <$.1^108, $.1^95>, <$.1^47, $.1^89>, <$.1^65, $.1^82>, <$.1^119, $.1^114>, <$.1^18, $.1^90>, <$.1^89, $.1^49>, <$.1^77, $.1^102>, <$.1^123, $.1^50>, <$.1^47, $.1^49>, <$.1^10, $.1^82>, <$.1^52, $.1^18>, <$.1^44, $.1^91>, <3, $.1^78>, <$.1^38, $.1^61>, <$.1^122, $.1^96>, <$.1^109, $.1^79>, <$.1^108, $.1^39>, <$.1^123, $.1^66>, <$.1^38, $.1^81>, <$.1^91, $.1^67>, <$.1^29, 3>, <$.1^59, $.1^25>, <$.1^122, 1>, <$.1^28, $.1^88>, <$.1^74, $.1^44>, <$.1^77, $.1^78>, <1, $.1^35>, <$.1^27, $.1^123>, <4, $.1 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:22:14 2004 Input: q:=7; r:=3; exp_t := [ q^i : i in [r-1..0 by -1] ]; exp_n := &+(exp_t); R := GF(7,3); polinomi_t:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exp_t }; puntsolav := :[ a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) ]; Output: Magma V2.10-6 Mon Mar 15 2004 12:22:11 on modular [Seed = 1753075223] ------------------------------------- >> puntsolav := :[ a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) ^ User error: bad syntax Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:22:28 2004 Input: q:=7; r:=3; exp_t := [ q^i : i in [r-1..0 by -1] ]; exp_n := &+(exp_t); R := GF(7,3); polinomi_t:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exp_t }; puntsolav := [ a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) ]; Output: Magma V2.10-6 Mon Mar 15 2004 12:22:26 on modular [Seed = 1635043087] ------------------------------------- >> puntsolav := [ a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) ^ User error: bad syntax Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee13.uab.es. (158.109.66.13) Time: Mon Mar 15 12:22:52 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; puntsOlav:=func: a in GF(q,r), b in GF(q,r)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; exemples:=function(q,r) pol:=polinomit(q,r); xsum:=polinomin(q,r); print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r,pol,xsum)); end function; exemples(2,3); exemples(3,3); exemples(5,3); exemples(3,4); exemples(2,4); puntsOlav2:=func: a in GF(q,r), b in GF(q,r), a in GF(q), b in GF(q)|Evaluate(pol,a) eq Evaluate(xsum,b)}>; pol:=polinomit(2,3); xsum:=polinomin(2,3); puntsOlav2(2,3,pol,xsum); Output: Magma V2.10-6 Mon Mar 15 2004 12:22:48 on modular [Seed = 1531903247] ------------------------------------- [ 49, 7, 1 ] q^(2*r-1) és igual a: 32 El cardinal dels punts Olav en aquest exemple és: 32 q^(2*r-1) és igual a: 243 El cardinal dels punts Olav en aquest exemple és: 243 q^(2*r-1) és igual a: 3125 El cardinal dels punts Olav en aquest exemple és: 3125 q^(2*r-1) és igual a: 2187 El cardinal dels punts Olav en aquest exemple és: 2187 q^(2*r-1) és igual a: 128 El cardinal dels punts Olav en aquest exemple és: 128 { <1, $.1^4>, <$.1^3, $.1^3>, <$.1^3, $.1^6>, <$.1^6, 1>, <$.1^6, $.1^2>, <1, $.1>, <$.1^5, 1>, <$.1^6, $.1^3>, <$.1^3, $.1^2>, <1, $.1^3>, <1, $.1^2>, <$.1^3, $.1^5>, <$.1, 0>, <0, 0>, <$.1^6, $.1^4>, <$.1^5, $.1^5>, <$.1^3, 1>, <1, $.1^5>, <$.1^5, $.1>, <$.1^5, $.1^4>, <$.1^6, $.1>, <$.1^3, $.1^4>, <1, 1>, <$.1^5, $.1^2>, <$.1^6, $.1^5>, <$.1^5, $.1^6>, <$.1^3, $.1>, <1, $.1^6>, <$.1^5, $.1^3>, <$.1^6, $.1^6>, <$.1^2, 0>, <$.1^4, 0> } Total time: 3.489 seconds, Total memory usage: 2.13MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:23:01 2004 Input: q:=7; r:=3; exp_t := [ q^i : i in [r-1..0 by -1] ]; exp_n := &+(exp_t); R := GF(7,3); polinomi_t:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exp_t }; puntsolav := [: a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) ]; Output: Magma V2.10-6 Mon Mar 15 2004 12:22:58 on modular [Seed = 1280961026] ------------------------------------- >> puntsolav := [: a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) ^ User error: bad syntax Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 12:23:40 2004 Input: n73 = x^57; n53; Output: Magma V2.10-6 Mon Mar 15 2004 12:23:37 on modular [Seed = 1096083428] ------------------------------------- >> n73 = x^57; ^ User error: Identifier 'x' has not been declared or assigned >> n53;; ^ User error: Identifier 'n53' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:24:02 2004 Input: q:=7; r:=3; exp_t := [ q^i : i in [r-1..0 by -1] ]; exp_n := &+(exp_t); R := GF(7,3); polinomi_t:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exp_t }; puntsolav := [a,b: a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) ]; Output: Magma V2.10-6 Mon Mar 15 2004 12:23:59 on modular [Seed = 3132038185] ------------------------------------- >> puntsolav := [a,b: a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t ^ User error: bad syntax Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:24:31 2004 Input: q:=7; r:=3; exp_t := [ q^i : i in [r-1..0 by -1] ]; exp_n := &+(exp_t); R := GF(7,3); polinomi_t:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exp_t }; puntsolav := {a,b: a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a)}; Output: Magma V2.10-6 Mon Mar 15 2004 12:24:28 on modular [Seed = 3014006083] ------------------------------------- >> puntsolav := {a,b: a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:25:25 2004 Input: q:=7; r:=3; exp_t := [ q^i : i in [r-1..0 by -1] ]; exp_n := &+(exp_t); R := GF(7,3); polinomi_t:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exp_t }; puntsolav:=[: a,b in R | Evaluate(polinomi_n,a) eq Evaluate(polinomi_t,b)]; Output: Magma V2.10-6 Mon Mar 15 2004 12:25:22 on modular [Seed = 2712929951] ------------------------------------- >> puntsolav:=[: a,b in R | Evaluate(polinomi_n,a) eq Evaluate(polinomi_t,b)]; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 12:25:35 2004 Input: x=GF(4) n73 = x^57; n53; Output: Magma V2.10-6 Mon Mar 15 2004 12:25:32 on modular [Seed = 2593078698] ------------------------------------- >> n73 = x^57; ^ User error: bad syntax >> n53;; ^ User error: Identifier 'n53' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 12:25:45 2004 Input: x=GF(4); n73 = x^57; n53; Output: Magma V2.10-6 Mon Mar 15 2004 12:25:42 on modular [Seed = 2475046073] ------------------------------------- >> x=GF(4); ^ User error: Identifier 'x' has not been declared or assigned >> n73 = x^57; ^ User error: Identifier 'x' has not been declared or assigned >> n53;; ^ User error: Identifier 'n53' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:26:42 2004 Input: q:=7; r:=3; exp_t := [ q^i : i in [r-1..0 by -1] ]; exp_n := &+(exp_t); R := GF(7,3); polinomi_n := PolynomialRing(R); polinomi_n := x^exp_n; polinomi_t:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exp_t }; puntsolav:=[: a,b in R | Evaluate(polinomi_n,a) eq Evaluate(polinomi_t,b)]; Output: Magma V2.10-6 Mon Mar 15 2004 12:26:39 on modular [Seed = 2240815862] ------------------------------------- >> puntsolav:=[: a,b in R | Evaluate(polinomi_n,a) eq Evaluate(polinomi_t,b)]; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 12:27:49 2004 Input: n73:=PolynomialRing(Z); n73 = x^57; n53; Output: Magma V2.10-6 Mon Mar 15 2004 12:27:46 on modular [Seed = 4276836688] ------------------------------------- >> n73:=PolynomialRing(Z); ^ User error: Identifier 'Z' has not been declared or assigned >> n73 = x^57; ^ User error: Identifier 'x' has not been declared or assigned >> n53;; ^ User error: Identifier 'n53' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:28:09 2004 Input: q:=7; r:=3; exp_t := [ q^i : i in [r-1..0 by -1] ]; exp_n := &+(exp_t); R := GF(7,3); polinomi_n := PolynomialRing(R); polinomi_n := x^exp_n; polinomi_t:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exp_t }; puntsolav:=[: a,b [in R] | Evaluate(polinomi_n,a) eq Evaluate(polinomi_t,b)]; Output: Magma V2.10-6 Mon Mar 15 2004 12:28:06 on modular [Seed = 4158804077] ------------------------------------- >> puntsolav:=[: a,b [in R] | Evaluate(polinomi_n,a) eq Evaluate(polinomi_t,b) ^ User error: bad syntax Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:28:24 2004 Input: q:=7; r:=3; exp_t := [ q^i : i in [r-1..0 by -1] ]; exp_n := &+(exp_t); R := GF(7,3); polinomi_n := PolynomialRing(R); polinomi_n := x^exp_n; polinomi_t:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exp_t }; puntsolav:=[(a,b): (a,b) [in R] | Evaluate(polinomi_n,a) eq Evaluate(polinomi_t,b)]; Output: Magma V2.10-6 Mon Mar 15 2004 12:28:21 on modular [Seed = 3908915041] ------------------------------------- >> puntsolav:=[(a,b): (a,b) [in R] | Evaluate(polinomi_n,a) eq Evaluate(polino ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:28:39 2004 Input: q:=7; r:=3; exp_t := [ q^i : i in [r-1..0 by -1] ]; exp_n := &+(exp_t); R := GF(7,3); polinomi_n := PolynomialRing(R); polinomi_n := x^exp_n; polinomi_t:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exp_t }; puntsolav:=[(a,b): a,b [in R] | Evaluate(polinomi_n,a) eq Evaluate(polinomi_t,b)]; Output: Magma V2.10-6 Mon Mar 15 2004 12:28:37 on modular [Seed = 3790882328] ------------------------------------- >> puntsolav:=[(a,b): a,b [in R] | Evaluate(polinomi_n,a) eq Evaluate(polinomi ^ User error: bad syntax Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:28:53 2004 Input: q:=7; r:=3; exp_t := [ q^i : i in [r-1..0 by -1] ]; exp_n := &+(exp_t); R := GF(7,3); polinomi_n := PolynomialRing(R); polinomi_n := x^exp_n; polinomi_t:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exp_t }; puntsolav:=[(a,b): a,b in R | Evaluate(polinomi_n,a) eq Evaluate(polinomi_t,b)]; Output: Magma V2.10-6 Mon Mar 15 2004 12:28:50 on modular [Seed = 3671031092] ------------------------------------- >> puntsolav:=[(a,b): a,b in R | Evaluate(polinomi_n,a) eq Evaluate(polinomi_t ^ Runtime error in elt< ... >: Bad arguments Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 12:29:31 2004 Input: Z=Integers(); n73:=PolynomialRing(Z); n73 = x^57; n53; Output: Magma V2.10-6 Mon Mar 15 2004 12:29:28 on modular [Seed = 3552998423] ------------------------------------- >> Z=Integers(); ^ User error: Identifier 'Z' has not been declared or assigned >> n73:=PolynomialRing(Z); ^ User error: Identifier 'Z' has not been declared or assigned >> n73 = x^57; ^ User error: Identifier 'x' has not been declared or assigned >> n53;; ^ User error: Identifier 'n53' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 12:29:40 2004 Input: Z:=Integers(); n73:=PolynomialRing(Z); n73 = x^57; n53; Output: Magma V2.10-6 Mon Mar 15 2004 12:29:37 on modular [Seed = 3318771192] ------------------------------------- >> n73 = x^57; ^ Runtime error in elt< ... >: LHS and RHS of relation constructor are not compatible >> n53;; ^ User error: Identifier 'n53' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 12:30:37 2004 Input: Z=Integers(100); n73:=PolynomialRing(Z); n73 = x^57; n53; Output: Magma V2.10-6 Mon Mar 15 2004 12:30:34 on modular [Seed = 925015856] ------------------------------------- >> Z=Integers(100); ^ User error: Identifier 'Z' has not been declared or assigned >> n73:=PolynomialRing(Z); ^ User error: Identifier 'Z' has not been declared or assigned >> n73 = x^57; ^ User error: Identifier 'x' has not been declared or assigned >> n53;; ^ User error: Identifier 'n53' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 12:30:47 2004 Input: Z:=Integers(100); n73:=PolynomialRing(Z); n73 = x^57; n53; Output: Magma V2.10-6 Mon Mar 15 2004 12:30:44 on modular [Seed = 775652951] ------------------------------------- >> n73 = x^57; ^ Runtime error in elt< ... >: LHS and RHS of relation constructor are not compatible >> n53;; ^ User error: Identifier 'n53' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 12:31:00 2004 Input: Z:=Integers(100); n73:=PolynomialRing(Z); n73 := x^57; n53; Output: Magma V2.10-6 Mon Mar 15 2004 12:30:57 on modular [Seed = 557091149] ------------------------------------- >> n53;; ^ User error: Identifier 'n53' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 12:31:13 2004 Input: Z:=Integers(100); n73:=PolynomialRing(Z); n73 := x^57; n73; Output: Magma V2.10-6 Mon Mar 15 2004 12:31:10 on modular [Seed = 403550331] ------------------------------------- x^57 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:33:03 2004 Input: q:=7; r:=3; exp_t := [ q^i : i in [r-1..0 by -1] ]; exp_n := &+(exp_t); R := GF(7,3); polinomi_n := PolynomialRing(R); polinomi_n := x^exp_n; polinomi_t:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exp_t }; puntsolav:=[ a: a in R | Evaluate(polinomi_n,a) eq Evaluate(polinomi_t,a)]; Output: Magma V2.10-6 Mon Mar 15 2004 12:33:00 on modular [Seed = 302496483] ------------------------------------- Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:33:20 2004 Input: q:=7; r:=3; exp_t := [ q^i : i in [r-1..0 by -1] ]; exp_n := &+(exp_t); R := GF(7,3); polinomi_n := PolynomialRing(R); polinomi_n := x^exp_n; polinomi_t:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exp_t }; puntsolav:=[ a: a in R | Evaluate(polinomi_n,a) eq Evaluate(polinomi_t,a)]; print puntsolav; Output: Magma V2.10-6 Mon Mar 15 2004 12:33:17 on modular [Seed = 84979173] ------------------------------------- [ R.1^34, R.1^41, R.1^66, R.1^67, R.1^69, R.1^73, R.1^86, R.1^89, R.1^90, R.1^110, R.1^116, R.1^117, R.1^120, R.1^127, R.1^128, R.1^132, R.1^135, R.1^141, R.1^156, R.1^157, R.1^169, R.1^205, R.1^212, R.1^237, R.1^238, R.1^240, R.1^244, R.1^257, R.1^260, R.1^261, R.1^281, R.1^287, R.1^288, R.1^291, R.1^298, R.1^299, R.1^303, R.1^306, R.1^312, R.1^327, R.1^328, R.1^340, 0 ] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host n137.ryd.student.liu.se. (130.236.215.137) Time: Mon Mar 15 12:33:47 2004 Input: A:=18319763876343075050046105985912487254390312955286319004804732883115032524903434566144196732390020367631712413634262994560146483287673; B:=10435002940608220263898092413744390893080003350854617124834186840832200737042490450426489234027559725460028244813617063564169606995640; p:=196820335922932778101683691741; E:=ChangeRing(EllipticCurve([A,B]),GF(p)); print(E); go:=Order(E); Factorization(go); Output: Magma V2.10-6 Mon Mar 15 2004 12:33:42 on modular [Seed = 2087310519] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 191197958891932074542120853762*x + 177675878358404135490302349428 over GF(196820335922932778101683691741) [ <2, 14>, <3, 3>, <5, 1>, <103, 1>, <28697, 1>, <44203, 1>, <102101, 1>, <6670537, 1> ] Total time: 4.879 seconds, Total memory usage: 3.48MB ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Mon Mar 15 12:34:00 2004 Input: K := GF(4); M22 := MatrixRing(K,2); Mt := { m : m in M22 | Trace(m) eq 0 }; Mf := { m : m in M22 | m[1] eq m[2] }; Mtf := Mt meet Mf; Output: Magma V2.10-6 Mon Mar 15 2004 12:33:57 on modular [Seed = 2002968143] ------------------------------------- Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:34:11 2004 Input: q:=7; r:=3; exp_t := [ q^i : i in [r-1..0 by -1] ]; exp_n := &+(exp_t); R := GF(7,3); polinomi_n := PolynomialRing(R); polinomi_n := x^exp_n; polinomi_t:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exp_t }; puntsolav:=[ a,b: a,b in R | Evaluate(polinomi_n,a) eq Evaluate(polinomi_t,b)]; print puntsolav; Output: Magma V2.10-6 Mon Mar 15 2004 12:34:08 on modular [Seed = 1853605699] ------------------------------------- >> puntsolav:=[ a,b: a,b in R | Evaluate(polinomi_n,a) eq Evaluate(polinomi_t, ^ User error: bad syntax >> print puntsolav; ^ User error: Identifier 'puntsolav' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Mon Mar 15 12:34:24 2004 Input: K := GF(4); M22 := MatrixRing(K,2); Mt := { m : m in M22 | Trace(m) eq 0 }; Mf := { m : m in M22 | m[1] eq m[2] }; Mtf := Mt meet Mf; print(Mtf); Output: Magma V2.10-6 Mon Mar 15 2004 12:34:21 on modular [Seed = 1635043393] ------------------------------------- { [ 0 0] [ 0 0], [K.1^2 K.1^2] [K.1^2 K.1^2], [ K.1 K.1] [ K.1 K.1], [ 1 1] [ 1 1] } Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Mon Mar 15 12:37:08 2004 Input: K := GF(4); M22 := MatrixRing(K,2); Mt := { m : m in M22 | Trace(m) eq 0 }; Mf := { m : m in M22 | m[1] eq m[2] }; Mtf := Mt meet Mf; rnd := [Random(M22) : i in {1..100000}]; Mt2 := { m : m in rnd | Trace(m) eq 0 }; Mf2 := { m : m in rnd | m[1] eq m[2] }; Mtf2 := Mt2 meet Mf2; #(M22); #(Mt); #(Mf); #(Mtf); #(rnd); #(Mt2); #(Mf2); #(Mtf2); Output: Magma V2.10-6 Mon Mar 15 2004 12:37:03 on modular [Seed = 1447296939] ------------------------------------- 256 64 16 4 100000 64 16 4 Total time: 4.909 seconds, Total memory usage: 6.95MB ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Mon Mar 15 12:37:34 2004 Input: K := GF(4); M22 := MatrixRing(K,2); Mt := { m : m in M22 | Trace(m) eq 0 }; Mf := { m : m in M22 | m[1] eq m[2] }; Mtf := Mt meet Mf; rnd := [Random(M22) : i in [1..100000]]; Mt2 := { m : m in rnd | Trace(m) eq 0 }; Mf2 := { m : m in rnd | m[1] eq m[2] }; Mtf2 := Mt2 meet Mf2; #(M22); #(Mt); #(Mf); #(Mtf); #(rnd); #(Mt2); #(Mf2); #(Mtf2); Output: Magma V2.10-6 Mon Mar 15 2004 12:37:29 on modular [Seed = 1230823597] ------------------------------------- 256 64 16 4 100000 64 16 4 Total time: 4.909 seconds, Total memory usage: 6.95MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:39:31 2004 Input: { a,b in [1..7 by 1] | a eq b }; Output: Magma V2.10-6 Mon Mar 15 2004 12:39:28 on modular [Seed = 1129769262] ------------------------------------- >> { a,b in [1..7 by 1] | a eq b }; ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:39:44 2004 Input: { a,b: a,b in [1..7 by 1] | a eq b }; Output: Magma V2.10-6 Mon Mar 15 2004 12:39:41 on modular [Seed = 3132035290] ------------------------------------- >> { a,b: a,b in [1..7 by 1] | a eq b }; ^ User error: bad syntax Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:39:57 2004 Input: { (a,b): a,b in [1..7 by 1] | a eq b }; Output: Magma V2.10-6 Mon Mar 15 2004 12:39:54 on modular [Seed = 2914519034] ------------------------------------- >> { (a,b): a,b in [1..7 by 1] | a eq b }; ^ Runtime error in elt< ... >: No permutation group context in which to create cycle Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:41:19 2004 Input: { {a,b}: a,b in [1..7 by 1] | a eq b }; Output: Magma V2.10-6 Mon Mar 15 2004 12:41:16 on modular [Seed = 2676634910] ------------------------------------- { { 1 }, { 2 }, { 3 }, { 4 }, { 7 }, { 5 }, { 6 } } Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Mon Mar 15 12:41:29 2004 Input: K := GF(4); M22 := MatrixRing(K,2); Mt := { m : m in M22 | Trace(m) eq 0 }; Mf := { m : m in M22 | m[1] eq m[2] }; Mtf := Mt meet Mf; rnd := [Random(M22) : i in [1..100000]]; Mt2 := [ m : m in rnd | Trace(m) eq 0 ]; Mf2 := [ m : m in rnd | m[1] eq m[2] ]; Mtf2 := Mt2 meet Mf2; #(M22); #(Mt); #(Mf); #(Mtf); #(rnd); #(Mt2); #(Mf2); #(Mtf2); Output: Magma V2.10-6 Mon Mar 15 2004 12:41:24 on modular [Seed = 2525183087] ------------------------------------- >> Mtf2 := Mt2 meet Mf2; ^ Runtime error in 'meet': Bad argument types Argument types given: SeqEnum[AlgMatElt], SeqEnum[AlgMatElt] 256 64 16 4 100000 25194 6263 >> #(Mtf2); ^ User error: Identifier 'Mtf2' has not been declared or assigned Total time: 4.859 seconds, Total memory usage: 6.95MB ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Mon Mar 15 12:42:40 2004 Input: K := GF(4); M22 := MatrixRing(K,2); Mt := { m : m in M22 | Trace(m) eq 0 }; Mf := { m : m in M22 | m[1] eq m[2] }; Mtf := Mt meet Mf; rnd := [Random(M22) : i in [1..100000]]; Mt2 := [ m : m in rnd | Trace(m) eq 0 ]; Mf2 := [ m : m in rnd | m[1] eq m[2] ]; Mtf2 := [ m : m in rnd | m[1] eq m[2] ]; #(M22); #(Mt); #(Mf); #(Mtf); #(rnd); #(Mt2); #(Mf2); #(Mtf2); Output: Magma V2.10-6 Mon Mar 15 2004 12:42:34 on modular [Seed = 2308711102] ------------------------------------- 256 64 16 4 100000 24939 6327 6327 Total time: 5.979 seconds, Total memory usage: 6.95MB ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Mon Mar 15 12:42:53 2004 Input: K := GF(4); M22 := MatrixRing(K,2); Mt := { m : m in M22 | Trace(m) eq 0 }; Mf := { m : m in M22 | m[1] eq m[2] }; Mtf := Mt meet Mf; rnd := [Random(M22) : i in [1..100000]]; Mt2 := [ m : m in rnd | Trace(m) eq 0 ]; Mf2 := [ m : m in rnd | m[1] eq m[2] ]; Mtf2 := [ m : m in Mt2 | m[1] eq m[2] ]; #(M22); #(Mt); #(Mf); #(Mtf); #(rnd); #(Mt2); #(Mf2); #(Mtf2); Output: Magma V2.10-6 Mon Mar 15 2004 12:42:48 on modular [Seed = 2157259685] ------------------------------------- 256 64 16 4 100000 24894 6284 1626 Total time: 5.129 seconds, Total memory usage: 6.95MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:42:58 2004 Input: q:=7; r:=3; exp_t := [ q^i : i in [r-1..0 by -1] ]; exp_n := &+(exp_t); R := GF(q,r); polinomi_t:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exp_t }; polinomi_n := PolynomialRing(R); polinomi_n := x^exp_n; puntsolav := { {a,b}:a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) }; Output: Magma V2.10-6 Mon Mar 15 2004 12:42:53 on modular [Seed = 4243150812] ------------------------------------- Total time: 4.239 seconds, Total memory usage: 6.11MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:43:17 2004 Input: q:=7; r:=3; exp_t := [ q^i : i in [r-1..0 by -1] ]; exp_n := &+(exp_t); R := GF(q,r); polinomi_t:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exp_t }; polinomi_n := PolynomialRing(R); polinomi_n := x^exp_n; puntsolav := { {a,b}:a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) }; print puntsolav; Output: Magma V2.10-6 Mon Mar 15 2004 12:43:12 on modular [Seed = 4075248127] ------------------------------------- { { R.1^212, R.1^152 }, { R.1^55, R.1^160 }, { R.1^199, R.1^138 }, { R.1^59, R.1^183 }, { R.1^36, R.1^127 }, { R.1^77, R.1^294 }, { R.1^194, R.1^329 }, { R.1^71, R.1^20 }, { R.1^231, 2 }, { R.1^170, R.1^270 }, { R.1^160, R.1^153 }, { R.1^112, R.1^312 }, { R.1^319, R.1^194 }, { R.1^47, R.1^314 }, { R.1^94, R.1^241 }, { R.1^66, 5 }, { R.1^282, R.1^175 }, { R.1^200, R.1^151 }, { R.1^333, R.1^283 }, { R.1^46, R.1^281 }, { R.1^13, R.1^281 }, { R.1, R.1^168 }, { R.1^157, R.1^316 }, { R.1^34, R.1^136 }, { R.1^240, R.1^42 }, { R.1^231, R.1^155 }, { R.1^112, R.1^270 }, { R.1^203, R.1^73 }, { R.1^314, R.1^30 }, { R.1^99, R.1^161 }, { R.1^325, R.1^262 }, { R.1^157, R.1^295 }, { R.1^146, R.1^260 }, { R.1^178, R.1^153 }, { R.1^61, R.1^118 }, { R.1^306, R.1^318 }, { R.1^272, R.1^130 }, { R.1^232, R.1^307 }, { R.1^105, R.1^261 }, { R.1^220, R.1^33 }, { R.1^40, R.1^317 }, { R.1^67, R.1^216 }, { R.1^242, R.1^232 }, { R.1^78, R.1^70 }, { R.1^310, R.1^315 }, { R.1^82, R.1^283 }, { R.1^189, R.1^223 }, { R.1^319, R.1^141 }, { R.1^90, R.1^294 }, { R.1^103, R.1^108 }, { R.1^302, R.1^39 }, { R.1^277, R.1^3 }, { R.1^89, R.1^203 }, { R.1^258, R.1^207 }, { R.1^55, R.1^41 }, { R.1^223, R.1^250 }, { R.1^6, R.1^160 }, { R.1^188, R.1^270 }, { R.1^11, R.1^75 }, { R.1^89, R.1^292 }, { R.1^154, R.1^109 }, { R.1^216, R.1^271 }, { R.1^341, R.1^292 }, { R.1^106, R.1^294 }, { R.1^81, R.1^226 }, { R.1^239, R.1^296 }, { R.1^260, R.1^272 }, { R.1^210, R.1^83 }, { 1, R.1^148 }, { R.1^198, R.1^339 }, { R.1^158, R.1^151 }, { R.1^145, R.1^238 }, { R.1^104, R.1^291 }, { R.1^210, R.1^159 }, { R.1^99, R.1^47 }, { R.1^112, R.1^328 }, { R.1^67, R.1^325 }, { R.1^253, R.1^112 }, { R.1^319, R.1^256 }, { R.1^72, R.1^263 }, { R.1^269, R.1^140 }, { R.1^143, R.1^310 }, { R.1^194, R.1^109 }, { 3, R.1^338 }, { R.1^105, R.1^274 }, { R.1^242, R.1^274 }, { R.1^47, R.1^30 }, { R.1^292, R.1^215 }, { R.1^178, R.1^318 }, { R.1^140, R.1^239 }, { R.1^326, R.1^184 }, { R.1^308, R.1^267 }, { R.1^145, R.1^328 }, { R.1^145, R.1^118 }, { R.1^222, R.1^137 }, { R.1^32, R.1^76 }, { R.1^81, R.1^94 }, { R.1^275, R.1^18 }, { R.1^178, R.1^225 }, { R.1^308, R.1^86 }, { R.1^135, R.1^159 }, { R.1^151, R.1^296 }, { R.1^302, R.1^117 }, { R.1^341, R.1^287 }, { R.1^264, R.1^299 }, { R.1^90, R.1^102 }, { R.1^165, R.1^172 }, { 3, R.1^4 }, { R.1^334, R.1^207 }, { R.1^309, R.1^212 }, { R.1^176, R.1^201 }, { R.1^148, 6 }, { 1, R.1^109 }, { R.1^17, R.1^118 }, { R.1^55, R.1^173 }, { R.1^204, R.1^307 }, { R.1^167, R.1^129 }, { R.1^270, R.1^116 }, { R.1^323, R.1^75 }, { R.1^35, R.1^86 }, { R.1^105, R.1^62 }, { R.1^138, R.1^120 }, { R.1^83, R.1^75 }, { R.1^320, R.1^19 }, { R.1^25, R.1^94 }, { R.1^34, R.1^340 }, { R.1^314, R.1^6 }, { R.1^210, R.1^314 }, { R.1^35, R.1^281 }, { R.1^44, R.1^163 }, { R.1^56, R.1^234 }, { R.1^187, R.1^68 }, { R.1^306, R.1^186 }, { R.1^70, R.1^174 }, { R.1^187, R.1^94 }, { R.1^156, R.1^336 }, { R.1^123, R.1^247 }, { R.1^190, R.1^153 }, { R.1^34, R.1^239 }, { R.1^207, R.1^142 }, { R.1^137, R.1^54 }, { R.1^277, R.1^130 }, { R.1^299, R.1^9 }, { R.1^11, R.1^295 }, { R.1^203, R.1^140 }, { R.1^298, R.1^64 }, { R.1^101, 4 }, { R.1^101, R.1^292 }, { R.1^245, R.1^63 }, { R.1^133, R.1^290 }, { R.1^44, R.1^63 }, { R.1^232, R.1^193 }, { R.1^288, R.1^267 }, { R.1^81, R.1^16 }, { R.1^22, R.1^315 }, { 1, R.1 }, { R.1^155, R.1^301 }, { R.1^255, R.1^185 }, { R.1^91, R.1^64 }, { R.1^115, R.1^98 }, { R.1^25, R.1^72 }, { R.1^245, R.1^116 }, { R.1^288, R.1^294 }, { R.1^160, R.1^97 }, { R.1^94, R.1^307 }, { R.1^110, R.1^309 }, { R.1^292, R.1^305 }, { R.1^24, R.1^51 }, { R.1^62, R.1^184 }, { R.1^93, R.1^116 }, { R.1^78, R.1^195 }, { R.1^281, R.1^140 }, { R.1^101, R.1^28 }, { R.1^62, R.1^86 }, { R.1^204, R.1^20 }, { R.1^258, R.1^120 }, { R.1^115, R.1^104 }, { R.1^234, R.1^16 }, { R.1^136, R.1^340 }, { R.1^143, R.1^206 }, { R.1^308, R.1^117 }, { R.1^105, R.1^241 }, { R.1^249, R.1^227 }, { R.1^24, R.1^146 }, { R.1^298, R.1^207 }, { R.1^91, R.1^329 }, { R.1^131, R.1^318 }, { R.1^242, R.1^311 }, { R.1^248, R.1^262 }, { R.1^53, R.1^296 }, { R.1^99, R.1^311 }, { R.1^55, R.1^299 }, { R.1^122, R.1^311 }, { R.1^67, R.1^97 }, { R.1^310, R.1^317 }, { R.1^322, R.1^293 }, { R.1^332, R.1^37 }, { R.1^97, R.1^120 }, { R.1^140, R.1^86 }, { R.1^330, R.1^7 }, { R.1^255, R.1^47 }, { R.1^117, R.1^273 }, { R.1^220, R.1^85 }, { R.1^5, R.1^164 }, { R.1^210, R.1^29 }, { R.1^242, R.1^286 }, { R.1^2, R.1^31 }, { R.1^305, R.1^340 }, { R.1^255, R.1^83 }, { R.1^223, R.1^70 }, { R.1^202, R.1^335 }, { R.1^177, R.1^235 }, { R.1^137, 4 }, { R.1^289, R.1^314 }, { R.1^136, R.1^15 }, { R.1^137, R.1^292 }, { R.1^258, R.1^97 }, { R.1^16, R.1^306 }, { R.1^173, R.1^142 }, { R.1^81, R.1^40 }, { R.1^199, R.1^210 }, { R.1^7, R.1^186 }, { R.1^135, R.1^291 }, { R.1^168, R.1^93 }, { R.1^188, R.1^307 }, { R.1^68, R.1^246 }, { R.1^308, R.1^165 }, { R.1^3, R.1^196 }, { R.1^290, R.1^43 }, { R.1^324, R.1^259 }, { R.1^325, R.1^40 }, { R.1^199, R.1^6 }, { R.1^170, R.1^163 }, { R.1^255, R.1^237 }, { R.1^266, R.1^246 }, { R.1^100, R.1^224 }, { R.1^277, R.1^172 }, { R.1^240, R.1^10 }, { R.1^332, R.1^295 }, { R.1^178, R.1^229 }, { R.1^265, R.1^147 }, { R.1^73, R.1^163 }, { R.1^25, R.1^60 }, { R.1^254, R.1^289 }, { R.1^79, R.1^38 }, { R.1^205, R.1^283 }, { 1, R.1^97 }, { R.1^291, R.1^150 }, { R.1^2, R.1^125 }, { R.1^79, R.1^71 }, { R.1^91, R.1^324 }, { R.1^189, R.1^7 }, { R.1^220, 6 }, { R.1^5, R.1^152 }, { R.1^12, R.1^32 }, { R.1^15, R.1^261 }, { R.1^3, R.1^4 }, { R.1^198, R.1^166 }, { R.1^266, R.1^245 }, { R.1^66, R.1^267 }, { R.1^155, R.1^25 }, { R.1^135, R.1^237 }, { R.1^265, R.1^124 }, { R.1^222, R.1^267 }, { R.1^242, R.1^270 }, { R.1^88, R.1^145 }, { R.1^180, R.1^104 }, { R.1^166, 5 }, { R.1^253, R.1^202 }, { R.1^286, R.1^81 }, { R.1^220, R.1^207 }, { R.1^270, R.1^307 }, { R.1^123, R.1^172 }, { R.1^6, R.1^76 }, { R.1^246, R.1^137 }, { R.1^224, R.1^106 }, { R.1^334, R.1^126 }, { R.1^37, R.1^18 }, { R.1^232, R.1^247 }, { R.1^326, R.1^328 }, { R.1^231, R.1^241 }, { R.1^203, R.1^175 }, { R.1^242, R.1^130 }, { R.1^189, R.1^289 }, { R.1, R.1^120 }, { R.1^94, R.1^239 }, { R.1^264, R.1^53 }, { R.1^45, R.1^268 }, { R.1^189, R.1^135 }, { R.1^270, R.1^197 }, { R.1^13, R.1^65 }, { R.1^78, R.1^306 }, { R.1^224, R.1^280 }, { R.1^290, R.1^184 }, { R.1^96, R.1^141 }, { R.1^255, R.1^135 }, { R.1^194, R.1^295 }, { R.1^247, R.1^73 }, { R.1^14, R.1^192 }, { R.1^56, R.1^260 }, { R.1^277, R.1^4 }, { R.1^33, R.1^248 }, { R.1^176, R.1^299 }, { R.1^281, R.1^282 }, { R.1^248, R.1^9 }, { R.1^235, R.1^205 }, { R.1^187, R.1^82 }, { R.1^69, R.1^27 }, { R.1^281, R.1^305 }, { R.1^322, R.1^269 }, { R.1^133, R.1^73 }, { R.1^315, R.1^52 }, { R.1^192, R.1^262 }, { R.1^319, R.1^67 }, { R.1^5, R.1^314 }, { R.1^89, R.1^95 }, { R.1^7, R.1^30 }, { R.1^100, R.1^315 }, { R.1^316, R.1^32 }, { R.1^277, R.1^190 }, { R.1^7, R.1^318 }, { 1, R.1^2 }, { R.1^204, R.1^260 }, { R.1^163, R.1^218 }, { R.1^226, R.1^239 }, { R.1^217, R.1^230 }, { R.1^239, R.1^328 }, { R.1^18, R.1^98 }, { R.1^44, R.1^321 }, { R.1^36, R.1^229 }, { R.1^286, R.1^323 }, { R.1^77, R.1^41 }, { R.1^210, R.1^89 }, { R.1^110, R.1^180 }, { R.1^195, R.1^306 }, { R.1^200, R.1^260 }, { R.1^37, R.1^318 }, { R.1^289, R.1^316 }, { R.1^341, R.1^91 }, { R.1^44, R.1^237 }, { R.1^159, R.1^28 }, { R.1^3, R.1^229 }, { R.1^211, R.1^98 }, { R.1^232, R.1^103 }, { R.1^67, R.1^7 }, { R.1^112, R.1^326 }, { R.1^27, R.1^205 }, { R.1^39, R.1^20 }, { R.1^22, R.1^207 }, { R.1^169, R.1^241 }, { R.1^234, R.1^259 }, { R.1^111, R.1^74 }, { R.1^155, R.1^145 }, { R.1^59, R.1^9 }, { R.1^188, R.1^191 }, { R.1^37, 2 }, { R.1^216, R.1^295 }, { R.1^34, R.1^16 }, { R.1^286, R.1^265 }, { R.1^222, R.1^49 }, { R.1^157, R.1^97 }, { R.1^132, R.1^267 }, { R.1^260, R.1^8 }, { R.1^293, R.1^9 }, { R.1^249, R.1^317 }, { R.1^299, R.1^142 }, { R.1^286, R.1^119 }, { R.1^271, R.1^273 }, { R.1^291, R.1^208 }, { R.1^290, R.1^229 }, { R.1^203, R.1^61 }, { R.1^101, R.1^82 }, { R.1^35, R.1^14 }, { R.1^200, R.1^214 }, { R.1^112, R.1^156 }, { R.1^3, R.1^31 }, { R.1^138, R.1^173 }, { R.1^190, R.1^318 }, { R.1^158, R.1^305 }, { R.1^2, R.1^324 }, { R.1^4, R.1^328 }, { R.1^59, R.1^103 }, { R.1^89, R.1^118 }, { R.1^80, R.1^335 }, { R.1^80, R.1^60 }, { R.1^220, R.1^309 }, { R.1^147, R.1^37 }, { R.1^71, R.1^313 }, { R.1^159, R.1^258 }, { R.1^172, R.1^261 }, { R.1^224, R.1^214 }, { R.1^234, R.1^92 }, { R.1^118, R.1^305 }, { R.1^287, R.1^17 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:44:47 2004 Input: ptqr := function (q,r) exponents_t := { q^i : i in [r-1..0 by -1] }; return {exponents_t}; end function; ptqr(7,3); Output: Magma V2.10-6 Mon Mar 15 2004 12:44:44 on modular [Seed = 3841019733] ------------------------------------- { { 1, 7, 49 } } Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:45:03 2004 Input: ptqr := function (q,r) exponents_t := { q^i : i in [r-1..0 by -1] }; return {exponents_t}; end function; ptqr(2,2); Output: Magma V2.10-6 Mon Mar 15 2004 12:45:00 on modular [Seed = 3687739514] ------------------------------------- { { 1, 2 } } Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 12:46:12 2004 Input: Z:=Integers(100); n73:=PolynomialRing(Z); r:=3 q:=7 equis:= [x^(q^r-1)] for i:=2 to r do equis cat [x^(q^r-i)] end do; Output: Magma V2.10-6 Mon Mar 15 2004 12:46:09 on modular [Seed = 3453511185] ------------------------------------- >> q:=7 ^ User error: bad syntax >> for i:=2 to r do equis cat [x^(q^r-i)] end do;; ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 12:46:35 2004 Input: Z:=Integers(100); n73:=PolynomialRing(Z); r:=3; q:=7; equis:= [x^(q^r-1)]; for i:=2 to r do equis:= equis cat [x^(q^r-i)] end do; Output: Magma V2.10-6 Mon Mar 15 2004 12:46:32 on modular [Seed = 3302059777] ------------------------------------- >> for i:=2 to r do equis:= equis cat [x^(q^r-i)] end do;; ^ User error: bad syntax Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 12:46:47 2004 Input: Z:=Integers(100); n73:=PolynomialRing(Z); r:=3; q:=7; equis:= [x^(q^r-1)]; for i:=2 to r do equis:= equis cat [x^(q^r-i)]; end do; Output: Magma V2.10-6 Mon Mar 15 2004 12:46:44 on modular [Seed = 1009356806] ------------------------------------- >> for i:=2 to r do equis:= equis cat [x^(q^r-i)]; end do;; ^ User error: bad syntax Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 12:47:12 2004 Input: Z:=Integers(100); n73:=PolynomialRing(Z); r:=3; q:=7; equis:= [q^r-1]; for i:=2 to r do equis:= equis cat [q^r-i]; end do; Output: Magma V2.10-6 Mon Mar 15 2004 12:47:09 on modular [Seed = 891328790] ------------------------------------- >> for i:=2 to r do equis:= equis cat [q^r-i]; end do;; ^ User error: bad syntax Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:47:33 2004 Input: crear_polinomis := function (q,r) R := GF(q,r); exponents_t := { q^i : i in [r-1..0 by -1] }; exponents_n := &+(exponents_t); polinomi_t:= PolynomialRing(R); polinomi_n:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exponents_t }; polinomi_n := x^exponents_n; return { polinomi_n , polinomi_t}; end function; crear_polinomis(7,3); Output: Magma V2.10-6 Mon Mar 15 2004 12:47:30 on modular [Seed = 708806182] ------------------------------------- { x^57, x^49 + x^7 + x } Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 12:47:49 2004 Input: Z:=Integers(100); n73:=PolynomialRing(Z); r:=3; q:=7; equis:= [q^r-1]; for i:=2 to r do equis:= equis cat [q^r-i; end for; Output: Magma V2.10-6 Mon Mar 15 2004 12:47:46 on modular [Seed = 590778207] ------------------------------------- >> for i:=2 to r do equis:= equis cat [q^r-i; end for;; ^ User error: bad syntax Total time: 3.149 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:47:52 2004 Input: crear_polinomis := function (q,r) R := GF(q,r); exponents_t := { q^i : i in [r-1..0 by -1] }; exponents_n := &+(exponents_t); polinomi_t:= PolynomialRing(R); polinomi_n:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exponents_t }; polinomi_n := x^exponents_n; return { polinomi_n , polinomi_t}; end function; crear_polinomis(2,2); Output: Magma V2.10-6 Mon Mar 15 2004 12:47:48 on modular [Seed = 504083044] ------------------------------------- { x^3, x^2 + x } Total time: 3.129 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 12:47:57 2004 Input: Z:=Integers(100); n73:=PolynomialRing(Z); r:=3; q:=7; equis:= [q^r-1]; for i:=2 to r do equis:= equis cat [q^r-i]; end for; Output: Magma V2.10-6 Mon Mar 15 2004 12:47:54 on modular [Seed = 285523301] ------------------------------------- Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:48:05 2004 Input: crear_polinomis := function (q,r) R := GF(q,r); exponents_t := { q^i : i in [r-1..0 by -1] }; exponents_n := &+(exponents_t); polinomi_t:= PolynomialRing(R); polinomi_n:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exponents_t }; polinomi_n := x^exponents_n; return { polinomi_n , polinomi_t}; end function; crear_polinomis(3,3); Output: Magma V2.10-6 Mon Mar 15 2004 12:48:02 on modular [Seed = 118664043] ------------------------------------- { x^13, x^9 + x^3 + x } Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 12:48:12 2004 Input: Z:=Integers(100); n73:=PolynomialRing(Z); r:=3; q:=7; equis:= [q^r-1]; for i:=2 to r do equis:= equis cat [q^r-i]; end for; equis; Output: Magma V2.10-6 Mon Mar 15 2004 12:48:09 on modular [Seed = 2087309339] ------------------------------------- [ 342, 341, 340 ] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 12:49:16 2004 Input: Z:=Integers(100); n73:=PolynomialRing(Z); r:=3; q:=7; equis:= [q^(r-1)]; for i:=2 to r do equis:= equis cat [q^(r-i)]; end for; equis; Output: Magma V2.10-6 Mon Mar 15 2004 12:49:13 on modular [Seed = 1969281490] ------------------------------------- [ 49, 7, 1 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:49:37 2004 Input: crear_polinomis := function (q,r) R := GF(q,r); exponents_t := { q^i : i in [r-1..0 by -1] }; exponents_n := &+(exponents_t); polinomi_t:= PolynomialRing(R); polinomi_n:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exponents_t }; polinomi_n := x^exponents_n; return { polinomi_n , polinomi_t}; end function; olav := function (q,r) gfqr := GF(q,r); polinomi_n, polinomi_t := crear_polinomis(q,r); puntsolav := { {a,b}:a,b in gfqr | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) }; return {puntsolav}; end function; olav(7,3); Output: Magma V2.10-6 Mon Mar 15 2004 12:49:34 on modular [Seed = 1786758906] ------------------------------------- [
:13]( q: 7, r: 3 ) >> polinomi_n, polinomi_t := crear_polinomis(q,r); ^ Runtime error in :=: Expected to assign 2 value(s) but only computed 1 value(s) Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 12:49:56 2004 Input: Z:=Integers(100); n73:=PolynomialRing(Z); r:=3; q:=7; coef:= [q^(r-1)]; for i:=2 to r do coef:= coef cat [q^(r-i)]; end for; coef; Output: Magma V2.10-6 Mon Mar 15 2004 12:49:53 on modular [Seed = 1668730780] ------------------------------------- [ 49, 7, 1 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:51:43 2004 Input: olav := function (q,r) R := GF(q,r); exponents_t := { q^i : i in [r-1..0 by -1] }; exponents_n := &+(exponents_t); polinomi_t:= PolynomialRing(R); polinomi_n:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exponents_t }; polinomi_n := x^exponents_n; puntsolav := { {a,b}:a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) }; return {puntsolav}; end function; olav(7,3); Output: Magma V2.10-6 Mon Mar 15 2004 12:51:39 on modular [Seed = 1346764101] ------------------------------------- { { { $.1^212, $.1^152 }, { $.1^55, $.1^160 }, { $.1^199, $.1^138 }, { $.1^59, $.1^183 }, { $.1^36, $.1^127 }, { $.1^77, $.1^294 }, { $.1^194, $.1^329 }, { $.1^71, $.1^20 }, { $.1^231, 2 }, { $.1^170, $.1^270 }, { $.1^160, $.1^153 }, { $.1^112, $.1^312 }, { $.1^319, $.1^194 }, { $.1^47, $.1^314 }, { $.1^94, $.1^241 }, { $.1^66, 5 }, { $.1^282, $.1^175 }, { $.1^200, $.1^151 }, { $.1^333, $.1^283 }, { $.1^46, $.1^281 }, { $.1^13, $.1^281 }, { $.1, $.1^168 }, { $.1^157, $.1^316 }, { $.1^34, $.1^136 }, { $.1^240, $.1^42 }, { $.1^231, $.1^155 }, { $.1^112, $.1^270 }, { $.1^203, $.1^73 }, { $.1^314, $.1^30 }, { $.1^99, $.1^161 }, { $.1^325, $.1^262 }, { $.1^157, $.1^295 }, { $.1^146, $.1^260 }, { $.1^178, $.1^153 }, { $.1^61, $.1^118 }, { $.1^306, $.1^318 }, { $.1^272, $.1^130 }, { $.1^232, $.1^307 }, { $.1^105, $.1^261 }, { $.1^220, $.1^33 }, { $.1^40, $.1^317 }, { $.1^67, $.1^216 }, { $.1^242, $.1^232 }, { $.1^78, $.1^70 }, { $.1^310, $.1^315 }, { $.1^82, $.1^283 }, { $.1^189, $.1^223 }, { $.1^319, $.1^141 }, { $.1^90, $.1^294 }, { $.1^103, $.1^108 }, { $.1^302, $.1^39 }, { $.1^277, $.1^3 }, { $.1^89, $.1^203 }, { $.1^258, $.1^207 }, { $.1^55, $.1^41 }, { $.1^223, $.1^250 }, { $.1^6, $.1^160 }, { $.1^188, $.1^270 }, { $.1^11, $.1^75 }, { $.1^89, $.1^292 }, { $.1^154, $.1^109 }, { $.1^216, $.1^271 }, { $.1^341, $.1^292 }, { $.1^106, $.1^294 }, { $.1^81, $.1^226 }, { $.1^239, $.1^296 }, { $.1^260, $.1^272 }, { $.1^210, $.1^83 }, { 1, $.1^148 }, { $.1^198, $.1^339 }, { $.1^158, $.1^151 }, { $.1^145, $.1^238 }, { $.1^104, $.1^291 }, { $.1^210, $.1^159 }, { $.1^99, $.1^47 }, { $.1^112, $.1^328 }, { $.1^67, $.1^325 }, { $.1^253, $.1^112 }, { $.1^319, $.1^256 }, { $.1^72, $.1^263 }, { $.1^269, $.1^140 }, { $.1^143, $.1^310 }, { $.1^194, $.1^109 }, { 3, $.1^338 }, { $.1^105, $.1^274 }, { $.1^242, $.1^274 }, { $.1^47, $.1^30 }, { $.1^292, $.1^215 }, { $.1^178, $.1^318 }, { $.1^140, $.1^239 }, { $.1^326, $.1^184 }, { $.1^308, $.1^267 }, { $.1^145, $.1^328 }, { $.1^145, $.1^118 }, { $.1^222, $.1^137 }, { $.1^32, $.1^76 }, { $.1^81, $.1^94 }, { $.1^275, $.1^18 }, { $.1^178, $.1^225 }, { $.1^308, $.1^86 }, { $.1^135, $.1^159 }, { $.1^151, $.1^296 }, { $.1^302, $.1^117 }, { $.1^341, $.1^287 }, { $.1^264, $.1^299 }, { $.1^90, $.1^102 }, { $.1^165, $.1^172 }, { 3, $.1^4 }, { $.1^334, $.1^207 }, { $.1^309, $.1^212 }, { $.1^176, $.1^201 }, { $.1^148, 6 }, { 1, $.1^109 }, { $.1^17, $.1^118 }, { $.1^55, $.1^173 }, { $.1^204, $.1^307 }, { $.1^167, $.1^129 }, { $.1^270, $.1^116 }, { $.1^323, $.1^75 }, { $.1^35, $.1^86 }, { $.1^105, $.1^62 }, { $.1^138, $.1^120 }, { $.1^83, $.1^75 }, { $.1^320, $.1^19 }, { $.1^25, $.1^94 }, { $.1^34, $.1^340 }, { $.1^314, $.1^6 }, { $.1^210, $.1^314 }, { $.1^35, $.1^281 }, { $.1^44, $.1^163 }, { $.1^56, $.1^234 }, { $.1^187, $.1^68 }, { $.1^306, $.1^186 }, { $.1^70, $.1^174 }, { $.1^187, $.1^94 }, { $.1^156, $.1^336 }, { $.1^123, $.1^247 }, { $.1^190, $.1^153 }, { $.1^34, $.1^239 }, { $.1^207, $.1^142 }, { $.1^137, $.1^54 }, { $.1^277, $.1^130 }, { $.1^299, $.1^9 }, { $.1^11, $.1^295 }, { $.1^203, $.1^140 }, { $.1^298, $.1^64 }, { $.1^101, 4 }, { $.1^101, $.1^292 }, { $.1^245, $.1^63 }, { $.1^133, $.1^290 }, { $.1^44, $.1^63 }, { $.1^232, $.1^193 }, { $.1^288, $.1^267 }, { $.1^81, $.1^16 }, { $.1^22, $.1^315 }, { 1, $.1 }, { $.1^155, $.1^301 }, { $.1^255, $.1^185 }, { $.1^91, $.1^64 }, { $.1^115, $.1^98 }, { $.1^25, $.1^72 }, { $.1^245, $.1^116 }, { $.1^288, $.1^294 }, { $.1^160, $.1^97 }, { $.1^94, $.1^307 }, { $.1^110, $.1^309 }, { $.1^292, $.1^305 }, { $.1^24, $.1^51 }, { $.1^62, $.1^184 }, { $.1^93, $.1^116 }, { $.1^78, $.1^195 }, { $.1^281, $.1^140 }, { $.1^101, $.1^28 }, { $.1^62, $.1^86 }, { $.1^204, $.1^20 }, { $.1^258, $.1^120 }, { $.1^115, $.1^104 }, { $.1^234, $.1^16 }, { $.1^136, $.1^340 }, { $.1^143, $.1^206 }, { $.1^308, $.1^117 }, { $.1^105, $.1^241 }, { $.1^249, $.1^227 }, { $.1^24, $.1^146 }, { $.1^298, $.1^207 }, { $.1^91, $.1^329 }, { $.1^131, $.1^318 }, { $.1^242, $.1^311 }, { $.1^248, $.1^262 }, { $.1^53, $.1^296 }, { $.1^99, $.1^311 }, { $.1^55, $.1^299 }, { $.1^122, $.1^311 }, { $.1^67, $.1^97 }, { $.1^310, $.1^317 }, { $.1^322, $.1^293 }, { $.1^332, $.1^37 }, { $.1^97, $.1^120 }, { $.1^140, $.1^86 }, { $.1^330, $.1^7 }, { $.1^255, $.1^47 }, { $.1^117, $.1^273 }, { $.1^220, $.1^85 }, { $.1^5, $.1^164 }, { $.1^210, $.1^29 }, { $.1^242, $.1^286 }, { $.1^2, $.1^31 }, { $.1^305, $.1^340 }, { $.1^255, $.1^83 }, { $.1^223, $.1^70 }, { $.1^202, $.1^335 }, { $.1^177, $.1^235 }, { $.1^137, 4 }, { $.1^289, $.1^314 }, { $.1^136, $.1^15 }, { $.1^137, $.1^292 }, { $.1^258, $.1^97 }, { $.1^16, $.1^306 }, { $.1^173, $.1^142 }, { $.1^81, $.1^40 }, { $.1^199, $.1^210 }, { $.1^7, $.1^186 }, { $.1^135, $.1^291 }, { $.1^168, $.1^93 }, { $.1^188, $.1^307 }, { $.1^68, $.1^246 }, { $.1^308, $.1^165 }, { $.1^3, $.1^196 }, { $.1^290, $.1^43 }, { $.1^324, $.1^259 }, { $.1^325, $.1^40 }, { $.1^199, $.1^6 }, { $.1^170, $.1^163 }, { $.1^255, $.1^237 }, { $.1^266, $.1^246 }, { $.1^100, $.1^224 }, { $.1^277, $.1^172 }, { $.1^240, $.1^10 }, { $.1^332, $.1^295 }, { $.1^178, $.1^229 }, { $.1^265, $.1^147 }, { $.1^73, $.1^163 }, { $.1^25, $.1^60 }, { $.1^254, $.1^289 }, { $.1^79, $.1^38 }, { $.1^205, $.1^283 }, { 1, $.1^97 }, { $.1^291, $.1^150 }, { $.1^2, $.1^125 }, { $.1^79, $.1^71 }, { $.1^91, $.1^324 }, { $.1^189, $.1^7 }, { $.1^220, 6 }, { $.1^5, $.1^152 }, { $.1^12, $.1^32 }, { $.1^15, $.1^261 }, { $.1^3, $.1^4 }, { $.1^198, $.1^166 }, { $.1^266, $.1^245 }, { $.1^66, $.1^267 }, { $.1^155, $.1^25 }, { $.1^135, $.1^237 }, { $.1^265, $.1^124 }, { $.1^222, $.1^267 }, { $.1^242, $.1^270 }, { $.1^88, $.1^145 }, { $.1^180, $.1^104 }, { $.1^166, 5 }, { $.1^253, $.1^202 }, { $.1^286, $.1^81 }, { $.1^220, $.1^207 }, { $.1^270, $.1^307 }, { $.1^123, $.1^172 }, { $.1^6, $.1^76 }, { $.1^246, $.1^137 }, { $.1^224, $.1^106 }, { $.1^334, $.1^126 }, { $.1^37, $.1^18 }, { $.1^232, $.1^247 }, { $.1^326, $.1^328 }, { $.1^231, $.1^241 }, { $.1^203, $.1^175 }, { $.1^242, $.1^130 }, { $.1^189, $.1^289 }, { $.1, $.1^120 }, { $.1^94, $.1^239 }, { $.1^264, $.1^53 }, { $.1^45, $.1^268 }, { $.1^189, $.1^135 }, { $.1^270, $.1^197 }, { $.1^13, $.1^65 }, { $.1^78, $.1^306 }, { $.1^224, $.1^280 }, { $.1^290, $.1^184 }, { $.1^96, $.1^141 }, { $.1^255, $.1^135 }, { $.1^194, $.1^295 }, { $.1^247, $.1^73 }, { $.1^14, $.1^192 }, { $.1^56, $.1^260 }, { $.1^277, $.1^4 }, { $.1^33, $.1^248 }, { $.1^176, $.1^299 }, { $.1^281, $.1^282 }, { $.1^248, $.1^9 }, { $.1^235, $.1^205 }, { $.1^187, $.1^82 }, { $.1^69, $.1^27 }, { $.1^281, $.1^305 }, { $.1^322, $.1^269 }, { $.1^133, $.1^73 }, { $.1^315, $.1^52 }, { $.1^192, $.1^262 }, { $.1^319, $.1^67 }, { $.1^5, $.1^314 }, { $.1^89, $.1^95 }, { $.1^7, $.1^30 }, { $.1^100, $.1^315 }, { $.1^316, $.1^32 }, { $.1^277, $.1^190 }, { $.1^7, $.1^318 }, { 1, $.1^2 }, { $.1^204, $.1^260 }, { $.1^163, $.1^218 }, { $.1^226, $.1^239 }, { $.1^217, $.1^230 }, { $.1^239, $.1^328 }, { $.1^18, $.1^98 }, { $.1^44, $.1^321 }, { $.1^36, $.1^229 }, { $.1^286, $.1^323 }, { $.1^77, $.1^41 }, { $.1^210, $.1^89 }, { $.1^110, $.1^180 }, { $.1^195, $.1^306 }, { $.1^200, $.1^260 }, { $.1^37, $.1^318 }, { $.1^289, $.1^316 }, { $.1^341, $.1^91 }, { $.1 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:52:00 2004 Input: olav := function (q,r) R := GF(q,r); exponents_t := { q^i : i in [r-1..0 by -1] }; exponents_n := &+(exponents_t); polinomi_t:= PolynomialRing(R); polinomi_n:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exponents_t }; polinomi_n := x^exponents_n; puntsolav := { {a,b}:a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) }; return {puntsolav}; end function; olav(2,2); Output: Magma V2.10-6 Mon Mar 15 2004 12:51:57 on modular [Seed = 1179904837] ------------------------------------- { { { $.1 }, { 1, $.1 }, { 1, $.1^2 }, { $.1^2 }, { 1, 0 }, { 0 }, { $.1, $.1^2 } } } Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:54:52 2004 Input: olav := function (q,r) R := GF(q,r); exponents_t := { q^i : i in [r-1..0 by -1] }; exponents_n := &+(exponents_t); polinomi_t:= PolynomialRing(R); polinomi_n:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exponents_t }; polinomi_n := x^exponents_n; puntsolav := { {a,b}:a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) }; return {puntsolav}; end function; numpunts := olav(2,2); #{numpunts}; Output: Magma V2.10-6 Mon Mar 15 2004 12:54:49 on modular [Seed = 3165196651] ------------------------------------- 1 Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:55:09 2004 Input: olav := function (q,r) R := GF(q,r); exponents_t := { q^i : i in [r-1..0 by -1] }; exponents_n := &+(exponents_t); polinomi_t:= PolynomialRing(R); polinomi_n:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exponents_t }; polinomi_n := x^exponents_n; puntsolav := { {a,b}:a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) }; return {puntsolav}; end function; numpunts := olav(2,2); #numpunts; Output: Magma V2.10-6 Mon Mar 15 2004 12:55:06 on modular [Seed = 2980322421] ------------------------------------- 1 Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:55:49 2004 Input: olav := function (q,r) R := GF(q,r); exponents_t := { q^i : i in [r-1..0 by -1] }; exponents_n := &+(exponents_t); polinomi_t:= PolynomialRing(R); polinomi_n:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exponents_t }; polinomi_n := x^exponents_n; puntsolav := { {a,b}:a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) }; return {puntsolav}; end function; numpunts := olav(2,2); #Prune(numpunts); Output: Magma V2.10-6 Mon Mar 15 2004 12:55:46 on modular [Seed = 2813462971] ------------------------------------- >> #Prune(numpunts); ^ Runtime error in 'Prune': Bad argument types Argument types given: SetEnum[SetEnum] Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 12:57:55 2004 Input: olav := function (q,r) R := GF(q,r); exponents_t := { q^i : i in [r-1..0 by -1] }; exponents_n := &+(exponents_t); polinomi_t:= PolynomialRing(R); polinomi_n:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exponents_t }; polinomi_n := x^exponents_n; puntsolav := { {a,b}:a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) }; return {puntsolav}; end function; olav(2,2); Output: Magma V2.10-6 Mon Mar 15 2004 12:57:52 on modular [Seed = 2642948867] ------------------------------------- { { { $.1 }, { 1, $.1 }, { 1, $.1^2 }, { $.1^2 }, { 1, 0 }, { 0 }, { $.1, $.1^2 } } } Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 12:58:22 2004 Input: t:= func ; Z:=Integers(100); n73:=PolynomialRing(Z); lista:=t(7,3); lista; Output: Magma V2.10-6 Mon Mar 15 2004 12:58:19 on modular [Seed = 2458336279] ------------------------------------- >> t:= func > then coef:= [q^(r-1)]; ^ User error: bad syntax >> for i:=2 to r do coef:= coef cat [q^(r-i)]; end for; end if;>; ^ User error: Identifier 'r' has not been declared or assigned >> for i:=2 to r do coef:= coef cat [q^(r-i)]; end for; end if;>; ^ User error: bad syntax >> lista:=t(7,3); ^ User error: Identifier 't' has not been declared or assigned >> lista;; ^ User error: Identifier 'lista' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 13:00:00 2004 Input: t:= func ; Z:=Integers(100); n73:=PolynomialRing(Z); lista:=t(7,3); lista; Output: Magma V2.10-6 Mon Mar 15 2004 12:59:57 on modular [Seed = 2342397096] ------------------------------------- >> select coef:= [q^(r-1)]; ^ User error: bad syntax >> for i:=2 to r do coef:= coef cat [q^(r-i)]; end for; end if;>; ^ User error: Identifier 'r' has not been declared or assigned >> for i:=2 to r do coef:= coef cat [q^(r-i)]; end for; end if;>; ^ User error: bad syntax >> lista:=t(7,3); ^ User error: Identifier 't' has not been declared or assigned >> lista;; ^ User error: Identifier 'lista' has not been declared or assigned Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 13:01:02 2004 Input: olav := function (q,r) R := GF(q,r); exponents_t := { q^i : i in [r-1..0 by -1] }; exponents_n := &+(exponents_t); polinomi_t:= PolynomialRing(R); polinomi_n:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exponents_t }; polinomi_n := x^exponents_n; puntsolav := { {a,b}:a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) }; return {puntsolav}; end function; punts := olav(2,2); punts2 := Position(punts,1); print punts2; Output: Magma V2.10-6 Mon Mar 15 2004 13:00:59 on modular [Seed = 4142094739] ------------------------------------- >> punts2 := Position(punts,1); ^ Runtime error in 'Position': Bad argument types Argument types given: SetEnum[SetEnum], RngIntElt >> print punts2; ^ User error: Identifier 'punts2' has not been declared or assigned Total time: 3.039 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 13:01:54 2004 Input: olav := function (q,r) R := GF(q,r); exponents_t := { q^i : i in [r-1..0 by -1] }; exponents_n := &+(exponents_t); polinomi_t:= PolynomialRing(R); polinomi_n:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exponents_t }; polinomi_n := x^exponents_n; puntsolav := [ {a,b}:a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) ]; return {puntsolav}; end function; punts := olav(2,2); punts2 := Position(punts,1); print punts2; Output: Magma V2.10-6 Mon Mar 15 2004 13:01:51 on modular [Seed = 3720901228] ------------------------------------- >> punts2 := Position(punts,1); ^ Runtime error in 'Position': Bad argument types Argument types given: SetEnum[SeqEnum], RngIntElt >> print punts2; ^ User error: Identifier 'punts2' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 13:02:09 2004 Input: olav := function (q,r) R := GF(q,r); exponents_t := { q^i : i in [r-1..0 by -1] }; exponents_n := &+(exponents_t); polinomi_t:= PolynomialRing(R); polinomi_n:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exponents_t }; polinomi_n := x^exponents_n; puntsolav := [ {a,b}:a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) ]; return {puntsolav}; end function; punts := olav(2,2); print punts; punts2 := Position(punts,1); print punts2; Output: Magma V2.10-6 Mon Mar 15 2004 13:02:06 on modular [Seed = 3536289138] ------------------------------------- { [ { 1, 0 }, { 1, $.1 }, { $.1 }, { $.1, $.1^2 }, { 1, $.1^2 }, { $.1, $.1^2 }, { $.1^2 }, { 0 } ] } >> punts2 := Position(punts,1); ^ Runtime error in 'Position': Bad argument types Argument types given: SetEnum[SeqEnum], RngIntElt >> print punts2; ^ User error: Identifier 'punts2' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 13:02:39 2004 Input: t:= function (q,r) if (r gt 0) and IsInteger(r) and isPrime(q) then coef:= [q^(r-1)]; for i:=2 to r do coef:= coef cat [q^(r-i)]; end for; end if; return coef; end function; Z:=Integers(100); n73:=PolynomialRing(Z); lista:=t(7,3); lista; Output: Magma V2.10-6 Mon Mar 15 2004 13:02:36 on modular [Seed = 3420349513] ------------------------------------- >> t:= function (q,r) if (r gt 0) and IsInteger(r) and isPrime(q) ^ User error: Identifier 'IsInteger' has not been declared or assigned >> lista:=t(7,3); ^ User error: Identifier 't' has not been declared or assigned >> lista;; ^ User error: Identifier 'lista' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 13:02:52 2004 Input: t:= function (q,r) if (r gt 0) and isInteger(r) and isPrime(q) then coef:= [q^(r-1)]; for i:=2 to r do coef:= coef cat [q^(r-i)]; end for; end if; return coef; end function; Z:=Integers(100); n73:=PolynomialRing(Z); lista:=t(7,3); lista; Output: Magma V2.10-6 Mon Mar 15 2004 13:02:48 on modular [Seed = 3235213110] ------------------------------------- >> t:= function (q,r) if (r gt 0) and isInteger(r) and isPrime(q) ^ User error: Identifier 'isInteger' has not been declared or assigned >> lista:=t(7,3); ^ User error: Identifier 't' has not been declared or assigned >> lista;; ^ User error: Identifier 'lista' has not been declared or assigned Total time: 3.609 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 13:02:52 2004 Input: olav := function (q,r) R := GF(q,r); exponents_t := { q^i : i in [r-1..0 by -1] }; exponents_n := &+(exponents_t); polinomi_t:= PolynomialRing(R); polinomi_n:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exponents_t }; polinomi_n := x^exponents_n; puntsolav := [ {a,b}:a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) ]; return puntsolav; end function; punts := olav(2,2); print punts; punts2 := Position(punts,1); print punts2; Output: Magma V2.10-6 Mon Mar 15 2004 13:02:48 on modular [Seed = 1043042760] ------------------------------------- [ { 1, 0 }, { 1, $.1 }, { $.1 }, { $.1, $.1^2 }, { 1, $.1^2 }, { $.1, $.1^2 }, { $.1^2 }, { 0 } ] >> punts2 := Position(punts,1); ^ Runtime error in 'Position': Could not lift element into sequence >> print punts2; ^ User error: Identifier 'punts2' has not been declared or assigned Total time: 3.559 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 13:03:17 2004 Input: olav := function (q,r) R := GF(q,r); exponents_t := { q^i : i in [r-1..0 by -1] }; exponents_n := &+(exponents_t); polinomi_t:= PolynomialRing(R); polinomi_n:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exponents_t }; polinomi_n := x^exponents_n; puntsolav := { {a,b}:a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) }; return puntsolav; end function; punts := olav(2,2); print punts; #punts punts2 := Position(punts,1); print punts2; Output: Magma V2.10-6 Mon Mar 15 2004 13:03:15 on modular [Seed = 775651826] ------------------------------------- { { $.1 }, { 1, $.1 }, { 1, $.1^2 }, { $.1^2 }, { 1, 0 }, { 0 }, { $.1, $.1^2 } } >> punts2 := Position(punts,1); ^ User error: bad syntax >> print punts2; ^ User error: Identifier 'punts2' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 13:03:54 2004 Input: olav := function (q,r) R := GF(q,r); exponents_t := { q^i : i in [r-1..0 by -1] }; exponents_n := &+(exponents_t); polinomi_t:= PolynomialRing(R); polinomi_n:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exponents_t }; polinomi_n := x^exponents_n; puntsolav := { {a,b}:a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) }; return puntsolav; end function; punts := olav(2,2); #{punts} punts2 := Position(punts,1); print punts2; Output: Magma V2.10-6 Mon Mar 15 2004 13:03:51 on modular [Seed = 623940893] ------------------------------------- >> punts2 := Position(punts,1); ^ User error: bad syntax >> print punts2; ^ User error: Identifier 'punts2' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 13:04:29 2004 Input: olav := function (q,r) R := GF(q,r); exponents_t := { q^i : i in [r-1..0 by -1] }; exponents_n := &+(exponents_t); polinomi_t:= PolynomialRing(R); polinomi_n:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exponents_t }; polinomi_n := x^exponents_n; puntsolav := { {a,b}:a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) }; return puntsolav; end function; punts := olav(2,2); #{punts}; punts2 := Position(punts,1); print punts2; Output: Magma V2.10-6 Mon Mar 15 2004 13:04:26 on modular [Seed = 470395913] ------------------------------------- 1 >> punts2 := Position(punts,1); ^ Runtime error in 'Position': Bad argument types Argument types given: SetEnum[SetEnum], RngIntElt >> print punts2; ^ User error: Identifier 'punts2' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 13:04:46 2004 Input: olav := function (q,r) R := GF(q,r); exponents_t := { q^i : i in [r-1..0 by -1] }; exponents_n := &+(exponents_t); polinomi_t:= PolynomialRing(R); polinomi_n:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exponents_t }; polinomi_n := x^exponents_n; puntsolav := [ {a,b}:a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) ]; return puntsolav; end function; punts := olav(2,2); #{punts}; punts2 := Position(punts,1); print punts2; Output: Magma V2.10-6 Mon Mar 15 2004 13:04:43 on modular [Seed = 319202071] ------------------------------------- 1 >> punts2 := Position(punts,1); ^ Runtime error in 'Position': Could not lift element into sequence >> print punts2; ^ User error: Identifier 'punts2' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 13:05:11 2004 Input: olav := function (q,r) R := GF(q,r); exponents_t := { q^i : i in [r-1..0 by -1] }; exponents_n := &+(exponents_t); polinomi_t:= PolynomialRing(R); polinomi_n:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exponents_t }; polinomi_n := x^exponents_n; puntsolav := [ {a,b}:a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) ]; return puntsolav; end function; punts := olav(2,2); print punts; #{punts}; punts2 := Position(punts,1); print punts2; Output: Magma V2.10-6 Mon Mar 15 2004 13:05:08 on modular [Seed = 101955181] ------------------------------------- [ { 1, 0 }, { 1, $.1 }, { $.1 }, { $.1, $.1^2 }, { 1, $.1^2 }, { $.1, $.1^2 }, { $.1^2 }, { 0 } ] 1 >> punts2 := Position(punts,1); ^ Runtime error in 'Position': Could not lift element into sequence >> print punts2; ^ User error: Identifier 'punts2' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 13:05:32 2004 Input: olav := function (q,r) R := GF(q,r); exponents_t := { q^i : i in [r-1..0 by -1] }; exponents_n := &+(exponents_t); polinomi_t:= PolynomialRing(R); polinomi_n:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exponents_t }; polinomi_n := x^exponents_n; puntsolav := [ {a,b}:a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) ]; return puntsolav; end function; punts := olav(2,2); print punts; #{punts}; punts2 := Position(punts,0); print punts2; Output: Magma V2.10-6 Mon Mar 15 2004 13:05:30 on modular [Seed = 2087308329] ------------------------------------- [ { 1, 0 }, { 1, $.1 }, { $.1 }, { $.1, $.1^2 }, { 1, $.1^2 }, { $.1, $.1^2 }, { $.1^2 }, { 0 } ] 1 >> punts2 := Position(punts,0); ^ Runtime error in 'Position': Could not lift element into sequence >> print punts2; ^ User error: Identifier 'punts2' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 13:06:06 2004 Input: olav := function (q,r) R := GF(q,r); exponents_t := { q^i : i in [r-1..0 by -1] }; exponents_n := &+(exponents_t); polinomi_t:= PolynomialRing(R); polinomi_n:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exponents_t }; polinomi_n := x^exponents_n; puntsolav := [ {a,b}:a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) ]; return puntsolav; end function; punts := olav(2,2); print punts; #(punts); punts2 := Position(punts,0); print punts2; Output: Magma V2.10-6 Mon Mar 15 2004 13:06:03 on modular [Seed = 1919402694] ------------------------------------- [ { 1, 0 }, { 1, $.1 }, { $.1 }, { $.1, $.1^2 }, { 1, $.1^2 }, { $.1, $.1^2 }, { $.1^2 }, { 0 } ] 8 >> punts2 := Position(punts,0); ^ Runtime error in 'Position': Could not lift element into sequence >> print punts2; ^ User error: Identifier 'punts2' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 13:06:43 2004 Input: olav := function (q,r) R := GF(q,r); exponents_t := { q^i : i in [r-1..0 by -1] }; exponents_n := &+(exponents_t); polinomi_t:= PolynomialRing(R); polinomi_n:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exponents_t }; polinomi_n := x^exponents_n; puntsolav := [ {a,b}:a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) ]; return puntsolav; end function; punts := olav(7,3); print punts; #(punts); punts2 := Position(punts,0); print punts2; Output: Magma V2.10-6 Mon Mar 15 2004 13:06:38 on modular [Seed = 1769789945] ------------------------------------- [ { 1, $.1 }, { 1, $.1^7 }, { 1, $.1^13 }, { 1, $.1^19 }, { 1, $.1^25 }, { 1, $.1^31 }, { 1, $.1^37 }, { 1, $.1^43 }, { 1, $.1^49 }, { 1, $.1^55 }, { 1, $.1^61 }, { 1, $.1^67 }, { 1, $.1^73 }, { 1, $.1^79 }, { 1, $.1^85 }, { 1, $.1^91 }, { 1, $.1^97 }, { 1, $.1^103 }, { 1, $.1^109 }, { 1, $.1^115 }, { 1, $.1^121 }, { 1, $.1^127 }, { 1, $.1^133 }, { 1, $.1^139 }, { 1, $.1^145 }, { 1, $.1^151 }, { 1, $.1^157 }, { 1, $.1^163 }, { 1, $.1^169 }, { 1, $.1^175 }, { 1, $.1^181 }, { 1, $.1^187 }, { 1, $.1^193 }, { 1, $.1^199 }, { 1, $.1^205 }, { 1, $.1^211 }, { 1, $.1^217 }, { 1, $.1^223 }, { 1, $.1^229 }, { 1, $.1^235 }, { 1, $.1^241 }, { 1, $.1^247 }, { 1, $.1^253 }, { 1, $.1^259 }, { 1, $.1^265 }, { 1, $.1^271 }, { 1, $.1^277 }, { 1, $.1^283 }, { 1, $.1^289 }, { 1, $.1^295 }, { 1, $.1^301 }, { 1, $.1^307 }, { 1, $.1^313 }, { 1, $.1^319 }, { 1, $.1^325 }, { 1, $.1^331 }, { 1, $.1^337 }, { 1, $.1 }, { $.1, $.1^6 }, { $.1, $.1^12 }, { $.1, $.1^18 }, { $.1, $.1^24 }, { $.1, $.1^30 }, { $.1, $.1^36 }, { $.1, $.1^42 }, { $.1, $.1^48 }, { $.1, $.1^54 }, { $.1, $.1^60 }, { $.1^66, $.1 }, { $.1, $.1^72 }, { $.1, $.1^78 }, { $.1, $.1^84 }, { $.1, $.1^90 }, { $.1, $.1^96 }, { $.1, $.1^102 }, { $.1, $.1^108 }, { $.1, 2 }, { $.1, $.1^120 }, { $.1, $.1^126 }, { $.1^132, $.1 }, { $.1, $.1^138 }, { $.1, $.1^144 }, { $.1, $.1^150 }, { $.1, $.1^156 }, { $.1, $.1^162 }, { $.1, $.1^168 }, { $.1, $.1^174 }, { $.1, $.1^180 }, { $.1, $.1^186 }, { $.1, $.1^192 }, { $.1^198, $.1 }, { $.1, $.1^204 }, { $.1, $.1^210 }, { $.1, $.1^216 }, { $.1, $.1^222 }, { $.1, 4 }, { $.1, $.1^234 }, { $.1, $.1^240 }, { $.1, $.1^246 }, { $.1, $.1^252 }, { $.1, $.1^258 }, { $.1^264, $.1 }, { $.1, $.1^270 }, { $.1, $.1^276 }, { $.1, $.1^282 }, { $.1, $.1^288 }, { $.1, $.1^294 }, { $.1, $.1^300 }, { $.1, $.1^306 }, { $.1, $.1^312 }, { $.1, $.1^318 }, { $.1, $.1^324 }, { $.1^330, $.1 }, { $.1, $.1^336 }, { 1, $.1^2 }, { $.1^2, $.1^6 }, { $.1^12, $.1^2 }, { $.1^2, $.1^18 }, { $.1^2, $.1^24 }, { $.1^2, $.1^30 }, { $.1^2, $.1^36 }, { $.1^2, $.1^42 }, { $.1^2, $.1^48 }, { $.1^2, $.1^54 }, { $.1^2, $.1^60 }, { $.1^66, $.1^2 }, { $.1^2, $.1^72 }, { $.1^78, $.1^2 }, { $.1^2, $.1^84 }, { $.1^2, $.1^90 }, { $.1^2, $.1^96 }, { $.1^2, $.1^102 }, { $.1^2, $.1^108 }, { $.1^2, 2 }, { $.1^2, $.1^120 }, { $.1^2, $.1^126 }, { $.1^132, $.1^2 }, { $.1^2, $.1^138 }, { $.1^144, $.1^2 }, { $.1^2, $.1^150 }, { $.1^2, $.1^156 }, { $.1^2, $.1^162 }, { $.1^2, $.1^168 }, { $.1^2, $.1^174 }, { $.1^2, $.1^180 }, { $.1^2, $.1^186 }, { $.1^2, $.1^192 }, { $.1^198, $.1^2 }, { $.1^2, $.1^204 }, { $.1^210, $.1^2 }, { $.1^2, $.1^216 }, { $.1^2, $.1^222 }, { $.1^2, 4 }, { $.1^2, $.1^234 }, { $.1^2, $.1^240 }, { $.1^2, $.1^246 }, { $.1^2, $.1^252 }, { $.1^2, $.1^258 }, { $.1^264, $.1^2 }, { $.1^2, $.1^270 }, { $.1^276, $.1^2 }, { $.1^2, $.1^282 }, { $.1^2, $.1^288 }, { $.1^2, $.1^294 }, { $.1^2, $.1^300 }, { $.1^2, $.1^306 }, { $.1^2, $.1^312 }, { $.1^2, $.1^318 }, { $.1^2, $.1^324 }, { $.1^330, $.1^2 }, { $.1^2, $.1^336 }, { $.1, $.1^3 }, { $.1^3, $.1^7 }, { $.1^13, $.1^3 }, { $.1^3, $.1^19 }, { $.1^3, $.1^25 }, { $.1^3, $.1^31 }, { $.1^3, $.1^37 }, { $.1^3, $.1^43 }, { $.1^3, $.1^49 }, { $.1^55, $.1^3 }, { $.1^3, $.1^61 }, { $.1^67, $.1^3 }, { $.1^3, $.1^73 }, { $.1^79, $.1^3 }, { $.1^3, $.1^85 }, { $.1^3, $.1^91 }, { $.1^3, $.1^97 }, { $.1^3, $.1^103 }, { $.1^3, $.1^109 }, { $.1^3, $.1^115 }, { $.1^121, $.1^3 }, { $.1^3, $.1^127 }, { $.1^133, $.1^3 }, { $.1^3, $.1^139 }, { $.1^145, $.1^3 }, { $.1^3, $.1^151 }, { $.1^3, $.1^157 }, { $.1^3, $.1^163 }, { $.1^3, $.1^169 }, { $.1^3, $.1^175 }, { $.1^3, $.1^181 }, { $.1^187, $.1^3 }, { $.1^3, $.1^193 }, { $.1^199, $.1^3 }, { $.1^3, $.1^205 }, { $.1^211, $.1^3 }, { $.1^3, $.1^217 }, { $.1^3, $.1^223 }, { $.1^3, $.1^229 }, { $.1^3, $.1^235 }, { $.1^3, $.1^241 }, { $.1^3, $.1^247 }, { $.1^253, $.1^3 }, { $.1^3, $.1^259 }, { $.1^265, $.1^3 }, { $.1^3, $.1^271 }, { $.1^277, $.1^3 }, { $.1^3, $.1^283 }, { $.1^3, $.1^289 }, { $.1^3, $.1^295 }, { $.1^3, $.1^301 }, { $.1^3, $.1^307 }, { $.1^3, $.1^313 }, { $.1^319, $.1^3 }, { $.1^3, $.1^325 }, { $.1^331, $.1^3 }, { $.1^3, $.1^337 }, { $.1^3, $.1^4 }, { $.1^4, $.1^9 }, { $.1^4, $.1^15 }, { $.1^4, $.1^21 }, { $.1^4, $.1^27 }, { $.1^33, $.1^4 }, { $.1^4, $.1^39 }, { $.1^45, $.1^4 }, { $.1^4, $.1^51 }, { 3, $.1^4 }, { $.1^4, $.1^63 }, { $.1^69, $.1^4 }, { $.1^4, $.1^75 }, { $.1^4, $.1^81 }, { $.1^4, $.1^87 }, { $.1^4, $.1^93 }, { $.1^99, $.1^4 }, { $.1^4, $.1^105 }, { $.1^111, $.1^4 }, { $.1^4, $.1^117 }, { $.1^123, $.1^4 }, { $.1^4, $.1^129 }, { $.1^135, $.1^4 }, { $.1^4, $.1^141 }, { $.1^4, $.1^147 }, { $.1^4, $.1^153 }, { $.1^4, $.1^159 }, { $.1^165, $.1^4 }, { $.1^4, 6 }, { $.1^177, $.1^4 }, { $.1^4, $.1^183 }, { $.1^189, $.1^4 }, { $.1^4, $.1^195 }, { $.1^201, $.1^4 }, { $.1^4, $.1^207 }, { $.1^4, $.1^213 }, { $.1^4, $.1^219 }, { $.1^4, $.1^225 }, { $.1^231, $.1^4 }, { $.1^4, $.1^237 }, { $.1^243, $.1^4 }, { $.1^4, $.1^249 }, { $.1^255, $.1^4 }, { $.1^4, $.1^261 }, { $.1^267, $.1^4 }, { $.1^4, $.1^273 }, { $.1^4, $.1^279 }, { $.1^4, 5 }, { $.1^4, $.1^291 }, { $.1^297, $.1^4 }, { $.1^4, $.1^303 }, { $.1^309, $.1^4 }, { $.1^4, $.1^315 }, { $.1^321, $.1^4 }, { $.1^4, $.1^327 }, { $.1^333, $.1^4 }, { $.1^4, $.1^339 }, { $.1^2, $.1^5 }, { $.1^5, $.1^8 }, { $.1^14, $.1^5 }, { $.1^5, $.1^20 }, { $.1^26, $.1^5 }, { $.1^5, $.1^32 }, { $.1^5, $.1^38 }, { $.1^44, $.1^5 }, { $.1^5, $.1^50 }, { $.1^56, $.1^5 }, { $.1^5, $.1^62 }, { $.1^68, $.1^5 }, { $.1^5, $.1^74 }, { $.1^80, $.1^5 }, { $.1^5, $.1^86 }, { $.1^92, $.1^5 }, { $.1^5, $.1^98 }, { $.1^5, $.1^104 }, { $.1^110, $.1^5 }, { $.1^5, $.1^116 }, { $.1^122, $.1^5 }, { $.1^5, $.1^128 }, { $.1^134, $.1^5 }, { $.1^5, $.1^140 }, { $.1^146, $.1^5 }, { $.1^5, $.1^152 }, { $.1^158, $.1^5 }, { $.1^5, $.1^164 }, { $.1^5, $.1^170 }, { $.1^176, $.1^5 }, { $.1^5, $.1^182 }, { $.1^188, $.1^5 }, { $.1^5, $.1^194 }, { $.1^200, $.1^5 }, { $.1^5, $.1^206 }, { $.1^212, $.1^5 }, { $.1^5, $.1^218 }, { $.1^224, $.1^5 }, { $.1^5, $.1^230 }, { $.1^5, $.1^236 }, { $.1^242, $.1^5 }, { $.1^5, $.1^248 }, { $.1^254, $.1^5 }, { $.1^5, $.1^260 }, { $.1^266, $.1^5 }, { $.1^5, $.1^272 }, { $.1^278, $.1^5 }, { $.1^5, $.1^284 }, { $.1^290, $.1^5 }, { $.1^5, $.1^296 }, { $.1^5, $.1^302 }, { $.1^308, $.1^5 }, { $.1^5, $.1^314 }, { $.1^320, $.1^5 }, { $.1^5, $.1^326 }, { $.1^332, $.1^5 }, { $.1^5, $.1^338 }, { $.1^4, $.1^6 }, { $.1^6, $.1^10 }, { $.1^16, $.1^6 }, { $.1^22, $.1^6 }, { $.1^6, $.1^28 }, { $.1^34, $.1^6 }, { $.1^6, $.1^40 }, { $.1^46, $.1^6 }, { $.1^6, $.1^52 }, { $.1^58, $.1^6 }, { $.1^6, $.1^64 }, { $.1^70, $.1^6 }, { $.1^6, $.1^76 }, { $.1^82, $.1^6 }, { $.1^88, $.1^6 }, { $.1^6, $.1^94 }, { $.1^100, $.1^6 }, { $.1^6, $.1^106 }, { $.1^112, $.1^6 }, { $.1^6, $.1^118 }, { $.1^124, $.1^6 }, { $.1^6, $.1^130 }, { $.1^136, $.1^6 }, { $.1^6, $.1^142 }, { $.1^148, $.1^6 }, { $.1^154, $.1^6 }, { $.1^6, $.1^160 }, { $.1^166, $.1^6 }, { $.1^6, $.1^172 }, { $.1^178, $.1^6 }, { $.1^6, $.1^184 }, { $.1^190, $.1^6 }, { $.1^6, $.1^196 }, { $.1^202, $.1^6 }, { $.1^6, $.1^208 }, { $.1^214, $.1^6 }, { $.1^220, $.1^6 }, { $.1^6, $.1^226 }, { $.1^232, $.1^6 }, { $.1^6, $.1^238 }, { $.1^244, $.1^6 }, { $.1^6, $.1^250 }, { $.1^256, $.1^6 }, { $.1^6, $.1^262 }, { $.1^268, $.1^6 }, { $.1^6, $.1^274 }, { $.1^280, $.1^6 }, { $.1^286, $.1^6 }, { $.1^6, $.1^292 }, { $.1^298, $.1^6 }, { $.1^6, $.1^304 }, { $.1^310, $.1^6 }, { $.1^6, $.1^316 }, { $.1^322, $.1^6 }, { $.1^6, $.1^328 }, { $.1^334, $.1^6 }, { $.1^6, $.1^340 }, { 1, $.1^7 }, { $.1^6, $.1^7 }, { $.1^12, $.1^7 }, { $.1^7, $.1^18 }, { $.1^24, $.1^7 }, { $.1^7, $.1^30 }, { $.1^36, $.1^7 }, { $.1^7, $.1^42 }, { $.1^48, $.1^7 }, { $.1^7, $.1^54 }, { $.1^60, $.1^7 }, { $.1^66, $.1^7 }, { $.1^72, $.1^7 }, { $.1^78, $.1^7 }, { $.1^7, $.1^84 }, { $.1^90, $.1^7 }, { $.1^7, $.1^96 }, { $.1^102, $.1^7 }, { $.1^7, $.1^108 }, { 2, $.1^7 }, { $.1^7, $.1^120 }, { $.1^126, $.1^7 }, { $.1^132, $.1^7 }, { $.1^138, $.1^7 }, { $.1^144, $.1^7 }, { $.1^7, $.1^150 }, { $.1^156, $.1^7 }, { $.1^7, $.1^162 }, { $.1^168, $.1^7 }, { $.1^7, $.1^174 }, { $.1^180, $.1^7 }, { $.1^7, $.1^186 }, { $.1^192, $.1^7 }, { $.1^198, $.1^7 }, { $.1^204, $.1^7 }, { $.1^210, $.1^7 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 13:07:11 2004 Input: olav := function (q,r) R := GF(q,r); exponents_t := { q^i : i in [r-1..0 by -1] }; exponents_n := &+(exponents_t); polinomi_t:= PolynomialRing(R); polinomi_n:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exponents_t }; polinomi_n := x^exponents_n; puntsolav := [ {a,b}:a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) ]; return puntsolav; end function; punts := olav(7,3); #(punts); punts2 := Position(punts,0); print punts2; Output: Magma V2.10-6 Mon Mar 15 2004 13:07:07 on modular [Seed = 1618333844] ------------------------------------- 16807 >> punts2 := Position(punts,0); ^ Runtime error in 'Position': Could not lift element into sequence >> print punts2; ^ User error: Identifier 'punts2' has not been declared or assigned Total time: 4.269 seconds, Total memory usage: 6.11MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 13:07:45 2004 Input: t:= function (q,r) if (r gt 0) and isPrime(q) then coef:= [q^(r-1)]; for i:=2 to r do coef:= coef cat [q^(r-i)]; end for; end if; return coef; end function; Z:=Integers(100); n73:=PolynomialRing(Z); lista:=t(7,3); lista; Output: Magma V2.10-6 Mon Mar 15 2004 13:07:42 on modular [Seed = 1464002438] ------------------------------------- >> t:= function (q,r) if (r gt 0) and isPrime(q) ^ User error: Identifier 'isPrime' has not been declared or assigned >> lista:=t(7,3); ^ User error: Identifier 't' has not been declared or assigned >> lista;; ^ User error: Identifier 'lista' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 13:07:54 2004 Input: olav := function (q,r) R := GF(q,r); exponents_t := { q^i : i in [r-1..0 by -1] }; exponents_n := &+(exponents_t); polinomi_t:= PolynomialRing(R); polinomi_n:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exponents_t }; polinomi_n := x^exponents_n; puntsolav := [ {a,b}:a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) ]; return puntsolav; end function; punts := olav(3,3); #(punts); Output: Magma V2.10-6 Mon Mar 15 2004 13:07:51 on modular [Seed = 1314651782] ------------------------------------- 243 Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 13:08:04 2004 Input: t:= function (q,r) if ((r gt 0) and isPrime(q)) then coef:= [q^(r-1)]; for i:=2 to r do coef:= coef cat [q^(r-i)]; end for; end if; return coef; end function; Z:=Integers(100); n73:=PolynomialRing(Z); lista:=t(7,3); lista; Output: Magma V2.10-6 Mon Mar 15 2004 13:08:01 on modular [Seed = 1162933371] ------------------------------------- >> t:= function (q,r) if ((r gt 0) and isPrime(q)) ^ User error: Identifier 'isPrime' has not been declared or assigned >> lista:=t(7,3); ^ User error: Identifier 't' has not been declared or assigned >> lista;; ^ User error: Identifier 'lista' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 13:08:33 2004 Input: t:= function (q,r) if ((r gt 0) and IsPrime(q)) then coef:= [q^(r-1)]; for i:=2 to r do coef:= coef cat [q^(r-i)]; end for; end if; return coef; end function; Z:=Integers(100); n73:=PolynomialRing(Z); lista:=t(7,3); lista; Output: Magma V2.10-6 Mon Mar 15 2004 13:08:30 on modular [Seed = 3165195677] ------------------------------------- [ 49, 7, 1 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 13:09:16 2004 Input: t:= function (q,r) if ((r gt 0) and IsPrime(q)) then coef:= [q^(r-1)]; for i:=2 to r do coef:= coef cat [q^(r-i)]; end for; end if; return coef; end function; Z:=Integers(100); n73:=PolynomialRing(Z); lista:=t(7,3); t73:=P!lista; Output: Magma V2.10-6 Mon Mar 15 2004 13:09:13 on modular [Seed = 2997289924] ------------------------------------- >> t73:=P!lista;; ^ User error: Identifier 'P' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee13.uab.es. (158.109.66.13) Time: Mon Mar 15 13:09:34 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; puntsOlav:=func: a,b in GF(q,r)|Evaluate(polinomit(q,r),a) eq Evaluate(polinomin(q,r),b)}>; exemples:=function(q,r) print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r)); end function; exemples(2,3); exemples(3,3); exemples(5,3); exemples(3,4); exemples(2,4); Output: Magma V2.10-6 Mon Mar 15 2004 13:09:28 on modular [Seed = 2847676622] ------------------------------------- [ 49, 7, 1 ] q^(2*r-1) és igual a: 32 El cardinal dels punts Olav en aquest exemple és: 32 q^(2*r-1) és igual a: 243 El cardinal dels punts Olav en aquest exemple és: 243 q^(2*r-1) és igual a: 3125 El cardinal dels punts Olav en aquest exemple és: 3125 q^(2*r-1) és igual a: 2187 El cardinal dels punts Olav en aquest exemple és: 2187 q^(2*r-1) és igual a: 128 El cardinal dels punts Olav en aquest exemple és: 128 Total time: 5.779 seconds, Total memory usage: 2.13MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 13:09:35 2004 Input: t:= function (q,r) if ((r gt 0) and IsPrime(q)) then coef:= [q^(r-1)]; for i:=2 to r do coef:= coef cat [q^(r-i)]; end for; end if; return coef; end function; Z:=Integers(100); n73:=PolynomialRing(Z); lista:=t(7,3); t73:=n73!lista; Output: Magma V2.10-6 Mon Mar 15 2004 13:09:32 on modular [Seed = 2796754885] ------------------------------------- Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Mon Mar 15 13:09:56 2004 Input: K := GF(7,3); P := PolynomialRing(K); n73 := x^&+(xp); print(n73); Output: Magma V2.10-6 Mon Mar 15 2004 13:09:53 on modular [Seed = 2541889241] ------------------------------------- >> n73 := x^&+(xp); ^ User error: Identifier 'xp' has not been declared or assigned >> print(n73);; ^ User error: Identifier 'n73' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 13:10:06 2004 Input: t:= function (q,r) if ((r gt 0) and IsPrime(q)) then coef:= [q^(r-1)]; for i:=2 to r do coef:= coef cat [q^(r-i)]; end for; end if; return coef; end function; Z:=Integers(100); PT:=PolynomialRing(Z); lista:=t(7,3); t73:=PT!lista; Output: Magma V2.10-6 Mon Mar 15 2004 13:10:03 on modular [Seed = 2274506435] ------------------------------------- Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 13:10:15 2004 Input: t:= function (q,r) if ((r gt 0) and IsPrime(q)) then coef:= [q^(r-1)]; for i:=2 to r do coef:= coef cat [q^(r-i)]; end for; end if; return coef; end function; Z:=Integers(100); PT:=PolynomialRing(Z); lista:=t(7,3); t73:=PT!lista; t73; Output: Magma V2.10-6 Mon Mar 15 2004 13:10:12 on modular [Seed = 4276834117] ------------------------------------- x^2 + 7*x + 49 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Mon Mar 15 13:10:25 2004 Input: K := GF(7,3); P := PolynomialRing(K); xp := [7^i : i in [2..0 by -1]]; n73 := x^&+(xp); print(n73); Output: Magma V2.10-6 Mon Mar 15 2004 13:10:22 on modular [Seed = 4108404037] ------------------------------------- x^57 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Mon Mar 15 13:11:10 2004 Input: K := GF(7,3); P := PolynomialRing(K); xp := [7^i : i in [2..0 by -1]]; t73 := &+[x^i : i in xp]; print(t73); Output: Magma V2.10-6 Mon Mar 15 2004 13:11:07 on modular [Seed = 3959315055] ------------------------------------- x^49 + x^7 + x Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 13:11:52 2004 Input: olav := function (q,r) R := GF(q,r); exponents_t := { q^i : i in [r-1..0 by -1] }; exponents_n := &+(exponents_t); polinomi_t:= PolynomialRing(R); polinomi_n:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exponents_t }; polinomi_n := x^exponents_n; puntsolav := [ {a,b}:a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) ]; return puntsolav; end function; punts2 := olav(2,2); print punts2; #{ {a,b}:a,b in punts2 | a in GF(2) and b in GF(2) }; Output: Magma V2.10-6 Mon Mar 15 2004 13:11:49 on modular [Seed = 3807859512] ------------------------------------- [ { 1, 0 }, { 1, $.1 }, { $.1 }, { $.1, $.1^2 }, { 1, $.1^2 }, { $.1, $.1^2 }, { $.1^2 }, { 0 } ] >> #{ {a,b}:a,b in punts2 | a in GF(2) and b in GF(2) }; ^ Runtime error in 'in': Bad argument types Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee13.uab.es. (158.109.66.13) Time: Mon Mar 15 13:12:29 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; puntsOlav:=func: a,b in GF(q,r)|Evaluate(polinomit(q,r),a) eq Evaluate(polinomin(q,r),b)}>; exemples:=function(q,r) print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r)); end function; print "Exemple amb q=2 i r=3" exemples(2,3); print "Exemple amb q=3 i r=3" exemples(3,3); print "Exemple amb q=5 i r=3" exemples(5,3); print "Exemple amb q=3 i r=4" exemples(3,4); print "Exemple amb q=2 i r=4" exemples(2,4); Output: Magma V2.10-6 Mon Mar 15 2004 13:12:26 on modular [Seed = 3637340909] ------------------------------------- [ 49, 7, 1 ] >> exemples(2,3); ^ User error: bad syntax >> exemples(3,3); ^ User error: bad syntax >> exemples(5,3); ^ User error: bad syntax >> exemples(3,4); ^ User error: bad syntax >> exemples(2,4); ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 13:13:06 2004 Input: olav := function (q,r) R := GF(q,r); exponents_t := { q^i : i in [r-1..0 by -1] }; exponents_n := &+(exponents_t); polinomi_t:= PolynomialRing(R); polinomi_n:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exponents_t }; polinomi_n := x^exponents_n; puntsolav := [ {a,b}:a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) ]; return puntsolav; end function; punts2 := olav(2,2); print punts2; #{ {a,b}:a,b in punts2 | Include(GF(2),a) and Include(GF(2),b) }; Output: Magma V2.10-6 Mon Mar 15 2004 13:13:03 on modular [Seed = 3487202783] ------------------------------------- [ { 1, 0 }, { 1, $.1 }, { $.1 }, { $.1, $.1^2 }, { 1, $.1^2 }, { $.1, $.1^2 }, { $.1^2 }, { 0 } ] >> #{ {a,b}:a,b in punts2 | Include(GF(2),a) and Include(GF(2),b) }; ^ Runtime error in 'Include': Bad argument types Argument types given: FldFin, SetEnum[FldFinElt] Total time: 2.859 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee13.uab.es. (158.109.66.13) Time: Mon Mar 15 13:13:24 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; puntsOlav:=func: a,b in GF(q,r)|Evaluate(polinomit(q,r),a) eq Evaluate(polinomin(q,r),b)}>; exemples:=function(q,r) print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r)); end function; print "Exemple amb q=2 i r=3"; exemples(2,3); print "Exemple amb q=3 i r=3"; exemples(3,3); print "Exemple amb q=5 i r=3"; exemples(5,3); print "Exemple amb q=3 i r=4"; exemples(3,4); print "Exemple amb q=2 i r=4"; exemples(2,4); Output: Magma V2.10-6 Mon Mar 15 2004 13:13:18 on modular [Seed = 3335746759] ------------------------------------- [ 49, 7, 1 ] Exemple amb q=2 i r=3 q^(2*r-1) és igual a: 32 El cardinal dels punts Olav en aquest exemple és: 32 Exemple amb q=3 i r=3 q^(2*r-1) és igual a: 243 El cardinal dels punts Olav en aquest exemple és: 243 Exemple amb q=5 i r=3 q^(2*r-1) és igual a: 3125 El cardinal dels punts Olav en aquest exemple és: 3125 Exemple amb q=3 i r=4 q^(2*r-1) és igual a: 2187 El cardinal dels punts Olav en aquest exemple és: 2187 Exemple amb q=2 i r=4 q^(2*r-1) és igual a: 128 El cardinal dels punts Olav en aquest exemple és: 128 Total time: 5.770 seconds, Total memory usage: 2.13MB ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Mon Mar 15 13:13:40 2004 Input: K := GF(7,3); P := PolynomialRing(K); xp := [7^i : i in [2..0 by -1]]; n73 := x^&+(xp); t73 := &+[x^i : i in xp]; polav := [ : a,b in K | Evaluate(n73,a) eq Evaluate(t73,b)]; print(polav); Output: Magma V2.10-6 Mon Mar 15 2004 13:13:36 on modular [Seed = 1870323070] ------------------------------------- [ <1, K.1>, <1, K.1^2>, <1, K.1^7>, <1, K.1^10>, <1, K.1^11>, <1, K.1^14>, <1, K.1^16>, <1, K.1^25>, <1, K.1^37>, <1, K.1^49>, <1, K.1^66>, <1, K.1^70>, <1, K.1^77>, <1, K.1^87>, <1, K.1^90>, <1, K.1^97>, <1, K.1^98>, <1, K.1^100>, <1, K.1^103>, <1, K.1^112>, <1, K.1^120>, <1, K.1^131>, <1, K.1^132>, <1, K.1^137>, <1, K.1^146>, <1, K.1^148>, <1, K.1^156>, <1, K.1^159>, <1, K.1^175>, <1, K.1^195>, <1, K.1^197>, <1, K.1^199>, <1, K.1^215>, <1, K.1^233>, <1, K.1^240>, <1, K.1^259>, <1, K.1^263>, <1, K.1^267>, <1, K.1^275>, <1, 5>, <1, K.1^288>, <1, K.1^306>, <1, K.1^307>, <1, K.1^312>, <1, K.1^314>, <1, K.1^321>, <1, K.1^337>, <1, K.1^338>, <1, K.1^339>, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , :=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; puntsOlav:=func: a,b in GF(q,r)|Evaluate(polinomit(q,r),a) eq Evaluate(polinomin(q,r),b)}>; exemples:=function(q,r) print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r)); end function; print "Exemple amb q=2 i r=3"; exemples(2,3); print "Exemple amb q=3 i r=3"; exemples(3,3); print "nExemple amb q=5 i r=3"; exemples(5,3); print "Exemple amb q=3 i r=4"; exemples(3,4); print "Exemple amb q=2 i r=4"; exemples(2,4); Output: Magma V2.10-6 Mon Mar 15 2004 13:14:00 on modular [Seed = 1986249823] ------------------------------------- [ 49, 7, 1 ] Exemple amb q=2 i r=3 q^(2*r-1) és igual a: 32 El cardinal dels punts Olav en aquest exemple és: 32 Exemple amb q=3 i r=3 q^(2*r-1) és igual a: 243 El cardinal dels punts Olav en aquest exemple és: 243 nExemple amb q=5 i r=3 q^(2*r-1) és igual a: 3125 El cardinal dels punts Olav en aquest exemple és: 3125 Exemple amb q=3 i r=4 q^(2*r-1) és igual a: 2187 El cardinal dels punts Olav en aquest exemple és: 2187 Exemple amb q=2 i r=4 q^(2*r-1) és igual a: 128 El cardinal dels punts Olav en aquest exemple és: 128 Total time: 5.859 seconds, Total memory usage: 2.13MB ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Mon Mar 15 13:14:24 2004 Input: K := GF(7,3); P := PolynomialRing(K); xp := [7^i : i in [2..0 by -1]]; n73 := x^&+(xp); t73 := &+[x^i : i in xp]; polav := [ : a,b in K | Evaluate(n73,a) eq Evaluate(t73,b)]; #(polav); Output: Magma V2.10-6 Mon Mar 15 2004 13:14:20 on modular [Seed = 18133820] ------------------------------------- 16807 Total time: 4.119 seconds, Total memory usage: 2.73MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 13:16:23 2004 Input: olav := function (q,r) R := GF(q,r); exponents_t := { q^i : i in [r-1..0 by -1] }; exponents_n := &+(exponents_t); polinomi_t:= PolynomialRing(R); polinomi_n:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exponents_t }; polinomi_n := x^exponents_n; puntsolav := [ {a,b}:a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) ]; return puntsolav; end function; punts2 := olav(2,2); print punts2; ab := { {a,b}:a,b in punts2 }; print ab; /*{ {a,b}:a,b in punts2 | Include(GF(2),a) and Include(GF(2),b) };*/ Output: Magma V2.10-6 Mon Mar 15 2004 13:16:20 on modular [Seed = 319201702] ------------------------------------- [ { 1, 0 }, { 1, $.1 }, { $.1 }, { $.1, $.1^2 }, { 1, $.1^2 }, { $.1, $.1^2 }, { $.1^2 }, { 0 } ] { { { 1, $.1 }, { 1, 0 } }, { { $.1 } }, { { 1, $.1^2 }, { $.1, $.1^2 } }, { { 1, 0 } }, { { 1, $.1^2 }, { 0 } }, { { 1, $.1 }, { 0 } }, { { 1, $.1^2 }, { 1, 0 } }, { { $.1, $.1^2 } }, { { 1, $.1 }, { $.1^2 } }, { { 0 }, { $.1, $.1^2 } }, { { $.1^2 }, { 0 } }, { { $.1 }, { 0 } }, { { 1, $.1 }, { $.1, $.1^2 } }, { { 1, 0 }, { 0 } }, { { $.1^2 } }, { { 1, 0 }, { $.1, $.1^2 } }, { { $.1 }, { 1, 0 } }, { { $.1 }, { 1, $.1 } }, { { $.1 }, { 1, $.1^2 } }, { { $.1^2 }, { $.1, $.1^2 } }, { { 1, $.1^2 } }, { { $.1^2 }, { 1, 0 } }, { { $.1 }, { $.1^2 } }, { { 1, $.1 } }, { { 1, $.1^2 }, { $.1^2 } }, { { $.1 }, { $.1, $.1^2 } }, { { 1, $.1 }, { 1, $.1^2 } }, { { 0 } } } Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee13.uab.es. (158.109.66.13) Time: Mon Mar 15 13:16:32 2004 Input: polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; puntsOlav:=func: a,b in GF(q,r)|Evaluate(polinomit(q,r),a) eq Evaluate(polinomin(q,r),b)}>; exemples:=function(q,r) print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r)); end function; print "Exemple amb q=2 i r=3"; exemples(2,3); print "Exemple amb q=3 i r=3";print""; exemples(3,3); print "Exemple amb q=5 i r=3"; exemples(5,3); print "Exemple amb q=3 i r=4"; exemples(3,4); print "Exemple amb q=2 i r=4"; exemples(2,4); Output: Magma V2.10-6 Mon Mar 15 2004 13:16:29 on modular [Seed = 437233830] ------------------------------------- [ 49, 7, 1 ] >> return x^sum; ^ User error: Identifier 'x' has not been declared or assigned >> pol:=pol+x^newlist[i]; ^ User error: Identifier 'x' has not been declared or assigned >> puntsOlav:=func: a,b in GF(q,r)|Evaluate(polinomit(q,r),a) eq Ev ^ User error: Identifier 'polinomit' has not been declared or assigned >> return #(puntsOlav(q,r)); ^ User error: Identifier 'puntsOlav' has not been declared or assigned Exemple amb q=2 i r=3 >> exemples(2,3); ^ User error: Identifier 'exemples' has not been declared or assigned Exemple amb q=3 i r=3 >> exemples(3,3); ^ User error: Identifier 'exemples' has not been declared or assigned Exemple amb q=5 i r=3 >> exemples(5,3); ^ User error: Identifier 'exemples' has not been declared or assigned Exemple amb q=3 i r=4 >> exemples(3,4); ^ User error: Identifier 'exemples' has not been declared or assigned Exemple amb q=2 i r=4 >> exemples(2,4);; ^ User error: Identifier 'exemples' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee13.uab.es. (158.109.66.13) Time: Mon Mar 15 13:17:19 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; puntsOlav:=func: a,b in GF(q,r)|Evaluate(polinomit(q,r),a) eq Evaluate(polinomin(q,r),b)}>; exemples:=function(q,r) print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r)); end function; print "Exemple amb q=2 i r=3"; exemples(2,3); print "Exemple amb q=3 i r=3";print""; exemples(3,3); print "Exemple amb q=5 i r=3"; exemples(5,3); print "Exemple amb q=3 i r=4"; exemples(3,4); print "Exemple amb q=2 i r=4"; exemples(2,4); Output: Magma V2.10-6 Mon Mar 15 2004 13:17:13 on modular [Seed = 623941197] ------------------------------------- [ 49, 7, 1 ] Exemple amb q=2 i r=3 q^(2*r-1) és igual a: 32 El cardinal dels punts Olav en aquest exemple és: 32 Exemple amb q=3 i r=3 q^(2*r-1) és igual a: 243 El cardinal dels punts Olav en aquest exemple és: 243 Exemple amb q=5 i r=3 q^(2*r-1) és igual a: 3125 El cardinal dels punts Olav en aquest exemple és: 3125 Exemple amb q=3 i r=4 q^(2*r-1) és igual a: 2187 El cardinal dels punts Olav en aquest exemple és: 2187 Exemple amb q=2 i r=4 q^(2*r-1) és igual a: 128 El cardinal dels punts Olav en aquest exemple és: 128 Total time: 5.749 seconds, Total memory usage: 2.13MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 13:17:43 2004 Input: olav := function (q,r) R := GF(q,r); exponents_t := { q^i : i in [r-1..0 by -1] }; exponents_n := &+(exponents_t); polinomi_t:= PolynomialRing(R); polinomi_n:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exponents_t }; polinomi_n := x^exponents_n; puntsolav := [ {a,b}:a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) ]; return puntsolav; end function; punts2 := olav(2,2); print punts2[0]; /*{ {a,b}:a,b in punts2 | Include(GF(2),a) and Include(GF(2),b) };*/ Output: Magma V2.10-6 Mon Mar 15 2004 13:17:40 on modular [Seed = 741973801] ------------------------------------- >> print punts2[0]; ^ Runtime error in '[]': Sequence element 0 not defined Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 13:17:56 2004 Input: olav := function (q,r) R := GF(q,r); exponents_t := { q^i : i in [r-1..0 by -1] }; exponents_n := &+(exponents_t); polinomi_t:= PolynomialRing(R); polinomi_n:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exponents_t }; polinomi_n := x^exponents_n; puntsolav := [ {a,b}:a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) ]; return puntsolav; end function; punts2 := olav(2,2); print punts2[1]; /*{ {a,b}:a,b in punts2 | Include(GF(2),a) and Include(GF(2),b) };*/ Output: Magma V2.10-6 Mon Mar 15 2004 13:17:53 on modular [Seed = 925008935] ------------------------------------- { 1, 0 } Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Mon Mar 15 13:18:21 2004 Input: xptfun := fun; print(xptfun(7,3)); Output: Magma V2.10-6 Mon Mar 15 2004 13:18:17 on modular [Seed = 3235214312] ------------------------------------- >> xptfun := fun; ^ User error: bad syntax >> print(xptfun(7,3)); ^ User error: Identifier 'xptfun' has not been declared or assigned Total time: 3.649 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee13.uab.es. (158.109.66.13) Time: Mon Mar 15 13:18:24 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; puntsOlav:=func: a,b in GF(q,r)|Evaluate(polinomit(q,r),a) eq Evaluate(polinomin(q,r),b)}>; exemples:=function(q,r) print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r)); end function; print"";print "Exemple amb q=2 i r=3"; exemples(2,3); print"";print "Exemple amb q=3 i r=3"; exemples(3,3); print"";print "Exemple amb q=5 i r=3"; exemples(5,3); print"";print "Exemple amb q=3 i r=4"; exemples(3,4); print"";print "Exemple amb q=2 i r=4"; exemples(2,4); Output: Magma V2.10-6 Mon Mar 15 2004 13:18:17 on modular [Seed = 3268899306] ------------------------------------- [ 49, 7, 1 ] Exemple amb q=2 i r=3 q^(2*r-1) és igual a: 32 El cardinal dels punts Olav en aquest exemple és: 32 Exemple amb q=3 i r=3 q^(2*r-1) és igual a: 243 El cardinal dels punts Olav en aquest exemple és: 243 Exemple amb q=5 i r=3 q^(2*r-1) és igual a: 3125 El cardinal dels punts Olav en aquest exemple és: 3125 Exemple amb q=3 i r=4 q^(2*r-1) és igual a: 2187 El cardinal dels punts Olav en aquest exemple és: 2187 Exemple amb q=2 i r=4 q^(2*r-1) és igual a: 128 El cardinal dels punts Olav en aquest exemple és: 128 Total time: 6.509 seconds, Total memory usage: 2.13MB ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Mon Mar 15 13:18:35 2004 Input: xptfun := func; print(xptfun(7,3)); Output: Magma V2.10-6 Mon Mar 15 2004 13:18:32 on modular [Seed = 3552993514] ------------------------------------- >> xptfun := func; ^ User error: bad syntax >> print(xptfun(7,3)); ^ User error: Identifier 'xptfun' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 13:18:41 2004 Input: olav := function (q,r) R := GF(q,r); exponents_t := { q^i : i in [r-1..0 by -1] }; exponents_n := &+(exponents_t); polinomi_t:= PolynomialRing(R); polinomi_n:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exponents_t }; polinomi_n := x^exponents_n; puntsolav := [ {a,b}:a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) ]; return puntsolav; end function; punts2 := olav(2,2); print punts2[2]; /*{ {a,b}:a,b in punts2 | Include(GF(2),a) and Include(GF(2),b) };*/ Output: Magma V2.10-6 Mon Mar 15 2004 13:18:38 on modular [Seed = 3671026149] ------------------------------------- { 1, $.1 } Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Mon Mar 15 13:18:53 2004 Input: xptfun := func; print(xptfun(7,3)); Output: Magma V2.10-6 Mon Mar 15 2004 13:18:50 on modular [Seed = 3857733166] ------------------------------------- [ 1, 7, 49 ] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 13:19:15 2004 Input: t:= function (q,r) if ((r gt 0) and IsPrime(q)) then coef:= [q^(r-1)]; for i:=2 to r do coef:= coef cat [q^(r-i)]; end for; end if; return coef; end function; Z:=Integers(100); PT:=PolynomialRing(Z); lista:=t(7,3); for i:=1 to #(lista) do t73:=t73 + PT![1]^lista[i]; end for; t73; n:= (q,r) t(q,r) Output: Magma V2.10-6 Mon Mar 15 2004 13:19:12 on modular [Seed = 3975765773] ------------------------------------- >> for i:=1 to #(lista) do t73:=t73 + PT![1]^lista[i]; end for; ^ User error: Identifier 't73' has not been declared or assigned >> t73; ^ User error: Identifier 't73' has not been declared or assigned >> n:= (q,r) t(q,r); ^ User error: bad syntax Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Mon Mar 15 13:19:32 2004 Input: xptfun := func; print(xptfun(7,3)); Output: Magma V2.10-6 Mon Mar 15 2004 13:19:29 on modular [Seed = 4158800903] ------------------------------------- [ 49, 7, 1 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 13:19:37 2004 Input: olav := function (q,r) R := GF(q,r); exponents_t := { q^i : i in [r-1..0 by -1] }; exponents_n := &+(exponents_t); polinomi_t:= PolynomialRing(R); polinomi_n:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exponents_t }; polinomi_n := x^exponents_n; puntsolav := [ {a,b}:a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) ]; return puntsolav; end function; punts2 := olav(2,2); print punts2[2]; { {a,b}:a,b in punts2[1] | Include(GF(2),a) and Include(GF(2),b) }; Output: Magma V2.10-6 Mon Mar 15 2004 13:19:34 on modular [Seed = 4276833545] ------------------------------------- { 1, $.1 } >> { {a,b}:a,b in punts2[1] | Include(GF(2),a) and Include(GF(2),b) }; ^ Runtime error in 'Include': Bad argument types Argument types given: FldFin, FldFinElt Total time: 3.129 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 13:19:39 2004 Input: t:= function (q,r) if ((r gt 0) and IsPrime(q)) then coef:= [q^(r-1)]; for i:=2 to r do coef:= coef cat [q^(r-i)]; end for; end if; return coef; end function; Z:=Integers(100); PT:=PolynomialRing(Z); lista:=t(7,3); t73:=0; for i:=1 to #(lista) do t73:=t73 + PT![1]^lista[i]; end for; t73; n:= (q,r) t(q,r) Output: Magma V2.10-6 Mon Mar 15 2004 13:19:36 on modular [Seed = 2207658106] ------------------------------------- 3 >> n:= (q,r) t(q,r); ^ User error: bad syntax Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 13:19:59 2004 Input: t:= function (q,r) if ((r gt 0) and IsPrime(q)) then coef:= [q^(r-1)]; for i:=2 to r do coef:= coef cat [q^(r-i)]; end for; end if; return coef; end function; Z:=Integers(100); PT:=PolynomialRing(Z); lista:=t(7,3); t73:=0; for i:=1 to #(lista) do t73:=t73 + PT![1]^lista[i]; end for; t73; Output: Magma V2.10-6 Mon Mar 15 2004 13:19:56 on modular [Seed = 2424644381] ------------------------------------- 3 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Mon Mar 15 13:20:09 2004 Input: xptfun := func; print({23,12,4,23}); Output: Magma V2.10-6 Mon Mar 15 2004 13:20:06 on modular [Seed = 2696221495] ------------------------------------- { 4, 12, 23 } Total time: 3.259 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 13:20:11 2004 Input: t:= function (q,r) if ((r gt 0) and IsPrime(q)) then coef:= [q^(r-1)]; for i:=2 to r do coef:= coef cat [q^(r-i)]; end for; end if; return coef; end function; Z:=Integers(100); PT:=PolynomialRing(Z); lista:=t(7,3); lista; t73:=0; for i:=1 to #(lista) do t73:=t73 + PT![1]^lista[i]; end for; t73; Output: Magma V2.10-6 Mon Mar 15 2004 13:20:07 on modular [Seed = 2779780668] ------------------------------------- [ 49, 7, 1 ] 3 Total time: 3.309 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Mon Mar 15 13:20:26 2004 Input: xptfun := func; print([23,12,4,23]); Output: Magma V2.10-6 Mon Mar 15 2004 13:20:23 on modular [Seed = 3047163411] ------------------------------------- [ 23, 12, 4, 23 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 13:20:35 2004 Input: olav := function (q,r) R := GF(q,r); exponents_t := { q^i : i in [r-1..0 by -1] }; exponents_n := &+(exponents_t); polinomi_t:= PolynomialRing(R); polinomi_n:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exponents_t }; polinomi_n := x^exponents_n; puntsolav := [ {a,b}:a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) ]; return puntsolav; end function; punts2 := olav(2,2); print punts2[2]; gf2 := { m:m in GF(2) }; { {a,b}:a,b in punts2[1] | Include(gf2,a) and Include(gf2,b) }; Output: Magma V2.10-6 Mon Mar 15 2004 13:20:31 on modular [Seed = 3165196045] ------------------------------------- { 1, $.1 } >> { {a,b}:a,b in punts2[1] | Include(gf2,a) and Include(gf2,b) }; ^ Runtime error: Expected a logical for the 'and' operator Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 13:20:38 2004 Input: t:= function (q,r) if ((r gt 0) and IsPrime(q)) then coef:= [q^(r-1)]; for i:=2 to r do coef:= coef cat [q^(r-i)]; end for; end if; return coef; end function; Z:=Integers(100); PT:=PolynomialRing(Z); lista:=t(7,3); lista; t73:=0; PT![1]^lista[1]; for i:=1 to #(lista) do t73:=t73 + PT![1]^lista[i]; end for; t73; Output: Magma V2.10-6 Mon Mar 15 2004 13:20:35 on modular [Seed = 1196618998] ------------------------------------- [ 49, 7, 1 ] 1 3 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 13:20:52 2004 Input: t:= function (q,r) if ((r gt 0) and IsPrime(q)) then coef:= [q^(r-1)]; for i:=2 to r do coef:= coef cat [q^(r-i)]; end for; end if; return coef; end function; Z:=Integers(100); PT:=PolynomialRing(Z); lista:=t(7,3); lista; t73:=0; PT![2]^lista[1]; for i:=1 to #(lista) do t73:=t73 + PT![1]^lista[i]; end for; t73; Output: Magma V2.10-6 Mon Mar 15 2004 13:20:49 on modular [Seed = 1297676558] ------------------------------------- [ 49, 7, 1 ] 12 3 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 13:21:09 2004 Input: olav := function (q,r) R := GF(q,r); exponents_t := { q^i : i in [r-1..0 by -1] }; exponents_n := &+(exponents_t); polinomi_t:= PolynomialRing(R); polinomi_n:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exponents_t }; polinomi_n := x^exponents_n; puntsolav := [ {a,b}:a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) ]; return puntsolav; end function; punts2 := olav(2,2); print punts2[2]; gf2 := { m:m in GF(2) }; { {a,b}:a,b in punts2[1] | Include(gf2,a) eq Include(gf2,b) }; Output: Magma V2.10-6 Mon Mar 15 2004 13:21:06 on modular [Seed = 1515187722] ------------------------------------- { 1, $.1 } { { 1 }, { 1, 0 }, { 0 } } Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 13:21:18 2004 Input: t:= function (q,r) if ((r gt 0) and IsPrime(q)) then coef:= [q^(r-1)]; for i:=2 to r do coef:= coef cat [q^(r-i)]; end for; end if; return coef; end function; Z:=Integers(100); PT:=PolynomialRing(Z); lista:=t(7,3); lista; t73:=0; PT![2]^lista[0,1]; for i:=1 to #(lista) do t73:=t73 + PT![1]^lista[i]; end for; t73; Output: Magma V2.10-6 Mon Mar 15 2004 13:21:15 on modular [Seed = 1668732730] ------------------------------------- [ 49, 7, 1 ] >> PT![2]^lista[0,1]; ^ Runtime error in '[]': Sequence element 0 not defined 3 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Mon Mar 15 13:21:42 2004 Input: xptfun := func; print(xptfun(8,4)); Output: Magma V2.10-6 Mon Mar 15 2004 13:21:39 on modular [Seed = 1753078809] ------------------------------------- [ 512, 64, 8, 1 ] Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 13:21:55 2004 Input: t:= function (q,r) if ((r gt 0) and IsPrime(q)) then coef:= [q^(r-1)]; for i:=2 to r do coef:= coef cat [q^(r-i)]; end for; end if; return coef; end function; Z:=Integers(100); PT:=PolynomialRing(Z); lista:=t(7,3); lista; t73:=0; PT![0,1]^lista[1]; for i:=1 to #(lista) do t73:=t73 + PT![0,1]^lista[i]; end for; t73; Output: Magma V2.10-6 Mon Mar 15 2004 13:21:52 on modular [Seed = 1986249332] ------------------------------------- [ 49, 7, 1 ] x^49 x^49 + x^7 + x Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 13:22:03 2004 Input: olav := function (q,r) R := GF(q,r); exponents_t := { q^i : i in [r-1..0 by -1] }; exponents_n := &+(exponents_t); polinomi_t:= PolynomialRing(R); polinomi_n:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exponents_t }; polinomi_n := x^exponents_n; puntsolav := [ {a,b}:a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) ]; return puntsolav; end function; punts2 := olav(2,2); print punts2[2]; gf2 := { m:m in GF(2) }; { {a,b}:a,b in punts2 | Include(gf2,a) eq Include(gf2,b) }; Output: Magma V2.10-6 Mon Mar 15 2004 13:22:00 on modular [Seed = 2137705333] ------------------------------------- { 1, $.1 } >> { {a,b}:a,b in punts2 | Include(gf2,a) eq Include(gf2,b) }; ^ Runtime error in 'Include': Illegal coercion Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 13:22:34 2004 Input: olav := function (q,r) R := GF(q,r); exponents_t := { q^i : i in [r-1..0 by -1] }; exponents_n := &+(exponents_t); polinomi_t:= PolynomialRing(R); polinomi_n:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exponents_t }; polinomi_n := x^exponents_n; puntsolav := [ {a,b}:a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) ]; return puntsolav; end function; punts2 := olav(2,2); print punts2[2]; gf2 := { m:m in GF(2) }; { {a,b}:a,b in punts2[4] | Include(gf2,a) eq Include(gf2,b) }; Output: Magma V2.10-6 Mon Mar 15 2004 13:22:31 on modular [Seed = 68268065] ------------------------------------- { 1, $.1 } >> { {a,b}:a,b in punts2[4] | Include(gf2,a) eq Include(gf2,b) }; ^ Runtime error in 'Include': No embedding known into LHS field Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee13.uab.es. (158.109.66.13) Time: Mon Mar 15 13:22:53 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; puntsOlav:=func: a,b in GF(q,r)|Evaluate(polinomit(q,r),a) eq Evaluate(polinomin(q,r),b)}>; exemples:=function(q,r) print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r)); end function; print"";print "Exemple amb q=2 i r=3"; exemples(2,3); print"";print "Exemple amb q=3 i r=3"; exemples(3,3); print"";print "Exemple amb q=5 i r=3"; exemples(5,3); print"";print "Exemple amb q=3 i r=4"; exemples(3,4); print"";print "Exemple amb q=2 i r=4"; exemples(2,4); puntsOlav2:=func: a,b in GF(q,r) a in GF(q), b in GF(q)|Evaluate(polinomit(q,r),a) eq Evaluate(polinomin(q,r),b)}> Output: Magma V2.10-6 Mon Mar 15 2004 13:22:47 on modular [Seed = 219724088] ------------------------------------- [ 49, 7, 1 ] Exemple amb q=2 i r=3 q^(2*r-1) és igual a: 32 El cardinal dels punts Olav en aquest exemple és: 32 Exemple amb q=3 i r=3 q^(2*r-1) és igual a: 243 El cardinal dels punts Olav en aquest exemple és: 243 Exemple amb q=5 i r=3 q^(2*r-1) és igual a: 3125 El cardinal dels punts Olav en aquest exemple és: 3125 Exemple amb q=3 i r=4 q^(2*r-1) és igual a: 2187 El cardinal dels punts Olav en aquest exemple és: 2187 Exemple amb q=2 i r=4 q^(2*r-1) és igual a: 128 El cardinal dels punts Olav en aquest exemple és: 128 >> puntsOlav2:=func: a,b in GF(q,r) a in GF(q), b in GF(q)|Evaluate ^ User error: bad syntax Total time: 5.819 seconds, Total memory usage: 2.13MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 13:23:08 2004 Input: olav := function (q,r) R := GF(q,r); exponents_t := { q^i : i in [r-1..0 by -1] }; exponents_n := &+(exponents_t); polinomi_t:= PolynomialRing(R); polinomi_n:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exponents_t }; polinomi_n := x^exponents_n; puntsolav := [ {a,b}:a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) ]; return puntsolav; end function; punts2 := olav(2,2); print punts2[2]; gf2 := { m:m in GF(2) }; { {a,b}:a,b in punts2[1] | Include(gf2,a) eq Include(gf2,b) }; Output: Magma V2.10-6 Mon Mar 15 2004 13:23:05 on modular [Seed = 437235409] ------------------------------------- { 1, $.1 } { { 1 }, { 1, 0 }, { 0 } } Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 13:23:30 2004 Input: olav := function (q,r) R := GF(q,r); exponents_t := { q^i : i in [r-1..0 by -1] }; exponents_n := &+(exponents_t); polinomi_t:= PolynomialRing(R); polinomi_n:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exponents_t }; polinomi_n := x^exponents_n; puntsolav := [ {a,b}:a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) ]; return puntsolav; end function; punts2 := olav(2,2); print punts2[1]; gf2 := { m:m in GF(2) }; { {a,b}:a,b in punts2[1] | Include(gf2,a) eq Include(gf2,b) }; Output: Magma V2.10-6 Mon Mar 15 2004 13:23:27 on modular [Seed = 640914171] ------------------------------------- { 1, 0 } { { 1 }, { 1, 0 }, { 0 } } Total time: 3.399 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee13.uab.es. (158.109.66.13) Time: Mon Mar 15 13:23:31 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; puntsOlav:=func: a,b in GF(q,r)|Evaluate(polinomit(q,r),a) eq Evaluate(polinomin(q,r),b)}>; exemples:=function(q,r) print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r)); end function; print"";print "Exemple amb q=2 i r=3"; exemples(2,3); print"";print "Exemple amb q=3 i r=3"; exemples(3,3); print"";print "Exemple amb q=5 i r=3"; exemples(5,3); print"";print "Exemple amb q=3 i r=4"; exemples(3,4); print"";print "Exemple amb q=2 i r=4"; exemples(2,4); puntsOlav2:=func: a,b in GF(q,r), a,b in GF(q)|Evaluate(polinomit(q,r),a) eq Evaluate(polinomin(q,r),b)}> Output: Magma V2.10-6 Mon Mar 15 2004 13:23:25 on modular [Seed = 590780412] ------------------------------------- [ 49, 7, 1 ] Exemple amb q=2 i r=3 q^(2*r-1) és igual a: 32 El cardinal dels punts Olav en aquest exemple és: 32 Exemple amb q=3 i r=3 q^(2*r-1) és igual a: 243 El cardinal dels punts Olav en aquest exemple és: 243 Exemple amb q=5 i r=3 q^(2*r-1) és igual a: 3125 El cardinal dels punts Olav en aquest exemple és: 3125 Exemple amb q=3 i r=4 q^(2*r-1) és igual a: 2187 El cardinal dels punts Olav en aquest exemple és: 2187 Exemple amb q=2 i r=4 q^(2*r-1) és igual a: 128 El cardinal dels punts Olav en aquest exemple és: 128 Total time: 6.239 seconds, Total memory usage: 2.13MB ************** MAGMA ***************** Host aula-a-siee13.uab.es. (158.109.66.13) Time: Mon Mar 15 13:23:55 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; puntsOlav:=func: a,b in GF(q,r)|Evaluate(polinomit(q,r),a) eq Evaluate(polinomin(q,r),b)}>; exemples:=function(q,r) print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r)); end function; print"";print "Exemple amb q=2 i r=3"; exemples(2,3); print"";print "Exemple amb q=3 i r=3"; exemples(3,3); print"";print "Exemple amb q=5 i r=3"; exemples(5,3); print"";print "Exemple amb q=3 i r=4"; exemples(3,4); print"";print "Exemple amb q=2 i r=4"; exemples(2,4); puntsOlav2:=func: a,b in GF(q,r), a,b in GF(q)|Evaluate(polinomit(q,r),a) eq Evaluate(polinomin(q,r),b)}> puntsOlav(2,3); Output: Magma V2.10-6 Mon Mar 15 2004 13:23:50 on modular [Seed = 824477125] ------------------------------------- [ 49, 7, 1 ] Exemple amb q=2 i r=3 q^(2*r-1) és igual a: 32 El cardinal dels punts Olav en aquest exemple és: 32 Exemple amb q=3 i r=3 q^(2*r-1) és igual a: 243 El cardinal dels punts Olav en aquest exemple és: 243 Exemple amb q=5 i r=3 q^(2*r-1) és igual a: 3125 El cardinal dels punts Olav en aquest exemple és: 3125 Exemple amb q=3 i r=4 q^(2*r-1) és igual a: 2187 El cardinal dels punts Olav en aquest exemple és: 2187 Exemple amb q=2 i r=4 q^(2*r-1) és igual a: 128 El cardinal dels punts Olav en aquest exemple és: 128 >> puntsOlav(2,3);; ^ User error: bad syntax Total time: 5.750 seconds, Total memory usage: 2.13MB ************** MAGMA ***************** Host aula-a-siee13.uab.es. (158.109.66.13) Time: Mon Mar 15 13:24:50 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; puntsOlav:=func: a,b in GF(q,r)|Evaluate(polinomit(q,r),a) eq Evaluate(polinomin(q,r),b)}>; exemples:=function(q,r) print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r)); end function; print"";print "Exemple amb q=2 i r=3"; exemples(2,3); print"";print "Exemple amb q=3 i r=3"; exemples(3,3); print"";print "Exemple amb q=5 i r=3"; exemples(5,3); print"";print "Exemple amb q=3 i r=4"; exemples(3,4); print"";print "Exemple amb q=2 i r=4"; exemples(2,4); puntsOlav2:=func: a,b in GF(q,r), a,b in GF(q)|Evaluate(polinomit(q,r),a) eq Evaluate(polinomin(q,r),b)}>; puntsOlav(2,3); puntsOlav2(2,3); Output: Magma V2.10-6 Mon Mar 15 2004 13:24:44 on modular [Seed = 1043040912] ------------------------------------- [ 49, 7, 1 ] Exemple amb q=2 i r=3 q^(2*r-1) és igual a: 32 El cardinal dels punts Olav en aquest exemple és: 32 Exemple amb q=3 i r=3 q^(2*r-1) és igual a: 243 El cardinal dels punts Olav en aquest exemple és: 243 Exemple amb q=5 i r=3 q^(2*r-1) és igual a: 3125 El cardinal dels punts Olav en aquest exemple és: 3125 Exemple amb q=3 i r=4 q^(2*r-1) és igual a: 2187 El cardinal dels punts Olav en aquest exemple és: 2187 Exemple amb q=2 i r=4 q^(2*r-1) és igual a: 128 El cardinal dels punts Olav en aquest exemple és: 128 { <1, $.1^4>, <$.1^3, $.1^3>, <$.1^3, $.1^6>, <$.1^6, 1>, <$.1^6, $.1^2>, <1, $.1>, <$.1^5, 1>, <$.1^6, $.1^3>, <$.1^3, $.1^2>, <1, $.1^3>, <1, $.1^2>, <$.1, 0>, <$.1^3, $.1^5>, <0, 0>, <$.1^5, $.1^5>, <$.1^6, $.1^4>, <$.1^3, 1>, <1, $.1^5>, <$.1^5, $.1>, <$.1^5, $.1^4>, <$.1^6, $.1>, <$.1^3, $.1^4>, <1, 1>, <$.1^5, $.1^2>, <$.1^5, $.1^6>, <$.1^6, $.1^5>, <$.1^3, $.1>, <1, $.1^6>, <$.1^4, 0>, <$.1^5, $.1^3>, <$.1^2, 0>, <$.1^6, $.1^6> } { <1, $.1^4>, <$.1^3, $.1^3>, <$.1^3, $.1^6>, <$.1^6, 1>, <$.1^6, $.1^2>, <1, $.1>, <$.1^5, 1>, <$.1^6, $.1^3>, <$.1^3, $.1^2>, <1, $.1^3>, <1, $.1^2>, <$.1, 0>, <$.1^3, $.1^5>, <0, 0>, <$.1^5, $.1^5>, <$.1^6, $.1^4>, <$.1^3, 1>, <1, $.1^5>, <$.1^5, $.1>, <$.1^5, $.1^4>, <$.1^6, $.1>, <$.1^3, $.1^4>, <1, 1>, <$.1^5, $.1^2>, <$.1^5, $.1^6>, <$.1^6, $.1^5>, <$.1^3, $.1>, <1, $.1^6>, <$.1^4, 0>, <$.1^5, $.1^3>, <$.1^2, 0>, <$.1^6, $.1^6> } Total time: 5.919 seconds, Total memory usage: 2.13MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 13:28:44 2004 Input: coeft:= function (q,r) if ((r gt 0) and IsPrime(q)) then coef:= [q^(r-1)]; for i:=2 to r do coef:= coef cat [q^(r-i)]; end for; end if; return coef; end function; Z:=Integers(100); PT:=PolynomialRing(Z); t := function (q,r) lista:=coeft(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + PT![0,1]^lista[i]; end for; return poly; end function; t(7,3); Output: Magma V2.10-6 Mon Mar 15 2004 13:28:41 on modular [Seed = 3487201876] ------------------------------------- x^49 + x^7 + x Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 13:29:00 2004 Input: coeft:= function (q,r) if ((r gt 0) and IsPrime(q)) then coef:= [q^(r-1)]; for i:=2 to r do coef:= coef cat [q^(r-i)]; end for; end if; return coef; end function; Z:=Integers(100); PT:=PolynomialRing(Z); t := function (q,r) lista:=coeft(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + PT![0,1]^lista[i]; end for; return poly; end function; t(7,3); t(5,4); Output: Magma V2.10-6 Mon Mar 15 2004 13:28:57 on modular [Seed = 3586154622] ------------------------------------- x^49 + x^7 + x x^125 + x^25 + x^5 + x Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Mon Mar 15 13:29:18 2004 Input: Pn := function(q,r) K := GF(q,r); P := PolynomialRing(K); xp := [q^i : i in [r-1..0 by -1]]; pol := x^&+(xp); return(pol); end function; Pt := function(q,r) K := GF(q,r); P := PolynomialRing(K); xp := [q^i : i in [r-1..0 by -1]]; pol := &+[x^i : i in xp]; return(pol); end function; print(Pn(8,4)); print(Pt(8,4)); Output: Magma V2.10-6 Mon Mar 15 2004 13:29:15 on modular [Seed = 3807860571] ------------------------------------- [
:3]( q: 8, r: 4 ) >> K := GF(q,r); ^ Runtime error in 'GF': Argument 1 (8) should be prime [
:10]( q: 8, r: 4 ) >> K := GF(q,r); ^ Runtime error in 'GF': Argument 1 (8) should be prime Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Mon Mar 15 13:30:13 2004 Input: Pn := function(q,r) K := GF(q,r); P := PolynomialRing(K); xp := [q^i : i in [r-1..0 by -1]]; pol := x^&+(xp); return(pol); end function; Pt := function(q,r) K := GF(q,r); P := PolynomialRing(K); xp := [q^i : i in [r-1..0 by -1]]; pol := &+[x^i : i in xp]; return(pol); end function; print(Pn(11,4)); print(Pt(11,4)); Output: Magma V2.10-6 Mon Mar 15 2004 13:30:10 on modular [Seed = 4041557632] ------------------------------------- x^1464 x^1331 + x^121 + x^11 + x Total time: 2.899 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host aula-a-siee05.uab.es. (158.109.66.5) Time: Mon Mar 15 13:30:36 2004 Input: olav := function (q,r) R := GF(q,r); exponents_t := { q^i : i in [r-1..0 by -1] }; exponents_n := &+(exponents_t); polinomi_t:= PolynomialRing(R); polinomi_n:= PolynomialRing(R); polinomi_t := &+{ x^i : i in exponents_t }; polinomi_n := x^exponents_n; puntsolav := [ {a,b}:a,b in R | Evaluate(polinomi_n,b) eq Evaluate(polinomi_t,a) ]; return puntsolav; end function; punts2 := olav(2,2); #(punts2); print punts2[1]; gf2 := { m:m in GF(2) }; { {a,b}:a,b in punts2[1] | Include(gf2,a) eq Include(gf2,b) }; Output: Magma V2.10-6 Mon Mar 15 2004 13:30:33 on modular [Seed = 4276832501] ------------------------------------- 8 { 1, 0 } { { 1 }, { 1, 0 }, { 0 } } Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee13.uab.es. (158.109.66.13) Time: Mon Mar 15 13:31:00 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; puntsOlav:=func: a,b in GF(q,r)|Evaluate(polinomit(q,r),a) eq Evaluate(polinomin(q,r),b)}>; exemples:=function(q,r) print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r)); end function; print"";print "Exemple amb q=2 i r=3"; exemples(2,3); print"";print "Exemple amb q=3 i r=3"; exemples(3,3); print"";print "Exemple amb q=5 i r=3"; exemples(5,3); print"";print "Exemple amb q=3 i r=4"; exemples(3,4); print"";print "Exemple amb q=2 i r=4"; exemples(2,4); puntsOlav2:=function(q,r) po2:=[po:po in puntsOlav(q,r)|po[1] in GF(q), po[2] in GF(q)]; return #(po2); end function; puntsOlav2(2,3); Output: Magma V2.10-6 Mon Mar 15 2004 13:30:54 on modular [Seed = 2274505115] ------------------------------------- [ 49, 7, 1 ] Exemple amb q=2 i r=3 q^(2*r-1) és igual a: 32 El cardinal dels punts Olav en aquest exemple és: 32 Exemple amb q=3 i r=3 q^(2*r-1) és igual a: 243 El cardinal dels punts Olav en aquest exemple és: 243 Exemple amb q=5 i r=3 q^(2*r-1) és igual a: 3125 El cardinal dels punts Olav en aquest exemple és: 3125 Exemple amb q=3 i r=4 q^(2*r-1) és igual a: 2187 El cardinal dels punts Olav en aquest exemple és: 2187 Exemple amb q=2 i r=4 q^(2*r-1) és igual a: 128 El cardinal dels punts Olav en aquest exemple és: 128 >> po2:=[po:po in puntsOlav(q,r)|po[1] in GF(q), po[2] in GF(q)]; ^ User error: bad syntax >> return #(po2); ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> puntsOlav2(2,3);; ^ User error: Identifier 'puntsOlav2' has not been declared or assigned Total time: 5.879 seconds, Total memory usage: 2.13MB ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Mon Mar 15 13:31:32 2004 Input: xptfun := func; print(xptfun(11,4)); Output: Magma V2.10-6 Mon Mar 15 2004 13:31:30 on modular [Seed = 2358852172] ------------------------------------- [ 1331, 121, 11, 1 ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 13:31:48 2004 Input: coef:= function (q,r) if ((r gt 0) and IsPrime(q)) then co:= [q^(r-1)]; for i:=2 to r do co:= co cat [q^(r-i)]; end for; end if; return co; end function; Z:=Integers(100); PT:=PolynomialRing(Z); t := function (q,r) lista:=coef(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + PT![0,1]^lista[i]; end for; return poly; end function; t(7,3); n := function (q,r) lista:=coef(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=PT![0,1]^exp; return poly; end function; n(7,3); Output: Magma V2.10-6 Mon Mar 15 2004 13:31:45 on modular [Seed = 2508202822] ------------------------------------- x^49 + x^7 + x x^57 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 13:32:03 2004 Input: coef:= function (q,r) if ((r gt 0) and IsPrime(q)) then co:= [q^(r-1)]; for i:=2 to r do co:= co cat [q^(r-i)]; end for; end if; return co; end function; Z:=Integers(100); PT:=PolynomialRing(Z); t := function (q,r) lista:=coef(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + PT![0,1]^lista[i]; end for; return poly; end function; t(7,3); n := function (q,r) lista:=coef(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=PT![0,1]^exp; return poly; end function; n(7,3); n(5,4); Output: Magma V2.10-6 Mon Mar 15 2004 13:32:01 on modular [Seed = 2729907265] ------------------------------------- x^49 + x^7 + x x^57 x^156 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee13.uab.es. (158.109.66.13) Time: Mon Mar 15 13:32:29 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; puntsOlav:=func: a,b in GF(q,r)|Evaluate(polinomit(q,r),a) eq Evaluate(polinomin(q,r),b)}>; exemples:=function(q,r) print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r)); end function; print"";print "Exemple amb q=2 i r=3"; exemples(2,3); print"";print "Exemple amb q=3 i r=3"; exemples(3,3); print"";print "Exemple amb q=5 i r=3"; exemples(5,3); print"";print "Exemple amb q=3 i r=4"; exemples(3,4); print"";print "Exemple amb q=2 i r=4"; exemples(2,4); puntsOlav2:=function(q,r) po2:=[po:po in puntsOlav(q,r)|po[1] in GF(q) and po[2] in GF(q)]; return #(po2); end function; puntsOlav2(2,3); Output: Magma V2.10-6 Mon Mar 15 2004 13:32:24 on modular [Seed = 2830966354] ------------------------------------- [ 49, 7, 1 ] Exemple amb q=2 i r=3 q^(2*r-1) és igual a: 32 El cardinal dels punts Olav en aquest exemple és: 32 Exemple amb q=3 i r=3 q^(2*r-1) és igual a: 243 El cardinal dels punts Olav en aquest exemple és: 243 Exemple amb q=5 i r=3 q^(2*r-1) és igual a: 3125 El cardinal dels punts Olav en aquest exemple és: 3125 Exemple amb q=3 i r=4 q^(2*r-1) és igual a: 2187 El cardinal dels punts Olav en aquest exemple és: 2187 Exemple amb q=2 i r=4 q^(2*r-1) és igual a: 128 El cardinal dels punts Olav en aquest exemple és: 128 2 Total time: 5.869 seconds, Total memory usage: 2.13MB ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Mon Mar 15 13:33:54 2004 Input: Olav := func : a, b in GF(q,r) | Evaluate(Pn(q,r),a) eq Evaluate(Pt(q,r),b)]>; #(Olav(7,3)); Output: Magma V2.10-6 Mon Mar 15 2004 13:33:51 on modular [Seed = 3047162616] ------------------------------------- >> Olav := func : a, b in GF(q,r) | Evaluate(Pn(q,r),a) eq Evalua ^ User error: Identifier 'Pn' has not been declared or assigned >> #(Olav(7,3));; ^ User error: Identifier 'Olav' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Mon Mar 15 13:35:13 2004 Input: Pn := function(q,r) K := GF(q,r); P := PolynomialRing(K); xp := [q^i : i in [r-1..0 by -1]]; pol := x^&+(xp); return(pol); end function; Pt := function(q,r) K := GF(q,r); P := PolynomialRing(K); xp := [q^i : i in [r-1..0 by -1]]; pol := &+[x^i : i in xp]; return(pol); end function; Olav := func : a, b in GF(q,r) | Evaluate(Pn(q,r),a) eq Evaluate(Pt(q,r),b)]>; #(Olav(7,3)); Output: Magma V2.10-6 Mon Mar 15 2004 13:34:55 on modular [Seed = 1129772111] ------------------------------------- 16807 Total time: 18.199 seconds, Total memory usage: 2.73MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 13:37:55 2004 Input: coef:= function (q,r) if ((r gt 0) and IsPrime(q)) then co:= [q^(r-1)]; for i:=2 to r do co:= co cat [q^(r-i)]; end for; end if; return co; end function; Z:=Integers(100); PT:=PolynomialRing(Z); t := function (q,r) lista:=coef(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + PT![0,1]^lista[i]; end for; return poly; end function; t(7,3); n := function (q,r) lista:=coef(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=PT![0,1]^exp; return poly; end function; n(7,3); punts_olav:=function (q,r) Field:=GF(q,r); punts:=[: a,b in Field | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; return punts; end function; punts_olav(7,3); Output: Magma V2.10-6 Mon Mar 15 2004 13:37:52 on modular [Seed = 1280963599] ------------------------------------- x^49 + x^7 + x x^57 >> punts:=[: a,b in Field | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; ^ User error: bad syntax >> return punts; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> punts_olav(7,3);; ^ User error: Identifier 'punts_olav' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee13.uab.es. (158.109.66.13) Time: Mon Mar 15 13:38:13 2004 Input: R:=Integers(); P:=PolynomialRing(R); polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; puntsOlav:=func: a,b in GF(q,r)|Evaluate(polinomit(q,r),a) eq Evaluate(polinomin(q,r),b)}>; exemples:=function(q,r) print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r)); end function; print"";print "Exemple amb q=2 i r=3"; exemples(2,3); print"";print "Exemple amb q=3 i r=3"; exemples(3,3); print"";print "Exemple amb q=5 i r=3"; exemples(5,3); print"";print "Exemple amb q=3 i r=4"; exemples(3,4); print"";print "Exemple amb q=2 i r=4"; exemples(2,4); puntsOlav2:=function(q,r) po2:=[po:po in puntsOlav(q,r)|po[1] in GF(q) and po[2] in GF(q)]; return #(po2); end function; print"";print "Exemple amb q=2 i r=3"; puntsOlav2(2,3); print"";print "Exemple amb q=3 i r=3"; puntsOlav2(3,3); print"";print "Exemple amb q=5 i r=3"; puntsOlav2(5,3); print"";print "Exemple amb q=3 i r=4"; puntsOlav2(3,4); print"";print "Exemple amb q=2 i r=4"; puntsOlav2(2,4); /*Veiem que hi hauran q punts que pertanyin a GF(q)*/ Output: Magma V2.10-6 Mon Mar 15 2004 13:38:04 on modular [Seed = 1531896596] ------------------------------------- [ 49, 7, 1 ] Exemple amb q=2 i r=3 q^(2*r-1) és igual a: 32 El cardinal dels punts Olav en aquest exemple és: 32 Exemple amb q=3 i r=3 q^(2*r-1) és igual a: 243 El cardinal dels punts Olav en aquest exemple és: 243 Exemple amb q=5 i r=3 q^(2*r-1) és igual a: 3125 El cardinal dels punts Olav en aquest exemple és: 3125 Exemple amb q=3 i r=4 q^(2*r-1) és igual a: 2187 El cardinal dels punts Olav en aquest exemple és: 2187 Exemple amb q=2 i r=4 q^(2*r-1) és igual a: 128 El cardinal dels punts Olav en aquest exemple és: 128 Exemple amb q=2 i r=3 2 Exemple amb q=3 i r=3 3 Exemple amb q=5 i r=3 5 Exemple amb q=3 i r=4 3 Exemple amb q=2 i r=4 2 Total time: 8.799 seconds, Total memory usage: 2.15MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 13:38:23 2004 Input: coef:= function (q,r) if ((r gt 0) and IsPrime(q)) then co:= [q^(r-1)]; for i:=2 to r do co:= co cat [q^(r-i)]; end for; end if; return co; end function; Z:=Integers(100); PT:=PolynomialRing(Z); t := function (q,r) lista:=coef(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + PT![0,1]^lista[i]; end for; return poly; end function; t(7,3); n := function (q,r) lista:=coef(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=PT![0,1]^exp; return poly; end function; n(7,3); punts_olav:=function (q,r) Field:=GF(q,r); punts:=[ a,b in Field | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; return punts; end function; punts_olav(7,3); Output: Magma V2.10-6 Mon Mar 15 2004 13:38:20 on modular [Seed = 1652021821] ------------------------------------- x^49 + x^7 + x x^57 >> punts:=[ a,b in Field | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; ^ User error: bad syntax >> return punts; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> punts_olav(7,3);; ^ User error: Identifier 'punts_olav' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Mon Mar 15 13:38:55 2004 Input: Pn := function(q,r) K := GF(q,r); P := PolynomialRing(K); xp := [q^i : i in [r-1..0 by -1]]; pol := x^&+(xp); return(pol); end function; Pt := function(q,r) K := GF(q,r); P := PolynomialRing(K); xp := [q^i : i in [r-1..0 by -1]]; pol := &+[x^i : i in xp]; return(pol); end function; Olav := func : a, b in GF(q,r) | Evaluate(Pn(q,r),a) eq Evaluate(Pt(q,r),b)]>; #(Olav(7,3)); 7^(3-1); #(Olav(11,4)); 11^(4-1); #(Olav(5,7)); 5^(7-1); #(Olav(1,3)); 1^(3-1); #(Olav(13,5)); 13^(5-1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Mar 15 2004 13:38:32 on modular [Seed = 1753075715] ------------------------------------- 16807 49 Errors: /home/mfd/gomagma: line 2: 811 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Mon Mar 15 13:40:11 2004 Input: Pn := function(q,r) K := GF(q,r); P := PolynomialRing(K); xp := [q^i : i in [r-1..0 by -1]]; pol := x^&+(xp); return(pol); end function; Pt := function(q,r) K := GF(q,r); P := PolynomialRing(K); xp := [q^i : i in [r-1..0 by -1]]; pol := &+[x^i : i in xp]; return(pol); end function; Olav := func : a, b in GF(q,r) | Evaluate(Pn(q,r),a) eq Evaluate(Pt(q,r),b)]>; #(Olav(7,3)); 7^(3-1); #(Olav(11,4)); 11^(4-1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Mar 15 2004 13:39:48 on modular [Seed = 1969278274] ------------------------------------- 16807 49 Errors: /home/mfd/gomagma: line 2: 822 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 13:40:17 2004 Input: coef:= function (q,r) if ((r gt 0) and IsPrime(q)) then co:= [q^(r-1)]; for i:=2 to r do co:= co cat [q^(r-i)]; end for; end if; return co; end function; Z:=Integers(100); PT:=PolynomialRing(Z); t := function (q,r) lista:=coef(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + PT![0,1]^lista[i]; end for; return poly; end function; t(7,3); n := function (q,r) lista:=coef(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=PT![0,1]^exp; return poly; end function; n(7,3); punts_olav:=function (q,r) Field:=GF(q,r); punts:=[ a,b: a in Field and b in Field | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; return punts; end function; punts_olav(7,3); Output: Magma V2.10-6 Mon Mar 15 2004 13:40:15 on modular [Seed = 68271304] ------------------------------------- x^49 + x^7 + x x^57 >> punts:=[ a,b: a in Field and b in Field | Evaluate(n(q,r),a) eq Evaluate(t( ^ User error: bad syntax >> return punts; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> punts_olav(7,3);; ^ User error: Identifier 'punts_olav' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Mon Mar 15 13:40:51 2004 Input: Pn := function(q,r) K := GF(q,r); P := PolynomialRing(K); xp := [q^i : i in [r-1..0 by -1]]; pol := x^&+(xp); return(pol); end function; Pt := function(q,r) K := GF(q,r); P := PolynomialRing(K); xp := [q^i : i in [r-1..0 by -1]]; pol := &+[x^i : i in xp]; return(pol); end function; Olav := func : a, b in GF(q,r) | Evaluate(Pn(q,r),a) eq Evaluate(Pt(q,r),b)]>; #(Olav(7,3)); 7^(6-1); Output: Magma V2.10-6 Mon Mar 15 2004 13:40:32 on modular [Seed = 302492401] ------------------------------------- 16807 16807 Total time: 18.389 seconds, Total memory usage: 2.73MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 13:40:54 2004 Input: coef:= function (q,r) if ((r gt 0) and IsPrime(q)) then co:= [q^(r-1)]; for i:=2 to r do co:= co cat [q^(r-i)]; end for; end if; return co; end function; Z:=Integers(100); PT:=PolynomialRing(Z); t := function (q,r) lista:=coef(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + PT![0,1]^lista[i]; end for; return poly; end function; t(7,3); n := function (q,r) lista:=coef(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=PT![0,1]^exp; return poly; end function; n(7,3); punts_olav:=function (q,r) Field:=GF(q,r); punts:=[ : a in Field and b in Field | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; return punts; end function; punts_olav(7,3); Output: Magma V2.10-6 Mon Mar 15 2004 13:40:51 on modular [Seed = 437232362] ------------------------------------- x^49 + x^7 + x x^57 >> punts:=[ : a in Field and b in Field | Evaluate(n(q,r),a) eq Evaluate( ^ User error: Identifier 'b' has not been declared or assigned >> punts_olav(7,3);; ^ User error: Identifier 'punts_olav' has not been declared or assigned Total time: 2.849 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee13.uab.es. (158.109.66.13) Time: Mon Mar 15 13:40:57 2004 Input: PRINT "EXERCICI 1" X:=[1..366 by 1]; Y:=[]; for i := 4 to 366 by 7 do Y:=Include(Y,X[i]); end for; Y; PRINT "EXERCICI 2" K:=GF(4); M:=MatrixRing(K,2); Mt := { x : x in M | Trace(x) eq 0 }; Mf := { y : y in M | Submatrix(y,1,1,1,2) eq Submatrix(y,2,1,1,2)}; Mtf := Mt meet Mf; L:=[Random(M):n in [1..10]]; #([z : z in L | z in Mt]); #([z : z in L | z in Mf]); #([z : z in L | z in Mtf]); print "EXERCICI 3" print "apartat i)" llista:=[]; for i:= 2 to 0 by -1 do llista:=Include(llista, 7^i); end for; llista; print "apartat ii)" R:=Integers(); P:=PolynomialRing(R); sum:=0; for i:= 2 to 0 by -1 do sum:=sum+7^i; end for; x^sum; pol:=0; for i:=1 to #(llista) do pol:=pol+x^llista[i]; end for; pol; print "apartat iii)" {: a in GF(7,3), b in GF(7,3)|Evaluate(pol,a) eq Evaluate(x^sum,b)}; print "apartat iv)" polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); print "apartat v)" polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; print "apartat vi)" puntsOlav:=func: a,b in GF(q,r)|Evaluate(polinomit(q,r),a) eq Evaluate(polinomin(q,r),b)}>; print "apartat vii)" exemples:=function(q,r) print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r)); end function; print"";print "Exemple amb q=2 i r=3"; exemples(2,3); print"";print "Exemple amb q=3 i r=3"; exemples(3,3); print"";print "Exemple amb q=5 i r=3"; exemples(5,3); print"";print "Exemple amb q=3 i r=4"; exemples(3,4); print"";print "Exemple amb q=2 i r=4"; exemples(2,4); print "apartat viii)" puntsOlav2:=function(q,r) po2:=[po:po in puntsOlav(q,r)|po[1] in GF(q) and po[2] in GF(q)]; return #(po2); end function; print"";print "Exemple amb q=2 i r=3"; puntsOlav2(2,3); print"";print "Exemple amb q=3 i r=3"; puntsOlav2(3,3); print"";print "Exemple amb q=5 i r=3"; puntsOlav2(5,3); print"";print "Exemple amb q=3 i r=4"; puntsOlav2(3,4); print"";print "Exemple amb q=2 i r=4"; puntsOlav2(2,4); /*Veiem que hi hauran q punts que pertanyin a GF(q)*/ Output: Magma V2.10-6 Mon Mar 15 2004 13:40:54 on modular [Seed = 557095380] ------------------------------------- >> PRINT "EXERCICI 1" ^ User error: bad syntax [ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] >> PRINT "EXERCICI 2" ^ User error: bad syntax 3 0 0 >> print "apartat i)" ^ User error: bad syntax [ 49, 7, 1 ] >> R:=Integers(); ^ User error: bad syntax >> P:=PolynomialRing(R); ^ User error: Identifier 'R' has not been declared or assigned >> x^sum; ^ User error: Identifier 'x' has not been declared or assigned >> pol:=pol+x^llista[i]; ^ User error: Identifier 'x' has not been declared or assigned 0 >> {: a in GF(7,3), b in GF(7,3)|Evaluate(pol,a) eq Evaluate(x^sum,b)}; ^ User error: bad syntax >> polinomitexp:=function(q,r) ^ User error: bad syntax >> for i:= r-1 to 0 by -1 do ^ User error: Identifier 'r' has not been declared or assigned >> return llista; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> polinomitexp(7,3); ^ User error: Identifier 'polinomitexp' has not been declared or assigned >> polinomin:=function(q,r) ^ User error: bad syntax >> for i:=r-1 to 0 by -1 do ^ User error: Identifier 'r' has not been declared or assigned >> return x^sum; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> newlist:=polinomitexp(q,r); ^ User error: Identifier 'polinomitexp' has not been declared or assigned >> puntsOlav:=func: a,b in GF(q,r)|Evaluate(polinomit(q,r),a) eq Ev ^ User error: bad syntax >> exemples:=function(q,r) ^ User error: bad syntax q^(2*r-1) és igual a: >> print q^(2*r-1); ^ User error: Identifier 'q' has not been declared or assigned El cardinal dels punts Olav en aquest exemple és: >> return #(puntsOlav(q,r)); ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax Exemple amb q=2 i r=3 >> exemples(2,3); ^ User error: Identifier 'exemples' has not been declared or assigned Exemple amb q=3 i r=3 >> exemples(3,3); ^ User error: Identifier 'exemples' has not been declared or assigned Exemple amb q=5 i r=3 >> exemples(5,3); ^ User error: Identifier 'exemples' has not been declared or assigned Exemple amb q=3 i r=4 >> exemples(3,4); ^ User error: Identifier 'exemples' has not been declared or assigned Exemple amb q=2 i r=4 >> exemples(2,4); ^ User error: Identifier 'exemples' has not been declared or assigned >> puntsOlav2:=function(q,r) ^ User error: bad syntax >> po2:=[po:po in puntsOlav(q,r)|po[1] in GF(q) and po[2] in GF(q)]; ^ User error: Identifier 'q' has not been declared or assigned >> return #(po2); ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax Exemple amb q=2 i r=3 >> puntsOlav2(2,3); ^ User error: Identifier 'puntsOlav2' has not been declared or assigned Exemple amb q=3 i r=3 >> puntsOlav2(3,3); ^ User error: Identifier 'puntsOlav2' has not been declared or assigned Exemple amb q=5 i r=3 >> puntsOlav2(5,3); ^ User error: Identifier 'puntsOlav2' has not been declared or assigned Exemple amb q=3 i r=4 >> puntsOlav2(3,4); ^ User error: Identifier 'puntsOlav2' has not been declared or assigned Exemple amb q=2 i r=4 >> puntsOlav2(2,4); ^ User error: Identifier 'puntsOlav2' has not been declared or assigned Total time: 3.039 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 13:41:09 2004 Input: coef:= function (q,r) if ((r gt 0) and IsPrime(q)) then co:= [q^(r-1)]; for i:=2 to r do co:= co cat [q^(r-i)]; end for; end if; return co; end function; Z:=Integers(100); PT:=PolynomialRing(Z); t := function (q,r) lista:=coef(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + PT![0,1]^lista[i]; end for; return poly; end function; t(7,3); n := function (q,r) lista:=coef(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=PT![0,1]^exp; return poly; end function; n(7,3); punts_olav:=function (q,r) Field:=GF(q,r); punts:=[ : a,b in Field | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; return punts; end function; punts_olav(7,3); Output: Magma V2.10-6 Mon Mar 15 2004 13:41:06 on modular [Seed = 792369071] ------------------------------------- x^49 + x^7 + x x^57 [
:18]( q: 7, r: 3 ) >> punts:=[ : a,b in Field | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; ^ Runtime error in 'Evaluate': Incompatible rings Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee13.uab.es. (158.109.66.13) Time: Mon Mar 15 13:41:36 2004 Input: print "EXERCICI 1" X:=[1..366 by 1]; Y:=[]; for i := 4 to 366 by 7 do Y:=Include(Y,X[i]); end for; Y; print "EXERCICI 2" K:=GF(4); M:=MatrixRing(K,2); Mt := { x : x in M | Trace(x) eq 0 }; Mf := { y : y in M | Submatrix(y,1,1,1,2) eq Submatrix(y,2,1,1,2)}; Mtf := Mt meet Mf; L:=[Random(M):n in [1..10]]; #([z : z in L | z in Mt]); #([z : z in L | z in Mf]); #([z : z in L | z in Mtf]); print "EXERCICI 3" print "apartat i)" llista:=[]; for i:= 2 to 0 by -1 do llista:=Include(llista, 7^i); end for; llista; print "apartat ii)" R:=Integers(); P:=PolynomialRing(R); sum:=0; for i:= 2 to 0 by -1 do sum:=sum+7^i; end for; x^sum; pol:=0; for i:=1 to #(llista) do pol:=pol+x^llista[i]; end for; pol; print "apartat iii)" {: a in GF(7,3), b in GF(7,3)|Evaluate(pol,a) eq Evaluate(x^sum,b)}; print "apartat iv)" polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); print "apartat v)" polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; print "apartat vi)" puntsOlav:=func: a,b in GF(q,r)|Evaluate(polinomit(q,r),a) eq Evaluate(polinomin(q,r),b)}>; print "apartat vii)" exemples:=function(q,r) print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r)); end function; print"";print "Exemple amb q=2 i r=3"; exemples(2,3); print"";print "Exemple amb q=3 i r=3"; exemples(3,3); print"";print "Exemple amb q=5 i r=3"; exemples(5,3); print"";print "Exemple amb q=3 i r=4"; exemples(3,4); print"";print "Exemple amb q=2 i r=4"; exemples(2,4); print "apartat viii)" puntsOlav2:=function(q,r) po2:=[po:po in puntsOlav(q,r)|po[1] in GF(q) and po[2] in GF(q)]; return #(po2); end function; print"";print "Exemple amb q=2 i r=3"; puntsOlav2(2,3); print"";print "Exemple amb q=3 i r=3"; puntsOlav2(3,3); print"";print "Exemple amb q=5 i r=3"; puntsOlav2(5,3); print"";print "Exemple amb q=3 i r=4"; puntsOlav2(3,4); print"";print "Exemple amb q=2 i r=4"; puntsOlav2(2,4); /*Veiem que hi hauran q punts que pertanyin a GF(q)*/ Output: Magma V2.10-6 Mon Mar 15 2004 13:41:32 on modular [Seed = 992904100] ------------------------------------- >> X:=[1..366 by 1]; ^ User error: bad syntax >> for i := 4 to 366 by 7 do Y:=Include(Y,X[i]); end for; ^ User error: Identifier 'X' has not been declared or assigned [] >> K:=GF(4); ^ User error: bad syntax >> M:=MatrixRing(K,2); ^ User error: Identifier 'K' has not been declared or assigned >> Mt := { x : x in M | Trace(x) eq 0 }; ^ User error: Identifier 'M' has not been declared or assigned >> Mf := { y : y in M | Submatrix(y,1,1,1,2) eq Submatrix(y,2,1,1,2)}; ^ User error: Identifier 'M' has not been declared or assigned >> Mtf := Mt meet Mf; ^ User error: Identifier 'Mt' has not been declared or assigned >> L:=[Random(M):n in [1..10]]; ^ User error: Identifier 'M' has not been declared or assigned >> #([z : z in L | z in Mt]); ^ User error: Identifier 'L' has not been declared or assigned >> #([z : z in L | z in Mf]); ^ User error: Identifier 'L' has not been declared or assigned >> #([z : z in L | z in Mtf]); ^ User error: Identifier 'L' has not been declared or assigned >> print "apartat i)" ^ User error: bad syntax [ 49, 7, 1 ] >> R:=Integers(); ^ User error: bad syntax >> P:=PolynomialRing(R); ^ User error: Identifier 'R' has not been declared or assigned >> x^sum; ^ User error: Identifier 'x' has not been declared or assigned >> pol:=pol+x^llista[i]; ^ User error: Identifier 'x' has not been declared or assigned 0 >> {: a in GF(7,3), b in GF(7,3)|Evaluate(pol,a) eq Evaluate(x^sum,b)}; ^ User error: bad syntax >> polinomitexp:=function(q,r) ^ User error: bad syntax >> for i:= r-1 to 0 by -1 do ^ User error: Identifier 'r' has not been declared or assigned >> return llista; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> polinomitexp(7,3); ^ User error: Identifier 'polinomitexp' has not been declared or assigned >> polinomin:=function(q,r) ^ User error: bad syntax >> for i:=r-1 to 0 by -1 do ^ User error: Identifier 'r' has not been declared or assigned >> return x^sum; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> newlist:=polinomitexp(q,r); ^ User error: Identifier 'polinomitexp' has not been declared or assigned >> puntsOlav:=func: a,b in GF(q,r)|Evaluate(polinomit(q,r),a) eq Ev ^ User error: bad syntax >> exemples:=function(q,r) ^ User error: bad syntax q^(2*r-1) és igual a: >> print q^(2*r-1); ^ User error: Identifier 'q' has not been declared or assigned El cardinal dels punts Olav en aquest exemple és: >> return #(puntsOlav(q,r)); ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax Exemple amb q=2 i r=3 >> exemples(2,3); ^ User error: Identifier 'exemples' has not been declared or assigned Exemple amb q=3 i r=3 >> exemples(3,3); ^ User error: Identifier 'exemples' has not been declared or assigned Exemple amb q=5 i r=3 >> exemples(5,3); ^ User error: Identifier 'exemples' has not been declared or assigned Exemple amb q=3 i r=4 >> exemples(3,4); ^ User error: Identifier 'exemples' has not been declared or assigned Exemple amb q=2 i r=4 >> exemples(2,4); ^ User error: Identifier 'exemples' has not been declared or assigned >> puntsOlav2:=function(q,r) ^ User error: bad syntax >> po2:=[po:po in puntsOlav(q,r)|po[1] in GF(q) and po[2] in GF(q)]; ^ User error: Identifier 'q' has not been declared or assigned >> return #(po2); ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax Exemple amb q=2 i r=3 >> puntsOlav2(2,3); ^ User error: Identifier 'puntsOlav2' has not been declared or assigned Exemple amb q=3 i r=3 >> puntsOlav2(3,3); ^ User error: Identifier 'puntsOlav2' has not been declared or assigned Exemple amb q=5 i r=3 >> puntsOlav2(5,3); ^ User error: Identifier 'puntsOlav2' has not been declared or assigned Exemple amb q=3 i r=4 >> puntsOlav2(3,4); ^ User error: Identifier 'puntsOlav2' has not been declared or assigned Exemple amb q=2 i r=4 >> puntsOlav2(2,4); ^ User error: Identifier 'puntsOlav2' has not been declared or assigned Total time: 3.569 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.42.170.proxycache.rima-tde.net. (80.58.42.170) Time: Mon Mar 15 13:41:55 2004 Input: Pn := function(q,r) K := GF(q,r); P := PolynomialRing(K); xp := [q^i : i in [r-1..0 by -1]]; pol := x^&+(xp); return(pol); end function; Pt := function(q,r) K := GF(q,r); P := PolynomialRing(K); xp := [q^i : i in [r-1..0 by -1]]; pol := &+[x^i : i in xp]; return(pol); end function; Olav := func : a, b in GF(q,r) | Evaluate(Pn(q,r),a) eq Evaluate(Pt(q,r),b)]>; #(Olav(11,4)); 11^(4-1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Mar 15 2004 13:41:31 on modular [Seed = 908299950] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 885 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 13:42:19 2004 Input: coef:= function (q,r) if ((r gt 0) and IsPrime(q)) then co:= [q^(r-1)]; for i:=2 to r do co:= co cat [q^(r-i)]; end for; end if; return co; end function; Z:=Integers(100); PT:=PolynomialRing(Z); t := function (q,r) lista:=coef(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + PT![0,1]^lista[i]; end for; return poly; end function; t(7,3); n := function (q,r) lista:=coef(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=PT![0,1]^exp; return poly; end function; n(7,3); n73=n(7,3); t73=t(7,3); punts_olav:=function (q,r) Field:=GF(q,r); punts:=[ : a,b in Field | Evaluate(n73,a) eq Evaluate(t73,b)]; return punts; end function; punts_olav(7,3); Output: Magma V2.10-6 Mon Mar 15 2004 13:42:16 on modular [Seed = 3302063503] ------------------------------------- x^49 + x^7 + x x^57 >> n73=n(7,3); ^ User error: Identifier 'n73' has not been declared or assigned >> t73=t(7,3); ^ User error: Identifier 't73' has not been declared or assigned >> punts:=[ : a,b in Field | Evaluate(n73,a) eq Evaluate(t73,b)]; ^ User error: Identifier 'n73' has not been declared or assigned >> punts_olav(7,3);; ^ User error: Identifier 'punts_olav' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee13.uab.es. (158.109.66.13) Time: Mon Mar 15 13:42:36 2004 Input: print "EXERCICI 3" print "apartat i)" llista:=[]; for i:= 2 to 0 by -1 do llista:=Include(llista, 7^i); end for; llista; print "apartat ii)" R:=Integers(); P:=PolynomialRing(R); sum:=0; for i:= 2 to 0 by -1 do sum:=sum+7^i; end for; x^sum; pol:=0; for i:=1 to #(llista) do pol:=pol+x^llista[i]; end for; pol; print "apartat iii)" {: a in GF(7,3), b in GF(7,3)|Evaluate(pol,a) eq Evaluate(x^sum,b)}; print "apartat iv)" polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); print "apartat v)" polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; print "apartat vi)" puntsOlav:=func: a,b in GF(q,r)|Evaluate(polinomit(q,r),a) eq Evaluate(polinomin(q,r),b)}>; print "apartat vii)" exemples:=function(q,r) print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r)); end function; print"";print "Exemple amb q=2 i r=3"; exemples(2,3); print"";print "Exemple amb q=3 i r=3"; exemples(3,3); print"";print "Exemple amb q=5 i r=3"; exemples(5,3); print"";print "Exemple amb q=3 i r=4"; exemples(3,4); print"";print "Exemple amb q=2 i r=4"; exemples(2,4); print "apartat viii)" puntsOlav2:=function(q,r) po2:=[po:po in puntsOlav(q,r)|po[1] in GF(q) and po[2] in GF(q)]; return #(po2); end function; print"";print "Exemple amb q=2 i r=3"; puntsOlav2(2,3); print"";print "Exemple amb q=3 i r=3"; puntsOlav2(3,3); print"";print "Exemple amb q=5 i r=3"; puntsOlav2(5,3); print"";print "Exemple amb q=3 i r=4"; puntsOlav2(3,4); print"";print "Exemple amb q=2 i r=4"; puntsOlav2(2,4); /*Veiem que hi hauran q punts que pertanyin a GF(q)*/ Output: Magma V2.10-6 Mon Mar 15 2004 13:42:33 on modular [Seed = 3552995977] ------------------------------------- >> print "apartat i)" ^ User error: bad syntax [ 49, 7, 1 ] >> R:=Integers(); ^ User error: bad syntax >> P:=PolynomialRing(R); ^ User error: Identifier 'R' has not been declared or assigned >> x^sum; ^ User error: Identifier 'x' has not been declared or assigned >> pol:=pol+x^llista[i]; ^ User error: Identifier 'x' has not been declared or assigned 0 >> {: a in GF(7,3), b in GF(7,3)|Evaluate(pol,a) eq Evaluate(x^sum,b)}; ^ User error: bad syntax >> polinomitexp:=function(q,r) ^ User error: bad syntax >> for i:= r-1 to 0 by -1 do ^ User error: Identifier 'r' has not been declared or assigned >> return llista; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> polinomitexp(7,3); ^ User error: Identifier 'polinomitexp' has not been declared or assigned >> polinomin:=function(q,r) ^ User error: bad syntax >> for i:=r-1 to 0 by -1 do ^ User error: Identifier 'r' has not been declared or assigned >> return x^sum; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> newlist:=polinomitexp(q,r); ^ User error: Identifier 'polinomitexp' has not been declared or assigned >> puntsOlav:=func: a,b in GF(q,r)|Evaluate(polinomit(q,r),a) eq Ev ^ User error: bad syntax >> exemples:=function(q,r) ^ User error: bad syntax q^(2*r-1) és igual a: >> print q^(2*r-1); ^ User error: Identifier 'q' has not been declared or assigned El cardinal dels punts Olav en aquest exemple és: >> return #(puntsOlav(q,r)); ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax Exemple amb q=2 i r=3 >> exemples(2,3); ^ User error: Identifier 'exemples' has not been declared or assigned Exemple amb q=3 i r=3 >> exemples(3,3); ^ User error: Identifier 'exemples' has not been declared or assigned Exemple amb q=5 i r=3 >> exemples(5,3); ^ User error: Identifier 'exemples' has not been declared or assigned Exemple amb q=3 i r=4 >> exemples(3,4); ^ User error: Identifier 'exemples' has not been declared or assigned Exemple amb q=2 i r=4 >> exemples(2,4); ^ User error: Identifier 'exemples' has not been declared or assigned >> puntsOlav2:=function(q,r) ^ User error: bad syntax >> po2:=[po:po in puntsOlav(q,r)|po[1] in GF(q) and po[2] in GF(q)]; ^ User error: Identifier 'q' has not been declared or assigned >> return #(po2); ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax Exemple amb q=2 i r=3 >> puntsOlav2(2,3); ^ User error: Identifier 'puntsOlav2' has not been declared or assigned Exemple amb q=3 i r=3 >> puntsOlav2(3,3); ^ User error: Identifier 'puntsOlav2' has not been declared or assigned Exemple amb q=5 i r=3 >> puntsOlav2(5,3); ^ User error: Identifier 'puntsOlav2' has not been declared or assigned Exemple amb q=3 i r=4 >> puntsOlav2(3,4); ^ User error: Identifier 'puntsOlav2' has not been declared or assigned Exemple amb q=2 i r=4 >> puntsOlav2(2,4); ^ User error: Identifier 'puntsOlav2' has not been declared or assigned Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 13:42:44 2004 Input: coef:= function (q,r) if ((r gt 0) and IsPrime(q)) then co:= [q^(r-1)]; for i:=2 to r do co:= co cat [q^(r-i)]; end for; end if; return co; end function; Z:=Integers(100); PT:=PolynomialRing(Z); t := function (q,r) lista:=coef(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + PT![0,1]^lista[i]; end for; return poly; end function; t(7,3); n := function (q,r) lista:=coef(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=PT![0,1]^exp; return poly; end function; n(7,3); n73:=n(7,3); t73:=t(7,3); punts_olav:=function (q,r) Field:=GF(q,r); punts:=[ : a,b in Field | Evaluate(n73,a) eq Evaluate(t73,b)]; return punts; end function; punts_olav(7,3); Output: Magma V2.10-6 Mon Mar 15 2004 13:42:41 on modular [Seed = 3671024568] ------------------------------------- x^49 + x^7 + x x^57 [
:20]( q: 7, r: 3 ) >> punts:=[ : a,b in Field | Evaluate(n73,a) eq Evaluate(t73,b)]; ^ Runtime error in 'Evaluate': Incompatible rings Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 13:43:00 2004 Input: coef:= function (q,r) if ((r gt 0) and IsPrime(q)) then co:= [q^(r-1)]; for i:=2 to r do co:= co cat [q^(r-i)]; end for; end if; return co; end function; Z:=Integers(100); PT:=PolynomialRing(Z); t := function (q,r) lista:=coef(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + PT![0,1]^lista[i]; end for; return poly; end function; t(7,3); n := function (q,r) lista:=coef(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=PT![0,1]^exp; return poly; end function; n(7,3); n73:=n(7,3); t73:=t(7,3); punts_olav:=function (q,r) Field:=GF(q,r); punts:=[ : a,b in Field | Evaluate(n73,a) eq Evaluate(t73,b)]; return {punts}; end function; punts_olav(7,3); Output: Magma V2.10-6 Mon Mar 15 2004 13:42:57 on modular [Seed = 3790887059] ------------------------------------- x^49 + x^7 + x x^57 [
:20]( q: 7, r: 3 ) >> punts:=[ : a,b in Field | Evaluate(n73,a) eq Evaluate(t73,b)]; ^ Runtime error in 'Evaluate': Incompatible rings Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee13.uab.es. (158.109.66.13) Time: Mon Mar 15 13:43:17 2004 Input: print "EXERCICI 3" R:=Integers(); P:=PolynomialRing(R); sum:=0; for i:= 2 to 0 by -1 do sum:=sum+7^i; end for; x^sum; pol:=0; for i:=1 to #(llista) do pol:=pol+x^llista[i]; end for; pol; print "apartat iii)" {: a in GF(7,3), b in GF(7,3)|Evaluate(pol,a) eq Evaluate(x^sum,b)}; print "apartat iv)" polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); print "apartat v)" polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; print "apartat vi)" puntsOlav:=func: a,b in GF(q,r)|Evaluate(polinomit(q,r),a) eq Evaluate(polinomin(q,r),b)}>; print "apartat vii)" exemples:=function(q,r) print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r)); end function; print"";print "Exemple amb q=2 i r=3"; exemples(2,3); print"";print "Exemple amb q=3 i r=3"; exemples(3,3); print"";print "Exemple amb q=5 i r=3"; exemples(5,3); print"";print "Exemple amb q=3 i r=4"; exemples(3,4); print"";print "Exemple amb q=2 i r=4"; exemples(2,4); print "apartat viii)" puntsOlav2:=function(q,r) po2:=[po:po in puntsOlav(q,r)|po[1] in GF(q) and po[2] in GF(q)]; return #(po2); end function; print"";print "Exemple amb q=2 i r=3"; puntsOlav2(2,3); print"";print "Exemple amb q=3 i r=3"; puntsOlav2(3,3); print"";print "Exemple amb q=5 i r=3"; puntsOlav2(5,3); print"";print "Exemple amb q=3 i r=4"; puntsOlav2(3,4); print"";print "Exemple amb q=2 i r=4"; puntsOlav2(2,4); /*Veiem que hi hauran q punts que pertanyin a GF(q)*/ Output: Magma V2.10-6 Mon Mar 15 2004 13:43:14 on modular [Seed = 3908915689] ------------------------------------- >> R:=Integers(); ^ User error: bad syntax >> P:=PolynomialRing(R); ^ User error: Identifier 'R' has not been declared or assigned >> x^sum; ^ User error: Identifier 'x' has not been declared or assigned >> for i:=1 to #(llista) do ^ User error: Identifier 'llista' has not been declared or assigned 0 >> {: a in GF(7,3), b in GF(7,3)|Evaluate(pol,a) eq Evaluate(x^sum,b)}; ^ User error: bad syntax >> polinomitexp:=function(q,r) ^ User error: bad syntax >> for i:= r-1 to 0 by -1 do ^ User error: Identifier 'r' has not been declared or assigned >> return llista; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> polinomitexp(7,3); ^ User error: Identifier 'polinomitexp' has not been declared or assigned >> polinomin:=function(q,r) ^ User error: bad syntax >> for i:=r-1 to 0 by -1 do ^ User error: Identifier 'r' has not been declared or assigned >> return x^sum; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> newlist:=polinomitexp(q,r); ^ User error: Identifier 'polinomitexp' has not been declared or assigned >> puntsOlav:=func: a,b in GF(q,r)|Evaluate(polinomit(q,r),a) eq Ev ^ User error: bad syntax >> exemples:=function(q,r) ^ User error: bad syntax q^(2*r-1) és igual a: >> print q^(2*r-1); ^ User error: Identifier 'q' has not been declared or assigned El cardinal dels punts Olav en aquest exemple és: >> return #(puntsOlav(q,r)); ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax Exemple amb q=2 i r=3 >> exemples(2,3); ^ User error: Identifier 'exemples' has not been declared or assigned Exemple amb q=3 i r=3 >> exemples(3,3); ^ User error: Identifier 'exemples' has not been declared or assigned Exemple amb q=5 i r=3 >> exemples(5,3); ^ User error: Identifier 'exemples' has not been declared or assigned Exemple amb q=3 i r=4 >> exemples(3,4); ^ User error: Identifier 'exemples' has not been declared or assigned Exemple amb q=2 i r=4 >> exemples(2,4); ^ User error: Identifier 'exemples' has not been declared or assigned >> puntsOlav2:=function(q,r) ^ User error: bad syntax >> po2:=[po:po in puntsOlav(q,r)|po[1] in GF(q) and po[2] in GF(q)]; ^ User error: Identifier 'q' has not been declared or assigned >> return #(po2); ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax Exemple amb q=2 i r=3 >> puntsOlav2(2,3); ^ User error: Identifier 'puntsOlav2' has not been declared or assigned Exemple amb q=3 i r=3 >> puntsOlav2(3,3); ^ User error: Identifier 'puntsOlav2' has not been declared or assigned Exemple amb q=5 i r=3 >> puntsOlav2(5,3); ^ User error: Identifier 'puntsOlav2' has not been declared or assigned Exemple amb q=3 i r=4 >> puntsOlav2(3,4); ^ User error: Identifier 'puntsOlav2' has not been declared or assigned Exemple amb q=2 i r=4 >> puntsOlav2(2,4); ^ User error: Identifier 'puntsOlav2' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee13.uab.es. (158.109.66.13) Time: Mon Mar 15 13:44:39 2004 Input: print "EXERCICI 1"; X:=[1..366 by 1]; Y:=[]; for i := 4 to 366 by 7 do Y:=Include(Y,X[i]); end for; Y; print "EXERCICI 2"; K:=GF(4); M:=MatrixRing(K,2); Mt := { x : x in M | Trace(x) eq 0 }; Mf := { y : y in M | Submatrix(y,1,1,1,2) eq Submatrix(y,2,1,1,2)}; Mtf := Mt meet Mf; L:=[Random(M):n in [1..10]]; #([z : z in L | z in Mt]); #([z : z in L | z in Mf]); #([z : z in L | z in Mtf]); print "EXERCICI 3"; print "apartat i)"; llista:=[]; for i:= 2 to 0 by -1 do llista:=Include(llista, 7^i); end for; llista; print "apartat ii)"; R:=Integers(); P:=PolynomialRing(R); sum:=0; for i:= 2 to 0 by -1 do sum:=sum+7^i; end for; x^sum; pol:=0; for i:=1 to #(llista) do pol:=pol+x^llista[i]; end for; pol; print "apartat iii)"; {: a in GF(7,3), b in GF(7,3)|Evaluate(pol,a) eq Evaluate(x^sum,b)}; print "apartat iv)"; polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); print "apartat v)"; polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; print "apartat vi)"; puntsOlav:=func: a,b in GF(q,r)|Evaluate(polinomit(q,r),a) eq Evaluate(polinomin(q,r),b)}>; print "apartat vii)"; exemples:=function(q,r) print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r)); end function; print"";print "Exemple amb q=2 i r=3"; exemples(2,3); print"";print "Exemple amb q=3 i r=3"; exemples(3,3); print"";print "Exemple amb q=5 i r=3"; exemples(5,3); print"";print "Exemple amb q=3 i r=4"; exemples(3,4); print"";print "Exemple amb q=2 i r=4"; exemples(2,4); print "apartat viii)"; puntsOlav2:=function(q,r) po2:=[po:po in puntsOlav(q,r)|po[1] in GF(q) and po[2] in GF(q)]; return #(po2); end function; print"";print "Exemple amb q=2 i r=3"; puntsOlav2(2,3); print"";print "Exemple amb q=3 i r=3"; puntsOlav2(3,3); print"";print "Exemple amb q=5 i r=3"; puntsOlav2(5,3); print"";print "Exemple amb q=3 i r=4"; puntsOlav2(3,4); print"";print "Exemple amb q=2 i r=4"; puntsOlav2(2,4); /*Veiem que hi hauran q punts que pertanyin a GF(q)*/ Output: Magma V2.10-6 Mon Mar 15 2004 13:44:25 on modular [Seed = 4142092092] ------------------------------------- EXERCICI 1 [ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] EXERCICI 2 3 2 1 EXERCICI 3 apartat i) [ 49, 7, 1 ] apartat ii) x^57 x^49 + x^7 + x apartat iii) { <$.1^205, $.1^175>, <$.1^172, 3>, <1, $.1^7>, <$.1^85, $.1^58>, <$.1^23, $.1^112>, <$.1^36, $.1^295>, <$.1^110, $.1^68>, <$.1^301, $.1^95>, <$.1^310, $.1^65>, <$.1^111, $.1^140>, <$.1^88, $.1^177>, <$.1^198, $.1^4>, <$.1^281, $.1^317>, <$.1^131, $.1^174>, <$.1^330, $.1^255>, <$.1^83, $.1^184>, <$.1^145, $.1^214>, <$.1^154, $.1^181>, <$.1^172, $.1^237>, <$.1^264, $.1^23>, <$.1^150, $.1^129>, <$.1^103, $.1^168>, <$.1^83, $.1^256>, <$.1^7, $.1^126>, <$.1^198, $.1^286>, <$.1^66, $.1^180>, <$.1^67, $.1^193>, <$.1^41, $.1^41>, <$.1^193, $.1^208>, <$.1^17, $.1^340>, <$.1^97, $.1^132>, <$.1^195, $.1^282>, <$.1^91, $.1^335>, <$.1^296, $.1^335>, <$.1^80, $.1^119>, <$.1^237, $.1^327>, <$.1^160, $.1^223>, <$.1^96, $.1^99>, <$.1^302, $.1^273>, <$.1^88, 5>, <$.1^139, $.1^62>, <$.1^150, $.1^63>, <$.1^149, $.1^40>, <$.1^316, $.1^169>, <$.1^252, $.1^151>, <$.1^255, $.1^53>, <$.1^42, $.1^112>, <$.1^176, $.1^251>, <$.1^226, $.1^38>, <$.1^124, $.1^182>, <$.1^34, $.1^322>, <$.1^327, $.1^39>, <$.1^161, $.1^340>, <$.1^135, $.1^51>, <$.1^28, $.1^21>, <$.1^332, $.1^73>, <$.1^187, $.1^21>, <$.1^311, $.1^62>, <$.1^102, $.1^131>, <$.1^319, $.1^3>, <$.1^314, $.1^246>, <$.1^44, $.1^69>, <$.1^100, 4>, <$.1^267, $.1^168>, <$.1^224, $.1^280>, <$.1^315, $.1^82>, <$.1^292, $.1^137>, <$.1^200, $.1^280>, <$.1^176, $.1^155>, <$.1^18, $.1^160>, <$.1^121, $.1^230>, <$.1^147, $.1^217>, <$.1^62, $.1^129>, <$.1^318, $.1^88>, <$.1^235, $.1^244>, <$.1^294, $.1^52>, <$.1^270, $.1^92>, <$.1^309, $.1^284>, <$.1^232, $.1^187>, <$.1^67, $.1^103>, <$.1^325, $.1^214>, <$.1^69, $.1^315>, <$.1^24, $.1^303>, <$.1^145, $.1^130>, <$.1^309, $.1^224>, <$.1^46, $.1^83>, <$.1^272, $.1^277>, <$.1^303, $.1^225>, <$.1^311, $.1^2>, <$.1^183, $.1^125>, <$.1^17, $.1^130>, <2, $.1^165>, <$.1^207, $.1^76>, <$.1^318, $.1^208>, <$.1^40, $.1^11>, <$.1^200, $.1^166>, <$.1^119, $.1^244>, <$.1^3, $.1^319>, <3, $.1^38>, <$.1^251, $.1^152>, <$.1^25, $.1^282>, <$.1^174, $.1^16>, <$.1^132, $.1^156>, <$.1^121, $.1^338>, <$.1^88, $.1^303>, <$.1^321, $.1^282>, <$.1^81, $.1^94>, <$.1^149, $.1^262>, <$.1^4, $.1^315>, <$.1^177, $.1^133>, <$.1^136, $.1^3>, <$.1^180, $.1^14>, <$.1^7, $.1^174>, <$.1^121, $.1^26>, <$.1^294, $.1^136>, <$.1^7, $.1^24>, <$.1^308, $.1^189>, <$.1^65, 0>, <$.1^218, $.1^23>, <$.1^132, 2>, <$.1^263, $.1^318>, <$.1^181, $.1^75>, <$.1^35, $.1^32>, <$.1^166, $.1^3>, <$.1^281, $.1^167>, <$.1^220, $.1^303>, <$.1^213, $.1^85>, <$.1, $.1^294>, <1, $.1^175>, <$.1^230, $.1^100>, <$.1^193, $.1^4>, <$.1^267, $.1^60>, <$.1^126, $.1^322>, <$.1^128, $.1^146>, <3, $.1^122>, <$.1^248, $.1^261>, <$.1^92, $.1^213>, <$.1^216, $.1^331>, <2, $.1^129>, <$.1^131, $.1^12>, <$.1^174, $.1^100>, <$.1^20, $.1^323>, <$.1^274, $.1^81>, <$.1^91, $.1^173>, <$.1^197, $.1^216>, <$.1^288, $.1^36>, <$.1^78, $.1^152>, <$.1^150, $.1^339>, <$.1^160, $.1^181>, <$.1^340, $.1^184>, <$.1^239, $.1^112>, <$.1^235, $.1^142>, <$.1^206, $.1^149>, <$.1^232, $.1^19>, <$.1^307, $.1^330>, <$.1, $.1^330>, <$.1^239, $.1^226>, <$.1^116, $.1^266>, <$.1^168, $.1^291>, <$.1^25, $.1^252>, <$.1^244, $.1^226>, <$.1^119, $.1^64>, <$.1^36, $.1^199>, <$.1^127, $.1^31>, <$.1^340, $.1^196>, <$.1^330, $.1^75>, <$.1^288, $.1^60>, <$.1^161, $.1^106>, <$.1^178, $.1^267>, <$.1^298, $.1^40>, <$.1^250, $.1^35>, <$.1^255, $.1^101>, <$.1^194, $.1^25>, <$.1^159, $.1^24>, <$.1^267, $.1^150>, <$.1^16, $.1^150>, <$.1^274, $.1^243>, <$.1^195, $.1^300>, <$.1^30, $.1^245>, <$.1^269, $.1^105>, <$.1^307, $.1^108>, <$.1^181, $.1^21>, <$.1^53, $.1^55>, <$.1^11, $.1^174>, <$.1^225, $.1^34>, <$.1^191, $.1^212>, <$.1^263, $.1^18>, <$.1^6, $.1^304>, <$.1^330, $.1^309>, <$.1^232, $.1^163>, <$.1^292, $.1^5>, <$.1^37, $.1^126>, <$.1^153, $.1^76>, <$.1^156, $.1^282>, <$.1^201, $.1^176>, <$.1^49, $.1^132>, <$.1^290, $.1^169>, <$.1^220, $.1^105>, <$.1^251, $.1^296>, <$.1^231, $.1^77>, <$.1^149, $.1^112>, <$.1^202, $.1^161>, <$.1^273, $.1^284>, <$.1^99, $.1^263>, <$.1^320, $.1^187>, <$.1^34, $.1^172>, <$.1^327, $.1^321>, <$.1^61, $.1^268>, <$.1^93, $.1^296>, <$.1^37, $.1^36>, <$.1^242, $.1^34>, <$.1^320, $.1>, <$.1^22, $.1^79>, <$.1^13, $.1^119>, <$.1^37, $.1^12>, <$.1^24, $.1^69>, <$.1^41, $.1^59>, <$.1^70, $.1^96>, <$.1^200, $.1^10>, <$.1^46, $.1^65>, <$.1^136, $.1^177>, <$.1^193, $.1^160>, <$.1^189, $.1^313>, <$.1^193, $.1^106>, <$.1^107, 0>, <$.1^216, $.1^193>, <$.1^267, $.1^192>, <$.1^249, $.1^257>, <$.1^262, $.1^320>, <$.1^23, $.1^118>, <6, $.1^22>, <$.1^183, $.1^203>, <$.1^207, $.1^10>, <$.1^260, $.1^332>, <$.1^308, $.1^219>, <$.1^145, $.1^124>, <$.1^106, $.1^127>, <$.1^189, $.1^271>, <$.1^138, $.1^245>, <$.1^84, $.1^266>, <$.1^45, $.1^262>, <$.1^235, $.1^304>, <$.1^245, $.1^194>, <$.1^257, $.1^41>, <$.1^24, $.1^249>, <$.1^100, $.1^330>, <$.1^136, $.1^183>, <$.1^62, $.1^99>, <$.1^315, $.1^52>, <$.1^62, $.1^177>, <$.1^242, $.1^82>, <$.1^127, $.1^193>, <$.1^155, $.1^85>, <$.1^158, $.1^167>, <$.1^9, $.1^5>, <$.1^194, $.1^127>, <$.1^42, $.1^268>, <$.1^140, $.1^227>, <$.1^45, $.1^298>, <$.1^196, $.1^213>, <$.1^224, $.1^268>, <$.1^145, $.1^226>, <$.1^3, $.1^259>, <$.1^52, $.1^19>, <$.1^224, $.1^46>, <$.1^23, $.1^196>, <$.1^239, $.1^304>, <$.1^12, $.1^8>, <$.1^325, $.1^22>, <$.1^47, $.1^80>, <$.1^185, $.1^87>, <$.1^169, $.1^7>, <$.1^120, $.1^330>, <$.1, $.1^138>, <$.1^329, $.1^140>, <$.1^55, $.1^23>, <$.1^201, $.1^296>, <$.1^271, $.1^243>, <$.1^58, $.1^103>, <$.1^99, $.1^203>, <$.1^188, $.1^247>, <$.1^144, $.1^85>, <$.1^338, $.1^246>, <$.1^150, $.1^147>, <$.1^58, $.1^97>, <$.1^208, $.1^207>, <$.1^196, $.1^297>, <$.1^315, $.1^106>, <$.1^173, $.1^183>, <$.1^53, $.1^73>, <2, $.1^33>, <$.1^47, $.1^20>, <$.1^185, $.1^213>, <$.1^20, $.1^287>, <$.1^29, $.1^265>, <$.1^259, $.1^330>, <$.1^30, $.1^191>, <$.1^34, $.1^244>, <$.1^144, $.1^13>, <$.1^180, $.1^146>, <$.1^325, $.1^142>, <$.1^150, $.1^249>, <$.1^271, $.1^339>, <$.1^159, 1>, <$.1^264, $.1^83>, <$.1^167, $.1^33>, <$.1^169, $.1^19>, <$.1^140, $.1^173>, <$.1^6, $.1^298>, <$.1^321, $.1^24>, <$.1^173, $.1^237>, <$.1^117, $.1^87>, <4, $.1^107>, <$.1^138, $.1^161>, <$.1^182, $.1^261>, <$.1^206, $.1^227>, <$.1^256, $.1^121>, <$.1^301, $.1^311>, <$.1^310, $.1^179>, <$.1^21, $.1^121>, <$.1^294, $.1^34>, <$.1^155, $.1^163>, <$.1^92, $.1^201>, <$.1^198, $.1^244>, <$.1^88, $.1^141>, <$.1^189, $.1^97>, <$.1^180, $.1^320>, <$.1^241, $.1^201>, <$.1^102, $.1^137>, <$.1^123, $.1^103>, <$.1^220, $.1^153>, <$.1^314, $.1^306>, <$.1^138, $.1^179>, <$.1^68, $.1^199>, <$.1^39, $.1^44>, <$.1^245, $.1^290>, <$.1^89, $.1^83>, <$.1^212, $.1^110>, <$.1^181, $.1^237>, <$.1^53, $.1^217>, <$.1^87, $.1^72>, <$.1^187, $.1^183>, <$.1^309, $.1^92>, <$.1^275, $.1^258>, <$.1^307, $.1^126>, <$.1^231, $.1^221>, <$.1^242, $.1^154>, <$.1^25, $.1^144>, <$.1^80, $.1^161>, <$.1^251, $.1^2>, <$.1^98, $.1^282>, <5, $.1^6>, <$.1^337, $.1^300>, <$.1^45, $.1^244>, <$.1^116, $.1^320>, <$.1^290, $.1^313>, <$.1^123, $.1^7>, <$.1^58, $.1^55>, <$.1^289, $.1^2>, <$.1^284, 0>, <$.1^248, $.1^177>, <$.1^241, $.1^267>, <$.1^218, $.1^263>, <$.1^134, $.1^187>, <$.1^207, $.1^130>, <$.1^20, $.1^263>, <$.1^44, $.1^255>, <6, $.1^322>, <$.1^220, $.1^129>, <6, $.1^82>, <$.1^101, $.1^10>, <$.1^226, $.1^230>, <$.1^145, $.1^136>, <$.1^178, $.1^237>, <$.1^261, $.1^21>, <$.1^241, $.1^273>, <$.1^2, $.1^300>, <$.1^192, $.1^76>, <$.1^260, $.1^98>, <$.1^41, $.1^311>, <$.1^313, $.1^230>, <$.1^339, $.1^270>, <$.1^299, $.1^71>, <$.1^178, $.1^189>, <$.1^156, $.1^60>, <$.1^223, $.1^298>, <$.1^102, $.1^47>, <$.1^308, $.1^99>, <$.1^82, $.1^97>, <$.1^326, $.1^268>, <$.1^21, $.1^241>, <$.1^148, $.1^174>, <$.1^78, $.1^146>, <1, $.1^133>, <$.1^240, $.1^288>, <$.1^229, $.1^196>, <$.1^34, $.1^46>, <$.1^39, $.1^8>, <$.1^177, $.1^139>, <$.1^89, $.1^131>, <$.1^178, $.1^3>, <$.1^80, $.1^71>, <$.1^117, $.1^327>, <$.1^246, $.1^200>, <$.1^137, $.1^216>, <$.1^205, $.1^217>, <$.1^112, $.1^66>, <$.1^317, $.1^159>, <$.1^297, $.1^73>, <$.1^309, $.1^74>, <$.1^86, $.1^50>, <$.1^294, $.1^76>, <$.1^259, $.1^6>, <$.1^302, $.1^333>, <$.1^339, $.1^120>, <$.1^100, $.1^312>, <$.1^86, $.1^200>, <$.1^242, $.1^172>, <$.1^257, $.1^209>, <$.1^337, $.1^324>, <$.1^260, $.1^152>, <$.1^116, $.1^290>, <$.1^43, $.1^95>, <$.1^31, $.1^2>, <$.1^326, $.1^40>, <$.1^93, $.1^326>, <$.1^319, $.1^189>, <$.1^43, $.1^173>, <$.1^261, $.1^33>, <$.1^287, $.1^107>, <$.1^142, $.1^245>, <$.1^43, $.1^185>, <$.1^185, $.1^69>, <$.1^132, $.1^234>, <$.1^326, $.1^304>, <$.1^197, $.1^252>, <$.1^21, $.1^127>, <$.1^9, $.1^281>, <$.1^147, $.1>, <$.1^100, $.1^186>, <$.1^110, $.1^290>, <$.1^290, $.1^43>, <$.1^255, $.1^191>, <$.1^328, $.1^226>, <$.1^253, $.1^124>, <$.1^70, $.1^252>, <$.1^268, $.1^267>, <$.1^71, $.1^157>, <$.1^185, $.1^45>, <$.1^174, $.1^304>, <$.1^16, $.1^270>, <$.1^47, $.1^188>, <$.1^109, $.1^218>, <$.1^258, $.1^243>, <$.1^187, $.1^147>, <$.1^281, $.1^173>, <1, $.1^127>, <$.1^81, $.1^64>, <$.1^314, $.1^222>, <$.1^85, $.1^148>, <$.1^235, $.1^190>, <$.1^143, $.1^279>, <$.1^25, $.1^324>, <$.1^157, $.1^295>, <$.1^202, $.1^89>, <$.1^75, $.1^239>, <$.1^59, $.1^13>, <$.1^151, $.1^128>, <$.1^313, $.1^170>, <$.1^118, $.1^323>, <$.1^22, $.1^85>, <$.1^206, $.1^65>, <$.1^169, $.1^187>, <$.1^296, $.1^41>, <$.1^255, $.1^155>, <$.1^224, $.1^226>, <$.1^339, $.1^264>, <$.1^64, $.1^175>, <$.1^121, $.1^128>, <$.1^24, $.1^147>, <$.1^199, $.1^294>, <$.1^216, $.1^295>, <$.1^177, $.1^127>, <$.1^282, $.1^59>, <$.1^187, $.1^3>, <$.1^309, $.1^152>, <$.1^119, $.1^46>, <$.1^281, $.1^323>, <$.1^148, $.1^216>, <$.1^67, $.1^313>, <$.1^326, $.1^100>, <$.1^334, $.1^125>, <$.1^151, $.1^302>, <$.1 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 13:45:33 2004 Input: coef:= function (q,r) if ((r gt 0) and IsPrime(q)) then co:= [q^(r-1)]; for i:=2 to r do co:= co cat [q^(r-i)]; end for; end if; return co; end function; Z:=Integers(100); PT:=PolynomialRing(Z); t := function (q,r) lista:=coef(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + PT![0,1]^lista[i]; end for; return poly; end function; t(7,3); n := function (q,r) lista:=coef(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=PT![0,1]^exp; return poly; end function; n(7,3); n73:=n(7,3); t73:=t(7,3); Evaluate(n(q,r),x); punts_olav:=function (q,r) punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; return punts; end function; punts_olav(7,3); Output: Magma V2.10-6 Mon Mar 15 2004 13:45:30 on modular [Seed = 2274508302] ------------------------------------- x^49 + x^7 + x x^57 >> Evaluate(n(q,r),x); ^ User error: Identifier 'q' has not been declared or assigned [
:21]( q: 7, r: 3 ) >> punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; ^ Runtime error in 'Evaluate': Incompatible rings Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 13:45:55 2004 Input: coef:= function (q,r) if ((r gt 0) and IsPrime(q)) then co:= [q^(r-1)]; for i:=2 to r do co:= co cat [q^(r-i)]; end for; end if; return co; end function; Z:=Integers(100); PT:=PolynomialRing(Z); t := function (q,r) lista:=coef(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + PT![0,1]^lista[i]; end for; return poly; end function; t(7,3); n := function (q,r) lista:=coef(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=PT![0,1]^exp; return poly; end function; n(7,3); n73:=n(7,3); t73:=t(7,3); Evaluate(n(7,3),x); punts_olav:=function (q,r) punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; return punts; end function; punts_olav(7,3); Output: Magma V2.10-6 Mon Mar 15 2004 13:45:52 on modular [Seed = 2375562286] ------------------------------------- x^49 + x^7 + x x^57 x^57 [
:21]( q: 7, r: 3 ) >> punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; ^ Runtime error in 'Evaluate': Incompatible rings Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 13:46:25 2004 Input: coef:= function (q,r) if ((r gt 0) and IsPrime(q)) then co:= [q^(r-1)]; for i:=2 to r do co:= co cat [q^(r-i)]; end for; end if; return co; end function; Z:=Integers(100); PT:=PolynomialRing(Z); t := function (q,r) lista:=coef(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + PT![0,1]^lista[i]; end for; return poly; end function; t(7,3); n := function (q,r) lista:=coef(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=PT![0,1]^exp; return poly; end function; n(7,3); n73:=n(7,3); t73:=t(7,3); ev:=Evaluate(n(7,3),x); ev; x; punts_olav:=function (q,r) punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; return punts; end function; punts_olav(7,3); Output: Magma V2.10-6 Mon Mar 15 2004 13:46:22 on modular [Seed = 2559385893] ------------------------------------- x^49 + x^7 + x x^57 x^57 x [
:23]( q: 7, r: 3 ) >> punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; ^ Runtime error in 'Evaluate': Incompatible rings Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee13.uab.es. (158.109.66.13) Time: Mon Mar 15 13:46:29 2004 Input: print "";print "EXERCICI 1"; X:=[1..366 by 1]; Y:=[]; for i := 4 to 366 by 7 do Y:=Include(Y,X[i]); end for; Y; print "";print "EXERCICI 2"; K:=GF(4); M:=MatrixRing(K,2); Mt := { x : x in M | Trace(x) eq 0 }; Mf := { y : y in M | Submatrix(y,1,1,1,2) eq Submatrix(y,2,1,1,2)}; Mtf := Mt meet Mf; L:=[Random(M):n in [1..10]]; #([z : z in L | z in Mt]); #([z : z in L | z in Mf]); #([z : z in L | z in Mtf]); print "";print "EXERCICI 3"; print "";print "apartat i)"; llista:=[]; for i:= 2 to 0 by -1 do llista:=Include(llista, 7^i); end for; llista; print "";print "apartat ii)"; R:=Integers(); P:=PolynomialRing(R); sum:=0; for i:= 2 to 0 by -1 do sum:=sum+7^i; end for; x^sum; pol:=0; for i:=1 to #(llista) do pol:=pol+x^llista[i]; end for; pol; print "";print "apartat iii)"; {: a in GF(7,3), b in GF(7,3)|Evaluate(pol,a) eq Evaluate(x^sum,b)}; print "";print "apartat iv)"; polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); print "";print "apartat v)"; polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; print "";print "apartat vi)"; puntsOlav:=func: a,b in GF(q,r)|Evaluate(polinomit(q,r),a) eq Evaluate(polinomin(q,r),b)}>; print "";print "apartat vii)"; exemples:=function(q,r) print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r)); end function; print"";print "Exemple amb q=2 i r=3"; exemples(2,3); print"";print "Exemple amb q=3 i r=3"; exemples(3,3); print"";print "Exemple amb q=5 i r=3"; exemples(5,3); print"";print "Exemple amb q=3 i r=4"; exemples(3,4); print"";print "Exemple amb q=2 i r=4"; exemples(2,4); print "apartat viii)"; puntsOlav2:=function(q,r) po2:=[po:po in puntsOlav(q,r)|po[1] in GF(q) and po[2] in GF(q)]; return #(po2); end function; print"";print "Exemple amb q=2 i r=3"; puntsOlav2(2,3); print"";print "Exemple amb q=3 i r=3"; puntsOlav2(3,3); print"";print "Exemple amb q=5 i r=3"; puntsOlav2(5,3); print"";print "Exemple amb q=3 i r=4"; puntsOlav2(3,4); print"";print "Exemple amb q=2 i r=4"; puntsOlav2(2,4); /*Veiem que hi hauran q punts que pertanyin a GF(q)*/ Output: Magma V2.10-6 Mon Mar 15 2004 13:46:15 on modular [Seed = 2609783343] ------------------------------------- EXERCICI 1 [ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] EXERCICI 2 5 2 2 EXERCICI 3 apartat i) [ 49, 7, 1 ] apartat ii) x^57 x^49 + x^7 + x apartat iii) { <$.1^205, $.1^175>, <$.1^172, 3>, <1, $.1^7>, <$.1^85, $.1^58>, <$.1^23, $.1^112>, <$.1^36, $.1^295>, <$.1^110, $.1^68>, <$.1^301, $.1^95>, <$.1^310, $.1^65>, <$.1^111, $.1^140>, <$.1^88, $.1^177>, <$.1^198, $.1^4>, <$.1^281, $.1^317>, <$.1^131, $.1^174>, <$.1^330, $.1^255>, <$.1^83, $.1^184>, <$.1^145, $.1^214>, <$.1^154, $.1^181>, <$.1^172, $.1^237>, <$.1^264, $.1^23>, <$.1^150, $.1^129>, <$.1^103, $.1^168>, <$.1^83, $.1^256>, <$.1^7, $.1^126>, <$.1^198, $.1^286>, <$.1^66, $.1^180>, <$.1^67, $.1^193>, <$.1^41, $.1^41>, <$.1^193, $.1^208>, <$.1^17, $.1^340>, <$.1^97, $.1^132>, <$.1^195, $.1^282>, <$.1^91, $.1^335>, <$.1^296, $.1^335>, <$.1^80, $.1^119>, <$.1^237, $.1^327>, <$.1^160, $.1^223>, <$.1^96, $.1^99>, <$.1^302, $.1^273>, <$.1^88, 5>, <$.1^139, $.1^62>, <$.1^150, $.1^63>, <$.1^149, $.1^40>, <$.1^316, $.1^169>, <$.1^252, $.1^151>, <$.1^255, $.1^53>, <$.1^42, $.1^112>, <$.1^176, $.1^251>, <$.1^226, $.1^38>, <$.1^124, $.1^182>, <$.1^34, $.1^322>, <$.1^327, $.1^39>, <$.1^161, $.1^340>, <$.1^135, $.1^51>, <$.1^28, $.1^21>, <$.1^332, $.1^73>, <$.1^187, $.1^21>, <$.1^311, $.1^62>, <$.1^102, $.1^131>, <$.1^319, $.1^3>, <$.1^314, $.1^246>, <$.1^44, $.1^69>, <$.1^100, 4>, <$.1^267, $.1^168>, <$.1^224, $.1^280>, <$.1^315, $.1^82>, <$.1^292, $.1^137>, <$.1^200, $.1^280>, <$.1^176, $.1^155>, <$.1^18, $.1^160>, <$.1^121, $.1^230>, <$.1^147, $.1^217>, <$.1^62, $.1^129>, <$.1^318, $.1^88>, <$.1^235, $.1^244>, <$.1^294, $.1^52>, <$.1^270, $.1^92>, <$.1^309, $.1^284>, <$.1^232, $.1^187>, <$.1^67, $.1^103>, <$.1^325, $.1^214>, <$.1^69, $.1^315>, <$.1^24, $.1^303>, <$.1^145, $.1^130>, <$.1^309, $.1^224>, <$.1^46, $.1^83>, <$.1^272, $.1^277>, <$.1^303, $.1^225>, <$.1^311, $.1^2>, <$.1^183, $.1^125>, <$.1^17, $.1^130>, <2, $.1^165>, <$.1^207, $.1^76>, <$.1^318, $.1^208>, <$.1^40, $.1^11>, <$.1^200, $.1^166>, <$.1^119, $.1^244>, <$.1^3, $.1^319>, <3, $.1^38>, <$.1^251, $.1^152>, <$.1^25, $.1^282>, <$.1^174, $.1^16>, <$.1^132, $.1^156>, <$.1^121, $.1^338>, <$.1^88, $.1^303>, <$.1^321, $.1^282>, <$.1^81, $.1^94>, <$.1^149, $.1^262>, <$.1^4, $.1^315>, <$.1^177, $.1^133>, <$.1^136, $.1^3>, <$.1^180, $.1^14>, <$.1^7, $.1^174>, <$.1^121, $.1^26>, <$.1^294, $.1^136>, <$.1^7, $.1^24>, <$.1^308, $.1^189>, <$.1^65, 0>, <$.1^218, $.1^23>, <$.1^132, 2>, <$.1^263, $.1^318>, <$.1^181, $.1^75>, <$.1^35, $.1^32>, <$.1^166, $.1^3>, <$.1^281, $.1^167>, <$.1^220, $.1^303>, <$.1^213, $.1^85>, <$.1, $.1^294>, <1, $.1^175>, <$.1^230, $.1^100>, <$.1^193, $.1^4>, <$.1^267, $.1^60>, <$.1^126, $.1^322>, <$.1^128, $.1^146>, <3, $.1^122>, <$.1^248, $.1^261>, <$.1^92, $.1^213>, <$.1^216, $.1^331>, <2, $.1^129>, <$.1^131, $.1^12>, <$.1^174, $.1^100>, <$.1^20, $.1^323>, <$.1^274, $.1^81>, <$.1^91, $.1^173>, <$.1^197, $.1^216>, <$.1^288, $.1^36>, <$.1^78, $.1^152>, <$.1^150, $.1^339>, <$.1^160, $.1^181>, <$.1^340, $.1^184>, <$.1^239, $.1^112>, <$.1^235, $.1^142>, <$.1^206, $.1^149>, <$.1^232, $.1^19>, <$.1^307, $.1^330>, <$.1, $.1^330>, <$.1^239, $.1^226>, <$.1^116, $.1^266>, <$.1^168, $.1^291>, <$.1^25, $.1^252>, <$.1^244, $.1^226>, <$.1^119, $.1^64>, <$.1^36, $.1^199>, <$.1^127, $.1^31>, <$.1^340, $.1^196>, <$.1^330, $.1^75>, <$.1^288, $.1^60>, <$.1^161, $.1^106>, <$.1^178, $.1^267>, <$.1^298, $.1^40>, <$.1^250, $.1^35>, <$.1^255, $.1^101>, <$.1^194, $.1^25>, <$.1^159, $.1^24>, <$.1^267, $.1^150>, <$.1^16, $.1^150>, <$.1^274, $.1^243>, <$.1^195, $.1^300>, <$.1^30, $.1^245>, <$.1^269, $.1^105>, <$.1^307, $.1^108>, <$.1^181, $.1^21>, <$.1^53, $.1^55>, <$.1^11, $.1^174>, <$.1^225, $.1^34>, <$.1^191, $.1^212>, <$.1^263, $.1^18>, <$.1^6, $.1^304>, <$.1^330, $.1^309>, <$.1^232, $.1^163>, <$.1^292, $.1^5>, <$.1^37, $.1^126>, <$.1^153, $.1^76>, <$.1^156, $.1^282>, <$.1^201, $.1^176>, <$.1^49, $.1^132>, <$.1^290, $.1^169>, <$.1^220, $.1^105>, <$.1^251, $.1^296>, <$.1^231, $.1^77>, <$.1^149, $.1^112>, <$.1^202, $.1^161>, <$.1^273, $.1^284>, <$.1^99, $.1^263>, <$.1^320, $.1^187>, <$.1^34, $.1^172>, <$.1^327, $.1^321>, <$.1^61, $.1^268>, <$.1^93, $.1^296>, <$.1^37, $.1^36>, <$.1^242, $.1^34>, <$.1^320, $.1>, <$.1^22, $.1^79>, <$.1^13, $.1^119>, <$.1^37, $.1^12>, <$.1^24, $.1^69>, <$.1^41, $.1^59>, <$.1^70, $.1^96>, <$.1^200, $.1^10>, <$.1^46, $.1^65>, <$.1^136, $.1^177>, <$.1^193, $.1^160>, <$.1^189, $.1^313>, <$.1^193, $.1^106>, <$.1^107, 0>, <$.1^216, $.1^193>, <$.1^267, $.1^192>, <$.1^249, $.1^257>, <$.1^262, $.1^320>, <$.1^23, $.1^118>, <6, $.1^22>, <$.1^183, $.1^203>, <$.1^207, $.1^10>, <$.1^260, $.1^332>, <$.1^308, $.1^219>, <$.1^145, $.1^124>, <$.1^106, $.1^127>, <$.1^189, $.1^271>, <$.1^138, $.1^245>, <$.1^84, $.1^266>, <$.1^45, $.1^262>, <$.1^235, $.1^304>, <$.1^245, $.1^194>, <$.1^257, $.1^41>, <$.1^24, $.1^249>, <$.1^100, $.1^330>, <$.1^136, $.1^183>, <$.1^62, $.1^99>, <$.1^315, $.1^52>, <$.1^62, $.1^177>, <$.1^242, $.1^82>, <$.1^127, $.1^193>, <$.1^155, $.1^85>, <$.1^158, $.1^167>, <$.1^9, $.1^5>, <$.1^194, $.1^127>, <$.1^42, $.1^268>, <$.1^140, $.1^227>, <$.1^45, $.1^298>, <$.1^196, $.1^213>, <$.1^224, $.1^268>, <$.1^145, $.1^226>, <$.1^3, $.1^259>, <$.1^52, $.1^19>, <$.1^224, $.1^46>, <$.1^23, $.1^196>, <$.1^239, $.1^304>, <$.1^12, $.1^8>, <$.1^325, $.1^22>, <$.1^47, $.1^80>, <$.1^185, $.1^87>, <$.1^169, $.1^7>, <$.1^120, $.1^330>, <$.1, $.1^138>, <$.1^329, $.1^140>, <$.1^55, $.1^23>, <$.1^201, $.1^296>, <$.1^271, $.1^243>, <$.1^58, $.1^103>, <$.1^99, $.1^203>, <$.1^188, $.1^247>, <$.1^144, $.1^85>, <$.1^338, $.1^246>, <$.1^150, $.1^147>, <$.1^58, $.1^97>, <$.1^208, $.1^207>, <$.1^196, $.1^297>, <$.1^315, $.1^106>, <$.1^173, $.1^183>, <$.1^53, $.1^73>, <2, $.1^33>, <$.1^47, $.1^20>, <$.1^185, $.1^213>, <$.1^20, $.1^287>, <$.1^29, $.1^265>, <$.1^259, $.1^330>, <$.1^30, $.1^191>, <$.1^34, $.1^244>, <$.1^144, $.1^13>, <$.1^180, $.1^146>, <$.1^325, $.1^142>, <$.1^150, $.1^249>, <$.1^271, $.1^339>, <$.1^159, 1>, <$.1^264, $.1^83>, <$.1^167, $.1^33>, <$.1^169, $.1^19>, <$.1^140, $.1^173>, <$.1^6, $.1^298>, <$.1^321, $.1^24>, <$.1^173, $.1^237>, <$.1^117, $.1^87>, <4, $.1^107>, <$.1^138, $.1^161>, <$.1^182, $.1^261>, <$.1^206, $.1^227>, <$.1^256, $.1^121>, <$.1^301, $.1^311>, <$.1^310, $.1^179>, <$.1^21, $.1^121>, <$.1^294, $.1^34>, <$.1^155, $.1^163>, <$.1^92, $.1^201>, <$.1^198, $.1^244>, <$.1^88, $.1^141>, <$.1^189, $.1^97>, <$.1^180, $.1^320>, <$.1^241, $.1^201>, <$.1^102, $.1^137>, <$.1^123, $.1^103>, <$.1^220, $.1^153>, <$.1^314, $.1^306>, <$.1^138, $.1^179>, <$.1^68, $.1^199>, <$.1^39, $.1^44>, <$.1^245, $.1^290>, <$.1^89, $.1^83>, <$.1^212, $.1^110>, <$.1^181, $.1^237>, <$.1^53, $.1^217>, <$.1^87, $.1^72>, <$.1^187, $.1^183>, <$.1^309, $.1^92>, <$.1^275, $.1^258>, <$.1^307, $.1^126>, <$.1^231, $.1^221>, <$.1^242, $.1^154>, <$.1^25, $.1^144>, <$.1^80, $.1^161>, <$.1^251, $.1^2>, <$.1^98, $.1^282>, <5, $.1^6>, <$.1^337, $.1^300>, <$.1^45, $.1^244>, <$.1^116, $.1^320>, <$.1^290, $.1^313>, <$.1^123, $.1^7>, <$.1^58, $.1^55>, <$.1^289, $.1^2>, <$.1^284, 0>, <$.1^248, $.1^177>, <$.1^241, $.1^267>, <$.1^218, $.1^263>, <$.1^134, $.1^187>, <$.1^207, $.1^130>, <$.1^20, $.1^263>, <$.1^44, $.1^255>, <6, $.1^322>, <$.1^220, $.1^129>, <6, $.1^82>, <$.1^101, $.1^10>, <$.1^226, $.1^230>, <$.1^145, $.1^136>, <$.1^178, $.1^237>, <$.1^261, $.1^21>, <$.1^241, $.1^273>, <$.1^2, $.1^300>, <$.1^192, $.1^76>, <$.1^260, $.1^98>, <$.1^41, $.1^311>, <$.1^313, $.1^230>, <$.1^339, $.1^270>, <$.1^299, $.1^71>, <$.1^178, $.1^189>, <$.1^156, $.1^60>, <$.1^223, $.1^298>, <$.1^102, $.1^47>, <$.1^308, $.1^99>, <$.1^82, $.1^97>, <$.1^326, $.1^268>, <$.1^21, $.1^241>, <$.1^148, $.1^174>, <$.1^78, $.1^146>, <1, $.1^133>, <$.1^240, $.1^288>, <$.1^229, $.1^196>, <$.1^34, $.1^46>, <$.1^39, $.1^8>, <$.1^177, $.1^139>, <$.1^89, $.1^131>, <$.1^178, $.1^3>, <$.1^80, $.1^71>, <$.1^117, $.1^327>, <$.1^246, $.1^200>, <$.1^137, $.1^216>, <$.1^205, $.1^217>, <$.1^112, $.1^66>, <$.1^317, $.1^159>, <$.1^297, $.1^73>, <$.1^309, $.1^74>, <$.1^86, $.1^50>, <$.1^294, $.1^76>, <$.1^259, $.1^6>, <$.1^302, $.1^333>, <$.1^339, $.1^120>, <$.1^100, $.1^312>, <$.1^86, $.1^200>, <$.1^242, $.1^172>, <$.1^257, $.1^209>, <$.1^337, $.1^324>, <$.1^260, $.1^152>, <$.1^116, $.1^290>, <$.1^43, $.1^95>, <$.1^31, $.1^2>, <$.1^326, $.1^40>, <$.1^93, $.1^326>, <$.1^319, $.1^189>, <$.1^43, $.1^173>, <$.1^261, $.1^33>, <$.1^287, $.1^107>, <$.1^142, $.1^245>, <$.1^43, $.1^185>, <$.1^185, $.1^69>, <$.1^132, $.1^234>, <$.1^326, $.1^304>, <$.1^197, $.1^252>, <$.1^21, $.1^127>, <$.1^9, $.1^281>, <$.1^147, $.1>, <$.1^100, $.1^186>, <$.1^110, $.1^290>, <$.1^290, $.1^43>, <$.1^255, $.1^191>, <$.1^328, $.1^226>, <$.1^253, $.1^124>, <$.1^70, $.1^252>, <$.1^268, $.1^267>, <$.1^71, $.1^157>, <$.1^185, $.1^45>, <$.1^174, $.1^304>, <$.1^16, $.1^270>, <$.1^47, $.1^188>, <$.1^109, $.1^218>, <$.1^258, $.1^243>, <$.1^187, $.1^147>, <$.1^281, $.1^173>, <1, $.1^127>, <$.1^81, $.1^64>, <$.1^314, $.1^222>, <$.1^85, $.1^148>, <$.1^235, $.1^190>, <$.1^143, $.1^279>, <$.1^25, $.1^324>, <$.1^157, $.1^295>, <$.1^202, $.1^89>, <$.1^75, $.1^239>, <$.1^59, $.1^13>, <$.1^151, $.1^128>, <$.1^313, $.1^170>, <$.1^118, $.1^323>, <$.1^22, $.1^85>, <$.1^206, $.1^65>, <$.1^169, $.1^187>, <$.1^296, $.1^41>, <$.1^255, $.1^155>, <$.1^224, $.1^226>, <$.1^339, $.1^264>, <$.1^64, $.1^175>, <$.1^121, $.1^128>, <$.1^24, $.1^147>, <$.1^199, $.1^294>, <$.1^216, $.1^295>, <$.1^177, $.1^127>, <$.1^282, $.1^59>, <$.1^187, $.1^3>, <$.1^309, $.1^152>, <$.1^119, $.1^46>, <$.1^281, $.1^323>, <$.1^148, $.1^216>, <$.1^67, $.1^313>, <$.1^326, $.1^100>, <$.1^334, $.1^125>, <$.1^151, $.1^302> ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host aula-a-siee13.uab.es. (158.109.66.13) Time: Mon Mar 15 13:47:13 2004 Input: print "";print "EXERCICI 1"; X:=[1..366 by 1]; Y:=[]; for i := 4 to 366 by 7 do Y:=Include(Y,X[i]); end for; Y; print "";print "EXERCICI 2"; K:=GF(4); M:=MatrixRing(K,2); Mt := { x : x in M | Trace(x) eq 0 }; Mf := { y : y in M | Submatrix(y,1,1,1,2) eq Submatrix(y,2,1,1,2)}; Mtf := Mt meet Mf; L:=[Random(M):n in [1..10]]; #([z : z in L | z in Mt]); #([z : z in L | z in Mf]); #([z : z in L | z in Mtf]); print "";print "EXERCICI 3"; print "";print "apartat i)"; llista:=[]; for i:= 2 to 0 by -1 do llista:=Include(llista, 7^i); end for; llista; print "";print "apartat ii)"; R:=Integers(); P:=PolynomialRing(R); sum:=0; for i:= 2 to 0 by -1 do sum:=sum+7^i; end for; x^sum; pol:=0; for i:=1 to #(llista) do pol:=pol+x^llista[i]; end for; pol; print "";print "apartat iii)"; {: a in GF(7,3), b in GF(7,3)|Evaluate(pol,a) eq Evaluate(x^sum,b)}; print "";print "apartat iv)"; polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); print "";print "apartat v)"; polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; print "";print "apartat vi)"; puntsOlav:=func: a,b in GF(q,r)|Evaluate(polinomit(q,r),a) eq Evaluate(polinomin(q,r),b)}>; print "";print "apartat vii)"; exemples:=function(q,r) print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r)); end function; print"";print "Exemple amb q=2 i r=3"; exemples(2,3); print"";print "Exemple amb q=3 i r=3"; exemples(3,3); print"";print "Exemple amb q=5 i r=3"; exemples(5,3); print"";print "Exemple amb q=3 i r=4"; exemples(3,4); print"";print "Exemple amb q=2 i r=4"; exemples(2,4); print "apartat viii)"; puntsOlav2:=function(q,r) po2:=[po:po in puntsOlav(q,r)|po[1] in GF(q) and po[2] in GF(q)]; return #(po2); end function; print"";print "Exemple amb q=2 i r=3"; puntsOlav2(2,3); print"";print "Exemple amb q=3 i r=3"; puntsOlav2(3,3); print"";print "Exemple amb q=5 i r=3"; puntsOlav2(5,3); print"";print "Exemple amb q=3 i r=4"; puntsOlav2(3,4); print"";print "Exemple amb q=2 i r=4"; puntsOlav2(2,4); /*Veiem que hi hauran q punts que pertanyin a GF(q)*/ Output: Magma V2.10-6 Mon Mar 15 2004 13:46:59 on modular [Seed = 2847675337] ------------------------------------- EXERCICI 1 [ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] EXERCICI 2 2 0 0 EXERCICI 3 apartat i) [ 49, 7, 1 ] apartat ii) x^57 x^49 + x^7 + x apartat iii) { <$.1^205, $.1^175>, <$.1^172, 3>, <1, $.1^7>, <$.1^85, $.1^58>, <$.1^23, $.1^112>, <$.1^36, $.1^295>, <$.1^110, $.1^68>, <$.1^301, $.1^95>, <$.1^310, $.1^65>, <$.1^111, $.1^140>, <$.1^88, $.1^177>, <$.1^198, $.1^4>, <$.1^281, $.1^317>, <$.1^131, $.1^174>, <$.1^330, $.1^255>, <$.1^83, $.1^184>, <$.1^145, $.1^214>, <$.1^154, $.1^181>, <$.1^172, $.1^237>, <$.1^264, $.1^23>, <$.1^150, $.1^129>, <$.1^103, $.1^168>, <$.1^83, $.1^256>, <$.1^7, $.1^126>, <$.1^198, $.1^286>, <$.1^66, $.1^180>, <$.1^67, $.1^193>, <$.1^41, $.1^41>, <$.1^193, $.1^208>, <$.1^17, $.1^340>, <$.1^97, $.1^132>, <$.1^195, $.1^282>, <$.1^91, $.1^335>, <$.1^296, $.1^335>, <$.1^80, $.1^119>, <$.1^237, $.1^327>, <$.1^160, $.1^223>, <$.1^96, $.1^99>, <$.1^302, $.1^273>, <$.1^88, 5>, <$.1^139, $.1^62>, <$.1^150, $.1^63>, <$.1^149, $.1^40>, <$.1^316, $.1^169>, <$.1^252, $.1^151>, <$.1^255, $.1^53>, <$.1^42, $.1^112>, <$.1^176, $.1^251>, <$.1^226, $.1^38>, <$.1^124, $.1^182>, <$.1^34, $.1^322>, <$.1^327, $.1^39>, <$.1^161, $.1^340>, <$.1^135, $.1^51>, <$.1^28, $.1^21>, <$.1^332, $.1^73>, <$.1^187, $.1^21>, <$.1^311, $.1^62>, <$.1^102, $.1^131>, <$.1^319, $.1^3>, <$.1^314, $.1^246>, <$.1^44, $.1^69>, <$.1^100, 4>, <$.1^267, $.1^168>, <$.1^224, $.1^280>, <$.1^315, $.1^82>, <$.1^292, $.1^137>, <$.1^200, $.1^280>, <$.1^176, $.1^155>, <$.1^18, $.1^160>, <$.1^121, $.1^230>, <$.1^147, $.1^217>, <$.1^62, $.1^129>, <$.1^318, $.1^88>, <$.1^235, $.1^244>, <$.1^294, $.1^52>, <$.1^270, $.1^92>, <$.1^309, $.1^284>, <$.1^232, $.1^187>, <$.1^67, $.1^103>, <$.1^325, $.1^214>, <$.1^69, $.1^315>, <$.1^24, $.1^303>, <$.1^145, $.1^130>, <$.1^309, $.1^224>, <$.1^46, $.1^83>, <$.1^272, $.1^277>, <$.1^303, $.1^225>, <$.1^311, $.1^2>, <$.1^183, $.1^125>, <$.1^17, $.1^130>, <2, $.1^165>, <$.1^207, $.1^76>, <$.1^318, $.1^208>, <$.1^40, $.1^11>, <$.1^200, $.1^166>, <$.1^119, $.1^244>, <$.1^3, $.1^319>, <3, $.1^38>, <$.1^251, $.1^152>, <$.1^25, $.1^282>, <$.1^174, $.1^16>, <$.1^132, $.1^156>, <$.1^121, $.1^338>, <$.1^88, $.1^303>, <$.1^321, $.1^282>, <$.1^81, $.1^94>, <$.1^149, $.1^262>, <$.1^4, $.1^315>, <$.1^177, $.1^133>, <$.1^136, $.1^3>, <$.1^180, $.1^14>, <$.1^7, $.1^174>, <$.1^121, $.1^26>, <$.1^294, $.1^136>, <$.1^7, $.1^24>, <$.1^308, $.1^189>, <$.1^65, 0>, <$.1^218, $.1^23>, <$.1^132, 2>, <$.1^263, $.1^318>, <$.1^181, $.1^75>, <$.1^35, $.1^32>, <$.1^166, $.1^3>, <$.1^281, $.1^167>, <$.1^220, $.1^303>, <$.1^213, $.1^85>, <$.1, $.1^294>, <1, $.1^175>, <$.1^230, $.1^100>, <$.1^193, $.1^4>, <$.1^267, $.1^60>, <$.1^126, $.1^322>, <$.1^128, $.1^146>, <3, $.1^122>, <$.1^248, $.1^261>, <$.1^92, $.1^213>, <$.1^216, $.1^331>, <2, $.1^129>, <$.1^131, $.1^12>, <$.1^174, $.1^100>, <$.1^20, $.1^323>, <$.1^274, $.1^81>, <$.1^91, $.1^173>, <$.1^197, $.1^216>, <$.1^288, $.1^36>, <$.1^78, $.1^152>, <$.1^150, $.1^339>, <$.1^160, $.1^181>, <$.1^340, $.1^184>, <$.1^239, $.1^112>, <$.1^235, $.1^142>, <$.1^206, $.1^149>, <$.1^232, $.1^19>, <$.1^307, $.1^330>, <$.1, $.1^330>, <$.1^239, $.1^226>, <$.1^116, $.1^266>, <$.1^168, $.1^291>, <$.1^25, $.1^252>, <$.1^244, $.1^226>, <$.1^119, $.1^64>, <$.1^36, $.1^199>, <$.1^127, $.1^31>, <$.1^340, $.1^196>, <$.1^330, $.1^75>, <$.1^288, $.1^60>, <$.1^161, $.1^106>, <$.1^178, $.1^267>, <$.1^298, $.1^40>, <$.1^250, $.1^35>, <$.1^255, $.1^101>, <$.1^194, $.1^25>, <$.1^159, $.1^24>, <$.1^267, $.1^150>, <$.1^16, $.1^150>, <$.1^274, $.1^243>, <$.1^195, $.1^300>, <$.1^30, $.1^245>, <$.1^269, $.1^105>, <$.1^307, $.1^108>, <$.1^181, $.1^21>, <$.1^53, $.1^55>, <$.1^11, $.1^174>, <$.1^225, $.1^34>, <$.1^191, $.1^212>, <$.1^263, $.1^18>, <$.1^6, $.1^304>, <$.1^330, $.1^309>, <$.1^232, $.1^163>, <$.1^292, $.1^5>, <$.1^37, $.1^126>, <$.1^153, $.1^76>, <$.1^156, $.1^282>, <$.1^201, $.1^176>, <$.1^49, $.1^132>, <$.1^290, $.1^169>, <$.1^220, $.1^105>, <$.1^251, $.1^296>, <$.1^231, $.1^77>, <$.1^149, $.1^112>, <$.1^202, $.1^161>, <$.1^273, $.1^284>, <$.1^99, $.1^263>, <$.1^320, $.1^187>, <$.1^34, $.1^172>, <$.1^327, $.1^321>, <$.1^61, $.1^268>, <$.1^93, $.1^296>, <$.1^37, $.1^36>, <$.1^242, $.1^34>, <$.1^320, $.1>, <$.1^22, $.1^79>, <$.1^13, $.1^119>, <$.1^37, $.1^12>, <$.1^24, $.1^69>, <$.1^41, $.1^59>, <$.1^70, $.1^96>, <$.1^200, $.1^10>, <$.1^46, $.1^65>, <$.1^136, $.1^177>, <$.1^193, $.1^160>, <$.1^189, $.1^313>, <$.1^193, $.1^106>, <$.1^107, 0>, <$.1^216, $.1^193>, <$.1^267, $.1^192>, <$.1^249, $.1^257>, <$.1^262, $.1^320>, <$.1^23, $.1^118>, <6, $.1^22>, <$.1^183, $.1^203>, <$.1^207, $.1^10>, <$.1^260, $.1^332>, <$.1^308, $.1^219>, <$.1^145, $.1^124>, <$.1^106, $.1^127>, <$.1^189, $.1^271>, <$.1^138, $.1^245>, <$.1^84, $.1^266>, <$.1^45, $.1^262>, <$.1^235, $.1^304>, <$.1^245, $.1^194>, <$.1^257, $.1^41>, <$.1^24, $.1^249>, <$.1^100, $.1^330>, <$.1^136, $.1^183>, <$.1^62, $.1^99>, <$.1^315, $.1^52>, <$.1^62, $.1^177>, <$.1^242, $.1^82>, <$.1^127, $.1^193>, <$.1^155, $.1^85>, <$.1^158, $.1^167>, <$.1^9, $.1^5>, <$.1^194, $.1^127>, <$.1^42, $.1^268>, <$.1^140, $.1^227>, <$.1^45, $.1^298>, <$.1^196, $.1^213>, <$.1^224, $.1^268>, <$.1^145, $.1^226>, <$.1^3, $.1^259>, <$.1^52, $.1^19>, <$.1^224, $.1^46>, <$.1^23, $.1^196>, <$.1^239, $.1^304>, <$.1^12, $.1^8>, <$.1^325, $.1^22>, <$.1^47, $.1^80>, <$.1^185, $.1^87>, <$.1^169, $.1^7>, <$.1^120, $.1^330>, <$.1, $.1^138>, <$.1^329, $.1^140>, <$.1^55, $.1^23>, <$.1^201, $.1^296>, <$.1^271, $.1^243>, <$.1^58, $.1^103>, <$.1^99, $.1^203>, <$.1^188, $.1^247>, <$.1^144, $.1^85>, <$.1^338, $.1^246>, <$.1^150, $.1^147>, <$.1^58, $.1^97>, <$.1^208, $.1^207>, <$.1^196, $.1^297>, <$.1^315, $.1^106>, <$.1^173, $.1^183>, <$.1^53, $.1^73>, <2, $.1^33>, <$.1^47, $.1^20>, <$.1^185, $.1^213>, <$.1^20, $.1^287>, <$.1^29, $.1^265>, <$.1^259, $.1^330>, <$.1^30, $.1^191>, <$.1^34, $.1^244>, <$.1^144, $.1^13>, <$.1^180, $.1^146>, <$.1^325, $.1^142>, <$.1^150, $.1^249>, <$.1^271, $.1^339>, <$.1^159, 1>, <$.1^264, $.1^83>, <$.1^167, $.1^33>, <$.1^169, $.1^19>, <$.1^140, $.1^173>, <$.1^6, $.1^298>, <$.1^321, $.1^24>, <$.1^173, $.1^237>, <$.1^117, $.1^87>, <4, $.1^107>, <$.1^138, $.1^161>, <$.1^182, $.1^261>, <$.1^206, $.1^227>, <$.1^256, $.1^121>, <$.1^301, $.1^311>, <$.1^310, $.1^179>, <$.1^21, $.1^121>, <$.1^294, $.1^34>, <$.1^155, $.1^163>, <$.1^92, $.1^201>, <$.1^198, $.1^244>, <$.1^88, $.1^141>, <$.1^189, $.1^97>, <$.1^180, $.1^320>, <$.1^241, $.1^201>, <$.1^102, $.1^137>, <$.1^123, $.1^103>, <$.1^220, $.1^153>, <$.1^314, $.1^306>, <$.1^138, $.1^179>, <$.1^68, $.1^199>, <$.1^39, $.1^44>, <$.1^245, $.1^290>, <$.1^89, $.1^83>, <$.1^212, $.1^110>, <$.1^181, $.1^237>, <$.1^53, $.1^217>, <$.1^87, $.1^72>, <$.1^187, $.1^183>, <$.1^309, $.1^92>, <$.1^275, $.1^258>, <$.1^307, $.1^126>, <$.1^231, $.1^221>, <$.1^242, $.1^154>, <$.1^25, $.1^144>, <$.1^80, $.1^161>, <$.1^251, $.1^2>, <$.1^98, $.1^282>, <5, $.1^6>, <$.1^337, $.1^300>, <$.1^45, $.1^244>, <$.1^116, $.1^320>, <$.1^290, $.1^313>, <$.1^123, $.1^7>, <$.1^58, $.1^55>, <$.1^289, $.1^2>, <$.1^284, 0>, <$.1^248, $.1^177>, <$.1^241, $.1^267>, <$.1^218, $.1^263>, <$.1^134, $.1^187>, <$.1^207, $.1^130>, <$.1^20, $.1^263>, <$.1^44, $.1^255>, <6, $.1^322>, <$.1^220, $.1^129>, <6, $.1^82>, <$.1^101, $.1^10>, <$.1^226, $.1^230>, <$.1^145, $.1^136>, <$.1^178, $.1^237>, <$.1^261, $.1^21>, <$.1^241, $.1^273>, <$.1^2, $.1^300>, <$.1^192, $.1^76>, <$.1^260, $.1^98>, <$.1^41, $.1^311>, <$.1^313, $.1^230>, <$.1^339, $.1^270>, <$.1^299, $.1^71>, <$.1^178, $.1^189>, <$.1^156, $.1^60>, <$.1^223, $.1^298>, <$.1^102, $.1^47>, <$.1^308, $.1^99>, <$.1^82, $.1^97>, <$.1^326, $.1^268>, <$.1^21, $.1^241>, <$.1^148, $.1^174>, <$.1^78, $.1^146>, <1, $.1^133>, <$.1^240, $.1^288>, <$.1^229, $.1^196>, <$.1^34, $.1^46>, <$.1^39, $.1^8>, <$.1^177, $.1^139>, <$.1^89, $.1^131>, <$.1^178, $.1^3>, <$.1^80, $.1^71>, <$.1^117, $.1^327>, <$.1^246, $.1^200>, <$.1^137, $.1^216>, <$.1^205, $.1^217>, <$.1^112, $.1^66>, <$.1^317, $.1^159>, <$.1^297, $.1^73>, <$.1^309, $.1^74>, <$.1^86, $.1^50>, <$.1^294, $.1^76>, <$.1^259, $.1^6>, <$.1^302, $.1^333>, <$.1^339, $.1^120>, <$.1^100, $.1^312>, <$.1^86, $.1^200>, <$.1^242, $.1^172>, <$.1^257, $.1^209>, <$.1^337, $.1^324>, <$.1^260, $.1^152>, <$.1^116, $.1^290>, <$.1^43, $.1^95>, <$.1^31, $.1^2>, <$.1^326, $.1^40>, <$.1^93, $.1^326>, <$.1^319, $.1^189>, <$.1^43, $.1^173>, <$.1^261, $.1^33>, <$.1^287, $.1^107>, <$.1^142, $.1^245>, <$.1^43, $.1^185>, <$.1^185, $.1^69>, <$.1^132, $.1^234>, <$.1^326, $.1^304>, <$.1^197, $.1^252>, <$.1^21, $.1^127>, <$.1^9, $.1^281>, <$.1^147, $.1>, <$.1^100, $.1^186>, <$.1^110, $.1^290>, <$.1^290, $.1^43>, <$.1^255, $.1^191>, <$.1^328, $.1^226>, <$.1^253, $.1^124>, <$.1^70, $.1^252>, <$.1^268, $.1^267>, <$.1^71, $.1^157>, <$.1^185, $.1^45>, <$.1^174, $.1^304>, <$.1^16, $.1^270>, <$.1^47, $.1^188>, <$.1^109, $.1^218>, <$.1^258, $.1^243>, <$.1^187, $.1^147>, <$.1^281, $.1^173>, <1, $.1^127>, <$.1^81, $.1^64>, <$.1^314, $.1^222>, <$.1^85, $.1^148>, <$.1^235, $.1^190>, <$.1^143, $.1^279>, <$.1^25, $.1^324>, <$.1^157, $.1^295>, <$.1^202, $.1^89>, <$.1^75, $.1^239>, <$.1^59, $.1^13>, <$.1^151, $.1^128>, <$.1^313, $.1^170>, <$.1^118, $.1^323>, <$.1^22, $.1^85>, <$.1^206, $.1^65>, <$.1^169, $.1^187>, <$.1^296, $.1^41>, <$.1^255, $.1^155>, <$.1^224, $.1^226>, <$.1^339, $.1^264>, <$.1^64, $.1^175>, <$.1^121, $.1^128>, <$.1^24, $.1^147>, <$.1^199, $.1^294>, <$.1^216, $.1^295>, <$.1^177, $.1^127>, <$.1^282, $.1^59>, <$.1^187, $.1^3>, <$.1^309, $.1^152>, <$.1^119, $.1^46>, <$.1^281, $.1^323>, <$.1^148, $.1^216>, <$.1^67, $.1^313>, <$.1^326, $.1^100>, <$.1^334, $.1^125>, <$.1^151, $.1^302> ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host aula-a-siee13.uab.es. (158.109.66.13) Time: Mon Mar 15 13:48:56 2004 Input: R:=Integers(); P:=PolynomialRing(R); print "";print "apartat iv)"; polinomitexp:=function(q,r) llista:=[]; for i:= r-1 to 0 by -1 do llista:=Include(llista, q^i); end for; return llista; end function; polinomitexp(7,3); print "";print "apartat v)"; polinomin:=function(q,r) sum:=0; for i:=r-1 to 0 by -1 do sum:=sum+q^i; end for; return x^sum; end function; polinomit:=function(q,r) pol:=0; newlist:=polinomitexp(q,r); for i:=1 to #(newlist) do pol:=pol+x^newlist[i]; end for; return pol; end function; print "";print "apartat vi)"; puntsOlav:=func: a,b in GF(q,r)|Evaluate(polinomit(q,r),a) eq Evaluate(polinomin(q,r),b)}>; print "";print "apartat vii)"; exemples:=function(q,r) print("q^(2*r-1) és igual a:"); print q^(2*r-1); print("El cardinal dels punts Olav en aquest exemple és:"); return #(puntsOlav(q,r)); end function; print"";print "Exemple amb q=2 i r=3"; exemples(2,3); print"";print "Exemple amb q=3 i r=3"; exemples(3,3); print"";print "Exemple amb q=5 i r=3"; exemples(5,3); print"";print "Exemple amb q=3 i r=4"; exemples(3,4); print"";print "Exemple amb q=2 i r=4"; exemples(2,4); print "apartat viii)"; puntsOlav2:=function(q,r) po2:=[po:po in puntsOlav(q,r)|po[1] in GF(q) and po[2] in GF(q)]; return #(po2); end function; print"";print "Exemple amb q=2 i r=3"; puntsOlav2(2,3); print"";print "Exemple amb q=3 i r=3"; puntsOlav2(3,3); print"";print "Exemple amb q=5 i r=3"; puntsOlav2(5,3); print"";print "Exemple amb q=3 i r=4"; puntsOlav2(3,4); print"";print "Exemple amb q=2 i r=4"; puntsOlav2(2,4); /*Veiem que hi hauran q punts que pertanyin a GF(q)*/ Output: Magma V2.10-6 Mon Mar 15 2004 13:48:48 on modular [Seed = 3080850788] ------------------------------------- apartat iv) [ 49, 7, 1 ] apartat v) apartat vi) apartat vii) Exemple amb q=2 i r=3 q^(2*r-1) és igual a: 32 El cardinal dels punts Olav en aquest exemple és: 32 Exemple amb q=3 i r=3 q^(2*r-1) és igual a: 243 El cardinal dels punts Olav en aquest exemple és: 243 Exemple amb q=5 i r=3 q^(2*r-1) és igual a: 3125 El cardinal dels punts Olav en aquest exemple és: 3125 Exemple amb q=3 i r=4 q^(2*r-1) és igual a: 2187 El cardinal dels punts Olav en aquest exemple és: 2187 Exemple amb q=2 i r=4 q^(2*r-1) és igual a: 128 El cardinal dels punts Olav en aquest exemple és: 128 apartat viii) Exemple amb q=2 i r=3 2 Exemple amb q=3 i r=3 3 Exemple amb q=5 i r=3 5 Exemple amb q=3 i r=4 3 Exemple amb q=2 i r=4 2 Total time: 8.719 seconds, Total memory usage: 2.15MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 13:49:36 2004 Input: coef:= function (q,r) if ((r gt 0) and IsPrime(q)) then co:= [q^(r-1)]; for i:=2 to r do co:= co cat [q^(r-i)]; end for; end if; return co; end function; Z:=Integers(100); PT:=PolynomialRing(Z); t := function (q,r) lista:=coef(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + PT![0,1]^lista[i]; end for; return poly; end function; t(7,3); n := function (q,r) lista:=coef(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=PT![0,1]^exp; return poly; end function; n(7,3); n73:=n(7,3); t73:=t(7,3); punts_olav:=function (q,r) punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; return{punts}; end function; punts_olav(7,3); Output: Magma V2.10-6 Mon Mar 15 2004 13:49:33 on modular [Seed = 3198878784] ------------------------------------- x^49 + x^7 + x x^57 [
:20]( q: 7, r: 3 ) >> punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; ^ Runtime error in 'Evaluate': Incompatible rings Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 13:57:25 2004 Input: coef:= function (q,r) if ((r gt 0) and IsPrime(q)) then co:= [q^(r-1)]; for i:=2 to r do co:= co cat [q^(r-i)]; end for; end if; return co; end function; Z:=Integers(100); PT:=PolynomialRing(Z); t := function (q,r) lista:=coef(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + PT![0,1]^lista[i]; end for; return poly; end function; t(7,3); n := function (q,r) lista:=coef(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=PT![0,1]^exp; return poly; end function; n(7,3); n73:=n(7,3); t73:=t(7,3); punts_olav:=function (q,r) punts:=[ : a,b in GF(Z) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; return{punts}; end function; punts_olav(7,3); Output: Magma V2.10-6 Mon Mar 15 2004 13:57:22 on modular [Seed = 1515185804] ------------------------------------- x^49 + x^7 + x x^57 [
:20]( q: 7, r: 3 ) >> punts:=[ : a,b in GF(Z) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; ^ Runtime error in 'GF': Bad argument types Argument types given: RngIntRes Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 13:57:50 2004 Input: coef:= function (q,r) if ((r gt 0) and IsPrime(q)) then co:= [q^(r-1)]; for i:=2 to r do co:= co cat [q^(r-i)]; end for; end if; return co; end function; Z:=Integers(100); PT:=PolynomialRing(Z); t := function (q,r) lista:=coef(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + PT![0,1]^lista[i]; end for; return poly; end function; t(7,3); n := function (q,r) lista:=coef(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=PT![0,1]^exp; return poly; end function; n(7,3); n73:=n(7,3); t73:=t(7,3); punts_olav:=function (q,r) punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; return{punts}; end function; punts_olav(7,3); Output: Magma V2.10-6 Mon Mar 15 2004 13:57:47 on modular [Seed = 1668734860] ------------------------------------- x^49 + x^7 + x x^57 [
:20]( q: 7, r: 3 ) >> punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; ^ Runtime error in 'Evaluate': Incompatible rings Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 13:58:04 2004 Input: coef:= function (q,r) if ((r gt 0) and IsPrime(q)) then co:= [q^(r-1)]; for i:=2 to r do co:= co cat [q^(r-i)]; end for; end if; return co; end function; Z:=Integers(100); PT:=PolynomialRing(Z); t := function (q,r) lista:=coef(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + PT![0,1]^lista[i]; end for; return poly; end function; t(7,3); n := function (q,r) lista:=coef(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=PT![0,1]^exp; return poly; end function; n(7,3); n73:=n(7,3); t73:=t(7,3); punts_olav:=function (q,r) punts:=[ : a,b in GF(q^r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; return{punts}; end function; punts_olav(7,3); Output: Magma V2.10-6 Mon Mar 15 2004 13:58:01 on modular [Seed = 1952565385] ------------------------------------- x^49 + x^7 + x x^57 [
:20]( q: 7, r: 3 ) >> punts:=[ : a,b in GF(q^r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; ^ Runtime error in 'Evaluate': Incompatible rings Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 14:00:35 2004 Input: coef:= function (q,r) if ((r gt 0) and IsPrime(q)) then co:= [q^(r-1)]; for i:=2 to r do co:= co cat [q^(r-i)]; end for; end if; return co; end function; Z:=Integers(100); PT:=PolynomialRing(Z); t := function (q,r) lista:=coef(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + PT![0,1]^lista[i]; end for; return poly; end function; t(7,3); n := function (q,r) lista:=coef(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=PT![0,1]^exp; return poly; end function; n(7,3); n73:=n(7,3); t73:=t(7,3); punts_olav:=function (q,r) punts:=[ : a,b in GF(q,r) | Evaluate(PT![0,1]^3,a) eq Evaluate(PT![0,1]^3,b)]; return{punts}; end function; punts_olav(7,3); Output: Magma V2.10-6 Mon Mar 15 2004 14:00:32 on modular [Seed = 35110678] ------------------------------------- x^49 + x^7 + x x^57 [
:20]( q: 7, r: 3 ) >> punts:=[ : a,b in GF(q,r) | Evaluate(PT![0,1]^3,a) eq Evaluate(PT![0,1 ^ Runtime error in 'Evaluate': Incompatible rings Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 14:02:10 2004 Input: coef:= function (q,r) if ((r gt 0) and IsPrime(q)) then co:= [q^(r-1)]; for i:=2 to r do co:= co cat [q^(r-i)]; end for; end if; return co; end function; Z:=Integers(100); PT:=PolynomialRing(Z); t := function (q,r) lista:=coef(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + PT![0,1]^lista[i]; end for; return poly; end function; t(7,3); n := function (q,r) lista:=coef(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=PT![0,1]^exp; return poly; end function; n(7,3); n73:=n(7,3); t73:=t(7,3); Evaluate(n(7,3),x); punts_olav:=function (q,r) punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; return{punts}; end function; punts_olav(7,3); Output: Magma V2.10-6 Mon Mar 15 2004 14:02:07 on modular [Seed = 623941838] ------------------------------------- x^49 + x^7 + x x^57 x^57 [
:21]( q: 7, r: 3 ) >> punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)] ^ Runtime error in 'Evaluate': Incompatible rings Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 14:02:30 2004 Input: coef:= function (q,r) if ((r gt 0) and IsPrime(q)) then co:= [q^(r-1)]; for i:=2 to r do co:= co cat [q^(r-i)]; end for; end if; return co; end function; Z:=Integers(100); PT:=PolynomialRing(Z); t := function (q,r) lista:=coef(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + PT![0,1]^lista[i]; end for; return poly; end function; t(7,3); n := function (q,r) lista:=coef(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=PT![0,1]^exp; return poly; end function; n(7,3); n73:=n(7,3); t73:=t(7,3); Evaluate(n(7,2),x); punts_olav:=function (q,r) punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; return{punts}; end function; punts_olav(7,3); Output: Magma V2.10-6 Mon Mar 15 2004 14:02:27 on modular [Seed = 792367784] ------------------------------------- x^49 + x^7 + x x^57 x^8 [
:21]( q: 7, r: 3 ) >> punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)] ^ Runtime error in 'Evaluate': Incompatible rings Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 14:04:07 2004 Input: coef:= function (q,r) if ((r gt 0) and IsPrime(q)) then co:= [q^(r-1)]; for i:=2 to r do co:= co cat [q^(r-i)]; end for; end if; return co; end function; Z:=Integers(100); PT:=PolynomialRing(Z); t := function (q,r) lista:=coef(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + PT![0,1]^lista[i]; end for; return poly; end function; t(7,3); n := function (q,r) lista:=coef(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=PT![0,1]^exp; return poly; end function; n(7,3); n73:=n(7,3); t73:=t(7,3); punts_olav:=function (q,r) punts:=[ : a,b in GF(q,r) | ( (Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)) and (a,b in Z) )]; return{punts}; end function; punts_olav(7,3); Output: Magma V2.10-6 Mon Mar 15 2004 14:04:04 on modular [Seed = 824479569] ------------------------------------- x^49 + x^7 + x x^57 [
:20]( q: 7, r: 3 ) >> punts:=[ : a,b in GF(q,r) | ( (Evaluate(n(q,r),a) eq Evaluate(t(q,r), ^ Runtime error in 'Evaluate': Incompatible rings Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 14:07:58 2004 Input: coef:= function (q,r) if ((r gt 0) and IsPrime(q)) then co:= [q^(r-1)]; for i:=2 to r do co:= co cat [q^(r-i)]; end for; end if; return co; end function; coe:=coef(7,3); Z:=Integers(100); PT:=PolynomialRing(Z); t := function (q,r) lista:=coef(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + PT![0,1]^lista[i]; end for; return poly; end function; t(7,3); n := function (q,r) lista:=coef(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=PT![0,1]^exp; return poly; end function; n(7,3); n73:=n(7,3); t73:=t(7,3); punts_olav:=function (q,r) punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; return{punts}; end function; punts_olav(7,3); Output: Magma V2.10-6 Mon Mar 15 2004 14:07:55 on modular [Seed = 3235217295] ------------------------------------- x^49 + x^7 + x x^57 [
:21]( q: 7, r: 3 ) >> punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)] ^ Runtime error in 'Evaluate': Incompatible rings Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 14:08:10 2004 Input: coef:= function (q,r) if ((r gt 0) and IsPrime(q)) then co:= [q^(r-1)]; for i:=2 to r do co:= co cat [q^(r-i)]; end for; end if; return co; end function; coe:=coef(7,3);coe; Z:=Integers(100); PT:=PolynomialRing(Z); t := function (q,r) lista:=coef(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + PT![0,1]^lista[i]; end for; return poly; end function; t(7,3); n := function (q,r) lista:=coef(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=PT![0,1]^exp; return poly; end function; n(7,3); n73:=n(7,3); t73:=t(7,3); punts_olav:=function (q,r) punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; return{punts}; end function; punts_olav(7,3); Output: Magma V2.10-6 Mon Mar 15 2004 14:08:06 on modular [Seed = 3386668698] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x x^57 [
:21]( q: 7, r: 3 ) >> punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)] ^ Runtime error in 'Evaluate': Incompatible rings Total time: 3.289 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 14:08:12 2004 Input: coef:= function (q,r) if ((r gt 0) and IsPrime(q)) then co:= [q^(r-1)]; for i:=2 to r do co:= co cat [q^(r-i)]; end for; end if; return co; end function; coe:=coef(7,3);coe; Z:=Integers(100); PT:=PolynomialRing(Z); t := function (q,r) lista:=coef(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + PT![0,1]^lista[i]; end for; return poly; end function; t(7,3); n := function (q,r) lista:=coef(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=PT![0,1]^exp; return poly; end function; n(7,3); n73:=n(7,3); t73:=t(7,3); punts_olav:=function (q,r) punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; return{punts}; end function; punts_olav(7,3); Output: Magma V2.10-6 Mon Mar 15 2004 14:08:08 on modular [Seed = 3569445768] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x x^57 [
:21]( q: 7, r: 3 ) >> punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)] ^ Runtime error in 'Evaluate': Incompatible rings Total time: 3.239 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee38.uab.es. (158.109.66.38) Time: Mon Mar 15 14:09:04 2004 Input: expo:= function (q,r) if ((r gt 0) and IsPrime(q)) then exp:= [q^(r-1)]; for i:=2 to r do exp:= exp cat [q^(r-i)]; end for; end if; return exp; end function; Z:=Integers(100); PT:=PolynomialRing(Z); t := function (q,r) lista:=expo(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + PT![0,1]^lista[i]; end for; return poly; end function; t(7,3); n := function (q,r) lista:=expo(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=PT![0,1]^exp; return poly; end function; n(7,3); n73:=n(7,3); t73:=t(7,3); punts_olav:=function (q,r) punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; return{punts}; end function; punts_olav(7,3); Output: Magma V2.10-6 Mon Mar 15 2004 14:09:01 on modular [Seed = 3687736530] ------------------------------------- x^49 + x^7 + x x^57 [
:20]( q: 7, r: 3 ) >> punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)] ^ Runtime error in 'Evaluate': Incompatible rings Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.49.169) Time: Mon Mar 15 16:50:13 2004 Input: n7_3:=PolynomialRing(Integers()); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Integers()); t7_3:=x^49+x^7+x; n7_3; t7_3; Olav:={ : a,b in GF(7^3) | Evaluate(n7_3,a) eq Evaluate(t7_3,b)}; Output: Magma V2.10-6 Mon Mar 15 2004 16:50:06 on modular [Seed = 1565210645] ------------------------------------- x^57 x^49 + x^7 + x Total time: 6.879 seconds, Total memory usage: 2.98MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.49.169) Time: Mon Mar 15 16:50:35 2004 Input: n7_3:=PolynomialRing(Integers()); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Integers()); t7_3:=x^49+x^7+x; n7_3; t7_3; Olav:={ : a,b in GF(7^3) | Evaluate(n7_3,a) eq Evaluate(t7_3,b)}; Olav; Output: Magma V2.10-6 Mon Mar 15 2004 16:50:28 on modular [Seed = 1668613633] ------------------------------------- x^57 x^49 + x^7 + x { <$.1^189, $.1^104>, <$.1^268, $.1^223>, <$.1^266, $.1^125>, <$.1^340, $.1^294>, <$.1^245, $.1^281>, <$.1^173, $.1^218>, <1, $.1^7>, <$.1^85, $.1^58>, <$.1^167, $.1^140>, <$.1^108, $.1^100>, <$.1^330, $.1^66>, <$.1^10, $.1^326>, <$.1^303, $.1^319>, <$.1^87, $.1^261>, <$.1^214, $.1^244>, <$.1^20, $.1^201>, <$.1^116, $.1^270>, <$.1^222, $.1^156>, <$.1^338, $.1^201>, <4, $.1^10>, <$.1^19, $.1^188>, <$.1^204, $.1^70>, <$.1^301, $.1^147>, <$.1^56, $.1^311>, <$.1^101, $.1^210>, <$.1^311, $.1^210>, <$.1^238, $.1^229>, <$.1^41, $.1^41>, <$.1^63, $.1^261>, <4, $.1^195>, <$.1^219, $.1^303>, <$.1^144, $.1^339>, <$.1^329, $.1^43>, <$.1^319, $.1^154>, <3, $.1^150>, <$.1^56, $.1^78>, <$.1^237, $.1^327>, <$.1^134, $.1^262>, <$.1^147, $.1^167>, <$.1^160, $.1^223>, <$.1^284, $.1^329>, <$.1^302, $.1^273>, <$.1^239, $.1^140>, <$.1^196, $.1^42>, <$.1^8, $.1^262>, <$.1^250, $.1^318>, <$.1^294, $.1^11>, <$.1^149, $.1^40>, <$.1^22, $.1^119>, <$.1^339, $.1^308>, <$.1^238, $.1^126>, <$.1^48, $.1^197>, <$.1^328, $.1^32>, <$.1^32, $.1^273>, <$.1^97, $.1^205>, <$.1^184, $.1^174>, <$.1^42, $.1^112>, <$.1^176, $.1^251>, <$.1^133, $.1^82>, <$.1^53, $.1^202>, <$.1^135, $.1^167>, <$.1^218, $.1^86>, <$.1^311, $.1^89>, <$.1^87, $.1^28>, <$.1^187, $.1^21>, <$.1^98, $.1^111>, <$.1^104, $.1^214>, <$.1^102, $.1^131>, <$.1^319, $.1^3>, <$.1^314, $.1^246>, <$.1^42, $.1^275>, <$.1^27, $.1^196>, <$.1^267, $.1^168>, <$.1^249, $.1^168>, <$.1^81, $.1^117>, <$.1^291, $.1^271>, <$.1^72, $.1^197>, <$.1^293, $.1^43>, <$.1^297, $.1^135>, <$.1^26, $.1^151>, <$.1^289, $.1^52>, <$.1^239, $.1^295>, <$.1^268, $.1^277>, <$.1^319, $.1^232>, <$.1^122, $.1^226>, <$.1^93, $.1^178>, <$.1^212, $.1^204>, <$.1^82, $.1^244>, <$.1^217, $.1^64>, <$.1^327, $.1^92>, <$.1^272, $.1^214>, <$.1^72, $.1^148>, <$.1^49, $.1^123>, <$.1^200, $.1^211>, <$.1^146, $.1^311>, <$.1^106, $.1^18>, <$.1^46, $.1^83>, <$.1^223, $.1^155>, <$.1^159, $.1^69>, <$.1^37, $.1^59>, <$.1^147, 2>, <$.1^240, $.1^49>, <$.1^294, $.1^338>, <$.1^294, $.1^215>, <$.1^3, $.1^319>, <$.1^177, $.1^172>, <$.1^277, 1>, <$.1^152, $.1^234>, <$.1^116, $.1^214>, <$.1^174, $.1^16>, <$.1^132, $.1^156>, <$.1^72, $.1^195>, <$.1^45, $.1^330>, <$.1^4, $.1^315>, <$.1^34, $.1^6>, <$.1^303, $.1^92>, <$.1^180, $.1^14>, <$.1^307, $.1^82>, <$.1^83, $.1^20>, <0, $.1^300>, <$.1^273, $.1^319>, <$.1^241, $.1^256>, <$.1^29, $.1^9>, <$.1^331, $.1^147>, <$.1^72, $.1^199>, <$.1^180, $.1^77>, <$.1^293, $.1^63>, <$.1^19, $.1^73>, <1, $.1^175>, <$.1^20, $.1^184>, <$.1^303, $.1^28>, <$.1^31, $.1^216>, <$.1^198, $.1^25>, <$.1^209, $.1^334>, <$.1^47, $.1^334>, <$.1^277, $.1^188>, <$.1^85, $.1^332>, <$.1^281, $.1^292>, <$.1^276, $.1^215>, <$.1^212, $.1^245>, <$.1^187, $.1^22>, <$.1^264, $.1^159>, <$.1^184, $.1^101>, <$.1^91, $.1^256>, <$.1^304, $.1^83>, <$.1^183, $.1^117>, <$.1^14, $.1^311>, <$.1^98, $.1^212>, <$.1^222, $.1^146>, <$.1^174, $.1^100>, <$.1^12, $.1^37>, <$.1^274, $.1^81>, <$.1^80, $.1^93>, <$.1^81, $.1^62>, <$.1^313, $.1^59>, <$.1^200, $.1^309>, <$.1^150, $.1^339>, <$.1^277, $.1^71>, <$.1^64, $.1^6>, <$.1^31, $.1^21>, <$.1^150, $.1^314>, <$.1^262, $.1^294>, <$.1^25, $.1^252>, <$.1^339, $.1^248>, <$.1^8, $.1^12>, <$.1^36, $.1^199>, <$.1^222, $.1^233>, <$.1^108, $.1^120>, <$.1^289, $.1^216>, <$.1^194, $.1^60>, <$.1^133, $.1^68>, <$.1^274, $.1^224>, <$.1^101, $.1^41>, <$.1^141, $.1^88>, <$.1^21, $.1^96>, <$.1^8, $.1^5>, <$.1^109, $.1^169>, <$.1^247, $.1^71>, <$.1^126, $.1^321>, <$.1^159, $.1^24>, <$.1^279, $.1^135>, <$.1^104, $.1^191>, <$.1^284, $.1^262>, <$.1^267, $.1^150>, <$.1^204, $.1^233>, <$.1^300, $.1^199>, <$.1^294, $.1^240>, <$.1^131, $.1^33>, <$.1^181, $.1^21>, <$.1^53, $.1^55>, <$.1^91, $.1^254>, <$.1^221, $.1^99>, <$.1^117, $.1^62>, <$.1^32, $.1^79>, <$.1^258, $.1^137>, <$.1^96, $.1>, <$.1^270, $.1^288>, <$.1^202, $.1^85>, <$.1^270, $.1^132>, <$.1^10, $.1^149>, <$.1^229, $.1^127>, <$.1^108, $.1^288>, <$.1^72, $.1^338>, <$.1^170, $.1^130>, <$.1^284, $.1^163>, <$.1^251, $.1^296>, <$.1^259, $.1^320>, <$.1^109, $.1^189>, <$.1^80, $.1^151>, <$.1^135, $.1^178>, <$.1^275, $.1^13>, <$.1^319, $.1^256>, <$.1^323, $.1^138>, <$.1^276, $.1^148>, <$.1^230, $.1^251>, <$.1^33, $.1^24>, <$.1^202, $.1^161>, <$.1^175, $.1^232>, <$.1^248, $.1^78>, <$.1^78, $.1^148>, <$.1^311, $.1^75>, <$.1^29, $.1^75>, <$.1^225, $.1^241>, <$.1^239, $.1^33>, <$.1^37, $.1^36>, <$.1^28, $.1^242>, <$.1^23, $.1^287>, <$.1^238, $.1^225>, <$.1^259, $.1^64>, <$.1^317, $.1^206>, <$.1^64, $.1^298>, <$.1^193, $.1^160>, <$.1^255, $.1^291>, <$.1^275, $.1^142>, <$.1^125, $.1^75>, <$.1^104, $.1^204>, <$.1^92, $.1^84>, <$.1^193, $.1^106>, <$.1^78, $.1^337>, <$.1^112, $.1^235>, <$.1^169, $.1^123>, <$.1^277, $.1^67>, <$.1^9, 2>, <$.1^173, $.1^334>, <$.1^110, $.1^245>, <$.1^18, $.1^2>, <$.1^23, $.1^118>, <$.1^103, $.1^232>, <$.1^106, $.1^32>, <$.1^53, $.1^210>, <$.1^71, $.1^9>, <$.1^189, $.1^271>, <$.1^151, $.1^324>, <$.1^304, $.1^253>, <$.1^257, $.1^41>, <$.1^174, $.1^321>, <$.1^330, $.1^100>, <$.1^104, $.1^262>, <$.1^51, $.1^327>, <$.1^186, $.1^240>, <$.1^208, $.1^239>, <$.1^249, $.1^308>, <$.1^253, $.1^169>, <$.1^147, $.1^248>, <$.1^8, $.1^124>, <$.1^181, $.1^82>, <$.1^20, $.1^124>, <$.1^73, $.1^59>, <$.1^88, $.1^198>, <$.1^150, $.1^70>, <$.1^289, $.1^213>, <$.1^325, $.1^169>, <$.1^209, $.1^264>, <$.1^295, $.1^134>, <$.1^11, $.1^41>, <$.1^209, $.1^158>, <$.1^99, $.1^104>, <$.1^277, $.1^54>, <$.1^204, $.1^25>, <$.1^12, $.1^7>, <$.1^203, $.1^299>, <$.1^172, $.1^223>, <$.1^325, $.1^22>, <$.1^47, $.1^80>, <$.1^203, $.1^250>, <$.1^275, $.1^218>, <$.1^46, $.1^229>, <$.1^9, $.1^24>, <$.1^292, $.1^81>, <$.1^329, $.1^140>, <$.1^115, $.1^67>, <$.1^224, $.1^12>, <2, $.1^120>, <6, 2>, <$.1^317, $.1^250>, <$.1^338, $.1^246>, <$.1^132, $.1>, <$.1^326, $.1^151>, <$.1^247, $.1^254>, <$.1^208, $.1^207>, <$.1^221, $.1^310>, <$.1^173, $.1^183>, <$.1^206, $.1^128>, <$.1^238, $.1^230>, <$.1^36, $.1^2>, <$.1^50, $.1^116>, <$.1^47, $.1^20>, <$.1^50, $.1^329>, <$.1^58, $.1^305>, <$.1^2, $.1^273>, <$.1^39, $.1^28>, <6, $.1^187>, <$.1^306, $.1^159>, <$.1^333, $.1^24>, <$.1^323, $.1^301>, <$.1^157, $.1^177>, <$.1^34, $.1^244>, <$.1^50, $.1^79>, <$.1^212, $.1^184>, <$.1^132, $.1^137>, <$.1^310, $.1^207>, <$.1^180, $.1^146>, <$.1^336, $.1^137>, <$.1^239, $.1^299>, <$.1^338, $.1^110>, <$.1^18, $.1^131>, <$.1^147, $.1^291>, <2, $.1^14>, <$.1^214, $.1^235>, <$.1^53, $.1^287>, <$.1^167, $.1^33>, <$.1^321, $.1^24>, <$.1^206, $.1^84>, <$.1^162, $.1^267>, <$.1^161, $.1^299>, <$.1^34, $.1^230>, <$.1^92, $.1^201>, <$.1^312, $.1^263>, <$.1^239, $.1^218>, <$.1^155, $.1^206>, <$.1^220, $.1^153>, <$.1^102, $.1^137>, <$.1^128, $.1^246>, <$.1^271, $.1^320>, <$.1^288, $.1^49>, <$.1^179, $.1^264>, <$.1^39, $.1^44>, <$.1^217, $.1^232>, <$.1^202, $.1^81>, <$.1^146, $.1^273>, <$.1^297, 2>, <$.1^164, $.1^251>, <$.1^212, $.1^110>, <$.1^268, $.1^224>, <$.1^182, $.1^204>, <$.1^309, $.1^92>, <$.1^134, $.1^184>, <$.1^184, $.1^328>, <$.1^74, $.1^115>, <$.1^25, $.1^144>, <$.1^220, $.1^331>, <$.1^248, $.1^214>, <$.1^75, $.1^178>, <$.1^58, $.1^340>, <$.1^216, $.1^314>, <$.1^47, $.1^30>, <$.1^38, $.1^204>, <$.1^32, $.1^245>, <$.1^290, $.1^313>, <$.1^216, $.1^11>, <$.1^81, $.1^150>, <$.1^219, $.1^261>, <$.1^291, $.1^274>, <$.1^230, $.1^245>, <$.1^84, $.1^87>, <$.1^154, $.1^18>, <$.1^226, $.1^230>, <$.1^190, $.1^223>, <$.1^25, $.1^213>, <2, $.1^10>, <$.1^12, $.1^159>, <$.1^280, $.1^294>, <$.1^101, $.1^91>, <$.1^47, $.1^255>, <$.1^28, $.1^305>, <$.1^58, $.1^101>, <$.1^220, $.1^253>, <$.1^196, $.1^23>, <$.1^43, $.1^290>, <$.1^21, $.1^241>, <$.1^182, $.1^191>, <$.1^324, $.1^159>, <$.1^47, $.1^287>, <$.1^226, $.1^253>, <$.1^174, $.1^77>, <$.1^148, $.1^174>, <6, $.1^283>, <$.1^78, $.1^146>, <$.1^339, $.1^268>, <$.1^240, $.1^288>, <4, $.1^312>, <$.1^84, $.1^195>, <$.1^117, $.1^327>, <$.1^158, $.1^111>, <$.1^28, $.1^277>, <$.1^16, $.1^225>, <$.1^322, $.1^253>, <5, $.1^135>, <$.1^320, $.1^47>, <$.1^191, $.1^250>, <$.1^282, $.1^156>, <$.1, $.1^189>, <$.1^140, $.1^270>, <$.1^161, $.1^287>, <$.1^100, $.1^326>, <$.1^139, $.1^82>, <$.1^337, $.1^324>, <$.1^13, $.1^73>, <$.1^254, $.1^128>, <$.1^170, $.1^212>, <$.1^319, $.1^189>, <$.1^338, $.1^115>, <$.1^336, $.1^49>, <$.1^73, $.1^3>, <$.1^130, $.1^45>, <$.1^289, $.1^160>, <$.1^260, $.1^12>, <$.1^59, $.1^249>, <$.1^317, $.1^91>, <$.1^173, $.1^287>, <$.1^320, $.1^60>, <$.1^18, $.1^337>, <$.1^251, $.1^255>, <$.1^289, $.1^22>, <$.1^123, $.1^291>, <$.1^258, $.1^146>, <$.1^187, $.1^147>, <$.1^87, $.1^269>, <$.1^73, $.1^290>, <$.1^184, $.1^145>, <$.1^96, $.1^240>, <$.1^25, $.1^324>, <$.1^48, $.1^37>, <$.1^272, $.1^226>, <$.1^321, $.1^44>, <$.1^102, $.1^132>, <$.1^331, $.1^205>, <$.1^198, $.1^307>, <$.1^45, $.1^24>, <$.1^51, $.1^269>, <$.1^59, $.1^13>, <$.1^9, $.1^258>, <$.1^110, $.1^329>, <$.1^186, 5>, <$.1^22, $.1^85>, <$.1^126, $.1>, <$.1^198, $.1^14>, <$.1^224, $.1^226>, <$.1^299, $.1^250>, <$.1^27, $.1^117>, <$.1^253, $.1^36>, <$.1^235, $.1^27>, <$.1^124, $.1^225>, <$.1^160, $.1^81>, <$.1^277, $.1^123>, <$.1^49, $.1^21>, <$.1^293, $.1^80>, <$.1^52, $.1^200>, <$.1^277, $.1^194>, <$.1^84, $.1^90>, <$.1^303, $.1^302>, <$.1^187, $.1^3>, <$.1^186, $.1^132>, <$.1^151, $.1^316>, <$.1^119, $.1^46>, <$.1^238, $.1^326>, <$.1^142, $.1^326>, <$.1^157, $.1^320>, <$.1^279, $.1^308>, <$.1^270, $.1>, <$.1^290, $.1^47>, <$.1^74, $.1^110>, <$.1^9, $.1^268>, <$.1^111, $.1^319>, <$.1^218, $.1^139>, <$.1^275, $.1^41>, <$.1^78, $.1^156>, <$.1^240, $.1^337>, <$.1^216, $.1>, <$.1^273, $.1^4>, <$.1^211, $.1^134>, <$.1^143, $.1^99>, <$.1^61, $.1^123>, <$.1^276, $.1^16>, <$.1^129, $.1^241>, <$.1^7, $.1^68>, <$.1^256, $.1^174>, <$.1^31, $.1^203>, <$.1^254, $.1^217>, <$.1^39, 2>, <$.1^212, $.1^151>, <$.1^19, $.1^106>, <$.1^164, $.1^93>, <$.1^339, $.1^258>, <$.1^156, $.1^131>, <$.1^13, $.1^68>, <$.1^204, $.1^10>, <$.1^288, $.1^337>, <$.1^266, $.1^78>, <$.1^332, $.1^163>, <$.1^335, $ ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 3(NXDOMAIN) (204.76.113.254) Time: Mon Mar 15 17:20:41 2004 Input: x+(x/100*15)=17000 Output: Magma V2.10-6 Mon Mar 15 2004 17:20:38 on modular [Seed = 975984202] ------------------------------------- >> x+(x/100*15)=17000; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (204.76.113.254) Time: Mon Mar 15 17:21:50 2004 Input: x*x Output: Magma V2.10-6 Mon Mar 15 2004 17:21:47 on modular [Seed = 3386877428] ------------------------------------- >> x*x; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.49.169) Time: Mon Mar 15 17:28:02 2004 Input: //SERGIO DIAZ GONZALEZ //DAVID PORTABELLA CANADELL //Grup lliurament: C-4 //Pregunta 1 > res := {i:i in [4..366 by 7]}; > res; { 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 } //Pregunta 2 //2.1 Mt := {m: m in M | Trace(m) eq 0}; > #Mt; 64 //2.2 > Mf := {m: m in M | (m[1,1] eq m[2,1]) and (m[1,2] eq m[2,2])}; > #Mf; 16 //2.3 > Mtf:=Mt meet Mf; > #Mtf; 4 //2.4 > M4:=[ Random(M) : i in [1..100000] ]; > M4f:=[i:i in M4 | i in Mf]; > #M4f; 6385 > M4t:=[i:i in M4 | i in Mt]; > #M4t; 25050 > M4tf:=[i:i in M4 | i in Mtf]; > #M4tf; 1575 // Sí que és raonable, ja que es mantenen les proporcions inicials on hi ha més matrius pertanyents a M4t. //Pregunta 3 //3.1 > t7_3:=PolynomialRing(Integers()); > t7_3:=x^49+x^7+x; > Coefficients(t7_3); [ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] //3.2 > n7_3:=PolynomialRing(Integers()); > n7_3:=x^(49+7+1); > t7_3:=PolynomialRing(Integers()); > t7_3:=x^49+x^7+x; > n7_3; x^57 > t7_3; x^49 + x^7 + x //3.3 > Olav:={ : a,b in GF(7^3) | Evaluate(n7_3,a) eq Evaluate(t7_3,b)}; //3.4 > exp:= func ; > exp(7,3); [ 1, 7, 49 ] //3.5 > nq_r:= function (q,r) P:=PolynomialRing(Integers()); exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; > nq_r(7,3); x^57 > tq_r:= function (q,r) P:=PolynomialRing(Integers()); exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; > tq_r(7,3); x^49 + x^7 + x //3.6 > olavq_r:= function (q,r) P:=PolynomialRing(Integers()); exp:= func ; return ( { : a,b in GF(q^r) | Evaluate(nq_r(q,r),a) eq Evaluate(tq_r(q,r),b)}); end function; //3.7 > #olavq_r(2,1) eq 2^(2*1-1); true > #olavq_r(4,2) eq 2^(2*2-1); true > #olavq_r(5,3) eq 5^(2*3-1); true > #olavq_r(1,2) eq 1^(2*2-1); true > #olavq_r(2,6) eq 2^(2*6-1); true //3.8 > olav_q:= function (q,r) return ( { : a,b in GF(q) | in olavq_r(q,r) }); end function; Output: Magma V2.10-6 Mon Mar 15 2004 17:27:59 on modular [Seed = 3891366478] ------------------------------------- { 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 } >> Mt := {m: m in M | Trace(m) eq 0}; ^ User error: bad syntax >> #Mt; ^ User error: Identifier 'Mt' has not been declared or assigned >> Mf := {m: m in M | (m[1,1] eq m[2,1]) and (m[1,2] eq m[2,2])}; ^ User error: bad syntax >> #Mf; ^ User error: Identifier 'Mf' has not been declared or assigned >> Mtf:=Mt meet Mf; ^ User error: bad syntax >> #Mtf; ^ User error: Identifier 'Mtf' has not been declared or assigned >> M4:=[ Random(M) : i in [1..100000] ]; ^ User error: bad syntax >> M4f:=[i:i in M4 | i in Mf]; ^ User error: Identifier 'M4' has not been declared or assigned >> #M4f; ^ User error: Identifier 'M4f' has not been declared or assigned >> M4t:=[i:i in M4 | i in Mt]; ^ User error: bad syntax >> #M4t; ^ User error: Identifier 'M4t' has not been declared or assigned >> M4tf:=[i:i in M4 | i in Mtf]; ^ User error: bad syntax >> #M4tf; ^ User error: Identifier 'M4tf' has not been declared or assigned >> t7_3:=PolynomialRing(Integers()); ^ User error: bad syntax >> t7_3:=x^49+x^7+x; ^ User error: Identifier 'x' has not been declared or assigned >> Coefficients(t7_3); ^ User error: Identifier 't7_3' has not been declared or assigned >> n7_3:=PolynomialRing(Integers()); ^ User error: bad syntax >> n7_3:=x^(49+7+1); ^ User error: Identifier 'x' has not been declared or assigned >> n7_3; ^ User error: Identifier 'n7_3' has not been declared or assigned >> t7_3; ^ User error: bad syntax >> Olav:={ : a,b in GF(7^3) | Evaluate(n7_3,a) eq Evaluate(t7_3,b)}; ^ User error: bad syntax [ 1, 7, 49 ] >> nq_r:= function (q,r) ^ User error: bad syntax >> return ( x^(&+[j : j in exp(q,r)]) ); ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> nq_r(7,3); ^ User error: Identifier 'nq_r' has not been declared or assigned >> tq_r:= function (q,r) ^ User error: bad syntax >> return ( &+[x^i : i in exp(q,r)] ); ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> tq_r(7,3); ^ User error: Identifier 'tq_r' has not been declared or assigned >> olavq_r:= function (q,r) ^ User error: bad syntax >> return ( { : a,b in GF(q^r) | Evaluate(nq_r(q,r),a) eq Evalua ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> #olavq_r(2,1) eq 2^(2*1-1); ^ User error: Identifier 'olavq_r' has not been declared or assigned >> #olavq_r(4,2) eq 2^(2*2-1); ^ User error: bad syntax >> #olavq_r(5,3) eq 5^(2*3-1); ^ User error: bad syntax >> #olavq_r(1,2) eq 1^(2*2-1); ^ User error: bad syntax >> #olavq_r(2,6) eq 2^(2*6-1); ^ User error: bad syntax >> olav_q:= function (q,r) ^ User error: bad syntax >> return ( { : a,b in GF(q) | in olavq_r(q,r) }); ^ User error: A 'return' can only be used inside a procedure or function >> end function;; ^ User error: bad syntax Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.49.169) Time: Mon Mar 15 17:31:44 2004 Input: t7_3:=PolynomialRing(Integers()); t7_3:=x^49+x^7+x; Coefficients(t7_3); n7_3:=PolynomialRing(Integers()); n7_3:=x^(49+7+1); t7_3:=PolynomialRing(Integers()); t7_3:=x^49+x^7+x; n7_3; t7_3; Olav:={ : a,b in GF(7^3) | Evaluate(n7_3,a) eq Evaluate(t7_3,b)}; exp:= func ; exp(7,3); nq_r:= function (q,r) P:=PolynomialRing(Integers()); exp:= func ; return ( x^(&+[j : j in exp(q,r)]) ); end function; nq_r(7,3); tq_r:= function (q,r) P:=PolynomialRing(Integers()); exp:= func ; return ( &+[x^i : i in exp(q,r)] ); end function; tq_r(7,3); olavq_r:= function (q,r) P:=PolynomialRing(Integers()); exp:= func ; return ( { : a,b in GF(q^r) | Evaluate(nq_r(q,r),a) eq Evaluate(tq_r(q,r),b)}); end function; #olavq_r(2,1) eq 2^(2*1-1); #olavq_r(4,2) eq 2^(2*2-1); #olavq_r(5,3) eq 5^(2*3-1); #olavq_r(1,2) eq 1^(2*2-1); #olavq_r(2,6) eq 2^(2*6-1); olav_q:= function (q,r) return ( { : a,b in GF(q) | in olavq_r(q,r) }); end function; olav_q(5,3); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Mar 15 2004 17:31:21 on modular [Seed = 4125334282] ------------------------------------- [ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] x^57 x^49 + x^7 + x [ 1, 7, 49 ] x^57 x^49 + x^7 + x true false true [
:27]( q: 1, r: 2 ) >> return ( { : a,b in GF(q^r) | Evaluate(nq_r(q,r),a) eq Evalua ^ Runtime error in 'GF': Argument 1 (1) should be >= 2 true Errors: /home/mfd/gomagma: line 2: 1715 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Mon Mar 15 18:21:57 2004 Input: P3 := PolynomialRing(Integers(3)); f := P3 ! [ 2, 2, 1]; P2 := PolynomialRing(Integers(2)); g := P2 ! [ 1, 1, 0, 0, 1]; P5 := PolynomialRing(Integers(5)); h := P5 ! [ 3, 2, 1]; i := P3 ! [ 1, 2, 1]; G9 := ext < P3 | f>; Output: Magma V2.10-6 Mon Mar 15 2004 18:21:54 on modular [Seed = 1952583329] ------------------------------------- >> G9 := ext < P3 | f>; ^ Runtime error: No constructor provided for this type of object Total time: 2.979 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Mon Mar 15 18:23:17 2004 Input: P3 := PolynomialRing(Integers(3)); f := P3 ! [ 2, 2, 1]; P2 := PolynomialRing(Integers(2)); g := P2 ! [ 1, 1, 0, 0, 1]; P5 := PolynomialRing(Integers(5)); h := P5 ! [ 3, 2, 1]; i := P3 ! [ 1, 2, 1]; K := GF(9); G9 := ext < K | f>; Output: Magma V2.10-6 Mon Mar 15 2004 18:23:14 on modular [Seed = 2053898463] ------------------------------------- >> G9 := ext < K | f>; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 3.049 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Mon Mar 15 18:23:37 2004 Input: P3 := PolynomialRing(Integers(3)); f := P3 ! [ 2, 2, 1]; P2 := PolynomialRing(Integers(2)); g := P2 ! [ 1, 1, 0, 0, 1]; P5 := PolynomialRing(Integers(5)); h := P5 ! [ 3, 2, 1]; IsIrreducible(f); i := P3 ! [ 1, 2, 1]; K := GF(9); G9 := ext < K | f>; Output: Magma V2.10-6 Mon Mar 15 2004 18:23:34 on modular [Seed = 1473201] ------------------------------------- true >> G9 := ext < K | f>; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 2.909 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host vpn-9-15.umd.edu. (128.8.9.15) Time: Tue Mar 16 01:30:05 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Tue Mar 16 2004 01:30:02 on modular [Seed = 453887419] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee85.uab.es. (158.109.66.85) Time: Tue Mar 16 04:10:51 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; p:=0; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(~C, [i,j]); p:=p+1; end if; end for; end for; return C,p; end function; polavqr(7,3); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Mar 16 2004 04:10:28 on modular [Seed = 85164492] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 3400 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host aula-b-siee85.uab.es. (158.109.66.85) Time: Tue Mar 16 04:11:02 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; p:=0; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(~C, [i,j]); p:=p+1; end if; end for; end for; return C,p; end function; polavqr(7,3); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Mar 16 2004 04:10:38 on modular [Seed = 101745349] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 3403 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host aula-b-siee85.uab.es. (158.109.66.85) Time: Tue Mar 16 04:11:23 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; p:=0; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(~C, [i,j]); p:=p+1; end if; end for; end for; return C,p; end function; polavqr(7,3); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Mar 16 2004 04:10:59 on modular [Seed = 503880432] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 3411 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host aula-b-siee85.uab.es. (158.109.66.85) Time: Tue Mar 16 04:11:43 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; p:=0; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(~C, [i,j]); p:=p+1; end if; end for; end for; return C,p; end function; polavqr(7,3); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Mar 16 2004 04:11:19 on modular [Seed = 369136355] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 3419 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host aula-b-siee85.uab.es. (158.109.66.85) Time: Tue Mar 16 04:12:24 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; p:=0; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(~C, [i,j]); p:=p+1; end if; end for; end for; return C,p; end function; polavqr(7,3); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Mar 16 2004 04:12:00 on modular [Seed = 607297673] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 3433 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host aula-b-siee85.uab.es. (158.109.66.85) Time: Tue Mar 16 04:12:45 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; p:=0; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(~C, [i,j]); p:=p+1; end if; end for; end for; return C,p; end function; Output: Magma V2.10-6 Tue Mar 16 2004 04:12:41 on modular [Seed = 1059699323] ------------------------------------- Total time: 3.430 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee85.uab.es. (158.109.66.85) Time: Tue Mar 16 04:13:40 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; p:=0; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(~C, [i,j]); p:=p+1; end if; end for; end for; return C,p; end function; polavqr(2,2); Output: Magma V2.10-6 Tue Mar 16 2004 04:13:36 on modular [Seed = 908112699] ------------------------------------- [ [ 1, $.1 ], [ 1, $.1^2 ], [ $.1, $.1 ], [ $.1, $.1^2 ], [ $.1^2, $.1 ], [ $.1^2, $.1^2 ], [ 0, 1 ], [ 0, 0 ] ] 8 Total time: 3.679 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee85.uab.es. (158.109.66.85) Time: Tue Mar 16 04:14:30 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(~C, [i,j]); end if; end for; end for; return C; end function; #polavqr(1,2); 1^(2*2-1); Output: Magma V2.10-6 Tue Mar 16 2004 04:14:27 on modular [Seed = 4176379334] ------------------------------------- [
:19]( q: 1, r: 2 ) >> for i in GF(q^r) do ^ Runtime error in 'GF': Argument 1 (1) should be >= 2 1 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee85.uab.es. (158.109.66.85) Time: Tue Mar 16 04:14:54 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(~C, [i,j]); end if; end for; end for; return C; end function; #polavqr(2,1); 1^(2*2-1); Output: Magma V2.10-6 Tue Mar 16 2004 04:14:51 on modular [Seed = 4091901493] ------------------------------------- 2 1 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee85.uab.es. (158.109.66.85) Time: Tue Mar 16 04:15:27 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(~C, [i,j]); end if; end for; end for; return C; end function; #polavqr(2,1); 2^(2*1-1); Output: Magma V2.10-6 Tue Mar 16 2004 04:15:24 on modular [Seed = 2174157920] ------------------------------------- 2 2 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee85.uab.es. (158.109.66.85) Time: Tue Mar 16 04:16:21 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(~C, [i,j]); end if; end for; end for; return C; end function; #polavqr(7,3); 7^(3*2-1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Mar 16 2004 04:15:58 on modular [Seed = 2592874265] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 3543 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host aula-b-siee85.uab.es. (158.109.66.85) Time: Tue Mar 16 04:19:41 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(~C, [i,j]); end if; end for; end for; return C; end function; polavqr(2,2); Output: Magma V2.10-6 Tue Mar 16 2004 04:19:38 on modular [Seed = 2914724682] ------------------------------------- [ [ 1, $.1 ], [ 1, $.1^2 ], [ $.1, $.1 ], [ $.1, $.1^2 ], [ $.1^2, $.1 ], [ $.1^2, $.1^2 ], [ 0, 1 ], [ 0, 0 ] ] Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee85.uab.es. (158.109.66.85) Time: Tue Mar 16 04:20:44 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(~C, [i,j]); end if; end for; end for; return C; end function; tqr:= function (q,r) function> C:=[]; function> for i in {1..r} do Include(~C,q^(r-i)); end for;return C; end function; tqr(3,4); Output: Magma V2.10-6 Tue Mar 16 2004 04:20:42 on modular [Seed = 3165272603] ------------------------------------- >> function> C:=[]; ^ User error: bad syntax >> function> for i in {1..r} do Include(~C,q^(r-i)); end for;return C; end fun ^ User error: bad syntax >> tqr(3,4);; ^ User error: Identifier 'tqr' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee85.uab.es. (158.109.66.85) Time: Tue Mar 16 04:21:15 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(~C, [i,j]); end if; end for; end for; return C; end function; tqr:= function (q,r) C:=[]; for i in {1..r} do Include(~C,q^(r-i)); end for;return C; end function; tqr(3,4); Output: Magma V2.10-6 Tue Mar 16 2004 04:21:12 on modular [Seed = 3080794354] ------------------------------------- [ 27, 9, 3, 1 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee85.uab.es. (158.109.66.85) Time: Tue Mar 16 04:32:24 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(~C, [i,j]); end if; end for; end for; return C; end function; spolav:= [k : k in polavqr(2,2) | k[1] in GF(2) and k[2] in GF(2) ]; #spolav; Output: Magma V2.10-6 Tue Mar 16 2004 04:32:21 on modular [Seed = 1481560499] ------------------------------------- 2 Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee85.uab.es. (158.109.66.85) Time: Tue Mar 16 04:32:37 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(~C, [i,j]); end if; end for; end for; return C; end function; spolav:= [k : k in polavqr(2,3) | k[1] in GF(2) and k[2] in GF(2) ]; #spolav; Output: Magma V2.10-6 Tue Mar 16 2004 04:32:34 on modular [Seed = 1363663021] ------------------------------------- 2 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee85.uab.es. (158.109.66.85) Time: Tue Mar 16 04:33:07 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(~C, [i,j]); end if; end for; end for; return C; end function; spolav:= [k : k in polavqr(3,5) | k[1] in GF(2) and k[2] in GF(2) ]; #spolav; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Mar 16 2004 04:32:44 on modular [Seed = 1718677396] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 3624 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host aula-b-siee85.uab.es. (158.109.66.85) Time: Tue Mar 16 04:33:31 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(~C, [i,j]); end if; end for; end for; return C; end function; spolav:= [k : k in polavqr(3,4) | k[1] in GF(2) and k[2] in GF(2) ]; #spolav; Output: Magma V2.10-6 Tue Mar 16 2004 04:33:23 on modular [Seed = 2137650898] ------------------------------------- >> spolav:= [k : k in polavqr(3,4) | k[1] in GF(2) and k[2] in GF(2) ]; ^ Runtime error in 'in': Arguments have no covering structure >> #spolav; ^ User error: Identifier 'spolav' has not been declared or assigned Total time: 7.629 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host aula-b-siee85.uab.es. (158.109.66.85) Time: Tue Mar 16 04:34:01 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(~C, [i,j]); end if; end for; end for; return C; end function; polavqr(3,4); spolav:= [k : k in polavqr(3,4) | k[1] in GF(2) and k[2] in GF(2) ]; #spolav; Output: Magma V2.10-6 Tue Mar 16 2004 04:33:48 on modular [Seed = 1952644550] ------------------------------------- [ [ 1, 1 ], [ 1, $.1 ], [ 1, $.1^2 ], [ 1, $.1^3 ], [ 1, $.1^6 ], [ 1, $.1^8 ], [ 1, $.1^9 ], [ 1, $.1^11 ], [ 1, $.1^18 ], [ 1, $.1^19 ], [ 1, $.1^23 ], [ 1, $.1^24 ], [ 1, $.1^27 ], [ 1, $.1^33 ], [ 1, $.1^44 ], [ 1, $.1^47 ], [ 1, $.1^50 ], [ 1, $.1^52 ], [ 1, $.1^54 ], [ 1, $.1^56 ], [ 1, $.1^57 ], [ 1, $.1^61 ], [ 1, $.1^68 ], [ 1, $.1^69 ], [ 1, $.1^70 ], [ 1, $.1^72 ], [ 1, $.1^76 ], [ $.1, $.1^4 ], [ $.1, $.1^7 ], [ $.1, $.1^10 ], [ $.1, $.1^12 ], [ $.1, $.1^14 ], [ $.1, $.1^16 ], [ $.1, $.1^17 ], [ $.1, $.1^21 ], [ $.1, $.1^28 ], [ $.1, $.1^29 ], [ $.1, $.1^30 ], [ $.1, $.1^32 ], [ $.1, $.1^36 ], [ $.1, 2 ], [ $.1, $.1^41 ], [ $.1, $.1^42 ], [ $.1, $.1^43 ], [ $.1, $.1^46 ], [ $.1, $.1^48 ], [ $.1, $.1^49 ], [ $.1, $.1^51 ], [ $.1, $.1^58 ], [ $.1, $.1^59 ], [ $.1, $.1^63 ], [ $.1, $.1^64 ], [ $.1, $.1^67 ], [ $.1, $.1^73 ], [ $.1^2, 1 ], [ $.1^2, $.1 ], [ $.1^2, $.1^2 ], [ $.1^2, $.1^3 ], [ $.1^2, $.1^6 ], [ $.1^2, $.1^8 ], [ $.1^2, $.1^9 ], [ $.1^2, $.1^11 ], [ $.1^2, $.1^18 ], [ $.1^2, $.1^19 ], [ $.1^2, $.1^23 ], [ $.1^2, $.1^24 ], [ $.1^2, $.1^27 ], [ $.1^2, $.1^33 ], [ $.1^2, $.1^44 ], [ $.1^2, $.1^47 ], [ $.1^2, $.1^50 ], [ $.1^2, $.1^52 ], [ $.1^2, $.1^54 ], [ $.1^2, $.1^56 ], [ $.1^2, $.1^57 ], [ $.1^2, $.1^61 ], [ $.1^2, $.1^68 ], [ $.1^2, $.1^69 ], [ $.1^2, $.1^70 ], [ $.1^2, $.1^72 ], [ $.1^2, $.1^76 ], [ $.1^3, $.1^4 ], [ $.1^3, $.1^7 ], [ $.1^3, $.1^10 ], [ $.1^3, $.1^12 ], [ $.1^3, $.1^14 ], [ $.1^3, $.1^16 ], [ $.1^3, $.1^17 ], [ $.1^3, $.1^21 ], [ $.1^3, $.1^28 ], [ $.1^3, $.1^29 ], [ $.1^3, $.1^30 ], [ $.1^3, $.1^32 ], [ $.1^3, $.1^36 ], [ $.1^3, 2 ], [ $.1^3, $.1^41 ], [ $.1^3, $.1^42 ], [ $.1^3, $.1^43 ], [ $.1^3, $.1^46 ], [ $.1^3, $.1^48 ], [ $.1^3, $.1^49 ], [ $.1^3, $.1^51 ], [ $.1^3, $.1^58 ], [ $.1^3, $.1^59 ], [ $.1^3, $.1^63 ], [ $.1^3, $.1^64 ], [ $.1^3, $.1^67 ], [ $.1^3, $.1^73 ], [ $.1^4, 1 ], [ $.1^4, $.1 ], [ $.1^4, $.1^2 ], [ $.1^4, $.1^3 ], [ $.1^4, $.1^6 ], [ $.1^4, $.1^8 ], [ $.1^4, $.1^9 ], [ $.1^4, $.1^11 ], [ $.1^4, $.1^18 ], [ $.1^4, $.1^19 ], [ $.1^4, $.1^23 ], [ $.1^4, $.1^24 ], [ $.1^4, $.1^27 ], [ $.1^4, $.1^33 ], [ $.1^4, $.1^44 ], [ $.1^4, $.1^47 ], [ $.1^4, $.1^50 ], [ $.1^4, $.1^52 ], [ $.1^4, $.1^54 ], [ $.1^4, $.1^56 ], [ $.1^4, $.1^57 ], [ $.1^4, $.1^61 ], [ $.1^4, $.1^68 ], [ $.1^4, $.1^69 ], [ $.1^4, $.1^70 ], [ $.1^4, $.1^72 ], [ $.1^4, $.1^76 ], [ $.1^5, $.1^4 ], [ $.1^5, $.1^7 ], [ $.1^5, $.1^10 ], [ $.1^5, $.1^12 ], [ $.1^5, $.1^14 ], [ $.1^5, $.1^16 ], [ $.1^5, $.1^17 ], [ $.1^5, $.1^21 ], [ $.1^5, $.1^28 ], [ $.1^5, $.1^29 ], [ $.1^5, $.1^30 ], [ $.1^5, $.1^32 ], [ $.1^5, $.1^36 ], [ $.1^5, 2 ], [ $.1^5, $.1^41 ], [ $.1^5, $.1^42 ], [ $.1^5, $.1^43 ], [ $.1^5, $.1^46 ], [ $.1^5, $.1^48 ], [ $.1^5, $.1^49 ], [ $.1^5, $.1^51 ], [ $.1^5, $.1^58 ], [ $.1^5, $.1^59 ], [ $.1^5, $.1^63 ], [ $.1^5, $.1^64 ], [ $.1^5, $.1^67 ], [ $.1^5, $.1^73 ], [ $.1^6, 1 ], [ $.1^6, $.1 ], [ $.1^6, $.1^2 ], [ $.1^6, $.1^3 ], [ $.1^6, $.1^6 ], [ $.1^6, $.1^8 ], [ $.1^6, $.1^9 ], [ $.1^6, $.1^11 ], [ $.1^6, $.1^18 ], [ $.1^6, $.1^19 ], [ $.1^6, $.1^23 ], [ $.1^6, $.1^24 ], [ $.1^6, $.1^27 ], [ $.1^6, $.1^33 ], [ $.1^6, $.1^44 ], [ $.1^6, $.1^47 ], [ $.1^6, $.1^50 ], [ $.1^6, $.1^52 ], [ $.1^6, $.1^54 ], [ $.1^6, $.1^56 ], [ $.1^6, $.1^57 ], [ $.1^6, $.1^61 ], [ $.1^6, $.1^68 ], [ $.1^6, $.1^69 ], [ $.1^6, $.1^70 ], [ $.1^6, $.1^72 ], [ $.1^6, $.1^76 ], [ $.1^7, $.1^4 ], [ $.1^7, $.1^7 ], [ $.1^7, $.1^10 ], [ $.1^7, $.1^12 ], [ $.1^7, $.1^14 ], [ $.1^7, $.1^16 ], [ $.1^7, $.1^17 ], [ $.1^7, $.1^21 ], [ $.1^7, $.1^28 ], [ $.1^7, $.1^29 ], [ $.1^7, $.1^30 ], [ $.1^7, $.1^32 ], [ $.1^7, $.1^36 ], [ $.1^7, 2 ], [ $.1^7, $.1^41 ], [ $.1^7, $.1^42 ], [ $.1^7, $.1^43 ], [ $.1^7, $.1^46 ], [ $.1^7, $.1^48 ], [ $.1^7, $.1^49 ], [ $.1^7, $.1^51 ], [ $.1^7, $.1^58 ], [ $.1^7, $.1^59 ], [ $.1^7, $.1^63 ], [ $.1^7, $.1^64 ], [ $.1^7, $.1^67 ], [ $.1^7, $.1^73 ], [ $.1^8, 1 ], [ $.1^8, $.1 ], [ $.1^8, $.1^2 ], [ $.1^8, $.1^3 ], [ $.1^8, $.1^6 ], [ $.1^8, $.1^8 ], [ $.1^8, $.1^9 ], [ $.1^8, $.1^11 ], [ $.1^8, $.1^18 ], [ $.1^8, $.1^19 ], [ $.1^8, $.1^23 ], [ $.1^8, $.1^24 ], [ $.1^8, $.1^27 ], [ $.1^8, $.1^33 ], [ $.1^8, $.1^44 ], [ $.1^8, $.1^47 ], [ $.1^8, $.1^50 ], [ $.1^8, $.1^52 ], [ $.1^8, $.1^54 ], [ $.1^8, $.1^56 ], [ $.1^8, $.1^57 ], [ $.1^8, $.1^61 ], [ $.1^8, $.1^68 ], [ $.1^8, $.1^69 ], [ $.1^8, $.1^70 ], [ $.1^8, $.1^72 ], [ $.1^8, $.1^76 ], [ $.1^9, $.1^4 ], [ $.1^9, $.1^7 ], [ $.1^9, $.1^10 ], [ $.1^9, $.1^12 ], [ $.1^9, $.1^14 ], [ $.1^9, $.1^16 ], [ $.1^9, $.1^17 ], [ $.1^9, $.1^21 ], [ $.1^9, $.1^28 ], [ $.1^9, $.1^29 ], [ $.1^9, $.1^30 ], [ $.1^9, $.1^32 ], [ $.1^9, $.1^36 ], [ $.1^9, 2 ], [ $.1^9, $.1^41 ], [ $.1^9, $.1^42 ], [ $.1^9, $.1^43 ], [ $.1^9, $.1^46 ], [ $.1^9, $.1^48 ], [ $.1^9, $.1^49 ], [ $.1^9, $.1^51 ], [ $.1^9, $.1^58 ], [ $.1^9, $.1^59 ], [ $.1^9, $.1^63 ], [ $.1^9, $.1^64 ], [ $.1^9, $.1^67 ], [ $.1^9, $.1^73 ], [ $.1^10, 1 ], [ $.1^10, $.1 ], [ $.1^10, $.1^2 ], [ $.1^10, $.1^3 ], [ $.1^10, $.1^6 ], [ $.1^10, $.1^8 ], [ $.1^10, $.1^9 ], [ $.1^10, $.1^11 ], [ $.1^10, $.1^18 ], [ $.1^10, $.1^19 ], [ $.1^10, $.1^23 ], [ $.1^10, $.1^24 ], [ $.1^10, $.1^27 ], [ $.1^10, $.1^33 ], [ $.1^10, $.1^44 ], [ $.1^10, $.1^47 ], [ $.1^10, $.1^50 ], [ $.1^10, $.1^52 ], [ $.1^10, $.1^54 ], [ $.1^10, $.1^56 ], [ $.1^10, $.1^57 ], [ $.1^10, $.1^61 ], [ $.1^10, $.1^68 ], [ $.1^10, $.1^69 ], [ $.1^10, $.1^70 ], [ $.1^10, $.1^72 ], [ $.1^10, $.1^76 ], [ $.1^11, $.1^4 ], [ $.1^11, $.1^7 ], [ $.1^11, $.1^10 ], [ $.1^11, $.1^12 ], [ $.1^11, $.1^14 ], [ $.1^11, $.1^16 ], [ $.1^11, $.1^17 ], [ $.1^11, $.1^21 ], [ $.1^11, $.1^28 ], [ $.1^11, $.1^29 ], [ $.1^11, $.1^30 ], [ $.1^11, $.1^32 ], [ $.1^11, $.1^36 ], [ $.1^11, 2 ], [ $.1^11, $.1^41 ], [ $.1^11, $.1^42 ], [ $.1^11, $.1^43 ], [ $.1^11, $.1^46 ], [ $.1^11, $.1^48 ], [ $.1^11, $.1^49 ], [ $.1^11, $.1^51 ], [ $.1^11, $.1^58 ], [ $.1^11, $.1^59 ], [ $.1^11, $.1^63 ], [ $.1^11, $.1^64 ], [ $.1^11, $.1^67 ], [ $.1^11, $.1^73 ], [ $.1^12, 1 ], [ $.1^12, $.1 ], [ $.1^12, $.1^2 ], [ $.1^12, $.1^3 ], [ $.1^12, $.1^6 ], [ $.1^12, $.1^8 ], [ $.1^12, $.1^9 ], [ $.1^12, $.1^11 ], [ $.1^12, $.1^18 ], [ $.1^12, $.1^19 ], [ $.1^12, $.1^23 ], [ $.1^12, $.1^24 ], [ $.1^12, $.1^27 ], [ $.1^12, $.1^33 ], [ $.1^12, $.1^44 ], [ $.1^12, $.1^47 ], [ $.1^12, $.1^50 ], [ $.1^12, $.1^52 ], [ $.1^12, $.1^54 ], [ $.1^12, $.1^56 ], [ $.1^12, $.1^57 ], [ $.1^12, $.1^61 ], [ $.1^12, $.1^68 ], [ $.1^12, $.1^69 ], [ $.1^12, $.1^70 ], [ $.1^12, $.1^72 ], [ $.1^12, $.1^76 ], [ $.1^13, $.1^4 ], [ $.1^13, $.1^7 ], [ $.1^13, $.1^10 ], [ $.1^13, $.1^12 ], [ $.1^13, $.1^14 ], [ $.1^13, $.1^16 ], [ $.1^13, $.1^17 ], [ $.1^13, $.1^21 ], [ $.1^13, $.1^28 ], [ $.1^13, $.1^29 ], [ $.1^13, $.1^30 ], [ $.1^13, $.1^32 ], [ $.1^13, $.1^36 ], [ $.1^13, 2 ], [ $.1^13, $.1^41 ], [ $.1^13, $.1^42 ], [ $.1^13, $.1^43 ], [ $.1^13, $.1^46 ], [ $.1^13, $.1^48 ], [ $.1^13, $.1^49 ], [ $.1^13, $.1^51 ], [ $.1^13, $.1^58 ], [ $.1^13, $.1^59 ], [ $.1^13, $.1^63 ], [ $.1^13, $.1^64 ], [ $.1^13, $.1^67 ], [ $.1^13, $.1^73 ], [ $.1^14, 1 ], [ $.1^14, $.1 ], [ $.1^14, $.1^2 ], [ $.1^14, $.1^3 ], [ $.1^14, $.1^6 ], [ $.1^14, $.1^8 ], [ $.1^14, $.1^9 ], [ $.1^14, $.1^11 ], [ $.1^14, $.1^18 ], [ $.1^14, $.1^19 ], [ $.1^14, $.1^23 ], [ $.1^14, $.1^24 ], [ $.1^14, $.1^27 ], [ $.1^14, $.1^33 ], [ $.1^14, $.1^44 ], [ $.1^14, $.1^47 ], [ $.1^14, $.1^50 ], [ $.1^14, $.1^52 ], [ $.1^14, $.1^54 ], [ $.1^14, $.1^56 ], [ $.1^14, $.1^57 ], [ $.1^14, $.1^61 ], [ $.1^14, $.1^68 ], [ $.1^14, $.1^69 ], [ $.1^14, $.1^70 ], [ $.1^14, $.1^72 ], [ $.1^14, $.1^76 ], [ $.1^15, $.1^4 ], [ $.1^15, $.1^7 ], [ $.1^15, $.1^10 ], [ $.1^15, $.1^12 ], [ $.1^15, $.1^14 ], [ $.1^15, $.1^16 ], [ $.1^15, $.1^17 ], [ $.1^15, $.1^21 ], [ $.1^15, $.1^28 ], [ $.1^15, $.1^29 ], [ $.1^15, $.1^30 ], [ $.1^15, $.1^32 ], [ $.1^15, $.1^36 ], [ $.1^15, 2 ], [ $.1^15, $.1^41 ], [ $.1^15, $.1^42 ], [ $.1^15, $.1^43 ], [ $.1^15, $.1^46 ], [ $.1^15, $.1^48 ], [ $.1^15, $.1^49 ], [ $.1^15, $.1^51 ], [ $.1^15, $.1^58 ], [ $.1^15, $.1^59 ], [ $.1^15, $.1^63 ], [ $.1^15, $.1^64 ], [ $.1^15, $.1^67 ], [ $.1^15, $.1^73 ], [ $.1^16, 1 ], [ $.1^16, $.1 ], [ $.1^16, $.1^2 ], [ $.1^16, $.1^3 ], [ $.1^16, $.1^6 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host aula-b-siee85.uab.es. (158.109.66.85) Time: Tue Mar 16 04:34:30 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(~C, [i,j]); end if; end for; end for; return C; end function; spolav:= [k : k in polavqr(3,4) | k[1] in GF(3) and k[2] in GF(3) ]; #spolav; Output: Magma V2.10-6 Tue Mar 16 2004 04:34:22 on modular [Seed = 219907933] ------------------------------------- 3 Total time: 7.770 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host aula-b-siee85.uab.es. (158.109.66.85) Time: Tue Mar 16 04:34:51 2004 Input: pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(~C, [i,j]); end if; end for; end for; return C; end function; spolav:= [k : k in polavqr(2,3) | k[1] in GF(2) and k[2] in GF(2) ]; #spolav; Output: Magma V2.10-6 Tue Mar 16 2004 04:34:48 on modular [Seed = 34900084] ------------------------------------- 2 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Tue Mar 16 04:49:15 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, x^12*y^3, x^12*y^4, x^12*y^5, x^12*y^6, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x^13*y^3, x^13*y^4, x^13*y^5, x^13*y^6, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^14*y^6, x^14*y^3, x^14*y^4, x^14*y^5, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^12, x^3*y^11, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^10*y^7, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^11*y^5, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^5*y^9, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; L := [ x^4*y^11]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Tue Mar 16 2004 04:49:12 on modular [Seed = 692036863] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] [ x^4*y^11 ] [ false ] Total time: 2.979 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Tue Mar 16 04:49:52 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, x^12*y^3, x^12*y^4, x^12*y^5, x^12*y^6, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x^13*y^3, x^13*y^4, x^13*y^5, x^13*y^6, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^14*y^6, x^14*y^3, x^14*y^4, x^14*y^5, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^12, x^3*y^11, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^13*y^5, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^11*y^5, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^5*y^9, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; L := [ x^4*y^11]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Tue Mar 16 2004 04:49:49 on modular [Seed = 1042854861] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] [ x^4*y^11 ] [ false ] Total time: 2.919 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Tue Mar 16 04:50:54 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, x^12*y^3, x^12*y^4, x^12*y^5, x^12*y^6, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x^13*y^3, x^13*y^4, x^13*y^5, x^13*y^6, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^14*y^6, x^14*y^3, x^14*y^4, x^14*y^5, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^12, x^3*y^11, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^11*y^7, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^11*y^5, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^5*y^9, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; L := [ x^5*y^11]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Tue Mar 16 2004 04:50:51 on modular [Seed = 3487122042] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] [ x^5*y^11 ] [ false ] Total time: 2.919 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Tue Mar 16 04:51:30 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, x^12*y^3, x^12*y^4, x^12*y^5, x^12*y^6, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x^13*y^3, x^13*y^4, x^13*y^5, x^13*y^6, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^14*y^6, x^14*y^3, x^14*y^4, x^14*y^5, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^12, x^3*y^11, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^14*y^5, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^11*y^5, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^5*y^9, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; L := [ x^5*y^11]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Tue Mar 16 2004 04:51:27 on modular [Seed = 3302115989] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] [ x^5*y^11 ] [ false ] Total time: 2.989 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Tue Mar 16 04:52:35 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, x^12*y^3, x^12*y^4, x^12*y^5, x^12*y^6, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x^13*y^3, x^13*y^4, x^13*y^5, x^13*y^6, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^14*y^6, x^14*y^3, x^14*y^4, x^14*y^5, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^12, x^3*y^11, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^9*y^9, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^11*y^5, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^5*y^9, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; L := [ x^6*y^11]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Tue Mar 16 2004 04:52:32 on modular [Seed = 3721090035] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] [ x^6*y^11 ] [ false ] Total time: 2.969 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Tue Mar 16 04:53:20 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, x^12*y^3, x^12*y^4, x^12*y^5, x^12*y^6, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x^13*y^3, x^13*y^4, x^13*y^5, x^13*y^6, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^14*y^6, x^14*y^3, x^14*y^4, x^14*y^5, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^12, x^3*y^11, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^12*y^5, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^11*y^5, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^5*y^9, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; L := [ x^6*y^11]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Tue Mar 16 2004 04:53:17 on modular [Seed = 3536083985] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] [ x^6*y^11 ] [ false ] Total time: 2.999 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Tue Mar 16 04:58:38 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, x^12*y^3, x^12*y^4, x^12*y^5, x^12*y^6, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x^13*y^3, x^13*y^4, x^13*y^5, x^13*y^6, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^14*y^6, x^14*y^3, x^14*y^4, x^14*y^5, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^12, x^3*y^11, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^10*y^9, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^11*y^5, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^5*y^9, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; L := [ x^7*y^11]; L; B, V := HomogeneousModuleTest(P, S, L); B; Output: Magma V2.10-6 Tue Mar 16 2004 04:58:35 on modular [Seed = 3841092449] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 0 [] [ x^7*y^11 ] [ false ] Total time: 2.999 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host host213-123-166-1.in-addr.btopenworld.com. (213.123.166.1) Time: Tue Mar 16 05:06:06 2004 Input: sdsdasda Output: Magma V2.10-6 Tue Mar 16 2004 05:06:03 on modular [Seed = 1281023368] ------------------------------------- >> sdsdasda; ^ User error: Identifier 'sdsdasda' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host host213-123-166-1.in-addr.btopenworld.com. (213.123.166.1) Time: Tue Mar 16 05:06:41 2004 Input: printf("%d", 5); Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed. ************** MAGMA ***************** Host 3(NXDOMAIN) (193.254.155.48) Time: Tue Mar 16 07:53:07 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Tue Mar 16 2004 07:53:04 on modular [Seed = 3569511476] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ouzel.dpmms.cam.ac.uk. (131.111.24.219) Time: Tue Mar 16 08:25:41 2004 Input: D:=CremonaDatabase(); E:=EllipticCurve(D,"37A"); two:=MultiplicationByMMap(E,2); SelmerGroup(two); Output: Magma V2.10-6 Tue Mar 16 2004 08:25:36 on modular [Seed = 2308884873] ------------------------------------- >> SelmerGroup(two);; ^ Runtime error in 'SelmerGroup': not implemented Total time: 2.939 seconds, Total memory usage: 2.70MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 16 09:14:16 2004 Input: dia:=1; dia:=dia+3; domingos:=[]; while dia le 366 do domingos:=domingos cat [dia];dia:=dia+7; end while; print domingos; Output: Magma V2.10-6 Tue Mar 16 2004 09:14:13 on modular [Seed = 302340598] ------------------------------------- [ 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 16 09:16:00 2004 Input: K:=GF(4); M22:=MatrixRing(K,2); m:=M22![1,1,1,1]; m[1,2]:=K.1; Trace(0); m; Mt:={n : n in M22 | Trace(n)eq 0}; Mt; Output: Magma V2.10-6 Tue Mar 16 2004 09:15:57 on modular [Seed = 34950734] ------------------------------------- 0 [ 1 K.1] [ 1 1] { [ 0 0] [ 0 0], [ 0 0] [K.1^2 0], [ 0 0] [ K.1 0], [ 0 0] [ 1 0], [K.1^2 0] [ 0 K.1^2], [K.1^2 0] [K.1^2 K.1^2], [K.1^2 0] [ K.1 K.1^2], [K.1^2 0] [ 1 K.1^2], [ 1 0] [ 0 1], [ 1 0] [K.1^2 1], [ 1 0] [ K.1 1], [ 1 0] [ 1 1], [ K.1 0] [ 0 K.1], [ K.1 0] [K.1^2 K.1], [ K.1 0] [ K.1 K.1], [ K.1 0] [ 1 K.1], [ 0 K.1^2] [ 0 0], [ 0 K.1^2] [K.1^2 0], [ 0 K.1^2] [ K.1 0], [ 0 K.1^2] [ 1 0], [K.1^2 K.1^2] [ 0 K.1^2], [K.1^2 K.1^2] [K.1^2 K.1^2], [K.1^2 K.1^2] [ K.1 K.1^2], [K.1^2 K.1^2] [ 1 K.1^2], [ 1 K.1^2] [ 0 1], [ 1 K.1^2] [K.1^2 1], [ 1 K.1^2] [ K.1 1], [ 1 K.1^2] [ 1 1], [ K.1 K.1^2] [ 0 K.1], [ K.1 K.1^2] [K.1^2 K.1], [ K.1 K.1^2] [ K.1 K.1], [ K.1 K.1^2] [ 1 K.1], [ 0 K.1] [ 0 0], [ 0 K.1] [K.1^2 0], [ 0 K.1] [ K.1 0], [ 0 K.1] [ 1 0], [K.1^2 K.1] [ 0 K.1^2], [K.1^2 K.1] [K.1^2 K.1^2], [K.1^2 K.1] [ K.1 K.1^2], [K.1^2 K.1] [ 1 K.1^2], [ 1 K.1] [ 0 1], [ 1 K.1] [K.1^2 1], [ 1 K.1] [ K.1 1], [ 1 K.1] [ 1 1], [ K.1 K.1] [ 0 K.1], [ K.1 K.1] [K.1^2 K.1], [ K.1 K.1] [ K.1 K.1], [ K.1 K.1] [ 1 K.1], [ 0 1] [ 0 0], [ 0 1] [K.1^2 0], [ 0 1] [ K.1 0], [ 0 1] [ 1 0], [K.1^2 1] [ 0 K.1^2], [K.1^2 1] [K.1^2 K.1^2], [K.1^2 1] [ K.1 K.1^2], [K.1^2 1] [ 1 K.1^2], [ 1 1] [ 0 1], [ 1 1] [K.1^2 1], [ 1 1] [ K.1 1], [ 1 1] [ 1 1], [ K.1 1] [ 0 K.1], [ K.1 1] [K.1^2 K.1], [ K.1 1] [ K.1 K.1], [ K.1 1] [ 1 K.1] } Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 16 09:17:59 2004 Input: K:=GF(4); M22:=MatrixRing(K,2); Mt:={n : n in M22 | Trace(n)eq 0}; Mt; Output: Magma V2.10-6 Tue Mar 16 2004 09:17:56 on modular [Seed = 203112649] ------------------------------------- { [ 0 0] [ 0 0], [ 0 0] [K.1^2 0], [ 0 0] [ K.1 0], [ 0 0] [ 1 0], [K.1^2 0] [ 0 K.1^2], [K.1^2 0] [K.1^2 K.1^2], [K.1^2 0] [ K.1 K.1^2], [K.1^2 0] [ 1 K.1^2], [ 1 0] [ 0 1], [ 1 0] [K.1^2 1], [ 1 0] [ K.1 1], [ 1 0] [ 1 1], [ K.1 0] [ 0 K.1], [ K.1 0] [K.1^2 K.1], [ K.1 0] [ K.1 K.1], [ K.1 0] [ 1 K.1], [ 0 K.1^2] [ 0 0], [ 0 K.1^2] [K.1^2 0], [ 0 K.1^2] [ K.1 0], [ 0 K.1^2] [ 1 0], [K.1^2 K.1^2] [ 0 K.1^2], [K.1^2 K.1^2] [K.1^2 K.1^2], [K.1^2 K.1^2] [ K.1 K.1^2], [K.1^2 K.1^2] [ 1 K.1^2], [ 1 K.1^2] [ 0 1], [ 1 K.1^2] [K.1^2 1], [ 1 K.1^2] [ K.1 1], [ 1 K.1^2] [ 1 1], [ K.1 K.1^2] [ 0 K.1], [ K.1 K.1^2] [K.1^2 K.1], [ K.1 K.1^2] [ K.1 K.1], [ K.1 K.1^2] [ 1 K.1], [ 0 K.1] [ 0 0], [ 0 K.1] [K.1^2 0], [ 0 K.1] [ K.1 0], [ 0 K.1] [ 1 0], [K.1^2 K.1] [ 0 K.1^2], [K.1^2 K.1] [K.1^2 K.1^2], [K.1^2 K.1] [ K.1 K.1^2], [K.1^2 K.1] [ 1 K.1^2], [ 1 K.1] [ 0 1], [ 1 K.1] [K.1^2 1], [ 1 K.1] [ K.1 1], [ 1 K.1] [ 1 1], [ K.1 K.1] [ 0 K.1], [ K.1 K.1] [K.1^2 K.1], [ K.1 K.1] [ K.1 K.1], [ K.1 K.1] [ 1 K.1], [ 0 1] [ 0 0], [ 0 1] [K.1^2 0], [ 0 1] [ K.1 0], [ 0 1] [ 1 0], [K.1^2 1] [ 0 K.1^2], [K.1^2 1] [K.1^2 K.1^2], [K.1^2 1] [ K.1 K.1^2], [K.1^2 1] [ 1 K.1^2], [ 1 1] [ 0 1], [ 1 1] [K.1^2 1], [ 1 1] [ K.1 1], [ 1 1] [ 1 1], [ K.1 1] [ 0 K.1], [ K.1 1] [K.1^2 K.1], [ K.1 1] [ K.1 K.1], [ K.1 1] [ 1 K.1] } Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 16 09:18:08 2004 Input: K:=GF(4); M22:=MatrixRing(K,2); Mt:={n : n in M22 | Trace(n)eq 0}; Mt; Output: Magma V2.10-6 Tue Mar 16 2004 09:18:05 on modular [Seed = 924875771] ------------------------------------- { [ 0 0] [ 0 0], [ 0 0] [K.1^2 0], [ 0 0] [ K.1 0], [ 0 0] [ 1 0], [K.1^2 0] [ 0 K.1^2], [K.1^2 0] [K.1^2 K.1^2], [K.1^2 0] [ K.1 K.1^2], [K.1^2 0] [ 1 K.1^2], [ 1 0] [ 0 1], [ 1 0] [K.1^2 1], [ 1 0] [ K.1 1], [ 1 0] [ 1 1], [ K.1 0] [ 0 K.1], [ K.1 0] [K.1^2 K.1], [ K.1 0] [ K.1 K.1], [ K.1 0] [ 1 K.1], [ 0 K.1^2] [ 0 0], [ 0 K.1^2] [K.1^2 0], [ 0 K.1^2] [ K.1 0], [ 0 K.1^2] [ 1 0], [K.1^2 K.1^2] [ 0 K.1^2], [K.1^2 K.1^2] [K.1^2 K.1^2], [K.1^2 K.1^2] [ K.1 K.1^2], [K.1^2 K.1^2] [ 1 K.1^2], [ 1 K.1^2] [ 0 1], [ 1 K.1^2] [K.1^2 1], [ 1 K.1^2] [ K.1 1], [ 1 K.1^2] [ 1 1], [ K.1 K.1^2] [ 0 K.1], [ K.1 K.1^2] [K.1^2 K.1], [ K.1 K.1^2] [ K.1 K.1], [ K.1 K.1^2] [ 1 K.1], [ 0 K.1] [ 0 0], [ 0 K.1] [K.1^2 0], [ 0 K.1] [ K.1 0], [ 0 K.1] [ 1 0], [K.1^2 K.1] [ 0 K.1^2], [K.1^2 K.1] [K.1^2 K.1^2], [K.1^2 K.1] [ K.1 K.1^2], [K.1^2 K.1] [ 1 K.1^2], [ 1 K.1] [ 0 1], [ 1 K.1] [K.1^2 1], [ 1 K.1] [ K.1 1], [ 1 K.1] [ 1 1], [ K.1 K.1] [ 0 K.1], [ K.1 K.1] [K.1^2 K.1], [ K.1 K.1] [ K.1 K.1], [ K.1 K.1] [ 1 K.1], [ 0 1] [ 0 0], [ 0 1] [K.1^2 0], [ 0 1] [ K.1 0], [ 0 1] [ 1 0], [K.1^2 1] [ 0 K.1^2], [K.1^2 1] [K.1^2 K.1^2], [K.1^2 1] [ K.1 K.1^2], [K.1^2 1] [ 1 K.1^2], [ 1 1] [ 0 1], [ 1 1] [K.1^2 1], [ 1 1] [ K.1 1], [ 1 1] [ 1 1], [ K.1 1] [ 0 K.1], [ K.1 1] [K.1^2 K.1], [ K.1 1] [ K.1 K.1], [ K.1 1] [ 1 K.1] } Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 16 09:21:06 2004 Input: K:=GF(4); M22:=MatrixRing(K,2); Mf:={n : n in M22 | (n[1,1]eq n[2,1]) and (n[1,2] eq n[2,2])}; Mf; Output: Magma V2.10-6 Tue Mar 16 2004 09:21:03 on modular [Seed = 691954743] ------------------------------------- { [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ K.1 0] [ K.1 0], [ 0 K.1^2] [ 0 K.1^2], [ K.1 K.1^2] [ K.1 K.1^2], [ 0 K.1] [ 0 K.1], [ K.1 K.1] [ K.1 K.1], [ 0 1] [ 0 1], [ K.1 1] [ K.1 1], [K.1^2 0] [K.1^2 0], [ 1 0] [ 1 0], [K.1^2 K.1^2] [K.1^2 K.1^2], [ 1 K.1^2] [ 1 K.1^2], [K.1^2 K.1] [K.1^2 K.1], [ 1 K.1] [ 1 K.1], [K.1^2 1] [K.1^2 1] } Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 16 09:22:15 2004 Input: K:=GF(4); M22:=MatrixRing(K,2); Mf:={n : n in M22 | (n[1,1]eq n[2,1]) and (n[1,2] eq n[2,2])}; Mt:={n : n in M22 | Trace(n)eq 0}; Mtf:={n : n in M22 | (n in Mf) and (n in Mt)}; Mtf; Output: Magma V2.10-6 Tue Mar 16 2004 09:22:12 on modular [Seed = 3502742805] ------------------------------------- { [ 0 0] [ 0 0], [K.1^2 K.1^2] [K.1^2 K.1^2], [ K.1 K.1] [ K.1 K.1], [ 1 1] [ 1 1] } Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 16 09:24:56 2004 Input: K:=GF(4); M22:=MatrixRing(K,2); Mf:={n : n in M22 | (n[1,1]eq n[2,1]) and (n[1,2] eq n[2,2])}; Mt:={n : n in M22 | Trace(n)eq 0}; Mtf:={n : n in M22 | (n in Mf) and (n in Mt)}; SEQ:=[Random(M22) : n in [1..S100000]]; m1:=[n : n in M22 | (n in SEQ) and (n in Mt)]; m2:=[n : n in M22 | (n in SEQ) and (n in Mf)]; m3:=[n : n in M22 | (n in SEQ) and (n in Mtf)]; print "RESULTATS:"; print "Matrius que pertanyen a Mt"; #(m1); print "Matrius que pertanyen a Mf"; #(m2); print "Matrius que pertanyen a Mtf"; #(m3); Output: Magma V2.10-6 Tue Mar 16 2004 09:24:53 on modular [Seed = 3670906046] ------------------------------------- >> SEQ:=[Random(M22) : n in [1..S100000]]; ^ User error: Identifier 'S100000' has not been declared or assigned >> m1:=[n : n in M22 | (n in SEQ) and (n in Mt)]; ^ User error: Identifier 'SEQ' has not been declared or assigned >> m2:=[n : n in M22 | (n in SEQ) and (n in Mf)]; ^ User error: Identifier 'SEQ' has not been declared or assigned >> m3:=[n : n in M22 | (n in SEQ) and (n in Mtf)]; ^ User error: Identifier 'SEQ' has not been declared or assigned RESULTATS: Matrius que pertanyen a Mt >> #(m1); ^ User error: Identifier 'm1' has not been declared or assigned Matrius que pertanyen a Mf >> #(m2); ^ User error: Identifier 'm2' has not been declared or assigned Matrius que pertanyen a Mtf >> #(m3);; ^ User error: Identifier 'm3' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 16 09:25:21 2004 Input: K:=GF(4); M22:=MatrixRing(K,2); Mf:={n : n in M22 | (n[1,1]eq n[2,1]) and (n[1,2] eq n[2,2])}; Mt:={n : n in M22 | Trace(n)eq 0}; Mtf:={n : n in M22 | (n in Mf) and (n in Mt)}; SEQ:=[Random(M22) : n in [1..100000]]; m1:=[n : n in M22 | (n in SEQ) and (n in Mt)]; m2:=[n : n in M22 | (n in SEQ) and (n in Mf)]; m3:=[n : n in M22 | (n in SEQ) and (n in Mtf)]; print "RESULTATS:"; print "Matrius que pertanyen a Mt"; #(m1); print "Matrius que pertanyen a Mf"; #(m2); print "Matrius que pertanyen a Mtf"; #(m3); Output: Magma V2.10-6 Tue Mar 16 2004 09:25:17 on modular [Seed = 3386804181] ------------------------------------- RESULTATS: Matrius que pertanyen a Mt 64 Matrius que pertanyen a Mf 16 Matrius que pertanyen a Mtf 4 Total time: 3.539 seconds, Total memory usage: 6.95MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 16 09:33:01 2004 Input: expo:= function (q,r) if ((r gt 0) and IsPrime(q)) then exp:= [q^(r-1)]; for i:=2 to r do exp:= exp cat [q^(r-i)]; end for; end if; return exp; end function; expo(7,3); Output: Magma V2.10-6 Tue Mar 16 2004 09:32:58 on modular [Seed = 3824464808] ------------------------------------- [ 49, 7, 1 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 16 09:34:55 2004 Input: Z:=Integers(100); PT:=PolynomialRing(Z); expo:= function (q,r) if ((r gt 0) and IsPrime(q)) then exp:= [q^(r-1)]; for i:=2 to r do exp:= exp cat [q^(r-i)]; end for; end if; return exp; end function; t := function (q,r) lista:=expo(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + PT![0,1]^lista[i]; end for; return poly; end function; t(7,3); n := function (q,r) lista:=expo(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=PT![0,1]^exp; return poly; end function; n(7,3); Output: Magma V2.10-6 Tue Mar 16 2004 09:34:52 on modular [Seed = 3942496823] ------------------------------------- x^49 + x^7 + x x^57 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 09:38:35 2004 Input: K := GF(6); Output: Magma V2.10-6 Tue Mar 16 2004 09:38:32 on modular [Seed = 2559560097] ------------------------------------- >> K := GF(6);; ^ Runtime error in 'GF': Argument 1 (6) is not a prime power Total time: 3.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 09:39:14 2004 Input: K := GF(3); Output: Magma V2.10-6 Tue Mar 16 2004 09:39:11 on modular [Seed = 2207568477] ------------------------------------- Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 09:39:22 2004 Input: K := GF(3); K; Output: Magma V2.10-6 Tue Mar 16 2004 09:39:19 on modular [Seed = 2325601100] ------------------------------------- Finite field of size 3 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 09:39:40 2004 Input: K := GF(3); K; S := FiniteField(3); S; Output: Magma V2.10-6 Tue Mar 16 2004 09:39:37 on modular [Seed = 3047351373] ------------------------------------- Finite field of size 3 Finite field of size 3 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 09:40:27 2004 Input: K := GF(3); K; F := ext; F; Output: Magma V2.10-6 Tue Mar 16 2004 09:40:24 on modular [Seed = 2779968556] ------------------------------------- Finite field of size 3 >> F := ext; ^ User error: Identifier 'x' has not been declared or assigned >> F;; ^ User error: Identifier 'F' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 09:42:19 2004 Input: P3 := PolynomialRing(Integers(3)); f := P3 ! [ 2, 2, 1]; P2 := PolynomialRing(Integers(2)); g := P2 ! [ 1, 1, 0, 0, 1]; P5 := PolynomialRing(Integers(5)); h := P5 ! [ 3, 2, 1]; i := P3 ! [ 1, 2, 1]; K := GF(3); K; F := ext; F; Output: Magma V2.10-6 Tue Mar 16 2004 09:42:16 on modular [Seed = 2948136374] ------------------------------------- Finite field of size 3 >> F := ext; ^ Runtime error in ext< ... >: Argument is not a polynomial over LHS >> F;; ^ User error: Identifier 'F' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 09:42:35 2004 Input: P3 := PolynomialRing(Integers(3)); f := P3 ! [ 2, 2, 1]; P2 := PolynomialRing(Integers(2)); g := P2 ! [ 1, 1, 0, 0, 1]; P5 := PolynomialRing(Integers(5)); h := P5 ! [ 3, 2, 1]; i := P3 ! [ 1, 2, 1]; K := GF(3); K; f; F := ext; F; Output: Magma V2.10-6 Tue Mar 16 2004 09:42:32 on modular [Seed = 1430390623] ------------------------------------- Finite field of size 3 x^2 + 2*x + 2 Finite field of size 3^2 Total time: 2.919 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 09:43:30 2004 Input: P3 := PolynomialRing(Integers(3)); f := P3 ! [ 2, 2, 1]; P2 := PolynomialRing(Integers(2)); g := P2 ! [ 1, 1, 0, 0, 1]; P5 := PolynomialRing(Integers(5)); h := P5 ! [ 3, 2, 1]; i := P3 ! [ 1, 2, 1]; K := GF(3); K; f; F := ext< GF(3) | f >; F; Output: Magma V2.10-6 Tue Mar 16 2004 09:43:27 on modular [Seed = 1112871071] ------------------------------------- Finite field of size 3 x^2 + 2*x + 2 Finite field of size 3^2 Total time: 2.979 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 16 09:47:07 2004 Input: P:=PolynomialRing(Integers()); Output: Magma V2.10-6 Tue Mar 16 2004 09:47:04 on modular [Seed = 1281040246] ------------------------------------- Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 16 09:47:11 2004 Input: P:=PolynomialRing(Integers()); Output: Magma V2.10-6 Tue Mar 16 2004 09:47:08 on modular [Seed = 1952655178] ------------------------------------- Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 09:48:49 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G9; G16 := ext < GF(2) | g > ; G16; G25 := ext < GF(5) | j >; G25; G9b := ext < GF(3) | k >; G9b; Output: Magma V2.10-6 Tue Mar 16 2004 09:48:46 on modular [Seed = 1635136253] ------------------------------------- Finite field of size 3^2 Finite field of size 2^4 Finite field of size 5^2 >> G9b := ext < GF(3) | k >; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b;; ^ User error: Identifier 'G9b' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 16 09:49:32 2004 Input: P:=PolynomialRing(Integers()); n:=x^((7^2)+7+7^0) Output: Magma V2.10-6 Tue Mar 16 2004 09:49:27 on modular [Seed = 1853439435] ------------------------------------- Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 16 09:49:46 2004 Input: P:=PolynomialRing(Integers()); n:=x^((7^2)+7+7^0); print(n); Output: Magma V2.10-6 Tue Mar 16 2004 09:49:43 on modular [Seed = 385893186] ------------------------------------- x^57 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 16 09:50:13 2004 Input: expo:= function (q,r) if ((r gt 0) and IsPrime(q)) then exp:= [q^(r-1)]; for i:=2 to r do exp:= exp cat [q^(r-i)]; end for; end if; return exp; end function; t := function (q,r) Z:=Integers(); PT:=PolynomialRing(Z); lista:=expo(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + PT![0,1]^lista[i]; end for; return poly; end function; t(7,3); Output: Magma V2.10-6 Tue Mar 16 2004 09:50:10 on modular [Seed = 118510455] ------------------------------------- x^49 + x^7 + x Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 16 09:51:05 2004 Input: P:=PolynomialRing(Integers()); n:=x^((7^2)+7+7^0); t:=(x^(7^2))+(x^(7))+x; print(n); print(t); Output: Magma V2.10-6 Tue Mar 16 2004 09:51:02 on modular [Seed = 219830537] ------------------------------------- x^57 x^49 + x^7 + x Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 16 09:51:44 2004 Input: PuntsOlav:=function(q,r) kf:=GF(q,r); punts:=[:a,b in kf | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b)]; return (punts); end function; PuntsOlav(7,3); Output: Magma V2.10-6 Tue Mar 16 2004 09:51:41 on modular [Seed = 1042901521] ------------------------------------- >> punts:=[:a,b in kf | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r) ^ User error: Identifier 'nqr' has not been declared or assigned >> PuntsOlav(7,3);; ^ User error: Identifier 'PuntsOlav' has not been declared or assigned Total time: 2.849 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 16 09:53:24 2004 Input: P:=PolynomialRing(Integers()); n:=x^((7^2)+7+7^0); t:=(x^(7^2))+(x^(7))+x; llista := [i : i in [1..3]|(7^i)] print(n); print(t); Output: Magma V2.10-6 Tue Mar 16 2004 09:53:21 on modular [Seed = 657486740] ------------------------------------- >> print(n); ^ User error: bad syntax x^49 + x^7 + x Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 16 09:53:33 2004 Input: P:=PolynomialRing(Integers()); n:=x^((7^2)+7+7^0); t:=(x^(7^2))+(x^(7))+x; llista := [i : i in [1..3]|(7^i)]; print(n); print(t); Output: Magma V2.10-6 Tue Mar 16 2004 09:53:30 on modular [Seed = 742094996] ------------------------------------- >> llista := [i : i in [1..3]|(7^i)]; ^ Runtime error in sequence construction: Logical expected x^57 x^49 + x^7 + x Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 16 09:54:13 2004 Input: P:=PolynomialRing(Integers()); n:=x^((7^2)+7+7^0); t:=(x^(7^2))+(x^(7))+x; llista:=[i : i in [1..3] by (7^i)]; print(n); print(t); Output: Magma V2.10-6 Tue Mar 16 2004 09:54:10 on modular [Seed = 3670904730] ------------------------------------- >> llista:=[i : i in [1..3] by (7^i)]; ^ User error: bad syntax x^57 x^49 + x^7 + x Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 16 09:54:22 2004 Input: P:=PolynomialRing(Integers()); n:=x^((7^2)+7+7^0); t:=(x^(7^2))+(x^(7))+x; print(n); print(t); Output: Magma V2.10-6 Tue Mar 16 2004 09:54:19 on modular [Seed = 3285489290] ------------------------------------- x^57 x^49 + x^7 + x Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 16 09:54:48 2004 Input: P:=PolynomialRing(Integers()); n:=x^((7^2)+7+7^0); t:=(x^(7^2))+(x^(7))+x; print(n); print(t); polav:=function (q,r); KQR:=GF(q,r); punts:=[: a,b in KQR | Evaluate(n73,a) eq Evaluate(t73,b)]; return{punts}; end function; Output: Magma V2.10-6 Tue Mar 16 2004 09:54:45 on modular [Seed = 3370098095] ------------------------------------- x^57 x^49 + x^7 + x >> punts:=[: a,b in KQR | Evaluate(n73,a) eq Evaluate(t73,b)]; ^ User error: bad syntax >> return{punts}; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 16 09:55:13 2004 Input: K:=GF(4); M22:=MatrixRing(K,2); Mf:={n : n in M22 | (n[1,1]eq n[2,1]) and (n[1,2] eq n[2,2])}; Mt:={n : n in M22 | Trace(n)eq 0}; Mtf:={n : n in M22 | (n in Mf) and (n in Mt)}; SEQ:=[Random(M22) : n in [1..100000]]; m1:=[n : n in M22 | (n in SEQ) and (n in Mt)]; m2:=[n : n in M22 | (n in SEQ) and (n in Mf)]; m3:=[n : n in M22 | (n in SEQ) and (n in Mtf)]; print "Matrius que pertanyen a Mt"; #(m1); print "Matrius que pertanyen a Mf"; #(m2); print "Matrius que pertanyen a Mtf"; #(m3); Output: Magma V2.10-6 Tue Mar 16 2004 09:55:09 on modular [Seed = 4125270250] ------------------------------------- Matrius que pertanyen a Mt 64 Matrius que pertanyen a Mf 16 Matrius que pertanyen a Mtf 4 Total time: 3.479 seconds, Total memory usage: 6.95MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 16 09:55:22 2004 Input: K:=GF(4); M22:=MatrixRing(K,2); Mf:={n : n in M22 | (n[1,1]eq n[2,1]) and (n[1,2] eq n[2,2])}; Mt:={n : n in M22 | Trace(n)eq 0}; Mtf:={n : n in M22 | (n in Mf) and (n in Mt)}; SEQ:=[Random(M22) : n in [1..100000 by 1]]; m1:=[n : n in M22 | (n in SEQ) and (n in Mt)]; m2:=[n : n in M22 | (n in SEQ) and (n in Mf)]; m3:=[n : n in M22 | (n in SEQ) and (n in Mtf)]; print "Matrius que pertanyen a Mt"; #(m1); print "Matrius que pertanyen a Mf"; #(m2); print "Matrius que pertanyen a Mtf"; #(m3); Output: Magma V2.10-6 Tue Mar 16 2004 09:55:18 on modular [Seed = 3807754214] ------------------------------------- Matrius que pertanyen a Mt 64 Matrius que pertanyen a Mf 16 Matrius que pertanyen a Mtf 4 Total time: 3.539 seconds, Total memory usage: 7.09MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 09:59:38 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; G25 ! 3; Output: Magma V2.10-6 Tue Mar 16 2004 09:59:35 on modular [Seed = 3909074669] ------------------------------------- 3 Total time: 3.019 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 09:59:51 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; G25 ! 5; Output: Magma V2.10-6 Tue Mar 16 2004 09:59:48 on modular [Seed = 2508374947] ------------------------------------- 0 Total time: 2.989 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 10:00:01 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; G25 ! 13; Output: Magma V2.10-6 Tue Mar 16 2004 09:59:58 on modular [Seed = 2190857406] ------------------------------------- 3 Total time: 3.129 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 10:01:06 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; G25 ! 13; Output: Magma V2.10-6 Tue Mar 16 2004 10:01:03 on modular [Seed = 2713122652] ------------------------------------- 3 Total time: 2.999 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 10:01:18 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; G25 ! 2; Output: Magma V2.10-6 Tue Mar 16 2004 10:01:15 on modular [Seed = 2931423303] ------------------------------------- 2 Total time: 2.989 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 10:02:02 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; G25 ! 2; Generator(G259; Output: Magma V2.10-6 Tue Mar 16 2004 10:01:59 on modular [Seed = 1447100642] ------------------------------------- 2 >> Generator(G259; ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 10:02:07 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; G25 ! 2; Generator(G259; Output: Magma V2.10-6 Tue Mar 16 2004 10:02:04 on modular [Seed = 1565133794] ------------------------------------- 2 >> Generator(G259; ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 10:02:15 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; G25 ! 2; Generator(G259; Output: Magma V2.10-6 Tue Mar 16 2004 10:02:12 on modular [Seed = 1146295011] ------------------------------------- 2 >> Generator(G259; ^ User error: bad syntax Total time: 3.019 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 10:02:25 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; G25 ! 2; Generator(G25); Output: Magma V2.10-6 Tue Mar 16 2004 10:02:22 on modular [Seed = 1935943134] ------------------------------------- 2 alpha Total time: 3.009 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 16 10:03:33 2004 Input: P:=PolynomialRing(Integers()); n:=x^((7^2)+7+7^0); t:=(x^(7^2))+(x^(7))+x; print(n); print(t); polav:=function (q,r); KQR:=GF(q,r); punts:=[ a,b in KQR | Evaluate(n73,a) eq Evaluate(t73,b)]; return{punts}; end function; Output: Magma V2.10-6 Tue Mar 16 2004 10:03:30 on modular [Seed = 2053975403] ------------------------------------- x^57 x^49 + x^7 + x >> punts:=[ a,b in KQR | Evaluate(n73,a) eq Evaluate(t73,b)]; ^ User error: bad syntax >> return{punts}; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 16 10:04:13 2004 Input: expo:= function (q,r) if ((r gt 0) and IsPrime(q)) then exp:= [q^(r-1)]; for i:=2 to r do exp:= exp cat [q^(r-i)]; end for; end if; return exp; end function; t := function (q,r) Z:=Integers(100); PT:=PolynomialRing(Z); lista:=expo(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + PT![0,1]^lista[i]; end for; return poly; end function; n := function (q,r) Z:=Integers(100); PT:=PolynomialRing(Z); lista:=expo(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=PT![0,1]^exp; return poly; end function; punts_olav:=function (q,r) punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; return{punts}; end function; Output: Magma V2.10-6 Tue Mar 16 2004 10:04:10 on modular [Seed = 1635137112] ------------------------------------- Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 16 10:04:32 2004 Input: expo:= function (q,r) if ((r gt 0) and IsPrime(q)) then exp:= [q^(r-1)]; for i:=2 to r do exp:= exp cat [q^(r-i)]; end for; end if; return exp; end function; t := function (q,r) Z:=Integers(100); PT:=PolynomialRing(Z); lista:=expo(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + PT![0,1]^lista[i]; end for; return poly; end function; n := function (q,r) Z:=Integers(100); PT:=PolynomialRing(Z); lista:=expo(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=PT![0,1]^exp; return poly; end function; punts_olav:=function (q,r) punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; return{punts}; end function; punt_olav(7,3); Output: Magma V2.10-6 Tue Mar 16 2004 10:04:29 on modular [Seed = 1753169734] ------------------------------------- >> punt_olav(7,3); ^ User error: Identifier 'punt_olav' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 16 10:04:42 2004 Input: expo:= function (q,r) if ((r gt 0) and IsPrime(q)) then exp:= [q^(r-1)]; for i:=2 to r do exp:= exp cat [q^(r-i)]; end for; end if; return exp; end function; t := function (q,r) Z:=Integers(100); PT:=PolynomialRing(Z); lista:=expo(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + PT![0,1]^lista[i]; end for; return poly; end function; n := function (q,r) Z:=Integers(100); PT:=PolynomialRing(Z); lista:=expo(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=PT![0,1]^exp; return poly; end function; punts_olav:=function (q,r) punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; return{punts}; end function; punts_olav(7,3); Output: Magma V2.10-6 Tue Mar 16 2004 10:04:39 on modular [Seed = 385892547] ------------------------------------- [
:16]( q: 7, r: 3 ) >> punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)] ^ Runtime error in 'Evaluate': Incompatible rings Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 16 10:05:49 2004 Input: expo:= function (q,r) if ((r gt 0) and IsPrime(q)) then exp:= [q^(r-1)]; for i:=2 to r do exp:= exp cat [q^(r-i)]; end for; end if; return exp; end function; t := function (q,r) Z:=Integers(); PT:=PolynomialRing(Z); lista:=expo(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + PT![0,1]^lista[i]; end for; return poly; end function; n := function (q,r) Z:=Integers(); PT:=PolynomialRing(Z); lista:=expo(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=PT![0,1]^exp; return poly; end function; punts_olav:=function (q,r) punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; return{punts}; end function; punts_olav(7,3); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Mar 16 2004 10:05:26 on modular [Seed = 34952679] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 4945 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 16 10:06:09 2004 Input: P:=PolynomialRing(Integers()); n73:=x^((7^2)+7+7^0); t73:=(x^(7^2))+(x^(7))+x; print(n); print(t); polav:=function (q,r); KQR:=GF(q,r); punts:=[ a,b in KQR | Evaluate(n73,a) eq Evaluate(t73,b)]; return{punts}; end function; Output: Magma V2.10-6 Tue Mar 16 2004 10:06:06 on modular [Seed = 136273797] ------------------------------------- >> print(n); ^ User error: Identifier 'n' has not been declared or assigned >> print(t); ^ User error: Identifier 't' has not been declared or assigned >> punts:=[ a,b in KQR | Evaluate(n73,a) eq Evaluate(t73,b)]; ^ User error: bad syntax >> return{punts}; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 16 10:06:21 2004 Input: P:=PolynomialRing(Integers()); n73:=x^((7^2)+7+7^0); t73:=(x^(7^2))+(x^(7))+x; print(n73); print(t73); polav:=function (q,r); KQR:=GF(q,r); punts:=[ a,b in KQR | Evaluate(n73,a) eq Evaluate(t73,b)]; return{punts}; end function; Output: Magma V2.10-6 Tue Mar 16 2004 10:06:18 on modular [Seed = 924868750] ------------------------------------- x^57 x^49 + x^7 + x >> punts:=[ a,b in KQR | Evaluate(n73,a) eq Evaluate(t73,b)]; ^ User error: bad syntax >> return{punts}; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 16 10:06:41 2004 Input: P:=PolynomialRing(Integers()); n73:=x^((7^2)+7+7^0); t73:=(x^(7^2))+(x^(7))+x; print(n73); print(t73); polav:=function (q,r); KQR:=GF(q,r); punts:=[ (a,b) in KQR | Evaluate(n73,a) eq Evaluate(t73,b)]; return{punts}; end function; Output: Magma V2.10-6 Tue Mar 16 2004 10:06:38 on modular [Seed = 590640270] ------------------------------------- x^57 x^49 + x^7 + x >> punts:=[ (a,b) in KQR | Evaluate(n73,a) eq Evaluate(t73,b)]; ^ User error: Identifier 'a' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 16 10:06:46 2004 Input: expo:= function (q,r) if ((r gt 0) and IsPrime(q)) then exp:= [q^(r-1)]; for i:=2 to r do exp:= exp cat [q^(r-i)]; end for; end if; return exp; end function; t := function (q,r) Z:=Integers(); PT:=PolynomialRing(Z); lista:=expo(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + PT![0,1]^lista[i]; end for; return poly; end function; n := function (q,r) Z:=Integers(); PT:=PolynomialRing(Z); lista:=expo(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=PT![0,1]^exp; return poly; end function; punts_olav:=function (q,r) punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; return{punts}; end function; punts_olav(7,3); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Mar 16 2004 10:06:23 on modular [Seed = 1042901378] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 4973 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 16 10:06:54 2004 Input: P:=PolynomialRing(Integers()); n73:=x^((7^2)+7+7^0); t73:=(x^(7^2))+(x^(7))+x; print(n73); print(t73); polav:=function (q,r); KQR:=GF(q,r); punts:=[ a,b in KQR | Evaluate(n73,a) eq Evaluate(t73,b)]; return{punts}; end function; Output: Magma V2.10-6 Tue Mar 16 2004 10:06:51 on modular [Seed = 742093940] ------------------------------------- x^57 x^49 + x^7 + x >> punts:=[ a,b in KQR | Evaluate(n73,a) eq Evaluate(t73,b)]; ^ User error: bad syntax >> return{punts}; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 16 10:07:04 2004 Input: P:=PolynomialRing(Integers()); n73:=x^((7^2)+7+7^0); t73:=(x^(7^2))+(x^(7))+x; print(n73); print(t73); polav:=function (q,r); KQR:=GF(q,r); punts:=[ a,b in KQR | Evaluate(n73,a) eq Evaluate(t73,b)]; return{punts}; end function; Output: Magma V2.10-6 Tue Mar 16 2004 10:07:01 on modular [Seed = 3687613341] ------------------------------------- x^57 x^49 + x^7 + x >> punts:=[ a,b in KQR | Evaluate(n73,a) eq Evaluate(t73,b)]; ^ User error: bad syntax >> return{punts}; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 16 10:08:07 2004 Input: n73:=x^57; t73:=x^49 + x^7 +x; k:=GF(7,3); punts:= [: a,b in k | Evaluate(n73,a) eq Evaluate(t73,b)]; punts; Output: Magma V2.10-6 Tue Mar 16 2004 10:08:04 on modular [Seed = 3268778693] ------------------------------------- >> n73:=x^57; ^ User error: Identifier 'x' has not been declared or assigned >> t73:=x^49 + x^7 +x; ^ User error: Identifier 'x' has not been declared or assigned >> punts:= [: a,b in k | Evaluate(n73,a) eq Evaluate(t73,b)]; ^ User error: Identifier 'n73' has not been declared or assigned >> punts;; ^ User error: Identifier 'punts' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 10:08:22 2004 Input: P2 := PolynomialRing(GF(2)); P3 := PolynomialRing(GF(3)); P5 := PolynomialRing(GF(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; G25 ! 2; Generator(G25); Output: Magma V2.10-6 Tue Mar 16 2004 10:08:19 on modular [Seed = 3386806777] ------------------------------------- 2 alpha Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 16 10:08:33 2004 Input: P:=PolynomialRing(Integers()); n73:=x^57; t73:=x^49 + x^7 +x; k:=GF(7,3); punts:= [: a,b in k | Evaluate(n73,a) eq Evaluate(t73,b)]; punts; Output: Magma V2.10-6 Tue Mar 16 2004 10:08:26 on modular [Seed = 4041713865] ------------------------------------- [ <1, k.1>, <1, k.1^2>, <1, k.1^7>, <1, k.1^10>, <1, k.1^11>, <1, k.1^14>, <1, k.1^16>, <1, k.1^25>, <1, k.1^37>, <1, k.1^49>, <1, k.1^66>, <1, k.1^70>, <1, k.1^77>, <1, k.1^87>, <1, k.1^90>, <1, k.1^97>, <1, k.1^98>, <1, k.1^100>, <1, k.1^103>, <1, k.1^112>, <1, k.1^120>, <1, k.1^131>, <1, k.1^132>, <1, k.1^137>, <1, k.1^146>, <1, k.1^148>, <1, k.1^156>, <1, k.1^159>, <1, k.1^175>, <1, k.1^195>, <1, k.1^197>, <1, k.1^199>, <1, k.1^215>, <1, k.1^233>, <1, k.1^240>, <1, k.1^259>, <1, k.1^263>, <1, k.1^267>, <1, k.1^275>, <1, 5>, <1, k.1^288>, <1, k.1^306>, <1, k.1^307>, <1, k.1^312>, <1, k.1^314>, <1, k.1^321>, <1, k.1^337>, <1, k.1^338>, <1, k.1^339>, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , := PolynomialRing(GF(2)); P3 := PolynomialRing(GF(3)); P5 := PolynomialRing(GF(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; G25 ! 11; Generator(G25); Output: Magma V2.10-6 Tue Mar 16 2004 10:08:35 on modular [Seed = 4176453848] ------------------------------------- 1 alpha Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 16 10:10:35 2004 Input: expo:= function (q,r) if ((r gt 0) and IsPrime(q)) then exp:= [q^(r-1)]; for i:=2 to r do exp:= exp cat [q^(r-i)]; end for; end if; return exp; end function; Z:=Integers(); PT:=PolynomialRing(Z); t := function (q,r) lista:=expo(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + x^lista[i]; end for; return poly; end function; n := function (q,r) lista:=expo(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=x^exp; return poly; end function; t(7,3); n(7,3); Output: Magma V2.10-6 Tue Mar 16 2004 10:10:32 on modular [Seed = 4009342549] ------------------------------------- x^49 + x^7 + x x^57 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 10:11:20 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; G25 ! 11; Generator(G25); IrreduciblePolynomial(G25,2); Output: Magma V2.10-6 Tue Mar 16 2004 10:11:17 on modular [Seed = 2508377299] ------------------------------------- 1 alpha $.1^2 + alpha^15*$.1 + alpha^5 Total time: 2.899 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 16 10:11:54 2004 Input: expo:= function (q,r) if ((r gt 0) and IsPrime(q)) then exp:= [q^(r-1)]; for i:=2 to r do exp:= exp cat [q^(r-i)]; end for; end if; return exp; end function; t := function (q,r) Z:=Integers(); PT:=PolynomialRing(Z); lista:=expo(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + x^lista[i]; end for; return poly; end function; n := function (q,r) Z:=Integers(); PT:=PolynomialRing(Z); lista:=expo(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=x^exp; return poly; end function; t(7,3); n(7,3); Output: Magma V2.10-6 Tue Mar 16 2004 10:11:51 on modular [Seed = 2626405880] ------------------------------------- x^49 + x^7 + x x^57 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 10:12:23 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; G25 ! 11; Generator(G25); IrreduciblePolynomial(G25,1); Output: Magma V2.10-6 Tue Mar 16 2004 10:12:20 on modular [Seed = 2342310540] ------------------------------------- 1 alpha $.1 Total time: 2.989 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 16 10:12:42 2004 Input: expo:= function (q,r) if ((r gt 0) and IsPrime(q)) then exp:= [q^(r-1)]; for i:=2 to r do exp:= exp cat [q^(r-i)]; end for; end if; return exp; end function; t := function (q,r) Z:=Integers(); PT:=PolynomialRing(Z); lista:=expo(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + x^lista[i]; end for; return poly; end function; n := function (q,r) Z:=Integers(); PT:=PolynomialRing(Z); lista:=expo(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=x^exp; return poly; end function; t(7,3); n(7,3); punts_olav:=function (q,r) punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; return{punts}; end function; punts(7,3); Output: Magma V2.10-6 Tue Mar 16 2004 10:12:39 on modular [Seed = 2997218182] ------------------------------------- x^49 + x^7 + x x^57 >> punts(7,3);; ^ User error: Identifier 'punts' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 10:13:09 2004 Input: P2 := PolynomialRing(GF(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G16; G25 := ext < GF(5) | j >; G25 ! 11; IrreduciblePolynomial(G25,1); Output: Magma V2.10-6 Tue Mar 16 2004 10:13:06 on modular [Seed = 3198805871] ------------------------------------- Finite field of size 2^4 1 $.1 Total time: 2.999 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 16 10:13:20 2004 Input: expo:= function (q,r) if ((r gt 0) and IsPrime(q)) then exp:= [q^(r-1)]; for i:=2 to r do exp:= exp cat [q^(r-i)]; end for; end if; return exp; end function; t := function (q,r) Z:=Integers(); PT:=PolynomialRing(Z); lista:=expo(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + x^lista[i]; end for; return poly; end function; n := function (q,r) Z:=Integers(); PT:=PolynomialRing(Z); lista:=expo(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=x^exp; return poly; end function; t(7,3); n(7,3); punts_olav:=function (q,r) punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; return{punts}; end function; punts_olav(7,3); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Mar 16 2004 10:12:57 on modular [Seed = 3115245715] ------------------------------------- x^49 + x^7 + x x^57 Errors: /home/mfd/gomagma: line 2: 5098 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 10:14:22 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; G25 ! 11; F := GF(27); F!6; Output: Magma V2.10-6 Tue Mar 16 2004 10:14:19 on modular [Seed = 2948134455] ------------------------------------- 1 0 Total time: 2.969 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 10:14:51 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; F := GF(27); F; F!7; Output: Magma V2.10-6 Tue Mar 16 2004 10:14:48 on modular [Seed = 1363544301] ------------------------------------- Finite field of size 3^3 1 Total time: 2.989 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 16 10:15:26 2004 Input: expo:= function (q,r) if ((r gt 0) and IsPrime(q)) then exp:= [q^(r-1)]; for i:=2 to r do exp:= exp cat [q^(r-i)]; end for; end if; return exp; end function; t := function (q,r) Z:=Integers(); PT:=PolynomialRing(Z); lista:=expo(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + x^lista[i]; end for; return poly; end function; n := function (q,r) Z:=Integers(); PT:=PolynomialRing(Z); lista:=expo(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=x^exp; return poly; end function; t(7,3); n(7,3); punts_olav:=function (q,r) punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; return punts; end function; punts_olav(7,3); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Mar 16 2004 10:15:03 on modular [Seed = 1179721701] ------------------------------------- x^49 + x^7 + x x^57 Errors: /home/mfd/gomagma: line 2: 5138 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host aula-etse013.uab.es. (158.109.66.132) Time: Tue Mar 16 10:15:45 2004 Input: G2:=GF(2); G3:=GF(3); G5:=GF(5); /* Z9 no es un cos, ja que nou no es un nombre primer */ Z9:=Integers(9); /* [a]m pertanyent a Zm es invertible sii mcd(a,m)=1*/ IsInvertible(Z9!3); Output: Magma V2.10-6 Tue Mar 16 2004 10:15:41 on modular [Seed = 1214190081] ------------------------------------- false Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 16 10:16:37 2004 Input: P:=PolynomialRing(Integers()); n73:=x^((7^2)+7+7^0); t73:=(x^(7^2))+(x^(7))+x; polav:=function (q,r); KQR:=GF(Integers(q),Integers(r)); punts:=[ a,b in KQR | Evaluate(n73,a) eq Evaluate(t73,b)]; return{punts}; end function; Output: Magma V2.10-6 Tue Mar 16 2004 10:16:34 on modular [Seed = 1935944053] ------------------------------------- >> punts:=[ a,b in KQR | Evaluate(n73,a) eq Evaluate(t73,b)]; ^ User error: bad syntax >> return{punts}; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 16 10:16:59 2004 Input: expo:= function (q,r) if ((r gt 0) and IsPrime(q)) then exp:= [q^(r-1)]; for i:=2 to r do exp:= exp cat [q^(r-i)]; end for; end if; return exp; end function; Z:=Integers(); PT:=PolynomialRing(Z); t := function (q,r) lista:=expo(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + x^lista[i]; end for; return poly; end function; n := function (q,r) lista:=expo(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=x^exp; return poly; end function; t(7,3); n(7,3); punts_olav:=function (q,r) punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; return punts; end function; punts_olav(7,3); Output: Magma V2.10-6 Tue Mar 16 2004 10:16:37 on modular [Seed = 1685274213] ------------------------------------- x^49 + x^7 + x x^57 [ <1, $.1>, <1, $.1^2>, <1, $.1^7>, <1, $.1^10>, <1, $.1^11>, <1, $.1^14>, <1, $.1^16>, <1, $.1^25>, <1, $.1^37>, <1, $.1^49>, <1, $.1^66>, <1, $.1^70>, <1, $.1^77>, <1, $.1^87>, <1, $.1^90>, <1, $.1^97>, <1, $.1^98>, <1, $.1^100>, <1, $.1^103>, <1, $.1^112>, <1, $.1^120>, <1, $.1^131>, <1, $.1^132>, <1, $.1^137>, <1, $.1^146>, <1, $.1^148>, <1, $.1^156>, <1, $.1^159>, <1, $.1^175>, <1, $.1^195>, <1, $.1^197>, <1, $.1^199>, <1, $.1^215>, <1, $.1^233>, <1, $.1^240>, <1, $.1^259>, <1, $.1^263>, <1, $.1^267>, <1, $.1^275>, <1, 5>, <1, $.1^288>, <1, $.1^306>, <1, $.1^307>, <1, $.1^312>, <1, $.1^314>, <1, $.1^321>, <1, $.1^337>, <1, $.1^338>, <1, $.1^339>, <$.1, 1>, <$.1, $.1^3>, <$.1, $.1^21>, <$.1, $.1^22>, <$.1, $.1^27>, <$.1, $.1^29>, <$.1, $.1^36>, <$.1, $.1^52>, <$.1, $.1^53>, <$.1, $.1^54>, <$.1, $.1^58>, <$.1, $.1^59>, <$.1, $.1^64>, <$.1, $.1^67>, <$.1, $.1^68>, <$.1, $.1^71>, <$.1, $.1^73>, <$.1, $.1^82>, <$.1, $.1^94>, <$.1, $.1^106>, <$.1, $.1^123>, <$.1, $.1^127>, <$.1, $.1^134>, <$.1, $.1^144>, <$.1, $.1^147>, <$.1, $.1^154>, <$.1, $.1^155>, <$.1, $.1^157>, <$.1, $.1^160>, <$.1, $.1^169>, <$.1, $.1^177>, <$.1, $.1^188>, <$.1, $.1^189>, <$.1, $.1^194>, <$.1, $.1^203>, <$.1, $.1^205>, <$.1, $.1^213>, <$.1, $.1^216>, <$.1, $.1^232>, <$.1, $.1^252>, <$.1, $.1^254>, <$.1, $.1^256>, <$.1, $.1^272>, <$.1, $.1^290>, <$.1, $.1^297>, <$.1, $.1^316>, <$.1, $.1^320>, <$.1, $.1^324>, <$.1, $.1^332>, <$.1^2, $.1^5>, <$.1^2, $.1^12>, <$.1^2, $.1^31>, <$.1^2, $.1^35>, <$.1^2, $.1^39>, <$.1^2, $.1^47>, <$.1^2, 3>, <$.1^2, $.1^60>, <$.1^2, $.1^78>, <$.1^2, $.1^79>, <$.1^2, $.1^84>, <$.1^2, $.1^86>, <$.1^2, $.1^93>, <$.1^2, $.1^109>, <$.1^2, $.1^110>, <$.1^2, $.1^111>, <$.1^2, $.1^115>, <$.1^2, $.1^116>, <$.1^2, $.1^121>, <$.1^2, $.1^124>, <$.1^2, $.1^125>, <$.1^2, $.1^128>, <$.1^2, $.1^130>, <$.1^2, $.1^139>, <$.1^2, $.1^151>, <$.1^2, $.1^163>, <$.1^2, $.1^180>, <$.1^2, $.1^184>, <$.1^2, $.1^191>, <$.1^2, $.1^201>, <$.1^2, $.1^204>, <$.1^2, $.1^211>, <$.1^2, $.1^212>, <$.1^2, $.1^214>, <$.1^2, $.1^217>, <$.1^2, $.1^226>, <$.1^2, $.1^234>, <$.1^2, $.1^245>, <$.1^2, $.1^246>, <$.1^2, $.1^251>, <$.1^2, $.1^260>, <$.1^2, $.1^262>, <$.1^2, $.1^270>, <$.1^2, $.1^273>, <$.1^2, $.1^289>, <$.1^2, $.1^309>, <$.1^2, $.1^311>, <$.1^2, $.1^313>, <$.1^2, $.1^329>, <$.1^3, $.1^4>, <$.1^3, $.1^24>, <$.1^3, $.1^26>, <$.1^3, $.1^28>, <$.1^3, $.1^44>, <$.1^3, $.1^62>, <$.1^3, $.1^69>, <$.1^3, $.1^88>, <$.1^3, $.1^92>, <$.1^3, $.1^96>, <$.1^3, $.1^104>, <$.1^3, 2>, <$.1^3, $.1^117>, <$.1^3, $.1^135>, <$.1^3, $.1^136>, <$.1^3, $.1^141>, <$.1^3, $.1^143>, <$.1^3, $.1^150>, <$.1^3, $.1^166>, <$.1^3, $.1^167>, <$.1^3, $.1^168>, <$.1^3, $.1^172>, <$.1^3, $.1^173>, <$.1^3, $.1^178>, <$.1^3, $.1^181>, <$.1^3, $.1^182>, <$.1^3, $.1^185>, <$.1^3, $.1^187>, <$.1^3, $.1^196>, <$.1^3, $.1^208>, <$.1^3, $.1^220>, <$.1^3, $.1^237>, <$.1^3, $.1^241>, <$.1^3, $.1^248>, <$.1^3, $.1^258>, <$.1^3, $.1^261>, <$.1^3, $.1^268>, <$.1^3, $.1^269>, <$.1^3, $.1^271>, <$.1^3, $.1^274>, <$.1^3, $.1^283>, <$.1^3, $.1^291>, <$.1^3, $.1^302>, <$.1^3, $.1^303>, <$.1^3, $.1^308>, <$.1^3, $.1^317>, <$.1^3, $.1^319>, <$.1^3, $.1^327>, <$.1^3, $.1^330>, <$.1^4, $.1^6>, <$.1^4, $.1^17>, <$.1^4, $.1^18>, <$.1^4, $.1^23>, <$.1^4, $.1^32>, <$.1^4, $.1^34>, <$.1^4, $.1^42>, <$.1^4, $.1^45>, <$.1^4, $.1^61>, <$.1^4, $.1^81>, <$.1^4, $.1^83>, <$.1^4, $.1^85>, <$.1^4, $.1^101>, <$.1^4, $.1^119>, <$.1^4, $.1^126>, <$.1^4, $.1^145>, <$.1^4, $.1^149>, <$.1^4, $.1^153>, <$.1^4, $.1^161>, <$.1^4, 6>, <$.1^4, $.1^174>, <$.1^4, $.1^192>, <$.1^4, $.1^193>, <$.1^4, $.1^198>, <$.1^4, $.1^200>, <$.1^4, $.1^207>, <$.1^4, $.1^223>, <$.1^4, $.1^224>, <$.1^4, $.1^225>, <$.1^4, $.1^229>, <$.1^4, $.1^230>, <$.1^4, $.1^235>, <$.1^4, $.1^238>, <$.1^4, $.1^239>, <$.1^4, $.1^242>, <$.1^4, $.1^244>, <$.1^4, $.1^253>, <$.1^4, $.1^265>, <$.1^4, $.1^277>, <$.1^4, $.1^294>, <$.1^4, $.1^298>, <$.1^4, $.1^305>, <$.1^4, $.1^315>, <$.1^4, $.1^318>, <$.1^4, $.1^325>, <$.1^4, $.1^326>, <$.1^4, $.1^328>, <$.1^4, $.1^331>, <$.1^4, $.1^340>, <$.1^5, $.1^9>, <$.1^5, $.1^13>, <$.1^5, $.1^20>, <$.1^5, $.1^30>, <$.1^5, $.1^33>, <$.1^5, $.1^40>, <$.1^5, $.1^41>, <$.1^5, $.1^43>, <$.1^5, $.1^46>, <$.1^5, $.1^55>, <$.1^5, $.1^63>, <$.1^5, $.1^74>, <$.1^5, $.1^75>, <$.1^5, $.1^80>, <$.1^5, $.1^89>, <$.1^5, $.1^91>, <$.1^5, $.1^99>, <$.1^5, $.1^102>, <$.1^5, $.1^118>, <$.1^5, $.1^138>, <$.1^5, $.1^140>, <$.1^5, $.1^142>, <$.1^5, $.1^158>, <$.1^5, $.1^176>, <$.1^5, $.1^183>, <$.1^5, $.1^202>, <$.1^5, $.1^206>, <$.1^5, $.1^210>, <$.1^5, $.1^218>, <$.1^5, 4>, <$.1^5, $.1^231>, <$.1^5, $.1^249>, <$.1^5, $.1^250>, <$.1^5, $.1^255>, <$.1^5, $.1^257>, <$.1^5, $.1^264>, <$.1^5, $.1^280>, <$.1^5, $.1^281>, <$.1^5, $.1^282>, <$.1^5, $.1^286>, <$.1^5, $.1^287>, <$.1^5, $.1^292>, <$.1^5, $.1^295>, <$.1^5, $.1^296>, <$.1^5, $.1^299>, <$.1^5, $.1^301>, <$.1^5, $.1^310>, <$.1^5, $.1^322>, <$.1^5, $.1^334>, <$.1^6, $.1>, <$.1^6, $.1^2>, <$.1^6, $.1^7>, <$.1^6, $.1^10>, <$.1^6, $.1^11>, <$.1^6, $.1^14>, <$.1^6, $.1^16>, <$.1^6, $.1^25>, <$.1^6, $.1^37>, <$.1^6, $.1^49>, <$.1^6, $.1^66>, <$.1^6, $.1^70>, <$.1^6, $.1^77>, <$.1^6, $.1^87>, <$.1^6, $.1^90>, <$.1^6, $.1^97>, <$.1^6, $.1^98>, <$.1^6, $.1^100>, <$.1^6, $.1^103>, <$.1^6, $.1^112>, <$.1^6, $.1^120>, <$.1^6, $.1^131>, <$.1^6, $.1^132>, <$.1^6, $.1^137>, <$.1^6, $.1^146>, <$.1^6, $.1^148>, <$.1^6, $.1^156>, <$.1^6, $.1^159>, <$.1^6, $.1^175>, <$.1^6, $.1^195>, <$.1^6, $.1^197>, <$.1^6, $.1^199>, <$.1^6, $.1^215>, <$.1^6, $.1^233>, <$.1^6, $.1^240>, <$.1^6, $.1^259>, <$.1^6, $.1^263>, <$.1^6, $.1^267>, <$.1^6, $.1^275>, <$.1^6, 5>, <$.1^6, $.1^288>, <$.1^6, $.1^306>, <$.1^6, $.1^307>, <$.1^6, $.1^312>, <$.1^6, $.1^314>, <$.1^6, $.1^321>, <$.1^6, $.1^337>, <$.1^6, $.1^338>, <$.1^6, $.1^339>, <$.1^7, 1>, <$.1^7, $.1^3>, <$.1^7, $.1^21>, <$.1^7, $.1^22>, <$.1^7, $.1^27>, <$.1^7, $.1^29>, <$.1^7, $.1^36>, <$.1^7, $.1^52>, <$.1^7, $.1^53>, <$.1^7, $.1^54>, <$.1^7, $.1^58>, <$.1^7, $.1^59>, <$.1^7, $.1^64>, <$.1^7, $.1^67>, <$.1^7, $.1^68>, <$.1^7, $.1^71>, <$.1^7, $.1^73>, <$.1^7, $.1^82>, <$.1^7, $.1^94>, <$.1^7, $.1^106>, <$.1^7, $.1^123>, <$.1^7, $.1^127>, <$.1^7, $.1^134>, <$.1^7, $.1^144>, <$.1^7, $.1^147>, <$.1^7, $.1^154>, <$.1^7, $.1^155>, <$.1^7, $.1^157>, <$.1^7, $.1^160>, <$.1^7, $.1^169>, <$.1^7, $.1^177>, <$.1^7, $.1^188>, <$.1^7, $.1^189>, <$.1^7, $.1^194>, <$.1^7, $.1^203>, <$.1^7, $.1^205>, <$.1^7, $.1^213>, <$.1^7, $.1^216>, <$.1^7, $.1^232>, <$.1^7, $.1^252>, <$.1^7, $.1^254>, <$.1^7, $.1^256>, <$.1^7, $.1^272>, <$.1^7, $.1^290>, <$.1^7, $.1^297>, <$.1^7, $.1^316>, <$.1^7, $.1^320>, <$.1^7, $.1^324>, <$.1^7, $.1^332>, <$.1^8, $.1^5>, <$.1^8, $.1^12>, <$.1^8, $.1^31>, <$.1^8, $.1^35>, <$.1^8, $.1^39>, <$.1^8, $.1^47>, <$.1^8, 3>, <$.1^8, $.1^60>, <$.1^8, $.1^78>, <$.1^8, $.1^79>, <$.1^8, $.1^84>, <$.1^8, $.1^86>, <$.1^8, $.1^93>, <$.1^8, $.1^109>, <$.1^8, $.1^110>, <$.1^8, $.1^111>, <$.1^8, $.1^115>, <$.1^8, $.1^116>, <$.1^8, $.1^121>, <$.1^8, $.1^124>, <$.1^8, $.1^125>, <$.1^8, $.1^128>, <$.1^8, $.1^130>, <$.1^8, $.1^139>, <$.1^8, $.1^151>, <$.1^8, $.1^163>, <$.1^8, $.1^180>, <$.1^8, $.1^184>, <$.1^8, $.1^191>, <$.1^8, $.1^201>, <$.1^8, $.1^204>, <$.1^8, $.1^211>, <$.1^8, $.1^212>, <$.1^8, $.1^214>, <$.1^8, $.1^217>, <$.1^8, $.1^226>, <$.1^8, $.1^234>, <$.1^8, $.1^245>, <$.1^8, $.1^246>, <$.1^8, $.1^251>, <$.1^8, $.1^260>, <$.1^8, $.1^262>, <$.1^8, $.1^270>, <$.1^8, $.1^273>, <$.1^8, $.1^289>, <$.1^8, $.1^309>, <$.1^8, $.1^311>, <$.1^8, $.1^313>, <$.1^8, $.1^329>, <$.1^9, $.1^4>, <$.1^9, $.1^24>, <$.1^9, $.1^26>, <$.1^9, $.1^28>, <$.1^9, $.1^44>, <$.1^9, $.1^62>, <$.1^9, $.1^69>, <$.1^9, $.1^88>, <$.1^9, $.1^92>, <$.1^9, $.1^96>, <$.1^9, $.1^104>, <$.1^9, 2>, <$.1^9, $.1^117>, <$.1^9, $.1^135>, <$.1^9, $.1^136>, <$.1^9, $.1^141>, <$.1^9, $.1^143>, <$.1^9, $.1^150>, <$.1^9, $.1^166>, <$.1^9, $.1^167>, <$.1^9, $.1^168>, <$.1^9, $.1^172>, <$.1^9, $.1^173>, <$.1^9, $.1^178>, <$.1^9, $.1^181>, <$.1^9, $.1^182>, <$.1^9, $.1^185>, <$.1^9, $.1^187>, <$.1^9, $.1^196>, <$.1^9, $.1^208>, <$.1^9, $.1^220>, <$.1^9, $.1^237>, <$.1^9, $.1^241>, <$.1^9, $.1^248>, <$.1^9, $.1^258>, <$.1^9, $.1^261>, <$.1^9, $.1^268>, <$.1^9, $.1^269>, <$.1^9, $.1^271>, <$.1^9, $.1^274>, <$.1^9, $.1^283>, <$.1^9, $.1^291>, <$.1^9, $.1^302>, <$.1^9, $.1^303>, <$.1^9, $.1^308>, <$.1^9, $.1^317>, <$.1^9, $.1^319>, <$.1^9, $.1^327>, <$.1^9, $.1^330>, <$.1^10, $.1^6>, <$.1^10, $.1^17>, <$.1^10, $.1^18>, <$.1^10, $.1^23>, <$.1^10, $.1^32>, <$.1^10, $.1^34>, <$.1^10, $.1^42>, <$.1^10, $.1^45>, <$.1^10, $.1^61>, <$.1^10, $.1^81>, <$.1^10, $.1^83>, <$.1^10, $.1^85>, <$.1^10, $.1^101>, <$.1^10, $.1^119>, <$.1^10, $.1^126>, <$.1^10, $.1^145>, <$.1^10, $.1^149>, <$.1^10, $.1^153>, <$.1^10, $.1^161>, <$.1^10, 6>, <$.1^10, $.1^174>, <$.1^10, $.1^192>, <$.1^10, $.1^193>, <$.1^10, $.1^198>, <$.1^10, $.1^200>, <$.1^10, $.1^207>, <$.1^10, $.1^223>, <$.1^10, $.1^224>, <$.1^10, $.1^225>, <$.1^10, $.1^229>, <$.1^10, $.1^230>, <$.1^10, $.1^235>, <$.1^10, $.1^238>, <$.1^10, $.1^239>, <$.1^10, $.1^242>, <$.1^10, $.1^244>, <$.1^10, $.1^253>, <$.1^10, $.1^265>, <$.1^10, $.1^277>, <$.1^10, $.1^294>, <$.1^10, $.1^298>, <$.1^10, $.1^305>, <$.1^10, $.1^315>, <$.1^10, $.1^318>, <$.1^10, $.1^325>, <$.1^10, $.1^326>, <$.1^10, $.1^328>, <$.1^10, $.1^331>, <$.1^10, $.1^340>, <$.1^11, $.1^9>, <$.1^11, $.1^13>, <$.1^11, $.1^20>, <$.1^11, $.1^30>, <$.1^11, $.1^33>, <$.1^11, $.1^40>, <$.1^11, $.1^41>, <$.1^11, $.1^43>, <$.1^11, $.1^46>, <$.1^11, $.1^55>, <$.1^11, $.1^63>, <$.1^11, $.1^74>, <$.1^11, $.1^75>, <$.1^11, $.1^80>, <$.1^11, $.1^89>, <$.1^11, $.1^91>, <$.1^11, $.1^99>, <$.1^11, $.1^102>, <$.1^11, $.1^118>, <$.1^11, $.1^138>, <$.1^11, $.1^140>, <$.1^11, $.1^142>, <$.1^11, $.1^158>, <$.1^11, $.1^176>, <$.1^11, $.1^183>, <$.1^11, $.1^202>, <$.1^11, $.1^206>, <$.1^11, $.1^210>, <$.1^11, ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 16 10:17:04 2004 Input: P:=PolynomialRing(Integers()); n73:=x^((7^2)+7+7^0); t73:=(x^(7^2))+(x^(7))+x; polav:=function (q,r); KQR:=GF(Integers(q),Integers(r)); punts:=[ a,b in KQR | (Evaluate(n73,a) eq Evaluate(t73,b))]; return{punts}; end function; Output: Magma V2.10-6 Tue Mar 16 2004 10:17:01 on modular [Seed = 1836726100] ------------------------------------- >> punts:=[ a,b in KQR | (Evaluate(n73,a) eq Evaluate(t73,b))]; ^ User error: bad syntax >> return{punts}; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 16 10:17:15 2004 Input: P:=PolynomialRing(Integers()); n73:=x^((7^2)+7+7^0); t73:=(x^(7^2))+(x^(7))+x; polav:=function (q,r); KQR:=GF(Integers(q),Integers(r)); punts:=[: a,b in KQR | (Evaluate(n73,a) eq Evaluate(t73,b))]; return{punts}; end function; Output: Magma V2.10-6 Tue Mar 16 2004 10:17:12 on modular [Seed = 369183802] ------------------------------------- >> punts:=[: a,b in KQR | (Evaluate(n73,a) eq Evaluate(t73,b))]; ^ User error: bad syntax >> return{punts}; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse013.uab.es. (158.109.66.132) Time: Tue Mar 16 10:18:00 2004 Input: G2:=GF(2); G3:=GF(3); G5:=GF(5); /* Z9 no es un cos, ja que nou no es un nombre primer */ Z9:=Integers(9); /* [a]m pertanyent a Zm es invertible sii mcd(a,m)=1*/ IsInvertible(Z9!3); s:=GF(3^2); p:=PolynomialRing(s); f:= 2+2*x+x^2; Factorization(f); Output: Magma V2.10-6 Tue Mar 16 2004 10:17:57 on modular [Seed = 520635886] ------------------------------------- false [ , ] Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-etse013.uab.es. (158.109.66.132) Time: Tue Mar 16 10:18:16 2004 Input: G2:=GF(2); G3:=GF(3); G5:=GF(5); /* Z9 no es un cos, ja que nou no es un nombre primer */ Z9:=Integers(9); /* [a]m pertanyent a Zm es invertible sii mcd(a,m)=1*/ IsInvertible(Z9!3); s:=GF(3^2); p:=PolynomialRing(s); f:= 2+2*x+x^2; Factorization(f); Output: Magma V2.10-6 Tue Mar 16 2004 10:18:12 on modular [Seed = 51665379] ------------------------------------- false [ , ] Total time: 3.749 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 16 10:18:16 2004 Input: P:=PolynomialRing(Integers()); n73:=x^((7^2)+7+7^0); t73:=(x^(7^2))+(x^(7))+x; polav:=function (q,r); KQR:=GF(Integers(q),Integers(r)); punts:=[: a,b in KQR | (Evaluate(n73,a) eq Evaluate(t73,b))]; return(punts); end function; Output: Magma V2.10-6 Tue Mar 16 2004 10:18:12 on modular [Seed = 18242529] ------------------------------------- >> punts:=[: a,b in KQR | (Evaluate(n73,a) eq Evaluate(t73,b))]; ^ User error: bad syntax >> return(punts); ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax Total time: 3.729 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse013.uab.es. (158.109.66.132) Time: Tue Mar 16 10:18:54 2004 Input: G2:=GF(2); G3:=GF(3); G5:=GF(5); /* Z9 no es un cos, ja que nou no es un nombre primer */ Z9:=Integers(9); /* [a]m pertanyent a Zm es invertible sii mcd(a,m)=1*/ IsInvertible(Z9!3); s:=GF(3^2); p:=PolynomialRing(s); f:= 2+2*x+x^2; Factorization(f); Roots(f); Output: Magma V2.10-6 Tue Mar 16 2004 10:18:51 on modular [Seed = 841312445] ------------------------------------- false [ , ] [ , ] Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-etse013.uab.es. (158.109.66.132) Time: Tue Mar 16 10:19:12 2004 Input: G2:=GF(2); G3:=GF(3); G5:=GF(5); /* Z9 no es un cos, ja que nou no es un nombre primer */ Z9:=Integers(9); /* [a]m pertanyent a Zm es invertible sii mcd(a,m)=1*/ IsInvertible(Z9!3); s:=GF(3,2); p:=PolynomialRing(s); f:= 2+2*x+x^2; Factorization(f); Roots(f); Output: Magma V2.10-6 Tue Mar 16 2004 10:19:08 on modular [Seed = 992764290] ------------------------------------- false [ , ] [ , ] Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-etse013.uab.es. (158.109.66.132) Time: Tue Mar 16 10:20:01 2004 Input: G2:=GF(2); G3:=GF(3); G5:=GF(5); /* Z9 no es un cos, ja que nou no es un nombre primer */ Z9:=Integers(9); /* [a]m pertanyent a Zm es invertible sii mcd(a,m)=1*/ IsInvertible(Z9!3); s:=GF(3,2); p:=PolynomialRing(s); f:= 2+2*x+x^2; Factorization(f); Output: Magma V2.10-6 Tue Mar 16 2004 10:19:58 on modular [Seed = 742094694] ------------------------------------- false [ , ] Total time: 3.059 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 16 10:20:22 2004 Input: P:=PolynomialRing(Integers()); n73:=x^((7^2)+7+7^0); t73:=(x^(7^2))+(x^(7))+x; polav:=function (q,r); KQR:=GF(q,r); punts:=[: a,b in KQR | (Evaluate(n73,a) eq Evaluate(t73,b))]; return(punts); end function; Output: Magma V2.10-6 Tue Mar 16 2004 10:20:18 on modular [Seed = 3704326074] ------------------------------------- >> punts:=[: a,b in KQR | (Evaluate(n73,a) eq Evaluate(t73,b))]; ^ User error: bad syntax >> return(punts); ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax Total time: 3.709 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse013.uab.es. (158.109.66.132) Time: Tue Mar 16 10:20:22 2004 Input: G2:=GF(2); G3:=GF(3); G5:=GF(5); /* Z9 no es un cos, ja que nou no es un nombre primer */ Z9:=Integers(9); /* [a]m pertanyent a Zm es invertible sii mcd(a,m)=1*/ IsInvertible(Z9!3); s:=GF(3,2); p:=PolynomialRing(s); f:= 2+2*x+x^2; Factorization(f); Roots(f,s); Output: Magma V2.10-6 Tue Mar 16 2004 10:20:18 on modular [Seed = 3754460344] ------------------------------------- false [ , ] [ , ] Total time: 3.769 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 16 10:20:32 2004 Input: P:=PolynomialRing(Integers()); n73:=x^((7^2)+7+7^0); t73:=(x^(7^2))+(x^(7))+x; polav:=function (q,r); KQR:=GF(q,r); punts:=[ a,b in KQR | (Evaluate(n73,a) eq Evaluate(t73,b))]; return(punts); end function; Output: Magma V2.10-6 Tue Mar 16 2004 10:20:29 on modular [Seed = 3470366119] ------------------------------------- >> punts:=[ a,b in KQR | (Evaluate(n73,a) eq Evaluate(t73,b))]; ^ User error: bad syntax >> return(punts); ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse013.uab.es. (158.109.66.132) Time: Tue Mar 16 10:20:41 2004 Input: G2:=GF(2); G3:=GF(3); G5:=GF(5); /* Z9 no es un cos, ja que nou no es un nombre primer */ Z9:=Integers(9); /* [a]m pertanyent a Zm es invertible sii mcd(a,m)=1*/ IsInvertible(Z9!3); s:=GF(3,2); p:=PolynomialRing(s); f:= 2+2*x+x^2; Factorization(f); Roots(f,s); IsIrreducible(f); Output: Magma V2.10-6 Tue Mar 16 2004 10:20:38 on modular [Seed = 4041714658] ------------------------------------- false [ , ] [ , ] false Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 210-BAR2-X75.libre.retevision.es. (62.82.151.210) Time: Tue Mar 16 10:20:50 2004 Input: spolav:= [k : k in polavqr(2,3) | k[1] in GF(2) and k[2] in GF(2) ]; #spolav; Output: Magma V2.10-6 Tue Mar 16 2004 10:20:47 on modular [Seed = 4193166050] ------------------------------------- >> spolav:= [k : k in polavqr(2,3) | k[1] in GF(2) and k[2] in GF(2) ]; ^ User error: Identifier 'polavqr' has not been declared or assigned >> #spolav;; ^ User error: Identifier 'spolav' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 16 10:21:00 2004 Input: /*P:=PolynomialRing(Integers()); n73:=x^((7^2)+7+7^0); t73:=(x^(7^2))+(x^(7))+x;*/ polav:=function (q,r); KQR:=GF(q,r); punts:=[ a,b in KQR | (Evaluate(n73,a) eq Evaluate(t73,b))]; return(punts); end function; Output: Magma V2.10-6 Tue Mar 16 2004 10:20:57 on modular [Seed = 3807754735] ------------------------------------- >> punts:=[ a,b in KQR | (Evaluate(n73,a) eq Evaluate(t73,b))]; ^ User error: bad syntax >> return(punts); ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse013.uab.es. (158.109.66.132) Time: Tue Mar 16 10:21:25 2004 Input: G2:=GF(2); G3:=GF(3); G5:=GF(5); /* Z9 no es un cos, ja que nou no es un nombre primer */ Z9:=Integers(9); /* [a]m pertanyent a Zm es invertible sii mcd(a,m)=1*/ IsInvertible(Z9!3); s:=GF(3,2); p:=PolynomialRing(s); f:= 2+2*x+x^2; Factorization(f); Roots(f,s); IsIrreducible(f); s1:=GF(2,4); p1:=PolynomialRing(s1); f1:= 1+x+x^4; Factorization(f1); Roots(f1,s1); IsIrreducible(f1); Output: Magma V2.10-6 Tue Mar 16 2004 10:21:22 on modular [Seed = 3959206093] ------------------------------------- false [ , ] [ , ] false [ , , , ] [ , , , ] false Total time: 3.489 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host aula-a-siee29.uab.es. (158.109.66.29) Time: Tue Mar 16 10:21:26 2004 Input: polav := function (q,r); KQR:=GF(q,r); punts:=[ a,b in KQR | (Evaluate(n73,a) eq Evaluate(t73,b))]; return(punts); end function; Output: Magma V2.10-6 Tue Mar 16 2004 10:21:23 on modular [Seed = 2525089201] ------------------------------------- >> punts:=[ a,b in KQR | (Evaluate(n73,a) eq Evaluate(t73,b))]; ^ User error: bad syntax >> return(punts); ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax Total time: 3.479 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 210-BAR2-X75.libre.retevision.es. (62.82.151.210) Time: Tue Mar 16 10:21:36 2004 Input: polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(~C, [i,j]);end if; end for;end for; return C; end function; spolav:= [k : k in polavqr(2,3) | k[1] in GF(2) and k[2] in GF(2) ]; #spolav; Output: Magma V2.10-6 Tue Mar 16 2004 10:21:32 on modular [Seed = 2240994989] ------------------------------------- >> if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(~C, [i,j] ^ User error: Identifier 'pnqr' has not been declared or assigned >> spolav:= [k : k in polavqr(2,3) | k[1] in GF(2) and k[2] in GF(2) ]; ^ User error: Identifier 'polavqr' has not been declared or assigned >> #spolav;; ^ User error: Identifier 'spolav' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 16 10:22:13 2004 Input: GF2 := GF (2); print GF2; Output: Magma V2.10-6 Tue Mar 16 2004 10:22:10 on modular [Seed = 2392446328] ------------------------------------- Finite field of size 2 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse013.uab.es. (158.109.66.132) Time: Tue Mar 16 10:22:21 2004 Input: G2:=GF(2); G3:=GF(3); G5:=GF(5); /* Z9 no es un cos, ja que nou no es un nombre primer */ Z9:=Integers(9); /* [a]m pertanyent a Zm es invertible sii mcd(a,m)=1*/ IsInvertible(Z9!3); s:=GF(3,2); p:=PolynomialRing(s); f:= 2+2*x+x^2; Factorization(f); Roots(f,s); IsIrreducible(f); s1=GF(2,4); p1:=PolynomialRing(s1); f1:= 1+x+x^4; Factorization(f1); Roots(f1,s1); IsIrreducible(f1); Output: Magma V2.10-6 Tue Mar 16 2004 10:22:17 on modular [Seed = 2997217615] ------------------------------------- false [ , ] [ , ] false >> s1=GF(2,4); ^ User error: Identifier 's1' has not been declared or assigned >> p1:=PolynomialRing(s1); ^ User error: Identifier 's1' has not been declared or assigned [ , ] >> Roots(f1,s1); ^ User error: Identifier 's1' has not been declared or assigned false Total time: 3.179 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 16 10:22:37 2004 Input: expo:= function (q,r) if ((r gt 0) and IsPrime(q)) then exp:= [q^(r-1)]; for i:=2 to r do exp:= exp cat [q^(r-i)]; end for; end if; return exp; end function; Z:=Integers(); PT:=PolynomialRing(Z); t := function (q,r) lista:=expo(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + x^lista[i]; end for; return poly; end function; n := function (q,r) lista:=expo(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=x^exp; return poly; end function; punts_olav:=function (q,r) punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; return punts; end function; punts_olav(7,3); Output: Magma V2.10-6 Tue Mar 16 2004 10:22:15 on modular [Seed = 3080776772] ------------------------------------- [ <1, $.1>, <1, $.1^2>, <1, $.1^7>, <1, $.1^10>, <1, $.1^11>, <1, $.1^14>, <1, $.1^16>, <1, $.1^25>, <1, $.1^37>, <1, $.1^49>, <1, $.1^66>, <1, $.1^70>, <1, $.1^77>, <1, $.1^87>, <1, $.1^90>, <1, $.1^97>, <1, $.1^98>, <1, $.1^100>, <1, $.1^103>, <1, $.1^112>, <1, $.1^120>, <1, $.1^131>, <1, $.1^132>, <1, $.1^137>, <1, $.1^146>, <1, $.1^148>, <1, $.1^156>, <1, $.1^159>, <1, $.1^175>, <1, $.1^195>, <1, $.1^197>, <1, $.1^199>, <1, $.1^215>, <1, $.1^233>, <1, $.1^240>, <1, $.1^259>, <1, $.1^263>, <1, $.1^267>, <1, $.1^275>, <1, 5>, <1, $.1^288>, <1, $.1^306>, <1, $.1^307>, <1, $.1^312>, <1, $.1^314>, <1, $.1^321>, <1, $.1^337>, <1, $.1^338>, <1, $.1^339>, <$.1, 1>, <$.1, $.1^3>, <$.1, $.1^21>, <$.1, $.1^22>, <$.1, $.1^27>, <$.1, $.1^29>, <$.1, $.1^36>, <$.1, $.1^52>, <$.1, $.1^53>, <$.1, $.1^54>, <$.1, $.1^58>, <$.1, $.1^59>, <$.1, $.1^64>, <$.1, $.1^67>, <$.1, $.1^68>, <$.1, $.1^71>, <$.1, $.1^73>, <$.1, $.1^82>, <$.1, $.1^94>, <$.1, $.1^106>, <$.1, $.1^123>, <$.1, $.1^127>, <$.1, $.1^134>, <$.1, $.1^144>, <$.1, $.1^147>, <$.1, $.1^154>, <$.1, $.1^155>, <$.1, $.1^157>, <$.1, $.1^160>, <$.1, $.1^169>, <$.1, $.1^177>, <$.1, $.1^188>, <$.1, $.1^189>, <$.1, $.1^194>, <$.1, $.1^203>, <$.1, $.1^205>, <$.1, $.1^213>, <$.1, $.1^216>, <$.1, $.1^232>, <$.1, $.1^252>, <$.1, $.1^254>, <$.1, $.1^256>, <$.1, $.1^272>, <$.1, $.1^290>, <$.1, $.1^297>, <$.1, $.1^316>, <$.1, $.1^320>, <$.1, $.1^324>, <$.1, $.1^332>, <$.1^2, $.1^5>, <$.1^2, $.1^12>, <$.1^2, $.1^31>, <$.1^2, $.1^35>, <$.1^2, $.1^39>, <$.1^2, $.1^47>, <$.1^2, 3>, <$.1^2, $.1^60>, <$.1^2, $.1^78>, <$.1^2, $.1^79>, <$.1^2, $.1^84>, <$.1^2, $.1^86>, <$.1^2, $.1^93>, <$.1^2, $.1^109>, <$.1^2, $.1^110>, <$.1^2, $.1^111>, <$.1^2, $.1^115>, <$.1^2, $.1^116>, <$.1^2, $.1^121>, <$.1^2, $.1^124>, <$.1^2, $.1^125>, <$.1^2, $.1^128>, <$.1^2, $.1^130>, <$.1^2, $.1^139>, <$.1^2, $.1^151>, <$.1^2, $.1^163>, <$.1^2, $.1^180>, <$.1^2, $.1^184>, <$.1^2, $.1^191>, <$.1^2, $.1^201>, <$.1^2, $.1^204>, <$.1^2, $.1^211>, <$.1^2, $.1^212>, <$.1^2, $.1^214>, <$.1^2, $.1^217>, <$.1^2, $.1^226>, <$.1^2, $.1^234>, <$.1^2, $.1^245>, <$.1^2, $.1^246>, <$.1^2, $.1^251>, <$.1^2, $.1^260>, <$.1^2, $.1^262>, <$.1^2, $.1^270>, <$.1^2, $.1^273>, <$.1^2, $.1^289>, <$.1^2, $.1^309>, <$.1^2, $.1^311>, <$.1^2, $.1^313>, <$.1^2, $.1^329>, <$.1^3, $.1^4>, <$.1^3, $.1^24>, <$.1^3, $.1^26>, <$.1^3, $.1^28>, <$.1^3, $.1^44>, <$.1^3, $.1^62>, <$.1^3, $.1^69>, <$.1^3, $.1^88>, <$.1^3, $.1^92>, <$.1^3, $.1^96>, <$.1^3, $.1^104>, <$.1^3, 2>, <$.1^3, $.1^117>, <$.1^3, $.1^135>, <$.1^3, $.1^136>, <$.1^3, $.1^141>, <$.1^3, $.1^143>, <$.1^3, $.1^150>, <$.1^3, $.1^166>, <$.1^3, $.1^167>, <$.1^3, $.1^168>, <$.1^3, $.1^172>, <$.1^3, $.1^173>, <$.1^3, $.1^178>, <$.1^3, $.1^181>, <$.1^3, $.1^182>, <$.1^3, $.1^185>, <$.1^3, $.1^187>, <$.1^3, $.1^196>, <$.1^3, $.1^208>, <$.1^3, $.1^220>, <$.1^3, $.1^237>, <$.1^3, $.1^241>, <$.1^3, $.1^248>, <$.1^3, $.1^258>, <$.1^3, $.1^261>, <$.1^3, $.1^268>, <$.1^3, $.1^269>, <$.1^3, $.1^271>, <$.1^3, $.1^274>, <$.1^3, $.1^283>, <$.1^3, $.1^291>, <$.1^3, $.1^302>, <$.1^3, $.1^303>, <$.1^3, $.1^308>, <$.1^3, $.1^317>, <$.1^3, $.1^319>, <$.1^3, $.1^327>, <$.1^3, $.1^330>, <$.1^4, $.1^6>, <$.1^4, $.1^17>, <$.1^4, $.1^18>, <$.1^4, $.1^23>, <$.1^4, $.1^32>, <$.1^4, $.1^34>, <$.1^4, $.1^42>, <$.1^4, $.1^45>, <$.1^4, $.1^61>, <$.1^4, $.1^81>, <$.1^4, $.1^83>, <$.1^4, $.1^85>, <$.1^4, $.1^101>, <$.1^4, $.1^119>, <$.1^4, $.1^126>, <$.1^4, $.1^145>, <$.1^4, $.1^149>, <$.1^4, $.1^153>, <$.1^4, $.1^161>, <$.1^4, 6>, <$.1^4, $.1^174>, <$.1^4, $.1^192>, <$.1^4, $.1^193>, <$.1^4, $.1^198>, <$.1^4, $.1^200>, <$.1^4, $.1^207>, <$.1^4, $.1^223>, <$.1^4, $.1^224>, <$.1^4, $.1^225>, <$.1^4, $.1^229>, <$.1^4, $.1^230>, <$.1^4, $.1^235>, <$.1^4, $.1^238>, <$.1^4, $.1^239>, <$.1^4, $.1^242>, <$.1^4, $.1^244>, <$.1^4, $.1^253>, <$.1^4, $.1^265>, <$.1^4, $.1^277>, <$.1^4, $.1^294>, <$.1^4, $.1^298>, <$.1^4, $.1^305>, <$.1^4, $.1^315>, <$.1^4, $.1^318>, <$.1^4, $.1^325>, <$.1^4, $.1^326>, <$.1^4, $.1^328>, <$.1^4, $.1^331>, <$.1^4, $.1^340>, <$.1^5, $.1^9>, <$.1^5, $.1^13>, <$.1^5, $.1^20>, <$.1^5, $.1^30>, <$.1^5, $.1^33>, <$.1^5, $.1^40>, <$.1^5, $.1^41>, <$.1^5, $.1^43>, <$.1^5, $.1^46>, <$.1^5, $.1^55>, <$.1^5, $.1^63>, <$.1^5, $.1^74>, <$.1^5, $.1^75>, <$.1^5, $.1^80>, <$.1^5, $.1^89>, <$.1^5, $.1^91>, <$.1^5, $.1^99>, <$.1^5, $.1^102>, <$.1^5, $.1^118>, <$.1^5, $.1^138>, <$.1^5, $.1^140>, <$.1^5, $.1^142>, <$.1^5, $.1^158>, <$.1^5, $.1^176>, <$.1^5, $.1^183>, <$.1^5, $.1^202>, <$.1^5, $.1^206>, <$.1^5, $.1^210>, <$.1^5, $.1^218>, <$.1^5, 4>, <$.1^5, $.1^231>, <$.1^5, $.1^249>, <$.1^5, $.1^250>, <$.1^5, $.1^255>, <$.1^5, $.1^257>, <$.1^5, $.1^264>, <$.1^5, $.1^280>, <$.1^5, $.1^281>, <$.1^5, $.1^282>, <$.1^5, $.1^286>, <$.1^5, $.1^287>, <$.1^5, $.1^292>, <$.1^5, $.1^295>, <$.1^5, $.1^296>, <$.1^5, $.1^299>, <$.1^5, $.1^301>, <$.1^5, $.1^310>, <$.1^5, $.1^322>, <$.1^5, $.1^334>, <$.1^6, $.1>, <$.1^6, $.1^2>, <$.1^6, $.1^7>, <$.1^6, $.1^10>, <$.1^6, $.1^11>, <$.1^6, $.1^14>, <$.1^6, $.1^16>, <$.1^6, $.1^25>, <$.1^6, $.1^37>, <$.1^6, $.1^49>, <$.1^6, $.1^66>, <$.1^6, $.1^70>, <$.1^6, $.1^77>, <$.1^6, $.1^87>, <$.1^6, $.1^90>, <$.1^6, $.1^97>, <$.1^6, $.1^98>, <$.1^6, $.1^100>, <$.1^6, $.1^103>, <$.1^6, $.1^112>, <$.1^6, $.1^120>, <$.1^6, $.1^131>, <$.1^6, $.1^132>, <$.1^6, $.1^137>, <$.1^6, $.1^146>, <$.1^6, $.1^148>, <$.1^6, $.1^156>, <$.1^6, $.1^159>, <$.1^6, $.1^175>, <$.1^6, $.1^195>, <$.1^6, $.1^197>, <$.1^6, $.1^199>, <$.1^6, $.1^215>, <$.1^6, $.1^233>, <$.1^6, $.1^240>, <$.1^6, $.1^259>, <$.1^6, $.1^263>, <$.1^6, $.1^267>, <$.1^6, $.1^275>, <$.1^6, 5>, <$.1^6, $.1^288>, <$.1^6, $.1^306>, <$.1^6, $.1^307>, <$.1^6, $.1^312>, <$.1^6, $.1^314>, <$.1^6, $.1^321>, <$.1^6, $.1^337>, <$.1^6, $.1^338>, <$.1^6, $.1^339>, <$.1^7, 1>, <$.1^7, $.1^3>, <$.1^7, $.1^21>, <$.1^7, $.1^22>, <$.1^7, $.1^27>, <$.1^7, $.1^29>, <$.1^7, $.1^36>, <$.1^7, $.1^52>, <$.1^7, $.1^53>, <$.1^7, $.1^54>, <$.1^7, $.1^58>, <$.1^7, $.1^59>, <$.1^7, $.1^64>, <$.1^7, $.1^67>, <$.1^7, $.1^68>, <$.1^7, $.1^71>, <$.1^7, $.1^73>, <$.1^7, $.1^82>, <$.1^7, $.1^94>, <$.1^7, $.1^106>, <$.1^7, $.1^123>, <$.1^7, $.1^127>, <$.1^7, $.1^134>, <$.1^7, $.1^144>, <$.1^7, $.1^147>, <$.1^7, $.1^154>, <$.1^7, $.1^155>, <$.1^7, $.1^157>, <$.1^7, $.1^160>, <$.1^7, $.1^169>, <$.1^7, $.1^177>, <$.1^7, $.1^188>, <$.1^7, $.1^189>, <$.1^7, $.1^194>, <$.1^7, $.1^203>, <$.1^7, $.1^205>, <$.1^7, $.1^213>, <$.1^7, $.1^216>, <$.1^7, $.1^232>, <$.1^7, $.1^252>, <$.1^7, $.1^254>, <$.1^7, $.1^256>, <$.1^7, $.1^272>, <$.1^7, $.1^290>, <$.1^7, $.1^297>, <$.1^7, $.1^316>, <$.1^7, $.1^320>, <$.1^7, $.1^324>, <$.1^7, $.1^332>, <$.1^8, $.1^5>, <$.1^8, $.1^12>, <$.1^8, $.1^31>, <$.1^8, $.1^35>, <$.1^8, $.1^39>, <$.1^8, $.1^47>, <$.1^8, 3>, <$.1^8, $.1^60>, <$.1^8, $.1^78>, <$.1^8, $.1^79>, <$.1^8, $.1^84>, <$.1^8, $.1^86>, <$.1^8, $.1^93>, <$.1^8, $.1^109>, <$.1^8, $.1^110>, <$.1^8, $.1^111>, <$.1^8, $.1^115>, <$.1^8, $.1^116>, <$.1^8, $.1^121>, <$.1^8, $.1^124>, <$.1^8, $.1^125>, <$.1^8, $.1^128>, <$.1^8, $.1^130>, <$.1^8, $.1^139>, <$.1^8, $.1^151>, <$.1^8, $.1^163>, <$.1^8, $.1^180>, <$.1^8, $.1^184>, <$.1^8, $.1^191>, <$.1^8, $.1^201>, <$.1^8, $.1^204>, <$.1^8, $.1^211>, <$.1^8, $.1^212>, <$.1^8, $.1^214>, <$.1^8, $.1^217>, <$.1^8, $.1^226>, <$.1^8, $.1^234>, <$.1^8, $.1^245>, <$.1^8, $.1^246>, <$.1^8, $.1^251>, <$.1^8, $.1^260>, <$.1^8, $.1^262>, <$.1^8, $.1^270>, <$.1^8, $.1^273>, <$.1^8, $.1^289>, <$.1^8, $.1^309>, <$.1^8, $.1^311>, <$.1^8, $.1^313>, <$.1^8, $.1^329>, <$.1^9, $.1^4>, <$.1^9, $.1^24>, <$.1^9, $.1^26>, <$.1^9, $.1^28>, <$.1^9, $.1^44>, <$.1^9, $.1^62>, <$.1^9, $.1^69>, <$.1^9, $.1^88>, <$.1^9, $.1^92>, <$.1^9, $.1^96>, <$.1^9, $.1^104>, <$.1^9, 2>, <$.1^9, $.1^117>, <$.1^9, $.1^135>, <$.1^9, $.1^136>, <$.1^9, $.1^141>, <$.1^9, $.1^143>, <$.1^9, $.1^150>, <$.1^9, $.1^166>, <$.1^9, $.1^167>, <$.1^9, $.1^168>, <$.1^9, $.1^172>, <$.1^9, $.1^173>, <$.1^9, $.1^178>, <$.1^9, $.1^181>, <$.1^9, $.1^182>, <$.1^9, $.1^185>, <$.1^9, $.1^187>, <$.1^9, $.1^196>, <$.1^9, $.1^208>, <$.1^9, $.1^220>, <$.1^9, $.1^237>, <$.1^9, $.1^241>, <$.1^9, $.1^248>, <$.1^9, $.1^258>, <$.1^9, $.1^261>, <$.1^9, $.1^268>, <$.1^9, $.1^269>, <$.1^9, $.1^271>, <$.1^9, $.1^274>, <$.1^9, $.1^283>, <$.1^9, $.1^291>, <$.1^9, $.1^302>, <$.1^9, $.1^303>, <$.1^9, $.1^308>, <$.1^9, $.1^317>, <$.1^9, $.1^319>, <$.1^9, $.1^327>, <$.1^9, $.1^330>, <$.1^10, $.1^6>, <$.1^10, $.1^17>, <$.1^10, $.1^18>, <$.1^10, $.1^23>, <$.1^10, $.1^32>, <$.1^10, $.1^34>, <$.1^10, $.1^42>, <$.1^10, $.1^45>, <$.1^10, $.1^61>, <$.1^10, $.1^81>, <$.1^10, $.1^83>, <$.1^10, $.1^85>, <$.1^10, $.1^101>, <$.1^10, $.1^119>, <$.1^10, $.1^126>, <$.1^10, $.1^145>, <$.1^10, $.1^149>, <$.1^10, $.1^153>, <$.1^10, $.1^161>, <$.1^10, 6>, <$.1^10, $.1^174>, <$.1^10, $.1^192>, <$.1^10, $.1^193>, <$.1^10, $.1^198>, <$.1^10, $.1^200>, <$.1^10, $.1^207>, <$.1^10, $.1^223>, <$.1^10, $.1^224>, <$.1^10, $.1^225>, <$.1^10, $.1^229>, <$.1^10, $.1^230>, <$.1^10, $.1^235>, <$.1^10, $.1^238>, <$.1^10, $.1^239>, <$.1^10, $.1^242>, <$.1^10, $.1^244>, <$.1^10, $.1^253>, <$.1^10, $.1^265>, <$.1^10, $.1^277>, <$.1^10, $.1^294>, <$.1^10, $.1^298>, <$.1^10, $.1^305>, <$.1^10, $.1^315>, <$.1^10, $.1^318>, <$.1^10, $.1^325>, <$.1^10, $.1^326>, <$.1^10, $.1^328>, <$.1^10, $.1^331>, <$.1^10, $.1^340>, <$.1^11, $.1^9>, <$.1^11, $.1^13>, <$.1^11, $.1^20>, <$.1^11, $.1^30>, <$.1^11, $.1^33>, <$.1^11, $.1^40>, <$.1^11, $.1^41>, <$.1^11, $.1^43>, <$.1^11, $.1^46>, <$.1^11, $.1^55>, <$.1^11, $.1^63>, <$.1^11, $.1^74>, <$.1^11, $.1^75>, <$.1^11, $.1^80>, <$.1^11, $.1^89>, <$.1^11, $.1^91>, <$.1^11, $.1^99>, <$.1^11, $.1^102>, <$.1^11, $.1^118>, <$.1^11, $.1^138>, <$.1^11, $.1^140>, <$.1^11, $.1^142>, <$.1^11, $.1^158>, <$.1^11, $.1^176>, <$.1^11, $.1^183>, <$.1^11, $.1^202>, <$.1^11, $.1^206>, <$.1^11, $.1^210>, <$.1^11, $.1^218>, <$.1^11, 4 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 210-BAR2-X75.libre.retevision.es. (62.82.151.210) Time: Tue Mar 16 10:22:44 2004 Input: ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(~C, [i,j]);end if; end for;end for; return C; end function; spolav:= [k : k in polavqr(2,3) | k[1] in GF(2) and k[2] in GF(2) ]; #spolav; Output: Magma V2.10-6 Tue Mar 16 2004 10:22:41 on modular [Seed = 2713123380] ------------------------------------- 2 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse013.uab.es. (158.109.66.132) Time: Tue Mar 16 10:22:51 2004 Input: G2:=GF(2); G3:=GF(3); G5:=GF(5); /* Z9 no es un cos, ja que nou no es un nombre primer */ Z9:=Integers(9); /* [a]m pertanyent a Zm es invertible sii mcd(a,m)=1*/ IsInvertible(Z9!3); s:=GF(3,2); p:=PolynomialRing(s); f:= 2+2*x+x^2; Factorization(f); Roots(f,s); IsIrreducible(f); s1:=GF(2,4); p1:=PolynomialRing(s1); f1:= 1+x+x^4; Factorization(f1); Roots(f1,s1); IsIrreducible(f1); Output: Magma V2.10-6 Tue Mar 16 2004 10:22:48 on modular [Seed = 2847863349] ------------------------------------- false [ , ] [ , ] false [ , , , ] [ , , , ] false Total time: 2.919 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host aula-etse013.uab.es. (158.109.66.132) Time: Tue Mar 16 10:23:14 2004 Input: G2:=GF(2); G3:=GF(3); G5:=GF(5); /* Z9 no es un cos, ja que nou no es un nombre primer */ Z9:=Integers(9); /* [a]m pertanyent a Zm es invertible sii mcd(a,m)=1*/ IsInvertible(Z9!3); s:=GF(3,2); p:=PolynomialRing(s); f:= 2+2*x+x^2; Factorization(f); Roots(f,s); IsIrreducible(f); s1=GF(2,4); p1:=PolynomialRing(s1); f1:= 1+x+x^4; Factorization(f1); IsIrreducible(f1); Output: Magma V2.10-6 Tue Mar 16 2004 10:23:11 on modular [Seed = 1380256216] ------------------------------------- false [ , ] [ , ] false >> s1=GF(2,4); ^ User error: Identifier 's1' has not been declared or assigned >> p1:=PolynomialRing(s1); ^ User error: Identifier 's1' has not been declared or assigned [ , ] false Total time: 2.869 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 10:23:43 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; F := GF(27); F; Order(F!7); Output: Magma V2.10-6 Tue Mar 16 2004 10:23:40 on modular [Seed = 1163009772] ------------------------------------- Finite field of size 3^3 1 Total time: 3.049 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host aula-etse013.uab.es. (158.109.66.132) Time: Tue Mar 16 10:24:30 2004 Input: G2:=GF(2); G3:=GF(3); G5:=GF(5); /* Z9 no es un cos, ja que nou no es un nombre primer */ Z9:=Integers(9); /* [a]m pertanyent a Zm es invertible sii mcd(a,m)=1*/ IsInvertible(Z9!3); s:=GF(3,2); p:=PolynomialRing(s); f:= 2+2*x+x^2; Factorization(f); Roots(f,s); IsIrreducible(f); s1:=GF(2,4); p1:=PolynomialRing(s1); f1:= 1+x+x^4; Factorization(f1); Roots(f1,s1); IsIrreducible(f1); s2:=GF(5,2); p2:=PolynomialRing(s2); f2:= 3+2*x+x^2; Factorization(f2); Roots(f2,s2); IsIrreducible(f2); Output: Magma V2.10-6 Tue Mar 16 2004 10:24:27 on modular [Seed = 1281036338] ------------------------------------- false [ , ] [ , ] false [ , , , ] [ , , , ] false [ , ] [ , ] false Total time: 2.969 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 16 10:24:45 2004 Input: generator (F); f:= GF (2); Output: Magma V2.10-6 Tue Mar 16 2004 10:24:39 on modular [Seed = 1935945489] ------------------------------------- >> generator (F); ^ User error: Identifier 'F' has not been declared or assigned Total time: 3.359 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 210-BAR2-X75.libre.retevision.es. (62.82.151.210) Time: Tue Mar 16 10:24:56 2004 Input: ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(~C, [i,j]);end if; end for;end for; return C; end function; spolav:= [k : k in polavqr(2,3) | k[1] in GF(2) and k[2] in GF(2) ]; #polavqr(2,7); 2^(7*2-1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Mar 16 2004 10:24:34 on modular [Seed = 2002791184] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 5410 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 16 10:25:06 2004 Input: P:=PolynomialRing(Integers()); ExponentsTqr:=function(q,r) i:=1; exp:=[]; while (r-i ge 0) do exp:=exp cat [q^(r-i)]; i:=i+1; end while; return (exp); end function; nqr:=function(q,r) sum:=0; i:=1; exp:=ExponentsTqr(q,r); while i le #(exp) do sum:=sum+exp[i]; i:=i+1; end while; return (x^sum); end function; tqr:=function(q,r) pol:=0; i:=1; exp:=ExponentsTqr(q,r); while i le #(exp) do pol:=pol+x^(exp[i]); i:=i+1; end while; return (pol); end function; PuntsOlav:=function(q,r) kf:=GF(q,r); punts:=[:a,b in kf | Evaluate(nqr(q,r),a) eq Evaluate(tqr(q,r),b)]; return (punts); end function; PuntsOlav(7,3); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Mar 16 2004 10:24:41 on modular [Seed = 2104107281] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 5416 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 16 10:25:24 2004 Input: generator (F); F:= GF (2); Output: Magma V2.10-6 Tue Mar 16 2004 10:25:21 on modular [Seed = 335759392] ------------------------------------- >> generator (F); ^ User error: Identifier 'F' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 16 10:25:35 2004 Input: generator (F); F:= GF (2); Output: Magma V2.10-6 Tue Mar 16 2004 10:25:32 on modular [Seed = 503923239] ------------------------------------- >> generator (F); ^ User error: Identifier 'F' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 16 10:25:56 2004 Input: Generator (F); F:= GF (2); Output: Magma V2.10-6 Tue Mar 16 2004 10:25:53 on modular [Seed = 18243029] ------------------------------------- >> Generator (F); ^ User error: Identifier 'F' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 210-BAR2-X75.libre.retevision.es. (62.82.151.210) Time: Tue Mar 16 10:26:14 2004 Input: ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(~C, [i,j]);end if; end for;end for; return C; end function; spolav:= [k : k in polavqr(2,3) | k[1] in GF(2) and k[2] in GF(2) ]; #polavqr(2,5); 2^(5*2-1); Output: Magma V2.10-6 Tue Mar 16 2004 10:26:11 on modular [Seed = 136271054] ------------------------------------- 512 512 Total time: 3.339 seconds, Total memory usage: 1.91MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 10:26:27 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; F := GF(27); F; Order(F!7); [Order(G25!i: i in [1..24]]; Output: Magma V2.10-6 Tue Mar 16 2004 10:26:24 on modular [Seed = 858025926] ------------------------------------- Finite field of size 3^3 1 >> [Order(G25!i: i in [1..24]]; ^ User error: bad syntax Total time: 2.989 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host aula-etse013.uab.es. (158.109.66.132) Time: Tue Mar 16 10:26:54 2004 Input: G2:=GF(2); G3:=GF(3); G5:=GF(5); /* Z9 no es un cos, ja que nou no es un nombre primer */ Z9:=Integers(9); /* [a]m pertanyent a Zm es invertible sii mcd(a,m)=1*/ IsInvertible(Z9!3); s:=GF(3,2); p:=PolynomialRing(s); f:= 2+2*x+x^2; Factorization(f); Roots(f,s); IsIrreducible(f); s1:=GF(2,4); p1:=PolynomialRing(s1); f1:= 1+x+x^4; Factorization(f1); Roots(f1,s1); IsIrreducible(f1); s2:=PolynomialRing(s2); f2:= 3+2*x+x^2; Factorization(f2); Roots(f2,s2); IsIrreducible(f2); Output: Magma V2.10-6 Tue Mar 16 2004 10:26:50 on modular [Seed = 976053973] ------------------------------------- false [ , ] [ , ] false [ , , , ] [ , , , ] false >> s2> p2:=PolynomialRing(s2); ^ User error: Identifier 's2' has not been declared or assigned [ ] >> Roots(f2,s2); ^ User error: Identifier 's2' has not been declared or assigned false Total time: 3.319 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 10:27:01 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; F := GF(27); F; Order(F!7); [Order(G25!i) : i in [1..24]]; Output: Magma V2.10-6 Tue Mar 16 2004 10:26:58 on modular [Seed = 775516857] ------------------------------------- Finite field of size 3^3 1 >> [Order(G25!i) : i in [1..24]]; ^ Runtime error in 'Order': Can not take order of zero element Total time: 3.019 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 16 10:27:05 2004 Input: GF2 := GF(2); Generator (GF2); GF2:= GF (2); Output: Magma V2.10-6 Tue Mar 16 2004 10:27:00 on modular [Seed = 725383098] ------------------------------------- 1 Total time: 3.099 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse013.uab.es. (158.109.66.132) Time: Tue Mar 16 10:27:07 2004 Input: G2:=GF(2); G3:=GF(3); G5:=GF(5); /* Z9 no es un cos, ja que nou no es un nombre primer */ Z9:=Integers(9); /* [a]m pertanyent a Zm es invertible sii mcd(a,m)=1*/ IsInvertible(Z9!3); s:=GF(3,2); p:=PolynomialRing(s); f:= 2+2*x+x^2; Factorization(f); Roots(f,s); IsIrreducible(f); s1:=GF(2,4); p1:=PolynomialRing(s1); f1:= 1+x+x^4; Factorization(f1); Roots(f1,s1); IsIrreducible(f1); s2:=GF(5,2); p2:=PolynomialRing(s2); f2:= 3+2*x+x^2; Factorization(f2); Roots(f2,s2); IsIrreducible(f2); Output: Magma V2.10-6 Tue Mar 16 2004 10:27:03 on modular [Seed = 3536162368] ------------------------------------- false [ , ] [ , ] false [ , , , ] [ , , , ] false [ , ] [ , ] false Total time: 2.959 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 16 10:27:15 2004 Input: Z:=Integers(); PT:=PolynomialRing(Z); expo:= function (q,r) if ((r gt 0) and IsPrime(q)) then exp:= [q^(r-1)]; for i:=2 to r do exp:= exp cat [q^(r-i)]; end for; end if; return exp; end function; t := function (q,r) lista:=expo(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + x^lista[i]; end for; return poly; end function; n := function (q,r) lista:=expo(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=x^exp; return poly; end function; punts_olav:=function (q,r) punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; return punts; end function; #punts_olav(7,3); Output: Magma V2.10-6 Tue Mar 16 2004 10:26:52 on modular [Seed = 657488846] ------------------------------------- 16807 Total time: 21.799 seconds, Total memory usage: 2.73MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 16 10:27:25 2004 Input: GF2 := GF(2); Generator (GF2); /*GF2:= GF (2);*/ Output: Magma V2.10-6 Tue Mar 16 2004 10:27:21 on modular [Seed = 3403519558] ------------------------------------- 1 Total time: 3.389 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 210-BAR2-X75.libre.retevision.es. (62.82.151.210) Time: Tue Mar 16 10:27:36 2004 Input: ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(~C, [i,j]);end if; end for;end for; return C; end function; spolav:= [k : k in polavqr(2,3) | k[1] in GF(2) and k[2] in GF(2) ]; #polavqr(3,5); 3^(5*2-1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Mar 16 2004 10:27:13 on modular [Seed = 3285491527] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 5526 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 10:27:36 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; F := GF(27); F; Order(F!7); Order(G25!1); [Order(G25!i) : i in [1..24]]; Output: Magma V2.10-6 Tue Mar 16 2004 10:27:33 on modular [Seed = 4260012365] ------------------------------------- Finite field of size 3^3 1 1 >> [Order(G25!i) : i in [1..24]]; ^ Runtime error in 'Order': Can not take order of zero element Total time: 3.499 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 16 10:28:02 2004 Input: GF2 := GF(2); Generator (GF2); GF2:= GF (2); print GF2; Output: Magma V2.10-6 Tue Mar 16 2004 10:27:59 on modular [Seed = 3807755848] ------------------------------------- 1 >> print GF2;; ^ User error: bad syntax Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-etse013.uab.es. (158.109.66.132) Time: Tue Mar 16 10:28:05 2004 Input: G2:=GF(2); G3:=GF(3); G5:=GF(5); /* Z9 no es un cos, ja que nou no es un nombre primer */ Z9:=Integers(9); /* [a]m pertanyent a Zm es invertible sii mcd(a,m)=1*/ IsInvertible(Z9!3); s:=GF(3,2); p:=PolynomialRing(s); f:= 2+2*x+x^2; Factorization(f); Roots(f,s); IsIrreducible(f); s1:=GF(2,4); p1:=PolynomialRing(s1); f1:= 1+x+x^4; Factorization(f1); Roots(f1,s1); IsIrreducible(f1); s2:=GF(5,2); p2:=PolynomialRing(s2); f2:= 3+2*x+x^2; Factorization(f2); Roots(f2,s2); IsIrreducible(f2); s3:=GF(3,2); p3:=PolynomialRing(s3); f3:= 1+2*x+x^2; Factorization(f3); Roots(f3,s3); IsIrreducible(f3); Output: Magma V2.10-6 Tue Mar 16 2004 10:28:02 on modular [Seed = 2508376258] ------------------------------------- false [ , ] [ , ] false [ , , , ] [ , , , ] false [ , ] [ , ] false [ ] [ <2, 2> ] false Total time: 2.979 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 10:28:08 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; F := GF(27); F; G25!1; Order(G25!1); /*[Order(G25!i) : i in [1..24]];*/ Output: Magma V2.10-6 Tue Mar 16 2004 10:28:05 on modular [Seed = 2626404812] ------------------------------------- Finite field of size 3^3 1 1 Total time: 2.929 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 16 10:28:17 2004 Input: GF2 := GF(2); Generator (GF2); GF2:= GF (2); print GF2; Output: Magma V2.10-6 Tue Mar 16 2004 10:28:14 on modular [Seed = 2257705949] ------------------------------------- 1 Finite field of size 2 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 210-BAR2-X75.libre.retevision.es. (62.82.151.210) Time: Tue Mar 16 10:28:20 2004 Input: ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(~C, [i,j]);end if; end for;end for; return C; end function; spolav:= [k : k in polavqr(2,3) | k[1] in GF(2) and k[2] in GF(2) ]; #polavqr(3,2); 3^(2*2-1); Output: Magma V2.10-6 Tue Mar 16 2004 10:28:17 on modular [Seed = 2157436356] ------------------------------------- 27 27 Total time: 3.129 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 10:28:40 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; F := GF(27); F; G25!1; Order(G25!24); /*[Order(G25!i) : i in [1..24]];*/ Output: Magma V2.10-6 Tue Mar 16 2004 10:28:37 on modular [Seed = 2980506817] ------------------------------------- Finite field of size 3^3 1 2 Total time: 2.999 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 10:28:59 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; F := GF(27); F; G25!1; Order(G25!24); [Order(G25!i) : i in [1..24]]; Output: Magma V2.10-6 Tue Mar 16 2004 10:28:56 on modular [Seed = 3098535381] ------------------------------------- Finite field of size 3^3 1 2 >> [Order(G25!i) : i in [1..24]]; ^ Runtime error in 'Order': Can not take order of zero element Total time: 2.969 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 10:29:16 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; F := GF(27); F; G25!1; Order(G25!24); [(Order(G25!i)) : i in [1..24]]; Output: Magma V2.10-6 Tue Mar 16 2004 10:29:13 on modular [Seed = 2746547903] ------------------------------------- Finite field of size 3^3 1 2 >> [(Order(G25!i)) : i in [1..24]]; ^ Runtime error in 'Order': Can not take order of zero element Total time: 3.709 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 16 10:29:17 2004 Input: GF2 := GF(2); Generator (GF2); GF2:= GF (2); print GF2; GF3 := GF(3); Generator (GF3); GF3:= GF (3); print GF3; Output: Magma V2.10-6 Tue Mar 16 2004 10:29:13 on modular [Seed = 2897998256] ------------------------------------- 1 Finite field of size 2 1 Finite field of size 3 Total time: 3.619 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 10:29:27 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; F := GF(27); F; G25!1; Order(G25!24); [(Order(G25!i)) : i in [2..24]]; Output: Magma V2.10-6 Tue Mar 16 2004 10:29:24 on modular [Seed = 1581843292] ------------------------------------- Finite field of size 3^3 1 2 >> [(Order(G25!i)) : i in [2..24]]; ^ Runtime error in 'Order': Can not take order of zero element Total time: 2.939 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host aula-etse013.uab.es. (158.109.66.132) Time: Tue Mar 16 10:29:39 2004 Input: G2:=GF(2); G3:=GF(3); G5:=GF(5); /* Z9 no es un cos, ja que nou no es un nombre primer */ Z9:=Integers(9); /* [a]m pertanyent a Zm es invertible sii mcd(a,m)=1*/ IsInvertible(Z9!3); s:=GF(3,2); p:=PolynomialRing(s); f:= 2+2*x+x^2; Factorization(f); Roots(f,s); IsIrreducible(f); s1:=GF(2,4); p1:=PolynomialRing(s1); f1:= 1+x+x^4; Factorization(f1); Roots(f1,s1); IsIrreducible(f1); s2:=GF(5,2); p2:=PolynomialRing(s2); f2:= 3+2*x+x^2; Factorization(f2); Roots(f2,s2); IsIrreducible(f2); s3:=GF(3,2); p3:=PolynomialRing(s3); f3:= 1+2*x+x^2; Factorization(f3); Roots(f3,Integers(3)); IsIrreducible(f3); Output: Magma V2.10-6 Tue Mar 16 2004 10:29:36 on modular [Seed = 1196431985] ------------------------------------- false [ , ] [ , ] false [ , , , ] [ , , , ] false [ , ] [ , ] false [ ] >> Roots(f3,Integers(3)); ^ Runtime error in 'Roots': Argument 1 cannot be coerced to be over argument 2 false Total time: 3.009 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 16 10:29:53 2004 Input: GF2 := GF(2); Generator (GF2); GF2:= GF (2); print GF2; GF3 := GF(3); Generator (GF3); GF3:= GF (3); print GF3; GF5 := GF(5); Generator (GF5); GF5:= GF (5); print GF5; Output: Magma V2.10-6 Tue Mar 16 2004 10:29:50 on modular [Seed = 1264326259] ------------------------------------- 1 Finite field of size 2 1 Finite field of size 3 1 Finite field of size 5 Total time: 3.169 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 210-BAR2-X75.libre.retevision.es. (62.82.151.210) Time: Tue Mar 16 10:29:56 2004 Input: ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(~C, [i,j]);end if; end for;end for; return C; end function; spolav:= [k : k in polavqr(2,3) | k[1] in GF(2) and k[2] in GF(2) ]; #polavqr(3,4); 3^(4*2-1); Output: Magma V2.10-6 Tue Mar 16 2004 10:29:47 on modular [Seed = 1281036657] ------------------------------------- 2187 2187 Total time: 8.119 seconds, Total memory usage: 2.24MB ************** MAGMA ***************** Host aula-etse013.uab.es. (158.109.66.132) Time: Tue Mar 16 10:30:08 2004 Input: G2:=GF(2); G3:=GF(3); G5:=GF(5); /* Z9 no es un cos, ja que nou no es un nombre primer */ Z9:=Integers(9); /* [a]m pertanyent a Zm es invertible sii mcd(a,m)=1*/ IsInvertible(Z9!3); s:=GF(3,2); p:=PolynomialRing(s); f:= 2+2*x+x^2; Factorization(f); Roots(f,s); IsIrreducible(f); s1:=GF(2,4); p1:=PolynomialRing(s1); f1:= 1+x+x^4; Factorization(f1); Roots(f1,s1); IsIrreducible(f1); s2:=GF(5,2); p2:=PolynomialRing(s2); f2:= 3+2*x+x^2; Factorization(f2); Roots(f2,s2); IsIrreducible(f2); s3:=GF(3,2); p3:=PolynomialRing(s3); f3:= 1+2*x+x^2; Factorization(f3); Roots(f3); IsIrreducible(f3); Output: Magma V2.10-6 Tue Mar 16 2004 10:30:05 on modular [Seed = 1701984334] ------------------------------------- false [ , ] [ , ] false [ , , , ] [ , , , ] false [ , ] [ , ] false [ ] [ <2, 2> ] false Total time: 2.999 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 16 10:30:17 2004 Input: GF2 := GF(2); Generator (GF2); GF2:= GF (2); print GF2; GF3 := GF(3); Generator (GF3); GF3:= GF (3); print GF3; GF5 := GF(5); Generator (GF5); GF5:= GF (5); print GF5; GF20 := GF(20); Generator (GF20); GF20:= GF (20); print GF20; Output: Magma V2.10-6 Tue Mar 16 2004 10:30:14 on modular [Seed = 1786591162] ------------------------------------- 1 Finite field of size 2 1 Finite field of size 3 1 Finite field of size 5 >> GF20 := GF(20); ^ Runtime error in 'GF': Argument 1 (20) is not a prime power >> Generator (GF20); ^ User error: Identifier 'GF20' has not been declared or assigned >> GF20:= GF (20); ^ Runtime error in 'GF': Argument 1 (20) is not a prime power >> print GF20; ^ User error: Identifier 'GF20' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 10:30:46 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; F := GF(27); F; G25!1; Order(G25!24); [Order(G25!i) : i in [1..24] | i mod 5 ne 0]; Output: Magma V2.10-6 Tue Mar 16 2004 10:30:43 on modular [Seed = 268914149] ------------------------------------- Finite field of size 3^3 1 2 [ 1, 4, 4, 2, 1, 4, 4, 2, 1, 4, 4, 2, 1, 4, 4, 2, 1, 4, 4, 2 ] Total time: 2.949 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 16 10:30:50 2004 Input: GF2 := GF(2); Generator (GF2); GF2:= GF (2); print GF2; GF3 := GF(3); Generator (GF3); GF3:= GF (3); print GF3; GF5 := GF(5); Generator (GF5); GF5:= GF (5); print GF5; GF23 := GF(23); Generator (GF23); GF23:= GF (23); print GF23; Output: Magma V2.10-6 Tue Mar 16 2004 10:30:47 on modular [Seed = 403654121] ------------------------------------- 1 Finite field of size 2 1 Finite field of size 3 1 Finite field of size 5 1 Finite field of size 23 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 16 10:31:28 2004 Input: Generator (F); Output: Magma V2.10-6 Tue Mar 16 2004 10:31:25 on modular [Seed = 236540821] ------------------------------------- >> Generator (F);; ^ User error: Identifier 'F' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 210-BAR2-X75.libre.retevision.es. (62.82.151.210) Time: Tue Mar 16 10:31:36 2004 Input: ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(~C, [i,j]);end if; end for;end for; return C; end function; spolav:= [k : k in polavqr(2,3) | k[1] in GF(2) and k[2] in GF(2) ]; #polavqr(2,1); 2^(1*2-1); Output: Magma V2.10-6 Tue Mar 16 2004 10:31:32 on modular [Seed = 924871349] ------------------------------------- 2 2 Total time: 3.629 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 10:31:36 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; F := GF(27); F; G25!1; Order(G25!24); [print"ordre de", i,Order(G25!i) : i in [1..24] | i mod 5 ne 0]; Output: Magma V2.10-6 Tue Mar 16 2004 10:31:33 on modular [Seed = 841314225] ------------------------------------- Finite field of size 3^3 1 2 >> [print"ordre de", i,Order(G25!i) : i in [1..24] | i mod 5 ne 0]; ^ User error: bad syntax Total time: 3.699 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 10:32:02 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; F := GF(27); F; G25!1; Order(G25!24); [print"ordre de"; i,Order(G25!i) : i in [1..24] | i mod 5 ne 0]; Output: Magma V2.10-6 Tue Mar 16 2004 10:31:59 on modular [Seed = 624064668] ------------------------------------- Finite field of size 3^3 1 2 >> [print"ordre de"; i,Order(G25!i) : i in [1..24] | i mod 5 ne 0]; ^ User error: bad syntax Total time: 2.889 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 16 10:32:11 2004 Input: k := GF(2); Output: Magma V2.10-6 Tue Mar 16 2004 10:32:08 on modular [Seed = 708671364] ------------------------------------- Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 10:32:18 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; F := GF(27); F; G25!1; Order(G25!24); [i,Order(G25!i) : i in [1..24] | i mod 5 ne 0]; Output: Magma V2.10-6 Tue Mar 16 2004 10:32:15 on modular [Seed = 3552874106] ------------------------------------- Finite field of size 3^3 1 2 >> [i,Order(G25!i) : i in [1..24] | i mod 5 ne 0]; ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 210-BAR2-X75.libre.retevision.es. (62.82.151.210) Time: Tue Mar 16 10:32:33 2004 Input: ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(~C, [i,j]);end if; end for;end for; return C; end function; spolav:= [k : k in polavqr(2,3) | k[1] in GF(2) and k[2] in GF(2) ]; #polavqr(1,3); 1^(3*2-1); Output: Magma V2.10-6 Tue Mar 16 2004 10:32:30 on modular [Seed = 3637479040] ------------------------------------- [
:19]( q: 1, r: 3 ) >> for i in GF(q^r) do ^ Runtime error in 'GF': Argument 1 (1) should be >= 2 1 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 10:32:38 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; F := GF(27); F; G25!1; Order(G25!24); [ : i in [1..24] | i mod 5 ne 0]; Output: Magma V2.10-6 Tue Mar 16 2004 10:32:35 on modular [Seed = 3235356293] ------------------------------------- Finite field of size 3^3 1 2 [ <1, 1>, <2, 4>, <3, 4>, <4, 2>, <6, 1>, <7, 4>, <8, 4>, <9, 2>, <11, 1>, <12, 4>, <13, 4>, <14, 2>, <16, 1>, <17, 4>, <18, 4>, <19, 2>, <21, 1>, <22, 4>, <23, 4>, <24, 2> ] Total time: 3.069 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 210-BAR2-X75.libre.retevision.es. (62.82.151.210) Time: Tue Mar 16 10:33:20 2004 Input: ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(~C, [i,j]);end if; end for;end for; return C; end function; spolav:= [k : k in polavqr(2,3) | k[1] in GF(2) and k[2] in GF(2) ]; #polavqr(5,3); 5^(3*2-1); Output: Magma V2.10-6 Tue Mar 16 2004 10:33:07 on modular [Seed = 4141983891] ------------------------------------- 3125 3125 Total time: 13.169 seconds, Total memory usage: 2.31MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 10:33:47 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; F := GF(27); F; G25!1; Order(G25!24); [ : i in [1..24] | (G25!i) ne 0]; Output: Magma V2.10-6 Tue Mar 16 2004 10:33:44 on modular [Seed = 4293435889] ------------------------------------- Finite field of size 3^3 1 2 [ <1, 1>, <2, 4>, <3, 4>, <4, 2>, <6, 1>, <7, 4>, <8, 4>, <9, 2>, <11, 1>, <12, 4>, <13, 4>, <14, 2>, <16, 1>, <17, 4>, <18, 4>, <19, 2>, <21, 1>, <22, 4>, <23, 4>, <24, 2> ] Total time: 3.039 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 210-BAR2-X75.libre.retevision.es. (62.82.151.210) Time: Tue Mar 16 10:34:46 2004 Input: ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(~C, [i,j]);end if; end for;end for; return C; end function; spolav:= [k : k in polavqr(2,3) | k[1] in GF(2) and k[2] in GF(2) ]; polav73:=function() C:=[]; for i in GF(7^3) do for j in GF(7^3) do if (Evaluate(pn73(),i) eq Evaluate(pt73(),j) ) then Include(~C, [i,j]); end if; end for; end for; return C; end function; polav73(); Output: Magma V2.10-6 Tue Mar 16 2004 10:34:43 on modular [Seed = 3841178145] ------------------------------------- >> if (Evaluate(pn73(),i) eq Evaluate(pt73(),j) ) then Include(~C, [i,j]); ^ User error: Identifier 'pn73' has not been declared or assigned >> polav73(); ^ User error: Identifier 'polav73' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 210-BAR2-X75.libre.retevision.es. (62.82.151.210) Time: Tue Mar 16 10:36:51 2004 Input: ptqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+x^(q^(r-i)); end for; return C; end function; pnqr:=function (q,r) P:=PolynomialRing(GF(q^r)); C:=0; for i in {1..r} do C:=C+(q^(r-i)); end for; return x^C; end function; polavqr:=function(q,r) C:=[]; for i in GF(q^r) do for j in GF(q^r) do if (Evaluate(pnqr(q,r),i) eq Evaluate(ptqr(q,r),j) ) then Include(~C, [i,j]);end if; end for;end for; return C; end function; spolav:= [k : k in polavqr(2,3) | k[1] in GF(2) and k[2] in GF(2) ]; pt73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+x^(7^(3-i)); end for; return C; end function; pn73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+(7^(3-i)); end for; return x^C; end function; polav73:=function() C:=[]; for i in GF(7^3) do for j in GF(7^3) do if (Evaluate(pn73(),i) eq Evaluate(pt73(),j) ) then Include(~C, [i,j]); end if; end for; end for; return C; end function; polav73(); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Mar 16 2004 10:36:28 on modular [Seed = 2525087804] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 5824 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 16 10:37:27 2004 Input: Z:=Integers(); PT:=PolynomialRing(Z); expo:= function (q,r) if ((r gt 0) and IsPrime(q)) then exp:= [q^(r-1)]; for i:=2 to r do exp:= exp cat [q^(r-i)]; end for; end if; return exp; end function; t := function (q,r) lista:=expo(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + x^lista[i]; end for; return poly; end function; n := function (q,r) lista:=expo(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=x^exp; return poly; end function; punts_olav:=function (q,r) punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; return punts; end function; #punts_olav(7,3); 7^5 Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Mar 16 2004 10:37:03 on modular [Seed = 2676539606] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 5833 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 10:37:27 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; F := GF(27); F; G25!1; Order(G25!24); ordre_elements := [ : i in [1..24] | (G25!i) ne 0]; [tupla[2]: tupla in ordre_elements | tupla[2] eq 25-1 ]; Output: Magma V2.10-6 Tue Mar 16 2004 10:37:22 on modular [Seed = 2576271101] ------------------------------------- Finite field of size 3^3 1 2 [] Total time: 3.009 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 16 10:37:37 2004 Input: Z:=Integers(); PT:=PolynomialRing(Z); expo:= function (q,r) if ((r gt 0) and IsPrime(q)) then exp:= [q^(r-1)]; for i:=2 to r do exp:= exp cat [q^(r-i)]; end for; end if; return exp; end function; t := function (q,r) lista:=expo(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + x^lista[i]; end for; return poly; end function; n := function (q,r) lista:=expo(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=x^exp; return poly; end function; punts_olav:=function (q,r) punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; return punts; end function; #punts_olav(7,3); 7^5; Output: Magma V2.10-6 Tue Mar 16 2004 10:37:16 on modular [Seed = 2592982496] ------------------------------------- 16807 16807 Total time: 21.190 seconds, Total memory usage: 2.73MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 10:38:07 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; F := GF(27); F; G25!1; Order(G25!24); /*ordre_elements := [ : i in [1..24] | (G25!i) ne 0]; */ ordre_elements:= [<3,24>, <2,48>, <9,24>]; [tupla[2]: tupla in ordre_elements | tupla[2] eq 25-1 ]; Output: Magma V2.10-6 Tue Mar 16 2004 10:38:04 on modular [Seed = 3047353023] ------------------------------------- Finite field of size 3^3 1 2 [ 24, 24 ] Total time: 2.929 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 16 10:38:21 2004 Input: k := GF(2); print k; Output: Magma V2.10-6 Tue Mar 16 2004 10:38:18 on modular [Seed = 3131958662] ------------------------------------- Finite field of size 2 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 10:38:50 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; F := GF(27); F; G25!1; Order(G25!24); /*ordre_elements := [<(G25!i),Order(G25!i)> : i in [1..24] | (G25!i) ne 0]; */ ordre_elements:= [<3,24>, <2,48>, <9,24>]; [tupla[1]: tupla in ordre_elements | tupla[2] eq 25-1 ]; Output: Magma V2.10-6 Tue Mar 16 2004 10:38:46 on modular [Seed = 2931421566] ------------------------------------- Finite field of size 3^3 1 2 [ 3, 9 ] Total time: 3.409 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 210-BAR2-X75.libre.retevision.es. (62.82.151.210) Time: Tue Mar 16 10:38:57 2004 Input: pt73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+x^(7^(3-i)); end for; return C; end function; pn73:=function () P:=PolynomialRing(GF(7^3)); C:=0; for i in {1..3} do C:=C+(7^(3-i)); end for; return x^C; end function; polav73:=function() C:=[]; for i in GF(7^3) do for j in GF(7^3) do if (Evaluate(pn73(),i) eq Evaluate(pt73(),j) ) then Include(~C, [i,j]); end if; end for; end for; return C; end function; polav73(); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Mar 16 2004 10:38:34 on modular [Seed = 2746547343] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 5877 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 16 10:40:10 2004 Input: Z:=Integers(); PT:=PolynomialRing(Z); expo:= function (q,r) if ((r gt 0) and IsPrime(q)) then exp:= [q^(r-1)]; for i:=2 to r do exp:= exp cat [q^(r-i)]; end for; end if; return exp; end function; t := function (q,r) lista:=expo(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + x^lista[i]; end for; return poly; end function; n := function (q,r) lista:=expo(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=x^exp; return poly; end function; punts_olav:=function (q,r) punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; return punts; end function; #punts_olav(7,3); 7^5; #punts_olav(5,3); 5^5; #punts_olav(7,2); 7^3; #punts_olav(5,2); 5^3; #punts_olav(7,1) 7^1; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Mar 16 2004 10:39:47 on modular [Seed = 1346834372] ------------------------------------- 16807 16807 Errors: /home/mfd/gomagma: line 2: 5895 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 16 10:40:59 2004 Input: Z:=Integers(); PT:=PolynomialRing(Z); expo:= function (q,r) if ((r gt 0) and IsPrime(q)) then exp:= [q^(r-1)]; for i:=2 to r do exp:= exp cat [q^(r-i)]; end for; end if; return exp; end function; t := function (q,r) lista:=expo(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + x^lista[i]; end for; return poly; end function; n := function (q,r) lista:=expo(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=x^exp; return poly; end function; punts_olav:=function (q,r) punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; return punts; end function; #punts_olav(7,3); 7^(3*2-1); Output: Magma V2.10-6 Tue Mar 16 2004 10:40:38 on modular [Seed = 1331171566] ------------------------------------- 16807 16807 Total time: 21.189 seconds, Total memory usage: 2.73MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 16 10:42:10 2004 Input: Z:=Integers(); PT:=PolynomialRing(Z); expo:= function (q,r) if ((r gt 0) and IsPrime(q)) then exp:= [q^(r-1)]; for i:=2 to r do exp:= exp cat [q^(r-i)]; end for; end if; return exp; end function; t := function (q,r) lista:=expo(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + x^lista[i]; end for; return poly; end function; n := function (q,r) lista:=expo(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=x^exp; return poly; end function; punts_olav:=function (q,r) punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; return punts; end function; #punts_olav(5,3); 5^(3*2-1); Output: Magma V2.10-6 Tue Mar 16 2004 10:42:05 on modular [Seed = 1986074220] ------------------------------------- 3125 3125 Total time: 5.269 seconds, Total memory usage: 2.12MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 16 10:43:04 2004 Input: Z:=Integers(); PT:=PolynomialRing(Z); expo:= function (q,r) if ((r gt 0) and IsPrime(q)) then exp:= [q^(r-1)]; for i:=2 to r do exp:= exp cat [q^(r-i)]; end for; end if; return exp; end function; t := function (q,r) lista:=expo(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + x^lista[i]; end for; return poly; end function; n := function (q,r) lista:=expo(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=x^exp; return poly; end function; punts_olav:=function (q,r) punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; return punts; end function; #punts_olav(7,2); 7^(2*2-1); #punts_olav(5,2); 5^(2*2-1); Output: Magma V2.10-6 Tue Mar 16 2004 10:43:01 on modular [Seed = 2104106415] ------------------------------------- 343 343 125 125 Total time: 3.209 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 16 10:43:45 2004 Input: Z:=Integers(); PT:=PolynomialRing(Z); expo:= function (q,r) if ((r gt 0) and IsPrime(q)) then exp:= [q^(r-1)]; for i:=2 to r do exp:= exp cat [q^(r-i)]; end for; end if; return exp; end function; t := function (q,r) lista:=expo(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + x^lista[i]; end for; return poly; end function; n := function (q,r) lista:=expo(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=x^exp; return poly; end function; punts_olav:=function (q,r) punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; return punts; end function; #punts_olav(7,1); 7^(1*2-1); Output: Magma V2.10-6 Tue Mar 16 2004 10:43:41 on modular [Seed = 1685259421] ------------------------------------- 7 7 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 16 10:46:07 2004 Input: Z:=Integers(); PT:=PolynomialRing(Z); expo:= function (q,r) if ((r gt 0) and IsPrime(q)) then exp:= [q^(r-1)]; for i:=2 to r do exp:= exp cat [q^(r-i)]; end for; end if; return exp; end function; t := function (q,r) lista:=expo(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + x^lista[i]; end for; return poly; end function; n := function (q,r) lista:=expo(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=x^exp; return poly; end function; punts_olav:=function (q,r) punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; return punts; end function; [: a,b in GF(5) | a,b in punts_olav(5,2)] Output: Magma V2.10-6 Tue Mar 16 2004 10:46:04 on modular [Seed = 369194877] ------------------------------------- >> [: a,b in GF(5) | a,b in punts_olav(5,2)] ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 16 10:46:44 2004 Input: Z:=Integers(); PT:=PolynomialRing(Z); expo:= function (q,r) if ((r gt 0) and IsPrime(q)) then exp:= [q^(r-1)]; for i:=2 to r do exp:= exp cat [q^(r-i)]; end for; end if; return exp; end function; t := function (q,r) lista:=expo(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + x^lista[i]; end for; return poly; end function; n := function (q,r) lista:=expo(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=x^exp; return poly; end function; punts_olav:=function (q,r) punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; return punts; end function; [: a,b in GF(5) | in punts_olav(5,2)] Output: Magma V2.10-6 Tue Mar 16 2004 10:46:39 on modular [Seed = 487226389] ------------------------------------- [ <0, 0>, <1, 3>, <2, 2>, <3, 2>, <4, 3> ] Total time: 4.589 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 16 10:47:29 2004 Input: Z:=Integers(); PT:=PolynomialRing(Z); expo:= function (q,r) if ((r gt 0) and IsPrime(q)) then exp:= [q^(r-1)]; for i:=2 to r do exp:= exp cat [q^(r-i)]; end for; end if; return exp; end function; t := function (q,r) lista:=expo(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + x^lista[i]; end for; return poly; end function; n := function (q,r) lista:=expo(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=x^exp; return poly; end function; punts_olav:=function (q,r) punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; return punts; end function; llista:=[: a,b in GF(5) | in punts_olav(5,2)] llista; #(llista); Output: Magma V2.10-6 Tue Mar 16 2004 10:47:26 on modular [Seed = 68380125] ------------------------------------- >> llista; ^ User error: bad syntax >> #(llista); ^ User error: Identifier 'llista' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 16 10:49:22 2004 Input: Z:=Integers(); PT:=PolynomialRing(Z); expo:= function (q,r) if ((r gt 0) and IsPrime(q)) then exp:= [q^(r-1)]; for i:=2 to r do exp:= exp cat [q^(r-i)]; end for; end if; return exp; end function; t := function (q,r) lista:=expo(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + x^lista[i]; end for; return poly; end function; n := function (q,r) lista:=expo(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=x^exp; return poly; end function; punts_olav:=function (q,r) punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; return punts; end function; punts:=[: a,b in GF(5) | in punts_olav(5,2)] punts; #(punts); Output: Magma V2.10-6 Tue Mar 16 2004 10:49:19 on modular [Seed = 186411683] ------------------------------------- >> punts; ^ User error: bad syntax >> #(punts); ^ User error: Identifier 'punts' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 16 10:49:35 2004 Input: Z:=Integers(); PT:=PolynomialRing(Z); expo:= function (q,r) if ((r gt 0) and IsPrime(q)) then exp:= [q^(r-1)]; for i:=2 to r do exp:= exp cat [q^(r-i)]; end for; end if; return exp; end function; t := function (q,r) lista:=expo(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + x^lista[i]; end for; return poly; end function; n := function (q,r) lista:=expo(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=x^exp; return poly; end function; punts_olav:=function (q,r) punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; return punts; end function; punts:=[: a,b in GF(5) | in punts_olav(5,2)]; punts; #(punts); Output: Magma V2.10-6 Tue Mar 16 2004 10:49:30 on modular [Seed = 841306223] ------------------------------------- [ <0, 0>, <1, 3>, <2, 2>, <3, 2>, <4, 3> ] 5 Total time: 4.629 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 10:51:24 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; F := GF(27); F; phi := func < n | #[i: i in [0..n-1] | GCD(i,n) eq 1 ] >; Output: Magma V2.10-6 Tue Mar 16 2004 10:51:21 on modular [Seed = 557204239] ------------------------------------- Finite field of size 3^3 Total time: 2.939 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 10:51:41 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; F := GF(27); F; phi := func < n | #[i: i in [0..n-1] | GCD(i,n) eq 1 ] >; phi(22); Output: Magma V2.10-6 Tue Mar 16 2004 10:51:38 on modular [Seed = 675236597] ------------------------------------- Finite field of size 3^3 10 Total time: 2.929 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 10:51:59 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; F := GF(27); F; phi := func < n | #[i: i in [0..n-1] | GCD(i,n) eq 1 ] >; phi(24); Output: Magma V2.10-6 Tue Mar 16 2004 10:51:55 on modular [Seed = 3754474772] ------------------------------------- Finite field of size 3^3 8 Total time: 2.939 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 16 10:52:19 2004 Input: Z:=Integers(); PT:=PolynomialRing(Z); expo:= function (q,r) if ((r gt 0) and IsPrime(q)) then exp:= [q^(r-1)]; for i:=2 to r do exp:= exp cat [q^(r-i)]; end for; end if; return exp; end function; t := function (q,r) lista:=expo(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + x^lista[i]; end for; return poly; end function; n := function (q,r) lista:=expo(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=x^exp; return poly; end function; punts_olav:=function (q,r) punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; return punts; end function; po72:=punts_olav(7,2); llista72:=[: a,b in GF(7) | in po72]; llista72; #(llista72); Output: Magma V2.10-6 Tue Mar 16 2004 10:52:16 on modular [Seed = 3335627809] ------------------------------------- [ <0, 0>, <1, 4>, <2, 2>, <3, 1>, <4, 1>, <5, 2>, <6, 4> ] 7 Total time: 3.209 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 16 10:53:39 2004 Input: Z:=Integers(); PT:=PolynomialRing(Z); expo:= function (q,r) if ((r gt 0) and IsPrime(q)) then exp:= [q^(r-1)]; for i:=2 to r do exp:= exp cat [q^(r-i)]; end for; end if; return exp; end function; t := function (q,r) lista:=expo(q,r); poly:=0; for i:=1 to #(lista) do poly:=poly + x^lista[i]; end for; return poly; end function; n := function (q,r) lista:=expo(q,r); exp:=0; for i:=1 to #(lista) do exp:=exp + lista[i]; end for; poly:=x^exp; return poly; end function; punts_olav:=function (q,r) punts:=[ : a,b in GF(q,r) | Evaluate(n(q,r),a) eq Evaluate(t(q,r),b)]; return punts; end function; po112:=punts_olav(11,2); llista112:=[: a,b in GF(11) | in po112]; llista112; #(llista112); Output: Magma V2.10-6 Tue Mar 16 2004 10:53:34 on modular [Seed = 3420236130] ------------------------------------- [ <0, 0>, <1, 6>, <2, 2>, <3, 10>, <4, 8>, <5, 7>, <6, 7>, <7, 8>, <8, 10>, <9, 2>, <10, 6> ] 11 Total time: 4.579 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 10:57:58 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; Generator(G25); phi := func < n | #[i: i in [0..n-1] | GCD(i,n) eq 1 ] >; phi(24); Output: Magma V2.10-6 Tue Mar 16 2004 10:57:55 on modular [Seed = 4260010409] ------------------------------------- gamma 8 Total time: 2.909 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 10:59:58 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; Generator(G25); ElementToSequence (gamma^24); Output: Magma V2.10-6 Tue Mar 16 2004 10:59:55 on modular [Seed = 3841163464] ------------------------------------- gamma [ 1, 0 ] Total time: 2.929 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 11:03:04 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; ejemplo := P3 ! [1,1,2]; Gej := ext < GF(3) | ejemplo >; Gej; Generator(Gej); /*ElementToSequence (gamma^24);*/ Output: Magma V2.10-6 Tue Mar 16 2004 11:03:01 on modular [Seed = 2174149859] ------------------------------------- >> Gej := ext < GF(3) | ejemplo >; ^ Runtime error in ext< ... >: Argument 1 is not monic >> Gej; ^ User error: Identifier 'Gej' has not been declared or assigned >> Generator(Gej); ^ User error: Identifier 'Gej' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 11:03:40 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; ejemplo := P3 ! [2,1,1]; Gej := ext < GF(3) | ejemplo >; Gej; Generator(Gej); /*ElementToSequence (gamma^24);*/ Output: Magma V2.10-6 Tue Mar 16 2004 11:03:37 on modular [Seed = 2292182406] ------------------------------------- Finite field of size 3^2 z Total time: 2.949 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 11:04:06 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; ejemplo := P3 ! [2,1,1]; Gej := ext < GF(3) | ejemplo >; Gej; Generator(Gej); ElementToSequence (z^7); Output: Magma V2.10-6 Tue Mar 16 2004 11:04:03 on modular [Seed = 3215514267] ------------------------------------- Finite field of size 3^2 z [ 1, 1 ] Total time: 2.939 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 11:04:22 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; ejemplo := P3 ! [2,1,1]; Gej := ext < GF(3) | ejemplo >; Gej; Generator(Gej); ElementToSequence (z^5); Output: Magma V2.10-6 Tue Mar 16 2004 11:04:19 on modular [Seed = 2796667762] ------------------------------------- Finite field of size 3^2 z [ 0, 2 ] Total time: 2.939 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 11:04:40 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; ejemplo := P3 ! [2,1,1]; Gej := ext < GF(3) | ejemplo >; Gej; Generator(Gej); ElementToSequence (z^3); Output: Magma V2.10-6 Tue Mar 16 2004 11:04:37 on modular [Seed = 2914699375] ------------------------------------- Finite field of size 3^2 z [ 2, 2 ] Total time: 2.999 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 11:05:09 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; ejemplo := P3 ! [2,1,1]; Gej := ext < GF(3) | ejemplo >; Gej; Generator(Gej); ElementToSequence (z^3); PrimitiveElement(Gej); Output: Magma V2.10-6 Tue Mar 16 2004 11:05:06 on modular [Seed = 1598569140] ------------------------------------- Finite field of size 3^2 z [ 2, 2 ] z Total time: 2.919 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 11:06:41 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; ejemplo := P3 ! [2,1,1]; Gej := ext < GF(3) | ejemplo >; Gej; Generator(Gej); ElementToSequence (z^3); PrimitiveElement(Gej); elt ; Output: Magma V2.10-6 Tue Mar 16 2004 11:06:38 on modular [Seed = 1230909214] ------------------------------------- Finite field of size 3^2 z [ 2, 2 ] z z^3 Total time: 2.919 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 11:07:57 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; ejemplo := P3 ! [2,1,1]; Gej := ext < GF(3) | ejemplo >; Gej; Generator(Gej); ElementToSequence (z^3); PrimitiveElement(Gej); Order(elt ); Output: Magma V2.10-6 Tue Mar 16 2004 11:07:54 on modular [Seed = 1112876096] ------------------------------------- Finite field of size 3^2 z [ 2, 2 ] z 8 Total time: 2.919 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 11:09:08 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; ejemplo := P3 ! [2,1,1]; Gej := ext < GF(3) | ejemplo >; Gej; Generator(Gej); ElementToSequence (z^3); elt ; Order(z^3); Output: Magma V2.10-6 Tue Mar 16 2004 11:09:05 on modular [Seed = 2070683010] ------------------------------------- Finite field of size 3^2 z [ 2, 2 ] z^3 8 Total time: 2.989 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 11:09:23 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; ejemplo := P3 ! [2,1,1]; Gej := ext < GF(3) | ejemplo >; Gej; Generator(Gej); ElementToSequence (z^3); elt ; Order(z^5); Output: Magma V2.10-6 Tue Mar 16 2004 11:09:20 on modular [Seed = 1952649884] ------------------------------------- Finite field of size 3^2 z [ 2, 2 ] z^3 8 Total time: 2.879 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 11:09:57 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; ejemplo := P3 ! [2,1,1]; Gej := ext < GF(3) | ejemplo >; Gej; Generator(Gej); ElementToSequence (z^3); Order(elt ); Order(z^5); Output: Magma V2.10-6 Tue Mar 16 2004 11:09:54 on modular [Seed = 1836714983] ------------------------------------- Finite field of size 3^2 z [ 2, 2 ] 2 8 Total time: 2.929 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 11:10:09 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; ejemplo := P3 ! [2,1,1]; Gej := ext < GF(3) | ejemplo >; Gej; Generator(Gej); ElementToSequence (z^3); Order(elt ); Order(z^5); Output: Magma V2.10-6 Tue Mar 16 2004 11:10:05 on modular [Seed = 487226264] ------------------------------------- Finite field of size 3^2 z [ 2, 2 ] 2 8 Total time: 2.999 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 16 11:11:21 2004 Input: k:= GF(2); print k; Output: Magma V2.10-6 Tue Mar 16 2004 11:11:18 on modular [Seed = 385904745] ------------------------------------- Finite field of size 2 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 11:18:02 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; /*ordre_elements := [<(G25!i),Order(G25!i)> : i in [1..24] | (G25!i) ne 0]; ordre_elements := [ElementToSequence(gamma^]; */ print "gamma"; Order(gamma); ejemplo := P3 ! [2,1,1]; Gej := ext < GF(3) | ejemplo >; Gej; Generator(Gej); ElementToSequence (z^3); Order(elt ); Order(z^5); Output: Magma V2.10-6 Tue Mar 16 2004 11:17:59 on modular [Seed = 992760788] ------------------------------------- gamma 24 Finite field of size 3^2 z [ 2, 2 ] 2 8 Total time: 2.939 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 16 11:18:45 2004 Input: f := GF (3); 2+2*alpha+alpha^2; Output: Magma V2.10-6 Tue Mar 16 2004 11:18:42 on modular [Seed = 874732686] ------------------------------------- 2 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 16 11:19:34 2004 Input: F := GF (3); 2+2*alpha+alpha^2; PrimitiveElement (F); Output: Magma V2.10-6 Tue Mar 16 2004 11:19:31 on modular [Seed = 758793318] ------------------------------------- 2 2 Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 11:19:59 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; /*ordre_elements := [<(G25!i),Order(G25!i)> : i in [1..24] | (G25!i) ne 0]; */ ordre_elements := [: i in [0..24]]; print "gamma"; Order(gamma); /* es 24, per tant es element primitiu*/ ejemplo := P3 ! [2,1,1]; Gej := ext < GF(3) | ejemplo >; Gej; Generator(Gej); ElementToSequence (z^3); Order(elt ); Order(z^5); Output: Magma V2.10-6 Tue Mar 16 2004 11:19:56 on modular [Seed = 640765778] ------------------------------------- >> ordre_elements := [ := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; /*ordre_elements := [<(G25!i),Order(G25!i)> : i in [1..24] | (G25!i) ne 0]; */ ordre_elements := [: i in [0..24]]; print "gamma"; Order(gamma); /* es 24, per tant es element primitiu*/ ejemplo := P3 ! [2,1,1]; Gej := ext < GF(3) | ejemplo >; Gej; Generator(Gej); ElementToSequence (z^3); Order(elt ); Order(z^5); Output: Magma V2.10-6 Tue Mar 16 2004 11:20:23 on modular [Seed = 3603021769] ------------------------------------- gamma 24 Finite field of size 3^2 z [ 2, 2 ] 2 8 Total time: 2.919 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 16 11:21:14 2004 Input: F := GF (3); 2+2*alpha+alpha^2; PrimitiveElement (F); G := GF (2); 1+alpha+alpha^4; PrimitiveElement (G); Output: Magma V2.10-6 Tue Mar 16 2004 11:21:11 on modular [Seed = 3235359215] ------------------------------------- 2 2 1 1 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 11:21:19 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; /*ordre_elements := [<(G25!i),Order(G25!i)> : i in [1..24] | (G25!i) ne 0]; */ ordre_elements := [: i in [0..24]]; ElementToSequence(gamma^1); ElementToSequence(gamma^2); ElementToSequence(gamma^3); ElementToSequence(gamma^4); print "gamma"; Order(gamma); /* es 24, per tant es element primitiu*/ ejemplo := P3 ! [2,1,1]; Gej := ext < GF(3) | ejemplo >; Gej; Generator(Gej); ElementToSequence (z^3); Order(elt ); Order(z^5); Output: Magma V2.10-6 Tue Mar 16 2004 11:21:16 on modular [Seed = 4193161437] ------------------------------------- [ 0, 1 ] [ 3, 1 ] [ 3, 4 ] [ 2, 2 ] gamma 24 Finite field of size 3^2 z [ 2, 2 ] 2 8 Total time: 2.979 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 16 11:22:44 2004 Input: F := GF (3); 2+2*alpha+alpha^2; PrimitiveElement (F); G := GF (2); 1+alpha+alpha^4; PrimitiveElement (G); H := GF (5); 3+2*alpha+alpha^2; PrimitiveElement (H); Output: Magma V2.10-6 Tue Mar 16 2004 11:22:41 on modular [Seed = 4075133819] ------------------------------------- 2 2 1 1 1 2 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 11:23:18 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; /*ordre_elements := [<(G25!i),Order(G25!i)> : i in [1..24] | (G25!i) ne 0]; */ ordre_elements := [: i in [1..24]]; ElementToSequence(gamma^1); ElementToSequence(gamma^2); ElementToSequence(gamma^3); ElementToSequence(gamma^4); print "gamma"; Order(gamma); /* es 24, per tant es element primitiu*/ ejemplo := P3 ! [2,1,1]; Gej := ext < GF(3) | ejemplo >; Gej; Generator(Gej); ElementToSequence (z^3); Order(elt ); Order(z^5); Output: Magma V2.10-6 Tue Mar 16 2004 11:23:15 on modular [Seed = 3959194176] ------------------------------------- [ 0, 1 ] [ 3, 1 ] [ 3, 4 ] [ 2, 2 ] gamma 24 Finite field of size 3^2 z [ 2, 2 ] 2 8 Total time: 2.939 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 16 11:23:58 2004 Input: F := GF (3); 2+2*alpha+alpha^2; PrimitiveElement (F); G1 := GF (3); 1+2*alpha+alpha^2; PrimitiveElement (G1); G := GF (2); 1+alpha+alpha^4; PrimitiveElement (G); H := GF (5); 3+2*alpha+alpha^2; PrimitiveElement (H); Output: Magma V2.10-6 Tue Mar 16 2004 11:23:55 on modular [Seed = 3841167015] ------------------------------------- 2 2 1 2 1 1 1 2 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 11:24:40 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; /*ordre_elements := [<(G25!i),Order(G25!i)> : i in [1..24] | (G25!i) ne 0]; */ ordre_elements := [: i in [1..24]]; ElementToSequence(gamma^1); ElementToSequence(gamma^2); ElementToSequence(gamma^3); ElementToSequence(gamma^4); print "gamma"; Order(gamma); /* es 24, per tant es element primitiu*/ ejemplo := P3 ! [2,1,1]; Gej := ext < GF(3) | ejemplo >; Gej; Generator(Gej); ElementToSequence (z^3); Order(elt ); Order(z^5); Output: Magma V2.10-6 Tue Mar 16 2004 11:24:37 on modular [Seed = 2643130240] ------------------------------------- [ 0, 1 ] [ 3, 1 ] [ 3, 4 ] [ 2, 2 ] gamma 24 Finite field of size 3^2 z [ 2, 2 ] 2 8 Total time: 3.039 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 11:25:08 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; /*ordre_elements := [<(G25!i),Order(G25!i)> : i in [1..24] | (G25!i) ne 0]; */ ordre_elements := [: i in [1..24]]; print "hola"; Order(gamma^3); print "gamma"; Order(gamma); /* es 24, per tant es element primitiu*/ ejemplo := P3 ! [2,1,1]; Gej := ext < GF(3) | ejemplo >; Gej; Generator(Gej); ElementToSequence (z^3); Order(elt ); Order(z^5); Output: Magma V2.10-6 Tue Mar 16 2004 11:25:05 on modular [Seed = 2325602483] ------------------------------------- hola 8 gamma 24 Finite field of size 3^2 z [ 2, 2 ] 2 8 Total time: 2.929 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 11:25:30 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; /*ordre_elements := [<(G25!i),Order(G25!i)> : i in [1..24] | (G25!i) ne 0]; */ ordre_elements := [: i in [1..24]]; ordre_elements; print "hola"; Order(gamma^3); print "gamma"; Order(gamma); /* es 24, per tant es element primitiu*/ ejemplo := P3 ! [2,1,1]; Gej := ext < GF(3) | ejemplo >; Gej; Generator(Gej); ElementToSequence (z^3); Order(elt ); Order(z^5); Output: Magma V2.10-6 Tue Mar 16 2004 11:25:27 on modular [Seed = 2207574444] ------------------------------------- [ , , , , , <2, 4>, , , , , , <4, 2>, , , , , , <3, 4>, , , , , , <1, 1> ] hola 8 gamma 24 Finite field of size 3^2 z [ 2, 2 ] 2 8 Total time: 2.899 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 11:29:38 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; ordre_elements := [: i in [1..24]]; ordre_elements; elem_primitius := [tupla[1]: tupla in ordre_elements | tupla[2] eq 25-1 ]; elem_primitius; ejemplo := P3 ! [2,1,1]; Gej := ext < GF(3) | ejemplo >; Gej; Generator(Gej); ElementToSequence (z^3); Order(elt ); Order(z^5); Output: Magma V2.10-6 Tue Mar 16 2004 11:29:35 on modular [Seed = 3182089866] ------------------------------------- [ , , , , , <2, 4>, , , , , , <4, 2>, , , , , , <3, 4>, , , , , , <1, 1> ] [ gamma, gamma^5, gamma^7, gamma^11, gamma^13, gamma^17, gamma^19, gamma^23 ] Finite field of size 3^2 z [ 2, 2 ] 2 8 Total time: 3.019 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 16 11:29:43 2004 Input: k:= Gf(5); DefiningPolynomila (k); Output: Magma V2.10-6 Tue Mar 16 2004 11:29:40 on modular [Seed = 3064061338] ------------------------------------- >> k:= Gf(5); DefiningPolynomila (k);; ^ User error: Identifier 'Gf' has not been declared or assigned >> k:= Gf(5); DefiningPolynomila (k);; ^ User error: Identifier 'k' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 16 11:30:00 2004 Input: k:= GF(5); DefiningPolynomial (k); Output: Magma V2.10-6 Tue Mar 16 2004 11:29:56 on modular [Seed = 2948121714] ------------------------------------- $.1 + 4 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 16 11:30:16 2004 Input: k:= GF(2); DefiningPolynomial (k); Output: Magma V2.10-6 Tue Mar 16 2004 11:30:13 on modular [Seed = 1581856146] ------------------------------------- $.1 + 1 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 16 11:33:10 2004 Input: k:= GF(3);DefiningPolynomial (k); Output: Magma V2.10-6 Tue Mar 16 2004 11:33:07 on modular [Seed = 1281040470] ------------------------------------- $.1 + 2 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 16 11:33:54 2004 Input: k:= GF(5);DefiningPolynomial (k); Output: Magma V2.10-6 Tue Mar 16 2004 11:33:51 on modular [Seed = 1196436337] ------------------------------------- $.1 + 4 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 16 11:36:04 2004 Input: F := GF (3); 2+2*alpha+alpha^2; Output: Magma V2.10-6 Tue Mar 16 2004 11:36:01 on modular [Seed = 1969363421] ------------------------------------- 2 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 11:36:22 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; ordre_elements := [: i in [1..24]]; ordre_elements; elem_primitius := [tupla[1]: tupla in ordre_elements | tupla[2] eq 25-1 ]; #elem_primitius; ejemplo := P3 ! [2,1,1]; Gej := ext < GF(3) | ejemplo >; Gej; Generator(Gej); ElementToSequence (z^3); Order(elt ); Order(z^5); Output: Magma V2.10-6 Tue Mar 16 2004 11:36:19 on modular [Seed = 1820000566] ------------------------------------- [ , , , , , <2, 4>, , , , , , <4, 2>, , , , , , <3, 4>, , , , , , <1, 1> ] 8 Finite field of size 3^2 z [ 2, 2 ] 2 8 Total time: 3.009 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 16 11:38:46 2004 Input: F := GF (3); G9:= 2+2*alpha+alpha^2; F := GF (2); G16:= 1+alpha+alpha^4; F := GF (3); G25:= 2+4*alpha+alpha^2; F := GF (3); G9b := 1+2*alpha+alpha^2; Output: Magma V2.10-6 Tue Mar 16 2004 11:38:43 on modular [Seed = 1718684588] ------------------------------------- Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 16 11:39:12 2004 Input: F := GF (3); G9:= 2+2*alpha+alpha^2; print G9; F := GF (2); G16:= 1+alpha+alpha^4; F := GF (3); G25:= 2+4*alpha+alpha^2; F := GF (3); G9b := 1+2*alpha+alpha^2; Output: Magma V2.10-6 Tue Mar 16 2004 11:39:09 on modular [Seed = 268926436] ------------------------------------- 2 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 16 11:39:39 2004 Input: F := GF (3); G9:= 2+2*alpha+alpha^2; print G9; F := GF (2); G16:= 1+alpha+alpha^4; print G16; F := GF (3); G25:= 2+4*alpha+alpha^2; print G25; F := GF (3); G9b := 1+2*alpha+alpha^2; print G9b; Output: Magma V2.10-6 Tue Mar 16 2004 11:39:36 on modular [Seed = 186410650] ------------------------------------- 2 1 1 1 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 16 11:56:05 2004 Input: F := GF (3); G9:= 2+2*alpha+alpha^2; print G9; F := GF (2); G16:= 1+alpha+alpha^4; print G16; F := GF (3); G25:= 2+4*alpha+alpha^2; print G25; Order (G25); F := GF (3); G9b := 1+2*alpha+alpha^2; print G9b; Output: Magma V2.10-6 Tue Mar 16 2004 11:56:02 on modular [Seed = 540496347] ------------------------------------- 2 1 1 1 1 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 16 12:04:37 2004 Input: G25 := GF(5); 2+4*alpha+alpha^2; Order (G25); Output: Magma V2.10-6 Tue Mar 16 2004 12:04:34 on modular [Seed = 3352343612] ------------------------------------- 2 >> G25 := GF(5); 2+4*alpha+alpha^2; Order (G25); ; ^ Runtime error in 'Order': Bad argument types Argument types given: FldFin Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 16 12:06:16 2004 Input: G25 := GF(5); g25:= 2+4*alpha+alpha^2; Order (g25); Output: Magma V2.10-6 Tue Mar 16 2004 12:06:13 on modular [Seed = 4125262249] ------------------------------------- 4 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (160.80.10.129) Time: Tue Mar 16 12:06:56 2004 Input: PF := PolynomialRing(GF(13, 2)); P := PolynomialRing(PF); FF1 := ext; P := PolynomialRing(FF1); FF2 := ext; ClassNumber(FF2); Output: Magma V2.10-6 Tue Mar 16 2004 12:06:42 on modular [Seed = 3975911575] ------------------------------------- 1 Total time: 11.449 seconds, Total memory usage: 5.02MB ************** MAGMA ***************** Host 3(NXDOMAIN) (160.80.10.129) Time: Tue Mar 16 12:21:11 2004 Input: PF:= PolynomialRing(GF(5)); FF1:= ext; ClassNumber(FF1); Output: Magma V2.10-6 Tue Mar 16 2004 12:21:08 on modular [Seed = 2359032657] ------------------------------------- >> FF1:= ext; ^ User error: Identifier 'y' has not been declared or assigned >> ClassNumber(FF1);; ^ User error: Identifier 'FF1' has not been declared or assigned Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (160.80.10.129) Time: Tue Mar 16 12:21:55 2004 Input: PF:= PolynomialRing(GF(5)); FF1:= ext; ClassNumber(FF1); Output: Magma V2.10-6 Tue Mar 16 2004 12:21:52 on modular [Seed = 2274422894] ------------------------------------- >> FF1:= ext; ^ User error: Identifier 'y' has not been declared or assigned >> ClassNumber(FF1);; ^ User error: Identifier 'FF1' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 12:25:56 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; ordre_elements := [: i in [1..24]]; ordre_elements; elem_primitius := [tupla[1]: tupla in ordre_elements | tupla[2] eq 25-1 ]; #elem_primitius; ejemplo := P3 ! [2,1,1]; Gej := ext < GF(3) | ejemplo >; Gej; Generator(Gej); ElementToSequence (z^3); MinimalPolynomial(elt ); Order(z^5); Output: Magma V2.10-6 Tue Mar 16 2004 12:25:53 on modular [Seed = 3030633548] ------------------------------------- [ , , , , , <2, 4>, , , , , , <4, 2>, , , , , , <3, 4>, , , , , , <1, 1> ] 8 Finite field of size 3^2 z [ 2, 2 ] $.1 + 1 8 Total time: 2.929 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host aula-a-siee40.uab.es. (158.109.66.40) Time: Tue Mar 16 12:27:17 2004 Input: diumenge := { n : n in [4..366 by 7] }; print diumenge; Output: Magma V2.10-6 Tue Mar 16 2004 12:27:14 on modular [Seed = 2948126468] ------------------------------------- { 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 } Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee40.uab.es. (158.109.66.40) Time: Tue Mar 16 12:28:31 2004 Input: diumenge := { n : n in [1..366 by 7] }; print diumenge; Output: Magma V2.10-6 Tue Mar 16 2004 12:28:27 on modular [Seed = 1515004731] ------------------------------------- { 1, 8, 15, 22, 29, 36, 43, 50, 57, 64, 71, 78, 85, 92, 99, 106, 113, 120, 127, 134, 141, 148, 155, 162, 169, 176, 183, 190, 197, 204, 211, 218, 225, 232, 239, 246, 253, 260, 267, 274, 281, 288, 295, 302, 309, 316, 323, 330, 337, 344, 351, 358, 365 } Total time: 3.699 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 12:28:31 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; ordre_elements := [: i in [1..24]]; ordre_elements; elem_primitius := [tupla[1]: tupla in ordre_elements | tupla[2] eq 25-1 ]; #elem_primitius; ejemplo := P3 ! [2,1,1]; Gej := ext < GF(3) | ejemplo >; Gej; Generator(Gej); ElementToSequence (z^3); print "eoh"; MinimalPolynomial(elt ); Order(z^5); Output: Magma V2.10-6 Tue Mar 16 2004 12:28:28 on modular [Seed = 1481580862] ------------------------------------- [ , , , , , <2, 4>, , , , , , <4, 2>, , , , , , <3, 4>, , , , , , <1, 1> ] 8 Finite field of size 3^2 z [ 2, 2 ] eoh $.1 + 1 8 Total time: 3.649 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host aula-a-siee40.uab.es. (158.109.66.40) Time: Tue Mar 16 12:28:51 2004 Input: diumenge := { n : n in [4..366 by 7] }; print diumenge; Output: Magma V2.10-6 Tue Mar 16 2004 12:28:48 on modular [Seed = 1264333377] ------------------------------------- { 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 333, 340, 347, 354, 361 } Total time: 3.289 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 12:28:53 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; ordre_elements := [: i in [1..24]]; ordre_elements; elem_primitius := [tupla[1]: tupla in ordre_elements | tupla[2] eq 25-1 ]; #elem_primitius; ejemplo := P3 ! [2,1,1]; Gej := ext < GF(3) | ejemplo >; Gej; Generator(Gej); ElementToSequence (z^3); print "eoh"; MinimalPolynomial(elt , Gej); Order(z^5); Output: Magma V2.10-6 Tue Mar 16 2004 12:28:50 on modular [Seed = 1314469702] ------------------------------------- [ , , , , , <2, 4>, , , , , , <4, 2>, , , , , , <3, 4>, , , , , , <1, 1> ] 8 Finite field of size 3^2 z [ 2, 2 ] eoh $.1 + 1 8 Total time: 3.329 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 16 12:36:42 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Tue Mar 16 2004 12:36:39 on modular [Seed = 1853429011] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 12:37:58 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; ordre_elements := [: i in [1..24]]; ordre_elements; elem_primitius := [tupla[1]: tupla in ordre_elements | tupla[2] eq 25-1 ]; #elem_primitius; ejemplo := P2 ! [1,1,1]; Gej := ext < GF(2) | ejemplo >; Gej; Generator(Gej); print "eoh"; MinimalPolynomial(elt , Gej); Output: Magma V2.10-6 Tue Mar 16 2004 12:37:55 on modular [Seed = 1735400526] ------------------------------------- [ , , , , , <2, 4>, , , , , , <4, 2>, , , , , , <3, 4>, , , , , , <1, 1> ] 8 Finite field of size 2^2 z eoh $.1 Total time: 3.019 seconds, Total memory usage: 2.29MB ************** MAGMA ***************** Host aula-a-siee40.uab.es. (158.109.66.40) Time: Tue Mar 16 12:38:42 2004 Input: SetEchoInput(true); Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed. ************** MAGMA ***************** Host aula-a-siee40.uab.es. (158.109.66.40) Time: Tue Mar 16 12:39:18 2004 Input: M22:=MatrixRing(GF(4),2); Output: Magma V2.10-6 Tue Mar 16 2004 12:39:15 on modular [Seed = 385903758] ------------------------------------- Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee40.uab.es. (158.109.66.40) Time: Tue Mar 16 12:39:34 2004 Input: M22:=MatrixRing(GF(4),2); print M22; Output: Magma V2.10-6 Tue Mar 16 2004 12:39:31 on modular [Seed = 203126661] ------------------------------------- Full Matrix Algebra of degree 2 over GF(2^2) Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee40.uab.es. (158.109.66.40) Time: Tue Mar 16 12:40:42 2004 Input: M22:=MatrixRing(GF(4),2); print M22; /* i) Subconjunt Mt de M que tenen traça 0 */ Mt := {m:m in M22 | Trace(m) eq 0}; /* ii) Subconjunt Mf de M amb la primera fila igual a la segona */ Mf := {m:m in M22 | m[1] eq m[2]}; /* iii) Utilitar Mt i Mf per trobar Mtf (traça igual a 0 i fila1 igual a fila2) */ Mtf := { Mt meet Mf }; /* o */ Mtf := {m:m in M22 | Trace(m) eq 0 and m[1] eq m[2]}; print Mt; print Mf; print Mtf; Output: Magma V2.10-6 Tue Mar 16 2004 12:40:39 on modular [Seed = 1026179440] ------------------------------------- Full Matrix Algebra of degree 2 over GF(2^2) { [ 0 0] [ 0 0], [ 0 0] [$.1^2 0], [ 0 0] [ $.1 0], [ 0 0] [ 1 0], [$.1^2 0] [ 0 $.1^2], [$.1^2 0] [$.1^2 $.1^2], [$.1^2 0] [ $.1 $.1^2], [$.1^2 0] [ 1 $.1^2], [ 1 0] [ 0 1], [ 1 0] [$.1^2 1], [ 1 0] [ $.1 1], [ 1 0] [ 1 1], [ $.1 0] [ 0 $.1], [ $.1 0] [$.1^2 $.1], [ $.1 0] [ $.1 $.1], [ $.1 0] [ 1 $.1], [ 0 $.1^2] [ 0 0], [ 0 $.1^2] [$.1^2 0], [ 0 $.1^2] [ $.1 0], [ 0 $.1^2] [ 1 0], [$.1^2 $.1^2] [ 0 $.1^2], [$.1^2 $.1^2] [$.1^2 $.1^2], [$.1^2 $.1^2] [ $.1 $.1^2], [$.1^2 $.1^2] [ 1 $.1^2], [ 1 $.1^2] [ 0 1], [ 1 $.1^2] [$.1^2 1], [ 1 $.1^2] [ $.1 1], [ 1 $.1^2] [ 1 1], [ $.1 $.1^2] [ 0 $.1], [ $.1 $.1^2] [$.1^2 $.1], [ $.1 $.1^2] [ $.1 $.1], [ $.1 $.1^2] [ 1 $.1], [ 0 $.1] [ 0 0], [ 0 $.1] [$.1^2 0], [ 0 $.1] [ $.1 0], [ 0 $.1] [ 1 0], [$.1^2 $.1] [ 0 $.1^2], [$.1^2 $.1] [$.1^2 $.1^2], [$.1^2 $.1] [ $.1 $.1^2], [$.1^2 $.1] [ 1 $.1^2], [ 1 $.1] [ 0 1], [ 1 $.1] [$.1^2 1], [ 1 $.1] [ $.1 1], [ 1 $.1] [ 1 1], [ $.1 $.1] [ 0 $.1], [ $.1 $.1] [$.1^2 $.1], [ $.1 $.1] [ $.1 $.1], [ $.1 $.1] [ 1 $.1], [ 0 1] [ 0 0], [ 0 1] [$.1^2 0], [ 0 1] [ $.1 0], [ 0 1] [ 1 0], [$.1^2 1] [ 0 $.1^2], [$.1^2 1] [$.1^2 $.1^2], [$.1^2 1] [ $.1 $.1^2], [$.1^2 1] [ 1 $.1^2], [ 1 1] [ 0 1], [ 1 1] [$.1^2 1], [ 1 1] [ $.1 1], [ 1 1] [ 1 1], [ $.1 1] [ 0 $.1], [ $.1 1] [$.1^2 $.1], [ $.1 1] [ $.1 $.1], [ $.1 1] [ 1 $.1] } { [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ $.1 0] [ $.1 0], [ 0 $.1^2] [ 0 $.1^2], [ $.1 $.1^2] [ $.1 $.1^2], [ 0 $.1] [ 0 $.1], [ $.1 $.1] [ $.1 $.1], [ 0 1] [ 0 1], [ $.1 1] [ $.1 1], [$.1^2 0] [$.1^2 0], [ 1 0] [ 1 0], [$.1^2 $.1^2] [$.1^2 $.1^2], [ 1 $.1^2] [ 1 $.1^2], [$.1^2 $.1] [$.1^2 $.1], [ 1 $.1] [ 1 $.1], [$.1^2 1] [$.1^2 1] } { [ 0 0] [ 0 0], [$.1^2 $.1^2] [$.1^2 $.1^2], [ $.1 $.1] [ $.1 $.1], [ 1 1] [ 1 1] } Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 12:41:08 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; ordre_elements := [: i in [1..24]]; ordre_elements; elem_primitius := [tupla[1]: tupla in ordre_elements | tupla[2] eq 25-1 ]; #elem_primitius; ejemplo := P3 ! [1,1]; Gej := ext < GF(3) | ejemplo >; Gej; print "eoh"; MinimalPolynomial(elt , Gej); Output: Magma V2.10-6 Tue Mar 16 2004 12:41:06 on modular [Seed = 708662850] ------------------------------------- [ , , , , , <2, 4>, , , , , , <4, 2>, , , , , , <3, 4>, , , , , , <1, 1> ] 8 Finite field of size 3 eoh $.1 + 1 Total time: 2.929 seconds, Total memory usage: 2.29MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 16 12:43:13 2004 Input: M22:=MatrixRing(F,2); Output: Magma V2.10-6 Tue Mar 16 2004 12:43:10 on modular [Seed = 590634967] ------------------------------------- >> M22:=MatrixRing(F,2);; ^ User error: Identifier 'F' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 16 12:43:43 2004 Input: /* Problema 1*/ [i : i in [1..366]|((i+3) mod 7) eq 0] [i : i in [4..366 by 7]]; /*Problema 2*/ /*(i)*/ M22:=MatrixRing(F,2); F:=GF(4); Mt:={i:i in M22|Trace(i) eq 0}; /*(ii)*/ Mf:={i:i in M22| i[1] eq i[2]}; /*(iii)*/ Mtf:={i:i in M22| (Trace(i) eq 0) and (i[1] eq i[2] )}; Output: Magma V2.10-6 Tue Mar 16 2004 12:43:40 on modular [Seed = 3637486670] ------------------------------------- >> [i : i in [4..366 by 7]]; ^ User error: bad syntax >> M22:=MatrixRing(F,2); ^ User error: Identifier 'F' has not been declared or assigned >> Mt:={i:i in M22|Trace(i) eq 0}; ^ User error: Identifier 'M22' has not been declared or assigned >> Mf:={i:i in M22| i[1] eq i[2]}; ^ User error: Identifier 'M22' has not been declared or assigned >> Mtf:={i:i in M22| (Trace(i) eq 0) and (i[1] eq i[2] )};; ^ User error: Identifier 'M22' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 16 12:44:10 2004 Input: /* Problema 1*/ [i:i in [1..366]|((i+3) mod 7) eq 0] [i:i in [4..366 by 7]]; /*Problema 2*/ /*(i)*/ M22:=MatrixRing(F,2); F:=GF(4); Mt:={i:i in M22|Trace(i) eq 0}; /*(ii)*/ Mf:={i:i in M22| i[1] eq i[2]}; /*(iii)*/ Mtf:={i:i in M22| (Trace(i) eq 0) and (i[1] eq i[2] )}; Output: Magma V2.10-6 Tue Mar 16 2004 12:44:07 on modular [Seed = 3519458668] ------------------------------------- >> [i:i in [4..366 by 7]]; ^ User error: bad syntax >> M22:=MatrixRing(F,2); ^ User error: Identifier 'F' has not been declared or assigned >> Mt:={i:i in M22|Trace(i) eq 0}; ^ User error: Identifier 'M22' has not been declared or assigned >> Mf:={i:i in M22| i[1] eq i[2]}; ^ User error: Identifier 'M22' has not been declared or assigned >> Mtf:={i:i in M22| (Trace(i) eq 0) and (i[1] eq i[2] )};; ^ User error: Identifier 'M22' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 16 12:45:02 2004 Input: /*Problema 2*/ /*(i)*/ M22:=MatrixRing(F,2); F:=GF(4); Mt:={i:i in M22|Trace(i) eq 0}; /*(ii)*/ Mf:={i:i in M22| i[1] eq i[2]}; /*(iii)*/ Mtf:={i:i in M22| (Trace(i) eq 0) and (i[1] eq i[2] )}; Output: Magma V2.10-6 Tue Mar 16 2004 12:44:59 on modular [Seed = 3470373775] ------------------------------------- >> M22:=MatrixRing(F,2); ^ User error: Identifier 'F' has not been declared or assigned >> Mt:={i:i in M22|Trace(i) eq 0}; ^ User error: Identifier 'M22' has not been declared or assigned >> Mf:={i:i in M22| i[1] eq i[2]}; ^ User error: Identifier 'M22' has not been declared or assigned >> Mtf:={i:i in M22| (Trace(i) eq 0) and (i[1] eq i[2] )};; ^ User error: Identifier 'M22' has not been declared or assigned Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host EPC-dhcp-89.Lib.UH.EDU. (129.7.156.89) Time: Tue Mar 16 12:45:46 2004 Input: kd1:=MultiPartiteGraph([3,3,3]); kd2:=LineGraph(kd1); kd2; Output: Magma V2.10-6 Tue Mar 16 2004 12:45:42 on modular [Seed = 4176446948] ------------------------------------- >> kd1:=MultiPartiteGraph([3,3,3]); ^ User error: Identifier 'MultiPartiteGraph' has not been declared or assigned >> kd2:=LineGraph(kd1); ^ User error: Identifier 'kd1' has not been declared or assigned >> kd2;; ^ User error: Identifier 'kd2' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host EPC-dhcp-89.Lib.UH.EDU. (129.7.156.89) Time: Tue Mar 16 12:45:59 2004 Input: kd1:=MultipartiteGraph([3,3,3]); kd2:=LineGraph(kd1); kd2; Output: Magma V2.10-6 Tue Mar 16 2004 12:45:56 on modular [Seed = 4058418431] ------------------------------------- Graph Vertex Neighbours 1 2 3 4 7 10 13 16 19 22 25 ; 2 1 3 5 8 11 13 17 19 23 25 ; 3 1 2 6 9 12 13 18 19 24 25 ; 4 1 5 6 7 10 14 16 20 22 26 ; 5 2 4 6 8 11 14 17 20 23 26 ; 6 3 4 5 9 12 14 18 20 24 26 ; 7 1 4 8 9 10 15 16 21 22 27 ; 8 2 5 7 9 11 15 17 21 23 27 ; 9 3 6 7 8 12 15 18 21 24 27 ; 10 1 4 7 11 12 13 14 15 16 22 ; 11 2 5 8 10 12 13 14 15 17 23 ; 12 3 6 9 10 11 13 14 15 18 24 ; 13 1 2 3 10 11 12 14 15 19 25 ; 14 4 5 6 10 11 12 13 15 20 26 ; 15 7 8 9 10 11 12 13 14 21 27 ; 16 1 4 7 10 17 18 19 20 21 22 ; 17 2 5 8 11 16 18 19 20 21 23 ; 18 3 6 9 12 16 17 19 20 21 24 ; 19 1 2 3 13 16 17 18 20 21 25 ; 20 4 5 6 14 16 17 18 19 21 26 ; 21 7 8 9 15 16 17 18 19 20 27 ; 22 1 4 7 10 16 23 24 25 26 27 ; 23 2 5 8 11 17 22 24 25 26 27 ; 24 3 6 9 12 18 22 23 25 26 27 ; 25 1 2 3 13 19 22 23 24 26 27 ; 26 4 5 6 14 20 22 23 24 25 27 ; 27 7 8 9 15 21 22 23 24 25 26 ; Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee40.uab.es. (158.109.66.40) Time: Tue Mar 16 12:46:54 2004 Input: M:=MatrixRing(GF(4),2); Mt := {m:m in M | Trace(m) eq 0}; Mf := {m:m in M | m[1] eq m[2]}; Mtf := { Mt meet Mf }; print Mt; print Mf; print Mtf; Output: Magma V2.10-6 Tue Mar 16 2004 12:46:51 on modular [Seed = 4009333567] ------------------------------------- { [ 0 0] [ 0 0], [ 0 0] [$.1^2 0], [ 0 0] [ $.1 0], [ 0 0] [ 1 0], [$.1^2 0] [ 0 $.1^2], [$.1^2 0] [$.1^2 $.1^2], [$.1^2 0] [ $.1 $.1^2], [$.1^2 0] [ 1 $.1^2], [ 1 0] [ 0 1], [ 1 0] [$.1^2 1], [ 1 0] [ $.1 1], [ 1 0] [ 1 1], [ $.1 0] [ 0 $.1], [ $.1 0] [$.1^2 $.1], [ $.1 0] [ $.1 $.1], [ $.1 0] [ 1 $.1], [ 0 $.1^2] [ 0 0], [ 0 $.1^2] [$.1^2 0], [ 0 $.1^2] [ $.1 0], [ 0 $.1^2] [ 1 0], [$.1^2 $.1^2] [ 0 $.1^2], [$.1^2 $.1^2] [$.1^2 $.1^2], [$.1^2 $.1^2] [ $.1 $.1^2], [$.1^2 $.1^2] [ 1 $.1^2], [ 1 $.1^2] [ 0 1], [ 1 $.1^2] [$.1^2 1], [ 1 $.1^2] [ $.1 1], [ 1 $.1^2] [ 1 1], [ $.1 $.1^2] [ 0 $.1], [ $.1 $.1^2] [$.1^2 $.1], [ $.1 $.1^2] [ $.1 $.1], [ $.1 $.1^2] [ 1 $.1], [ 0 $.1] [ 0 0], [ 0 $.1] [$.1^2 0], [ 0 $.1] [ $.1 0], [ 0 $.1] [ 1 0], [$.1^2 $.1] [ 0 $.1^2], [$.1^2 $.1] [$.1^2 $.1^2], [$.1^2 $.1] [ $.1 $.1^2], [$.1^2 $.1] [ 1 $.1^2], [ 1 $.1] [ 0 1], [ 1 $.1] [$.1^2 1], [ 1 $.1] [ $.1 1], [ 1 $.1] [ 1 1], [ $.1 $.1] [ 0 $.1], [ $.1 $.1] [$.1^2 $.1], [ $.1 $.1] [ $.1 $.1], [ $.1 $.1] [ 1 $.1], [ 0 1] [ 0 0], [ 0 1] [$.1^2 0], [ 0 1] [ $.1 0], [ 0 1] [ 1 0], [$.1^2 1] [ 0 $.1^2], [$.1^2 1] [$.1^2 $.1^2], [$.1^2 1] [ $.1 $.1^2], [$.1^2 1] [ 1 $.1^2], [ 1 1] [ 0 1], [ 1 1] [$.1^2 1], [ 1 1] [ $.1 1], [ 1 1] [ 1 1], [ $.1 1] [ 0 $.1], [ $.1 1] [$.1^2 $.1], [ $.1 1] [ $.1 $.1], [ $.1 1] [ 1 $.1] } { [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ $.1 0] [ $.1 0], [ 0 $.1^2] [ 0 $.1^2], [ $.1 $.1^2] [ $.1 $.1^2], [ 0 $.1] [ 0 $.1], [ $.1 $.1] [ $.1 $.1], [ 0 1] [ 0 1], [ $.1 1] [ $.1 1], [$.1^2 0] [$.1^2 0], [ 1 0] [ 1 0], [$.1^2 $.1^2] [$.1^2 $.1^2], [ 1 $.1^2] [ 1 $.1^2], [$.1^2 $.1] [$.1^2 $.1], [ 1 $.1] [ 1 $.1], [$.1^2 1] [$.1^2 1] } { { [ 0 0] [ 0 0], [$.1^2 $.1^2] [$.1^2 $.1^2], [ $.1 $.1] [ $.1 $.1], [ 1 1] [ 1 1] } } Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host EPC-dhcp-89.Lib.UH.EDU. (129.7.156.89) Time: Tue Mar 16 12:47:28 2004 Input: kd1:=MultipartiteGraph([3,3,3]); kd2:=LineGraph(kd1); kd2; A:=AdjacencyMatrix(kd2); m:=Rank(A); n:=Rank(Transpose(A)); m; n; Output: Magma V2.10-6 Tue Mar 16 2004 12:47:25 on modular [Seed = 3891304976] ------------------------------------- Graph Vertex Neighbours 1 2 3 4 7 10 13 16 19 22 25 ; 2 1 3 5 8 11 13 17 19 23 25 ; 3 1 2 6 9 12 13 18 19 24 25 ; 4 1 5 6 7 10 14 16 20 22 26 ; 5 2 4 6 8 11 14 17 20 23 26 ; 6 3 4 5 9 12 14 18 20 24 26 ; 7 1 4 8 9 10 15 16 21 22 27 ; 8 2 5 7 9 11 15 17 21 23 27 ; 9 3 6 7 8 12 15 18 21 24 27 ; 10 1 4 7 11 12 13 14 15 16 22 ; 11 2 5 8 10 12 13 14 15 17 23 ; 12 3 6 9 10 11 13 14 15 18 24 ; 13 1 2 3 10 11 12 14 15 19 25 ; 14 4 5 6 10 11 12 13 15 20 26 ; 15 7 8 9 10 11 12 13 14 21 27 ; 16 1 4 7 10 17 18 19 20 21 22 ; 17 2 5 8 11 16 18 19 20 21 23 ; 18 3 6 9 12 16 17 19 20 21 24 ; 19 1 2 3 13 16 17 18 20 21 25 ; 20 4 5 6 14 16 17 18 19 21 26 ; 21 7 8 9 15 16 17 18 19 20 27 ; 22 1 4 7 10 16 23 24 25 26 27 ; 23 2 5 8 11 17 22 24 25 26 27 ; 24 3 6 9 12 18 22 23 25 26 27 ; 25 1 2 3 13 19 22 23 24 26 27 ; 26 4 5 6 14 20 22 23 24 25 27 ; 27 7 8 9 15 21 22 23 24 25 26 ; 27 27 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee40.uab.es. (158.109.66.40) Time: Tue Mar 16 12:47:46 2004 Input: M:=MatrixRing(GF(4),2); Mt := {m:m in M | Trace(m) eq 0}; Mf := {m:m in M | m[1] eq m[2]}; Mtf := { Mt meet Mf }; #(MTF); print Mt; print Mf; print Mtf; Output: Magma V2.10-6 Tue Mar 16 2004 12:47:43 on modular [Seed = 2626412921] ------------------------------------- >> #(MTF); ^ User error: Identifier 'MTF' has not been declared or assigned { [ 0 0] [ 0 0], [ 0 0] [$.1^2 0], [ 0 0] [ $.1 0], [ 0 0] [ 1 0], [$.1^2 0] [ 0 $.1^2], [$.1^2 0] [$.1^2 $.1^2], [$.1^2 0] [ $.1 $.1^2], [$.1^2 0] [ 1 $.1^2], [ 1 0] [ 0 1], [ 1 0] [$.1^2 1], [ 1 0] [ $.1 1], [ 1 0] [ 1 1], [ $.1 0] [ 0 $.1], [ $.1 0] [$.1^2 $.1], [ $.1 0] [ $.1 $.1], [ $.1 0] [ 1 $.1], [ 0 $.1^2] [ 0 0], [ 0 $.1^2] [$.1^2 0], [ 0 $.1^2] [ $.1 0], [ 0 $.1^2] [ 1 0], [$.1^2 $.1^2] [ 0 $.1^2], [$.1^2 $.1^2] [$.1^2 $.1^2], [$.1^2 $.1^2] [ $.1 $.1^2], [$.1^2 $.1^2] [ 1 $.1^2], [ 1 $.1^2] [ 0 1], [ 1 $.1^2] [$.1^2 1], [ 1 $.1^2] [ $.1 1], [ 1 $.1^2] [ 1 1], [ $.1 $.1^2] [ 0 $.1], [ $.1 $.1^2] [$.1^2 $.1], [ $.1 $.1^2] [ $.1 $.1], [ $.1 $.1^2] [ 1 $.1], [ 0 $.1] [ 0 0], [ 0 $.1] [$.1^2 0], [ 0 $.1] [ $.1 0], [ 0 $.1] [ 1 0], [$.1^2 $.1] [ 0 $.1^2], [$.1^2 $.1] [$.1^2 $.1^2], [$.1^2 $.1] [ $.1 $.1^2], [$.1^2 $.1] [ 1 $.1^2], [ 1 $.1] [ 0 1], [ 1 $.1] [$.1^2 1], [ 1 $.1] [ $.1 1], [ 1 $.1] [ 1 1], [ $.1 $.1] [ 0 $.1], [ $.1 $.1] [$.1^2 $.1], [ $.1 $.1] [ $.1 $.1], [ $.1 $.1] [ 1 $.1], [ 0 1] [ 0 0], [ 0 1] [$.1^2 0], [ 0 1] [ $.1 0], [ 0 1] [ 1 0], [$.1^2 1] [ 0 $.1^2], [$.1^2 1] [$.1^2 $.1^2], [$.1^2 1] [ $.1 $.1^2], [$.1^2 1] [ 1 $.1^2], [ 1 1] [ 0 1], [ 1 1] [$.1^2 1], [ 1 1] [ $.1 1], [ 1 1] [ 1 1], [ $.1 1] [ 0 $.1], [ $.1 1] [$.1^2 $.1], [ $.1 1] [ $.1 $.1], [ $.1 1] [ 1 $.1] } { [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ $.1 0] [ $.1 0], [ 0 $.1^2] [ 0 $.1^2], [ $.1 $.1^2] [ $.1 $.1^2], [ 0 $.1] [ 0 $.1], [ $.1 $.1] [ $.1 $.1], [ 0 1] [ 0 1], [ $.1 1] [ $.1 1], [$.1^2 0] [$.1^2 0], [ 1 0] [ 1 0], [$.1^2 $.1^2] [$.1^2 $.1^2], [ 1 $.1^2] [ 1 $.1^2], [$.1^2 $.1] [$.1^2 $.1], [ 1 $.1] [ 1 $.1], [$.1^2 1] [$.1^2 1] } { { [ 0 0] [ 0 0], [$.1^2 $.1^2] [$.1^2 $.1^2], [ $.1 $.1] [ $.1 $.1], [ 1 1] [ 1 1] } } Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee40.uab.es. (158.109.66.40) Time: Tue Mar 16 12:47:56 2004 Input: M:=MatrixRing(GF(4),2); Mt := {m:m in M | Trace(m) eq 0}; Mf := {m:m in M | m[1] eq m[2]}; Mtf := { Mt meet Mf }; #(Mtf); print Mt; print Mf; print Mtf; Output: Magma V2.10-6 Tue Mar 16 2004 12:47:54 on modular [Seed = 2508384261] ------------------------------------- 1 { [ 0 0] [ 0 0], [ 0 0] [$.1^2 0], [ 0 0] [ $.1 0], [ 0 0] [ 1 0], [$.1^2 0] [ 0 $.1^2], [$.1^2 0] [$.1^2 $.1^2], [$.1^2 0] [ $.1 $.1^2], [$.1^2 0] [ 1 $.1^2], [ 1 0] [ 0 1], [ 1 0] [$.1^2 1], [ 1 0] [ $.1 1], [ 1 0] [ 1 1], [ $.1 0] [ 0 $.1], [ $.1 0] [$.1^2 $.1], [ $.1 0] [ $.1 $.1], [ $.1 0] [ 1 $.1], [ 0 $.1^2] [ 0 0], [ 0 $.1^2] [$.1^2 0], [ 0 $.1^2] [ $.1 0], [ 0 $.1^2] [ 1 0], [$.1^2 $.1^2] [ 0 $.1^2], [$.1^2 $.1^2] [$.1^2 $.1^2], [$.1^2 $.1^2] [ $.1 $.1^2], [$.1^2 $.1^2] [ 1 $.1^2], [ 1 $.1^2] [ 0 1], [ 1 $.1^2] [$.1^2 1], [ 1 $.1^2] [ $.1 1], [ 1 $.1^2] [ 1 1], [ $.1 $.1^2] [ 0 $.1], [ $.1 $.1^2] [$.1^2 $.1], [ $.1 $.1^2] [ $.1 $.1], [ $.1 $.1^2] [ 1 $.1], [ 0 $.1] [ 0 0], [ 0 $.1] [$.1^2 0], [ 0 $.1] [ $.1 0], [ 0 $.1] [ 1 0], [$.1^2 $.1] [ 0 $.1^2], [$.1^2 $.1] [$.1^2 $.1^2], [$.1^2 $.1] [ $.1 $.1^2], [$.1^2 $.1] [ 1 $.1^2], [ 1 $.1] [ 0 1], [ 1 $.1] [$.1^2 1], [ 1 $.1] [ $.1 1], [ 1 $.1] [ 1 1], [ $.1 $.1] [ 0 $.1], [ $.1 $.1] [$.1^2 $.1], [ $.1 $.1] [ $.1 $.1], [ $.1 $.1] [ 1 $.1], [ 0 1] [ 0 0], [ 0 1] [$.1^2 0], [ 0 1] [ $.1 0], [ 0 1] [ 1 0], [$.1^2 1] [ 0 $.1^2], [$.1^2 1] [$.1^2 $.1^2], [$.1^2 1] [ $.1 $.1^2], [$.1^2 1] [ 1 $.1^2], [ 1 1] [ 0 1], [ 1 1] [$.1^2 1], [ 1 1] [ $.1 1], [ 1 1] [ 1 1], [ $.1 1] [ 0 $.1], [ $.1 1] [$.1^2 $.1], [ $.1 1] [ $.1 $.1], [ $.1 1] [ 1 $.1] } { [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ $.1 0] [ $.1 0], [ 0 $.1^2] [ 0 $.1^2], [ $.1 $.1^2] [ $.1 $.1^2], [ 0 $.1] [ 0 $.1], [ $.1 $.1] [ $.1 $.1], [ 0 1] [ 0 1], [ $.1 1] [ $.1 1], [$.1^2 0] [$.1^2 0], [ 1 0] [ 1 0], [$.1^2 $.1^2] [$.1^2 $.1^2], [ 1 $.1^2] [ 1 $.1^2], [$.1^2 $.1] [$.1^2 $.1], [ 1 $.1] [ 1 $.1], [$.1^2 1] [$.1^2 1] } { { [ 0 0] [ 0 0], [$.1^2 $.1^2] [$.1^2 $.1^2], [ $.1 $.1] [ $.1 $.1], [ 1 1] [ 1 1] } } Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee40.uab.es. (158.109.66.40) Time: Tue Mar 16 12:49:01 2004 Input: M:=MatrixRing(GF(4),2); Mt := {m:m in M | Trace(m) eq 0}; Mf := {m:m in M | m[1] eq m[2]}; Mtf := { Mt meet Mf }; Ma := {Random(M):m in [1..100000] }; Output: Magma V2.10-6 Tue Mar 16 2004 12:48:57 on modular [Seed = 2190867665] ------------------------------------- Total time: 3.079 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 12:49:13 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; ordre_elements := [: i in [1..24]]; ordre_elements; elem_primitius := [tupla[1]: tupla in ordre_elements | tupla[2] eq 25-1 ]; #elem_primitius; print "eoh"; MinimalPolynomial(alpha, G25); Output: Magma V2.10-6 Tue Mar 16 2004 12:49:09 on modular [Seed = 3148662260] ------------------------------------- [ , , , , , <2, 4>, , , , , , <4, 2>, , , , , , <3, 4>, , , , , , <1, 1> ] 8 eoh >> MinimalPolynomial(alpha, G25); ^ Runtime error in 'MinimalPolynomial': Argument 2 is not a subfield of the parent of argument 1 Total time: 3.169 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host aula-a-siee40.uab.es. (158.109.66.40) Time: Tue Mar 16 12:49:15 2004 Input: M:=MatrixRing(GF(4),2); Mt := {m:m in M | Trace(m) eq 0}; Mf := {m:m in M | m[1] eq m[2]}; Mtf := { Mt meet Mf }; Ma := {Random(M):m in [1..100000] }; print Ma; Output: Magma V2.10-6 Tue Mar 16 2004 12:49:12 on modular [Seed = 3198796028] ------------------------------------- { [ 0 0] [ 0 0], [$.1^2 0] [ 0 $.1], [ 0 0] [$.1^2 0], [$.1^2 0] [$.1^2 $.1], [$.1^2 0] [ $.1 $.1], [ 0 0] [ $.1 0], [ 0 0] [ 1 0], [$.1^2 0] [ 1 $.1], [ 0 0] [ 0 $.1^2], [$.1^2 0] [ 0 1], [$.1^2 0] [$.1^2 1], [ 0 0] [$.1^2 $.1^2], [ 0 0] [ $.1 $.1^2], [$.1^2 0] [ $.1 1], [$.1^2 0] [ 1 1], [ 0 0] [ 1 $.1^2], [ 0 0] [ 0 $.1], [$.1^2 0] [ 0 0], [ 0 0] [$.1^2 $.1], [$.1^2 0] [$.1^2 0], [$.1^2 0] [ $.1 0], [ 0 0] [ $.1 $.1], [ 0 0] [ 1 $.1], [$.1^2 0] [ 1 0], [ 0 0] [ 0 1], [$.1^2 0] [ 0 $.1^2], [$.1^2 0] [$.1^2 $.1^2], [ 0 0] [$.1^2 1], [$.1^2 0] [ $.1 $.1^2], [ 0 0] [ $.1 1], [ 0 0] [ 1 1], [$.1^2 0] [ 1 $.1^2], [ 1 0] [ 0 $.1], [ $.1 0] [ 0 0], [ $.1 0] [$.1^2 0], [ 1 0] [$.1^2 $.1], [ $.1 0] [ $.1 0], [ 1 0] [ $.1 $.1], [ 1 0] [ 1 $.1], [ $.1 0] [ 1 0], [ 1 0] [ 0 1], [ $.1 0] [ 0 $.1^2], [ 1 0] [$.1^2 1], [ $.1 0] [$.1^2 $.1^2], [ $.1 0] [ $.1 $.1^2], [ 1 0] [ $.1 1], [ $.1 0] [ 1 $.1^2], [ 1 0] [ 1 1], [ 1 0] [ 0 0], [ $.1 0] [ 0 $.1], [ 1 0] [$.1^2 0], [ $.1 0] [$.1^2 $.1], [ $.1 0] [ $.1 $.1], [ 1 0] [ $.1 0], [ $.1 0] [ 1 $.1], [ 1 0] [ 1 0], [ 1 0] [ 0 $.1^2], [ $.1 0] [ 0 1], [ $.1 0] [$.1^2 1], [ 1 0] [$.1^2 $.1^2], [ 1 0] [ $.1 $.1^2], [ $.1 0] [ $.1 1], [ $.1 0] [ 1 1], [ 1 0] [ 1 $.1^2], [$.1^2 $.1^2] [ 0 $.1], [ 0 $.1^2] [ 0 0], [ 0 $.1^2] [$.1^2 0], [$.1^2 $.1^2] [$.1^2 $.1], [$.1^2 $.1^2] [ $.1 $.1], [ 0 $.1^2] [ $.1 0], [ 0 $.1^2] [ 1 0], [$.1^2 $.1^2] [ 1 $.1], [$.1^2 $.1^2] [ 0 1], [ 0 $.1^2] [ 0 $.1^2], [$.1^2 $.1^2] [$.1^2 1], [ 0 $.1^2] [$.1^2 $.1^2], [$.1^2 $.1^2] [ $.1 1], [ 0 $.1^2] [ $.1 $.1^2], [ 0 $.1^2] [ 1 $.1^2], [$.1^2 $.1^2] [ 1 1], [ 0 $.1^2] [ 0 $.1], [$.1^2 $.1^2] [ 0 0], [ 0 $.1^2] [$.1^2 $.1], [$.1^2 $.1^2] [$.1^2 0], [ 0 $.1^2] [ $.1 $.1], [$.1^2 $.1^2] [ $.1 0], [$.1^2 $.1^2] [ 1 0], [ 0 $.1^2] [ 1 $.1], [$.1^2 $.1^2] [ 0 $.1^2], [ 0 $.1^2] [ 0 1], [ 0 $.1^2] [$.1^2 1], [$.1^2 $.1^2] [$.1^2 $.1^2], [$.1^2 $.1^2] [ $.1 $.1^2], [ 0 $.1^2] [ $.1 1], [$.1^2 $.1^2] [ 1 $.1^2], [ 0 $.1^2] [ 1 1], [ 1 $.1^2] [ 0 $.1], [ $.1 $.1^2] [ 0 0], [ 1 $.1^2] [$.1^2 $.1], [ $.1 $.1^2] [$.1^2 0], [ $.1 $.1^2] [ $.1 0], [ 1 $.1^2] [ $.1 $.1], [ $.1 $.1^2] [ 1 0], [ 1 $.1^2] [ 1 $.1], [ 1 $.1^2] [ 0 1], [ $.1 $.1^2] [ 0 $.1^2], [ $.1 $.1^2] [$.1^2 $.1^2], [ 1 $.1^2] [$.1^2 1], [ 1 $.1^2] [ $.1 1], [ $.1 $.1^2] [ $.1 $.1^2], [ $.1 $.1^2] [ 1 $.1^2], [ 1 $.1^2] [ 1 1], [ $.1 $.1^2] [ 0 $.1], [ 1 $.1^2] [ 0 0], [ 1 $.1^2] [$.1^2 0], [ $.1 $.1^2] [$.1^2 $.1], [ 1 $.1^2] [ $.1 0], [ $.1 $.1^2] [ $.1 $.1], [ $.1 $.1^2] [ 1 $.1], [ 1 $.1^2] [ 1 0], [ $.1 $.1^2] [ 0 1], [ 1 $.1^2] [ 0 $.1^2], [ $.1 $.1^2] [$.1^2 1], [ 1 $.1^2] [$.1^2 $.1^2], [ $.1 $.1^2] [ $.1 1], [ 1 $.1^2] [ $.1 $.1^2], [ 1 $.1^2] [ 1 $.1^2], [ $.1 $.1^2] [ 1 1], [$.1^2 $.1] [ 0 $.1], [ 0 $.1] [ 0 0], [ 0 $.1] [$.1^2 0], [$.1^2 $.1] [$.1^2 $.1], [$.1^2 $.1] [ $.1 $.1], [ 0 $.1] [ $.1 0], [ 0 $.1] [ 1 0], [$.1^2 $.1] [ 1 $.1], [ 0 $.1] [ 0 $.1^2], [$.1^2 $.1] [ 0 1], [$.1^2 $.1] [$.1^2 1], [ 0 $.1] [$.1^2 $.1^2], [$.1^2 $.1] [ $.1 1], [ 0 $.1] [ $.1 $.1^2], [ 0 $.1] [ 1 $.1^2], [$.1^2 $.1] [ 1 1], [$.1^2 $.1] [ 0 0], [ 0 $.1] [ 0 $.1], [$.1^2 $.1] [$.1^2 0], [ 0 $.1] [$.1^2 $.1], [$.1^2 $.1] [ $.1 0], [ 0 $.1] [ $.1 $.1], [ 0 $.1] [ 1 $.1], [$.1^2 $.1] [ 1 0], [$.1^2 $.1] [ 0 $.1^2], [ 0 $.1] [ 0 1], [$.1^2 $.1] [$.1^2 $.1^2], [ 0 $.1] [$.1^2 1], [$.1^2 $.1] [ $.1 $.1^2], [ 0 $.1] [ $.1 1], [$.1^2 $.1] [ 1 $.1^2], [ 0 $.1] [ 1 1], [ 1 $.1] [ 0 $.1], [ $.1 $.1] [ 0 0], [ $.1 $.1] [$.1^2 0], [ 1 $.1] [$.1^2 $.1], [ 1 $.1] [ $.1 $.1], [ $.1 $.1] [ $.1 0], [ 1 $.1] [ 1 $.1], [ $.1 $.1] [ 1 0], [ 1 $.1] [ 0 1], [ $.1 $.1] [ 0 $.1^2], [ $.1 $.1] [$.1^2 $.1^2], [ 1 $.1] [$.1^2 1], [ 1 $.1] [ $.1 1], [ $.1 $.1] [ $.1 $.1^2], [ $.1 $.1] [ 1 $.1^2], [ 1 $.1] [ 1 1], [ $.1 $.1] [ 0 $.1], [ 1 $.1] [ 0 0], [ 1 $.1] [$.1^2 0], [ $.1 $.1] [$.1^2 $.1], [ $.1 $.1] [ $.1 $.1], [ 1 $.1] [ $.1 0], [ $.1 $.1] [ 1 $.1], [ 1 $.1] [ 1 0], [ $.1 $.1] [ 0 1], [ 1 $.1] [ 0 $.1^2], [ $.1 $.1] [$.1^2 1], [ 1 $.1] [$.1^2 $.1^2], [ $.1 $.1] [ $.1 1], [ 1 $.1] [ $.1 $.1^2], [ 1 $.1] [ 1 $.1^2], [ $.1 $.1] [ 1 1], [ 0 1] [ 0 0], [$.1^2 1] [ 0 $.1], [ 0 1] [$.1^2 0], [$.1^2 1] [$.1^2 $.1], [$.1^2 1] [ $.1 $.1], [ 0 1] [ $.1 0], [ 0 1] [ 1 0], [$.1^2 1] [ 1 $.1], [$.1^2 1] [ 0 1], [ 0 1] [ 0 $.1^2], [$.1^2 1] [$.1^2 1], [ 0 1] [$.1^2 $.1^2], [$.1^2 1] [ $.1 1], [ 0 1] [ $.1 $.1^2], [$.1^2 1] [ 1 1], [ 0 1] [ 1 $.1^2], [$.1^2 1] [ 0 0], [ 0 1] [ 0 $.1], [ 0 1] [$.1^2 $.1], [$.1^2 1] [$.1^2 0], [ 0 1] [ $.1 $.1], [$.1^2 1] [ $.1 0], [$.1^2 1] [ 1 0], [ 0 1] [ 1 $.1], [$.1^2 1] [ 0 $.1^2], [ 0 1] [ 0 1], [$.1^2 1] [$.1^2 $.1^2], [ 0 1] [$.1^2 1], [$.1^2 1] [ $.1 $.1^2], [ 0 1] [ $.1 1], [$.1^2 1] [ 1 $.1^2], [ 0 1] [ 1 1], [ 1 1] [ 0 $.1], [ $.1 1] [ 0 0], [ 1 1] [$.1^2 $.1], [ $.1 1] [$.1^2 0], [ 1 1] [ $.1 $.1], [ $.1 1] [ $.1 0], [ 1 1] [ 1 $.1], [ $.1 1] [ 1 0], [ 1 1] [ 0 1], [ $.1 1] [ 0 $.1^2], [ $.1 1] [$.1^2 $.1^2], [ 1 1] [$.1^2 1], [ $.1 1] [ $.1 $.1^2], [ 1 1] [ $.1 1], [ $.1 1] [ 1 $.1^2], [ 1 1] [ 1 1], [ 1 1] [ 0 0], [ $.1 1] [ 0 $.1], [ 1 1] [$.1^2 0], [ $.1 1] [$.1^2 $.1], [ $.1 1] [ $.1 $.1], [ 1 1] [ $.1 0], [ 1 1] [ 1 0], [ $.1 1] [ 1 $.1], [ $.1 1] [ 0 1], [ 1 1] [ 0 $.1^2], [ $.1 1] [$.1^2 1], [ 1 1] [$.1^2 $.1^2], [ $.1 1] [ $.1 1], [ 1 1] [ $.1 $.1^2], [ 1 1] [ 1 $.1^2], [ $.1 1] [ 1 1] } Total time: 3.669 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host EPC-dhcp-89.Lib.UH.EDU. (129.7.156.89) Time: Tue Mar 16 12:49:31 2004 Input: kd1:=MultipartiteGraph([3,3,3]); kd2:=LineGraph(kd1); kd2; A:=AdjacencyMatrix(kd2); M:=PolynomialRing(GF(2)); M!A; m:=Rank(A); n:=Rank(Transpose(A)); Output: Magma V2.10-6 Tue Mar 16 2004 12:49:28 on modular [Seed = 2847856603] ------------------------------------- Graph Vertex Neighbours 1 2 3 4 7 10 13 16 19 22 25 ; 2 1 3 5 8 11 13 17 19 23 25 ; 3 1 2 6 9 12 13 18 19 24 25 ; 4 1 5 6 7 10 14 16 20 22 26 ; 5 2 4 6 8 11 14 17 20 23 26 ; 6 3 4 5 9 12 14 18 20 24 26 ; 7 1 4 8 9 10 15 16 21 22 27 ; 8 2 5 7 9 11 15 17 21 23 27 ; 9 3 6 7 8 12 15 18 21 24 27 ; 10 1 4 7 11 12 13 14 15 16 22 ; 11 2 5 8 10 12 13 14 15 17 23 ; 12 3 6 9 10 11 13 14 15 18 24 ; 13 1 2 3 10 11 12 14 15 19 25 ; 14 4 5 6 10 11 12 13 15 20 26 ; 15 7 8 9 10 11 12 13 14 21 27 ; 16 1 4 7 10 17 18 19 20 21 22 ; 17 2 5 8 11 16 18 19 20 21 23 ; 18 3 6 9 12 16 17 19 20 21 24 ; 19 1 2 3 13 16 17 18 20 21 25 ; 20 4 5 6 14 16 17 18 19 21 26 ; 21 7 8 9 15 16 17 18 19 20 27 ; 22 1 4 7 10 16 23 24 25 26 27 ; 23 2 5 8 11 17 22 24 25 26 27 ; 24 3 6 9 12 18 22 23 25 26 27 ; 25 1 2 3 13 19 22 23 24 26 27 ; 26 4 5 6 14 20 22 23 24 25 27 ; 27 7 8 9 15 21 22 23 24 25 26 ; >> M!A; ^ Runtime error in '!': Illegal coercion Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 12:49:48 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; ordre_elements := [: i in [1..24]]; ordre_elements; elem_primitius := [tupla[1]: tupla in ordre_elements | tupla[2] eq 25-1 ]; #elem_primitius; print "eoh"; MinimalPolynomial(gamma, G25); Output: Magma V2.10-6 Tue Mar 16 2004 12:49:45 on modular [Seed = 2796673221] ------------------------------------- [ , , , , , <2, 4>, , , , , , <4, 2>, , , , , , <3, 4>, , , , , , <1, 1> ] 8 eoh $.1 + gamma^13 Total time: 2.969 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host aula-a-siee40.uab.es. (158.109.66.40) Time: Tue Mar 16 12:51:27 2004 Input: M:=MatrixRing(GF(4),2); Mt := {m:m in M | Trace(m) eq 0}; Mf := {m:m in M | m[1] eq m[2]}; Mtf := { Mt meet Mf }; Ma := {Random(M):m in [1..100000] }; print Ma; Random(M); Output: Magma V2.10-6 Tue Mar 16 2004 12:51:23 on modular [Seed = 1447110806] ------------------------------------- { [$.1^2 0] [ 0 $.1], [ 0 0] [ 0 0], [$.1^2 0] [$.1^2 $.1], [ 0 0] [$.1^2 0], [ 0 0] [ $.1 0], [$.1^2 0] [ $.1 $.1], [ 0 0] [ 1 0], [$.1^2 0] [ 1 $.1], [ 0 0] [ 0 $.1^2], [$.1^2 0] [ 0 1], [$.1^2 0] [$.1^2 1], [ 0 0] [$.1^2 $.1^2], [ 0 0] [ $.1 $.1^2], [$.1^2 0] [ $.1 1], [$.1^2 0] [ 1 1], [ 0 0] [ 1 $.1^2], [$.1^2 0] [ 0 0], [ 0 0] [ 0 $.1], [ 0 0] [$.1^2 $.1], [$.1^2 0] [$.1^2 0], [ 0 0] [ $.1 $.1], [$.1^2 0] [ $.1 0], [ 0 0] [ 1 $.1], [$.1^2 0] [ 1 0], [$.1^2 0] [ 0 $.1^2], [ 0 0] [ 0 1], [$.1^2 0] [$.1^2 $.1^2], [ 0 0] [$.1^2 1], [$.1^2 0] [ $.1 $.1^2], [ 0 0] [ $.1 1], [$.1^2 0] [ 1 $.1^2], [ 0 0] [ 1 1], [ 1 0] [ 0 $.1], [ $.1 0] [ 0 0], [ 1 0] [$.1^2 $.1], [ $.1 0] [$.1^2 0], [ 1 0] [ $.1 $.1], [ $.1 0] [ $.1 0], [ 1 0] [ 1 $.1], [ $.1 0] [ 1 0], [ 1 0] [ 0 1], [ $.1 0] [ 0 $.1^2], [ $.1 0] [$.1^2 $.1^2], [ 1 0] [$.1^2 1], [ $.1 0] [ $.1 $.1^2], [ 1 0] [ $.1 1], [ $.1 0] [ 1 $.1^2], [ 1 0] [ 1 1], [ $.1 0] [ 0 $.1], [ 1 0] [ 0 0], [ 1 0] [$.1^2 0], [ $.1 0] [$.1^2 $.1], [ 1 0] [ $.1 0], [ $.1 0] [ $.1 $.1], [ $.1 0] [ 1 $.1], [ 1 0] [ 1 0], [ $.1 0] [ 0 1], [ 1 0] [ 0 $.1^2], [ 1 0] [$.1^2 $.1^2], [ $.1 0] [$.1^2 1], [ 1 0] [ $.1 $.1^2], [ $.1 0] [ $.1 1], [ 1 0] [ 1 $.1^2], [ $.1 0] [ 1 1], [$.1^2 $.1^2] [ 0 $.1], [ 0 $.1^2] [ 0 0], [$.1^2 $.1^2] [$.1^2 $.1], [ 0 $.1^2] [$.1^2 0], [ 0 $.1^2] [ $.1 0], [$.1^2 $.1^2] [ $.1 $.1], [ 0 $.1^2] [ 1 0], [$.1^2 $.1^2] [ 1 $.1], [$.1^2 $.1^2] [ 0 1], [ 0 $.1^2] [ 0 $.1^2], [ 0 $.1^2] [$.1^2 $.1^2], [$.1^2 $.1^2] [$.1^2 1], [$.1^2 $.1^2] [ $.1 1], [ 0 $.1^2] [ $.1 $.1^2], [ 0 $.1^2] [ 1 $.1^2], [$.1^2 $.1^2] [ 1 1], [$.1^2 $.1^2] [ 0 0], [ 0 $.1^2] [ 0 $.1], [$.1^2 $.1^2] [$.1^2 0], [ 0 $.1^2] [$.1^2 $.1], [$.1^2 $.1^2] [ $.1 0], [ 0 $.1^2] [ $.1 $.1], [ 0 $.1^2] [ 1 $.1], [$.1^2 $.1^2] [ 1 0], [$.1^2 $.1^2] [ 0 $.1^2], [ 0 $.1^2] [ 0 1], [$.1^2 $.1^2] [$.1^2 $.1^2], [ 0 $.1^2] [$.1^2 1], [ 0 $.1^2] [ $.1 1], [$.1^2 $.1^2] [ $.1 $.1^2], [ 0 $.1^2] [ 1 1], [$.1^2 $.1^2] [ 1 $.1^2], [ 1 $.1^2] [ 0 $.1], [ $.1 $.1^2] [ 0 0], [ $.1 $.1^2] [$.1^2 0], [ 1 $.1^2] [$.1^2 $.1], [ 1 $.1^2] [ $.1 $.1], [ $.1 $.1^2] [ $.1 0], [ $.1 $.1^2] [ 1 0], [ 1 $.1^2] [ 1 $.1], [ $.1 $.1^2] [ 0 $.1^2], [ 1 $.1^2] [ 0 1], [ 1 $.1^2] [$.1^2 1], [ $.1 $.1^2] [$.1^2 $.1^2], [ $.1 $.1^2] [ $.1 $.1^2], [ 1 $.1^2] [ $.1 1], [ $.1 $.1^2] [ 1 $.1^2], [ 1 $.1^2] [ 1 1], [ 1 $.1^2] [ 0 0], [ $.1 $.1^2] [ 0 $.1], [ 1 $.1^2] [$.1^2 0], [ $.1 $.1^2] [$.1^2 $.1], [ 1 $.1^2] [ $.1 0], [ $.1 $.1^2] [ $.1 $.1], [ $.1 $.1^2] [ 1 $.1], [ 1 $.1^2] [ 1 0], [ $.1 $.1^2] [ 0 1], [ 1 $.1^2] [ 0 $.1^2], [ $.1 $.1^2] [$.1^2 1], [ 1 $.1^2] [$.1^2 $.1^2], [ $.1 $.1^2] [ $.1 1], [ 1 $.1^2] [ $.1 $.1^2], [ 1 $.1^2] [ 1 $.1^2], [ $.1 $.1^2] [ 1 1], [$.1^2 $.1] [ 0 $.1], [ 0 $.1] [ 0 0], [$.1^2 $.1] [$.1^2 $.1], [ 0 $.1] [$.1^2 0], [$.1^2 $.1] [ $.1 $.1], [ 0 $.1] [ $.1 0], [$.1^2 $.1] [ 1 $.1], [ 0 $.1] [ 1 0], [$.1^2 $.1] [ 0 1], [ 0 $.1] [ 0 $.1^2], [$.1^2 $.1] [$.1^2 1], [ 0 $.1] [$.1^2 $.1^2], [$.1^2 $.1] [ $.1 1], [ 0 $.1] [ $.1 $.1^2], [$.1^2 $.1] [ 1 1], [ 0 $.1] [ 1 $.1^2], [ 0 $.1] [ 0 $.1], [$.1^2 $.1] [ 0 0], [$.1^2 $.1] [$.1^2 0], [ 0 $.1] [$.1^2 $.1], [$.1^2 $.1] [ $.1 0], [ 0 $.1] [ $.1 $.1], [ 0 $.1] [ 1 $.1], [$.1^2 $.1] [ 1 0], [ 0 $.1] [ 0 1], [$.1^2 $.1] [ 0 $.1^2], [$.1^2 $.1] [$.1^2 $.1^2], [ 0 $.1] [$.1^2 1], [ 0 $.1] [ $.1 1], [$.1^2 $.1] [ $.1 $.1^2], [$.1^2 $.1] [ 1 $.1^2], [ 0 $.1] [ 1 1], [ $.1 $.1] [ 0 0], [ 1 $.1] [ 0 $.1], [ 1 $.1] [$.1^2 $.1], [ $.1 $.1] [$.1^2 0], [ $.1 $.1] [ $.1 0], [ 1 $.1] [ $.1 $.1], [ 1 $.1] [ 1 $.1], [ $.1 $.1] [ 1 0], [ 1 $.1] [ 0 1], [ $.1 $.1] [ 0 $.1^2], [ $.1 $.1] [$.1^2 $.1^2], [ 1 $.1] [$.1^2 1], [ 1 $.1] [ $.1 1], [ $.1 $.1] [ $.1 $.1^2], [ $.1 $.1] [ 1 $.1^2], [ 1 $.1] [ 1 1], [ $.1 $.1] [ 0 $.1], [ 1 $.1] [ 0 0], [ 1 $.1] [$.1^2 0], [ $.1 $.1] [$.1^2 $.1], [ 1 $.1] [ $.1 0], [ $.1 $.1] [ $.1 $.1], [ $.1 $.1] [ 1 $.1], [ 1 $.1] [ 1 0], [ 1 $.1] [ 0 $.1^2], [ $.1 $.1] [ 0 1], [ 1 $.1] [$.1^2 $.1^2], [ $.1 $.1] [$.1^2 1], [ 1 $.1] [ $.1 $.1^2], [ $.1 $.1] [ $.1 1], [ $.1 $.1] [ 1 1], [ 1 $.1] [ 1 $.1^2], [ 0 1] [ 0 0], [$.1^2 1] [ 0 $.1], [ 0 1] [$.1^2 0], [$.1^2 1] [$.1^2 $.1], [ 0 1] [ $.1 0], [$.1^2 1] [ $.1 $.1], [ 0 1] [ 1 0], [$.1^2 1] [ 1 $.1], [$.1^2 1] [ 0 1], [ 0 1] [ 0 $.1^2], [$.1^2 1] [$.1^2 1], [ 0 1] [$.1^2 $.1^2], [$.1^2 1] [ $.1 1], [ 0 1] [ $.1 $.1^2], [ 0 1] [ 1 $.1^2], [$.1^2 1] [ 1 1], [ 0 1] [ 0 $.1], [$.1^2 1] [ 0 0], [ 0 1] [$.1^2 $.1], [$.1^2 1] [$.1^2 0], [ 0 1] [ $.1 $.1], [$.1^2 1] [ $.1 0], [$.1^2 1] [ 1 0], [ 0 1] [ 1 $.1], [$.1^2 1] [ 0 $.1^2], [ 0 1] [ 0 1], [$.1^2 1] [$.1^2 $.1^2], [ 0 1] [$.1^2 1], [ 0 1] [ $.1 1], [$.1^2 1] [ $.1 $.1^2], [$.1^2 1] [ 1 $.1^2], [ 0 1] [ 1 1], [ 1 1] [ 0 $.1], [ $.1 1] [ 0 0], [ 1 1] [$.1^2 $.1], [ $.1 1] [$.1^2 0], [ $.1 1] [ $.1 0], [ 1 1] [ $.1 $.1], [ 1 1] [ 1 $.1], [ $.1 1] [ 1 0], [ $.1 1] [ 0 $.1^2], [ 1 1] [ 0 1], [ $.1 1] [$.1^2 $.1^2], [ 1 1] [$.1^2 1], [ 1 1] [ $.1 1], [ $.1 1] [ $.1 $.1^2], [ 1 1] [ 1 1], [ $.1 1] [ 1 $.1^2], [ 1 1] [ 0 0], [ $.1 1] [ 0 $.1], [ 1 1] [$.1^2 0], [ $.1 1] [$.1^2 $.1], [ $.1 1] [ $.1 $.1], [ 1 1] [ $.1 0], [ $.1 1] [ 1 $.1], [ 1 1] [ 1 0], [ 1 1] [ 0 $.1^2], [ $.1 1] [ 0 1], [ 1 1] [$.1^2 $.1^2], [ $.1 1] [$.1^2 1], [ $.1 1] [ $.1 1], [ 1 1] [ $.1 $.1^2], [ 1 1] [ 1 $.1^2], [ $.1 1] [ 1 1] } [ 1 $.1] [ $.1 $.1^2] Total time: 3.369 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee40.uab.es. (158.109.66.40) Time: Tue Mar 16 12:51:37 2004 Input: M:=MatrixRing(GF(4),2); Mt := {m:m in M | Trace(m) eq 0}; Mf := {m:m in M | m[1] eq m[2]}; Mtf := { Mt meet Mf }; Ma := {Random(M):m in [1..100000] }; print Ma; Random(M); Output: Magma V2.10-6 Tue Mar 16 2004 12:51:33 on modular [Seed = 1297757107] ------------------------------------- { [ 0 0] [ 0 0], [$.1^2 0] [ 0 $.1], [$.1^2 0] [$.1^2 $.1], [ 0 0] [$.1^2 0], [ 0 0] [ $.1 0], [$.1^2 0] [ $.1 $.1], [ 0 0] [ 1 0], [$.1^2 0] [ 1 $.1], [$.1^2 0] [ 0 1], [ 0 0] [ 0 $.1^2], [ 0 0] [$.1^2 $.1^2], [$.1^2 0] [$.1^2 1], [ 0 0] [ $.1 $.1^2], [$.1^2 0] [ $.1 1], [$.1^2 0] [ 1 1], [ 0 0] [ 1 $.1^2], [ 0 0] [ 0 $.1], [$.1^2 0] [ 0 0], [ 0 0] [$.1^2 $.1], [$.1^2 0] [$.1^2 0], [$.1^2 0] [ $.1 0], [ 0 0] [ $.1 $.1], [$.1^2 0] [ 1 0], [ 0 0] [ 1 $.1], [$.1^2 0] [ 0 $.1^2], [ 0 0] [ 0 1], [$.1^2 0] [$.1^2 $.1^2], [ 0 0] [$.1^2 1], [$.1^2 0] [ $.1 $.1^2], [ 0 0] [ $.1 1], [$.1^2 0] [ 1 $.1^2], [ 0 0] [ 1 1], [ $.1 0] [ 0 0], [ 1 0] [ 0 $.1], [ 1 0] [$.1^2 $.1], [ $.1 0] [$.1^2 0], [ $.1 0] [ $.1 0], [ 1 0] [ $.1 $.1], [ $.1 0] [ 1 0], [ 1 0] [ 1 $.1], [ 1 0] [ 0 1], [ $.1 0] [ 0 $.1^2], [ 1 0] [$.1^2 1], [ $.1 0] [$.1^2 $.1^2], [ $.1 0] [ $.1 $.1^2], [ 1 0] [ $.1 1], [ 1 0] [ 1 1], [ $.1 0] [ 1 $.1^2], [ $.1 0] [ 0 $.1], [ 1 0] [ 0 0], [ 1 0] [$.1^2 0], [ $.1 0] [$.1^2 $.1], [ $.1 0] [ $.1 $.1], [ 1 0] [ $.1 0], [ $.1 0] [ 1 $.1], [ 1 0] [ 1 0], [ $.1 0] [ 0 1], [ 1 0] [ 0 $.1^2], [ 1 0] [$.1^2 $.1^2], [ $.1 0] [$.1^2 1], [ $.1 0] [ $.1 1], [ 1 0] [ $.1 $.1^2], [ 1 0] [ 1 $.1^2], [ $.1 0] [ 1 1], [$.1^2 $.1^2] [ 0 $.1], [ 0 $.1^2] [ 0 0], [ 0 $.1^2] [$.1^2 0], [$.1^2 $.1^2] [$.1^2 $.1], [$.1^2 $.1^2] [ $.1 $.1], [ 0 $.1^2] [ $.1 0], [ 0 $.1^2] [ 1 0], [$.1^2 $.1^2] [ 1 $.1], [$.1^2 $.1^2] [ 0 1], [ 0 $.1^2] [ 0 $.1^2], [ 0 $.1^2] [$.1^2 $.1^2], [$.1^2 $.1^2] [$.1^2 1], [ 0 $.1^2] [ $.1 $.1^2], [$.1^2 $.1^2] [ $.1 1], [$.1^2 $.1^2] [ 1 1], [ 0 $.1^2] [ 1 $.1^2], [ 0 $.1^2] [ 0 $.1], [$.1^2 $.1^2] [ 0 0], [$.1^2 $.1^2] [$.1^2 0], [ 0 $.1^2] [$.1^2 $.1], [$.1^2 $.1^2] [ $.1 0], [ 0 $.1^2] [ $.1 $.1], [ 0 $.1^2] [ 1 $.1], [$.1^2 $.1^2] [ 1 0], [ 0 $.1^2] [ 0 1], [$.1^2 $.1^2] [ 0 $.1^2], [$.1^2 $.1^2] [$.1^2 $.1^2], [ 0 $.1^2] [$.1^2 1], [$.1^2 $.1^2] [ $.1 $.1^2], [ 0 $.1^2] [ $.1 1], [$.1^2 $.1^2] [ 1 $.1^2], [ 0 $.1^2] [ 1 1], [ $.1 $.1^2] [ 0 0], [ 1 $.1^2] [ 0 $.1], [ 1 $.1^2] [$.1^2 $.1], [ $.1 $.1^2] [$.1^2 0], [ $.1 $.1^2] [ $.1 0], [ 1 $.1^2] [ $.1 $.1], [ $.1 $.1^2] [ 1 0], [ 1 $.1^2] [ 1 $.1], [ $.1 $.1^2] [ 0 $.1^2], [ 1 $.1^2] [ 0 1], [ 1 $.1^2] [$.1^2 1], [ $.1 $.1^2] [$.1^2 $.1^2], [ 1 $.1^2] [ $.1 1], [ $.1 $.1^2] [ $.1 $.1^2], [ 1 $.1^2] [ 1 1], [ $.1 $.1^2] [ 1 $.1^2], [ 1 $.1^2] [ 0 0], [ $.1 $.1^2] [ 0 $.1], [ $.1 $.1^2] [$.1^2 $.1], [ 1 $.1^2] [$.1^2 0], [ 1 $.1^2] [ $.1 0], [ $.1 $.1^2] [ $.1 $.1], [ 1 $.1^2] [ 1 0], [ $.1 $.1^2] [ 1 $.1], [ $.1 $.1^2] [ 0 1], [ 1 $.1^2] [ 0 $.1^2], [ $.1 $.1^2] [$.1^2 1], [ 1 $.1^2] [$.1^2 $.1^2], [ 1 $.1^2] [ $.1 $.1^2], [ $.1 $.1^2] [ $.1 1], [ 1 $.1^2] [ 1 $.1^2], [ $.1 $.1^2] [ 1 1], [$.1^2 $.1] [ 0 $.1], [ 0 $.1] [ 0 0], [ 0 $.1] [$.1^2 0], [$.1^2 $.1] [$.1^2 $.1], [ 0 $.1] [ $.1 0], [$.1^2 $.1] [ $.1 $.1], [ 0 $.1] [ 1 0], [$.1^2 $.1] [ 1 $.1], [$.1^2 $.1] [ 0 1], [ 0 $.1] [ 0 $.1^2], [$.1^2 $.1] [$.1^2 1], [ 0 $.1] [$.1^2 $.1^2], [ 0 $.1] [ $.1 $.1^2], [$.1^2 $.1] [ $.1 1], [$.1^2 $.1] [ 1 1], [ 0 $.1] [ 1 $.1^2], [$.1^2 $.1] [ 0 0], [ 0 $.1] [ 0 $.1], [$.1^2 $.1] [$.1^2 0], [ 0 $.1] [$.1^2 $.1], [ 0 $.1] [ $.1 $.1], [$.1^2 $.1] [ $.1 0], [ 0 $.1] [ 1 $.1], [$.1^2 $.1] [ 1 0], [ 0 $.1] [ 0 1], [$.1^2 $.1] [ 0 $.1^2], [$.1^2 $.1] [$.1^2 $.1^2], [ 0 $.1] [$.1^2 1], [$.1^2 $.1] [ $.1 $.1^2], [ 0 $.1] [ $.1 1], [ 0 $.1] [ 1 1], [$.1^2 $.1] [ 1 $.1^2], [ $.1 $.1] [ 0 0], [ 1 $.1] [ 0 $.1], [ $.1 $.1] [$.1^2 0], [ 1 $.1] [$.1^2 $.1], [ $.1 $.1] [ $.1 0], [ 1 $.1] [ $.1 $.1], [ $.1 $.1] [ 1 0], [ 1 $.1] [ 1 $.1], [ $.1 $.1] [ 0 $.1^2], [ 1 $.1] [ 0 1], [ $.1 $.1] [$.1^2 $.1^2], [ 1 $.1] [$.1^2 1], [ $.1 $.1] [ $.1 $.1^2], [ 1 $.1] [ $.1 1], [ 1 $.1] [ 1 1], [ $.1 $.1] [ 1 $.1^2], [ 1 $.1] [ 0 0], [ $.1 $.1] [ 0 $.1], [ $.1 $.1] [$.1^2 $.1], [ 1 $.1] [$.1^2 0], [ $.1 $.1] [ $.1 $.1], [ 1 $.1] [ $.1 0], [ 1 $.1] [ 1 0], [ $.1 $.1] [ 1 $.1], [ $.1 $.1] [ 0 1], [ 1 $.1] [ 0 $.1^2], [ $.1 $.1] [$.1^2 1], [ 1 $.1] [$.1^2 $.1^2], [ $.1 $.1] [ $.1 1], [ 1 $.1] [ $.1 $.1^2], [ 1 $.1] [ 1 $.1^2], [ $.1 $.1] [ 1 1], [$.1^2 1] [ 0 $.1], [ 0 1] [ 0 0], [ 0 1] [$.1^2 0], [$.1^2 1] [$.1^2 $.1], [$.1^2 1] [ $.1 $.1], [ 0 1] [ $.1 0], [$.1^2 1] [ 1 $.1], [ 0 1] [ 1 0], [$.1^2 1] [ 0 1], [ 0 1] [ 0 $.1^2], [ 0 1] [$.1^2 $.1^2], [$.1^2 1] [$.1^2 1], [$.1^2 1] [ $.1 1], [ 0 1] [ $.1 $.1^2], [$.1^2 1] [ 1 1], [ 0 1] [ 1 $.1^2], [$.1^2 1] [ 0 0], [ 0 1] [ 0 $.1], [ 0 1] [$.1^2 $.1], [$.1^2 1] [$.1^2 0], [$.1^2 1] [ $.1 0], [ 0 1] [ $.1 $.1], [ 0 1] [ 1 $.1], [$.1^2 1] [ 1 0], [ 0 1] [ 0 1], [$.1^2 1] [ 0 $.1^2], [ 0 1] [$.1^2 1], [$.1^2 1] [$.1^2 $.1^2], [$.1^2 1] [ $.1 $.1^2], [ 0 1] [ $.1 1], [ 0 1] [ 1 1], [$.1^2 1] [ 1 $.1^2], [ 1 1] [ 0 $.1], [ $.1 1] [ 0 0], [ $.1 1] [$.1^2 0], [ 1 1] [$.1^2 $.1], [ 1 1] [ $.1 $.1], [ $.1 1] [ $.1 0], [ $.1 1] [ 1 0], [ 1 1] [ 1 $.1], [ 1 1] [ 0 1], [ $.1 1] [ 0 $.1^2], [ $.1 1] [$.1^2 $.1^2], [ 1 1] [$.1^2 1], [ 1 1] [ $.1 1], [ $.1 1] [ $.1 $.1^2], [ $.1 1] [ 1 $.1^2], [ 1 1] [ 1 1], [ $.1 1] [ 0 $.1], [ 1 1] [ 0 0], [ 1 1] [$.1^2 0], [ $.1 1] [$.1^2 $.1], [ $.1 1] [ $.1 $.1], [ 1 1] [ $.1 0], [ 1 1] [ 1 0], [ $.1 1] [ 1 $.1], [ $.1 1] [ 0 1], [ 1 1] [ 0 $.1^2], [ $.1 1] [$.1^2 1], [ 1 1] [$.1^2 $.1^2], [ $.1 1] [ $.1 1], [ 1 1] [ $.1 $.1^2], [ $.1 1] [ 1 1], [ 1 1] [ 1 $.1^2] } [$.1^2 0] [ $.1 $.1^2] Total time: 3.379 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee40.uab.es. (158.109.66.40) Time: Tue Mar 16 12:52:02 2004 Input: M:=MatrixRing(GF(4),2); Mt := {m:m in M | Trace(m) eq 0}; Mf := {m:m in M | m[1] eq m[2]}; Mtf := { Mt meet Mf }; Ma := {Random(M):m in [1..100000] }; print Ma; #(Random(M)); Output: Magma V2.10-6 Tue Mar 16 2004 12:51:59 on modular [Seed = 1146305184] ------------------------------------- { [ 0 0] [ 0 0], [$.1^2 0] [ 0 $.1], [ 0 0] [$.1^2 0], [$.1^2 0] [$.1^2 $.1], [$.1^2 0] [ $.1 $.1], [ 0 0] [ $.1 0], [ 0 0] [ 1 0], [$.1^2 0] [ 1 $.1], [ 0 0] [ 0 $.1^2], [$.1^2 0] [ 0 1], [$.1^2 0] [$.1^2 1], [ 0 0] [$.1^2 $.1^2], [$.1^2 0] [ $.1 1], [ 0 0] [ $.1 $.1^2], [ 0 0] [ 1 $.1^2], [$.1^2 0] [ 1 1], [ 0 0] [ 0 $.1], [$.1^2 0] [ 0 0], [ 0 0] [$.1^2 $.1], [$.1^2 0] [$.1^2 0], [$.1^2 0] [ $.1 0], [ 0 0] [ $.1 $.1], [ 0 0] [ 1 $.1], [$.1^2 0] [ 1 0], [$.1^2 0] [ 0 $.1^2], [ 0 0] [ 0 1], [$.1^2 0] [$.1^2 $.1^2], [ 0 0] [$.1^2 1], [ 0 0] [ $.1 1], [$.1^2 0] [ $.1 $.1^2], [$.1^2 0] [ 1 $.1^2], [ 0 0] [ 1 1], [ 1 0] [ 0 $.1], [ $.1 0] [ 0 0], [ 1 0] [$.1^2 $.1], [ $.1 0] [$.1^2 0], [ $.1 0] [ $.1 0], [ 1 0] [ $.1 $.1], [ $.1 0] [ 1 0], [ 1 0] [ 1 $.1], [ 1 0] [ 0 1], [ $.1 0] [ 0 $.1^2], [ 1 0] [$.1^2 1], [ $.1 0] [$.1^2 $.1^2], [ $.1 0] [ $.1 $.1^2], [ 1 0] [ $.1 1], [ 1 0] [ 1 1], [ $.1 0] [ 1 $.1^2], [ $.1 0] [ 0 $.1], [ 1 0] [ 0 0], [ $.1 0] [$.1^2 $.1], [ 1 0] [$.1^2 0], [ $.1 0] [ $.1 $.1], [ 1 0] [ $.1 0], [ $.1 0] [ 1 $.1], [ 1 0] [ 1 0], [ $.1 0] [ 0 1], [ 1 0] [ 0 $.1^2], [ 1 0] [$.1^2 $.1^2], [ $.1 0] [$.1^2 1], [ $.1 0] [ $.1 1], [ 1 0] [ $.1 $.1^2], [ $.1 0] [ 1 1], [ 1 0] [ 1 $.1^2], [$.1^2 $.1^2] [ 0 $.1], [ 0 $.1^2] [ 0 0], [ 0 $.1^2] [$.1^2 0], [$.1^2 $.1^2] [$.1^2 $.1], [ 0 $.1^2] [ $.1 0], [$.1^2 $.1^2] [ $.1 $.1], [$.1^2 $.1^2] [ 1 $.1], [ 0 $.1^2] [ 1 0], [ 0 $.1^2] [ 0 $.1^2], [$.1^2 $.1^2] [ 0 1], [ 0 $.1^2] [$.1^2 $.1^2], [$.1^2 $.1^2] [$.1^2 1], [$.1^2 $.1^2] [ $.1 1], [ 0 $.1^2] [ $.1 $.1^2], [$.1^2 $.1^2] [ 1 1], [ 0 $.1^2] [ 1 $.1^2], [ 0 $.1^2] [ 0 $.1], [$.1^2 $.1^2] [ 0 0], [ 0 $.1^2] [$.1^2 $.1], [$.1^2 $.1^2] [$.1^2 0], [ 0 $.1^2] [ $.1 $.1], [$.1^2 $.1^2] [ $.1 0], [$.1^2 $.1^2] [ 1 0], [ 0 $.1^2] [ 1 $.1], [ 0 $.1^2] [ 0 1], [$.1^2 $.1^2] [ 0 $.1^2], [$.1^2 $.1^2] [$.1^2 $.1^2], [ 0 $.1^2] [$.1^2 1], [$.1^2 $.1^2] [ $.1 $.1^2], [ 0 $.1^2] [ $.1 1], [ 0 $.1^2] [ 1 1], [$.1^2 $.1^2] [ 1 $.1^2], [ 1 $.1^2] [ 0 $.1], [ $.1 $.1^2] [ 0 0], [ 1 $.1^2] [$.1^2 $.1], [ $.1 $.1^2] [$.1^2 0], [ $.1 $.1^2] [ $.1 0], [ 1 $.1^2] [ $.1 $.1], [ $.1 $.1^2] [ 1 0], [ 1 $.1^2] [ 1 $.1], [ $.1 $.1^2] [ 0 $.1^2], [ 1 $.1^2] [ 0 1], [ 1 $.1^2] [$.1^2 1], [ $.1 $.1^2] [$.1^2 $.1^2], [ 1 $.1^2] [ $.1 1], [ $.1 $.1^2] [ $.1 $.1^2], [ 1 $.1^2] [ 1 1], [ $.1 $.1^2] [ 1 $.1^2], [ 1 $.1^2] [ 0 0], [ $.1 $.1^2] [ 0 $.1], [ $.1 $.1^2] [$.1^2 $.1], [ 1 $.1^2] [$.1^2 0], [ 1 $.1^2] [ $.1 0], [ $.1 $.1^2] [ $.1 $.1], [ 1 $.1^2] [ 1 0], [ $.1 $.1^2] [ 1 $.1], [ $.1 $.1^2] [ 0 1], [ 1 $.1^2] [ 0 $.1^2], [ 1 $.1^2] [$.1^2 $.1^2], [ $.1 $.1^2] [$.1^2 1], [ $.1 $.1^2] [ $.1 1], [ 1 $.1^2] [ $.1 $.1^2], [ 1 $.1^2] [ 1 $.1^2], [ $.1 $.1^2] [ 1 1], [ 0 $.1] [ 0 0], [$.1^2 $.1] [ 0 $.1], [$.1^2 $.1] [$.1^2 $.1], [ 0 $.1] [$.1^2 0], [$.1^2 $.1] [ $.1 $.1], [ 0 $.1] [ $.1 0], [$.1^2 $.1] [ 1 $.1], [ 0 $.1] [ 1 0], [$.1^2 $.1] [ 0 1], [ 0 $.1] [ 0 $.1^2], [ 0 $.1] [$.1^2 $.1^2], [$.1^2 $.1] [$.1^2 1], [$.1^2 $.1] [ $.1 1], [ 0 $.1] [ $.1 $.1^2], [ 0 $.1] [ 1 $.1^2], [$.1^2 $.1] [ 1 1], [$.1^2 $.1] [ 0 0], [ 0 $.1] [ 0 $.1], [ 0 $.1] [$.1^2 $.1], [$.1^2 $.1] [$.1^2 0], [$.1^2 $.1] [ $.1 0], [ 0 $.1] [ $.1 $.1], [$.1^2 $.1] [ 1 0], [ 0 $.1] [ 1 $.1], [ 0 $.1] [ 0 1], [$.1^2 $.1] [ 0 $.1^2], [ 0 $.1] [$.1^2 1], [$.1^2 $.1] [$.1^2 $.1^2], [ 0 $.1] [ $.1 1], [$.1^2 $.1] [ $.1 $.1^2], [ 0 $.1] [ 1 1], [$.1^2 $.1] [ 1 $.1^2], [ $.1 $.1] [ 0 0], [ 1 $.1] [ 0 $.1], [ $.1 $.1] [$.1^2 0], [ 1 $.1] [$.1^2 $.1], [ 1 $.1] [ $.1 $.1], [ $.1 $.1] [ $.1 0], [ $.1 $.1] [ 1 0], [ 1 $.1] [ 1 $.1], [ 1 $.1] [ 0 1], [ $.1 $.1] [ 0 $.1^2], [ $.1 $.1] [$.1^2 $.1^2], [ 1 $.1] [$.1^2 1], [ 1 $.1] [ $.1 1], [ $.1 $.1] [ $.1 $.1^2], [ $.1 $.1] [ 1 $.1^2], [ 1 $.1] [ 1 1], [ 1 $.1] [ 0 0], [ $.1 $.1] [ 0 $.1], [ $.1 $.1] [$.1^2 $.1], [ 1 $.1] [$.1^2 0], [ $.1 $.1] [ $.1 $.1], [ 1 $.1] [ $.1 0], [ 1 $.1] [ 1 0], [ $.1 $.1] [ 1 $.1], [ $.1 $.1] [ 0 1], [ 1 $.1] [ 0 $.1^2], [ 1 $.1] [$.1^2 $.1^2], [ $.1 $.1] [$.1^2 1], [ $.1 $.1] [ $.1 1], [ 1 $.1] [ $.1 $.1^2], [ 1 $.1] [ 1 $.1^2], [ $.1 $.1] [ 1 1], [ 0 1] [ 0 0], [$.1^2 1] [ 0 $.1], [$.1^2 1] [$.1^2 $.1], [ 0 1] [$.1^2 0], [ 0 1] [ $.1 0], [$.1^2 1] [ $.1 $.1], [ 0 1] [ 1 0], [$.1^2 1] [ 1 $.1], [$.1^2 1] [ 0 1], [ 0 1] [ 0 $.1^2], [ 0 1] [$.1^2 $.1^2], [$.1^2 1] [$.1^2 1], [$.1^2 1] [ $.1 1], [ 0 1] [ $.1 $.1^2], [ 0 1] [ 1 $.1^2], [$.1^2 1] [ 1 1], [$.1^2 1] [ 0 0], [ 0 1] [ 0 $.1], [ 0 1] [$.1^2 $.1], [$.1^2 1] [$.1^2 0], [ 0 1] [ $.1 $.1], [$.1^2 1] [ $.1 0], [ 0 1] [ 1 $.1], [$.1^2 1] [ 1 0], [ 0 1] [ 0 1], [$.1^2 1] [ 0 $.1^2], [ 0 1] [$.1^2 1], [$.1^2 1] [$.1^2 $.1^2], [ 0 1] [ $.1 1], [$.1^2 1] [ $.1 $.1^2], [ 0 1] [ 1 1], [$.1^2 1] [ 1 $.1^2], [ $.1 1] [ 0 0], [ 1 1] [ 0 $.1], [ $.1 1] [$.1^2 0], [ 1 1] [$.1^2 $.1], [ 1 1] [ $.1 $.1], [ $.1 1] [ $.1 0], [ 1 1] [ 1 $.1], [ $.1 1] [ 1 0], [ $.1 1] [ 0 $.1^2], [ 1 1] [ 0 1], [ 1 1] [$.1^2 1], [ $.1 1] [$.1^2 $.1^2], [ $.1 1] [ $.1 $.1^2], [ 1 1] [ $.1 1], [ 1 1] [ 1 1], [ $.1 1] [ 1 $.1^2], [ 1 1] [ 0 0], [ $.1 1] [ 0 $.1], [ 1 1] [$.1^2 0], [ $.1 1] [$.1^2 $.1], [ $.1 1] [ $.1 $.1], [ 1 1] [ $.1 0], [ $.1 1] [ 1 $.1], [ 1 1] [ 1 0], [ $.1 1] [ 0 1], [ 1 1] [ 0 $.1^2], [ $.1 1] [$.1^2 1], [ 1 1] [$.1^2 $.1^2], [ $.1 1] [ $.1 1], [ 1 1] [ $.1 $.1^2], [ $.1 1] [ 1 1], [ 1 1] [ 1 $.1^2] } >> #(Random(M));; ^ Runtime error in '#': Bad argument types Argument types given: AlgMatElt Total time: 3.429 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee40.uab.es. (158.109.66.40) Time: Tue Mar 16 12:52:20 2004 Input: M:=MatrixRing(GF(4),2); Mt := {m:m in M | Trace(m) eq 0}; Mf := {m:m in M | m[1] eq m[2]}; Mtf := { Mt meet Mf }; Ma := {Random(M):m in [1..100000] }; print Ma; #(M); Output: Magma V2.10-6 Tue Mar 16 2004 12:52:16 on modular [Seed = 1935937016] ------------------------------------- { [ 0 0] [ 0 0], [$.1^2 0] [ 0 $.1], [ 0 0] [$.1^2 0], [$.1^2 0] [$.1^2 $.1], [ 0 0] [ $.1 0], [$.1^2 0] [ $.1 $.1], [ 0 0] [ 1 0], [$.1^2 0] [ 1 $.1], [ 0 0] [ 0 $.1^2], [$.1^2 0] [ 0 1], [$.1^2 0] [$.1^2 1], [ 0 0] [$.1^2 $.1^2], [$.1^2 0] [ $.1 1], [ 0 0] [ $.1 $.1^2], [$.1^2 0] [ 1 1], [ 0 0] [ 1 $.1^2], [ 0 0] [ 0 $.1], [$.1^2 0] [ 0 0], [ 0 0] [$.1^2 $.1], [$.1^2 0] [$.1^2 0], [$.1^2 0] [ $.1 0], [ 0 0] [ $.1 $.1], [$.1^2 0] [ 1 0], [ 0 0] [ 1 $.1], [ 0 0] [ 0 1], [$.1^2 0] [ 0 $.1^2], [$.1^2 0] [$.1^2 $.1^2], [ 0 0] [$.1^2 1], [ 0 0] [ $.1 1], [$.1^2 0] [ $.1 $.1^2], [ 0 0] [ 1 1], [$.1^2 0] [ 1 $.1^2], [ 1 0] [ 0 $.1], [ $.1 0] [ 0 0], [ $.1 0] [$.1^2 0], [ 1 0] [$.1^2 $.1], [ $.1 0] [ $.1 0], [ 1 0] [ $.1 $.1], [ 1 0] [ 1 $.1], [ $.1 0] [ 1 0], [ $.1 0] [ 0 $.1^2], [ 1 0] [ 0 1], [ 1 0] [$.1^2 1], [ $.1 0] [$.1^2 $.1^2], [ 1 0] [ $.1 1], [ $.1 0] [ $.1 $.1^2], [ $.1 0] [ 1 $.1^2], [ 1 0] [ 1 1], [ $.1 0] [ 0 $.1], [ 1 0] [ 0 0], [ 1 0] [$.1^2 0], [ $.1 0] [$.1^2 $.1], [ 1 0] [ $.1 0], [ $.1 0] [ $.1 $.1], [ $.1 0] [ 1 $.1], [ 1 0] [ 1 0], [ 1 0] [ 0 $.1^2], [ $.1 0] [ 0 1], [ $.1 0] [$.1^2 1], [ 1 0] [$.1^2 $.1^2], [ 1 0] [ $.1 $.1^2], [ $.1 0] [ $.1 1], [ $.1 0] [ 1 1], [ 1 0] [ 1 $.1^2], [$.1^2 $.1^2] [ 0 $.1], [ 0 $.1^2] [ 0 0], [$.1^2 $.1^2] [$.1^2 $.1], [ 0 $.1^2] [$.1^2 0], [ 0 $.1^2] [ $.1 0], [$.1^2 $.1^2] [ $.1 $.1], [$.1^2 $.1^2] [ 1 $.1], [ 0 $.1^2] [ 1 0], [ 0 $.1^2] [ 0 $.1^2], [$.1^2 $.1^2] [ 0 1], [ 0 $.1^2] [$.1^2 $.1^2], [$.1^2 $.1^2] [$.1^2 1], [$.1^2 $.1^2] [ $.1 1], [ 0 $.1^2] [ $.1 $.1^2], [ 0 $.1^2] [ 1 $.1^2], [$.1^2 $.1^2] [ 1 1], [$.1^2 $.1^2] [ 0 0], [ 0 $.1^2] [ 0 $.1], [$.1^2 $.1^2] [$.1^2 0], [ 0 $.1^2] [$.1^2 $.1], [ 0 $.1^2] [ $.1 $.1], [$.1^2 $.1^2] [ $.1 0], [ 0 $.1^2] [ 1 $.1], [$.1^2 $.1^2] [ 1 0], [$.1^2 $.1^2] [ 0 $.1^2], [ 0 $.1^2] [ 0 1], [ 0 $.1^2] [$.1^2 1], [$.1^2 $.1^2] [$.1^2 $.1^2], [$.1^2 $.1^2] [ $.1 $.1^2], [ 0 $.1^2] [ $.1 1], [$.1^2 $.1^2] [ 1 $.1^2], [ 0 $.1^2] [ 1 1], [ $.1 $.1^2] [ 0 0], [ 1 $.1^2] [ 0 $.1], [ 1 $.1^2] [$.1^2 $.1], [ $.1 $.1^2] [$.1^2 0], [ $.1 $.1^2] [ $.1 0], [ 1 $.1^2] [ $.1 $.1], [ 1 $.1^2] [ 1 $.1], [ $.1 $.1^2] [ 1 0], [ $.1 $.1^2] [ 0 $.1^2], [ 1 $.1^2] [ 0 1], [ 1 $.1^2] [$.1^2 1], [ $.1 $.1^2] [$.1^2 $.1^2], [ 1 $.1^2] [ $.1 1], [ $.1 $.1^2] [ $.1 $.1^2], [ 1 $.1^2] [ 1 1], [ $.1 $.1^2] [ 1 $.1^2], [ $.1 $.1^2] [ 0 $.1], [ 1 $.1^2] [ 0 0], [ $.1 $.1^2] [$.1^2 $.1], [ 1 $.1^2] [$.1^2 0], [ $.1 $.1^2] [ $.1 $.1], [ 1 $.1^2] [ $.1 0], [ $.1 $.1^2] [ 1 $.1], [ 1 $.1^2] [ 1 0], [ 1 $.1^2] [ 0 $.1^2], [ $.1 $.1^2] [ 0 1], [ 1 $.1^2] [$.1^2 $.1^2], [ $.1 $.1^2] [$.1^2 1], [ 1 $.1^2] [ $.1 $.1^2], [ $.1 $.1^2] [ $.1 1], [ $.1 $.1^2] [ 1 1], [ 1 $.1^2] [ 1 $.1^2], [$.1^2 $.1] [ 0 $.1], [ 0 $.1] [ 0 0], [ 0 $.1] [$.1^2 0], [$.1^2 $.1] [$.1^2 $.1], [$.1^2 $.1] [ $.1 $.1], [ 0 $.1] [ $.1 0], [ 0 $.1] [ 1 0], [$.1^2 $.1] [ 1 $.1], [$.1^2 $.1] [ 0 1], [ 0 $.1] [ 0 $.1^2], [$.1^2 $.1] [$.1^2 1], [ 0 $.1] [$.1^2 $.1^2], [$.1^2 $.1] [ $.1 1], [ 0 $.1] [ $.1 $.1^2], [ 0 $.1] [ 1 $.1^2], [$.1^2 $.1] [ 1 1], [ 0 $.1] [ 0 $.1], [$.1^2 $.1] [ 0 0], [$.1^2 $.1] [$.1^2 0], [ 0 $.1] [$.1^2 $.1], [$.1^2 $.1] [ $.1 0], [ 0 $.1] [ $.1 $.1], [ 0 $.1] [ 1 $.1], [$.1^2 $.1] [ 1 0], [ 0 $.1] [ 0 1], [$.1^2 $.1] [ 0 $.1^2], [ 0 $.1] [$.1^2 1], [$.1^2 $.1] [$.1^2 $.1^2], [ 0 $.1] [ $.1 1], [$.1^2 $.1] [ $.1 $.1^2], [$.1^2 $.1] [ 1 $.1^2], [ 0 $.1] [ 1 1], [ 1 $.1] [ 0 $.1], [ $.1 $.1] [ 0 0], [ $.1 $.1] [$.1^2 0], [ 1 $.1] [$.1^2 $.1], [ 1 $.1] [ $.1 $.1], [ $.1 $.1] [ $.1 0], [ 1 $.1] [ 1 $.1], [ $.1 $.1] [ 1 0], [ $.1 $.1] [ 0 $.1^2], [ 1 $.1] [ 0 1], [ $.1 $.1] [$.1^2 $.1^2], [ 1 $.1] [$.1^2 1], [ 1 $.1] [ $.1 1], [ $.1 $.1] [ $.1 $.1^2], [ 1 $.1] [ 1 1], [ $.1 $.1] [ 1 $.1^2], [ 1 $.1] [ 0 0], [ $.1 $.1] [ 0 $.1], [ 1 $.1] [$.1^2 0], [ $.1 $.1] [$.1^2 $.1], [ 1 $.1] [ $.1 0], [ $.1 $.1] [ $.1 $.1], [ $.1 $.1] [ 1 $.1], [ 1 $.1] [ 1 0], [ $.1 $.1] [ 0 1], [ 1 $.1] [ 0 $.1^2], [ 1 $.1] [$.1^2 $.1^2], [ $.1 $.1] [$.1^2 1], [ $.1 $.1] [ $.1 1], [ 1 $.1] [ $.1 $.1^2], [ $.1 $.1] [ 1 1], [ 1 $.1] [ 1 $.1^2], [ 0 1] [ 0 0], [$.1^2 1] [ 0 $.1], [ 0 1] [$.1^2 0], [$.1^2 1] [$.1^2 $.1], [ 0 1] [ $.1 0], [$.1^2 1] [ $.1 $.1], [$.1^2 1] [ 1 $.1], [ 0 1] [ 1 0], [$.1^2 1] [ 0 1], [ 0 1] [ 0 $.1^2], [$.1^2 1] [$.1^2 1], [ 0 1] [$.1^2 $.1^2], [$.1^2 1] [ $.1 1], [ 0 1] [ $.1 $.1^2], [$.1^2 1] [ 1 1], [ 0 1] [ 1 $.1^2], [$.1^2 1] [ 0 0], [ 0 1] [ 0 $.1], [ 0 1] [$.1^2 $.1], [$.1^2 1] [$.1^2 0], [$.1^2 1] [ $.1 0], [ 0 1] [ $.1 $.1], [$.1^2 1] [ 1 0], [ 0 1] [ 1 $.1], [$.1^2 1] [ 0 $.1^2], [ 0 1] [ 0 1], [$.1^2 1] [$.1^2 $.1^2], [ 0 1] [$.1^2 1], [$.1^2 1] [ $.1 $.1^2], [ 0 1] [ $.1 1], [$.1^2 1] [ 1 $.1^2], [ 0 1] [ 1 1], [ 1 1] [ 0 $.1], [ $.1 1] [ 0 0], [ 1 1] [$.1^2 $.1], [ $.1 1] [$.1^2 0], [ 1 1] [ $.1 $.1], [ $.1 1] [ $.1 0], [ 1 1] [ 1 $.1], [ $.1 1] [ 1 0], [ 1 1] [ 0 1], [ $.1 1] [ 0 $.1^2], [ $.1 1] [$.1^2 $.1^2], [ 1 1] [$.1^2 1], [ 1 1] [ $.1 1], [ $.1 1] [ $.1 $.1^2], [ 1 1] [ 1 1], [ $.1 1] [ 1 $.1^2], [ 1 1] [ 0 0], [ $.1 1] [ 0 $.1], [ 1 1] [$.1^2 0], [ $.1 1] [$.1^2 $.1], [ 1 1] [ $.1 0], [ $.1 1] [ $.1 $.1], [ $.1 1] [ 1 $.1], [ 1 1] [ 1 0], [ $.1 1] [ 0 1], [ 1 1] [ 0 $.1^2], [ $.1 1] [$.1^2 1], [ 1 1] [$.1^2 $.1^2], [ $.1 1] [ $.1 1], [ 1 1] [ $.1 $.1^2], [ $.1 1] [ 1 1], [ 1 1] [ 1 $.1^2] } 256 Total time: 3.349 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee40.uab.es. (158.109.66.40) Time: Tue Mar 16 12:53:25 2004 Input: M:=MatrixRing(GF(4),2); Mt := {m:m in M | Trace(m) eq 0}; Mf := {m:m in M | m[1] eq m[2]}; Mtf := { Mt meet Mf }; Ma := {Random(M):m in [1..100000] }; #(Ma); Output: Magma V2.10-6 Tue Mar 16 2004 12:53:22 on modular [Seed = 1786582307] ------------------------------------- 256 Total time: 3.249 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.33.170.proxycache.rima-tde.net. (80.58.33.170) Time: Tue Mar 16 12:54:35 2004 Input: [i: i in [i..366] by 7] 2- R:=GF(4); M:=MatrixRing(R,2); Mt={A: A in M | trace(A) eq 0} Mf:={A: A in M | A[1] eq A[2]} Mtf:=Mt meet Mf seq:={Random(M): num in [1..100000]}; #([A:A in seq | A in Mt]); Output: Magma V2.10-6 Tue Mar 16 2004 12:54:32 on modular [Seed = 1635130978] ------------------------------------- >> [i: i in [i..366] by 7] ^ User error: bad syntax >> R:=GF(4); ^ User error: Illegal left hand side of an assignment statement >> M:=MatrixRing(R,2); ^ User error: Identifier 'R' has not been declared or assigned >> Mf:={A: A in M | A[1] eq A[2]} ^ User error: bad syntax >> seq:={Random(M): num in [1..100000]}; ^ User error: bad syntax >> #([A:A in seq | A in Mt]);; ^ User error: Identifier 'seq' has not been declared or assigned Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.33.170.proxycache.rima-tde.net. (80.58.33.170) Time: Tue Mar 16 12:55:07 2004 Input: k:=GF(4); M22:=MatrixRing(k,2); Mt:={M:M in M22|Trace(M) eq 0}; Mt; Output: Magma V2.10-6 Tue Mar 16 2004 12:55:04 on modular [Seed = 470508351] ------------------------------------- { [ 0 0] [ 0 0], [ 0 0] [k.1^2 0], [ 0 0] [ k.1 0], [ 0 0] [ 1 0], [k.1^2 0] [ 0 k.1^2], [k.1^2 0] [k.1^2 k.1^2], [k.1^2 0] [ k.1 k.1^2], [k.1^2 0] [ 1 k.1^2], [ 1 0] [ 0 1], [ 1 0] [k.1^2 1], [ 1 0] [ k.1 1], [ 1 0] [ 1 1], [ k.1 0] [ 0 k.1], [ k.1 0] [k.1^2 k.1], [ k.1 0] [ k.1 k.1], [ k.1 0] [ 1 k.1], [ 0 k.1^2] [ 0 0], [ 0 k.1^2] [k.1^2 0], [ 0 k.1^2] [ k.1 0], [ 0 k.1^2] [ 1 0], [k.1^2 k.1^2] [ 0 k.1^2], [k.1^2 k.1^2] [k.1^2 k.1^2], [k.1^2 k.1^2] [ k.1 k.1^2], [k.1^2 k.1^2] [ 1 k.1^2], [ 1 k.1^2] [ 0 1], [ 1 k.1^2] [k.1^2 1], [ 1 k.1^2] [ k.1 1], [ 1 k.1^2] [ 1 1], [ k.1 k.1^2] [ 0 k.1], [ k.1 k.1^2] [k.1^2 k.1], [ k.1 k.1^2] [ k.1 k.1], [ k.1 k.1^2] [ 1 k.1], [ 0 k.1] [ 0 0], [ 0 k.1] [k.1^2 0], [ 0 k.1] [ k.1 0], [ 0 k.1] [ 1 0], [k.1^2 k.1] [ 0 k.1^2], [k.1^2 k.1] [k.1^2 k.1^2], [k.1^2 k.1] [ k.1 k.1^2], [k.1^2 k.1] [ 1 k.1^2], [ 1 k.1] [ 0 1], [ 1 k.1] [k.1^2 1], [ 1 k.1] [ k.1 1], [ 1 k.1] [ 1 1], [ k.1 k.1] [ 0 k.1], [ k.1 k.1] [k.1^2 k.1], [ k.1 k.1] [ k.1 k.1], [ k.1 k.1] [ 1 k.1], [ 0 1] [ 0 0], [ 0 1] [k.1^2 0], [ 0 1] [ k.1 0], [ 0 1] [ 1 0], [k.1^2 1] [ 0 k.1^2], [k.1^2 1] [k.1^2 k.1^2], [k.1^2 1] [ k.1 k.1^2], [k.1^2 1] [ 1 k.1^2], [ 1 1] [ 0 1], [ 1 1] [k.1^2 1], [ 1 1] [ k.1 1], [ 1 1] [ 1 1], [ k.1 1] [ 0 k.1], [ k.1 1] [k.1^2 k.1], [ k.1 1] [ k.1 k.1], [ k.1 1] [ 1 k.1] } Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee40.uab.es. (158.109.66.40) Time: Tue Mar 16 12:58:45 2004 Input: M:=MatrixRing(GF(4),2); Mt := {m:m in M | Trace(m) eq 0}; Mf := {m:m in M | m[1] eq m[2]}; Mtf := { Mt meet Mf }; Ma := {Random(M):m in [1..100000] }; #(M); #(Ma); Output: Magma V2.10-6 Tue Mar 16 2004 12:58:41 on modular [Seed = 169675264] ------------------------------------- 256 256 Total time: 3.369 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee40.uab.es. (158.109.66.40) Time: Tue Mar 16 12:59:08 2004 Input: M:=MatrixRing(GF(4),2); Mt := {m:m in M | Trace(m) eq 0}; Mf := {m:m in M | m[1] eq m[2]}; Mtf := { Mt meet Mf }; Ma := {Random(M):m in [1..100000]by 1 }; #(M); #(Ma); Output: Magma V2.10-6 Tue Mar 16 2004 12:59:05 on modular [Seed = 101778996] ------------------------------------- >> Ma := {Random(M):m in [1..100000]by 1 }; ^ User error: bad syntax 256 >> #(Ma);; ^ User error: Identifier 'Ma' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 13:04:52 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; ordre_elements := [: i in [1..24]]; ordre_elements; elem_primitius := [tupla[1]: tupla in ordre_elements | tupla[2] eq 25-1 ]; #elem_primitius; print "eoh"; MinimalPolynomial(gamma^2, G25); Output: Magma V2.10-6 Tue Mar 16 2004 13:04:49 on modular [Seed = 3670924096] ------------------------------------- [ , , , , , <2, 4>, , , , , , <4, 2>, , , , , , <3, 4>, , , , , , <1, 1> ] 8 eoh $.1 + gamma^14 Total time: 2.919 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Tue Mar 16 13:05:16 2004 Input: P2 := PolynomialRing(Integers(2)); P3 := PolynomialRing(Integers(3)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g > ; G25 := ext < GF(5) | j >; ordre_elements := [: i in [1..24]]; ordre_elements; elem_primitius := [tupla[1]: tupla in ordre_elements | tupla[2] eq 25-1 ]; #elem_primitius; print "eoh"; MinimalPolynomial(gamma, G25); Output: Magma V2.10-6 Tue Mar 16 2004 13:05:13 on modular [Seed = 3586315351] ------------------------------------- [ , , , , , <2, 4>, , , , , , <4, 2>, , , , , , <3, 4>, , , , , , <1, 1> ] 8 eoh $.1 + gamma^13 Total time: 2.929 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host aula-a-siee40.uab.es. (158.109.66.40) Time: Tue Mar 16 13:06:39 2004 Input: M:=MatrixRing(GF(4),2); Mt := {m:m in M | Trace(m) eq 0}; Mf := {m:m in M | m[1] eq m[2]}; Mtf := { Mt meet Mf }; print Mtf; Ma := {Random(M):m in [1..100000] by 1 }; #(M); #(Ma); Output: Magma V2.10-6 Tue Mar 16 2004 13:06:36 on modular [Seed = 3285500340] ------------------------------------- { { [ 0 0] [ 0 0], [$.1^2 $.1^2] [$.1^2 $.1^2], [ $.1 $.1] [ $.1 $.1], [ 1 1] [ 1 1] } } >> Ma := {Random(M):m in [1..100000] by 1 }; ^ User error: bad syntax 256 >> #(Ma);; ^ User error: Identifier 'Ma' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee40.uab.es. (158.109.66.40) Time: Tue Mar 16 13:15:45 2004 Input: M:=MatrixRing(GF(4),2); Mt := {m:m in M | Trace(m) eq 0}; Mf := {m:m in M | m[1] eq m[2]}; Mtf := Mt meet Mf ; print Mtf; Ma := [Random(M22):m in [1..100000]]; #(M); #(Ma); Output: Magma V2.10-6 Tue Mar 16 2004 13:15:42 on modular [Seed = 3959222270] ------------------------------------- { [ 0 0] [ 0 0], [$.1^2 $.1^2] [$.1^2 $.1^2], [ $.1 $.1] [ $.1 $.1], [ 1 1] [ 1 1] } >> Ma := [Random(M22):m in [1..100000]]; ^ User error: Identifier 'M22' has not been declared or assigned 256 >> #(Ma);; ^ User error: Identifier 'Ma' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee40.uab.es. (158.109.66.40) Time: Tue Mar 16 13:16:02 2004 Input: M:=MatrixRing(GF(4),2); Mt := {m:m in M | Trace(m) eq 0}; Mf := {m:m in M | m[1] eq m[2]}; Mtf := Mt meet Mf ; print Mtf; Ma := [Random(M):m in [1..100000]]; #(M); #(Ma); Output: Magma V2.10-6 Tue Mar 16 2004 13:15:58 on modular [Seed = 3774342373] ------------------------------------- { [ 0 0] [ 0 0], [$.1^2 $.1^2] [$.1^2 $.1^2], [ $.1 $.1] [ $.1 $.1], [ 1 1] [ 1 1] } 256 100000 Total time: 3.479 seconds, Total memory usage: 7.09MB ************** MAGMA ***************** Host 192-BAR2-X96.libre.retevision.es. (62.82.155.192) Time: Tue Mar 16 14:45:11 2004 Input: v:=[1..366]; Output: Magma V2.10-6 Tue Mar 16 2004 14:45:08 on modular [Seed = 4293453542] ------------------------------------- Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 192-BAR2-X96.libre.retevision.es. (62.82.155.192) Time: Tue Mar 16 14:45:24 2004 Input: v:=[1..366]; print v; Output: Magma V2.10-6 Tue Mar 16 2004 14:45:21 on modular [Seed = 4142002170] ------------------------------------- [ 1 .. 366 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 192-BAR2-X96.libre.retevision.es. (62.82.155.192) Time: Tue Mar 16 14:47:30 2004 Input: v:=[1..366]; Include(v,367); print v; Output: Magma V2.10-6 Tue Mar 16 2004 14:47:27 on modular [Seed = 3959222905] ------------------------------------- [ 1 .. 367 ] [ 1 .. 366 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 192-BAR2-X96.libre.retevision.es. (62.82.155.192) Time: Tue Mar 16 14:47:47 2004 Input: v:=[1..366]; Include(v,367); Output: Magma V2.10-6 Tue Mar 16 2004 14:47:44 on modular [Seed = 3807771487] ------------------------------------- [ 1 .. 367 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 192-BAR2-X96.libre.retevision.es. (62.82.155.192) Time: Tue Mar 16 14:48:24 2004 Input: v:=[1..366]; Include(C,367); Output: Magma V2.10-6 Tue Mar 16 2004 14:48:21 on modular [Seed = 2508361677] ------------------------------------- >> Include(C,367); ^ User error: Identifier 'C' has not been declared or assigned Total time: 2.869 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 192-BAR2-X96.libre.retevision.es. (62.82.155.192) Time: Tue Mar 16 14:48:46 2004 Input: v:=[1..366]; C:=[]; Include(C,367); Output: Magma V2.10-6 Tue Mar 16 2004 14:48:43 on modular [Seed = 2409141705] ------------------------------------- [ 367 ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 192-BAR2-X96.libre.retevision.es. (62.82.155.192) Time: Tue Mar 16 14:50:30 2004 Input: v:=[1..366]; C:=[]; length(v); /*for i:=1 to i:=lengthInclude(C,367);*/ Output: Magma V2.10-6 Tue Mar 16 2004 14:50:27 on modular [Seed = 3148652901] ------------------------------------- >> length(v); ^ User error: Identifier 'length' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 192-BAR2-X96.libre.retevision.es. (62.82.155.192) Time: Tue Mar 16 14:52:28 2004 Input: v:=[1..366]; C:=[]; for i:=1 to i:=366 do { if (i mod 7)-4 eq 0 then Include(C,i); } end for; Output: Magma V2.10-6 Tue Mar 16 2004 14:52:25 on modular [Seed = 2897982984] ------------------------------------- >> for i:=1 to i:=366 do ^ User error: bad syntax >> if (i mod 7)-4 eq 0 then Include(C,i); ^ User error: bad syntax >> } ^ User error: bad syntax >> end for;; ^ User error: bad syntax Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 192-BAR2-X96.libre.retevision.es. (62.82.155.192) Time: Tue Mar 16 14:55:43 2004 Input: v:=[1..366]; C:=[]; for i:=1 to 366 do if (i mod 7)-4 eq 0 then Include(C,i); end for; Output: Magma V2.10-6 Tue Mar 16 2004 14:55:40 on modular [Seed = 1598571709] ------------------------------------- >> end for;; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 192-BAR2-X96.libre.retevision.es. (62.82.155.192) Time: Tue Mar 16 14:56:04 2004 Input: v:=[1..366]; C:=[]; for i:=1 to 366 do if (i mod 7)-4 eq 0 then Include(C,i); end for Output: Magma V2.10-6 Tue Mar 16 2004 14:56:01 on modular [Seed = 1413697499] ------------------------------------- >> end for; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 192-BAR2-X96.libre.retevision.es. (62.82.155.192) Time: Tue Mar 16 14:56:21 2004 Input: v:=[1..366]; C:=[]; for i:=1 to 366 do if (i mod 7)-4 eq 0 then Include(C,i); endfor; Output: Magma V2.10-6 Tue Mar 16 2004 14:56:18 on modular [Seed = 1297766129] ------------------------------------- User error: syntax error at end of input Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 192-BAR2-X96.libre.retevision.es. (62.82.155.192) Time: Tue Mar 16 14:56:38 2004 Input: v:=[1..366]; C:=[]; for i:=1 to 366 do if (i mod 7)-4 eq 0 then Include(C,i); endfor; ; Output: Magma V2.10-6 Tue Mar 16 2004 14:56:35 on modular [Seed = 1112889839] ------------------------------------- User error: syntax error at end of input Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 192-BAR2-X96.libre.retevision.es. (62.82.155.192) Time: Tue Mar 16 14:57:16 2004 Input: v:=[1..366]; C:=[]; for i:=1 to 366 do if (i mod 7)-4 eq 0 then Include(C,i); endfor; ; Output: Magma V2.10-6 Tue Mar 16 2004 14:57:13 on modular [Seed = 2070701884] ------------------------------------- User error: syntax error at end of input Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 192-BAR2-X96.libre.retevision.es. (62.82.155.192) Time: Tue Mar 16 14:57:36 2004 Input: v:=[1..366]; C:=[]; for i:=1 to 366 do if (i mod 7)-4 eq 0 then Include(C,i); endfor;; Output: Magma V2.10-6 Tue Mar 16 2004 14:57:33 on modular [Seed = 1885826051] ------------------------------------- User error: syntax error at end of input Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 192-BAR2-X96.libre.retevision.es. (62.82.155.192) Time: Tue Mar 16 14:59:04 2004 Input: v:=[1..366]; C:=[]; for i:=1 to 366 do if (i mod 7)-4 eq 0 then Include(C,i); endfor Output: Magma V2.10-6 Tue Mar 16 2004 14:59:01 on modular [Seed = 1769895346] ------------------------------------- User error: syntax error at end of input Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 192-BAR2-X96.libre.retevision.es. (62.82.155.192) Time: Tue Mar 16 15:00:55 2004 Input: /*v:=[1..366];*/ C:=[]; for i:=1 to 366 do if (i mod 7)-4 eq 0 then Include(C,i); endfor Output: Magma V2.10-6 Tue Mar 16 2004 15:00:52 on modular [Seed = 385878972] ------------------------------------- User error: syntax error at end of input Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 192-BAR2-X96.libre.retevision.es. (62.82.155.192) Time: Tue Mar 16 15:02:20 2004 Input: /*v:=[1..366];*/ C:=[]; for i:=1 to 366 do if (i mod 7)-4 eq 0 then Include(C,i) endif; endfor; Output: Magma V2.10-6 Tue Mar 16 2004 15:02:17 on modular [Seed = 992749100] ------------------------------------- >> if (i mod 7)-4 eq 0 then Include(C,i) endif; ^ User error: bad syntax >> endfor;; ^ User error: Identifier 'endfor' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 192-BAR2-X96.libre.retevision.es. (62.82.155.192) Time: Tue Mar 16 15:02:31 2004 Input: /*v:=[1..366];*/ C:=[]; for i:=1 to 366 do if (i mod 7)-4 eq 0 then Include(C,i) end if; endfor; Output: Magma V2.10-6 Tue Mar 16 2004 15:02:28 on modular [Seed = 807873850] ------------------------------------- >> if (i mod 7)-4 eq 0 then Include(C,i) end if; ^ User error: bad syntax >> endfor;; ^ User error: Identifier 'endfor' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 192-BAR2-X96.libre.retevision.es. (62.82.155.192) Time: Tue Mar 16 15:04:41 2004 Input: k:=GF(4); Output: Magma V2.10-6 Tue Mar 16 2004 15:04:38 on modular [Seed = 691942561] ------------------------------------- Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 202-BARC-X66.libre.retevision.es. (62.82.36.202) Time: Tue Mar 16 15:31:43 2004 Input: v:=[1..366]; [i-4 : i in v | i mod 7 eq 0]; Output: Magma V2.10-6 Tue Mar 16 2004 15:31:39 on modular [Seed = 3774334101] ------------------------------------- [ 3, 10, 17, 24, 31, 38, 45, 52, 59, 66, 73, 80, 87, 94, 101, 108, 115, 122, 129, 136, 143, 150, 157, 164, 171, 178, 185, 192, 199, 206, 213, 220, 227, 234, 241, 248, 255, 262, 269, 276, 283, 290, 297, 304, 311, 318, 325, 332, 339, 346, 353, 360 ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 202-BARC-X66.libre.retevision.es. (62.82.36.202) Time: Tue Mar 16 15:35:21 2004 Input: K:=GF(4); PrimeField(K); Output: Magma V2.10-6 Tue Mar 16 2004 15:35:18 on modular [Seed = 2458236874] ------------------------------------- Finite field of size 2 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 202-BARC-X66.libre.retevision.es. (62.82.36.202) Time: Tue Mar 16 15:36:35 2004 Input: K:=GF(4); M22:=KMatrixSpace(K,2,2); Output: Magma V2.10-6 Tue Mar 16 2004 15:36:32 on modular [Seed = 2308877447] ------------------------------------- Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 202-BARC-X66.libre.retevision.es. (62.82.36.202) Time: Tue Mar 16 15:39:28 2004 Input: K:=GF(4); M:=MatrixRing(K,2); print M[1]; Output: Magma V2.10-6 Tue Mar 16 2004 15:39:25 on modular [Seed = 3198786333] ------------------------------------- >> print M[1]; ^ Runtime error in '[]': Bad argument types Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 202-BARC-X66.libre.retevision.es. (62.82.36.202) Time: Tue Mar 16 15:41:07 2004 Input: K:=GF(4); M:=MatrixRing(K,2); M; Output: Magma V2.10-6 Tue Mar 16 2004 15:41:04 on modular [Seed = 2897971859] ------------------------------------- Full Matrix Algebra of degree 2 over GF(2^2) Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 202-BARC-X66.libre.retevision.es. (62.82.36.202) Time: Tue Mar 16 15:41:33 2004 Input: K:=GF(4); M:=MatrixRing(K,2); M[1]; Output: Magma V2.10-6 Tue Mar 16 2004 15:41:30 on modular [Seed = 2779939713] ------------------------------------- >> M[1]; ^ Runtime error in '[]': Bad argument types Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 202-BARC-X66.libre.retevision.es. (62.82.36.202) Time: Tue Mar 16 15:43:03 2004 Input: K:=GF(4); M:=MatrixRing(K,2); M; Output: Magma V2.10-6 Tue Mar 16 2004 15:43:00 on modular [Seed = 1515027665] ------------------------------------- Full Matrix Algebra of degree 2 over GF(2^2) Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Tue Mar 16 18:19:56 2004 Input: {: a in GF(7,3), b in GF(7,3)|Evaluate(pol,a) eq Evaluate(x^sum,b)}; Output: Magma V2.10-6 Tue Mar 16 2004 18:19:53 on modular [Seed = 2157398905] ------------------------------------- >> {: a in GF(7,3), b in GF(7,3)|Evaluate(pol,a) eq Evaluate(x^sum,b)}; ^ User error: Identifier 'pol' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 16 20:29:09 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^2 - 5); M := ExtensionField(N, w^2 - 3); Output: Magma V2.10-6 Tue Mar 16 2004 20:29:06 on modular [Seed = 1651870690] ------------------------------------- >> M := ExtensionField(N, w^2 - 3); ^ User error: Identifier 'ExtensionField' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 16 20:29:33 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^2 - 5); M := NumberField(w^2 - 3); Output: Magma V2.10-6 Tue Mar 16 2004 20:29:29 on modular [Seed = 1753186803] ------------------------------------- >> M := NumberField(w^2 - 3); ^ Runtime error in 'NumberField': Bad argument types Argument types given: FldNumElt Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 16 20:31:42 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^2 - 5); M := RadicalExtension(N, 2, -3); Output: Magma V2.10-6 Tue Mar 16 2004 20:31:39 on modular [Seed = 2104137572] ------------------------------------- Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 16 20:31:58 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^2 - 5); M := RadicalExtension(N, 2, -3); UnitGroup(M); Output: Magma V2.10-6 Tue Mar 16 2004 20:31:55 on modular [Seed = 1247649955] ------------------------------------- Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 to Maximal Order of Equation Order with defining polynomial x^2 + [3, 0] over its ground order Total time: 3.029 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 16 20:33:49 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^2 - 5); M := RadicalExtension(N, 2, -3); G, phi := UnitGroup(M); G; Output: Magma V2.10-6 Tue Mar 16 2004 20:33:46 on modular [Seed = 1346878152] ------------------------------------- Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*G.1 = 0 Total time: 3.039 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 16 20:36:12 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^2 + 5); M := NumberField(x^2 + 3); K := MergeField(N, M); G, phi := UnitGroup(K); G; Output: Magma V2.10-6 Tue Mar 16 2004 20:36:09 on modular [Seed = 573950410] ------------------------------------- >> K := MergeField(N, M); ^ User error: Identifier 'MergeField' has not been declared or assigned >> G, phi := UnitGroup(K); ^ User error: Identifier 'K' has not been declared or assigned >> G;; ^ User error: Identifier 'G' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 16 20:36:34 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^2 + 5); M := NumberField(x^2 + 3); K := MergeFields(N, M); G, phi := UnitGroup(K); G; Output: Magma V2.10-6 Tue Mar 16 2004 20:36:31 on modular [Seed = 675267541] ------------------------------------- >> G, phi := UnitGroup(K); ^ Runtime error in 'UnitGroup': Bad argument types Argument types given: SeqEnum[FldNum] >> G;; ^ User error: Identifier 'G' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 16 20:37:42 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^2 + 3); M := RadicalField(N, 2, -5); G, phi := UnitGroup(M); G; Output: Magma V2.10-6 Tue Mar 16 2004 20:37:39 on modular [Seed = 824629936] ------------------------------------- >> M := RadicalField(N, 2, -5); ^ User error: Identifier 'RadicalField' has not been declared or assigned >> G, phi := UnitGroup(M); ^ User error: Identifier 'M' has not been declared or assigned >> G;; ^ User error: Identifier 'G' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 16 20:37:59 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^2 + 3); M := RadicalExtension(N, 2, -5); G, phi := UnitGroup(M); G; Output: Magma V2.10-6 Tue Mar 16 2004 20:37:56 on modular [Seed = 1042929064] ------------------------------------- Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*G.1 = 0 Total time: 2.929 seconds, Total memory usage: 1.97MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 16 20:38:16 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^2 + 3); M := RadicalExtension(N, 2, 5); G, phi := UnitGroup(N); G; Output: Magma V2.10-6 Tue Mar 16 2004 20:38:13 on modular [Seed = 118549344] ------------------------------------- Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*G.1 = 0 Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 16 20:40:30 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^2 + 3); M := ext; G, phi := UnitGroup(M); G; Output: Magma V2.10-6 Tue Mar 16 2004 20:40:27 on modular [Seed = 335804669] ------------------------------------- >> M := ext; ^ User error: bad syntax >> G, phi := UnitGroup(M); ^ User error: Identifier 'M' has not been declared or assigned >> G;; ^ User error: Identifier 'G' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 16 20:41:09 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^2 + 3); M := ext; G, phi := UnitGroup(M); G; Output: Magma V2.10-6 Tue Mar 16 2004 20:41:06 on modular [Seed = 3807710770] ------------------------------------- Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*G.1 = 0 Total time: 3.039 seconds, Total memory usage: 1.97MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 16 20:43:11 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^2 + 3); M := ext; G, phi := UnitGroup(M); G; u1 := M!phi(G.1); u1; u2 := M!phi(G.2); u2 Output: Magma V2.10-6 Tue Mar 16 2004 20:43:08 on modular [Seed = 3909027238] ------------------------------------- Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*G.1 = 0 -1 >> u2 := M!phi(G.2); u2; ^ Runtime error in '.': Argument 2 (2) should be in the range [-1 .. 1] >> u2 := M!phi(G.2); u2; ^ User error: Identifier 'u2' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.97MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 16 20:43:17 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^2 + 3); M := ext; G, phi := UnitGroup(M); G; u1 := M!phi(G.1); u1; u2 := M!phi(G.2); u2; Output: Magma V2.10-6 Tue Mar 16 2004 20:43:14 on modular [Seed = 4058389664] ------------------------------------- Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*G.1 = 0 -1 >> u2 := M!phi(G.2); u2;; ^ Runtime error in '.': Argument 2 (2) should be in the range [-1 .. 1] >> u2 := M!phi(G.2); u2;; ^ User error: Identifier 'u2' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.97MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 16 20:43:54 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^2 + 3); M := ext; MinimalPolynomial(M); G, phi := UnitGroup(M); G; u1 := M!phi(G.1); u1; u2 := M!phi(G.2); u2; Output: Magma V2.10-6 Tue Mar 16 2004 20:43:51 on modular [Seed = 4276687819] ------------------------------------- >> MinimalPolynomial(M); ^ Runtime error in 'MinimalPolynomial': Bad argument types Argument types given: FldNum Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*G.1 = 0 -1 >> u2 := M!phi(G.2); u2;; ^ Runtime error in '.': Argument 2 (2) should be in the range [-1 .. 1] >> u2 := M!phi(G.2); u2;; ^ User error: Identifier 'u2' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.97MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 16 20:45:51 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^2 + 3); M := ext; M; G, phi := UnitGroup(M); G; u1 := M!phi(G.1); u1; u2 := M!phi(G.2); u2; Output: Magma V2.10-6 Tue Mar 16 2004 20:45:48 on modular [Seed = 3386778727] ------------------------------------- Number Field with defining polynomial $.1^2 + 5 over N Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*G.1 = 0 -1 >> u2 := M!phi(G.2); u2;; ^ Runtime error in '.': Argument 2 (2) should be in the range [-1 .. 1] >> u2 := M!phi(G.2); u2;; ^ User error: Identifier 'u2' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.97MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 16 20:47:11 2004 Input: F := PolynomialRing(RationalField()); M := ext; M; G, phi := UnitGroup(M); G; Output: Magma V2.10-6 Tue Mar 16 2004 20:47:08 on modular [Seed = 3602987176] ------------------------------------- >> M := ext; ^ Runtime error: No constructor provided for this type of object >> M; ^ User error: Identifier 'M' has not been declared or assigned >> G, phi := UnitGroup(M); ^ User error: Identifier 'M' has not been declared or assigned >> G; ^ User error: Identifier 'G' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 16 20:47:23 2004 Input: F := PolynomialRing(RationalField()); M := ext; M; G, phi := UnitGroup(M); G; Output: Magma V2.10-6 Tue Mar 16 2004 20:47:20 on modular [Seed = 3754439061] ------------------------------------- Number Field with defining polynomial $.1^2 + 5 over its ground field Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*G.1 = 0 Total time: 2.999 seconds, Total memory usage: 1.97MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 16 20:50:06 2004 Input: F := PolynomialRing(RationalField()); M:=NumberField([x^2+ 5, x^2+3]) M; G, phi := UnitGroup(M); G; Output: Magma V2.10-6 Tue Mar 16 2004 20:50:03 on modular [Seed = 2897953285] ------------------------------------- >> M; ^ User error: bad syntax >> G, phi := UnitGroup(M); ^ User error: Identifier 'M' has not been declared or assigned >> G; ^ User error: Identifier 'G' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 16 20:50:33 2004 Input: F := PolynomialRing(RationalField()); M:=NumberField([x^2+ 5, x^2+3]); M; G, phi := UnitGroup(M); G; Output: Magma V2.10-6 Tue Mar 16 2004 20:50:30 on modular [Seed = 3047316273] ------------------------------------- Number Field with defining polynomial $.1^2 + 5 over its ground field Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*G.1 = 0 Total time: 2.949 seconds, Total memory usage: 1.97MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 16 20:52:27 2004 Input: F := PolynomialRing(RationalField()); M:=NumberField([x^2+ 5, x^2+3]); M; G, phi := UnitGroup(M); G; OK:=MaximalOrder(M); Output: Magma V2.10-6 Tue Mar 16 2004 20:52:24 on modular [Seed = 2157408186] ------------------------------------- Number Field with defining polynomial $.1^2 + 5 over its ground field Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*G.1 = 0 Total time: 3.009 seconds, Total memory usage: 1.97MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 16 20:52:44 2004 Input: F := PolynomialRing(RationalField()); M:=NumberField([x^2+ 5, x^2+3]); M; G, phi := UnitGroup(M); G; OK:=MaximalOrder(M); IntegralBasis(OK); Output: Magma V2.10-6 Tue Mar 16 2004 20:52:40 on modular [Seed = 2308859523] ------------------------------------- Number Field with defining polynomial $.1^2 + 5 over its ground field Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*G.1 = 0 >> IntegralBasis(OK); ^ Runtime error in 'IntegralBasis': Bad argument types Argument types given: RngOrd Total time: 3.009 seconds, Total memory usage: 1.97MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 16 20:52:57 2004 Input: F := PolynomialRing(RationalField()); M:=NumberField([x^2+ 5, x^2+3]); M; G, phi := UnitGroup(M); G; OK:=MaximalOrder(M); IntegralBasis(M); Output: Magma V2.10-6 Tue Mar 16 2004 20:52:54 on modular [Seed = 2525067650] ------------------------------------- Number Field with defining polynomial $.1^2 + 5 over its ground field Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*G.1 = 0 [ 1, w ] Total time: 3.029 seconds, Total memory usage: 1.97MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 16 20:54:38 2004 Input: F := PolynomialRing(RationalField()); M:=NumberField([x^2+ 7, x^2+3]); M; G, phi := UnitGroup(M); G; OK:=MaximalOrder(M); IntegralBasis(M); Output: Magma V2.10-6 Tue Mar 16 2004 20:54:35 on modular [Seed = 2626384677] ------------------------------------- Number Field with defining polynomial $.1^2 + 7 over its ground field Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*G.1 = 0 [ 1, 1/2*w + 1/2 ] Total time: 3.029 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Mar 16 20:55:10 2004 Input: F := PolynomialRing(RationalField()); M:=NumberField([x^4+3]); M; G, phi := UnitGroup(M); G; OK:=MaximalOrder(M); IntegralBasis(M); Output: Magma V2.10-6 Tue Mar 16 2004 20:55:07 on modular [Seed = 1753188336] ------------------------------------- Number Field with defining polynomial x^4 + 3 over the Rational Field Abelian Group isomorphic to Z/6 + Z Defined on 2 generators Relations: 6*G.1 = 0 [ 1, w, 1/2*(w^2 - 1), 1/2*(w^3 + w^2 + w + 1) ] Total time: 3.089 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host ALagny-102-1-3-216.w80-11.abo.wanadoo.fr. (80.11.127.216) Time: Wed Mar 17 03:58:11 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Wed Mar 17 2004 03:58:08 on modular [Seed = 1652175141] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (160.80.10.129) Time: Wed Mar 17 04:26:43 2004 Input: PF:= PolynomialRing(GF(5)); P:= PolynomialRing(PF); FF1:= ext; ClassNumber(FF1); Output: Magma V2.10-6 Wed Mar 17 2004 04:26:39 on modular [Seed = 758477963] ------------------------------------- 6 Total time: 3.279 seconds, Total memory usage: 2.15MB ************** MAGMA ***************** Host 3(NXDOMAIN) (160.80.10.129) Time: Wed Mar 17 04:59:14 2004 Input: PF:= PolynomialRing(GF(5)); P:= PolynomialRing(PF); FF1:= ext; ClassNumber(FF1); Output: Magma V2.10-6 Wed Mar 17 2004 04:59:11 on modular [Seed = 3924920559] ------------------------------------- 6 Total time: 3.099 seconds, Total memory usage: 2.15MB ************** MAGMA ***************** Host 3(NXDOMAIN) (160.80.10.129) Time: Wed Mar 17 04:59:26 2004 Input: PF:= PolynomialRing(GF(5)); P:= PolynomialRing(PF); FF1:= ext; ClassNumber(FF1); Output: Magma V2.10-6 Wed Mar 17 2004 04:59:23 on modular [Seed = 3774382578] ------------------------------------- 6 Total time: 3.169 seconds, Total memory usage: 2.15MB ************** MAGMA ***************** Host 3(NXDOMAIN) (160.80.10.129) Time: Wed Mar 17 04:59:38 2004 Input: PF:= PolynomialRing(GF(5)); P:= PolynomialRing(PF); FF1:= ext; ClassNumber(FF1); Output: Magma V2.10-6 Wed Mar 17 2004 04:59:35 on modular [Seed = 4225997333] ------------------------------------- 6 Total time: 3.119 seconds, Total memory usage: 2.15MB ************** MAGMA ***************** Host 3(NXDOMAIN) (160.80.10.129) Time: Wed Mar 17 04:59:49 2004 Input: PF:= PolynomialRing(GF(5)); P:= PolynomialRing(PF); FF1:= ext; ClassNumber(FF1); Output: Magma V2.10-6 Wed Mar 17 2004 04:59:46 on modular [Seed = 4075459337] ------------------------------------- 6 Total time: 3.149 seconds, Total memory usage: 2.15MB ************** MAGMA ***************** Host 3(NXDOMAIN) (160.80.10.129) Time: Wed Mar 17 05:00:12 2004 Input: PF:= PolynomialRing(GF(5)); P:= PolynomialRing(PF); FF1:= ext; ClassNumber(FF1); Output: Magma V2.10-6 Wed Mar 17 2004 05:00:09 on modular [Seed = 3269108482] ------------------------------------- 6 Total time: 3.139 seconds, Total memory usage: 2.15MB ************** MAGMA ***************** Host 3(NXDOMAIN) (160.80.10.129) Time: Wed Mar 17 05:00:26 2004 Input: PF:= PolynomialRing(GF(5)); P:= PolynomialRing(PF); FF1:= ext; ClassNumber(FF1); Output: Magma V2.10-6 Wed Mar 17 2004 05:00:22 on modular [Seed = 3720723458] ------------------------------------- 6 Total time: 3.199 seconds, Total memory usage: 2.15MB ************** MAGMA ***************** Host 3(NXDOMAIN) (160.80.10.129) Time: Wed Mar 17 05:01:03 2004 Input: PF:= PolynomialRing(GF(5)); P:= PolynomialRing(PF); FF1:= ext; ClassNumber(FF1); Output: Magma V2.10-6 Wed Mar 17 2004 05:00:59 on modular [Seed = 3620714085] ------------------------------------- Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Wed Apr 23 11:13:24 EST 2003 Initial seed: 3620714085 Time to this point: 3.49 Error in Riemann-Roch space computation Total time: 3.469 seconds, Total memory usage: 6.93MB ************** MAGMA ***************** Host 3(NXDOMAIN) (160.80.10.129) Time: Wed Mar 17 05:01:46 2004 Input: PF:= PolynomialRing(GF(5)); P:= PolynomialRing(PF); FF1:= ext; ClassNumber(FF1); Output: Magma V2.10-6 Wed Mar 17 2004 05:01:43 on modular [Seed = 2963854046] ------------------------------------- 6 Total time: 3.119 seconds, Total memory usage: 2.15MB ************** MAGMA ***************** Host 3(NXDOMAIN) (160.80.10.129) Time: Wed Mar 17 05:02:00 2004 Input: PF:= PolynomialRing(GF(5)); P:= PolynomialRing(PF); FF1:= ext; ClassNumber(FF1); Output: Magma V2.10-6 Wed Mar 17 2004 05:01:57 on modular [Seed = 2341726711] ------------------------------------- 6 Total time: 3.269 seconds, Total memory usage: 2.15MB ************** MAGMA ***************** Host 3(NXDOMAIN) (160.80.10.129) Time: Wed Mar 17 05:02:27 2004 Input: PF:= PolynomialRing(GF(5)); P:= PolynomialRing(PF); FF1:= ext; ClassNumber(FF1); Output: Magma V2.10-6 Wed Mar 17 2004 05:02:24 on modular [Seed = 2241718236] ------------------------------------- 6 Total time: 3.219 seconds, Total memory usage: 2.15MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 05:19:51 2004 Input: /*Sessio 2*/ G2:=GF(2); G3:=GF(3); G5:=GF(5); /* Z9 no es un cos, ja que nou no es un nombre primer */ Z9:=Integers(9); /* [a]m pertanyent a Zm es invertible sii mcd(a,m)=1*/ IsInvertible(Z9!3); s:=GF(3,2); p:=PolynomialRing(s); f:= 2+2*x+x^2; Factorization(f); Roots(f,s); IsIrreducible(f); s1:=GF(2,4); p1:=PolynomialRing(s1); f1:= 1+x+x^4; Factorization(f1); Roots(f1,s1); IsIrreducible(f1); s2:=GF(5,2); p2:=PolynomialRing(s2); f2:= 3+2*x+x^2; Factorization(f2); Roots(f2,s2); IsIrreducible(f2); s3:=GF(3,2); p3:=PolynomialRing(s3); f3:= 1+2*x+x^2; Factorization(f3); Roots(f3); IsIrreducible(f3); Output: Magma V2.10-6 Wed Mar 17 2004 05:19:48 on modular [Seed = 1702691659] ------------------------------------- false [ , ] [ , ] false [ , , , ] [ , , , ] false [ , ] [ , ] false [ ] [ <2, 2> ] false Total time: 2.969 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 05:20:56 2004 Input: /*Sessio 2*/ /*Pregunta 1*/ /*Apartat 1*/ GF(2); GF(3); GF(5); /*Apartat 2*/ /* Z9 no es un cos, ja que nou no es un nombre primer */ Z9:=Integers(9); /* [a]m pertanyent a Zm es invertible sii mcd(a,m)=1*/ IsInvertible(Z9!3); s:=GF(3,2); p:=PolynomialRing(s); f:= 2+2*x+x^2; Factorization(f); Roots(f,s); IsIrreducible(f); s1:=GF(2,4); p1:=PolynomialRing(s1); f1:= 1+x+x^4; Factorization(f1); Roots(f1,s1); IsIrreducible(f1); s2:=GF(5,2); p2:=PolynomialRing(s2); f2:= 3+2*x+x^2; Factorization(f2); Roots(f2,s2); IsIrreducible(f2); s3:=GF(3,2); p3:=PolynomialRing(s3); f3:= 1+2*x+x^2; Factorization(f3); Roots(f3); IsIrreducible(f3); Output: Magma V2.10-6 Wed Mar 17 2004 05:20:53 on modular [Seed = 1246899365] ------------------------------------- Finite field of size 2 Finite field of size 3 Finite field of size 5 false [ , ] [ , ] false [ , , , ] [ , , , ] false [ , ] [ , ] false [ ] [ <2, 2> ] false Total time: 2.929 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 05:21:20 2004 Input: /*Sessio 2*/ /*Pregunta 1*/ /*Apartat 1*/ G2 := GF(2); G3 := GF(3); G5 := GF(5); /*Apartat 2*/ /* Z9 no es un cos, ja que nou no es un nombre primer */ Z9:=Integers(9); /* [a]m pertanyent a Zm es invertible sii mcd(a,m)=1*/ IsInvertible(Z9!3); s:=GF(3,2); p:=PolynomialRing(s); f:= 2+2*x+x^2; Factorization(f); Roots(f,s); IsIrreducible(f); s1:=GF(2,4); p1:=PolynomialRing(s1); f1:= 1+x+x^4; Factorization(f1); Roots(f1,s1); IsIrreducible(f1); s2:=GF(5,2); p2:=PolynomialRing(s2); f2:= 3+2*x+x^2; Factorization(f2); Roots(f2,s2); IsIrreducible(f2); s3:=GF(3,2); p3:=PolynomialRing(s3); f3:= 1+2*x+x^2; Factorization(f3); Roots(f3); IsIrreducible(f3); Output: Magma V2.10-6 Wed Mar 17 2004 05:21:17 on modular [Seed = 1130046900] ------------------------------------- false [ , ] [ , ] false [ , , , ] [ , , , ] false [ , ] [ , ] false [ ] [ <2, 2> ] false Total time: 3.009 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 05:27:22 2004 Input: /*Sessio 2*/ /*Pregunta 1*/ /*Apartat 1*/ G2 := GF(2); G3 := GF(3); G5 := GF(5); Terms(G2); Terms(G3); Terms(G5); /*Apartat 2*/ /* Z9 no es un cos, ja que nou no es un nombre primer */ Z9:=Integers(9); /* [a]m pertanyent a Zm es invertible sii mcd(a,m)=1*/ IsInvertible(Z9!3); /*Apartat 3*/ s:=GF(3,2); p:=PolynomialRing(s); f:= 2+2*x+x^2; Factorization(f); Roots(f,s); IsIrreducible(f); s1:=GF(2,4); p1:=PolynomialRing(s1); f1:= 1+x+x^4; Factorization(f1); Roots(f1,s1); IsIrreducible(f1); s2:=GF(5,2); p2:=PolynomialRing(s2); f2:= 3+2*x+x^2; Factorization(f2); Roots(f2,s2); IsIrreducible(f2); s3:=GF(3,2); p3:=PolynomialRing(s3); f3:= 1+2*x+x^2; Factorization(f3); Roots(f3); IsIrreducible(f3); Output: Magma V2.10-6 Wed Mar 17 2004 05:27:19 on modular [Seed = 1447968315] ------------------------------------- >> Terms(G2); Terms(G3); Terms(G5); ^ Runtime error in 'Terms': Bad argument types Argument types given: FldFin >> Terms(G2); Terms(G3); Terms(G5); ^ Runtime error in 'Terms': Bad argument types Argument types given: FldFin >> Terms(G2); Terms(G3); Terms(G5); ^ Runtime error in 'Terms': Bad argument types Argument types given: FldFin false [ , ] [ , ] false [ , , , ] [ , , , ] false [ , ] [ , ] false [ ] [ <2, 2> ] false Total time: 3.199 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (160.80.10.129) Time: Wed Mar 17 05:27:33 2004 Input: PF:= PolynomialRing(GF(5)); P:= PolynomialRing(PF); FF1:= ext; ClassNumber(FF1); Output: Magma V2.10-6 Wed Mar 17 2004 05:27:15 on modular [Seed = 1397439293] ------------------------------------- 107226 Total time: 15.679 seconds, Total memory usage: 5.13MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 05:28:04 2004 Input: /*Sessio 2*/ /*Pregunta 1*/ /*Apartat 1*/ G2 := GF(2); G3 := GF(3); G5 := GF(5); /*Apartat 2*/ /* Z9 no es un cos, ja que nou no es un nombre primer */ Z9:=Integers(9); /* [a]m pertanyent a Zm es invertible sii mcd(a,m)=1*/ IsInvertible(Z9!3); /*Apartat 3*/ s:=GF(3,2); p:=PolynomialRing(s); f:= 2+2*x+x^2; Factorization(f); Roots(f,s); IsIrreducible(f); s1:=GF(2,4); p1:=PolynomialRing(s1); f1:= 1+x+x^4; Factorization(f1); Roots(f1,s1); IsIrreducible(f1); s2:=GF(5,2); p2:=PolynomialRing(s2); f2:= 3+2*x+x^2; Factorization(f2); Roots(f2,s2); IsIrreducible(f2); s3:=GF(3,2); p3:=PolynomialRing(s3); f3:= 1+2*x+x^2; Factorization(f3); Roots(f3); IsIrreducible(f3); Output: Magma V2.10-6 Wed Mar 17 2004 05:28:01 on modular [Seed = 1042699877] ------------------------------------- false [ , ] [ , ] false [ , , , ] [ , , , ] false [ , ] [ , ] false [ ] [ <2, 2> ] false Total time: 2.989 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (160.80.10.129) Time: Wed Mar 17 05:28:58 2004 Input: PF:= PolynomialRing(GF(5)); P:= PolynomialRing(PF); FF1:= ext; ClassNumber(FF1); Output: Magma V2.10-6 Wed Mar 17 2004 05:28:39 on modular [Seed = 925851402] ------------------------------------- 157104 Total time: 18.299 seconds, Total memory usage: 5.64MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 05:28:58 2004 Input: /*Sessio 2*/ /*Pregunta 1*/ /*Apartat 1*/ G2 := GF(2); G3 := GF(3); G5 := GF(5); G2; /*Apartat 2*/ /* Z9 no es un cos, ja que nou no es un nombre primer */ Z9:=Integers(9); /* [a]m pertanyent a Zm es invertible sii mcd(a,m)=1*/ IsInvertible(Z9!3); /*Apartat 3*/ s:=GF(3,2); p:=PolynomialRing(s); f:= 2+2*x+x^2; Factorization(f); Roots(f,s); IsIrreducible(f); s1:=GF(2,4); p1:=PolynomialRing(s1); f1:= 1+x+x^4; Factorization(f1); Roots(f1,s1); IsIrreducible(f1); s2:=GF(5,2); p2:=PolynomialRing(s2); f2:= 3+2*x+x^2; Factorization(f2); Roots(f2,s2); IsIrreducible(f2); s3:=GF(3,2); p3:=PolynomialRing(s3); f3:= 1+2*x+x^2; Factorization(f3); Roots(f3); IsIrreducible(f3); Output: Magma V2.10-6 Wed Mar 17 2004 05:28:54 on modular [Seed = 168976902] ------------------------------------- Finite field of size 2 false [ , ] [ , ] false [ , , , ] [ , , , ] false [ , ] [ , ] false [ ] [ <2, 2> ] false Total time: 4.299 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 05:29:40 2004 Input: /*Sessio 2*/ /*Pregunta 1*/ /*Apartat 1*/ G2 := GF(2); G3 := GF(3); G5 := GF(5); G2!1; /*Apartat 2*/ /* Z9 no es un cos, ja que nou no es un nombre primer */ Z9:=Integers(9); /* [a]m pertanyent a Zm es invertible sii mcd(a,m)=1*/ IsInvertible(Z9!3); /*Apartat 3*/ s:=GF(3,2); p:=PolynomialRing(s); f:= 2+2*x+x^2; Factorization(f); Roots(f,s); IsIrreducible(f); s1:=GF(2,4); p1:=PolynomialRing(s1); f1:= 1+x+x^4; Factorization(f1); Roots(f1,s1); IsIrreducible(f1); s2:=GF(5,2); p2:=PolynomialRing(s2); f2:= 3+2*x+x^2; Factorization(f2); Roots(f2,s2); IsIrreducible(f2); s3:=GF(3,2); p3:=PolynomialRing(s3); f3:= 1+2*x+x^2; Factorization(f3); Roots(f3); IsIrreducible(f3); Output: Magma V2.10-6 Wed Mar 17 2004 05:29:37 on modular [Seed = 436368097] ------------------------------------- 1 false [ , ] [ , ] false [ , , , ] [ , , , ] false [ , ] [ , ] false [ ] [ <2, 2> ] false Total time: 3.119 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 05:29:49 2004 Input: /*Sessio 2*/ /*Pregunta 1*/ /*Apartat 1*/ G2 := GF(2); G3 := GF(3); G5 := GF(5); G2!2; /*Apartat 2*/ /* Z9 no es un cos, ja que nou no es un nombre primer */ Z9:=Integers(9); /* [a]m pertanyent a Zm es invertible sii mcd(a,m)=1*/ IsInvertible(Z9!3); /*Apartat 3*/ s:=GF(3,2); p:=PolynomialRing(s); f:= 2+2*x+x^2; Factorization(f); Roots(f,s); IsIrreducible(f); s1:=GF(2,4); p1:=PolynomialRing(s1); f1:= 1+x+x^4; Factorization(f1); Roots(f1,s1); IsIrreducible(f1); s2:=GF(5,2); p2:=PolynomialRing(s2); f2:= 3+2*x+x^2; Factorization(f2); Roots(f2,s2); IsIrreducible(f2); s3:=GF(3,2); p3:=PolynomialRing(s3); f3:= 1+2*x+x^2; Factorization(f3); Roots(f3); IsIrreducible(f3); Output: Magma V2.10-6 Wed Mar 17 2004 05:29:45 on modular [Seed = 370048741] ------------------------------------- 0 false [ , ] [ , ] false [ , , , ] [ , , , ] false [ , ] [ , ] false [ ] [ <2, 2> ] false Total time: 3.199 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (160.80.10.129) Time: Wed Mar 17 05:29:57 2004 Input: PF:= PolynomialRing(GF(5)); P:= PolynomialRing(PF); FF1:= ext; ClassNumber(FF1); Output: Magma V2.10-6 Wed Mar 17 2004 05:29:40 on modular [Seed = 419525095] ------------------------------------- 73152 Total time: 16.869 seconds, Total memory usage: 5.11MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 05:30:04 2004 Input: /*Sessio 2*/ /*Pregunta 1*/ /*Apartat 1*/ G2 := GF(2); G3 := GF(3); G5 := GF(5); G2!3; /*Apartat 2*/ /* Z9 no es un cos, ja que nou no es un nombre primer */ Z9:=Integers(9); /* [a]m pertanyent a Zm es invertible sii mcd(a,m)=1*/ IsInvertible(Z9!3); /*Apartat 3*/ s:=GF(3,2); p:=PolynomialRing(s); f:= 2+2*x+x^2; Factorization(f); Roots(f,s); IsIrreducible(f); s1:=GF(2,4); p1:=PolynomialRing(s1); f1:= 1+x+x^4; Factorization(f1); Roots(f1,s1); IsIrreducible(f1); s2:=GF(5,2); p2:=PolynomialRing(s2); f2:= 3+2*x+x^2; Factorization(f2); Roots(f2,s2); IsIrreducible(f2); s3:=GF(3,2); p3:=PolynomialRing(s3); f3:= 1+2*x+x^2; Factorization(f3); Roots(f3); IsIrreducible(f3); Output: Magma V2.10-6 Wed Mar 17 2004 05:30:01 on modular [Seed = 4175466555] ------------------------------------- 1 false [ , ] [ , ] false [ , , , ] [ , , , ] false [ , ] [ , ] false [ ] [ <2, 2> ] false Total time: 3.049 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (160.80.10.129) Time: Wed Mar 17 05:31:01 2004 Input: PF:= PolynomialRing(GF(5)); P:= PolynomialRing(PF); FF1:= ext; ClassNumber(FF1); Output: Magma V2.10-6 Wed Mar 17 2004 05:30:41 on modular [Seed = 4142833229] ------------------------------------- 98586 Total time: 19.920 seconds, Total memory usage: 5.73MB ************** MAGMA ***************** Host 3(NXDOMAIN) (160.80.10.129) Time: Wed Mar 17 05:32:01 2004 Input: PF:= PolynomialRing(GF(5)); P:= PolynomialRing(PF); FF1:= ext; ClassNumber(FF1); Output: Magma V2.10-6 Wed Mar 17 2004 05:31:40 on modular [Seed = 3436488106] ------------------------------------- 98136 Total time: 20.329 seconds, Total memory usage: 5.76MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 05:32:23 2004 Input: /*Sessio 2*/ /*Pregunta 1*/ /*Apartat 1*/ G2 := GF(2); G3 := GF(3); G5 := GF(5); G2!0;G2!1;G2!2; G3!0;G3!1;G3!2;G3!3; /*Apartat 2*/ /* Z9 no es un cos, ja que nou no es un nombre primer */ Z9:=Integers(9); /* [a]m pertanyent a Zm es invertible sii mcd(a,m)=1*/ IsInvertible(Z9!3); /*Apartat 3*/ s:=GF(3,2); p:=PolynomialRing(s); f:= 2+2*x+x^2; Factorization(f); Roots(f,s); IsIrreducible(f); s1:=GF(2,4); p1:=PolynomialRing(s1); f1:= 1+x+x^4; Factorization(f1); Roots(f1,s1); IsIrreducible(f1); s2:=GF(5,2); p2:=PolynomialRing(s2); f2:= 3+2*x+x^2; Factorization(f2); Roots(f2,s2); IsIrreducible(f2); s3:=GF(3,2); p3:=PolynomialRing(s3); f3:= 1+2*x+x^2; Factorization(f3); Roots(f3); IsIrreducible(f3); Output: Magma V2.10-6 Wed Mar 17 2004 05:32:20 on modular [Seed = 3319639195] ------------------------------------- 0 1 0 0 1 2 0 false [ , ] [ , ] false [ , , , ] [ , , , ] false [ , ] [ , ] false [ ] [ <2, 2> ] false Total time: 2.929 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (160.80.10.129) Time: Wed Mar 17 05:32:57 2004 Input: PF:= PolynomialRing(GF(5)); P:= PolynomialRing(PF); FF1:= ext; ClassNumber(FF1); Output: Magma V2.10-6 Wed Mar 17 2004 05:32:39 on modular [Seed = 3536501759] ------------------------------------- 84240 Total time: 18.010 seconds, Total memory usage: 5.33MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 05:33:29 2004 Input: /*Apartat 2*/ /* Z9 no es un cos, ja que nou no es un nombre primer */ Z9:=Integers(9); /* [a]m pertanyent a Zm es invertible sii mcd(a,m)=1*/ IsInvertible(Z9!3); /*Apartat 3*/ s:=GF(3,2); p:=PolynomialRing(s); f:= 2+2*x+x^2; Factorization(f); Roots(f,s); IsIrreducible(f); s1:=GF(2,4); p1:=PolynomialRing(s1); f1:= 1+x+x^4; Factorization(f1); Roots(f1,s1); IsIrreducible(f1); s2:=GF(5,2); p2:=PolynomialRing(s2); f2:= 3+2*x+x^2; Factorization(f2); Roots(f2,s2); IsIrreducible(f2); s3:=GF(3,2); p3:=PolynomialRing(s3); f3:= 1+2*x+x^2; Factorization(f3); Roots(f3); IsIrreducible(f3); Output: Magma V2.10-6 Wed Mar 17 2004 05:33:26 on modular [Seed = 2880684727] ------------------------------------- false [ , ] [ , ] false [ , , , ] [ , , , ] false [ , ] [ , ] false [ ] [ <2, 2> ] false Total time: 2.919 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 05:34:09 2004 Input: /*Apartat 3*/ s:=GF(3,2); p:=PolynomialRing(s); f:= 2+2*x+x^2; Factorization(f); Roots(f,s); IsIrreducible(f); s1:=GF(2,4); p1:=PolynomialRing(s1); f1:= 1+x+x^4; Factorization(f1); Roots(f1,s1); IsIrreducible(f1); s2:=GF(5,2); p2:=PolynomialRing(s2); f2:= 3+2*x+x^2; Factorization(f2); Roots(f2,s2); IsIrreducible(f2); s3:=GF(3,2); p3:=PolynomialRing(s3); f3:= 1+2*x+x^2; Factorization(f3); Roots(f3); IsIrreducible(f3); Output: Magma V2.10-6 Wed Mar 17 2004 05:34:06 on modular [Seed = 2814365267] ------------------------------------- [ , ] [ , ] false [ , , , ] [ , , , ] false [ , ] [ , ] false [ ] [ <2, 2> ] false Total time: 3.219 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (160.80.10.129) Time: Wed Mar 17 05:34:15 2004 Input: PF:= PolynomialRing(GF(5)); P:= PolynomialRing(PF); FF1:= ext; ClassNumber(FF1); Output: Magma V2.10-6 Wed Mar 17 2004 05:33:59 on modular [Seed = 2696464733] ------------------------------------- 106938 Total time: 15.239 seconds, Total memory usage: 4.82MB ************** MAGMA ***************** Host 3(NXDOMAIN) (160.80.10.129) Time: Wed Mar 17 05:34:56 2004 Input: PF:= PolynomialRing(GF(5)); P:= PolynomialRing(PF); FF1:= ext; ClassNumber(FF1); Output: Magma V2.10-6 Wed Mar 17 2004 05:34:38 on modular [Seed = 3081756259] ------------------------------------- 122418 Total time: 17.119 seconds, Total memory usage: 5.54MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 05:35:19 2004 Input: s:=GF(3,2); p:=PolynomialRing(s); f:= 2+2*x+x^2; Factorization(f); Roots(f,s); IsIrreducible(f); Output: Magma V2.10-6 Wed Mar 17 2004 05:35:16 on modular [Seed = 2157504782] ------------------------------------- [ , ] [ , ] false Total time: 2.889 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (160.80.10.129) Time: Wed Mar 17 05:35:36 2004 Input: PF:= PolynomialRing(GF(5)); P:= PolynomialRing(PF); FF1:= ext; ClassNumber(FF1); Output: Magma V2.10-6 Wed Mar 17 2004 05:35:20 on modular [Seed = 2575429659] ------------------------------------- 93024 Total time: 15.359 seconds, Total memory usage: 5.07MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 05:35:52 2004 Input: s:=GF(3); p:=PolynomialRing(s); f:= 2+2*x+x^2; Factorization(f); Roots(f,s); IsIrreducible(f); Output: Magma V2.10-6 Wed Mar 17 2004 05:35:49 on modular [Seed = 2542796280] ------------------------------------- [ ] [] true Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 05:36:15 2004 Input: s:=GF(3); p:=PolynomialRing(s); f:= 2+2*x+x^2; Factorization(f); Roots(f,s); IsIrreducible(f); Output: Magma V2.10-6 Wed Mar 17 2004 05:36:12 on modular [Seed = 1652164629] ------------------------------------- [ ] [] true Total time: 3.169 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (160.80.10.129) Time: Wed Mar 17 05:36:19 2004 Input: PF:= PolynomialRing(GF(5)); P:= PolynomialRing(PF); FF1:= ext; ClassNumber(FF1); Output: Magma V2.10-6 Wed Mar 17 2004 05:36:05 on modular [Seed = 1836386067] ------------------------------------- 94284 Total time: 14.459 seconds, Total memory usage: 4.95MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 05:36:35 2004 Input: f:= 2+2*x+x^2; Factorization(f); Roots(f,s); IsIrreducible(f); Output: Magma V2.10-6 Wed Mar 17 2004 05:36:32 on modular [Seed = 1936398632] ------------------------------------- >> f:= 2+2*x+x^2; ^ User error: Identifier 'x' has not been declared or assigned >> Factorization(f); ^ User error: Identifier 'f' has not been declared or assigned >> Roots(f,s); ^ User error: Identifier 'f' has not been declared or assigned >> IsIrreducible(f);; ^ User error: Identifier 'f' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 05:36:44 2004 Input: s:=GF(3); p:=PolynomialRing(s); f:= 2+2*x+x^2; Factorization(f); Roots(f,s); IsIrreducible(f); Output: Magma V2.10-6 Wed Mar 17 2004 05:36:41 on modular [Seed = 1246896152] ------------------------------------- [ ] [] true Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 05:37:00 2004 Input: s1:=GF(2,4); p1:=PolynomialRing(s1); f1:= 1+x+x^4; Factorization(f1); Roots(f1,s1); IsIrreducible(f1); Output: Magma V2.10-6 Wed Mar 17 2004 05:36:57 on modular [Seed = 1096362851] ------------------------------------- [ , , , ] [ , , , ] false Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 05:37:07 2004 Input: s1:=GF(2); p1:=PolynomialRing(s1); f1:= 1+x+x^4; Factorization(f1); Roots(f1,s1); IsIrreducible(f1); Output: Magma V2.10-6 Wed Mar 17 2004 05:37:04 on modular [Seed = 1480602211] ------------------------------------- [ ] [] true Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (160.80.10.129) Time: Wed Mar 17 05:37:24 2004 Input: PF:= PolynomialRing(GF(5)); P:= PolynomialRing(PF); FF1:= ext; ClassNumber(FF1); Output: Magma V2.10-6 Wed Mar 17 2004 05:37:09 on modular [Seed = 1464810857] ------------------------------------- 93024 Total time: 15.309 seconds, Total memory usage: 5.08MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 05:37:33 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); f2:= 3+2*x+x^2; Factorization(f2); Roots(f2,s2); IsIrreducible(f2); Output: Magma V2.10-6 Wed Mar 17 2004 05:37:30 on modular [Seed = 775308335] ------------------------------------- [ ] [] true Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 05:38:01 2004 Input: s3:=GF(3); p3:=PolynomialRing(s3); f3:= 1+2*x+x^2; Factorization(f3); Roots(f3); IsIrreducible(f3); Output: Magma V2.10-6 Wed Mar 17 2004 05:37:57 on modular [Seed = 624775115] ------------------------------------- [ ] [ <2, 2> ] false Total time: 3.629 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 05:38:14 2004 Input: s3:=GF(5); p3:=PolynomialRing(s3); f3:= 1+2*x+x^2; Factorization(f3); Roots(f3); IsIrreducible(f3); Output: Magma V2.10-6 Wed Mar 17 2004 05:38:10 on modular [Seed = 824794056] ------------------------------------- [ ] [ <4, 2> ] false Total time: 3.639 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (160.80.10.129) Time: Wed Mar 17 05:38:15 2004 Input: PF:= PolynomialRing(GF(5)); P:= PolynomialRing(PF); FF1:= ext; ClassNumber(FF1); Output: Magma V2.10-6 Wed Mar 17 2004 05:37:58 on modular [Seed = 975327447] ------------------------------------- 93006 Total time: 16.629 seconds, Total memory usage: 5.11MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 05:38:23 2004 Input: s3:=GF(7); p3:=PolynomialRing(s3); f3:= 1+2*x+x^2; Factorization(f3); Roots(f3); IsIrreducible(f3); Output: Magma V2.10-6 Wed Mar 17 2004 05:38:20 on modular [Seed = 35285237] ------------------------------------- [ ] [ <6, 2> ] false Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 05:38:41 2004 Input: s3:=GF(2); p3:=PolynomialRing(s3); f3:= 1+2*x+x^2; Factorization(f3); Roots(f3); IsIrreducible(f3); Output: Magma V2.10-6 Wed Mar 17 2004 05:38:38 on modular [Seed = 419525596] ------------------------------------- [ ] [ <1, 2> ] false Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 05:39:09 2004 Input: s3:=GF(3); p3:=PolynomialRing(s3); f3:= 1+2*x+x^2; Factorization(f3); Roots(f3); IsIrreducible(f3); Output: Magma V2.10-6 Wed Mar 17 2004 05:39:06 on modular [Seed = 268991153] ------------------------------------- [ ] [ <2, 2> ] false Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (160.80.10.129) Time: Wed Mar 17 05:41:47 2004 Input: PF:= PolynomialRing(GF(5)); P:= PolynomialRing(PF); FF1:= ext; ClassNumber(FF1); Output: Magma V2.10-6 Wed Mar 17 2004 05:41:43 on modular [Seed = 3875442154] ------------------------------------- 879 Total time: 3.949 seconds, Total memory usage: 2.25MB ************** MAGMA ***************** Host 3(NXDOMAIN) (160.80.10.129) Time: Wed Mar 17 05:42:27 2004 Input: PF:= PolynomialRing(GF(5)); P:= PolynomialRing(PF); FF1:= ext; ClassNumber(FF1); Output: Magma V2.10-6 Wed Mar 17 2004 05:42:24 on modular [Seed = 4259681798] ------------------------------------- >> 4 + 7*x^3 + 5*x^2 + 4*x + 1)>; ^ User error: bad syntax >> ClassNumber(FF1);; ^ User error: Identifier 'FF1' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (160.80.10.129) Time: Wed Mar 17 05:42:43 2004 Input: PF:= PolynomialRing(GF(5)); P:= PolynomialRing(PF); FF1:= ext; ClassNumber(FF1); Output: Magma V2.10-6 Wed Mar 17 2004 05:42:39 on modular [Seed = 4109147904] ------------------------------------- 987 Total time: 4.009 seconds, Total memory usage: 2.35MB ************** MAGMA ***************** Host 3(NXDOMAIN) (160.80.10.129) Time: Wed Mar 17 05:43:36 2004 Input: PF:= PolynomialRing(GF(5)); P:= PolynomialRing(PF); FF1:= ext; ClassNumber(FF1); Output: Magma V2.10-6 Wed Mar 17 2004 05:43:32 on modular [Seed = 3285952636] ------------------------------------- 987 Total time: 4.109 seconds, Total memory usage: 2.35MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 05:43:38 2004 Input: s:=GF(3); p:=PolynomialRing(s3); G9 := ext < p | 2+2*x+x^2 >; Output: Magma V2.10-6 Wed Mar 17 2004 05:43:35 on modular [Seed = 3235425148] ------------------------------------- >> p:=PolynomialRing(s3); ^ User error: Identifier 's3' has not been declared or assigned >> G9 := ext < p | 2+2*x+x^2 >; ^ User error: Identifier 'p' has not been declared or assigned Total time: 3.109 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 05:44:00 2004 Input: s:=GF(3); p:=PolynomialRing(s); G9 := ext < p | 2+2*x+x^2 >; Output: Magma V2.10-6 Wed Mar 17 2004 05:43:57 on modular [Seed = 3603873104] ------------------------------------- >> G9 := ext < p | 2+2*x+x^2 >; ^ Runtime error: No constructor provided for this type of object Total time: 3.499 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (160.80.10.129) Time: Wed Mar 17 05:44:01 2004 Input: PF:= PolynomialRing(GF(5)); P:= PolynomialRing(PF); FF1:= ext; ClassNumber(FF1); Output: Magma V2.10-6 Wed Mar 17 2004 05:43:56 on modular [Seed = 3519658582] ------------------------------------- 663 Total time: 5.250 seconds, Total memory usage: 2.65MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 05:44:20 2004 Input: s:=GF(3); p:=PolynomialRing(s); G9 := ext< p | 2+2*x+x^2 >; Output: Magma V2.10-6 Wed Mar 17 2004 05:44:17 on modular [Seed = 2797521612] ------------------------------------- >> G9 := ext< p | 2+2*x+x^2 >; ^ Runtime error: No constructor provided for this type of object Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 05:44:45 2004 Input: s:=GF(3); p:=PolynomialRing(s); G9 := ext< s | 2+2*x+x^2 >; Output: Magma V2.10-6 Wed Mar 17 2004 05:44:42 on modular [Seed = 3181760972] ------------------------------------- Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (160.80.10.129) Time: Wed Mar 17 05:44:49 2004 Input: PF:= PolynomialRing(GF(5)); P:= PolynomialRing(PF); FF1:= ext; ClassNumber(FF1); Output: Magma V2.10-6 Wed Mar 17 2004 05:44:45 on modular [Seed = 3031226562] ------------------------------------- 987 Total time: 4.009 seconds, Total memory usage: 2.35MB ************** MAGMA ***************** Host 3(NXDOMAIN) (160.80.10.129) Time: Wed Mar 17 05:45:12 2004 Input: PF:= PolynomialRing(GF(5)); P:= PolynomialRing(PF); FF1:= ext; ClassNumber(FF1); Output: Magma V2.10-6 Wed Mar 17 2004 05:45:08 on modular [Seed = 2275404760] ------------------------------------- 864 Total time: 4.009 seconds, Total memory usage: 2.35MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 05:45:30 2004 Input: s:=GF(3); p:=PolynomialRing(s); G9 := ext< s | 2+2*x+x^2 >; s1:=GF(3); p1:=PolynomialRing(s1); G9b := ext< s1 | 1+2*x+x^2 >; Output: Magma V2.10-6 Wed Mar 17 2004 05:45:27 on modular [Seed = 2659644082] ------------------------------------- >> G9b := ext< s1 | 1+2*x+x^2 >; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 05:47:30 2004 Input: s2:=GF(2); G16 := ext< s | 1+x+x^4 >; Output: Magma V2.10-6 Wed Mar 17 2004 05:47:27 on modular [Seed = 1819541695] ------------------------------------- >> G16 := ext< s | 1+x+x^4 >;; ^ User error: Identifier 's' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 05:47:37 2004 Input: s2:=GF(2); G16 := ext< s2 | 1+x+x^4 >; Output: Magma V2.10-6 Wed Mar 17 2004 05:47:34 on modular [Seed = 1702693327] ------------------------------------- >> G16 := ext< s2 | 1+x+x^4 >;; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 05:47:58 2004 Input: s2:=GF(2); p2:=PolynomialRing(s2); G16 := ext< s2 | 1+x+x^4 >; Output: Magma V2.10-6 Wed Mar 17 2004 05:47:55 on modular [Seed = 2120618697] ------------------------------------- Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 05:49:12 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; Output: Magma V2.10-6 Wed Mar 17 2004 05:49:09 on modular [Seed = 2003769918] ------------------------------------- Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 05:49:31 2004 Input: s4:=GF(3); G9b := ext< s4 | 1+2*x+x^2 >; Output: Magma V2.10-6 Wed Mar 17 2004 05:49:28 on modular [Seed = 1213211932] ------------------------------------- >> G9b := ext< s4 | 1+2*x+x^2 >;; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 05:49:47 2004 Input: s4:=GF(3); p4:=PolynomialRing(s4); G9b := ext< s4 | 1+2*x+x^2 >; Output: Magma V2.10-6 Wed Mar 17 2004 05:49:44 on modular [Seed = 1096363109] ------------------------------------- >> G9b := ext< s4 | 1+2*x+x^2 >;; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (160.80.10.129) Time: Wed Mar 17 05:52:15 2004 Input: PF:= PolynomialRing(GF(7)); P:= PolynomialRing(PF); FF1:= ext; ClassNumber(FF1); Output: Magma V2.10-6 Wed Mar 17 2004 05:52:08 on modular [Seed = 1397440231] ------------------------------------- 929100 Total time: 7.919 seconds, Total memory usage: 3.42MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 05:52:32 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; Output: Magma V2.10-6 Wed Mar 17 2004 05:52:29 on modular [Seed = 607930789] ------------------------------------- Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (160.80.10.129) Time: Wed Mar 17 05:54:24 2004 Input: PF:= PolynomialRing(GF(7)); P:= PolynomialRing(PF); FF1:= ext; ClassNumber(FF1); Output: Magma V2.10-6 Wed Mar 17 2004 05:54:16 on modular [Seed = 1042698250] ------------------------------------- 929100 Total time: 7.509 seconds, Total memory usage: 3.42MB ************** MAGMA ***************** Host 3(NXDOMAIN) (160.80.10.129) Time: Wed Mar 17 05:56:01 2004 Input: PF:= PolynomialRing(GF(7)); P:= PolynomialRing(PF); FF1:= ext; ClassNumber(FF1); Output: Magma V2.10-6 Wed Mar 17 2004 05:55:57 on modular [Seed = 219505628] ------------------------------------- 3 Total time: 3.099 seconds, Total memory usage: 2.12MB ************** MAGMA ***************** Host 3(NXDOMAIN) (160.80.10.129) Time: Wed Mar 17 05:56:14 2004 Input: PF:= PolynomialRing(GF(7)); P:= PolynomialRing(PF); FF1:= ext; ClassNumber(FF1); Output: Magma V2.10-6 Wed Mar 17 2004 05:56:10 on modular [Seed = 102656160] ------------------------------------- 9 Total time: 3.369 seconds, Total memory usage: 2.12MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 05:56:42 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; {Order(n) : n in G25 | n ne 0 }; Output: Magma V2.10-6 Wed Mar 17 2004 05:56:39 on modular [Seed = 520581524] ------------------------------------- { 1, 2, 3, 4, 6, 8, 12, 24 } Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 05:58:06 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; {Order(n) : n in G25 | n ne 0 }; {n : n in G25 | IsPrimitive(n) }; Output: Magma V2.10-6 Wed Mar 17 2004 05:58:03 on modular [Seed = 319519812] ------------------------------------- { 1, 2, 3, 4, 6, 8, 12, 24 } { G25.1^11, G25.1, G25.1^23, G25.1^13, G25.1^5, G25.1^17, G25.1^7, G25.1^19 } Total time: 3.499 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (160.80.10.129) Time: Wed Mar 17 05:58:11 2004 Input: PF:= PolynomialRing(GF(7)); P:= PolynomialRing(PF); FF1:= ext; ClassNumber(FF1); Output: Magma V2.10-6 Wed Mar 17 2004 05:58:02 on modular [Seed = 268992326] ------------------------------------- 1034532 Total time: 8.869 seconds, Total memory usage: 3.62MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 05:58:49 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; {Order(n) : n in G25 | n ne 0 }; m := {n : n in G25 | IsPrimitive(n) }; #m; Output: Magma V2.10-6 Wed Mar 17 2004 05:58:46 on modular [Seed = 4276523508] ------------------------------------- { 1, 2, 3, 4, 6, 8, 12, 24 } 8 Total time: 3.419 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (160.80.10.129) Time: Wed Mar 17 05:58:52 2004 Input: PF:= PolynomialRing(GF(7)); P:= PolynomialRing(PF); FF1:= ext; ClassNumber(FF1); Output: Magma V2.10-6 Wed Mar 17 2004 05:58:44 on modular [Seed = 3824913643] ------------------------------------- 1379376 Total time: 7.809 seconds, Total memory usage: 3.42MB ************** MAGMA ***************** Host 3(NXDOMAIN) (160.80.10.129) Time: Wed Mar 17 06:00:00 2004 Input: PF:= PolynomialRing(GF(7)); P:= PolynomialRing(PF); FF1:= ext; ClassNumber(FF1); Output: Magma V2.10-6 Wed Mar 17 2004 05:59:52 on modular [Seed = 3453329929] ------------------------------------- 1379376 Total time: 7.329 seconds, Total memory usage: 3.32MB ************** MAGMA ***************** Host 3(NXDOMAIN) (160.80.10.129) Time: Wed Mar 17 06:00:38 2004 Input: PF:= PolynomialRing(GF(7)); P:= PolynomialRing(PF); FF1:= ext; ClassNumber(FF1); Output: Magma V2.10-6 Wed Mar 17 2004 06:00:29 on modular [Seed = 3653351032] ------------------------------------- 1034532 Total time: 8.539 seconds, Total memory usage: 3.62MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 06:01:18 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; PrimitiveElement(G25); Output: Magma V2.10-6 Wed Mar 17 2004 06:01:14 on modular [Seed = 2780678707] ------------------------------------- G25.1 Total time: 3.809 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (160.80.10.129) Time: Wed Mar 17 06:01:25 2004 Input: PF:= PolynomialRing(GF(7)); P:= PolynomialRing(PF); FF1:= ext; ClassNumber(FF1); Output: Magma V2.10-6 Wed Mar 17 2004 06:01:14 on modular [Seed = 2830157630] ------------------------------------- 761589 Total time: 9.879 seconds, Total memory usage: 3.42MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 06:01:35 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; PrimitiveElement(G25); Output: Magma V2.10-6 Wed Mar 17 2004 06:01:31 on modular [Seed = 2308045294] ------------------------------------- alpha Total time: 3.119 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 06:02:31 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; PrimitiveElement(G25); MinimalPolynomial(alpha); Output: Magma V2.10-6 Wed Mar 17 2004 06:02:20 on modular [Seed = 2191192786] ------------------------------------- alpha x^2 + 4*x + 2 Total time: 3.579 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 06:02:37 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; PrimitiveElement(G25); MinimalPolynomial(alpha); Output: Magma V2.10-6 Wed Mar 17 2004 06:02:33 on modular [Seed = 2525947571] ------------------------------------- alpha x^2 + 4*x + 2 Total time: 3.429 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (160.80.10.129) Time: Wed Mar 17 06:02:38 2004 Input: PF:= PolynomialRing(GF(7)); P:= PolynomialRing(PF); FF1:= ext; ClassNumber(FF1); Output: Magma V2.10-6 Wed Mar 17 2004 06:02:23 on modular [Seed = 2642800078] ------------------------------------- 982281 Total time: 9.019 seconds, Total memory usage: 3.52MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 06:02:48 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; PrimitiveElement(G25); MinimalPolynomial(alpha,G25); Output: Magma V2.10-6 Wed Mar 17 2004 06:02:44 on modular [Seed = 1685853277] ------------------------------------- alpha $.1 + alpha^13 Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 06:02:57 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; PrimitiveElement(G25); MinimalPolynomial(alpha); Output: Magma V2.10-6 Wed Mar 17 2004 06:02:54 on modular [Seed = 2137460556] ------------------------------------- alpha x^2 + 4*x + 2 Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 06:03:51 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; PrimitiveElement(G25); MinimalPolynomial(alpha); Order(alpha); Output: Magma V2.10-6 Wed Mar 17 2004 06:03:23 on modular [Seed = 1986922080] ------------------------------------- alpha x^2 + 4*x + 2 24 Total time: 4.119 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 06:03:52 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; PrimitiveElement(G25); MinimalPolynomial(alpha); Order(alpha); Output: Magma V2.10-6 Wed Mar 17 2004 06:03:47 on modular [Seed = 1936393101] ------------------------------------- alpha x^2 + 4*x + 2 24 Total time: 3.709 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 06:09:28 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; PrimitiveElement(G25); f:=MinimalPolynomial(alpha); Order(alpha); Output: Magma V2.10-6 Wed Mar 17 2004 06:09:24 on modular [Seed = 1514286035] ------------------------------------- alpha 24 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 06:09:35 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; PrimitiveElement(G25); f:=MinimalPolynomial(alpha); f; Order(alpha); Output: Magma V2.10-6 Wed Mar 17 2004 06:09:32 on modular [Seed = 758471852] ------------------------------------- alpha x^2 + 4*x + 2 24 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee113.uab.es. (158.109.66.113) Time: Wed Mar 17 06:09:48 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; PrimitiveElement(G25); f:=MinimalPolynomial(alpha); f; Degree(f); Order(alpha); Output: Magma V2.10-6 Wed Mar 17 2004 06:09:45 on modular [Seed = 607933872] ------------------------------------- alpha x^2 + 4*x + 2 2 24 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee110.uab.es. (158.109.66.110) Time: Wed Mar 17 06:16:20 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; PrimitiveElement(G25); f:=MinimalPolynomial(alpha); f; Degree(f); Order(alpha); Output: Magma V2.10-6 Wed Mar 17 2004 06:16:17 on modular [Seed = 236355042] ------------------------------------- alpha x^2 + 4*x + 2 2 24 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee110.uab.es. (158.109.66.110) Time: Wed Mar 17 06:16:41 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; Z5 := Integer(5); PrimitiveElement(G25); f:=MinimalPolynomial(alpha); f; Degree(f); Order(alpha); Output: Magma V2.10-6 Wed Mar 17 2004 06:16:39 on modular [Seed = 18445051] ------------------------------------- >> Z5 := Integer(5); ^ User error: Identifier 'Integer' has not been declared or assigned alpha x^2 + 4*x + 2 2 24 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee110.uab.es. (158.109.66.110) Time: Wed Mar 17 06:17:02 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; Z5 := Integers(5); PrimitiveElement(G25); f:=MinimalPolynomial(alpha); f; Degree(f); Order(alpha); Output: Magma V2.10-6 Wed Mar 17 2004 06:16:59 on modular [Seed = 402680798] ------------------------------------- alpha x^2 + 4*x + 2 2 24 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee110.uab.es. (158.109.66.110) Time: Wed Mar 17 06:17:38 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; Z5 := Integers(5); PrimitiveElement(G25); f:=MinimalPolynomial(alpha); f; Degree(f); Order(alpha); Roots(f,Z5); Roots(f,G25); Output: Magma V2.10-6 Wed Mar 17 2004 06:17:35 on modular [Seed = 302670256] ------------------------------------- alpha x^2 + 4*x + 2 2 24 [] [ , ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee110.uab.es. (158.109.66.110) Time: Wed Mar 17 06:19:47 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; Z5 := Integers(5); PrimitiveElement(G25); f:=MinimalPolynomial(alpha); Output: Magma V2.10-6 Wed Mar 17 2004 06:19:44 on modular [Seed = 3858600408] ------------------------------------- alpha Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee110.uab.es. (158.109.66.110) Time: Wed Mar 17 06:20:56 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; Z5 := Integers(5); PrimitiveElement(G25); f:=MinimalPolynomial(alpha); 2*(alpha^(-3))-(alpha^5) + ((alpha^6)/(alpha+2)) Output: Magma V2.10-6 Wed Mar 17 2004 06:20:53 on modular [Seed = 4159669007] ------------------------------------- alpha alpha^17 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee110.uab.es. (158.109.66.110) Time: Wed Mar 17 06:23:15 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; Z5 := Integers(5); PrimitiveElement(G25); f:=MinimalPolynomial(alpha); h:= 2*(alpha^(-3))-(alpha^5) + ((alpha^6)/(alpha+2)); h; Output: Magma V2.10-6 Wed Mar 17 2004 06:23:12 on modular [Seed = 3470179203] ------------------------------------- alpha alpha^17 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee110.uab.es. (158.109.66.110) Time: Wed Mar 17 06:23:44 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; Z5 := Integers(5); PrimitiveElement(G25); f:=MinimalPolynomial(alpha); h:= 2*(alpha^(-3))-(alpha^5) + ((alpha^6)/(alpha+2)); h; GCD(h,2+4*x+x^2); Output: Magma V2.10-6 Wed Mar 17 2004 06:23:41 on modular [Seed = 3235427728] ------------------------------------- alpha alpha^17 >> GCD(h,2+4*x+x^2);; ^ Runtime error in 'GCD': Bad argument types Argument types given: FldFinElt, RngUPolElt Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee110.uab.es. (158.109.66.110) Time: Wed Mar 17 06:24:58 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; Z5 := Integers(5); PrimitiveElement(G25); f:=MinimalPolynomial(alpha); h:= 2*(alpha^(-3))-(alpha^5) + ((alpha^6)/(alpha+2)); h; XGCD(h,2+4*x+x^2); Output: Magma V2.10-6 Wed Mar 17 2004 06:24:55 on modular [Seed = 3687034417] ------------------------------------- alpha alpha^17 >> XGCD(h,2+4*x+x^2);; ^ Runtime error in 'XGCD': Bad argument types Argument types given: FldFinElt, RngUPolElt Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee110.uab.es. (158.109.66.110) Time: Wed Mar 17 06:25:12 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; Z5 := Integers(5); PrimitiveElement(G25); f:=MinimalPolynomial(alpha); h:= 2*(alpha^(-3))-(alpha^5) + ((alpha^6)/(alpha+2)); h; XGCD(x,2+4*x+x^2); Output: Magma V2.10-6 Wed Mar 17 2004 06:25:09 on modular [Seed = 2931219286] ------------------------------------- alpha alpha^17 1 2*x + 3 3 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h0050da316214.ne.client2.attbi.com. (65.96.168.112) Time: Wed Mar 17 06:56:07 2004 Input: 1+1 Output: Magma V2.10-6 Wed Mar 17 2004 06:56:03 on modular [Seed = 1719540443] ------------------------------------- 2 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host n137.ryd.student.liu.se. (130.236.215.137) Time: Wed Mar 17 08:13:04 2004 Input: A:=24163217246705688308009538130645762342186558132943627795095664583283721955988776447394282015366066227; B:=7815527163768586341449473718100818075486473271302551938574007413902677216320779959777336503026038858; p:=151033361501104476498848307103061710384035503479961; E:=ChangeRing(EllipticCurve([A,B]),GF(p)); print(E); go:=Order(E); Factorization(go); Output: Magma V2.10-6 Wed Mar 17 2004 08:12:42 on modular [Seed = 3198595098] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 87893907476578502879744438504737425992870\ 012736387*x + 41376363411560991298522007781027615875889438019175 over GF(151033361501104476498848307103061710384035503479961) [ <2, 4>, <3, 4>, <7, 1>, <29, 1>, <109, 1>, <151, 1>, <3947, 1>, <9649, 1>, <14627, 1>, <32507, 1>, <195271, 1>, <488161, 1>, <686731, 1>, <29423839, 1> ] Total time: 21.539 seconds, Total memory usage: 3.85MB ************** MAGMA ***************** Host sl-5.splius.lt. (62.80.224.5) Time: Wed Mar 17 10:53:16 2004 Input: simas Output: Magma V2.10-6 Wed Mar 17 2004 10:53:13 on modular [Seed = 2897516725] ------------------------------------- >> simas; ^ User error: Identifier 'simas' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sl-5.splius.lt. (62.80.224.5) Time: Wed Mar 17 10:53:45 2004 Input: 123 Output: Magma V2.10-6 Wed Mar 17 2004 10:53:42 on modular [Seed = 2659625576] ------------------------------------- 123 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sl-5.splius.lt. (62.80.224.5) Time: Wed Mar 17 10:54:00 2004 Input: 12345 Output: Magma V2.10-6 Wed Mar 17 2004 10:53:57 on modular [Seed = 2275390306] ------------------------------------- 12345 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sl-5.splius.lt. (62.80.224.5) Time: Wed Mar 17 10:54:26 2004 Input: 123451232132132132465465465498654654564 Output: Magma V2.10-6 Wed Mar 17 2004 10:54:23 on modular [Seed = 2019576998] ------------------------------------- 123451232132132132465465465498654654564 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.194.89.11) Time: Wed Mar 17 11:05:14 2004 Input: series(tan(x),x=0,5); Output: Magma V2.10-6 Wed Mar 17 2004 11:05:11 on modular [Seed = 1213234958] ------------------------------------- >> series(tan(x),x=0,5); ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee18.uab.es. (158.109.66.18) Time: Wed Mar 17 11:51:13 2004 Input: print "Exercici 1. i)"; G2:=GF(2); G3:=GF(3); G5:=GF(5); [x:x in G2]; [x:x in G3]; [x:x in G5]; Output: Magma V2.10-6 Wed Mar 17 2004 11:51:10 on modular [Seed = 3235381583] ------------------------------------- Exercici 1. i) [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee42.uab.es. (158.109.66.42) Time: Wed Mar 17 13:11:11 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; {Order(n) : n in G25 | n ne 0 }; m := {n : n in G25 | IsPrimitive(n) }; #m; Output: Magma V2.10-6 Wed Mar 17 2004 13:11:08 on modular [Seed = 1627342] ------------------------------------- { 1, 2, 3, 4, 6, 8, 12, 24 } 8 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee42.uab.es. (158.109.66.42) Time: Wed Mar 17 13:12:39 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; {n : n in G25 | n ne 0 }; m := {n : n in G25 | IsPrimitive(n) }; #m; Output: Magma V2.10-6 Wed Mar 17 2004 13:12:36 on modular [Seed = 236378984] ------------------------------------- { 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 2, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 3, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23 } 8 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee42.uab.es. (158.109.66.42) Time: Wed Mar 17 13:12:49 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; {n : n in G25 | n ne 0 }; m := {n : n in G25 | IsPrimitive(n) }; #m; Output: Magma V2.10-6 Wed Mar 17 2004 13:12:47 on modular [Seed = 4159644314] ------------------------------------- { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 2, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 3, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } 8 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee42.uab.es. (158.109.66.42) Time: Wed Mar 17 13:13:04 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; #{n : n in G25 | n ne 0 }; m := {n : n in G25 | IsPrimitive(n) }; #m; Output: Magma V2.10-6 Wed Mar 17 2004 13:13:01 on modular [Seed = 4242811299] ------------------------------------- 24 8 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee42.uab.es. (158.109.66.42) Time: Wed Mar 17 13:13:32 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; {Order(n) : n in G25 | n ne 0 }; m := {n : n in G25 | IsPrimitive(n) }; #m; Output: Magma V2.10-6 Wed Mar 17 2004 13:13:29 on modular [Seed = 3858575582] ------------------------------------- { 1, 2, 3, 4, 6, 8, 12, 24 } 8 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee42.uab.es. (158.109.66.42) Time: Wed Mar 17 13:13:58 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; {Order(n) : n in G25 | n ne 0 }; m := {n : n in G25 | IsPrimitive(n) }; #m; m; Output: Magma V2.10-6 Wed Mar 17 2004 13:13:55 on modular [Seed = 3536455619] ------------------------------------- { 1, 2, 3, 4, 6, 8, 12, 24 } 8 { alpha^11, alpha, alpha^23, alpha^13, alpha^5, alpha^17, alpha^7, alpha^19 } Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee42.uab.es. (158.109.66.42) Time: Wed Mar 17 13:14:22 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; {Order(n) : n in G25 | n ne 0 }; m := {n : n in G25 | IsPrimitive(n) }; #m; m; (alpha^7)^24 Output: Magma V2.10-6 Wed Mar 17 2004 13:14:19 on modular [Seed = 3686993618] ------------------------------------- { 1, 2, 3, 4, 6, 8, 12, 24 } 8 { alpha^11, alpha, alpha^23, alpha^13, alpha^5, alpha^17, alpha^7, alpha^19 } 1 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee42.uab.es. (158.109.66.42) Time: Wed Mar 17 13:14:33 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; {Order(n) : n in G25 | n ne 0 }; m := {n : n in G25 | IsPrimitive(n) }; #m; m; (alpha^11)^24 Output: Magma V2.10-6 Wed Mar 17 2004 13:14:30 on modular [Seed = 3235386676] ------------------------------------- { 1, 2, 3, 4, 6, 8, 12, 24 } 8 { alpha^11, alpha, alpha^23, alpha^13, alpha^5, alpha^17, alpha^7, alpha^19 } 1 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee42.uab.es. (158.109.66.42) Time: Wed Mar 17 13:14:41 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; {Order(n) : n in G25 | n ne 0 }; m := {n : n in G25 | IsPrimitive(n) }; #m; m; (alpha)^24 Output: Magma V2.10-6 Wed Mar 17 2004 13:14:38 on modular [Seed = 3385924661] ------------------------------------- { 1, 2, 3, 4, 6, 8, 12, 24 } 8 { alpha^11, alpha, alpha^23, alpha^13, alpha^5, alpha^17, alpha^7, alpha^19 } 1 Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee42.uab.es. (158.109.66.42) Time: Wed Mar 17 13:19:28 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; h:= 2*(alpha^(-3))-(alpha^5) + ((alpha^6)/(alpha+2)); h; IsInvertible(h); { n : n in G25 | IsInvertible(n)}; #{ n : n in G25 | IsInvertible(n)}; #{ n : n in Integers(9) | IsInvertible(n)}; EulerPhi(8); #{ n : n in Integers(3) | IsInvertible(n)}; EulerPhi(2); EulerPhi(3); EulerPhi((5^2)-1); Output: Magma V2.10-6 Wed Mar 17 2004 13:19:25 on modular [Seed = 3198576737] ------------------------------------- alpha^17 true alpha^7 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 2, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 3, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } 24 6 4 2 1 2 8 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee42.uab.es. (158.109.66.42) Time: Wed Mar 17 13:20:32 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; h:= 2*(alpha^(-3))-(alpha^5) + ((alpha^6)/(alpha+2)); h; IsInvertible(h); (alpha^(17+7)) { n : n in G25 | IsInvertible(n)}; #{ n : n in G25 | IsInvertible(n)}; #{ n : n in Integers(9) | IsInvertible(n)}; EulerPhi(8); #{ n : n in Integers(3) | IsInvertible(n)}; EulerPhi(2); EulerPhi(3); EulerPhi((5^2)-1); Output: Magma V2.10-6 Wed Mar 17 2004 13:20:29 on modular [Seed = 2931193905] ------------------------------------- alpha^17 true alpha^7 >> { n : n in G25 | IsInvertible(n)}; ^ User error: bad syntax 24 6 4 2 1 2 8 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee42.uab.es. (158.109.66.42) Time: Wed Mar 17 13:20:49 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; h:= 2*(alpha^(-3))-(alpha^5) + ((alpha^6)/(alpha+2)); h; IsInvertible(h); (alpha^(17+7)); { n : n in G25 | IsInvertible(n)}; #{ n : n in G25 | IsInvertible(n)}; #{ n : n in Integers(9) | IsInvertible(n)}; EulerPhi(8); #{ n : n in Integers(3) | IsInvertible(n)}; EulerPhi(2); EulerPhi(3); EulerPhi((5^2)-1); Output: Magma V2.10-6 Wed Mar 17 2004 13:20:46 on modular [Seed = 2492219928] ------------------------------------- alpha^17 true alpha^7 1 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 2, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 3, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } 24 6 4 2 1 2 8 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee42.uab.es. (158.109.66.42) Time: Wed Mar 17 13:21:52 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; h:= 2*(alpha^(-3))-(alpha^5) + ((alpha^6)/(alpha+2)); h; IsInvertible(h); { n : n in G25 | IsInvertible(n)}; #{ n : n in G25 | IsInvertible(n)}; #{ n : n in Integers(9) | IsInvertible(n)}; EulerPhi(8); #{ n : n in Integers(3) | IsInvertible(n)}; EulerPhi(2); EulerPhi(3); EulerPhi((5^2)-1); Output: Magma V2.10-6 Wed Mar 17 2004 13:21:49 on modular [Seed = 2642758354] ------------------------------------- alpha^17 true alpha^7 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 2, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 3, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } 24 6 4 2 1 2 8 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee42.uab.es. (158.109.66.42) Time: Wed Mar 17 13:22:39 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; h:= 2*(alpha^(-3))-(alpha^5) + ((alpha^6)/(alpha+2)); h; IsInvertible(h); { n : n in G25 | IsInvertible(n)}; #{ n : n in G25 | IsInvertible(n)}; Output: Magma V2.10-6 Wed Mar 17 2004 13:22:36 on modular [Seed = 2324848020] ------------------------------------- alpha^17 true alpha^7 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 2, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 3, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } 24 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee42.uab.es. (158.109.66.42) Time: Wed Mar 17 13:24:52 2004 Input: G16 := GF(16); { ElementToSequence(n) : n in G16 }; Output: Magma V2.10-6 Wed Mar 17 2004 13:24:49 on modular [Seed = 1986961908] ------------------------------------- { [ 0, 0, 0, 0 ], [ 0, 0, 0, 1 ], [ 1, 0, 0, 0 ], [ 1, 0, 0, 1 ], [ 0, 1, 1, 0 ], [ 0, 1, 1, 1 ], [ 1, 1, 1, 0 ], [ 1, 1, 1, 1 ], [ 0, 0, 1, 0 ], [ 0, 0, 1, 1 ], [ 1, 0, 1, 0 ], [ 1, 0, 1, 1 ], [ 0, 1, 0, 0 ], [ 0, 1, 0, 1 ], [ 1, 1, 0, 0 ], [ 1, 1, 0, 1 ] } Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee42.uab.es. (158.109.66.42) Time: Wed Mar 17 13:25:11 2004 Input: G16 := GF(16); { : n in G16 }; Output: Magma V2.10-6 Wed Mar 17 2004 13:25:08 on modular [Seed = 1635367190] ------------------------------------- { <[ 1, 0, 1, 0 ], G16.1^8>, <[ 1, 1, 1, 1 ], G16.1^12>, <[ 0, 1, 0, 1 ], G16.1^9>, <[ 0, 1, 1, 1 ], G16.1^11>, <[ 0, 0, 1, 0 ], G16.1^2>, <[ 0, 1, 1, 0 ], G16.1^5>, <[ 1, 0, 0, 0 ], 1>, <[ 1, 0, 1, 1 ], G16.1^13>, <[ 1, 0, 0, 1 ], G16.1^14>, <[ 1, 1, 1, 0 ], G16.1^10>, <[ 0, 0, 0, 0 ], 0>, <[ 0, 1, 0, 0 ], G16.1>, <[ 0, 0, 0, 1 ], G16.1^3>, <[ 1, 1, 0, 0 ], G16.1^4>, <[ 0, 0, 1, 1 ], G16.1^6>, <[ 1, 1, 0, 1 ], G16.1^7> } Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee42.uab.es. (158.109.66.42) Time: Wed Mar 17 13:25:21 2004 Input: G16 := GF(16); { : n in G16 }; Output: Magma V2.10-6 Wed Mar 17 2004 13:25:19 on modular [Seed = 1752215572] ------------------------------------- { <[ 1, 0, 1, 0 ], alpha^8>, <[ 1, 1, 1, 1 ], alpha^12>, <[ 0, 1, 0, 1 ], alpha^9>, <[ 0, 1, 1, 1 ], alpha^11>, <[ 0, 0, 1, 0 ], alpha^2>, <[ 0, 1, 1, 0 ], alpha^5>, <[ 1, 0, 0, 0 ], 1>, <[ 1, 0, 1, 1 ], alpha^13>, <[ 1, 0, 0, 1 ], alpha^14>, <[ 1, 1, 1, 0 ], alpha^10>, <[ 0, 0, 0, 0 ], 0>, <[ 0, 1, 0, 0 ], alpha>, <[ 0, 0, 0, 1 ], alpha^3>, <[ 1, 1, 0, 0 ], alpha^4>, <[ 0, 0, 1, 1 ], alpha^6>, <[ 1, 1, 0, 1 ], alpha^7> } Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee42.uab.es. (158.109.66.42) Time: Wed Mar 17 13:25:41 2004 Input: G16 := GF(16); #{ : n in G16 }; Output: Magma V2.10-6 Wed Mar 17 2004 13:25:38 on modular [Seed = 1464831750] ------------------------------------- 16 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee42.uab.es. (158.109.66.42) Time: Wed Mar 17 13:26:01 2004 Input: G16 := GF(16); { : n in G16 }; Output: Magma V2.10-6 Wed Mar 17 2004 13:25:58 on modular [Seed = 1564837144] ------------------------------------- { <[ 1, 0, 1, 0 ], alpha^8>, <[ 1, 1, 1, 1 ], alpha^12>, <[ 0, 1, 0, 1 ], alpha^9>, <[ 0, 1, 1, 1 ], alpha^11>, <[ 0, 0, 1, 0 ], alpha^2>, <[ 0, 1, 1, 0 ], alpha^5>, <[ 1, 0, 0, 0 ], 1>, <[ 1, 0, 1, 1 ], alpha^13>, <[ 1, 0, 0, 1 ], alpha^14>, <[ 1, 1, 1, 0 ], alpha^10>, <[ 0, 0, 0, 0 ], 0>, <[ 0, 1, 0, 0 ], alpha>, <[ 0, 0, 0, 1 ], alpha^3>, <[ 1, 1, 0, 0 ], alpha^4>, <[ 0, 0, 1, 1 ], alpha^6>, <[ 1, 1, 0, 1 ], alpha^7> } Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee42.uab.es. (158.109.66.42) Time: Wed Mar 17 13:26:57 2004 Input: G25 := GF(25); { : n in G25 }; Output: Magma V2.10-6 Wed Mar 17 2004 13:26:54 on modular [Seed = 1146920025] ------------------------------------- { <[ 3, 4 ], alpha^3>, <[ 2, 3 ], alpha^11>, <[ 4, 0 ], 4>, <[ 1, 4 ], alpha^5>, <[ 4, 4 ], alpha^10>, <[ 2, 2 ], alpha^4>, <[ 3, 3 ], alpha^16>, <[ 1, 0 ], 1>, <[ 1, 1 ], alpha^22>, <[ 4, 3 ], alpha^20>, <[ 3, 2 ], alpha^23>, <[ 2, 0 ], 2>, <[ 3, 0 ], 3>, <[ 0, 1 ], alpha>, <[ 2, 4 ], alpha^14>, <[ 1, 2 ], alpha^8>, <[ 1, 3 ], alpha^9>, <[ 0, 3 ], alpha^19>, <[ 4, 1 ], alpha^17>, <[ 4, 2 ], alpha^21>, <[ 0, 4 ], alpha^13>, <[ 0, 0 ], 0>, <[ 3, 1 ], alpha^2>, <[ 0, 2 ], alpha^7>, <[ 2, 1 ], alpha^15> } Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee42.uab.es. (158.109.66.42) Time: Wed Mar 17 13:29:03 2004 Input: G2:= GF(2); G4:= GF(2,2); G8:= GF(8); G16b:= GF(16); { n : n in G2}; { n : n in G4}; { n : n in G8}; { n : n in G16b}; Output: Magma V2.10-6 Wed Mar 17 2004 13:29:00 on modular [Seed = 858516396] ------------------------------------- { 0, 1 } { 1, alpha, alpha^2, 0 } { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, 0 } { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, alpha^12, alpha^13, alpha^14, 0 } Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee42.uab.es. (158.109.66.42) Time: Wed Mar 17 13:29:59 2004 Input: G2:= GF(2); G4:= GF(2,2); G8:= GF(8); G16b:= GF(16); { n : n in G2}; { n : n in G4}; { n : n in G8}; { n : n in G16b}; G2 subset G4; G2 subset G8; G4 subset G8; G2 subset G16b; G4 subset G16b; GF(8) subset GF(64); Output: Magma V2.10-6 Wed Mar 17 2004 13:29:56 on modular [Seed = 975364973] ------------------------------------- { 0, 1 } { 1, alpha, alpha^2, 0 } { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, 0 } { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, alpha^12, alpha^13, alpha^14, 0 } true true false true true true Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee42.uab.es. (158.109.66.42) Time: Wed Mar 17 13:39:19 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; h:= 2*(alpha^(-3))-(alpha^5) + ((alpha^6)/(alpha+2)); h; IsInvertible(h); { n : n in G25 | IsInvertible(n)}; #{ n : n in G25 | IsInvertible(n)}; Output: Magma V2.10-6 Wed Mar 17 2004 13:39:16 on modular [Seed = 302696757] ------------------------------------- alpha^17 true alpha^7 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 2, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 3, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } 24 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee42.uab.es. (158.109.66.42) Time: Wed Mar 17 13:39:43 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; h:= 2*(alpha^(-3))-(alpha^5) + ((alpha^6)/(alpha+2)); h; IsInvertible(h); { n : n in G25 | IsInvertible(n)}; #{ n : n in G25 | IsInvertible(n)}; GCD(alpha^10,25); Output: Magma V2.10-6 Wed Mar 17 2004 13:39:40 on modular [Seed = 419545606] ------------------------------------- alpha^17 true alpha^7 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 2, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 3, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } 24 >> GCD(alpha^10,25);; ^ Runtime error in 'GCD': Bad argument types Argument types given: FldFinElt, FldFinElt Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee42.uab.es. (158.109.66.42) Time: Wed Mar 17 13:40:47 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; h:= 2*(alpha^(-3))-(alpha^5) + ((alpha^6)/(alpha+2)); h; IsInvertible(h); { n : n in G25 | IsInvertible(n)}; #{ n : n in G25 | IsInvertible(n)}; GCD(alpha^10,2+4*x+x^2); Output: Magma V2.10-6 Wed Mar 17 2004 13:40:44 on modular [Seed = 135320535] ------------------------------------- alpha^17 true alpha^7 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 2, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 3, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } 24 >> GCD(alpha^10,2+4*x+x^2);; ^ Runtime error in 'GCD': Bad argument types Argument types given: FldFinElt, RngUPolElt Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee42.uab.es. (158.109.66.42) Time: Wed Mar 17 13:40:59 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; h:= 2*(alpha^(-3))-(alpha^5) + ((alpha^6)/(alpha+2)); h; IsInvertible(h); { n : n in G25 | IsInvertible(n)}; #{ n : n in G25 | IsInvertible(n)}; GCD(alpha^10,alpha); Output: Magma V2.10-6 Wed Mar 17 2004 13:40:56 on modular [Seed = 4159646780] ------------------------------------- alpha^17 true alpha^7 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 2, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 3, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } 24 >> GCD(alpha^10,alpha);; ^ Runtime error in 'GCD': Bad argument types Argument types given: FldFinElt, FldFinElt Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee42.uab.es. (158.109.66.42) Time: Wed Mar 17 13:41:15 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; h:= 2*(alpha^(-3))-(alpha^5) + ((alpha^6)/(alpha+2)); h; IsInvertible(h); { n : n in G25 | IsInvertible(n)}; #{ n : n in G25 | IsInvertible(n)}; XGCD(alpha^10,alpha); Output: Magma V2.10-6 Wed Mar 17 2004 13:41:12 on modular [Seed = 4276495685] ------------------------------------- alpha^17 true alpha^7 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 2, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 3, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } 24 >> XGCD(alpha^10,alpha);; ^ Runtime error in 'XGCD': Bad argument types Argument types given: FldFinElt, FldFinElt Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee42.uab.es. (158.109.66.42) Time: Wed Mar 17 13:41:40 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; h:= 2*(alpha^(-3))-(alpha^5) + ((alpha^6)/(alpha+2)); h; IsInvertible(h); { n : n in G25 | IsInvertible(n)}; #{ n : n in G25 | IsInvertible(n)}; GCD(x^10,2+4*x+x^2); Output: Magma V2.10-6 Wed Mar 17 2004 13:41:37 on modular [Seed = 3858579063] ------------------------------------- alpha^17 true alpha^7 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 2, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 3, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } 24 1 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee42.uab.es. (158.109.66.42) Time: Wed Mar 17 13:42:00 2004 Input: s2:=GF(5); p2:=PolynomialRing(s2); G25 := ext< s2 | 2+4*x+x^2 >; h:= 2*(alpha^(-3))-(alpha^5) + ((alpha^6)/(alpha+2)); h; IsInvertible(h); { n : n in G25 | IsInvertible(n)}; #{ n : n in G25 | IsInvertible(n)}; GCD(x^10,2+4*x+x^2); GCD(x^20,2+4*x+x^2); Output: Magma V2.10-6 Wed Mar 17 2004 13:41:57 on modular [Seed = 3975427946] ------------------------------------- alpha^17 true alpha^7 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 2, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 3, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } 24 1 1 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee42.uab.es. (158.109.66.42) Time: Wed Mar 17 13:49:56 2004 Input: G25 := GF(25); p := PolynomialRing(kk); IsFinite(pp); > pp; Univariate Polynomial Ring in x over GF(5^2) > #pp; >> #pp; ^ Runtime error in '#': Cardinality is infinite or not feasibly computable Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed. ************** MAGMA ***************** Host aula-a-siee42.uab.es. (158.109.66.42) Time: Wed Mar 17 13:50:23 2004 Input: G25 := GF(25); p := PolynomialRing(kk); IsFinite(pp); pp; #pp; Output: Magma V2.10-6 Wed Mar 17 2004 13:50:20 on modular [Seed = 3453292626] ------------------------------------- >> p := PolynomialRing(kk); ^ User error: Identifier 'kk' has not been declared or assigned >> IsFinite(pp); ^ User error: Identifier 'pp' has not been declared or assigned >> pp; ^ User error: Identifier 'pp' has not been declared or assigned >> #pp; ^ User error: Identifier 'pp' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee42.uab.es. (158.109.66.42) Time: Wed Mar 17 13:50:53 2004 Input: G25 := GF(25); p := PolynomialRing(G25); IsFinite(p); p; #p; Output: Magma V2.10-6 Wed Mar 17 2004 13:50:50 on modular [Seed = 3148047810] ------------------------------------- false Univariate Polynomial Ring in x over GF(5^2) >> #p; ^ Runtime error in '#': Cardinality is infinite or not feasibly computable Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee42.uab.es. (158.109.66.42) Time: Wed Mar 17 13:54:16 2004 Input: G5 := GF(5); a := PrimitiveElement(G25); b := PrimitiveElement(G5); p1 := ((a^2)+ a*x + b * (x^2)); p2 := 1 + a * x; Output: Magma V2.10-6 Wed Mar 17 2004 13:54:13 on modular [Seed = 2863821836] ------------------------------------- >> a := PrimitiveElement(G25); ^ User error: Identifier 'G25' has not been declared or assigned >> p1 := ((a^2)+ a*x + b * (x^2)); ^ User error: Identifier 'a' has not been declared or assigned >> p2 := 1 + a * x;; ^ User error: Identifier 'a' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee42.uab.es. (158.109.66.42) Time: Wed Mar 17 13:54:54 2004 Input: G5 := GF(5); G25 := GF(25); a := PrimitiveElement(G25); b := PrimitiveElement(G5); p1 := ((a^2)+ a*x + b * (x^2)); p2 := 1 + a * x; Output: Magma V2.10-6 Wed Mar 17 2004 13:54:51 on modular [Seed = 2424851992] ------------------------------------- >> p1 := ((a^2)+ a*x + b * (x^2)); ^ User error: Identifier 'x' has not been declared or assigned >> p2 := 1 + a * x;; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee42.uab.es. (158.109.66.42) Time: Wed Mar 17 13:55:30 2004 Input: /*Apartat 1*/ G25 := GF(25); p := PolynomialRing(G25); G5 := GF(5); a := PrimitiveElement(G25); b := PrimitiveElement(G5); p1 := ((a^2)+ a*x + b * (x^2)); p2 := 1 + a * x; Output: Magma V2.10-6 Wed Mar 17 2004 13:55:27 on modular [Seed = 2207997167] ------------------------------------- Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee42.uab.es. (158.109.66.42) Time: Wed Mar 17 14:01:41 2004 Input: /*Apartat 1*/ G25 := GF(25); p := PolynomialRing(G25); G5 := GF(5); a := PrimitiveElement(G25); b := PrimitiveElement(G5); p1 := ((a^2)+ a*x + b * (x^2)); p2 := 1 + a * x; /*Apartat 3*/ p1 + p2 ; p1 * p2 ; /*Apartat 4*/ Quotrem(p1,p2); /*Apartat 5*/ XGCD(p1,p2); /*Si que son coprimers, ja que el mcd entre ells es igual a 1*/ /*Apartat 6*/ (alpha^4)*p1 + ((alpha^21)*x + 4)*p2; /*Apartat 7*/ dd := (1/(alpha^4))-(alpha^(-3))*x + (alpha^5)*x^2; Factorization(dd); Evaluate(dd,-alpha^21); Evaluate(dd,-3); Output: Magma V2.10-6 Wed Mar 17 2004 14:01:38 on modular [Seed = 1752205454] ------------------------------------- 2*x^2 + alpha^7*x + alpha^17 alpha^7*x^3 + alpha*x^2 + 3*x + alpha^2 alpha^5*x + alpha^20 alpha^20 1 alpha^4 alpha^21*x + 4 1 [ , ] 0 0 Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (210.77.25.176) Time: Wed Mar 17 14:11:12 2004 Input: F:=EllipticCurve([0, 17]); F; Output: Magma V2.10-6 Wed Mar 17 2004 14:11:09 on modular [Seed = 591118746] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 17 over Rational Field Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (210.77.25.176) Time: Wed Mar 17 14:12:00 2004 Input: F:=EllipticCurve([0, 17]); F; MW, f := MordellWeilGroup(F); MW; Output: Magma V2.10-6 Wed Mar 17 2004 14:11:56 on modular [Seed = 336393884] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 17 over Rational Field Abelian Group isomorphic to Z + Z Defined on 2 generators (free) Total time: 3.649 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Wed Mar 17 14:28:35 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^4+x^3+x^3+x^2+x+1); UnitGroup(K); Output: Magma V2.10-6 Wed Mar 17 2004 14:28:32 on modular [Seed = 4225965423] ------------------------------------- >> K:=NumberField(x^4+x^3+x^3+x^2+x+1); ^ Runtime error in 'NumberField': Argument 1 is not irreducible >> UnitGroup(K);; ^ User error: Identifier 'K' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Wed Mar 17 14:28:59 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^4+x^3+x^2+x+1); UnitGroup(K); Output: Magma V2.10-6 Wed Mar 17 2004 14:28:56 on modular [Seed = 3975416416] ------------------------------------- Abelian Group isomorphic to Z/10 + Z Defined on 2 generators Relations: 10*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/10 + Z Defined on 2 generators Relations: 10*$.1 = 0 to Maximal Equation Order with defining polynomial x^4 + x^3 + x^2 + x + 1 over its ground order Total time: 2.999 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Wed Mar 17 14:29:42 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^4+x^3+x^2+x+1); G, phi := UnitGroup(K); G; Output: Magma V2.10-6 Wed Mar 17 2004 14:29:38 on modular [Seed = 3603837313] ------------------------------------- Abelian Group isomorphic to Z/10 + Z Defined on 2 generators Relations: 10*G.1 = 0 Total time: 3.039 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Wed Mar 17 14:31:22 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^4+x^3+x^2+x+1); G, phi := UnitGroup(K); G; K!phi(G.1); K!phi(G.2); Output: Magma V2.10-6 Wed Mar 17 2004 14:31:19 on modular [Seed = 3235391283] ------------------------------------- Abelian Group isomorphic to Z/10 + Z Defined on 2 generators Relations: 10*G.1 = 0 -a^2 a^3 + a + 1 Total time: 2.989 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host pubmac2.math.harvard.edu. (140.247.29.135) Time: Wed Mar 17 15:23:35 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^4+10*x+1); UnitGroup(K); Output: Magma V2.10-6 Wed Mar 17 2004 15:23:31 on modular [Seed = 992200845] ------------------------------------- Abelian Group isomorphic to Z/2 + Z + Z Defined on 3 generators Relations: 2*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/2 + Z + Z Defined on 3 generators Relations: 2*$.1 = 0 to Maximal Order of Equation Order with defining polynomial x^4 + 10*x + 1 over its ground order Total time: 3.419 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host pubmac2.math.harvard.edu. (140.247.29.135) Time: Wed Mar 17 15:24:28 2004 Input: R:=PolynomialRing(RationalField()); IsIrreducible(x^4+10*x+1); Output: Magma V2.10-6 Wed Mar 17 2004 15:24:25 on modular [Seed = 775347618] ------------------------------------- true Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host pubmac2.math.harvard.edu. (140.247.29.135) Time: Wed Mar 17 15:25:31 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^4+10*x^2+1); UnitGroup(K); Output: Magma V2.10-6 Wed Mar 17 2004 15:25:27 on modular [Seed = 486926687] ------------------------------------- Abelian Group isomorphic to Z/6 + Z Defined on 2 generators Relations: 6*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/6 + Z Defined on 2 generators Relations: 6*$.1 = 0 to Maximal Order of Equation Order with defining polynomial x^4 + 10*x^2 + 1 over its ground order Total time: 3.089 seconds, Total memory usage: 2.07MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Wed Mar 17 19:48:40 2004 Input: R:=PolynomialRing(RationalField()); Isirreducible(x^4+10*x^2+1); K:=NumberField(x^4+10*x^2+1); UnitGroup(K); Output: Magma V2.10-6 Wed Mar 17 2004 19:48:37 on modular [Seed = 1497491652] ------------------------------------- >> Isirreducible(x^4+10*x^2+1); ^ User error: Identifier 'Isirreducible' has not been declared or assigned Abelian Group isomorphic to Z/6 + Z Defined on 2 generators Relations: 6*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/6 + Z Defined on 2 generators Relations: 6*$.1 = 0 to Maximal Order of Equation Order with defining polynomial x^4 + 10*x^2 + 1 over its ground order Total time: 3.119 seconds, Total memory usage: 2.07MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Wed Mar 17 19:48:53 2004 Input: R:=PolynomialRing(RationalField()); IsIrreducible(x^4+10*x^2+1); K:=NumberField(x^4+10*x^2+1); UnitGroup(K); Output: Magma V2.10-6 Wed Mar 17 2004 19:48:50 on modular [Seed = 1380639704] ------------------------------------- true Abelian Group isomorphic to Z/6 + Z Defined on 2 generators Relations: 6*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/6 + Z Defined on 2 generators Relations: 6*$.1 = 0 to Maximal Order of Equation Order with defining polynomial x^4 + 10*x^2 + 1 over its ground order Total time: 3.089 seconds, Total memory usage: 2.07MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Wed Mar 17 19:49:41 2004 Input: R:=PolynomialRing(RationalField()); IsIrreducible(x^4+10*x^2+1); K:=NumberField(x^4+10*x^2+1); G:=UnitGroup(K); G; Output: Magma V2.10-6 Wed Mar 17 2004 19:49:37 on modular [Seed = 1263794449] ------------------------------------- true Abelian Group isomorphic to Z/6 + Z Defined on 2 generators Relations: 6*G.1 = 0 Total time: 3.069 seconds, Total memory usage: 2.07MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Wed Mar 17 22:14:55 2004 Input: F := PolynomialRing(RationalField()); M:=NumberField([x^4+3]); M; G, phi := UnitGroup(M); G; OK:=MaximalOrder(M); IntegralBasis(M); Output: Magma V2.10-6 Wed Mar 17 2004 22:14:52 on modular [Seed = 1042770539] ------------------------------------- Number Field with defining polynomial x^4 + 3 over the Rational Field Abelian Group isomorphic to Z/6 + Z Defined on 2 generators Relations: 6*G.1 = 0 [ 1, w, 1/2*(w^2 - 1), 1/2*(w^3 + w^2 + w + 1) ] Total time: 3.129 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Wed Mar 17 22:15:50 2004 Input: F := PolynomialRing(RationalField()); M:=NumberField([x^4 + x^3 + x^2 + x + 1]); M; G, phi := UnitGroup(M); G; OK:=MaximalOrder(M); IntegralBasis(M); Output: Magma V2.10-6 Wed Mar 17 2004 22:15:47 on modular [Seed = 775387700] ------------------------------------- Number Field with defining polynomial x^4 + x^3 + x^2 + x + 1 over the Rational Field Abelian Group isomorphic to Z/10 + Z Defined on 2 generators Relations: 10*G.1 = 0 [ 1, w, w^2, w^3 ] Total time: 3.049 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Wed Mar 17 23:16:44 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^3-3*x+1); G, phi:=UnitGroup(K); G; K!phi(G.1); Output: Magma V2.10-6 Wed Mar 17 2004 23:16:41 on modular [Seed = 2931281022] ------------------------------------- Abelian Group isomorphic to Z/2 + Z + Z Defined on 3 generators Relations: 2*G.1 = 0 -1 Total time: 2.999 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Wed Mar 17 23:17:09 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^3-3*x+1); G, phi:=UnitGroup(K); G; K!phi(G.1); K!phi(G.2); K!phi(G.3); Output: Magma V2.10-6 Wed Mar 17 2004 23:17:06 on modular [Seed = 2558655011] ------------------------------------- Abelian Group isomorphic to Z/2 + Z + Z Defined on 3 generators Relations: 2*G.1 = 0 -1 a^2 + a - 1 -a + 1 Total time: 3.019 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Wed Mar 17 23:51:12 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^3-3*x+1); G, phi:=UnitGroup(K); G; u1:=K!phi(G.1); u2:=K!phi(G.2); u3:=K!phi(G.3); Logs(u1); Logs(u2); Logs(u3); Output: Magma V2.10-6 Wed Mar 17 2004 23:51:09 on modular [Seed = 1397373332] ------------------------------------- Abelian Group isomorphic to Z/2 + Z + Z Defined on 3 generators Relations: 2*G.1 = 0 [ 0.E-57, 0.E-57, 0.E-57 ] [ -0.6309447242020459512812798775193268885471288643833906999998, 1.057576813574934871730201141801213067891478387455999999999694, -0.42663208937288892044892126428188617934434952307285679999996 ] [ -0.42663208937288892044892126428188617934434952307285679999996, -0.6309447242020459512812798775193268885471288643833906999998, 1.057576813574934871730201141801213067891478387455999999999694 ] Total time: 2.989 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Mar 18 03:25:22 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^4 + x^3 + x^2 + x + 1); G, phi := UnitGroup(K); G; Output: Magma V2.10-6 Thu Mar 18 2004 03:25:19 on modular [Seed = 1280659679] ------------------------------------- Abelian Group isomorphic to Z/10 + Z Defined on 2 generators Relations: 10*G.1 = 0 Total time: 2.989 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Mar 18 03:26:08 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^4 + x^3 + x^2 + x + 1); G, phi := UnitGroup(K); G; K!phi(G.1); K!phi(G.2); Output: Magma V2.10-6 Thu Mar 18 2004 03:26:05 on modular [Seed = 1197365798] ------------------------------------- Abelian Group isomorphic to Z/10 + Z Defined on 2 generators Relations: 10*G.1 = 0 -a^2 a^3 + a + 1 Total time: 3.029 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Mar 18 03:28:13 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^4 + x^3 + x^2 + x + 1); G, phi := UnitGroup(K); G; K!phi(G.1); K!phi(G.2); MinimalPolynomial(a^3 + a + 1); Output: Magma V2.10-6 Thu Mar 18 2004 03:28:10 on modular [Seed = 992093917] ------------------------------------- Abelian Group isomorphic to Z/10 + Z Defined on 2 generators Relations: 10*G.1 = 0 -a^2 a^3 + a + 1 x^4 - 2*x^3 + 4*x^2 - 3*x + 1 Total time: 2.999 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Mar 18 03:38:21 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^4 + x^3 + x^2 + x + 1); G, phi := UnitGroup(K); G; K!phi(G.1); K!phi(G.2); Logs(-a^3); Logs(a^3 + a + 1); Output: Magma V2.10-6 Thu Mar 18 2004 03:38:18 on modular [Seed = 520487065] ------------------------------------- Abelian Group isomorphic to Z/10 + Z Defined on 2 generators Relations: 10*G.1 = 0 -a^2 a^3 + a + 1 [ -4.9999999999999999999999999999999999999999999999999999999987E-53, -4.9999999999999999999999999999999999999999999999999999999987E-53 ] [ -0.48121182505960344749775891342436842313518433438566049999996, 0.48121182505960344749775891342436842313518433438566049999996 ] Total time: 2.949 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Mar 18 03:47:23 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3 - 3x + 1); G, phi := UnitGroup(K); G; K!phi(G.1); K!phi(G.2); K!phi(G.3); Output: Magma V2.10-6 Thu Mar 18 2004 03:47:20 on modular [Seed = 1647204] ------------------------------------- >> K := NumberField(x^3 - 3x + 1); ^ User error: bad syntax >> G, phi := UnitGroup(K); ^ User error: Identifier 'K' has not been declared or assigned >> G; ^ User error: Identifier 'G' has not been declared or assigned >> K!phi(G.1); ^ User error: Identifier 'K' has not been declared or assigned >> K!phi(G.2); ^ User error: Identifier 'K' has not been declared or assigned >> K!phi(G.3);; ^ User error: Identifier 'K' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Mar 18 03:47:33 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3 - 3*x + 1); G, phi := UnitGroup(K); G; K!phi(G.1); K!phi(G.2); K!phi(G.3); Output: Magma V2.10-6 Thu Mar 18 2004 03:47:30 on modular [Seed = 4192263079] ------------------------------------- Abelian Group isomorphic to Z/2 + Z + Z Defined on 3 generators Relations: 2*G.1 = 0 -1 a^2 + a - 1 -a + 1 Total time: 2.969 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Mar 18 03:52:29 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3 - 3*x + 1); G, phi := UnitGroup(K); G; K!phi(G.1); K!phi(G.2); K!phi(G.3); Logs(-a+1); Logs(a^2 + a - 1); Output: Magma V2.10-6 Thu Mar 18 2004 03:52:26 on modular [Seed = 3841837010] ------------------------------------- Abelian Group isomorphic to Z/2 + Z + Z Defined on 3 generators Relations: 2*G.1 = 0 -1 a^2 + a - 1 -a + 1 [ -0.42663208937288892044892126428188617934434952307285679999996, -0.6309447242020459512812798775193268885471288643833906999998, 1.057576813574934871730201141801213067891478387455999999999694 ] [ -0.6309447242020459512812798775193268885471288643833906999998, 1.057576813574934871730201141801213067891478387455999999999694, -0.42663208937288892044892126428188617934434952307285679999996 ] Total time: 3.029 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Mar 18 04:23:42 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^4 + 10*x + 1); G, phi := UnitGroup(K); G; Output: Magma V2.10-6 Thu Mar 18 2004 04:23:39 on modular [Seed = 2542714226] ------------------------------------- Abelian Group isomorphic to Z/2 + Z + Z Defined on 3 generators Relations: 2*G.1 = 0 Total time: 3.269 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Mar 18 04:24:40 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^4 + 10*x^2 + 1); G, phi := UnitGroup(K); G; Output: Magma V2.10-6 Thu Mar 18 2004 04:24:37 on modular [Seed = 2358617639] ------------------------------------- Abelian Group isomorphic to Z/6 + Z Defined on 2 generators Relations: 6*G.1 = 0 Total time: 3.099 seconds, Total memory usage: 1.97MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Mar 18 04:49:30 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^4 + 10*x^2 + 1); C := Class(K); C; G, phi := UnitGroup(K); G; Output: Magma V2.10-6 Thu Mar 18 2004 04:49:27 on modular [Seed = 1581739654] ------------------------------------- >> C := Class(K); ^ Runtime error in 'Class': Bad argument types Argument types given: FldNum >> C; ^ User error: Identifier 'C' has not been declared or assigned Abelian Group isomorphic to Z/6 + Z Defined on 2 generators Relations: 6*G.1 = 0 Total time: 3.089 seconds, Total memory usage: 1.97MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Mar 18 04:49:39 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^4 + 10*x^2 + 1); C := ClassGroup(K); C; G, phi := UnitGroup(K); G; Output: Magma V2.10-6 Thu Mar 18 2004 04:49:36 on modular [Seed = 1431070106] ------------------------------------- Abelian Group of order 1 Abelian Group isomorphic to Z/6 + Z Defined on 2 generators Relations: 6*G.1 = 0 Total time: 3.339 seconds, Total memory usage: 2.07MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Mar 18 04:50:10 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^4 + 10*x^2 + 1); C := ClassGroup(K); C; Output: Magma V2.10-6 Thu Mar 18 2004 04:50:06 on modular [Seed = 1163687412] ------------------------------------- Abelian Group of order 1 Total time: 3.329 seconds, Total memory usage: 1.97MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Mar 18 04:51:22 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^4 + 10*x^2 + 1); G, phi := UnitGroup(K); G; Output: Magma V2.10-6 Thu Mar 18 2004 04:51:19 on modular [Seed = 909051742] ------------------------------------- Abelian Group isomorphic to Z/6 + Z Defined on 2 generators Relations: 6*G.1 = 0 Total time: 3.159 seconds, Total memory usage: 1.97MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Mar 18 04:52:55 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^10 - x^6 - x^5 - x^4 + 1); G, phi := UnitGroup(K); G; Output: Magma V2.10-6 Thu Mar 18 2004 04:52:50 on modular [Seed = 758389793] ------------------------------------- Abelian Group isomorphic to Z/2 + Z (5 copies) Defined on 6 generators Relations: 2*G.1 = 0 Total time: 4.409 seconds, Total memory usage: 2.29MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Mar 18 04:54:06 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^10 - x^6 - x^5 - x^4 + 1); C := ClassGroup(K); C; Output: Magma V2.10-6 Thu Mar 18 2004 04:54:02 on modular [Seed = 607983073] ------------------------------------- Abelian Group of order 1 Total time: 3.859 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Mar 18 04:57:02 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^20 - 5); C := ClassGroup(K); C; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 18 2004 04:56:39 on modular [Seed = 353118013] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 16234 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Mar 18 04:57:25 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^20 - 5); C := ClassGroup(K); C; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 18 2004 04:57:02 on modular [Seed = 202718749] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 16243 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Mar 18 04:57:39 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^15 - 5); C := ClassGroup(K); C; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 18 2004 04:57:16 on modular [Seed = 152058634] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 16246 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Mar 18 04:58:01 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^10 - 5); C := ClassGroup(K); C; Output: Magma V2.10-6 Thu Mar 18 2004 04:57:49 on modular [Seed = 4225943833] ------------------------------------- Abelian Group of order 1 Total time: 11.250 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Mar 18 04:59:23 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^10 - 5); G,phi := UnitGroup(K); G; Output: Magma V2.10-6 Thu Mar 18 2004 04:59:16 on modular [Seed = 4058563450] ------------------------------------- Abelian Group isomorphic to Z/2 + Z (5 copies) Defined on 6 generators Relations: 2*G.1 = 0 Total time: 7.369 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Mar 18 05:01:09 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^10 - 5); G,phi := UnitGroup(K); G; K!phi(G.2); K!phi(G.3); Output: Magma V2.10-6 Thu Mar 18 2004 05:01:01 on modular [Seed = 3620660469] ------------------------------------- Abelian Group isomorphic to Z/2 + Z (5 copies) Defined on 6 generators Relations: 2*G.1 = 0 1/2*(-a^5 + 1) 1/2*(-a^6 + a^5 - 2*a^3 + 2*a^2 - a - 1) Total time: 7.299 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Mar 18 05:01:59 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^10 - 5); G,phi := UnitGroup(K); G; K!phi(G.1); K!phi(G.2); K!phi(G.3); K!phi(G.4); K!phi(G.5); K!phi(G.6); Output: Magma V2.10-6 Thu Mar 18 2004 05:01:52 on modular [Seed = 3302881067] ------------------------------------- Abelian Group isomorphic to Z/2 + Z (5 copies) Defined on 6 generators Relations: 2*G.1 = 0 -1 1/2*(-a^5 + 1) 1/2*(-a^6 + a^5 - 2*a^3 + 2*a^2 - a - 1) 1/2*(-a^5 - 2*a^4 - 2*a^3 - 2*a^2 - 2*a - 1) 1/2*(a^8 - a^7 + 2*a^4 - a^3 + a^2 - 2*a + 2) 1/2*(-a^9 - 2*a^8 + 2*a^6 + 2*a^5 - a^4 - 4*a^3 - 2*a^2 + 6*a + 6) Total time: 7.419 seconds, Total memory usage: 3.09MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Mar 18 05:22:21 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^10 + 5); G,phi := UnitGroup(K); G; K!phi(G.1); K!phi(G.2); K!phi(G.3); K!phi(G.4); K!phi(G.5); K!phi(G.6); Output: Magma V2.10-6 Thu Mar 18 2004 05:22:09 on modular [Seed = 2575344055] ------------------------------------- Abelian Group isomorphic to Z/2 + Z + Z + Z + Z Defined on 5 generators Relations: 2*G.1 = 0 -1 -a^7 + a^6 - 1 -a^7 - a^6 + 1 -4*a^8 + 3*a^6 + 5*a^4 - 10*a^2 - 1 -4*a^9 - 2*a^8 + 6*a^7 + 8*a^6 + 5*a^5 - 5*a^4 - 15*a^3 - 10*a^2 + 24 >> K!phi(G.6);; ^ Runtime error in '.': Argument 2 (6) should be in the range [-5 .. 5] Total time: 11.420 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Mar 18 05:22:51 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^10 + 5); G,phi := UnitGroup(K); G; K!phi(G.1); K!phi(G.2); K!phi(G.3); K!phi(G.4); K!phi(G.5); Output: Magma V2.10-6 Thu Mar 18 2004 05:22:40 on modular [Seed = 2409019264] ------------------------------------- Abelian Group isomorphic to Z/2 + Z + Z + Z + Z Defined on 5 generators Relations: 2*G.1 = 0 -1 -a^7 + a^6 - 1 -a^7 - a^6 + 1 -4*a^8 + 3*a^6 + 5*a^4 - 10*a^2 - 1 -4*a^9 - 2*a^8 + 6*a^7 + 8*a^6 + 5*a^5 - 5*a^4 - 15*a^3 - 10*a^2 + 24 Total time: 11.399 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Mar 18 05:24:02 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^10 + 5); C := ClassGroup(K); C; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 18 2004 05:23:39 on modular [Seed = 2258615890] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 16377 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Mar 18 05:25:13 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^10 + 7); G,phi := UnitGroup(K); G; K!phi(G.1); K!phi(G.2); K!phi(G.3); K!phi(G.4); K!phi(G.5); Output: Magma V2.10-6 Thu Mar 18 2004 05:25:07 on modular [Seed = 135344395] ------------------------------------- Abelian Group isomorphic to Z/2 + Z + Z + Z + Z Defined on 5 generators Relations: 2*G.1 = 0 -1 1/10*(-2*a^8 - a^6 - 5*a^5 + 2*a^4 - 4*a^2 + 5*a + 3) 1/10*(-a^9 - a^8 + 2*a^7 + 2*a^6 - 4*a^5 + a^4 + 3*a^3 - 2*a^2 - 6*a + 4) 1/10*(-a^9 + a^8 + 2*a^7 - 2*a^6 - 4*a^5 - a^4 + 3*a^3 + 2*a^2 - 6*a - 4) 1/10*(a^9 - 3*a^8 - 2*a^7 + 6*a^6 + 4*a^5 - 7*a^4 - 3*a^3 + 14*a^2 + 6*a - 18) Total time: 6.179 seconds, Total memory usage: 2.59MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Mar 18 05:26:19 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^10+7); C := ClassGroup(K); C; Output: Magma V2.10-6 Thu Mar 18 2004 05:26:13 on modular [Seed = 419438684] ------------------------------------- Abelian Group of order 1 Total time: 6.619 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Mar 18 05:27:28 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^10-7); C := ClassGroup(K); C; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 18 2004 05:27:05 on modular [Seed = 591010394] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 16419 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Mar 18 05:28:25 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^10 - 7); G, phi := UnitGroup(K); G; K!phi(G.1); K!phi(G.2); K!phi(G.3); K!phi(G.4); K!phi(G.5); Output: Magma V2.10-6 Thu Mar 18 2004 05:28:19 on modular [Seed = 1263694472] ------------------------------------- Abelian Group isomorphic to Z/2 + Z (5 copies) Defined on 6 generators Relations: 2*G.1 = 0 -1 1/5*(a^9 - 2*a^8 + 2*a^7 + a^6 - a^5 + 2*a^4 - 7*a^3 + 4*a^2 + a - 2) 1/5*(-a^9 - 2*a^8 - 2*a^7 + a^6 + a^5 + 2*a^4 + 7*a^3 + 4*a^2 - a - 2) 1/5*(3*a^8 - 4*a^6 + 2*a^4 + 4*a^2 - 12) 1/5*(2*a^9 + 2*a^8 + 4*a^7 + 4*a^6 + 3*a^5 + 8*a^4 + 6*a^3 + 6*a^2 + 12*a + 12) Total time: 6.499 seconds, Total memory usage: 2.89MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Mar 18 05:29:07 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^10 - 7); G, phi := UnitGroup(K); G; K!phi(G.1); K!phi(G.2); K!phi(G.3); K!phi(G.4); K!phi(G.5); K!phi(G.6); Output: Magma V2.10-6 Thu Mar 18 2004 05:29:00 on modular [Seed = 1431071929] ------------------------------------- Abelian Group isomorphic to Z/2 + Z (5 copies) Defined on 6 generators Relations: 2*G.1 = 0 -1 1/5*(a^9 - 2*a^8 + 2*a^7 + a^6 - a^5 + 2*a^4 - 7*a^3 + 4*a^2 + a - 2) 1/5*(-a^9 - 2*a^8 - 2*a^7 + a^6 + a^5 + 2*a^4 + 7*a^3 + 4*a^2 - a - 2) 1/5*(3*a^8 - 4*a^6 + 2*a^4 + 4*a^2 - 12) 1/5*(2*a^9 + 2*a^8 + 4*a^7 + 4*a^6 + 3*a^5 + 8*a^4 + 6*a^3 + 6*a^2 + 12*a + 12) 1/5*(7*a^9 - 10*a^8 + 4*a^7 + 5*a^6 - 7*a^5 + a^3 + 10*a^2 - 18*a - 5) Total time: 6.499 seconds, Total memory usage: 2.89MB ************** MAGMA ***************** Host qlink-ppp135.tele.QueensU.CA. (130.15.245.135) Time: Thu Mar 18 08:28:49 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Thu Mar 18 2004 08:28:46 on modular [Seed = 4192214518] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.109 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Thu Mar 18 08:59:51 2004 Input: P:=PolynomialRing(RationalField()); K:=NumberField(x^4+x^3+x^2+x+1); G, f:=UnitGroup(K); G; Abelian Group isomorphic to Z/10 + Z Defined on 2 generators Relations: 10*G.1 = 0 u1:=K!f(G.1); u1; u2:=K!f(G.2); u2; Norm(u1); Norm(u2); Logs(u1); Logs(u2); Output: Magma V2.10-6 Thu Mar 18 2004 08:59:47 on modular [Seed = 708034940] ------------------------------------- Abelian Group isomorphic to Z/10 + Z Defined on 2 generators Relations: 10*G.1 = 0 >> Abelian Group isomorphic to Z/10 + Z ^ User error: bad syntax >> Defined on 2 generators ^ User error: bad syntax >> 10*G.1 = 0 ^ User error: bad syntax -a^2 a^3 + a + 1 1 1 [ 0.E-57, -7.49999999999999999999999999999999999999999999999999999999872E-53 ] [ -0.48121182505960344749775891342436842313518433438566049999996, 0.48121182505960344749775891342436842313518433438566049999996 ] Total time: 3.099 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Thu Mar 18 09:00:09 2004 Input: P:=PolynomialRing(RationalField()); K:=NumberField(x^4+x^3+x^2+x+1); G, f:=UnitGroup(K); G; u1:=K!f(G.1); u1; u2:=K!f(G.2); u2; Norm(u1); Norm(u2); Logs(u1); Logs(u2); Output: Magma V2.10-6 Thu Mar 18 2004 09:00:06 on modular [Seed = 941740892] ------------------------------------- Abelian Group isomorphic to Z/10 + Z Defined on 2 generators Relations: 10*G.1 = 0 -a^2 a^3 + a + 1 1 1 [ 0.E-57, -7.49999999999999999999999999999999999999999999999999999999872E-53 ] [ -0.48121182505960344749775891342436842313518433438566049999996, 0.48121182505960344749775891342436842313518433438566049999996 ] Total time: 3.039 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Thu Mar 18 09:20:28 2004 Input: P:=PolynomialRing(RationalField()); K:=NumberField(x^3-3*x+1); G, f:=UnitGroup(K); G; u1:=K!f(G.1); u1; u2:=K!f(G.2); u2; u3:=K!f(G.3); u3; Norm(u1); Norm(u2); Norm(u3); Logs(u1); Logs(u2); Logs(u3); Output: Magma V2.10-6 Thu Mar 18 2004 09:20:24 on modular [Seed = 1936360281] ------------------------------------- Abelian Group isomorphic to Z/2 + Z + Z Defined on 3 generators Relations: 2*G.1 = 0 -1 a^2 + a - 1 -a + 1 -1 -1 -1 [ 0.E-57, 0.E-57, 0.E-57 ] [ -0.6309447242020459512812798775193268885471288643833906999998, 1.057576813574934871730201141801213067891478387455999999999694, -0.42663208937288892044892126428188617934434952307285679999996 ] [ -0.42663208937288892044892126428188617934434952307285679999996, -0.6309447242020459512812798775193268885471288643833906999998, 1.057576813574934871730201141801213067891478387455999999999694 ] Total time: 3.059 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 09:40:32 2004 Input: V:=[1..366]; [i-4:i in V | i mod 7 eq 0]; Output: Magma V2.10-6 Thu Mar 18 2004 09:40:29 on modular [Seed = 2659674689] ------------------------------------- [ 3, 10, 17, 24, 31, 38, 45, 52, 59, 66, 73, 80, 87, 94, 101, 108, 115, 122, 129, 136, 143, 150, 157, 164, 171, 178, 185, 192, 199, 206, 213, 220, 227, 234, 241, 248, 255, 262, 269, 276, 283, 290, 297, 304, 311, 318, 325, 332, 339, 346, 353, 360 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 09:48:03 2004 Input: /*SetLogFile("p3.txt");*/ K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ l:=[1..49]; l2:=[0]cat[1 : x in l]; /* (ii)*/ tqr:=P!l2; nqr:=x^&+l; Output: WARNING: MAGMA command contains unsafe command 'file', so it will not be executed. ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 09:48:41 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ l:=[1..49]; l2:=[0]cat[1 : x in l]; /* (ii)*/ tqr:=P!l2; nqr:=x^&+l; Output: Magma V2.10-6 Thu Mar 18 2004 09:48:38 on modular [Seed = 3131264126] ------------------------------------- Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 09:49:02 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ l:=[1..49]; l2:=[0]cat[1 : x in l]; /* (ii)*/ tqr:=P!l2; nqr:=x^&+l; tqr; Output: Magma V2.10-6 Thu Mar 18 2004 09:48:59 on modular [Seed = 3285857562] ------------------------------------- x^49 + x^48 + x^47 + x^46 + x^45 + x^44 + x^43 + x^42 + x^41 + x^40 + x^39 + x^38 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 09:49:27 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ l:=[1..49]; l2:=[0]cat[1 : x in l]; /* (ii)*/ tqr:=P!l2; nqr:=x^&+l; tqr; nqr; Output: Magma V2.10-6 Thu Mar 18 2004 09:49:24 on modular [Seed = 3369156158] ------------------------------------- x^49 + x^48 + x^47 + x^46 + x^45 + x^44 + x^43 + x^42 + x^41 + x^40 + x^39 + x^38 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x x^1225 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 09:51:51 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ l:=[1..49]; l; l2:=[0]cat[1 : x in l]; /* (ii)*/ tqr:=P!l2; nqr:=x^&+l; /*tqr; nqr;*/ Output: Magma V2.10-6 Thu Mar 18 2004 09:51:48 on modular [Seed = 3653250655] ------------------------------------- [ 1 .. 49 ] Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 09:57:27 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ l:=[1..49]; /*l;*/ l2:=[0]cat[1 : x in l]; /* (ii)*/ tqr:=P!l2; nqr:=x^&+l; Evaluate(nqr,1); /*tqr; nqr;*/ /* (iii)*/ [(a,b):a in P Output: Magma V2.10-6 Thu Mar 18 2004 09:57:24 on modular [Seed = 3958510397] ------------------------------------- 1 >> [(a,b):a in P; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 09:58:03 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ l:=[1..49]; /*l;*/ l2:=[0]cat[1 : x in l]; /* (ii)*/ tqr:=P!l2; nqr:=x^2; Evaluate(nqr,2); /*tqr; nqr;*/ /* (iii)*/ /*[(a,b):a in P*/ Output: Magma V2.10-6 Thu Mar 18 2004 09:58:00 on modular [Seed = 4041803786] ------------------------------------- 4 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 09:59:44 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ l:=[1..49]; /*l;*/ l2:=[0]cat[1 : x in l]; /* (ii)*/ tqr:=P!l2; nqr:=x^&+l; /*tqr; nqr;*/ /* (iii)*/ [(a,b):a,b in P|Evaluate(tqr,a) eq Evaluate (nqr,b)]; Output: Magma V2.10-6 Thu Mar 18 2004 09:59:41 on modular [Seed = 4192207014] ------------------------------------- >> [(a,b):a,b in P|Evaluate(tqr,a) eq Evaluate (nqr,b)];; ^ Runtime error in for: Iteration is not possible over this object Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 10:01:40 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ l:=[1..49]; /*l;*/ l2:=[0]cat[1 : x in l]; /* (ii)*/ tqr:=P!l2; nqr:=x^&+l; /*tqr; nqr;*/ /* (iii)*/ [:a,b in P|Evaluate(tqr,a) eq Evaluate (nqr,b)]; Output: Magma V2.10-6 Thu Mar 18 2004 10:01:37 on modular [Seed = 486859983] ------------------------------------- >> [:a,b in P|Evaluate(tqr,a) eq Evaluate (nqr,b)];; ^ Runtime error in for: Iteration is not possible over this object Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 10:03:06 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ l:=[1..49]; /*l;*/ l2:=[0]cat[1 : x in l]; /* (ii)*/ tqr:=P!l2; nqr:=x^&+l; /*tqr; nqr;*/ /* (iii)*/ [: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)]; Output: Magma V2.10-6 Thu Mar 18 2004 10:02:54 on modular [Seed = 608034361] ------------------------------------- [ <1, 0>, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , <3, 3>, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , <2, 2>, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , <6, 6>, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , <4, 4>, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , <5, 5>, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , <0, 0> ] Total time: 11.849 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 10:17:21 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ l:=[1..49]; /*l;*/ l2:=[0]cat[1 : x in l]; /* (ii)*/ tqr:=P!l2; nqr:=x^&+l; /*tqr; nqr;*/ /* (iii)*/ /*[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ ex_iv := function (q,r) K_iv := GF(q,r); exp_max := q^r-1; l:=[1..exp_max]; return l; end function; Output: Magma V2.10-6 Thu Mar 18 2004 10:17:18 on modular [Seed = 1197390394] ------------------------------------- Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 10:17:46 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ l:=[1..49]; /*l;*/ l2:=[0]cat[1 : x in l]; /* (ii)*/ tqr:=P!l2; nqr:=x^&+l; /*tqr; nqr;*/ /* (iii)*/ /*[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ ex_iv := function (q,r) K_iv := GF(q,r); exp_max := q^r-1; l:=[1..exp_max]; return l; end function; ex_iv(7,3); Output: Magma V2.10-6 Thu Mar 18 2004 10:17:43 on modular [Seed = 1314370522] ------------------------------------- [ 1 .. 342 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 10:18:30 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ l:=[1..49]; /*l;*/ l2:=[0]cat[1 : x in l]; /* (ii)*/ tqr:=P!l2; nqr:=x^&+l; /*tqr; nqr;*/ /* (iii)*/ /*[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ ex_iv := function (q,r) K_iv := GF(q,r); exp_max := q^(r-1); l:=[1..exp_max]; return l; end function; ex_iv(7,3); Output: Magma V2.10-6 Thu Mar 18 2004 10:18:27 on modular [Seed = 1431087253] ------------------------------------- [ 1 .. 49 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 10:25:24 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ l:=[1..49]; /*l;*/ l2:=[0]cat[1 : x in l]; /* (ii)*/ tqr:=P!l2; nqr:=x^&+l; /*tqr; nqr;*/ /* (iii)*/ /*[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ ex_iv := function (q,r) K_iv := GF(q,r); exp_max := q^(r-1); l:=[1..exp_max]; return l; end function; CalculNqr := function (q,r) K_v := GF(q,r); P:=PolinomialRing(K_v); exponents:=CalculExponents(q,r); nqr:=x^&+exponents; return nqr; end function; CalculNqr(7,3); Output: Magma V2.10-6 Thu Mar 18 2004 10:25:21 on modular [Seed = 1752274698] ------------------------------------- >> P:=PolinomialRing(K_v); ^ User error: Identifier 'PolinomialRing' has not been declared or assigned >> CalculNqr(7,3); ^ User error: Identifier 'CalculNqr' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 10:26:01 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ l:=[1..49]; /*l;*/ l2:=[0]cat[1 : x in l]; /* (ii)*/ tqr:=P!l2; nqr:=x^&+l; /*tqr; nqr;*/ /* (iii)*/ /*[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ ex_iv := function (q,r) K_iv := GF(q,r); exp_max := q^(r-1); l:=[1..exp_max]; return l; end function; CalculNqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); nqr:=x^&+exponents; return nqr; end function; CalculNqr(7,3); Output: Magma V2.10-6 Thu Mar 18 2004 10:25:58 on modular [Seed = 1987021299] ------------------------------------- >> exponents:=CalculExponents(q,r); ^ User error: Identifier 'CalculExponents' has not been declared or assigned >> CalculNqr(7,3); ^ User error: Identifier 'CalculNqr' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 10:26:26 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ l:=[1..49]; /*l;*/ l2:=[0]cat[1 : x in l]; /* (ii)*/ tqr:=P!l2; nqr:=x^&+l; /*tqr; nqr;*/ /* (iii)*/ /*[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ ex_iv := function (q,r) K_iv := GF(q,r); exp_max := q^(r-1); l:=[1..exp_max]; return l; end function; CalculNqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=ex_iv(q,r); nqr:=x^&+exponents; return nqr; end function; CalculNqr(7,3); Output: Magma V2.10-6 Thu Mar 18 2004 10:26:23 on modular [Seed = 2103739105] ------------------------------------- x^1225 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 10:28:32 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ l:=[1..49]; /*l;*/ l2:=[0]cat[1 : x in l]; /* (ii)*/ tqr:=P!l2; nqr:=x^&+l; /*tqr; nqr;*/ /* (iii)*/ /*[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ ex_iv := function (q,r) K_iv := GF(q,r); exp_max := q^(r-1); l:=[1..exp_max]; return l; end function; CalculNqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=ex_iv(q,r); nqr:=x^&+exponents; return nqr; end function; CalculTqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=ex_iv(q,r); e2:=[0]cat[1 : x in exponents]; tqr:=P!e2; return tqr; end function; CalculTqr(7,3); Output: Magma V2.10-6 Thu Mar 18 2004 10:28:29 on modular [Seed = 2224882842] ------------------------------------- x^49 + x^48 + x^47 + x^46 + x^45 + x^44 + x^43 + x^42 + x^41 + x^40 + x^39 + x^38 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 10:32:31 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ l:=[1..49]; /*l;*/ l2:=[0]cat[1 : x in l]; /* (ii)*/ tqr:=P!l2; nqr:=x^&+l; /*tqr; nqr;*/ /* (iii)*/ /*[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ ex_iv := function (q,r) K_iv := GF(q,r); exp_max := q^(r-1); l:=[1..exp_max]; return l; end function; CalculNqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=ex_iv(q,r); nqr:=x^&+exponents; return nqr; end function; CalculTqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=ex_iv(q,r); e2:=[0]cat[1 : x in exponents]; tqr:=P!e2; return tqr; end function; /*CalculTqr(7,3);*/ CalculOlav := function(q,r) K_vi := GF(q,r); tqr;=CalculTqr(q,r); nqr:=CalculNqr(q,r); resposta:=[: a,b in K_vi|Evaluate(tqr,a) eq Evaluate (nqr,b)]; return resposta; end function; Output: Magma V2.10-6 Thu Mar 18 2004 10:32:28 on modular [Seed = 2608994964] ------------------------------------- >> tqr;=CalculTqr(q,r); ^ User error: bad syntax >> nqr:=CalculNqr(q,r); ^ User error: Identifier 'q' has not been declared or assigned >> resposta:=[: a,b in K_vi|Evaluate(tqr,a) eq Evaluate (nqr,b)]; ^ User error: Identifier 'K_vi' has not been declared or assigned >> return resposta; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 10:32:49 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ l:=[1..49]; /*l;*/ l2:=[0]cat[1 : x in l]; /* (ii)*/ tqr:=P!l2; nqr:=x^&+l; /*tqr; nqr;*/ /* (iii)*/ /*[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ ex_iv := function (q,r) K_iv := GF(q,r); exp_max := q^(r-1); l:=[1..exp_max]; return l; end function; CalculNqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=ex_iv(q,r); nqr:=x^&+exponents; return nqr; end function; CalculTqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=ex_iv(q,r); e2:=[0]cat[1 : x in exponents]; tqr:=P!e2; return tqr; end function; /*CalculTqr(7,3);*/ CalculOlav := function(q,r) K_vi := GF(q,r); tqr:=CalculTqr(q,r); nqr:=CalculNqr(q,r); resposta:=[: a,b in K_vi|Evaluate(tqr,a) eq Evaluate (nqr,b)]; return resposta; end function; Output: Magma V2.10-6 Thu Mar 18 2004 10:32:46 on modular [Seed = 2730173375] ------------------------------------- Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 10:33:19 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ l:=[1..49]; /*l;*/ l2:=[0]cat[1 : x in l]; /* (ii)*/ tqr:=P!l2; nqr:=x^&+l; /*tqr; nqr;*/ /* (iii)*/ /*[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ ex_iv := function (q,r) K_iv := GF(q,r); exp_max := q^(r-1); l:=[1..exp_max]; return l; end function; CalculNqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=ex_iv(q,r); nqr:=x^&+exponents; return nqr; end function; CalculTqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=ex_iv(q,r); e2:=[0]cat[1 : x in exponents]; tqr:=P!e2; return tqr; end function; /*CalculTqr(7,3);*/ CalculOlav := function(q,r) K_vi := GF(q,r); tqr:=CalculTqr(q,r); nqr:=CalculNqr(q,r); resposta:=[: a,b in K_vi|Evaluate(tqr,a) eq Evaluate (nqr,b)]; return resposta; end function; CalculOlav(7,3); Output: Magma V2.10-6 Thu Mar 18 2004 10:33:07 on modular [Seed = 2846894233] ------------------------------------- [ <1, 0>, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , <3, 3>, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , <2, 2>, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , <6, 6>, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , <4, 4>, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , <5, 5>, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , <0, 0> ] Total time: 11.729 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 10:33:52 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ l:=[1..49]; /*l;*/ l2:=[0]cat[1 : x in l]; /* (ii)*/ tqr:=P!l2; nqr:=x^&+l; /*tqr; nqr;*/ /* (iii)*/ /*[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ ex_iv := function (q,r) K_iv := GF(q,r); exp_max := q^(r-1); l:=[1..exp_max]; return l; end function; CalculNqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=ex_iv(q,r); nqr:=x^&+exponents; return nqr; end function; CalculTqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=ex_iv(q,r); e2:=[0]cat[1 : x in exponents]; tqr:=P!e2; return tqr; end function; /*CalculTqr(7,3);*/ CalculOlav := function(q,r) K_vi := GF(q,r); tqr:=CalculTqr(q,r); nqr:=CalculNqr(q,r); resposta:=[: a,b in K_vi|Evaluate(tqr,a) eq Evaluate (nqr,b)]; return resposta; end function; CalculOlav(7,3); Output: Magma V2.10-6 Thu Mar 18 2004 10:33:40 on modular [Seed = 2963878375] ------------------------------------- [ <1, 0>, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , <3, 3>, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , <2, 2>, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , <6, 6>, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , <4, 4>, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , <5, 5>, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , <0, 0> ] Total time: 11.789 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (147.83.14.242) Time: Thu Mar 18 10:35:32 2004 Input: GF(9); Output: Magma V2.10-6 Thu Mar 18 2004 10:35:28 on modular [Seed = 3285860864] ------------------------------------- Finite field of size 3^2 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (147.83.14.242) Time: Thu Mar 18 10:36:04 2004 Input: K:=GF(9); Set(K); Output: Magma V2.10-6 Thu Mar 18 2004 10:36:01 on modular [Seed = 3385870379] ------------------------------------- { 1, K.1, K.1^2, K.1^3, 2, K.1^5, K.1^6, K.1^7, 0 } Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 10:39:56 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ l:=[1..49]; Length(l); /*l;*/ l2:=[0]cat[1 : x in l]; /* (ii)*/ tqr:=P!l2; nqr:=x^&+l; /*tqr; nqr;*/ /* (iii)*/ /*[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ ex_iv := function (q,r) K_iv := GF(q,r); exp_max := q^(r-1); l:=[1..exp_max]; return l; end function; CalculNqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=ex_iv(q,r); nqr:=x^&+exponents; return nqr; end function; CalculTqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=ex_iv(q,r); e2:=[0]cat[1 : x in exponents]; tqr:=P!e2; return tqr; end function; /*CalculTqr(7,3);*/ CalculOlav := function(q,r) K_vi := GF(q,r); tqr:=CalculTqr(q,r); nqr:=CalculNqr(q,r); resposta:=[: a,b in K_vi|Evaluate(tqr,a) eq Evaluate (nqr,b)]; return resposta; end function; /*CalculOlav(7,3);*/ Output: Magma V2.10-6 Thu Mar 18 2004 10:39:53 on modular [Seed = 3620623645] ------------------------------------- >> Length(l); ^ Runtime error in 'Length': Bad argument types Argument types given: SeqEnum[RngIntElt] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 10:40:39 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ l:=[1..49]; Length l; /*l;*/ l2:=[0]cat[1 : x in l]; /* (ii)*/ tqr:=P!l2; nqr:=x^&+l; /*tqr; nqr;*/ /* (iii)*/ /*[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ ex_iv := function (q,r) K_iv := GF(q,r); exp_max := q^(r-1); l:=[1..exp_max]; return l; end function; CalculNqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=ex_iv(q,r); nqr:=x^&+exponents; return nqr; end function; CalculTqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=ex_iv(q,r); e2:=[0]cat[1 : x in exponents]; tqr:=P!e2; return tqr; end function; /*CalculTqr(7,3);*/ CalculOlav := function(q,r) K_vi := GF(q,r); tqr:=CalculTqr(q,r); nqr:=CalculNqr(q,r); resposta:=[: a,b in K_vi|Evaluate(tqr,a) eq Evaluate (nqr,b)]; return resposta; end function; /*CalculOlav(7,3);*/ Output: Magma V2.10-6 Thu Mar 18 2004 10:40:36 on modular [Seed = 3892208912] ------------------------------------- >> Length l; ^ User error: bad syntax Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 10:52:10 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ l:=[1..49]; Length l; /*l;*/ l2:=[0]cat[1 : x in l]; /* (ii)*/ tqr:=P!l2; nqr:=x^&+l; /*tqr; nqr;*/ /* (iii)*/ /*[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ ex_iv := function (q,r) K_iv := GF(q,r); exp_max := q^(r-1); l:=[1..exp_max]; return l; end function; CalculNqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=ex_iv(q,r); nqr:=x^&+exponents; return nqr; end function; CalculTqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=ex_iv(q,r); e2:=[0]cat[1 : x in exponents]; tqr:=P!e2; return tqr; end function; /*CalculTqr(7,3);*/ CalculOlav := function(q,r) K_vi := GF(q,r); tqr:=CalculTqr(q,r); nqr:=CalculNqr(q,r); resposta:=[: a,b in K_vi|Evaluate(tqr,a) eq Evaluate (nqr,b)]; return resposta; end function; /*CalculOlav(7,3);*/ Ex1:=CalculOlav(7,3); ultim:=Prune(Ex1); Append(Ex1,ultim); long1:=Position(Ex1,ultim); long1 eq 7^(2*3 -1); Output: Magma V2.10-6 Thu Mar 18 2004 10:51:58 on modular [Seed = 4175527269] ------------------------------------- >> Length l; ^ User error: bad syntax >> Append(Ex1,ultim); ^ Runtime error in 'Append': Could not lift element into sequence >> long1:=Position(Ex1,ultim); ^ Runtime error in 'Position': Could not lift element into sequence >> long1 eq 7^(2*3 -1); ^ User error: Identifier 'long1' has not been declared or assigned Total time: 11.679 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 10:52:54 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ l:=[1..49]; /*l;*/ l2:=[0]cat[1 : x in l]; /* (ii)*/ tqr:=P!l2; nqr:=x^&+l; /*tqr; nqr;*/ /* (iii)*/ /*[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ ex_iv := function (q,r) K_iv := GF(q,r); exp_max := q^(r-1); l:=[1..exp_max]; return l; end function; CalculNqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=ex_iv(q,r); nqr:=x^&+exponents; return nqr; end function; CalculTqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=ex_iv(q,r); e2:=[0]cat[1 : x in exponents]; tqr:=P!e2; return tqr; end function; /*CalculTqr(7,3);*/ CalculOlav := function(q,r) K_vi := GF(q,r); tqr:=CalculTqr(q,r); nqr:=CalculNqr(q,r); resposta:=[: a,b in K_vi|Evaluate(tqr,a) eq Evaluate (nqr,b)]; return resposta; end function; /*CalculOlav(7,3);*/ Ex1:=CalculOlav(7,3); ultim:=Prune(Ex1); Append(Ex1,ultim); long1:=Position(Ex1,ultim); long1 eq 7^(2*3 -1); Output: Magma V2.10-6 Thu Mar 18 2004 10:52:42 on modular [Seed = 1672654] ------------------------------------- >> Append(Ex1,ultim); ^ Runtime error in 'Append': Could not lift element into sequence >> long1:=Position(Ex1,ultim); ^ Runtime error in 'Position': Could not lift element into sequence >> long1 eq 7^(2*3 -1); ^ User error: Identifier 'long1' has not been declared or assigned Total time: 11.729 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 10:56:06 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ l:=[1..49]; /*l;*/ l2:=[0]cat[1 : x in l]; /* (ii)*/ tqr:=P!l2; nqr:=x^&+l; /*tqr; nqr;*/ /* (iii)*/ /*[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ ex_iv := function (q,r) K_iv := GF(q,r); exp_max := q^(r-1); l:=[1..exp_max]; return l; end function; CalculNqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=ex_iv(q,r); nqr:=x^&+exponents; return nqr; end function; CalculTqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=ex_iv(q,r); e2:=[0]cat[1 : x in exponents]; tqr:=P!e2; return tqr; end function; /*CalculTqr(7,3);*/ CalculOlav := function(q,r) K_vi := GF(q,r); tqr:=CalculTqr(q,r); nqr:=CalculNqr(q,r); resposta:=[: a,b in K_vi|Evaluate(tqr,a) eq Evaluate (nqr,b)]; return resposta; end function; /*CalculOlav(7,3);*/ Ex1:=CalculOlav(7,3); long1:=&+[1 : i in Ex1]; long1 eq 7^(2*3 -1); Output: Magma V2.10-6 Thu Mar 18 2004 10:55:54 on modular [Seed = 353145755] ------------------------------------- false Total time: 11.769 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 10:57:02 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ l:=[1..49]; /*l;*/ l2:=[0]cat[1 : x in l]; /* (ii)*/ tqr:=P!l2; nqr:=x^&+l; /*tqr; nqr;*/ /* (iii)*/ /*[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ ex_iv := function (q,r) K_iv := GF(q,r); exp_max := q^(r-1); l:=[1..exp_max]; return l; end function; CalculNqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=ex_iv(q,r); nqr:=x^&+exponents; return nqr; end function; CalculTqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=ex_iv(q,r); e2:=[0]cat[1 : x in exponents]; tqr:=P!e2; return tqr; end function; /*CalculTqr(7,3);*/ CalculOlav := function(q,r) K_vi := GF(q,r); tqr:=CalculTqr(q,r); nqr:=CalculNqr(q,r); resposta:=[: a,b in K_vi|Evaluate(tqr,a) eq Evaluate (nqr,b)]; return resposta; end function; /*CalculOlav(7,3);*/ Ex1:=CalculOlav(7,3); long1:=&+[1 : i in Ex1]; long1 eq 7^(2*(3 -1)); Output: Magma V2.10-6 Thu Mar 18 2004 10:56:50 on modular [Seed = 520526297] ------------------------------------- false Total time: 11.719 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 10:57:40 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ l:=[1..49]; /*l;*/ l2:=[0]cat[1 : x in l]; /* (ii)*/ tqr:=P!l2; nqr:=x^&+l; /*tqr; nqr;*/ /* (iii)*/ /*[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ ex_iv := function (q,r) K_iv := GF(q,r); exp_max := q^(r-1); l:=[1..exp_max]; return l; end function; CalculNqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=ex_iv(q,r); nqr:=x^&+exponents; return nqr; end function; CalculTqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=ex_iv(q,r); e2:=[0]cat[1 : x in exponents]; tqr:=P!e2; return tqr; end function; /*CalculTqr(7,3);*/ CalculOlav := function(q,r) K_vi := GF(q,r); tqr:=CalculTqr(q,r); nqr:=CalculNqr(q,r); resposta:=[: a,b in K_vi|Evaluate(tqr,a) eq Evaluate (nqr,b)]; return resposta; end function; /*CalculOlav(7,3);*/ Ex1:=CalculOlav(7,3); long1:=&+[1 : i in Ex1]; long1; /*long1 eq */7^(2*(3 -1)); Output: Magma V2.10-6 Thu Mar 18 2004 10:57:29 on modular [Seed = 540649165] ------------------------------------- 343 2401 Total time: 11.669 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 10:58:59 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ l:=[1..49]; /*l;*/ l2:=[0]cat[1 : x in l]; /* (ii)*/ tqr:=P!l2; nqr:=x^&+l; /*tqr; nqr;*/ /* (iii)*/ /*[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ ex_iv := function (q,r) K_iv := GF(q,r); exp_max := q^(r-1); l:=[1..exp_max]; return l; end function; CalculNqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=ex_iv(q,r); nqr:=x^&+exponents; return nqr; end function; CalculTqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=ex_iv(q,r); e2:=[0]cat[1 : x in exponents]; tqr:=P!e2; return tqr; end function; /*CalculTqr(7,3);*/ CalculOlav := function(q,r) K_vi := GF(q,r); tqr:=CalculTqr(q,r); nqr:=CalculNqr(q,r); resposta:=[: a,b in K_vi|Evaluate(tqr,a) eq Evaluate (nqr,b)]; return resposta; end function; /*CalculOlav(7,3);*/ Ex1:=CalculOlav(7,3); long1:=&+[1 : i in Ex1]; long1; /*long1 eq */7^(2*3 -1); Output: Magma V2.10-6 Thu Mar 18 2004 10:58:47 on modular [Seed = 691056154] ------------------------------------- 343 16807 Total time: 11.709 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 11:02:29 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ l:=[1..49]; /*l;*/ l2:=[0]cat[1 : x in l]; /* (ii)*/ tqr:=P!l2; nqr:=x^&+l; /*tqr; nqr;*/ /* (iii)*/ /*[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ ex_iv := function (q,r) K_iv := GF(q,r); exp_max := q^(r-1); l:=[1..exp_max]; return l; end function; CalculNqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=ex_iv(q,r); nqr:=x^&+exponents; return nqr; end function; CalculTqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=ex_iv(q,r); e2:=[0]cat[1 : x in exponents]; tqr:=P!e2; return tqr; end function; /*CalculTqr(7,3);*/ CalculOlav := function(q,r) K_vi := GF(q,r); tqr:=CalculTqr(q,r); nqr:=CalculNqr(q,r); resposta:=[: a,b in K_vi|Evaluate(tqr,a) eq Evaluate (nqr,b)]; return resposta; end function; /*CalculOlav(7,3);*/ Ex1:=CalculOlav(7,3); #(Ex1); /*long1 eq */7^(2*3 -1); Output: Magma V2.10-6 Thu Mar 18 2004 11:02:17 on modular [Seed = 1414388825] ------------------------------------- 343 16807 Total time: 11.759 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 11:06:45 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ l:=[1..49]; /*l;*/ l2:=[0]cat[1 : x in l]; /* (ii)*/ tqr:=P!l2; nqr:=x^&+l; /*tqr; nqr;*/ /* (iii)*/ /*[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ ex_iv := function (q,r) K_iv := GF(q,r); exp_max := q^(r-1); l:=[1..exp_max]; return l; end function; CalculNqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=ex_iv(q,r); nqr:=x^&+exponents; return nqr; end function; CalculTqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=ex_iv(q,r); e2:=[0]cat[1 : x in exponents]; tqr:=P!e2; return tqr; end function; /*CalculTqr(7,3);*/ CalculOlav := function(q,r) K_vi := GF(q,r); tqr:=CalculTqr(q,r); nqr:=CalculNqr(q,r); resposta:=[: a,b in K_vi|Evaluate(tqr,a) eq Evaluate (nqr,b)]; return resposta; end function; /*CalculOlav(7,3);*/ /*Ex1:=CalculOlav(7,3);*/ /*#(Ex1);*/ /*long1 eq */7^(2*3 -1); exponents:=[7^(3-x):x in [1..3]]; exponents; e2:=[0]cat[1 : x in exponents]; /* (ii)*/ tqr:=P!e2; Output: Magma V2.10-6 Thu Mar 18 2004 11:06:42 on modular [Seed = 1514394444] ------------------------------------- 16807 [ 49, 7, 1 ] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 11:07:49 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ exponents:=[7^(3-x):x in [1..3]]; exponents; e2:=[0]cat[1 : x in exponents]; /* (ii)*/ tqr:=P!e2; nqr:=x^&+exponents; tqr; nqr; Output: Magma V2.10-6 Thu Mar 18 2004 11:07:46 on modular [Seed = 1668999733] ------------------------------------- [ 49, 7, 1 ] x^3 + x^2 + x x^57 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 11:13:43 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ exponents:=[7^(3-x):x in [1..3]]; exponents; /* (ii)*/ tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; tqr; nqr:=x^&+exponents; tqr; nqr; Output: Magma V2.10-6 Thu Mar 18 2004 11:13:40 on modular [Seed = 2087057100] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x x^49 + x^7 + x x^57 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 11:15:15 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ exponents:=[7^(3-x):x in [1..3]]; exponents; /* (ii)*/ tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; tqr; nqr:=x^&+exponents; nqr; Output: Magma V2.10-6 Thu Mar 18 2004 11:15:12 on modular [Seed = 2174225045] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x x^57 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 11:15:50 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ exponents:=[7^(3-x):x in [1..3]]; exponents; /* (ii)*/ tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; tqr; nqr:=x^&+exponents; nqr; [: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)]; Output: Magma V2.10-6 Thu Mar 18 2004 11:15:44 on modular [Seed = 2324890046] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x x^57 [ <1, alpha>, <1, alpha^7>, <1, alpha^13>, <1, alpha^19>, <1, alpha^25>, <1, alpha^31>, <1, alpha^37>, <1, alpha^43>, <1, alpha^49>, <1, alpha^55>, <1, alpha^61>, <1, alpha^67>, <1, alpha^73>, <1, alpha^79>, <1, alpha^85>, <1, alpha^91>, <1, alpha^97>, <1, alpha^103>, <1, alpha^109>, <1, alpha^115>, <1, alpha^121>, <1, alpha^127>, <1, alpha^133>, <1, alpha^139>, <1, alpha^145>, <1, alpha^151>, <1, alpha^157>, <1, alpha^163>, <1, alpha^169>, <1, alpha^175>, <1, alpha^181>, <1, alpha^187>, <1, alpha^193>, <1, alpha^199>, <1, alpha^205>, <1, alpha^211>, <1, alpha^217>, <1, alpha^223>, <1, alpha^229>, <1, alpha^235>, <1, alpha^241>, <1, alpha^247>, <1, alpha^253>, <1, alpha^259>, <1, alpha^265>, <1, alpha^271>, <1, alpha^277>, <1, alpha^283>, <1, alpha^289>, <1, alpha^295>, <1, alpha^301>, <1, alpha^307>, <1, alpha^313>, <1, alpha^319>, <1, alpha^325>, <1, alpha^331>, <1, alpha^337>, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , :=GF(7,3); P:=PolynomialRing(K); /* (i)*/ exponents:=[7^(3-x):x in [1..3]]; exponents; /* (ii)*/ tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; tqr; nqr:=x^&+exponents; nqr; a:=[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)]; #(a); Output: Magma V2.10-6 Thu Mar 18 2004 11:16:24 on modular [Seed = 2659653058] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x x^57 16807 Total time: 4.139 seconds, Total memory usage: 2.73MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 11:16:56 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ exponents:=[7^(3-x):x in [1..3]]; exponents; /* (ii)*/ tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; tqr; nqr:=x^&+exponents; nqr; a:=[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)]; #(a); 7^(2*3-1); Output: Magma V2.10-6 Thu Mar 18 2004 11:16:52 on modular [Seed = 2814258391] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x x^57 16807 16807 Total time: 4.029 seconds, Total memory usage: 2.73MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 11:19:08 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ exponents:=[7^(3-x):x in [1..3]]; exponents; /* (ii)*/ tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; tqr; nqr:=x^&+exponents; nqr; /*[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ CalculExponents := function (q,r) K_iv := GF(q,r); l:=[q^(r-x):x in [1..r]]; return l; end function; CalculExponents(7,3); Output: Magma V2.10-6 Thu Mar 18 2004 11:19:05 on modular [Seed = 3047964232] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x x^57 [ 49, 7, 1 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 11:20:13 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ exponents:=[7^(3-x):x in [1..3]]; exponents; /* (ii)*/ tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; tqr; nqr:=x^&+exponents; nqr; /*[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ CalculExponents := function (q,r) K_iv := GF(q,r); l:=[q^(r-x):x in [1..r]]; return l; end function; CalculExponents(7,3); CalculTqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; return tqr; end function; CalculTqr(7,3); Output: Magma V2.10-6 Thu Mar 18 2004 11:20:10 on modular [Seed = 3319548411] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x x^57 [ 49, 7, 1 ] x^49 + x^7 + x Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 11:20:40 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ exponents:=[7^(3-x):x in [1..3]]; exponents; /* (ii)*/ tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; tqr; nqr:=x^&+exponents; nqr; /*[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ CalculExponents := function (q,r) K_iv := GF(q,r); l:=[q^(r-x):x in [1..r]]; return l; end function; CalculExponents(7,3); CalculTqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; return tqr; end function; CalculTqr(7,3); CalculNqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); nqr:=x^&+exponents; return nqr; end function; CalculNqr(7,3); Output: Magma V2.10-6 Thu Mar 18 2004 11:20:37 on modular [Seed = 3470213791] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x x^57 [ 49, 7, 1 ] x^49 + x^7 + x x^57 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 11:21:38 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ exponents:=[7^(3-x):x in [1..3]]; exponents; /* (ii)*/ tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; tqr; nqr:=x^&+exponents; nqr; /*[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ CalculExponents := function (q,r) K_iv := GF(q,r); l:=[q^(r-x):x in [1..r]]; return l; end function; CalculExponents(7,3); CalculTqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; return tqr; end function; CalculTqr(7,3); CalculNqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); nqr:=x^&+exponents; return nqr; end function; CalculNqr(7,3); CalculOlav := function(q,r) K_vi := GF(q,r); tqr:=CalculTqr(q,r); nqr:=CalculNqr(q,r); resposta:=[: a,b in K_vi|Evaluate(tqr,a) eq Evaluate (nqr,b)]; return resposta; end function; r:=CalculOlav(7,3); r; Output: Magma V2.10-6 Thu Mar 18 2004 11:21:34 on modular [Seed = 3502857306] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x x^57 [ 49, 7, 1 ] x^49 + x^7 + x x^57 [ <1, alpha>, <1, alpha^7>, <1, alpha^13>, <1, alpha^19>, <1, alpha^25>, <1, alpha^31>, <1, alpha^37>, <1, alpha^43>, <1, alpha^49>, <1, alpha^55>, <1, alpha^61>, <1, alpha^67>, <1, alpha^73>, <1, alpha^79>, <1, alpha^85>, <1, alpha^91>, <1, alpha^97>, <1, alpha^103>, <1, alpha^109>, <1, alpha^115>, <1, alpha^121>, <1, alpha^127>, <1, alpha^133>, <1, alpha^139>, <1, alpha^145>, <1, alpha^151>, <1, alpha^157>, <1, alpha^163>, <1, alpha^169>, <1, alpha^175>, <1, alpha^181>, <1, alpha^187>, <1, alpha^193>, <1, alpha^199>, <1, alpha^205>, <1, alpha^211>, <1, alpha^217>, <1, alpha^223>, <1, alpha^229>, <1, alpha^235>, <1, alpha^241>, <1, alpha^247>, <1, alpha^253>, <1, alpha^259>, <1, alpha^265>, <1, alpha^271>, <1, alpha^277>, <1, alpha^283>, <1, alpha^289>, <1, alpha^295>, <1, alpha^301>, <1, alpha^307>, <1, alpha^313>, <1, alpha^319>, <1, alpha^325>, <1, alpha^331>, <1, alpha^337>, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , :=GF(7,3); P:=PolynomialRing(K); /* (i)*/ exponents:=[7^(3-x):x in [1..3]]; exponents; /* (ii)*/ tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; tqr; nqr:=x^&+exponents; nqr; /*[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ CalculExponents := function (q,r) K_iv := GF(q,r); l:=[q^(r-x):x in [1..r]]; return l; end function; CalculExponents(7,3); CalculTqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; return tqr; end function; CalculTqr(7,3); CalculNqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); nqr:=x^&+exponents; return nqr; end function; CalculNqr(7,3); CalculOlav := function(q,r) K_vi := GF(q,r); tqr:=CalculTqr(q,r); nqr:=CalculNqr(q,r); resposta:=[: a,b in K_vi|Evaluate(tqr,a) eq Evaluate (nqr,b)]; return resposta; end function; r:=CalculOlav(7,3); #(r); Output: Magma V2.10-6 Thu Mar 18 2004 11:21:59 on modular [Seed = 3653260666] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x x^57 [ 49, 7, 1 ] x^49 + x^7 + x x^57 16807 Total time: 4.079 seconds, Total memory usage: 2.73MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 11:25:06 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ exponents:=[7^(3-x):x in [1..3]]; exponents; /* (ii)*/ tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; tqr; nqr:=x^&+exponents; nqr; /*[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ CalculExponents := function (q,r) K_iv := GF(q,r); l:=[q^(r-x):x in [1..r]]; return l; end function; CalculExponents(7,3); CalculTqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; return tqr; end function; CalculTqr(7,3); CalculNqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); nqr:=x^&+exponents; return nqr; end function; CalculNqr(7,3); CalculOlav := function(q,r) K_vi := GF(q,r); tqr:=CalculTqr(q,r); nqr:=CalculNqr(q,r); resposta:=[: a,b in K_vi|Evaluate(tqr,a) eq Evaluate (nqr,b)]; return resposta; end function; r:=CalculOlav(7,3); #(r); Ex1:=CalculOlav(7,3); long1:=#(Ex1); long1 eq 7^(2*3 -1); Ex2:=CalculOlav(4,3); long2:=#(Ex2); long2 eq 4^(2*3 -1); Ex3:=CalculOlav(6,2); long3:=#(Ex3); long3 eq 6^(2*2 -1); Ex4:=CalculOlav(9,4); long4:=#(Ex4); long4 eq 9^(2*4 -1); Ex5:=CalculOlav(7,5); long5:=#(Ex5); long5 eq 7^(2*5 -1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 18 2004 11:24:43 on modular [Seed = 3808128941] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x x^57 [ 49, 7, 1 ] x^49 + x^7 + x x^57 16807 true [
:38]( q: 4, r: 3 ) >> K_vi := GF(q,r); ^ Runtime error in 'GF': Argument 1 (4) should be prime >> long2:=#(Ex2); ^ User error: Identifier 'Ex2' has not been declared or assigned >> long2 eq 4^(2*3 -1); ^ User error: Identifier 'long2' has not been declared or assigned [
:38]( q: 6, r: 2 ) >> K_vi := GF(q,r); ^ Runtime error in 'GF': Argument 1 (6) should be prime >> long3:=#(Ex3); ^ User error: Identifier 'Ex3' has not been declared or assigned >> long3 eq 6^(2*2 -1); ^ User error: Identifier 'long3' has not been declared or assigned [
:38]( q: 9, r: 4 ) >> K_vi := GF(q,r); ^ Runtime error in 'GF': Argument 1 (9) should be prime >> long4:=#(Ex4); ^ User error: Identifier 'Ex4' has not been declared or assigned >> long4 eq 9^(2*4 -1); ^ User error: Identifier 'long4' has not been declared or assigned Errors: /home/mfd/gomagma: line 2: 17638 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 11:26:11 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ exponents:=[7^(3-x):x in [1..3]]; exponents; /* (ii)*/ tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; tqr; nqr:=x^&+exponents; nqr; /*[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ CalculExponents := function (q,r) K_iv := GF(q,r); l:=[q^(r-x):x in [1..r]]; return l; end function; CalculExponents(7,3); CalculTqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; return tqr; end function; CalculTqr(7,3); CalculNqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); nqr:=x^&+exponents; return nqr; end function; CalculNqr(7,3); CalculOlav := function(q,r) K_vi := GF(q,r); tqr:=CalculTqr(q,r); nqr:=CalculNqr(q,r); resposta:=[: a,b in K_vi|Evaluate(tqr,a) eq Evaluate (nqr,b)]; return resposta; end function; r:=CalculOlav(7,3); #(r); Ex1:=CalculOlav(7,3); long1:=#(Ex1); long1 eq 7^(2*3 -1); Ex2:=CalculOlav(4,1); long2:=#(Ex2); long2 eq 4^(2*1 -1); Output: Magma V2.10-6 Thu Mar 18 2004 11:26:06 on modular [Seed = 4041833834] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x x^57 [ 49, 7, 1 ] x^49 + x^7 + x x^57 16807 true [
:38]( q: 4, r: 1 ) >> K_vi := GF(q,r); ^ Runtime error in 'GF': Argument 1 (4) should be prime >> long2:=#(Ex2); ^ User error: Identifier 'Ex2' has not been declared or assigned >> long2 eq 4^(2*1 -1);; ^ User error: Identifier 'long2' has not been declared or assigned Total time: 5.339 seconds, Total memory usage: 3.67MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 11:28:41 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ exponents:=[7^(3-x):x in [1..3]]; exponents; /* (ii)*/ tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; tqr; nqr:=x^&+exponents; nqr; /*[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ CalculExponents := function (q,r) K_iv := GF(q,r); l:=[q^(r-x):x in [1..r]]; return l; end function; CalculExponents(7,3); CalculTqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; return tqr; end function; CalculTqr(7,3); CalculNqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); nqr:=x^&+exponents; return nqr; end function; CalculNqr(7,3); CalculOlav := function(q,r) K_vi := GF(q,r); tqr:=CalculTqr(q,r); nqr:=CalculNqr(q,r); resposta:=[: a,b in K_vi|Evaluate(tqr,a) eq Evaluate (nqr,b)]; return resposta; end function; r:=CalculOlav(7,3); #(r); Ex1:=CalculOlav(7,3); long1:=#(Ex1); long1 eq 7^(2*3 -1); Ex2:=CalculOlav(13,5); long2:=#(Ex2); long2 eq 13^(2*5 -1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 18 2004 11:28:18 on modular [Seed = 4192237535] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x x^57 [ 49, 7, 1 ] x^49 + x^7 + x x^57 16807 true Errors: /home/mfd/gomagma: line 2: 17661 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 11:29:25 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ exponents:=[7^(3-x):x in [1..3]]; exponents; /* (ii)*/ tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; tqr; nqr:=x^&+exponents; nqr; /*[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ CalculExponents := function (q,r) K_iv := GF(q,r); l:=[q^(r-x):x in [1..r]]; return l; end function; CalculExponents(7,3); CalculTqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; return tqr; end function; CalculTqr(7,3); CalculNqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); nqr:=x^&+exponents; return nqr; end function; CalculNqr(7,3); CalculOlav := function(q,r) K_vi := GF(q,r); tqr:=CalculTqr(q,r); nqr:=CalculNqr(q,r); resposta:=[: a,b in K_vi|Evaluate(tqr,a) eq Evaluate (nqr,b)]; return resposta; end function; r:=CalculOlav(7,3); #(r); Ex2:=CalculOlav(13,5); long2:=#(Ex2); long2 eq 13^(2*5 -1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 18 2004 11:29:02 on modular [Seed = 52071752] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x x^57 [ 49, 7, 1 ] x^49 + x^7 + x x^57 16807 Errors: /home/mfd/gomagma: line 2: 17670 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 11:29:51 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ exponents:=[7^(3-x):x in [1..3]]; exponents; /* (ii)*/ tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; tqr; nqr:=x^&+exponents; nqr; /*[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ CalculExponents := function (q,r) K_iv := GF(q,r); l:=[q^(r-x):x in [1..r]]; return l; end function; CalculExponents(7,3); CalculTqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; return tqr; end function; CalculTqr(7,3); CalculNqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); nqr:=x^&+exponents; return nqr; end function; CalculNqr(7,3); CalculOlav := function(q,r) K_vi := GF(q,r); tqr:=CalculTqr(q,r); nqr:=CalculNqr(q,r); resposta:=[: a,b in K_vi|Evaluate(tqr,a) eq Evaluate (nqr,b)]; return resposta; end function; r:=CalculOlav(7,3); #(r); Ex2:=CalculOlav(3,5); long2:=#(Ex2); long2 eq 3^(2*5 -1); Output: Magma V2.10-6 Thu Mar 18 2004 11:29:46 on modular [Seed = 169051253] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x x^57 [ 49, 7, 1 ] x^49 + x^7 + x x^57 16807 true Total time: 4.949 seconds, Total memory usage: 4.21MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 11:31:35 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ exponents:=[7^(3-x):x in [1..3]]; exponents; /* (ii)*/ tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; tqr; nqr:=x^&+exponents; nqr; /*[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ CalculExponents := function (q,r) K_iv := GF(q,r); l:=[q^(r-x):x in [1..r]]; return l; end function; CalculExponents(7,3); CalculTqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; return tqr; end function; CalculTqr(7,3); CalculNqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); nqr:=x^&+exponents; return nqr; end function; CalculNqr(7,3); CalculOlav := function(q,r) K_vi := GF(q,r); tqr:=CalculTqr(q,r); nqr:=CalculNqr(q,r); resposta:=[: a,b in K_vi|Evaluate(tqr,a) eq Evaluate (nqr,b)]; return resposta; end function; r:=CalculOlav(7,3); #(r); Ex3:=CalculOlav(5,3); long3:=#(Ex3); long3 eq 5^(2*3 -1); Ex4:=CalculOlav(7,5); long4:=#(Ex4); long4 eq 7^(2*5 -1); Ex5:=CalculOlav(3,7); long5:=#(Ex5); long5 eq 3^(2*7 -1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 18 2004 11:31:12 on modular [Seed = 624733168] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x x^57 [ 49, 7, 1 ] x^49 + x^7 + x x^57 16807 true Errors: /home/mfd/gomagma: line 2: 17696 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 11:32:17 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ exponents:=[7^(3-x):x in [1..3]]; exponents; /* (ii)*/ tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; tqr; nqr:=x^&+exponents; nqr; /*[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ CalculExponents := function (q,r) K_iv := GF(q,r); l:=[q^(r-x):x in [1..r]]; return l; end function; CalculExponents(7,3); CalculTqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; return tqr; end function; CalculTqr(7,3); CalculNqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); nqr:=x^&+exponents; return nqr; end function; CalculNqr(7,3); CalculOlav := function(q,r) K_vi := GF(q,r); tqr:=CalculTqr(q,r); nqr:=CalculNqr(q,r); resposta:=[: a,b in K_vi|Evaluate(tqr,a) eq Evaluate (nqr,b)]; return resposta; end function; r:=CalculOlav(7,3); #(r); Ex4:=CalculOlav(7,5); long4:=#(Ex4); long4 eq 7^(2*5 -1); Ex5:=CalculOlav(3,7); long5:=#(Ex5); long5 eq 3^(2*7 -1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 18 2004 11:31:54 on modular [Seed = 741712595] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x x^57 [ 49, 7, 1 ] x^49 + x^7 + x x^57 16807 Errors: /home/mfd/gomagma: line 2: 17705 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 11:34:12 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ exponents:=[7^(3-x):x in [1..3]]; exponents; /* (ii)*/ tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; tqr; nqr:=x^&+exponents; nqr; /*[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ CalculExponents := function (q,r) K_iv := GF(q,r); l:=[q^(r-x):x in [1..r]]; return l; end function; CalculExponents(7,3); CalculTqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; return tqr; end function; CalculTqr(7,3); CalculNqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); nqr:=x^&+exponents; return nqr; end function; CalculNqr(7,3); CalculOlav := function(q,r) K_vi := GF(q,r); tqr:=CalculTqr(q,r); nqr:=CalculNqr(q,r); resposta:=[: a,b in K_vi|Evaluate(tqr,a) eq Evaluate (nqr,b)]; return resposta; end function; r:=CalculOlav(7,3); #(r); Ex4:=CalculOlav(7,1); long4:=#(Ex4); long4 eq 7^(2*1 -1); Ex5:=CalculOlav(3,7); long5:=#(Ex5); long5 eq 3^(2*7 -1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 18 2004 11:33:49 on modular [Seed = 925808735] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x x^57 [ 49, 7, 1 ] x^49 + x^7 + x x^57 16807 true Errors: /home/mfd/gomagma: line 2: 17714 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 11:35:28 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ exponents:=[7^(3-x):x in [1..3]]; exponents; /* (ii)*/ tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; tqr; nqr:=x^&+exponents; nqr; /*[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ CalculExponents := function (q,r) K_iv := GF(q,r); l:=[q^(r-x):x in [1..r]]; return l; end function; CalculExponents(7,3); CalculTqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; return tqr; end function; CalculTqr(7,3); CalculNqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); nqr:=x^&+exponents; return nqr; end function; CalculNqr(7,3); CalculOlav := function(q,r) K_vi := GF(q,r); tqr:=CalculTqr(q,r); nqr:=CalculNqr(q,r); resposta:=[: a,b in K_vi|Evaluate(tqr,a) eq Evaluate (nqr,b)]; return resposta; end function; r:=CalculOlav(7,3); #(r); Ex4:=CalculOlav(7,1); long4:=#(Ex4); long4 eq 7^(2*1 -1); Ex5:=CalculOlav(3,1); long5:=#(Ex5); long5 eq 3^(2*1 -1); Output: Magma V2.10-6 Thu Mar 18 2004 11:35:24 on modular [Seed = 1163709068] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x x^57 [ 49, 7, 1 ] x^49 + x^7 + x x^57 16807 true true Total time: 4.089 seconds, Total memory usage: 2.83MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 11:35:58 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ exponents:=[7^(3-x):x in [1..3]]; exponents; /* (ii)*/ tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; tqr; nqr:=x^&+exponents; nqr; /*[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ CalculExponents := function (q,r) K_iv := GF(q,r); l:=[q^(r-x):x in [1..r]]; return l; end function; CalculExponents(7,3); CalculTqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; return tqr; end function; CalculTqr(7,3); CalculNqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); nqr:=x^&+exponents; return nqr; end function; CalculNqr(7,3); CalculOlav := function(q,r) K_vi := GF(q,r); tqr:=CalculTqr(q,r); nqr:=CalculNqr(q,r); resposta:=[: a,b in K_vi|Evaluate(tqr,a) eq Evaluate (nqr,b)]; return resposta; end function; r:=CalculOlav(7,3); #(r); Ex1:=CalculOlav(7,3); long1:=#(Ex1); long1 eq 7^(2*3 -1); Ex2:=CalculOlav(3,5); long2:=#(Ex2); long2 eq 3^(2*5 -1); /* Han de ser primers???? A part hem agafat numeros petits pq l'interpret ens donava el missatge:Errors: /home/mfd/gomagma: line 2: 17714 Alarm clock /usr/local/bin/magma*/ Ex3:=CalculOlav(5,3); long3:=#(Ex3); long3 eq 5^(2*3 -1); Ex4:=CalculOlav(7,1); long4:=#(Ex4); long4 eq 7^(2*1 -1); Ex5:=CalculOlav(3,1); long5:=#(Ex5); long5 eq 3^(2*1 -1); Output: WARNING: MAGMA command contains unsafe command 'alarm', so it will not be executed. ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 11:38:55 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ exponents:=[7^(3-x):x in [1..3]]; exponents; /* (ii)*/ tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; tqr; nqr:=x^&+exponents; nqr; /*[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ CalculExponents := function (q,r) K_iv := GF(q,r); l:=[q^(r-x):x in [1..r]]; return l; end function; CalculExponents(7,3); CalculTqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; return tqr; end function; CalculTqr(7,3); CalculNqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); nqr:=x^&+exponents; return nqr; end function; CalculNqr(7,3); CalculOlav := function(q,r) K_vi := GF(q,r); tqr:=CalculTqr(q,r); nqr:=CalculNqr(q,r); resposta:=[: a,b in K_vi|Evaluate(tqr,a) eq Evaluate (nqr,b)]; return resposta; end function; r:=CalculOlav(7,3); #(r); Ex3:=CalculOlav(5,3); long3:=#(Ex3); long3 eq 5^(2*3 -1); [: in Ex3|a,b in GF(5)]; Output: Magma V2.10-6 Thu Mar 18 2004 11:38:50 on modular [Seed = 2103766499] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x x^57 [ 49, 7, 1 ] x^49 + x^7 + x x^57 16807 true >> [: in Ex3|a,b in GF(5)];; ^ User error: bad syntax Total time: 4.159 seconds, Total memory usage: 3.07MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 11:40:55 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ exponents:=[7^(3-x):x in [1..3]]; exponents; /* (ii)*/ tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; tqr; nqr:=x^&+exponents; nqr; /*[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ CalculExponents := function (q,r) K_iv := GF(q,r); l:=[q^(r-x):x in [1..r]]; return l; end function; CalculExponents(7,3); CalculTqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; return tqr; end function; CalculTqr(7,3); CalculNqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); nqr:=x^&+exponents; return nqr; end function; CalculNqr(7,3); CalculOlav := function(q,r) K_vi := GF(q,r); tqr:=CalculTqr(q,r); nqr:=CalculNqr(q,r); resposta:=[: a,b in K_vi|Evaluate(tqr,a) eq Evaluate (nqr,b)]; return resposta; end function; r:=CalculOlav(7,3); #(r); Ex3:=CalculOlav(5,3); long3:=#(Ex3); long3 eq 5^(2*3 -1); [x:=:x in Ex3|a,b in GF(5)]; Output: Magma V2.10-6 Thu Mar 18 2004 11:40:50 on modular [Seed = 2492269955] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x x^57 [ 49, 7, 1 ] x^49 + x^7 + x x^57 16807 true >> [x:=:x in Ex3|a,b in GF(5)];; ^ User error: bad syntax Total time: 4.309 seconds, Total memory usage: 3.07MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 11:45:43 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ exponents:=[7^(3-x):x in [1..3]]; exponents; /* (ii)*/ tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; tqr; nqr:=x^&+exponents; nqr; /*[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ CalculExponents := function (q,r) K_iv := GF(q,r); l:=[q^(r-x):x in [1..r]]; return l; end function; CalculExponents(7,3); CalculTqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; return tqr; end function; CalculTqr(7,3); CalculNqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); nqr:=x^&+exponents; return nqr; end function; CalculNqr(7,3); CalculOlav := function(q,r) K_vi := GF(q,r); tqr:=CalculTqr(q,r); nqr:=CalculNqr(q,r); resposta:=[: a,b in K_vi|Evaluate(tqr,a) eq Evaluate (nqr,b)]; return resposta; end function; r:=CalculOlav(7,3); #(r); Ex3:=CalculOlav(5,3); long3:=#(Ex3); long3 eq 5^(2*3 -1); [:a,b in GF(5)| in Ex3]; Output: Magma V2.10-6 Thu Mar 18 2004 11:45:39 on modular [Seed = 319455526] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x x^57 [ 49, 7, 1 ] x^49 + x^7 + x x^57 16807 true [ <0, 0>, <1, 2>, <2, 1>, <3, 4>, <4, 3> ] Total time: 4.239 seconds, Total memory usage: 3.07MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 11:46:12 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ exponents:=[7^(3-x):x in [1..3]]; exponents; /* (ii)*/ tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; tqr; nqr:=x^&+exponents; nqr; /*[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ CalculExponents := function (q,r) K_iv := GF(q,r); l:=[q^(r-x):x in [1..r]]; return l; end function; CalculExponents(7,3); CalculTqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; return tqr; end function; CalculTqr(7,3); CalculNqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); nqr:=x^&+exponents; return nqr; end function; CalculNqr(7,3); CalculOlav := function(q,r) K_vi := GF(q,r); tqr:=CalculTqr(q,r); nqr:=CalculNqr(q,r); resposta:=[: a,b in K_vi|Evaluate(tqr,a) eq Evaluate (nqr,b)]; return resposta; end function; r:=CalculOlav(7,3); #(r); Ex3:=CalculOlav(5,3); long3:=#(Ex3); long3 eq 5^(2*3 -1); Ex3; [:a,b in GF(5)| in Ex3]; Output: Magma V2.10-6 Thu Mar 18 2004 11:46:07 on modular [Seed = 608024173] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x x^57 [ 49, 7, 1 ] x^49 + x^7 + x x^57 16807 true [ <1, alpha^3>, <1, alpha^7>, <1, alpha^11>, <1, alpha^15>, <1, alpha^19>, <1, alpha^23>, <1, alpha^27>, <1, 2>, <1, alpha^35>, <1, alpha^39>, <1, alpha^43>, <1, alpha^47>, <1, alpha^51>, <1, alpha^55>, <1, alpha^59>, <1, alpha^63>, <1, alpha^67>, <1, alpha^71>, <1, alpha^75>, <1, alpha^79>, <1, alpha^83>, <1, alpha^87>, <1, alpha^91>, <1, alpha^95>, <1, alpha^99>, <1, alpha^103>, <1, alpha^107>, <1, alpha^111>, <1, alpha^115>, <1, alpha^119>, <1, alpha^123>, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 11:47:55 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ exponents:=[7^(3-x):x in [1..3]]; exponents; /* (ii)*/ tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; tqr; nqr:=x^&+exponents; nqr; /*[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ CalculExponents := function (q,r) K_iv := GF(q,r); l:=[q^(r-x):x in [1..r]]; return l; end function; CalculExponents(7,3); CalculTqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; return tqr; end function; CalculTqr(7,3); CalculNqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); nqr:=x^&+exponents; return nqr; end function; CalculNqr(7,3); CalculOlav := function(q,r) K_vi := GF(q,r); tqr:=CalculTqr(q,r); nqr:=CalculNqr(q,r); resposta:=[: a,b in K_vi|Evaluate(tqr,a) eq Evaluate (nqr,b)]; return resposta; end function; r:=CalculOlav(7,3); #(r); Ex3:=CalculOlav(5,3); long3:=#(Ex3); long3 eq 5^(2*3 -1); [:a,b in GF(5)| in Ex3]; Output: Magma V2.10-6 Thu Mar 18 2004 11:47:51 on modular [Seed = 691059608] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x x^57 [ 49, 7, 1 ] x^49 + x^7 + x x^57 16807 true [ <0, 0>, <1, 2>, <2, 1>, <3, 4>, <4, 3> ] Total time: 4.299 seconds, Total memory usage: 3.07MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 11:48:41 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ exponents:=[7^(3-x):x in [1..3]]; exponents; /* (ii)*/ tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; tqr; nqr:=x^&+exponents; nqr; /*[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ CalculExponents := function (q,r) K_iv := GF(q,r); l:=[q^(r-x):x in [1..r]]; return l; end function; CalculExponents(7,3); CalculTqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; return tqr; end function; CalculTqr(7,3); CalculNqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); nqr:=x^&+exponents; return nqr; end function; CalculNqr(7,3); CalculOlav := function(q,r) K_vi := GF(q,r); tqr:=CalculTqr(q,r); nqr:=CalculNqr(q,r); resposta:=[: a,b in K_vi|Evaluate(tqr,a) eq Evaluate (nqr,b)]; return resposta; end function; r:=CalculOlav(7,3); #(r); Ex3:=CalculOlav(3,3); long3:=#(Ex3); long3 eq 3^(2*3 -1); [:a,b in GF(5)| in Ex3]; Output: Magma V2.10-6 Thu Mar 18 2004 11:48:37 on modular [Seed = 1042787549] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x x^57 [ 49, 7, 1 ] x^49 + x^7 + x x^57 16807 true >> [:a,b in GF(5)| in Ex3];; ^ Runtime error in 'in': Could not lift element into sequence universe Total time: 4.139 seconds, Total memory usage: 2.83MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 11:49:05 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); /* (i)*/ exponents:=[7^(3-x):x in [1..3]]; exponents; /* (ii)*/ tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; tqr; nqr:=x^&+exponents; nqr; /*[: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ CalculExponents := function (q,r) K_iv := GF(q,r); l:=[q^(r-x):x in [1..r]]; return l; end function; CalculExponents(7,3); CalculTqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; return tqr; end function; CalculTqr(7,3); CalculNqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); nqr:=x^&+exponents; return nqr; end function; CalculNqr(7,3); CalculOlav := function(q,r) K_vi := GF(q,r); tqr:=CalculTqr(q,r); nqr:=CalculNqr(q,r); resposta:=[: a,b in K_vi|Evaluate(tqr,a) eq Evaluate (nqr,b)]; return resposta; end function; r:=CalculOlav(7,3); #(r); Ex3:=CalculOlav(3,3); long3:=#(Ex3); long3 eq 3^(2*3 -1); [:a,b in GF(3)| in Ex3]; Output: Magma V2.10-6 Thu Mar 18 2004 11:49:01 on modular [Seed = 1197397436] ------------------------------------- [ 49, 7, 1 ] x^49 + x^7 + x x^57 [ 49, 7, 1 ] x^49 + x^7 + x x^57 16807 true [ <0, 0>, <1, 0>, <2, 0> ] Total time: 4.089 seconds, Total memory usage: 2.83MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 11:57:28 2004 Input: V:=[1..366]; [i-4:i in V | i mod 7 eq 0]; Output: Magma V2.10-6 Thu Mar 18 2004 11:57:25 on modular [Seed = 1548077231] ------------------------------------- [ 3, 10, 17, 24, 31, 38, 45, 52, 59, 66, 73, 80, 87, 94, 101, 108, 115, 122, 129, 136, 143, 150, 157, 164, 171, 178, 185, 192, 199, 206, 213, 220, 227, 234, 241, 248, 255, 262, 269, 276, 283, 290, 297, 304, 311, 318, 325, 332, 339, 346, 353, 360 ] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 11:58:15 2004 Input: K:=GF(4); M2:=MatrixRing(K,2); Mt:={x:x in M2|Trace(x) eq 0}; Mt; Output: Magma V2.10-6 Thu Mar 18 2004 11:58:12 on modular [Seed = 1669002817] ------------------------------------- { [ 0 0] [ 0 0], [ 0 0] [alpha^2 0], [ 0 0] [ alpha 0], [ 0 0] [ 1 0], [alpha^2 0] [ 0 alpha^2], [alpha^2 0] [alpha^2 alpha^2], [alpha^2 0] [ alpha alpha^2], [alpha^2 0] [ 1 alpha^2], [ 1 0] [ 0 1], [ 1 0] [alpha^2 1], [ 1 0] [ alpha 1], [ 1 0] [ 1 1], [ alpha 0] [ 0 alpha], [ alpha 0] [alpha^2 alpha], [ alpha 0] [ alpha alpha], [ alpha 0] [ 1 alpha], [ 0 alpha^2] [ 0 0], [ 0 alpha^2] [alpha^2 0], [ 0 alpha^2] [ alpha 0], [ 0 alpha^2] [ 1 0], [alpha^2 alpha^2] [ 0 alpha^2], [alpha^2 alpha^2] [alpha^2 alpha^2], [alpha^2 alpha^2] [ alpha alpha^2], [alpha^2 alpha^2] [ 1 alpha^2], [ 1 alpha^2] [ 0 1], [ 1 alpha^2] [alpha^2 1], [ 1 alpha^2] [ alpha 1], [ 1 alpha^2] [ 1 1], [ alpha alpha^2] [ 0 alpha], [ alpha alpha^2] [alpha^2 alpha], [ alpha alpha^2] [ alpha alpha], [ alpha alpha^2] [ 1 alpha], [ 0 alpha] [ 0 0], [ 0 alpha] [alpha^2 0], [ 0 alpha] [ alpha 0], [ 0 alpha] [ 1 0], [alpha^2 alpha] [ 0 alpha^2], [alpha^2 alpha] [alpha^2 alpha^2], [alpha^2 alpha] [ alpha alpha^2], [alpha^2 alpha] [ 1 alpha^2], [ 1 alpha] [ 0 1], [ 1 alpha] [alpha^2 1], [ 1 alpha] [ alpha 1], [ 1 alpha] [ 1 1], [ alpha alpha] [ 0 alpha], [ alpha alpha] [alpha^2 alpha], [ alpha alpha] [ alpha alpha], [ alpha alpha] [ 1 alpha], [ 0 1] [ 0 0], [ 0 1] [alpha^2 0], [ 0 1] [ alpha 0], [ 0 1] [ 1 0], [alpha^2 1] [ 0 alpha^2], [alpha^2 1] [alpha^2 alpha^2], [alpha^2 1] [ alpha alpha^2], [alpha^2 1] [ 1 alpha^2], [ 1 1] [ 0 1], [ 1 1] [alpha^2 1], [ 1 1] [ alpha 1], [ 1 1] [ 1 1], [ alpha 1] [ 0 alpha], [ alpha 1] [alpha^2 alpha], [ alpha 1] [ alpha alpha], [ alpha 1] [ 1 alpha] } Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 11:59:07 2004 Input: K:=GF(4); M2:=MatrixRing(K,2); Mt:={x:x in M2|Trace(x) eq 0}; Mf:={x:x in M2|x[1] eq x[2]}; Mf; Output: Magma V2.10-6 Thu Mar 18 2004 11:59:04 on modular [Seed = 1752300854] ------------------------------------- { [ 1 1] [ 1 1], [ 0 0] [ 0 0], [ alpha 0] [ alpha 0], [ 0 alpha^2] [ 0 alpha^2], [ alpha alpha^2] [ alpha alpha^2], [ 0 alpha] [ 0 alpha], [ alpha alpha] [ alpha alpha], [ 0 1] [ 0 1], [ alpha 1] [ alpha 1], [alpha^2 0] [alpha^2 0], [ 1 0] [ 1 0], [alpha^2 alpha^2] [alpha^2 alpha^2], [ 1 alpha^2] [ 1 alpha^2], [alpha^2 alpha] [alpha^2 alpha], [ 1 alpha] [ 1 alpha], [alpha^2 1] [alpha^2 1] } Total time: 3.069 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 11:59:52 2004 Input: K:=GF(4); M2:=MatrixRing(K,2); Mt:={x:x in M2|Trace(x) eq 0}; Mf:={x:x in M2|x[1] eq x[2]}; Mtf:=Mt meet Mf; Mtf; Output: Magma V2.10-6 Thu Mar 18 2004 11:59:48 on modular [Seed = 2070081273] ------------------------------------- { [ 0 0] [ 0 0], [alpha^2 alpha^2] [alpha^2 alpha^2], [ alpha alpha] [ alpha alpha], [ 1 1] [ 1 1] } Total time: 3.089 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 12:00:36 2004 Input: K:=GF(4); M2:=MatrixRing(K,2); Mt:={x:x in M2|Trace(x) eq 0}; Mf:={x:x in M2|x[1] eq x[2]}; Mtf:=Mt meet Mf; for i:=1 to 100000 do y[i]:=Random(M2); end for; numMt:=0; numMf:=0; numMtf:=0; for i:=1 to 100000 do if y[i] in Mt then numMt:=numMt+1;end if; if y[i] in Mf then numMf:=numMf+1;end if; if y[i] in Mtf then numMtf:=numMtf+1;end if; end for; numMt; numMf; numMtf; Output: Magma V2.10-6 Thu Mar 18 2004 12:00:33 on modular [Seed = 2458584869] ------------------------------------- >> for i:=1 to 100000 do y[i]:=Random(M2); end for; ^ User error: Identifier 'y' has not been declared or assigned >> if y[i] in Mt then numMt:=numMt+1;end if; ^ User error: Identifier 'y' has not been declared or assigned 0 0 0 Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 12:01:27 2004 Input: K:=GF(4); M2:=MatrixRing(K,2); Mt:={x:x in M2|Trace(x) eq 0}; Mf:={x:x in M2|x[1] eq x[2]}; Mtf:=Mt meet Mf; y:=[]; for i:=1 to 100000 do y[i]:=Random(M2); end for; numMt:=0; numMf:=0; numMtf:=0; for i:=1 to 100000 do if y[i] in Mt then numMt:=numMt+1;end if; if y[i] in Mf then numMf:=numMf+1;end if; if y[i] in Mtf then numMtf:=numMtf+1;end if; end for; numMt; numMf; numMtf; Output: Magma V2.10-6 Thu Mar 18 2004 12:01:23 on modular [Seed = 3064931155] ------------------------------------- 25058 6266 1597 Total time: 4.129 seconds, Total memory usage: 7.09MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 12:03:39 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); exponents:=[7^(3-x):x in [1..3]]; exponents; Output: Magma V2.10-6 Thu Mar 18 2004 12:03:36 on modular [Seed = 3215337937] ------------------------------------- [ 49, 7, 1 ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 12:04:20 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); exponents:=[7^(3-x):x in [1..3]]; tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; tqr; nqr:=x^&+exponents; nqr; Output: Magma V2.10-6 Thu Mar 18 2004 12:04:17 on modular [Seed = 3319550802] ------------------------------------- x^49 + x^7 + x x^57 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 12:05:01 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); exponents:=[7^(3-x):x in [1..3]]; tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; nqr:=x^&+exponents; [: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)]; Output: Magma V2.10-6 Thu Mar 18 2004 12:04:56 on modular [Seed = 3402849396] ------------------------------------- [ <1, alpha>, <1, alpha^7>, <1, alpha^13>, <1, alpha^19>, <1, alpha^25>, <1, alpha^31>, <1, alpha^37>, <1, alpha^43>, <1, alpha^49>, <1, alpha^55>, <1, alpha^61>, <1, alpha^67>, <1, alpha^73>, <1, alpha^79>, <1, alpha^85>, <1, alpha^91>, <1, alpha^97>, <1, alpha^103>, <1, alpha^109>, <1, alpha^115>, <1, alpha^121>, <1, alpha^127>, <1, alpha^133>, <1, alpha^139>, <1, alpha^145>, <1, alpha^151>, <1, alpha^157>, <1, alpha^163>, <1, alpha^169>, <1, alpha^175>, <1, alpha^181>, <1, alpha^187>, <1, alpha^193>, <1, alpha^199>, <1, alpha^205>, <1, alpha^211>, <1, alpha^217>, <1, alpha^223>, <1, alpha^229>, <1, alpha^235>, <1, alpha^241>, <1, alpha^247>, <1, alpha^253>, <1, alpha^259>, <1, alpha^265>, <1, alpha^271>, <1, alpha^277>, <1, alpha^283>, <1, alpha^289>, <1, alpha^295>, <1, alpha^301>, <1, alpha^307>, <1, alpha^313>, <1, alpha^319>, <1, alpha^325>, <1, alpha^331>, <1, alpha^337>, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , :=GF(7,3); P:=PolynomialRing(K); exponents:=[7^(3-x):x in [1..3]]; tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; nqr:=x^&+exponents; /*: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ CalculExponents := function (q,r) K_iv := GF(q,r); l:=[q^(r-x):x in [1..r]]; return l; end function; CalculExponents(7,3); Output: Magma V2.10-6 Thu Mar 18 2004 12:06:35 on modular [Seed = 3636547525] ------------------------------------- [ 49, 7, 1 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 12:07:26 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); exponents:=[7^(3-x):x in [1..3]]; tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; nqr:=x^&+exponents; /*: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ CalculExponents := function (q,r) K_iv := GF(q,r); l:=[q^(r-x):x in [1..r]]; return l; end function; CalculNqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); nqr:=x^&+exponents; return nqr; end function; CalculNqr(7,3); CalculTqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; return tqr; end function; CalculTqr(7,3); Output: Magma V2.10-6 Thu Mar 18 2004 12:07:23 on modular [Seed = 4009195939] ------------------------------------- x^57 x^49 + x^7 + x Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 12:09:04 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); exponents:=[7^(3-x):x in [1..3]]; tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; nqr:=x^&+exponents; /*: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ CalculExponents := function (q,r) K_iv := GF(q,r); l:=[q^(r-x):x in [1..r]]; return l; end function; CalculNqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); nqr:=x^&+exponents; return nqr; end function; CalculTqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; return tqr; end function; CalculOlav := function(q,r) K_vi := GF(q,r); tqr:=CalculTqr(q,r); nqr:=CalculNqr(q,r); resposta:=[: a,b in K_vi|Evaluate(tqr,a) eq Evaluate (nqr,b)]; return resposta; end function; [:a,b in GF(5)| in Ex3]; [:a,b in GF(3)| in Ex5]; Output: Magma V2.10-6 Thu Mar 18 2004 12:09:01 on modular [Seed = 4159594588] ------------------------------------- >> [:a,b in GF(5)| in Ex3]; ^ User error: Identifier 'Ex3' has not been declared or assigned >> [:a,b in GF(3)| in Ex5]; ^ User error: Identifier 'Ex5' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 208-BARC-X49.libre.retevision.es. (62.82.19.208) Time: Thu Mar 18 12:09:41 2004 Input: K:=GF(7,3); P:=PolynomialRing(K); exponents:=[7^(3-x):x in [1..3]]; tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; nqr:=x^&+exponents; /*: a,b in K|Evaluate(tqr,a) eq Evaluate (nqr,b)];*/ CalculExponents := function (q,r) K_iv := GF(q,r); l:=[q^(r-x):x in [1..r]]; return l; end function; CalculNqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); nqr:=x^&+exponents; return nqr; end function; CalculTqr := function (q,r) K_v := GF(q,r); P:=PolynomialRing(K_v); exponents:=CalculExponents(q,r); tqr:=0; for i in exponents do tqr:=tqr + x ^ i;end for; return tqr; end function; CalculOlav := function(q,r) K_vi := GF(q,r); tqr:=CalculTqr(q,r); nqr:=CalculNqr(q,r); resposta:=[: a,b in K_vi|Evaluate(tqr,a) eq Evaluate (nqr,b)]; return resposta; end function; Ex3:=CalculOlav(5,3); long3:=#(Ex3); long3 eq 5^(2*3 -1); Ex5:=CalculOlav(3,1); long5:=#(Ex5); long5 eq 3^(2*1 -1); [:a,b in GF(5)| in Ex3]; [:a,b in GF(3)| in Ex5]; Output: Magma V2.10-6 Thu Mar 18 2004 12:09:38 on modular [Seed = 4242893608] ------------------------------------- true true [ <0, 0>, <1, 2>, <2, 1>, <3, 4>, <4, 3> ] [ <0, 0>, <1, 1>, <2, 2> ] Total time: 3.119 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host dsl81-215-29661.adsl.ttnet.net.tr. (81.215.115.221) Time: Thu Mar 18 14:15:18 2004 Input: UEUHF88RFEII9 IIFG9I 43FUJ9RIFIU8239 92FR9IH8U4RJU Output: Magma V2.10-6 Thu Mar 18 2004 14:15:15 on modular [Seed = 185777728] ------------------------------------- >> UEUHF88RFEII9 IIFG9I 43FUJ9RIFIU8239 92FR9IH8U4RJU; ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host chaucer.math.psu.edu. (146.186.131.57) Time: Thu Mar 18 14:28:59 2004 Input: A:=[2,3;1,4]; JordanForm(A); Output: Magma V2.10-6 Thu Mar 18 2004 14:28:56 on modular [Seed = 540645456] ------------------------------------- >> A:=[2,3;1,4]; ^ User error: bad syntax >> JordanForm(A);; ^ User error: Identifier 'A' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host chaucer.math.psu.edu. (146.186.131.57) Time: Thu Mar 18 14:29:11 2004 Input: A:=Matrix([2,3;1,4]); JordanForm(A); Output: Magma V2.10-6 Thu Mar 18 2004 14:29:08 on modular [Seed = 941719732] ------------------------------------- >> A:=Matrix([2,3;1,4]); ^ User error: bad syntax >> JordanForm(A);; ^ User error: Identifier 'A' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host chaucer.math.psu.edu. (146.186.131.57) Time: Thu Mar 18 14:29:28 2004 Input: A:=Matrix([[2,3],[1,4]]); JordanForm(A); Output: Magma V2.10-6 Thu Mar 18 2004 14:29:25 on modular [Seed = 808028333] ------------------------------------- >> JordanForm(A);; ^ Runtime error in 'JordanForm': Coefficient ring of argument 1 is not a field Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host chaucer.math.psu.edu. (146.186.131.57) Time: Thu Mar 18 14:30:50 2004 Input: R:=MatrixAlgebra(Rationals(),2); A:=Matrix([[2,3],[1,4]]); JordanForm(A); Output: Magma V2.10-6 Thu Mar 18 2004 14:30:47 on modular [Seed = 1331099552] ------------------------------------- >> JordanForm(A);; ^ Runtime error in 'JordanForm': Coefficient ring of argument 1 is not a field Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host chaucer.math.psu.edu. (146.186.131.57) Time: Thu Mar 18 14:31:02 2004 Input: R:=MatrixAlgebra(Rationals(),2); A:=R!Matrix([[2,3],[1,4]]); JordanForm(A); Output: Magma V2.10-6 Thu Mar 18 2004 14:30:59 on modular [Seed = 1197408188] ------------------------------------- [5 0] [0 1] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host chaucer.math.psu.edu. (146.186.131.57) Time: Thu Mar 18 14:32:02 2004 Input: R:=MatrixAlgebra(Rationals(),2); A:=R!Matrix([[2,3],[1,4]]); J,T:=JordanForm(A); J; T; Output: Magma V2.10-6 Thu Mar 18 2004 14:31:59 on modular [Seed = 1363732598] ------------------------------------- [5 0] [0 1] [ 1 3] [-3 3] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 66-126-189-162.centralsan.dst.ca.us. (66.126.189.162) Time: Thu Mar 18 14:47:57 2004 Input: log(131071) Output: Magma V2.10-6 Thu Mar 18 2004 14:47:54 on modular [Seed = 2392273516] ------------------------------------- >> log(131071); ^ User error: Identifier 'log' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Thu Mar 18 16:49:16 2004 Input: n*(n^2-9*n+2)/2 Output: Magma V2.10-6 Thu Mar 18 2004 16:49:13 on modular [Seed = 2863723514] ------------------------------------- >> n*(n^2-9*n+2)/2; ^ User error: Identifier 'n' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Thu Mar 18 16:49:40 2004 Input: n=1204288 n*(n^2-9*n+2)/2 Output: Magma V2.10-6 Thu Mar 18 2004 16:49:37 on modular [Seed = 2780822749] ------------------------------------- >> n*(n^2-9*n+2)/2; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Thu Mar 18 16:50:01 2004 Input: n=1204288; n*(n^2-9*n+2)/2 Output: Magma V2.10-6 Thu Mar 18 2004 16:49:57 on modular [Seed = 3165054256] ------------------------------------- >> n=1204288; ^ User error: Identifier 'n' has not been declared or assigned >> n*(n^2-9*n+2)/2; ^ User error: Identifier 'n' has not been declared or assigned Total time: 3.119 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host c-67-163-82-183.client.comcast.net. (67.163.82.183) Time: Thu Mar 18 20:28:21 2004 Input: x=2y^3-y^4 Output: Magma V2.10-6 Thu Mar 18 2004 20:28:18 on modular [Seed = 2441846056] ------------------------------------- >> x=2y^3-y^4; ^ User error: bad syntax Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host c-67-163-82-183.client.comcast.net. (67.163.82.183) Time: Thu Mar 18 20:28:48 2004 Input: x=2(y^3)-(y^4) Output: Magma V2.10-6 Thu Mar 18 2004 20:28:46 on modular [Seed = 2830279789] ------------------------------------- >> x=2(y^3)-(y^4); ^ User error: Identifier 'y' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host c-67-163-82-183.client.comcast.net. (67.163.82.183) Time: Thu Mar 18 20:29:11 2004 Input: x=2(y^3)-(y^4),y Output: Magma V2.10-6 Thu Mar 18 2004 20:29:08 on modular [Seed = 2814225224] ------------------------------------- >> x=2(y^3)-(y^4),y; ^ User error: Identifier 'y' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (192.146.136.129) Time: Thu Mar 18 20:38:16 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Thu Mar 18 2004 20:38:13 on modular [Seed = 3386099399] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (192.146.136.129) Time: Thu Mar 18 20:39:23 2004 Input: > W1 := CoxeterGroup( GrpFPCox, "B4" ); > W2 := CoxeterGroup( GrpFPCox, "C4" ); > IsCoxeterIsomorphic( W1, W2 ); Output: Magma V2.10-6 Thu Mar 18 2004 20:39:19 on modular [Seed = 3235565452] ------------------------------------- true [ 1, 2, 3, 4 ] Total time: 3.049 seconds, Total memory usage: 2.39MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Mar 18 21:16:54 2004 Input: F := PolynomialRing(RationalField()); N := NumberField(x^2 + 5); M := NumberField(x^2 + 3); K := MergeField(N, M); G, phi := UnitGroup(K); G; Output: Magma V2.10-6 Thu Mar 18 2004 21:16:50 on modular [Seed = 641482296] ------------------------------------- >> K := MergeField(N, M); ^ User error: Identifier 'MergeField' has not been declared or assigned >> G, phi := UnitGroup(K); ^ User error: Identifier 'K' has not been declared or assigned >> G;; ^ User error: Identifier 'G' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Mar 18 21:21:08 2004 Input: Q := PolynomialRing(RationalField()); K := NumberField(x^2+3, x^2+2 default:=true); G, phi := UnitGroup(K); G; Output: Magma V2.10-6 Thu Mar 18 2004 21:21:05 on modular [Seed = 808069421] ------------------------------------- >> K := NumberField(x^2+3, x^2+2 default:=true); ^ User error: bad syntax >> G, phi := UnitGroup(K); ^ User error: Identifier 'K' has not been declared or assigned >> G;; ^ User error: Identifier 'G' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Mar 18 21:21:21 2004 Input: Q := PolynomialRing(RationalField()); K := NumberField(x^2+3, x^2+2, default:=true); G, phi := UnitGroup(K); G; Output: Magma V2.10-6 Thu Mar 18 2004 21:21:18 on modular [Seed = 1230196827] ------------------------------------- >> K := NumberField(x^2+3, x^2+2, default:=true); ^ User error: bad syntax >> G, phi := UnitGroup(K); ^ User error: Identifier 'K' has not been declared or assigned >> G;; ^ User error: Identifier 'G' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Mar 18 21:21:35 2004 Input: Q := PolynomialRing(RationalField()); K := NumberField(x^2+3, x^2+2 Default:=true); G, phi := UnitGroup(K); G; Output: Magma V2.10-6 Thu Mar 18 2004 21:21:32 on modular [Seed = 1113086818] ------------------------------------- >> K := NumberField(x^2+3, x^2+2 Default:=true); ^ User error: bad syntax >> G, phi := UnitGroup(K); ^ User error: Identifier 'K' has not been declared or assigned >> G;; ^ User error: Identifier 'G' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Mar 18 21:24:14 2004 Input: F := PolynomialRing(RationalField()); M := ext; M; G, phi := UnitGroup(M); G; Output: Magma V2.10-6 Thu Mar 18 2004 21:24:11 on modular [Seed = 1414417811] ------------------------------------- Number Field with defining polynomial $.1^2 + 2 over its ground field Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*G.1 = 0 Total time: 2.959 seconds, Total memory usage: 1.97MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Mar 18 21:25:58 2004 Input: K:=CyclotomicField(5); G,phi:=UnitGroup(K); G; Output: Magma V2.10-6 Thu Mar 18 2004 21:25:54 on modular [Seed = 1785753684] ------------------------------------- Abelian Group isomorphic to Z/10 + Z Defined on 2 generators Relations: 10*G.1 = 0 Total time: 3.059 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Mar 18 21:39:59 2004 Input: K:=CyclotomicField(5); G,phi:=UnitGroup(K); G; u:=K!phi(G.2); u; Output: Magma V2.10-6 Thu Mar 18 2004 21:39:56 on modular [Seed = 2291308024] ------------------------------------- Abelian Group isomorphic to Z/10 + Z Defined on 2 generators Relations: 10*G.1 = 0 zeta_5^3 + zeta_5 + 1 Total time: 3.039 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Mar 18 21:40:34 2004 Input: K:=CyclotomicField(5); G,phi:=UnitGroup(K); G; u:=K!phi(G.2); u; v:=K!phi(G.1); v; Output: Magma V2.10-6 Thu Mar 18 2004 21:40:31 on modular [Seed = 2575533066] ------------------------------------- Abelian Group isomorphic to Z/10 + Z Defined on 2 generators Relations: 10*G.1 = 0 zeta_5^3 + zeta_5 + 1 -zeta_5^2 Total time: 3.049 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Mar 18 21:43:11 2004 Input: K:=CyclotomicField(5); G,phi:=UnitGroup(K); G; u:=K!phi(G.2); u; v:=K!phi(G.1); v; Logs(u); Logs(v); Output: Magma V2.10-6 Thu Mar 18 2004 21:43:08 on modular [Seed = 2897654428] ------------------------------------- Abelian Group isomorphic to Z/10 + Z Defined on 2 generators Relations: 10*G.1 = 0 zeta_5^3 + zeta_5 + 1 -zeta_5^2 [ -0.48121182505960344749775891342436842313518433438566049999996, 0.48121182505960344749775891342436842313518433438566049999996 ] [ 0.E-57, -7.49999999999999999999999999999999999999999999999999999999872E-53 ] Total time: 3.069 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Mar 18 22:02:46 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^4+10*x^2+1); UnitGroup(K); Output: Magma V2.10-6 Thu Mar 18 2004 22:02:43 on modular [Seed = 3653499654] ------------------------------------- Abelian Group isomorphic to Z/6 + Z Defined on 2 generators Relations: 6*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/6 + Z Defined on 2 generators Relations: 6*$.1 = 0 to Maximal Order of Equation Order with defining polynomial x^4 + 10*x^2 + 1 over its ground order Total time: 3.039 seconds, Total memory usage: 2.07MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Mar 18 22:03:01 2004 Input: Q:=PolynomialRing(RationalField()); K:=NumberField(x^4+10*x^2+1); UnitGroup(K); Output: Magma V2.10-6 Thu Mar 18 2004 22:02:58 on modular [Seed = 3536384060] ------------------------------------- Abelian Group isomorphic to Z/6 + Z Defined on 2 generators Relations: 6*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/6 + Z Defined on 2 generators Relations: 6*$.1 = 0 to Maximal Order of Equation Order with defining polynomial x^4 + 10*x^2 + 1 over its ground order Total time: 3.079 seconds, Total memory usage: 2.07MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Mar 18 22:05:55 2004 Input: Q:=PolynomialRing(RationalField()); K:=NumberField(x^4+10*x^2+1); UnitGroup(K);R:=PolynomialRing(RationalField()); K:=NumberField(x^3-3*x+1); G, phi:=UnitGroup(K); G; u1:=K!phi(G.1); u2:=K!phi(G.2); u3:=K!phi(G.3); Logs(u1); Logs(u2); Logs(u3); Output: Magma V2.10-6 Thu Mar 18 2004 22:05:51 on modular [Seed = 3892167780] ------------------------------------- Abelian Group isomorphic to Z/6 + Z Defined on 2 generators Relations: 6*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/6 + Z Defined on 2 generators Relations: 6*$.1 = 0 to Maximal Order of Equation Order with defining polynomial x^4 + 10*x^2 + 1 over its ground order Abelian Group isomorphic to Z/2 + Z + Z Defined on 3 generators Relations: 2*G.1 = 0 [ 0.E-57, 0.E-57, 0.E-57 ] [ -0.6309447242020459512812798775193268885471288643833906999998, 1.057576813574934871730201141801213067891478387455999999999694, -0.42663208937288892044892126428188617934434952307285679999996 ] [ -0.42663208937288892044892126428188617934434952307285679999996, -0.6309447242020459512812798775193268885471288643833906999998, 1.057576813574934871730201141801213067891478387455999999999694 ] Total time: 3.199 seconds, Total memory usage: 2.07MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Mar 18 22:06:15 2004 Input: Q:=PolynomialRing(RationalField()); K:=NumberField(x^3-3*x+1); G, phi:=UnitGroup(K); G; u1:=K!phi(G.1); u2:=K!phi(G.2); u3:=K!phi(G.3); Logs(u1); Logs(u2); Logs(u3); Output: Magma V2.10-6 Thu Mar 18 2004 22:06:11 on modular [Seed = 4192459345] ------------------------------------- Abelian Group isomorphic to Z/2 + Z + Z Defined on 3 generators Relations: 2*G.1 = 0 [ 0.E-57, 0.E-57, 0.E-57 ] [ -0.6309447242020459512812798775193268885471288643833906999998, 1.057576813574934871730201141801213067891478387455999999999694, -0.42663208937288892044892126428188617934434952307285679999996 ] [ -0.42663208937288892044892126428188617934434952307285679999996, -0.6309447242020459512812798775193268885471288643833906999998, 1.057576813574934871730201141801213067891478387455999999999694 ] Total time: 3.019 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Mar 18 22:13:58 2004 Input: K:=CyclotomicField(10); K; Output: Magma V2.10-6 Thu Mar 18 2004 22:13:55 on modular [Seed = 18556031] ------------------------------------- Cyclotomic Field of order 10 and degree 4 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Thu Mar 18 22:22:45 2004 Input: log(9999399973 Output: Magma V2.10-6 Thu Mar 18 2004 22:22:35 on modular [Seed = 1548122922] ------------------------------------- >> log(9999399973; ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Thu Mar 18 22:23:01 2004 Input: log(9999399973); Output: Magma V2.10-6 Thu Mar 18 2004 22:22:58 on modular [Seed = 1347057615] ------------------------------------- >> log(9999399973);; ^ User error: Identifier 'log' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Thu Mar 18 22:24:44 2004 Input: log 100 Output: Magma V2.10-6 Thu Mar 18 2004 22:24:41 on modular [Seed = 1702838930] ------------------------------------- >> log 100; ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Thu Mar 18 22:27:24 2004 Input: Log(100) Output: Magma V2.10-6 Thu Mar 18 2004 22:27:21 on modular [Seed = 2053133038] ------------------------------------- 4.60517018598809136803598290931 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Thu Mar 18 22:27:39 2004 Input: Log(9999399973) Output: Magma V2.10-6 Thu Mar 18 2004 22:27:36 on modular [Seed = 2375525672] ------------------------------------- 23.0257909254402228235737383381173 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Thu Mar 18 22:30:45 2004 Input: Exp(20.1304956) Output: Magma V2.10-6 Thu Mar 18 2004 22:30:42 on modular [Seed = 2642916594] ------------------------------------- 552793791.85993657777316487757365229965 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Thu Mar 18 22:34:26 2004 Input: Iroot(9999399973,6) Output: Magma V2.10-6 Thu Mar 18 2004 22:34:23 on modular [Seed = 2542648741] ------------------------------------- 46 Total time: 2.859 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Thu Mar 18 22:34:48 2004 Input: Iroot(9999399973,5) Output: Magma V2.10-6 Thu Mar 18 2004 22:34:46 on modular [Seed = 2931066101] ------------------------------------- 99 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Thu Mar 18 22:36:32 2004 Input: 9999399973 div 99 Output: Magma V2.10-6 Thu Mar 18 2004 22:36:29 on modular [Seed = 3165033996] ------------------------------------- 101004040 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Thu Mar 18 22:37:04 2004 Input: 9999399973 div 44 Output: Magma V2.10-6 Thu Mar 18 2004 22:37:01 on modular [Seed = 3081608551] ------------------------------------- 227259090 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Thu Mar 18 22:37:18 2004 Input: 9999399973 div 43 Output: Magma V2.10-6 Thu Mar 18 2004 22:37:15 on modular [Seed = 3470058536] ------------------------------------- 232544185 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Thu Mar 18 22:37:45 2004 Input: 9999399973 div 42 Output: Magma V2.10-6 Thu Mar 18 2004 22:37:42 on modular [Seed = 3252415178] ------------------------------------- 238080951 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Thu Mar 18 22:39:17 2004 Input: Round(9999399973 * 0.5) Output: Magma V2.10-6 Thu Mar 18 2004 22:39:14 on modular [Seed = 3636655031] ------------------------------------- 4999699987 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Thu Mar 18 22:50:59 2004 Input: Round( Root( 3 * Log(9999399973)/Log(Log(9999399973)),3)) Output: Magma V2.10-6 Thu Mar 18 2004 22:50:56 on modular [Seed = 4293251538] ------------------------------------- 3 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Mar 18 23:05:38 2004 Input: Q:=PolynomialRing(RationalField(); IsIrreducible(x^3-3*x+1); Output: Magma V2.10-6 Thu Mar 18 2004 23:05:35 on modular [Seed = 285941904] ------------------------------------- >> Q:=PolynomialRing(RationalField(); ^ User error: bad syntax >> IsIrreducible(x^3-3*x+1); ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Mar 18 23:08:04 2004 Input: R:=PolynomialRing(RationalField()); IsIrreducible(x^3-3*x+1); Output: Magma V2.10-6 Thu Mar 18 2004 23:08:01 on modular [Seed = 658314504] ------------------------------------- true Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Thu Mar 18 23:10:21 2004 Input: P := PolynomialRing(Integers(),2); F := P!0; F := 38*X^3+53*X^2*Y-208*X*Y^2+448*Y^3; Q := PolynomialRing(Integers()); f := Q!Evaluate(F,[X,1]); Evaluate(f,1075); Output: Magma V2.10-6 Thu Mar 18 2004 23:10:18 on modular [Seed = 1280737000] ------------------------------------- 47268306223 Total time: 2.869 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Thu Mar 18 23:11:08 2004 Input: P := PolynomialRing(Integers(),2); F := P!0; F := 38*X^3+53*X^2*Y-208*X*Y^2+448*Y^3; Q := PolynomialRing(Integers()); f := Q!Evaluate(F,[X,1]); Evaluate(F,[X,1]); Output: Magma V2.10-6 Thu Mar 18 2004 23:11:05 on modular [Seed = 1113092245] ------------------------------------- 38*X^3 + 53*X^2 - 208*X + 448 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Thu Mar 18 23:11:22 2004 Input: P:= FunctionField(GF(3)); Q:= PolynomialRing(P); f:=x^6+x+t; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Thu Mar 18 2004 23:11:19 on modular [Seed = 1531013554] ------------------------------------- x^6 + x + t Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 5, 6) (1, 2) 16 6 Total time: 3.039 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Thu Mar 18 23:11:43 2004 Input: P:= FunctionField(GF(3)); Q:= PolynomialRing(P); f:=x^6+x+t; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Thu Mar 18 2004 23:11:40 on modular [Seed = 1397318049] ------------------------------------- x^6 + x + t Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 5, 6) (1, 2) 16 6 Total time: 2.919 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Thu Mar 18 23:12:20 2004 Input: P:= FunctionField(GF(3)); Q:= PolynomialRing(P); f:=x^6+x^3-t^2; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Thu Mar 18 2004 23:12:17 on modular [Seed = 1635471950] ------------------------------------- x^6 + x^3 + 2*t^2 >> G, R:= GaloisGroup(f); ^ Runtime error in 'GaloisGroup': Polynomial is not separable >> print(G); ^ User error: Identifier 'G' has not been declared or assigned >> t1, t2:= TransitiveGroupIdentification(G); ^ User error: Identifier 'G' has not been declared or assigned >> print(t1); ^ User error: Identifier 't1' has not been declared or assigned >> print(t2);; ^ User error: Identifier 't2' has not been declared or assigned Total time: 3.449 seconds, Total memory usage: 8.26MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Thu Mar 18 23:12:30 2004 Input: P := PolynomialRing(Integers(),2); F := P!0; F := 38*X^3+53*X^2*Y-208*X*Y^2+448*Y^3; Q := PolynomialRing(Integers()); f := Q!Evaluate(F,[X,1]); Evaluate(F,[1075,1]); Output: Magma V2.10-6 Thu Mar 18 2004 23:12:27 on modular [Seed = 1986807123] ------------------------------------- 47268306223 Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Thu Mar 18 23:13:03 2004 Input: P := PolynomialRing(Integers(),2); F := P!0; F := 38*X^3+53*X^2*Y-208*X*Y^2+448*Y^3; Q := PolynomialRing(Integers()); f := Q!Evaluate(F,[X,1]); Q!Evaluate(F,[1075,1]); Output: Magma V2.10-6 Thu Mar 18 2004 23:13:00 on modular [Seed = 2408955085] ------------------------------------- 47268306223 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Thu Mar 18 23:15:02 2004 Input: P := PolynomialRing(Integers(),2); F := P!0; F := 8*X^3+53*X^2*Y-208*X*Y^2+448*Y^3; Q := PolynomialRing(Integers()); f := Q!Evaluate(F,[X,1]); Q!Evaluate(F,[1075,1]); Output: Magma V2.10-6 Thu Mar 18 2004 23:14:59 on modular [Seed = 2207887438] ------------------------------------- 9999399973 Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Thu Mar 18 23:15:11 2004 Input: P:= FunctionField(GF(3)); Q:= PolynomialRing(P); f:=x^6+x+t; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Thu Mar 18 2004 23:15:08 on modular [Seed = 2492376918] ------------------------------------- x^6 + x + t Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 5, 6) (1, 2) 16 6 Total time: 2.979 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Thu Mar 18 23:15:21 2004 Input: P := PolynomialRing(Integers(),2); F := P!0; F := 8*X^3+53*X^2*Y-208*X*Y^2+448*Y^3; Q := PolynomialRing(Integers()); f := Q!Evaluate(F,[X,1]); Q!Evaluate(f,1075); Output: Magma V2.10-6 Thu Mar 18 2004 23:15:18 on modular [Seed = 2914492021] ------------------------------------- 9999399973 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Thu Mar 18 23:15:36 2004 Input: P:= FunctionField(GF(3)); Q:= PolynomialRing(P); f:=x^6+2*x^3-t^2; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Thu Mar 18 2004 23:15:33 on modular [Seed = 2730004809] ------------------------------------- x^6 + 2*x^3 + 2*t^2 >> G, R:= GaloisGroup(f); ^ Runtime error in 'GaloisGroup': Polynomial is not separable >> print(G); ^ User error: Identifier 'G' has not been declared or assigned >> t1, t2:= TransitiveGroupIdentification(G); ^ User error: Identifier 'G' has not been declared or assigned >> print(t1); ^ User error: Identifier 't1' has not been declared or assigned >> print(t2);; ^ User error: Identifier 't2' has not been declared or assigned Total time: 3.479 seconds, Total memory usage: 8.26MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Thu Mar 18 23:16:00 2004 Input: P:= FunctionField(GF(3)); Q:= PolynomialRing(P); f:=x^6+2*x^3-t^2; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Thu Mar 18 2004 23:15:57 on modular [Seed = 2963964739] ------------------------------------- x^6 + 2*x^3 + 2*t^2 >> G, R:= GaloisGroup(f); ^ Runtime error in 'GaloisGroup': Polynomial is not separable >> print(G); ^ User error: Identifier 'G' has not been declared or assigned >> t1, t2:= TransitiveGroupIdentification(G); ^ User error: Identifier 'G' has not been declared or assigned >> print(t1); ^ User error: Identifier 't1' has not been declared or assigned >> print(t2);; ^ User error: Identifier 't2' has not been declared or assigned Total time: 3.539 seconds, Total memory usage: 8.26MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Thu Mar 18 23:16:18 2004 Input: P := PolynomialRing(Integers(),2); F := P!0; F := 8*X^3+53*X^2*Y-208*X*Y^2+448*Y^3; Q := PolynomialRing(Integers()); f := Q!Evaluate(F,[X,1]); Q!Evaluate(f,1075); K:=GF(3); Roots(f,K); Output: Magma V2.10-6 Thu Mar 18 2004 23:16:15 on modular [Seed = 3386113480] ------------------------------------- 9999399973 [] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Thu Mar 18 23:16:35 2004 Input: P := PolynomialRing(Integers(),2); F := P!0; F := 8*X^3+53*X^2*Y-208*X*Y^2+448*Y^3; Q := PolynomialRing(Integers()); f := Q!Evaluate(F,[X,1]); Q!Evaluate(f,1075); K:=GF(5); Roots(f,K); Output: Magma V2.10-6 Thu Mar 18 2004 23:16:32 on modular [Seed = 3737447152] ------------------------------------- 9999399973 [] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Thu Mar 18 23:16:44 2004 Input: P := PolynomialRing(Integers(),2); F := P!0; F := 8*X^3+53*X^2*Y-208*X*Y^2+448*Y^3; Q := PolynomialRing(Integers()); f := Q!Evaluate(F,[X,1]); Q!Evaluate(f,1075); K:=GF(7); Roots(f,K); Output: Magma V2.10-6 Thu Mar 18 2004 23:16:41 on modular [Seed = 3620594672] ------------------------------------- 9999399973 [ <0, 1>, <1, 1>, <2, 1> ] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Thu Mar 18 23:16:57 2004 Input: P := PolynomialRing(Integers(),2); F := P!0; F := 8*X^3+53*X^2*Y-208*X*Y^2+448*Y^3; Q := PolynomialRing(Integers()); f := Q!Evaluate(F,[X,1]); Q!Evaluate(f,1075); K:=GF(11); Roots(f,K); Output: Magma V2.10-6 Thu Mar 18 2004 23:16:54 on modular [Seed = 3975600340] ------------------------------------- 9999399973 [ <2, 1>, <3, 1>, <9, 1> ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Thu Mar 18 23:17:11 2004 Input: P := PolynomialRing(Integers(),2); F := P!0; F := 8*X^3+53*X^2*Y-208*X*Y^2+448*Y^3; Q := PolynomialRing(Integers()); f := Q!Evaluate(F,[X,1]); Q!Evaluate(f,1075); K:=GF(2); Roots(f,K); Output: Magma V2.10-6 Thu Mar 18 2004 23:17:08 on modular [Seed = 3858747823] ------------------------------------- 9999399973 [ <0, 2> ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Thu Mar 18 23:20:00 2004 Input: P:= FunctionField(GF(3)); Q:= PolynomialRing(P); f:=x^6+2*x^3+x^2-t^2; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Thu Mar 18 2004 23:19:56 on modular [Seed = 1717475] ------------------------------------- x^6 + 2*x^3 + x^2 + 2*t^2 Permutation group G acting on a set of cardinality 6 (1, 2)(3, 4, 5, 6) (1, 2, 3) 15 6 Total time: 3.529 seconds, Total memory usage: 8.27MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Thu Mar 18 23:22:44 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6+x+t; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Thu Mar 18 2004 23:22:40 on modular [Seed = 792009392] ------------------------------------- x^6 + x + t Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 2)(3, 4)(5, 6) 14 6 Total time: 3.359 seconds, Total memory usage: 6.62MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Thu Mar 18 23:24:30 2004 Input: P := PolynomialRing(Integers(),2); F := P!0; F := 8*X^3+53*X^2*Y-208*X*Y^2+448*Y^3; Q := PolynomialRing(Integers()); f := Q!Evaluate(F,[X,1]); K:=GF(7); Roots(f,K); Output: Magma V2.10-6 Thu Mar 18 2004 23:24:27 on modular [Seed = 658313939] ------------------------------------- [ <0, 1>, <1, 1>, <2, 1> ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Mar 18 23:25:40 2004 Input: Q:=PolynomialRing(RationalField()); K:=NumberField(x^2+3); UnitGroup(K); Output: Magma V2.10-6 Thu Mar 18 2004 23:25:37 on modular [Seed = 941756022] ------------------------------------- Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 to Maximal Order of Equation Order with defining polynomial x^2 + 3 over its ground order Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Mar 18 23:39:30 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^4 + 10*x^2 + 1); C := ClassGroup(K); K; Output: Magma V2.10-6 Thu Mar 18 2004 23:39:27 on modular [Seed = 1581541166] ------------------------------------- Number Field with defining polynomial x^4 + 10*x^2 + 1 over the Rational Field Total time: 3.279 seconds, Total memory usage: 1.97MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Mar 18 23:39:59 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^10 + 10*x^2 + 1); C := ClassGroup(K); K; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 18 2004 23:39:36 on modular [Seed = 1431268562] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 20314 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Mar 18 23:44:22 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^10 + 10*x^2 + 1); U := UnitGroup(K); K; Output: Magma V2.10-6 Thu Mar 18 2004 23:44:13 on modular [Seed = 1668897265] ------------------------------------- Number Field with defining polynomial x^10 + 10*x^2 + 1 over the Rational Field Total time: 9.069 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Mar 18 23:44:43 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^10 + 10*x^2 + 1); U := UnitGroup(K); U; Output: Magma V2.10-6 Thu Mar 18 2004 23:44:34 on modular [Seed = 2053128391] ------------------------------------- Abelian Group isomorphic to Z/2 + Z + Z + Z + Z Defined on 5 generators Relations: 2*U.1 = 0 Total time: 9.219 seconds, Total memory usage: 3.09MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Mar 18 23:47:35 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^8 + 10*x^2 + 1); U := ClassGroup(K); U; Output: Magma V2.10-6 Thu Mar 18 2004 23:47:24 on modular [Seed = 2358687711] ------------------------------------- Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*U.1 = 0 Total time: 11.239 seconds, Total memory usage: 2.59MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Mar 18 23:49:00 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^8 + 10*x^2 + 1); U := UnitGroup(K); U; Output: Magma V2.10-6 Thu Mar 18 2004 23:48:54 on modular [Seed = 2207889466] ------------------------------------- Abelian Group isomorphic to Z/2 + Z + Z + Z Defined on 4 generators Relations: 2*U.1 = 0 Total time: 5.429 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Mar 18 23:49:53 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^8 + 6*x^3-15*x^2 + 1); U := UnitGroup(K); U; Output: Magma V2.10-6 Thu Mar 18 2004 23:49:43 on modular [Seed = 2592121202] ------------------------------------- Abelian Group isomorphic to Z/2 + Z (5 copies) Defined on 6 generators Relations: 2*U.1 = 0 Total time: 9.159 seconds, Total memory usage: 2.73MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Mar 18 23:50:02 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5 + 6*x^3-15*x^2 + 1); U := UnitGroup(K); U; Output: Magma V2.10-6 Thu Mar 18 2004 23:49:58 on modular [Seed = 2441849448] ------------------------------------- Abelian Group isomorphic to Z/2 + Z + Z + Z Defined on 4 generators Relations: 2*U.1 = 0 Total time: 4.239 seconds, Total memory usage: 2.49MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Mar 18 23:50:39 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5 + 6*x^3-15*x^2 + 1); U := ClassGroup(K); U; Output: Magma V2.10-6 Thu Mar 18 2004 23:50:35 on modular [Seed = 2713427378] ------------------------------------- Abelian Group of order 1 Total time: 3.789 seconds, Total memory usage: 2.29MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Mar 18 23:51:49 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^15 + 6*x^3-15*x^2 + 1); U := ClassGroup(K); U; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 18 2004 23:51:26 on modular [Seed = 3081604086] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 20408 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Mar 18 23:52:24 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^15 + 6*x^3-15*x^2 + 1); U := UnitGroup(K); U; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 18 2004 23:52:01 on modular [Seed = 3470062256] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 20417 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Mar 18 23:53:07 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^12 + 6*x^3-15*x^2 + 1); U := UnitGroup(K); U; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 18 2004 23:52:44 on modular [Seed = 3319789910] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 20426 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Mar 18 23:53:36 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^11 + 6*x^3-15*x^2 + 1); U := UnitGroup(K); U; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 18 2004 23:53:13 on modular [Seed = 3587172707] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 20442 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Mar 18 23:54:05 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^11 -15*x^2 + 1); U := UnitGroup(K); U; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 18 2004 23:53:42 on modular [Seed = 3975598133] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 20451 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Mar 18 23:54:30 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^11 -3*x^2 + 1); U := UnitGroup(K); U; Output: Magma V2.10-6 Thu Mar 18 2004 23:54:23 on modular [Seed = 3824803564] ------------------------------------- Abelian Group isomorphic to Z/2 + Z (6 copies) Defined on 7 generators Relations: 2*U.1 = 0 Total time: 6.909 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Mar 18 23:55:28 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^11 -3*x^2 + 1); U := ClassGroup(K); U; Output: Magma V2.10-6 Thu Mar 18 2004 23:55:12 on modular [Seed = 4142713801] ------------------------------------- Abelian Group of order 1 Total time: 16.809 seconds, Total memory usage: 2.70MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Mar 18 23:55:58 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^13 -2*x^2 + 1); U := ClassGroup(K); U; Output: Magma V2.10-6 Thu Mar 18 2004 23:55:55 on modular [Seed = 302526297] ------------------------------------- >> K := NumberField(x^13 -2*x^2 + 1); ^ Runtime error in 'NumberField': Argument 1 is not irreducible >> U := ClassGroup(K); ^ User error: Identifier 'K' has not been declared or assigned >> U; ^ User error: Identifier 'U' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Mar 18 23:56:28 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^13 -2*x^2 + 2); U := ClassGroup(K); U; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 18 2004 23:56:05 on modular [Seed = 470163817] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 20492 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Mar 18 23:56:45 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^13 -2*x^2 + 2); U := UnitGroup(K); U; Output: Magma V2.10-6 Thu Mar 18 2004 23:56:36 on modular [Seed = 85932177] ------------------------------------- Abelian Group isomorphic to Z/2 + Z (6 copies) Defined on 7 generators Relations: 2*U.1 = 0 Total time: 8.880 seconds, Total memory usage: 3.00MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Fri Mar 19 00:01:35 2004 Input: 9999399973 div 99^3 Output: Magma V2.10-6 Fri Mar 19 2004 00:01:32 on modular [Seed = 691214229] ------------------------------------- 10305 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Mar 19 00:08:47 2004 Input: P:= FunctionField(GF(3)); Q:= PolynomialRing(P); f:=x^6+2*x^3+x^2-t^2; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Fri Mar 19 2004 00:08:43 on modular [Seed = 1531026192] ------------------------------------- x^6 + 2*x^3 + x^2 + 2*t^2 Permutation group G acting on a set of cardinality 6 (1, 2)(3, 4, 5, 6) (1, 2, 3) 15 6 Total time: 3.429 seconds, Total memory usage: 8.27MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Mar 19 00:10:29 2004 Input: P:= FunctionField(GF(3)); Q:= PolynomialRing(P); f:=x^6+x^3+t*x^2-t^2; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Fri Mar 19 2004 00:10:26 on modular [Seed = 1263635353] ------------------------------------- x^6 + x^3 + t*x^2 + 2*t^2 Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 Total time: 3.559 seconds, Total memory usage: 8.46MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Fri Mar 19 00:10:48 2004 Input: K:=CyclotomicField(9); U:UnitGroup(K); U; Output: Magma V2.10-6 Fri Mar 19 2004 00:10:45 on modular [Seed = 1953412273] ------------------------------------- >> U:UnitGroup(K); ^ User error: bad syntax >> U; ^ User error: Identifier 'U' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Fri Mar 19 00:10:59 2004 Input: K:=CyclotomicField(9); U:=UnitGroup(K); U; Output: Magma V2.10-6 Fri Mar 19 2004 00:10:56 on modular [Seed = 2103950733] ------------------------------------- Abelian Group isomorphic to Z/18 + Z + Z Defined on 3 generators Relations: 18*U.1 = 0 Total time: 3.119 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Fri Mar 19 00:12:51 2004 Input: 9999399973 div 1075^3 Output: Magma V2.10-6 Fri Mar 19 2004 00:12:48 on modular [Seed = 1869983279] ------------------------------------- 8 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Fri Mar 19 00:13:44 2004 Input: 9999399973 div 1070^3 Output: Magma V2.10-6 Fri Mar 19 2004 00:13:41 on modular [Seed = 2558679309] ------------------------------------- 8 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Fri Mar 19 00:13:56 2004 Input: 9999399973 div 1000^3 Output: Magma V2.10-6 Fri Mar 19 2004 00:13:53 on modular [Seed = 2174435328] ------------------------------------- 9 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Fri Mar 19 00:15:37 2004 Input: 9999399973 div 1077^3 Output: Magma V2.10-6 Fri Mar 19 2004 00:15:34 on modular [Seed = 2392084328] ------------------------------------- 8 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Fri Mar 19 00:16:04 2004 Input: 9999399973 div 879^3 Output: Magma V2.10-6 Fri Mar 19 2004 00:16:00 on modular [Seed = 3131078843] ------------------------------------- 14 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Mar 19 00:17:19 2004 Input: P:= FunctionField(GF(3)); Q:= PolynomialRing(P); f:=x^6+x^4+x^3-t^2; print(f); G, R:= GaloisGroup(f); print(G); print(Order(G)); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Fri Mar 19 2004 00:17:16 on modular [Seed = 2763941608] ------------------------------------- x^6 + x^4 + x^3 + 2*t^2 Permutation group G acting on a set of cardinality 6 (1, 2)(3, 4, 5, 6) (1, 2, 3) 360 15 6 Total time: 3.569 seconds, Total memory usage: 8.26MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Mar 19 00:17:58 2004 Input: P:= FunctionField(GF(3)); Q:= PolynomialRing(P); f:=x^6+x^4+x^3-t^2; print(f); G, R:= GaloisGroup(f); print(G); print(Order(G)); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Fri Mar 19 2004 00:17:55 on modular [Seed = 2897636927] ------------------------------------- x^6 + x^4 + x^3 + 2*t^2 Permutation group G acting on a set of cardinality 6 (1, 2)(3, 4, 5, 6) (1, 2, 3) 360 15 6 Total time: 3.419 seconds, Total memory usage: 8.26MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Fri Mar 19 00:19:00 2004 Input: n:=9999399973 d:=3 low_m1 := Iroot( Iroot( n, d+1 ) * Iroot( n, d ) , 2 ); high_m1 := Iroot( n, d ); n div high_m1^d; n div low_m1^d; Output: Magma V2.10-6 Fri Mar 19 2004 00:18:57 on modular [Seed = 3570275845] ------------------------------------- >> d:=3 ^ User error: bad syntax >> low_m1 := Iroot( Iroot( n, d+1 ) * Iroot( n, d ) , 2 ); ^ User error: Identifier 'n' has not been declared or assigned >> high_m1 := Iroot( n, d ); ^ User error: Identifier 'n' has not been declared or assigned >> n div high_m1^d; ^ User error: Identifier 'n' has not been declared or assigned >> n div low_m1^d;; ^ User error: Identifier 'n' has not been declared or assigned Total time: 3.239 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Mar 19 00:19:03 2004 Input: P:= FunctionField(GF(3)); Q:= PolynomialRing(P); f:=x^6+x^4+x^3-t^2; print(f); G, R:= GaloisGroup(f); print(G); print(Order(G)); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Fri Mar 19 2004 00:18:59 on modular [Seed = 3620541700] ------------------------------------- x^6 + x^4 + x^3 + 2*t^2 Permutation group G acting on a set of cardinality 6 (1, 2)(3, 4, 5, 6) (1, 2, 3) 360 15 6 Total time: 3.719 seconds, Total memory usage: 8.26MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Fri Mar 19 00:19:34 2004 Input: n := 9999399973 d := 3 low_m1 := Iroot( Iroot( n, d+1 ) * Iroot( n, d ) , 2 ); high_m1 := Iroot( n, d ); n div high_m1^d; n div low_m1^d; Output: Magma V2.10-6 Fri Mar 19 2004 00:19:31 on modular [Seed = 3336307765] ------------------------------------- >> d := 3 ^ User error: bad syntax >> low_m1 := Iroot( Iroot( n, d+1 ) * Iroot( n, d ) , 2 ); ^ User error: Identifier 'n' has not been declared or assigned >> high_m1 := Iroot( n, d ); ^ User error: Identifier 'n' has not been declared or assigned >> n div high_m1^d; ^ User error: Identifier 'n' has not been declared or assigned >> n div low_m1^d;; ^ User error: Identifier 'n' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Fri Mar 19 00:20:04 2004 Input: n := 9999399973; d := 3; low_m1 := Iroot( Iroot( n, d+1 ) * Iroot( n, d ) , 2 ); high_m1 := Iroot( n, d ); n div high_m1^d; n div low_m1^d; Output: Magma V2.10-6 Fri Mar 19 2004 00:20:01 on modular [Seed = 4142675431] ------------------------------------- 1 17 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Fri Mar 19 00:22:28 2004 Input: n := 9999399973; d := 3; a_d := 8; low_m1 := Iroot( Iroot( n, d+1 ) * Iroot( n, d ) , 2 ); high_m1 := Iroot( n, d ); n div high_m1^d; n div low_m1^d; Iroot( n div a_d, d ); Output: Magma V2.10-6 Fri Mar 19 2004 00:22:26 on modular [Seed = 3774489442] ------------------------------------- 1 17 1077 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Fri Mar 19 00:23:02 2004 Input: n := 9999399973; d := 3; a_d := 8; low_m1 := Iroot( Iroot( n, d+1 ) * Iroot( n, d ) , 2 ); high_m1 := Iroot( n, d ); n div high_m1^d; n div low_m1^d; Iroot( n div a_d, d ); (n - a_d*best_m1^d) div best_m1^(d-1); Output: Magma V2.10-6 Fri Mar 19 2004 00:22:59 on modular [Seed = 3925027402] ------------------------------------- 1 17 1077 >> (n - a_d*best_m1^d) div best_m1^(d-1);; ^ User error: Identifier 'best_m1' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Fri Mar 19 00:23:29 2004 Input: n := 9999399973; d := 3; a_d := 8; low_m1 := Iroot( Iroot( n, d+1 ) * Iroot( n, d ) , 2 ); high_m1 := Iroot( n, d ); n div high_m1^d; n div low_m1^d; best_m1 := Iroot( n div a_d, d ); (n - a_d*best_m1^d) div best_m1^(d-1); Output: Magma V2.10-6 Fri Mar 19 2004 00:23:26 on modular [Seed = 319410380] ------------------------------------- 1 17 4 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Mar 19 00:24:47 2004 Input: P:= FunctionField(GF(3)); Q:= PolynomialRing(P); f:=x^6+t*x^4+x^3-t^2; print(f); G, R:= GaloisGroup(f); print(G); print(Order(G)); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Fri Mar 19 2004 00:24:44 on modular [Seed = 436264471] ------------------------------------- x^6 + t*x^4 + x^3 + 2*t^2 Permutation group G acting on a set of cardinality 6 (1, 2)(3, 4, 5, 6) (1, 2, 3) 360 15 6 Total time: 3.429 seconds, Total memory usage: 8.46MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Fri Mar 19 00:24:55 2004 Input: n := 9999399973; d := 3; a_d := 8; low_m1 := Iroot( Iroot( n, d+1 ) * Iroot( n, d ) , 2 ); high_m1 := Iroot( n, d ); n div high_m1^d; n div low_m1^d; best_m1 := Iroot( n div a_d, d ); a_dminus1 := (n - a_d*best_m1^d) div best_m1^(d-1); coeff_bound := Round( best_m1 * 0.5 ); k := (coeff_bound - a_dminus1) div (a_d * d); Output: Magma V2.10-6 Fri Mar 19 2004 00:24:52 on modular [Seed = 85967152] ------------------------------------- 1 17 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Fri Mar 19 00:25:13 2004 Input: n := 9999399973; d := 3; a_d := 8; low_m1 := Iroot( Iroot( n, d+1 ) * Iroot( n, d ) , 2 ); high_m1 := Iroot( n, d ); n div high_m1^d; n div low_m1^d; best_m1 := Iroot( n div a_d, d ); a_dminus1 := (n - a_d*best_m1^d) div best_m1^(d-1); coeff_bound := Round( best_m1 * 0.5 ); (coeff_bound - a_dminus1) div (a_d * d); Output: Magma V2.10-6 Fri Mar 19 2004 00:25:10 on modular [Seed = 808121367] ------------------------------------- 1 17 22 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Fri Mar 19 00:26:46 2004 Input: n := 9999399973; d := 3; a_d := 8; low_m1 := Iroot( Iroot( n, d+1 ) * Iroot( n, d ) , 2 ); high_m1 := Iroot( n, d ); n div high_m1^d; n div low_m1^d; best_m1 := Iroot( n div a_d, d ); a_dminus1 := (n - a_d*best_m1^d) div best_m1^(d-1); coeff_bound := Round( best_m1 * 0.5 ); print coeff_bound (coeff_bound - a_dminus1) div (a_d * d); Output: Magma V2.10-6 Fri Mar 19 2004 00:26:43 on modular [Seed = 975240888] ------------------------------------- 1 17 >> (coeff_bound - a_dminus1) div (a_d * d); ^ Runtime error: Bad argument types Argument types given: RngIntElt, RngIntElt Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Fri Mar 19 00:26:53 2004 Input: n := 9999399973; d := 3; a_d := 8; low_m1 := Iroot( Iroot( n, d+1 ) * Iroot( n, d ) , 2 ); high_m1 := Iroot( n, d ); n div high_m1^d; n div low_m1^d; best_m1 := Iroot( n div a_d, d ); a_dminus1 := (n - a_d*best_m1^d) div best_m1^(d-1); coeff_bound := Round( best_m1 * 0.5 ); print coeff_bound; (coeff_bound - a_dminus1) div (a_d * d); Output: Magma V2.10-6 Fri Mar 19 2004 00:26:50 on modular [Seed = 624943534] ------------------------------------- 1 17 539 22 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Mar 19 00:28:45 2004 Input: P:= FunctionField(GF(3)); Q:= PolynomialRing(P); f:=x^6+t*x^4+x^3-t^2; print(f); G, R:= GaloisGroup(f); print(G); print(Order(G)); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Fri Mar 19 2004 00:28:42 on modular [Seed = 1464701516] ------------------------------------- x^6 + t*x^4 + x^3 + 2*t^2 Permutation group G acting on a set of cardinality 6 (1, 2)(3, 4, 5, 6) (1, 2, 3) 360 15 6 Total time: 3.419 seconds, Total memory usage: 8.46MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Fri Mar 19 00:29:19 2004 Input: n := 9999399973; d := 3; a_d := 8; low_m1 := Iroot( Iroot( n, d+1 ) * Iroot( n, d ) , 2 ); high_m1 := Iroot( n, d ); n div high_m1^d; n div low_m1^d; best_m1 := Iroot( n div a_d, d ); a_dminus1 := (n - a_d*best_m1^d) div best_m1^(d-1); coeff_bound := Round( best_m1 * 0.5 ); print coeff_bound; (coeff_bound - a_dminus1) div (a_d * d); n div 1055^d Output: Magma V2.10-6 Fri Mar 19 2004 00:29:16 on modular [Seed = 1581554531] ------------------------------------- 1 17 539 22 8 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Fri Mar 19 00:29:30 2004 Input: n := 9999399973; d := 3; a_d := 8; low_m1 := Iroot( Iroot( n, d+1 ) * Iroot( n, d ) , 2 ); high_m1 := Iroot( n, d ); n div high_m1^d; n div low_m1^d; best_m1 := Iroot( n div a_d, d ); a_dminus1 := (n - a_d*best_m1^d) div best_m1^(d-1); coeff_bound := Round( best_m1 * 0.5 ); print coeff_bound; (coeff_bound - a_dminus1) div (a_d * d); n div 1054^d Output: Magma V2.10-6 Fri Mar 19 2004 00:29:27 on modular [Seed = 1230212207] ------------------------------------- 1 17 539 22 8 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Fri Mar 19 00:29:44 2004 Input: n := 9999399973; d := 3; a_d := 8; low_m1 := Iroot( Iroot( n, d+1 ) * Iroot( n, d ) , 2 ); high_m1 := Iroot( n, d ); n div high_m1^d; n div low_m1^d; best_m1 := Iroot( n div a_d, d ); a_dminus1 := (n - a_d*best_m1^d) div best_m1^(d-1); coeff_bound := Round( best_m1 * 0.5 ); print coeff_bound; (coeff_bound - a_dminus1) div (a_d * d); n div 1053^d Output: Magma V2.10-6 Fri Mar 19 2004 00:29:41 on modular [Seed = 1886041380] ------------------------------------- 1 17 539 22 8 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host schnell.scsinternet.com. (216.129.11.6) Time: Fri Mar 19 00:29:55 2004 Input: n := 9999399973; d := 3; a_d := 8; low_m1 := Iroot( Iroot( n, d+1 ) * Iroot( n, d ) , 2 ); high_m1 := Iroot( n, d ); n div high_m1^d; n div low_m1^d; best_m1 := Iroot( n div a_d, d ); a_dminus1 := (n - a_d*best_m1^d) div best_m1^(d-1); coeff_bound := Round( best_m1 * 0.5 ); print coeff_bound; (coeff_bound - a_dminus1) div (a_d * d); n div 1050^d Output: Magma V2.10-6 Fri Mar 19 2004 00:29:52 on modular [Seed = 2070003258] ------------------------------------- 1 17 539 22 8 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.67.220.67) Time: Fri Mar 19 00:45:40 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Fri Mar 19 2004 00:45:37 on modular [Seed = 2224967060] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Mar 19 00:46:04 2004 Input: P:= FunctionField(GF(3)); Q:= PolynomialRing(P); f:=x^6+x^4+t*x^3-t^2; print(f); G, R:= GaloisGroup(f); print(G); print(Order(G)); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Fri Mar 19 2004 00:46:00 on modular [Seed = 2408924806] ------------------------------------- x^6 + x^4 + t*x^3 + 2*t^2 Permutation group G acting on a set of cardinality 6 (1, 2)(3, 4, 5, 6) (1, 2, 3) 360 15 6 Total time: 3.489 seconds, Total memory usage: 8.77MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Mar 19 01:07:36 2004 Input: P:= FunctionField(GF(3)); Q:= PolynomialRing(P); f:=x^6+x^4+t^2*x^3-t^2; print(f); G, R:= GaloisGroup(f); print(G); print(Order(G)); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Fri Mar 19 2004 01:07:32 on modular [Seed = 4242944713] ------------------------------------- x^6 + x^4 + t^2*x^3 + 2*t^2 Permutation group G acting on a set of cardinality 6 (1, 2)(3, 4, 5, 6) (1, 2, 3) 360 15 6 Total time: 3.499 seconds, Total memory usage: 8.27MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Mar 19 01:08:31 2004 Input: P:= FunctionField(GF(3)); Q:= PolynomialRing(P); f:=x^6+t*x^4+t^2*x^3-t^2; print(f); G, R:= GaloisGroup(f); print(G); print(Order(G)); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Fri Mar 19 2004 01:08:27 on modular [Seed = 3892128173] ------------------------------------- x^6 + t*x^4 + t^2*x^3 + 2*t^2 Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 60 12 6 Total time: 3.589 seconds, Total memory usage: 8.47MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Mar 19 01:10:02 2004 Input: P:= FunctionField(GF(3)); Q:= PolynomialRing(P); f:=x^6+t*x^4+x^3-t^2; print(f); G, R:= GaloisGroup(f); print(G); print(Order(G)); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Fri Mar 19 2004 01:09:57 on modular [Seed = 4008976458] ------------------------------------- x^6 + t*x^4 + x^3 + 2*t^2 Permutation group G acting on a set of cardinality 6 (1, 2)(3, 4, 5, 6) (1, 2, 3) 360 15 6 Total time: 3.659 seconds, Total memory usage: 8.46MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Mar 19 01:10:28 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6+x+t; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Fri Mar 19 2004 01:10:24 on modular [Seed = 487052255] ------------------------------------- x^6 + x + t Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 2)(3, 4)(5, 6) 14 6 Total time: 3.359 seconds, Total memory usage: 6.62MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Mar 19 01:10:58 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6+x+t; print(f); G, R:= GaloisGroup(f); print(G); print(Order(G)); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Fri Mar 19 2004 01:10:55 on modular [Seed = 168871159] ------------------------------------- x^6 + x + t Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 2)(3, 4)(5, 6) 120 14 6 Total time: 3.299 seconds, Total memory usage: 6.62MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Mar 19 01:11:16 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6+x+t^2; print(f); G, R:= GaloisGroup(f); print(G); print(Order(G)); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Fri Mar 19 2004 01:11:12 on modular [Seed = 808124195] ------------------------------------- x^6 + x + t^2 Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 60 12 6 Total time: 3.319 seconds, Total memory usage: 6.62MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Mar 19 01:11:44 2004 Input: P:= FunctionField(GF(3)); Q:= PolynomialRing(P); f:=x^6+t*x^4+x^3-t^2; print(f); G, R:= GaloisGroup(f); print(G); print(Order(G)); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Fri Mar 19 2004 01:11:40 on modular [Seed = 641526056] ------------------------------------- x^6 + t*x^4 + x^3 + 2*t^2 Permutation group G acting on a set of cardinality 6 (1, 2)(3, 4, 5, 6) (1, 2, 3) 360 15 6 Total time: 3.489 seconds, Total memory usage: 8.46MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Mar 19 01:12:05 2004 Input: P:= FunctionField(GF(3)); Q:= PolynomialRing(P); f:=x^6 + t*x^4 + t^2*x^3 + 2*t^2; print(f); G, R:= GaloisGroup(f); print(G); print(Order(G)); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Fri Mar 19 2004 01:12:02 on modular [Seed = 792059919] ------------------------------------- x^6 + t*x^4 + t^2*x^3 + 2*t^2 Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 60 12 6 Total time: 3.519 seconds, Total memory usage: 8.46MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Fri Mar 19 03:34:15 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-6 Fri Mar 19 2004 03:34:12 on modular [Seed = 1464707008] ------------------------------------- [ x^2 - 1, x*z - 2*y, 2*x - y*z, y^2 - 1, z^2 - 4 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Fri Mar 19 03:34:25 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-6 Fri Mar 19 2004 03:34:22 on modular [Seed = 1581559491] ------------------------------------- [ x^2 - 1, x*z - 2*y, 2*x - y*z, y^2 - 1, z^2 - 4 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Fri Mar 19 03:34:40 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-6 Fri Mar 19 2004 03:34:37 on modular [Seed = 1163900363] ------------------------------------- [ x^2*y^2 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Fri Mar 19 03:35:11 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-6 Fri Mar 19 2004 03:35:08 on modular [Seed = 1886027999] ------------------------------------- [ x^2*y^2 + z^2*w^2, x^2*w^2 + y^2*z^2, y^4*z^2 - z^2*w^4 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Fri Mar 19 03:35:59 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-6 Fri Mar 19 2004 03:35:56 on modular [Seed = 2137362304] ------------------------------------- [ x^2*y^2 + z^2*w^2, x^2*z^2 + y^2*w^2, x^2*w^2 + y^2*z^2, y^4*z^2 - z^2*w^4, y^4*w^2 - z^4*w^2, y^2*z^4 - y^2*w^4, z^6*w^2 - z^2*w^6 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (213.182.177.254) Time: Fri Mar 19 07:05:15 2004 Input: C:=BKLC(GF(2),23,12); Output: Magma V2.10-6 Fri Mar 19 2004 07:05:10 on modular [Seed = 841520082] ------------------------------------- Total time: 3.109 seconds, Total memory usage: 2.39MB ************** MAGMA ***************** Host 3(NXDOMAIN) (213.182.177.254) Time: Fri Mar 19 07:05:56 2004 Input: C:=BKLC(GF(2),23,12); C; Output: Magma V2.10-6 Fri Mar 19 2004 07:05:53 on modular [Seed = 958634767] ------------------------------------- [23, 12, 7] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 0] [0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1] [0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 0 0] [0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 0] [0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1] [0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1 0 0] [0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1 0] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1] [0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 1 1 0 0 0 1 1] [0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 0 1] Total time: 2.999 seconds, Total memory usage: 2.39MB ************** MAGMA ***************** Host 3(NXDOMAIN) (213.182.177.254) Time: Fri Mar 19 07:06:38 2004 Input: C:=BKLC(GF(2),18,9); C; Output: Magma V2.10-6 Fri Mar 19 2004 07:06:35 on modular [Seed = 792038771] ------------------------------------- [18, 9, 6] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 1 1] [0 1 0 0 0 0 0 0 0 1 0 0 1 1 1 1 0 0] [0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 1 1 0] [0 0 0 1 0 0 0 0 0 1 1 0 0 1 1 0 0 1] [0 0 0 0 1 0 0 0 0 0 1 1 0 0 1 1 0 1] [0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 1 1 1] [0 0 0 0 0 0 1 0 0 1 1 1 1 0 0 1 0 0] [0 0 0 0 0 0 0 1 0 0 1 1 1 1 0 0 1 0] [0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 1 1 1] Total time: 3.039 seconds, Total memory usage: 2.49MB ************** MAGMA ***************** Host 3(NXDOMAIN) (213.182.177.254) Time: Fri Mar 19 07:07:49 2004 Input: C:=BKLC(GF(2),18,9); C; WeightDistribution(C); Output: Magma V2.10-6 Fri Mar 19 2004 07:07:46 on modular [Seed = 1447883987] ------------------------------------- [18, 9, 6] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 1 1] [0 1 0 0 0 0 0 0 0 1 0 0 1 1 1 1 0 0] [0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 1 1 0] [0 0 0 1 0 0 0 0 0 1 1 0 0 1 1 0 0 1] [0 0 0 0 1 0 0 0 0 0 1 1 0 0 1 1 0 1] [0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 1 1 1] [0 0 0 0 0 0 1 0 0 1 1 1 1 0 0 1 0 0] [0 0 0 0 0 0 0 1 0 0 1 1 1 1 0 0 1 0] [0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 1 1 1] [ <0, 1>, <6, 102>, <8, 153>, <10, 153>, <12, 102>, <18, 1> ] Total time: 3.039 seconds, Total memory usage: 2.49MB ************** MAGMA ***************** Host 3(NXDOMAIN) (213.182.177.254) Time: Fri Mar 19 07:09:53 2004 Input: C:=BKLC(GF(2),24,14); C; WeightDistribution(C); Output: Magma V2.10-6 Fri Mar 19 2004 07:09:50 on modular [Seed = 1564999236] ------------------------------------- [24, 14, 6] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 0] [0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 1 0 1 0] [0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 1 1 1] [0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 1 1] [0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 1 0 0] [0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 1 1 1 1 0 1 1] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 1] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 1] [0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 1 0] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 1 1 0 1] [0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 0 1 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 1 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 1 1 1] [ <0, 1>, <6, 336>, <8, 1335>, <10, 3888>, <12, 5264>, <14, 3888>, <16, 1335>, <18, 336>, <24, 1> ] Total time: 3.049 seconds, Total memory usage: 2.29MB ************** MAGMA ***************** Host 3(NXDOMAIN) (213.182.177.254) Time: Fri Mar 19 07:10:41 2004 Input: C:=BKLC(GF(2),36,25); C; WeightDistribution(C); Output: Magma V2.10-6 Fri Mar 19 2004 07:10:38 on modular [Seed = 1297608292] ------------------------------------- [36, 25, 5] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 0] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 1 0] [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 1 0 0] [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 0] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 1 0] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1] [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 1 0] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 1 0 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 0 1 0 1 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 1 1 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 1 0 0 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 1 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 0 1 1 1] [ <0, 1>, <5, 236>, <6, 1160>, <7, 4276>, <8, 15064>, <9, 45556>, <10, 122648>, <11, 295024>, <12, 613776>, <13, 1120804>, <14, 1845840>, <15, 2729796>, <16, 3581378>, <17, 4192508>, <18, 4424112>, <19, 4200448>, <20, 3567808>, <21, 2714324>, <22, 1852968>, <23, 1129852>, <24, 612560>, <25, 294796>, <26, 124600>, <27, 45456>, <28, 14384>, <29, 3996>, <30, 896>, <31, 140>, <32, 21>, <33, 4> ] Total time: 2.989 seconds, Total memory usage: 2.29MB ************** MAGMA ***************** Host 3(NXDOMAIN) (213.182.177.254) Time: Fri Mar 19 07:11:09 2004 Input: C:=BKLC(GF(2),35,24); C; WeightDistribution(C); Output: Magma V2.10-6 Fri Mar 19 2004 07:11:06 on modular [Seed = 1936314430] ------------------------------------- [35, 24, 5] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 1 1 1] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 1] [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 1 0] [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 1 0 1 0] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 1] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 0 1 0] [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 1] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 1 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 1 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 1 1 0 0 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 1 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 1 0 1 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 0 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 1 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 1 1 0 0] [ <0, 1>, <5, 216>, <6, 1017>, <7, 3611>, <8, 12143>, <9, 34561>, <10, 88778>, <11, 206126>, <12, 409918>, <13, 711170>, <14, 1121319>, <15, 1593365>, <16, 1993939>, <17, 2213071>, <18, 2214732>, <19, 1990276>, <20, 1587876>, <21, 1127380>, <22, 716471>, <23, 405397>, <24, 203289>, <25, 90575>, <26, 35402>, <27, 11886>, <28, 3518>, <29, 946>, <30, 201>, <31, 27>, <32, 4>, <33, 1> ] Total time: 2.999 seconds, Total memory usage: 2.29MB ************** MAGMA ***************** Host 3(NXDOMAIN) (213.182.177.254) Time: Fri Mar 19 07:11:28 2004 Input: C:=BKLC(GF(2),34,23); C; WeightDistribution(C); Output: Magma V2.10-6 Fri Mar 19 2004 07:11:25 on modular [Seed = 2053167360] ------------------------------------- [34, 23, 6] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0 0 1] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 1 1 1] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 0] [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 1 0 1] [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 1 1] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 0 0 0] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 1 0] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 0 1 1 0] [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 1 1 0 1 0] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 1 0 0] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 1 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 1 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 0 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 1 0 0 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 1 1 1 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 1 0 0 1 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 0 1 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1 1 1] [ <0, 1>, <6, 1562>, <8, 17127>, <10, 128777>, <12, 535274>, <14, 1358940>, <16, 2152623>, <18, 2152623>, <20, 1358940>, <22, 535274>, <24, 128777>, <26, 17127>, <28, 1562>, <34, 1> ] Total time: 3.139 seconds, Total memory usage: 2.29MB ************** MAGMA ***************** Host 3(NXDOMAIN) (213.182.177.254) Time: Fri Mar 19 07:17:26 2004 Input: BKLCLowerBound(GF(2),36,25); BKLCUpperBound(GF(2),36,25); Output: Magma V2.10-6 Fri Mar 19 2004 07:17:23 on modular [Seed = 2542613331] ------------------------------------- 5 6 Total time: 2.989 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 3(NXDOMAIN) (213.182.177.254) Time: Fri Mar 19 07:17:57 2004 Input: BKLCLowerBound(GF(2),24,14); BKLCUpperBound(GF(2),24,14); Output: Magma V2.10-6 Fri Mar 19 2004 07:17:54 on modular [Seed = 2659465851] ------------------------------------- 6 6 Total time: 2.969 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 3(NXDOMAIN) (213.182.177.254) Time: Fri Mar 19 07:18:27 2004 Input: BKLCLowerBound(GF(2),34,23); BKLCUpperBound(GF(2),34,23); Output: Magma V2.10-6 Fri Mar 19 2004 07:18:24 on modular [Seed = 2241798274] ------------------------------------- 6 6 Total time: 2.999 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 3(NXDOMAIN) (213.182.177.254) Time: Fri Mar 19 07:18:44 2004 Input: BKLCLowerBound(GF(2),35,24); BKLCUpperBound(GF(2),35,24); Output: Magma V2.10-6 Fri Mar 19 2004 07:18:41 on modular [Seed = 2358651322] ------------------------------------- 5 6 Total time: 2.959 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 3(NXDOMAIN) (213.182.177.254) Time: Fri Mar 19 07:19:00 2004 Input: BKLCLowerBound(GF(2),36,25); BKLCUpperBound(GF(2),36,25); Output: Magma V2.10-6 Fri Mar 19 2004 07:18:57 on modular [Seed = 3215268505] ------------------------------------- 5 6 Total time: 3.109 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 3(NXDOMAIN) (213.182.177.254) Time: Fri Mar 19 07:19:17 2004 Input: BKLCLowerBound(GF(2),37,26); BKLCUpperBound(GF(2),37,26); Output: Magma V2.10-6 Fri Mar 19 2004 07:19:14 on modular [Seed = 2797339635] ------------------------------------- 5 6 Total time: 2.979 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 3(NXDOMAIN) (213.182.177.254) Time: Fri Mar 19 07:19:32 2004 Input: BKLCLowerBound(GF(2),38,27); BKLCUpperBound(GF(2),38,27); Output: Magma V2.10-6 Fri Mar 19 2004 07:19:29 on modular [Seed = 2914453739] ------------------------------------- 5 5 Total time: 2.999 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 3(NXDOMAIN) (213.182.177.254) Time: Fri Mar 19 07:23:46 2004 Input: BKLCLowerBound(GF(2),48,36); BKLCUpperBound(GF(2),48,36); Output: Magma V2.10-6 Fri Mar 19 2004 07:23:43 on modular [Seed = 3336331422] ------------------------------------- 6 6 Total time: 2.959 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 3(NXDOMAIN) (213.182.177.254) Time: Fri Mar 19 07:24:13 2004 Input: BKLCLowerBound(GF(2),49,37); BKLCUpperBound(GF(2),49,37); Output: Magma V2.10-6 Fri Mar 19 2004 07:24:10 on modular [Seed = 3453447088] ------------------------------------- 5 6 Total time: 2.969 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 3(NXDOMAIN) (213.182.177.254) Time: Fri Mar 19 07:25:25 2004 Input: C:=BKLC(GF(2),49,37); C; WeightDistribution(C); Output: Magma V2.10-6 Fri Mar 19 2004 07:25:21 on modular [Seed = 4242954842] ------------------------------------- [49, 37, 5] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 1 1 0 0 1] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 1 0 0 1 0] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 1 0 0 1] [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 0] [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 1 0 0 0] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 1 0 0] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 1 0] [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 1] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 1 0 1 0 0] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 1 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 1 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 1 0 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 1 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 0 0 1 0 0 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1 1 1 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 1 0 1 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 0 1 1 1 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 0 1 1 1 0 1] [ <0, 1>, <5, 535>, <6, 3625>, <7, 20520>, <8, 110360>, <9, 503190>, <10, 2001594>, <11, 7110009>, <12, 22544453>, <13, 64113149>, <14, 164809391>, <15, 384667641>, <16, 817487630>, <17, 1586718776>, <18, 2820765608>, <19, 4602490132>, <20, 6903787172>, <21, 9533640438>, <22, 12133698266>, <23, 14244015348>, <24, 15431005772>, <25, 15430944724>, <26, 14244000748>, <27, 12133807934>, <28, 9533628934>, <29, 6903652586>, <30, 4602508958>, <31, 2820889934>, <32, 1586700697>, <33, 817398744>, <34, 384682696>, <35, 164858020>, <36, 64102708>, <37, 22525155>, <38, 7115437>, <39, 2006428>, <40, 501236>, <41, 109958>, <42, 20970>, <43, 3473>, <44, 477>, <45, 41>, <46, 3>, <47, 1> ] Total time: 3.049 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 3(NXDOMAIN) (213.182.177.254) Time: Fri Mar 19 07:25:50 2004 Input: C:=BKLC(GF(2),48,36); C; WeightDistribution(C); Output: Magma V2.10-6 Fri Mar 19 2004 07:25:47 on modular [Seed = 3824764223] ------------------------------------- [48, 36, 6] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0 1] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 1] [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 1 0 0 0 0] [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 0 0 0 1] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 0 0 1 0] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 0 0] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 0 1 1 1] [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 1 0 1] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 1 1 0 0] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 0 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 1 0 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 1 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 1 1 0 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 1 0 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0] [ <0, 1>, <6, 6768>, <8, 181290>, <10, 3199728>, <12, 34013760>, <14, 235496640>, <16, 1101037263>, <18, 3569211328>, <20, 8171728320>, <22, 13371954720>, <24, 15745817100>, <26, 13371954720>, <28, 8171728320>, <30, 3569211328>, <32, 1101037263>, <34, 235496640>, <36, 34013760>, <38, 3199728>, <40, 181290>, <42, 6768>, <48, 1> ] Total time: 3.009 seconds, Total memory usage: 2.29MB ************** MAGMA ***************** Host ALagny-102-1-3-199.w80-11.abo.wanadoo.fr. (80.11.127.199) Time: Fri Mar 19 08:46:41 2004 Input: (a+b)*(c+d) Output: Magma V2.10-6 Fri Mar 19 2004 08:46:38 on modular [Seed = 1986842577] ------------------------------------- >> (a+b)*(c+d); ^ User error: Identifier 'a' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ALagny-102-1-3-199.w80-11.abo.wanadoo.fr. (80.11.127.199) Time: Fri Mar 19 08:46:57 2004 Input: expand((a+b)*(c+d)) Output: Magma V2.10-6 Fri Mar 19 2004 08:46:54 on modular [Seed = 1635506358] ------------------------------------- >> expand((a+b)*(c+d)); ^ User error: Identifier 'a' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host gw1.btc.transwitch.com. (63.149.68.2) Time: Fri Mar 19 12:13:12 2004 Input: R := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 + 14*x^8 - 1)); Output: Magma V2.10-6 Fri Mar 19 2004 12:13:04 on modular [Seed = 1025922817] ------------------------------------- 144 16 Total time: 7.459 seconds, Total memory usage: 4.61MB ************** MAGMA ***************** Host gw1.btc.transwitch.com. (63.149.68.2) Time: Fri Mar 19 12:13:59 2004 Input: R := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 57*x^14 + 1212*x^12 - 12385*x^10 + 64261*x^8 - 162395*x^6 + 159448*x^4 - 6131*x^2 + 1)); Output: Magma V2.10-6 Fri Mar 19 2004 12:13:51 on modular [Seed = 908942437] ------------------------------------- 77 16 Total time: 7.989 seconds, Total memory usage: 5.39MB ************** MAGMA ***************** Host gw1.btc.transwitch.com. (63.149.68.2) Time: Fri Mar 19 12:14:51 2004 Input: R := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 32*x^14 + 368*x^12 - 1920*x^10 + 4848*x^8 - 5952*x^6 + 3328*x^4 - 768*x^2 + 56)); Output: Magma V2.10-6 Fri Mar 19 2004 12:14:44 on modular [Seed = 791954871] ------------------------------------- 144 16 Total time: 6.399 seconds, Total memory usage: 3.61MB ************** MAGMA ***************** Host gw1.btc.transwitch.com. (63.149.68.2) Time: Fri Mar 19 12:19:21 2004 Input: R := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 48*x^14 + 792*x^12 - 5472*x^10 + 15174*x^8 - 17520*x^6 + 7272*x^4 - 288*x^2 + 3)); Output: Magma V2.10-6 Fri Mar 19 2004 12:19:13 on modular [Seed = 1598305490] ------------------------------------- 136 16 Total time: 7.899 seconds, Total memory usage: 12.38MB ************** MAGMA ***************** Host gw1.btc.transwitch.com. (63.149.68.2) Time: Fri Mar 19 12:19:45 2004 Input: R := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 288*x^14 + 20664*x^12 - 461616*x^10 + 3440310*x^8 - 8576640*x^6 + 6072024*x^4 - 10704*x^2 + 3)); Output: Magma V2.10-6 Fri Mar 19 2004 12:19:38 on modular [Seed = 1347107814] ------------------------------------- 136 16 Total time: 7.359 seconds, Total memory usage: 5.48MB ************** MAGMA ***************** Host gw1.btc.transwitch.com. (63.149.68.2) Time: Fri Mar 19 12:20:06 2004 Input: R := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 88*x^14 + 2032*x^12 - 12592*x^10 + 35548*x^8 - 52816*x^6 + 42112*x^4 - 16672*x^2 + 2500)); Output: Magma V2.10-6 Fri Mar 19 2004 12:19:57 on modular [Seed = 1230119656] ------------------------------------- 12 16 Total time: 8.659 seconds, Total memory usage: 12.04MB ************** MAGMA ***************** Host gw1.btc.transwitch.com. (63.149.68.2) Time: Fri Mar 19 12:25:08 2004 Input: R := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 136*x^14 + 6834*x^12 - 156536*x^10 + 1601451*x^8 - 6077024*x^6 + 7580368*x^4 - 1447040*x^2 + 2176)); Output: Magma V2.10-6 Fri Mar 19 2004 12:25:01 on modular [Seed = 1986861703] ------------------------------------- 136 16 Total time: 6.779 seconds, Total memory usage: 4.11MB ************** MAGMA ***************** Host gw1.btc.transwitch.com. (63.149.68.2) Time: Fri Mar 19 12:25:27 2004 Input: R := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 136*x^14 + 6358*x^12 - 113288*x^10 + 538339*x^8 - 854624*x^6 + 406096*x^4 - 54400*x^2 + 2176)); Output: Magma V2.10-6 Fri Mar 19 2004 12:25:19 on modular [Seed = 1869874060] ------------------------------------- 136 16 Total time: 7.529 seconds, Total memory usage: 5.72MB ************** MAGMA ***************** Host gw1.btc.transwitch.com. (63.149.68.2) Time: Fri Mar 19 12:25:39 2004 Input: R := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 136*x^14 + 5950*x^12 - 103768*x^10 + 800955*x^8 - 2514640*x^6 + 1893732*x^4 - 409904*x^2 + 136)); Output: Magma V2.10-6 Fri Mar 19 2004 12:25:32 on modular [Seed = 1618677104] ------------------------------------- 136 16 Total time: 6.619 seconds, Total memory usage: 4.22MB ************** MAGMA ***************** Host gw1.btc.transwitch.com. (63.149.68.2) Time: Fri Mar 19 12:26:07 2004 Input: R := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 128*x^14 + 6420*x^12 - 160016*x^10 + 2075022*x^8 - 13437152*x^6 + 38371748*x^4 - 31835280*x^2 + 2042041)); Output: Magma V2.10-6 Fri Mar 19 2004 12:25:58 on modular [Seed = 2592208800] ------------------------------------- 12 16 Total time: 8.819 seconds, Total memory usage: 11.26MB ************** MAGMA ***************** Host gw1.btc.transwitch.com. (63.149.68.2) Time: Fri Mar 19 12:26:58 2004 Input: R := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 108*x^14 + 4440*x^12 - 88056*x^10 + 871412*x^8 - 4048416*x^6 + 8377248*x^4 - 6048000*x^2 + 40000)); Output: Magma V2.10-6 Fri Mar 19 2004 12:26:48 on modular [Seed = 2358763976] ------------------------------------- 26 16 Total time: 10.119 seconds, Total memory usage: 4.59MB ************** MAGMA ***************** Host gw1.btc.transwitch.com. (63.149.68.2) Time: Fri Mar 19 12:27:18 2004 Input: R := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 164*x^14 + 7160*x^12 - 103432*x^10 + 577652*x^8 - 1188128*x^6 + 1031072*x^4 - 371200*x^2 + 40000)); Output: Magma V2.10-6 Fri Mar 19 2004 12:27:10 on modular [Seed = 2157702642] ------------------------------------- 26 16 Total time: 7.899 seconds, Total memory usage: 4.19MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Fri Mar 19 13:21:33 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-6 Fri Mar 19 2004 13:21:30 on modular [Seed = 841566213] ------------------------------------- [ 4*x^2*y^2 + z^2*w^2, x^2*z^2 + y^2*w^2, x^2*w^2 + y^2*z^2, 4*y^4*z^2 - z^2*w^4, 4*y^4*w^2 - z^4*w^2, y^2*z^4 - y^2*w^4, z^6*w^2 - z^2*w^6 ] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Fri Mar 19 13:21:49 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-6 Fri Mar 19 2004 13:21:46 on modular [Seed = 624844546] ------------------------------------- [ 4*x^2*y^2 + 9*z^2*w^2, x^2*z^2 + y^2*w^2, x^2*w^2 + y^2*z^2, 4*y^4*z^2 - 9*z^2*w^4, 4*y^4*w^2 - 9*z^4*w^2, y^2*z^4 - y^2*w^4, 9*z^6*w^2 - 9*z^2*w^6 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host v198-169-189-225.online-age.net. (198.169.189.225) Time: Fri Mar 19 15:26:09 2004 Input: 5*a+9*b + (2*(2*a+5*b)) Output: Magma V2.10-6 Fri Mar 19 2004 15:26:06 on modular [Seed = 624833125] ------------------------------------- >> 5*a+9*b + (2*(2*a+5*b)); ^ User error: Identifier 'a' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Sat Mar 20 03:20:47 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > 2*x*y*z*w in I; Output: Magma V2.10-6 Sat Mar 20 2004 03:20:42 on modular [Seed = 3235610169] ------------------------------------- [ 4*x^2*y^2 + 9*z^2*w^2, x^2*z^2 + y^2*w^2, x^2*w^2 + y^2*z^2, 4*y^4*z^2 - 9*z^2*w^4, 4*y^4*w^2 - 9*z^4*w^2, y^2*z^4 - y^2*w^4, 9*z^6*w^2 - 9*z^2*w^6 ] false Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ppp-62-11-143-127.dialup.tiscali.it. (62.11.143.127) Time: Sat Mar 20 05:24:08 2004 Input: a:=[1,2,3,21,3,13,1,31] Output: Magma V2.10-6 Sat Mar 20 2004 05:24:05 on modular [Seed = 252925165] ------------------------------------- Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ppp-62-11-143-127.dialup.tiscali.it. (62.11.143.127) Time: Sat Mar 20 05:24:26 2004 Input: a:=[1,2,3,21,3,13,1,31] Output: Magma V2.10-6 Sat Mar 20 2004 05:24:23 on modular [Seed = 369774054] ------------------------------------- Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ppp-62-11-143-127.dialup.tiscali.it. (62.11.143.127) Time: Sat Mar 20 05:25:23 2004 Input: LLL([1,2,3,21,3,13,1,31]) Output: Magma V2.10-6 Sat Mar 20 2004 05:25:20 on modular [Seed = 2003512128] ------------------------------------- >> LLL([1,2,3,21,3,13,1,31]) ^ Runtime error in 'LLL': Bad argument types Argument types given: SeqEnum[RngIntElt] Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dsl-203-33-165-136.NSW.netspace.net.au. (203.33.165.136) Time: Sat Mar 20 08:04:25 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Sat Mar 20 2004 08:04:21 on modular [Seed = 2575669479] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.849 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 08:47:24 2004 Input: G2 := GF(2); [element: element in G2]; G3 := GF(3); [element: element in G3]; G5 := GF(5); [element: element in G5]; Output: Magma V2.10-6 Sat Mar 20 2004 08:47:21 on modular [Seed = 725033067] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 08:47:45 2004 Input: G2 := GF(2); G2; [element: element in G2]; G3 := GF(3); G3; [element: element in G3]; G5 := GF(5); G5; [element: element in G5]; Output: Magma V2.10-6 Sat Mar 20 2004 08:47:42 on modular [Seed = 574499189] ------------------------------------- Finite field of size 2 [ 0, 1 ] Finite field of size 3 [ 0, 1, 2 ] Finite field of size 5 [ 0, 1, 2, 3, 4 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 08:50:08 2004 Input: Z9 := Integers(9); Z9; IsField(Z9); Output: Magma V2.10-6 Sat Mar 20 2004 08:50:05 on modular [Seed = 841891350] ------------------------------------- Residue class ring of integers modulo 9 false Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 08:53:52 2004 Input: Z9 := Integers(9); Z9; IsField(Z9); Order(6,9); Output: Magma V2.10-6 Sat Mar 20 2004 08:53:49 on modular [Seed = 252904395] ------------------------------------- Residue class ring of integers modulo 9 false 0 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 08:57:42 2004 Input: P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); Output: Magma V2.10-6 Sat Mar 20 2004 08:57:39 on modular [Seed = 469766630] ------------------------------------- true true true false Total time: 3.009 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 09:01:17 2004 Input: P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; G9b := ext < GF(3) | k >; Output: Magma V2.10-6 Sat Mar 20 2004 09:01:14 on modular [Seed = 1919843569] ------------------------------------- true true true false >> G9b := ext < GF(3) | k >;; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 2.949 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 09:05:45 2004 Input: P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; IsPrimitive(j); Output: Magma V2.10-6 Sat Mar 20 2004 09:05:42 on modular [Seed = 1130319068] ------------------------------------- true true true false >> IsPrimitive(j);; ^ Runtime error in 'IsPrimitive': Coefficient ring of argument 1 is not a finite field Total time: 2.989 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 09:06:16 2004 Input: P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; IsPrimitive(j); Output: Magma V2.10-6 Sat Mar 20 2004 09:06:13 on modular [Seed = 1564562081] ------------------------------------- true true true false >> IsPrimitive(j);; ^ Runtime error in 'IsPrimitive': Coefficient ring of argument 1 is not a finite field Total time: 2.939 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 09:06:36 2004 Input: P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; IsPrimitive(j); Output: Magma V2.10-6 Sat Mar 20 2004 09:06:33 on modular [Seed = 1414028180] ------------------------------------- true true true false x^2 + 4*x + 2 >> IsPrimitive(j);; ^ Runtime error in 'IsPrimitive': Coefficient ring of argument 1 is not a finite field Total time: 2.949 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 09:09:17 2004 Input: P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; Order(alpha); Output: Magma V2.10-6 Sat Mar 20 2004 09:09:14 on modular [Seed = 2930949645] ------------------------------------- true true true false x^2 + 4*x + 2 24 Total time: 3.019 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 09:09:23 2004 Input: P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; Order(alpha); Output: Magma V2.10-6 Sat Mar 20 2004 09:09:20 on modular [Seed = 2797254175] ------------------------------------- true true true false x^2 + 4*x + 2 24 Total time: 3.009 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 09:10:29 2004 Input: P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; Order(alpha); ordre_elements := [: i in [1..24]]; ordre_elements; Output: Magma V2.10-6 Sat Mar 20 2004 09:10:26 on modular [Seed = 3064637005] ------------------------------------- true true true false x^2 + 4*x + 2 24 [ , , , , , <2, 4>, , , , , , <4, 2>, , , , , , <3, 4>, , , , , , <1, 1> ] Total time: 2.969 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 09:12:50 2004 Input: P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; Order(alpha); ordre_elements := [: i in [1..24]]; ordre_elements; elem_primitius := [tupla[1]: tupla in ordre_elements | tupla[2] eq 25-1 ]; Output: Magma V2.10-6 Sat Mar 20 2004 09:12:47 on modular [Seed = 2208273141] ------------------------------------- true true true false x^2 + 4*x + 2 24 [ , , , , , <2, 4>, , , , , , <4, 2>, , , , , , <3, 4>, , , , , , <1, 1> ] Total time: 2.929 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 09:13:18 2004 Input: P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; Order(alpha); ordre_elements := [: i in [1..24]]; ordre_elements; elem_primitius := [tupla[1]: tupla in ordre_elements | tupla[2] eq 25-1 ]; elem_primitius; Output: Magma V2.10-6 Sat Mar 20 2004 09:13:15 on modular [Seed = 2592508872] ------------------------------------- true true true false x^2 + 4*x + 2 24 [ , , , , , <2, 4>, , , , , , <4, 2>, , , , , , <3, 4>, , , , , , <1, 1> ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] Total time: 2.909 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 09:16:45 2004 Input: P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; Order(alpha); ordre_elements := [: i in [1..24]]; ordre_elements; elem_primitius := [tupla[1]: tupla in ordre_elements | tupla[2] eq 25-1 ]; elem_primitius; EulerPhi(24); Output: Magma V2.10-6 Sat Mar 20 2004 09:16:42 on modular [Seed = 3992059790] ------------------------------------- true true true false x^2 + 4*x + 2 24 [ , , , , , <2, 4>, , , , , , <4, 2>, , , , , , <3, 4>, , , , , , <1, 1> ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 Total time: 2.929 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 09:19:34 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; Order(alpha); ordre_elements := [: i in [1..24]]; ordre_elements; elem_primitius := [tupla[1]: tupla in ordre_elements | tupla[2] eq 25-1 ]; elem_primitius; EulerPhi(24); s := MinimalPolynomial(alpha, G5); s; Output: Magma V2.10-6 Sat Mar 20 2004 09:19:31 on modular [Seed = 3841521214] ------------------------------------- true true true false x^2 + 4*x + 2 24 [ , , , , , <2, 4>, , , , , , <4, 2>, , , , , , <3, 4>, , , , , , <1, 1> ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 $.1^2 + 4*$.1 + 2 Total time: 2.989 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 09:22:31 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; Order(alpha); ordre_elements := [: i in [1..24]]; ordre_elements; elem_primitius := [tupla[1]: tupla in ordre_elements | tupla[2] eq 25-1 ]; elem_primitius; EulerPhi(24); s := MinimalPolynomial(alpha, G5); s; Degree(s); Output: Magma V2.10-6 Sat Mar 20 2004 09:22:27 on modular [Seed = 4142589308] ------------------------------------- true true true false x^2 + 4*x + 2 24 [ , , , , , <2, 4>, , , , , , <4, 2>, , , , , , <3, 4>, , , , , , <1, 1> ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 $.1^2 + 4*$.1 + 2 2 Total time: 3.009 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 09:25:20 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); Roots(s,G25); Z5 := Integers(5); Roots(s,Z5); Output: Magma V2.10-6 Sat Mar 20 2004 09:25:17 on modular [Seed = 3302543520] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 [ , ] [] Total time: 2.999 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 09:50:05 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); Roots(s,G25)[1]; Z5 := Integers(5); Roots(s,Z5)[1]; Output: Magma V2.10-6 Sat Mar 20 2004 09:50:02 on modular [Seed = 891891461] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 >> Roots(s,Z5)[1];; ^ Runtime error in '[]': Sequence element 1 not defined Total time: 2.969 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 09:51:41 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); 2*alpha^(-3) - alpha^5 + (1/ (alpha + 2)) * alpha^6; Output: Magma V2.10-6 Sat Mar 20 2004 09:51:38 on modular [Seed = 52369747] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 alpha^17 Total time: 2.949 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 09:52:29 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); 2*alpha^(-3) - alpha^5 + (1/ (alpha + 2)) * alpha^6; 1/(alpha^17); Output: Magma V2.10-6 Sat Mar 20 2004 09:52:26 on modular [Seed = 402915992] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 alpha^17 alpha^7 Total time: 3.039 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 09:53:32 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); 2*alpha^(-3) - alpha^5 + (1/ (alpha + 2)) * alpha^6; 1/(alpha^17); alpha^17 * alpha^7; Output: Magma V2.10-6 Sat Mar 20 2004 09:53:28 on modular [Seed = 286067667] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 alpha^17 alpha^7 1 Total time: 3.079 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 09:55:03 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); 2*alpha^(-3) - alpha^5 + (1/ (alpha + 2)) * alpha^6; 1/(alpha^17); alpha^17 * alpha^7; elements_invertibles := [element in G25 | IsInvertible(element)]; Output: Magma V2.10-6 Sat Mar 20 2004 09:55:00 on modular [Seed = 1869837313] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 alpha^17 alpha^7 1 >> elements_invertibles := [element in G25 | IsInvertible(element)];; ^ User error: Identifier 'element' has not been declared or assigned Total time: 3.069 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 09:55:30 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); 2*alpha^(-3) - alpha^5 + (1/ (alpha + 2)) * alpha^6; 1/(alpha^17); alpha^17 * alpha^7; elements_invertibles := [element in G25 | IsInvertible(element) eq true]; elements_invertibles; Output: Magma V2.10-6 Sat Mar 20 2004 09:55:27 on modular [Seed = 2120377611] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 alpha^17 alpha^7 1 >> elements_invertibles := [element in G25 | IsInvertible(element) eq true]; ^ User error: Identifier 'element' has not been declared or assigned >> elements_invertibles;; ^ User error: Identifier 'elements_invertibles' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 09:56:14 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); 2*alpha^(-3) - alpha^5 + (1/ (alpha + 2)) * alpha^6; 1/(alpha^17); alpha^17 * alpha^7; IsInvertible(alpha^17); Output: Magma V2.10-6 Sat Mar 20 2004 09:56:11 on modular [Seed = 2003528918] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 alpha^17 alpha^7 1 true alpha^7 Total time: 3.039 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 09:56:59 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); 2*alpha^(-3) - alpha^5 + (1/ (alpha + 2)) * alpha^6; 1/(alpha^17); alpha^17 * alpha^7; IsInvertible(alpha^17); elements_invertibles := [element: element in G25 | IsInvertible(element)]; elements_invertibles; Output: Magma V2.10-6 Sat Mar 20 2004 09:56:56 on modular [Seed = 1297176287] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 alpha^17 alpha^7 1 true alpha^7 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 2, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 3, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] Total time: 2.999 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 10:03:55 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); 2*alpha^(-3) - alpha^5 + (1/ (alpha + 2)) * alpha^6; 1/(alpha^17); alpha^17 * alpha^7; IsInvertible(alpha^17); elements_invertibles := [element: element in G25 | IsInvertible(element)]; elements_invertibles; Order(alpha^17); Output: Magma V2.10-6 Sat Mar 20 2004 10:03:52 on modular [Seed = 2797255636] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 alpha^17 alpha^7 1 true alpha^7 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 2, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 3, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] 24 Total time: 2.999 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 10:05:59 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); 2*alpha^(-3) - alpha^5 + (1/ (alpha + 2)) * alpha^6; 1/(alpha^17); alpha^17 * alpha^7; IsInvertible(alpha^17); elements_invertibles := [element: element in G25 | IsInvertible(element)]; elements_invertibles; Order(alpha^17); hola := [a: a in G25]; Output: Magma V2.10-6 Sat Mar 20 2004 10:05:56 on modular [Seed = 3014635085] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 alpha^17 alpha^7 1 true alpha^7 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 2, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 3, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] 24 Total time: 2.989 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 10:06:33 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); [a: a in G25]; Output: Magma V2.10-6 Sat Mar 20 2004 10:06:30 on modular [Seed = 2308281429] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 2, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 3, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] Total time: 2.999 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 10:08:41 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); rep_vect25 := [ElementToSequence(x): x in G25]; rep_vect25; rep_exp25 := [x: x in G25]; rep_exp25; Output: Magma V2.10-6 Sat Mar 20 2004 10:08:38 on modular [Seed = 2275121627] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 [ [ 1, 0 ], [ 0, 1 ], [ 3, 1 ], [ 3, 4 ], [ 2, 2 ], [ 1, 4 ], [ 2, 0 ], [ 0, 2 ], [ 1, 2 ], [ 1, 3 ], [ 4, 4 ], [ 2, 3 ], [ 4, 0 ], [ 0, 4 ], [ 2, 4 ], [ 2, 1 ], [ 3, 3 ], [ 4, 1 ], [ 3, 0 ], [ 0, 3 ], [ 4, 3 ], [ 4, 2 ], [ 1, 1 ], [ 3, 2 ], [ 0, 0 ] ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 2, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 3, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] Total time: 3.059 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 10:10:12 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); rep_vect25 := [ElementToSequence(x): x in G25]; rep_vect25; rep_exp25 := [x: x in G25]; rep_exp25; Matrix([rep_vect25, rep_exp25]); Output: Magma V2.10-6 Sat Mar 20 2004 10:10:09 on modular [Seed = 2542504300] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 [ [ 1, 0 ], [ 0, 1 ], [ 3, 1 ], [ 3, 4 ], [ 2, 2 ], [ 1, 4 ], [ 2, 0 ], [ 0, 2 ], [ 1, 2 ], [ 1, 3 ], [ 4, 4 ], [ 2, 3 ], [ 4, 0 ], [ 0, 4 ], [ 2, 4 ], [ 2, 1 ], [ 3, 3 ], [ 4, 1 ], [ 3, 0 ], [ 0, 3 ], [ 4, 3 ], [ 4, 2 ], [ 1, 1 ], [ 3, 2 ], [ 0, 0 ] ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 2, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 3, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] >> Matrix([rep_vect25, rep_exp25]);; ^ Runtime error in [ ... ]: Could not find a valid universe Total time: 2.949 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 10:12:06 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); rep_vect25 := [ElementToSequence(x): x in G25]; rep_vect25; rep_exp25 := [x: x in G25]; rep_exp25; /* Matrix([rep_vect25, rep_exp25]);*/ hola:=[1,2,3]; Matrix([hola,[1,2,3]]); Output: Magma V2.10-6 Sat Mar 20 2004 10:12:03 on modular [Seed = 3875207567] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 [ [ 1, 0 ], [ 0, 1 ], [ 3, 1 ], [ 3, 4 ], [ 2, 2 ], [ 1, 4 ], [ 2, 0 ], [ 0, 2 ], [ 1, 2 ], [ 1, 3 ], [ 4, 4 ], [ 2, 3 ], [ 4, 0 ], [ 0, 4 ], [ 2, 4 ], [ 2, 1 ], [ 3, 3 ], [ 4, 1 ], [ 3, 0 ], [ 0, 3 ], [ 4, 3 ], [ 4, 2 ], [ 1, 1 ], [ 3, 2 ], [ 0, 0 ] ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 2, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 3, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [1 2 3] [1 2 3] Total time: 2.989 seconds, Total memory usage: 2.22MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 10:12:37 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); rep_vect25 := [ElementToSequence(x): x in G25]; #rep_vect25; rep_exp25 := [x: x in G25]; #rep_exp25; /* Matrix([rep_vect25, rep_exp25]);*/ hola:=[1,2,3]; Matrix([hola,[1,2,3]]); Output: Magma V2.10-6 Sat Mar 20 2004 10:12:34 on modular [Seed = 4293124279] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 25 25 [1 2 3] [1 2 3] Total time: 2.889 seconds, Total memory usage: 2.22MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 10:12:59 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); rep_vect25 := [ElementToSequence(x): x in G25]; #rep_vect25; rep_exp25 := [x: x in G25]; #rep_exp25; /* Matrix([rep_vect25, rep_exp25]);*/ hola:=[1,2,3]; Matrix([hola,hola]); Output: Magma V2.10-6 Sat Mar 20 2004 10:12:55 on modular [Seed = 4108905385] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 25 25 [1 2 3] [1 2 3] Total time: 3.049 seconds, Total memory usage: 2.22MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 10:14:23 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); rep_vect25 := [ElementToSequence(x): x in G25]; #rep_vect25; rep_exp25 := [x: x in G25]; #rep_exp25; /* Matrix([rep_vect25, rep_exp25]);*/ hola:=[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]; Matrix([hola,hola]); Output: Magma V2.10-6 Sat Mar 20 2004 10:14:20 on modular [Seed = 3453080107] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 25 25 [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15] [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15] Total time: 2.999 seconds, Total memory usage: 2.22MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 10:14:42 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); rep_vect25 := [ElementToSequence(x): x in G25]; #rep_vect25; rep_exp25 := [x: x in G25]; #rep_exp25; /* Matrix([rep_vect25, rep_exp25]);*/ hola:=[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]; Matrix([hola,hola]); Output: Magma V2.10-6 Sat Mar 20 2004 10:14:39 on modular [Seed = 3670459695] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 25 25 [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21] [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21] Total time: 2.939 seconds, Total memory usage: 2.22MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 10:14:56 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); rep_vect25 := [ElementToSequence(x): x in G25]; #rep_vect25; rep_exp25 := [x: x in G25]; #rep_exp25; /* Matrix([rep_vect25, rep_exp25]);*/ hola:=[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25]; Matrix([hola,hola]); Output: Magma V2.10-6 Sat Mar 20 2004 10:14:53 on modular [Seed = 3553610772] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 25 25 [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25] [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25] Total time: 2.969 seconds, Total memory usage: 2.22MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 10:15:17 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); rep_vect25 := [ElementToSequence(x): x in G25]; #rep_vect25; rep_exp25 := [x: x in G25]; #rep_exp25; /* Matrix([rep_vect25, rep_exp25]);*/ hola:=[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35]; Matrix([hola,hola]); Output: Magma V2.10-6 Sat Mar 20 2004 10:15:14 on modular [Seed = 758189316] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 25 25 [1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35] [1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35] Total time: 3.029 seconds, Total memory usage: 2.22MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 10:15:59 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); rep_vect25 := [ElementToSequence(x): x in G25]; #rep_vect25; rep_exp25 := [x: x in G25]; #rep_exp25; /* Matrix([rep_vect25, rep_exp25]);*/ hola:=[1,2,3,4,5]; hola1 := [a,b,c,d,e]; Matrix([hola,hola1]); Output: Magma V2.10-6 Sat Mar 20 2004 10:15:56 on modular [Seed = 958732606] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 25 25 >> hola1 := [a,b,c,d,e]; ^ User error: Identifier 'a' has not been declared or assigned >> Matrix([hola,hola1]);; ^ User error: Identifier 'hola1' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 10:16:37 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); rep_vect25 := [ElementToSequence(x): x in G25]; #rep_vect25; rep_exp25 := [x: x in G25]; #rep_exp25; /* Matrix([rep_vect25, rep_exp25]);*/ hola:=[1,2,3,4,5]; hola1 := [alpha,alpha^2,alpha^3,alpha^4,alpha^5]; Matrix([hola,hola1]); Output: Magma V2.10-6 Sat Mar 20 2004 10:16:33 on modular [Seed = 1843322] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 25 25 [ 1 2 3 4 0] [ alpha alpha^2 alpha^3 alpha^4 alpha^5] Total time: 2.999 seconds, Total memory usage: 2.22MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 10:17:10 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); rep_vect25 := [ElementToSequence(x): x in G25]; #rep_vect25; rep_exp25 := [x: x in G25]; #rep_exp25; /* Matrix([rep_vect25, rep_exp25]);*/ hola:=[1,2,3,4,6]; hola1 := [alpha,alpha^2,alpha^3,alpha^4,alpha^5]; Matrix([hola,hola1]); Output: Magma V2.10-6 Sat Mar 20 2004 10:17:07 on modular [Seed = 2019842080] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 25 25 [ 1 2 3 4 1] [ alpha alpha^2 alpha^3 alpha^4 alpha^5] Total time: 3.079 seconds, Total memory usage: 2.22MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 10:18:03 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); rep_vec25 := [ElementToSequence(x): x in G25]; #rep_vec25; rep_exp25 := [x: x in G25]; #rep_exp25; Matrix([rep_vec25, rep_exp25]); hola:=[1,2,3,4,6]; hola1 := [alpha,alpha^2,alpha^3,alpha^4,alpha^5]; Matrix([hola,hola1]); Output: Magma V2.10-6 Sat Mar 20 2004 10:18:00 on modular [Seed = 2003523572] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 25 25 >> Matrix([rep_vec25, rep_exp25]); ^ Runtime error in [ ... ]: Could not find a valid universe [ 1 2 3 4 1] [ alpha alpha^2 alpha^3 alpha^4 alpha^5] Total time: 3.009 seconds, Total memory usage: 2.22MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 10:19:25 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); rep_vec25 := [ElementToSequence(x): x in G25]; rep_vec25; rep_exp25 := [x: x in G25]; rep_exp25; Matrix([rep_vec25, rep_exp25]); Output: Magma V2.10-6 Sat Mar 20 2004 10:19:22 on modular [Seed = 1314025119] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 [ [ 1, 0 ], [ 0, 1 ], [ 3, 1 ], [ 3, 4 ], [ 2, 2 ], [ 1, 4 ], [ 2, 0 ], [ 0, 2 ], [ 1, 2 ], [ 1, 3 ], [ 4, 4 ], [ 2, 3 ], [ 4, 0 ], [ 0, 4 ], [ 2, 4 ], [ 2, 1 ], [ 3, 3 ], [ 4, 1 ], [ 3, 0 ], [ 0, 3 ], [ 4, 3 ], [ 4, 2 ], [ 1, 1 ], [ 3, 2 ], [ 0, 0 ] ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 2, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 3, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] >> Matrix([rep_vec25, rep_exp25]); ^ Runtime error in [ ... ]: Could not find a valid universe Total time: 2.989 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 10:22:56 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); rep_vec25 := [ElementToSequence(x): x in G25]; rep_vec25; rep_exp25 := [x: x in G25]; rep_exp25; Matrix([rep_vec25, rep_exp25]); G16 := ext < GF(2) | g >; rep_vect16 := [ElementToSequence(x): x in G16]; rep_vect16; rep_exp16 := [x: x in G16]; rep_exp16; Output: Magma V2.10-6 Sat Mar 20 2004 10:22:53 on modular [Seed = 1547730362] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 [ [ 1, 0 ], [ 0, 1 ], [ 3, 1 ], [ 3, 4 ], [ 2, 2 ], [ 1, 4 ], [ 2, 0 ], [ 0, 2 ], [ 1, 2 ], [ 1, 3 ], [ 4, 4 ], [ 2, 3 ], [ 4, 0 ], [ 0, 4 ], [ 2, 4 ], [ 2, 1 ], [ 3, 3 ], [ 4, 1 ], [ 3, 0 ], [ 0, 3 ], [ 4, 3 ], [ 4, 2 ], [ 1, 1 ], [ 3, 2 ], [ 0, 0 ] ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 2, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 3, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] >> Matrix([rep_vec25, rep_exp25]); ^ Runtime error in [ ... ]: Could not find a valid universe [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 1, 1, 0, 0 ], [ 0, 1, 1, 0 ], [ 0, 0, 1, 1 ], [ 1, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 0, 1, 0, 1 ], [ 1, 1, 1, 0 ], [ 0, 1, 1, 1 ], [ 1, 1, 1, 1 ], [ 1, 0, 1, 1 ], [ 1, 0, 0, 1 ], [ 0, 0, 0, 0 ] ] [ 1, gamma, gamma^2, gamma^3, gamma^4, gamma^5, gamma^6, gamma^7, gamma^8, gamma^9, gamma^10, gamma^11, gamma^12, gamma^13, gamma^14, 0 ] Total time: 2.929 seconds, Total memory usage: 2.22MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 10:30:11 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); rep_vec25 := [ElementToSequence(x): x in G25]; rep_vec25; rep_exp25 := [x: x in G25]; rep_exp25; Matrix([rep_vec25, rep_exp25]); G16 := ext < GF(2) | g >; G2 := GF(2); G4 := GF(4); G8 := GF(8); G16 := GF(16); [elem: elem in GF(2)]; [elem: elem in GF(4)]; [elem: elem in GF(8)]; [elem: elem in GF(16)]; G2 subset G4; G2 subset G8; G2 subset G16; G4 subset G2; G4 subset G8; G4 subset G16; G8 subset G2; G8 subset G4; G8 subset G16; G16 subset G2; G16 subset G4; G16 subset G8; Output: Magma V2.10-6 Sat Mar 20 2004 10:30:08 on modular [Seed = 2780399118] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 [ [ 1, 0 ], [ 0, 1 ], [ 3, 1 ], [ 3, 4 ], [ 2, 2 ], [ 1, 4 ], [ 2, 0 ], [ 0, 2 ], [ 1, 2 ], [ 1, 3 ], [ 4, 4 ], [ 2, 3 ], [ 4, 0 ], [ 0, 4 ], [ 2, 4 ], [ 2, 1 ], [ 3, 3 ], [ 4, 1 ], [ 3, 0 ], [ 0, 3 ], [ 4, 3 ], [ 4, 2 ], [ 1, 1 ], [ 3, 2 ], [ 0, 0 ] ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 2, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 3, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] >> Matrix([rep_vec25, rep_exp25]); ^ Runtime error in [ ... ]: Could not find a valid universe [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] true true true false false true false false false false false false Total time: 2.939 seconds, Total memory usage: 2.22MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 10:31:11 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); rep_vec25 := [ElementToSequence(x): x in G25]; rep_vec25; rep_exp25 := [x: x in G25]; rep_exp25; Matrix([rep_vec25, rep_exp25]); G16 := ext < GF(2) | g >; G2 := GF(2); G4 := GF(4); G8 := GF(8); G16 := GF(16); [elem: elem in GF(2)]; [elem1: elem1 in GF(4)]; [elem2: elem2 in GF(8)]; [elem3: elem3 in GF(16)]; G2 subset G4; G2 subset G8; G2 subset G16; G4 subset G2; G4 subset G8; G4 subset G16; G8 subset G2; G8 subset G4; G8 subset G16; G16 subset G2; G16 subset G4; G16 subset G8; Output: Magma V2.10-6 Sat Mar 20 2004 10:31:08 on modular [Seed = 3164643115] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 [ [ 1, 0 ], [ 0, 1 ], [ 3, 1 ], [ 3, 4 ], [ 2, 2 ], [ 1, 4 ], [ 2, 0 ], [ 0, 2 ], [ 1, 2 ], [ 1, 3 ], [ 4, 4 ], [ 2, 3 ], [ 4, 0 ], [ 0, 4 ], [ 2, 4 ], [ 2, 1 ], [ 3, 3 ], [ 4, 1 ], [ 3, 0 ], [ 0, 3 ], [ 4, 3 ], [ 4, 2 ], [ 1, 1 ], [ 3, 2 ], [ 0, 0 ] ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 2, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 3, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] >> Matrix([rep_vec25, rep_exp25]); ^ Runtime error in [ ... ]: Could not find a valid universe [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] true true true false false true false false false false false false Total time: 2.949 seconds, Total memory usage: 2.22MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 10:34:08 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); rep_vec25 := [ElementToSequence(x): x in G25]; rep_vec25; rep_exp25 := [x: x in G25]; rep_exp25; Matrix([rep_vec25, rep_exp25]); G16 := ext < GF(2) | g >; G2 := GF(2); G4 := GF(4); G8 := GF(8); G16 := GF(16); [elem: elem in G2]; [elem1: elem1 in G4]; [elem2: elem2 in G8]; [elem3: elem3 in G16]; G2 subset G4; G2 subset G8; G2 subset G16; G4 subset G2; G4 subset G8; G4 subset G16; G8 subset G2; G8 subset G4; G8 subset G16; G16 subset G2; G16 subset G4; G16 subset G8; Output: Magma V2.10-6 Sat Mar 20 2004 10:34:05 on modular [Seed = 2308287951] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 [ [ 1, 0 ], [ 0, 1 ], [ 3, 1 ], [ 3, 4 ], [ 2, 2 ], [ 1, 4 ], [ 2, 0 ], [ 0, 2 ], [ 1, 2 ], [ 1, 3 ], [ 4, 4 ], [ 2, 3 ], [ 4, 0 ], [ 0, 4 ], [ 2, 4 ], [ 2, 1 ], [ 3, 3 ], [ 4, 1 ], [ 3, 0 ], [ 0, 3 ], [ 4, 3 ], [ 4, 2 ], [ 1, 1 ], [ 3, 2 ], [ 0, 0 ] ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 2, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 3, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] >> Matrix([rep_vec25, rep_exp25]); ^ Runtime error in [ ... ]: Could not find a valid universe [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] true true true false false true false false false false false false Total time: 3.009 seconds, Total memory usage: 2.22MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 10:34:49 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); rep_vec25 := [ElementToSequence(x): x in G25]; rep_vec25; rep_exp25 := [x: x in G25]; rep_exp25; G16 := ext < GF(2) | g >; cosfinit2 := GF(2); cosfinit4 := GF(4); G8 := GF(8); G16 := GF(16); [elem: elem in cosfinit2]; [elem1: elem1 in cosfinit4]; [elem2: elem2 in G8]; [elem3: elem3 in G16]; G2 subset G4; G2 subset G8; G2 subset G16; G4 subset G2; G4 subset G8; G4 subset G16; G8 subset G2; G8 subset G4; G8 subset G16; G16 subset G2; G16 subset G4; G16 subset G8; Output: Magma V2.10-6 Sat Mar 20 2004 10:34:46 on modular [Seed = 2157749309] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 [ [ 1, 0 ], [ 0, 1 ], [ 3, 1 ], [ 3, 4 ], [ 2, 2 ], [ 1, 4 ], [ 2, 0 ], [ 0, 2 ], [ 1, 2 ], [ 1, 3 ], [ 4, 4 ], [ 2, 3 ], [ 4, 0 ], [ 0, 4 ], [ 2, 4 ], [ 2, 1 ], [ 3, 3 ], [ 4, 1 ], [ 3, 0 ], [ 0, 3 ], [ 4, 3 ], [ 4, 2 ], [ 1, 1 ], [ 3, 2 ], [ 0, 0 ] ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 2, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 3, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 0, 1 ] [ 1, cosfinit4.1, cosfinit4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] >> G2 subset G4; ^ User error: Identifier 'G4' has not been declared or assigned >> G2 subset G8; ^ Runtime error in 'subset': Bad argument types Argument types given: Intrinsic, FldFin >> G2 subset G16; ^ Runtime error in 'subset': Bad argument types Argument types given: Intrinsic, FldFin >> G4 subset G2; ^ User error: Identifier 'G4' has not been declared or assigned >> G4 subset G8; ^ User error: Identifier 'G4' has not been declared or assigned >> G4 subset G16; ^ User error: Identifier 'G4' has not been declared or assigned >> G8 subset G2; ^ Runtime error in 'subset': Bad argument types Argument types given: FldFin, Intrinsic >> G8 subset G4; ^ User error: Identifier 'G4' has not been declared or assigned false >> G16 subset G2; ^ Runtime error in 'subset': Bad argument types Argument types given: FldFin, Intrinsic >> G16 subset G4; ^ User error: Identifier 'G4' has not been declared or assigned false Total time: 3.009 seconds, Total memory usage: 2.22MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 10:36:29 2004 Input: cosfinit2 := GF(2); cosfinit4 := GF(4); cosfinit8 := GF(8); cosfinit16 := GF(16); [elem: elem in cosfinit2]; [elem: elem in cosfinit4]; [elem: elem in GF(8)]; [elem: elem in GF(16)]; Output: Magma V2.10-6 Sat Mar 20 2004 10:36:26 on modular [Seed = 2458826307] ------------------------------------- [ 0, 1 ] [ 1, cosfinit4.1, cosfinit4.1^2, 0 ] [ 1, cosfinit8.1, cosfinit8.1^2, cosfinit8.1^3, cosfinit8.1^4, cosfinit8.1^5, cosfinit8.1^6, 0 ] [ 1, cosfinit16.1, cosfinit16.1^2, cosfinit16.1^3, cosfinit16.1^4, cosfinit16.1^5, cosfinit16.1^6, cosfinit16.1^7, cosfinit16.1^8, cosfinit16.1^9, cosfinit16.1^10, cosfinit16.1^11, cosfinit16.1^12, cosfinit16.1^13, cosfinit16.1^14, 0 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 10:36:54 2004 Input: cosfinit2 := GF(2); cosfinit4 := GF(4); cosfinit8 := GF(8); cosfinit16 := GF(16); cos3 := GF(3) [elem: elem in cosfinit2]; [elem: elem in cosfinit4]; [elem: elem in cos3]; [elem: elem in GF(16)]; Output: Magma V2.10-6 Sat Mar 20 2004 10:36:52 on modular [Seed = 3925200086] ------------------------------------- >> [elem: elem in cosfinit2]; ^ User error: bad syntax [ 1, cosfinit4.1, cosfinit4.1^2, 0 ] >> [elem: elem in cos3]; ^ User error: Identifier 'cos3' has not been declared or assigned [ 1, cosfinit16.1, cosfinit16.1^2, cosfinit16.1^3, cosfinit16.1^4, cosfinit16.1^5, cosfinit16.1^6, cosfinit16.1^7, cosfinit16.1^8, cosfinit16.1^9, cosfinit16.1^10, cosfinit16.1^11, cosfinit16.1^12, cosfinit16.1^13, cosfinit16.1^14, 0 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 10:37:27 2004 Input: cosfinit2 := GF(2); cosfinit4 := GF(4); cosfinit8 := GF(8); cosfinit16 := GF(16); cos3 := GF(3) [elem: elem in cos3]; [elem: elem in cosfinit4]; [elem: elem in cos3]; [elem: elem in GF(16)]; Output: Magma V2.10-6 Sat Mar 20 2004 10:37:24 on modular [Seed = 3892036344] ------------------------------------- >> [elem: elem in cos3]; ^ User error: bad syntax [ 1, cosfinit4.1, cosfinit4.1^2, 0 ] >> [elem: elem in cos3]; ^ User error: Identifier 'cos3' has not been declared or assigned [ 1, cosfinit16.1, cosfinit16.1^2, cosfinit16.1^3, cosfinit16.1^4, cosfinit16.1^5, cosfinit16.1^6, cosfinit16.1^7, cosfinit16.1^8, cosfinit16.1^9, cosfinit16.1^10, cosfinit16.1^11, cosfinit16.1^12, cosfinit16.1^13, cosfinit16.1^14, 0 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 10:38:19 2004 Input: G2 := GF(2); G4 := GF(4); G8 := GF(8); G16 := GF(16); G3 := GF(3) [elem: elem in G3]; [elem: elem in G4]; [elem: elem in cos3]; [elem: elem in G16]; Output: Magma V2.10-6 Sat Mar 20 2004 10:38:16 on modular [Seed = 4276280253] ------------------------------------- >> [elem: elem in G3]; ^ User error: bad syntax [ 1, G4.1, G4.1^2, 0 ] >> [elem: elem in cos3]; ^ User error: Identifier 'cos3' has not been declared or assigned [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 10:38:38 2004 Input: G2 := GF(2); G4 := GF(4); G8 := GF(8); G16 := GF(16); G3 := GF(3) [elem: elem in G3]; /* [elem: elem in G4]; [elem: elem in cos3]; [elem: elem in G16]; */ Output: Magma V2.10-6 Sat Mar 20 2004 10:38:35 on modular [Seed = 4125741221] ------------------------------------- >> [elem: elem in G3]; ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 10:40:00 2004 Input: /*G2 := GF(2); G4 := GF(4); G8 := GF(8); G16 := GF(16); G3 := GF(3) */ G2 := GF(2); [element: element in G2]; G3 := GF(3); [element: element in G3]; G5 := GF(5); [element: element in G5]; /* [elem: elem in G3]; [elem: elem in G4]; [elem: elem in cos3]; [elem: elem in G16]; */ Output: Magma V2.10-6 Sat Mar 20 2004 10:39:57 on modular [Seed = 3436243242] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 10:40:46 2004 Input: G4 := GF(4); G8 := GF(8); G16 := GF(16); G2 := GF(2); [element: element in G2]; G3 := GF(3); [element: element in G3]; G5 := GF(5); [element: element in G5]; [elem: elem in G4]; [elem: elem in G16]; Output: Magma V2.10-6 Sat Mar 20 2004 10:40:43 on modular [Seed = 3703634188] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 10:41:54 2004 Input: G4 := GF(4); G8 := GF(8); G16 := GF(16); G2 := GF(2); G3 := GF(3); G5 := GF(5); G9 := GF(9); [element: element in G2]; [element: element in G3]; [element: element in G5]; [elem: elem in G4]; [elem: elem in G16]; [elem: elem in G9]; Output: Magma V2.10-6 Sat Mar 20 2004 10:41:51 on modular [Seed = 775030845] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 10:42:13 2004 Input: G4 := GF(4); G8 := GF(8); G16 := GF(16); G2 := GF(2); G3 := GF(3); G5 := GF(5); G9 := GF(7); [element: element in G2]; [element: element in G3]; [element: element in G5]; [elem: elem in G4]; [elem: elem in G16]; [elem: elem in G7]; Output: Magma V2.10-6 Sat Mar 20 2004 10:42:10 on modular [Seed = 658178393] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] >> [elem: elem in G7];; ^ User error: Identifier 'G7' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 10:42:26 2004 Input: G4 := GF(4); G8 := GF(8); G16 := GF(16); G2 := GF(2); G3 := GF(3); G5 := GF(5); G7 := GF(7); [element: element in G2]; [element: element in G3]; [element: element in G5]; [elem: elem in G4]; [elem: elem in G16]; [elem: elem in G7]; Output: Magma V2.10-6 Sat Mar 20 2004 10:42:23 on modular [Seed = 941891147] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 0, 1, 2, 3, 4, 5, 6 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 10:42:44 2004 Input: G4 := GF(4); G8 := GF(8); G16 := GF(16); G2 := GF(2); G3 := GF(3); G5 := GF(5); G21 := GF(21); [element: element in G2]; [element: element in G3]; [element: element in G5]; [elem: elem in G4]; [elem: elem in G16]; [elem: elem in G21]; Output: Magma V2.10-6 Sat Mar 20 2004 10:42:41 on modular [Seed = 825038700] ------------------------------------- >> G21 := GF(21); ^ Runtime error in 'GF': Argument 1 (21) is not a prime power [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] >> [elem: elem in G21];; ^ User error: Identifier 'G21' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 10:43:07 2004 Input: G4 := GF(4); G8 := GF(8); G16 := GF(16); G2 := GF(2); G3 := GF(3); G5 := GF(5); G21 := GF(27); [element: element in G2]; [element: element in G3]; [element: element in G5]; [elem: elem in G4]; [elem: elem in G16]; [elem: elem in G21]; Output: Magma V2.10-6 Sat Mar 20 2004 10:43:04 on modular [Seed = 169225390] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G21.1, G21.1^2, G21.1^3, G21.1^4, G21.1^5, G21.1^6, G21.1^7, G21.1^8, G21.1^9, G21.1^10, G21.1^11, G21.1^12, 2, G21.1^14, G21.1^15, G21.1^16, G21.1^17, G21.1^18, G21.1^19, G21.1^20, G21.1^21, G21.1^22, G21.1^23, G21.1^24, G21.1^25, 0 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 10:43:58 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); rep_vec25 := [ElementToSequence(x): x in G25]; rep_vec25; rep_exp25 := [x: x in G25]; rep_exp25; G16 := ext < GF(2) | g >; G2 := GF(2); G4 := GF(4); G8 := GF(8); G16 := GF(16); [elem: elem in G2]; [elem: elem1 in G4]; [elem: elem2 in G8]; [elem: elem3 in G16]; G2 subset G4; G2 subset G8; G2 subset G16; G4 subset G2; G4 subset G8; G4 subset G16; G8 subset G2; G8 subset G4; G8 subset G16; G16 subset G2; G16 subset G4; G16 subset G8; Output: Magma V2.10-6 Sat Mar 20 2004 10:43:55 on modular [Seed = 52372884] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 [ [ 1, 0 ], [ 0, 1 ], [ 3, 1 ], [ 3, 4 ], [ 2, 2 ], [ 1, 4 ], [ 2, 0 ], [ 0, 2 ], [ 1, 2 ], [ 1, 3 ], [ 4, 4 ], [ 2, 3 ], [ 4, 0 ], [ 0, 4 ], [ 2, 4 ], [ 2, 1 ], [ 3, 3 ], [ 4, 1 ], [ 3, 0 ], [ 0, 3 ], [ 4, 3 ], [ 4, 2 ], [ 1, 1 ], [ 3, 2 ], [ 0, 0 ] ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 2, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 3, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 0, 1 ] >> [elem: elem1 in G4]; ^ User error: Identifier 'elem' has not been declared or assigned >> [elem: elem2 in G8]; ^ User error: Identifier 'elem' has not been declared or assigned >> [elem: elem3 in G16]; ^ User error: Identifier 'elem' has not been declared or assigned true true true false false true false false false false false false Total time: 3.049 seconds, Total memory usage: 2.22MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 10:44:25 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); rep_vec25 := [ElementToSequence(x): x in G25]; rep_vec25; rep_exp25 := [x: x in G25]; rep_exp25; G16 := ext < GF(2) | g >; G2 := GF(2); G4 := GF(4); G8 := GF(8); G16 := GF(16); [elem: elem in G2]; [elem: elem in G4]; [elem: elem in G8]; [elem: elem in G16]; G2 subset G4; G2 subset G8; G2 subset G16; G4 subset G2; G4 subset G8; G4 subset G16; G8 subset G2; G8 subset G4; G8 subset G16; G16 subset G2; G16 subset G4; G16 subset G8; Output: Magma V2.10-6 Sat Mar 20 2004 10:44:21 on modular [Seed = 336081645] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 [ [ 1, 0 ], [ 0, 1 ], [ 3, 1 ], [ 3, 4 ], [ 2, 2 ], [ 1, 4 ], [ 2, 0 ], [ 0, 2 ], [ 1, 2 ], [ 1, 3 ], [ 4, 4 ], [ 2, 3 ], [ 4, 0 ], [ 0, 4 ], [ 2, 4 ], [ 2, 1 ], [ 3, 3 ], [ 4, 1 ], [ 3, 0 ], [ 0, 3 ], [ 4, 3 ], [ 4, 2 ], [ 1, 1 ], [ 3, 2 ], [ 0, 0 ] ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 2, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 3, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] true true true false false true false false false false false false Total time: 3.029 seconds, Total memory usage: 2.22MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 10:51:19 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); rep_vec25 := [ElementToSequence(x): x in G25]; rep_vec25; rep_exp25 := [x: x in G25]; rep_exp25; G16 := ext < GF(2) | g >; G2 := GF(2); G4 := GF(4); G8 := GF(8); G16 := GF(16); [elem: elem in G2]; [elem: elem in G4]; [elem: elem in G8]; [elem: elem in G16]; PG25 := PolynomialRing(G25); IsFinite(PG25); Output: Magma V2.10-6 Sat Mar 20 2004 10:51:16 on modular [Seed = 2086687780] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 [ [ 1, 0 ], [ 0, 1 ], [ 3, 1 ], [ 3, 4 ], [ 2, 2 ], [ 1, 4 ], [ 2, 0 ], [ 0, 2 ], [ 1, 2 ], [ 1, 3 ], [ 4, 4 ], [ 2, 3 ], [ 4, 0 ], [ 0, 4 ], [ 2, 4 ], [ 2, 1 ], [ 3, 3 ], [ 4, 1 ], [ 3, 0 ], [ 0, 3 ], [ 4, 3 ], [ 4, 2 ], [ 1, 1 ], [ 3, 2 ], [ 0, 0 ] ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 2, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 3, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] false Total time: 2.949 seconds, Total memory usage: 2.22MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 10:53:38 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); rep_vec25 := [ElementToSequence(x): x in G25]; rep_vec25; rep_exp25 := [x: x in G25]; rep_exp25; G16 := ext < GF(2) | g >; G2 := GF(2); G4 := GF(4); G8 := GF(8); G16 := GF(16); [elem: elem in G2]; [elem: elem in G4]; [elem: elem in G8]; [elem: elem in G16]; PG25 := PolynomialRing(G25); IsFinite(PG25); beta := PrimitiveElement(G5); p1 := alpha^2 + alpha^x + beta*x^2; p2 := 1 + alpha*x; Output: Magma V2.10-6 Sat Mar 20 2004 10:53:35 on modular [Seed = 1986682533] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 [ [ 1, 0 ], [ 0, 1 ], [ 3, 1 ], [ 3, 4 ], [ 2, 2 ], [ 1, 4 ], [ 2, 0 ], [ 0, 2 ], [ 1, 2 ], [ 1, 3 ], [ 4, 4 ], [ 2, 3 ], [ 4, 0 ], [ 0, 4 ], [ 2, 4 ], [ 2, 1 ], [ 3, 3 ], [ 4, 1 ], [ 3, 0 ], [ 0, 3 ], [ 4, 3 ], [ 4, 2 ], [ 1, 1 ], [ 3, 2 ], [ 0, 0 ] ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 2, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 3, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] false >> p1 := alpha^2 + alpha^x + beta*x^2; ^ Runtime error in '^': Bad argument types Argument types given: RngUPolElt, RngUPolElt Total time: 2.949 seconds, Total memory usage: 2.22MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 10:54:52 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); G16 := ext < GF(2) | g >; PG25 := PolynomialRing(G25); beta := PrimitiveElement(G5); p1 := alpha^2 + alpha^x + beta*x^2; p2 := 1 + alpha*x; Output: Magma V2.10-6 Sat Mar 20 2004 10:54:49 on modular [Seed = 1330865706] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 >> p1 := alpha^2 + alpha^x + beta*x^2; ^ Runtime error in '^': Bad argument types Argument types given: RngUPolElt, RngUPolElt Total time: 2.919 seconds, Total memory usage: 2.22MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 10:55:31 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); G16 := ext < GF(2) | g >; PG25 := PolynomialRing(G25); beta := PrimitiveElement(G5); p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; Output: Magma V2.10-6 Sat Mar 20 2004 10:55:28 on modular [Seed = 1547728128] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 Total time: 2.999 seconds, Total memory usage: 2.22MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 10:56:02 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); G16 := ext < GF(2) | g >; PG25 := PolynomialRing(G25); beta := PrimitiveElement(G5); p1 := alpha^2 + alpha*x + beta*x^2; p1; p2 := 1 + alpha*x; p2; Output: Magma V2.10-6 Sat Mar 20 2004 10:55:59 on modular [Seed = 1430879478] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 2*x^2 + alpha*x + alpha^2 alpha*x + 1 Total time: 3.099 seconds, Total memory usage: 2.22MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 10:58:28 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); G16 := ext < GF(2) | g >; PG25 := PolynomialRing(G25); beta := PrimitiveElement(G5); p1 := alpha^2 + alpha*x + beta*x^2; p1; p2 := 1 + alpha*x; p2; beta; Output: Magma V2.10-6 Sat Mar 20 2004 10:58:25 on modular [Seed = 2830402213] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 2*x^2 + alpha*x + alpha^2 alpha*x + 1 2 Total time: 3.019 seconds, Total memory usage: 2.22MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 10:59:27 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); G16 := ext < GF(2) | g >; PG25 := PolynomialRing(G25); beta := PrimitiveElement(G5); p1 := alpha^2 + alpha*x + beta*x^2; p1; p2 := 1 + alpha*x; p2; beta; p1 + p2; p1 * p2; Output: Magma V2.10-6 Sat Mar 20 2004 10:59:24 on modular [Seed = 2713553873] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 2*x^2 + alpha*x + alpha^2 alpha*x + 1 2 2*x^2 + alpha^7*x + alpha^17 alpha^7*x^3 + alpha*x^2 + 3*x + alpha^2 Total time: 2.979 seconds, Total memory usage: 2.22MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 11:00:26 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); G16 := ext < GF(2) | g >; PG25 := PolynomialRing(G25); beta := PrimitiveElement(G5); p1 := alpha^2 + alpha*x + beta*x^2; p1; p2 := 1 + alpha*x; p2; beta; p1 + p2; p1 * p2; Quotrem(p1,p2); Output: Magma V2.10-6 Sat Mar 20 2004 11:00:23 on modular [Seed = 2980944650] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 2*x^2 + alpha*x + alpha^2 alpha*x + 1 2 2*x^2 + alpha^7*x + alpha^17 alpha^7*x^3 + alpha*x^2 + 3*x + alpha^2 alpha^5*x + alpha^20 alpha^20 Total time: 2.959 seconds, Total memory usage: 2.22MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 11:00:49 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); G16 := ext < GF(2) | g >; PG25 := PolynomialRing(G25); beta := PrimitiveElement(G5); p1 := alpha^2 + alpha*x + beta*x^2; p1; p2 := 1 + alpha*x; p2; beta; Quotrem(p1,p2); Output: Magma V2.10-6 Sat Mar 20 2004 11:00:46 on modular [Seed = 2325127176] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 2*x^2 + alpha*x + alpha^2 alpha*x + 1 2 alpha^5*x + alpha^20 alpha^20 Total time: 2.999 seconds, Total memory usage: 2.22MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 11:01:50 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); G16 := ext < GF(2) | g >; PG25 := PolynomialRing(G25); beta := PrimitiveElement(G5); p1 := alpha^2 + alpha*x + beta*x^2; p1; p2 := 1 + alpha*x; p2; beta; quocient, residu: Quotrem(p1,p2); quocient; residu; Output: Magma V2.10-6 Sat Mar 20 2004 11:01:47 on modular [Seed = 4025730344] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 2*x^2 + alpha*x + alpha^2 alpha*x + 1 2 >> quocient, residu: Quotrem(p1,p2); ^ User error: bad syntax >> quocient; ^ User error: Identifier 'quocient' has not been declared or assigned >> residu;; ^ User error: Identifier 'residu' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 2.22MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 11:02:06 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); G16 := ext < GF(2) | g >; PG25 := PolynomialRing(G25); beta := PrimitiveElement(G5); p1 := alpha^2 + alpha*x + beta*x^2; p1; p2 := 1 + alpha*x; p2; beta; quocient, residu:= Quotrem(p1,p2); quocient; residu; Output: Magma V2.10-6 Sat Mar 20 2004 11:02:03 on modular [Seed = 3774663223] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 2*x^2 + alpha*x + alpha^2 alpha*x + 1 2 alpha^5*x + alpha^20 alpha^20 Total time: 3.019 seconds, Total memory usage: 2.22MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 11:04:52 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); G16 := ext < GF(2) | g >; PG25 := PolynomialRing(G25); beta := PrimitiveElement(G5); p1 := alpha^2 + alpha*x + beta*x^2; p1; p2 := 1 + alpha*x; p2; beta; quocient, residu:= Quotrem(p1,p2); quocient; residu; GCD (p1, p2); LCM (p1, p2); Output: Magma V2.10-6 Sat Mar 20 2004 11:04:48 on modular [Seed = 4209430902] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 2*x^2 + alpha*x + alpha^2 alpha*x + 1 2 alpha^5*x + alpha^20 alpha^20 1 x^3 + 3*x^2 + alpha^11*x + alpha^19 Total time: 3.029 seconds, Total memory usage: 2.22MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 11:06:29 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); G16 := ext < GF(2) | g >; PG25 := PolynomialRing(G25); beta := PrimitiveElement(G5); p1 := alpha^2 + alpha*x + beta*x^2; p1; p2 := 1 + alpha*x; p2; beta; quocient, residu:= Quotrem(p1,p2); quocient; residu; GCD (p1, p2); LCM (p1, p2); d, a, b := XGCD (p1,p2); d; a; b; 1 eq a*p1 + b*p2; Output: Magma V2.10-6 Sat Mar 20 2004 11:06:26 on modular [Seed = 3369395430] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 2*x^2 + alpha*x + alpha^2 alpha*x + 1 2 alpha^5*x + alpha^20 alpha^20 1 x^3 + 3*x^2 + alpha^11*x + alpha^19 1 alpha^4 alpha^21*x + 4 true Total time: 3.149 seconds, Total memory usage: 2.22MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 11:11:48 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); G16 := ext < GF(2) | g >; PG25 := PolynomialRing(G25); beta := PrimitiveElement(G5); p1 := alpha^2 + alpha*x + beta*x^2; p1; p2 := 1 + alpha*x; p2; beta; quocient, residu:= Quotrem(p1,p2); quocient; residu; GCD (p1, p2); LCM (p1, p2); d, a, b := XGCD (p1,p2); d; a; b; 1 eq a*p1 + b*p2; polinomi := 1/(alpha^4) - alpha^(-3)*x + alpha^5 *x^2; Factorization(polinomi); Roots(polinomi, G25); Comprovem que són arrels de manera que en evaluar 'polinomi' en aquests valors, s'anul·larà: Evaluate(polinomi, -3); Evaluate(polinomi, -alpha^21); Output: Magma V2.10-6 Sat Mar 20 2004 11:11:45 on modular [Seed = 3519937724] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 2*x^2 + alpha*x + alpha^2 alpha*x + 1 2 alpha^5*x + alpha^20 alpha^20 1 x^3 + 3*x^2 + alpha^11*x + alpha^19 1 alpha^4 alpha^21*x + 4 true [ , ] [ <2, 1>, ] >> Comprovem que s^3n arrels de manera que en evaluar 'polinomi' en aquests va ^ User error: bad syntax 0 0 Total time: 3.069 seconds, Total memory usage: 2.22MB ************** MAGMA ***************** Host 149-210-ADSL.red.retevision.es. (80.224.210.149) Time: Sat Mar 20 11:12:29 2004 Input: G5 := GF(5); P3 := PolynomialRing(Integers(3)); P2 := PolynomialRing(Integers(2)); P5 := PolynomialRing(Integers(5)); f := P3 ! [ 2, 2, 1 ]; g := P2 ! [ 1, 1, 0, 0, 1 ]; h := P5 ! [ 3, 2, 1 ]; i := P3 ! [ 1, 2, 1 ]; IsIrreducible(f); IsIrreducible(g); IsIrreducible(h); IsIrreducible(i); j := P5 ! [ 2, 4, 1 ]; k := P3 ! [ 1, 2, 1 ]; G9 := ext < GF(3) | f >; G16 := ext < GF(2) | g >; G25 := ext < GF(5) | j >; j; s := MinimalPolynomial(alpha, G5); s; Degree(s); G16 := ext < GF(2) | g >; PG25 := PolynomialRing(G25); beta := PrimitiveElement(G5); p1 := alpha^2 + alpha*x + beta*x^2; p1; p2 := 1 + alpha*x; p2; beta; quocient, residu:= Quotrem(p1,p2); quocient; residu; GCD (p1, p2); LCM (p1, p2); d, a, b := XGCD (p1,p2); d; a; b; 1 eq a*p1 + b*p2; polinomi := 1/(alpha^4) - alpha^(-3)*x + alpha^5 *x^2; Factorization(polinomi); Roots(polinomi, G25); Evaluate(polinomi, -3); Evaluate(polinomi, -alpha^21); Output: Magma V2.10-6 Sat Mar 20 2004 11:12:26 on modular [Seed = 725026412] ------------------------------------- true true true false x^2 + 4*x + 2 $.1^2 + 4*$.1 + 2 2 2*x^2 + alpha*x + alpha^2 alpha*x + 1 2 alpha^5*x + alpha^20 alpha^20 1 x^3 + 3*x^2 + alpha^11*x + alpha^19 1 alpha^4 alpha^21*x + 4 true [ , ] [ <2, 1>, ] 0 0 Total time: 3.049 seconds, Total memory usage: 2.22MB ************** MAGMA ***************** Host balder.cpd.ufv.br. (200.17.79.42) Time: Sat Mar 20 11:31:54 2004 Input: gl3 := LieAlgebra(Algebra(MatrixRing(Rationals(), 3))); sl3 := gl3 * gl3; sl3; Output: Magma V2.10-6 Sat Mar 20 2004 11:31:50 on modular [Seed = 469773767] ------------------------------------- Lie Algebra of dimension 8 with base ring Rational Field Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-158-214-34.alt.east.verizon.net. (141.158.214.34) Time: Sat Mar 20 12:59:52 2004 Input: R:=MatrixAlgebra(Rationals(),2); A:=R!Matrix([[2,3],[1,4]); J,T:=JordanForm(A); J; T; Output: Magma V2.10-6 Sat Mar 20 2004 12:59:49 on modular [Seed = 3436186228] ------------------------------------- >> A:=R!Matrix([[2,3],[1,4]); ^ User error: bad syntax >> J,T:=JordanForm(A); J; T; ^ User error: Identifier 'A' has not been declared or assigned >> J,T:=JordanForm(A); J; T; ^ User error: Identifier 'J' has not been declared or assigned >> J,T:=JordanForm(A); J; T; ^ User error: Identifier 'T' has not been declared or assigned Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-158-214-34.alt.east.verizon.net. (141.158.214.34) Time: Sat Mar 20 13:00:15 2004 Input: R:=MatrixAlgebra(Rationals(),2); A:=R!Matrix([[2,3],[1,4]]); J,T:=JordanForm(A); J; T; Output: Magma V2.10-6 Sat Mar 20 2004 13:00:12 on modular [Seed = 3754105182] ------------------------------------- [5 0] [0 1] [ 1 3] [-3 3] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-158-214-34.alt.east.verizon.net. (141.158.214.34) Time: Sat Mar 20 13:41:00 2004 Input: R:=MatrixAlgebra(Rationals(),2); A:=R!Matrix([[2,3,4],[1,4,2],[1,1,1]]); J,T:=JordanForm(A); J; T; Output: Magma V2.10-6 Sat Mar 20 2004 13:40:57 on modular [Seed = 1230346590] ------------------------------------- >> A:=R!Matrix([[2,3,4],[1,4,2],[1,1,1]]); ^ Runtime error in '!': Arguments 1 and 2 have incompatible degrees >> J,T:=JordanForm(A); J; T; ^ User error: Identifier 'A' has not been declared or assigned >> J,T:=JordanForm(A); J; T; ^ User error: Identifier 'J' has not been declared or assigned >> J,T:=JordanForm(A); J; T; ^ User error: Identifier 'T' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-158-214-34.alt.east.verizon.net. (141.158.214.34) Time: Sat Mar 20 13:41:15 2004 Input: R:=MatrixAlgebra(Rationals(),3); A:=R!Matrix([[2,3,4],[1,4,2],[1,1,1]]); J,T:=JordanForm(A); J; T; Output: Magma V2.10-6 Sat Mar 20 2004 13:41:12 on modular [Seed = 1598263097] ------------------------------------- [ 0 1 0] [ 0 0 1] [-5 -5 7] [ 1 0 0] [ 2 3 4] [11 22 18] Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host host229-46.pool8249.interbusiness.it. (82.49.46.229) Time: Sat Mar 20 13:42:27 2004 Input: x+1=0 Output: Magma V2.10-6 Sat Mar 20 2004 13:42:24 on modular [Seed = 3215159041] ------------------------------------- >> x+1=0; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-215-194-55.aep.bellsouth.net. (68.215.194.55) Time: Sat Mar 20 20:30:45 2004 Input: 2^(1/2) Output: Magma V2.10-6 Sat Mar 20 2004 20:30:41 on modular [Seed = 1480910891] ------------------------------------- 1.414213562373095048801689 Total time: 3.159 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-215-194-55.aep.bellsouth.net. (68.215.194.55) Time: Sat Mar 20 20:30:47 2004 Input: 2^(1/2) Output: Magma V2.10-6 Sat Mar 20 2004 20:30:44 on modular [Seed = 1598287657] ------------------------------------- 1.414213562373095048801689 Total time: 3.289 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-215-194-55.aep.bellsouth.net. (68.215.194.55) Time: Sat Mar 20 20:30:51 2004 Input: 2^(1/2) Output: Magma V2.10-6 Sat Mar 20 2004 20:30:48 on modular [Seed = 2980905419] ------------------------------------- 1.414213562373095048801689 Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-215-194-55.aep.bellsouth.net. (68.215.194.55) Time: Sat Mar 20 20:30:54 2004 Input: 2^(1/2) Output: Magma V2.10-6 Sat Mar 20 2004 20:30:51 on modular [Seed = 3030910157] ------------------------------------- 1.414213562373095048801689 Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-215-194-55.aep.bellsouth.net. (68.215.194.55) Time: Sat Mar 20 20:31:05 2004 Input: 2^(1/2*2) Output: Magma V2.10-6 Sat Mar 20 2004 20:31:02 on modular [Seed = 2797213378] ------------------------------------- 2 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-215-194-55.aep.bellsouth.net. (68.215.194.55) Time: Sat Mar 20 20:31:08 2004 Input: 2^(1/2*2) Output: Magma V2.10-6 Sat Mar 20 2004 20:31:05 on modular [Seed = 2930908869] ------------------------------------- 2 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-215-194-55.aep.bellsouth.net. (68.215.194.55) Time: Sat Mar 20 20:31:22 2004 Input: 2^1/2 Output: Magma V2.10-6 Sat Mar 20 2004 20:31:19 on modular [Seed = 2224567505] ------------------------------------- 1 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-215-194-55.aep.bellsouth.net. (68.215.194.55) Time: Sat Mar 20 20:31:47 2004 Input: 2^165*3^110*5^66*11^30 Output: Magma V2.10-6 Sat Mar 20 2004 20:31:44 on modular [Seed = 4075700800] ------------------------------------- 3365798748776771055021735745225708539201175499714289329302312493001360549271892\ 8678263219572408787075925846209331200000000000000000000000000000000000000000000\ 0000000000000000000000 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-215-194-55.aep.bellsouth.net. (68.215.194.55) Time: Sat Mar 20 20:32:26 2004 Input: ((2^165*3^110*5^66*11^30)/2)^(1/2) Output: Magma V2.10-6 Sat Mar 20 2004 20:32:23 on modular [Seed = 3774632053] ------------------------------------- 4.1023156562950949100516512e89 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-215-194-55.aep.bellsouth.net. (68.215.194.55) Time: Sat Mar 20 20:32:48 2004 Input: ((2^165*3^110*5^66*11^30)/2) Output: Magma V2.10-6 Sat Mar 20 2004 20:32:45 on modular [Seed = 3925170534] ------------------------------------- 1682899374388385527510867872612854269600587749857144664651156246500680274635946\ 4339131609786204393537962923104665600000000000000000000000000000000000000000000\ 0000000000000000000000 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-215-194-55.aep.bellsouth.net. (68.215.194.55) Time: Sat Mar 20 20:33:24 2004 Input: sqrt(168289937438838552751086787261285426960058774985714466465115624650068027463594643391316097862043935379629231046656000000000000000000000000000000000000000000000000000000000000000000) Output: Magma V2.10-6 Sat Mar 20 2004 20:33:21 on modular [Seed = 3620431620] ------------------------------------- >> sqrt(1682899374388385527510867872612854269600587749857144664651156246500680 ^ User error: Identifier 'sqrt' has not been declared or assigned Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-215-194-55.aep.bellsouth.net. (68.215.194.55) Time: Sat Mar 20 20:33:39 2004 Input: (168289937438838552751086787261285426960058774985714466465115624650068027463594643391316097862043935379629231046656000000000000000000000000000000000000000000000000000000000000000000)^(1/2) Output: Magma V2.10-6 Sat Mar 20 2004 20:33:36 on modular [Seed = 3703598110] ------------------------------------- 4.1023156562950949100516512e89 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 200-153-190-163.dsl.telesp.net.br. (200.153.190.163) Time: Sun Mar 21 09:32:37 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Sun Mar 21 2004 09:32:32 on modular [Seed = 1919915393] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 200-153-190-163.dsl.telesp.net.br. (200.153.190.163) Time: Sun Mar 21 09:33:05 2004 Input: Miguel Angel Hernandez Torres Output: Magma V2.10-6 Sun Mar 21 2004 09:33:01 on modular [Seed = 2036637335] ------------------------------------- >> Miguel Angel Hernandez Torres; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 200-153-190-163.dsl.telesp.net.br. (200.153.190.163) Time: Sun Mar 21 09:33:51 2004 Input: 2=3 Output: Magma V2.10-6 Sun Mar 21 2004 09:33:47 on modular [Seed = 1447801326] ------------------------------------- 2 = 3 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host c-67-169-131-252.client.comcast.net. (67.169.131.252) Time: Sun Mar 21 15:17:11 2004 Input: a(n)= { n=n2+1; return(((2*n)!/(n!*2^n))^2) } a(3) Output: Magma V2.10-6 Sun Mar 21 2004 15:17:08 on modular [Seed = 4259333583] ------------------------------------- >> a(n)= { n=n2+1; return(((2*n)!/(n!*2^n))^2) } ^ User error: bad syntax >> a(3); ^ User error: Identifier 'a' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host its-wn-prox1.its.rmit.edu.au. (131.170.6.141) Time: Sun Mar 21 22:48:44 2004 Input: Z:=IntegerRing(); Output: Magma V2.10-6 Sun Mar 21 2004 22:48:40 on modular [Seed = 4059026322] ------------------------------------- Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Sun Mar 21 23:59:10 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > 2*x*y*z*w in I; Output: Magma V2.10-6 Sun Mar 21 2004 23:59:07 on modular [Seed = 1414162100] ------------------------------------- [ 4*x^2*y^2 + 9*z^2*w^2, 196*x^2*z^2 + y^2*w^2, x^2*w^2 + 289*y^2*z^2, 289*y^6*z^2 + 42483*y^2*z^6 - 3*y^2*z^2*w^4, 1156*y^4*z^2 - 9*z^2*w^4, y^4*w^2 - 441*z^4*w^2, 56644*y^2*z^4 - y^2*w^4, 509796*z^6*w^2 - 9*z^2*w^6 ] false Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Sun Mar 21 23:59:27 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > 2*x*y*z*w in I; Output: Magma V2.10-6 Sun Mar 21 2004 23:59:24 on modular [Seed = 1130197396] ------------------------------------- [ 4*x^2*y^2 + 9*z^2*w^2, 196*x^2*z^2 + 121*y^2*w^2, x^2*w^2 + 289*y^2*z^2, 289*y^6*z^2 + 42483*y^2*z^6 - 93*y^2*z^2*w^4, y^4*z^2*w^2 + 235935*z^6*w^2 - 504*z^2*w^6, 1156*y^4*z^2 - 9*z^2*w^4, 121*y^4*w^2 - 441*z^4*w^2, 56644*y^2*z^4 - 121*y^2*w^4, 509796*z^6*w^2 - 1089*z^2*w^6 ] false Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 01:22:42 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > 2124125151251*x*y*z*w in I; Output: Magma V2.10-6 Mon Mar 22 2004 01:22:39 on modular [Seed = 2157856468] ------------------------------------- [ 4*x^2*y^2 + 9*z^2*w^2, 196*x^2*z^2 + 121*y^2*w^2, x^2*w^2 + 289*y^2*z^2, 289*y^6*z^2 + 42483*y^2*z^6 - 93*y^2*z^2*w^4, y^4*z^2*w^2 + 235935*z^6*w^2 - 504*z^2*w^6, 1156*y^4*z^2 - 9*z^2*w^4, 121*y^4*w^2 - 441*z^4*w^2, 56644*y^2*z^4 - 121*y^2*w^4, 509796*z^6*w^2 - 1089*z^2*w^6 ] false Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 03:29:34 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > 2124125151251*x*y*z*w in I; Output: Magma V2.10-6 Mon Mar 22 2004 03:29:31 on modular [Seed = 252832921] ------------------------------------- >> I := ideal; ^ User error: bad syntax >> GroebnerBasis(I); ^ User error: Identifier 'I' has not been declared or assigned >> 2124125151251*x*y*z*w in I;; ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 03:30:01 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > 2124125151251*x*y*z*w in I; Output: Magma V2.10-6 Mon Mar 22 2004 03:29:58 on modular [Seed = 102294141] ------------------------------------- [ x^2 + 1, y^2 + 1, 2 ] false Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 03:34:55 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (1+x^2)*(3+2*y) +2*x*y^2*(1+y) in I; Output: Magma V2.10-6 Mon Mar 22 2004 03:34:52 on modular [Seed = 4042134945] ------------------------------------- [ x^2 + 1, y^2 + 1, 2 ] true Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 03:35:07 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (3+2*y) +2*x*y^2*(1+y) in I; Output: Magma V2.10-6 Mon Mar 22 2004 03:35:04 on modular [Seed = 3891856034] ------------------------------------- [ x^2 + 1, y^2 + 1, 2 ] false Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee83.uab.es. (158.109.66.83) Time: Mon Mar 22 05:01:41 2004 Input: p:=5; eulerphi(p-1); Output: Magma V2.10-6 Mon Mar 22 2004 05:01:37 on modular [Seed = 1163640004] ------------------------------------- >> eulerphi(p-1); ^ User error: Identifier 'eulerphi' has not been declared or assigned Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee83.uab.es. (158.109.66.83) Time: Mon Mar 22 05:02:54 2004 Input: p:=5; EulerPhi(p-1); Output: Magma V2.10-6 Mon Mar 22 2004 05:02:51 on modular [Seed = 1347332507] ------------------------------------- 2 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee83.uab.es. (158.109.66.83) Time: Mon Mar 22 05:03:57 2004 Input: Z5:=PolynomialRing(GF(5)); // Univariate Polynomial Ring in x over GF(5) pol3:=Z5![3,2,1]; G25:= ext ; EulerPhi(G25); Output: Magma V2.10-6 Mon Mar 22 2004 05:03:54 on modular [Seed = 1497867091] ------------------------------------- >> G25:= ext ; ^ User error: Identifier 'G5' has not been declared or assigned >> EulerPhi(G25);; ^ User error: Identifier 'G25' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee83.uab.es. (158.109.66.83) Time: Mon Mar 22 05:04:14 2004 Input: G5:=GF(5); Z5:=PolynomialRing(GF(5)); // Univariate Polynomial Ring in x over GF(5) pol3:=Z5![3,2,1]; G25:= ext ; EulerPhi(G25); Output: Magma V2.10-6 Mon Mar 22 2004 05:04:11 on modular [Seed = 1652332665] ------------------------------------- >> EulerPhi(G25);; ^ Runtime error in 'EulerPhi': Bad argument types Argument types given: FldFin Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee83.uab.es. (158.109.66.83) Time: Mon Mar 22 05:04:36 2004 Input: G5:=GF(5); Z5:=PolynomialRing(GF(5)); // Univariate Polynomial Ring in x over GF(5) pol3:=Z5![3,2,1]; G25:= ext ; EulerPhi(#G25); Output: Magma V2.10-6 Mon Mar 22 2004 05:04:33 on modular [Seed = 1802867034] ------------------------------------- 20 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee83.uab.es. (158.109.66.83) Time: Mon Mar 22 05:05:38 2004 Input: p:=5; n:=2; EulerPhi(p^n-1); Output: Magma V2.10-6 Mon Mar 22 2004 05:05:35 on modular [Seed = 2019983895] ------------------------------------- 8 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host m201.math.metu.edu.tr. (144.122.136.201) Time: Mon Mar 22 06:13:58 2004 Input: a:=5; a+a; Output: Magma V2.10-6 Mon Mar 22 2004 06:13:53 on modular [Seed = 369663078] ------------------------------------- 10 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host m201.math.metu.edu.tr. (144.122.136.201) Time: Mon Mar 22 06:14:17 2004 Input: a:=5; a+a; a^2; Output: Magma V2.10-6 Mon Mar 22 2004 06:14:14 on modular [Seed = 557820838] ------------------------------------- 10 25 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee96.uab.es. (158.109.66.96) Time: Mon Mar 22 09:03:50 2004 Input: ElementToSequence (G16); Output: Magma V2.10-6 Mon Mar 22 2004 09:03:47 on modular [Seed = 3235803777] ------------------------------------- >> ElementToSequence (G16); ^ User error: Identifier 'G16' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee96.uab.es. (158.109.66.96) Time: Mon Mar 22 09:07:18 2004 Input: ElementToSequence (1); Output: Magma V2.10-6 Mon Mar 22 2004 09:07:15 on modular [Seed = 3503186881] ------------------------------------- [ 1 ] Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee96.uab.es. (158.109.66.96) Time: Mon Mar 22 09:07:33 2004 Input: ElementToSequence (1,2); Output: Magma V2.10-6 Mon Mar 22 2004 09:07:30 on modular [Seed = 3653724921] ------------------------------------- >> ElementToSequence (1,2); ^ Runtime error in 'ElementToSequence': Bad argument types Argument types given: RngIntElt, RngIntElt Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee96.uab.es. (158.109.66.96) Time: Mon Mar 22 09:10:47 2004 Input: ElementToSequence (23); Output: Magma V2.10-6 Mon Mar 22 2004 09:10:44 on modular [Seed = 3925301775] ------------------------------------- [ 23 ] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee96.uab.es. (158.109.66.96) Time: Mon Mar 22 09:19:22 2004 Input: GF2:= GF(2); [x : x in GF2]; GF4:= GF(4); [x : x in GF4]; GF8:= GF(8); [x : x in GF8]; GF16:= GF(16); [x : x in GF16]; Output: Magma V2.10-6 Mon Mar 22 2004 09:19:19 on modular [Seed = 52279015] ------------------------------------- [ 0, 1 ] [ 1, GF4.1, GF4.1^2, 0 ] [ 1, GF8.1, GF8.1^2, GF8.1^3, GF8.1^4, GF8.1^5, GF8.1^6, 0 ] [ 1, GF16.1, GF16.1^2, GF16.1^3, GF16.1^4, GF16.1^5, GF16.1^6, GF16.1^7, GF16.1^8, GF16.1^9, GF16.1^10, GF16.1^11, GF16.1^12, GF16.1^13, GF16.1^14, 0 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee96.uab.es. (158.109.66.96) Time: Mon Mar 22 09:23:33 2004 Input: GF2:= GF(2); [x : x in GF2]; GF4:= GF(4); [x : x in GF4]; GF8:= GF(8); [x : x in GF8]; GF16:= GF(16); [x : x in GF16]; GF25:= GF(25); P := PolynomialRing (G25); Output: Magma V2.10-6 Mon Mar 22 2004 09:23:30 on modular [Seed = 286238704] ------------------------------------- [ 0, 1 ] [ 1, GF4.1, GF4.1^2, 0 ] [ 1, GF8.1, GF8.1^2, GF8.1^3, GF8.1^4, GF8.1^5, GF8.1^6, 0 ] [ 1, GF16.1, GF16.1^2, GF16.1^3, GF16.1^4, GF16.1^5, GF16.1^6, GF16.1^7, GF16.1^8, GF16.1^9, GF16.1^10, GF16.1^11, GF16.1^12, GF16.1^13, GF16.1^14, 0 ] >> P := PolynomialRing (G25); ^ User error: Identifier 'G25' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee96.uab.es. (158.109.66.96) Time: Mon Mar 22 09:24:17 2004 Input: GF2:= GF(2); [x : x in GF2]; GF4:= GF(4); [x : x in GF4]; GF8:= GF(8); [x : x in GF8]; GF16:= GF(16); [x : x in GF16]; GF25:= GF(25); P := PolynomialRing (GF25); Output: Magma V2.10-6 Mon Mar 22 2004 09:24:14 on modular [Seed = 403091221] ------------------------------------- [ 0, 1 ] [ 1, GF4.1, GF4.1^2, 0 ] [ 1, GF8.1, GF8.1^2, GF8.1^3, GF8.1^4, GF8.1^5, GF8.1^6, 0 ] [ 1, GF16.1, GF16.1^2, GF16.1^3, GF16.1^4, GF16.1^5, GF16.1^6, GF16.1^7, GF16.1^8, GF16.1^9, GF16.1^10, GF16.1^11, GF16.1^12, GF16.1^13, GF16.1^14, 0 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee96.uab.es. (158.109.66.96) Time: Mon Mar 22 09:25:14 2004 Input: GF2:= GF(2); [x : x in GF2]; GF4:= GF(4); [x : x in GF4]; GF8:= GF(8); [x : x in GF8]; GF16:= GF(16); [x : x in GF16]; GF25:= GF(25); GF5:= GF(5); P := PolynomialRing (GF25); Q := PolynomialRing (GF5); Output: Magma V2.10-6 Mon Mar 22 2004 09:25:11 on modular [Seed = 708091246] ------------------------------------- [ 0, 1 ] [ 1, GF4.1, GF4.1^2, 0 ] [ 1, GF8.1, GF8.1^2, GF8.1^3, GF8.1^4, GF8.1^5, GF8.1^6, 0 ] [ 1, GF16.1, GF16.1^2, GF16.1^3, GF16.1^4, GF16.1^5, GF16.1^6, GF16.1^7, GF16.1^8, GF16.1^9, GF16.1^10, GF16.1^11, GF16.1^12, GF16.1^13, GF16.1^14, 0 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 11:46:56 2004 Input: [x: x in GF(2)]; [ 0, 1 ] [x: x in GF(3)]; [ 0, 1, 2 ] [x: x in GF(5)]; [ 0, 1, 2, 3, 4 ] z9 := Integers (9); [x : x in z9]; [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] IsInvertible(z9!0); false IsInvertible(z9!1); true 1 IsInvertible(z9!2); true 5 IsInvertible(z9!3); false IsInvertible(z9!4); true 7 z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); true z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); true z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); true P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); false G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] Ordre:= [Order(lista[i]) : i in [0..23]]; print Ordre; [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] lista:=[x: x in G25 | IsPrimitive (x)]; lista; [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] # lista; 8 /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); 8 lista; [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] MinimalPolynomial(G25.1); $.1^2 + 2*$.1 + 3 /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; $.1^2 + 2*$.1 + 3 Roots (polinomi,G25); [ , ] Roots (polinomi,GF(5)); [] F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; alpha^13 Output: Magma V2.10-6 Mon Mar 22 2004 11:46:53 on modular [Seed = 3252591032] ------------------------------------- [ 0, 1 ] >> [x: x in GF(3)]; ^ User error: bad syntax >> [x: x in GF(5)]; ^ User error: bad syntax >> z9 := Integers (9); ^ User error: bad syntax >> [x : x in z9]; ^ User error: Identifier 'z9' has not been declared or assigned >> IsInvertible(z9!0); ^ User error: bad syntax >> IsInvertible(z9!1); ^ User error: bad syntax >> true 1 ^ User error: bad syntax >> IsInvertible(z9!2); ^ User error: Identifier 'z9' has not been declared or assigned >> true 5 ^ User error: bad syntax >> IsInvertible(z9!3); ^ User error: Identifier 'z9' has not been declared or assigned >> IsInvertible(z9!4); ^ User error: bad syntax >> true 7 ^ User error: bad syntax true >> z2:= Integers(2); ^ User error: bad syntax >> P := PolynomialRing (z2); ^ User error: Identifier 'z2' has not been declared or assigned false >> z5:= Integers(5); ^ User error: bad syntax >> P := PolynomialRing (z5); ^ User error: Identifier 'z5' has not been declared or assigned false >> P := PolynomialRing (z3); ^ User error: bad syntax false >> G3 := GF(3); ^ User error: bad syntax >> G9:= ext < G3 |f>; ^ User error: Identifier 'G3' has not been declared or assigned >> [x : x in G9]; ^ User error: Identifier 'G9' has not been declared or assigned >> G2 := GF(2); ^ User error: bad syntax >> G16:= ext < G2 | g >; ^ Runtime error: No constructor provided for this type of object >> [x : x in G16]; ^ User error: Identifier 'G16' has not been declared or assigned >> G5 := GF(5); ^ User error: bad syntax >> G25:= ext < G5 |h>; ^ User error: Identifier 'G5' has not been declared or assigned >> [x : x in G25]; ^ User error: Identifier 'G25' has not been declared or assigned >> G9b:= ext < G3 |j>; ^ User error: bad syntax >> G9b:= ext < G3 |j>; ^ User error: Identifier 'G3' has not been declared or assigned >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax >> lista:=[x: x in G25]; ^ User error: Identifier 'G25' has not been declared or assigned >> print lista; ^ User error: Identifier 'lista' has not been declared or assigned >> Ordre:= [Order(lista[i]) : i in [0..23]]; ^ User error: bad syntax >> print Ordre; ^ User error: Identifier 'Ordre' has not been declared or assigned >> lista:=[x: x in G25 | IsPrimitive (x)]; ^ User error: bad syntax >> lista; ^ User error: Identifier 'lista' has not been declared or assigned >> # lista; ^ User error: bad syntax >> elements := func < p,n | EulerPhi (p^n -1)>; ^ User error: bad syntax >> elements (5,2); ^ User error: Identifier 'elements' has not been declared or assigned >> lista; ^ User error: bad syntax >> MinimalPolynomial(G25.1); ^ User error: bad syntax >> polinomi := MinimalPolynomial(G25.1); ^ User error: bad syntax >> polinomi; ^ User error: Identifier 'polinomi' has not been declared or assigned >> Roots (polinomi,G25); ^ User error: bad syntax >> Roots (polinomi,GF(5)); ^ User error: bad syntax >> F := G25; ^ User error: bad syntax >> pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; ^ User error: Identifier 'alpha' has not been declared or assigned >> pol; ^ User error: Identifier 'pol' has not been declared or assigned >> alpha^13 ^ User error: Identifier 'alpha' has not been declared or assigned Total time: 3.029 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 11:47:47 2004 Input: [x : x in GF(2)]; [ 0, 1 ] [x : x in GF(3)]; [ 0, 1, 2 ] [x : x in GF(5)]; [ 0, 1, 2, 3, 4 ] z9 := Integers (9); [x : x in z9]; [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] IsInvertible(z9!0); false IsInvertible(z9!1); true 1 IsInvertible(z9!2); true 5 IsInvertible(z9!3); false IsInvertible(z9!4); true 7 z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); true z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); true z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); true P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); false G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] Ordre:= [Order(lista[i]) : i in [0..23]]; print Ordre; [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] lista:=[x: x in G25 | IsPrimitive (x)]; lista; [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] # lista; 8 /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); 8 lista; [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] MinimalPolynomial(G25.1); $.1^2 + 2*$.1 + 3 /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; $.1^2 + 2*$.1 + 3 Roots (polinomi,G25); [ , ] Roots (polinomi,GF(5)); [] F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; alpha^13 Output: Magma V2.10-6 Mon Mar 22 2004 11:47:44 on modular [Seed = 3402994302] ------------------------------------- [ 0, 1 ] >> [x : x in GF(3)]; ^ User error: bad syntax >> [x : x in GF(5)]; ^ User error: bad syntax >> z9 := Integers (9); ^ User error: bad syntax >> [x : x in z9]; ^ User error: Identifier 'z9' has not been declared or assigned >> IsInvertible(z9!0); ^ User error: bad syntax >> IsInvertible(z9!1); ^ User error: bad syntax >> true 1 ^ User error: bad syntax >> IsInvertible(z9!2); ^ User error: Identifier 'z9' has not been declared or assigned >> true 5 ^ User error: bad syntax >> IsInvertible(z9!3); ^ User error: Identifier 'z9' has not been declared or assigned >> IsInvertible(z9!4); ^ User error: bad syntax >> true 7 ^ User error: bad syntax true >> z2:= Integers(2); ^ User error: bad syntax >> P := PolynomialRing (z2); ^ User error: Identifier 'z2' has not been declared or assigned false >> z5:= Integers(5); ^ User error: bad syntax >> P := PolynomialRing (z5); ^ User error: Identifier 'z5' has not been declared or assigned false >> P := PolynomialRing (z3); ^ User error: bad syntax false >> G3 := GF(3); ^ User error: bad syntax >> G9:= ext < G3 |f>; ^ User error: Identifier 'G3' has not been declared or assigned >> [x : x in G9]; ^ User error: Identifier 'G9' has not been declared or assigned >> G2 := GF(2); ^ User error: bad syntax >> G16:= ext < G2 | g >; ^ Runtime error: No constructor provided for this type of object >> [x : x in G16]; ^ User error: Identifier 'G16' has not been declared or assigned >> G5 := GF(5); ^ User error: bad syntax >> G25:= ext < G5 |h>; ^ User error: Identifier 'G5' has not been declared or assigned >> [x : x in G25]; ^ User error: Identifier 'G25' has not been declared or assigned >> G9b:= ext < G3 |j>; ^ User error: bad syntax >> G9b:= ext < G3 |j>; ^ User error: Identifier 'G3' has not been declared or assigned >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax >> lista:=[x: x in G25]; ^ User error: Identifier 'G25' has not been declared or assigned >> print lista; ^ User error: Identifier 'lista' has not been declared or assigned >> Ordre:= [Order(lista[i]) : i in [0..23]]; ^ User error: bad syntax >> print Ordre; ^ User error: Identifier 'Ordre' has not been declared or assigned >> lista:=[x: x in G25 | IsPrimitive (x)]; ^ User error: bad syntax >> lista; ^ User error: Identifier 'lista' has not been declared or assigned >> # lista; ^ User error: bad syntax >> elements := func < p,n | EulerPhi (p^n -1)>; ^ User error: bad syntax >> elements (5,2); ^ User error: Identifier 'elements' has not been declared or assigned >> lista; ^ User error: bad syntax >> MinimalPolynomial(G25.1); ^ User error: bad syntax >> polinomi := MinimalPolynomial(G25.1); ^ User error: bad syntax >> polinomi; ^ User error: Identifier 'polinomi' has not been declared or assigned >> Roots (polinomi,G25); ^ User error: bad syntax >> Roots (polinomi,GF(5)); ^ User error: bad syntax >> F := G25; ^ User error: bad syntax >> pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; ^ User error: Identifier 'alpha' has not been declared or assigned >> pol; ^ User error: Identifier 'pol' has not been declared or assigned >> alpha^13 ^ User error: Identifier 'alpha' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 11:48:18 2004 Input: [x : x in GF(2)]; Output: Magma V2.10-6 Mon Mar 22 2004 11:48:15 on modular [Seed = 3553397528] ------------------------------------- [ 0, 1 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 11:48:46 2004 Input: [x : x in GF(2)]; [ 0, 1 ] [x : x in GF(3)]; [ 0, 1, 2 ] [x : x in GF(5)]; [ 0, 1, 2, 3, 4 ] z9 := Integers (9); [x : x in z9]; [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] IsInvertible(z9!0); false IsInvertible(z9!1); true 1 IsInvertible(z9!2); true 5 IsInvertible(z9!3); false IsInvertible(z9!4); true 7 z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); true z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); true z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); true P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); false G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] Ordre:= [Order(lista[i]) : i in [0..23]]; print Ordre; [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] lista:=[x: x in G25 | IsPrimitive (x)]; lista; [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] # lista; 8 /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); 8 lista; [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] MinimalPolynomial(G25.1); $.1^2 + 2*$.1 + 3 /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; $.1^2 + 2*$.1 + 3 Roots (polinomi,G25); [ , ] Roots (polinomi,GF(5)); [] F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; alpha^13 Output: Magma V2.10-6 Mon Mar 22 2004 11:48:43 on modular [Seed = 3774855183] ------------------------------------- [ 0, 1 ] >> [x : x in GF(3)]; ^ User error: bad syntax >> [x : x in GF(5)]; ^ User error: bad syntax >> z9 := Integers (9); ^ User error: bad syntax >> [x : x in z9]; ^ User error: Identifier 'z9' has not been declared or assigned >> IsInvertible(z9!0); ^ User error: bad syntax >> IsInvertible(z9!1); ^ User error: bad syntax >> true 1 ^ User error: bad syntax >> IsInvertible(z9!2); ^ User error: Identifier 'z9' has not been declared or assigned >> true 5 ^ User error: bad syntax >> IsInvertible(z9!3); ^ User error: Identifier 'z9' has not been declared or assigned >> IsInvertible(z9!4); ^ User error: bad syntax >> true 7 ^ User error: bad syntax true >> z2:= Integers(2); ^ User error: bad syntax >> P := PolynomialRing (z2); ^ User error: Identifier 'z2' has not been declared or assigned false >> z5:= Integers(5); ^ User error: bad syntax >> P := PolynomialRing (z5); ^ User error: Identifier 'z5' has not been declared or assigned false >> P := PolynomialRing (z3); ^ User error: bad syntax false >> G3 := GF(3); ^ User error: bad syntax >> G9:= ext < G3 |f>; ^ User error: Identifier 'G3' has not been declared or assigned >> [x : x in G9]; ^ User error: Identifier 'G9' has not been declared or assigned >> G2 := GF(2); ^ User error: bad syntax >> G16:= ext < G2 | g >; ^ Runtime error: No constructor provided for this type of object >> [x : x in G16]; ^ User error: Identifier 'G16' has not been declared or assigned >> G5 := GF(5); ^ User error: bad syntax >> G25:= ext < G5 |h>; ^ User error: Identifier 'G5' has not been declared or assigned >> [x : x in G25]; ^ User error: Identifier 'G25' has not been declared or assigned >> G9b:= ext < G3 |j>; ^ User error: bad syntax >> G9b:= ext < G3 |j>; ^ User error: Identifier 'G3' has not been declared or assigned >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax >> lista:=[x: x in G25]; ^ User error: Identifier 'G25' has not been declared or assigned >> print lista; ^ User error: Identifier 'lista' has not been declared or assigned >> Ordre:= [Order(lista[i]) : i in [0..23]]; ^ User error: bad syntax >> print Ordre; ^ User error: Identifier 'Ordre' has not been declared or assigned >> lista:=[x: x in G25 | IsPrimitive (x)]; ^ User error: bad syntax >> lista; ^ User error: Identifier 'lista' has not been declared or assigned >> # lista; ^ User error: bad syntax >> elements := func < p,n | EulerPhi (p^n -1)>; ^ User error: bad syntax >> elements (5,2); ^ User error: Identifier 'elements' has not been declared or assigned >> lista; ^ User error: bad syntax >> MinimalPolynomial(G25.1); ^ User error: bad syntax >> polinomi := MinimalPolynomial(G25.1); ^ User error: bad syntax >> polinomi; ^ User error: Identifier 'polinomi' has not been declared or assigned >> Roots (polinomi,G25); ^ User error: bad syntax >> Roots (polinomi,GF(5)); ^ User error: bad syntax >> F := G25; ^ User error: bad syntax >> pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; ^ User error: Identifier 'alpha' has not been declared or assigned >> pol; ^ User error: Identifier 'pol' has not been declared or assigned >> alpha^13 ^ User error: Identifier 'alpha' has not been declared or assigned Total time: 3.139 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 11:49:17 2004 Input: [x : x in GF(2)]; [ 0, 1 ] [y : y in GF(3)]; [ 0, 1, 2 ] [z : z in GF(5)]; [ 0, 1, 2, 3, 4 ] z9 := Integers (9); [x : x in z9]; [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] IsInvertible(z9!0); false IsInvertible(z9!1); true 1 IsInvertible(z9!2); true 5 IsInvertible(z9!3); false IsInvertible(z9!4); true 7 z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); true z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); true z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); true P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); false G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] Ordre:= [Order(lista[i]) : i in [0..23]]; print Ordre; [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] lista:=[x: x in G25 | IsPrimitive (x)]; lista; [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] # lista; 8 /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); 8 lista; [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] MinimalPolynomial(G25.1); $.1^2 + 2*$.1 + 3 /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; $.1^2 + 2*$.1 + 3 Roots (polinomi,G25); [ , ] Roots (polinomi,GF(5)); [] F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; alpha^13 Output: Magma V2.10-6 Mon Mar 22 2004 11:49:14 on modular [Seed = 3925258471] ------------------------------------- [ 0, 1 ] >> [y : y in GF(3)]; ^ User error: bad syntax >> [z : z in GF(5)]; ^ User error: bad syntax >> z9 := Integers (9); ^ User error: bad syntax >> [x : x in z9]; ^ User error: Identifier 'z9' has not been declared or assigned >> IsInvertible(z9!0); ^ User error: bad syntax >> IsInvertible(z9!1); ^ User error: bad syntax >> true 1 ^ User error: bad syntax >> IsInvertible(z9!2); ^ User error: Identifier 'z9' has not been declared or assigned >> true 5 ^ User error: bad syntax >> IsInvertible(z9!3); ^ User error: Identifier 'z9' has not been declared or assigned >> IsInvertible(z9!4); ^ User error: bad syntax >> true 7 ^ User error: bad syntax true >> z2:= Integers(2); ^ User error: bad syntax >> P := PolynomialRing (z2); ^ User error: Identifier 'z2' has not been declared or assigned false >> z5:= Integers(5); ^ User error: bad syntax >> P := PolynomialRing (z5); ^ User error: Identifier 'z5' has not been declared or assigned false >> P := PolynomialRing (z3); ^ User error: bad syntax false >> G3 := GF(3); ^ User error: bad syntax >> G9:= ext < G3 |f>; ^ User error: Identifier 'G3' has not been declared or assigned >> [x : x in G9]; ^ User error: Identifier 'G9' has not been declared or assigned >> G2 := GF(2); ^ User error: bad syntax >> G16:= ext < G2 | g >; ^ Runtime error: No constructor provided for this type of object >> [x : x in G16]; ^ User error: Identifier 'G16' has not been declared or assigned >> G5 := GF(5); ^ User error: bad syntax >> G25:= ext < G5 |h>; ^ User error: Identifier 'G5' has not been declared or assigned >> [x : x in G25]; ^ User error: Identifier 'G25' has not been declared or assigned >> G9b:= ext < G3 |j>; ^ User error: bad syntax >> G9b:= ext < G3 |j>; ^ User error: Identifier 'G3' has not been declared or assigned >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax >> lista:=[x: x in G25]; ^ User error: Identifier 'G25' has not been declared or assigned >> print lista; ^ User error: Identifier 'lista' has not been declared or assigned >> Ordre:= [Order(lista[i]) : i in [0..23]]; ^ User error: bad syntax >> print Ordre; ^ User error: Identifier 'Ordre' has not been declared or assigned >> lista:=[x: x in G25 | IsPrimitive (x)]; ^ User error: bad syntax >> lista; ^ User error: Identifier 'lista' has not been declared or assigned >> # lista; ^ User error: bad syntax >> elements := func < p,n | EulerPhi (p^n -1)>; ^ User error: bad syntax >> elements (5,2); ^ User error: Identifier 'elements' has not been declared or assigned >> lista; ^ User error: bad syntax >> MinimalPolynomial(G25.1); ^ User error: bad syntax >> polinomi := MinimalPolynomial(G25.1); ^ User error: bad syntax >> polinomi; ^ User error: Identifier 'polinomi' has not been declared or assigned >> Roots (polinomi,G25); ^ User error: bad syntax >> Roots (polinomi,GF(5)); ^ User error: bad syntax >> F := G25; ^ User error: bad syntax >> pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; ^ User error: Identifier 'alpha' has not been declared or assigned >> pol; ^ User error: Identifier 'pol' has not been declared or assigned >> alpha^13 ^ User error: Identifier 'alpha' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 11:49:50 2004 Input: [x : x in GF(2)]; [ 0, 1 ] [ x : x in GF(3)]; [ 0, 1, 2 ] Output: Magma V2.10-6 Mon Mar 22 2004 11:49:47 on modular [Seed = 4075662301] ------------------------------------- [ 0, 1 ] >> [ x : x in GF(3)]; ^ User error: bad syntax [ 0, 1, 2 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 11:50:02 2004 Input: [x : x in GF(2)]; [ x : x in GF(3)]; Output: Magma V2.10-6 Mon Mar 22 2004 11:49:59 on modular [Seed = 4226065096] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] Total time: 3.179 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 11:52:49 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [0..23]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista:=[x: x in G25 | IsPrimitive (x)]; lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ Output: Magma V2.10-6 Mon Mar 22 2004 11:52:46 on modular [Seed = 336285135] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> Ordre:= [Order(lista[i]) : i in [0..23]]; ^ Runtime error in '[]': Sequence element 0 not defined >> print Ordre; ^ User error: Identifier 'Ordre' has not been declared or assigned [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 8 8 [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 Total time: 3.039 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 11:53:43 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista:=[x: x in G25 | IsPrimitive (x)]; lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ Output: Magma V2.10-6 Mon Mar 22 2004 11:53:39 on modular [Seed = 520111369] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 8 8 [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 Total time: 3.049 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 11:55:47 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista:=[x: x in G25 | IsPrimitive (x)]; lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ inverse (pol); Output: Magma V2.10-6 Mon Mar 22 2004 11:55:44 on modular [Seed = 758282168] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 8 8 [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 >> inverse (pol); ^ User error: Identifier 'inverse' has not been declared or assigned Total time: 3.029 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 11:56:10 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista:=[x: x in G25 | IsPrimitive (x)]; lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ Inverse (pol); Output: Magma V2.10-6 Mon Mar 22 2004 11:56:07 on modular [Seed = 875261590] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 8 8 [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 >> Inverse (pol); ^ Runtime error in 'Inverse': Bad argument types Argument types given: FldFinElt Total time: 3.039 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 12:00:50 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista:=[x: x in G25 | IsPrimitive (x)]; lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; Output: Magma V2.10-6 Mon Mar 22 2004 12:00:47 on modular [Seed = 1079974906] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 8 8 [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] Total time: 3.019 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 12:01:34 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista:=[x: x in G25 | IsPrimitive (x)]; lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ Inverse (alpha^13); lista2:=[x: x in G25 | IsInvertible (x)]; lista2; Output: Magma V2.10-6 Mon Mar 22 2004 12:01:31 on modular [Seed = 1702510219] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 8 8 [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 >> Inverse (alpha^13); ^ Runtime error in 'Inverse': Bad argument types Argument types given: FldFinElt [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] Total time: 3.029 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 12:02:06 2004 Input: Inverse (9); Output: Magma V2.10-6 Mon Mar 22 2004 12:02:03 on modular [Seed = 1869624161] ------------------------------------- >> Inverse (9);; ^ Runtime error in 'Inverse': Bad argument types Argument types given: RngIntElt Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 12:02:50 2004 Input: Inverse (3); Output: Magma V2.10-6 Mon Mar 22 2004 12:02:47 on modular [Seed = 1986603588] ------------------------------------- >> Inverse (3);; ^ Runtime error in 'Inverse': Bad argument types Argument types given: RngIntElt Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 12:03:07 2004 Input: InverseOp (3); Output: Magma V2.10-6 Mon Mar 22 2004 12:03:04 on modular [Seed = 2224806089] ------------------------------------- >> InverseOp (3);; ^ User error: Identifier 'InverseOp' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 12:03:48 2004 Input: InverseOp(3) O; Output: Magma V2.10-6 Mon Mar 22 2004 12:03:45 on modular [Seed = 2408633339] ------------------------------------- >> InverseOp(3) O;; ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 12:04:04 2004 Input: InverseOp(3); Output: Magma V2.10-6 Mon Mar 22 2004 12:04:01 on modular [Seed = 2525612562] ------------------------------------- >> InverseOp(3);; ^ User error: Identifier 'InverseOp' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 12:04:18 2004 Input: Inverse(3); Output: Magma V2.10-6 Mon Mar 22 2004 12:04:15 on modular [Seed = 2575746323] ------------------------------------- >> Inverse(3);; ^ Runtime error in 'Inverse': Bad argument types Argument types given: RngIntElt Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 12:05:11 2004 Input: [x : x in GF(2)]; [x : x in GF(4)]; [x : x in GF(8)]; [x : x in GF(16)]; Output: Magma V2.10-6 Mon Mar 22 2004 12:05:08 on modular [Seed = 2897473645] ------------------------------------- [ 0, 1 ] [ 1, $.1, $.1^2, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, $.1^7, $.1^8, $.1^9, $.1^10, $.1^11, $.1^12, $.1^13, $.1^14, 0 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 12:08:45 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista:=[x: x in G25 | IsPrimitive (x)]; lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ InverseDefiningPolynomials (alpha^13); lista2:=[x: x in G25 | IsInvertible (x)]; lista2; Output: Magma V2.10-6 Mon Mar 22 2004 12:08:42 on modular [Seed = 2981030958] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 8 8 [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 >> InverseDefiningPolynomials (alpha^13); ^ Runtime error in 'InverseDefiningPolynomials': Bad argument types Argument types given: FldFinElt [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] Total time: 3.029 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 12:13:52 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); G5 := GF(5); G25:= ext < G5 |h>; Output: Magma V2.10-6 Mon Mar 22 2004 12:13:49 on modular [Seed = 3286015243] ------------------------------------- true Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 12:14:23 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); G5 := GF(5); G25:= ext < G5 |h>; P:= PolynomialRing (G25); IsFinite (P); Output: Magma V2.10-6 Mon Mar 22 2004 12:14:20 on modular [Seed = 3402994723] ------------------------------------- true false Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 12:17:10 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; [x : x in GF(2)]; [x : x in GF(4)]; [x : x in GF(8)]; [x : x in GF(16)]; /*els elements de GF(2) pertanyen a GF(4). Els elements d'aquest a GF(8) i aquests a GF(16)*/ P:= PolynomialRing (G25); IsFinite (P); /*false*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; Output: Magma V2.10-6 Mon Mar 22 2004 12:17:07 on modular [Seed = 3858414195] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 25 8 [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] [ 0, 1 ] [ 1, $.1, $.1^2, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, $.1^7, $.1^8, $.1^9, $.1^10, $.1^11, $.1^12, $.1^13, $.1^14, 0 ] false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] Total time: 2.999 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 12:21:23 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; [x : x in GF(2)]; [x : x in GF(4)]; [x : x in GF(8)]; [x : x in GF(16)]; /*els elements de GF(2) pertanyen a GF(4). Els elements d'aquest a GF(8) i aquests a GF(16)*/ P:= PolynomialRing (G25); IsFinite (P); /*false*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; p1 := alpha^2 + alpha*x + 2*x^2; Output: Magma V2.10-6 Mon Mar 22 2004 12:21:19 on modular [Seed = 4109079678] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 25 8 [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] [ 0, 1 ] [ 1, $.1, $.1^2, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, $.1^7, $.1^8, $.1^9, $.1^10, $.1^11, $.1^12, $.1^13, $.1^14, 0 ] false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] >> p1 := alpha^2 + alpha*x + 2*x^2; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt Total time: 3.039 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 12:22:24 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); G5 := GF(5); G25:= ext < G5 |h>; P:= PolynomialRing (G25); IsFinite (P); Output: Magma V2.10-6 Mon Mar 22 2004 12:22:21 on modular [Seed = 4276198966] ------------------------------------- true false Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 12:22:49 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; [x : x in GF(2)]; [x : x in GF(4)]; [x : x in GF(8)]; [x : x in GF(16)]; /*els elements de GF(2) pertanyen a GF(4). Els elements d'aquest a GF(8) i aquests a GF(16)*/ P:= PolynomialRing (G25); IsFinite (P); /*false*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; p1 := alpha^2 + alpha*x + 2*x^2; Output: Magma V2.10-6 Mon Mar 22 2004 12:22:46 on modular [Seed = 52192227] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 25 8 [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] [ 0, 1 ] [ 1, $.1, $.1^2, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, $.1^7, $.1^8, $.1^9, $.1^10, $.1^11, $.1^12, $.1^13, $.1^14, 0 ] false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] Total time: 2.989 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 12:26:14 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); G5 := GF(5); G25:= ext < G5 |h>; P:= PolynomialRing (G25); IsFinite (P); sum (9,4); Output: Magma V2.10-6 Mon Mar 22 2004 12:26:11 on modular [Seed = 353006752] ------------------------------------- true false >> sum (9,4);; ^ User error: Identifier 'sum' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 12:29:11 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); G5 := GF(5); G25:= ext < G5 |h>; P:= PolynomialRing (G25); IsFinite (P); sum [9,4]; Output: Magma V2.10-6 Mon Mar 22 2004 12:29:08 on modular [Seed = 403143290] ------------------------------------- true false >> sum [9,4];; ^ User error: Identifier 'sum' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 12:30:54 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); G5 := GF(5); G25:= ext < G5 |h>; P:= PolynomialRing (G25); IsFinite (P); 9+4; Output: Magma V2.10-6 Mon Mar 22 2004 12:30:51 on modular [Seed = 674712293] ------------------------------------- true false 13 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 12:31:12 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; [x : x in GF(2)]; [x : x in GF(4)]; [x : x in GF(8)]; [x : x in GF(16)]; /*els elements de GF(2) pertanyen a GF(4). Els elements d'aquest a GF(8) i aquests a GF(16)*/ P:= PolynomialRing (G25); IsFinite (P); /*false*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; p1 := alpha^2 + alpha*x + 2*x^2; p2 := 1 + alpha*x; p1 + p2; Output: Magma V2.10-6 Mon Mar 22 2004 12:31:09 on modular [Seed = 825119722] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 25 8 [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] [ 0, 1 ] [ 1, $.1, $.1^2, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, $.1^7, $.1^8, $.1^9, $.1^10, $.1^11, $.1^12, $.1^13, $.1^14, 0 ] false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] 2*x^2 + alpha^19*x + alpha^9 Total time: 3.049 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 12:31:42 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; [x : x in GF(2)]; [x : x in GF(4)]; [x : x in GF(8)]; [x : x in GF(16)]; /*els elements de GF(2) pertanyen a GF(4). Els elements d'aquest a GF(8) i aquests a GF(16)*/ P:= PolynomialRing (G25); IsFinite (P); /*false*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; p1 := alpha^2 + alpha*x + 2*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; Output: Magma V2.10-6 Mon Mar 22 2004 12:31:39 on modular [Seed = 1196959162] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 25 8 [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] [ 0, 1 ] [ 1, $.1, $.1^2, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, $.1^7, $.1^8, $.1^9, $.1^10, $.1^11, $.1^12, $.1^13, $.1^14, 0 ] false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] 2*x^2 + alpha^19*x + alpha^9 Total time: 2.989 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 12:32:40 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; [x : x in GF(2)]; [x : x in GF(4)]; [x : x in GF(8)]; [x : x in GF(16)]; /*els elements de GF(2) pertanyen a GF(4). Els elements d'aquest a GF(8) i aquests a GF(16)*/ P:= PolynomialRing (G25); IsFinite (P); /*false*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; p1 := alpha^2 + alpha*x + 2*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; producte := p1 * p2; producte; Output: Magma V2.10-6 Mon Mar 22 2004 12:32:37 on modular [Seed = 1297231486] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 25 8 [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] [ 0, 1 ] [ 1, $.1, $.1^2, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, $.1^7, $.1^8, $.1^9, $.1^10, $.1^11, $.1^12, $.1^13, $.1^14, 0 ] false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] 2*x^2 + alpha^19*x + alpha^9 alpha^19*x^3 + alpha^22*x^2 + alpha^10*x + alpha^2 Total time: 3.049 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 12:34:36 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; [x : x in GF(2)]; [x : x in GF(4)]; [x : x in GF(8)]; [x : x in GF(16)]; /*els elements de GF(2) pertanyen a GF(4). Els elements d'aquest a GF(8) i aquests a GF(16)*/ P:= PolynomialRing (G25); IsFinite (P); /*false*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; p1 := alpha^2 + alpha*x + 2*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; producte := p1 * p2; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; Output: Magma V2.10-6 Mon Mar 22 2004 12:34:33 on modular [Seed = 1397502204] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 25 8 [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] [ 0, 1 ] [ 1, $.1, $.1^2, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, $.1^7, $.1^8, $.1^9, $.1^10, $.1^11, $.1^12, $.1^13, $.1^14, 0 ] false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] 2*x^2 + alpha^19*x + alpha^9 alpha^19*x^3 + alpha^22*x^2 + alpha^10*x + alpha^2 alpha^17*x + alpha^5 alpha^15 Total time: 3.049 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 12:38:05 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; [x : x in GF(2)]; [x : x in GF(4)]; [x : x in GF(8)]; [x : x in GF(16)]; /*els elements de GF(2) pertanyen a GF(4). Els elements d'aquest a GF(8) i aquests a GF(16)*/ P:= PolynomialRing (G25); IsFinite (P); /*false*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; p1 := alpha^2 + alpha*x + 2*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; producte := p1 * p2; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; mcd := GCD (p1,p2); mcd; mcm := LCM (p1,p2); mcm; Output: Magma V2.10-6 Mon Mar 22 2004 12:38:02 on modular [Seed = 1652360734] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 25 8 [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] [ 0, 1 ] [ 1, $.1, $.1^2, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, $.1^7, $.1^8, $.1^9, $.1^10, $.1^11, $.1^12, $.1^13, $.1^14, 0 ] false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] 2*x^2 + alpha^19*x + alpha^9 alpha^19*x^3 + alpha^22*x^2 + alpha^10*x + alpha^2 alpha^17*x + alpha^5 alpha^15 1 x^3 + alpha^3*x^2 + alpha^15*x + alpha^7 Total time: 2.989 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 12:45:42 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; [x : x in GF(2)]; [x : x in GF(4)]; [x : x in GF(8)]; [x : x in GF(16)]; /*els elements de GF(2) pertanyen a GF(4). Els elements d'aquest a GF(8) i aquests a GF(16)*/ P:= PolynomialRing (G25); IsFinite (P); /*false*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; p1 := alpha^2 + alpha*x + 2*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; producte := p1 * p2; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; mcd := GCD (p1,p2); mcd; mcm := LCM (p1,p2); mcm; Factorization ((1/alpha^4) - alpha^-3 * x + alpha^5 * x^2); Output: Magma V2.10-6 Mon Mar 22 2004 12:45:38 on modular [Seed = 2103581497] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 25 8 [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] [ 0, 1 ] [ 1, $.1, $.1^2, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, $.1^7, $.1^8, $.1^9, $.1^10, $.1^11, $.1^12, $.1^13, $.1^14, 0 ] false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] 2*x^2 + alpha^19*x + alpha^9 alpha^19*x^3 + alpha^22*x^2 + alpha^10*x + alpha^2 alpha^17*x + alpha^5 alpha^15 1 x^3 + alpha^3*x^2 + alpha^15*x + alpha^7 [ ] Total time: 3.049 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 12:47:20 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; [x : x in GF(2)]; [x : x in GF(4)]; [x : x in GF(8)]; [x : x in GF(16)]; /*els elements de GF(2) pertanyen a GF(4). Els elements d'aquest a GF(8) i aquests a GF(16)*/ P:= PolynomialRing (G25); IsFinite (P); /*false*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; p1 := alpha^2 + alpha*x + 2*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; producte := p1 * p2; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; mcd := GCD (p1,p2); mcd; mcm := LCM (p1,p2); mcm; Factorization ((1/alpha^4) - alpha^-3 * x + alpha^5 * x^2,G25); Output: Magma V2.10-6 Mon Mar 22 2004 12:47:17 on modular [Seed = 2208097568] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 25 8 [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] [ 0, 1 ] [ 1, $.1, $.1^2, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, $.1^7, $.1^8, $.1^9, $.1^10, $.1^11, $.1^12, $.1^13, $.1^14, 0 ] false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] 2*x^2 + alpha^19*x + alpha^9 alpha^19*x^3 + alpha^22*x^2 + alpha^10*x + alpha^2 alpha^17*x + alpha^5 alpha^15 1 x^3 + alpha^3*x^2 + alpha^15*x + alpha^7 >> Factorization ((1/alpha^4) - alpha^-3 * x + alpha^5 * x^2,G25);; ^ Runtime error in 'Factorization': Bad argument types Argument types given: RngUPolElt, FldFin Total time: 3.169 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 12:48:41 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; [x : x in GF(2)]; [x : x in GF(4)]; [x : x in GF(8)]; [x : x in GF(16)]; /*els elements de GF(2) pertanyen a GF(4). Els elements d'aquest a GF(8) i aquests a GF(16)*/ P:= PolynomialRing (G25); IsFinite (P); /*false*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; p1 := alpha^2 + alpha*x + 2*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; producte := p1 * p2; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; mcd := GCD (p1,p2); mcd; mcm := LCM (p1,p2); mcm; a := (1/alpha^4) - alpha^-3 * x + alpha^5 * x^2 b := Factorization (a); Roots (b); Output: Magma V2.10-6 Mon Mar 22 2004 12:48:38 on modular [Seed = 2308370297] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 25 8 [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] [ 0, 1 ] [ 1, $.1, $.1^2, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, $.1^7, $.1^8, $.1^9, $.1^10, $.1^11, $.1^12, $.1^13, $.1^14, 0 ] false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] 2*x^2 + alpha^19*x + alpha^9 alpha^19*x^3 + alpha^22*x^2 + alpha^10*x + alpha^2 alpha^17*x + alpha^5 alpha^15 1 x^3 + alpha^3*x^2 + alpha^15*x + alpha^7 >> b := Factorization (a); ^ User error: bad syntax >> Roots (b);; ^ User error: Identifier 'b' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 12:49:42 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; [x : x in GF(2)]; [x : x in GF(4)]; [x : x in GF(8)]; [x : x in GF(16)]; /*els elements de GF(2) pertanyen a GF(4). Els elements d'aquest a GF(8) i aquests a GF(16)*/ P:= PolynomialRing (G25); IsFinite (P); /*false*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; p1 := alpha^2 + alpha*x + 2*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; producte := p1 * p2; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; mcd := GCD (p1,p2); mcd; mcm := LCM (p1,p2); mcm; a := (1/alpha^4) - alpha^-3 * x + alpha^5 * x^2 fact := Factorization (a); Roots (fact); Output: Magma V2.10-6 Mon Mar 22 2004 12:49:39 on modular [Seed = 2659318187] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 25 8 [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] [ 0, 1 ] [ 1, $.1, $.1^2, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, $.1^7, $.1^8, $.1^9, $.1^10, $.1^11, $.1^12, $.1^13, $.1^14, 0 ] false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] 2*x^2 + alpha^19*x + alpha^9 alpha^19*x^3 + alpha^22*x^2 + alpha^10*x + alpha^2 alpha^17*x + alpha^5 alpha^15 1 x^3 + alpha^3*x^2 + alpha^15*x + alpha^7 >> fact := Factorization (a); ^ User error: bad syntax >> Roots (fact);; ^ User error: Identifier 'fact' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 12:50:13 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; [x : x in GF(2)]; [x : x in GF(4)]; [x : x in GF(8)]; [x : x in GF(16)]; /*els elements de GF(2) pertanyen a GF(4). Els elements d'aquest a GF(8) i aquests a GF(16)*/ P:= PolynomialRing (G25); IsFinite (P); /*false*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; p1 := alpha^2 + alpha*x + 2*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; producte := p1 * p2; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; mcd := GCD (p1,p2); mcd; mcm := LCM (p1,p2); mcm; a := (1/alpha^4) - alpha^-3 * x + alpha^5 * x^2 Factorization (a); /*Roots (fact);*/ Output: Magma V2.10-6 Mon Mar 22 2004 12:50:10 on modular [Seed = 2947598587] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 25 8 [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] [ 0, 1 ] [ 1, $.1, $.1^2, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, $.1^7, $.1^8, $.1^9, $.1^10, $.1^11, $.1^12, $.1^13, $.1^14, 0 ] false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] 2*x^2 + alpha^19*x + alpha^9 alpha^19*x^3 + alpha^22*x^2 + alpha^10*x + alpha^2 alpha^17*x + alpha^5 alpha^15 1 x^3 + alpha^3*x^2 + alpha^15*x + alpha^7 >> Factorization (a); ^ User error: bad syntax Total time: 3.079 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 12:50:49 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; [x : x in GF(2)]; [x : x in GF(4)]; [x : x in GF(8)]; [x : x in GF(16)]; /*els elements de GF(2) pertanyen a GF(4). Els elements d'aquest a GF(8) i aquests a GF(16)*/ P:= PolynomialRing (G25); IsFinite (P); /*false*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; p1 := alpha^2 + alpha*x + 2*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; producte := p1 * p2; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; mcd := GCD (p1,p2); mcd; mcm := LCM (p1,p2); mcm; a := (1/alpha^4) - alpha^-3 * x + alpha^5 * x^2; b := Factorization (a); Roots (b); Output: Magma V2.10-6 Mon Mar 22 2004 12:50:45 on modular [Seed = 3031159751] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 25 8 [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] [ 0, 1 ] [ 1, $.1, $.1^2, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, $.1^7, $.1^8, $.1^9, $.1^10, $.1^11, $.1^12, $.1^13, $.1^14, 0 ] false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] 2*x^2 + alpha^19*x + alpha^9 alpha^19*x^3 + alpha^22*x^2 + alpha^10*x + alpha^2 alpha^17*x + alpha^5 alpha^15 1 x^3 + alpha^3*x^2 + alpha^15*x + alpha^7 >> Roots (b);; ^ Runtime error in 'Roots': Bad argument types Argument types given: SeqEnum[Tup] Total time: 3.059 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 12:51:22 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; [x : x in GF(2)]; [x : x in GF(4)]; [x : x in GF(8)]; [x : x in GF(16)]; /*els elements de GF(2) pertanyen a GF(4). Els elements d'aquest a GF(8) i aquests a GF(16)*/ P:= PolynomialRing (G25); IsFinite (P); /*false*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; p1 := alpha^2 + alpha*x + 2*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; producte := p1 * p2; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; mcd := GCD (p1,p2); mcd; mcm := LCM (p1,p2); mcm; a := (1/alpha^4) - alpha^-3 * x + alpha^5 * x^2; b := Factorization (a); Roots (b,G25); Output: Magma V2.10-6 Mon Mar 22 2004 12:51:19 on modular [Seed = 3181566508] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 25 8 [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] [ 0, 1 ] [ 1, $.1, $.1^2, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, $.1^7, $.1^8, $.1^9, $.1^10, $.1^11, $.1^12, $.1^13, $.1^14, 0 ] false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] 2*x^2 + alpha^19*x + alpha^9 alpha^19*x^3 + alpha^22*x^2 + alpha^10*x + alpha^2 alpha^17*x + alpha^5 alpha^15 1 x^3 + alpha^3*x^2 + alpha^15*x + alpha^7 >> Roots (b,G25);; ^ Runtime error in 'Roots': Bad argument types Argument types given: SeqEnum[Tup], FldFin Total time: 3.069 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 12:52:17 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; [x : x in GF(2)]; [x : x in GF(4)]; [x : x in GF(8)]; [x : x in GF(16)]; /*els elements de GF(2) pertanyen a GF(4). Els elements d'aquest a GF(8) i aquests a GF(16)*/ P:= PolynomialRing (G25); IsFinite (P); /*false*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; p1 := alpha^2 + alpha*x + 2*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; producte := p1 * p2; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; mcd := GCD (p1,p2); mcd; mcm := LCM (p1,p2); mcm; a := (1/alpha^4) - alpha^-3 * x + alpha^5 * x^2; b := Factorization (a); b; Output: Magma V2.10-6 Mon Mar 22 2004 12:52:14 on modular [Seed = 3286017035] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 25 8 [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] [ 0, 1 ] [ 1, $.1, $.1^2, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, $.1^7, $.1^8, $.1^9, $.1^10, $.1^11, $.1^12, $.1^13, $.1^14, 0 ] false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] 2*x^2 + alpha^19*x + alpha^9 alpha^19*x^3 + alpha^22*x^2 + alpha^10*x + alpha^2 alpha^17*x + alpha^5 alpha^15 1 x^3 + alpha^3*x^2 + alpha^15*x + alpha^7 [ ] Total time: 3.049 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 12:52:46 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; [x : x in GF(2)]; [x : x in GF(4)]; [x : x in GF(8)]; [x : x in GF(16)]; /*els elements de GF(2) pertanyen a GF(4). Els elements d'aquest a GF(8) i aquests a GF(16)*/ P:= PolynomialRing (G25); IsFinite (P); /*false*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; p1 := alpha^2 + alpha*x + 2*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; producte := p1 * p2; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; mcd := GCD (p1,p2); mcd; mcm := LCM (p1,p2); mcm; a := (1/alpha^4) - alpha^-3 * x + alpha^5 * x^2; b := Factorization (a); b; Roots (b); Output: Magma V2.10-6 Mon Mar 22 2004 12:52:43 on modular [Seed = 3386289700] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 25 8 [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] [ 0, 1 ] [ 1, $.1, $.1^2, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, $.1^7, $.1^8, $.1^9, $.1^10, $.1^11, $.1^12, $.1^13, $.1^14, 0 ] false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] 2*x^2 + alpha^19*x + alpha^9 alpha^19*x^3 + alpha^22*x^2 + alpha^10*x + alpha^2 alpha^17*x + alpha^5 alpha^15 1 x^3 + alpha^3*x^2 + alpha^15*x + alpha^7 [ ] >> Roots (b);; ^ Runtime error in 'Roots': Bad argument types Argument types given: SeqEnum[Tup] Total time: 3.059 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 13:06:25 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; G25:= ext < G5 |h>; P:= PolynomialRing (G25); Output: Magma V2.10-6 Mon Mar 22 2004 13:06:22 on modular [Seed = 4192637665] ------------------------------------- >> G25:= ext < G5 |h>; ^ User error: Identifier 'G5' has not been declared or assigned >> P:= PolynomialRing (G25); ^ User error: Identifier 'G25' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 13:07:00 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; G5 := GF(5); G25:= ext < G5 |h>; P:= PolynomialRing (G25); Output: Magma V2.10-6 Mon Mar 22 2004 13:06:57 on modular [Seed = 236021064] ------------------------------------- Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 13:07:15 2004 Input: z5:= Integers(5); Q := PolynomialRing (z5); h:= 3+2*x+x^2; G5 := GF(5); G25:= ext < G5 |h>; P:= PolynomialRing (G25); Output: Magma V2.10-6 Mon Mar 22 2004 13:07:12 on modular [Seed = 353009218] ------------------------------------- Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 13:07:51 2004 Input: z5:= Integers(5); Q := PolynomialRing (z5); h:= 3+2*x+x^2; G5 := GF(5); G25:= ext < G5 |h>; P:= PolynomialRing (G25); p1 := alpha^2 + alpha*x + 2*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; Output: Magma V2.10-6 Mon Mar 22 2004 13:07:48 on modular [Seed = 469989231] ------------------------------------- >> p1 := alpha^2 + alpha*x + 2*x^2; ^ User error: Identifier 'alpha' has not been declared or assigned >> p2 := 1 + alpha*x; ^ User error: Identifier 'alpha' has not been declared or assigned >> suma := p1 + p2; ^ User error: Identifier 'p1' has not been declared or assigned >> suma;; ^ User error: Identifier 'suma' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 13:08:38 2004 Input: z5:= Integers(5); Q := PolynomialRing (z5); h:= 3+2*x+x^2; G5 := GF(5); G25:= ext < G5 |h>; P:= PolynomialRing (G25); F := G25; p1 := alpha^2 + alpha*x + 2*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; Output: Magma V2.10-6 Mon Mar 22 2004 13:08:35 on modular [Seed = 574441862] ------------------------------------- 2*x^2 + alpha^19*x + alpha^9 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 13:09:34 2004 Input: z5:= Integers(5); Q := PolynomialRing (z5); h:= 3+2*x+x^2; G5 := GF(5); G25:= ext < G5 |h>; P:= PolynomialRing (G25); F := G25; G := G5; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; Output: Magma V2.10-6 Mon Mar 22 2004 13:09:31 on modular [Seed = 908680682] ------------------------------------- x^2 + alpha^19*x + alpha^9 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 13:11:15 2004 Input: z5:= Integers(5); Q := PolynomialRing (z5); h:= 3+2*x+x^2; G5 := GF(5); G25:= ext < G5 |h>; P:= PolynomialRing (G25); F := G25; G := G5; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; producte := p1 * p2; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; Output: Magma V2.10-6 Mon Mar 22 2004 13:11:12 on modular [Seed = 1163536642] ------------------------------------- x^2 + alpha^19*x + alpha^9 alpha*x^3 + alpha^9*x^2 + alpha^10*x + alpha^2 alpha^23*x + alpha^21 alpha Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 13:13:28 2004 Input: z5:= Integers(5); Q := PolynomialRing (z5); h:= 3+2*x+x^2; G5 := GF(5); G25:= ext < G5 |h>; P:= PolynomialRing (G25); F := G25; G := G5; IsPrimitive (alpha); p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; producte := p1 * p2; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; Output: Magma V2.10-6 Mon Mar 22 2004 13:13:25 on modular [Seed = 1464351637] ------------------------------------- true x^2 + alpha^19*x + alpha^9 alpha*x^3 + alpha^9*x^2 + alpha^10*x + alpha^2 alpha^23*x + alpha^21 alpha Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 13:13:47 2004 Input: z5:= Integers(5); Q := PolynomialRing (z5); h:= 3+2*x+x^2; G5 := GF(5); G25:= ext < G5 |h>; P:= PolynomialRing (G25); F := G25; G := G5; IsPrimitive (beta); p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; producte := p1 * p2; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; Output: Magma V2.10-6 Mon Mar 22 2004 13:13:44 on modular [Seed = 1514485381] ------------------------------------- false x^2 + alpha^19*x + alpha^9 alpha*x^3 + alpha^9*x^2 + alpha^10*x + alpha^2 alpha^23*x + alpha^21 alpha Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 13:14:11 2004 Input: z5:= Integers(5); Q := PolynomialRing (z5); h:= 3+2*x+x^2; G5 := GF(5); G25:= ext < G5 |h>; P:= PolynomialRing (G25); F := G25; G := G5; IsPrimitive (beta,G5); p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; producte := p1 * p2; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; Output: Magma V2.10-6 Mon Mar 22 2004 13:14:08 on modular [Seed = 1635650966] ------------------------------------- >> IsPrimitive (beta,G5); ^ Runtime error in 'IsPrimitive': Bad argument types Argument types given: FldFinElt, FldFin x^2 + alpha^19*x + alpha^9 alpha*x^3 + alpha^9*x^2 + alpha^10*x + alpha^2 alpha^23*x + alpha^21 alpha Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 13:15:19 2004 Input: z5:= Integers(5); Q := PolynomialRing (z5); h:= 3+2*x+x^2; G5 := GF(5); G25:= ext < G5 |h>; P:= PolynomialRing (G25); F := G25; G := G5; lista_primitius_G25:=[alpha: alpha in G25 | IsPrimitive (x)]; lista_primitius_G25; lista_primitius_G5:=[beta: beta in G5 | IsPrimitive (x)]; lista_primitius_G5; /*[2,3]*/ p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; producte := p1 * p2; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; Output: Magma V2.10-6 Mon Mar 22 2004 13:15:16 on modular [Seed = 1953175879] ------------------------------------- [] [] x^2 + alpha^19*x + alpha^9 alpha*x^3 + alpha^9*x^2 + alpha^10*x + alpha^2 alpha^23*x + alpha^21 alpha Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 13:16:20 2004 Input: z5:= Integers(5); Q := PolynomialRing (z5); h:= 3+2*x+x^2; G5 := GF(5); G25:= ext < G5 |h>; P:= PolynomialRing (G25); F := G25; G := G5; lista_primitius_G25:=[alpha: alpha in G25 | IsPrimitive (alpha)]; lista_primitius_G25; lista_primitius_G5:=[beta: beta in G5 | IsPrimitive (beta)]; lista_primitius_G5; /*[2,3]*/ p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; producte := p1 * p2; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; Output: Magma V2.10-6 Mon Mar 22 2004 13:16:17 on modular [Seed = 2020021518] ------------------------------------- [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] x^2 + alpha^19*x + alpha^9 alpha*x^3 + alpha^9*x^2 + alpha^10*x + alpha^2 alpha^23*x + alpha^21 alpha Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 13:16:46 2004 Input: z5:= Integers(5); Q := PolynomialRing (z5); h:= 3+2*x+x^2; G5 := GF(5); G25:= ext < G5 |h>; P:= PolynomialRing (G25); lista_primitius_G25:=[alpha: alpha in G25 | IsPrimitive (alpha)]; lista_primitius_G25; lista_primitius_G5:=[beta: beta in G5 | IsPrimitive (beta)]; lista_primitius_G5; /*[2,3]*/ p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; producte := p1 * p2; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; Output: Magma V2.10-6 Mon Mar 22 2004 13:16:43 on modular [Seed = 2408636931] ------------------------------------- [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] [ 2, 3 ] >> p1 := alpha^2 + alpha*x + beta*x^2; ^ User error: Identifier 'alpha' has not been declared or assigned >> p2 := 1 + alpha*x; ^ User error: Identifier 'alpha' has not been declared or assigned >> suma := p1 + p2; ^ User error: Identifier 'p1' has not been declared or assigned >> suma; ^ User error: Identifier 'suma' has not been declared or assigned >> producte := p1 * p2; ^ User error: Identifier 'p1' has not been declared or assigned >> producte; ^ User error: Identifier 'producte' has not been declared or assigned >> quocient := p1 div p2; ^ User error: Identifier 'p1' has not been declared or assigned >> quocient; ^ User error: Identifier 'quocient' has not been declared or assigned >> residu := p1 mod p2; ^ User error: Identifier 'p1' has not been declared or assigned >> residu;; ^ User error: Identifier 'residu' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 13:18:13 2004 Input: z5:= Integers(5); Q := PolynomialRing (z5); h:= 3+2*x+x^2; G5 := GF(5); G25:= ext < G5 |h>; P:= PolynomialRing (G25); G := G25; G := G5; lista_primitius_G25:=[alpha: alpha in G25 | IsPrimitive (alpha)]; lista_primitius_G25; alpha; lista_primitius_G5:=[beta: beta in G5 | IsPrimitive (beta)]; lista_primitius_G5; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; producte := p1 * p2; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; Output: Magma V2.10-6 Mon Mar 22 2004 13:18:10 on modular [Seed = 2508912752] ------------------------------------- [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] alpha [ 2, 3 ] x^2 + alpha^19*x + alpha^9 alpha*x^3 + alpha^9*x^2 + alpha^10*x + alpha^2 alpha^23*x + alpha^21 alpha Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 69-162-195-137.bflony.adelphia.net. (69.162.195.137) Time: Mon Mar 22 13:25:37 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Mon Mar 22 2004 13:25:34 on modular [Seed = 2930884919] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 13:29:52 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; [x : x in GF(2)]; [x : x in GF(4)]; [x : x in GF(8)]; [x : x in GF(16)]; /*els elements de GF(2) pertanyen a GF(4). Els elements d'aquest a GF(8) i aquests a GF(16)*/ P := PolynomialRing (G25); IsFinite (P); /*false*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; /*[2,3]*/ G := G5; p1 := alpha^2 + alpha*x + 2*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; /*x^2 + alpha^19*x + alpha^9*/ producte := p1 * p2; producte; /*alpha*x^3 + alpha^9*x^2 + alpha^10*x + alpha^2*/ quocient := p1 div p2; quocient; /*alpha^23*x + alpha^21*/ residu := p1 mod p2; residu; /* alpha*/ mcd := GCD (p1,p2); mcd; /*1 */ mcm := LCM (p1,p2); mcm; /*x^3 + alpha^3*x^2 + alpha^15*x + alpha^7*/ /*p1 i p2 són coprimers, ja que el maxim comu divisor es 1*/ Factorization ((1/alpha^4) - alpha^-3 * x + alpha^5 * x^2); /*[ ]*/ Output: Magma V2.10-6 Mon Mar 22 2004 13:29:49 on modular [Seed = 3014443817] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 25 8 [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] [ 0, 1 ] [ 1, $.1, $.1^2, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, $.1^7, $.1^8, $.1^9, $.1^10, $.1^11, $.1^12, $.1^13, $.1^14, 0 ] false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] 2*x^2 + alpha^19*x + alpha^9 alpha^19*x^3 + alpha^22*x^2 + alpha^10*x + alpha^2 alpha^17*x + alpha^5 alpha^15 1 x^3 + alpha^3*x^2 + alpha^15*x + alpha^7 [ ] Total time: 3.009 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 13:31:26 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; [x : x in GF(2)]; [x : x in GF(4)]; [x : x in GF(8)]; [x : x in GF(16)]; /*els elements de GF(2) pertanyen a GF(4). Els elements d'aquest a GF(8) i aquests a GF(16)*/ P := PolynomialRing (G25); IsFinite (P); /*false*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; /*[2,3]*/ G := G5; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; /*x^2 + alpha^19*x + alpha^9*/ producte := p1 * p2; producte; /*alpha*x^3 + alpha^9*x^2 + alpha^10*x + alpha^2*/ quocient := p1 div p2; quocient; /*alpha^23*x + alpha^21*/ residu := p1 mod p2; residu; /* alpha*/ mcd := GCD (p1,p2); mcd; /*1 */ mcm := LCM (p1,p2); mcm; /*x^3 + alpha^3*x^2 + alpha^15*x + alpha^7*/ /*p1 i p2 són coprimers, ja que el maxim comu divisor es 1*/ Factorization ((1/alpha^4) - alpha^-3 * x + alpha^5 * x^2); /*[ ]*/ Output: Magma V2.10-6 Mon Mar 22 2004 13:31:23 on modular [Seed = 3269308990] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 25 8 [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] [ 0, 1 ] [ 1, $.1, $.1^2, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, $.1^7, $.1^8, $.1^9, $.1^10, $.1^11, $.1^12, $.1^13, $.1^14, 0 ] false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] x^2 + alpha^19*x + alpha^9 alpha*x^3 + alpha^9*x^2 + alpha^10*x + alpha^2 alpha^23*x + alpha^21 alpha 1 x^3 + alpha^8*x^2 + alpha^9*x + alpha [ ] Total time: 3.049 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 13:33:34 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; [x : x in GF(2)]; [x : x in GF(4)]; [x : x in GF(8)]; [x : x in GF(16)]; /*els elements de GF(2) pertanyen a GF(4). Els elements d'aquest a GF(8) i aquests a GF(16)*/ P := PolynomialRing (G25); IsFinite (P); /*false*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; /*[2,3]*/ G := G5; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; /*x^2 + alpha^19*x + alpha^9*/ producte := p1 * p2; producte; /*alpha*x^3 + alpha^9*x^2 + alpha^10*x + alpha^2*/ quocient := p1 div p2; quocient; /*alpha^23*x + alpha^21*/ residu := p1 mod p2; residu; /* alpha*/ mcd := GCD (p1,p2); mcd; /*1 */ mcm := LCM (p1,p2); mcm; /*x^3 + alpha^3*x^2 + alpha^15*x + alpha^7*/ /*p1 i p2 són coprimers, ja que el maxim comu divisor es 1*/ Factorization ((1/alpha^4) - alpha^-3 * x + alpha^5 * x^2); /*[ ]*/ IsPrimitive (alpha); IsPrimitive (beta); Output: Magma V2.10-6 Mon Mar 22 2004 13:33:31 on modular [Seed = 3369580980] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 25 8 [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] [ 0, 1 ] [ 1, $.1, $.1^2, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, $.1^7, $.1^8, $.1^9, $.1^10, $.1^11, $.1^12, $.1^13, $.1^14, 0 ] false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] x^2 + alpha^19*x + alpha^9 alpha*x^3 + alpha^9*x^2 + alpha^10*x + alpha^2 alpha^23*x + alpha^21 alpha 1 x^3 + alpha^8*x^2 + alpha^9*x + alpha [ ] true false Total time: 3.079 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 13:35:17 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; [x : x in GF(2)]; [x : x in GF(4)]; [x : x in GF(8)]; [x : x in GF(16)]; /*els elements de GF(2) pertanyen a GF(4). Els elements d'aquest a GF(8) i aquests a GF(16)*/ P := PolynomialRing (G25); IsFinite (P); /*false*/ lista_primitius_G25:=[alpha: alpha in G25 | IsPrimitive (alpha)]; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ lista_primitius_G5:=[beta: beta in G5 | IsPrimitive (beta)]; lista_primitius_G5; /*[2,3]*/ G := G5; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; /*x^2 + alpha^19*x + alpha^9*/ producte := p1 * p2; producte; /*alpha*x^3 + alpha^9*x^2 + alpha^10*x + alpha^2*/ quocient := p1 div p2; quocient; /*alpha^23*x + alpha^21*/ residu := p1 mod p2; residu; /* alpha*/ mcd := GCD (p1,p2); mcd; /*1 */ mcm := LCM (p1,p2); mcm; /*x^3 + alpha^3*x^2 + alpha^15*x + alpha^7*/ /*p1 i p2 són coprimers, ja que el maxim comu divisor es 1*/ Factorization ((1/alpha^4) - alpha^-3 * x + alpha^5 * x^2); /*[ ]*/ IsPrimitive (alpha); IsPrimitive (beta); Output: Magma V2.10-6 Mon Mar 22 2004 13:35:14 on modular [Seed = 3670387519] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 25 8 [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] [ 0, 1 ] [ 1, $.1, $.1^2, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, $.1^7, $.1^8, $.1^9, $.1^10, $.1^11, $.1^12, $.1^13, $.1^14, 0 ] false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] x^2 + alpha^19*x + alpha^9 alpha*x^3 + alpha^9*x^2 + alpha^10*x + alpha^2 alpha^23*x + alpha^21 alpha 1 x^3 + alpha^8*x^2 + alpha^9*x + alpha [ ] true false Total time: 3.069 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 13:36:12 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; [x : x in GF(2)]; [x : x in GF(4)]; [x : x in GF(8)]; [x : x in GF(16)]; /*els elements de GF(2) pertanyen a GF(4). Els elements d'aquest a GF(8) i aquests a GF(16)*/ P := PolynomialRing (G25); IsFinite (P); /*false*/ lista_primitius_G25:=[alpha: alpha in G25 | IsPrimitive (alpha)]; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ lista_primitius_G5:=[beta: beta in G5 | IsPrimitive (beta)]; lista_primitius_G5; /*[2,3]*/ G := G5; G; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; /*x^2 + alpha^19*x + alpha^9*/ producte := p1 * p2; producte; /*alpha*x^3 + alpha^9*x^2 + alpha^10*x + alpha^2*/ quocient := p1 div p2; quocient; /*alpha^23*x + alpha^21*/ residu := p1 mod p2; residu; /* alpha*/ mcd := GCD (p1,p2); mcd; /*1 */ mcm := LCM (p1,p2); mcm; /*x^3 + alpha^3*x^2 + alpha^15*x + alpha^7*/ /*p1 i p2 són coprimers, ja que el maxim comu divisor es 1*/ Factorization ((1/alpha^4) - alpha^-3 * x + alpha^5 * x^2); /*[ ]*/ IsPrimitive (alpha); IsPrimitive (beta); Output: Magma V2.10-6 Mon Mar 22 2004 13:36:09 on modular [Seed = 3791557631] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 25 8 [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] [ 0, 1 ] [ 1, $.1, $.1^2, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, $.1^7, $.1^8, $.1^9, $.1^10, $.1^11, $.1^12, $.1^13, $.1^14, 0 ] false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] Finite field of size 5 x^2 + alpha^19*x + alpha^9 alpha*x^3 + alpha^9*x^2 + alpha^10*x + alpha^2 alpha^23*x + alpha^21 alpha 1 x^3 + alpha^8*x^2 + alpha^9*x + alpha [ ] true false Total time: 3.039 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 13:37:57 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; [x : x in GF(2)]; [x : x in GF(4)]; [x : x in GF(8)]; [x : x in GF(16)]; /*els elements de GF(2) pertanyen a GF(4). Els elements d'aquest a GF(8) i aquests a GF(16)*/ P := PolynomialRing (G25); IsFinite (P); /*false*/ lista_primitius_G25:=[alpha: alpha in G25 | IsPrimitive (alpha)]; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ alpha; lista_primitius_G5:=[beta: beta in G5 | IsPrimitive (beta)]; lista_primitius_G5; /*[2,3]*/ beta; G := G5; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; /*x^2 + alpha^19*x + alpha^9*/ producte := p1 * p2; producte; /*alpha*x^3 + alpha^9*x^2 + alpha^10*x + alpha^2*/ quocient := p1 div p2; quocient; /*alpha^23*x + alpha^21*/ residu := p1 mod p2; residu; /* alpha*/ mcd := GCD (p1,p2); mcd; /*1 */ mcm := LCM (p1,p2); mcm; /*x^3 + alpha^3*x^2 + alpha^15*x + alpha^7*/ /*p1 i p2 són coprimers, ja que el maxim comu divisor es 1*/ Factorization ((1/alpha^4) - alpha^-3 * x + alpha^5 * x^2); /*[ ]*/ IsPrimitive (alpha); IsPrimitive (beta); Output: Magma V2.10-6 Mon Mar 22 2004 13:37:54 on modular [Seed = 4159210866] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 25 8 [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] [ 0, 1 ] [ 1, $.1, $.1^2, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, $.1^7, $.1^8, $.1^9, $.1^10, $.1^11, $.1^12, $.1^13, $.1^14, 0 ] false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] alpha [ 2, 3 ] >> beta; ^ User error: Identifier 'beta' has not been declared or assigned x^2 + alpha^19*x + alpha^9 alpha*x^3 + alpha^9*x^2 + alpha^10*x + alpha^2 alpha^23*x + alpha^21 alpha 1 x^3 + alpha^8*x^2 + alpha^9*x + alpha [ ] true false Total time: 3.159 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 22 13:38:47 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; [x : x in GF(2)]; [x : x in GF(4)]; [x : x in GF(8)]; [x : x in GF(16)]; /*els elements de GF(2) pertanyen a GF(4). Els elements d'aquest a GF(8) i aquests a GF(16)*/ P := PolynomialRing (G25); IsFinite (P); /*false*/ lista_primitius_G25:=[alpha: alpha in G25 | IsPrimitive (alpha)]; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ alpha; lista_primitius_G5:=[beta: beta in G5 | IsPrimitive (beta)]; lista_primitius_G5; /*[2,3]*/ G := G5; beta; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; /*x^2 + alpha^19*x + alpha^9*/ producte := p1 * p2; producte; /*alpha*x^3 + alpha^9*x^2 + alpha^10*x + alpha^2*/ quocient := p1 div p2; quocient; /*alpha^23*x + alpha^21*/ residu := p1 mod p2; residu; /* alpha*/ mcd := GCD (p1,p2); mcd; /*1 */ mcm := LCM (p1,p2); mcm; /*x^3 + alpha^3*x^2 + alpha^15*x + alpha^7*/ /*p1 i p2 són coprimers, ja que el maxim comu divisor es 1*/ Factorization ((1/alpha^4) - alpha^-3 * x + alpha^5 * x^2); /*[ ]*/ IsPrimitive (alpha); IsPrimitive (beta); Output: Magma V2.10-6 Mon Mar 22 2004 13:38:44 on modular [Seed = 4276194381] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 25 8 [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] [ 0, 1 ] [ 1, $.1, $.1^2, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, $.1^7, $.1^8, $.1^9, $.1^10, $.1^11, $.1^12, $.1^13, $.1^14, 0 ] false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] alpha [ 2, 3 ] 1 x^2 + alpha^19*x + alpha^9 alpha*x^3 + alpha^9*x^2 + alpha^10*x + alpha^2 alpha^23*x + alpha^21 alpha 1 x^3 + alpha^8*x^2 + alpha^9*x + alpha [ ] true false Total time: 3.159 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 14:23:44 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (3+2*y) +2*x*y^2*(1+y) in I; Output: Magma V2.10-6 Mon Mar 22 2004 14:23:40 on modular [Seed = 1669078614] ------------------------------------- >> I := ideal; ^ Runtime error: Bad argument types Argument types given: RngMPolElt, RngIntElt >> GroebnerBasis(I); ^ User error: Identifier 'I' has not been declared or assigned >> (3+2*y) +2*x*y^2*(1+y) in I;; ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 14:23:51 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (3+2*y) +2*x*y^2*(1+y) in I; Output: Magma V2.10-6 Mon Mar 22 2004 14:23:48 on modular [Seed = 2086863152] ------------------------------------- [ 2*x^2 + 2, 4 ] false Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 14:25:47 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > ((1+x)*(1+y)+(1-x)*(1-y)) in I; Output: Magma V2.10-6 Mon Mar 22 2004 14:25:44 on modular [Seed = 3453137021] ------------------------------------- [ 2*x^2 + 2, 2*y^2 + 2, 4 ] false Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 14:25:55 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > ((1+x)*(1+y)+(1-x)*(1-y))^2 in I; Output: Magma V2.10-6 Mon Mar 22 2004 14:25:52 on modular [Seed = 3503271192] ------------------------------------- [ 2*x^2 + 2, 2*y^2 + 2, 4 ] true Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 14:26:08 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > ((1+x)*(1+y)+(1-x)*(1-y))^3 in I; Output: Magma V2.10-6 Mon Mar 22 2004 14:26:04 on modular [Seed = 4025520683] ------------------------------------- [ 2*x^2 + 2, 2*y^2 + 2, 4 ] true Total time: 3.739 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 14:34:31 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > ((1+x)*(1+y)+(1-x)*(1-y))^3 in I; Output: Magma V2.10-6 Mon Mar 22 2004 14:34:28 on modular [Seed = 4125788729] ------------------------------------- >> I := ideal; ^ User error: bad syntax >> GroebnerBasis(I); ^ User error: Identifier 'I' has not been declared or assigned >> ((1+x)*(1+y)+(1-x)*(1-y))^3 in I;; ^ User error: Identifier 'I' has not been declared or assigned Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 14:34:41 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > ((1+x)*(1+y)+(1-x)*(1-y))^3 in I; Output: Magma V2.10-6 Mon Mar 22 2004 14:34:38 on modular [Seed = 252735688] ------------------------------------- >> I := ideal; ^ Runtime error: Bad argument types Argument types given: RngMPolElt, RngIntElt >> GroebnerBasis(I); ^ User error: Identifier 'I' has not been declared or assigned >> ((1+x)*(1+y)+(1-x)*(1-y))^3 in I;; ^ User error: Identifier 'I' has not been declared or assigned Total time: 3.119 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 14:34:50 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > ((1+x)*(1+y)+(1-x)*(1-y))^3 in I; Output: Magma V2.10-6 Mon Mar 22 2004 14:34:47 on modular [Seed = 102332888] ------------------------------------- [ 2*x^2*y^2 + x^2 + 2*x*y^4 + 2*x*y^2 + y^4 ] false Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 14:35:12 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > ((1+x)*(1+y)+(1-x)*(1-y))^3 in I; Output: Magma V2.10-6 Mon Mar 22 2004 14:35:09 on modular [Seed = 353004273] ------------------------------------- [ x^2*y + 2*x^2 + 4*x*y^2 + 4*y^12 - 2*y^11 - 4*y^10 + y^9 + 2*y^8 - 2*y^6 + 2*y^4, 3*x^2 + 4*x*y^2 + 4*y^12 - 6*y^10 + 2*y^8 + y^7 - y^6 - y^5 + 2*y^4, x*y^6 + x*y^4 - 2*x*y^2 + 2*y^13 - 2*y^12 - y^11 - y^9 + 2*y^8 + y^7 + y^6 - y^5 - y^4, 2*x*y^3 - 2*x*y^2 - 2*y^8 + 2*y^7 + y^6 - y^4, 4*y^13 - 4*y^12 - y^9 + 3*y^8 - 3*y^7 + y^6 ] false Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 14:35:54 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > ((1+x)*(1+y)+(1-x)*(1-y))^3 in I; Output: Magma V2.10-6 Mon Mar 22 2004 14:35:49 on modular [Seed = 791686963] ------------------------------------- [ x^2 + 4*x*y^2 + 908*y^3 + 911*y^2, 2*x*y^3 + 6*x*y^2 + 1166*y^3 + 1170*y^2, 8*x*y^2 + 144*y^3 + 152*y^2, y^4 + 1020*y^3 + 1019*y^2, 1480*y^3 + 1480*y^2 ] false Total time: 3.149 seconds, Total memory usage: 1.94MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 14:37:27 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > ((1+x)*(1+y)+(1-x)*(1-y))^3 in I; Output: Magma V2.10-6 Mon Mar 22 2004 14:37:24 on modular [Seed = 958806340] ------------------------------------- [ x^2 + 3*y^2, 2*x*y^2 + 2*y^2, y^4 + 3*y^2, 2*y^3 + 2*y^2, 4*y^2 ] false Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 14:38:33 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > ((1+x)*(1+y)+(1-x)*(1-y))^3 in I; Output: Magma V2.10-6 Mon Mar 22 2004 14:38:30 on modular [Seed = 808398991] ------------------------------------- [ x^2 + y^7 - y^6 - y^5, x*y^6 + x*y^4 + 2*y^6, 2*x*y^2 + y^7 - y^6 + y^5 + y^4, y^8 - y^6, 2*y^7 - 2*y^6 ] false Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:03:02 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (x+y^2)*(x+y^3)+x*y^2*x*y^3 in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:02:59 on modular [Seed = 2525597932] ------------------------------------- [ x^2 + y^7 - y^6 - y^5, x*y^6 + x*y^4 + 2*y^6, 2*x*y^2 + y^7 - y^6 + y^5 + y^4, y^8 - y^6, 2*y^7 - 2*y^6 ] false Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:03:27 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > ((x+y^2)*(x+y^3)+x*y^2*x*y^3)^2 in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:03:24 on modular [Seed = 2713626404] ------------------------------------- [ x^2 + y^7 - y^6 - y^5, x*y^6 + x*y^4 + 2*y^6, 2*x*y^2 + y^7 - y^6 + y^5 + y^4, y^8 - y^6, 2*y^7 - 2*y^6 ] false Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:10:51 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > ((x+y^2)*(x+y^3)+x*y^2*x*y^3)^2 in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:10:48 on modular [Seed = 3064577783] ------------------------------------- [ x^2 - y^5, x*y^4 + y^6, 2*x*y^2 + y^5 + y^4, y^7 - y^6 ] false Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:12:03 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > ((x+y^2)*(x+y^3)+x*y^2*x*y^3)^2 in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:12:00 on modular [Seed = 3235891289] ------------------------------------- [ x^2 - y^5, x*y^4, 2*x*y^2 + y^5 + y^4, y^6 ] true Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:14:27 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (1+x)(1+x*y)+ x^2*y in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:14:23 on modular [Seed = 3620265665] ------------------------------------- [ x^2 + 1, y^2 + 1, 2 ] >> (1+x)(1+x*y)+ x^2*y in I;; ^ Runtime error: Bad argument types Argument types given: RngMPolElt, RngMPolElt Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:14:44 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (1+x)*(1+x*y)+ x^2*y in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:14:41 on modular [Seed = 3791579353] ------------------------------------- [ x^2 + 1, y^2 + 1, 2 ] false Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:14:59 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > ((1+x)*(1+x*y)+ x^2*y)^2 in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:14:56 on modular [Seed = 4175950257] ------------------------------------- [ x^2 + 1, y^2 + 1, 2 ] false Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:15:40 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (1+ x^2*y)^2 in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:15:37 on modular [Seed = 4159241879] ------------------------------------- [ x^2 + 1, y^2 + 1, 2 ] true Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:16:18 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (1+ x^2*y)^2 in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:16:14 on modular [Seed = 52169351] ------------------------------------- [ x^2 + y^2 + 1, y^4 + y^2 + 1, 2 ] false Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:16:39 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (1+ (x+y)*x*y)^2 in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:16:36 on modular [Seed = 403116470] ------------------------------------- [ x^2 + y^2 + 1, y^4 + y^2 + 1, 2 ] true Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:16:55 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (1+ (x+y)*x*y)^2 in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:16:52 on modular [Seed = 369696680] ------------------------------------- [ x^2 + y^2 + 1, y^4 + y^2 + 1, 2 ] true Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:17:16 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (1+ (x+y)*x*y)^2 in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:17:13 on modular [Seed = 791684844] ------------------------------------- [ x^2 + y^2 + 1, y^4 + y^2 + 1, 2 ] true Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:18:24 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (1+ (x+y)*x*y)^2 in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:18:21 on modular [Seed = 607858211] ------------------------------------- [ x^2 + 1, 2 ] false Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:19:09 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (1+ (x+y)*x*y)^2 in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:19:06 on modular [Seed = 808401408] ------------------------------------- [ x^2 + y^2, 2*x*y, 2*y^3 ] false Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:19:58 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (1+ (x+y)*x*y)^2 in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:19:55 on modular [Seed = 1313948719] ------------------------------------- [ x^2 + y^2, 2*x*y, 2*y^3 ] false Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:21:25 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (1+ (x+y)*x*y)^2 in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:21:22 on modular [Seed = 1802789283] ------------------------------------- [ x^2 + y^2, 2*x*y, 2*y^3 ] false Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:22:11 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (1+ (x+y)*x*y)^2 in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:22:08 on modular [Seed = 2103605127] ------------------------------------- [ x^2 + y^2, 2*x*y, 6*x + 6*y + 36, 2*y^3, 6*y^2 + 36*y, 54 ] false Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:23:00 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > x*(x-3)+y*(y-3) in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:22:57 on modular [Seed = 2325053857] ------------------------------------- [ x^2 + y^2, 2*x*y, 6*x + 6*y + 36, 2*y^3, 6*y^2 + 36*y, 54 ] false Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:23:13 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (x*(x-3)+y*(y-3))^2 in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:23:10 on modular [Seed = 2157939620] ------------------------------------- [ x^2 + y^2, 2*x*y, 6*x + 6*y + 36, 2*y^3, 6*y^2 + 36*y, 54 ] true Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:24:21 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (x*(x-3)+y*(y-3))^2 in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:24:18 on modular [Seed = 2575733473] ------------------------------------- [ x^2 + y^2, 2*x*y, 2*y^3, 8*y^2 ] true Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:24:44 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (x*(3*x)+y*(y))^2 in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:24:41 on modular [Seed = 2525601045] ------------------------------------- [ x^2 + y^2, 2*x*y, 2*y^3, 8*y^2 ] true Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:26:16 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (x*(3*x)+y*(y))^2 in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:26:13 on modular [Seed = 2813897800] ------------------------------------- [ x^2 + 121, 22*x, 2662 ] false Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:26:57 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (x*(3*x)+y*(y))^2 in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:26:54 on modular [Seed = 2964307124] ------------------------------------- [ x^2 + 121, 22*x, y^2 + 121, 22*y, 2662 ] true Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:27:41 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (121+x*y)^2 in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:27:38 on modular [Seed = 3469853438] ------------------------------------- [ x^2 + 121, 22*x, y^2 + 121, 22*y, 2662 ] true Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:28:28 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (11*(x+y))^2 in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:28:25 on modular [Seed = 3319450022] ------------------------------------- [ x^2 + 121, 22*x, y^2 + 121, 22*y, 2662 ] true Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:28:48 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (11*(x+y))^2 in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:28:45 on modular [Seed = 3503283367] ------------------------------------- [ x^2 + 1, y^2 + 1, 2 ] true Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:29:11 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (11*(x+y))^2 in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:29:08 on modular [Seed = 4025541489] ------------------------------------- [ x^2 + 1, y^2 + 1, 2 ] true Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:29:26 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (11*(x+y))^2 in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:29:23 on modular [Seed = 3841714253] ------------------------------------- >> I := ideal; ^ User error: bad syntax >> GroebnerBasis(I); ^ User error: Identifier 'I' has not been declared or assigned >> (11*(x+y))^2 in I;; ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:29:35 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (11*(x+y))^2 in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:29:32 on modular [Seed = 4259508571] ------------------------------------- [ x^2 + 121, 11*x*y^2 + 11*x, 22*x, 121*y^2 + 2541, 2662 ] false Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:30:05 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (11*(x+x*y))^2 in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:30:02 on modular [Seed = 202571981] ------------------------------------- [ x^2 + 121, 11*x*y^2 + 11*x, 22*x, 121*y^2 + 2541, 2662 ] true Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:32:34 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (11*(x+x*y))^2 in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:32:30 on modular [Seed = 520098378] ------------------------------------- [ x^3 + 1, 3 ] false Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:34:28 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (11*(x+x*y))^2 in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:34:25 on modular [Seed = 369695692] ------------------------------------- [ x^3 + 1, y^3 + 1, 3 ] false Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:34:57 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (1+2*x*y^2+2*y*x^2)^2 in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:34:54 on modular [Seed = 758259912] ------------------------------------- [ x^3 + 1, y^3 + 1, 3 ] true Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:35:19 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (1+2*x*y+2*y^2*x^2)^2 in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:35:16 on modular [Seed = 942093879] ------------------------------------- [ x^3 + 1, y^3 + 1, 3 ] false Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:35:57 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (1+2*x*y+2*y^2*x^2)^2 in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:35:54 on modular [Seed = 908670999] ------------------------------------- [ 2*x^3 + 1, y^3 + 1, 3 ] false Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:36:19 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (1+4*x*y+8*y^2*x^2)^2 in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:36:15 on modular [Seed = 1297236857] ------------------------------------- [ 2*x^3 + 1, y^3 + 1, 3 ] false Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:37:40 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (1+4*x*y+8*y^2*x^2)^2 in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:37:37 on modular [Seed = 1531205057] ------------------------------------- [ 2*x^3 + 1, y^3 + 1, 3 ] false Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:44:11 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (1+8*x*y+4*y^2*x^2)^2 in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:44:08 on modular [Seed = 1752660091] ------------------------------------- [ 2*x^3 + 1, y^3 + 1, 3 ] true Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:44:59 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (1+4*x*y^2+8*y*x^2)^2 in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:44:56 on modular [Seed = 1735948068] ------------------------------------- [ 2*x^3 + 1, y^3 + 1, 3 ] true Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:47:43 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (1+4*x*y^2+8*y*x^2)^2 in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:47:40 on modular [Seed = 1886347415] ------------------------------------- >> I := ideal; ^ Runtime error: Bad argument types Argument types given: RngMPolElt, RngMPolElt >> GroebnerBasis(I); ^ User error: Identifier 'I' has not been declared or assigned >> (1+4*x*y^2+8*y*x^2)^2 in I;; ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:47:53 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (1+4*x*y^2+8*y*x^2)^2 in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:47:50 on modular [Seed = 2408619890] ------------------------------------- [ x^2 + 2*x + 1, 10*x + 10 ] false Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:48:04 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (1+4*x*y^2+8*y*x^2)^2 in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:48:01 on modular [Seed = 2258212748] ------------------------------------- [ x^2 + 2*x + 1, 10*x + 10 ] false Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:48:13 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (1+4*x*y^2+8*y*x^2)^2 in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:48:11 on modular [Seed = 2642578589] ------------------------------------- [ x^2 + 2*x + 1 ] false Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:49:01 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (1+x^3)(1+x^5) in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:48:58 on modular [Seed = 2492171685] ------------------------------------- [ x^2 + 2*x + 1 ] >> (1+x^3)(1+x^5) in I;; ^ Runtime error: Bad argument types Argument types given: RngMPolElt, RngMPolElt Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:49:10 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (1+x^3)*(1+x^5) in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:49:07 on modular [Seed = 2747052779] ------------------------------------- [ x^2 + 2*x + 1 ] true Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:49:26 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (1+x^3)*(1+x^5) in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:49:23 on modular [Seed = 3131419618] ------------------------------------- [ x^2 + 54*x + 1347701, 484*x + 6513672, 7086244 ] false Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 15:49:35 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (1+3*x^3)*(1+x^5) in I; Output: Magma V2.10-6 Mon Mar 22 2004 15:49:32 on modular [Seed = 2981011686] ------------------------------------- [ x^2 + 54*x + 1347701, 484*x + 6513672, 7086244 ] false Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 16:10:12 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (1+3*x^3)*(1+x^5) in I; Output: Magma V2.10-6 Mon Mar 22 2004 16:10:09 on modular [Seed = 252713266] ------------------------------------- [ x^2 + 2*x + 1, 2*x*y + 2*x + 2*y + 2, y^2 + 2*y + 1, 4 ] false Total time: 3.069 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 16:10:22 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (1+3*x^3)*(1+x^5)*(1+y^5) in I; Output: Magma V2.10-6 Mon Mar 22 2004 16:10:18 on modular [Seed = 2037302] ------------------------------------- [ x^2 + 2*x + 1, 2*x*y + 2*x + 2*y + 2, y^2 + 2*y + 1, 4 ] true Total time: 3.029 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 16:10:51 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (1+3*x^3)*(1+x^5)*(1+y^5) in I; Output: Magma V2.10-6 Mon Mar 22 2004 16:10:48 on modular [Seed = 419827533] ------------------------------------- [ x^2 + 54*x + 1347701, 484*x + 6513672, y^2 + 54*y + 1347701, 484*y + 6513672, 7086244 ] false Total time: 2.989 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 16:11:08 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (1+3*x^3)*(1+x^5)*(1+y^5)*(1+3*y^3) in I; Output: Magma V2.10-6 Mon Mar 22 2004 16:11:05 on modular [Seed = 302842999] ------------------------------------- [ x^2 + 54*x + 1347701, 484*x + 6513672, y^2 + 54*y + 1347701, 484*y + 6513672, 7086244 ] true Total time: 2.959 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 16:16:28 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (1+3*x^3)*(1+x^5)*(1+y^5)*(1+3*y^3) in I; Output: Magma V2.10-6 Mon Mar 22 2004 16:16:25 on modular [Seed = 591148166] ------------------------------------- [ 11*x^2*y + 3211*y^3, 121*x^2 + 169*y^2, 26*x*y^3, 286*x*y, 4394*y^3 ] false Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 16:17:33 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > in I; Output: Magma V2.10-6 Mon Mar 22 2004 16:17:30 on modular [Seed = 891953875] ------------------------------------- [ x^2*y^2 + 3211*y^2, 11*x^2*y + 169*y^3, 121*x^2 + 169*y^2, 26*x*y^3, 286*x*y, 169*y^4 + 1859*y^2, 338*y^3, 3718*y^2 ] >> in I;; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 16:18:52 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (121*x^3 +(13*y)^2) in I; Output: Magma V2.10-6 Mon Mar 22 2004 16:18:49 on modular [Seed = 1330665338] ------------------------------------- [ x^2*y^2 + 3211*y^2, 11*x^2*y + 169*y^3, 121*x^2 + 169*y^2, 26*x*y^3, 286*x*y, 169*y^4 + 1859*y^2, 338*y^3, 3718*y^2 ] false Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 16:19:02 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (121*x^3 +(13*y)^2)^2 in I; Output: Magma V2.10-6 Mon Mar 22 2004 16:18:59 on modular [Seed = 1079990287] ------------------------------------- [ x^2*y^2 + 3211*y^2, 11*x^2*y + 169*y^3, 121*x^2 + 169*y^2, 26*x*y^3, 286*x*y, 169*y^4 + 1859*y^2, 338*y^3, 3718*y^2 ] true Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 16:20:07 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (121*x^3 +(13*y)^2)^2 in I; Output: Magma V2.10-6 Mon Mar 22 2004 16:20:04 on modular [Seed = 1397509083] ------------------------------------- [ x^2 + 3*y^2, 2*x*y - 2*y^2, 8*y^3 ] false Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Mon Mar 22 18:07:59 2004 Input: n:=1807082088687404805951656164405905566278102516769401349170127021450056662540244048387341127590812303371781887966563182013214880557; m:= 540525112162133938753086; coeff = n div (m^5); print coeff; P := PolynomialRingh(Integers(),2); F := P!0; F := Output: Magma V2.10-6 Mon Mar 22 2004 18:07:56 on modular [Seed = 1852923823] ------------------------------------- >> coeff = n div (m^5); ^ User error: Identifier 'coeff' has not been declared or assigned >> print coeff; ^ User error: Identifier 'coeff' has not been declared or assigned >> P := PolynomialRingh(Integers(),2); ^ User error: Identifier 'PolynomialRingh' has not been declared or assigned >> F := P!0; ^ User error: Identifier 'P' has not been declared or assigned >> F := ; ^ User error: bad syntax Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Mon Mar 22 18:08:15 2004 Input: n:=1807082088687404805951656164405905566278102516769401349170127021450056662540244048387341127590812303371781887966563182013214880557; m:= 540525112162133938753086; coeff := n div (m^5); print coeff; P := PolynomialRingh(Integers(),2); F := P!0; F := Output: Magma V2.10-6 Mon Mar 22 2004 18:08:12 on modular [Seed = 1635668144] ------------------------------------- 39165033600 >> P := PolynomialRingh(Integers(),2); ^ User error: Identifier 'PolynomialRingh' has not been declared or assigned >> F := P!0; ^ User error: Identifier 'P' has not been declared or assigned >> F := ; ^ User error: bad syntax Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Mon Mar 22 18:08:27 2004 Input: n:=1807082088687404805951656164405905566278102516769401349170127021450056662540244048387341127590812303371781887966563182013214880557; m:= 540525112162133938753086; coeff := n div (m^5); print coeff; P := PolynomialRing(Integers(),2); F := P!0; F := Output: Magma V2.10-6 Mon Mar 22 2004 18:08:24 on modular [Seed = 2020034973] ------------------------------------- 39165033600 >> F := ; ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Mon Mar 22 18:16:23 2004 Input: n:=1807082088687404805951656164405905566278102516769401349170127021450056662540244048387341127590812303371781887966563182013214880557; m:= 540525112162133938753086; rem :=; coeffs :=[]; for i := 5 to 0 by -1 do temp := m^i; coeff := rem div temp; Append (~coeffs, coeff); rem -=: coeff*temp; end for; print coeffs; P := PolynomialRing(Integers(),2); F := P!0; F := Output: Magma V2.10-6 Mon Mar 22 2004 18:16:20 on modular [Seed = 2174661192] ------------------------------------- >> rem :=; ^ User error: bad syntax >> rem -=: coeff*temp; ^ User error: bad syntax >> end for; ^ User error: bad syntax [] >> F := ; ^ User error: bad syntax Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Mon Mar 22 18:16:42 2004 Input: n:=1807082088687404805951656164405905566278102516769401349170127021450056662540244048387341127590812303371781887966563182013214880557; m:= 540525112162133938753086; rem := n; coeffs :=[]; for i := 5 to 0 by -1 do temp := m^i; coeff := rem div temp; Append (~coeffs, coeff); rem -=: coeff*temp; end for; print coeffs; P := PolynomialRing(Integers(),2); F := P!0; F := Output: Magma V2.10-6 Mon Mar 22 2004 18:16:39 on modular [Seed = 2559028034] ------------------------------------- >> rem -=: coeff*temp; ^ User error: bad syntax >> end for; ^ User error: bad syntax [] >> F := ; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Mon Mar 22 18:16:59 2004 Input: n:=1807082088687404805951656164405905566278102516769401349170127021450056662540244048387341127590812303371781887966563182013214880557; m:= 540525112162133938753086; rem := n; coeffs :=[]; for i := 5 to 0 by -1 do temp := m^i; coeff := rem div temp; Append (~coeffs, coeff); rem -:= coeff*temp; end for; print coeffs; P := PolynomialRing(Integers(),2); F := P!0; F := Output: Magma V2.10-6 Mon Mar 22 2004 18:16:56 on modular [Seed = 2458755447] ------------------------------------- [ 39165033600, 20503845316952, 368918762230643496796164, 80542667093060343063245, 10787315896624763483886, 198918697357741052852725 ] >> F := ; ^ User error: bad syntax Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Mon Mar 22 18:18:43 2004 Input: n:=1807082088687404805951656164405905566278102516769401349170127021450056662540244048387341127590812303371781887966563182013214880557; m:= 540525112162133938753086; rem := n; coeffs :=[]; for i := 5 to 0 by -1 do temp := m^i; coeff := rem div temp; Append (~coeffs, coeff); rem -:= coeff*temp; end for; mdiv2 := m div 2; for i := d+1 to 2 by -1 do if coeffs[i] gt mdiv2 then coeffs[i] -:= m; coeffs[i-1] += 1; end if; end for print coeffs; P := PolynomialRing(Integers(),2); F := P!0; F := Output: Magma V2.10-6 Mon Mar 22 2004 18:18:40 on modular [Seed = 2780467704] ------------------------------------- >> coeffs[i-1] += 1; ^ User error: bad syntax >> end if; ^ User error: bad syntax >> end for ^ User error: bad syntax [ 39165033600, 20503845316952, 368918762230643496796164, 80542667093060343063245, 10787315896624763483886, 198918697357741052852725 ] >> F := ; ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Mon Mar 22 18:18:57 2004 Input: n:=1807082088687404805951656164405905566278102516769401349170127021450056662540244048387341127590812303371781887966563182013214880557; m:= 540525112162133938753086; rem := n; coeffs :=[]; for i := 5 to 0 by -1 do temp := m^i; coeff := rem div temp; Append (~coeffs, coeff); rem -:= coeff*temp; end for; mdiv2 := m div 2; for i := d+1 to 2 by -1 do if coeffs[i] gt mdiv2 then coeffs[i] -:= m; coeffs[i-1] +:= 1; end if; end for print coeffs; P := PolynomialRing(Integers(),2); F := P!0; F := Output: Magma V2.10-6 Mon Mar 22 2004 18:18:54 on modular [Seed = 3164834031] ------------------------------------- >> print coeffs; ^ User error: bad syntax >> F := ; ^ User error: bad syntax Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Mon Mar 22 18:19:21 2004 Input: n:=1807082088687404805951656164405905566278102516769401349170127021450056662540244048387341127590812303371781887966563182013214880557; m:= 540525112162133938753086; rem := n; coeffs :=[]; for i := 5 to 0 by -1 do temp := m^i; coeff := rem div temp; Append (~coeffs, coeff); rem -:= coeff*temp; end for; mdiv2 := m div 2; for i := d+1 to 2 by -1 do if coeffs[i] gt mdiv2 then coeffs[i] -:= m; coeffs[i-1] +:= 1; end if; end for; print coeffs; P := PolynomialRing(Integers(),2); F := P!0; F := Output: Magma V2.10-6 Mon Mar 22 2004 18:19:18 on modular [Seed = 3081274316] ------------------------------------- >> for i := d+1 to 2 by -1 do ^ User error: Identifier 'd' has not been declared or assigned [ 39165033600, 20503845316952, 368918762230643496796164, 80542667093060343063245, 10787315896624763483886, 198918697357741052852725 ] >> F := ; ^ User error: bad syntax Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Mon Mar 22 18:19:38 2004 Input: n:=1807082088687404805951656164405905566278102516769401349170127021450056662540244048387341127590812303371781887966563182013214880557; m:= 540525112162133938753086; rem := n; coeffs :=[]; for i := 5 to 0 by -1 do temp := m^i; coeff := rem div temp; Append (~coeffs, coeff); rem -:= coeff*temp; end for; mdiv2 := m div 2; for i := 6 to 2 by -1 do if coeffs[i] gt mdiv2 then coeffs[i] -:= m; coeffs[i-1] +:= 1; end if; end for; print coeffs; P := PolynomialRing(Integers(),2); F := P!0; F := Output: Magma V2.10-6 Mon Mar 22 2004 18:19:35 on modular [Seed = 3469867588] ------------------------------------- [ 39165033600, 20503845316953, -171606349931490441956922, 80542667093060343063245, 10787315896624763483886, 198918697357741052852725 ] >> F := ; ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Mon Mar 22 18:21:45 2004 Input: n:=1807082088687404805951656164405905566278102516769401349170127021450056662540244048387341127590812303371781887966563182013214880557; m:= 540525112162133938753086; d:=5; rem := n; coeffs :=[]; for i := 5 to 0 by -1 do temp := m^i; coeff := rem div temp; Append (~coeffs, coeff); rem -:= coeff*temp; end for; mdiv2 := m div 2; for i := 6 to 2 by -1 do if coeffs[i] gt mdiv2 then coeffs[i] -:= m; coeffs[i-1] +:= 1; end if; end for; print coeffs; P := PolynomialRing(Integers(),2); F := P!0; for i in [0..5] do F +:= coeffs[i+1]*X^(d-i)*Y^i; end for; print F; Output: Magma V2.10-6 Mon Mar 22 2004 18:21:41 on modular [Seed = 3737250773] ------------------------------------- [ 39165033600, 20503845316953, -171606349931490441956922, 80542667093060343063245, 10787315896624763483886, 198918697357741052852725 ] 39165033600*X^5 + 20503845316953*X^4*Y - 171606349931490441956922*X^3*Y^2 + 80542667093060343063245*X^2*Y^3 + 10787315896624763483886*X*Y^4 + 198918697357741052852725*Y^5 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Mon Mar 22 18:22:42 2004 Input: n:=1807082088687404805951656164405905566278102516769401349170127021450056662540244048387341127590812303371781887966563182013214880557; m:= 540525112162133938753086; d:=5; rem := n; coeffs :=[]; for i := 5 to 0 by -1 do temp := m^i; coeff := rem div temp; Append (~coeffs, coeff); rem -:= coeff*temp; end for; mdiv2 := m div 2; for i := 6 to 2 by -1 do if coeffs[i] gt mdiv2 then coeffs[i] -:= m; coeffs[i-1] +:= 1; end if; end for; print coeffs; P := PolynomialRing(Integers(),2); F := P!0; for i in [0..5] do F +:= coeffs[i+1]*X^(d-i)*Y^i; end for; print F; Evaluate F[m,1]; Output: Magma V2.10-6 Mon Mar 22 2004 18:22:38 on modular [Seed = 3503285731] ------------------------------------- [ 39165033600, 20503845316953, -171606349931490441956922, 80542667093060343063245, 10787315896624763483886, 198918697357741052852725 ] 39165033600*X^5 + 20503845316953*X^4*Y - 171606349931490441956922*X^3*Y^2 + 80542667093060343063245*X^2*Y^3 + 10787315896624763483886*X*Y^4 + 198918697357741052852725*Y^5 >> Evaluate F[m,1];; ^ User error: bad syntax Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Mon Mar 22 18:23:37 2004 Input: n:=1807082088687404805951656164405905566278102516769401349170127021450056662540244048387341127590812303371781887966563182013214880557; m:= 540525112162133938753086; d:=5; rem := n; coeffs :=[]; for i := 5 to 0 by -1 do temp := m^i; coeff := rem div temp; Append (~coeffs, coeff); rem -:= coeff*temp; end for; mdiv2 := m div 2; for i := 6 to 2 by -1 do if coeffs[i] gt mdiv2 then coeffs[i] -:= m; coeffs[i-1] +:= 1; end if; end for; print coeffs; P := PolynomialRing(Integers(),2); F := P!0; for i in [0..5] do F +:= coeffs[i+1]*X^(d-i)*Y^i; end for; print F; Evaluate (F,[m,1]); Output: Magma V2.10-6 Mon Mar 22 2004 18:23:34 on modular [Seed = 3958693520] ------------------------------------- [ 39165033600, 20503845316953, -171606349931490441956922, 80542667093060343063245, 10787315896624763483886, 198918697357741052852725 ] 39165033600*X^5 + 20503845316953*X^4*Y - 171606349931490441956922*X^3*Y^2 + 80542667093060343063245*X^2*Y^3 + 10787315896624763483886*X*Y^4 + 198918697357741052852725*Y^5 1807082088687404805951656164405905566278102516769401349170127021450056662540244\ 048387341127590812303371781887966563182013214880557 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Mon Mar 22 18:24:10 2004 Input: n:=1807082088687404805951656164405905566278102516769401349170127021450056662540244048387341127590812303371781887966563182013214880557; m:= 540525112162133938753086; d:=5; rem := n; coeffs :=[]; for i := 5 to 0 by -1 do temp := m^i; coeff := rem div temp; Append (~coeffs, coeff); rem -:= coeff*temp; end for; mdiv2 := m div 2; for i := 6 to 2 by -1 do if coeffs[i] gt mdiv2 then coeffs[i] -:= m; coeffs[i-1] +:= 1; end if; end for; P := PolynomialRing(Integers(),2); F := P!0; for i in [0..5] do F +:= coeffs[i+1]*X^(d-i)*Y^i; end for; print F; Output: Magma V2.10-6 Mon Mar 22 2004 18:24:07 on modular [Seed = 3808286584] ------------------------------------- 39165033600*X^5 + 20503845316953*X^4*Y - 171606349931490441956922*X^3*Y^2 + 80542667093060343063245*X^2*Y^3 + 10787315896624763483886*X*Y^4 + 198918697357741052852725*Y^5 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Mon Mar 22 18:25:48 2004 Input: n:=1807082088687404805951656164405905566278102516769401349170127021450056662540244048387341127590812303371781887966563182013214880557; m:= 540525112162133938753086; d:=5; rem := n; coeffs :=[]; for i := 5 to 0 by -1 do temp := m^i; coeff := rem div temp; Append (~coeffs, coeff); rem -:= coeff*temp; end for; mdiv2 := m div 2; for i := 6 to 2 by -1 do if coeffs[i] gt mdiv2 then coeffs[i] -:= m; coeffs[i-1] +:= 1; end if; end for; P := PolynomialRing(Integers(),2); F := P!0; for i in [0..5] do F +:= coeffs[i+1]*X^(d-i)*Y^i; end for; print F; F2 := X - Y*m; print F2; Output: Magma V2.10-6 Mon Mar 22 2004 18:25:45 on modular [Seed = 4058956805] ------------------------------------- 39165033600*X^5 + 20503845316953*X^4*Y - 171606349931490441956922*X^3*Y^2 + 80542667093060343063245*X^2*Y^3 + 10787315896624763483886*X*Y^4 + 198918697357741052852725*Y^5 X - 540525112162133938753086*Y Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Mon Mar 22 18:27:55 2004 Input: n:=1807082088687404805951656164405905566278102516769401349170127021450056662540244048387341127590812303371781887966563182013214880557; m:= 540525112162133938753086; d:=5; dlogd = d*Log(d); temp := 1.0/d * Log(n); e := dlgod + Sqrt(dlogd^2 + 4*temp*Log(temp)); B := Round(Exp(0.5*e); print B; rem := n; coeffs :=[]; for i := 5 to 0 by -1 do temp := m^i; coeff := rem div temp; Append (~coeffs, coeff); rem -:= coeff*temp; end for; mdiv2 := m div 2; for i := 6 to 2 by -1 do if coeffs[i] gt mdiv2 then coeffs[i] -:= m; coeffs[i-1] +:= 1; end if; end for; P := PolynomialRing(Integers(),2); F := P!0; for i in [0..5] do F +:= coeffs[i+1]*X^(d-i)*Y^i; end for; print F; F2 := X - Y*m; print F2; Output: Magma V2.10-6 Mon Mar 22 2004 18:27:51 on modular [Seed = 135741041] ------------------------------------- >> dlogd = d*Log(d); ^ User error: Identifier 'dlogd' has not been declared or assigned >> e := dlgod + Sqrt(dlogd^2 + 4*temp*Log(temp)); ^ User error: Identifier 'dlgod' has not been declared or assigned >> B := Round(Exp(0.5*e); ^ User error: bad syntax >> print B; ^ User error: Identifier 'B' has not been declared or assigned 39165033600*X^5 + 20503845316953*X^4*Y - 171606349931490441956922*X^3*Y^2 + 80542667093060343063245*X^2*Y^3 + 10787315896624763483886*X*Y^4 + 198918697357741052852725*Y^5 X - 540525112162133938753086*Y Total time: 3.269 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Mon Mar 22 18:28:05 2004 Input: n:=1807082088687404805951656164405905566278102516769401349170127021450056662540244048387341127590812303371781887966563182013214880557; m:= 540525112162133938753086; d:=5; dlogd := d*Log(d); temp := 1.0/d * Log(n); e := dlgod + Sqrt(dlogd^2 + 4*temp*Log(temp)); B := Round(Exp(0.5*e); print B; rem := n; coeffs :=[]; for i := 5 to 0 by -1 do temp := m^i; coeff := rem div temp; Append (~coeffs, coeff); rem -:= coeff*temp; end for; mdiv2 := m div 2; for i := 6 to 2 by -1 do if coeffs[i] gt mdiv2 then coeffs[i] -:= m; coeffs[i-1] +:= 1; end if; end for; P := PolynomialRing(Integers(),2); F := P!0; for i in [0..5] do F +:= coeffs[i+1]*X^(d-i)*Y^i; end for; print F; F2 := X - Y*m; print F2; Output: Magma V2.10-6 Mon Mar 22 2004 18:28:02 on modular [Seed = 453258647] ------------------------------------- >> e := dlgod + Sqrt(dlogd^2 + 4*temp*Log(temp)); ^ User error: Identifier 'dlgod' has not been declared or assigned >> B := Round(Exp(0.5*e); ^ User error: bad syntax >> print B; ^ User error: Identifier 'B' has not been declared or assigned 39165033600*X^5 + 20503845316953*X^4*Y - 171606349931490441956922*X^3*Y^2 + 80542667093060343063245*X^2*Y^3 + 10787315896624763483886*X*Y^4 + 198918697357741052852725*Y^5 X - 540525112162133938753086*Y Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Mon Mar 22 18:28:18 2004 Input: n:=1807082088687404805951656164405905566278102516769401349170127021450056662540244048387341127590812303371781887966563182013214880557; m:= 540525112162133938753086; d:=5; dlogd := d*Log(d); temp := 1.0/d * Log(n); e := dlogd + Sqrt(dlogd^2 + 4*temp*Log(temp)); B := Round(Exp(0.5*e); print B; rem := n; coeffs :=[]; for i := 5 to 0 by -1 do temp := m^i; coeff := rem div temp; Append (~coeffs, coeff); rem -:= coeff*temp; end for; mdiv2 := m div 2; for i := 6 to 2 by -1 do if coeffs[i] gt mdiv2 then coeffs[i] -:= m; coeffs[i-1] +:= 1; end if; end for; P := PolynomialRing(Integers(),2); F := P!0; for i in [0..5] do F +:= coeffs[i+1]*X^(d-i)*Y^i; end for; print F; F2 := X - Y*m; print F2; Output: Magma V2.10-6 Mon Mar 22 2004 18:28:15 on modular [Seed = 269428369] ------------------------------------- >> B := Round(Exp(0.5*e); ^ User error: bad syntax >> print B; ^ User error: Identifier 'B' has not been declared or assigned 39165033600*X^5 + 20503845316953*X^4*Y - 171606349931490441956922*X^3*Y^2 + 80542667093060343063245*X^2*Y^3 + 10787315896624763483886*X*Y^4 + 198918697357741052852725*Y^5 X - 540525112162133938753086*Y Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Mon Mar 22 18:28:39 2004 Input: n:=1807082088687404805951656164405905566278102516769401349170127021450056662540244048387341127590812303371781887966563182013214880557; m:= 540525112162133938753086; d:=5; dlogd := d*Log(d); temp := 1.0/d * Log(n); e := dlogd + Sqrt(dlogd^2 + 4*temp*Log(temp)); B := Round(Exp(0.5*e)); print B; rem := n; coeffs :=[]; for i := 5 to 0 by -1 do temp := m^i; coeff := rem div temp; Append (~coeffs, coeff); rem -:= coeff*temp; end for; mdiv2 := m div 2; for i := 6 to 2 by -1 do if coeffs[i] gt mdiv2 then coeffs[i] -:= m; coeffs[i-1] +:= 1; end if; end for; P := PolynomialRing(Integers(),2); F := P!0; for i in [0..5] do F +:= coeffs[i+1]*X^(d-i)*Y^i; end for; print F; F2 := X - Y*m; print F2; Output: Magma V2.10-6 Mon Mar 22 2004 18:28:36 on modular [Seed = 691412867] ------------------------------------- 552793791 39165033600*X^5 + 20503845316953*X^4*Y - 171606349931490441956922*X^3*Y^2 + 80542667093060343063245*X^2*Y^3 + 10787315896624763483886*X*Y^4 + 198918697357741052852725*Y^5 X - 540525112162133938753086*Y Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Mon Mar 22 18:37:56 2004 Input: n:=1807082088687404805951656164405905566278102516769401349170127021450056662540244048387341127590812303371781887966563182013214880557; m:= 540525112162133938753086; d:=5; alpha = -1.212611257; function ADR(u); if u le 1.0 then return 1.0; end if; return u^-u; end function; dlogd := d*Log(d); temp := 1.0/d * Log(n); e := dlogd + Sqrt(dlogd^2 + 4*temp*Log(temp)); B := Round(Exp(0.5*e)); print B; rem := n; coeffs :=[]; for i := 5 to 0 by -1 do temp := m^i; coeff := rem div temp; Append (~coeffs, coeff); rem -:= coeff*temp; end for; mdiv2 := m div 2; for i := 6 to 2 by -1 do if coeffs[i] gt mdiv2 then coeffs[i] -:= m; coeffs[i-1] +:= 1; end if; end for; P := PolynomialRing(Integers(),2); F1 := P!0; for i in [0..5] do F1 +:= coeffs[i+1]*X^(d-i)*Y^i; end for; print F1; F2 := X - Y*m; print F2; pi := Pi(RealField()); K := 1000; rating := 0.0; logB := Log(B); for i in [1..K] do theta := pi/K*(i-0.5); tmp := Abs(Evaluate(F1, [Cos(theta),Sin(theta)])); u1 := (Log(tmp)+alpha)/logB + d; tmp := Abs(Evaluate(F2, [Cos(theta),Sin(theta)])); u2 := Log(tmp) / logB + 1.0; rating +:= ADR(u1) * ADR(u2); end for; print rating; Output: Magma V2.10-6 Mon Mar 22 2004 18:37:52 on modular [Seed = 1096710559] ------------------------------------- >> alpha = -1.212611257; ^ User error: Identifier 'alpha' has not been declared or assigned 552793791 39165033600*X^5 + 20503845316953*X^4*Y - 171606349931490441956922*X^3*Y^2 + 80542667093060343063245*X^2*Y^3 + 10787315896624763483886*X*Y^4 + 198918697357741052852725*Y^5 X - 540525112162133938753086*Y >> u1 := (Log(tmp)+alpha)/logB + d; ^ User error: Identifier 'alpha' has not been declared or assigned 0.E-29 Total time: 3.119 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Mon Mar 22 18:38:35 2004 Input: n:=1807082088687404805951656164405905566278102516769401349170127021450056662540244048387341127590812303371781887966563182013214880557; m:= 540525112162133938753086; d:=5; alpha := -1.212611257; function ADR(u); if u le 1.0 then return 1.0; end if; return u^-u; end function; dlogd := d*Log(d); temp := 1.0/d * Log(n); e := dlogd + Sqrt(dlogd^2 + 4*temp*Log(temp)); B := Round(Exp(0.5*e)); print B; rem := n; coeffs :=[]; for i := 5 to 0 by -1 do temp := m^i; coeff := rem div temp; Append (~coeffs, coeff); rem -:= coeff*temp; end for; mdiv2 := m div 2; for i := 6 to 2 by -1 do if coeffs[i] gt mdiv2 then coeffs[i] -:= m; coeffs[i-1] +:= 1; end if; end for; P := PolynomialRing(Integers(),2); F1 := P!0; for i in [0..5] do F1 +:= coeffs[i+1]*X^(d-i)*Y^i; end for; print F1; F2 := X - Y*m; print F2; pi := Pi(RealField()); K := 1000; rating := 0.0; logB := Log(B); for i in [1..K] do theta := pi/K*(i-0.5); tmp := Abs(Evaluate(F1, [Cos(theta),Sin(theta)])); u1 := (Log(tmp)+alpha)/logB + d; tmp := Abs(Evaluate(F2, [Cos(theta),Sin(theta)])); u2 := Log(tmp) / logB + 1.0; rating +:= ADR(u1) * ADR(u2); end for; print rating; Output: Magma V2.10-6 Mon Mar 22 2004 18:38:31 on modular [Seed = 1447653039] ------------------------------------- 552793791 39165033600*X^5 + 20503845316953*X^4*Y - 171606349931490441956922*X^3*Y^2 + 80542667093060343063245*X^2*Y^3 + 10787315896624763483886*X*Y^4 + 198918697357741052852725*Y^5 X - 540525112162133938753086*Y 0.00000238580250515333119932401441110 Total time: 4.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Mon Mar 22 18:46:46 2004 Input: n:=1807082088687404805951656164405905566278102516769401349170127021450056662540244048387341127590812303371781887966563182013214880557; m:= 540525112162133938753086; d:=5; alpha := -1.212611257; function ADR(u); if u le 1.0 then return 1.0; end if; return u^-u; end function; dlogd := d*Log(d); temp := 1.0/d * Log(n); e := dlogd + Sqrt(dlogd^2 + 4*temp*Log(temp)); B := Round(Exp(0.5*e)); print B; rem := n; coeffs :=[]; for i := 5 to 0 by -1 do temp := m^i; coeff := rem div temp; Append (~coeffs, coeff); rem -:= coeff*temp; end for; mdiv2 := m div 2; for i := 6 to 2 by -1 do if coeffs[i] gt mdiv2 then coeffs[i] -:= m; coeffs[i-1] +:= 1; end if; end for; P := PolynomialRing(Integers(),2); F1 := P!0; for i in [0..5] do F1 +:= coeffs[i+1]*X^(d-i)*Y^i; end for; print F1; F2 := X - Y*m; print F2; pi := Pi(RealField()); K := 5; rating := 0.0; logB := Log(B); for i in [1..K] do theta := pi/K*(i-0.5); print theta; tmp := Abs(Evaluate(F1, [Cos(theta),Sin(theta)])); print tmp; u1 := (Log(tmp)+alpha)/logB + d; print u1; tmp := Abs(Evaluate(F2, [Cos(theta),Sin(theta)])); print tmp; u2 := Log(tmp) / logB + 1.0; print u2; rating +:= ADR(u1) * ADR(u2); print rating; end for; Output: Magma V2.10-6 Mon Mar 22 2004 18:46:43 on modular [Seed = 2103592848] ------------------------------------- 552793791 39165033600*X^5 + 20503845316953*X^4*Y - 171606349931490441956922*X^3*Y^2 + 80542667093060343063245*X^2*Y^3 + 10787315896624763483886*X*Y^4 + 198918697357741052852725*Y^5 X - 540525112162133938753086*Y 0.314159265358979323846264338325 11292881581228151885354.6253685951 7.462226924922737449292014047839049946073 167031445544523968846653.14435958862 3.65629173324337306592515302119 0.00000000267803326305375467176057723549 0.94247779607693797153879301497 63580635198533061111107.14758195380248695371 7.548073612544916215659157419512805747016 437294001625590938223196.50763162803196770767 3.70410097099475658666562719425 0.00000000452972939911782344109226591351 1.57079632679489661923132169162 198918697357741052852725. 7.604733282631076199538861997318096133864 540525112162133938753086.00000000000 3.71462904540126645597575735765 0.0000000060522626834080352319723461896 2.199114857512855266923850368252 103766061335620468102639.78942545819682807817 7.572406347266487288518570477314853533548 437294001625590938223197.68320554380994558130 3.70410097099475658666562732779 0.0000000077726450369750288290224071227 2.82743338823081391461637904490 16713390221760801717136.8748812675 7.481701737515437258943925934006610034889 167031445544523968846655.04647827148 3.65629173324337306592515358690 0.0000000102981497705605779934930583642 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Mon Mar 22 19:03:18 2004 Input: n:=1807082088687404805951656164405905566278102516769401349170127021450056662540244048387341127590812303371781887966563182013214880557; m:= 514358562175166398546636; d:=5; alpha := -1.381646445 function ADR(u); if u le 1.0 then return 1.0; end if; return u^-u; end function; dlogd := d*Log(d); temp := 1.0/d * Log(n); e := dlogd + Sqrt(dlogd^2 + 4*temp*Log(temp)); B := Round(Exp(0.5*e)); print B; rem := n; coeffs :=[]; for i := 5 to 0 by -1 do temp := m^i; coeff := rem div temp; Append (~coeffs, coeff); rem -:= coeff*temp; end for; mdiv2 := m div 2; for i := 6 to 2 by -1 do if coeffs[i] gt mdiv2 then coeffs[i] -:= m; coeffs[i-1] +:= 1; end if; end for; P := PolynomialRing(Integers(),2); F1 := P!0; for i in [0..5] do F1 +:= coeffs[i+1]*X^(d-i)*Y^i; end for; print F1; F2 := X - Y*m; print F2; pi := Pi(RealField()); K := 1000; rating := 0.0; logB := Log(B); for i in [1..K] do theta := pi/K*(i-0.5); // print theta; tmp := Abs(Evaluate(F1, [Cos(theta),Sin(theta)])); // print tmp; u1 := (Log(tmp)+alpha)/logB + d; // print u1; tmp := Abs(Evaluate(F2, [Cos(theta),Sin(theta)])); // print tmp; u2 := Log(tmp) / logB + 1.0; // print u2; rating +:= ADR(u1) * ADR(u2); // print rating; end for; print rating; Output: Magma V2.10-6 Mon Mar 22 2004 19:03:15 on modular [Seed = 3469864963] ------------------------------------- >> function ADR(u); ^ User error: bad syntax >> if u le 1.0 then ^ User error: Identifier 'u' has not been declared or assigned >> return u^-u; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax 552793791 50193561600*X^5 + 64765082860480*X^4*Y + 143762033203997405985440*X^3*Y^2 - 35729104839883107152522*X^2*Y^3 + 62547591101890478191896*X*Y^4 + 98976029826532472331693*Y^5 X - 514358562175166398546636*Y >> u1 := (Log(tmp)+alpha)/logB + d; ^ User error: Identifier 'alpha' has not been declared or assigned 0.E-29 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Mon Mar 22 19:03:37 2004 Input: n:=1807082088687404805951656164405905566278102516769401349170127021450056662540244048387341127590812303371781887966563182013214880557; m:= 514358562175166398546636; d:=5; alpha := -1.381646445; function ADR(u); if u le 1.0 then return 1.0; end if; return u^-u; end function; dlogd := d*Log(d); temp := 1.0/d * Log(n); e := dlogd + Sqrt(dlogd^2 + 4*temp*Log(temp)); B := Round(Exp(0.5*e)); print B; rem := n; coeffs :=[]; for i := 5 to 0 by -1 do temp := m^i; coeff := rem div temp; Append (~coeffs, coeff); rem -:= coeff*temp; end for; mdiv2 := m div 2; for i := 6 to 2 by -1 do if coeffs[i] gt mdiv2 then coeffs[i] -:= m; coeffs[i-1] +:= 1; end if; end for; P := PolynomialRing(Integers(),2); F1 := P!0; for i in [0..5] do F1 +:= coeffs[i+1]*X^(d-i)*Y^i; end for; print F1; F2 := X - Y*m; print F2; pi := Pi(RealField()); K := 1000; rating := 0.0; logB := Log(B); for i in [1..K] do theta := pi/K*(i-0.5); // print theta; tmp := Abs(Evaluate(F1, [Cos(theta),Sin(theta)])); // print tmp; u1 := (Log(tmp)+alpha)/logB + d; // print u1; tmp := Abs(Evaluate(F2, [Cos(theta),Sin(theta)])); // print tmp; u2 := Log(tmp) / logB + 1.0; // print u2; rating +:= ADR(u1) * ADR(u2); // print rating; end for; print rating; Output: Magma V2.10-6 Mon Mar 22 2004 19:03:32 on modular [Seed = 3352885533] ------------------------------------- 552793791 50193561600*X^5 + 64765082860480*X^4*Y + 143762033203997405985440*X^3*Y^2 - 35729104839883107152522*X^2*Y^3 + 62547591101890478191896*X*Y^4 + 98976029826532472331693*Y^5 X - 514358562175166398546636*Y 0.00000258504459060183889596422401589 Total time: 4.199 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Mon Mar 22 19:06:22 2004 Input: n:=1807082088687404805951656164405905566278102516769401349170127021450056662540244048387341127590812303371781887966563182013214880557; m:= 514358562175166398546636; d:=5; alpha := -1.381646445; function ADR(u); if u le 1.0 then return 1.0; end if; return u^-u; end function; dlogd := d*Log(d); temp := 1.0/d * Log(n); e := dlogd + Sqrt(dlogd^2 + 4*temp*Log(temp)); B := Round(Exp(0.5*e)); print B; rem := n; coeffs :=[]; for i := 5 to 0 by -1 do temp := m^i; coeff := rem div temp; Append (~coeffs, coeff); rem -:= coeff*temp; end for; mdiv2 := m div 2; for i := 6 to 2 by -1 do if coeffs[i] gt mdiv2 then coeffs[i] -:= m; coeffs[i-1] +:= 1; end if; end for; P := PolynomialRing(Integers(),2); F1 := P!0; for i in [0..5] do F1 +:= coeffs[i+1]*X^(d-i)*Y^i; end for; print F1; F2 := X - Y*m; print F2; pi := Pi(RealField()); K := 1000; rating := 0.0; logB := Log(B); for i in [1..K] do theta := pi/K*(i-0.5); // print theta; tmp := Abs(Evaluate(F1, [Cos(theta),Sin(theta)])); // print tmp; u1 := (Log(tmp)+alpha)/logB + d; // print u1; tmp := Abs(Evaluate(F2, [Cos(theta),Sin(theta)])); // print tmp; u2 := Log(tmp) / logB + 1.0; // print u2; rating +:= ADR(u1) * ADR(u2); // print rating; end for; print rating/K; Output: Magma V2.10-6 Mon Mar 22 2004 19:06:17 on modular [Seed = 3636979631] ------------------------------------- 552793791 50193561600*X^5 + 64765082860480*X^4*Y + 143762033203997405985440*X^3*Y^2 - 35729104839883107152522*X^2*Y^3 + 62547591101890478191896*X*Y^4 + 98976029826532472331693*Y^5 X - 514358562175166398546636*Y 0.00000000258504459060183889596422401583 Total time: 4.169 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Mon Mar 22 20:59:50 2004 Input: > F := EllipticCurve([0, -2]); > F; Output: Magma V2.10-6 Mon Mar 22 2004 20:59:47 on modular [Seed = 3352829403] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 2 over Rational Field Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Mon Mar 22 21:00:18 2004 Input: > F := EllipticCurve([0, -2]); > F; > MW, f := MordellWeilGroup(F); > MW; Output: Magma V2.10-6 Mon Mar 22 2004 21:00:15 on modular [Seed = 3570077428] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 2 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) Total time: 3.149 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Mon Mar 22 21:02:10 2004 Input: > F := EllipticCurve([0, -2]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i in [-4..4] | > IsIntegral(pt) where pt is i*a; > intpts; > #intpts; Output: Magma V2.10-6 Mon Mar 22 2004 21:02:07 on modular [Seed = 4109053540] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 2 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (3 : 5 : 1) >> IsIntegral(pt) where pt is i*a; ^ User error: bad syntax >> intpts; ^ User error: Identifier 'intpts' has not been declared or assigned >> #intpts;; ^ User error: Identifier 'intpts' has not been declared or assigned Total time: 3.199 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Mon Mar 22 21:02:58 2004 Input: > F := EllipticCurve([0, -2]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i in [-4..4] | > IsIntegral(pt) where pt is i*a]; > intpts; > #intpts; Output: Magma V2.10-6 Mon Mar 22 2004 21:02:55 on modular [Seed = 336318155] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 2 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (3 : 5 : 1) [ (3 : -5 : 1), (3 : 5 : 1) ] 2 Total time: 3.159 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Mon Mar 22 21:03:47 2004 Input: > F := EllipticCurve([0, -128]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i in [-4..4] | > IsIntegral(pt) where pt is i*a]; > intpts; > #intpts; Output: Magma V2.10-6 Mon Mar 22 2004 21:03:44 on modular [Seed = 18799121] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 128 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (12 : 40 : 1) [ (12 : -40 : 1), (12 : 40 : 1) ] 2 Total time: 3.099 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Mon Mar 22 21:04:06 2004 Input: > F := EllipticCurve([0, -128]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i in [-40..40] | > IsIntegral(pt) where pt is i*a]; > intpts; > #intpts; Output: Magma V2.10-6 Mon Mar 22 2004 21:04:03 on modular [Seed = 169201929] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 128 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (12 : 40 : 1) [ (12 : -40 : 1), (12 : 40 : 1) ] 2 Total time: 3.389 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Mon Mar 22 21:04:38 2004 Input: > F := EllipticCurve([0, -1458]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i in [-40..40] | > IsIntegral(pt) where pt is i*a]; > intpts; > #intpts; Output: Magma V2.10-6 Mon Mar 22 2004 21:04:34 on modular [Seed = 925428757] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 1458 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (27 : 135 : 1) [ (27 : -135 : 1), (27 : 135 : 1) ] 2 Total time: 3.369 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Mon Mar 22 21:05:28 2004 Input: > F := EllipticCurve([0, -31250]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i in [-40..40] | > IsIntegral(pt) where pt is i*a]; > intpts; > #intpts; Output: Magma V2.10-6 Mon Mar 22 2004 21:05:25 on modular [Seed = 607911761] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 31250 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (75 : 625 : 1) [ (75 : -625 : 1), (75 : 625 : 1) ] 2 Total time: 3.389 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Mon Mar 22 21:08:15 2004 Input: > F := EllipticCurve([0, -2]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i in [-4..4] | > pt is i*a]; > intpts; Output: Magma V2.10-6 Mon Mar 22 2004 21:08:12 on modular [Seed = 775025202] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 2 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (3 : 5 : 1) >> pt is i*a]; ^ User error: bad syntax >> intpts;; ^ User error: Identifier 'intpts' has not been declared or assigned Total time: 3.139 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Mon Mar 22 21:09:30 2004 Input: > F := EllipticCurve([0, -2]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > rtlpts := [ pt : i in [-4..4] | > pt is i*a]; > rtlpts; Output: Magma V2.10-6 Mon Mar 22 2004 21:09:26 on modular [Seed = 1464371985] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 2 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (3 : 5 : 1) >> pt is i*a]; ^ User error: bad syntax >> rtlpts;; ^ User error: Identifier 'rtlpts' has not been declared or assigned Total time: 3.179 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Mon Mar 22 21:09:47 2004 Input: > F := EllipticCurve([0, -2]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > rtlpts := [ pt : i in [-4..4] | where pt is i*a]; > rtlpts; Output: Magma V2.10-6 Mon Mar 22 2004 21:09:44 on modular [Seed = 1080007736] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 2 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (3 : 5 : 1) >> rtlpts := [ pt : i in [-4..4] | where pt is i*a]; ^ User error: bad syntax >> rtlpts;; ^ User error: Identifier 'rtlpts' has not been declared or assigned Total time: 3.209 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Mon Mar 22 21:10:09 2004 Input: > F := EllipticCurve([0, -2]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > rtlpts := [ pt : i in [-4..4] | > where pt is i*a]; > rtlpts; Output: Magma V2.10-6 Mon Mar 22 2004 21:10:06 on modular [Seed = 1886366750] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 2 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (3 : 5 : 1) >> where pt is i*a]; ^ User error: bad syntax >> rtlpts;; ^ User error: Identifier 'rtlpts' has not been declared or assigned Total time: 3.089 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Mon Mar 22 21:11:06 2004 Input: > F := EllipticCurve([0, -2]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i in [-4..4] ]; > intpts; Output: Magma V2.10-6 Mon Mar 22 2004 21:11:03 on modular [Seed = 2036770270] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 2 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (3 : 5 : 1) >> intpts := [ pt : i in [-4..4] ]; ^ User error: Identifier 'pt' has not been declared or assigned >> intpts;; ^ User error: Identifier 'intpts' has not been declared or assigned Total time: 3.139 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Mon Mar 22 21:13:10 2004 Input: > F := EllipticCurve([0, -2]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i in [-4..4] | pt is i*a ]; > intpts; Output: Magma V2.10-6 Mon Mar 22 2004 21:13:07 on modular [Seed = 1669119552] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 2 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (3 : 5 : 1) >> intpts := [ pt : i in [-4..4] | pt is i*a ]; ^ User error: bad syntax >> intpts;; ^ User error: Identifier 'intpts' has not been declared or assigned Total time: 3.149 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Mon Mar 22 21:13:34 2004 Input: > F := EllipticCurve([0, -2]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i in [-4..4] | pt where pt is i*a ]; > intpts; Output: Magma V2.10-6 Mon Mar 22 2004 21:13:31 on modular [Seed = 1819521335] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 2 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (3 : 5 : 1) >> intpts := [ pt : i in [-4..4] | pt where pt is i*a ]; ^ Runtime error in sequence construction: Logical expected >> intpts;; ^ User error: Identifier 'intpts' has not been declared or assigned Total time: 3.189 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Mon Mar 22 21:14:04 2004 Input: > F := EllipticCurve([0, -2]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i in [-4..4] | IsIntegral(pt) where pt is i*a ]; > intpts; Output: Magma V2.10-6 Mon Mar 22 2004 21:14:01 on modular [Seed = 2508867820] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 2 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (3 : 5 : 1) [ (3 : -5 : 1), (3 : 5 : 1) ] Total time: 3.099 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Mon Mar 22 21:14:25 2004 Input: > F := EllipticCurve([0, -2]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i in [-4..4] | IsRational(pt) where pt is i*a ]; > intpts; Output: Magma V2.10-6 Mon Mar 22 2004 21:14:22 on modular [Seed = 2659271664] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 2 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (3 : 5 : 1) >> intpts := [ pt : i in [-4..4] | IsRational(pt) where pt is i*a ]; ^ User error: Identifier 'IsRational' has not been declared or assigned >> intpts;; ^ User error: Identifier 'intpts' has not been declared or assigned Total time: 3.179 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Mon Mar 22 21:20:53 2004 Input: > F := EllipticCurve([0, -2]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; >2*a; >3*a; Output: Magma V2.10-6 Mon Mar 22 2004 21:20:50 on modular [Seed = 3148113065] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 2 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (3 : 5 : 1) (129/100 : -383/1000 : 1) (164323/29241 : -66234835/5000211 : 1) Total time: 3.189 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Mon Mar 22 21:22:39 2004 Input: > F := EllipticCurve([0, -2000000]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; >2*a; >3*a; Output: Magma V2.10-6 Mon Mar 22 2004 21:22:36 on modular [Seed = 2864018902] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 2000000 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (300 : 5000 : 1) (129 : -383 : 1) (16432300/29241 : -66234835000/5000211 : 1) Total time: 3.239 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Mon Mar 22 21:24:19 2004 Input: > F := EllipticCurve([0, -2000000*(171)^6]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; >2*a; >3*a; Output: Magma V2.10-6 Mon Mar 22 2004 21:24:16 on modular [Seed = 3553365011] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 50004220089042000000 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (8772300 : 25001055000 : 1) (3772089 : -1915080813 : 1) (16432300 : -66234835000 : 1) Total time: 3.099 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Mon Mar 22 21:26:29 2004 Input: > F := EllipticCurve([0, -2000000*(171)^6]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i, j in [-10..10] | > IsIntegral(pt) where pt is i*a + j*b] ; > intpts; Output: Magma V2.10-6 Mon Mar 22 2004 21:26:26 on modular [Seed = 3808232096] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 50004220089042000000 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (8772300 : 25001055000 : 1) >> IsIntegral(pt) where pt is i*a + j*b] ; ^ User error: Identifier 'b' has not been declared or assigned >> intpts;; ^ User error: Identifier 'intpts' has not been declared or assigned Total time: 3.209 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Mon Mar 22 21:26:49 2004 Input: > F := EllipticCurve([0, -2000000*(171)^6]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i in [-10..10] | > IsIntegral(pt) where pt is i*a] ; > intpts; Output: Magma V2.10-6 Mon Mar 22 2004 21:26:46 on modular [Seed = 4008775320] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 50004220089042000000 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (8772300 : 25001055000 : 1) [ (16432300 : 66234835000 : 1), (3772089 : 1915080813 : 1), (8772300 : -25001055000 : 1), (8772300 : 25001055000 : 1), (3772089 : -1915080813 : 1), (16432300 : -66234835000 : 1) ] Total time: 3.139 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Mon Mar 22 21:27:34 2004 Input: > F := EllipticCurve([0, -2000000*(171)^6]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i in [-40..100] | > IsIntegral(pt) where pt is i*a] ; > intpts; Output: Magma V2.10-6 Mon Mar 22 2004 21:27:27 on modular [Seed = 419887495] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 50004220089042000000 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (8772300 : 25001055000 : 1) [ (16432300 : 66234835000 : 1), (3772089 : 1915080813 : 1), (8772300 : -25001055000 : 1), (8772300 : 25001055000 : 1), (3772089 : -1915080813 : 1), (16432300 : -66234835000 : 1) ] Total time: 7.579 seconds, Total memory usage: 2.42MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 21:55:37 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-6 Mon Mar 22 2004 21:55:34 on modular [Seed = 1581365609] ------------------------------------- >> I := ideal; ^ User error: Identifier 'x1' has not been declared or assigned >> GroebnerBasis(I); ^ User error: Identifier 'I' has not been declared or assigned Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 21:56:20 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-6 Mon Mar 22 2004 21:56:17 on modular [Seed = 1230417417] ------------------------------------- [ x^2*y^2 + 2*x*y*z*w + z^2*w^2, x^2*z^2 + 2*x*y*z*w + y^2*w^2, x^2*w^2 + 2*x*y*z*w + y^2*z^2, x*y^4*w^2 - x*z^4*w^2 + 2*y^3*z*w^3 - 2*y*z^3*w^3, 2*x*y^3*z*w - 2*x*y*z*w^3 + y^4*w^2 + y^2*z^4 - y^2*w^4 - z^4*w^2, x*y^2*z^4 - x*y^2*w^4 + 2*y^3*z^3*w - 2*y^3*z*w^3, 2*x*y^2*z^2*w^3 - 2*x*z^2*w^5 - y^5*z*w^2 - y^3*z^5 + 4*y^3*z^3*w^2 + y^3*z*w^4 + y*z^5*w^2 - 4*y*z^3*w^4, 2*x*y^2*z*w^4 - 2*x*z^5*w^2 - y^5*w^3 - y^3*z^4*w + 4*y^3*z^2*w^3 + y^3*w^5 - 3*y*z^4*w^3, 2*x*y^2*w^5 - 2*x*z^2*w^5 - y^5*z*w^2 + 4*y^3*z*w^4 + y*z^5*w^2 - 4*y*z^3*w^4, 2*x*y*z^3*w - 2*x*y*z*w^3 + y^2*z^4 - y^2*w^4, x*z^6*w^2 - x*z^2*w^6 + 2*y*z^5*w^3 - 2*y*z^3*w^5, 2*x*z^5*w^3 - 2*x*z^3*w^5 + y*z^6*w^2 - y*z^2*w^6, 2*x*z^4*w^5 - 2*x*z^2*w^7 - y*z^7*w^2 + 4*y*z^5*w^4 - 3*y*z^3*w^6, y^6*z*w^2 - 3*y^4*z*w^4 + y^2*z^7 - 3*y^2*z^5*w^2 + 3*y^2*z^3*w^4 + 2*y^2*z*w^6 - z^7*w^2 + 3*z^5*w^4 - 3*z^3*w^6, y^6*w^3 - 3*y^4*w^5 + 3*y^2*w^7 - z^6*w^3 + 3*z^4*w^5 - 3*z^2*w^7, y^4*z^2 - y^4*w^2 - y^2*z^4 + y^2*w^4 + z^4*w^2 - z^2*w^4, y^3*z^6 - 3*y^3*z^4*w^2 + 3*y^3*z^2*w^4 - y^3*w^6, y^2*z^8 - 2*y^2*z^6*w^2 + 2*y^2*z^2*w^6 - y^2*w^8 - z^8*w^2 + 3*z^6*w^4 - 3*z^4*w^6 + z^2*w^8, y^2*z^7*w - 3*y^2*z^5*w^3 + 3*y^2*z^3*w^5 - y^2*z*w^7, y^2*z^6*w^3 - 3*y^2*z^4*w^5 + 3*y^2*z^2*w^7 - y^2*w^9 - z^8*w^3 + 3*z^6*w^5 - 3*z^4*w^7 + z^2*w^9, y*z^8*w^2 - 3*y*z^6*w^4 + 3*y*z^4*w^6 - y*z^2*w^8, z^9*w^3 - 3*z^7*w^5 + 3*z^5*w^7 - z^3*w^9 ] Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 21:56:59 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (x*y+z*w)*(x*z+y*w)*(x*w+y*z) in I; Output: Magma V2.10-6 Mon Mar 22 2004 21:56:56 on modular [Seed = 1936495642] ------------------------------------- [ x^2*y^2 + 2*x*y*z*w + z^2*w^2, x^2*z^2 + 2*x*y*z*w + y^2*w^2, x^2*w^2 + 2*x*y*z*w + y^2*z^2, x*y^4*w^2 - x*z^4*w^2 + 2*y^3*z*w^3 - 2*y*z^3*w^3, 2*x*y^3*z*w - 2*x*y*z*w^3 + y^4*w^2 + y^2*z^4 - y^2*w^4 - z^4*w^2, x*y^2*z^4 - x*y^2*w^4 + 2*y^3*z^3*w - 2*y^3*z*w^3, 2*x*y^2*z^2*w^3 - 2*x*z^2*w^5 - y^5*z*w^2 - y^3*z^5 + 4*y^3*z^3*w^2 + y^3*z*w^4 + y*z^5*w^2 - 4*y*z^3*w^4, 2*x*y^2*z*w^4 - 2*x*z^5*w^2 - y^5*w^3 - y^3*z^4*w + 4*y^3*z^2*w^3 + y^3*w^5 - 3*y*z^4*w^3, 2*x*y^2*w^5 - 2*x*z^2*w^5 - y^5*z*w^2 + 4*y^3*z*w^4 + y*z^5*w^2 - 4*y*z^3*w^4, 2*x*y*z^3*w - 2*x*y*z*w^3 + y^2*z^4 - y^2*w^4, x*z^6*w^2 - x*z^2*w^6 + 2*y*z^5*w^3 - 2*y*z^3*w^5, 2*x*z^5*w^3 - 2*x*z^3*w^5 + y*z^6*w^2 - y*z^2*w^6, 2*x*z^4*w^5 - 2*x*z^2*w^7 - y*z^7*w^2 + 4*y*z^5*w^4 - 3*y*z^3*w^6, y^6*z*w^2 - 3*y^4*z*w^4 + y^2*z^7 - 3*y^2*z^5*w^2 + 3*y^2*z^3*w^4 + 2*y^2*z*w^6 - z^7*w^2 + 3*z^5*w^4 - 3*z^3*w^6, y^6*w^3 - 3*y^4*w^5 + 3*y^2*w^7 - z^6*w^3 + 3*z^4*w^5 - 3*z^2*w^7, y^4*z^2 - y^4*w^2 - y^2*z^4 + y^2*w^4 + z^4*w^2 - z^2*w^4, y^3*z^6 - 3*y^3*z^4*w^2 + 3*y^3*z^2*w^4 - y^3*w^6, y^2*z^8 - 2*y^2*z^6*w^2 + 2*y^2*z^2*w^6 - y^2*w^8 - z^8*w^2 + 3*z^6*w^4 - 3*z^4*w^6 + z^2*w^8, y^2*z^7*w - 3*y^2*z^5*w^3 + 3*y^2*z^3*w^5 - y^2*z*w^7, y^2*z^6*w^3 - 3*y^2*z^4*w^5 + 3*y^2*z^2*w^7 - y^2*w^9 - z^8*w^3 + 3*z^6*w^5 - 3*z^4*w^7 + z^2*w^9, y*z^8*w^2 - 3*y*z^6*w^4 + 3*y*z^4*w^6 - y*z^2*w^8, z^9*w^3 - 3*z^7*w^5 + 3*z^5*w^7 - z^3*w^9 ] false Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 22:18:17 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (x*y+z*w)*(x*z+y*w)*(x*w+y*z) in I; Output: Magma V2.10-6 Mon Mar 22 2004 22:18:13 on modular [Seed = 2391892714] ------------------------------------- [ x^2*y^2 + 2*x*y*z*w + z^2*w^2, x^2*z^2 + 2*x*y*z*w + y^2*w^2, x^2*w^2 + 2*x*y*z*w + y^2*z^2, x*y^4*w^2 - x*z^4*w^2 + 2*y^3*z*w^3 - 2*y*z^3*w^3, 20*x*y^3*z^3 + 60480*y^2*z^2*w^3 - 55440*y^2*w^5 - 4620*z^4*w^3, 120*x*y^3*z^2 + 240*y^2*z^3*w - 220*z^3*w^3, 2*x*y^3*z*w + 218*x*y*z*w^3 + y^4*w^2 + y^2*z^4 + 120*y^2*z^2*w^2 - y^2*w^4 - z^4*w^2, 20*x*y^3*w^4 + 40*y^2*z*w^5 + 420*z^5*w^3 + 460*z^3*w^5, 220*x*y^3*w^3 + 1440*y^2*z*w^4 + 120*z^5*w^2 - 1440*z^3*w^4, x*y^2*z^4 + 119*x*y^2*w^4 + 2*y^3*z^3*w + 18*y^3*z*w^3, 120*x*y^2*z^3 + 240*y^3*z^2*w - 220*y^3*w^3, 2*x*y^2*z^2*w^3 + 18*x*z^2*w^5 + 9*y^5*z*w^2 + 9*y^3*z^5 + 384*y^3*z^3*w^2 + 491*y^3*z*w^4 + 491*y*z^5*w^2 + 36*y*z^3*w^4, 20*x*y^2*z^2*w + 420*y^3*z^3, 2*x*y^2*z*w^4 + 18*x*z^5*w^2 + 9*y^5*w^3 + 9*y^3*z^4*w + 384*y^3*z^2*w^3 + 491*y^3*w^5 + 27*y*z^4*w^3, 20*x*y^2*z*w^3 + 4920*y^3*z^2*w^2 - 4500*y^3*w^4, 2*x*y^2*w^5 + 18*x*z^2*w^5 + 9*y^5*z*w^2 + 384*y^3*z*w^4 + 491*y*z^5*w^2 + 36*y*z^3*w^4, 120*x*y^2*w^4 + 20*y^3*z*w^3, 2*x*y*z^3*w + 218*x*y*z*w^3 + y^2*z^4 + 120*y^2*z^2*w^2 - y^2*w^4, 20*x*y*z^2*w^3 + 4920*y^2*z^3*w^2 - 4500*z^3*w^4, 20*x*y*z*w^4 + 58920*y^2*z^2*w^3 - 54000*y^2*w^5 - 4500*z^4*w^3, 220*x*y*z*w + 120*y^2*z^2, x*z^6*w^2 + 19*x*z^2*w^6 + 2*y*z^5*w^3 + 418*y*z^3*w^5, 2*x*z^5*w^3 + 18*x*z^3*w^5 + y*z^6*w^2 + 420*y*z^4*w^4 + 499*y*z^2*w^6, 20*x*z^5*w^2 + 40*y*z^4*w^3 + 380*y*z^2*w^5, 2*x*z^4*w^5 + 18*x*z^2*w^7 + 9*y*z^7*w^2 + 384*y*z^5*w^4 + 27*y*z^3*w^6, 20*x*z^4*w^3 + 420*y*z^5*w^2, 20*x*z^3*w^4 + 420*y*z^4*w^3, 220*x*z^3*w^3 + 120*y*z^4*w^2, 20*x*z^2*w^5 + 420*y*z^3*w^4, 120*x*z^2*w^4 + 20*y*z^3*w^3, y^6*z*w^2 + 7*y^4*z*w^4 + y^2*z^7 + 7*y^2*z^5*w^2 + 383*y^2*z^3*w^4 + 492*y^2*z*w^6 + 9*z^7*w^2 + 373*z^5*w^4 + 227*z^3*w^6, y^6*w^3 + 7*y^4*w^5 + 383*y^2*w^7 + 9*z^6*w^3 + 373*z^4*w^5 + 5227*z^2*w^7, y^4*z^2 + 9*y^4*w^2 + 9*y^2*z^4 - 120*y^2*z^2*w^2 - 9*y^2*w^4 - 9*z^4*w^2 + 119*z^2*w^4, 10*y^4*w^2 - 120*y^2*w^4 - 10*z^4*w^2 + 120*z^2*w^4, y^3*z^6 + 7*y^3*z^4*w^2 + 383*y^3*z^2*w^4 + 109*y^3*w^6, 500*y^3*z^3, 500*y^3*z^2*w^3, 6000*y^3*z^2*w^2 - 5500*y^3*w^4, 500*y^3*z*w^4, 500*y^3*w^5, y^2*z^8 + 8*y^2*z^6*w^2 + 172*y^2*z^2*w^6 + 319*y^2*w^8 + 9*z^8*w^2 + 3*z^6*w^4 + 167*z^4*w^6 + 2321*z^2*w^8, y^2*z^7*w + 7*y^2*z^5*w^3 + 383*y^2*z^3*w^5 + 109*y^2*z*w^7, y^2*z^6*w^3 + 7*y^2*z^4*w^5 + 383*y^2*z^2*w^7 + 109*y^2*w^9 + 9*z^8*w^3 + 3*z^6*w^5 + 167*z^4*w^7 + 1321*z^2*w^9, 10*y^2*z^4 - 120*y^2*z^2*w^2 + 110*y^2*w^4, 500*y^2*z^3*w^3, 6000*y^2*z^3*w^2 - 5500*z^3*w^4, 72000*y^2*z^2*w^3 - 66000*y^2*w^5 - 5500*z^4*w^3, 500*y^2*z*w^5, 500*y^2*w^7 + 5000*z^2*w^7, y*z^8*w^2 + 7*y*z^6*w^4 + 383*y*z^4*w^6 + 109*y*z^2*w^8, 500*y*z^5*w^2, 500*y*z^4*w^3, 500*y*z^3*w^4, 500*y*z^2*w^5, z^9*w^3 + 7*z^7*w^5 + 383*z^5*w^7 + 109*z^3*w^9, 10*z^6*w^2 - 120*z^4*w^4 + 110*z^2*w^6, 500*z^5*w^3, 500*z^3*w^5, 5500*z^2*w^7 ] false Total time: 3.069 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Mon Mar 22 22:18:32 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (x*y+z*w)*(x*z+y*w)*(x*w+y*z)*(11*x*w+y*z) in I; Output: Magma V2.10-6 Mon Mar 22 2004 22:18:29 on modular [Seed = 3114685741] ------------------------------------- [ x^2*y^2 + 2*x*y*z*w + z^2*w^2, x^2*z^2 + 2*x*y*z*w + y^2*w^2, x^2*w^2 + 2*x*y*z*w + y^2*z^2, x*y^4*w^2 - x*z^4*w^2 + 2*y^3*z*w^3 - 2*y*z^3*w^3, 20*x*y^3*z^3 + 60480*y^2*z^2*w^3 - 55440*y^2*w^5 - 4620*z^4*w^3, 120*x*y^3*z^2 + 240*y^2*z^3*w - 220*z^3*w^3, 2*x*y^3*z*w + 218*x*y*z*w^3 + y^4*w^2 + y^2*z^4 + 120*y^2*z^2*w^2 - y^2*w^4 - z^4*w^2, 20*x*y^3*w^4 + 40*y^2*z*w^5 + 420*z^5*w^3 + 460*z^3*w^5, 220*x*y^3*w^3 + 1440*y^2*z*w^4 + 120*z^5*w^2 - 1440*z^3*w^4, x*y^2*z^4 + 119*x*y^2*w^4 + 2*y^3*z^3*w + 18*y^3*z*w^3, 120*x*y^2*z^3 + 240*y^3*z^2*w - 220*y^3*w^3, 2*x*y^2*z^2*w^3 + 18*x*z^2*w^5 + 9*y^5*z*w^2 + 9*y^3*z^5 + 384*y^3*z^3*w^2 + 491*y^3*z*w^4 + 491*y*z^5*w^2 + 36*y*z^3*w^4, 20*x*y^2*z^2*w + 420*y^3*z^3, 2*x*y^2*z*w^4 + 18*x*z^5*w^2 + 9*y^5*w^3 + 9*y^3*z^4*w + 384*y^3*z^2*w^3 + 491*y^3*w^5 + 27*y*z^4*w^3, 20*x*y^2*z*w^3 + 4920*y^3*z^2*w^2 - 4500*y^3*w^4, 2*x*y^2*w^5 + 18*x*z^2*w^5 + 9*y^5*z*w^2 + 384*y^3*z*w^4 + 491*y*z^5*w^2 + 36*y*z^3*w^4, 120*x*y^2*w^4 + 20*y^3*z*w^3, 2*x*y*z^3*w + 218*x*y*z*w^3 + y^2*z^4 + 120*y^2*z^2*w^2 - y^2*w^4, 20*x*y*z^2*w^3 + 4920*y^2*z^3*w^2 - 4500*z^3*w^4, 20*x*y*z*w^4 + 58920*y^2*z^2*w^3 - 54000*y^2*w^5 - 4500*z^4*w^3, 220*x*y*z*w + 120*y^2*z^2, x*z^6*w^2 + 19*x*z^2*w^6 + 2*y*z^5*w^3 + 418*y*z^3*w^5, 2*x*z^5*w^3 + 18*x*z^3*w^5 + y*z^6*w^2 + 420*y*z^4*w^4 + 499*y*z^2*w^6, 20*x*z^5*w^2 + 40*y*z^4*w^3 + 380*y*z^2*w^5, 2*x*z^4*w^5 + 18*x*z^2*w^7 + 9*y*z^7*w^2 + 384*y*z^5*w^4 + 27*y*z^3*w^6, 20*x*z^4*w^3 + 420*y*z^5*w^2, 20*x*z^3*w^4 + 420*y*z^4*w^3, 220*x*z^3*w^3 + 120*y*z^4*w^2, 20*x*z^2*w^5 + 420*y*z^3*w^4, 120*x*z^2*w^4 + 20*y*z^3*w^3, y^6*z*w^2 + 7*y^4*z*w^4 + y^2*z^7 + 7*y^2*z^5*w^2 + 383*y^2*z^3*w^4 + 492*y^2*z*w^6 + 9*z^7*w^2 + 373*z^5*w^4 + 227*z^3*w^6, y^6*w^3 + 7*y^4*w^5 + 383*y^2*w^7 + 9*z^6*w^3 + 373*z^4*w^5 + 5227*z^2*w^7, y^4*z^2 + 9*y^4*w^2 + 9*y^2*z^4 - 120*y^2*z^2*w^2 - 9*y^2*w^4 - 9*z^4*w^2 + 119*z^2*w^4, 10*y^4*w^2 - 120*y^2*w^4 - 10*z^4*w^2 + 120*z^2*w^4, y^3*z^6 + 7*y^3*z^4*w^2 + 383*y^3*z^2*w^4 + 109*y^3*w^6, 500*y^3*z^3, 500*y^3*z^2*w^3, 6000*y^3*z^2*w^2 - 5500*y^3*w^4, 500*y^3*z*w^4, 500*y^3*w^5, y^2*z^8 + 8*y^2*z^6*w^2 + 172*y^2*z^2*w^6 + 319*y^2*w^8 + 9*z^8*w^2 + 3*z^6*w^4 + 167*z^4*w^6 + 2321*z^2*w^8, y^2*z^7*w + 7*y^2*z^5*w^3 + 383*y^2*z^3*w^5 + 109*y^2*z*w^7, y^2*z^6*w^3 + 7*y^2*z^4*w^5 + 383*y^2*z^2*w^7 + 109*y^2*w^9 + 9*z^8*w^3 + 3*z^6*w^5 + 167*z^4*w^7 + 1321*z^2*w^9, 10*y^2*z^4 - 120*y^2*z^2*w^2 + 110*y^2*w^4, 500*y^2*z^3*w^3, 6000*y^2*z^3*w^2 - 5500*z^3*w^4, 72000*y^2*z^2*w^3 - 66000*y^2*w^5 - 5500*z^4*w^3, 500*y^2*z*w^5, 500*y^2*w^7 + 5000*z^2*w^7, y*z^8*w^2 + 7*y*z^6*w^4 + 383*y*z^4*w^6 + 109*y*z^2*w^8, 500*y*z^5*w^2, 500*y*z^4*w^3, 500*y*z^3*w^4, 500*y*z^2*w^5, z^9*w^3 + 7*z^7*w^5 + 383*z^5*w^7 + 109*z^3*w^9, 10*z^6*w^2 - 120*z^4*w^4 + 110*z^2*w^6, 500*z^5*w^3, 500*z^3*w^5, 5500*z^2*w^7 ] false Total time: 3.069 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host genoa.ucc.usyd.edu.au. (129.78.228.114) Time: Mon Mar 22 22:23:55 2004 Input: 1; Output: Magma V2.10-6 Mon Mar 22 2004 22:23:52 on modular [Seed = 2947564150] ------------------------------------- 1 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Tue Mar 23 02:13:25 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (x*y+z*w)*(x*z+y*w)*(x*w+y*z)*(11*x*w+y*z) in I; Output: Magma V2.10-6 Tue Mar 23 2004 02:13:22 on modular [Seed = 2897415981] ------------------------------------- [ x^2*y^2 + z^2*w^2, x^2*z^2 + y^2*w^2, x^2*w^2 + y^2*z^2, 2*x*y^2*w^4, 2*x*y*z, 2*x*z^2*w^4, y^4*z^2 - z^2*w^4, y^4*w^2 + z^4*w^2, 2*y^3*z^3, 2*y^3*w^2, y^2*z^4 - y^2*w^4, 2*y^2*z*w^4, 2*y^2*w^6, 2*y*z^2*w^4, z^6*w^2 + z^2*w^6, 2*z^3*w^2, 2*z^2*w^6 ] true Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Tue Mar 23 02:25:08 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > Output: Magma V2.10-6 Tue Mar 23 2004 02:25:05 on modular [Seed = 3453119375] ------------------------------------- [ x^2*y^2*w^2 + 343*y^4*z^2 - 342*z^2*w^4, 9*x^2*y^2 + 9*z^2*w^2, x^2*z^2*w^2 + 1176*y^2*z^4 - 1175*y^2*w^4, 25*x^2*z^2 + 25*y^2*w^2, 49*x^2*w^2 + 49*y^2*z^2, 1225*x*y^2*w^4, x*y*z, 441*x*z^2*w^4, 49*y^5*z^2 + 126*y*z^2*w^4, y^4*z^2*w^2 + 6174*z^2*w^6, 441*y^4*z^2 - 441*z^2*w^4, y^3*z^3*w^2, 49*y^3*z^3, 25*y^3*w^2, 49*y^2*z^5 + 50*y^2*z*w^4, y^2*z^4*w^2 + 9800*y^2*w^6, 1225*y^2*z^4 - 1225*y^2*w^4, 225*y^2*z*w^4, 11025*y^2*w^6, 225*y*z^2*w^4, 9*z^3*w^2, 11025*z^2*w^6 ] Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Tue Mar 23 02:25:23 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > Output: Magma V2.10-6 Tue Mar 23 2004 02:25:20 on modular [Seed = 4109062791] ------------------------------------- [ x^2*y^2*z^2 + 100*y^4*w^2 - 99*z^4*w^2, x^2*y^2*w^2 + 343*y^4*z^2 - 342*z^2*w^4, 9*x^2*y^2 + 9*z^2*w^2, x^2*z^2*w^2 + 1176*y^2*z^4 - 1175*y^2*w^4, 25*x^2*z^2 + 25*y^2*w^2, 49*x^2*w^2 + 49*y^2*z^2, 1225*x*y^2*w^5, x*y*z*w, 225*x*z^5*w^2, 441*x*z^2*w^5, y^5*z^2*w^2 + 342*y*z^6*w^2 + 99*y*z^2*w^6, 49*y^5*z^2*w + 126*y*z^2*w^5, 25*y^5*z*w^2 + 171*y*z^5*w^2, y^4*z^2*w^3 + 6174*z^2*w^7, 9*y^4*z^2*w^2 + 10575*z^6*w^2 - 10584*z^2*w^6, 441*y^4*z^2 - 441*z^2*w^4, 225*y^4*w^2 - 225*z^4*w^2, y^3*z^3*w^3, 49*y^3*z^3, 25*y^3*w^3, 49*y^2*z^5*w + 50*y^2*z*w^5, y^2*z^4*w^3 + 9800*y^2*w^7, 1225*y^2*z^4 - 1225*y^2*w^4, 225*y^2*z*w^5, 11025*y^2*w^7, 441*y*z^5*w^2, 225*y*z^2*w^5, 11025*z^6*w^2 - 11025*z^2*w^6, 9*z^3*w^3, 11025*z^2*w^7 ] Total time: 2.919 seconds, Total memory usage: 1.92MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Tue Mar 23 02:53:11 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > Output: Magma V2.10-6 Tue Mar 23 2004 02:53:08 on modular [Seed = 825138625] ------------------------------------- [ x^2*z^2 + 1, y^2 + 1, 2 ] Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Tue Mar 23 02:54:00 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > Output: Magma V2.10-6 Tue Mar 23 2004 02:53:57 on modular [Seed = 975542075] ------------------------------------- [ x^2 + 1, y^2 + 1, z^2 + 1, 2 ] Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host tweedledum.its.utas.edu.au. (131.217.6.3) Time: Tue Mar 23 03:02:51 2004 Input: 2+2 Output: Magma V2.10-6 Tue Mar 23 2004 03:02:48 on modular [Seed = 2003359819] ------------------------------------- 4 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Tue Mar 23 03:06:39 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > Output: Magma V2.10-6 Tue Mar 23 2004 03:06:36 on modular [Seed = 1719260798] ------------------------------------- [ x^3 + 2, y^3 + 2, z^3 + 1, 3 ] Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Tue Mar 23 03:07:05 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > Output: Magma V2.10-6 Tue Mar 23 2004 03:07:02 on modular [Seed = 1752684634] ------------------------------------- [ 1 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-151-201-57-45.pitt.east.verizon.net. (151.201.57.45) Time: Tue Mar 23 03:08:09 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > Output: Magma V2.10-6 Tue Mar 23 2004 03:08:06 on modular [Seed = 2442011107] ------------------------------------- [ x^3 + 2, y^3 + 2, z^3 + 2, 3 ] Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee26.uab.es. (158.109.66.26) Time: Tue Mar 23 05:03:39 2004 Input: Inverse (9); Output: Magma V2.10-6 Tue Mar 23 2004 05:03:36 on modular [Seed = 2035888662] ------------------------------------- >> Inverse (9);; ^ Runtime error in 'Inverse': Bad argument types Argument types given: RngIntElt Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee26.uab.es. (158.109.66.26) Time: Tue Mar 23 05:08:55 2004 Input: Inverse (x^2+x+1); Output: Magma V2.10-6 Tue Mar 23 2004 05:08:52 on modular [Seed = 1783244489] ------------------------------------- >> Inverse (x^2+x+1);; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee26.uab.es. (158.109.66.26) Time: Tue Mar 23 05:09:34 2004 Input: P := PolynomialRing (GF(2)); Inverse (x^2+x+1); Output: Magma V2.10-6 Tue Mar 23 2004 05:09:31 on modular [Seed = 2427509852] ------------------------------------- >> Inverse (x^2+x+1);; ^ Runtime error in 'Inverse': Bad argument types Argument types given: RngUPolElt Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee26.uab.es. (158.109.66.26) Time: Tue Mar 23 05:11:32 2004 Input: P := PolynomialRing (GF(2)); Inverse (GF(2)); Output: Magma V2.10-6 Tue Mar 23 2004 05:11:29 on modular [Seed = 2158022086] ------------------------------------- >> Inverse (GF(2));; ^ Runtime error in 'Inverse': Bad argument types Argument types given: FldFin Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee26.uab.es. (158.109.66.26) Time: Tue Mar 23 05:15:03 2004 Input: F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; Output: Magma V2.10-6 Tue Mar 23 2004 05:14:59 on modular [Seed = 3046505345] ------------------------------------- >> F := G25; ^ User error: Identifier 'G25' has not been declared or assigned >> pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; ^ User error: Identifier 'alpha' has not been declared or assigned >> pol; ^ User error: Identifier 'pol' has not been declared or assigned >> lista2:=[x: x in G25 | IsInvertible (x)]; ^ User error: Identifier 'G25' has not been declared or assigned >> lista2;; ^ User error: Identifier 'lista2' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee26.uab.es. (158.109.66.26) Time: Tue Mar 23 05:15:46 2004 Input: G5 := GF(5); G25:= ext < G5 |h>; F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; Output: Magma V2.10-6 Tue Mar 23 2004 05:15:43 on modular [Seed = 2810702335] ------------------------------------- >> G25:= ext < G5 |h>; ^ User error: Identifier 'h' has not been declared or assigned >> F := G25; ^ User error: Identifier 'G25' has not been declared or assigned >> pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; ^ User error: Identifier 'alpha' has not been declared or assigned >> pol; ^ User error: Identifier 'pol' has not been declared or assigned >> lista2:=[x: x in G25 | IsInvertible (x)]; ^ User error: Identifier 'G25' has not been declared or assigned >> lista2;; ^ User error: Identifier 'lista2' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee26.uab.es. (158.109.66.26) Time: Tue Mar 23 05:16:17 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; G5 := GF(5); G25:= ext < G5 |h>; F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; Output: Magma V2.10-6 Tue Mar 23 2004 05:16:14 on modular [Seed = 2894914261] ------------------------------------- alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee26.uab.es. (158.109.66.26) Time: Tue Mar 23 05:16:56 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; G5 := GF(5); G25:= ext < G5 |h>; F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); Output: Magma V2.10-6 Tue Mar 23 2004 05:16:53 on modular [Seed = 3555958097] ------------------------------------- alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee26.uab.es. (158.109.66.26) Time: Tue Mar 23 05:18:55 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; G5 := GF(5); G25:= ext < G5 |h>; F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); ElementToSequence (1); Output: Magma V2.10-6 Tue Mar 23 2004 05:18:51 on modular [Seed = 3657012930] ------------------------------------- alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 [ 1 ] Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee26.uab.es. (158.109.66.26) Time: Tue Mar 23 05:19:04 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; G5 := GF(5); G25:= ext < G5 |h>; F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); ElementToSequence (1,2); Output: Magma V2.10-6 Tue Mar 23 2004 05:19:01 on modular [Seed = 3488579789] ------------------------------------- alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 >> ElementToSequence (1,2);; ^ Runtime error in 'ElementToSequence': Bad argument types Argument types given: RngIntElt, RngIntElt Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee26.uab.es. (158.109.66.26) Time: Tue Mar 23 05:29:26 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); /*true alpha ^11,com que és invertibla, té invers i es alpha^11*/ Output: Magma V2.10-6 Tue Mar 23 2004 05:29:23 on modular [Seed = 3871782770] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 25 8 [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 Total time: 2.979 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host aula-a-siee26.uab.es. (158.109.66.26) Time: Tue Mar 23 05:31:56 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); /*true alpha ^11,com que és invertibla, té invers i es alpha^11*/ IsPrimitive (alpha); /*lista_exponencial:=[x: x in G25 | IsPrimitive (x)];*/ Output: Magma V2.10-6 Tue Mar 23 2004 05:31:53 on modular [Seed = 423185176] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 25 8 [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 true Total time: 3.149 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host aula-a-siee26.uab.es. (158.109.66.26) Time: Tue Mar 23 05:35:30 2004 Input: ElementToSequence (0); ElementToSequence (1); Output: Magma V2.10-6 Tue Mar 23 2004 05:35:27 on modular [Seed = 153705470] ------------------------------------- [ 0 ] [ 1 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee26.uab.es. (158.109.66.26) Time: Tue Mar 23 05:35:55 2004 Input: llista := ElementToSequence (0); llista := ElementToSequence (1); Output: Magma V2.10-6 Tue Mar 23 2004 05:35:52 on modular [Seed = 69490452] ------------------------------------- Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee26.uab.es. (158.109.66.26) Time: Tue Mar 23 05:36:05 2004 Input: llista := ElementToSequence (0); llista := ElementToSequence (1); llista; Output: Magma V2.10-6 Tue Mar 23 2004 05:36:02 on modular [Seed = 1025338935] ------------------------------------- [ 1 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee26.uab.es. (158.109.66.26) Time: Tue Mar 23 05:36:43 2004 Input: llista2 := ElementToSequence (0); llista1 := ElementToSequence (1); llista1 cat llista2; Output: Magma V2.10-6 Tue Mar 23 2004 05:36:40 on modular [Seed = 907437334] ------------------------------------- [ 1, 0 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee26.uab.es. (158.109.66.26) Time: Tue Mar 23 05:37:58 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); /*true alpha ^11,com que és invertibla, té invers i es alpha^11*/ IsPrimitive (alpha); lista_exponencial := function (p,n) llista1 := ElementToSequence (0); for i:=0 to (p^n)-2 do llista2 := ElementToSequence (alpha^i); llista1 := llista1 cat llista2; end for; return llista1; end function; Output: Magma V2.10-6 Tue Mar 23 2004 05:37:55 on modular [Seed = 536900539] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 25 8 [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 true Total time: 2.989 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host aula-a-siee26.uab.es. (158.109.66.26) Time: Tue Mar 23 05:38:25 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); /*true alpha ^11,com que és invertibla, té invers i es alpha^11*/ IsPrimitive (alpha); lista_exponencial := function (p,n) llista1 := ElementToSequence (0); for i:=0 to (p^n)-2 do llista2 := ElementToSequence (alpha^i); llista1 := llista1 cat llista2; end for; return llista1; end function; lista_exponencial (5,2); Output: Magma V2.10-6 Tue Mar 23 2004 05:38:22 on modular [Seed = 1501104863] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 25 8 [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 true [ 0, 1, 0, 0, 1, 2, 3, 1, 1, 2, 4, 3, 4, 3, 0, 0, 3, 1, 4, 3, 3, 1, 2, 4, 2, 4, 0, 0, 4, 3, 2, 4, 4, 3, 1, 2, 1, 2, 0, 0, 2, 4, 1, 2, 2, 4, 3, 1, 3 ] Total time: 2.979 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host aula-a-siee26.uab.es. (158.109.66.26) Time: Tue Mar 23 05:39:13 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); /*true alpha ^11,com que és invertibla, té invers i es alpha^11*/ IsPrimitive (alpha); lista_exponencial := function (p,n) llista1 := ElementToSequence (0); for i:=0 to (p^n)-2 do llista2 := ElementToSequence (alpha^i); llista1 := llista1 cat llista2; end for; return llista1; end function; lista_exponencial (3,2); Output: Magma V2.10-6 Tue Mar 23 2004 05:39:10 on modular [Seed = 1400045701] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 25 8 [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 true [ 0, 1, 0, 0, 1, 2, 3, 1, 1, 2, 4, 3, 4, 3, 0, 0, 3 ] Total time: 3.069 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host aula-a-siee26.uab.es. (158.109.66.26) Time: Tue Mar 23 05:39:59 2004 Input: llista2 := ElementToSequence (alpha^2); llista1 := ElementToSequence (alpha^1); llista1 cat llista2; Output: Magma V2.10-6 Tue Mar 23 2004 05:39:55 on modular [Seed = 1282154408] ------------------------------------- >> llista2 := ElementToSequence (alpha^2); ^ User error: Identifier 'alpha' has not been declared or assigned >> llista1 := ElementToSequence (alpha^1); ^ User error: Identifier 'alpha' has not been declared or assigned >> llista1 cat llista2;; ^ User error: Identifier 'llista1' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee26.uab.es. (158.109.66.26) Time: Tue Mar 23 05:43:38 2004 Input: z3:= Integers(3); P := PolynomialRing (z3); h:= x^2 +1 ; G9 := GF(3); G9b:= ext < G9 |h>; F := G9b; llista2 := ElementToSequence (alpha^2); llista1 := ElementToSequence (alpha^1); llista:= llista1 cat llista2; llista; Output: Magma V2.10-6 Tue Mar 23 2004 05:43:35 on modular [Seed = 2120100529] ------------------------------------- [ 0, 1, 2, 0 ] Total time: 2.929 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host aula-a-siee26.uab.es. (158.109.66.26) Time: Tue Mar 23 05:44:35 2004 Input: z3:= Integers(3); P := PolynomialRing (z3); h:= x^2 +1 ; G9 := GF(3); G9b:= ext < G9 |h>; F := G9b; llista2 := ElementToSequence (alpha^2); llista2; llista1 := ElementToSequence (alpha^1); llista1; llista:= llista1 cat llista2; llista; Output: Magma V2.10-6 Tue Mar 23 2004 05:44:31 on modular [Seed = 2002199136] ------------------------------------- [ 2, 0 ] [ 0, 1 ] [ 0, 1, 2, 0 ] Total time: 2.929 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host aula-a-siee26.uab.es. (158.109.66.26) Time: Tue Mar 23 05:46:20 2004 Input: z3:= Integers(3); P := PolynomialRing (z3); h:= x^2 +1 ; G9 := GF(3); G9b:= ext < G9 |h>; F := G9b; llista2 := ElementToSequence (3*alpha^2); llista2; llista1 := ElementToSequence (alpha^1); llista1; llista:= llista1 cat llista2; llista; Output: Magma V2.10-6 Tue Mar 23 2004 05:46:17 on modular [Seed = 1699033092] ------------------------------------- [ 0, 0 ] [ 0, 1 ] [ 0, 1, 0, 0 ] Total time: 2.919 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host aula-a-siee26.uab.es. (158.109.66.26) Time: Tue Mar 23 05:46:47 2004 Input: z3:= Integers(3); P := PolynomialRing (z3); h:= x^2 +1 ; G9 := GF(3); G9b:= ext < G9 |h>; F := G9b; llista2 := ElementToSequence (2*alpha+1); llista2; llista1 := ElementToSequence (alpha^1); llista1; llista:= llista1 cat llista2; llista; Output: Magma V2.10-6 Tue Mar 23 2004 05:46:44 on modular [Seed = 2663303954] ------------------------------------- [ 1, 2 ] [ 0, 1 ] [ 0, 1, 1, 2 ] Total time: 2.889 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host aula-a-siee26.uab.es. (158.109.66.26) Time: Tue Mar 23 05:47:11 2004 Input: z3:= Integers(3); P := PolynomialRing (z3); h:= x^2 +1 ; G9 := GF(3); G9b:= ext < G9 |h>; F := G9b; llista2 := ElementToSequence (2*alpha^5+1); llista2; llista1 := ElementToSequence (alpha^1); llista1; llista:= llista1 cat llista2; llista; Output: Magma V2.10-6 Tue Mar 23 2004 05:47:08 on modular [Seed = 2545402403] ------------------------------------- [ 1, 2 ] [ 0, 1 ] [ 0, 1, 1, 2 ] Total time: 2.969 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host aula-a-siee26.uab.es. (158.109.66.26) Time: Tue Mar 23 05:48:12 2004 Input: z3:= Integers(3); P := PolynomialRing (z3); h:= x^2 +1 ; G9 := GF(3); G9b:= ext < G9 |h>; F := G9b; llista2 := ElementToSequence (2*alpha+1)^6; llista2; llista1 := ElementToSequence (alpha^1); llista1; llista:= llista1 cat llista2; llista; Output: Magma V2.10-6 Tue Mar 23 2004 05:48:09 on modular [Seed = 2174866544] ------------------------------------- >> llista2 := ElementToSequence (2*alpha+1)^6; ^ Runtime error in '^': Bad argument types Argument types given: SeqEnum[FldFinElt], RngIntElt >> llista2; ^ User error: Identifier 'llista2' has not been declared or assigned [ 0, 1 ] >> llista:= llista1 cat llista2; ^ User error: Identifier 'llista2' has not been declared or assigned >> llista;; ^ User error: Identifier 'llista' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host aula-a-siee26.uab.es. (158.109.66.26) Time: Tue Mar 23 05:48:23 2004 Input: z3:= Integers(3); P := PolynomialRing (z3); h:= x^2 +1 ; G9 := GF(3); G9b:= ext < G9 |h>; F := G9b; llista2 := ElementToSequence ((2*alpha+1)^6); llista2; llista1 := ElementToSequence (alpha^1); llista1; llista:= llista1 cat llista2; llista; Output: Magma V2.10-6 Tue Mar 23 2004 05:48:20 on modular [Seed = 3130715990] ------------------------------------- [ 0, 2 ] [ 0, 1 ] [ 0, 1, 0, 2 ] Total time: 2.979 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host aula-a-siee26.uab.es. (158.109.66.26) Time: Tue Mar 23 05:48:41 2004 Input: z3:= Integers(3); P := PolynomialRing (z3); h:= x^2 +1 ; G9 := GF(3); G9b:= ext < G9 |h>; F := G9b; llista2 := ElementToSequence ((2*alpha+1)^7); llista2; llista1 := ElementToSequence (alpha^1); llista1; llista:= llista1 cat llista2; llista; Output: Magma V2.10-6 Tue Mar 23 2004 05:48:38 on modular [Seed = 3029656234] ------------------------------------- [ 2, 2 ] [ 0, 1 ] [ 0, 1, 2, 2 ] Total time: 2.939 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host aula-a-siee26.uab.es. (158.109.66.26) Time: Tue Mar 23 05:54:09 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); /*true alpha ^11,com que és invertibla, té invers i es alpha^11*/ IsPrimitive (alpha); lista_vectorial := function (p,n) llista1 := [[0,0]]; for i:=0 to (p^n)-2 do llista2 := ElementToSequence (alpha^i); llista1 := llista2 Include llista1; end for; return llista1; end function; lista_exponencial (3,2); Output: Magma V2.10-6 Tue Mar 23 2004 05:54:06 on modular [Seed = 2793861616] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 25 8 [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 true >> llista1 := llista2 Include llista1; ^ User error: bad syntax >> end for; ^ User error: bad syntax >> return llista1; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> lista_exponencial (3,2); ^ User error: Identifier 'lista_exponencial' has not been declared or assigned Total time: 3.059 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host aula-a-siee26.uab.es. (158.109.66.26) Time: Tue Mar 23 05:54:32 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); /*true alpha ^11,com que és invertibla, té invers i es alpha^11*/ IsPrimitive (alpha); lista_vectorial := function (p,n) llista1 := [[0,0]]; for i:=0 to (p^n)-2 do llista2 := ElementToSequence (alpha^i); llista1 := llista2 Include llista1; end for; return llista1; end function; lista_vectorial (3,2); Output: Magma V2.10-6 Tue Mar 23 2004 05:54:29 on modular [Seed = 3758065826] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 25 8 [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 true >> llista1 := llista2 Include llista1; ^ User error: bad syntax >> end for; ^ User error: bad syntax >> return llista1; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> lista_vectorial (3,2); ^ User error: Identifier 'lista_vectorial' has not been declared or assigned Total time: 3.109 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host aula-a-siee26.uab.es. (158.109.66.26) Time: Tue Mar 23 05:56:01 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); /*true alpha ^11,com que és invertibla, té invers i es alpha^11*/ IsPrimitive (alpha); lista_vectorial := function (p,n) llista1 := [[0,0]]; for i:=0 to (p^n)-2 do llista2 := ElementToSequence (alpha^i); llista1 := Include (llista1,llista2); end for; return llista1; end function; lista_vectorial (3,2); Output: Magma V2.10-6 Tue Mar 23 2004 05:55:58 on modular [Seed = 3454900843] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 25 8 [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 true [ [ 0, 0 ], [ 1, 0 ], [ 0, 1 ], [ 2, 3 ], [ 1, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 0 ], [ 0, 3 ] ] Total time: 2.989 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host aula-a-siee26.uab.es. (158.109.66.26) Time: Tue Mar 23 05:56:58 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); /*true alpha ^11,com que és invertibla, té invers i es alpha^11*/ IsPrimitive (alpha); lista_vectorial := function (p,n) llista1 := [[0,0]]; for i:=0 to (p^n)-2 do llista2 := ElementToSequence ((2*alpha+1)^i); llista1 := Include (llista1,llista2); end for; return llista1; end function; lista_vectorial (3,2); Output: Magma V2.10-6 Tue Mar 23 2004 05:56:55 on modular [Seed = 3336999209] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 25 8 [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 true [ [ 0, 0 ], [ 1, 0 ], [ 1, 2 ], [ 4, 1 ], [ 3, 0 ], [ 3, 1 ], [ 2, 3 ], [ 4, 0 ], [ 4, 3 ] ] Total time: 3.059 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host aula-a-siee26.uab.es. (158.109.66.26) Time: Tue Mar 23 05:57:41 2004 Input: z3:= Integers(3); P := PolynomialRing (z3); h:= x^2 +1 ; G9 := GF(3); G9b:= ext < G9 |h>; F := G9b; lista_vectorial := function (p,n) llista1 := [[0,0]]; for i:=0 to (p^n)-2 do llista2 := ElementToSequence ((2*alpha+1)^i); llista1 := Include (llista1,llista2); end for; return llista1; end function; lista_vectorial (3,2); Output: Magma V2.10-6 Tue Mar 23 2004 05:57:38 on modular [Seed = 4040206538] ------------------------------------- [ [ 0, 0 ], [ 1, 0 ], [ 1, 2 ], [ 0, 1 ], [ 1, 1 ], [ 2, 0 ], [ 2, 1 ], [ 0, 2 ], [ 2, 2 ] ] Total time: 2.969 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host aula-a-siee26.uab.es. (158.109.66.26) Time: Tue Mar 23 05:59:59 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); /*true alpha ^11,com que és invertibla, té invers i es alpha^11*/ IsPrimitive (alpha); lista_vectorial := function (p,n) llista1 := [[0,0]]; for i:=0 to (p^n)-2 do llista2 := ElementToSequence (alpha^i); llista1 := Include (llista1,llista2); end for; return llista1; end function; lista_vectorial (5,2); Output: Magma V2.10-6 Tue Mar 23 2004 05:59:56 on modular [Seed = 3939152478] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 25 8 [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 true [ [ 0, 0 ], [ 1, 0 ], [ 0, 1 ], [ 2, 3 ], [ 1, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 0 ], [ 0, 3 ], [ 1, 4 ], [ 3, 3 ], [ 1, 2 ], [ 4, 2 ], [ 4, 0 ], [ 0, 4 ], [ 3, 2 ], [ 4, 4 ], [ 3, 1 ], [ 2, 1 ], [ 2, 0 ], [ 0, 2 ], [ 4, 1 ], [ 2, 2 ], [ 4, 3 ], [ 1, 3 ] ] Total time: 3.009 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host aula-a-siee26.uab.es. (158.109.66.26) Time: Tue Mar 23 06:08:22 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); /*true alpha ^11,com que és invertibla, té invers i es alpha^11*/ IsPrimitive (alpha); lista_vectorial := function (p,n) llista1 := [[0,0]]; for i:=0 to (p^n)-2 do llista2 := ElementToSequence (alpha^i); llista1 := Include (llista1,llista2); end for; return llista1; end function; lista_vectorial (5,2); lista_exponencial := function (p,n) llista1 := [alpha]; for i:=2 to (p^n)-2 do llista2 := (alpha^i); llista1 := Include (llista1,llista2); end for; return llista1; end function; lista_exponencial(5,2); Output: Magma V2.10-6 Tue Mar 23 2004 06:08:16 on modular [Seed = 991650178] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 25 8 [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 true [ [ 0, 0 ], [ 1, 0 ], [ 0, 1 ], [ 2, 3 ], [ 1, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 0 ], [ 0, 3 ], [ 1, 4 ], [ 3, 3 ], [ 1, 2 ], [ 4, 2 ], [ 4, 0 ], [ 0, 4 ], [ 3, 2 ], [ 4, 4 ], [ 3, 1 ], [ 2, 1 ], [ 2, 0 ], [ 0, 2 ], [ 4, 1 ], [ 2, 2 ], [ 4, 3 ], [ 1, 3 ] ] [ alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] Total time: 3.660 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host aula-a-siee26.uab.es. (158.109.66.26) Time: Tue Mar 23 06:08:53 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); /*true alpha ^11,com que és invertibla, té invers i es alpha^11*/ IsPrimitive (alpha); lista_vectorial := function (p,n) llista1 := [[0,0]]; for i:=0 to (p^n)-2 do llista2 := ElementToSequence (alpha^i); llista1 := Include (llista1,llista2); end for; return llista1; end function; lista_vectorial (5,2); lista_exponencial := function (p,n) llista1 := [alpha]; for i:=2 to (p^n)-2 do llista2 := [alpha^i]; llista1 := Include (llista1,llista2); end for; return llista1; end function; lista_exponencial(5,2); Output: Magma V2.10-6 Tue Mar 23 2004 06:08:49 on modular [Seed = 924282351] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 25 8 [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 true [ [ 0, 0 ], [ 1, 0 ], [ 0, 1 ], [ 2, 3 ], [ 1, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 0 ], [ 0, 3 ], [ 1, 4 ], [ 3, 3 ], [ 1, 2 ], [ 4, 2 ], [ 4, 0 ], [ 0, 4 ], [ 3, 2 ], [ 4, 4 ], [ 3, 1 ], [ 2, 1 ], [ 2, 0 ], [ 0, 2 ], [ 4, 1 ], [ 2, 2 ], [ 4, 3 ], [ 1, 3 ] ] [
:111]( p: 5, n: 2 ) >> llista1 := Include (llista1,llista2); ^ Runtime error in 'Include': Cannot lift element into sequence Total time: 3.139 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host aula-a-siee26.uab.es. (158.109.66.26) Time: Tue Mar 23 06:09:16 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); /*true alpha ^11,com que és invertibla, té invers i es alpha^11*/ IsPrimitive (alpha); lista_vectorial := function (p,n) llista1 := [[0,0]]; for i:=0 to (p^n)-2 do llista2 := ElementToSequence (alpha^i); llista1 := Include (llista1,llista2); end for; return llista1; end function; lista_vectorial (5,2); lista_exponencial := function (p,n) llista1 := [alpha]; for i:=2 to (p^n)-2 do llista2 := (alpha^i); llista1 := Include (llista1,llista2); end for; return llista1; end function; lista_exponencial(5,2); Output: Magma V2.10-6 Tue Mar 23 2004 06:09:13 on modular [Seed = 772699374] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 25 8 [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 true [ [ 0, 0 ], [ 1, 0 ], [ 0, 1 ], [ 2, 3 ], [ 1, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 0 ], [ 0, 3 ], [ 1, 4 ], [ 3, 3 ], [ 1, 2 ], [ 4, 2 ], [ 4, 0 ], [ 0, 4 ], [ 3, 2 ], [ 4, 4 ], [ 3, 1 ], [ 2, 1 ], [ 2, 0 ], [ 0, 2 ], [ 4, 1 ], [ 2, 2 ], [ 4, 3 ], [ 1, 3 ] ] [ alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] Total time: 2.969 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host aula-a-siee44.uab.es. (158.109.66.44) Time: Tue Mar 23 06:09:47 2004 Input: P2:=PolynomialRing(G2); > P3:=PolynomialRing(G3); > P5:=PolynomialRing(G5); > P3x:=elt; > P2x:=elt; > P3bx:=elt; > P5x:=elt; > IsIrreducible(P3x); true > IsIrreducible(P2x); true > IsIrreducible(P5x); false > IsIrreducible(P5x); true Output: Magma V2.10-6 Tue Mar 23 2004 06:09:44 on modular [Seed = 1501103032] ------------------------------------- >> P2:=PolynomialRing(G2); ^ Runtime error in 'PolynomialRing': Bad argument types Argument types given: Intrinsic >> P3:=PolynomialRing(G3); ^ User error: Identifier 'G3' has not been declared or assigned >> P5:=PolynomialRing(G5); ^ User error: Identifier 'G5' has not been declared or assigned >> P3x:=elt; ^ User error: Identifier 'P3' has not been declared or assigned >> P2x:=elt; ^ User error: Identifier 'P2' has not been declared or assigned >> P3bx:=elt; ^ User error: Identifier 'P3' has not been declared or assigned >> P5x:=elt; ^ User error: Identifier 'P5' has not been declared or assigned >> IsIrreducible(P3x); ^ User error: Identifier 'P3x' has not been declared or assigned >> IsIrreducible(P2x); ^ User error: bad syntax >> IsIrreducible(P5x); ^ User error: bad syntax >> IsIrreducible(P5x); ^ User error: bad syntax true Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee44.uab.es. (158.109.66.44) Time: Tue Mar 23 06:10:46 2004 Input: P2:=PolynomialRing(G2); > P3:=PolynomialRing(G3); > P5:=PolynomialRing(G5); > P3x:=elt; > P2x:=elt; > P3bx:=elt; > P5x:=elt; > IsIrreducible(P3x); > IsIrreducible(P2x); > IsIrreducible(P5x); > IsIrreducible(P3bx); Output: Magma V2.10-6 Tue Mar 23 2004 06:10:43 on modular [Seed = 1080040298] ------------------------------------- >> P2:=PolynomialRing(G2); ^ Runtime error in 'PolynomialRing': Bad argument types Argument types given: Intrinsic >> P3:=PolynomialRing(G3); ^ User error: Identifier 'G3' has not been declared or assigned >> P5:=PolynomialRing(G5); ^ User error: Identifier 'G5' has not been declared or assigned >> P3x:=elt; ^ User error: Identifier 'P3' has not been declared or assigned >> P2x:=elt; ^ User error: Identifier 'P2' has not been declared or assigned >> P3bx:=elt; ^ User error: Identifier 'P3' has not been declared or assigned >> P5x:=elt; ^ User error: Identifier 'P5' has not been declared or assigned >> IsIrreducible(P3x); ^ User error: Identifier 'P3x' has not been declared or assigned >> IsIrreducible(P2x); ^ User error: Identifier 'P2x' has not been declared or assigned >> IsIrreducible(P5x); ^ User error: Identifier 'P5x' has not been declared or assigned >> IsIrreducible(P3bx); ^ User error: Identifier 'P3bx' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee44.uab.es. (158.109.66.44) Time: Tue Mar 23 06:11:00 2004 Input: >P2:=PolynomialRing(G2); > P3:=PolynomialRing(G3); > P5:=PolynomialRing(G5); > P3x:=elt; > P2x:=elt; > P3bx:=elt; > P5x:=elt; > IsIrreducible(P3x); > IsIrreducible(P2x); > IsIrreducible(P5x); > IsIrreducible(P3bx); Output: Magma V2.10-6 Tue Mar 23 2004 06:10:57 on modular [Seed = 1917987114] ------------------------------------- >> P2:=PolynomialRing(G2); ^ Runtime error in 'PolynomialRing': Bad argument types Argument types given: Intrinsic >> P3:=PolynomialRing(G3); ^ User error: Identifier 'G3' has not been declared or assigned >> P5:=PolynomialRing(G5); ^ User error: Identifier 'G5' has not been declared or assigned >> P3x:=elt; ^ User error: Identifier 'P3' has not been declared or assigned >> P2x:=elt; ^ User error: Identifier 'P2' has not been declared or assigned >> P3bx:=elt; ^ User error: Identifier 'P3' has not been declared or assigned >> P5x:=elt; ^ User error: Identifier 'P5' has not been declared or assigned >> IsIrreducible(P3x); ^ User error: Identifier 'P3x' has not been declared or assigned >> IsIrreducible(P2x); ^ User error: Identifier 'P2x' has not been declared or assigned >> IsIrreducible(P5x); ^ User error: Identifier 'P5x' has not been declared or assigned >> IsIrreducible(P3bx); ^ User error: Identifier 'P3bx' has not been declared or assigned Total time: 3.199 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee44.uab.es. (158.109.66.44) Time: Tue Mar 23 06:11:20 2004 Input: P2:=PolynomialRing(G2); P3:=PolynomialRing(G3); P5:=PolynomialRing(G5); P3x:=elt; P2x:=elt; P3bx:=elt; P5x:=elt; IsIrreducible(P3x); IsIrreducible(P2x); IsIrreducible(P5x); IsIrreducible(P3bx); Output: Magma V2.10-6 Tue Mar 23 2004 06:11:17 on modular [Seed = 1850619170] ------------------------------------- >> P2:=PolynomialRing(G2); ^ Runtime error in 'PolynomialRing': Bad argument types Argument types given: Intrinsic >> P3:=PolynomialRing(G3); ^ User error: Identifier 'G3' has not been declared or assigned >> P5:=PolynomialRing(G5); ^ User error: Identifier 'G5' has not been declared or assigned >> P3x:=elt; ^ User error: Identifier 'P3' has not been declared or assigned >> P2x:=elt; ^ User error: Identifier 'P2' has not been declared or assigned >> P3bx:=elt; ^ User error: Identifier 'P3' has not been declared or assigned >> P5x:=elt; ^ User error: Identifier 'P5' has not been declared or assigned >> IsIrreducible(P3x); ^ User error: Identifier 'P3x' has not been declared or assigned >> IsIrreducible(P2x); ^ User error: Identifier 'P2x' has not been declared or assigned >> IsIrreducible(P5x); ^ User error: Identifier 'P5x' has not been declared or assigned >> IsIrreducible(P3bx); ^ User error: Identifier 'P3bx' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee26.uab.es. (158.109.66.26) Time: Tue Mar 23 06:11:27 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); /*true alpha ^11,com que és invertibla, té invers i es alpha^11*/ IsPrimitive (alpha); lista_vectorial := function (p,n) llista1 := [[0,0]]; for i:=0 to (p^n)-2 do llista2 := ElementToSequence (alpha^i); llista1 := Include (llista1,llista2); end for; return llista1; end function; lista_exponencial := function (p,n) llista1 := [alpha]; for i:=2 to (p^n)-2 do llista2 := (alpha^i); llista1 := Include (llista1,llista2); end for; return llista1; end function; lista_vectorial (2,4); lista_exponencial (2,4); lista_vectorial (5,2); lista_exponencial(5,2); Output: Magma V2.10-6 Tue Mar 23 2004 06:11:24 on modular [Seed = 2579088092] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 25 8 [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 true [ [ 0, 0 ], [ 1, 0 ], [ 0, 1 ], [ 2, 3 ], [ 1, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 0 ], [ 0, 3 ], [ 1, 4 ], [ 3, 3 ], [ 1, 2 ], [ 4, 2 ], [ 4, 0 ], [ 0, 4 ], [ 3, 2 ] ] [ alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14 ] [ [ 0, 0 ], [ 1, 0 ], [ 0, 1 ], [ 2, 3 ], [ 1, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 0 ], [ 0, 3 ], [ 1, 4 ], [ 3, 3 ], [ 1, 2 ], [ 4, 2 ], [ 4, 0 ], [ 0, 4 ], [ 3, 2 ], [ 4, 4 ], [ 3, 1 ], [ 2, 1 ], [ 2, 0 ], [ 0, 2 ], [ 4, 1 ], [ 2, 2 ], [ 4, 3 ], [ 1, 3 ] ] [ alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] Total time: 3.129 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host aula-a-siee44.uab.es. (158.109.66.44) Time: Tue Mar 23 06:11:56 2004 Input: G2:=GF(2); G3:=GF(3); G5:=GF(5); P2:=PolynomialRing(G2); P3:=PolynomialRing(G3); P5:=PolynomialRing(G5); P3x:=elt; P2x:=elt; P3bx:=elt; P5x:=elt; IsIrreducible(P3x); IsIrreducible(P2x); IsIrreducible(P5x); IsIrreducible(P3bx); Output: Magma V2.10-6 Tue Mar 23 2004 06:11:53 on modular [Seed = 2309608169] ------------------------------------- true true true false Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee26.uab.es. (158.109.66.26) Time: Tue Mar 23 06:12:26 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); /*true alpha ^11,com que és invertibla, té invers i es alpha^11*/ IsPrimitive (alpha); lista_vectorial := function (p,n) llista1 := [[0,0]]; for i:=0 to (p^n)-2 do llista2 := ElementToSequence (alpha^i); llista1 := Include (llista1,llista2); end for; return llista1; end function; lista_exponencial := function (p,n) llista1 := [alpha]; for i:=1 to (p^n)-2 do llista2 := (alpha^i); llista1 := Include (llista1,llista2); end for; return llista1; end function; lista_vectorial (2,4); lista_exponencial (2,4); lista_vectorial (5,2); lista_exponencial(5,2); Output: Magma V2.10-6 Tue Mar 23 2004 06:12:23 on modular [Seed = 2208552973] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 25 8 [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 true [ [ 0, 0 ], [ 1, 0 ], [ 0, 1 ], [ 2, 3 ], [ 1, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 0 ], [ 0, 3 ], [ 1, 4 ], [ 3, 3 ], [ 1, 2 ], [ 4, 2 ], [ 4, 0 ], [ 0, 4 ], [ 3, 2 ] ] [ alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14 ] [ [ 0, 0 ], [ 1, 0 ], [ 0, 1 ], [ 2, 3 ], [ 1, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 0 ], [ 0, 3 ], [ 1, 4 ], [ 3, 3 ], [ 1, 2 ], [ 4, 2 ], [ 4, 0 ], [ 0, 4 ], [ 3, 2 ], [ 4, 4 ], [ 3, 1 ], [ 2, 1 ], [ 2, 0 ], [ 0, 2 ], [ 4, 1 ], [ 2, 2 ], [ 4, 3 ], [ 1, 3 ] ] [ alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] Total time: 2.959 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host aula-a-siee26.uab.es. (158.109.66.26) Time: Tue Mar 23 06:13:31 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); /*true alpha ^11,com que és invertibla, té invers i es alpha^11*/ IsPrimitive (alpha); lista_vectorial := function (p,n) llista1 := [[0,0]]; for i:=0 to (p^n)-1 do llista2 := ElementToSequence (alpha^i); llista1 := Include (llista1,llista2); end for; return llista1; end function; lista_exponencial := function (p,n) llista1 := [alpha]; for i:=1 to (p^n)-1 do llista2 := (alpha^i); llista1 := Include (llista1,llista2); end for; return llista1; end function; lista_vectorial (2,4); lista_exponencial (2,4); lista_vectorial (5,2); lista_exponencial(5,2); Output: Magma V2.10-6 Tue Mar 23 2004 06:13:28 on modular [Seed = 3130712443] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 25 8 [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 true [ [ 0, 0 ], [ 1, 0 ], [ 0, 1 ], [ 2, 3 ], [ 1, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 0 ], [ 0, 3 ], [ 1, 4 ], [ 3, 3 ], [ 1, 2 ], [ 4, 2 ], [ 4, 0 ], [ 0, 4 ], [ 3, 2 ], [ 4, 4 ] ] [ alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15 ] [ [ 0, 0 ], [ 1, 0 ], [ 0, 1 ], [ 2, 3 ], [ 1, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 0 ], [ 0, 3 ], [ 1, 4 ], [ 3, 3 ], [ 1, 2 ], [ 4, 2 ], [ 4, 0 ], [ 0, 4 ], [ 3, 2 ], [ 4, 4 ], [ 3, 1 ], [ 2, 1 ], [ 2, 0 ], [ 0, 2 ], [ 4, 1 ], [ 2, 2 ], [ 4, 3 ], [ 1, 3 ] ] [ alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 1 ] Total time: 2.969 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host aula-a-siee44.uab.es. (158.109.66.44) Time: Tue Mar 23 06:14:31 2004 Input: G2:=GF(2); G3:=GF(3); G5:=GF(5); P2:=PolynomialRing(G2); P3:=PolynomialRing(G3); P5:=PolynomialRing(G5); P3x:=elt; P2x:=elt; P3bx:=elt; P5x:=elt; G9:=ext; G16:=ext; G25:ext; Output: Magma V2.10-6 Tue Mar 23 2004 06:14:28 on modular [Seed = 3046500792] ------------------------------------- >> G25:ext; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee44.uab.es. (158.109.66.44) Time: Tue Mar 23 06:15:05 2004 Input: G2:=GF(2); G3:=GF(3); G5:=GF(5); P2:=PolynomialRing(G2); P3:=PolynomialRing(G3); P5:=PolynomialRing(G5); P3x:=elt; P2x:=elt; P3bx:=elt; P5x:=elt; G9:=ext; G16:=ext; G25:=ext>; Output: Magma V2.10-6 Tue Mar 23 2004 06:15:01 on modular [Seed = 2726493838] ------------------------------------- Total time: 3.599 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee26.uab.es. (158.109.66.26) Time: Tue Mar 23 06:15:05 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); /*true alpha ^11,com que és invertibla, té invers i es alpha^11*/ IsPrimitive (alpha); lista_vectorial := function (p,n) llista1 := [[0,0]]; for i:=0 to (p^n)-1 do llista2 := ElementToSequence (alpha^i); llista1 := Include (llista1,llista2); end for; return llista1; end function; lista_exponencial := function (p,n) llista1 := [alpha]; for i:=1 to (p^n)-1 do llista2 := (alpha^i); llista1 := Include (llista1,llista2); end for; return llista1; end function; /*lista_vectorial (2,4); lista_exponencial (2,4);*/ lista_vectorial (5,2); lista_exponencial(5,2); Output: Magma V2.10-6 Tue Mar 23 2004 06:15:02 on modular [Seed = 2760177803] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 25 8 [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 true [ [ 0, 0 ], [ 1, 0 ], [ 0, 1 ], [ 2, 3 ], [ 1, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 0 ], [ 0, 3 ], [ 1, 4 ], [ 3, 3 ], [ 1, 2 ], [ 4, 2 ], [ 4, 0 ], [ 0, 4 ], [ 3, 2 ], [ 4, 4 ], [ 3, 1 ], [ 2, 1 ], [ 2, 0 ], [ 0, 2 ], [ 4, 1 ], [ 2, 2 ], [ 4, 3 ], [ 1, 3 ] ] [ alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 1 ] Total time: 3.679 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host aula-a-siee44.uab.es. (158.109.66.44) Time: Tue Mar 23 06:15:49 2004 Input: G2:=GF(2); G3:=GF(3); G5:=GF(5); P2:=PolynomialRing(G2); P3:=PolynomialRing(G3); P5:=PolynomialRing(G5); P3x:=elt; P2x:=elt; P3bx:=elt; P5x:=elt; G9:=ext; G16:=ext; G25:=ext>; G9b:=ext; Output: Magma V2.10-6 Tue Mar 23 2004 06:15:46 on modular [Seed = 3589638574] ------------------------------------- >> G9b:=ext;; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee26.uab.es. (158.109.66.26) Time: Tue Mar 23 06:20:42 2004 Input: [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ lista:=[x: x in G25]; print lista; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; /*[ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ]*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ # lista; /*8*/ /*un cos de p^n te fi(p^n-1) elements primitius, on */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ lista; /*[ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ]*/ MinimalPolynomial(G25.1); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ polinomi := MinimalPolynomial(G25.1); polinomi; /*$.1^2 + 2*$.1 + 3*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ F := G25; pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); /*true alpha ^11,com que és invertibla, té invers i es alpha^11*/ IsPrimitive (alpha); lista_vectorial := function (p,n) llista1 := [[0,0]]; for i:=0 to (p^n)-1 do llista2 := ElementToSequence (alpha^i); llista1 := Include (llista1,llista2); end for; return llista1; end function; lista_exponencial := function (p,n) llista1 := [alpha]; for i:=1 to (p^n)-1 do llista2 := (alpha^i); llista1 := Include (llista1,llista2); end for; return llista1; end function; lista_vectorial (2,4); lista_exponencial (2,4); lista_vectorial (5,2); lista_exponencial(5,2); Output: Magma V2.10-6 Tue Mar 23 2004 06:20:39 on modular [Seed = 4242317666] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 25 8 [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ] $.1^2 + 2*$.1 + 3 $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 true [ [ 0, 0 ], [ 1, 0 ], [ 0, 1 ], [ 2, 3 ], [ 1, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 0 ], [ 0, 3 ], [ 1, 4 ], [ 3, 3 ], [ 1, 2 ], [ 4, 2 ], [ 4, 0 ], [ 0, 4 ], [ 3, 2 ], [ 4, 4 ] ] [ alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15 ] [ [ 0, 0 ], [ 1, 0 ], [ 0, 1 ], [ 2, 3 ], [ 1, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 0 ], [ 0, 3 ], [ 1, 4 ], [ 3, 3 ], [ 1, 2 ], [ 4, 2 ], [ 4, 0 ], [ 0, 4 ], [ 3, 2 ], [ 4, 4 ], [ 3, 1 ], [ 2, 1 ], [ 2, 0 ], [ 0, 2 ], [ 4, 1 ], [ 2, 2 ], [ 4, 3 ], [ 1, 3 ] ] [ alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 1 ] Total time: 2.999 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host aula-a-siee44.uab.es. (158.109.66.44) Time: Tue Mar 23 06:22:38 2004 Input: [Order(k):k in G25|k ne 0]; Output: Magma V2.10-6 Tue Mar 23 2004 06:22:35 on modular [Seed = 3922310155] ------------------------------------- >> [Order(k):k in G25|k ne 0]; ^ User error: Identifier 'G25' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee44.uab.es. (158.109.66.44) Time: Tue Mar 23 06:23:38 2004 Input: G25:=ext>; [Order(k):k in G25|k ne 0]; Output: Magma V2.10-6 Tue Mar 23 2004 06:23:35 on modular [Seed = 3770728142] ------------------------------------- >> G25:=ext>; ^ User error: Identifier 'P5' has not been declared or assigned >> [Order(k):k in G25|k ne 0]; ^ User error: Identifier 'G25' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee44.uab.es. (158.109.66.44) Time: Tue Mar 23 06:24:04 2004 Input: P5:=PolynomialRing(G5); G25:=ext>; [Order(k):k in G25|k ne 0]; Output: Magma V2.10-6 Tue Mar 23 2004 06:24:01 on modular [Seed = 406341203] ------------------------------------- >> P5:=PolynomialRing(G5); ^ User error: Identifier 'G5' has not been declared or assigned >> G25:=ext>; ^ User error: Identifier 'P5' has not been declared or assigned >> [Order(k):k in G25|k ne 0]; ^ User error: Identifier 'G25' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee44.uab.es. (158.109.66.44) Time: Tue Mar 23 06:24:23 2004 Input: G5:=GF(5); P5:=PolynomialRing(G5); G25:=ext>; [Order(k):k in G25|k ne 0]; Output: Magma V2.10-6 Tue Mar 23 2004 06:24:20 on modular [Seed = 288444271] ------------------------------------- [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee44.uab.es. (158.109.66.44) Time: Tue Mar 23 06:45:00 2004 Input: G5:=GF(5); P5:=PolynomialRing(G5); G25:=ext>; [Order(k):k in G25|k ne 0]; Roots(MinimalPolynomial(G25.1,G25),G5); Output: Magma V2.10-6 Tue Mar 23 2004 06:44:57 on modular [Seed = 789531660] ------------------------------------- [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] >> Roots(MinimalPolynomial(G25.1,G25),G5); ^ Runtime error in 'Roots': Argument 1 cannot be coerced to be over argument 2 Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee44.uab.es. (158.109.66.44) Time: Tue Mar 23 06:45:51 2004 Input: G5:=GF(5); P5:=PolynomialRing(G5); G25:=ext>; [Order(k):k in G25|k ne 0]; > 2*G25.1^(-3)-G25.1^5+G25.1^6/(G25.1+2); Output: Magma V2.10-6 Tue Mar 23 2004 06:45:48 on modular [Seed = 1484274478] ------------------------------------- [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] G25.1^17 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (213.182.177.254) Time: Tue Mar 23 07:42:14 2004 Input: C:=BKLC(GF(2),48,36); C; WeightDistribution(C); BKLCLowerBound(GF(2),48,36), BKLCUpperBound(GF(2),48,36); Output: Magma V2.10-6 Tue Mar 23 2004 07:42:10 on modular [Seed = 3387537777] ------------------------------------- [48, 36, 6] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0 1] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 1] [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 1 0 0 0 0] [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 0 0 0 1] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 0 0 1 0] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 0 0] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 0 1 1 1] [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 1 0 1] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 1 1 0 0] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 0 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 1 0 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 1 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 1 1 0 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 1 0 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0] [ <0, 1>, <6, 6768>, <8, 181290>, <10, 3199728>, <12, 34013760>, <14, 235496640>, <16, 1101037263>, <18, 3569211328>, <20, 8171728320>, <22, 13371954720>, <24, 15745817100>, <26, 13371954720>, <28, 8171728320>, <30, 3569211328>, <32, 1101037263>, <34, 235496640>, <36, 34013760>, <38, 3199728>, <40, 181290>, <42, 6768>, <48, 1> ] 6 6 Total time: 3.079 seconds, Total memory usage: 2.29MB ************** MAGMA ***************** Host 3(NXDOMAIN) (213.182.177.254) Time: Tue Mar 23 07:44:14 2004 Input: C:=BKLC(GF(2),36,25); C; WeightDistribution(C); BKLCLowerBound(GF(2),36,25), BKLCUpperBound(GF(2),36,25); Output: Magma V2.10-6 Tue Mar 23 2004 07:44:11 on modular [Seed = 3353851590] ------------------------------------- [36, 25, 5] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 0] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 1 0] [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 1 0 0] [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 0] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 1 0] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1] [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 1 0] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 1 0 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 0 1 0 1 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 1 1 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 1 0 0 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 1 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 0 1 1 1] [ <0, 1>, <5, 236>, <6, 1160>, <7, 4276>, <8, 15064>, <9, 45556>, <10, 122648>, <11, 295024>, <12, 613776>, <13, 1120804>, <14, 1845840>, <15, 2729796>, <16, 3581378>, <17, 4192508>, <18, 4424112>, <19, 4200448>, <20, 3567808>, <21, 2714324>, <22, 1852968>, <23, 1129852>, <24, 612560>, <25, 294796>, <26, 124600>, <27, 45456>, <28, 14384>, <29, 3996>, <30, 896>, <31, 140>, <32, 21>, <33, 4> ] 5 6 Total time: 3.109 seconds, Total memory usage: 2.29MB ************** MAGMA ***************** Host 3(NXDOMAIN) (213.182.177.254) Time: Tue Mar 23 07:45:36 2004 Input: C:=BKLC(GF(2),72,59); C; WeightDistribution(C); BKLCLowerBound(GF(2),72,59), BKLCUpperBound(GF(2),72,59); Output: Magma V2.10-6 Tue Mar 23 2004 07:45:33 on modular [Seed = 4158097024] ------------------------------------- [72, 59, 5] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1 1 1 0] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 1 1 0 0 1 0] [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 1 0] [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 1 1 0 1 0 0] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 0] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 1 1] [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 1 1] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 1 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 1 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 1 0 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 0 1 0 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 0 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 1 1 0 1 1 1 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 1 1 0 0 0 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 0 1 0 0 1 0 1 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 0 0 1 0 0 1 1 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 0 1 0 0 1 1 0 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 1 1 0 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 0 1 0 0 0 0 1 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1 1 1 1 0 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 0 0 0 1 1 0 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 1 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 1 1 0 0 1 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 1 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 0 0 0 0 0 1 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 0 1 0 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 0 1 0] [ <0, 1>, <5, 1128>, <6, 26860>, <7, 136085>, <8, 1727617>, <9, 8860595>, <10, 72894979>, <11, 337226581>, <12, 1995618017>, <13, 8249826787>, <14, 37701458267>, <15, 137745581421>, <16, 510421564589>, <17, 1638264388027>, <18, 5089447841435>, <19, 14322910055725>, <20, 38160216078729>, <21, 94257482859787>, <22, 218674445757027>, <23, 475443408728665>, <24, 970203439687365>, <25, 1863834659615695>, <26, 3367745181257727>, <27, 5739158175130777>, <28, 9222811854381045>, <29, 13992658891545535>, <30, 20058454048820471>, <31, 27172342827651073>, <32, 34818318130442907>, <33, 42201675795927815>, <34, 48407593329417735>, <35, 52559709334701121>, <36, 54015175607956717>, <37, 52559709276925351>, <38, 48407593220331495>, <39, 42201675828283295>, <40, 34818318308068227>, <41, 27172342829017273>, <42, 20058453862532201>, <43, 13992658867445215>, <44, 9222811999666755>, <45, 5739158203763017>, <46, 3367745096762097>, <47, 1863834638769415>, <48, 970203472768335> ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 3(NXDOMAIN) (213.182.177.254) Time: Tue Mar 23 07:46:18 2004 Input: C:=BKLC(GF(2),72,59); WeightDistribution(C); BKLCLowerBound(GF(2),72,59), BKLCUpperBound(GF(2),72,59); Output: Magma V2.10-6 Tue Mar 23 2004 07:46:15 on modular [Seed = 3972832609] ------------------------------------- [ <0, 1>, <5, 1128>, <6, 26860>, <7, 136085>, <8, 1727617>, <9, 8860595>, <10, 72894979>, <11, 337226581>, <12, 1995618017>, <13, 8249826787>, <14, 37701458267>, <15, 137745581421>, <16, 510421564589>, <17, 1638264388027>, <18, 5089447841435>, <19, 14322910055725>, <20, 38160216078729>, <21, 94257482859787>, <22, 218674445757027>, <23, 475443408728665>, <24, 970203439687365>, <25, 1863834659615695>, <26, 3367745181257727>, <27, 5739158175130777>, <28, 9222811854381045>, <29, 13992658891545535>, <30, 20058454048820471>, <31, 27172342827651073>, <32, 34818318130442907>, <33, 42201675795927815>, <34, 48407593329417735>, <35, 52559709334701121>, <36, 54015175607956717>, <37, 52559709276925351>, <38, 48407593220331495>, <39, 42201675828283295>, <40, 34818318308068227>, <41, 27172342829017273>, <42, 20058453862532201>, <43, 13992658867445215>, <44, 9222811999666755>, <45, 5739158203763017>, <46, 3367745096762097>, <47, 1863834638769415>, <48, 970203472768335>, <49, 475443419338225>, <50, 218674441447761>, <51, 94257479119687>, <52, 38160211133595>, <53, 14322910853665>, <54, 5089452368905>, <55, 1638264347059>, <56, 510419473143>, <57, 137745561221>, <58, 37702036053>, <59, 8249821555>, <60, 1995551527>, <61, 337234901>, <62, 72877949>, <63, 8857163>, <64, 1737128>, <65, 136845>, <66, 24909>, <67, 1035>, <68, 175>, <69, 5>, <70, 1> ] 5 6 Total time: 3.189 seconds, Total memory usage: 2.29MB ************** MAGMA ***************** Host 3(NXDOMAIN) (213.182.177.254) Time: Tue Mar 23 07:47:10 2004 Input: C:=BKLC(GF(2),96,82); WeightDistribution(C); BKLCLowerBound(GF(2),96,82), BKLCUpperBound(GF(2),96,82); Output: Magma V2.10-6 Tue Mar 23 2004 07:47:07 on modular [Seed = 3854930996] ------------------------------------- [ <0, 1>, <5, 3909>, <6, 58767>, <7, 726194>, <8, 8084539>, <9, 79135145>, <10, 688463964>, <11, 5382665268>, <12, 38126997141>, <13, 246356860988>, <14, 1460546783914>, <15, 7984330691404>, <16, 40420658174599>, <17, 190214859442746>, <18, 834831955585436>, <19, 3427204737279552>, <20, 13194737977667550>, <21, 47752385896603689>, <22, 162792225412896219>, <23, 523766287300729402>, <24, 1593122455401864901>, <25, 4588192680350917969>, <26, 12529295399518400960>, <27, 32483358424003147564>, <28, 80048276113219690713>, <29, 187699406092565175034>, <30, 419195340270041337144>, <31, 892480401814481393680>, <32, 1812850816209043696874>, <33, 3515831886050200898840>, <34, 6514629671150042194160>, <35, 11540201131655558858560>, <36, 19554229695409350758696>, <37, 31709561668375728097626>, <38, 49233266800777426070382>, <39, 73218704472736768787524>, <40, 104336653873722147844494>, <41, 142508600413158166442706>, <42, 186618405303008372262856>, <43, 234357997357026611061960>, <44, 282294860452529841723930>, <45, 326207394300770759759616>, <46, 361664719768663425627516>, <47, 384749701881776839102920>, <48, 392765320670497464495630>, <49, 384749701880785168223100>, <50, 361664719768363101117000>, <51, 326207394301566671645376>, <52, 282294860452993698996660>, <53, 234357997356534444081450>, <54, 186618405302561024096670>, <55, 142508600413357862684580>, <56, 104336653874035419616362>, <57, 73218704472734688086186>, <58, 49233266800614543740496>, <59, 31709561668292421818520>, <60, 19554229695471510544042>, <61, 11540201131744699983148>, <62, 6514629671130755230904>, <63, 3515831885988930685712>, <64, 1812850816218892546821>, <65, 892480401846218890200>, <66, 419195340260386172720>, <67, 187699406079832391104>, <68, 80048276121492805544>, <69, 32483358427814782113>, <70, 12529295394291034691>, <71, 4588192679652052362>, <72, 1593122457886538311>, <73, 523766287262804133>, <74, 162792224506950204>, <75, 47752385990291652>, <76, 13194738231303441>, <77, 3427204692172436>, <78, 834831902198762>, <79, 190214873791436>, <80, 40420666185595>, <81, 7984327367514>, <82, 1460545991676>, <83, 246357393920>, <84, 38127075230>, <85, 5382622061>, <86, 688435015>, <87, 79131554>, <88, 8094913>, <89, 727781>, <90, 56720>, <91, 3708>, <92, 189>, <93, 10> ] 5 6 Total time: 3.559 seconds, Total memory usage: 2.29MB ************** MAGMA ***************** Host 3(NXDOMAIN) (213.182.177.254) Time: Tue Mar 23 07:47:49 2004 Input: BKLCLowerBound(GF(2),96,82), BKLCUpperBound(GF(2),96,82); Output: Magma V2.10-6 Tue Mar 23 2004 07:47:46 on modular [Seed = 288448760] ------------------------------------- 5 6 Total time: 3.029 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 3(NXDOMAIN) (213.182.177.254) Time: Tue Mar 23 07:48:26 2004 Input: BKLCLowerBound(GF(2),144,129), BKLCUpperBound(GF(2),144,129); Output: Magma V2.10-6 Tue Mar 23 2004 07:48:23 on modular [Seed = 221085441] ------------------------------------- 5 6 Total time: 2.979 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 3(NXDOMAIN) (213.182.177.254) Time: Tue Mar 23 07:48:55 2004 Input: BKLCLowerBound(GF(2),192,176), BKLCUpperBound(GF(2),192,176); Output: Magma V2.10-6 Tue Mar 23 2004 07:48:52 on modular [Seed = 69498411] ------------------------------------- 5 6 Total time: 3.019 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 3(NXDOMAIN) (213.182.177.254) Time: Tue Mar 23 07:49:17 2004 Input: BKLCLowerBound(GF(2),192,176), BKLCUpperBound(GF(2),192,176); Output: Magma V2.10-6 Tue Mar 23 2004 07:49:14 on modular [Seed = 856899938] ------------------------------------- 5 6 Total time: 3.029 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 3(NXDOMAIN) (213.182.177.254) Time: Tue Mar 23 07:55:37 2004 Input: BKLCLowerBound(GF(2),24,14), BKLCUpperBound(GF(2),24,14); Output: Magma V2.10-6 Tue Mar 23 2004 07:55:34 on modular [Seed = 2410675282] ------------------------------------- 6 6 Total time: 3.039 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 3(NXDOMAIN) (213.182.177.254) Time: Tue Mar 23 07:57:03 2004 Input: BKLCLowerBound(GF(2),23,14), BKLCUpperBound(GF(2),23,14); Output: Magma V2.10-6 Tue Mar 23 2004 07:57:00 on modular [Seed = 2259088001] ------------------------------------- 5 5 Total time: 3.059 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 3(NXDOMAIN) (213.182.177.254) Time: Tue Mar 23 07:57:33 2004 Input: BKLCLowerBound(GF(2),36,25), BKLCUpperBound(GF(2),36,25); Output: Magma V2.10-6 Tue Mar 23 2004 07:57:30 on modular [Seed = 3012806546] ------------------------------------- 5 6 Total time: 2.959 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 3(NXDOMAIN) (213.182.177.254) Time: Tue Mar 23 07:57:50 2004 Input: BKLCLowerBound(GF(2),35,25), BKLCUpperBound(GF(2),35,25); Output: Magma V2.10-6 Tue Mar 23 2004 07:57:47 on modular [Seed = 2861227770] ------------------------------------- 4 5 Total time: 2.959 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 3(NXDOMAIN) (213.182.177.254) Time: Tue Mar 23 07:58:45 2004 Input: BKLCLowerBound(GF(2),34,23), BKLCUpperBound(GF(2),34,23); Output: Magma V2.10-6 Tue Mar 23 2004 07:58:42 on modular [Seed = 2709640504] ------------------------------------- 6 6 Total time: 3.029 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 3(NXDOMAIN) (213.182.177.254) Time: Tue Mar 23 07:59:04 2004 Input: BKLCLowerBound(GF(2),33,23), BKLCUpperBound(GF(2),33,23); Output: Magma V2.10-6 Tue Mar 23 2004 07:59:01 on modular [Seed = 3640175702] ------------------------------------- 5 5 Total time: 3.019 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 3(NXDOMAIN) (213.182.177.254) Time: Tue Mar 23 08:00:00 2004 Input: BKLCLowerBound(GF(2),34,24), BKLCUpperBound(GF(2),34,24); Output: Magma V2.10-6 Tue Mar 23 2004 07:59:57 on modular [Seed = 3623330561] ------------------------------------- 4 5 Total time: 3.029 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.32.172.proxycache.rima-tde.net. (80.58.32.172) Time: Tue Mar 23 12:39:49 2004 Input: G1:=GF(1); Output: Magma V2.10-6 Tue Mar 23 2004 12:39:46 on modular [Seed = 4073899149] ------------------------------------- >> G1:=GF(1);; ^ Runtime error in 'GF': Argument 1 (1) should be >= 2 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.172.proxycache.rima-tde.net. (80.58.32.172) Time: Tue Mar 23 12:44:40 2004 Input: G2:=GF(2); MinimalPolynomial(G2); Output: Magma V2.10-6 Tue Mar 23 2004 12:44:37 on modular [Seed = 507390341] ------------------------------------- >> MinimalPolynomial(G2);; ^ Runtime error in 'MinimalPolynomial': Bad argument types Argument types given: FldFin Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.172.proxycache.rima-tde.net. (80.58.32.172) Time: Tue Mar 23 12:48:29 2004 Input: G2:=GF(2); MinimalPolynomial(G2); z2:= Integers (2); P := PolynomialRing (z2); f:= x+1; IsIrreducible (f); Output: Magma V2.10-6 Tue Mar 23 2004 12:48:26 on modular [Seed = 823200069] ------------------------------------- >> MinimalPolynomial(G2); ^ Runtime error in 'MinimalPolynomial': Bad argument types Argument types given: FldFin true Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.32.172.proxycache.rima-tde.net. (80.58.32.172) Time: Tue Mar 23 12:48:53 2004 Input: G2:=GF(2); z2:= Integers (2); P := PolynomialRing (z2); f:= x+1; IsIrreducible (f); Output: Magma V2.10-6 Tue Mar 23 2004 12:48:50 on modular [Seed = 553720253] ------------------------------------- true Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.32.172.proxycache.rima-tde.net. (80.58.32.172) Time: Tue Mar 23 12:50:04 2004 Input: G2:=GF(2); z2:= Integers (2); P := PolynomialRing (z2); f:= x+1; IsIrreducible (f); Gf2:= ext < G2 |f>; Output: Magma V2.10-6 Tue Mar 23 2004 12:50:01 on modular [Seed = 1366387078] ------------------------------------- true Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.32.172.proxycache.rima-tde.net. (80.58.32.172) Time: Tue Mar 23 12:50:55 2004 Input: G2:=GF(2); z2:= Integers (2); P := PolynomialRing (z2); f:= x+1; IsIrreducible (f); Gf2:= ext < G2 |f>; [x : x in Gf2]; Output: Magma V2.10-6 Tue Mar 23 2004 12:50:51 on modular [Seed = 1181122211] ------------------------------------- true [ 0, 1 ] Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.32.172.proxycache.rima-tde.net. (80.58.32.172) Time: Tue Mar 23 12:53:15 2004 Input: G2:=GF(2); z2:= Integers (2); P := PolynomialRing (z2); f:= x^2+1; IsIrreducible (f); Gf4:= ext < G2 |f>; [x : x in Gf2]; Output: Magma V2.10-6 Tue Mar 23 2004 12:53:12 on modular [Seed = 2086421994] ------------------------------------- false >> Gf4:= ext < G2 |f>; ^ Runtime error in ext< ... >: Argument is not irreducible >> [x : x in Gf2];; ^ User error: Identifier 'Gf2' has not been declared or assigned Total time: 3.099 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.32.172.proxycache.rima-tde.net. (80.58.32.172) Time: Tue Mar 23 12:53:30 2004 Input: G2:=GF(2); z2:= Integers (2); P := PolynomialRing (z2); f:= x^2; IsIrreducible (f); Gf4:= ext < G2 |f>; [x : x in Gf2]; Output: Magma V2.10-6 Tue Mar 23 2004 12:53:27 on modular [Seed = 1968524540] ------------------------------------- false >> Gf4:= ext < G2 |f>; ^ Runtime error in ext< ... >: Argument is not irreducible >> [x : x in Gf2];; ^ User error: Identifier 'Gf2' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.32.172.proxycache.rima-tde.net. (80.58.32.172) Time: Tue Mar 23 12:54:34 2004 Input: G2:=GF(2); z2:= Integers (2); P := PolynomialRing (z2); f:= x^2+x+1; IsIrreducible (f); Gf4:= ext < G2 |f>; [x : x in Gf2]; Output: Magma V2.10-6 Tue Mar 23 2004 12:54:31 on modular [Seed = 1783255971] ------------------------------------- true >> [x : x in Gf2];; ^ User error: Identifier 'Gf2' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.32.172.proxycache.rima-tde.net. (80.58.32.172) Time: Tue Mar 23 12:54:53 2004 Input: G2:=GF(2); z2:= Integers (2); P := PolynomialRing (z2); f:= x^2+x+1; IsIrreducible (f); Gf4:= ext < G2 |f>; [x : x in Gf4]; Output: Magma V2.10-6 Tue Mar 23 2004 12:54:50 on modular [Seed = 1665358487] ------------------------------------- true [ 1, Gf4.1, Gf4.1^2, 0 ] Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.32.172.proxycache.rima-tde.net. (80.58.32.172) Time: Tue Mar 23 12:57:39 2004 Input: G2:=GF(2); z2:= Integers (2); P := PolynomialRing (z2); f:= x^3+x+1; IsIrreducible (f); Gf8:= ext < G2 |f>; [x : x in Gf8]; Output: Magma V2.10-6 Tue Mar 23 2004 12:57:36 on modular [Seed = 2461181980] ------------------------------------- true [ 1, Gf8.1, Gf8.1^2, Gf8.1^3, Gf8.1^4, Gf8.1^5, Gf8.1^6, 0 ] Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.32.172.proxycache.rima-tde.net. (80.58.32.172) Time: Tue Mar 23 12:58:50 2004 Input: G2:=GF(2); z2:= Integers (2); P := PolynomialRing (z2); f:= x^4+x+1; IsIrreducible (f); Gf16:= ext < G2 |f>; [x : x in Gf16]; Output: Magma V2.10-6 Tue Mar 23 2004 12:58:47 on modular [Seed = 2343285058] ------------------------------------- true [ 1, Gf16.1, Gf16.1^2, Gf16.1^3, Gf16.1^4, Gf16.1^5, Gf16.1^6, Gf16.1^7, Gf16.1^8, Gf16.1^9, Gf16.1^10, Gf16.1^11, Gf16.1^12, Gf16.1^13, Gf16.1^14, 0 ] Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.32.172.proxycache.rima-tde.net. (80.58.32.172) Time: Tue Mar 23 13:03:22 2004 Input: G2:=GF(2); z2:= Integers (2); P := PolynomialRing (z2); f:= x^4+x+1; IsIrreducible (f); Gf16:= ext < G2 |f>; [x : x in Gf16]; G2:=GF(2); z2:= Integers (2); P := PolynomialRing (z2); f:= x^2+x+1; Gf4:= ext < G2 |f>; [x : x in Gf4]; Gf4 subset Gf16; Output: Magma V2.10-6 Tue Mar 23 2004 13:03:19 on modular [Seed = 2709625432] ------------------------------------- true [ 1, Gf16.1, Gf16.1^2, Gf16.1^3, Gf16.1^4, Gf16.1^5, Gf16.1^6, Gf16.1^7, Gf16.1^8, Gf16.1^9, Gf16.1^10, Gf16.1^11, Gf16.1^12, Gf16.1^13, Gf16.1^14, 0 ] [ 1, Gf4.1, Gf4.1^2, 0 ] >> Gf4 subset Gf16;; ^ Runtime error in 'subset': Arguments have no covering field Total time: 3.049 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.32.172.proxycache.rima-tde.net. (80.58.32.172) Time: Tue Mar 23 13:03:40 2004 Input: G2:=GF(2); z2:= Integers (2); P := PolynomialRing (z2); f:= x^4+x+1; IsIrreducible (f); Gf16:= ext < G2 |f>; [x : x in Gf16]; G2:=GF(2); z2:= Integers (2); P := PolynomialRing (z2); f:= x^2+x+1; Gf4:= ext < G2 |f>; [x : x in Gf4]; Gf16 subset Gf4; Output: Magma V2.10-6 Tue Mar 23 2004 13:03:37 on modular [Seed = 3606506801] ------------------------------------- true [ 1, Gf16.1, Gf16.1^2, Gf16.1^3, Gf16.1^4, Gf16.1^5, Gf16.1^6, Gf16.1^7, Gf16.1^8, Gf16.1^9, Gf16.1^10, Gf16.1^11, Gf16.1^12, Gf16.1^13, Gf16.1^14, 0 ] [ 1, Gf4.1, Gf4.1^2, 0 ] >> Gf16 subset Gf4;; ^ Runtime error in 'subset': Arguments have no covering field Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.32.172.proxycache.rima-tde.net. (80.58.32.172) Time: Tue Mar 23 13:13:44 2004 Input: G5 := GF(5); h:= 3+2*x+x^2; G25:= ext < G5 |h>; F := G25; Output: Magma V2.10-6 Tue Mar 23 2004 13:13:41 on modular [Seed = 4292854196] ------------------------------------- >> h:= 3+2*x+x^2; ^ User error: Identifier 'x' has not been declared or assigned >> G25:= ext < G5 |h>; ^ User error: Identifier 'h' has not been declared or assigned >> F := G25;; ^ User error: Identifier 'G25' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.172.proxycache.rima-tde.net. (80.58.32.172) Time: Tue Mar 23 13:15:02 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); G5 := GF(5); h:= 3+2*x+x^2; G25:= ext < G5 |h>; F := G25; G := G5; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; Output: Magma V2.10-6 Tue Mar 23 2004 13:14:59 on modular [Seed = 4107586121] ------------------------------------- >> p1 := alpha^2 + alpha*x + beta*x^2; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt >> p2 := 1 + alpha*x;; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.172.proxycache.rima-tde.net. (80.58.32.172) Time: Tue Mar 23 13:17:20 2004 Input: [x : x in GF(2)]; [x : x in GF(4)]; [x : x in GF(8)]; [x : x in GF(16)]; Output: Magma V2.10-6 Tue Mar 23 2004 13:17:17 on modular [Seed = 3854949078] ------------------------------------- [ 0, 1 ] [ 1, $.1, $.1^2, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, $.1^7, $.1^8, $.1^9, $.1^10, $.1^11, $.1^12, $.1^13, $.1^14, 0 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.172.proxycache.rima-tde.net. (80.58.32.172) Time: Tue Mar 23 13:19:04 2004 Input: P := PolynomialRing (G25); IsFinite (P); /*false*/ /*EXERCICI 2.ii*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; /*[2,3]*/ G := G5; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; /*EXERCICI 2.iii*/ suma := p1 + p2; suma; /*x^2 + alpha^19*x + alpha^9*/ producte := p1 * p2; producte; /*alpha*x^3 + alpha^9*x^2 + alpha^10*x + alpha^2*/ /*EXERCICI 2.iv*/ quocient := p1 div p2; quocient; /*alpha^23*x + alpha^21*/ residu := p1 mod p2; residu; /* alpha*/ /*EXERCICI 2.v*/ mcd := GCD (p1,p2); mcd; /*1 */ mcm := LCM (p1,p2); mcm; Output: Magma V2.10-6 Tue Mar 23 2004 13:19:01 on modular [Seed = 440018320] ------------------------------------- >> P := PolynomialRing (G25); ^ User error: Identifier 'G25' has not been declared or assigned >> IsFinite (P); ^ User error: Identifier 'P' has not been declared or assigned >> lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; ^ User error: Identifier 'G25' has not been declared or assigned >> lista_primitius_G25; ^ User error: Identifier 'lista_primitius_G25' has not been declared or assigned >> lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; ^ User error: Identifier 'G5' has not been declared or assigned >> lista_primitius_G5; ^ User error: Identifier 'lista_primitius_G5' has not been declared or assigned >> G := G5; ^ User error: Identifier 'G5' has not been declared or assigned >> p1 := alpha^2 + alpha*x + beta*x^2; ^ User error: Identifier 'alpha' has not been declared or assigned >> p2 := 1 + alpha*x; ^ User error: Identifier 'alpha' has not been declared or assigned >> suma := p1 + p2; ^ User error: Identifier 'p1' has not been declared or assigned >> suma; ^ User error: Identifier 'suma' has not been declared or assigned >> producte := p1 * p2; ^ User error: Identifier 'p1' has not been declared or assigned >> producte; ^ User error: Identifier 'producte' has not been declared or assigned >> quocient := p1 div p2; ^ User error: Identifier 'p1' has not been declared or assigned >> quocient; ^ User error: Identifier 'quocient' has not been declared or assigned >> residu := p1 mod p2; ^ User error: Identifier 'p1' has not been declared or assigned >> residu; ^ User error: Identifier 'residu' has not been declared or assigned >> mcd := GCD (p1,p2); ^ User error: Identifier 'p1' has not been declared or assigned >> mcd; ^ User error: Identifier 'mcd' has not been declared or assigned >> mcm := LCM (p1,p2); ^ User error: Identifier 'p1' has not been declared or assigned >> mcm;; ^ User error: Identifier 'mcm' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.172.proxycache.rima-tde.net. (80.58.32.172) Time: Tue Mar 23 13:19:53 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); G5 := GF(5); h:= 3+2*x+x^2; G25:= ext < G5 |h>; F := G25; P := PolynomialRing (G25); IsFinite (P); /*false*/ /*EXERCICI 2.ii*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; /*[2,3]*/ G := G5; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; /*EXERCICI 2.iii*/ suma := p1 + p2; suma; /*x^2 + alpha^19*x + alpha^9*/ producte := p1 * p2; producte; /*alpha*x^3 + alpha^9*x^2 + alpha^10*x + alpha^2*/ /*EXERCICI 2.iv*/ quocient := p1 div p2; quocient; /*alpha^23*x + alpha^21*/ residu := p1 mod p2; residu; /* alpha*/ /*EXERCICI 2.v*/ mcd := GCD (p1,p2); mcd; /*1 */ mcm := LCM (p1,p2); mcm; Output: Magma V2.10-6 Tue Mar 23 2004 13:19:50 on modular [Seed = 288435912] ------------------------------------- false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] x^2 + alpha^19*x + alpha^9 alpha*x^3 + alpha^9*x^2 + alpha^10*x + alpha^2 alpha^23*x + alpha^21 alpha 1 x^3 + alpha^8*x^2 + alpha^9*x + alpha Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.172.proxycache.rima-tde.net. (80.58.32.172) Time: Tue Mar 23 13:20:47 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); G5 := GF(5); h:= 3+2*x+x^2; G25:= ext < G5 |h>; F := G25; P := PolynomialRing (G25); IsFinite (P); /*false*/ /*EXERCICI 2.ii*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; /*[2,3]*/ G := G5; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; Output: Magma V2.10-6 Tue Mar 23 2004 13:20:44 on modular [Seed = 18956002] ------------------------------------- false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.172.proxycache.rima-tde.net. (80.58.32.172) Time: Tue Mar 23 13:21:22 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); G5 := GF(5); h:= 3+2*x+x^2; G25:= ext < G5 |h>; F := G25; P := PolynomialRing (G25); G := G5; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; Output: Magma V2.10-6 Tue Mar 23 2004 13:21:19 on modular [Seed = 941160504] ------------------------------------- Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.172.proxycache.rima-tde.net. (80.58.32.172) Time: Tue Mar 23 13:22:32 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); G5 := GF(5); h:= 3+2*x+x^2; G25:= ext < G5 |h>; F := G25; P := PolynomialRing (G25); G := G5; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; XGCD(p1,p2); Output: Magma V2.10-6 Tue Mar 23 2004 13:22:29 on modular [Seed = 705358416] ------------------------------------- 1 alpha^23 alpha^10*x + alpha^8 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.172.proxycache.rima-tde.net. (80.58.32.172) Time: Tue Mar 23 13:25:07 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); G5 := GF(5); h:= 3+2*x+x^2; G25:= ext < G5 |h>; F := G25; P := PolynomialRing (G25); G := G5; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; XGCD(p1,p2); alpha^23*p1+(alpha^10*x + alpha^8)*p2; Output: Magma V2.10-6 Tue Mar 23 2004 13:25:04 on modular [Seed = 1568513090] ------------------------------------- 1 alpha^23 alpha^10*x + alpha^8 1 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.172.proxycache.rima-tde.net. (80.58.32.172) Time: Tue Mar 23 13:33:45 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); G5 := GF(5); h:= 3+2*x+x^2; G25:= ext < G5 |h>; F := G25; P := PolynomialRing (G25); G := G5; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; Factorization ((1/alpha^4) - alpha^-3 * x + alpha^5 * x^2); Output: Magma V2.10-6 Tue Mar 23 2004 13:33:42 on modular [Seed = 1214810961] ------------------------------------- [ ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 23 13:34:12 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x^6+x^2+1); Points(C); Output: Magma V2.10-6 Tue Mar 23 2004 13:34:09 on modular [Seed = 2136980545] ------------------------------------- >> Points(C);; ^ Runtime error in 'Points': A positive height bound must be given Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.172.proxycache.rima-tde.net. (80.58.32.172) Time: Tue Mar 23 13:34:44 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); G5 := GF(5); h:= 3+2*x+x^2; G25:= ext < G5 |h>; F := G25; P := PolynomialRing (G25); G := G5; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; polinomi:=Factorization ((1/alpha^4) - alpha^-3 * x + alpha^5 * x^2); Roots (polinomi,G25); Output: Magma V2.10-6 Tue Mar 23 2004 13:34:41 on modular [Seed = 1985393960] ------------------------------------- >> Roots (polinomi,G25); ^ Runtime error in 'Roots': Bad argument types Argument types given: SeqEnum[Tup], FldFin Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 23 13:34:56 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x^6+x^2+1); Points(C : Bound:=4); Output: Magma V2.10-6 Tue Mar 23 2004 13:34:53 on modular [Seed = 1833807423] ------------------------------------- {@ (1 : -1 : 0), (1 : 1 : 0), (0 : -1 : 1), (0 : 1 : 1), (-1 : -9 : 2), (-1 : 9 : 2), (1 : -9 : 2), (1 : 9 : 2) @} Total time: 2.909 seconds, Total memory usage: 29.52MB ************** MAGMA ***************** Host 80.58.32.172.proxycache.rima-tde.net. (80.58.32.172) Time: Tue Mar 23 13:35:23 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); G5 := GF(5); h:= 3+2*x+x^2; G25:= ext < G5 |h>; F := G25; P := PolynomialRing (G25); G := G5; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; polinomi:=Factorization ((1/alpha^4) - alpha^-3 * x + alpha^5 * x^2); Roots (polinomi[0],G25); Output: Magma V2.10-6 Tue Mar 23 2004 13:35:20 on modular [Seed = 2680118504] ------------------------------------- >> Roots (polinomi[0],G25); ^ Runtime error in '[]': Sequence element 0 not defined Total time: 3.249 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 23 13:35:25 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x^3-1); Points(C : Bound:=4); Output: Magma V2.10-6 Tue Mar 23 2004 13:35:22 on modular [Seed = 2629591017] ------------------------------------- {@ (1 : 0 : 0), (1 : 0 : 1) @} Total time: 3.319 seconds, Total memory usage: 29.52MB ************** MAGMA ***************** Host 80.58.32.172.proxycache.rima-tde.net. (80.58.32.172) Time: Tue Mar 23 13:35:40 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); G5 := GF(5); h:= 3+2*x+x^2; G25:= ext < G5 |h>; F := G25; P := PolynomialRing (G25); G := G5; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; polinomi:=Factorization ((1/alpha^4) - alpha^-3 * x + alpha^5 * x^2); Roots (polinomi[1],G25); Output: Magma V2.10-6 Tue Mar 23 2004 13:35:37 on modular [Seed = 2376945387] ------------------------------------- >> Roots (polinomi[1],G25); ^ Runtime error in 'Roots': Bad argument types Argument types given: Tup, FldFin Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 23 13:36:06 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x^3-1); #(Points(C : Bound:=4)); Output: Magma V2.10-6 Tue Mar 23 2004 13:36:03 on modular [Seed = 2225358600] ------------------------------------- 2 Total time: 2.989 seconds, Total memory usage: 29.52MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 23 13:37:36 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x^3-1); #(Points(C : Bound:=4)); ZetaFunction(C); Output: Magma V2.10-6 Tue Mar 23 2004 13:37:33 on modular [Seed = 3130685768] ------------------------------------- 2 >> ZetaFunction(C);; ^ Runtime error in 'ZetaFunction': Base field of argument must be finite. Total time: 2.909 seconds, Total memory usage: 29.52MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 23 13:38:20 2004 Input: C := HyperellipticCurve(x^3-1); ZetaFunction(C); Output: Magma V2.10-6 Tue Mar 23 2004 13:38:17 on modular [Seed = 2962257078] ------------------------------------- >> C := HyperellipticCurve(x^3-1); ^ User error: Identifier 'x' has not been declared or assigned >> ZetaFunction(C);; ^ User error: Identifier 'C' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.172.proxycache.rima-tde.net. (80.58.32.172) Time: Tue Mar 23 13:38:44 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); G5 := GF(5); h:= 3+2*x+x^2; G25:= ext < G5 |h>; F := G25; P := PolynomialRing (G25); G := G5; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; Factorization ((1/alpha^4) - alpha^-3 * x + alpha^5 * x^2); Output: Magma V2.10-6 Tue Mar 23 2004 13:38:41 on modular [Seed = 2810667913] ------------------------------------- [ ] Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.172.proxycache.rima-tde.net. (80.58.32.172) Time: Tue Mar 23 13:39:42 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); G5 := GF(5); h:= 3+2*x+x^2; G25:= ext < G5 |h>; F := G25; P := PolynomialRing (G25); G := G5; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; algo:=XGCD(p1,p2); Factorization ((1/alpha^4) - alpha^-3 * x + alpha^5 * x^2); Output: Magma V2.10-6 Tue Mar 23 2004 13:39:39 on modular [Seed = 3741194922] ------------------------------------- [ ] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.172.proxycache.rima-tde.net. (80.58.32.172) Time: Tue Mar 23 13:40:00 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); G5 := GF(5); h:= 3+2*x+x^2; G25:= ext < G5 |h>; F := G25; P := PolynomialRing (G25); G := G5; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; algo:=XGCD(p1,p2); algo; Factorization ((1/alpha^4) - alpha^-3 * x + alpha^5 * x^2); Output: Magma V2.10-6 Tue Mar 23 2004 13:39:57 on modular [Seed = 3589607863] ------------------------------------- 1 [ ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.172.proxycache.rima-tde.net. (80.58.32.172) Time: Tue Mar 23 13:40:42 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); G5 := GF(5); h:= 3+2*x+x^2; G25:= ext < G5 |h>; F := G25; P := PolynomialRing (G25); G := G5; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; [d,a,b]:=XGCD(p1,p2); Factorization ((1/alpha^4) - alpha^-3 * x + alpha^5 * x^2); Output: Magma V2.10-6 Tue Mar 23 2004 13:40:39 on modular [Seed = 3320119677] ------------------------------------- >> [d,a,b]:=XGCD(p1,p2); ^ User error: Illegal left hand side of an assignment statement [ ] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.172.proxycache.rima-tde.net. (80.58.32.172) Time: Tue Mar 23 13:41:04 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); G5 := GF(5); h:= 3+2*x+x^2; G25:= ext < G5 |h>; F := G25; P := PolynomialRing (G25); G := G5; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; :=XGCD(p1,p2); Factorization ((1/alpha^4) - alpha^-3 * x + alpha^5 * x^2); Output: Magma V2.10-6 Tue Mar 23 2004 13:41:01 on modular [Seed = 4242290782] ------------------------------------- >> :=XGCD(p1,p2); ^ User error: Illegal left hand side of an assignment statement [ ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 23 13:41:55 2004 Input: F7 := FiniteField(7); C := HyperellipticCurve(x^3-1); ZetaFunction(C); Output: Magma V2.10-6 Tue Mar 23 2004 13:41:52 on modular [Seed = 4073862685] ------------------------------------- >> C := HyperellipticCurve(x^3-1); ^ User error: Identifier 'x' has not been declared or assigned >> ZetaFunction(C);; ^ User error: Identifier 'C' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 23 13:42:20 2004 Input: F7 := FiniteField(7); C := HyperellipticCurve(x^3-1); ZetaFunction(C); Output: Magma V2.10-6 Tue Mar 23 2004 13:42:17 on modular [Seed = 3905433086] ------------------------------------- >> C := HyperellipticCurve(x^3-1); ^ Runtime error in 'HyperellipticCurve': Bad argument types Argument types given: FldFinElt >> ZetaFunction(C);; ^ User error: Identifier 'C' has not been declared or assigned Total time: 3.159 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.172.proxycache.rima-tde.net. (80.58.32.172) Time: Tue Mar 23 13:42:22 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); G5 := GF(5); h:= 3+2*x+x^2; G25:= ext < G5 |h>; F := G25; P := PolynomialRing (G25); G := G5; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; (d,a,b):=XGCD(p1,p2); Factorization ((1/alpha^4) - alpha^-3 * x + alpha^5 * x^2); Output: Magma V2.10-6 Tue Mar 23 2004 13:42:19 on modular [Seed = 3854901489] ------------------------------------- >> (d,a,b):=XGCD(p1,p2); ^ User error: Illegal left hand side of an assignment statement [ ] Total time: 3.209 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 23 13:42:47 2004 Input: F7 := PolynomialRing(FiniteField(7)); C := HyperellipticCurve(x^3-1); ZetaFunction(C); Output: Magma V2.10-6 Tue Mar 23 2004 13:42:43 on modular [Seed = 840103729] ------------------------------------- (7*$.1^2 - 4*$.1 + 1)/(7*$.1^2 - 8*$.1 + 1) Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.32.172.proxycache.rima-tde.net. (80.58.32.172) Time: Tue Mar 23 13:43:55 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); G5 := GF(5); h:= 3+2*x+x^2; G25:= ext < G5 |h>; F := G25; P := PolynomialRing (G25); G := G5; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; algo:=[XGCD(p1,p2)]; Factorization ((1/alpha^4) - alpha^-3 * x + alpha^5 * x^2); Output: Magma V2.10-6 Tue Mar 23 2004 13:43:52 on modular [Seed = 991690355] ------------------------------------- [ ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 23 13:44:01 2004 Input: F7 := PolynomialRing(FiniteField(5)); C := HyperellipticCurve(x^5+x^3+1); ZetaFunction(C); Output: Magma V2.10-6 Tue Mar 23 2004 13:43:58 on modular [Seed = 69517642] ------------------------------------- (25*$.1^4 + 15*$.1^3 + 10*$.1^2 + 3*$.1 + 1)/(5*$.1^2 - 6*$.1 + 1) Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.32.172.proxycache.rima-tde.net. (80.58.32.172) Time: Tue Mar 23 13:44:22 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); G5 := GF(5); h:= 3+2*x+x^2; G25:= ext < G5 |h>; F := G25; P := PolynomialRing (G25); G := G5; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; algo:=[XGCD(p1,p2)]; algo; Factorization ((1/alpha^4) - alpha^-3 * x + alpha^5 * x^2); Output: Magma V2.10-6 Tue Mar 23 2004 13:44:19 on modular [Seed = 237947821] ------------------------------------- [ 1 ] [ ] Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 23 13:44:28 2004 Input: F7 := PolynomialRing(FiniteField(5)); C := HyperellipticCurve(x^4+x^2+1); ZetaFunction(C); Output: Magma V2.10-6 Tue Mar 23 2004 13:44:25 on modular [Seed = 389534398] ------------------------------------- (5*$.1^2 + 2*$.1 + 1)/(5*$.1^2 - 6*$.1 + 1) Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 23 13:44:41 2004 Input: F7 := PolynomialRing(FiniteField(7)); C := HyperellipticCurve(x^4+x^2+1); ZetaFunction(C); Output: Magma V2.10-6 Tue Mar 23 2004 13:44:38 on modular [Seed = 1614849494] ------------------------------------- (7*$.1^2 + 1)/(7*$.1^2 - 8*$.1 + 1) Total time: 2.889 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.32.172.proxycache.rima-tde.net. (80.58.32.172) Time: Tue Mar 23 13:45:00 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); G5 := GF(5); h:= 3+2*x+x^2; G25:= ext < G5 |h>; F := G25; P := PolynomialRing (G25); G := G5; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; [x: x in XGCD(p1,p2)]; Factorization ((1/alpha^4) - alpha^-3 * x + alpha^5 * x^2); Output: Magma V2.10-6 Tue Mar 23 2004 13:44:57 on modular [Seed = 1766436064] ------------------------------------- >> [x: x in XGCD(p1,p2)]; ^ Runtime error in for: Iteration is not possible over this object [ ] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 23 13:56:18 2004 Input: F7 := PolynomialRing(FiniteField(7)); C := HyperellipticCurve(x^3-1); #(Points(C : Bound:=4)); Output: Magma V2.10-6 Tue Mar 23 2004 13:56:15 on modular [Seed = 1181126185] ------------------------------------- 4 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.172.proxycache.rima-tde.net. (80.58.32.172) Time: Tue Mar 23 13:56:24 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); G5 := GF(5); h:= 3+2*x+x^2; G25:= ext < G5 |h>; F := G25; P := PolynomialRing (G25); G := G5; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; pol:=(1/alpha^4) - alpha^-3 * x + alpha^5 * x^2; Factorization ((1/alpha^4) - alpha^-3 * x + alpha^5 * x^2); Evaluate(pol,1); Output: Magma V2.10-6 Tue Mar 23 2004 13:56:21 on modular [Seed = 1332709178] ------------------------------------- [ ] alpha^7 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 23 13:56:28 2004 Input: F7 := PolynomialRing(FiniteField(5)); C := HyperellipticCurve(x^3-1); #(Points(C : Bound:=4)); Output: Magma V2.10-6 Tue Mar 23 2004 13:56:25 on modular [Seed = 1467457326] ------------------------------------- 6 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 23 13:56:36 2004 Input: F7 := PolynomialRing(FiniteField(5^2)); C := HyperellipticCurve(x^3-1); #(Points(C : Bound:=4)); Output: Magma V2.10-6 Tue Mar 23 2004 13:56:33 on modular [Seed = 2709613024] ------------------------------------- 36 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 23 13:56:45 2004 Input: F7 := PolynomialRing(FiniteField(5^3)); C := HyperellipticCurve(x^3-1); #(Points(C : Bound:=4)); Output: Magma V2.10-6 Tue Mar 23 2004 13:56:42 on modular [Seed = 2861196000] ------------------------------------- 126 Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 23 13:56:56 2004 Input: F7 := PolynomialRing(FiniteField(5^4)); C := HyperellipticCurve(x^3-1); #(Points(C : Bound:=4)); Output: Magma V2.10-6 Tue Mar 23 2004 13:56:53 on modular [Seed = 3029630177] ------------------------------------- 576 Total time: 2.959 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 80.58.32.172.proxycache.rima-tde.net. (80.58.32.172) Time: Tue Mar 23 13:57:28 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); G5 := GF(5); h:= 3+2*x+x^2; G25:= ext < G5 |h>; F := G25; P := PolynomialRing (G25); G := G5; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; pol:=(1/alpha^4) - alpha^-3 * x + alpha^5 * x^2; Factorization ((1/alpha^4) - alpha^-3 * x + alpha^5 * x^2); Evaluate(pol,1); Evaluate(pol,x^2 + alpha^4*x + alpha^15); Output: Magma V2.10-6 Tue Mar 23 2004 13:57:25 on modular [Seed = 3198055947] ------------------------------------- [ ] alpha^7 alpha^5*x^4 + alpha^3*x^3 + alpha^8*x^2 + alpha^4*x + alpha^22 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 23 13:57:52 2004 Input: FiniteField(5^4); Output: Magma V2.10-6 Tue Mar 23 2004 13:57:49 on modular [Seed = 2427475997] ------------------------------------- Finite field of size 5^4 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 23 14:06:21 2004 Input: F7 := PolynomialRing(FiniteField(7)); C := HyperellipticCurve(x^3-1); ZetaFunction(C); Output: Magma V2.10-6 Tue Mar 23 2004 14:06:18 on modular [Seed = 4191761267] ------------------------------------- (7*$.1^2 - 4*$.1 + 1)/(7*$.1^2 - 8*$.1 + 1) Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 23 14:07:57 2004 Input: F7 := PolynomialRing(FiniteField(7)); C := HyperellipticCurve(x^3-1); #(Points(C : Bound:=4)); Output: Magma V2.10-6 Tue Mar 23 2004 14:07:55 on modular [Seed = 3303280623] ------------------------------------- 4 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 23 14:12:14 2004 Input: for p in [2..10] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^3-1); #(Points(C : Bound:=4)); end if; end for; Output: Magma V2.10-6 Tue Mar 23 2004 14:12:11 on modular [Seed = 3589609982] ------------------------------------- HyperellipticCurve( f: x^3 + 1 ) In file "/usr/local/magma/package/Geometry/CrvHyp/curve.m", line 257, column 30: >> return HyperellipticCurve(f, Parent(f)!0); ^ Runtime error in 'HyperellipticCurve': Curve is not reduced Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 23 14:12:37 2004 Input: for p in [2..10] do if IsPrime(p) eq 1 then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^3-1); #(Points(C : Bound:=4)); end if; end for; Output: Magma V2.10-6 Tue Mar 23 2004 14:12:34 on modular [Seed = 3758035933] ------------------------------------- >> if IsPrime(p) eq 1 then ^ Runtime error in 'eq': Bad argument types Argument types given: BoolElt, RngIntElt Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 23 14:12:59 2004 Input: for p in [2..10] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^3-1); #(Points(C : Bound:=4)); end if; end for; Output: Magma V2.10-6 Tue Mar 23 2004 14:12:56 on modular [Seed = 671671345] ------------------------------------- HyperellipticCurve( f: x^3 + 1 ) In file "/usr/local/magma/package/Geometry/CrvHyp/curve.m", line 257, column 30: >> return HyperellipticCurve(f, Parent(f)!0); ^ Runtime error in 'HyperellipticCurve': Curve is not reduced Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 23 14:13:21 2004 Input: for p in [5..10] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^3-1); #(Points(C : Bound:=4)); end if; end for; Output: Magma V2.10-6 Tue Mar 23 2004 14:13:18 on modular [Seed = 840105565] ------------------------------------- 6 4 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 23 14:13:40 2004 Input: for p in [5..20] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^3-1); #(Points(C : Bound:=4)); end if; end for; Output: Magma V2.10-6 Tue Mar 23 2004 14:13:37 on modular [Seed = 103205446] ------------------------------------- 6 4 12 12 18 28 Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 23 14:14:06 2004 Input: for p in [5..20] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^3-1); #(Points(C : Bound:=4)); F := PolynomialRing(FiniteField(p^2)); C := HyperellipticCurve(x^3-1); #(Points(C : Bound:=4)); end if; end for; Output: Magma V2.10-6 Tue Mar 23 2004 14:14:03 on modular [Seed = 288480587] ------------------------------------- 6 36 4 48 12 144 12 192 18 324 28 336 Total time: 2.939 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 23 14:15:49 2004 Input: for p in [5..200] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^3-1); #(Points(C : Bound:=4)); F := PolynomialRing(FiniteField(p^2)); C := HyperellipticCurve(x^3-1); #(Points(C : Bound:=4)); end if; end for; Output: Magma V2.10-6 Tue Mar 23 2004 14:15:41 on modular [Seed = 524276707] ------------------------------------- 6 36 4 48 12 144 12 192 18 324 28 336 24 576 30 900 28 1008 48 1344 42 1764 52 1872 48 2304 54 2916 60 3600 48 3648 52 4368 72 5184 84 5376 76 6384 84 7056 90 8100 84 9408 102 10404 124 10416 108 11664 108 12096 114 12996 148 15984 132 17424 138 19044 124 19344 150 22500 148 23088 144 24768 172 26832 168 28224 174 30276 180 32400 156 32448 192 36864 192 37632 198 39204 172 39216 Total time: 8.209 seconds, Total memory usage: 7.74MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 23 15:08:19 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+1, x^2-2, true); Output: Magma V2.10-6 Tue Mar 23 2004 15:08:16 on modular [Seed = 3905434105] ------------------------------------- >> K:=NumberField(x^2+1, x^2-2, true);; ^ Runtime error in 'NumberField': Bad argument types Argument types given: RngUPolElt, RngUPolElt, BoolElt Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 23 15:10:59 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2+1, x^2-2]); Output: Magma V2.10-6 Tue Mar 23 2004 15:10:56 on modular [Seed = 4225442314] ------------------------------------- Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 23 15:11:32 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2+1, x^2-2]); OK:=MaximalOrder(K); Factorization(2*OK); Output: Magma V2.10-6 Tue Mar 23 2004 15:11:28 on modular [Seed = 3269597971] ------------------------------------- [ ] Total time: 3.879 seconds, Total memory usage: 1.98MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 23 15:12:54 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2+3, x^2+3*x+3]); OK:=MaximalOrder(K); Factorization(2*OK); Output: Magma V2.10-6 Tue Mar 23 2004 15:12:51 on modular [Seed = 3522235315] ------------------------------------- >> K:=NumberField([x^2+3, x^2+3*x+3]); ^ Runtime error in 'NumberField': Argument 1 is not irreducible >> OK:=MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> Factorization(2*OK);; ^ User error: Identifier 'OK' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 23 15:13:36 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+3); OK:=MaximalOrder(K); Factorization(2*OK); Output: Magma V2.10-6 Tue Mar 23 2004 15:13:33 on modular [Seed = 3690660247] ------------------------------------- [ ] Total time: 2.929 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 23 15:13:46 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+3); OK:=MaximalOrder(K); Factorization(3*OK); Output: Magma V2.10-6 Tue Mar 23 2004 15:13:43 on modular [Seed = 553778036] ------------------------------------- [ ] Total time: 2.899 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 23 15:14:01 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+3*x+3); OK:=MaximalOrder(K); Factorization(3*OK); Output: Magma V2.10-6 Tue Mar 23 2004 15:13:58 on modular [Seed = 772732042] ------------------------------------- [ ] Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 23 15:14:22 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2+3, x^2+3*x+3]); OK:=MaximalOrder(K); Factorization(3*OK); Output: Magma V2.10-6 Tue Mar 23 2004 15:14:19 on modular [Seed = 924315022] ------------------------------------- >> K:=NumberField([x^2+3, x^2+3*x+3]); ^ Runtime error in 'NumberField': Argument 1 is not irreducible >> OK:=MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> Factorization(3*OK);; ^ User error: Identifier 'OK' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 23 15:14:44 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2+3, x^3+3*x+3]); OK:=MaximalOrder(K); Factorization(3*OK); Output: Magma V2.10-6 Tue Mar 23 2004 15:14:40 on modular [Seed = 1008527022] ------------------------------------- [ ] Total time: 3.219 seconds, Total memory usage: 2.04MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 23 15:15:11 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2+3, x^3+6*x+6]); OK:=MaximalOrder(K); Factorization(3*OK); Output: Magma V2.10-6 Tue Mar 23 2004 15:15:07 on modular [Seed = 153736160] ------------------------------------- [ ] Total time: 4.139 seconds, Total memory usage: 2.15MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 23 15:15:52 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^5+15, x^3+15*x+15]); OK:=MaximalOrder(K); Factorization(3*OK); Output: Magma V2.10-6 Tue Mar 23 2004 15:15:45 on modular [Seed = 389533124] ------------------------------------- [ ] Total time: 6.689 seconds, Total memory usage: 2.38MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 23 15:16:08 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^5+15, x^3+15*x+15]); OK:=MaximalOrder(K); Factorization(15*OK); Output: Magma V2.10-6 Tue Mar 23 2004 15:16:01 on modular [Seed = 1648539969] ------------------------------------- [ , ] Total time: 7.629 seconds, Total memory usage: 2.38MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 23 15:47:24 2004 Input: for p in [5..20] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^3-1); #(Points(C : Bound:=4)); end if; end for; Output: Magma V2.10-6 Tue Mar 23 2004 15:47:20 on modular [Seed = 1568522022] ------------------------------------- 6 4 12 12 18 28 Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 23 15:47:35 2004 Input: for p in [5..250] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^3-1); #(Points(C : Bound:=4)); end if; end for; Output: Magma V2.10-6 Tue Mar 23 2004 15:47:32 on modular [Seed = 2861189356] ------------------------------------- 6 4 12 12 18 28 24 30 28 48 42 52 48 54 60 48 52 72 84 76 84 90 84 102 124 108 108 114 148 132 138 124 150 148 144 172 168 174 180 156 192 192 198 172 196 196 228 252 234 240 228 Total time: 3.089 seconds, Total memory usage: 2.39MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 23 15:48:07 2004 Input: for p in [5..25000] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^3-1); #(Points(C : Bound:=4)); end if; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Mar 23 2004 15:47:44 on modular [Seed = 3012776417] ------------------------------------- 6 4 12 12 18 28 24 30 28 48 42 52 48 54 60 48 52 72 84 76 84 90 84 102 124 108 108 114 148 132 138 124 150 148 144 172 168 174 180 156 192 192 198 172 196 196 228 252 234 240 228 252 258 264 270 244 252 282 316 294 292 312 336 318 364 372 348 336 354 360 364 336 388 384 390 432 402 372 420 444 432 432 412 444 450 468 462 484 468 480 532 492 532 504 510 522 532 588 508 558 564 570 556 624 588 594 600 576 628 624 618 652 676 642 604 648 654 660 624 624 678 684 700 702 732 720 772 684 724 744 700 732 762 768 774 844 798 810 868 822 772 828 876 840 912 858 916 864 912 882 892 888 868 912 868 930 912 942 948 954 988 972 978 984 1036 1008 948 1014 1020 1008 1032 1092 988 1050 988 1062 1036 1008 1084 1092 1116 1098 1104 1110 1164 1156 1092 1152 1092 1164 1108 1182 1188 1194 1200 1164 1218 1224 1230 1300 1308 1236 1260 1278 1252 1284 1290 1348 1344 1302 1372 1308 1320 1344 1324 1362 1368 1374 1308 1468 1410 1444 1428 1488 1434 1440 1372 1452 1452 1516 1396 1482 1444 1488 1524 1494 1500 1512 1524 1468 1492 1488 1554 1560 1612 1572 1612 1584 1548 1602 1608 1668 1614 1620 1596 1708 1638 1728 1732 1668 1596 1776 1698 1636 1710 1722 1684 1734 1776 1828 1764 1708 1764 1756 1788 1872 1728 1812 1824 1900 1848 1776 1924 1872 1956 1878 1876 1890 1902 1908 1914 1932 1872 1950 1876 1974 1980 1948 2064 1998 1948 2004 1924 2052 2028 2028 2040 2064 2064 2070 2082 1996 2088 2052 2100 2112 2196 2130 2164 2064 2142 2236 2154 2100 2092 2212 2208 2214 2316 2238 2308 2244 2236 2268 2352 2274 2196 2308 2352 2298 2310 2236 2334 2340 2268 2284 2352 2358 2428 2388 2382 2356 2352 2394 2400 2412 2418 2424 2352 2442 2448 2460 2548 2496 2478 2404 2496 2532 2548 2544 2550 2500 2604 2580 2592 2496 2610 2532 2622 2634 2548 2658 2716 2664 2716 2748 2764 2688 2628 2694 2700 2812 2712 2676 2692 2730 2836 2742 2736 2754 2692 2778 2790 2884 2892 2802 2716 2820 2736 2838 2844 2956 2964 2862 2880 2884 2898 2904 2910 3024 2928 2940 3024 2958 2964 2970 3028 3000 3108 3012 2932 3024 2928 3042 2964 3024 3172 3052 3084 3090 3216 3120 3108 3138 3052 3168 3072 3276 3268 3192 3204 3210 3108 3222 3276 3252 3324 3258 3172 3268 3300 3216 3364 3252 3244 3324 3330 3316 3412 3348 3360 3396 3372 3276 3390 3508 3408 3414 3396 3450 3348 3462 3436 3468 3468 3492 3388 3628 3504 3528 3648 3534 3540 3600 3484 3558 3508 3676 3582 3484 3594 3724 3504 3618 3624 3556 3612 3532 3660 3672 3792 3678 3700 3648 3702 3792 3720 3844 3612 3724 3762 3768 3648 3780 3684 3798 3804 3822 3724 3834 3724 3852 3756 3864 3792 3882 3888 3844 3912 3918 3796 3924 3930 3964 3892 3948 3892 3990 4002 3892 4008 4014 4020 3900 4132 4050 4108 4032 4074 4080 4092 4044 4228 4108 4128 4032 4134 4140 4032 4158 4204 4212 4116 4212 4218 4108 4230 4348 4242 4372 4254 4260 4368 4272 4404 4284 4290 4368 4252 4338 4468 4350 4368 4396 4374 4392 4398 4410 4422 4492 4368 4564 4452 4458 4464 4482 4564 4494 4468 4464 4518 4396 4524 4548 4464 4656 4564 4584 4636 4464 4732 4656 4638 4732 4644 4650 4516 4788 4684 4674 4680 4692 4704 4722 4612 4788 4734 4752 4732 4732 4788 4656 4794 4800 4800 4944 4818 4900 4908 4872 4878 4890 5044 5004 4920 4932 5052 4938 4944 5068 4908 4968 4944 4974 4852 5124 5092 5004 5010 4900 5022 4924 5040 5052 5068 4944 5082 5088 5100 5004 5092 5184 5044 5148 5154 5044 5172 5308 5190 5328 5328 5332 5232 5376 5238 5262 5274 5280 5376 5298 5304 5310 5212 5334 5404 5352 5382 5388 5394 5400 5548 5436 5418 5548 5308 5292 5442 5404 5328 5472 5478 5332 5484 5502 5356 5508 5520 5376 5572 5532 5628 5572 5652 5574 5616 5592 5476 5640 5700 5668 5652 5616 5658 5548 5670 5812 5556 5694 5628 5712 5718 5652 5742 5716 5628 5932 5784 5884 5802 5808 5814 5868 5884 5692 5844 5850 6004 5844 5862 5868 5772 5880 5988 5898 5904 6076 5928 5940 6084 5982 5988 5932 6012 6030 6192 5956 6048 6054 6004 5952 6076 6090 6100 6102 6114 6276 6132 6192 6144 6004 6244 6174 6198 6268 6204 6076 6084 6222 6384 6364 6258 6264 6270 6244 6384 6288 6300 6156 6312 6318 6324 6330 6384 6196 6354 6360 6516 6244 6384 6484 Errors: /home/mfd/gomagma: line 2: 25233 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 23 15:49:08 2004 Input: print p; Output: Magma V2.10-6 Tue Mar 23 2004 15:49:05 on modular [Seed = 3113835354] ------------------------------------- >> print p;; ^ User error: Identifier 'p' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 23 15:49:19 2004 Input: print "p"; Output: Magma V2.10-6 Tue Mar 23 2004 15:49:16 on modular [Seed = 2259051624] ------------------------------------- p Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 23 15:49:32 2004 Input: for p in [5..2500] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^3-1); #(Points(C : Bound:=4)); end if; end for; Output: Magma V2.10-6 Tue Mar 23 2004 15:49:26 on modular [Seed = 2410638715] ------------------------------------- 6 4 12 12 18 28 24 30 28 48 42 52 48 54 60 48 52 72 84 76 84 90 84 102 124 108 108 114 148 132 138 124 150 148 144 172 168 174 180 156 192 192 198 172 196 196 228 252 234 240 228 252 258 264 270 244 252 282 316 294 292 312 336 318 364 372 348 336 354 360 364 336 388 384 390 432 402 372 420 444 432 432 412 444 450 468 462 484 468 480 532 492 532 504 510 522 532 588 508 558 564 570 556 624 588 594 600 576 628 624 618 652 676 642 604 648 654 660 624 624 678 684 700 702 732 720 772 684 724 744 700 732 762 768 774 844 798 810 868 822 772 828 876 840 912 858 916 864 912 882 892 888 868 912 868 930 912 942 948 954 988 972 978 984 1036 1008 948 1014 1020 1008 1032 1092 988 1050 988 1062 1036 1008 1084 1092 1116 1098 1104 1110 1164 1156 1092 1152 1092 1164 1108 1182 1188 1194 1200 1164 1218 1224 1230 1300 1308 1236 1260 1278 1252 1284 1290 1348 1344 1302 1372 1308 1320 1344 1324 1362 1368 1374 1308 1468 1410 1444 1428 1488 1434 1440 1372 1452 1452 1516 1396 1482 1444 1488 1524 1494 1500 1512 1524 1468 1492 1488 1554 1560 1612 1572 1612 1584 1548 1602 1608 1668 1614 1620 1596 1708 1638 1728 1732 1668 1596 1776 1698 1636 1710 1722 1684 1734 1776 1828 1764 1708 1764 1756 1788 1872 1728 1812 1824 1900 1848 1776 1924 1872 1956 1878 1876 1890 1902 1908 1914 1932 1872 1950 1876 1974 1980 1948 2064 1998 1948 2004 1924 2052 2028 2028 2040 2064 2064 2070 2082 1996 2088 2052 2100 2112 2196 2130 2164 2064 2142 2236 2154 2100 2092 2212 2208 2214 2316 2238 2308 2244 2236 2268 2352 2274 2196 2308 2352 2298 2310 2236 2334 2340 2268 2284 2352 2358 2428 2388 2382 2356 2352 2394 2400 2412 2418 2424 2352 2442 2448 2460 2548 2496 2478 Total time: 5.899 seconds, Total memory usage: 2.39MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 23 15:49:58 2004 Input: for p in [5..5000] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^3-1); #(Points(C : Bound:=4)); end if; end for; Output: Magma V2.10-6 Tue Mar 23 2004 15:49:43 on modular [Seed = 2494854737] ------------------------------------- 6 4 12 12 18 28 24 30 28 48 42 52 48 54 60 48 52 72 84 76 84 90 84 102 124 108 108 114 148 132 138 124 150 148 144 172 168 174 180 156 192 192 198 172 196 196 228 252 234 240 228 252 258 264 270 244 252 282 316 294 292 312 336 318 364 372 348 336 354 360 364 336 388 384 390 432 402 372 420 444 432 432 412 444 450 468 462 484 468 480 532 492 532 504 510 522 532 588 508 558 564 570 556 624 588 594 600 576 628 624 618 652 676 642 604 648 654 660 624 624 678 684 700 702 732 720 772 684 724 744 700 732 762 768 774 844 798 810 868 822 772 828 876 840 912 858 916 864 912 882 892 888 868 912 868 930 912 942 948 954 988 972 978 984 1036 1008 948 1014 1020 1008 1032 1092 988 1050 988 1062 1036 1008 1084 1092 1116 1098 1104 1110 1164 1156 1092 1152 1092 1164 1108 1182 1188 1194 1200 1164 1218 1224 1230 1300 1308 1236 1260 1278 1252 1284 1290 1348 1344 1302 1372 1308 1320 1344 1324 1362 1368 1374 1308 1468 1410 1444 1428 1488 1434 1440 1372 1452 1452 1516 1396 1482 1444 1488 1524 1494 1500 1512 1524 1468 1492 1488 1554 1560 1612 1572 1612 1584 1548 1602 1608 1668 1614 1620 1596 1708 1638 1728 1732 1668 1596 1776 1698 1636 1710 1722 1684 1734 1776 1828 1764 1708 1764 1756 1788 1872 1728 1812 1824 1900 1848 1776 1924 1872 1956 1878 1876 1890 1902 1908 1914 1932 1872 1950 1876 1974 1980 1948 2064 1998 1948 2004 1924 2052 2028 2028 2040 2064 2064 2070 2082 1996 2088 2052 2100 2112 2196 2130 2164 2064 2142 2236 2154 2100 2092 2212 2208 2214 2316 2238 2308 2244 2236 2268 2352 2274 2196 2308 2352 2298 2310 2236 2334 2340 2268 2284 2352 2358 2428 2388 2382 2356 2352 2394 2400 2412 2418 2424 2352 2442 2448 2460 2548 2496 2478 2404 2496 2532 2548 2544 2550 2500 2604 2580 2592 2496 2610 2532 2622 2634 2548 2658 2716 2664 2716 2748 2764 2688 2628 2694 2700 2812 2712 2676 2692 2730 2836 2742 2736 2754 2692 2778 2790 2884 2892 2802 2716 2820 2736 2838 2844 2956 2964 2862 2880 2884 2898 2904 2910 3024 2928 2940 3024 2958 2964 2970 3028 3000 3108 3012 2932 3024 2928 3042 2964 3024 3172 3052 3084 3090 3216 3120 3108 3138 3052 3168 3072 3276 3268 3192 3204 3210 3108 3222 3276 3252 3324 3258 3172 3268 3300 3216 3364 3252 3244 3324 3330 3316 3412 3348 3360 3396 3372 3276 3390 3508 3408 3414 3396 3450 3348 3462 3436 3468 3468 3492 3388 3628 3504 3528 3648 3534 3540 3600 3484 3558 3508 3676 3582 3484 3594 3724 3504 3618 3624 3556 3612 3532 3660 3672 3792 3678 3700 3648 3702 3792 3720 3844 3612 3724 3762 3768 3648 3780 3684 3798 3804 3822 3724 3834 3724 3852 3756 3864 3792 3882 3888 3844 3912 3918 3796 3924 3930 3964 3892 3948 3892 3990 4002 3892 4008 4014 4020 3900 4132 4050 4108 4032 4074 4080 4092 4044 4228 4108 4128 4032 4134 4140 4032 4158 4204 4212 4116 4212 4218 4108 4230 4348 4242 4372 4254 4260 4368 4272 4404 4284 4290 4368 4252 4338 4468 4350 4368 4396 4374 4392 4398 4410 4422 4492 4368 4564 4452 4458 4464 4482 4564 4494 4468 4464 4518 4396 4524 4548 4464 4656 4564 4584 4636 4464 4732 4656 4638 4732 4644 4650 4516 4788 4684 4674 4680 4692 4704 4722 4612 4788 4734 4752 4732 4732 4788 4656 4794 4800 4800 4944 4818 4900 4908 4872 4878 4890 5044 5004 4920 4932 5052 4938 4944 5068 4908 4968 4944 4974 4852 5124 5092 Total time: 14.719 seconds, Total memory usage: 2.49MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 23 15:50:53 2004 Input: for p in [5..5000] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^5-x^3+1); #(Points(C : Bound:=4)); end if; end for; Output: Magma V2.10-6 Tue Mar 23 2004 15:50:50 on modular [Seed = 3838052332] ------------------------------------- 8 HyperellipticCurve( f: x^5 + 6*x^3 + 1 ) In file "/usr/local/magma/package/Geometry/CrvHyp/curve.m", line 257, column 30: >> return HyperellipticCurve(f, Parent(f)!0); ^ Runtime error in 'HyperellipticCurve': Curve has a finite singularity Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 23 15:51:12 2004 Input: for p in [5..5000] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^5-x^3+2); #(Points(C : Bound:=4)); end if; end for; Output: Magma V2.10-6 Tue Mar 23 2004 15:51:07 on modular [Seed = 3989638900] ------------------------------------- 3 9 10 13 11 19 25 21 31 38 43 37 53 49 58 52 68 77 80 78 84 85 103 100 101 93 99 114 127 120 148 130 141 161 159 145 184 166 152 199 201 192 216 202 198 222 235 253 252 246 212 263 268 277 291 278 271 255 270 284 306 323 319 330 322 307 381 344 342 370 374 351 376 361 439 415 371 405 418 426 432 439 435 428 453 461 466 477 479 492 528 489 487 507 477 568 560 557 536 524 576 581 531 575 603 600 543 562 583 607 615 615 613 701 629 673 657 639 721 711 680 684 656 725 672 750 727 717 712 746 749 761 762 789 741 809 789 874 811 782 857 866 824 804 862 873 867 832 853 873 834 871 922 925 883 933 994 957 914 982 923 969 980 1005 986 995 1005 1043 965 1037 1065 975 1058 1075 1004 1095 1078 1097 1091 1113 1098 1086 1073 1101 1106 1091 1148 1111 1134 1174 1237 1241 1207 1199 1193 1287 1222 1181 1266 1169 1250 1235 1225 1209 1296 1260 1244 1321 1285 1326 1338 1293 1274 1304 1351 1356 1367 1410 1385 1407 1455 1516 1448 1423 1417 1460 1478 1479 1473 1472 1439 1461 1394 1474 1438 1533 1501 1539 1462 1517 1520 HyperellipticCurve( f: x^5 + 1548*x^3 + 2 ) In file "/usr/local/magma/package/Geometry/CrvHyp/curve.m", line 257, column 30: >> return HyperellipticCurve(f, Parent(f)!0); ^ Runtime error in 'HyperellipticCurve': Curve has a finite singularity Total time: 4.199 seconds, Total memory usage: 2.39MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 23 15:51:31 2004 Input: for p in [5..5000] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^5-x^4+2); #(Points(C : Bound:=4)); end if; end for; Output: Magma V2.10-6 Tue Mar 23 2004 15:51:28 on modular [Seed = 4208597384] ------------------------------------- 4 9 11 12 18 10 22 22 32 HyperellipticCurve( f: x^5 + 36*x^4 + 2 ) In file "/usr/local/magma/package/Geometry/CrvHyp/curve.m", line 257, column 30: >> return HyperellipticCurve(f, Parent(f)!0); ^ Runtime error in 'HyperellipticCurve': Curve has a finite singularity Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 23 15:51:57 2004 Input: for p in [5..5000] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^5-x^4+2*x-2); #(Points(C : Bound:=4)); end if; end for; Output: Magma V2.10-6 Tue Mar 23 2004 15:51:41 on modular [Seed = 3286442172] ------------------------------------- 6 10 16 12 24 16 20 34 34 36 36 48 44 62 54 76 62 68 66 78 88 94 118 94 110 106 92 110 138 130 128 138 130 126 152 156 184 174 170 168 200 206 222 202 218 194 236 232 250 224 242 220 246 240 274 306 288 258 306 318 306 320 318 326 326 370 344 348 362 348 378 352 356 384 406 360 412 422 436 416 420 450 434 420 456 446 514 466 436 484 510 490 530 516 502 532 476 536 528 570 580 580 562 610 594 586 604 602 602 664 618 634 614 704 648 636 650 662 648 674 634 672 660 666 704 740 730 736 782 728 786 736 736 830 758 780 798 800 856 842 822 770 820 852 832 836 860 832 860 898 908 912 932 880 886 924 922 962 1002 948 954 956 1036 984 978 980 1062 1046 1034 1008 1024 1066 1026 1046 1062 1050 1050 1076 1054 1092 1044 1074 1168 1118 1080 1126 1130 1160 1178 1150 1198 1166 1170 1190 1234 1208 1218 1192 1210 1238 1236 1242 1320 1306 1314 1292 1282 1332 1310 1314 1394 1302 1340 1346 1354 1424 1368 1402 1436 1382 1476 1398 1500 1384 1442 1428 1442 1466 1460 1456 1474 1454 1492 1492 1478 1466 1496 1492 1608 1558 1554 1576 1606 1652 1562 1534 1638 1512 1612 1558 1636 1614 1598 1654 1588 1690 1578 1658 1614 1698 1716 1688 1676 1662 1718 1742 1720 1754 1652 1722 1766 1782 1822 1782 1788 1752 1754 1830 1876 1898 1868 1880 1872 1848 1882 1974 1922 1942 1922 1834 1934 1950 1900 1994 1950 1934 1976 1996 1998 2046 2042 1946 2032 2002 2012 2056 2036 1960 2032 2022 2104 2080 2056 2158 2102 2156 2146 2142 2114 2174 2178 2114 2124 2230 2248 2248 2192 2194 2236 2202 2234 2270 2242 2276 2272 2222 2290 2318 2200 2244 2290 2306 2334 2404 2356 2378 2356 2362 2356 2334 2394 2362 2392 2394 2376 2418 2312 2392 2484 2458 2424 2380 2498 2474 2414 2570 2506 2568 2564 2544 2542 2674 2576 2576 2664 2498 2580 2642 2590 2664 2694 2626 2712 2688 2762 2696 2750 2700 2674 2718 2678 2688 2648 2758 2734 2724 2684 2746 2720 2716 2798 2764 2826 2782 2740 2748 2736 2880 2866 2926 2900 2836 2754 2878 2888 2858 2844 2820 2982 2976 2880 2940 2966 2926 2992 2978 3132 2956 3106 3066 3064 2980 3052 3068 3026 3068 3004 3194 3092 3142 3204 3124 3142 3162 3214 3132 3126 3196 3230 3156 3198 3224 3222 3194 3212 3140 3368 3218 3212 3326 3322 3252 3376 3146 3322 3342 3304 3242 3238 3346 3364 3350 3450 3264 3378 3342 3348 3494 3506 3474 3446 3562 3502 3552 3352 3528 3594 3642 3524 3420 3490 3594 3564 3476 3642 3534 3582 3484 3638 3674 3576 3702 3612 3700 3612 3638 3692 3606 3632 3636 3722 3698 3652 3742 3618 3764 3672 3746 3728 3674 3778 3688 3650 3862 3722 3914 3798 3818 3822 3822 3890 3808 3888 3972 3880 3996 3858 3974 3808 3950 4022 3914 3984 3890 3918 4002 3986 3914 3890 3998 4056 3950 4094 4104 4056 4098 3980 4114 4104 4040 3950 4136 4050 4074 4128 4214 4118 4098 4138 4214 4158 4202 4090 4100 4166 4114 4306 4338 4340 4238 4202 4208 4336 4216 4282 4314 4098 4190 4270 4400 4266 4254 4308 4362 4406 4312 4406 4362 4398 4314 4430 4454 4486 4598 4340 4502 4482 4546 4520 4442 4558 4446 4630 4518 4536 4594 4686 4480 4662 4592 4658 4628 4670 4622 4672 4600 4532 4658 4646 4632 4628 4622 4632 4766 4666 4686 4702 4876 4814 4798 4842 4912 4668 4688 4810 4704 4810 4886 5068 4884 4682 4768 4914 4784 4952 4886 4952 5002 4956 4942 4976 4932 4910 5042 4948 4938 4974 Total time: 15.339 seconds, Total memory usage: 2.49MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 23 15:55:00 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2-5, x^2-10]); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Tue Mar 23 2004 15:54:57 on modular [Seed = 3488558028] ------------------------------------- [ ] Total time: 3.279 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 23 15:55:38 2004 Input: for p in [5..5000] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^2)); C := HyperellipticCurve(x^5-x^4+2*x-2); #(Points(C : Bound:=4)); end if; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Mar 23 2004 15:55:15 on modular [Seed = 3640147145] ------------------------------------- 34 42 118 186 322 406 542 906 1002 1330 1746 1830 2342 2906 3570 3810 4706 5174 5422 6490 7014 8078 9534 10426 10762 11650 12074 12670 15994 17122 18914 19314 22242 22842 24978 26758 28302 30034 31890 33178 36198 37046 38986 39930 44674 50010 52022 52410 54382 57766 58502 63302 65694 69334 72362 73834 77050 78958 80498 86426 95074 97526 98790 101114 Errors: /home/mfd/gomagma: line 2: 25338 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 23 15:56:20 2004 Input: for p in [5..1000] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^2)); C := HyperellipticCurve(x^5-x^4+2*x-2); #(Points(C : Bound:=4)); end if; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Mar 23 2004 15:55:57 on modular [Seed = 536921182] ------------------------------------- 34 42 118 186 322 406 542 906 1002 1330 1746 1830 2342 2906 3570 3810 4706 5174 5422 6490 7014 8078 9534 10426 10762 11650 12074 12670 15994 17122 18914 19314 22242 22842 24978 26758 28302 30034 31890 33178 36198 37046 38986 39930 44674 50010 52022 52410 54382 57766 58502 63302 65694 69334 72362 73834 77050 78958 80498 86426 95074 97526 Errors: /home/mfd/gomagma: line 2: 25347 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 23 15:56:22 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2+5, x^2-10]); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Tue Mar 23 2004 15:56:16 on modular [Seed = 621134198] ------------------------------------- [ ] Total time: 3.689 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 23 15:56:49 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2+5, x^2+10]); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Tue Mar 23 2004 15:56:46 on modular [Seed = 907465371] ------------------------------------- [ ] Total time: 3.639 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 23 15:57:24 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2+3, x^2+10]); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Tue Mar 23 2004 15:57:21 on modular [Seed = 2155666] ------------------------------------- [ ] Total time: 3.359 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 23 15:57:44 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2+1, x^2+10]); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Tue Mar 23 2004 15:57:41 on modular [Seed = 254798825] ------------------------------------- [ , ] Total time: 3.479 seconds, Total memory usage: 1.95MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 23 15:58:56 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2+1, x^2+10]); OK:=MaximalOrder(K); Factorization(3*OK); Output: Magma V2.10-6 Tue Mar 23 2004 15:58:52 on modular [Seed = 355856442] ------------------------------------- [ , ] Total time: 3.429 seconds, Total memory usage: 2.05MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Tue Mar 23 15:59:21 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+10); OK:=MaximalOrder(K); Factorization(3*OK); Output: Magma V2.10-6 Tue Mar 23 2004 15:59:18 on modular [Seed = 473757977] ------------------------------------- [ ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 16:52:51 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2+1, x^2+10]); OK:=MaximalOrder(K); Factorization(3*OK); Output: Magma V2.10-6 Tue Mar 23 2004 16:52:47 on modular [Seed = 2528536346] ------------------------------------- [ , ] Total time: 3.429 seconds, Total memory usage: 2.05MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 16:53:48 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+1); OK:=MaximalOrder(K); Factorization(3*OK); Output: Magma V2.10-6 Tue Mar 23 2004 16:53:45 on modular [Seed = 2629594454] ------------------------------------- [ ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 16:54:07 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+10); OK:=MaximalOrder(K); Factorization(3*OK); Output: Magma V2.10-6 Tue Mar 23 2004 16:54:04 on modular [Seed = 3955956276] ------------------------------------- [ ] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 16:57:16 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2+3, x^2+10]); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Tue Mar 23 2004 16:57:13 on modular [Seed = 4107535982] ------------------------------------- [ ] Total time: 3.279 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 16:58:03 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+3); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Tue Mar 23 2004 16:58:00 on modular [Seed = 3269603337] ------------------------------------- [ ] Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 16:58:17 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+10); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Tue Mar 23 2004 16:58:14 on modular [Seed = 3454877464] ------------------------------------- [ ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 16:58:59 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+1); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Tue Mar 23 2004 16:58:56 on modular [Seed = 3572770775] ------------------------------------- [ , ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 16:59:09 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+2); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Tue Mar 23 2004 16:59:06 on modular [Seed = 604297002] ------------------------------------- [ ] Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 16:59:19 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+3); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Tue Mar 23 2004 16:59:16 on modular [Seed = 772726078] ------------------------------------- [ ] Total time: 2.889 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 16:59:29 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+4); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Tue Mar 23 2004 16:59:25 on modular [Seed = 924304429] ------------------------------------- [ , ] Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 16:59:38 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+11); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Tue Mar 23 2004 16:59:35 on modular [Seed = 941149019] ------------------------------------- [ , ] Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 16:59:48 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+12); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Tue Mar 23 2004 16:59:45 on modular [Seed = 19001972] ------------------------------------- [ ] Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 17:00:01 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+13); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Tue Mar 23 2004 16:59:58 on modular [Seed = 170588528] ------------------------------------- [ ] Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 17:00:09 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+14); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Tue Mar 23 2004 17:00:06 on modular [Seed = 440068440] ------------------------------------- [ , ] Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 17:00:20 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+10); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Tue Mar 23 2004 17:00:18 on modular [Seed = 1665372213] ------------------------------------- [ ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 17:00:41 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+10); OK:=MaximalOrder(K); Factorization(3*OK); Output: Magma V2.10-6 Tue Mar 23 2004 17:00:38 on modular [Seed = 1951696854] ------------------------------------- [ ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 17:00:50 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+1); OK:=MaximalOrder(K); Factorization(3*OK); Output: Magma V2.10-6 Tue Mar 23 2004 17:00:47 on modular [Seed = 2103283414] ------------------------------------- [ ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 17:00:57 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+3); OK:=MaximalOrder(K); Factorization(3*OK); Output: Magma V2.10-6 Tue Mar 23 2004 17:00:54 on modular [Seed = 1181136372] ------------------------------------- [ ] Total time: 2.989 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 17:01:12 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+4); OK:=MaximalOrder(K); Factorization(3*OK); Output: Magma V2.10-6 Tue Mar 23 2004 17:01:09 on modular [Seed = 1501145816] ------------------------------------- [ ] Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 17:01:19 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+5); OK:=MaximalOrder(K); Factorization(3*OK); Output: Magma V2.10-6 Tue Mar 23 2004 17:01:16 on modular [Seed = 2726449450] ------------------------------------- [ , ] Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 17:01:26 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+6); OK:=MaximalOrder(K); Factorization(3*OK); Output: Magma V2.10-6 Tue Mar 23 2004 17:01:23 on modular [Seed = 2878036028] ------------------------------------- [ ] Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 17:01:52 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2+6, x^2+3]); OK:=MaximalOrder(K); Factorization(3*OK); Output: Magma V2.10-6 Tue Mar 23 2004 17:01:48 on modular [Seed = 3164360532] ------------------------------------- [ ] Total time: 3.039 seconds, Total memory usage: 2.07MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 17:02:16 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2+9); OK:=MaximalOrder(K); Factorization(3*OK); Output: Magma V2.10-6 Tue Mar 23 2004 17:02:13 on modular [Seed = 2242213444] ------------------------------------- >> K:=NumberField([x^2+9); ^ User error: bad syntax >> OK:=MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> Factorization(3*OK); ^ User error: Identifier 'OK' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 17:02:22 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+9); OK:=MaximalOrder(K); Factorization(3*OK); Output: Magma V2.10-6 Tue Mar 23 2004 17:02:19 on modular [Seed = 2393800001] ------------------------------------- [ ] Total time: 2.979 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 17:02:30 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+12); OK:=MaximalOrder(K); Factorization(3*OK); Output: Magma V2.10-6 Tue Mar 23 2004 17:02:27 on modular [Seed = 2545378368] ------------------------------------- [ ] Total time: 2.969 seconds, Total memory usage: 1.91MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 17:02:54 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2+12,x^2+3]); OK:=MaximalOrder(K); Factorization(3*OK); Output: Magma V2.10-6 Tue Mar 23 2004 17:02:51 on modular [Seed = 2562223287] ------------------------------------- >> K:=NumberField([x^2+12,x^2+3]); ^ Runtime error in 'NumberField': Argument 1 is not irreducible >> OK:=MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> Factorization(3*OK); ^ User error: Identifier 'OK' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 17:03:18 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2+12,x^2+6]); OK:=MaximalOrder(K); Factorization(3*OK); Output: Magma V2.10-6 Tue Mar 23 2004 17:03:15 on modular [Seed = 3787527654] ------------------------------------- [ ] Total time: 3.809 seconds, Total memory usage: 2.07MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 17:03:50 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+15); OK:=MaximalOrder(K); Factorization(3*OK); Output: Magma V2.10-6 Tue Mar 23 2004 17:03:47 on modular [Seed = 3955957644] ------------------------------------- [ ] Total time: 2.909 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 17:04:08 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2+15,x^2+12]); OK:=MaximalOrder(K); Factorization(3*OK); Output: Magma V2.10-6 Tue Mar 23 2004 17:04:05 on modular [Seed = 4242278541] ------------------------------------- [ ] Total time: 3.179 seconds, Total memory usage: 2.04MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 17:04:17 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2+15,x^2+3]); OK:=MaximalOrder(K); Factorization(3*OK); Output: Magma V2.10-6 Tue Mar 23 2004 17:04:14 on modular [Seed = 3320132031] ------------------------------------- [ ] Total time: 3.159 seconds, Total memory usage: 2.04MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 17:04:27 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2+15,x^2+6]); OK:=MaximalOrder(K); Factorization(3*OK); Output: Magma V2.10-6 Tue Mar 23 2004 17:04:23 on modular [Seed = 3471719053] ------------------------------------- [ , ] Total time: 3.659 seconds, Total memory usage: 2.14MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 17:05:10 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2+15,x^2+12]); OK:=MaximalOrder(K); Factorization(3*OK); Output: Magma V2.10-6 Tue Mar 23 2004 17:05:07 on modular [Seed = 3555927908] ------------------------------------- [ ] Total time: 3.139 seconds, Total memory usage: 2.04MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 17:05:22 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2+15,x^2+6]); OK:=MaximalOrder(K); Factorization(3*OK); Output: Magma V2.10-6 Tue Mar 23 2004 17:05:18 on modular [Seed = 621138334] ------------------------------------- [ , ] Total time: 3.619 seconds, Total memory usage: 2.14MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 17:08:16 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+15); OK:=MaximalOrder(K); Factorization(3*OK); Output: Magma V2.10-6 Tue Mar 23 2004 17:08:13 on modular [Seed = 772725574] ------------------------------------- [ ] Total time: 2.979 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 17:08:55 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+6); OK:=MaximalOrder(K); Factorization(3*OK); Output: Magma V2.10-6 Tue Mar 23 2004 17:08:52 on modular [Seed = 823247968] ------------------------------------- [ ] Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 17:10:40 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+6); OK:=MaximalOrder(K); Factorization(2*OK); Output: Magma V2.10-6 Tue Mar 23 2004 17:10:37 on modular [Seed = 2160120] ------------------------------------- [ ] Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 17:10:51 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+6); OK:=MaximalOrder(K); Factorization(4*OK); Output: Magma V2.10-6 Tue Mar 23 2004 17:10:48 on modular [Seed = 187432646] ------------------------------------- [ ] Total time: 3.049 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 17:10:57 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+6); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Tue Mar 23 2004 17:10:54 on modular [Seed = 305326041] ------------------------------------- [ , ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 17:11:14 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+7); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Tue Mar 23 2004 17:11:11 on modular [Seed = 1699057855] ------------------------------------- [ ] Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 17:11:25 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+10); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Tue Mar 23 2004 17:11:22 on modular [Seed = 1816959555] ------------------------------------- [ ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 17:11:38 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+8); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Tue Mar 23 2004 17:11:35 on modular [Seed = 2002223429] ------------------------------------- [ ] Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 17:11:55 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+12); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Tue Mar 23 2004 17:11:52 on modular [Seed = 2120124531] ------------------------------------- [ ] Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 17:12:06 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+13); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Tue Mar 23 2004 17:12:03 on modular [Seed = 1096922967] ------------------------------------- [ ] Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 17:12:14 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+14); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Tue Mar 23 2004 17:12:11 on modular [Seed = 1214824022] ------------------------------------- [ , ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 17:12:44 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2+14,x^2+6]); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Tue Mar 23 2004 17:12:40 on modular [Seed = 1383244847] ------------------------------------- [ , , , ] Total time: 3.589 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 17:13:10 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2+14,x^2+6]); OK:=MaximalOrder(K); Factorization(3*OK); Output: Magma V2.10-6 Tue Mar 23 2004 17:13:07 on modular [Seed = 2760135410] ------------------------------------- [ , ] Total time: 3.619 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host c211-28-55-6.brodm1.vic.optusnet.com.au. (211.28.55.6) Time: Tue Mar 23 18:17:49 2004 Input: 2+3; Output: Magma V2.10-6 Tue Mar 23 2004 18:17:46 on modular [Seed = 823243917] ------------------------------------- 5 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host c211-28-55-6.brodm1.vic.optusnet.com.au. (211.28.55.6) Time: Tue Mar 23 18:18:11 2004 Input: a:=3; a+3; Output: Magma V2.10-6 Tue Mar 23 2004 18:18:08 on modular [Seed = 103187344] ------------------------------------- 6 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A17-64-46-46.apple.com. (17.64.46.46) Time: Tue Mar 23 19:49:18 2004 Input: ln(2^2048) Output: Magma V2.10-6 Tue Mar 23 2004 19:49:14 on modular [Seed = 3787553484] ------------------------------------- >> ln(2^2048) ^ User error: Identifier 'ln' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A17-64-46-46.apple.com. (17.64.46.46) Time: Tue Mar 23 19:50:24 2004 Input: log(2^2048) Output: Magma V2.10-6 Tue Mar 23 2004 19:50:21 on modular [Seed = 3336986029] ------------------------------------- >> log(2^2048); ^ User error: Identifier 'log' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host A17-64-46-46.apple.com. (17.64.46.46) Time: Tue Mar 23 19:53:36 2004 Input: B:=log(2^2048); B; Output: Magma V2.10-6 Tue Mar 23 2004 19:53:33 on modular [Seed = 3438039271] ------------------------------------- >> B:=log(2^2048); ^ User error: Identifier 'log' has not been declared or assigned >> B;; ^ User error: Identifier 'B' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 21:42:41 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-7); OK:=MaximalOrder(K); IntegralBasis(OK); Output: Magma V2.10-6 Tue Mar 23 2004 21:42:38 on modular [Seed = 2545361454] ------------------------------------- >> IntegralBasis(OK);; ^ Runtime error in 'IntegralBasis': Bad argument types Argument types given: RngOrd Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 21:43:15 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-7); OK:=MaximalOrder(K); IntegerBasis(OK); Output: Magma V2.10-6 Tue Mar 23 2004 21:43:12 on modular [Seed = 2663263097] ------------------------------------- >> IntegerBasis(OK);; ^ User error: Identifier 'IntegerBasis' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 21:43:24 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-7); OK:=MaximalOrder(K); Basis(OK); Output: Magma V2.10-6 Tue Mar 23 2004 21:43:21 on modular [Seed = 3854913547] ------------------------------------- [ OK.1, OK.2 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 21:44:48 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-7); OK:=MaximalOrder(K); [K!OK.i : i in [1, 2]]; Output: Magma V2.10-6 Tue Mar 23 2004 21:44:45 on modular [Seed = 3972815574] ------------------------------------- [ 1, a ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 21:44:57 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^3-7); OK:=MaximalOrder(K); [K!OK.i : i in [1, 2]]; Output: Magma V2.10-6 Tue Mar 23 2004 21:44:54 on modular [Seed = 4090709490] ------------------------------------- [ 1, a ] Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 21:45:05 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^3-7); OK:=MaximalOrder(K); [K!OK.i : i in [1, 2, 3]]; Output: Magma V2.10-6 Tue Mar 23 2004 21:45:02 on modular [Seed = 3336990927] ------------------------------------- [ 1, a, a^2 ] Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 21:45:19 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^17-7); OK:=MaximalOrder(K); [K!OK.i : i in [1..17]]; Output: Magma V2.10-6 Tue Mar 23 2004 21:45:16 on modular [Seed = 3454893014] ------------------------------------- [ 1, a, a^2, a^3, a^4, a^5, a^6, a^7, a^8, a^9, a^10, a^11, a^12, a^13, a^14, a^15, a^16 ] Total time: 2.929 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 21:45:29 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^16-7); OK:=MaximalOrder(K); [K!OK.i : i in [1..17]]; Output: Magma V2.10-6 Tue Mar 23 2004 21:45:26 on modular [Seed = 3572785845] ------------------------------------- >> [K!OK.i : i in [1..17]];; ^ Runtime error in '.': Value for name index (17) should be in the range [1..16] Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 21:45:39 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^16-7); OK:=MaximalOrder(K); [K!OK.i : i in [1..16]]; Output: Magma V2.10-6 Tue Mar 23 2004 21:45:36 on modular [Seed = 3690687916] ------------------------------------- [ 1, a, a^2, a^3, a^4, a^5, a^6, a^7, a^8, a^9, a^10, a^11, a^12, a^13, a^14, a^15 ] Total time: 2.889 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 21:48:44 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^16-7); OK:=MaximalOrder(K); [K!OK.i : i in [1..16]]; Discriminant(OK); Output: Magma V2.10-6 Tue Mar 23 2004 21:48:41 on modular [Seed = 772708623] ------------------------------------- [ 1, a, a^2, a^3, a^4, a^5, a^6, a^7, a^8, a^9, a^10, a^11, a^12, a^13, a^14, a^15 ] -87577052148112605759278455717888 Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host CPE0004e2574a13-CM014120007623.cpe.net.cable.rogers.com. (24.103.3.214) Time: Tue Mar 23 22:26:15 2004 Input: 0xba12^2 Output: Magma V2.10-6 Tue Mar 23 2004 22:26:12 on modular [Seed = 1096941245] ------------------------------------- >> 0xba12^2; ^ User error: bad syntax Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 22:41:17 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+1); OK:=MaximalOrder(K); I:=2*OK; ResidueClassField(OK,I); Output: Magma V2.10-6 Tue Mar 23 2004 22:41:14 on modular [Seed = 3130784200] ------------------------------------- >> ResidueClassField(OK,I); ^ Runtime error in 'ResidueClassField': Ideal must be prime Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 22:42:55 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+1); OK:=MaximalOrder(K); I:=2*OK; F:=Factorization(I); ResidueClassField(OK,F[1][1]); Output: Magma V2.10-6 Tue Mar 23 2004 22:42:52 on modular [Seed = 3046438433] ------------------------------------- Finite field of size 2 Mapping from: RngOrd: OK to GF(2) given by the ideal Prime Ideal of OK Two element generators: [2, 0] [3, 1] Total time: 2.909 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 22:44:44 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+1); OK:=MaximalOrder(K); I:=3*OK; F:=Factorization(I); ResidueClassField(OK,F[1][1]); Output: Magma V2.10-6 Tue Mar 23 2004 22:44:41 on modular [Seed = 2410597262] ------------------------------------- Finite field of size 3^2 Mapping from: RngOrd: OK to GF(3^2) given by the ideal Principal Prime Ideal of OK Generator: [3, 0] Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 22:46:41 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+2); OK:=MaximalOrder(K); I:=2*OK; F:=Factorization(I); ResidueClassField(OK,F[1][1]); Output: Magma V2.10-6 Tue Mar 23 2004 22:46:38 on modular [Seed = 2629687338] ------------------------------------- Finite field of size 2 Mapping from: RngOrd: OK to GF(2) given by the ideal Prime Ideal of OK Two element generators: [2, 0] [2, 1] Total time: 2.919 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 22:47:03 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2+2,x^2+1]); OK:=MaximalOrder(K); I:=2*OK; F:=Factorization(I); ResidueClassField(OK,F[1][1]); Output: Magma V2.10-6 Tue Mar 23 2004 22:46:59 on modular [Seed = 2528629261] ------------------------------------- Finite field of size 2 Mapping from: RngOrd: OK to GF(2) given by the ideal Prime Ideal of OK Two element generators: [[2, 0], [0, 0]] [[4, 1], [3, 1]] Total time: 3.439 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 22:47:51 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+3); OK:=MaximalOrder(K); I:=2*OK; F:=Factorization(I); ResidueClassField(OK,F[1][1]); Output: Magma V2.10-6 Tue Mar 23 2004 22:47:48 on modular [Seed = 3770786860] ------------------------------------- Finite field of size 2^2 Mapping from: RngOrd: OK to GF(2^2) given by the ideal Principal Prime Ideal of OK Generator: [2, 0] Total time: 2.969 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 22:48:23 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2+2,x^2+1]); OK:=MaximalOrder(K); I:=2*OK; F:=Factorization(I); ResidueClassField(OK,F[1][1]); Output: Magma V2.10-6 Tue Mar 23 2004 22:48:20 on modular [Seed = 4191730901] ------------------------------------- Finite field of size 2 Mapping from: RngOrd: OK to GF(2) given by the ideal Prime Ideal of OK Two element generators: [[2, 0], [0, 0]] [[2, 1], [-1, 1]] Total time: 3.439 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 22:49:52 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2+2,x^2+1]); OK:=MaximalOrder(K); I:=2*OK; F:=Factorization(I); ResidueClassField(OK,F[1][1]); Output: Magma V2.10-6 Tue Mar 23 2004 22:49:48 on modular [Seed = 4073961350] ------------------------------------- Finite field of size 2 Mapping from: RngOrd: OK to GF(2) given by the ideal Prime Ideal of OK Two element generators: [[2, 0], [0, 0]] [[3, 2], [1, -1]] Total time: 3.439 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 22:50:06 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+4); OK:=MaximalOrder(K); I:=2*OK; F:=Factorization(I); ResidueClassField(OK,F[1][1]); Output: Magma V2.10-6 Tue Mar 23 2004 22:50:03 on modular [Seed = 3269691265] ------------------------------------- Finite field of size 2 Mapping from: RngOrd: OK to GF(2) given by the ideal Prime Ideal of OK Two element generators: [2, 0] [1, 1] Total time: 2.979 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 22:50:23 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2+4,x^2+1]); OK:=MaximalOrder(K); I:=2*OK; F:=Factorization(I); ResidueClassField(OK,F[1][1]); Output: Magma V2.10-6 Tue Mar 23 2004 22:50:20 on modular [Seed = 3690634895] ------------------------------------- >> K:=NumberField([x^2+4,x^2+1]); ^ Runtime error in 'NumberField': Argument 1 is not irreducible >> OK:=MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> I:=2*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> F:=Factorization(I); ^ User error: Identifier 'I' has not been declared or assigned >> ResidueClassField(OK,F[1][1]); ^ User error: Identifier 'OK' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 22:50:33 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2+4,x^2+2]); OK:=MaximalOrder(K); I:=2*OK; F:=Factorization(I); ResidueClassField(OK,F[1][1]); Output: Magma V2.10-6 Tue Mar 23 2004 22:50:29 on modular [Seed = 3572863353] ------------------------------------- Finite field of size 2 Mapping from: RngOrd: OK to GF(2) given by the ideal Prime Ideal of OK Two element generators: [[2, 0], [0, 0]] [[-1, -1], [4, -1]] Total time: 4.049 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 22:50:57 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2+6,x^2+2]); OK:=MaximalOrder(K); I:=2*OK; F:=Factorization(I); ResidueClassField(OK,F[1][1]); Output: Magma V2.10-6 Tue Mar 23 2004 22:50:54 on modular [Seed = 739076507] ------------------------------------- Finite field of size 2 Mapping from: RngOrd: OK to GF(2) given by the ideal Prime Ideal of OK Two element generators: [[2, 0], [0, 0]] [[1, 2], [1, 0]] Total time: 3.499 seconds, Total memory usage: 1.97MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 22:51:07 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2+6,x^2+2]); OK:=MaximalOrder(K); I:=3*OK; F:=Factorization(I); ResidueClassField(OK,F[1][1]); Output: Magma V2.10-6 Tue Mar 23 2004 22:51:04 on modular [Seed = 654729894] ------------------------------------- Finite field of size 3 Mapping from: RngOrd: OK to GF(3) given by the ideal Prime Ideal of OK Two element generators: [[3, 0], [0, 0]] [[5, 0], [-2, -1]] Total time: 3.359 seconds, Total memory usage: 2.07MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 22:51:19 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2+3,x^2+2]); OK:=MaximalOrder(K); I:=3*OK; F:=Factorization(I); ResidueClassField(OK,F[1][1]); Output: Magma V2.10-6 Tue Mar 23 2004 22:51:15 on modular [Seed = 823162027] ------------------------------------- Finite field of size 3 Mapping from: RngOrd: OK to GF(3) given by the ideal Prime Ideal of OK Two element generators: [[3, 0], [0, 0]] [[-1, 0], [0, -2]] Total time: 3.269 seconds, Total memory usage: 2.07MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 22:51:27 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2+3,x^2+9]); OK:=MaximalOrder(K); I:=3*OK; F:=Factorization(I); ResidueClassField(OK,F[1][1]); Output: Magma V2.10-6 Tue Mar 23 2004 22:51:23 on modular [Seed = 136924570] ------------------------------------- Finite field of size 3^2 Mapping from: RngOrd: OK to GF(3^2) given by the ideal Prime Ideal of OK Two element generators: [[3, 0], [0, 0]] [[2, -3], [2, 0]] Total time: 3.289 seconds, Total memory usage: 2.07MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 22:51:47 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+9); OK:=MaximalOrder(K); I:=3*OK; F:=Factorization(I); ResidueClassField(OK,F[1][1]); Output: Magma V2.10-6 Tue Mar 23 2004 22:51:44 on modular [Seed = 52578042] ------------------------------------- Finite field of size 3^2 Mapping from: RngOrd: OK to GF(3^2) given by the ideal Principal Prime Ideal of OK Generator: [3, 0] Total time: 2.909 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 22:52:00 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+6); OK:=MaximalOrder(K); I:=3*OK; F:=Factorization(I); ResidueClassField(OK,F[1][1]); Output: Magma V2.10-6 Tue Mar 23 2004 22:51:57 on modular [Seed = 440098798] ------------------------------------- Finite field of size 3 Mapping from: RngOrd: OK to GF(3) given by the ideal Prime Ideal of OK Two element generators: [3, 0] [3, 1] Total time: 2.929 seconds, Total memory usage: 1.98MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 22:52:08 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+4); OK:=MaximalOrder(K); I:=3*OK; F:=Factorization(I); ResidueClassField(OK,F[1][1]); Output: Magma V2.10-6 Tue Mar 23 2004 22:52:05 on modular [Seed = 355750105] ------------------------------------- Finite field of size 3^2 Mapping from: RngOrd: OK to GF(3^2) given by the ideal Principal Prime Ideal of OK Generator: [3, 0] Total time: 2.929 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 22:52:17 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+1); OK:=MaximalOrder(K); I:=3*OK; F:=Factorization(I); ResidueClassField(OK,F[1][1]); Output: Magma V2.10-6 Tue Mar 23 2004 22:52:14 on modular [Seed = 1816996267] ------------------------------------- Finite field of size 3^2 Mapping from: RngOrd: OK to GF(3^2) given by the ideal Principal Prime Ideal of OK Generator: [3, 0] Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 22:52:26 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+2); OK:=MaximalOrder(K); I:=3*OK; F:=Factorization(I); ResidueClassField(OK,F[1][1]); Output: Magma V2.10-6 Tue Mar 23 2004 22:52:22 on modular [Seed = 1715938233] ------------------------------------- Finite field of size 3 Mapping from: RngOrd: OK to GF(3) given by the ideal Prime Ideal of OK Two element generators: [3, 0] [4, 1] Total time: 2.909 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 22:52:42 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2+2, x^2+6]); OK:=MaximalOrder(K); I:=3*OK; F:=Factorization(I); ResidueClassField(OK,F[1][1]); Output: Magma V2.10-6 Tue Mar 23 2004 22:52:39 on modular [Seed = 1901082463] ------------------------------------- Finite field of size 3 Mapping from: RngOrd: OK to GF(3) given by the ideal Prime Ideal of OK Two element generators: [[3, 0], [0, 0]] [[-1, -3], [-2, -2]] Total time: 3.449 seconds, Total memory usage: 1.98MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 22:52:56 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2+2, x^2+12]); OK:=MaximalOrder(K); I:=3*OK; F:=Factorization(I); ResidueClassField(OK,F[1][1]); Output: Magma V2.10-6 Tue Mar 23 2004 22:52:53 on modular [Seed = 1214844532] ------------------------------------- Finite field of size 3 Mapping from: RngOrd: OK to GF(3) given by the ideal Prime Ideal of OK Two element generators: [[3, 0], [0, 0]] [[9, 4], [2, 2]] Total time: 2.989 seconds, Total memory usage: 2.05MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 22:53:06 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2+12, x^2+6]); OK:=MaximalOrder(K); I:=3*OK; F:=Factorization(I); ResidueClassField(OK,F[1][1]); Output: Magma V2.10-6 Tue Mar 23 2004 22:53:02 on modular [Seed = 1130497396] ------------------------------------- Finite field of size 3^2 Mapping from: RngOrd: OK to GF(3^2) given by the ideal Prime Ideal of OK Two element generators: [[3, 0], [0, 0]] [[12, 4], [4, 1]] / 4 Total time: 3.759 seconds, Total memory usage: 2.07MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 22:53:20 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+12); OK:=MaximalOrder(K); I:=3*OK; F:=Factorization(I); ResidueClassField(OK,F[1][1]); Output: Magma V2.10-6 Tue Mar 23 2004 22:53:17 on modular [Seed = 1518017630] ------------------------------------- Finite field of size 3 Mapping from: RngOrd: OK to GF(3) given by the ideal Prime Ideal of OK Two element generators: [3, 0] [5, 4] Total time: 2.939 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 22:56:44 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+6); OK:=MaximalOrder(K); I:=3*OK; F:=Factorization(I); ResidueClassField(OK,F[1][1]); Output: Magma V2.10-6 Tue Mar 23 2004 22:56:41 on modular [Seed = 2861296762] ------------------------------------- Finite field of size 3 Mapping from: RngOrd: OK to GF(3) given by the ideal Prime Ideal of OK Two element generators: [3, 0] [3, 1] Total time: 2.909 seconds, Total memory usage: 1.98MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Mar 23 22:59:19 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2+12); OK:=MaximalOrder(K); I:=3*OK; F:=Factorization(I); ResidueClassField(OK,F[1][1]); Output: Magma V2.10-6 Tue Mar 23 2004 22:59:16 on modular [Seed = 2760237849] ------------------------------------- Finite field of size 3 Mapping from: RngOrd: OK to GF(3) given by the ideal Prime Ideal of OK Two element generators: [3, 0] [5, 4] Total time: 2.959 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host 211-21-160-69.HINET-IP.hinet.net. (211.21.160.69) Time: Tue Mar 23 23:04:30 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Tue Mar 23 2004 23:04:27 on modular [Seed = 2612712313] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host fwsmb10.nlb.si. (193.201.212.157) Time: Wed Mar 24 05:37:04 2004 Input: 435435435*435435435345 Output: Magma V2.10-6 Wed Mar 24 2004 05:37:01 on modular [Seed = 3097074779] ------------------------------------- 189604018203864450075 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host fwsmb10.nlb.si. (193.201.212.157) Time: Wed Mar 24 05:37:31 2004 Input: 43543543543543543534543534543534543534534543435435435345 * 934583945943958439589345943594598495849358439589438598459485983495 Output: Magma V2.10-6 Wed Mar 24 2004 05:37:29 on modular [Seed = 2393877065] ------------------------------------- 4069509674530749961334704292845870210640612919115779637770917725208384823493905\ 3045901425919539291171758293353070809630775 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host fwsmb10.nlb.si. (193.201.212.157) Time: Wed Mar 24 05:37:55 2004 Input: 435435435435435435345435345435345435345345434354354353455465464565465465465 * 934583945943958439589345943594598495849358439589438598459485983495 Output: Magma V2.10-6 Wed Mar 24 2004 05:37:52 on modular [Seed = 2275844777] ------------------------------------- 4069509674530749961334704292845870210640612919115779637821997079608480792277791\ 33344281155318541003407501525534866852984976990281643482500175 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Wed Mar 24 06:41:35 2004 Input: G2:=GF(2); G4:=GF(4); G8:=GF(8); G16:=GF(16); Output: Magma V2.10-6 Wed Mar 24 2004 06:41:31 on modular [Seed = 170605006] ------------------------------------- Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Wed Mar 24 06:42:17 2004 Input: G2:=GF(2); G4:=GF(4); G8:=GF(8); G16:=GF(16); [i: i in G2]; [i: i in G4]; [i: i in G8]; [i: i in G16]; Output: Magma V2.10-6 Wed Mar 24 2004 06:42:14 on modular [Seed = 18887992] ------------------------------------- [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Wed Mar 24 06:46:42 2004 Input: G25 := ext < GF(5)|(2+4*z+z^2) >; W:=PolynomialRing(G25); W; Output: Magma V2.10-6 Wed Mar 24 2004 06:46:39 on modular [Seed = 322053667] ------------------------------------- >> G25 := ext < GF(5)|(2+4*z+z^2) >; ^ User error: Identifier 'z' has not been declared or assigned >> W:=PolynomialRing(G25); ^ User error: Identifier 'G25' has not been declared or assigned >> W;; ^ User error: Identifier 'W' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Wed Mar 24 06:47:31 2004 Input: R:=PolynomialRing(GF(5)); G25 := ext < GF(5)|(2+4*z+z^2) >; W:=PolynomialRing(G25); W; Output: Magma V2.10-6 Wed Mar 24 2004 06:47:28 on modular [Seed = 1783324437] ------------------------------------- Univariate Polynomial Ring over GF(5^2) Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Wed Mar 24 06:48:16 2004 Input: R:=PolynomialRing(GF(5)); G25 := ext < GF(5)|(2+4*z+z^2) >; W:=PolynomialRing(G25); Terms(W); Output: Magma V2.10-6 Wed Mar 24 2004 06:48:13 on modular [Seed = 1614894385] ------------------------------------- >> Terms(W);; ^ Runtime error in 'Terms': Bad argument types Argument types given: RngUPol Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Wed Mar 24 06:54:09 2004 Input: alpha:=PrimitiveElement(G25); beta:=PrimitiveElement(G5); p1:=alpha^2 + alpha*x + beta*(x^2); p2:=1 + alpha*x; Output: Magma V2.10-6 Wed Mar 24 2004 06:54:06 on modular [Seed = 1332640190] ------------------------------------- >> alpha:=PrimitiveElement(G25); ^ User error: Identifier 'G25' has not been declared or assigned >> beta:=PrimitiveElement(G5); ^ User error: Identifier 'G5' has not been declared or assigned >> p1:=alpha^2 + alpha*x + beta*(x^2); ^ User error: Identifier 'alpha' has not been declared or assigned >> p2:=1 + alpha*x;; ^ User error: Identifier 'alpha' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Wed Mar 24 06:55:14 2004 Input: G5:=GF(5); R:=PolynomialRing(GF(5)); G25 := ext < GF(5)|(2+4*z+z^2) >; alpha:=PrimitiveElement(G25); beta:=PrimitiveElement(G5); p1:=alpha^2 + alpha*z + beta*(z^2); p2:=1 + alpha*z; Output: Magma V2.10-6 Wed Mar 24 2004 06:55:11 on modular [Seed = 1113814386] ------------------------------------- >> p1:=alpha^2 + alpha*z + beta*(z^2); ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt >> p2:=1 + alpha*z;; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Wed Mar 24 06:59:36 2004 Input: G5:=GF(5); R:=PolynomialRing(GF(5)); G25 := ext < GF(5)|(2+4*z+z^2) >; alpha:=PrimitiveElement(G25); beta:=PrimitiveElement(G5); p1:=alpha^2 + alpha * z + beta*(z^2); p2:=1 + alpha*z; Output: Magma V2.10-6 Wed Mar 24 2004 06:59:33 on modular [Seed = 1467379549] ------------------------------------- >> p1:=alpha^2 + alpha * z + beta*(z^2); ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt >> p2:=1 + alpha*z;; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Wed Mar 24 07:00:56 2004 Input: G5:=GF(5); R:=PolynomialRing(GF(5)); G25 := ext < GF(5)|(2+4*z+z^2) >; W:=PolynomialRing(G25); IsFinit(W); Output: Magma V2.10-6 Wed Mar 24 2004 07:00:53 on modular [Seed = 2776931839] ------------------------------------- >> IsFinit(W);; ^ User error: Identifier 'IsFinit' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Wed Mar 24 07:01:54 2004 Input: G5:=GF(5); R:=PolynomialRing(GF(5)); G25 := ext < GF(5)|(2+4*z+z^2) >; W:=PolynomialRing(G25); IsFinite(W); Output: Magma V2.10-6 Wed Mar 24 2004 07:01:51 on modular [Seed = 2326508042] ------------------------------------- false Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Wed Mar 24 07:04:04 2004 Input: G2 subset G4; G2 subset G8; G2 subset G16; G4 subset G8; G4 subset G16; G8 subset G16; Output: Magma V2.10-6 Wed Mar 24 2004 07:04:01 on modular [Seed = 2158082462] ------------------------------------- >> G2 subset G4; ^ User error: Identifier 'G4' has not been declared or assigned >> G2 subset G8; ^ User error: Identifier 'G8' has not been declared or assigned >> G2 subset G16; ^ User error: Identifier 'G16' has not been declared or assigned >> G4 subset G8; ^ User error: Identifier 'G4' has not been declared or assigned >> G4 subset G16; ^ User error: Identifier 'G4' has not been declared or assigned >> G8 subset G16;; ^ User error: Identifier 'G8' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Wed Mar 24 07:04:32 2004 Input: G2:=GF(2); G4:=GF(4); G8:=GF(8); G16:=GF(16); G2 subset G4; G2 subset G8; G2 subset G16; G4 subset G8; G4 subset G16; G8 subset G16; Output: Magma V2.10-6 Wed Mar 24 2004 07:04:29 on modular [Seed = 2545331957] ------------------------------------- true true true false true false Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Wed Mar 24 07:07:53 2004 Input: G5:=GF(5); R:=PolynomialRing(GF(5)); G25 := ext < GF(5)|(2+4*z+z^2) >; alpha:=PrimitiveElement(G25); beta:=PrimitiveElement(G5); p1:=alpha^2 + alpha*z + beta*(z^2); p2:=1 + alpha*z; Output: Magma V2.10-6 Wed Mar 24 2004 07:07:50 on modular [Seed = 3922252752] ------------------------------------- >> p1:=alpha^2 + alpha*z + beta*(z^2); ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt >> p2:=1 + alpha*z;; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Wed Mar 24 07:08:16 2004 Input: G5:=GF(5); R:=PolynomialRing(GF(5)); G25 := ext < GF(5)|(2+4*z+z^2) >; alph:=PrimitiveElement(G25); beta:=PrimitiveElement(G5); p1:=alph^2 + alph*z + beta*(z^2); p2:=1 + alph*z; Output: Magma V2.10-6 Wed Mar 24 2004 07:08:13 on modular [Seed = 3770800866] ------------------------------------- >> p1:=alph^2 + alph*z + beta*(z^2); ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt >> p2:=1 + alph*z;; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Wed Mar 24 07:08:35 2004 Input: G5:=GF(5); R:=PolynomialRing(GF(5)); G25 := ext < GF(5)|(2+4*z+z^2) >; alpha:=PrimitiveElement(G25); beta:=PrimitiveElement(G5); p1:=alpha^2 + (alpha)*z + beta*(z^2); p2:=1 + alph*z; Output: Magma V2.10-6 Wed Mar 24 2004 07:08:32 on modular [Seed = 4056992670] ------------------------------------- >> p1:=alpha^2 + (alpha)*z + beta*(z^2); ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt >> p2:=1 + alph*z;; ^ User error: Identifier 'alph' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Wed Mar 24 07:08:49 2004 Input: G5:=GF(5); R:=PolynomialRing(GF(5)); G25 := ext < GF(5)|(2+4*z+z^2) >; alpha:=PrimitiveElement(G25); beta:=PrimitiveElement(G5); p1:=alpha^2 + alpha*z + beta*(z^2); p2:=1 + alph*z; Output: Magma V2.10-6 Wed Mar 24 2004 07:08:46 on modular [Seed = 3370775209] ------------------------------------- >> p1:=alpha^2 + alpha*z + beta*(z^2); ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt >> p2:=1 + alph*z;; ^ User error: Identifier 'alph' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Wed Mar 24 07:08:57 2004 Input: G5:=GF(5); R:=PolynomialRing(GF(5)); G25 := ext < GF(5)|(2+4*z+z^2) >; alpha:=PrimitiveElement(G25); beta:=PrimitiveElement(G5); p1:=alpha^2 + alpha + beta*(z^2); p2:=1 + alph*z; Output: Magma V2.10-6 Wed Mar 24 2004 07:08:54 on modular [Seed = 3758024102] ------------------------------------- >> p1:=alpha^2 + alpha + beta*(z^2); ^ Runtime error in '+': Bad argument types Argument types given: FldFinElt, RngUPolElt >> p2:=1 + alph*z;; ^ User error: Identifier 'alph' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Wed Mar 24 07:09:54 2004 Input: G5:=GF(5); R:=PolynomialRing(GF(5)); G25 := ext < GF(5)|(2+4*z+z^2) >; alpha:=PrimitiveElement(G25); beta:=PrimitiveElement(G5); p1:=alpha^2 + alpha*z + beta*(z^2); p2:=1 + alph*z; Output: Magma V2.10-6 Wed Mar 24 2004 07:09:52 on modular [Seed = 3572887147] ------------------------------------- >> p1:=alpha^2 + alpha*z + beta*(z^2); ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt >> p2:=1 + alph*z;; ^ User error: Identifier 'alph' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Wed Mar 24 07:10:20 2004 Input: G5:=GF(5); R:=PolynomialRing(GF(5)); G25 := ext < GF(5)|(2+4*z+z^2) >; alpha:=PrimitiveElement(G25); beta:=PrimitiveElement(G5); p2:=1 + alpha*z; Output: Magma V2.10-6 Wed Mar 24 2004 07:10:17 on modular [Seed = 991560098] ------------------------------------- >> p2:=1 + alpha*z;; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Wed Mar 24 07:10:31 2004 Input: G5:=GF(5); R:=PolynomialRing(GF(5)); G25 := ext < GF(5)|(2+4*z+z^2) >; alpha:=PrimitiveElement(G25); beta:=PrimitiveElement(G5); p1:=alpha^2 + alpha*z + beta*(z^2); p2:=1 + alpha*z; Output: Magma V2.10-6 Wed Mar 24 2004 07:10:28 on modular [Seed = 604315296] ------------------------------------- >> p1:=alpha^2 + alpha*z + beta*(z^2); ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt >> p2:=1 + alpha*z;; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Wed Mar 24 07:11:18 2004 Input: G5:=GF(5); R:=PolynomialRing(GF(5)); G25 := ext < GF(5)|(2+4*z+z^2) >; alpha:=PrimitiveElement(G25); beta:=PrimitiveElement(G5); alpha^2 + alpha*z + beta*(z^2); 1 + alpha*z; Output: Magma V2.10-6 Wed Mar 24 2004 07:11:16 on modular [Seed = 755767289] ------------------------------------- >> alpha^2 + alpha*z + beta*(z^2); ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt >> 1 + alpha*z;; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Wed Mar 24 07:11:36 2004 Input: G5:=GF(5); R:=PolynomialRing(GF(5)); G25 := ext < GF(5)|(2+4*z+z^2) >; alpha:=PrimitiveElement(G25); beta:=PrimitiveElement(G5); alpha; p1:=alpha^2 + alpha*z + beta*(z^2); p2:=1 + alpha*z; Output: Magma V2.10-6 Wed Mar 24 2004 07:11:33 on modular [Seed = 372714707] ------------------------------------- G25.1 >> p1:=alpha^2 + alpha*z + beta*(z^2); ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt >> p2:=1 + alpha*z;; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Wed Mar 24 07:11:53 2004 Input: G5:=GF(5); R:=PolynomialRing(GF(5)); G25 := ext < GF(5)|(2+4*z+z^2) >; alpha:=PrimitiveElement(G25); beta:=PrimitiveElement(G5); alpha; p1:=alpha^2 + G25.1*z + beta*(z^2); p2:=1 + alpha*z; Output: Magma V2.10-6 Wed Mar 24 2004 07:11:50 on modular [Seed = 524166185] ------------------------------------- G25.1 >> p1:=alpha^2 + G25.1*z + beta*(z^2); ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt >> p2:=1 + alpha*z;; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Wed Mar 24 07:12:06 2004 Input: G5:=GF(5); R:=PolynomialRing(GF(5)); G25 := ext < GF(5)|(2+4*z+z^2) >; alpha:=PrimitiveElement(G25); beta:=PrimitiveElement(G5); alpha; p1:=alpha^2 + alpha*x + beta*(z^2); p2:=1 + alpha*z; Output: Magma V2.10-6 Wed Mar 24 2004 07:12:03 on modular [Seed = 136917803] ------------------------------------- G25.1 >> p1:=alpha^2 + alpha*x + beta*(z^2); ^ User error: Identifier 'x' has not been declared or assigned >> p2:=1 + alpha*z;; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee125.uab.es. (158.109.66.125) Time: Wed Mar 24 07:12:18 2004 Input: G5:=GF(5); R:=PolynomialRing(GF(5)); G25 := ext < GF(5)|(2+4*z+z^2) >; alpha:=PrimitiveElement(G25); beta:=PrimitiveElement(G5); p1:=alpha^2 + alpha*z + beta*(z^2); p2:=1 + alpha*z; Output: Magma V2.10-6 Wed Mar 24 2004 07:12:15 on modular [Seed = 1901087326] ------------------------------------- >> p1:=alpha^2 + alpha*z + beta*(z^2); ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt >> p2:=1 + alpha*z;; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cfpbc1.gs.com. (204.4.130.140) Time: Wed Mar 24 08:08:12 2004 Input: 2+3 Output: Magma V2.10-6 Wed Mar 24 2004 08:08:09 on modular [Seed = 1231585601] ------------------------------------- 5 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cfpbc1.gs.com. (204.4.130.140) Time: Wed Mar 24 08:08:35 2004 Input: 2^3+3 Output: Magma V2.10-6 Wed Mar 24 2004 08:08:32 on modular [Seed = 3147461594] ------------------------------------- 11 Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 24 10:59:12 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); true IsIrreducible(q1); true IsIrreducible(q2); false IsIrreducible(r1); true G9:=ext; G16:=ext; G25:=ext; //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es reductible. //apartat iv) for a:=1 to 24 do llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; Output: Magma V2.10-6 Wed Mar 24 2004 10:59:09 on modular [Seed = 170654324] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] >> Z9 no ^)s un cos finit perqu^( el '9' no ^)s primer. ^ User error: bad syntax { 0, 3, 6 } true >> IsIrreducible(q1); ^ User error: bad syntax >> IsIrreducible(q2); ^ User error: bad syntax >> IsIrreducible(r1); ^ User error: bad syntax >> G9:=ext; ^ User error: bad syntax >> for a:=1 to 24 do ^ User error: bad syntax [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 24 11:00:23 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no es un cos finit perque el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); true IsIrreducible(q1); true IsIrreducible(q2); false IsIrreducible(r1); true G9:=ext; G16:=ext; G25:=ext; //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es reductible. //apartat iv) for a:=1 to 24 do llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; Output: Magma V2.10-6 Wed Mar 24 2004 11:00:20 on modular [Seed = 2052819677] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true >> IsIrreducible(q1); ^ User error: bad syntax >> IsIrreducible(q2); ^ User error: bad syntax >> IsIrreducible(r1); ^ User error: bad syntax >> G9:=ext; ^ User error: bad syntax >> for a:=1 to 24 do ^ User error: bad syntax [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 24 11:01:44 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no es un cos finit perque el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) for a:=1 to 24 do llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; Output: Magma V2.10-6 Wed Mar 24 2004 11:01:41 on modular [Seed = 1450681984] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true User error: syntax error at end of input Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 24 11:02:28 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no es un cos finit perque el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) //for a:=1 to 24 do //llista:=[x : x in G25]; //[Order(x): x in G25 | x ne 0 ]; //#[x: x in G25 | IsPrimitive(x)]; Output: Magma V2.10-6 Wed Mar 24 2004 11:02:25 on modular [Seed = 1568451711] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 24 11:03:41 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no es un cos finit perque el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) //for a:=1 to 24 do llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; Output: Magma V2.10-6 Wed Mar 24 2004 11:03:38 on modular [Seed = 1265285666] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 24 11:38:21 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no es un cos finit perque el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) //for a:=1 to 24 do llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; MinimalPolynomial(a,G25); Output: Magma V2.10-6 Wed Mar 24 2004 11:38:18 on modular [Seed = 4292740790] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 >> MinimalPolynomial(a,G25);; ^ User error: Identifier 'a' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 24 11:41:52 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no es un cos finit perque el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) //for a:=1 to 24 do llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) [MinimalPolynomial(x,G25): x in G25|IsPrimitive(x)]; Output: Magma V2.10-6 Wed Mar 24 2004 11:41:49 on modular [Seed = 4006548624] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ $.1 + G25.1^13, $.1 + G25.1^17, $.1 + G25.1^19, $.1 + G25.1^23, $.1 + G25.1, $.1 + G25.1^5, $.1 + G25.1^7, $.1 + G25.1^11 ] Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 24 11:57:47 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no es un cos finit perque el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) //for a:=1 to 24 do llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; [x: x in G25 | IsPrimitive(x)]; //apartat v) [MinimalPolynomial(x,G25): x in G25|IsPrimitive(x)]; Output: Magma V2.10-6 Wed Mar 24 2004 11:57:44 on modular [Seed = 890555145] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] [ $.1 + G25.1^13, $.1 + G25.1^17, $.1 + G25.1^19, $.1 + G25.1^23, $.1 + G25.1, $.1 + G25.1^5, $.1 + G25.1^7, $.1 + G25.1^11 ] Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 24 12:00:14 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no es un cos finit perque el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) //for a:=1 to 24 do llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) [MinimalPolynomial(x,G25): x in G25|IsPrimitive(x)]; MinimalPolynomial(G25.1^5,G25); Output: Magma V2.10-6 Wed Mar 24 2004 12:00:11 on modular [Seed = 536993423] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ $.1 + G25.1^13, $.1 + G25.1^17, $.1 + G25.1^19, $.1 + G25.1^23, $.1 + G25.1, $.1 + G25.1^5, $.1 + G25.1^7, $.1 + G25.1^11 ] $.1 + G25.1^17 Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 24 12:11:33 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no es un cos finit perque el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) //for a:=1 to 24 do llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) [MinimalPolynomial(x,G25): x in G25|IsPrimitive(x)]; MinimalPolynomial(G25.1^7,G25); Output: Magma V2.10-6 Wed Mar 24 2004 12:11:30 on modular [Seed = 1715988240] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ $.1 + G25.1^13, $.1 + G25.1^17, $.1 + G25.1^19, $.1 + G25.1^23, $.1 + G25.1, $.1 + G25.1^5, $.1 + G25.1^7, $.1 + G25.1^11 ] $.1 + G25.1^19 Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 24 12:30:12 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no es un cos finit perque el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) //for a:=1 to 24 do llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) F := G25; MinimalPolynomial(alpha,G25); //[MinimalPolynomial(x,G25): x in G25|IsPrimitive(x)]; //MinimalPolynomial(G25.1^7,G25); Output: Magma V2.10-6 Wed Mar 24 2004 12:30:08 on modular [Seed = 3164420393] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 $.1 + alpha^13 Total time: 3.089 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 24 12:30:42 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no es un cos finit perque el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) //for a:=1 to 24 do llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) F := G25; MinimalPolynomial(alpha,G25); //[MinimalPolynomial(x,G25): x in G25|IsPrimitive(x)]; //MinimalPolynomial(G25.1^7,G25); Output: Magma V2.10-6 Wed Mar 24 2004 12:30:39 on modular [Seed = 2225406223] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 $.1 + alpha^13 Total time: 3.139 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 24 12:36:14 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no es un cos finit perque el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) //for a:=1 to 24 do llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) F := G25; MinimalPolynomial(alpha,G25); IsPrimitive(alpha); Output: Magma V2.10-6 Wed Mar 24 2004 12:36:11 on modular [Seed = 4158025928] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 $.1 + alpha^13 true Total time: 3.079 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 24 12:38:21 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no es un cos finit perque el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) //for a:=1 to 24 do llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) F := G25; MinimalPolynomial(alpha,G25); print alpha; Output: Magma V2.10-6 Wed Mar 24 2004 12:38:18 on modular [Seed = 4191714887] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 $.1 + alpha^13 alpha Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 24 12:40:49 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no es un cos finit perque el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) //for a:=1 to 24 do llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) F := G25; MinimalPolynomial(alpha,G25); Roots (polinomi,G25); Roots (polinomi,Z5); Output: Magma V2.10-6 Wed Mar 24 2004 12:40:46 on modular [Seed = 3939197632] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 $.1 + alpha^13 >> Roots (polinomi,G25); ^ User error: Identifier 'polinomi' has not been declared or assigned >> Roots (polinomi,Z5);; ^ User error: Identifier 'polinomi' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 24 12:41:15 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no es un cos finit perque el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) //for a:=1 to 24 do llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) F := G25; Minpol:=MinimalPolynomial(alpha,G25); Roots (Minpol,G25); Roots (Minpol,Z5); Output: Magma V2.10-6 Wed Mar 24 2004 12:41:12 on modular [Seed = 3555875807] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ ] >> Roots (Minpol,Z5);; ^ User error: Identifier 'Z5' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 24 12:41:41 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no es un cos finit perque el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) //for a:=1 to 24 do llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) F := G25; Minpol:=MinimalPolynomial(alpha,G25); Roots (Minpol,G25); Roots (Minpol,z5); Output: Magma V2.10-6 Wed Mar 24 2004 12:41:38 on modular [Seed = 3303361698] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ ] >> Roots (Minpol,z5);; ^ Runtime error in 'Roots': Argument 1 cannot be coerced to be over argument 2 Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 24 12:42:38 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no es un cos finit perque el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) //for a:=1 to 24 do llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) F := G25; Minpol:=MinimalPolynomial(alpha,G25); Roots (Minpol,G25); Roots (Minpol,GF(5)); Output: Magma V2.10-6 Wed Mar 24 2004 12:42:35 on modular [Seed = 3471787633] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ ] >> Roots (Minpol,GF(5));; ^ Runtime error in 'Roots': Argument 1 cannot be coerced to be over argument 2 Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 24 12:50:30 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no es un cos finit perque el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) //for a:=1 to 24 do llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) F := G25; Minpol:=MinimalPolynomial(alpha,G25); Roots (Minpol,G25); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; Output: Magma V2.10-6 Wed Mar 24 2004 12:50:27 on modular [Seed = 772777080] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ ] Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 24 12:50:46 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no es un cos finit perque el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) //for a:=1 to 24 do llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) F := G25; Minpol:=MinimalPolynomial(alpha,G25); Roots (Minpol,G25); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; Output: Magma V2.10-6 Wed Mar 24 2004 12:50:43 on modular [Seed = 288398167] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ ] alpha^13 Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 24 12:53:28 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no es un cos finit perque el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) //for a:=1 to 24 do llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) F := G25; Minpol:=MinimalPolynomial(alpha,G25); Roots (Minpol,G25); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); Output: Magma V2.10-6 Wed Mar 24 2004 12:53:25 on modular [Seed = 440111418] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ ] alpha^13 true alpha^11 Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 24 12:54:49 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no es un cos finit perque el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) //for a:=1 to 24 do llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) F := G25; Minpol:=MinimalPolynomial(alpha,G25); Roots (Minpol,G25); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; Output: Magma V2.10-6 Wed Mar 24 2004 12:54:46 on modular [Seed = 204310367] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 24 12:57:29 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no es un cos finit perque el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) //for a:=1 to 24 do llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) F := G25; Minpol:=MinimalPolynomial(alpha,G25); Roots (Minpol,G25); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; {x:x in G25} Output: Magma V2.10-6 Wed Mar 24 2004 12:57:26 on modular [Seed = 1918107201] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 } Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 24 12:57:42 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no es un cos finit perque el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) //for a:=1 to 24 do llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) F := G25; Minpol:=MinimalPolynomial(alpha,G25); Roots (Minpol,G25); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; {x:x in G25}; Output: Magma V2.10-6 Wed Mar 24 2004 12:57:39 on modular [Seed = 1699014979] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 } Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Wed Mar 24 13:05:26 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no es un cos finit perque el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) //for a:=1 to 24 do llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) F := G25; Minpol:=MinimalPolynomial(alpha,G25); Roots (Minpol,G25); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; Output: Magma V2.10-6 Wed Mar 24 2004 13:05:22 on modular [Seed = 1315947416] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:26:48 2004 Input: > F := EllipticCurve([0, 17]); > F; > MW, f := MordellWeilGroup(F); > MW; %> a := f(MW.1); %> b := f(MW.2); %> a, b; %> intpts := [ pt : i, j in [-4..4] | %> IsIntegral(pt) where pt is i*a + j*b] ; %> intpts; > #intpts; Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed. ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:28:00 2004 Input: > F := EllipticCurve([0, 3]); > F; > MW, f := MordellWeilGroup(F); > MW; Output: Magma V2.10-6 Wed Mar 24 2004 13:27:57 on modular [Seed = 2208436379] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 3 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) Total time: 3.239 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:29:36 2004 Input: > F := EllipticCurve([0, 3]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i in [-40..40] | > IsIntegral(pt) where pt is i*a] ; > intpts; > #intpts; Output: Magma V2.10-6 Wed Mar 24 2004 13:29:33 on modular [Seed = 4124337741] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 3 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (1 : 2 : 1) [ (1 : -2 : 1), (1 : 2 : 1) ] 2 Total time: 3.289 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:30:30 2004 Input: > F := EllipticCurve([0, 5]); > F; > MW, f := MordellWeilGroup(F); > MW; Output: Magma V2.10-6 Wed Mar 24 2004 13:30:27 on modular [Seed = 3854857747] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 5 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) Total time: 3.239 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:30:51 2004 Input: > F := EllipticCurve([0, 7]); > F; > MW, f := MordellWeilGroup(F); > MW; Output: Magma V2.10-6 Wed Mar 24 2004 13:30:48 on modular [Seed = 3972890369] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 7 over Rational Field Abelian Group of order 1 Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:31:59 2004 Input: > F := EllipticCurve([0, 11]); > F; > MW, f := MordellWeilGroup(F); > MW; Output: Magma V2.10-6 Wed Mar 24 2004 13:31:56 on modular [Seed = 3623240702] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 11 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) Total time: 3.119 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:32:38 2004 Input: > F := EllipticCurve([0, 13]); > F; > MW, f := MordellWeilGroup(F); > MW; Output: Magma V2.10-6 Wed Mar 24 2004 13:32:35 on modular [Seed = 3656928687] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 13 over Rational Field Abelian Group of order 1 Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:33:05 2004 Input: > F := EllipticCurve([0, 17]); > F; > MW, f := MordellWeilGroup(F); > MW; Output: Magma V2.10-6 Wed Mar 24 2004 13:33:02 on modular [Seed = 3286390696] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 17 over Rational Field Abelian Group isomorphic to Z + Z Defined on 2 generators (free) Total time: 3.619 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:33:28 2004 Input: > F := EllipticCurve([0, 19]); > F; > MW, f := MordellWeilGroup(F); > MW; Output: Magma V2.10-6 Wed Mar 24 2004 13:33:25 on modular [Seed = 3404422794] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 19 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) Total time: 3.129 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:33:49 2004 Input: > F := EllipticCurve([0, 23]); > F; > MW, f := MordellWeilGroup(F); > MW; Output: Magma V2.10-6 Wed Mar 24 2004 13:33:46 on modular [Seed = 1042262658] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 23 over Rational Field Abelian Group of order 1 Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:34:07 2004 Input: > F := EllipticCurve([0, 29]); > F; > MW, f := MordellWeilGroup(F); > MW; Output: Magma V2.10-6 Wed Mar 24 2004 13:34:04 on modular [Seed = 654750605] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 29 over Rational Field Abelian Group of order 1 Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:34:29 2004 Input: > F := EllipticCurve([0, 31]); > F; > MW, f := MordellWeilGroup(F); > MW; Output: Magma V2.10-6 Wed Mar 24 2004 13:34:26 on modular [Seed = 739096744] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 31 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) Total time: 3.119 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:34:51 2004 Input: > F := EllipticCurve([0, 37]); > F; > MW, f := MordellWeilGroup(F); > MW; Output: Magma V2.10-6 Wed Mar 24 2004 13:34:47 on modular [Seed = 355762660] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 37 over Rational Field Abelian Group isomorphic to Z + Z Defined on 2 generators (free) Total time: 3.329 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:35:13 2004 Input: > F := EllipticCurve([0, 41]); > F; > MW, f := MordellWeilGroup(F); > MW; Output: Magma V2.10-6 Wed Mar 24 2004 13:35:10 on modular [Seed = 103256814] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 41 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) Total time: 3.129 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:35:33 2004 Input: > F := EllipticCurve([0, 43]); > F; > MW, f := MordellWeilGroup(F); > MW; Output: Magma V2.10-6 Wed Mar 24 2004 13:35:29 on modular [Seed = 204314827] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 43 over Rational Field Abelian Group isomorphic to Z + Z Defined on 2 generators (free) Total time: 3.579 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:35:55 2004 Input: > F := EllipticCurve([0, 47]); > F; > MW, f := MordellWeilGroup(F); > MW; Output: Magma V2.10-6 Wed Mar 24 2004 13:35:52 on modular [Seed = 1968496715] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 47 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) Total time: 3.139 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:36:51 2004 Input: > F := EllipticCurve([0, 53]); > F; > MW, f := MordellWeilGroup(F); > MW; Output: Magma V2.10-6 Wed Mar 24 2004 13:36:48 on modular [Seed = 2052845324] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 53 over Rational Field Abelian Group of order 1 Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:37:13 2004 Input: > F := EllipticCurve([0, 59]); > F; > MW, f := MordellWeilGroup(F); > MW; Output: Magma V2.10-6 Wed Mar 24 2004 13:37:10 on modular [Seed = 1867446799] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 59 over Rational Field Abelian Group of order 1 Total time: 3.039 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:37:32 2004 Input: > F := EllipticCurve([0, 61]); > F; > MW, f := MordellWeilGroup(F); > MW; Output: Magma V2.10-6 Wed Mar 24 2004 13:37:29 on modular [Seed = 1417003275] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 61 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) Total time: 3.079 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:37:51 2004 Input: > F := EllipticCurve([0, 67]); > F; > MW, f := MordellWeilGroup(F); > MW; Output: Magma V2.10-6 Wed Mar 24 2004 13:37:48 on modular [Seed = 1518063376] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 67 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) Total time: 3.129 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:38:11 2004 Input: > F := EllipticCurve([0, 71]); > F; > MW, f := MordellWeilGroup(F); > MW; Output: Magma V2.10-6 Wed Mar 24 2004 13:38:07 on modular [Seed = 1130551034] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 71 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) Total time: 3.139 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:38:32 2004 Input: > F := EllipticCurve([0, 73]); > F; > MW, f := MordellWeilGroup(F); > MW; Output: Magma V2.10-6 Wed Mar 24 2004 13:38:28 on modular [Seed = 1214897626] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 73 over Rational Field Abelian Group isomorphic to Z + Z Defined on 2 generators (free) Total time: 3.479 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:40:06 2004 Input: > F := EllipticCurve([0, 79]); > F; > MW, f := MordellWeilGroup(F); > MW; Output: Magma V2.10-6 Wed Mar 24 2004 13:40:03 on modular [Seed = 3113758604] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 79 over Rational Field Abelian Group isomorphic to Z + Z Defined on 2 generators (free) Total time: 3.409 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:40:27 2004 Input: > F := EllipticCurve([0, 83]); > F; > MW, f := MordellWeilGroup(F); > MW; Output: Magma V2.10-6 Wed Mar 24 2004 13:40:24 on modular [Seed = 2928621696] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 83 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) Total time: 3.119 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:40:47 2004 Input: > F := EllipticCurve([0, 89]); > F; > MW, f := MordellWeilGroup(F); > MW; Output: Magma V2.10-6 Wed Mar 24 2004 13:40:43 on modular [Seed = 2545287562] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 89 over Rational Field Abelian Group isomorphic to Z + Z Defined on 2 generators (free) Total time: 3.449 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:41:13 2004 Input: > F := EllipticCurve([0, 91]); > F; > MW, f := MordellWeilGroup(F); > MW; Output: Magma V2.10-6 Wed Mar 24 2004 13:41:10 on modular [Seed = 2629634796] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 91 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) Total time: 3.149 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:41:32 2004 Input: > F := EllipticCurve([0, 97]); > F; > MW, f := MordellWeilGroup(F); > MW; Output: Magma V2.10-6 Wed Mar 24 2004 13:41:29 on modular [Seed = 2242122730] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 97 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) Total time: 3.109 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:42:05 2004 Input: > F := EllipticCurve([0, 101]); > F; > MW, f := MordellWeilGroup(F); > MW; Output: Magma V2.10-6 Wed Mar 24 2004 13:42:02 on modular [Seed = 2326469830] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 101 over Rational Field Abelian Group isomorphic to Z + Z Defined on 2 generators (free) Total time: 3.409 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:42:30 2004 Input: > F := EllipticCurve([0, 103]); > F; > MW, f := MordellWeilGroup(F); > MW; Output: Magma V2.10-6 Wed Mar 24 2004 13:42:27 on modular [Seed = 4090651990] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 103 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) Total time: 3.079 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:43:46 2004 Input: > F := EllipticCurve([0, 101]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > b := f(MW.2); > a, b; > intpts := [ pt : i, j in [-40..40] | > IsIntegral(pt) where pt is i*a + j*b] ; > intpts; > #intpts; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Wed Mar 24 2004 13:43:23 on modular [Seed = 3888541978] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 101 over Rational Field Abelian Group isomorphic to Z + Z Defined on 2 generators (free) (-1 : 10 : 1) (95 : 926 : 1) Errors: /home/mfd/gomagma: line 2: 30417 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:44:12 2004 Input: > F := EllipticCurve([0, 101]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > b := f(MW.2); > a, b; > intpts := [ pt : i, j in [-10..20] | > IsIntegral(pt) where pt is i*a + j*b] ; > intpts; > #intpts; Output: Magma V2.10-6 Wed Mar 24 2004 13:44:04 on modular [Seed = 3972889134] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 101 over Rational Field Abelian Group isomorphic to Z + Z Defined on 2 generators (free) (-1 : 10 : 1) (95 : 926 : 1) [ (-1 : -10 : 1), (95 : -926 : 1), (95 : 926 : 1), (-1 : 10 : 1) ] 4 Total time: 7.189 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:44:34 2004 Input: > F := EllipticCurve([0, 89]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > b := f(MW.2); > a, b; > intpts := [ pt : i, j in [-10..20] | > IsIntegral(pt) where pt is i*a + j*b] ; > intpts; > #intpts; Output: Magma V2.10-6 Wed Mar 24 2004 13:44:30 on modular [Seed = 3589554925] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 89 over Rational Field Abelian Group isomorphic to Z + Z Defined on 2 generators (free) (-2 : -9 : 1) (-4 : 5 : 1) [ (55 : -408 : 1), (-2 : 9 : 1), (10 : -33 : 1), (-4 : -5 : 1), (-4 : 5 : 1), (10 : 33 : 1), (-2 : -9 : 1), (55 : 408 : 1) ] 8 Total time: 4.649 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:45:11 2004 Input: > F := EllipticCurve([0, 79]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > b := f(MW.2); > a, b; > intpts := [ pt : i, j in [-10..20] | > IsIntegral(pt) where pt is i*a + j*b] ; > intpts; > #intpts; Output: Magma V2.10-6 Wed Mar 24 2004 13:45:04 on modular [Seed = 3337048512] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 79 over Rational Field Abelian Group isomorphic to Z + Z Defined on 2 generators (free) (-15/4 : 41/8 : 1) (45 : -302 : 1) [ (45 : 302 : 1), (45 : -302 : 1) ] 2 Total time: 7.659 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:45:39 2004 Input: > F := EllipticCurve([0, 73]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > b := f(MW.2); > a, b; > intpts := [ pt : i, j in [-10..20] | > IsIntegral(pt) where pt is i*a + j*b] ; > intpts; > #intpts; Output: Magma V2.10-6 Wed Mar 24 2004 13:45:35 on modular [Seed = 3488503990] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 73 over Rational Field Abelian Group isomorphic to Z + Z Defined on 2 generators (free) (2 : 9 : 1) (-4 : 3 : 1) [ (356 : -6717 : 1), (3 : 10 : 1), (2 : -9 : 1), (6 : 17 : 1), (72 : 611 : 1), (-4 : -3 : 1), (-4 : 3 : 1), (72 : -611 : 1), (6 : -17 : 1), (2 : 9 : 1), (3 : -10 : 1), (356 : 6717 : 1) ] 12 Total time: 4.279 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:46:04 2004 Input: > F := EllipticCurve([0, 43]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > b := f(MW.2); > a, b; > intpts := [ pt : i, j in [-10..20] | > IsIntegral(pt) where pt is i*a + j*b] ; > intpts; > #intpts; Output: Magma V2.10-6 Wed Mar 24 2004 13:45:58 on modular [Seed = 890544740] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 43 over Rational Field Abelian Group isomorphic to Z + Z Defined on 2 generators (free) (-3 : 4 : 1) (9/4 : -59/8 : 1) [ (-3 : -4 : 1), (-3 : 4 : 1) ] 2 Total time: 5.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:46:31 2004 Input: > F := EllipticCurve([0, 37]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > b := f(MW.2); > a, b; > intpts := [ pt : i, j in [-10..20] | > IsIntegral(pt) where pt is i*a + j*b] ; > intpts; > #intpts; Output: Magma V2.10-6 Wed Mar 24 2004 13:46:27 on modular [Seed = 991603855] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 37 over Rational Field Abelian Group isomorphic to Z + Z Defined on 2 generators (free) (-1 : -6 : 1) (3 : -8 : 1) [ (243 : -3788 : 1), (-1 : 6 : 1), (3 : 8 : 1), (3 : -8 : 1), (-1 : -6 : 1), (243 : 3788 : 1) ] 6 Total time: 4.709 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:46:54 2004 Input: > F := EllipticCurve([0, 17]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > b := f(MW.2); > a, b; > intpts := [ pt : i, j in [-10..20] | > IsIntegral(pt) where pt is i*a + j*b] ; > intpts; > #intpts; Output: Magma V2.10-6 Wed Mar 24 2004 13:46:50 on modular [Seed = 570668431] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 17 over Rational Field Abelian Group isomorphic to Z + Z Defined on 2 generators (free) (-2 : 3 : 1) (4 : 9 : 1) [ (52 : -375 : 1), (8 : 23 : 1), (5234 : 378661 : 1), (-1 : 4 : 1), (-2 : -3 : 1), (2 : -5 : 1), (43 : -282 : 1), (4 : -9 : 1), (4 : 9 : 1), (43 : 282 : 1), (2 : 5 : 1), (-2 : 3 : 1), (-1 : -4 : 1), (5234 : -378661 : 1), (8 : -23 : 1), (52 : 375 : 1) ] 16 Total time: 4.159 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:48:00 2004 Input: > F := EllipticCurve([0, 5]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i in [-20..30] | > IsIntegral(pt) where pt is i*a ] ; > intpts; > #intpts; Output: Magma V2.10-6 Wed Mar 24 2004 13:47:57 on modular [Seed = 671727554] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 5 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (-1 : 2 : 1) [ (-1 : -2 : 1), (-1 : 2 : 1) ] 2 Total time: 3.189 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:48:18 2004 Input: > F := EllipticCurve([0, 11]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i in [-20..30] | > IsIntegral(pt) where pt is i*a ] ; > intpts; > #intpts; Output: Magma V2.10-6 Wed Mar 24 2004 13:48:14 on modular [Seed = 524191942] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 11 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (-7/4 : -19/8 : 1) [] 0 Total time: 3.209 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:49:17 2004 Input: > F := EllipticCurve([0, 11]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i in [-40..70] | > IsIntegral(pt) where pt is i*a ] ; > intpts; > #intpts; Output: Magma V2.10-6 Wed Mar 24 2004 13:49:10 on modular [Seed = 103259671] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 11 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (-7/4 : -19/8 : 1) [] 0 Total time: 6.489 seconds, Total memory usage: 2.55MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:49:39 2004 Input: > F := EllipticCurve([0, 19]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i in [-40..70] | > IsIntegral(pt) where pt is i*a ] ; > intpts; > #intpts; Output: Magma V2.10-6 Wed Mar 24 2004 13:49:34 on modular [Seed = 204313605] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 19 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (5 : 12 : 1) [ (5 : -12 : 1), (5 : 12 : 1) ] 2 Total time: 4.319 seconds, Total memory usage: 2.21MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:50:00 2004 Input: > F := EllipticCurve([0, 31]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i in [-40..70] | > IsIntegral(pt) where pt is i*a ] ; > intpts; > #intpts; Output: Magma V2.10-6 Wed Mar 24 2004 13:49:55 on modular [Seed = 1934813975] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 31 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (-3 : 2 : 1) [ (-3 : -2 : 1), (-3 : 2 : 1) ] 2 Total time: 4.699 seconds, Total memory usage: 2.30MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:50:25 2004 Input: > F := EllipticCurve([0, 41]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i in [-40..70] | > IsIntegral(pt) where pt is i*a ] ; > intpts; > #intpts; Output: Magma V2.10-6 Wed Mar 24 2004 13:50:20 on modular [Seed = 1665334072] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 41 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (2 : 7 : 1) [ (2 : -7 : 1), (2 : 7 : 1) ] 2 Total time: 4.259 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:50:51 2004 Input: > F := EllipticCurve([0, 47]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i in [-40..70] | > IsIntegral(pt) where pt is i*a ] ; > intpts; > #intpts; Output: Magma V2.10-6 Wed Mar 24 2004 13:50:43 on modular [Seed = 1783362270] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 47 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (17/4 : 89/8 : 1) [] 0 Total time: 7.879 seconds, Total memory usage: 2.87MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:51:15 2004 Input: > F := EllipticCurve([0, 61]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i in [-40..70] | > IsIntegral(pt) where pt is i*a ] ; > intpts; > #intpts; Output: Magma V2.10-6 Wed Mar 24 2004 13:51:07 on modular [Seed = 1366346237] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 61 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (-15/4 : -23/8 : 1) [] 0 Total time: 7.659 seconds, Total memory usage: 2.90MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:51:43 2004 Input: > F := EllipticCurve([0, 67]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i in [-40..70] | > IsIntegral(pt) where pt is i*a ] ; > intpts; > #intpts; Output: Magma V2.10-6 Wed Mar 24 2004 13:51:29 on modular [Seed = 1484374238] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 67 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (49/36 : -1801/216 : 1) [] 0 Total time: 13.590 seconds, Total memory usage: 3.03MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:52:02 2004 Input: > F := EllipticCurve([0, 71]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i in [-40..70] | > IsIntegral(pt) where pt is i*a ] ; > intpts; > #intpts; Output: Magma V2.10-6 Wed Mar 24 2004 13:51:57 on modular [Seed = 1332664245] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 71 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (5 : 14 : 1) [ (5 : -14 : 1), (5 : 14 : 1) ] 2 Total time: 5.449 seconds, Total memory usage: 2.32MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:52:41 2004 Input: > F := EllipticCurve([0, 83]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i in [-40..70] | > IsIntegral(pt) where pt is i*a ] ; > intpts; > #intpts; Output: Magma V2.10-6 Wed Mar 24 2004 13:52:19 on modular [Seed = 3063361122] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 83 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (2641/36 : -135737/216 : 1) [] 0 Total time: 22.399 seconds, Total memory usage: 5.21MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:53:03 2004 Input: > F := EllipticCurve([0, 91]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i in [-40..70] | > IsIntegral(pt) where pt is i*a ] ; > intpts; > #intpts; Output: Magma V2.10-6 Wed Mar 24 2004 13:52:58 on modular [Seed = 3130729351] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 91 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (-3 : 8 : 1) [ (-3 : -8 : 1), (-3 : 8 : 1) ] 2 Total time: 5.169 seconds, Total memory usage: 2.22MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:53:19 2004 Input: > F := EllipticCurve([0, 97]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i in [-40..70] | > IsIntegral(pt) where pt is i*a ] ; > intpts; > #intpts; Output: Magma V2.10-6 Wed Mar 24 2004 13:53:12 on modular [Seed = 2709534863] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 97 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (18 : 77 : 1) [ (18 : -77 : 1), (18 : 77 : 1) ] 2 Total time: 6.219 seconds, Total memory usage: 2.50MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:53:51 2004 Input: > F := EllipticCurve([0, 103]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > a; > intpts := [ pt : i in [-40..70] | > IsIntegral(pt) where pt is i*a ] ; > intpts; > #intpts; Output: Magma V2.10-6 Wed Mar 24 2004 13:53:41 on modular [Seed = 2827563434] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 103 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) (13/9 : 278/27 : 1) [] 0 Total time: 10.009 seconds, Total memory usage: 3.26MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:55:47 2004 Input: > F := EllipticCurve([0, 17]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > b := f(MW.2); > a, b; > intpts := [ pt : i, j in [-40..40] | > IsIntegral(pt) where pt is i*a + j*b] ; > intpts; > #intpts; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Wed Mar 24 2004 13:55:24 on modular [Seed = 2612658736] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 17 over Rational Field Abelian Group isomorphic to Z + Z Defined on 2 generators (free) (-2 : 3 : 1) (4 : 9 : 1) Errors: /home/mfd/gomagma: line 2: 30636 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:56:00 2004 Input: > F := EllipticCurve([0, 17]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > b := f(MW.2); > a, b; > intpts := [ pt : i, j in [-10..20] | > IsIntegral(pt) where pt is i*a + j*b] ; > intpts; > #intpts; Output: Magma V2.10-6 Wed Mar 24 2004 13:55:56 on modular [Seed = 2191727369] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 17 over Rational Field Abelian Group isomorphic to Z + Z Defined on 2 generators (free) (-2 : 3 : 1) (4 : 9 : 1) [ (52 : -375 : 1), (8 : 23 : 1), (5234 : 378661 : 1), (-1 : 4 : 1), (-2 : -3 : 1), (2 : -5 : 1), (43 : -282 : 1), (4 : -9 : 1), (4 : 9 : 1), (43 : 282 : 1), (2 : 5 : 1), (-2 : 3 : 1), (-1 : -4 : 1), (5234 : -378661 : 1), (8 : -23 : 1), (52 : 375 : 1) ] 16 Total time: 4.119 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host pcd595076.netvigator.com. (218.102.127.76) Time: Wed Mar 24 13:56:34 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Wed Mar 24 2004 13:56:31 on modular [Seed = 4040255768] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:56:48 2004 Input: > F := EllipticCurve([0, 17]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > b := f(MW.2); > a, b; > intpts := [ pt : i, j in [-8..8] | > IsIntegral(pt) where pt is i*a + j*b] ; > intpts; > #intpts; Output: Magma V2.10-6 Wed Mar 24 2004 13:56:45 on modular [Seed = 3888545341] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 17 over Rational Field Abelian Group isomorphic to Z + Z Defined on 2 generators (free) (-2 : 3 : 1) (4 : 9 : 1) [ (52 : -375 : 1), (8 : 23 : 1), (5234 : 378661 : 1), (-1 : 4 : 1), (-2 : -3 : 1), (2 : -5 : 1), (43 : -282 : 1), (4 : -9 : 1), (4 : 9 : 1), (43 : 282 : 1), (2 : 5 : 1), (-2 : 3 : 1), (-1 : -4 : 1), (5234 : -378661 : 1), (8 : -23 : 1), (52 : 375 : 1) ] 16 Total time: 3.679 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host pcd595076.netvigator.com. (218.102.127.76) Time: Wed Mar 24 13:57:19 2004 Input: 13^11791 mod 18865 Output: Magma V2.10-6 Wed Mar 24 2004 13:57:15 on modular [Seed = 4006573266] ------------------------------------- 9792 Total time: 3.299 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-58-34.vc.shawcable.net. (24.81.58.34) Time: Wed Mar 24 13:57:22 2004 Input: > F := EllipticCurve([0, 17]); > F; > MW, f := MordellWeilGroup(F); > MW; > a := f(MW.1); > b := f(MW.2); > a, b; > intpts := [ pt : i, j in [-4..4] | > IsIntegral(pt) where pt is i*a + j*b] ; > intpts; > #intpts; Output: Magma V2.10-6 Wed Mar 24 2004 13:57:18 on modular [Seed = 3955913170] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 17 over Rational Field Abelian Group isomorphic to Z + Z Defined on 2 generators (free) (-2 : 3 : 1) (4 : 9 : 1) [ (52 : -375 : 1), (8 : 23 : 1), (5234 : 378661 : 1), (-1 : 4 : 1), (-2 : -3 : 1), (2 : -5 : 1), (43 : -282 : 1), (4 : -9 : 1), (4 : 9 : 1), (43 : 282 : 1), (2 : 5 : 1), (-2 : 3 : 1), (-1 : -4 : 1), (5234 : -378661 : 1), (8 : -23 : 1), (52 : 375 : 1) ] 16 Total time: 3.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host pcd595076.netvigator.com. (218.102.127.76) Time: Wed Mar 24 13:57:41 2004 Input: 13^11791 mod 18865 Output: Magma V2.10-6 Wed Mar 24 2004 13:57:38 on modular [Seed = 3286391254] ------------------------------------- 9792 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Wed Mar 24 14:44:21 2004 Input: F := PolynomialRing(FiniteField(5^4)); C := HyperellipticCurve(x^3-1); #(Points(C : Bound:=4)); Output: Magma V2.10-6 Wed Mar 24 2004 14:44:18 on modular [Seed = 1417015678] ------------------------------------- 576 Total time: 2.979 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Wed Mar 24 14:44:33 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); c=0; d=0; f:=x^6 +2*c*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Wed Mar 24 2004 14:44:30 on modular [Seed = 1298983019] ------------------------------------- >> c=0; d=0; ^ User error: Identifier 'c' has not been declared or assigned >> c=0; d=0; ^ User error: Identifier 'd' has not been declared or assigned >> f:=x^6 +2*c*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 ^ User error: Identifier 'c' has not been declared or assigned >> print(f); ^ User error: Identifier 'f' has not been declared or assigned >> G, R:= GaloisGroup(f); ^ User error: Identifier 'f' has not been declared or assigned >> print(G); ^ User error: Identifier 'G' has not been declared or assigned >> t1, t2:= TransitiveGroupIdentification(G); ^ User error: Identifier 'G' has not been declared or assigned >> print(t1); ^ User error: Identifier 't1' has not been declared or assigned >> print(t2);; ^ User error: Identifier 't2' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Wed Mar 24 14:44:46 2004 Input: F := PolynomialRing(FiniteField(5^1)); C := HyperellipticCurve(x^3-1); #(Points(C : Bound:=4)); Output: Magma V2.10-6 Wed Mar 24 2004 14:44:43 on modular [Seed = 1181213525] ------------------------------------- 6 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Wed Mar 24 14:44:55 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); c:=0; d:=0; f:=x^6 +2*c*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Wed Mar 24 2004 14:44:51 on modular [Seed = 3214809779] ------------------------------------- x^6 + 2*x^4 + (4*b + 2)*x^3 + 2*b*x^2 + (2*b + 1)*x + 4*b + 1 Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 Total time: 3.389 seconds, Total memory usage: 6.53MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Wed Mar 24 14:45:29 2004 Input: F := PolynomialRing(FiniteField(5^1)); C := HyperellipticCurve(x^4-1); #(Points(C : Bound:=4)); Output: Magma V2.10-6 Wed Mar 24 2004 14:45:26 on modular [Seed = 2692810190] ------------------------------------- 8 Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Wed Mar 24 14:46:11 2004 Input: F := PolynomialRing(FiniteField(5^10)); C := HyperellipticCurve(x^4-1); #(Points(C : Bound:=4)); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Wed Mar 24 2004 14:45:48 on modular [Seed = 2578988237] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 30881 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Wed Mar 24 14:46:21 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); c:=0; d:=0; f:=x^6 +2*c*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); print(f); G, R:= GaloisGroup(f); print(G); print(order(G)); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Wed Mar 24 2004 14:46:17 on modular [Seed = 2461218595] ------------------------------------- x^6 + 2*x^4 + (4*b + 2)*x^3 + 2*b*x^2 + (2*b + 1)*x + 4*b + 1 Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) >> print(order(G)); ^ User error: Identifier 'order' has not been declared or assigned 12 6 Total time: 3.839 seconds, Total memory usage: 6.53MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Wed Mar 24 14:46:22 2004 Input: F := PolynomialRing(FiniteField(5^5)); C := HyperellipticCurve(x^4-1); #(Points(C : Bound:=4)); Output: Magma V2.10-6 Wed Mar 24 2004 14:46:18 on modular [Seed = 2511613991] ------------------------------------- 3208 Total time: 3.659 seconds, Total memory usage: 2.30MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Wed Mar 24 14:46:35 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); c:=0; d:=0; f:=x^6 +2*c*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); print(f); G, R:= GaloisGroup(f); print(G); print(Order(G)); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Wed Mar 24 2004 14:46:32 on modular [Seed = 2225414436] ------------------------------------- x^6 + 2*x^4 + (4*b + 2)*x^3 + 2*b*x^2 + (2*b + 1)*x + 4*b + 1 Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 60 12 6 Total time: 3.349 seconds, Total memory usage: 6.53MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Wed Mar 24 14:46:40 2004 Input: F := PolynomialRing(FiniteField(5^5)); C := HyperellipticCurve(x^7-x^4+1); #(Points(C : Bound:=4)); Output: Magma V2.10-6 Wed Mar 24 2004 14:46:36 on modular [Seed = 4259076185] ------------------------------------- 3257 Total time: 2.999 seconds, Total memory usage: 2.30MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Wed Mar 24 14:46:56 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); c:=1; d:=0; f:=x^6 +2*c*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); print(f); G, R:= GaloisGroup(f); print(G); print(Order(G)); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Wed Mar 24 2004 14:46:53 on modular [Seed = 4141306723] ------------------------------------- x^6 + 2*x^5 + (4*b + 1)*x^3 + 2*b*x^2 + (2*b + 3)*x + 4*b + 1 Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 60 12 6 Total time: 3.259 seconds, Total memory usage: 6.53MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Wed Mar 24 14:47:09 2004 Input: F := PolynomialRing(FiniteField(5^5)); C := HyperellipticCurve(x^7-x^4-2*x+1); #(Points(C : Bound:=4)); Output: Magma V2.10-6 Wed Mar 24 2004 14:47:06 on modular [Seed = 4023274092] ------------------------------------- 3071 Total time: 2.939 seconds, Total memory usage: 2.30MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Wed Mar 24 14:52:09 2004 Input: F := PolynomialRing(FiniteField(5^5)); C := HyperellipticCurve(x^20-x^4-2*x+1); #(Points(C : Bound:=4)); Output: Magma V2.10-6 Wed Mar 24 2004 14:52:06 on modular [Seed = 3505485326] ------------------------------------- HyperellipticCurve( f: x^20 + 4*x^4 + 3*x + 1 ) In file "/usr/local/magma/package/Geometry/CrvHyp/curve.m", line 257, column 30: >> return HyperellipticCurve(f, Parent(f)!0); ^ Runtime error in 'HyperellipticCurve': Curve has a finite singularity >> #(Points(C : Bound:=4));; ^ User error: Identifier 'C' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Wed Mar 24 14:52:33 2004 Input: F := PolynomialRing(FiniteField(5^4)); C := HyperellipticCurve(x^20-x^4-2*x+1); #(Points(C : Bound:=4)); Output: Magma V2.10-6 Wed Mar 24 2004 14:52:30 on modular [Seed = 3387453199] ------------------------------------- HyperellipticCurve( f: x^20 + 4*x^4 + 3*x + 1 ) In file "/usr/local/magma/package/Geometry/CrvHyp/curve.m", line 257, column 30: >> return HyperellipticCurve(f, Parent(f)!0); ^ Runtime error in 'HyperellipticCurve': Curve has a finite singularity >> #(Points(C : Bound:=4));; ^ User error: Identifier 'C' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Wed Mar 24 14:52:47 2004 Input: F := PolynomialRing(FiniteField(5^4)); C := HyperellipticCurve(x^21-x^4-2*x+1); #(Points(C : Bound:=4)); Output: Magma V2.10-6 Wed Mar 24 2004 14:52:44 on modular [Seed = 3286394103] ------------------------------------- 639 Total time: 2.919 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Wed Mar 24 15:01:38 2004 Input: F := PolynomialRing(FiniteField(5^3)); C := HyperellipticCurve(x^3-1); #(Points(C : Bound:=4)); Output: Magma V2.10-6 Wed Mar 24 2004 15:01:35 on modular [Seed = 524203577] ------------------------------------- 126 Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 24 15:15:11 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^5+7*x^4+3*x^2-x+1); OK:=MaximalOrder(K); I:=5*OK; Factorization(I); Output: Magma V2.10-6 Wed Mar 24 2004 15:15:08 on modular [Seed = 2019152909] ------------------------------------- [ , , ] Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 24 15:35:35 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2+12, x^2+6]); OK:=MaximalOrder(K); I:=3*OK; F:=Factorization(I); ResidueClassField(OK,F[1][1]); +7*x^4+3*x^2-x+1); Output: Magma V2.10-6 Wed Mar 24 2004 15:35:32 on modular [Seed = 1602154098] ------------------------------------- Finite field of size 3^2 Mapping from: RngOrd: OK to GF(3^2) given by the ideal Prime Ideal of OK Two element generators: [[3, 0], [0, 0]] [[0, -16], [-1, 1]] / 4 >> +7*x^4+3*x^2-x+1); ^ User error: bad syntax Total time: 3.799 seconds, Total memory usage: 2.16MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Mar 24 15:36:01 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2+12, x^2+6]); OK:=MaximalOrder(K); I:=3*OK; F:=Factorization(I); ResidueClassField(OK,F[1][1]); Output: Magma V2.10-6 Wed Mar 24 2004 15:35:57 on modular [Seed = 1231616093] ------------------------------------- Finite field of size 3^2 Mapping from: RngOrd: OK to GF(3^2) given by the ideal Prime Ideal of OK Two element generators: [[3, 0], [0, 0]] [[-12, -16], [1, 1]] / 4 Total time: 3.749 seconds, Total memory usage: 2.16MB ************** MAGMA ***************** Host pcd595076.netvigator.com. (218.102.127.76) Time: Wed Mar 24 15:39:43 2004 Input: 3^110 mode 100 Output: Magma V2.10-6 Wed Mar 24 2004 15:39:40 on modular [Seed = 1130557814] ------------------------------------- >> 3^110 mode 100 ^ User error: bad syntax Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pcd595076.netvigator.com. (218.102.127.76) Time: Wed Mar 24 15:39:52 2004 Input: 3^110 mod 100 Output: Magma V2.10-6 Wed Mar 24 2004 15:39:49 on modular [Seed = 3130722454] ------------------------------------- 49 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Wed Mar 24 16:55:52 2004 Input: coeffs[5] := -5142225622472630020004; coeffs[4] := -3356924353646091366162; coeffs[3] := 6545365626333869758617; coeffs[2] := -4722668925346720843884; coeffs[1] := -514856715582822510304; coeffs[0] := 237866611103421300000; m1_Value := 617119742304446938751913; P := PolynomialRing(Integers(),2); F := P!0; for i in [0..d] do F +:= coeffs[i+1]*X^(d-i)*Y^i; end for; eval := Evaluate(F,[m1_Value,1]); print eval; Output: Magma V2.10-6 Wed Mar 24 2004 16:55:49 on modular [Seed = 823358190] ------------------------------------- >> coeffs[5] := -5142225622472630020004; ^ User error: Identifier 'coeffs' has not been declared or assigned >> coeffs[4] := -3356924353646091366162; ^ User error: Identifier 'coeffs' has not been declared or assigned >> coeffs[3] := 6545365626333869758617; ^ User error: Identifier 'coeffs' has not been declared or assigned >> coeffs[2] := -4722668925346720843884; ^ User error: Identifier 'coeffs' has not been declared or assigned >> coeffs[1] := -514856715582822510304; ^ User error: Identifier 'coeffs' has not been declared or assigned >> coeffs[0] := 237866611103421300000; ^ User error: Identifier 'coeffs' has not been declared or assigned >> for i in [0..d] do ^ User error: Identifier 'd' has not been declared or assigned 0 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Wed Mar 24 16:56:33 2004 Input: d := 5; coeffs := []; coeffs[5] := -5142225622472630020004; coeffs[4] := -3356924353646091366162; coeffs[3] := 6545365626333869758617; coeffs[2] := -4722668925346720843884; coeffs[1] := -514856715582822510304; coeffs[0] := 237866611103421300000; m1_Value := 617119742304446938751913; P := PolynomialRing(Integers(),2); F := P!0; for i in [0..d] do F +:= coeffs[i+1]*X^(d-i)*Y^i; end for; eval := Evaluate(F,[m1_Value,1]); print eval; Output: Magma V2.10-6 Wed Mar 24 2004 16:56:30 on modular [Seed = 772565530] ------------------------------------- >> coeffs[0] := 237866611103421300000; ^ Runtime error in :=: Bad sequence index >> F +:= coeffs[i+1]*X^(d-i)*Y^i; ^ Runtime error in '[]': Sequence element 6 not defined -460822401366877760461978107162342271934773062174824510424972792556661307934182\ 25925921073887864974387717147741093749335668955075930315980977 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Wed Mar 24 16:57:04 2004 Input: d := 5; coeffs := []; coeffs[6] := -5142225622472630020004; coeffs[5] := -3356924353646091366162; coeffs[4] := 6545365626333869758617; coeffs[3] := -4722668925346720843884; coeffs[2] := -514856715582822510304; coeffs[1] := 237866611103421300000; m1_Value := 617119742304446938751913; P := PolynomialRing(Integers(),2); F := P!0; for i in [0..d] do F +:= coeffs[i+1]*X^(d-i)*Y^i; end for; eval := Evaluate(F,[m1_Value,1]); print eval; Output: Magma V2.10-6 Wed Mar 24 2004 16:57:01 on modular [Seed = 654664496] ------------------------------------- 2129024631825875754749788201627151749780670396327721627823338321538194998405649\ 5911366573853021918316783107387995317230889569230873441936471 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mundroo.cs.mu.OZ.AU. (128.250.37.89) Time: Wed Mar 24 21:04:25 2004 Input: lkjlkjlk Output: Magma V2.10-6 Wed Mar 24 2004 21:04:21 on modular [Seed = 473850374] ------------------------------------- >> lkjlkjlk; ^ User error: Identifier 'lkjlkjlk' has not been declared or assigned Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Wed Mar 24 21:09:10 2004 Input: R:=PolynomialRing(RationalField()); M:=NumberField([x^2-7,x^2-13] : Abs := true); OM:=MaximalOrder(M); Factorization(3*OM); Output: Magma V2.10-6 Wed Mar 24 2004 21:09:07 on modular [Seed = 305163629] ------------------------------------- Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Wed Apr 23 11:13:24 EST 2003 Initial seed: 305163629 Time to this point: 3.07 Segmentation fault Errors: Magma: Fatal Error: Magma: Irrecoverable error; exiting ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Wed Mar 24 21:09:29 2004 Input: 1+1; Output: Magma V2.10-6 Wed Mar 24 2004 21:09:26 on modular [Seed = 187266145] ------------------------------------- 2 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Wed Mar 24 22:57:01 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2+1); OK:=MaximalOrder(K); Factorization(3*OK); Output: Magma V2.10-6 Wed Mar 24 2004 22:56:58 on modular [Seed = 4208517709] ------------------------------------- [ ] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Wed Mar 24 22:57:31 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2+10); OK:=MaximalOrder(K); Factorization(3*OK); Output: Magma V2.10-6 Wed Mar 24 2004 22:57:28 on modular [Seed = 3989828985] ------------------------------------- [ ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Wed Mar 24 22:58:44 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2+1, x^2+10]); OK:=MaximalOrder(K); Factorization(3*OK); Output: Magma V2.10-6 Wed Mar 24 2004 22:58:41 on modular [Seed = 3888512811] ------------------------------------- [ , ] Total time: 3.499 seconds, Total memory usage: 2.05MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Wed Mar 24 22:59:36 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2+6, x^2+10]); OK:=MaximalOrder(K); Factorization(3*OK); Output: Magma V2.10-6 Wed Mar 24 2004 22:59:33 on modular [Seed = 3741108166] ------------------------------------- [ ] Total time: 3.459 seconds, Total memory usage: 1.95MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Wed Mar 24 23:00:04 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2+6, x^2+2]); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Wed Mar 24 2004 23:00:01 on modular [Seed = 3471628210] ------------------------------------- [ , ] Total time: 3.339 seconds, Total memory usage: 1.97MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Wed Mar 24 23:00:43 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2+5); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Wed Mar 24 2004 23:00:40 on modular [Seed = 3252934804] ------------------------------------- [ ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Wed Mar 24 23:01:24 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2+10); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Wed Mar 24 2004 23:01:21 on modular [Seed = 688599174] ------------------------------------- [ ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Wed Mar 24 23:02:02 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2+1,x^2+10]); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Wed Mar 24 2004 23:01:58 on modular [Seed = 507250582] ------------------------------------- [ , ] Total time: 3.559 seconds, Total memory usage: 1.95MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Wed Mar 24 23:02:21 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-5, x^2+10]); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Wed Mar 24 2004 23:02:17 on modular [Seed = 389353184] ------------------------------------- [ ] Total time: 3.369 seconds, Total memory usage: 2.08MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Wed Mar 24 23:02:38 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2+5, x^2+10]); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Wed Mar 24 2004 23:02:35 on modular [Seed = 204346857] ------------------------------------- [ ] Total time: 3.499 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Thu Mar 25 00:05:57 2004 Input: function ComputeCont_p( p, disc, bound, F, f ); if disc mod p eq 0 then /* estimate using some small sample space */ cont_p := 0; upper_limit := bound^2; for i in [1..bound] do repeat a := Random( upper_limit ); b := Random( upper_limit ); until Gcd( a, b ) eq 1; value := Evaluate( F, [a, b] ); while value mod p eq 0 do value div:= p; cont_p +:= 1; end while; end for; cont_p := cont_p / (0.0 + bound); else K := GF(p); roots_mod_p := Roots( f, K ); q_p := #roots_mod_p; /* add in the contribution of the projective roots */ d := Degree( f ); if Coefficient(f, d) mod p eq 0 then q_p +:= 1; end if; cont_p := q_p * p / (p * p - 1.0); end if; return cont_p; end function; function ComputeAlpha( F, bound, abort_p, abort_alpha, max_p ); Q := PolynomialRing(Integers()); f := Q!Evaluate( F, [X, 1] ); disc := Discriminant( f ); a_d := Coefficient(f, Degree(f)); primes := [p : p in [1..max_p] | IsPrime(p)]; alpha := 0.0; for p in primes do cont_p := ComputeCont_p( p, disc, bound, F, f ); alpha +:= (1.0/(p-1) - cont_p)*Log(p); /* early-abort strategy */ if p eq abort_p and alpha gt abort_alpha then break; end if; end for; return alpha; end function; d := 5; coeffs := []; coeffs[6] := -5142225622472630020004; coeffs[5] := -3356924353646091366162; coeffs[4] := 6545365626333869758617; coeffs[3] := -4722668925346720843884; coeffs[2] := -514856715582822510304; coeffs[1] := 237866611103421300000; m1_Value := 617119742304446938751913; P := PolynomialRing(Integers(),2); F := P!0; for i in [0..d] do F +:= coeffs[i+1]*X^(d-i)*Y^i; end for; eval := Evaluate(F,[m1_Value,1]); print eval; alpha := ComputeAlpha( F, 2500, 11, max_alpha+0.5, 100 ); print alpha; alpha := ComputeAlpha( F, 10000, 0, 0, 2000 ); print alpha; Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed. ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Thu Mar 25 00:08:10 2004 Input: function CalcCont_p( p, disc, bound, F, f ); if disc mod p eq 0 then /* estimate using some small sample space */ cont_p := 0; upper_limit := bound^2; for i in [1..bound] do repeat a := Random( upper_limit ); b := Random( upper_limit ); until Gcd( a, b ) eq 1; value := Evaluate( F, [a, b] ); while value mod p eq 0 do value div:= p; cont_p +:= 1; end while; end for; cont_p := cont_p / (0.0 + bound); else K := GF(p); roots_mod_p := Roots( f, K ); q_p := #roots_mod_p; /* add in the contribution of the projective roots */ d := Degree( f ); if Coefficient(f, d) mod p eq 0 then q_p +:= 1; end if; cont_p := q_p * p / (p * p - 1.0); end if; return cont_p; end function; function CalcAlpha( F, bound, abort_p, abort_alpha, max_p ); Q := PolynomialRing(Integers()); f := Q!Evaluate( F, [X, 1] ); disc := Discriminant( f ); a_d := Coefficient(f, Degree(f)); primes := [p : p in [1..max_p] | IsPrime(p)]; alpha := 0.0; for p in primes do cont_p := CalcCont_p( p, disc, bound, F, f ); alpha +:= (1.0/(p-1) - cont_p)*Log(p); /* early-abort strategy */ if p eq abort_p and alpha gt abort_alpha then break; end if; end for; return alpha; end function; d := 5; coeffs := []; coeffs[6] := -5142225622472630020004; coeffs[5] := -3356924353646091366162; coeffs[4] := 6545365626333869758617; coeffs[3] := -4722668925346720843884; coeffs[2] := -514856715582822510304; coeffs[1] := 237866611103421300000; m1_Value := 617119742304446938751913; P := PolynomialRing(Integers(),2); F := P!0; for i in [0..d] do F +:= coeffs[i+1]*X^(d-i)*Y^i; end for; eval := Evaluate(F,[m1_Value,1]); print eval; alpha := CalcAlpha( F, 2500, 11, max_alpha+0.5, 100 ); print alpha; alpha := CalcAlpha( F, 10000, 0, 0, 2000 ); print alpha; Output: Magma V2.10-6 Thu Mar 25 2004 00:08:05 on modular [Seed = 2158143883] ------------------------------------- 2129024631825875754749788201627151749780670396327721627823338321538194998405649\ 5911366573853021918316783107387995317230889569230873441936471 >> alpha := CalcAlpha( F, 2500, 11, max_alpha+0.5, 100 ); ^ User error: Identifier 'max_alpha' has not been declared or assigned >> print alpha; ^ User error: Identifier 'alpha' has not been declared or assigned -4.182432612893593995540572417282 Total time: 5.069 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Thu Mar 25 00:08:45 2004 Input: function CalcCont_p( p, disc, bound, F, f ); if disc mod p eq 0 then /* estimate using some small sample space */ cont_p := 0; upper_limit := bound^2; for i in [1..bound] do repeat a := Random( upper_limit ); b := Random( upper_limit ); until Gcd( a, b ) eq 1; value := Evaluate( F, [a, b] ); while value mod p eq 0 do value div:= p; cont_p +:= 1; end while; end for; cont_p := cont_p / (0.0 + bound); else K := GF(p); roots_mod_p := Roots( f, K ); q_p := #roots_mod_p; /* add in the contribution of the projective roots */ d := Degree( f ); if Coefficient(f, d) mod p eq 0 then q_p +:= 1; end if; cont_p := q_p * p / (p * p - 1.0); end if; return cont_p; end function; function CalcAlpha( F, bound, abort_p, abort_alpha, max_p ); Q := PolynomialRing(Integers()); f := Q!Evaluate( F, [X, 1] ); disc := Discriminant( f ); a_d := Coefficient(f, Degree(f)); primes := [p : p in [1..max_p] | IsPrime(p)]; alpha := 0.0; for p in primes do cont_p := CalcCont_p( p, disc, bound, F, f ); alpha +:= (1.0/(p-1) - cont_p)*Log(p); /* early-abort strategy */ if p eq abort_p and alpha gt abort_alpha then break; end if; end for; return alpha; end function; d := 5; coeffs := []; coeffs[6] := -5142225622472630020004; coeffs[5] := -3356924353646091366162; coeffs[4] := 6545365626333869758617; coeffs[3] := -4722668925346720843884; coeffs[2] := -514856715582822510304; coeffs[1] := 237866611103421300000; m1_Value := 617119742304446938751913; P := PolynomialRing(Integers(),2); F := P!0; for i in [0..d] do F +:= coeffs[i+1]*X^(d-i)*Y^i; end for; eval := Evaluate(F,[m1_Value,1]); print eval; alpha := CalcAlpha( F, 2500, 11, -0.5, 100 ); print alpha; alpha := CalcAlpha( F, 10000, 0, 0, 2000 ); print alpha; Output: Magma V2.10-6 Thu Mar 25 2004 00:08:40 on modular [Seed = 4191932575] ------------------------------------- 2129024631825875754749788201627151749780670396327721627823338321538194998405649\ 5911366573853021918316783107387995317230889569230873441936471 -3.89858619138623751099994092070 -4.179526890197887473457763063972 Total time: 5.619 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Thu Mar 25 00:11:01 2004 Input: function CalcCont_p( p, disc, bound, F, f ); if disc mod p eq 0 then /* estimate using some small sample space */ cont_p := 0; upper_limit := bound^2; for i in [1..bound] do repeat a := Random( upper_limit ); b := Random( upper_limit ); until Gcd( a, b ) eq 1; value := Evaluate( F, [a, b] ); while value mod p eq 0 do value div:= p; cont_p +:= 1; end while; end for; cont_p := cont_p / (0.0 + bound); else K := GF(p); roots_mod_p := Roots( f, K ); q_p := #roots_mod_p; print "roots mod p", q_p; /* add in the contribution of the projective roots */ d := Degree( f ); if Coefficient(f, d) mod p eq 0 then q_p +:= 1; end if; cont_p := q_p * p / (p * p - 1.0); end if; return cont_p; end function; function CalcAlpha( F, bound, abort_p, abort_alpha, max_p ); Q := PolynomialRing(Integers()); f := Q!Evaluate( F, [X, 1] ); disc := Discriminant( f ); a_d := Coefficient(f, Degree(f)); primes := [p : p in [1..max_p] | IsPrime(p)]; alpha := 0.0; for p in primes do cont_p := CalcCont_p( p, disc, bound, F, f ); alpha +:= (1.0/(p-1) - cont_p)*Log(p); /* early-abort strategy */ if p eq abort_p and alpha gt abort_alpha then break; end if; end for; return alpha; end function; d := 5; coeffs := []; coeffs[6] := -5142225622472630020004; coeffs[5] := -3356924353646091366162; coeffs[4] := 6545365626333869758617; coeffs[3] := -4722668925346720843884; coeffs[2] := -514856715582822510304; coeffs[1] := 237866611103421300000; m1_Value := 617119742304446938751913; P := PolynomialRing(Integers(),2); F := P!0; for i in [0..d] do F +:= coeffs[i+1]*X^(d-i)*Y^i; end for; eval := Evaluate(F,[m1_Value,1]); print eval; alpha := CalcAlpha( F, 2500, 11, -0.5, 100 ); print alpha; alpha := CalcAlpha( F, 10000, 0, 0, 2000 ); print alpha; Output: Magma V2.10-6 Thu Mar 25 2004 00:10:56 on modular [Seed = 3922444343] ------------------------------------- 2129024631825875754749788201627151749780670396327721627823338321538194998405649\ 5911366573853021918316783107387995317230889569230873441936471 roots mod p 2 roots mod p 1 roots mod p 2 roots mod p 2 roots mod p 1 roots mod p 2 roots mod p 0 roots mod p 0 roots mod p 2 roots mod p 2 roots mod p 3 roots mod p 1 roots mod p 3 roots mod p 2 roots mod p 0 roots mod p 1 roots mod p 0 roots mod p 3 roots mod p 1 roots mod p 2 roots mod p 0 -3.88784426992597633874659450367 roots mod p 2 roots mod p 1 roots mod p 2 roots mod p 2 roots mod p 1 roots mod p 2 roots mod p 0 roots mod p 0 roots mod p 2 roots mod p 2 roots mod p 3 roots mod p 1 roots mod p 3 roots mod p 2 roots mod p 0 roots mod p 1 roots mod p 0 roots mod p 3 roots mod p 1 roots mod p 2 roots mod p 0 roots mod p 2 roots mod p 2 roots mod p 1 roots mod p 1 roots mod p 3 roots mod p 0 roots mod p 2 roots mod p 1 roots mod p 0 roots mod p 1 roots mod p 3 roots mod p 0 roots mod p 0 roots mod p 1 roots mod p 1 roots mod p 2 roots mod p 1 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 2 roots mod p 0 roots mod p 1 roots mod p 3 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 3 roots mod p 2 roots mod p 2 roots mod p 0 roots mod p 2 roots mod p 2 roots mod p 0 roots mod p 1 roots mod p 1 roots mod p 1 roots mod p 1 roots mod p 1 roots mod p 0 roots mod p 2 roots mod p 2 roots mod p 1 roots mod p 0 roots mod p 1 roots mod p 1 roots mod p 1 roots mod p 2 roots mod p 1 roots mod p 2 roots mod p 3 roots mod p 1 roots mod p 1 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 1 roots mod p 1 roots mod p 3 roots mod p 2 roots mod p 0 roots mod p 0 roots mod p 1 roots mod p 0 roots mod p 2 roots mod p 1 roots mod p 1 roots mod p 1 roots mod p 3 roots mod p 3 roots mod p 0 roots mod p 1 roots mod p 0 roots mod p 1 roots mod p 2 roots mod p 0 roots mod p 1 roots mod p 3 roots mod p 0 roots mod p 1 roots mod p 2 roots mod p 1 roots mod p 0 roots mod p 1 roots mod p 0 roots mod p 1 roots mod p 0 roots mod p 1 roots mod p 1 roots mod p 3 roots mod p 1 roots mod p 1 roots mod p 1 roots mod p 0 roots mod p 2 roots mod p 1 roots mod p 1 roots mod p 0 roots mod p 0 roots mod p 1 roots mod p 0 roots mod p 1 roots mod p 3 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 1 roots mod p 2 roots mod p 0 roots mod p 1 roots mod p 0 roots mod p 2 roots mod p 2 roots mod p 0 roots mod p 0 roots mod p 3 roots mod p 3 roots mod p 2 roots mod p 1 roots mod p 3 roots mod p 3 roots mod p 1 roots mod p 1 roots mod p 2 roots mod p 1 roots mod p 1 roots mod p 1 roots mod p 0 roots mod p 3 roots mod p 1 roots mod p 1 roots mod p 0 roots mod p 5 roots mod p 0 roots mod p 1 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 2 roots mod p 3 roots mod p 0 roots mod p 0 roots mod p 2 roots mod p 0 roots mod p 2 roots mod p 3 roots mod p 1 roots mod p 3 roots mod p 3 roots mod p 0 roots mod p 1 roots mod p 1 roots mod p 1 roots mod p 3 roots mod p 3 roots mod p 2 roots mod p 3 roots mod p 1 roots mod p 1 roots mod p 1 roots mod p 0 roots mod p 2 roots mod p 0 roots mod p 2 roots mod p 2 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 1 roots mod p 1 roots mod p 3 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 1 roots mod p 0 roots mod p 2 roots mod p 3 roots mod p 1 roots mod p 0 roots mod p 0 roots mod p 2 roots mod p 1 roots mod p 1 roots mod p 1 roots mod p 1 roots mod p 1 roots mod p 1 roots mod p 0 roots mod p 1 roots mod p 0 roots mod p 0 roots mod p 3 roots mod p 1 roots mod p 0 roots mod p 0 roots mod p 3 roots mod p 1 roots mod p 5 roots mod p 0 roots mod p 0 roots mod p 1 roots mod p 0 roots mod p 3 roots mod p 2 roots mod p 1 roots mod p 2 roots mod p 1 roots mod p 0 roots mod p 2 roots mod p 2 roots mod p 2 roots mod p 1 roots mod p 1 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 1 roots mod p 2 roots mod p 0 roots mod p 2 roots mod p 1 roots mod p 1 roots mod p 2 roots mod p 1 roots mod p 1 roots mod p 0 roots mod p 2 roots mod p 0 roots mod p 1 roots mod p 3 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 2 roots mod p 1 roots mod p 0 roots mod p 2 roots mod p 0 roots mod p 2 roots mod p 0 roots mod p 2 roots mod p 2 roots mod p 2 roots mod p 0 roots mod p 1 roots mod p 0 roots mod p 0 roots mod p 2 roots mod p 0 roots mod p 2 roots mod p 0 roots mod p 1 roots mod p 1 roots mod p 3 roots mod p 2 roots mod p 0 roots mod p 2 roots mod p 1 roots mod p 0 roots mod p 1 roots mod p 1 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 3 roots mod p 0 roots mod p 0 roots mod p 3 roots mod p 0 roots mod p 0 -4.171675974432168873402101182122 Total time: 5.569 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Thu Mar 25 00:12:06 2004 Input: function CalcCont_p( p, disc, bound, F, f ); if disc mod p eq 0 then /* estimate using some small sample space */ cont_p := 0; upper_limit := bound^2; for i in [1..bound] do repeat a := Random( upper_limit ); b := Random( upper_limit ); until Gcd( a, b ) eq 1; value := Evaluate( F, [a, b] ); while value mod p eq 0 do value div:= p; cont_p +:= 1; end while; end for; cont_p := cont_p / (0.0 + bound); else K := GF(p); roots_mod_p := Roots( f, K ); q_p := #roots_mod_p; print "roots mod p", q_p; /* add in the contribution of the projective roots */ d := Degree( f ); if Coefficient(f, d) mod p eq 0 then q_p +:= 1; end if; cont_p := q_p * p / (p * p - 1.0); end if; return cont_p; end function; function CalcAlpha( F, bound, abort_p, abort_alpha, max_p ); Q := PolynomialRing(Integers()); f := Q!Evaluate( F, [X, 1] ); disc := Discriminant( f ); a_d := Coefficient(f, Degree(f)); primes := [p : p in [1..max_p] | IsPrime(p)]; alpha := 0.0; for p in primes do cont_p := CalcCont_p( p, disc, bound, F, f ); print "cont_p = ", cont_p; alpha +:= (1.0/(p-1) - cont_p)*Log(p); /* early-abort strategy */ if p eq abort_p and alpha gt abort_alpha then break; end if; end for; return alpha; end function; d := 5; coeffs := []; coeffs[6] := -5142225622472630020004; coeffs[5] := -3356924353646091366162; coeffs[4] := 6545365626333869758617; coeffs[3] := -4722668925346720843884; coeffs[2] := -514856715582822510304; coeffs[1] := 237866611103421300000; m1_Value := 617119742304446938751913; P := PolynomialRing(Integers(),2); F := P!0; for i in [0..d] do F +:= coeffs[i+1]*X^(d-i)*Y^i; end for; eval := Evaluate(F,[m1_Value,1]); print eval; alpha := CalcAlpha( F, 2500, 11, -0.5, 100 ); print alpha; alpha := CalcAlpha( F, 10000, 0, 0, 2000 ); print alpha; Output: Magma V2.10-6 Thu Mar 25 2004 00:12:00 on modular [Seed = 3741119680] ------------------------------------- 2129024631825875754749788201627151749780670396327721627823338321538194998405649\ 5911366573853021918316783107387995317230889569230873441936471 cont_p = 2.00479999999999999999999999999999999999121 roots mod p 2 cont_p = 1.1250000000000000000000000000000000000000 roots mod p 1 cont_p = 0.416666666666666666666666666666666666666 cont_p = 0.579599999999999999999999999999999999997 cont_p = 0.2099999999999999999999999999999999999999 roots mod p 2 cont_p = 0.2321428571428571428571428571428571428566 cont_p = 0.1263999999999999999999999999999999999998 roots mod p 2 cont_p = 0.1583333333333333333333333333333333333332 roots mod p 1 cont_p = 0.0435606060606060606060606060606060606059 roots mod p 2 cont_p = 0.0690476190476190476190476190476190476188 roots mod p 0 cont_p = 0 roots mod p 0 cont_p = 0 roots mod p 2 cont_p = 0.0488095238095238095238095238095238095235 roots mod p 2 cont_p = 0.0465367965367965367965367965367965367963 roots mod p 3 cont_p = 0.0638586956521739130434782608695652173910 roots mod p 1 cont_p = 0.01887464387464387464387464387464387464373 roots mod p 3 cont_p = 0.0508620689655172413793103448275862068962 roots mod p 2 cont_p = 0.0327956989247311827956989247311827956987 roots mod p 0 cont_p = 0 roots mod p 1 cont_p = 0.01408730158730158730158730158730158730149 roots mod p 0 cont_p = 0 roots mod p 3 cont_p = 0.0379807692307692307692307692307692307690 roots mod p 1 cont_p = 0.01204994192799070847851335656213704994189 roots mod p 2 cont_p = 0.02247474747474747474747474747474747474746 roots mod p 0 cont_p = 0 -4.00095494049547062338010904529672 cont_p = 1.991899999999999999999999999999999999996 roots mod p 2 cont_p = 1.1250000000000000000000000000000000000000 roots mod p 1 cont_p = 0.416666666666666666666666666666666666666 cont_p = 0.567899999999999999999999999999999999997 cont_p = 0.1821999999999999999999999999999999999999 roots mod p 2 cont_p = 0.2321428571428571428571428571428571428566 cont_p = 0.1141999999999999999999999999999999999999 roots mod p 2 cont_p = 0.1583333333333333333333333333333333333332 roots mod p 1 cont_p = 0.0435606060606060606060606060606060606059 roots mod p 2 cont_p = 0.0690476190476190476190476190476190476188 roots mod p 0 cont_p = 0 roots mod p 0 cont_p = 0 roots mod p 2 cont_p = 0.0488095238095238095238095238095238095235 roots mod p 2 cont_p = 0.0465367965367965367965367965367965367963 roots mod p 3 cont_p = 0.0638586956521739130434782608695652173910 roots mod p 1 cont_p = 0.01887464387464387464387464387464387464373 roots mod p 3 cont_p = 0.0508620689655172413793103448275862068962 roots mod p 2 cont_p = 0.0327956989247311827956989247311827956987 roots mod p 0 cont_p = 0 roots mod p 1 cont_p = 0.01408730158730158730158730158730158730149 roots mod p 0 cont_p = 0 roots mod p 3 cont_p = 0.0379807692307692307692307692307692307690 roots mod p 1 cont_p = 0.01204994192799070847851335656213704994189 roots mod p 2 cont_p = 0.02247474747474747474747474747474747474746 roots mod p 0 cont_p = 0 roots mod p 2 cont_p = 0.01980392156862745098039215686274509803915 roots mod p 2 cont_p = 0.01941930618401206636500754147812971342376 roots mod p 1 cont_p = 0.00934661076170510132774283717679944095035 roots mod p 1 cont_p = 0.00917508417508417508417508417508417508410 roots mod p 3 cont_p = 0.0265507518796992481203007518796992481202 roots mod p 0 cont_p = 0 roots mod p 2 cont_p = 0.01526806526806526806526806526806526806524 roots mod p 1 cont_p = 0.00729965899403239556692242114236999147479 roots mod p 0 cont_p = 0 roots mod p 1 cont_p = 0.00671171171171171171171171171171171171165 roots mod p 3 cont_p = 0.01986842105263157894736842105263157894729 roots mod p 0 cont_p = 0 roots mod p 0 cont_p = 0 roots mod p 1 cont_p = 0.00598823866896156052782558806655192197359 roots mod p 1 cont_p = 0.00578053996257685110932905640203154236831 roots mod p 2 cont_p = 0.01117353308364544319600499375780274656678 roots mod p 1 cont_p = 0.00552503052503052503052503052503052503051 roots mod p 0 cont_p = 0 roots mod p 0 cont_p = 0 roots mod p 0 cont_p = 0 roots mod p 2 cont_p = 0.01005050505050505050505050505050505050501 roots mod p 0 cont_p = 0 roots mod p 1 cont_p = 0.00448439510939510939510939510939510939509 roots mod p 3 cont_p = 0.01321611551001397298556124825337680484389 roots mod p 0 cont_p = 0 roots mod p 0 cont_p = 0 roots mod p 0 cont_p = 0 roots mod p 3 cont_p = 0.01244834710743801652892561983471074380162 roots mod p 2 cont_p = 0.00796825396825396825396825396825396825390 roots mod p 2 cont_p = 0.00778221899224806201550387596899224806196 roots mod p 0 cont_p = 0 roots mod p 2 cont_p = 0.00743504698728579325594250967385295743500 roots mod p 2 cont_p = 0.00738017429193899782135076252723311546839 roots mod p 0 cont_p = 0 roots mod p 1 cont_p = 0.00355876393110435663627152988855116514689 roots mod p 1 cont_p = 0.00353361302567176106283088602537209070021 roots mod p 1 cont_p = 0.00341300903923213120864784269872332494639 roots mod p 1 cont_p = 0.00325736355148119854002206943383413971648 roots mod p 1 cont_p = 0.00321546732837055417700578990901571546730 roots mod p 0 cont_p = 0 roots mod p 2 cont_p = 0.00630921105007563092110500756309211050072 roots mod p 2 cont_p = 0.00604235122307411464037970062066447608610 roots mod p 1 cont_p = 0.00296738517892364046210200056353902507746 roots mod p 0 cont_p = 0 roots mod p 1 cont_p = 0.00286535303776683087027914614121510673232 roots mod p 1 cont_p = 0.00283288392398561890087313816127375449408 roots mod p 1 cont_p = 0.00278553693358162631905648665425201738049 roots mod p 2 cont_p = 0.00544963174150629603231171299596103587548 roots mod p 1 cont_p = 0.00268098441722730147777586107756885745498 roots mod p 2 cont_p = 0.00527708159287106655527708159287106655524 roots mod p 3 cont_p = 0.00783295157068062827225130890052356020935 roots mod p 1 cont_p = 0.00257071107586571504097277293153581813373 roots mod p 1 cont_p = 0.00251890766966143850565961118724937820414 roots mod p 0 cont_p = 0 roots mod p 0 cont_p = 0 roots mod p 0 cont_p = 0 roots mod p 0 cont_p = 0 roots mod p 0 cont_p = 0 roots mod p 1 cont_p = 0.002309481140126301416623997269158559481126 roots mod p 1 cont_p = 0.002277916147779161477791614777916147779145 roots mod p 3 cont_p = 0.00677204353674941910236027883086706616116 roots mod p 2 cont_p = 0.00445436507936507936507936507936507936504 roots mod p 0 cont_p = 0 roots mod p 0 cont_p = 0 roots mod p 1 cont_p = 0.002159837289147633975220182116733840871756 roots mod p 0 cont_p = 0 roots mod p 2 cont_p = 0.00417538354253835425383542538354253835424 roots mod p 1 cont_p = 0.002053396748296566147203669972340281994180 roots mod p 1 cont_p = 0.002036668325866932138709142193462750954035 roots mod p 1 cont_p = 0.002004016064257028112449799196787148594366 roots mod p 3 cont_p = 0.00596423828495541642952001517738569531395 roots mod p 3 cont_p = 0.00589393237610004631773969430291801760069 roots mod p 0 cont_p = 0 roots mod p 1 cont_p = 0.001912052879412710947325319528530899944426 roots mod p 0 cont_p = 0 roots mod p 1 cont_p = 0.001828159674875003342156626828159674874991 roots mod p 2 cont_p = 0.00359067584641963848276217735489028132330 roots mod p 0 cont_p = 0 roots mod p 1 cont_p = 0.001757474672596985421299728193723745984675 roots mod p 3 cont_p = 0.00525395656974604343025395656974604343021 roots mod p 0 cont_p = 0 roots mod p 1 cont_p = 0.001703582456873534396693831116064173109514 roots mod p 2 cont_p = 0.00337269087269087269087269087269087269085 roots mod p 1 cont_p = 0.001669453734671125975473801560758082497208 roots mod p 0 cont_p = 0 roots mod p 1 cont_p = 0.001647450929303456661455619246135139829764 roots mod p 0 cont_p = 0 roots mod p 1 cont_p = 0.001620749800361450846887740091623586769209 roots mod p 0 cont_p = 0 roots mod p 1 cont_p = 0.001584790034157122764717701426562186055846 roots mod p 1 cont_p = 0.001560066199376947040498442367601246105913 roots mod p 3 cont_p = 0.00466564114471469205317234573634411098855 roots mod p 1 cont_p = 0.001545598746321140541986775216909375836097 roots mod p 1 cont_p = 0.001531397159527963828070767903041218738852 roots mod p 1 cont_p = 0.001517454177028645113751496730220134475451 roots mod p 0 cont_p = 0 roots mod p 2 cont_p = 0.00297177476331779002402147802741274551361 roots mod p 1 cont_p = 0.001477108097257859000541097205494754848046 roots mod p 1 cont_p = 0.001464131981958807086141551336797516763551 roots mod p 0 cont_p = 0 roots mod p 0 cont_p = 0 roots mod p 1 cont_p = 0.001410440041378212779501869976923689026807 roots mod p 0 cont_p = 0 roots mod p 1 cont_p = 0.001375518420972966427511882057336602791138 roots mod p 3 cont_p = 0.00409277705811408406664582123553848215479 roots mod p 0 cont_p = 0 roots mod p 0 cont_p = 0 roots mod p 0 cont_p = 0 roots mod p 1 cont_p = 0.001321006268235819687007022099370384330797 roots mod p 2 cont_p = 0.00262812543168945987014781047105953861028 roots mod p 0 cont_p = 0 roots mod p 1 cont_p = 0.001293663225823727088939765165816497302211 roots mod p 0 cont_p = 0 roots mod p 2 cont_p = 0.00250941423911537638065011775670331607912 roots mod p 2 cont_p = 0.002472191663610805524996944138858330277458 roots mod p 0 cont_p = 0 roots mod p 0 cont_p = 0 roots mod p 3 cont_p = 0.00364520586776273828927786832967188718018 roots mod p 3 cont_p = 0.00362757483243850229848756009404498719160 roots mod p 2 cont_p = 0.002412548745707467551364879809091438216613 roots mod p 1 cont_p = 0.001191896806455279008978292987839527218996 roots mod p 3 cont_p = 0.00351700366131213510571626480192631197017 roots mod p 3 cont_p = 0.00350058819684987909286974707535455199005 roots mod p 1 cont_p = 0.001164145931587792052908331978099419959880 roots mod p 1 cont_p = 0.001158750107416000687462404399759388158456 roots mod p 2 cont_p = 0.0022805046754246367314673240344910079986 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Thu Mar 25 00:12:48 2004 Input: function CalcCont_p( p, disc, bound, F, f ); if disc mod p eq 0 then /* estimate using some small sample space */ cont_p := 0; upper_limit := bound^2; for i in [1..bound] do repeat a := Random( upper_limit ); b := Random( upper_limit ); until Gcd( a, b ) eq 1; value := Evaluate( F, [a, b] ); while value mod p eq 0 do value div:= p; cont_p +:= 1; end while; end for; cont_p := cont_p / (0.0 + bound); else K := GF(p); roots_mod_p := Roots( f, K ); q_p := #roots_mod_p; print "roots mod p", q_p; /* add in the contribution of the projective roots */ d := Degree( f ); if Coefficient(f, d) mod p eq 0 then q_p +:= 1; end if; cont_p := q_p * p / (p * p - 1.0); end if; return cont_p; end function; function CalcAlpha( F, bound, abort_p, abort_alpha, max_p ); Q := PolynomialRing(Integers()); f := Q!Evaluate( F, [X, 1] ); disc := Discriminant( f ); a_d := Coefficient(f, Degree(f)); primes := [p : p in [1..max_p] | IsPrime(p)]; alpha := 0.0; for p in primes do cont_p := CalcCont_p( p, disc, bound, F, f ); // print "cont_p = ", cont_p; alpha +:= (1.0/(p-1) - cont_p)*Log(p); /* early-abort strategy */ if p eq abort_p and alpha gt abort_alpha then break; end if; end for; return alpha; end function; d := 5; coeffs := []; coeffs[6] := -5142225622472630020004; coeffs[5] := -3356924353646091366162; coeffs[4] := 6545365626333869758617; coeffs[3] := -4722668925346720843884; coeffs[2] := -514856715582822510304; coeffs[1] := 237866611103421300000; m1_Value := 617119742304446938751913; P := PolynomialRing(Integers(),2); F := P!0; for i in [0..d] do F +:= coeffs[i+1]*X^(d-i)*Y^i; end for; eval := Evaluate(F,[m1_Value,1]); print eval; alpha := CalcAlpha( F, 2500, 11, -0.5, 100 ); print alpha; alpha := CalcAlpha( F, 10000, 0, 0, 2000 ); print alpha; Output: Magma V2.10-6 Thu Mar 25 2004 00:12:42 on modular [Seed = 3572956832] ------------------------------------- 2129024631825875754749788201627151749780670396327721627823338321538194998405649\ 5911366573853021918316783107387995317230889569230873441936471 roots mod p 2 roots mod p 1 roots mod p 2 roots mod p 2 roots mod p 1 roots mod p 2 roots mod p 0 roots mod p 0 roots mod p 2 roots mod p 2 roots mod p 3 roots mod p 1 roots mod p 3 roots mod p 2 roots mod p 0 roots mod p 1 roots mod p 0 roots mod p 3 roots mod p 1 roots mod p 2 roots mod p 0 -3.90881012130615512822979159143 roots mod p 2 roots mod p 1 roots mod p 2 roots mod p 2 roots mod p 1 roots mod p 2 roots mod p 0 roots mod p 0 roots mod p 2 roots mod p 2 roots mod p 3 roots mod p 1 roots mod p 3 roots mod p 2 roots mod p 0 roots mod p 1 roots mod p 0 roots mod p 3 roots mod p 1 roots mod p 2 roots mod p 0 roots mod p 2 roots mod p 2 roots mod p 1 roots mod p 1 roots mod p 3 roots mod p 0 roots mod p 2 roots mod p 1 roots mod p 0 roots mod p 1 roots mod p 3 roots mod p 0 roots mod p 0 roots mod p 1 roots mod p 1 roots mod p 2 roots mod p 1 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 2 roots mod p 0 roots mod p 1 roots mod p 3 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 3 roots mod p 2 roots mod p 2 roots mod p 0 roots mod p 2 roots mod p 2 roots mod p 0 roots mod p 1 roots mod p 1 roots mod p 1 roots mod p 1 roots mod p 1 roots mod p 0 roots mod p 2 roots mod p 2 roots mod p 1 roots mod p 0 roots mod p 1 roots mod p 1 roots mod p 1 roots mod p 2 roots mod p 1 roots mod p 2 roots mod p 3 roots mod p 1 roots mod p 1 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 1 roots mod p 1 roots mod p 3 roots mod p 2 roots mod p 0 roots mod p 0 roots mod p 1 roots mod p 0 roots mod p 2 roots mod p 1 roots mod p 1 roots mod p 1 roots mod p 3 roots mod p 3 roots mod p 0 roots mod p 1 roots mod p 0 roots mod p 1 roots mod p 2 roots mod p 0 roots mod p 1 roots mod p 3 roots mod p 0 roots mod p 1 roots mod p 2 roots mod p 1 roots mod p 0 roots mod p 1 roots mod p 0 roots mod p 1 roots mod p 0 roots mod p 1 roots mod p 1 roots mod p 3 roots mod p 1 roots mod p 1 roots mod p 1 roots mod p 0 roots mod p 2 roots mod p 1 roots mod p 1 roots mod p 0 roots mod p 0 roots mod p 1 roots mod p 0 roots mod p 1 roots mod p 3 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 1 roots mod p 2 roots mod p 0 roots mod p 1 roots mod p 0 roots mod p 2 roots mod p 2 roots mod p 0 roots mod p 0 roots mod p 3 roots mod p 3 roots mod p 2 roots mod p 1 roots mod p 3 roots mod p 3 roots mod p 1 roots mod p 1 roots mod p 2 roots mod p 1 roots mod p 1 roots mod p 1 roots mod p 0 roots mod p 3 roots mod p 1 roots mod p 1 roots mod p 0 roots mod p 5 roots mod p 0 roots mod p 1 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 2 roots mod p 3 roots mod p 0 roots mod p 0 roots mod p 2 roots mod p 0 roots mod p 2 roots mod p 3 roots mod p 1 roots mod p 3 roots mod p 3 roots mod p 0 roots mod p 1 roots mod p 1 roots mod p 1 roots mod p 3 roots mod p 3 roots mod p 2 roots mod p 3 roots mod p 1 roots mod p 1 roots mod p 1 roots mod p 0 roots mod p 2 roots mod p 0 roots mod p 2 roots mod p 2 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 1 roots mod p 1 roots mod p 3 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 1 roots mod p 0 roots mod p 2 roots mod p 3 roots mod p 1 roots mod p 0 roots mod p 0 roots mod p 2 roots mod p 1 roots mod p 1 roots mod p 1 roots mod p 1 roots mod p 1 roots mod p 1 roots mod p 0 roots mod p 1 roots mod p 0 roots mod p 0 roots mod p 3 roots mod p 1 roots mod p 0 roots mod p 0 roots mod p 3 roots mod p 1 roots mod p 5 roots mod p 0 roots mod p 0 roots mod p 1 roots mod p 0 roots mod p 3 roots mod p 2 roots mod p 1 roots mod p 2 roots mod p 1 roots mod p 0 roots mod p 2 roots mod p 2 roots mod p 2 roots mod p 1 roots mod p 1 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 1 roots mod p 2 roots mod p 0 roots mod p 2 roots mod p 1 roots mod p 1 roots mod p 2 roots mod p 1 roots mod p 1 roots mod p 0 roots mod p 2 roots mod p 0 roots mod p 1 roots mod p 3 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 2 roots mod p 1 roots mod p 0 roots mod p 2 roots mod p 0 roots mod p 2 roots mod p 0 roots mod p 2 roots mod p 2 roots mod p 2 roots mod p 0 roots mod p 1 roots mod p 0 roots mod p 0 roots mod p 2 roots mod p 0 roots mod p 2 roots mod p 0 roots mod p 1 roots mod p 1 roots mod p 3 roots mod p 2 roots mod p 0 roots mod p 2 roots mod p 1 roots mod p 0 roots mod p 1 roots mod p 1 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 3 roots mod p 0 roots mod p 0 roots mod p 3 roots mod p 0 roots mod p 0 -4.187350381476560979560234128867 Total time: 5.459 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Thu Mar 25 00:13:17 2004 Input: function CalcCont_p( p, disc, bound, F, f ); if disc mod p eq 0 then /* estimate using some small sample space */ cont_p := 0; upper_limit := bound^2; for i in [1..bound] do repeat a := Random( upper_limit ); b := Random( upper_limit ); until Gcd( a, b ) eq 1; value := Evaluate( F, [a, b] ); while value mod p eq 0 do value div:= p; cont_p +:= 1; end while; end for; cont_p := cont_p / (0.0 + bound); else K := GF(p); roots_mod_p := Roots( f, K ); q_p := #roots_mod_p; print "roots mod p", q_p; /* add in the contribution of the projective roots */ d := Degree( f ); if Coefficient(f, d) mod p eq 0 then q_p +:= 1; end if; cont_p := q_p * p / (p * p - 1.0); end if; return cont_p; end function; function CalcAlpha( F, bound, abort_p, abort_alpha, max_p ); Q := PolynomialRing(Integers()); f := Q!Evaluate( F, [X, 1] ); disc := Discriminant( f ); a_d := Coefficient(f, Degree(f)); primes := [p : p in [1..max_p] | IsPrime(p)]; alpha := 0.0; for p in primes do cont_p := CalcCont_p( p, disc, bound, F, f ); // print "cont_p = ", cont_p; alpha +:= (1.0/(p-1) - cont_p)*Log(p); /* early-abort strategy */ if p eq abort_p and alpha gt abort_alpha then break; end if; end for; return alpha; end function; d := 5; coeffs := []; coeffs[6] := -5142225622472630020004; coeffs[5] := -3356924353646091366162; coeffs[4] := 6545365626333869758617; coeffs[3] := -4722668925346720843884; coeffs[2] := -514856715582822510304; coeffs[1] := 237866611103421300000; m1_Value := 617119742304446938751913; P := PolynomialRing(Integers(),2); F := P!0; for i in [0..d] do F +:= coeffs[i+1]*X^(d-i)*Y^i; end for; eval := Evaluate(F,[m1_Value,1]); print eval; alpha := CalcAlpha( F, 2500, 11, -0.5, 100 ); print alpha; alpha := CalcAlpha( F, 10000, 0, 0, 2000 ); print alpha; Output: Magma V2.10-6 Thu Mar 25 2004 00:13:12 on modular [Seed = 3404259484] ------------------------------------- 2129024631825875754749788201627151749780670396327721627823338321538194998405649\ 5911366573853021918316783107387995317230889569230873441936471 roots mod p 2 roots mod p 1 roots mod p 2 roots mod p 2 roots mod p 1 roots mod p 2 roots mod p 0 roots mod p 0 roots mod p 2 roots mod p 2 roots mod p 3 roots mod p 1 roots mod p 3 roots mod p 2 roots mod p 0 roots mod p 1 roots mod p 0 roots mod p 3 roots mod p 1 roots mod p 2 roots mod p 0 -3.89775285966827332692022513600 roots mod p 2 roots mod p 1 roots mod p 2 roots mod p 2 roots mod p 1 roots mod p 2 roots mod p 0 roots mod p 0 roots mod p 2 roots mod p 2 roots mod p 3 roots mod p 1 roots mod p 3 roots mod p 2 roots mod p 0 roots mod p 1 roots mod p 0 roots mod p 3 roots mod p 1 roots mod p 2 roots mod p 0 roots mod p 2 roots mod p 2 roots mod p 1 roots mod p 1 roots mod p 3 roots mod p 0 roots mod p 2 roots mod p 1 roots mod p 0 roots mod p 1 roots mod p 3 roots mod p 0 roots mod p 0 roots mod p 1 roots mod p 1 roots mod p 2 roots mod p 1 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 2 roots mod p 0 roots mod p 1 roots mod p 3 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 3 roots mod p 2 roots mod p 2 roots mod p 0 roots mod p 2 roots mod p 2 roots mod p 0 roots mod p 1 roots mod p 1 roots mod p 1 roots mod p 1 roots mod p 1 roots mod p 0 roots mod p 2 roots mod p 2 roots mod p 1 roots mod p 0 roots mod p 1 roots mod p 1 roots mod p 1 roots mod p 2 roots mod p 1 roots mod p 2 roots mod p 3 roots mod p 1 roots mod p 1 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 1 roots mod p 1 roots mod p 3 roots mod p 2 roots mod p 0 roots mod p 0 roots mod p 1 roots mod p 0 roots mod p 2 roots mod p 1 roots mod p 1 roots mod p 1 roots mod p 3 roots mod p 3 roots mod p 0 roots mod p 1 roots mod p 0 roots mod p 1 roots mod p 2 roots mod p 0 roots mod p 1 roots mod p 3 roots mod p 0 roots mod p 1 roots mod p 2 roots mod p 1 roots mod p 0 roots mod p 1 roots mod p 0 roots mod p 1 roots mod p 0 roots mod p 1 roots mod p 1 roots mod p 3 roots mod p 1 roots mod p 1 roots mod p 1 roots mod p 0 roots mod p 2 roots mod p 1 roots mod p 1 roots mod p 0 roots mod p 0 roots mod p 1 roots mod p 0 roots mod p 1 roots mod p 3 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 1 roots mod p 2 roots mod p 0 roots mod p 1 roots mod p 0 roots mod p 2 roots mod p 2 roots mod p 0 roots mod p 0 roots mod p 3 roots mod p 3 roots mod p 2 roots mod p 1 roots mod p 3 roots mod p 3 roots mod p 1 roots mod p 1 roots mod p 2 roots mod p 1 roots mod p 1 roots mod p 1 roots mod p 0 roots mod p 3 roots mod p 1 roots mod p 1 roots mod p 0 roots mod p 5 roots mod p 0 roots mod p 1 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 2 roots mod p 3 roots mod p 0 roots mod p 0 roots mod p 2 roots mod p 0 roots mod p 2 roots mod p 3 roots mod p 1 roots mod p 3 roots mod p 3 roots mod p 0 roots mod p 1 roots mod p 1 roots mod p 1 roots mod p 3 roots mod p 3 roots mod p 2 roots mod p 3 roots mod p 1 roots mod p 1 roots mod p 1 roots mod p 0 roots mod p 2 roots mod p 0 roots mod p 2 roots mod p 2 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 1 roots mod p 1 roots mod p 3 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 1 roots mod p 0 roots mod p 2 roots mod p 3 roots mod p 1 roots mod p 0 roots mod p 0 roots mod p 2 roots mod p 1 roots mod p 1 roots mod p 1 roots mod p 1 roots mod p 1 roots mod p 1 roots mod p 0 roots mod p 1 roots mod p 0 roots mod p 0 roots mod p 3 roots mod p 1 roots mod p 0 roots mod p 0 roots mod p 3 roots mod p 1 roots mod p 5 roots mod p 0 roots mod p 0 roots mod p 1 roots mod p 0 roots mod p 3 roots mod p 2 roots mod p 1 roots mod p 2 roots mod p 1 roots mod p 0 roots mod p 2 roots mod p 2 roots mod p 2 roots mod p 1 roots mod p 1 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 1 roots mod p 2 roots mod p 0 roots mod p 2 roots mod p 1 roots mod p 1 roots mod p 2 roots mod p 1 roots mod p 1 roots mod p 0 roots mod p 2 roots mod p 0 roots mod p 1 roots mod p 3 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 2 roots mod p 1 roots mod p 0 roots mod p 2 roots mod p 0 roots mod p 2 roots mod p 0 roots mod p 2 roots mod p 2 roots mod p 2 roots mod p 0 roots mod p 1 roots mod p 0 roots mod p 0 roots mod p 2 roots mod p 0 roots mod p 2 roots mod p 0 roots mod p 1 roots mod p 1 roots mod p 3 roots mod p 2 roots mod p 0 roots mod p 2 roots mod p 1 roots mod p 0 roots mod p 1 roots mod p 1 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 0 roots mod p 3 roots mod p 0 roots mod p 0 roots mod p 3 roots mod p 0 roots mod p 0 -4.142702252107597934350662319072 Total time: 5.469 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Thu Mar 25 00:17:46 2004 Input: function CalcCont_p( p, disc, bound, F, f ); if disc mod p eq 0 then /* estimate using some small sample space */ cont_p := 0; upper_limit := bound^2; for i in [1..bound] do repeat a := Random( upper_limit ); b := Random( upper_limit ); until Gcd( a, b ) eq 1; value := Evaluate( F, [a, b] ); while value mod p eq 0 do value div:= p; cont_p +:= 1; end while; end for; cont_p := cont_p / (0.0 + bound); else K := GF(p); roots_mod_p := Roots( f, K ); q_p := #roots_mod_p; print "roots mod p", p,q_p; /* add in the contribution of the projective roots */ d := Degree( f ); if Coefficient(f, d) mod p eq 0 then q_p +:= 1; end if; cont_p := q_p * p / (p * p - 1.0); end if; return cont_p; end function; function CalcAlpha( F, bound, abort_p, abort_alpha, max_p ); Q := PolynomialRing(Integers()); f := Q!Evaluate( F, [X, 1] ); disc := Discriminant( f ); a_d := Coefficient(f, Degree(f)); primes := [p : p in [1..max_p] | IsPrime(p)]; alpha := 0.0; for p in primes do cont_p := CalcCont_p( p, disc, bound, F, f ); // print "cont_p = ", cont_p; alpha +:= (1.0/(p-1) - cont_p)*Log(p); /* early-abort strategy */ if p eq abort_p and alpha gt abort_alpha then break; end if; end for; return alpha; end function; d := 5; coeffs := []; coeffs[6] := -5142225622472630020004; coeffs[5] := -3356924353646091366162; coeffs[4] := 6545365626333869758617; coeffs[3] := -4722668925346720843884; coeffs[2] := -514856715582822510304; coeffs[1] := 237866611103421300000; m1_Value := 617119742304446938751913; P := PolynomialRing(Integers(),2); F := P!0; for i in [0..d] do F +:= coeffs[i+1]*X^(d-i)*Y^i; end for; eval := Evaluate(F,[m1_Value,1]); print eval; alpha := CalcAlpha( F, 2500, 11, -0.5, 100 ); print alpha; alpha := CalcAlpha( F, 10000, 0, 0, 2000 ); print alpha; Output: Magma V2.10-6 Thu Mar 25 2004 00:17:40 on modular [Seed = 1008605047] ------------------------------------- 2129024631825875754749788201627151749780670396327721627823338321538194998405649\ 5911366573853021918316783107387995317230889569230873441936471 roots mod p 3 2 roots mod p 5 1 roots mod p 13 2 roots mod p 19 2 roots mod p 23 1 roots mod p 29 2 roots mod p 31 0 roots mod p 37 0 roots mod p 41 2 roots mod p 43 2 roots mod p 47 3 roots mod p 53 1 roots mod p 59 3 roots mod p 61 2 roots mod p 67 0 roots mod p 71 1 roots mod p 73 0 roots mod p 79 3 roots mod p 83 1 roots mod p 89 2 roots mod p 97 0 -3.79565703810878203197694936192 roots mod p 3 2 roots mod p 5 1 roots mod p 13 2 roots mod p 19 2 roots mod p 23 1 roots mod p 29 2 roots mod p 31 0 roots mod p 37 0 roots mod p 41 2 roots mod p 43 2 roots mod p 47 3 roots mod p 53 1 roots mod p 59 3 roots mod p 61 2 roots mod p 67 0 roots mod p 71 1 roots mod p 73 0 roots mod p 79 3 roots mod p 83 1 roots mod p 89 2 roots mod p 97 0 roots mod p 101 2 roots mod p 103 2 roots mod p 107 1 roots mod p 109 1 roots mod p 113 3 roots mod p 127 0 roots mod p 131 2 roots mod p 137 1 roots mod p 139 0 roots mod p 149 1 roots mod p 151 3 roots mod p 157 0 roots mod p 163 0 roots mod p 167 1 roots mod p 173 1 roots mod p 179 2 roots mod p 181 1 roots mod p 191 0 roots mod p 193 0 roots mod p 197 0 roots mod p 199 2 roots mod p 211 0 roots mod p 223 1 roots mod p 227 3 roots mod p 229 0 roots mod p 233 0 roots mod p 239 0 roots mod p 241 3 roots mod p 251 2 roots mod p 257 2 roots mod p 263 0 roots mod p 269 2 roots mod p 271 2 roots mod p 277 0 roots mod p 281 1 roots mod p 283 1 roots mod p 293 1 roots mod p 307 1 roots mod p 311 1 roots mod p 313 0 roots mod p 317 2 roots mod p 331 2 roots mod p 337 1 roots mod p 347 0 roots mod p 349 1 roots mod p 353 1 roots mod p 359 1 roots mod p 367 2 roots mod p 373 1 roots mod p 379 2 roots mod p 383 3 roots mod p 389 1 roots mod p 397 1 roots mod p 401 0 roots mod p 409 0 roots mod p 419 0 roots mod p 421 0 roots mod p 431 0 roots mod p 433 1 roots mod p 439 1 roots mod p 443 3 roots mod p 449 2 roots mod p 457 0 roots mod p 461 0 roots mod p 463 1 roots mod p 467 0 roots mod p 479 2 roots mod p 487 1 roots mod p 491 1 roots mod p 499 1 roots mod p 503 3 roots mod p 509 3 roots mod p 521 0 roots mod p 523 1 roots mod p 541 0 roots mod p 547 1 roots mod p 557 2 roots mod p 563 0 roots mod p 569 1 roots mod p 571 3 roots mod p 577 0 roots mod p 587 1 roots mod p 593 2 roots mod p 599 1 roots mod p 601 0 roots mod p 607 1 roots mod p 613 0 roots mod p 617 1 roots mod p 619 0 roots mod p 631 1 roots mod p 641 1 roots mod p 643 3 roots mod p 647 1 roots mod p 653 1 roots mod p 659 1 roots mod p 661 0 roots mod p 673 2 roots mod p 677 1 roots mod p 683 1 roots mod p 691 0 roots mod p 701 0 roots mod p 709 1 roots mod p 719 0 roots mod p 727 1 roots mod p 733 3 roots mod p 739 0 roots mod p 743 0 roots mod p 751 0 roots mod p 757 1 roots mod p 761 2 roots mod p 769 0 roots mod p 773 1 roots mod p 787 0 roots mod p 797 2 roots mod p 809 2 roots mod p 811 0 roots mod p 821 0 roots mod p 823 3 roots mod p 827 3 roots mod p 829 2 roots mod p 839 1 roots mod p 853 3 roots mod p 857 3 roots mod p 859 1 roots mod p 863 1 roots mod p 877 2 roots mod p 881 1 roots mod p 883 1 roots mod p 887 1 roots mod p 907 0 roots mod p 911 3 roots mod p 919 1 roots mod p 929 1 roots mod p 937 0 roots mod p 941 5 roots mod p 947 0 roots mod p 953 1 roots mod p 967 0 roots mod p 971 0 roots mod p 977 0 roots mod p 983 2 roots mod p 991 3 roots mod p 997 0 roots mod p 1009 0 roots mod p 1013 2 roots mod p 1019 0 roots mod p 1021 2 roots mod p 1031 3 roots mod p 1033 1 roots mod p 1039 3 roots mod p 1049 3 roots mod p 1051 0 roots mod p 1061 1 roots mod p 1063 1 roots mod p 1069 1 roots mod p 1087 3 roots mod p 1091 3 roots mod p 1093 2 roots mod p 1097 3 roots mod p 1103 1 roots mod p 1109 1 roots mod p 1117 1 roots mod p 1123 0 roots mod p 1129 2 roots mod p 1151 0 roots mod p 1153 2 roots mod p 1163 2 roots mod p 1171 0 roots mod p 1181 0 roots mod p 1187 0 roots mod p 1193 0 roots mod p 1201 0 roots mod p 1213 1 roots mod p 1217 1 roots mod p 1223 3 roots mod p 1229 0 roots mod p 1231 0 roots mod p 1237 0 roots mod p 1249 1 roots mod p 1259 0 roots mod p 1277 2 roots mod p 1279 3 roots mod p 1283 1 roots mod p 1289 0 roots mod p 1291 0 roots mod p 1297 2 roots mod p 1301 1 roots mod p 1303 1 roots mod p 1307 1 roots mod p 1319 1 roots mod p 1321 1 roots mod p 1327 1 roots mod p 1361 0 roots mod p 1367 1 roots mod p 1373 0 roots mod p 1381 0 roots mod p 1399 3 roots mod p 1409 1 roots mod p 1423 0 roots mod p 1427 0 roots mod p 1429 3 roots mod p 1433 1 roots mod p 1439 5 roots mod p 1447 0 roots mod p 1451 0 roots mod p 1453 1 roots mod p 1459 0 roots mod p 1471 3 roots mod p 1481 2 roots mod p 1483 1 roots mod p 1487 2 roots mod p 1489 1 roots mod p 1493 0 roots mod p 1499 2 roots mod p 1511 2 roots mod p 1523 2 roots mod p 1531 1 roots mod p 1543 1 roots mod p 1549 0 roots mod p 1553 0 roots mod p 1559 0 roots mod p 1567 1 roots mod p 1571 2 roots mod p 1579 0 roots mod p 1583 2 roots mod p 1597 1 roots mod p 1601 1 roots mod p 1607 2 roots mod p 1609 1 roots mod p 1613 1 roots mod p 1619 0 roots mod p 1621 2 roots mod p 1627 0 roots mod p 1637 1 roots mod p 1657 3 roots mod p 1663 0 roots mod p 1667 0 roots mod p 1669 0 roots mod p 1693 0 roots mod p 1697 2 roots mod p 1699 1 roots mod p 1709 0 roots mod p 1721 2 roots mod p 1723 0 roots mod p 1733 2 roots mod p 1741 0 roots mod p 1747 2 roots mod p 1753 2 roots mod p 1759 2 roots mod p 1777 0 roots mod p 1783 1 roots mod p 1787 0 roots mod p 1789 0 roots mod p 1801 2 roots mod p 1811 0 roots mod p 1823 2 roots mod p 1831 0 roots mod p 1847 1 roots mod p 1861 1 roots mod p 1867 3 roots mod p 1871 2 roots mod p 1873 0 roots mod p 1877 2 roots mod p 1879 1 roots mod p 1889 0 roots mod p 1901 1 roots mod p 1907 1 roots mod p 1913 0 roots mod p 1931 0 roots mod p 1933 0 roots mod p 1949 0 roots mod p 1951 0 roots mod p 1973 3 roots mod p 1979 0 roots mod p 1987 0 roots mod p 1993 3 roots mod p 1997 0 roots mod p 1999 0 -4.224931315205598270672479336411 Total time: 5.519 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Thu Mar 25 00:26:08 2004 Input: function CalcCont_p( p, disc, bound, F, f ); if disc mod p eq 0 then /* estimate using some small sample space */ cont_p := 0; upper_limit := bound^2; for i in [1..bound] do repeat a := Random( upper_limit ); b := Random( upper_limit ); until Gcd( a, b ) eq 1; value := Evaluate( F, [a, b] ); while value mod p eq 0 do value div:= p; cont_p +:= 1; end while; end for; cont_p := cont_p / (0.0 + bound); else K := GF(p); roots_mod_p := Roots( f, K ); q_p := #roots_mod_p; print "roots mod p", p,q_p; /* add in the contribution of the projective roots */ d := Degree( f ); if Coefficient(f, d) mod p eq 0 then q_p +:= 1; end if; cont_p := q_p * p / (p * p - 1.0); end if; return cont_p; end function; function CalcAlpha( F, bound, abort_p, abort_alpha, max_p ); Q := PolynomialRing(Integers()); f := Q!Evaluate( F, [X, 1] ); disc := Discriminant( f ); print "discriminant = ", disc; a_d := Coefficient(f, Degree(f)); primes := [p : p in [1..max_p] | IsPrime(p)]; alpha := 0.0; for p in primes do cont_p := CalcCont_p( p, disc, bound, F, f ); // print "cont_p = ", cont_p; alpha +:= (1.0/(p-1) - cont_p)*Log(p); /* early-abort strategy */ if p eq abort_p and alpha gt abort_alpha then break; end if; end for; return alpha; end function; d := 5; coeffs := []; coeffs[6] := -5142225622472630020004; coeffs[5] := -3356924353646091366162; coeffs[4] := 6545365626333869758617; coeffs[3] := -4722668925346720843884; coeffs[2] := -514856715582822510304; coeffs[1] := 237866611103421300000; m1_Value := 617119742304446938751913; P := PolynomialRing(Integers(),2); F := P!0; for i in [0..d] do F +:= coeffs[i+1]*X^(d-i)*Y^i; end for; eval := Evaluate(F,[m1_Value,1]); print eval; alpha := CalcAlpha( F, 2500, 11, -0.5, 100 ); print alpha; alpha := CalcAlpha( F, 10000, 0, 0, 2000 ); print alpha; Output: Magma V2.10-6 Thu Mar 25 2004 00:26:02 on modular [Seed = 637799283] ------------------------------------- 2129024631825875754749788201627151749780670396327721627823338321538194998405649\ 5911366573853021918316783107387995317230889569230873441936471 discriminant = -32527601918733866616892681658291466483997745425215021341917914\ 2095185174185308559529094399575371274387767935197645089523743844999337331162148\ 9235318265483060291098235794518016 roots mod p 3 2 roots mod p 5 1 roots mod p 13 2 roots mod p 19 2 roots mod p 23 1 roots mod p 29 2 roots mod p 31 0 roots mod p 37 0 roots mod p 41 2 roots mod p 43 2 roots mod p 47 3 roots mod p 53 1 roots mod p 59 3 roots mod p 61 2 roots mod p 67 0 roots mod p 71 1 roots mod p 73 0 roots mod p 79 3 roots mod p 83 1 roots mod p 89 2 roots mod p 97 0 -3.86344219482930414594083005659 discriminant = -32527601918733866616892681658291466483997745425215021341917914\ 2095185174185308559529094399575371274387767935197645089523743844999337331162148\ 9235318265483060291098235794518016 roots mod p 3 2 roots mod p 5 1 roots mod p 13 2 roots mod p 19 2 roots mod p 23 1 roots mod p 29 2 roots mod p 31 0 roots mod p 37 0 roots mod p 41 2 roots mod p 43 2 roots mod p 47 3 roots mod p 53 1 roots mod p 59 3 roots mod p 61 2 roots mod p 67 0 roots mod p 71 1 roots mod p 73 0 roots mod p 79 3 roots mod p 83 1 roots mod p 89 2 roots mod p 97 0 roots mod p 101 2 roots mod p 103 2 roots mod p 107 1 roots mod p 109 1 roots mod p 113 3 roots mod p 127 0 roots mod p 131 2 roots mod p 137 1 roots mod p 139 0 roots mod p 149 1 roots mod p 151 3 roots mod p 157 0 roots mod p 163 0 roots mod p 167 1 roots mod p 173 1 roots mod p 179 2 roots mod p 181 1 roots mod p 191 0 roots mod p 193 0 roots mod p 197 0 roots mod p 199 2 roots mod p 211 0 roots mod p 223 1 roots mod p 227 3 roots mod p 229 0 roots mod p 233 0 roots mod p 239 0 roots mod p 241 3 roots mod p 251 2 roots mod p 257 2 roots mod p 263 0 roots mod p 269 2 roots mod p 271 2 roots mod p 277 0 roots mod p 281 1 roots mod p 283 1 roots mod p 293 1 roots mod p 307 1 roots mod p 311 1 roots mod p 313 0 roots mod p 317 2 roots mod p 331 2 roots mod p 337 1 roots mod p 347 0 roots mod p 349 1 roots mod p 353 1 roots mod p 359 1 roots mod p 367 2 roots mod p 373 1 roots mod p 379 2 roots mod p 383 3 roots mod p 389 1 roots mod p 397 1 roots mod p 401 0 roots mod p 409 0 roots mod p 419 0 roots mod p 421 0 roots mod p 431 0 roots mod p 433 1 roots mod p 439 1 roots mod p 443 3 roots mod p 449 2 roots mod p 457 0 roots mod p 461 0 roots mod p 463 1 roots mod p 467 0 roots mod p 479 2 roots mod p 487 1 roots mod p 491 1 roots mod p 499 1 roots mod p 503 3 roots mod p 509 3 roots mod p 521 0 roots mod p 523 1 roots mod p 541 0 roots mod p 547 1 roots mod p 557 2 roots mod p 563 0 roots mod p 569 1 roots mod p 571 3 roots mod p 577 0 roots mod p 587 1 roots mod p 593 2 roots mod p 599 1 roots mod p 601 0 roots mod p 607 1 roots mod p 613 0 roots mod p 617 1 roots mod p 619 0 roots mod p 631 1 roots mod p 641 1 roots mod p 643 3 roots mod p 647 1 roots mod p 653 1 roots mod p 659 1 roots mod p 661 0 roots mod p 673 2 roots mod p 677 1 roots mod p 683 1 roots mod p 691 0 roots mod p 701 0 roots mod p 709 1 roots mod p 719 0 roots mod p 727 1 roots mod p 733 3 roots mod p 739 0 roots mod p 743 0 roots mod p 751 0 roots mod p 757 1 roots mod p 761 2 roots mod p 769 0 roots mod p 773 1 roots mod p 787 0 roots mod p 797 2 roots mod p 809 2 roots mod p 811 0 roots mod p 821 0 roots mod p 823 3 roots mod p 827 3 roots mod p 829 2 roots mod p 839 1 roots mod p 853 3 roots mod p 857 3 roots mod p 859 1 roots mod p 863 1 roots mod p 877 2 roots mod p 881 1 roots mod p 883 1 roots mod p 887 1 roots mod p 907 0 roots mod p 911 3 roots mod p 919 1 roots mod p 929 1 roots mod p 937 0 roots mod p 941 5 roots mod p 947 0 roots mod p 953 1 roots mod p 967 0 roots mod p 971 0 roots mod p 977 0 roots mod p 983 2 roots mod p 991 3 roots mod p 997 0 roots mod p 1009 0 roots mod p 1013 2 roots mod p 1019 0 roots mod p 1021 2 roots mod p 1031 3 roots mod p 1033 1 roots mod p 1039 3 roots mod p 1049 3 roots mod p 1051 0 roots mod p 1061 1 roots mod p 1063 1 roots mod p 1069 1 roots mod p 1087 3 roots mod p 1091 3 roots mod p 1093 2 roots mod p 1097 3 roots mod p 1103 1 roots mod p 1109 1 roots mod p 1117 1 roots mod p 1123 0 roots mod p 1129 2 roots mod p 1151 0 roots mod p 1153 2 roots mod p 1163 2 roots mod p 1171 0 roots mod p 1181 0 roots mod p 1187 0 roots mod p 1193 0 roots mod p 1201 0 roots mod p 1213 1 roots mod p 1217 1 roots mod p 1223 3 roots mod p 1229 0 roots mod p 1231 0 roots mod p 1237 0 roots mod p 1249 1 roots mod p 1259 0 roots mod p 1277 2 roots mod p 1279 3 roots mod p 1283 1 roots mod p 1289 0 roots mod p 1291 0 roots mod p 1297 2 roots mod p 1301 1 roots mod p 1303 1 roots mod p 1307 1 roots mod p 1319 1 roots mod p 1321 1 roots mod p 1327 1 roots mod p 1361 0 roots mod p 1367 1 roots mod p 1373 0 roots mod p 1381 0 roots mod p 1399 3 roots mod p 1409 1 roots mod p 1423 0 roots mod p 1427 0 roots mod p 1429 3 roots mod p 1433 1 roots mod p 1439 5 roots mod p 1447 0 roots mod p 1451 0 roots mod p 1453 1 roots mod p 1459 0 roots mod p 1471 3 roots mod p 1481 2 roots mod p 1483 1 roots mod p 1487 2 roots mod p 1489 1 roots mod p 1493 0 roots mod p 1499 2 roots mod p 1511 2 roots mod p 1523 2 roots mod p 1531 1 roots mod p 1543 1 roots mod p 1549 0 roots mod p 1553 0 roots mod p 1559 0 roots mod p 1567 1 roots mod p 1571 2 roots mod p 1579 0 roots mod p 1583 2 roots mod p 1597 1 roots mod p 1601 1 roots mod p 1607 2 roots mod p 1609 1 roots mod p 1613 1 roots mod p 1619 0 roots mod p 1621 2 roots mod p 1627 0 roots mod p 1637 1 roots mod p 1657 3 roots mod p 1663 0 roots mod p 1667 0 roots mod p 1669 0 roots mod p 1693 0 roots mod p 1697 2 roots mod p 1699 1 roots mod p 1709 0 roots mod p 1721 2 roots mod p 1723 0 roots mod p 1733 2 roots mod p 1741 0 roots mod p 1747 2 roots mod p 1753 2 roots mod p 1759 2 roots mod p 1777 0 roots mod p 1783 1 roots mod p 1787 0 roots mod p 1789 0 roots mod p 1801 2 roots mod p 1811 0 roots mod p 1823 2 roots mod p 1831 0 roots mod p 1847 1 roots mod p 1861 1 roots mod p 1867 3 roots mod p 1871 2 roots mod p 1873 0 roots mod p 1877 2 roots mod p 1879 1 roots mod p 1889 0 roots mod p 1901 1 roots mod p 1907 1 roots mod p 1913 0 roots mod p 1931 0 roots mod p 1933 0 roots mod p 1949 0 roots mod p 1951 0 roots mod p 1973 3 roots mod p 1979 0 roots mod p 1987 0 roots mod p 1993 3 roots mod p 1997 0 roots mod p 1999 0 -4.166431735660589174135761850444 Total time: 5.589 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Thu Mar 25 00:30:09 2004 Input: function CalcCont_p( p, disc, bound, F, f ); if disc mod p eq 0 then /* estimate using some small sample space */ cont_p := 0; upper_limit := bound^2; for i in [1..bound] do repeat a := Random( upper_limit ); b := Random( upper_limit ); until Gcd( a, b ) eq 1; value := Evaluate( F, [a, b] ); while value mod p eq 0 do value div:= p; cont_p +:= 1; end while; end for; cont_p := cont_p / (0.0 + bound); else K := GF(p); roots_mod_p := Roots( f, K ); q_p := #roots_mod_p; // print "roots mod p", p,q_p; /* add in the contribution of the projective roots */ d := Degree( f ); if Coefficient(f, d) mod p eq 0 then q_p +:= 1; end if; cont_p := q_p * p / (p * p - 1.0); print "cont_p = ", cont_p; end if; return cont_p; end function; function CalcAlpha( F, bound, abort_p, abort_alpha, max_p ); Q := PolynomialRing(Integers()); f := Q!Evaluate( F, [X, 1] ); disc := Discriminant( f ); // print "discriminant = ", disc; a_d := Coefficient(f, Degree(f)); primes := [p : p in [1..max_p] | IsPrime(p)]; alpha := 0.0; for p in primes do cont_p := CalcCont_p( p, disc, bound, F, f ); // print "cont_p = ", cont_p; alpha +:= (1.0/(p-1) - cont_p)*Log(p); /* early-abort strategy */ if p eq abort_p and alpha gt abort_alpha then break; end if; end for; return alpha; end function; d := 5; coeffs := []; coeffs[6] := -5142225622472630020004; coeffs[5] := -3356924353646091366162; coeffs[4] := 6545365626333869758617; coeffs[3] := -4722668925346720843884; coeffs[2] := -514856715582822510304; coeffs[1] := 237866611103421300000; m1_Value := 617119742304446938751913; P := PolynomialRing(Integers(),2); F := P!0; for i in [0..d] do F +:= coeffs[i+1]*X^(d-i)*Y^i; end for; eval := Evaluate(F,[m1_Value,1]); print eval; alpha := CalcAlpha( F, 2500, 11, -0.5, 100 ); print alpha; alpha := CalcAlpha( F, 10000, 0, 0, 2000 ); print alpha; Output: Magma V2.10-6 Thu Mar 25 2004 00:30:03 on modular [Seed = 355941233] ------------------------------------- 2129024631825875754749788201627151749780670396327721627823338321538194998405649\ 5911366573853021918316783107387995317230889569230873441936471 cont_p = 1.1250000000000000000000000000000000000000 cont_p = 0.416666666666666666666666666666666666666 cont_p = 0.2321428571428571428571428571428571428566 cont_p = 0.1583333333333333333333333333333333333332 cont_p = 0.0435606060606060606060606060606060606059 cont_p = 0.0690476190476190476190476190476190476188 cont_p = 0 cont_p = 0 cont_p = 0.0488095238095238095238095238095238095235 cont_p = 0.0465367965367965367965367965367965367963 cont_p = 0.0638586956521739130434782608695652173910 cont_p = 0.01887464387464387464387464387464387464373 cont_p = 0.0508620689655172413793103448275862068962 cont_p = 0.0327956989247311827956989247311827956987 cont_p = 0 cont_p = 0.01408730158730158730158730158730158730149 cont_p = 0 cont_p = 0.0379807692307692307692307692307692307690 cont_p = 0.01204994192799070847851335656213704994189 cont_p = 0.02247474747474747474747474747474747474746 cont_p = 0 -3.74648856434595782265077196456 cont_p = 1.1250000000000000000000000000000000000000 cont_p = 0.416666666666666666666666666666666666666 cont_p = 0.2321428571428571428571428571428571428566 cont_p = 0.1583333333333333333333333333333333333332 cont_p = 0.0435606060606060606060606060606060606059 cont_p = 0.0690476190476190476190476190476190476188 cont_p = 0 cont_p = 0 cont_p = 0.0488095238095238095238095238095238095235 cont_p = 0.0465367965367965367965367965367965367963 cont_p = 0.0638586956521739130434782608695652173910 cont_p = 0.01887464387464387464387464387464387464373 cont_p = 0.0508620689655172413793103448275862068962 cont_p = 0.0327956989247311827956989247311827956987 cont_p = 0 cont_p = 0.01408730158730158730158730158730158730149 cont_p = 0 cont_p = 0.0379807692307692307692307692307692307690 cont_p = 0.01204994192799070847851335656213704994189 cont_p = 0.02247474747474747474747474747474747474746 cont_p = 0 cont_p = 0.01980392156862745098039215686274509803915 cont_p = 0.01941930618401206636500754147812971342376 cont_p = 0.00934661076170510132774283717679944095035 cont_p = 0.00917508417508417508417508417508417508410 cont_p = 0.0265507518796992481203007518796992481202 cont_p = 0 cont_p = 0.01526806526806526806526806526806526806524 cont_p = 0.00729965899403239556692242114236999147479 cont_p = 0 cont_p = 0.00671171171171171171171171171171171171165 cont_p = 0.01986842105263157894736842105263157894729 cont_p = 0 cont_p = 0 cont_p = 0.00598823866896156052782558806655192197359 cont_p = 0.00578053996257685110932905640203154236831 cont_p = 0.01117353308364544319600499375780274656678 cont_p = 0.00552503052503052503052503052503052503051 cont_p = 0 cont_p = 0 cont_p = 0 cont_p = 0.01005050505050505050505050505050505050501 cont_p = 0 cont_p = 0.00448439510939510939510939510939510939509 cont_p = 0.01321611551001397298556124825337680484389 cont_p = 0 cont_p = 0 cont_p = 0 cont_p = 0.01244834710743801652892561983471074380162 cont_p = 0.00796825396825396825396825396825396825390 cont_p = 0.00778221899224806201550387596899224806196 cont_p = 0 cont_p = 0.00743504698728579325594250967385295743500 cont_p = 0.00738017429193899782135076252723311546839 cont_p = 0 cont_p = 0.00355876393110435663627152988855116514689 cont_p = 0.00353361302567176106283088602537209070021 cont_p = 0.00341300903923213120864784269872332494639 cont_p = 0.00325736355148119854002206943383413971648 cont_p = 0.00321546732837055417700578990901571546730 cont_p = 0 cont_p = 0.00630921105007563092110500756309211050072 cont_p = 0.00604235122307411464037970062066447608610 cont_p = 0.00296738517892364046210200056353902507746 cont_p = 0 cont_p = 0.00286535303776683087027914614121510673232 cont_p = 0.00283288392398561890087313816127375449408 cont_p = 0.00278553693358162631905648665425201738049 cont_p = 0.00544963174150629603231171299596103587548 cont_p = 0.00268098441722730147777586107756885745498 cont_p = 0.00527708159287106655527708159287106655524 cont_p = 0.00783295157068062827225130890052356020935 cont_p = 0.00257071107586571504097277293153581813373 cont_p = 0.00251890766966143850565961118724937820414 cont_p = 0 cont_p = 0 cont_p = 0 cont_p = 0 cont_p = 0 cont_p = 0.002309481140126301416623997269158559481126 cont_p = 0.002277916147779161477791614777916147779145 cont_p = 0.00677204353674941910236027883086706616116 cont_p = 0.00445436507936507936507936507936507936504 cont_p = 0 cont_p = 0 cont_p = 0.002159837289147633975220182116733840871756 cont_p = 0 cont_p = 0.00417538354253835425383542538354253835424 cont_p = 0.002053396748296566147203669972340281994180 cont_p = 0.002036668325866932138709142193462750954035 cont_p = 0.002004016064257028112449799196787148594366 cont_p = 0.00596423828495541642952001517738569531395 cont_p = 0.00589393237610004631773969430291801760069 cont_p = 0 cont_p = 0.001912052879412710947325319528530899944426 cont_p = 0 cont_p = 0.001828159674875003342156626828159674874991 cont_p = 0.00359067584641963848276217735489028132330 cont_p = 0 cont_p = 0.001757474672596985421299728193723745984675 cont_p = 0.00525395656974604343025395656974604343021 cont_p = 0 cont_p = 0.001703582456873534396693831116064173109514 cont_p = 0.00337269087269087269087269087269087269085 cont_p = 0.001669453734671125975473801560758082497208 cont_p = 0 cont_p = 0.001647450929303456661455619246135139829764 cont_p = 0 cont_p = 0.001620749800361450846887740091623586769209 cont_p = 0 cont_p = 0.001584790034157122764717701426562186055846 cont_p = 0.001560066199376947040498442367601246105913 cont_p = 0.00466564114471469205317234573634411098855 cont_p = 0.001545598746321140541986775216909375836097 cont_p = 0.001531397159527963828070767903041218738852 cont_p = 0.001517454177028645113751496730220134475451 cont_p = 0 cont_p = 0.00297177476331779002402147802741274551361 cont_p = 0.001477108097257859000541097205494754848046 cont_p = 0.001464131981958807086141551336797516763551 cont_p = 0 cont_p = 0 cont_p = 0.001410440041378212779501869976923689026807 cont_p = 0 cont_p = 0.001375518420972966427511882057336602791138 cont_p = 0.00409277705811408406664582123553848215479 cont_p = 0 cont_p = 0 cont_p = 0 cont_p = 0.001321006268235819687007022099370384330797 cont_p = 0.00262812543168945987014781047105953861028 cont_p = 0 cont_p = 0.001293663225823727088939765165816497302211 cont_p = 0 cont_p = 0.00250941423911537638065011775670331607912 cont_p = 0.002472191663610805524996944138858330277458 cont_p = 0 cont_p = 0 cont_p = 0.00364520586776273828927786832967188718018 cont_p = 0.00362757483243850229848756009404498719160 cont_p = 0.002412548745707467551364879809091438216613 cont_p = 0.001191896806455279008978292987839527218996 cont_p = 0.00351700366131213510571626480192631197017 cont_p = 0.00350058819684987909286974707535455199005 cont_p = 0.001164145931587792052908331978099419959880 cont_p = 0.001158750107416000687462404399759388158456 cont_p = 0.002280504675424636731467324034491007998652 cont_p = 0.001135075242218099360956503813646670789519 cont_p = 0.001132504283764787966468638737546300571504 cont_p = 0.001127397148841844101437780896020173672541 cont_p = 0 cont_p = 0.00329308849045691150954308849045691150953 cont_p = 0.001088140570237756938524201951311925736474 cont_p = 0.001076427512050426399703374119391916944748 cont_p = 0 cont_p = 0.00531350228124858833626959389257803677099 cont_p = 0 cont_p = 0.001049319098708665856279618765745291827419 cont_p = 0 cont_p = 0 cont_p = 0 cont_p = 0.002034590101501829682247942642359213816157 cont_p = 0.00302724828934506353861192570869990224827 cont_p = 0 cont_p = 0 cont_p = 0.001974335586375720154984369031191773666669 cont_p = 0 cont_p = 0.001958865738076052338743716664748091017221 cont_p = 0.00290979905170467374125084669225558816886 cont_p = 0.000968055118228299821570479660534089034826 cont_p = 0.00288739439751000444642063139172965762559 cont_p = 0.00285986913849509269356597600872410032713 cont_p = 0 cont_p = 0.000942507906051238318587215293323384145254 cont_p = 0.000940734604873766336745819350636478201146 cont_p = 0.000935454513633658861003185270748013581152 cont_p = 0.00275989194020149496262593435164120896975 cont_p = 0.00274977316261719931444702086903921766305 cont_p = 0.001829827698200641527881015998017826171376 cont_p = 0.00273473335726536635953890949702843923255 cont_p = 0.000906619058891606828164864935953076093525 cont_p = 0.000901713988356587634565973916154421569579 cont_p = 0.000895255865248363372894505677701476651208 cont_p = 0 cont_p = 0.001771480574907424841523881252745873344614 cont_p = 0 cont_p = 0.001734606682072020026959368380512227999221 cont_p = 0.001719691727144217518084118506426294278726 cont_p = 0 cont_p = 0 cont_p = 0 cont_p = 0 cont_p = 0 cont_p = 0.000824402868622941371567140239559376036442 cont_p = 0.000821693241725002160573848414138795264015 cont_p = 0.002452986104425403549308430409807130708239 cont_p = 0 cont_p = 0 cont_p = 0 cont_p = 0.000800641025641025641025641025641025641019 cont_p = 0 cont_p = 0.001566171673019657478132465990649574913770 cont_p = 0.002345583920187793427230046948356807511722 cont_p = 0.000779423700312498481247661121398126953111 cont_p = 0 cont_p = 0 cont_p = 0.001542020962924917727177614183263900778015 cont_p = 0.000768639962188349285123478671865768639956 cont_p = 0.000767460160395050559309415434489647828256 cont_p = 0.000765111388978649470100360135062356285499 cont_p = 0.000758150549501080608819607302156619303807 cont_p = 0.000757002704809058818135973960482281208450 cont_p = 0.000753579930582056733722219193516146032084 cont_p = 0 cont_p = 0.000731529286857945253568278920825734419010 cont_p = 0 cont_p = 0 cont_p = 0.0021443899448191293684855916615573267933 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Thu Mar 25 00:36:55 2004 Input: function CalcCont_p( p, disc, bound, F, f ); if disc mod p eq 0 then /* estimate using some small sample space */ cont_p := 0; upper_limit := bound^2; for i in [1..bound] do repeat a := Random( upper_limit ); b := Random( upper_limit ); until Gcd( a, b ) eq 1; value := Evaluate( F, [a, b] ); while value mod p eq 0 do value div:= p; cont_p +:= 1; end while; end for; cont_p := cont_p / (0.0 + bound); else K := GF(p); roots_mod_p := Roots( f, K ); q_p := #roots_mod_p; // print "roots mod p", p,q_p; /* add in the contribution of the projective roots */ d := Degree( f ); if Coefficient(f, d) mod p eq 0 then q_p +:= 1; end if; cont_p := q_p * p / (p * p - 1.0); end if; return cont_p; end function; function CalcAlpha( F, bound, abort_p, abort_alpha, max_p ); Q := PolynomialRing(Integers()); f := Q!Evaluate( F, [X, 1] ); print bound^2; disc := Discriminant( f ); // print "discriminant = ", disc; a_d := Coefficient(f, Degree(f)); primes := [p : p in [1..max_p] | IsPrime(p)]; alpha := 0.0; for p in primes do cont_p := CalcCont_p( p, disc, bound, F, f ); // print "cont_p = ", cont_p; alpha +:= (1.0/(p-1) - cont_p)*Log(p); /* early-abort strategy */ if p eq abort_p and alpha gt abort_alpha then break; end if; end for; return alpha; end function; d := 5; coeffs := []; coeffs[6] := -5142225622472630020004; coeffs[5] := -3356924353646091366162; coeffs[4] := 6545365626333869758617; coeffs[3] := -4722668925346720843884; coeffs[2] := -514856715582822510304; coeffs[1] := 237866611103421300000; m1_Value := 617119742304446938751913; P := PolynomialRing(Integers(),2); F := P!0; for i in [0..d] do F +:= coeffs[i+1]*X^(d-i)*Y^i; end for; eval := Evaluate(F,[m1_Value,1]); print eval; alpha := CalcAlpha( F, 2500, 11, -0.5, 100 ); print alpha; alpha := CalcAlpha( F, 10000, 0, 0, 2000 ); print alpha; Output: Magma V2.10-6 Thu Mar 25 2004 00:36:49 on modular [Seed = 119875785] ------------------------------------- 2129024631825875754749788201627151749780670396327721627823338321538194998405649\ 5911366573853021918316783107387995317230889569230873441936471 6250000 -3.86292790467483358584440603817 100000000 -4.166352853311354675436329269998 Total time: 5.479 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Thu Mar 25 00:39:17 2004 Input: function CalcCont_p( p, disc, bound, F, f ); if disc mod p eq 0 then /* estimate using some small sample space */ cont_p := 0; upper_limit := bound^2; for i in [1..bound] do repeat a := Random( upper_limit ); b := Random( upper_limit ); until Gcd( a, b ) eq 1; print a,b; value := Evaluate( F, [a, b] ); while value mod p eq 0 do value div:= p; cont_p +:= 1; end while; end for; cont_p := cont_p / (0.0 + bound); else K := GF(p); roots_mod_p := Roots( f, K ); q_p := #roots_mod_p; // print "roots mod p", p,q_p; /* add in the contribution of the projective roots */ d := Degree( f ); if Coefficient(f, d) mod p eq 0 then q_p +:= 1; end if; cont_p := q_p * p / (p * p - 1.0); end if; return cont_p; end function; function CalcAlpha( F, bound, abort_p, abort_alpha, max_p ); Q := PolynomialRing(Integers()); f := Q!Evaluate( F, [X, 1] ); print bound^2; disc := Discriminant( f ); // print "discriminant = ", disc; a_d := Coefficient(f, Degree(f)); primes := [p : p in [1..max_p] | IsPrime(p)]; alpha := 0.0; for p in primes do cont_p := CalcCont_p( p, disc, bound, F, f ); // print "cont_p = ", cont_p; alpha +:= (1.0/(p-1) - cont_p)*Log(p); /* early-abort strategy */ if p eq abort_p and alpha gt abort_alpha then break; end if; end for; return alpha; end function; d := 5; coeffs := []; coeffs[6] := -5142225622472630020004; coeffs[5] := -3356924353646091366162; coeffs[4] := 6545365626333869758617; coeffs[3] := -4722668925346720843884; coeffs[2] := -514856715582822510304; coeffs[1] := 237866611103421300000; m1_Value := 617119742304446938751913; P := PolynomialRing(Integers(),2); F := P!0; for i in [0..d] do F +:= coeffs[i+1]*X^(d-i)*Y^i; end for; eval := Evaluate(F,[m1_Value,1]); print eval; alpha := CalcAlpha( F, 2500, 11, -0.5, 100 ); print alpha; alpha := CalcAlpha( F, 10000, 0, 0, 2000 ); print alpha; Output: Magma V2.10-6 Thu Mar 25 2004 00:39:11 on modular [Seed = 2103397693] ------------------------------------- 2129024631825875754749788201627151749780670396327721627823338321538194998405649\ 5911366573853021918316783107387995317230889569230873441936471 6250000 2994117 631769 1665143 2338996 4372688 4295491 2796895 4007202 4260982 2135295 6098712 773279 6008199 566450 4117598 2324649 5947741 5826539 800327 4770666 4320295 5709574 696181 3947497 5720422 5743383 2549765 2052364 5918677 2292255 1671295 600177 3782584 5505243 2175967 5160111 1792099 1305600 1719197 117152 4489571 1799810 2978947 5429736 1250981 4851035 1649840 2135129 3359639 4038080 962361 5600572 4193315 5835414 6153717 3105286 5193920 4207677 5811532 1445719 2007853 6200246 471232 5815485 590467 5146200 1357257 876163 1500427 2236489 3155111 1913159 137469 2011816 5847974 3363271 2675037 3978139 1407275 4987892 3938648 6013583 6201163 2390035 2430853 1949091 185535 308806 4392947 2337940 1184756 3688389 2531058 3758231 5220868 334881 3858323 4653430 4494737 74613 5507165 4323571 4202539 969741 938865 3947239 5635253 3560012 1245989 4969731 5968178 4012955 913423 5222859 1754620 4560841 3967246 5353913 5871503 3923547 4764908 1138695 5060349 908735 418271 4703308 1206813 1485454 778087 129700 1910319 4078744 2554393 2645916 2942611 2637828 5244343 5480258 1034585 1872498 5643118 4257689 5884665 4792972 2057792 3508151 4881883 5770606 5753887 3623143 4351209 4741361 920189 1834056 2874623 2212957 4784363 2189716 3881544 2298745 863509 4143947 2308630 634439 3206335 2633442 172570 5770347 4239729 5208659 5100827 1189273 124329 3304642 1370120 5420021 4235216 2851277 3649627 2795585 1807501 278593 5218552 4014299 1631678 5152873 1881726 2056787 2880157 725251 942477 4817132 2647996 473479 5333899 984937 4801574 3094355 1019819 4026682 274813 1559134 6054259 1453795 5478384 559709 5716587 1723613 3524683 4151700 5278528 843661 3331421 5896922 5739044 1972873 2062580 6081963 2471516 2371883 727863 146866 323561 1035148 2741163 5490848 5229199 1060471 3384418 3448239 2184381 2194744 6249117 3378425 1114114 637577 3861353 1196557 3139386 4189999 4174489 2285879 2362086 4436081 2248510 2513397 5772477 655930 2900737 4192060 343219 1599910 4283110 5384003 970727 2246758 2283114 3313247 4200567 3508180 3762007 3694535 2870091 927781 6105813 4728806 4017301 1769398 160475 3600232 241963 1490048 4422941 5370635 5835448 5322285 2546248 583489 100387 3899697 4656298 1267785 5998755 4727381 3059702 1571083 3698707 3519814 2739308 2529115 1343499 1138999 2804933 5112588 872466 4346645 3098860 6232521 4562209 1459516 2235841 3895112 4984309 771406 4135031 2643648 3742515 3222262 1042873 1870069 2533764 3092419 3219514 6191589 2906189 6023224 4863632 2160555 4646446 1345697 6060427 4591115 2285541 1305980 3895331 6049992 4133427 1507997 2882780 5950433 2114592 1570601 1669249 6099091 2061898 1482583 377674 1171967 3658350 2494267 2099840 3175691 4356061 3101266 2616656 1647041 1695299 1134720 5738252 2694685 1026975 2713172 3459417 1471508 574813 2297992 4176188 4033497 4777341 3657572 1263289 5537876 5374865 3811142 3228541 1463171 513605 5476302 1092391 5539081 3900945 2975039 2083699 5653362 5388871 3249414 4644274 2926583 1363300 2375917 3546983 3888030 5551541 4047274 2142256 2942385 5840312 857603 4396361 5114877 3045157 93996 4565926 825349 4170361 994470 2978017 3529611 3381731 839543 1073308 3140277 4626556 2837625 1096145 5151831 521897 5149345 839986 913343 830621 2025269 4618045 5787882 726115 779382 768880 3871857 3656607 3461740 1049129 3894375 1765679 2762182 1333671 1620595 2620976 3371923 3598597 1237356 4016011 5236944 5175306 1759379 5592942 463877 2453459 2172883 923799 1307323 6119472 3097151 4751637 62867 6018287 1937241 1233113 5587328 3731941 2210709 382639 1125741 3946582 2429159 4390291 4236216 3624304 2662451 5794756 584889 4143039 4960367 1089411 5948998 2152877 3898798 1907902 1192265 4989377 6170511 2772725 1726959 5148614 6184515 3421219 699787 5184887 3922000 333360 4115309 3701360 5448689 3313186 1556547 3171793 1959438 3438769 2353645 6198995 6172546 6211963 3456815 1952918 156085 5569337 3288552 5789629 4461447 2190767 5320616 3393184 1131053 6000308 1725863 5132799 5074001 677350 4001429 3137914 71985 1054319 3448031 4673875 168069 4821121 3201539 2345839 4406877 1690937 5178093 883795 5389634 1146047 6207461 2525345 5519393 6177901 3190780 1073780 1645789 2464944 3477799 1474709 5815026 2974913 4816352 947776 5455155 5720035 2005961 1447036 3561653 6193787 4270316 2547044 810203 3076419 2948623 4611275 5680719 1579797 5091328 6246823 5821855 2895865 5746609 436855 4249813 5582815 230358 2023069 1414348 3064825 33163 1179053 2380501 4951517 5627052 4708173 5238395 1345999 854748 1546716 4750543 842578 1954057 4722109 1551434 1605233 3116543 192887 2602330 1753217 5045383 5142045 186212 6160565 836106 354599 3774087 5841359 3060585 1796231 6042461 4914231 1602835 4349109 3046112 937217 5587895 2693756 2663831 5525532 4554847 229394 1186021 4013731 3126926 4937219 5222255 2787632 3710207 4330507 5612969 2327948 1879195 202145 1965858 3749996 3411571 1386829 3654785 4144711 5566546 4036633 377508 4507963 908673 5918505 2629807 2720152 238637 3371083 1416178 2364662 1820169 4957287 1263191 692776 1064345 2982344 803041 295561 3940149 2345980 4535539 1986935 5117646 301757 1256984 2566105 1723701 1532433 6182066 5319199 175279 2157171 2379653 4452755 1085204 4124153 4971803 6180646 5260893 2054605 2875594 3720830 1375253 2288780 1636291 4213391 5607491 2301985 5470918 4990919 1059981 5093813 5820273 6021590 224877 3377515 2239883 3571722 1628677 4553868 5550881 2631913 3350162 171811 321732 4366942 4310247 5709979 5403459 795860 4352627 1217089 1918071 5842165 1710967 5963212 5719727 2669509 1116498 3419836 5749881 1573999 3080964 982419 306554 4754825 4887719 4501859 4887744 1607407 1635012 6237785 1666599 218035 1419042 1880053 5883446 4737978 3070253 1949872 1741831 1775751 908366 513647 4481204 3080705 353846 2894589 1697764 4867351 3579424 3234300 3101627 3444858 5561485 4306329 5090039 1867196 2602177 2573354 4294539 4082811 4473215 1510130 3683729 544992 6112453 5013686 1857661 976684 115829 5342593 5726563 1718696 125143 2967979 5779545 3728608 1442253 5039653 1925731 650264 2944829 5899567 2611029 2588343 4030903 5400733 5223709 1599853 2825359 353497 4211376 810751 4819416 351698 2435603 4702609 552549 4316374 1385601 5997941 1760871 2907253 2796424 6026747 3157833 2297126 5303567 5758571 3602962 505553 4409269 3101204 2035979 4319058 1746421 150339 2765293 3465657 2553056 5250938 715063 2191517 424410 320293 3449048 2236187 2756117 1571065 525492 4188076 4844905 5898624 4378735 951262 1747209 4482981 471682 603715 3825267 5201397 4521778 1395133 2325550 2228959 221231 1244821 3569725 3693156 3011675 3749981 5463172 18657 133081 5002723 1977042 3787567 1904947 226859 110742 5452196 6042943 3457528 5097947 653607 4590430 1900802 991603 2584268 1780819 6163338 3975743 5055972 1536955 738539 358675 3770051 4939855 6054149 4606025 2897888 55625 1900087 3696946 4225175 4263133 4513058 4899175 5747207 5999642 1282175 811391 4962683 1762100 3000604 4394947 2703235 5913619 1211483 422281 4429441 3350897 2381684 5720789 2791366 1422177 525152 2265737 400027 1317979 899175 2442256 592730 3417871 3035659 707217 6065752 5591121 1663999 3410369 4539644 2867479 534133 4809459 426593 2878149 322646 5218077 4949362 3034805 5264711 5370240 2581173 4843130 4187194 2938021 5001376 770295 3312880 1076101 2400341 18210 644599 5550587 7591 3993717 4876203 4723745 1785346 3145619 1573103 3362423 3048825 2712746 4092551 3604357 5578527 620581 56191 4459574 2269453 4528604 3369565 526272 2297991 3059510 2667922 1080529 2144318 593317 2581172 4771017 2493495 107003 6057011 3950923 5371733 3507829 3160431 5505268 611436 1613215 5892779 4546901 1237163 1721151 5988025 3690038 4542699 4237838 1614551 2036859 617889 2886109 187127 912725 6183995 2386038 5721619 1029172 3884867 5131195 4060693 5390881 407104 1415941 4809214 3934911 3884189 2282923 4620430 5327639 2311147 1711597 5506577 591036 2868036 304883 1973099 5384520 1970066 5001569 4008443 428530 2262141 1237135 5448809 4364113 961739 5038596 1386891 5193131 3459087 1253836 2936570 1579577 3626431 2693181 4756897 417623 3288943 965645 4092616 809697 5518374 4053767 433575 2195968 5909100 1076813 5701138 1101233 5401387 5372958 1172049 2745251 1667213 2979420 1830255 4384463 5508857 4622847 4897569 2749201 5106905 6026121 2291891 4730794 2987186 6002975 4850956 5377007 4104781 5764164 1758824 5523181 6055513 4633522 3281206 3782309 2047142 675011 1679857 3888380 5084017 701201 5374506 387563 2021975 5264421 1009707 3968534 5644041 625216 3689212 1765799 3462988 1864897 3212718 900607 6067233 4558334 5329002 2132357 504632 4527201 1265771 3612606 6232044 3330763 3494131 6003513 2863229 717074 4779562 1413955 2409862 3261613 2780229 1080295 6129476 374337 6057955 4047332 5197438 3556149 1611394 1685941 3813990 5179211 2374655 4708647 1581125 6188058 268239 1810873 5799719 3971659 4560176 4275695 3080692 2166319 2562811 164032 6210277 2867896 3112963 1195920 529808 4706997 3272371 1660808 2879498 1319977 977078 3247565 1814318 481815 1819007 703027 2391742 5748983 4918027 2220295 4951882 1174067 3097777 5884274 3061133 4711528 4737703 1915737 513959 5111313 4801051 5234687 291895 326061 366157 5171399 4551857 5010492 2563448 1402867 4956549 5335537 4802511 2872741 4061264 1209653 5569475 2613076 5571200 3266411 1466740 1862397 3583973 1749995 2524770 315883 5256991 1975692 2992735 4643987 981976 5413411 2431640 5455387 199493 1940956 4882443 6088775 5267709 4812419 488999 125621 2747173 5363218 2216081 5263407 762299 5541128 469987 2128491 2697457 1859810 5945834 2940071 1482075 227644 3400924 4880529 1542783 4453253 1881986 2628257 6067022 1136329 3715214 524055 3025752 49153 5104457 2673081 2713190 1311189 5373711 5930584 1529149 2131762 4112926 5423275 718720 4160989 4022171 744436 2521837 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host pcd595076.netvigator.com. (218.102.127.76) Time: Thu Mar 25 00:51:09 2004 Input: 108809 mod 291452 Output: Magma V2.10-6 Thu Mar 25 2004 00:51:06 on modular [Seed = 1614959381] ------------------------------------- 108809 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pcd595076.netvigator.com. (218.102.127.76) Time: Thu Mar 25 00:51:25 2004 Input: 108809 mod 291452 Output: Magma V2.10-6 Thu Mar 25 2004 00:51:22 on modular [Seed = 1315732779] ------------------------------------- 108809 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pcd595076.netvigator.com. (218.102.127.76) Time: Thu Mar 25 00:52:11 2004 Input: 8107 * 108809 mod 291452 Output: Magma V2.10-6 Thu Mar 25 2004 00:52:08 on modular [Seed = 1147566067] ------------------------------------- 180811 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pcd595076.netvigator.com. (218.102.127.76) Time: Thu Mar 25 00:52:52 2004 Input: 17*33 mod 35 Output: Magma V2.10-6 Thu Mar 25 2004 00:52:49 on modular [Seed = 3147401269] ------------------------------------- 1 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Thu Mar 25 01:06:33 2004 Input: function CalcCont_p( p, disc, bound, F, f ); if disc mod p eq 0 then /* estimate using some small sample space */ cont_p := 0; upper_limit := bound^2; for i in [1..bound] do repeat a := Random( upper_limit ); b := Random( upper_limit ); until Gcd( a, b ) eq 1; // print a,b; value := Evaluate( F, [a, b] ); while value mod p eq 0 do value div:= p; cont_p +:= 1; end while; end for; cont_p := cont_p / (0.0 + bound); else K := GF(p); roots_mod_p := Roots( f, K ); q_p := #roots_mod_p; // print "roots mod p", p,q_p; /* add in the contribution of the projective roots */ d := Degree( f ); if Coefficient(f, d) mod p eq 0 then q_p +:= 1; end if; cont_p := q_p * p / (p * p - 1.0); end if; print cont_p; return cont_p; end function; function CalcAlpha( F, bound, abort_p, abort_alpha, max_p ); Q := PolynomialRing(Integers()); f := Q!Evaluate( F, [X, 1] ); print bound^2; disc := Discriminant( f ); // print "discriminant = ", disc; a_d := Coefficient(f, Degree(f)); primes := [p : p in [1..max_p] | IsPrime(p)]; alpha := 0.0; for p in primes do cont_p := CalcCont_p( p, disc, bound, F, f ); // print "cont_p = ", cont_p; alpha +:= (1.0/(p-1) - cont_p)*Log(p); /* early-abort strategy */ if p eq abort_p and alpha gt abort_alpha then break; end if; end for; return alpha; end function; d := 5; coeffs := []; coeffs[6] := -5142225622472630020004; coeffs[5] := -3356924353646091366162; coeffs[4] := 6545365626333869758617; coeffs[3] := -4722668925346720843884; coeffs[2] := -514856715582822510304; coeffs[1] := 237866611103421300000; m1_Value := 617119742304446938751913; P := PolynomialRing(Integers(),2); F := P!0; for i in [0..d] do F +:= coeffs[i+1]*X^(d-i)*Y^i; end for; eval := Evaluate(F,[m1_Value,1]); print eval; alpha := CalcAlpha( F, 2500, 11, -0.5, 100 ); print alpha; alpha := CalcAlpha( F, 10000, 0, 0, 2000 ); print alpha; Output: Magma V2.10-6 Thu Mar 25 2004 01:06:27 on modular [Seed = 3707693568] ------------------------------------- 2129024631825875754749788201627151749780670396327721627823338321538194998405649\ 5911366573853021918316783107387995317230889569230873441936471 6250000 2.0419999999999999999999999999999999999966 1.1250000000000000000000000000000000000000 0.416666666666666666666666666666666666666 0.547999999999999999999999999999999999997 0.1727999999999999999999999999999999999997 0.2321428571428571428571428571428571428566 0.0971999999999999999999999999999999999999 0.1583333333333333333333333333333333333332 0.0435606060606060606060606060606060606059 0.0690476190476190476190476190476190476188 0 0 0.0488095238095238095238095238095238095235 0.0465367965367965367965367965367965367963 0.0638586956521739130434782608695652173910 0.01887464387464387464387464387464387464373 0.0508620689655172413793103448275862068962 0.0327956989247311827956989247311827956987 0 0.01408730158730158730158730158730158730149 0 0.0379807692307692307692307692307692307690 0.01204994192799070847851335656213704994189 0.02247474747474747474747474747474747474746 0 -3.79331772110761179466671022155 100000000 2.001899999999999999999999999999999999994809 1.1250000000000000000000000000000000000000 0.416666666666666666666666666666666666666 0.561199999999999999999999999999999999999 0.1825999999999999999999999999999999999996 0.2321428571428571428571428571428571428566 0.1144999999999999999999999999999999999997 0.1583333333333333333333333333333333333332 0.0435606060606060606060606060606060606059 0.0690476190476190476190476190476190476188 0 0 0.0488095238095238095238095238095238095235 0.0465367965367965367965367965367965367963 0.0638586956521739130434782608695652173910 0.01887464387464387464387464387464387464373 0.0508620689655172413793103448275862068962 0.0327956989247311827956989247311827956987 0 0.01408730158730158730158730158730158730149 0 0.0379807692307692307692307692307692307690 0.01204994192799070847851335656213704994189 0.02247474747474747474747474747474747474746 0 0.01980392156862745098039215686274509803915 0.01941930618401206636500754147812971342376 0.00934661076170510132774283717679944095035 0.00917508417508417508417508417508417508410 0.0265507518796992481203007518796992481202 0 0.01526806526806526806526806526806526806524 0.00729965899403239556692242114236999147479 0 0.00671171171171171171171171171171171171165 0.01986842105263157894736842105263157894729 0 0 0.00598823866896156052782558806655192197359 0.00578053996257685110932905640203154236831 0.01117353308364544319600499375780274656678 0.00552503052503052503052503052503052503051 0 0 0 0.01005050505050505050505050505050505050501 0 0.00448439510939510939510939510939510939509 0.01321611551001397298556124825337680484389 0 0 0 0.01244834710743801652892561983471074380162 0.00796825396825396825396825396825396825390 0.00778221899224806201550387596899224806196 0 0.00743504698728579325594250967385295743500 0.00738017429193899782135076252723311546839 0 0.00355876393110435663627152988855116514689 0.00353361302567176106283088602537209070021 0.00341300903923213120864784269872332494639 0.00325736355148119854002206943383413971648 0.00321546732837055417700578990901571546730 0 0.00630921105007563092110500756309211050072 0.00604235122307411464037970062066447608610 0.00296738517892364046210200056353902507746 0 0.00286535303776683087027914614121510673232 0.00283288392398561890087313816127375449408 0.00278553693358162631905648665425201738049 0.00544963174150629603231171299596103587548 0.00268098441722730147777586107756885745498 0.00527708159287106655527708159287106655524 0.00783295157068062827225130890052356020935 0.00257071107586571504097277293153581813373 0.00251890766966143850565961118724937820414 0 0 0 0 0 0.002309481140126301416623997269158559481126 0.002277916147779161477791614777916147779145 0.00677204353674941910236027883086706616116 0.00445436507936507936507936507936507936504 0 0 0.002159837289147633975220182116733840871756 0 0.00417538354253835425383542538354253835424 0.002053396748296566147203669972340281994180 0.002036668325866932138709142193462750954035 0.002004016064257028112449799196787148594366 0.00596423828495541642952001517738569531395 0.00589393237610004631773969430291801760069 0 0.001912052879412710947325319528530899944426 0 0.001828159674875003342156626828159674874991 0.00359067584641963848276217735489028132330 0 0.001757474672596985421299728193723745984675 0.00525395656974604343025395656974604343021 0 0.001703582456873534396693831116064173109514 0.00337269087269087269087269087269087269085 0.001669453734671125975473801560758082497208 0 0.001647450929303456661455619246135139829764 0 0.001620749800361450846887740091623586769209 0 0.001584790034157122764717701426562186055846 0.001560066199376947040498442367601246105913 0.00466564114471469205317234573634411098855 0.001545598746321140541986775216909375836097 0.001531397159527963828070767903041218738852 0.001517454177028645113751496730220134475451 0 0.00297177476331779002402147802741274551361 0.001477108097257859000541097205494754848046 0.001464131981958807086141551336797516763551 0 0 0.001410440041378212779501869976923689026807 0 0.001375518420972966427511882057336602791138 0.00409277705811408406664582123553848215479 0 0 0 0.001321006268235819687007022099370384330797 0.00262812543168945987014781047105953861028 0 0.001293663225823727088939765165816497302211 0 0.00250941423911537638065011775670331607912 0.002472191663610805524996944138858330277458 0 0 0.00364520586776273828927786832967188718018 0.00362757483243850229848756009404498719160 0.002412548745707467551364879809091438216613 0.001191896806455279008978292987839527218996 0.00351700366131213510571626480192631197017 0.00350058819684987909286974707535455199005 0.001164145931587792052908331978099419959880 0.001158750107416000687462404399759388158456 0.002280504675424636731467324034491007998652 0.001135075242218099360956503813646670789519 0.001132504283764787966468638737546300571504 0.001127397148841844101437780896020173672541 0 0.00329308849045691150954308849045691150953 0.001088140570237756938524201951311925736474 0.001076427512050426399703374119391916944748 0 0.00531350228124858833626959389257803677099 0 0.001049319098708665856279618765745291827419 0 0 0 0.002034590101501829682247942642359213816157 0.00302724828934506353861192570869990224827 0 0 0.001974335586375720154984369031191773666669 0 0.001958865738076052338743716664748091017221 0.00290979905170467374125084669225558816886 0.000968055118228299821570479660534089034826 0.00288739439751000444642063139172965762559 0.00285986913849509269356597600872410032713 0 0.000942507906051238318587215293323384145254 0.000940734604873766336745819350636478201146 0.000935454513633658861003185270748013581152 0.00275989194020149496262593435164120896975 0.00274977316261719931444702086903921766305 0.001829827698200641527881015998017826171376 0.00273473335726536635953890949702843923255 0.000906619058891606828164864935953076093525 0.000901713988356587634565973916154421569579 0.000895255865248363372894505677701476651208 0 0.001771480574907424841523881252745873344614 0 0.001734606682072020026959368380512227999221 0.001719691727144217518084118506426294278726 0 0 0 0 0 0.000824402868622941371567140239559376036442 0.000821693241725002160573848414138795264015 0.002452986104425403549308430409807130708239 0 0 0 0.000800641025641025641025641025641025641019 0 0.001566171673019657478132465990649574913770 0.002345583920187793427230046948356807511722 0.000779423700312498481247661121398126953111 0 0 0.001542020962924917727177614183263900778015 0.000768639962188349285123478671865768639956 0.000767460160395050559309415434489647828256 0.000765111388978649470100360135062356285499 0.000758150549501080608819607302156619303807 0.000757002704809058818135973960482281208450 0.000753579930582056733722219193516146032084 0 0.000731529286857945253568278920825734419010 0 0 0.002144389944819129368485591661557326793366 0.000709723565441650548033526756931012250156 0 0 0.002099371217018275841805253569959452312378 0.000697837046040687844292248116375649626384 0.00347463684129191778704991500540874671609 0 0 0.000688231571687867798909439524670236187049 0 0.002039429902395740905057675244010647737342 0.001350439508334245176350439508334245176340 0.000674309140048961300202611026841414130386 0.001344990520846900823456200523886018610972 0.000671591975175001804142310745471602800025 0 0.001334223408989764129951045838896306186016 0.001323627317004800448509057780580959388899 0.001313198202392900624609834414587795448036 0.000653168142801071690643185037287325722277 0.000648088412195990672231070610135548342438 0 0 0 0.000638162353063830896343211614147574738700 0.001273074990680864167517544286154195231829 0 0.001263424382893409442082008453689869619064 0.000626174321912415582134309490873617084003 0.000624609862671660424469413233458177278397 0.001244555553490331654306301617689881848533 0.000621504279843020920243502981984487500382 0.000619963040517063781244138601135843011363 0 0.001233806761961303679347246959248603309423 0 0.000610873777132945837102316319920231900665 0.001810501564657960525165643957273474239949 0 0 0 0 0.001178550792275040558259439518190101562321 0.000588581722441626827409408993279290514787 0 0.001162115441752424168759960024849417929392 0 0.001154068474285516407350876772390793024174 0 0.001144820066002448224251050455962107569827 0.001140901683301833252630647235542504282438 0.001137010032061226600475747233426414313779 0 0.000560852672212911375841121730508875501398 0 0 0.001110494512270316931804168208163768652109 0 0.001097093034452211758815259884068018564519 0 0.000541418675221492122900573604798956911629 0.000537345668318261090514304193663883210324 0.001606856379572698417070030364163401887940 0.001068947392476804241510123863065039535624 0 0.001065530403664016748752812841316012361738 0.000532198128384655473228649763215734257805 0 0.000526039072444518235652222037744202778233 0.000524383993171733970403514445170387 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Thu Mar 25 01:09:56 2004 Input: function CalcCont_p( p, disc, bound, F, f ); if disc mod p eq 0 then /* estimate using some small sample space */ cont_p := 0; upper_limit := bound^2; for i in [1..bound] do repeat a := Random( upper_limit ); b := Random( upper_limit ); until Gcd( a, b ) eq 1; // print a,b; value := Evaluate( F, [a, b] ); while value mod p eq 0 do value div:= p; cont_p +:= 1; end while; end for; cont_p := cont_p / (0.0 + bound); else K := GF(p); roots_mod_p := Roots( f, K ); q_p := #roots_mod_p; // print "roots mod p", p,q_p; /* add in the contribution of the projective roots */ d := Degree( f ); if Coefficient(f, d) mod p eq 0 then q_p +:= 1; end if; cont_p := q_p * p / (p * p - 1.0); end if; print p,cont_p; return cont_p; end function; function CalcAlpha( F, bound, abort_p, abort_alpha, max_p ); Q := PolynomialRing(Integers()); f := Q!Evaluate( F, [X, 1] ); print bound^2; disc := Discriminant( f ); // print "discriminant = ", disc; a_d := Coefficient(f, Degree(f)); primes := [p : p in [1..max_p] | IsPrime(p)]; alpha := 0.0; for p in primes do cont_p := CalcCont_p( p, disc, bound, F, f ); // print "cont_p = ", cont_p; alpha +:= (1.0/(p-1) - cont_p)*Log(p); /* early-abort strategy */ if p eq abort_p and alpha gt abort_alpha then break; end if; end for; return alpha; end function; d := 5; coeffs := []; coeffs[6] := -5142225622472630020004; coeffs[5] := -3356924353646091366162; coeffs[4] := 6545365626333869758617; coeffs[3] := -4722668925346720843884; coeffs[2] := -514856715582822510304; coeffs[1] := 237866611103421300000; m1_Value := 617119742304446938751913; P := PolynomialRing(Integers(),2); F := P!0; for i in [0..d] do F +:= coeffs[i+1]*X^(d-i)*Y^i; end for; eval := Evaluate(F,[m1_Value,1]); print eval; alpha := CalcAlpha( F, 2500, 11, -0.5, 100 ); print alpha; alpha := CalcAlpha( F, 10000, 0, 0, 2000 ); print alpha; Output: Magma V2.10-6 Thu Mar 25 2004 01:09:51 on modular [Seed = 3539002690] ------------------------------------- 2129024631825875754749788201627151749780670396327721627823338321538194998405649\ 5911366573853021918316783107387995317230889569230873441936471 6250000 2 1.996799999999999999999999999999999999996 3 1.1250000000000000000000000000000000000000 5 0.416666666666666666666666666666666666666 7 0.581599999999999999999999999999999999997 11 0.1607999999999999999999999999999999999996 13 0.2321428571428571428571428571428571428566 17 0.1163999999999999999999999999999999999996 19 0.1583333333333333333333333333333333333332 23 0.0435606060606060606060606060606060606059 29 0.0690476190476190476190476190476190476188 31 0 37 0 41 0.0488095238095238095238095238095238095235 43 0.0465367965367965367965367965367965367963 47 0.0638586956521739130434782608695652173910 53 0.01887464387464387464387464387464387464373 59 0.0508620689655172413793103448275862068962 61 0.0327956989247311827956989247311827956987 67 0 71 0.01408730158730158730158730158730158730149 73 0 79 0.0379807692307692307692307692307692307690 83 0.01204994192799070847851335656213704994189 89 0.02247474747474747474747474747474747474746 97 0 -3.85299300248685969594463892356 100000000 2 1.981499999999999999999999999999999999999 3 1.1250000000000000000000000000000000000000 5 0.416666666666666666666666666666666666666 7 0.567999999999999999999999999999999999999 11 0.1715999999999999999999999999999999999997 13 0.2321428571428571428571428571428571428566 17 0.1091999999999999999999999999999999999996 19 0.1583333333333333333333333333333333333332 23 0.0435606060606060606060606060606060606059 29 0.0690476190476190476190476190476190476188 31 0 37 0 41 0.0488095238095238095238095238095238095235 43 0.0465367965367965367965367965367965367963 47 0.0638586956521739130434782608695652173910 53 0.01887464387464387464387464387464387464373 59 0.0508620689655172413793103448275862068962 61 0.0327956989247311827956989247311827956987 67 0 71 0.01408730158730158730158730158730158730149 73 0 79 0.0379807692307692307692307692307692307690 83 0.01204994192799070847851335656213704994189 89 0.02247474747474747474747474747474747474746 97 0 101 0.01980392156862745098039215686274509803915 103 0.01941930618401206636500754147812971342376 107 0.00934661076170510132774283717679944095035 109 0.00917508417508417508417508417508417508410 113 0.0265507518796992481203007518796992481202 127 0 131 0.01526806526806526806526806526806526806524 137 0.00729965899403239556692242114236999147479 139 0 149 0.00671171171171171171171171171171171171165 151 0.01986842105263157894736842105263157894729 157 0 163 0 167 0.00598823866896156052782558806655192197359 173 0.00578053996257685110932905640203154236831 179 0.01117353308364544319600499375780274656678 181 0.00552503052503052503052503052503052503051 191 0 193 0 197 0 199 0.01005050505050505050505050505050505050501 211 0 223 0.00448439510939510939510939510939510939509 227 0.01321611551001397298556124825337680484389 229 0 233 0 239 0 241 0.01244834710743801652892561983471074380162 251 0.00796825396825396825396825396825396825390 257 0.00778221899224806201550387596899224806196 263 0 269 0.00743504698728579325594250967385295743500 271 0.00738017429193899782135076252723311546839 277 0 281 0.00355876393110435663627152988855116514689 283 0.00353361302567176106283088602537209070021 293 0.00341300903923213120864784269872332494639 307 0.00325736355148119854002206943383413971648 311 0.00321546732837055417700578990901571546730 313 0 317 0.00630921105007563092110500756309211050072 331 0.00604235122307411464037970062066447608610 337 0.00296738517892364046210200056353902507746 347 0 349 0.00286535303776683087027914614121510673232 353 0.00283288392398561890087313816127375449408 359 0.00278553693358162631905648665425201738049 367 0.00544963174150629603231171299596103587548 373 0.00268098441722730147777586107756885745498 379 0.00527708159287106655527708159287106655524 383 0.00783295157068062827225130890052356020935 389 0.00257071107586571504097277293153581813373 397 0.00251890766966143850565961118724937820414 401 0 409 0 419 0 421 0 431 0 433 0.002309481140126301416623997269158559481126 439 0.002277916147779161477791614777916147779145 443 0.00677204353674941910236027883086706616116 449 0.00445436507936507936507936507936507936504 457 0 461 0 463 0.002159837289147633975220182116733840871756 467 0 479 0.00417538354253835425383542538354253835424 487 0.002053396748296566147203669972340281994180 491 0.002036668325866932138709142193462750954035 499 0.002004016064257028112449799196787148594366 503 0.00596423828495541642952001517738569531395 509 0.00589393237610004631773969430291801760069 521 0 523 0.001912052879412710947325319528530899944426 541 0 547 0.001828159674875003342156626828159674874991 557 0.00359067584641963848276217735489028132330 563 0 569 0.001757474672596985421299728193723745984675 571 0.00525395656974604343025395656974604343021 577 0 587 0.001703582456873534396693831116064173109514 593 0.00337269087269087269087269087269087269085 599 0.001669453734671125975473801560758082497208 601 0 607 0.001647450929303456661455619246135139829764 613 0 617 0.001620749800361450846887740091623586769209 619 0 631 0.001584790034157122764717701426562186055846 641 0.001560066199376947040498442367601246105913 643 0.00466564114471469205317234573634411098855 647 0.001545598746321140541986775216909375836097 653 0.001531397159527963828070767903041218738852 659 0.001517454177028645113751496730220134475451 661 0 673 0.00297177476331779002402147802741274551361 677 0.001477108097257859000541097205494754848046 683 0.001464131981958807086141551336797516763551 691 0 701 0 709 0.001410440041378212779501869976923689026807 719 0 727 0.001375518420972966427511882057336602791138 733 0.00409277705811408406664582123553848215479 739 0 743 0 751 0 757 0.001321006268235819687007022099370384330797 761 0.00262812543168945987014781047105953861028 769 0 773 0.001293663225823727088939765165816497302211 787 0 797 0.00250941423911537638065011775670331607912 809 0.002472191663610805524996944138858330277458 811 0 821 0 823 0.00364520586776273828927786832967188718018 827 0.00362757483243850229848756009404498719160 829 0.002412548745707467551364879809091438216613 839 0.001191896806455279008978292987839527218996 853 0.00351700366131213510571626480192631197017 857 0.00350058819684987909286974707535455199005 859 0.001164145931587792052908331978099419959880 863 0.001158750107416000687462404399759388158456 877 0.002280504675424636731467324034491007998652 881 0.001135075242218099360956503813646670789519 883 0.001132504283764787966468638737546300571504 887 0.001127397148841844101437780896020173672541 907 0 911 0.00329308849045691150954308849045691150953 919 0.001088140570237756938524201951311925736474 929 0.001076427512050426399703374119391916944748 937 0 941 0.00531350228124858833626959389257803677099 947 0 953 0.001049319098708665856279618765745291827419 967 0 971 0 977 0 983 0.002034590101501829682247942642359213816157 991 0.00302724828934506353861192570869990224827 997 0 1009 0 1013 0.001974335586375720154984369031191773666669 1019 0 1021 0.001958865738076052338743716664748091017221 1031 0.00290979905170467374125084669225558816886 1033 0.000968055118228299821570479660534089034826 1039 0.00288739439751000444642063139172965762559 1049 0.00285986913849509269356597600872410032713 1051 0 1061 0.000942507906051238318587215293323384145254 1063 0.000940734604873766336745819350636478201146 1069 0.000935454513633658861003185270748013581152 1087 0.00275989194020149496262593435164120896975 1091 0.00274977316261719931444702086903921766305 1093 0.001829827698200641527881015998017826171376 1097 0.00273473335726536635953890949702843923255 1103 0.000906619058891606828164864935953076093525 1109 0.000901713988356587634565973916154421569579 1117 0.000895255865248363372894505677701476651208 1123 0 1129 0.001771480574907424841523881252745873344614 1151 0 1153 0.001734606682072020026959368380512227999221 1163 0.001719691727144217518084118506426294278726 1171 0 1181 0 1187 0 1193 0 1201 0 1213 0.000824402868622941371567140239559376036442 1217 0.000821693241725002160573848414138795264015 1223 0.002452986104425403549308430409807130708239 1229 0 1231 0 1237 0 1249 0.000800641025641025641025641025641025641019 1259 0 1277 0.001566171673019657478132465990649574913770 1279 0.002345583920187793427230046948356807511722 1283 0.000779423700312498481247661121398126953111 1289 0 1291 0 1297 0.001542020962924917727177614183263900778015 1301 0.000768639962188349285123478671865768639956 1303 0.000767460160395050559309415434489647828256 1307 0.000765111388978649470100360135062356285499 1319 0.000758150549501080608819607302156619303807 1321 0.000757002704809058818135973960482281208450 1327 0.000753579930582056733722219193516146032084 1361 0 1367 0.000731529286857945253568278920825734419010 1373 0 1381 0 1399 0.002144389944819129368485591661557326793366 1409 0.000709723565441650548033526756931012250156 1423 0 1427 0 1429 0.002099371217018275841805253569959452312378 1433 0.000697837046040687844292248116375649626384 1439 0.00347463684129191778704991500540874671609 1447 0 1451 0 1453 0.000688231571687867798909439524670236187049 1459 0 1471 0.002039429902395740905057675244010647737342 1481 0.001350439508334245176350439508334245176340 1483 0.000674309140048961300202611026841414130386 1487 0.001344990520846900823456200523886018610972 1489 0.000671591975175001804142310745471602800025 1493 0 1499 0.001334223408989764129951045838896306186016 1511 0.001323627317004800448509057780580959388899 1523 0.001313198202392900624609834414587795448036 1531 0.000653168142801071690643185037287325722277 1543 0.000648088412195990672231070610135548342438 1549 0 1553 0 1559 0 1567 0.000638162353063830896343211614147574738700 1571 0.001273074990680864167517544286154195231829 1579 0 1583 0.001263424382893409442082008453689869619064 1597 0.000626174321912415582134309490873617084003 1601 0.000624609862671660 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host pcd595076.netvigator.com. (218.102.127.76) Time: Thu Mar 25 01:15:59 2004 Input: 107381 * 108809 mod 291452 Output: Magma V2.10-6 Thu Mar 25 2004 01:15:56 on modular [Seed = 1901283372] ------------------------------------- 1 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pcd595076.netvigator.com. (218.102.127.76) Time: Thu Mar 25 01:16:09 2004 Input: 108809 mod 291452 Output: Magma V2.10-6 Thu Mar 25 2004 01:16:06 on modular [Seed = 2019180831] ------------------------------------- 108809 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pcd595076.netvigator.com. (218.102.127.76) Time: Thu Mar 25 01:16:31 2004 Input: 107381 * 108809 mod 291452 Output: Magma V2.10-6 Thu Mar 25 2004 01:16:28 on modular [Seed = 52509310] ------------------------------------- 1 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Thu Mar 25 01:30:05 2004 Input: function CalcCont_p( p, disc, bound, F, f ); if disc mod p eq 0 then /* estimate using some small sample space */ cont_p := 0; upper_limit := bound^2; for i in [1..bound] do repeat a := Random( upper_limit ); b := Random( upper_limit ); until Gcd( a, b ) eq 1; // print a,b; value := Evaluate( F, [a, b] ); while value mod p eq 0 do value div:= p; cont_p +:= 1; end while; end for; cont_p := cont_p / (0.0 + bound); else K := GF(p); roots_mod_p := Roots( f, K ); q_p := #roots_mod_p; // print "roots mod p", p,q_p; /* add in the contribution of the projective roots */ d := Degree( f ); if Coefficient(f, d) mod p eq 0 then q_p +:= 1; end if; cont_p := q_p * p / (p * p - 1.0); end if; // print p,cont_p; return cont_p; end function; function CalcAlpha( F, bound, abort_p, abort_alpha, max_p ); Q := PolynomialRing(Integers()); f := Q!Evaluate( F, [X, 1] ); print bound^2; disc := Discriminant( f ); // print "discriminant = ", disc; a_d := Coefficient(f, Degree(f)); primes := [p : p in [1..max_p] | IsPrime(p)]; alpha := 0.0; for p in primes do cont_p := CalcCont_p( p, disc, bound, F, f ); // print "cont_p = ", cont_p; alpha +:= (1.0/(p-1) - cont_p)*Log(p); /* early-abort strategy */ if p eq abort_p and alpha gt abort_alpha then break; end if; end for; return alpha; end function; function RatePolynomials( F1, F2, alpha, B1, B2, d ) pi := Pi(RealField()); K := 1000; rating := 0.0; logB1 := Log( B1 ); logB2 := Log( B2 ); for i in [1..K] do theta := pi/K*(i - 0.5); tmp := Abs( Evaluate( F1, [Cos( theta ), Sin( theta ) ] ) ); u1 := ( Log( tmp ) + alpha ) / logB1 + d; tmp := Abs( Evaluate( F2, [Cos( theta ), Sin( theta ) ] ) ); u2 := Log( tmp ) / logB2 + 1.0; rating +:= ApproxDickmanRho( u1 ) * ApproxDickmanRho( u2 ); end for; return rating/K; end function; n:=21290246318258757547497882016271517497806703963277216278233383215381949984056495911366573853021918316783107387995317230889569230873441936471 d := Round( Root( 3 * Log(n)/Log(Log(n)) , 3 ) ); print "degree ", d; dlogd := d*Log(d); temp := 1.0/d * Log( n ); e := dlogd + Sqrt( dlogd^2 + 4*temp*Log(temp) ); B := Round( Exp( 0.5*e ) ); //d := 5; coeffs := []; coeffs[6] := -5142225622472630020004; coeffs[5] := -3356924353646091366162; coeffs[4] := 6545365626333869758617; coeffs[3] := -4722668925346720843884; coeffs[2] := -514856715582822510304; coeffs[1] := 237866611103421300000; m1_Value := 617119742304446938751913; P := PolynomialRing(Integers(),2); F := P!0; for i in [0..d] do F +:= coeffs[i+1]*X^(d-i)*Y^i; end for; eval := Evaluate(F,[m1_Value,1]); print eval; F2 := X*1 - Y*m1_Value; alpha := CalcAlpha( F, 2500, 11, -0.5, 100 ); print alpha; alpha := CalcAlpha( F, 10000, 0, 0, 2000 ); print alpha; rating := RatePolynomials( F, F2, alpha, B, B, d ); print rating; Output: Magma V2.10-6 Thu Mar 25 2004 01:30:02 on modular [Seed = 553852170] ------------------------------------- >> rating +:= ApproxDickmanRho( u1 ) * ApproxDickmanRho( u2 ); ^ User error: Identifier 'ApproxDickmanRho' has not been declared or assigned >> d := Round( Root( 3 * Log(n)/Log(Log(n)) , 3 ) ); ^ User error: bad syntax >> print "degree ", d; ^ User error: Identifier 'd' has not been declared or assigned >> dlogd := d*Log(d); ^ User error: Identifier 'd' has not been declared or assigned >> temp := 1.0/d * Log( n ); ^ User error: Identifier 'd' has not been declared or assigned >> e := dlogd + Sqrt( dlogd^2 + 4*temp*Log(temp) ); ^ User error: Identifier 'dlogd' has not been declared or assigned >> B := Round( Exp( 0.5*e ) ); ^ User error: Identifier 'e' has not been declared or assigned >> for i in [0..d] do ^ User error: Identifier 'd' has not been declared or assigned 0 6250000 CalcAlpha( F: 0, bound: 2500, abort_p: 11, abort_alpha: -0.50000000000000000000000000000, max_p: 100 ) >> disc := Discriminant( f ); ^ Runtime error in 'Discriminant': Degree of argument is less than 1 >> print alpha; ^ User error: Identifier 'alpha' has not been declared or assigned 100000000 CalcAlpha( F: 0, bound: 10000, abort_p: 0, abort_alpha: 0, max_p: 2000 ) >> disc := Discriminant( f ); ^ Runtime error in 'Discriminant': Degree of argument is less than 1 >> print alpha; ^ User error: Identifier 'alpha' has not been declared or assigned >> rating := RatePolynomials( F, F2, alpha, B, B, d ); ^ User error: Identifier 'alpha' has not been declared or assigned >> print rating;; ^ User error: Identifier 'rating' has not been declared or assigned Total time: 3.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Thu Mar 25 01:30:31 2004 Input: function CalcCont_p( p, disc, bound, F, f ); if disc mod p eq 0 then /* estimate using some small sample space */ cont_p := 0; upper_limit := bound^2; for i in [1..bound] do repeat a := Random( upper_limit ); b := Random( upper_limit ); until Gcd( a, b ) eq 1; // print a,b; value := Evaluate( F, [a, b] ); while value mod p eq 0 do value div:= p; cont_p +:= 1; end while; end for; cont_p := cont_p / (0.0 + bound); else K := GF(p); roots_mod_p := Roots( f, K ); q_p := #roots_mod_p; // print "roots mod p", p,q_p; /* add in the contribution of the projective roots */ d := Degree( f ); if Coefficient(f, d) mod p eq 0 then q_p +:= 1; end if; cont_p := q_p * p / (p * p - 1.0); end if; // print p,cont_p; return cont_p; end function; function CalcAlpha( F, bound, abort_p, abort_alpha, max_p ); Q := PolynomialRing(Integers()); f := Q!Evaluate( F, [X, 1] ); print bound^2; disc := Discriminant( f ); // print "discriminant = ", disc; a_d := Coefficient(f, Degree(f)); primes := [p : p in [1..max_p] | IsPrime(p)]; alpha := 0.0; for p in primes do cont_p := CalcCont_p( p, disc, bound, F, f ); // print "cont_p = ", cont_p; alpha +:= (1.0/(p-1) - cont_p)*Log(p); /* early-abort strategy */ if p eq abort_p and alpha gt abort_alpha then break; end if; end for; return alpha; end function; function ApproxDickmanRho( u ); if u le 1.0 then return 1.0; end if; return u^-u; end function; function RatePolynomials( F1, F2, alpha, B1, B2, d ) pi := Pi(RealField()); K := 1000; rating := 0.0; logB1 := Log( B1 ); logB2 := Log( B2 ); for i in [1..K] do theta := pi/K*(i - 0.5); tmp := Abs( Evaluate( F1, [Cos( theta ), Sin( theta ) ] ) ); u1 := ( Log( tmp ) + alpha ) / logB1 + d; tmp := Abs( Evaluate( F2, [Cos( theta ), Sin( theta ) ] ) ); u2 := Log( tmp ) / logB2 + 1.0; rating +:= ApproxDickmanRho( u1 ) * ApproxDickmanRho( u2 ); end for; return rating/K; end function; n:=21290246318258757547497882016271517497806703963277216278233383215381949984056495911366573853021918316783107387995317230889569230873441936471 d := Round( Root( 3 * Log(n)/Log(Log(n)) , 3 ) ); print "degree ", d; dlogd := d*Log(d); temp := 1.0/d * Log( n ); e := dlogd + Sqrt( dlogd^2 + 4*temp*Log(temp) ); B := Round( Exp( 0.5*e ) ); //d := 5; coeffs := []; coeffs[6] := -5142225622472630020004; coeffs[5] := -3356924353646091366162; coeffs[4] := 6545365626333869758617; coeffs[3] := -4722668925346720843884; coeffs[2] := -514856715582822510304; coeffs[1] := 237866611103421300000; m1_Value := 617119742304446938751913; P := PolynomialRing(Integers(),2); F := P!0; for i in [0..d] do F +:= coeffs[i+1]*X^(d-i)*Y^i; end for; eval := Evaluate(F,[m1_Value,1]); print eval; F2 := X*1 - Y*m1_Value; alpha := CalcAlpha( F, 2500, 11, -0.5, 100 ); print alpha; alpha := CalcAlpha( F, 10000, 0, 0, 2000 ); print alpha; rating := RatePolynomials( F, F2, alpha, B, B, d ); print rating; Output: Magma V2.10-6 Thu Mar 25 2004 01:30:28 on modular [Seed = 671749357] ------------------------------------- >> d := Round( Root( 3 * Log(n)/Log(Log(n)) , 3 ) ); ^ User error: bad syntax >> print "degree ", d; ^ User error: Identifier 'd' has not been declared or assigned >> dlogd := d*Log(d); ^ User error: Identifier 'd' has not been declared or assigned >> temp := 1.0/d * Log( n ); ^ User error: Identifier 'd' has not been declared or assigned >> e := dlogd + Sqrt( dlogd^2 + 4*temp*Log(temp) ); ^ User error: Identifier 'dlogd' has not been declared or assigned >> B := Round( Exp( 0.5*e ) ); ^ User error: Identifier 'e' has not been declared or assigned >> for i in [0..d] do ^ User error: Identifier 'd' has not been declared or assigned 0 6250000 CalcAlpha( F: 0, bound: 2500, abort_p: 11, abort_alpha: -0.50000000000000000000000000000, max_p: 100 ) >> disc := Discriminant( f ); ^ Runtime error in 'Discriminant': Degree of argument is less than 1 >> print alpha; ^ User error: Identifier 'alpha' has not been declared or assigned 100000000 CalcAlpha( F: 0, bound: 10000, abort_p: 0, abort_alpha: 0, max_p: 2000 ) >> disc := Discriminant( f ); ^ Runtime error in 'Discriminant': Degree of argument is less than 1 >> print alpha; ^ User error: Identifier 'alpha' has not been declared or assigned >> rating := RatePolynomials( F, F2, alpha, B, B, d ); ^ User error: Identifier 'alpha' has not been declared or assigned >> print rating;; ^ User error: Identifier 'rating' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Thu Mar 25 01:31:03 2004 Input: function CalcCont_p( p, disc, bound, F, f ); if disc mod p eq 0 then /* estimate using some small sample space */ cont_p := 0; upper_limit := bound^2; for i in [1..bound] do repeat a := Random( upper_limit ); b := Random( upper_limit ); until Gcd( a, b ) eq 1; // print a,b; value := Evaluate( F, [a, b] ); while value mod p eq 0 do value div:= p; cont_p +:= 1; end while; end for; cont_p := cont_p / (0.0 + bound); else K := GF(p); roots_mod_p := Roots( f, K ); q_p := #roots_mod_p; // print "roots mod p", p,q_p; /* add in the contribution of the projective roots */ d := Degree( f ); if Coefficient(f, d) mod p eq 0 then q_p +:= 1; end if; cont_p := q_p * p / (p * p - 1.0); end if; // print p,cont_p; return cont_p; end function; function CalcAlpha( F, bound, abort_p, abort_alpha, max_p ); Q := PolynomialRing(Integers()); f := Q!Evaluate( F, [X, 1] ); print bound^2; disc := Discriminant( f ); // print "discriminant = ", disc; a_d := Coefficient(f, Degree(f)); primes := [p : p in [1..max_p] | IsPrime(p)]; alpha := 0.0; for p in primes do cont_p := CalcCont_p( p, disc, bound, F, f ); // print "cont_p = ", cont_p; alpha +:= (1.0/(p-1) - cont_p)*Log(p); /* early-abort strategy */ if p eq abort_p and alpha gt abort_alpha then break; end if; end for; return alpha; end function; function ApproxDickmanRho( u ); if u le 1.0 then return 1.0; end if; return u^-u; end function; function RatePolynomials( F1, F2, alpha, B1, B2, d ) pi := Pi(RealField()); K := 1000; rating := 0.0; logB1 := Log( B1 ); logB2 := Log( B2 ); for i in [1..K] do theta := pi/K*(i - 0.5); tmp := Abs( Evaluate( F1, [Cos( theta ), Sin( theta ) ] ) ); u1 := ( Log( tmp ) + alpha ) / logB1 + d; tmp := Abs( Evaluate( F2, [Cos( theta ), Sin( theta ) ] ) ); u2 := Log( tmp ) / logB2 + 1.0; rating +:= ApproxDickmanRho( u1 ) * ApproxDickmanRho( u2 ); end for; return rating/K; end function; n:=21290246318258757547497882016271517497806703963277216278233383215381949984056495911366573853021918316783107387995317230889569230873441936471; d := Round( Root( 3 * Log(n)/Log(Log(n)) , 3 ) ); print "degree ", d; dlogd := d*Log(d); temp := 1.0/d * Log( n ); e := dlogd + Sqrt( dlogd^2 + 4*temp*Log(temp) ); B := Round( Exp( 0.5*e ) ); //d := 5; coeffs := []; coeffs[6] := -5142225622472630020004; coeffs[5] := -3356924353646091366162; coeffs[4] := 6545365626333869758617; coeffs[3] := -4722668925346720843884; coeffs[2] := -514856715582822510304; coeffs[1] := 237866611103421300000; m1_Value := 617119742304446938751913; P := PolynomialRing(Integers(),2); F := P!0; for i in [0..d] do F +:= coeffs[i+1]*X^(d-i)*Y^i; end for; eval := Evaluate(F,[m1_Value,1]); print eval; F2 := X*1 - Y*m1_Value; alpha := CalcAlpha( F, 2500, 11, -0.5, 100 ); print alpha; alpha := CalcAlpha( F, 10000, 0, 0, 2000 ); print alpha; rating := RatePolynomials( F, F2, alpha, B, B, d ); print rating; Output: Magma V2.10-6 Thu Mar 25 2004 01:30:54 on modular [Seed = 856756204] ------------------------------------- degree 6 >> F +:= coeffs[i+1]*X^(d-i)*Y^i; ^ Runtime error in '[]': Sequence element 7 not defined 1313863132152204466382051090234893558534586335500945145792213080387521049833677\ 5916989232081187776967305025225215964788462414308960448255995267042655128822575\ 719023 6250000 -7.444049468347039377150624295555 100000000 -10.60328274604207470865761389290 0.00000000128929131518728645905498726144 Total time: 8.229 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Thu Mar 25 01:31:52 2004 Input: function CalcCont_p( p, disc, bound, F, f ); if disc mod p eq 0 then /* estimate using some small sample space */ cont_p := 0; upper_limit := bound^2; for i in [1..bound] do repeat a := Random( upper_limit ); b := Random( upper_limit ); until Gcd( a, b ) eq 1; // print a,b; value := Evaluate( F, [a, b] ); while value mod p eq 0 do value div:= p; cont_p +:= 1; end while; end for; cont_p := cont_p / (0.0 + bound); else K := GF(p); roots_mod_p := Roots( f, K ); q_p := #roots_mod_p; // print "roots mod p", p,q_p; /* add in the contribution of the projective roots */ d := Degree( f ); if Coefficient(f, d) mod p eq 0 then q_p +:= 1; end if; cont_p := q_p * p / (p * p - 1.0); end if; // print p,cont_p; return cont_p; end function; function CalcAlpha( F, bound, abort_p, abort_alpha, max_p ); Q := PolynomialRing(Integers()); f := Q!Evaluate( F, [X, 1] ); print bound^2; disc := Discriminant( f ); // print "discriminant = ", disc; a_d := Coefficient(f, Degree(f)); primes := [p : p in [1..max_p] | IsPrime(p)]; alpha := 0.0; for p in primes do cont_p := CalcCont_p( p, disc, bound, F, f ); // print "cont_p = ", cont_p; alpha +:= (1.0/(p-1) - cont_p)*Log(p); /* early-abort strategy */ if p eq abort_p and alpha gt abort_alpha then break; end if; end for; return alpha; end function; function ApproxDickmanRho( u ); if u le 1.0 then return 1.0; end if; return u^-u; end function; function RatePolynomials( F1, F2, alpha, B1, B2, d ) pi := Pi(RealField()); K := 1000; rating := 0.0; logB1 := Log( B1 ); logB2 := Log( B2 ); for i in [1..K] do theta := pi/K*(i - 0.5); tmp := Abs( Evaluate( F1, [Cos( theta ), Sin( theta ) ] ) ); u1 := ( Log( tmp ) + alpha ) / logB1 + d; tmp := Abs( Evaluate( F2, [Cos( theta ), Sin( theta ) ] ) ); u2 := Log( tmp ) / logB2 + 1.0; rating +:= ApproxDickmanRho( u1 ) * ApproxDickmanRho( u2 ); end for; return rating/K; end function; n:=21290246318258757547497882016271517497806703963277216278233383215381949984056495911366573853021918316783107387995317230889569230873441936471; d := 5 print "degree ", d; dlogd := d*Log(d); temp := 1.0/d * Log( n ); e := dlogd + Sqrt( dlogd^2 + 4*temp*Log(temp) ); B := Round( Exp( 0.5*e ) ); coeffs := []; coeffs[6] := -5142225622472630020004; coeffs[5] := -3356924353646091366162; coeffs[4] := 6545365626333869758617; coeffs[3] := -4722668925346720843884; coeffs[2] := -514856715582822510304; coeffs[1] := 237866611103421300000; m1_Value := 617119742304446938751913; P := PolynomialRing(Integers(),2); F := P!0; for i in [0..d] do F +:= coeffs[i+1]*X^(d-i)*Y^i; end for; eval := Evaluate(F,[m1_Value,1]); print eval; F2 := X*1 - Y*m1_Value; alpha := CalcAlpha( F, 2500, 11, -0.5, 100 ); print alpha; alpha := CalcAlpha( F, 10000, 0, 0, 2000 ); print alpha; rating := RatePolynomials( F, F2, alpha, B, B, d ); print rating; Output: Magma V2.10-6 Thu Mar 25 2004 01:31:49 on modular [Seed = 974653102] ------------------------------------- >> print "degree ", d; ^ User error: bad syntax >> dlogd := d*Log(d); ^ User error: Identifier 'd' has not been declared or assigned >> temp := 1.0/d * Log( n ); ^ User error: Identifier 'd' has not been declared or assigned >> e := dlogd + Sqrt( dlogd^2 + 4*temp*Log(temp) ); ^ User error: Identifier 'dlogd' has not been declared or assigned >> B := Round( Exp( 0.5*e ) ); ^ User error: Identifier 'e' has not been declared or assigned >> for i in [0..d] do ^ User error: Identifier 'd' has not been declared or assigned 0 6250000 CalcAlpha( F: 0, bound: 2500, abort_p: 11, abort_alpha: -0.50000000000000000000000000000, max_p: 100 ) >> disc := Discriminant( f ); ^ Runtime error in 'Discriminant': Degree of argument is less than 1 >> print alpha; ^ User error: Identifier 'alpha' has not been declared or assigned 100000000 CalcAlpha( F: 0, bound: 10000, abort_p: 0, abort_alpha: 0, max_p: 2000 ) >> disc := Discriminant( f ); ^ Runtime error in 'Discriminant': Degree of argument is less than 1 >> print alpha; ^ User error: Identifier 'alpha' has not been declared or assigned >> rating := RatePolynomials( F, F2, alpha, B, B, d ); ^ User error: Identifier 'alpha' has not been declared or assigned >> print rating;; ^ User error: Identifier 'rating' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Thu Mar 25 01:32:15 2004 Input: function CalcCont_p( p, disc, bound, F, f ); if disc mod p eq 0 then /* estimate using some small sample space */ cont_p := 0; upper_limit := bound^2; for i in [1..bound] do repeat a := Random( upper_limit ); b := Random( upper_limit ); until Gcd( a, b ) eq 1; // print a,b; value := Evaluate( F, [a, b] ); while value mod p eq 0 do value div:= p; cont_p +:= 1; end while; end for; cont_p := cont_p / (0.0 + bound); else K := GF(p); roots_mod_p := Roots( f, K ); q_p := #roots_mod_p; // print "roots mod p", p,q_p; /* add in the contribution of the projective roots */ d := Degree( f ); if Coefficient(f, d) mod p eq 0 then q_p +:= 1; end if; cont_p := q_p * p / (p * p - 1.0); end if; // print p,cont_p; return cont_p; end function; function CalcAlpha( F, bound, abort_p, abort_alpha, max_p ); Q := PolynomialRing(Integers()); f := Q!Evaluate( F, [X, 1] ); print bound^2; disc := Discriminant( f ); // print "discriminant = ", disc; a_d := Coefficient(f, Degree(f)); primes := [p : p in [1..max_p] | IsPrime(p)]; alpha := 0.0; for p in primes do cont_p := CalcCont_p( p, disc, bound, F, f ); // print "cont_p = ", cont_p; alpha +:= (1.0/(p-1) - cont_p)*Log(p); /* early-abort strategy */ if p eq abort_p and alpha gt abort_alpha then break; end if; end for; return alpha; end function; function ApproxDickmanRho( u ); if u le 1.0 then return 1.0; end if; return u^-u; end function; function RatePolynomials( F1, F2, alpha, B1, B2, d ) pi := Pi(RealField()); K := 1000; rating := 0.0; logB1 := Log( B1 ); logB2 := Log( B2 ); for i in [1..K] do theta := pi/K*(i - 0.5); tmp := Abs( Evaluate( F1, [Cos( theta ), Sin( theta ) ] ) ); u1 := ( Log( tmp ) + alpha ) / logB1 + d; tmp := Abs( Evaluate( F2, [Cos( theta ), Sin( theta ) ] ) ); u2 := Log( tmp ) / logB2 + 1.0; rating +:= ApproxDickmanRho( u1 ) * ApproxDickmanRho( u2 ); end for; return rating/K; end function; n:=21290246318258757547497882016271517497806703963277216278233383215381949984056495911366573853021918316783107387995317230889569230873441936471; d := 5; print "degree ", d; dlogd := d*Log(d); temp := 1.0/d * Log( n ); e := dlogd + Sqrt( dlogd^2 + 4*temp*Log(temp) ); B := Round( Exp( 0.5*e ) ); coeffs := []; coeffs[6] := -5142225622472630020004; coeffs[5] := -3356924353646091366162; coeffs[4] := 6545365626333869758617; coeffs[3] := -4722668925346720843884; coeffs[2] := -514856715582822510304; coeffs[1] := 237866611103421300000; m1_Value := 617119742304446938751913; P := PolynomialRing(Integers(),2); F := P!0; for i in [0..d] do F +:= coeffs[i+1]*X^(d-i)*Y^i; end for; eval := Evaluate(F,[m1_Value,1]); print eval; F2 := X*1 - Y*m1_Value; alpha := CalcAlpha( F, 2500, 11, -0.5, 100 ); print alpha; alpha := CalcAlpha( F, 10000, 0, 0, 2000 ); print alpha; rating := RatePolynomials( F, F2, alpha, B, B, d ); print rating; Output: Magma V2.10-6 Thu Mar 25 2004 01:32:08 on modular [Seed = 3320314220] ------------------------------------- degree 5 2129024631825875754749788201627151749780670396327721627823338321538194998405649\ 5911366573853021918316783107387995317230889569230873441936471 6250000 -3.82524086325160008864837622704 100000000 -4.155583280478002685412394880510 0.0000000091070087430810672658395285346 Total time: 6.789 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host pcd595076.netvigator.com. (218.102.127.76) Time: Thu Mar 25 02:34:08 2004 Input: 10738688 * 8759677 mod 97485575 Output: Magma V2.10-6 Thu Mar 25 2004 02:34:04 on modular [Seed = 1164414571] ------------------------------------- 1 Total time: 3.189 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Thu Mar 25 02:36:00 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2+6, x^2+5]); OK:=MaximalOrder(K); Factorization(3*OK); Output: Magma V2.10-6 Thu Mar 25 2004 02:35:57 on modular [Seed = 1450483145] ------------------------------------- [ , ] Total time: 3.499 seconds, Total memory usage: 2.07MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Thu Mar 25 02:36:39 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2+1); OK:=MaximalOrder(K); Factorization(3*OK); Output: Magma V2.10-6 Thu Mar 25 2004 02:36:36 on modular [Seed = 1602065177] ------------------------------------- [ ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Thu Mar 25 02:36:59 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2+1); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Thu Mar 25 2004 02:36:56 on modular [Seed = 1682352190] ------------------------------------- [ , ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Thu Mar 25 02:37:15 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2+6); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Thu Mar 25 2004 02:37:12 on modular [Seed = 1833935111] ------------------------------------- [ , ] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Thu Mar 25 02:37:43 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2+6, x^2+1]); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Thu Mar 25 2004 02:37:39 on modular [Seed = 2052634235] ------------------------------------- [ , , , ] Total time: 3.249 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Thu Mar 25 02:38:12 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2+5, x^2+1]); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Thu Mar 25 2004 02:38:09 on modular [Seed = 2280483] ------------------------------------- [ , ] Total time: 3.279 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Thu Mar 25 02:38:28 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-3, x^2+1]); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Thu Mar 25 2004 02:38:25 on modular [Seed = 153863482] ------------------------------------- [ , ] Total time: 3.309 seconds, Total memory usage: 1.97MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Thu Mar 25 02:38:47 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-3); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Thu Mar 25 2004 02:38:44 on modular [Seed = 372562640] ------------------------------------- [ ] Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Thu Mar 25 02:39:01 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Thu Mar 25 2004 02:38:58 on modular [Seed = 524145615] ------------------------------------- [ ] Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Thu Mar 25 02:39:24 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-5, x^2+1]); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Thu Mar 25 2004 02:39:20 on modular [Seed = 604432590] ------------------------------------- [ , ] Total time: 3.319 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Thu Mar 25 02:39:38 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2+2, x^2+1]); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Thu Mar 25 2004 02:39:35 on modular [Seed = 756015576] ------------------------------------- [ , ] Total time: 3.269 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Thu Mar 25 02:39:53 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2+2); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Thu Mar 25 2004 02:39:50 on modular [Seed = 974714558] ------------------------------------- [ ] Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Thu Mar 25 02:40:03 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2+7); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Thu Mar 25 2004 02:40:00 on modular [Seed = 3370779738] ------------------------------------- [ ] Total time: 3.189 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Thu Mar 25 02:40:11 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-7); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Thu Mar 25 2004 02:40:08 on modular [Seed = 3606321740] ------------------------------------- [ ] Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Thu Mar 25 02:40:20 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-6); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Thu Mar 25 2004 02:40:17 on modular [Seed = 3757904764] ------------------------------------- [ , ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Thu Mar 25 02:40:41 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-6, x^2+1); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Thu Mar 25 2004 02:40:38 on modular [Seed = 3855034705] ------------------------------------- >> K:=NumberField(x^2-6, x^2+1); ^ Runtime error in 'NumberField': Bad argument types Argument types given: RngUPolElt, RngUPolElt >> OK:=MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> Factorization(5*OK);; ^ User error: Identifier 'OK' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Thu Mar 25 02:41:00 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-6, x^2+1]); OK:=MaximalOrder(K); Factorization(5*OK); Output: Magma V2.10-6 Thu Mar 25 2004 02:40:56 on modular [Seed = 4073734072] ------------------------------------- [ , , , ] Total time: 3.219 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Thu Mar 25 02:41:24 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-3, x^2+1]); OK:=MaximalOrder(K); Factorization(2*OK); Output: Magma V2.10-6 Thu Mar 25 2004 02:41:21 on modular [Seed = 4225316504] ------------------------------------- [ ] Total time: 3.449 seconds, Total memory usage: 1.98MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Thu Mar 25 02:41:42 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-3); OK:=MaximalOrder(K); Factorization(2*OK); Output: Magma V2.10-6 Thu Mar 25 2004 02:41:39 on modular [Seed = 2158120433] ------------------------------------- [ ] Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Thu Mar 25 02:42:52 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2+1); OK:=MaximalOrder(K); Factorization(2*OK); Output: Magma V2.10-6 Thu Mar 25 2004 02:42:49 on modular [Seed = 2309702834] ------------------------------------- [ ] Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Thu Mar 25 02:45:02 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2+1, x^2-3]); OK:=MaximalOrder(K); Factorization(2*OK); Output: Magma V2.10-6 Thu Mar 25 2004 02:44:58 on modular [Seed = 2545244719] ------------------------------------- [ ] Total time: 3.539 seconds, Total memory usage: 1.98MB ************** MAGMA ***************** Host sv4.ictp.trieste.it. (140.105.16.64) Time: Thu Mar 25 05:27:28 2004 Input: R:= PolynomialRing(Rationals()); f:=x^2-x+1; K:=NumberField(f); P:=MaximalOrder(K); M:=MatrixRing( P , 15 ) ! [ 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, 0, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1-w, 0, 1-w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, -w, 0, 0, w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -w, -1, 0, 0, 0, 1-w, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1-w, 0, 1, -1+w, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 1-w, -1+w, 1, w, -w, 1-w, 1, 1-w, 3, 0, 0, 0, 0, 0, 0, 1, 1+w, 1, 1, -1, -1+w, -w, 0, 1-w, 3, 0, 0, 0, 0, 0, 1-w, -1+w, w, 1-w, 1-w, 0, -w, w, 0, 1, 3, 0, 0, 0, 0, 1-w, 1-w, 2-w, 1, w, 0, 0, 1-w, 1-w, 1-w, 0, 3, 0, 0, 0, -w, -1+w, 1, w, -w, -1, 1, 1-w, 1, w, 0, 0, 3, 0, 0, -1, -1+w, 0, 0, 1-w, 0, -1, -w, 0, 0, 1-w, -w, 1, 3, 0, 1-w, w, 1, 0, -w, -1, -1, 1, 1-w, 1, 2-w, 1, w, w, 3 ]; for i := 1 to 15 do for j := i+1 to 15 do M[i,j]:=Trace(M[j,i])-M[j,i]; end for; end for; N:= MatrixRing( Integers() , 30 ) ! 0; for i := 1 to 15 do for j := 1 to 15 do N[i,j]:=Trace(M[i,j]); N[15+i,15+j]:=N[i,j]; N[15+i,j]:=Trace(w*M[i,j]); N[j,15+i]:=N[15+i,j]; end for; end for; L := LatticeWithGram(N); LL, T := PairReduce(L); G2 := AutomorphismGroup(L : Stabilizer := 1); #G2; FactoredOrder(G2); GG2 := AutomorphismGroup(LL : Stabilizer := 1); #GG2; FactoredOrder(GG2); Z := IntegerRing(); H := MatrixGroup< 13, Z | G2, [T^-1*g*T : g in Generators(GG2) ] >; #H; FactoredOrder(H); MatrixRing(Z, 13) ! -1 in H; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 25 2004 05:27:03 on modular [Seed = 3097119493] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 1533 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 05:43:38 2004 Input: for p in [5..20] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^5-1); #(Points(C : Bound:=4)); end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 05:43:35 on modular [Seed = 1732612342] ------------------------------------- HyperellipticCurve( f: x^5 + 4 ) In file "/usr/local/magma/package/Geometry/CrvHyp/curve.m", line 257, column 30: >> return HyperellipticCurve(f, Parent(f)!0); ^ Runtime error in 'HyperellipticCurve': Curve has a finite singularity Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 05:43:56 2004 Input: for p in [5..20] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^5+1); #(Points(C : Bound:=4)); end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 05:43:53 on modular [Seed = 1817091011] ------------------------------------- HyperellipticCurve( f: x^5 + 1 ) In file "/usr/local/magma/package/Geometry/CrvHyp/curve.m", line 257, column 30: >> return HyperellipticCurve(f, Parent(f)!0); ^ Runtime error in 'HyperellipticCurve': Curve has a finite singularity Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 05:44:10 2004 Input: for p in [5..20] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^5-x^4+1); #(Points(C : Bound:=4)); end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 05:44:07 on modular [Seed = 1968669380] ------------------------------------- 7 9 9 11 23 HyperellipticCurve( f: x^5 + 18*x^4 + 1 ) In file "/usr/local/magma/package/Geometry/CrvHyp/curve.m", line 257, column 30: >> return HyperellipticCurve(f, Parent(f)!0); ^ Runtime error in 'HyperellipticCurve': Curve has a finite singularity Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 05:49:47 2004 Input: for p in [5..20] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^3+1); #(Points(C : Bound:=4)); end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 05:49:44 on modular [Seed = 86506507] ------------------------------------- 6 12 12 12 18 12 Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 05:50:51 2004 Input: for p in [5..200] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^3+1); Print(#(Points(C : Bound:=4),","); end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 05:50:48 on modular [Seed = 355986651] ------------------------------------- >> Print(#(Points(C : Bound:=4),","); ^ User error: bad syntax >> end if; ^ User error: bad syntax >> end for;; ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 05:51:08 2004 Input: for p in [5..200] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^3+1); print(#(Points(C : Bound:=4),","); end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 05:51:05 on modular [Seed = 439935941] ------------------------------------- >> print(#(Points(C : Bound:=4),","); ^ User error: bad syntax >> end if; ^ User error: bad syntax >> end for;; ^ User error: bad syntax Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 05:54:31 2004 Input: for p in [5..200] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^3+1); print#(Points(C : Bound:=4), ","; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 05:54:28 on modular [Seed = 772592653] ------------------------------------- >> print#(Points(C : Bound:=4), ","; ^ User error: bad syntax >> end if; ^ User error: bad syntax >> end for;; ^ User error: bad syntax Total time: 2.869 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 05:54:40 2004 Input: for p in [5..200] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^3+1); print #(Points(C : Bound:=4), ","; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 05:54:37 on modular [Seed = 924175644] ------------------------------------- >> print #(Points(C : Bound:=4), ","; ^ User error: bad syntax >> end if; ^ User error: bad syntax >> end for;; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 05:54:55 2004 Input: for p in [5..200] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^3+1); print #(Points(C : Bound:=4); end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 05:54:52 on modular [Seed = 1008649734] ------------------------------------- >> print #(Points(C : Bound:=4); ^ User error: bad syntax >> end if; ^ User error: bad syntax >> end for;; ^ User error: bad syntax Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 05:55:14 2004 Input: for p in [5..200] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^3+1); number:=#(Points(C : Bound:=4); print number; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 05:55:11 on modular [Seed = 3252894472] ------------------------------------- >> number:=#(Points(C : Bound:=4); ^ User error: bad syntax >> print number; ^ User error: Identifier 'number' has not been declared or assigned >> end if; ^ User error: bad syntax >> end for;; ^ User error: bad syntax Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 05:55:39 2004 Input: for p in [5..200] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^3+1); num:=#(Points(C : Bound:=4); print num; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 05:55:36 on modular [Seed = 3606326328] ------------------------------------- >> num:=#(Points(C : Bound:=4); ^ User error: bad syntax >> print num; ^ User error: Identifier 'num' has not been declared or assigned >> end if; ^ User error: bad syntax >> end for;; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 05:56:23 2004 Input: for p in [5..20] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^3+1); Points(C : Bound:=4); end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 05:56:20 on modular [Seed = 3707643470] ------------------------------------- {@ (1 : 0 : 0), (0 : 1 : 1), (0 : 4 : 1), (2 : 3 : 1), (2 : 2 : 1), (4 : 0 : 1) @} {@ (1 : 0 : 0), (0 : 1 : 1), (0 : 6 : 1), (1 : 4 : 1), (1 : 3 : 1), (2 : 4 : 1), (2 : 3 : 1), (3 : 0 : 1), (4 : 4 : 1), (4 : 3 : 1), (5 : 0 : 1), (6 : 0 : 1) @} {@ (1 : 0 : 0), (0 : 1 : 1), (0 : 10 : 1), (2 : 3 : 1), (2 : 8 : 1), (5 : 4 : 1), (5 : 7 : 1), (7 : 5 : 1), (7 : 6 : 1), (9 : 9 : 1), (9 : 2 : 1), (10 : 0 : 1) @} {@ (1 : 0 : 0), (0 : 1 : 1), (0 : 12 : 1), (2 : 3 : 1), (2 : 10 : 1), (4 : 0 : 1), (5 : 3 : 1), (5 : 10 : 1), (6 : 3 : 1), (6 : 10 : 1), (10 : 0 : 1), (12 : 0 : 1) @} {@ (1 : 0 : 0), (0 : 1 : 1), (0 : 16 : 1), (1 : 11 : 1), (1 : 6 : 1), (2 : 3 : 1), (2 : 14 : 1), (6 : 9 : 1), (6 : 8 : 1), (7 : 15 : 1), (7 : 2 : 1), (9 : 4 : 1), (9 : 13 : 1), (10 : 7 : 1), (10 : 10 : 1), (14 : 12 : 1), (14 : 5 : 1), (16 : 0 : 1) @} {@ (1 : 0 : 0), (0 : 1 : 1), (0 : 18 : 1), (2 : 16 : 1), (2 : 3 : 1), (3 : 16 : 1), (3 : 3 : 1), (8 : 0 : 1), (12 : 0 : 1), (14 : 16 : 1), (14 : 3 : 1), (18 : 0 : 1) @} Total time: 2.979 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 05:56:35 2004 Input: for p in [5..20] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^3+1); #Points(C : Bound:=4); end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 05:56:32 on modular [Seed = 3855032131] ------------------------------------- 6 12 12 12 18 12 Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 05:56:52 2004 Input: for p in [5..20] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^3+1); #Points(C : Bound:=4); print ,; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 05:56:49 on modular [Seed = 3938979933] ------------------------------------- >> #Points(C : Bound:=4); print ,; ^ User error: bad syntax >> end if; ^ User error: bad syntax >> end for;; ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 05:57:00 2004 Input: for p in [5..20] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^3+1); #Points(C : Bound:=4); print ","; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 05:56:57 on modular [Seed = 4090562892] ------------------------------------- 6 , 12 , 12 , 12 , 18 , 12 , Total time: 3.089 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 05:57:20 2004 Input: for p in [5..20] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^3+1); print #Points(C : Bound:=4) ","; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 05:57:17 on modular [Seed = 4175037363] ------------------------------------- >> print #Points(C : Bound:=4) ","; ^ User error: bad syntax >> end if; ^ User error: bad syntax >> end for;; ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 05:57:32 2004 Input: for p in [5..20] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^3+1); print #Points(C : Bound:=4), ","; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 05:57:29 on modular [Seed = 2174974686] ------------------------------------- 6 , 12 , 12 , 12 , 18 , 12 , Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 05:57:42 2004 Input: for p in [5..20] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^3+1); print #Points(C : Bound:=4),","; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 05:57:39 on modular [Seed = 2528407027] ------------------------------------- 6 , 12 , 12 , 12 , 18 , 12 , Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 05:58:30 2004 Input: for p in [5..20] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); print #Points(C : Bound:=4),","; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 05:58:27 on modular [Seed = 2629724041] ------------------------------------- 6 , 16 , 12 , 10 , 18 , 4 , Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 05:58:46 2004 Input: for p in [5..200] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); print #Points(C : Bound:=4),","; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 05:58:43 on modular [Seed = 2777112192] ------------------------------------- 6 , 16 , 12 , 10 , 18 , 4 , 24 , 30 , 40 , 58 , 42 , 28 , 48 , 54 , 60 , 34 , 100 , 72 , 94 , 88 , 84 , 90 , 70 , 102 , 64 , 108 , 106 , 114 , 88 , 132 , 138 , 172 , 150 , 160 , 130 , 148 , 168 , 174 , 180 , 130 , 192 , 190 , 198 , 256 , Total time: 3.049 seconds, Total memory usage: 2.29MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 05:59:05 2004 Input: for p in [5..2000] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); print #Points(C : Bound:=4),","; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 05:59:00 on modular [Seed = 2877903001] ------------------------------------- 6 , 16 , 12 , 10 , 18 , 4 , 24 , 30 , 40 , 58 , 42 , 28 , 48 , 54 , 60 , 34 , 100 , 72 , 94 , 88 , 84 , 90 , 70 , 102 , 64 , 108 , 106 , 114 , 88 , 132 , 138 , 172 , 150 , 160 , 130 , 148 , 168 , 174 , 180 , 130 , 192 , 190 , 198 , 256 , 244 , 280 , 228 , 274 , 234 , 240 , 214 , 252 , 258 , 264 , 270 , 328 , 226 , 282 , 220 , 294 , 340 , 312 , 358 , 318 , 268 , 406 , 348 , 322 , 354 , 360 , 376 , 298 , 364 , 384 , 390 , 466 , 402 , 334 , 420 , 466 , 432 , 430 , 496 , 444 , 450 , 478 , 462 , 424 , 468 , 480 , 400 , 492 , 436 , 504 , 510 , 522 , 508 , 634 , 628 , 558 , 564 , 570 , 604 , 670 , 588 , 594 , 600 , 550 , 568 , 634 , 618 , 556 , 544 , 642 , 724 , 648 , 654 , 660 , 586 , 574 , 678 , 684 , 676 , 702 , 754 , 720 , 640 , 634 , 772 , 744 , 856 , 706 , 762 , 766 , 774 , 676 , 798 , 810 , 700 , 822 , 928 , 828 , 922 , 840 , 970 , 858 , 748 , 864 , 946 , 882 , 868 , 888 , 988 , 912 , 1024 , 930 , 886 , 942 , 948 , 954 , 928 , 972 , 978 , 984 , 904 , 1018 , 886 , 1014 , 1020 , 994 , 1032 , 1150 , 1144 , 1050 , 1180 , 1062 , 1120 , 946 , 1096 , 1092 , 1138 , 1098 , 1104 , 1110 , 1210 , 1060 , 1054 , 1152 , 1030 , 1164 , 1300 , 1182 , 1188 , 1194 , 1198 , 1114 , 1218 , 1224 , 1230 , 1096 , 1378 , 1222 , 1260 , 1278 , 1336 , 1284 , 1290 , 1180 , 1390 , 1302 , 1168 , 1308 , 1320 , 1366 , 1336 , 1362 , 1368 , 1374 , 1234 , 1264 , 1410 , 1384 , 1428 , 1546 , 1434 , 1440 , 1600 , 1452 , 1450 , 1348 , 1624 , 1482 , 1564 , 1488 , 1558 , 1494 , 1500 , 1512 , 1524 , 1660 , 1648 , 1426 , 1554 , 1560 , 1480 , 1572 , 1516 , 1584 , 1498 , 1602 , 1608 , 1726 , 1614 , 1620 , 1570 , 1468 , 1638 , 1798 , 1528 , 1668 , 1522 , 1858 , 1698 , 1828 , 1710 , 1722 , 1804 , 1734 , 1810 , 1588 , 1774 , 1864 , 1750 , 1840 , 1788 , 1954 , 1654 , 1812 , 1824 , 1696 , 1848 , 1690 , 1756 , 1872 , 2038 , 1878 , 1888 , 1890 , 1902 , 1908 , 1914 , 1932 , 1810 , 1950 , 2104 , 1974 , 1980 , 2068 , 2134 , 1998 , 2104 , Total time: 5.029 seconds, Total memory usage: 2.39MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 06:01:16 2004 Input: for p in [2001..4000] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); print #Points(C : Bound:=4),","; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 06:01:03 on modular [Seed = 1568646901] ------------------------------------- 2004 , 2188 , 2086 , 2028 , 2026 , 2040 , 2074 , 2064 , 2070 , 2082 , 2260 , 2088 , 2014 , 2100 , 2112 , 2278 , 2130 , 2068 , 1990 , 2142 , 1960 , 2154 , 2038 , 2356 , 2188 , 2208 , 2214 , 2410 , 2238 , 2104 , 2244 , 2284 , 2268 , 2434 , 2274 , 2110 , 2248 , 2410 , 2298 , 2310 , 2464 , 2334 , 2340 , 2194 , 2476 , 2352 , 2358 , 2260 , 2398 , 2382 , 2440 , 2314 , 2394 , 2400 , 2412 , 2418 , 2424 , 2266 , 2442 , 2448 , 2460 , 2308 , 2518 , 2478 , 2704 , 2470 , 2532 , 2524 , 2544 , 2550 , 2656 , 2650 , 2580 , 2592 , 2398 , 2610 , 2446 , 2622 , 2634 , 2848 , 2658 , 2548 , 2664 , 2584 , 2818 , 2524 , 2688 , 2566 , 2694 , 2700 , 2500 , 2712 , 2638 , 2776 , 2730 , 2524 , 2742 , 2722 , 2754 , 2920 , 2778 , 2790 , 2608 , 2986 , 2802 , 2980 , 2820 , 2638 , 2838 , 2844 , 2644 , 3070 , 2862 , 2880 , 2896 , 2898 , 2904 , 2910 , 3130 , 2928 , 2940 , 3094 , 2958 , 2964 , 2970 , 2860 , 3000 , 3214 , 3012 , 3196 , 3024 , 2818 , 3042 , 2878 , 2986 , 2860 , 3136 , 3084 , 3090 , 3322 , 3120 , 3094 , 3138 , 3388 , 3168 , 2974 , 3370 , 3028 , 3192 , 3204 , 3210 , 2998 , 3222 , 3322 , 3252 , 3394 , 3258 , 3436 , 3280 , 3300 , 3130 , 3196 , 3190 , 3472 , 3324 , 3330 , 3364 , 3208 , 3348 , 3360 , 3430 , 3372 , 3178 , 3390 , 3160 , 3408 , 3414 , 3358 , 3450 , 3238 , 3462 , 3520 , 3468 , 3466 , 3492 , 3724 , 3280 , 3490 , 3528 , 3766 , 3534 , 3540 , 3658 , 3676 , 3558 , 3664 , 3364 , 3582 , 3784 , 3594 , 3376 , 3394 , 3618 , 3624 , 3784 , 3586 , 3868 , 3660 , 3672 , 3910 , 3678 , 3676 , 3598 , 3702 , 3874 , 3720 , 3496 , 3490 , 3772 , 3762 , 3768 , 3526 , 3780 , 3574 , 3798 , 3804 , 3822 , 4024 , 3834 , 4096 , 3852 , 3658 , 3864 , 3706 , 3882 , 3886 , 4036 , 3912 , 3918 , 4168 , 3924 , 3930 , 3868 , 4048 , 3948 , 4120 , 3990 , Total time: 9.409 seconds, Total memory usage: 2.33MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 06:03:16 2004 Input: for p in [4001..5000] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); print #Points(C : Bound:=4),","; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 06:03:05 on modular [Seed = 1648401996] ------------------------------------- 4002 , 4228 , 4008 , 4014 , 4020 , 3778 , 3820 , 4050 , 3940 , 4006 , 4074 , 4080 , 4092 , 3994 , 3844 , 4120 , 4128 , 3934 , 4134 , 4140 , 3910 , 4158 , 4072 , 4246 , 4030 , 4212 , 4218 , 4444 , 4230 , 4000 , 4242 , 3988 , 4254 , 4260 , 4474 , 4272 , 4534 , 4284 , 4290 , 4438 , 4480 , 4338 , 4084 , 4350 , 4378 , 4300 , 4374 , 4392 , 4398 , 4410 , 4422 , 4288 , 4294 , 4216 , 4452 , 4458 , 4464 , 4482 , 4324 , 4494 , 4588 , 4414 , 4518 , 4768 , 4524 , 4548 , 4378 , 4750 , 4576 , 4584 , 4504 , 4330 , 4348 , 4690 , 4638 , 4456 , 4644 , 4650 , 4924 , 4918 , 4624 , 4674 , 4680 , 4692 , 4704 , 4722 , 4948 , 4846 , 4734 , 4752 , 4816 , 4888 , 4788 , 4522 , 4794 , 4800 , 4798 , 5074 , 4818 , 4696 , 4954 , 4872 , 4878 , 4890 , 4624 , 5098 , 4920 , 4932 , 5170 , 4938 , 4944 , 4720 , 4858 , 4968 , 4918 , 4974 , 5260 , 5254 , 4816 , Total time: 10.589 seconds, Total memory usage: 2.54MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 07:47:18 2004 Input: for p in [5..20] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); ZetaFunction(C); print #Points(C : Bound:=4),","; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 07:47:15 on modular [Seed = 153853330] ------------------------------------- (25*$.1^4 + 10*$.1^2 + 1)/(5*$.1^2 - 6*$.1 + 1) 6 , (49*$.1^4 + 56*$.1^3 + 30*$.1^2 + 8*$.1 + 1)/(7*$.1^2 - 8*$.1 + 1) 16 , (121*$.1^4 + 22*$.1^2 + 1)/(11*$.1^2 - 12*$.1 + 1) 12 , (169*$.1^4 - 52*$.1^3 + 30*$.1^2 - 4*$.1 + 1)/(13*$.1^2 - 14*$.1 + 1) 10 , (289*$.1^4 + 34*$.1^2 + 1)/(17*$.1^2 - 18*$.1 + 1) 18 , (361*$.1^4 - 304*$.1^3 + 102*$.1^2 - 16*$.1 + 1)/(19*$.1^2 - 20*$.1 + 1) 4 , Total time: 3.019 seconds, Total memory usage: 2.29MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 07:48:14 2004 Input: for p in [5..10] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); #C print #Points(C : Bound:=4),","; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 07:48:11 on modular [Seed = 52532800] ------------------------------------- >> print #Points(C : Bound:=4),","; ^ User error: bad syntax >> end if; ^ User error: bad syntax >> end for;; ^ User error: bad syntax Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 07:48:24 2004 Input: for p in [5..10] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); #C; print #Points(C : Bound:=4),","; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 07:48:21 on modular [Seed = 473860417] ------------------------------------- 6 6 , 16 16 , Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 07:48:37 2004 Input: for p in [5..10] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); print #C; print #Points(C : Bound:=4),","; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 07:48:34 on modular [Seed = 372540284] ------------------------------------- 6 6 , 16 16 , Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 07:48:57 2004 Input: for p in [5..10] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); print #C, ","; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 07:48:54 on modular [Seed = 789428817] ------------------------------------- 6 , 16 , Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 07:50:19 2004 Input: for p in [5..10] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); print #C, ","; Jacobian(C); end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 07:50:16 on modular [Seed = 806528496] ------------------------------------- 6 , Jacobian of Hyperelliptic Curve defined by y^2 = x^6 + 1 over GF(5) 16 , Jacobian of Hyperelliptic Curve defined by y^2 = x^6 + 1 over GF(7) Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 07:50:54 2004 Input: for p in [5..10] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); print #C, ","; print Jacobian(C); end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 07:50:51 on modular [Seed = 3404226345] ------------------------------------- 6 , Jacobian of Hyperelliptic Curve defined by y^2 = x^6 + 1 over GF(5) 16 , Jacobian of Hyperelliptic Curve defined by y^2 = x^6 + 1 over GF(7) Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 07:51:09 2004 Input: for p in [5..10] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); print #C, ","; print Dimension(Jacobian(C)); end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 07:51:06 on modular [Seed = 3286324785] ------------------------------------- 6 , 2 16 , 2 Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 07:59:29 2004 Input: for p in [5..10] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); print #C, ","; ZetaFunction(C); end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 07:59:26 on modular [Seed = 3589751347] ------------------------------------- 6 , (25*$.1^4 + 10*$.1^2 + 1)/(5*$.1^2 - 6*$.1 + 1) 16 , (49*$.1^4 + 56*$.1^3 + 30*$.1^2 + 8*$.1 + 1)/(7*$.1^2 - 8*$.1 + 1) Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 07:59:42 2004 Input: for p in [5..10] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); print #C, ","; Denominator(ZetaFunction(C)); end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 07:59:39 on modular [Seed = 4006377757] ------------------------------------- 6 , 5*$.1^2 - 6*$.1 + 1 16 , 7*$.1^2 - 8*$.1 + 1 Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:00:18 2004 Input: for p in [5..10] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); print #C, ","; Nominator(ZetaFunction(C)); end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 08:00:15 on modular [Seed = 4040320871] ------------------------------------- >> Nominator(ZetaFunction(C)); ^ User error: Identifier 'Nominator' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:01:00 2004 Input: for p in [5..10] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); print #C, ","; Numerator(ZetaFunction(C)); end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 08:00:57 on modular [Seed = 2309689800] ------------------------------------- 6 , 25*$.1^4 + 10*$.1^2 + 1 16 , 49*$.1^4 + 56*$.1^3 + 30*$.1^2 + 8*$.1 + 1 Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:01:49 2004 Input: for p in [5..10] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); print #C, ","; Roots(Numerator(ZetaFunction(C))); end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 08:01:46 on modular [Seed = 2494958822] ------------------------------------- 6 , [] 16 , [] Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:02:26 2004 Input: for p in [5..10] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); print #C, ","; Roots(Numerator(ZetaFunction(C)), ComplexField()); end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 08:02:23 on modular [Seed = 2928424633] ------------------------------------- 6 , [ <-0.447213595499957939281834733746255247086*i, 2>, <0.447213595499957939281834733746255247086*i, 2> ] 16 , [ <-0.285714285714285714285714285714285714285 - 0.2474358296526967562182066202151246238479*i, 2>, <-0.285714285714285714285714285714285714285 + 0.2474358296526967562182066202151246238479*i, 2> ] Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:02:47 2004 Input: for p in [5..10] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); print #C, ","; Numerator(ZetaFunction(C)), Roots(Numerator(ZetaFunction(C)), ComplexField()); end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 08:02:44 on modular [Seed = 2810527643] ------------------------------------- 6 , 25*$.1^4 + 10*$.1^2 + 1 [ <-0.447213595499957939281834733746255247086*i, 2>, <0.447213595499957939281834733746255247086*i, 2> ] 16 , 49*$.1^4 + 56*$.1^3 + 30*$.1^2 + 8*$.1 + 1 [ <-0.285714285714285714285714285714285714285 - 0.2474358296526967562182066202151246238479*i, 2>, <-0.285714285714285714285714285714285714285 + 0.2474358296526967562182066202151246238479*i, 2> ] Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:04:41 2004 Input: for p in [5..10] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); print #C, ","; R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); summe:=0; for i in [1..Length(R)] do summe:=summe+1/R[i]^2; end for; print summe; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 08:04:38 on modular [Seed = 2995792412] ------------------------------------- 6 , >> for i in [1..Length(R)] do ^ Runtime error in 'Length': Bad argument types Argument types given: SeqEnum[Tup] Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:05:29 2004 Input: F := PolynomialRing(FiniteField(5)); C := HyperellipticCurve(x^6+1); print #C, ","; R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); Output: Magma V2.10-6 Thu Mar 25 2004 08:05:26 on modular [Seed = 1315755793] ------------------------------------- 6 , Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:05:51 2004 Input: F := PolynomialRing(FiniteField(5)); C := HyperellipticCurve(x^6+1); print #C, ","; R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); print R; Output: Magma V2.10-6 Thu Mar 25 2004 08:05:48 on modular [Seed = 1501282364] ------------------------------------- 6 , [ <-0.447213595499957939281834733746255247086*i, 2>, <0.447213595499957939281834733746255247086*i, 2> ] Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:06:09 2004 Input: F := PolynomialRing(FiniteField(5)); C := HyperellipticCurve(x^6+1); print #C, ","; R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); print R[1][1]; Output: Magma V2.10-6 Thu Mar 25 2004 08:06:06 on modular [Seed = 1349699879] ------------------------------------- 6 , -0.447213595499957939281834733746255247086*i Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:06:57 2004 Input: for p in [5..10] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); print #C, ","; R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); summe:=0; for i in [1..Length(R)/2] do summe:=summe+1/R[i][1]^2; end for; print summe; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 08:06:54 on modular [Seed = 1783165773] ------------------------------------- 6 , >> for i in [1..Length(R)/2] do ^ Runtime error in 'Length': Bad argument types Argument types given: SeqEnum[Tup] Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:07:17 2004 Input: F := PolynomialRing(FiniteField(5)); C := HyperellipticCurve(x^6+1); print #C, ","; R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); print R[1][1]; print Length(R); Output: Magma V2.10-6 Thu Mar 25 2004 08:07:14 on modular [Seed = 1699216558] ------------------------------------- 6 , -0.447213595499957939281834733746255247086*i >> print Length(R); ^ Runtime error in 'Length': Bad argument types Argument types given: SeqEnum[Tup] Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:08:06 2004 Input: F := PolynomialRing(FiniteField(5)); C := HyperellipticCurve(x^6+1); print #C, ","; R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); print R[1][1]; print #R; Output: Magma V2.10-6 Thu Mar 25 2004 08:08:03 on modular [Seed = 2136860293] ------------------------------------- 6 , -0.447213595499957939281834733746255247086*i 2 Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:09:45 2004 Input: for p in [5..10] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); print #C, ","; R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); summe:=0; for i in [1..#R/2] do summe:=summe+2/R[i][1]^2; end for; print summe; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 08:09:42 on modular [Seed = 153850710] ------------------------------------- 6 , >> for i in [1..#R/2] do ^ Runtime error in [ ... ]: Sequence range does not consist of integers Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:10:16 2004 Input: for p in [5..10] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); print #C, ","; R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); summe:=0; for i in [1..(#R)/2] do summe:=summe+2/R[i][1]^2; end for; print summe; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 08:10:13 on modular [Seed = 423330661] ------------------------------------- 6 , >> for i in [1..(#R)/2] do ^ Runtime error in [ ... ]: Sequence range does not consist of integers Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:10:46 2004 Input: for p in [5..10] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); print #C, ","; R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); rootNumber:=#R; summe:=0; for i in [1..rootNumber] do summe:=summe+2/R[i][1]^2; end for; print summe; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 08:10:43 on modular [Seed = 271747594] ------------------------------------- 6 , -20.00000000000000000000000000000000000018807909613 + 0.E-37*i 16 , 4.00000000000000000000000000000000000011754943508 + 0.E-37*i Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:11:30 2004 Input: for p in [5..5] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); print #C, ","; R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); rootNumber:=#R; summe:=0; for i in [1..rootNumber] do summe:=summe+2/R[i][1]^2; end for; print p^2+1-summe; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 08:11:27 on modular [Seed = 722055453] ------------------------------------- 6 , 46.00000000000000000000000000000000000018807909613 + 0.E-37*i Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:11:46 2004 Input: for p in [5..5] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); # print #C, ","; R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); rootNumber:=#R; summe:=0; for i in [1..rootNumber] do summe:=summe+2/R[i][1]^2; end for; print p^2+1-summe; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 08:11:43 on modular [Seed = 570472676] ------------------------------------- >> # print #C, ","; ^ User error: bad syntax >> R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); ^ User error: Identifier 'C' has not been declared or assigned >> rootNumber:=#R; ^ User error: Identifier 'R' has not been declared or assigned >> for i in [1..rootNumber] do ^ User error: Identifier 'rootNumber' has not been declared or assigned >> print p^2+1-summe; ^ User error: Identifier 'p' has not been declared or assigned >> end if; ^ User error: bad syntax >> end for;; ^ User error: bad syntax Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:11:55 2004 Input: for p in [5..5] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); print #C, ","; R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); rootNumber:=#R; summe:=0; for i in [1..rootNumber] do summe:=summe+2/R[i][1]^2; end for; print p^2+1-summe; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 08:11:52 on modular [Seed = 1008641772] ------------------------------------- 6 , 46.00000000000000000000000000000000000018807909613 + 0.E-37*i Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:12:06 2004 Input: for p in [5..5] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); rootNumber:=#R; summe:=0; for i in [1..rootNumber] do summe:=summe+2/R[i][1]^2; end for; print p^2+1-summe; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 08:12:03 on modular [Seed = 924167645] ------------------------------------- 46.00000000000000000000000000000000000018807909613 + 0.E-37*i Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:12:37 2004 Input: for p in [5..5] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); rootNumber:=#R; summe:=0; for i in [1..rootNumber] do summe:=summe+2/R[i][1]^2; end for; numberOfPoints:=p^2+1-summe; print Round(numberOfPoints); end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 08:12:34 on modular [Seed = 3252902730] ------------------------------------- 46 Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:12:50 2004 Input: for p in [5..100] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); rootNumber:=#R; summe:=0; for i in [1..rootNumber] do summe:=summe+2/R[i][1]^2; end for; numberOfPoints:=p^2+1-summe; print Round(numberOfPoints); end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 08:12:47 on modular [Seed = 3640279646] ------------------------------------- 46 46 166 214 358 310 622 958 1054 1318 1846 1894 2398 3022 3718 3574 4246 5326 5422 6526 7222 8278 9406 Total time: 3.109 seconds, Total memory usage: 3.49MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:13:42 2004 Input: for p in [5..20] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); rootNumber:=#R; summe:=0; for i in [1..rootNumber] do summe:=summe+2/R[i][1]^2; end for; numberOfPoints:=p^2+1-summe; print Round(numberOfPoints); end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 08:13:39 on modular [Seed = 3538962840] ------------------------------------- 46 46 166 214 358 310 Total time: 2.999 seconds, Total memory usage: 2.39MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:13:53 2004 Input: for p in [5..20] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^2)); C := HyperellipticCurve(x^3-1); #(Points(C : Bound:=4)); end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 08:13:50 on modular [Seed = 3989796522] ------------------------------------- 36 48 144 192 324 336 Total time: 2.959 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:14:12 2004 Input: for p in [5..20] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); rootNumber:=#R; summe:=0; for i in [1..rootNumber] do summe:=summe+1/R[i][1]^2; end for; numberOfPoints:=p^2+1-summe; print Round(numberOfPoints); end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 08:14:08 on modular [Seed = 3888479374] ------------------------------------- 36 48 144 192 324 336 Total time: 2.989 seconds, Total memory usage: 2.39MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:14:47 2004 Input: for p in [5..20] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); numberOfRoots:=#R; summe:=0; for i in [1..numberOfRoots] do summe:=summe+1/R[i][1]^2; end for; numberOfPoints:=p^2+1-summe; print Round(numberOfPoints); end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 08:14:44 on modular [Seed = 4275856883] ------------------------------------- 36 48 144 192 324 336 Total time: 2.939 seconds, Total memory usage: 2.39MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:15:31 2004 Input: for p in [5..20] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^2)); C := HyperellipticCurve(x^6+1); #(Points(C : Bound:=4)); end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 08:15:28 on modular [Seed = 2377062068] ------------------------------------- 46 46 166 214 358 310 Total time: 2.929 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:15:47 2004 Input: for p in [5..20] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); numberOfRoots:=#R; summe:=0; for i in [1..numberOfRoots] do summe:=summe+2/R[i][1]^2; end for; numberOfPoints:=p^2+1-summe; print Round(numberOfPoints); end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 08:15:44 on modular [Seed = 2225479501] ------------------------------------- 46 46 166 214 358 310 Total time: 3.009 seconds, Total memory usage: 2.39MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:16:54 2004 Input: for p in [5..2000] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); numberOfRoots:=#R; summe:=0; for i in [1..numberOfRoots] do summe:=summe+2/R[i][1]^2; end for; numberOfPoints:=p^2+1-summe; print Round(numberOfPoints); end if; end for; Output: ** WARNING: Computation used more memory than allowed. ** Magma V2.10-6 Thu Mar 25 2004 08:16:36 on modular [Seed = 2444429932] ------------------------------------- 46 46 166 214 358 310 622 958 1054 1318 1846 1894 2398 3022 3718 3574 4246 5326 5422 6526 7222 8278 9406 10606 10222 11878 12310 13222 15838 17686 19318 19366 22798 23374 24886 27094 28558 30622 32758 32134 37246 38014 39598 38830 44854 49054 52438 52390 55222 58078 58654 64006 67078 70222 73438 72958 76486 80086 79174 87022 94966 97966 98254 101758 108838 112606 121798 122806 126022 130318 136126 137734 145030 148222 152878 156886 162406 166030 177238 177958 187486 189214 192910 198022 203398 210478 214366 215422 219958 231358 235246 243046 248950 255022 261118 Current total memory usage: 94.4MB, failed memory request: 1.0MB System Error: User memory limit has been reached Total time: 18.049 seconds, Total memory usage: 99.00MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:17:55 2004 Input: for p in [5..1000] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); numberOfRoots:=#R; summe:=0; for i in [1..numberOfRoots] do summe:=summe+2/R[i][1]^2; end for; numberOfPoints:=p^2+1-summe; print Round(numberOfPoints); end if; end for; Output: ** WARNING: Computation used more memory than allowed. ** Magma V2.10-6 Thu Mar 25 2004 08:17:37 on modular [Seed = 2827629328] ------------------------------------- 46 46 166 214 358 310 622 958 1054 1318 1846 1894 2398 3022 3718 3574 4246 5326 5422 6526 7222 8278 9406 10606 10222 11878 12310 13222 15838 17686 19318 19366 22798 23374 24886 27094 28558 30622 32758 32134 37246 38014 39598 38830 44854 49054 52438 52390 55222 58078 58654 64006 67078 70222 73438 72958 76486 80086 79174 87022 94966 97966 98254 101758 108838 112606 121798 122806 126022 130318 136126 137734 145030 148222 152878 156886 162406 166030 177238 177958 187486 189214 192910 198022 203398 210478 214366 215422 219958 231358 235246 243046 248950 255022 261118 Current total memory usage: 94.4MB, failed memory request: 1.0MB System Error: User memory limit has been reached Total time: 17.930 seconds, Total memory usage: 98.99MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:18:21 2004 Input: for p in [5..500] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); numberOfRoots:=#R; summe:=0; for i in [1..numberOfRoots] do summe:=summe+2/R[i][1]^2; end for; numberOfPoints:=p^2+1-summe; print Round(numberOfPoints); end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 08:18:04 on modular [Seed = 2726313703] ------------------------------------- 46 46 166 214 358 310 622 958 1054 1318 1846 1894 2398 3022 3718 3574 4246 5326 5422 6526 7222 8278 9406 10606 10222 11878 12310 13222 15838 17686 19318 19366 22798 23374 24886 27094 28558 30622 32758 32134 37246 38014 39598 38830 44854 49054 52438 52390 55222 58078 58654 64006 67078 70222 73438 72958 76486 80086 79174 87022 94966 97966 98254 101758 108838 112606 121798 122806 126022 130318 136126 137734 145030 148222 152878 156886 162406 166030 177238 177958 187486 189214 192910 198022 203398 210478 214366 215422 219958 231358 235246 243046 248950 Total time: 16.850 seconds, Total memory usage: 91.86MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:19:04 2004 Input: for p in [5..500] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); numberOfRoots:=#R; summe:=0; for i in [1..numberOfRoots] do summe:=summe+2/R[i][1]^2; end for; numberOfPoints:=p^2+1-summe; print Round(numberOfPoints), ","; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 08:18:46 on modular [Seed = 3164479683] ------------------------------------- 46 , 46 , 166 , 214 , 358 , 310 , 622 , 958 , 1054 , 1318 , 1846 , 1894 , 2398 , 3022 , 3718 , 3574 , 4246 , 5326 , 5422 , 6526 , 7222 , 8278 , 9406 , 10606 , 10222 , 11878 , 12310 , 13222 , 15838 , 17686 , 19318 , 19366 , 22798 , 23374 , 24886 , 27094 , 28558 , 30622 , 32758 , 32134 , 37246 , 38014 , 39598 , 38830 , 44854 , 49054 , 52438 , 52390 , 55222 , 58078 , 58654 , 64006 , 67078 , 70222 , 73438 , 72958 , 76486 , 80086 , 79174 , 87022 , 94966 , 97966 , 98254 , 101758 , 108838 , 112606 , 121798 , 122806 , 126022 , 130318 , 136126 , 137734 , 145030 , 148222 , 152878 , 156886 , 162406 , 166030 , 177238 , 177958 , 187486 , 189214 , 192910 , 198022 , 203398 , 210478 , 214366 , 215422 , 219958 , 231358 , 235246 , 243046 , 248950 , Total time: 16.949 seconds, Total memory usage: 91.86MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:19:57 2004 Input: for p in [501..1000] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); numberOfRoots:=#R; summe:=0; for i in [1..numberOfRoots] do summe:=summe+2/R[i][1]^2; end for; numberOfPoints:=p^2+1-summe; print Round(numberOfPoints), ","; end if; end for; Output: ** WARNING: Computation used more memory than allowed. ** Magma V2.10-6 Thu Mar 25 2004 08:19:38 on modular [Seed = 3080006548] ------------------------------------- 255022 , 261118 , 273526 , 275494 , 290614 , 298198 , 312478 , 319222 , 326038 , 327814 , 331006 , 346918 , 354022 , 361198 , 362254 , 370078 , 378022 , 383158 , 383590 , 396814 , 413446 , 412822 , 421198 , Current total memory usage: 94.7MB, failed memory request: 1.6MB System Error: User memory limit has been reached Total time: 19.600 seconds, Total memory usage: 99.28MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:20:36 2004 Input: for p in [501..750] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); numberOfRoots:=#R; summe:=0; for i in [1..numberOfRoots] do summe:=summe+2/R[i][1]^2; end for; numberOfPoints:=p^2+1-summe; print Round(numberOfPoints), ","; end if; end for; Output: ** WARNING: Computation used more memory than allowed. ** Magma V2.10-6 Thu Mar 25 2004 08:20:16 on modular [Seed = 1147590814] ------------------------------------- 255022 , 261118 , 273526 , 275494 , 290614 , 298198 , 312478 , 319222 , 326038 , 327814 , 331006 , 346918 , 354022 , 361198 , 362254 , 370078 , 378022 , 383158 , 383590 , 396814 , 413446 , 412822 , 421198 , Current total memory usage: 94.7MB, failed memory request: 1.6MB System Error: User memory limit has been reached Total time: 19.520 seconds, Total memory usage: 99.28MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:21:22 2004 Input: for p in [501..750] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^2)); C := HyperellipticCurve(x^6+1); #(Points(C : Bound:=4)); end if; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 25 2004 08:20:59 on modular [Seed = 1568653740] ------------------------------------- 255022 261118 273526 275494 290614 298198 Errors: /home/mfd/gomagma: line 2: 2583 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:22:12 2004 Input: for p in [501..600] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); numberOfRoots:=#R; summe:=0; for i in [1..numberOfRoots] do summe:=summe+2/R[i][1]^2; end for; numberOfPoints:=p^2+1-summe; print Round(numberOfPoints), ","; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 08:22:00 on modular [Seed = 1783166680] ------------------------------------- 255022 , 261118 , 273526 , 275494 , 290614 , 298198 , 312478 , 319222 , 326038 , 327814 , 331006 , 346918 , 354022 , 361198 , Total time: 11.829 seconds, Total memory usage: 53.74MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:23:18 2004 Input: for p in [601..700] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); numberOfRoots:=#R; summe:=0; for i in [1..numberOfRoots] do summe:=summe+2/R[i][1]^2; end for; numberOfPoints:=p^2+1-summe; print Round(numberOfPoints), ","; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 08:23:01 on modular [Seed = 1631845406] ------------------------------------- 362254 , 370078 , 378022 , 383158 , 383590 , 396814 , 413446 , 412822 , 421198 , 429022 , 436918 , 436678 , 450622 , 461038 , 469222 , 480118 , Total time: 17.270 seconds, Total memory usage: 81.94MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:25:04 2004 Input: for p in [701..800] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); numberOfRoots:=#R; summe:=0; for i in [1..numberOfRoots] do summe:=summe+2/R[i][1]^2; end for; numberOfPoints:=p^2+1-summe; print Round(numberOfPoints), ","; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 08:24:44 on modular [Seed = 2120016808] ------------------------------------- 494206 , 504550 , 519838 , 527566 , 535222 , 548566 , 555022 , 561598 , 574726 , 582166 , 594430 , 600622 , 616246 , 638398 , Total time: 19.559 seconds, Total memory usage: 95.99MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:26:01 2004 Input: for p in [801..900] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); numberOfRoots:=#R; summe:=0; for i in [1..numberOfRoots] do summe:=summe+2/R[i][1]^2; end for; numberOfPoints:=p^2+1-summe; print Round(numberOfPoints), ","; end if; end for; Output: ** WARNING: Computation used more memory than allowed. ** Magma V2.10-6 Thu Mar 25 2004 08:25:41 on modular [Seed = 187274900] ------------------------------------- 657718 , 654694 , 677326 , 675214 , 687238 , 686326 , 707278 , 724294 , 737878 , 735046 , 748222 , Current total memory usage: 92.7MB, failed memory request: 2.9MB System Error: User memory limit has been reached Total time: 19.329 seconds, Total memory usage: 97.25MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:27:21 2004 Input: for p in [801..850] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); numberOfRoots:=#R; summe:=0; for i in [1..numberOfRoots] do summe:=summe+2/R[i][1]^2; end for; numberOfPoints:=p^2+1-summe; print Round(numberOfPoints), ","; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 08:27:08 on modular [Seed = 69638754] ------------------------------------- 657718 , 654694 , 677326 , 675214 , 687238 , 686326 , 707278 , Total time: 12.960 seconds, Total memory usage: 58.84MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:28:05 2004 Input: for p in [851..900] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); numberOfRoots:=#R; summe:=0; for i in [1..numberOfRoots] do summe:=summe+2/R[i][1]^2; end for; numberOfPoints:=p^2+1-summe; print Round(numberOfPoints), ","; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 08:27:49 on modular [Seed = 305171469] ------------------------------------- 724294 , 737878 , 735046 , 748222 , 770326 , 779686 , 783094 , 790318 , Total time: 15.519 seconds, Total memory usage: 74.65MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:29:22 2004 Input: for p in [901..950] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); numberOfRoots:=#R; summe:=0; for i in [1..numberOfRoots] do summe:=summe+2/R[i][1]^2; end for; numberOfPoints:=p^2+1-summe; print Round(numberOfPoints), ","; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 08:29:06 on modular [Seed = 739160772] ------------------------------------- 823078 , 833566 , 842830 , 866758 , 880366 , 889246 , 900598 , Total time: 16.219 seconds, Total memory usage: 74.22MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:30:14 2004 Input: for p in [951..1000] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); numberOfRoots:=#R; summe:=0; for i in [1..numberOfRoots] do summe:=summe+2/R[i][1]^2; end for; numberOfPoints:=p^2+1-summe; print Round(numberOfPoints), ","; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 08:29:56 on modular [Seed = 621263803] ------------------------------------- 912022 , 938158 , 946726 , 958438 , 970222 , 982174 , 997798 , Total time: 17.180 seconds, Total memory usage: 82.17MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:32:19 2004 Input: for p in [1..100] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); numberOfRoots:=#R; summe:=0; for i in [1..numberOfRoots] do summe:=summe+2/R[i][1]^2; end for; numberOfPoints:=p^2+1-summe; print Round(numberOfPoints), ","; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 08:32:16 on modular [Seed = 3404223968] ------------------------------------- HyperellipticCurve( f: x^6 + 1 ) In file "/usr/local/magma/package/Geometry/CrvHyp/curve.m", line 257, column 30: >> return HyperellipticCurve(f, Parent(f)!0); ^ Runtime error in 'HyperellipticCurve': Curve is not reduced Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:32:36 2004 Input: for p in [5..100] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); numberOfRoots:=#R; summe:=0; for i in [1..numberOfRoots] do summe:=summe+2/R[i][1]^2; end for; numberOfPoints:=p^2+1-summe; print Round(numberOfPoints), ","; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 08:32:33 on modular [Seed = 3286326520] ------------------------------------- 46 , 46 , 166 , 214 , 358 , 310 , 622 , 958 , 1054 , 1318 , 1846 , 1894 , 2398 , 3022 , 3718 , 3574 , 4246 , 5326 , 5422 , 6526 , 7222 , 8278 , 9406 , Total time: 3.089 seconds, Total memory usage: 3.49MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:41:07 2004 Input: for p in [5..20] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^2)); C := HyperellipticCurve(x^3-1); #(Points(C : Bound:=4)); end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 08:41:04 on modular [Seed = 3955837649] ------------------------------------- 36 48 144 192 324 336 Total time: 2.929 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:41:32 2004 Input: for p in [5..20] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^2)); C := HyperellipticCurve(x^3-1); print #C, ","; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 08:41:29 on modular [Seed = 3770827043] ------------------------------------- 36 , 48 , 144 , 192 , 324 , 336 , Total time: 2.959 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:42:11 2004 Input: for p in [5..200] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^2)); C := HyperellipticCurve(x^3-1); print #C, ","; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 08:42:07 on modular [Seed = 4191901724] ------------------------------------- 36 , 48 , 144 , 192 , 324 , 336 , 576 , 900 , 1008 , 1344 , 1764 , 1872 , 2304 , 2916 , 3600 , 3648 , 4368 , 5184 , 5376 , 6384 , 7056 , 8100 , 9408 , 10404 , 10416 , 11664 , 12096 , 12996 , 15984 , 17424 , 19044 , 19344 , 22500 , 23088 , 24768 , 26832 , 28224 , 30276 , 32400 , 32448 , 36864 , 37632 , 39204 , 39216 , Total time: 3.749 seconds, Total memory usage: 3.39MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:42:56 2004 Input: for p in [5..1000] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^2)); C := HyperellipticCurve(x^3-1); print #C, ","; end if; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 25 2004 08:42:33 on modular [Seed = 4157953652] ------------------------------------- 36 , 48 , 144 , 192 , 324 , 336 , 576 , 900 , 1008 , 1344 , 1764 , 1872 , 2304 , 2916 , 3600 , 3648 , 4368 , 5184 , 5376 , 6384 , 7056 , 8100 , 9408 , 10404 , 10416 , 11664 , 12096 , 12996 , 15984 , 17424 , 19044 , 19344 , 22500 , 23088 , 24768 , 26832 , 28224 , 30276 , 32400 , 32448 , 36864 , 37632 , 39204 , 39216 , 44688 , 49392 , 51984 , 52416 , 54756 , 57600 , 58368 , 63504 , 66564 , 69696 , 72900 , 73200 , 76608 , 79524 , 79632 , 86436 , 94608 , 97344 , 98112 , 101124 , 109200 , 113088 , 121104 , 122304 , 125316 , 129600 , 135408 , 138432 , 144336 , 147456 , 152100 , 157248 , 161604 , 166656 , 176400 , 177600 , 186624 , 188352 , 192816 , 197136 , 202500 , 209664 , 213444 , 214896 , 219024 , 230400 , 236208 , 242064 , 248976 , 254016 , 260100 , 272484 , 274512 , 291648 , 298704 , 311364 , 318096 , 324900 , 326928 , 331968 , 345744 , 352836 , 360000 , 361728 , 369264 , Errors: /home/mfd/gomagma: line 2: 2749 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:43:39 2004 Input: FiniteField(p^2) Output: Magma V2.10-6 Thu Mar 25 2004 08:43:35 on modular [Seed = 2377068495] ------------------------------------- >> FiniteField(p^2); ^ User error: Identifier 'p' has not been declared or assigned Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:43:48 2004 Input: FiniteField(5^2) Output: Magma V2.10-6 Thu Mar 25 2004 08:43:45 on modular [Seed = 2595764417] ------------------------------------- Finite field of size 5^2 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:44:27 2004 Input: for p in [5..750] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^2)); C := HyperellipticCurve(x^3-1); print #C, ","; end if; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 25 2004 08:44:04 on modular [Seed = 2477863421] ------------------------------------- 36 , 48 , 144 , 192 , 324 , 336 , 576 , 900 , 1008 , 1344 , 1764 , 1872 , 2304 , 2916 , 3600 , 3648 , 4368 , 5184 , 5376 , 6384 , 7056 , 8100 , 9408 , 10404 , 10416 , 11664 , 12096 , 12996 , 15984 , 17424 , 19044 , 19344 , 22500 , 23088 , 24768 , 26832 , 28224 , 30276 , 32400 , 32448 , 36864 , 37632 , 39204 , 39216 , 44688 , 49392 , 51984 , 52416 , 54756 , 57600 , 58368 , 63504 , 66564 , 69696 , 72900 , 73200 , 76608 , 79524 , 79632 , 86436 , 94608 , 97344 , 98112 , 101124 , 109200 , 113088 , 121104 , 122304 , 125316 , 129600 , 135408 , 138432 , 144336 , 147456 , 152100 , 157248 , 161604 , 166656 , 176400 , 177600 , 186624 , 188352 , 192816 , 197136 , 202500 , 209664 , 213444 , 214896 , 219024 , 230400 , 236208 , 242064 , 248976 , 254016 , 260100 , 272484 , 274512 , 291648 , 298704 , 311364 , 318096 , 324900 , 326928 , 331968 , 345744 , 352836 , 360000 , 361728 , 369264 , 376896 , Errors: /home/mfd/gomagma: line 2: 2777 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:44:49 2004 Input: for p in [5..500] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^2)); C := HyperellipticCurve(x^3-1); print #C, ","; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 08:44:35 on modular [Seed = 2827618977] ------------------------------------- 36 , 48 , 144 , 192 , 324 , 336 , 576 , 900 , 1008 , 1344 , 1764 , 1872 , 2304 , 2916 , 3600 , 3648 , 4368 , 5184 , 5376 , 6384 , 7056 , 8100 , 9408 , 10404 , 10416 , 11664 , 12096 , 12996 , 15984 , 17424 , 19044 , 19344 , 22500 , 23088 , 24768 , 26832 , 28224 , 30276 , 32400 , 32448 , 36864 , 37632 , 39204 , 39216 , 44688 , 49392 , 51984 , 52416 , 54756 , 57600 , 58368 , 63504 , 66564 , 69696 , 72900 , 73200 , 76608 , 79524 , 79632 , 86436 , 94608 , 97344 , 98112 , 101124 , 109200 , 113088 , 121104 , 122304 , 125316 , 129600 , 135408 , 138432 , 144336 , 147456 , 152100 , 157248 , 161604 , 166656 , 176400 , 177600 , 186624 , 188352 , 192816 , 197136 , 202500 , 209664 , 213444 , 214896 , 219024 , 230400 , 236208 , 242064 , 248976 , Total time: 13.829 seconds, Total memory usage: 8.94MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:45:32 2004 Input: for p in [501..750] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^2)); C := HyperellipticCurve(x^3-1); print #C, ","; end if; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 25 2004 08:45:09 on modular [Seed = 2777089930] ------------------------------------- 254016 , 260100 , 272484 , 274512 , 291648 , 298704 , 311364 , 318096 , 324900 , 326928 , 331968 , 345744 , 352836 , 360000 , 361728 , 369264 , 376896 , 381924 , 383376 , 397488 , 412164 , 413136 , 419904 , 427716 , 435600 , 436800 , 451776 , 459684 , 467856 , 478800 , 492804 , Errors: /home/mfd/gomagma: line 2: 2799 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:46:45 2004 Input: for p in [501..600] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^2)); C := HyperellipticCurve(x^3-1); print #C, ","; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 08:46:35 on modular [Seed = 3012628802] ------------------------------------- 254016 , 260100 , 272484 , 274512 , 291648 , 298704 , 311364 , 318096 , 324900 , 326928 , 331968 , 345744 , 352836 , 360000 , Total time: 10.159 seconds, Total memory usage: 13.99MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:49:09 2004 Input: for p in [601..700] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^2)); C := HyperellipticCurve(x^3-1); print #C, ","; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 08:48:54 on modular [Seed = 1214966597] ------------------------------------- 361728 , 369264 , 376896 , 381924 , 383376 , 397488 , 412164 , 413136 , 419904 , 427716 , 435600 , 436800 , 451776 , 459684 , 467856 , 478800 , Total time: 14.729 seconds, Total memory usage: 18.68MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:49:41 2004 Input: for p in [701..800] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^2)); C := HyperellipticCurve(x^3-1); print #C, ","; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 08:49:24 on modular [Seed = 1197859944] ------------------------------------- 492804 , 503616 , 518400 , 528048 , 536256 , 547344 , 553536 , 562800 , 573888 , 580644 , 592896 , 599076 , 617808 , 636804 , Total time: 16.619 seconds, Total memory usage: 26.66MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:50:30 2004 Input: for p in [801..900] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^2)); C := HyperellipticCurve(x^3-1); print #C, ","; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 08:50:08 on modular [Seed = 1450505613] ------------------------------------- 656100 , 656208 , 675684 , 676272 , 685584 , 686784 , 705600 , 725952 , 736164 , 736464 , 746496 , 769728 , 777924 , 781392 , 788544 , Total time: 21.389 seconds, Total memory usage: 30.92MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:51:10 2004 Input: for p in [901..1000] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^2)); C := HyperellipticCurve(x^3-1); print #C, ","; end if; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Mar 25 2004 08:50:47 on modular [Seed = 1833946769] ------------------------------------- 822864 , 831744 , 843696 , 864900 , 879168 , 887364 , 898704 , 910116 , 936624 , 944784 , 956484 , 968256 , Errors: /home/mfd/gomagma: line 2: 2854 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:51:33 2004 Input: for p in [901..950] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^2)); C := HyperellipticCurve(x^3-1); print #C, ","; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 08:51:18 on modular [Seed = 1682360313] ------------------------------------- 822864 , 831744 , 843696 , 864900 , 879168 , 887364 , 898704 , Total time: 14.019 seconds, Total memory usage: 31.92MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Mar 25 08:52:06 2004 Input: for p in [951..1000] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^2)); C := HyperellipticCurve(x^3-1); print #C, ","; end if; end for; Output: Magma V2.10-6 Thu Mar 25 2004 08:51:52 on modular [Seed = 1934741696] ------------------------------------- 910116 , 936624 , 944784 , 956484 , 968256 , 982128 , 995904 , Total time: 14.619 seconds, Total memory usage: 43.17MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Mar 25 11:18:11 2004 Input: (x^6+(2*c)*x^5+(2+2*c+c^2+b*d)*x^4+(2-b+2*c+2*c^2+d+2*b*d)*x^3+(2*b-c+c^2+b*d)*x^2+(1+2*b+2*c)*x+(1-b))^2 Output: Magma V2.10-6 Thu Mar 25 2004 11:18:08 on modular [Seed = 389304603] ------------------------------------- >> (x^6+(2*c)*x^5+(2+2*c+c^2+b*d)*x^4+(2-b+2*c+2*c^2+d+2*b*d)*x^3+(2*b-c+c^2+b ^ User error: Identifier 'x' has not been declared or assigned Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Mar 25 11:19:32 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); R:= PolynomialRing(Q); S:= PolynomialRing(R); (x^6+(2*c)*x^5+(2+2*c+c^2+b*d)*x^4+(2-b+2*c+2*c^2+d+2*b*d)*x^3+(2*b-c+c^2+b*d)*x^2+(1+2*b+2*c)*x+(1-b))^2 Output: Magma V2.10-6 Thu Mar 25 2004 11:19:28 on modular [Seed = 671837941] ------------------------------------- x^12 + 4*c*x^11 + (2*b*d + (c^2 + 4*c + 4))*x^10 + (((4*c + 4)*b + 2)*d + (3*b + (4*c^3 + 2*c^2 + 2*c + 4)))*x^9 + (b^2*d^2 + ((2*c^2 + 2*c + 1)*b + 4*c)*d + ((c + 4)*b + (c^4 + 2*c^3 + 3*c^2 + 4*c + 4)))*x^8 + ((4*b^2 + 2*b)*d^2 + (3*b^2 + (3*c^2 + c + 2)*b + (2*c^2 + 4*c + 4))*d + ((3*c^2 + 4*c)*b + (4*c^4 + c^3 + c^2)))*x^7 + ((b^2 + 4*b + 1)*d^2 + (2*c^2*b + (4*c^2 + 4*c + 4))*d + (b^2 + (2*c + 2)*b + (c^4 + 3*c + 1)))*x^6 + ((4*b^2 + 2*b)*d^2 + ((3*c^2 + 4*c)*b + (2*c^2 + 3*c))*d + (b^2 + (4*c + 1)*b + (4*c^4 + 4*c^3 + 2*c + 4)))*x^5 + (b^2*d^2 + ((2*c^2 + c)*b + (4*c + 2))*d + ((c + 2)*b + (c^4 + c^3 + c + 3)))*x^4 + (((4*c + 4)*b + 2)*d + (3*b + (4*c^3 + 2*c^2 + 2*c + 4)))*x^3 + ((3*b^2 + 2*b)*d + ((3*c^2 + 3)*b + (c^2 + 2*c + 1)))*x^2 + (b^2 + (c + 2)*b + (4*c + 2))*x + b^2 + 3*b + 1 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Mar 25 11:20:00 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); R:= PolynomialRing(Q); S:= PolynomialRing(R); (x^6+(2*c)*x^5+(2+2*c+c^2+b*d)*x^4+(2-b+2*c+2*c^2+d+2*b*d)*x^3+(2*b-c+c^2+b*d)*x^2+(1+2*b+2*c)*x+(1-b))^2 Output: Magma V2.10-6 Thu Mar 25 2004 11:19:57 on modular [Seed = 553805760] ------------------------------------- >> R:= PolynomialRing(Q); ^ Runtime error in 'AssignNames': Argument 2 must have length 1 >> (x^6+(2*c)*x^5+(2+2*c+c^2+b*d)*x^4+(2-b+2*c+2*c^2+d+2*b*d)*x^3+(2*b-c+c^2+b ^ User error: Identifier 'd' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Mar 25 11:20:13 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); R:= PolynomialRing(Q); S:= PolynomialRing(R); (x^6+(2*c)*x^5+(2+2*c+c^2+b*d)*x^4+(2-b+2*c+2*c^2+d+2*b*d)*x^3+(2*b-c+c^2+b*d)*x^2+(1+2*b+2*c)*x+(1-b))^2 Output: Magma V2.10-6 Thu Mar 25 2004 11:20:10 on modular [Seed = 823293895] ------------------------------------- x^12 + 4*c*x^11 + (2*b*d + (c^2 + 4*c + 4))*x^10 + (((4*c + 4)*b + 2)*d + (3*b + (4*c^3 + 2*c^2 + 2*c + 4)))*x^9 + (b^2*d^2 + ((2*c^2 + 2*c + 1)*b + 4*c)*d + ((c + 4)*b + (c^4 + 2*c^3 + 3*c^2 + 4*c + 4)))*x^8 + ((4*b^2 + 2*b)*d^2 + (3*b^2 + (3*c^2 + c + 2)*b + (2*c^2 + 4*c + 4))*d + ((3*c^2 + 4*c)*b + (4*c^4 + c^3 + c^2)))*x^7 + ((b^2 + 4*b + 1)*d^2 + (2*c^2*b + (4*c^2 + 4*c + 4))*d + (b^2 + (2*c + 2)*b + (c^4 + 3*c + 1)))*x^6 + ((4*b^2 + 2*b)*d^2 + ((3*c^2 + 4*c)*b + (2*c^2 + 3*c))*d + (b^2 + (4*c + 1)*b + (4*c^4 + 4*c^3 + 2*c + 4)))*x^5 + (b^2*d^2 + ((2*c^2 + c)*b + (4*c + 2))*d + ((c + 2)*b + (c^4 + c^3 + c + 3)))*x^4 + (((4*c + 4)*b + 2)*d + (3*b + (4*c^3 + 2*c^2 + 2*c + 4)))*x^3 + ((3*b^2 + 2*b)*d + ((3*c^2 + 3)*b + (c^2 + 2*c + 1)))*x^2 + (b^2 + (c + 2)*b + (4*c + 2))*x + b^2 + 3*b + 1 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Mar 25 11:20:53 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); R:= PolynomialRing(Q); S:= PolynomialRing(R); (x^6+(2*c)*x^5+(2+2*c+c^2+b*d)*x^4+(2-b+2*c+2*c^2+d+2*b*d)*x^3+(2*b-c+c^2+b*d)*x^2+(1+2*b+2*c)*x+(1-b))^2; G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Thu Mar 25 2004 11:20:50 on modular [Seed = 3404303460] ------------------------------------- x^12 + 4*c*x^11 + (2*b*d + (c^2 + 4*c + 4))*x^10 + (((4*c + 4)*b + 2)*d + (3*b + (4*c^3 + 2*c^2 + 2*c + 4)))*x^9 + (b^2*d^2 + ((2*c^2 + 2*c + 1)*b + 4*c)*d + ((c + 4)*b + (c^4 + 2*c^3 + 3*c^2 + 4*c + 4)))*x^8 + ((4*b^2 + 2*b)*d^2 + (3*b^2 + (3*c^2 + c + 2)*b + (2*c^2 + 4*c + 4))*d + ((3*c^2 + 4*c)*b + (4*c^4 + c^3 + c^2)))*x^7 + ((b^2 + 4*b + 1)*d^2 + (2*c^2*b + (4*c^2 + 4*c + 4))*d + (b^2 + (2*c + 2)*b + (c^4 + 3*c + 1)))*x^6 + ((4*b^2 + 2*b)*d^2 + ((3*c^2 + 4*c)*b + (2*c^2 + 3*c))*d + (b^2 + (4*c + 1)*b + (4*c^4 + 4*c^3 + 2*c + 4)))*x^5 + (b^2*d^2 + ((2*c^2 + c)*b + (4*c + 2))*d + ((c + 2)*b + (c^4 + c^3 + c + 3)))*x^4 + (((4*c + 4)*b + 2)*d + (3*b + (4*c^3 + 2*c^2 + 2*c + 4)))*x^3 + ((3*b^2 + 2*b)*d + ((3*c^2 + 3)*b + (c^2 + 2*c + 1)))*x^2 + (b^2 + (c + 2)*b + (4*c + 2))*x + b^2 + 3*b + 1 >> G, R:= GaloisGroup(f); ^ User error: Identifier 'f' has not been declared or assigned >> print(G); ^ User error: Identifier 'G' has not been declared or assigned >> t1, t2:= TransitiveGroupIdentification(G); ^ User error: Identifier 'G' has not been declared or assigned >> print(t1); ^ User error: Identifier 't1' has not been declared or assigned >> print(t2); ^ User error: Identifier 't2' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Mar 25 11:21:10 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); R:= PolynomialRing(Q); S:= PolynomialRing(R); f:=(x^6+(2*c)*x^5+(2+2*c+c^2+b*d)*x^4+(2-b+2*c+2*c^2+d+2*b*d)*x^3+(2*b-c+c^2+b*d)*x^2+(1+2*b+2*c)*x+(1-b))^2; G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Thu Mar 25 2004 11:21:07 on modular [Seed = 3286271356] ------------------------------------- >> G, R:= GaloisGroup(f); ^ Runtime error in 'GaloisGroup': This coefficient ring is not supported yet >> print(G); ^ User error: Identifier 'G' has not been declared or assigned >> t1, t2:= TransitiveGroupIdentification(G); ^ User error: Identifier 'G' has not been declared or assigned >> print(t1); ^ User error: Identifier 't1' has not been declared or assigned >> print(t2);; ^ User error: Identifier 't2' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Mar 25 11:21:29 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); R:= PolynomialRing(Q); S:= PolynomialRing(R); f:=(x^6+(2*c)*x^5+(2+2*c+c^2+b*d)*x^4+(2-b+2*c+2*c^2+d+2*b*d)*x^3+(2*b-c+c^2+b*d)*x^2+(1+2*b+2*c)*x+(1-b))^2 Output: Magma V2.10-6 Thu Mar 25 2004 11:21:26 on modular [Seed = 3572994974] ------------------------------------- Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Mar 25 11:22:05 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); R:= PolynomialRing(Q); S:= PolynomialRing(R); f:=(x^6+(2*c)*x^5+(2+2*c+c^2+b*d)*x^4+(2-b+2*c+2*c^2+d+2*b*d)*x^3+(2*b-c+c^2+b*d)*x^2+(1+2*b+2*c)*x+(1-b))^2; print(f); Output: Magma V2.10-6 Thu Mar 25 2004 11:22:01 on modular [Seed = 3989744267] ------------------------------------- x^12 + 4*c*x^11 + (2*b*d + (c^2 + 4*c + 4))*x^10 + (((4*c + 4)*b + 2)*d + (3*b + (4*c^3 + 2*c^2 + 2*c + 4)))*x^9 + (b^2*d^2 + ((2*c^2 + 2*c + 1)*b + 4*c)*d + ((c + 4)*b + (c^4 + 2*c^3 + 3*c^2 + 4*c + 4)))*x^8 + ((4*b^2 + 2*b)*d^2 + (3*b^2 + (3*c^2 + c + 2)*b + (2*c^2 + 4*c + 4))*d + ((3*c^2 + 4*c)*b + (4*c^4 + c^3 + c^2)))*x^7 + ((b^2 + 4*b + 1)*d^2 + (2*c^2*b + (4*c^2 + 4*c + 4))*d + (b^2 + (2*c + 2)*b + (c^4 + 3*c + 1)))*x^6 + ((4*b^2 + 2*b)*d^2 + ((3*c^2 + 4*c)*b + (2*c^2 + 3*c))*d + (b^2 + (4*c + 1)*b + (4*c^4 + 4*c^3 + 2*c + 4)))*x^5 + (b^2*d^2 + ((2*c^2 + c)*b + (4*c + 2))*d + ((c + 2)*b + (c^4 + c^3 + c + 3)))*x^4 + (((4*c + 4)*b + 2)*d + (3*b + (4*c^3 + 2*c^2 + 2*c + 4)))*x^3 + ((3*b^2 + 2*b)*d + ((3*c^2 + 3)*b + (c^2 + 2*c + 1)))*x^2 + (b^2 + (c + 2)*b + (4*c + 2))*x + b^2 + 3*b + 1 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Mar 25 11:26:46 2004 Input: P:= FunctionField(GF(3)); Q:= PolynomialRing(P); R:= PolynomialRing(Q); S:= PolynomialRing(R); f:=(x^6+(2*c)*x^5+(2+2*c+c^2+b*d)*x^4+(2-b+2*c+2*c^2+d+2*b*d)*x^3+(2*b-c+c^2+b*d)*x^2+(1+2*b+2*c)*x+(1-b))^2; print(f); Output: Magma V2.10-6 Thu Mar 25 2004 11:26:43 on modular [Seed = 3821054956] ------------------------------------- x^12 + c*x^11 + (2*b*d + (c + 1))*x^10 + (((c + 1)*b + 2)*d + (b + (c^3 + 1)))*x^9 + (b^2*d^2 + (2*c^2*b + c)*d + ((2*c + 1)*b + (c^4 + 2*c + 1)))*x^8 + ((b^2 + 2*b)*d^2 + (b^2 + (2*c^2 + c)*b + (2*c^2 + c + 1))*d + ((c^2 + c)*b + (c^4 + c^3 + c^2 + 2*c + 1)))*x^7 + ((b + 1)*d^2 + ((c + 1)*b + (c^2 + c + 1))*d + (b^2 + 2*b + (c^3 + 2*c^2 + 2*c)))*x^6 + ((b^2 + 2*b)*d^2 + (b^2 + (2*c^2 + c + 1)*b + (2*c^2 + c))*d + (2*b^2 + (c^2 + 2*c + 1)*b + (c^4 + c^3 + c^2 + 1)))*x^5 + (b^2*d^2 + (b^2 + (2*c^2 + 1)*b + (c + 2))*d + ((c^2 + 2*c + 2)*b + (c^4 + c + 2)))*x^4 + (((c + 1)*b + 2)*d + (b^2 + b + (c^3 + 2*c^2 + 2*c + 1)))*x^3 + ((b^2 + 2*b)*d + ((c^2 + c + 2)*b + (2*c + 1)))*x^2 + (2*b^2 + (2*c + 2)*b + (c + 2))*x + b^2 + b + 1 Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Mar 25 11:27:00 2004 Input: P:= FunctionField(GF(3)); Q:= PolynomialRing(P); R:= PolynomialRing(Q); S:= PolynomialRing(R); f:=(x^6+(2*c)*x^5+(2+2*c+c^2+b*d)*x^4+(2-b+2*c+2*c^2+d+2*b*d)*x^3+(2*b-c+c^2+b*d)*x^2+(1+2*b+2*c)*x+(1-b)); print(f); Output: Magma V2.10-6 Thu Mar 25 2004 11:26:57 on modular [Seed = 4107779305] ------------------------------------- x^6 + 2*c*x^5 + (b*d + (c^2 + 2*c + 2))*x^4 + ((2*b + 1)*d + (2*b + (2*c^2 + 2*c + 2)))*x^3 + (b*d + (2*b + (c^2 + 2*c)))*x^2 + (2*b + (2*c + 1))*x + 2*b + 1 Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Mar 25 11:27:30 2004 Input: P:= FunctionField(GF(3)); Q:= PolynomialRing(P); R:= PolynomialRing(Q); S:= PolynomialRing(R); f:=(x^6 +2*c*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1)); print(f); Output: Magma V2.10-6 Thu Mar 25 2004 11:27:27 on modular [Seed = 2377041326] ------------------------------------- x^6 + 2*c*x^5 + (2*b*d + (c^2 + 2*c + 2))*x^4 + ((b + 2)*d + (b + (2*c^2 + 2*c + 2)))*x^3 + (2*b*d + (c^2 + c + 2))*x^2 + 2*c*x + b + 1 Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Mar 25 11:28:12 2004 Input: p:=3; P:= FunctionField(GF(p)); Q:= PolynomialRing(P); R:= PolynomialRing(Q); S:= PolynomialRing(R); f:=(x^6 +2*c*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1))^((p-1)/2); print(f); Output: Magma V2.10-6 Thu Mar 25 2004 11:28:09 on modular [Seed = 2158217301] ------------------------------------- >> 12*b+2*c)*x +(4*b+1))^((p-1)/2); ^ Runtime error in '^': Bad argument types Argument types given: RngUPolElt, RngUPolElt >> print(f);; ^ User error: Identifier 'f' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Mar 25 11:29:40 2004 Input: p:=3; s:=(p-1)/2; P:= FunctionField(GF(p)); Q:= PolynomialRing(P); R:= PolynomialRing(Q); S:= PolynomialRing(R); f:=x^6 +(2*c)*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); print(f); Output: Magma V2.10-6 Thu Mar 25 2004 11:29:37 on modular [Seed = 2595869223] ------------------------------------- x^6 + 2*c*x^5 + (2*b*d + (c^2 + 2*c + 2))*x^4 + ((b + 2)*d + (b + (2*c^2 + 2*c + 2)))*x^3 + (2*b*d + (c^2 + c + 2))*x^2 + 2*c*x + b + 1 Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Mar 25 11:29:52 2004 Input: p:=3; s:=(p-1)/2; P:= FunctionField(GF(p)); Q:= PolynomialRing(P); R:= PolynomialRing(Q); S:= PolynomialRing(R); f:=x^6 +(2*c)*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); print(f^s); Output: Magma V2.10-6 Thu Mar 25 2004 11:29:49 on modular [Seed = 2477841186] ------------------------------------- >> print(f^s);; ^ Runtime error in '^': Bad argument types Argument types given: RngUPolElt, RngUPolElt Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Mar 25 11:30:18 2004 Input: p:=3; s:=(p-1)/2; P:= FunctionField(GF(p)); Q:= PolynomialRing(P); R:= PolynomialRing(Q); S:= PolynomialRing(R); f:=x^6 +(2*c)*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); print(s); print(f^s); Output: Magma V2.10-6 Thu Mar 25 2004 11:30:15 on modular [Seed = 2743134968] ------------------------------------- 1 >> print(f^s);; ^ Runtime error in '^': Bad argument types Argument types given: RngUPolElt, RngUPolElt Total time: 3.029 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Mar 25 11:30:34 2004 Input: p:=3; s:=(p-1)/2; P:= FunctionField(GF(p)); Q:= PolynomialRing(P); R:= PolynomialRing(Q); S:= PolynomialRing(R); f:=x^6 +(2*c)*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); print(s); print(Pow(f,s)); Output: Magma V2.10-6 Thu Mar 25 2004 11:30:31 on modular [Seed = 3029859807] ------------------------------------- 1 >> print(Pow(f,s));; ^ User error: Identifier 'Pow' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Mar 25 11:35:38 2004 Input: p:=3; s:=(p-1)/2; P:= FunctionField(GF(p)); Q:= PolynomialRing(P); R:= PolynomialRing(Q); S:= PolynomialRing(R); f:=x^6 +(2*c)*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); print(s); print((f)^s); Output: Magma V2.10-6 Thu Mar 25 2004 11:35:35 on modular [Seed = 570517560] ------------------------------------- 1 >> print((f)^s);; ^ Runtime error in '^': Bad argument types Argument types given: RngUPolElt, RngUPolElt Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Mar 25 11:41:55 2004 Input: Z:=Integers() p:=3; s:=(p-1)/2; print(s in Z); P:= FunctionField(GF(p)); Q:= PolynomialRing(P); R:= PolynomialRing(Q); S:= PolynomialRing(R); f:=x^6 +(2*c)*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); print(s); print((f)^s); Output: Magma V2.10-6 Thu Mar 25 2004 11:41:52 on modular [Seed = 3286272094] ------------------------------------- >> p:=3; ^ User error: bad syntax >> s:=(p-1)/2; ^ User error: Identifier 'p' has not been declared or assigned >> print(s in Z); ^ User error: Identifier 's' has not been declared or assigned >> P:= FunctionField(GF(p)); ^ User error: Identifier 'p' has not been declared or assigned >> Q:= PolynomialRing(P); ^ User error: Identifier 'P' has not been declared or assigned >> R:= PolynomialRing(Q); ^ User error: Identifier 'Q' has not been declared or assigned >> S:= PolynomialRing(R); ^ User error: Identifier 'R' has not been declared or assigned >> f:=x^6 +(2*c)*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 ^ User error: Identifier 'x' has not been declared or assigned >> print(s); ^ User error: Identifier 's' has not been declared or assigned >> print((f)^s);; ^ User error: Identifier 'f' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Mar 25 11:42:08 2004 Input: Z:=Integers(); p:=3; s:=(p-1)/2; print(s in Z); P:= FunctionField(GF(p)); Q:= PolynomialRing(P); R:= PolynomialRing(Q); S:= PolynomialRing(R); f:=x^6 +(2*c)*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); print(s); print((f)^s); Output: Magma V2.10-6 Thu Mar 25 2004 11:42:05 on modular [Seed = 3589709381] ------------------------------------- true 1 >> print((f)^s);; ^ Runtime error in '^': Bad argument types Argument types given: RngUPolElt, RngUPolElt Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Mar 25 11:42:31 2004 Input: Z:=Integers(); p:=3; s:=(p-1)/2; print(s in Z); P:= FunctionField(GF(p)); Q:= PolynomialRing(P); R:= PolynomialRing(Q); S:= PolynomialRing(R); f:=x^6 +(2*c)*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); print(s); print(f^2); Output: Magma V2.10-6 Thu Mar 25 2004 11:42:28 on modular [Seed = 3973031765] ------------------------------------- true 1 x^12 + c*x^11 + (b*d + (c + 1))*x^10 + (((2*c + 2)*b + 1)*d + (2*b + (c^3 + 1)))*x^9 + (b^2*d^2 + (c^2*b + 2*c)*d + (c*b + (c^4 + 2)))*x^8 + ((b^2 + 2*b)*d^2 + (b^2 + (c^2 + 2*c)*b + (c^2 + 2*c + 2))*d + ((2*c^2 + c + 1)*b + (c^4 + c^3 + c + 2)))*x^7 + ((b + 1)*d^2 + (2*b^2 + c*b + (2*c^2 + 2*c + 2))*d + (b^2 + (c^2 + c)*b + (2*c^3 + 2*c^2 + 2*c + 2)))*x^6 + ((b^2 + 2*b)*d^2 + (b^2 + c^2*b + (c^2 + c + 2))*d + ((2*c^2 + 1)*b + (c^4 + 2)))*x^5 + (b^2*d^2 + (b^2 + (c^2 + 2*c)*b + 2*c)*d + ((2*c^2 + 2*c + 1)*b + (c^4 + c^3 + c + 2)))*x^4 + ((2*b^2 + 2*c*b + 1)*d + (2*b^2 + (c^2 + c)*b + (c^3 + 2*c^2 + 1)))*x^3 + ((b^2 + b)*d + ((2*c^2 + 2*c + 1)*b + (2*c + 1)))*x^2 + (c*b + c)*x + b^2 + 2*b + 1 Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Mar 25 11:42:44 2004 Input: Z:=Integers(); p:=3; s:=(p-1)/2; print(s in Z); P:= FunctionField(GF(p)); Q:= PolynomialRing(P); R:= PolynomialRing(Q); S:= PolynomialRing(R); f:=x^6 +(2*c)*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); print(s); print(f^s); Output: Magma V2.10-6 Thu Mar 25 2004 11:42:41 on modular [Seed = 3888425899] ------------------------------------- true 1 >> print(f^s);; ^ Runtime error in '^': Bad argument types Argument types given: RngUPolElt, RngUPolElt Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Mar 25 11:44:08 2004 Input: Z:=Integers(); p:=3; s:=elt< Z | (p-1)/2>; P:= FunctionField(GF(p)); Q:= PolynomialRing(P); R:= PolynomialRing(Q); S:= PolynomialRing(R); f:=x^6 +(2*c)*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); print(s); print(f^s); Output: Magma V2.10-6 Thu Mar 25 2004 11:44:05 on modular [Seed = 4191860193] ------------------------------------- >> s:=elt< Z | (p-1)/2>; ^ Runtime error in elt< ... >: Bad arguments >> print(s); ^ User error: Identifier 's' has not been declared or assigned >> print(f^s);; ^ User error: Identifier 's' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Mar 25 11:44:31 2004 Input: Z:=Integers(); p:=elt< Z | 3 >; s:=elt< Z | (p-1)/2 >; P:= FunctionField(GF(p)); Q:= PolynomialRing(P); R:= PolynomialRing(Q); S:= PolynomialRing(R); f:=x^6 +(2*c)*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); print(s); print(f^s); Output: Magma V2.10-6 Thu Mar 25 2004 11:44:28 on modular [Seed = 4040408273] ------------------------------------- >> s:=elt< Z | (p-1)/2 >; ^ Runtime error in elt< ... >: Bad arguments >> print(s); ^ User error: Identifier 's' has not been declared or assigned >> print(f^s);; ^ User error: Identifier 's' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Mar 25 11:44:46 2004 Input: Z:=Integers(); p:=elt< Z | 3 >; s:=(p-1)/2; P:= FunctionField(GF(p)); Q:= PolynomialRing(P); R:= PolynomialRing(Q); S:= PolynomialRing(R); f:=x^6 +(2*c)*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); print(s); print(f^s); Output: Magma V2.10-6 Thu Mar 25 2004 11:44:43 on modular [Seed = 2343094205] ------------------------------------- 1 >> print(f^s);; ^ Runtime error in '^': Bad argument types Argument types given: RngUPolElt, RngUPolElt Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Mar 25 11:45:08 2004 Input: Z:=Integers(); p:=elt< Z | 3 >; s:=(p-1)/2; P:= FunctionField(GF(p)); Q:= PolynomialRing(P); R:= PolynomialRing(Q); T:= PolynomialRing(R); f:=x^6 +(2*c)*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); print(s); print(f^s); Output: Magma V2.10-6 Thu Mar 25 2004 11:45:05 on modular [Seed = 2663240258] ------------------------------------- 1 >> print(f^s);; ^ Runtime error in '^': Bad argument types Argument types given: RngUPolElt, RngUPolElt Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Mar 25 11:45:21 2004 Input: Z:=Integers(); p:=elt< Z | 3 >; s:=(p-1)/2; P:= FunctionField(GF(p)); Q:= PolynomialRing(P); R:= PolynomialRing(Q); S:= PolynomialRing(R); f:=x^6 +(2*c)*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); print(s); print(f^s); Output: Magma V2.10-6 Thu Mar 25 2004 11:45:19 on modular [Seed = 2444418371] ------------------------------------- 1 >> print(f^s);; ^ Runtime error in '^': Bad argument types Argument types given: RngUPolElt, RngUPolElt Total time: 2.889 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Mar 25 11:46:17 2004 Input: Z:=Integers(); p:=elt< Z | 3 >; s:=(p-1)/2; P:= FunctionField(GF(p)); Q:= PolynomialRing(P); R:= PolynomialRing(Q); S:= PolynomialRing(R); f:=x^6 +(2*c)*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); print(f); Output: Magma V2.10-6 Thu Mar 25 2004 11:46:14 on modular [Seed = 2877876016] ------------------------------------- x^6 + 2*c*x^5 + (2*b*d + (c^2 + 2*c + 2))*x^4 + ((b + 2)*d + (b + (2*c^2 + 2*c + 2)))*x^3 + (2*b*d + (c^2 + c + 2))*x^2 + 2*c*x + b + 1 Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Mar 25 11:46:40 2004 Input: Z:=Integers(); p:=elt< Z | 3 >; s:=(p-1)/2; P:= FunctionField(GF(p)); Q:= PolynomialRing(P); R:= PolynomialRing(Q); S:= PolynomialRing(R); f:=x^6 +(2*c)*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); c:=0; print(f); Output: Magma V2.10-6 Thu Mar 25 2004 11:46:37 on modular [Seed = 2726424066] ------------------------------------- x^6 + 2*c*x^5 + (2*b*d + (c^2 + 2*c + 2))*x^4 + ((b + 2)*d + (b + (2*c^2 + 2*c + 2)))*x^3 + (2*b*d + (c^2 + c + 2))*x^2 + 2*c*x + b + 1 Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Mar 25 11:46:56 2004 Input: Z:=Integers(); p:=elt< Z | 3 >; s:=(p-1)/2; P:= FunctionField(GF(p)); Q:= PolynomialRing(P); R:= PolynomialRing(Q); S:= PolynomialRing(R); f:=x^6 +(2*c)*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); print(f); Output: Magma V2.10-6 Thu Mar 25 2004 11:46:53 on modular [Seed = 3046570245] ------------------------------------- x^6 + 2*c*x^5 + (2*b*d + (c^2 + 2*c + 2))*x^4 + ((b + 2)*d + (b + (2*c^2 + 2*c + 2)))*x^3 + (2*b*d + (c^2 + c + 2))*x^2 + 2*c*x + b + 1 Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Mar 25 11:47:41 2004 Input: Z:=Integers(); p:=elt< Z | 5 >; s:=(p-1)/2; P:= FunctionField(GF(p)); Q:= PolynomialRing(P); R:= PolynomialRing(Q); S:= PolynomialRing(R); f:=x^6 +(2*c)*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); print(f^2); Output: Magma V2.10-6 Thu Mar 25 2004 11:47:38 on modular [Seed = 1265108526] ------------------------------------- x^12 + 4*c*x^11 + (2*b*d + (c^2 + 4*c + 4))*x^10 + (((4*c + 4)*b + 2)*d + (3*b + (4*c^3 + 2*c^2 + 2*c + 4)))*x^9 + (b^2*d^2 + ((2*c^2 + 2*c + 1)*b + 4*c)*d + ((c + 4)*b + (c^4 + 2*c^3 + 3*c^2 + 4*c + 4)))*x^8 + ((4*b^2 + 2*b)*d^2 + (3*b^2 + (3*c^2 + c + 2)*b + (2*c^2 + 4*c + 4))*d + ((3*c^2 + 4*c)*b + (4*c^4 + c^3 + c^2)))*x^7 + ((b^2 + 4*b + 1)*d^2 + (2*c^2*b + (4*c^2 + 4*c + 4))*d + (b^2 + (2*c + 2)*b + (c^4 + 3*c + 1)))*x^6 + ((4*b^2 + 2*b)*d^2 + ((3*c^2 + 4*c)*b + (2*c^2 + 3*c))*d + (b^2 + (4*c + 1)*b + (4*c^4 + 4*c^3 + 2*c + 4)))*x^5 + (b^2*d^2 + ((2*c^2 + c)*b + (4*c + 2))*d + ((c + 2)*b + (c^4 + c^3 + c + 3)))*x^4 + (((4*c + 4)*b + 2)*d + (3*b + (4*c^3 + 2*c^2 + 2*c + 4)))*x^3 + ((3*b^2 + 2*b)*d + ((3*c^2 + 3)*b + (c^2 + 2*c + 1)))*x^2 + (b^2 + (c + 2)*b + (4*c + 2))*x + b^2 + 3*b + 1 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Mar 25 11:52:19 2004 Input: Z:=Integers(); p:=elt< Z | 5 >; s:=(p-1)/2; P:= FunctionField(GF(p)); Q:= PolynomialRing(P); R:= PolynomialRing(Q); S:= PolynomialRing(R); X := Matrix(R, 2, 2, [(b^2*d^2 + ((2*c^2 + c)*b + (4*c + 2))*d + ((c + 2)*b + (c^4 + c^3 + c + 3))), (((4*c + 4)*b + 2)*d + (3*b + (4*c^3 + 2*c^2 + 2*c + 4))), (((4*c + 4)*b + 2)*d + (3*b + (4*c^3 + 2*c^2 + 2*c + 4))), (b^2*d^2 + ((2*c^2 + 2*c + 1)*b + 4*c)*d + ((c + 4)*b + (c^4 + 2*c^3 + 3*c^2 + 4*c + 4)))]); print(X); Output: Magma V2.10-6 Thu Mar 25 2004 11:52:16 on modular [Seed = 1817125474] ------------------------------------- [b^2*d^2 + ((2*c^2 + c)*b + (4*c + 2))*d + (c + 2)*b + c^4 + c^3 + c + 3 ((4*c + 4)*b + 2)*d + 3*b + 4*c^3 + 2*c^2 + 2*c + 4] [((4*c + 4)*b + 2)*d + 3*b + 4*c^3 + 2*c^2 + 2*c + 4 b^2*d^2 + ((2*c^2 + 2*c + 1)*b + 4*c)*d + (c + 4)*b + c^4 + 2*c^3 + 3*c^2 + 4*c + 4] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Mar 25 11:54:15 2004 Input: Z:=Integers(); p:=elt< Z | 5 >; s:=(p-1)/2; P:= FunctionField(GF(p)); Q:= PolynomialRing(P); R:= PolynomialRing(Q); S:= PolynomialRing(R); X := Matrix(R, 2, 2, [(b^2*d^2 + ((2*c^2 + c)*b + (4*c + 2))*d + ((c + 2)*b + (c^4 + c^3 + c + 3))), (((4*c + 4)*b + 2)*d + (3*b + (4*c^3 + 2*c^2 + 2*c + 4))), (((4*c + 4)*b + 2)*d + (3*b + (4*c^3 + 2*c^2 + 2*c + 4))), (b^2*d^2 + ((2*c^2 + 2*c + 1)*b + 4*c)*d + ((c + 4)*b + (c^4 + 2*c^3 + 3*c^2 + 4*c + 4)))]); print(X); print(Determinant(X)); Output: Magma V2.10-6 Thu Mar 25 2004 11:54:12 on modular [Seed = 1648438424] ------------------------------------- [b^2*d^2 + ((2*c^2 + c)*b + (4*c + 2))*d + (c + 2)*b + c^4 + c^3 + c + 3 ((4*c + 4)*b + 2)*d + 3*b + 4*c^3 + 2*c^2 + 2*c + 4] [((4*c + 4)*b + 2)*d + 3*b + 4*c^3 + 2*c^2 + 2*c + 4 b^2*d^2 + ((2*c^2 + 2*c + 1)*b + 4*c)*d + (c + 4)*b + c^4 + 2*c^3 + 3*c^2 + 4*c + 4] b^4*d^4 + ((4*c^2 + 3*c + 1)*b^3 + (3*c + 2)*b^2)*d^3 + ((2*c + 1)*b^3 + (c^4 + 4*c^3 + c^2 + 4*c + 1)*b^2 + (c^3 + c^2 + 2*c + 1)*b + (c^2 + 3*c + 1))*d^2 + ((4*c^3 + 3)*b^2 + (4*c^6 + 4*c^5 + 4*c^4 + c^3 + c^2 + 4*c + 2)*b + (3*c^5 + 4*c^4 + 3*c^2 + 3*c + 2))*d + (c^2 + c + 4)*b^2 + (2*c^5 + 4*c^4 + 2*c^3 + 4*c^2 + 2*c + 1)*b + c^8 + 3*c^7 + 4*c^6 + 2*c^5 + 3*c^4 + 3*c^3 + 3*c^2 + 1 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Mar 25 11:54:35 2004 Input: Z:=Integers(); p:=elt< Z | 5 >; s:=(p-1)/2; P:= FunctionField(GF(p)); Q:= PolynomialRing(P); R:= PolynomialRing(Q); S:= PolynomialRing(R); X := Matrix(R, 2, 2, [(b^2*d^2 + ((2*c^2 + c)*b + (4*c + 2))*d + ((c + 2)*b + (c^4 + c^3 + c + 3))), (((4*c + 4)*b + 2)*d + (3*b + (4*c^3 + 2*c^2 + 2*c + 4))), (((4*c + 4)*b + 2)*d + (3*b + (4*c^3 + 2*c^2 + 2*c + 4))), (b^2*d^2 + ((2*c^2 + 2*c + 1)*b + 4*c)*d + ((c + 4)*b + (c^4 + 2*c^3 + 3*c^2 + 4*c + 4)))]); print(X); print(); print(Determinant(X)); Output: Magma V2.10-6 Thu Mar 25 2004 11:54:32 on modular [Seed = 2069378557] ------------------------------------- [b^2*d^2 + ((2*c^2 + c)*b + (4*c + 2))*d + (c + 2)*b + c^4 + c^3 + c + 3 ((4*c + 4)*b + 2)*d + 3*b + 4*c^3 + 2*c^2 + 2*c + 4] [((4*c + 4)*b + 2)*d + 3*b + 4*c^3 + 2*c^2 + 2*c + 4 b^2*d^2 + ((2*c^2 + 2*c + 1)*b + 4*c)*d + (c + 4)*b + c^4 + 2*c^3 + 3*c^2 + 4*c + 4] >> print(); ^ User error: bad syntax b^4*d^4 + ((4*c^2 + 3*c + 1)*b^3 + (3*c + 2)*b^2)*d^3 + ((2*c + 1)*b^3 + (c^4 + 4*c^3 + c^2 + 4*c + 1)*b^2 + (c^3 + c^2 + 2*c + 1)*b + (c^2 + 3*c + 1))*d^2 + ((4*c^3 + 3)*b^2 + (4*c^6 + 4*c^5 + 4*c^4 + c^3 + c^2 + 4*c + 2)*b + (3*c^5 + 4*c^4 + 3*c^2 + 3*c + 2))*d + (c^2 + c + 4)*b^2 + (2*c^5 + 4*c^4 + 2*c^3 + 4*c^2 + 2*c + 1)*b + c^8 + 3*c^7 + 4*c^6 + 2*c^5 + 3*c^4 + 3*c^3 + 3*c^2 + 1 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Mar 25 11:54:48 2004 Input: Z:=Integers(); p:=elt< Z | 5 >; s:=(p-1)/2; P:= FunctionField(GF(p)); Q:= PolynomialRing(P); R:= PolynomialRing(Q); S:= PolynomialRing(R); X := Matrix(R, 2, 2, [(b^2*d^2 + ((2*c^2 + c)*b + (4*c + 2))*d + ((c + 2)*b + (c^4 + c^3 + c + 3))), (((4*c + 4)*b + 2)*d + (3*b + (4*c^3 + 2*c^2 + 2*c + 4))), (((4*c + 4)*b + 2)*d + (3*b + (4*c^3 + 2*c^2 + 2*c + 4))), (b^2*d^2 + ((2*c^2 + 2*c + 1)*b + 4*c)*d + ((c + 4)*b + (c^4 + 2*c^3 + 3*c^2 + 4*c + 4)))]); print(X); print(""); print(Determinant(X)); Output: Magma V2.10-6 Thu Mar 25 2004 11:54:45 on modular [Seed = 1884503787] ------------------------------------- [b^2*d^2 + ((2*c^2 + c)*b + (4*c + 2))*d + (c + 2)*b + c^4 + c^3 + c + 3 ((4*c + 4)*b + 2)*d + 3*b + 4*c^3 + 2*c^2 + 2*c + 4] [((4*c + 4)*b + 2)*d + 3*b + 4*c^3 + 2*c^2 + 2*c + 4 b^2*d^2 + ((2*c^2 + 2*c + 1)*b + 4*c)*d + (c + 4)*b + c^4 + 2*c^3 + 3*c^2 + 4*c + 4] b^4*d^4 + ((4*c^2 + 3*c + 1)*b^3 + (3*c + 2)*b^2)*d^3 + ((2*c + 1)*b^3 + (c^4 + 4*c^3 + c^2 + 4*c + 1)*b^2 + (c^3 + c^2 + 2*c + 1)*b + (c^2 + 3*c + 1))*d^2 + ((4*c^3 + 3)*b^2 + (4*c^6 + 4*c^5 + 4*c^4 + c^3 + c^2 + 4*c + 2)*b + (3*c^5 + 4*c^4 + 3*c^2 + 3*c + 2))*d + (c^2 + c + 4)*b^2 + (2*c^5 + 4*c^4 + 2*c^3 + 4*c^2 + 2*c + 1)*b + c^8 + 3*c^7 + 4*c^6 + 2*c^5 + 3*c^4 + 3*c^3 + 3*c^2 + 1 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host c-24-6-87-110.client.comcast.net. (24.6.87.110) Time: Thu Mar 25 12:10:50 2004 Input: q:=16; F:=FiniteField(q); PP,Pts,Lns:=ProjectivePlane(F); Output: Magma V2.10-6 Thu Mar 25 2004 12:10:47 on modular [Seed = 3236139545] ------------------------------------- >> PP,Pts,Lns:=ProjectivePlane(F); ^ Runtime error in :=: Expected to assign 3 value(s) but only computed 1 value(s) Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host c-24-6-87-110.client.comcast.net. (24.6.87.110) Time: Thu Mar 25 13:58:34 2004 Input: FF:=FiniteField(16); Output: Magma V2.10-6 Thu Mar 25 2004 13:58:31 on modular [Seed = 553798310] ------------------------------------- Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-138-89-136-75.nwrk.east.verizon.net. (138.89.136.75) Time: Thu Mar 25 16:08:55 2004 Input: gayxsfakjdhlkj121+ajfhlakdl=asljfljs;iuoiuwoejoiru Output: Magma V2.10-6 Thu Mar 25 2004 16:08:52 on modular [Seed = 2191624375] ------------------------------------- >> gayxsfakjdhlkj121+ajfhlakdl=asljfljs;iuoiuwoejoiru; ^ User error: Identifier 'asljfljs' has not been declared or assigned >> gayxsfakjdhlkj121+ajfhlakdl=asljfljs;iuoiuwoejoiru; ^ User error: Identifier 'iuoiuwoejoiru' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-138-89-136-75.nwrk.east.verizon.net. (138.89.136.75) Time: Thu Mar 25 16:09:31 2004 Input: 3x+1=3x-4 Output: Magma V2.10-6 Thu Mar 25 2004 16:09:28 on modular [Seed = 2377025364] ------------------------------------- >> 3x+1=3x-4; ^ User error: bad syntax Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Thu Mar 25 16:25:41 2004 Input: function CalcCont_p( p, disc, bound, F, f ); if disc mod p eq 0 then /* estimate using some small sample space */ cont_p := 0; upper_limit := bound^2; for i in [1..bound] do repeat a := Random( upper_limit ); b := Random( upper_limit ); until Gcd( a, b ) eq 1; // print a,b; value := Evaluate( F, [a, b] ); while value mod p eq 0 do value div:= p; cont_p +:= 1; end while; end for; cont_p := cont_p / (0.0 + bound); else K := GF(p); roots_mod_p := Roots( f, K ); q_p := #roots_mod_p; // print "roots mod p", p,q_p; /* add in the contribution of the projective roots */ d := Degree( f ); if Coefficient(f, d) mod p eq 0 then q_p +:= 1; end if; cont_p := q_p * p / (p * p - 1.0); end if; // print p,cont_p; return cont_p; end function; function CalcAlpha( F, bound, abort_p, abort_alpha, max_p ); Q := PolynomialRing(Integers()); f := Q!Evaluate( F, [X, 1] ); print bound^2; disc := Discriminant( f ); // print "discriminant = ", disc; a_d := Coefficient(f, Degree(f)); primes := [p : p in [1..max_p] | IsPrime(p)]; alpha := 0.0; for p in primes do cont_p := CalcCont_p( p, disc, bound, F, f ); // print "cont_p = ", cont_p; alpha +:= (1.0/(p-1) - cont_p)*Log(p); /* early-abort strategy */ if p eq abort_p and alpha gt abort_alpha then break; end if; end for; return alpha; end function; function ApproxDickmanRho( u ); if u le 1.0 then return 1.0; end if; return u^-u; end function; function RatePolynomials( F1, F2, alpha, B1, B2, d ) pi := Pi(RealField()); K := 1000; rating := 0.0; logB1 := Log( B1 ); logB2 := Log( B2 ); for i in [1..K] do theta := pi/K*(i - 0.5); tmp := Abs( Evaluate( F1, [Cos( theta ), Sin( theta ) ] ) ); u1 := ( Log( tmp ) + alpha ) / logB1 + d; tmp := Abs( Evaluate( F2, [Cos( theta ), Sin( theta ) ] ) ); u2 := Log( tmp ) / logB2 + 1.0; rating +:= ApproxDickmanRho( u1 ) * ApproxDickmanRho( u2 ); end for; return rating/K; end function; n:=21290246318258757547497882016271517497806703963277216278233383215381949984056495911366573853021918316783107387995317230889569230873441936471; d := 5; print "degree ", d; dlogd := d*Log(d); temp := 1.0/(d+1) * Log( n ); e := dlogd + Sqrt( dlogd^2 + 4*temp*Log(temp) ); B := Round( Exp( 0.5*e ) ); coeffs := []; coeffs[6] := -5142225622472630020004; coeffs[5] := -3356924353646091366162; coeffs[4] := 6545365626333869758617; coeffs[3] := -4722668925346720843884; coeffs[2] := -514856715582822510304; coeffs[1] := 237866611103421300000; m1_Value := 617119742304446938751913; P := PolynomialRing(Integers(),2); F := P!0; for i in [0..d] do F +:= coeffs[i+1]*X^(d-i)*Y^i; end for; eval := Evaluate(F,[m1_Value,1]); print eval; F2 := X*1 - Y*m1_Value; alpha := CalcAlpha( F, 2500, 11, -0.5, 100 ); print alpha; alpha := CalcAlpha( F, 10000, 0, 0, 2000 ); print alpha; rating := RatePolynomials( F, F2, alpha, B, B, d ); print rating; Output: Magma V2.10-6 Thu Mar 25 2004 16:25:34 on modular [Seed = 1181042778] ------------------------------------- degree 5 2129024631825875754749788201627151749780670396327721627823338321538194998405649\ 5911366573853021918316783107387995317230889569230873441936471 6250000 -3.86600742809144357782688067283 100000000 -4.191107268340705635467937738339 0.00000000311265081232425900262895631698 Total time: 6.799 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Thu Mar 25 16:32:56 2004 Input: function CalcCont_p( p, disc, bound, F, f ); if disc mod p eq 0 then /* estimate using some small sample space */ cont_p := 0; upper_limit := bound^2; for i in [1..bound] do repeat a := Random( upper_limit ); b := Random( upper_limit ); until Gcd( a, b ) eq 1; // print a,b; value := Evaluate( F, [a, b] ); while value mod p eq 0 do value div:= p; cont_p +:= 1; end while; end for; cont_p := cont_p / (0.0 + bound); else K := GF(p); roots_mod_p := Roots( f, K ); q_p := #roots_mod_p; // print "roots mod p", p,q_p; /* add in the contribution of the projective roots */ d := Degree( f ); if Coefficient(f, d) mod p eq 0 then q_p +:= 1; end if; cont_p := q_p * p / (p * p - 1.0); end if; // print p,cont_p; return cont_p; end function; function CalcAlpha( F, bound, abort_p, abort_alpha, max_p ); Q := PolynomialRing(Integers()); f := Q!Evaluate( F, [X, 1] ); print bound^2; disc := Discriminant( f ); // print "discriminant = ", disc; a_d := Coefficient(f, Degree(f)); primes := [p : p in [1..max_p] | IsPrime(p)]; alpha := 0.0; for p in primes do cont_p := CalcCont_p( p, disc, bound, F, f ); // print "cont_p = ", cont_p; alpha +:= (1.0/(p-1) - cont_p)*Log(p); /* early-abort strategy */ if p eq abort_p and alpha gt abort_alpha then break; end if; end for; return alpha; end function; function ApproxDickmanRho( u ); if u le 1.0 then return 1.0; end if; return u^-u; end function; function RatePolynomials( F1, F2, alpha, B1, B2, d ) pi := Pi(RealField()); K := 1000; rating := 0.0; logB1 := Log( B1 ); logB2 := Log( B2 ); for i in [1..K] do theta := pi/K*(i - 0.5); tmp := Abs( Evaluate( F1, [Cos( theta ), Sin( theta ) ] ) ); u1 := ( Log( tmp ) + alpha ) / logB1 + d; tmp := Abs( Evaluate( F2, [Cos( theta ), Sin( theta ) ] ) ); u2 := Log( tmp ) / logB2 + 1.0; rating +:= ApproxDickmanRho( u1 ) * ApproxDickmanRho( u2 ); end for; return rating/K; end function; n:=21290246318258757547497882016271517497806703963277216278233383215381949984056495911366573853021918316783107387995317230889569230873441936471; d := 5; print "degree ", d; dlogd := d*Log(d); temp := 1.0/(d+1) * Log( n ); e := dlogd + Sqrt( dlogd^2 + 4*temp*Log(temp) ); B := Round( Exp( 0.5*e ) ); print "Bound = ", B; coeffs := []; coeffs[6] := -5142225622472630020004; coeffs[5] := -3356924353646091366162; coeffs[4] := 6545365626333869758617; coeffs[3] := -4722668925346720843884; coeffs[2] := -514856715582822510304; coeffs[1] := 237866611103421300000; m1_Value := 617119742304446938751913; P := PolynomialRing(Integers(),2); F := P!0; for i in [0..d] do F +:= coeffs[i+1]*X^(d-i)*Y^i; end for; eval := Evaluate(F,[m1_Value,1]); print eval; F2 := X*1 - Y*m1_Value; alpha := CalcAlpha( F, 2500, 11, -0.5, 100 ); print alpha; alpha := CalcAlpha( F, 10000, 0, 0, 2000 ); print alpha; rating := RatePolynomials( F, F2, alpha, B, B, d ); print rating; Output: Magma V2.10-6 Thu Mar 25 2004 16:32:50 on modular [Seed = 2120052270] ------------------------------------- degree 5 Bound = 208332754 2129024631825875754749788201627151749780670396327721627823338321538194998405649\ 5911366573853021918316783107387995317230889569230873441936471 6250000 -3.89974326926211791062181585492 100000000 -4.186529779134550176345389926042 0.00000000311043167285862803098085807164 Total time: 6.679 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Thu Mar 25 16:33:26 2004 Input: function CalcCont_p( p, disc, bound, F, f ); if disc mod p eq 0 then /* estimate using some small sample space */ cont_p := 0; upper_limit := bound^2; for i in [1..bound] do repeat a := Random( upper_limit ); b := Random( upper_limit ); until Gcd( a, b ) eq 1; // print a,b; value := Evaluate( F, [a, b] ); while value mod p eq 0 do value div:= p; cont_p +:= 1; end while; end for; cont_p := cont_p / (0.0 + bound); else K := GF(p); roots_mod_p := Roots( f, K ); q_p := #roots_mod_p; // print "roots mod p", p,q_p; /* add in the contribution of the projective roots */ d := Degree( f ); if Coefficient(f, d) mod p eq 0 then q_p +:= 1; end if; cont_p := q_p * p / (p * p - 1.0); end if; // print p,cont_p; return cont_p; end function; function CalcAlpha( F, bound, abort_p, abort_alpha, max_p ); Q := PolynomialRing(Integers()); f := Q!Evaluate( F, [X, 1] ); print bound^2; disc := Discriminant( f ); // print "discriminant = ", disc; a_d := Coefficient(f, Degree(f)); primes := [p : p in [1..max_p] | IsPrime(p)]; alpha := 0.0; for p in primes do cont_p := CalcCont_p( p, disc, bound, F, f ); // print "cont_p = ", cont_p; alpha +:= (1.0/(p-1) - cont_p)*Log(p); /* early-abort strategy */ if p eq abort_p and alpha gt abort_alpha then break; end if; end for; return alpha; end function; function ApproxDickmanRho( u ); if u le 1.0 then return 1.0; end if; return u^-u; end function; function RatePolynomials( F1, F2, alpha, B1, B2, d ) pi := Pi(RealField()); K := 1000; rating := 0.0; logB1 := Log( B1 ); logB2 := Log( B2 ); for i in [1..K] do theta := pi/K*(i - 0.5); tmp := Abs( Evaluate( F1, [Cos( theta ), Sin( theta ) ] ) ); u1 := ( Log( tmp ) + alpha ) / logB1 + d; tmp := Abs( Evaluate( F2, [Cos( theta ), Sin( theta ) ] ) ); u2 := Log( tmp ) / logB2 + 1.0; rating +:= ApproxDickmanRho( u1 ) * ApproxDickmanRho( u2 ); end for; return rating/K; end function; n:=21290246318258757547497882016271517497806703963277216278233383215381949984056495911366573853021918316783107387995317230889569230873441936471; d := 5; print "degree ", d; dlogd := d*Log(d); temp := 1.0/(d) * Log( n ); e := dlogd + Sqrt( dlogd^2 + 4*temp*Log(temp) ); B := Round( Exp( 0.5*e ) ); print "Bound = ", B; coeffs := []; coeffs[6] := -5142225622472630020004; coeffs[5] := -3356924353646091366162; coeffs[4] := 6545365626333869758617; coeffs[3] := -4722668925346720843884; coeffs[2] := -514856715582822510304; coeffs[1] := 237866611103421300000; m1_Value := 617119742304446938751913; P := PolynomialRing(Integers(),2); F := P!0; for i in [0..d] do F +:= coeffs[i+1]*X^(d-i)*Y^i; end for; eval := Evaluate(F,[m1_Value,1]); print eval; F2 := X*1 - Y*m1_Value; alpha := CalcAlpha( F, 2500, 11, -0.5, 100 ); print alpha; alpha := CalcAlpha( F, 10000, 0, 0, 2000 ); print alpha; rating := RatePolynomials( F, F2, alpha, B, B, d ); print rating; Output: Magma V2.10-6 Thu Mar 25 2004 16:33:19 on modular [Seed = 1682404393] ------------------------------------- degree 5 Bound = 1137513005 2129024631825875754749788201627151749780670396327721627823338321538194998405649\ 5911366573853021918316783107387995317230889569230873441936471 6250000 -3.95594283801962022233954413140 100000000 -4.160733818294657488609570126275 0.0000000091136676420387322776467370159 Total time: 6.689 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Thu Mar 25 16:34:29 2004 Input: function CalcCont_p( p, disc, bound, F, f ); if disc mod p eq 0 then /* estimate using some small sample space */ cont_p := 0; upper_limit := bound^2; for i in [1..bound] do repeat a := Random( upper_limit ); b := Random( upper_limit ); until Gcd( a, b ) eq 1; // print a,b; value := Evaluate( F, [a, b] ); while value mod p eq 0 do value div:= p; cont_p +:= 1; end while; end for; cont_p := cont_p / (0.0 + bound); else K := GF(p); roots_mod_p := Roots( f, K ); q_p := #roots_mod_p; // print "roots mod p", p,q_p; /* add in the contribution of the projective roots */ d := Degree( f ); if Coefficient(f, d) mod p eq 0 then q_p +:= 1; end if; cont_p := q_p * p / (p * p - 1.0); end if; // print p,cont_p; return cont_p; end function; function CalcAlpha( F, bound, abort_p, abort_alpha, max_p ); Q := PolynomialRing(Integers()); f := Q!Evaluate( F, [X, 1] ); print bound^2; disc := Discriminant( f ); // print "discriminant = ", disc; a_d := Coefficient(f, Degree(f)); primes := [p : p in [1..max_p] | IsPrime(p)]; alpha := 0.0; for p in primes do cont_p := CalcCont_p( p, disc, bound, F, f ); // print "cont_p = ", cont_p; alpha +:= (1.0/(p-1) - cont_p)*Log(p); /* early-abort strategy */ if p eq abort_p and alpha gt abort_alpha then break; end if; end for; return alpha; end function; function ApproxDickmanRho( u ); if u le 1.0 then return 1.0; end if; return u^-u; end function; function RatePolynomials( F1, F2, alpha, B1, B2, d ) pi := Pi(RealField()); K := 1000; rating := 0.0; logB1 := Log( B1 ); logB2 := Log( B2 ); for i in [1..K] do theta := pi/K*(i - 0.5); tmp := Abs( Evaluate( F1, [Cos( theta ), Sin( theta ) ] ) ); u1 := ( Log( tmp ) + alpha ) / logB1 + d; tmp := Abs( Evaluate( F2, [Cos( theta ), Sin( theta ) ] ) ); u2 := Log( tmp ) / logB2 + 1.0; rating +:= ApproxDickmanRho( u1 ) * ApproxDickmanRho( u2 ); end for; return rating/K; end function; n:=21290246318258757547497882016271517497806703963277216278233383215381949984056495911366573853021918316783107387995317230889569230873441936471; d := 5; print "degree ", d; dlogd := d*Log(d); temp := 1.0/(d+1) * Log( n ); e := dlogd + Sqrt( dlogd^2 + 4*temp*Log(temp) ); B := Round( Exp( 0.5*e ) ); print "Bound = ", B; coeffs := []; coeffs[6] := -5142225622472630020004; coeffs[5] := -3356924353646091366162; coeffs[4] := 6545365626333869758617; coeffs[3] := -4722668925346720843884; coeffs[2] := -514856715582822510304; coeffs[1] := 237866611103421300000; m1_Value := 617119742304446938751913; P := PolynomialRing(Integers(),2); F := P!0; for i in [0..d] do F +:= coeffs[i+1]*X^(d-i)*Y^i; end for; eval := Evaluate(F,[m1_Value,1]); print eval; F2 := X*1 - Y*m1_Value; alpha := CalcAlpha( F, 2500, 11, -0.5, 100 ); print alpha; alpha := CalcAlpha( F, 10000, 0, 0, 2000 ); print alpha; rating := RatePolynomials( F, F2, alpha, B, B, d ); print rating; Output: Magma V2.10-6 Thu Mar 25 2004 16:34:22 on modular [Seed = 305201694] ------------------------------------- degree 5 Bound = 208332754 2129024631825875754749788201627151749780670396327721627823338321538194998405649\ 5911366573853021918316783107387995317230889569230873441936471 6250000 -3.87023635860140505097237120607 100000000 -4.104850007983155630984207795367 0.00000000307109468563465717768394401732 Total time: 6.639 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.48.221) Time: Thu Mar 25 17:00:54 2004 Input: R:=PolynomialRing(GF(5)); G25 := ext < GF(5)|(2+4*z+z^2) >; alpha:=PrimitiveElement(G25); beta:=PrimitiveElement(G5); p1:=alpha^2 + alpha*z + beta*(z^2); p2:=1 + alpha*z; Output: Magma V2.10-6 Thu Mar 25 2004 17:00:51 on modular [Seed = 587216354] ------------------------------------- >> beta:=PrimitiveElement(G5); ^ User error: Identifier 'G5' has not been declared or assigned >> p1:=alpha^2 + alpha*z + beta*(z^2); ^ User error: Identifier 'beta' has not been declared or assigned >> p2:=1 + alpha*z;; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.48.221) Time: Thu Mar 25 17:01:25 2004 Input: G5:=GF(5); R:=PolynomialRing(GF(5)); G25 := ext < GF(5)|(2+4*z+z^2) >; alpha:=PrimitiveElement(G25); beta:=PrimitiveElement(G5); p1:=alpha^2 + alpha*z + beta*(z^2); p2:=1 + alpha*z; Output: Magma V2.10-6 Thu Mar 25 2004 17:01:22 on modular [Seed = 3741173822] ------------------------------------- >> p1:=alpha^2 + alpha*z + beta*(z^2); ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt >> p2:=1 + alpha*z;; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.48.221) Time: Thu Mar 25 17:01:49 2004 Input: G5:=GF(5); R:=PolynomialRing(GF(5)); G25:= ext < GF(5)|(2+4*z+z^2) >; alpha:=PrimitiveElement(G25); beta:=PrimitiveElement(G5); p1:=alpha^2 + alpha*z + beta*(z^2); p2:=1 + alpha*z; Output: Magma V2.10-6 Thu Mar 25 2004 17:01:46 on modular [Seed = 3353661791] ------------------------------------- >> p1:=alpha^2 + alpha*z + beta*(z^2); ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt >> p2:=1 + alpha*z;; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.48.221) Time: Thu Mar 25 17:04:24 2004 Input: G5:=GF(5); R:=PolynomialRing(GF(5)); G25:= ext < GF(5)|(2+4*z+z^2) >; P:=PolynomialRing(G25); alpha:=PrimitiveElement(G25); beta:=PrimitiveElement(G5); p1:=alpha^2 + alpha*x + beta*(x^2); p2:=1 + alpha*x; Output: Magma V2.10-6 Thu Mar 25 2004 17:04:21 on modular [Seed = 3454982906] ------------------------------------- Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.48.221) Time: Thu Mar 25 17:05:37 2004 Input: G5:=GF(5); G25:= ext < GF(5)|(2+4*z+z^2) >; P:=PolynomialRing(G25); alpha:=PrimitiveElement(G25); beta:=PrimitiveElement(G5); p1:=alpha^2 + alpha*x + beta*(x^2); p2:=1 + alpha*x; Output: Magma V2.10-6 Thu Mar 25 2004 17:05:34 on modular [Seed = 4275955970] ------------------------------------- >> G25:= ext < GF(5)|(2+4*z+z^2) >; ^ User error: Identifier 'z' has not been declared or assigned >> P:=PolynomialRing(G25); ^ User error: Identifier 'G25' has not been declared or assigned >> alpha:=PrimitiveElement(G25); ^ User error: Identifier 'G25' has not been declared or assigned >> p1:=alpha^2 + alpha*x + beta*(x^2); ^ User error: Identifier 'alpha' has not been declared or assigned >> p2:=1 + alpha*x;; ^ User error: Identifier 'alpha' has not been declared or assigned Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.48.221) Time: Thu Mar 25 17:06:42 2004 Input: G5:=GF(5); R:=PolynomialRing(GF(5)); G25:= ext < GF(5)|(2+4*z+z^2) >; P:=PolynomialRing(G25); alpha:=PrimitiveElement(G25); beta:=PrimitiveElement(G5); p1:=alpha^2 + alpha*x + beta*(x^2); p2:=1 + alpha*x; p1+p2; Output: Magma V2.10-6 Thu Mar 25 2004 17:06:39 on modular [Seed = 3888443482] ------------------------------------- 2*x^2 + alpha^7*x + alpha^17 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.48.221) Time: Thu Mar 25 17:08:51 2004 Input: G5:=GF(5); R:=PolynomialRing(GF(5)); G25:= ext < GF(5)|(2+4*z+z^2) >; P:=PolynomialRing(G25); alpha:=PrimitiveElement(G25); beta:=PrimitiveElement(G5); p1:=alpha^2 + alpha*x + beta*(x^2); p2:=1 + alpha*x; p1; p2; p1+p2; Output: Magma V2.10-6 Thu Mar 25 2004 17:08:48 on modular [Seed = 3989763535] ------------------------------------- 2*x^2 + alpha*x + alpha^2 alpha*x + 1 2*x^2 + alpha^7*x + alpha^17 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.48.221) Time: Thu Mar 25 17:10:15 2004 Input: G25 := ext < GF(5)|(x^2+2*x+3) >; [Order(i): i in G25 | i ne 0 ]; Output: Magma V2.10-6 Thu Mar 25 2004 17:10:12 on modular [Seed = 2646508811] ------------------------------------- >> G25 := ext < GF(5)|(x^2+2*x+3) >; ^ User error: Identifier 'x' has not been declared or assigned >> [Order(i): i in G25 | i ne 0 ]; ^ User error: Identifier 'G25' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.48.221) Time: Thu Mar 25 17:11:10 2004 Input: R:=PolynomialRing(GF(5)); G25 := ext < GF(5)|(z^2+2*z+3) >; [Order(i): i in G25 | i ne 0 ]; Output: Magma V2.10-6 Thu Mar 25 2004 17:11:07 on modular [Seed = 2326368803] ------------------------------------- [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.48.221) Time: Thu Mar 25 17:11:38 2004 Input: R:=PolynomialRing(GF(5)); G25 := ext < GF(5)|(z^2+2*z+3) >; #[i: i in G25 | IsPrimitive(i)]; Output: Magma V2.10-6 Thu Mar 25 2004 17:11:35 on modular [Seed = 3012602614] ------------------------------------- 8 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.48.221) Time: Thu Mar 25 17:12:08 2004 Input: R:=PolynomialRing(GF(5)); G25 := ext < GF(5)|(z^2+2*z+3) >; #[i: i in G25]; Output: Magma V2.10-6 Thu Mar 25 2004 17:12:05 on modular [Seed = 3097207263] ------------------------------------- 25 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.48.221) Time: Thu Mar 25 17:12:35 2004 Input: R:=PolynomialRing(GF(5)); G25 := ext < GF(5)|(z^2+2*z+3) >; MinimalPolynomial(G25.1^5); Output: Magma V2.10-6 Thu Mar 25 2004 17:12:32 on modular [Seed = 2709698723] ------------------------------------- z^2 + 2*z + 3 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.48.221) Time: Thu Mar 25 17:12:56 2004 Input: R:=PolynomialRing(GF(5)); G25 := ext < GF(5)|(z^2+2*z+3) >; Degree(MinimalPolynomial(G25.1^5)); Output: Magma V2.10-6 Thu Mar 25 2004 17:12:53 on modular [Seed = 2928523161] ------------------------------------- 2 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.48.221) Time: Thu Mar 25 17:13:07 2004 Input: R:=PolynomialRing(GF(5)); G25 := ext < GF(5)|(z^2+2*z+3) >; CoefficientRing(MinimalPolynomial(G25.1^5)); Output: Magma V2.10-6 Thu Mar 25 2004 17:13:04 on modular [Seed = 1450528629] ------------------------------------- Finite field of size 5 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.48.221) Time: Thu Mar 25 17:13:56 2004 Input: R:=PolynomialRing(GF(5)); G25 := ext < GF(5)|(z^2+2*z+3) >; Roots(MinimalPolynomial(G25.1^5),G25); Output: Magma V2.10-6 Thu Mar 25 2004 17:13:53 on modular [Seed = 1551844782] ------------------------------------- [ , ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.48.221) Time: Thu Mar 25 17:14:36 2004 Input: R:=PolynomialRing(GF(5)); G25 := ext < GF(5)|(z^2+2*z+3) >; Roots(MinimalPolynomial(G25.1^5),GF(5)); Output: Magma V2.10-6 Thu Mar 25 2004 17:14:33 on modular [Seed = 1265128145] ------------------------------------- [] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.48.221) Time: Thu Mar 25 17:15:03 2004 Input: R:=PolynomialRing(GF(5)); G25 := ext < GF(5)|(z^2+2*z+3) >; alpha:=PrimitiveElement(G25); 2*(alpha^-3) - (alpha^5) + ((alpha^6)/(alpha+2)); Output: Magma V2.10-6 Thu Mar 25 2004 17:15:00 on modular [Seed = 1985310657] ------------------------------------- G25.1^8 Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.48.221) Time: Thu Mar 25 17:15:49 2004 Input: R:=PolynomialRing(GF(5)); G25 := ext < GF(5)|(z^2+2*z+3) >; alpha:=PrimitiveElement(G25); b:=2*(alpha^-3) - (alpha^5) + ((alpha^6)/(alpha+2)); IsInvertible(b); Output: Magma V2.10-6 Thu Mar 25 2004 17:15:46 on modular [Seed = 2103338812] ------------------------------------- true G25.1^16 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.48.221) Time: Thu Mar 25 17:16:22 2004 Input: R:=PolynomialRing(GF(5)); G25 := ext < GF(5)|(z^2+2*z+3) >; [i:i in G25 | IsInvertible(i)]; Output: Magma V2.10-6 Thu Mar 25 2004 17:16:19 on modular [Seed = 1783197706] ------------------------------------- [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23 ] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.48.221) Time: Thu Mar 25 17:16:43 2004 Input: R:=PolynomialRing(GF(5)); G25 := ext < GF(5)|(z^2+2*z+3) >; [ElementToSequence(i): i in G25]; Output: Magma V2.10-6 Thu Mar 25 2004 17:16:40 on modular [Seed = 288492298] ------------------------------------- [ [ 1, 0 ], [ 0, 1 ], [ 2, 3 ], [ 1, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 0 ], [ 0, 3 ], [ 1, 4 ], [ 3, 3 ], [ 1, 2 ], [ 4, 2 ], [ 4, 0 ], [ 0, 4 ], [ 3, 2 ], [ 4, 4 ], [ 3, 1 ], [ 2, 1 ], [ 2, 0 ], [ 0, 2 ], [ 4, 1 ], [ 2, 2 ], [ 4, 3 ], [ 1, 3 ], [ 0, 0 ] ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.48.221) Time: Thu Mar 25 17:17:39 2004 Input: R:=PolynomialRing(GF(5)); G25 := ext < GF(5)|(z^2+2*z+3) >; W:=PolynomialRing(G25); IsFinite(W); Output: Magma V2.10-6 Thu Mar 25 2004 17:17:36 on modular [Seed = 524027340] ------------------------------------- false Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.48.221) Time: Thu Mar 25 17:18:12 2004 Input: R:=PolynomialRing(GF(5)); G5:=GF(5); G25:= ext < GF(5)|(2+4*z+z^2) >; P:=PolynomialRing(G25); alpha:=PrimitiveElement(G25); beta:=PrimitiveElement(G5); p1:=alpha^2 + alpha*x + beta*(x^2); p2:=1 + alpha*x; Output: Magma V2.10-6 Thu Mar 25 2004 17:18:10 on modular [Seed = 86384628] ------------------------------------- Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.48.221) Time: Thu Mar 25 17:18:33 2004 Input: R:=PolynomialRing(GF(5)); G5:=GF(5); G25:= ext < GF(5)|(2+4*z+z^2) >; P:=PolynomialRing(G25); alpha:=PrimitiveElement(G25); beta:=PrimitiveElement(G5); p1:=alpha^2 + alpha*x + beta*(x^2); p2:=1 + alpha*x; p1+p2; Output: Magma V2.10-6 Thu Mar 25 2004 17:18:30 on modular [Seed = 856697302] ------------------------------------- 2*x^2 + alpha^7*x + alpha^17 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.48.221) Time: Thu Mar 25 17:19:42 2004 Input: R:=PolynomialRing(GF(5)); G5:=GF(5); G25:= ext < GF(5)|(z^2+2*z+3) >; P:=PolynomialRing(G25); alpha:=PrimitiveElement(G25); beta:=PrimitiveElement(G5); p1:=alpha^2 + alpha*x + beta*(x^2); p2:=1 + alpha*x; p1+p2; Output: Magma V2.10-6 Thu Mar 25 2004 17:19:39 on modular [Seed = 974725266] ------------------------------------- 2*x^2 + alpha^19*x + alpha^9 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.48.221) Time: Thu Mar 25 17:20:26 2004 Input: R:=PolynomialRing(GF(5)); G5:=GF(5); G25:= ext < GF(5)|(z^2+2*z+3) >; P:=PolynomialRing(G25); alpha:=PrimitiveElement(G25); beta:=PrimitiveElement(G5); p1:=alpha^2 + alpha*x + beta*(x^2); p2:=1 + alpha*x; p1*p2; Output: Magma V2.10-6 Thu Mar 25 2004 17:20:23 on modular [Seed = 705245534] ------------------------------------- alpha^19*x^3 + alpha^22*x^2 + alpha^10*x + alpha^2 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.48.221) Time: Thu Mar 25 17:21:43 2004 Input: R:=PolynomialRing(GF(5)); G5:=GF(5); G25:= ext < GF(5)|(z^2+2*z+3) >; P:=PolynomialRing(G25); alpha:=PrimitiveElement(G25); beta:=PrimitiveElement(G5); p1:=alpha^2 + alpha*x + beta*(x^2); p2:=1 + alpha*x; Quotrem(p1,p2); Output: Magma V2.10-6 Thu Mar 25 2004 17:21:40 on modular [Seed = 3623144688] ------------------------------------- alpha^17*x + alpha^5 alpha^15 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.48.221) Time: Thu Mar 25 17:24:32 2004 Input: R:=PolynomialRing(GF(5)); G5:=GF(5); G25:= ext < GF(5)|(z^2+2*z+3) >; P:=PolynomialRing(G25); alpha:=PrimitiveElement(G25); beta:=PrimitiveElement(G5); p1:=alpha^2 + alpha*x + beta*(x^2); p2:=1 + alpha*x; GCD(p1,p2); Output: Magma V2.10-6 Thu Mar 25 2004 17:24:29 on modular [Seed = 3707748498] ------------------------------------- 1 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.48.221) Time: Thu Mar 25 17:28:49 2004 Input: R:=PolynomialRing(GF(5)); G5:=GF(5); G25:= ext < GF(5)|(z^2+2*z+3) >; P:=PolynomialRing(G25); alpha:=PrimitiveElement(G25); beta:=PrimitiveElement(G5); p1:=alpha^2 + alpha*x + beta*(x^2); p2:=1 + alpha*x; LCM(p1,p2); Output: Magma V2.10-6 Thu Mar 25 2004 17:28:46 on modular [Seed = 3454980224] ------------------------------------- x^3 + alpha^3*x^2 + alpha^15*x + alpha^7 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.48.221) Time: Thu Mar 25 17:29:44 2004 Input: R:=PolynomialRing(GF(5)); G5:=GF(5); G25:= ext < GF(5)|(z^2+2*z+3) >; P:=PolynomialRing(G25); alpha:=PrimitiveElement(G25); beta:=PrimitiveElement(G5); p1:=alpha^2 + alpha*x + beta*(x^2); p2:=1 + alpha*x; XGCD(p1,p2); Output: Magma V2.10-6 Thu Mar 25 2004 17:29:41 on modular [Seed = 4107790834] ------------------------------------- 1 alpha^9 alpha^14*x + alpha^2 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.48.221) Time: Thu Mar 25 17:30:52 2004 Input: R:=PolynomialRing(GF(5)); G5:=GF(5); G25:= ext < GF(5)|(z^2+2*z+3) >; P:=PolynomialRing(G25); alpha:=PrimitiveElement(G25); beta:=PrimitiveElement(G5); p1:=alpha^2 + alpha*x + beta*(x^2); p2:=1 + alpha*x; 1=alpha^9*p1+(alpha^14*x + alpha^2)*p2; Output: Magma V2.10-6 Thu Mar 25 2004 17:30:49 on modular [Seed = 3838310702] ------------------------------------- 1 = 1 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.48.221) Time: Thu Mar 25 17:32:31 2004 Input: R:=PolynomialRing(GF(5)); G5:=GF(5); G25:= ext < GF(5)|(z^2+2*z+3) >; P:=PolynomialRing(G25); alpha:=PrimitiveElement(G25); beta:=PrimitiveElement(G5); p1:=alpha^2 + alpha*x + beta*(x^2); p2:=1 + alpha*x; p3:=(1/alpha^4)-alpha^(-3)*z+alpha^5*x^2; Factorization(p3); Output: Magma V2.10-6 Thu Mar 25 2004 17:32:28 on modular [Seed = 2461110077] ------------------------------------- >> p3:=(1/alpha^4)-alpha^(-3)*z+alpha^5*x^2; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt >> Factorization(p3);; ^ User error: Identifier 'p3' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.48.221) Time: Thu Mar 25 17:32:52 2004 Input: R:=PolynomialRing(GF(5)); G5:=GF(5); G25:= ext < GF(5)|(z^2+2*z+3) >; P:=PolynomialRing(G25); alpha:=PrimitiveElement(G25); beta:=PrimitiveElement(G5); p1:=alpha^2 + alpha*x + beta*(x^2); p2:=1 + alpha*x; p3:=(1/alpha^4)-alpha^(-3)*x+alpha^5*x^2; Factorization(p3); Output: Magma V2.10-6 Thu Mar 25 2004 17:32:49 on modular [Seed = 2579138523] ------------------------------------- [ ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.48.221) Time: Thu Mar 25 17:48:39 2004 Input: R:=PolynomialRing(GF(5)); G5:=GF(5); G25:= ext < GF(5)|(z^2+2*z+3) >; P:=PolynomialRing(G25); alpha:=PrimitiveElement(G25); beta:=PrimitiveElement(G5); p1:=alpha^2 + alpha*x + beta*(x^2); p2:=1 + alpha*x; p3:=(1/alpha^4)-alpha^(-3)*x+alpha^5*x^2; Roots(p3); Output: Magma V2.10-6 Thu Mar 25 2004 17:48:36 on modular [Seed = 3181288490] ------------------------------------- [] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host a212-113-164-105.netcabo.pt. (212.113.164.105) Time: Thu Mar 25 19:08:40 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Thu Mar 25 2004 19:08:37 on modular [Seed = 974720746] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host a212-113-164-105.netcabo.pt. (212.113.164.105) Time: Thu Mar 25 19:11:08 2004 Input: /* * An implementation of the Number Field Sieve as described in * "Factoring Integers with the Number Field Sieve" by J.P. Buhler, * H.W. Lenstra, and Carl Pomerance. (Algorithm 11.1) * * This code is not at all optimized - it is demonstration of the * Magma computer algebra package, and to for people who want to * learn the Number Field Sieve algorithm or how to code it. Note * that the algebraic square root code is available only for the * most recent release of Magma. * * This code is best demonstrated for numbers around 20-digits. * Larger numbers will cause the program to take up too much memory, * and numbers that are too small do not work well with this algorithm. * * "print" statements that can be ommitted are left justified. * * by Contini - Fri March 3rd, 2000. */ function SelectPolynomial(n); /* select a degree according to the asymptotic formula */ d := Round( Root( 3 * Log(n)/Log(Log(n)) , 3 ) ); print "degree ", d; m := Iroot( n, d ); print "m := ", m, ";"; coeffs := []; for i := d to 0 by -1 do temp2 := m^i; coeff := n div temp2; /* Append (~coeffs, coeff); */ coeffs[i+1] := coeff; n -:= coeff*temp2; end for; P := PolynomialRing( IntegerRing() ); f := P!coeffs; return f, m, d; end function; procedure RationalSieve( ~sieve_array, y, FB, log_primes, ~prev_roots, m_mod_p, sieve_len); /* * RATIONAL SIEVE */ sieve_array := [0 : i in [1..sieve_len]]; for i in [1..#FB] do p := FB[i]; logp := log_primes[i]; /* * Compute loc - the first location in the sieve array * where p divides the corresponding residue */ loc := prev_roots[i] - m_mod_p[i]; if loc lt 0 then loc +:= p; end if; prev_roots[i] := loc; /* sieve begins at location 1, so skip location 0 */ if loc eq 0 then loc := p; end if; /* MAIN SIEVE LOOP */ while loc le sieve_len do sieve_array[loc] +:= logp; loc +:= p; end while; end for; end procedure; procedure AlgebraicSieve( ~nf_sieve_array, y, ~nf_prev_roots, log_primes, R_p_set, sieve_len ); /* * NUMBER FIELD SIEVE */ nf_sieve_array := [0 : i in [1..sieve_len]]; for i in [1..#R_p_set] do R_p := R_p_set[i]; p := R_p[1]; r := R_p[2]; logp := R_p[3]; loc := nf_prev_roots[i] - r; if loc lt 0 then loc +:= p; end if; nf_prev_roots[i] := loc; if loc eq 0 then loc := p; end if; /* MAIN SIEVE LOOP */ while loc le sieve_len do nf_sieve_array[loc] +:= logp; loc +:= p; end while; end for; end procedure; procedure ScanSieveArray( J, b, bm, y, d, sieve_array, nf_sieve_array, error_term, ~num_rels, sieve_len, ~M, FB, prev_roots, nf_prev_roots, R_p_set, enough_rels, ~smooth_alg_elts, char_cols, char_offset ); /* scan sieve array */ threshold := Round( Log( bm ) ) - error_term; zero := [0: i in [1..d]]; x := zero; x[1] := 1; x[2] := b; nf_threshold := Round( Log( Abs( Norm( J!x ) ) ) ) - error_term; for a in [1..sieve_len] do if sieve_array[a] ge threshold then /* rational side appears to be smooth */ if nf_sieve_array[a] ge nf_threshold then /* number field side appears to be smooth */ if Gcd(b, a) ne 1 then /* relation is redundant */ continue; end if; /* see if it really is smooth */ relation := []; rational_side := a + bm; for i in [1..#FB] do p := FB[i]; if a mod p eq prev_roots[i] then e := 0; quot, rem := Quotrem( rational_side, p ); repeat rational_side := quot; e +:= 1; quot, rem := Quotrem( rational_side, p ); until rem ne 0; Append( ~relation, [i, e] ); end if; end for; if Abs(rational_side) ne 1 then /* rational side is not smooth :-( */ continue; end if; /* try algebraic side */ x := zero; x[1] := a; x[2] := b; alg_elt := J!x; norm := IntegerRing()!Norm(alg_elt); for i in [1..#R_p_set] do R_p := R_p_set[i]; p := R_p[1]; if a mod p eq nf_prev_roots[i] then e := 0; quot, rem := Quotrem( norm, p ); repeat norm := quot; e +:= 1; quot, rem := Quotrem( norm, p ); until rem ne 0; Append( ~relation, [i+#FB, e] ); end if; end for; if Abs(norm) ne 1 then /* algebraic side is not smooth :-( */ continue; end if; /* The relation is a keeper! */ print "a := ", a, "; b:= ", b,";"; num_rels +:= 1; /* Compute the character columns corresponding to alg_elt */ for i in [1..#char_cols] do p := char_cols[i][1]; r := char_cols[i][2]; if LegendreSymbol( (a + b*r) mod p, p ) eq -1 then M[num_rels, i + char_offset] := 1; end if; end for; /* store the algebraic element */ Append( ~smooth_alg_elts, alg_elt ); /* store relation in matrix */ for j in [1..#relation] do M[num_rels, relation[j, 1]] := relation[j, 2]; end for; if num_rels eq enough_rels then break; end if; /* update the nf_threshold - since the norms grow somewhat quickly, we waste a lot of time on false reports if this update is not made */ x := zero; x[1] := a; x[2] := b; nf_threshold := Round( Log( Abs( Norm( J!x ) ) ) ); nf_threshold -:= error_term; end if; end if; end for; end procedure; function NFS( n ) f, m, d := SelectPolynomial(n); fprime := Derivative( f ); J := NumberField( f ); /* choose y - the bound for smoothness */ dlogd := d*Log(d); temp := 1.0/d * Log( n ); e := dlogd + Sqrt( dlogd^2 + 4*temp*Log(temp) ); y := Round( Exp( 0.5*e ) ); print "smoothness bound is ", y; /* prepare data for rational sieve */ FB := [p : p in [2..y] | IsPrime( p ) ]; log_primes := [Round(Log(p)) : p in FB]; prev_roots := [0: p in FB]; m_mod_p := [m mod p: p in FB]; /* prepare data for the algebraic sieve */ cols := #FB; R_p_set := []; nf_prev_roots := []; for p in FB do K := GF(p); roots_mod_p := Roots( f, K ); for i in [1..#roots_mod_p] do r := IntegerRing()!roots_mod_p[i][1]; /* also include the rounded logarithm of p in the storage */ Append( ~R_p_set, [p, r, Round(Log(p))] ); Append( ~nf_prev_roots, 0 ); cols +:= 1; end for; end for; smooth_alg_elts := []; /* create the character columns */ char_offset := cols; num_char_cols := 3 * Ilog2( n ); char_cols := []; p := NextPrime( y ); i := 0; repeat K := GF(p); roots_mod_p := Roots( f, K ); for j in [1..#roots_mod_p] do r := IntegerRing()!roots_mod_p[j][1]; Append( ~char_cols, [p, r] ); i +:= 1; if i eq num_char_cols then break; end if; end for; p := NextPrime( p ); until i eq num_char_cols; cols +:= num_char_cols; enough_rels := cols+50; print "will quit after", enough_rels," relations"; /* allow for an error in the sieve threshold */ error_term := 3; /* set up matrix */ M := RMatrixSpace (IntegerRing(), enough_rels, cols)!0; num_rels := 0; b := 1; /* bm = b*m */ bm := m; sieve_len := y * 25; while true do RationalSieve( ~sieve_array, y, FB, log_primes, ~prev_roots, m_mod_p, sieve_len ); AlgebraicSieve( ~nf_sieve_array, y, ~nf_prev_roots, log_primes, R_p_set, sieve_len ); ScanSieveArray( J, b, bm, y, d, sieve_array, nf_sieve_array, error_term, ~num_rels, sieve_len, ~M, FB, prev_roots, nf_prev_roots, R_p_set, enough_rels, ~smooth_alg_elts, char_cols, char_offset ); bm +:= m; b +:= 1; print "Number of relations: ", num_rels; if num_rels ge enough_rels then break; end if; end while; print "matrix size: ",num_rels," by ", cols; print "finding null space"; gf2 := GF(2); Mprime := RMatrixSpace (gf2, num_rels, cols)!M; time null_space := NullSpace( Mprime ); /* "free" Mprime */ Mprime := 0; for j in [1..Dimension(null_space)] do print "trying null space vector #",j; /* get the first element of the solution vector */ soln := ChangeUniverse (Eltseq (null_space.j), IntegerRing()); /* compute the exponents of a relation that involves an algebraic square and an integer square */ exps := RSpace(IntegerRing(), cols)!0; for i in [1..num_rels] do if soln[i] eq 1 then exps +:= M[i]; end if; end for; /* compute the square root x of the integer element of the relation */ x := 1; for i in [1..#FB] do e := exps[i]; if e gt 0 then x := (x * ( FB[i]^(e div 2) ) ) mod n; end if; end for; x := ( x * Evaluate( fprime, m ) ) mod n; print x,"^2 mod n = ", x^2 mod n; list := []; for i in [1..num_rels] do if soln[i] eq 1 then Append( ~list, smooth_alg_elts[i] ); end if; end for; Append( ~list, Evaluate( fprime, alpha )^2 ); /* Compute the square root beta of the algebraic element */ ok, l := Root(2, list, []); if ok eq false then print "Element is not a square... continuing!"; continue; end if; /* map the sqrt to an integer v modulo n */ v := 1; for i in [1..#l] do list := l[i]; prod_list := 1; for j in [1..#list] do seq := Eltseq( list[j] ); elt := 0; for k in [0..d-1] do num := Numerator( seq[k+1] ) mod n; den := Denominator( seq[k+1] ) mod n; elt +:= ( ( num * Modinv( den, n ) mod n) * Modexp( m, k, n ) ) mod n; end for; prod_list := (prod_list * elt) mod n; end for; v := v * Modexp( Modinv( prod_list, n ), 2^(i-1), n ) mod n; end for; print v,"^2 mod n = ", v^2 mod n; gcd := Gcd(x-v, n); print "Gcd of ",x-v," and ",v," is ", gcd; if gcd ne 1 and gcd ne n then print "FACTOR: ", gcd; return gcd; end if; end for; print "no factor found :-( "; return 0; end function; Output: WARNING: MAGMA command contains unsafe command 'memory', so it will not be executed. ************** MAGMA ***************** Host ika.cs.mu.OZ.AU. (128.250.37.70) Time: Thu Mar 25 22:06:53 2004 Input: 2*3 Output: Magma V2.10-6 Thu Mar 25 2004 22:06:49 on modular [Seed = 2962452143] ------------------------------------- 6 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee94.uab.es. (158.109.66.94) Time: Fri Mar 26 05:23:38 2004 Input: P5 := PolynomialRing(Integers(5)); j := P5 ! [ 2, 4, 1 ]; G25 := ext < GF(5) | j >; rep_vect25 := [ElementToSequence(x): x in G25]; rep_exp25 := [x: x in G25]; Output: Magma V2.10-6 Fri Mar 26 2004 05:23:34 on modular [Seed = 654533597] ------------------------------------- Total time: 3.189 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee94.uab.es. (158.109.66.94) Time: Fri Mar 26 05:24:11 2004 Input: P5 := PolynomialRing(Integers(5)); j := P5 ! [ 2, 4, 1 ]; G25 := ext < GF(5) | j >; rep_vect25 := [ElementToSequence(x): x in G25]; rep_vect25; rep_exp25 := [x: x in G25]; rep_exp25; Output: Magma V2.10-6 Fri Mar 26 2004 05:24:08 on modular [Seed = 3657276749] ------------------------------------- [ [ 1, 0 ], [ 0, 1 ], [ 3, 1 ], [ 3, 4 ], [ 2, 2 ], [ 1, 4 ], [ 2, 0 ], [ 0, 2 ], [ 1, 2 ], [ 1, 3 ], [ 4, 4 ], [ 2, 3 ], [ 4, 0 ], [ 0, 4 ], [ 2, 4 ], [ 2, 1 ], [ 3, 3 ], [ 4, 1 ], [ 3, 0 ], [ 0, 3 ], [ 4, 3 ], [ 4, 2 ], [ 1, 1 ], [ 3, 2 ], [ 0, 0 ] ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 2, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 3, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee94.uab.es. (158.109.66.94) Time: Fri Mar 26 05:27:53 2004 Input: P5 := PolynomialRing(Integers(5)); j := P5 ! [ 2, 4, 1 ]; G25 := ext < GF(5) | j >; rep_vect25 := [ElementToSequence(x): x in G25]; rep_exp25 := [x: x in G25]; a:=[2,4,6,8]; a; Include(a,5); a; Output: Magma V2.10-6 Fri Mar 26 2004 05:27:50 on modular [Seed = 3253044283] ------------------------------------- [ 2, 4, 6, 8 ] [ 2, 4, 6, 8, 5 ] [ 2, 4, 6, 8 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee94.uab.es. (158.109.66.94) Time: Fri Mar 26 05:28:57 2004 Input: P5 := PolynomialRing(Integers(5)); j := P5 ! [ 2, 4, 1 ]; G25 := ext < GF(5) | j >; rep_vect25 := [ElementToSequence(x): x in G25]; rep_exp25 := [x: x in G25]; a:=[2,4,6,8]; b:=[1,3,5,7]; [: c in a | d in b ]; Output: Magma V2.10-6 Fri Mar 26 2004 05:28:54 on modular [Seed = 3989416023] ------------------------------------- >> [: c in a | d in b ]; ^ User error: Identifier 'd' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee94.uab.es. (158.109.66.94) Time: Fri Mar 26 05:29:16 2004 Input: P5 := PolynomialRing(Integers(5)); j := P5 ! [ 2, 4, 1 ]; G25 := ext < GF(5) | j >; rep_vect25 := [ElementToSequence(x): x in G25]; rep_exp25 := [x: x in G25]; a:=[2,4,6,8]; b:=[1,3,5,7]; [: c in a, d in b ]; Output: Magma V2.10-6 Fri Mar 26 2004 05:29:13 on modular [Seed = 3871515459] ------------------------------------- [ <2, 1>, <4, 1>, <6, 1>, <8, 1>, <2, 3>, <4, 3>, <6, 3>, <8, 3>, <2, 5>, <4, 5>, <6, 5>, <8, 5>, <2, 7>, <4, 7>, <6, 7>, <8, 7> ] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee94.uab.es. (158.109.66.94) Time: Fri Mar 26 05:31:04 2004 Input: P5 := PolynomialRing(Integers(5)); j := P5 ! [ 2, 4, 1 ]; G25 := ext < GF(5) | j >; rep_vect25 := [ElementToSequence(x): x in G25]; rep_exp25 := [x: x in G25]; a:=[2,4,6,8]; b:=[1,3,5,7]; [: c eq a[i], d eq b[i] | i in [0.. #a] ]; Output: Magma V2.10-6 Fri Mar 26 2004 05:31:01 on modular [Seed = 2208810426] ------------------------------------- >> [: c eq a[i], d eq b[i] | i in [0.. #a] ]; ^ User error: bad syntax Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee94.uab.es. (158.109.66.94) Time: Fri Mar 26 05:31:36 2004 Input: P5 := PolynomialRing(Integers(5)); j := P5 ! [ 2, 4, 1 ]; G25 := ext < GF(5) | j >; rep_vect25 := [ElementToSequence(x): x in G25]; rep_exp25 := [x: x in G25]; a:=[2,4,6,8]; b:=[1,3,5,7]; a[0]; 2 in a[0]; [: c eq a[i], d eq b[i] | i in [0.. #a] ]; Output: Magma V2.10-6 Fri Mar 26 2004 05:31:33 on modular [Seed = 3029398125] ------------------------------------- >> a[0]; ^ Runtime error in '[]': Sequence element 0 not defined >> 2 in a[0]; ^ Runtime error in '[]': Sequence element 0 not defined >> [: c eq a[i], d eq b[i] | i in [0.. #a] ]; ^ User error: bad syntax Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee94.uab.es. (158.109.66.94) Time: Fri Mar 26 05:31:51 2004 Input: P5 := PolynomialRing(Integers(5)); j := P5 ! [ 2, 4, 1 ]; G25 := ext < GF(5) | j >; rep_vect25 := [ElementToSequence(x): x in G25]; rep_exp25 := [x: x in G25]; a:=[2,4,6,8]; b:=[1,3,5,7]; a[1]; 2 in a[1]; [: c eq a[i], d eq b[i] | i in [1.. #a] ]; Output: Magma V2.10-6 Fri Mar 26 2004 05:31:49 on modular [Seed = 2911497060] ------------------------------------- 2 >> 2 in a[1]; ^ Runtime error in 'in': Bad argument types Argument types given: RngIntElt, RngIntElt >> [: c eq a[i], d eq b[i] | i in [1.. #a] ]; ^ User error: bad syntax Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee94.uab.es. (158.109.66.94) Time: Fri Mar 26 05:32:02 2004 Input: P5 := PolynomialRing(Integers(5)); j := P5 ! [ 2, 4, 1 ]; G25 := ext < GF(5) | j >; rep_vect25 := [ElementToSequence(x): x in G25]; rep_exp25 := [x: x in G25]; a:=[2,4,6,8]; b:=[1,3,5,7]; a[1]; 2 eq a[1]; [: c eq a[i], d eq b[i] | i in [1.. #a] ]; Output: Magma V2.10-6 Fri Mar 26 2004 05:31:59 on modular [Seed = 2793594981] ------------------------------------- 2 true >> [: c eq a[i], d eq b[i] | i in [1.. #a] ]; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 05:33:48 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); true IsIrreducible(q1); true IsIrreducible(q2); false IsIrreducible(r1); true G9:=ext; G16:=ext; G25:=ext; IsIrreductible(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; Output: Magma V2.10-6 Fri Mar 26 2004 05:33:45 on modular [Seed = 1484529420] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true >> IsIrreducible(q1); ^ User error: bad syntax >> IsIrreducible(q2); ^ User error: bad syntax >> IsIrreducible(r1); ^ User error: bad syntax >> G9:=ext; ^ User error: bad syntax >> IsIrreductible(alpha); ^ User error: Identifier 'IsIrreductible' has not been declared or assigned [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 05:34:29 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsIrreductible(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; Output: Magma V2.10-6 Fri Mar 26 2004 05:34:26 on modular [Seed = 1400312892] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true >> IsIrreductible(alpha); ^ User error: Identifier 'IsIrreductible' has not been declared or assigned [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 05:35:22 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; Output: Magma V2.10-6 Fri Mar 26 2004 05:35:19 on modular [Seed = 1180828028] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 05:36:01 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) {<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25} Output: Magma V2.10-6 Fri Mar 26 2004 05:35:58 on modular [Seed = 2036154026] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } >> {<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25} ^ Runtime error in '^': Bad argument types Argument types given: FldFinElt, FldFinElt Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 05:37:01 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; ElementToSequence(alpha^20); Output: Magma V2.10-6 Fri Mar 26 2004 05:36:58 on modular [Seed = 1935095012] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } [ 4, 1 ] Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 05:37:18 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) {<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; Output: Magma V2.10-6 Fri Mar 26 2004 05:37:15 on modular [Seed = 1783508460] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } >> {<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; ^ Runtime error in '^': Bad argument types Argument types given: FldFinElt, FldFinElt Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 05:37:45 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) {<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; Output: Magma V2.10-6 Fri Mar 26 2004 05:37:42 on modular [Seed = 490298038] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } >> {<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; ^ Runtime error in '^': Bad argument types Argument types given: FldFinElt, FldFinElt Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee94.uab.es. (158.109.66.94) Time: Fri Mar 26 05:39:03 2004 Input: P5 := PolynomialRing(Integers(5)); j := P5 ! [ 2, 4, 1 ]; G25 := ext < GF(5) | j >; rep_vect25 := [ElementToSequence(x): x in G25]; rep_exp25 := [x: x in G25]; a:=[2,4,6,8]; b:=[1,3,5,7]; a[1]; 2 eq a[1]; [: i in [1..4] | c eq a[i], d eq b[i] | i in [1.. #a] ]; Output: Magma V2.10-6 Fri Mar 26 2004 05:39:00 on modular [Seed = 389242638] ------------------------------------- 2 true >> [: i in [1..4] | c eq a[i], d eq b[i] | i in [1.. #a] ]; ^ User error: bad syntax Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 05:39:07 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; {[ElementToSequence(alpha^i)] : i in G25} Output: Magma V2.10-6 Fri Mar 26 2004 05:39:04 on modular [Seed = 237651483] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } >> {[ElementToSequence(alpha^i)] : i in G25} ^ Runtime error in '^': Bad argument types Argument types given: FldFinElt, FldFinElt Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee94.uab.es. (158.109.66.94) Time: Fri Mar 26 05:39:21 2004 Input: P5 := PolynomialRing(Integers(5)); j := P5 ! [ 2, 4, 1 ]; G25 := ext < GF(5) | j >; rep_vect25 := [ElementToSequence(x): x in G25]; rep_exp25 := [x: x in G25]; a:=[2,4,6,8]; b:=[1,3,5,7]; a[1]; 2 eq a[1]; [: i in [1..4] | c eq a[i], d eq b[i] ]; Output: Magma V2.10-6 Fri Mar 26 2004 05:39:18 on modular [Seed = 19220746] ------------------------------------- 2 true >> [: i in [1..4] | c eq a[i], d eq b[i] ]; ^ User error: bad syntax Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 05:39:28 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; {[ElementToSequence(alpha^x)] : x in G25} Output: Magma V2.10-6 Fri Mar 26 2004 05:39:25 on modular [Seed = 941387832] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } >> {[ElementToSequence(alpha^x)] : x in G25} ^ Runtime error in '^': Bad argument types Argument types given: FldFinElt, FldFinElt Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 05:39:49 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; {[ElementToSequence(alpha^z)] : x in G25} Output: Magma V2.10-6 Fri Mar 26 2004 05:39:46 on modular [Seed = 840333853] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } >> {[ElementToSequence(alpha^z)] : x in G25} ^ Runtime error in '^': Bad argument types Argument types given: FldFinElt, RngUPolElt Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee94.uab.es. (158.109.66.94) Time: Fri Mar 26 05:39:52 2004 Input: P5 := PolynomialRing(Integers(5)); j := P5 ! [ 2, 4, 1 ]; G25 := ext < GF(5) | j >; rep_vect25 := [ElementToSequence(x): x in G25]; rep_exp25 := [x: x in G25]; a:=[2,4,6,8]; b:=[1,3,5,7]; a[1]; 2 eq a[1]; [: i in [1..4]]; Output: Magma V2.10-6 Fri Mar 26 2004 05:39:49 on modular [Seed = 620850445] ------------------------------------- 2 true [ <2, 1>, <4, 3>, <6, 5>, <8, 7> ] Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 05:40:34 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; [ElementToSequence(alpha^20)] Output: Magma V2.10-6 Fri Mar 26 2004 05:40:31 on modular [Seed = 3589381399] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } [ [ 4, 1 ] ] Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 05:40:54 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; ElementToSequence(alpha^20); Output: Magma V2.10-6 Fri Mar 26 2004 05:40:51 on modular [Seed = 3488319265] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } [ 4, 1 ] Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee94.uab.es. (158.109.66.94) Time: Fri Mar 26 05:41:30 2004 Input: P5 := PolynomialRing(Integers(5)); j := P5 ! [ 2, 4, 1 ]; G25 := ext < GF(5) | j >; rep_vect25 := [ElementToSequence(x): x in G25]; rep_exp25 := [x: x in G25]; a:=[2,4,6,8]; b:=[1,3,5,7]; a[1]; 2 eq a[1]; [: i in [1..4]]; [x in G25]; [x in G25]; Output: Magma V2.10-6 Fri Mar 26 2004 05:41:27 on modular [Seed = 3336736332] ------------------------------------- 2 true [ <2, 1>, <4, 3>, <6, 5>, <8, 7> ] >> [x in G25]; ^ User error: Identifier 'x' has not been declared or assigned >> [x in G25];; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee94.uab.es. (158.109.66.94) Time: Fri Mar 26 05:41:53 2004 Input: P5 := PolynomialRing(Integers(5)); j := P5 ! [ 2, 4, 1 ]; G25 := ext < GF(5) | j >; rep_vect25 := [ElementToSequence(x): x in G25]; rep_exp25 := [x: x in G25]; a:=[2,4,6,8]; b:=[1,3,5,7]; a[1]; 2 eq a[1]; [: i in [1..4]]; [x:x in G25]; [x:x in G25]; Output: Magma V2.10-6 Fri Mar 26 2004 05:41:50 on modular [Seed = 4192055626] ------------------------------------- 2 true [ <2, 1>, <4, 3>, <6, 5>, <8, 7> ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 2, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 3, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 2, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 3, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 05:42:11 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; {[ElementToSequence(alpha^r)]: r in G25}; Output: Magma V2.10-6 Fri Mar 26 2004 05:42:07 on modular [Seed = 4040472658] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } >> {[ElementToSequence(alpha^r)]: r in G25}; ^ Runtime error in '^': Bad argument types Argument types given: FldFinElt, FldFinElt Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 05:42:28 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; {ElementToSequence(alpha^r): r in G25}; Output: Magma V2.10-6 Fri Mar 26 2004 05:42:25 on modular [Seed = 3956253351] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } >> {ElementToSequence(alpha^r): r in G25}; ^ Runtime error in '^': Bad argument types Argument types given: FldFinElt, FldFinElt Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee94.uab.es. (158.109.66.94) Time: Fri Mar 26 05:42:47 2004 Input: P5 := PolynomialRing(Integers(5)); j := P5 ! [ 2, 4, 1 ]; G25 := ext < GF(5) | j >; rep_vect25 := [ElementToSequence(x): x in G25]; rep_exp25 := [x: x in G25]; [: i in [1..#rep_vect25]]; Output: Magma V2.10-6 Fri Mar 26 2004 05:42:44 on modular [Seed = 3804670875] ------------------------------------- [ <[ 1, 0 ], 1>, <[ 0, 1 ], alpha>, <[ 3, 1 ], alpha^2>, <[ 3, 4 ], alpha^3>, <[ 2, 2 ], alpha^4>, <[ 1, 4 ], alpha^5>, <[ 2, 0 ], 2>, <[ 0, 2 ], alpha^7>, <[ 1, 2 ], alpha^8>, <[ 1, 3 ], alpha^9>, <[ 4, 4 ], alpha^10>, <[ 2, 3 ], alpha^11>, <[ 4, 0 ], 4>, <[ 0, 4 ], alpha^13>, <[ 2, 4 ], alpha^14>, <[ 2, 1 ], alpha^15>, <[ 3, 3 ], alpha^16>, <[ 4, 1 ], alpha^17>, <[ 3, 0 ], 3>, <[ 0, 3 ], alpha^19>, <[ 4, 3 ], alpha^20>, <[ 4, 2 ], alpha^21>, <[ 1, 1 ], alpha^22>, <[ 3, 2 ], alpha^23>, <[ 0, 0 ], 0> ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 05:46:41 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; {[ElementToSequence(alpha^r)]: r in [0..24]}; Output: Magma V2.10-6 Fri Mar 26 2004 05:46:38 on modular [Seed = 2461456577] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } { [ [ 0, 1 ] ], [ [ 0, 2 ] ], [ [ 0, 3 ] ], [ [ 4, 0 ] ], [ [ 0, 4 ] ], [ [ 4, 1 ] ], [ [ 4, 2 ] ], [ [ 4, 3 ] ], [ [ 4, 4 ] ], [ [ 1, 0 ] ], [ [ 1, 1 ] ], [ [ 1, 2 ] ], [ [ 1, 3 ] ], [ [ 1, 4 ] ], [ [ 2, 0 ] ], [ [ 2, 1 ] ], [ [ 2, 2 ] ], [ [ 2, 3 ] ], [ [ 2, 4 ] ], [ [ 3, 0 ] ], [ [ 3, 1 ] ], [ [ 3, 2 ] ], [ [ 3, 3 ] ], [ [ 3, 4 ] ] } Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 05:47:02 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; {ElementToSequence(alpha^r): r in [0..24]}; Output: Magma V2.10-6 Fri Mar 26 2004 05:46:59 on modular [Seed = 2241974267] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } { [ 0, 1 ], [ 0, 2 ], [ 0, 3 ], [ 4, 0 ], [ 0, 4 ], [ 4, 1 ], [ 4, 2 ], [ 4, 3 ], [ 4, 4 ], [ 1, 0 ], [ 1, 1 ], [ 1, 2 ], [ 1, 3 ], [ 1, 4 ], [ 2, 0 ], [ 2, 1 ], [ 2, 2 ], [ 2, 3 ], [ 2, 4 ], [ 3, 0 ], [ 3, 1 ], [ 3, 2 ], [ 3, 3 ], [ 3, 4 ] } Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 05:47:37 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; {[0,0] cat ElementToSequence(alpha^r): r in [0..24]}; Output: Magma V2.10-6 Fri Mar 26 2004 05:47:34 on modular [Seed = 3164141223] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } { [ 0, 0, 0, 1 ], [ 0, 0, 0, 2 ], [ 0, 0, 0, 3 ], [ 0, 0, 4, 0 ], [ 0, 0, 0, 4 ], [ 0, 0, 4, 1 ], [ 0, 0, 4, 2 ], [ 0, 0, 4, 3 ], [ 0, 0, 4, 4 ], [ 0, 0, 1, 0 ], [ 0, 0, 1, 1 ], [ 0, 0, 1, 2 ], [ 0, 0, 1, 3 ], [ 0, 0, 1, 4 ], [ 0, 0, 2, 0 ], [ 0, 0, 2, 1 ], [ 0, 0, 2, 2 ], [ 0, 0, 2, 3 ], [ 0, 0, 2, 4 ], [ 0, 0, 3, 0 ], [ 0, 0, 3, 1 ], [ 0, 0, 3, 2 ], [ 0, 0, 3, 3 ], [ 0, 0, 3, 4 ] } Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 05:48:04 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; {[0,0] cat [ElementToSequence(alpha^r)]: r in [0..24]}; Output: Magma V2.10-6 Fri Mar 26 2004 05:48:01 on modular [Seed = 3079929227] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } >> {[0,0] cat [ElementToSequence(alpha^r)]: r in [0..24]}; ^ Runtime error in 'cat': Incompatible sequences Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee94.uab.es. (158.109.66.94) Time: Fri Mar 26 05:48:13 2004 Input: P2 := PolynomialRing(Integers(2)); g := P2 ! [ 1, 1, 0, 0, 1 ]; G16 := ext < GF(2) | g >; rep_vect16 := [ElementToSequence(x): x in G16]; rep_exp16 := [x: x in G16]; [: i in [1..#rep_vect16]]; Output: Magma V2.10-6 Fri Mar 26 2004 05:48:10 on modular [Seed = 2844648350] ------------------------------------- [ <[ 1, 0, 0, 0 ], 1>, <[ 0, 1, 0, 0 ], gamma>, <[ 0, 0, 1, 0 ], gamma^2>, <[ 0, 0, 0, 1 ], gamma^3>, <[ 1, 1, 0, 0 ], gamma^4>, <[ 0, 1, 1, 0 ], gamma^5>, <[ 0, 0, 1, 1 ], gamma^6>, <[ 1, 1, 0, 1 ], gamma^7>, <[ 1, 0, 1, 0 ], gamma^8>, <[ 0, 1, 0, 1 ], gamma^9>, <[ 1, 1, 1, 0 ], gamma^10>, <[ 0, 1, 1, 1 ], gamma^11>, <[ 1, 1, 1, 1 ], gamma^12>, <[ 1, 0, 1, 1 ], gamma^13>, <[ 1, 0, 0, 1 ], gamma^14>, <[ 0, 0, 0, 0 ], 0> ] Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 05:48:40 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; {<[0,0]> cat <[ElementToSequence(alpha^r)]>: r in [0..24]}; Output: Magma V2.10-6 Fri Mar 26 2004 05:48:37 on modular [Seed = 2693065336] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } >> {<[0,0]> cat <[ElementToSequence(alpha^r)]>: r in [0..24]}; ^ Runtime error in 'cat': Bad argument types Argument types given: Tup, Tup Total time: 3.049 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 05:49:06 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; {[0,0] cat ElementToSequence(alpha^r): r in [0..24]}; Output: Magma V2.10-6 Fri Mar 26 2004 05:49:03 on modular [Seed = 1484526233] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } { [ 0, 0, 0, 1 ], [ 0, 0, 0, 2 ], [ 0, 0, 0, 3 ], [ 0, 0, 4, 0 ], [ 0, 0, 0, 4 ], [ 0, 0, 4, 1 ], [ 0, 0, 4, 2 ], [ 0, 0, 4, 3 ], [ 0, 0, 4, 4 ], [ 0, 0, 1, 0 ], [ 0, 0, 1, 1 ], [ 0, 0, 1, 2 ], [ 0, 0, 1, 3 ], [ 0, 0, 1, 4 ], [ 0, 0, 2, 0 ], [ 0, 0, 2, 1 ], [ 0, 0, 2, 2 ], [ 0, 0, 2, 3 ], [ 0, 0, 2, 4 ], [ 0, 0, 3, 0 ], [ 0, 0, 3, 1 ], [ 0, 0, 3, 2 ], [ 0, 0, 3, 3 ], [ 0, 0, 3, 4 ] } Total time: 3.059 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 05:50:06 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; {<[0],[0,0]> cat <[r],ElementToSequence(alpha^r)>: r in [0..24]}; Output: Magma V2.10-6 Fri Mar 26 2004 05:50:03 on modular [Seed = 1231881164] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } >> {<[0],[0,0]> cat <[r],ElementToSequence(alpha^r)>: r in [0..24]}; ^ Runtime error in 'cat': Bad argument types Argument types given: Tup, Tup Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 05:51:08 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; {<[0],[0,0]> cat <[r],ElementToSequence(alpha^r)>: r in [0..24]}; Output: Magma V2.10-6 Fri Mar 26 2004 05:51:05 on modular [Seed = 2119841081] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } >> {<[0],[0,0]> cat <[r],ElementToSequence(alpha^r)>: r in [0..24]}; ^ Runtime error in 'cat': Bad argument types Argument types given: Tup, Tup Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 05:51:33 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; {<[0],[0,0]> cat <[r],ElementToSequence(alpha^r)>: r in [0..24]}; Output: Magma V2.10-6 Fri Mar 26 2004 05:51:30 on modular [Seed = 2001943579] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } >> {<[0],[0,0]> cat <[r],ElementToSequence(alpha^r)>: r in [0..24]}; ^ Runtime error in 'cat': Bad argument types Argument types given: Tup, Tup Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 05:52:16 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; {<0,[0,0]> cat : r in [0..24]}; Output: Magma V2.10-6 Fri Mar 26 2004 05:52:13 on modular [Seed = 1816668015] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } >> {<0,[0,0]> cat : r in [0..24]}; ^ Runtime error in 'cat': Bad argument types Argument types given: Tup, Tup Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 05:52:34 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; {<0,[0,0]> cat : r in [0..24]}; Output: Magma V2.10-6 Fri Mar 26 2004 05:52:31 on modular [Seed = 1648765267] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } >> {<0,[0,0]> cat : r in [0..24]}; ^ Runtime error in 'cat': Bad argument types Argument types given: Tup, Tup Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 05:53:36 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; //{<0,[0,0]> cat : r in [0..24]}; {<[0],[0,0]> cat <[1],[3,3]>; Output: Magma V2.10-6 Fri Mar 26 2004 05:53:33 on modular [Seed = 406606827] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } >> {<[0],[0,0]> cat <[1],[3,3]>; ; ^ User error: bad syntax Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 05:53:55 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; //{<0,[0,0]> cat : r in [0..24]}; <[0],[0,0]> cat <[1],[3,3]>; Output: Magma V2.10-6 Fri Mar 26 2004 05:53:52 on modular [Seed = 288709263] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } >> <[0],[0,0]> cat <[1],[3,3]>; ; ^ Runtime error in 'cat': Bad argument types Argument types given: Tup, Tup Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 05:54:21 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; //{<0,[0,0]> cat : r in [0..24]}; [0],[0,0] cat [1],[3,3]; Output: Magma V2.10-6 Fri Mar 26 2004 05:54:18 on modular [Seed = 102911362] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } [ 0 ] [ 0, 0, 1 ] [ 3, 3 ] Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 05:54:59 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; //{<0,[0,0]> cat : r in [0..24]}; <0,[0,0]> cat <1,[3,3]>; Output: Magma V2.10-6 Fri Mar 26 2004 05:54:56 on modular [Seed = 1058763617] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } >> <0,[0,0]> cat <1,[3,3]>; ; ^ Runtime error in 'cat': Bad argument types Argument types given: Tup, Tup Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 05:55:40 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; //{<0,[0,0]> cat : r in [0..24]}; <0,[0,0]> cat <1,[3,3]>; [0] cat [1]; Output: Magma V2.10-6 Fri Mar 26 2004 05:55:37 on modular [Seed = 806648903] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } >> <0,[0,0]> cat <1,[3,3]>; ^ Runtime error in 'cat': Bad argument types Argument types given: Tup, Tup [ 0, 1 ] Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 05:56:27 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; //{<0,[0,0]> cat : r in [0..24]}; <0,[0,0]> cat <1,[3,3]>; [0,[0]] cat [1]; Output: Magma V2.10-6 Fri Mar 26 2004 05:56:24 on modular [Seed = 637692448] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } >> <0,[0,0]> cat <1,[3,3]>; ^ Runtime error in 'cat': Bad argument types Argument types given: Tup, Tup >> [0,[0]] cat [1];; ^ User error: Could not find a valid universe for the sequence Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 05:56:55 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; //{<0,[0,0]> cat : r in [0..24]}; <0,[0,0]> cat <1,[3,3]>; 0 cat 1; Output: Magma V2.10-6 Fri Mar 26 2004 05:56:52 on modular [Seed = 3757806581] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } >> <0,[0,0]> cat <1,[3,3]>; ^ Runtime error in 'cat': Bad argument types Argument types given: Tup, Tup >> 0 cat 1;; ^ Runtime error in 'cat': Bad argument types Argument types given: RngIntElt, RngIntElt Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 05:57:25 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; //{<0,[0,0]> cat : r in [0..24]}; <0,[0,0]> cat <1,[3,3]>; [0,1] cat [1,0]; Output: Magma V2.10-6 Fri Mar 26 2004 05:57:22 on modular [Seed = 3572537368] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } >> <0,[0,0]> cat <1,[3,3]>; ^ Runtime error in 'cat': Bad argument types Argument types given: Tup, Tup [ 0, 1, 1, 0 ] Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 05:58:08 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; //{<0,[0,0]> cat : r in [0..24]}; <0,[0,0]> cat <1,[3,3]>; <[0,1]> cat <[1,0]>; Output: Magma V2.10-6 Fri Mar 26 2004 05:58:05 on modular [Seed = 4141005333] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } >> <0,[0,0]> cat <1,[3,3]>; ^ Runtime error in 'cat': Bad argument types Argument types given: Tup, Tup >> <[0,1]> cat <[1,0]>;; ^ Runtime error in 'cat': Bad argument types Argument types given: Tup, Tup Total time: 3.109 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 05:58:33 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; //{<0,[0,0]> cat : r in [0..24]}; <0,[0,0]> cat <1,[3,3]>; [<[0,1]>] cat [<[1,0]>]; Output: Magma V2.10-6 Fri Mar 26 2004 05:58:29 on modular [Seed = 3871517293] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } >> <0,[0,0]> cat <1,[3,3]>; ^ Runtime error in 'cat': Bad argument types Argument types given: Tup, Tup [ <[ 0, 1 ]>, <[ 1, 0 ]> ] Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 05:59:07 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; //{<0,[0,0]> cat : r in [0..24]}; <0,[0,0]> cat <1,[3,3]>; [[0,1]] cat [<[1,0]>]; Output: Magma V2.10-6 Fri Mar 26 2004 05:59:03 on modular [Seed = 2528303664] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } >> <0,[0,0]> cat <1,[3,3]>; ^ Runtime error in 'cat': Bad argument types Argument types given: Tup, Tup >> [[0,1]] cat [<[1,0]>];; ^ Runtime error in 'cat': Incompatible sequences Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 05:59:21 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; //{<0,[0,0]> cat : r in [0..24]}; <0,[0,0]> cat <1,[3,3]>; [[0,1]] cat [[1,0]]; Output: Magma V2.10-6 Fri Mar 26 2004 05:59:18 on modular [Seed = 2410398423] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } >> <0,[0,0]> cat <1,[3,3]>; ^ Runtime error in 'cat': Bad argument types Argument types given: Tup, Tup [ [ 0, 1 ], [ 1, 0 ] ] Total time: 3.029 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 06:00:00 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; //{<0,[0,0]> cat : r in [0..24]}; <0,[0,0]> cat <1,[3,3]>; [[0,[1]]] cat [[1,[0]]]; Output: Magma V2.10-6 Fri Mar 26 2004 05:59:56 on modular [Seed = 2225129974] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } >> <0,[0,0]> cat <1,[3,3]>; ^ Runtime error in 'cat': Bad argument types Argument types given: Tup, Tup >> [[0,[1]]] cat [[1,[0]]];; ^ User error: Could not find a valid universe for the sequence Total time: 3.089 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 06:01:08 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; //{<0,[0,0]> cat : r in [0..24]}; {<0,[0,0]>} cat {<1,[3,3]>}; Output: Magma V2.10-6 Fri Mar 26 2004 06:01:04 on modular [Seed = 2894651778] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } >> {<0,[0,0]>} cat {<1,[3,3]>}; ^ Runtime error in 'cat': Bad argument types Argument types given: SetEnum[Tup], SetEnum[Tup] Total time: 3.339 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 06:02:00 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; //{<0,[0,0]> cat : r in [0..24]}; [<0,[0,0]> cat {<1,[3,3]>]; Output: Magma V2.10-6 Fri Mar 26 2004 06:01:37 on modular [Seed = 1467161241] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } >> [<0,[0,0]> cat {<1,[3,3]>]; ^ User error: bad syntax Total time: 3.510 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 06:02:29 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; //{<0,[0,0]> cat : r in [0..24]}; [<0,[0,0]> cat <1,[3,3]>]; Output: Magma V2.10-6 Fri Mar 26 2004 06:02:25 on modular [Seed = 1298727123] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } >> [<0,[0,0]> cat <1,[3,3]>]; ^ Runtime error in 'cat': Bad argument types Argument types given: Tup, Tup Total time: 3.509 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 06:02:56 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; //{<0,[0,0]> cat : r in [0..24]}; <0,[0,0]> cat <1,[3,3]>; Output: Magma V2.10-6 Fri Mar 26 2004 06:02:53 on modular [Seed = 1147144646] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } >> <0,[0,0]> cat <1,[3,3]>; ^ Runtime error in 'cat': Bad argument types Argument types given: Tup, Tup Total time: 3.119 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 06:03:36 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; //{<0,[0,0]> cat : r in [0..24]}; <[0],[0,0]> cat <[1],[3,3]>; Output: Magma V2.10-6 Fri Mar 26 2004 06:03:31 on modular [Seed = 2052994086] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } >> <[0],[0,0]> cat <[1],[3,3]>; ^ Runtime error in 'cat': Bad argument types Argument types given: Tup, Tup Total time: 5.100 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 06:03:59 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; //{<0,[0,0]> cat : r in [0..24]}; <[[0],[0,0]]> cat <[[1],[3,3]]>; Output: Magma V2.10-6 Fri Mar 26 2004 06:03:55 on modular [Seed = 1884569140] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } >> <[[0],[0,0]]> cat <[[1],[3,3]]>; ^ Runtime error in 'cat': Bad argument types Argument types given: Tup, Tup Total time: 3.349 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 06:04:57 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; [<0,[0,0]> cat : r in [0..24]]; Output: Magma V2.10-6 Fri Mar 26 2004 06:04:54 on modular [Seed = 1732454766] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } >> [<0,[0,0]> cat : r in [0..24]]; ^ Runtime error in 'cat': Bad argument types Argument types given: Tup, Tup Total time: 3.409 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 06:06:25 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; [[<0,[0,0]>] cat []: r in [0..24]]; Output: Magma V2.10-6 Fri Mar 26 2004 06:06:22 on modular [Seed = 372398311] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } [ [ <0, [ 0, 0 ]>, <0, [ 1, 0 ]> ], [ <0, [ 0, 0 ]>, <1, [ 0, 1 ]> ], [ <0, [ 0, 0 ]>, <2, [ 2, 3 ]> ], [ <0, [ 0, 0 ]>, <3, [ 1, 1 ]> ], [ <0, [ 0, 0 ]>, <4, [ 2, 4 ]> ], [ <0, [ 0, 0 ]>, <5, [ 3, 4 ]> ], [ <0, [ 0, 0 ]>, <6, [ 3, 0 ]> ], [ <0, [ 0, 0 ]>, <7, [ 0, 3 ]> ], [ <0, [ 0, 0 ]>, <8, [ 1, 4 ]> ], [ <0, [ 0, 0 ]>, <9, [ 3, 3 ]> ], [ <0, [ 0, 0 ]>, <10, [ 1, 2 ]> ], [ <0, [ 0, 0 ]>, <11, [ 4, 2 ]> ], [ <0, [ 0, 0 ]>, <12, [ 4, 0 ]> ], [ <0, [ 0, 0 ]>, <13, [ 0, 4 ]> ], [ <0, [ 0, 0 ]>, <14, [ 3, 2 ]> ], [ <0, [ 0, 0 ]>, <15, [ 4, 4 ]> ], [ <0, [ 0, 0 ]>, <16, [ 3, 1 ]> ], [ <0, [ 0, 0 ]>, <17, [ 2, 1 ]> ], [ <0, [ 0, 0 ]>, <18, [ 2, 0 ]> ], [ <0, [ 0, 0 ]>, <19, [ 0, 2 ]> ], [ <0, [ 0, 0 ]>, <20, [ 4, 1 ]> ], [ <0, [ 0, 0 ]>, <21, [ 2, 2 ]> ], [ <0, [ 0, 0 ]>, <22, [ 4, 3 ]> ], [ <0, [ 0, 0 ]>, <23, [ 1, 3 ]> ], [ <0, [ 0, 0 ]>, <24, [ 1, 0 ]> ] ] Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 06:06:49 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; {[<0,[0,0]>] cat []: r in [0..24]}; Output: Magma V2.10-6 Fri Mar 26 2004 06:06:46 on modular [Seed = 220808084] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } { [ <0, [ 0, 0 ]>, <9, [ 3, 3 ]> ], [ <0, [ 0, 0 ]>, <16, [ 3, 1 ]> ], [ <0, [ 0, 0 ]>, <3, [ 1, 1 ]> ], [ <0, [ 0, 0 ]>, <5, [ 3, 4 ]> ], [ <0, [ 0, 0 ]>, <2, [ 2, 3 ]> ], [ <0, [ 0, 0 ]>, <4, [ 2, 4 ]> ], [ <0, [ 0, 0 ]>, <11, [ 4, 2 ]> ], [ <0, [ 0, 0 ]>, <0, [ 1, 0 ]> ], [ <0, [ 0, 0 ]>, <17, [ 2, 1 ]> ], [ <0, [ 0, 0 ]>, <23, [ 1, 3 ]> ], [ <0, [ 0, 0 ]>, <13, [ 0, 4 ]> ], [ <0, [ 0, 0 ]>, <10, [ 1, 2 ]> ], [ <0, [ 0, 0 ]>, <6, [ 3, 0 ]> ], [ <0, [ 0, 0 ]>, <1, [ 0, 1 ]> ], [ <0, [ 0, 0 ]>, <18, [ 2, 0 ]> ], [ <0, [ 0, 0 ]>, <22, [ 4, 3 ]> ], [ <0, [ 0, 0 ]>, <15, [ 4, 4 ]> ], [ <0, [ 0, 0 ]>, <24, [ 1, 0 ]> ], [ <0, [ 0, 0 ]>, <12, [ 4, 0 ]> ], [ <0, [ 0, 0 ]>, <19, [ 0, 2 ]> ], [ <0, [ 0, 0 ]>, <8, [ 1, 4 ]> ], [ <0, [ 0, 0 ]>, <7, [ 0, 3 ]> ], [ <0, [ 0, 0 ]>, <21, [ 2, 2 ]> ], [ <0, [ 0, 0 ]>, <14, [ 3, 2 ]> ], [ <0, [ 0, 0 ]>, <20, [ 4, 1 ]> ] } Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 06:07:47 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; {[<0,[0,0]>] cat []: r in [0..24]}; Output: Magma V2.10-6 Fri Mar 26 2004 06:07:44 on modular [Seed = 69225307] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } { [ <0, [ 0, 0 ]>, ], [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]> ], [ <0, [ 0, 0 ]>, ], [ <0, [ 0, 0 ]>, ], [ <0, [ 0, 0 ]>, ], [ <0, [ 0, 0 ]>, ], [ <0, [ 0, 0 ]>, ], [ <0, [ 0, 0 ]>, ], [ <0, [ 0, 0 ]>, <2, [ 2, 0 ]> ], [ <0, [ 0, 0 ]>, ], [ <0, [ 0, 0 ]>, <4, [ 4, 0 ]> ], [ <0, [ 0, 0 ]>, ], [ <0, [ 0, 0 ]>, ], [ <0, [ 0, 0 ]>, ], [ <0, [ 0, 0 ]>, ], [ <0, [ 0, 0 ]>, ], [ <0, [ 0, 0 ]>, ], [ <0, [ 0, 0 ]>, ], [ <0, [ 0, 0 ]>, ], [ <0, [ 0, 0 ]>, ], [ <0, [ 0, 0 ]>, ], [ <0, [ 0, 0 ]>, ], [ <0, [ 0, 0 ]>, <3, [ 3, 0 ]> ], [ <0, [ 0, 0 ]>, ] } Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 06:08:32 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; [<0,[0,0]>] cat {[]: r in [0..24]}; Output: Magma V2.10-6 Fri Mar 26 2004 06:08:29 on modular [Seed = 975074632] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } >> [<0,[0,0]>] cat {[]: r in [0..24]}; ^ Runtime error in 'cat': Bad argument types Argument types given: SeqEnum[Tup], SetEnum[SeqEnum] Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 06:08:55 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; [<0,[0,0]>] cat [{]: r in [0..24]}]; Output: Magma V2.10-6 Fri Mar 26 2004 06:08:53 on modular [Seed = 806649642] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } >> [<0,[0,0]>] cat [{]: r in [0..24]}]; ^ User error: bad syntax Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 06:09:21 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; [<0,[0,0]>] cat [{: r in [0..24]}]; Output: Magma V2.10-6 Fri Mar 26 2004 06:09:18 on modular [Seed = 654534694] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } >> [<0,[0,0]>] cat [{: r in [0..24]}]; ^ Runtime error in 'cat': Incompatible sequences Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 06:09:59 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) //{<[0],[0,0]> cat <[i],[ElementToSequence(alpha^i)]> : i in G25}; [<0,[0,0]>] cat [: r in [0..24]]; Output: Magma V2.10-6 Fri Mar 26 2004 06:09:56 on modular [Seed = 3740963077] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , , <1, [ 1, 0 ]> ] Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 06:11:49 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) [<0,[0,0]>] cat [: r in [0..24]]; [<0,[0,0]>] cat [: r in [0..24]]; Output: Magma V2.10-6 Fri Mar 26 2004 06:11:46 on modular [Seed = 3454632544] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , , <1, [ 1, 0 ]> ] [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , , <1, [ 1, 0 ]> ] Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 06:12:10 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) [<0,[0,0]>] cat [: r in [0..24]]; [<0,[0,0]>] cat [: r in [0..15]]; Output: Magma V2.10-6 Fri Mar 26 2004 06:12:07 on modular [Seed = 3303052444] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , , <1, [ 1, 0 ]> ] [ <0, [ 0, 0 ]>, <1, [ 1, 0, 0, 0 ]>, , , , , , , , , , , , , , , <1, [ 1, 0, 0, 0 ]> ] Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 06:12:57 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) [<0,[0,0]>] cat [: r in [0..24]]; [<0,[0,0]>] cat [: r in [0..15]]; ElementToSequence(beta^14); Output: Magma V2.10-6 Fri Mar 26 2004 06:12:54 on modular [Seed = 4225739666] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , , <1, [ 1, 0 ]> ] [ <0, [ 0, 0 ]>, <1, [ 1, 0, 0, 0 ]>, , , , , , , , , , , , , , , <1, [ 1, 0, 0, 0 ]> ] [ 1, 0, 0, 1 ] Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 06:20:43 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) [<0,[0,0]>] cat [: r in [0..24]]; [<0,[0,0]>] cat [: r in [0..15]]; G2; Output: Magma V2.10-6 Fri Mar 26 2004 06:20:40 on modular [Seed = 3787830198] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , , <1, [ 1, 0 ]> ] [ <0, [ 0, 0 ]>, <1, [ 1, 0, 0, 0 ]>, , , , , , , , , , , , , , , <1, [ 1, 0, 0, 0 ]> ] Finite field of size 2 Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 06:21:26 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) [<0,[0,0]>] cat [: r in [0..24]]; [<0,[0,0]>] cat [: r in [0..15]]; //exercici viii) G4:=ext; Output: Magma V2.10-6 Fri Mar 26 2004 06:21:23 on modular [Seed = 2562509556] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , , <1, [ 1, 0 ]> ] [ <0, [ 0, 0 ]>, <1, [ 1, 0, 0, 0 ]>, , , , , , , , , , , , , , , <1, [ 1, 0, 0, 0 ]> ] Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 06:21:38 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) [<0,[0,0]>] cat [: r in [0..24]]; [<0,[0,0]>] cat [: r in [0..15]]; //exercici viii) G4:=ext; G4; Output: Magma V2.10-6 Fri Mar 26 2004 06:21:35 on modular [Seed = 2393562350] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , , <1, [ 1, 0 ]> ] [ <0, [ 0, 0 ]>, <1, [ 1, 0, 0, 0 ]>, , , , , , , , , , , , , , , <1, [ 1, 0, 0, 0 ]> ] Finite field of size 2^2 Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 06:22:23 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) [<0,[0,0]>] cat [: r in [0..24]]; [<0,[0,0]>] cat [: r in [0..15]]; //exercici viii) G4:=ext; G8:=ext; Output: Magma V2.10-6 Fri Mar 26 2004 06:22:20 on modular [Seed = 2241976246] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , , <1, [ 1, 0 ]> ] [ <0, [ 0, 0 ]>, <1, [ 1, 0, 0, 0 ]>, , , , , , , , , , , , , , , <1, [ 1, 0, 0, 0 ]> ] Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 06:22:33 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) [<0,[0,0]>] cat [: r in [0..24]]; [<0,[0,0]>] cat [: r in [0..15]]; //exercici viii) G4:=ext; G8:=ext; G8; Output: Magma V2.10-6 Fri Mar 26 2004 06:22:30 on modular [Seed = 3164139157] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , , <1, [ 1, 0 ]> ] [ <0, [ 0, 0 ]>, <1, [ 1, 0, 0, 0 ]>, , , , , , , , , , , , , , , <1, [ 1, 0, 0, 0 ]> ] Finite field of size 2^3 Total time: 3.059 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 06:23:14 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) [<0,[0,0]>] cat [: r in [0..24]]; [<0,[0,0]>] cat [: r in [0..15]]; //exercici viii) G4:=ext; G8:=ext; G16:=ext; G16; Output: Magma V2.10-6 Fri Mar 26 2004 06:23:11 on modular [Seed = 3013075315] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , , <1, [ 1, 0 ]> ] [ <0, [ 0, 0 ]>, <1, [ 1, 0, 0, 0 ]>, , , , , , , , , , , , , , , <1, [ 1, 0, 0, 0 ]> ] Finite field of size 2^4 Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 06:24:15 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) [<0,[0,0]>] cat [: r in [0..24]]; [<0,[0,0]>] cat [: r in [0..15]]; //exercici viii) G4:=ext; G8:=ext; G16:=ext; [x: x in G2]; [x: x in G4]; [x: x in G8]; [x: x in G16]; Output: Magma V2.10-6 Fri Mar 26 2004 06:24:12 on modular [Seed = 2844654378] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , , <1, [ 1, 0 ]> ] [ <0, [ 0, 0 ]>, <1, [ 1, 0, 0, 0 ]>, , , , , , , , , , , , , , , <1, [ 1, 0, 0, 0 ]> ] [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 06:28:20 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) [<0,[0,0]>] cat [: r in [0..24]]; [<0,[0,0]>] cat [: r in [0..15]]; //exercici viii) G4:=ext; G8:=ext; G16:=ext; [x: x in G2]; [x: x in G4]; [x: x in G8]; [x: x in G16]; //apartat 1 R:=PolynomialRing(G25); Output: Magma V2.10-6 Fri Mar 26 2004 06:28:17 on modular [Seed = 1715615191] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , , <1, [ 1, 0 ]> ] [ <0, [ 0, 0 ]>, <1, [ 1, 0, 0, 0 ]>, , , , , , , , , , , , , , , <1, [ 1, 0, 0, 0 ]> ] [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 06:28:46 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) [<0,[0,0]>] cat [: r in [0..24]]; [<0,[0,0]>] cat [: r in [0..15]]; //exercici viii) G4:=ext; G8:=ext; G16:=ext; [x: x in G2]; [x: x in G4]; [x: x in G8]; [x: x in G16]; //apartat 1 R:=PolynomialRing(G25); R; Output: Magma V2.10-6 Fri Mar 26 2004 06:28:43 on modular [Seed = 1867201764] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , , <1, [ 1, 0 ]> ] [ <0, [ 0, 0 ]>, <1, [ 1, 0, 0, 0 ]>, , , , , , , , , , , , , , , <1, [ 1, 0, 0, 0 ]> ] [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] Univariate Polynomial Ring in s over GF(5^2) Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Fri Mar 26 06:38:36 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //exercici vii) [<0,[0,0]>] cat [: r in [0..24]]; [<0,[0,0]>] cat [: r in [0..15]]; //exercici viii) G4:=ext; G8:=ext; G16:=ext; [x: x in G2]; [x: x in G4]; [x: x in G8]; [x: x in G16]; //apartat i IsFinite(R); R:=PolynomialRing(G25); //apartat ii Output: Magma V2.10-6 Fri Mar 26 2004 06:38:33 on modular [Seed = 1215045137] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , , <1, [ 1, 0 ]> ] [ <0, [ 0, 0 ]>, <1, [ 1, 0, 0, 0 ]>, , , , , , , , , , , , , , , <1, [ 1, 0, 0, 0 ]> ] [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] false Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host pool-141-158-212-241.alt.east.verizon.net. (141.158.212.241) Time: Fri Mar 26 07:38:57 2004 Input: R:=MatrixAlgebra(Rationals(),3); A:=R!Matrix([[0,-1,2],[3,-4,6],[2,-2,3]); J,T:=JordanForm(A); J; T; Output: Magma V2.10-6 Fri Mar 26 2004 07:38:54 on modular [Seed = 3353584633] ------------------------------------- >> A:=R!Matrix([[0,-1,2],[3,-4,6],[2,-2,3]); ^ User error: bad syntax >> J,T:=JordanForm(A); J; T;; ^ User error: Identifier 'A' has not been declared or assigned >> J,T:=JordanForm(A); J; T;; ^ User error: Identifier 'J' has not been declared or assigned >> J,T:=JordanForm(A); J; T;; ^ User error: Identifier 'T' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-158-212-241.alt.east.verizon.net. (141.158.212.241) Time: Fri Mar 26 07:39:32 2004 Input: R:=MatrixAlgebra(Rationals(),3); A:=R!Matrix([[0,-1,2],[3,-4,6],[2,-2,3]); J,T:=JordanForm(A); J; T; Output: Magma V2.10-6 Fri Mar 26 2004 07:39:30 on modular [Seed = 3505697842] ------------------------------------- >> A:=R!Matrix([[0,-1,2],[3,-4,6],[2,-2,3]); ^ User error: bad syntax >> J,T:=JordanForm(A); J; T;; ^ User error: Identifier 'A' has not been declared or assigned >> J,T:=JordanForm(A); J; T;; ^ User error: Identifier 'J' has not been declared or assigned >> J,T:=JordanForm(A); J; T;; ^ User error: Identifier 'T' has not been declared or assigned Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-158-212-241.alt.east.verizon.net. (141.158.212.241) Time: Fri Mar 26 07:39:54 2004 Input: R:=MatrixAlgebra(Rationals(),3); A:=R!Matrix([[0,-1,2],[3,-4,6],[2,-2,3]]); J,T:=JordanForm(A); J; T; Output: Magma V2.10-6 Fri Mar 26 2004 07:39:51 on modular [Seed = 3657284910] ------------------------------------- [ 1 0 0] [ 0 -1 0] [ 0 0 -1] [ 1 -1 2] [-1 -1 2] [ 1 -1 1] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-158-212-241.alt.east.verizon.net. (141.158.212.241) Time: Fri Mar 26 07:42:03 2004 Input: R:=MatrixAlgebra(Rationals(),3); A:=R!Matrix([[0,-1,2],[3,-4,6],[2,-2,3]]); F,T:=RationalForm(A); F; T; Output: Magma V2.10-6 Fri Mar 26 2004 07:42:00 on modular [Seed = 2861486034] ------------------------------------- [-1 0 0] [ 0 0 1] [ 0 1 0] [ -1 -1 2] [ 0 0 1/2] [ 1 -1 3/2] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-158-212-241.alt.east.verizon.net. (141.158.212.241) Time: Fri Mar 26 07:43:55 2004 Input: R:=MatrixAlgebra(Rationals(),3); A:=R!Matrix([[0,0.1],[1,0,-1],[0,1,1]]); F,T:=RationalForm(A); F; T; Output: Magma V2.10-6 Fri Mar 26 2004 07:43:52 on modular [Seed = 3029389660] ------------------------------------- >> A:=R!Matrix([[0,0.1],[1,0,-1],[0,1,1]]); ^ Runtime error in 'Matrix': Element 2 of sequence does not have length 2 >> F,T:=RationalForm(A); F; T;; ^ User error: Identifier 'A' has not been declared or assigned >> F,T:=RationalForm(A); F; T;; ^ User error: Identifier 'F' has not been declared or assigned >> F,T:=RationalForm(A); F; T;; ^ User error: Identifier 'T' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-158-212-241.alt.east.verizon.net. (141.158.212.241) Time: Fri Mar 26 07:44:25 2004 Input: R:=MatrixAlgebra(Rationals(),3); A:=R!Matrix([[0,0,1],[1,0,-1],[0,1,1]]); F,T:=RationalForm(A); F; T; Output: Magma V2.10-6 Fri Mar 26 2004 07:44:22 on modular [Seed = 3197819769] ------------------------------------- [ 0 1 0] [ 0 0 1] [ 1 -1 1] [1 0 0] [0 0 1] [0 1 1] Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host pool-141-158-212-241.alt.east.verizon.net. (141.158.212.241) Time: Fri Mar 26 07:46:00 2004 Input: R:=MatrixAlgebra(Rationals(),4); A:=R!Matrix([[2,0,0,0],[3,2,0,-2],[0,0,2,0],[0,0,2,2]); F,T:=RationalForm(A); F; T; Output: Magma V2.10-6 Fri Mar 26 2004 07:45:57 on modular [Seed = 2359880425] ------------------------------------- >> A:=R!Matrix([[2,0,0,0],[3,2,0,-2],[0,0,2,0],[0,0,2,2]); ^ User error: bad syntax >> F,T:=RationalForm(A); F; T;; ^ User error: Identifier 'A' has not been declared or assigned >> F,T:=RationalForm(A); F; T;; ^ User error: Identifier 'F' has not been declared or assigned >> F,T:=RationalForm(A); F; T;; ^ User error: Identifier 'T' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-158-212-241.alt.east.verizon.net. (141.158.212.241) Time: Fri Mar 26 07:46:16 2004 Input: R:=MatrixAlgebra(Rationals(),4); A:=R!Matrix([[2,0,0,0],[3,2,0,-2],[0,0,2,0],[0,0,2,2]]); F,T:=RationalForm(A); F; T; Output: Magma V2.10-6 Fri Mar 26 2004 07:46:13 on modular [Seed = 2511467488] ------------------------------------- [ 2 0 0 0] [ 0 0 1 0] [ 0 0 0 1] [ 0 8 -12 6] [ 1 0 0 0] [ 0 1 0 0] [ 3 2 0 -2] [12 4 -4 -8] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-158-212-241.alt.east.verizon.net. (141.158.212.241) Time: Fri Mar 26 07:53:55 2004 Input: R:=MatrixAlgebra(Rationals(),4); A:=R!Matrix([[2,0,0,0],[0,2,0,-2],[0,0,2,0],[0,0,2,2]]); F,T:=RationalForm(A); F; T; Output: Magma V2.10-6 Fri Mar 26 2004 07:53:52 on modular [Seed = 1749815273] ------------------------------------- [ 2 0 0 0] [ 0 0 1 0] [ 0 0 0 1] [ 0 8 -12 6] [ 1 0 0 0] [ 0 1 0 0] [ 0 2 0 -2] [ 0 4 -4 -8] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-158-212-241.alt.east.verizon.net. (141.158.212.241) Time: Fri Mar 26 07:55:26 2004 Input: R:=MatrixAlgebra(Rationals(),4); A:=R!Matrix([[1,-2,-1,0],[1,0,-3,0],[-1,-2,1,0],[1,2,1,2]]); F,T:=RationalForm(A); F; T; Output: Magma V2.10-6 Fri Mar 26 2004 07:55:23 on modular [Seed = 1985093164] ------------------------------------- [ 2 0 0 0] [ 0 0 1 0] [ 0 0 0 1] [ 0 -8 4 2] [ -2 0 3 1] [ 0 5/16 0 3/16] [ 1/2 3/8 -3/4 3/8] [ 2 5/4 -2 3/4] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-158-212-241.alt.east.verizon.net. (141.158.212.241) Time: Fri Mar 26 07:57:01 2004 Input: R:=MatrixAlgebra(Rationals(),3); A:=R!Matrix([[0,0,1],[1,0,-1],[0,1,1]]); F,T:=RationalForm(A); F; T; Output: Magma V2.10-6 Fri Mar 26 2004 07:56:58 on modular [Seed = 1097148858] ------------------------------------- [ 0 1 0] [ 0 0 1] [ 1 -1 1] [1 0 0] [0 0 1] [0 1 1] Total time: 3.059 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:10:35 2004 Input: /*1*/ /*(i)*/ print "Exercici 1"; print "apartat (i)"; G2:=GF(2); G3:=GF(3); G5:=GF(5); elements := procedure (cos,numelementos) for i:=0 to (numelementos-1) do cos!i; end for; end procedure; print "elements de G2"; elements(G2,2); print "elements de G3"; elements(G3,3); print "elements de G5"; elements(G5,5); Output: Magma V2.10-6 Fri Mar 26 2004 09:10:32 on modular [Seed = 3130966787] ------------------------------------- Exercici 1 apartat (i) elements de G2 0 1 elements de G3 0 1 2 elements de G5 0 1 2 3 4 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:10:59 2004 Input: print "apartat (ii)"; Z9:=Integers(9); /* Z9 no es un cos pq te elements no invertibles a part del zero. Són aquests:*/ for i:=0 to 8 do if(IsInvertible(Z9!i) eq false) then Z9!i; end if; end for; Output: Magma V2.10-6 Fri Mar 26 2004 09:10:56 on modular [Seed = 2241985556] ------------------------------------- apartat (ii) 0 3 6 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:11:23 2004 Input: print "apartat (iii)"; P1:=PolynomialRing(GF(3)); IsIrreducible(2+2*x+x^2); P2:=PolynomialRing(GF(2)); IsIrreducible(1+y+y^4); P3:=PolynomialRing(GF(5)); IsIrreducible(3+2*z+z^2); P4:=PolynomialRing(GF(3)); IsIrreducible(1+2*t+t^2); Output: Magma V2.10-6 Fri Mar 26 2004 09:11:20 on modular [Seed = 2410411494] ------------------------------------- apartat (iii) true true true false Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:11:33 2004 Input: print "apartat (iii)"; P1:=PolynomialRing(GF(3)); IsIrreducible(2+2*x+x^2); P2:=PolynomialRing(GF(2)); IsIrreducible(1+y+y^4); P3:=PolynomialRing(GF(5)); IsIrreducible(3+2*z+z^2); P4:=PolynomialRing(GF(3)); IsIrreducible(1+2*t+t^2); Output: Magma V2.10-6 Fri Mar 26 2004 09:11:30 on modular [Seed = 2528308453] ------------------------------------- apartat (iii) true true true false Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:14:19 2004 Input: G9:=GF(3); G9x:=ext< G9 | 2+2*a+a^2>; Output: Magma V2.10-6 Fri Mar 26 2004 09:14:16 on modular [Seed = 1615076026] ------------------------------------- >> G9x:=ext< G9 | 2+2*a+a^2>; ^ Runtime error in ext< ... >: Rhs argument 1 is invalid for this constructor Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:14:45 2004 Input: G9:=GF(3); G9x:=ext < G9 | 2+2*a+a^2>; Output: Magma V2.10-6 Fri Mar 26 2004 09:14:42 on modular [Seed = 1850348766] ------------------------------------- >> G9x:=ext < G9 | 2+2*a+a^2>; ^ Runtime error in ext< ... >: Rhs argument 1 is invalid for this constructor Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:15:14 2004 Input: G9:=GF(3); G9x:=ext< G9 | 2+2*a+a^2 >; Output: Magma V2.10-6 Fri Mar 26 2004 09:15:11 on modular [Seed = 2036138996] ------------------------------------- >> G9x:=ext< G9 | 2+2*a+a^2 >; ^ Runtime error in ext< ... >: Rhs argument 1 is invalid for this constructor Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:15:39 2004 Input: G9:=ext< GF(3) | 2+2*a+a^2 >; Output: Magma V2.10-6 Fri Mar 26 2004 09:15:36 on modular [Seed = 1180843308] ------------------------------------- >> G9:=ext< GF(3) | 2+2*a+a^2 >; ^ User error: Identifier 'a' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:16:20 2004 Input: G9:=GF(3); G9:=ext< GF(3) | 2+2*a+a^2 >; Output: Magma V2.10-6 Fri Mar 26 2004 09:16:17 on modular [Seed = 1298740766] ------------------------------------- >> G9:=ext< GF(3) | 2+2*a+a^2 >; ^ User error: Identifier 'a' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:16:36 2004 Input: G9:=GF(3); G9:=ext< G9 | 2+2*a+a^2 >; Output: Magma V2.10-6 Fri Mar 26 2004 09:16:33 on modular [Seed = 1518215545] ------------------------------------- >> G9:=ext< G9 | 2+2*a+a^2 >; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:16:46 2004 Input: G9:=GF(3); G9x:=ext< G9 | 2+2*a+a^2 >; Output: Magma V2.10-6 Fri Mar 26 2004 09:16:43 on modular [Seed = 587683850] ------------------------------------- >> G9x:=ext< G9 | 2+2*a+a^2 >; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:16:54 2004 Input: G9:=GF(3); G9x:=ext< G9 | 2+2*a+a^2 >; Output: Magma V2.10-6 Fri Mar 26 2004 09:16:51 on modular [Seed = 671896345] ------------------------------------- >> G9x:=ext< G9 | 2+2*a+a^2 >; ^ Runtime error in ext< ... >: Rhs argument 1 is invalid for this constructor Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:17:03 2004 Input: G9:=GF(3); G9x:=ext< G9 | 2+2*a+a^2 >; Output: Magma V2.10-6 Fri Mar 26 2004 09:17:00 on modular [Seed = 823478799] ------------------------------------- >> G9x:=ext< G9 | 2+2*a+a^2 >; ^ Runtime error in ext< ... >: Rhs argument 1 is invalid for this constructor Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:17:12 2004 Input: G9:=GF(3); G9x:=ext < G9 | 2+2*a+a^2 >; Output: Magma V2.10-6 Fri Mar 26 2004 09:17:09 on modular [Seed = 1041909049] ------------------------------------- >> G9x:=ext < G9 | 2+2*a+a^2 >; ^ Runtime error in ext< ... >: Rhs argument 1 is invalid for this constructor Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:17:46 2004 Input: G9:=GF(3); PrimeField(G9); Output: Magma V2.10-6 Fri Mar 26 2004 09:17:43 on modular [Seed = 69238753] ------------------------------------- Finite field of size 3 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:19:33 2004 Input: G9:=GF(3); PrimeField(G9); Generator(G9); Output: Magma V2.10-6 Fri Mar 26 2004 09:19:30 on modular [Seed = 305555842] ------------------------------------- Finite field of size 3 1 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:23:09 2004 Input: G9:=GF(3); G9x:=ext< G9 | 2+2*a+a^2>; PrimeField(G9x); Generator(G9x); Output: Magma V2.10-6 Fri Mar 26 2004 09:23:06 on modular [Seed = 3821510475] ------------------------------------- >> G9x:=ext< G9 | 2+2*a+a^2>; ^ User error: Identifier 'a' has not been declared or assigned >> PrimeField(G9x); ^ User error: Identifier 'G9x' has not been declared or assigned >> Generator(G9x); ^ User error: Identifier 'G9x' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:23:19 2004 Input: G9:=GF(3); G9x:=ext< G9 | 2+2*beta+beta^2>; PrimeField(G9x); Generator(G9x); Output: Magma V2.10-6 Fri Mar 26 2004 09:23:16 on modular [Seed = 3922564447] ------------------------------------- >> G9x:=ext< G9 | 2+2*beta+beta^2>; ^ User error: Identifier 'beta' has not been declared or assigned >> PrimeField(G9x); ^ User error: Identifier 'G9x' has not been declared or assigned >> Generator(G9x); ^ User error: Identifier 'G9x' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:23:34 2004 Input: G9:=GF(3); G9x:=ext< G9 | 2+2*alpha+alpha^2>; PrimeField(G9x); Generator(G9x); Output: Magma V2.10-6 Fri Mar 26 2004 09:23:31 on modular [Seed = 4140993143] ------------------------------------- >> G9x:=ext< G9 | 2+2*alpha+alpha^2>; ^ Runtime error in ext< ... >: Rhs argument 1 is invalid for this constructor >> PrimeField(G9x); ^ User error: Identifier 'G9x' has not been declared or assigned >> Generator(G9x); ^ User error: Identifier 'G9x' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:23:56 2004 Input: G9:=GF(3); G9x:=ext< G9 | f >; PrimeField(G9x); Generator(G9x); Output: Magma V2.10-6 Fri Mar 26 2004 09:23:53 on modular [Seed = 4242047079] ------------------------------------- >> G9x:=ext< G9 | f >; ^ User error: Identifier 'f' has not been declared or assigned >> PrimeField(G9x); ^ User error: Identifier 'G9x' has not been declared or assigned >> Generator(G9x); ^ User error: Identifier 'G9x' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:25:30 2004 Input: P:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreductible(f); /* G9:=GF(3); G9x:=ext< G9 | f >; PrimeField(G9x); Generator(G9x); */ Output: Magma V2.10-6 Fri Mar 26 2004 09:25:27 on modular [Seed = 3387798780] ------------------------------------- >> IsIrreductible(f); ^ User error: Identifier 'IsIrreductible' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:25:44 2004 Input: P:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); /* G9:=GF(3); G9x:=ext< G9 | f >; PrimeField(G9x); Generator(G9x); */ Output: Magma V2.10-6 Fri Mar 26 2004 09:25:41 on modular [Seed = 3606227921] ------------------------------------- true Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:26:06 2004 Input: P:=PolynomialRing(GF(3)); f:=2+2*x+x^2; G9:=GF(3); G9x:=ext< G9 | f >; PrimeField(G9x); Generator(G9x); Output: Magma V2.10-6 Fri Mar 26 2004 09:26:03 on modular [Seed = 3757810374] ------------------------------------- Finite field of size 3 beta Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:28:39 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); Output: Magma V2.10-6 Fri Mar 26 2004 09:28:36 on modular [Seed = 2861487324] ------------------------------------- apartat (iii) true true true false Total time: 3.029 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:29:38 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G9:=GF(3); G9x:=ext< G9 | f >; Output: Magma V2.10-6 Fri Mar 26 2004 09:29:35 on modular [Seed = 3013070238] ------------------------------------- apartat (iii) true true true false Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:30:07 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G9:=GF(3); G9x:=ext< G9 | f >; Generator(G9x); Output: Magma V2.10-6 Fri Mar 26 2004 09:30:03 on modular [Seed = 2158296713] ------------------------------------- apartat (iii) true true true false beta Total time: 3.119 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:31:17 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G9:=GF(3); G9x:=ext< G9 | f >; Generator(G9x); G16:=GF(2); G16x:=ext< G16 | g >; Generator(G16x); Output: Magma V2.10-6 Fri Mar 26 2004 09:31:14 on modular [Seed = 2309879641] ------------------------------------- apartat (iii) true true true false beta beta Total time: 3.089 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:32:17 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G9:=GF(3); G9x:=ext< G9 | f >; Generator(G9x); G16:=GF(2); G16x:=ext< G16 | g >; Generator(G16x); G25:=GF(5); G25x:=ext< G25 | h >; Generator(G25x); Output: Magma V2.10-6 Fri Mar 26 2004 09:32:15 on modular [Seed = 2528307227] ------------------------------------- apartat (iii) true true true false beta beta beta Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:33:16 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G9:=GF(3); G9x:=ext< G9 | f >; Generator(G9x); G16:=GF(2); G16x:=ext< G16 | g >; Generator(G16x); G25:=GF(5); G25x:=ext< G25 | h >; Generator(G25x); G9y:=ext< G9 | k >; Generator(G9y); Output: Magma V2.10-6 Fri Mar 26 2004 09:33:13 on modular [Seed = 1615077162] ------------------------------------- apartat (iii) true true true false beta beta beta >> G9y:=ext< G9 | k >; ^ Runtime error in ext< ... >: Argument is not irreducible >> Generator(G9y); ^ User error: Identifier 'G9y' has not been declared or assigned Total time: 3.039 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:35:31 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G9:=GF(3); G9x:=ext< G9 | f >; Generator(G9x); G16:=GF(2); G16x:=ext< G16 | g >; Generator(G16x); G25:=GF(5); G25x:=ext< G25 | h >; Generator(G25x); G9y:=ext< G9 | k >; Generator(G9y); Output: Magma V2.10-6 Fri Mar 26 2004 09:35:28 on modular [Seed = 1935084704] ------------------------------------- apartat (iii) true true true false G9x.1 G16x.1 G25x.1 >> G9y:=ext< G9 | k >; ^ Runtime error in ext< ... >: Argument is not irreducible >> Generator(G9y); ^ User error: Identifier 'G9y' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:37:48 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; G9b:=ext< G3 | k >; Output: Magma V2.10-6 Fri Mar 26 2004 09:37:45 on modular [Seed = 2036168995] ------------------------------------- apartat (iii) true true true false >> G9b:=ext< G3 | k >; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:39:00 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ Order(G25); Output: Magma V2.10-6 Fri Mar 26 2004 09:38:57 on modular [Seed = 1197688741] ------------------------------------- apartat (iii) true true true false >> Order(G25); ^ Runtime error in 'Order': Bad argument types Argument types given: FldFin Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:39:46 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ G25!10; Output: Magma V2.10-6 Fri Mar 26 2004 09:39:43 on modular [Seed = 1298746753] ------------------------------------- apartat (iii) true true true false 0 Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:39:58 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ G25!11; Output: Magma V2.10-6 Fri Mar 26 2004 09:39:55 on modular [Seed = 1416647820] ------------------------------------- apartat (iii) true true true false 1 Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:41:51 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ PrimeField(G25); GroundField(G25); Order(G25!2); Output: Magma V2.10-6 Fri Mar 26 2004 09:41:49 on modular [Seed = 671885670] ------------------------------------- apartat (iii) true true true false Finite field of size 5 Finite field of size 5 4 Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:42:21 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ G25!2; Order(G25!2); Output: Magma V2.10-6 Fri Mar 26 2004 09:42:18 on modular [Seed = 907163423] ------------------------------------- apartat (iii) true true true false 2 4 Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:42:55 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ for i from 1 to 5 do G25!2; Order(G25!2); end do; Output: Magma V2.10-6 Fri Mar 26 2004 09:42:52 on modular [Seed = 1025063986] ------------------------------------- apartat (iii) true true true false >> for i from 1 to 5 do G25!2; Order(G25!2); end do;; ^ User error: bad syntax Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:43:12 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ for i:=1 to 5 do G25!2; Order(G25!2); end do; Output: Magma V2.10-6 Fri Mar 26 2004 09:43:09 on modular [Seed = 69207322] ------------------------------------- apartat (iii) true true true false >> for i:=1 to 5 do G25!2; Order(G25!2); end do;; ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:43:31 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ for i:=1 to 5 do G25!2; Order(G25!2); end for; Output: Magma V2.10-6 Fri Mar 26 2004 09:43:28 on modular [Seed = 305533921] ------------------------------------- apartat (iii) true true true false 2 4 2 4 2 4 2 4 2 4 Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:43:45 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ for i:=1 to 5 do G25!i; Order(G25!i); end for; Output: Magma V2.10-6 Fri Mar 26 2004 09:43:42 on modular [Seed = 423434468] ------------------------------------- apartat (iii) true true true false 1 1 2 4 3 4 4 2 0 >> for i:=1 to 5 do G25!i; Order(G25!i); end for;; ^ Runtime error in 'Order': Can not take order of zero element Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:44:12 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ for i:=1 to 4 do G25!i; Order(G25!i); end for; Output: Magma V2.10-6 Fri Mar 26 2004 09:44:09 on modular [Seed = 3770999098] ------------------------------------- apartat (iii) true true true false 1 1 2 4 3 4 4 2 Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:45:08 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ PrimitiveElement(G25); Output: Magma V2.10-6 Fri Mar 26 2004 09:45:05 on modular [Seed = 4091015777] ------------------------------------- apartat (iii) true true true false G25.1 Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:52:23 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ Generator(G25); PrimitiveElement(G25); Output: Magma V2.10-6 Fri Mar 26 2004 09:52:20 on modular [Seed = 3421489164] ------------------------------------- apartat (iii) true true true false G25.1 G25.1 Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:52:35 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ Generator(G5,G25); PrimitiveElement(G25); Output: Magma V2.10-6 Fri Mar 26 2004 09:52:32 on modular [Seed = 3539390721] ------------------------------------- apartat (iii) true true true false >> Generator(G5,G25); ^ Runtime error in 'Generator': Argument 2 is not a subfield of argument 1 G25.1 Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:53:57 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ for i:=1 to 4 do IsPrimitive(G25!i); end for; Output: Magma V2.10-6 Fri Mar 26 2004 09:53:54 on modular [Seed = 3640450233] ------------------------------------- apartat (iii) true true true false false false false false Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:55:25 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ G25; Output: Magma V2.10-6 Fri Mar 26 2004 09:55:22 on modular [Seed = 2861477523] ------------------------------------- apartat (iii) true true true false Finite field of size 5^2 Total time: 3.079 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:56:24 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ for i:=0 to 24 do G25!i; end for; Output: Magma V2.10-6 Fri Mar 26 2004 09:56:21 on modular [Seed = 2979378503] ------------------------------------- apartat (iii) true true true false 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:57:07 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ DefiningPolynomial(G25); Output: Magma V2.10-6 Fri Mar 26 2004 09:57:04 on modular [Seed = 3097279515] ------------------------------------- apartat (iii) true true true false z^2 + 2*z + 3 Total time: 3.079 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:58:13 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ DefiningPolynomial(G25); MinimalPolynimial(G25!1); Output: Magma V2.10-6 Fri Mar 26 2004 09:58:10 on modular [Seed = 2258797543] ------------------------------------- apartat (iii) true true true false z^2 + 2*z + 3 >> MinimalPolynimial(G25!1);; ^ User error: Identifier 'MinimalPolynimial' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:58:20 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ DefiningPolynomial(G25); MinimalPolynimial(G25!1); Output: Magma V2.10-6 Fri Mar 26 2004 09:58:17 on modular [Seed = 2359855590] ------------------------------------- apartat (iii) true true true false z^2 + 2*z + 3 >> MinimalPolynimial(G25!1);; ^ User error: Identifier 'MinimalPolynimial' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 09:58:34 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ DefiningPolynomial(G25); MinimalPolynomial(G25!1); Output: Magma V2.10-6 Fri Mar 26 2004 09:58:31 on modular [Seed = 2613026543] ------------------------------------- apartat (iii) true true true false z^2 + 2*z + 3 z + 4 Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 10:02:45 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ DefiningPolynomial(G25); MinimalPolynomial(G25!1); PrimitivePolynomial(G25); Output: Magma V2.10-6 Fri Mar 26 2004 10:02:42 on modular [Seed = 2136701193] ------------------------------------- apartat (iii) true true true false z^2 + 2*z + 3 z + 4 >> PrimitivePolynomial(G25);; ^ Runtime error in 'PrimitivePolynomial': Bad argument types Argument types given: FldFin Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 10:03:26 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ DefiningPolynomial(G25); for i:=0 to 24 do MinimalPolynomial(G25!i); end for; PrimitivePolynomial(G25,2); Output: Magma V2.10-6 Fri Mar 26 2004 10:03:23 on modular [Seed = 1097156382] ------------------------------------- apartat (iii) true true true false z^2 + 2*z + 3 z z + 4 z + 3 z + 2 z + 1 z z + 4 z + 3 z + 2 z + 1 z z + 4 z + 3 z + 2 z + 1 z z + 4 z + 3 z + 2 z + 1 z z + 4 z + 3 z + 2 z + 1 $.1^2 + G25.1^9*$.1 + G25.1^19 Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 10:03:46 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ DefiningPolynomial(G25); for i:=0 to 4 do MinimalPolynomial(G25!i); end for; PrimitivePolynomial(G25,2); Output: Magma V2.10-6 Fri Mar 26 2004 10:03:43 on modular [Seed = 1248742497] ------------------------------------- apartat (iii) true true true false z^2 + 2*z + 3 z z + 4 z + 3 z + 2 z + 1 $.1^2 + G25.1^9*$.1 + G25.1^19 Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 10:04:20 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ DefiningPolynomial(G25); for i:=0 to 4 do MinimalPolynomial(G25!i); end for; Output: Magma V2.10-6 Fri Mar 26 2004 10:04:18 on modular [Seed = 1551391306] ------------------------------------- apartat (iii) true true true false z^2 + 2*z + 3 z z + 4 z + 3 z + 2 z + 1 Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 10:09:49 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ a:=PrimitiveElement(G25); a; MinimalPolynomial(a); EulerPhi(a); Output: Magma V2.10-6 Fri Mar 26 2004 10:09:46 on modular [Seed = 587670781] ------------------------------------- apartat (iii) true true true false G25.1 z^2 + 2*z + 3 >> EulerPhi(a);; ^ Runtime error in 'EulerPhi': Bad argument types Argument types given: FldFinElt Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 10:13:22 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ a:=PrimitiveElement(G25); a; mpa:=MinimalPolynomial(a); Coefficients(mpa); Output: Magma V2.10-6 Fri Mar 26 2004 10:13:19 on modular [Seed = 1025062358] ------------------------------------- apartat (iii) true true true false G25.1 [ 3, 2, 1 ] Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 10:13:58 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ a:=PrimitiveElement(G25); a; mpa:=MinimalPolynomial(a); mpa; CoefficientRing(mpa); Output: Magma V2.10-6 Fri Mar 26 2004 10:13:55 on modular [Seed = 102895313] ------------------------------------- apartat (iii) G25.1 z^2 + 2*z + 3 Finite field of size 5 Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 10:15:31 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ a:=PrimitiveElement(G25); a; mpa:=MinimalPolynomial(a); mpa; CoefficientRing(mpa); Roots(mpa,G25); Roots(mpa,Integers(5)); Output: Magma V2.10-6 Fri Mar 26 2004 10:15:28 on modular [Seed = 338697568] ------------------------------------- apartat (iii) G25.1 z^2 + 2*z + 3 Finite field of size 5 [ , ] [] Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 10:16:30 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ a:=PrimitiveElement(G25); a; mpa:=MinimalPolynomial(a); mpa; Degree(mpa); CoefficientRing(mpa); Roots(mpa,G25); Roots(mpa,Integers(5)); Output: Magma V2.10-6 Fri Mar 26 2004 10:16:27 on modular [Seed = 523966000] ------------------------------------- apartat (iii) G25.1 z^2 + 2*z + 3 2 Finite field of size 5 [ , ] [] Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host dialup-4.155.9.191.Dial1.Baltimore1.Level3.net. (4.155.9.191) Time: Fri Mar 26 10:17:46 2004 Input: F:=GF(2); P:=PolynomialRing(F); g:=x^5+x^2+1; IsPrimitive(g); Output: Magma V2.10-6 Fri Mar 26 2004 10:17:44 on modular [Seed = 3787843613] ------------------------------------- true Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dialup-4.155.9.191.Dial1.Baltimore1.Level3.net. (4.155.9.191) Time: Fri Mar 26 10:19:52 2004 Input: F:=GF(2); P:=PolynomialRing(F); g:=x^5+x^2+1; IsPrimitive(g); EF:=ext; EP:=PolynomialRing(EF); Output: Magma V2.10-6 Fri Mar 26 2004 10:19:49 on modular [Seed = 3956269466] ------------------------------------- true Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dialup-4.155.9.191.Dial1.Baltimore1.Level3.net. (4.155.9.191) Time: Fri Mar 26 10:20:53 2004 Input: F:=GF(2); P:=PolynomialRing(F); g:=x^5+x^2+1; IsPrimitive(g); EF:=ext; EP:=PolynomialRing(EF); (X+1)*(X^4+X^3+1); Output: Magma V2.10-6 Fri Mar 26 2004 10:20:50 on modular [Seed = 3303067379] ------------------------------------- true X^5 + X^3 + X + 1 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dialup-4.155.9.191.Dial1.Baltimore1.Level3.net. (4.155.9.191) Time: Fri Mar 26 10:21:33 2004 Input: F:=GF(2); P:=PolynomialRing(F); g:=x^5+x^2+1; IsPrimitive(g); EF:=ext; EP:=PolynomialRing(EF); (X+1)*(X^4+X^3+1); (X^5 + X^3 + X + 1) mod (X+1); Output: Magma V2.10-6 Fri Mar 26 2004 10:21:30 on modular [Seed = 3454650323] ------------------------------------- true X^5 + X^3 + X + 1 0 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dialup-4.155.9.191.Dial1.Baltimore1.Level3.net. (4.155.9.191) Time: Fri Mar 26 10:22:10 2004 Input: F:=GF(2); P:=PolynomialRing(F); g:=x^5+x^2+1; IsPrimitive(g); EF:=ext; EP:=PolynomialRing(EF); (X+1)*(X^14+X^3+1); (X^5 + X^3 + X + 1) mod (X+1); Output: Magma V2.10-6 Fri Mar 26 2004 10:22:07 on modular [Seed = 3606240301] ------------------------------------- true X^15 + X^14 + X^4 + X^3 + X + 1 0 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dialup-4.155.9.191.Dial1.Baltimore1.Level3.net. (4.155.9.191) Time: Fri Mar 26 10:22:38 2004 Input: F:=GF(2); P:=PolynomialRing(F); g:=x^5+x^2+1; IsPrimitive(g); EF:=ext; EP:=PolynomialRing(EF); (X+1)*(X^14+X^3+1); (X^15 + X^14 + X^4 + X^3 + X + 1) mod (X+1); Output: Magma V2.10-6 Fri Mar 26 2004 10:22:35 on modular [Seed = 3757823232] ------------------------------------- true X^15 + X^14 + X^4 + X^3 + X + 1 0 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dialup-4.155.9.191.Dial1.Baltimore1.Level3.net. (4.155.9.191) Time: Fri Mar 26 10:23:44 2004 Input: F:=GF(2); P:=PolynomialRing(F); g:=x^5+x^2+1; IsPrimitive(g); EF:=ext; EP:=PolynomialRing(EF); IrreduciblePolynomial(EF,2); (X+1)*(X^14+X^3+1); (X^15 + X^14 + X^4 + X^3 + X + 1) mod (X+1); Output: Magma V2.10-6 Fri Mar 26 2004 10:23:41 on modular [Seed = 2709891896] ------------------------------------- true X^2 + alpha^2*X + alpha^16 X^15 + X^14 + X^4 + X^3 + X + 1 0 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dialup-4.155.9.191.Dial1.Baltimore1.Level3.net. (4.155.9.191) Time: Fri Mar 26 10:24:29 2004 Input: F:=GF(2); P:=PolynomialRing(F); g:=x^5+x^2+1; IsPrimitive(g); EF:=ext; EP:=PolynomialRing(EF); G:=IrreduciblePolynomial(EF,2); IsPrimitive(G); (X+1)*(X^14+X^3+1); (X^15 + X^14 + X^4 + X^3 + X + 1) mod (X+1); Output: Magma V2.10-6 Fri Mar 26 2004 10:24:26 on modular [Seed = 2861474276] ------------------------------------- true true X^15 + X^14 + X^4 + X^3 + X + 1 0 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dialup-4.155.9.191.Dial1.Baltimore1.Level3.net. (4.155.9.191) Time: Fri Mar 26 10:25:03 2004 Input: F:=GF(2); P:=PolynomialRing(F); g:=x^5+x^2+1; IsPrimitive(g); EF:=ext; EP:=PolynomialRing(EF); G:=IrreduciblePolynomial(EF,2); IsPrimitive(G); (G)*(X^14+X^3+1); (X^15 + X^14 + X^4 + X^3 + X + 1) mod (X+1); Output: Magma V2.10-6 Fri Mar 26 2004 10:25:00 on modular [Seed = 3013064859] ------------------------------------- true true X^16 + alpha^2*X^15 + alpha^16*X^14 + X^5 + alpha^2*X^4 + alpha^16*X^3 + X^2 + alpha^2*X + alpha^16 0 Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 10:25:22 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; p^n-1; Output: Magma V2.10-6 Fri Mar 26 2004 10:25:19 on modular [Seed = 2175109818] ------------------------------------- apartat (iii) 24 Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host dialup-4.155.9.191.Dial1.Baltimore1.Level3.net. (4.155.9.191) Time: Fri Mar 26 10:25:59 2004 Input: F:=GF(2); P:=PolynomialRing(F); g:=x^5+x^2+1; IsPrimitive(g); EF:=ext; EP:=PolynomialRing(EF); G:=IrreduciblePolynomial(EF,2); IsPrimitive(G); (G)*(X^14+X^3+1); (X^16 + alpha^2*X^15 + alpha^16*X^14 + X^5 + alpha^2*X^4 + alpha^16*X^3 + X^2 + alpha^2*X + alpha^16) mod (G); Output: Magma V2.10-6 Fri Mar 26 2004 10:25:56 on modular [Seed = 2326692202] ------------------------------------- true true X^16 + alpha^2*X^15 + alpha^16*X^14 + X^5 + alpha^2*X^4 + alpha^16*X^3 + X^2 + alpha^2*X + alpha^16 0 Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 10:26:12 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; p^n-1; for i:=1 to 24 Order(G25!i); end for; Output: Magma V2.10-6 Fri Mar 26 2004 10:26:09 on modular [Seed = 2478282854] ------------------------------------- apartat (iii) 24 >> for i:=1 to 24 Order(G25!i); end for;; ^ User error: bad syntax Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host dialup-4.155.9.191.Dial1.Baltimore1.Level3.net. (4.155.9.191) Time: Fri Mar 26 10:26:17 2004 Input: F:=GF(2); P:=PolynomialRing(F); g:=x^5+x^2+1; IsPrimitive(g); EF:=ext; EP:=PolynomialRing(EF); G:=IrreduciblePolynomial(EF,2); G; IsPrimitive(G); (G)*(X^14+X^3+1); (X^16 + alpha^2*X^15 + alpha^16*X^14 + X^5 + alpha^2*X^4 + alpha^16*X^3 + X^2 + alpha^2*X + alpha^16) mod (G); Output: Magma V2.10-6 Fri Mar 26 2004 10:26:14 on modular [Seed = 1698786966] ------------------------------------- true X^2 + alpha^2*X + alpha^16 true X^16 + alpha^2*X^15 + alpha^16*X^14 + X^5 + alpha^2*X^4 + alpha^16*X^3 + X^2 + alpha^2*X + alpha^16 0 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 10:26:24 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; p^n-1; for i:=1 to 24 do Order(G25!i); end for; Output: Magma V2.10-6 Fri Mar 26 2004 10:26:21 on modular [Seed = 1816684436] ------------------------------------- apartat (iii) 24 1 4 4 2 >> for i:=1 to 24 do Order(G25!i); end for;; ^ Runtime error in 'Order': Can not take order of zero element Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 10:27:06 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; p^n-1; for i:=1 to 4 do Order(G25!i); end for; Output: Magma V2.10-6 Fri Mar 26 2004 10:27:03 on modular [Seed = 2001960149] ------------------------------------- apartat (iii) 24 1 4 4 2 Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host dialup-4.155.9.191.Dial1.Baltimore1.Level3.net. (4.155.9.191) Time: Fri Mar 26 10:27:36 2004 Input: F:=GF(2); P:=PolynomialRing(F); g:=x^5+x^2+1; IsPrimitive(g); EF:=ext; EP:=PolynomialRing(EF); G:=X^2 + alpha^2*X + alpha^16; (X^16 + alpha^2*X^15 + alpha^16*X^14 + X^5 + alpha^2*X^4 + alpha^16*X^3 + X^2 + alpha^2*X + alpha^16) mod (G); Output: Magma V2.10-6 Fri Mar 26 2004 10:27:33 on modular [Seed = 2119857662] ------------------------------------- true 0 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 10:28:35 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; p^n-1; pe:=PrimitiveElement(G25); pe; Order(pe); for i:=1 to 4 do Order(G25!i); end for; Output: Magma V2.10-6 Fri Mar 26 2004 10:28:32 on modular [Seed = 1332429578] ------------------------------------- apartat (iii) 24 G25.1 24 1 4 4 2 Total time: 2.889 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 10:30:44 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; p^n-1; pe:=PrimitiveElement(G25); pe; Order(pe); F![1,1,1]; Order(F![1,1,1]); /*for i:=1 to 4 do F![1,1,1]; end for;*/ Output: Magma V2.10-6 Fri Mar 26 2004 10:30:41 on modular [Seed = 1601917851] ------------------------------------- apartat (iii) 24 G25.1 24 >> F![1,1,1]; ^ User error: Identifier 'F' has not been declared or assigned >> Order(F![1,1,1]); ^ User error: Identifier 'F' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 10:31:01 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; p^n-1; pe:=PrimitiveElement(G25); pe; Order(pe); G25![1,1,1]; Order(G25![1,1,1]); /*for i:=1 to 4 do F![1,1,1]; end for;*/ Output: Magma V2.10-6 Fri Mar 26 2004 10:30:58 on modular [Seed = 637676273] ------------------------------------- apartat (iii) 24 G25.1 24 >> G25![1,1,1]; ^ Runtime error in '!': Sequence must have length 2 to lift into this finite field LHS: FldFin RHS: [RngIntElt] >> Order(G25![1,1,1]); ^ Runtime error in '!': Sequence must have length 2 to lift into this finite field LHS: FldFin RHS: [RngIntElt] Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 10:31:25 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; p^n-1; pe:=PrimitiveElement(G25); pe; Order(pe); G25![1,1,1]; Order(G25![1,1,1]); /*for i:=1 to 4 do F![1,1]; end for;*/ Output: Magma V2.10-6 Fri Mar 26 2004 10:31:22 on modular [Seed = 671884423] ------------------------------------- apartat (iii) 24 G25.1 24 >> G25![1,1,1]; ^ Runtime error in '!': Sequence must have length 2 to lift into this finite field LHS: FldFin RHS: [RngIntElt] >> Order(G25![1,1,1]); ^ Runtime error in '!': Sequence must have length 2 to lift into this finite field LHS: FldFin RHS: [RngIntElt] Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 10:31:40 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; p^n-1; pe:=PrimitiveElement(G25); pe; Order(pe); G25![1,1]; Order(G25![1,1]); /*for i:=1 to 4 do F![1,1]; end for;*/ Output: Magma V2.10-6 Fri Mar 26 2004 10:31:37 on modular [Seed = 857161615] ------------------------------------- apartat (iii) 24 G25.1 24 G25.1^3 8 Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 10:33:31 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ alpha+alpha^2; Output: Magma V2.10-6 Fri Mar 26 2004 10:33:28 on modular [Seed = 86050856] ------------------------------------- apartat (iii) 2 Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 10:34:43 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ alpha5+alpha5^2; Output: Magma V2.10-6 Fri Mar 26 2004 10:34:40 on modular [Seed = 254477050] ------------------------------------- apartat (iii) 2 Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 10:35:36 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ G25![0,0,1]; Output: Magma V2.10-6 Fri Mar 26 2004 10:35:33 on modular [Seed = 305536946] ------------------------------------- apartat (iii) >> G25![0,0,1];; ^ Runtime error in '!': Sequence must have length 2 to lift into this finite field LHS: FldFin RHS: [RngIntElt] Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 10:36:49 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ for i:=0 to 4 do for j:=0 to 4 do G25![j,i]; end for; end for; Output: Magma V2.10-6 Fri Mar 26 2004 10:36:46 on modular [Seed = 3854691214] ------------------------------------- apartat (iii) 0 1 2 3 4 G25.1 G25.1^3 G25.1^17 G25.1^16 G25.1^20 G25.1^19 G25.1^10 G25.1^21 G25.1^14 G25.1^11 G25.1^7 G25.1^23 G25.1^2 G25.1^9 G25.1^22 G25.1^13 G25.1^8 G25.1^4 G25.1^5 G25.1^15 Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Fri Mar 26 10:36:56 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Fri Mar 26 2004 10:36:53 on modular [Seed = 3972588188] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Fri Mar 26 10:40:22 2004 Input: F ! [1,2]; Output: Magma V2.10-6 Fri Mar 26 2004 10:40:19 on modular [Seed = 4225758589] ------------------------------------- >> F ! [1,2];; ^ User error: Identifier 'F' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Fri Mar 26 10:40:56 2004 Input: /*1*/ /*(i)*/ print "Exercici 1"; print "apartat (i)"; G2:=GF(2); G3:=GF(3); G5:=GF(5); elements := procedure (cos,numelementos) for i:=0 to (numelementos-1) do cos!i; end for; end procedure; print "elements de G2"; elements(G2,2); print "elements de G3"; elements(G3,3); print "elements de G5"; elements(G5,5); /*(ii)*/ print "apartat (ii)"; Z9:=Integers(9); /* Z9 no es un cos pq te elements no invertibles a part del zero. Són aquests:*/ for i:=0 to 8 do if(IsInvertible(Z9!i) eq false) then Z9!i; end if; end for; /*(iii)*/ print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; G9b:=ext< G3 | k >; /*En aquest últim cas el polinomi k no es irreductible i no podem definir el cos finit G9b com a extensió de G9 fent servir aquest polinomi*/ /*(iv)*/ print "apartat (iv)"; for i:=1 to 4 do Order(G25!i); end for; F ! [1,2]; Output: Magma V2.10-6 Fri Mar 26 2004 10:40:53 on modular [Seed = 3404645802] ------------------------------------- Exercici 1 apartat (i) elements de G2 0 1 elements de G3 0 1 2 elements de G5 0 1 2 3 4 apartat (ii) 0 3 6 apartat (iii) true true true false >> G9b:=ext< G3 | k >; ^ Runtime error in ext< ... >: Argument is not irreducible apartat (iv) 1 4 4 2 >> F ! [1,2];; ^ User error: Identifier 'F' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 10:41:49 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ for i:=0 to 4 do for j:=0 to 4 do el:=G25![j,i]; el; if (el ne 0) then Order(el); end if; end for; end for; Output: Magma V2.10-6 Fri Mar 26 2004 10:41:46 on modular [Seed = 3724137090] ------------------------------------- apartat (iii) 0 1 1 2 4 3 4 4 2 G25.1 24 G25.1^3 8 G25.1^17 24 G25.1^16 3 G25.1^20 6 G25.1^19 24 G25.1^10 12 G25.1^21 8 G25.1^14 12 G25.1^11 24 G25.1^7 24 G25.1^23 24 G25.1^2 12 G25.1^9 8 G25.1^22 12 G25.1^13 24 G25.1^8 3 G25.1^4 6 G25.1^5 24 G25.1^15 8 Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 10:42:50 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ for i:=0 to 4 do for j:=0 to 4 do el:=G25![j,i]; if (el ne 0) then Order(el); end if; end for; end for; Output: Magma V2.10-6 Fri Mar 26 2004 10:42:47 on modular [Seed = 2759895990] ------------------------------------- apartat (iii) 1 4 4 2 24 8 24 3 6 24 12 8 12 24 24 24 12 8 12 24 3 6 24 8 Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Fri Mar 26 10:43:54 2004 Input: /*1*/ /*(i)*/ print "Exercici 1"; print "apartat (i)"; G2:=GF(2); G3:=GF(3); G5:=GF(5); elements := procedure (cos,numelementos) for i:=0 to (numelementos-1) do cos!i; end for; end procedure; print "elements de G2"; elements(G2,2); print "elements de G3"; elements(G3,3); print "elements de G5"; elements(G5,5); /*(ii)*/ print "apartat (ii)"; Z9:=Integers(9); /* Z9 no es un cos pq te elements no invertibles a part del zero. Són aquests:*/ for i:=0 to 8 do if(IsInvertible(Z9!i) eq false) then Z9!i; end if; end for; /*(iii)*/ print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; G9b:=ext< G3 | k >; /*En aquest últim cas el polinomi k no es irreductible i no podem definir el cos finit G9b com a extensió de G9 fent servir aquest polinomi*/ /*(iv)*/ print "apartat (iv)"; for i:=1 to 4 do Order(G25!i); end for; G25 ! [1,2]; Output: Magma V2.10-6 Fri Mar 26 2004 10:43:51 on modular [Seed = 2844632699] ------------------------------------- Exercici 1 apartat (i) elements de G2 0 1 elements de G3 0 1 2 elements de G5 0 1 2 3 4 apartat (ii) 0 3 6 apartat (iii) true true true false >> G9b:=ext< G3 | k >; ^ Runtime error in ext< ... >: Argument is not irreducible apartat (iv) 1 4 4 2 G25.1^10 Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 10:47:21 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ llista:=[]; p:=5; n:=2; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n - 1)) then llista:=llista cat el; end if; end if; end for; end for; Output: Magma V2.10-6 Fri Mar 26 2004 10:47:18 on modular [Seed = 3097274459] ------------------------------------- apartat (iii) >> ; if (el ne 0) then if (Order(el) eq (p^n - 1)) then llista:=llista cat el; ^ Runtime error in 'cat': Bad argument types Argument types given: SeqEnum[], FldFinElt Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 10:47:57 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ llista:=[]; p:=5; n:=2; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n - 1)) then llista:=llista cat [el]; end if; end if; end for; end for; Output: Magma V2.10-6 Fri Mar 26 2004 10:47:54 on modular [Seed = 2208797516] ------------------------------------- apartat (iii) Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 10:48:22 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ llista:=[]; p:=5; n:=2; p^n-1; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n - 1)) then llista:=llista cat [el]; end if; end if; end for; end for; Output: Magma V2.10-6 Fri Mar 26 2004 10:48:19 on modular [Seed = 2511439156] ------------------------------------- apartat (iii) 24 Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 10:49:05 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ llista:=[]; p:=5; n:=2; p^n-1; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; llista; Output: Magma V2.10-6 Fri Mar 26 2004 10:49:02 on modular [Seed = 2629340183] ------------------------------------- apartat (iii) 24 [ G25.1, G25.1^17, G25.1^19, G25.1^11, G25.1^7, G25.1^23, G25.1^13, G25.1^5 ] Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 10:54:19 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then Order(el); end if; end for; end for; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; llista; Output: Magma V2.10-6 Fri Mar 26 2004 10:54:16 on modular [Seed = 1985111096] ------------------------------------- apartat (iii) 1 4 4 2 24 8 24 3 6 24 12 8 12 24 24 24 12 8 12 24 3 6 24 8 [ G25.1, G25.1^17, G25.1^19, G25.1^11, G25.1^7, G25.1^23, G25.1^13, G25.1^5 ] Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 10:55:11 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; llista; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; llista; Output: Magma V2.10-6 Fri Mar 26 2004 10:55:08 on modular [Seed = 2069850433] ------------------------------------- apartat (iii) [ 1, 4, 4, 2, 24, 8, 24, 3, 6, 24, 12, 8, 12, 24, 24, 24, 12, 8, 12, 24, 3, 6, 24, 8 ] [ G25.1, G25.1^17, G25.1^19, G25.1^11, G25.1^7, G25.1^23, G25.1^13, G25.1^5 ] Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 10:58:03 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; print("Ordre dels elements de G25 diferents de 0"); llista; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25); llista; Output: Magma V2.10-6 Fri Mar 26 2004 10:58:00 on modular [Seed = 603993930] ------------------------------------- apartat (iii) Ordre dels elements de G25 diferents de 0 [ 1, 4, 4, 2, 24, 8, 24, 3, 6, 24, 12, 8, 12, 24, 24, 24, 12, 8, 12, 24, 3, 6, 24, 8 ] >> quit; ^ User error: Unterminated string Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 10:58:22 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; print("Ordre dels elements de G25 diferents de 0"); llista; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; Output: Magma V2.10-6 Fri Mar 26 2004 10:58:19 on modular [Seed = 705575255] ------------------------------------- apartat (iii) Ordre dels elements de G25 diferents de 0 [ 1, 4, 4, 2, 24, 8, 24, 3, 6, 24, 12, 8, 12, 24, 24, 24, 12, 8, 12, 24, 3, 6, 24, 8 ] Elements primitius de G25 [ G25.1, G25.1^17, G25.1^19, G25.1^11, G25.1^7, G25.1^23, G25.1^13, G25.1^5 ] Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 11:01:29 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; print("Ordre dels elements de G25 diferents de 0"); llista; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; Output: Magma V2.10-6 Fri Mar 26 2004 11:01:26 on modular [Seed = 389219495] ------------------------------------- apartat (iii) Ordre dels elements de G25 diferents de 0 [ 1, 4, 4, 2, 24, 8, 24, 3, 6, 24, 12, 8, 12, 24, 24, 24, 12, 8, 12, 24, 3, 6, 24, 8 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Fri Mar 26 11:02:14 2004 Input: /*1*/ /*(i)*/ print "Exercici 1"; print "apartat (i)"; G2:=GF(2); G3:=GF(3); G5:=GF(5); elements := procedure (cos,numelementos) for i:=0 to (numelementos-1) do cos!i; end for; end procedure; print "elements de G2"; elements(G2,2); print "elements de G3"; elements(G3,3); print "elements de G5"; elements(G5,5); /*(ii)*/ print "apartat (ii)"; Z9:=Integers(9); /* Z9 no es un cos pq te elements no invertibles a part del zero. Són aquests:*/ for i:=0 to 8 do if(IsInvertible(Z9!i) eq false) then Z9!i; end if; end for; /*(iii)*/ print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; G9b:=ext< G3 | k >; /*En aquest últim cas el polinomi k no es irreductible i no podem definir el cos finit G9b com a extensió de G9 fent servir aquest polinomi*/ /*(iv)*/ print "apartat (iv)"; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; print("Ordre dels elements de G25 diferents de 0"); llista; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; Output: Magma V2.10-6 Fri Mar 26 2004 11:02:11 on modular [Seed = 473434233] ------------------------------------- Exercici 1 apartat (i) elements de G2 0 1 elements de G3 0 1 2 elements de G5 0 1 2 3 4 apartat (ii) 0 3 6 apartat (iii) true true true false >> G9b:=ext< G3 | k >; ^ Runtime error in ext< ... >: Argument is not irreducible apartat (iv) Ordre dels elements de G25 diferents de 0 [ 1, 4, 4, 2, 24, 8, 24, 3, 6, 24, 12, 8, 12, 24, 24, 24, 12, 8, 12, 24, 3, 6, 24, 8 ] Elements primitius de G25 [ G25.1, G25.1^17, G25.1^19, G25.1^11, G25.1^7, G25.1^23, G25.1^13, G25.1^5 ] Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 11:02:44 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; print("Ordre dels elements de G25 diferents de 0"); llista; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; Output: Magma V2.10-6 Fri Mar 26 2004 11:02:41 on modular [Seed = 3804690085] ------------------------------------- apartat (iii) >> G9; ^ User error: bad syntax Ordre dels elements de G25 diferents de 0 [ 1, 4, 4, 2, 24, 8, 24, 3, 6, 24, 12, 8, 12, 24, 24, 24, 12, 8, 12, 24, 3, 6, 24, 8 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 11:02:57 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; print("Ordre dels elements de G25 diferents de 0"); llista; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; Output: Magma V2.10-6 Fri Mar 26 2004 11:02:54 on modular [Seed = 3956277155] ------------------------------------- apartat (iii) Ordre dels elements de G25 diferents de 0 [ 1, 4, 4, 2, 24, 8, 24, 3, 6, 24, 12, 8, 12, 24, 24, 24, 12, 8, 12, 24, 3, 6, 24, 8 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 11:05:11 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ print "apartat (iv)"; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; print("Ordre dels elements de G25 diferents de 0"); llista; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; Output: Magma V2.10-6 Fri Mar 26 2004 11:05:08 on modular [Seed = 4208913960] ------------------------------------- apartat (iii) true true true false apartat (iv) Ordre dels elements de G25 diferents de 0 [ 1, 4, 4, 2, 24, 8, 24, 3, 6, 24, 12, 8, 12, 24, 24, 24, 12, 8, 12, 24, 3, 6, 24, 8 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 11:05:48 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ print "apartat (iv)"; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; print("Ordre dels elements de G25 diferents de 0"); llista; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; Output: Magma V2.10-6 Fri Mar 26 2004 11:05:45 on modular [Seed = 3286751100] ------------------------------------- apartat (iii) true true true false apartat (iv) Ordre dels elements de G25 diferents de 0 [ 24, 24, 24, 24, 1, 8, 12, 24, 3, 4, 24, 8, 12, 6, 4, 3, 12, 8, 24, 2, 6, 24, 12, 8 ] Elements primitius de G25 [ alfa, alfa^19, alfa^7, alfa^13, alfa^23, alfa^17, alfa^5, alfa^11 ] Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 11:07:59 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ print "apartat (iv)"; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; print("Ordre dels elements de G25 diferents de 0"); llista; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; 3+alfa; Output: Magma V2.10-6 Fri Mar 26 2004 11:07:56 on modular [Seed = 3370966514] ------------------------------------- apartat (iii) true true true false apartat (iv) Ordre dels elements de G25 diferents de 0 [ 24, 24, 24, 24, 1, 8, 12, 24, 3, 4, 24, 8, 12, 6, 4, 3, 12, 8, 24, 2, 6, 24, 12, 8 ] Elements primitius de G25 [ alfa, alfa^19, alfa^7, alfa^13, alfa^23, alfa^17, alfa^5, alfa^11 ] alfa^16 Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 11:08:16 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ print "apartat (iv)"; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; print("Ordre dels elements de G25 diferents de 0"); llista; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; 3+alfa; alfa^16; Output: Magma V2.10-6 Fri Mar 26 2004 11:08:13 on modular [Seed = 3740978133] ------------------------------------- apartat (iii) true true true false apartat (iv) Ordre dels elements de G25 diferents de 0 [ 24, 24, 24, 24, 1, 8, 12, 24, 3, 4, 24, 8, 12, 6, 4, 3, 12, 8, 24, 2, 6, 24, 12, 8 ] Elements primitius de G25 [ alfa, alfa^19, alfa^7, alfa^13, alfa^23, alfa^17, alfa^5, alfa^11 ] alfa^16 alfa^16 Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 11:08:44 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ print "apartat (iv)"; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; print("Ordre dels elements de G25 diferents de 0"); llista; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; 3+alfa; MinimalPolynomial(alfa^16); Output: Magma V2.10-6 Fri Mar 26 2004 11:08:41 on modular [Seed = 2693051727] ------------------------------------- apartat (iii) true true true false apartat (iv) Ordre dels elements de G25 diferents de 0 [ 24, 24, 24, 24, 1, 8, 12, 24, 3, 4, 24, 8, 12, 6, 4, 3, 12, 8, 24, 2, 6, 24, 12, 8 ] Elements primitius de G25 [ alfa, alfa^19, alfa^7, alfa^13, alfa^23, alfa^17, alfa^5, alfa^11 ] alfa^16 z^2 + z + 1 Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Fri Mar 26 11:10:09 2004 Input: /*1*/ /*(i)*/ print "Exercici 1"; print "apartat (i)"; G2:=GF(2); G3:=GF(3); G5:=GF(5); elements := procedure (cos,numelementos) for i:=0 to (numelementos-1) do cos!i; end for; end procedure; print "elements de G2"; elements(G2,2); print "elements de G3"; elements(G3,3); print "elements de G5"; elements(G5,5); /*(ii)*/ print "apartat (ii)"; Z9:=Integers(9); /* Z9 no es un cos pq te elements no invertibles a part del zero. Són aquests:*/ for i:=0 to 8 do if(IsInvertible(Z9!i) eq false) then Z9!i; end if; end for; /*(iii)*/ print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; G9b:=ext< G3 | k >; /*En aquest últim cas el polinomi k no es irreductible i no podem definir el cos finit G9b com a extensió de G9 fent servir aquest polinomi*/ /*(iv)*/ print "apartat (iv)"; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; print("Ordre dels elements de G25 diferents de 0"); llista; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end for; end for; print("Elements primitius de G25"); llista; Output: Magma V2.10-6 Fri Mar 26 2004 11:10:06 on modular [Seed = 2962531592] ------------------------------------- Exercici 1 apartat (i) elements de G2 0 1 elements de G3 0 1 2 elements de G5 0 1 2 3 4 apartat (ii) 0 3 6 apartat (iii) true true true false >> G9b:=ext< G3 | k >; ^ Runtime error in ext< ... >: Argument is not irreducible apartat (iv) Ordre dels elements de G25 diferents de 0 [ 1, 4, 4, 2, 24, 8, 24, 3, 6, 24, 12, 8, 12, 24, 24, 24, 12, 8, 12, 24, 3, 6, 24, 8 ] >> for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (Order(el) eq ( ^ Runtime error in 'Order': Can not take order of zero element Elements primitius de G25 [] Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 11:10:49 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ print "apartat (iv)"; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; print("Ordre dels elements de G25 diferents de 0"); llista; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; prim_el:=llista[1]; prim_el; mp:=MinimalPolynomial(prim_el); mp; Degree(mp); CoefficientRing(mp); Roots(mp,G25); Roots(mpa,Integers(5)); MinimalPolynomial(alfa^16); Output: Magma V2.10-6 Fri Mar 26 2004 11:10:46 on modular [Seed = 3114119129] ------------------------------------- apartat (iii) true true true false apartat (iv) Ordre dels elements de G25 diferents de 0 [ 24, 24, 24, 24, 1, 8, 12, 24, 3, 4, 24, 8, 12, 6, 4, 3, 12, 8, 24, 2, 6, 24, 12, 8 ] Elements primitius de G25 [ alfa, alfa^19, alfa^7, alfa^13, alfa^23, alfa^17, alfa^5, alfa^11 ] alfa z^2 + 2*z + 3 2 Finite field of size 5 [ , ] >> Roots(mpa,Integers(5)); ^ User error: Identifier 'mpa' has not been declared or assigned z^2 + z + 1 Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 11:11:00 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ print "apartat (iv)"; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; print("Ordre dels elements de G25 diferents de 0"); llista; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; print "apartat (v)"; prim_el:=llista[1]; prim_el; mp:=MinimalPolynomial(prim_el); mp; Degree(mp); CoefficientRing(mp); Roots(mp,G25); Roots(mpa,Integers(5)); MinimalPolynomial(alfa^16); Output: Magma V2.10-6 Fri Mar 26 2004 11:10:57 on modular [Seed = 2393544953] ------------------------------------- apartat (iii) true true true false apartat (iv) Ordre dels elements de G25 diferents de 0 [ 24, 24, 24, 24, 1, 8, 12, 24, 3, 4, 24, 8, 12, 6, 4, 3, 12, 8, 24, 2, 6, 24, 12, 8 ] Elements primitius de G25 [ alfa, alfa^19, alfa^7, alfa^13, alfa^23, alfa^17, alfa^5, alfa^11 ] apartat (v) alfa z^2 + 2*z + 3 2 Finite field of size 5 [ , ] >> Roots(mpa,Integers(5)); ^ User error: Identifier 'mpa' has not been declared or assigned z^2 + z + 1 Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Fri Mar 26 11:11:15 2004 Input: /*1*/ /*(i)*/ print "Exercici 1"; print "apartat (i)"; G2:=GF(2); G3:=GF(3); G5:=GF(5); elements := procedure (cos,numelementos) for i:=0 to (numelementos-1) do cos!i; end for; end procedure; print "elements de G2"; elements(G2,2); print "elements de G3"; elements(G3,3); print "elements de G5"; elements(G5,5); /*(ii)*/ print "apartat (ii)"; Z9:=Integers(9); /* Z9 no es un cos pq te elements no invertibles a part del zero. Són aquests:*/ for i:=0 to 8 do if(IsInvertible(Z9!i) eq false) then Z9!i; end if; end for; /*(iii)*/ print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; G9b:=ext< G3 | k >; /*En aquest últim cas el polinomi k no es irreductible i no podem definir el cos finit G9b com a extensió de G9 fent servir aquest polinomi*/ /*(iv)*/ print "apartat (iv)"; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; print("Ordre dels elements de G25 diferents de 0"); llista; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; Output: Magma V2.10-6 Fri Mar 26 2004 11:11:11 on modular [Seed = 2545123822] ------------------------------------- Exercici 1 apartat (i) elements de G2 0 1 elements de G3 0 1 2 elements de G5 0 1 2 3 4 apartat (ii) 0 3 6 apartat (iii) true true true false >> G9b:=ext< G3 | k >; ^ Runtime error in ext< ... >: Argument is not irreducible apartat (iv) Ordre dels elements de G25 diferents de 0 [ 1, 4, 4, 2, 24, 8, 24, 3, 6, 24, 12, 8, 12, 24, 24, 24, 12, 8, 12, 24, 3, 6, 24, 8 ] Elements primitius de G25 [ G25.1, G25.1^17, G25.1^19, G25.1^11, G25.1^7, G25.1^23, G25.1^13, G25.1^5 ] Total time: 3.179 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 11:11:17 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ print "apartat (iv)"; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; print("Ordre dels elements de G25 diferents de 0"); llista; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; print "apartat (v)"; prim_el:=llista[1]; prim_el; mp:=MinimalPolynomial(prim_el); mp; Degree(mp); CoefficientRing(mp); Roots(mp,G25); Roots(mp,Integers(5)); MinimalPolynomial(alfa^16); Output: Magma V2.10-6 Fri Mar 26 2004 11:11:14 on modular [Seed = 2461435094] ------------------------------------- apartat (iii) true true true false apartat (iv) Ordre dels elements de G25 diferents de 0 [ 24, 24, 24, 24, 1, 8, 12, 24, 3, 4, 24, 8, 12, 6, 4, 3, 12, 8, 24, 2, 6, 24, 12, 8 ] Elements primitius de G25 [ alfa, alfa^19, alfa^7, alfa^13, alfa^23, alfa^17, alfa^5, alfa^11 ] apartat (v) alfa z^2 + 2*z + 3 2 Finite field of size 5 [ , ] [] z^2 + z + 1 Total time: 3.229 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 11:11:26 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ print "apartat (iv)"; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; print("Ordre dels elements de G25 diferents de 0"); llista; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; print "apartat (v)"; prim_el:=llista[1]; prim_el; mp:=MinimalPolynomial(prim_el); mp; Degree(mp); CoefficientRing(mp); Roots(mp,G25); Roots(mp,Integers(5)); Output: Magma V2.10-6 Fri Mar 26 2004 11:11:23 on modular [Seed = 1681945128] ------------------------------------- apartat (iii) true true true false apartat (iv) Ordre dels elements de G25 diferents de 0 [ 24, 24, 24, 24, 1, 8, 12, 24, 3, 4, 24, 8, 12, 6, 4, 3, 12, 8, 24, 2, 6, 24, 12, 8 ] Elements primitius de G25 [ alfa, alfa^19, alfa^7, alfa^13, alfa^23, alfa^17, alfa^5, alfa^11 ] apartat (v) alfa z^2 + 2*z + 3 2 Finite field of size 5 [ , ] [] Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 11:12:18 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ print "apartat (iv)"; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; print("Ordre dels elements de G25 diferents de 0"); llista; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; print "apartat (v)"; prim_el:=llista[2]; prim_el; mp:=MinimalPolynomial(prim_el); mp; Degree(mp); CoefficientRing(mp); Roots(mp,G25); Roots(mp,Integers(5)); Output: Magma V2.10-6 Fri Mar 26 2004 11:12:15 on modular [Seed = 1800371539] ------------------------------------- apartat (iii) true true true false apartat (iv) Ordre dels elements de G25 diferents de 0 [ 24, 24, 24, 24, 1, 8, 12, 24, 3, 4, 24, 8, 12, 6, 4, 3, 12, 8, 24, 2, 6, 24, 12, 8 ] Elements primitius de G25 [ alfa, alfa^19, alfa^7, alfa^13, alfa^23, alfa^17, alfa^5, alfa^11 ] apartat (v) alfa^19 z^2 + 4*z + 2 2 Finite field of size 5 [ , ] [] Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 11:14:00 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ print "apartat (iv)"; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; print("Ordre dels elements de G25 diferents de 0"); llista; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; print "apartat (v)"; for i:=1 to 8 do print "element" i; prim_el:=llista[i]; prim_el; mp:=MinimalPolynomial(prim_el); mp; Degree(mp); CoefficientRing(mp); Roots(mp,G25); Roots(mp,Integers(5)); Output: Magma V2.10-6 Fri Mar 26 2004 11:13:57 on modular [Seed = 1884579538] ------------------------------------- apartat (iii) true true true false apartat (iv) Ordre dels elements de G25 diferents de 0 [ 24, 24, 24, 24, 1, 8, 12, 24, 3, 4, 24, 8, 12, 6, 4, 3, 12, 8, 24, 2, 6, 24, 12, 8 ] Elements primitius de G25 [ alfa, alfa^19, alfa^7, alfa^13, alfa^23, alfa^17, alfa^5, alfa^11 ] apartat (v) >> print "element" i; ^ User error: bad syntax >> prim_el:=llista[i]; ^ User error: Identifier 'i' has not been declared or assigned >> prim_el; ^ User error: Identifier 'prim_el' has not been declared or assigned >> mp:=MinimalPolynomial(prim_el); ^ User error: Identifier 'prim_el' has not been declared or assigned >> mp; ^ User error: Identifier 'mp' has not been declared or assigned >> Degree(mp); ^ User error: Identifier 'mp' has not been declared or assigned >> CoefficientRing(mp); ^ User error: Identifier 'mp' has not been declared or assigned >> Roots(mp,G25); ^ User error: Identifier 'mp' has not been declared or assigned >> Roots(mp,Integers(5)); ^ User error: Identifier 'mp' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 11:14:32 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; print "apartat (v)"; for i:=1 to 8 do print "element" i; prim_el:=llista[i]; prim_el; mp:=MinimalPolynomial(prim_el); mp; Degree(mp); CoefficientRing(mp); Roots(mp,G25); Roots(mp,Integers(5)); end for; Output: Magma V2.10-6 Fri Mar 26 2004 11:14:29 on modular [Seed = 1197691333] ------------------------------------- apartat (iii) Elements primitius de G25 [ alfa, alfa^19, alfa^7, alfa^13, alfa^23, alfa^17, alfa^5, alfa^11 ] apartat (v) >> print "element" i; ^ User error: bad syntax >> prim_el:=llista[i]; ^ User error: Identifier 'i' has not been declared or assigned >> prim_el; ^ User error: Identifier 'prim_el' has not been declared or assigned >> mp:=MinimalPolynomial(prim_el); ^ User error: Identifier 'prim_el' has not been declared or assigned >> mp; ^ User error: Identifier 'mp' has not been declared or assigned >> Degree(mp); ^ User error: Identifier 'mp' has not been declared or assigned >> CoefficientRing(mp); ^ User error: Identifier 'mp' has not been declared or assigned >> Roots(mp,G25); ^ User error: Identifier 'mp' has not been declared or assigned >> Roots(mp,Integers(5)); ^ User error: Identifier 'mp' has not been declared or assigned >> end for; ^ User error: bad syntax Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 11:15:29 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; print "apartat (v)"; for i:=1 to 8 do i; prim_el:=llista[i]; prim_el; mp:=MinimalPolynomial(prim_el); mp; Degree(mp); CoefficientRing(mp); Roots(mp,G25); Roots(mp,Integers(5)); end for; Output: Magma V2.10-6 Fri Mar 26 2004 11:15:26 on modular [Seed = 1248746803] ------------------------------------- apartat (iii) Elements primitius de G25 [ alfa, alfa^19, alfa^7, alfa^13, alfa^23, alfa^17, alfa^5, alfa^11 ] apartat (v) 1 alfa z^2 + 2*z + 3 2 Finite field of size 5 [ , ] [] 2 alfa^19 z^2 + 4*z + 2 2 Finite field of size 5 [ , ] [] 3 alfa^7 z^2 + z + 2 2 Finite field of size 5 [ , ] [] 4 alfa^13 z^2 + 3*z + 3 2 Finite field of size 5 [ , ] [] 5 alfa^23 z^2 + 4*z + 2 2 Finite field of size 5 [ , ] [] 6 alfa^17 z^2 + 3*z + 3 2 Finite field of size 5 [ , ] [] 7 alfa^5 z^2 + 2*z + 3 2 Finite field of size 5 [ , ] [] 8 alfa^11 z^2 + z + 2 2 Finite field of size 5 [ , ] [] Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 11:20:58 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; print "apartat (v)"; for i:=1 to 8 do i; prim_el:=llista[i]; prim_el; mp:=MinimalPolynomial(prim_el); mp; Degree(prim_el); CoefficientRing(mp); Roots(mp,G25); Roots(mp,Integers(5)); end for; Output: Magma V2.10-6 Fri Mar 26 2004 11:20:54 on modular [Seed = 772421166] ------------------------------------- apartat (iii) Elements primitius de G25 [ alfa, alfa^19, alfa^7, alfa^13, alfa^23, alfa^17, alfa^5, alfa^11 ] apartat (v) 1 alfa z^2 + 2*z + 3 >> Degree(prim_el); ^ Runtime error in 'Degree': Bad argument types Argument types given: FldFinElt Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 11:25:30 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; print "apartat (v)"; for i:=1 to 8 do i; prim_el:=llista[i]; prim_el; mp:=MinimalPolynomial(prim_el); mp; EulerPhi(prim_el); CoefficientRing(mp); Roots(mp,G25); Roots(mp,Integers(5)); end for; Output: Magma V2.10-6 Fri Mar 26 2004 11:25:27 on modular [Seed = 69213460] ------------------------------------- apartat (iii) Elements primitius de G25 [ alfa, alfa^19, alfa^7, alfa^13, alfa^23, alfa^17, alfa^5, alfa^11 ] apartat (v) 1 alfa z^2 + 2*z + 3 >> EulerPhi(prim_el); ^ Runtime error in 'EulerPhi': Bad argument types Argument types given: FldFinElt Total time: 3.169 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 11:50:04 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; beta:=2*alfa^(-3) - alfa^5 + (1/(alfa+2))*alfa^6; Output: Magma V2.10-6 Fri Mar 26 2004 11:50:00 on modular [Seed = 3404649877] ------------------------------------- apartat (iii) Elements primitius de G25 [ alfa, alfa^19, alfa^7, alfa^13, alfa^23, alfa^17, alfa^5, alfa^11 ] Total time: 3.279 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 11:52:46 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; beta:=2*alfa^(-3) - alfa^5 + (1/(alfa+2))*alfa^6; beta; Output: Magma V2.10-6 Fri Mar 26 2004 11:52:42 on modular [Seed = 2878321686] ------------------------------------- apartat (iii) Elements primitius de G25 [ alfa, alfa^19, alfa^7, alfa^13, alfa^23, alfa^17, alfa^5, alfa^11 ] alfa^8 Total time: 4.709 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 11:53:36 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; beta:=2*alfa^(-3) - alfa^5 + (1/(alfa+2))*alfa^6; beta; alfa^(-3); Output: Magma V2.10-6 Fri Mar 26 2004 11:53:33 on modular [Seed = 3147799505] ------------------------------------- apartat (iii) Elements primitius de G25 [ alfa, alfa^19, alfa^7, alfa^13, alfa^23, alfa^17, alfa^5, alfa^11 ] alfa^8 alfa^21 Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 11:53:52 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; beta:=2*alfa^(-3) - alfa^5 + (1/(alfa+2))*alfa^6; beta; 2*alfa^(-3); Output: Magma V2.10-6 Fri Mar 26 2004 11:53:49 on modular [Seed = 2191958776] ------------------------------------- apartat (iii) Elements primitius de G25 [ alfa, alfa^19, alfa^7, alfa^13, alfa^23, alfa^17, alfa^5, alfa^11 ] alfa^8 alfa^15 Total time: 3.169 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 11:54:22 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; beta:=2*alfa^(-3) - alfa^5 + (1/(alfa+2))*alfa^6; beta; 2*alfa^(-3)-alfa^5; Output: Magma V2.10-6 Fri Mar 26 2004 11:54:19 on modular [Seed = 2293016788] ------------------------------------- apartat (iii) Elements primitius de G25 [ alfa, alfa^19, alfa^7, alfa^13, alfa^23, alfa^17, alfa^5, alfa^11 ] alfa^8 1 Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 11:54:43 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; beta:=2*alfa^(-3) - alfa^5 + (1/(alfa+2))*alfa^6; beta; 2*alfa^(-3)-alfa^5; alfa^5; Output: Magma V2.10-6 Fri Mar 26 2004 11:54:40 on modular [Seed = 2679881640] ------------------------------------- apartat (iii) Elements primitius de G25 [ alfa, alfa^19, alfa^7, alfa^13, alfa^23, alfa^17, alfa^5, alfa^11 ] alfa^8 1 alfa^5 Total time: 3.089 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 11:55:38 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; beta:=2*alfa^(-3) - alfa^5 + (1/(alfa+2))*alfa^6; beta; 2*alfa^(-3)-alfa^5; alfa^5; ElementToSequence(alfa^8); ElementToSequence(alfa^5); Output: Magma V2.10-6 Fri Mar 26 2004 11:55:35 on modular [Seed = 1850363521] ------------------------------------- apartat (iii) Elements primitius de G25 [ alfa, alfa^19, alfa^7, alfa^13, alfa^23, alfa^17, alfa^5, alfa^11 ] alfa^8 1 alfa^5 [ 1, 4 ] [ 3, 4 ] Total time: 3.099 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 11:57:26 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; beta:=2*alfa^(-3) - alfa^5 + (1/(alfa+2))*alfa^6; beta; 2*alfa^(-3)-alfa^5; alfa^5; ElementToSequence(alfa^8); ElementToSequence(alfa^5); alfa^(-3) Output: Magma V2.10-6 Fri Mar 26 2004 11:57:23 on modular [Seed = 1732462588] ------------------------------------- apartat (iii) Elements primitius de G25 [ alfa, alfa^19, alfa^7, alfa^13, alfa^23, alfa^17, alfa^5, alfa^11 ] alfa^8 1 alfa^5 [ 1, 4 ] [ 3, 4 ] alfa^21 Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 11:57:47 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; beta:=2*alfa^(-3) - alfa^5 + (1/(alfa+2))*alfa^6; beta; 2*alfa^(-3)-alfa^5; alfa^5; ElementToSequence(alfa^8); ElementToSequence(alfa^5); alfa^(-3) ElementToSequence(alfa^21); Output: Magma V2.10-6 Fri Mar 26 2004 11:57:44 on modular [Seed = 1884573968] ------------------------------------- apartat (iii) Elements primitius de G25 [ alfa, alfa^19, alfa^7, alfa^13, alfa^23, alfa^17, alfa^5, alfa^11 ] alfa^8 1 alfa^5 [ 1, 4 ] [ 3, 4 ] >> ElementToSequence(alfa^21); ^ User error: bad syntax Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 11:58:02 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; beta:=2*alfa^(-3) - alfa^5 + (1/(alfa+2))*alfa^6; beta; 2*alfa^(-3)-alfa^5; alfa^5; ElementToSequence(alfa^8); ElementToSequence(alfa^5); alfa^(-3); ElementToSequence(alfa^21); Output: Magma V2.10-6 Fri Mar 26 2004 11:57:59 on modular [Seed = 1231906870] ------------------------------------- apartat (iii) Elements primitius de G25 [ alfa, alfa^19, alfa^7, alfa^13, alfa^23, alfa^17, alfa^5, alfa^11 ] alfa^8 1 alfa^5 [ 1, 4 ] [ 3, 4 ] alfa^21 [ 2, 2 ] Total time: 3.099 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 11:59:11 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; beta:=2*alfa^(-3) - alfa^5 + (1/(alfa+2))*alfa^6; beta; 2*alfa^(-3)-alfa^5; alfa^5; ElementToSequence(alfa^8); ElementToSequence(alfa^5); alfa^(-3); ElementToSequence(alfa^21); 2*alfa^21; ElementToSequence(2*alfa^21); Output: Magma V2.10-6 Fri Mar 26 2004 11:59:07 on modular [Seed = 1484552555] ------------------------------------- apartat (iii) Elements primitius de G25 [ alfa, alfa^19, alfa^7, alfa^13, alfa^23, alfa^17, alfa^5, alfa^11 ] alfa^8 1 alfa^5 [ 1, 4 ] [ 3, 4 ] alfa^21 [ 2, 2 ] alfa^15 [ 4, 4 ] Total time: 3.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (206.81.131.14) Time: Fri Mar 26 11:59:14 2004 Input: 2^20996011-1 Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Mar 26 2004 11:58:51 on modular [Seed = 1164010598] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 10285 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 12:00:49 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![i,j]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do llista:= llista cat [G25![i,j]]; end for; end for; print("Elements primitius de G25"); llista; beta:=2*alfa^(-3) - alfa^5 + (1/(alfa+2))*alfa^6; beta; alfa^(-3); ElementToSequence(alfa^21); 2*alfa^21; ElementToSequence(2*alfa^21); Output: Magma V2.10-6 Fri Mar 26 2004 12:00:46 on modular [Seed = 537133558] ------------------------------------- apartat (iii) Elements primitius de G25 [ 0, alfa, alfa^19, alfa^7, alfa^13, 1, alfa^3, alfa^10, alfa^23, alfa^8, 2, alfa^17, alfa^21, alfa^2, alfa^4, 3, alfa^16, alfa^14, alfa^9, alfa^5, 4, alfa^20, alfa^11, alfa^22, alfa^15 ] alfa^8 alfa^21 [ 2, 2 ] alfa^15 [ 4, 4 ] Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 12:01:34 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do llista:= llista cat [G25![j,i]]; end for; end for; print("Elements primitius de G25"); llista; beta:=2*alfa^(-3) - alfa^5 + (1/(alfa+2))*alfa^6; beta; alfa^(-3); ElementToSequence(alfa^21); 2*alfa^21; ElementToSequence(2*alfa^21); Output: Magma V2.10-6 Fri Mar 26 2004 12:01:31 on modular [Seed = 237645709] ------------------------------------- apartat (iii) Elements primitius de G25 [ 0, 1, 2, 3, 4, alfa, alfa^3, alfa^17, alfa^16, alfa^20, alfa^19, alfa^10, alfa^21, alfa^14, alfa^11, alfa^7, alfa^23, alfa^2, alfa^9, alfa^22, alfa^13, alfa^8, alfa^4, alfa^5, alfa^15 ] alfa^8 alfa^21 [ 2, 2 ] alfa^15 [ 4, 4 ] Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 12:02:10 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do llista:= llista cat [G25![j,i]]; end for; end for; print("Elements primitius de G25"); llista; beta:=2*alfa^(-3) - alfa^5 + (1/(alfa+2))*alfa^6; beta; alfa^(-3); ElementToSequence(alfa^21); 2*alfa^21; ElementToSequence(2*alfa^21); ElementToSequence(alfa^3); Output: Magma V2.10-6 Fri Mar 26 2004 12:02:07 on modular [Seed = 406600319] ------------------------------------- apartat (iii) Elements primitius de G25 [ 0, 1, 2, 3, 4, alfa, alfa^3, alfa^17, alfa^16, alfa^20, alfa^19, alfa^10, alfa^21, alfa^14, alfa^11, alfa^7, alfa^23, alfa^2, alfa^9, alfa^22, alfa^13, alfa^8, alfa^4, alfa^5, alfa^15 ] alfa^8 alfa^21 [ 2, 2 ] alfa^15 [ 4, 4 ] [ 1, 1 ] Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 12:03:20 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do llista:= llista cat [G25![j,i]]; end for; end for; print("Elements primitius de G25"); llista; beta:=2*alfa^(-3) - alfa^5 + (1/(alfa+2))*alfa^6; beta; alfa^(-3); ElementToSequence(alfa^21); 2*alfa^21; ElementToSequence(2*alfa^21); ElementToSequence(alfa^3); 3+alfa; Output: Magma V2.10-6 Fri Mar 26 2004 12:03:17 on modular [Seed = 305541167] ------------------------------------- apartat (iii) Elements primitius de G25 [ 0, 1, 2, 3, 4, alfa, alfa^3, alfa^17, alfa^16, alfa^20, alfa^19, alfa^10, alfa^21, alfa^14, alfa^11, alfa^7, alfa^23, alfa^2, alfa^9, alfa^22, alfa^13, alfa^8, alfa^4, alfa^5, alfa^15 ] alfa^8 alfa^21 [ 2, 2 ] alfa^15 [ 4, 4 ] [ 1, 1 ] alfa^16 Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 12:03:29 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do llista:= llista cat [G25![j,i]]; end for; end for; print("Elements primitius de G25"); llista; beta:=2*alfa^(-3) - alfa^5 + (1/(alfa+2))*alfa^6; beta; alfa^(-3); ElementToSequence(alfa^21); 2*alfa^21; ElementToSequence(2*alfa^21); ElementToSequence(alfa^3); 1+alfa; Output: Magma V2.10-6 Fri Mar 26 2004 12:03:26 on modular [Seed = 3956263389] ------------------------------------- apartat (iii) Elements primitius de G25 [ 0, 1, 2, 3, 4, alfa, alfa^3, alfa^17, alfa^16, alfa^20, alfa^19, alfa^10, alfa^21, alfa^14, alfa^11, alfa^7, alfa^23, alfa^2, alfa^9, alfa^22, alfa^13, alfa^8, alfa^4, alfa^5, alfa^15 ] alfa^8 alfa^21 [ 2, 2 ] alfa^15 [ 4, 4 ] [ 1, 1 ] alfa^3 Total time: 3.059 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 12:05:00 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do llista:= llista cat [G25![j,i]]; end for; end for; print("Elements primitius de G25"); llista; beta:=2*alfa^(-3) - alfa^5 + (1/(alfa+2))*alfa^6; beta; Output: Magma V2.10-6 Fri Mar 26 2004 12:04:57 on modular [Seed = 3854681908] ------------------------------------- apartat (iii) Elements primitius de G25 [ 0, 1, 2, 3, 4, alfa, alfa^3, alfa^17, alfa^16, alfa^20, alfa^19, alfa^10, alfa^21, alfa^14, alfa^11, alfa^7, alfa^23, alfa^2, alfa^9, alfa^22, alfa^13, alfa^8, alfa^4, alfa^5, alfa^15 ] alfa^8 Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 12:08:05 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ beta:=2*alfa^(-3) - alfa^5 + (1/(alfa+2))*alfa^6; beta; for i:=0 to (p-1) do for j:=0 to (p-1) do if(IsInvertible(G25![j,i]) eq true) then G25![j,i]; end if; end for; end for; Output: Magma V2.10-6 Fri Mar 26 2004 12:08:02 on modular [Seed = 4141012460] ------------------------------------- apartat (iii) alfa^8 1 2 3 4 alfa alfa^3 alfa^17 alfa^16 alfa^20 alfa^19 alfa^10 alfa^21 alfa^14 alfa^11 alfa^7 alfa^23 alfa^2 alfa^9 alfa^22 alfa^13 alfa^8 alfa^4 alfa^5 alfa^15 Total time: 3.029 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 12:09:01 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ beta:=2*alfa^(-3) - alfa^5 + (1/(alfa+2))*alfa^6; beta; for i:=0 to (p-1) do for j:=0 to (p-1) do if(IsInvertible(G25![j,i]) eq true) then G25![j,i]; end if; end for; end for; IsInvertible(G25![0,0]); Output: Magma V2.10-6 Fri Mar 26 2004 12:08:58 on modular [Seed = 3236225794] ------------------------------------- apartat (iii) alfa^8 1 2 3 4 alfa alfa^3 alfa^17 alfa^16 alfa^20 alfa^19 alfa^10 alfa^21 alfa^14 alfa^11 alfa^7 alfa^23 alfa^2 alfa^9 alfa^22 alfa^13 alfa^8 alfa^4 alfa^5 alfa^15 false Total time: 3.069 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 12:10:27 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ beta:=2*alfa^(-3) - alfa^5 + (1/(alfa+2))*alfa^6; beta; beta^(-1); alfa^(-8); Output: Magma V2.10-6 Fri Mar 26 2004 12:10:24 on modular [Seed = 3505714360] ------------------------------------- apartat (iii) alfa^8 alfa^16 alfa^16 Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 12:12:09 2004 Input: print "apartat (iii)"; P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ print "apartat (vi)"; beta:=2*alfa^(-3) - alfa^5 + (1/(alfa+2))*alfa^6; print("Solucio de beta"); beta; print("Invers"); beta^(-1); Output: Magma V2.10-6 Fri Mar 26 2004 12:12:06 on modular [Seed = 2861469348] ------------------------------------- apartat (iii) apartat (vi) Solucio de beta alfa^8 Invers alfa^16 Total time: 3.039 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 12:14:17 2004 Input: P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ print "apartat (vi)"; beta:=2*alfa^(-3) - alfa^5 + (1/(alfa+2))*alfa^6; print("Solucio de beta"); beta; print("Invers"); beta^(-1); Output: Magma V2.10-6 Fri Mar 26 2004 12:14:13 on modular [Seed = 2776727848] ------------------------------------- apartat (vi) Solucio de beta alfa^8 Invers alfa^16 Total time: 3.119 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 12:17:39 2004 Input: P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; for i:=0 to (p^n-1) do ElementToSequence(alfa^i) end for; Output: Magma V2.10-6 Fri Mar 26 2004 12:17:36 on modular [Seed = 3046215789] ------------------------------------- >> for i:=0 to (p^n-1) do ElementToSequence(alfa^i) end for; ^ User error: bad syntax Total time: 3.169 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 12:17:51 2004 Input: P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; for i:=0 to (p^n-1) do ElementToSequence(alfa^i); end for; Output: Magma V2.10-6 Fri Mar 26 2004 12:17:48 on modular [Seed = 2393549658] ------------------------------------- [ 1, 0 ] [ 0, 1 ] [ 2, 3 ] [ 1, 1 ] [ 2, 4 ] [ 3, 4 ] [ 3, 0 ] [ 0, 3 ] [ 1, 4 ] [ 3, 3 ] [ 1, 2 ] [ 4, 2 ] [ 4, 0 ] [ 0, 4 ] [ 3, 2 ] [ 4, 4 ] [ 3, 1 ] [ 2, 1 ] [ 2, 0 ] [ 0, 2 ] [ 4, 1 ] [ 2, 2 ] [ 4, 3 ] [ 1, 3 ] [ 1, 0 ] Total time: 3.109 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 12:19:22 2004 Input: P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; /*for i:=0 to (p^n-1) do ElementToSequence(alfa^i); end for;*/ G25![0,0]; Output: Magma V2.10-6 Fri Mar 26 2004 12:19:18 on modular [Seed = 2562506470] ------------------------------------- 0 Total time: 3.149 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 12:21:29 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5b:=O![2,4,1]; G25:=ext; Output: Magma V2.10-6 Fri Mar 26 2004 12:21:25 on modular [Seed = 1665615263] ------------------------------------- Total time: 3.479 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 12:21:31 2004 Input: P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; ElementToSequence(0); for i:=0 to (p^n-1) do ElementToSequence(alfa^i); end for; Output: Magma V2.10-6 Fri Mar 26 2004 12:21:28 on modular [Seed = 1681932949] ------------------------------------- [ 0 ] [ 1, 0 ] [ 0, 1 ] [ 2, 3 ] [ 1, 1 ] [ 2, 4 ] [ 3, 4 ] [ 3, 0 ] [ 0, 3 ] [ 1, 4 ] [ 3, 3 ] [ 1, 2 ] [ 4, 2 ] [ 4, 0 ] [ 0, 4 ] [ 3, 2 ] [ 4, 4 ] [ 3, 1 ] [ 2, 1 ] [ 2, 0 ] [ 0, 2 ] [ 4, 1 ] [ 2, 2 ] [ 4, 3 ] [ 1, 3 ] [ 1, 0 ] Total time: 3.309 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 12:21:46 2004 Input: P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; ElementToSequence(0*alfa); for i:=0 to (p^n-1) do ElementToSequence(alfa^i); end for; Output: Magma V2.10-6 Fri Mar 26 2004 12:21:43 on modular [Seed = 1968264123] ------------------------------------- [ 0, 0 ] [ 1, 0 ] [ 0, 1 ] [ 2, 3 ] [ 1, 1 ] [ 2, 4 ] [ 3, 4 ] [ 3, 0 ] [ 0, 3 ] [ 1, 4 ] [ 3, 3 ] [ 1, 2 ] [ 4, 2 ] [ 4, 0 ] [ 0, 4 ] [ 3, 2 ] [ 4, 4 ] [ 3, 1 ] [ 2, 1 ] [ 2, 0 ] [ 0, 2 ] [ 4, 1 ] [ 2, 2 ] [ 4, 3 ] [ 1, 3 ] [ 1, 0 ] Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 12:23:05 2004 Input: P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; ElementToSequence(0*alfa); for i:=0 to (p^n-2) do ElementToSequence(alfa^i); end for; Output: Magma V2.10-6 Fri Mar 26 2004 12:23:02 on modular [Seed = 1197695448] ------------------------------------- [ 0, 0 ] [ 1, 0 ] [ 0, 1 ] [ 2, 3 ] [ 1, 1 ] [ 2, 4 ] [ 3, 4 ] [ 3, 0 ] [ 0, 3 ] [ 1, 4 ] [ 3, 3 ] [ 1, 2 ] [ 4, 2 ] [ 4, 0 ] [ 0, 4 ] [ 3, 2 ] [ 4, 4 ] [ 3, 1 ] [ 2, 1 ] [ 2, 0 ] [ 0, 2 ] [ 4, 1 ] [ 2, 2 ] [ 4, 3 ] [ 1, 3 ] Total time: 3.069 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 12:24:21 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5b:=O![2,4,1]; pz5:=O![3,2,1]; G25:=ext; Output: Magma V2.10-6 Fri Mar 26 2004 12:24:18 on modular [Seed = 1349810043] ------------------------------------- Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 12:24:51 2004 Input: P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; print("exp , vect"); < 0 , ElementToSequence(0*alfa)>; for i:=0 to (p^n-2) do < alfa^i , ElementToSequence(alfa^i)>; end for; Output: Magma V2.10-6 Fri Mar 26 2004 12:24:48 on modular [Seed = 671878945] ------------------------------------- exp , vect <0, [ 0, 0 ]> <1, [ 1, 0 ]> <3, [ 3, 0 ]> <4, [ 4, 0 ]> <2, [ 2, 0 ]> Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 12:32:05 2004 Input: P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; k:=1+2*x+x^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; /*G9b:=ext< G3 | k >;*/ p:=5; n:=2; print("G25"); print("exponencial , vectorial"); < 0 , ElementToSequence(0*alfa)>; for i:=0 to (p^n-2) do < alfa^i , ElementToSequence(alfa^i)>; end for; p:=2; n:=4; print("G16"); print("exponencial , vectorial"); < 0 , ElementToSequence(0*alfa2)>; for i:=0 to (p^n-2) do < alfa2^i , ElementToSequence(alfa2^i)>; end for; Output: Magma V2.10-6 Fri Mar 26 2004 12:32:02 on modular [Seed = 187638384] ------------------------------------- G25 exponencial , vectorial <0, [ 0, 0 ]> <1, [ 1, 0 ]> <3, [ 3, 0 ]> <4, [ 4, 0 ]> <2, [ 2, 0 ]> G16 exponencial , vectorial <0, [ 0, 0, 0, 0 ]> <1, [ 1, 0, 0, 0 ]> Total time: 3.029 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 12:36:56 2004 Input: CF2:=GF(2); CF4:=GF(2,2); CF8:=GF(2,3); CF16:=GF(2,4); CF2!0; Output: Magma V2.10-6 Fri Mar 26 2004 12:36:53 on modular [Seed = 457126215] ------------------------------------- 0 Total time: 3.119 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 12:37:24 2004 Input: CF2:=GF(2); CF4:=GF(2,2); CF8:=GF(2,3); CF16:=GF(2,4); for i:=0 to 2 do CF2!i; end for; Output: Magma V2.10-6 Fri Mar 26 2004 12:37:21 on modular [Seed = 305543210] ------------------------------------- 0 1 0 Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 12:37:50 2004 Input: CF2:=GF(2); CF4:=GF(2,2); CF8:=GF(2,3); CF16:=GF(2,4); for i:=0 to 1 do CF2!i; end for; elements(CF2); Output: Magma V2.10-6 Fri Mar 26 2004 12:37:47 on modular [Seed = 3989424111] ------------------------------------- 0 1 >> elements(CF2); ^ User error: Identifier 'elements' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 12:38:12 2004 Input: CF2:=GF(2); CF4:=GF(2,2); CF8:=GF(2,3); CF16:=GF(2,4); for i:=0 to 1 do CF2!i; end for; elements(CF2,2); Output: Magma V2.10-6 Fri Mar 26 2004 12:38:08 on modular [Seed = 3837840909] ------------------------------------- 0 1 >> elements(CF2,2); ^ User error: Identifier 'elements' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 12:42:15 2004 Input: CF2:=GF(2); CF4:=GF(2,2); CF8:=GF(2,3); CF16:=GF(2,4); print("Elements de CF2"); CF2!0; CF2!1; print("Elements de CF4"); CF4![0 0]; CF4![1 0]; CF4![0 1]; CF4![1 1]; Output: Magma V2.10-6 Fri Mar 26 2004 12:42:12 on modular [Seed = 3387810516] ------------------------------------- Elements de CF2 0 1 Elements de CF4 >> CF4![0 0]; ^ User error: bad syntax >> CF4![1 0]; ^ User error: bad syntax >> CF4![0 1]; ^ User error: bad syntax >> CF4![1 1]; ^ User error: bad syntax Total time: 3.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 12:42:34 2004 Input: CF2:=GF(2); CF4:=GF(2,2); CF8:=GF(2,3); CF16:=GF(2,4); print("Elements de CF2"); CF2!0; CF2!1; print("Elements de CF4"); CF4!0; CF4!1; CF4!2; CF4!3; Output: Magma V2.10-6 Fri Mar 26 2004 12:42:30 on modular [Seed = 3236227887] ------------------------------------- Elements de CF2 0 1 Elements de CF4 0 1 0 1 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 12:45:05 2004 Input: CF2:=GF(2); CF4:=GF(2,2); CF8:=GF(2,3); CF16:=GF(2,4); print("Elements de CF2"); p:=2 n:=1; for i:=0 to p^n-1 do CF2!i; end for; print("Elements de CF4"); p:=2 n:=2; for i:=0 to p^n-1 do CF4!i; end for; print("Elements de CF8"); p:=2 n:=3; for i:=0 to p^n-1 do CF8!i; end for; print("Elements de CF16"); p:=2 n:=4; for i:=0 to p^n-1 do CF16!i; end for; Output: Magma V2.10-6 Fri Mar 26 2004 12:45:02 on modular [Seed = 3740988073] ------------------------------------- Elements de CF2 >> n:=1; ^ User error: bad syntax >> for i:=0 to p^n-1 do CF2!i; end for; ^ User error: Identifier 'p' has not been declared or assigned Elements de CF4 >> n:=2; ^ User error: bad syntax >> for i:=0 to p^n-1 do CF4!i; end for; ^ User error: Identifier 'p' has not been declared or assigned Elements de CF8 >> n:=3; ^ User error: bad syntax >> for i:=0 to p^n-1 do CF8!i; end for; ^ User error: Identifier 'p' has not been declared or assigned Elements de CF16 >> n:=4; ^ User error: bad syntax >> for i:=0 to p^n-1 do CF16!i; end for; ^ User error: Identifier 'p' has not been declared or assigned Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 12:45:25 2004 Input: CF2:=GF(2); CF4:=GF(2,2); CF8:=GF(2,3); CF16:=GF(2,4); print("Elements de CF2"); p:=2; n:=1; for i:=0 to p^n-1 do CF2!i; end for; print("Elements de CF4"); p:=2; n:=2; for i:=0 to p^n-1 do CF4!i; end for; print("Elements de CF8"); p:=2; n:=3; for i:=0 to p^n-1 do CF8!i; end for; print("Elements de CF16"); p:=2; n:=4; for i:=0 to p^n-1 do CF16!i; end for; Output: Magma V2.10-6 Fri Mar 26 2004 12:45:22 on modular [Seed = 2827781363] ------------------------------------- Elements de CF2 0 1 Elements de CF4 0 1 0 1 Elements de CF8 0 1 0 1 0 1 0 1 Elements de CF16 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 12:46:42 2004 Input: CF2:=GF(2); CF4:=GF(2,2); CF8:=GF(2,3); CF16:=GF(2,4); print("Elements de CF2"); p:=2; n:=1; for i:=0 to p^n-1 do CF2!i; end for; print("Elements de CF4"); p:=2; n:=2; for i:=0 to p^n-1 do CF4!i; end for; print("Elements de CF8"); p:=2; n:=3; for i:=0 to p^n-1 do CF8!i; end for; print("Elements de CF16"); p:=2; n:=4; for i:=0 to p^n-1 do CF16!i; end for; CF2 subset CF16; Output: Magma V2.10-6 Fri Mar 26 2004 12:46:39 on modular [Seed = 2743570357] ------------------------------------- Elements de CF2 0 1 Elements de CF4 0 1 0 1 Elements de CF8 0 1 0 1 0 1 0 1 Elements de CF16 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 true Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 12:48:31 2004 Input: CF2:=GF(2); CF4:=GF(2,2); CF8:=GF(2,3); CF16:=GF(2,4); CF2 subset CF16; CF2 subset CF8; CF2 subset CF4; CF2 subset CF2; CF4 subset CF16; CF4 subset CF8; CF4 subset CF4; CF4 subset CF2; CF8 subset CF16; CF8 subset CF8; CF8 subset CF4; CF8 subset CF2; CF16 subset CF16; CF16 subset CF8; CF16 subset CF4; CF16 subset CF2; Output: Magma V2.10-6 Fri Mar 26 2004 12:48:28 on modular [Seed = 3164115001] ------------------------------------- true true true true true false true false false true false false true false false false Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Fri Mar 26 12:49:31 2004 Input: CF2:=GF(2); CF4:=GF(2,2); CF8:=GF(2,3); CF16:=GF(2,4); print "CF2 subset"; CF2 subset CF16; CF2 subset CF8; CF2 subset CF4; CF2 subset CF2; print "CF4 subset"; CF4 subset CF16; CF4 subset CF8; CF4 subset CF4; CF4 subset CF2; print "CF8 subset"; CF8 subset CF16; CF8 subset CF8; CF8 subset CF4; CF8 subset CF2; print "CF16 subset"; CF16 subset CF16; CF16 subset CF8; CF16 subset CF4; CF16 subset CF2; Output: Magma V2.10-6 Fri Mar 26 2004 12:49:28 on modular [Seed = 3079903990] ------------------------------------- CF2 subset true true true true CF4 subset true false true false CF8 subset false true false false CF16 subset true false false false Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 12:53:22 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=ext; Output: Magma V2.10-6 Fri Mar 26 2004 12:53:19 on modular [Seed = 2579347455] ------------------------------------- Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 12:53:57 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=ext; [Order(i) : i in G25 | i ne 0]; Output: Magma V2.10-6 Fri Mar 26 2004 12:53:54 on modular [Seed = 2427764427] ------------------------------------- [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 12:54:21 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=ext; [j : j in G25 | j ne 0 and Order(j) eq 24]; Output: Magma V2.10-6 Fri Mar 26 2004 12:54:18 on modular [Seed = 1715619910] ------------------------------------- [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 12:55:24 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=ext; [j : j in G25 | IsPrimitive(j)]; Output: Magma V2.10-6 Fri Mar 26 2004 12:55:22 on modular [Seed = 1884577424] ------------------------------------- [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 12:56:02 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=ext; #[j : j in G25 | IsPrimitive(j)]; Output: Magma V2.10-6 Fri Mar 26 2004 12:55:59 on modular [Seed = 1231906707] ------------------------------------- 8 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 12:57:15 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=ext; MinimalPolynomial(alpha); Output: Magma V2.10-6 Fri Mar 26 2004 12:57:12 on modular [Seed = 1180854484] ------------------------------------- z^2 + 2*z + 3 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 12:57:40 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=ext; MinimalPolynomial(alpha); DefiningPolynomial(G25); Output: Magma V2.10-6 Fri Mar 26 2004 12:57:37 on modular [Seed = 1551397671] ------------------------------------- z^2 + 2*z + 3 z^2 + 2*z + 3 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 12:58:32 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=ext; pmalpha:=DefiningPolynomial(G25); CoefficientRing(pmalpha); Output: Magma V2.10-6 Fri Mar 26 2004 12:58:29 on modular [Seed = 705561861] ------------------------------------- Finite field of size 5 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 12:58:57 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=ext; pmalpha:=DefiningPolynomial(G25); CoefficientRing(pmalpha); Roots(pmalpha,G5); Output: Magma V2.10-6 Fri Mar 26 2004 12:58:54 on modular [Seed = 587664407] ------------------------------------- Finite field of size 5 [] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 12:59:41 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=ext; pmalpha:=DefiningPolynomial(G25); CoefficientRing(pmalpha); Roots(pmalpha,G5); Roots(pmalpha,G25); Output: Magma V2.10-6 Fri Mar 26 2004 12:59:38 on modular [Seed = 941365208] ------------------------------------- Finite field of size 5 [] [ , ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 13:00:18 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=ext; p:=2*alpha^(-3)-alpha^5+(1/(alpha+2))*(alpha^6); p; Output: Magma V2.10-6 Fri Mar 26 2004 13:00:15 on modular [Seed = 153953996] ------------------------------------- alpha^8 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 13:00:41 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=ext; p:=2*alpha^(-3)-alpha^5+(1/(alpha+2))*(alpha^6); p; IsInvertible(p); Output: Magma V2.10-6 Fri Mar 26 2004 13:00:38 on modular [Seed = 102902186] ------------------------------------- alpha^8 true alpha^16 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 13:01:16 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=ext; [i: i in G25 | IsInvertible(i)]; Output: Magma V2.10-6 Fri Mar 26 2004 13:01:13 on modular [Seed = 3804679521] ------------------------------------- [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 13:02:04 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=ext; [: i in G25]; Output: Magma V2.10-6 Fri Mar 26 2004 13:02:01 on modular [Seed = 4225747848] ------------------------------------- [ <[ 1, 0 ], 1>, <[ 0, 1 ], alpha>, <[ 2, 3 ], alpha^2>, <[ 1, 1 ], alpha^3>, <[ 2, 4 ], alpha^4>, <[ 3, 4 ], alpha^5>, <[ 3, 0 ], 3>, <[ 0, 3 ], alpha^7>, <[ 1, 4 ], alpha^8>, <[ 3, 3 ], alpha^9>, <[ 1, 2 ], alpha^10>, <[ 4, 2 ], alpha^11>, <[ 4, 0 ], 4>, <[ 0, 4 ], alpha^13>, <[ 3, 2 ], alpha^14>, <[ 4, 4 ], alpha^15>, <[ 3, 1 ], alpha^16>, <[ 2, 1 ], alpha^17>, <[ 2, 0 ], 2>, <[ 0, 2 ], alpha^19>, <[ 4, 1 ], alpha^20>, <[ 2, 2 ], alpha^21>, <[ 4, 3 ], alpha^22>, <[ 1, 3 ], alpha^23>, <[ 0, 0 ], 0> ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 13:14:03 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=ext; [: i in G25]; P:=PolynomialRing(R); p1=alpha^2+alpha*x+beta*x^2; p2=1 + alpha*x; Output: Magma V2.10-6 Fri Mar 26 2004 13:14:00 on modular [Seed = 3336762436] ------------------------------------- [ <[ 1, 0 ], 1>, <[ 0, 1 ], alpha>, <[ 2, 3 ], alpha^2>, <[ 1, 1 ], alpha^3>, <[ 2, 4 ], alpha^4>, <[ 3, 4 ], alpha^5>, <[ 3, 0 ], 3>, <[ 0, 3 ], alpha^7>, <[ 1, 4 ], alpha^8>, <[ 3, 3 ], alpha^9>, <[ 1, 2 ], alpha^10>, <[ 4, 2 ], alpha^11>, <[ 4, 0 ], 4>, <[ 0, 4 ], alpha^13>, <[ 3, 2 ], alpha^14>, <[ 4, 4 ], alpha^15>, <[ 3, 1 ], alpha^16>, <[ 2, 1 ], alpha^17>, <[ 2, 0 ], 2>, <[ 0, 2 ], alpha^19>, <[ 4, 1 ], alpha^20>, <[ 2, 2 ], alpha^21>, <[ 4, 3 ], alpha^22>, <[ 1, 3 ], alpha^23>, <[ 0, 0 ], 0> ] >> P:=PolynomialRing(R); ^ User error: Identifier 'R' has not been declared or assigned >> p1=alpha^2+alpha*x+beta*x^2; ^ User error: Identifier 'x' has not been declared or assigned >> p2=1 + alpha*x; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 13:14:13 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=ext; P:=PolynomialRing(R); p1=alpha^2+alpha*x+beta*x^2; p2=1 + alpha*x; Output: Magma V2.10-6 Fri Mar 26 2004 13:14:10 on modular [Seed = 3757829447] ------------------------------------- >> P:=PolynomialRing(R); ^ User error: Identifier 'R' has not been declared or assigned >> p1=alpha^2+alpha*x+beta*x^2; ^ User error: Identifier 'x' has not been declared or assigned >> p2=1 + alpha*x; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 13:14:58 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=ext; R:=Reals(); P:=PolynomialRing(R); p1=alpha^2+alpha*x+beta*x^2; p2=1 + alpha*x; Output: Magma V2.10-6 Fri Mar 26 2004 13:14:55 on modular [Seed = 3572557729] ------------------------------------- >> R:=Reals(); ^ User error: Identifier 'Reals' has not been declared or assigned >> P:=PolynomialRing(R); ^ User error: Identifier 'R' has not been declared or assigned >> p1=alpha^2+alpha*x+beta*x^2; ^ User error: Identifier 'x' has not been declared or assigned >> p2=1 + alpha*x; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 13:15:10 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=ext; R:=Integers(); P:=PolynomialRing(R); p1=alpha^2+alpha*x+beta*x^2; p2=1 + alpha*x; Output: Magma V2.10-6 Fri Mar 26 2004 13:15:07 on modular [Seed = 2709885664] ------------------------------------- >> p1=alpha^2+alpha*x+beta*x^2; ^ User error: Identifier 'p1' has not been declared or assigned >> p2=1 + alpha*x; ^ User error: Identifier 'p2' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 13:15:22 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=ext; R:=Integers(); P:=PolynomialRing(R); p1:=alpha^2+alpha*x+beta*x^2; p2:=1 + alpha*x; Output: Magma V2.10-6 Fri Mar 26 2004 13:15:19 on modular [Seed = 3197799907] ------------------------------------- >> p1:=alpha^2+alpha*x+beta*x^2; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt >> p2:=1 + alpha*x; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 13:17:00 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=ext; R:=Integers(); P:=PolynomialRing(R); p1:=P![alpha^2,alpha,beta]; p1:=alpha^2+alpha*x+beta*x^2; p2:=1 + alpha*x; Output: Magma V2.10-6 Fri Mar 26 2004 13:16:57 on modular [Seed = 2326706553] ------------------------------------- >> p1:=P![alpha^2,alpha,beta]; ^ Runtime error in '!': Can't coerce sequence element 1 into the coefficient ring >> p1:=alpha^2+alpha*x+beta*x^2; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt >> p2:=1 + alpha*x; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 13:20:22 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=ext; R:=Integers(); P:=PolynomialRing(R); p1:=P![alpha,alpha,beta]; p1:=alpha^2+alpha*x+beta*x^2; p2:=1 + alpha*x; Output: Magma V2.10-6 Fri Mar 26 2004 13:20:19 on modular [Seed = 2562501777] ------------------------------------- >> p1:=P![alpha,alpha,beta]; ^ Runtime error in '!': Can't coerce sequence element 1 into the coefficient ring >> p1:=alpha^2+alpha*x+beta*x^2; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt >> p2:=1 + alpha*x; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 13:20:32 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=ext; R:=Integers(); P:=PolynomialRing(R); p1:=P![alpha,alpha,beta]; p1:=alpha^2+alpha*x+beta*x^2; p2:=1 + alpha*x; Output: Magma V2.10-6 Fri Mar 26 2004 13:20:29 on modular [Seed = 2444600726] ------------------------------------- >> p1:=P![alpha,alpha,beta]; ^ Runtime error in '!': Can't coerce sequence element 1 into the coefficient ring >> p1:=alpha^2+alpha*x+beta*x^2; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt >> p2:=1 + alpha*x; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 13:20:48 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=ext; R:=Integers(); P:=PolynomialRing(R); p1:=P![beta,beta,beta]; p1:=alpha^2+alpha*x+beta*x^2; p2:=1 + alpha*x; Output: Magma V2.10-6 Fri Mar 26 2004 13:20:45 on modular [Seed = 1867209593] ------------------------------------- >> p1:=alpha^2+alpha*x+beta*x^2; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt >> p2:=1 + alpha*x; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 13:34:53 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=GF(25); Output: Magma V2.10-6 Fri Mar 26 2004 13:34:50 on modular [Seed = 1951417301] ------------------------------------- Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 13:35:26 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=GF(25); P:=PolynomialRing(Integers()); p1:=P![beta,beta,beta]; p1:=alpha^2+alpha*x+beta*x^2; p2:=1 + alpha*x; Output: Magma V2.10-6 Fri Mar 26 2004 13:35:23 on modular [Seed = 1180856774] ------------------------------------- >> p1:=alpha^2+alpha*x+beta*x^2; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt >> p2:=1 + alpha*x;; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 13:36:00 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=GF(25); P:=PolynomialRing(Integers()); p1:=P![beta,beta,beta]; Output: Magma V2.10-6 Fri Mar 26 2004 13:35:57 on modular [Seed = 1568236859] ------------------------------------- Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 13:36:14 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=GF(25); P:=PolynomialRing(Integers()); p1:=P![beta,beta,beta]; p1; Output: Magma V2.10-6 Fri Mar 26 2004 13:36:11 on modular [Seed = 1416653860] ------------------------------------- x^2 + x + 1 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 13:36:34 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=GF(25); P:=PolynomialRing(Integers()); p1:=P![beta,beta,beta]; alpha;beta; p1; Output: Magma V2.10-6 Fri Mar 26 2004 13:36:31 on modular [Seed = 587668327] ------------------------------------- alpha 1 x^2 + x + 1 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 13:36:51 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=GF(25); P:=PolynomialRing(Integers()); p1:=P![alpha,beta,beta]; alpha;beta; p1; Output: Magma V2.10-6 Fri Mar 26 2004 13:36:48 on modular [Seed = 975045137] ------------------------------------- >> p1:=P![alpha,beta,beta]; ^ Runtime error in '!': Can't coerce sequence element 0 into the coefficient ring alpha 1 >> p1; ^ User error: Identifier 'p1' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 13:44:02 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=GF(25); a1:=PrimitiveElement(G5); a1; Output: Magma V2.10-6 Fri Mar 26 2004 13:43:59 on modular [Seed = 220804233] ------------------------------------- 2 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 13:44:11 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=GF(25); a1:=PrimitiveElement(G5); a1; Output: Magma V2.10-6 Fri Mar 26 2004 13:44:08 on modular [Seed = 69221783] ------------------------------------- 2 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 13:44:34 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=GF(25); a:=PrimitiveElement(G5); a; b:=PrimitiveElement(G25); Output: Magma V2.10-6 Fri Mar 26 2004 13:44:31 on modular [Seed = 322382184] ------------------------------------- 2 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 13:44:42 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=GF(25); a:=PrimitiveElement(G5); a; b:=PrimitiveElement(G25); b; Output: Magma V2.10-6 Fri Mar 26 2004 13:44:39 on modular [Seed = 3922580373] ------------------------------------- 2 alpha Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 13:45:32 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=ext; a:=PrimitiveElement(G5); a; b:=PrimitiveElement(G25); b; Output: Magma V2.10-6 Fri Mar 26 2004 13:45:29 on modular [Seed = 3837845190] ------------------------------------- 2 alpha Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 13:46:24 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=ext; b:=PrimitiveElement(G5); a:=PrimitiveElement(G25); p1:=a^2+a*x+b*x^2; p1; Output: Magma V2.10-6 Fri Mar 26 2004 13:46:21 on modular [Seed = 4091005413] ------------------------------------- >> p1:=a^2+a*x+b*x^2; ^ User error: Identifier 'x' has not been declared or assigned >> p1;; ^ User error: Identifier 'p1' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 13:47:11 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=ext; b:=PrimitiveElement(G5); a:=PrimitiveElement(G25); P:=PolynomialRing(Integers()); p1:=a^2+a*x+b*x^2; p1; Output: Magma V2.10-6 Fri Mar 26 2004 13:47:08 on modular [Seed = 3404656653] ------------------------------------- >> p1:=a^2+a*x+b*x^2; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt >> p1;; ^ User error: Identifier 'p1' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 13:47:37 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=ext; b:=PrimitiveElement(G5); a:=PrimitiveElement(G25); P:=PolynomialRing(G25); p1:=a^2+a*x+b*x^2; p1; Output: Magma V2.10-6 Fri Mar 26 2004 13:47:34 on modular [Seed = 3253074796] ------------------------------------- 2*x^2 + alpha*x + alpha^2 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 13:48:06 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=ext; b:=PrimitiveElement(G5); a:=PrimitiveElement(G25); P:=PolynomialRing(G25); p1:=alpha^2+alpha*x+beta*x^2; p1; Output: Magma V2.10-6 Fri Mar 26 2004 13:48:03 on modular [Seed = 3757827415] ------------------------------------- x^2 + alpha*x + alpha^2 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 13:48:37 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=ext; b:=PrimitiveElement(G5); a:=PrimitiveElement(G25); P:=PolynomialRing(G5); p1:=alpha^2+alpha*x+beta*x^2; p1; Output: Magma V2.10-6 Fri Mar 26 2004 13:48:34 on modular [Seed = 3589402300] ------------------------------------- >> p1:=alpha^2+alpha*x+beta*x^2; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt >> p1;; ^ User error: Identifier 'p1' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 13:49:03 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=ext; b:=PrimitiveElement(G5); a:=PrimitiveElement(G25); P:=PolynomialRing(G25); p1:=alpha^2+alpha*x+beta*x^2; p2:=1+alpha*x; Output: Magma V2.10-6 Fri Mar 26 2004 13:49:00 on modular [Seed = 2894632923] ------------------------------------- Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 13:49:19 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=ext; b:=PrimitiveElement(G5); a:=PrimitiveElement(G25); P:=PolynomialRing(G25); p1:=alpha^2+alpha*x+beta*x^2; p1; p2:=1+alpha*x; p2; Output: Magma V2.10-6 Fri Mar 26 2004 13:49:16 on modular [Seed = 3147792636] ------------------------------------- x^2 + alpha*x + alpha^2 alpha*x + 1 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 13:51:05 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=ext; b:=PrimitiveElement(G5); a:=PrimitiveElement(G25); P:=PolynomialRing(G25); p1:=alpha^2+alpha*x+beta*x^2; p1; p2:=1+alpha*x; p2; suma:=p1+p2; suma; Output: Magma V2.10-6 Fri Mar 26 2004 13:51:02 on modular [Seed = 2326704503] ------------------------------------- x^2 + alpha*x + alpha^2 alpha*x + 1 x^2 + alpha^19*x + alpha^9 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 13:52:30 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=ext; b:=PrimitiveElement(G5); a:=PrimitiveElement(G25); P:=PolynomialRing(G25); p1:=alpha^2+alpha*x+beta*x^2; p2:=1+alpha*x; suma:=p1+p2; prod:=p1*p2; prod; Output: Magma V2.10-6 Fri Mar 26 2004 13:52:27 on modular [Seed = 2175121921] ------------------------------------- alpha*x^3 + alpha^9*x^2 + alpha^10*x + alpha^2 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 13:54:00 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=ext; b:=PrimitiveElement(G5); a:=PrimitiveElement(G25); P:=PolynomialRing(G25); p1:=alpha^2+alpha*x+beta*x^2; p2:=1+alpha*x; suma:=p1+p2; prod:=p1*p2; prod; quotrem(p1,p2); Output: Magma V2.10-6 Fri Mar 26 2004 13:53:57 on modular [Seed = 2679874481] ------------------------------------- alpha*x^3 + alpha^9*x^2 + alpha^10*x + alpha^2 >> quotrem(p1,p2);; ^ User error: Identifier 'quotrem' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 13:54:19 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=ext; b:=PrimitiveElement(G5); a:=PrimitiveElement(G25); P:=PolynomialRing(G25); p1:=alpha^2+alpha*x+beta*x^2; p2:=1+alpha*x; suma:=p1+p2; prod:=p1*p2; prod; Quotrem(p1,p2); Output: Magma V2.10-6 Fri Mar 26 2004 13:54:16 on modular [Seed = 2511448486] ------------------------------------- alpha*x^3 + alpha^9*x^2 + alpha^10*x + alpha^2 alpha^23*x + alpha^21 alpha Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 13:54:52 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=ext; b:=PrimitiveElement(G5); a:=PrimitiveElement(G25); P:=PolynomialRing(G25); p1:=alpha^2+alpha*x+beta*x^2; p2:=1+alpha*x; suma:=p1+p2; prod:=p1*p2; divi:=p1/p2; divi; Quotrem(p1,p2); Output: Magma V2.10-6 Fri Mar 26 2004 13:54:49 on modular [Seed = 1800361854] ------------------------------------- (alpha^23*x^2 + x + alpha)/(x + alpha^23) alpha^23*x + alpha^21 alpha Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.0.13.255) Time: Fri Mar 26 13:57:30 2004 Input: G5:=GF(5); O:=PolynomialRing(G5); pz5:=O![3,2,1]; G25:=ext; b:=PrimitiveElement(G5); a:=PrimitiveElement(G25); P:=PolynomialRing(G25); p1:=alpha^2+alpha*x+beta*x^2; p2:=1+alpha*x; suma:=p1+p2; prod:=p1*p2; divi:=p1 div p2; divi; Quotrem(p1,p2); Output: Magma V2.10-6 Fri Mar 26 2004 13:57:27 on modular [Seed = 2036155394] ------------------------------------- alpha^23*x + alpha^21 alpha^23*x + alpha^21 alpha Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.120.170.5) Time: Fri Mar 26 15:25:59 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Fri Mar 26 2004 15:25:56 on modular [Seed = 2596162338] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.120.170.5) Time: Fri Mar 26 15:29:47 2004 Input: IntegerRing(16) Output: Magma V2.10-6 Fri Mar 26 2004 15:29:44 on modular [Seed = 1816706745] ------------------------------------- Residue class ring of integers modulo 16 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.120.170.5) Time: Fri Mar 26 15:31:28 2004 Input: k=IntegerRing(16) Output: Magma V2.10-6 Fri Mar 26 2004 15:31:25 on modular [Seed = 2086186764] ------------------------------------- >> k=IntegerRing(16) ^ User error: Identifier 'k' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.120.170.5) Time: Fri Mar 26 15:37:31 2004 Input: k:=IntegerRing(16) R=k[x] Output: Magma V2.10-6 Fri Mar 26 2004 15:37:28 on modular [Seed = 1315609259] ------------------------------------- >> R=k[x]; ^ User error: bad syntax Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.120.170.5) Time: Fri Mar 26 15:37:49 2004 Input: k:=IntegerRing(16) R:=k[x] Output: Magma V2.10-6 Fri Mar 26 2004 15:37:46 on modular [Seed = 1097176502] ------------------------------------- >> R:=k[x]; ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.120.170.5) Time: Fri Mar 26 15:42:11 2004 Input: k:=IntegerRing(16) R:= PolynomialRing(k,6) Output: Magma V2.10-6 Fri Mar 26 2004 15:42:08 on modular [Seed = 1383499679] ------------------------------------- >> R:= PolynomialRing(k,6) ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.120.170.5) Time: Fri Mar 26 15:42:30 2004 Input: k:=IntegerRing(16) A:= PolynomialRing(k,6) Output: Magma V2.10-6 Fri Mar 26 2004 15:42:27 on modular [Seed = 620884219] ------------------------------------- >> A:= PolynomialRing(k,6) ^ User error: bad syntax Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.120.170.5) Time: Fri Mar 26 15:46:36 2004 Input: k:=IntegerRing(16) R> R:= PolynomialRing(k,2) Output: Magma V2.10-6 Fri Mar 26 2004 15:46:46 on modular [Seed = 220847062] ------------------------------------- >> R:= PolynomialRing(k,2) ^ User error: bad syntax Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.120.170.5) Time: Fri Mar 26 15:51:03 2004 Input: k:=IntegerRing(16) A:= PolynomialRing(k,2) Output: Magma V2.10-6 Fri Mar 26 2004 15:51:00 on modular [Seed = 507169222] ------------------------------------- >> A:= PolynomialRing(k,2) ^ User error: bad syntax Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.120.170.5) Time: Fri Mar 26 15:54:15 2004 Input: k :=IntegerRing(16) R := PolynomialRing(k,2) Output: Magma V2.10-6 Fri Mar 26 2004 15:54:12 on modular [Seed = 3922538992] ------------------------------------- >> R := PolynomialRing(k,2) ^ User error: bad syntax Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.120.170.5) Time: Fri Mar 26 15:54:31 2004 Input: k :=IntegerRing(16); R := PolynomialRing(k,2) Output: Magma V2.10-6 Fri Mar 26 2004 15:54:28 on modular [Seed = 3770955785] ------------------------------------- Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.120.170.5) Time: Fri Mar 26 15:54:51 2004 Input: k :=IntegerRing(16); R := PolynomialRing(k,2); R; Output: Magma V2.10-6 Fri Mar 26 2004 15:54:48 on modular [Seed = 4225704718] ------------------------------------- Polynomial ring of rank 2 over IntegerRing(16) Lexicographical Order Variables: x, y Total time: 3.029 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.120.170.5) Time: Fri Mar 26 15:55:04 2004 Input: k :=IntegerRing(16); R := PolynomialRing(k,2); R;k; Output: Magma V2.10-6 Fri Mar 26 2004 15:55:01 on modular [Seed = 3471447558] ------------------------------------- Polynomial ring of rank 2 over IntegerRing(16) Lexicographical Order Variables: x, y Residue class ring of integers modulo 16 Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Fri Mar 26 19:52:32 2004 Input: n:=21290246318258757547497882016271517497806703963277216278233383215381949984056495911366573853021918316783107387995317230889569230873441936471; X1 := 0.02; X2 := 0.5; low_m1 := Exp((log(n) - log(X2))/(d+1)); high_m1 := Exp((log(n) - log(X1))/(d+1)); print low_m1; print high_m1; Output: Magma V2.10-6 Fri Mar 26 2004 19:52:28 on modular [Seed = 3404618473] ------------------------------------- >> low_m1 := Exp((log(n) - log(X2))/(d+1)); ^ User error: Identifier 'log' has not been declared or assigned >> high_m1 := Exp((log(n) - log(X1))/(d+1)); ^ User error: Identifier 'log' has not been declared or assigned >> print low_m1; ^ User error: Identifier 'low_m1' has not been declared or assigned >> print high_m1; ^ User error: Identifier 'high_m1' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Fri Mar 26 19:52:51 2004 Input: n:=21290246318258757547497882016271517497806703963277216278233383215381949984056495911366573853021918316783107387995317230889569230873441936471; X1 := 0.02; X2 := 0.5; low_m1 := Exp((Log(n) - Log(X2))/(d+1)); high_m1 := Exp((Log(n) - Log(X1))/(d+1)); print low_m1; print high_m1; Output: Magma V2.10-6 Fri Mar 26 2004 19:52:48 on modular [Seed = 3253031374] ------------------------------------- >> low_m1 := Exp((Log(n) - Log(X2))/(d+1)); ^ User error: Identifier 'd' has not been declared or assigned >> high_m1 := Exp((Log(n) - Log(X1))/(d+1)); ^ User error: Identifier 'd' has not been declared or assigned >> print low_m1; ^ User error: Identifier 'low_m1' has not been declared or assigned >> print high_m1; ^ User error: Identifier 'high_m1' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Fri Mar 26 19:53:14 2004 Input: n:=21290246318258757547497882016271517497806703963277216278233383215381949984056495911366573853021918316783107387995317230889569230873441936471; X1 := 0.02; X2 := 0.5; d := 3; low_m1 := Exp((Log(n) - Log(X2)) div (d+1)); high_m1 := Exp((Log(n) - Log(X1)) div (d+1)); print low_m1; print high_m1; Output: Magma V2.10-6 Fri Mar 26 2004 19:53:11 on modular [Seed = 3640412352] ------------------------------------- >> low_m1 := Exp((Log(n) - Log(X2)) div (d+1)); ^ Runtime error in 'div': Bad argument types Argument types given: FldPrElt, FldPrElt >> high_m1 := Exp((Log(n) - Log(X1)) div (d+1)); ^ Runtime error in 'div': Bad argument types Argument types given: FldPrElt, FldPrElt >> print low_m1; ^ User error: Identifier 'low_m1' has not been declared or assigned >> print high_m1; ^ User error: Identifier 'high_m1' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Fri Mar 26 19:53:46 2004 Input: n:=21290246318258757547497882016271517497806703963277216278233383215381949984056495911366573853021918316783107387995317230889569230873441936471; X1 := 0.02; X2 := 0.5; d := 3; low_m1 := Exp((Log(n) - Log(X2)) / (d+1)); high_m1 := Exp((Log(n) - Log(X1)) / (d+1)); print low_m1; print high_m1; Output: Magma V2.10-6 Fri Mar 26 2004 19:53:43 on modular [Seed = 2928295510] ------------------------------------- 8.077978081368073257567384173809E34 1.80629081106923391743234091933E35 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Fri Mar 26 19:55:03 2004 Input: n:=21290246318258757547497882016271517497806703963277216278233383215381949984056495911366573853021918316783107387995317230889569230873441936471; X1 := 0.02; X2 := 0.5; d := 3; low_m1 := Round(Exp((Log(n) - Log(X2)) / (d+1))); high_m1 := Round(Exp((Log(n) - Log(X1)) / (d+1))); print low_m1; print high_m1; Output: Magma V2.10-6 Fri Mar 26 2004 19:55:00 on modular [Seed = 2776708398] ------------------------------------- Round( x: 8.077978081368073257567384173809E34 ) In file "/usr/local/magma/package/Ring/RngInt/misc.m", line 29, column 25: >> return RoundReal(x); ^ Runtime error in 'RoundReal': Not enough precision to compute floor Round( x: 1.80629081106923391743234091933E35 ) In file "/usr/local/magma/package/Ring/RngInt/misc.m", line 29, column 25: >> return RoundReal(x); ^ Runtime error in 'RoundReal': Not enough precision to compute floor >> print low_m1; ^ User error: Identifier 'low_m1' has not been declared or assigned >> print high_m1; ^ User error: Identifier 'high_m1' has not been declared or assigned Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Fri Mar 26 19:56:53 2004 Input: n:=21290246318258757547497882016271517497806703963277216278233383215381949984056495911366573853021918316783107387995317230889569230873441936471; X1 := 0.02; X2 := 0.5; d := 3; temp := Log(n) - Log(X2); e := temp / (d+1); low_m1 := Round(Exp(e)); high_m1 := Round(Exp((Log(n) - Log(X1)) / (d+1))); print low_m1; print high_m1; Output: Magma V2.10-6 Fri Mar 26 2004 19:56:50 on modular [Seed = 3079874186] ------------------------------------- Round( x: 8.077978081368073257567384173809E34 ) In file "/usr/local/magma/package/Ring/RngInt/misc.m", line 29, column 25: >> return RoundReal(x); ^ Runtime error in 'RoundReal': Not enough precision to compute floor Round( x: 1.80629081106923391743234091933E35 ) In file "/usr/local/magma/package/Ring/RngInt/misc.m", line 29, column 25: >> return RoundReal(x); ^ Runtime error in 'RoundReal': Not enough precision to compute floor >> print low_m1; ^ User error: Identifier 'low_m1' has not been declared or assigned >> print high_m1; ^ User error: Identifier 'high_m1' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Fri Mar 26 19:57:51 2004 Input: n:=21290246318258757547497882016271517497806703963277216278233383215381949984056495911366573853021918316783107387995317230889569230873441936471; X1 := 0.02; X2 := 0.5; d := 3; temp := Log(n) - Log(X2); e := temp / (d+1); low_m1 := Round(Exp(e)); temp := Log(n) - Log(X1); e := temp / (d+1); high_m1 := Round(Exp(e)); print low_m1; print high_m1; Output: Magma V2.10-6 Fri Mar 26 2004 19:57:48 on modular [Seed = 2393513837] ------------------------------------- Round( x: 8.077978081368073257567384173809E34 ) In file "/usr/local/magma/package/Ring/RngInt/misc.m", line 29, column 25: >> return RoundReal(x); ^ Runtime error in 'RoundReal': Not enough precision to compute floor Round( x: 1.80629081106923391743234091933E35 ) In file "/usr/local/magma/package/Ring/RngInt/misc.m", line 29, column 25: >> return RoundReal(x); ^ Runtime error in 'RoundReal': Not enough precision to compute floor >> print low_m1; ^ User error: Identifier 'low_m1' has not been declared or assigned >> print high_m1; ^ User error: Identifier 'high_m1' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Fri Mar 26 20:28:03 2004 Input: n:=21290246318258757547497882016271517497806703963277216278233383215381949984056495911366573853021918316783107387995317230889569230873441936471; X1 := 0.02; X2 := 0.5; d := 3; temp := Log(n) - Log(X2); e := temp / (d+1.0); low_m1 := Round(Exp(e)); temp := Log(n) - Log(X1); e := temp / (d+1); high_m1 := Round(Exp(e)); print low_m1; print high_m1; Output: Magma V2.10-6 Fri Mar 26 2004 20:28:00 on modular [Seed = 1601947535] ------------------------------------- Round( x: 8.077978081368073257567384173809E34 ) In file "/usr/local/magma/package/Ring/RngInt/misc.m", line 29, column 25: >> return RoundReal(x); ^ Runtime error in 'RoundReal': Not enough precision to compute floor Round( x: 1.80629081106923391743234091933E35 ) In file "/usr/local/magma/package/Ring/RngInt/misc.m", line 29, column 25: >> return RoundReal(x); ^ Runtime error in 'RoundReal': Not enough precision to compute floor >> print low_m1; ^ User error: Identifier 'low_m1' has not been declared or assigned >> print high_m1; ^ User error: Identifier 'high_m1' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Fri Mar 26 20:28:56 2004 Input: n:=21290246318258757547497882016271517497806703963277216278233383215381949984056495911366573853021918316783107387995317230889569230873441936471; X1 := 0.02; X2 := 0.5; d := 3; temp := Log(n) - Log(X2); print temp; Output: Magma V2.10-6 Fri Mar 26 2004 20:28:53 on modular [Seed = 1231933932] ------------------------------------- 321.50813906224597966393892462838 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Fri Mar 26 20:29:33 2004 Input: n:=21290246318258757547497882016271517497806703963277216278233383215381949984056495911366573853021918316783107387995317230889569230873441936471; X1 := 0.02; X2 := 0.5; d := 3; temp := Log(n) - Log(X2); e := temp/(d+1); print temp; print e; Output: Magma V2.10-6 Fri Mar 26 2004 20:29:30 on modular [Seed = 840346296] ------------------------------------- 321.50813906224597966393892462838 80.377034765561494915984731157096 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Fri Mar 26 20:30:00 2004 Input: n:=21290246318258757547497882016271517497806703963277216278233383215381949984056495911366573853021918316783107387995317230889569230873441936471; X1 := 0.02; X2 := 0.5; d := 3; temp := Log(n) - Log(X2); e := temp/(d+1); low_m1 := Exp(e); print temp; print e; print low_m1; Output: Magma V2.10-6 Fri Mar 26 2004 20:29:57 on modular [Seed = 991928926] ------------------------------------- 321.50813906224597966393892462838 80.377034765561494915984731157096 8.077978081368073257567384173809E34 Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Fri Mar 26 20:30:45 2004 Input: n:=21290246318258757547497882016271517497806703963277216278233383215381949984056495911366573853021918316783107387995317230889569230873441936471; X1 := 0.02; X2 := 0.5; d := 3; temp := Log(n) - Log(X2); e := temp/(d+1); low_m1 := Round(Exp(e)); print temp; print e; print low_m1; Output: Magma V2.10-6 Fri Mar 26 2004 20:30:42 on modular [Seed = 738768158] ------------------------------------- Round( x: 8.077978081368073257567384173809E34 ) In file "/usr/local/magma/package/Ring/RngInt/misc.m", line 29, column 25: >> return RoundReal(x); ^ Runtime error in 'RoundReal': Not enough precision to compute floor 321.50813906224597966393892462838 80.377034765561494915984731157096 >> print low_m1; ^ User error: Identifier 'low_m1' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host nn5.ody.ca. (216.99.108.5) Time: Fri Mar 26 20:31:04 2004 Input: n:=21290246318258757547497882016271517497806703963277216278233383215381949984056495911366573853021918316783107387995317230889569230873441936471; X1 := 0.02; X2 := 0.5; d := 3; temp := Log(n) - Log(X2); e := temp/(d+1); low_m1 := Floor(Exp(e)); print temp; print e; print low_m1; Output: Magma V2.10-6 Fri Mar 26 2004 20:31:01 on modular [Seed = 355568688] ------------------------------------- >> low_m1 := Floor(Exp(e)); ^ Runtime error in 'Floor': Not enough precision to compute floor 321.50813906224597966393892462838 80.377034765561494915984731157096 >> print low_m1; ^ User error: Identifier 'low_m1' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.59.164) Time: Fri Mar 26 23:36:07 2004 Input: >Q := QuadraticField(7537543); // arbitrary choice > Q := QuadraticForms(Discriminant(Q)); > C, m := ClassGroup(Q); > C; Output: Magma V2.10-6 Fri Mar 26 2004 23:35:55 on modular [Seed = 1433407884] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/76 Defined on 2 generators Relations: 2*C.1 = 0 76*C.2 = 0 Total time: 11.599 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.59.164) Time: Fri Mar 26 23:36:41 2004 Input: >Q := QuadraticField(15); // arbitrary choice > Q := QuadraticForms(Discriminant(Q)); > C, m := ClassGroup(Q); > C; Output: Magma V2.10-6 Fri Mar 26 2004 23:36:38 on modular [Seed = 1114048230] ------------------------------------- Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*C.1 = 0 Total time: 3.129 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.59.164) Time: Fri Mar 26 23:36:57 2004 Input: >Q := QuadraticField(-15); // arbitrary choice > Q := QuadraticForms(Discriminant(Q)); > C, m := ClassGroup(Q); > C; Output: Magma V2.10-6 Fri Mar 26 2004 23:36:54 on modular [Seed = 1265504223] ------------------------------------- Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*C.1 = 0 Total time: 3.029 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.59.164) Time: Fri Mar 26 23:37:32 2004 Input: >Q := QuadraticField(-119); // arbitrary choice > Q := QuadraticForms(Discriminant(Q)); > C, m := ClassGroup(Q); > C; Output: Magma V2.10-6 Fri Mar 26 2004 23:37:29 on modular [Seed = 806712651] ------------------------------------- Abelian Group isomorphic to Z/10 Defined on 1 generator Relations: 10*C.1 = 0 Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.59.164) Time: Fri Mar 26 23:38:13 2004 Input: >Q := QuadraticField(-139); // arbitrary choice > Q := QuadraticForms(Discriminant(Q)); > C, m := ClassGroup(Q); > C; Output: Magma V2.10-6 Fri Mar 26 2004 23:38:10 on modular [Seed = 1041988478] ------------------------------------- Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*C.1 = 0 Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.59.164) Time: Fri Mar 26 23:39:00 2004 Input: >Q := QuadraticField(-14955); // arbitrary choice > Q := QuadraticForms(Discriminant(Q)); > C, m := ClassGroup(Q); > C; Output: Magma V2.10-6 Fri Mar 26 2004 23:38:57 on modular [Seed = 604070199] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/18 Defined on 2 generators Relations: 2*C.1 = 0 18*C.2 = 0 Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.59.164) Time: Fri Mar 26 23:39:43 2004 Input: >Q := QuadraticField(-399); // arbitrary choice > Q := QuadraticForms(Discriminant(Q)); > C, m := ClassGroup(Q); > C; Output: Magma V2.10-6 Fri Mar 26 2004 23:39:40 on modular [Seed = 755525843] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.59.164) Time: Fri Mar 26 23:40:09 2004 Input: >Q := QuadraticField(-407); // arbitrary choice > Q := QuadraticForms(Discriminant(Q)); > C, m := ClassGroup(Q); > C; Output: Magma V2.10-6 Fri Mar 26 2004 23:40:06 on modular [Seed = 490232009] ------------------------------------- Abelian Group isomorphic to Z/16 Defined on 1 generator Relations: 16*C.1 = 0 Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.59.164) Time: Fri Mar 26 23:40:33 2004 Input: >Q := QuadraticField(-14995); // arbitrary choice > Q := QuadraticForms(Discriminant(Q)); > C, m := ClassGroup(Q); > C; Output: Magma V2.10-6 Fri Mar 26 2004 23:40:30 on modular [Seed = 170872774] ------------------------------------- Abelian Group isomorphic to Z/16 Defined on 1 generator Relations: 16*C.1 = 0 Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.141.69.153) Time: Sat Mar 27 03:52:11 2004 Input: (2+3)*(3-7) Output: Magma V2.10-6 Sat Mar 27 2004 03:52:07 on modular [Seed = 4141086261] ------------------------------------- -20 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:31:15 2004 Input: >Q(z):=QuadraticField(21835); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); Output: Magma V2.10-6 Sat Mar 27 2004 05:31:11 on modular [Seed = 507185542] ------------------------------------- >> Q(z):=QuadraticField(21835); ^ User error: Illegal left hand side of an assignment statement >> Q:=QuadraticForms(Discriminant(Q)); ^ User error: Identifier 'Q' has not been declared or assigned >> C,m:=ClassGroup(Q);; ^ User error: Identifier 'Q' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:32:06 2004 Input: >Q(z):=QuadraticField(-21835); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); Output: Magma V2.10-6 Sat Mar 27 2004 05:32:03 on modular [Seed = 85990737] ------------------------------------- >> Q(z):=QuadraticField(-21835); ^ User error: Illegal left hand side of an assignment statement >> Q:=QuadraticForms(Discriminant(Q)); ^ User error: Identifier 'Q' has not been declared or assigned >> C,m:=ClassGroup(Q);; ^ User error: Identifier 'Q' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:34:15 2004 Input: >Q:=QuadraticField(21835); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); Output: Magma V2.10-6 Sat Mar 27 2004 05:34:07 on modular [Seed = 187569123] ------------------------------------- Total time: 7.759 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:34:49 2004 Input: >Q:=QuadraticField(-21835); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:34:46 on modular [Seed = 4057262400] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:35:31 2004 Input: >Q:=QuadraticField(-22243); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:35:28 on modular [Seed = 3837918307] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 3.039 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:36:23 2004 Input: >Q:=QuadraticField(-27307); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:36:20 on modular [Seed = 3956208312] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:36:59 2004 Input: >Q:=QuadraticField(-19987); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:36:56 on modular [Seed = 3539454957] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:37:24 2004 Input: >Q:=QuadraticField(-20155); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:37:21 on modular [Seed = 3640508878] ------------------------------------- Abelian Group isomorphic to Z/4 + Z/4 Defined on 2 generators Relations: 4*C.1 = 0 4*C.2 = 0 Total time: 3.029 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:37:50 2004 Input: >Q:=QuadraticField(-21715); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:37:47 on modular [Seed = 3488274115] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:38:21 2004 Input: >Q:=QuadraticField(-18907); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:38:18 on modular [Seed = 3046157400] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:38:33 2004 Input: >Q:=QuadraticField(-18907); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:38:30 on modular [Seed = 3164185965] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:39:05 2004 Input: >Q:=QuadraticField(-19195); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:39:01 on modular [Seed = 2743515666] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:39:26 2004 Input: >Q:=QuadraticField(-19947); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:39:23 on modular [Seed = 2861544198] ------------------------------------- Abelian Group isomorphic to Z/4 + Z/4 Defined on 2 generators Relations: 4*C.1 = 0 4*C.2 = 0 Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:39:51 2004 Input: >Q:=QuadraticField(-17515); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:39:48 on modular [Seed = 2444527634] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:40:17 2004 Input: >Q:=QuadraticField(-18403); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:40:14 on modular [Seed = 2175048696] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:40:39 2004 Input: >Q:=QuadraticField(-18715); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:40:36 on modular [Seed = 2019385892] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 3.029 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:41:02 2004 Input: >Q:=QuadraticField(-17227); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:40:59 on modular [Seed = 1901357874] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:41:29 2004 Input: >Q:=QuadraticField(-17347); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:41:26 on modular [Seed = 1783590980] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 3.029 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:41:50 2004 Input: >Q:=QuadraticField(-17427); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:41:46 on modular [Seed = 1665562993] ------------------------------------- Abelian Group isomorphic to Z/4 + Z/4 Defined on 2 generators Relations: 4*C.1 = 0 4*C.2 = 0 Total time: 3.039 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:42:16 2004 Input: >Q:=QuadraticField(-16027); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:42:13 on modular [Seed = 1551451809] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:42:45 2004 Input: >Q:=QuadraticField(-16195); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:42:42 on modular [Seed = 1433423759] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:43:16 2004 Input: >Q:=QuadraticField(-16555); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:43:13 on modular [Seed = 1315656951] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/2 + Z/4 Defined on 3 generators Relations: 2*C.1 = 0 2*C.2 = 0 4*C.3 = 0 Total time: 3.039 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:43:55 2004 Input: >Q:=QuadraticField(-15715); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:43:52 on modular [Seed = 958145449] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:44:21 2004 Input: >Q:=QuadraticField(-15387); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:44:18 on modular [Seed = 840378696] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:44:47 2004 Input: >Q:=QuadraticField(-15067); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:44:44 on modular [Seed = 722350159] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:45:11 2004 Input: >Q:=QuadraticField(-14707); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:45:08 on modular [Seed = 406651732] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:45:35 2004 Input: >Q:=QuadraticField(-14547); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:45:32 on modular [Seed = 288623141] ------------------------------------- Abelian Group isomorphic to Z/4 + Z/4 Defined on 2 generators Relations: 4*C.1 = 0 4*C.2 = 0 Total time: 3.099 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:46:00 2004 Input: >Q:=QuadraticField(-14155); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:45:57 on modular [Seed = 170856727] ------------------------------------- Abelian Group isomorphic to Z/4 + Z/4 Defined on 2 generators Relations: 4*C.1 = 0 4*C.2 = 0 Total time: 3.029 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:46:28 2004 Input: >Q:=QuadraticField(-13827); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:46:24 on modular [Seed = 52828411] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:46:49 2004 Input: >Q:=QuadraticField(-13795); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:46:46 on modular [Seed = 4242138898] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 3.059 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:47:13 2004 Input: >Q:=QuadraticField(-13363); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:47:10 on modular [Seed = 4141083936] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:47:37 2004 Input: >Q:=QuadraticField(-12859); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:47:34 on modular [Seed = 4023055441] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:48:04 2004 Input: >Q:=QuadraticField(-12835); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:48:01 on modular [Seed = 3640509249] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:48:27 2004 Input: >Q:=QuadraticField(-12772); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:48:24 on modular [Seed = 3539454290] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:48:49 2004 Input: >Q:=QuadraticField(-12747); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:48:46 on modular [Seed = 3421427645] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:49:22 2004 Input: >Q:=QuadraticField(-12595); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:49:18 on modular [Seed = 3303135379] ------------------------------------- Abelian Group isomorphic to Z/4 + Z/4 Defined on 2 generators Relations: 4*C.1 = 0 4*C.2 = 0 Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:49:55 2004 Input: >Q:=QuadraticField(-12259); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:49:52 on modular [Seed = 3180896661] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:50:30 2004 Input: >Q:=QuadraticField(-12027); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:50:27 on modular [Seed = 2928390821] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:51:14 2004 Input: >Q:=QuadraticField(-11635); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:51:11 on modular [Seed = 2810362688] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 3.029 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:51:37 2004 Input: >Q:=QuadraticField(-11523); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:51:34 on modular [Seed = 2427817054] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:52:00 2004 Input: >Q:=QuadraticField(-11635); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:51:57 on modular [Seed = 2309788988] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:52:23 2004 Input: >Q:=QuadraticField(-10635); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:52:20 on modular [Seed = 2192023070] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:52:50 2004 Input: >Q:=QuadraticField(-10563); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:52:47 on modular [Seed = 2053072636] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:53:16 2004 Input: >Q:=QuadraticField(-10387); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:53:13 on modular [Seed = 1968203797] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 3.059 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:53:45 2004 Input: >Q:=QuadraticField(-10227); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:53:42 on modular [Seed = 1850438433] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:54:09 2004 Input: >Q:=QuadraticField(-10203); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:54:05 on modular [Seed = 1501316206] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 3.029 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:54:29 2004 Input: >Q:=QuadraticField(-9955); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:54:26 on modular [Seed = 1349864779] ------------------------------------- Abelian Group isomorphic to Z/4 + Z/4 Defined on 2 generators Relations: 4*C.1 = 0 4*C.2 = 0 Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:54:54 2004 Input: >Q:=QuadraticField(-9835); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:54:51 on modular [Seed = 1265522249] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:55:16 2004 Input: >Q:=QuadraticField(-9483); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:55:13 on modular [Seed = 1180916654] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:55:34 2004 Input: >Q:=QuadraticField(-9219); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:55:31 on modular [Seed = 823405803] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:55:56 2004 Input: >Q:=QuadraticField(-8643); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:55:53 on modular [Seed = 671954408] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:56:50 2004 Input: >Q:=QuadraticField(-8635); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:56:47 on modular [Seed = 570900404] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 3.039 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:57:07 2004 Input: >Q:=QuadraticField(-8515); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:57:04 on modular [Seed = 490210148] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:57:31 2004 Input: >Q:=QuadraticField(-8283); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:57:28 on modular [Seed = 338758261] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 3.039 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:57:58 2004 Input: >Q:=QuadraticField(-8043); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:57:55 on modular [Seed = 254415170] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:58:16 2004 Input: >Q:=QuadraticField(-7923); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:58:12 on modular [Seed = 4225689030] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:58:37 2004 Input: >Q:=QuadraticField(-7843); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:58:34 on modular [Seed = 4124109782] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 2.749 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:58:53 2004 Input: >Q:=QuadraticField(-7707); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:58:50 on modular [Seed = 3972657919] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:59:11 2004 Input: >Q:=QuadraticField(-7579); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:59:08 on modular [Seed = 3888314850] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 05:59:42 2004 Input: >Q:=QuadraticField(-7491); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 05:59:39 on modular [Seed = 3522481971] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 06:00:05 2004 Input: >Q:=QuadraticField(-7347); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 06:00:02 on modular [Seed = 3319847694] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 3.199 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 06:00:30 2004 Input: >Q:=QuadraticField(-7315); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 06:00:22 on modular [Seed = 3164185091] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/2 + Z/4 Defined on 3 generators Relations: 2*C.1 = 0 2*C.2 = 0 4*C.3 = 0 Total time: 3.389 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 06:01:01 2004 Input: >Q:=QuadraticField(-6923); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 06:00:55 on modular [Seed = 3079842089] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 3.229 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 06:01:21 2004 Input: >Q:=QuadraticField(-6771); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 06:01:17 on modular [Seed = 2427817492] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 3.299 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 06:02:01 2004 Input: >Q:=QuadraticField(-6747); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 06:01:37 on modular [Seed = 2343474403] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 3.349 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 06:02:20 2004 Input: >Q:=QuadraticField(-6355); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 06:02:16 on modular [Seed = 2192022979] ------------------------------------- Abelian Group isomorphic to Z/4 + Z/4 Defined on 2 generators Relations: 4*C.1 = 0 4*C.2 = 0 Total time: 3.579 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 06:02:52 2004 Input: >Q:=QuadraticField(-5907); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 06:02:44 on modular [Seed = 2119917904] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 3.369 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 06:03:22 2004 Input: >Q:=QuadraticField(-5883); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 06:03:18 on modular [Seed = 1968204409] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 3.719 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 06:03:41 2004 Input: >Q:=QuadraticField(-4899); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 06:03:37 on modular [Seed = 1665563792] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 3.149 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 06:04:00 2004 Input: >Q:=QuadraticField(-4683); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 06:03:56 on modular [Seed = 1484605374] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 3.419 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 06:04:32 2004 Input: >Q:=QuadraticField(-4521); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 06:04:27 on modular [Seed = 1366576784] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/2 + Z/18 Defined on 3 generators Relations: 2*C.1 = 0 2*C.2 = 0 18*C.3 = 0 Total time: 3.579 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 06:05:10 2004 Input: >Q:=QuadraticField(-4551); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 06:05:00 on modular [Seed = 1114070501] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/28 Defined on 2 generators Relations: 2*C.1 = 0 28*C.2 = 0 Total time: 5.589 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 06:05:24 2004 Input: >Q:=QuadraticField(-4251); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 06:05:12 on modular [Seed = 975119784] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 6.540 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 06:05:47 2004 Input: >Q:=QuadraticField(-4179); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 06:05:44 on modular [Seed = 907220548] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 3.029 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 06:06:06 2004 Input: >Q:=QuadraticField(-3939); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 06:06:03 on modular [Seed = 738790477] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 06:06:28 2004 Input: >Q:=QuadraticField(-3819); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 06:06:25 on modular [Seed = 620758382] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 3.049 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 06:06:46 2004 Input: >Q:=QuadraticField(-3531); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 06:06:43 on modular [Seed = 305607211] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 06:07:03 2004 Input: >Q:=QuadraticField(-3363); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 06:07:00 on modular [Seed = 187575077] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 3.029 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 06:07:26 2004 Input: >Q:=QuadraticField(-3171); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 06:07:22 on modular [Seed = 2433040] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 06:07:50 2004 Input: >Q:=QuadraticField(-2739); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 06:07:47 on modular [Seed = 4192000256] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 06:08:11 2004 Input: >Q:=QuadraticField(-2379); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 06:08:07 on modular [Seed = 4141078043] ------------------------------------- Abelian Group isomorphic to Z/4 + Z/4 Defined on 2 generators Relations: 4*C.1 = 0 4*C.2 = 0 Total time: 3.109 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 06:08:35 2004 Input: >Q:=QuadraticField(-2211); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 06:08:32 on modular [Seed = 3972647974] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 3.059 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 06:08:58 2004 Input: >Q:=QuadraticField(-1565); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 06:08:55 on modular [Seed = 3854615896] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/14 Defined on 2 generators Relations: 2*C.1 = 0 14*C.2 = 0 Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 06:09:02 2004 Input: >Q:=QuadraticField(-1595); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 06:08:59 on modular [Seed = 3724082540] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 06:09:16 2004 Input: >Q:=QuadraticField(-1595); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 06:09:13 on modular [Seed = 3421432680] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 06:09:31 2004 Input: >Q:=QuadraticField(-1023); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 06:09:28 on modular [Seed = 3236290642] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 06:09:53 2004 Input: >Q:=QuadraticField(-1015); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 06:09:50 on modular [Seed = 3114047805] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 3.029 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 06:10:15 2004 Input: >Q:=QuadraticField(-903); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 06:10:12 on modular [Seed = 2844559559] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 3.089 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 06:10:53 2004 Input: >Q:=QuadraticField(-663); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 06:10:50 on modular [Seed = 2793637863] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 06:11:14 2004 Input: >Q:=QuadraticField(-399); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 06:11:11 on modular [Seed = 2679815850] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 06:11:50 2004 Input: >Q:=QuadraticField(-399); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 06:11:47 on modular [Seed = 2494674333] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*C.1 = 0 8*C.2 = 0 Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.48.32) Time: Sat Mar 27 06:12:04 2004 Input: >Q:=QuadraticField(-111); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 06:12:01 on modular [Seed = 2376641654] ------------------------------------- Abelian Group isomorphic to Z/8 Defined on 1 generator Relations: 8*C.1 = 0 Total time: 3.029 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 06:20:16 2004 Input: G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; Output: Magma V2.10-6 Sat Mar 27 2004 06:20:13 on modular [Seed = 1766607487] ------------------------------------- >> G25:= ext < G5 |h>; ^ User error: Identifier 'h' has not been declared or assigned >> [x : x in G25];; ^ User error: Identifier 'G25' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 06:20:37 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; Output: Magma V2.10-6 Sat Mar 27 2004 06:20:34 on modular [Seed = 1698711196] ------------------------------------- [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 06:23:19 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ Output: Magma V2.10-6 Sat Mar 27 2004 06:23:16 on modular [Seed = 1383560717] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] Total time: 3.009 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 06:26:19 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; Output: Magma V2.10-6 Sat Mar 27 2004 06:26:16 on modular [Seed = 1281976559] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] Total time: 2.969 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 06:27:39 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [ : i in [1..24]]; print Ordre; Output: Magma V2.10-6 Sat Mar 27 2004 06:27:36 on modular [Seed = 991829608] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ , , , , , <3, 24>, , , , , , <4, 24>, , , , , , <2, 24>, , , , , , <1, 24> ] Total time: 3.019 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 06:30:09 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[] : i in [1..24]]; print Ordre; Output: Magma V2.10-6 Sat Mar 27 2004 06:30:06 on modular [Seed = 688655596] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ ], [ ], [ ], [ ], [ ], [ <3, 24> ], [ ], [ ], [ ], [ ], [ ], [ <4, 24> ], [ ], [ ], [ ], [ ], [ ], [ <2, 24> ], [ ], [ ], [ ], [ ], [ ], [ <1, 24> ] ] Total time: 2.989 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 06:31:26 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; Output: Magma V2.10-6 Sat Mar 27 2004 06:31:23 on modular [Seed = 654442839] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] Total time: 3.029 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 06:33:45 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; Output: Magma V2.10-6 Sat Mar 27 2004 06:33:42 on modular [Seed = 490224624] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 Total time: 2.999 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 06:35:57 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ MinimalPolynomial(alpha); /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ Output: Magma V2.10-6 Sat Mar 27 2004 06:35:54 on modular [Seed = 254421102] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 Total time: 3.019 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 06:36:54 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ Output: Magma V2.10-6 Sat Mar 27 2004 06:36:51 on modular [Seed = 102965550] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 Total time: 3.019 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 06:38:05 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ Output: Magma V2.10-6 Sat Mar 27 2004 06:38:02 on modular [Seed = 4242135837] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 [ , ] [] Total time: 2.959 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 06:39:01 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; Output: Magma V2.10-6 Sat Mar 27 2004 06:38:58 on modular [Seed = 3939487043] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 Total time: 2.949 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 06:39:32 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); Output: Magma V2.10-6 Sat Mar 27 2004 06:39:29 on modular [Seed = 3787769451] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 Total time: 3.039 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 06:43:09 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); llista_primitius1:=[x: x in G25 | IsPrimitive (x)]; llista_primitius1; llista_primitius2:=[x: x in G16 | IsPrimitive (x)]; llista_primitius2; Output: Magma V2.10-6 Sat Mar 27 2004 06:43:06 on modular [Seed = 3505780833] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ beta, beta^2, beta^4, beta^7, beta^8, beta^11, beta^13, beta^14 ] Total time: 3.029 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 06:47:44 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); llista_primitius1:=[x: x in G25 | IsPrimitive (x)]; llista_primitius1; llista_primitius2:=[x: x in G16 | IsPrimitive (x)]; llista_primitius2; lista_vectorial := function (p,n) llista1 := [0,0]; for i:=0 to (p^n)-2 do llista2 :=[alpha^i,ElementToSequence (alpha^i)]; llista1 := llista1 cat llista2; end for; return llista1; end function; Output: Magma V2.10-6 Sat Mar 27 2004 06:47:41 on modular [Seed = 3236292966] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ beta, beta^2, beta^4, beta^7, beta^8, beta^11, beta^13, beta^14 ] Total time: 2.969 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 06:48:39 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); llista_primitius1:=[x: x in G25 | IsPrimitive (x)]; llista_primitius1; llista_primitius2:=[x: x in G16 | IsPrimitive (x)]; llista_primitius2; lista_vectorial := function (p,n) llista1 := [0,0]; for i:=0 to (p^n)-2 do llista2 :=[alpha^i,ElementToSequence (alpha^i)]; llista1 := llista1 cat llista2; end for; return llista1; end function; lista_vectorial (2,4); Output: Magma V2.10-6 Sat Mar 27 2004 06:48:35 on modular [Seed = 3197867217] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ beta, beta^2, beta^4, beta^7, beta^8, beta^11, beta^13, beta^14 ] [
:88]( p: 2, n: 4 ) >> for i:=0 to (p^n)-2 do llista2 :=[alpha^i,ElementToSequence (alpha^i)]; ^ Runtime error in [ ... ]: Could not find a valid universe Total time: 3.029 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 06:49:56 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); llista_primitius1:=[x: x in G25 | IsPrimitive (x)]; llista_primitius1; llista_primitius2:=[x: x in G16 | IsPrimitive (x)]; llista_primitius2; lista_vectorial := function (p,n) llista1 := [<0,0>]; for i:=0 to (p^n)-2 do llista2 :=[]; llista1 := llista1 cat llista2; end for; return llista1; end function; lista_vectorial (2,4); Output: Magma V2.10-6 Sat Mar 27 2004 06:49:53 on modular [Seed = 3046154159] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ beta, beta^2, beta^4, beta^7, beta^8, beta^11, beta^13, beta^14 ] [
:88]( p: 2, n: 4 ) >> llista1 := llista1 cat llista2; ^ Runtime error in 'cat': Incompatible sequences Total time: 2.959 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 06:51:01 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); llista_primitius1:=[x: x in G25 | IsPrimitive (x)]; llista_primitius1; llista_primitius2:=[x: x in G16 | IsPrimitive (x)]; llista_primitius2; lista_vectorial := function (p,n) llista1 := [<0,0>]; for i:=0 to (p^n)-2 do llista2 :=[]; llista1 := [llista1] cat [llista2]; end for; return llista1; end function; lista_vectorial (2,4); Output: Magma V2.10-6 Sat Mar 27 2004 06:50:58 on modular [Seed = 2759954045] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ beta, beta^2, beta^4, beta^7, beta^8, beta^11, beta^13, beta^14 ] [
:88]( p: 2, n: 4 ) >> llista1 := [llista1] cat [llista2]; ^ Runtime error in 'cat': Incompatible sequences Total time: 2.969 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 06:52:48 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); llista_primitius1:=[x: x in G25 | IsPrimitive (x)]; llista_primitius1; llista_primitius2:=[x: x in G16 | IsPrimitive (x)]; llista_primitius2; lista_vectorial := function (p,n) llista1 := [0,0]; for i:=0 to (p^n)-2 do llista2 :=[alpha^i,ElementToSequence (alpha^i)]; llista1 := [llista1] cat [llista2]; end for; return llista1; end function; lista_vectorial (2,4); Output: Magma V2.10-6 Sat Mar 27 2004 06:52:45 on modular [Seed = 2478225637] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ beta, beta^2, beta^4, beta^7, beta^8, beta^11, beta^13, beta^14 ] [
:88]( p: 2, n: 4 ) >> for i:=0 to (p^n)-2 do llista2 :=[alpha^i,ElementToSequence (alpha^i)]; ^ Runtime error in [ ... ]: Could not find a valid universe Total time: 2.969 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 06:53:21 2004 Input: 1 cat 2 Output: Magma V2.10-6 Sat Mar 27 2004 06:53:18 on modular [Seed = 2309792476] ------------------------------------- >> 1 cat 2; ^ Runtime error in 'cat': Bad argument types Argument types given: RngIntElt, RngIntElt Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 06:53:40 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); llista_primitius1:=[x: x in G25 | IsPrimitive (x)]; llista_primitius1; llista_primitius2:=[x: x in G16 | IsPrimitive (x)]; llista_primitius2; lista_vectorial := function (p,n) llista1 := [0,0]; for i:=0 to (p^n)-2 do llista2 :=[]; llista1 := [llista1] cat [llista2]; end for; return llista1; end function; lista_vectorial (2,4); Output: Magma V2.10-6 Sat Mar 27 2004 06:53:37 on modular [Seed = 2275585213] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ beta, beta^2, beta^4, beta^7, beta^8, beta^11, beta^13, beta^14 ] [
:88]( p: 2, n: 4 ) >> llista1 := [llista1] cat [llista2]; ^ Runtime error in 'cat': Incompatible sequences Total time: 3.029 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 06:53:57 2004 Input: [1] cat [2] Output: Magma V2.10-6 Sat Mar 27 2004 06:53:54 on modular [Seed = 2036093527] ------------------------------------- [ 1, 2 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 06:54:43 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); llista_primitius1:=[x: x in G25 | IsPrimitive (x)]; llista_primitius1; llista_primitius2:=[x: x in G16 | IsPrimitive (x)]; llista_primitius2; lista_vectorial := function (p,n) llista1 := [<0,0>]; for i:=0 to (p^n)-2 do llista2 :=[]; llista1 := {llista1} cat {llista2}; end for; return llista1; end function; lista_vectorial (2,4); Output: Magma V2.10-6 Sat Mar 27 2004 06:54:40 on modular [Seed = 1918327182] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ beta, beta^2, beta^4, beta^7, beta^8, beta^11, beta^13, beta^14 ] [
:88]( p: 2, n: 4 ) >> llista1 := {llista1} cat {llista2}; ^ Runtime error in 'cat': Bad argument types Argument types given: SetEnum[SeqEnum], SetEnum[SeqEnum] Total time: 3.029 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 06:54:54 2004 Input: {1} cat {2} Output: Magma V2.10-6 Sat Mar 27 2004 06:54:51 on modular [Seed = 1800290460] ------------------------------------- >> {1} cat {2}; ^ Runtime error in 'cat': Bad argument types Argument types given: SetEnum[RngIntElt], SetEnum[RngIntElt] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 06:55:32 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); llista_primitius1:=[x: x in G25 | IsPrimitive (x)]; llista_primitius1; llista_primitius2:=[x: x in G16 | IsPrimitive (x)]; llista_primitius2; lista_vectorial := function (p,n) llista1 := [<0,0>]; for i:=0 to (p^n)-2 do llista2 :=[]; llista3 := [llista1] cat [llista2]; end for; return llista3; end function; lista_vectorial (2,4); Output: Magma V2.10-6 Sat Mar 27 2004 06:55:29 on modular [Seed = 1484616597] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ beta, beta^2, beta^4, beta^7, beta^8, beta^11, beta^13, beta^14 ] [
:88]( p: 2, n: 4 ) >> llista3 := [llista1] cat [llista2]; ^ Runtime error in 'cat': Incompatible sequences Total time: 3.039 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 06:55:59 2004 Input: a := [1,2]; b:= [3,4]; a cat b; Output: Magma V2.10-6 Sat Mar 27 2004 06:55:56 on modular [Seed = 1366588129] ------------------------------------- [ 1, 2, 3, 4 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 06:56:24 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); llista_primitius1:=[x: x in G25 | IsPrimitive (x)]; llista_primitius1; llista_primitius2:=[x: x in G16 | IsPrimitive (x)]; llista_primitius2; lista_vectorial := function (p,n) llista1 := [<0,0>]; for i:=0 to (p^n)-2 do llista2 :=[]; llista3 := llista1 cat llista2; end for; return llista3; end function; lista_vectorial (2,4); Output: Magma V2.10-6 Sat Mar 27 2004 06:56:21 on modular [Seed = 1248813523] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ beta, beta^2, beta^4, beta^7, beta^8, beta^11, beta^13, beta^14 ] [
:88]( p: 2, n: 4 ) >> llista3 := llista1 cat llista2; ^ Runtime error in 'cat': Incompatible sequences Total time: 2.959 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 06:57:13 2004 Input: lista_vectorial := function (p,n) llista1 := [<0,0>]; for i:=0 to (p^n)-2 do llista2 :=[]; llista1 := llista2 cat llista1; end for; return llista1; end function; Output: Magma V2.10-6 Sat Mar 27 2004 06:57:10 on modular [Seed = 1024987479] ------------------------------------- >> for i:=0 to (p^n)-2 do llista2 :=[]; ^ User error: Identifier 'alpha' has not been declared or assigned Total time: 3.619 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 06:57:14 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); llista_primitius1:=[x: x in G25 | IsPrimitive (x)]; llista_primitius1; llista_primitius2:=[x: x in G16 | IsPrimitive (x)]; llista_primitius2; lista_vectorial := function (p,n) llista1 := [<0,0>]; for i:=0 to (p^n)-2 do llista2 :=[]; llista3 := llista2 cat llista1; end for; return llista3; end function; lista_vectorial (2,4); Output: Magma V2.10-6 Sat Mar 27 2004 06:57:10 on modular [Seed = 1058673493] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ beta, beta^2, beta^4, beta^7, beta^8, beta^11, beta^13, beta^14 ] [
:88]( p: 2, n: 4 ) >> llista3 := llista2 cat llista1; ^ Runtime error in 'cat': Incompatible sequences Total time: 3.669 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 06:58:19 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; G5 := GF(5); G25:= ext < G5 |h>; lista_vectorial := function (p,n) llista1 := [<0,0>]; for i:=0 to (p^n)-2 do llista2 :=[]; llista1 := llista2 cat llista1; end for; return llista1; end function; Output: Magma V2.10-6 Sat Mar 27 2004 06:58:16 on modular [Seed = 789185291] ------------------------------------- Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 06:58:37 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; G5 := GF(5); G25:= ext < G5 |h>; lista_vectorial := function (p,n) llista1 := [<0,0>]; for i:=0 to (p^n)-2 do llista2 :=[]; llista1 := llista2 cat llista1; end for; return llista1; end function; Output: Magma V2.10-6 Sat Mar 27 2004 06:58:34 on modular [Seed = 537201718] ------------------------------------- Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 06:59:14 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; G5 := GF(5); G25:= ext < G5 |h>; lista_vectorial := function (p,n) llista1 := [<0,0>]; for i:=0 to (p^n)-2 do llista2 :=[]; llista1 := llista2 cat llista1; end for; return llista1; end function; lista_vectorial (2,4); Output: Magma V2.10-6 Sat Mar 27 2004 06:59:11 on modular [Seed = 423376362] ------------------------------------- [
:8]( p: 2, n: 4 ) >> llista1 := llista2 cat llista1; ^ Runtime error in 'cat': Incompatible sequences Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 07:00:08 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; G5 := GF(5); G25:= ext < G5 |h>; lista_vectorial := function (p,n) llista1 := [<0,ElementToSequence (alpha^0)>]; for i:=0 to (p^n)-2 do llista2 :=[]; llista1 := llista2 cat llista1; end for; return llista1; end function; lista_vectorial (2,4); Output: Magma V2.10-6 Sat Mar 27 2004 07:00:05 on modular [Seed = 187574194] ------------------------------------- [ , , <4, [ 4, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <1, [ 1, 0 ]>, <0, [ 1, 0 ]> ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 07:01:07 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; G5 := GF(5); G25:= ext < G5 |h>; lista_vectorial := function (p,n) llista1 := [<0,ElementToSequence (0)>]; for i:=(p^n)-2 to 0 by (-1) do llista2 :=[]; llista1 := llista2 cat llista1; end for; return llista1; end function; lista_vectorial (2,4); Output: Magma V2.10-6 Sat Mar 27 2004 07:01:04 on modular [Seed = 4006331282] ------------------------------------- [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , <0, [ 0 ]> ] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 07:01:44 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; G5 := GF(5); G25:= ext < G5 |h>; lista_vectorial := function (p,n) llista1 := [0,ElementToSequence (0)]; for i:=(p^n)-2 to 0 by (-1) do llista2 :=[alpha^i,ElementToSequence(alpha^i)]; llista1 := llista2 cat llista1; end for; return llista1; end function; lista_vectorial (2,4); Output: Magma V2.10-6 Sat Mar 27 2004 07:01:41 on modular [Seed = 3888302782] ------------------------------------- [
:8]( p: 2, n: 4 ) >> llista1 := [0,ElementToSequence (0)]; ^ Runtime error in [ ... ]: Could not find a valid universe Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 07:02:35 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; G5 := GF(5); G25:= ext < G5 |h>; lista_vectorial := function (p,n) llista1 := [[0,ElementToSequence (0)]]; for i:=(p^n)-2 to 0 by (-1) do llista2 :=[[alpha^i,ElementToSequence(alpha^i)]]; llista1 := llista2 cat llista1; end for; return llista1; end function; lista_vectorial (2,4); Output: Magma V2.10-6 Sat Mar 27 2004 07:02:32 on modular [Seed = 3640522236] ------------------------------------- [
:8]( p: 2, n: 4 ) >> llista1 := [[0,ElementToSequence (0)]]; ^ Runtime error in [ ... ]: Could not find a valid universe Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 07:03:18 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; G5 := GF(5); G25:= ext < G5 |h>; lista_vectorial := function (p,n) llista1 := [<0,ElementToSequence (0)>]; for i:=(p^n)-2 to 0 by (-1) do llista2 :=[]; llista1 := llista2 cat llista1; end for; return llista1; end function; lista_vectorial (2,4); Output: Magma V2.10-6 Sat Mar 27 2004 07:03:15 on modular [Seed = 3556179500] ------------------------------------- [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , <0, [ 0 ]> ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 07:03:37 2004 Input: a := [[2]]; Output: Magma V2.10-6 Sat Mar 27 2004 07:03:34 on modular [Seed = 3303139630] ------------------------------------- Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 07:04:41 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; G5 := GF(5); G25:= ext < G5 |h>; lista_vectorial := function (p,n) llista1 := [<0,ElementToSequence (0)>]; for i:=(p^n)-2 to 0 by (-1) do llista2 :=[]; llista1 := llista1 cat llista2; end for; return llista1; end function; lista_vectorial (2,4); Output: Magma V2.10-6 Sat Mar 27 2004 07:04:38 on modular [Seed = 3180892183] ------------------------------------- [ <0, [ 0 ]>, , , <4, [ 4, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <1, [ 1, 0 ]> ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 07:05:42 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; G5 := GF(5); G25:= ext < G5 |h>; lista_vectorial := function (p,n) llista1 := [<0,ElementToSequence (0)>]; for i:=0 to (p^n)-2 do llista2 :=[]; llista1 := llista1 cat llista2; end for; return llista1; end function; lista_vectorial (2,4); Output: Magma V2.10-6 Sat Mar 27 2004 07:05:39 on modular [Seed = 2996280541] ------------------------------------- [ <0, [ 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 07:06:27 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; G5 := GF(5); G25:= ext < G5 |h>; lista_vectorial := function (p,n) llista1 := [<0,0>]; for i:=0 to (p^n)-2 do llista2 :=[]; llista1 := llista1 cat llista2; end for; return llista1; end function; lista_vectorial (2,4); Output: Magma V2.10-6 Sat Mar 27 2004 07:06:24 on modular [Seed = 2759953048] ------------------------------------- [
:8]( p: 2, n: 4 ) >> llista1 := llista1 cat llista2; ^ Runtime error in 'cat': Incompatible sequences Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 07:06:49 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; G5 := GF(5); G25:= ext < G5 |h>; lista_vectorial := function (p,n) llista1 := [<0,[0,0]>]; for i:=0 to (p^n)-2 do llista2 :=[]; llista1 := llista1 cat llista2; end for; return llista1; end function; lista_vectorial (2,4); Output: Magma V2.10-6 Sat Mar 27 2004 07:06:46 on modular [Seed = 2646127543] ------------------------------------- [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 07:07:18 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; G5 := GF(5); G25:= ext < G5 |h>; lista_vectorial := function (p,n) llista1 := [0,[0,0]]; for i:=0 to (p^n)-2 do llista2 :=[alpha^i,ElementToSequence(alpha^i)]; llista1 := llista1 cat llista2; end for; return llista1; end function; lista_vectorial (2,4); Output: Magma V2.10-6 Sat Mar 27 2004 07:07:15 on modular [Seed = 2528360601] ------------------------------------- >> llista1 := [0,[0,0]]; ^ User error: Could not find a valid universe for the sequence >> for i:=0 to (p^n)-2 do llista2 :=[alpha^i,ElementToSequence(alpha^i)]; ^ User error: Identifier 'p' has not been declared or assigned >> return llista1; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> lista_vectorial (2,4);; ^ User error: Identifier 'lista_vectorial' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 07:07:43 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; G5 := GF(5); G25:= ext < G5 |h>; lista_vectorial := function (p,n) llista1 := [<0,[0,0]>]; for i:=0 to (p^n)-2 do llista2 :=[]; llista1 := llista1 cat llista2; end for; return llista1; end function; lista_vectorial (2,4); Output: Magma V2.10-6 Sat Mar 27 2004 07:07:40 on modular [Seed = 2410324351] ------------------------------------- [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 07:08:57 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; G5 := GF(5); G25:= ext < G5 |h>; lista_vectorial := function (p,n) llista1 := [[0,0]]; for i:=0 to (p^n)-2 do llista2 :=[]; llista1 := llista1 cat llista2; end for; return llista1; end function; lista_vectorial (2,4); Output: Magma V2.10-6 Sat Mar 27 2004 07:08:54 on modular [Seed = 2175053611] ------------------------------------- [
:8]( p: 2, n: 4 ) >> llista1 := llista1 cat llista2; ^ Runtime error in 'cat': Incompatible sequences Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 07:09:39 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; G5 := GF(5); G25:= ext < G5 |h>; lista_vectorial := function (p,n) llista1 := [<0,[0,0]>]; for i:=0 to (p^n)-2 do llista2 :=[]; llista1 := llista1 cat llista2; end for; return llista1; end function; lista_vectorial (2,4); Taula := function (p,n) llista1 := [<0,[0,0]>]; for i:=0 to (p^n)-2 do llista2 :=[]; llista1 := llista1 cat llista2; end for; return llista1; end function; Taula (2,4); Output: Magma V2.10-6 Sat Mar 27 2004 07:09:36 on modular [Seed = 2069779462] ------------------------------------- [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , ] [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , ] Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 07:11:28 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; G5 := GF(5); G25:= ext < G5 |h>; Taula := function (p,n) llista1 := [<0,[0,0]>]; for i:=0 to (p^n)-2 do llista2 :=[]; llista1 := llista1 cat llista2; end for; return llista1; end function; Taula (5,2); Output: Magma V2.10-6 Sat Mar 27 2004 07:11:25 on modular [Seed = 1783580026] ------------------------------------- [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 07:13:49 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); llista_primitius1:=[x: x in G25 | IsPrimitive (x)]; llista_primitius1; llista_primitius2:=[x: x in G16 | IsPrimitive (x)]; llista_primitius2; [x : x in GF(2)]; [x : x in GF(4)]; [x : x in GF(8)]; [x : x in GF(16)]; Output: Magma V2.10-6 Sat Mar 27 2004 07:13:46 on modular [Seed = 1601859800] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ beta, beta^2, beta^4, beta^7, beta^8, beta^11, beta^13, beta^14 ] [ 0, 1 ] [ 1, $.1, $.1^2, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, 0 ] [ 1, $.1, $.1^2, $.1^3, $.1^4, $.1^5, $.1^6, $.1^7, $.1^8, $.1^9, $.1^10, $.1^11, $.1^12, $.1^13, $.1^14, 0 ] Total time: 3.109 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 07:15:43 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); llista_primitius1:=[x: x in G25 | IsPrimitive (x)]; llista_primitius1; llista_primitius2:=[x: x in G16 | IsPrimitive (x)]; llista_primitius2; G2 := GF(2); [x : x in G2]; G4 := GF (4); [x : x in G4]; G8 := GF (8); [x : x in G8]; G16b := GF (16); [x : x in G16b]; Output: Magma V2.10-6 Sat Mar 27 2004 07:15:40 on modular [Seed = 1383555651] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ beta, beta^2, beta^4, beta^7, beta^8, beta^11, beta^13, beta^14 ] [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16b.1, G16b.1^2, G16b.1^3, G16b.1^4, G16b.1^5, G16b.1^6, G16b.1^7, G16b.1^8, G16b.1^9, G16b.1^10, G16b.1^11, G16b.1^12, G16b.1^13, G16b.1^14, 0 ] Total time: 2.959 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 07:19:18 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); llista_primitius1:=[x: x in G25 | IsPrimitive (x)]; llista_primitius1; llista_primitius2:=[x: x in G16 | IsPrimitive (x)]; llista_primitius2; G2 := GF(2); [x : x in G2]; G4 := GF (4); [x : x in G4]; G8 := GF (8); [x : x in G8]; G16b := GF (16); [x : x in G16b]; G2 subset G4; G2 subset G8; G2 subset G16b; G4 subset G2; G4 subset G8; G4 subset G16b; G8 subset G2; G8 subset G4; G8 subset G16b; G16b subset G2; G16b subset G4; G16b subset G8; Output: Magma V2.10-6 Sat Mar 27 2004 07:19:15 on modular [Seed = 1097101439] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ beta, beta^2, beta^4, beta^7, beta^8, beta^11, beta^13, beta^14 ] [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16b.1, G16b.1^2, G16b.1^3, G16b.1^4, G16b.1^5, G16b.1^6, G16b.1^7, G16b.1^8, G16b.1^9, G16b.1^10, G16b.1^11, G16b.1^12, G16b.1^13, G16b.1^14, 0 ] true true true false false true false false false false false false Total time: 2.989 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 07:26:08 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); llista_primitius1:=[x: x in G25 | IsPrimitive (x)]; llista_primitius1; llista_primitius2:=[x: x in G16 | IsPrimitive (x)]; llista_primitius2; G2 := GF(2); [x : x in G2]; G4 := GF (4); [x : x in G4]; G8 := GF (8); [x : x in G8]; G16b := GF (16); [x : x in G16b]; G2 subset G4; G2 subset G8; G2 subset G16b; G4 subset G2; Output: Magma V2.10-6 Sat Mar 27 2004 07:26:05 on modular [Seed = 688659337] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ beta, beta^2, beta^4, beta^7, beta^8, beta^11, beta^13, beta^14 ] [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16b.1, G16b.1^2, G16b.1^3, G16b.1^4, G16b.1^5, G16b.1^6, G16b.1^7, G16b.1^8, G16b.1^9, G16b.1^10, G16b.1^11, G16b.1^12, G16b.1^13, G16b.1^14, 0 ] true true true false Total time: 2.969 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 07:26:36 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); llista_primitius1:=[x: x in G25 | IsPrimitive (x)]; llista_primitius1; llista_primitius2:=[x: x in G16 | IsPrimitive (x)]; llista_primitius2; G2 := GF(2); [x : x in G2]; G4 := GF (4); [x : x in G4]; G8 := GF (8); [x : x in G8]; G16b := GF (16); [x : x in G16b]; G2 subset G4; G2 subset G8; G2 subset G16b; G4 subset G2; G4 subset G8; Output: Magma V2.10-6 Sat Mar 27 2004 07:26:33 on modular [Seed = 537203364] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ beta, beta^2, beta^4, beta^7, beta^8, beta^11, beta^13, beta^14 ] [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16b.1, G16b.1^2, G16b.1^3, G16b.1^4, G16b.1^5, G16b.1^6, G16b.1^7, G16b.1^8, G16b.1^9, G16b.1^10, G16b.1^11, G16b.1^12, G16b.1^13, G16b.1^14, 0 ] true true true false false Total time: 2.969 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 07:27:01 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); llista_primitius1:=[x: x in G25 | IsPrimitive (x)]; llista_primitius1; llista_primitius2:=[x: x in G16 | IsPrimitive (x)]; llista_primitius2; G2 := GF(2); [x : x in G2]; G4 := GF (4); [x : x in G4]; G8 := GF (8); [x : x in G8]; G16b := GF (16); [x : x in G16b]; G2 subset G4; G2 subset G8; G2 subset G16b; G4 subset G2; G4 subset G8; G4 subset G16b; Output: Magma V2.10-6 Sat Mar 27 2004 07:26:58 on modular [Seed = 457058420] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ beta, beta^2, beta^4, beta^7, beta^8, beta^11, beta^13, beta^14 ] [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16b.1, G16b.1^2, G16b.1^3, G16b.1^4, G16b.1^5, G16b.1^6, G16b.1^7, G16b.1^8, G16b.1^9, G16b.1^10, G16b.1^11, G16b.1^12, G16b.1^13, G16b.1^14, 0 ] true true true false false true Total time: 2.959 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 07:27:28 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); llista_primitius1:=[x: x in G25 | IsPrimitive (x)]; llista_primitius1; llista_primitius2:=[x: x in G16 | IsPrimitive (x)]; llista_primitius2; G2 := GF(2); [x : x in G2]; G4 := GF (4); [x : x in G4]; G8 := GF (8); [x : x in G8]; G16b := GF (16); [x : x in G16b]; G2 subset G4; G2 subset G8; G2 subset G16b; G4 subset G2; G4 subset G8; G4 subset G16b; G8 subset G2; Output: Magma V2.10-6 Sat Mar 27 2004 07:27:24 on modular [Seed = 305602882] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ beta, beta^2, beta^4, beta^7, beta^8, beta^11, beta^13, beta^14 ] [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16b.1, G16b.1^2, G16b.1^3, G16b.1^4, G16b.1^5, G16b.1^6, G16b.1^7, G16b.1^8, G16b.1^9, G16b.1^10, G16b.1^11, G16b.1^12, G16b.1^13, G16b.1^14, 0 ] true true true false false true false Total time: 3.039 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 07:27:50 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); llista_primitius1:=[x: x in G25 | IsPrimitive (x)]; llista_primitius1; llista_primitius2:=[x: x in G16 | IsPrimitive (x)]; llista_primitius2; G2 := GF(2); [x : x in G2]; G4 := GF (4); [x : x in G4]; G8 := GF (8); [x : x in G8]; G16b := GF (16); [x : x in G16b]; G2 subset G4; G2 subset G8; G2 subset G16b; G4 subset G2; G4 subset G8; G4 subset G16b; G8 subset G2; Output: Magma V2.10-6 Sat Mar 27 2004 07:27:47 on modular [Seed = 85997115] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ beta, beta^2, beta^4, beta^7, beta^8, beta^11, beta^13, beta^14 ] [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16b.1, G16b.1^2, G16b.1^3, G16b.1^4, G16b.1^5, G16b.1^6, G16b.1^7, G16b.1^8, G16b.1^9, G16b.1^10, G16b.1^11, G16b.1^12, G16b.1^13, G16b.1^14, 0 ] true true true false false true false Total time: 3.009 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 07:28:26 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); llista_primitius1:=[x: x in G25 | IsPrimitive (x)]; llista_primitius1; llista_primitius2:=[x: x in G16 | IsPrimitive (x)]; llista_primitius2; G2 := GF(2); [x : x in G2]; G4 := GF (4); [x : x in G4]; G8 := GF (8); [x : x in G8]; G16b := GF (16); [x : x in G16b]; G2 subset G4; G2 subset G8; G2 subset G16b; G4 subset G2; G4 subset G8; G4 subset G16b; G8 subset G2; G8 subset G4; Output: Magma V2.10-6 Sat Mar 27 2004 07:28:23 on modular [Seed = 4292529381] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ beta, beta^2, beta^4, beta^7, beta^8, beta^11, beta^13, beta^14 ] [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16b.1, G16b.1^2, G16b.1^3, G16b.1^4, G16b.1^5, G16b.1^6, G16b.1^7, G16b.1^8, G16b.1^9, G16b.1^10, G16b.1^11, G16b.1^12, G16b.1^13, G16b.1^14, 0 ] true true true false false true false false Total time: 3.089 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 07:28:54 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); llista_primitius1:=[x: x in G25 | IsPrimitive (x)]; llista_primitius1; llista_primitius2:=[x: x in G16 | IsPrimitive (x)]; llista_primitius2; G2 := GF(2); [x : x in G2]; G4 := GF (4); [x : x in G4]; G8 := GF (8); [x : x in G8]; G16b := GF (16); [x : x in G16b]; G2 subset G4; G2 subset G8; G2 subset G16b; G4 subset G2; G4 subset G8; G4 subset G16b; G8 subset G2; G8 subset G4; G8 subset G16b; Output: Magma V2.10-6 Sat Mar 27 2004 07:28:51 on modular [Seed = 4141073672] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ beta, beta^2, beta^4, beta^7, beta^8, beta^11, beta^13, beta^14 ] [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16b.1, G16b.1^2, G16b.1^3, G16b.1^4, G16b.1^5, G16b.1^6, G16b.1^7, G16b.1^8, G16b.1^9, G16b.1^10, G16b.1^11, G16b.1^12, G16b.1^13, G16b.1^14, 0 ] true true true false false true false false false Total time: 2.989 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 07:29:21 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); llista_primitius1:=[x: x in G25 | IsPrimitive (x)]; llista_primitius1; llista_primitius2:=[x: x in G16 | IsPrimitive (x)]; llista_primitius2; G2 := GF(2); [x : x in G2]; G4 := GF (4); [x : x in G4]; G8 := GF (8); [x : x in G8]; G16b := GF (16); [x : x in G16b]; G2 subset G4; G2 subset G8; G2 subset G16b; G4 subset G2; G4 subset G8; G4 subset G16b; G8 subset G2; G8 subset G4; G8 subset G16b; G16b subset G2; G16b subset G4; G16b subset G8; Output: Magma V2.10-6 Sat Mar 27 2004 07:29:18 on modular [Seed = 3905805067] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ beta, beta^2, beta^4, beta^7, beta^8, beta^11, beta^13, beta^14 ] [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16b.1, G16b.1^2, G16b.1^3, G16b.1^4, G16b.1^5, G16b.1^6, G16b.1^7, G16b.1^8, G16b.1^9, G16b.1^10, G16b.1^11, G16b.1^12, G16b.1^13, G16b.1^14, 0 ] true true true false false true false false false false false false Total time: 2.989 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 07:32:37 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); llista_primitius1:=[x: x in G25 | IsPrimitive (x)]; llista_primitius1; llista_primitius2:=[x: x in G16 | IsPrimitive (x)]; llista_primitius2; G2 := GF(2); [x : x in G2]; G4 := GF (4); [x : x in G4]; G8 := GF (8); [x : x in G8]; G16b := GF (16); [x : x in G16b]; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; Output: Magma V2.10-6 Sat Mar 27 2004 07:32:34 on modular [Seed = 3690917828] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ beta, beta^2, beta^4, beta^7, beta^8, beta^11, beta^13, beta^14 ] [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16b.1, G16b.1^2, G16b.1^3, G16b.1^4, G16b.1^5, G16b.1^6, G16b.1^7, G16b.1^8, G16b.1^9, G16b.1^10, G16b.1^11, G16b.1^12, G16b.1^13, G16b.1^14, 0 ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] Total time: 3.069 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 07:34:33 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); llista_primitius1:=[x: x in G25 | IsPrimitive (x)]; llista_primitius1; llista_primitius2:=[x: x in G16 | IsPrimitive (x)]; llista_primitius2; G2 := GF(2); [x : x in G2]; G4 := GF (4); [x : x in G4]; G8 := GF (8); [x : x in G8]; G16b := GF (16); [x : x in G16b]; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; G5 := GF(5); lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; Output: Magma V2.10-6 Sat Mar 27 2004 07:34:30 on modular [Seed = 3454597478] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ beta, beta^2, beta^4, beta^7, beta^8, beta^11, beta^13, beta^14 ] [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16b.1, G16b.1^2, G16b.1^3, G16b.1^4, G16b.1^5, G16b.1^6, G16b.1^7, G16b.1^8, G16b.1^9, G16b.1^10, G16b.1^11, G16b.1^12, G16b.1^13, G16b.1^14, 0 ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] Total time: 3.049 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 07:35:31 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); llista_primitius1:=[x: x in G25 | IsPrimitive (x)]; llista_primitius1; llista_primitius2:=[x: x in G16 | IsPrimitive (x)]; llista_primitius2; G2 := GF(2); [x : x in G2]; G4 := GF (4); [x : x in G4]; G8 := GF (8); [x : x in G8]; G16b := GF (16); [x : x in G16b]; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; G5 := GF(5); lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; Output: Magma V2.10-6 Sat Mar 27 2004 07:35:28 on modular [Seed = 3236296109] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ beta, beta^2, beta^4, beta^7, beta^8, beta^11, beta^13, beta^14 ] [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16b.1, G16b.1^2, G16b.1^3, G16b.1^4, G16b.1^5, G16b.1^6, G16b.1^7, G16b.1^8, G16b.1^9, G16b.1^10, G16b.1^11, G16b.1^12, G16b.1^13, G16b.1^14, 0 ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] >> p1 := alpha^2 + alpha*x + beta*x^2; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt >> p2 := 1 + alpha*x; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt >> suma := p1 + p2; ^ User error: Identifier 'p1' has not been declared or assigned >> suma; ^ User error: Identifier 'suma' has not been declared or assigned Total time: 3.039 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 07:36:25 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); llista_primitius1:=[x: x in G25 | IsPrimitive (x)]; llista_primitius1; llista_primitius2:=[x: x in G16 | IsPrimitive (x)]; llista_primitius2; G2 := GF(2); [x : x in G2]; G4 := GF (4); [x : x in G4]; G8 := GF (8); [x : x in G8]; G16b := GF (16); [x : x in G16b]; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; G5 := GF(5); lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; Output: Magma V2.10-6 Sat Mar 27 2004 07:36:22 on modular [Seed = 3131019137] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ beta, beta^2, beta^4, beta^7, beta^8, beta^11, beta^13, beta^14 ] [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16b.1, G16b.1^2, G16b.1^3, G16b.1^4, G16b.1^5, G16b.1^6, G16b.1^7, G16b.1^8, G16b.1^9, G16b.1^10, G16b.1^11, G16b.1^12, G16b.1^13, G16b.1^14, 0 ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] >> p1 := alpha^2 + alpha*x + beta*x^2; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt >> p2 := 1 + alpha*x; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt >> suma := p1 + p2; ^ User error: Identifier 'p1' has not been declared or assigned >> suma; ^ User error: Identifier 'suma' has not been declared or assigned Total time: 3.089 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 07:37:11 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); llista_primitius1:=[x: x in G25 | IsPrimitive (x)]; llista_primitius1; llista_primitius2:=[x: x in G16 | IsPrimitive (x)]; llista_primitius2; G2 := GF(2); [x : x in G2]; G4 := GF (4); [x : x in G4]; G8 := GF (8); [x : x in G8]; G16b := GF (16); [x : x in G16b]; P := PolynomialRing (G25); IsFinite (P); lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; G5 := GF(5); lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; Output: Magma V2.10-6 Sat Mar 27 2004 07:37:08 on modular [Seed = 2911410340] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ beta, beta^2, beta^4, beta^7, beta^8, beta^11, beta^13, beta^14 ] [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16b.1, G16b.1^2, G16b.1^3, G16b.1^4, G16b.1^5, G16b.1^6, G16b.1^7, G16b.1^8, G16b.1^9, G16b.1^10, G16b.1^11, G16b.1^12, G16b.1^13, G16b.1^14, 0 ] false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] x^2 + alpha^19*x + alpha^9 Total time: 3.069 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 07:38:24 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); llista_primitius1:=[x: x in G25 | IsPrimitive (x)]; llista_primitius1; llista_primitius2:=[x: x in G16 | IsPrimitive (x)]; llista_primitius2; G2 := GF(2); [x : x in G2]; G4 := GF (4); [x : x in G4]; G8 := GF (8); [x : x in G8]; G16b := GF (16); [x : x in G16b]; P := PolynomialRing (G25); IsFinite (P); lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; G5 := GF(5); lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; producte := p1 * p2; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; mcd := GCD (p1,p2); mcd; mcm := LCM (p1,p2); mcm; Output: Magma V2.10-6 Sat Mar 27 2004 07:38:21 on modular [Seed = 2810352231] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ beta, beta^2, beta^4, beta^7, beta^8, beta^11, beta^13, beta^14 ] [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16b.1, G16b.1^2, G16b.1^3, G16b.1^4, G16b.1^5, G16b.1^6, G16b.1^7, G16b.1^8, G16b.1^9, G16b.1^10, G16b.1^11, G16b.1^12, G16b.1^13, G16b.1^14, 0 ] false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] x^2 + alpha^19*x + alpha^9 alpha*x^3 + alpha^9*x^2 + alpha^10*x + alpha^2 alpha^23*x + alpha^21 alpha 1 x^3 + alpha^8*x^2 + alpha^9*x + alpha Total time: 2.999 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 07:39:45 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); llista_primitius1:=[x: x in G25 | IsPrimitive (x)]; llista_primitius1; llista_primitius2:=[x: x in G16 | IsPrimitive (x)]; llista_primitius2; G2 := GF(2); [x : x in G2]; G4 := GF (4); [x : x in G4]; G8 := GF (8); [x : x in G8]; G16b := GF (16); [x : x in G16b]; P := PolynomialRing (G25); IsFinite (P); lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; G5 := GF(5); lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; producte := p1 * p2; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; mcd := GCD (p1,p2); mcd; mcm := LCM (p1,p2); mcm; combinacio := XGCD(p1,p2); combinacio; Output: Magma V2.10-6 Sat Mar 27 2004 07:39:41 on modular [Seed = 2579279849] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ beta, beta^2, beta^4, beta^7, beta^8, beta^11, beta^13, beta^14 ] [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16b.1, G16b.1^2, G16b.1^3, G16b.1^4, G16b.1^5, G16b.1^6, G16b.1^7, G16b.1^8, G16b.1^9, G16b.1^10, G16b.1^11, G16b.1^12, G16b.1^13, G16b.1^14, 0 ] false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] x^2 + alpha^19*x + alpha^9 alpha*x^3 + alpha^9*x^2 + alpha^10*x + alpha^2 alpha^23*x + alpha^21 alpha 1 x^3 + alpha^8*x^2 + alpha^9*x + alpha 1 Total time: 3.099 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 07:41:53 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); llista_primitius1:=[x: x in G25 | IsPrimitive (x)]; llista_primitius1; llista_primitius2:=[x: x in G16 | IsPrimitive (x)]; llista_primitius2; G2 := GF(2); [x : x in G2]; G4 := GF (4); [x : x in G4]; G8 := GF (8); [x : x in G8]; G16b := GF (16); [x : x in G16b]; P := PolynomialRing (G25); IsFinite (P); lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; G5 := GF(5); lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; producte := p1 * p2; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; mcd := GCD (p1,p2); mcd; mcm := LCM (p1,p2); mcm; XGCD(p1,p2); Output: Magma V2.10-6 Sat Mar 27 2004 07:41:50 on modular [Seed = 2309799802] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ beta, beta^2, beta^4, beta^7, beta^8, beta^11, beta^13, beta^14 ] [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16b.1, G16b.1^2, G16b.1^3, G16b.1^4, G16b.1^5, G16b.1^6, G16b.1^7, G16b.1^8, G16b.1^9, G16b.1^10, G16b.1^11, G16b.1^12, G16b.1^13, G16b.1^14, 0 ] false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] x^2 + alpha^19*x + alpha^9 alpha*x^3 + alpha^9*x^2 + alpha^10*x + alpha^2 alpha^23*x + alpha^21 alpha 1 x^3 + alpha^8*x^2 + alpha^9*x + alpha 1 alpha^23 alpha^10*x + alpha^8 Total time: 3.049 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 07:42:59 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); llista_primitius1:=[x: x in G25 | IsPrimitive (x)]; llista_primitius1; llista_primitius2:=[x: x in G16 | IsPrimitive (x)]; llista_primitius2; G2 := GF(2); [x : x in G2]; G4 := GF (4); [x : x in G4]; G8 := GF (8); [x : x in G8]; G16b := GF (16); [x : x in G16b]; P := PolynomialRing (G25); IsFinite (P); lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; G5 := GF(5); lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; producte := p1 * p2; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; mcd := GCD (p1,p2); mcd; mcm := LCM (p1,p2); mcm; XGCD(p1,p2); pol:=(1/alpha^4) - alpha^-3 * x + alpha^5 * x^2; Factorization (pol); Output: Magma V2.10-6 Sat Mar 27 2004 07:42:56 on modular [Seed = 2208740654] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ beta, beta^2, beta^4, beta^7, beta^8, beta^11, beta^13, beta^14 ] [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16b.1, G16b.1^2, G16b.1^3, G16b.1^4, G16b.1^5, G16b.1^6, G16b.1^7, G16b.1^8, G16b.1^9, G16b.1^10, G16b.1^11, G16b.1^12, G16b.1^13, G16b.1^14, 0 ] false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] x^2 + alpha^19*x + alpha^9 alpha*x^3 + alpha^9*x^2 + alpha^10*x + alpha^2 alpha^23*x + alpha^21 alpha 1 x^3 + alpha^8*x^2 + alpha^9*x + alpha 1 alpha^23 alpha^10*x + alpha^8 [ ] Total time: 3.049 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 07:44:18 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); llista_primitius1:=[x: x in G25 | IsPrimitive (x)]; llista_primitius1; llista_primitius2:=[x: x in G16 | IsPrimitive (x)]; llista_primitius2; G2 := GF(2); [x : x in G2]; G4 := GF (4); [x : x in G4]; G8 := GF (8); [x : x in G8]; G16b := GF (16); [x : x in G16b]; P := PolynomialRing (G25); IsFinite (P); lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; G5 := GF(5); lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; producte := p1 * p2; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; mcd := GCD (p1,p2); mcd; mcm := LCM (p1,p2); mcm; XGCD(p1,p2); pol:=(alpha^(-4) - alpha^(-3) * x + alpha^5 * x^2; Factorization (pol); Output: Magma V2.10-6 Sat Mar 27 2004 07:44:14 on modular [Seed = 1985167638] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ beta, beta^2, beta^4, beta^7, beta^8, beta^11, beta^13, beta^14 ] [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16b.1, G16b.1^2, G16b.1^3, G16b.1^4, G16b.1^5, G16b.1^6, G16b.1^7, G16b.1^8, G16b.1^9, G16b.1^10, G16b.1^11, G16b.1^12, G16b.1^13, G16b.1^14, 0 ] false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] x^2 + alpha^19*x + alpha^9 alpha*x^3 + alpha^9*x^2 + alpha^10*x + alpha^2 alpha^23*x + alpha^21 alpha 1 x^3 + alpha^8*x^2 + alpha^9*x + alpha 1 alpha^23 alpha^10*x + alpha^8 >> pol:=(alpha^(-4) - alpha^(-3) * x + alpha^5 * x^2; ^ User error: bad syntax >> Factorization (pol);; ^ Runtime error in 'Factorization': Bad argument types Argument types given: FldFinElt Total time: 3.059 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 07:45:01 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); llista_primitius1:=[x: x in G25 | IsPrimitive (x)]; llista_primitius1; llista_primitius2:=[x: x in G16 | IsPrimitive (x)]; llista_primitius2; G2 := GF(2); [x : x in G2]; G4 := GF (4); [x : x in G4]; G8 := GF (8); [x : x in G8]; G16b := GF (16); [x : x in G16b]; P := PolynomialRing (G25); IsFinite (P); lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; G5 := GF(5); lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; producte := p1 * p2; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; mcd := GCD (p1,p2); mcd; mcm := LCM (p1,p2); mcm; XGCD(p1,p2); pol:=alpha^(-4) - alpha^(-3) * x + alpha^5 * x^2; Factorization (pol); Output: Magma V2.10-6 Sat Mar 27 2004 07:44:58 on modular [Seed = 1867143259] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ beta, beta^2, beta^4, beta^7, beta^8, beta^11, beta^13, beta^14 ] [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16b.1, G16b.1^2, G16b.1^3, G16b.1^4, G16b.1^5, G16b.1^6, G16b.1^7, G16b.1^8, G16b.1^9, G16b.1^10, G16b.1^11, G16b.1^12, G16b.1^13, G16b.1^14, 0 ] false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] x^2 + alpha^19*x + alpha^9 alpha*x^3 + alpha^9*x^2 + alpha^10*x + alpha^2 alpha^23*x + alpha^21 alpha 1 x^3 + alpha^8*x^2 + alpha^9*x + alpha 1 alpha^23 alpha^10*x + alpha^8 [ ] Total time: 3.149 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 07:46:14 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); llista_primitius1:=[x: x in G25 | IsPrimitive (x)]; llista_primitius1; llista_primitius2:=[x: x in G16 | IsPrimitive (x)]; llista_primitius2; G2 := GF(2); [x : x in G2]; G4 := GF (4); [x : x in G4]; G8 := GF (8); [x : x in G8]; G16b := GF (16); [x : x in G16b]; P := PolynomialRing (G25); IsFinite (P); lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; G5 := GF(5); lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; producte := p1 * p2; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; mcd := GCD (p1,p2); mcd; mcm := LCM (p1,p2); mcm; XGCD(p1,p2); pol:=alpha^(-4) - alpha^(-3) * x + alpha^5 * x^2; Factorization (pol); Evaluate(pol,x^2 + alpha^4*x + alpha^15); Output: Magma V2.10-6 Sat Mar 27 2004 07:46:11 on modular [Seed = 1631868556] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ beta, beta^2, beta^4, beta^7, beta^8, beta^11, beta^13, beta^14 ] [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16b.1, G16b.1^2, G16b.1^3, G16b.1^4, G16b.1^5, G16b.1^6, G16b.1^7, G16b.1^8, G16b.1^9, G16b.1^10, G16b.1^11, G16b.1^12, G16b.1^13, G16b.1^14, 0 ] false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] x^2 + alpha^19*x + alpha^9 alpha*x^3 + alpha^9*x^2 + alpha^10*x + alpha^2 alpha^23*x + alpha^21 alpha 1 x^3 + alpha^8*x^2 + alpha^9*x + alpha 1 alpha^23 alpha^10*x + alpha^8 [ ] alpha^5*x^4 + alpha^3*x^3 + alpha^8*x^2 + alpha^4*x + alpha^22 Total time: 3.059 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 07:48:04 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); llista_primitius1:=[x: x in G25 | IsPrimitive (x)]; llista_primitius1; llista_primitius2:=[x: x in G16 | IsPrimitive (x)]; llista_primitius2; G2 := GF(2); [x : x in G2]; G4 := GF (4); [x : x in G4]; G8 := GF (8); [x : x in G8]; G16b := GF (16); [x : x in G16b]; P := PolynomialRing (G25); IsFinite (P); lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; G5 := GF(5); lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; producte := p1 * p2; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; mcd := GCD (p1,p2); mcd; mcm := LCM (p1,p2); mcm; XGCD(p1,p2); pol:=alpha^(-4) - alpha^(-3) * x + alpha^5 * x^2; Factorization (pol,G25); Evaluate(pol,x^2 + alpha^4*x + alpha^15); Output: Magma V2.10-6 Sat Mar 27 2004 07:48:01 on modular [Seed = 1450405417] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ beta, beta^2, beta^4, beta^7, beta^8, beta^11, beta^13, beta^14 ] [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16b.1, G16b.1^2, G16b.1^3, G16b.1^4, G16b.1^5, G16b.1^6, G16b.1^7, G16b.1^8, G16b.1^9, G16b.1^10, G16b.1^11, G16b.1^12, G16b.1^13, G16b.1^14, 0 ] false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] x^2 + alpha^19*x + alpha^9 alpha*x^3 + alpha^9*x^2 + alpha^10*x + alpha^2 alpha^23*x + alpha^21 alpha 1 x^3 + alpha^8*x^2 + alpha^9*x + alpha 1 alpha^23 alpha^10*x + alpha^8 >> Factorization (pol,G25); ^ Runtime error in 'Factorization': Bad argument types Argument types given: RngUPolElt, FldFin alpha^5*x^4 + alpha^3*x^3 + alpha^8*x^2 + alpha^4*x + alpha^22 Total time: 3.089 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 07:53:00 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); llista_primitius1:=[x: x in G25 | IsPrimitive (x)]; llista_primitius1; llista_primitius2:=[x: x in G16 | IsPrimitive (x)]; llista_primitius2; G2 := GF(2); [x : x in G2]; G4 := GF (4); [x : x in G4]; G8 := GF (8); [x : x in G8]; G16b := GF (16); [x : x in G16b]; P := PolynomialRing (G25); IsFinite (P); lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; G5 := GF(5); lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; producte := p1 * p2; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; mcd := GCD (p1,p2); mcd; mcm := LCM (p1,p2); mcm; XGCD(p1,p2); pol:=alpha^(-4) - alpha^(-3) * x + alpha^5 * x^2; Factorization (G25,pol); Evaluate(pol,x^2 + alpha^4*x + alpha^15); Output: Magma V2.10-6 Sat Mar 27 2004 07:52:57 on modular [Seed = 1163951122] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ beta, beta^2, beta^4, beta^7, beta^8, beta^11, beta^13, beta^14 ] [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16b.1, G16b.1^2, G16b.1^3, G16b.1^4, G16b.1^5, G16b.1^6, G16b.1^7, G16b.1^8, G16b.1^9, G16b.1^10, G16b.1^11, G16b.1^12, G16b.1^13, G16b.1^14, 0 ] false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] x^2 + alpha^19*x + alpha^9 alpha*x^3 + alpha^9*x^2 + alpha^10*x + alpha^2 alpha^23*x + alpha^21 alpha 1 x^3 + alpha^8*x^2 + alpha^9*x + alpha 1 alpha^23 alpha^10*x + alpha^8 >> Factorization (G25,pol); ^ Runtime error in 'Factorization': Bad argument types Argument types given: FldFin, RngUPolElt alpha^5*x^4 + alpha^3*x^3 + alpha^8*x^2 + alpha^4*x + alpha^22 Total time: 3.079 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 07:56:37 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; G5 := GF(5); G25:= ext < G5 |h>; Output: Magma V2.10-6 Sat Mar 27 2004 07:56:34 on modular [Seed = 873533000] ------------------------------------- Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 07:57:46 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; G5 := GF(5); G25:= ext < G5 |h>; P := PolynomialRing (G25); pol:=alpha^(-4) - alpha^(-3) * y + alpha^5 * y^2; Factorization (pol); Output: Magma V2.10-6 Sat Mar 27 2004 07:57:43 on modular [Seed = 755504916] ------------------------------------- [ ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 07:58:15 2004 Input: z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; G5 := GF(5); G25:= ext < G5 |h>; P := PolynomialRing (G25); pol:=alpha^(-4) - alpha^(-3) * y + alpha^5 * y^2; Factorization (pol,G25); Output: Magma V2.10-6 Sat Mar 27 2004 07:58:12 on modular [Seed = 587602233] ------------------------------------- >> Factorization (pol,G25);; ^ Runtime error in 'Factorization': Bad argument types Argument types given: RngUPolElt, FldFin Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 07:58:53 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); llista_primitius1:=[x: x in G25 | IsPrimitive (x)]; llista_primitius1; llista_primitius2:=[x: x in G16 | IsPrimitive (x)]; llista_primitius2; G2 := GF(2); [x : x in G2]; G4 := GF (4); [x : x in G4]; G8 := GF (8); [x : x in G8]; G16b := GF (16); [x : x in G16b]; P := PolynomialRing (G25); IsFinite (P); lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; G5 := GF(5); lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; producte := p1 * p2; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; mcd := GCD (p1,p2); mcd; mcm := LCM (p1,p2); mcm; XGCD(p1,p2); P := PolynomialRing (G25); pol:=alpha^(-4) - alpha^(-3) * x + alpha^5 * x^2; Factorization (pol); Roots (pol,G25); Evaluate(pol,x^2 + alpha^4*x + alpha^15); Output: Magma V2.10-6 Sat Mar 27 2004 07:58:50 on modular [Seed = 423371757] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ beta, beta^2, beta^4, beta^7, beta^8, beta^11, beta^13, beta^14 ] [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16b.1, G16b.1^2, G16b.1^3, G16b.1^4, G16b.1^5, G16b.1^6, G16b.1^7, G16b.1^8, G16b.1^9, G16b.1^10, G16b.1^11, G16b.1^12, G16b.1^13, G16b.1^14, 0 ] false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] x^2 + alpha^19*x + alpha^9 alpha*x^3 + alpha^9*x^2 + alpha^10*x + alpha^2 alpha^23*x + alpha^21 alpha 1 x^3 + alpha^8*x^2 + alpha^9*x + alpha 1 alpha^23 alpha^10*x + alpha^8 [ ] [] alpha^5*x^4 + alpha^3*x^3 + alpha^8*x^2 + alpha^4*x + alpha^22 Total time: 3.049 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 08:03:16 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); llista_primitius1:=[x: x in G25 | IsPrimitive (x)]; llista_primitius1; llista_primitius2:=[x: x in G16 | IsPrimitive (x)]; llista_primitius2; G2 := GF(2); [x : x in G2]; G4 := GF (4); [x : x in G4]; G8 := GF (8); [x : x in G8]; G16b := GF (16); [x : x in G16b]; P := PolynomialRing (G25); IsFinite (P); lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; G5 := GF(5); lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; producte := p1 * p2; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; mcd := GCD (p1,p2); mcd; mcm := LCM (p1,p2); mcm; XGCD(p1,p2); P := PolynomialRing (G25); pol:=alpha^(-4) - alpha^(-3) * x + alpha^5 * x^2; Factorization (pol); Roots (pol,G25); IsIrreductible(pol); Output: Magma V2.10-6 Sat Mar 27 2004 08:03:13 on modular [Seed = 4074227997] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ beta, beta^2, beta^4, beta^7, beta^8, beta^11, beta^13, beta^14 ] [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16b.1, G16b.1^2, G16b.1^3, G16b.1^4, G16b.1^5, G16b.1^6, G16b.1^7, G16b.1^8, G16b.1^9, G16b.1^10, G16b.1^11, G16b.1^12, G16b.1^13, G16b.1^14, 0 ] false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] x^2 + alpha^19*x + alpha^9 alpha*x^3 + alpha^9*x^2 + alpha^10*x + alpha^2 alpha^23*x + alpha^21 alpha 1 x^3 + alpha^8*x^2 + alpha^9*x + alpha 1 alpha^23 alpha^10*x + alpha^8 [ ] [] >> IsIrreductible(pol);; ^ User error: Identifier 'IsIrreductible' has not been declared or assigned Total time: 3.079 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 08:04:01 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; cardinal := # lista_primitius_G25; cardinal; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*grau es 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; lista2:=[x: x in G25 | IsInvertible (x)]; lista2; IsInvertible (pol); llista_primitius1:=[x: x in G25 | IsPrimitive (x)]; llista_primitius1; llista_primitius2:=[x: x in G16 | IsPrimitive (x)]; llista_primitius2; G2 := GF(2); [x : x in G2]; G4 := GF (4); [x : x in G4]; G8 := GF (8); [x : x in G8]; G16b := GF (16); [x : x in G16b]; P := PolynomialRing (G25); IsFinite (P); lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; G5 := GF(5); lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; suma := p1 + p2; suma; producte := p1 * p2; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; mcd := GCD (p1,p2); mcd; mcm := LCM (p1,p2); mcm; XGCD(p1,p2); P := PolynomialRing (G25); pol:=alpha^(-4) - alpha^(-3) * x + alpha^5 * x^2; Factorization (pol); Roots (pol,G25); IsIrreducible(pol); Output: Magma V2.10-6 Sat Mar 27 2004 08:03:57 on modular [Seed = 3905803051] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 [ , ] [] alpha^13 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] true alpha^11 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ beta, beta^2, beta^4, beta^7, beta^8, beta^11, beta^13, beta^14 ] [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16b.1, G16b.1^2, G16b.1^3, G16b.1^4, G16b.1^5, G16b.1^6, G16b.1^7, G16b.1^8, G16b.1^9, G16b.1^10, G16b.1^11, G16b.1^12, G16b.1^13, G16b.1^14, 0 ] false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] x^2 + alpha^19*x + alpha^9 alpha*x^3 + alpha^9*x^2 + alpha^10*x + alpha^2 alpha^23*x + alpha^21 alpha 1 x^3 + alpha^8*x^2 + alpha^9*x + alpha 1 alpha^23 alpha^10*x + alpha^8 [ ] [] true Total time: 3.109 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 08:12:20 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i, Order(lista[i])] : i in [1..24]]; print Ordre; Output: Magma V2.10-6 Sat Mar 27 2004 08:12:17 on modular [Seed = 3505777951] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] Total time: 3.009 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 08:12:52 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [Order(lista[i]) : i in [1..24]]; print Ordre; Output: Magma V2.10-6 Sat Mar 27 2004 08:12:49 on modular [Seed = 3387749478] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] Total time: 2.959 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 08:13:30 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [ : i in [1..24]]; print Ordre; Output: Magma V2.10-6 Sat Mar 27 2004 08:13:27 on modular [Seed = 3214574134] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] >> Ordre:= [ : i in [1..24]]; ^ User error: Identifier 'aplha' has not been declared or assigned >> print Ordre;; ^ User error: Identifier 'Ordre' has not been declared or assigned Total time: 3.029 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 08:14:03 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [ : i in [1..24]]; print Ordre; Output: Magma V2.10-6 Sat Mar 27 2004 08:14:00 on modular [Seed = 3046149075] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ , , , , , <3, 24>, , , , , , <4, 24>, , , , , , <2, 24>, , , , , , <1, 24> ] Total time: 3.089 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 08:14:42 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i,Order(lista[i]]> : i in [1..24]]; print Ordre; Output: Magma V2.10-6 Sat Mar 27 2004 08:14:39 on modular [Seed = 2861536491] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] >> Ordre:= [[alpha^i,Order(lista[i]]> : i in [1..24]]; ^ User error: bad syntax >> print Ordre;; ^ User error: Identifier 'Ordre' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 08:15:21 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i,Order(lista[i])]> : i in [1..24]]; print Ordre; Output: Magma V2.10-6 Sat Mar 27 2004 08:15:18 on modular [Seed = 2679808391] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] >> Ordre:= [[alpha^i,Order(lista[i])]> : i in [1..24]]; ^ User error: bad syntax >> print Ordre;; ^ User error: Identifier 'Ordre' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 08:15:48 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[alpha^i,Order(lista[i])] : i in [1..24]]; print Ordre; Output: Magma V2.10-6 Sat Mar 27 2004 08:15:45 on modular [Seed = 2494671467] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ alpha, 1 ], [ alpha^2, 4 ], [ alpha^3, 2 ], [ alpha^4, 3 ], [ alpha^5, 1 ], [ 3, 4 ], [ alpha^7, 4 ], [ alpha^8, 4 ], [ alpha^9, 3 ], [ alpha^10, 3 ], [ alpha^11, 2 ], [ 4, 4 ], [ alpha^13, 2 ], [ alpha^14, 4 ], [ alpha^15, 2 ], [ alpha^16, 3 ], [ alpha^17, 3 ], [ 2, 4 ], [ alpha^19, 4 ], [ alpha^20, 4 ], [ alpha^21, 1 ], [ alpha^22, 3 ], [ alpha^23, 2 ], [ 1, 4 ] ] Total time: 3.019 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 08:16:21 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[] : i in [1..24]]; print Ordre; Output: Magma V2.10-6 Sat Mar 27 2004 08:16:18 on modular [Seed = 2343482711] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ ], [ ], [ ], [ ], [ ], [ <3, 24> ], [ ], [ ], [ ], [ ], [ ], [ <4, 24> ], [ ], [ ], [ ], [ ], [ ], [ <2, 24> ], [ ], [ ], [ ], [ ], [ ], [ <1, 24> ] ] Total time: 2.949 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 08:19:30 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[] : i in [0..24]]; print Ordre; Output: Magma V2.10-6 Sat Mar 27 2004 08:19:27 on modular [Seed = 2136621151] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] >> Ordre:= [[] : i in [0..24]]; ^ Runtime error in '[]': Sequence element 0 not defined >> print Ordre;; ^ User error: Identifier 'Ordre' has not been declared or assigned Total time: 3.029 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 08:20:24 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[<0,0>] cat [] : i in [1..24]]; print Ordre; Output: Magma V2.10-6 Sat Mar 27 2004 08:20:21 on modular [Seed = 1867141253] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ <0, 0>, ], [ <0, 0>, ], [ <0, 0>, ], [ <0, 0>, ], [ <0, 0>, ], [ <0, 0>, <3, 24> ], [ <0, 0>, ], [ <0, 0>, ], [ <0, 0>, ], [ <0, 0>, ], [ <0, 0>, ], [ <0, 0>, <4, 24> ], [ <0, 0>, ], [ <0, 0>, ], [ <0, 0>, ], [ <0, 0>, ], [ <0, 0>, ], [ <0, 0>, <2, 24> ], [ <0, 0>, ], [ <0, 0>, ], [ <0, 0>, ], [ <0, 0>, ], [ <0, 0>, ], [ <0, 0>, <1, 24> ] ] Total time: 3.039 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 08:21:44 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[] : i in [1..24]]; print Ordre; IsPrimitive (alpha^2); Output: Magma V2.10-6 Sat Mar 27 2004 08:21:41 on modular [Seed = 1698716415] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ ], [ ], [ ], [ ], [ ], [ <3, 24> ], [ ], [ ], [ ], [ ], [ ], [ <4, 24> ], [ ], [ ], [ ], [ ], [ ], [ <2, 24> ], [ ], [ ], [ ], [ ], [ ], [ <1, 24> ] ] false Total time: 3.009 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 08:22:38 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[] : i in [1..24]]; print Ordre; IsPrimitive (alpha^2); Order (alpha); Output: Magma V2.10-6 Sat Mar 27 2004 08:22:35 on modular [Seed = 1551473720] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ ], [ ], [ ], [ ], [ ], [ <3, 24> ], [ ], [ ], [ ], [ ], [ ], [ <4, 24> ], [ ], [ ], [ ], [ ], [ ], [ <2, 24> ], [ ], [ ], [ ], [ ], [ ], [ <1, 24> ] ] false 24 Total time: 2.979 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 08:24:13 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[] : i in [1..24]]; print Ordre; IsPrimitive (alpha^2); Order (alpha); Output: Magma V2.10-6 Sat Mar 27 2004 08:24:10 on modular [Seed = 1366593876] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] >> Ordre:= [[] : i in [1..24]]; ^ Runtime error in 'Order': Can not take order of zero element >> print Ordre; ^ User error: Identifier 'Ordre' has not been declared or assigned false 24 Total time: 3.019 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 08:24:54 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[] : i in [1..24]]; print Ordre; IsPrimitive (alpha^2); Order (alpha); Output: Magma V2.10-6 Sat Mar 27 2004 08:24:51 on modular [Seed = 1215137940] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ ], [ ], [ ], [ ], [ ], [ <3, 24> ], [ ], [ ], [ ], [ ], [ ], [ <4, 24> ], [ ], [ ], [ ], [ ], [ ], [ <2, 24> ], [ ], [ ], [ ], [ ], [ ], [ <1, 24> ] ] false 24 Total time: 3.109 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 08:25:23 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[] : i in [2..24]]; print Ordre; IsPrimitive (alpha^2); Order (alpha); Output: Magma V2.10-6 Sat Mar 27 2004 08:25:20 on modular [Seed = 991886212] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ ], [ ], [ ], [ ], [ <3, 24> ], [ ], [ ], [ ], [ ], [ ], [ <4, 24> ], [ ], [ ], [ ], [ ], [ ], [ <2, 24> ], [ ], [ ], [ ], [ ], [ ], [ <1, 24> ] ] false 24 Total time: 3.019 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 08:25:55 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[] : i in [1..24]]; print Ordre; IsPrimitive (alpha^2); Order (alpha); Output: Magma V2.10-6 Sat Mar 27 2004 08:25:52 on modular [Seed = 840430253] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] >> Ordre:= [[] : i in [1..24]]; ^ Runtime error in 'Order': Can not take order of zero element >> print Ordre; ^ User error: Identifier 'Ordre' has not been declared or assigned false 24 Total time: 3.029 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 08:26:44 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no es un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 ]*/ lista:=[x: x in G25]; print lista; Ordre:= [[] : i in [1..23]]; print Ordre; IsPrimitive (alpha^2); Order (alpha); Output: Magma V2.10-6 Sat Mar 27 2004 08:26:41 on modular [Seed = 688711751] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, omega, omega^2, omega^3, 2, omega^5, omega^6, omega^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ ], [ ], [ ], [ ], [ ], [ <3, 4> ], [ ], [ ], [ ], [ ], [ ], [ <4, 2> ], [ ], [ ], [ ], [ ], [ ], [ <2, 4> ], [ ], [ ], [ ], [ ], [ ] ] false 24 Total time: 3.049 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 09:37:12 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no és un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, gamma, gamma^2, gamma^3, 2, gamma^5, gamma^6, gamma^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ /*EXERCICI 1.iv*/ lista:=[x: x in G25]; print lista; /*[ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] */ Ordre:= [[] : i in [1..23]]; print Ordre; /* [ [ ], [ ], [ ], [ ], [ ], [ <3, 4> ], [ ], [ ], [ ], [ ], [ ], [ <4, 2> ], [ ], [ ], [ ], [ ], [ ], [ <2, 4> ], [ ], [ ], [ ], [ ], [ ] ] */ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ /* Podem comprovar que els elements primitius d'un cos són aquells que el seu ordre és 24 */ cardinal:= # lista_primitius_G25; cardinal; /*8*/ /*un cos de p^n te phi(p^n-1) elements primitius*/ /*Si apliquem la fòrmula al nostre cas: */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ /*EXERCICI 1.V*/ lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); Output: Magma V2.10-6 Sat Mar 27 2004 09:37:09 on modular [Seed = 2528331644] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, gamma, gamma^2, gamma^3, 2, gamma^5, gamma^6, gamma^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ ], [ ], [ ], [ ], [ ], [ <3, 24> ], [ ], [ ], [ ], [ ], [ ], [ <4, 24> ], [ ], [ ], [ ], [ ], [ ], [ <2, 24> ], [ ], [ ], [ ], [ ], [ ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] Total time: 3.039 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 09:38:09 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no és un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, gamma, gamma^2, gamma^3, 2, gamma^5, gamma^6, gamma^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ /*EXERCICI 1.iv*/ lista:=[x: x in G25]; print lista; /*[ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] */ Ordre:= [[] : i in [1..23]]; print Ordre; /* [ [ ], [ ], [ ], [ ], [ ], [ <3, 4> ], [ ], [ ], [ ], [ ], [ ], [ <4, 2> ], [ ], [ ], [ ], [ ], [ ], [ <2, 4> ], [ ], [ ], [ ], [ ], [ ] ] */ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ /* Podem comprovar que els elements primitius d'un cos són aquells que el seu ordre és 24 */ cardinal:= # lista_primitius_G25; cardinal; /*8*/ /*un cos de p^n te phi(p^n-1) elements primitius*/ /*Si apliquem la fòrmula al nostre cas: */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ /*EXERCICI 1.V*/ lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; Output: Magma V2.10-6 Sat Mar 27 2004 09:38:06 on modular [Seed = 2309773368] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, gamma, gamma^2, gamma^3, 2, gamma^5, gamma^6, gamma^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ ], [ ], [ ], [ ], [ ], [ <3, 24> ], [ ], [ ], [ ], [ ], [ ], [ <4, 24> ], [ ], [ ], [ ], [ ], [ ], [ <2, 24> ], [ ], [ ], [ ], [ ], [ ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 Total time: 3.019 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 09:40:44 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no és un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, gamma, gamma^2, gamma^3, 2, gamma^5, gamma^6, gamma^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ /*EXERCICI 1.iv*/ lista:=[x: x in G25]; print lista; /*[ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] */ Ordre:= [[] : i in [1..23]]; print Ordre; /* [ [ ], [ ], [ ], [ ], [ ], [ <3, 4> ], [ ], [ ], [ ], [ ], [ ], [ <4, 2> ], [ ], [ ], [ ], [ ], [ ], [ <2, 4> ], [ ], [ ], [ ], [ ], [ ] ] */ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ /* Podem comprovar que els elements primitius d'un cos són aquells que el seu ordre és 24 */ cardinal:= # lista_primitius_G25; cardinal; /*8*/ /*un cos de p^n te phi(p^n-1) elements primitius*/ /*Si apliquem la fòrmula al nostre cas: */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ /*EXERCICI 1.V*/ lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; Roots (polinomi, G25); Evaluate (polinomi, alpha); Output: Magma V2.10-6 Sat Mar 27 2004 09:40:41 on modular [Seed = 170907747] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, gamma, gamma^2, gamma^3, 2, gamma^5, gamma^6, gamma^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ ], [ ], [ ], [ ], [ ], [ <3, 24> ], [ ], [ ], [ ], [ ], [ ], [ <4, 24> ], [ ], [ ], [ ], [ ], [ ], [ <2, 24> ], [ ], [ ], [ ], [ ], [ ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 [ , ] 0 Total time: 3.039 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 09:43:23 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no és un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, gamma, gamma^2, gamma^3, 2, gamma^5, gamma^6, gamma^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ /*EXERCICI 1.iv*/ lista:=[x: x in G25]; print lista; /*[ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] */ Ordre:= [[] : i in [1..23]]; print Ordre; /* [ [ ], [ ], [ ], [ ], [ ], [ <3, 4> ], [ ], [ ], [ ], [ ], [ ], [ <4, 2> ], [ ], [ ], [ ], [ ], [ ], [ <2, 4> ], [ ], [ ], [ ], [ ], [ ] ] */ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ /* Podem comprovar que els elements primitius d'un cos són aquells que el seu ordre és 24 */ cardinal:= # lista_primitius_G25; cardinal; /*8*/ /*un cos de p^n te phi(p^n-1) elements primitius*/ /*Si apliquem la fòrmula al nostre cas: */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ /*EXERCICI 1.V*/ lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; Evaluate (polinomi, alpha); IsIrreducible (polinomi, G25); Output: Magma V2.10-6 Sat Mar 27 2004 09:43:19 on modular [Seed = 355517981] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, gamma, gamma^2, gamma^3, 2, gamma^5, gamma^6, gamma^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ ], [ ], [ ], [ ], [ ], [ <3, 24> ], [ ], [ ], [ ], [ ], [ ], [ <4, 24> ], [ ], [ ], [ ], [ ], [ ], [ <2, 24> ], [ ], [ ], [ ], [ ], [ ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 0 >> IsIrreducible (polinomi, G25);; ^ Runtime error in 'IsIrreducible': Bad argument types Argument types given: RngUPolElt, FldFin Total time: 3.029 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 09:43:47 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no és un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, gamma, gamma^2, gamma^3, 2, gamma^5, gamma^6, gamma^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ /*EXERCICI 1.iv*/ lista:=[x: x in G25]; print lista; /*[ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] */ Ordre:= [[] : i in [1..23]]; print Ordre; /* [ [ ], [ ], [ ], [ ], [ ], [ <3, 4> ], [ ], [ ], [ ], [ ], [ ], [ <4, 2> ], [ ], [ ], [ ], [ ], [ ], [ <2, 4> ], [ ], [ ], [ ], [ ], [ ] ] */ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ /* Podem comprovar que els elements primitius d'un cos són aquells que el seu ordre és 24 */ cardinal:= # lista_primitius_G25; cardinal; /*8*/ /*un cos de p^n te phi(p^n-1) elements primitius*/ /*Si apliquem la fòrmula al nostre cas: */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ /*EXERCICI 1.V*/ lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; Evaluate (polinomi, alpha); IsIrreducible (polinomi); Output: Magma V2.10-6 Sat Mar 27 2004 09:43:44 on modular [Seed = 507235646] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, gamma, gamma^2, gamma^3, 2, gamma^5, gamma^6, gamma^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ ], [ ], [ ], [ ], [ ], [ <3, 24> ], [ ], [ ], [ ], [ ], [ ], [ <4, 24> ], [ ], [ ], [ ], [ ], [ ], [ <2, 24> ], [ ], [ ], [ ], [ ], [ ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 0 true Total time: 2.979 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 09:52:59 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no és un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, gamma, gamma^2, gamma^3, 2, gamma^5, gamma^6, gamma^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ /*EXERCICI 1.iv*/ lista:=[x: x in G25]; print lista; /*[ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] */ Ordre:= [[] : i in [1..23]]; print Ordre; /* [ [ ], [ ], [ ], [ ], [ ], [ <3, 4> ], [ ], [ ], [ ], [ ], [ ], [ <4, 2> ], [ ], [ ], [ ], [ ], [ ], [ <2, 4> ], [ ], [ ], [ ], [ ], [ ] ] */ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ /* Podem comprovar que els elements primitius d'un cos són aquells que el seu ordre és 24 */ cardinal:= # lista_primitius_G25; cardinal; /*8*/ /*un cos de p^n te phi(p^n-1) elements primitius*/ /*Si apliquem la fòrmula al nostre cas: */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ /*EXERCICI 1.V*/ lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*Podem comprovar que el polinomi mínim d'alpha és aquest, ja que és el polinomi que té com arrel alpha i a més és irreductible a Z5*/ Evaluate (polinomi, alpha); /*0*/ IsIrreducible (polinomi, G25); /*true*/ /*El grau del polinomi és 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ /*EXERCICI 1.vi*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ IsInvertible (pol); /*true alpha ^11*/ /*El polinomi és invertible,per tant té invers i és alpha^11*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; /* [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] */ /*EXERCICI 1.vii*/ /*considerem alpha un element primitiu del cos*/ Taula := function (p,n) llista1 := [<0,[0,0]>]; for i:=0 to (p^n)-2 do llista2 :=[]; llista1 := llista1 cat llista2; end for; return llista1; end function; Taula (2,4); /* [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , ] */ Taula (5,2); /* [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , ] */ /*EXERCICI 1.viii*/ G2 := GF(2); [x : x in G2]; /*[ 0, 1 ]*/ G4 := GF (4); [x : x in G4]; /*[ 1, G4.1, G4.1^2, 0 ]*/ G8 := GF (8); [x : x in G8]; /*[ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ]*/ G16b := GF (16); [x : x in G16b]; /*[ 1, G16b.1, G16b.1^2, G16b.1^3, G16b.1^4, G16b.1^5, G16b.1^6, G16b.1^7, G16b.1^8, G16b.1^9, G16b.1^10, G16b.1^11, G16b.1^12, G16b.1^13, G16b.1^14, 0 ]*/ G2 subset G4; /*true*/ G2 subset G8; /*true*/ G2 subset G16b; /*true*/ G4 subset G2; /*false*/ G4 subset G8; /*false*/ G4 subset G16b; /*true*/ G8 subset G2; /*false*/ G8 subset G4; /*false*/ G8 subset G16b; /*false*/ G16b subset G2; /*false*/ G16b subset G4; /*false*/ G16b subset G8; /*false*/ /*G2 és un subcos de G4, G8 i G16b*/ /*G4 és un subcos de G16b*/ /*EXERCICI 2.i*/ P := PolynomialRing (G25); IsFinite (P); /*false*/ /*EXERCICI 2.ii*/ /*Mirem la llista d'elements primitius del cossos*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ G5 := GF(5); lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; Output: Magma V2.10-6 Sat Mar 27 2004 09:52:56 on modular [Seed = 941485424] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, gamma, gamma^2, gamma^3, 2, gamma^5, gamma^6, gamma^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ ], [ ], [ ], [ ], [ ], [ <3, 24> ], [ ], [ ], [ ], [ ], [ ], [ <4, 24> ], [ ], [ ], [ ], [ ], [ ], [ <2, 24> ], [ ], [ ], [ ], [ ], [ ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 0 >> IsIrreducible (polinomi, G25); ^ Runtime error in 'IsIrreducible': Bad argument types Argument types given: RngUPolElt, FldFin [ , ] [] alpha^13 true alpha^11 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , ] [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , ] [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16b.1, G16b.1^2, G16b.1^3, G16b.1^4, G16b.1^5, G16b.1^6, G16b.1^7, G16b.1^8, G16b.1^9, G16b.1^10, G16b.1^11, G16b.1^12, G16b.1^13, G16b.1^14, 0 ] true true true false false true false false false false false false false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] Total time: 3.109 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 09:54:11 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no és un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, gamma, gamma^2, gamma^3, 2, gamma^5, gamma^6, gamma^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ /*EXERCICI 1.iv*/ lista:=[x: x in G25]; print lista; /*[ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] */ Ordre:= [[] : i in [1..23]]; print Ordre; /* [ [ ], [ ], [ ], [ ], [ ], [ <3, 4> ], [ ], [ ], [ ], [ ], [ ], [ <4, 2> ], [ ], [ ], [ ], [ ], [ ], [ <2, 4> ], [ ], [ ], [ ], [ ], [ ] ] */ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ /* Podem comprovar que els elements primitius d'un cos són aquells que el seu ordre és 24 */ cardinal:= # lista_primitius_G25; cardinal; /*8*/ /*un cos de p^n te phi(p^n-1) elements primitius*/ /*Si apliquem la fòrmula al nostre cas: */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ /*EXERCICI 1.V*/ lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*Podem comprovar que el polinomi mínim d'alpha és aquest, ja que és el polinomi que té com arrel alpha i a més és irreductible a Z5*/ Evaluate (polinomi, alpha); /*0*/ IsIrreducible (polinomi, G25); /*true*/ /*El grau del polinomi és 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ /*EXERCICI 1.vi*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ IsInvertible (pol); /*true alpha ^11*/ /*El polinomi és invertible,per tant té invers i és alpha^11*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; /* [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] */ /*EXERCICI 1.vii*/ /*considerem alpha un element primitiu del cos*/ Taula := function (p,n) llista1 := [<0,[0,0]>]; for i:=0 to (p^n)-2 do llista2 :=[]; llista1 := llista1 cat llista2; end for; return llista1; end function; Taula (2,4); /* [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , ] */ Taula (5,2); /* [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , ] */ /*EXERCICI 1.viii*/ G2 := GF(2); [x : x in G2]; /*[ 0, 1 ]*/ G4 := GF (4); [x : x in G4]; /*[ 1, G4.1, G4.1^2, 0 ]*/ G8 := GF (8); [x : x in G8]; /*[ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ]*/ G16b := GF (16); [x : x in G16b]; /*[ 1, G16b.1, G16b.1^2, G16b.1^3, G16b.1^4, G16b.1^5, G16b.1^6, G16b.1^7, G16b.1^8, G16b.1^9, G16b.1^10, G16b.1^11, G16b.1^12, G16b.1^13, G16b.1^14, 0 ]*/ G2 subset G4; /*true*/ G2 subset G8; /*true*/ G2 subset G16b; /*true*/ G4 subset G2; /*false*/ G4 subset G8; /*false*/ G4 subset G16b; /*true*/ G8 subset G2; /*false*/ G8 subset G4; /*false*/ G8 subset G16b; /*false*/ G16b subset G2; /*false*/ G16b subset G4; /*false*/ G16b subset G8; /*false*/ /*G2 és un subcos de G4, G8 i G16b*/ /*G4 és un subcos de G16b*/ /*EXERCICI 2.i*/ P := PolynomialRing (G25); IsFinite (P); /*false*/ /*EXERCICI 2.ii*/ /*Mirem la llista d'elements primitius del cossos*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ G5 := GF(5); lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; IsPrimitive (beta); Output: Magma V2.10-6 Sat Mar 27 2004 09:54:08 on modular [Seed = 1130796755] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, gamma, gamma^2, gamma^3, 2, gamma^5, gamma^6, gamma^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ ], [ ], [ ], [ ], [ ], [ <3, 24> ], [ ], [ ], [ ], [ ], [ ], [ <4, 24> ], [ ], [ ], [ ], [ ], [ ], [ <2, 24> ], [ ], [ ], [ ], [ ], [ ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 0 >> IsIrreducible (polinomi, G25); ^ Runtime error in 'IsIrreducible': Bad argument types Argument types given: RngUPolElt, FldFin [ , ] [] alpha^13 true alpha^11 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , ] [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , ] [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16b.1, G16b.1^2, G16b.1^3, G16b.1^4, G16b.1^5, G16b.1^6, G16b.1^7, G16b.1^8, G16b.1^9, G16b.1^10, G16b.1^11, G16b.1^12, G16b.1^13, G16b.1^14, 0 ] true true true false false true false false false false false false false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] false Total time: 2.999 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 09:57:26 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no és un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, gamma, gamma^2, gamma^3, 2, gamma^5, gamma^6, gamma^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ /*EXERCICI 1.iv*/ lista:=[x: x in G25]; print lista; /*[ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] */ Ordre:= [[] : i in [1..23]]; print Ordre; /* [ [ ], [ ], [ ], [ ], [ ], [ <3, 4> ], [ ], [ ], [ ], [ ], [ ], [ <4, 2> ], [ ], [ ], [ ], [ ], [ ], [ <2, 4> ], [ ], [ ], [ ], [ ], [ ] ] */ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ /* Podem comprovar que els elements primitius d'un cos són aquells que el seu ordre és 24 */ cardinal:= # lista_primitius_G25; cardinal; /*8*/ /*un cos de p^n te phi(p^n-1) elements primitius*/ /*Si apliquem la fòrmula al nostre cas: */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ /*EXERCICI 1.V*/ lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*Podem comprovar que el polinomi mínim d'alpha és aquest, ja que és el polinomi que té com arrel alpha i a més és irreductible a Z5*/ Evaluate (polinomi, alpha); /*0*/ IsIrreducible (polinomi, G25); /*true*/ /*El grau del polinomi és 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ /*EXERCICI 1.vi*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ IsInvertible (pol); /*true alpha ^11*/ /*El polinomi és invertible,per tant té invers i és alpha^11*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; /* [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] */ /*EXERCICI 1.vii*/ /*considerem alpha un element primitiu del cos*/ Taula := function (p,n) llista1 := [<0,[0,0]>]; for i:=0 to (p^n)-2 do llista2 :=[]; llista1 := llista1 cat llista2; end for; return llista1; end function; Taula (2,4); /* [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , ] */ Taula (5,2); /* [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , ] */ /*EXERCICI 1.viii*/ G2 := GF(2); [x : x in G2]; /*[ 0, 1 ]*/ G4 := GF (4); [x : x in G4]; /*[ 1, G4.1, G4.1^2, 0 ]*/ G8 := GF (8); [x : x in G8]; /*[ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ]*/ G16b := GF (16); [x : x in G16b]; /*[ 1, G16b.1, G16b.1^2, G16b.1^3, G16b.1^4, G16b.1^5, G16b.1^6, G16b.1^7, G16b.1^8, G16b.1^9, G16b.1^10, G16b.1^11, G16b.1^12, G16b.1^13, G16b.1^14, 0 ]*/ G2 subset G4; /*true*/ G2 subset G8; /*true*/ G2 subset G16b; /*true*/ G4 subset G2; /*false*/ G4 subset G8; /*false*/ G4 subset G16b; /*true*/ G8 subset G2; /*false*/ G8 subset G4; /*false*/ G8 subset G16b; /*false*/ G16b subset G2; /*false*/ G16b subset G4; /*false*/ G16b subset G8; /*false*/ /*G2 és un subcos de G4, G8 i G16b*/ /*G4 és un subcos de G16b*/ /*EXERCICI 2.i*/ P := PolynomialRing (G25); IsFinite (P); /*false*/ /*EXERCICI 2.ii*/ /*Mirem la llista d'elements primitius del cossos*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ G5 := GF(5); lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; IsPrimitive (beta); beta:= 2; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; /*EXERCICI 2.iii*/ suma := p1 + p2; suma; /*x^2 + alpha^19*x + alpha^9*/ producte := p1 * p2; producte; /*alpha*x^3 + alpha^9*x^2 + alpha^10*x + alpha^2*/ /*EXERCICI 2.iv*/ quocient := p1 div p2; quocient; /*alpha^23*x + alpha^21*/ residu := p1 mod p2; residu; /* alpha*/ /*EXERCICI 2.v*/ mcd := GCD (p1,p2); mcd; /*1 */ mcm := LCM (p1,p2); mcm; /*x^3 + alpha^8*x^2 + alpha^9*x + alpha*/ /*p1 i p2 són coprimers, ja que el maxim comu divisor es 1*/ Output: Magma V2.10-6 Sat Mar 27 2004 09:57:22 on modular [Seed = 1366591235] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, gamma, gamma^2, gamma^3, 2, gamma^5, gamma^6, gamma^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ ], [ ], [ ], [ ], [ ], [ <3, 24> ], [ ], [ ], [ ], [ ], [ ], [ <4, 24> ], [ ], [ ], [ ], [ ], [ ], [ <2, 24> ], [ ], [ ], [ ], [ ], [ ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 0 >> IsIrreducible (polinomi, G25); ^ Runtime error in 'IsIrreducible': Bad argument types Argument types given: RngUPolElt, FldFin [ , ] [] alpha^13 true alpha^11 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , ] [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , ] [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16b.1, G16b.1^2, G16b.1^3, G16b.1^4, G16b.1^5, G16b.1^6, G16b.1^7, G16b.1^8, G16b.1^9, G16b.1^10, G16b.1^11, G16b.1^12, G16b.1^13, G16b.1^14, 0 ] true true true false false true false false false false false false false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] false 2*x^2 + alpha^19*x + alpha^9 alpha^19*x^3 + alpha^22*x^2 + alpha^10*x + alpha^2 alpha^17*x + alpha^5 alpha^15 1 x^3 + alpha^3*x^2 + alpha^15*x + alpha^7 Total time: 3.059 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Sat Mar 27 10:00:42 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no és un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, gamma, gamma^2, gamma^3, 2, gamma^5, gamma^6, gamma^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ /*EXERCICI 1.iv*/ lista:=[x: x in G25]; print lista; /*[ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] */ Ordre:= [[] : i in [1..23]]; print Ordre; /* [ [ ], [ ], [ ], [ ], [ ], [ <3, 4> ], [ ], [ ], [ ], [ ], [ ], [ <4, 2> ], [ ], [ ], [ ], [ ], [ ], [ <2, 4> ], [ ], [ ], [ ], [ ], [ ] ] */ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ /* Podem comprovar que els elements primitius d'un cos són aquells que el seu ordre és 24 */ cardinal:= # lista_primitius_G25; cardinal; /*8*/ /*un cos de p^n te phi(p^n-1) elements primitius*/ /*Si apliquem la fòrmula al nostre cas: */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ /*EXERCICI 1.V*/ lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*Podem comprovar que el polinomi mínim d'alpha és aquest, ja que és el polinomi que té com arrel alpha i a més és irreductible a Z5*/ Evaluate (polinomi, alpha); /*0*/ IsIrreducible (polinomi, G25); /*true*/ /*El grau del polinomi és 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ /*EXERCICI 1.vi*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ IsInvertible (pol); /*true alpha ^11*/ /*El polinomi és invertible,per tant té invers i és alpha^11*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; /* [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] */ /*EXERCICI 1.vii*/ /*considerem alpha un element primitiu del cos*/ Taula := function (p,n) llista1 := [<0,[0,0]>]; for i:=0 to (p^n)-2 do llista2 :=[]; llista1 := llista1 cat llista2; end for; return llista1; end function; Taula (2,4); /* [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , ] */ Taula (5,2); /* [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , ] */ /*EXERCICI 1.viii*/ G2 := GF(2); [x : x in G2]; /*[ 0, 1 ]*/ G4 := GF (4); [x : x in G4]; /*[ 1, G4.1, G4.1^2, 0 ]*/ G8 := GF (8); [x : x in G8]; /*[ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ]*/ G16b := GF (16); [x : x in G16b]; /*[ 1, G16b.1, G16b.1^2, G16b.1^3, G16b.1^4, G16b.1^5, G16b.1^6, G16b.1^7, G16b.1^8, G16b.1^9, G16b.1^10, G16b.1^11, G16b.1^12, G16b.1^13, G16b.1^14, 0 ]*/ G2 subset G4; /*true*/ G2 subset G8; /*true*/ G2 subset G16b; /*true*/ G4 subset G2; /*false*/ G4 subset G8; /*false*/ G4 subset G16b; /*true*/ G8 subset G2; /*false*/ G8 subset G4; /*false*/ G8 subset G16b; /*false*/ G16b subset G2; /*false*/ G16b subset G4; /*false*/ G16b subset G8; /*false*/ /*G2 és un subcos de G4, G8 i G16b*/ /*G4 és un subcos de G16b*/ /*EXERCICI 2.i*/ P := PolynomialRing (G25); IsFinite (P); /*false*/ /*EXERCICI 2.ii*/ /*Mirem la llista d'elements primitius del cossos*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ G5 := GF(5); lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; IsPrimitive (beta); beta:= 2; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; /*EXERCICI 2.iii*/ suma := p1 + p2; suma; /*x^2 + alpha^19*x + alpha^9*/ producte := p1 * p2; producte; /*alpha*x^3 + alpha^9*x^2 + alpha^10*x + alpha^2*/ /*EXERCICI 2.iv*/ quocient := p1 div p2; quocient; /*alpha^23*x + alpha^21*/ residu := p1 mod p2; residu; /* alpha*/ /*EXERCICI 2.v*/ mcd := GCD (p1,p2); mcd; /*1 */ mcm := LCM (p1,p2); mcm; /*x^3 + alpha^8*x^2 + alpha^9*x + alpha*/ /*p1 i p2 són coprimers, ja que el maxim comu divisor es 1*/ XGCD(p1,p2); Output: Magma V2.10-6 Sat Mar 27 2004 10:00:39 on modular [Seed = 1648866677] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, gamma, gamma^2, gamma^3, 2, gamma^5, gamma^6, gamma^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ ], [ ], [ ], [ ], [ ], [ <3, 24> ], [ ], [ ], [ ], [ ], [ ], [ <4, 24> ], [ ], [ ], [ ], [ ], [ ], [ <2, 24> ], [ ], [ ], [ ], [ ], [ ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 0 >> IsIrreducible (polinomi, G25); ^ Runtime error in 'IsIrreducible': Bad argument types Argument types given: RngUPolElt, FldFin [ , ] [] alpha^13 true alpha^11 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , ] [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , ] [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16b.1, G16b.1^2, G16b.1^3, G16b.1^4, G16b.1^5, G16b.1^6, G16b.1^7, G16b.1^8, G16b.1^9, G16b.1^10, G16b.1^11, G16b.1^12, G16b.1^13, G16b.1^14, 0 ] true true true false false true false false false false false false false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] false 2*x^2 + alpha^19*x + alpha^9 alpha^19*x^3 + alpha^22*x^2 + alpha^10*x + alpha^2 alpha^17*x + alpha^5 alpha^15 1 x^3 + alpha^3*x^2 + alpha^15*x + alpha^7 1 alpha^9 alpha^14*x + alpha^2 Total time: 3.159 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Sat Mar 27 11:41:50 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; L := [x^27 *y^13]; HomogeneousModuleTestBasis(P, S, L ) ; Output: Magma V2.10-6 Sat Mar 27 2004 11:41:46 on modular [Seed = 1008325367] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] [] Total time: 3.589 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Sat Mar 27 11:43:38 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; L := [x^7 *y^13]; HomogeneousModuleTestBasis(P, S, L ) ; Output: Magma V2.10-6 Sat Mar 27 2004 11:43:35 on modular [Seed = 1180936560] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] [] Total time: 3.629 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Sat Mar 27 11:44:22 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; L := [x^27 *y^19]; HomogeneousModuleTestBasis(P, S, L ) ; Output: Magma V2.10-6 Sat Mar 27 2004 11:44:18 on modular [Seed = 1349893939] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] [] Total time: 3.589 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Sat Mar 27 11:44:54 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; L := [x^30 *y^13]; HomogeneousModuleTestBasis(P, S, L ) ; Output: Magma V2.10-6 Sat Mar 27 2004 11:44:50 on modular [Seed = 1535030488] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] [] Total time: 3.669 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Sat Mar 27 11:45:19 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; L := [x^26 *y^13]; HomogeneousModuleTestBasis(P, S, L ) ; Output: Magma V2.10-6 Sat Mar 27 2004 11:45:15 on modular [Seed = 1715702268] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] [] Total time: 3.609 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Sat Mar 27 11:46:50 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S; L := [x^26 *y^13]; HomogeneousModuleTestBasis(P, S, L ) ; Output: Magma V2.10-6 Sat Mar 27 2004 11:46:46 on modular [Seed = 1884659590] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] [ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, y^11, y^12, y^13, y^14, y^15, y^16, y^17, y^18, y^19, y^20, y^21, y^22, y^23, y^24, y^25, y^26, y^27, y^28, y^29, y^30, y^31, y^32, y^33, y^34, y^35, y^36, y^37, y^38, y^39, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x*y^11, x*y^12, x*y^13, x*y^14, x*y^15, x*y^16, x*y^17, x*y^18, x*y^19, x*y^20, x*y^21, x*y^22, x*y^23, x*y^24, x*y^25, x*y^26, x*y^27, x*y^28, x*y^29, x*y^30, x*y^31, x*y^32, x*y^33, x*y^34, x*y^35, x*y^36, x*y^37, x*y^38, x*y^39, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^2*y^11, x^2*y^12, x^2*y^13, x^2*y^14, x^2*y^15, x^2*y^16, x^2*y^17, x^2*y^18, x^2*y^19, x^2*y^20, x^2*y^21, x^2*y^22, x^2*y^23, x^2*y^24, x^2*y^25, x^2*y^26, x^2*y^27, x^2*y^28, x^2*y^29, x^2*y^30, x^2*y^31, x^2*y^32, x^2*y^33, x^2*y^34, x^2*y^35, x^2*y^36, x^2*y^37, x^2*y^38, x^2*y^39, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^3*y^13, x^3*y^14, x^3*y^15, x^3*y^16, x^3*y^17, x^3*y^18, x^3*y^19, x^3*y^20, x^3*y^21, x^3*y^22, x^3*y^23, x^3*y^24, x^3*y^25, x^3*y^26, x^3*y^27, x^3*y^28, x^3*y^29, x^3*y^30, x^3*y^31, x^3*y^32, x^3*y^33, x^3*y^34, x^3*y^35, x^3*y^36, x^3*y^37, x^3*y^38, x^3*y^39, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^4*y^15, x^4*y^16, x^4*y^17, x^4*y^18, x^4*y^19, x^4*y^20, x^4*y^21, x^4*y^22, x^4*y^23, x^4*y^24, x^4*y^25, x^4*y^26, x^4*y^27, x^4*y^28, x^4*y^29, x^4*y^30, x^4*y^31, x^4*y^32, x^4*y^33, x^4*y^34, x^4*y^35, x^4*y^36, x^4*y^37, x^4*y^38, x^4*y^39, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^5*y^15, x^5*y^16, x^5*y^17, x^5*y^18, x^5*y^19, x^5*y^20, x^5*y^21, x^5*y^22, x^5*y^23, x^5*y^24, x^5*y^25, x^5*y^26, x^5*y^27, x^5*y^28, x^5*y^29, x^5*y^30, x^5*y^31, x^5*y^32, x^5*y^33, x^5*y^34, x^5*y^35, x^5*y^36, x^5*y^37, x^5*y^38, x^5*y^39, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^6*y^15, x^6*y^16, x^6*y^17, x^6*y^18, x^6*y^19, x^6*y^20, x^6*y^21, x^6*y^22, x^6*y^23, x^6*y^24, x^6*y^25, x^6*y^26, x^6*y^27, x^6*y^28, x^6*y^29, x^6*y^30, x^6*y^31, x^6*y^32, x^6*y^33, x^6*y^34, x^6*y^35, x^6*y^36, x^6*y^37, x^6*y^38, x^6*y^39, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^7*y^15, x^7*y^16, x^7*y^17, x^7*y^18, x^7*y^19, x^7*y^20, x^7*y^21, x^7*y^22, x^7*y^23, x^7*y^24, x^7*y^25, x^7*y^26, x^7*y^27, x^7*y^28, x^7*y^29, x^7*y^30, x^7*y^31, x^7*y^32, x^7*y^33, x^7*y^34, x^7*y^35, x^7*y^36, x^7*y^37, x^7*y^38, x^7*y^39, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^8*y^7, x^8*y^8, x^8*y^9, x^8*y^10, x^8*y^11, x^8*y^12, x^8*y^13, x^8*y^14, x^8*y^15, x^8*y^16, x^8*y^17, x^8*y^18, x^8*y^19, x^8*y^20, x^8*y^21, x^8*y^22, x^8*y^23, x^8*y^24, x^8*y^25, x^8*y^26, x^8*y^27, x^8*y^28, x^8*y^29, x^8*y^30, x^8*y^31, x^8*y^32, x^8*y^33, x^8*y^34, x^8*y^35, x^8*y^36, x^8*y^37, x^8*y^38, x^8*y^39, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^9*y^7, x^9*y^8, x^9*y^9, x^9*y^10, x^9*y^11, x^9*y^12, x^9*y^13, x^9*y^14, x^9*y^15, x^9*y^16, x^9*y^17, x^9*y^18, x^9*y^19, x^9*y^20, x^9*y^21, x^9*y^22, x^9*y^23, x^9*y^24, x^9*y^25, x^9*y^26, x^9*y^27, x^9*y^28, x^9*y^29, x^9*y^30, x^9*y^31, x^9*y^32, x^9*y^33, x^9*y^34, x^9*y^35, x^9*y^36, x^9*y^37, x^9*y^38, x^9*y^39, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^10*y^7, x^10*y^8, x^10*y^9, x^10*y^10, x^10*y^11, x^10*y^12, x^10*y^13, x^10*y^14, x^10*y^15, x^10*y^16, x^10*y^17, x^10*y^18, x^10*y^19, x^10*y^20, x^10*y^21, x^10*y^22, x^10*y^23, x^10*y^24, x^10*y^25, x^10*y^26, x^10*y^27, x^10*y^28, x^10*y^29, x^10*y^30, x^10*y^31, x^10*y^32, x^10*y^33, x^10*y^34, x^10*y^35, x^10*y^36, x^10*y^37, x^10*y^38, x^10*y^39, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^11*y^5, x^11*y^6, x^11*y^7, x^11*y^8, x^11*y^9, x^11*y^10, x^11*y^11, x^11*y^12, x^11*y^13, x^11*y^14, x^11*y^15, x^11*y^16, x^11*y^17, x^11*y^18, x^11*y^19, x^11*y^20, x^11*y^21, x^11*y^22, x^11*y^23, x^11*y^24, x^11*y^25, x^11*y^26, x^11*y^27, x^11*y^28, x^11*y^29, x^11*y^30, x^11*y^31, x^11*y^32, x^11*y^33, x^11*y^34, x^11*y^35, x^11*y^36, x^11*y^37, x^11*y^38, x^11*y^39, x^12, x^12*y, x^12*y^2, x^12*y^3, x^12*y^4, x^12*y^5, x^12*y^6, x^12*y^7, x^12*y^8, x^12*y^9, x^12*y^10, x^12*y^11, x^12*y^12, x^12*y^13, x^12*y^14, x^12*y^15, x^12*y^16, x^12*y^17, x^12*y^18, x^12*y^19, x^12*y^20, x^12*y^21, x^12*y^22, x^12*y^23, x^12*y^24, x^12*y^25, x^12*y^26, x^12*y^27, x^12*y^28, x^12*y^29, x^12*y^30, x^12*y^31, x^12*y^32, x^12*y^33, x^12*y^34, x^12*y^35, x^12*y^36, x^12*y^37, x^12*y^38, x^12*y^39, x^13, x^13*y, x^13*y^2, x^13*y^3, x^13*y^4, x^13*y^5, x^13*y^6, x^13*y^7, x^13*y^8, x^13*y^9, x^13*y^10, x^13*y^11, x^13*y^12, x^13*y^13, x^13*y^14, x^13*y^15, x^13*y^16, x^13*y^17, x^13*y^18, x^13*y^19, x^13*y^20, x^13*y^21, x^13*y^22, x^13*y^23, x^13*y^24, x^13*y^25, x^13*y^26, x^13*y^27, x^13*y^28, x^13*y^29, x^13*y^30, x^13*y^31, x^13*y^32, x^13*y^33, x^13*y^34, x^13*y^35, x^13*y^36, x^13*y^37, x^13*y^38, x^13*y^39, x^14, x^14*y, x^14*y^2, x^14*y^3, x^14*y^4, x^14*y^5, x^14*y^6, x^14*y^7, x^14*y^8, x^14*y^9, x^14*y^10, x^14*y^11, x^14*y^12, x^14*y^13, x^14*y^14, x^14*y^15, x^14*y^16, x^14*y^17, x^14*y^18, x^14*y^19, x^14*y^20, x^14*y^21, x^14*y^22, x^14*y^23, x^14*y^24, x^14*y^25, x^14*y^26, x^14*y^27, x^14*y^28, x^14*y^29, x^14*y^30, x^14*y^31, x^14*y^32, x^14*y^33, x^14*y^34, x^14*y^35, x^14*y^36, x^14*y^37, x^14*y^38, x^14*y^39, x^15, x^15*y, x^15*y^2, x^15*y^3, x^15*y^4, x^15*y^5, x^15*y^6, x^15*y^7, x^15*y^8, x^15*y^9, x^15*y^10, x^15*y^11, x^15*y^12, x^15*y^13, x^15*y^14, x^15*y^15, x^15*y^16, x^15*y^17, x^15*y^18, x^15*y^19, x^15*y^20, x^15*y^21, x^15*y^22, x^15*y^23, x^15*y^24, x^15*y^25, x^15*y^26, x^15*y^27, x^15*y^28, x^15*y^29, x^15*y^30, x^15*y^31, x^15*y^32, x^15*y^33, x^15*y^34, x^15*y^35, x^15*y^36, x^15*y^37, x^15*y^38, x^15*y^39, x^16, x^16*y, x^16*y^2, x^16*y^3, x^16*y^4, x^16*y^5, x^16*y^6, x^16*y^7, x^16*y^8, x^16*y^9, x^16*y^10, x^16*y^11, x^16*y^12, x^16*y^13, x^16*y^14, x^16*y^15, x^16*y^16, x^16*y^17, x^16*y^18, x^16*y^19, x^16*y^20, x^16*y^21, x^16*y^22, x^16*y^23, x^16*y^24, x^16*y^25, x^16*y^26, x^16*y^27, x^16*y^28, x^16*y^29, x^16*y^30, x^16*y^31, x^16*y^32, x^16*y^33, x^16*y^34, x^16*y^35, x^16*y^36, x^16*y^37, x^16*y^38, x^16*y^39, x^17, x^17*y, x^17*y^2, x^17*y^3, x^17*y^4, x^17*y^5, x^17*y^6, x^17*y^7, x^17*y^8, x^17*y^9, x^17*y^10, x^17*y^11, x^17*y^12, x^17*y^13, x^17*y^14, x^17*y^15, x^17*y^16, x^17*y^17, x^17*y^18, x^17*y^19, x^17*y^20, x^17*y^21, x^17*y^22, x^17*y^23, x^17*y^24, x^17*y^25, x^17*y^26, x^17*y^27, x^17*y^28, x^17*y^29, x^17*y^30, x^17*y^3 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Sat Mar 27 11:52:37 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; L := [x^26 *y^13]; L subset S; L; HomogeneousModuleTestBasis(P, S, L ) ; Output: Magma V2.10-6 Sat Mar 27 2004 11:52:33 on modular [Seed = 2275571415] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] true [ x^26*y^13 ] [] Total time: 3.649 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Sat Mar 27 11:53:09 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; L := [x^27 *y^13]; L subset S; L; HomogeneousModuleTestBasis(P, S, L ) ; Output: Magma V2.10-6 Sat Mar 27 2004 11:53:05 on modular [Seed = 2393604094] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] false [ x^27*y^13 ] [] Total time: 3.459 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Sat Mar 27 11:53:34 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; L := [x^27 *y^19]; L subset S; L; HomogeneousModuleTestBasis(P, S, L ) ; Output: Magma V2.10-6 Sat Mar 27 2004 11:53:31 on modular [Seed = 2562550034] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] false [ x^27*y^19 ] [] Total time: 3.659 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Sat Mar 27 11:53:56 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; L := [x^28 *y^13]; L subset S; L; HomogeneousModuleTestBasis(P, S, L ) ; Output: Magma V2.10-6 Sat Mar 27 2004 11:53:52 on modular [Seed = 2743489026] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] false [ x^28*y^13 ] [] Total time: 3.599 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Sat Mar 27 11:54:34 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; L := [x^35 *y^13]; L subset S; L; HomogeneousModuleTestBasis(P, S, L ) ; Output: Magma V2.10-6 Sat Mar 27 2004 11:54:30 on modular [Seed = 2911394922] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] false [ x^35*y^13 ] [] Total time: 3.619 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Sat Mar 27 11:54:55 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; L := [x^35 *y^12]; L subset S; L; HomogeneousModuleTestBasis(P, S, L ) ; Output: Magma V2.10-6 Sat Mar 27 2004 11:54:51 on modular [Seed = 3029419374] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] true [ x^35*y^12 ] [] Total time: 3.609 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Sat Mar 27 11:55:47 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; L := [x^36 *y^12]; L subset S; L; HomogeneousModuleTestBasis(P, S, L ) ; Output: Magma V2.10-6 Sat Mar 27 2004 11:55:44 on modular [Seed = 3286643154] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] false [ x^36*y^12 ] [] Total time: 3.669 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Sat Mar 27 11:56:13 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; L := [x^35 *y^12]; L subset S; L; HomogeneousModuleTestBasis(P, S, L ) ; Output: Magma V2.10-6 Sat Mar 27 2004 11:56:09 on modular [Seed = 3404675298] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] true [ x^35*y^12 ] [] Total time: 3.699 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Sat Mar 27 11:56:54 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; L := [x^36 *y^9]; L subset S; L; HomogeneousModuleTestBasis(P, S, L ) ; Output: Magma V2.10-6 Sat Mar 27 2004 11:56:51 on modular [Seed = 3589285767] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] false [ x^36*y^9 ] [] Total time: 3.589 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Sat Mar 27 11:57:17 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; L := [x^36 *y^6]; L subset S; L; HomogeneousModuleTestBasis(P, S, L ) ; Output: Magma V2.10-6 Sat Mar 27 2004 11:57:13 on modular [Seed = 3707317940] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] false [ x^36*y^6 ] [] Total time: 3.659 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Sat Mar 27 11:57:38 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; L := [x^36 *y^3]; L subset S; L; HomogeneousModuleTestBasis(P, S, L ) ; Output: Magma V2.10-6 Sat Mar 27 2004 11:57:34 on modular [Seed = 3871544473] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] true [ x^36*y^3 ] [] Total time: 3.619 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Sat Mar 27 11:57:57 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; L := [x^36 *y^4]; L subset S; L; HomogeneousModuleTestBasis(P, S, L ) ; Output: Magma V2.10-6 Sat Mar 27 2004 11:57:54 on modular [Seed = 4057203554] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] false [ x^36*y^4 ] [] Total time: 3.679 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Sat Mar 27 11:58:48 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; L := [x^37 *y^3]; L subset S; L; HomogeneousModuleTestBasis(P, S, L ) ; Output: Magma V2.10-6 Sat Mar 27 2004 11:58:44 on modular [Seed = 4225632574] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] true [ x^37*y^3 ] [] Total time: 3.579 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Sat Mar 27 11:59:11 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; L := [x^37 *y^4]; L subset S; L; HomogeneousModuleTestBasis(P, S, L ) ; Output: Magma V2.10-6 Sat Mar 27 2004 11:59:07 on modular [Seed = 19198936] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] false [ x^37*y^4 ] [] Total time: 3.609 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Sat Mar 27 11:59:41 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; L := [x^39 *y^2]; L subset S; L; HomogeneousModuleTestBasis(P, S, L ) ; Output: Magma V2.10-6 Sat Mar 27 2004 11:59:37 on modular [Seed = 237763829] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] false [ x^39*y^2 ] [] Total time: 3.649 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Sat Mar 27 11:59:52 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; L := [x^39 *y]; L subset S; L; HomogeneousModuleTestBasis(P, S, L ) ; Output: Magma V2.10-6 Sat Mar 27 2004 11:59:48 on modular [Seed = 389211153] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] false [ x^39*y ] [] Total time: 3.589 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Sat Mar 27 12:00:10 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; L := [x^38 *y]; L subset S; L; HomogeneousModuleTestBasis(P, S, L ) ; Output: Magma V2.10-6 Sat Mar 27 2004 12:00:06 on modular [Seed = 620811825] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] true [ x^38*y ] [] Total time: 3.609 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Sat Mar 27 12:00:23 2004 Input: K := GF(3); R := PolynomialRing(K, [6, 8, 162, 216, 234]); R; P := [z, w, u, y*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9)+y^(1+27)*x^3, x*(u -w*x^3 +z*x^12 -z*y^9 -x^39 +x^27 *y^9 ) +y^3 *(w -z*x^9 +x^36 -y^27 )+x^4*y^27 ] ; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; L := [x^38 *y^3]; L subset S; L; HomogeneousModuleTestBasis(P, S, L ) ; Output: Magma V2.10-6 Sat Mar 27 2004 12:00:20 on modular [Seed = 840417556] ------------------------------------- Graded Polynomial ring of rank 5 over GF(3) Lexicographical Order Variables: x, y, z, w, u Variable weights: 6 8 162 216 234 0 [] true [ x^38*y^3 ] [] Total time: 3.659 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host b138.bernhard.wmich.edu. (141.218.133.138) Time: Sat Mar 27 16:43:46 2004 Input: k:=IntegerRing(16); R :=PolinomialRing(k,6); I:=ideal; Output: Magma V2.10-6 Sat Mar 27 2004 16:43:43 on modular [Seed = 2241867790] ------------------------------------- >> R :=PolinomialRing(k,6); ^ User error: Identifier 'PolinomialRing' has not been declared or assigned >> I:=ideal; ^ User error: Identifier 'R' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host b138.bernhard.wmich.edu. (141.218.133.138) Time: Sat Mar 27 16:44:35 2004 Input: k:=IntegerRing(16); R:=PolinomialRing(k,6); I:=ideal; Output: Magma V2.10-6 Sat Mar 27 2004 16:44:32 on modular [Seed = 2393586506] ------------------------------------- >> R:=PolinomialRing(k,6); ^ User error: Identifier 'PolinomialRing' has not been declared or assigned >> I:=ideal; ^ User error: Identifier 'R' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host b138.bernhard.wmich.edu. (141.218.133.138) Time: Sat Mar 27 16:44:46 2004 Input: k:=IntegerRing(16); R:=PolynomialRing(k,6); I:=ideal; Output: Magma V2.10-6 Sat Mar 27 2004 16:44:43 on modular [Seed = 2545033816] ------------------------------------- Total time: 2.889 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host b138.bernhard.wmich.edu. (141.218.133.138) Time: Sat Mar 27 16:46:21 2004 Input: k:=IntegerRing(16); R:=PolynomialRing(k,6); I:=ideal; J:=ideal; L:=(I meet J)/(I*J); Output: Magma V2.10-6 Sat Mar 27 2004 16:46:18 on modular [Seed = 2776634251] ------------------------------------- >> L:=(I meet J)/(I*J);; ^ Runtime error in '/': Argument 1 is not a full polynomial ring Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host b138.bernhard.wmich.edu. (141.218.133.138) Time: Sat Mar 27 16:52:40 2004 Input: k:=IntegerRing(16); R:=PolynomialRing(k,6); I:=module; J:=module; Output: Magma V2.10-6 Sat Mar 27 2004 16:52:37 on modular [Seed = 2962556689] ------------------------------------- >> I:=module; ^ User error: bad syntax >> J:=module; ^ User error: bad syntax Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host b138.bernhard.wmich.edu. (141.218.133.138) Time: Sat Mar 27 16:53:32 2004 Input: k:=IntegerRing(16); R:=PolynomialRing(k,6); I:=sub; J:=sub; Output: Magma V2.10-6 Sat Mar 27 2004 16:53:29 on modular [Seed = 3147697254] ------------------------------------- Total time: 3.039 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host b138.bernhard.wmich.edu. (141.218.133.138) Time: Sat Mar 27 16:53:42 2004 Input: k:=IntegerRing(16); R:=PolynomialRing(k,6); I:=sub; J:=sub; I; Output: Magma V2.10-6 Sat Mar 27 2004 16:53:39 on modular [Seed = 3437853483] ------------------------------------- Subring of Polynomial ring of rank 6 over IntegerRing(16) Lexicographical Order Variables: x, y, z, a, b, c Generators: [ 2, x^2, y^2, z^2, x*a + y*b + z*c ] Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host b138.bernhard.wmich.edu. (141.218.133.138) Time: Sat Mar 27 16:55:12 2004 Input: k:=IntegerRing(16); R:=PolynomialRing(k,6); M:=Module(R,1); I:=sub; J:=sub; I; Output: Magma V2.10-6 Sat Mar 27 2004 16:55:09 on modular [Seed = 3522456040] ------------------------------------- >> I:=sub; ^ Runtime error in sub< ... >: Rhs argument 1 is invalid for this constructor >> J:=sub; ^ User error: Identifier 'N' has not been declared or assigned >> I;; ^ User error: Identifier 'I' has not been declared or assigned Total time: 3.069 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host b138.bernhard.wmich.edu. (141.218.133.138) Time: Sat Mar 27 16:56:19 2004 Input: k:=IntegerRing(16); R:=PolynomialRing(k,6); M:=Module(R,1); I:=sub; J:=sub; I; Output: Magma V2.10-6 Sat Mar 27 2004 16:56:16 on modular [Seed = 3674169950] ------------------------------------- >> I:=sub; ^ Runtime error in sub< ... >: Rhs argument 1 is invalid for this constructor >> J:=sub; ^ Runtime error in sub< ... >: Rhs argument 1 is invalid for this constructor >> I;; ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host b138.bernhard.wmich.edu. (141.218.133.138) Time: Sat Mar 27 16:56:56 2004 Input: k:=IntegerRing(16); R:=PolynomialRing(k,6); M:=Module(R); I:=sub; J:=sub; I; Output: Magma V2.10-6 Sat Mar 27 2004 16:56:53 on modular [Seed = 3821427522] ------------------------------------- >> M:=Module(R); ^ Runtime error in 'Module': Bad argument types Argument types given: RngMPol >> I:=sub; ^ User error: Identifier 'M' has not been declared or assigned >> J:=sub; ^ User error: Identifier 'M' has not been declared or assigned >> I;; ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host b138.bernhard.wmich.edu. (141.218.133.138) Time: Sat Mar 27 16:58:38 2004 Input: k:=IntegerRing(16); R:=PolynomialRing(k,6); M:=Module(R,1); I:=sub; J:=sub; I; Output: Magma V2.10-6 Sat Mar 27 2004 16:58:35 on modular [Seed = 4141043705] ------------------------------------- >> I:=sub; ^ Runtime error in sub< ... >: Rhs argument 1 is invalid for this constructor >> J:=sub; ^ Runtime error in sub< ... >: Rhs argument 1 is invalid for this constructor >> I;; ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host b138.bernhard.wmich.edu. (141.218.133.138) Time: Sat Mar 27 17:00:12 2004 Input: k:=IntegerRing(16); R:=PolynomialRing(k,6); M:=Module(R,1); I:=sub; J:=sub; I; Output: Magma V2.10-6 Sat Mar 27 2004 17:00:09 on modular [Seed = 119717483] ------------------------------------- >> I:=sub; ^ Runtime error in sub< ... >: Rhs argument 1 is invalid for this constructor >> J:=sub; ^ Runtime error in sub< ... >: Rhs argument 1 is invalid for this constructor >> I;; ^ User error: Identifier 'I' has not been declared or assigned Total time: 3.059 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host b138.bernhard.wmich.edu. (141.218.133.138) Time: Sat Mar 27 17:01:32 2004 Input: k:=IntegerRing(16); R:=PolynomialRing(k,6); M:=Module(R,1); I:=sub; J:=sub; I; Output: Magma V2.10-6 Sat Mar 27 2004 17:01:30 on modular [Seed = 406692263] ------------------------------------- >> I:=sub; ^ Runtime error in sub< ... >: Rhs argument 1 is invalid for this constructor >> J:=sub; ^ Runtime error in sub< ... >: Rhs argument 1 is invalid for this constructor >> I;; ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host b138.bernhard.wmich.edu. (141.218.133.138) Time: Sat Mar 27 17:02:33 2004 Input: k:=IntegerRing(16); R:=PolynomialRing(k,6); M:=Module(R,1); M; I:=sub; J:=sub; Output: Magma V2.10-6 Sat Mar 27 2004 17:02:30 on modular [Seed = 570923985] ------------------------------------- Full Module of degree 1 TOP Order Coefficient ring: Polynomial ring of rank 6 over IntegerRing(16) Lexicographical Order Variables: x, y, z, a, b, c >> I:=sub; ^ Runtime error in sub< ... >: Rhs argument 1 is invalid for this constructor >> J:=sub; ^ Runtime error in sub< ... >: Rhs argument 1 is invalid for this constructor Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host b138.bernhard.wmich.edu. (141.218.133.138) Time: Sat Mar 27 17:04:14 2004 Input: k:=IntegerRing(16); R:=PolynomialRing(k,6); M:=Module(R,1); M; I:=sub; J:=sub; Output: Magma V2.10-6 Sat Mar 27 2004 17:04:11 on modular [Seed = 873565802] ------------------------------------- Full Module of degree 1 TOP Order Coefficient ring: Polynomial ring of rank 6 over IntegerRing(16) Lexicographical Order Variables: x, y, z, a, b, c >> J:=sub; ^ Runtime error in sub< ... >: Rhs argument 1 is invalid for this constructor Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host b138.bernhard.wmich.edu. (141.218.133.138) Time: Sat Mar 27 17:07:45 2004 Input: k:=IntegerRing(16); R:=PolynomialRing(k,6); I:=ideal; J:=ideal; M:=Module(R,1); N:=sub; Output: Magma V2.10-6 Sat Mar 27 2004 17:07:42 on modular [Seed = 1180958061] ------------------------------------- >> N:=sub; ^ Runtime error in sub< ... >: Rhs argument 1 is invalid for this constructor Total time: 3.049 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host b138.bernhard.wmich.edu. (141.218.133.138) Time: Sat Mar 27 17:15:07 2004 Input: k:=IntegerRing(16); R:=PolynomialRing(k,6); I:=ideal; J:=ideal; A:=I meet J; B:=I*J; M:=Module(R,1); A; B; Output: Magma V2.10-6 Sat Mar 27 2004 17:15:04 on modular [Seed = 1585177267] ------------------------------------- Ideal of Polynomial ring of rank 6 over IntegerRing(16) Lexicographical Order Variables: x, y, z, a, b, c Basis: [ x*a + y*b + z*c, 2 ] Ideal of Polynomial ring of rank 6 over IntegerRing(16) Lexicographical Order Variables: x, y, z, a, b, c Basis: [ 4, 2*a^2, 2*b^2, 2*c^2, 2*x*a + 2*y*b + 2*z*c, 2*x^2, x^2*a^2, x^2*b^2, x^2*c^2, x^3*a + x^2*y*b + x^2*z*c, 2*y^2, y^2*a^2, y^2*b^2, y^2*c^2, x*y^2*a + y^3*b + y^2*z*c, 2*z^2, z^2*a^2, z^2*b^2, z^2*c^2, x*z^2*a + y*z^2*b + z^3*c, 2*x*a + 2*y*b + 2*z*c, x*a^3 + y*a^2*b + z*a^2*c, x*a*b^2 + y*b^3 + z*b^2*c, x*a*c^2 + y*b*c^2 + z*c^3, x^2*a^2 + 2*x*y*a*b + 2*x*z*a*c + y^2*b^2 + 2*y*z*b*c + z^2*c^2 ] Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host b138.bernhard.wmich.edu. (141.218.133.138) Time: Sat Mar 27 17:21:21 2004 Input: k:=IntegerRing(16); R:=PolynomialRing(k,6); I:=ideal; J:=ideal; M:=Module(R,1); A:=I meet J; A; Output: Magma V2.10-6 Sat Mar 27 2004 17:21:18 on modular [Seed = 1968229166] ------------------------------------- Ideal of Polynomial ring of rank 6 over IntegerRing(16) Lexicographical Order Variables: x, y, z, a, b, c Basis: [ x*a + y*b + z*c, 2 ] Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host b138.bernhard.wmich.edu. (141.218.133.138) Time: Sat Mar 27 17:21:45 2004 Input: k:=IntegerRing(16); R:=PolynomialRing(k,6); I:=ideal; J:=ideal; M:=Module(R,1); A:=I meet J; A; Output: Magma V2.10-6 Sat Mar 27 2004 17:21:42 on modular [Seed = 2086257167] ------------------------------------- Ideal of Polynomial ring of rank 6 over IntegerRing(16) Lexicographical Order Variables: x, y, z, a, b, c Basis: [ x*y*z*b^2*c, 2*y*z*b^3*c, x*y*z*c^3, 2*y*z*b*c^3, y^3*a*b + y^2*z*a*c, y^2*z*a*b + y*z^2*a*c, y*z^2*a*b + z^3*a*c, x*y*b^3 + x*z*b^2*c, y^2*a*b*c, z^2*a*b*c, x*y*b*c^2 + x*z*c^3, y^2*a^2, z^2*a^2, x^2*b^2, y^2*b^2, z^2*b^2, 2*x*y*z*c, 4*y*z*b*c, x^2*c^2, y^2*c^2, z^2*c^2, 2*x*y*b + 2*x*z*c, 2*x^2, 2*y^2, 2*z^2, x*a + y*b + z*c ] Total time: 2.989 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host b138.bernhard.wmich.edu. (141.218.133.138) Time: Sat Mar 27 17:22:29 2004 Input: k:=IntegerRing(16); R:=PolynomialRing(k,6); I:=ideal; J:=ideal; M:=Module(R,1); A:=I meet J; A; Output: Magma V2.10-6 Sat Mar 27 2004 17:22:26 on modular [Seed = 2275555616] ------------------------------------- Ideal of Polynomial ring of rank 6 over IntegerRing(16) Lexicographical Order Variables: x, y, z, a, b, c Basis: [ x*a + y*b + z*c, 2 ] Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host b138.bernhard.wmich.edu. (141.218.133.138) Time: Sat Mar 27 17:25:16 2004 Input: k:=IntegerRing(16); R:=PolynomialRing(k,6); I:=ideal; J:=ideal; M:=Module(R,1); A:=I meet J; A; Output: Magma V2.10-6 Sat Mar 27 2004 17:25:13 on modular [Seed = 2494639064] ------------------------------------- Ideal of Polynomial ring of rank 6 over IntegerRing(16) Lexicographical Order Variables: x, y, z, a, b, c Basis: [ x*a + y*b + z*c, 2 ] Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host b138.bernhard.wmich.edu. (141.218.133.138) Time: Sat Mar 27 17:25:45 2004 Input: k:=IntegerRing(64); R:=PolynomialRing(k,6); I:=ideal; J:=ideal; M:=Module(R,1); A:=I meet J; A; Output: Magma V2.10-6 Sat Mar 27 2004 17:25:42 on modular [Seed = 2679775484] ------------------------------------- Ideal of Polynomial ring of rank 6 over IntegerRing(64) Lexicographical Order Variables: x, y, z, a, b, c Basis: [ x*a + y*b + z*c, 2 ] Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host b138.bernhard.wmich.edu. (141.218.133.138) Time: Sat Mar 27 17:26:04 2004 Input: k:=IntegerRing(64); R:=PolynomialRing(k,6); I:=ideal; J:=ideal; M:=Module(R,1); A:=I meet J; A; Output: Magma V2.10-6 Sat Mar 27 2004 17:26:01 on modular [Seed = 2793609690] ------------------------------------- Ideal of Polynomial ring of rank 6 over IntegerRing(64) Lexicographical Order Variables: x, y, z, a, b, c Basis: [ 2 ] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host b138.bernhard.wmich.edu. (141.218.133.138) Time: Sat Mar 27 17:27:25 2004 Input: k:=IntegerRing(16); R:=PolynomialRing(k,6); I:=ideal; J:=ideal; M:=Module(R,1); A:=I meet J; A; Output: Magma V2.10-6 Sat Mar 27 2004 17:27:22 on modular [Seed = 3046115962] ------------------------------------- Ideal of Polynomial ring of rank 6 over IntegerRing(16) Lexicographical Order Variables: x, y, z, a, b, c Basis: [ x*a + y*b + z*c, 2 ] Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host b138.bernhard.wmich.edu. (141.218.133.138) Time: Sat Mar 27 17:30:38 2004 Input: k:=IntegerRing(); R:=PolynomialRing(k,6); I:=ideal; J:=ideal; M:=Module(R,1); A:=I meet J; A; Output: Magma V2.10-6 Sat Mar 27 2004 17:30:35 on modular [Seed = 3336603208] ------------------------------------- Ideal of Polynomial ring of rank 6 over Integer Ring Lexicographical Order Variables: x, y, z, a, b, c Basis: [ x*a + y*b + z*c, 2 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host b138.bernhard.wmich.edu. (141.218.133.138) Time: Sat Mar 27 17:31:52 2004 Input: k:=IntegerRing(); R:=PolynomialRing(k,6); I:=ideal; J:=ideal; M:=Module(R,1); A:=(I meet J); A; Output: Magma V2.10-6 Sat Mar 27 2004 17:31:49 on modular [Seed = 3387918617] ------------------------------------- Ideal of Polynomial ring of rank 6 over Integer Ring Lexicographical Order Variables: x, y, z, a, b, c Basis: [ x*a + y*b + z*c, 2 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host b138.bernhard.wmich.edu. (141.218.133.138) Time: Sat Mar 27 17:34:10 2004 Input: k:=IntegerRing(); R:=PolynomialRing(k,6); I:=ideal; J:=ideal; A := I meet J; Output: Magma V2.10-6 Sat Mar 27 2004 17:34:07 on modular [Seed = 3640564098] ------------------------------------- Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host b138.bernhard.wmich.edu. (141.218.133.138) Time: Sat Mar 27 17:34:21 2004 Input: k:=IntegerRing(); R:=PolynomialRing(k,6); I:=ideal; J:=ideal; A := I meet J; A; Output: Magma V2.10-6 Sat Mar 27 2004 17:34:18 on modular [Seed = 3821380236] ------------------------------------- Ideal of Polynomial ring of rank 6 over Integer Ring Lexicographical Order Variables: x, y, z, a, b, c Basis: [ x^2*a^2 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host b138.bernhard.wmich.edu. (141.218.133.138) Time: Sat Mar 27 17:34:38 2004 Input: k:=IntegerRing(); R:=PolynomialRing(k,6); I:=ideal; J:=ideal; A := I meet J; A; Output: Magma V2.10-6 Sat Mar 27 2004 17:34:35 on modular [Seed = 3939281812] ------------------------------------- Ideal of Polynomial ring of rank 6 over Integer Ring Lexicographical Order Variables: x, y, z, a, b, c Basis: [ 2 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host b138.bernhard.wmich.edu. (141.218.133.138) Time: Sat Mar 27 17:34:58 2004 Input: k:=IntegerRing(); R:=PolynomialRing(k,6); I:=ideal; J:=ideal; A := I meet J; A; Output: Magma V2.10-6 Sat Mar 27 2004 17:34:55 on modular [Seed = 4259036279] ------------------------------------- Ideal of Polynomial ring of rank 6 over Integer Ring Lexicographical Order Variables: x, y, z, a, b, c Basis: [ 2*x^2, 3*a^2, 6 ] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host b138.bernhard.wmich.edu. (141.218.133.138) Time: Sat Mar 27 17:39:06 2004 Input: k:=IntegerRing(); R:=PolynomialRing(k,6); I:=ideal; J:=ideal; A := I meet J; A; Output: Magma V2.10-6 Sat Mar 27 2004 17:39:02 on modular [Seed = 187517323] ------------------------------------- Ideal of Polynomial ring of rank 6 over Integer Ring Lexicographical Order Variables: x, y, z, a, b, c Basis: [ 2 ] Total time: 3.489 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host b138.bernhard.wmich.edu. (141.218.133.138) Time: Sat Mar 27 17:39:26 2004 Input: k:=IntegerRing(); R:=PolynomialRing(k,6); I:=ideal; J:=ideal; I; A := I meet J; A; Output: Magma V2.10-6 Sat Mar 27 2004 17:39:23 on modular [Seed = 923891114] ------------------------------------- Ideal of Polynomial ring of rank 6 over Integer Ring Lexicographical Order Variables: x, y, z, a, b, c Basis: [ 2, x^2 ] Ideal of Polynomial ring of rank 6 over Integer Ring Lexicographical Order Variables: x, y, z, a, b, c Basis: [ 2 ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host b138.bernhard.wmich.edu. (141.218.133.138) Time: Sat Mar 27 17:40:50 2004 Input: k:=IntegerRing(); R:=PolynomialRing(k,6); I:=ideal; J:=ideal; A := I meet J; x^2*a^2 in A; Output: Magma V2.10-6 Sat Mar 27 2004 17:40:47 on modular [Seed = 1215171233] ------------------------------------- false Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host b138.bernhard.wmich.edu. (141.218.133.138) Time: Sat Mar 27 17:41:10 2004 Input: k:=IntegerRing(); R:=PolynomialRing(k,6); I:=ideal; J:=ideal; A := I meet J; x^2*a^2 in A; Output: Magma V2.10-6 Sat Mar 27 2004 17:41:07 on modular [Seed = 1366757972] ------------------------------------- >> I:=ideal; ^ Runtime error in '^': Bad argument types Argument types given: RngMPolElt, RngMPolElt >> J:=ideal; ^ Runtime error in '^': Bad argument types Argument types given: RngMPolElt, RngMPolElt >> A := I meet J; ^ User error: Identifier 'I' has not been declared or assigned >> x^2*a^2 in A;; ^ User error: Identifier 'A' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host b138.bernhard.wmich.edu. (141.218.133.138) Time: Sat Mar 27 17:41:25 2004 Input: k:=IntegerRing(); R:=PolynomialRing(k,6); I:=ideal; J:=ideal; A := I meet J; x^2*a^2 in A; Output: Magma V2.10-6 Sat Mar 27 2004 17:41:22 on modular [Seed = 1715479922] ------------------------------------- false Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host b138.bernhard.wmich.edu. (141.218.133.138) Time: Sat Mar 27 17:42:55 2004 Input: k:=IntegerRing(); R:=PolynomialRing(k,6); I:=ideal; J:=ideal; A := I meet J; x^2*a^2 in A; Output: Magma V2.10-6 Sat Mar 27 2004 17:42:52 on modular [Seed = 1867066373] ------------------------------------- true Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host b138.bernhard.wmich.edu. (141.218.133.138) Time: Sat Mar 27 17:44:24 2004 Input: k:=IntegerRing(); R:=PolynomialRing(k,6); I:=ideal; J:=ideal; A := I meet J; x^2*a^2 in A; Output: Magma V2.10-6 Sat Mar 27 2004 17:44:21 on modular [Seed = 1918120369] ------------------------------------- false Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.61.168) Time: Sat Mar 27 18:48:23 2004 Input: >Q:=QuadraticField(-9435); >Q:=QudraticForms(Discriminant(Q); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 18:48:19 on modular [Seed = 4275612732] ------------------------------------- >> Q:=QudraticForms(Discriminant(Q); ^ User error: bad syntax Abelian Group isomorphic to Z/2 + Z/2 + Z/8 Defined on 3 generators Relations: 2*C.1 = 0 2*C.2 = 0 8*C.3 = 0 Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.61.168) Time: Sat Mar 27 18:48:41 2004 Input: >Q:=QuadraticField(-9435); >Q:=QudraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 18:48:38 on modular [Seed = 102782167] ------------------------------------- >> Q:=QudraticForms(Discriminant(Q)); ^ User error: Identifier 'QudraticForms' has not been declared or assigned Abelian Group isomorphic to Z/2 + Z/2 + Z/8 Defined on 3 generators Relations: 2*C.1 = 0 2*C.2 = 0 8*C.3 = 0 Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.61.168) Time: Sat Mar 27 18:49:27 2004 Input: >Q:=QuadraticField(-9435); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 18:49:24 on modular [Seed = 220945934] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/2 + Z/8 Defined on 3 generators Relations: 2*C.1 = 0 2*C.2 = 0 8*C.3 = 0 Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.61.168) Time: Sat Mar 27 18:49:52 2004 Input: >Q:=QuadraticField(-8295); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 18:49:49 on modular [Seed = 338839310] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/2 + Z/16 Defined on 3 generators Relations: 2*C.1 = 0 2*C.2 = 0 16*C.3 = 0 Total time: 3.049 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.61.168) Time: Sat Mar 27 18:50:17 2004 Input: >Q:=QuadraticField(-9735); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 18:50:14 on modular [Seed = 604141333] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/2 + Z/16 Defined on 3 generators Relations: 2*C.1 = 0 2*C.2 = 0 16*C.3 = 0 Total time: 3.049 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.54.11) Time: Sat Mar 27 20:45:49 2004 Input: >Q:=QuadraticField(-11571); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 20:45:46 on modular [Seed = 1551512094] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/2 + Z/8 Defined on 3 generators Relations: 2*C.1 = 0 2*C.2 = 0 8*C.3 = 0 Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.54.11) Time: Sat Mar 27 20:46:11 2004 Input: >Q:=QuadraticField(-11739); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 20:46:08 on modular [Seed = 1450195006] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/2 + Z/8 Defined on 3 generators Relations: 2*C.1 = 0 2*C.2 = 0 8*C.3 = 0 Total time: 3.069 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.54.11) Time: Sat Mar 27 20:46:46 2004 Input: >Q:=QuadraticField(-13515); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 20:46:43 on modular [Seed = 1615204075] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/2 + Z/8 Defined on 3 generators Relations: 2*C.1 = 0 2*C.2 = 0 8*C.3 = 0 Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.54.11) Time: Sat Mar 27 20:47:07 2004 Input: >Q:=QuadraticField(-13755); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 20:47:04 on modular [Seed = 2036275177] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/2 + Z/8 Defined on 3 generators Relations: 2*C.1 = 0 2*C.2 = 0 8*C.3 = 0 Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.54.11) Time: Sat Mar 27 20:47:29 2004 Input: >Q:=QuadraticField(-18291); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 20:47:26 on modular [Seed = 1918115028] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/2 + Z/8 Defined on 3 generators Relations: 2*C.1 = 0 2*C.2 = 0 8*C.3 = 0 Total time: 3.039 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.54.11) Time: Sat Mar 27 20:47:52 2004 Input: >Q:=QuadraticField(-19227); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 20:47:49 on modular [Seed = 2343429446] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/2 + Z/8 Defined on 3 generators Relations: 2*C.1 = 0 2*C.2 = 0 8*C.3 = 0 Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.54.11) Time: Sat Mar 27 20:48:15 2004 Input: >Q:=QuadraticField(-19635); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 20:48:12 on modular [Seed = 2225269328] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/4 Defined on 4 generators Relations: 2*C.1 = 0 2*C.2 = 0 2*C.3 = 0 4*C.4 = 0 Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.54.11) Time: Sat Mar 27 20:48:49 2004 Input: >Q:=QuadraticField(-16835); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 20:48:46 on modular [Seed = 2662920296] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/2 + Z/8 Defined on 3 generators Relations: 2*C.1 = 0 2*C.2 = 0 8*C.3 = 0 Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.54.11) Time: Sat Mar 27 20:49:21 2004 Input: >Q:=QuadraticField(-16995); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 20:49:18 on modular [Seed = 2827929534] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/2 + Z/8 Defined on 3 generators Relations: 2*C.1 = 0 2*C.2 = 0 8*C.3 = 0 Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.54.11) Time: Sat Mar 27 20:49:42 2004 Input: >Q:=QuadraticField(-17115); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 20:49:39 on modular [Seed = 2710032026] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/2 + Z/8 Defined on 3 generators Relations: 2*C.1 = 0 2*C.2 = 0 8*C.3 = 0 Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.54.11) Time: Sat Mar 27 20:50:07 2004 Input: >Q:=QuadraticField(-17355); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 20:50:04 on modular [Seed = 2979520245] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/2 + Z/8 Defined on 3 generators Relations: 2*C.1 = 0 2*C.2 = 0 8*C.3 = 0 Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.54.11) Time: Sat Mar 27 20:50:30 2004 Input: >Q:=QuadraticField(-13335); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 20:50:27 on modular [Seed = 3404506529] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/2 + Z/16 Defined on 3 generators Relations: 2*C.1 = 0 2*C.2 = 0 16*C.3 = 0 Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.54.11) Time: Sat Mar 27 20:50:53 2004 Input: >Q:=QuadraticField(-17535); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 20:50:50 on modular [Seed = 3286609073] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/2 + Z/16 Defined on 3 generators Relations: 2*C.1 = 0 2*C.2 = 0 16*C.3 = 0 Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.54.11) Time: Sat Mar 27 20:51:15 2004 Input: >Q:=QuadraticField(-18655); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 20:51:12 on modular [Seed = 3707417412] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/2 + Z/16 Defined on 3 generators Relations: 2*C.1 = 0 2*C.2 = 0 16*C.3 = 0 Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (221.14.54.11) Time: Sat Mar 27 20:51:38 2004 Input: >Q:=QuadraticField(-19019); >Q:=QuadraticForms(Discriminant(Q)); >C,m:=ClassGroup(Q); >C; Output: Magma V2.10-6 Sat Mar 27 2004 20:51:35 on modular [Seed = 3589519994] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/2 + Z/16 Defined on 3 generators Relations: 2*C.1 = 0 2*C.2 = 0 16*C.3 = 0 Total time: 3.069 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 05:54:54 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //apartat vii) [<0,[0,0]>] cat [: r in [0..24]]; [<0,[0,0]>] cat [: r in [0..15]]; //apartat viii) G4:=ext; G8:=ext; G16:=ext; G2 subset G4; G2 subset G8; G2 subset G16; G4 subset G2; G4 subset G8; G4 subset G16; G8 subset G2; G8 subset G4; G8 subset G16; G16 subset G2; G16 subset G4; G16 subset G8; //subset //exercici 2 //apartat i R:=PolynomialRing(G25); IsFinite(R); //apartat ii Bheta:=PrimitiveElement(G5); p1:=alpha^2+alpha*x+Bheta*(x^2); p2:=1+alpha*x; //apartat iii) print (p1+p2); print (p1*p2); //apartat iv) print (p1/p2); Output: Magma V2.10-6 Sun Mar 28 2004 05:54:51 on modular [Seed = 69397176] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , , <1, [ 1, 0 ]> ] [ <0, [ 0, 0 ]>, <1, [ 1, 0, 0, 0 ]>, , , , , , , , , , , , , , , <1, [ 1, 0, 0, 0 ]> ] true true true false false true false false false false false false false >> p1:=alpha^2+alpha*x+Bheta*(x^2); ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt >> p2:=1+alpha*x; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt >> print (p1+p2); ^ User error: Identifier 'p2' has not been declared or assigned >> print (p1*p2); ^ User error: Identifier 'p2' has not been declared or assigned >> print (p1/p2);; ^ User error: Identifier 'p2' has not been declared or assigned Total time: 3.209 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 06:01:46 2004 Input: P:= PolynomialRing (Integers(3)); G25 := ext < GF(3) | P![3,2,1] >; Seq := {a : a in G25 | a ne 0 and Order(a) eq 24}; Seq; Output: Magma V2.10-6 Sun Mar 28 2004 06:01:42 on modular [Seed = 907069159] ------------------------------------- >> G25 := ext < GF(3) | P![3,2,1] >; ^ Runtime error in ext< ... >: Argument is not irreducible >> Seq := {a : a in G25 | a ne 0 and Order(a) eq 24}; ^ User error: Identifier 'G25' has not been declared or assigned Intrinsic 'Seq' Signatures: ( M) -> SeqEnum [ Search: "BFS" | "DFS" ] The (explicitly enumerated) sequence of words, w, in M with 0 <= length(w) <= #M. ( M, a, b) -> SeqEnum [ Search: "BFS" | "DFS" ] The (explicitly enumerated) sequence of words, w, in M with a <= length(w) <= b. Total time: 3.229 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 06:02:06 2004 Input: P:= PolynomialRing (Integers(3)); G25 := ext < GF(5) | P![3,2,1] >; Seq := {a : a in G25 | a ne 0 and Order(a) eq 24}; Seq; Output: Magma V2.10-6 Sun Mar 28 2004 06:02:02 on modular [Seed = 1025232336] ------------------------------------- >> G25 := ext < GF(5) | P![3,2,1] >; ^ Runtime error in ext< ... >: Argument is not a polynomial over LHS >> Seq := {a : a in G25 | a ne 0 and Order(a) eq 24}; ^ User error: Identifier 'G25' has not been declared or assigned Intrinsic 'Seq' Signatures: ( M) -> SeqEnum [ Search: "BFS" | "DFS" ] The (explicitly enumerated) sequence of words, w, in M with 0 <= length(w) <= #M. ( M, a, b) -> SeqEnum [ Search: "BFS" | "DFS" ] The (explicitly enumerated) sequence of words, w, in M with a <= length(w) <= b. Total time: 3.189 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 06:02:36 2004 Input: P:= PolynomialRing (Integers(5)); G25 := ext < GF(5) | P![3,2,1] >; Seq := {a : a in G25 | a ne 0 and Order(a) eq 24}; Seq; Output: Magma V2.10-6 Sun Mar 28 2004 06:02:31 on modular [Seed = 3253154113] ------------------------------------- { G25.1^11, G25.1, G25.1^23, G25.1^13, G25.1^5, G25.1^17, G25.1^7, G25.1^19 } Total time: 4.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 06:02:36 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //apartat vii) [<0,[0,0]>] cat [: r in [0..24]]; [<0,[0,0]>] cat [: r in [0..15]]; //apartat viii) G4:=ext; G8:=ext; G16:=ext; G2 subset G4; G2 subset G8; G2 subset G16; G4 subset G2; G4 subset G8; G4 subset G16; G8 subset G2; G8 subset G4; G8 subset G16; G16 subset G2; G16 subset G4; G16 subset G8; //subset //exercici 2 //apartat i R:=PolynomialRing(G25); IsFinite(R); //apartat ii Bheta:=PrimitiveElement(G5); p1:=alpha^2+alpha*s+Bheta*(s^2); p2:=1+alpha*s; //apartat iii) print (p1+p2); print (p1*p2); //apartat iv) print (p1/p2); Output: Magma V2.10-6 Sun Mar 28 2004 06:02:31 on modular [Seed = 3286577987] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , , <1, [ 1, 0 ]> ] [ <0, [ 0, 0 ]>, <1, [ 1, 0, 0, 0 ]>, , , , , , , , , , , , , , , <1, [ 1, 0, 0, 0 ]> ] true true true false false true false false false false false false false 2*s^2 + alpha^19*s + alpha^9 alpha^19*s^3 + alpha^22*s^2 + alpha^10*s + alpha^2 (alpha^17*s^2 + s + alpha)/(s + alpha^23) Total time: 3.869 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 06:03:19 2004 Input: P:= PolynomialRing (Integers()); G25 := ext < GF(5) | P![3,2,1] >; Seq := {a : a in G25 | a ne 0 and Order(a) eq 24}; Seq; Output: Magma V2.10-6 Sun Mar 28 2004 06:03:15 on modular [Seed = 3539214950] ------------------------------------- { G25.1^11, G25.1, G25.1^23, G25.1^13, G25.1^5, G25.1^17, G25.1^7, G25.1^19 } Total time: 3.329 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 06:03:40 2004 Input: P:= PolynomialRing (Integers()); G25 := ext < GF(5) | P![3,2,1] >; Seq := {a : a in G25 | a ne 0 and Order(a) eq 24}; Seq; #Seq; Output: Magma V2.10-6 Sun Mar 28 2004 06:03:36 on modular [Seed = 3640535447] ------------------------------------- { G25.1^11, G25.1, G25.1^23, G25.1^13, G25.1^5, G25.1^17, G25.1^7, G25.1^19 } 8 Total time: 3.289 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 06:03:51 2004 Input: P:= PolynomialRing (Integers(5)); G25 := ext < GF(5) | P![3,2,1] >; Seq := {a : a in G25 | a ne 0 and Order(a) eq 24}; Seq; #Seq; Output: Magma V2.10-6 Sun Mar 28 2004 06:03:47 on modular [Seed = 4022935227] ------------------------------------- { G25.1^11, G25.1, G25.1^23, G25.1^13, G25.1^5, G25.1^17, G25.1^7, G25.1^19 } 8 Total time: 3.219 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 06:04:05 2004 Input: P:= PolynomialRing (Integers()); G25 := ext < GF(5) | P![3,2,1] >; Seq := {a : a in G25 | a ne 0 and Order(a) eq 24}; Seq; #Seq; Output: Magma V2.10-6 Sun Mar 28 2004 06:04:02 on modular [Seed = 4124247184] ------------------------------------- { G25.1^11, G25.1, G25.1^23, G25.1^13, G25.1^5, G25.1^17, G25.1^7, G25.1^19 } 8 Total time: 3.369 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 06:05:02 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //apartat vii) [<0,[0,0]>] cat [: r in [0..24]]; [<0,[0,0]>] cat [: r in [0..15]]; //apartat viii) G4:=ext; G8:=ext; G16:=ext; G2 subset G4; G2 subset G8; G2 subset G16; G4 subset G2; G4 subset G8; G4 subset G16; G8 subset G2; G8 subset G4; G8 subset G16; G16 subset G2; G16 subset G4; G16 subset G8; //subset //exercici 2 //apartat i R:=PolynomialRing(G25); IsFinite(R); //apartat ii Bheta:=PrimitiveElement(G5); p1:=alpha^2+alpha*s+Bheta*(s^2); p2:=1+alpha*s; //apartat iii) print (p1+p2); print (p1*p2); //apartat iv) p3:=p1/p2; print p3; Output: Magma V2.10-6 Sun Mar 28 2004 06:04:58 on modular [Seed = 4242148833] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , , <1, [ 1, 0 ]> ] [ <0, [ 0, 0 ]>, <1, [ 1, 0, 0, 0 ]>, , , , , , , , , , , , , , , <1, [ 1, 0, 0, 0 ]> ] true true true false false true false false false false false false false 2*s^2 + alpha^19*s + alpha^9 alpha^19*s^3 + alpha^22*s^2 + alpha^10*s + alpha^2 (alpha^17*s^2 + s + alpha)/(s + alpha^23) Total time: 3.369 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 06:05:21 2004 Input: P:= PolynomialRing (Integers()); G25 := ext < GF(3) | P![1,2,1] >; Seq := {a : a in G25 | a ne 0 and Order(a) eq 24}; Seq; #Seq; Output: Magma V2.10-6 Sun Mar 28 2004 06:05:18 on modular [Seed = 2410249894] ------------------------------------- >> G25 := ext < GF(3) | P![1,2,1] >; ^ Runtime error in ext< ... >: Argument is not irreducible >> Seq := {a : a in G25 | a ne 0 and Order(a) eq 24}; ^ User error: Identifier 'G25' has not been declared or assigned Intrinsic 'Seq' Signatures: ( M) -> SeqEnum [ Search: "BFS" | "DFS" ] The (explicitly enumerated) sequence of words, w, in M with 0 <= length(w) <= #M. ( M, a, b) -> SeqEnum [ Search: "BFS" | "DFS" ] The (explicitly enumerated) sequence of words, w, in M with a <= length(w) <= b. >> #Seq;; ^ Runtime error in '#': Bad argument types Argument types given: Intrinsic Total time: 3.439 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 06:05:37 2004 Input: P:= PolynomialRing (Integers()); G25 := ext < GF(5) | P![3,2,1] >; Seq := {a : a in G25 | a ne 0 and Order(a) eq 24}; Seq; #Seq; Output: Magma V2.10-6 Sun Mar 28 2004 06:05:31 on modular [Seed = 2528143274] ------------------------------------- { G25.1^11, G25.1, G25.1^23, G25.1^13, G25.1^5, G25.1^17, G25.1^7, G25.1^19 } 8 Total time: 6.000 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 06:06:17 2004 Input: P:= PolynomialRing (Integers()); G25 := ext < GF(5) | P![3,2,1] >; Seq := {a : a in G25 | a ne 0 and Order(a) eq 25}; Seq; #Seq; Output: Magma V2.10-6 Sun Mar 28 2004 06:06:13 on modular [Seed = 2629463422] ------------------------------------- {} 0 Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 06:06:26 2004 Input: P:= PolynomialRing (Integers()); G25 := ext < GF(5) | P![3,2,1] >; Seq := {a : a in G25 | a ne 0 and Order(a) eq 24}; Seq; #Seq; Output: Magma V2.10-6 Sun Mar 28 2004 06:06:22 on modular [Seed = 2743423563] ------------------------------------- { G25.1^11, G25.1, G25.1^23, G25.1^13, G25.1^5, G25.1^17, G25.1^7, G25.1^19 } 8 Total time: 3.219 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 06:08:23 2004 Input: P:= PolynomialRing (Integers()); G25 := ext < GF(5) | P![3,2,1] >; Seq := {a : a in G25 }; Seq; #Seq; Output: Magma V2.10-6 Sun Mar 28 2004 06:08:02 on modular [Seed = 2844744700] ------------------------------------- { 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23, 0 } 25 Total time: 5.269 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 06:08:46 2004 Input: P:= PolynomialRing (Integers()); G25 := ext < GF(5) | P![3,2,1] >; Seq := {a : a in G25 | a ne 0 and Order(a) eq 24}; Seq; #Seq; Output: Magma V2.10-6 Sun Mar 28 2004 06:08:39 on modular [Seed = 3214495183] ------------------------------------- { G25.1^11, G25.1, G25.1^23, G25.1^13, G25.1^5, G25.1^17, G25.1^7, G25.1^19 } 8 Total time: 4.389 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 06:10:23 2004 Input: P:= PolynomialRing (Integers()); G9 := ext < GF(3) | P![2,2,1] >; Seq := {a : a in G9 | a ne 0 and Order(a) eq 8}; Seq; #Seq; G16 := ext < GF(2) | P![1,1,0,0,1] >; Seq := {a : a in G16 | a ne 0 and Order(a) eq 15}; Seq; #Seq; G25 := ext < GF(5) | P![3,2,1] >; Seq := {a : a in G25 | a ne 0 and Order(a) eq 24}; Seq; #Seq; Output: Magma V2.10-6 Sun Mar 28 2004 06:10:19 on modular [Seed = 1147319959] ------------------------------------- { G9.1, G9.1^3, G9.1^5, G9.1^7 } 4 { G16.1^11, G16.1, G16.1^2, G16.1^13, G16.1^14, G16.1^4, G16.1^7, G16.1^8 } 8 { G25.1^11, G25.1, G25.1^23, G25.1^13, G25.1^5, G25.1^17, G25.1^7, G25.1^19 } 8 Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 06:14:38 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //apartat vii) [<0,[0,0]>] cat [: r in [0..24]]; [<0,[0,0]>] cat [: r in [0..15]]; //apartat viii) G4:=ext; G8:=ext; G16:=ext; G2 subset G4; G2 subset G8; G2 subset G16; G4 subset G2; G4 subset G8; G4 subset G16; G8 subset G2; G8 subset G4; G8 subset G16; G16 subset G2; G16 subset G4; G16 subset G8; //subset //exercici 2 //apartat i R:=PolynomialRing(G25); IsFinite(R); //apartat ii Bheta:=PrimitiveElement(G5); p1:=alpha^2+alpha*s+Bheta*(s^2); p2:=1+alpha*s; //apartat iii) print (p1+p2); print (p1*p2); //apartat iv) print(s^2+1 div s); print (p1 div p2); print (p1 mod p2); Output: Magma V2.10-6 Sun Mar 28 2004 06:14:35 on modular [Seed = 1601809548] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , , <1, [ 1, 0 ]> ] [ <0, [ 0, 0 ]>, <1, [ 1, 0, 0, 0 ]>, , , , , , , , , , , , , , , <1, [ 1, 0, 0, 0 ]> ] true true true false false true false false false false false false false 2*s^2 + alpha^19*s + alpha^9 alpha^19*s^3 + alpha^22*s^2 + alpha^10*s + alpha^2 s^2 alpha^17*s + alpha^5 alpha^15 Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 06:15:09 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //apartat vii) [<0,[0,0]>] cat [: r in [0..24]]; [<0,[0,0]>] cat [: r in [0..15]]; //apartat viii) G4:=ext; G8:=ext; G16:=ext; G2 subset G4; G2 subset G8; G2 subset G16; G4 subset G2; G4 subset G8; G4 subset G16; G8 subset G2; G8 subset G4; G8 subset G16; G16 subset G2; G16 subset G4; G16 subset G8; //subset //exercici 2 //apartat i R:=PolynomialRing(G25); IsFinite(R); //apartat ii Bheta:=PrimitiveElement(G5); p1:=alpha^2+alpha*s+Bheta*(s^2); p2:=1+alpha*s; //apartat iii) print (p1+p2); print (p1*p2); //apartat iv) print(s^2+s div s); print (p1 div p2); print (p1 mod p2); Output: Magma V2.10-6 Sun Mar 28 2004 06:15:06 on modular [Seed = 1816829854] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , , <1, [ 1, 0 ]> ] [ <0, [ 0, 0 ]>, <1, [ 1, 0, 0, 0 ]>, , , , , , , , , , , , , , , <1, [ 1, 0, 0, 0 ]> ] true true true false false true false false false false false false false 2*s^2 + alpha^19*s + alpha^9 alpha^19*s^3 + alpha^22*s^2 + alpha^10*s + alpha^2 s^2 + 1 alpha^17*s + alpha^5 alpha^15 Total time: 3.069 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 06:15:32 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //apartat vii) [<0,[0,0]>] cat [: r in [0..24]]; [<0,[0,0]>] cat [: r in [0..15]]; //apartat viii) G4:=ext; G8:=ext; G16:=ext; G2 subset G4; G2 subset G8; G2 subset G16; G4 subset G2; G4 subset G8; G4 subset G16; G8 subset G2; G8 subset G4; G8 subset G16; G16 subset G2; G16 subset G4; G16 subset G8; //subset //exercici 2 //apartat i R:=PolynomialRing(G25); IsFinite(R); //apartat ii Bheta:=PrimitiveElement(G5); p1:=alpha^2+alpha*s+Bheta*(s^2); p2:=1+alpha*s; //apartat iii) print (p1+p2); print (p1*p2); //apartat iv) print((s^2+s) div s); print (p1 div p2); print (p1 mod p2); Output: Magma V2.10-6 Sun Mar 28 2004 06:15:29 on modular [Seed = 1698928380] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , , <1, [ 1, 0 ]> ] [ <0, [ 0, 0 ]>, <1, [ 1, 0, 0, 0 ]>, , , , , , , , , , , , , , , <1, [ 1, 0, 0, 0 ]> ] true true true false false true false false false false false false false 2*s^2 + alpha^19*s + alpha^9 alpha^19*s^3 + alpha^22*s^2 + alpha^10*s + alpha^2 s + 1 alpha^17*s + alpha^5 alpha^15 Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 06:17:00 2004 Input: P:= PolynomialRing (Integers()); G25 := ext < GF(5) | P![3,2,1] >; Seq := {a : a in G25 | a ne 0 and Order(a) eq 24}; alpha := Seq[1]; sol := MinimalPolynomial(alpha); sol; Output: Magma V2.10-6 Sun Mar 28 2004 06:16:57 on modular [Seed = 1901561104] ------------------------------------- >> alpha := Seq[1]; ^ Runtime error in '[]': Bad argument types >> sol := MinimalPolynomial(alpha); ^ User error: Identifier 'alpha' has not been declared or assigned >> sol;; ^ User error: Identifier 'sol' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 06:17:49 2004 Input: P:= PolynomialRing (Integers()); G25 := ext < GF(5) | P![3,2,1] >; Seq := [a : a in G25 | a ne 0 and Order(a) eq 24]; Seq; #Seq; Output: Magma V2.10-6 Sun Mar 28 2004 06:17:46 on modular [Seed = 170720792] ------------------------------------- [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 8 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 06:18:14 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //apartat vii) [<0,[0,0]>] cat [: r in [0..24]]; [<0,[0,0]>] cat [: r in [0..15]]; //apartat viii) G4:=ext; G8:=ext; G16:=ext; G2 subset G4; G2 subset G8; G2 subset G16; G4 subset G2; G4 subset G8; G4 subset G16; G8 subset G2; G8 subset G4; G8 subset G16; G16 subset G2; G16 subset G4; G16 subset G8; //subset //exercici 2 //apartat i R:=PolynomialRing(G25); IsFinite(R); //apartat ii Bheta:=PrimitiveElement(G5); p1:=alpha^2+alpha*s+Bheta*(s^2); p2:=1+alpha*s; //apartat iii) print (p1+p2); print (p1*p2); //apartat iv) print (p1 div p2); print (p1 mod p2); //apartat v) print (GCD(p1,p2)); print (LCM(p1,p2)); //apartat vi) print(XGCD(p1,p2)); //apartat vii) Output: Magma V2.10-6 Sun Mar 28 2004 06:18:11 on modular [Seed = 52819768] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , , <1, [ 1, 0 ]> ] [ <0, [ 0, 0 ]>, <1, [ 1, 0, 0, 0 ]>, , , , , , , , , , , , , , , <1, [ 1, 0, 0, 0 ]> ] true true true false false true false false false false false false false 2*s^2 + alpha^19*s + alpha^9 alpha^19*s^3 + alpha^22*s^2 + alpha^10*s + alpha^2 alpha^17*s + alpha^5 alpha^15 1 s^3 + alpha^3*s^2 + alpha^15*s + alpha^7 1 alpha^9 alpha^14*s + alpha^2 Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 06:18:17 2004 Input: P:= PolynomialRing (Integers(5)); G25 := ext < GF(5) | P![3,2,1] >; Seq := [a : a in G25 | a ne 0 and Order(a) eq 24]; Seq; #Seq; Output: Magma V2.10-6 Sun Mar 28 2004 06:18:14 on modular [Seed = 406776870] ------------------------------------- [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 8 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 06:18:43 2004 Input: P:= PolynomialRing (Integers()); G9 := ext < GF(3) | P![2,2,1] >; Seq := [a : a in G9 | a ne 0 and Order(a) eq 8]; Seq; #Seq; G16 := ext < GF(2) | P![1,1,0,0,1] >; Seq := [a : a in G16 | a ne 0 and Order(a) eq 15]; Seq; #Seq; G25 := ext < GF(5) | P![3,2,1] >; Seq := [a : a in G25 | a ne 0 and Order(a) eq 24]; Seq; #Seq; Output: Magma V2.10-6 Sun Mar 28 2004 06:18:40 on modular [Seed = 389145551] ------------------------------------- [ G9.1, G9.1^3, G9.1^5, G9.1^7 ] 4 [ G16.1, G16.1^2, G16.1^4, G16.1^7, G16.1^8, G16.1^11, G16.1^13, G16.1^14 ] 8 [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 8 Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 06:18:53 2004 Input: P:= PolynomialRing (Integers(3)); G9 := ext < GF(3) | P![2,2,1] >; Seq := [a : a in G9 | a ne 0 and Order(a) eq 8]; Seq; #Seq; G16 := ext < GF(2) | P![1,1,0,0,1] >; Seq := [a : a in G16 | a ne 0 and Order(a) eq 15]; Seq; #Seq; G25 := ext < GF(5) | P![3,2,1] >; Seq := [a : a in G25 | a ne 0 and Order(a) eq 24]; Seq; #Seq; Output: Magma V2.10-6 Sun Mar 28 2004 06:18:50 on modular [Seed = 537318642] ------------------------------------- [ G9.1, G9.1^3, G9.1^5, G9.1^7 ] 4 >> G16 := ext < GF(2) | P![1,1,0,0,1] >; ^ Runtime error in ext< ... >: Argument is not a polynomial over LHS >> Seq := [a : a in G16 | a ne 0 and Order(a) eq 15]; ^ User error: Identifier 'G16' has not been declared or assigned [ G9.1, G9.1^3, G9.1^5, G9.1^7 ] 4 >> G25 := ext < GF(5) | P![3,2,1] >; ^ Runtime error in ext< ... >: Argument is not a polynomial over LHS >> Seq := [a : a in G25 | a ne 0 and Order(a) eq 24]; ^ User error: Identifier 'G25' has not been declared or assigned [ G9.1, G9.1^3, G9.1^5, G9.1^7 ] 4 Total time: 2.979 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 06:20:26 2004 Input: P:= PolynomialRing (Integers()); G25 := ext < GF(5) | P![3,2,1] >; Seq := [a : a in G25 | a ne 0 and Order(a) eq 24]; alpha := Seq[1]; sol := MinimalPolynomial(alpha); sol; Output: Magma V2.10-6 Sun Mar 28 2004 06:20:23 on modular [Seed = 840222349] ------------------------------------- $.1^2 + 2*$.1 + 3 Total time: 2.849 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 06:20:51 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //apartat vii) [<0,[0,0]>] cat [: r in [0..24]]; [<0,[0,0]>] cat [: r in [0..15]]; //apartat viii) G4:=ext; G8:=ext; G16:=ext; G2 subset G4; G2 subset G8; G2 subset G16; G4 subset G2; G4 subset G8; G4 subset G16; G8 subset G2; G8 subset G4; G8 subset G16; G16 subset G2; G16 subset G4; G16 subset G8; //subset //exercici 2 //apartat i R:=PolynomialRing(G25); IsFinite(R); //apartat ii Bheta:=PrimitiveElement(G5); p1:=alpha^2+alpha*s+Bheta*(s^2); p2:=1+alpha*s; //apartat iii) //print (p1+p2); //print (p1*p2); //apartat iv) //print (p1 div p2); //print (p1 mod p2); //apartat v) //print (GCD(p1,p2)); //print (LCM(p1,p2)); //apartat vi) //print(XGCD(p1,p2)); //apartat vii) Output: Magma V2.10-6 Sun Mar 28 2004 06:20:48 on modular [Seed = 3421322899] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , , <1, [ 1, 0 ]> ] [ <0, [ 0, 0 ]>, <1, [ 1, 0, 0, 0 ]>, , , , , , , , , , , , , , , <1, [ 1, 0, 0, 0 ]> ] true true true false false true false false false false false false false Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 06:21:12 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //apartat vii) [<0,[0,0]>] cat [: r in [0..24]]; [<0,[0,0]>] cat [: r in [0..15]]; //apartat viii) G4:=ext; G8:=ext; G16:=ext; G2 subset G4; G2 subset G8; G2 subset G16; G4 subset G2; G4 subset G8; G4 subset G16; G8 subset G2; G8 subset G4; G8 subset G16; G16 subset G2; G16 subset G4; G16 subset G8; //subset //exercici 2 //apartat i R:=PolynomialRing(G25); IsFinite(R); //apartat ii Bheta:=PrimitiveElement(G5); p1:=alpha^2+alpha*s+Bheta*(s^2); p2:=1+alpha*s; //apartat iii) print (p1+p2); print (p1*p2); //apartat iv) //print (p1 div p2); //print (p1 mod p2); //apartat v) //print (GCD(p1,p2)); //print (LCM(p1,p2)); //apartat vi) //print(XGCD(p1,p2)); //apartat vii) Output: Magma V2.10-6 Sun Mar 28 2004 06:21:09 on modular [Seed = 3303158185] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , , <1, [ 1, 0 ]> ] [ <0, [ 0, 0 ]>, <1, [ 1, 0, 0, 0 ]>, , , , , , , , , , , , , , , <1, [ 1, 0, 0, 0 ]> ] true true true false false true false false false false false false false 2*s^2 + alpha^19*s + alpha^9 alpha^19*s^3 + alpha^22*s^2 + alpha^10*s + alpha^2 Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 06:21:19 2004 Input: P:= PolynomialRing (Integers()); G25 := ext < GF(5) | P![3,2,1] >; Seq := [a : a in G25 | a ne 0 and Order(a) eq 24]; alpha := Seq[1]; sol := MinimalPolynomial(alpha); sol; Output: Magma V2.10-6 Sun Mar 28 2004 06:21:16 on modular [Seed = 3740806074] ------------------------------------- $.1^2 + 2*$.1 + 3 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 06:21:37 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //apartat vii) [<0,[0,0]>] cat [: r in [0..24]]; [<0,[0,0]>] cat [: r in [0..15]]; //apartat viii) G4:=ext; G8:=ext; G16:=ext; G2 subset G4; G2 subset G8; G2 subset G16; G4 subset G2; G4 subset G8; G4 subset G16; G8 subset G2; G8 subset G4; G8 subset G16; G16 subset G2; G16 subset G4; G16 subset G8; //subset //exercici 2 //apartat i R:=PolynomialRing(G25); IsFinite(R); //apartat ii Bheta:=PrimitiveElement(G5); p1:=alpha^2+alpha*s+Bheta*(s^2); p2:=1+alpha*s; //apartat iii) print (p1+p2); print (p1*p2); //apartat iv) print (p1 div p2); print (p1 mod p2); //apartat v) //print (GCD(p1,p2)); //print (LCM(p1,p2)); //apartat vi) //print(XGCD(p1,p2)); //apartat vii) Output: Magma V2.10-6 Sun Mar 28 2004 06:21:34 on modular [Seed = 3622904481] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , , <1, [ 1, 0 ]> ] [ <0, [ 0, 0 ]>, <1, [ 1, 0, 0, 0 ]>, , , , , , , , , , , , , , , <1, [ 1, 0, 0, 0 ]> ] true true true false false true false false false false false false false 2*s^2 + alpha^19*s + alpha^9 alpha^19*s^3 + alpha^22*s^2 + alpha^10*s + alpha^2 alpha^17*s + alpha^5 alpha^15 Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 06:21:48 2004 Input: P:= PolynomialRing (Integers()); G25 := ext < GF(5) | P![3,2,1] >; Seq := [a : a in G25 | a ne 0 and Order(a) eq 24]; alpha := Seq[1]; sol := MinimalPolynomial(alpha); sol; Output: Magma V2.10-6 Sun Mar 28 2004 06:21:45 on modular [Seed = 3771078113] ------------------------------------- $.1^2 + 2*$.1 + 3 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 06:22:05 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //apartat vii) [<0,[0,0]>] cat [: r in [0..24]]; [<0,[0,0]>] cat [: r in [0..15]]; //apartat viii) G4:=ext; G8:=ext; G16:=ext; G2 subset G4; G2 subset G8; G2 subset G16; G4 subset G2; G4 subset G8; G4 subset G16; G8 subset G2; G8 subset G4; G8 subset G16; G16 subset G2; G16 subset G4; G16 subset G8; //subset //exercici 2 //apartat i R:=PolynomialRing(G25); IsFinite(R); //apartat ii Bheta:=PrimitiveElement(G5); p1:=alpha^2+alpha*s+Bheta*(s^2); p2:=1+alpha*s; //apartat iii) print (p1+p2); print (p1*p2); //apartat iv) print (p1 div p2); print (p1 mod p2); //apartat v) print (GCD(p1,p2)); //print (LCM(p1,p2)); //apartat vi) //print(XGCD(p1,p2)); //apartat vii) Output: Magma V2.10-6 Sun Mar 28 2004 06:22:02 on modular [Seed = 4192144619] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , , <1, [ 1, 0 ]> ] [ <0, [ 0, 0 ]>, <1, [ 1, 0, 0, 0 ]>, , , , , , , , , , , , , , , <1, [ 1, 0, 0, 0 ]> ] true true true false false true false false false false false false false 2*s^2 + alpha^19*s + alpha^9 alpha^19*s^3 + alpha^22*s^2 + alpha^10*s + alpha^2 alpha^17*s + alpha^5 alpha^15 1 Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 06:22:19 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //apartat vii) [<0,[0,0]>] cat [: r in [0..24]]; [<0,[0,0]>] cat [: r in [0..15]]; //apartat viii) G4:=ext; G8:=ext; G16:=ext; G2 subset G4; G2 subset G8; G2 subset G16; G4 subset G2; G4 subset G8; G4 subset G16; G8 subset G2; G8 subset G4; G8 subset G16; G16 subset G2; G16 subset G4; G16 subset G8; //subset //exercici 2 //apartat i R:=PolynomialRing(G25); IsFinite(R); //apartat ii Bheta:=PrimitiveElement(G5); p1:=alpha^2+alpha*s+Bheta*(s^2); p2:=1+alpha*s; //apartat iii) print (p1+p2); print (p1*p2); //apartat iv) print (p1 div p2); print (p1 mod p2); //apartat v) print (GCD(p1,p2)); print (LCM(p1,p2)); //apartat vi) //print(XGCD(p1,p2)); //apartat vii) Output: Magma V2.10-6 Sun Mar 28 2004 06:22:16 on modular [Seed = 4073981906] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , , <1, [ 1, 0 ]> ] [ <0, [ 0, 0 ]>, <1, [ 1, 0, 0, 0 ]>, , , , , , , , , , , , , , , <1, [ 1, 0, 0, 0 ]> ] true true true false false true false false false false false false false 2*s^2 + alpha^19*s + alpha^9 alpha^19*s^3 + alpha^22*s^2 + alpha^10*s + alpha^2 alpha^17*s + alpha^5 alpha^15 1 s^3 + alpha^3*s^2 + alpha^15*s + alpha^7 Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 06:22:37 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //apartat vii) [<0,[0,0]>] cat [: r in [0..24]]; [<0,[0,0]>] cat [: r in [0..15]]; //apartat viii) G4:=ext; G8:=ext; G16:=ext; G2 subset G4; G2 subset G8; G2 subset G16; G4 subset G2; G4 subset G8; G4 subset G16; G8 subset G2; G8 subset G4; G8 subset G16; G16 subset G2; G16 subset G4; G16 subset G8; //subset //exercici 2 //apartat i R:=PolynomialRing(G25); IsFinite(R); //apartat ii Bheta:=PrimitiveElement(G5); p1:=alpha^2+alpha*s+Bheta*(s^2); p2:=1+alpha*s; //apartat iii) print (p1+p2); print (p1*p2); //apartat iv) print (p1 div p2); print (p1 mod p2); //apartat v) print (GCD(p1,p2)); print (LCM(p1,p2)); //apartat vi) print(XGCD(p1,p2)); //apartat vii) Output: Magma V2.10-6 Sun Mar 28 2004 06:22:34 on modular [Seed = 2343403193] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , , <1, [ 1, 0 ]> ] [ <0, [ 0, 0 ]>, <1, [ 1, 0, 0, 0 ]>, , , , , , , , , , , , , , , <1, [ 1, 0, 0, 0 ]> ] true true true false false true false false false false false false false 2*s^2 + alpha^19*s + alpha^9 alpha^19*s^3 + alpha^22*s^2 + alpha^10*s + alpha^2 alpha^17*s + alpha^5 alpha^15 1 s^3 + alpha^3*s^2 + alpha^15*s + alpha^7 1 alpha^9 alpha^14*s + alpha^2 Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 06:23:02 2004 Input: P:= PolynomialRing (Integers()); G25 := ext < GF(5) | P![3,2,1] >; Seq := [a : a in G25 | a ne 0 and Order(a) eq 24]; alpha := Seq[1]; sol := MinimalPolynomial(alpha); ElementToSequence(sol); Output: Magma V2.10-6 Sun Mar 28 2004 06:22:59 on modular [Seed = 2242080862] ------------------------------------- [ 3, 2, 1 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 06:24:32 2004 Input: P:= PolynomialRing (Integers()); G25 := ext < GF(5) | P![3,2,1] >; Seq := [a : a in G25 | a ne 0 and Order(a) eq 24]; alpha := Seq[1]; sol := MinimalPolynomial(alpha); ElementToSequence(sol); PrimeField(sol); Output: Magma V2.10-6 Sun Mar 28 2004 06:24:29 on modular [Seed = 2679728698] ------------------------------------- [ 3, 2, 1 ] >> PrimeField(sol);; ^ Runtime error in 'PrimeField': Bad argument types Argument types given: RngUPolElt Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 06:25:26 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //apartat vii) [<0,[0,0]>] cat [: r in [0..24]]; [<0,[0,0]>] cat [: r in [0..15]]; //apartat viii) G4:=ext; G8:=ext; G16:=ext; G2 subset G4; G2 subset G8; G2 subset G16; G4 subset G2; G4 subset G8; G4 subset G16; G8 subset G2; G8 subset G4; G8 subset G16; G16 subset G2; G16 subset G4; G16 subset G8; //subset //exercici 2 //apartat i R:=PolynomialRing(G25); IsFinite(R); //apartat ii Bheta:=PrimitiveElement(G5); p1:=alpha^2+alpha*s+Bheta*(s^2); p2:=1+alpha*s; //apartat iii) print (p1+p2); print (p1*p2); //apartat iv) print (p1 div p2); print (p1 mod p2); //apartat v) print (GCD(p1,p2)); print (LCM(p1,p2)); //apartat vi) print(XGCD(p1,p2)); //apartat vii) p3:=(1/(alpha^4))-(alpha^(-3))*s+(alpha^5)*(x^2); factorizacion(p3); Output: Magma V2.10-6 Sun Mar 28 2004 06:25:23 on modular [Seed = 2911591366] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , , <1, [ 1, 0 ]> ] [ <0, [ 0, 0 ]>, <1, [ 1, 0, 0, 0 ]>, , , , , , , , , , , , , , , <1, [ 1, 0, 0, 0 ]> ] true true true false false true false false false false false false false 2*s^2 + alpha^19*s + alpha^9 alpha^19*s^3 + alpha^22*s^2 + alpha^10*s + alpha^2 alpha^17*s + alpha^5 alpha^15 1 s^3 + alpha^3*s^2 + alpha^15*s + alpha^7 1 alpha^9 alpha^14*s + alpha^2 >> p3:=(1/(alpha^4))-(alpha^(-3))*s+(alpha^5)*(x^2); ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt >> factorizacion(p3);; ^ User error: Identifier 'p3' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 06:25:41 2004 Input: P:= PolynomialRing (Integers()); G25 := ext < GF(5) | P![3,2,1] >; Seq := [a : a in G25 | a ne 0 and Order(a) eq 24]; alpha := Seq[1]; sol := MinimalPolynomial(alpha); ElementToSequence(sol); sol in P; Output: Magma V2.10-6 Sun Mar 28 2004 06:25:38 on modular [Seed = 2793427164] ------------------------------------- [ 3, 2, 1 ] >> sol in P;; ^ Runtime error in 'in': Arguments are not compatible Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 06:25:58 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //apartat vii) [<0,[0,0]>] cat [: r in [0..24]]; [<0,[0,0]>] cat [: r in [0..15]]; //apartat viii) G4:=ext; G8:=ext; G16:=ext; G2 subset G4; G2 subset G8; G2 subset G16; G4 subset G2; G4 subset G8; G4 subset G16; G8 subset G2; G8 subset G4; G8 subset G16; G16 subset G2; G16 subset G4; G16 subset G8; //subset //exercici 2 //apartat i R:=PolynomialRing(G25); IsFinite(R); //apartat ii Bheta:=PrimitiveElement(G5); p1:=alpha^2+alpha*s+Bheta*(s^2); p2:=1+alpha*s; //apartat iii) print (p1+p2); print (p1*p2); //apartat iv) print (p1 div p2); print (p1 mod p2); //apartat v) print (GCD(p1,p2)); print (LCM(p1,p2)); //apartat vi) print(XGCD(p1,p2)); //apartat vii) p3:=(1/(alpha^4))-(alpha^(-3))*s+(alpha^5)*(s^2); factorizacion(p3); Output: Magma V2.10-6 Sun Mar 28 2004 06:25:55 on modular [Seed = 3214494132] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , , <1, [ 1, 0 ]> ] [ <0, [ 0, 0 ]>, <1, [ 1, 0, 0, 0 ]>, , , , , , , , , , , , , , , <1, [ 1, 0, 0, 0 ]> ] true true true false false true false false false false false false false 2*s^2 + alpha^19*s + alpha^9 alpha^19*s^3 + alpha^22*s^2 + alpha^10*s + alpha^2 alpha^17*s + alpha^5 alpha^15 1 s^3 + alpha^3*s^2 + alpha^15*s + alpha^7 1 alpha^9 alpha^14*s + alpha^2 >> factorizacion(p3);; ^ User error: Identifier 'factorizacion' has not been declared or assigned Total time: 3.059 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 06:26:19 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //apartat vii) [<0,[0,0]>] cat [: r in [0..24]]; [<0,[0,0]>] cat [: r in [0..15]]; //apartat viii) G4:=ext; G8:=ext; G16:=ext; G2 subset G4; G2 subset G8; G2 subset G16; G4 subset G2; G4 subset G8; G4 subset G16; G8 subset G2; G8 subset G4; G8 subset G16; G16 subset G2; G16 subset G4; G16 subset G8; //subset //exercici 2 //apartat i R:=PolynomialRing(G25); IsFinite(R); //apartat ii Bheta:=PrimitiveElement(G5); p1:=alpha^2+alpha*s+Bheta*(s^2); p2:=1+alpha*s; //apartat iii) print (p1+p2); print (p1*p2); //apartat iv) print (p1 div p2); print (p1 mod p2); //apartat v) print (GCD(p1,p2)); print (LCM(p1,p2)); //apartat vi) print(XGCD(p1,p2)); //apartat vii) p3:=(1/(alpha^4))-(alpha^(-3))*s+(alpha^5)*(s^2); Factorizacion(p3); Output: Magma V2.10-6 Sun Mar 28 2004 06:26:16 on modular [Seed = 1215217241] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , , <1, [ 1, 0 ]> ] [ <0, [ 0, 0 ]>, <1, [ 1, 0, 0, 0 ]>, , , , , , , , , , , , , , , <1, [ 1, 0, 0, 0 ]> ] true true true false false true false false false false false false false 2*s^2 + alpha^19*s + alpha^9 alpha^19*s^3 + alpha^22*s^2 + alpha^10*s + alpha^2 alpha^17*s + alpha^5 alpha^15 1 s^3 + alpha^3*s^2 + alpha^15*s + alpha^7 1 alpha^9 alpha^14*s + alpha^2 >> Factorizacion(p3);; ^ User error: Identifier 'Factorizacion' has not been declared or assigned Total time: 3.029 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 06:26:40 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //apartat vii) [<0,[0,0]>] cat [: r in [0..24]]; [<0,[0,0]>] cat [: r in [0..15]]; //apartat viii) G4:=ext; G8:=ext; G16:=ext; G2 subset G4; G2 subset G8; G2 subset G16; G4 subset G2; G4 subset G8; G4 subset G16; G8 subset G2; G8 subset G4; G8 subset G16; G16 subset G2; G16 subset G4; G16 subset G8; //subset //exercici 2 //apartat i R:=PolynomialRing(G25); IsFinite(R); //apartat ii Bheta:=PrimitiveElement(G5); p1:=alpha^2+alpha*s+Bheta*(s^2); p2:=1+alpha*s; //apartat iii) print (p1+p2); print (p1*p2); //apartat iv) print (p1 div p2); print (p1 mod p2); //apartat v) print (GCD(p1,p2)); print (LCM(p1,p2)); //apartat vi) print(XGCD(p1,p2)); //apartat vii) p3:=(1/(alpha^4))-(alpha^(-3))*s+(alpha^5)*(s^2); Factorizacion(p3); Output: Magma V2.10-6 Sun Mar 28 2004 06:26:37 on modular [Seed = 1130739047] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , , <1, [ 1, 0 ]> ] [ <0, [ 0, 0 ]>, <1, [ 1, 0, 0, 0 ]>, , , , , , , , , , , , , , , <1, [ 1, 0, 0, 0 ]> ] true true true false false true false false false false false false false 2*s^2 + alpha^19*s + alpha^9 alpha^19*s^3 + alpha^22*s^2 + alpha^10*s + alpha^2 alpha^17*s + alpha^5 alpha^15 1 s^3 + alpha^3*s^2 + alpha^15*s + alpha^7 1 alpha^9 alpha^14*s + alpha^2 >> Factorizacion(p3);; ^ User error: Identifier 'Factorizacion' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 06:26:58 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //apartat vii) [<0,[0,0]>] cat [: r in [0..24]]; [<0,[0,0]>] cat [: r in [0..15]]; //apartat viii) G4:=ext; G8:=ext; G16:=ext; G2 subset G4; G2 subset G8; G2 subset G16; G4 subset G2; G4 subset G8; G4 subset G16; G8 subset G2; G8 subset G4; G8 subset G16; G16 subset G2; G16 subset G4; G16 subset G8; //subset //exercici 2 //apartat i R:=PolynomialRing(G25); IsFinite(R); //apartat ii Bheta:=PrimitiveElement(G5); p1:=alpha^2+alpha*s+Bheta*(s^2); p2:=1+alpha*s; //apartat iii) print (p1+p2); print (p1*p2); //apartat iv) print (p1 div p2); print (p1 mod p2); //apartat v) print (GCD(p1,p2)); print (LCM(p1,p2)); //apartat vi) print(XGCD(p1,p2)); //apartat vii) p3:=(1/(alpha^4))-(alpha^(-3))*s+(alpha^5)*(s^2); Factorization(p3); Output: Magma V2.10-6 Sun Mar 28 2004 06:26:55 on modular [Seed = 1518120044] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , , <1, [ 1, 0 ]> ] [ <0, [ 0, 0 ]>, <1, [ 1, 0, 0, 0 ]>, , , , , , , , , , , , , , , <1, [ 1, 0, 0, 0 ]> ] true true true false false true false false false false false false false 2*s^2 + alpha^19*s + alpha^9 alpha^19*s^3 + alpha^22*s^2 + alpha^10*s + alpha^2 alpha^17*s + alpha^5 alpha^15 1 s^3 + alpha^3*s^2 + alpha^15*s + alpha^7 1 alpha^9 alpha^14*s + alpha^2 [ ] Total time: 3.139 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 06:27:00 2004 Input: P:= PolynomialRing (Integers()); G25 := ext < GF(5) | P![3,2,1] >; Seq := [a : a in G25 | a ne 0 and Order(a) eq 24]; alpha := Seq[1]; sol := MinimalPolynomial(alpha); ElementToSequence(sol); G25[3,2,1]; Output: Magma V2.10-6 Sun Mar 28 2004 06:26:57 on modular [Seed = 1601808791] ------------------------------------- [ 3, 2, 1 ] >> G25[3,2,1]; ^ Runtime error in '[]': Bad argument types Total time: 3.099 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 06:27:11 2004 Input: P:= PolynomialRing (Integers()); G25 := ext < GF(5) | P![3,2,1] >; Seq := [a : a in G25 | a ne 0 and Order(a) eq 24]; alpha := Seq[1]; sol := MinimalPolynomial(alpha); ElementToSequence(sol); G25![3,2,1]; Output: Magma V2.10-6 Sun Mar 28 2004 06:27:08 on modular [Seed = 1816828585] ------------------------------------- [ 3, 2, 1 ] >> G25![3,2,1]; ^ Runtime error in '!': Sequence must have length 2 to lift into this finite field LHS: FldFin RHS: [RngIntElt] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 06:27:40 2004 Input: P:= PolynomialRing (Integers()); G25 := ext < GF(5) | P![3,2,1] >; Seq := [a : a in G25 | a ne 0 and Order(a) eq 24]; alpha := Seq[3]; sol := MinimalPolynomial(alpha); ElementToSequence(sol); Output: Magma V2.10-6 Sun Mar 28 2004 06:27:37 on modular [Seed = 1732350343] ------------------------------------- [ 2, 1, 1 ] Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 06:27:57 2004 Input: P:= PolynomialRing (Integers()); G25 := ext < GF(5) | P![3,2,1] >; Seq := [a : a in G25 | a ne 0 and Order(a) eq 24]; alpha := Seq[8]; sol := MinimalPolynomial(alpha); ElementToSequence(sol); Output: Magma V2.10-6 Sun Mar 28 2004 06:27:54 on modular [Seed = 2119731341] ------------------------------------- [ 2, 4, 1 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 06:28:46 2004 Input: P:= PolynomialRing (Integers()); G25 := ext < GF(5) | P![3,2,1] >; Seq := [a : a in G25 | a ne 0 and Order(a) eq 24]; alpha := Seq[8]; ElementToSequence(alpha); sol := MinimalPolynomial(alpha); ElementToSequence(sol); Output: Magma V2.10-6 Sun Mar 28 2004 06:28:43 on modular [Seed = 137297578] ------------------------------------- [ 1, 3 ] [ 2, 4, 1 ] Total time: 3.459 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 06:28:48 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //apartat vii) [<0,[0,0]>] cat [: r in [0..24]]; [<0,[0,0]>] cat [: r in [0..15]]; //apartat viii) G4:=ext; G8:=ext; G16:=ext; G2 subset G4; G2 subset G8; G2 subset G16; G4 subset G2; G4 subset G8; G4 subset G16; G8 subset G2; G8 subset G4; G8 subset G16; G16 subset G2; G16 subset G4; G16 subset G8; //subset //exercici 2 //apartat i R:=PolynomialRing(G25); IsFinite(R); //apartat ii Bheta:=PrimitiveElement(G5); p1:=alpha^2+alpha*s+Bheta*(s^2); p2:=1+alpha*s; //apartat iii) print (p1+p2); print (p1*p2); //apartat iv) print (p1 div p2); print (p1 mod p2); //apartat v) print (GCD(p1,p2)); print (LCM(p1,p2)); //apartat vi) print(XGCD(p1,p2)); //apartat vii) p3:=(1/(alpha^4))-(alpha^(-3))*s+(alpha^5)*(s^2); Factorization(p3); Roots(p3); Output: Magma V2.10-6 Sun Mar 28 2004 06:28:44 on modular [Seed = 220986280] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , , <1, [ 1, 0 ]> ] [ <0, [ 0, 0 ]>, <1, [ 1, 0, 0, 0 ]>, , , , , , , , , , , , , , , <1, [ 1, 0, 0, 0 ]> ] true true true false false true false false false false false false false 2*s^2 + alpha^19*s + alpha^9 alpha^19*s^3 + alpha^22*s^2 + alpha^10*s + alpha^2 alpha^17*s + alpha^5 alpha^15 1 s^3 + alpha^3*s^2 + alpha^15*s + alpha^7 1 alpha^9 alpha^14*s + alpha^2 [ ] [] Total time: 3.549 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 06:31:14 2004 Input: P:= PolynomialRing (Integers()); G25 := ext < GF(5) | P![3,2,1] >; Seq := [a : a in G25 | a ne 0 and Order(a) eq 24]; alpha := Seq[8]; sol := MinimalPolynomial(alpha); ElementToSequence(sol); roots(sol,GF(5)); roots(sol,G25); Output: Magma V2.10-6 Sun Mar 28 2004 06:31:11 on modular [Seed = 305456420] ------------------------------------- [ 2, 4, 1 ] >> roots(sol,GF(5)); ^ User error: Identifier 'roots' has not been declared or assigned >> roots(sol,G25); ^ User error: Identifier 'roots' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 06:31:29 2004 Input: P:= PolynomialRing (Integers()); G25 := ext < GF(5) | P![3,2,1] >; Seq := [a : a in G25 | a ne 0 and Order(a) eq 24]; alpha := Seq[8]; sol := MinimalPolynomial(alpha); ElementToSequence(sol); Roots(sol,GF(5)); Roots(sol,G25); Output: Magma V2.10-6 Sun Mar 28 2004 06:31:26 on modular [Seed = 755751658] ------------------------------------- [ 2, 4, 1 ] [] [ , ] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 06:31:52 2004 Input: P:= PolynomialRing (Integers(5)); G25 := ext < GF(5) | P![3,2,1] >; Seq := [a : a in G25 | a ne 0 and Order(a) eq 24]; alpha := Seq[8]; sol := MinimalPolynomial(alpha); ElementToSequence(sol); Roots(sol,GF(5)); Roots(sol,G25); Output: Magma V2.10-6 Sun Mar 28 2004 06:31:49 on modular [Seed = 604165064] ------------------------------------- [ 2, 4, 1 ] [] [ , ] Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 06:32:01 2004 Input: P:= PolynomialRing (Integers()); G25 := ext < GF(5) | P![3,2,1] >; Seq := [a : a in G25 | a ne 0 and Order(a) eq 24]; alpha := Seq[8]; sol := MinimalPolynomial(alpha); ElementToSequence(sol); Roots(sol,GF(5)); Roots(sol,G25); Output: Magma V2.10-6 Sun Mar 28 2004 06:31:58 on modular [Seed = 1041811929] ------------------------------------- [ 2, 4, 1 ] [] [ , ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 06:32:12 2004 Input: P:= PolynomialRing (Integers()); G25 := ext < GF(5) | P![3,2,1] >; Seq := [a : a in G25 | a ne 0 and Order(a) eq 24]; alpha := Seq[6]; sol := MinimalPolynomial(alpha); ElementToSequence(sol); Roots(sol,GF(5)); Roots(sol,G25); Output: Magma V2.10-6 Sun Mar 28 2004 06:32:08 on modular [Seed = 3387899448] ------------------------------------- [ 3, 3, 1 ] [] [ , ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 06:32:53 2004 Input: P:= PolynomialRing (Integers()); G25 := ext < GF(5) | P![3,2,1] >; Seq := [a : a in G25 | a ne 0 and Order(a) eq 24]; alpha := Seq[6]; sol := MinimalPolynomial(alpha); ElementToSequence(sol);ç Degree(sol); Roots(sol,GF(5)); Roots(sol,G25); Output: Magma V2.10-6 Sun Mar 28 2004 06:32:50 on modular [Seed = 3269735785] ------------------------------------- [ 3, 3, 1 ] >> ElementToSequence(sol);^' ^ User error: Unknown character (ascii value -25) 2 [] [ , ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 06:33:04 2004 Input: P:= PolynomialRing (Integers()); G25 := ext < GF(5) | P![3,2,1] >; Seq := [a : a in G25 | a ne 0 and Order(a) eq 24]; alpha := Seq[6]; sol := MinimalPolynomial(alpha); ElementToSequence(sol); Degree(sol); Roots(sol,GF(5)); Roots(sol,G25); Output: Magma V2.10-6 Sun Mar 28 2004 06:33:01 on modular [Seed = 3724225145] ------------------------------------- [ 3, 3, 1 ] 2 [] [ , ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 06:43:46 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //apartat vii) [<0,[0,0]>] cat [: r in [0..24]]; [<0,[0,0]>] cat [: r in [0..15]]; //apartat viii) G4:=ext; G8:=ext; G16:=ext; G2 subset G4; G2 subset G8; G2 subset G16; G4 subset G2; G4 subset G8; G4 subset G16; G8 subset G2; G8 subset G4; G8 subset G16; G16 subset G2; G16 subset G4; G16 subset G8; //subset //exercici 2 //apartat i R:=PolynomialRing(G25); IsFinite(R); //apartat ii Bheta:=PrimitiveElement(G5); p1:=alpha^2+alpha*s+Bheta*(s^2); p2:=1+alpha*s; //apartat iii) print (p1+p2); print (p1*p2); //apartat iv) print (p1 div p2); print (p1 mod p2); //apartat v) print (GCD(p1,p2)); print (LCM(p1,p2)); //apartat vi) print(XGCD(p1,p2)); //apartat vii) p3:=(1/(alpha^4))-(alpha^(-3))*s+(alpha^5)*(s^2); Factorization(p3); Roots(p3); (alpha^19*s^3 + alpha^22*s^2 + alpha^10*s + alpha^2)*(alpha^(-19)); Output: Magma V2.10-6 Sun Mar 28 2004 06:43:43 on modular [Seed = 4258990043] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , , <1, [ 1, 0 ]> ] [ <0, [ 0, 0 ]>, <1, [ 1, 0, 0, 0 ]>, , , , , , , , , , , , , , , <1, [ 1, 0, 0, 0 ]> ] true true true false false true false false false false false false false 2*s^2 + alpha^19*s + alpha^9 alpha^19*s^3 + alpha^22*s^2 + alpha^10*s + alpha^2 alpha^17*s + alpha^5 alpha^15 1 s^3 + alpha^3*s^2 + alpha^15*s + alpha^7 1 alpha^9 alpha^14*s + alpha^2 [ ] [] s^3 + alpha^3*s^2 + alpha^15*s + alpha^7 Total time: 3.039 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 06:53:07 2004 Input: P:= PolynomialRing (Integers()); G25 := ext < GF(5) | P![3,2,1] >; Seq := [a : a in G25 | a ne 0 and Order(a) eq 24]; alpha := Seq[6]; sol := 2*alpha^(-3) - alpha^5 + alpha^6 / (alpha + 2); sol; Output: Magma V2.10-6 Sun Mar 28 2004 06:53:04 on modular [Seed = 2242083180] ------------------------------------- G25.1^19 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 07:10:25 2004 Input: P:= PolynomialRing (Integers()); G25 := ext < GF(5) | P![3,2,1] >; Seq := [a : a in G25 | a ne 0 and Order(a) eq 24]; alpha := Seq[6]; sol := 2*alpha^(-3) - alpha^5 + alpha^6 / (alpha + 2); sol; IsInvertible(sol); Output: Magma V2.10-6 Sun Mar 28 2004 07:10:22 on modular [Seed = 1130742695] ------------------------------------- G25.1^19 true G25.1^5 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 07:11:38 2004 Input: P:= PolynomialRing (Integers()); G25 := ext < GF(5) | P![3,2,1] >; Seq := [a : a in G25 | a ne 0 and Order(a) eq 24]; alpha := Seq[6]; sol := 2*alpha^(-3) - alpha^5 + alpha^6 / (alpha + 2); sol; IsInvertible(sol); Inv := [IsInvertible(a) : a in G25 | a ne 0 and Order(a) eq 24]; Output: Magma V2.10-6 Sun Mar 28 2004 07:11:35 on modular [Seed = 1484708069] ------------------------------------- G25.1^19 true G25.1^5 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 07:11:57 2004 Input: P:= PolynomialRing (Integers()); G25 := ext < GF(5) | P![3,2,1] >; Seq := [a : a in G25 | a ne 0 and Order(a) eq 24]; alpha := Seq[6]; sol := 2*alpha^(-3) - alpha^5 + alpha^6 / (alpha + 2); sol; IsInvertible(sol); Inv := [IsInvertible(a) : a in G25 | a ne 0 and Order(a) eq 24]; Inv; Output: Magma V2.10-6 Sun Mar 28 2004 07:11:54 on modular [Seed = 1366806545] ------------------------------------- G25.1^19 true G25.1^5 [ true, true, true, true, true, true, true, true ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 07:12:25 2004 Input: P:= PolynomialRing (Integers()); G25 := ext < GF(5) | P![3,2,1] >; Seq := [a : a in G25 | a ne 0 and Order(a) eq 24]; alpha := Seq[6]; sol := 2*alpha^(-3) - alpha^5 + alpha^6 / (alpha + 2); sol; IsInvertible(sol); Inv := [(a,IsInvertible(a)) : a in G25]; Inv; Output: Magma V2.10-6 Sun Mar 28 2004 07:12:22 on modular [Seed = 1850273538] ------------------------------------- G25.1^19 true G25.1^5 >> Inv := [(a,IsInvertible(a)) : a in G25]; ^ Runtime error: No constructor provided for this type of object >> Inv;; ^ User error: Identifier 'Inv' has not been declared or assigned Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 07:12:43 2004 Input: P:= PolynomialRing (Integers()); G25 := ext < GF(5) | P![3,2,1] >; Seq := [a : a in G25 | a ne 0 and Order(a) eq 24]; alpha := Seq[6]; sol := 2*alpha^(-3) - alpha^5 + alpha^6 / (alpha + 2); sol; IsInvertible(sol); Inv := [{a,IsInvertible(a)} : a in G25]; Inv; Output: Magma V2.10-6 Sun Mar 28 2004 07:12:40 on modular [Seed = 1732371989] ------------------------------------- G25.1^19 true G25.1^5 >> Inv := [{a,IsInvertible(a)} : a in G25]; ^ Runtime error in { ... }: Can't coerce argument 2 into the universe >> Inv;; ^ User error: Identifier 'Inv' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 07:13:08 2004 Input: P:= PolynomialRing (Integers()); G25 := ext < GF(5) | P![3,2,1] >; Seq := [a : a in G25 | a ne 0 and Order(a) eq 24]; alpha := Seq[6]; sol := 2*alpha^(-3) - alpha^5 + alpha^6 / (alpha + 2); sol; IsInvertible(sol); Inv := [[a,IsInvertible(a)] : a in G25 | a ne 0]; Inv; Output: Magma V2.10-6 Sun Mar 28 2004 07:13:05 on modular [Seed = 2103180390] ------------------------------------- G25.1^19 true G25.1^5 >> Inv := [[a,IsInvertible(a)] : a in G25 | a ne 0]; ^ Runtime error in [ ... ]: Could not find a valid universe >> Inv;; ^ User error: Identifier 'Inv' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 07:13:27 2004 Input: P:= PolynomialRing (Integers()); G25 := ext < GF(5) | P![3,2,1] >; Seq := [a : a in G25 | a ne 0 and Order(a) eq 24]; alpha := Seq[6]; sol := 2*alpha^(-3) - alpha^5 + alpha^6 / (alpha + 2); sol; IsInvertible(sol); Inv := [IsInvertible(a) : a in G25 | a ne 0]; Inv; Output: Magma V2.10-6 Sun Mar 28 2004 07:13:24 on modular [Seed = 187533861] ------------------------------------- G25.1^19 true G25.1^5 [ true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 07:19:28 2004 Input: G2 := GF(2); Seq := [a : a in G2]; G3 := GF(3); Seq := [a : a in G3]; G5 := GF(5); Seq := [a : a in G5]; Output: Magma V2.10-6 Sun Mar 28 2004 07:19:25 on modular [Seed = 423599006] ------------------------------------- Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 07:19:42 2004 Input: G2 := GF(2); [a : a in G2]; G3 := GF(3); Seq := [a : a in G3]; G5 := GF(5); Seq := [a : a in G5]; Output: Magma V2.10-6 Sun Mar 28 2004 07:19:39 on modular [Seed = 372282503] ------------------------------------- [ 0, 1 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 07:19:52 2004 Input: G2 := GF(2); [a : a in G2]; G3 := GF(3); [a : a in G3]; G5 := GF(5); [a : a in G5]; Output: Magma V2.10-6 Sun Mar 28 2004 07:19:49 on modular [Seed = 789163392] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 07:22:08 2004 Input: Z9 := Integers(9); IsField(Z9); IsInvertible(Z9); Output: Magma V2.10-6 Sun Mar 28 2004 07:22:05 on modular [Seed = 1058651160] ------------------------------------- false >> IsInvertible(Z9);; ^ Runtime error in 'IsInvertible': Bad argument types Argument types given: RngIntRes Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 07:22:26 2004 Input: Z9 := Integers(9); IsField(Z9); IsInvertible(Z9!3); Output: Magma V2.10-6 Sun Mar 28 2004 07:22:23 on modular [Seed = 890484224] ------------------------------------- false false Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 07:29:12 2004 Input: P3:= PolynomialRing (Integers(3)); P2:= PolynomialRing (Integers(2)); P5:= PolynomialRing (Integers(5)); IsInvertible(P3![2,2,1]); IsInvertible(P2![1,1,0,0,1]); IsInvertible(P5![1,2,1]); IsInvertible(P3![1,2,1]); Output: Magma V2.10-6 Sun Mar 28 2004 07:29:09 on modular [Seed = 3690815108] ------------------------------------- false false false false Total time: 2.899 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 07:32:01 2004 Input: P3:= PolynomialRing (Integers(3)); P2:= PolynomialRing (Integers(2)); P5:= PolynomialRing (Integers(5)); IsIrreducible(P3![2,2,1]); IsIrreducible(P2![1,1,0,0,1]); IsIrreducible(P5![1,2,1]); IsIrreducible(P3![1,2,1]); Output: Magma V2.10-6 Sun Mar 28 2004 07:31:58 on modular [Seed = 3905842460] ------------------------------------- true true false false Total time: 2.969 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 07:32:22 2004 Input: P3:= PolynomialRing (Integers(3)); P2:= PolynomialRing (Integers(2)); P5:= PolynomialRing (Integers(5)); IsIrreducible(P3![2,2,1]); IsIrreducible(P2![1,1,0,0,1]); IsIrreducible(P5![3,2,1]); IsIrreducible(P3![1,2,1]); Output: Magma V2.10-6 Sun Mar 28 2004 07:32:19 on modular [Seed = 3787940984] ------------------------------------- true true true false Total time: 2.989 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 07:33:57 2004 Input: P3:= PolynomialRing (Integers(3)); P2:= PolynomialRing (Integers(2)); P5:= PolynomialRing (Integers(5)); IsIrreducible(P3![2,2,1]); IsIrreducible(P2![1,1,0,0,1]); IsIrreducible(P5![3,2,1]); IsIrreducible(P3![1,2,1]); G9 := ext < GF(3) | P3![2,2,1] >; G16 := ext < GF(2) | P2![1,1,0,0,1] >; G25 := ext < GF(5) | P5![3,2,1] >; G9b := ext < GF(3) | P3![2,2,1] >; Output: Magma V2.10-6 Sun Mar 28 2004 07:33:54 on modular [Seed = 4292442503] ------------------------------------- true true true false Total time: 2.959 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 07:34:59 2004 Input: P3:= PolynomialRing (Integers(3)); P2:= PolynomialRing (Integers(2)); P5:= PolynomialRing (Integers(5)); IsIrreducible(P3![2,2,1]); IsIrreducible(P2![1,1,0,0,1]); IsIrreducible(P5![3,2,1]); IsIrreducible(P3![1,2,1]); G9 := ext < GF(3) | P3![2,2,1] >; G16 := ext < GF(2) | P2![1,1,0,0,1] >; G25 := ext < GF(5) | P5![3,2,1] >; G9b := ext < GF(3) | P3![2,2,1] >; Seq := {a : a in G9b} Output: Magma V2.10-6 Sun Mar 28 2004 07:34:56 on modular [Seed = 4124275663] ------------------------------------- true true true false Total time: 2.939 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 07:35:10 2004 Input: P3:= PolynomialRing (Integers(3)); P2:= PolynomialRing (Integers(2)); P5:= PolynomialRing (Integers(5)); IsIrreducible(P3![2,2,1]); IsIrreducible(P2![1,1,0,0,1]); IsIrreducible(P5![3,2,1]); IsIrreducible(P3![1,2,1]); G9 := ext < GF(3) | P3![2,2,1] >; G16 := ext < GF(2) | P2![1,1,0,0,1] >; G25 := ext < GF(5) | P5![3,2,1] >; G9b := ext < GF(3) | P3![2,2,1] >; Seq := {a : a in G9b}; Output: Magma V2.10-6 Sun Mar 28 2004 07:35:07 on modular [Seed = 2258632887] ------------------------------------- true true true false Total time: 2.999 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 07:35:20 2004 Input: P3:= PolynomialRing (Integers(3)); P2:= PolynomialRing (Integers(2)); P5:= PolynomialRing (Integers(5)); IsIrreducible(P3![2,2,1]); IsIrreducible(P2![1,1,0,0,1]); IsIrreducible(P5![3,2,1]); IsIrreducible(P3![1,2,1]); G9 := ext < GF(3) | P3![2,2,1] >; G16 := ext < GF(2) | P2![1,1,0,0,1] >; G25 := ext < GF(5) | P5![3,2,1] >; G9b := ext < GF(3) | P3![2,2,1] >; Seq := {a : a in G9b}; Seq; Output: Magma V2.10-6 Sun Mar 28 2004 07:35:16 on modular [Seed = 2679707985] ------------------------------------- true true true false { 1, G9b.1, G9b.1^2, G9b.1^3, 2, G9b.1^5, G9b.1^6, G9b.1^7, 0 } Total time: 3.009 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 07:35:42 2004 Input: P3:= PolynomialRing (Integers(3)); P2:= PolynomialRing (Integers(2)); P5:= PolynomialRing (Integers(5)); IsIrreducible(P3![2,2,1]); IsIrreducible(P2![1,1,0,0,1]); IsIrreducible(P5![3,2,1]); IsIrreducible(P3![1,2,1]); G9 := ext < GF(3) | P3![2,2,1] >; G16 := ext < GF(2) | P2![1,1,0,0,1] >; G25 := ext < GF(5) | P5![3,2,1] >; G9b := ext < GF(3) | P3![1,2,1] >; Output: Magma V2.10-6 Sun Mar 28 2004 07:35:39 on modular [Seed = 2494698053] ------------------------------------- true true true false >> G9b := ext < GF(3) | P3![1,2,1] >; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 2.999 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 08:16:57 2004 Input: G25 := ext < GF(5) | P![3,2,1] >; Seq := {Order(a) : a in G25 | a ne 0}; Seq; Seq := {a : a in G25 | a ne 0 and Order(a) eq 24}; Seq; #Seq; Output: Magma V2.10-6 Sun Mar 28 2004 08:16:54 on modular [Seed = 1951589497] ------------------------------------- >> G25 := ext < GF(5) | P![3,2,1] >; ^ User error: Identifier 'P' has not been declared or assigned >> Seq := {Order(a) : a in G25 | a ne 0}; ^ User error: Identifier 'G25' has not been declared or assigned Intrinsic 'Seq' Signatures: ( M) -> SeqEnum [ Search: "BFS" | "DFS" ] The (explicitly enumerated) sequence of words, w, in M with 0 <= length(w) <= #M. ( M, a, b) -> SeqEnum [ Search: "BFS" | "DFS" ] The (explicitly enumerated) sequence of words, w, in M with a <= length(w) <= b. >> Seq := {a : a in G25 | a ne 0 and Order(a) eq 24}; ^ User error: Identifier 'G25' has not been declared or assigned Intrinsic 'Seq' Signatures: ( M) -> SeqEnum [ Search: "BFS" | "DFS" ] The (explicitly enumerated) sequence of words, w, in M with 0 <= length(w) <= #M. ( M, a, b) -> SeqEnum [ Search: "BFS" | "DFS" ] The (explicitly enumerated) sequence of words, w, in M with a <= length(w) <= b. >> #Seq;; ^ Runtime error in '#': Bad argument types Argument types given: Intrinsic Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 08:17:50 2004 Input: P5:= PolynomialRing (Integers(5)); G25 := ext < GF(5) | P5![3,2,1] >; Seq := {Order(a) : a in G25 | a ne 0}; Seq; Seq := {a : a in G25 | a ne 0 and Order(a) eq 24}; Seq; #Seq; Output: Magma V2.10-6 Sun Mar 28 2004 08:17:48 on modular [Seed = 52794164] ------------------------------------- { 1, 2, 3, 4, 6, 8, 12, 24 } { G25.1^11, G25.1, G25.1^23, G25.1^13, G25.1^5, G25.1^17, G25.1^7, G25.1^19 } 8 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 08:18:21 2004 Input: P5:= PolynomialRing (Integers(5)); G25 := ext < GF(5) | P5![3,2,1] >; Seq := [Order(a) : a in G25 | a ne 0]; Seq; Seq := [a : a in G25 | a ne 0 and Order(a) eq 24]; Seq; #Seq; Output: Magma V2.10-6 Sun Mar 28 2004 08:18:18 on modular [Seed = 440175307] ------------------------------------- [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] 8 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 08:22:58 2004 Input: P5:= PolynomialRing (Integers(5)); G25 := ext < GF(5) | P5![3,2,1] >; Seq := [a : a in G25 | a ne 0 and Order(a) eq 24]; alpha := Seq[6]; sol := MinimalPolynomial(alpha); sol; Degree(sol); Roots(sol,GF(5)); Roots(sol,G25); Output: Magma V2.10-6 Sun Mar 28 2004 08:22:55 on modular [Seed = 789167819] ------------------------------------- $.1^2 + 3*$.1 + 3 2 [] [ , ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 08:23:48 2004 Input: P5:= PolynomialRing (Integers(5)); G25 := ext < GF(5) | P5![3,2,1] >; Seq := [a : a in G25 | a ne 0 and Order(a) eq 24]; alpha := Seq[6]; sol := MinimalPolynomial(alpha); sol; Degree(sol); Roots(sol,GF(5)); Roots(sol,G25); Output: Magma V2.10-6 Sun Mar 28 2004 08:23:45 on modular [Seed = 620999823] ------------------------------------- x^2 + 3*x + 3 2 [] [ , ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 08:24:26 2004 Input: P5:= PolynomialRing (Integers(5)); G25 := ext < GF(5) | P5![3,2,1] >; Seq := [a : a in G25 | a ne 0 and Order(a) eq 24]; alpha := Seq[6]; sol := MinimalPolynomial(alpha); sol; Degree(sol); Roots(sol,GF(5)); Roots(sol,G25); Output: Magma V2.10-6 Sun Mar 28 2004 08:24:23 on modular [Seed = 1008381552] ------------------------------------- x^2 + 3*x + 3 2 [] [ , ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 08:25:29 2004 Input: P5:= PolynomialRing (Integers(5)); G25 := ext < GF(5) | P5![3,2,1] >; Seq := [a : a in G25 | a ne 0 and Order(a) eq 24]; Seq; alpha := Seq[6]; sol := MinimalPolynomial(alpha); sol; Degree(sol); Roots(sol,GF(5)); Roots(sol,G25); Output: Magma V2.10-6 Sun Mar 28 2004 08:25:26 on modular [Seed = 3471334595] ------------------------------------- [ x, x^5, x^7, x^11, x^13, x^17, x^19, x^23 ] x^2 + 3*x + 3 2 [] [ , ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 08:28:09 2004 Input: P5:= PolynomialRing (Integers(5)); G25 := ext < GF(5) | P5![3,2,1] >; Seq := [a : a in G25 | a ne 0 and Order(a) eq 24]; alpha := Seq[6]; sol := 2*alpha^(-3) - alpha^5 + alpha^6 / (alpha + 2); sol; IsInvertible(sol); Inv := [IsInvertible(a) : a in G25 | a ne 0]; Inv; Output: Magma V2.10-6 Sun Mar 28 2004 08:28:06 on modular [Seed = 3303167593] ------------------------------------- x^19 true x^5 [ true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true ] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 08:33:50 2004 Input: P5:= PolynomialRing (Integers(5)); P2:= PolynomialRing (Integers(2)); G25 := ext < GF(5) | P5![3,2,1] >; G16 := ext < GF(2) | P2![1,1,0,0,1] >; TG25 := [a,ElementToSequence(a) : a in G25]; TG25; Output: Magma V2.10-6 Sun Mar 28 2004 08:33:47 on modular [Seed = 3922689433] ------------------------------------- >> TG25 := [a,ElementToSequence(a) : a in G25]; ^ User error: bad syntax >> TG25;; ^ User error: Identifier 'TG25' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 08:34:57 2004 Input: P5:= PolynomialRing (Integers(5)); P2:= PolynomialRing (Integers(2)); G25 := ext < GF(5) | P5![3,2,1] >; G16 := ext < GF(2) | P2![1,1,0,0,1] >; TG25 := [ [a,ElementToSequence(a)] : a in G25]; TG25; Output: Magma V2.10-6 Sun Mar 28 2004 08:34:54 on modular [Seed = 3888214994] ------------------------------------- >> TG25 := [ [a,ElementToSequence(a)] : a in G25]; ^ Runtime error in [ ... ]: Could not find a valid universe >> TG25;; ^ User error: Identifier 'TG25' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 08:35:11 2004 Input: P5:= PolynomialRing (Integers(5)); P2:= PolynomialRing (Integers(2)); G25 := ext < GF(5) | P5![3,2,1] >; G16 := ext < GF(2) | P2![1,1,0,0,1] >; TG25 := [ : a in G25]; TG25; Output: Magma V2.10-6 Sun Mar 28 2004 08:35:08 on modular [Seed = 4074006069] ------------------------------------- [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , , <0, [ 0, 0 ]> ] Total time: 2.969 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 08:36:12 2004 Input: P5:= PolynomialRing (Integers(5)); P2:= PolynomialRing (Integers(2)); G25 := ext < GF(5) | P5![3,2,1] >; G16 := ext < GF(2) | P2![1,1,0,0,1] >; TG25 := [ : a in G25]; TG25; Output: Magma V2.10-6 Sun Mar 28 2004 08:36:09 on modular [Seed = 2309954827] ------------------------------------- [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , , <0, [ 0, 0 ]> ] Total time: 2.919 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 08:36:41 2004 Input: P5:= PolynomialRing (Integers(5)); P2:= PolynomialRing (Integers(2)); G25

:= ext < GF(5) | P5![3,2,1] >; G16

:= ext < GF(2) | P2![1,1,0,0,1] >; TG25 := [ : a in G25]; TG25; Output: Magma V2.10-6 Sun Mar 28 2004 08:36:38 on modular [Seed = 2158367789] ------------------------------------- [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , , <0, [ 0, 0 ]> ] Total time: 2.959 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 08:37:57 2004 Input: P5:= PolynomialRing (Integers(5)); P2:= PolynomialRing (Integers(2)); G25

:= ext < GF(5) | P5![3,2,1] >; G16

:= ext < GF(2) | P2![1,1,0,0,1] >; Seq := [a : a in G25 | a ne 0 and Order(a) eq 24]; alpha := Seq[6]; sol := MinimalPolynomial(alpha); sol; Degree(sol); Roots(sol,GF(5)); Roots(sol,G25); TG25 := [ : a in G25]; TG25; Output: Magma V2.10-6 Sun Mar 28 2004 08:37:54 on modular [Seed = 2662861799] ------------------------------------- x^2 + 3*x + 3 2 [] [ , ] [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , , <0, [ 0, 0 ]> ] Total time: 2.979 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 08:38:33 2004 Input: P5:= PolynomialRing (Integers(5)); P2:= PolynomialRing (Integers(2)); G25

:= ext < GF(5) | P5![3,2,1] >; G16

:= ext < GF(2) | P2![1,1,0,0,1] >; [ : a in G25]; Output: Magma V2.10-6 Sun Mar 28 2004 08:38:30 on modular [Seed = 2494693769] ------------------------------------- [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , , <0, [ 0, 0 ]> ] Total time: 2.969 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 08:39:45 2004 Input: P5:= PolynomialRing (Integers(5)); P2:= PolynomialRing (Integers(2)); G25

:= ext < GF(5) | P5![3,2,1] >; G16

:= ext < GF(2) | P2![1,1,0,0,1] >; [ : a in G16]; [ : a in G25]; Output: Magma V2.10-6 Sun Mar 28 2004 08:39:43 on modular [Seed = 2743416439] ------------------------------------- [ <1, [ 1, 0, 0, 0 ]>, , , , , , , , , , , , , , , <0, [ 0, 0, 0, 0 ]> ] [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , , <0, [ 0, 0 ]> ] Total time: 2.899 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 08:42:10 2004 Input: G2 := GF(2); G4 := GF(4); G8 := GF(8); G16 := GF(16); [a : a in G2]; [a : a in G4]; [a : a in G8]; [a : a in G16]; Output: Magma V2.10-6 Sun Mar 28 2004 08:42:07 on modular [Seed = 2996053206] ------------------------------------- [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 08:42:28 2004 Input: G2 := GF(2); G4 := GF(4); G8 := GF(8); G16 := GF(16); [a : a in G2]; [a : a in G4]; [a : a in G8]; [a : a in G16]; Output: Magma V2.10-6 Sun Mar 28 2004 08:42:25 on modular [Seed = 1315493955] ------------------------------------- [ 0, 1 ] [ 1, x, x^2, 0 ] [ 1, x, x^2, x^3, x^4, x^5, x^6, 0 ] [ 1, x, x^2, x^3, x^4, x^5, x^6, x^7, x^8, x^9, x^10, x^11, x^12, x^13, x^14, 0 ] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 08:43:07 2004 Input: G2 := GF(2); G4 := GF(2,2); G8 := GF(8); G16 := GF(16); [a : a in G2]; [a : a in G4]; [a : a in G8]; [a : a in G16]; Output: Magma V2.10-6 Sun Mar 28 2004 08:43:04 on modular [Seed = 1197592931] ------------------------------------- [ 0, 1 ] [ 1, x, x^2, 0 ] [ 1, x, x^2, x^3, x^4, x^5, x^6, 0 ] [ 1, x, x^2, x^3, x^4, x^5, x^6, x^7, x^8, x^9, x^10, x^11, x^12, x^13, x^14, 0 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 08:43:19 2004 Input: G2 := GF(2); G4 := GF(4); G8 := GF(8); G16 := GF(16); [a : a in G2]; [a : a in G4]; [a : a in G8]; [a : a in G16]; Output: Magma V2.10-6 Sun Mar 28 2004 08:43:16 on modular [Seed = 1484705376] ------------------------------------- [ 0, 1 ] [ 1, x, x^2, 0 ] [ 1, x, x^2, x^3, x^4, x^5, x^6, 0 ] [ 1, x, x^2, x^3, x^4, x^5, x^6, x^7, x^8, x^9, x^10, x^11, x^12, x^13, x^14, 0 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 08:45:07 2004 Input: G2 := GF(2); G4 := GF(4); G8 := GF(8); G16 := GF(16); [a : a in G2]; [a : a in G4]; [a : a in G8]; [a : a in G16]; G16 subset G2 Output: Magma V2.10-6 Sun Mar 28 2004 08:45:04 on modular [Seed = 1867119043] ------------------------------------- [ 0, 1 ] [ 1, x, x^2, 0 ] [ 1, x, x^2, x^3, x^4, x^5, x^6, 0 ] [ 1, x, x^2, x^3, x^4, x^5, x^6, x^7, x^8, x^9, x^10, x^11, x^12, x^13, x^14, 0 ] false Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 08:45:15 2004 Input: G2 := GF(2); G4 := GF(4); G8 := GF(8); G16 := GF(16); [a : a in G2]; [a : a in G4]; [a : a in G8]; [a : a in G16]; G16 subset G2 Output: Magma V2.10-6 Sun Mar 28 2004 08:45:12 on modular [Seed = 1615263428] ------------------------------------- [ 0, 1 ] [ 1, x, x^2, 0 ] [ 1, x, x^2, x^3, x^4, x^5, x^6, 0 ] [ 1, x, x^2, x^3, x^4, x^5, x^6, x^7, x^8, x^9, x^10, x^11, x^12, x^13, x^14, 0 ] false Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 08:45:23 2004 Input: G2 := GF(2); G4 := GF(4); G8 := GF(8); G16 := GF(16); [a : a in G2]; [a : a in G4]; [a : a in G8]; [a : a in G16]; G16 subset G2; Output: Magma V2.10-6 Sun Mar 28 2004 08:45:20 on modular [Seed = 2052910278] ------------------------------------- [ 0, 1 ] [ 1, x, x^2, 0 ] [ 1, x, x^2, x^3, x^4, x^5, x^6, 0 ] [ 1, x, x^2, x^3, x^4, x^5, x^6, x^7, x^8, x^9, x^10, x^11, x^12, x^13, x^14, 0 ] false Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 08:45:31 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; PR25:=PolynomialRing(G25); Output: Magma V2.10-6 Sun Mar 28 2004 08:45:28 on modular [Seed = 1935009223] ------------------------------------- Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 08:45:37 2004 Input: G2 := GF(2); G4 := GF(4); G8 := GF(8); G16 := GF(16); [a : a in G2]; [a : a in G4]; [a : a in G8]; [a : a in G16]; G2 subset G16; Output: Magma V2.10-6 Sun Mar 28 2004 08:45:34 on modular [Seed = 69374646] ------------------------------------- [ 0, 1 ] [ 1, x, x^2, 0 ] [ 1, x, x^2, x^3, x^4, x^5, x^6, 0 ] [ 1, x, x^2, x^3, x^4, x^5, x^6, x^7, x^8, x^9, x^10, x^11, x^12, x^13, x^14, 0 ] true Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 08:45:58 2004 Input: G2 := GF(2); G4 := GF(4); G8 := GF(8); G16 := GF(16); [a : a in G2]; [a : a in G4]; [a : a in G8]; [a : a in G16]; G4 subset G16; Output: Magma V2.10-6 Sun Mar 28 2004 08:45:55 on modular [Seed = 490441282] ------------------------------------- [ 0, 1 ] [ 1, x, x^2, 0 ] [ 1, x, x^2, x^3, x^4, x^5, x^6, 0 ] [ 1, x, x^2, x^3, x^4, x^5, x^6, x^7, x^8, x^9, x^10, x^11, x^12, x^13, x^14, 0 ] true Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 08:49:11 2004 Input: G2 := GF(2); G4 := GF(4); G8 := GF(8); G16 := GF(16); [a : a in G2]; [a : a in G4]; [a : a in G8]; [a : a in G16]; G2 subset G4; G2 subset G8; G2 subset G16; G4 subset G2; G4 subset G8; G4 subset G16; G8 subset G2; G8 subset G4; G8 subset G16; G16 subset G2; G16 subset G4; G16 subset G8; Output: Magma V2.10-6 Sun Mar 28 2004 08:49:08 on modular [Seed = 272009096] ------------------------------------- [ 0, 1 ] [ 1, x, x^2, 0 ] [ 1, x, x^2, x^3, x^4, x^5, x^6, 0 ] [ 1, x, x^2, x^3, x^4, x^5, x^6, x^7, x^8, x^9, x^10, x^11, x^12, x^13, x^14, 0 ] true true true false false true false false false false false false Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 08:54:12 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; P25:=PolynomialRing(G25); CoefficientRing(P25); Output: Magma V2.10-6 Sun Mar 28 2004 08:54:09 on modular [Seed = 570735471] ------------------------------------- Finite field of size 5^2 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 08:55:05 2004 Input: G2 := GF(2); G4 := GF(4); G8 := GF(8); G16 := GF(16); [a : a in G2]; [a : a in G4]; [a : a in G8]; [a : a in G16]; G2 subset G4; G2 subset G8; G2 subset G16; G4 subset G8; G4 subset G16; G8 subset G16; Output: Magma V2.10-6 Sun Mar 28 2004 08:55:02 on modular [Seed = 806791498] ------------------------------------- [ 0, 1 ] [ 1, x, x^2, 0 ] [ 1, x, x^2, x^3, x^4, x^5, x^6, 0 ] [ 1, x, x^2, x^3, x^4, x^5, x^6, x^7, x^8, x^9, x^10, x^11, x^12, x^13, x^14, 0 ] true true true false true false Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 08:57:19 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; Output: Magma V2.10-6 Sun Mar 28 2004 08:57:15 on modular [Seed = 3387904062] ------------------------------------- Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 08:58:42 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G5"); llista; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; Output: Magma V2.10-6 Sun Mar 28 2004 08:58:39 on modular [Seed = 3707389599] ------------------------------------- >> der(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; en ^ User error: bad syntax Elements primitius de G5 [ 2, 3 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 08:59:15 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; Output: Magma V2.10-6 Sun Mar 28 2004 08:59:12 on modular [Seed = 3589492649] ------------------------------------- Elements primitius de G5 [ 2, 3 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 09:00:08 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; alpha:=llista[1]; beta; alpha; Output: Magma V2.10-6 Sun Mar 28 2004 09:00:05 on modular [Seed = 3821369802] ------------------------------------- Elements primitius de G5 [ 2, 3 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] 2 alfa Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 09:01:33 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*x+x^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; p1:=alfa^2+alfa*x+beta*x^2; p2:=1+alfa*x; p1; p2; Output: Magma V2.10-6 Sun Mar 28 2004 09:01:29 on modular [Seed = 2191792247] ------------------------------------- Elements primitius de G5 [ 2, 3 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] >> p1:=alfa^2+alfa*x+beta*x^2; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt >> p2:=1+alfa*x; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt >> p1; ^ User error: Identifier 'p1' has not been declared or assigned >> p2;; ^ User error: Identifier 'p2' has not been declared or assigned Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 09:02:10 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; p1:=alfa^2+alfa*x+beta*x^2; p2:=1+alfa*x; p1; p2; Output: Magma V2.10-6 Sun Mar 28 2004 09:02:06 on modular [Seed = 2612855049] ------------------------------------- Elements primitius de G5 [ 2, 3 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] >> p1:=alfa^2+alfa*x+beta*x^2; ^ User error: Identifier 'x' has not been declared or assigned >> p2:=1+alfa*x; ^ User error: Identifier 'x' has not been declared or assigned >> p1; ^ User error: Identifier 'p1' has not been declared or assigned >> p2;; ^ User error: Identifier 'p2' has not been declared or assigned Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 09:03:26 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; PR5:=PolynomialRing(G25); p1:=alfa^2+alfa*x+beta*x^2; p2:=1+alfa*x; p1; p2; Output: Magma V2.10-6 Sun Mar 28 2004 09:03:22 on modular [Seed = 2928162248] ------------------------------------- Elements primitius de G5 [ 2, 3 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] 2*x^2 + alfa*x + alfa^2 alfa*x + 1 Total time: 3.359 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 09:03:58 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; PR5:=PolynomialRing(G25); print " "; p1:=alfa^2+alfa*x+beta*x^2; p2:=1+alfa*x; p1; p2; Output: Magma V2.10-6 Sun Mar 28 2004 09:03:54 on modular [Seed = 2810264737] ------------------------------------- Elements primitius de G5 [ 2, 3 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] 2*x^2 + alfa*x + alfa^2 alfa*x + 1 Total time: 3.209 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 09:04:59 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; PR5:=PolynomialRing(G25); print " "; p1:=alfa^2+alfa*x+beta*x^2; p2:=1+alfa*x; p1; p2; suma:=p1+p2; suma; Output: Magma V2.10-6 Sun Mar 28 2004 09:04:55 on modular [Seed = 3114214002] ------------------------------------- Elements primitius de G5 [ 2, 3 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] 2*x^2 + alfa*x + alfa^2 alfa*x + 1 2*x^2 + alfa^19*x + alfa^9 Total time: 4.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 09:10:18 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; PR5:=PolynomialRing(G25); print " "; p1:=alfa^2+alfa*x+beta*x^2; p2:=1+alfa*x; p1; p2; p1+p2; p1*p2; Output: Magma V2.10-6 Sun Mar 28 2004 09:10:15 on modular [Seed = 1113906888] ------------------------------------- Elements primitius de G5 [ 2, 3 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] 2*x^2 + alfa*x + alfa^2 alfa*x + 1 2*x^2 + alfa^19*x + alfa^9 alfa^19*x^3 + alfa^22*x^2 + alfa^10*x + alfa^2 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 09:11:07 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; PR5:=PolynomialRing(G25); print " "; p1:=alfa^2+alfa*x+beta*x^2; p2:=1+alfa*x; print "Polinomis"; p1; p2; print "Suma"; p1+p2; print "Producte"; p1*p2; Output: Magma V2.10-6 Sun Mar 28 2004 09:11:04 on modular [Seed = 1433651680] ------------------------------------- Elements primitius de G5 [ 2, 3 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Polinomis 2*x^2 + alfa*x + alfa^2 alfa*x + 1 Suma 2*x^2 + alfa^19*x + alfa^9 Producte alfa^19*x^3 + alfa^22*x^2 + alfa^10*x + alfa^2 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 09:12:43 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; PR5:=PolynomialRing(G25); print " "; p1:=alfa^2+alfa*x+beta*x^2; p2:=1+alfa*x; print "Polinomis"; p1; p2; print "Suma"; p1+p2; print "Producte"; p1*p2; print "Quocient de p1/p2"; 5/3; print "Residu de p1/p2"; 5%3; Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed. ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 09:12:59 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; PR5:=PolynomialRing(G25); print " "; p1:=alfa^2+alfa*x+beta*x^2; p2:=1+alfa*x; print "Polinomis"; p1; p2; print "Suma"; p1+p2; print "Producte"; p1*p2; print "Quocient de p1/p2"; 5/3; print "Residu de p1/p2"; 5 mod 3; Output: Magma V2.10-6 Sun Mar 28 2004 09:12:56 on modular [Seed = 1698953280] ------------------------------------- Elements primitius de G5 [ 2, 3 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Polinomis 2*x^2 + alfa*x + alfa^2 alfa*x + 1 Suma 2*x^2 + alfa^19*x + alfa^9 Producte alfa^19*x^3 + alfa^22*x^2 + alfa^10*x + alfa^2 Quocient de p1/p2 5/3 Residu de p1/p2 2 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 09:14:00 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; PR5:=PolynomialRing(G25); print " "; p1:=alfa^2+alfa*x+beta*x^2; p2:=1+alfa*x; print "Polinomis"; p1; p2; print "Suma"; p1+p2; print "Producte"; p1*p2; print "Quocient de p1/p2"; 5 div 3; print "Residu de p1/p2"; 5 mod 3; Output: Magma V2.10-6 Sun Mar 28 2004 09:13:57 on modular [Seed = 2119754646] ------------------------------------- Elements primitius de G5 [ 2, 3 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Polinomis 2*x^2 + alfa*x + alfa^2 alfa*x + 1 Suma 2*x^2 + alfa^19*x + alfa^9 Producte alfa^19*x^3 + alfa^22*x^2 + alfa^10*x + alfa^2 Quocient de p1/p2 1 Residu de p1/p2 2 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 09:14:28 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; PR5:=PolynomialRing(G25); print " "; p1:=alfa^2+alfa*x+beta*x^2; p2:=1+alfa*x; print "Polinomis"; p1; p2; print "Suma"; p1+p2; print "Producte"; p1*p2; print "Quocient de p1/p2"; p1 div p2; print "Residu de p1/p2"; p1 mod p2; Output: Magma V2.10-6 Sun Mar 28 2004 09:14:25 on modular [Seed = 1901587709] ------------------------------------- Elements primitius de G5 [ 2, 3 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Polinomis 2*x^2 + alfa*x + alfa^2 alfa*x + 1 Suma 2*x^2 + alfa^19*x + alfa^9 Producte alfa^19*x^3 + alfa^22*x^2 + alfa^10*x + alfa^2 Quocient de p1/p2 alfa^17*x + alfa^5 Residu de p1/p2 alfa^15 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 09:15:17 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; PR5:=PolynomialRing(G25); print " "; p1:=alfa^2+alfa*x+beta*x^2; p2:=1+alfa*x; print "Polinomis"; p1; p2; print "Suma"; p1+p2; print "Producte"; p1*p2; print "Quocient de p1/p2"; p1 div p2; print "Residu de p1/p2"; p1 mod p2; ((alfa^17*x + alfa^5)*p2)+alfa^15; Output: Magma V2.10-6 Sun Mar 28 2004 09:15:14 on modular [Seed = 69376443] ------------------------------------- Elements primitius de G5 [ 2, 3 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Polinomis 2*x^2 + alfa*x + alfa^2 alfa*x + 1 Suma 2*x^2 + alfa^19*x + alfa^9 Producte alfa^19*x^3 + alfa^22*x^2 + alfa^10*x + alfa^2 Quocient de p1/p2 alfa^17*x + alfa^5 Residu de p1/p2 alfa^15 2*x^2 + alfa*x + alfa^2 Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 09:15:48 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; PR5:=PolynomialRing(G25); print " "; p1:=alfa^2+alfa*x+beta*x^2; p2:=1+alfa*x; print "Polinomis"; p1; p2; print "Suma"; p1+p2; print "Producte"; p1*p2; print "Quocient de p1/p2"; p1 div p2; print "Residu de p1/p2"; p1 mod p2; Output: Magma V2.10-6 Sun Mar 28 2004 09:15:45 on modular [Seed = 523862339] ------------------------------------- Elements primitius de G5 [ 2, 3 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Polinomis 2*x^2 + alfa*x + alfa^2 alfa*x + 1 Suma 2*x^2 + alfa^19*x + alfa^9 Producte alfa^19*x^3 + alfa^22*x^2 + alfa^10*x + alfa^2 Quocient de p1/p2 alfa^17*x + alfa^5 Residu de p1/p2 alfa^15 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 09:18:18 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; PR5:=PolynomialRing(G25); print " "; p1:=alfa^2+alfa*x+beta*x^2; p2:=1+alfa*x; print "Polinomis"; p1; p2; print "Suma"; p1+p2; print "Producte"; p1*p2; print "Quocient de p1/p2"; p1 div p2; print "Residu de p1/p2"; p1 mod p2; print "Maxim Comu Divisor de p1 i p2"; GCD(p1,p2); print "Minim Comu Multiple de p1 i p2"; LCM(p1,p2); Output: Magma V2.10-6 Sun Mar 28 2004 09:18:14 on modular [Seed = 322276856] ------------------------------------- Elements primitius de G5 [ 2, 3 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Polinomis 2*x^2 + alfa*x + alfa^2 alfa*x + 1 Suma 2*x^2 + alfa^19*x + alfa^9 Producte alfa^19*x^3 + alfa^22*x^2 + alfa^10*x + alfa^2 Quocient de p1/p2 alfa^17*x + alfa^5 Residu de p1/p2 alfa^15 Maxim Comu Divisor de p1 i p2 1 Minim Comu Multiple de p1 i p2 x^3 + alfa^3*x^2 + alfa^15*x + alfa^7 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 09:29:18 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; PR5:=PolynomialRing(G25); print " "; p1:=alfa^2+alfa*x+beta*x^2; p2:=1+alfa*x; print "Polinomis"; p1; p2; print "Suma"; p1+p2; print "Producte"; p1*p2; print "Quocient de p1/p2"; p1 div p2; print "Residu de p1/p2"; p1 mod p2; print "Maxim Comu Divisor de p1 i p2"; GCD(p1,p2); print "Minim Comu Multiple de p1 i p2"; LCM(p1,p2); print "Maxim Comu Divisor com a combinacio lineal de p1 i p2"; XGCD(p1,p2); Output: Magma V2.10-6 Sun Mar 28 2004 09:29:15 on modular [Seed = 974953292] ------------------------------------- Elements primitius de G5 [ 2, 3 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Polinomis 2*x^2 + alfa*x + alfa^2 alfa*x + 1 Suma 2*x^2 + alfa^19*x + alfa^9 Producte alfa^19*x^3 + alfa^22*x^2 + alfa^10*x + alfa^2 Quocient de p1/p2 alfa^17*x + alfa^5 Residu de p1/p2 alfa^15 Maxim Comu Divisor de p1 i p2 1 Minim Comu Multiple de p1 i p2 x^3 + alfa^3*x^2 + alfa^15*x + alfa^7 Maxim Comu Divisor com a combinacio lineal de p1 i p2 1 alfa^9 alfa^14*x + alfa^2 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 09:30:08 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; PR5:=PolynomialRing(G25); print " "; p1:=alfa^2+alfa*x+beta*x^2; p2:=1+alfa*x; print "Polinomis"; p1; p2; print "Suma"; p1+p2; print "Producte"; p1*p2; print "Quocient de p1/p2"; p1 div p2; print "Residu de p1/p2"; p1 mod p2; print "Maxim Comu Divisor de p1 i p2"; GCD(p1,p2); print "Minim Comu Multiple de p1 i p2"; LCM(p1,p2); print "Maxim Comu Divisor com a combinacio lineal de p1 i p2"; [d,a,b]:=XGCD(p1,p2); Output: Magma V2.10-6 Sun Mar 28 2004 09:30:05 on modular [Seed = 3320014053] ------------------------------------- Elements primitius de G5 [ 2, 3 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Polinomis 2*x^2 + alfa*x + alfa^2 alfa*x + 1 Suma 2*x^2 + alfa^19*x + alfa^9 Producte alfa^19*x^3 + alfa^22*x^2 + alfa^10*x + alfa^2 Quocient de p1/p2 alfa^17*x + alfa^5 Residu de p1/p2 alfa^15 Maxim Comu Divisor de p1 i p2 1 Minim Comu Multiple de p1 i p2 x^3 + alfa^3*x^2 + alfa^15*x + alfa^7 Maxim Comu Divisor com a combinacio lineal de p1 i p2 >> [d,a,b]:=XGCD(p1,p2); ^ User error: Illegal left hand side of an assignment statement Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 09:30:43 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; PR5:=PolynomialRing(G25); print " "; p1:=alfa^2+alfa*x+beta*x^2; p2:=1+alfa*x; print "Polinomis"; p1; p2; print "Suma"; p1+p2; print "Producte"; p1*p2; print "Quocient de p1/p2"; p1 div p2; print "Residu de p1/p2"; p1 mod p2; print "Maxim Comu Divisor de p1 i p2"; GCD(p1,p2); print "Minim Comu Multiple de p1 i p2"; LCM(p1,p2); print "Maxim Comu Divisor com a combinacio lineal de p1 i p2"; :=XGCD(p1,p2); Output: Magma V2.10-6 Sun Mar 28 2004 09:30:40 on modular [Seed = 3707403521] ------------------------------------- Elements primitius de G5 [ 2, 3 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Polinomis 2*x^2 + alfa*x + alfa^2 alfa*x + 1 Suma 2*x^2 + alfa^19*x + alfa^9 Producte alfa^19*x^3 + alfa^22*x^2 + alfa^10*x + alfa^2 Quocient de p1/p2 alfa^17*x + alfa^5 Residu de p1/p2 alfa^15 Maxim Comu Divisor de p1 i p2 1 Minim Comu Multiple de p1 i p2 x^3 + alfa^3*x^2 + alfa^15*x + alfa^7 Maxim Comu Divisor com a combinacio lineal de p1 i p2 >> :=XGCD(p1,p2); ^ User error: Illegal left hand side of an assignment statement Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 09:31:05 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; PR5:=PolynomialRing(G25); print " "; p1:=alfa^2+alfa*x+beta*x^2; p2:=1+alfa*x; print "Polinomis"; p1; p2; print "Suma"; p1+p2; print "Producte"; p1*p2; print "Quocient de p1/p2"; p1 div p2; print "Residu de p1/p2"; p1 mod p2; print "Maxim Comu Divisor de p1 i p2"; GCD(p1,p2); print "Minim Comu Multiple de p1 i p2"; LCM(p1,p2); print "Maxim Comu Divisor com a combinacio lineal de p1 i p2"; XGCD(p1,p2)[1]; Output: Magma V2.10-6 Sun Mar 28 2004 09:31:02 on modular [Seed = 3622925884] ------------------------------------- Elements primitius de G5 [ 2, 3 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Polinomis 2*x^2 + alfa*x + alfa^2 alfa*x + 1 Suma 2*x^2 + alfa^19*x + alfa^9 Producte alfa^19*x^3 + alfa^22*x^2 + alfa^10*x + alfa^2 Quocient de p1/p2 alfa^17*x + alfa^5 Residu de p1/p2 alfa^15 Maxim Comu Divisor de p1 i p2 1 Minim Comu Multiple de p1 i p2 x^3 + alfa^3*x^2 + alfa^15*x + alfa^7 Maxim Comu Divisor com a combinacio lineal de p1 i p2 >> XGCD(p1,p2)[1]; ^ Runtime error in '[]': Bad argument types Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 09:31:38 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; PR5:=PolynomialRing(G25); print " "; p1:=alfa^2+alfa*x+beta*x^2; p2:=1+alfa*x; print "Polinomis"; p1; p2; print "Suma"; p1+p2; print "Producte"; p1*p2; print "Quocient de p1/p2"; p1 div p2; print "Residu de p1/p2"; p1 mod p2; print "Maxim Comu Divisor de p1 i p2"; GCD(p1,p2); print "Minim Comu Multiple de p1 i p2"; LCM(p1,p2); print "Maxim Comu Divisor com a combinacio lineal de p1 i p2"; XGCD(p1,p2); Output: Magma V2.10-6 Sun Mar 28 2004 09:31:35 on modular [Seed = 4006104932] ------------------------------------- Elements primitius de G5 [ 2, 3 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Polinomis 2*x^2 + alfa*x + alfa^2 alfa*x + 1 Suma 2*x^2 + alfa^19*x + alfa^9 Producte alfa^19*x^3 + alfa^22*x^2 + alfa^10*x + alfa^2 Quocient de p1/p2 alfa^17*x + alfa^5 Residu de p1/p2 alfa^15 Maxim Comu Divisor de p1 i p2 1 Minim Comu Multiple de p1 i p2 x^3 + alfa^3*x^2 + alfa^15*x + alfa^7 Maxim Comu Divisor com a combinacio lineal de p1 i p2 1 alfa^9 alfa^14*x + alfa^2 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 09:35:04 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; PR5:=PolynomialRing(G25); print " "; p1:=alfa^2+alfa*x+beta*x^2; p2:=1+alfa*x; print "Polinomis"; p1; p2; print "Suma"; p1+p2; print "Producte"; p1*p2; print "Quocient de p1/p2"; p1 div p2; print "Residu de p1/p2"; p1 mod p2; print "Maxim Comu Divisor de p1 i p2"; GCD(p1,p2); print "Minim Comu Multiple de p1 i p2"; LCM(p1,p2); print "Maxim Comu Divisor com a combinacio lineal de p1 i p2"; XGCD(p1,p2); print " "; alfa^9*p1 + (alfa^14*x + alfa^2)*p2 Output: Magma V2.10-6 Sun Mar 28 2004 09:35:01 on modular [Seed = 4292435239] ------------------------------------- Elements primitius de G5 [ 2, 3 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Polinomis 2*x^2 + alfa*x + alfa^2 alfa*x + 1 Suma 2*x^2 + alfa^19*x + alfa^9 Producte alfa^19*x^3 + alfa^22*x^2 + alfa^10*x + alfa^2 Quocient de p1/p2 alfa^17*x + alfa^5 Residu de p1/p2 alfa^15 Maxim Comu Divisor de p1 i p2 1 Minim Comu Multiple de p1 i p2 x^3 + alfa^3*x^2 + alfa^15*x + alfa^7 Maxim Comu Divisor com a combinacio lineal de p1 i p2 1 alfa^9 alfa^14*x + alfa^2 1 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 09:38:56 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; PR5:=PolynomialRing(G25); print " "; p1:=alfa^2+alfa*x+beta*x^2; p2:=1+alfa*x; print "Polinomis"; p1; p2; print "Suma"; p1+p2; print "Producte"; p1*p2; print "Quocient de p1/p2"; p1 div p2; print "Residu de p1/p2"; p1 mod p2; print "Maxim Comu Divisor de p1 i p2"; GCD(p1,p2); print "Minim Comu Multiple de p1 i p2"; LCM(p1,p2); print "Maxim Comu Divisor com a combinacio lineal de p1 i p2"; XGCD(p1,p2); print " "; print "Polinomi sobre G25"; poli:= 1/alfa^4 - alfa^(-3) * x + alfa^5*x^2; poli; Output: Magma V2.10-6 Sun Mar 28 2004 09:38:53 on modular [Seed = 4040577984] ------------------------------------- Elements primitius de G5 [ 2, 3 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Polinomis 2*x^2 + alfa*x + alfa^2 alfa*x + 1 Suma 2*x^2 + alfa^19*x + alfa^9 Producte alfa^19*x^3 + alfa^22*x^2 + alfa^10*x + alfa^2 Quocient de p1/p2 alfa^17*x + alfa^5 Residu de p1/p2 alfa^15 Maxim Comu Divisor de p1 i p2 1 Minim Comu Multiple de p1 i p2 x^3 + alfa^3*x^2 + alfa^15*x + alfa^7 Maxim Comu Divisor com a combinacio lineal de p1 i p2 1 alfa^9 alfa^14*x + alfa^2 Polinomi sobre G25 alfa^5*x^2 + alfa^9*x + alfa^20 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 09:40:59 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; PR5:=PolynomialRing(G25); print " "; p1:=alfa^2+alfa*x+beta*x^2; p2:=1+alfa*x; print "Polinomis"; p1; p2; print "Suma"; p1+p2; print "Producte"; p1*p2; print "Quocient de p1/p2"; p1 div p2; print "Residu de p1/p2"; p1 mod p2; print "Maxim Comu Divisor de p1 i p2"; GCD(p1,p2); print "Minim Comu Multiple de p1 i p2"; LCM(p1,p2); print "Maxim Comu Divisor com a combinacio lineal de p1 i p2"; XGCD(p1,p2); print " "; print "Polinomi sobre G25"; poli:= 1/alfa^4 - alfa^(-3) * x + alfa^5*x^2; poli; print "Factorització"; Factorization(poli); Output: Magma V2.10-6 Sun Mar 28 2004 09:40:56 on modular [Seed = 2158371637] ------------------------------------- Elements primitius de G5 [ 2, 3 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Polinomis 2*x^2 + alfa*x + alfa^2 alfa*x + 1 Suma 2*x^2 + alfa^19*x + alfa^9 Producte alfa^19*x^3 + alfa^22*x^2 + alfa^10*x + alfa^2 Quocient de p1/p2 alfa^17*x + alfa^5 Residu de p1/p2 alfa^15 Maxim Comu Divisor de p1 i p2 1 Minim Comu Multiple de p1 i p2 x^3 + alfa^3*x^2 + alfa^15*x + alfa^7 Maxim Comu Divisor com a combinacio lineal de p1 i p2 1 alfa^9 alfa^14*x + alfa^2 Polinomi sobre G25 alfa^5*x^2 + alfa^9*x + alfa^20 Factorització [ ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 09:49:28 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; PR5:=PolynomialRing(G25); print " "; p1:=alfa^2+alfa*x+beta*x^2; p2:=1+alfa*x; print "Polinomis"; p1; p2; print "Suma"; p1+p2; print "Producte"; p1*p2; print "Quocient de p1/p2"; p1 div p2; print "Residu de p1/p2"; p1 mod p2; print "Maxim Comu Divisor de p1 i p2"; GCD(p1,p2); print "Minim Comu Multiple de p1 i p2"; LCM(p1,p2); print "Maxim Comu Divisor com a combinacio lineal de p1 i p2"; XGCD(p1,p2); print " "; print "Polinomi sobre G25"; poli:= 1/alfa^4 - alfa^(-3) * x + alfa^5*x^2; poli; print "Factorització"; Evaluate(poli=0); Output: Magma V2.10-6 Sun Mar 28 2004 09:49:25 on modular [Seed = 2478126635] ------------------------------------- Elements primitius de G5 [ 2, 3 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Polinomis 2*x^2 + alfa*x + alfa^2 alfa*x + 1 Suma 2*x^2 + alfa^19*x + alfa^9 Producte alfa^19*x^3 + alfa^22*x^2 + alfa^10*x + alfa^2 Quocient de p1/p2 alfa^17*x + alfa^5 Residu de p1/p2 alfa^15 Maxim Comu Divisor de p1 i p2 1 Minim Comu Multiple de p1 i p2 x^3 + alfa^3*x^2 + alfa^15*x + alfa^7 Maxim Comu Divisor com a combinacio lineal de p1 i p2 1 alfa^9 alfa^14*x + alfa^2 Polinomi sobre G25 alfa^5*x^2 + alfa^9*x + alfa^20 Factorització >> Evaluate(poli=0); ^ Runtime error in 'Evaluate': Bad argument types Argument types given: RelElt Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 09:49:59 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; PR5:=PolynomialRing(G25); print " "; p1:=alfa^2+alfa*x+beta*x^2; p2:=1+alfa*x; print "Polinomis"; p1; p2; print "Suma"; p1+p2; print "Producte"; p1*p2; print "Quocient de p1/p2"; p1 div p2; print "Residu de p1/p2"; p1 mod p2; print "Maxim Comu Divisor de p1 i p2"; GCD(p1,p2); print "Minim Comu Multiple de p1 i p2"; LCM(p1,p2); print "Maxim Comu Divisor com a combinacio lineal de p1 i p2"; XGCD(p1,p2); print " "; print "Polinomi sobre G25"; poli:= 1/alfa^4 - alfa^(-3) * x + alfa^5*x^2; poli; print "Factorització"; Factorization(poli); Output: Magma V2.10-6 Sun Mar 28 2004 09:49:56 on modular [Seed = 2776826876] ------------------------------------- Elements primitius de G5 [ 2, 3 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Polinomis 2*x^2 + alfa*x + alfa^2 alfa*x + 1 Suma 2*x^2 + alfa^19*x + alfa^9 Producte alfa^19*x^3 + alfa^22*x^2 + alfa^10*x + alfa^2 Quocient de p1/p2 alfa^17*x + alfa^5 Residu de p1/p2 alfa^15 Maxim Comu Divisor de p1 i p2 1 Minim Comu Multiple de p1 i p2 x^3 + alfa^3*x^2 + alfa^15*x + alfa^7 Maxim Comu Divisor com a combinacio lineal de p1 i p2 1 alfa^9 alfa^14*x + alfa^2 Polinomi sobre G25 alfa^5*x^2 + alfa^9*x + alfa^20 Factorització [ ] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 09:51:50 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; PR5:=PolynomialRing(G25); print " "; p1:=alfa^2+alfa*x+beta*x^2; p2:=1+alfa*x; print "Polinomis"; p1; p2; print "Suma"; p1+p2; print "Producte"; p1*p2; print "Quocient de p1/p2"; p1 div p2; print "Residu de p1/p2"; p1 mod p2; print "Maxim Comu Divisor de p1 i p2"; GCD(p1,p2); print "Minim Comu Multiple de p1 i p2"; LCM(p1,p2); print "Maxim Comu Divisor com a combinacio lineal de p1 i p2"; XGCD(p1,p2); print " "; print "Polinomi sobre G25"; poli:= 1/alfa^4 - alfa^(-3) * x + alfa^5*x^2; poli; print "Factorització"; Factorization(poli); print "Arrel?"; PrimitiveRoot(poli); Output: Magma V2.10-6 Sun Mar 28 2004 09:51:47 on modular [Seed = 3046314875] ------------------------------------- Elements primitius de G5 [ 2, 3 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Polinomis 2*x^2 + alfa*x + alfa^2 alfa*x + 1 Suma 2*x^2 + alfa^19*x + alfa^9 Producte alfa^19*x^3 + alfa^22*x^2 + alfa^10*x + alfa^2 Quocient de p1/p2 alfa^17*x + alfa^5 Residu de p1/p2 alfa^15 Maxim Comu Divisor de p1 i p2 1 Minim Comu Multiple de p1 i p2 x^3 + alfa^3*x^2 + alfa^15*x + alfa^7 Maxim Comu Divisor com a combinacio lineal de p1 i p2 1 alfa^9 alfa^14*x + alfa^2 Polinomi sobre G25 alfa^5*x^2 + alfa^9*x + alfa^20 Factorització [ ] Arrel? >> PrimitiveRoot(poli);; ^ Runtime error in 'PrimitiveRoot': Bad argument types Argument types given: RngUPolElt Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 09:53:55 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; PR5:=PolynomialRing(G25); print " "; p1:=alfa^2+alfa*x+beta*x^2; p2:=1+alfa*x; print "Polinomis"; p1; p2; print "Suma"; p1+p2; print "Producte"; p1*p2; print "Quocient de p1/p2"; p1 div p2; print "Residu de p1/p2"; p1 mod p2; print "Maxim Comu Divisor de p1 i p2"; GCD(p1,p2); print "Minim Comu Multiple de p1 i p2"; LCM(p1,p2); print "Maxim Comu Divisor com a combinacio lineal de p1 i p2"; XGCD(p1,p2); print " "; print "Polinomi sobre G25"; poli:= 1/alfa^4 - alfa^(-3) * x + alfa^5*x^2; poli; print "Factorització"; Factorization(poli); print "Arrel?"; Evaluate(poli); Output: Magma V2.10-6 Sun Mar 28 2004 09:53:52 on modular [Seed = 1282075394] ------------------------------------- Elements primitius de G5 [ 2, 3 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Polinomis 2*x^2 + alfa*x + alfa^2 alfa*x + 1 Suma 2*x^2 + alfa^19*x + alfa^9 Producte alfa^19*x^3 + alfa^22*x^2 + alfa^10*x + alfa^2 Quocient de p1/p2 alfa^17*x + alfa^5 Residu de p1/p2 alfa^15 Maxim Comu Divisor de p1 i p2 1 Minim Comu Multiple de p1 i p2 x^3 + alfa^3*x^2 + alfa^15*x + alfa^7 Maxim Comu Divisor com a combinacio lineal de p1 i p2 1 alfa^9 alfa^14*x + alfa^2 Polinomi sobre G25 alfa^5*x^2 + alfa^9*x + alfa^20 Factorització [ ] Arrel? >> Evaluate(poli);; ^ Runtime error in 'Evaluate': Bad argument types Argument types given: RngUPolElt Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 09:58:32 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; PR5:=PolynomialRing(G25); print " "; p1:=alfa^2+alfa*x+beta*x^2; p2:=1+alfa*x; print "Polinomis"; p1; p2; print "Suma"; p1+p2; print "Producte"; p1*p2; print "Quocient de p1/p2"; p1 div p2; print "Residu de p1/p2"; p1 mod p2; print "Maxim Comu Divisor de p1 i p2"; GCD(p1,p2); print "Minim Comu Multiple de p1 i p2"; LCM(p1,p2); print "Maxim Comu Divisor com a combinacio lineal de p1 i p2"; XGCD(p1,p2); print " "; print "Polinomi sobre G25"; poli:= 1/alfa^4 - alfa^(-3) * x + alfa^5*x^2; poli; print "Factorització"; Factorization(poli); print "Irreductible"; IsIrreducible(poli); Output: Magma V2.10-6 Sun Mar 28 2004 09:58:29 on modular [Seed = 1551561735] ------------------------------------- Elements primitius de G5 [ 2, 3 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Polinomis 2*x^2 + alfa*x + alfa^2 alfa*x + 1 Suma 2*x^2 + alfa^19*x + alfa^9 Producte alfa^19*x^3 + alfa^22*x^2 + alfa^10*x + alfa^2 Quocient de p1/p2 alfa^17*x + alfa^5 Residu de p1/p2 alfa^15 Maxim Comu Divisor de p1 i p2 1 Minim Comu Multiple de p1 i p2 x^3 + alfa^3*x^2 + alfa^15*x + alfa^7 Maxim Comu Divisor com a combinacio lineal de p1 i p2 1 alfa^9 alfa^14*x + alfa^2 Polinomi sobre G25 alfa^5*x^2 + alfa^9*x + alfa^20 Factorització [ ] Irreductible true Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 10:02:57 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; PR5:=PolynomialRing(G25); print " "; p1:=alfa^2+alfa*x+beta*x^2; p2:=1+alfa*x; print "Polinomis"; p1; p2; print "Suma"; p1+p2; print "Producte"; p1*p2; print "Quocient de p1/p2"; p1 div p2; print "Residu de p1/p2"; p1 mod p2; print "Maxim Comu Divisor de p1 i p2"; GCD(p1,p2); print "Minim Comu Multiple de p1 i p2"; LCM(p1,p2); print "Maxim Comu Divisor com a combinacio lineal de p1 i p2"; XGCD(p1,p2); print " "; print "Polinomi sobre G25"; poli:= 1/alfa^4 - alfa^(-3) * x + alfa^5*x^2; poli; print "Factorització"; Factorization(poli); print "És irreductible?"; IsIrreducible(poli); Output: Magma V2.10-6 Sun Mar 28 2004 10:02:54 on modular [Seed = 2069746219] ------------------------------------- Elements primitius de G5 [ 2, 3 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Polinomis 2*x^2 + alfa*x + alfa^2 alfa*x + 1 Suma 2*x^2 + alfa^19*x + alfa^9 Producte alfa^19*x^3 + alfa^22*x^2 + alfa^10*x + alfa^2 Quocient de p1/p2 alfa^17*x + alfa^5 Residu de p1/p2 alfa^15 Maxim Comu Divisor de p1 i p2 1 Minim Comu Multiple de p1 i p2 x^3 + alfa^3*x^2 + alfa^15*x + alfa^7 Maxim Comu Divisor com a combinacio lineal de p1 i p2 1 alfa^9 alfa^14*x + alfa^2 Polinomi sobre G25 alfa^5*x^2 + alfa^9*x + alfa^20 Factorització [ ] És irreductible? true Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 10:09:33 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; PR5:=PolynomialRing(G25); print " "; p1:=alfa^2+alfa*x+beta*x^2; p2:=1+alfa*x; print "Polinomis"; p1; p2; print "Suma"; p1+p2; print "Producte"; p1*p2; print "Quocient de p1/p2"; p1 div p2; print "Residu de p1/p2"; p1 mod p2; print "Maxim Comu Divisor de p1 i p2"; GCD(p1,p2); print "Minim Comu Multiple de p1 i p2"; LCM(p1,p2); print "Maxim Comu Divisor com a combinacio lineal de p1 i p2"; XGCD(p1,p2); print " "; print "Polinomi sobre G25"; poli:= 1/alfa^4 - alfa^(-3) * x + alfa^5*x^2; poli; print "Factorització"; Factorization(poli); print "És irreductible?"; IsIrreducible(poli); Evaluate(alfa^5*x^2 + alfa^9*x + alfa^20 = 0) Output: Magma V2.10-6 Sun Mar 28 2004 10:09:30 on modular [Seed = 137274092] ------------------------------------- Elements primitius de G5 [ 2, 3 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Polinomis 2*x^2 + alfa*x + alfa^2 alfa*x + 1 Suma 2*x^2 + alfa^19*x + alfa^9 Producte alfa^19*x^3 + alfa^22*x^2 + alfa^10*x + alfa^2 Quocient de p1/p2 alfa^17*x + alfa^5 Residu de p1/p2 alfa^15 Maxim Comu Divisor de p1 i p2 1 Minim Comu Multiple de p1 i p2 x^3 + alfa^3*x^2 + alfa^15*x + alfa^7 Maxim Comu Divisor com a combinacio lineal de p1 i p2 1 alfa^9 alfa^14*x + alfa^2 Polinomi sobre G25 alfa^5*x^2 + alfa^9*x + alfa^20 Factorització [ ] És irreductible? true >> Evaluate(alfa^5*x^2 + alfa^9*x + alfa^20 = 0) ^ Runtime error in 'Evaluate': Bad argument types Argument types given: RelElt Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 10:09:53 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; PR5:=PolynomialRing(G25); print " "; p1:=alfa^2+alfa*x+beta*x^2; p2:=1+alfa*x; print "Polinomis"; p1; p2; print "Suma"; p1+p2; print "Producte"; p1*p2; print "Quocient de p1/p2"; p1 div p2; print "Residu de p1/p2"; p1 mod p2; print "Maxim Comu Divisor de p1 i p2"; GCD(p1,p2); print "Minim Comu Multiple de p1 i p2"; LCM(p1,p2); print "Maxim Comu Divisor com a combinacio lineal de p1 i p2"; XGCD(p1,p2); print " "; print "Polinomi sobre G25"; poli:= 1/alfa^4 - alfa^(-3) * x + alfa^5*x^2; poli; print "Factorització"; Factorization(poli); print "És irreductible?"; IsIrreducible(poli); print "Evaluem"; Evaluate(alfa^5*x^2 + alfa^9*x + alfa^20 = 0); Output: Magma V2.10-6 Sun Mar 28 2004 10:09:50 on modular [Seed = 19377137] ------------------------------------- Elements primitius de G5 [ 2, 3 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Polinomis 2*x^2 + alfa*x + alfa^2 alfa*x + 1 Suma 2*x^2 + alfa^19*x + alfa^9 Producte alfa^19*x^3 + alfa^22*x^2 + alfa^10*x + alfa^2 Quocient de p1/p2 alfa^17*x + alfa^5 Residu de p1/p2 alfa^15 Maxim Comu Divisor de p1 i p2 1 Minim Comu Multiple de p1 i p2 x^3 + alfa^3*x^2 + alfa^15*x + alfa^7 Maxim Comu Divisor com a combinacio lineal de p1 i p2 1 alfa^9 alfa^14*x + alfa^2 Polinomi sobre G25 alfa^5*x^2 + alfa^9*x + alfa^20 Factorització [ ] És irreductible? true Evaluem >> Evaluate(alfa^5*x^2 + alfa^9*x + alfa^20 = 0); ^ Runtime error in 'Evaluate': Bad argument types Argument types given: RelElt Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 10:10:19 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; PR5:=PolynomialRing(G25); print " "; p1:=alfa^2+alfa*x+beta*x^2; p2:=1+alfa*x; print "Polinomis"; p1; p2; print "Suma"; p1+p2; print "Producte"; p1*p2; print "Quocient de p1/p2"; p1 div p2; print "Residu de p1/p2"; p1 mod p2; print "Maxim Comu Divisor de p1 i p2"; GCD(p1,p2); print "Minim Comu Multiple de p1 i p2"; LCM(p1,p2); print "Maxim Comu Divisor com a combinacio lineal de p1 i p2"; XGCD(p1,p2); print " "; print "Polinomi sobre G25"; poli:= 1/alfa^4 - alfa^(-3) * x + alfa^5*x^2; poli; print "Factorització"; Factorization(poli); print "És irreductible?"; IsIrreducible(poli); print "Evaluem"; Evaluate(alfa^5*x^2 + alfa^9*x + alfa^20,x); Output: Magma V2.10-6 Sun Mar 28 2004 10:10:15 on modular [Seed = 288865159] ------------------------------------- Elements primitius de G5 [ 2, 3 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Polinomis 2*x^2 + alfa*x + alfa^2 alfa*x + 1 Suma 2*x^2 + alfa^19*x + alfa^9 Producte alfa^19*x^3 + alfa^22*x^2 + alfa^10*x + alfa^2 Quocient de p1/p2 alfa^17*x + alfa^5 Residu de p1/p2 alfa^15 Maxim Comu Divisor de p1 i p2 1 Minim Comu Multiple de p1 i p2 x^3 + alfa^3*x^2 + alfa^15*x + alfa^7 Maxim Comu Divisor com a combinacio lineal de p1 i p2 1 alfa^9 alfa^14*x + alfa^2 Polinomi sobre G25 alfa^5*x^2 + alfa^9*x + alfa^20 Factorització [ ] És irreductible? true Evaluem alfa^5*x^2 + alfa^9*x + alfa^20 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 10:10:38 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; PR5:=PolynomialRing(G25); print " "; p1:=alfa^2+alfa*x+beta*x^2; p2:=1+alfa*x; print "Polinomis"; p1; p2; print "Suma"; p1+p2; print "Producte"; p1*p2; print "Quocient de p1/p2"; p1 div p2; print "Residu de p1/p2"; p1 mod p2; print "Maxim Comu Divisor de p1 i p2"; GCD(p1,p2); print "Minim Comu Multiple de p1 i p2"; LCM(p1,p2); print "Maxim Comu Divisor com a combinacio lineal de p1 i p2"; XGCD(p1,p2); print " "; print "Polinomi sobre G25"; poli:= 1/alfa^4 - alfa^(-3) * x + alfa^5*x^2; poli; print "Factorització"; Factorization(poli); print "És irreductible?"; IsIrreducible(poli); print "Evaluem"; Evaluate(alfa^5*x^2 + alfa^9*x + alfa^20=0,x); Output: Magma V2.10-6 Sun Mar 28 2004 10:10:34 on modular [Seed = 637570179] ------------------------------------- Elements primitius de G5 [ 2, 3 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Polinomis 2*x^2 + alfa*x + alfa^2 alfa*x + 1 Suma 2*x^2 + alfa^19*x + alfa^9 Producte alfa^19*x^3 + alfa^22*x^2 + alfa^10*x + alfa^2 Quocient de p1/p2 alfa^17*x + alfa^5 Residu de p1/p2 alfa^15 Maxim Comu Divisor de p1 i p2 1 Minim Comu Multiple de p1 i p2 x^3 + alfa^3*x^2 + alfa^15*x + alfa^7 Maxim Comu Divisor com a combinacio lineal de p1 i p2 1 alfa^9 alfa^14*x + alfa^2 Polinomi sobre G25 alfa^5*x^2 + alfa^9*x + alfa^20 Factorització [ ] És irreductible? true Evaluem >> Evaluate(alfa^5*x^2 + alfa^9*x + alfa^20=0,x); ^ Runtime error in 'Evaluate': Bad argument types Argument types given: RelElt, RngUPolElt Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 10:11:07 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; PR5:=PolynomialRing(G25); print " "; p1:=alfa^2+alfa*x+beta*x^2; p2:=1+alfa*x; print "Polinomis"; p1; p2; print "Suma"; p1+p2; print "Producte"; p1*p2; print "Quocient de p1/p2"; p1 div p2; print "Residu de p1/p2"; p1 mod p2; print "Maxim Comu Divisor de p1 i p2"; GCD(p1,p2); print "Minim Comu Multiple de p1 i p2"; LCM(p1,p2); print "Maxim Comu Divisor com a combinacio lineal de p1 i p2"; XGCD(p1,p2); print " "; print "Polinomi sobre G25"; poli:= 1/alfa^4 - alfa^(-3) * x + alfa^5*x^2; poli; print "Factorització"; Factorization(poli); print "És irreductible?"; IsIrreducible(poli); print "Evaluem"; Evaluate(alfa^9*x,x); Output: Magma V2.10-6 Sun Mar 28 2004 10:11:04 on modular [Seed = 1058641017] ------------------------------------- Elements primitius de G5 [ 2, 3 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Polinomis 2*x^2 + alfa*x + alfa^2 alfa*x + 1 Suma 2*x^2 + alfa^19*x + alfa^9 Producte alfa^19*x^3 + alfa^22*x^2 + alfa^10*x + alfa^2 Quocient de p1/p2 alfa^17*x + alfa^5 Residu de p1/p2 alfa^15 Maxim Comu Divisor de p1 i p2 1 Minim Comu Multiple de p1 i p2 x^3 + alfa^3*x^2 + alfa^15*x + alfa^7 Maxim Comu Divisor com a combinacio lineal de p1 i p2 1 alfa^9 alfa^14*x + alfa^2 Polinomi sobre G25 alfa^5*x^2 + alfa^9*x + alfa^20 Factorització [ ] És irreductible? true Evaluem alfa^9*x Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 10:11:30 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; PR5:=PolynomialRing(G25); print " "; p1:=alfa^2+alfa*x+beta*x^2; p2:=1+alfa*x; print "Polinomis"; p1; p2; print "Suma"; p1+p2; print "Producte"; p1*p2; print "Quocient de p1/p2"; p1 div p2; print "Residu de p1/p2"; p1 mod p2; print "Maxim Comu Divisor de p1 i p2"; GCD(p1,p2); print "Minim Comu Multiple de p1 i p2"; LCM(p1,p2); print "Maxim Comu Divisor com a combinacio lineal de p1 i p2"; XGCD(p1,p2); print " "; print "Polinomi sobre G25"; poli:= 1/alfa^4 - alfa^(-3) * x + alfa^5*x^2; poli; print "Factorització"; Factorization(poli); print "És irreductible?"; IsIrreducible(poli); print "Evaluem"; Evaluate(1+2*x,x); Output: Magma V2.10-6 Sun Mar 28 2004 10:11:27 on modular [Seed = 873635685] ------------------------------------- Elements primitius de G5 [ 2, 3 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Polinomis 2*x^2 + alfa*x + alfa^2 alfa*x + 1 Suma 2*x^2 + alfa^19*x + alfa^9 Producte alfa^19*x^3 + alfa^22*x^2 + alfa^10*x + alfa^2 Quocient de p1/p2 alfa^17*x + alfa^5 Residu de p1/p2 alfa^15 Maxim Comu Divisor de p1 i p2 1 Minim Comu Multiple de p1 i p2 x^3 + alfa^3*x^2 + alfa^15*x + alfa^7 Maxim Comu Divisor com a combinacio lineal de p1 i p2 1 alfa^9 alfa^14*x + alfa^2 Polinomi sobre G25 alfa^5*x^2 + alfa^9*x + alfa^20 Factorització [ ] És irreductible? true Evaluem 2*x + 1 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 10:12:25 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; PR5:=PolynomialRing(G25); print " "; p1:=alfa^2+alfa*x+beta*x^2; p2:=1+alfa*x; print "Polinomis"; p1; p2; print "Suma"; p1+p2; print "Producte"; p1*p2; print "Quocient de p1/p2"; p1 div p2; print "Residu de p1/p2"; p1 mod p2; print "Maxim Comu Divisor de p1 i p2"; GCD(p1,p2); print "Minim Comu Multiple de p1 i p2"; LCM(p1,p2); print "Maxim Comu Divisor com a combinacio lineal de p1 i p2"; XGCD(p1,p2); print " "; print "Polinomi sobre G25"; poli:= 1/alfa^4 - alfa^(-3) * x + alfa^5*x^2; poli; print "Factorització"; Factorization(poli); print "És irreductible?"; IsIrreducible(poli); print "Evaluem"; Evaluate(alfa^5*x^2 + alfa^9*x + alfa^20,a); Output: Magma V2.10-6 Sun Mar 28 2004 10:12:22 on modular [Seed = 3404489171] ------------------------------------- Elements primitius de G5 [ 2, 3 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Polinomis 2*x^2 + alfa*x + alfa^2 alfa*x + 1 Suma 2*x^2 + alfa^19*x + alfa^9 Producte alfa^19*x^3 + alfa^22*x^2 + alfa^10*x + alfa^2 Quocient de p1/p2 alfa^17*x + alfa^5 Residu de p1/p2 alfa^15 Maxim Comu Divisor de p1 i p2 1 Minim Comu Multiple de p1 i p2 x^3 + alfa^3*x^2 + alfa^15*x + alfa^7 Maxim Comu Divisor com a combinacio lineal de p1 i p2 1 alfa^9 alfa^14*x + alfa^2 Polinomi sobre G25 alfa^5*x^2 + alfa^9*x + alfa^20 Factorització [ ] És irreductible? true Evaluem >> Evaluate(alfa^5*x^2 + alfa^9*x + alfa^20,a); ^ User error: Identifier 'a' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 10:12:41 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; PR5:=PolynomialRing(G25); print " "; p1:=alfa^2+alfa*x+beta*x^2; p2:=1+alfa*x; print "Polinomis"; p1; p2; print "Suma"; p1+p2; print "Producte"; p1*p2; print "Quocient de p1/p2"; p1 div p2; print "Residu de p1/p2"; p1 mod p2; print "Maxim Comu Divisor de p1 i p2"; GCD(p1,p2); print "Minim Comu Multiple de p1 i p2"; LCM(p1,p2); print "Maxim Comu Divisor com a combinacio lineal de p1 i p2"; XGCD(p1,p2); print " "; print "Polinomi sobre G25"; poli:= 1/alfa^4 - alfa^(-3) * x + alfa^5*x^2; poli; print "Factorització"; Factorization(poli); print "És irreductible?"; IsIrreducible(poli); print "Evaluem"; Evaluate(alfa^5*x^2 + alfa^9*x + alfa^20,x); Output: Magma V2.10-6 Sun Mar 28 2004 10:12:38 on modular [Seed = 3286591723] ------------------------------------- Elements primitius de G5 [ 2, 3 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Polinomis 2*x^2 + alfa*x + alfa^2 alfa*x + 1 Suma 2*x^2 + alfa^19*x + alfa^9 Producte alfa^19*x^3 + alfa^22*x^2 + alfa^10*x + alfa^2 Quocient de p1/p2 alfa^17*x + alfa^5 Residu de p1/p2 alfa^15 Maxim Comu Divisor de p1 i p2 1 Minim Comu Multiple de p1 i p2 x^3 + alfa^3*x^2 + alfa^15*x + alfa^7 Maxim Comu Divisor com a combinacio lineal de p1 i p2 1 alfa^9 alfa^14*x + alfa^2 Polinomi sobre G25 alfa^5*x^2 + alfa^9*x + alfa^20 Factorització [ ] És irreductible? true Evaluem alfa^5*x^2 + alfa^9*x + alfa^20 Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 10:13:33 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; PR5:=PolynomialRing(G25); print " "; p1:=alfa^2+alfa*x+beta*x^2; p2:=1+alfa*x; print "Polinomis"; p1; p2; print "Suma"; p1+p2; print "Producte"; p1*p2; print "Quocient de p1/p2"; p1 div p2; print "Residu de p1/p2"; p1 mod p2; print "Maxim Comu Divisor de p1 i p2"; GCD(p1,p2); print "Minim Comu Multiple de p1 i p2"; LCM(p1,p2); print "Maxim Comu Divisor com a combinacio lineal de p1 i p2"; XGCD(p1,p2); print " "; print "Polinomi sobre G25"; poli:= 1/alfa^4 - alfa^(-3) * x + alfa^5*x^2; poli; print "Factorització"; Factorization(poli); print "És irreductible?"; IsIrreducible(poli); print "Evaluem"; Evaluate(alfa^5*x^2 + alfa^9*x + alfa^20,x); PX:=PolynomialRing(GF(5)); Evaluate(y+2,y); Output: Magma V2.10-6 Sun Mar 28 2004 10:13:30 on modular [Seed = 3657396749] ------------------------------------- Elements primitius de G5 [ 2, 3 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Polinomis 2*x^2 + alfa*x + alfa^2 alfa*x + 1 Suma 2*x^2 + alfa^19*x + alfa^9 Producte alfa^19*x^3 + alfa^22*x^2 + alfa^10*x + alfa^2 Quocient de p1/p2 alfa^17*x + alfa^5 Residu de p1/p2 alfa^15 Maxim Comu Divisor de p1 i p2 1 Minim Comu Multiple de p1 i p2 x^3 + alfa^3*x^2 + alfa^15*x + alfa^7 Maxim Comu Divisor com a combinacio lineal de p1 i p2 1 alfa^9 alfa^14*x + alfa^2 Polinomi sobre G25 alfa^5*x^2 + alfa^9*x + alfa^20 Factorització [ ] És irreductible? true Evaluem alfa^5*x^2 + alfa^9*x + alfa^20 y + 2 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 10:17:09 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; PR5:=PolynomialRing(G25); print " "; p1:=alfa^2+alfa*x+beta*x^2; p2:=1+alfa*x; print "Polinomis"; p1; p2; print "Suma"; p1+p2; print "Producte"; p1*p2; print "Quocient de p1/p2"; p1 div p2; print "Residu de p1/p2"; p1 mod p2; print "Maxim Comu Divisor de p1 i p2"; GCD(p1,p2); print "Minim Comu Multiple de p1 i p2"; LCM(p1,p2); print "Maxim Comu Divisor com a combinacio lineal de p1 i p2"; XGCD(p1,p2); print " "; print "Polinomi sobre G25"; poli:= 1/alfa^4 - alfa^(-3) * x + alfa^5*x^2; poli; print "Factorització"; Factorization(poli); print "És irreductible?"; IsIrreducible(poli); print "Evaluem"; Evaluate(alfa^5*x^2 + alfa^9*x + alfa^20,x); PX:=PolynomialRing(GF(5)); Evaluate(y+2,0); Output: Magma V2.10-6 Sun Mar 28 2004 10:17:06 on modular [Seed = 3871361754] ------------------------------------- Elements primitius de G5 [ 2, 3 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Polinomis 2*x^2 + alfa*x + alfa^2 alfa*x + 1 Suma 2*x^2 + alfa^19*x + alfa^9 Producte alfa^19*x^3 + alfa^22*x^2 + alfa^10*x + alfa^2 Quocient de p1/p2 alfa^17*x + alfa^5 Residu de p1/p2 alfa^15 Maxim Comu Divisor de p1 i p2 1 Minim Comu Multiple de p1 i p2 x^3 + alfa^3*x^2 + alfa^15*x + alfa^7 Maxim Comu Divisor com a combinacio lineal de p1 i p2 1 alfa^9 alfa^14*x + alfa^2 Polinomi sobre G25 alfa^5*x^2 + alfa^9*x + alfa^20 Factorització [ ] És irreductible? true Evaluem alfa^5*x^2 + alfa^9*x + alfa^20 2 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 10:17:45 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; PR5:=PolynomialRing(G25); print " "; p1:=alfa^2+alfa*x+beta*x^2; p2:=1+alfa*x; print "Polinomis"; p1; p2; print "Suma"; p1+p2; print "Producte"; p1*p2; print "Quocient de p1/p2"; p1 div p2; print "Residu de p1/p2"; p1 mod p2; print "Maxim Comu Divisor de p1 i p2"; GCD(p1,p2); print "Minim Comu Multiple de p1 i p2"; LCM(p1,p2); print "Maxim Comu Divisor com a combinacio lineal de p1 i p2"; XGCD(p1,p2); print " "; print "Polinomi sobre G25"; poli:= 1/alfa^4 - alfa^(-3) * x + alfa^5*x^2; poli; print "Factorització"; Factorization(poli); print "És irreductible?"; IsIrreducible(poli); print "Evaluem"; Evaluate(alfa^5*x^2 + alfa^9*x + alfa^20,0); Output: Magma V2.10-6 Sun Mar 28 2004 10:17:42 on modular [Seed = 4292432679] ------------------------------------- Elements primitius de G5 [ 2, 3 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Polinomis 2*x^2 + alfa*x + alfa^2 alfa*x + 1 Suma 2*x^2 + alfa^19*x + alfa^9 Producte alfa^19*x^3 + alfa^22*x^2 + alfa^10*x + alfa^2 Quocient de p1/p2 alfa^17*x + alfa^5 Residu de p1/p2 alfa^15 Maxim Comu Divisor de p1 i p2 1 Minim Comu Multiple de p1 i p2 x^3 + alfa^3*x^2 + alfa^15*x + alfa^7 Maxim Comu Divisor com a combinacio lineal de p1 i p2 1 alfa^9 alfa^14*x + alfa^2 Polinomi sobre G25 alfa^5*x^2 + alfa^9*x + alfa^20 Factorització [ ] És irreductible? true Evaluem alfa^20 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 10:18:07 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; PR5:=PolynomialRing(G25); print " "; p1:=alfa^2+alfa*x+beta*x^2; p2:=1+alfa*x; print "Polinomis"; p1; p2; print "Suma"; p1+p2; print "Producte"; p1*p2; print "Quocient de p1/p2"; p1 div p2; print "Residu de p1/p2"; p1 mod p2; print "Maxim Comu Divisor de p1 i p2"; GCD(p1,p2); print "Minim Comu Multiple de p1 i p2"; LCM(p1,p2); print "Maxim Comu Divisor com a combinacio lineal de p1 i p2"; XGCD(p1,p2); print " "; print "Polinomi sobre G25"; poli:= 1/alfa^4 - alfa^(-3) * x + alfa^5*x^2; poli; print "Factorització"; Factorization(poli); print "És irreductible?"; IsIrreducible(poli); print "Evaluem"; Evaluate(poli,0); Output: Magma V2.10-6 Sun Mar 28 2004 10:18:04 on modular [Seed = 4107425814] ------------------------------------- Elements primitius de G5 [ 2, 3 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Polinomis 2*x^2 + alfa*x + alfa^2 alfa*x + 1 Suma 2*x^2 + alfa^19*x + alfa^9 Producte alfa^19*x^3 + alfa^22*x^2 + alfa^10*x + alfa^2 Quocient de p1/p2 alfa^17*x + alfa^5 Residu de p1/p2 alfa^15 Maxim Comu Divisor de p1 i p2 1 Minim Comu Multiple de p1 i p2 x^3 + alfa^3*x^2 + alfa^15*x + alfa^7 Maxim Comu Divisor com a combinacio lineal de p1 i p2 1 alfa^9 alfa^14*x + alfa^2 Polinomi sobre G25 alfa^5*x^2 + alfa^9*x + alfa^20 Factorització [ ] És irreductible? true Evaluem alfa^20 Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 10:23:09 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; PR5:=PolynomialRing(G25); print " "; p1:=alfa^2+alfa*x+beta*x^2; p2:=1+alfa*x; print "Polinomis"; p1; p2; print "Suma"; p1+p2; print "Producte"; p1*p2; print "Quocient de p1/p2"; p1 div p2; print "Residu de p1/p2"; p1 mod p2; Quotrem(p1,p2); print "Maxim Comu Divisor de p1 i p2"; GCD(p1,p2); print "Minim Comu Multiple de p1 i p2"; LCM(p1,p2); print "Maxim Comu Divisor com a combinacio lineal de p1 i p2"; XGCD(p1,p2); print " "; print "Polinomi sobre G25"; poli:= 1/alfa^4 - alfa^(-3) * x + alfa^5*x^2; poli; print "Factorització"; Factorization(poli); print "És irreductible?"; IsIrreducible(poli); print "Evaluem"; Evaluate(poli,0); Output: Magma V2.10-6 Sun Mar 28 2004 10:23:05 on modular [Seed = 2208640532] ------------------------------------- Elements primitius de G5 [ 2, 3 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Polinomis 2*x^2 + alfa*x + alfa^2 alfa*x + 1 Suma 2*x^2 + alfa^19*x + alfa^9 Producte alfa^19*x^3 + alfa^22*x^2 + alfa^10*x + alfa^2 Quocient de p1/p2 alfa^17*x + alfa^5 Residu de p1/p2 alfa^15 alfa^17*x + alfa^5 alfa^15 Maxim Comu Divisor de p1 i p2 1 Minim Comu Multiple de p1 i p2 x^3 + alfa^3*x^2 + alfa^15*x + alfa^7 Maxim Comu Divisor com a combinacio lineal de p1 i p2 1 alfa^9 alfa^14*x + alfa^2 Polinomi sobre G25 alfa^5*x^2 + alfa^9*x + alfa^20 Factorització [ ] És irreductible? true Evaluem alfa^20 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 10:24:07 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; PR5:=PolynomialRing(G25); print " "; p1:=alfa^2+alfa*x+beta*x^2; p2:=1+alfa*x; print "Polinomis"; p1; p2; print "Suma"; p1+p2; print "Producte"; p1*p2; print "Quocient i Residu de p1/p2"; Quotrem(p1,p2); print "Maxim Comu Divisor de p1 i p2"; GCD(p1,p2); print "Minim Comu Multiple de p1 i p2"; LCM(p1,p2); print "Maxim Comu Divisor com a combinacio lineal de p1 i p2"; XGCD(p1,p2); print " "; print "Polinomi sobre G25"; poli:= 1/alfa^4 - alfa^(-3) * x + alfa^5*x^2; poli; print "Factorització"; Factorization(poli); print "És irreductible?"; IsIrreducible(poli); print "Evaluem"; Evaluate(poli,0); Output: Magma V2.10-6 Sun Mar 28 2004 10:24:04 on modular [Seed = 2579445699] ------------------------------------- Elements primitius de G5 [ 2, 3 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Polinomis 2*x^2 + alfa*x + alfa^2 alfa*x + 1 Suma 2*x^2 + alfa^19*x + alfa^9 Producte alfa^19*x^3 + alfa^22*x^2 + alfa^10*x + alfa^2 Quocient i Residu de p1/p2 alfa^17*x + alfa^5 alfa^15 Maxim Comu Divisor de p1 i p2 1 Minim Comu Multiple de p1 i p2 x^3 + alfa^3*x^2 + alfa^15*x + alfa^7 Maxim Comu Divisor com a combinacio lineal de p1 i p2 1 alfa^9 alfa^14*x + alfa^2 Polinomi sobre G25 alfa^5*x^2 + alfa^9*x + alfa^20 Factorització [ ] És irreductible? true Evaluem alfa^20 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 10:49:34 2004 Input: print "EXERCICI 1"; print "apartat (i)"; /* CODI ----*/ G2:=GF(2); G3:=GF(3); G5:=GF(5); elements := procedure (cos,numelementos) for i:=0 to (numelementos-1) do cos!i; end for; end procedure; print "elements de G2"; elements(G2,2); print "elements de G3"; elements(G3,3); print "elements de G5"; elements(G5,5); Output: Magma V2.10-6 Sun Mar 28 2004 10:49:31 on modular [Seed = 1180758530] ------------------------------------- EXERCICI 1 apartat (i) elements de G2 0 1 elements de G3 0 1 2 elements de G5 0 1 2 3 4 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 10:51:21 2004 Input: print "EXERCICI 1"; print "apartat (i)"; /* CODI ----*/ G2:=GF(2); G3:=GF(3); G5:=GF(5); elements := procedure (cos,numelementos) for i:=0 to (numelementos-1) do cos!i; end for; end procedure; print "elements de G2"; elements(G2,2); print "elements de G3"; elements(G3,3); print "elements de G5"; elements(G5,5); Z9:=Integers(9); /* Z9 no es un cos pq te elements no invertibles a part del zero. Són aquests:*/ for i:=0 to 8 do if(IsInvertible(Z9!i) eq false) then Z9!i; end if; end for; Output: Magma V2.10-6 Sun Mar 28 2004 10:51:18 on modular [Seed = 1433657708] ------------------------------------- EXERCICI 1 apartat (i) elements de G2 0 1 elements de G3 0 1 2 elements de G5 0 1 2 3 4 0 3 6 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 10:51:45 2004 Input: print "apartat (ii)"; /* CODI ----*/ Z9:=Integers(9); /* Z9 no es un cos pq te elements no invertibles a part del zero. Són aquests:*/ for i:=0 to 8 do if(IsInvertible(Z9!i) eq false) then Z9!i; end if; end for; Output: Magma V2.10-6 Sun Mar 28 2004 10:51:42 on modular [Seed = 1766841768] ------------------------------------- apartat (ii) 0 3 6 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 10:52:32 2004 Input: print "apartat (ii)"; /* CODI ----*/ Z9:=Integers(9); /* Z9 no es un cos pq te elements no invertibles a part del zero. Són aquests:*/ print "Elements no invertibles a Z9"; for i:=0 to 8 do if(IsInvertible(Z9!i) eq false) then Z9!i; end if; end for; Output: Magma V2.10-6 Sun Mar 28 2004 10:52:29 on modular [Seed = 2052902536] ------------------------------------- apartat (ii) Elements no invertibles a Z9 0 3 6 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 10:53:37 2004 Input: print "apartat (iii)"; /* CODI ----*/ P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; IsIrreducible(f); P2:=PolynomialRing(GF(2)); g:=1+y+y^4; IsIrreducible(g); P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; IsIrreducible(h); k:=1+2*x+x^2; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; G9b:=ext< G3 | k >; /*En aquest últim cas el polinomi k no es irreductible i no podem definir el cos finit G9b com a extensió de G9 fent servir aquest polinomi*/ Output: Magma V2.10-6 Sun Mar 28 2004 10:53:34 on modular [Seed = 1884734657] ------------------------------------- apartat (iii) true true true false >> G9b:=ext< G3 | k >; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 10:56:01 2004 Input: print "apartat (iii)"; /* CODI ----*/ P3:=PolynomialRing(GF(3)); print "Polinomi 1"; f:=2+2*x+x^2; f; print "És irreductible?"; IsIrreducible(f); P2:=PolynomialRing(GF(2)); print "Polinomi 2"; g:=1+y+y^4; g; print "És irreductible?"; IsIrreducible(g); P5:=PolynomialRing(GF(5)); print "Polinomi 3"; h:=3+2*z+z^2; h; print "És irreductible?"; IsIrreducible(h); print "Polinomi 4"; k:=1+2*x+x^2; print "És irreductible?"; IsIrreducible(k); G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; G9b:=ext< G3 | k >; /*En aquest últim cas el polinomi k no es irreductible i no podem definir el cos finit G9b com a extensió de G9 fent servir aquest polinomi*/ Output: Magma V2.10-6 Sun Mar 28 2004 10:55:58 on modular [Seed = 35960771] ------------------------------------- apartat (iii) Polinomi 1 x^2 + 2*x + 2 És irreductible? true Polinomi 2 y^4 + y + 1 És irreductible? true Polinomi 3 z^2 + 2*z + 3 És irreductible? true Polinomi 4 És irreductible? false >> G9b:=ext< G3 | k >; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 11:01:12 2004 Input: G2:=GF(2); Output: Magma V2.10-6 Sun Mar 28 2004 11:01:08 on modular [Seed = 1041795253] ------------------------------------- Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 11:01:40 2004 Input: P5:=PolynomialRing(GF(5)); print "Polinomi 3"; h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; /*(iv)*/ print "apartat (iv)"; /* CODI ----*/ p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; print("Ordre dels elements de G25 diferents de 0"); llista; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; Output: Magma V2.10-6 Sun Mar 28 2004 11:01:37 on modular [Seed = 890471323] ------------------------------------- Polinomi 3 apartat (iv) Ordre dels elements de G25 diferents de 0 [ 1, 4, 4, 2, 24, 8, 24, 3, 6, 24, 12, 8, 12, 24, 24, 24, 12, 8, 12, 24, 3, 6, 24, 8 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Total time: 3.299 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 11:01:42 2004 Input: G2:=GF(2); elementsG2:=[A : A in G2] Output: Magma V2.10-6 Sun Mar 28 2004 11:01:38 on modular [Seed = 840205471] ------------------------------------- Total time: 3.289 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 11:01:55 2004 Input: G2:=GF(2); elementsG2:=[A : A in G2]; elementsG2; Output: Magma V2.10-6 Sun Mar 28 2004 11:01:52 on modular [Seed = 3286594940] ------------------------------------- [ 0, 1 ] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 11:02:18 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; /*(iv)*/ print "apartat (iv)"; /* CODI ----*/ p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; print("Ordre dels elements de G25 diferents de 0"); llista; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; Output: Magma V2.10-6 Sun Mar 28 2004 11:02:15 on modular [Seed = 3673976210] ------------------------------------- apartat (iv) Ordre dels elements de G25 diferents de 0 [ 1, 4, 4, 2, 24, 8, 24, 3, 6, 24, 12, 8, 12, 24, 24, 24, 12, 8, 12, 24, 3, 6, 24, 8 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 11:03:24 2004 Input: G3:=GF(3); elementsG3:=[A : A in G3]; elementsG3; Output: Magma V2.10-6 Sun Mar 28 2004 11:03:21 on modular [Seed = 3505809366] ------------------------------------- [ 0, 1, 2 ] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 11:04:00 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; /*(iv)*/ print "apartat (iv)"; /* CODI ----*/ p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; print("Ordre dels elements de G25 diferents de 0"); llista; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print("Elements primitius de G25"); llista; #llista; Output: Magma V2.10-6 Sun Mar 28 2004 11:03:57 on modular [Seed = 3871363524] ------------------------------------- apartat (iv) Ordre dels elements de G25 diferents de 0 [ 1, 4, 4, 2, 24, 8, 24, 3, 6, 24, 12, 8, 12, 24, 24, 24, 12, 8, 12, 24, 3, 6, 24, 8 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] 8 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 11:04:19 2004 Input: G5:=GF(5); elementsG5:=[A : A in G5]; elementsG5; Output: Magma V2.10-6 Sun Mar 28 2004 11:04:16 on modular [Seed = 4259007026] ------------------------------------- [ 0, 1, 2, 3, 4 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 11:04:33 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; /*(iv)*/ print "apartat (iv)"; /* CODI ----*/ p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; print "Ordre dels elements de G25 diferents de 0"; llista; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print "Elements primitius de G25"; llista; print "Nombre d'elements primitius de G25 #llista; Output: Magma V2.10-6 Sun Mar 28 2004 11:04:30 on modular [Seed = 4107420469] ------------------------------------- apartat (iv) Ordre dels elements de G25 diferents de 0 [ 1, 4, 4, 2, 24, 8, 24, 3, 6, 24, 12, 8, 12, 24, 24, 24, 12, 8, 12, 24, 3, 6, 24, 8 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] >> quit; ^ User error: Unterminated string Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 11:04:49 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; /*(iv)*/ print "apartat (iv)"; /* CODI ----*/ p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; print "Ordre dels elements de G25 diferents de 0"; llista; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print "Elements primitius de G25"; llista; print "Nombre d'elements primitius de G25"; #llista; Output: Magma V2.10-6 Sun Mar 28 2004 11:04:46 on modular [Seed = 2343386202] ------------------------------------- apartat (iv) Ordre dels elements de G25 diferents de 0 [ 1, 4, 4, 2, 24, 8, 24, 3, 6, 24, 12, 8, 12, 24, 24, 24, 12, 8, 12, 24, 3, 6, 24, 8 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Nombre d'elements primitius de G25 8 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 11:07:18 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; /*(iv)*/ print "apartat (iv)"; /* CODI ----*/ p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; print "Ordre dels elements de G25 diferents de 0"; llista; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print "Elements primitius de G25"; llista; print "Nombre d'elements primitius de G25"; #llista; EulerPhi(G25); Output: Magma V2.10-6 Sun Mar 28 2004 11:07:15 on modular [Seed = 2646287841] ------------------------------------- apartat (iv) Ordre dels elements de G25 diferents de 0 [ 1, 4, 4, 2, 24, 8, 24, 3, 6, 24, 12, 8, 12, 24, 24, 24, 12, 8, 12, 24, 3, 6, 24, 8 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Nombre d'elements primitius de G25 8 >> EulerPhi(G25); ^ Runtime error in 'EulerPhi': Bad argument types Argument types given: FldFin Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 11:07:28 2004 Input: Z9:=Integers(9); IsInvertible(Z9!3); Output: Magma V2.10-6 Sun Mar 28 2004 11:07:25 on modular [Seed = 2494704870] ------------------------------------- false Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 11:07:51 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; /*(iv)*/ print "apartat (iv)"; /* CODI ----*/ p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; print "Ordre dels elements de G25 diferents de 0"; llista; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print "Elements primitius de G25"; llista; print "Nombre d'elements primitius de G25"; #llista; EulerPhi(5,2); Output: Magma V2.10-6 Sun Mar 28 2004 11:07:48 on modular [Seed = 2878149552] ------------------------------------- apartat (iv) Ordre dels elements de G25 diferents de 0 [ 1, 4, 4, 2, 24, 8, 24, 3, 6, 24, 12, 8, 12, 24, 24, 24, 12, 8, 12, 24, 3, 6, 24, 8 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Nombre d'elements primitius de G25 8 >> EulerPhi(5,2); ^ Runtime error in 'EulerPhi': Bad argument types Argument types given: RngIntElt, RngIntElt Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 11:08:04 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; /*(iv)*/ print "apartat (iv)"; /* CODI ----*/ p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; print "Ordre dels elements de G25 diferents de 0"; llista; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print "Elements primitius de G25"; llista; print "Nombre d'elements primitius de G25"; #llista; EulerPhi(25); Output: Magma V2.10-6 Sun Mar 28 2004 11:08:01 on modular [Seed = 2726566540] ------------------------------------- apartat (iv) Ordre dels elements de G25 diferents de 0 [ 1, 4, 4, 2, 24, 8, 24, 3, 6, 24, 12, 8, 12, 24, 24, 24, 12, 8, 12, 24, 3, 6, 24, 8 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Nombre d'elements primitius de G25 8 20 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 11:13:37 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; /*(iv)*/ print "apartat (iv)"; /* CODI ----*/ p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; print "Ordre dels elements de G25 diferents de 0"; llista; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print "Elements primitius de G25"; llista; print "Nombre d'elements primitius de G25"; #llista; EulerPhi(5); Output: Magma V2.10-6 Sun Mar 28 2004 11:13:34 on modular [Seed = 1366812847] ------------------------------------- apartat (iv) Ordre dels elements de G25 diferents de 0 [ 1, 4, 4, 2, 24, 8, 24, 3, 6, 24, 12, 8, 12, 24, 24, 24, 12, 8, 12, 24, 3, 6, 24, 8 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Nombre d'elements primitius de G25 8 4 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 11:15:35 2004 Input: Z5:=Integers(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; IsIrreductible(p); Output: Magma V2.10-6 Sun Mar 28 2004 11:15:32 on modular [Seed = 1584981034] ------------------------------------- >> IsIrreductible(p);; ^ User error: Identifier 'IsIrreductible' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 11:16:52 2004 Input: Z5:=Integers(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; IsIrreducible(p); Output: Magma V2.10-6 Sun Mar 28 2004 11:16:49 on modular [Seed = 1248653419] ------------------------------------- true Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 11:21:38 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; /*(iv)*/ print "apartat (iv)"; /* CODI ----*/ p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then llista:=llista cat [Order(el)]; end if; end for; end for; print "Ordre dels elements de G25 diferents de 0"; llista; /*Un element primitiu es tot element beta de GF(p^n) que té ordre és p^n - 1*/ llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; print "Elements primitius de G25"; llista; print "Nombre d'elements primitius de G25"; #llista; EulerPhi(5); EulerPhi(9); Output: Magma V2.10-6 Sun Mar 28 2004 11:21:35 on modular [Seed = 2086324131] ------------------------------------- apartat (iv) Ordre dels elements de G25 diferents de 0 [ 1, 4, 4, 2, 24, 8, 24, 3, 6, 24, 12, 8, 12, 24, 24, 24, 12, 8, 12, 24, 3, 6, 24, 8 ] Elements primitius de G25 [ alfa, alfa^17, alfa^19, alfa^11, alfa^7, alfa^23, alfa^13, alfa^5 ] Nombre d'elements primitius de G25 8 4 6 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 11:25:37 2004 Input: Z3:=GF(3); p:=PolynomialRing(Z3); p:=2+2*x+x^2; G9:=ext; G9; Output: Magma V2.10-6 Sun Mar 28 2004 11:25:34 on modular [Seed = 1800263493] ------------------------------------- Finite field of size 3^2 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 11:25:47 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; /*(iv)*/ print "apartat (iv)"; /* CODI ----*/ p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; /*(v)*/ print "apartat (v)"; /* CODI ----*/ prim_el:=llista[1]; mpa:=MinimalPolynomial(a); print("Polinomi minim"); mpa; print("Grau de l'element primitiu"); Degree(mpa); print("Cos sobre el que esta definit el polinomi minim"); CoefficientRing(mpa); print("Arrels a G25"); Roots(mpa,G25); print("Arrels a Z5"); Roots(mpa,Integers(5)); Output: Magma V2.10-6 Sun Mar 28 2004 11:25:44 on modular [Seed = 338864332] ------------------------------------- apartat (iv) apartat (v) >> mpa:=MinimalPolynomial(a); ^ User error: Identifier 'a' has not been declared or assigned Polinomi minim >> mpa; ^ User error: Identifier 'mpa' has not been declared or assigned Grau de l'element primitiu >> Degree(mpa); ^ User error: Identifier 'mpa' has not been declared or assigned Cos sobre el que esta definit el polinomi minim >> CoefficientRing(mpa); ^ User error: Identifier 'mpa' has not been declared or assigned Arrels a G25 >> Roots(mpa,G25); ^ User error: Identifier 'mpa' has not been declared or assigned Arrels a Z5 >> Roots(mpa,Integers(5)); ^ User error: Identifier 'mpa' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 11:26:05 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; /*(iv)*/ print "apartat (iv)"; /* CODI ----*/ p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; /*(v)*/ print "apartat (v)"; /* CODI ----*/ prim_el:=llista[1]; mpa:=MinimalPolynomial(prim_el); print("Polinomi minim"); mpa; print("Grau de l'element primitiu"); Degree(mpa); print("Cos sobre el que esta definit el polinomi minim"); CoefficientRing(mpa); print("Arrels a G25"); Roots(mpa,G25); print("Arrels a Z5"); Roots(mpa,Integers(5)); Output: Magma V2.10-6 Sun Mar 28 2004 11:26:02 on modular [Seed = 490447319] ------------------------------------- apartat (iv) apartat (v) Polinomi minim z^2 + 2*z + 3 Grau de l'element primitiu 2 Cos sobre el que esta definit el polinomi minim Finite field of size 5 Arrels a G25 [ , ] Arrels a Z5 [] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 11:26:24 2004 Input: Z3:=GF(3); p:=2+2*x+x^2; G9:=ext; G9; Output: Magma V2.10-6 Sun Mar 28 2004 11:26:21 on modular [Seed = 102808315] ------------------------------------- >> p:=2+2*x+x^2; ^ User error: Identifier 'x' has not been declared or assigned >> G9:=ext; ^ User error: Identifier 'p' has not been declared or assigned >> G9;; ^ User error: Identifier 'G9' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 11:26:35 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; /*(v)*/ print "apartat (v)"; /* CODI ----*/ prim_el:=llista[1]; mpa:=MinimalPolynomial(prim_el); print("Polinomi minim"); mpa; print("Grau de l'element primitiu"); Degree(mpa); print("Cos sobre el que esta definit el polinomi minim"); CoefficientRing(mpa); print("Arrels a G25"); Roots(mpa,G25); print("Arrels a Z5"); Roots(mpa,Integers(5)); Output: Magma V2.10-6 Sun Mar 28 2004 11:26:32 on modular [Seed = 254391271] ------------------------------------- apartat (v) Polinomi minim z^2 + 2*z + 3 Grau de l'element primitiu 2 Cos sobre el que esta definit el polinomi minim Finite field of size 5 Arrels a G25 [ , ] Arrels a Z5 [] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 11:26:40 2004 Input: Z3:=GF(3); p:=PolynomialRing(Z3); p:=2+2*x+x^2; G9:=ext; Output: Magma V2.10-6 Sun Mar 28 2004 11:26:37 on modular [Seed = 941524181] ------------------------------------- Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 11:29:50 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; /*(v)*/ print "apartat (v)"; /* CODI ----*/ prim_el:=llista[1]; mpa:=MinimalPolynomial(a); print "Polinomi minim"; mpa; print "Grau"; Degree(mpa); print "Cos sobre el que esta definit el polinomi minim"; CoefficientRing(mpa); print "Arrels a G25"; Roots(mpa,G25); print "Arrels a Z5" ; Roots(mpa,Integers(5)); Output: Magma V2.10-6 Sun Mar 28 2004 11:29:47 on modular [Seed = 587570696] ------------------------------------- apartat (v) >> mpa:=MinimalPolynomial(a); ^ User error: Identifier 'a' has not been declared or assigned Polinomi minim >> mpa; ^ User error: Identifier 'mpa' has not been declared or assigned Grau >> Degree(mpa); ^ User error: Identifier 'mpa' has not been declared or assigned Cos sobre el que esta definit el polinomi minim >> CoefficientRing(mpa); ^ User error: Identifier 'mpa' has not been declared or assigned Arrels a G25 >> Roots(mpa,G25); ^ User error: Identifier 'mpa' has not been declared or assigned Arrels a Z5 >> Roots(mpa,Integers(5));; ^ User error: Identifier 'mpa' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 11:30:25 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; /*(v)*/ print "apartat (v)"; /* CODI ----*/ prim_el:=llista[1]; mpa:=MinimalPolynomial(prim_el); print "Polinomi minim"; mpa; print "Grau"; Degree(mpa); print "Cos sobre el que esta definit el polinomi minim"; CoefficientRing(mpa); print "Arrels a G25"; Roots(mpa,G25); print "Arrels a Z5" ; Roots(mpa,Integers(5)); Output: Magma V2.10-6 Sun Mar 28 2004 11:30:22 on modular [Seed = 3556077085] ------------------------------------- apartat (v) Polinomi minim z^2 + 2*z + 3 Grau 2 Cos sobre el que esta definit el polinomi minim Finite field of size 5 Arrels a G25 [ , ] Arrels a Z5 [] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 11:32:14 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do el:=G25![j,i]; if (el ne 0) then if (Order(el) eq (p^n-1)) then llista:=llista cat [el]; end if; end if; end for; end for; beta:=2*alfa^(-3) - alfa^5 + (1/(alfa+2))*alfa^6; print("Solucio de beta"); beta; print("Invers"); beta^(-1); Output: Magma V2.10-6 Sun Mar 28 2004 11:32:11 on modular [Seed = 3707396743] ------------------------------------- Solucio de beta alfa^8 Invers alfa^16 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 11:32:32 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; print "apartat (vi)"; /* CODI ----*/ beta:=2*alfa^(-3) - alfa^5 + (1/(alfa+2))*alfa^6; print("Solucio de beta"); beta; print("Invers"); beta^(-1); Output: Magma V2.10-6 Sun Mar 28 2004 11:32:29 on modular [Seed = 3320019848] ------------------------------------- apartat (vi) Solucio de beta alfa^8 Invers alfa^16 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 11:37:16 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; print "apartat (vi)"; /* CODI ----*/ beta:=2*alfa^(-3) - alfa^5 + (1/(alfa+2))*alfa^6; print("Solucio de beta"); beta; print("Invers"); beta^(-1); print "Elements invertibles a G25"; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do if(IsInvertible(G25![j,i]) eq true) then llista:=llista cat [G25![j,i]]; end if; end for; end for; llista; Output: Magma V2.10-6 Sun Mar 28 2004 11:37:13 on modular [Seed = 4107422621] ------------------------------------- apartat (vi) Solucio de beta alfa^8 Invers alfa^16 Elements invertibles a G25 [ 1, 2, 3, 4, alfa, alfa^3, alfa^17, alfa^16, alfa^20, alfa^19, alfa^10, alfa^21, alfa^14, alfa^11, alfa^7, alfa^23, alfa^2, alfa^9, alfa^22, alfa^13, alfa^8, alfa^4, alfa^5, alfa^15 ] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 11:38:12 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; print "apartat (vi)"; /* CODI ----*/ beta:=2*alfa^(-3) - alfa^5 + (1/(alfa+2))*alfa^6; print("Solucio de beta"); beta; print("Invers"); beta^(-1); print "Elements invertibles a G25"; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do if(IsInvertible(G25![j,i]) eq true) then llista:=llista cat [G25![j,i]]; end if; end for; end for; llista; print "Nombre d'elements invertibles de G25"; EulerPhi(25); #llista; Output: Magma V2.10-6 Sun Mar 28 2004 11:38:09 on modular [Seed = 4259005148] ------------------------------------- apartat (vi) Solucio de beta alfa^8 Invers alfa^16 Elements invertibles a G25 [ 1, 2, 3, 4, alfa, alfa^3, alfa^17, alfa^16, alfa^20, alfa^19, alfa^10, alfa^21, alfa^14, alfa^11, alfa^7, alfa^23, alfa^2, alfa^9, alfa^22, alfa^13, alfa^8, alfa^4, alfa^5, alfa^15 ] Nombre d'elements invertibles de G25 20 24 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 11:39:38 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; print "apartat (vi)"; /* CODI ----*/ beta:=2*alfa^(-3) - alfa^5 + (1/(alfa+2))*alfa^6; print("Solucio de beta"); beta; print("Invers"); beta^(-1); print "Elements invertibles a G25"; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do if(IsInvertible(G25![j,i]) eq true) then llista:=llista cat [G25![j,i]]; end if; end for; end for; llista; print "Nombre d'elements invertibles de G25"; EulerPhi(p^n-1); #llista; Output: Magma V2.10-6 Sun Mar 28 2004 11:39:35 on modular [Seed = 3905836927] ------------------------------------- apartat (vi) Solucio de beta alfa^8 Invers alfa^16 Elements invertibles a G25 [ 1, 2, 3, 4, alfa, alfa^3, alfa^17, alfa^16, alfa^20, alfa^19, alfa^10, alfa^21, alfa^14, alfa^11, alfa^7, alfa^23, alfa^2, alfa^9, alfa^22, alfa^13, alfa^8, alfa^4, alfa^5, alfa^15 ] Nombre d'elements invertibles de G25 8 24 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 11:40:28 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; print "apartat (vi)"; /* CODI ----*/ beta:=2*alfa^(-3) - alfa^5 + (1/(alfa+2))*alfa^6; print("Solucio de beta"); beta; print("Invers"); beta^(-1); print "Elements invertibles a G25"; llista:=[]; for i:=0 to (p-1) do for j:=0 to (p-1) do if(IsInvertible(G25![j,i]) eq true) then llista:=llista cat [G25![j,i]]; end if; end for; end for; llista; print "Nombre d'elements invertibles de G25"; #llista; Output: Magma V2.10-6 Sun Mar 28 2004 11:40:25 on modular [Seed = 2562598705] ------------------------------------- apartat (vi) Solucio de beta alfa^8 Invers alfa^16 Elements invertibles a G25 [ 1, 2, 3, 4, alfa, alfa^3, alfa^17, alfa^16, alfa^20, alfa^19, alfa^10, alfa^21, alfa^14, alfa^11, alfa^7, alfa^23, alfa^2, alfa^9, alfa^22, alfa^13, alfa^8, alfa^4, alfa^5, alfa^15 ] Nombre d'elements invertibles de G25 24 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 11:43:56 2004 Input: Z2:=GF(2); p:=PolynomialRing(Z2); p:=1+x+x^4; G16:=ext; Output: Magma V2.10-6 Sun Mar 28 2004 11:43:53 on modular [Seed = 2208613146] ------------------------------------- Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 11:46:14 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; Output: Magma V2.10-6 Sun Mar 28 2004 11:46:11 on modular [Seed = 2979459250] ------------------------------------- Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 11:47:23 2004 Input: Z3:=GF(3); p:=PolynomialRing(Z3); p:=1+2*x+x^2; G9b:=ext; Output: Magma V2.10-6 Sun Mar 28 2004 11:47:20 on modular [Seed = 3130915698] ------------------------------------- >> G9b:=ext;; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 11:47:45 2004 Input: P2:=PolynomialRing(GF(2)); g:=1+y+y^4; G2:=GF(2); G16:=ext< G2 | g >; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; /*(vii)*/ print "apartat (vii)"; /* CODI ----*/ p:=5; n:=2; print("G25"); print("exponencial , vectorial"); < 0 , ElementToSequence(0*alfa)>; for i:=0 to (p^n-2) do < alfa^i , ElementToSequence(alfa^i)>; end for; p:=2; n:=4; print("G16"); print("exponencial , vectorial"); < 0 , ElementToSequence(0*alfa2)>; for i:=0 to (p^n-2) do < alfa2^i , ElementToSequence(alfa2^i)>; end for; Output: Magma V2.10-6 Sun Mar 28 2004 11:47:42 on modular [Seed = 2743394909] ------------------------------------- apartat (vii) G25 exponencial , vectorial <0, [ 0, 0 ]> <1, [ 1, 0 ]> <3, [ 3, 0 ]> <4, [ 4, 0 ]> <2, [ 2, 0 ]> G16 exponencial , vectorial <0, [ 0, 0, 0, 0 ]> <1, [ 1, 0, 0, 0 ]> Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 11:49:01 2004 Input: CF2:=GF(2); CF4:=GF(2,2); CF8:=GF(2,3); CF16:=GF(2,4); print("Elements de CF2"); p:=2; n:=1; for i:=0 to p^n-1 do CF2!i; end for; print("Elements de CF4"); p:=2; n:=2; for i:=0 to p^n-1 do CF4!i; end for; print("Elements de CF8"); p:=2; n:=3; for i:=0 to p^n-1 do CF8!i; end for; print("Elements de CF16"); p:=2; n:=4; for i:=0 to p^n-1 do CF16!i; end for; Output: Magma V2.10-6 Sun Mar 28 2004 11:48:58 on modular [Seed = 2911562759] ------------------------------------- Elements de CF2 0 1 Elements de CF4 0 1 0 1 Elements de CF8 0 1 0 1 0 1 0 1 Elements de CF16 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 11:52:05 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; elements:=[A:A in G25]; ordre:=[Order(A):A in elements | A ne 0]; ordre; Output: Magma V2.10-6 Sun Mar 28 2004 11:52:02 on modular [Seed = 1601707452] ------------------------------------- [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 11:54:40 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; elements:=[A:A in G25]; primitius:=[A:A in elements | IsPrimitive(A) eq true]; primitius; Output: Magma V2.10-6 Sun Mar 28 2004 11:54:37 on modular [Seed = 1215236948] ------------------------------------- [ G25.1, G25.1^5, G25.1^7, G25.1^11, G25.1^13, G25.1^17, G25.1^19, G25.1^23 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 11:55:35 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; elements:=[A:A in G25]; primitius:=[A:A in elements | IsPrimitive(A) eq true]; #(primitius); Output: Magma V2.10-6 Sun Mar 28 2004 11:55:32 on modular [Seed = 1985033635] ------------------------------------- 8 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 11:58:51 2004 Input: CF2:=GF(2); CF4:=GF(2,2); CF8:=GF(2,3); CF16:=GF(2,4); print("Elements de CF2"); p:=2; n:=1; for i:=0 to p^n-1 do CF2!i; end for; print("Elements de CF4"); p:=2; n:=2; for i:=0 to p^n-1 do CF4!i; end for; print("Elements de CF8"); p:=2; n:=3; for i:=0 to p^n-1 do CF8!i; end for; print("Elements de CF16"); p:=2; n:=4; for i:=0 to p^n-1 do CF16!i; end for; CF2 subset CF16; CF2 subset CF8; CF2 subset CF4; CF4 subset CF16; CF4 subset CF8; CF4 subset CF2; CF8 subset CF16; CF8 subset CF4; CF8 subset CF2; CF16 subset CF8; CF16 subset CF4; CF16 subset CF2; Output: Magma V2.10-6 Sun Mar 28 2004 11:58:48 on modular [Seed = 1665410938] ------------------------------------- Elements de CF2 0 1 Elements de CF4 0 1 0 1 Elements de CF8 0 1 0 1 0 1 0 1 Elements de CF16 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 true true true true false false false false false false false false Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 12:02:10 2004 Input: CF2:=GF(2); CF4:=GF(2,2); CF8:=GF(2,3); CF16:=GF(2,4); print("Elements de CF2"); p:=2; n:=1; for i:=0 to p^n-1 do CF2!i; end for; print("Elements de CF4"); p:=2; n:=2; for i:=0 to p^n-1 do CF4!i; end for; print("Elements de CF8"); p:=2; n:=3; for i:=0 to p^n-1 do CF8!i; end for; print("Elements de CF16"); p:=2; n:=4; for i:=0 to p^n-1 do CF16!i; end for; print "CF2"; CF2 subset CF16; CF2 subset CF8; CF2 subset CF4; print "CF4"; CF4 subset CF16; CF4 subset CF8; CF4 subset CF2; print "CF8"; CF8 subset CF16; CF8 subset CF4; CF8 subset CF2; print "CF16"; CF16 subset CF8; CF16 subset CF4; CF16 subset CF2; Output: Magma V2.10-6 Sun Mar 28 2004 12:02:06 on modular [Seed = 119554648] ------------------------------------- Elements de CF2 0 1 Elements de CF4 0 1 0 1 Elements de CF8 0 1 0 1 0 1 0 1 Elements de CF16 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 CF2 true true true CF4 true false false CF8 false false false CF16 false false false Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 12:04:34 2004 Input: CF2:=GF(2); CF4:=GF(2,2); CF8:=GF(2,3); CF16:=GF(2,4); elements := procedure (cos,numelementos) for i:=0 to (numelementos-1) do cos!i; end for; end procedure; print("Elements de CF2"); elements(CF2,2); print("Elements de CF4"); elements(CF4,4); print("Elements de CF8"); elements(CF8,8); print("Elements de CF16"); elements(CF16,16); print "CF2"; CF2 subset CF16; CF2 subset CF8; CF2 subset CF4; print "CF4"; CF4 subset CF16; CF4 subset CF8; CF4 subset CF2; print "CF8"; CF8 subset CF16; CF8 subset CF4; CF8 subset CF2; print "CF16"; CF16 subset CF8; CF16 subset CF4; CF16 subset CF2; Output: Magma V2.10-6 Sun Mar 28 2004 12:04:31 on modular [Seed = 806843902] ------------------------------------- Elements de CF2 0 1 Elements de CF4 0 1 0 1 Elements de CF8 0 1 0 1 0 1 0 1 Elements de CF16 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 CF2 true true true CF4 true false false CF8 false false false CF16 false false false Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 12:10:01 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; /*EXERCICI 2*/ /*(i)*/ print "EXERCICI 2"; print "apartat(i); PR5:=PolynomialRing(G25); Output: Magma V2.10-6 Sun Mar 28 2004 12:09:58 on modular [Seed = 554067862] ------------------------------------- EXERCICI 2 >> quit; ^ User error: Unterminated string Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 12:10:15 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; /*EXERCICI 2*/ /*(i)*/ print "EXERCICI 2"; print "apartat(i)"; PR5:=PolynomialRing(G25); Output: Magma V2.10-6 Sun Mar 28 2004 12:10:12 on modular [Seed = 3522598772] ------------------------------------- EXERCICI 2 apartat(i) Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 12:10:49 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; /*EXERCICI 2*/ /*(i)*/ print "EXERCICI 2"; print "apartat(i)"; PR5:=PolynomialRing(G25); IsFinite(PR5); Output: Magma V2.10-6 Sun Mar 28 2004 12:10:46 on modular [Seed = 3640631199] ------------------------------------- EXERCICI 2 apartat(i) false Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 12:11:12 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; /*EXERCICI 2*/ /*(i)*/ print "EXERCICI 2"; print "apartat(i)"; PR5:=PolynomialRing(G25); print "És finit?"; IsFinite(PR5); Output: Magma V2.10-6 Sun Mar 28 2004 12:11:09 on modular [Seed = 3286533311] ------------------------------------- EXERCICI 2 apartat(i) És finit? false Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 12:13:07 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; PR5:=PolynomialRing(G25); /*(ii)*/ print "apartat (ii)"; /* CODI ----*/ p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; p1:=alfa^2+alfa*x+beta*x^2; p2:=1+alfa*x; Output: Magma V2.10-6 Sun Mar 28 2004 12:13:04 on modular [Seed = 3454700092] ------------------------------------- apartat (ii) Elements primitius de G5 [ 2, 3 ] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 12:14:06 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; PR5:=PolynomialRing(G25); /*(ii)*/ print "apartat (ii)"; /* CODI ----*/ p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; print "Polinomi p1"; p1:=alfa^2+alfa*x+beta*x^2; p1; print "Polinomi p2"; p2:=1+alfa*x; p2; Output: Magma V2.10-6 Sun Mar 28 2004 12:14:03 on modular [Seed = 4157649021] ------------------------------------- apartat (ii) Elements primitius de G5 [ 2, 3 ] Polinomi p1 2*x^2 + alfa*x + alfa^2 Polinomi p2 alfa*x + 1 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 12:16:35 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; PR5:=PolynomialRing(G25); /*(ii)*/ print "apartat (ii)"; /* CODI ----*/ p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; print "Polinomi p1"; p1:=alfa^2+alfa*x+beta*x^2; p1; print "Polinomi p2"; p2:=1+alfa*x; p2; print "Suma"; p1+p2; print "Producte"; p1*p2; Output: Magma V2.10-6 Sun Mar 28 2004 12:16:32 on modular [Seed = 3888164806] ------------------------------------- apartat (ii) Elements primitius de G5 [ 2, 3 ] Polinomi p1 2*x^2 + alfa*x + alfa^2 Polinomi p2 alfa*x + 1 Suma 2*x^2 + alfa^19*x + alfa^9 Producte alfa^19*x^3 + alfa^22*x^2 + alfa^10*x + alfa^2 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 12:16:49 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; PR5:=PolynomialRing(G25); /*(ii)*/ print "apartat (ii)"; /* CODI ----*/ p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; print "Polinomi p1"; p1:=alfa^2+alfa*x+beta*x^2; p1; print "Polinomi p2"; p2:=1+alfa*x; p2; /*(iii)*/ print "apartat (iii)"; /* CODI ----*/ print "Suma"; p1+p2; print "Producte"; p1*p2; Output: Magma V2.10-6 Sun Mar 28 2004 12:16:46 on modular [Seed = 4006192833] ------------------------------------- apartat (ii) Elements primitius de G5 [ 2, 3 ] Polinomi p1 2*x^2 + alfa*x + alfa^2 Polinomi p2 alfa*x + 1 apartat (iii) Suma 2*x^2 + alfa^19*x + alfa^9 Producte alfa^19*x^3 + alfa^22*x^2 + alfa^10*x + alfa^2 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 12:19:51 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; PR5:=PolynomialRing(G25); /*(ii)*/ print "apartat (ii)"; /* CODI ----*/ p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; print "Polinomi p1"; p1:=alfa^2+alfa*x+beta*x^2; p1; print "Polinomi p2"; p2:=1+alfa*x; p2; /*(iii)*/ print "apartat (iii)"; /* CODI ----*/ print "Suma"; p1+p2; print "Producte"; p1*p2; /*(iv)*/ print "apartat (iv)"; /* CODI ----*/ print "Quocient i Residu de p1/p2"; Quotrem(p1,p2); Output: Magma V2.10-6 Sun Mar 28 2004 12:19:48 on modular [Seed = 2612843262] ------------------------------------- apartat (ii) Elements primitius de G5 [ 2, 3 ] Polinomi p1 2*x^2 + alfa*x + alfa^2 Polinomi p2 alfa*x + 1 apartat (iii) Suma 2*x^2 + alfa^19*x + alfa^9 Producte alfa^19*x^3 + alfa^22*x^2 + alfa^10*x + alfa^2 apartat (iv) Quocient i Residu de p1/p2 alfa^17*x + alfa^5 alfa^15 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 12:20:43 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; PR5:=PolynomialRing(G25); /*(ii)*/ print "apartat (ii)"; /* CODI ----*/ p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; print "Polinomi p1"; p1:=alfa^2+alfa*x+beta*x^2; p1; print "Polinomi p2"; p2:=1+alfa*x; p2; /*(iii)*/ print "apartat (iii)"; /* CODI ----*/ print "Suma"; p1+p2; print "Producte"; p1*p2; /*(iv)*/ print "apartat (iv)"; /* CODI ----*/ print "Quocient i Residu de p1/p2"; Quotrem(p1,p2); /*(v)*/ print "apartat (v)"; /* CODI ----*/ print "Maxim Comu Divisor de p1 i p2"; GCD(p1,p2); print "Minim Comu Multiple de p1 i p2"; LCM(p1,p2); Output: Magma V2.10-6 Sun Mar 28 2004 12:20:40 on modular [Seed = 2343355058] ------------------------------------- apartat (ii) Elements primitius de G5 [ 2, 3 ] Polinomi p1 2*x^2 + alfa*x + alfa^2 Polinomi p2 alfa*x + 1 apartat (iii) Suma 2*x^2 + alfa^19*x + alfa^9 Producte alfa^19*x^3 + alfa^22*x^2 + alfa^10*x + alfa^2 apartat (iv) Quocient i Residu de p1/p2 alfa^17*x + alfa^5 alfa^15 apartat (v) Maxim Comu Divisor de p1 i p2 1 Minim Comu Multiple de p1 i p2 x^3 + alfa^3*x^2 + alfa^15*x + alfa^7 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 12:21:33 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; elements:=[A:A in G25]; primitius:=[A:A in elements | IsPrimitive(A) eq true]; primitius[2]; Output: Magma V2.10-6 Sun Mar 28 2004 12:21:30 on modular [Seed = 2996173689] ------------------------------------- G25.1^5 Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 12:22:02 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; PR5:=PolynomialRing(G25); /*(ii)*/ print "apartat (ii)"; /* CODI ----*/ p:=5; n:=2; llista:=[]; for i:=0 to (p-1) do el:=G5!i; if (el ne 0) then if (Order(el) eq (p-1)) then llista:=llista cat [el]; end if; end if; end for; print("Elements primitius de G5"); llista; beta:=llista[1]; print "Polinomi p1"; p1:=alfa^2+alfa*x+beta*x^2; p1; print "Polinomi p2"; p2:=1+alfa*x; p2; /*(iii)*/ print "apartat (iii)"; /* CODI ----*/ print "Suma"; p1+p2; print "Producte"; p1*p2; /*(iv)*/ print "apartat (iv)"; /* CODI ----*/ print "Quocient i Residu de p1/p2"; Quotrem(p1,p2); /*(v)*/ print "apartat (v)"; /* CODI ----*/ print "Maxim Comu Divisor de p1 i p2"; GCD(p1,p2); print "Minim Comu Multiple de p1 i p2"; LCM(p1,p2); /*(vi)*/ print "apartat (vi)"; /* CODI ----*/ print "Maxim Comu Divisor com a combinacio lineal de p1 i p2"; XGCD(p1,p2); Output: Magma V2.10-6 Sun Mar 28 2004 12:21:59 on modular [Seed = 3181048923] ------------------------------------- apartat (ii) Elements primitius de G5 [ 2, 3 ] Polinomi p1 2*x^2 + alfa*x + alfa^2 Polinomi p2 alfa*x + 1 apartat (iii) Suma 2*x^2 + alfa^19*x + alfa^9 Producte alfa^19*x^3 + alfa^22*x^2 + alfa^10*x + alfa^2 apartat (iv) Quocient i Residu de p1/p2 alfa^17*x + alfa^5 alfa^15 apartat (v) Maxim Comu Divisor de p1 i p2 1 Minim Comu Multiple de p1 i p2 x^3 + alfa^3*x^2 + alfa^15*x + alfa^7 apartat (vi) Maxim Comu Divisor com a combinacio lineal de p1 i p2 1 alfa^9 alfa^14*x + alfa^2 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 12:22:25 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; elements:=[A:A in G25]; primitius:=[A:A in elements | IsPrimitive(A) eq true]; primitius[2]; polmin:=MinimalPolynomial(primitius[2],Z5); polmin; Output: Magma V2.10-6 Sun Mar 28 2004 12:22:21 on modular [Seed = 2810244664] ------------------------------------- G25.1^5 x^2 + 2*x + 3 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 12:23:27 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; PR5:=PolynomialRing(G25); /*(vii)*/ print "apartat (vi)"; /* CODI ----*/ print "Polinomi sobre G25"; poli:= 1/alfa^4 - alfa^(-3) * x + alfa^5*x^2; poli; print "Factorització"; Factorization(poli); Output: Magma V2.10-6 Sun Mar 28 2004 12:23:24 on modular [Seed = 1383405580] ------------------------------------- apartat (vi) Polinomi sobre G25 alfa^5*x^2 + alfa^9*x + alfa^20 Factorització [ ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 12:23:37 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; elements:=[A:A in G25]; primitius:=[A:A in elements | IsPrimitive(A) eq true]; primitius[2]; polmin:=MinimalPolynomial(primitius[2],Z5); polmin; Degree(polmin); Output: Magma V2.10-6 Sun Mar 28 2004 12:23:34 on modular [Seed = 1534857503] ------------------------------------- G25.1^5 x^2 + 2*x + 3 2 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 12:23:52 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; PR5:=PolynomialRing(G25); /*(vii)*/ print "apartat (vi)"; /* CODI ----*/ print "Polinomi sobre G25"; poli:= 1/alfa^4 - alfa^(-3) * x + alfa^5*x^2; poli; print "Factorització"; Factorization(poli); Roots(poli); Output: Magma V2.10-6 Sun Mar 28 2004 12:23:49 on modular [Seed = 1080494647] ------------------------------------- apartat (vi) Polinomi sobre G25 alfa^5*x^2 + alfa^9*x + alfa^20 Factorització [ ] [] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 12:24:19 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; PR5:=PolynomialRing(G25); /*(vii)*/ print "apartat (vi)"; /* CODI ----*/ print "Polinomi sobre G25"; poli:= 1/alfa^4 - alfa^(-3) * x + alfa^5*x^2; poli; print "Factorització"; Factorization(poli); print "Arrels"; Roots(poli); Output: Magma V2.10-6 Sun Mar 28 2004 12:24:16 on modular [Seed = 1231946587] ------------------------------------- apartat (vi) Polinomi sobre G25 alfa^5*x^2 + alfa^9*x + alfa^20 Factorització [ ] Arrels [] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 12:24:59 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; PR5:=PolynomialRing(G25); /*(vii)*/ print "apartat (vi)"; /* CODI ----*/ print "Polinomi sobre G25"; poli:= 1/alfa^4 - alfa^(-3) * x + alfa^5*x^2; poli; print "Factorització"; Factorization(poli); print "Arrels"; Roots(poli,G25); Output: Magma V2.10-6 Sun Mar 28 2004 12:24:56 on modular [Seed = 1985035340] ------------------------------------- apartat (vi) Polinomi sobre G25 alfa^5*x^2 + alfa^9*x + alfa^20 Factorització [ ] Arrels [] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 12:25:11 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; PR5:=PolynomialRing(G25); /*(vii)*/ print "apartat (vi)"; /* CODI ----*/ print "Polinomi sobre G25"; poli:= 1/alfa^4 - alfa^(-3) * x + alfa^5*x^2; poli; print "Factorització"; Factorization(poli,G25); print "Arrels"; Roots(poli,G25); Output: Magma V2.10-6 Sun Mar 28 2004 12:25:08 on modular [Seed = 1665411397] ------------------------------------- apartat (vi) Polinomi sobre G25 alfa^5*x^2 + alfa^9*x + alfa^20 Factorització >> Factorization(poli,G25); ^ Runtime error in 'Factorization': Bad argument types Argument types given: RngUPolElt, FldFin Arrels [] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 12:25:26 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; PR5:=PolynomialRing(G25); /*(vii)*/ print "apartat (vi)"; /* CODI ----*/ print "Polinomi sobre G25"; poli:= 1/alfa^4 - alfa^(-3) * x + alfa^5*x^2; poli; print "Factorització"; Factorization(poli); print "Arrels"; Roots(poli,G25); Output: Magma V2.10-6 Sun Mar 28 2004 12:25:23 on modular [Seed = 1750016697] ------------------------------------- apartat (vi) Polinomi sobre G25 alfa^5*x^2 + alfa^9*x + alfa^20 Factorització [ ] Arrels [] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 12:28:11 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; PR5:=PolynomialRing(G25); /*(vii)*/ print "apartat (vi)"; /* CODI ----*/ print "Polinomi sobre G25"; poli:= 1/alfa^4 - alfa^(-3) * x + alfa^5*x^2; poli; print "Factorització"; Factorization(poli); print "Arrels"; Roots(poli,G25); for i:=0 to 4 do for j:=0 to 4 do Evaluate(poli,G25![j,i]) end for; end for; Output: Magma V2.10-6 Sun Mar 28 2004 12:28:08 on modular [Seed = 372333932] ------------------------------------- apartat (vi) Polinomi sobre G25 alfa^5*x^2 + alfa^9*x + alfa^20 Factorització [ ] Arrels [] >> for i:=0 to 4 do for j:=0 to 4 do Evaluate(poli,G25![j,i]) end for; end for ^ User error: bad syntax Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 12:28:25 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; PR5:=PolynomialRing(G25); /*(vii)*/ print "apartat (vi)"; /* CODI ----*/ print "Polinomi sobre G25"; poli:= 1/alfa^4 - alfa^(-3) * x + alfa^5*x^2; poli; print "Factorització"; Factorization(poli); print "Arrels"; Roots(poli,G25); for i:=0 to 4 do for j:=0 to 4 do Evaluate(poli,G25![j,i]); end for; end for; Output: Magma V2.10-6 Sun Mar 28 2004 12:28:22 on modular [Seed = 473651064] ------------------------------------- apartat (vi) Polinomi sobre G25 alfa^5*x^2 + alfa^9*x + alfa^20 Factorització [ ] Arrels [] alfa^20 alfa^7 alfa^2 alfa alfa^11 alfa alfa^2 alfa^7 alfa^20 alfa^11 alfa^10 alfa^15 alfa^5 alfa^14 alfa^22 alfa^4 alfa^3 alfa^3 alfa^4 4 alfa^14 alfa^5 alfa^15 alfa^10 alfa^22 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 12:29:12 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; PR5:=PolynomialRing(G25); /*(vii)*/ print "apartat (vi)"; /* CODI ----*/ print "Polinomi sobre G25"; poli:= 1/alfa^4 - alfa^(-3) * x + alfa^5*x^2; poli; print "Factorització"; Factorization(poli); print "Arrels"; Roots(poli,G25); for i:=0 to 4 do for j:=0 to 4 do if(Evaluate(poli,G25![j,i]) eq 0) then G25![j,i]; end for; end for; Output: Magma V2.10-6 Sun Mar 28 2004 12:29:09 on modular [Seed = 86134322] ------------------------------------- apartat (vi) Polinomi sobre G25 alfa^5*x^2 + alfa^9*x + alfa^20 Factorització [ ] Arrels [] >> [j,i]) eq 0) then G25![j,i]; end for; end for; ^ User error: bad syntax Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 12:29:30 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; PR5:=PolynomialRing(G25); /*(vii)*/ print "apartat (vi)"; /* CODI ----*/ print "Polinomi sobre G25"; poli:= 1/alfa^4 - alfa^(-3) * x + alfa^5*x^2; poli; print "Factorització"; Factorization(poli); print "Arrels"; Roots(poli,G25); for i:=0 to 4 do for j:=0 to 4 do if(Evaluate(poli,G25![j,i]) eq 0) then G25![j,i]; end if; end for; end for; Output: Magma V2.10-6 Sun Mar 28 2004 12:29:26 on modular [Seed = 840268054] ------------------------------------- apartat (vi) Polinomi sobre G25 alfa^5*x^2 + alfa^9*x + alfa^20 Factorització [ ] Arrels [] Total time: 3.589 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 12:29:31 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; PR5:=PolynomialRing(G25); /*(vii)*/ print "apartat (vi)"; /* CODI ----*/ print "Polinomi sobre G25"; poli:= 1/alfa^4 - alfa^(-3) * x + alfa^5*x^2; poli; print "Factorització"; Factorization(poli); print "Arrels"; Roots(poli,G25); for i:=0 to 4 do for j:=0 to 4 do if(Evaluate(poli,G25![j,i]) eq 0) then G25![j,i]; end if; end for; end for; Output: Magma V2.10-6 Sun Mar 28 2004 12:29:27 on modular [Seed = 823556628] ------------------------------------- apartat (vi) Polinomi sobre G25 alfa^5*x^2 + alfa^9*x + alfa^20 Factorització [ ] Arrels [] Total time: 3.709 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 12:29:33 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; elements:=[A:A in G25]; primitius:=[A:A in elements | IsPrimitive(A) eq true]; primitius[2]; polmin:=MinimalPolynomial(primitius[2],Z5); polmin; Degree(polmin); Roots(polmin, Z5); Output: Magma V2.10-6 Sun Mar 28 2004 12:29:30 on modular [Seed = 890404381] ------------------------------------- G25.1^5 x^2 + 2*x + 3 2 [] Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 12:30:12 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; elements:=[A:A in G25]; primitius:=[A:A in elements | IsPrimitive(A) eq true]; primitius[2]; polmin:=MinimalPolynomial(primitius[2],Z5); polmin; Degree(polmin); Roots(polmin, G25); Output: Magma V2.10-6 Sun Mar 28 2004 12:30:09 on modular [Seed = 3505888035] ------------------------------------- G25.1^5 x^2 + 2*x + 3 2 [ , ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 12:30:27 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; PR5:=PolynomialRing(G25); /*(vii)*/ print "apartat (vi)"; /* CODI ----*/ print "Polinomi sobre G25"; poli:= 1/alfa^4 - alfa^(-3) * x + alfa^5*x^2; poli; print "Factorització"; Factorization(poli); print "Arrels"; Roots(poli,G25); print "Comprovació amb Evaluate"; for i:=0 to 4 do for j:=0 to 4 do if(Evaluate(poli,G25![j,i]) eq 0) then G25![j,i]; end if; end for; end for; Output: Magma V2.10-6 Sun Mar 28 2004 12:30:24 on modular [Seed = 3657339451] ------------------------------------- apartat (vi) Polinomi sobre G25 alfa^5*x^2 + alfa^9*x + alfa^20 Factorització [ ] Arrels [] Comprovació amb Evaluate Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 12:31:03 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; PR5:=PolynomialRing(G25); /*(vii)*/ print "apartat (vi)"; /* CODI ----*/ print "Polinomi sobre G25"; poli:= 1/alfa^4 - alfa^(-3) * x + alfa^5*x^2; poli; print "Factorització"; Factorization(poli); print "Arrels"; Roots(poli,G25); print "Comprovació amb Evaluate"; for i:=0 to 4 do for j:=0 to 4 do if(Evaluate(poli,G25![j,i]) eq 0) then G25![j,i]; end if; end for; end for; Output: Magma V2.10-6 Sun Mar 28 2004 12:31:00 on modular [Seed = 3336670528] ------------------------------------- apartat (vi) Polinomi sobre G25 alfa^5*x^2 + alfa^9*x + alfa^20 Factorització [ ] Arrels [] Comprovació amb Evaluate Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 12:31:16 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; PR5:=PolynomialRing(G25); /*(vii)*/ print "apartat (vi)"; /* CODI ----*/ print "Polinomi sobre G25"; poli:= 1/alfa^4 - alfa^(-3) * x + alfa^5*x^2; poli; print "Factorització"; Factorization(poli); print "Arrels"; Roots(poli,G25); print "Comprovació amb Evaluate"; for i:=0 to 4 do for j:=0 to 4 do if(Evaluate(poli,G25![j,i]) eq 0) then G25![j,i]; end if; end for; end for; llista; Output: Magma V2.10-6 Sun Mar 28 2004 12:31:13 on modular [Seed = 3488121980] ------------------------------------- apartat (vi) Polinomi sobre G25 alfa^5*x^2 + alfa^9*x + alfa^20 Factorització [ ] Arrels [] Comprovació amb Evaluate >> llista; ^ User error: Identifier 'llista' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Sun Mar 28 12:31:39 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; PR5:=PolynomialRing(G25); /*(vii)*/ print "apartat (vi)"; /* CODI ----*/ print "Polinomi sobre G25"; poli:= 1/alfa^4 - alfa^(-3) * x + alfa^5*x^2; poli; print "Factorització"; Factorization(poli); print "Arrels"; Roots(poli,G25); print "Comprovació amb Evaluate"; llista:=[]; for i:=0 to 4 do for j:=0 to 4 do if(Evaluate(poli,G25![j,i]) eq 0) then llista:=llista cat [G25![j,i]]; end if; end for; end for; llista; Output: Magma V2.10-6 Sun Mar 28 2004 12:31:36 on modular [Seed = 4107517790] ------------------------------------- apartat (vi) Polinomi sobre G25 alfa^5*x^2 + alfa^9*x + alfa^20 Factorització [ ] Arrels [] Comprovació amb Evaluate [] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 12:33:19 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; elements:=[A:A in G25]; primitius:=[A:A in elements | IsPrimitive(A) eq true]; primitius[2]; equ := (2*alpha^-3) - (alpha^5) + (alpha^6/(alpha+2)); equ; Output: Magma V2.10-6 Sun Mar 28 2004 12:33:16 on modular [Seed = 3804606188] ------------------------------------- G25.1^5 >> equ := (2*alpha^-3) - (alpha^5) + (alpha^6/(alpha+2)); ^ User error: Identifier 'alpha' has not been declared or assigned >> equ; ^ User error: Identifier 'equ' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 12:34:29 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; elements:=[A:A in G25]; primitius:=[A:A in elements | IsPrimitive(A) eq true]; alpha:=primitius[2]; equ := (2*alpha^-3) - (alpha^5) + (alpha^6/(alpha+2)); equ; Output: Magma V2.10-6 Sun Mar 28 2004 12:34:26 on modular [Seed = 3905922072] ------------------------------------- G25.1^16 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 12:37:26 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; elements:=[A:A in G25]; primitius:=[A:A in elements | IsPrimitive(A) eq true]; alpha:=primitius[2]; equ := (2*alpha^-3) - (alpha^5) + (alpha^6/(alpha+2)); equ; Isinvertible(equ); Output: Magma V2.10-6 Sun Mar 28 2004 12:37:23 on modular [Seed = 2596132763] ------------------------------------- G25.1^16 >> Isinvertible(equ); ^ User error: Identifier 'Isinvertible' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 12:38:03 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; elements:=[A:A in G25]; primitius:=[A:A in elements | IsPrimitive(A) eq true]; alpha:=primitius[2]; equ := (2*alpha^-3) - (alpha^5) + (alpha^6/(alpha+2)); equ; IsInvertible(equ); Output: Magma V2.10-6 Sun Mar 28 2004 12:38:00 on modular [Seed = 2208616105] ------------------------------------- G25.1^16 true G25.1^8 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 12:40:50 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; elements:=[A:A in G25]; primitius:=[A:A in elements | IsPrimitive(A) eq true]; alpha:=primitius[2]; equ := (2*alpha^-3) - (alpha^5) + (alpha^6/(alpha+2)); equ; IsInvertible(equ); invertibles:=[A : A in G25 | IsInvertible(A) eq true]; Output: Magma V2.10-6 Sun Mar 28 2004 12:40:47 on modular [Seed = 2979463164] ------------------------------------- G25.1^16 true G25.1^8 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 12:41:11 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; elements:=[A:A in G25]; primitius:=[A:A in elements | IsPrimitive(A) eq true]; alpha:=primitius[2]; equ := (2*alpha^-3) - (alpha^5) + (alpha^6/(alpha+2)); equ; IsInvertible(equ); invertibles:=[A : A in G25 | IsInvertible(A) eq true]; invertibles; Output: Magma V2.10-6 Sun Mar 28 2004 12:41:08 on modular [Seed = 3197759704] ------------------------------------- G25.1^16 true G25.1^8 [ 1, G25.1, G25.1^2, G25.1^3, G25.1^4, G25.1^5, 3, G25.1^7, G25.1^8, G25.1^9, G25.1^10, G25.1^11, 4, G25.1^13, G25.1^14, G25.1^15, G25.1^16, G25.1^17, 2, G25.1^19, G25.1^20, G25.1^21, G25.1^22, G25.1^23 ] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 12:50:07 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; elements:=[A:A in G25]; tupla:={[ : x in G25 ]; Output: Magma V2.10-6 Sun Mar 28 2004 12:50:04 on modular [Seed = 1450247753] ------------------------------------- >> tupla:={[ : x in G25 ]; ^ User error: bad syntax Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 12:50:28 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; elements:=[A:A in G25]; tupla:={[ : x in G25 ]}; Output: Magma V2.10-6 Sun Mar 28 2004 12:50:25 on modular [Seed = 1568279919] ------------------------------------- Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 12:50:47 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; elements:=[A:A in G25]; tupla:={[ : x in G25 ]}; tupla; Output: Magma V2.10-6 Sun Mar 28 2004 12:50:44 on modular [Seed = 1147343971] ------------------------------------- { [ <[ 1, 0 ], 1>, <[ 0, 1 ], G25.1>, <[ 2, 3 ], G25.1^2>, <[ 1, 1 ], G25.1^3>, <[ 2, 4 ], G25.1^4>, <[ 3, 4 ], G25.1^5>, <[ 3, 0 ], 3>, <[ 0, 3 ], G25.1^7>, <[ 1, 4 ], G25.1^8>, <[ 3, 3 ], G25.1^9>, <[ 1, 2 ], G25.1^10>, <[ 4, 2 ], G25.1^11>, <[ 4, 0 ], 4>, <[ 0, 4 ], G25.1^13>, <[ 3, 2 ], G25.1^14>, <[ 4, 4 ], G25.1^15>, <[ 3, 1 ], G25.1^16>, <[ 2, 1 ], G25.1^17>, <[ 2, 0 ], 2>, <[ 0, 2 ], G25.1^19>, <[ 4, 1 ], G25.1^20>, <[ 2, 2 ], G25.1^21>, <[ 4, 3 ], G25.1^22>, <[ 1, 3 ], G25.1^23>, <[ 0, 0 ], 0> ] } Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 12:54:12 2004 Input: Z2:=GF(2); p:=PolynomialRing(Z2); p:=1+x+x^4; G16:=ext; tupla:={[ : x in G16 ]}; Output: Magma V2.10-6 Sun Mar 28 2004 12:54:09 on modular [Seed = 1901469795] ------------------------------------- Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 12:54:22 2004 Input: Z2:=GF(2); p:=PolynomialRing(Z2); p:=1+x+x^4; G16:=ext; tupla:={[ : x in G16 ]}; tupla; Output: Magma V2.10-6 Sun Mar 28 2004 12:54:19 on modular [Seed = 2019502432] ------------------------------------- { [ <[ 1, 0, 0, 0 ], 1>, <[ 0, 1, 0, 0 ], G16.1>, <[ 0, 0, 1, 0 ], G16.1^2>, <[ 0, 0, 0, 1 ], G16.1^3>, <[ 1, 1, 0, 0 ], G16.1^4>, <[ 0, 1, 1, 0 ], G16.1^5>, <[ 0, 0, 1, 1 ], G16.1^6>, <[ 1, 1, 0, 1 ], G16.1^7>, <[ 1, 0, 1, 0 ], G16.1^8>, <[ 0, 1, 0, 1 ], G16.1^9>, <[ 1, 1, 1, 0 ], G16.1^10>, <[ 0, 1, 1, 1 ], G16.1^11>, <[ 1, 1, 1, 1 ], G16.1^12>, <[ 1, 0, 1, 1 ], G16.1^13>, <[ 1, 0, 0, 1 ], G16.1^14>, <[ 0, 0, 0, 0 ], 0> ] } Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 13:25:52 2004 Input: G4:=GF(4); elementsG4:=[A : A in G4]; elementsG4; Output: Magma V2.10-6 Sun Mar 28 2004 13:25:49 on modular [Seed = 772372176] ------------------------------------- [ 1, alpha, alpha^2, 0 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 13:26:51 2004 Input: G8:=GF(8); elementsG8:=[A : A in G8]; elementsG8; Output: Magma V2.10-6 Sun Mar 28 2004 13:26:48 on modular [Seed = 3572730991] ------------------------------------- [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, 0 ] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 13:27:43 2004 Input: G16:=GF(16); elementsG16:=[A : A in G16]; elementsG16; Output: Magma V2.10-6 Sun Mar 28 2004 13:27:40 on modular [Seed = 3286538892] ------------------------------------- [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, alpha^12, alpha^13, alpha^14, 0 ] Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 13:34:46 2004 Input: GF(4) subset GF(16); Output: Magma V2.10-6 Sun Mar 28 2004 13:34:43 on modular [Seed = 4040665696] ------------------------------------- true Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 13:39:36 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; P:=PolynomialRing(G25); Output: Magma V2.10-6 Sun Mar 28 2004 13:39:33 on modular [Seed = 3771186006] ------------------------------------- Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 13:40:21 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; P25:=PolynomialRing(G25); Isfinite(P25); Output: Magma V2.10-6 Sun Mar 28 2004 13:40:18 on modular [Seed = 2427964625] ------------------------------------- >> Isfinite(P25); ^ User error: Identifier 'Isfinite' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 13:40:47 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; P25:=PolynomialRing(G25); IsFinite(P25); Output: Magma V2.10-6 Sun Mar 28 2004 13:40:44 on modular [Seed = 2679686112] ------------------------------------- false Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 13:44:22 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; P25:=PolynomialRing(G25); elementsP25:=[A:A in P25]; elementsP25[2]; Output: Magma V2.10-6 Sun Mar 28 2004 13:44:19 on modular [Seed = 2225330644] ------------------------------------- >> elementsP25:=[A:A in P25]; ^ Runtime error in for: Iteration is not possible over this object >> elementsP25[2]; ^ User error: Identifier 'elementsP25' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 13:45:33 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; P25:=PolynomialRing(G25); elementsP25:=[A : A in G25]; elementsP25[2]; Output: Magma V2.10-6 Sun Mar 28 2004 13:45:30 on modular [Seed = 3079727790] ------------------------------------- G25.1 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 13:45:53 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; P25:=PolynomialRing(G25); elementsP25:=[A : A in G25]; elementsP25[3]; Output: Magma V2.10-6 Sun Mar 28 2004 13:45:50 on modular [Seed = 3197756339] ------------------------------------- G25.1^2 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 13:48:38 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; P25:=PolynomialRing(G25); alpha:=G25.1^2; beta:=2; p1 := alpha ^2 + alpha*x + beta* x^2; p1; Output: Magma V2.10-6 Sun Mar 28 2004 13:48:35 on modular [Seed = 2878141947] ------------------------------------- 2*x^2 + G25.1^2*x + G25.1^4 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 13:49:39 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; P25:=PolynomialRing(G25); alpha:=G25.1^2; beta:=2; p1 := alpha ^2 + alpha*x + beta* x^2; p1; p2 := 1 + alpha *x; p2; Output: Magma V2.10-6 Sun Mar 28 2004 13:49:36 on modular [Seed = 1433537345] ------------------------------------- 2*x^2 + G25.1^2*x + G25.1^4 G25.1^2*x + 1 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 13:50:29 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; P25:=PolynomialRing(G25); alpha:=G25.1^2; beta:=2; p1 := alpha ^2 + alpha*x + beta* x^2; p2 := 1 + alpha *x; p1+p2; Output: Magma V2.10-6 Sun Mar 28 2004 13:50:26 on modular [Seed = 1180768352] ------------------------------------- 2*x^2 + G25.1^20*x + G25.1^5 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host styx.uwa.edu.au. (130.95.128.51) Time: Sun Mar 28 13:51:14 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Sun Mar 28 2004 13:51:11 on modular [Seed = 1332220292] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 13:51:35 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; P25:=PolynomialRing(G25); alpha:=G25.1^2; beta:=2; p1 := alpha ^2 + alpha*x + beta* x^2; p2 := 1 + alpha *x; p1*p2; Output: Magma V2.10-6 Sun Mar 28 2004 13:51:32 on modular [Seed = 1884761744] ------------------------------------- G25.1^20*x^3 + G25.1^15*x^2 + G25.1^7*x + G25.1^4 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 13:52:49 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; P25:=PolynomialRing(G25); alpha:=G25.1^2; beta:=2; p1 := alpha ^2 + alpha*x + beta* x^2; p2 := 1 + alpha *x; Quotrem(p1,p2); Output: Magma V2.10-6 Sun Mar 28 2004 13:52:46 on modular [Seed = 2036213715] ------------------------------------- G25.1^16*x + G25.1^9 G25.1^20 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 13:54:51 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; P25:=PolynomialRing(G25); alpha:=G25.1^2; beta:=2; p1 := alpha ^2 + alpha*x + beta* x^2; p2 := 1 + alpha *x; Quotrem(p1,p2); p1 div p2; p1 mod p2; Output: Magma V2.10-6 Sun Mar 28 2004 13:54:48 on modular [Seed = 1816867649] ------------------------------------- G25.1^16*x + G25.1^9 G25.1^20 G25.1^16*x + G25.1^9 G25.1^20 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 13:55:49 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; P25:=PolynomialRing(G25); alpha:=G25.1^2; beta:=2; p1 := alpha ^2 + alpha*x + beta* x^2; p2 := 1 + alpha *x; GCD(p1,p2); Output: Magma V2.10-6 Sun Mar 28 2004 13:55:46 on modular [Seed = 288771831] ------------------------------------- 1 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 13:56:20 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; P25:=PolynomialRing(G25); alpha:=G25.1^2; beta:=2; p1 := alpha ^2 + alpha*x + beta* x^2; p2 := 1 + alpha *x; LCM(p1,p2); Output: Magma V2.10-6 Sun Mar 28 2004 13:56:17 on modular [Seed = 440223135] ------------------------------------- x^3 + G25.1^19*x^2 + G25.1^11*x + G25.1^8 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 13:57:40 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; P25:=PolynomialRing(G25); alpha:=G25.1^2; beta:=2; p1 := alpha ^2 + alpha*x + beta* x^2; p2 := 1 + alpha *x; XGCD(p1,p2); Output: Magma V2.10-6 Sun Mar 28 2004 13:57:37 on modular [Seed = 204172409] ------------------------------------- 1 G25.1^4 G25.1^8*x + G25.1 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 13:59:39 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; P25:=PolynomialRing(G25); alpha:=G25.1^2; beta:=2; p1 := alpha ^2 + alpha*x + beta* x^2; p2 := 1 + alpha *x; p3 := (1/alpha^4) - ((alpha^-3)*x) + ((alpha^5)*x^2); Factorization(p3); Output: Magma V2.10-6 Sun Mar 28 2004 13:59:36 on modular [Seed = 907106042] ------------------------------------- [ ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 14:00:29 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; P25:=PolynomialRing(G25); alpha:=G25.1^2; beta:=2; p1 := alpha ^2 + alpha*x + beta* x^2; p2 := 1 + alpha *x; p3 := (1/alpha^4) - ((alpha^-3)*x) + ((alpha^5)*x^2); Factorization(p3); Roots(p3,G25); Output: Magma V2.10-6 Sun Mar 28 2004 14:00:26 on modular [Seed = 654329785] ------------------------------------- [ ] [] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 14:00:40 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; P25:=PolynomialRing(G25); alpha:=G25.1^2; beta:=2; p1 := alpha ^2 + alpha*x + beta* x^2; p2 := 1 + alpha *x; p3 := (1/alpha^4) - ((alpha^-3)*x) + ((alpha^5)*x^2); Factorization(p3); Roots(p3); Output: Magma V2.10-6 Sun Mar 28 2004 14:00:37 on modular [Seed = 672090281] ------------------------------------- [ ] [] Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 14:00:52 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; P25:=PolynomialRing(G25); alpha:=G25.1^2; beta:=2; p1 := alpha ^2 + alpha*x + beta* x^2; p2 := 1 + alpha *x; p3 := (1/alpha^4) - ((alpha^-3)*x) + ((alpha^5)*x^2); Factorization(p3); Roots(p3,G25); Output: Magma V2.10-6 Sun Mar 28 2004 14:00:49 on modular [Seed = 3522605412] ------------------------------------- [ ] [] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 14:04:22 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; P25:=PolynomialRing(G25); alpha:=G25.1^2; beta:=2; p1 := alpha ^2 + alpha*x + beta* x^2; p2 := 1 + alpha *x; p3 := (1/alpha^4) - ((alpha^-3)*x) + ((alpha^5)*x^2); Factorization(p3); Roots(p3,G25); Generator(G25); Output: Magma V2.10-6 Sun Mar 28 2004 14:04:18 on modular [Seed = 4140930833] ------------------------------------- [ ] [] G25.1 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 14:04:50 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; P25:=PolynomialRing(G25); Generator(G25); beta:=2; p1 := alpha ^2 + alpha*x + beta* x^2; p2 := 1 + alpha *x; p3 := (1/alpha^4) - ((alpha^-3)*x) + ((alpha^5)*x^2); Factorization(p3); Roots(p3,G25); Output: Magma V2.10-6 Sun Mar 28 2004 14:04:47 on modular [Seed = 4292386404] ------------------------------------- G25.1 >> p1 := alpha ^2 + alpha*x + beta* x^2; ^ User error: Identifier 'alpha' has not been declared or assigned >> p2 := 1 + alpha *x; ^ User error: Identifier 'alpha' has not been declared or assigned >> p3 := (1/alpha^4) - ((alpha^-3)*x) + ((alpha^5)*x^2); ^ User error: Identifier 'alpha' has not been declared or assigned >> Factorization(p3); ^ User error: Identifier 'p3' has not been declared or assigned >> Roots(p3,G25); ^ User error: Identifier 'p3' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 14:05:08 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; P25:=PolynomialRing(G25); alpha:=Generator(G25); beta:=2; p1 := alpha ^2 + alpha*x + beta* x^2; p2 := 1 + alpha *x; p3 := (1/alpha^4) - ((alpha^-3)*x) + ((alpha^5)*x^2); Factorization(p3); Roots(p3,G25); Output: Magma V2.10-6 Sun Mar 28 2004 14:05:05 on modular [Seed = 3972762969] ------------------------------------- [ ] [] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 14:08:48 2004 Input: G5:=GF(5); Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; P25:=PolynomialRing(G25); alpha:=Generator(G25); beta:=Generator(G5); p1 := alpha ^2 + alpha*x + beta* x^2; p2 := 1 + alpha *x; Output: Magma V2.10-6 Sun Mar 28 2004 14:08:45 on modular [Seed = 2544956798] ------------------------------------- Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 14:10:19 2004 Input: G5:=GF(5); Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; P25:=PolynomialRing(G25); alpha:=Generator(G25); beta:=Generator(G5); alpaha; p1 := alpha ^2 + alpha*x + beta* x^2; p2 := 1 + alpha *x; Output: Magma V2.10-6 Sun Mar 28 2004 14:10:16 on modular [Seed = 2275468491] ------------------------------------- >> alpaha; ^ User error: Identifier 'alpaha' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 14:12:38 2004 Input: G5:=GF(5); Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; alpha:=Generator(G25); beta:=Generator(G5) p1 := alpha ^2 + alpha*x + beta* x^2; p1; Output: Magma V2.10-6 Sun Mar 28 2004 14:12:35 on modular [Seed = 2309941886] ------------------------------------- >> p1 := alpha ^2 + alpha*x + beta* x^2; ^ User error: bad syntax >> p1;; ^ User error: Identifier 'p1' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 14:13:00 2004 Input: G5:=GF(5); Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; alpha:=Generator(G25); beta:=Generator(G5); p1 := alpha ^2 + alpha*x + beta* x^2; p1; Output: Magma V2.10-6 Sun Mar 28 2004 14:12:57 on modular [Seed = 2996162911] ------------------------------------- >> p1 := alpha ^2 + alpha*x + beta* x^2; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt >> p1;; ^ User error: Identifier 'p1' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 14:14:03 2004 Input: G5:=GF(5); Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; alpha:=Generator(G25); p1 := alpha ^2 + alpha*x + beta* x^2; p1; Output: Magma V2.10-6 Sun Mar 28 2004 14:14:00 on modular [Seed = 2760099592] ------------------------------------- >> p1 := alpha ^2 + alpha*x + beta* x^2; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt >> p1;; ^ User error: Identifier 'p1' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 14:15:11 2004 Input: G5:=GF(5); Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; P25 := PolynomialRing(G25); alpha:=Generator(G25); p1 := alpha ^2 + alpha*x + beta* x^2; p1; Output: Magma V2.10-6 Sun Mar 28 2004 14:15:08 on modular [Seed = 2861420226] ------------------------------------- x^2 + G25.1*x + G25.1^2 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 14:15:46 2004 Input: G5:=GF(5); Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; P25 := PolynomialRing(G25); alpha:=Generator(G25); p1 := alpha ^2 + alpha*x + beta* x^2; p1; Output: Magma V2.10-6 Sun Mar 28 2004 14:15:43 on modular [Seed = 1383413336] ------------------------------------- x^2 + G25.1*x + G25.1^2 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 14:15:56 2004 Input: G5:=GF(5); Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; P25 := PolynomialRing(G25); alpha:=Generator(G25); p1 := alpha ^2 + alpha*x + beta* x^2; p1; Output: Magma V2.10-6 Sun Mar 28 2004 14:15:53 on modular [Seed = 1147347064] ------------------------------------- x^2 + G25.1*x + G25.1^2 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 14:18:42 2004 Input: G5:=GF(5); Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; P25 := PolynomialRing(G25); alpha:=Generator(G25); p1 := alpha ^2 + alpha*x + beta* x^2; p1; p2 := 1 + alpha *x; p2; Output: Magma V2.10-6 Sun Mar 28 2004 14:18:39 on modular [Seed = 1231957011] ------------------------------------- x^2 + G25.1*x + G25.1^2 G25.1*x + 1 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 14:19:18 2004 Input: G5:=GF(5); Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; P25 := PolynomialRing(G25); alpha:=Generator(G25); p1 := alpha ^2 + alpha*x + beta* x^2; p2 := 1 + alpha *x; p1+p2; p1*p2; Output: Magma V2.10-6 Sun Mar 28 2004 14:19:15 on modular [Seed = 1884755222] ------------------------------------- x^2 + G25.1^19*x + G25.1^9 G25.1*x^3 + G25.1^9*x^2 + G25.1^10*x + G25.1^2 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 14:19:59 2004 Input: G5:=GF(5); Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; P25 := PolynomialRing(G25); alpha:=Generator(G25); p1 := alpha ^2 + alpha*x + beta* x^2; p2 := 1 + alpha *x; Quotrem(p1,p2); p1 div p2; p1 mod p2; Output: Magma V2.10-6 Sun Mar 28 2004 14:19:56 on modular [Seed = 2052923251] ------------------------------------- G25.1^23*x + G25.1^21 G25.1 G25.1^23*x + G25.1^21 G25.1 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 14:20:27 2004 Input: G5:=GF(5); Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; P25 := PolynomialRing(G25); alpha:=Generator(G25); p1 := alpha ^2 + alpha*x + beta* x^2; p2 := 1 + alpha *x; GCD(p1,p2); Output: Magma V2.10-6 Sun Mar 28 2004 14:20:24 on modular [Seed = 1783435079] ------------------------------------- 1 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 14:20:46 2004 Input: G5:=GF(5); Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; P25 := PolynomialRing(G25); alpha:=Generator(G25); p1 := alpha ^2 + alpha*x + beta* x^2; p2 := 1 + alpha *x; LCM(p1,p2); Output: Magma V2.10-6 Sun Mar 28 2004 14:20:43 on modular [Seed = 490371268] ------------------------------------- x^3 + G25.1^8*x^2 + G25.1^9*x + G25.1 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 14:21:11 2004 Input: G5:=GF(5); Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; P25 := PolynomialRing(G25); alpha:=Generator(G25); p1 := alpha ^2 + alpha*x + beta* x^2; p2 := 1 + alpha *x; XGCD(p1,p2); Output: Magma V2.10-6 Sun Mar 28 2004 14:21:08 on modular [Seed = 69427700] ------------------------------------- 1 G25.1^23 G25.1^10*x + G25.1^8 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 14:22:10 2004 Input: G5:=GF(5); Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; P25 := PolynomialRing(G25); alpha:=Generator(G25); p3 := (1/alpha^4) - ((alpha^-3)*x) + ((alpha^5)*x^2); Factorization(p3); Output: Magma V2.10-6 Sun Mar 28 2004 14:22:07 on modular [Seed = 254306949] ------------------------------------- [ ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Sun Mar 28 14:22:39 2004 Input: G5:=GF(5); Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; P25 := PolynomialRing(G25); alpha:=Generator(G25); p3 := (1/alpha^4) - ((alpha^-3)*x) + ((alpha^5)*x^2); Roots(p3,G25); Output: Magma V2.10-6 Sun Mar 28 2004 14:22:36 on modular [Seed = 907105183] ------------------------------------- [] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 15:04:56 2004 Input: P5:= PolynomialRing (Integers(5)); G25

:= ext < GF(5) | P5![3,2,1] >; P25 := PolynomialRing (G25); [a : a in P25]; Output: Magma V2.10-6 Sun Mar 28 2004 15:04:53 on modular [Seed = 2662986030] ------------------------------------- >> [a : a in P25];; ^ Runtime error in for: Iteration is not possible over this object Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 15:05:20 2004 Input: P5:= PolynomialRing (Integers(5)); G25

:= ext < GF(5) | P5![3,2,1] >; P25 := PolynomialRing (G25); P25!1; Output: Magma V2.10-6 Sun Mar 28 2004 15:05:17 on modular [Seed = 2376786469] ------------------------------------- 1 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 15:05:31 2004 Input: P5:= PolynomialRing (Integers(5)); G25

:= ext < GF(5) | P5![3,2,1] >; P25 := PolynomialRing (G25); P25!10; Output: Magma V2.10-6 Sun Mar 28 2004 15:05:28 on modular [Seed = 3029583081] ------------------------------------- 0 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 15:05:46 2004 Input: P5:= PolynomialRing (Integers(5)); G25

:= ext < GF(5) | P5![3,2,1] >; P25 := PolynomialRing (G25); P25!5; Output: Magma V2.10-6 Sun Mar 28 2004 15:05:43 on modular [Seed = 3214462973] ------------------------------------- 0 Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 15:06:40 2004 Input: P5:= PolynomialRing (Integers(5)); G25

:= ext < GF(5) | P5![3,2,1] >; P25 := PolynomialRing (G25); P25!2; Output: Magma V2.10-6 Sun Mar 28 2004 15:06:37 on modular [Seed = 2709967289] ------------------------------------- 2 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 15:06:49 2004 Input: P5:= PolynomialRing (Integers(5)); G25

:= ext < GF(5) | P5![3,2,1] >; P25 := PolynomialRing (G25); P25!3; Output: Magma V2.10-6 Sun Mar 28 2004 15:06:46 on modular [Seed = 2827999403] ------------------------------------- 3 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 15:07:04 2004 Input: P5:= PolynomialRing (Integers(5)); G25

:= ext < GF(5) | P5![3,2,1] >; P25 := PolynomialRing (G25); P25!8; Output: Magma V2.10-6 Sun Mar 28 2004 15:07:01 on modular [Seed = 1349984355] ------------------------------------- 3 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 15:07:11 2004 Input: P5:= PolynomialRing (Integers(5)); G25

:= ext < GF(5) | P5![3,2,1] >; P25 := PolynomialRing (G25); P25!9; Output: Magma V2.10-6 Sun Mar 28 2004 15:07:08 on modular [Seed = 1501440355] ------------------------------------- 4 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 15:07:36 2004 Input: P5:= PolynomialRing (Integers(5)); G25

:= ext < GF(5) | P5![3,2,1] >; P25 := PolynomialRing (G25); #P25; Output: Magma V2.10-6 Sun Mar 28 2004 15:07:33 on modular [Seed = 1315520157] ------------------------------------- >> #P25; ^ Runtime error in '#': Cardinality is infinite or not feasibly computable Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 15:13:03 2004 Input: P5:= PolynomialRing (Integers(5)); G25

:= ext < GF(5) | P5![3,2,1] >; Seq := [a : a in G25 | a ne 0 and Order(a) eq 24]; alpha := Seq[6]; sol := MinimalPolynomial(alpha); CoefficientRing(sol); Output: Magma V2.10-6 Sun Mar 28 2004 15:12:59 on modular [Seed = 2103053543] ------------------------------------- Finite field of size 5 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 15:15:08 2004 Input: P5:= PolynomialRing (Integers(5)); G25

:= ext < GF(5) | P5![3,2,1] >; alpha := PrimitiveElement(G25); alpha; Output: Magma V2.10-6 Sun Mar 28 2004 15:15:05 on modular [Seed = 1866997104] ------------------------------------- p Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 15:17:37 2004 Input: P5:= PolynomialRing (Integers(5)); G25

:= ext < GF(5) | P5![3,2,1] >; G5 := GF(5); alpha := PrimitiveElement(G25); beta := PrimitiveElement(G5); p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; Output: Magma V2.10-6 Sun Mar 28 2004 15:17:34 on modular [Seed = 322199963] ------------------------------------- >> p1 := alpha^2 + alpha*x + beta*x^2; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt >> p2 := 1 + alpha*x; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 15:18:04 2004 Input: P5:= PolynomialRing (Integers(5)); G25

:= ext < GF(5) | P5![3,2,1] >; G5 := GF(5); alpha := PrimitiveElement(G25); beta := PrimitiveElement(G5); p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; Output: Magma V2.10-6 Sun Mar 28 2004 15:18:01 on modular [Seed = 406809271] ------------------------------------- >> p1 := alpha^2 + alpha*x + beta*x^2; ^ User error: Identifier 'x' has not been declared or assigned >> p2 := 1 + alpha*x; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 15:18:31 2004 Input: P5:= PolynomialRing (Integers(5)); G25

:= ext < GF(5) | P5![3,2,1] >; G5 := GF(5); alpha := PrimitiveElement(G25); beta := PrimitiveElement(G5); p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; Output: Magma V2.10-6 Sun Mar 28 2004 15:18:28 on modular [Seed = 237600076] ------------------------------------- >> p1 := alpha^2 + alpha*x + beta*x^2; ^ User error: Identifier 'x' has not been declared or assigned >> p2 := 1 + alpha*x; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 15:21:15 2004 Input: P5:= PolynomialRing (Integers(5)); G25

:= ext < GF(5) | P5![3,2,1] >; G5 := GF(5); P := PolynomialRing (Integers()); alpha := PrimitiveElement(G25); beta := PrimitiveElement(G5); p1 := P![alpha^2,alpha,beta*x^2); p2 := P![1,alpha]; p1; p2; Output: Magma V2.10-6 Sun Mar 28 2004 15:21:12 on modular [Seed = 1058557137] ------------------------------------- >> p1 := P![alpha^2,alpha,beta*x^2); ^ User error: bad syntax >> p2 := P![1,alpha]; ^ Runtime error in '!': Can't coerce sequence element 1 into the coefficient ring >> p1; ^ User error: Identifier 'p1' has not been declared or assigned >> p2; ^ User error: Identifier 'p2' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 15:22:39 2004 Input: P5:= PolynomialRing (Integers(5)); G25

:= ext < GF(5) | P5![3,2,1] >; G5 := GF(5); P := PolynomialRing (Integers()); alpha := PrimitiveElement(G25); beta := PrimitiveElement(G5); p1 := P![alpha^2,alpha,beta); p2 := P![1,alpha]; p1; p2; Output: Magma V2.10-6 Sun Mar 28 2004 15:22:36 on modular [Seed = 3740904068] ------------------------------------- >> p1 := P![alpha^2,alpha,beta); ^ User error: bad syntax >> p2 := P![1,alpha]; ^ Runtime error in '!': Can't coerce sequence element 1 into the coefficient ring >> p1; ^ User error: Identifier 'p1' has not been declared or assigned >> p2; ^ User error: Identifier 'p2' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 15:22:51 2004 Input: P5:= PolynomialRing (Integers(5)); G25

:= ext < GF(5) | P5![3,2,1] >; G5 := GF(5); P := PolynomialRing (Integers()); alpha := PrimitiveElement(G25); beta := PrimitiveElement(G5); p1 := P![alpha^2,alpha,beta]; p2 := P![1,alpha]; p1; p2; Output: Magma V2.10-6 Sun Mar 28 2004 15:22:48 on modular [Seed = 3353392009] ------------------------------------- >> p1 := P![alpha^2,alpha,beta]; ^ Runtime error in '!': Can't coerce sequence element 1 into the coefficient ring >> p2 := P![1,alpha]; ^ Runtime error in '!': Can't coerce sequence element 1 into the coefficient ring >> p1; ^ User error: Identifier 'p1' has not been declared or assigned >> p2; ^ User error: Identifier 'p2' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 15:23:17 2004 Input: P5:= PolynomialRing (Integers(5)); G25

:= ext < GF(5) | P5![3,2,1] >; G5 := GF(5); P := PolynomialRing (); alpha := PrimitiveElement(G25); beta := PrimitiveElement(G5); p1 := P![alpha^2,alpha,beta]; p2 := P![1,alpha]; p1; p2; Output: Magma V2.10-6 Sun Mar 28 2004 15:23:14 on modular [Seed = 3438000296] ------------------------------------- >> P := PolynomialRing (); ^ Runtime error in 'PolynomialRing': Bad argument types Argument types given: >> p1 := P![alpha^2,alpha,beta]; ^ User error: Identifier 'P' has not been declared or assigned >> p2 := P![1,alpha]; ^ User error: Identifier 'P' has not been declared or assigned >> p1; ^ User error: Identifier 'p1' has not been declared or assigned >> p2; ^ User error: Identifier 'p2' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 15:24:45 2004 Input: P5:= PolynomialRing (Integers(5)); G25

:= ext < GF(5) | P5![3,2,1] >; G5 := GF(5); P := PolynomialRing (G25); alpha := PrimitiveElement(G25); beta := PrimitiveElement(G5); p1 := P![alpha^2,alpha,beta]; p2 := P![1,alpha]; p1; p2; Output: Magma V2.10-6 Sun Mar 28 2004 15:24:42 on modular [Seed = 4074079790] ------------------------------------- 2*x^2 + p*x + p^2 p*x + 1 Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 15:25:59 2004 Input: P5:= PolynomialRing (Integers(5)); G25

:= ext < GF(5) | P5![3,2,1] >; G5 := GF(5); P := PolynomialRing (G25); alpha := PrimitiveElement(G25); beta := PrimitiveElement(G5); beta; p1 := P![alpha^2,alpha,beta]; p2 := P![1,alpha]; p1; p2; Output: Magma V2.10-6 Sun Mar 28 2004 15:25:56 on modular [Seed = 3838021734] ------------------------------------- 2 2*x^2 + p*x + p^2 p*x + 1 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 15:27:38 2004 Input: P5:= PolynomialRing (Integers(5)); G25

:= ext < GF(5) | P5![3,2,1] >; G5 := GF(5); P := PolynomialRing (G25); alpha := PrimitiveElement(G25); beta := PrimitiveElement(G5); alpha; beta; p1 := P![alpha^2,alpha,beta]; p2 := P![1,alpha]; p1; p2; Output: Magma V2.10-6 Sun Mar 28 2004 15:27:35 on modular [Seed = 3989477516] ------------------------------------- p 2 2*x^2 + p*x + p^2 p*x + 1 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 15:28:54 2004 Input: P5:= PolynomialRing (Integers(5)); G25

:= ext < GF(5) | P5![3,2,1] >; G5 := GF(5); P := PolynomialRing (G25); alpha := PrimitiveElement(G25); beta := PrimitiveElement(G5); p1 := P![alpha^2,alpha,beta]; p2 := P![1,alpha]; p1+p2; p1*p2; Output: Magma V2.10-6 Sun Mar 28 2004 15:28:51 on modular [Seed = 2427970885] ------------------------------------- 2*x^2 + p^19*x + p^9 p^19*x^3 + p^22*x^2 + p^10*x + p^2 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 15:30:22 2004 Input: P5:= PolynomialRing (Integers(5)); G25

:= ext < GF(5) | P5![3,2,1] >; G5 := GF(5); P := PolynomialRing (G25); alpha := PrimitiveElement(G25); beta := PrimitiveElement(G5); p1 := P![alpha^2,alpha,beta]; p2 := P![1,alpha]; p1 div p2; p1 mod p2; Output: Magma V2.10-6 Sun Mar 28 2004 15:30:19 on modular [Seed = 2158490893] ------------------------------------- p^17*x + p^5 p^15 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Sun Mar 28 15:34:18 2004 Input: P5:= PolynomialRing (Integers(5)); G25

:= ext < GF(5) | P5![3,2,1] >; G5 := GF(5); P := PolynomialRing (G25); alpha := PrimitiveElement(G25); beta := PrimitiveElement(G5); p1 := P![alpha^2,alpha,beta]; p2 := P![1,alpha]; GCD(p1,p2); LCM(p1,p2); Output: Magma V2.10-6 Sun Mar 28 2004 15:34:15 on modular [Seed = 3029582373] ------------------------------------- 1 x^3 + p^3*x^2 + p^15*x + p^7 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Mon Mar 29 00:41:05 2004 Input: K := GF(2); R := PolynomialRing(K, [7, 6, 4, 1016, 1008, 992, 960, 896, 768, 512]); R; P := [a, b, c, d, e, f, g , x*(a- b*z^2 -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2)), y*(a- b*z^(2) -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2)) + x^2 *(b- c*z^(2^2) -d*y^(2^3) +d*z^(2^3 +2^2) -e*x^(2^4) +e*z^(2^4)*y^(2^3) -e*z^(2^4 +2^3 +2^2)), z*(a- b*z^(2) -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2)) + y^2 *(b- c*z^(2^2) -d*y^(2^3) +d*z^(2^3 +2^2) -e*x^(2^4) +e*z^(2^4)*y^(2^3) -e*z^(2^4 +2^3 +2^2)) + x^(2^2) *(c- d*z^(2^3) -e*y^(2^4) +e*z^(2^4 +2^3) -f*x^(2^5) +f*z^(2^5)*y^(2^4) -f*z^(2^5 +2^4 +2^3)) ] ; P; [IsHomogeneous(f): f in P]; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S; Output: Magma V2.10-6 Mon Mar 29 2004 00:41:02 on modular [Seed = 941608589] ------------------------------------- Graded Polynomial ring of rank 10 over GF(2) Lexicographical Order Variables: x, y, z, a, b, c, d, e, f, g Variable weights: 7 6 4 1016 1008 992 960 896 768 512 [ a, b, c, d, e, f, g, x^9*d + x*y^4*z^8*d + x*y^4*c + x*z^14*d + x*z^6*c + x*z^2*b + x*a, x^18*e + x^8*y*d + x^2*y^8*z^16*e + x^2*y^8*d + x^2*z^28*e + x^2*z^12*d + x^2*z^4*c + x^2*b + y^5*z^8*d + y^5*c + y*z^14*d + y*z^6*c + y*z^2*b + y*a, x^36*f + x^16*y^2*e + x^8*z*d + x^4*y^16*z^32*f + x^4*y^16*e + x^4*z^56*f + x^4*z^24*e + x^4*z^8*d + x^4*c + y^10*z^16*e + y^10*d + y^4*z^9*d + y^4*z*c + y^2*z^28*e + y^2*z^12*d + y^2*z^4*c + y^2*b + z^15*d + z^7*c + z^3*b + z*a ] [ true, true, true, true, true, true, true, true, true, true ] 3 [ 1, 2, 3 ] >> V,phi:=VectorSpace(quo); ^ Runtime error in 'VectorSpace': Quotient does not have finite dimension >> S:=[R!(v@@phi ): v in Basis(V)]; ^ User error: Identifier 'V' has not been declared or assigned >> S;; ^ User error: Identifier 'S' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 1.92MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Mon Mar 29 01:00:22 2004 Input: K := GF(2); R := PolynomialRing(K, [4, 6, 7, 248, 240, 224, 192, 128]); R; P := [w, u, v, e, o, z(w-u*x^2+u*x^6-v*y^4-e*x^14-e*z^8+e*x^8*y^4+e*x^2*y^8+o*x^30-o*y^16*x^6+o*z^8*x^16+o*y^20+o*z^16*x^2-x^62+y^32*x^14-x^2*y^40-o*y^4*x^24-z^32*x^6+z^32*y^4-z^16*x^34+y^32*z^8+y^16*x^38-y^20*x^32-y^36*x^8-z^8*x^48-y^20*x^32+y^4*x^56+y^8*x^50-o*y^8*x^18), z^2*(u-v*x^4+e*x^12-e*y^8-o*x^28-o*z^16+o*y^16*x^4+o*y^8*x^16+x^60-y^32*x^12+y^40+z^32*x^4+x^32*z^16-y^16*x^36-y^8*x^48)+y*(w-u*x^2+u*x^6-v*y^4-e*x^14-e*z^8+e*x^8*y^4+e*x^2*y^8+o*x^30-o*y^16*x^6+o*z^8*x^16+o*y^20+o*z^16*x^2-x^62+y^32*x^14-x^2*y^40-o*y^4*x^24-z^32*x^6+z^32*y^4-z^16*x^34+y^32*z^8+y^16*x^38-y^20*x^32-y^36*x^8-z^8*x^48-y^20*x^32+y^4*x^56+y^8*x^50-o*y^8*x^18), z^4*(v-e*x^8+o*x^24-o*y^16-z^32+y^32*x^8-x^56+y^16*x^32)+y^2*(u-v*x^4+e*x^12-e*y^8-o*x^28-o*z^16+o*y^16*x^4+o*y^8*x^16+x^60-y^32*x^12+y^40+z^32*x^4+x^32*z^16-y^16*x^36-y^8*x^48)+x*(w-u*x^2+u*x^6-v*y^4-e*x^14-e*z^8+e*x^8*y^4+e*x^2*y^8+o*x^30-o*y^16*x^6+o*z^8*x^16+o*y^20+o*z^16*x^2-x^62+y^32*x^14-x^2*y^40-o*y^4*x^24-z^32*x^6+z^32*y^4-z^16*x^34+y^32*z^8+y^16*x^38-y^20*x^32-y^36*x^8-z^8*x^48-y^20*x^32+y^4*x^56+y^8*x^50-o*y^8*x^18) ]; P; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S; Output: Magma V2.10-6 Mon Mar 29 2004 01:00:19 on modular [Seed = 3606130174] ------------------------------------- Graded Polynomial ring of rank 8 over GF(2) Lexicographical Order Variables: x, y, z, w, u, v, e, o Variable weights: 4 6 7 248 240 224 192 128 >> P := [w, u, v, e, o, z(w-u*x^2+u*x^6-v*y^4-e*x^14-e*z^8+e*x^8*y^4+e*x^2*y^8 ^ Runtime error: Bad argument types Argument types given: RngMPolElt, RngMPolElt >> P; ^ User error: Identifier 'P' has not been declared or assigned >> I:=ideal; ^ User error: Identifier 'P' has not been declared or assigned >> Dimension(I); ^ User error: Identifier 'I' has not been declared or assigned >> V,phi:=VectorSpace(quo); ^ User error: Identifier 'I' has not been declared or assigned >> S:=[R!(v@@phi ): v in Basis(V)]; ^ User error: Identifier 'V' has not been declared or assigned >> S;; ^ User error: Identifier 'S' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Mon Mar 29 02:49:17 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > Output: Magma V2.10-6 Mon Mar 29 2004 02:49:14 on modular [Seed = 1833630154] ------------------------------------- [ a1^2 - 2*a1*a2^2*x2 - 4*a1*a2 + 2*a2^3*x2 + 3*a2^2, a1*x1^2 - a1*x2^2 + 2*x1 - 2*x2, 2*a1*x1 - 2*a1*x2 - 2*a2*x1 + 2*a2*x2, a2^2*x2^2 + 2*a2*x2 + 1, a2*x1^2 - a2*x2^2 + 2*x1 - 2*x2, 2*a2*x1*x2^2 - 2*a2*x2^3 - x1^2 + 4*x1*x2 - 3*x2^2, x1^3 - 3*x1^2*x2 + 3*x1*x2^2 - x2^3 ] Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Mon Mar 29 02:50:11 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (1+a1*x1)(1+a1*x2)(1+a2*x1)(1+a2*x2) in I; Output: Magma V2.10-6 Mon Mar 29 2004 02:50:08 on modular [Seed = 473663857] ------------------------------------- [ a1^2 - 2*a1*a2^2*x2 - 4*a1*a2 + 2*a2^3*x2 + 3*a2^2, a1*x1^2 - a1*x2^2 + 2*x1 - 2*x2, 2*a1*x1 - 2*a1*x2 - 2*a2*x1 + 2*a2*x2, a2^2*x2^2 + 2*a2*x2 + 1, a2*x1^2 - a2*x2^2 + 2*x1 - 2*x2, 2*a2*x1*x2^2 - 2*a2*x2^3 - x1^2 + 4*x1*x2 - 3*x2^2, x1^3 - 3*x1^2*x2 + 3*x1*x2^2 - x2^3 ] >> (1+a1*x1)(1+a1*x2)(1+a2*x1)(1+a2*x2) in I; ^ Runtime error: Bad argument types Argument types given: RngMPolElt, RngMPolElt Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Mon Mar 29 02:50:29 2004 Input: > P := PolynomialRing(IntegerRing(), 4); > I := ideal; > GroebnerBasis(I); > (1+a1*x1)*(1+a1*x2)*(1+a2*x1)*(1+a2*x2) in I; Output: Magma V2.10-6 Mon Mar 29 2004 02:50:26 on modular [Seed = 389054984] ------------------------------------- [ a1^2 - 2*a1*a2^2*x2 - 4*a1*a2 + 2*a2^3*x2 + 3*a2^2, a1*x1^2 - a1*x2^2 + 2*x1 - 2*x2, 2*a1*x1 - 2*a1*x2 - 2*a2*x1 + 2*a2*x2, a2^2*x2^2 + 2*a2*x2 + 1, a2*x1^2 - a2*x2^2 + 2*x1 - 2*x2, 2*a2*x1*x2^2 - 2*a2*x2^3 - x1^2 + 4*x1*x2 - 3*x2^2, x1^3 - 3*x1^2*x2 + 3*x1*x2^2 - x2^3 ] true Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Mon Mar 29 04:15:03 2004 Input: K := GF(2); R := PolynomialRing(K, [7, 6, 4, 1016, 1008, 992, 960, 896, 768, 512]); R; P := [a, b, c, d, e, f, g , x*(a- b*z^2 -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2)), y*(a- b*z^(2) -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2)) + x^2 *(b- c*z^(2^2) -d*y^(2^3) +d*z^(2^3 +2^2) -e*x^(2^4) +e*z^(2^4)*y^(2^3) -e*z^(2^4 +2^3 +2^2)), z*(a- b*z^(2) -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2)) + y^2 *(b- c*z^(2^2) -d*y^(2^3) +d*z^(2^3 +2^2) -e*x^(2^4) +e*z^(2^4)*y^(2^3) -e*z^(2^4 +2^3 +2^2)) + x^(2^2) *(c- d*z^(2^3) -e*y^(2^4) +e*z^(2^4 +2^3) -f*x^(2^5) +f*z^(2^5)*y^(2^4) -f*z^(2^5 +2^4 +2^3)), y*(a- b*z^(2) -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2) +e*(x^(2^4)*z^2 +y^(2^4)*y^(2^2) -y^(2^4)*z^(2^2 +2) +z^(2^4 + 2^3 + 2^2 +2) ) + f*(x^(2^5)*y^(2^2) - x^(2^5)*z^(2^2 +2) - y^(2^5 +2^3)*z^(2) + y^(2^5)*z^( 2^3 + 2^2 +2) -z^(2^5 +2^4 + 2^3 + 2^2 +2) ) + g*(x^(2^6 +2^3) -x^(2^6)*y^(2^3)*z^2 + x^(2^6)*z^(2^3 +2^2 +2) -y^(2^6 + 2^4 + 2^2 ) + y^(2^6 +2^4)*z^(2^2 +2) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2) ) - z^2 *(x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^4 +2^3 +2^2) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^3 +2^2) - y^(2^7)*z^(2^5 + 2^4 +2^3 + 2^2 ) +z^(2^7 +2^6 +2^5 +2^4 + 2^3 + 2^2 ) )- x^(2^7)*y^(2^2 +2^4) ) ) + x^2 *(b- c*z^(2^2) -d*y^(2^3) +d*z^(2^3 +2^2) -e*x^(2^4) +e*z^(2^4)*y^(2^3) -e*z^(2^4 +2^3 +2^2) + f*( x^(2^5)*z^(2^2) +y^(2^5)*y^(2^3) -y^(2^5)*z^(2^2 +2^3) +z^(2^4 + 2^3 + 2^2 +2^5)) + g*( x^(2^6)*y^(2^3) - x^(2^6)*z^(2^2 +2^3) - y^(2^6 +2^4)*z^(2^2) + y^(2^6)*z^( 2^3 + 2^2 +2^4) -z^(2^5 +2^4 + 2^3 + 2^2 +2^6))+ x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^3 +2^2 +2^4) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^2 +2^3) - y^(2^7)*z^( 2^4 +2^3 + 2^2 +2^5) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2^7) ), z*(a- b*z^(2) -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2) +e*(x^(2^4)*z^2 +y^(2^4)*y^(2^2) -y^(2^4)*z^(2^2 +2) +z^(2^4 + 2^3 + 2^2 +2) ) + f*(x^(2^5)*y^(2^2) - x^(2^5)*z^(2^2 +2) - y^(2^5 +2^3)*z^(2) + y^(2^5)*z^( 2^3 + 2^2 +2) -z^(2^5 +2^4 + 2^3 + 2^2 +2) ) + g*(x^(2^6 +2^3) -x^(2^6)*y^(2^3)*z^2 + x^(2^6)*z^(2^3 +2^2 +2) -y^(2^6 + 2^4 + 2^2 ) + y^(2^6 +2^4)*z^(2^2 +2) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2) ) - z^2 *(x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^4 +2^3 +2^2) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^3 +2^2) - y^(2^7)*z^(2^5 + 2^4 +2^3 + 2^2 ) +z^(2^7 +2^6 +2^5 +2^4 + 2^3 + 2^2 ) )- x^(2^7)*y^(2^2 +2^4) ) ) + y^2 *(b- c*z^(2^2) -d*y^(2^3) +d*z^(2^3 +2^2) -e*x^(2^4) +e*z^(2^4)*y^(2^3) -e*z^(2^4 +2^3 +2^2) + f*( x^(2^5)*z^(2^2) +y^(2^5)*y^(2^3) -y^(2^5)*z^(2^2 +2^3) +z^(2^4 + 2^3 + 2^2 +2^5)) + g*( x^(2^6)*y^(2^3) - x^(2^6)*z^(2^2 +2^3) - y^(2^6 +2^4)*z^(2^2) + y^(2^6)*z^( 2^3 + 2^2 +2^4) -z^(2^5 +2^4 + 2^3 + 2^2 +2^6))+ x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^3 +2^2 +2^4) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^2 +2^3) - y^(2^7)*z^( 2^4 +2^3 + 2^2 +2^5) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2^7) ) + x^(2^2) *(c- d*z^(2^3) -e*y^(2^4) +e*z^(2^4 +2^3) -f*x^(2^5) +f*z^(2^5)*y^(2^4) -f*z^(2^5 +2^4 +2^3) + f*(y^(2^5)*z^(2^3) -x^(2^5) -z^(2^3 +2^4 +2^5) ) +g*(x^(2^6)*z^(2^3) +y^(2^6)*y^(2^4) -y^(2^6)*z^(2^4 +2^3) +z^(2^4 + 2^3 + 2^6 +2^5) ) + x^(2^7)*y^(2^4) - x^(2^7)*z^(2^4 +2^3) - y^(2^7 +2^5)*z^(2^3) + y^(2^7)*z^( 2^3 + 2^5 +2^4) -z^(2^5 +2^4 + 2^3 + 2^7 +2^6)) ] ; P; [IsHomogeneous(f): f in P]; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S; Output: Magma V2.10-6 Mon Mar 29 2004 04:15:00 on modular [Seed = 1665452567] ------------------------------------- Graded Polynomial ring of rank 10 over GF(2) Lexicographical Order Variables: x, y, z, a, b, c, d, e, f, g Variable weights: 7 6 4 1016 1008 992 960 896 768 512 >> x^(2^7)*y^(2^2 +2^4) ) ) + ^ User error: bad syntax >> x^(2^7)*y^(2^2 +2^4) ) ) + ^ User error: bad syntax >> ] ; ^ User error: bad syntax >> P; ^ User error: Identifier 'P' has not been declared or assigned >> [IsHomogeneous(f): f in P]; ^ User error: Identifier 'P' has not been declared or assigned >> I:=ideal; ^ User error: Identifier 'P' has not been declared or assigned >> Dimension(I); ^ User error: Identifier 'I' has not been declared or assigned >> V,phi:=VectorSpace(quo); ^ User error: Identifier 'I' has not been declared or assigned >> S:=[R!(v@@phi ): v in Basis(V)]; ^ User error: Identifier 'V' has not been declared or assigned >> S; ^ User error: Identifier 'S' has not been declared or assigned Total time: 3.059 seconds, Total memory usage: 1.91MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Mon Mar 29 04:19:32 2004 Input: K := GF(2); R := PolynomialRing(K, [7, 6, 4, 1016, 1008, 992, 960, 896, 768, 512]); R; P := [a, b, c, d, e, f, g , x*(a- b*z^2 -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2)), y*(a- b*z^(2) -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2)) + x^2 *(b- c*z^(2^2) -d*y^(2^3) +d*z^(2^3 +2^2) -e*x^(2^4) +e*z^(2^4)*y^(2^3) -e*z^(2^4 +2^3 +2^2)), z*(a- b*z^(2) -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2)) + y^2 *(b- c*z^(2^2) -d*y^(2^3) +d*z^(2^3 +2^2) -e*x^(2^4) +e*z^(2^4)*y^(2^3) -e*z^(2^4 +2^3 +2^2)) + x^(2^2) *(c- d*z^(2^3) -e*y^(2^4) +e*z^(2^4 +2^3) -f*x^(2^5) +f*z^(2^5)*y^(2^4) -f*z^(2^5 +2^4 +2^3)), y*(a- b*z^(2) -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2) +e*(x^(2^4)*z^2 +y^(2^4)*y^(2^2) -y^(2^4)*z^(2^2 +2) +z^(2^4 + 2^3 + 2^2 +2) ) + f*(x^(2^5)*y^(2^2) - x^(2^5)*z^(2^2 +2) - y^(2^5 +2^3)*z^(2) + y^(2^5)*z^( 2^3 + 2^2 +2) -z^(2^5 +2^4 + 2^3 + 2^2 +2) ) + g*(x^(2^6 +2^3) -x^(2^6)*y^(2^3)*z^2 + x^(2^6)*z^(2^3 +2^2 +2) -y^(2^6 + 2^4 + 2^2 ) + y^(2^6 +2^4)*z^(2^2 +2) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2) ) - z^2 *(x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^4 +2^3 +2^2) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^3 +2^2) - y^(2^7)*z^(2^5 + 2^4 +2^3 + 2^2 ) +z^(2^7 +2^6 +2^5 +2^4 + 2^3 + 2^2 ) )- x^(2^7)*y^(2^2 +2^4) ) + x^2 *(b- c*z^(2^2) -d*y^(2^3) +d*z^(2^3 +2^2) -e*x^(2^4) +e*z^(2^4)*y^(2^3) -e*z^(2^4 +2^3 +2^2) + f*( x^(2^5)*z^(2^2) +y^(2^5)*y^(2^3) -y^(2^5)*z^(2^2 +2^3) +z^(2^4 + 2^3 + 2^2 +2^5)) + g*( x^(2^6)*y^(2^3) - x^(2^6)*z^(2^2 +2^3) - y^(2^6 +2^4)*z^(2^2) + y^(2^6)*z^( 2^3 + 2^2 +2^4) -z^(2^5 +2^4 + 2^3 + 2^2 +2^6))+ x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^3 +2^2 +2^4) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^2 +2^3) - y^(2^7)*z^( 2^4 +2^3 + 2^2 +2^5) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2^7) ), z*(a- b*z^(2) -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2) +e*(x^(2^4)*z^2 +y^(2^4)*y^(2^2) -y^(2^4)*z^(2^2 +2) +z^(2^4 + 2^3 + 2^2 +2) ) + f*(x^(2^5)*y^(2^2) - x^(2^5)*z^(2^2 +2) - y^(2^5 +2^3)*z^(2) + y^(2^5)*z^( 2^3 + 2^2 +2) -z^(2^5 +2^4 + 2^3 + 2^2 +2) ) + g*(x^(2^6 +2^3) -x^(2^6)*y^(2^3)*z^2 + x^(2^6)*z^(2^3 +2^2 +2) -y^(2^6 + 2^4 + 2^2 ) + y^(2^6 +2^4)*z^(2^2 +2) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2) ) - z^2 *(x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^4 +2^3 +2^2) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^3 +2^2) - y^(2^7)*z^(2^5 + 2^4 +2^3 + 2^2 ) +z^(2^7 +2^6 +2^5 +2^4 + 2^3 + 2^2 ) )- x^(2^7)*y^(2^2 +2^4) ) + y^2 *(b- c*z^(2^2) -d*y^(2^3) +d*z^(2^3 +2^2) -e*x^(2^4) +e*z^(2^4)*y^(2^3) -e*z^(2^4 +2^3 +2^2) + f*( x^(2^5)*z^(2^2) +y^(2^5)*y^(2^3) -y^(2^5)*z^(2^2 +2^3) +z^(2^4 + 2^3 + 2^2 +2^5)) + g*( x^(2^6)*y^(2^3) - x^(2^6)*z^(2^2 +2^3) - y^(2^6 +2^4)*z^(2^2) + y^(2^6)*z^( 2^3 + 2^2 +2^4) -z^(2^5 +2^4 + 2^3 + 2^2 +2^6))+ x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^3 +2^2 +2^4) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^2 +2^3) - y^(2^7)*z^( 2^4 +2^3 + 2^2 +2^5) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2^7) ) + x^(2^2) *(c- d*z^(2^3) -e*y^(2^4) +e*z^(2^4 +2^3) -f*x^(2^5) +f*z^(2^5)*y^(2^4) -f*z^(2^5 +2^4 +2^3) + f*(y^(2^5)*z^(2^3) -x^(2^5) -z^(2^3 +2^4 +2^5) ) +g*(x^(2^6)*z^(2^3) +y^(2^6)*y^(2^4) -y^(2^6)*z^(2^4 +2^3) +z^(2^4 + 2^3 + 2^6 +2^5) ) + x^(2^7)*y^(2^4) - x^(2^7)*z^(2^4 +2^3) - y^(2^7 +2^5)*z^(2^3) + y^(2^7)*z^( 2^3 + 2^5 +2^4) -z^(2^5 +2^4 + 2^3 + 2^7 +2^6)) ] ; P; [IsHomogeneous(f): f in P]; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Mar 29 2004 04:19:09 on modular [Seed = 1901517596] ------------------------------------- Graded Polynomial ring of rank 10 over GF(2) Lexicographical Order Variables: x, y, z, a, b, c, d, e, f, g Variable weights: 7 6 4 1016 1008 992 960 896 768 512 [ a, b, c, d, e, f, g, x^9*d + x*y^4*z^8*d + x*y^4*c + x*z^14*d + x*z^6*c + x*z^2*b + x*a, x^18*e + x^8*y*d + x^2*y^8*z^16*e + x^2*y^8*d + x^2*z^28*e + x^2*z^12*d + x^2*z^4*c + x^2*b + y^5*z^8*d + y^5*c + y*z^14*d + y*z^6*c + y*z^2*b + y*a, x^36*f + x^16*y^2*e + x^8*z*d + x^4*y^16*z^32*f + x^4*y^16*e + x^4*z^56*f + x^4*z^24*e + x^4*z^8*d + x^4*c + y^10*z^16*e + y^10*d + y^4*z^9*d + y^4*z*c + y^2*z^28*e + y^2*z^12*d + y^2*z^4*c + y^2*b + z^15*d + z^7*c + z^3*b + z*a, x^146 + x^144*y*z^2 + x^130*y^16*z^4 + x^130*z^28 + x^128*y^21 + x^128*y^17*z^6 + x^128*y*z^30 + x^72*y*g + x^66*y^8*g + x^66*z^12*g + x^64*y^9*z^2*g + x^64*y*z^14*g + x^34*z^4*f + x^32*y^5*f + x^32*y*z^6*f + x^18*e + x^16*y*z^2*e + x^8*y*d + x^2*y^168 + x^2*y^160*z^12 + x^2*y^128*z^60 + x^2*y^80*z^4*g + x^2*y^64*z^28*g + x^2*y^40*f + x^2*y^32*z^12*f + x^2*y^8*z^16*e + x^2*y^8*d + x^2*z^252 + x^2*z^124*g + x^2*z^60*f + x^2*z^28*e + x^2*z^12*d + x^2*z^4*c + x^2*b + y^169*z^2 + y^161*z^14 + y^129*z^62 + y^85*g + y^81*z^6*g + y^65*z^30*g + y^41*z^2*f + y^33*z^14*f + y^21*e + y^17*z^6*e + y^5*z^8*d + y^5*c + y*z^254 + y*z^126*g + y*z^62*f + y*z^30*e + y*z^14*d + y*z^6*c + y*z^2*b + y*a, x^144*y^2 + x^144*z^3 + x^132*y^16 + x^132*z^24 + x^128*y^20*z + x^128*y^18*z^4 + x^128*y^16*z^7 + x^128*y^2*z^28 + x^128*z^31 + x^72*z*g + x^68*z^8*g + x^64*y^10*g + x^64*y^8*z^3*g + x^64*y^2*z^12*g + x^64*z^15*g + x^32*y^4*z*f + x^32*y^2*z^4*f + x^32*z^7*f + x^16*y^2*e + x^16*z^3*e + x^8*z*d + x^4*y^160*z^8 + x^4*y^128*z^56 + x^4*y^80*g + x^4*y^64*z^24*g + x^4*y^32*z^8*f + x^4*y^16*z^32*f + x^4*y^16*e + x^4*z^248 + x^4*z^120*g + x^4*z^24*e + x^4*z^8*d + x^4*c + y^170 + y^168*z^3 + y^162*z^12 + y^160*z^15 + y^130*z^60 + y^128*z^63 + y^84*z*g + y^82*z^4*g + y^80*z^7*g + y^66*z^28*g + y^64*z^31*g + y^42*f + y^40*z^3*f + y^34*z^12*f + y^32*z^15*f + y^20*z*e + y^16*z^7*e + y^10*z^16*e + y^10*d + y^4*z^9*d + y^4*z*c + y^2*z^252 + y^2*z^124*g + y^2*z^60*f + y^2*z^28*e + y^2*z^12*d + y^2*z^4*c + y^2*b + z^255 + z^127*g + z^63*f + z^31*e + z^15*d + z^7*c + z^3*b + z*a ] [ true, true, true, true, true, true, true, true, true, true, true, true ] 1 [ 2 ] Errors: /home/mfd/gomagma: line 2: 8209 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (80.103.148.24) Time: Mon Mar 29 04:29:25 2004 Input: Z4=Integers(4); Output: Magma V2.10-6 Mon Mar 29 2004 04:29:22 on modular [Seed = 1265428313] ------------------------------------- >> Z4=Integers(4); ^ User error: Identifier 'Z4' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.103.148.24) Time: Mon Mar 29 04:29:52 2004 Input: Z4:=Integers(4); Output: Magma V2.10-6 Mon Mar 29 2004 04:29:50 on modular [Seed = 1416886458] ------------------------------------- Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.103.148.24) Time: Mon Mar 29 04:30:13 2004 Input: Z4:=Integers(4); Z$; Output: Magma V2.10-6 Mon Mar 29 2004 04:30:10 on modular [Seed = 604211430] ------------------------------------- >> Z$; ^ User error: bad syntax Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.103.148.24) Time: Mon Mar 29 04:30:23 2004 Input: Z4:=Integers(4); Z4; Output: Magma V2.10-6 Mon Mar 29 2004 04:30:20 on modular [Seed = 755663329] ------------------------------------- Residue class ring of integers modulo 4 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Mon Mar 29 04:39:20 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; [IsHomogeneous(f): f in P]; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; L := [x^14*y^7]; B, V := HomogeneousModuleTest(P, S, L); B; V; Output: Magma V2.10-6 Mon Mar 29 2004 04:39:17 on modular [Seed = 1058574746] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 [ true, true, true, true, true ] 0 [] [ true ] [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, t4, t3, 0, 0, 0, t1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, t5, 0, 0, 0, 0, 0, t4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] ] Total time: 2.909 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.103.148.24) Time: Mon Mar 29 04:47:24 2004 Input: Z4:=Integers(4); Z4; f:={x:x in Z4}; Output: Magma V2.10-6 Mon Mar 29 2004 04:47:21 on modular [Seed = 4022886182] ------------------------------------- Residue class ring of integers modulo 4 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.103.148.24) Time: Mon Mar 29 04:47:44 2004 Input: Z4:=Integers(4); Z4; f:={x:x in Z4}; f; Output: Magma V2.10-6 Mon Mar 29 2004 04:47:41 on modular [Seed = 4175382565] ------------------------------------- Residue class ring of integers modulo 4 { 0, 1, 2, 3 } Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Mon Mar 29 04:57:04 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; [IsHomogeneous(f): f in P]; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S; L := [x^14*y^7]; B, V := HomogeneousModuleTest(P, S, L); B; V; Output: Magma V2.10-6 Mon Mar 29 2004 04:57:01 on modular [Seed = 3522585436] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 [ true, true, true, true, true ] 0 [] [ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, y^11, y^12, y^13, y^14, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x*y^11, x*y^12, x*y^13, x*y^14, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^2*y^11, x^2*y^12, x^2*y^13, x^2*y^14, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^11*y^5, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ] [ true ] [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, t4, t3, 0, 0, 0, t1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, t5, 0, 0, 0, 0, 0, t4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] ] Total time: 3.059 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.103.148.24) Time: Mon Mar 29 04:59:50 2004 Input: R:=RealField(); Output: Magma V2.10-6 Mon Mar 29 2004 04:59:47 on modular [Seed = 3707465519] ------------------------------------- Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.103.148.24) Time: Mon Mar 29 05:00:42 2004 Input: R:=RealField(); P:=PolynomialRing(R); Output: Magma V2.10-6 Mon Mar 29 2004 05:00:39 on modular [Seed = 2894798603] ------------------------------------- Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Mon Mar 29 05:29:49 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; [IsHomogeneous(f): f in P]; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S; L := [x^14*y^7]; B, V := HomogeneousModuleTest(P, S, L); B; V; P[4]*S[91]+P[3]*S[92]+P[1]*S[96]+P[5]*S[120]+P[4]*S[126] eq L[1]; Output: Magma V2.10-6 Mon Mar 29 2004 05:29:46 on modular [Seed = 570792153] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 [ true, true, true, true, true ] 0 [] [ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, y^11, y^12, y^13, y^14, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x*y^11, x*y^12, x*y^13, x*y^14, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^2*y^11, x^2*y^12, x^2*y^13, x^2*y^14, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^11*y^5, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ] [ true ] [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, t4, t3, 0, 0, 0, t1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, t5, 0, 0, 0, 0, 0, t4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] ] false Total time: 2.929 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 05:40:48 2004 Input: for p in [5..20] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^2)); C := HyperellipticCurve(x^3-1); #(Points(C : Bound:=4)); end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 05:40:44 on modular [Seed = 102873930] ------------------------------------- 36 48 144 192 324 336 Total time: 2.969 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 05:41:22 2004 Input: for p in [5..20] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^20)); C := HyperellipticCurve(x^3-1); #(Points(C : Bound:=4)); end if; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Mar 29 2004 05:40:59 on modular [Seed = 288795723] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 8560 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 05:41:53 2004 Input: for p in [5..20] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^5)); C := HyperellipticCurve(x^3-1); #(Points(C : Bound:=4)); end if; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Mar 29 2004 05:41:30 on modular [Seed = 406824227] ------------------------------------- 3126 17044 161052 370092 Errors: /home/mfd/gomagma: line 2: 8569 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 05:42:50 2004 Input: for p in [5..200] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^2)); C := HyperellipticCurve(x^3-1); #(Points(C : Bound:=4)); end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 05:42:42 on modular [Seed = 3821297184] ------------------------------------- 36 48 144 192 324 336 576 900 1008 1344 1764 1872 2304 2916 3600 3648 4368 5184 5376 6384 7056 8100 9408 10404 10416 11664 12096 12996 15984 17424 19044 19344 22500 23088 24768 26832 28224 30276 32400 32448 36864 37632 39204 39216 Total time: 8.000 seconds, Total memory usage: 7.74MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 05:44:30 2004 Input: for p in [5..100] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); numberOfRoots:=#R; summe:=0; for i in [1..numberOfRoots] do summe:=summe+2/R[i][1]^2; end for; numberOfPoints:=p^2+1-summe; print Round(numberOfPoints), ","; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 05:44:27 on modular [Seed = 3989459847] ------------------------------------- 46 , 46 , 166 , 214 , 358 , 310 , 622 , 958 , 1054 , 1318 , 1846 , 1894 , 2398 , 3022 , 3718 , 3574 , 4246 , 5326 , 5422 , 6526 , 7222 , 8278 , 9406 , Total time: 3.189 seconds, Total memory usage: 3.49MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 05:45:19 2004 Input: for p in [5..20] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^3-1); #(Points(C : Bound:=4)); end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 05:45:15 on modular [Seed = 4175382178] ------------------------------------- 6 4 12 12 18 28 Total time: 3.059 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 05:45:55 2004 Input: n:=2; for p in [5..20] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^n)); C := HyperellipticCurve(x^3-1); #(Points(C : Bound:=4)); end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 05:45:52 on modular [Seed = 3286531522] ------------------------------------- 36 48 144 192 324 336 Total time: 2.919 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 05:46:03 2004 Input: n:=1; for p in [5..20] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^n)); C := HyperellipticCurve(x^3-1); #(Points(C : Bound:=4)); end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 05:46:00 on modular [Seed = 3404559555] ------------------------------------- 6 4 12 12 18 28 Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 05:46:20 2004 Input: n:=1; for p in [5..20] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^n)); C := HyperellipticCurve(x^3-1); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 05:46:17 on modular [Seed = 3589434317] ------------------------------------- 6 4 12 12 18 28 Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 05:49:45 2004 Input: m:=1; upperBound:=10; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^3-1); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 05:49:42 on modular [Seed = 3740885497] ------------------------------------- 6 4 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 05:52:04 2004 Input: upperBound:=20; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); numberOfRoots:=#R; summe:=0; for i in [1..numberOfRoots] do summe:=summe+2/R[i][1]^2; end for; numberOfPoints:=p^2+1-summe; print Round(numberOfPoints), ","; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 05:52:01 on modular [Seed = 2979401217] ------------------------------------- 46 , 46 , 166 , 214 , 358 , 310 , Total time: 2.999 seconds, Total memory usage: 2.39MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 05:52:08 2004 Input: m:=1; upperBound:=20; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^3-1); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 05:52:05 on modular [Seed = 3097429772] ------------------------------------- 6 4 12 12 18 28 Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 05:52:36 2004 Input: upperBound:=20; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^2)); C := HyperellipticCurve(x^6+1); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); numberOfRoots:=#R; summe:=0; for i in [1..numberOfRoots] do summe:=summe+2/R[i][1]^2; end for; numberOfPoints:=p^2+1-summe; print Round(numberOfPoints), ","; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 05:52:32 on modular [Seed = 2208578578] ------------------------------------- -24 , 238 , -120 , -122 , -288 , 454 , Total time: 3.389 seconds, Total memory usage: 5.53MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 05:52:51 2004 Input: m:=1; upperBound:=20; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^6+1); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 05:52:48 on modular [Seed = 2325924587] ------------------------------------- 6 16 12 10 18 4 Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 05:53:05 2004 Input: m:=1; upperBound:=20; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^6+1); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 05:53:02 on modular [Seed = 2495403259] ------------------------------------- 6 16 12 10 18 4 Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 05:53:16 2004 Input: m:=2; upperBound:=20; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^6+1); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 05:53:13 on modular [Seed = 2679627751] ------------------------------------- 46 46 166 214 358 310 Total time: 3.009 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 05:53:34 2004 Input: upperBound:=20; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); numberOfRoots:=#R; summe:=0; for i in [1..numberOfRoots] do summe:=summe+2/R[i][1]^2; end for; numberOfPoints:=p^2+1-summe; print Round(numberOfPoints), ","; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 05:53:31 on modular [Seed = 1699554604] ------------------------------------- 46 , 46 , 166 , 214 , 358 , 310 , Total time: 2.939 seconds, Total memory usage: 2.39MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 05:56:37 2004 Input: m:=2; upperBound:=50; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^6+1); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 05:56:34 on modular [Seed = 2052209402] ------------------------------------- 46 46 166 214 358 310 622 958 1054 1318 1846 1894 2398 Total time: 3.029 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 05:56:41 2004 Input: upperBound:=50; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); numberOfRoots:=#R; summe:=0; for i in [1..numberOfRoots] do summe:=summe+2/R[i][1]^2; end for; numberOfPoints:=p^2+1-summe; print Round(numberOfPoints), ","; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 05:56:38 on modular [Seed = 1080557764] ------------------------------------- 46 , 46 , 166 , 214 , 358 , 310 , 622 , 958 , 1054 , 1318 , 1846 , 1894 , 2398 , Total time: 3.039 seconds, Total memory usage: 2.49MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 06:00:27 2004 Input: m:=1; upperBound:=50; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^6+1); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 06:00:23 on modular [Seed = 1517427711] ------------------------------------- 6 16 12 10 18 4 24 30 40 58 42 28 48 Total time: 3.299 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 06:01:16 2004 Input: m:=2; upperBound:=50; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^6+1); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 06:01:13 on modular [Seed = 823750826] ------------------------------------- 46 46 166 214 358 310 622 958 1054 1318 1846 1894 2398 Total time: 3.089 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.90.160.162) Time: Mon Mar 29 06:10:51 2004 Input: gcd(879,4355) Output: Magma V2.10-6 Mon Mar 29 2004 06:10:48 on modular [Seed = 3147038689] ------------------------------------- >> gcd(879,4355); ^ User error: Identifier 'gcd' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.90.160.162) Time: Mon Mar 29 06:11:15 2004 Input: GCD(879,4355) Output: Magma V2.10-6 Mon Mar 29 2004 06:11:12 on modular [Seed = 2158544050] ------------------------------------- 1 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.90.160.162) Time: Mon Mar 29 06:11:29 2004 Input: GCD(8790,4355) Output: Magma V2.10-6 Mon Mar 29 2004 06:11:26 on modular [Seed = 2309082549] ------------------------------------- 5 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.90.160.162) Time: Mon Mar 29 06:11:46 2004 Input: FACT(6565678) Output: Magma V2.10-6 Mon Mar 29 2004 06:11:43 on modular [Seed = 2529088155] ------------------------------------- >> FACT(6565678); ^ User error: Identifier 'FACT' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.90.160.162) Time: Mon Mar 29 06:11:58 2004 Input: FACTOR(6565678) Output: Magma V2.10-6 Mon Mar 29 2004 06:11:55 on modular [Seed = 2679626630] ------------------------------------- >> FACTOR(6565678); ^ User error: Identifier 'FACTOR' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.90.160.162) Time: Mon Mar 29 06:12:12 2004 Input: FACTORIZE(6565678) Output: Magma V2.10-6 Mon Mar 29 2004 06:12:09 on modular [Seed = 1682710670] ------------------------------------- >> FACTORIZE(6565678); ^ User error: Identifier 'FACTORIZE' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.90.160.162) Time: Mon Mar 29 06:12:28 2004 Input: FACTORISE(6565678) Output: Magma V2.10-6 Mon Mar 29 2004 06:12:25 on modular [Seed = 1935357833] ------------------------------------- >> FACTORISE(6565678); ^ User error: Identifier 'FACTORISE' has not been declared or assigned Total time: 2.869 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.90.160.162) Time: Mon Mar 29 06:12:51 2004 Input: PRIME(6565678) Output: Magma V2.10-6 Mon Mar 29 2004 06:12:48 on modular [Seed = 2052210345] ------------------------------------- >> PRIME(6565678); ^ User error: Identifier 'PRIME' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 07:48:36 2004 Input: F := PolynomialRing(FiniteField(5^1)); C := HyperellipticCurve(x^3-1); #C; Output: Magma V2.10-6 Mon Mar 29 2004 07:48:33 on modular [Seed = 1833252392] ------------------------------------- 6 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 07:48:44 2004 Input: F := PolynomialRing(FiniteField(5^2)); C := HyperellipticCurve(x^3-1); #C; Output: Magma V2.10-6 Mon Mar 29 2004 07:48:41 on modular [Seed = 1985883451] ------------------------------------- 36 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 07:48:53 2004 Input: F := PolynomialRing(FiniteField(5^3)); C := HyperellipticCurve(x^3-1); #C; Output: Magma V2.10-6 Mon Mar 29 2004 07:48:50 on modular [Seed = 2018517806] ------------------------------------- 126 Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 07:49:11 2004 Input: F := PolynomialRing(FiniteField(5^4)); C := HyperellipticCurve(x^3-1); #C; Output: Magma V2.10-6 Mon Mar 29 2004 07:49:08 on modular [Seed = 1097407073] ------------------------------------- 576 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee107.uab.es. (158.109.66.107) Time: Mon Mar 29 08:28:05 2004 Input: K:=GF(25); F:= ext; Output: Magma V2.10-6 Mon Mar 29 2004 08:28:02 on modular [Seed = 3955462125] ------------------------------------- >> F:= ext;; ^ User error: bad syntax Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Mon Mar 29 09:02:01 2004 Input: K := GF(2); R := PolynomialRing(K, [7, 6, 4, 1016, 1008, 992, 960, 896, 768, 512]); R; P := [a, b, c, d, e, f, g , x*(a- b*z^2 -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2) +e*(x^(2^4)*z^2 +y^(2^4)*y^(2^2) -y^(2^4)*z^(2^2 +2) +z^(2^4 + 2^3 + 2^2 +2) ) + f*(x^(2^5)*y^(2^2) - x^(2^5)*z^(2^2 +2) - y^(2^5 +2^3)*z^(2) + y^(2^5)*z^( 2^3 + 2^2 +2) -z^(2^5 +2^4 + 2^3 + 2^2 +2) ) + g*(x^(2^6 +2^3) -x^(2^6)*y^(2^3)*z^2 + x^(2^6)*z^(2^3 +2^2 +2) -y^(2^6 + 2^4 + 2^2 ) + y^(2^6 +2^4)*z^(2^2 +2) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2) ) - z^2 *(x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^4 +2^3 +2^2) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^3 +2^2) - y^(2^7)*z^(2^5 + 2^4 +2^3 + 2^2 ) +z^(2^7 +2^6 +2^5 +2^4 + 2^3 + 2^2 ) )- x^(2^7)*y^(2^2 +2^4) ), y*(a- b*z^(2) -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2) +e*(x^(2^4)*z^2 +y^(2^4)*y^(2^2) -y^(2^4)*z^(2^2 +2) +z^(2^4 + 2^3 + 2^2 +2) ) + f*(x^(2^5)*y^(2^2) - x^(2^5)*z^(2^2 +2) - y^(2^5 +2^3)*z^(2) + y^(2^5)*z^( 2^3 + 2^2 +2) -z^(2^5 +2^4 + 2^3 + 2^2 +2) ) + g*(x^(2^6 +2^3) -x^(2^6)*y^(2^3)*z^2 + x^(2^6)*z^(2^3 +2^2 +2) -y^(2^6 + 2^4 + 2^2 ) + y^(2^6 +2^4)*z^(2^2 +2) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2) ) - z^2 *(x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^4 +2^3 +2^2) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^3 +2^2) - y^(2^7)*z^(2^5 + 2^4 +2^3 + 2^2 ) +z^(2^7 +2^6 +2^5 +2^4 + 2^3 + 2^2 ) )- x^(2^7)*y^(2^2 +2^4) ) ) + x^2 *(b- c*z^(2^2) -d*y^(2^3) +d*z^(2^3 +2^2) -e*x^(2^4) +e*z^(2^4)*y^(2^3) -e*z^(2^4 +2^3 +2^2) + f*( x^(2^5)*z^(2^2) +y^(2^5)*y^(2^3) -y^(2^5)*z^(2^2 +2^3) +z^(2^4 + 2^3 + 2^2 +2^5)) + g*( x^(2^6)*y^(2^3) - x^(2^6)*z^(2^2 +2^3) - y^(2^6 +2^4)*z^(2^2) + y^(2^6)*z^( 2^3 + 2^2 +2^4) -z^(2^5 +2^4 + 2^3 + 2^2 +2^6))+ x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^3 +2^2 +2^4) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^2 +2^3) - y^(2^7)*z^( 2^4 +2^3 + 2^2 +2^5) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2^7) ), z*(a- b*z^(2) -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2) +e*(x^(2^4)*z^2 +y^(2^4)*y^(2^2) -y^(2^4)*z^(2^2 +2) +z^(2^4 + 2^3 + 2^2 +2) ) + f*(x^(2^5)*y^(2^2) - x^(2^5)*z^(2^2 +2) - y^(2^5 +2^3)*z^(2) + y^(2^5)*z^( 2^3 + 2^2 +2) -z^(2^5 +2^4 + 2^3 + 2^2 +2) ) + g*(x^(2^6 +2^3) -x^(2^6)*y^(2^3)*z^2 + x^(2^6)*z^(2^3 +2^2 +2) -y^(2^6 + 2^4 + 2^2 ) + y^(2^6 +2^4)*z^(2^2 +2) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2) ) - z^2 *(x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^4 +2^3 +2^2) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^3 +2^2) - y^(2^7)*z^(2^5 + 2^4 +2^3 + 2^2 ) +z^(2^7 +2^6 +2^5 +2^4 + 2^3 + 2^2 ) )- x^(2^7)*y^(2^2 +2^4) ) ) + y^2 *(b- c*z^(2^2) -d*y^(2^3) +d*z^(2^3 +2^2) -e*x^(2^4) +e*z^(2^4)*y^(2^3) -e*z^(2^4 +2^3 +2^2) + f*( x^(2^5)*z^(2^2) +y^(2^5)*y^(2^3) -y^(2^5)*z^(2^2 +2^3) +z^(2^4 + 2^3 + 2^2 +2^5)) + g*( x^(2^6)*y^(2^3) - x^(2^6)*z^(2^2 +2^3) - y^(2^6 +2^4)*z^(2^2) + y^(2^6)*z^( 2^3 + 2^2 +2^4) -z^(2^5 +2^4 + 2^3 + 2^2 +2^6))+ x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^3 +2^2 +2^4) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^2 +2^3) - y^(2^7)*z^( 2^4 +2^3 + 2^2 +2^5) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2^7) ) + x^(2^2) *(c- d*z^(2^3) -e*y^(2^4) +e*z^(2^4 +2^3) -f*x^(2^5) +f*z^(2^5)*y^(2^4) -f*z^(2^5 +2^4 +2^3) + f*(y^(2^5)*z^(2^3) -x^(2^5) -z^(2^3 +2^4 +2^5) ) +g*(x^(2^6)*z^(2^3) +y^(2^6)*y^(2^4) -y^(2^6)*z^(2^4 +2^3) +z^(2^4 + 2^3 + 2^6 +2^5) ) + x^(2^7)*y^(2^4) - x^(2^7)*z^(2^4 +2^3) - y^(2^7 +2^5)*z^(2^3) + y^(2^7)*z^( 2^3 + 2^5 +2^4) -z^(2^5 +2^4 + 2^3 + 2^7 +2^6)) ] ; P; [IsHomogeneous(f): f in P]; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S; Output: Magma V2.10-6 Mon Mar 29 2004 09:01:58 on modular [Seed = 2325931704] ------------------------------------- Graded Polynomial ring of rank 10 over GF(2) Lexicographical Order Variables: x, y, z, a, b, c, d, e, f, g Variable weights: 7 6 4 1016 1008 992 960 896 768 512 >> x^(2^7)*y^(2^2 +2^4) ) ) + ^ User error: bad syntax >> x^(2^7)*y^(2^2 +2^4) ) ) + ^ User error: bad syntax >> ] ; ^ User error: bad syntax >> P; ^ User error: Identifier 'P' has not been declared or assigned >> [IsHomogeneous(f): f in P]; ^ User error: Identifier 'P' has not been declared or assigned >> I:=ideal; ^ User error: Identifier 'P' has not been declared or assigned >> Dimension(I); ^ User error: Identifier 'I' has not been declared or assigned >> V,phi:=VectorSpace(quo); ^ User error: Identifier 'I' has not been declared or assigned >> S:=[R!(v@@phi ): v in Basis(V)]; ^ User error: Identifier 'V' has not been declared or assigned >> S; ^ User error: Identifier 'S' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.92MB ************** MAGMA ***************** Host aula-b-siee107.uab.es. (158.109.66.107) Time: Mon Mar 29 09:03:04 2004 Input: k:=GF(25); f:=x^2+4*x+2; F:=ext; MinimalPolynomiual(alpha); Output: Magma V2.10-6 Mon Mar 29 2004 09:03:01 on modular [Seed = 2478571362] ------------------------------------- >> f:=x^2+4*x+2; ^ User error: Identifier 'x' has not been declared or assigned >> F:=ext; ^ User error: Identifier 'f' has not been declared or assigned >> MinimalPolynomiual(alpha);; ^ User error: Identifier 'alpha' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee107.uab.es. (158.109.66.107) Time: Mon Mar 29 09:03:55 2004 Input: k:=GF(25); P:=PolynomialRing(k); f:=x^2+4*x+2; F:=ext; MinimalPolynomiual(alpha); Output: Magma V2.10-6 Mon Mar 29 2004 09:03:52 on modular [Seed = 1682704585] ------------------------------------- >> F:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible >> MinimalPolynomiual(alpha);; ^ User error: Identifier 'alpha' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Mon Mar 29 09:04:08 2004 Input: K := GF(2); R := PolynomialRing(K, [7, 6, 4, 1016, 1008, 992, 960, 896, 768, 512]); R; P := [a, b, c, d, e, f, g , x*(a- b*z^2 -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2) +e*(x^(2^4)*z^2 +y^(2^4)*y^(2^2) -y^(2^4)*z^(2^2 +2) +z^(2^4 + 2^3 + 2^2 +2) ) + f*(x^(2^5)*y^(2^2) - x^(2^5)*z^(2^2 +2) - y^(2^5 +2^3)*z^(2) + y^(2^5)*z^( 2^3 + 2^2 +2) -z^(2^5 +2^4 + 2^3 + 2^2 +2) ) + g*(x^(2^6 +2^3) -x^(2^6)*y^(2^3)*z^2 + x^(2^6)*z^(2^3 +2^2 +2) -y^(2^6 + 2^4 + 2^2 ) + y^(2^6 +2^4)*z^(2^2 +2) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2) ) - z^2 *(x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^4 +2^3 +2^2) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^3 +2^2) - y^(2^7)*z^(2^5 + 2^4 +2^3 + 2^2 ) +z^(2^7 +2^6 +2^5 +2^4 + 2^3 + 2^2 ) )- x^(2^7)*y^(2^2 +2^4) ), y*(a- b*z^(2) -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2) +e*(x^(2^4)*z^2 +y^(2^4)*y^(2^2) -y^(2^4)*z^(2^2 +2) +z^(2^4 + 2^3 + 2^2 +2) ) + f*(x^(2^5)*y^(2^2) - x^(2^5)*z^(2^2 +2) - y^(2^5 +2^3)*z^(2) + y^(2^5)*z^( 2^3 + 2^2 +2) -z^(2^5 +2^4 + 2^3 + 2^2 +2) ) + g*(x^(2^6 +2^3) -x^(2^6)*y^(2^3)*z^2 + x^(2^6)*z^(2^3 +2^2 +2) -y^(2^6 + 2^4 + 2^2 ) + y^(2^6 +2^4)*z^(2^2 +2) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2) ) - z^2 *(x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^4 +2^3 +2^2) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^3 +2^2) - y^(2^7)*z^(2^5 + 2^4 +2^3 + 2^2 ) +z^(2^7 +2^6 +2^5 +2^4 + 2^3 + 2^2 ) )- x^(2^7)*y^(2^2 +2^4) ) + x^2 *(b- c*z^(2^2) -d*y^(2^3) +d*z^(2^3 +2^2) -e*x^(2^4) +e*z^(2^4)*y^(2^3) -e*z^(2^4 +2^3 +2^2) + f*( x^(2^5)*z^(2^2) +y^(2^5)*y^(2^3) -y^(2^5)*z^(2^2 +2^3) +z^(2^4 + 2^3 + 2^2 +2^5)) + g*( x^(2^6)*y^(2^3) - x^(2^6)*z^(2^2 +2^3) - y^(2^6 +2^4)*z^(2^2) + y^(2^6)*z^( 2^3 + 2^2 +2^4) -z^(2^5 +2^4 + 2^3 + 2^2 +2^6))+ x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^3 +2^2 +2^4) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^2 +2^3) - y^(2^7)*z^( 2^4 +2^3 + 2^2 +2^5) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2^7) ), z*(a- b*z^(2) -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2) +e*(x^(2^4)*z^2 +y^(2^4)*y^(2^2) -y^(2^4)*z^(2^2 +2) +z^(2^4 + 2^3 + 2^2 +2) ) + f*(x^(2^5)*y^(2^2) - x^(2^5)*z^(2^2 +2) - y^(2^5 +2^3)*z^(2) + y^(2^5)*z^( 2^3 + 2^2 +2) -z^(2^5 +2^4 + 2^3 + 2^2 +2) ) + g*(x^(2^6 +2^3) -x^(2^6)*y^(2^3)*z^2 + x^(2^6)*z^(2^3 +2^2 +2) -y^(2^6 + 2^4 + 2^2 ) + y^(2^6 +2^4)*z^(2^2 +2) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2) ) - z^2 *(x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^4 +2^3 +2^2) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^3 +2^2) - y^(2^7)*z^(2^5 + 2^4 +2^3 + 2^2 ) +z^(2^7 +2^6 +2^5 +2^4 + 2^3 + 2^2 ) )- x^(2^7)*y^(2^2 +2^4) ) + y^2 *(b- c*z^(2^2) -d*y^(2^3) +d*z^(2^3 +2^2) -e*x^(2^4) +e*z^(2^4)*y^(2^3) -e*z^(2^4 +2^3 +2^2) + f*( x^(2^5)*z^(2^2) +y^(2^5)*y^(2^3) -y^(2^5)*z^(2^2 +2^3) +z^(2^4 + 2^3 + 2^2 +2^5)) + g*( x^(2^6)*y^(2^3) - x^(2^6)*z^(2^2 +2^3) - y^(2^6 +2^4)*z^(2^2) + y^(2^6)*z^( 2^3 + 2^2 +2^4) -z^(2^5 +2^4 + 2^3 + 2^2 +2^6))+ x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^3 +2^2 +2^4) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^2 +2^3) - y^(2^7)*z^( 2^4 +2^3 + 2^2 +2^5) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2^7) ) + x^(2^2) *(c- d*z^(2^3) -e*y^(2^4) +e*z^(2^4 +2^3) -f*x^(2^5) +f*z^(2^5)*y^(2^4) -f*z^(2^5 +2^4 +2^3) + f*(y^(2^5)*z^(2^3) -x^(2^5) -z^(2^3 +2^4 +2^5) ) +g*(x^(2^6)*z^(2^3) +y^(2^6)*y^(2^4) -y^(2^6)*z^(2^4 +2^3) +z^(2^4 + 2^3 + 2^6 +2^5) ) + x^(2^7)*y^(2^4) - x^(2^7)*z^(2^4 +2^3) - y^(2^7 +2^5)*z^(2^3) + y^(2^7)*z^( 2^3 + 2^5 +2^4) -z^(2^5 +2^4 + 2^3 + 2^7 +2^6)) ] ; P; [IsHomogeneous(f): f in P]; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S; Output: Magma V2.10-6 Mon Mar 29 2004 09:04:01 on modular [Seed = 1866925019] ------------------------------------- Graded Polynomial ring of rank 10 over GF(2) Lexicographical Order Variables: x, y, z, a, b, c, d, e, f, g Variable weights: 7 6 4 1016 1008 992 960 896 768 512 [ a, b, c, d, e, f, g, x^145*z^2 + x^129*y^20 + x^129*y^16*z^6 + x^129*z^30 + x^73*g + x^65*y^8*z^2*g + x^65*z^14*g + x^33*y^4*f + x^33*z^6*f + x^17*z^2*e + x^9*d + x*y^168*z^2 + x*y^160*z^14 + x*y^128*z^62 + x*y^84*g + x*y^80*z^6*g + x*y^64*z^30*g + x*y^40*z^2*f + x*y^32*z^14*f + x*y^20*e + x*y^16*z^6*e + x*y^4*z^8*d + x*y^4*c + x*z^254 + x*z^126*g + x*z^62*f + x*z^30*e + x*z^14*d + x*z^6*c + x*z^2*b + x*a, x^146 + x^144*y*z^2 + x^130*y^16*z^4 + x^130*z^28 + x^128*y^21 + x^128*y^17*z^6 + x^128*y*z^30 + x^72*y*g + x^66*y^8*g + x^66*z^12*g + x^64*y^9*z^2*g + x^64*y*z^14*g + x^34*z^4*f + x^32*y^5*f + x^32*y*z^6*f + x^18*e + x^16*y*z^2*e + x^8*y*d + x^2*y^168 + x^2*y^160*z^12 + x^2*y^128*z^60 + x^2*y^80*z^4*g + x^2*y^64*z^28*g + x^2*y^40*f + x^2*y^32*z^12*f + x^2*y^8*z^16*e + x^2*y^8*d + x^2*z^252 + x^2*z^124*g + x^2*z^60*f + x^2*z^28*e + x^2*z^12*d + x^2*z^4*c + x^2*b + y^169*z^2 + y^161*z^14 + y^129*z^62 + y^85*g + y^81*z^6*g + y^65*z^30*g + y^41*z^2*f + y^33*z^14*f + y^21*e + y^17*z^6*e + y^5*z^8*d + y^5*c + y*z^254 + y*z^126*g + y*z^62*f + y*z^30*e + y*z^14*d + y*z^6*c + y*z^2*b + y*a, x^144*y^2 + x^144*z^3 + x^132*y^16 + x^132*z^24 + x^128*y^20*z + x^128*y^18*z^4 + x^128*y^16*z^7 + x^128*y^2*z^28 + x^128*z^31 + x^72*z*g + x^68*z^8*g + x^64*y^10*g + x^64*y^8*z^3*g + x^64*y^2*z^12*g + x^64*z^15*g + x^32*y^4*z*f + x^32*y^2*z^4*f + x^32*z^7*f + x^16*y^2*e + x^16*z^3*e + x^8*z*d + x^4*y^160*z^8 + x^4*y^128*z^56 + x^4*y^80*g + x^4*y^64*z^24*g + x^4*y^32*z^8*f + x^4*y^16*z^32*f + x^4*y^16*e + x^4*z^248 + x^4*z^120*g + x^4*z^24*e + x^4*z^8*d + x^4*c + y^170 + y^168*z^3 + y^162*z^12 + y^160*z^15 + y^130*z^60 + y^128*z^63 + y^84*z*g + y^82*z^4*g + y^80*z^7*g + y^66*z^28*g + y^64*z^31*g + y^42*f + y^40*z^3*f + y^34*z^12*f + y^32*z^15*f + y^20*z*e + y^16*z^7*e + y^10*z^16*e + y^10*d + y^4*z^9*d + y^4*z*c + y^2*z^252 + y^2*z^124*g + y^2*z^60*f + y^2*z^28*e + y^2*z^12*d + y^2*z^4*c + y^2*b + z^255 + z^127*g + z^63*f + z^31*e + z^15*d + z^7*c + z^3*b + z*a ] [ true, true, true, true, true, true, true, true, true, true ] 1 [ 2 ] >> V,phi:=VectorSpace(quo); ^ Runtime error in 'VectorSpace': Quotient does not have finite dimension >> S:=[R!(v@@phi ): v in Basis(V)]; ^ User error: Identifier 'V' has not been declared or assigned >> S; ^ User error: Identifier 'S' has not been declared or assigned Total time: 7.369 seconds, Total memory usage: 2.58MB ************** MAGMA ***************** Host aula-b-siee107.uab.es. (158.109.66.107) Time: Mon Mar 29 09:04:25 2004 Input: k:=GF(25); P:=PolynomialRing(k); f:=x^2+4*x+2; F:=ext< k | f >; MinimalPolynomiual(alpha); Output: Magma V2.10-6 Mon Mar 29 2004 09:04:22 on modular [Seed = 1985878773] ------------------------------------- >> F:=ext< k | f >; ^ Runtime error in ext< ... >: Argument is not irreducible >> MinimalPolynomiual(alpha);; ^ User error: Identifier 'alpha' has not been declared or assigned Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee107.uab.es. (158.109.66.107) Time: Mon Mar 29 09:05:24 2004 Input: k:=GF(25); P:=PolynomialRing(k); f:=x^2+4*x+2; F:=ext< k | f >; MinimalPolynomiual(alpha); Output: Magma V2.10-6 Mon Mar 29 2004 09:05:21 on modular [Seed = 1147939072] ------------------------------------- >> F:=ext< k | f >; ^ Runtime error in ext< ... >: Argument is not irreducible >> MinimalPolynomiual(alpha);; ^ User error: Identifier 'MinimalPolynomiual' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee107.uab.es. (158.109.66.107) Time: Mon Mar 29 09:05:46 2004 Input: k:=GF(25); P:=PolynomialRing(k); f:=x^2+4*x+2; F:= ext < k | f >; MinimalPolynomiual(alpha); Output: Magma V2.10-6 Mon Mar 29 2004 09:05:43 on modular [Seed = 1332159005] ------------------------------------- >> F:= ext < k | f >; ^ Runtime error in ext< ... >: Argument is not irreducible >> MinimalPolynomiual(alpha);; ^ User error: Identifier 'MinimalPolynomiual' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee107.uab.es. (158.109.66.107) Time: Mon Mar 29 09:06:01 2004 Input: k:=GF(25); P:=PolynomialRing(k); f:=x^2+4*x+2; F:= ext< k | f >; MinimalPolynomiual(alpha); Output: Magma V2.10-6 Mon Mar 29 2004 09:05:58 on modular [Seed = 1451113333] ------------------------------------- >> F:= ext< k | f >; ^ Runtime error in ext< ... >: Argument is not irreducible >> MinimalPolynomiual(alpha);; ^ User error: Identifier 'MinimalPolynomiual' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee107.uab.es. (158.109.66.107) Time: Mon Mar 29 09:06:41 2004 Input: k:=GF(25); P:=PolynomialRing(k); f:=x^2+4*x+2; F:= ext< k | f >; MinimalPolynomial(alpha); Output: Magma V2.10-6 Mon Mar 29 2004 09:06:38 on modular [Seed = 1500591186] ------------------------------------- >> F:= ext< k | f >; ^ Runtime error in ext< ... >: Argument is not irreducible $.1^2 + 4*$.1 + 2 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee107.uab.es. (158.109.66.107) Time: Mon Mar 29 09:07:18 2004 Input: k:=GF(25); P:=PolynomialRing(k); f:=x^2+4*x+2; F:= ext< k | f >; poli:=MinimalPolynomial(alpha); poli; Output: Magma V2.10-6 Mon Mar 29 2004 09:07:15 on modular [Seed = 537415126] ------------------------------------- >> F:= ext< k | f >; ^ Runtime error in ext< ... >: Argument is not irreducible $.1^2 + 4*$.1 + 2 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee107.uab.es. (158.109.66.107) Time: Mon Mar 29 09:10:49 2004 Input: k:=GF(25); P:=PolynomialRing(k); f:=x^2+4*x+2; F:= ext< k | f >; poli:=MinimalPolynomial(1); poli; Output: Magma V2.10-6 Mon Mar 29 2004 09:10:46 on modular [Seed = 840588337] ------------------------------------- >> F:= ext< k | f >; ^ Runtime error in ext< ... >: Argument is not irreducible $.1 - 1 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee107.uab.es. (158.109.66.107) Time: Mon Mar 29 09:12:24 2004 Input: k:=GF(25); P:=PolynomialRing(k); f:=x^2+2*x+1; F:= ext< k | f >; poli:=MinimalPolynomial(1); poli; Output: Magma V2.10-6 Mon Mar 29 2004 09:12:21 on modular [Seed = 70019748] ------------------------------------- >> F:= ext< k | f >; ^ Runtime error in ext< ... >: Argument is not irreducible $.1 - 1 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee107.uab.es. (158.109.66.107) Time: Mon Mar 29 09:12:51 2004 Input: k:=GF(25); P:=PolynomialRing(k); f:=x^2+2*x+1; F:= ext< k | f >; poli:=MinimalPolynomial(1); poli; Output: Magma V2.10-6 Mon Mar 29 2004 09:12:48 on modular [Seed = 254239114] ------------------------------------- >> F:= ext< k | f >; ^ Runtime error in ext< ... >: Argument is not irreducible $.1 - 1 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee107.uab.es. (158.109.66.107) Time: Mon Mar 29 09:19:47 2004 Input: F:=GF(25); 2*alpha^(-3)-alpha^5+(1/(alpha+2))*alpha^6; Output: Magma V2.10-6 Mon Mar 29 2004 09:19:44 on modular [Seed = 3855455488] ------------------------------------- alpha^17 Total time: 3.619 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Mon Mar 29 09:19:51 2004 Input: K := GF(2); R := PolynomialRing(K, [7, 6, 4, 1016, 1008, 992, 960, 896, 768, 512]); R; P := [a, b, c, d, e, f, g , x*(a- b*z^2 -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2) +e*(x^(2^4)*z^2 +y^(2^4)*y^(2^2) -y^(2^4)*z^(2^2 +2) +z^(2^4 + 2^3 + 2^2 +2) ) + f*(x^(2^5)*y^(2^2) - x^(2^5)*z^(2^2 +2) - y^(2^5 +2^3)*z^(2) + y^(2^5)*z^( 2^3 + 2^2 +2) -z^(2^5 +2^4 + 2^3 + 2^2 +2) ) + g*(x^(2^6 +2^3) -x^(2^6)*y^(2^3)*z^2 + x^(2^6)*z^(2^3 +2^2 +2) -y^(2^6 + 2^4 + 2^2 ) + y^(2^6 +2^4)*z^(2^2 +2) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2) ) - z^2 *(x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^4 +2^3 +2^2) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^3 +2^2) - y^(2^7)*z^(2^5 + 2^4 +2^3 + 2^2 ) +z^(2^7 +2^6 +2^5 +2^4 + 2^3 + 2^2 ) )- x^(2^7)*y^(2^2 +2^4) ), y*(a- b*z^(2) -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2) +e*(x^(2^4)*z^2 +y^(2^4)*y^(2^2) -y^(2^4)*z^(2^2 +2) +z^(2^4 + 2^3 + 2^2 +2) ) + f*(x^(2^5)*y^(2^2) - x^(2^5)*z^(2^2 +2) - y^(2^5 +2^3)*z^(2) + y^(2^5)*z^( 2^3 + 2^2 +2) -z^(2^5 +2^4 + 2^3 + 2^2 +2) ) + g*(x^(2^6 +2^3) -x^(2^6)*y^(2^3)*z^2 + x^(2^6)*z^(2^3 +2^2 +2) -y^(2^6 + 2^4 + 2^2 ) + y^(2^6 +2^4)*z^(2^2 +2) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2) ) - z^2 *(x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^4 +2^3 +2^2) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^3 +2^2) - y^(2^7)*z^(2^5 + 2^4 +2^3 + 2^2 ) +z^(2^7 +2^6 +2^5 +2^4 + 2^3 + 2^2 ) )- x^(2^7)*y^(2^2 +2^4) ) + x^2 *(b- c*z^(2^2) -d*y^(2^3) +d*z^(2^3 +2^2) -e*x^(2^4) +e*z^(2^4)*y^(2^3) -e*z^(2^4 +2^3 +2^2) + f*( x^(2^5)*z^(2^2) +y^(2^5)*y^(2^3) -y^(2^5)*z^(2^2 +2^3) +z^(2^4 + 2^3 + 2^2 +2^5)) + g*( x^(2^6)*y^(2^3) - x^(2^6)*z^(2^2 +2^3) - y^(2^6 +2^4)*z^(2^2) + y^(2^6)*z^( 2^3 + 2^2 +2^4) -z^(2^5 +2^4 + 2^3 + 2^2 +2^6))+ x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^3 +2^2 +2^4) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^2 +2^3) - y^(2^7)*z^( 2^4 +2^3 + 2^2 +2^5) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2^7) ), z*(a- b*z^(2) -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2) +e*(x^(2^4)*z^2 +y^(2^4)*y^(2^2) -y^(2^4)*z^(2^2 +2) +z^(2^4 + 2^3 + 2^2 +2) ) + f*(x^(2^5)*y^(2^2) - x^(2^5)*z^(2^2 +2) - y^(2^5 +2^3)*z^(2) + y^(2^5)*z^( 2^3 + 2^2 +2) -z^(2^5 +2^4 + 2^3 + 2^2 +2) ) + g*(x^(2^6 +2^3) -x^(2^6)*y^(2^3)*z^2 + x^(2^6)*z^(2^3 +2^2 +2) -y^(2^6 + 2^4 + 2^2 ) + y^(2^6 +2^4)*z^(2^2 +2) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2) ) - z^2 *(x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^4 +2^3 +2^2) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^3 +2^2) - y^(2^7)*z^(2^5 + 2^4 +2^3 + 2^2 ) +z^(2^7 +2^6 +2^5 +2^4 + 2^3 + 2^2 ) )- x^(2^7)*y^(2^2 +2^4) ) + y^2 *(b- c*z^(2^2) -d*y^(2^3) +d*z^(2^3 +2^2) -e*x^(2^4) +e*z^(2^4)*y^(2^3) -e*z^(2^4 +2^3 +2^2) + f*( x^(2^5)*z^(2^2) +y^(2^5)*y^(2^3) -y^(2^5)*z^(2^2 +2^3) +z^(2^4 + 2^3 + 2^2 +2^5)) + g*( x^(2^6)*y^(2^3) - x^(2^6)*z^(2^2 +2^3) - y^(2^6 +2^4)*z^(2^2) + y^(2^6)*z^( 2^3 + 2^2 +2^4) -z^(2^5 +2^4 + 2^3 + 2^2 +2^6))+ x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^3 +2^2 +2^4) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^2 +2^3) - y^(2^7)*z^( 2^4 +2^3 + 2^2 +2^5) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2^7) ) + x^(2^2) *(c- d*z^(2^3) -e*y^(2^4) +e*z^(2^4 +2^3) -f*x^(2^5) +f*z^(2^5)*y^(2^4) -f*z^(2^5 +2^4 +2^3) + f*(y^(2^5)*z^(2^3) -x^(2^5) -z^(2^3 +2^4 +2^5) ) +g*(x^(2^6)*z^(2^3) +y^(2^6)*y^(2^4) -y^(2^6)*z^(2^4 +2^3) +z^(2^4 + 2^3 + 2^6 +2^5) ) + x^(2^7)*y^(2^4) - x^(2^7)*z^(2^4 +2^3) - y^(2^7 +2^5)*z^(2^3) + y^(2^7)*z^( 2^3 + 2^5 +2^4) -z^(2^5 +2^4 + 2^3 + 2^7 +2^6)) ] ; P; [IsHomogeneous(f): f in P]; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S; Output: Magma V2.10-6 Mon Mar 29 2004 09:19:43 on modular [Seed = 405825538] ------------------------------------- Graded Polynomial ring of rank 10 over GF(2) Lexicographical Order Variables: x, y, z, a, b, c, d, e, f, g Variable weights: 7 6 4 1016 1008 992 960 896 768 512 [ a, b, c, d, e, f, g, x^145*z^2 + x^129*y^20 + x^129*y^16*z^6 + x^129*z^30 + x^73*g + x^65*y^8*z^2*g + x^65*z^14*g + x^33*y^4*f + x^33*z^6*f + x^17*z^2*e + x^9*d + x*y^168*z^2 + x*y^160*z^14 + x*y^128*z^62 + x*y^84*g + x*y^80*z^6*g + x*y^64*z^30*g + x*y^40*z^2*f + x*y^32*z^14*f + x*y^20*e + x*y^16*z^6*e + x*y^4*z^8*d + x*y^4*c + x*z^254 + x*z^126*g + x*z^62*f + x*z^30*e + x*z^14*d + x*z^6*c + x*z^2*b + x*a, x^146 + x^144*y*z^2 + x^130*y^16*z^4 + x^130*z^28 + x^128*y^21 + x^128*y^17*z^6 + x^128*y*z^30 + x^72*y*g + x^66*y^8*g + x^66*z^12*g + x^64*y^9*z^2*g + x^64*y*z^14*g + x^34*z^4*f + x^32*y^5*f + x^32*y*z^6*f + x^18*e + x^16*y*z^2*e + x^8*y*d + x^2*y^168 + x^2*y^160*z^12 + x^2*y^128*z^60 + x^2*y^80*z^4*g + x^2*y^64*z^28*g + x^2*y^40*f + x^2*y^32*z^12*f + x^2*y^8*z^16*e + x^2*y^8*d + x^2*z^252 + x^2*z^124*g + x^2*z^60*f + x^2*z^28*e + x^2*z^12*d + x^2*z^4*c + x^2*b + y^169*z^2 + y^161*z^14 + y^129*z^62 + y^85*g + y^81*z^6*g + y^65*z^30*g + y^41*z^2*f + y^33*z^14*f + y^21*e + y^17*z^6*e + y^5*z^8*d + y^5*c + y*z^254 + y*z^126*g + y*z^62*f + y*z^30*e + y*z^14*d + y*z^6*c + y*z^2*b + y*a, x^144*y^2 + x^144*z^3 + x^132*y^16 + x^132*z^24 + x^128*y^20*z + x^128*y^18*z^4 + x^128*y^16*z^7 + x^128*y^2*z^28 + x^128*z^31 + x^72*z*g + x^68*z^8*g + x^64*y^10*g + x^64*y^8*z^3*g + x^64*y^2*z^12*g + x^64*z^15*g + x^32*y^4*z*f + x^32*y^2*z^4*f + x^32*z^7*f + x^16*y^2*e + x^16*z^3*e + x^8*z*d + x^4*y^160*z^8 + x^4*y^128*z^56 + x^4*y^80*g + x^4*y^64*z^24*g + x^4*y^32*z^8*f + x^4*y^16*z^32*f + x^4*y^16*e + x^4*z^248 + x^4*z^120*g + x^4*z^24*e + x^4*z^8*d + x^4*c + y^170 + y^168*z^3 + y^162*z^12 + y^160*z^15 + y^130*z^60 + y^128*z^63 + y^84*z*g + y^82*z^4*g + y^80*z^7*g + y^66*z^28*g + y^64*z^31*g + y^42*f + y^40*z^3*f + y^34*z^12*f + y^32*z^15*f + y^20*z*e + y^16*z^7*e + y^10*z^16*e + y^10*d + y^4*z^9*d + y^4*z*c + y^2*z^252 + y^2*z^124*g + y^2*z^60*f + y^2*z^28*e + y^2*z^12*d + y^2*z^4*c + y^2*b + z^255 + z^127*g + z^63*f + z^31*e + z^15*d + z^7*c + z^3*b + z*a ] [ true, true, true, true, true, true, true, true, true, true ] 1 [ 2 ] >> V,phi:=VectorSpace(quo); ^ Runtime error in 'VectorSpace': Quotient does not have finite dimension >> S:=[R!(v@@phi ): v in Basis(V)]; ^ User error: Identifier 'V' has not been declared or assigned >> S; ^ User error: Identifier 'S' has not been declared or assigned Total time: 7.699 seconds, Total memory usage: 2.58MB ************** MAGMA ***************** Host aula-b-siee107.uab.es. (158.109.66.107) Time: Mon Mar 29 09:22:58 2004 Input: F:=GF(25); f:=2*alpha^(-3)-alpha^5+(1/(alpha+2))*alpha^6; f; ElementToSequence(f); Output: Magma V2.10-6 Mon Mar 29 2004 09:22:55 on modular [Seed = 4074406824] ------------------------------------- alpha^17 [ 4, 1 ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee107.uab.es. (158.109.66.107) Time: Mon Mar 29 09:25:09 2004 Input: F:=GF(25); F![4,1]; Output: Magma V2.10-6 Mon Mar 29 2004 09:25:06 on modular [Seed = 3287003748] ------------------------------------- alpha^17 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee107.uab.es. (158.109.66.107) Time: Mon Mar 29 09:26:00 2004 Input: k:=GF(25); P:=PolynomialRing(k); f:=x^2+4*x+2; F:= ext< k | f >; MinimalPolynomial(1); Output: Magma V2.10-6 Mon Mar 29 2004 09:25:57 on modular [Seed = 3403856730] ------------------------------------- >> F:= ext< k | f >; ^ Runtime error in ext< ... >: Argument is not irreducible $.1 - 1 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee107.uab.es. (158.109.66.107) Time: Mon Mar 29 09:28:39 2004 Input: F:=GF(16); f:=2*alpha^(-3)-alpha^5+(1/(alpha+2))*alpha^6; f; ElementToSequence(f); Output: Magma V2.10-6 Mon Mar 29 2004 09:28:35 on modular [Seed = 3707022890] ------------------------------------- 0 [ 0, 0, 0, 0 ] Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee107.uab.es. (158.109.66.107) Time: Mon Mar 29 09:29:12 2004 Input: F:=GF(16); 2*alpha^(-3)-alpha^5+(1/(alpha+2))*alpha^6; Output: Magma V2.10-6 Mon Mar 29 2004 09:29:09 on modular [Seed = 2794378358] ------------------------------------- 0 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee107.uab.es. (158.109.66.107) Time: Mon Mar 29 09:29:50 2004 Input: F:=GF(16); F![0]; Output: Magma V2.10-6 Mon Mar 29 2004 09:29:47 on modular [Seed = 2843859735] ------------------------------------- 0 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Mon Mar 29 09:39:33 2004 Input: K := GF(2); R := PolynomialRing(K, [7, 6, 4, 1016, 1008, 992, 960, 896, 768, 512]); R; P := [a, b, c, d, e, f, g , x*(a- b*z^2 -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2) +e*(x^(2^4)*z^2 +y^(2^4)*y^(2^2) -y^(2^4)*z^(2^2 +2) +z^(2^4 + 2^3 + 2^2 +2) ) + f*(x^(2^5)*y^(2^2) - x^(2^5)*z^(2^2 +2) - y^(2^5 +2^3)*z^(2) + y^(2^5)*z^( 2^3 + 2^2 +2) -z^(2^5 +2^4 + 2^3 + 2^2 +2) ) + g*(x^(2^6 +2^3) -x^(2^6)*y^(2^3)*z^2 + x^(2^6)*z^(2^3 +2^2 +2) -y^(2^6 + 2^4 + 2^2 ) + y^(2^6 +2^4)*z^(2^2 +2) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2) ) - z^2 *(x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^4 +2^3 +2^2) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^3 +2^2) - y^(2^7)*z^(2^5 + 2^4 +2^3 + 2^2 ) +z^(2^7 +2^6 +2^5 +2^4 + 2^3 + 2^2 ) )- x^(2^7)*y^(2^2 +2^4) ), y*(a- b*z^(2) -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2) +e*(x^(2^4)*z^2 +y^(2^4)*y^(2^2) -y^(2^4)*z^(2^2 +2) +z^(2^4 + 2^3 + 2^2 +2) ) + f*(x^(2^5)*y^(2^2) - x^(2^5)*z^(2^2 +2) - y^(2^5 +2^3)*z^(2) + y^(2^5)*z^( 2^3 + 2^2 +2) -z^(2^5 +2^4 + 2^3 + 2^2 +2) ) + g*(x^(2^6 +2^3) -x^(2^6)*y^(2^3)*z^2 + x^(2^6)*z^(2^3 +2^2 +2) -y^(2^6 + 2^4 + 2^2 ) + y^(2^6 +2^4)*z^(2^2 +2) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2) ) - z^2 *(x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^4 +2^3 +2^2) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^3 +2^2) - y^(2^7)*z^(2^5 + 2^4 +2^3 + 2^2 ) +z^(2^7 +2^6 +2^5 +2^4 + 2^3 + 2^2 ) )- x^(2^7)*y^(2^2 +2^4) ) + x^2 *(b- c*z^(2^2) -d*y^(2^3) +d*z^(2^3 +2^2) -e*x^(2^4) +e*z^(2^4)*y^(2^3) -e*z^(2^4 +2^3 +2^2) + f*( x^(2^5)*z^(2^2) +y^(2^5)*y^(2^3) -y^(2^5)*z^(2^2 +2^3) +z^(2^4 + 2^3 + 2^2 +2^5)) + g*( x^(2^6)*y^(2^3) - x^(2^6)*z^(2^2 +2^3) - y^(2^6 +2^4)*z^(2^2) + y^(2^6)*z^( 2^3 + 2^2 +2^4) -z^(2^5 +2^4 + 2^3 + 2^2 +2^6))+ x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^3 +2^2 +2^4) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^2 +2^3) - y^(2^7)*z^( 2^4 +2^3 + 2^2 +2^5) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2^7) ), z*(a- b*z^(2) -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2) +e*(x^(2^4)*z^2 +y^(2^4)*y^(2^2) -y^(2^4)*z^(2^2 +2) +z^(2^4 + 2^3 + 2^2 +2) ) + f*(x^(2^5)*y^(2^2) - x^(2^5)*z^(2^2 +2) - y^(2^5 +2^3)*z^(2) + y^(2^5)*z^( 2^3 + 2^2 +2) -z^(2^5 +2^4 + 2^3 + 2^2 +2) ) + g*(x^(2^6 +2^3) -x^(2^6)*y^(2^3)*z^2 + x^(2^6)*z^(2^3 +2^2 +2) -y^(2^6 + 2^4 + 2^2 ) + y^(2^6 +2^4)*z^(2^2 +2) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2) ) - z^2 *(x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^4 +2^3 +2^2) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^3 +2^2) - y^(2^7)*z^(2^5 + 2^4 +2^3 + 2^2 ) +z^(2^7 +2^6 +2^5 +2^4 + 2^3 + 2^2 ) )- x^(2^7)*y^(2^2 +2^4) ) + y^2 *(b- c*z^(2^2) -d*y^(2^3) +d*z^(2^3 +2^2) -e*x^(2^4) +e*z^(2^4)*y^(2^3) -e*z^(2^4 +2^3 +2^2) + f*( x^(2^5)*z^(2^2) +y^(2^5)*y^(2^3) -y^(2^5)*z^(2^2 +2^3) +z^(2^4 + 2^3 + 2^2 +2^5)) + g*( x^(2^6)*y^(2^3) - x^(2^6)*z^(2^2 +2^3) - y^(2^6 +2^4)*z^(2^2) + y^(2^6)*z^( 2^3 + 2^2 +2^4) -z^(2^5 +2^4 + 2^3 + 2^2 +2^6))+ x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^3 +2^2 +2^4) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^2 +2^3) - y^(2^7)*z^( 2^4 +2^3 + 2^2 +2^5) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2^7) ) + x^(2^2) *(c- d*z^(2^3) -e*y^(2^4) +e*z^(2^4 +2^3) -f*x^(2^5) +f*z^(2^5)*y^(2^4) -f*z^(2^5 +2^4 +2^3) +g*(x^(2^6)*z^(2^3) +y^(2^6)*y^(2^4) -y^(2^6)*z^(2^4 +2^3) +z^(2^4 + 2^3 + 2^6 +2^5) ) + x^(2^7)*y^(2^4) - x^(2^7)*z^(2^4 +2^3) - y^(2^7 +2^5)*z^(2^3) + y^(2^7)*z^( 2^3 + 2^5 +2^4) -z^(2^5 +2^4 + 2^3 + 2^7 +2^6)) ] ; P; [IsHomogeneous(f): f in P]; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S; Output: Magma V2.10-6 Mon Mar 29 2004 09:39:26 on modular [Seed = 2158556667] ------------------------------------- Graded Polynomial ring of rank 10 over GF(2) Lexicographical Order Variables: x, y, z, a, b, c, d, e, f, g Variable weights: 7 6 4 1016 1008 992 960 896 768 512 [ a, b, c, d, e, f, g, x^145*z^2 + x^129*y^20 + x^129*y^16*z^6 + x^129*z^30 + x^73*g + x^65*y^8*z^2*g + x^65*z^14*g + x^33*y^4*f + x^33*z^6*f + x^17*z^2*e + x^9*d + x*y^168*z^2 + x*y^160*z^14 + x*y^128*z^62 + x*y^84*g + x*y^80*z^6*g + x*y^64*z^30*g + x*y^40*z^2*f + x*y^32*z^14*f + x*y^20*e + x*y^16*z^6*e + x*y^4*z^8*d + x*y^4*c + x*z^254 + x*z^126*g + x*z^62*f + x*z^30*e + x*z^14*d + x*z^6*c + x*z^2*b + x*a, x^146 + x^144*y*z^2 + x^130*y^16*z^4 + x^130*z^28 + x^128*y^21 + x^128*y^17*z^6 + x^128*y*z^30 + x^72*y*g + x^66*y^8*g + x^66*z^12*g + x^64*y^9*z^2*g + x^64*y*z^14*g + x^34*z^4*f + x^32*y^5*f + x^32*y*z^6*f + x^18*e + x^16*y*z^2*e + x^8*y*d + x^2*y^168 + x^2*y^160*z^12 + x^2*y^128*z^60 + x^2*y^80*z^4*g + x^2*y^64*z^28*g + x^2*y^40*f + x^2*y^32*z^12*f + x^2*y^8*z^16*e + x^2*y^8*d + x^2*z^252 + x^2*z^124*g + x^2*z^60*f + x^2*z^28*e + x^2*z^12*d + x^2*z^4*c + x^2*b + y^169*z^2 + y^161*z^14 + y^129*z^62 + y^85*g + y^81*z^6*g + y^65*z^30*g + y^41*z^2*f + y^33*z^14*f + y^21*e + y^17*z^6*e + y^5*z^8*d + y^5*c + y*z^254 + y*z^126*g + y*z^62*f + y*z^30*e + y*z^14*d + y*z^6*c + y*z^2*b + y*a, x^144*y^2 + x^144*z^3 + x^132*y^16 + x^132*z^24 + x^128*y^20*z + x^128*y^18*z^4 + x^128*y^16*z^7 + x^128*y^2*z^28 + x^128*z^31 + x^72*z*g + x^68*z^8*g + x^64*y^10*g + x^64*y^8*z^3*g + x^64*y^2*z^12*g + x^64*z^15*g + x^36*f + x^32*y^4*z*f + x^32*y^2*z^4*f + x^32*z^7*f + x^16*y^2*e + x^16*z^3*e + x^8*z*d + x^4*y^160*z^8 + x^4*y^128*z^56 + x^4*y^80*g + x^4*y^64*z^24*g + x^4*y^16*z^32*f + x^4*y^16*e + x^4*z^248 + x^4*z^120*g + x^4*z^56*f + x^4*z^24*e + x^4*z^8*d + x^4*c + y^170 + y^168*z^3 + y^162*z^12 + y^160*z^15 + y^130*z^60 + y^128*z^63 + y^84*z*g + y^82*z^4*g + y^80*z^7*g + y^66*z^28*g + y^64*z^31*g + y^42*f + y^40*z^3*f + y^34*z^12*f + y^32*z^15*f + y^20*z*e + y^16*z^7*e + y^10*z^16*e + y^10*d + y^4*z^9*d + y^4*z*c + y^2*z^252 + y^2*z^124*g + y^2*z^60*f + y^2*z^28*e + y^2*z^12*d + y^2*z^4*c + y^2*b + z^255 + z^127*g + z^63*f + z^31*e + z^15*d + z^7*c + z^3*b + z*a ] [ true, true, true, true, true, true, true, true, true, true ] 1 [ 2 ] >> V,phi:=VectorSpace(quo); ^ Runtime error in 'VectorSpace': Quotient does not have finite dimension >> S:=[R!(v@@phi ): v in Basis(V)]; ^ User error: Identifier 'V' has not been declared or assigned >> S; ^ User error: Identifier 'S' has not been declared or assigned Total time: 7.889 seconds, Total memory usage: 2.58MB ************** MAGMA ***************** Host aula-b-siee107.uab.es. (158.109.66.107) Time: Mon Mar 29 09:43:33 2004 Input: dos:=GF(2); cuatro:=GF(4); ocho:=GF(8); diezseis:=GF(16); [x:x in dos]; [x:x in cuatro]; [x:x in ocho]; [x:x in diezseis]; Output: Magma V2.10-6 Mon Mar 29 2004 09:43:30 on modular [Seed = 2478564836] ------------------------------------- [ 0, 1 ] [ 1, cuatro.1, cuatro.1^2, 0 ] [ 1, ocho.1, ocho.1^2, ocho.1^3, ocho.1^4, ocho.1^5, ocho.1^6, 0 ] [ 1, diezseis.1, diezseis.1^2, diezseis.1^3, diezseis.1^4, diezseis.1^5, diezseis.1^6, diezseis.1^7, diezseis.1^8, diezseis.1^9, diezseis.1^10, diezseis.1^11, diezseis.1^12, diezseis.1^13, diezseis.1^14, 0 ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Mon Mar 29 09:54:48 2004 Input: K := GF(2); R := PolynomialRing(K, [7, 6, 4, 1016, 1008, 992, 960, 896, 768, 512]); R; P := [a, b, c, d, e, f, g , x*(a- b*z^2 -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2) +e*(x^(2^4)*z^2 +y^(2^4)*y^(2^2) -y^(2^4)*z^(2^2 +2) +z^(2^4 + 2^3 + 2^2 +2) ) + f*(x^(2^5)*y^(2^2) - x^(2^5)*z^(2^2 +2) - y^(2^5 +2^3)*z^(2) + y^(2^5)*z^( 2^3 + 2^2 +2) -z^(2^5 +2^4 + 2^3 + 2^2 +2) ) + g*(x^(2^6 +2^3) -x^(2^6)*y^(2^3)*z^2 + x^(2^6)*z^(2^3 +2^2 +2) -y^(2^6 + 2^4 + 2^2 ) + y^(2^6 +2^4)*z^(2^2 +2) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2) ) - z^2 *(x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^4 +2^3 +2^2) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^3 +2^2) - y^(2^7)*z^(2^5 + 2^4 +2^3 + 2^2 ) +z^(2^7 +2^6 +2^5 +2^4 + 2^3 + 2^2 ) )- x^(2^7)*y^(2^2 +2^4) ), y*(a- b*z^(2) -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2) +e*(x^(2^4)*z^2 +y^(2^4)*y^(2^2) -y^(2^4)*z^(2^2 +2) +z^(2^4 + 2^3 + 2^2 +2) ) + f*(x^(2^5)*y^(2^2) - x^(2^5)*z^(2^2 +2) - y^(2^5 +2^3)*z^(2) + y^(2^5)*z^( 2^3 + 2^2 +2) -z^(2^5 +2^4 + 2^3 + 2^2 +2) ) + g*(x^(2^6 +2^3) -x^(2^6)*y^(2^3)*z^2 + x^(2^6)*z^(2^3 +2^2 +2) -y^(2^6 + 2^4 + 2^2 ) + y^(2^6 +2^4)*z^(2^2 +2) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2) ) - z^2 *(x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^4 +2^3 +2^2) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^3 +2^2) - y^(2^7)*z^(2^5 + 2^4 +2^3 + 2^2 ) +z^(2^7 +2^6 +2^5 +2^4 + 2^3 + 2^2 ) )- x^(2^7)*y^(2^2 +2^4) ) + x^2 *(b- c*z^(2^2) -d*y^(2^3) +d*z^(2^3 +2^2) -e*x^(2^4) +e*z^(2^4)*y^(2^3) -e*z^(2^4 +2^3 +2^2) + f*( x^(2^5)*z^(2^2) +y^(2^5)*y^(2^3) -y^(2^5)*z^(2^2 +2^3) +z^(2^4 + 2^3 + 2^2 +2^5)) + g*( x^(2^6)*y^(2^3) - x^(2^6)*z^(2^2 +2^3) - y^(2^6 +2^4)*z^(2^2) + y^(2^6)*z^( 2^3 + 2^2 +2^4) -z^(2^5 +2^4 + 2^3 + 2^2 +2^6))+ x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^3 +2^2 +2^4) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^2 +2^3) - y^(2^7)*z^( 2^4 +2^3 + 2^2 +2^5) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2^7) ), z*(a- b*z^(2) -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2) +e*(x^(2^4)*z^2 +y^(2^4)*y^(2^2) -y^(2^4)*z^(2^2 +2) +z^(2^4 + 2^3 + 2^2 +2) ) + f*(x^(2^5)*y^(2^2) - x^(2^5)*z^(2^2 +2) - y^(2^5 +2^3)*z^(2) + y^(2^5)*z^( 2^3 + 2^2 +2) -z^(2^5 +2^4 + 2^3 + 2^2 +2) ) + g*(x^(2^6 +2^3) -x^(2^6)*y^(2^3)*z^2 + x^(2^6)*z^(2^3 +2^2 +2) -y^(2^6 + 2^4 + 2^2 ) + y^(2^6 +2^4)*z^(2^2 +2) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2) ) - z^2 *(x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^4 +2^3 +2^2) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^3 +2^2) - y^(2^7)*z^(2^5 + 2^4 +2^3 + 2^2 ) +z^(2^7 +2^6 +2^5 +2^4 + 2^3 + 2^2 ) )- x^(2^7)*y^(2^2 +2^4) ) + y^2 *(b- c*z^(2^2) -d*y^(2^3) +d*z^(2^3 +2^2) -e*x^(2^4) +e*z^(2^4)*y^(2^3) -e*z^(2^4 +2^3 +2^2) + f*( x^(2^5)*z^(2^2) +y^(2^5)*y^(2^3) -y^(2^5)*z^(2^2 +2^3) +z^(2^4 + 2^3 + 2^2 +2^5)) + g*( x^(2^6)*y^(2^3) - x^(2^6)*z^(2^2 +2^3) - y^(2^6 +2^4)*z^(2^2) + y^(2^6)*z^( 2^3 + 2^2 +2^4) -z^(2^5 +2^4 + 2^3 + 2^2 +2^6))+ x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^3 +2^2 +2^4) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^2 +2^3) - y^(2^7)*z^( 2^4 +2^3 + 2^2 +2^5) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2^7) ) + x^(2^2) *(c- d*z^(2^3) -e*y^(2^4) +e*z^(2^4 +2^3) -f*x^(2^5) +f*z^(2^5)*y^(2^4) -f*z^(2^5 +2^4 +2^3) +g*(x^(2^6)*z^(2^3) +y^(2^6)*y^(2^4) -y^(2^6)*z^(2^4 +2^3) +z^(2^4 + 2^3 + 2^6 +2^5) ) + x^(2^7)*y^(2^4) - x^(2^7)*z^(2^4 +2^3) - y^(2^7 +2^5)*z^(2^3) + y^(2^7)*z^( 2^3 + 2^5 +2^4) -z^(2^5 +2^4 + 2^3 + 2^7 +2^6)), y ] ; P; [IsHomogeneous(f): f in P]; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Mar 29 2004 09:54:25 on modular [Seed = 1765872046] ------------------------------------- Graded Polynomial ring of rank 10 over GF(2) Lexicographical Order Variables: x, y, z, a, b, c, d, e, f, g Variable weights: 7 6 4 1016 1008 992 960 896 768 512 [ a, b, c, d, e, f, g, x^145*z^2 + x^129*y^20 + x^129*y^16*z^6 + x^129*z^30 + x^73*g + x^65*y^8*z^2*g + x^65*z^14*g + x^33*y^4*f + x^33*z^6*f + x^17*z^2*e + x^9*d + x*y^168*z^2 + x*y^160*z^14 + x*y^128*z^62 + x*y^84*g + x*y^80*z^6*g + x*y^64*z^30*g + x*y^40*z^2*f + x*y^32*z^14*f + x*y^20*e + x*y^16*z^6*e + x*y^4*z^8*d + x*y^4*c + x*z^254 + x*z^126*g + x*z^62*f + x*z^30*e + x*z^14*d + x*z^6*c + x*z^2*b + x*a, x^146 + x^144*y*z^2 + x^130*y^16*z^4 + x^130*z^28 + x^128*y^21 + x^128*y^17*z^6 + x^128*y*z^30 + x^72*y*g + x^66*y^8*g + x^66*z^12*g + x^64*y^9*z^2*g + x^64*y*z^14*g + x^34*z^4*f + x^32*y^5*f + x^32*y*z^6*f + x^18*e + x^16*y*z^2*e + x^8*y*d + x^2*y^168 + x^2*y^160*z^12 + x^2*y^128*z^60 + x^2*y^80*z^4*g + x^2*y^64*z^28*g + x^2*y^40*f + x^2*y^32*z^12*f + x^2*y^8*z^16*e + x^2*y^8*d + x^2*z^252 + x^2*z^124*g + x^2*z^60*f + x^2*z^28*e + x^2*z^12*d + x^2*z^4*c + x^2*b + y^169*z^2 + y^161*z^14 + y^129*z^62 + y^85*g + y^81*z^6*g + y^65*z^30*g + y^41*z^2*f + y^33*z^14*f + y^21*e + y^17*z^6*e + y^5*z^8*d + y^5*c + y*z^254 + y*z^126*g + y*z^62*f + y*z^30*e + y*z^14*d + y*z^6*c + y*z^2*b + y*a, x^144*y^2 + x^144*z^3 + x^132*y^16 + x^132*z^24 + x^128*y^20*z + x^128*y^18*z^4 + x^128*y^16*z^7 + x^128*y^2*z^28 + x^128*z^31 + x^72*z*g + x^68*z^8*g + x^64*y^10*g + x^64*y^8*z^3*g + x^64*y^2*z^12*g + x^64*z^15*g + x^36*f + x^32*y^4*z*f + x^32*y^2*z^4*f + x^32*z^7*f + x^16*y^2*e + x^16*z^3*e + x^8*z*d + x^4*y^160*z^8 + x^4*y^128*z^56 + x^4*y^80*g + x^4*y^64*z^24*g + x^4*y^16*z^32*f + x^4*y^16*e + x^4*z^248 + x^4*z^120*g + x^4*z^56*f + x^4*z^24*e + x^4*z^8*d + x^4*c + y^170 + y^168*z^3 + y^162*z^12 + y^160*z^15 + y^130*z^60 + y^128*z^63 + y^84*z*g + y^82*z^4*g + y^80*z^7*g + y^66*z^28*g + y^64*z^31*g + y^42*f + y^40*z^3*f + y^34*z^12*f + y^32*z^15*f + y^20*z*e + y^16*z^7*e + y^10*z^16*e + y^10*d + y^4*z^9*d + y^4*z*c + y^2*z^252 + y^2*z^124*g + y^2*z^60*f + y^2*z^28*e + y^2*z^12*d + y^2*z^4*c + y^2*b + z^255 + z^127*g + z^63*f + z^31*e + z^15*d + z^7*c + z^3*b + z*a, y ] [ true, true, true, true, true, true, true, true, true, true, true ] 0 [] Errors: /home/mfd/gomagma: line 2: 9743 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Mon Mar 29 09:55:45 2004 Input: K := GF(2); R := PolynomialRing(K, [7, 6, 4, 1016, 1008, 992, 960, 896, 768, 512]); R; P := [a, b, c, d, e, f, g , x*(a- b*z^2 -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2) +e*(x^(2^4)*z^2 +y^(2^4)*y^(2^2) -y^(2^4)*z^(2^2 +2) +z^(2^4 + 2^3 + 2^2 +2) ) + f*(x^(2^5)*y^(2^2) - x^(2^5)*z^(2^2 +2) - y^(2^5 +2^3)*z^(2) + y^(2^5)*z^( 2^3 + 2^2 +2) -z^(2^5 +2^4 + 2^3 + 2^2 +2) ) + g*(x^(2^6 +2^3) -x^(2^6)*y^(2^3)*z^2 + x^(2^6)*z^(2^3 +2^2 +2) -y^(2^6 + 2^4 + 2^2 ) + y^(2^6 +2^4)*z^(2^2 +2) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2) ) - z^2 *(x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^4 +2^3 +2^2) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^3 +2^2) - y^(2^7)*z^(2^5 + 2^4 +2^3 + 2^2 ) +z^(2^7 +2^6 +2^5 +2^4 + 2^3 + 2^2 ) )- x^(2^7)*y^(2^2 +2^4) ), y*(a- b*z^(2) -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2) +e*(x^(2^4)*z^2 +y^(2^4)*y^(2^2) -y^(2^4)*z^(2^2 +2) +z^(2^4 + 2^3 + 2^2 +2) ) + f*(x^(2^5)*y^(2^2) - x^(2^5)*z^(2^2 +2) - y^(2^5 +2^3)*z^(2) + y^(2^5)*z^( 2^3 + 2^2 +2) -z^(2^5 +2^4 + 2^3 + 2^2 +2) ) + g*(x^(2^6 +2^3) -x^(2^6)*y^(2^3)*z^2 + x^(2^6)*z^(2^3 +2^2 +2) -y^(2^6 + 2^4 + 2^2 ) + y^(2^6 +2^4)*z^(2^2 +2) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2) ) - z^2 *(x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^4 +2^3 +2^2) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^3 +2^2) - y^(2^7)*z^(2^5 + 2^4 +2^3 + 2^2 ) +z^(2^7 +2^6 +2^5 +2^4 + 2^3 + 2^2 ) )- x^(2^7)*y^(2^2 +2^4) ) + x^2 *(b- c*z^(2^2) -d*y^(2^3) +d*z^(2^3 +2^2) -e*x^(2^4) +e*z^(2^4)*y^(2^3) -e*z^(2^4 +2^3 +2^2) + f*( x^(2^5)*z^(2^2) +y^(2^5)*y^(2^3) -y^(2^5)*z^(2^2 +2^3) +z^(2^4 + 2^3 + 2^2 +2^5)) + g*( x^(2^6)*y^(2^3) - x^(2^6)*z^(2^2 +2^3) - y^(2^6 +2^4)*z^(2^2) + y^(2^6)*z^( 2^3 + 2^2 +2^4) -z^(2^5 +2^4 + 2^3 + 2^2 +2^6))+ x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^3 +2^2 +2^4) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^2 +2^3) - y^(2^7)*z^( 2^4 +2^3 + 2^2 +2^5) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2^7) ), z*(a- b*z^(2) -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2) +e*(x^(2^4)*z^2 +y^(2^4)*y^(2^2) -y^(2^4)*z^(2^2 +2) +z^(2^4 + 2^3 + 2^2 +2) ) + f*(x^(2^5)*y^(2^2) - x^(2^5)*z^(2^2 +2) - y^(2^5 +2^3)*z^(2) + y^(2^5)*z^( 2^3 + 2^2 +2) -z^(2^5 +2^4 + 2^3 + 2^2 +2) ) + g*(x^(2^6 +2^3) -x^(2^6)*y^(2^3)*z^2 + x^(2^6)*z^(2^3 +2^2 +2) -y^(2^6 + 2^4 + 2^2 ) + y^(2^6 +2^4)*z^(2^2 +2) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2) ) - z^2 *(x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^4 +2^3 +2^2) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^3 +2^2) - y^(2^7)*z^(2^5 + 2^4 +2^3 + 2^2 ) +z^(2^7 +2^6 +2^5 +2^4 + 2^3 + 2^2 ) )- x^(2^7)*y^(2^2 +2^4) ) + y^2 *(b- c*z^(2^2) -d*y^(2^3) +d*z^(2^3 +2^2) -e*x^(2^4) +e*z^(2^4)*y^(2^3) -e*z^(2^4 +2^3 +2^2) + f*( x^(2^5)*z^(2^2) +y^(2^5)*y^(2^3) -y^(2^5)*z^(2^2 +2^3) +z^(2^4 + 2^3 + 2^2 +2^5)) + g*( x^(2^6)*y^(2^3) - x^(2^6)*z^(2^2 +2^3) - y^(2^6 +2^4)*z^(2^2) + y^(2^6)*z^( 2^3 + 2^2 +2^4) -z^(2^5 +2^4 + 2^3 + 2^2 +2^6))+ x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^3 +2^2 +2^4) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^2 +2^3) - y^(2^7)*z^( 2^4 +2^3 + 2^2 +2^5) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2^7) ) + x^(2^2) *(c- d*z^(2^3) -e*y^(2^4) +e*z^(2^4 +2^3) -f*x^(2^5) +f*z^(2^5)*y^(2^4) -f*z^(2^5 +2^4 +2^3) +g*(x^(2^6)*z^(2^3) +y^(2^6)*y^(2^4) -y^(2^6)*z^(2^4 +2^3) +z^(2^4 + 2^3 + 2^6 +2^5) ) + x^(2^7)*y^(2^4) - x^(2^7)*z^(2^4 +2^3) - y^(2^7 +2^5)*z^(2^3) + y^(2^7)*z^( 2^3 + 2^5 +2^4) -z^(2^5 +2^4 + 2^3 + 2^7 +2^6)), y^2 ] ; P; [IsHomogeneous(f): f in P]; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Mar 29 2004 09:55:22 on modular [Seed = 1231106549] ------------------------------------- Graded Polynomial ring of rank 10 over GF(2) Lexicographical Order Variables: x, y, z, a, b, c, d, e, f, g Variable weights: 7 6 4 1016 1008 992 960 896 768 512 [ a, b, c, d, e, f, g, x^145*z^2 + x^129*y^20 + x^129*y^16*z^6 + x^129*z^30 + x^73*g + x^65*y^8*z^2*g + x^65*z^14*g + x^33*y^4*f + x^33*z^6*f + x^17*z^2*e + x^9*d + x*y^168*z^2 + x*y^160*z^14 + x*y^128*z^62 + x*y^84*g + x*y^80*z^6*g + x*y^64*z^30*g + x*y^40*z^2*f + x*y^32*z^14*f + x*y^20*e + x*y^16*z^6*e + x*y^4*z^8*d + x*y^4*c + x*z^254 + x*z^126*g + x*z^62*f + x*z^30*e + x*z^14*d + x*z^6*c + x*z^2*b + x*a, x^146 + x^144*y*z^2 + x^130*y^16*z^4 + x^130*z^28 + x^128*y^21 + x^128*y^17*z^6 + x^128*y*z^30 + x^72*y*g + x^66*y^8*g + x^66*z^12*g + x^64*y^9*z^2*g + x^64*y*z^14*g + x^34*z^4*f + x^32*y^5*f + x^32*y*z^6*f + x^18*e + x^16*y*z^2*e + x^8*y*d + x^2*y^168 + x^2*y^160*z^12 + x^2*y^128*z^60 + x^2*y^80*z^4*g + x^2*y^64*z^28*g + x^2*y^40*f + x^2*y^32*z^12*f + x^2*y^8*z^16*e + x^2*y^8*d + x^2*z^252 + x^2*z^124*g + x^2*z^60*f + x^2*z^28*e + x^2*z^12*d + x^2*z^4*c + x^2*b + y^169*z^2 + y^161*z^14 + y^129*z^62 + y^85*g + y^81*z^6*g + y^65*z^30*g + y^41*z^2*f + y^33*z^14*f + y^21*e + y^17*z^6*e + y^5*z^8*d + y^5*c + y*z^254 + y*z^126*g + y*z^62*f + y*z^30*e + y*z^14*d + y*z^6*c + y*z^2*b + y*a, x^144*y^2 + x^144*z^3 + x^132*y^16 + x^132*z^24 + x^128*y^20*z + x^128*y^18*z^4 + x^128*y^16*z^7 + x^128*y^2*z^28 + x^128*z^31 + x^72*z*g + x^68*z^8*g + x^64*y^10*g + x^64*y^8*z^3*g + x^64*y^2*z^12*g + x^64*z^15*g + x^36*f + x^32*y^4*z*f + x^32*y^2*z^4*f + x^32*z^7*f + x^16*y^2*e + x^16*z^3*e + x^8*z*d + x^4*y^160*z^8 + x^4*y^128*z^56 + x^4*y^80*g + x^4*y^64*z^24*g + x^4*y^16*z^32*f + x^4*y^16*e + x^4*z^248 + x^4*z^120*g + x^4*z^56*f + x^4*z^24*e + x^4*z^8*d + x^4*c + y^170 + y^168*z^3 + y^162*z^12 + y^160*z^15 + y^130*z^60 + y^128*z^63 + y^84*z*g + y^82*z^4*g + y^80*z^7*g + y^66*z^28*g + y^64*z^31*g + y^42*f + y^40*z^3*f + y^34*z^12*f + y^32*z^15*f + y^20*z*e + y^16*z^7*e + y^10*z^16*e + y^10*d + y^4*z^9*d + y^4*z*c + y^2*z^252 + y^2*z^124*g + y^2*z^60*f + y^2*z^28*e + y^2*z^12*d + y^2*z^4*c + y^2*b + z^255 + z^127*g + z^63*f + z^31*e + z^15*d + z^7*c + z^3*b + z*a, y^2 ] [ true, true, true, true, true, true, true, true, true, true, true ] 0 [] Errors: /home/mfd/gomagma: line 2: 9775 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 09:56:05 2004 Input: test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if ((-a)^n eq 1) then return false; else w=RootOfUnity(n,K); val:={}; wj:=1; r:=k modulo n; for j in [0..n-1] do val:=val join { (wj+a)^l*wj^r }; if (#val neq (j+1)) then return false; end if; wj:=wj*w; end for; end if; return true; end function; q := 125; K := GF(q); R := PolynomialRing(K); test_niederreiter(85,31,1,K,R); Output: Magma V2.10-6 Mon Mar 29 2004 09:56:02 on modular [Seed = 738481480] ------------------------------------- >> r:=k modulo n; ^ User error: bad syntax >> if (#val neq (j+1)) then return false; end if; ^ User error: bad syntax >> wj:=wj*w; ^ User error: Identifier 'wj' has not been declared or assigned >> end for; ^ User error: bad syntax >> end if; ^ User error: bad syntax >> return true; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> test_niederreiter(85,31,1,K,R);; ^ User error: Identifier 'test_niederreiter' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 09:56:24 2004 Input: test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if ((-a)^n eq 1) then return false; else w=RootOfUnity(n,K); val:={}; wj:=1; r:=k mod n; for j in [0..n-1] do val:=val join { (wj+a)^l*wj^r }; if (#val neq (j+1)) then return false; end if; wj:=wj*w; end for; end if; return true; end function; q := 125; K := GF(q); R := PolynomialRing(K); test_niederreiter(85,31,1,K,R); Output: Magma V2.10-6 Mon Mar 29 2004 09:56:20 on modular [Seed = 940589386] ------------------------------------- >> if (#val neq (j+1)) then return false; end if; ^ User error: bad syntax >> wj:=wj*w; ^ User error: Identifier 'wj' has not been declared or assigned >> end for; ^ User error: bad syntax >> end if; ^ User error: bad syntax >> return true; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> test_niederreiter(85,31,1,K,R);; ^ User error: Identifier 'test_niederreiter' has not been declared or assigned Total time: 3.489 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Mon Mar 29 09:56:45 2004 Input: K := GF(2); R := PolynomialRing(K, [7, 6, 4, 1016, 1008, 992, 960, 896, 768, 512]); R; P := [a, b, c, d, e, f, g , x*(a- b*z^2 -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2) +e*(x^(2^4)*z^2 +y^(2^4)*y^(2^2) -y^(2^4)*z^(2^2 +2) +z^(2^4 + 2^3 + 2^2 +2) ) + f*(x^(2^5)*y^(2^2) - x^(2^5)*z^(2^2 +2) - y^(2^5 +2^3)*z^(2) + y^(2^5)*z^( 2^3 + 2^2 +2) -z^(2^5 +2^4 + 2^3 + 2^2 +2) ) + g*(x^(2^6 +2^3) -x^(2^6)*y^(2^3)*z^2 + x^(2^6)*z^(2^3 +2^2 +2) -y^(2^6 + 2^4 + 2^2 ) + y^(2^6 +2^4)*z^(2^2 +2) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2) ) - z^2 *(x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^4 +2^3 +2^2) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^3 +2^2) - y^(2^7)*z^(2^5 + 2^4 +2^3 + 2^2 ) +z^(2^7 +2^6 +2^5 +2^4 + 2^3 + 2^2 ) )- x^(2^7)*y^(2^2 +2^4) ), y*(a- b*z^(2) -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2) +e*(x^(2^4)*z^2 +y^(2^4)*y^(2^2) -y^(2^4)*z^(2^2 +2) +z^(2^4 + 2^3 + 2^2 +2) ) + f*(x^(2^5)*y^(2^2) - x^(2^5)*z^(2^2 +2) - y^(2^5 +2^3)*z^(2) + y^(2^5)*z^( 2^3 + 2^2 +2) -z^(2^5 +2^4 + 2^3 + 2^2 +2) ) + g*(x^(2^6 +2^3) -x^(2^6)*y^(2^3)*z^2 + x^(2^6)*z^(2^3 +2^2 +2) -y^(2^6 + 2^4 + 2^2 ) + y^(2^6 +2^4)*z^(2^2 +2) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2) ) - z^2 *(x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^4 +2^3 +2^2) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^3 +2^2) - y^(2^7)*z^(2^5 + 2^4 +2^3 + 2^2 ) +z^(2^7 +2^6 +2^5 +2^4 + 2^3 + 2^2 ) )- x^(2^7)*y^(2^2 +2^4) ) + x^2 *(b- c*z^(2^2) -d*y^(2^3) +d*z^(2^3 +2^2) -e*x^(2^4) +e*z^(2^4)*y^(2^3) -e*z^(2^4 +2^3 +2^2) + f*( x^(2^5)*z^(2^2) +y^(2^5)*y^(2^3) -y^(2^5)*z^(2^2 +2^3) +z^(2^4 + 2^3 + 2^2 +2^5)) + g*( x^(2^6)*y^(2^3) - x^(2^6)*z^(2^2 +2^3) - y^(2^6 +2^4)*z^(2^2) + y^(2^6)*z^( 2^3 + 2^2 +2^4) -z^(2^5 +2^4 + 2^3 + 2^2 +2^6))+ x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^3 +2^2 +2^4) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^2 +2^3) - y^(2^7)*z^( 2^4 +2^3 + 2^2 +2^5) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2^7) ), z*(a- b*z^(2) -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2) +e*(x^(2^4)*z^2 +y^(2^4)*y^(2^2) -y^(2^4)*z^(2^2 +2) +z^(2^4 + 2^3 + 2^2 +2) ) + f*(x^(2^5)*y^(2^2) - x^(2^5)*z^(2^2 +2) - y^(2^5 +2^3)*z^(2) + y^(2^5)*z^( 2^3 + 2^2 +2) -z^(2^5 +2^4 + 2^3 + 2^2 +2) ) + g*(x^(2^6 +2^3) -x^(2^6)*y^(2^3)*z^2 + x^(2^6)*z^(2^3 +2^2 +2) -y^(2^6 + 2^4 + 2^2 ) + y^(2^6 +2^4)*z^(2^2 +2) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2) ) - z^2 *(x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^4 +2^3 +2^2) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^3 +2^2) - y^(2^7)*z^(2^5 + 2^4 +2^3 + 2^2 ) +z^(2^7 +2^6 +2^5 +2^4 + 2^3 + 2^2 ) )- x^(2^7)*y^(2^2 +2^4) ) + y^2 *(b- c*z^(2^2) -d*y^(2^3) +d*z^(2^3 +2^2) -e*x^(2^4) +e*z^(2^4)*y^(2^3) -e*z^(2^4 +2^3 +2^2) + f*( x^(2^5)*z^(2^2) +y^(2^5)*y^(2^3) -y^(2^5)*z^(2^2 +2^3) +z^(2^4 + 2^3 + 2^2 +2^5)) + g*( x^(2^6)*y^(2^3) - x^(2^6)*z^(2^2 +2^3) - y^(2^6 +2^4)*z^(2^2) + y^(2^6)*z^( 2^3 + 2^2 +2^4) -z^(2^5 +2^4 + 2^3 + 2^2 +2^6))+ x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^3 +2^2 +2^4) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^2 +2^3) - y^(2^7)*z^( 2^4 +2^3 + 2^2 +2^5) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2^7) ) + x^(2^2) *(c- d*z^(2^3) -e*y^(2^4) +e*z^(2^4 +2^3) -f*x^(2^5) +f*z^(2^5)*y^(2^4) -f*z^(2^5 +2^4 +2^3) +g*(x^(2^6)*z^(2^3) +y^(2^6)*y^(2^4) -y^(2^6)*z^(2^4 +2^3) +z^(2^4 + 2^3 + 2^6 +2^5) ) + x^(2^7)*y^(2^4) - x^(2^7)*z^(2^4 +2^3) - y^(2^7 +2^5)*z^(2^3) + y^(2^7)*z^( 2^3 + 2^5 +2^4) -z^(2^5 +2^4 + 2^3 + 2^7 +2^6)), y^3 ] ; P; [IsHomogeneous(f): f in P]; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Mar 29 2004 09:56:21 on modular [Seed = 120553076] ------------------------------------- Graded Polynomial ring of rank 10 over GF(2) Lexicographical Order Variables: x, y, z, a, b, c, d, e, f, g Variable weights: 7 6 4 1016 1008 992 960 896 768 512 [ a, b, c, d, e, f, g, x^145*z^2 + x^129*y^20 + x^129*y^16*z^6 + x^129*z^30 + x^73*g + x^65*y^8*z^2*g + x^65*z^14*g + x^33*y^4*f + x^33*z^6*f + x^17*z^2*e + x^9*d + x*y^168*z^2 + x*y^160*z^14 + x*y^128*z^62 + x*y^84*g + x*y^80*z^6*g + x*y^64*z^30*g + x*y^40*z^2*f + x*y^32*z^14*f + x*y^20*e + x*y^16*z^6*e + x*y^4*z^8*d + x*y^4*c + x*z^254 + x*z^126*g + x*z^62*f + x*z^30*e + x*z^14*d + x*z^6*c + x*z^2*b + x*a, x^146 + x^144*y*z^2 + x^130*y^16*z^4 + x^130*z^28 + x^128*y^21 + x^128*y^17*z^6 + x^128*y*z^30 + x^72*y*g + x^66*y^8*g + x^66*z^12*g + x^64*y^9*z^2*g + x^64*y*z^14*g + x^34*z^4*f + x^32*y^5*f + x^32*y*z^6*f + x^18*e + x^16*y*z^2*e + x^8*y*d + x^2*y^168 + x^2*y^160*z^12 + x^2*y^128*z^60 + x^2*y^80*z^4*g + x^2*y^64*z^28*g + x^2*y^40*f + x^2*y^32*z^12*f + x^2*y^8*z^16*e + x^2*y^8*d + x^2*z^252 + x^2*z^124*g + x^2*z^60*f + x^2*z^28*e + x^2*z^12*d + x^2*z^4*c + x^2*b + y^169*z^2 + y^161*z^14 + y^129*z^62 + y^85*g + y^81*z^6*g + y^65*z^30*g + y^41*z^2*f + y^33*z^14*f + y^21*e + y^17*z^6*e + y^5*z^8*d + y^5*c + y*z^254 + y*z^126*g + y*z^62*f + y*z^30*e + y*z^14*d + y*z^6*c + y*z^2*b + y*a, x^144*y^2 + x^144*z^3 + x^132*y^16 + x^132*z^24 + x^128*y^20*z + x^128*y^18*z^4 + x^128*y^16*z^7 + x^128*y^2*z^28 + x^128*z^31 + x^72*z*g + x^68*z^8*g + x^64*y^10*g + x^64*y^8*z^3*g + x^64*y^2*z^12*g + x^64*z^15*g + x^36*f + x^32*y^4*z*f + x^32*y^2*z^4*f + x^32*z^7*f + x^16*y^2*e + x^16*z^3*e + x^8*z*d + x^4*y^160*z^8 + x^4*y^128*z^56 + x^4*y^80*g + x^4*y^64*z^24*g + x^4*y^16*z^32*f + x^4*y^16*e + x^4*z^248 + x^4*z^120*g + x^4*z^56*f + x^4*z^24*e + x^4*z^8*d + x^4*c + y^170 + y^168*z^3 + y^162*z^12 + y^160*z^15 + y^130*z^60 + y^128*z^63 + y^84*z*g + y^82*z^4*g + y^80*z^7*g + y^66*z^28*g + y^64*z^31*g + y^42*f + y^40*z^3*f + y^34*z^12*f + y^32*z^15*f + y^20*z*e + y^16*z^7*e + y^10*z^16*e + y^10*d + y^4*z^9*d + y^4*z*c + y^2*z^252 + y^2*z^124*g + y^2*z^60*f + y^2*z^28*e + y^2*z^12*d + y^2*z^4*c + y^2*b + z^255 + z^127*g + z^63*f + z^31*e + z^15*d + z^7*c + z^3*b + z*a, y^3 ] [ true, true, true, true, true, true, true, true, true, true, true ] 0 [] Errors: /home/mfd/gomagma: line 2: 9825 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Mon Mar 29 09:57:23 2004 Input: K := GF(2); R := PolynomialRing(K, [7, 6, 4, 1016, 1008, 992, 960, 896, 768, 512]); R; P := [a, b, c, d, e, f, g , x*(a- b*z^2 -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2) +e*(x^(2^4)*z^2 +y^(2^4)*y^(2^2) -y^(2^4)*z^(2^2 +2) +z^(2^4 + 2^3 + 2^2 +2) ) + f*(x^(2^5)*y^(2^2) - x^(2^5)*z^(2^2 +2) - y^(2^5 +2^3)*z^(2) + y^(2^5)*z^( 2^3 + 2^2 +2) -z^(2^5 +2^4 + 2^3 + 2^2 +2) ) + g*(x^(2^6 +2^3) -x^(2^6)*y^(2^3)*z^2 + x^(2^6)*z^(2^3 +2^2 +2) -y^(2^6 + 2^4 + 2^2 ) + y^(2^6 +2^4)*z^(2^2 +2) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2) ) - z^2 *(x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^4 +2^3 +2^2) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^3 +2^2) - y^(2^7)*z^(2^5 + 2^4 +2^3 + 2^2 ) +z^(2^7 +2^6 +2^5 +2^4 + 2^3 + 2^2 ) )- x^(2^7)*y^(2^2 +2^4) ), y*(a- b*z^(2) -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2) +e*(x^(2^4)*z^2 +y^(2^4)*y^(2^2) -y^(2^4)*z^(2^2 +2) +z^(2^4 + 2^3 + 2^2 +2) ) + f*(x^(2^5)*y^(2^2) - x^(2^5)*z^(2^2 +2) - y^(2^5 +2^3)*z^(2) + y^(2^5)*z^( 2^3 + 2^2 +2) -z^(2^5 +2^4 + 2^3 + 2^2 +2) ) + g*(x^(2^6 +2^3) -x^(2^6)*y^(2^3)*z^2 + x^(2^6)*z^(2^3 +2^2 +2) -y^(2^6 + 2^4 + 2^2 ) + y^(2^6 +2^4)*z^(2^2 +2) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2) ) - z^2 *(x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^4 +2^3 +2^2) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^3 +2^2) - y^(2^7)*z^(2^5 + 2^4 +2^3 + 2^2 ) +z^(2^7 +2^6 +2^5 +2^4 + 2^3 + 2^2 ) )- x^(2^7)*y^(2^2 +2^4) ) + x^2 *(b- c*z^(2^2) -d*y^(2^3) +d*z^(2^3 +2^2) -e*x^(2^4) +e*z^(2^4)*y^(2^3) -e*z^(2^4 +2^3 +2^2) + f*( x^(2^5)*z^(2^2) +y^(2^5)*y^(2^3) -y^(2^5)*z^(2^2 +2^3) +z^(2^4 + 2^3 + 2^2 +2^5)) + g*( x^(2^6)*y^(2^3) - x^(2^6)*z^(2^2 +2^3) - y^(2^6 +2^4)*z^(2^2) + y^(2^6)*z^( 2^3 + 2^2 +2^4) -z^(2^5 +2^4 + 2^3 + 2^2 +2^6))+ x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^3 +2^2 +2^4) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^2 +2^3) - y^(2^7)*z^( 2^4 +2^3 + 2^2 +2^5) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2^7) ), z*(a- b*z^(2) -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2) +e*(x^(2^4)*z^2 +y^(2^4)*y^(2^2) -y^(2^4)*z^(2^2 +2) +z^(2^4 + 2^3 + 2^2 +2) ) + f*(x^(2^5)*y^(2^2) - x^(2^5)*z^(2^2 +2) - y^(2^5 +2^3)*z^(2) + y^(2^5)*z^( 2^3 + 2^2 +2) -z^(2^5 +2^4 + 2^3 + 2^2 +2) ) + g*(x^(2^6 +2^3) -x^(2^6)*y^(2^3)*z^2 + x^(2^6)*z^(2^3 +2^2 +2) -y^(2^6 + 2^4 + 2^2 ) + y^(2^6 +2^4)*z^(2^2 +2) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2) ) - z^2 *(x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^4 +2^3 +2^2) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^3 +2^2) - y^(2^7)*z^(2^5 + 2^4 +2^3 + 2^2 ) +z^(2^7 +2^6 +2^5 +2^4 + 2^3 + 2^2 ) )- x^(2^7)*y^(2^2 +2^4) ) + y^2 *(b- c*z^(2^2) -d*y^(2^3) +d*z^(2^3 +2^2) -e*x^(2^4) +e*z^(2^4)*y^(2^3) -e*z^(2^4 +2^3 +2^2) + f*( x^(2^5)*z^(2^2) +y^(2^5)*y^(2^3) -y^(2^5)*z^(2^2 +2^3) +z^(2^4 + 2^3 + 2^2 +2^5)) + g*( x^(2^6)*y^(2^3) - x^(2^6)*z^(2^2 +2^3) - y^(2^6 +2^4)*z^(2^2) + y^(2^6)*z^( 2^3 + 2^2 +2^4) -z^(2^5 +2^4 + 2^3 + 2^2 +2^6))+ x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^3 +2^2 +2^4) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^2 +2^3) - y^(2^7)*z^( 2^4 +2^3 + 2^2 +2^5) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2^7) ) + x^(2^2) *(c- d*z^(2^3) -e*y^(2^4) +e*z^(2^4 +2^3) -f*x^(2^5) +f*z^(2^5)*y^(2^4) -f*z^(2^5 +2^4 +2^3) +g*(x^(2^6)*z^(2^3) +y^(2^6)*y^(2^4) -y^(2^6)*z^(2^4 +2^3) +z^(2^4 + 2^3 + 2^6 +2^5) ) + x^(2^7)*y^(2^4) - x^(2^7)*z^(2^4 +2^3) - y^(2^7 +2^5)*z^(2^3) + y^(2^7)*z^( 2^3 + 2^5 +2^4) -z^(2^5 +2^4 + 2^3 + 2^7 +2^6)), y^4 ] ; P; [IsHomogeneous(f): f in P]; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Mar 29 2004 09:57:00 on modular [Seed = 3838614974] ------------------------------------- Graded Polynomial ring of rank 10 over GF(2) Lexicographical Order Variables: x, y, z, a, b, c, d, e, f, g Variable weights: 7 6 4 1016 1008 992 960 896 768 512 [ a, b, c, d, e, f, g, x^145*z^2 + x^129*y^20 + x^129*y^16*z^6 + x^129*z^30 + x^73*g + x^65*y^8*z^2*g + x^65*z^14*g + x^33*y^4*f + x^33*z^6*f + x^17*z^2*e + x^9*d + x*y^168*z^2 + x*y^160*z^14 + x*y^128*z^62 + x*y^84*g + x*y^80*z^6*g + x*y^64*z^30*g + x*y^40*z^2*f + x*y^32*z^14*f + x*y^20*e + x*y^16*z^6*e + x*y^4*z^8*d + x*y^4*c + x*z^254 + x*z^126*g + x*z^62*f + x*z^30*e + x*z^14*d + x*z^6*c + x*z^2*b + x*a, x^146 + x^144*y*z^2 + x^130*y^16*z^4 + x^130*z^28 + x^128*y^21 + x^128*y^17*z^6 + x^128*y*z^30 + x^72*y*g + x^66*y^8*g + x^66*z^12*g + x^64*y^9*z^2*g + x^64*y*z^14*g + x^34*z^4*f + x^32*y^5*f + x^32*y*z^6*f + x^18*e + x^16*y*z^2*e + x^8*y*d + x^2*y^168 + x^2*y^160*z^12 + x^2*y^128*z^60 + x^2*y^80*z^4*g + x^2*y^64*z^28*g + x^2*y^40*f + x^2*y^32*z^12*f + x^2*y^8*z^16*e + x^2*y^8*d + x^2*z^252 + x^2*z^124*g + x^2*z^60*f + x^2*z^28*e + x^2*z^12*d + x^2*z^4*c + x^2*b + y^169*z^2 + y^161*z^14 + y^129*z^62 + y^85*g + y^81*z^6*g + y^65*z^30*g + y^41*z^2*f + y^33*z^14*f + y^21*e + y^17*z^6*e + y^5*z^8*d + y^5*c + y*z^254 + y*z^126*g + y*z^62*f + y*z^30*e + y*z^14*d + y*z^6*c + y*z^2*b + y*a, x^144*y^2 + x^144*z^3 + x^132*y^16 + x^132*z^24 + x^128*y^20*z + x^128*y^18*z^4 + x^128*y^16*z^7 + x^128*y^2*z^28 + x^128*z^31 + x^72*z*g + x^68*z^8*g + x^64*y^10*g + x^64*y^8*z^3*g + x^64*y^2*z^12*g + x^64*z^15*g + x^36*f + x^32*y^4*z*f + x^32*y^2*z^4*f + x^32*z^7*f + x^16*y^2*e + x^16*z^3*e + x^8*z*d + x^4*y^160*z^8 + x^4*y^128*z^56 + x^4*y^80*g + x^4*y^64*z^24*g + x^4*y^16*z^32*f + x^4*y^16*e + x^4*z^248 + x^4*z^120*g + x^4*z^56*f + x^4*z^24*e + x^4*z^8*d + x^4*c + y^170 + y^168*z^3 + y^162*z^12 + y^160*z^15 + y^130*z^60 + y^128*z^63 + y^84*z*g + y^82*z^4*g + y^80*z^7*g + y^66*z^28*g + y^64*z^31*g + y^42*f + y^40*z^3*f + y^34*z^12*f + y^32*z^15*f + y^20*z*e + y^16*z^7*e + y^10*z^16*e + y^10*d + y^4*z^9*d + y^4*z*c + y^2*z^252 + y^2*z^124*g + y^2*z^60*f + y^2*z^28*e + y^2*z^12*d + y^2*z^4*c + y^2*b + z^255 + z^127*g + z^63*f + z^31*e + z^15*d + z^7*c + z^3*b + z*a, y^4 ] [ true, true, true, true, true, true, true, true, true, true, true ] 0 [] Errors: /home/mfd/gomagma: line 2: 9858 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 09:57:36 2004 Input: test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if ((-a)^n eq 1) then return false; else w:=RootOfUnity(n,K); val:={}; wj:=1; r:=k mod n; for j in [0..n-1] do val:=val join { (wj+a)^l*wj^r }; if (#val neq (j+1)) then return false; end if; wj:=wj*w; end for; end if; return true; end function; q := 125; K := GF(q); R := PolynomialRing(K); test_niederreiter(85,31,1,K,R); Output: Magma V2.10-6 Mon Mar 29 2004 09:57:33 on modular [Seed = 3904934352] ------------------------------------- >> if (#val neq (j+1)) then return false; end if; ^ User error: bad syntax >> wj:=wj*w; ^ User error: Identifier 'wj' has not been declared or assigned >> end for; ^ User error: bad syntax >> end if; ^ User error: bad syntax >> return true; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> test_niederreiter(85,31,1,K,R);; ^ User error: Identifier 'test_niederreiter' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Mon Mar 29 09:58:01 2004 Input: K := GF(2); R := PolynomialRing(K, [7, 6, 4, 1016, 1008, 992, 960, 896, 768, 512]); R; P := [a, b, c, d, e, f, g , x*(a- b*z^2 -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2) +e*(x^(2^4)*z^2 +y^(2^4)*y^(2^2) -y^(2^4)*z^(2^2 +2) +z^(2^4 + 2^3 + 2^2 +2) ) + f*(x^(2^5)*y^(2^2) - x^(2^5)*z^(2^2 +2) - y^(2^5 +2^3)*z^(2) + y^(2^5)*z^( 2^3 + 2^2 +2) -z^(2^5 +2^4 + 2^3 + 2^2 +2) ) + g*(x^(2^6 +2^3) -x^(2^6)*y^(2^3)*z^2 + x^(2^6)*z^(2^3 +2^2 +2) -y^(2^6 + 2^4 + 2^2 ) + y^(2^6 +2^4)*z^(2^2 +2) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2) ) - z^2 *(x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^4 +2^3 +2^2) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^3 +2^2) - y^(2^7)*z^(2^5 + 2^4 +2^3 + 2^2 ) +z^(2^7 +2^6 +2^5 +2^4 + 2^3 + 2^2 ) )- x^(2^7)*y^(2^2 +2^4) ), y*(a- b*z^(2) -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2) +e*(x^(2^4)*z^2 +y^(2^4)*y^(2^2) -y^(2^4)*z^(2^2 +2) +z^(2^4 + 2^3 + 2^2 +2) ) + f*(x^(2^5)*y^(2^2) - x^(2^5)*z^(2^2 +2) - y^(2^5 +2^3)*z^(2) + y^(2^5)*z^( 2^3 + 2^2 +2) -z^(2^5 +2^4 + 2^3 + 2^2 +2) ) + g*(x^(2^6 +2^3) -x^(2^6)*y^(2^3)*z^2 + x^(2^6)*z^(2^3 +2^2 +2) -y^(2^6 + 2^4 + 2^2 ) + y^(2^6 +2^4)*z^(2^2 +2) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2) ) - z^2 *(x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^4 +2^3 +2^2) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^3 +2^2) - y^(2^7)*z^(2^5 + 2^4 +2^3 + 2^2 ) +z^(2^7 +2^6 +2^5 +2^4 + 2^3 + 2^2 ) )- x^(2^7)*y^(2^2 +2^4) ) + x^2 *(b- c*z^(2^2) -d*y^(2^3) +d*z^(2^3 +2^2) -e*x^(2^4) +e*z^(2^4)*y^(2^3) -e*z^(2^4 +2^3 +2^2) + f*( x^(2^5)*z^(2^2) +y^(2^5)*y^(2^3) -y^(2^5)*z^(2^2 +2^3) +z^(2^4 + 2^3 + 2^2 +2^5)) + g*( x^(2^6)*y^(2^3) - x^(2^6)*z^(2^2 +2^3) - y^(2^6 +2^4)*z^(2^2) + y^(2^6)*z^( 2^3 + 2^2 +2^4) -z^(2^5 +2^4 + 2^3 + 2^2 +2^6))+ x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^3 +2^2 +2^4) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^2 +2^3) - y^(2^7)*z^( 2^4 +2^3 + 2^2 +2^5) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2^7) ), z*(a- b*z^(2) -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2) +e*(x^(2^4)*z^2 +y^(2^4)*y^(2^2) -y^(2^4)*z^(2^2 +2) +z^(2^4 + 2^3 + 2^2 +2) ) + f*(x^(2^5)*y^(2^2) - x^(2^5)*z^(2^2 +2) - y^(2^5 +2^3)*z^(2) + y^(2^5)*z^( 2^3 + 2^2 +2) -z^(2^5 +2^4 + 2^3 + 2^2 +2) ) + g*(x^(2^6 +2^3) -x^(2^6)*y^(2^3)*z^2 + x^(2^6)*z^(2^3 +2^2 +2) -y^(2^6 + 2^4 + 2^2 ) + y^(2^6 +2^4)*z^(2^2 +2) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2) ) - z^2 *(x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^4 +2^3 +2^2) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^3 +2^2) - y^(2^7)*z^(2^5 + 2^4 +2^3 + 2^2 ) +z^(2^7 +2^6 +2^5 +2^4 + 2^3 + 2^2 ) )- x^(2^7)*y^(2^2 +2^4) ) + y^2 *(b- c*z^(2^2) -d*y^(2^3) +d*z^(2^3 +2^2) -e*x^(2^4) +e*z^(2^4)*y^(2^3) -e*z^(2^4 +2^3 +2^2) + f*( x^(2^5)*z^(2^2) +y^(2^5)*y^(2^3) -y^(2^5)*z^(2^2 +2^3) +z^(2^4 + 2^3 + 2^2 +2^5)) + g*( x^(2^6)*y^(2^3) - x^(2^6)*z^(2^2 +2^3) - y^(2^6 +2^4)*z^(2^2) + y^(2^6)*z^( 2^3 + 2^2 +2^4) -z^(2^5 +2^4 + 2^3 + 2^2 +2^6))+ x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^3 +2^2 +2^4) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^2 +2^3) - y^(2^7)*z^( 2^4 +2^3 + 2^2 +2^5) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2^7) ) + x^(2^2) *(c- d*z^(2^3) -e*y^(2^4) +e*z^(2^4 +2^3) -f*x^(2^5) +f*z^(2^5)*y^(2^4) -f*z^(2^5 +2^4 +2^3) +g*(x^(2^6)*z^(2^3) +y^(2^6)*y^(2^4) -y^(2^6)*z^(2^4 +2^3) +z^(2^4 + 2^3 + 2^6 +2^5) ) + x^(2^7)*y^(2^4) - x^(2^7)*z^(2^4 +2^3) - y^(2^7 +2^5)*z^(2^3) + y^(2^7)*z^( 2^3 + 2^5 +2^4) -z^(2^5 +2^4 + 2^3 + 2^7 +2^6)), y^10 ] ; P; [IsHomogeneous(f): f in P]; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Mar 29 2004 09:57:38 on modular [Seed = 4040722932] ------------------------------------- Graded Polynomial ring of rank 10 over GF(2) Lexicographical Order Variables: x, y, z, a, b, c, d, e, f, g Variable weights: 7 6 4 1016 1008 992 960 896 768 512 [ a, b, c, d, e, f, g, x^145*z^2 + x^129*y^20 + x^129*y^16*z^6 + x^129*z^30 + x^73*g + x^65*y^8*z^2*g + x^65*z^14*g + x^33*y^4*f + x^33*z^6*f + x^17*z^2*e + x^9*d + x*y^168*z^2 + x*y^160*z^14 + x*y^128*z^62 + x*y^84*g + x*y^80*z^6*g + x*y^64*z^30*g + x*y^40*z^2*f + x*y^32*z^14*f + x*y^20*e + x*y^16*z^6*e + x*y^4*z^8*d + x*y^4*c + x*z^254 + x*z^126*g + x*z^62*f + x*z^30*e + x*z^14*d + x*z^6*c + x*z^2*b + x*a, x^146 + x^144*y*z^2 + x^130*y^16*z^4 + x^130*z^28 + x^128*y^21 + x^128*y^17*z^6 + x^128*y*z^30 + x^72*y*g + x^66*y^8*g + x^66*z^12*g + x^64*y^9*z^2*g + x^64*y*z^14*g + x^34*z^4*f + x^32*y^5*f + x^32*y*z^6*f + x^18*e + x^16*y*z^2*e + x^8*y*d + x^2*y^168 + x^2*y^160*z^12 + x^2*y^128*z^60 + x^2*y^80*z^4*g + x^2*y^64*z^28*g + x^2*y^40*f + x^2*y^32*z^12*f + x^2*y^8*z^16*e + x^2*y^8*d + x^2*z^252 + x^2*z^124*g + x^2*z^60*f + x^2*z^28*e + x^2*z^12*d + x^2*z^4*c + x^2*b + y^169*z^2 + y^161*z^14 + y^129*z^62 + y^85*g + y^81*z^6*g + y^65*z^30*g + y^41*z^2*f + y^33*z^14*f + y^21*e + y^17*z^6*e + y^5*z^8*d + y^5*c + y*z^254 + y*z^126*g + y*z^62*f + y*z^30*e + y*z^14*d + y*z^6*c + y*z^2*b + y*a, x^144*y^2 + x^144*z^3 + x^132*y^16 + x^132*z^24 + x^128*y^20*z + x^128*y^18*z^4 + x^128*y^16*z^7 + x^128*y^2*z^28 + x^128*z^31 + x^72*z*g + x^68*z^8*g + x^64*y^10*g + x^64*y^8*z^3*g + x^64*y^2*z^12*g + x^64*z^15*g + x^36*f + x^32*y^4*z*f + x^32*y^2*z^4*f + x^32*z^7*f + x^16*y^2*e + x^16*z^3*e + x^8*z*d + x^4*y^160*z^8 + x^4*y^128*z^56 + x^4*y^80*g + x^4*y^64*z^24*g + x^4*y^16*z^32*f + x^4*y^16*e + x^4*z^248 + x^4*z^120*g + x^4*z^56*f + x^4*z^24*e + x^4*z^8*d + x^4*c + y^170 + y^168*z^3 + y^162*z^12 + y^160*z^15 + y^130*z^60 + y^128*z^63 + y^84*z*g + y^82*z^4*g + y^80*z^7*g + y^66*z^28*g + y^64*z^31*g + y^42*f + y^40*z^3*f + y^34*z^12*f + y^32*z^15*f + y^20*z*e + y^16*z^7*e + y^10*z^16*e + y^10*d + y^4*z^9*d + y^4*z*c + y^2*z^252 + y^2*z^124*g + y^2*z^60*f + y^2*z^28*e + y^2*z^12*d + y^2*z^4*c + y^2*b + z^255 + z^127*g + z^63*f + z^31*e + z^15*d + z^7*c + z^3*b + z*a, y^10 ] [ true, true, true, true, true, true, true, true, true, true, true ] 0 [] Errors: /home/mfd/gomagma: line 2: 9878 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host aula-b-siee107.uab.es. (158.109.66.107) Time: Mon Mar 29 09:58:15 2004 Input: k:=GF(25); P:=PolynomialRing(k); Output: Magma V2.10-6 Mon Mar 29 2004 09:58:12 on modular [Seed = 3403854632] ------------------------------------- Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Mon Mar 29 09:58:22 2004 Input: K := GF(2); R := PolynomialRing(K, [7, 6, 4, 1016, 1008, 992, 960, 896, 768, 512]); R; P := [a, b, c, d, e, f, g , x*(a- b*z^2 -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2) +e*(x^(2^4)*z^2 +y^(2^4)*y^(2^2) -y^(2^4)*z^(2^2 +2) +z^(2^4 + 2^3 + 2^2 +2) ) + f*(x^(2^5)*y^(2^2) - x^(2^5)*z^(2^2 +2) - y^(2^5 +2^3)*z^(2) + y^(2^5)*z^( 2^3 + 2^2 +2) -z^(2^5 +2^4 + 2^3 + 2^2 +2) ) + g*(x^(2^6 +2^3) -x^(2^6)*y^(2^3)*z^2 + x^(2^6)*z^(2^3 +2^2 +2) -y^(2^6 + 2^4 + 2^2 ) + y^(2^6 +2^4)*z^(2^2 +2) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2) ) - z^2 *(x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^4 +2^3 +2^2) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^3 +2^2) - y^(2^7)*z^(2^5 + 2^4 +2^3 + 2^2 ) +z^(2^7 +2^6 +2^5 +2^4 + 2^3 + 2^2 ) )- x^(2^7)*y^(2^2 +2^4) ), y*(a- b*z^(2) -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2) +e*(x^(2^4)*z^2 +y^(2^4)*y^(2^2) -y^(2^4)*z^(2^2 +2) +z^(2^4 + 2^3 + 2^2 +2) ) + f*(x^(2^5)*y^(2^2) - x^(2^5)*z^(2^2 +2) - y^(2^5 +2^3)*z^(2) + y^(2^5)*z^( 2^3 + 2^2 +2) -z^(2^5 +2^4 + 2^3 + 2^2 +2) ) + g*(x^(2^6 +2^3) -x^(2^6)*y^(2^3)*z^2 + x^(2^6)*z^(2^3 +2^2 +2) -y^(2^6 + 2^4 + 2^2 ) + y^(2^6 +2^4)*z^(2^2 +2) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2) ) - z^2 *(x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^4 +2^3 +2^2) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^3 +2^2) - y^(2^7)*z^(2^5 + 2^4 +2^3 + 2^2 ) +z^(2^7 +2^6 +2^5 +2^4 + 2^3 + 2^2 ) )- x^(2^7)*y^(2^2 +2^4) ) + x^2 *(b- c*z^(2^2) -d*y^(2^3) +d*z^(2^3 +2^2) -e*x^(2^4) +e*z^(2^4)*y^(2^3) -e*z^(2^4 +2^3 +2^2) + f*( x^(2^5)*z^(2^2) +y^(2^5)*y^(2^3) -y^(2^5)*z^(2^2 +2^3) +z^(2^4 + 2^3 + 2^2 +2^5)) + g*( x^(2^6)*y^(2^3) - x^(2^6)*z^(2^2 +2^3) - y^(2^6 +2^4)*z^(2^2) + y^(2^6)*z^( 2^3 + 2^2 +2^4) -z^(2^5 +2^4 + 2^3 + 2^2 +2^6))+ x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^3 +2^2 +2^4) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^2 +2^3) - y^(2^7)*z^( 2^4 +2^3 + 2^2 +2^5) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2^7) ), z*(a- b*z^(2) -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2) +e*(x^(2^4)*z^2 +y^(2^4)*y^(2^2) -y^(2^4)*z^(2^2 +2) +z^(2^4 + 2^3 + 2^2 +2) ) + f*(x^(2^5)*y^(2^2) - x^(2^5)*z^(2^2 +2) - y^(2^5 +2^3)*z^(2) + y^(2^5)*z^( 2^3 + 2^2 +2) -z^(2^5 +2^4 + 2^3 + 2^2 +2) ) + g*(x^(2^6 +2^3) -x^(2^6)*y^(2^3)*z^2 + x^(2^6)*z^(2^3 +2^2 +2) -y^(2^6 + 2^4 + 2^2 ) + y^(2^6 +2^4)*z^(2^2 +2) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2) ) - z^2 *(x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^4 +2^3 +2^2) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^3 +2^2) - y^(2^7)*z^(2^5 + 2^4 +2^3 + 2^2 ) +z^(2^7 +2^6 +2^5 +2^4 + 2^3 + 2^2 ) )- x^(2^7)*y^(2^2 +2^4) ) + y^2 *(b- c*z^(2^2) -d*y^(2^3) +d*z^(2^3 +2^2) -e*x^(2^4) +e*z^(2^4)*y^(2^3) -e*z^(2^4 +2^3 +2^2) + f*( x^(2^5)*z^(2^2) +y^(2^5)*y^(2^3) -y^(2^5)*z^(2^2 +2^3) +z^(2^4 + 2^3 + 2^2 +2^5)) + g*( x^(2^6)*y^(2^3) - x^(2^6)*z^(2^2 +2^3) - y^(2^6 +2^4)*z^(2^2) + y^(2^6)*z^( 2^3 + 2^2 +2^4) -z^(2^5 +2^4 + 2^3 + 2^2 +2^6))+ x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^3 +2^2 +2^4) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^2 +2^3) - y^(2^7)*z^( 2^4 +2^3 + 2^2 +2^5) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2^7) ) + x^(2^2) *(c- d*z^(2^3) -e*y^(2^4) +e*z^(2^4 +2^3) -f*x^(2^5) +f*z^(2^5)*y^(2^4) -f*z^(2^5 +2^4 +2^3) +g*(x^(2^6)*z^(2^3) +y^(2^6)*y^(2^4) -y^(2^6)*z^(2^4 +2^3) +z^(2^4 + 2^3 + 2^6 +2^5) ) + x^(2^7)*y^(2^4) - x^(2^7)*z^(2^4 +2^3) - y^(2^7 +2^5)*z^(2^3) + y^(2^7)*z^( 2^3 + 2^5 +2^4) -z^(2^5 +2^4 + 2^3 + 2^7 +2^6)), x*y^10 ] ; P; [IsHomogeneous(f): f in P]; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S; Output: Magma V2.10-6 Mon Mar 29 2004 09:58:19 on modular [Seed = 3556485694] ------------------------------------- Graded Polynomial ring of rank 10 over GF(2) Lexicographical Order Variables: x, y, z, a, b, c, d, e, f, g Variable weights: 7 6 4 1016 1008 992 960 896 768 512 [ a, b, c, d, e, f, g, x^145*z^2 + x^129*y^20 + x^129*y^16*z^6 + x^129*z^30 + x^73*g + x^65*y^8*z^2*g + x^65*z^14*g + x^33*y^4*f + x^33*z^6*f + x^17*z^2*e + x^9*d + x*y^168*z^2 + x*y^160*z^14 + x*y^128*z^62 + x*y^84*g + x*y^80*z^6*g + x*y^64*z^30*g + x*y^40*z^2*f + x*y^32*z^14*f + x*y^20*e + x*y^16*z^6*e + x*y^4*z^8*d + x*y^4*c + x*z^254 + x*z^126*g + x*z^62*f + x*z^30*e + x*z^14*d + x*z^6*c + x*z^2*b + x*a, x^146 + x^144*y*z^2 + x^130*y^16*z^4 + x^130*z^28 + x^128*y^21 + x^128*y^17*z^6 + x^128*y*z^30 + x^72*y*g + x^66*y^8*g + x^66*z^12*g + x^64*y^9*z^2*g + x^64*y*z^14*g + x^34*z^4*f + x^32*y^5*f + x^32*y*z^6*f + x^18*e + x^16*y*z^2*e + x^8*y*d + x^2*y^168 + x^2*y^160*z^12 + x^2*y^128*z^60 + x^2*y^80*z^4*g + x^2*y^64*z^28*g + x^2*y^40*f + x^2*y^32*z^12*f + x^2*y^8*z^16*e + x^2*y^8*d + x^2*z^252 + x^2*z^124*g + x^2*z^60*f + x^2*z^28*e + x^2*z^12*d + x^2*z^4*c + x^2*b + y^169*z^2 + y^161*z^14 + y^129*z^62 + y^85*g + y^81*z^6*g + y^65*z^30*g + y^41*z^2*f + y^33*z^14*f + y^21*e + y^17*z^6*e + y^5*z^8*d + y^5*c + y*z^254 + y*z^126*g + y*z^62*f + y*z^30*e + y*z^14*d + y*z^6*c + y*z^2*b + y*a, x^144*y^2 + x^144*z^3 + x^132*y^16 + x^132*z^24 + x^128*y^20*z + x^128*y^18*z^4 + x^128*y^16*z^7 + x^128*y^2*z^28 + x^128*z^31 + x^72*z*g + x^68*z^8*g + x^64*y^10*g + x^64*y^8*z^3*g + x^64*y^2*z^12*g + x^64*z^15*g + x^36*f + x^32*y^4*z*f + x^32*y^2*z^4*f + x^32*z^7*f + x^16*y^2*e + x^16*z^3*e + x^8*z*d + x^4*y^160*z^8 + x^4*y^128*z^56 + x^4*y^80*g + x^4*y^64*z^24*g + x^4*y^16*z^32*f + x^4*y^16*e + x^4*z^248 + x^4*z^120*g + x^4*z^56*f + x^4*z^24*e + x^4*z^8*d + x^4*c + y^170 + y^168*z^3 + y^162*z^12 + y^160*z^15 + y^130*z^60 + y^128*z^63 + y^84*z*g + y^82*z^4*g + y^80*z^7*g + y^66*z^28*g + y^64*z^31*g + y^42*f + y^40*z^3*f + y^34*z^12*f + y^32*z^15*f + y^20*z*e + y^16*z^7*e + y^10*z^16*e + y^10*d + y^4*z^9*d + y^4*z*c + y^2*z^252 + y^2*z^124*g + y^2*z^60*f + y^2*z^28*e + y^2*z^12*d + y^2*z^4*c + y^2*b + z^255 + z^127*g + z^63*f + z^31*e + z^15*d + z^7*c + z^3*b + z*a, x*y^10 ] [ true, true, true, true, true, true, true, true, true, true, true ] 1 [ 2 ] >> V,phi:=VectorSpace(quo); ^ Runtime error in 'VectorSpace': Quotient does not have finite dimension >> S:=[R!(v@@phi ): v in Basis(V)]; ^ User error: Identifier 'V' has not been declared or assigned >> S; ^ User error: Identifier 'S' has not been declared or assigned Total time: 3.519 seconds, Total memory usage: 2.32MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 09:58:23 2004 Input: test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if ((-a)^n eq 1) then return false; else w:=RootOfUnity(n,K); val:={}; wj:=1; r:=k mod n; for j in [0..n-1] do val:=val join { (wj+a)^l*wj^r }; print #val; if (#val neq (j+1)) then return false; end if; wj:=wj*w; end for; end if; return true; end function; q := 125; K := GF(q); R := PolynomialRing(K); test_niederreiter(85,31,1,K,R); Output: Magma V2.10-6 Mon Mar 29 2004 09:58:20 on modular [Seed = 3740706612] ------------------------------------- >> if (#val neq (j+1)) then return false; end if; ^ User error: bad syntax >> wj:=wj*w; ^ User error: Identifier 'wj' has not been declared or assigned >> end for; ^ User error: bad syntax >> end if; ^ User error: bad syntax >> return true; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> test_niederreiter(85,31,1,K,R);; ^ User error: Identifier 'test_niederreiter' has not been declared or assigned Total time: 3.389 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Mon Mar 29 09:58:47 2004 Input: K := GF(2); R := PolynomialRing(K, [7, 6, 4, 1016, 1008, 992, 960, 896, 768, 512]); R; P := [a, b, c, d, e, f, g , x*(a- b*z^2 -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2) +e*(x^(2^4)*z^2 +y^(2^4)*y^(2^2) -y^(2^4)*z^(2^2 +2) +z^(2^4 + 2^3 + 2^2 +2) ) + f*(x^(2^5)*y^(2^2) - x^(2^5)*z^(2^2 +2) - y^(2^5 +2^3)*z^(2) + y^(2^5)*z^( 2^3 + 2^2 +2) -z^(2^5 +2^4 + 2^3 + 2^2 +2) ) + g*(x^(2^6 +2^3) -x^(2^6)*y^(2^3)*z^2 + x^(2^6)*z^(2^3 +2^2 +2) -y^(2^6 + 2^4 + 2^2 ) + y^(2^6 +2^4)*z^(2^2 +2) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2) ) - z^2 *(x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^4 +2^3 +2^2) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^3 +2^2) - y^(2^7)*z^(2^5 + 2^4 +2^3 + 2^2 ) +z^(2^7 +2^6 +2^5 +2^4 + 2^3 + 2^2 ) )- x^(2^7)*y^(2^2 +2^4) ), y*(a- b*z^(2) -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2) +e*(x^(2^4)*z^2 +y^(2^4)*y^(2^2) -y^(2^4)*z^(2^2 +2) +z^(2^4 + 2^3 + 2^2 +2) ) + f*(x^(2^5)*y^(2^2) - x^(2^5)*z^(2^2 +2) - y^(2^5 +2^3)*z^(2) + y^(2^5)*z^( 2^3 + 2^2 +2) -z^(2^5 +2^4 + 2^3 + 2^2 +2) ) + g*(x^(2^6 +2^3) -x^(2^6)*y^(2^3)*z^2 + x^(2^6)*z^(2^3 +2^2 +2) -y^(2^6 + 2^4 + 2^2 ) + y^(2^6 +2^4)*z^(2^2 +2) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2) ) - z^2 *(x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^4 +2^3 +2^2) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^3 +2^2) - y^(2^7)*z^(2^5 + 2^4 +2^3 + 2^2 ) +z^(2^7 +2^6 +2^5 +2^4 + 2^3 + 2^2 ) )- x^(2^7)*y^(2^2 +2^4) ) + x^2 *(b- c*z^(2^2) -d*y^(2^3) +d*z^(2^3 +2^2) -e*x^(2^4) +e*z^(2^4)*y^(2^3) -e*z^(2^4 +2^3 +2^2) + f*( x^(2^5)*z^(2^2) +y^(2^5)*y^(2^3) -y^(2^5)*z^(2^2 +2^3) +z^(2^4 + 2^3 + 2^2 +2^5)) + g*( x^(2^6)*y^(2^3) - x^(2^6)*z^(2^2 +2^3) - y^(2^6 +2^4)*z^(2^2) + y^(2^6)*z^( 2^3 + 2^2 +2^4) -z^(2^5 +2^4 + 2^3 + 2^2 +2^6))+ x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^3 +2^2 +2^4) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^2 +2^3) - y^(2^7)*z^( 2^4 +2^3 + 2^2 +2^5) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2^7) ), z*(a- b*z^(2) -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2) +e*(x^(2^4)*z^2 +y^(2^4)*y^(2^2) -y^(2^4)*z^(2^2 +2) +z^(2^4 + 2^3 + 2^2 +2) ) + f*(x^(2^5)*y^(2^2) - x^(2^5)*z^(2^2 +2) - y^(2^5 +2^3)*z^(2) + y^(2^5)*z^( 2^3 + 2^2 +2) -z^(2^5 +2^4 + 2^3 + 2^2 +2) ) + g*(x^(2^6 +2^3) -x^(2^6)*y^(2^3)*z^2 + x^(2^6)*z^(2^3 +2^2 +2) -y^(2^6 + 2^4 + 2^2 ) + y^(2^6 +2^4)*z^(2^2 +2) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2) ) - z^2 *(x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^4 +2^3 +2^2) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^3 +2^2) - y^(2^7)*z^(2^5 + 2^4 +2^3 + 2^2 ) +z^(2^7 +2^6 +2^5 +2^4 + 2^3 + 2^2 ) )- x^(2^7)*y^(2^2 +2^4) ) + y^2 *(b- c*z^(2^2) -d*y^(2^3) +d*z^(2^3 +2^2) -e*x^(2^4) +e*z^(2^4)*y^(2^3) -e*z^(2^4 +2^3 +2^2) + f*( x^(2^5)*z^(2^2) +y^(2^5)*y^(2^3) -y^(2^5)*z^(2^2 +2^3) +z^(2^4 + 2^3 + 2^2 +2^5)) + g*( x^(2^6)*y^(2^3) - x^(2^6)*z^(2^2 +2^3) - y^(2^6 +2^4)*z^(2^2) + y^(2^6)*z^( 2^3 + 2^2 +2^4) -z^(2^5 +2^4 + 2^3 + 2^2 +2^6))+ x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^3 +2^2 +2^4) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^2 +2^3) - y^(2^7)*z^( 2^4 +2^3 + 2^2 +2^5) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2^7) ) + x^(2^2) *(c- d*z^(2^3) -e*y^(2^4) +e*z^(2^4 +2^3) -f*x^(2^5) +f*z^(2^5)*y^(2^4) -f*z^(2^5 +2^4 +2^3) +g*(x^(2^6)*z^(2^3) +y^(2^6)*y^(2^4) -y^(2^6)*z^(2^4 +2^3) +z^(2^4 + 2^3 + 2^6 +2^5) ) + x^(2^7)*y^(2^4) - x^(2^7)*z^(2^4 +2^3) - y^(2^7 +2^5)*z^(2^3) + y^(2^7)*z^( 2^3 + 2^5 +2^4) -z^(2^5 +2^4 + 2^3 + 2^7 +2^6)), x*y^2 ] ; P; [IsHomogeneous(f): f in P]; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S; Output: Magma V2.10-6 Mon Mar 29 2004 09:58:44 on modular [Seed = 2693323106] ------------------------------------- Graded Polynomial ring of rank 10 over GF(2) Lexicographical Order Variables: x, y, z, a, b, c, d, e, f, g Variable weights: 7 6 4 1016 1008 992 960 896 768 512 [ a, b, c, d, e, f, g, x^145*z^2 + x^129*y^20 + x^129*y^16*z^6 + x^129*z^30 + x^73*g + x^65*y^8*z^2*g + x^65*z^14*g + x^33*y^4*f + x^33*z^6*f + x^17*z^2*e + x^9*d + x*y^168*z^2 + x*y^160*z^14 + x*y^128*z^62 + x*y^84*g + x*y^80*z^6*g + x*y^64*z^30*g + x*y^40*z^2*f + x*y^32*z^14*f + x*y^20*e + x*y^16*z^6*e + x*y^4*z^8*d + x*y^4*c + x*z^254 + x*z^126*g + x*z^62*f + x*z^30*e + x*z^14*d + x*z^6*c + x*z^2*b + x*a, x^146 + x^144*y*z^2 + x^130*y^16*z^4 + x^130*z^28 + x^128*y^21 + x^128*y^17*z^6 + x^128*y*z^30 + x^72*y*g + x^66*y^8*g + x^66*z^12*g + x^64*y^9*z^2*g + x^64*y*z^14*g + x^34*z^4*f + x^32*y^5*f + x^32*y*z^6*f + x^18*e + x^16*y*z^2*e + x^8*y*d + x^2*y^168 + x^2*y^160*z^12 + x^2*y^128*z^60 + x^2*y^80*z^4*g + x^2*y^64*z^28*g + x^2*y^40*f + x^2*y^32*z^12*f + x^2*y^8*z^16*e + x^2*y^8*d + x^2*z^252 + x^2*z^124*g + x^2*z^60*f + x^2*z^28*e + x^2*z^12*d + x^2*z^4*c + x^2*b + y^169*z^2 + y^161*z^14 + y^129*z^62 + y^85*g + y^81*z^6*g + y^65*z^30*g + y^41*z^2*f + y^33*z^14*f + y^21*e + y^17*z^6*e + y^5*z^8*d + y^5*c + y*z^254 + y*z^126*g + y*z^62*f + y*z^30*e + y*z^14*d + y*z^6*c + y*z^2*b + y*a, x^144*y^2 + x^144*z^3 + x^132*y^16 + x^132*z^24 + x^128*y^20*z + x^128*y^18*z^4 + x^128*y^16*z^7 + x^128*y^2*z^28 + x^128*z^31 + x^72*z*g + x^68*z^8*g + x^64*y^10*g + x^64*y^8*z^3*g + x^64*y^2*z^12*g + x^64*z^15*g + x^36*f + x^32*y^4*z*f + x^32*y^2*z^4*f + x^32*z^7*f + x^16*y^2*e + x^16*z^3*e + x^8*z*d + x^4*y^160*z^8 + x^4*y^128*z^56 + x^4*y^80*g + x^4*y^64*z^24*g + x^4*y^16*z^32*f + x^4*y^16*e + x^4*z^248 + x^4*z^120*g + x^4*z^56*f + x^4*z^24*e + x^4*z^8*d + x^4*c + y^170 + y^168*z^3 + y^162*z^12 + y^160*z^15 + y^130*z^60 + y^128*z^63 + y^84*z*g + y^82*z^4*g + y^80*z^7*g + y^66*z^28*g + y^64*z^31*g + y^42*f + y^40*z^3*f + y^34*z^12*f + y^32*z^15*f + y^20*z*e + y^16*z^7*e + y^10*z^16*e + y^10*d + y^4*z^9*d + y^4*z*c + y^2*z^252 + y^2*z^124*g + y^2*z^60*f + y^2*z^28*e + y^2*z^12*d + y^2*z^4*c + y^2*b + z^255 + z^127*g + z^63*f + z^31*e + z^15*d + z^7*c + z^3*b + z*a, x*y^2 ] [ true, true, true, true, true, true, true, true, true, true, true ] 1 [ 2 ] >> V,phi:=VectorSpace(quo); ^ Runtime error in 'VectorSpace': Quotient does not have finite dimension >> S:=[R!(v@@phi ): v in Basis(V)]; ^ User error: Identifier 'V' has not been declared or assigned >> S; ^ User error: Identifier 'S' has not been declared or assigned Total time: 3.039 seconds, Total memory usage: 2.32MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 09:59:02 2004 Input: test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if ((-a)^n eq 1) then return false; else w:=RootOfUnity(n,K); val:={}; wj:=1; r:=k mod n; for j in [0..n-1] do val:=val join {K| (wj+a)^l*wj^r }; if (#val neq (j+1)) then return false; end if; wj:=wj*w; end for; end if; return true; end function; q := 125; K := GF(q); R := PolynomialRing(K); test_niederreiter(85,31,1,K,R); Output: Magma V2.10-6 Mon Mar 29 2004 09:58:59 on modular [Seed = 3080703586] ------------------------------------- >> if (#val neq (j+1)) then return false; end if; ^ User error: bad syntax >> wj:=wj*w; ^ User error: Identifier 'wj' has not been declared or assigned >> end for; ^ User error: bad syntax >> end if; ^ User error: bad syntax >> return true; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> test_niederreiter(85,31,1,K,R);; ^ User error: Identifier 'test_niederreiter' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 09:59:20 2004 Input: test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if ((-a)^n eq 1) then return false; else w:=RootOfUnity(n,K); val:={}; wj:=1; r:=k mod n; for j in [0..n-1] do val:=val join {K| (wj+a)^l*wj^r }; if ((#val) neq (j+1)) then return false; end if; wj:=wj*w; end for; end if; return true; end function; q := 125; K := GF(q); R := PolynomialRing(K); test_niederreiter(85,31,1,K,R); Output: Magma V2.10-6 Mon Mar 29 2004 09:59:17 on modular [Seed = 3214394911] ------------------------------------- >> if ((#val) neq (j+1)) then return false; end if; ^ User error: bad syntax >> wj:=wj*w; ^ User error: Identifier 'wj' has not been declared or assigned >> end for; ^ User error: bad syntax >> end if; ^ User error: bad syntax >> return true; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax >> test_niederreiter(85,31,1,K,R);; ^ User error: Identifier 'test_niederreiter' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Mon Mar 29 10:00:07 2004 Input: K := GF(2); R := PolynomialRing(K, [7, 6, 4, 1016, 1008, 992, 960, 896, 768, 512]); R; P := [a, b, c, d, e, f, g , x*(a- b*z^2 -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2) +e*(x^(2^4)*z^2 +y^(2^4)*y^(2^2) -y^(2^4)*z^(2^2 +2) +z^(2^4 + 2^3 + 2^2 +2) ) + f*(x^(2^5)*y^(2^2) - x^(2^5)*z^(2^2 +2) - y^(2^5 +2^3)*z^(2) + y^(2^5)*z^( 2^3 + 2^2 +2) -z^(2^5 +2^4 + 2^3 + 2^2 +2) ) + g*(x^(2^6 +2^3) -x^(2^6)*y^(2^3)*z^2 + x^(2^6)*z^(2^3 +2^2 +2) -y^(2^6 + 2^4 + 2^2 ) + y^(2^6 +2^4)*z^(2^2 +2) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2) ) - z^2 *(x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^4 +2^3 +2^2) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^3 +2^2) - y^(2^7)*z^(2^5 + 2^4 +2^3 + 2^2 ) +z^(2^7 +2^6 +2^5 +2^4 + 2^3 + 2^2 ) )- x^(2^7)*y^(2^2 +2^4) ), y*(a- b*z^(2) -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2) +e*(x^(2^4)*z^2 +y^(2^4)*y^(2^2) -y^(2^4)*z^(2^2 +2) +z^(2^4 + 2^3 + 2^2 +2) ) + f*(x^(2^5)*y^(2^2) - x^(2^5)*z^(2^2 +2) - y^(2^5 +2^3)*z^(2) + y^(2^5)*z^( 2^3 + 2^2 +2) -z^(2^5 +2^4 + 2^3 + 2^2 +2) ) + g*(x^(2^6 +2^3) -x^(2^6)*y^(2^3)*z^2 + x^(2^6)*z^(2^3 +2^2 +2) -y^(2^6 + 2^4 + 2^2 ) + y^(2^6 +2^4)*z^(2^2 +2) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2) ) - z^2 *(x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^4 +2^3 +2^2) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^3 +2^2) - y^(2^7)*z^(2^5 + 2^4 +2^3 + 2^2 ) +z^(2^7 +2^6 +2^5 +2^4 + 2^3 + 2^2 ) )- x^(2^7)*y^(2^2 +2^4) ) + x^2 *(b- c*z^(2^2) -d*y^(2^3) +d*z^(2^3 +2^2) -e*x^(2^4) +e*z^(2^4)*y^(2^3) -e*z^(2^4 +2^3 +2^2) + f*( x^(2^5)*z^(2^2) +y^(2^5)*y^(2^3) -y^(2^5)*z^(2^2 +2^3) +z^(2^4 + 2^3 + 2^2 +2^5)) + g*( x^(2^6)*y^(2^3) - x^(2^6)*z^(2^2 +2^3) - y^(2^6 +2^4)*z^(2^2) + y^(2^6)*z^( 2^3 + 2^2 +2^4) -z^(2^5 +2^4 + 2^3 + 2^2 +2^6))+ x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^3 +2^2 +2^4) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^2 +2^3) - y^(2^7)*z^( 2^4 +2^3 + 2^2 +2^5) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2^7) ), z*(a- b*z^(2) -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) -d*z^(2^3 +2^2 +2) +e*(x^(2^4)*z^2 +y^(2^4)*y^(2^2) -y^(2^4)*z^(2^2 +2) +z^(2^4 + 2^3 + 2^2 +2) ) + f*(x^(2^5)*y^(2^2) - x^(2^5)*z^(2^2 +2) - y^(2^5 +2^3)*z^(2) + y^(2^5)*z^( 2^3 + 2^2 +2) -z^(2^5 +2^4 + 2^3 + 2^2 +2) ) + g*(x^(2^6 +2^3) -x^(2^6)*y^(2^3)*z^2 + x^(2^6)*z^(2^3 +2^2 +2) -y^(2^6 + 2^4 + 2^2 ) + y^(2^6 +2^4)*z^(2^2 +2) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2) ) - z^2 *(x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^4 +2^3 +2^2) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^3 +2^2) - y^(2^7)*z^(2^5 + 2^4 +2^3 + 2^2 ) +z^(2^7 +2^6 +2^5 +2^4 + 2^3 + 2^2 ) )- x^(2^7)*y^(2^2 +2^4) ) + y^2 *(b- c*z^(2^2) -d*y^(2^3) +d*z^(2^3 +2^2) -e*x^(2^4) +e*z^(2^4)*y^(2^3) -e*z^(2^4 +2^3 +2^2) + f*( x^(2^5)*z^(2^2) +y^(2^5)*y^(2^3) -y^(2^5)*z^(2^2 +2^3) +z^(2^4 + 2^3 + 2^2 +2^5)) + g*( x^(2^6)*y^(2^3) - x^(2^6)*z^(2^2 +2^3) - y^(2^6 +2^4)*z^(2^2) + y^(2^6)*z^( 2^3 + 2^2 +2^4) -z^(2^5 +2^4 + 2^3 + 2^2 +2^6))+ x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) + x^(2^7)*z^(2^3 +2^2 +2^4) -y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^2 +2^3) - y^(2^7)*z^( 2^4 +2^3 + 2^2 +2^5) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2^7) ) + x^(2^2) *(c- d*z^(2^3) -e*y^(2^4) +e*z^(2^4 +2^3) -f*x^(2^5) +f*z^(2^5)*y^(2^4) -f*z^(2^5 +2^4 +2^3) +g*(x^(2^6)*z^(2^3) +y^(2^6)*y^(2^4) -y^(2^6)*z^(2^4 +2^3) +z^(2^4 + 2^3 + 2^6 +2^5) ) + x^(2^7)*y^(2^4) - x^(2^7)*z^(2^4 +2^3) - y^(2^7 +2^5)*z^(2^3) + y^(2^7)*z^( 2^3 + 2^5 +2^4) -z^(2^5 +2^4 + 2^3 + 2^7 +2^6)), x ] ; P; [IsHomogeneous(f): f in P]; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S; Output: Magma V2.10-6 Mon Mar 29 2004 10:00:04 on modular [Seed = 2393306908] ------------------------------------- Graded Polynomial ring of rank 10 over GF(2) Lexicographical Order Variables: x, y, z, a, b, c, d, e, f, g Variable weights: 7 6 4 1016 1008 992 960 896 768 512 [ a, b, c, d, e, f, g, x^145*z^2 + x^129*y^20 + x^129*y^16*z^6 + x^129*z^30 + x^73*g + x^65*y^8*z^2*g + x^65*z^14*g + x^33*y^4*f + x^33*z^6*f + x^17*z^2*e + x^9*d + x*y^168*z^2 + x*y^160*z^14 + x*y^128*z^62 + x*y^84*g + x*y^80*z^6*g + x*y^64*z^30*g + x*y^40*z^2*f + x*y^32*z^14*f + x*y^20*e + x*y^16*z^6*e + x*y^4*z^8*d + x*y^4*c + x*z^254 + x*z^126*g + x*z^62*f + x*z^30*e + x*z^14*d + x*z^6*c + x*z^2*b + x*a, x^146 + x^144*y*z^2 + x^130*y^16*z^4 + x^130*z^28 + x^128*y^21 + x^128*y^17*z^6 + x^128*y*z^30 + x^72*y*g + x^66*y^8*g + x^66*z^12*g + x^64*y^9*z^2*g + x^64*y*z^14*g + x^34*z^4*f + x^32*y^5*f + x^32*y*z^6*f + x^18*e + x^16*y*z^2*e + x^8*y*d + x^2*y^168 + x^2*y^160*z^12 + x^2*y^128*z^60 + x^2*y^80*z^4*g + x^2*y^64*z^28*g + x^2*y^40*f + x^2*y^32*z^12*f + x^2*y^8*z^16*e + x^2*y^8*d + x^2*z^252 + x^2*z^124*g + x^2*z^60*f + x^2*z^28*e + x^2*z^12*d + x^2*z^4*c + x^2*b + y^169*z^2 + y^161*z^14 + y^129*z^62 + y^85*g + y^81*z^6*g + y^65*z^30*g + y^41*z^2*f + y^33*z^14*f + y^21*e + y^17*z^6*e + y^5*z^8*d + y^5*c + y*z^254 + y*z^126*g + y*z^62*f + y*z^30*e + y*z^14*d + y*z^6*c + y*z^2*b + y*a, x^144*y^2 + x^144*z^3 + x^132*y^16 + x^132*z^24 + x^128*y^20*z + x^128*y^18*z^4 + x^128*y^16*z^7 + x^128*y^2*z^28 + x^128*z^31 + x^72*z*g + x^68*z^8*g + x^64*y^10*g + x^64*y^8*z^3*g + x^64*y^2*z^12*g + x^64*z^15*g + x^36*f + x^32*y^4*z*f + x^32*y^2*z^4*f + x^32*z^7*f + x^16*y^2*e + x^16*z^3*e + x^8*z*d + x^4*y^160*z^8 + x^4*y^128*z^56 + x^4*y^80*g + x^4*y^64*z^24*g + x^4*y^16*z^32*f + x^4*y^16*e + x^4*z^248 + x^4*z^120*g + x^4*z^56*f + x^4*z^24*e + x^4*z^8*d + x^4*c + y^170 + y^168*z^3 + y^162*z^12 + y^160*z^15 + y^130*z^60 + y^128*z^63 + y^84*z*g + y^82*z^4*g + y^80*z^7*g + y^66*z^28*g + y^64*z^31*g + y^42*f + y^40*z^3*f + y^34*z^12*f + y^32*z^15*f + y^20*z*e + y^16*z^7*e + y^10*z^16*e + y^10*d + y^4*z^9*d + y^4*z*c + y^2*z^252 + y^2*z^124*g + y^2*z^60*f + y^2*z^28*e + y^2*z^12*d + y^2*z^4*c + y^2*b + z^255 + z^127*g + z^63*f + z^31*e + z^15*d + z^7*c + z^3*b + z*a, x ] [ true, true, true, true, true, true, true, true, true, true, true ] 1 [ 2 ] >> V,phi:=VectorSpace(quo); ^ Runtime error in 'VectorSpace': Quotient does not have finite dimension >> S:=[R!(v@@phi ): v in Basis(V)]; ^ User error: Identifier 'V' has not been declared or assigned >> S; ^ User error: Identifier 'S' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 2.32MB ************** MAGMA ***************** Host aula-b-siee107.uab.es. (158.109.66.107) Time: Mon Mar 29 10:00:26 2004 Input: k:=GF(25); P:=PolynomialRing(k); IsFinit(P); Output: Magma V2.10-6 Mon Mar 29 2004 10:00:23 on modular [Seed = 2545937910] ------------------------------------- >> IsFinit(P); ^ User error: Identifier 'IsFinit' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee107.uab.es. (158.109.66.107) Time: Mon Mar 29 10:00:36 2004 Input: k:=GF(25); P:=PolynomialRing(k); IsFinit(); Output: Magma V2.10-6 Mon Mar 29 2004 10:00:33 on modular [Seed = 2629101291] ------------------------------------- >> IsFinit(); ^ User error: Identifier 'IsFinit' has not been declared or assigned Total time: 3.439 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:00:38 2004 Input: val:={}; for j in [0..10] do val:=val join {j}; end for; print val; Output: Magma V2.10-6 Mon Mar 29 2004 10:00:34 on modular [Seed = 2612257263] ------------------------------------- { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 } Total time: 3.689 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 10:00:40 2004 Input: F := PolynomialRing(FiniteField(7)); C := HyperellipticCurve(x^4+1); ZetaFunction(C); Output: Magma V2.10-6 Mon Mar 29 2004 10:00:37 on modular [Seed = 1649022992] ------------------------------------- (7*$.1^2 + 1)/(7*$.1^2 - 8*$.1 + 1) Total time: 3.189 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:00:47 2004 Input: val:={}; for j in [0..10] do val:=val join {j}; end for; print #val; Output: Magma V2.10-6 Mon Mar 29 2004 10:00:44 on modular [Seed = 1935345928] ------------------------------------- 11 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 10:01:16 2004 Input: F := PolynomialRing(FiniteField(7^2)); C := HyperellipticCurve(x^4+1); ZetaFunction(C); Output: Magma V2.10-6 Mon Mar 29 2004 10:01:13 on modular [Seed = 1231106839] ------------------------------------- (49*$.1^2 + 14*$.1 + 1)/(49*$.1^2 - 50*$.1 + 1) Total time: 3.029 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 10:01:28 2004 Input: F := PolynomialRing(FiniteField(7^2)); C := HyperellipticCurve(x^5-1); ZetaFunction(C); Output: Magma V2.10-6 Mon Mar 29 2004 10:01:25 on modular [Seed = 1601643901] ------------------------------------- (2401*$.1^4 + 98*$.1^2 + 1)/(49*$.1^2 - 50*$.1 + 1) Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:01:39 2004 Input: q := 125; K := GF(q); R := PolynomialRing(K); val:={}; for j in [0..10] do val:=val join {K.1^j}; end for; print #val; Output: Magma V2.10-6 Mon Mar 29 2004 10:01:36 on modular [Seed = 638475281] ------------------------------------- 11 Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:01:50 2004 Input: q := 125; K := GF(q); R := PolynomialRing(K); val:={}; for j in [0..10] do val:=val join {K.1^j}; end for; print val; print #val; Output: Magma V2.10-6 Mon Mar 29 2004 10:01:47 on modular [Seed = 772166674] ------------------------------------- { 1, w, w^2, w^3, w^4, w^5, w^6, w^7, w^8, w^9, w^10 } 11 Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:02:44 2004 Input: q := 125; K := GF(q); R := PolynomialRing(K); val:={}; for j in [0..10] do val:=val join {K.1^j}; end for; print val; print #val; if (#val neq 12) then print "pqs 12"; end if; Output: Magma V2.10-6 Mon Mar 29 2004 10:02:41 on modular [Seed = 907955392] ------------------------------------- { 1, w, w^2, w^3, w^4, w^5, w^6, w^7, w^8, w^9, w^10 } 11 >> if (#val neq 12) then print "pqs 12"; end if;; ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:03:15 2004 Input: q := 125; K := GF(q); R := PolynomialRing(K); val:={}; for j in [0..10] do val:=val join {K.1^j}; end for; print val; print #val; c:=#val; if (c neq 12) then print "pas 12"; end if; Output: Magma V2.10-6 Mon Mar 29 2004 10:03:12 on modular [Seed = 1041646825] ------------------------------------- { 1, w, w^2, w^3, w^4, w^5, w^6, w^7, w^8, w^9, w^10 } 11 >> if (c neq 12) then print "pas 12"; end if;; ^ User error: bad syntax Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:03:40 2004 Input: q := 125; K := GF(q); R := PolynomialRing(K); val:={}; for j in [0..10] do val:=val join {K.1^j}; end for; print val; print #val; c:=#val; if (c eq 12) then print "pas 12"; end if; Output: Magma V2.10-6 Mon Mar 29 2004 10:03:37 on modular [Seed = 103709864] ------------------------------------- { 1, w, w^2, w^3, w^4, w^5, w^6, w^7, w^8, w^9, w^10 } 11 Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:03:50 2004 Input: q := 125; K := GF(q); R := PolynomialRing(K); val:={}; for j in [0..10] do val:=val join {K.1^j}; end for; print val; print #val; c:=#val; if (c eq 11) then print "pas 12"; end if; Output: Magma V2.10-6 Mon Mar 29 2004 10:03:46 on modular [Seed = 237401275] ------------------------------------- { 1, w, w^2, w^3, w^4, w^5, w^6, w^7, w^8, w^9, w^10 } 11 pas 12 Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:04:12 2004 Input: q := 125; K := GF(q); R := PolynomialRing(K); val:={}; for j in [0..10] do val:=val join {K.1^j}; end for; print val; print #val; c:=#val; if (#val ne 12) then print "pas 12"; end if; Output: Magma V2.10-6 Mon Mar 29 2004 10:04:09 on modular [Seed = 356347803] ------------------------------------- { 1, w, w^2, w^3, w^4, w^5, w^6, w^7, w^8, w^9, w^10 } 11 pas 12 Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:04:38 2004 Input: test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if ((-a)^n eq 1) then return false; else w:=RootOfUnity(n,K); val:={}; wj:=1; r:=k mod n; for j in [0..n-1] do val:=val join { (wj+a)^l*wj^r }; if (#val ne (j+1)) then return false; end if; wj:=wj*w; end for; end if; return true; end function; q := 125; K := GF(q); R := PolynomialRing(K); test_niederreiter(85,31,1,K,R); Output: Magma V2.10-6 Mon Mar 29 2004 10:04:35 on modular [Seed = 490038905] ------------------------------------- false Total time: 3.059 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:05:06 2004 Input: test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if ((-a)^n eq 1) then return false; else w:=RootOfUnity(n,K); val:={}; wj:=1; r:=k mod n; for j in [0..n-1] do val:=val join { (wj+a)^l*wj^r }; if (#val ne (j+1)) then return false; end if; wj:=wj*w; end for; end if; return true; end function; q := 125; K := GF(q); R := PolynomialRing(K); time test_niederreiter(85,31,1,K,R); Output: Magma V2.10-6 Mon Mar 29 2004 10:05:03 on modular [Seed = 3989149333] ------------------------------------- false Time: 0.000 Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 10:06:00 2004 Input: m:=2; upperBound:=10; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5-1); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 10:05:57 on modular [Seed = 4108095430] ------------------------------------- HyperellipticCurve( f: x^5 + 4 ) In file "/usr/local/magma/package/Geometry/CrvHyp/curve.m", line 257, column 30: >> return HyperellipticCurve(f, Parent(f)!0); ^ Runtime error in 'HyperellipticCurve': Curve has a finite singularity Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:06:07 2004 Input: test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if ((-a)^n eq 1) then return false; else w:=RootOfUnity(n,K); val:={}; wj:=1; r:=k mod n; for j in [0..n-1] do val:=val join { (wj+a)^l*wj^r }; if (#val ne (j+1)) then return false; end if; wj:=wj*w; end for; end if; return true; end function; q := 2^10; K := GF(q); R := PolynomialRing(K); print Factorization(2^10); time test_niederreiter(85,31,1,K,R); Output: Magma V2.10-6 Mon Mar 29 2004 10:06:04 on modular [Seed = 4224942272] ------------------------------------- [ <2, 10> ] false Time: 0.000 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 10:06:13 2004 Input: m:=2; upperBound:=10; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+1); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 10:06:10 on modular [Seed = 3287005382] ------------------------------------- HyperellipticCurve( f: x^5 + 1 ) In file "/usr/local/magma/package/Geometry/CrvHyp/curve.m", line 257, column 30: >> return HyperellipticCurve(f, Parent(f)!0); ^ Runtime error in 'HyperellipticCurve': Curve has a finite singularity Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:06:17 2004 Input: test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if ((-a)^n eq 1) then return false; else w:=RootOfUnity(n,K); val:={}; wj:=1; r:=k mod n; for j in [0..n-1] do val:=val join { (wj+a)^l*wj^r }; if (#val ne (j+1)) then return false; end if; wj:=wj*w; end for; end if; return true; end function; q := 2^10; K := GF(q); R := PolynomialRing(K); print Factorization(2^10-1); time test_niederreiter(85,31,1,K,R); Output: Magma V2.10-6 Mon Mar 29 2004 10:06:14 on modular [Seed = 3403854283] ------------------------------------- [ <3, 1>, <11, 1>, <31, 1> ] false Time: 0.000 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 10:06:22 2004 Input: m:=2; upperBound:=10; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+2); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 10:06:19 on modular [Seed = 3539642846] ------------------------------------- HyperellipticCurve( f: x^5 + 2 ) In file "/usr/local/magma/package/Geometry/CrvHyp/curve.m", line 257, column 30: >> return HyperellipticCurve(f, Parent(f)!0); ^ Runtime error in 'HyperellipticCurve': Curve has a finite singularity Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 10:06:33 2004 Input: m:=2; upperBound:=10; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 10:06:30 on modular [Seed = 3656491720] ------------------------------------- 46 46 Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 10:06:43 2004 Input: m:=2; upperBound:=20; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 10:06:40 on modular [Seed = 2693323591] ------------------------------------- 46 46 150 178 313 397 Total time: 3.019 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:07:17 2004 Input: test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if ((-a)^n eq 1) then return false; else w:=RootOfUnity(n,K); val:={}; wj:=1; r:=k mod n; for j in [0..n-1] do val:=val join { (wj+a)^l*wj^r }; if (#val ne (j+1)) then return false; end if; wj:=wj*w; end for; end if; return true; end function; q := 2^10; K := GF(q); R := PolynomialRing(K); print Factorization(2^10-1); time test_niederreiter(85,682,1,K,R); Output: Magma V2.10-6 Mon Mar 29 2004 10:07:14 on modular [Seed = 3080703090] ------------------------------------- [ <3, 1>, <11, 1>, <31, 1> ] false Time: 0.000 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:07:43 2004 Input: test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if ((-a)^n eq 1) then return false; else w:=RootOfUnity(n,K); val:={}; wj:=1; r:=k mod n; for j in [0..n-1] do val:=val join { (wj+a)^l*wj^r }; if (#val ne (j+1)) then return false; end if; wj:=wj*w; end for; end if; return true; end function; q := 2^10; K := GF(q); R := PolynomialRing(K); print Factorization(2^10-1); time test_niederreiter(85,3,1,K,R); Output: Magma V2.10-6 Mon Mar 29 2004 10:07:40 on modular [Seed = 3214394468] ------------------------------------- [ <3, 1>, <11, 1>, <31, 1> ] false Time: 0.000 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee107.uab.es. (158.109.66.107) Time: Mon Mar 29 10:08:13 2004 Input: k:=GF(25); P:=PolynomialRing(k); IsFinite(); Output: Magma V2.10-6 Mon Mar 29 2004 10:08:10 on modular [Seed = 2259615035] ------------------------------------- >> IsFinite(); ^ Runtime error in 'IsFinite': Bad argument types Argument types given: Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:08:21 2004 Input: test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if ((-a)^n eq 1) then print "etape 1"; return false; else w:=RootOfUnity(n,K); val:={}; wj:=1; r:=k mod n; for j in [0..n-1] do val:=val join { (wj+a)^l*wj^r }; if (#val ne (j+1)) then return false; end if; wj:=wj*w; end for; end if; return true; end function; q := 2^10; K := GF(q); R := PolynomialRing(K); print Factorization(2^10-1); time test_niederreiter(85,3,1,K,R); Output: Magma V2.10-6 Mon Mar 29 2004 10:08:18 on modular [Seed = 2376463880] ------------------------------------- [ <3, 1>, <11, 1>, <31, 1> ] false Time: 0.000 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee107.uab.es. (158.109.66.107) Time: Mon Mar 29 10:08:26 2004 Input: k:=GF(25); P:=PolynomialRing(k); IsFinite(P); Output: Magma V2.10-6 Mon Mar 29 2004 10:08:23 on modular [Seed = 2512252437] ------------------------------------- false Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 10:08:41 2004 Input: m:=2; upperBound:=20; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); ZetaFunction(C); #C; Print nn; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 10:08:38 on modular [Seed = 2629101325] ------------------------------------- >> Print nn; ^ User error: bad syntax >> end if; ^ User error: bad syntax >> end for;; ^ User error: bad syntax Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:08:48 2004 Input: test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if ((-a)^n eq 1) then print return false; else w:=RootOfUnity(n,K); val:={}; wj:=1; r:=k mod n; print n; for j in [0..n-1] do print j; val:=val join { (wj+a)^l*wj^r }; if (#val ne (j+1)) then return false; end if; wj:=wj*w; end for; end if; return true; end function; q := 2^10; K := GF(q); R := PolynomialRing(K); print Factorization(2^10-1); time test_niederreiter(85,3,1,K,R); Output: Magma V2.10-6 Mon Mar 29 2004 10:08:45 on modular [Seed = 1816401913] ------------------------------------- >> if ((-a)^n eq 1) then print return false; ^ User error: bad syntax >> else ^ User error: bad syntax >> w:=RootOfUnity(n,K); ^ User error: Identifier 'n' has not been declared or assigned >> r:=k mod n; ^ User error: Identifier 'k' has not been declared or assigned >> print n; ^ User error: Identifier 'n' has not been declared or assigned >> for j in [0..n-1] do ^ User error: Identifier 'n' has not been declared or assigned >> end if; ^ User error: bad syntax >> return true; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax [ <3, 1>, <11, 1>, <31, 1> ] >> time test_niederreiter(85,3,1,K,R);; ^ User error: Identifier 'test_niederreiter' has not been declared or assigned Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 10:08:52 2004 Input: m:=2; upperBound:=20; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); ZetaFunction(C); #C; Print "nn"; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 10:08:49 on modular [Seed = 1699551500] ------------------------------------- >> Print "nn"; ^ User error: bad syntax >> end if; ^ User error: bad syntax >> end for;; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:08:58 2004 Input: test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if ((-a)^n eq 1) then return false; else w:=RootOfUnity(n,K); val:={}; wj:=1; r:=k mod n; print n; for j in [0..n-1] do print j; val:=val join { (wj+a)^l*wj^r }; if (#val ne (j+1)) then return false; end if; wj:=wj*w; end for; end if; return true; end function; q := 2^10; K := GF(q); R := PolynomialRing(K); print Factorization(2^10-1); time test_niederreiter(85,3,1,K,R); Output: Magma V2.10-6 Mon Mar 29 2004 10:08:55 on modular [Seed = 2119565841] ------------------------------------- [ <3, 1>, <11, 1>, <31, 1> ] 341 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 false Time: 0.010 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 10:09:16 2004 Input: m:=2; upperBound:=20; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); ZetaFunction(C); #C; print ; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 10:09:13 on modular [Seed = 1985874439] ------------------------------------- >> print ; ^ User error: bad syntax >> end if; ^ User error: bad syntax >> end for;; ^ User error: bad syntax Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 10:09:24 2004 Input: m:=2; upperBound:=20; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); ZetaFunction(C); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 10:09:21 on modular [Seed = 1332163334] ------------------------------------- (625*$.1^4 + 500*$.1^3 + 150*$.1^2 + 20*$.1 + 1)/(25*$.1^2 - 26*$.1 + 1) 46 (2401*$.1^4 - 196*$.1^3 + 42*$.1^2 - 4*$.1 + 1)/(49*$.1^2 - 50*$.1 + 1) 46 (14641*$.1^4 + 3388*$.1^3 + 410*$.1^2 + 28*$.1 + 1)/(121*$.1^2 - 122*$.1 + 1) 150 (28561*$.1^4 + 1352*$.1^3 + 66*$.1^2 + 8*$.1 + 1)/(169*$.1^2 - 170*$.1 + 1) 178 (83521*$.1^4 + 6647*$.1^3 + 528*$.1^2 + 23*$.1 + 1)/(289*$.1^2 - 290*$.1 + 1) 313 (130321*$.1^4 + 12635*$.1^3 + 1008*$.1^2 + 35*$.1 + 1)/(361*$.1^2 - 362*$.1 + 1) 397 Total time: 3.339 seconds, Total memory usage: 5.44MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:10:04 2004 Input: test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if ((-a)^n eq 1) then return false; else w:=RootOfUnity(n,K); val:={}; wj:=1; r:=k mod n; print n; for j in [0..n-1] do print j; val:=val join { (wj+a)^l*wj^r }; if (#val ne (j+1)) then return false; end if; wj:=wj*w; end for; end if; return true; end function; q := 2^10; K := GF(q); R := PolynomialRing(K); print Factorization(2^10-1); time test_niederreiter(85,3,1,K,R); time IsProbablyPermutationPolynomial(x^85*(x^3+1)); Output: Magma V2.10-6 Mon Mar 29 2004 10:10:01 on modular [Seed = 1601643390] ------------------------------------- [ <3, 1>, <11, 1>, <31, 1> ] 341 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 false Time: 0.000 false Time: 0.000 Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 10:10:08 2004 Input: m:=1; upperBound:=10; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); ZetaFunction(C); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 10:10:05 on modular [Seed = 1467951986] ------------------------------------- (25*$.1^4 + 10*$.1^2 + 1)/(5*$.1^2 - 6*$.1 + 1) 6 (49*$.1^4 + 14*$.1^3 + 2*$.1 + 1)/(7*$.1^2 - 8*$.1 + 1) 10 Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:10:24 2004 Input: test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if ((-a)^n eq 1) then return false; else w:=RootOfUnity(n,K); val:={}; wj:=1; r:=k mod n; print n; for j in [0..n-1] do print j; val:=val join { (wj+a)^l*wj^r }; if (#val ne (j+1)) then return false; end if; wj:=wj*w; end for; end if; return true; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); print Factorization(2^10-1); time test_niederreiter(85,3,1,K,R); time IsProbablyPermutationPolynomial(x^85*(x^3+1)); Output: Magma V2.10-6 Mon Mar 29 2004 10:10:20 on modular [Seed = 537418772] ------------------------------------- [ <3, 1>, <11, 1>, <31, 1> ] 349525 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 false Time: 0.190 false Time: 0.010 Total time: 3.839 seconds, Total memory usage: 14.39MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 10:10:39 2004 Input: m:=2; upperBound:=10; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); ZetaFunction(C); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 10:10:36 on modular [Seed = 940590140] ------------------------------------- (625*$.1^4 + 500*$.1^3 + 150*$.1^2 + 20*$.1 + 1)/(25*$.1^2 - 26*$.1 + 1) 46 (2401*$.1^4 - 196*$.1^3 + 42*$.1^2 - 4*$.1 + 1)/(49*$.1^2 - 50*$.1 + 1) 46 Total time: 2.929 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host aula-b-siee107.uab.es. (158.109.66.107) Time: Mon Mar 29 10:10:54 2004 Input: k:=GF(25); F:= ext< k | f >; Output: Magma V2.10-6 Mon Mar 29 2004 10:10:51 on modular [Seed = 823741730] ------------------------------------- >> F:= ext< k | f >;; ^ User error: Identifier 'f' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 10:11:12 2004 Input: m:=3; upperBound:=10; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); ZetaFunction(C); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 10:11:09 on modular [Seed = 237400811] ------------------------------------- (15625*$.1^4 + 250*$.1^2 + 1)/(125*$.1^2 - 126*$.1 + 1) 126 (117649*$.1^4 + 17150*$.1^3 + 1176*$.1^2 + 50*$.1 + 1)/(343*$.1^2 - 344*$.1 + 1) 394 Total time: 3.209 seconds, Total memory usage: 3.60MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:11:28 2004 Input: test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if ((-a)^n eq 1) then return false; else w:=RootOfUnity(n,K); val:={}; wj:=1; r:=k mod n; print n; for j in [0..n-1] do print j; val:=val join { (wj+a)^l*wj^r }; if (#val ne (j+1)) then return false; end if; wj:=wj*w; end for; end if; return true; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); print Factorization(2^10-1); time test_niederreiter(85,2^20 div 3,1,K,R); time IsProbablyPermutationPolynomial(x^85*(x^(2^20 div 3)+1)); Output: Magma V2.10-6 Mon Mar 29 2004 10:11:23 on modular [Seed = 120552436] ------------------------------------- [ <3, 1>, <11, 1>, <31, 1> ] 3 0 1 2 false Time: 0.000 false Time: 0.770 Total time: 5.049 seconds, Total memory usage: 86.26MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 10:11:28 2004 Input: m:=2; upperBound:=10; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); ZetaFunction(C); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 10:11:24 on modular [Seed = 439510766] ------------------------------------- (625*$.1^4 + 500*$.1^3 + 150*$.1^2 + 20*$.1 + 1)/(25*$.1^2 - 26*$.1 + 1) 46 (2401*$.1^4 - 196*$.1^3 + 42*$.1^2 - 4*$.1 + 1)/(49*$.1^2 - 50*$.1 + 1) 46 Total time: 4.019 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:12:57 2004 Input: test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if ((-a)^n eq 1) then return false; else w:=RootOfUnity(n,K); val:={}; wj:=1; r:=k mod n; print n; for j in [0..n-1] do print j; val:=val join { (wj+a)^l*wj^r }; if (#val ne (j+1)) then return false; end if; wj:=wj*w; end for; end if; return true; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); print Factorization(2^10-1); time test_niederreiter(85,2^10-1,1,K,R); time IsProbablyPermutationPolynomial(x^85*(x^(2^10-1)+1)); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Mar 29 2004 10:12:34 on modular [Seed = 3904935010] ------------------------------------- [ <3, 1>, <11, 1>, <31, 1> ] 1025 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 true Time: 0.260 Errors: /home/mfd/gomagma: line 2: 10368 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host aula-b-siee107.uab.es. (158.109.66.107) Time: Mon Mar 29 10:12:59 2004 Input: F:=GF(25); F:=GF(5); p1:=alpha^2+alpha*x+beta*x^2; p2:=1+alpha*x; Output: Magma V2.10-6 Mon Mar 29 2004 10:12:55 on modular [Seed = 3955464052] ------------------------------------- >> p1:=alpha^2+alpha*x+beta*x^2; ^ User error: Identifier 'x' has not been declared or assigned >> p2:=1+alpha*x;; ^ User error: Identifier 'x' has not been declared or assigned Total time: 3.299 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 10:13:21 2004 Input: m:=1; upperBound:=100; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); ZetaFunction(C); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 10:13:17 on modular [Seed = 4191257756] ------------------------------------- (25*$.1^4 + 10*$.1^2 + 1)/(5*$.1^2 - 6*$.1 + 1) 6 (49*$.1^4 + 14*$.1^3 + 2*$.1 + 1)/(7*$.1^2 - 8*$.1 + 1) 10 (121*$.1^4 - 22*$.1^3 + 16*$.1^2 - 2*$.1 + 1)/(11*$.1^2 - 12*$.1 + 1) 10 (169*$.1^4 + 52*$.1^3 + 12*$.1^2 + 4*$.1 + 1)/(13*$.1^2 - 14*$.1 + 1) 18 (289*$.1^4 + 51*$.1^3 + 16*$.1^2 + 3*$.1 + 1)/(17*$.1^2 - 18*$.1 + 1) 21 (361*$.1^4 + 19*$.1^3 + 18*$.1^2 + $.1 + 1)/(19*$.1^2 - 20*$.1 + 1) 21 (529*$.1^4 + 253*$.1^3 + 70*$.1^2 + 11*$.1 + 1)/(23*$.1^2 - 24*$.1 + 1) 35 (841*$.1^4 - 87*$.1^3 + 48*$.1^2 - 3*$.1 + 1)/(29*$.1^2 - 30*$.1 + 1) 27 (961*$.1^4 + 155*$.1^3 + 26*$.1^2 + 5*$.1 + 1)/(31*$.1^2 - 32*$.1 + 1) 37 (1369*$.1^4 + 37*$.1^3 - 52*$.1^2 + $.1 + 1)/(37*$.1^2 - 38*$.1 + 1) 39 (1681*$.1^4 + 246*$.1^3 + 78*$.1^2 + 6*$.1 + 1)/(41*$.1^2 - 42*$.1 + 1) 48 (1849*$.1^4 - 344*$.1^3 + 78*$.1^2 - 8*$.1 + 1)/(43*$.1^2 - 44*$.1 + 1) 36 (2209*$.1^4 + 282*$.1^3 + 54*$.1^2 + 6*$.1 + 1)/(47*$.1^2 - 48*$.1 + 1) 54 (2809*$.1^4 + 212*$.1^3 + 82*$.1^2 + 4*$.1 + 1)/(53*$.1^2 - 54*$.1 + 1) 58 (3481*$.1^4 + 118*$.1^3 + 80*$.1^2 + 2*$.1 + 1)/(59*$.1^2 - 60*$.1 + 1) 62 (3721*$.1^4 - 122*$.1^3 - 14*$.1^2 - 2*$.1 + 1)/(61*$.1^2 - 62*$.1 + 1) 60 (4489*$.1^4 + 335*$.1^3 - 6*$.1^2 + 5*$.1 + 1)/(67*$.1^2 - 68*$.1 + 1) 73 (5041*$.1^4 + 78*$.1^2 + 1)/(71*$.1^2 - 72*$.1 + 1) 72 (5329*$.1^4 - 365*$.1^3 - 24*$.1^2 - 5*$.1 + 1)/(73*$.1^2 - 74*$.1 + 1) 69 (6241*$.1^4 - 158*$.1^3 - 2*$.1 + 1)/(79*$.1^2 - 80*$.1 + 1) 78 (6889*$.1^4 + 747*$.1^3 + 46*$.1^2 + 9*$.1 + 1)/(83*$.1^2 - 84*$.1 + 1) 93 (7921*$.1^4 + 890*$.1^3 + 146*$.1^2 + 10*$.1 + 1)/(89*$.1^2 - 90*$.1 + 1) 100 (9409*$.1^4 + 388*$.1^3 + 22*$.1^2 + 4*$.1 + 1)/(97*$.1^2 - 98*$.1 + 1) 102 Total time: 3.059 seconds, Total memory usage: 3.49MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:13:56 2004 Input: test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if ((-a)^n eq 1) then return false; else w:=RootOfUnity(n,K); val:={}; wj:=1; r:=k mod n; print n; for j in [0..n-1] do print j; val:=val join { (wj+a)^l*wj^r }; if (#val ne (j+1)) then return false; end if; wj:=wj*w; end for; end if; return true; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); print Factorization(q-1); time test_niederreiter(85,2^10-1,1,K,R); time IsProbablyPermutationPolynomial(x^85*(x^(2^10-1)+1)); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Mar 29 2004 10:13:33 on modular [Seed = 4091252358] ------------------------------------- [ <3, 1>, <5, 2>, <11, 1>, <31, 1>, <41, 1> ] 1025 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 true Time: 0.250 Errors: /home/mfd/gomagma: line 2: 10395 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:14:45 2004 Input: test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if ((-a)^n eq 1) then return false; else w:=RootOfUnity(n,K); val:={}; wj:=1; r:=k mod n; print n; for j in [0..n-1] do print j; val:=val join { (wj+a)^l*wj^r }; if (#val ne (j+1)) then return false; end if; wj:=wj*w; end for; end if; return true; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); time IsProbablyPermutationPolynomial(x^85*(x^(2^10-1)+1)); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Mar 29 2004 10:14:22 on modular [Seed = 3437539818] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 10404 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host aula-b-siee107.uab.es. (158.109.66.107) Time: Mon Mar 29 10:15:01 2004 Input: k:=GF(25); F:=k; j:=GF(5); F:=j; P:=PolynomialRing(); p1:=alpha^2+alpha*x+beta*x^2; p2:=1+alpha*x; Output: Magma V2.10-6 Mon Mar 29 2004 10:14:58 on modular [Seed = 3303848414] ------------------------------------- >> P:=PolynomialRing(); ^ Runtime error in 'PolynomialRing': Bad argument types Argument types given: >> p1:=alpha^2+alpha*x+beta*x^2; ^ User error: Identifier 'x' has not been declared or assigned >> p2:=1+alpha*x;; ^ User error: Identifier 'x' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 10:16:15 2004 Input: m:=4; upperBound:=10; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); ZetaFunction(C); #C; end if; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Mar 29 2004 10:15:52 on modular [Seed = 3539644178] ------------------------------------- (390625*$.1^4 - 62500*$.1^3 + 3750*$.1^2 - 100*$.1 + 1)/(625*$.1^2 - 626*$.1 + 1) 526 Errors: /home/mfd/gomagma: line 2: 10426 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host aula-b-siee107.uab.es. (158.109.66.107) Time: Mon Mar 29 10:16:41 2004 Input: RealField(); F:=GF(25); F:=GF(5); P:=PolynomialRing(R); p1:=alpha^2+alpha*x+beta*x^2; p2:=1+alpha*x; Output: Magma V2.10-6 Mon Mar 29 2004 10:16:38 on modular [Seed = 2894385426] ------------------------------------- Real Field >> P:=PolynomialRing(R); ^ User error: Identifier 'R' has not been declared or assigned >> p1:=alpha^2+alpha*x+beta*x^2; ^ User error: Identifier 'x' has not been declared or assigned >> p2:=1+alpha*x;; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee107.uab.es. (158.109.66.107) Time: Mon Mar 29 10:16:55 2004 Input: R:=RealField(); F:=GF(25); F:=GF(5); P:=PolynomialRing(R); p1:=alpha^2+alpha*x+beta*x^2; p2:=1+alpha*x; Output: Magma V2.10-6 Mon Mar 29 2004 10:16:52 on modular [Seed = 2777536553] ------------------------------------- >> p1:=alpha^2+alpha*x+beta*x^2; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt >> p2:=1+alpha*x;; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:17:39 2004 Input: test_bete:=function(p,K) return exists { a in K : a ne 0 and Degree(Gcd(PowerExp(x,q,p-a)-x)) ne 1 }; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); time test_bete(x^85*(x^(2^10-1)+1),K); Output: Magma V2.10-6 Mon Mar 29 2004 10:17:35 on modular [Seed = 3214393816] ------------------------------------- >> return exists { a in K : a ne 0 and Degree(Gcd(PowerExp(x,q,p-a)-x)) ne 1 } ^ User error: bad syntax >> end function; ^ User error: bad syntax >> time test_bete(x^85*(x^(2^10-1)+1),K);; ^ User error: Identifier 'test_bete' has not been declared or assigned Total time: 3.569 seconds, Total memory usage: 14.37MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:18:02 2004 Input: test_bete:=function(p,K) return exists {a: a in K | a ne 0 and Degree(Gcd(PowerExp(x,q,p-a)-x)) ne 1 }; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); time test_bete(x^85*(x^(2^10-1)+1),K); Output: Magma V2.10-6 Mon Mar 29 2004 10:17:59 on modular [Seed = 3080702456] ------------------------------------- >> return exists {a: a in K | a ne 0 and Degree(Gcd(PowerExp(x,q,p-a)-x)) ne ^ User error: Identifier 'x' has not been declared or assigned >> time test_bete(x^85*(x^(2^10-1)+1),K);; ^ User error: Identifier 'test_bete' has not been declared or assigned Total time: 3.569 seconds, Total memory usage: 14.37MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:18:42 2004 Input: test_bete:=function(p,K,R) return exists {a: a in K | a ne 0 and Degree(Gcd(PowerExp(R.1,q,p-a)-R.1)) ne 1 }; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); time test_bete(x^85*(x^(2^10-1)+1),K,R); Output: Magma V2.10-6 Mon Mar 29 2004 10:18:39 on modular [Seed = 2410148264] ------------------------------------- >> return exists {a: a in K | a ne 0 and Degree(Gcd(PowerExp(R.1,q,p-a)-R.1)) ^ User error: Identifier 'q' has not been declared or assigned >> time test_bete(x^85*(x^(2^10-1)+1),K,R);; ^ User error: Identifier 'test_bete' has not been declared or assigned Total time: 3.579 seconds, Total memory usage: 14.37MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 10:18:49 2004 Input: m:=4; upperBound:=5; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); ZetaFunction(C); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 10:18:45 on modular [Seed = 2276456890] ------------------------------------- (390625*$.1^4 - 62500*$.1^3 + 3750*$.1^2 - 100*$.1 + 1)/(625*$.1^2 - 626*$.1 + 1) 526 Total time: 3.709 seconds, Total memory usage: 6.62MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:18:57 2004 Input: test_bete:=function(p,K,R) return exists {a: a in K | a ne 0 and Degree(Gcd(PowerExp(R.1,#K,p-a)-R.1)) ne 1 }; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); time test_bete(x^85*(x^(2^10-1)+1),K,R); Output: Magma V2.10-6 Mon Mar 29 2004 10:18:54 on modular [Seed = 2444881831] ------------------------------------- >> return exists {a: a in K | a ne 0 and Degree(Gcd(PowerExp(R.1,#K,p-a)-R.1) ^ User error: Identifier 'PowerExp' has not been declared or assigned >> time test_bete(x^85*(x^(2^10-1)+1),K,R);; ^ User error: Identifier 'test_bete' has not been declared or assigned Total time: 3.559 seconds, Total memory usage: 14.37MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:19:16 2004 Input: test_bete:=function(p,K,R) return exists {a: a in K | a ne 0 and Degree(Gcd(PowerMod(R.1,#K,p-a)-R.1)) ne 1 }; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); time test_bete(x^85*(x^(2^10-1)+1),K,R); Output: Magma V2.10-6 Mon Mar 29 2004 10:19:12 on modular [Seed = 1749030513] ------------------------------------- >> return exists {a: a in K | a ne 0 and Degree(Gcd(PowerMod(R.1,#K,p-a)-R.1) ^ User error: Identifier 'PowerMod' has not been declared or assigned >> time test_bete(x^85*(x^(2^10-1)+1),K,R);; ^ User error: Identifier 'test_bete' has not been declared or assigned Total time: 3.719 seconds, Total memory usage: 14.37MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:19:24 2004 Input: test_bete:=function(p,K,R) return exists {a: a in K | a ne 0 and Degree(Gcd(Power(R.1,#K,p-a)-R.1)) ne 1 }; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); time test_bete(x^85*(x^(2^10-1)+1),K,R); Output: Magma V2.10-6 Mon Mar 29 2004 10:19:21 on modular [Seed = 1615339120] ------------------------------------- [

:3]( p: x^1108 + x^85, K: GF(2^20), R: Univariate Polynomial Ring in x over GF(2^20) ) >> return exists {a: a in K | a ne 0 and Degree(Gcd(Power(R.1,#K,p-a)-R.1)) n ^ Runtime error in 'Power': Bad argument types Argument types given: RngUPolElt, RngIntElt, RngUPolElt Total time: 3.569 seconds, Total memory usage: 14.38MB ************** MAGMA ***************** Host aula-b-siee107.uab.es. (158.109.66.107) Time: Mon Mar 29 10:20:40 2004 Input: F:=GF(25); F:=GF(5); P:=PolynomialRing(GF(5)); P:=PolynomialRing(GF(25)); p1:=alpha^2+alpha*x+beta*x^2; p2:=1+alpha*x; Output: Magma V2.10-6 Mon Mar 29 2004 10:20:37 on modular [Seed = 1901662173] ------------------------------------- Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-b-siee107.uab.es. (158.109.66.107) Time: Mon Mar 29 10:20:58 2004 Input: F:=GF(25); F:=GF(5); P:=PolynomialRing(GF(5)); P:=PolynomialRing(GF(25)); p1:=alpha^2+alpha*x+beta*x^2; p2:=1+alpha*x; p1; p2; Output: Magma V2.10-6 Mon Mar 29 2004 10:20:55 on modular [Seed = 1214265078] ------------------------------------- x^2 + alpha*x + alpha^2 alpha*x + 1 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:21:59 2004 Input: test_bete:=function(p,K,R) return exists {a: a in K | a ne 0 and Degree(Gcd(Modexp(R.1,#K,p-a)-R.1)) ne 1 }; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); time test_bete(x^85*(x^(2^10-1)+1),K,R); Output: Magma V2.10-6 Mon Mar 29 2004 10:21:55 on modular [Seed = 1114258744] ------------------------------------- [
:3]( p: x^1108 + x^85, K: GF(2^20), R: Univariate Polynomial Ring in x over GF(2^20) ) >> return exists {a: a in K | a ne 0 and Degree(Gcd(Modexp(R.1,#K,p-a)-R.1)) ^ Runtime error in 'Gcd': Bad argument types Argument types given: RngUPolElt Total time: 3.629 seconds, Total memory usage: 14.38MB ************** MAGMA ***************** Host aula-b-siee107.uab.es. (158.109.66.107) Time: Mon Mar 29 10:22:19 2004 Input: F:=GF(25); F:=GF(5); P:=PolynomialRing(GF(5)); p1:=alpha^2+alpha*x+beta*x^2; p2:=1+alpha*x; p1; p2; Output: Magma V2.10-6 Mon Mar 29 2004 10:22:15 on modular [Seed = 1517430043] ------------------------------------- >> p1:=alpha^2+alpha*x+beta*x^2; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt >> p2:=1+alpha*x; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt >> p1; ^ User error: Identifier 'p1' has not been declared or assigned >> p2;; ^ User error: Identifier 'p2' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:22:28 2004 Input: test_bete:=function(p,K,R) return exists {a: a in K | a ne 0 and Degree(Gcd(Modexp(R.1,#K,p-a)-R.1),p-a) ne 1 }; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); time test_bete(x^85*(x^(2^10-1)+1),K,R); Output: Magma V2.10-6 Mon Mar 29 2004 10:22:23 on modular [Seed = 1434266131] ------------------------------------- [
:3]( p: x^1108 + x^85, K: GF(2^20), R: Univariate Polynomial Ring in x over GF(2^20) ) >> return exists {a: a in K | a ne 0 and Degree(Gcd(Modexp(R.1,#K,p-a)-R.1),p ^ Runtime error in 'Gcd': Bad argument types Argument types given: RngUPolElt Total time: 3.599 seconds, Total memory usage: 14.38MB ************** MAGMA ***************** Host aula-b-siee107.uab.es. (158.109.66.107) Time: Mon Mar 29 10:22:34 2004 Input: F:=GF(25); F:=GF(5); P:=PolynomialRing(GF(25)); p1:=alpha^2+alpha*x+beta*x^2; p2:=1+alpha*x; p1; p2; Output: Magma V2.10-6 Mon Mar 29 2004 10:22:31 on modular [Seed = 755323507] ------------------------------------- x^2 + alpha*x + alpha^2 alpha*x + 1 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:22:47 2004 Input: test_bete:=function(p,K,R) return exists {a: a in K | a ne 0 and Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-1)) ne 1 }; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); time test_bete(x^85*(x^(2^10-1)+1),K,R); Output: Magma V2.10-6 Mon Mar 29 2004 10:22:43 on modular [Seed = 604789518] ------------------------------------- true Time: 0.070 Total time: 3.729 seconds, Total memory usage: 14.38MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 10:22:57 2004 Input: m:=2; upperBound:=10; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); ZetaFunction(C); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 10:22:53 on modular [Seed = 1007960859] ------------------------------------- (625*$.1^4 + 500*$.1^3 + 150*$.1^2 + 20*$.1 + 1)/(25*$.1^2 - 26*$.1 + 1) 46 (2401*$.1^4 - 196*$.1^3 + 42*$.1^2 - 4*$.1 + 1)/(49*$.1^2 - 50*$.1 + 1) 46 Total time: 3.499 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host aula-b-siee107.uab.es. (158.109.66.107) Time: Mon Mar 29 10:22:58 2004 Input: F:=GF(25); F:=GF(5); P:=PolynomialRing(GF(25),GF(5)); p1:=alpha^2+alpha*x+beta*x^2; p2:=1+alpha*x; p1; p2; Output: Magma V2.10-6 Mon Mar 29 2004 10:22:54 on modular [Seed = 823741975] ------------------------------------- >> P:=PolynomialRing(GF(25),GF(5)); ^ Runtime error in 'PolynomialRing': Bad argument types Argument types given: FldFin, FldFin >> p1:=alpha^2+alpha*x+beta*x^2; ^ User error: Identifier 'x' has not been declared or assigned >> p2:=1+alpha*x; ^ User error: Identifier 'x' has not been declared or assigned >> p1; ^ User error: Identifier 'p1' has not been declared or assigned >> p2;; ^ User error: Identifier 'p2' has not been declared or assigned Total time: 3.539 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:23:24 2004 Input: test_bete:=function(p,K,R) return exists {a: a in K | a ne 0 and Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) ne 1 }; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); time test_bete(x^85*(x^(2^10-1)+1),K,R); Output: Magma V2.10-6 Mon Mar 29 2004 10:23:20 on modular [Seed = 237400335] ------------------------------------- true Time: 0.070 Total time: 3.709 seconds, Total memory usage: 14.48MB ************** MAGMA ***************** Host aula-b-siee107.uab.es. (158.109.66.107) Time: Mon Mar 29 10:23:28 2004 Input: F:=GF(25); F:=GF(5); G:=PolynomialRing(GF(5)); P:=PolynomialRing(GF(25)); p1:=alpha^2+alpha*x+beta*x^2; p2:=1+alpha*x; p1; p2; Output: Magma V2.10-6 Mon Mar 29 2004 10:23:25 on modular [Seed = 103708930] ------------------------------------- x^2 + alpha*x + alpha^2 alpha*x + 1 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:24:46 2004 Input: test_bete:=function(p,K,R) return exists {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) ne 1 }; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); time test_bete(x^85*(x^(2^10-1)+1),K,R); Output: Magma V2.10-6 Mon Mar 29 2004 10:24:41 on modular [Seed = 272134080] ------------------------------------- true Time: 0.070 Total time: 4.539 seconds, Total memory usage: 14.48MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 10:24:46 2004 Input: for p in [5..10] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); numberOfRoots:=#R; summe:=0; for i in [1..numberOfRoots] do summe:=summe+2/R[i][1]^2; end for; numberOfPoints:=p^2+1-summe; print Round(numberOfPoints), ","; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 10:24:41 on modular [Seed = 356346565] ------------------------------------- 46 , 46 , Total time: 4.109 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:25:54 2004 Input: test_bete:=function(p,K,R) return exists {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) ne 1 }; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); p:=x^85*(x^(2^10-1)+1); time test_bete(p,K,R); {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) ne 1 }; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Mar 29 2004 10:25:31 on modular [Seed = 3872299364] ------------------------------------- true Time: 0.060 Errors: /home/mfd/gomagma: line 2: 10639 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:26:50 2004 Input: test_bete:=function(p,K,R) return exists {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) ne 1 }; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); p:=x^85*(x^(2^10-1)+1); time test_bete(p,K,R); for a in K do print Gcd(Modexp(R.1,#K,p-a)-R.1,p-a); end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Mar 29 2004 10:26:27 on modular [Seed = 4275502772] ------------------------------------- true Time: 0.070 1 x + w^735889 x + w^423203 x + w^797267 x + w^846406 x + w^479395 x + w^545959 x + w^699648 x + w^644237 x + w^661601 x + w^958790 x + w^757829 x + w^43343 x + w^732082 x + w^350721 x + w^320935 x + w^239899 x + w^244963 x + w^274627 x + w^823966 x + w^869005 x + w^889444 x + w^467083 x + w^1021547 x + w^86686 x + w^230125 x + w^415589 x + w^991578 x + w^701442 x + w^182731 x + w^641870 x + w^694084 x + w^479798 x + w^720612 x + w^489926 x + w^52190 x + w^549254 x + w^34643 x + w^599357 x + w^755096 x + w^689435 x + w^671949 x + w^730313 x + w^1032627 x + w^934166 Errors: /home/mfd/gomagma: line 2: 10647 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:28:06 2004 Input: test_bete:=function(p,K,R) return exists {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) ne 1 }; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); p:=x^85*(x^(2^10-1)+1); time test_bete(p,K,R); for a in K do print Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)); end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Mar 29 2004 10:27:43 on modular [Seed = 3420703693] ------------------------------------- true Time: 0.060 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Errors: /home/mfd/gomagma: line 2: 10658 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:29:02 2004 Input: test_bete:=function(p,K,R) return exists {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) ne 1 }; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); p:=x^85*(x^(2^10-1)+1); time test_bete(p,K,R); for a in K do print a; print Gcd(Modexp(R.1,#K,p-a)-R.1,p-a); end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Mar 29 2004 10:28:39 on modular [Seed = 3287008013] ------------------------------------- true Time: 0.070 1 1 w x + w^735889 w^2 x + w^423203 w^3 x + w^797267 w^4 x + w^846406 w^5 x + w^479395 w^6 x + w^545959 w^7 x + w^699648 w^8 x + w^644237 w^9 x + w^661601 w^10 x + w^958790 w^11 x + w^757829 w^12 x + w^43343 w^13 x + w^732082 w^14 x + w^350721 w^15 x + w^320935 w^16 x + w^239899 w^17 x + w^244963 w^18 x + w^274627 w^19 x + w^823966 w^20 x + w^869005 w^21 x + w^889444 w^22 x + w^467083 w^23 x + w^1021547 w^24 x + w^86686 w^25 x + w^230125 w^26 x + w^415589 w^27 x + w^991578 w^28 x + w^701442 w^29 x + w^182731 w^30 x + w^641870 w^31 x + w^694084 w^32 x + w^479798 w^33 x + w^720612 w^34 x + w^489926 w^35 x + w^52190 w^36 x + w^549254 w^37 x + w^34643 w^38 x + w^599357 w^39 x + w^755096 w^40 x + w^689435 w^41 x + w^671949 w^42 x + w^730313 w^43 x + w^1032627 w^44 x + w^934166 w^45 Errors: /home/mfd/gomagma: line 2: 10666 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:32:05 2004 Input: test_bete:=function(p,K,R) return exists {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) ne 1 }; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); p:=x^85*(x^(2^10-1)+1); time test_bete(p,K,R); for i in [46..100] do print Gcd(Modexp(R.1,#K,p-w^i)-R.1,p-w^i); end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Mar 29 2004 10:31:42 on modular [Seed = 3623868128] ------------------------------------- true Time: 0.060 x + w^994519 x + w^593683 x + w^173372 x + w^169211 x + w^460250 x + w^62489 x + w^831178 x + w^739892 x + w^934581 x + w^828945 x + w^354309 x + w^955923 x + w^365462 x + w^610376 x + w^235165 x + w^356054 x + w^339593 x + w^652157 x + w^959596 x + w^565935 x + w^392649 x + w^320838 x + w^979852 x + w^329941 x + w^104380 x + w^287794 x + w^49933 x + w^225147 x + w^69286 x + w^171725 x + w^150139 x + w^264878 x + w^461617 x + w^739331 x + w^330295 x + w^511659 x + w^295323 x + w^294237 x + w^412051 x + w^372015 x + w^1016679 x + w^367793 x + w^819757 x + w^20196 Errors: /home/mfd/gomagma: line 2: 10686 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:32:50 2004 Input: test_bete:=function(p,K,R) return exists {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) ne 1 }; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); p:=x^85*(x^(2^10-1)+1); time test_bete(p,K,R); for i in [46..100] do print i; print Gcd(Modexp(R.1,#K,p-w^i)-R.1,p-w^i); end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Mar 29 2004 10:32:27 on modular [Seed = 2928062284] ------------------------------------- true Time: 0.070 46 x + w^994519 47 x + w^593683 48 x + w^173372 49 x + w^169211 50 x + w^460250 51 x + w^62489 52 x + w^831178 53 x + w^739892 54 x + w^934581 55 x + w^828945 56 x + w^354309 57 x + w^955923 58 x + w^365462 59 x + w^610376 60 x + w^235165 61 x + w^356054 62 x + w^339593 63 x + w^652157 64 x + w^959596 65 x + w^565935 66 x + w^392649 67 x + w^320838 68 x + w^979852 69 x + w^329941 70 x + w^104380 71 x + w^287794 72 x + w^49933 73 x + w^225147 74 x + w^69286 75 x + w^171725 76 x + w^150139 77 x + w^264878 78 x + w^461617 79 x + w^739331 80 x + w^330295 81 x + w^511659 82 x + w^295323 83 x + w^294237 84 x + w^412051 85 x + w^372015 86 x + w^1016679 87 x + w^367793 88 x + w^819757 89 x + w^20196 90 Errors: /home/mfd/gomagma: line 2: 10695 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:33:50 2004 Input: test_bete:=function(p,K,R) return exists {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) ne 1 }; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); p:=x^85*(x^(2^10-1)+1); time test_bete(p,K,R); for i in [90..140] do print i; print Gcd(Modexp(R.1,#K,p-w^i)-R.1,p-w^i); end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Mar 29 2004 10:33:27 on modular [Seed = 2794366728] ------------------------------------- true Time: 0.070 90 x + w^677160 91 x + w^227124 92 x + w^940463 93 x + w^1019327 94 x + w^138791 95 x + w^276080 96 x + w^346744 97 x + w^1021133 98 x + w^338422 99 x + w^654061 100 x + w^920500 101 x + w^833314 102 x + w^124978 103 x + w^290967 104 x + w^613781 105 x + w^219095 106 x + w^431209 107 x + w^68298 108 x + w^820587 109 x + w^407451 110 x + w^609315 111 x + w^64979 112 x + w^708618 113 x + w^216557 114 x + w^863271 115 x + w^484985 116 x + w^730924 117 x + w^882563 118 x + w^172177 119 x + w^544191 120 x + w^470330 121 x + w^402619 122 x + w^712108 123 x + w^396347 124 x + w^679186 125 x + w^108200 126 x + w^255739 127 x + w^453503 128 x + w^870617 129 x + w^261706 130 x + w^83295 131 x + w^695159 132 x + w^785298 133 x + w^268637 134 Errors: /home/mfd/gomagma: line 2: 10703 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:34:29 2004 Input: test_bete:=function(p,K,R) return exists {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) ne 1 }; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); p:=x^85*(x^(2^10-1)+1); time test_bete(p,K,R); for i in [135..170] do print i; print Gcd(Modexp(R.1,#K,p-w^i)-R.1,p-w^i); end for; Output: Magma V2.10-6 Mon Mar 29 2004 10:34:10 on modular [Seed = 2979639338] ------------------------------------- true Time: 0.070 135 x + w^408940 136 x + w^911129 137 x + w^472368 138 x + w^659882 139 x + w^351296 140 x + w^208760 141 x + w^79549 142 x + w^575588 143 x + w^111202 144 x + w^99866 145 x + w^749655 146 x + w^450294 147 x + w^626533 148 x + w^138572 149 x + w^520836 150 x + w^343450 151 x + w^472539 152 x + w^300278 153 x + w^300217 154 x + w^529756 155 x + w^970445 156 x + w^923234 157 x + w^463973 158 x + w^430087 159 x + w^763151 160 x + w^660590 161 x + w^576479 162 x + w^1023318 163 x + w^355982 164 x + w^590646 165 x + w^149835 166 x + w^588474 167 x + w^675538 168 x + w^824102 169 x + w^966516 170 x + w^744030 Total time: 19.199 seconds, Total memory usage: 14.48MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:35:20 2004 Input: test_bete:=function(p,K,R) return exists {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) ne 1 }; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); p:=x^85*(x^(2^10-1)+1); time test_bete(p,K,R); for i in [171..240] do print i; print Gcd(Modexp(R.1,#K,p-w^i)-R.1,p-w^i); end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Mar 29 2004 10:34:57 on modular [Seed = 2309065665] ------------------------------------- true Time: 0.070 171 x + w^273494 172 x + w^984783 173 x + w^663897 174 x + w^735586 175 x + w^305025 176 x + w^590939 177 x + w^840978 178 x + w^40392 179 x + w^593831 180 x + w^305745 181 x + w^651109 182 x + w^454248 183 x + w^289162 184 x + w^832351 185 x + w^309540 186 x + w^990079 187 x + w^326843 188 x + w^277582 189 x + w^865871 190 x + w^552160 191 x + w^1008224 192 x + w^693488 193 x + w^438202 194 x + w^993691 195 x + w^544680 196 x + w^676844 197 x + w^146858 198 x + w^259547 199 x + w^1007736 200 x + w^792425 201 x + w^69739 202 x + w^618053 203 x + w^892692 204 x + w^249956 205 x + w^558420 206 x + w^581934 207 x + w^746898 208 x + w^178987 209 x + w^955876 210 x + w^438190 211 x + w^144979 212 x + w^862418 213 x + w^963832 214 x + w^136596 215 Errors: /home/mfd/gomagma: line 2: 10720 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:36:09 2004 Input: test_bete:=function(p,K,R) return exists {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) ne 1 }; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); p:=x^85*(x^(2^10-1)+1); time test_bete(p,K,R); print Gcd(Modexp(R.1,#K,p)-R.1,p); Output: Magma V2.10-6 Mon Mar 29 2004 10:36:05 on modular [Seed = 2225899144] ------------------------------------- true Time: 0.070 x^1024 + x Total time: 3.699 seconds, Total memory usage: 14.58MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:36:46 2004 Input: test_bete:=function(p,K,R) return exists {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) ne 1 }; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); p:=x^85*(x^(2^10-1)+1); time test_bete(p,K,R); Factorization(Gcd(Modexp(R.1,#K,p)-R.1,p)); Output: Magma V2.10-6 Mon Mar 29 2004 10:36:39 on modular [Seed = 2629082738] ------------------------------------- true Time: 0.070 [ , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , := GF(q); R := PolynomialRing(K); p:=x^85*(x^(2^10-1)+1); time test_bete(p,K,R); p(1); Factorization(Gcd(Modexp(R.1,#K,p)-R.1,p)); Output: Magma V2.10-6 Mon Mar 29 2004 10:41:23 on modular [Seed = 1833266851] ------------------------------------- true Time: 0.070 >> p(1); ^ Runtime error: Bad argument types Argument types given: RngIntElt, RngUPolElt [ , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:42:09 2004 Input: test_bete:=function(p,K,R) return exists {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) ne 1 }; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); p:=x^85*(x^(2^10-1)+1); time test_bete(p,K,R); Evaluate(p,-1); Factorization(Gcd(Modexp(R.1,#K,p)-R.1,p)); Output: Magma V2.10-6 Mon Mar 29 2004 10:42:02 on modular [Seed = 1699571397] ------------------------------------- true Time: 0.070 0 [ , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:42:45 2004 Input: test_bete:=function(p,K,R) return exists {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) ne 1 }; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); p:=x^85*(x^(2^10-1)+1); time test_bete(p,K,R); Evaluate(p,-w^1025); Output: Magma V2.10-6 Mon Mar 29 2004 10:42:42 on modular [Seed = 2102755045] ------------------------------------- true Time: 0.040 0 Total time: 3.649 seconds, Total memory usage: 14.48MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:43:53 2004 Input: test_bete:=function(p,K,R) return exists {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) ne 1 }; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); p:=x^85*(x^(2^10-1)+1); time test_bete(p,K,R); IsProbablyPermutationPolynomial(p); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Mar 29 2004 10:43:30 on modular [Seed = 1969058109] ------------------------------------- true Time: 0.070 Errors: /home/mfd/gomagma: line 2: 10783 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:44:19 2004 Input: test_bete:=function(p,K,R) return exists {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) ne 1 }; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); p:=x^85*(x^(2^10-1)+1); time test_bete(p,K,R); Gcd(85,2^10-1); Output: Magma V2.10-6 Mon Mar 29 2004 10:44:15 on modular [Seed = 1131104102] ------------------------------------- true Time: 0.070 1 Total time: 3.709 seconds, Total memory usage: 14.48MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:44:35 2004 Input: test_bete:=function(p,K,R) return exists {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) ne 1 }; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); p:=x^85*(x^(2^10-1)+1); time test_bete(p,K,R); Gcd(85,q-1); Output: Magma V2.10-6 Mon Mar 29 2004 10:44:31 on modular [Seed = 1534287726] ------------------------------------- true Time: 0.070 5 Total time: 3.689 seconds, Total memory usage: 14.48MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:45:06 2004 Input: test_bete:=function(p,K,R) return exists {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) ne 1 }; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); p:=x^85*(x^(2^10-1)+1); time test_bete(p,K,R); Gcd(87,q-1); Output: Magma V2.10-6 Mon Mar 29 2004 10:45:03 on modular [Seed = 1467962178] ------------------------------------- true Time: 0.060 3 Total time: 3.639 seconds, Total memory usage: 14.48MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:45:17 2004 Input: test_bete:=function(p,K,R) return exists {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) ne 1 }; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); p:=x^85*(x^(2^10-1)+1); time test_bete(p,K,R); Gcd(89,q-1); Output: Magma V2.10-6 Mon Mar 29 2004 10:45:12 on modular [Seed = 788999117] ------------------------------------- true Time: 0.070 1 Total time: 3.629 seconds, Total memory usage: 14.48MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:45:27 2004 Input: test_bete:=function(p,K,R) return exists {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) ne 1 }; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); p:=x^89*(x^(2^10-1)+1); time test_bete(p,K,R); Gcd(89,q-1); Output: Magma V2.10-6 Mon Mar 29 2004 10:45:23 on modular [Seed = 655303646] ------------------------------------- true Time: 0.060 1 Total time: 3.709 seconds, Total memory usage: 14.38MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:46:17 2004 Input: test_bete:=function(p,K,R) return exists {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) ne 1 }; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); p:=x^89*(x^(2^10-1)+1); time test_bete(p,K,R); time IsProbablyPermutationPolynomial(p); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Mar 29 2004 10:45:54 on modular [Seed = 1058487271] ------------------------------------- true Time: 0.070 Errors: /home/mfd/gomagma: line 2: 10837 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:47:10 2004 Input: test_bete:=function(p,K,R) return exists {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) ne 1 }; end function; test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if ((-a)^n eq 1) then return false; else w=RootOfUnity(n,K); val:={}; wj:=1; r:=k modulo n; for j in [0..n-1] do val:=val join { (wj+a)^l*wj^r }; if (#val neq (j+1)) then return false; end if; wj:=wj*w; end for; end if; return true; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); p:=x^89*(x^(2^10-1)+1); time test_bete(p,K,R); time test_niederreiter(89,2^10-1,K,R); Output: Magma V2.10-6 Mon Mar 29 2004 10:47:06 on modular [Seed = 924791719] ------------------------------------- >> r:=k modulo n; ^ User error: bad syntax >> if (#val neq (j+1)) then return false; end if; ^ User error: bad syntax >> wj:=wj*w; ^ User error: Identifier 'wj' has not been declared or assigned >> end for; ^ User error: bad syntax >> end if; ^ User error: bad syntax >> return true; ^ User error: A 'return' can only be used inside a procedure or function >> end function; ^ User error: bad syntax true Time: 0.070 >> time test_niederreiter(89,2^10-1,K,R);; ^ User error: Identifier 'test_niederreiter' has not been declared or assigned Total time: 3.629 seconds, Total memory usage: 14.48MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:47:41 2004 Input: test_bete:=function(p,K,R) return exists {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) ne 1 }; end function; test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if ((-a)^n eq 1) then return false; else w:=RootOfUnity(n,K); val:={}; wj:=1; r:=k mod n; for j in [0..n-1] do val:=val join { (wj+a)^l*wj^r }; if (#val ne (j+1)) then return false; end if; wj:=wj*w; end for; end if; return true; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); p:=x^89*(x^(2^10-1)+1); time test_bete(p,K,R); time test_niederreiter(89,2^10-1,K,R); Output: Magma V2.10-6 Mon Mar 29 2004 10:47:37 on modular [Seed = 203688319] ------------------------------------- true Time: 0.070 >> time test_niederreiter(89,2^10-1,K,R);; ^ Runtime error in procedure call: Number of arguments (4) does not equal expected number of arguments (5) Total time: 3.749 seconds, Total memory usage: 14.49MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:48:09 2004 Input: test_bete:=function(p,K,R) return exists {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) ne 1 }; end function; test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if ((-a)^n eq 1) then return false; else w:=RootOfUnity(n,K); val:={}; wj:=1; r:=k mod n; for j in [0..n-1] do val:=val join { (wj+a)^l*wj^r }; if (#val ne (j+1)) then return false; end if; wj:=wj*w; end for; end if; return true; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); p:=x^89*(x^(2^10-1)+1); time test_bete(p,K,R); time test_niederreiter(89,2^10-1,1,K,R); Output: Magma V2.10-6 Mon Mar 29 2004 10:48:05 on modular [Seed = 69992795] ------------------------------------- true Time: 0.070 true Time: 0.250 Total time: 4.039 seconds, Total memory usage: 14.49MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:48:48 2004 Input: test_bete:=function(p,K,R) return forall {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) eq 1 }; end function; test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if ((-a)^n eq 1) then return false; else w:=RootOfUnity(n,K); val:={}; wj:=1; r:=k mod n; for j in [0..n-1] do val:=val join { (wj+a)^l*wj^r }; if (#val ne (j+1)) then return false; end if; wj:=wj*w; end for; end if; return true; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); p:=x^89*(x^(2^10-1)+1); time test_bete(p,K,R); time test_niederreiter(89,2^10-1,1,K,R); Output: Magma V2.10-6 Mon Mar 29 2004 10:48:44 on modular [Seed = 473176363] ------------------------------------- false Time: 0.070 true Time: 0.240 Total time: 3.889 seconds, Total memory usage: 14.49MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:49:35 2004 Input: test_bete:=function(p,K,R) return forall {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) eq 1 }; end function; test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if ((-a)^n eq 1) then return false; else w:=RootOfUnity(n,K); val:={}; wj:=1; r:=k mod n; for j in [0..n-1] do val:=val join { (wj+a)^l*wj^r }; if (#val ne (j+1)) then return false; end if; wj:=wj*w; end for; end if; return true; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); p:=x^89*(x^(2^10-1)+1); time test_bete(p,K,R); time test_niederreiter(89,2^10-1,1,K,R); Gcd(#K-1,2^10-1); Output: Magma V2.10-6 Mon Mar 29 2004 10:49:31 on modular [Seed = 356323572] ------------------------------------- false Time: 0.070 true Time: 0.250 1023 Total time: 3.899 seconds, Total memory usage: 14.49MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:50:30 2004 Input: test_bete:=function(p,K,R) return forall {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) eq 1 }; end function; test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if ((-a)^n eq 1) then return false; else w:=RootOfUnity(n,K); val:={}; wj:=1; r:=k mod n; for j in [0..n-1] do val:=val join { (wj+a)^l*wj^r }; if (#val ne (j+1)) then return false; end if; wj:=wj*w; end for; end if; print #val; print val; return true; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); p:=x^89*(x^(2^10-1)+1); time test_bete(p,K,R); time test_niederreiter(89,2^10-1,1,K,R); Gcd(#K-1,2^10-1); Output: Magma V2.10-6 Mon Mar 29 2004 10:50:26 on modular [Seed = 3838632268] ------------------------------------- false Time: 0.070 1025 { w^970827, w^762135, w^553443, w^344751, w^136059, w^898194, w^689502, w^480810, w^272118, w^63426, w^1034253, w^825561, w^616869, w^408177, w^199485, w^961620, w^752928, w^544236, w^335544, w^126852, w^888987, w^680295, w^471603, w^262911, w^54219, w^1025046, w^816354, w^607662, w^398970, w^190278, w^952413, w^743721, w^535029, w^326337, w^117645, w^879780, w^671088, w^462396, w^253704, w^45012, w^1015839, w^807147, w^598455, w^389763, w^181071, w^943206, w^734514, w^525822, w^317130, w^108438, w^870573, w^661881, w^453189, w^244497, w^35805, w^1006632, w^797940, w^589248, w^380556, w^171864, w^933999, w^725307, w^516615, w^307923, w^99231, w^861366, w^652674, w^443982, w^235290, w^26598, w^997425, w^788733, w^580041, w^371349, w^162657, w^924792, w^716100, w^507408, w^298716, w^90024, w^852159, w^643467, w^434775, w^226083, w^17391, w^988218, w^779526, w^570834, w^362142, w^153450, w^915585, w^706893, w^498201, w^289509, w^80817, w^842952, w^634260, w^425568, w^216876, w^8184, w^979011, w^770319, w^561627, w^352935, w^144243, w^906378, w^697686, w^488994, w^280302, w^71610, w^1042437, w^833745, w^625053, w^416361, w^207669, w^969804, w^761112, w^552420, w^343728, w^135036, w^897171, w^688479, w^479787, w^271095, w^62403, w^1033230, w^824538, w^615846, w^407154, w^198462, w^960597, w^751905, w^543213, w^334521, w^125829, w^887964, w^679272, w^470580, w^261888, w^53196, w^1024023, w^815331, w^606639, w^397947, w^189255, w^951390, w^742698, w^534006, w^325314, w^116622, w^878757, w^670065, w^461373, w^252681, w^43989, w^1014816, w^806124, w^597432, w^388740, w^180048, w^942183, w^733491, w^524799, w^316107, w^107415, w^869550, w^660858, w^452166, w^243474, w^34782, w^1005609, w^796917, w^588225, w^379533, w^170841, w^932976, w^724284, w^515592, w^306900, w^98208, w^860343, w^651651, w^442959, w^234267, w^25575, w^996402, w^787710, w^579018, w^370326, w^161634, w^923769, w^715077, w^506385, w^297693, w^89001, w^851136, w^642444, w^433752, w^225060, w^16368, w^987195, w^778503, w^569811, w^361119, w^152427, w^914562, w^705870, w^497178, w^288486, w^79794, w^841929, w^633237, w^424545, w^215853, w^7161, w^977988, w^769296, w^560604, w^351912, w^143220, w^905355, w^696663, w^487971, w^279279, w^70587, w^1041414, w^832722, w^624030, w^415338, w^206646, w^968781, w^760089, w^551397, w^342705, w^134013, w^896148, w^687456, w^478764, w^270072, w^61380, w^1032207, w^823515, w^614823, w^406131, w^197439, w^959574, w^750882, w^542190, w^333498, w^124806, w^886941, w^678249, w^469557, w^260865, w^52173, w^1023000, w^814308, w^605616, w^396924, w^188232, w^950367, w^741675, w^532983, w^324291, w^115599, w^877734, w^669042, w^460350, w^251658, w^42966, w^1013793, w^805101, w^596409, w^387717, w^179025, w^941160, w^732468, w^523776, w^315084, w^106392, w^868527, w^659835, w^451143, w^242451, w^33759, w^1004586, w^795894, w^587202, w^378510, w^169818, w^931953, w^723261, w^514569, w^305877, w^97185, w^859320, w^650628, w^441936, w^233244, w^24552, w^995379, w^786687, w^577995, w^369303, w^160611, w^922746, w^714054, w^505362, w^296670, w^87978, w^850113, w^641421, w^432729, w^224037, w^15345, w^986172, w^777480, w^568788, w^360096, w^151404, w^913539, w^704847, w^496155, w^287463, w^78771, w^840906, w^632214, w^423522, w^214830, w^6138, w^976965, w^768273, w^559581, w^350889, w^142197, w^904332, w^695640, w^486948, w^278256, w^69564, w^1040391, w^831699, w^623007, w^414315, w^205623, w^967758, w^759066, w^550374, w^341682, w^132990, w^895125, w^686433, w^477741, w^269049, w^60357, w^1031184, w^822492, w^613800, w^405108, w^196416, w^958551, w^749859, w^541167, w^332475, w^123783, w^885918, w^677226, w^468534, w^259842, w^51150, w^1021977, w^813285, w^604593, w^395901, w^187209, w^949344, w^740652, w^531960, w^323268, w^114576, w^876711, w^668019, w^459327, w^250635, w^41943, w^1012770, w^804078, w^595386, w^386694, w^178002, w^940137, w^731445, w^522753, w^314061, w^105369, w^867504, w^658812, w^450120, w^241428, w^32736, w^1003563, w^794871, w^586179, w^377487, w^168795, w^930930, w^722238, w^513546, w^304854, w^96162, w^858297, w^649605, w^440913, w^232221, w^23529, w^994356, w^785664, w^576972, w^368280, w^159588, w^921723, w^713031, w^504339, w^295647, w^86955, w^849090, w^640398, w^431706, w^223014, w^14322, w^985149, w^776457, w^567765, w^359073, w^150381, w^912516, w^703824, w^495132, w^286440, w^77748, 0, w^839883, w^631191, w^422499, w^213807, w^5115, w^975942, w^767250, w^558558, w^349866, w^141174, w^903309, w^694617, w^485925, w^277233, w^68541, w^1039368, w^830676, w^621984, w^413292, w^204600, w^966735, w^758043, w^549351, w^340659, w^131967, w^894102, w^685410, w^476718, w^268026, w^59334, w^1030161, w^821469, w^612777, w^404085, w^195393, w^957528, w^748836, w^540144, w^331452, w^122760, w^884895, w^676203, w^467511, w^258819, w^50127, w^1020954, w^812262, w^603570, w^394878, w^186186, w^948321, w^739629, w^530937, w^322245, w^113553, w^875688, w^666996, w^458304, w^249612, w^40920, w^1011747, w^803055, w^594363, w^385671, w^176979, w^939114, w^730422, w^521730, w^313038, w^104346, w^866481, w^657789, w^449097, w^240405, w^31713, w^1002540, w^793848, w^585156, w^376464, w^167772, w^929907, w^721215, w^512523, w^303831, w^95139, w^857274, w^648582, w^439890, w^231198, w^22506, w^993333, w^784641, w^575949, w^367257, w^158565, w^920700, w^712008, w^503316, w^294624, w^85932, w^848067, w^639375, w^430683, w^221991, w^13299, w^984126, w^775434, w^566742, w^358050, w^149358, w^911493, w^702801, w^494109, w^285417, w^76725, w^1047552, w^838860, w^630168, w^421476, w^212784, w^4092, w^974919, w^766227, w^557535, w^348843, w^140151, w^902286, w^693594, w^484902, w^276210, w^67518, w^1038345, w^829653, w^620961, w^412269, w^203577, w^965712, w^757020, w^548328, w^339636, w^130944, w^893079, w^684387, w^475695, w^267003, w^58311, w^1029138, w^820446, w^611754, w^403062, w^194370, w^956505, w^747813, w^539121, w^330429, w^121737, w^883872, w^675180, w^466488, w^257796, w^49104, w^1019931, w^811239, w^602547, w^393855, w^185163, w^947298, w^738606, w^529914, w^321222, w^112530, w^874665, w^665973, w^457281, w^248589, w^39897, w^1010724, w^802032, w^593340, w^384648, w^175956, w^938091, w^729399, w^520707, w^312015, w^103323, w^865458, w^656766, w^448074, w^239382, w^30690, w^1001517, w^792825, w^584133, w^375441, w^166749, w^928884, w^720192, w^511500, w^302808, w^94116, w^856251, w^647559, w^438867, w^230175, w^21483, w^992310, w^783618, w^574926, w^366234, w^157542, w^919677, w^710985, w^502293, w^293601, w^84909, w^847044, w^638352, w^429660, w^220968, w^12276, w^983103, w^774411, w^565719, w^357027, w^148335, w^910470, w^701778, w^493086, w^284394, w^75702, w^1046529, w^837837, w^629145, w^420453, w^211761, w^3069, w^973896, w^765204, w^556512, w^347820, w^139128, w^901263, w^692571, w^483879, w^275187, w^66495, w^1037322, w^828630, w^619938, w^411246, w^202554, w^964689, w^755997, w^547305, w^338613, w^129921, w^892056, w^683364, w^474672, w^265980, w^57288, w^1028115, w^819423, w^610731, w^402039, w^193347, w^955482, w^746790, w^538098, w^329406, w^120714, w^882849, w^674157, w^465465, w^256773, w^48081, w^1018908, w^810216, w^601524, w^392832, w^184140, w^946275, w^737583, w^528891, w^320199, w^111507, w^873642, w^664950, w^456258, w^247566, w^38874, w^1009701, w^801009, w^592317, w^383625, w^174933, w^937068, w^728376, w^519684, w^310992, w^102300, w^864435, w^655743, w^447051, w^238359, w^29667, w^1000494, w^791802, w^583110, w^374418, w^165726, w^927861, w^719169, w^510477, w^301785, w^93093, w^855228, w^646536, w^437844, w^229152, w^20460, w^991287, w^782595, w^573903, w^365211, w^156519, w^918654, w^709962, w^501270, w^292578, w^83886, w^846021, w^637329, w^428637, w^219945, w^11253, w^982080, w^773388, w^564696, w^356004, w^147312, w^909447, w^700755, w^492063, w^283371, w^74679, w^1045506, w^836814, w^628122, w^419430, w^210738, w^2046, w^972873, w^764181, w^555489, w^346797, w^138105, w^900240, w^691548, w^482856, w^274164, w^65472, w^1036299, w^827607, w^618915, w^410223, w^201531, w^963666, w^754974, w^546282, w^337590, w^128898, w^891033, w^682341, w^473649, w^264957, w^56265, w^1027092, w^818400, w^609708, w^401016, w^192324, w^954459, w^745767, w^537075, w^328383, w^119691, w^881826, w^673134, w^464442, w^255750, w^47058, w^1017885, w^809193, w^600501, w^391809, w^183117, w^945252, w^736560, w^527868, w^319176, w^110484, w^872619, w^663927, w^455235, w^246543, w^37851, w^1008678, w^799986, w^591294, w^382602, w^173910, w^936045, w^727353, w^518661, w^309969, w^101277, w^863412, w^654720, w^446028, w^237336, w^28644, w^999471, w^790779, w^582087, w^373395, w^164703, w^926838, w^718146, w^509454, w^300762, w^92070, w^854205, w^645513, w^436821, w^228129, w^19437, w^990264, w^781572, w^572880, w^364188, w^155496, w^917631, w^708939, w^500247, w^291555, w^82863, w^844998, w^636306, w^427614, w^218922, w^10230, w^981057, w^772365, w^563673, w^354981, w^146289, w^908424, w^699732, w^491040, w^282348, w^73656, w^1044483, w^835791, w^627099, w^418407, w^209715, w^1023, w^971850, w^763158, w^554466, w^345774, w^137082, w^899217, w^690525, w^481833, w^273141, w^64449, w^1035276, w^826584, w^617892, w^409200, w^200508, w^962643, w^753951, w^545259, w^336567, w^127875, w^890010, w^681318, w^472626, w^263934, w^55242, w^1026069, w^817377, w^608685, w^399993, w^191301, w^953436, w^744744, w^536052, w^327360, w^118668, w^880803, w^672111, w^463419, w^254727, w^46035, w^1016862, w^808170, w^599478, w^390786, w^182094, w^944229, w^735537, w^526845, w^318153, w^109461, w^871596, w^662904, w^454212, w^245520, w^36828, w^1007655, w^798963, w^590271, w^381579, w^172887, w^935022, w^726330, w^517638, w^308946, w^100254, w^862389, w^653697, w^445005, w^236313, w^27621, w^9 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:51:20 2004 Input: test_bete:=function(p,K,R) return forall {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) eq 1 }; end function; test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if ((-a)^n eq 1) then return false; else w:=RootOfUnity(n,K); val:={}; wj:=1; r:=k mod n; for j in [0..n-1] do val:=val join { (wj+a)^l*wj^k }; if (#val ne (j+1)) then return false; end if; wj:=wj*w; end for; end if; print #val; print val; return true; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); p:=x^89*(x^(2^10-1)+1); time test_bete(p,K,R); time test_niederreiter(89,2^10-1,1,K,R); Gcd(#K-1,2^10-1); Output: Magma V2.10-6 Mon Mar 29 2004 10:51:16 on modular [Seed = 4241815906] ------------------------------------- false Time: 0.070 1025 { w^970827, w^762135, w^553443, w^344751, w^136059, w^898194, w^689502, w^480810, w^272118, w^63426, w^1034253, w^825561, w^616869, w^408177, w^199485, w^961620, w^752928, w^544236, w^335544, w^126852, w^888987, w^680295, w^471603, w^262911, w^54219, w^1025046, w^816354, w^607662, w^398970, w^190278, w^952413, w^743721, w^535029, w^326337, w^117645, w^879780, w^671088, w^462396, w^253704, w^45012, w^1015839, w^807147, w^598455, w^389763, w^181071, w^943206, w^734514, w^525822, w^317130, w^108438, w^870573, w^661881, w^453189, w^244497, w^35805, w^1006632, w^797940, w^589248, w^380556, w^171864, w^933999, w^725307, w^516615, w^307923, w^99231, w^861366, w^652674, w^443982, w^235290, w^26598, w^997425, w^788733, w^580041, w^371349, w^162657, w^924792, w^716100, w^507408, w^298716, w^90024, w^852159, w^643467, w^434775, w^226083, w^17391, w^988218, w^779526, w^570834, w^362142, w^153450, w^915585, w^706893, w^498201, w^289509, w^80817, w^842952, w^634260, w^425568, w^216876, w^8184, w^979011, w^770319, w^561627, w^352935, w^144243, w^906378, w^697686, w^488994, w^280302, w^71610, w^1042437, w^833745, w^625053, w^416361, w^207669, w^969804, w^761112, w^552420, w^343728, w^135036, w^897171, w^688479, w^479787, w^271095, w^62403, w^1033230, w^824538, w^615846, w^407154, w^198462, w^960597, w^751905, w^543213, w^334521, w^125829, w^887964, w^679272, w^470580, w^261888, w^53196, w^1024023, w^815331, w^606639, w^397947, w^189255, w^951390, w^742698, w^534006, w^325314, w^116622, w^878757, w^670065, w^461373, w^252681, w^43989, w^1014816, w^806124, w^597432, w^388740, w^180048, w^942183, w^733491, w^524799, w^316107, w^107415, w^869550, w^660858, w^452166, w^243474, w^34782, w^1005609, w^796917, w^588225, w^379533, w^170841, w^932976, w^724284, w^515592, w^306900, w^98208, w^860343, w^651651, w^442959, w^234267, w^25575, w^996402, w^787710, w^579018, w^370326, w^161634, w^923769, w^715077, w^506385, w^297693, w^89001, w^851136, w^642444, w^433752, w^225060, w^16368, w^987195, w^778503, w^569811, w^361119, w^152427, w^914562, w^705870, w^497178, w^288486, w^79794, w^841929, w^633237, w^424545, w^215853, w^7161, w^977988, w^769296, w^560604, w^351912, w^143220, w^905355, w^696663, w^487971, w^279279, w^70587, w^1041414, w^832722, w^624030, w^415338, w^206646, w^968781, w^760089, w^551397, w^342705, w^134013, w^896148, w^687456, w^478764, w^270072, w^61380, w^1032207, w^823515, w^614823, w^406131, w^197439, w^959574, w^750882, w^542190, w^333498, w^124806, w^886941, w^678249, w^469557, w^260865, w^52173, w^1023000, w^814308, w^605616, w^396924, w^188232, w^950367, w^741675, w^532983, w^324291, w^115599, w^877734, w^669042, w^460350, w^251658, w^42966, w^1013793, w^805101, w^596409, w^387717, w^179025, w^941160, w^732468, w^523776, w^315084, w^106392, w^868527, w^659835, w^451143, w^242451, w^33759, w^1004586, w^795894, w^587202, w^378510, w^169818, w^931953, w^723261, w^514569, w^305877, w^97185, w^859320, w^650628, w^441936, w^233244, w^24552, w^995379, w^786687, w^577995, w^369303, w^160611, w^922746, w^714054, w^505362, w^296670, w^87978, w^850113, w^641421, w^432729, w^224037, w^15345, w^986172, w^777480, w^568788, w^360096, w^151404, w^913539, w^704847, w^496155, w^287463, w^78771, w^840906, w^632214, w^423522, w^214830, w^6138, w^976965, w^768273, w^559581, w^350889, w^142197, w^904332, w^695640, w^486948, w^278256, w^69564, w^1040391, w^831699, w^623007, w^414315, w^205623, w^967758, w^759066, w^550374, w^341682, w^132990, w^895125, w^686433, w^477741, w^269049, w^60357, w^1031184, w^822492, w^613800, w^405108, w^196416, w^958551, w^749859, w^541167, w^332475, w^123783, w^885918, w^677226, w^468534, w^259842, w^51150, w^1021977, w^813285, w^604593, w^395901, w^187209, w^949344, w^740652, w^531960, w^323268, w^114576, w^876711, w^668019, w^459327, w^250635, w^41943, w^1012770, w^804078, w^595386, w^386694, w^178002, w^940137, w^731445, w^522753, w^314061, w^105369, w^867504, w^658812, w^450120, w^241428, w^32736, w^1003563, w^794871, w^586179, w^377487, w^168795, w^930930, w^722238, w^513546, w^304854, w^96162, w^858297, w^649605, w^440913, w^232221, w^23529, w^994356, w^785664, w^576972, w^368280, w^159588, w^921723, w^713031, w^504339, w^295647, w^86955, w^849090, w^640398, w^431706, w^223014, w^14322, w^985149, w^776457, w^567765, w^359073, w^150381, w^912516, w^703824, w^495132, w^286440, w^77748, 0, w^839883, w^631191, w^422499, w^213807, w^5115, w^975942, w^767250, w^558558, w^349866, w^141174, w^903309, w^694617, w^485925, w^277233, w^68541, w^1039368, w^830676, w^621984, w^413292, w^204600, w^966735, w^758043, w^549351, w^340659, w^131967, w^894102, w^685410, w^476718, w^268026, w^59334, w^1030161, w^821469, w^612777, w^404085, w^195393, w^957528, w^748836, w^540144, w^331452, w^122760, w^884895, w^676203, w^467511, w^258819, w^50127, w^1020954, w^812262, w^603570, w^394878, w^186186, w^948321, w^739629, w^530937, w^322245, w^113553, w^875688, w^666996, w^458304, w^249612, w^40920, w^1011747, w^803055, w^594363, w^385671, w^176979, w^939114, w^730422, w^521730, w^313038, w^104346, w^866481, w^657789, w^449097, w^240405, w^31713, w^1002540, w^793848, w^585156, w^376464, w^167772, w^929907, w^721215, w^512523, w^303831, w^95139, w^857274, w^648582, w^439890, w^231198, w^22506, w^993333, w^784641, w^575949, w^367257, w^158565, w^920700, w^712008, w^503316, w^294624, w^85932, w^848067, w^639375, w^430683, w^221991, w^13299, w^984126, w^775434, w^566742, w^358050, w^149358, w^911493, w^702801, w^494109, w^285417, w^76725, w^1047552, w^838860, w^630168, w^421476, w^212784, w^4092, w^974919, w^766227, w^557535, w^348843, w^140151, w^902286, w^693594, w^484902, w^276210, w^67518, w^1038345, w^829653, w^620961, w^412269, w^203577, w^965712, w^757020, w^548328, w^339636, w^130944, w^893079, w^684387, w^475695, w^267003, w^58311, w^1029138, w^820446, w^611754, w^403062, w^194370, w^956505, w^747813, w^539121, w^330429, w^121737, w^883872, w^675180, w^466488, w^257796, w^49104, w^1019931, w^811239, w^602547, w^393855, w^185163, w^947298, w^738606, w^529914, w^321222, w^112530, w^874665, w^665973, w^457281, w^248589, w^39897, w^1010724, w^802032, w^593340, w^384648, w^175956, w^938091, w^729399, w^520707, w^312015, w^103323, w^865458, w^656766, w^448074, w^239382, w^30690, w^1001517, w^792825, w^584133, w^375441, w^166749, w^928884, w^720192, w^511500, w^302808, w^94116, w^856251, w^647559, w^438867, w^230175, w^21483, w^992310, w^783618, w^574926, w^366234, w^157542, w^919677, w^710985, w^502293, w^293601, w^84909, w^847044, w^638352, w^429660, w^220968, w^12276, w^983103, w^774411, w^565719, w^357027, w^148335, w^910470, w^701778, w^493086, w^284394, w^75702, w^1046529, w^837837, w^629145, w^420453, w^211761, w^3069, w^973896, w^765204, w^556512, w^347820, w^139128, w^901263, w^692571, w^483879, w^275187, w^66495, w^1037322, w^828630, w^619938, w^411246, w^202554, w^964689, w^755997, w^547305, w^338613, w^129921, w^892056, w^683364, w^474672, w^265980, w^57288, w^1028115, w^819423, w^610731, w^402039, w^193347, w^955482, w^746790, w^538098, w^329406, w^120714, w^882849, w^674157, w^465465, w^256773, w^48081, w^1018908, w^810216, w^601524, w^392832, w^184140, w^946275, w^737583, w^528891, w^320199, w^111507, w^873642, w^664950, w^456258, w^247566, w^38874, w^1009701, w^801009, w^592317, w^383625, w^174933, w^937068, w^728376, w^519684, w^310992, w^102300, w^864435, w^655743, w^447051, w^238359, w^29667, w^1000494, w^791802, w^583110, w^374418, w^165726, w^927861, w^719169, w^510477, w^301785, w^93093, w^855228, w^646536, w^437844, w^229152, w^20460, w^991287, w^782595, w^573903, w^365211, w^156519, w^918654, w^709962, w^501270, w^292578, w^83886, w^846021, w^637329, w^428637, w^219945, w^11253, w^982080, w^773388, w^564696, w^356004, w^147312, w^909447, w^700755, w^492063, w^283371, w^74679, w^1045506, w^836814, w^628122, w^419430, w^210738, w^2046, w^972873, w^764181, w^555489, w^346797, w^138105, w^900240, w^691548, w^482856, w^274164, w^65472, w^1036299, w^827607, w^618915, w^410223, w^201531, w^963666, w^754974, w^546282, w^337590, w^128898, w^891033, w^682341, w^473649, w^264957, w^56265, w^1027092, w^818400, w^609708, w^401016, w^192324, w^954459, w^745767, w^537075, w^328383, w^119691, w^881826, w^673134, w^464442, w^255750, w^47058, w^1017885, w^809193, w^600501, w^391809, w^183117, w^945252, w^736560, w^527868, w^319176, w^110484, w^872619, w^663927, w^455235, w^246543, w^37851, w^1008678, w^799986, w^591294, w^382602, w^173910, w^936045, w^727353, w^518661, w^309969, w^101277, w^863412, w^654720, w^446028, w^237336, w^28644, w^999471, w^790779, w^582087, w^373395, w^164703, w^926838, w^718146, w^509454, w^300762, w^92070, w^854205, w^645513, w^436821, w^228129, w^19437, w^990264, w^781572, w^572880, w^364188, w^155496, w^917631, w^708939, w^500247, w^291555, w^82863, w^844998, w^636306, w^427614, w^218922, w^10230, w^981057, w^772365, w^563673, w^354981, w^146289, w^908424, w^699732, w^491040, w^282348, w^73656, w^1044483, w^835791, w^627099, w^418407, w^209715, w^1023, w^971850, w^763158, w^554466, w^345774, w^137082, w^899217, w^690525, w^481833, w^273141, w^64449, w^1035276, w^826584, w^617892, w^409200, w^200508, w^962643, w^753951, w^545259, w^336567, w^127875, w^890010, w^681318, w^472626, w^263934, w^55242, w^1026069, w^817377, w^608685, w^399993, w^191301, w^953436, w^744744, w^536052, w^327360, w^118668, w^880803, w^672111, w^463419, w^254727, w^46035, w^1016862, w^808170, w^599478, w^390786, w^182094, w^944229, w^735537, w^526845, w^318153, w^109461, w^871596, w^662904, w^454212, w^245520, w^36828, w^1007655, w^798963, w^590271, w^381579, w^172887, w^935022, w^726330, w^517638, w^308946, w^100254, w^862389, w^653697, w^445005, w^236313, w^27621, w^9 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:52:33 2004 Input: test_bete:=function(p,K,R) return forall {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) eq 1 }; end function; test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if ((-a)^n eq 1) then return false; else w:=RootOfUnity(n,K); val:={}; wj:=1; r:=k mod n; for j in [0..n-1] do val:=val join { (wj+a)^l*wj^k }; if (#val ne (j+1)) then return false; end if; wj:=wj*w; end for; end if; print #val; return true; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); p:=x^89*(x^(2^10-1)+1); time test_bete(p,K,R); time test_niederreiter(89,2^10-1,1,K,R); 2^20; Output: Magma V2.10-6 Mon Mar 29 2004 10:52:29 on modular [Seed = 4124963746] ------------------------------------- false Time: 0.060 1025 true Time: 0.250 1048576 Total time: 3.929 seconds, Total memory usage: 14.49MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:52:50 2004 Input: test_bete:=function(p,K,R) return forall {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) eq 1 }; end function; test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if ((-a)^n eq 1) then return false; else w:=RootOfUnity(n,K); val:={}; wj:=1; r:=k mod n; for j in [0..n-1] do val:=val join { (wj+a)^l*wj^k }; if (#val ne (j+1)) then return false; end if; wj:=wj*w; end for; end if; print #val; return true; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); p:=x^89*(x^(2^10-1)+1); time test_bete(p,K,R); time test_niederreiter(89,2^10-1,1,K,R); w^(2^20+5); Output: Magma V2.10-6 Mon Mar 29 2004 10:52:46 on modular [Seed = 3454389225] ------------------------------------- false Time: 0.070 1025 true Time: 0.250 w^6 Total time: 3.899 seconds, Total memory usage: 14.49MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:53:30 2004 Input: test_bete:=function(p,K,R) return forall {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) eq 1 }; end function; test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if ((-a)^n eq 1) then return false; else w:=RootOfUnity(n,K); val:={}; wj:=1; r:=k mod n; for j in [0..n-1] do val:=val join { (wj+a)^l*wj^k }; if (#val ne (j+1)) then return false; end if; wj:=wj*w; end for; end if; print #val; return true; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); p:=x^89*(x^(2^10-1)+1); time test_bete(p,K,R); time test_niederreiter(89,2^10-1,1,K,R); {1} join {1}; Output: Magma V2.10-6 Mon Mar 29 2004 10:53:26 on modular [Seed = 3320693721] ------------------------------------- false Time: 0.070 1025 true Time: 0.250 { 1 } Total time: 3.959 seconds, Total memory usage: 14.49MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:53:47 2004 Input: test_bete:=function(p,K,R) return forall {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) eq 1 }; end function; test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if ((-a)^n eq 1) then return false; else w:=RootOfUnity(n,K); val:={}; wj:=1; r:=k mod n; for j in [0..n-1] do val:=val join { (wj+a)^l*wj^k }; if (#val ne (j+1)) then return false; end if; wj:=wj*w; end for; end if; print #val; return true; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); p:=x^89*(x^(2^10-1)+1); time test_bete(p,K,R); time test_niederreiter(89,2^10-1,1,K,R); {w^1025} join {w}; Output: Magma V2.10-6 Mon Mar 29 2004 10:53:43 on modular [Seed = 3723877168] ------------------------------------- false Time: 0.070 1025 true Time: 0.250 { w, w^1025 } Total time: 3.959 seconds, Total memory usage: 14.49MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:54:02 2004 Input: test_bete:=function(p,K,R) return forall {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) eq 1 }; end function; test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if ((-a)^n eq 1) then return false; else w:=RootOfUnity(n,K); val:={}; wj:=1; r:=k mod n; for j in [0..n-1] do val:=val join { (wj+a)^l*wj^k }; if (#val ne (j+1)) then return false; end if; wj:=wj*w; end for; end if; print #val; return true; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); p:=x^89*(x^(2^10-1)+1); time test_bete(p,K,R); time test_niederreiter(89,2^10-1,1,K,R); {w^(2^20)} join {w}; Output: Magma V2.10-6 Mon Mar 29 2004 10:53:58 on modular [Seed = 2860690518] ------------------------------------- false Time: 0.060 1025 true Time: 0.250 { w } Total time: 3.919 seconds, Total memory usage: 14.49MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:54:31 2004 Input: test_bete:=function(p,K,R) return forall {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) eq 1 }; end function; test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if ((-a)^n eq 1) then return false; else w:=RootOfUnity(n,K); val:={}; wj:=1; r:=k mod n; for j in [0..n-1] do val:=val join { (wj+a)^l*wj^k }; if (#val ne (j+1)) then print j; return false; end if; wj:=wj*w; end for; end if; print #val; return true; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); p:=x^89*(x^(2^10-1)+1); time test_bete(p,K,R); time test_niederreiter(89,2^10-1,1,K,R); {w^(2^20)} join {w}; Output: Magma V2.10-6 Mon Mar 29 2004 10:54:27 on modular [Seed = 2726995068] ------------------------------------- false Time: 0.070 1025 true Time: 0.250 { w } Total time: 3.859 seconds, Total memory usage: 14.49MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:55:19 2004 Input: test_bete:=function(p,K,R) return forall {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) eq 1 }; end function; test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if ((-a)^n eq 1) then return false; else w:=RootOfUnity(n,K); val:={}; wj:=1; r:=k mod n; for j in [0..n-1] do val:=val join { (wj+a)^l*wj^k }; if (#val ne (j+1)) then print j; return false; end if; wj:=wj*w; end for; end if; print #val; return true; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); p:=x^89*(x^(2^10-1)+1); time test_bete(p,K,R); time test_niederreiter(89,2^10-1,1,K,R); Gcd(Modexp(x,q,p)-x,p); Output: Magma V2.10-6 Mon Mar 29 2004 10:55:15 on modular [Seed = 3197548599] ------------------------------------- false Time: 0.070 1025 true Time: 0.240 x^1024 + x Total time: 3.899 seconds, Total memory usage: 14.49MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:56:08 2004 Input: test_bete:=function(p,K,R) return forall {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) eq 1 }; end function; test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if ((-a)^n eq 1) then return false; else w:=RootOfUnity(n,K); val:={}; wj:=1; r:=k mod n; for j in [0..n-1] do val:=val join { (wj+a)^l*wj^k }; if (#val ne (j+1)) then print j; return false; end if; wj:=wj*w; end for; end if; print #val; return true; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); p:=x^89*(x^(2^10-1)+1); time test_bete(p,K,R); time test_niederreiter(89,2^10-1,1,K,R); Factorization(Gcd(Modexp(x,q,p)-x,p)); Output: Magma V2.10-6 Mon Mar 29 2004 10:56:00 on modular [Seed = 3080696013] ------------------------------------- false Time: 0.070 1025 true Time: 0.250 [ , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , := GF(q); R := PolynomialRing(K); p:=x^89*(x^(2^10-1)+1); 1023*1025; 2^20; Output: Magma V2.10-6 Mon Mar 29 2004 10:58:03 on modular [Seed = 2209055842] ------------------------------------- 1048575 1048576 Total time: 3.579 seconds, Total memory usage: 14.39MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 10:58:50 2004 Input: test_bete:=function(p,K,R) return forall {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) eq 1 }; end function; test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if ((-a)^n eq 1) then return false; else w:=RootOfUnity(n,K); val:={}; wj:=1; r:=k mod n; for j in [0..n-1] do val:=val join { (wj+a)^l*wj^k }; if (#val ne (j+1)) then print j; return false; end if; wj:=wj*w; end for; end if; print #val; return true; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); p:=x^89*(x^(2^10-1)+1); test_bete(p,K,R); Output: Magma V2.10-6 Mon Mar 29 2004 10:58:47 on modular [Seed = 2612239430] ------------------------------------- false Total time: 3.629 seconds, Total memory usage: 14.49MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 11:01:09 2004 Input: test_bete:=function(p,K,R) return forall {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) eq 1 }; end function; test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if IsOne((-a)^n) then return false; else w:=RootOfUnity(n,K); val:={}; wj:=1; r:=k mod n; for j in [0..n-1] do val:=val join { (wj+a)^l*wj^k }; if (#val ne (j+1)) then print j; return false; end if; wj:=wj*w; end for; end if; print #val; return true; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); p:=x^89*(x^(2^10-1)+1); test_bete(p,K,R); test_niederreiter(89,2^10-1,1,K,R); Output: Magma V2.10-6 Mon Mar 29 2004 11:01:05 on modular [Seed = 2136438613] ------------------------------------- false 1025 true Total time: 3.949 seconds, Total memory usage: 14.39MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 11:01:45 2004 Input: test_bete:=function(p,K,R) return forall {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) eq 1 }; end function; test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if IsOne((-a)^n) then return false; else w:=RootOfUnity(n,K); val:={}; wj:=1; r:=k mod n; for j in [0..n-1] do val:=val join { (wj+a)^l*wj^k }; if (#val ne (j+1)) then return false; end if; wj:=wj*w; end for; end if; return true; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); p:=x^89*(x^(2^10-1)+1); test_bete(p,K,R); test_niederreiter(89,2^10-1,1,K,R); Output: Magma V2.10-6 Mon Mar 29 2004 11:01:41 on modular [Seed = 2002747257] ------------------------------------- false true Total time: 3.889 seconds, Total memory usage: 14.49MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 11:03:16 2004 Input: m:=1; upperBound:=10; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); ZetaFunction(C); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 11:03:13 on modular [Seed = 1332168677] ------------------------------------- (25*$.1^4 + 10*$.1^2 + 1)/(5*$.1^2 - 6*$.1 + 1) 6 (49*$.1^4 + 14*$.1^3 + 2*$.1 + 1)/(7*$.1^2 - 8*$.1 + 1) 10 Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 11:03:23 2004 Input: test_bete:=function(p,K,R) return forall {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) eq 1 }; end function; test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if IsOne((-a)^n) then return false; else omega:=RootOfUnity(n,K); val:={}; omegaj:=1; r:=k mod n; for j in [0..n-1] do val:=val join { (omegaj+a)^l*omegaj^k }; if (#val ne (j+1)) then return false; end if; omegaj:=omegaj*w; end for; end if; return true; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); p:=x^89*(x^(2^10-1)+1); test_bete(p,K,R); test_niederreiter(89,2^10-1,1,K,R); Output: Magma V2.10-6 Mon Mar 29 2004 11:03:19 on modular [Seed = 1181634282] ------------------------------------- >> omegaj:=omegaj*w; ^ User error: Identifier 'w' has not been declared or assigned false >> test_niederreiter(89,2^10-1,1,K,R);; ^ User error: Identifier 'test_niederreiter' has not been declared or assigned Total time: 4.139 seconds, Total memory usage: 14.48MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 11:03:25 2004 Input: m:=3; upperBound:=10; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); ZetaFunction(C); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 11:03:21 on modular [Seed = 1517441784] ------------------------------------- (15625*$.1^4 + 250*$.1^2 + 1)/(125*$.1^2 - 126*$.1 + 1) 126 (117649*$.1^4 + 17150*$.1^3 + 1176*$.1^2 + 50*$.1 + 1)/(343*$.1^2 - 344*$.1 + 1) 394 Total time: 3.869 seconds, Total memory usage: 3.60MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 11:03:37 2004 Input: m:=2; upperBound:=10; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); ZetaFunction(C); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 11:03:34 on modular [Seed = 1417436393] ------------------------------------- (625*$.1^4 + 500*$.1^3 + 150*$.1^2 + 20*$.1 + 1)/(25*$.1^2 - 26*$.1 + 1) 46 (2401*$.1^4 - 196*$.1^3 + 42*$.1^2 - 4*$.1 + 1)/(49*$.1^2 - 50*$.1 + 1) 46 Total time: 3.039 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 11:04:05 2004 Input: test_bete:=function(p,K,R) return forall {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) eq 1 }; end function; test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if IsOne((-a)^n) then return false; else omega:=RootOfUnity(n,K); val:={}; wj:=1; r:=k mod n; for j in [0..n-1] do val:=val join { (wj+a)^l*wj^k }; if (#val ne (j+1)) then return false; end if; wj=wj*w; end for; end if; return true; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); p:=x^89*(x^(2^10-1)+1); test_bete(p,K,R); test_niederreiter(89,2^10-1,1,K,R); Output: Magma V2.10-6 Mon Mar 29 2004 11:04:02 on modular [Seed = 571091643] ------------------------------------- >> wj=wj*w; ^ User error: Identifier 'w' has not been declared or assigned false >> test_niederreiter(89,2^10-1,1,K,R);; ^ User error: Identifier 'test_niederreiter' has not been declared or assigned Total time: 3.709 seconds, Total memory usage: 14.48MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 11:04:17 2004 Input: test_bete:=function(p,K,R) return forall {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) eq 1 }; end function; test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if IsOne((-a)^n) then return false; else w:=RootOfUnity(n,K); val:={}; wj:=1; r:=k mod n; for j in [0..n-1] do val:=val join { (wj+a)^l*wj^k }; if (#val ne (j+1)) then return false; end if; wj=wj*w; end for; end if; return true; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); p:=x^89*(x^(2^10-1)+1); test_bete(p,K,R); test_niederreiter(89,2^10-1,1,K,R); Output: Magma V2.10-6 Mon Mar 29 2004 11:04:14 on modular [Seed = 974271151] ------------------------------------- false w^1023 = 1 false Total time: 3.679 seconds, Total memory usage: 14.49MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 11:04:44 2004 Input: test_bete:=function(p,K,R) return forall {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) eq 1 }; end function; test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if IsOne((-a)^n) then return false; else w:=RootOfUnity(n,K); val:={}; wj:=1; r:=k mod n; for j in [0..n-1] do val:=val join { (wj+a)^l*wj^k }; if (#val ne (j+1)) then return false; end if; wj:=wj*w; end for; end if; return true; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); p:=x^89*(x^(2^10-1)+1); test_bete(p,K,R); test_niederreiter(89,2^10-1,1,K,R); Output: Magma V2.10-6 Mon Mar 29 2004 11:04:40 on modular [Seed = 840579905] ------------------------------------- false true Total time: 3.859 seconds, Total memory usage: 14.49MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 11:05:25 2004 Input: test_bete:=function(p,K,R) return forall {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) eq 1 }; end function; test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if IsOne((-a)^n) then return false; else w:=RootOfUnity(n,K); val:={}; wj:=1; r:=k mod n; for j in [0..n] do val:=val join { (wj+a)^l*wj^k }; if (#val ne (j+1)) then return false; end if; wj:=wj*w; end for; end if; return true; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); p:=x^89*(x^(2^10-1)+1); test_bete(p,K,R); test_niederreiter(89,2^10-1,1,K,R); Output: Magma V2.10-6 Mon Mar 29 2004 11:05:21 on modular [Seed = 237373220] ------------------------------------- false false Total time: 3.939 seconds, Total memory usage: 14.49MB ************** MAGMA ***************** Host fontenay-4-81-56-42-102.fbx.proxad.net. (81.56.42.102) Time: Mon Mar 29 11:05:36 2004 Input: test_bete:=function(p,K,R) return forall {a: a in K | Degree(Gcd(Modexp(R.1,#K,p-a)-R.1,p-a)) eq 1 }; end function; test_niederreiter:=function(k,l,a,K,R) d:=Gcd(#K-1,l); n:=(#K-1) div d; if IsOne((-a)^n) then return false; else w:=RootOfUnity(n,K); val:={}; wj:=1; r:=k mod n; for j in [0..n-1] do val:=val join { (wj+a)^l*wj^k }; if (#val ne (j+1)) then return false; end if; wj:=wj*w; end for; end if; return true; end function; q := 2^20; K := GF(q); R := PolynomialRing(K); p:=x^89*(x^(2^10-1)+1); test_bete(p,K,R); test_niederreiter(89,2^10-1,1,K,R); Output: Magma V2.10-6 Mon Mar 29 2004 11:05:32 on modular [Seed = 103681825] ------------------------------------- false true Total time: 3.959 seconds, Total memory usage: 14.49MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 11:14:15 2004 Input: m:=2; upperBound:=20; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); ZetaFunction(C); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 11:14:12 on modular [Seed = 3938640341] ------------------------------------- (625*$.1^4 + 500*$.1^3 + 150*$.1^2 + 20*$.1 + 1)/(25*$.1^2 - 26*$.1 + 1) 46 (2401*$.1^4 - 196*$.1^3 + 42*$.1^2 - 4*$.1 + 1)/(49*$.1^2 - 50*$.1 + 1) 46 (14641*$.1^4 + 3388*$.1^3 + 410*$.1^2 + 28*$.1 + 1)/(121*$.1^2 - 122*$.1 + 1) 150 (28561*$.1^4 + 1352*$.1^3 + 66*$.1^2 + 8*$.1 + 1)/(169*$.1^2 - 170*$.1 + 1) 178 (83521*$.1^4 + 6647*$.1^3 + 528*$.1^2 + 23*$.1 + 1)/(289*$.1^2 - 290*$.1 + 1) 313 (130321*$.1^4 + 12635*$.1^3 + 1008*$.1^2 + 35*$.1 + 1)/(361*$.1^2 - 362*$.1 + 1) 397 Total time: 3.359 seconds, Total memory usage: 5.44MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 11:14:39 2004 Input: m:=1; upperBound:=20; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); ZetaFunction(C); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 11:14:36 on modular [Seed = 3788106470] ------------------------------------- (25*$.1^4 + 10*$.1^2 + 1)/(5*$.1^2 - 6*$.1 + 1) 6 (49*$.1^4 + 14*$.1^3 + 2*$.1 + 1)/(7*$.1^2 - 8*$.1 + 1) 10 (121*$.1^4 - 22*$.1^3 + 16*$.1^2 - 2*$.1 + 1)/(11*$.1^2 - 12*$.1 + 1) 10 (169*$.1^4 + 52*$.1^3 + 12*$.1^2 + 4*$.1 + 1)/(13*$.1^2 - 14*$.1 + 1) 18 (289*$.1^4 + 51*$.1^3 + 16*$.1^2 + 3*$.1 + 1)/(17*$.1^2 - 18*$.1 + 1) 21 (361*$.1^4 + 19*$.1^3 + 18*$.1^2 + $.1 + 1)/(19*$.1^2 - 20*$.1 + 1) 21 Total time: 2.969 seconds, Total memory usage: 2.29MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 11:15:06 2004 Input: m:=2; upperBound:=20; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); ZetaFunction(C); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 11:15:02 on modular [Seed = 4241815313] ------------------------------------- (625*$.1^4 + 500*$.1^3 + 150*$.1^2 + 20*$.1 + 1)/(25*$.1^2 - 26*$.1 + 1) 46 (2401*$.1^4 - 196*$.1^3 + 42*$.1^2 - 4*$.1 + 1)/(49*$.1^2 - 50*$.1 + 1) 46 (14641*$.1^4 + 3388*$.1^3 + 410*$.1^2 + 28*$.1 + 1)/(121*$.1^2 - 122*$.1 + 1) 150 (28561*$.1^4 + 1352*$.1^3 + 66*$.1^2 + 8*$.1 + 1)/(169*$.1^2 - 170*$.1 + 1) 178 (83521*$.1^4 + 6647*$.1^3 + 528*$.1^2 + 23*$.1 + 1)/(289*$.1^2 - 290*$.1 + 1) 313 (130321*$.1^4 + 12635*$.1^3 + 1008*$.1^2 + 35*$.1 + 1)/(361*$.1^2 - 362*$.1 + 1) 397 Total time: 3.399 seconds, Total memory usage: 5.44MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 11:15:46 2004 Input: for p in [5..10] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^2)); C := HyperellipticCurve(x^6+1); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); numberOfRoots:=#R; summe:=0; for i in [1..numberOfRoots] do summe:=summe+2/R[i][1]^2; end for; numberOfPoints:=p^2+1-summe; print Round(numberOfPoints), ","; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 11:15:43 on modular [Seed = 3420700687] ------------------------------------- -24 , 238 , Total time: 2.999 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 11:16:16 2004 Input: for p in [5..20] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^2)); C := HyperellipticCurve(x^5+x+2); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); numberOfRoots:=#R; summe:=0; for i in [1..numberOfRoots] do summe:=summe+2/R[i][1]^2; end for; numberOfPoints:=p^2+1-summe; print Round(numberOfPoints), ","; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 11:16:13 on modular [Seed = 3253324391] ------------------------------------- -24 , 186 , 194 , 306 , 1344 , 1944 , Total time: 3.569 seconds, Total memory usage: 5.53MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 11:16:58 2004 Input: for p in [5..20] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^1)); C := HyperellipticCurve(x^5+x+2); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); numberOfRoots:=#R; summe:=0; for i in [1..numberOfRoots] do summe:=summe+2/R[i][1]^2; end for; numberOfPoints:=p^2+1-summe; print Round(numberOfPoints), ","; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 11:16:55 on modular [Seed = 3740718402] ------------------------------------- 46 , 42 , 178 , 186 , 336 , 432 , Total time: 3.149 seconds, Total memory usage: 2.33MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 11:17:23 2004 Input: m:=1; upperBound:=10; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); ZetaFunction(C); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 11:17:20 on modular [Seed = 3590183342] ------------------------------------- (25*$.1^4 + 10*$.1^2 + 1)/(5*$.1^2 - 6*$.1 + 1) 6 (49*$.1^4 + 14*$.1^3 + 2*$.1 + 1)/(7*$.1^2 - 8*$.1 + 1) 10 Total time: 3.029 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 11:25:53 2004 Input: m:=3; upperBound:=20; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); ZetaFunction(C); #C; end if; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Mar 29 2004 11:25:31 on modular [Seed = 3180703789] ------------------------------------- (15625*$.1^4 + 250*$.1^2 + 1)/(125*$.1^2 - 126*$.1 + 1) 126 (117649*$.1^4 + 17150*$.1^3 + 1176*$.1^2 + 50*$.1 + 1)/(343*$.1^2 - 344*$.1 + 1) 394 Errors: /home/mfd/gomagma: line 2: 11222 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 11:26:36 2004 Input: m:=3; upperBound:=20; for p in [11..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); ZetaFunction(C); #C; end if; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Mar 29 2004 11:26:13 on modular [Seed = 3030170362] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 11231 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 11:27:14 2004 Input: m:=3; upperBound:=11; for p in [11..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); ZetaFunction(C); #C; end if; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Mar 29 2004 11:26:51 on modular [Seed = 2192215202] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 11241 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 11:27:28 2004 Input: m:=3; upperBound:=5; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); ZetaFunction(C); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 11:27:25 on modular [Seed = 2578552735] ------------------------------------- (15625*$.1^4 + 250*$.1^2 + 1)/(125*$.1^2 - 126*$.1 + 1) 126 Total time: 2.979 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 11:33:59 2004 Input: m:=1; upperBound:=100; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); ZetaFunction(C); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 11:33:56 on modular [Seed = 1682729980] ------------------------------------- (25*$.1^4 + 10*$.1^2 + 1)/(5*$.1^2 - 6*$.1 + 1) 6 (49*$.1^4 + 14*$.1^3 + 2*$.1 + 1)/(7*$.1^2 - 8*$.1 + 1) 10 (121*$.1^4 - 22*$.1^3 + 16*$.1^2 - 2*$.1 + 1)/(11*$.1^2 - 12*$.1 + 1) 10 (169*$.1^4 + 52*$.1^3 + 12*$.1^2 + 4*$.1 + 1)/(13*$.1^2 - 14*$.1 + 1) 18 (289*$.1^4 + 51*$.1^3 + 16*$.1^2 + 3*$.1 + 1)/(17*$.1^2 - 18*$.1 + 1) 21 (361*$.1^4 + 19*$.1^3 + 18*$.1^2 + $.1 + 1)/(19*$.1^2 - 20*$.1 + 1) 21 (529*$.1^4 + 253*$.1^3 + 70*$.1^2 + 11*$.1 + 1)/(23*$.1^2 - 24*$.1 + 1) 35 (841*$.1^4 - 87*$.1^3 + 48*$.1^2 - 3*$.1 + 1)/(29*$.1^2 - 30*$.1 + 1) 27 (961*$.1^4 + 155*$.1^3 + 26*$.1^2 + 5*$.1 + 1)/(31*$.1^2 - 32*$.1 + 1) 37 (1369*$.1^4 + 37*$.1^3 - 52*$.1^2 + $.1 + 1)/(37*$.1^2 - 38*$.1 + 1) 39 (1681*$.1^4 + 246*$.1^3 + 78*$.1^2 + 6*$.1 + 1)/(41*$.1^2 - 42*$.1 + 1) 48 (1849*$.1^4 - 344*$.1^3 + 78*$.1^2 - 8*$.1 + 1)/(43*$.1^2 - 44*$.1 + 1) 36 (2209*$.1^4 + 282*$.1^3 + 54*$.1^2 + 6*$.1 + 1)/(47*$.1^2 - 48*$.1 + 1) 54 (2809*$.1^4 + 212*$.1^3 + 82*$.1^2 + 4*$.1 + 1)/(53*$.1^2 - 54*$.1 + 1) 58 (3481*$.1^4 + 118*$.1^3 + 80*$.1^2 + 2*$.1 + 1)/(59*$.1^2 - 60*$.1 + 1) 62 (3721*$.1^4 - 122*$.1^3 - 14*$.1^2 - 2*$.1 + 1)/(61*$.1^2 - 62*$.1 + 1) 60 (4489*$.1^4 + 335*$.1^3 - 6*$.1^2 + 5*$.1 + 1)/(67*$.1^2 - 68*$.1 + 1) 73 (5041*$.1^4 + 78*$.1^2 + 1)/(71*$.1^2 - 72*$.1 + 1) 72 (5329*$.1^4 - 365*$.1^3 - 24*$.1^2 - 5*$.1 + 1)/(73*$.1^2 - 74*$.1 + 1) 69 (6241*$.1^4 - 158*$.1^3 - 2*$.1 + 1)/(79*$.1^2 - 80*$.1 + 1) 78 (6889*$.1^4 + 747*$.1^3 + 46*$.1^2 + 9*$.1 + 1)/(83*$.1^2 - 84*$.1 + 1) 93 (7921*$.1^4 + 890*$.1^3 + 146*$.1^2 + 10*$.1 + 1)/(89*$.1^2 - 90*$.1 + 1) 100 (9409*$.1^4 + 388*$.1^3 + 22*$.1^2 + 4*$.1 + 1)/(97*$.1^2 - 98*$.1 + 1) 102 Total time: 3.149 seconds, Total memory usage: 3.49MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 11:34:22 2004 Input: m:=1; upperBound:=100; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 11:34:18 on modular [Seed = 2102750491] ------------------------------------- 6 10 10 18 21 21 35 27 37 39 48 36 54 58 62 60 73 72 69 78 93 100 102 Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 11:34:39 2004 Input: m:=1; upperBound:=100; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); ZetaFunction(C); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 11:34:36 on modular [Seed = 1985897990] ------------------------------------- (25*$.1^4 + 10*$.1^2 + 1)/(5*$.1^2 - 6*$.1 + 1) 6 (49*$.1^4 + 14*$.1^3 + 2*$.1 + 1)/(7*$.1^2 - 8*$.1 + 1) 10 (121*$.1^4 - 22*$.1^3 + 16*$.1^2 - 2*$.1 + 1)/(11*$.1^2 - 12*$.1 + 1) 10 (169*$.1^4 + 52*$.1^3 + 12*$.1^2 + 4*$.1 + 1)/(13*$.1^2 - 14*$.1 + 1) 18 (289*$.1^4 + 51*$.1^3 + 16*$.1^2 + 3*$.1 + 1)/(17*$.1^2 - 18*$.1 + 1) 21 (361*$.1^4 + 19*$.1^3 + 18*$.1^2 + $.1 + 1)/(19*$.1^2 - 20*$.1 + 1) 21 (529*$.1^4 + 253*$.1^3 + 70*$.1^2 + 11*$.1 + 1)/(23*$.1^2 - 24*$.1 + 1) 35 (841*$.1^4 - 87*$.1^3 + 48*$.1^2 - 3*$.1 + 1)/(29*$.1^2 - 30*$.1 + 1) 27 (961*$.1^4 + 155*$.1^3 + 26*$.1^2 + 5*$.1 + 1)/(31*$.1^2 - 32*$.1 + 1) 37 (1369*$.1^4 + 37*$.1^3 - 52*$.1^2 + $.1 + 1)/(37*$.1^2 - 38*$.1 + 1) 39 (1681*$.1^4 + 246*$.1^3 + 78*$.1^2 + 6*$.1 + 1)/(41*$.1^2 - 42*$.1 + 1) 48 (1849*$.1^4 - 344*$.1^3 + 78*$.1^2 - 8*$.1 + 1)/(43*$.1^2 - 44*$.1 + 1) 36 (2209*$.1^4 + 282*$.1^3 + 54*$.1^2 + 6*$.1 + 1)/(47*$.1^2 - 48*$.1 + 1) 54 (2809*$.1^4 + 212*$.1^3 + 82*$.1^2 + 4*$.1 + 1)/(53*$.1^2 - 54*$.1 + 1) 58 (3481*$.1^4 + 118*$.1^3 + 80*$.1^2 + 2*$.1 + 1)/(59*$.1^2 - 60*$.1 + 1) 62 (3721*$.1^4 - 122*$.1^3 - 14*$.1^2 - 2*$.1 + 1)/(61*$.1^2 - 62*$.1 + 1) 60 (4489*$.1^4 + 335*$.1^3 - 6*$.1^2 + 5*$.1 + 1)/(67*$.1^2 - 68*$.1 + 1) 73 (5041*$.1^4 + 78*$.1^2 + 1)/(71*$.1^2 - 72*$.1 + 1) 72 (5329*$.1^4 - 365*$.1^3 - 24*$.1^2 - 5*$.1 + 1)/(73*$.1^2 - 74*$.1 + 1) 69 (6241*$.1^4 - 158*$.1^3 - 2*$.1 + 1)/(79*$.1^2 - 80*$.1 + 1) 78 (6889*$.1^4 + 747*$.1^3 + 46*$.1^2 + 9*$.1 + 1)/(83*$.1^2 - 84*$.1 + 1) 93 (7921*$.1^4 + 890*$.1^3 + 146*$.1^2 + 10*$.1 + 1)/(89*$.1^2 - 90*$.1 + 1) 100 (9409*$.1^4 + 388*$.1^3 + 22*$.1^2 + 4*$.1 + 1)/(97*$.1^2 - 98*$.1 + 1) 102 Total time: 3.059 seconds, Total memory usage: 3.49MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Mon Mar 29 11:36:31 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; [IsHomogeneous(f): f in P]; I:=ideal; Dimension(I); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, y^11, y^12, y^13, y^14, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x*y^11, x*y^12, x*y^13, x*y^14, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^2*y^11, x^2*y^12, x^2*y^13, x^2*y^14, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^11*y^5, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; L := [x^14 *y^3]; HomogeneousModuleTestBasis(P, S, L ) ; B, V := HomogeneousModuleTest(P, S, L); B; V; Output: Magma V2.10-6 Mon Mar 29 2004 11:36:28 on modular [Seed = 1147950244] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 [ true, true, true, true, true ] 0 [] [] [ true ] [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, t5, 0, t2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, t4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, t1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] ] Total time: 2.989 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 11:38:26 2004 Input: m:=2; upperBound:=10; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); ZetaFunction(C); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 11:38:23 on modular [Seed = 1567968718] ------------------------------------- (625*$.1^4 + 500*$.1^3 + 150*$.1^2 + 20*$.1 + 1)/(25*$.1^2 - 26*$.1 + 1) 46 (2401*$.1^4 - 196*$.1^3 + 42*$.1^2 - 4*$.1 + 1)/(49*$.1^2 - 50*$.1 + 1) 46 Total time: 2.899 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Mon Mar 29 11:58:53 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; [IsHomogeneous(f): f in P]; I:=ideal; Dimension(I); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, y^11, y^12, y^13, y^14, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x*y^11, x*y^12, x*y^13, x*y^14, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^2*y^11, x^2*y^12, x^2*y^13, x^2*y^14, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^11*y^5, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; L := [y^3]; HomogeneousModuleTestBasis(P, S, L ) ; B, V := HomogeneousModuleTest(P, S, L); B; V; Output: Magma V2.10-6 Mon Mar 29 2004 11:58:50 on modular [Seed = 69996962] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 [ true, true, true, true, true ] 0 [] [] [ true ] [ [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] ] Total time: 2.909 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Mon Mar 29 11:59:43 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; [IsHomogeneous(f): f in P]; I:=ideal; Dimension(I); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, y^11, y^12, y^13, y^14, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x*y^11, x*y^12, x*y^13, x*y^14, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^2*y^11, x^2*y^12, x^2*y^13, x^2*y^14, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^11*y^5, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; L := [y^2]; HomogeneousModuleTestBasis(P, S, L ) ; B, V := HomogeneousModuleTest(P, S, L); B; V; Output: Magma V2.10-6 Mon Mar 29 2004 11:59:40 on modular [Seed = 506858382] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 [ true, true, true, true, true ] 0 [] [] [ true ] [ [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] ] Total time: 2.949 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Mon Mar 29 12:00:10 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; [IsHomogeneous(f): f in P]; I:=ideal; Dimension(I); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, y^11, y^12, y^13, y^14, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x*y^11, x*y^12, x*y^13, x*y^14, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^2*y^11, x^2*y^12, x^2*y^13, x^2*y^14, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^11*y^5, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; L := [x^3]; HomogeneousModuleTestBasis(P, S, L ) ; B, V := HomogeneousModuleTest(P, S, L); B; V; Output: Magma V2.10-6 Mon Mar 29 2004 12:00:07 on modular [Seed = 3904962195] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 [ true, true, true, true, true ] 0 [] [] [ true ] [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] ] Total time: 2.979 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Mon Mar 29 12:07:47 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; [IsHomogeneous(f): f in P]; I:=ideal; Dimension(I); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, y^11, y^12, y^13, y^14, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x*y^11, x*y^12, x*y^13, x*y^14, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^2*y^11, x^2*y^12, x^2*y^13, x^2*y^14, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^11*y^5, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; L := [x^14*y^3]; HomogeneousModuleTestBasis(P, S, L ) ; B, V := HomogeneousModuleTest(P, S, L); B; V; Output: Magma V2.10-6 Mon Mar 29 2004 12:07:44 on modular [Seed = 3420707911] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 [ true, true, true, true, true ] 0 [] [] [ true ] [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, t5, 0, t2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, t4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, t1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] ] Total time: 2.969 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Mon Mar 29 12:17:18 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; [IsHomogeneous(f): f in P]; I:=ideal; Dimension(I); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, y^11, y^12, y^13, y^14, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x*y^11, x*y^12, x*y^13, x*y^14, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^2*y^11, x^2*y^12, x^2*y^13, x^2*y^14, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^11*y^5, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; L := [x^14*y^3]; HomogeneousModuleTestBasis(P, S, L ) ; B, V := HomogeneousModuleTest(P, S, L); B; V; P[5]*S[32] + P[2]*S[34] + S[42]*S[1] + P[4]*S[46] +P[1]*S[94] eq L[2]; Output: Magma V2.10-6 Mon Mar 29 2004 12:17:15 on modular [Seed = 2843849694] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 [ true, true, true, true, true ] 0 [] [] [ true ] [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, t5, 0, t2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, t4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, t1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] ] >> P[5]*S[32] + P[2]*S[34] + S[42]*S[1] + P[4]*S[46] +P[1]*S[94] eq L[2];; ^ Runtime error in '[]': Sequence element 2 not defined Total time: 2.979 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Mon Mar 29 12:17:36 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; [IsHomogeneous(f): f in P]; I:=ideal; Dimension(I); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, y^11, y^12, y^13, y^14, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x*y^11, x*y^12, x*y^13, x*y^14, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^2*y^11, x^2*y^12, x^2*y^13, x^2*y^14, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^11*y^5, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; L := [x^14*y^3]; HomogeneousModuleTestBasis(P, S, L ) ; B, V := HomogeneousModuleTest(P, S, L); B; V; P[5]*S[32] + P[2]*S[34] + S[42]*S[1] + P[4]*S[46] +P[1]*S[94] eq L[1]; Output: Magma V2.10-6 Mon Mar 29 2004 12:17:33 on modular [Seed = 2727000291] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 [ true, true, true, true, true ] 0 [] [] [ true ] [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, t5, 0, t2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, t4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, t1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] ] true Total time: 2.989 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Mon Mar 29 12:18:29 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; [IsHomogeneous(f): f in P]; I:=ideal; Dimension(I); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, y^11, y^12, y^13, y^14, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x*y^11, x*y^12, x*y^13, x*y^14, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^2*y^11, x^2*y^12, x^2*y^13, x^2*y^14, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^11*y^5, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; L := [x^14*y^3]; HomogeneousModuleTestBasis(P, S, L ) ; B, V := HomogeneousModuleTest(P, S, L); B; V; P[5]*S[32] + P[2]*S[34] + S[42]*S[1] + P[4]*S[46] +P[1]*S[94] eq L[1]; S[32]; Output: Magma V2.10-6 Mon Mar 29 2004 12:18:26 on modular [Seed = 3047010235] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 [ true, true, true, true, true ] 0 [] [] [ true ] [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, t5, 0, t2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, t4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, t1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] ] true x^2*y Total time: 2.959 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Mon Mar 29 12:20:27 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; [IsHomogeneous(f): f in P]; I:=ideal; Dimension(I); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, y^11, y^12, y^13, y^14, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x*y^11, x*y^12, x*y^13, x*y^14, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^2*y^11, x^2*y^12, x^2*y^13, x^2*y^14, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^11*y^5, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; L := [x^14*y^3]; HomogeneousModuleTestBasis(P, S, L ) ; B, V := HomogeneousModuleTest(P, S, L); B; V; P[5]*S[32] + P[2]*S[34] + S[42]*S[1] + P[4]*S[46] +P[1]*S[94] eq L[1]; S[32]; S[34]; S[42]; S[46]; S[94]; Output: Magma V2.10-6 Mon Mar 29 2004 12:20:24 on modular [Seed = 2259590194] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 [ true, true, true, true, true ] 0 [] [] [ true ] [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, t5, 0, t2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, t4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, t1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] ] true x^2*y x^2*y^3 x^2*y^11 x^3 x^6*y^3 Total time: 2.929 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Mon Mar 29 12:22:49 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; [IsHomogeneous(f): f in P]; I:=ideal; Dimension(I); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, y^11, y^12, y^13, y^14, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x*y^11, x*y^12, x*y^13, x*y^14, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^2*y^11, x^2*y^12, x^2*y^13, x^2*y^14, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^11*y^5, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; L := [x^14*y^7]; HomogeneousModuleTestBasis(P, S, L ) ; B, V := HomogeneousModuleTest(P, S, L); B; V; Output: Magma V2.10-6 Mon Mar 29 2004 12:22:46 on modular [Seed = 2561704850] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 [ true, true, true, true, true ] 0 [] [] [ true ] [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, t4, t3, 0, 0, 0, t1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, t5, 0, 0, 0, 0, 0, t4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] ] Total time: 2.999 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Mon Mar 29 12:28:10 2004 Input: K := GF(2); R := PolynomialRing(K, [2, 3, 16, 24, 28]); R; P := [z, w, u, y*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4)+y^(1+8)*x^2, x*(u -w*x^2 +z*x^6 -z*y^4 -x^14 +x^8 *y^4 ) +y^2 *(w -z*x^4 +x^12 -y^8 )+x^3*y^8 ] ; [IsHomogeneous(f): f in P]; I:=ideal; Dimension(I); S:=[ 1, y, y^2, y^3, y^4, y^5, y^6, y^7, y^8, y^9, y^10, y^11, y^12, y^13, y^14, x, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6, x*y^7, x*y^8, x*y^9, x*y^10, x*y^11, x*y^12, x*y^13, x*y^14, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^2*y^5, x^2*y^6, x^2*y^7, x^2*y^8, x^2*y^9, x^2*y^10, x^2*y^11, x^2*y^12, x^2*y^13, x^2*y^14, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^3*y^5, x^3*y^6, x^3*y^7, x^3*y^8, x^3*y^9, x^3*y^10, x^3*y^11, x^3*y^12, x^3*y^13, x^3*y^14, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4, x^4*y^5, x^4*y^6, x^4*y^7, x^4*y^8, x^4*y^9, x^4*y^10, x^4*y^11, x^4*y^12, x^4*y^13, x^4*y^14, x^5, x^5*y, x^5*y^2, x^5*y^3, x^5*y^4, x^5*y^5, x^5*y^6, x^5*y^7, x^5*y^8, x^5*y^9, x^5*y^10, x^5*y^11, x^5*y^12, x^5*y^13, x^5*y^14, x^6, x^6*y, x^6*y^2, x^6*y^3, x^6*y^4, x^6*y^5, x^6*y^6, x^6*y^7, x^6*y^8, x^6*y^9, x^6*y^10, x^6*y^11, x^6*y^12, x^6*y^13, x^6*y^14, x^7, x^7*y, x^7*y^2, x^7*y^3, x^7*y^4, x^7*y^5, x^7*y^6, x^7*y^7, x^7*y^8, x^7*y^9, x^7*y^10, x^7*y^11, x^7*y^12, x^7*y^13, x^7*y^14, x^8, x^8*y, x^8*y^2, x^8*y^3, x^8*y^4, x^8*y^5, x^8*y^6, x^9, x^9*y, x^9*y^2, x^9*y^3, x^9*y^4, x^9*y^5, x^9*y^6, x^10, x^10*y, x^10*y^2, x^10*y^3, x^10*y^4, x^10*y^5, x^10*y^6, x^11, x^11*y, x^11*y^2, x^11*y^3, x^11*y^4, x^11*y^5, x^11*y^6, x^12, x^12*y, x^12*y^2, x^13, x^13*y, x^13*y^2, x^14 ]; L := [x^14*y^7]; HomogeneousModuleTestBasis(P, S, L ) ; B, V := HomogeneousModuleTest(P, S, L); B; V; S[103]*P[4] + S[104]*P[3] + S[108]*P[1] + S[132]*P[5] + S[138]*P[4] eq L[1]; S[103]; S[104]; S[108]; S[132]; S[138]; Output: Magma V2.10-6 Mon Mar 29 2004 12:28:07 on modular [Seed = 1782740640] ------------------------------------- Graded Polynomial ring of rank 5 over GF(2) Lexicographical Order Variables: x, y, z, w, u Variable weights: 2 3 16 24 28 [ true, true, true, true, true ] 0 [] [] [ true ] [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, t4, t3, 0, 0, 0, t1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, t5, 0, 0, 0, 0, 0, t4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] ] false x^6*y^12 x^6*y^13 x^7*y^2 x^9*y^4 x^10*y^3 Total time: 2.909 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Mon Mar 29 12:29:20 2004 Input: G25:=GF(2,5); P:=PolynominalRing(G25); Output: Magma V2.10-6 Mon Mar 29 2004 12:29:17 on modular [Seed = 2136433663] ------------------------------------- >> P:=PolynominalRing(G25);; ^ User error: Identifier 'PolynominalRing' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Mon Mar 29 12:29:53 2004 Input: G25:=GF(2,5); P:=PolynomialRing(G25); Output: Magma V2.10-6 Mon Mar 29 2004 12:29:50 on modular [Seed = 1985899285] ------------------------------------- Total time: 3.369 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Mon Mar 29 12:29:54 2004 Input: G25:=GF(2,5); P:=PolynomialRing(G25); Output: Magma V2.10-6 Mon Mar 29 2004 12:29:51 on modular [Seed = 1935371793] ------------------------------------- Total time: 3.339 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee14.uab.es. (158.109.66.14) Time: Mon Mar 29 12:33:23 2004 Input: G2:=GF(2); G3:=GF(3); G5:=GF(5); #(G2); #(G3); #(G5); [x:x in G2]; [x:x in G3]; [x:x in G5]; Z9:=Integers(9); IsField(Z9); Output: Magma V2.10-6 Mon Mar 29 2004 12:33:20 on modular [Seed = 1500595412] ------------------------------------- 2 3 5 [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] false Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee14.uab.es. (158.109.66.14) Time: Mon Mar 29 12:37:49 2004 Input: G2:=GF(2); G3:=GF(3); G5:=GF(5); #(G2); #(G3); #(G5); [x:x in G2]; [x:x in G3]; [x:x in G5]; Z9:=Integers(9); IsField(Z9); /*Z9 no és cos perqué no és un número primer.*/ /*Només formen cos el enters primers, Zp, on p és primer*/ Z9!2; IsInvertible(Z9!6); /* 6 no és invertible perqué el MCD entre 9 i 6 es diferent de 1*/ P3:=PolynomialRing(G3); P3:=x^2+2*x+2; P3; IsIrreducible(P3); P2:=PolynomialRing(G2); P2:=x^4+x+1; P2; IsIrreducible(P2); P5:=PolynomialRing(G5); P5:=x^2+2*x+3; P5; IsIrreducible(P5); P3b:=PolynomialRing(G3); P3b:=x^2+2*x+1; P3b; IsIrreducible(P3b); P2b:=PolynomialRing(G5); P2b:=x^2+4*x+2; P2b; IsIrreducible(P2b); G9:=ext ; G16:=ext ; G25:=ext ; G9b:=ext ; /* No podem crear el cos G9b perqué el polinomi no és irreductible.*/ [Order(i):i in G25 | i ne 0]; #[Order(i):i in G25 | i ne 0 and Order(i) eq #(G25)-1]; /*En general un cos de p^n elements on p es primer té: */ /* Phi(p^n-1) elements primitius.*/ /*En el nostre cas és Phi(5^2-1)=8 */ PrimitiveElement(G25); pmin:=MinimalPolynomial(G25.1); CoefficientRing(pmin); Output: Magma V2.10-6 Mon Mar 29 2004 12:37:46 on modular [Seed = 506855577] ------------------------------------- 2 3 5 [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] false 2 false x^2 + 2*x + 2 true x^4 + x + 1 true x^2 + 2*x + 3 true x^2 + 2*x + 1 false x^2 + 4*x + 2 true >> G9b:=ext ; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 G25.1 Finite field of size 5 Total time: 3.059 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee14.uab.es. (158.109.66.14) Time: Mon Mar 29 12:40:45 2004 Input: Generator(G25); Output: Magma V2.10-6 Mon Mar 29 2004 12:40:42 on modular [Seed = 3855481362] ------------------------------------- >> Generator(G25); ^ User error: Identifier 'G25' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee14.uab.es. (158.109.66.14) Time: Mon Mar 29 12:41:21 2004 Input: PrimitiveElement(G25); pmin:=MinimalPolynomial(G25.1); CoefficientRing(pmin); Generator(G25); Output: Magma V2.10-6 Mon Mar 29 2004 12:41:18 on modular [Seed = 4241810223] ------------------------------------- >> PrimitiveElement(G25); ^ User error: Identifier 'G25' has not been declared or assigned >> pmin:=MinimalPolynomial(G25.1); ^ User error: Identifier 'G25' has not been declared or assigned >> CoefficientRing(pmin); ^ User error: Identifier 'pmin' has not been declared or assigned >> Generator(G25); ^ User error: Identifier 'G25' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee14.uab.es. (158.109.66.14) Time: Mon Mar 29 12:41:43 2004 Input: G25:=ext ; PrimitiveElement(G25); pmin:=MinimalPolynomial(G25.1); CoefficientRing(pmin); Generator(G25); Output: Magma V2.10-6 Mon Mar 29 2004 12:41:40 on modular [Seed = 4158646350] ------------------------------------- >> G25:=ext ; ^ User error: Identifier 'G5' has not been declared or assigned >> PrimitiveElement(G25); ^ User error: Identifier 'G25' has not been declared or assigned >> pmin:=MinimalPolynomial(G25.1); ^ User error: Identifier 'G25' has not been declared or assigned >> CoefficientRing(pmin); ^ User error: Identifier 'pmin' has not been declared or assigned >> Generator(G25); ^ User error: Identifier 'G25' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee14.uab.es. (158.109.66.14) Time: Mon Mar 29 12:42:35 2004 Input: G5:=GF(5); P2b:=PolynomialRing(G5); P2b:=x^2+4*x+2; P2b; G25:=ext ; PrimitiveElement(G25); pmin:=MinimalPolynomial(G25.1); CoefficientRing(pmin); Generator(G25); Output: Magma V2.10-6 Mon Mar 29 2004 12:42:32 on modular [Seed = 3471240875] ------------------------------------- x^2 + 4*x + 2 G25.1 Finite field of size 5 G25.1 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee14.uab.es. (158.109.66.14) Time: Mon Mar 29 12:42:54 2004 Input: Generator(G25); Output: Magma V2.10-6 Mon Mar 29 2004 12:42:51 on modular [Seed = 3253330359] ------------------------------------- >> Generator(G25); ^ User error: Identifier 'G25' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee14.uab.es. (158.109.66.14) Time: Mon Mar 29 12:43:19 2004 Input: G5:=GF(5); P2b:=PolynomialRing(G5); P2b:=x^2+4*x+2; G25:=ext ; PrimitiveElement(G25); pmin:=MinimalPolynomial(G25.1); CoefficientRing(pmin); Generator(G25); Output: Magma V2.10-6 Mon Mar 29 2004 12:43:16 on modular [Seed = 3639670913] ------------------------------------- G25.1 Finite field of size 5 G25.1 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Mon Mar 29 13:24:49 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; P25:=PolynomialRing(G25); G5:=GF(5); alpha:=Generator(G25); p3 := (1/alpha^4) - ((alpha^-3)*x) + ((alpha^5)*x^2); Factorization(p3); Output: Magma V2.10-6 Mon Mar 29 2004 13:24:46 on modular [Seed = 1665878755] ------------------------------------- [ ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Mon Mar 29 13:25:06 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; P25:=PolynomialRing(G25); G5:=GF(5); alpha:=Generator(G25); p3 := (1/alpha^4) - ((alpha^-3)*x) + ((alpha^5)*x^2); Factorization(p3,G25); Output: Magma V2.10-6 Mon Mar 29 2004 13:25:03 on modular [Seed = 1952210405] ------------------------------------- >> Factorization(p3,G25);; ^ Runtime error in 'Factorization': Bad argument types Argument types given: RngUPolElt, FldFin Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Mon Mar 29 13:25:57 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; P25:=PolynomialRing(G25); G5:=GF(5); alpha:=Generator(G25); p3 := (1/alpha^4) - ((alpha^-3)*x) + ((alpha^5)*x^2); Factorization(p3); Output: Magma V2.10-6 Mon Mar 29 2004 13:25:54 on modular [Seed = 1298491153] ------------------------------------- [ ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Mon Mar 29 13:26:18 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; P25:=PolynomialRing(G25); G5:=GF(5); p3 := (1/alpha^4) - ((alpha^-3)*x) + ((alpha^5)*x^2); Factorization(p3); Output: Magma V2.10-6 Mon Mar 29 2004 13:26:15 on modular [Seed = 1114269803] ------------------------------------- [ ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Mon Mar 29 13:27:24 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; P25:=PolynomialRing(G25); G5:=GF(5); p3 := (1/alpha^4) - ((alpha^-3)*x) + ((alpha^5)*x^2); Factorization(p3); arrels:=[A:A in G25 | Evaluate(p3,A) eq 0]; arrels Output: Magma V2.10-6 Mon Mar 29 2004 13:27:21 on modular [Seed = 1534292412] ------------------------------------- [ ] [] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.34.42.proxycache.rima-tde.net. (80.58.34.42) Time: Mon Mar 29 13:27:48 2004 Input: Z5:=GF(5); p:=PolynomialRing(Z5); p:=3+2*x+x^2; G25:=ext; P25:=PolynomialRing(G25); G5:=GF(5); p3 := (1/alpha^4) - ((alpha^-3)*x) + ((alpha^5)*x^2); Factorization(p3); arrels:=[A:A in G25 | Evaluate(p3,A) eq 1]; arrels Output: Magma V2.10-6 Mon Mar 29 2004 13:27:45 on modular [Seed = 1350072991] ------------------------------------- [ ] [] Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.12.239) Time: Mon Mar 29 14:29:57 2004 Input: P := PolynomialRing (G25); alpha := PrimitiveElement(G25); beta := PrimitiveElement(G5); alpha; beta; p1 := P![alpha^2,alpha,beta]; p2 := P![1,alpha]; p1^24; Output: Magma V2.10-6 Mon Mar 29 2004 14:29:53 on modular [Seed = 2693306878] ------------------------------------- >> P := PolynomialRing (G25); ^ User error: Identifier 'G25' has not been declared or assigned >> alpha := PrimitiveElement(G25); ^ User error: Identifier 'G25' has not been declared or assigned >> beta := PrimitiveElement(G5); ^ User error: Identifier 'G5' has not been declared or assigned >> alpha; ^ User error: Identifier 'alpha' has not been declared or assigned >> beta; ^ User error: Identifier 'beta' has not been declared or assigned >> p1 := P![alpha^2,alpha,beta]; ^ User error: Identifier 'P' has not been declared or assigned >> p2 := P![1,alpha]; ^ User error: Identifier 'P' has not been declared or assigned >> p1^24;; ^ User error: Identifier 'p1' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.12.239) Time: Mon Mar 29 14:30:32 2004 Input: P5:= PolynomialRing (Integers(5)); G25

:= ext < GF(5) | P5![3,2,1] >; P := PolynomialRing (G25); alpha := PrimitiveElement(G25); beta := PrimitiveElement(G5); alpha; beta; p1 := P![alpha^2,alpha,beta]; p2 := P![1,alpha]; p1^24; Output: Magma V2.10-6 Mon Mar 29 2004 14:30:29 on modular [Seed = 2962786698] ------------------------------------- >> beta := PrimitiveElement(G5); ^ User error: Identifier 'G5' has not been declared or assigned p >> beta; ^ User error: Identifier 'beta' has not been declared or assigned >> p1 := P![alpha^2,alpha,beta]; ^ User error: Identifier 'beta' has not been declared or assigned >> p1^24;; ^ User error: Identifier 'p1' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.12.239) Time: Mon Mar 29 14:31:34 2004 Input: G5 := GF(5); P5:= PolynomialRing (Integers(5)); G25

:= ext < GF(5) | P5![3,2,1] >; P := PolynomialRing (G25); alpha := PrimitiveElement(G25); beta := PrimitiveElement(G5); alpha; beta; p1 := P![alpha^2,alpha,beta]; p2 := P![1,alpha]; p1^24; Output: Magma V2.10-6 Mon Mar 29 2004 14:31:31 on modular [Seed = 2276441723] ------------------------------------- p 2 x^48 + p^19*x^47 + p^2*x^46 + p^3*x^45 + p^16*x^44 + 4*x^42 + p^7*x^41 + p^14*x^40 + p^15*x^39 + p^4*x^38 + x^36 + p^19*x^35 + p^2*x^34 + p^3*x^33 + p^16*x^32 + 4*x^30 + p^7*x^29 + p^14*x^28 + p^15*x^27 + p^4*x^26 + x^24 + p^20*x^22 + p^15*x^21 + p^22*x^20 + p^23*x^19 + 4*x^18 + p^8*x^16 + p^3*x^15 + p^10*x^14 + p^11*x^13 + x^12 + p^20*x^10 + p^15*x^9 + p^22*x^8 + p^23*x^7 + 4*x^6 + p^8*x^4 + p^3*x^3 + p^10*x^2 + p^11*x + 1 Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.12.239) Time: Mon Mar 29 14:31:53 2004 Input: G5 := GF(5); P5:= PolynomialRing (Integers(5)); G25

:= ext < GF(5) | P5![3,2,1] >; P := PolynomialRing (G25); alpha := PrimitiveElement(G25); beta := PrimitiveElement(G5); alpha; beta; p1 := P![alpha^2,alpha,beta]; p2 := P![1,alpha]; p1^25; Output: Magma V2.10-6 Mon Mar 29 2004 14:31:50 on modular [Seed = 2662770519] ------------------------------------- p 2 2*x^50 + p*x^25 + p^2 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.12.239) Time: Mon Mar 29 14:32:20 2004 Input: G5 := GF(5); P5:= PolynomialRing (Integers(5)); G25

:= ext < GF(5) | P5![3,2,1] >; P := PolynomialRing (G25); alpha := PrimitiveElement(G25); beta := PrimitiveElement(G5); p1 := P![alpha^2,alpha,beta]; p2 := P![1,alpha]; p1; p1^25; Output: Magma V2.10-6 Mon Mar 29 2004 14:32:17 on modular [Seed = 2512235579] ------------------------------------- 2*x^2 + p*x + p^2 2*x^50 + p*x^25 + p^2 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.12.239) Time: Mon Mar 29 14:34:26 2004 Input: G5 := GF(5); P5:= PolynomialRing (Integers(5)); G25

:= ext < GF(5) | P5![3,2,1] >; P := PolynomialRing (G25); alpha := PrimitiveElement(G25); beta := PrimitiveElement(G5); p1 := P![alpha^2,alpha,beta]; p2 := P![1,alpha]; p1; (1-p2)/p1; Output: Magma V2.10-6 Mon Mar 29 2004 14:34:23 on modular [Seed = 1969049402] ------------------------------------- 2*x^2 + p*x + p^2 p^19*x/(x^2 + p^7*x + p^8) Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.12.239) Time: Mon Mar 29 14:35:08 2004 Input: G5 := GF(5); P5:= PolynomialRing (Integers(5)); G25

:= ext < GF(5) | P5![3,2,1] >; P := PolynomialRing (G25); alpha := PrimitiveElement(G25); beta := PrimitiveElement(G5); p1 := P![alpha^2,alpha,beta]; p2 := P![1,alpha]; p1; a := (1-p2)/p1; a*p1+p2; Output: Magma V2.10-6 Mon Mar 29 2004 14:35:05 on modular [Seed = 1665882490] ------------------------------------- 2*x^2 + p*x + p^2 1 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.12.239) Time: Mon Mar 29 14:35:28 2004 Input: G5 := GF(5); P5:= PolynomialRing (Integers(5)); G25

:= ext < GF(5) | P5![3,2,1] >; P := PolynomialRing (G25); alpha := PrimitiveElement(G25); beta := PrimitiveElement(G5); p1 := P![alpha^2,alpha,beta]; p2 := P![1,alpha]; p1; a := (1-p2)/p1; a; Output: Magma V2.10-6 Mon Mar 29 2004 14:35:25 on modular [Seed = 1816417889] ------------------------------------- 2*x^2 + p*x + p^2 p^19*x/(x^2 + p^7*x + p^8) Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.12.239) Time: Mon Mar 29 14:35:49 2004 Input: G5 := GF(5); P5:= PolynomialRing (Integers(5)); G25

:= ext < GF(5) | P5![3,2,1] >; P := PolynomialRing (G25); alpha := PrimitiveElement(G25); beta := PrimitiveElement(G5); p1 := P![alpha^2,alpha,beta]; p2 := P![1,alpha]; p1; a := (1-p2)/p1; Evaluate(a); Output: Magma V2.10-6 Mon Mar 29 2004 14:35:46 on modular [Seed = 1434283959] ------------------------------------- 2*x^2 + p*x + p^2 >> Evaluate(a);; ^ Runtime error in 'Evaluate': Bad argument types Argument types given: FldFunRatUElt Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.12.239) Time: Mon Mar 29 14:36:30 2004 Input: G5 := GF(5); P5:= PolynomialRing (Integers(5)); G25

:= ext < GF(5) | P5![3,2,1] >; P := PolynomialRing (G25); alpha := PrimitiveElement(G25); beta := PrimitiveElement(G5); p1 := P![alpha^2,alpha,beta]; p2 := P![1,alpha]; p1; a := (1-p2)/p1; a; Output: Magma V2.10-6 Mon Mar 29 2004 14:36:27 on modular [Seed = 1584817301] ------------------------------------- 2*x^2 + p*x + p^2 p^19*x/(x^2 + p^7*x + p^8) Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.12.239) Time: Mon Mar 29 14:37:03 2004 Input: G5 := GF(5); P5:= PolynomialRing (Integers(5)); G25

:= ext < GF(5) | P5![3,2,1] >; P := PolynomialRing (G25); alpha := PrimitiveElement(G25); beta := PrimitiveElement(G5); p1 := P![alpha^2,alpha,beta]; p2 := P![1,alpha]; p2; p1; a := (1-p2)/p1; a; Output: Magma V2.10-6 Mon Mar 29 2004 14:37:00 on modular [Seed = 1198489067] ------------------------------------- p*x + 1 2*x^2 + p*x + p^2 p^19*x/(x^2 + p^7*x + p^8) Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.12.239) Time: Mon Mar 29 14:37:39 2004 Input: G5 := GF(5); P5:= PolynomialRing (Integers(5)); G25

:= ext < GF(5) | P5![3,2,1] >; P := PolynomialRing (G25); alpha := PrimitiveElement(G25); beta := PrimitiveElement(G5); p1 := P![alpha^2,alpha,beta]; p2 := P![1,alpha]; a := (1-p2)/p1; a*p1+p2; Output: Magma V2.10-6 Mon Mar 29 2004 14:37:36 on modular [Seed = 806882112] ------------------------------------- 1 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.12.239) Time: Mon Mar 29 14:44:21 2004 Input: G5 := GF(5); P5:= PolynomialRing (Integers(5)); G25

:= ext < GF(5) | P5![3,2,1] >; P := PolynomialRing (G25); alpha := PrimitiveElement(G25); fun := 1/alpha^4-alpha^(-3)x+alpha^5x^2+alpha^11x^3; Factoritzation(fun); Evaluate(fun); Output: Magma V2.10-6 Mon Mar 29 2004 14:44:19 on modular [Seed = 621615558] ------------------------------------- >> fun := 1/alpha^4-alpha^(-3)x+alpha^5x^2+alpha^11x^3; ^ User error: bad syntax >> Factoritzation(fun); ^ User error: Identifier 'fun' has not been declared or assigned >> Evaluate(fun);; ^ User error: Identifier 'fun' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.12.239) Time: Mon Mar 29 14:45:01 2004 Input: G5 := GF(5); P5:= PolynomialRing (Integers(5)); G25

:= ext < GF(5) | P5![3,2,1] >; P := PolynomialRing (G25); alpha := PrimitiveElement(G25); fun := 1/alpha^4-alpha^(-3)*x+alpha^5*x^2+alpha^11*x^3; Factoritzation(fun); Output: Magma V2.10-6 Mon Mar 29 2004 14:44:56 on modular [Seed = 772149990] ------------------------------------- >> Factoritzation(fun); ^ User error: Identifier 'Factoritzation' has not been declared or assigned Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.12.239) Time: Mon Mar 29 14:45:16 2004 Input: G5 := GF(5); P5:= PolynomialRing (Integers(5)); G25

:= ext < GF(5) | P5![3,2,1] >; P := PolynomialRing (G25); alpha := PrimitiveElement(G25); fun := 1/alpha^4-alpha^(-3)*x+alpha^5*x^2+alpha^11*x^3; Factorization(fun); Output: Magma V2.10-6 Mon Mar 29 2004 14:45:13 on modular [Seed = 456337314] ------------------------------------- [ , , ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.12.239) Time: Mon Mar 29 14:45:57 2004 Input: G5 := GF(5); P5:= PolynomialRing (Integers(5)); G25

:= ext < GF(5) | P5![3,2,1] >; P := PolynomialRing (G25); alpha := PrimitiveElement(G25); fun := 1/alpha^4-alpha^(-3)*x+alpha^5*x^2+alpha^11*x^3; Factorization(fun); fun(1); Output: Magma V2.10-6 Mon Mar 29 2004 14:45:54 on modular [Seed = 70006918] ------------------------------------- [ , , ] >> fun(1);; ^ Runtime error: Bad argument types Argument types given: RngIntElt, RngUPolElt Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.12.239) Time: Mon Mar 29 14:46:23 2004 Input: G5 := GF(5); P5:= PolynomialRing (Integers(5)); G25

:= ext < GF(5) | P5![3,2,1] >; P := PolynomialRing (G25); alpha := PrimitiveElement(G25); fun := 1/alpha^4-alpha^(-3)*x+alpha^5*x^2+alpha^11*x^3; Factorization(fun); Evaluate(fun,1); Output: Magma V2.10-6 Mon Mar 29 2004 14:46:20 on modular [Seed = 220541041] ------------------------------------- [ , , ] 4 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.61.12.239) Time: Mon Mar 29 14:47:11 2004 Input: G5 := GF(5); P5:= PolynomialRing (Integers(5)); G25

:= ext < GF(5) | P5![3,2,1] >; P := PolynomialRing (G25); alpha := PrimitiveElement(G25); fun := 1/alpha^4-alpha^(-3)*x+alpha^5*x^2+alpha^11*x^3; Factorization(fun); Evaluate(fun,-1); Evaluate(fun,-p); Evaluate(fun,-p^8); Output: Magma V2.10-6 Mon Mar 29 2004 14:47:08 on modular [Seed = 4141796282] ------------------------------------- [ , , ] 0 0 0 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 16:23:29 2004 Input: m:=1; upperBound:=20; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^3-1); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 16:23:23 on modular [Seed = 4224919664] ------------------------------------- 6 4 12 12 18 28 Total time: 3.149 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 16:23:46 2004 Input: m:=1; upperBound:=20; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 16:23:43 on modular [Seed = 2175357465] ------------------------------------- 6 10 10 18 21 21 Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 16:24:15 2004 Input: m:=3; upperBound:=10; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 16:24:12 on modular [Seed = 2996461833] ------------------------------------- 126 394 Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 16:24:37 2004 Input: m:=4; upperBound:=5; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 16:24:34 on modular [Seed = 3113315820] ------------------------------------- 526 Total time: 2.849 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 16:24:52 2004 Input: m:=4; upperBound:=7; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 16:24:49 on modular [Seed = 1332189990] ------------------------------------- 526 2470 Total time: 2.859 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 16:25:19 2004 Input: m:=4; upperBound:=10; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 16:25:16 on modular [Seed = 1451131426] ------------------------------------- 526 2470 Total time: 2.849 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 29 16:34:07 2004 Input: beta:= PrimitiveElement (G5); alpha := PrimitiveElement (G25); Output: Magma V2.10-6 Mon Mar 29 2004 16:34:03 on modular [Seed = 473221661] ------------------------------------- >> beta:= PrimitiveElement (G5); ^ User error: Identifier 'G5' has not been declared or assigned >> alpha := PrimitiveElement (G25);; ^ User error: Identifier 'G25' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 29 16:34:48 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no és un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, gamma, gamma^2, gamma^3, 2, gamma^5, gamma^6, gamma^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ /*EXERCICI 1.iv*/ lista:=[x: x in G25]; print lista; /*[ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] */ Ordre:= [[] : i in [1..23]]; print Ordre; /* [ [ ], [ ], [ ], [ ], [ ], [ <3, 4> ], [ ], [ ], [ ], [ ], [ ], [ <4, 2> ], [ ], [ ], [ ], [ ], [ ], [ <2, 4> ], [ ], [ ], [ ], [ ], [ ] ] */ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ /* Podem comprovar que els elements primitius d'un cos són aquells que el seu ordre és 24 */ cardinal:= # lista_primitius_G25; cardinal; /*8*/ /*un cos de p^n te phi(p^n-1) elements primitius*/ /*Si apliquem la fòrmula al nostre cas: */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ /*EXERCICI 1.V*/ lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*Podem comprovar que el polinomi mínim d'alpha és aquest, ja que és el polinomi que té com arrel alpha i a més és irreductible a Z5*/ Evaluate (polinomi, alpha); /*0*/ IsIrreducible (polinomi); /*true*/ /*El grau del polinomi és 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ /*EXERCICI 1.vi*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ IsInvertible (pol); /*true alpha ^11*/ /*El polinomi és invertible,per tant té invers i és alpha^11*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; /* [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] */ /*EXERCICI 1.vii*/ /*considerem alpha un element primitiu del cos*/ Taula := function (p,n) llista1 := [<0,[0,0]>]; for i:=0 to (p^n)-2 do llista2 :=[]; llista1 := llista1 cat llista2; end for; return llista1; end function; Taula (2,4); /* [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , ] */ Taula (5,2); /* [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , ] */ /*EXERCICI 1.viii*/ G2 := GF(2); [x : x in G2]; /*[ 0, 1 ]*/ G4 := GF (4); [x : x in G4]; /*[ 1, G4.1, G4.1^2, 0 ]*/ G8 := GF (8); [x : x in G8]; /*[ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ]*/ G16b := GF (16); [x : x in G16b]; /*[ 1, G16b.1, G16b.1^2, G16b.1^3, G16b.1^4, G16b.1^5, G16b.1^6, G16b.1^7, G16b.1^8, G16b.1^9, G16b.1^10, G16b.1^11, G16b.1^12, G16b.1^13, G16b.1^14, 0 ]*/ G2 subset G4; /*true*/ G2 subset G8; /*true*/ G2 subset G16b; /*true*/ G4 subset G2; /*false*/ G4 subset G8; /*false*/ G4 subset G16b; /*true*/ G8 subset G2; /*false*/ G8 subset G4; /*false*/ G8 subset G16b; /*false*/ G16b subset G2; /*false*/ G16b subset G4; /*false*/ G16b subset G8; /*false*/ /*G2 és un subcos de G4, G8 i G16b*/ /*G4 és un subcos de G16b*/ /*EXERCICI 2.i*/ P := PolynomialRing (G25); IsFinite (P); /*false*/ /*EXERCICI 2.ii*/ /*Mirem la llista d'elements primitius del cossos*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ G5 := GF(5); lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; /*[2,3]*/ beta:= PrimitiveElement (G5); alpha := PrimitiveElement (G25); Output: Magma V2.10-6 Mon Mar 29 2004 16:34:45 on modular [Seed = 3556443628] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, gamma, gamma^2, gamma^3, 2, gamma^5, gamma^6, gamma^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ ], [ ], [ ], [ ], [ ], [ <3, 24> ], [ ], [ ], [ ], [ ], [ ], [ <4, 24> ], [ ], [ ], [ ], [ ], [ ], [ <2, 24> ], [ ], [ ], [ ], [ ], [ ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 0 true [ , ] [] alpha^13 true alpha^11 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , ] [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , ] [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16b.1, G16b.1^2, G16b.1^3, G16b.1^4, G16b.1^5, G16b.1^6, G16b.1^7, G16b.1^8, G16b.1^9, G16b.1^10, G16b.1^11, G16b.1^12, G16b.1^13, G16b.1^14, 0 ] true true true false false true false false false false false false false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] Total time: 3.149 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 29 16:36:42 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no és un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, gamma, gamma^2, gamma^3, 2, gamma^5, gamma^6, gamma^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ /*EXERCICI 1.iv*/ lista:=[x: x in G25]; print lista; /*[ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] */ Ordre:= [[] : i in [1..23]]; print Ordre; /* [ [ ], [ ], [ ], [ ], [ ], [ <3, 4> ], [ ], [ ], [ ], [ ], [ ], [ <4, 2> ], [ ], [ ], [ ], [ ], [ ], [ <2, 4> ], [ ], [ ], [ ], [ ], [ ] ] */ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ /* Podem comprovar que els elements primitius d'un cos són aquells que el seu ordre és 24 */ cardinal:= # lista_primitius_G25; cardinal; /*8*/ /*un cos de p^n te phi(p^n-1) elements primitius*/ /*Si apliquem la fòrmula al nostre cas: */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ /*EXERCICI 1.V*/ lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*Podem comprovar que el polinomi mínim d'alpha és aquest, ja que és el polinomi que té com arrel alpha i a més és irreductible a Z5*/ Evaluate (polinomi, alpha); /*0*/ IsIrreducible (polinomi); /*true*/ /*El grau del polinomi és 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ /*EXERCICI 1.vi*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ IsInvertible (pol); /*true alpha ^11*/ /*El polinomi és invertible,per tant té invers i és alpha^11*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; /* [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] */ /*EXERCICI 1.vii*/ /*considerem alpha un element primitiu del cos*/ Taula := function (p,n) llista1 := [<0,[0,0]>]; for i:=0 to (p^n)-2 do llista2 :=[]; llista1 := llista1 cat llista2; end for; return llista1; end function; Taula (2,4); /* [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , ] */ Taula (5,2); /* [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , ] */ /*EXERCICI 1.viii*/ G2 := GF(2); [x : x in G2]; /*[ 0, 1 ]*/ G4 := GF (4); [x : x in G4]; /*[ 1, G4.1, G4.1^2, 0 ]*/ G8 := GF (8); [x : x in G8]; /*[ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ]*/ G16b := GF (16); [x : x in G16b]; /*[ 1, G16b.1, G16b.1^2, G16b.1^3, G16b.1^4, G16b.1^5, G16b.1^6, G16b.1^7, G16b.1^8, G16b.1^9, G16b.1^10, G16b.1^11, G16b.1^12, G16b.1^13, G16b.1^14, 0 ]*/ G2 subset G4; /*true*/ G2 subset G8; /*true*/ G2 subset G16b; /*true*/ G4 subset G2; /*false*/ G4 subset G8; /*false*/ G4 subset G16b; /*true*/ G8 subset G2; /*false*/ G8 subset G4; /*false*/ G8 subset G16b; /*false*/ G16b subset G2; /*false*/ G16b subset G4; /*false*/ G16b subset G8; /*false*/ /*G2 és un subcos de G4, G8 i G16b*/ /*G4 és un subcos de G16b*/ /*EXERCICI 2.i*/ P := PolynomialRing (G25); IsFinite (P); /*false*/ /*EXERCICI 2.ii*/ /*Mirem la llista d'elements primitius del cossos*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ G5 := GF(5); lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; /*[2,3]*/ beta:= PrimitiveElement (G5); alpha := PrimitiveElement (G25); IsPrimitive(alpha); IsPrimitive(beta); p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; /*EXERCICI 2.iii*/ suma := p1 + p2; suma; /*2*x^2 + alpha^19*x + alpha^9*/ producte := p1 * p2; producte; /*alpha^19*x^3 + alpha^22*x^2 + alpha^10*x + alpha^2*/ /*EXERCICI 2.iv*/ quocient := p1 div p2; quocient; /*alpha^17*x + alpha^5*/ residu := p1 mod p2; residu; /* alpha^15*/ /*EXERCICI 2.v*/ mcd := GCD (p1,p2); mcd; /*1 */ mcm := LCM (p1,p2); mcm; /*x^3 + alpha^3*x^2 + alpha^15*x + alpha^7*/ /*p1 i p2 són coprimers, ja que el maxim comu divisorentre ells és 1*/ /*EXERCICI 2.vi*/ XGCD(p1,p2); /* 1 alpha^9 alpha^14*x + alpha^2 */ alpha^9*p1+(alpha^14*x + alpha^2)*p2; /* 1 */ Output: Magma V2.10-6 Mon Mar 29 2004 16:36:39 on modular [Seed = 4174392917] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, gamma, gamma^2, gamma^3, 2, gamma^5, gamma^6, gamma^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ ], [ ], [ ], [ ], [ ], [ <3, 24> ], [ ], [ ], [ ], [ ], [ ], [ <4, 24> ], [ ], [ ], [ ], [ ], [ ], [ <2, 24> ], [ ], [ ], [ ], [ ], [ ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 0 true [ , ] [] alpha^13 true alpha^11 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , ] [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , ] [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16b.1, G16b.1^2, G16b.1^3, G16b.1^4, G16b.1^5, G16b.1^6, G16b.1^7, G16b.1^8, G16b.1^9, G16b.1^10, G16b.1^11, G16b.1^12, G16b.1^13, G16b.1^14, 0 ] true true true false false true false false false false false false false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] true true 2*x^2 + alpha^19*x + alpha^9 alpha^19*x^3 + alpha^22*x^2 + alpha^10*x + alpha^2 alpha^17*x + alpha^5 alpha^15 1 x^3 + alpha^3*x^2 + alpha^15*x + alpha^7 1 alpha^9 alpha^14*x + alpha^2 1 Total time: 3.049 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 16:37:20 2004 Input: m:=2; upperBound:=5; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 16:37:17 on modular [Seed = 2342739148] ------------------------------------- 46 Total time: 2.869 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.35.170.proxycache.rima-tde.net. (80.58.35.170) Time: Mon Mar 29 16:39:30 2004 Input: /*EXERCICI 1.i*/ [x : x in GF(2)]; /*[ 0, 1 ]*/ [x : x in GF(3)]; /*[ 0, 1, 2 ]*/ [x : x in GF(5)]; /*[ 0, 1, 2, 3, 4 ]*/ /*EXERCICI 1.ii*/ /* Z9 no és un cos, ja que 9 no és un nombre primer*/ z9 := Integers (9); [x : x in z9]; /*[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]*/ IsInvertible(z9!0); /*false*/ IsInvertible(z9!1); /*true 1*/ IsInvertible(z9!2); /*true 5*/ IsInvertible(z9!3); /*false*/ IsInvertible(z9!4); /*true 7*/ /*EXERCICI 1.iii*/ z3:= Integers (3); P := PolynomialRing (z3); f:= 2+2*x+x^2; IsIrreducible (f); /*true*/ z2:= Integers(2); P := PolynomialRing (z2); g:= 1+x+x^4; IsIrreducible (g); /*true*/ z5:= Integers(5); P := PolynomialRing (z5); h:= 3+2*x+x^2; IsIrreducible (h); /*true*/ P := PolynomialRing (z3); j:= 1+2*x+x^2; IsIrreducible (j); /*false*/ G3 := GF(3); G9:= ext < G3 |f>; [x : x in G9]; /*[ 1, gamma, gamma^2, gamma^3, 2, gamma^5, gamma^6, gamma^7, 0 ]*/ G2 := GF(2); G16:= ext < G2 | g >; [x : x in G16]; /*[ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ]*/ G5 := GF(5); G25:= ext < G5 |h>; [x : x in G25]; /*[ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ]*/ G9b:= ext < G3 |j>; G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible /* hi ha problemes perque el polinomi j no es irreductible a Z3*/ /*EXERCICI 1.iv*/ lista:=[x: x in G25]; print lista; /*[ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] */ Ordre:= [[] : i in [1..23]]; print Ordre; /* [ [ ], [ ], [ ], [ ], [ ], [ <3, 4> ], [ ], [ ], [ ], [ ], [ ], [ <4, 2> ], [ ], [ ], [ ], [ ], [ ], [ <2, 4> ], [ ], [ ], [ ], [ ], [ ] ] */ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ /* Podem comprovar que els elements primitius d'un cos són aquells que el seu ordre és 24 */ cardinal:= # lista_primitius_G25; cardinal; /*8*/ /*un cos de p^n te phi(p^n-1) elements primitius*/ /*Si apliquem la fòrmula al nostre cas: */ elements := func < p,n | EulerPhi (p^n -1)>; elements (5,2); /*8*/ /*EXERCICI 1.V*/ lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ polinomi:= MinimalPolynomial(alpha); polinomi; /*$.1^2 + 2*$.1 + 3*/ /*Podem comprovar que el polinomi mínim d'alpha és aquest, ja que és el polinomi que té com arrel alpha i a més és irreductible a Z5*/ Evaluate (polinomi, alpha); /*0*/ IsIrreducible (polinomi); /*true*/ /*El grau del polinomi és 2*/ /*sobre el cos GF(25)*/ Roots (polinomi,G25); /*[ , ]*/ Roots (polinomi,GF(5)); /*[]*/ /*EXERCICI 1.vi*/ pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; /*alpha^13*/ IsInvertible (pol); /*true alpha ^11*/ /*El polinomi és invertible,per tant té invers i és alpha^11*/ lista2:=[x: x in G25 | IsInvertible (x)]; lista2; /* [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] */ /*EXERCICI 1.vii*/ /*considerem alpha un element primitiu del cos*/ Taula := function (p,n) llista1 := [<0,[0,0]>]; for i:=0 to (p^n)-2 do llista2 :=[]; llista1 := llista1 cat llista2; end for; return llista1; end function; Taula (2,4); /* [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , ] */ Taula (5,2); /* [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , ] */ /*EXERCICI 1.viii*/ G2 := GF(2); [x : x in G2]; /*[ 0, 1 ]*/ G4 := GF (4); [x : x in G4]; /*[ 1, G4.1, G4.1^2, 0 ]*/ G8 := GF (8); [x : x in G8]; /*[ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ]*/ G16b := GF (16); [x : x in G16b]; /*[ 1, G16b.1, G16b.1^2, G16b.1^3, G16b.1^4, G16b.1^5, G16b.1^6, G16b.1^7, G16b.1^8, G16b.1^9, G16b.1^10, G16b.1^11, G16b.1^12, G16b.1^13, G16b.1^14, 0 ]*/ G2 subset G4; /*true*/ G2 subset G8; /*true*/ G2 subset G16b; /*true*/ G4 subset G2; /*false*/ G4 subset G8; /*false*/ G4 subset G16b; /*true*/ G8 subset G2; /*false*/ G8 subset G4; /*false*/ G8 subset G16b; /*false*/ G16b subset G2; /*false*/ G16b subset G4; /*false*/ G16b subset G8; /*false*/ /*G2 és un subcos de G4, G8 i G16b*/ /*G4 és un subcos de G16b*/ /*EXERCICI 2.i*/ P := PolynomialRing (G25); IsFinite (P); /*false*/ /*EXERCICI 2.ii*/ /*Mirem la llista d'elements primitius del cossos*/ lista_primitius_G25:=[x: x in G25 | IsPrimitive (x)]; lista_primitius_G25; /*[ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ]*/ G5 := GF(5); lista_primitius_G5:=[x: x in G5 | IsPrimitive (x)]; lista_primitius_G5; /*[2,3]*/ beta:= PrimitiveElement (G5); alpha := PrimitiveElement (G25); IsPrimitive(alpha); IsPrimitive(beta); p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; /*EXERCICI 2.iii*/ suma := p1 + p2; suma; /*2*x^2 + alpha^19*x + alpha^9*/ producte := p1 * p2; producte; /*alpha^19*x^3 + alpha^22*x^2 + alpha^10*x + alpha^2*/ /*EXERCICI 2.iv*/ quocient := p1 div p2; quocient; /*alpha^17*x + alpha^5*/ residu := p1 mod p2; residu; /* alpha^15*/ /*EXERCICI 2.v*/ mcd := GCD (p1,p2); mcd; /*1 */ mcm := LCM (p1,p2); mcm; /*x^3 + alpha^3*x^2 + alpha^15*x + alpha^7*/ /*p1 i p2 són coprimers, ja que el maxim comu divisorentre ells és 1*/ /*EXERCICI 2.vi*/ XGCD(p1,p2); Output: Magma V2.10-6 Mon Mar 29 2004 16:39:27 on modular [Seed = 3337490690] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] false true 1 true 5 false true 7 true true true false [ 1, gamma, gamma^2, gamma^3, 2, gamma^5, gamma^6, gamma^7, 0 ] [ 1, beta, beta^2, beta^3, beta^4, beta^5, beta^6, beta^7, beta^8, beta^9, beta^10, beta^11, beta^12, beta^13, beta^14, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> G9b:= ext < G3 |j>; ^ Runtime error in ext< ... >: Argument is not irreducible >> ^ ^ User error: bad syntax >> Runtime error in ext< ... >: Argument is not irreducible ^ User error: bad syntax [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23, 0 ] [ [ ], [ ], [ ], [ ], [ ], [ <3, 24> ], [ ], [ ], [ ], [ ], [ ], [ <4, 24> ], [ ], [ ], [ ], [ ], [ ], [ <2, 24> ], [ ], [ ], [ ], [ ], [ ] ] [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] 8 8 [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] $.1^2 + 2*$.1 + 3 0 true [ , ] [] alpha^13 true alpha^11 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , ] [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , ] [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16b.1, G16b.1^2, G16b.1^3, G16b.1^4, G16b.1^5, G16b.1^6, G16b.1^7, G16b.1^8, G16b.1^9, G16b.1^10, G16b.1^11, G16b.1^12, G16b.1^13, G16b.1^14, 0 ] true true true false false true false false false false false false false [ alpha, alpha^5, alpha^7, alpha^11, alpha^13, alpha^17, alpha^19, alpha^23 ] [ 2, 3 ] true true 2*x^2 + alpha^19*x + alpha^9 alpha^19*x^3 + alpha^22*x^2 + alpha^10*x + alpha^2 alpha^17*x + alpha^5 alpha^15 1 x^3 + alpha^3*x^2 + alpha^15*x + alpha^7 1 alpha^9 alpha^14*x + alpha^2 Total time: 3.059 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 16:40:24 2004 Input: for p in [5..5] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^5+x+2); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); numberOfRoots:=#R; summe:=0; for i in [1..numberOfRoots] do summe:=summe+2/R[i][1]^2; end for; numberOfPoints:=p^2+1-summe; print Round(numberOfPoints), ","; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 16:40:21 on modular [Seed = 2679588881] ------------------------------------- 46 , Total time: 3.109 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 16:41:20 2004 Input: for p in [5..5] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^5+x+2); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); print R; numberOfRoots:=#R; summe:=0; for i in [1..numberOfRoots] do summe:=summe+2/R[i][1]^2; end for; numberOfPoints:=p^2+1-summe; print Round(numberOfPoints), ","; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 16:41:17 on modular [Seed = 2710140439] ------------------------------------- [ <-0.447213595499957939281834733746255247086*i, 2>, <0.447213595499957939281834733746255247086*i, 2> ] 46 , Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 16:42:08 2004 Input: for p in [5..5] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^5+x+2); ZetaFunction(C); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); print R; numberOfRoots:=#R; summe:=0; for i in [1..numberOfRoots] do summe:=summe+2/R[i][1]^2; end for; numberOfPoints:=p^2+1-summe; print Round(numberOfPoints), ","; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 16:42:05 on modular [Seed = 1298502956] ------------------------------------- (25*$.1^4 + 10*$.1^2 + 1)/(5*$.1^2 - 6*$.1 + 1) [ <-0.447213595499957939281834733746255247086*i, 2>, <0.447213595499957939281834733746255247086*i, 2> ] 46 , Total time: 2.889 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 16:47:48 2004 Input: for p in [5..5] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^4+x+2); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); print R; numberOfRoots:=#R; summe:=0; for i in [1..numberOfRoots] do summe:=summe+2/R[i][1]^2; end for; numberOfPoints:=p^2+1-summe; print Round(numberOfPoints), ","; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 16:47:42 on modular [Seed = 2545897134] ------------------------------------- [ <-0.0999999999999999999999999999999999999997 - 0.435889894354067355223698198385961565910*i, 1>, <-0.0999999999999999999999999999999999999997 + 0.435889894354067355223698198385961565910*i, 1> ] 44 , Total time: 3.279 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 16:48:08 2004 Input: for p in [5..5] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^4+x+2); ZetaFunction(C); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); print R; numberOfRoots:=#R; summe:=0; for i in [1..numberOfRoots] do summe:=summe+2/R[i][1]^2; end for; numberOfPoints:=p^2+1-summe; print Round(numberOfPoints), ","; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 16:48:05 on modular [Seed = 2561687882] ------------------------------------- (5*$.1^2 + $.1 + 1)/(5*$.1^2 - 6*$.1 + 1) [ <-0.0999999999999999999999999999999999999997 - 0.435889894354067355223698198385961565910*i, 1>, <-0.0999999999999999999999999999999999999997 + 0.435889894354067355223698198385961565910*i, 1> ] 44 , Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 16:48:36 2004 Input: for p in [5..5] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^2)); C := HyperellipticCurve(x^4+x+2); ZetaFunction(C); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); print R; numberOfRoots:=#R; summe:=0; for i in [1..numberOfRoots] do summe:=summe+2/R[i][1]^2; end for; numberOfPoints:=p^2+1-summe; print Round(numberOfPoints), ","; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 16:48:33 on modular [Seed = 373215215] ------------------------------------- (25*$.1^2 + 9*$.1 + 1)/(25*$.1^2 - 26*$.1 + 1) [ <-0.179999999999999999999999999997 - 0.087177978870813471044739639675*i, 1>, <-0.179999999999999999999999999997 + 0.087177978870813471044739639675*i, 1> ] -36 , Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 16:49:37 2004 Input: m:=2; upperBound:=5; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 16:49:34 on modular [Seed = 891153555] ------------------------------------- 46 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 16:50:03 2004 Input: m:=2; upperBound:=5; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); ZetaFunction(C); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 16:49:59 on modular [Seed = 3253279630] ------------------------------------- (625*$.1^4 + 500*$.1^3 + 150*$.1^2 + 20*$.1 + 1)/(25*$.1^2 - 26*$.1 + 1) 46 Total time: 3.029 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 16:50:26 2004 Input: m:=2; upperBound:=5; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^4+x+2); ZetaFunction(C); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 16:50:23 on modular [Seed = 3989125050] ------------------------------------- (25*$.1^2 + 9*$.1 + 1)/(25*$.1^2 - 26*$.1 + 1) 35 Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 16:51:21 2004 Input: m:=2; upperBound:=5; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^4+x+2); ZetaFunction(C); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 16:51:17 on modular [Seed = 2376423312] ------------------------------------- (25*$.1^2 + 9*$.1 + 1)/(25*$.1^2 - 26*$.1 + 1) 35 Total time: 3.559 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 16:51:40 2004 Input: m:=2; upperBound:=5; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^4+x+2); ZetaFunction(C); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); print R; #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 16:51:36 on modular [Seed = 2561688249] ------------------------------------- (25*$.1^2 + 9*$.1 + 1)/(25*$.1^2 - 26*$.1 + 1) [ <-0.179999999999999999999999999997 - 0.087177978870813471044739639675*i, 1>, <-0.179999999999999999999999999997 + 0.087177978870813471044739639675*i, 1> ] 35 Total time: 3.309 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 16:52:08 2004 Input: m:=2; upperBound:=5; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); ZetaFunction(C); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); print R; #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 16:52:05 on modular [Seed = 2461681759] ------------------------------------- (625*$.1^4 + 500*$.1^3 + 150*$.1^2 + 20*$.1 + 1)/(25*$.1^2 - 26*$.1 + 1) [ <-0.199999999999999999999999999997, 4> ] 46 Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 16:55:39 2004 Input: for p in [5..5] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^2)); C := HyperellipticCurve(x^5+x+2); ZetaFunction(C); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); print R; numberOfRoots:=#R; summe:=0; for i in [1..numberOfRoots] do summe:=summe+2/R[i][1]^2; end for; numberOfPoints:=p^2+1-summe; print Round(numberOfPoints), ","; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 16:55:35 on modular [Seed = 3030151083] ------------------------------------- (625*$.1^4 + 500*$.1^3 + 150*$.1^2 + 20*$.1 + 1)/(25*$.1^2 - 26*$.1 + 1) [ <-0.199999999999999999999999999997, 4> ] -24 , Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 17:03:33 2004 Input: for p in [5..5] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^1)); C := HyperellipticCurve(x^5+x+2); ZetaFunction(C); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); print R; numberOfRoots:=#R; summe:=0; for i in [1..numberOfRoots] do summe:=summe+2/R[i][1]^2; end for; numberOfPoints:=p^2+1-summe; print Round(numberOfPoints), ","; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 17:03:30 on modular [Seed = 1632222234] ------------------------------------- (25*$.1^4 + 10*$.1^2 + 1)/(5*$.1^2 - 6*$.1 + 1) [ <-0.447213595499957939281834733746255247086*i, 2>, <0.447213595499957939281834733746255247086*i, 2> ] 46 , Total time: 3.369 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 17:03:55 2004 Input: m:=1; upperBound:=5; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); ZetaFunction(C); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); print R; #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 17:03:51 on modular [Seed = 2018551161] ------------------------------------- (25*$.1^4 + 10*$.1^2 + 1)/(5*$.1^2 - 6*$.1 + 1) [ <-0.447213595499957939281834733746255247086*i, 2>, <0.447213595499957939281834733746255247086*i, 2> ] 6 Total time: 3.509 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host s0202.math.lsa.umich.edu. (141.211.62.202) Time: Mon Mar 29 17:16:37 2004 Input: k=IntegerRing(4); Output: Magma V2.10-6 Mon Mar 29 2004 17:16:34 on modular [Seed = 322695960] ------------------------------------- >> k=IntegerRing(4); ^ User error: Identifier 'k' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host s0202.math.lsa.umich.edu. (141.211.62.202) Time: Mon Mar 29 17:16:59 2004 Input: k=IntegerRing(4); Output: Magma V2.10-6 Mon Mar 29 2004 17:16:56 on modular [Seed = 789040958] ------------------------------------- >> k=IntegerRing(4); ^ User error: Identifier 'k' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host s0202.math.lsa.umich.edu. (141.211.62.202) Time: Mon Mar 29 17:21:48 2004 Input: 1+1; Output: Magma V2.10-6 Mon Mar 29 2004 17:21:45 on modular [Seed = 840618754] ------------------------------------- 2 Total time: 3.359 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Mon Mar 29 17:21:50 2004 Input: m:=3; upperBound:=5; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); ZetaFunction(C); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); print R; #C; end if; end for; Output: Magma V2.10-6 Mon Mar 29 2004 17:21:46 on modular [Seed = 924833284] ------------------------------------- (15625*$.1^4 + 250*$.1^2 + 1)/(125*$.1^2 - 126*$.1 + 1) [ <-0.089442719099991587856366946747*i, 2>, <0.089442719099991587856366946747*i, 2> ] 126 Total time: 3.369 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host Toronto-HSE-ppp3836818.sympatico.ca. (67.69.188.185) Time: Mon Mar 29 18:08:16 2004 Input: E:=EllipticCurve([0,0,1,-1,0]); f:=ModularForm(E); time Coefficient(f,10000); Output: Magma V2.10-6 Mon Mar 29 2004 18:08:09 on modular [Seed = 3522772418] ------------------------------------- 76 Time: 3.420 Total time: 6.439 seconds, Total memory usage: 2.59MB ************** MAGMA ***************** Host Toronto-HSE-ppp3836818.sympatico.ca. (67.69.188.185) Time: Mon Mar 29 18:10:06 2004 Input: E:=EllipticCurve([0,0,1,-1,0]); f:=ModularForm(E); time Coefficient(f,50000); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Mar 29 2004 18:09:43 on modular [Seed = 4005954067] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 2724 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host adsl-241-86.ns.itd.umich.edu. (141.213.241.86) Time: Mon Mar 29 21:36:27 2004 Input: k:=ResidueClassRing(14) Output: Magma V2.10-6 Mon Mar 29 2004 21:36:24 on modular [Seed = 1517471550] ------------------------------------- Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-241-86.ns.itd.umich.edu. (141.213.241.86) Time: Mon Mar 29 21:36:49 2004 Input: k:=ResidueClassRing(14); k; Output: Magma V2.10-6 Mon Mar 29 2004 21:36:46 on modular [Seed = 1816457502] ------------------------------------- Residue class ring of integers modulo 14 Total time: 2.869 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-241-86.ns.itd.umich.edu. (141.213.241.86) Time: Mon Mar 29 21:37:22 2004 Input: k:=IntegerRing(14); k; Output: Magma V2.10-6 Mon Mar 29 2004 21:37:19 on modular [Seed = 1716452213] ------------------------------------- Residue class ring of integers modulo 14 Total time: 2.869 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Tue Mar 30 01:16:10 2004 Input: P5:= PolynomialRing (Integers(5)); G25

:= ext < GF(5) | P5![3,2,1] >; #[a: a in G25 | IsPrimitive(a)]; Output: Magma V2.10-6 Tue Mar 30 2004 01:16:07 on modular [Seed = 2529150588] ------------------------------------- 8 Total time: 2.859 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DWB-239-12.go.retevision.es. (81.61.12.239) Time: Tue Mar 30 01:16:26 2004 Input: P5:= PolynomialRing (Integers(5)); G25

:= ext < GF(5) | P5![3,2,1] >; [a: a in G25 | IsPrimitive(a)]; #[a: a in G25 | IsPrimitive(a)]; Output: Magma V2.10-6 Tue Mar 30 2004 01:16:23 on modular [Seed = 2843801939] ------------------------------------- [ p, p^5, p^7, p^11, p^13, p^17, p^19, p^23 ] 8 Total time: 2.869 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 30 02:10:39 2004 Input: for p in [5..100] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^6+1); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); numberOfRoots:=#R; summe:=0; for i in [1..numberOfRoots] do summe:=summe+2/R[i][1]^2; end for; numberOfPoints:=p^2+1-summe; print Round(numberOfPoints), ","; end if; end for; Output: Magma V2.10-6 Tue Mar 30 2004 02:10:35 on modular [Seed = 2710821] ------------------------------------- 46 , 46 , 166 , 214 , 358 , 310 , 622 , 958 , 1054 , 1318 , 1846 , 1894 , 2398 , 3022 , 3718 , 3574 , 4246 , 5326 , 5422 , 6526 , 7222 , 8278 , 9406 , Total time: 3.079 seconds, Total memory usage: 3.49MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 30 02:13:22 2004 Input: for p in [5..100] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^5+x+2); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); numberOfRoots:=#R; summe:=0; for i in [1..numberOfRoots] do summe:=summe+2/R[i][1]^2; end for; numberOfPoints:=p^2+1-summe; print Round(numberOfPoints), ","; end if; end for; Output: Magma V2.10-6 Tue Mar 30 2004 02:13:18 on modular [Seed = 3471282318] ------------------------------------- 46 , 42 , 178 , 186 , 336 , 432 , 568 , 1016 , 1016 , 1160 , 1922 , 2034 , 2354 , 3106 , 3794 , 3658 , 4416 , 5354 , 5184 , 6234 , 6912 , 8306 , 9466 , Total time: 3.469 seconds, Total memory usage: 3.53MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 30 02:14:01 2004 Input: for p in [5..50] do if IsPrime(p) then F := PolynomialRing(FiniteField(p)); C := HyperellipticCurve(x^5+x+2); R:=Roots(Numerator(ZetaFunction(C)), ComplexField()); numberOfRoots:=#R; summe:=0; for i in [1..numberOfRoots] do summe:=summe+2/R[i][1]^2; end for; numberOfPoints:=p^2+1-summe; print Round(numberOfPoints), ","; end if; end for; Output: Magma V2.10-6 Tue Mar 30 2004 02:13:58 on modular [Seed = 3354302911] ------------------------------------- 46 , 42 , 178 , 186 , 336 , 432 , 568 , 1016 , 1016 , 1160 , 1922 , 2034 , 2354 , Total time: 3.219 seconds, Total memory usage: 2.53MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 30 02:14:46 2004 Input: m:=2; upperBound:=50; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); #C; end if; end for; Output: Magma V2.10-6 Tue Mar 30 2004 02:14:43 on modular [Seed = 3707077361] ------------------------------------- 46 46 150 178 313 397 549 929 989 1265 1802 1942 2282 Total time: 2.959 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 30 02:15:21 2004 Input: m:=2; upperBound:=500; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); #C; end if; end for; Output: Magma V2.10-6 Tue Mar 30 2004 02:15:14 on modular [Seed = 3522727709] ------------------------------------- 46 46 150 178 313 397 549 929 989 1265 1802 1942 2282 2958 3638 3690 4453 5198 5257 6238 6901 8114 9438 10294 10858 11518 12145 12966 16234 16902 18890 19501 22182 22749 24817 26754 28386 30602 32126 33337 36830 37402 39250 39358 44930 50130 51526 52714 54393 57837 58390 63186 66193 69726 72241 74173 77350 79425 80694 85841 94254 96302 97550 100746 109770 113889 121294 HyperellipticCurve( f: x^5 + x + 2 ) In file "/usr/local/magma/package/Geometry/CrvHyp/curve.m", line 257, column 30: >> return HyperellipticCurve(f, Parent(f)!0); ^ Runtime error in 'HyperellipticCurve': Curve has a finite singularity Total time: 6.719 seconds, Total memory usage: 5.28MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 30 02:17:15 2004 Input: m:=2; upperBound:=500; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-7)); #C; end if; end for; Output: Magma V2.10-6 Tue Mar 30 2004 02:17:12 on modular [Seed = 3889084753] ------------------------------------- HyperellipticCurve( f: x^5 + 2*x^4 + 3*x^3 + 2*x^2 + 2*x ) In file "/usr/local/magma/package/Geometry/CrvHyp/curve.m", line 257, column 30: >> return HyperellipticCurve(f, Parent(f)!0); ^ Runtime error in 'HyperellipticCurve': Curve has a finite singularity Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 30 02:17:48 2004 Input: m:=2; upperBound:=500; for p in [11..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-7)); #C; end if; end for; Output: Magma V2.10-6 Tue Mar 30 2004 02:17:30 on modular [Seed = 4241859512] ------------------------------------- 166 182 286 342 510 854 990 1414 1710 1830 2318 2854 3382 3926 4630 5118 5518 6126 6934 8046 9662 10214 10574 11430 12214 12798 16062 17350 19214 19206 22502 22974 24406 26582 27838 30294 32566 32678 36846 37310 39462 39918 44486 50046 51638 53094 54670 57358 58558 63030 66366 69726 72022 74110 76742 78958 79782 85894 95254 96558 98574 101014 110582 113822 120582 121494 124446 129086 134174 139654 144982 146350 151878 157334 162110 168590 175814 176902 185998 187742 194062 195270 203166 208782 212598 215006 218326 229502 238350 241574 249862 Total time: 17.569 seconds, Total memory usage: 8.71MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 30 02:22:27 2004 Input: m:=4; upperBound:=50; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^3-1); #C; end if; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Mar 30 2004 02:22:04 on modular [Seed = 2376396255] ------------------------------------- 576 2496 14400 28416 82944 130368 278784 705600 923328 Errors: /home/mfd/gomagma: line 2: 3779 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 30 02:22:51 2004 Input: m:=4; upperBound:=50; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); #C; end if; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Mar 30 2004 02:22:28 on modular [Seed = 2242700799] ------------------------------------- 526 2470 14678 28630 84049 131113 280265 706641 924889 Errors: /home/mfd/gomagma: line 2: 3787 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 30 02:25:13 2004 Input: m:=5; upperBound:=10; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); #C; end if; end for; Output: Magma V2.10-6 Tue Mar 30 2004 02:25:10 on modular [Seed = 2529162766] ------------------------------------- 3126 16630 Total time: 2.969 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 30 02:25:39 2004 Input: m:=6; upperBound:=10; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); #C; end if; end for; Output: Magma V2.10-6 Tue Mar 30 2004 02:25:35 on modular [Seed = 2944847630] ------------------------------------- 16126 117502 Total time: 3.119 seconds, Total memory usage: 3.48MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 30 02:26:10 2004 Input: m:=10; upperBound:=10; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); #C; end if; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Mar 30 2004 02:25:47 on modular [Seed = 2760754193] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 3818 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 30 02:26:44 2004 Input: m:=10; upperBound:=5; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); #C; end if; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Mar 30 2004 02:26:21 on modular [Seed = 3180649710] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 3827 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 30 02:27:50 2004 Input: m:=8; upperBound:=5; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); #C; end if; end for; Output: Magma V2.10-6 Tue Mar 30 2004 02:27:47 on modular [Seed = 3013268110] ------------------------------------- 388126 Total time: 3.669 seconds, Total memory usage: 6.51MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 30 02:28:56 2004 Input: m:=2; upperBound:=10; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^7+x+2); #C; end if; end for; Output: Magma V2.10-6 Tue Mar 30 2004 02:28:53 on modular [Seed = 1231038643] ------------------------------------- 30 92 Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 30 02:54:10 2004 Input: m:=2; upperBound:=10; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^9+x+2); #C; end if; end for; Output: Magma V2.10-6 Tue Mar 30 2004 02:54:07 on modular [Seed = 2085952428] ------------------------------------- HyperellipticCurve( f: x^9 + x + 2 ) In file "/usr/local/magma/package/Geometry/CrvHyp/curve.m", line 257, column 30: >> return HyperellipticCurve(f, Parent(f)!0); ^ Runtime error in 'HyperellipticCurve': Curve has a finite singularity Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 30 02:54:21 2004 Input: m:=2; upperBound:=10; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^9+x^3+2); #C; end if; end for; Output: Magma V2.10-6 Tue Mar 30 2004 02:54:18 on modular [Seed = 1935283350] ------------------------------------- 48 HyperellipticCurve( f: x^9 + x^3 + 2 ) In file "/usr/local/magma/package/Geometry/CrvHyp/curve.m", line 257, column 30: >> return HyperellipticCurve(f, Parent(f)!0); ^ Runtime error in 'HyperellipticCurve': Curve has a finite singularity Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 30 02:54:31 2004 Input: m:=2; upperBound:=10; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^9+3*x+2); #C; end if; end for; Output: Magma V2.10-6 Tue Mar 30 2004 02:54:28 on modular [Seed = 170094065] ------------------------------------- 26 55 Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 30 02:54:50 2004 Input: m:=2; upperBound:=10; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^10+3*x+2); #C; end if; end for; Output: Magma V2.10-6 Tue Mar 30 2004 02:54:47 on modular [Seed = 19424905] ------------------------------------- 26 HyperellipticCurve( f: x^10 + 3*x + 2 ) In file "/usr/local/magma/package/Geometry/CrvHyp/curve.m", line 257, column 30: >> return HyperellipticCurve(f, Parent(f)!0); ^ Runtime error in 'HyperellipticCurve': Curve has a finite singularity Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-b-siee124.uab.es. (158.109.66.124) Time: Tue Mar 30 03:39:35 2004 Input: G9:=GF(9); [k:k,j in G9| k*j eq 1]; Output: Magma V2.10-6 Tue Mar 30 2004 03:39:30 on modular [Seed = 2209018254] ------------------------------------- [ 1, G9.1, G9.1^2, G9.1^3, 2, G9.1^5, G9.1^6, G9.1^7 ] Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host CPE-144-132-5-185.vic.bigpond.net.au. (144.132.5.185) Time: Tue Mar 30 05:29:32 2004 Input: inverse Output: Magma V2.10-6 Tue Mar 30 2004 05:29:29 on modular [Seed = 1350130698] ------------------------------------- >> inverse; ^ User error: Identifier 'inverse' has not been declared or assigned Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host CPE-144-132-5-185.vic.bigpond.net.au. (144.132.5.185) Time: Tue Mar 30 05:29:34 2004 Input: inverse; Output: Magma V2.10-6 Tue Mar 30 2004 05:29:31 on modular [Seed = 1434212621] ------------------------------------- >> inverse;; ^ User error: Identifier 'inverse' has not been declared or assigned Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (195.144.131.14) Time: Tue Mar 30 08:06:59 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Tue Mar 30 2004 08:06:56 on modular [Seed = 957352349] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.149 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (195.144.131.5) Time: Tue Mar 30 08:07:02 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Tue Mar 30 2004 08:06:58 on modular [Seed = 621548931] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.129 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host host213-52-168-66.wmrc.com. (213.52.168.66) Time: Tue Mar 30 08:58:58 2004 Input: factor(x^199-1) Output: Magma V2.10-6 Tue Mar 30 2004 08:58:55 on modular [Seed = 1935298105] ------------------------------------- >> factor(x^199-1) ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 30 09:04:09 2004 Input: print "EXERCICI 1"; print "apartat (i)"; /* CODI ----*/ G2:=GF(2); G3:=GF(3); G5:=GF(5); print "elements de G2"; [ el : el in G2 ] print "elements de G3"; [ el : el in G3 ] print "elements de G5"; [ el : el in G4 ] Output: Magma V2.10-6 Tue Mar 30 2004 09:04:06 on modular [Seed = 86784774] ------------------------------------- EXERCICI 1 apartat (i) elements de G2 >> print "elements de G3"; ^ User error: bad syntax >> print "elements de G5"; ^ User error: bad syntax >> [ el : el in G4 ]; ^ User error: Identifier 'G4' has not been declared or assigned Total time: 2.869 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 30 09:04:42 2004 Input: print "EXERCICI 1"; print "apartat (i)"; /* CODI ----*/ G2:=GF(2); G3:=GF(3); G5:=GF(5); print "elements de G2"; [ el : el in G2 ]; print "elements de G3"; [ el : el in G3 ]; print "elements de G5"; [ el : el in G5 ]; Output: Magma V2.10-6 Tue Mar 30 2004 09:04:39 on modular [Seed = 203764270] ------------------------------------- EXERCICI 1 apartat (i) elements de G2 [ 0, 1 ] elements de G3 [ 0, 1, 2 ] elements de G5 [ 0, 1, 2, 3, 4 ] Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 30 09:06:52 2004 Input: Z9:=Integers(9); /* Z9 no es un cos pq te elements no invertibles a part del zero. Són aquests:*/ print "Elements no invertibles a Z9"; [el: el in Z9 | IsInvertible(el) eq false); Output: Magma V2.10-6 Tue Mar 30 2004 09:06:49 on modular [Seed = 3639731828] ------------------------------------- Elements no invertibles a Z9 >> [el: el in Z9 | IsInvertible(el) eq false); ^ User error: bad syntax Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 30 09:07:02 2004 Input: Z9:=Integers(9); /* Z9 no es un cos pq te elements no invertibles a part del zero. Són aquests:*/ print "Elements no invertibles a Z9"; [el: el in Z9 | IsInvertible(el) eq false ]; Output: Magma V2.10-6 Tue Mar 30 2004 09:06:59 on modular [Seed = 3454333595] ------------------------------------- Elements no invertibles a Z9 [ 0, 3, 6 ] Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 30 09:11:40 2004 Input: p:=5; n:=2; print "Ordre dels elements de G25 diferents de 0"; [Order(el) : el in G25 | el ne 0]; print "Elements primitius de G25"; Elem25:=[el : el in G25 | (el ne 0) and (Order(el) eq (p^n-1))]; Elem25; Output: Magma V2.10-6 Tue Mar 30 2004 09:11:37 on modular [Seed = 4224859063] ------------------------------------- Ordre dels elements de G25 diferents de 0 >> [Order(el) : el in G25 | el ne 0]; ^ User error: Identifier 'G25' has not been declared or assigned Elements primitius de G25 >> Elem25:=[el : el in G25 | (el ne 0) and (Order(el) eq (p^n-1))]; ^ User error: Identifier 'G25' has not been declared or assigned >> Elem25; ^ User error: Identifier 'Elem25' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 30 09:12:35 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; print "Ordre dels elements de G25 diferents de 0"; [Order(el) : el in G25 | el ne 0]; print "Elements primitius de G25"; Elem25:=[el : el in G25 | (el ne 0) and (Order(el) eq (p^n-1))]; Elem25; Output: Magma V2.10-6 Tue Mar 30 2004 09:12:32 on modular [Seed = 3989057001] ------------------------------------- Ordre dels elements de G25 diferents de 0 [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] Elements primitius de G25 [ alfa, alfa^5, alfa^7, alfa^11, alfa^13, alfa^17, alfa^19, alfa^23 ] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 30 09:13:53 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; print "Ordre dels elements de G25 diferents de 0"; [Order(el) : el in G25 | el ne 0]; print "Elements primitius de G25"; Elem25:=[el : el in G25 | (el ne 0) and (Order(el) eq (p^n-1))]; Elem25; print "Nombre d'elements primitius de G25"; #Elem25; Output: Magma V2.10-6 Tue Mar 30 2004 09:13:51 on modular [Seed = 2428063834] ------------------------------------- Ordre dels elements de G25 diferents de 0 [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] Elements primitius de G25 [ alfa, alfa^5, alfa^7, alfa^11, alfa^13, alfa^17, alfa^19, alfa^23 ] Nombre d'elements primitius de G25 8 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee50.uab.es. (158.109.66.50) Time: Tue Mar 30 09:14:30 2004 Input: gcd(9,3); Output: Magma V2.10-6 Tue Mar 30 2004 09:14:26 on modular [Seed = 2595445261] ------------------------------------- >> gcd(9,3);; ^ User error: Identifier 'gcd' has not been declared or assigned Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 30 09:17:03 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; beta:=2*alfa^(-3) - alfa^5 + (1/(alfa+2))*alfa^6; print "Solucio de beta"; beta; print "Invers"; beta^(-1); Output: Magma V2.10-6 Tue Mar 30 2004 09:17:00 on modular [Seed = 2342668930] ------------------------------------- Solucio de beta alfa^8 Invers alfa^16 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 30 09:19:42 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; beta:=2*alfa^(-3) - alfa^5 + (1/(alfa+2))*alfa^6; print "Solucio de beta"; beta; print "Invers"; beta^(-1); print "Elements invertibles a G25"; Inv25:=[el : el in G25 | IsInvertible(el) eq true]; print "Nombre d'elements invertibles de G25"; #Inv25 Output: Magma V2.10-6 Tue Mar 30 2004 09:19:39 on modular [Seed = 2996531996] ------------------------------------- Solucio de beta alfa^8 Invers alfa^16 Elements invertibles a G25 Nombre d'elements invertibles de G25 24 Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 30 09:20:04 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; beta:=2*alfa^(-3) - alfa^5 + (1/(alfa+2))*alfa^6; print "Solucio de beta"; beta; print "Invers"; beta^(-1); print "Elements invertibles a G25"; Inv25:=[el : el in G25 | IsInvertible(el) eq true]; Inv25; print "Nombre d'elements invertibles de G25"; #Inv25 Output: Magma V2.10-6 Tue Mar 30 2004 09:20:01 on modular [Seed = 2727043302] ------------------------------------- Solucio de beta alfa^8 Invers alfa^16 Elements invertibles a G25 [ 1, alfa, alfa^2, alfa^3, alfa^4, alfa^5, 3, alfa^7, alfa^8, alfa^9, alfa^10, alfa^11, 4, alfa^13, alfa^14, alfa^15, alfa^16, alfa^17, 2, alfa^19, alfa^20, alfa^21, alfa^22, alfa^23 ] Nombre d'elements invertibles de G25 24 Total time: 2.869 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 30 09:24:11 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; G2:=GF(2); G16:=ext< G2 | g >; print "G25" ; print "exponencial , vectorial"; [ < el , ElementToSequence(el)> : el in G25]; print "G16"; print "exponencial , vectorial"; [ < el , ElementToSequence(el)> : el in G16]; Output: Magma V2.10-6 Tue Mar 30 2004 09:24:08 on modular [Seed = 1417516810] ------------------------------------- G25 exponencial , vectorial [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , , <0, [ 0, 0 ]> ] G16 exponencial , vectorial [ <1, [ 1, 0, 0, 0 ]>, , , , , , , , , , , , , , , <0, [ 0, 0, 0, 0 ]> ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 30 09:27:34 2004 Input: CF2:=GF(2); CF4:=GF(2,2); CF8:=GF(2,3); CF16:=GF(2,4); print("Elements de CF2"); [ el : el in CF2 ] print("Elements de CF4"); [ el : el in CF4 ] print("Elements de CF8"); [ el : el in CF8 ] print("Elements de CF16"); [ el : el in CF6 ] print "CF2"; CF2 subset CF16; CF2 subset CF8; CF2 subset CF4; print "CF4"; CF4 subset CF16; CF4 subset CF8; CF4 subset CF2; print "CF8"; CF8 subset CF16; CF8 subset CF4; CF8 subset CF2; print "CF16"; CF16 subset CF8; CF16 subset CF4; CF16 subset CF2; Output: Magma V2.10-6 Tue Mar 30 2004 09:27:31 on modular [Seed = 1198425282] ------------------------------------- Elements de CF2 >> print("Elements de CF4"); ^ User error: bad syntax >> print("Elements de CF8"); ^ User error: bad syntax >> print("Elements de CF16"); ^ User error: bad syntax >> print "CF2"; ^ User error: bad syntax true true true CF4 true false false CF8 false false false CF16 false false false Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 30 09:27:46 2004 Input: CF2:=GF(2); CF4:=GF(2,2); CF8:=GF(2,3); CF16:=GF(2,4); print("Elements de CF2"); [ el : el in CF2 ]; print("Elements de CF4"); [ el : el in CF4 ]; print("Elements de CF8"); [ el : el in CF8 ]; print("Elements de CF16"); [ el : el in CF6 ]; print "CF2"; CF2 subset CF16; CF2 subset CF8; CF2 subset CF4; print "CF4"; CF4 subset CF16; CF4 subset CF8; CF4 subset CF2; print "CF8"; CF8 subset CF16; CF8 subset CF4; CF8 subset CF2; print "CF16"; CF16 subset CF8; CF16 subset CF4; CF16 subset CF2; Output: Magma V2.10-6 Tue Mar 30 2004 09:27:43 on modular [Seed = 1281724357] ------------------------------------- Elements de CF2 [ 0, 1 ] Elements de CF4 [ 1, CF4.1, CF4.1^2, 0 ] Elements de CF8 [ 1, CF8.1, CF8.1^2, CF8.1^3, CF8.1^4, CF8.1^5, CF8.1^6, 0 ] Elements de CF16 >> [ el : el in CF6 ]; ^ User error: Identifier 'CF6' has not been declared or assigned CF2 true true true CF4 true false false CF8 false false false CF16 false false false Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 30 09:28:09 2004 Input: CF2:=GF(2); CF4:=GF(2,2); CF8:=GF(2,3); CF16:=GF(2,4); print("Elements de CF2"); [ el : el in CF2 ]; print("Elements de CF4"); [ el : el in CF4 ]; print("Elements de CF8"); [ el : el in CF8 ]; print("Elements de CF16"); [ el : el in CF16 ]; print "CF2"; CF2 subset CF16; CF2 subset CF8; CF2 subset CF4; print "CF4"; CF4 subset CF16; CF4 subset CF8; CF4 subset CF2; print "CF8"; CF8 subset CF16; CF8 subset CF4; CF8 subset CF2; print "CF16"; CF16 subset CF8; CF16 subset CF4; CF16 subset CF2; Output: Magma V2.10-6 Tue Mar 30 2004 09:28:06 on modular [Seed = 1969010389] ------------------------------------- Elements de CF2 [ 0, 1 ] Elements de CF4 [ 1, CF4.1, CF4.1^2, 0 ] Elements de CF8 [ 1, CF8.1, CF8.1^2, CF8.1^3, CF8.1^4, CF8.1^5, CF8.1^6, 0 ] Elements de CF16 [ 1, CF16.1, CF16.1^2, CF16.1^3, CF16.1^4, CF16.1^5, CF16.1^6, CF16.1^7, CF16.1^8, CF16.1^9, CF16.1^10, CF16.1^11, CF16.1^12, CF16.1^13, CF16.1^14, 0 ] CF2 true true true CF4 true false false CF8 false false false CF16 false false false Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 30 10:40:17 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; print "apartat (vi)"; /* CODI ----*/ print "Polinomi sobre G25"; poli:= 1/alfa^4 - alfa^(-3) * x + alfa^5*x^2; poli; print "Factorització"; Factorization(poli); print "Arrels"; Roots(poli,G25); print "Comprovació amb Evaluate"; [ el : el in G25 | Evaluate(poli,el) eq 0] Output: Magma V2.10-6 Tue Mar 30 2004 10:40:14 on modular [Seed = 2158580744] ------------------------------------- apartat (vi) Polinomi sobre G25 >> poli:= 1/alfa^4 - alfa^(-3) * x + alfa^5*x^2; ^ User error: Identifier 'x' has not been declared or assigned >> poli; ^ User error: Identifier 'poli' has not been declared or assigned Factorització >> Factorization(poli); ^ User error: Identifier 'poli' has not been declared or assigned Arrels >> Roots(poli,G25); ^ User error: Identifier 'poli' has not been declared or assigned Comprovació amb Evaluate >> [ el : el in G25 | Evaluate(poli,el) eq 0]; ^ User error: Identifier 'poli' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 30 10:41:08 2004 Input: P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G5:=GF(5); G25:=ext< G5 | h >; PR5:=PolynomialRing(G25); print "apartat (vi)"; /* CODI ----*/ print "Polinomi sobre G25"; poli:= 1/alfa^4 - alfa^(-3) * x + alfa^5*x^2; poli; print "Factorització"; Factorization(poli); print "Arrels"; Roots(poli,G25); print "Comprovació amb Evaluate"; [ el : el in G25 | Evaluate(poli,el) eq 0] Output: Magma V2.10-6 Tue Mar 30 2004 10:41:05 on modular [Seed = 2308988110] ------------------------------------- apartat (vi) Polinomi sobre G25 alfa^5*x^2 + alfa^9*x + alfa^20 Factorització [ ] Arrels [] Comprovació amb Evaluate [] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dumbo.mat.ub.es. (161.116.84.30) Time: Tue Mar 30 11:07:45 2004 Input: S4:=Sym(4); Output: Magma V2.10-6 Tue Mar 30 2004 11:07:41 on modular [Seed = 2052301152] ------------------------------------- Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dumbo.mat.ub.es. (161.116.84.30) Time: Tue Mar 30 11:08:13 2004 Input: S4:=Sym(4); Subgroups(S4); Output: Magma V2.10-6 Tue Mar 30 2004 11:08:10 on modular [Seed = 1632156252] ------------------------------------- Conjugacy classes of subgroups ------------------------------ [ 1] Order 1 Length 1 Permutation group acting on a set of cardinality 4 Order = 1 [ 2] Order 2 Length 3 Permutation group acting on a set of cardinality 4 Order = 2 (1, 4)(2, 3) [ 3] Order 2 Length 6 Permutation group acting on a set of cardinality 4 Order = 2 (3, 4) [ 4] Order 3 Length 4 Permutation group acting on a set of cardinality 4 Order = 3 (2, 3, 4) [ 5] Order 4 Length 1 Permutation group acting on a set of cardinality 4 Order = 4 = 2^2 (1, 4)(2, 3) (1, 3)(2, 4) [ 6] Order 4 Length 3 Permutation group acting on a set of cardinality 4 Order = 4 = 2^2 (1, 4, 2, 3) (1, 2)(3, 4) [ 7] Order 4 Length 3 Permutation group acting on a set of cardinality 4 Order = 4 = 2^2 (3, 4) (1, 2)(3, 4) [ 8] Order 6 Length 4 Permutation group acting on a set of cardinality 4 Order = 6 = 2 * 3 (3, 4) (2, 3, 4) [ 9] Order 8 Length 3 Permutation group acting on a set of cardinality 4 Order = 8 = 2^3 (3, 4) (1, 4)(2, 3) (1, 3)(2, 4) [10] Order 12 Length 1 Permutation group acting on a set of cardinality 4 Order = 12 = 2^2 * 3 (2, 3, 4) (1, 4)(2, 3) (1, 3)(2, 4) [11] Order 24 Length 1 Permutation group acting on a set of cardinality 4 Order = 24 = 2^3 * 3 (3, 4) (2, 3, 4) (1, 4)(2, 3) (1, 3)(2, 4) Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host dumbo.mat.ub.es. (161.116.84.30) Time: Tue Mar 30 11:09:30 2004 Input: S4:=Sym({"1","2","3","4"}); Subgroups(S4); Output: Magma V2.10-6 Tue Mar 30 2004 11:09:27 on modular [Seed = 339595252] ------------------------------------- Conjugacy classes of subgroups ------------------------------ [ 1] Order 1 Length 1 Permutation group acting on a set of cardinality 4 Order = 1 [ 2] Order 2 Length 3 Permutation group acting on a set of cardinality 4 Order = 2 (3, 4)(2, 1) [ 3] Order 2 Length 6 Permutation group acting on a set of cardinality 4 Order = 2 (1, 4) [ 4] Order 3 Length 4 Permutation group acting on a set of cardinality 4 Order = 3 (2, 1, 4) [ 5] Order 4 Length 1 Permutation group acting on a set of cardinality 4 Order = 4 = 2^2 (3, 4)(2, 1) (3, 1)(2, 4) [ 6] Order 4 Length 3 Permutation group acting on a set of cardinality 4 Order = 4 = 2^2 (3, 4, 2, 1) (3, 2)(1, 4) [ 7] Order 4 Length 3 Permutation group acting on a set of cardinality 4 Order = 4 = 2^2 (1, 4) (3, 2)(1, 4) [ 8] Order 6 Length 4 Permutation group acting on a set of cardinality 4 Order = 6 = 2 * 3 (1, 4) (2, 1, 4) [ 9] Order 8 Length 3 Permutation group acting on a set of cardinality 4 Order = 8 = 2^3 (1, 4) (3, 4)(2, 1) (3, 1)(2, 4) [10] Order 12 Length 1 Permutation group acting on a set of cardinality 4 Order = 12 = 2^2 * 3 (2, 1, 4) (3, 4)(2, 1) (3, 1)(2, 4) [11] Order 24 Length 1 Permutation group acting on a set of cardinality 4 Order = 24 = 2^3 * 3 (1, 4) (2, 1, 4) (3, 4)(2, 1) (3, 1)(2, 4) Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host dumbo.mat.ub.es. (161.116.84.30) Time: Tue Mar 30 11:14:51 2004 Input: S4:=Sym({"1","2","3","4"}); Subgroups(S4); ? Subgroups; Output: Magma V2.10-6 Tue Mar 30 2004 11:14:48 on modular [Seed = 36429485] ------------------------------------- Conjugacy classes of subgroups ------------------------------ [ 1] Order 1 Length 1 Permutation group acting on a set of cardinality 4 Order = 1 [ 2] Order 2 Length 3 Permutation group acting on a set of cardinality 4 Order = 2 (3, 4)(2, 1) [ 3] Order 2 Length 6 Permutation group acting on a set of cardinality 4 Order = 2 (1, 4) [ 4] Order 3 Length 4 Permutation group acting on a set of cardinality 4 Order = 3 (2, 1, 4) [ 5] Order 4 Length 1 Permutation group acting on a set of cardinality 4 Order = 4 = 2^2 (3, 4)(2, 1) (3, 1)(2, 4) [ 6] Order 4 Length 3 Permutation group acting on a set of cardinality 4 Order = 4 = 2^2 (3, 4, 2, 1) (3, 2)(1, 4) [ 7] Order 4 Length 3 Permutation group acting on a set of cardinality 4 Order = 4 = 2^2 (1, 4) (3, 2)(1, 4) [ 8] Order 6 Length 4 Permutation group acting on a set of cardinality 4 Order = 6 = 2 * 3 (1, 4) (2, 1, 4) [ 9] Order 8 Length 3 Permutation group acting on a set of cardinality 4 Order = 8 = 2^3 (1, 4) (3, 4)(2, 1) (3, 1)(2, 4) [10] Order 12 Length 1 Permutation group acting on a set of cardinality 4 Order = 12 = 2^2 * 3 (2, 1, 4) (3, 4)(2, 1) (3, 1)(2, 4) [11] Order 24 Length 1 Permutation group acting on a set of cardinality 4 Order = 24 = 2^3 * 3 (1, 4) (2, 1, 4) (3, 4)(2, 1) (3, 1)(2, 4) 55 matches: 1 S /magma/group/generic_abelian/subgroups 2 S /magma/group/GrpPSL2/Congruence-subgroups 3 S /magma/group/matrix/subgroups 4 S /magma/group/p-groups/subgroups 5 S /magma/group/permutation/\ characteristic-subgroup-normal-structure/normal-subgroups 6 S /magma/group/permutation/\ characteristic-subgroup-normal-structure/normal-subgroups 7 S /magma/group/permutation/\ characteristic-subgroup-normal-structure/normal-subgroups 8 S /magma/group/permutation/subgroup/subgroups-conditional 9 S /magma/group/soluble/normal-series/characteristic-subgroups 10 S /magma/group/soluble/subgroups 11 S /magma/lie-theory/finite-coxeter-groups/subgroups 12 I /magma/group/abelian/characteristic-subgroup-normal-structure/\ subgroup-structure/MaximalSubgroups 13 I /magma/group/abelian/characteristic-subgroup-normal-structure/\ subgroup-structure/Subgroups 14 I /magma/group/finitely-presented/subgroup/low-index-subgroup/\ LowIndexSubgroups 15 I /magma/group/finitely-presented/subgroup/low-index-subgroup/\ LowIndexSubgroups 16 I /magma/group/group-overview/\ characteristic-subgroup-normal-structure/subgroup-series/\ NormalSubgroups 17 I /magma/group/group-overview/subgroup/subgroup-classes/\ AbelianSubgroups 18 I /magma/group/group-overview/subgroup/subgroup-classes/\ CyclicSubgroups 19 I /magma/group/group-overview/subgroup/subgroup-classes/\ ElementaryAbelianSubgroups 20 I /magma/group/group-overview/subgroup/subgroup-classes/\ NilpotentSubgroups 21 I /magma/group/group-overview/subgroup/subgroup-classes/\ NonsolvableSubgroups 22 I /magma/group/group-overview/subgroup/subgroup-classes/\ PerfectSubgroups 23 I /magma/group/group-overview/subgroup/subgroup-classes/\ RegularSubgroups 24 I /magma/group/group-overview/subgroup/subgroup-classes/\ SimpleSubgroups 25 I /magma/group/group-overview/subgroup/subgroup-classes/\ SolubleSubgroups 26 I /magma/group/group-overview/subgroup/subgroup-classes/\ SolubleSubgroups 27 I /magma/group/group-overview/subgroup/subgroup-classes/\ SubgroupClasses 28 I /magma/group/group-overview/subgroup/subgroup-poset/\ class-information/MaximalSubgroups 29 I /magma/group/matrix/subgroups/quotient/LowIndexSubgroups 30 I /magma/group/p-groups/Misc/NumberOfSubgroupsAbelianPGroup 31 I /magma/group/permutation/\ characteristic-subgroup-normal-structure/normal-subgroups/\ MinimalNormalSubgroups 32 I /magma/group/permutation/\ characteristic-subgroup-normal-structure/normal-subgroups/\ NormalSubgroups 33 I /magma/group/permutation/subgroup/maximals/LowIndexSubgroups 34 I /magma/group/permutation/subgroup/maximals/LowIndexSubgroups 35 I /magma/group/permutation/subgroup/maximals/MaximalSubgroups 36 I /magma/group/permutation/subgroup/maximals/SubgroupClasses 37 I /magma/group/permutation/subgroup/maximals/SubgroupsLift 38 I /magma/group/permutation/subgroup/subgroups-conditional/\ AbelianSubgroups 39 I /magma/group/permutation/subgroup/subgroups-conditional/\ CyclicSubgroups 40 I /magma/group/permutation/subgroup/subgroups-conditional/\ ElementaryAbelianSubgroups 41 I /magma/group/permutation/subgroup/subgroups-conditional/\ NilpotentSubgroups 42 I /magma/group/permutation/subgroup/subgroups-conditional/\ NonsolvableSubgroups 43 I /magma/group/permutation/subgroup/subgroups-conditional/\ NormalSubgroups 44 I /magma/group/permutation/subgroup/subgroups-conditional/\ PerfectSubgroups 45 I /magma/group/permutation/subgroup/subgroups-conditional/\ SimpleSubgroups 46 I /magma/group/permutation/subgroup/subgroups-conditional/\ SolvableSubgroups 47 I /magma/group/soluble/normal-series/normals/NormalSubgroups 48 I /magma/group/soluble/subgroups/subgroup-classes/AbelianSubgroups 49 I /magma/group/soluble/subgroups/subgroup-classes/AbelianSubgroups 50 I /magma/group/soluble/subgroups/subgroup-classes/MaximalSubgroups 51 I /magma/group/soluble/subgroups/subgroup-classes/SubgroupClasses 52 E /magma/group/abelian/characteristic-subgroup-normal-structure/\ subgroup-structure/Example-Subgroups 53 E /magma/group/group-overview/subgroup/subgroup-classes/\ Example-Subgroups 54 E /magma/group/matrix/subgroups/construction-subgroup/\ Example-Subgroups 55 E /magma/group/permutation/subgroup/maximals/Example-Subgroups To view an entry, type ? followed by the number next to it Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host dumbo.mat.ub.es. (161.116.84.30) Time: Tue Mar 30 11:16:21 2004 Input: S4:=Sym({"1","2","3","4"}); Subgroups(S4); Output: Magma V2.10-6 Tue Mar 30 2004 11:16:18 on modular [Seed = 991094334] ------------------------------------- Conjugacy classes of subgroups ------------------------------ [ 1] Order 1 Length 1 Permutation group acting on a set of cardinality 4 Order = 1 [ 2] Order 2 Length 3 Permutation group acting on a set of cardinality 4 Order = 2 (3, 4)(2, 1) [ 3] Order 2 Length 6 Permutation group acting on a set of cardinality 4 Order = 2 (1, 4) [ 4] Order 3 Length 4 Permutation group acting on a set of cardinality 4 Order = 3 (2, 1, 4) [ 5] Order 4 Length 1 Permutation group acting on a set of cardinality 4 Order = 4 = 2^2 (3, 4)(2, 1) (3, 1)(2, 4) [ 6] Order 4 Length 3 Permutation group acting on a set of cardinality 4 Order = 4 = 2^2 (3, 4, 2, 1) (3, 2)(1, 4) [ 7] Order 4 Length 3 Permutation group acting on a set of cardinality 4 Order = 4 = 2^2 (1, 4) (3, 2)(1, 4) [ 8] Order 6 Length 4 Permutation group acting on a set of cardinality 4 Order = 6 = 2 * 3 (1, 4) (2, 1, 4) [ 9] Order 8 Length 3 Permutation group acting on a set of cardinality 4 Order = 8 = 2^3 (1, 4) (3, 4)(2, 1) (3, 1)(2, 4) [10] Order 12 Length 1 Permutation group acting on a set of cardinality 4 Order = 12 = 2^2 * 3 (2, 1, 4) (3, 4)(2, 1) (3, 1)(2, 4) [11] Order 24 Length 1 Permutation group acting on a set of cardinality 4 Order = 24 = 2^3 * 3 (1, 4) (2, 1, 4) (3, 4)(2, 1) (3, 1)(2, 4) Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host dumbo.mat.ub.es. (161.116.84.30) Time: Tue Mar 30 11:26:39 2004 Input: S4:=Sym({"1","2","3","4"}); S4; Output: Magma V2.10-6 Tue Mar 30 2004 11:26:36 on modular [Seed = 3556379704] ------------------------------------- Symmetric group S4 acting on a set of cardinality 4 Order = 24 = 2^3 * 3 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dumbo.mat.ub.es. (161.116.84.30) Time: Tue Mar 30 11:28:54 2004 Input: S4:=Sym({"1","2","3","4"}); S4; SubgroupClasses(S4); Output: Magma V2.10-6 Tue Mar 30 2004 11:28:51 on modular [Seed = 3639687372] ------------------------------------- Symmetric group S4 acting on a set of cardinality 4 Order = 24 = 2^3 * 3 Conjugacy classes of subgroups ------------------------------ [ 1] Order 1 Length 1 Permutation group acting on a set of cardinality 4 Order = 1 [ 2] Order 2 Length 3 Permutation group acting on a set of cardinality 4 Order = 2 (3, 4)(2, 1) [ 3] Order 2 Length 6 Permutation group acting on a set of cardinality 4 Order = 2 (1, 4) [ 4] Order 3 Length 4 Permutation group acting on a set of cardinality 4 Order = 3 (2, 1, 4) [ 5] Order 4 Length 1 Permutation group acting on a set of cardinality 4 Order = 4 = 2^2 (3, 4)(2, 1) (3, 1)(2, 4) [ 6] Order 4 Length 3 Permutation group acting on a set of cardinality 4 Order = 4 = 2^2 (3, 4, 2, 1) (3, 2)(1, 4) [ 7] Order 4 Length 3 Permutation group acting on a set of cardinality 4 Order = 4 = 2^2 (1, 4) (3, 2)(1, 4) [ 8] Order 6 Length 4 Permutation group acting on a set of cardinality 4 Order = 6 = 2 * 3 (1, 4) (2, 1, 4) [ 9] Order 8 Length 3 Permutation group acting on a set of cardinality 4 Order = 8 = 2^3 (1, 4) (3, 4)(2, 1) (3, 1)(2, 4) [10] Order 12 Length 1 Permutation group acting on a set of cardinality 4 Order = 12 = 2^2 * 3 (2, 1, 4) (3, 4)(2, 1) (3, 1)(2, 4) [11] Order 24 Length 1 Permutation group acting on a set of cardinality 4 Order = 24 = 2^3 * 3 (1, 4) (2, 1, 4) (3, 4)(2, 1) (3, 1)(2, 4) Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host dumbo.mat.ub.es. (161.116.84.30) Time: Tue Mar 30 11:31:34 2004 Input: S4:=Sym({"1","2","3","4"}); S4; SubgroupClasses(S4: Presentation:=true); Output: Magma V2.10-6 Tue Mar 30 2004 11:31:31 on modular [Seed = 3370199164] ------------------------------------- Symmetric group S4 acting on a set of cardinality 4 Order = 24 = 2^3 * 3 Conjugacy classes of subgroups ------------------------------ [ 1] Order 1 Length 1 Permutation group acting on a set of cardinality 4 Order = 1 Finitely presented group on 1 generator Relations $.1 = Id($) [ 2] Order 2 Length 3 Permutation group acting on a set of cardinality 4 Order = 2 (3, 4)(2, 1) Finitely presented group on 1 generator Relations $.1^2 = Id($) [ 3] Order 2 Length 6 Permutation group acting on a set of cardinality 4 Order = 2 (1, 4) Finitely presented group on 1 generator Relations $.1^2 = Id($) [ 4] Order 3 Length 4 Permutation group acting on a set of cardinality 4 Order = 3 (2, 1, 4) Finitely presented group on 1 generator Relations $.1^3 = Id($) [ 5] Order 4 Length 1 Permutation group acting on a set of cardinality 4 Order = 4 = 2^2 (3, 4)(2, 1) (3, 1)(2, 4) Finitely presented group on 2 generators Relations $.1^2 = Id($) $.2^2 = Id($) ($.1, $.2) = Id($) [ 6] Order 4 Length 3 Permutation group acting on a set of cardinality 4 Order = 4 = 2^2 (3, 4, 2, 1) (3, 2)(1, 4) Finitely presented group on 2 generators Relations $.1^2 = $.2 $.2^$.1 = $.2 $.2^2 = Id($) [ 7] Order 4 Length 3 Permutation group acting on a set of cardinality 4 Order = 4 = 2^2 (1, 4) (3, 2)(1, 4) Finitely presented group on 2 generators Relations $.1^2 = Id($) $.2^$.1 = $.2 $.2^2 = Id($) [ 8] Order 6 Length 4 Permutation group acting on a set of cardinality 4 Order = 6 = 2 * 3 (1, 4) (2, 1, 4) Finitely presented group on 2 generators Relations $.1^2 = Id($) $.2^$.1 = $.2^2 $.2^3 = Id($) [ 9] Order 8 Length 3 Permutation group acting on a set of cardinality 4 Order = 8 = 2^3 (1, 4) (3, 4)(2, 1) (3, 1)(2, 4) Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^$.1 = $.3 $.3^$.1 = $.2 $.2^2 = Id($) $.3^2 = Id($) ($.2, $.3) = Id($) [10] Order 12 Length 1 Permutation group acting on a set of cardinality 4 Order = 12 = 2^2 * 3 (2, 1, 4) (3, 4)(2, 1) (3, 1)(2, 4) Finitely presented group on 3 generators Relations $.1^3 = Id($) $.2^$.1 = $.2 * $.3 $.3^$.1 = $.2 $.2^2 = Id($) $.3^2 = Id($) ($.2, $.3) = Id($) [11] Order 24 Length 1 Permutation group acting on a set of cardinality 4 Order = 24 = 2^3 * 3 (1, 4) (2, 1, 4) (3, 4)(2, 1) (3, 1)(2, 4) Finitely presented group on 4 generators Relations $.1^2 = Id($) $.1^-1 * $.2 * $.1 * $.2^-2 = Id($) $.2^3 = Id($) $.3^$.1 = $.4 $.4^$.1 = $.3 $.3^$.2 = $.3 * $.4 $.4^$.2 = $.3 $.3^2 = Id($) $.4^2 = Id($) ($.3, $.4) = Id($) Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Tue Mar 30 11:32:14 2004 Input: G5:=GF(5); Output: Magma V2.10-6 Tue Mar 30 2004 11:32:11 on modular [Seed = 4275511202] ------------------------------------- Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Tue Mar 30 11:32:41 2004 Input: G5:=GF(5); [x:x in G5]; Output: Magma V2.10-6 Tue Mar 30 2004 11:32:38 on modular [Seed = 3838641557] ------------------------------------- [ 0, 1, 2, 3, 4 ] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Tue Mar 30 11:38:56 2004 Input: G5:=GF(5); [x:x in G5]; P2b:=x^2+4*x+2; Output: Magma V2.10-6 Tue Mar 30 2004 11:38:53 on modular [Seed = 2512156511] ------------------------------------- [ 0, 1, 2, 3, 4 ] >> P2b:=x^2+4*x+2;; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Tue Mar 30 11:39:29 2004 Input: G5:=GF(5); [x:x in G5]; P2b:=PolynomialRing(G5); P2b:=x^2+4*x+2; P2b; Output: Magma V2.10-6 Tue Mar 30 2004 11:39:26 on modular [Seed = 2629140085] ------------------------------------- [ 0, 1, 2, 3, 4 ] x^2 + 4*x + 2 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Tue Mar 30 11:39:58 2004 Input: G5:=GF(5); [x:x in G5]; P2b:=PolynomialRing(G5); P2b:=x^2+4*x+2; P2b; G25:=ext ; Output: Magma V2.10-6 Tue Mar 30 2004 11:39:55 on modular [Seed = 2208981263] ------------------------------------- [ 0, 1, 2, 3, 4 ] x^2 + 4*x + 2 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Tue Mar 30 11:40:08 2004 Input: G5:=GF(5); [x:x in G5]; P2b:=PolynomialRing(G5); P2b:=x^2+4*x+2; P2b; G25:=ext ; Output: Magma V2.10-6 Tue Mar 30 2004 11:40:05 on modular [Seed = 3013234945] ------------------------------------- [ 0, 1, 2, 3, 4 ] x^2 + 4*x + 2 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Tue Mar 30 11:41:04 2004 Input: P:=PolynomialRing(G25); Output: Magma V2.10-6 Tue Mar 30 2004 11:41:01 on modular [Seed = 3113245427] ------------------------------------- >> P:=PolynomialRing(G25);; ^ User error: Identifier 'G25' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dumbo.mat.ub.es. (161.116.84.30) Time: Tue Mar 30 11:42:42 2004 Input: s4:=Sym(4); Subgroups(s4: Al:=All); Output: Magma V2.10-6 Tue Mar 30 2004 11:42:39 on modular [Seed = 2944814215] ------------------------------------- >> Subgroups(s4: Al:=All);; ^ User error: Identifier 'All' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dumbo.mat.ub.es. (161.116.84.30) Time: Tue Mar 30 11:43:02 2004 Input: s4:=Sym(4); Subgroups(s4: Al:="All"); Output: Magma V2.10-6 Tue Mar 30 2004 11:42:58 on modular [Seed = 2018614194] ------------------------------------- Conjugacy classes of subgroups ------------------------------ [ 1] Order 1 Length 1 Permutation group acting on a set of cardinality 4 Order = 1 [ 2] Order 2 Length 3 Permutation group acting on a set of cardinality 4 Order = 2 (1, 4)(2, 3) [ 3] Order 2 Length 6 Permutation group acting on a set of cardinality 4 Order = 2 (3, 4) [ 4] Order 3 Length 4 Permutation group acting on a set of cardinality 4 Order = 3 (2, 3, 4) [ 5] Order 4 Length 1 Permutation group acting on a set of cardinality 4 Order = 4 = 2^2 (1, 4)(2, 3) (1, 3)(2, 4) [ 6] Order 4 Length 3 Permutation group acting on a set of cardinality 4 Order = 4 = 2^2 (1, 4, 2, 3) (1, 2)(3, 4) [ 7] Order 4 Length 3 Permutation group acting on a set of cardinality 4 Order = 4 = 2^2 (3, 4) (1, 2)(3, 4) [ 8] Order 6 Length 4 Permutation group acting on a set of cardinality 4 Order = 6 = 2 * 3 (3, 4) (2, 3, 4) [ 9] Order 8 Length 3 Permutation group acting on a set of cardinality 4 Order = 8 = 2^3 (3, 4) (1, 4)(2, 3) (1, 3)(2, 4) [10] Order 12 Length 1 Permutation group acting on a set of cardinality 4 Order = 12 = 2^2 * 3 (2, 3, 4) (1, 4)(2, 3) (1, 3)(2, 4) [11] Order 24 Length 1 Permutation group acting on a set of cardinality 4 Order = 24 = 2^3 * 3 (3, 4) (2, 3, 4) (1, 4)(2, 3) (1, 3)(2, 4) Total time: 3.179 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host aula-a-siee47.uab.es. (158.109.66.47) Time: Tue Mar 30 11:45:32 2004 Input: G5:=GF(5); P2b:=PolynomialRing(G5); P2b:=x^2+4*x+2; P2b; P:=PolynomialRing(G25); Output: Magma V2.10-6 Tue Mar 30 2004 11:45:29 on modular [Seed = 1782812184] ------------------------------------- x^2 + 4*x + 2 >> P:=PolynomialRing(G25);; ^ User error: Identifier 'G25' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD02.Math.McGill.CA. (132.206.150.202) Time: Tue Mar 30 11:46:41 2004 Input: E:=EllipticCuvre([0,0,1,-1,0]); w1,w2:=Periods(E); Volume([w1,w2]); Output: Magma V2.10-6 Tue Mar 30 2004 11:46:38 on modular [Seed = 1699512659] ------------------------------------- >> E:=EllipticCuvre([0,0,1,-1,0]); ^ User error: Identifier 'EllipticCuvre' has not been declared or assigned >> w1,w2:=Periods(E); ^ User error: Identifier 'E' has not been declared or assigned >> Volume([w1,w2]);; ^ User error: Identifier 'w1' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host MathD02.Math.McGill.CA. (132.206.150.202) Time: Tue Mar 30 11:46:54 2004 Input: E:=EllipticCurve([0,0,1,-1,0]); w1,w2:=Periods(E); Volume([w1,w2]); Output: Magma V2.10-6 Tue Mar 30 2004 11:46:51 on modular [Seed = 506985021] ------------------------------------- >> w1,w2:=Periods(E); ^ Runtime error in :=: Expected to assign 2 value(s) but only computed 1 value(s) >> Volume([w1,w2]);; ^ User error: Identifier 'w1' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host MathD02.Math.McGill.CA. (132.206.150.202) Time: Tue Mar 30 11:47:13 2004 Input: E:=EllipticCurve([0,0,1,-1,0]); w:=Periods(E); Volume(w); Output: Magma V2.10-6 Tue Mar 30 2004 11:47:10 on modular [Seed = 136441054] ------------------------------------- >> Volume(w);; ^ User error: Identifier 'Volume' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host MathD02.Math.McGill.CA. (132.206.150.202) Time: Tue Mar 30 11:47:37 2004 Input: E:=EllipticCurve([0,0,1,-1,0]); w:=Periods(E); Im(w[1]*Conjugate(w[2])); Output: Magma V2.10-6 Tue Mar 30 2004 11:47:34 on modular [Seed = 19457535] ------------------------------------- >> Im(w[1]*Conjugate(w[2])); ^ Runtime error in 'Conjugate': Bad argument types Argument types given: FldPrElt Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host MathD02.Math.McGill.CA. (132.206.150.202) Time: Tue Mar 30 11:47:47 2004 Input: E:=EllipticCurve([0,0,1,-1,0]); w:=Periods(E); Im(w[1]*ComplexConjugate(w[2])); Output: Magma V2.10-6 Tue Mar 30 2004 11:47:44 on modular [Seed = 974380754] ------------------------------------- -7.33813274078957673907072100333230558800617658612317901532588 Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host MathD02.Math.McGill.CA. (132.206.150.202) Time: Tue Mar 30 11:48:39 2004 Input: E:=EllipticCurve([0,0,1,-1,0]); F:=EllipticCuvre([0,1,-1,-23,-50]); w:=Periods(E); w2:=Periods(F); Im(w[1]*ComplexConjugate(w[2])); Im(w2[1]*ComplexConjugate(w2[2]); Output: Magma V2.10-6 Tue Mar 30 2004 11:48:36 on modular [Seed = 874369160] ------------------------------------- >> F:=EllipticCuvre([0,1,-1,-23,-50]); ^ User error: Identifier 'EllipticCuvre' has not been declared or assigned >> w2:=Periods(F); ^ User error: Identifier 'F' has not been declared or assigned -7.33813274078957673907072100333230558800617658612317901532588 >> Im(w2[1]*ComplexConjugate(w2[2]);; ^ User error: bad syntax Total time: 2.889 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host MathD02.Math.McGill.CA. (132.206.150.202) Time: Tue Mar 30 11:48:49 2004 Input: E:=EllipticCurve([0,0,1,-1,0]); F:=EllipticCurve([0,1,-1,-23,-50]); w:=Periods(E); w2:=Periods(F); Im(w[1]*ComplexConjugate(w[2])); Im(w2[1]*ComplexConjugate(w2[2]); Output: Magma V2.10-6 Tue Mar 30 2004 11:48:46 on modular [Seed = 755288475] ------------------------------------- -7.33813274078957673907072100333230558800617658612317901532588 >> Im(w2[1]*ComplexConjugate(w2[2]);; ^ User error: bad syntax Total time: 2.889 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host MathD02.Math.McGill.CA. (132.206.150.202) Time: Tue Mar 30 11:49:02 2004 Input: E:=EllipticCurve([0,0,1,-1,0]); F:=EllipticCurve([0,1,-1,-23,-50]); w:=Periods(E); w2:=Periods(F); Im(w[1]*ComplexConjugate(w[2])); Im(w2[1]*ComplexConjugate(w2[2])); Output: Magma V2.10-6 Tue Mar 30 2004 11:48:59 on modular [Seed = 638567045] ------------------------------------- -7.33813274078957673907072100333230558800617658612317901532588 -1.9240823823973966679020793993124540644761655384894164459404 Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host MathD02.Math.McGill.CA. (132.206.150.202) Time: Tue Mar 30 11:49:18 2004 Input: E:=EllipticCurve([0,0,1,-1,0]); F:=EllipticCurve([0,1,-1,-23,-50]); w:=Periods(E); w2:=Periods(F); Im(w[1]*ComplexConjugate(w[2]))/Im(w2[1]*ComplexConjugate(w2[2])); Output: Magma V2.10-6 Tue Mar 30 2004 11:49:15 on modular [Seed = 3757456012] ------------------------------------- 3.8138350041157288744961945588576825752062270982053019679509 Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host MathD02.Math.McGill.CA. (132.206.150.202) Time: Tue Mar 30 11:51:00 2004 Input: E:=EllipticCurve([0,0,1,-1,0]); F:=EllipticCurve([0,1,-1,-23,-50]); Conductor(E)/Conductor(F); w:=Periods(E); w2:=Periods(F); Im(w[1]*ComplexConjugate(w[2]))/Im(w2[1]*ComplexConjugate(w2[2])); Output: Magma V2.10-6 Tue Mar 30 2004 11:50:57 on modular [Seed = 3236505065] ------------------------------------- 1 3.8138350041157288744961945588576825752062270982053019679509 Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host MathD02.Math.McGill.CA. (132.206.150.202) Time: Tue Mar 30 11:52:18 2004 Input: E:=EllipticCurve([0,0,1,-1,0]); F:=EllipticCurve([0,1,-1,-23,-50]); w:=Periods(E); w2:=Periods(F); w,w2; Im(w[1]*ComplexConjugate(w[2]))/Im(w2[1]*ComplexConjugate(w2[2])); Output: Magma V2.10-6 Tue Mar 30 2004 11:52:15 on modular [Seed = 4208140061] ------------------------------------- [ 2.9934586462319596298320099794525081777975837913695972275547, 0.E-57 + 2.45138938198679006085422483186652522534961728914505005017054*i ] [ 1.08852159290422917350430831153959482310514050430141238853242, 0.E-57 + 1.7676106702337894758813231444978152337342893789853023023247*i ] 3.8138350041157288744961945588576825752062270982053019679509 Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host MathD02.Math.McGill.CA. (132.206.150.202) Time: Tue Mar 30 11:58:09 2004 Input: E:=EllipticCurve([0,0,1,-1,0]); F:=EllipticCurve([0,1,-1,-23,-50]); w:=Periods(E); w2:=Periods(F); w,w2; Im(w[1]*ComplexConjugate(w[2]))/Im(w2[1]*ComplexConjugate(w2[2])); 0.72568/0.305999; Output: Magma V2.10-6 Tue Mar 30 2004 11:58:06 on modular [Seed = 4022732969] ------------------------------------- [ 2.9934586462319596298320099794525081777975837913695972275547, 0.E-57 + 2.45138938198679006085422483186652522534961728914505005017054*i ] [ 1.08852159290422917350430831153959482310514050430141238853242, 0.E-57 + 1.7676106702337894758813231444978152337342893789853023023247*i ] 3.8138350041157288744961945588576825752062270982053019679509 2.371511018009862777329337677539 Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 30 12:06:14 2004 Input: P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; print "Ordre dels elements de G25 diferents de 0"; [Order(el) : el in G25 | el ne 0]; print "Elements primitius de G25"; Elem25:=[el : el in G25 | (el ne 0) and (Order(el) eq (p^n-1))]; Elem25; print "Nombre d'elements primitius de G25"; #Elem25; p:=2; n:=4; print "Ordre dels elements de G16 diferents de 0"; [Order(el) : el in G16 | el ne 0]; print "Elements primitius de G16"; Elem16:=[el : el in G16 | (el ne 0) and (Order(el) eq (p^n-1))]; Elem16; print "Nombre d'elements primitius de G16"; #Elem16; p:=3; n:=2; print "Ordre dels elements de G9 diferents de 0"; [Order(el) : el in G9 | el ne 0]; print "Elements primitius de G9"; Elem9:=[el : el in G9 | (el ne 0) and (Order(el) eq (p^n-1))]; Elem9; print "Nombre d'elements primitius de G9"; #Elem9; Output: Magma V2.10-6 Tue Mar 30 2004 12:06:11 on modular [Seed = 3146928864] ------------------------------------- Ordre dels elements de G25 diferents de 0 [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] Elements primitius de G25 [ alfa, alfa^5, alfa^7, alfa^11, alfa^13, alfa^17, alfa^19, alfa^23 ] Nombre d'elements primitius de G25 8 Ordre dels elements de G16 diferents de 0 [ 1, 15, 15, 5, 15, 3, 5, 15, 15, 5, 3, 15, 5, 15, 15 ] Elements primitius de G16 [ alfa2, alfa2^2, alfa2^4, alfa2^7, alfa2^8, alfa2^11, alfa2^13, alfa2^14 ] Nombre d'elements primitius de G16 8 Ordre dels elements de G9 diferents de 0 [ 1, 8, 4, 8, 2, 8, 4, 8 ] Elements primitius de G9 [ alfa3, alfa3^3, alfa3^5, alfa3^7 ] Nombre d'elements primitius de G9 4 Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 30 12:06:42 2004 Input: P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; print "Ordre dels elements de G25 diferents de 0"; [Order(el) : el in G25 | el ne 0]; print "Elements primitius de G25"; Elem25:=[el : el in G25 | (el ne 0) and (Order(el) eq (p^n-1))]; Elem25; print "Nombre d'elements primitius de G25"; #Elem25; p:=2; n:=4; print "Ordre dels elements de G16 diferents de 0"; [Order(el) : el in G16 | el ne 0]; print "Elements primitius de G16"; Elem16:=[el : el in G16 | (el ne 0) and (Order(el) eq (p^n-1))]; Elem16; print "Nombre d'elements primitius de G16"; #Elem16; p:=3; n:=2; print "Ordre dels elements de G9 diferents de 0"; [Order(el) : el in G9 | el ne 0]; print "Elements primitius de G9"; Elem9:=[el : el in G9 | (el ne 0) and (Order(el) eq (p^n-1))]; Elem9; print "Nombre d'elements primitius de G9"; #Elem9; Output: Magma V2.10-6 Tue Mar 30 2004 12:06:39 on modular [Seed = 3013237492] ------------------------------------- Ordre dels elements de G25 diferents de 0 [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] Elements primitius de G25 [ alfa, alfa^5, alfa^7, alfa^11, alfa^13, alfa^17, alfa^19, alfa^23 ] Nombre d'elements primitius de G25 8 Ordre dels elements de G16 diferents de 0 [ 1, 15, 15, 5, 15, 3, 5, 15, 15, 5, 3, 15, 5, 15, 15 ] Elements primitius de G16 [ alfa2, alfa2^2, alfa2^4, alfa2^7, alfa2^8, alfa2^11, alfa2^13, alfa2^14 ] Nombre d'elements primitius de G16 8 Ordre dels elements de G9 diferents de 0 [ 1, 8, 4, 8, 2, 8, 4, 8 ] Elements primitius de G9 [ alfa3, alfa3^3, alfa3^5, alfa3^7 ] Nombre d'elements primitius de G9 4 Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host MathD02.Math.McGill.CA. (132.206.150.202) Time: Tue Mar 30 12:10:23 2004 Input: E:=EllipticCurve([0,0,1,-1,0]); F:=EllipticCurve([0,1,-1,-23,-50]); w:=Periods(E); w2:=Periods(F); w,w2; Im(w[1]*ComplexConjugate(w[2]))/Im(w2[1]*ComplexConjugate(w2[2])); 0.72568/0.305999; x:=0; for i in [1..100] do x+:=Coefficient(ModularForm(F),i)/i; end for; x; Output: Magma V2.10-6 Tue Mar 30 2004 12:10:18 on modular [Seed = 1483846139] ------------------------------------- [ 2.9934586462319596298320099794525081777975837913695972275547, 0.E-57 + 2.45138938198679006085422483186652522534961728914505005017054*i ] [ 1.08852159290422917350430831153959482310514050430141238853242, 0.E-57 + 1.7676106702337894758813231444978152337342893789853023023247*i ] 3.8138350041157288744961945588576825752062270982053019679509 2.371511018009862777329337677539 227218087159347570489261707723211687085/348601876148562385822669044676561517784 Total time: 4.979 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host MathD02.Math.McGill.CA. (132.206.150.202) Time: Tue Mar 30 12:10:42 2004 Input: E:=EllipticCurve([0,0,1,-1,0]); F:=EllipticCurve([0,1,-1,-23,-50]); w:=Periods(E); w2:=Periods(F); w,w2; Im(w[1]*ComplexConjugate(w[2]))/Im(w2[1]*ComplexConjugate(w2[2])); 0.72568/0.305999; x:=0; for i in [1..100] do x+:=Coefficient(ModularForm(F),i)/i; end for; x*1.0; Output: Magma V2.10-6 Tue Mar 30 2004 12:10:37 on modular [Seed = 1400551687] ------------------------------------- [ 2.9934586462319596298320099794525081777975837913695972275547, 0.E-57 + 2.45138938198679006085422483186652522534961728914505005017054*i ] [ 1.08852159290422917350430831153959482310514050430141238853242, 0.E-57 + 1.7676106702337894758813231444978152337342893789853023023247*i ] 3.8138350041157288744961945588576825752062270982053019679509 2.371511018009862777329337677539 0.65179823376083859573592706669 Total time: 5.089 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host MathD02.Math.McGill.CA. (132.206.150.202) Time: Tue Mar 30 12:11:26 2004 Input: E:=EllipticCurve([0,0,1,-1,0]); F:=EllipticCurve([0,1,-1,-23,-50]); w:=Periods(E); w2:=Periods(F); w,w2; Im(w[1]*ComplexConjugate(w[2]))/Im(w2[1]*ComplexConjugate(w2[2])); 0.72568/0.305999; x:=0; f:=ModularForm(F) Coefficient(f,1000); for i in [1..1000] do x+:=Coefficient(f,i)/i; end for; x*1.0; Output: Magma V2.10-6 Tue Mar 30 2004 12:11:23 on modular [Seed = 1248043048] ------------------------------------- [ 2.9934586462319596298320099794525081777975837913695972275547, 0.E-57 + 2.45138938198679006085422483186652522534961728914505005017054*i ] [ 1.08852159290422917350430831153959482310514050430141238853242, 0.E-57 + 1.7676106702337894758813231444978152337342893789853023023247*i ] 3.8138350041157288744961945588576825752062270982053019679509 2.371511018009862777329337677539 >> Coefficient(f,1000); ^ User error: bad syntax >> x+:=Coefficient(f,i)/i; ^ User error: Identifier 'f' has not been declared or assigned 0 Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host MathD02.Math.McGill.CA. (132.206.150.202) Time: Tue Mar 30 12:11:37 2004 Input: E:=EllipticCurve([0,0,1,-1,0]); F:=EllipticCurve([0,1,-1,-23,-50]); w:=Periods(E); w2:=Periods(F); w,w2; Im(w[1]*ComplexConjugate(w[2]))/Im(w2[1]*ComplexConjugate(w2[2])); 0.72568/0.305999; x:=0; f:=ModularForm(F); Coefficient(f,1000); for i in [1..1000] do x+:=Coefficient(f,i)/i; end for; x*1.0; Output: Magma V2.10-6 Tue Mar 30 2004 12:11:33 on modular [Seed = 1164750681] ------------------------------------- [ 2.9934586462319596298320099794525081777975837913695972275547, 0.E-57 + 2.45138938198679006085422483186652522534961728914505005017054*i ] [ 1.08852159290422917350430831153959482310514050430141238853242, 0.E-57 + 1.7676106702337894758813231444978152337342893789853023023247*i ] 3.8138350041157288744961945588576825752062270982053019679509 2.371511018009862777329337677539 0 0.68357742326125002512588523259 Total time: 3.339 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host MathD02.Math.McGill.CA. (132.206.150.202) Time: Tue Mar 30 12:11:59 2004 Input: E:=EllipticCurve([0,0,1,-1,0]); F:=EllipticCurve([0,1,-1,-23,-50]); w:=Periods(E); w2:=Periods(F); w,w2; Im(w[1]*ComplexConjugate(w[2]))/Im(w2[1]*ComplexConjugate(w2[2])); 0.72568/0.305999; x:=0; f:=ModularForm(F); Coefficient(f,10000); for i in [1..10000] do x+:=Coefficient(f,i)/i; end for; x*1.0; Output: Magma V2.10-6 Tue Mar 30 2004 12:11:49 on modular [Seed = 2085983856] ------------------------------------- [ 2.9934586462319596298320099794525081777975837913695972275547, 0.E-57 + 2.45138938198679006085422483186652522534961728914505005017054*i ] [ 1.08852159290422917350430831153959482310514050430141238853242, 0.E-57 + 1.7676106702337894758813231444978152337342893789853023023247*i ] 3.8138350041157288744961945588576825752062270982053019679509 2.371511018009862777329337677539 100 0.72759644798150361983459236322 Total time: 9.439 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host MathD02.Math.McGill.CA. (132.206.150.202) Time: Tue Mar 30 12:12:47 2004 Input: E:=EllipticCurve([0,0,1,-1,0]); F:=EllipticCurve([0,1,-1,-23,-50]); w:=Periods(E); w2:=Periods(F); w,w2; Im(w[1]*ComplexConjugate(w[2]))/Im(w2[1]*ComplexConjugate(w2[2])); 0.72568/0.305999; x:=0; f:=ModularForm(F); Coefficient(f,20000); for i in [1..20000] do x+:=Coefficient(f,i)/i; end for; x*1.0; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Mar 30 2004 12:12:24 on modular [Seed = 1985977431] ------------------------------------- [ 2.9934586462319596298320099794525081777975837913695972275547, 0.E-57 + 2.45138938198679006085422483186652522534961728914505005017054*i ] [ 1.08852159290422917350430831153959482310514050430141238853242, 0.E-57 + 1.7676106702337894758813231444978152337342893789853023023247*i ] 3.8138350041157288744961945588576825752062270982053019679509 2.371511018009862777329337677539 0 Errors: /home/mfd/gomagma: line 2: 6447 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host MathD02.Math.McGill.CA. (132.206.150.202) Time: Tue Mar 30 12:13:39 2004 Input: E:=EllipticCurve([0,0,1,-1,0]); F:=EllipticCurve([0,1,-1,-23,-50]); w:=Periods(E); w2:=Periods(F); w,w2; Im(w[1]*ComplexConjugate(w[2]))/Im(w2[1]*ComplexConjugate(w2[2])); 0.72568/0.305999; x:=0; f:=ModularForm(F); Coefficient(f,15000); for i in [1..15000] do x+:=Coefficient(f,i)/i; end for; x*1.0; Output: Magma V2.10-6 Tue Mar 30 2004 12:13:23 on modular [Seed = 1632144267] ------------------------------------- [ 2.9934586462319596298320099794525081777975837913695972275547, 0.E-57 + 2.45138938198679006085422483186652522534961728914505005017054*i ] [ 1.08852159290422917350430831153959482310514050430141238853242, 0.E-57 + 1.7676106702337894758813231444978152337342893789853023023247*i ] 3.8138350041157288744961945588576825752062270982053019679509 2.371511018009862777329337677539 0 0.70011679418079819551789325870 Total time: 16.270 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host MathD02.Math.McGill.CA. (132.206.150.202) Time: Tue Mar 30 12:14:16 2004 Input: E:=EllipticCurve([0,0,1,-1,0]); F:=EllipticCurve([0,1,-1,-23,-50]); w:=Periods(E); w2:=Periods(F); w,w2; Im(w[1]*ComplexConjugate(w[2]))/Im(w2[1]*ComplexConjugate(w2[2])); 0.72568/0.305999; x:=0; f:=ModularForm(F); Coefficient(f,10000); for i in [1..10000] do x+:=Coefficient(f,i)/i; end for; x*1.0; Output: Magma V2.10-6 Tue Mar 30 2004 12:14:07 on modular [Seed = 405926558] ------------------------------------- [ 2.9934586462319596298320099794525081777975837913695972275547, 0.E-57 + 2.45138938198679006085422483186652522534961728914505005017054*i ] [ 1.08852159290422917350430831153959482310514050430141238853242, 0.E-57 + 1.7676106702337894758813231444978152337342893789853023023247*i ] 3.8138350041157288744961945588576825752062270982053019679509 2.371511018009862777329337677539 100 0.72759644798150361983459236322 Total time: 9.699 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 30 12:14:17 2004 Input: P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; print "Ordre dels elements de G25 diferents de 0"; [Order(el) : el in G25 | el ne 0]; print "Elements primitius de G25"; Elem25:=[el : el in G25 | (el ne 0) and (Order(el) eq (p^n-1))]; Elem25; print "Nombre d'elements primitius de G25"; #Elem25; print "Per euler"; EulerPhi(p^n-1); p:=2; n:=4; print "Ordre dels elements de G16 diferents de 0"; [Order(el) : el in G16 | el ne 0]; print "Elements primitius de G16"; Elem16:=[el : el in G16 | (el ne 0) and (Order(el) eq (p^n-1))]; Elem16; print "Nombre d'elements primitius de G16"; #Elem16; print "Per euler"; EulerPhi(p^n-1); p:=3; n:=2; print "Ordre dels elements de G9 diferents de 0"; [Order(el) : el in G9 | el ne 0]; print "Elements primitius de G9"; Elem9:=[el : el in G9 | (el ne 0) and (Order(el) eq (p^n-1))]; Elem9; print "Nombre d'elements primitius de G9"; #Elem9; print "Per euler"; EulerPhi(p^n-1); Output: Magma V2.10-6 Tue Mar 30 2004 12:14:13 on modular [Seed = 473298592] ------------------------------------- Ordre dels elements de G25 diferents de 0 [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] Elements primitius de G25 [ alfa, alfa^5, alfa^7, alfa^11, alfa^13, alfa^17, alfa^19, alfa^23 ] Nombre d'elements primitius de G25 8 Per euler 8 Ordre dels elements de G16 diferents de 0 [ 1, 15, 15, 5, 15, 3, 5, 15, 15, 5, 3, 15, 5, 15, 15 ] Elements primitius de G16 [ alfa2, alfa2^2, alfa2^4, alfa2^7, alfa2^8, alfa2^11, alfa2^13, alfa2^14 ] Nombre d'elements primitius de G16 8 Per euler 8 Ordre dels elements de G9 diferents de 0 [ 1, 8, 4, 8, 2, 8, 4, 8 ] Elements primitius de G9 [ alfa3, alfa3^3, alfa3^5, alfa3^7 ] Nombre d'elements primitius de G9 4 Per euler 4 Total time: 3.269 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 30 12:15:35 2004 Input: P3:=PolynomialRing(GF(3)); f:=2+2*x+x^2; P2:=PolynomialRing(GF(2)); g:=1+y+y^4; P5:=PolynomialRing(GF(5)); h:=3+2*z+z^2; G3:=GF(3); G9:=ext< G3 | f >; G2:=GF(2); G16:=ext< G2 | g >; G5:=GF(5); G25:=ext< G5 | h >; p:=5; n:=2; print "Ordre dels elements de G25 diferents de 0"; [Order(el) : el in G25 | el ne 0]; print "Elements primitius de G25"; Elem25:=[el : el in G25 | (el ne 0) and (Order(el) eq (p^n-1))]; Elem25; print "Nombre d'elements primitius de G25"; #Elem25; print "Si ho fem amb la funció d'euler..."; EulerPhi(p^n-1); Output: Magma V2.10-6 Tue Mar 30 2004 12:15:32 on modular [Seed = 19458668] ------------------------------------- Ordre dels elements de G25 diferents de 0 [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] Elements primitius de G25 [ alfa, alfa^5, alfa^7, alfa^11, alfa^13, alfa^17, alfa^19, alfa^23 ] Nombre d'elements primitius de G25 8 Si ho fem amb la funció d'euler... 8 Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host MathD02.Math.McGill.CA. (132.206.150.202) Time: Tue Mar 30 12:15:58 2004 Input: E:=EllipticCurve([0,0,1,-1,0]); F:=EllipticCurve([0,1,-1,-23,-50]); w:=Periods(E); w2:=Periods(F); w,w2; Im(w[1]*ComplexConjugate(w[2]))/Im(w2[1]*ComplexConjugate(w2[2])); 0.72568/0.305999; x:=0; f:=ModularForm(F); Coefficient(f,10000); for i in [1..10000] do x+:=-Coefficient(f,i)*Log(i)/i; end for; x*1.0; Output: Magma V2.10-6 Tue Mar 30 2004 12:15:47 on modular [Seed = 940692258] ------------------------------------- [ 2.9934586462319596298320099794525081777975837913695972275547, 0.E-57 + 2.45138938198679006085422483186652522534961728914505005017054*i ] [ 1.08852159290422917350430831153959482310514050430141238853242, 0.E-57 + 1.7676106702337894758813231444978152337342893789853023023247*i ] 3.8138350041157288744961945588576825752062270982053019679509 2.371511018009862777329337677539 100 0.425274335550962537056620818570 Total time: 11.130 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host MathD02.Math.McGill.CA. (132.206.150.202) Time: Tue Mar 30 12:16:30 2004 Input: E:=EllipticCurve([0,0,1,-1,0]); F:=EllipticCurve([0,1,-1,-23,-50]); w:=Periods(E); w2:=Periods(F); w,w2; Im(w[1]*ComplexConjugate(w[2]))/Im(w2[1]*ComplexConjugate(w2[2])); 0.72568/0.305999; x:=0; f:=ModularForm(F); Coefficient(f,15000); for i in [1..15000] do x+:=-Coefficient(f,i)*Log(i)/i; end for; x*1.0; Output: Magma V2.10-6 Tue Mar 30 2004 12:16:11 on modular [Seed = 857397297] ------------------------------------- [ 2.9934586462319596298320099794525081777975837913695972275547, 0.E-57 + 2.45138938198679006085422483186652522534961728914505005017054*i ] [ 1.08852159290422917350430831153959482310514050430141238853242, 0.E-57 + 1.7676106702337894758813231444978152337342893789853023023247*i ] 3.8138350041157288744961945588576825752062270982053019679509 2.371511018009862777329337677539 0 0.68799181218292956059416470310 Total time: 18.539 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host MathD02.Math.McGill.CA. (132.206.150.202) Time: Tue Mar 30 12:17:16 2004 Input: E:=EllipticCurve([0,0,1,-1,0]); F:=EllipticCurve([0,1,-1,-23,-50]); w:=Periods(E); w2:=Periods(F); w,w2; Im(w[1]*ComplexConjugate(w[2]))/Im(w2[1]*ComplexConjugate(w2[2])); 0.72568/0.305999; x:=0; f:=ModularForm(F); Coefficient(f,16000); for i in [1..16000] do x+:=-Coefficient(f,i)*Log(i)/i; end for; x*1.0; Output: Magma V2.10-6 Tue Mar 30 2004 12:16:55 on modular [Seed = 704889332] ------------------------------------- [ 2.9934586462319596298320099794525081777975837913695972275547, 0.E-57 + 2.45138938198679006085422483186652522534961728914505005017054*i ] [ 1.08852159290422917350430831153959482310514050430141238853242, 0.E-57 + 1.7676106702337894758813231444978152337342893789853023023247*i ] 3.8138350041157288744961945588576825752062270982053019679509 2.371511018009862777329337677539 0 -0.409237640791498245086081678451 Total time: 21.409 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host MathD02.Math.McGill.CA. (132.206.150.202) Time: Tue Mar 30 12:18:38 2004 Input: E:=EllipticCurve([0,0,1,-1,0]); F:=EllipticCurve([0,1,-1,-23,-50]); w:=Periods(E); w2:=Periods(F); w,w2; Im(w[1]*ComplexConjugate(w[2]))/Im(w2[1]*ComplexConjugate(w2[2])); 0.72568/0.305999; x:=0; f:=ModularForm(F); 3.8*0.3/0.4 //Coefficient(f,16000); //for i in [1..16000] do //x+:=-Coefficient(f,i)*Log(i)/i; //end for; //x*1.0; Output: Magma V2.10-6 Tue Mar 30 2004 12:18:35 on modular [Seed = 655281301] ------------------------------------- [ 2.9934586462319596298320099794525081777975837913695972275547, 0.E-57 + 2.45138938198679006085422483186652522534961728914505005017054*i ] [ 1.08852159290422917350430831153959482310514050430141238853242, 0.E-57 + 1.7676106702337894758813231444978152337342893789853023023247*i ] 3.8138350041157288744961945588576825752062270982053019679509 2.371511018009862777329337677539 >> quit; ^ User error: bad syntax Total time: 2.969 seconds, Total memory usage: 2.39MB ************** MAGMA ***************** Host MathD02.Math.McGill.CA. (132.206.150.202) Time: Tue Mar 30 12:19:05 2004 Input: E:=EllipticCurve([0,0,1,-1,0]); F:=EllipticCurve([0,1,-1,-23,-50]); w:=Periods(E); w2:=Periods(F); w,w2; Im(w[1]*ComplexConjugate(w[2]))/Im(w2[1]*ComplexConjugate(w2[2])); 0.72568/0.305999; x:=0; f:=ModularForm(F); 3.8*0.3/0.4 //Coefficient(f,16000); //for i in [1..16000] do //x+:=-Coefficient(f,i)*Log(i)/i; //end for; //x*1.0; Output: Magma V2.10-6 Tue Mar 30 2004 12:19:02 on modular [Seed = 3740742273] ------------------------------------- [ 2.9934586462319596298320099794525081777975837913695972275547, 0.E-57 + 2.45138938198679006085422483186652522534961728914505005017054*i ] [ 1.08852159290422917350430831153959482310514050430141238853242, 0.E-57 + 1.7676106702337894758813231444978152337342893789853023023247*i ] 3.8138350041157288744961945588576825752062270982053019679509 2.371511018009862777329337677539 >> quit; ^ User error: bad syntax Total time: 3.039 seconds, Total memory usage: 2.39MB ************** MAGMA ***************** Host MathD02.Math.McGill.CA. (132.206.150.202) Time: Tue Mar 30 12:19:18 2004 Input: E:=EllipticCurve([0,0,1,-1,0]); F:=EllipticCurve([0,1,-1,-23,-50]); w:=Periods(E); w2:=Periods(F); w,w2; Im(w[1]*ComplexConjugate(w[2]))/Im(w2[1]*ComplexConjugate(w2[2])); 0.72568/0.305999; x:=0; f:=ModularForm(F); 3.8*0.3/0.4; //Coefficient(f,16000); //for i in [1..16000] do //x+:=-Coefficient(f,i)*Log(i)/i; //end for; //x*1.0; Output: Magma V2.10-6 Tue Mar 30 2004 12:19:15 on modular [Seed = 3386910083] ------------------------------------- [ 2.9934586462319596298320099794525081777975837913695972275547, 0.E-57 + 2.45138938198679006085422483186652522534961728914505005017054*i ] [ 1.08852159290422917350430831153959482310514050430141238853242, 0.E-57 + 1.7676106702337894758813231444978152337342893789853023023247*i ] 3.8138350041157288744961945588576825752062270982053019679509 2.371511018009862777329337677539 2.84999999999999999999999999992 Total time: 3.019 seconds, Total memory usage: 2.39MB ************** MAGMA ***************** Host MathD02.Math.McGill.CA. (132.206.150.202) Time: Tue Mar 30 12:19:46 2004 Input: E:=EllipticCurve([0,0,1,-1,0]); F:=EllipticCurve([0,1,-1,-23,-50]); w:=Periods(E); w2:=Periods(F); w,w2; Im(w[1]*ComplexConjugate(w[2]))/Im(w2[1]*ComplexConjugate(w2[2])); 0.72568/0.305999; x:=0; f:=ModularForm(F); 3.8138*0.30599/0.6; //Coefficient(f,16000); //for i in [1..16000] do //x+:=-Coefficient(f,i)*Log(i)/i; //end for; //x*1.0; Output: Magma V2.10-6 Tue Mar 30 2004 12:19:43 on modular [Seed = 3236506806] ------------------------------------- [ 2.9934586462319596298320099794525081777975837913695972275547, 0.E-57 + 2.45138938198679006085422483186652522534961728914505005017054*i ] [ 1.08852159290422917350430831153959482310514050430141238853242, 0.E-57 + 1.7676106702337894758813231444978152337342893789853023023247*i ] 3.8138350041157288744961945588576825752062270982053019679509 2.371511018009862777329337677539 1.94497443666666666666666666662 Total time: 3.029 seconds, Total memory usage: 2.39MB ************** MAGMA ***************** Host MathD02.Math.McGill.CA. (132.206.150.202) Time: Tue Mar 30 12:21:08 2004 Input: E:=EllipticCurve([0,0,1,-1,0]); F:=EllipticCurve([0,1,-1,-23,-50]); w:=Periods(E); w2:=Periods(F); w,w2; Im(w[1]*ComplexConjugate(w[2]))/Im(w2[1]*ComplexConjugate(w2[2])); 0.72568/0.305999; x:=0; f:=ModularForm(F); 3.8138*0.30599/0.6; 0.30599/0.7256; //Coefficient(f,16000); //for i in [1..16000] do //x+:=-Coefficient(f,i)*Log(i)/i; //end for; //x*1.0; Output: Magma V2.10-6 Tue Mar 30 2004 12:21:05 on modular [Seed = 4091158315] ------------------------------------- [ 2.9934586462319596298320099794525081777975837913695972275547, 0.E-57 + 2.45138938198679006085422483186652522534961728914505005017054*i ] [ 1.08852159290422917350430831153959482310514050430141238853242, 0.E-57 + 1.7676106702337894758813231444978152337342893789853023023247*i ] 3.8138350041157288744961945588576825752062270982053019679509 2.371511018009862777329337677539 1.94497443666666666666666666662 0.421706174200661521499448732081 Total time: 2.969 seconds, Total memory usage: 2.39MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 30 14:14:41 2004 Input: G5:=GF(5); p1:=PolinomialRing(G5); G25:=ext; p2:=PolinimialRing(G25); p3:=PolinomialRing(Integers()); pol:=y^2+z*y+z*x^2; Output: Magma V2.10-6 Tue Mar 30 2004 14:14:38 on modular [Seed = 1298450952] ------------------------------------- >> p1:=PolinomialRing(G5); ^ User error: Identifier 'PolinomialRing' has not been declared or assigned >> G25:=ext; ^ User error: Identifier 'z' has not been declared or assigned >> p2:=PolinimialRing(G25); ^ User error: Identifier 'G25' has not been declared or assigned >> p3:=PolinomialRing(Integers()); ^ User error: Identifier 'PolinomialRing' has not been declared or assigned >> pol:=y^2+z*y+z*x^2;; ^ User error: Identifier 'y' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 30 14:15:22 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=y^2+z*y+z*x^2; Output: Magma V2.10-6 Tue Mar 30 2004 14:15:19 on modular [Seed = 2136406115] ------------------------------------- Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 30 14:20:02 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=y^2+z*y+z*x^2; pol1:=1+y*x; Output: Magma V2.10-6 Tue Mar 30 2004 14:19:59 on modular [Seed = 1952316528] ------------------------------------- Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 30 14:21:11 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=y^2+z*y+z*x^2; pol1:=1+y*x; pol2:=pol1+pol; Output: Magma V2.10-6 Tue Mar 30 2004 14:21:08 on modular [Seed = 974369477] ------------------------------------- Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 30 14:21:55 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=y^2+z*y+z*x^2; pol1:=1+y*x; pol2:=pol1+pol; pol2; Output: Magma V2.10-6 Tue Mar 30 2004 14:21:52 on modular [Seed = 772253349] ------------------------------------- y^3 + 3*y^2 + 1 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 30 14:25:04 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=y^2+z*y+z*x^2; pol1:=1+y*x; pol2:=pol1+pol; pol2; pol3:=pol1*pol; pol3; Output: Magma V2.10-6 Tue Mar 30 2004 14:25:01 on modular [Seed = 3757463049] ------------------------------------- y^3 + 3*y^2 + 1 y^5 + 2*y^4 + y^3 + 2*y^2 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 30 14:28:05 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=y^2+z*y+z*x^2; pol1:=1+y*x; pol2:=pol1+pol; pol2; pol3:=pol1*pol; pol3; pol4:=pol/pol1; pol4; Output: Magma V2.10-6 Tue Mar 30 2004 14:28:02 on modular [Seed = 3386917840] ------------------------------------- y^3 + 3*y^2 + 1 y^5 + 2*y^4 + y^3 + 2*y^2 y^2/(y + 3) Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 30 14:29:33 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=y^2+z*y+z*x^2; pol1:=1+y*x; pol2:=pol1+pol; pol2; pol3:=pol1*pol; pol3; pol4:=pol/pol1; pol4; pol5:=(pol)mod(pol1); pol5; Output: Magma V2.10-6 Tue Mar 30 2004 14:29:30 on modular [Seed = 3303886341] ------------------------------------- y^3 + 3*y^2 + 1 y^5 + 2*y^4 + y^3 + 2*y^2 y^2/(y + 3) 4*y + 3 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dhcp-129-64-53-12.math.brandeis.edu. (129.64.53.12) Time: Tue Mar 30 14:36:11 2004 Input: pari Output: Magma V2.10-6 Tue Mar 30 2004 14:36:08 on modular [Seed = 2645823982] ------------------------------------- >> pari; ^ User error: Identifier 'pari' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 30 14:54:04 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=y^2+z*y+z*x^2; pol1:=1+y*x; pol2:=pol1+pol; pol2; pol3:=pol1*pol; pol3; pol4:=pol/pol1; pol4; pol5:=(pol)mod(pol1); pol5; pol6:=GCD(pol1,pol); pol6; Output: Magma V2.10-6 Tue Mar 30 2004 14:54:01 on modular [Seed = 2944810925] ------------------------------------- y^3 + 3*y^2 + 1 y^5 + 2*y^4 + y^3 + 2*y^2 y^2/(y + 3) 4*y + 3 y + 2 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 30 14:55:38 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=y^2+z*y+z*x^2; pol1:=1+y*x; pol2:=pol1+pol; pol2; pol3:=pol1*pol; pol3; pol4:=pol/pol1; pol4; pol5:=(pol)mod(pol1); pol5; pol6:=GCD(pol1,pol); pol6; pol7:=LCD(pol1,pol); pol7; Output: Magma V2.10-6 Tue Mar 30 2004 14:55:35 on modular [Seed = 1584910005] ------------------------------------- y^3 + 3*y^2 + 1 y^5 + 2*y^4 + y^3 + 2*y^2 y^2/(y + 3) 4*y + 3 y + 2 >> pol7:=LCD(pol1,pol); ^ User error: Identifier 'LCD' has not been declared or assigned >> pol7;; ^ User error: Identifier 'pol7' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 30 14:55:58 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=y^2+z*y+z*x^2; pol1:=1+y*x; pol2:=pol1+pol; pol2; pol3:=pol1*pol; pol3; pol4:=pol/pol1; pol4; pol5:=(pol)mod(pol1); pol5; pol6:=GCD(pol1,pol); pol6; pol7:=LCM(pol1,pol); pol7; Output: Magma V2.10-6 Tue Mar 30 2004 14:55:55 on modular [Seed = 1467926464] ------------------------------------- y^3 + 3*y^2 + 1 y^5 + 2*y^4 + y^3 + 2*y^2 y^2/(y + 3) 4*y + 3 y + 2 y^4 + y^2 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 30 15:17:40 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=y^2+z*y+z*x^2; pol1:=1+y*x; pol2:=pol1+pol; pol2; pol3:=pol1*pol; pol3; pol4:=pol/pol1; pol4; pol5:=(pol)mod(pol1); pol5; pol6:=GCD(pol1,pol); pol6; pol7:=LCM(pol1,pol); pol7; XGCD(pol,pol1); a*pol + b*pol1; Output: Magma V2.10-6 Tue Mar 30 2004 15:17:37 on modular [Seed = 305891247] ------------------------------------- y^3 + 3*y^2 + 1 y^5 + 2*y^4 + y^3 + 2*y^2 y^2/(y + 3) 4*y + 3 y + 2 y^4 + y^2 y + 2 4 y + 2 >> a*pol + b*pol1;; ^ User error: Identifier 'a' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 30 15:18:12 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=y^2+z*y+z*x^2; pol1:=1+y*x; pol2:=pol1+pol; pol2; pol3:=pol1*pol; pol3; pol4:=pol/pol1; pol4; pol5:=(pol)mod(pol1); pol5; pol6:=GCD(pol1,pol); pol6; pol7:=LCM(pol1,pol); pol7; (a,b,c):=XGCD(pol,pol1); a*pol + b*pol1; Output: Magma V2.10-6 Tue Mar 30 2004 15:18:09 on modular [Seed = 186817878] ------------------------------------- y^3 + 3*y^2 + 1 y^5 + 2*y^4 + y^3 + 2*y^2 y^2/(y + 3) 4*y + 3 y + 2 y^4 + y^2 >> (a,b,c):=XGCD(pol,pol1); ^ User error: Illegal left hand side of an assignment statement >> a*pol + b*pol1;; ^ User error: Identifier 'a' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 30 15:19:35 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=y^2+z*y+z*x^2; pol1:=1+y*x; pol2:=pol1+pol; pol2; pol3:=pol1*pol; pol3; pol4:=pol/pol1; pol4; pol5:=(pol)mod(pol1); pol5; pol6:=GCD(pol1,pol); pol6; pol7:=LCM(pol1,pol); pol7; a,b,c=XGCD(pol,pol1); a*pol + b*pol1; Output: Magma V2.10-6 Tue Mar 30 2004 15:19:32 on modular [Seed = 1008052788] ------------------------------------- y^3 + 3*y^2 + 1 y^5 + 2*y^4 + y^3 + 2*y^2 y^2/(y + 3) 4*y + 3 y + 2 y^4 + y^2 >> a,b,c=XGCD(pol,pol1); ^ User error: Identifier 'a' has not been declared or assigned >> a*pol + b*pol1;; ^ User error: Identifier 'a' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 30 15:20:01 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=y^2+z*y+z*x^2; pol1:=1+y*x; pol2:=pol1+pol; pol2; pol3:=pol1*pol; pol3; pol4:=pol/pol1; pol4; pol5:=(pol)mod(pol1); pol5; pol6:=GCD(pol1,pol); pol6; pol7:=LCM(pol1,pol); pol7; a, b, c :=XGCD(pol,pol1); a*pol + b*pol1; Output: Magma V2.10-6 Tue Mar 30 2004 15:19:58 on modular [Seed = 891069191] ------------------------------------- y^3 + 3*y^2 + 1 y^5 + 2*y^4 + y^3 + 2*y^2 y^2/(y + 3) 4*y + 3 y + 2 y^4 + y^2 y^4 + 4*y^3 + 3*y^2 + 4 Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 30 15:20:49 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=y^2+z*y+z*x^2; pol1:=1+y*x; pol2:=pol1+pol; pol2; pol3:=pol1*pol; pol3; pol4:=pol/pol1; pol4; pol5:=(pol)mod(pol1); pol5; pol6:=GCD(pol1,pol); pol6; pol7:=LCM(pol1,pol); pol7; a, b, c :=XGCD(pol,pol1); pol6;a*pol + b*pol1; Output: Magma V2.10-6 Tue Mar 30 2004 15:20:46 on modular [Seed = 638562532] ------------------------------------- y^3 + 3*y^2 + 1 y^5 + 2*y^4 + y^3 + 2*y^2 y^2/(y + 3) 4*y + 3 y + 2 y^4 + y^2 y + 2 y^4 + 4*y^3 + 3*y^2 + 4 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 30 15:21:04 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=y^2+z*y+z*x^2; pol1:=1+y*x; pol2:=pol1+pol; pol2; pol3:=pol1*pol; pol3; pol4:=pol/pol1; pol4; pol5:=(pol)mod(pol1); pol5; pol6:=GCD(pol1,pol); pol6; pol7:=LCM(pol1,pol); pol7; a, b, c :=XGCD(pol,pol1); pol8;a*pol + b*pol1; Output: Magma V2.10-6 Tue Mar 30 2004 15:21:01 on modular [Seed = 3757459758] ------------------------------------- y^3 + 3*y^2 + 1 y^5 + 2*y^4 + y^3 + 2*y^2 y^2/(y + 3) 4*y + 3 y + 2 y^4 + y^2 >> pol8;a*pol + b*pol1;; ^ User error: Identifier 'pol8' has not been declared or assigned y^4 + 4*y^3 + 3*y^2 + 4 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 30 15:21:10 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=y^2+z*y+z*x^2; pol1:=1+y*x; pol2:=pol1+pol; pol2; pol3:=pol1*pol; pol3; pol4:=pol/pol1; pol4; pol5:=(pol)mod(pol1); pol5; pol6:=GCD(pol1,pol); pol6; pol7:=LCM(pol1,pol); pol7; a, b, c :=XGCD(pol,pol1); pol8:=a*pol + b*pol1; Output: Magma V2.10-6 Tue Mar 30 2004 15:21:07 on modular [Seed = 3623764280] ------------------------------------- y^3 + 3*y^2 + 1 y^5 + 2*y^4 + y^3 + 2*y^2 y^2/(y + 3) 4*y + 3 y + 2 y^4 + y^2 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 30 15:21:47 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=y^2+z*y+z*x^2; pol1:=1+y*x; pol2:=pol1+pol; pol2; pol3:=pol1*pol; pol3; pol4:=pol/pol1; pol4; pol5:=(pol)mod(pol1); pol5; pol6:=GCD(pol1,pol); pol6; pol7:=LCM(pol1,pol); pol7; a, b, c :=XGCD(pol,pol1); pol8:=a*pol + b*pol1; pol8; Output: Magma V2.10-6 Tue Mar 30 2004 15:21:44 on modular [Seed = 3370212940] ------------------------------------- y^3 + 3*y^2 + 1 y^5 + 2*y^4 + y^3 + 2*y^2 y^2/(y + 3) 4*y + 3 y + 2 y^4 + y^2 y^4 + 4*y^3 + 3*y^2 + 4 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 30 15:22:44 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=y^2+z*y+z*x^2; pol1:=1+y*x; pol2:=pol1+pol; pol2; pol3:=pol1*pol; pol3; pol4:=pol/pol1; pol4; pol5:=(pol)mod(pol1); pol5; pol6:=GCD(pol1,pol); pol6; pol7:=LCM(pol1,pol); pol7; a, b, c :=XGCD(pol1,pol); pol8:=a*pol + b*pol1; pol8; Output: Magma V2.10-6 Tue Mar 30 2004 15:22:41 on modular [Seed = 3270202767] ------------------------------------- y^3 + 3*y^2 + 1 y^5 + 2*y^4 + y^3 + 2*y^2 y^2/(y + 3) 4*y + 3 y + 2 y^4 + y^2 y^4 + y^2 + y + 2 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 30 15:23:21 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=y^2+z*y+z*x^2; pol1:=1+y*x; pol2:=pol1+pol; pol2; pol3:=pol1*pol; pol3; pol4:=pol/pol1; pol4; pol5:=(pol)mod(pol1); pol5; pol6:=GCD(pol1,pol); pol6; pol7:=LCM(pol1,pol); pol7; a, b, c :=XGCD(pol1,pol); pol8:=a*pol1 + b*pol; pol8; Output: Magma V2.10-6 Tue Mar 30 2004 15:23:18 on modular [Seed = 4224871569] ------------------------------------- y^3 + 3*y^2 + 1 y^5 + 2*y^4 + y^3 + 2*y^2 y^2/(y + 3) 4*y + 3 y + 2 y^4 + y^2 y^4 + y^2 + y + 2 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 30 15:23:30 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=y^2+z*y+z*x^2; pol1:=1+y*x; pol2:=pol1+pol; pol2; pol3:=pol1*pol; pol3; pol4:=pol/pol1; pol4; pol5:=(pol)mod(pol1); pol5; pol6:=GCD(pol1,pol); pol6; pol7:=LCM(pol1,pol); pol7; a, b, c :=XGCD(pol1,pol); pol8:=a*pol1 + b*pol; pol8; a; b; c; Output: Magma V2.10-6 Tue Mar 30 2004 15:23:27 on modular [Seed = 4091176080] ------------------------------------- y^3 + 3*y^2 + 1 y^5 + 2*y^4 + y^3 + 2*y^2 y^2/(y + 3) 4*y + 3 y + 2 y^4 + y^2 y^4 + y^2 + y + 2 y + 2 y + 2 4 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 30 15:24:41 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=y^2+z*y+z*x^2; pol1:=1+y*x; pol2:=pol1+pol; pol2; pol3:=pol1*pol; pol3; pol4:=pol/pol1; pol4; pol5:=(pol)mod(pol1); pol5; pol6:=GCD(pol1,pol); pol6; pol7:=LCM(pol1,pol); pol7; a, b, c :=XGCD(pol1,pol); pol8:=b*pol1 + c*pol; pol8; a; b; c; Output: Magma V2.10-6 Tue Mar 30 2004 15:24:38 on modular [Seed = 3855381055] ------------------------------------- y^3 + 3*y^2 + 1 y^5 + 2*y^4 + y^3 + 2*y^2 y^2/(y + 3) 4*y + 3 y + 2 y^4 + y^2 y + 2 y + 2 y + 2 4 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 30 15:25:05 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=y^2+z*y+z*x^2; pol1:=1+y*x; pol2:=pol1+pol; pol2; pol3:=pol1*pol; pol3; pol4:=pol/pol1; pol4; pol5:=(pol)mod(pol1); pol5; pol6:=GCD(pol1,pol); pol6; pol7:=LCM(pol1,pol); pol7; a, b, c :=XGCD(pol1,pol); pol8:=b*pol1 + c*pol; pol8; Output: Magma V2.10-6 Tue Mar 30 2004 15:25:02 on modular [Seed = 2595425624] ------------------------------------- y^3 + 3*y^2 + 1 y^5 + 2*y^4 + y^3 + 2*y^2 y^2/(y + 3) 4*y + 3 y + 2 y^4 + y^2 y + 2 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Tue Mar 30 15:25:35 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=y^2+z*y+z*x^2; pol1:=1+y*x; pol2:=pol1+pol; pol2; pol3:=pol1*pol; pol3; pol4:=pol/pol1; pol4; pol5:=(pol)mod(pol1); pol5; pol6:=GCD(pol1,pol); pol6; pol7:=LCM(pol1,pol); pol7; a, b, c :=XGCD(pol1,pol); pol8:=b*pol1 + c*pol; pol8; b; c; Output: Magma V2.10-6 Tue Mar 30 2004 15:25:32 on modular [Seed = 2478441587] ------------------------------------- y^3 + 3*y^2 + 1 y^5 + 2*y^4 + y^3 + 2*y^2 y^2/(y + 3) 4*y + 3 y + 2 y^4 + y^2 y + 2 y + 2 4 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dhcp-129-64-53-12.math.brandeis.edu. (129.64.53.12) Time: Tue Mar 30 15:38:56 2004 Input: G:=Gamma0(16); C:=CosetRepresentatives(G); H:=UpperHalfPlaneWithCusps(); Edge1:=[H|0,2]; Edge2:=[H|i,1/2*(i+1)]; point:=GeodesicsIntersection(Edge1,Edge2,H)[1]; triangle1:=[H|Infinity(),i,r]; triangle3:=[H|i,point,r]; triangle2:=[H|0,i,point]; Par:=Parent(triangle1); t:=G![1,1,0,1]; Polygons:=[Par|g*tri : g in C,tri in [triangle1,triangle2,triangle3]]; Polygons2:=[Par|t*g*tri : g in C,tri in [triangle3]]; Polygons3:=[Par|t^(-1)*g*tri : g in C,tri in [triangle3]]; purple:=[0.5,0,0.8]; blue:=[0.6,0.6,0.9]; yellow:=[1,0.8,0]; Colours:=[blue : i in C] cat [purple : i in C] cat [yellow : i in C] cat [purple : i in C] cat [yellow : i in C]; DisplayPolygons(Polygons cat Polygons2 cat Polygons3,"/tmp/pic.ps":Show:=true, Colours:=Colours,Size:=[-1,2,1.5,150]); Output: Magma V2.10-6 Tue Mar 30 2004 15:38:53 on modular [Seed = 2996512819] ------------------------------------- GeodesicsIntersection( x: [ 0, 2 ], y: [ root(-1), 1/2 + (1/2)*root(-1) ], H: Upper half complex plane union cusps ) ExtendGeodesic( z: [ root(-1), 1/2 + (1/2)*root(-1) ], H: Upper half complex plane union cusps ) In file "/usr/local/magma/package/Geometry/GrpPSL2/SpcHyp/geo_intersect.m", line 160, column 9: >> if a eq Infinity() then ^ Runtime error in 'eq': Bad argument types >> triangle3:=[H|i,point,r]; ^ User error: Identifier 'point' has not been declared or assigned >> triangle2:=[H|0,i,point]; ^ User error: Identifier 'point' has not been declared or assigned >> Polygons:=[Par|g*tri : g in C,tri in [triangle1,triangle2,triangle3]]; ^ User error: Identifier 'triangle2' has not been declared or assigned >> Polygons2:=[Par|t*g*tri : g in C,tri in [triangle3]]; ^ User error: Identifier 'triangle3' has not been declared or assigned >> Polygons3:=[Par|t^(-1)*g*tri : g in C,tri in [triangle3]]; ^ User error: Identifier 'triangle3' has not been declared or assigned >> DisplayPolygons(Polygons cat Polygons2 cat ^ User error: Identifier 'Polygons' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host dhcp-129-64-53-12.math.brandeis.edu. (129.64.53.12) Time: Tue Mar 30 15:39:33 2004 Input: G:=Gamma0(16); C:=CosetRepresentatives(G); H:=UpperHalfPlaneWithCusps(); Edge1:=[H|0,2]; Edge2:=[H|i,1/2*(i+1)]; point:=GeodesicsIntersection(Edge1,Edge2,H)[1]; triangle1:=[H|Infinity(),i,r]; triangle3:=[H|i,point,r]; triangle2:=[H|0,i,point]; Par:=Parent(triangle1); t:=G![1,1,0,1]; Polygons:=[Par|g*tri : g in C,tri in [triangle1,triangle2,triangle3]]; Polygons2:=[Par|t*g*tri : g in C,tri in [triangle3]]; Polygons3:=[Par|t^(-1)*g*tri : g in C,tri in [triangle3]]; purple:=[0.5,0,0.8]; blue:=[0.6,0.6,0.9]; yellow:=[1,0.8,0]; Colours:=[blue : i in C] cat [purple : i in C] cat [yellow : i in C] cat [purple : i in C] cat [yellow : i in C]; DisplayPolygons(Polygons cat Polygons2 cat Polygons3,"/tmp/pic.ps":Show:=true, Colours:=Colours,Size:=[-1,2,1.5,150]); Output: Magma V2.10-6 Tue Mar 30 2004 15:39:30 on modular [Seed = 1567933954] ------------------------------------- GeodesicsIntersection( x: [ 0, 2 ], y: [ root(-1), 1/2 + (1/2)*root(-1) ], H: Upper half complex plane union cusps ) ExtendGeodesic( z: [ root(-1), 1/2 + (1/2)*root(-1) ], H: Upper half complex plane union cusps ) In file "/usr/local/magma/package/Geometry/GrpPSL2/SpcHyp/geo_intersect.m", line 160, column 9: >> if a eq Infinity() then ^ Runtime error in 'eq': Bad argument types >> triangle3:=[H|i,point,r]; ^ User error: Identifier 'point' has not been declared or assigned >> triangle2:=[H|0,i,point]; ^ User error: Identifier 'point' has not been declared or assigned >> Polygons:=[Par|g*tri : g in C,tri in [triangle1,triangle2,triangle3]]; ^ User error: Identifier 'triangle2' has not been declared or assigned >> Polygons2:=[Par|t*g*tri : g in C,tri in [triangle3]]; ^ User error: Identifier 'triangle3' has not been declared or assigned >> Polygons3:=[Par|t^(-1)*g*tri : g in C,tri in [triangle3]]; ^ User error: Identifier 'triangle3' has not been declared or assigned >> DisplayPolygons(Polygons cat Polygons2 cat ^ User error: Identifier 'Polygons' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host dhcp-129-64-53-12.math.brandeis.edu. (129.64.53.12) Time: Tue Mar 30 15:41:46 2004 Input: G := GammaUpper0(2); H := UpperHalfPlaneWithCusps(); generators := Generators(G); M := generators cat [g^(-1) : g in generators] cat [G!1]; X := [1..#M]; L := [G!m : m in Set([Matrix(M[i]*M[j]*M[k]*M[l]*M[m]) : i in X, j in X, k in X, l in X, m in X])]; C := CosetRepresentatives(GammaUpper0(2)); tri1:=[H|Infinity(),i,r]; tri2:=[H|0,i,r]; Pols1:=[g*c*tri1 : c in C, g in L]; Pols2:=[g*c*tri2 : c in C, g in L]; pols := Pols1 cat Pols2; Colours := &cat[[[0.5,0.5,1],[1,0,0],[0,0.8,0]] : i in L]; Colours2 := &cat[[[0,0,1],[1,0.6,0.2],[0.5,1,0.5]] : i in L]; cols:=Colours cat Colours2; DisplayPolygons(pols,"/tmp/picture1.ps": Show := true,Size:=[-2,2,1.5,150], Colours:=cols,Outline:=false); Output: Magma V2.10-6 Tue Mar 30 2004 15:41:29 on modular [Seed = 1298454121] ------------------------------------- translation should be an integer [ -5.0000000000000000000000000000, 6.0000000000000000000000000000, 1.50000000000000000000000000000, 200 ] Total time: 16.760 seconds, Total memory usage: 4.42MB Errors: gv: Unable to open the display. ************** MAGMA ***************** Host dhcp-129-64-53-12.math.brandeis.edu. (129.64.53.12) Time: Tue Mar 30 15:43:18 2004 Input: G := GammaUpper0(2); H := UpperHalfPlaneWithCusps(); generators := Generators(G); M := generators cat [g^(-1) : g in generators] cat [G!1]; tri1 := [H|Infinity(),r-1,0,r,r+1]; tri2 := [H|Infinity(),i-1,0,i+1]; tri3 := FundamentalDomain(G); X := [1..#M]; L := [G!m : m in Set([Matrix(M[i]*M[j]*M[k]*M[l]*M[m]) : i in X, j in X, k in X, l in X, m in X])]; DisplayPolygons([g*tri1 : g in L],"/tmp/pic1.ps": Show := true, Size:=[-2,2,1.5,100]); DisplayPolygons([g*tri2 : g in L],"/tmp/pic2.ps": Show := true, Size:=[-2,2,1.5,100]); DisplayPolygons([g*tri3 : g in L],"/tmp/pic3.ps": Show := true, Size:=[-2,2,1.5,100]); Output: Magma V2.10-6 Tue Mar 30 2004 15:43:07 on modular [Seed = 1080679366] ------------------------------------- translation should be an integer [ -5.50000000000000000000000000000, 6.0000000000000000000000000000, 1.50000000000000000000000000000, 200 ] translation should be an integer [ -5.0000000000000000000000000000, 6.0000000000000000000000000000, 1.50000000000000000000000000000, 200 ] translation should be an integer [ -5.0000000000000000000000000000, 6.0000000000000000000000000000, 1.50000000000000000000000000000, 200 ] Total time: 11.639 seconds, Total memory usage: 2.46MB Errors: gv: Unable to open the display. gv: Unable to open the display. gv: Unable to open the display. ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 30 16:16:58 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible i per poder fer un cos finit am extenció d'un polinomi, el polinomi ha de ser irreductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! //apartat v) //F := G25; Minpol:=MinimalPolynomial(alpha); Roots (Minpol,G25); //Roots (Minpol,Z5); No es poden buscar arrels a Z5. //apartat vi) pol := 2*alpha^(-3) - alpha^5 + (1/alpha +2)*alpha ^6; pol; IsInvertible(G25!pol); {x: x in G25|IsInvertible(G25!x)}; //apartat vii) [<0,[0,0]>] cat [: r in [0..24]]; [<0,[0,0]>] cat [: r in [0..15]]; //apartat viii) G4:=ext; G8:=ext; G16:=ext; G2 subset G4; G2 subset G8; G2 subset G16; G4 subset G2; G4 subset G8; G4 subset G16; G8 subset G2; G8 subset G4; G8 subset G16; G16 subset G2; G16 subset G4; G16 subset G8; Output: Magma V2.10-6 Tue Mar 30 2004 16:16:55 on modular [Seed = 537494458] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 >> !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ^ User error: bad syntax [ , ] alpha^13 true alpha^11 { 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 } [ <0, [ 0, 0 ]>, <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , , <1, [ 1, 0 ]> ] [ <0, [ 0, 0 ]>, <1, [ 1, 0, 0, 0 ]>, , , , , , , , , , , , , , , <1, [ 1, 0, 0, 0 ]> ] true true true false false true false false false false false false Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 30 16:43:18 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible i per poder fer un cos finit am extenció d'un polinomi, el polinomi ha de ser irreductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; EulerPhi(G2); Output: Magma V2.10-6 Tue Mar 30 2004 16:43:15 on modular [Seed = 2612146741] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 >> EulerPhi(G2);; ^ Runtime error in 'EulerPhi': Bad argument types Argument types given: FldFin Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 30 16:44:19 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible i per poder fer un cos finit am extenció d'un polinomi, el polinomi ha de ser irreductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; EulerPhi(2); Output: Magma V2.10-6 Tue Mar 30 2004 16:44:16 on modular [Seed = 2376345568] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 1 Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 30 16:44:54 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible i per poder fer un cos finit am extenció d'un polinomi, el polinomi ha de ser irreductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; EulerPhi(3); Output: Magma V2.10-6 Tue Mar 30 2004 16:44:51 on modular [Seed = 2225942154] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 2 Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 80.58.50.44.proxycache.rima-tde.net. (80.58.50.44) Time: Tue Mar 30 16:45:24 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible i per poder fer un cos finit am extenció d'un polinomi, el polinomi ha de ser irreductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; EulerPhi(5); Output: Magma V2.10-6 Tue Mar 30 2004 16:45:21 on modular [Seed = 3146912151] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 4 Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Tue Mar 30 18:01:41 2004 Input: m:=4; upperBound:=50; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^5+x+2); #C; end if; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Mar 30 2004 18:01:18 on modular [Seed = 4208150170] ------------------------------------- 526 2470 14678 28630 84049 131113 280265 706641 924889 Errors: /home/mfd/gomagma: line 2: 7844 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (212.170.78.25) Time: Tue Mar 30 20:06:55 2004 Input: //Exercici 1 //apartat i) G2:=GF(2); G3:=GF(3); G5:=GF(5); [x: x in G2]; [x: x in G3]; [x: x in G5]; //apartat ii) //Z9 no és un cos finit perquè el '9' no és primer. Z9:=Integers(9); {x: x in Z9 | not(IsInvertible(x))}; //apartat iii) z2:=GF(2); z3:=GF(3); z5:=GF(5); P:=PolynomialRing(z2); p1:=P![1,1,0,0,1]; Q:=PolynomialRing(z3); q1:=Q![2,2,1]; q2:=Q![1,2,1]; R:=PolynomialRing(z5); r1:=R![3,2,1]; IsIrreducible(p1); //true IsIrreducible(q1); //true IsIrreducible(q2); //false IsIrreducible(r1); //true G9:=ext; G16:=ext; G25:=ext; IsPrimitive(alpha); //true //G9b:=ext; en aquest hi ha problemes perquè el polinomi q2 es //reductible. //apartat iv) llista:=[x : x in G25]; [Order(x): x in G25 | x ne 0 ]; #[x: x in G25 | IsPrimitive(x)]; Output: Magma V2.10-6 Tue Mar 30 2004 20:06:52 on modular [Seed = 3253442610] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] { 0, 3, 6 } true true false true true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] 8 Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host ip170.pm31.ts.paducah.hcis.net. (66.20.225.170) Time: Tue Mar 30 21:17:23 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Tue Mar 30 2004 21:17:13 on modular [Seed = 907828351] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-243-119.ns.itd.umich.edu. (141.213.243.119) Time: Wed Mar 31 01:43:04 2004 Input: k:=Integers(4); k; Output: Magma V2.10-6 Wed Mar 31 2004 01:43:01 on modular [Seed = 3757438920] ------------------------------------- Residue class ring of integers modulo 4 Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-243-119.ns.itd.umich.edu. (141.213.243.119) Time: Wed Mar 31 01:45:33 2004 Input: k:=Integers(4); k; R:=PolynomialRing(k,2); I:=ideal; I; Output: Magma V2.10-6 Wed Mar 31 2004 01:45:30 on modular [Seed = 2843967681] ------------------------------------- Residue class ring of integers modulo 4 Ideal of Polynomial ring of rank 2 over IntegerRing(4) Lexicographical Order Variables: x, y Basis: [ 2, x^2 ] Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host adsl-243-119.ns.itd.umich.edu. (141.213.243.119) Time: Wed Mar 31 01:46:28 2004 Input: k:=Integers(4); k; R:=PolynomialRing(k,2); I:=ideal; J:=ideal; L:=I meet J; L; Output: Magma V2.10-6 Wed Mar 31 2004 01:46:25 on modular [Seed = 3030293911] ------------------------------------- Residue class ring of integers modulo 4 Ideal of Polynomial ring of rank 2 over IntegerRing(4) Lexicographical Order Variables: x, y Basis: [ 2 ] Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host adsl-243-119.ns.itd.umich.edu. (141.213.243.119) Time: Wed Mar 31 01:49:29 2004 Input: k:=Integers(18); k; R:=PolynomialRing(k,2); I:=ideal; J:=ideal; L:=I meet J; L; Output: Magma V2.10-6 Wed Mar 31 2004 01:49:26 on modular [Seed = 2208934423] ------------------------------------- Residue class ring of integers modulo 18 Ideal of residue class ring of integers modulo 18 generated by 6 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-243-119.ns.itd.umich.edu. (141.213.243.119) Time: Wed Mar 31 01:49:48 2004 Input: k:=Integers(18); k; R:=PolynomialRing(k,2); I:=ideal; J:=ideal; L:=I meet J; L; Output: Magma V2.10-6 Wed Mar 31 2004 01:49:45 on modular [Seed = 2292359907] ------------------------------------- Residue class ring of integers modulo 18 Ideal of Polynomial ring of rank 2 over IntegerRing(18) Lexicographical Order Variables: x, y Basis: [ 6 ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-243-119.ns.itd.umich.edu. (141.213.243.119) Time: Wed Mar 31 01:53:34 2004 Input: k:=Integers(18); k; R:=PolynomialRing(k,2); I:=ideal; J:=ideal; L:=I meet J; L; Output: Magma V2.10-6 Wed Mar 31 2004 01:53:31 on modular [Seed = 2662642711] ------------------------------------- Residue class ring of integers modulo 18 Ideal of Polynomial ring of rank 2 over IntegerRing(18) Lexicographical Order Variables: x, y Basis: [ 3*x, 2*y, 6 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-243-119.ns.itd.umich.edu. (141.213.243.119) Time: Wed Mar 31 01:55:09 2004 Input: k:=Integers(18); k; R:=PolynomialRing(k,2); I:=ideal; J:=ideal; L:=I meet J; L; Output: Magma V2.10-6 Wed Mar 31 2004 01:55:06 on modular [Seed = 1782595907] ------------------------------------- Residue class ring of integers modulo 18 Ideal of Polynomial ring of rank 2 over IntegerRing(18) Lexicographical Order Variables: x, y Basis: [ 2 ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-243-119.ns.itd.umich.edu. (141.213.243.119) Time: Wed Mar 31 01:59:30 2004 Input: R:=Integers(4); R; S:=PolynomialRing(R,2); I:=ideal; J:=ideal; L:=I meet J; L; Output: Magma V2.10-6 Wed Mar 31 2004 01:59:27 on modular [Seed = 2018661460] ------------------------------------- Residue class ring of integers modulo 4 Ideal of Polynomial ring of rank 2 over IntegerRing(4) Lexicographical Order Variables: x, y Basis: [ 2 ] Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host adsl-243-119.ns.itd.umich.edu. (141.213.243.119) Time: Wed Mar 31 02:04:14 2004 Input: R:=Integers(4); S:=PolynomialRing(R,2); I:=ideal; J:=ideal; L:=I meet J; L; Output: Magma V2.10-6 Wed Mar 31 2004 02:04:11 on modular [Seed = 688063521] ------------------------------------- Ideal of Polynomial ring of rank 2 over IntegerRing(4) Lexicographical Order Variables: x, y Basis: [ 2 ] Total time: 3.029 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host adsl-243-119.ns.itd.umich.edu. (141.213.243.119) Time: Wed Mar 31 02:23:51 2004 Input: R:=Integers(4); S:=PolynomialRing(R,2); I:=ideal; J:=ideal; L:=I*J; L; Output: Magma V2.10-6 Wed Mar 31 2004 02:23:48 on modular [Seed = 289088374] ------------------------------------- Ideal of Polynomial ring of rank 2 over IntegerRing(4) Lexicographical Order Variables: x, y Basis: [ 0, 2*y, 2*x, x*y ] Total time: 2.889 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.194.89.11) Time: Wed Mar 31 03:33:25 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Wed Mar 31 2004 03:33:21 on modular [Seed = 1097565044] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.194.89.11) Time: Wed Mar 31 03:34:03 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Wed Mar 31 2004 03:34:00 on modular [Seed = 1264683351] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Wed Mar 31 10:31:44 2004 Input: m:=1; upperBound:=1000; for p in [5..upperBound] do if IsPrime(p) then F := PolynomialRing(FiniteField(p^m)); C := HyperellipticCurve(x^3-1); #C; end if; end for; Output: Magma V2.10-6 Wed Mar 31 2004 10:31:40 on modular [Seed = 2927889051] ------------------------------------- 6 4 12 12 18 28 24 30 28 48 42 52 48 54 60 48 52 72 84 76 84 90 84 102 124 108 108 114 148 132 138 124 150 148 144 172 168 174 180 156 192 192 198 172 196 196 228 252 234 240 228 252 258 264 270 244 252 282 316 294 292 312 336 318 364 372 348 336 354 360 364 336 388 384 390 432 402 372 420 444 432 432 412 444 450 468 462 484 468 480 532 492 532 504 510 522 532 588 508 558 564 570 556 624 588 594 600 576 628 624 618 652 676 642 604 648 654 660 624 624 678 684 700 702 732 720 772 684 724 744 700 732 762 768 774 844 798 810 868 822 772 828 876 840 912 858 916 864 912 882 892 888 868 912 868 930 912 942 948 954 988 972 978 984 1036 1008 Total time: 3.209 seconds, Total memory usage: 2.39MB ************** MAGMA ***************** Host d198-166-21-168.abhsia.telus.net. (198.166.21.168) Time: Wed Mar 31 12:32:47 2004 Input: A=[1, 1, 3; 1, 3, 1; 3, 1, 1] charpoly(A) mateigen(A) Output: Magma V2.10-6 Wed Mar 31 2004 12:32:44 on modular [Seed = 1247873693] ------------------------------------- >> A=[1, 1, 3; 1, 3, 1; 3, 1, 1] ^ User error: bad syntax >> mateigen(A) ^ User error: bad syntax Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ac219pc12.UMBC.EDU. (130.85.106.96) Time: Wed Mar 31 15:51:39 2004 Input: CyclicCode; ? Output: Magma V2.10-6 Wed Mar 31 2004 15:51:36 on modular [Seed = 1483945838] ------------------------------------- Intrinsic 'CyclicCode' Signatures: ( v) -> Code The cyclic code generated by v (the linear code generated by cyclic shifts of v). ( n, f) -> Code The cyclic code of length n generated by f(x) (the linear code generated by cyclic shifts of the vector corresponding to f(x)). ( n, R, K) -> Code Given a positive integer n and a set or sequence R of primitive n-th roots of unity from a field L, together with a subfield K of L, construct the cyclic code C over K of length n such that the generator polynomial for C is the polynomial of least degree having the elements of R as roots. =============================================================================== PATH: / KIND: Overview =============================================================================== You are reading about the Magma online help system. This system gives you information about Magma while you are at the computer. To see this help page at any time, all you have to do is to type ? ---------- The online help system comes in two modes: the single request mode and the Magma Help Browser. To enter the Browser, type ?? The Browser is useful if you intend to read several related help nodes, because you can exploit the tree structure of the online help. Once you are in the Browser, you can type help again to find out how to use the Browser, and for a more detailed explanation of the whole online help system. ---------- Single help requests begin with the ? character. Examples are: ?print ?magma ?ring ?example If your help request is ambiguous, Magma will return a numbered list of matches. To see the contents of one of them, type ? followed by its number. Some help pages suggest other pages that you might like to look at as well. They are prefixed by a code such as +3 or +5 . To read one of them, type ? followed by the code. You can also supply the full pathname of a help node, if you know it. For example: ?/system/quit ?/magma/module/homomorphism ---------- The online help system offers tab completion. If you type a few letters of your help request and then press the tab key, Magma will "complete" the request if there is a unique completion. Otherwise, it will complete the request as far as possible, and then emit a beep. Press the tab key again to see all the possibilities. ALWAYS PRESS TAB BEFORE THE END OF THE LINE, SO AS TO SEE EVERY RELEVANT HELP PAGE. (On a few operating systems, the tab completion feature cannot be made available.) ---------- The content of the online help system comes from two sources: the "Handbook of Magma Functions" (Bosma and Cannon) and specially-written overview nodes. You may also wish to consult the books "An Introduction to Algebraic Programming in Magma" (Cannon and Playoust) and "Solving Problems with Magma" (Bosma, Cannon, Playoust and Steel). ---------- The online help system is also available in an HTML form suitable for Internet browsers. To use this, move to a shell prompt (outside Magma) and type magmahelp ---------- To leave Magma, type quit; or -D. =============================================================================== Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ac219pc12.UMBC.EDU. (130.85.106.96) Time: Wed Mar 31 15:52:38 2004 Input: CyclicCode; ? Output: Magma V2.10-6 Wed Mar 31 2004 15:52:35 on modular [Seed = 772096467] ------------------------------------- Intrinsic 'CyclicCode' Signatures: ( v) -> Code The cyclic code generated by v (the linear code generated by cyclic shifts of v). ( n, f) -> Code The cyclic code of length n generated by f(x) (the linear code generated by cyclic shifts of the vector corresponding to f(x)). ( n, R, K) -> Code Given a positive integer n and a set or sequence R of primitive n-th roots of unity from a field L, together with a subfield K of L, construct the cyclic code C over K of length n such that the generator polynomial for C is the polynomial of least degree having the elements of R as roots. =============================================================================== PATH: / KIND: Overview =============================================================================== You are reading about the Magma online help system. This system gives you information about Magma while you are at the computer. To see this help page at any time, all you have to do is to type ? ---------- The online help system comes in two modes: the single request mode and the Magma Help Browser. To enter the Browser, type ?? The Browser is useful if you intend to read several related help nodes, because you can exploit the tree structure of the online help. Once you are in the Browser, you can type help again to find out how to use the Browser, and for a more detailed explanation of the whole online help system. ---------- Single help requests begin with the ? character. Examples are: ?print ?magma ?ring ?example If your help request is ambiguous, Magma will return a numbered list of matches. To see the contents of one of them, type ? followed by its number. Some help pages suggest other pages that you might like to look at as well. They are prefixed by a code such as +3 or +5 . To read one of them, type ? followed by the code. You can also supply the full pathname of a help node, if you know it. For example: ?/system/quit ?/magma/module/homomorphism ---------- The online help system offers tab completion. If you type a few letters of your help request and then press the tab key, Magma will "complete" the request if there is a unique completion. Otherwise, it will complete the request as far as possible, and then emit a beep. Press the tab key again to see all the possibilities. ALWAYS PRESS TAB BEFORE THE END OF THE LINE, SO AS TO SEE EVERY RELEVANT HELP PAGE. (On a few operating systems, the tab completion feature cannot be made available.) ---------- The content of the online help system comes from two sources: the "Handbook of Magma Functions" (Bosma and Cannon) and specially-written overview nodes. You may also wish to consult the books "An Introduction to Algebraic Programming in Magma" (Cannon and Playoust) and "Solving Problems with Magma" (Bosma, Cannon, Playoust and Steel). ---------- The online help system is also available in an HTML form suitable for Internet browsers. To use this, move to a shell prompt (outside Magma) and type magmahelp ---------- To leave Magma, type quit; or -D. =============================================================================== Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ac219pc12.UMBC.EDU. (130.85.106.96) Time: Wed Mar 31 15:53:14 2004 Input: CyclicCode(3,x+1); Output: Magma V2.10-6 Wed Mar 31 2004 15:53:11 on modular [Seed = 655116542] ------------------------------------- >> CyclicCode(3,x+1); ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host math.cudenver.edu. (132.194.16.89) Time: Wed Mar 31 16:09:51 2004 Input: G:=AbelianGroup;G; Output: Magma V2.10-6 Wed Mar 31 2004 16:09:48 on modular [Seed = 289039075] ------------------------------------- Abelian Group isomorphic to Z/5 + Z/5 Defined on 2 generators Relations: 5*a = 0 5*b = 0 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host math.cudenver.edu. (132.194.16.89) Time: Wed Mar 31 16:11:26 2004 Input: G:=AbelianGroup;G; H:=AutomorphismGroup(G); Output: Magma V2.10-6 Wed Mar 31 2004 16:11:23 on modular [Seed = 4258696808] ------------------------------------- Abelian Group isomorphic to Z/5 + Z/5 Defined on 2 generators Relations: 5*a = 0 5*b = 0 >> H:=AutomorphismGroup(G); ^ Runtime error in 'AutomorphismGroup': Bad argument types Argument types given: GrpAb Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Mar 31 17:12:41 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=1/alpha^4-alpha^(-3)x+alpha^5x^2+alpha^11x^3 Output: Magma V2.10-6 Wed Mar 31 2004 17:12:38 on modular [Seed = 254020918] ------------------------------------- >> pol:=1/alpha^4-alpha^(-3)x+alpha^5x^2+alpha^11x^3 ; ^ User error: bad syntax Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Mar 31 17:12:44 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=1/alpha^4-alpha^(-3)x+alpha^5x^2+alpha^11x^3; Output: Magma V2.10-6 Wed Mar 31 2004 17:12:41 on modular [Seed = 203886138] ------------------------------------- >> pol:=1/alpha^4-alpha^(-3)x+alpha^5x^2+alpha^11x^3;; ^ User error: bad syntax Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Mar 31 17:13:00 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=1/alpha^4-alpha^(-3)*x+alpha^5*x^2+alpha^11*x^3; Output: Magma V2.10-6 Wed Mar 31 2004 17:12:57 on modular [Seed = 506797080] ------------------------------------- >> pol:=1/alpha^4-alpha^(-3)*x+alpha^5*x^2+alpha^11*x^3;; ^ Runtime error in '^': Argument 2 (-3) should be >= 0 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Mar 31 17:14:03 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=1/alpha^4-alpha^(-3)*x+(alpha^5)*(x^2)+(alpha^11)*(x^3); Output: Magma V2.10-6 Wed Mar 31 2004 17:14:00 on modular [Seed = 3972525611] ------------------------------------- >> pol:=1/alpha^4-alpha^(-3)*x+(alpha^5)*(x^2)+(alpha^11)*(x^3);; ^ Runtime error in '^': Argument 2 (-3) should be >= 0 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Mar 31 17:15:27 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=1/alpha^4-1/(alpha^3)*x+(alpha^5)*(x^2)+(alpha^11)*(x^3); Output: Magma V2.10-6 Wed Mar 31 2004 17:15:24 on modular [Seed = 4275436653] ------------------------------------- >> pol:=1/alpha^4-1/(alpha^3)*x+(alpha^5)*(x^2)+(alpha^11)*(x^3);; ^ Runtime error in '*': Bad argument types Argument types given: FldFunRatUElt, RngUPolElt Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Mar 31 17:15:52 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=1/alpha^4-(1/(alpha^3))*x+(alpha^5)*(x^2)+(alpha^11)*(x^3); Output: Magma V2.10-6 Wed Mar 31 2004 17:15:49 on modular [Seed = 4125030031] ------------------------------------- >> pol:=1/alpha^4-(1/(alpha^3))*x+(alpha^5)*(x^2)+(alpha^11)*(x^3);; ^ Runtime error in '*': Bad argument types Argument types given: FldFunRatUElt, RngUPolElt Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Mar 31 17:16:10 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=1/alpha^4-(1/(alpha^3))+(alpha^5)*(x^2)+(alpha^11)*(x^3); Output: Magma V2.10-6 Wed Mar 31 2004 17:16:07 on modular [Seed = 3437744004] ------------------------------------- Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Mar 31 17:16:20 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=1/alpha^4-x*(1/(alpha^3))+(alpha^5)*(x^2)+(alpha^11)*(x^3); Output: Magma V2.10-6 Wed Mar 31 2004 17:16:17 on modular [Seed = 3286810781] ------------------------------------- >> pol:=1/alpha^4-x*(1/(alpha^3))+(alpha^5)*(x^2)+(alpha^11)*(x^3);; ^ Runtime error in '*': Bad argument types Argument types given: RngUPolElt, FldFunRatUElt Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Mar 31 17:16:35 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=1/alpha^4-(x)*(1/(alpha^3))+(alpha^5)*(x^2)+(alpha^11)*(x^3); Output: Magma V2.10-6 Wed Mar 31 2004 17:16:32 on modular [Seed = 3673283061] ------------------------------------- >> pol:=1/alpha^4-(x)*(1/(alpha^3))+(alpha^5)*(x^2)+(alpha^11)*(x^3);; ^ Runtime error in '*': Bad argument types Argument types given: RngUPolElt, FldFunRatUElt Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Mar 31 17:16:50 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=(1/alpha^4)-(x)*(1/(alpha^3))+(alpha^5)*(x^2)+(alpha^11)*(x^3); Output: Magma V2.10-6 Wed Mar 31 2004 17:16:47 on modular [Seed = 3522876145] ------------------------------------- >> pol:=(1/alpha^4)-(x)*(1/(alpha^3))+(alpha^5)*(x^2)+(alpha^11)*(x^3);; ^ Runtime error in '*': Bad argument types Argument types given: RngUPolElt, FldFunRatUElt Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Mar 31 17:17:07 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=(1/alpha^4)-((x/(alpha^3))+(alpha^5)*(x^2)+(alpha^11)*(x^3); Output: Magma V2.10-6 Wed Mar 31 2004 17:17:04 on modular [Seed = 2827201447] ------------------------------------- >> pol:=(1/alpha^4)-((x/(alpha^3))+(alpha^5)*(x^2)+(alpha^11)*(x^3);; ^ User error: bad syntax Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Mar 31 17:17:19 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=(1/alpha^4)-(x/(alpha^3)+(alpha^5)*(x^2)+(alpha^11)*(x^3); Output: Magma V2.10-6 Wed Mar 31 2004 17:17:16 on modular [Seed = 3197484477] ------------------------------------- >> pol:=(1/alpha^4)-(x/(alpha^3)+(alpha^5)*(x^2)+(alpha^11)*(x^3);; ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Mar 31 17:17:30 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=(1/alpha^4)-(x/(alpha^3)+(alpha^5)*(x^2)+(alpha^11)*(x^3) Output: Magma V2.10-6 Wed Mar 31 2004 17:17:27 on modular [Seed = 3030366124] ------------------------------------- >> pol:=(1/alpha^4)-(x/(alpha^3)+(alpha^5)*(x^2)+(alpha^11)*(x^3); ^ User error: bad syntax Total time: 2.869 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Mar 31 17:17:39 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=(1/alpha^4)-(x/(alpha^3)+(alpha^5)*(x^2)+(alpha^11)*(x^3); Output: Magma V2.10-6 Wed Mar 31 2004 17:17:36 on modular [Seed = 2342553700] ------------------------------------- >> pol:=(1/alpha^4)-(x/(alpha^3)+(alpha^5)*(x^2)+(alpha^11)*(x^3);; ^ User error: bad syntax Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Mar 31 17:17:51 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=(1/alpha^4)-(x/(alpha^3)+(alpha^5)*(x^2)+(alpha^11)*(x^3) Output: Magma V2.10-6 Wed Mar 31 2004 17:17:48 on modular [Seed = 2192146785] ------------------------------------- >> pol:=(1/alpha^4)-(x/(alpha^3)+(alpha^5)*(x^2)+(alpha^11)*(x^3); ^ User error: bad syntax Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Mar 31 17:18:06 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=(1/alpha^4)-(1/(alpha^3)+(alpha^5)*(x^2)+(alpha^11)*(x^3); Output: Magma V2.10-6 Wed Mar 31 2004 17:18:03 on modular [Seed = 2578618989] ------------------------------------- >> pol:=(1/alpha^4)-(1/(alpha^3)+(alpha^5)*(x^2)+(alpha^11)*(x^3);; ^ User error: bad syntax Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Mar 31 17:18:41 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=1/alpha^4-(x/(alpha^3))+(alpha^5)*(x^2)+(alpha^11)*(x^3); Output: Magma V2.10-6 Wed Mar 31 2004 17:18:38 on modular [Seed = 2428212033] ------------------------------------- Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Mar 31 17:18:59 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=1/alpha^4-(x/(alpha^3))+(alpha^5)*(x^2)+(alpha^11)*(x^3); Evaluate(pol); Output: Magma V2.10-6 Wed Mar 31 2004 17:18:56 on modular [Seed = 2018737112] ------------------------------------- >> Evaluate(pol);; ^ Runtime error in 'Evaluate': Bad argument types Argument types given: FldFunRatUElt Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Mar 31 17:19:31 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=1/alpha^4-(x/(alpha^3))+(alpha^5)*(x^2)+(alpha^11)*(x^3); pol; Output: Magma V2.10-6 Wed Mar 31 2004 17:19:28 on modular [Seed = 1632264929] ------------------------------------- (alpha^18 + alpha^11 + 4*alpha^2 + 1)/alpha^4 Total time: 2.869 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Mar 31 17:19:54 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=1/alpha^4-(x/(alpha^3))+(alpha^5)*(x^2)+(alpha^11)*(x^3); Evaluate(pol,3); Output: Magma V2.10-6 Wed Mar 31 2004 17:19:51 on modular [Seed = 1782672925] ------------------------------------- 3 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Mar 31 17:20:03 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=1/alpha^4-(x/(alpha^3))+(alpha^5)*(x^2)+(alpha^11)*(x^3); Evaluate(pol,6); Output: Magma V2.10-6 Wed Mar 31 2004 17:20:00 on modular [Seed = 1417629748] ------------------------------------- 2 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Mar 31 17:20:15 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=1/alpha^4-(x/(alpha^3))+(alpha^5)*(x^2)+(alpha^11)*(x^3); pol; Evaluate(pol,6); Output: Magma V2.10-6 Wed Mar 31 2004 17:20:12 on modular [Seed = 1148141608] ------------------------------------- (alpha^18 + alpha^11 + 4*alpha^2 + 1)/alpha^4 2 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217) Time: Wed Mar 31 18:40:32 2004 Input: ModularSymbols(389); Output: Magma V2.10-6 Wed Mar 31 2004 18:40:29 on modular [Seed = 1782676726] ------------------------------------- Full modular symbols space for Gamma_0(389) of weight 2 and dimension 65 over Rational Field Total time: 2.720 seconds, Total memory usage: 2.80MB ************** MAGMA ***************** Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217) Time: Wed Mar 31 18:48:50 2004 Input: ModularSymbols(389); Output: Magma V2.10-22 Wed Mar 31 2004 18:48:47 on modular [Seed = 186651557] ------------------------------------- Full modular symbols space for Gamma_0(389) of weight 2 and dimension 65 over Rational Field Total time: 2.789 seconds, Total memory usage: 2.90MB ************** MAGMA ***************** Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217) Time: Wed Mar 31 18:51:27 2004 Input: ModularSymbols(389); Output: Magma V2.10-22 Wed Mar 31 2004 18:51:24 on modular [Seed = 3689988822] ------------------------------------- Full modular symbols space for Gamma_0(389) of weight 2 and dimension 65 over Rational Field Total time: 2.709 seconds, Total memory usage: 2.90MB ************** MAGMA ***************** Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217) Time: Wed Mar 31 18:51:37 2004 Input: Factorial(69); Output: Magma V2.10-22 Wed Mar 31 2004 18:51:35 on modular [Seed = 3270105908] ------------------------------------- 1711224524281413113724683388812728390922705448935203693936480409232572797541406\ 47424000000000000000 Total time: 2.530 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217) Time: Wed Mar 31 18:55:21 2004 Input: SubgroupLattice(SymmetricGroup(5)); Output: Magma V2.10-22 Wed Mar 31 2004 18:55:19 on modular [Seed = 2962991782] ------------------------------------- Partially ordered set of subgroup classes ----------------------------------------- [ 1] Order 1 Length 1 Maximal Subgroups: --- [ 2] Order 2 Length 10 Maximal Subgroups: 1 [ 3] Order 2 Length 15 Maximal Subgroups: 1 [ 4] Order 3 Length 10 Maximal Subgroups: 1 [ 5] Order 5 Length 6 Maximal Subgroups: 1 --- [ 6] Order 4 Length 5 Maximal Subgroups: 3 [ 7] Order 4 Length 15 Maximal Subgroups: 3 [ 8] Order 4 Length 15 Maximal Subgroups: 2 3 [ 9] Order 6 Length 10 Maximal Subgroups: 3 4 [10] Order 6 Length 10 Maximal Subgroups: 2 4 [11] Order 6 Length 10 Maximal Subgroups: 2 4 [12] Order 10 Length 6 Maximal Subgroups: 3 5 --- [13] Order 8 Length 15 Maximal Subgroups: 6 7 8 [14] Order 12 Length 5 Maximal Subgroups: 4 6 [15] Order 12 Length 10 Maximal Subgroups: 8 9 10 11 [16] Order 20 Length 6 Maximal Subgroups: 7 12 --- [17] Order 24 Length 5 Maximal Subgroups: 10 13 14 [18] Order 60 Length 1 Maximal Subgroups: 9 12 14 --- [19] Order 120 Length 1 Maximal Subgroups: 15 16 17 18 Total time: 2.619 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217) Time: Wed Mar 31 18:56:52 2004 Input: R:=Integers(4); > R; > S:=PolynomialRing(R,2); > I:=ideal; > J:=ideal; > L:=I meet J; > L; Output: Magma V2.10-22 Wed Mar 31 2004 18:56:49 on modular [Seed = 2743646483] ------------------------------------- Residue class ring of integers modulo 4 Ideal of Polynomial ring of rank 2 over IntegerRing(4) Lexicographical Order Variables: x, y Basis: [ x*y, 2 ] Total time: 2.529 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host host57.200-117-215.telecom.net.ar. (200.117.215.57) Time: Thu Apr 1 00:18:28 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-22 Thu Apr 1 2004 00:18:25 on modular [Seed = 86958909] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.519 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Thu Apr 1 02:23:28 2004 Input: > P := PolynomialRing(IntegerRing(), 2); > I := ideal GroebnerBasis(I); > (1+a1*x1)*(1+a1*x2)*(1+a2*x1)*(1+a2*x2) in I; > Output: Magma V2.10-22 Thu Apr 1 2004 02:23:25 on modular [Seed = 153258622] ------------------------------------- >> I := ideal> GroebnerBasis(I); ^ User error: Identifier 'I' has not been declared or assigned >> (1+a1*x1)*(1+a1*x2)*(1+a2*x1)*(1+a2*x2) in I; ^ User error: Identifier 'a1' has not been declared or assigned Total time: 2.590 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Thu Apr 1 02:23:39 2004 Input: > P := PolynomialRing(IntegerRing(), 2); > I := ideal; > GroebnerBasis(I); > (1+a1*x1)*(1+a1*x2)*(1+a2*x1)*(1+a2*x2) in I; > Output: Magma V2.10-22 Thu Apr 1 2004 02:23:36 on modular [Seed = 103646564] ------------------------------------- [ 3*x^2*y + 48*y^3, 9*x^2 + 16*y^2, 8*x*y^3, 24*x*y, 128*y^3 ] >> (1+a1*x1)*(1+a1*x2)*(1+a2*x1)*(1+a2*x2) in I; ^ User error: Identifier 'a1' has not been declared or assigned Total time: 2.559 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Thu Apr 1 02:24:37 2004 Input: > P := PolynomialRing(IntegerRing(), 2); > I := ideal; > GroebnerBasis(I); > n=2 > Output: Magma V2.10-22 Thu Apr 1 2004 02:24:35 on modular [Seed = 1041612183] ------------------------------------- [ 3*x^2*y + 48*y^3, 9*x^2 + 16*y^2, 8*x*y^3, 24*x*y, 128*y^3 ] >> n=2 ^ User error: Identifier 'n' has not been declared or assigned Total time: 2.499 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Thu Apr 1 02:25:48 2004 Input: > P := PolynomialRing(IntegerRing(), 2); > I := ideal; > GroebnerBasis(I); > ( (3+x+4+y)^3+3(3+x+4+y)(3+x-4-y)^2 )/4 in I > Output: Magma V2.10-22 Thu Apr 1 2004 02:25:45 on modular [Seed = 704752073] ------------------------------------- [ 3*x^2*y + 48*y^3, 9*x^2 + 16*y^2, 8*x*y^3, 24*x*y, 128*y^3 ] >> ( (3+x+4+y)^3+3(3+x+4+y)(3+x-4-y)^2 )/4 in I ^ Runtime error: Bad argument types Argument types given: RngMPolElt, RngIntElt Total time: 2.609 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Thu Apr 1 02:26:02 2004 Input: > P := PolynomialRing(IntegerRing(), 2); > I := ideal; > GroebnerBasis(I); > ( (3+x+4+y)^3+3*(3+x+4+y)*(3+x-4-y)^2 )/4 in I > Output: Magma V2.10-22 Thu Apr 1 2004 02:25:59 on modular [Seed = 571057727] ------------------------------------- [ 3*x^2*y + 48*y^3, 9*x^2 + 16*y^2, 8*x*y^3, 24*x*y, 128*y^3 ] >> ( (3+x+4+y)^3+3*(3+x+4+y)*(3+x-4-y)^2 )/4 in I ^ Runtime error in '/': Coefficient ring of argument 1 is not a field Total time: 2.499 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Thu Apr 1 02:26:47 2004 Input: > P := PolynomialRing(IntegerRing(), 2); > I := ideal; > GroebnerBasis(I); > ( (3+x+4+y)^3+3*(3+x+4+y)*(3+x-4-y)^2 )*(0.25) in I > Output: Magma V2.10-22 Thu Apr 1 2004 02:26:44 on modular [Seed = 1400428413] ------------------------------------- [ 3*x^2*y + 48*y^3, 9*x^2 + 16*y^2, 8*x*y^3, 24*x*y, 128*y^3 ] >> ( (3+x+4+y)^3+3*(3+x+4+y)*(3+x-4-y)^2 )*(0.25) in I ^ Runtime error in '*': Bad argument types Argument types given: RngMPolElt, FldPrElt Total time: 2.509 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Thu Apr 1 02:27:10 2004 Input: > P := PolynomialRing(IntegerRing(), 2); > I := ideal; > GroebnerBasis(I); > ( (3+x+4+y)^3+3*(3+x+4+y)*(3+x-4-y)^2 )) div 4 in I > Output: Magma V2.10-22 Thu Apr 1 2004 02:27:08 on modular [Seed = 1264635677] ------------------------------------- [ 3*x^2*y + 48*y^3, 9*x^2 + 16*y^2, 8*x*y^3, 24*x*y, 128*y^3 ] >> ( (3+x+4+y)^3+3*(3+x+4+y)*(3+x-4-y)^2 )) div 4 in I ^ User error: bad syntax Total time: 2.479 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Thu Apr 1 02:27:27 2004 Input: > P := PolynomialRing(IntegerRing(), 2); > I := ideal; > GroebnerBasis(I); > ( (3+x+4+y)^3+3*(3+x+4+y)*(3+x-4-y)^2 ) div 4 in I > Output: Magma V2.10-22 Thu Apr 1 2004 02:27:24 on modular [Seed = 1080804358] ------------------------------------- [ 3*x^2*y + 48*y^3, 9*x^2 + 16*y^2, 8*x*y^3, 24*x*y, 128*y^3 ] false Total time: 2.559 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Thu Apr 1 02:27:50 2004 Input: > P := PolynomialRing(IntegerRing(), 2); > I := ideal; > GroebnerBasis(I); > ( (3+x+4+y)^7+7*(3+x+4+y)^3*(3+x-4-y)^4 ) div 4 in I > Output: Magma V2.10-22 Thu Apr 1 2004 02:27:47 on modular [Seed = 2035481872] ------------------------------------- [ 3*x^2*y + 48*y^3, 9*x^2 + 16*y^2, 8*x*y^3, 24*x*y, 128*y^3 ] false Total time: 2.550 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Thu Apr 1 02:28:15 2004 Input: > P := PolynomialRing(IntegerRing(), 2); > I := ideal; > GroebnerBasis(I); > ( (3+x+4+y)^7+7*(3+x+4+y)^3*(3+x-4-y)^4 ) div 8 in I > Output: Magma V2.10-22 Thu Apr 1 2004 02:28:13 on modular [Seed = 1901786598] ------------------------------------- [ 3*x^2*y + 48*y^3, 9*x^2 + 16*y^2, 8*x*y^3, 24*x*y, 128*y^3 ] false Total time: 2.549 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Thu Apr 1 02:28:57 2004 Input: > P := PolynomialRing(IntegerRing(), 2); > I := ideal; > GroebnerBasis(I); > ( (3+x+4+y)^15+15*(3+x+4+y)^7*(3+x-4-y)^8 ) div 16 in I > Output: Magma V2.10-22 Thu Apr 1 2004 02:28:54 on modular [Seed = 1765993924] ------------------------------------- [ 3*x^2*y + 48*y^3, 9*x^2 + 16*y^2, 8*x*y^3, 24*x*y, 128*y^3 ] false Total time: 2.520 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Thu Apr 1 02:52:47 2004 Input: > P := PolynomialRing(IntegerRing(), 2); > I := ideal; > GroebnerBasis(I); > ( (3*x+4*y)^15+15*(3*x+4*y)^7*(3*x-4*y)^8 ) div 16 in I > Output: Magma V2.10-22 Thu Apr 1 2004 02:52:44 on modular [Seed = 3013097957] ------------------------------------- [ 3*x^2*y + 48*y^3, 9*x^2 + 16*y^2, 8*x*y^3, 24*x*y, 128*y^3 ] true Total time: 2.510 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Thu Apr 1 02:53:04 2004 Input: > P := PolynomialRing(IntegerRing(), 2); > I := ideal; > GroebnerBasis(I); > ( (3*x+4*y)^7+7*(3*x+4*y)^3*(3*x-4*y)^4 ) div 16 in I > Output: Magma V2.10-22 Thu Apr 1 2004 02:53:02 on modular [Seed = 2877301231] ------------------------------------- [ 3*x^2*y + 48*y^3, 9*x^2 + 16*y^2, 8*x*y^3, 24*x*y, 128*y^3 ] >> ( (3*x+4*y)^7+7*(3*x+4*y)^3*(3*x-4*y)^4 ) div 16 in I ^ Runtime error in 'div': Argument 2 does not divide argument 1 Total time: 2.500 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Thu Apr 1 02:53:22 2004 Input: > P := PolynomialRing(IntegerRing(), 2); > I := ideal; > GroebnerBasis(I); > ( (3*x+4*y)^7+7*(3*x+4*y)^3*(3*x-4*y)^4 ) div 8 in I > Output: Magma V2.10-22 Thu Apr 1 2004 02:53:19 on modular [Seed = 2743609814] ------------------------------------- [ 3*x^2*y + 48*y^3, 9*x^2 + 16*y^2, 8*x*y^3, 24*x*y, 128*y^3 ] true Total time: 2.509 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Thu Apr 1 02:53:41 2004 Input: > P := PolynomialRing(IntegerRing(), 2); > I := ideal; > GroebnerBasis(I); > ( (3*x+4*y)^3+3*(3*x+4*y)^1*(3*x-4*y)^2 ) div 4 in I > Output: Magma V2.10-22 Thu Apr 1 2004 02:53:39 on modular [Seed = 3689959746] ------------------------------------- [ 3*x^2*y + 48*y^3, 9*x^2 + 16*y^2, 8*x*y^3, 24*x*y, 128*y^3 ] false Total time: 2.499 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Thu Apr 1 02:55:02 2004 Input: > P := PolynomialRing(IntegerRing(), 2); > I := ideal; > GroebnerBasis(I); > ( (5*x+4*y)^3+3*(5*x+4*y)^1*(5*x-4*y)^2 ) div 4 in I > Output: Magma V2.10-22 Thu Apr 1 2004 02:54:59 on modular [Seed = 3556268314] ------------------------------------- [ 5*x^2*y + 80*y^3, 25*x^2 + 16*y^2, 8*x*y^3, 40*x*y, 128*y^3 ] false Total time: 2.549 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Thu Apr 1 02:56:21 2004 Input: > P := PolynomialRing(IntegerRing(), 2); > I := ideal; > GroebnerBasis(I); > ( (5*(x-y)+4*y)^3+3*(5*(x-y)+4*y)^1*(5*(x-y)-4*y)^2 ) div 4 in I > Output: Magma V2.10-22 Thu Apr 1 2004 02:56:18 on modular [Seed = 3437709300] ------------------------------------- [ 5*x^2*y + 30*x*y^2 + 45*y^3, 25*x^2 + 30*x*y - 39*y^2, 8*x*y^3 + 120*y^4, 40*x*y - 40*y^2, 128*y^3 ] false Total time: 2.549 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Thu Apr 1 02:57:03 2004 Input: > P := PolynomialRing(IntegerRing(), 2); > I := ideal; > GroebnerBasis(I); > ( (5*(x-y)+4*y)^7+7*(5*(x-y)+4*y)^3*(5*(x-y)-4*y)^4 ) div 8 in I > Output: Magma V2.10-22 Thu Apr 1 2004 02:57:01 on modular [Seed = 3304017811] ------------------------------------- [ 5*x^2*y + 30*x*y^2 + 45*y^3, 25*x^2 + 30*x*y - 39*y^2, 8*x*y^3 + 120*y^4, 40*x*y - 40*y^2, 128*y^3 ] true Total time: 2.509 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host man002.math.klte.hu. (193.6.146.50) Time: Thu Apr 1 03:45:53 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-22 Thu Apr 1 2004 03:45:50 on modular [Seed = 1952441041] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.579 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host man002.math.klte.hu. (193.6.146.50) Time: Thu Apr 1 03:48:13 2004 Input: M:=CuspidalSubspace(ModularSymbols(1056,2,1)); D:=NewformDecomposition(M); Output: Magma V2.10-22 Thu Apr 1 2004 03:47:51 on modular [Seed = 1615591244] ------------------------------------- ************** MAGMA ***************** Host man002.math.klte.hu. (193.6.146.50) Time: Thu Apr 1 03:49:00 2004 Input: M:=CuspidalSubspace(ModularSymbols(1056,2,1)); D:=NewformDecomposition(M); #D; Output: Magma V2.10-22 Thu Apr 1 2004 03:48:37 on modular [Seed = 2561871846] ------------------------------------- ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Thu Apr 1 03:49:02 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > ( (5*(x)+4*y+6*z)^7+7*(5*(x)+4*y+6*z)^3*(5*(x)-4*y-6*z)^4 ) div 8 in I > Output: Magma V2.10-22 Thu Apr 1 2004 03:48:59 on modular [Seed = 2662664702] ------------------------------------- [ x^2*y + 14*x^2*z + 16*y^3 + 32*y^2*z + 36*y*z^2 + 72*z^3, 25*x^2 + 16*y^2 + 36*z^2, 8*x*y + 12*x*z, 128*y^3 + 192*y^2*z + 288*y*z^2 + 432*z^3 ] false Total time: 2.529 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Thu Apr 1 03:49:26 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > ( (5*(x)+4*y+6*z)^7+7*(5*(x)+4*y+6*z)^3*(5*(x)-4*y-6*z)^4 ) div 8 in I > Output: Magma V2.10-22 Thu Apr 1 2004 03:49:24 on modular [Seed = 2292391687] ------------------------------------- [ 5*x^2*y + 20*x^2*z + 80*y^3 + 128*y^2*z + 180*y*z^2 + 288*z^3, 25*x^2 + 16*y^2 + 36*z^2, 8*x*y^3 + 12*x*y^2*z + 8*x*y*z^2 + 12*x*z^3, 40*x*y + 60*x*z, 128*y^3 + 192*y^2*z + 288*y*z^2 + 432*z^3 ] false Total time: 2.510 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Thu Apr 1 03:49:51 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > ( (5*(x)+4*y+6*z)^15+15*(5*(x)+4*y+6*z)^7*(5*(x)-4*y-6*z)^8 ) div 16 in I > Output: Magma V2.10-22 Thu Apr 1 2004 03:49:48 on modular [Seed = 2158696247] ------------------------------------- [ 5*x^2*y + 20*x^2*z + 80*y^3 + 128*y^2*z + 180*y*z^2 + 288*z^3, 25*x^2 + 16*y^2 + 36*z^2, 8*x*y^3 + 12*x*y^2*z + 8*x*y*z^2 + 12*x*z^3, 40*x*y + 60*x*z, 128*y^3 + 192*y^2*z + 288*y*z^2 + 432*z^3 ] false Total time: 2.509 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Thu Apr 1 03:50:48 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > ( (5*(x)+4*y+6*z)^15+15*(5*(x)+4*y+6*z)^7*(5*(x)-4*y-6*z)^8 ) div 16 in I > Output: Magma V2.10-22 Thu Apr 1 2004 03:50:45 on modular [Seed = 2962958158] ------------------------------------- [ x^2*y*z^4 + x^2*z^5 + 16*y^2*z^5 + 36*y*z^6 + 900*z^7, 5*x^2*y + 20*x^2*z + 80*y^3 + 32*y^2*z + 36*y*z^2 + 288*z^3, 5*x^2*z^2 + 32*y^2*z^2 + 1044*z^4, 25*x^2 + 16*y^2 + 36*z^2, 8*x*y^3 + 4*x*y^2*z + 4*x*y*z^2 + 132*x*z^3, 4*x*y*z^4 + 24*x*z^5, 8*x*y*z + 300*x*z^2, 40*x*y + 60*x*z, 36*x*z^4, 180*x*z^3, 360*x*z^2, 16*y^3*z + 864*z^4, 128*y^3 + 432*z^3, 48*y*z, 1296*z^4 ] true Total time: 2.559 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (203.214.70.203) Time: Thu Apr 1 05:52:33 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-22 Thu Apr 1 2004 05:52:30 on modular [Seed = 2259497718] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.550 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 2(SERVFAIL) (203.214.70.203) Time: Thu Apr 1 05:52:41 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-22 Thu Apr 1 2004 05:52:38 on modular [Seed = 2175415785] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.509 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 2(SERVFAIL) (203.214.70.203) Time: Thu Apr 1 05:53:17 2004 Input: extgcd(100,3); Output: Magma V2.10-22 Thu Apr 1 2004 05:53:15 on modular [Seed = 3113356604] ------------------------------------- >> extgcd(100,3);; ^ User error: Identifier 'extgcd' has not been declared or assigned Total time: 2.560 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 2(SERVFAIL) (203.214.70.203) Time: Thu Apr 1 05:53:42 2004 Input: ?extgcd Output: Magma V2.10-22 Thu Apr 1 2004 05:53:39 on modular [Seed = 2979661084] ------------------------------------- No references for word "extgcd" Total time: 2.549 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 2(SERVFAIL) (203.214.70.203) Time: Thu Apr 1 05:54:23 2004 Input: ?gcd Output: Magma V2.10-22 Thu Apr 1 2004 05:54:20 on modular [Seed = 2843876715] ------------------------------------- 53 matches: 1 S /magma/ring-field-algebra/distributive-multivariate-polynomial/\ common/gcd-lcm 2 S /magma/ring-field-algebra/integer/gcd-lcm 3 S /magma/ring-field-algebra/univariate-polynomial/common/gcd-lcm 4 I /magma/geometry/algebraic-curve/divisors/divisor-arithmetic/\ divisors-coeff-arith/GCD 5 I /magma/geometry/algebraic-curve/divisors/divisor-arithmetic/\ divisors-coeff-arith/GCD 6 I /magma/geometry/algebraic-curve/divisors/divisor-arithmetic/\ divisors-coeff-arith/GCD 7 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ LeftGCD 8 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ LeftGCD 9 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ LeftGCD 10 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ LeftGCD 11 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ LeftGCD 12 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ LeftGCD 13 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ LeftGCD 14 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ LeftGCD 15 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ LeftGCD 16 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ RightGCD 17 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ RightGCD 18 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ RightGCD 19 I /magma/group/braid/braid-groups-elements/braid-groups-lattice/\ RightGCD 20 I /magma/ring-field-algebra/algebraic-field/ideal/ideal-arithmetic/\ GCD 21 I /magma/ring-field-algebra/algebraic-field/ideal/ideal-arithmetic/\ GCD 22 I /magma/ring-field-algebra/algebraic-field/ideal/ideal-arithmetic/\ GCD 23 I /magma/ring-field-algebra/detail/generic/predicate/HasGCD 24 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ common/gcd-lcm/GCD 25 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ common/gcd-lcm/GCD 26 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ common/gcd-lcm/GreatestCommonDivisor 27 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ common/gcd-lcm/GreatestCommonDivisor 28 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ common/gcd-lcm/GreatestCommonDivisor 29 I /magma/ring-field-algebra/function-field/Divisors/\ operation-element/arithmetic/GCD 30 I /magma/ring-field-algebra/function-field/Divisors/\ operation-element/arithmetic/GCD 31 I /magma/ring-field-algebra/function-field/ideals/\ ideal-ops-further/Gcd 32 I /magma/ring-field-algebra/integer/gcd-lcm/Gcd 33 I /magma/ring-field-algebra/integer/gcd-lcm/Gcd 34 I /magma/ring-field-algebra/integer/gcd-lcm/Gcd 35 I /magma/ring-field-algebra/integer/gcd-lcm/GreatestCommonDivisor 36 I /magma/ring-field-algebra/integer/gcd-lcm/GreatestCommonDivisor 37 I /magma/ring-field-algebra/integer/gcd-lcm/GreatestCommonDivisor 38 I /magma/ring-field-algebra/integer/residue-class-rings/ideal/\ GreatestCommonDivisor 39 I /magma/ring-field-algebra/integer/residue-class-rings/ideal/\ GreatestCommonDivisor 40 I /magma/ring-field-algebra/integer/residue-class-rings/ideal/\ GreatestCommonDivisor 41 I /magma/ring-field-algebra/integer/residue-class-rings/ideal/\ GreatestCommonDivisor 42 I /magma/ring-field-algebra/local/polynomials/operations/\ GreatestCommonDivisor 43 I /magma/ring-field-algebra/local/polynomials/operations/\ GreatestCommonDivisor 44 I /magma/ring-field-algebra/local/polynomials/operations/\ GreatestCommonDivisor 45 I /magma/ring-field-algebra/quadratic/elements/\ greatest-common-divisor/Gcd 46 I /magma/ring-field-algebra/quadratic/elements/\ greatest-common-divisor/Gcd 47 I /magma/ring-field-algebra/univariate-polynomial/common/gcd-lcm/\ GreatestCommonDivisor 48 I /magma/ring-field-algebra/univariate-polynomial/common/gcd-lcm/\ GreatestCommonDivisor 49 I /magma/ring-field-algebra/univariate-polynomial/common/gcd-lcm/\ GreatestCommonDivisor 50 I /magma/ring-field-algebra/valuation/element/other/\ GreatestCommonDivisor 51 I /magma/ring-field-algebra/valuation/element/other/\ GreatestCommonDivisor 52 I /magma/ring-field-algebra/valuation/element/other/\ GreatestCommonDivisor 53 E /magma/ring-field-algebra/local/polynomials/operations/Example-gcd To view an entry, type ? followed by the number next to it Total time: 2.559 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 2(SERVFAIL) (203.214.70.203) Time: Thu Apr 1 05:55:54 2004 Input: gcd(100,2); Output: Magma V2.10-22 Thu Apr 1 2004 05:55:51 on modular [Seed = 3673255923] ------------------------------------- >> gcd(100,2);; ^ User error: Identifier 'gcd' has not been declared or assigned Total time: 2.549 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 2(SERVFAIL) (203.214.70.203) Time: Thu Apr 1 05:56:12 2004 Input: gcd(100,2); Output: Magma V2.10-22 Thu Apr 1 2004 05:56:10 on modular [Seed = 3539560326] ------------------------------------- >> gcd(100,2);; ^ User error: Identifier 'gcd' has not been declared or assigned Total time: 2.550 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 2(SERVFAIL) (203.214.70.203) Time: Thu Apr 1 05:56:33 2004 Input: Gcd(100,2); Output: Magma V2.10-22 Thu Apr 1 2004 05:56:30 on modular [Seed = 3403775882] ------------------------------------- 2 Total time: 2.550 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 2(SERVFAIL) (203.214.70.203) Time: Thu Apr 1 05:57:59 2004 Input: ExtGcd(100,2); Output: Magma V2.10-22 Thu Apr 1 2004 05:57:56 on modular [Seed = 3286791785] ------------------------------------- >> ExtGcd(100,2);; ^ User error: Identifier 'ExtGcd' has not been declared or assigned Total time: 2.580 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 2(SERVFAIL) (203.214.70.203) Time: Thu Apr 1 05:58:11 2004 Input: ?ExtGcd(100,2); Output: Magma V2.10-22 Thu Apr 1 2004 05:58:09 on modular [Seed = 4224732708] ------------------------------------- No references for word "ExtGcd(100,2);" Total time: 2.509 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 2(SERVFAIL) (203.214.70.203) Time: Thu Apr 1 05:58:23 2004 Input: ?ExtGcd Output: Magma V2.10-22 Thu Apr 1 2004 05:58:21 on modular [Seed = 4091037216] ------------------------------------- No references for word "ExtGcd" Total time: 2.559 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 2(SERVFAIL) (203.214.70.203) Time: Thu Apr 1 05:58:37 2004 Input: ?ExactGcd Output: Magma V2.10-22 Thu Apr 1 2004 05:58:35 on modular [Seed = 3955252782] ------------------------------------- No references for word "ExactGcd" Total time: 2.559 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 2(SERVFAIL) (203.214.70.203) Time: Thu Apr 1 05:59:44 2004 Input: ?Exact Output: Magma V2.10-22 Thu Apr 1 2004 05:59:41 on modular [Seed = 3771422435] ------------------------------------- 25 matches: 1 I /magma/geometry/algebraic-curve/function_field/ff-diff/\ ff-diff-element-operations/IsExact 2 I /magma/group/GrpPSL2/upper-plane/predicates/ExactValue 3 I /magma/group/GrpPSL2/upper-plane/predicates/IsExact 4 I /magma/module-lattice/complexes/chainmaps/homologymaps/\ LongExactSequenceOnHomology 5 I /magma/module-lattice/complexes/chainmaps/Predicates/\ IsShortExactSequence 6 I /magma/module-lattice/complexes/complexes/extensions/\ ExactExtension 7 I /magma/module-lattice/complexes/complexes/extensions/\ LeftExactExtension 8 I /magma/module-lattice/complexes/complexes/extensions/\ RightExactExtension 9 I /magma/module-lattice/complexes/complexes/predicates/IsExact 10 I /magma/module-lattice/complexes/complexes/predicates/IsExact 11 I /magma/module-lattice/complexes/complexes/predicates/\ IsShortExactSequence 12 I /magma/module-lattice/lattice/lattice-properties/\ lattice-predicates/IsExact 13 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ operation-element/division/div 14 I /magma/ring-field-algebra/function-field/class-fields/properties/\ DegreeOfExactConstantField 15 I /magma/ring-field-algebra/function-field/class-fields/properties/\ DegreeOfExactConstantField 16 I /magma/ring-field-algebra/function-field/differentials/elt-ops/\ elt-pred/IsExact 17 I /magma/ring-field-algebra/function-field/Divisors/\ divisor-class-group/ClassGroupExactSequence 18 I /magma/ring-field-algebra/function-field/Divisors/\ divisor-class-group/SClassGroupExactSequence 19 I /magma/ring-field-algebra/function-field/global/\ ClassGroupExactSequence 20 I /magma/ring-field-algebra/function-field/structure-invar/\ DimensionOfExactConstantField 21 I /magma/ring-field-algebra/function-field/structure-invar/\ DimensionOfExactConstantField 22 I /magma/ring-field-algebra/function-field/structure-related/\ structure-related-other/ExactConstantField 23 I /magma/ring-field-algebra/integer/operation-element/arithmetic/\ ExactQuotient 24 I /magma/ring-field-algebra/real-complex/operation-element/roots/\ RootsNonExact 25 I /magma/ring-field-algebra/univariate-polynomial/\ operation-element/division/ExactQuotient To view an entry, type ? followed by the number next to it Total time: 2.559 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host ibmws6215.bc.edu. (136.167.76.227) Time: Thu Apr 1 09:53:40 2004 Input: 2+3 Output: Magma V2.10-22 Thu Apr 1 2004 09:53:37 on modular [Seed = 1248208537] ------------------------------------- 5 Total time: 2.629 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 11:46:58 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-22 Thu Apr 1 2004 11:46:53 on modular [Seed = 890843756] ------------------------------------- x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1 Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 Total time: 2.939 seconds, Total memory usage: 6.59MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 11:49:02 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1; print(f^2); print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-22 Thu Apr 1 2004 11:48:59 on modular [Seed = 1041381857] ------------------------------------- x^12 + 4*x^11 + 4*x^10 + (2*t + 2)*x^9 + (4*t + 4)*x^8 + x^7 + (t^2 + 2*t)*x^6 + 4*x^5 + (t + 1)*x^4 + (2*t + 2)*x^3 + 4*x^2 + x + 1 x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1 Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 Total time: 2.979 seconds, Total memory usage: 6.59MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 11:51:10 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1; print(f^2); print(f); q=[[1,2][3,4]]; print(q^2); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-22 Thu Apr 1 2004 11:51:07 on modular [Seed = 220267858] ------------------------------------- x^12 + 4*x^11 + 4*x^10 + (2*t + 2)*x^9 + (4*t + 4)*x^8 + x^7 + (t^2 + 2*t)*x^6 + 4*x^5 + (t + 1)*x^4 + (2*t + 2)*x^3 + 4*x^2 + x + 1 x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1 >> q=[[1,2][3,4]]; ^ User error: Identifier 'q' has not been declared or assigned >> print(q^2); ^ User error: Identifier 'q' has not been declared or assigned Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 Total time: 2.889 seconds, Total memory usage: 6.59MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 11:51:23 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1; print(f^2); print(f); q:=[[1,2][3,4]]; print(q^2); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-22 Thu Apr 1 2004 11:51:20 on modular [Seed = 356064697] ------------------------------------- x^12 + 4*x^11 + 4*x^10 + (2*t + 2)*x^9 + (4*t + 4)*x^8 + x^7 + (t^2 + 2*t)*x^6 + 4*x^5 + (t + 1)*x^4 + (2*t + 2)*x^3 + 4*x^2 + x + 1 x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1 >> q:=[[1,2][3,4]]; ^ Runtime error in '[]': Sequence element 3 not defined >> print(q^2); ^ User error: Identifier 'q' has not been declared or assigned Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 Total time: 2.900 seconds, Total memory usage: 6.59MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 11:51:33 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1; print(f^2); print(f); q:=[[1,2],[3,4]]; print(q^2); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-22 Thu Apr 1 2004 11:51:30 on modular [Seed = 489756075] ------------------------------------- x^12 + 4*x^11 + 4*x^10 + (2*t + 2)*x^9 + (4*t + 4)*x^8 + x^7 + (t^2 + 2*t)*x^6 + 4*x^5 + (t + 1)*x^4 + (2*t + 2)*x^3 + 4*x^2 + x + 1 x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1 >> print(q^2); ^ Runtime error in '^': Bad argument types Argument types given: SeqEnum[SeqEnum], RngIntElt Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 Total time: 2.929 seconds, Total memory usage: 6.59MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 11:56:58 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1; print(f^2); print(f); q:=elt; print(q^2); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-22 Thu Apr 1 2004 11:56:55 on modular [Seed = 1649306513] ------------------------------------- x^12 + 4*x^11 + 4*x^10 + (2*t + 2)*x^9 + (4*t + 4)*x^8 + x^7 + (t^2 + 2*t)*x^6 + 4*x^5 + (t + 1)*x^4 + (2*t + 2)*x^3 + 4*x^2 + x + 1 x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1 [1 2] [0 1] Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 Total time: 3.000 seconds, Total memory usage: 6.59MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 12:00:15 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1; print(f^2); print(f); q:=elt; p:=elt; print(q^2); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-22 Thu Apr 1 2004 12:00:12 on modular [Seed = 2085648068] ------------------------------------- x^12 + 4*x^11 + 4*x^10 + (2*t + 2)*x^9 + (4*t + 4)*x^8 + x^7 + (t^2 + 2*t)*x^6 + 4*x^5 + (t + 1)*x^4 + (2*t + 2)*x^3 + 4*x^2 + x + 1 x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1 [2*t^2 + 4*t + 2 4*t^2 + 3*t + 4] [ 3*t^2 + t + 3 3*t^2 + t + 3] Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 Total time: 2.879 seconds, Total memory usage: 6.60MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 12:00:28 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1; print(f^2); print(f); q:=elt; p:=elt; print(q*p); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-22 Thu Apr 1 2004 12:00:25 on modular [Seed = 1147686601] ------------------------------------- x^12 + 4*x^11 + 4*x^10 + (2*t + 2)*x^9 + (4*t + 4)*x^8 + x^7 + (t^2 + 2*t)*x^6 + 4*x^5 + (t + 1)*x^4 + (2*t + 2)*x^3 + 4*x^2 + x + 1 x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1 [ 2*t^6 + 2*t^5 + t + 1 4*t^6 + 4*t^5 + 4*t + 4] [3*t^6 + 3*t^5 + 4*t + 4 3*t^6 + 3*t^5 + 3*t + 3] Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 Total time: 2.949 seconds, Total memory usage: 6.60MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 12:01:58 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1; print(f^2); print(f); q:=elt; p:=elt; print(q*p); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-22 Thu Apr 1 2004 12:01:55 on modular [Seed = 1584551289] ------------------------------------- x^12 + 4*x^11 + 4*x^10 + (2*t + 2)*x^9 + (4*t + 4)*x^8 + x^7 + (t^2 + 2*t)*x^6 + 4*x^5 + (t + 1)*x^4 + (2*t + 2)*x^3 + 4*x^2 + x + 1 x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1 >> p:=elt; ^ User error: bad syntax >> print(q*p); ^ User error: Identifier 'p' has not been declared or assigned Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 Total time: 3.000 seconds, Total memory usage: 6.59MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 12:02:08 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1; print(f^2); print(f); q:=elt; p:=elt; print(q*p); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-22 Thu Apr 1 2004 12:02:05 on modular [Seed = 2794106255] ------------------------------------- x^12 + 4*x^11 + 4*x^10 + (2*t + 2)*x^9 + (4*t + 4)*x^8 + x^7 + (t^2 + 2*t)*x^6 + 4*x^5 + (t + 1)*x^4 + (2*t + 2)*x^3 + 4*x^2 + x + 1 x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1 [0 0] [0 0] Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 Total time: 2.899 seconds, Total memory usage: 6.60MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 12:04:56 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1; print(f^2); print(f); q:=elt; p:=elt; print(q); print(q*p); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-22 Thu Apr 1 2004 12:04:52 on modular [Seed = 2409858079] ------------------------------------- x^12 + 4*x^11 + 4*x^10 + (2*t + 2)*x^9 + (4*t + 4)*x^8 + x^7 + (t^2 + 2*t)*x^6 + 4*x^5 + (t + 1)*x^4 + (2*t + 2)*x^3 + 4*x^2 + x + 1 x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1 [ t + 1 2*t + 2] [2*t + 2 4*t + 4] [0 0] [0 0] Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 Total time: 3.269 seconds, Total memory usage: 6.60MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 12:09:41 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6 + 4*x^5 + 4*(t+1)*x^3 + 2* (t+1)*x^2 + 2*t*x + 4*t + 1 print(f^2); q:=elt; p:=elt; print(q); print(q*p); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-22 Thu Apr 1 2004 12:09:39 on modular [Seed = 3822055188] ------------------------------------- >> print(f^2); ^ User error: bad syntax [ t + 1 2*t + 2] [2*t + 2 4*t + 4] [0 0] [0 0] >> G, R:= GaloisGroup(f); ^ User error: Identifier 'f' has not been declared or assigned >> print(G); ^ User error: Identifier 'G' has not been declared or assigned >> t1, t2:= TransitiveGroupIdentification(G); ^ User error: Identifier 'G' has not been declared or assigned >> print(t1); ^ User error: Identifier 't1' has not been declared or assigned >> print(t2);; ^ User error: Identifier 't2' has not been declared or assigned Total time: 2.520 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 12:09:51 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6 + 4*x^5 + 4*(t+1)*x^3 + 2* (t+1)*x^2 + 2*t*x + 4*t + 1; print(f^2); q:=elt; p:=elt; print(q); print(q*p); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-22 Thu Apr 1 2004 12:09:48 on modular [Seed = 3955746579] ------------------------------------- x^12 + 3*x^11 + x^10 + (3*t + 3)*x^9 + (t + 1)*x^8 + x^7 + (t^2 + t + 3)*x^6 + (t^2 + 4*t + 4)*x^5 + (4*t + 4)*x^4 + (3*t + 3)*x^3 + 4*x^2 + (t^2 + 4*t)*x + t^2 + 3*t + 1 [ t + 1 2*t + 2] [2*t + 2 4*t + 4] [0 0] [0 0] Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 Total time: 2.929 seconds, Total memory usage: 6.60MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 12:12:16 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6 + 4*x^5 + 4*(t+1)*x^3 + 2* (t+1)*x^2 + 2*t*x + 4*t + 1; f2=f^2; print(f2[3]); print(f^2); q:=elt; p:=elt; print(q); print(q*p); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-22 Thu Apr 1 2004 12:12:13 on modular [Seed = 4208392115] ------------------------------------- >> f2=f^2; ^ User error: Identifier 'f2' has not been declared or assigned >> print(f2[3]); ^ User error: Identifier 'f2' has not been declared or assigned x^12 + 3*x^11 + x^10 + (3*t + 3)*x^9 + (t + 1)*x^8 + x^7 + (t^2 + t + 3)*x^6 + (t^2 + 4*t + 4)*x^5 + (4*t + 4)*x^4 + (3*t + 3)*x^3 + 4*x^2 + (t^2 + 4*t)*x + t^2 + 3*t + 1 [ t + 1 2*t + 2] [2*t + 2 4*t + 4] [0 0] [0 0] Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 Total time: 2.900 seconds, Total memory usage: 6.60MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 12:12:26 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6 + 4*x^5 + 4*(t+1)*x^3 + 2* (t+1)*x^2 + 2*t*x + 4*t + 1; f2:=f^2; print(f2[3]); print(f^2); q:=elt; p:=elt; print(q); print(q*p); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-22 Thu Apr 1 2004 12:12:23 on modular [Seed = 3270430609] ------------------------------------- >> print(f2[3]); ^ Runtime error in '[]': Bad argument types x^12 + 3*x^11 + x^10 + (3*t + 3)*x^9 + (t + 1)*x^8 + x^7 + (t^2 + t + 3)*x^6 + (t^2 + 4*t + 4)*x^5 + (4*t + 4)*x^4 + (3*t + 3)*x^3 + 4*x^2 + (t^2 + 4*t)*x + t^2 + 3*t + 1 [ t + 1 2*t + 2] [2*t + 2 4*t + 4] [0 0] [0 0] Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 Total time: 2.970 seconds, Total memory usage: 6.60MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 12:12:43 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6 + 4*x^5 + 4*(t+1)*x^3 + 2* (t+1)*x^2 + 2*t*x + 4*t + 1; f2:=f^2; print(coeff(f2, 3)); print(f^2); q:=elt; p:=elt; print(q); print(q*p); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-22 Thu Apr 1 2004 12:12:40 on modular [Seed = 3404121958] ------------------------------------- >> print(coeff(f2, 3)); ^ User error: Identifier 'coeff' has not been declared or assigned x^12 + 3*x^11 + x^10 + (3*t + 3)*x^9 + (t + 1)*x^8 + x^7 + (t^2 + t + 3)*x^6 + (t^2 + 4*t + 4)*x^5 + (4*t + 4)*x^4 + (3*t + 3)*x^3 + 4*x^2 + (t^2 + 4*t)*x + t^2 + 3*t + 1 [ t + 1 2*t + 2] [2*t + 2 4*t + 4] [0 0] [0 0] Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 Total time: 2.879 seconds, Total memory usage: 6.60MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 12:13:44 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6 + 4*x^5 + 4*(t+1)*x^3 + 2* (t+1)*x^2 + 2*t*x + 4*t + 1; f2:=f^2; print(Coeffinient(f2, 3)); print(f^2); q:=elt; p:=elt; print(q); print(q*p); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-22 Thu Apr 1 2004 12:13:41 on modular [Seed = 3556761137] ------------------------------------- >> print(Coeffinient(f2, 3)); ^ User error: Identifier 'Coeffinient' has not been declared or assigned x^12 + 3*x^11 + x^10 + (3*t + 3)*x^9 + (t + 1)*x^8 + x^7 + (t^2 + t + 3)*x^6 + (t^2 + 4*t + 4)*x^5 + (4*t + 4)*x^4 + (3*t + 3)*x^3 + 4*x^2 + (t^2 + 4*t)*x + t^2 + 3*t + 1 [ t + 1 2*t + 2] [2*t + 2 4*t + 4] [0 0] [0 0] Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 Total time: 2.879 seconds, Total memory usage: 6.60MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 12:13:51 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6 + 4*x^5 + 4*(t+1)*x^3 + 2* (t+1)*x^2 + 2*t*x + 4*t + 1; f2:=f^2; print(Coefficient(f2, 3)); print(f^2); q:=elt; p:=elt; print(q); print(q*p); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-22 Thu Apr 1 2004 12:13:48 on modular [Seed = 3690452531] ------------------------------------- 3*t + 3 x^12 + 3*x^11 + x^10 + (3*t + 3)*x^9 + (t + 1)*x^8 + x^7 + (t^2 + t + 3)*x^6 + (t^2 + 4*t + 4)*x^5 + (4*t + 4)*x^4 + (3*t + 3)*x^3 + 4*x^2 + (t^2 + 4*t)*x + t^2 + 3*t + 1 [ t + 1 2*t + 2] [2*t + 2 4*t + 4] [0 0] [0 0] Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 Total time: 2.930 seconds, Total memory usage: 6.60MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 12:17:32 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6 + 4*x^5 + 4*(t+1)*x^3 + 2* (t+1)*x^2 + 2*t*x + 4*t + 1; f2:=f^2; print(Coefficient(f2, 3)); print(f^2); c3:=Coefficient(f2, 3); c4:=Coefficient(f2, 4); c8:=Coefficient(f2, 8); c9:=Coefficient(f2, 9); m:=elt; n:=elt; print(m); print(m*n); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-22 Thu Apr 1 2004 12:17:29 on modular [Seed = 771891362] ------------------------------------- 3*t + 3 x^12 + 3*x^11 + x^10 + (3*t + 3)*x^9 + (t + 1)*x^8 + x^7 + (t^2 + t + 3)*x^6 + (t^2 + 4*t + 4)*x^5 + (4*t + 4)*x^4 + (3*t + 3)*x^3 + 4*x^2 + (t^2 + 4*t)*x + t^2 + 3*t + 1 [4*t + 4 3*t + 3] [3*t + 3 t + 1] [0 0] [0 0] Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 Total time: 2.929 seconds, Total memory usage: 6.60MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 12:17:57 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6 + 4*x^5 + 4*(t+1)*x^3 + 2* (t+1)*x^2 + 2*t*x + 4*t + 1; f2:=f^2; c3:=Coefficient(f2, 3); c4:=Coefficient(f2, 4); c8:=Coefficient(f2, 8); c9:=Coefficient(f2, 9); m:=elt; n:=elt; print(m); print(m*n); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-22 Thu Apr 1 2004 12:17:54 on modular [Seed = 824000470] ------------------------------------- [4*t + 4 3*t + 3] [3*t + 3 t + 1] [0 0] [0 0] Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 Total time: 2.929 seconds, Total memory usage: 6.60MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 12:30:40 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); x^6 + 2*x^5 + (t+2)*x^3 + 3*x + 1; f2:=f^2; c3:=Coefficient(f2, 3); c4:=Coefficient(f2, 4); c8:=Coefficient(f2, 8); c9:=Coefficient(f2, 9); m:=elt; n:=elt; print(m); print(m*n); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-22 Thu Apr 1 2004 12:30:37 on modular [Seed = 356058253] ------------------------------------- x^6 + 2*x^5 + (t + 2)*x^3 + 3*x + 1 >> f2:=f^2; ^ User error: Identifier 'f' has not been declared or assigned >> c3:=Coefficient(f2, 3); ^ User error: Identifier 'f2' has not been declared or assigned >> c4:=Coefficient(f2, 4); ^ User error: Identifier 'f2' has not been declared or assigned >> c8:=Coefficient(f2, 8); ^ User error: Identifier 'f2' has not been declared or assigned >> c9:=Coefficient(f2, 9); ^ User error: Identifier 'f2' has not been declared or assigned >> m:=elt; ^ User error: Identifier 'c4' has not been declared or assigned >> n:=elt; ^ User error: Identifier 'c4' has not been declared or assigned >> print(m); ^ User error: Identifier 'm' has not been declared or assigned >> print(m*n); ^ User error: Identifier 'm' has not been declared or assigned >> G, R:= GaloisGroup(f); ^ User error: Identifier 'f' has not been declared or assigned >> print(G); ^ User error: Identifier 'G' has not been declared or assigned >> t1, t2:= TransitiveGroupIdentification(G); ^ User error: Identifier 'G' has not been declared or assigned >> print(t1); ^ User error: Identifier 't1' has not been declared or assigned >> print(t2);; ^ User error: Identifier 't2' has not been declared or assigned Total time: 2.559 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 12:30:51 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6 + 2*x^5 + (t+2)*x^3 + 3*x + 1; f2:=f^2; c3:=Coefficient(f2, 3); c4:=Coefficient(f2, 4); c8:=Coefficient(f2, 8); c9:=Coefficient(f2, 9); m:=elt; n:=elt; print(m); print(m*n); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-22 Thu Apr 1 2004 12:30:48 on modular [Seed = 489753840] ------------------------------------- [ t + 2 2*t + 4] [2*t + 4 4*t + 3] [0 0] [0 0] Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 Total time: 3.009 seconds, Total memory usage: 6.60MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 12:36:25 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6 + 2*x^5 + (t+2)*x^3 + 3*x + 1; f2:=f^2; c3:=Coefficient(f2, 3); c4:=Coefficient(f2, 4); c8:=Coefficient(f2, 8); c9:=Coefficient(f2, 9); m:=elt; n:=elt; print(m); print(m*n); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-22 Thu Apr 1 2004 12:36:22 on modular [Seed = 1816166239] ------------------------------------- [ t + 2 2*t + 4] [2*t + 4 4*t + 3] [0 0] [0 0] Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 Total time: 2.869 seconds, Total memory usage: 6.60MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 12:36:42 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6 + 2*x^5 + (t+2)*x^3 + 3*x + 1; f2:=f^2; c3:=Coefficient(f2, 3); c4:=Coefficient(f2, 4); c8:=Coefficient(f2, 8); c9:=Coefficient(f2, 9); m:=elt; n:=elt; print(m*n); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-22 Thu Apr 1 2004 12:36:39 on modular [Seed = 1951950710] ------------------------------------- [0 0] [0 0] Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 Total time: 2.959 seconds, Total memory usage: 6.60MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 12:36:55 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6 + 2*x^5 + (t+2)*x^3 + 3*x + 1; print(f); f2:=f^2; c3:=Coefficient(f2, 3); c4:=Coefficient(f2, 4); c8:=Coefficient(f2, 8); c9:=Coefficient(f2, 9); m:=elt; n:=elt; print(m*n); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-22 Thu Apr 1 2004 12:36:52 on modular [Seed = 2085646189] ------------------------------------- x^6 + 2*x^5 + (t + 2)*x^3 + 3*x + 1 [0 0] [0 0] Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 Total time: 2.880 seconds, Total memory usage: 6.60MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 12:37:23 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6 + 2*x^5 + (t+1)*x^3 + 3*x + 1; print(f); f2:=f^2; c3:=Coefficient(f2, 3); c4:=Coefficient(f2, 4); c8:=Coefficient(f2, 8); c9:=Coefficient(f2, 9); m:=elt; n:=elt; print(m*n); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-22 Thu Apr 1 2004 12:37:20 on modular [Seed = 1147688753] ------------------------------------- x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1 [0 0] [0 0] Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 Total time: 2.890 seconds, Total memory usage: 6.60MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 12:37:39 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6 - x^5 - (t + 1)*x^3 + 2*(t+1)*x^2 + 2*t*x + (1-t); print(f); f2:=f^2; c3:=Coefficient(f2, 3); c4:=Coefficient(f2, 4); c8:=Coefficient(f2, 8); c9:=Coefficient(f2, 9); m:=elt; n:=elt; print(m*n); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-22 Thu Apr 1 2004 12:37:36 on modular [Seed = 1281384201] ------------------------------------- x^6 + 4*x^5 + (4*t + 4)*x^3 + (2*t + 2)*x^2 + 2*t*x + 4*t + 1 [0 0] [0 0] Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 Total time: 2.940 seconds, Total memory usage: 6.60MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 12:40:23 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6 - x^5 - (1)*x^3 + 2*(1)*x^2 + 2*x + (1); print(f); f2:=f^2; c3:=Coefficient(f2, 3); c4:=Coefficient(f2, 4); c8:=Coefficient(f2, 8); c9:=Coefficient(f2, 9); m:=elt; n:=elt; print(m*n); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-22 Thu Apr 1 2004 12:40:21 on modular [Seed = 1550862460] ------------------------------------- x^6 + 4*x^5 + 4*x^3 + 2*x^2 + 2*x + 1 [3 1] [3 4] >> G, R:= GaloisGroup(f); ^ Runtime error in 'GaloisGroup': Argument 1 is not irreducible >> print(G); ^ User error: Identifier 'G' has not been declared or assigned >> t1, t2:= TransitiveGroupIdentification(G); ^ User error: Identifier 'G' has not been declared or assigned >> print(t1); ^ User error: Identifier 't1' has not been declared or assigned >> print(t2);; ^ User error: Identifier 't2' has not been declared or assigned Total time: 2.530 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 12:40:32 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6 - x^5 - (1)*x^3 + 3*(1)*x^2 + 2*x + (1); print(f); f2:=f^2; c3:=Coefficient(f2, 3); c4:=Coefficient(f2, 4); c8:=Coefficient(f2, 8); c9:=Coefficient(f2, 9); m:=elt; n:=elt; print(m*n); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-22 Thu Apr 1 2004 12:40:29 on modular [Seed = 2760421516] ------------------------------------- x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 [0 0] [4 4] >> G, R:= GaloisGroup(f); ^ Runtime error in 'GaloisGroup': Argument 1 is not irreducible >> print(G); ^ User error: Identifier 'G' has not been declared or assigned >> t1, t2:= TransitiveGroupIdentification(G); ^ User error: Identifier 'G' has not been declared or assigned >> print(t1); ^ User error: Identifier 't1' has not been declared or assigned >> print(t2);; ^ User error: Identifier 't2' has not been declared or assigned Total time: 2.570 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 12:44:17 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6 - x^5 - (1)*x^3 + 3*(1)*x^2 + 2*x + (1); print(f); if (isIrreducible(f)) { f2:=f^2; c3:=Coefficient(f2, 3); c4:=Coefficient(f2, 4); c8:=Coefficient(f2, 8); c9:=Coefficient(f2, 9); m:=elt; n:=elt; print(m*n); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); } Output: Magma V2.10-22 Thu Apr 1 2004 12:44:14 on modular [Seed = 2944645988] ------------------------------------- x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 >> if (isIrreducible(f)) { ^ User error: bad syntax [0 0] [4 4] >> G, R:= GaloisGroup(f); ^ Runtime error in 'GaloisGroup': Argument 1 is not irreducible >> print(G); ^ User error: Identifier 'G' has not been declared or assigned >> t1, t2:= TransitiveGroupIdentification(G); ^ User error: Identifier 'G' has not been declared or assigned >> print(t1); ^ User error: Identifier 't1' has not been declared or assigned >> print(t2); ^ User error: Identifier 't2' has not been declared or assigned >> } ^ User error: bad syntax Total time: 2.560 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 12:44:27 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6 - x^5 - (1)*x^3 + 3*(1)*x^2 + 2*x + (1); print(f); if (IsIrreducible(f)) { f2:=f^2; c3:=Coefficient(f2, 3); c4:=Coefficient(f2, 4); c8:=Coefficient(f2, 8); c9:=Coefficient(f2, 9); m:=elt; n:=elt; print(m*n); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); } Output: Magma V2.10-22 Thu Apr 1 2004 12:44:25 on modular [Seed = 3080430443] ------------------------------------- x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 >> if (IsIrreducible(f)) { ^ User error: bad syntax [0 0] [4 4] >> G, R:= GaloisGroup(f); ^ Runtime error in 'GaloisGroup': Argument 1 is not irreducible >> print(G); ^ User error: Identifier 'G' has not been declared or assigned >> t1, t2:= TransitiveGroupIdentification(G); ^ User error: Identifier 'G' has not been declared or assigned >> print(t1); ^ User error: Identifier 't1' has not been declared or assigned >> print(t2); ^ User error: Identifier 't2' has not been declared or assigned >> }; ^ User error: bad syntax Total time: 2.559 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 12:46:22 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6 - x^5 - (1)*x^3 + 3*(1)*x^2 + 2*x + (1); print(f); if IsIrreducible(f) then f2:=f^2; c3:=Coefficient(f2, 3); c4:=Coefficient(f2, 4); c8:=Coefficient(f2, 8); c9:=Coefficient(f2, 9); m:=elt; n:=elt; print(m*n); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); end if Output: Magma V2.10-22 Thu Apr 1 2004 12:46:19 on modular [Seed = 3147280117] ------------------------------------- x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 Total time: 2.530 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 12:47:00 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6 - x^5 - (1)*x^3 + 3*(1)*x^2 + 2*x + (1); print(f); if IsIrreducible(f) then f2:=f^2; c3:=Coefficient(f2, 3); c4:=Coefficient(f2, 4); c8:=Coefficient(f2, 8); c9:=Coefficient(f2, 9); m:=elt; n:=elt; print(m*n); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); else print(f "not irreducible"); end if; Output: Magma V2.10-22 Thu Apr 1 2004 12:46:57 on modular [Seed = 2376177721] ------------------------------------- x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 >> print(f "not irreducible"); ^ User error: bad syntax >> end if;; ^ User error: bad syntax Total time: 2.570 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 12:47:10 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6 - x^5 - (1)*x^3 + 3*(1)*x^2 + 2*x + (1); print(f); if IsIrreducible(f) then f2:=f^2; c3:=Coefficient(f2, 3); c4:=Coefficient(f2, 4); c8:=Coefficient(f2, 8); c9:=Coefficient(f2, 9); m:=elt; n:=elt; print(m*n); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); else print(f, "not irreducible"); end if; Output: Magma V2.10-22 Thu Apr 1 2004 12:47:07 on modular [Seed = 2511962155] ------------------------------------- x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 >> print(f, "not irreducible"); ^ Runtime error: No constructor provided for this type of object Total time: 2.629 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 12:47:53 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6 - x^5 - (1)*x^3 + 3*(1)*x^2 + 2*x + (1); print f; if IsIrreducible(f) then f2:=f^2; c3:=Coefficient(f2, 3); c4:=Coefficient(f2, 4); c8:=Coefficient(f2, 8); c9:=Coefficient(f2, 9); m:=elt; n:=elt; print(m*n); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); else print f, "not irreducible"; end if; Output: Magma V2.10-22 Thu Apr 1 2004 12:47:51 on modular [Seed = 2628815230] ------------------------------------- x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 not irreducible Total time: 2.569 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 12:48:55 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6 - x^5 - (1)*x^3 + 3*(1)*x^2 + 2*x + (1); print f; if IsIrreducible(f) then f2:=f^2; c3:=Coefficient(f2, 3); c4:=Coefficient(f2, 4); c8:=Coefficient(f2, 8); c9:=Coefficient(f2, 9); m:=elt; n:=elt; print(m*n); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); else print f "not irreducible"; end if; Output: Magma V2.10-22 Thu Apr 1 2004 12:48:52 on modular [Seed = 3838374597] ------------------------------------- x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 >> print f "not irreducible"; ^ User error: bad syntax >> end if;; ^ User error: bad syntax Total time: 2.559 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 12:49:05 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6 - x^5 - (1)*x^3 + 3*(1)*x^2 + 2*x + (1); print f; if IsIrreducible(f) then f2:=f^2; c3:=Coefficient(f2, 3); c4:=Coefficient(f2, 4); c8:=Coefficient(f2, 8); c9:=Coefficient(f2, 9); m:=elt; n:=elt; print(m*n); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); else print f cat "not irreducible"; end if; Output: Magma V2.10-22 Thu Apr 1 2004 12:49:03 on modular [Seed = 3972070086] ------------------------------------- x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 >> print f cat "not irreducible"; ^ Runtime error in 'cat': Bad argument types Argument types given: RngUPolElt, MonStgElt Total time: 2.550 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 12:50:16 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6 - x^5 - (1)*x^3 + 3*(1)*x^2 + 2*x + (1); print f; if IsIrreducible(f) then f2:=f^2; c3:=Coefficient(f2, 3); c4:=Coefficient(f2, 4); c8:=Coefficient(f2, 8); c9:=Coefficient(f2, 9); m:=elt; n:=elt; print(m*n); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); else print "f" cat "not irreducible"; end if; Output: Magma V2.10-22 Thu Apr 1 2004 12:50:14 on modular [Seed = 4258392974] ------------------------------------- x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 fnot irreducible Total time: 2.559 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 12:51:45 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6 - x^5 - (1)*x^3 + 3*(1)*x^2 + 2*x + (1); print f; if IsIrreducible(f) then f2:=f^2; c3:=Coefficient(f2, 3); c4:=Coefficient(f2, 4); c8:=Coefficient(f2, 8); c9:=Coefficient(f2, 9); m:=elt; n:=elt; print(m*n); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); else print PolynomialToString(f) cat "not irreducible"; end if; Output: Magma V2.10-22 Thu Apr 1 2004 12:51:42 on modular [Seed = 3320435534] ------------------------------------- x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 >> print PolynomialToString(f) cat "not irreducible"; ^ User error: Identifier 'PolynomialToString' has not been declared or assigned Total time: 2.529 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 12:52:18 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6 - x^5 - (1)*x^3 + 3*(1)*x^2 + 2*x + (1); print f; if IsIrreducible(f) then f2:=f^2; c3:=Coefficient(f2, 3); c4:=Coefficient(f2, 4); c8:=Coefficient(f2, 8); c9:=Coefficient(f2, 9); m:=elt; n:=elt; print(m*n); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); else print PolynomialToString(f) cat "not irreducible"; end if; Output: Magma V2.10-22 Thu Apr 1 2004 12:52:15 on modular [Seed = 3404127264] ------------------------------------- x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 >> print PolynomialToString(f) cat "not irreducible"; ^ User error: Identifier 'PolynomialToString' has not been declared or assigned Total time: 2.530 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 12:52:42 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6 - x^5 - (1)*x^3 + 3*(1)*x^2 + 2*x + (1); print f; if IsIrreducible(f) then f2:=f^2; c3:=Coefficient(f2, 3); c4:=Coefficient(f2, 4); c8:=Coefficient(f2, 8); c9:=Coefficient(f2, 9); m:=elt; n:=elt; print(m*n); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); else print ToString(f) cat "not irreducible"; end if; Output: Magma V2.10-22 Thu Apr 1 2004 12:52:39 on modular [Seed = 3539911696] ------------------------------------- x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 >> print ToString(f) cat "not irreducible"; ^ User error: Identifier 'ToString' has not been declared or assigned Total time: 2.510 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 13:05:16 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); S := [ P | ]; for a in S do for b in S do for c in S do f:=x^6 - x^5 - (1)*x^3 + 3*(1)*x^2 + 2*x + (1); print f; if IsIrreducible(f) then f2:=f^2; c3:=Coefficient(f2, 3); c4:=Coefficient(f2, 4); c8:=Coefficient(f2, 8); c9:=Coefficient(f2, 9); m:=elt; n:=elt; print(m*n); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); end if; end for; end for; end for; Output: Magma V2.10-22 Thu Apr 1 2004 13:05:14 on modular [Seed = 86580473] ------------------------------------- Total time: 2.529 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 13:05:29 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); S := [ P | ]; print S; for a in S do for b in S do for c in S do f:=x^6 - x^5 - (1)*x^3 + 3*(1)*x^2 + 2*x + (1); print f; if IsIrreducible(f) then f2:=f^2; c3:=Coefficient(f2, 3); c4:=Coefficient(f2, 4); c8:=Coefficient(f2, 8); c9:=Coefficient(f2, 9); m:=elt; n:=elt; print(m*n); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); end if; end for; end for; end for; Output: Magma V2.10-22 Thu Apr 1 2004 13:05:26 on modular [Seed = 220271821] ------------------------------------- [] Total time: 2.570 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 13:05:46 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); S := [ P | ]; Append(~S, 1); Append(~S, 2); print S; for a in S do for b in S do for c in S do f:=x^6 - x^5 - (1)*x^3 + 3*(1)*x^2 + 2*x + (1); print f; if IsIrreducible(f) then f2:=f^2; c3:=Coefficient(f2, 3); c4:=Coefficient(f2, 4); c8:=Coefficient(f2, 8); c9:=Coefficient(f2, 9); m:=elt; n:=elt; print(m*n); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); end if; end for; end for; end for; Output: Magma V2.10-22 Thu Apr 1 2004 13:05:43 on modular [Seed = 356060356] ------------------------------------- [ 1, 2 ] x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 Total time: 2.559 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 13:08:04 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); S := [ P | ]; for r in [0..4] do for s in [0..4] do Append(~S, r*t+s); end if; end if; print S; for a in S do for b in S do for c in S do f:=x^6 - x^5 - (1)*x^3 + 3*(1)*x^2 + 2*x + (1); print f; if IsIrreducible(f) then f2:=f^2; c3:=Coefficient(f2, 3); c4:=Coefficient(f2, 4); c8:=Coefficient(f2, 8); c9:=Coefficient(f2, 9); m:=elt; n:=elt; print(m*n); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); end if; end for; end for; end for; Output: Magma V2.10-22 Thu Apr 1 2004 13:08:02 on modular [Seed = 1716157634] ------------------------------------- >> end if; ^ User error: bad syntax >> end if; ^ User error: bad syntax [] Total time: 2.630 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 13:08:24 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); S := [ P | ]; for r in [0..4] do for s in [0..4] do Append(~S, r*t+s); end for; end for; print S; for a in S do for b in S do for c in S do f:=x^6 - x^5 - (1)*x^3 + 3*(1)*x^2 + 2*x + (1); print f; if IsIrreducible(f) then f2:=f^2; c3:=Coefficient(f2, 3); c4:=Coefficient(f2, 4); c8:=Coefficient(f2, 8); c9:=Coefficient(f2, 9); m:=elt; n:=elt; print(m*n); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); end if; end for; end for; end for; Output: Magma V2.10-22 Thu Apr 1 2004 13:08:12 on modular [Seed = 1849849028] ------------------------------------- [ 0, 1, 2, 3, 4, t, t + 1, t + 2, t + 3, t + 4, 2*t, 2*t + 1, 2*t + 2, 2*t + 3, 2*t + 4, 3*t, 3*t + 1, 3*t + 2, 3*t + 3, 3*t + 4, 4*t, 4*t + 1, 4*t + 2, 4*t + 3, 4*t + 4 ] x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + 1 x^6 + 4*x^5 + 4*x^3 + 3*x^2 + 2*x + ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 13:13:42 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); S := [ P | ]; for r in [0..4] do for s in [0..4] do Append(~S, r*t+s); end for; end for; print S; zeromat := elt; for a in S do for b in S do for c in S do f:=x^6 - x^5 - (1)*x^3 + 3*(1)*x^2 + 2*x + (1); if IsIrreducible(f) then continue; end if; f2:=f^2; c3:=Coefficient(f2, 3); c4:=Coefficient(f2, 4); c8:=Coefficient(f2, 8); c9:=Coefficient(f2, 9); m:=elt; n:=elt; if m*n != zeromat then continue; end if; G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); end if; end for; end for; end for; Output: Magma V2.10-22 Thu Apr 1 2004 13:13:40 on modular [Seed = 2102486671] ------------------------------------- [ 0, 1, 2, 3, 4, t, t + 1, t + 2, t + 3, t + 4, 2*t, 2*t + 1, 2*t + 2, 2*t + 3, 2*t + 4, 3*t, 3*t + 1, 3*t + 2, 3*t + 3, 3*t + 4, 4*t, 4*t + 1, 4*t + 2, 4*t + 3, 4*t + 4 ] >> if m*n != zeromat then ^ User error: bad syntax >> continue; ^ User error: A 'continue' can only be used inside a loop >> end if; ^ User error: bad syntax >> G, R:= GaloisGroup(f); ^ User error: Identifier 'f' has not been declared or assigned >> print(G); ^ User error: Identifier 'G' has not been declared or assigned >> t1, t2:= TransitiveGroupIdentification(G); ^ User error: Identifier 'G' has not been declared or assigned >> print(t1); ^ User error: Identifier 't1' has not been declared or assigned >> print(t2); ^ User error: Identifier 't2' has not been declared or assigned >> end if; ^ User error: bad syntax >> end for; ^ User error: bad syntax >> end for; ^ User error: bad syntax >> end for; ^ User error: bad syntax Total time: 2.519 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 13:14:50 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); S := [ P | ]; for r in [0..4] do for s in [0..4] do Append(~S, r*t+s); end for; end for; print S; zeromat := elt; for a in S do for b in S do for c in S do f:=x^6 - x^5 - (1)*x^3 + 3*(1)*x^2 + 2*x + 1; if not IsIrreducible(f) then continue; end if; f2:=f^2; c3:=Coefficient(f2, 3); c4:=Coefficient(f2, 4); c8:=Coefficient(f2, 8); c9:=Coefficient(f2, 9); m:=elt; n:=elt; if not (m*n eq zeromat) then continue; end if; G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); end if; end for; end for; end for; Output: Magma V2.10-22 Thu Apr 1 2004 13:14:47 on modular [Seed = 1164532084] ------------------------------------- [ 0, 1, 2, 3, 4, t, t + 1, t + 2, t + 3, t + 4, 2*t, 2*t + 1, 2*t + 2, 2*t + 3, 2*t + 4, 3*t, 3*t + 1, 3*t + 2, 3*t + 3, 3*t + 4, 4*t, 4*t + 1, 4*t + 2, 4*t + 3, 4*t + 4 ] >> end if; ^ User error: bad syntax >> end for; ^ User error: bad syntax >> end for; ^ User error: bad syntax >> end for;; ^ User error: bad syntax Total time: 2.510 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host sartre.math.psu.edu. (146.186.131.109) Time: Thu Apr 1 13:17:49 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); S := [ P | ]; for r in [0..4] do for s in [0..4] do Append(~S, r*t+s); end for; end for; zeromat := elt; for a in S do for b in S do for c in S do f:=x^6 - x^5 - (1)*x^3 + 3*(1)*x^2 + 2*x + 1; if not IsIrreducible(f) then continue; end if; f2:=f^2; c3:=Coefficient(f2, 3); c4:=Coefficient(f2, 4); c8:=Coefficient(f2, 8); c9:=Coefficient(f2, 9); m:=elt; n:=elt; if m*n ne zeromat then continue; end if; G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); end if; end for; end for; end for; Output: Magma V2.10-22 Thu Apr 1 2004 13:17:46 on modular [Seed = 1450855098] ------------------------------------- >> end if; ^ User error: bad syntax >> end for; ^ User error: bad syntax >> end for; ^ User error: bad syntax >> end for;; ^ User error: bad syntax Total time: 2.529 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host client-146-186-121-110.mobility-up.psu.edu. (146.186.121.110) Time: Thu Apr 1 14:42:38 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); S := [ P | ]; for r in [0..4] do for s in [0..4] do Append(~S, r*t+s); end for; end for; zeromat := elt; G, R := GaloisGroup(x^6 + 2*x^5 + (t+2)*x^3 + 3*x + 1); print(G); print(R); for a in S do for b in S do for c in S do f:=x^6 - x^5 - (1)*x^3 + 3*(1)*x^2 + 2*x + (1); if IsIrreducible(f) then continue; end if; f2:=f^2; c3:=Coefficient(f2, 3); c4:=Coefficient(f2, 4); c8:=Coefficient(f2, 8); c9:=Coefficient(f2, 9); m:=elt; n:=elt; if m*n != zeromat then continue; end if; G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); end if; end for; end for; end for; Output: Magma V2.10-22 Thu Apr 1 2004 14:42:35 on modular [Seed = 721886119] ------------------------------------- Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) [ w^572*$.1^7 + 3*$.1^6 + w^286*$.1^5 + $.1^3 + w^182*$.1^2 + w^364*$.1 + w^52, w^520*$.1^7 + 4*$.1^6 + w^364*$.1^5 + 4*$.1^3 + 2*$.1^2 + w^520*$.1 + w^364, w^121*$.1^7 + w^377*$.1^6 + w^65*$.1^5 + w^512*$.1^3 + w^207*$.1^2 + w^622*$.1 + w^94, w^362*$.1^7 + w^274*$.1^6 + w^78*$.1^5 + w^64*$.1^3 + w^145*$.1^2 + w^610*$.1 + w^466, w^314*$.1^7 + w^610*$.1^6 + w^78*$.1^5 + w^352*$.1^3 + w^505*$.1^2 + w^274*$.1 + w^418, w^529*$.1^7 + w^65*$.1^6 + w^377*$.1^5 + w^320*$.1^3 + w^183*$.1^2 + w^574*$.1 + w^478 ] >> if m*n != zeromat then ^ User error: bad syntax >> continue; ^ User error: A 'continue' can only be used inside a loop >> end if; ^ User error: bad syntax >> G, R:= GaloisGroup(f); ^ User error: Identifier 'f' has not been declared or assigned Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 >> end if; ^ User error: bad syntax >> end for; ^ User error: bad syntax >> end for; ^ User error: bad syntax >> end for; ^ User error: bad syntax Total time: 2.909 seconds, Total memory usage: 6.60MB ************** MAGMA ***************** Host client-146-186-121-85.mobility-up.psu.edu. (146.186.121.85) Time: Thu Apr 1 14:50:47 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); S := [ P | ]; for r in [0..4] do for s in [0..4] do Append(~S, r*t+s); end for; end for; zeromat := elt; G1, R1 := GaloisGroup(x^6 + 2*x^5 + (t+2)*x^3 + 3*x + 1); for a in S do for b in S do for c in S do f = x^6 + (2*c)*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1) if IsIrreducible(f) then continue; end if; f2:=f^2; c3:=Coefficient(f2, 3); c4:=Coefficient(f2, 4); c8:=Coefficient(f2, 8); c9:=Coefficient(f2, 9); m:=elt; n:=elt; if m*n != zeromat then continue; end if; G, R:= GaloisGroup(f); if G eq G1 then print(f); end if; end if; end for; end for; end for; Output: Magma V2.10-22 Thu Apr 1 2004 14:50:44 on modular [Seed = 1114534129] ------------------------------------- >> if IsIrreducible(f) then ^ User error: bad syntax >> continue; ^ User error: A 'continue' can only be used inside a loop >> end if; ^ User error: bad syntax >> f2:=f^2; ^ User error: Identifier 'f' has not been declared or assigned >> c3:=Coefficient(f2, 3); ^ User error: Identifier 'f2' has not been declared or assigned >> c4:=Coefficient(f2, 4); ^ User error: Identifier 'f2' has not been declared or assigned >> c8:=Coefficient(f2, 8); ^ User error: Identifier 'f2' has not been declared or assigned >> c9:=Coefficient(f2, 9); ^ User error: Identifier 'f2' has not been declared or assigned >> m:=elt; ^ User error: Identifier 'c4' has not been declared or assigned >> n:=elt; ^ User error: Identifier 'c4' has not been declared or assigned >> if m*n != zeromat then ^ User error: bad syntax >> continue; ^ User error: A 'continue' can only be used inside a loop >> end if; ^ User error: bad syntax >> G, R:= GaloisGroup(f); ^ User error: Identifier 'f' has not been declared or assigned >> if G eq G1 then ^ User error: Identifier 'G' has not been declared or assigned >> end if; ^ User error: bad syntax >> end for; ^ User error: bad syntax >> end for; ^ User error: bad syntax >> end for;; ^ User error: bad syntax Total time: 3.060 seconds, Total memory usage: 6.60MB ************** MAGMA ***************** Host client-146-186-121-110.mobility-up.psu.edu. (146.186.121.110) Time: Thu Apr 1 14:52:04 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); S := [ P | ]; for r in [0..4] do for s in [0..4] do Append(~S, r*t+s); end for; end for; zeromat := elt; G1, R1 := GaloisGroup(x^6 + 2*x^5 + (t+2)*x^3 + 3*x + 1); for a in S do for b in S do for c in S do f = x^6 + (2*c)*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); if IsIrreducible(f) then continue; end if; f2:=f^2; c3:=Coefficient(f2, 3); c4:=Coefficient(f2, 4); c8:=Coefficient(f2, 8); c9:=Coefficient(f2, 9); m:=elt; n:=elt; if m*n != zeromat then continue; end if; G, R:= GaloisGroup(f); if G eq G1 then print(f); end if; end if; end for; end for; end for; Output: Magma V2.10-22 Thu Apr 1 2004 14:52:01 on modular [Seed = 2944638313] ------------------------------------- >> if m*n != zeromat then ^ User error: bad syntax >> continue; ^ User error: A 'continue' can only be used inside a loop >> end if; ^ User error: bad syntax >> G, R:= GaloisGroup(f); ^ User error: Identifier 'f' has not been declared or assigned >> if G eq G1 then ^ User error: Identifier 'G' has not been declared or assigned >> end if; ^ User error: bad syntax >> end for; ^ User error: bad syntax >> end for; ^ User error: bad syntax >> end for;; ^ User error: bad syntax Total time: 2.869 seconds, Total memory usage: 6.60MB ************** MAGMA ***************** Host client-146-186-121-110.mobility-up.psu.edu. (146.186.121.110) Time: Thu Apr 1 14:52:31 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); S := [ P | ]; for r in [0..4] do for s in [0..4] do Append(~S, r*t+s); end for; end for; zeromat := elt; G1, R1 := GaloisGroup(x^6 + 2*x^5 + (t+2)*x^3 + 3*x + 1); for a in S do for b in S do for c in S do f = x^6 + (2*c)*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); if IsIrreducible(f) then continue; end if; f2:=f^2; c3:=Coefficient(f2, 3); c4:=Coefficient(f2, 4); c8:=Coefficient(f2, 8); c9:=Coefficient(f2, 9); m:=elt; n:=elt; if m*n ne zeromat then continue; end if; G, R:= GaloisGroup(f); if G eq G1 then print(f); end if; end if; end for; end for; end for; Output: Magma V2.10-22 Thu Apr 1 2004 14:52:28 on modular [Seed = 3147270496] ------------------------------------- >> end if; ^ User error: bad syntax >> end for; ^ User error: bad syntax >> end for; ^ User error: bad syntax >> end for;; ^ User error: bad syntax Total time: 2.879 seconds, Total memory usage: 6.60MB ************** MAGMA ***************** Host client-146-186-121-110.mobility-up.psu.edu. (146.186.121.110) Time: Thu Apr 1 14:53:15 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); S := [ P | ]; for r in [0..4] do for s in [0..4] do Append(~S, r*t+s); end for; end for; zeromat := elt; G1, R1 := GaloisGroup(x^6 + 2*x^5 + (t+2)*x^3 + 3*x + 1); for a in S do for b in S do for c in S do f = x^6 + (2*c)*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); if IsIrreducible(f) then continue; end if; f2:=f^2; c3:=Coefficient(f2, 3); c4:=Coefficient(f2, 4); c8:=Coefficient(f2, 8); c9:=Coefficient(f2, 9); m:=elt; n:=elt; if m*n ne zeromat then continue; end if; G, R:= GaloisGroup(f); if G eq G1 then print(f); end if; end for; end for; end for; Output: Magma V2.10-22 Thu Apr 1 2004 14:53:12 on modular [Seed = 2528814489] ------------------------------------- >> +(2+2*c+c^2-4*b*d)*x^4 ^ User error: Identifier 'd' has not been declared or assigned Total time: 2.930 seconds, Total memory usage: 6.60MB ************** MAGMA ***************** Host client-146-186-121-110.mobility-up.psu.edu. (146.186.121.110) Time: Thu Apr 1 14:53:38 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); S := [ P | ]; for r in [0..4] do for s in [0..4] do Append(~S, r*t+s); end for; end for; zeromat := elt; G1, R1 := GaloisGroup(x^6 + 2*x^5 + (t+2)*x^3 + 3*x + 1); for b in S do for c in S do for d in S do f = x^6 + (2*c)*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); if IsIrreducible(f) then continue; end if; f2:=f^2; c3:=Coefficient(f2, 3); c4:=Coefficient(f2, 4); c8:=Coefficient(f2, 8); c9:=Coefficient(f2, 9); m:=elt; n:=elt; if m*n ne zeromat then continue; end if; G, R:= GaloisGroup(f); if G eq G1 then print(f); end if; end for; end for; end for; Output: Magma V2.10-22 Thu Apr 1 2004 14:53:35 on modular [Seed = 2662509958] ------------------------------------- >> f = x^6 ^ User error: Identifier 'f' has not been declared or assigned Total time: 2.869 seconds, Total memory usage: 6.60MB ************** MAGMA ***************** Host client-146-186-121-110.mobility-up.psu.edu. (146.186.121.110) Time: Thu Apr 1 14:54:10 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); S := [ P | ]; for r in [0..4] do for s in [0..4] do Append(~S, r*t+s); end for; end for; zeromat := elt; G1, R1 := GaloisGroup(x^6 + 2*x^5 + (t+2)*x^3 + 3*x + 1); for b in S do for c in S do for d in S do f := x^6 + (2*c)*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); if IsIrreducible(f) then continue; end if; f2:=f^2; c3:=Coefficient(f2, 3); c4:=Coefficient(f2, 4); c8:=Coefficient(f2, 8); c9:=Coefficient(f2, 9); m:=elt; n:=elt; if m*n ne zeromat then continue; end if; G, R:= GaloisGroup(f); if G eq G1 then print(f); end if; end for; end for; end for; Output: Magma V2.10-22 Thu Apr 1 2004 14:54:07 on modular [Seed = 3805204890] ------------------------------------- >> G, R:= GaloisGroup(f); ^ Runtime error in 'GaloisGroup': Argument 1 is not irreducible Total time: 2.880 seconds, Total memory usage: 6.60MB ************** MAGMA ***************** Host client-146-186-121-110.mobility-up.psu.edu. (146.186.121.110) Time: Thu Apr 1 14:55:44 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); S := [ P | ]; for r in [0..4] do for s in [0..4] do Append(~S, r*t+s); end for; end for; zeromat := elt; G1, R1 := GaloisGroup(x^6 + 2*x^5 + (t+2)*x^3 + 3*x + 1); for b in S do for c in S do for d in S do f := x^6 + (2*c)*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); if not IsIrreducible(f) then continue; end if; f2:=f^2; c3:=Coefficient(f2, 3); c4:=Coefficient(f2, 4); c8:=Coefficient(f2, 8); c9:=Coefficient(f2, 9); m:=elt; n:=elt; if m*n ne zeromat then continue; end if; G, R:= GaloisGroup(f); if G eq G1 then print(f); end if; end for; end for; end for; Output: Magma V2.10-22 Thu Apr 1 2004 14:55:22 on modular [Seed = 3370449733] ------------------------------------- x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + t*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + 2*t*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + 3*t*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + 4*t*x^3 + 3*x + 1 x^6 + 4*x^5 + (4*t + 4)*x^3 + (2*t + 2)*x^2 + 2*t*x + 4*t + 1 x^6 + 2*t*x^5 + (t + 2)*x^4 + (3*t + 1)*x^3 + (4*t + 1)*x + 4*t + 1 x^6 + (2*t + 3)*x^5 + (4*t + 1)*x^4 + (4*t + 1)*x^3 + (3*t + 2)*x^2 + (4*t + 4)*x + 4*t + 1 x^6 + (3*t + 1)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t + 1 x^6 + 4*x^5 + (4*t + 3)*x^3 + (2*t + 4)*x^2 + (2*t + 2)*x + 4*t x^6 + 2*t*x^5 + 4*t*x^4 + 4*t*x^3 + 3*t*x^2 + (4*t + 3)*x + 4*t x^6 + (2*t + 2)*x^5 + (t + 3)*x^4 + (3*t + 4)*x^3 + 4*t*x + 4*t x^6 + (3*t + 4)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t x^6 + 4*x^5 + (4*t + 2)*x^3 + (2*t + 1)*x^2 + (2*t + 4)*x + 4*t + 4 ************** MAGMA ***************** Host client-146-186-121-110.mobility-up.psu.edu. (146.186.121.110) Time: Thu Apr 1 14:56:07 2004 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); S := [ P | ]; for r in [0..4] do for s in [0..4] do Append(~S, r*t+s); end for; end for; zeromat := elt; G1, R1 := GaloisGroup(x^6 + 2*x^5 + (t+2)*x^3 + 3*x + 1); for b in S do for c in S do for d in S do f := x^6 + (2*c)*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); if not IsIrreducible(f) then continue; end if; f2:=f^2; c3:=Coefficient(f2, 3); c4:=Coefficient(f2, 4); c8:=Coefficient(f2, 8); c9:=Coefficient(f2, 9); m:=elt; n:=elt; if m*n ne zeromat then continue; end if; G, R:= GaloisGroup(f); if G eq G1 then print(f); end if; end for; end for; end for; Output: Magma V2.10-22 Thu Apr 1 2004 14:55:45 on modular [Seed = 3523076663] ------------------------------------- x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + t*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + 2*t*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + 3*t*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + 4*t*x^3 + 3*x + 1 x^6 + 4*x^5 + (4*t + 4)*x^3 + (2*t + 2)*x^2 + 2*t*x + 4*t + 1 x^6 + 2*t*x^5 + (t + 2)*x^4 + (3*t + 1)*x^3 + (4*t + 1)*x + 4*t + 1 x^6 + (2*t + 3)*x^5 + (4*t + 1)*x^4 + (4*t + 1)*x^3 + (3*t + 2)*x^2 + (4*t + 4)*x + 4*t + 1 x^6 + (3*t + 1)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t + 1 x^6 + 4*x^5 + (4*t + 3)*x^3 + (2*t + 4)*x^2 + (2*t + 2)*x + 4*t x^6 + 2*t*x^5 + 4*t*x^4 + 4*t*x^3 + 3*t*x^2 + (4*t + 3)*x + 4*t x^6 + (2*t + 2)*x^5 + (t + 3)*x^4 + (3*t + 4)*x^3 + 4*t*x + 4*t x^6 + (3*t + 4)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t x^6 + 4*x^5 + (4*t + 2)*x^3 + (2*t + 1)*x^2 + (2*t + 4)*x + 4*t + 4 ************** MAGMA ***************** Host client-146-186-121-68.mobility-up.psu.edu. (146.186.121.68) Time: Thu Apr 1 16:08:19 2004 Input: p:=5 P:= FunctionField(GF(p)); Q:= PolynomialRing(P); S := [ P | ]; for r in [0..p-1] do for s in [0..p-1] do Append(~S, r*t+s); end for; end for; zeromat := elt; G1, R1 := GaloisGroup(x^6 + 2*x^5 + (t+2)*x^3 + 3*x + 1); for b in S do for c in S do for d in S do f := x^6 + (2*c)*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); if not IsIrreducible(f) then continue; end if; f2:=f^2; c3:=Coefficient(f2, 3); c4:=Coefficient(f2, 4); c8:=Coefficient(f2, 8); c9:=Coefficient(f2, 9); m:=elt; n:=elt; if m*n ne zeromat then continue; end if; G, R:= GaloisGroup(f); if G eq G1 then print(f); end if; end for; end for; end for; Output: Magma V2.10-22 Thu Apr 1 2004 16:08:16 on modular [Seed = 2794086990] ------------------------------------- >> P:= FunctionField(GF(p)); ^ User error: bad syntax >> Q:= PolynomialRing(P); ^ User error: Identifier 'P' has not been declared or assigned >> S := [ P | ]; ^ User error: Identifier 'P' has not been declared or assigned >> for r in [0..p-1] do ^ User error: Identifier 'p' has not been declared or assigned >> zeromat := elt; ^ User error: Identifier 'Q' has not been declared or assigned >> G1, R1 := GaloisGroup(x^6 + 2*x^5 + (t+2)*x^3 + 3*x + 1); ^ User error: Identifier 'x' has not been declared or assigned >> for b in S do ^ User error: Identifier 'S' has not been declared or assigned Total time: 2.499 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host client-146-186-121-68.mobility-up.psu.edu. (146.186.121.68) Time: Thu Apr 1 16:08:35 2004 Input: p:=5 P:= FunctionField(GF(p)); Q:= PolynomialRing(P); S := [ P | ]; for r in [0..p-1] do for s in [0..p-1] do Append(~S, r*t+s); end for; end for; zeromat := elt; G1, R1 := GaloisGroup(x^6 + 2*x^5 + (t+2)*x^3 + 3*x + 1); for b in S do for c in S do for d in S do f := x^6 + (2*c)*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); if not IsIrreducible(f) then continue; end if; f2:=f^2; c3:=Coefficient(f2, 3); c4:=Coefficient(f2, 4); c8:=Coefficient(f2, 8); c9:=Coefficient(f2, 9); m:=elt; n:=elt; if m*n ne zeromat then continue; end if; G, R:= GaloisGroup(f); if G eq G1 then print(f); end if; end for; end for; end for; Output: Magma V2.10-22 Thu Apr 1 2004 16:08:33 on modular [Seed = 3197270599] ------------------------------------- >> P:= FunctionField(GF(p)); ^ User error: bad syntax >> Q:= PolynomialRing(P); ^ User error: Identifier 'P' has not been declared or assigned >> S := [ P | ]; ^ User error: Identifier 'P' has not been declared or assigned >> for r in [0..p-1] do ^ User error: Identifier 'p' has not been declared or assigned >> zeromat := elt; ^ User error: Identifier 'Q' has not been declared or assigned >> G1, R1 := GaloisGroup(x^6 + 2*x^5 + (t+2)*x^3 + 3*x + 1); ^ User error: Identifier 'x' has not been declared or assigned >> for b in S do ^ User error: Identifier 'S' has not been declared or assigned Total time: 2.509 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host client-146-186-121-68.mobility-up.psu.edu. (146.186.121.68) Time: Thu Apr 1 16:11:16 2004 Input: T := PolynomialRing(RationalField()); GA, RA := GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1); print(GA); quit; p:=5; P:= FunctionField(GF(p)); Q:= PolynomialRing(P); S := [ P | ]; for r in [0..p-1] do for s in [0..p-1] do Append(~S, r*t+s); end for; end for; zeromat := elt; G1, R1 := GaloisGroup(x^6 + 2*x^5 + (t+2)*x^3 + 3*x + 1); for b in S do for c in S do for d in S do f := x^6 + (2*c)*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); if not IsIrreducible(f) then continue; end if; f2:=f^2; c3:=Coefficient(f2, 3); c4:=Coefficient(f2, 4); c8:=Coefficient(f2, 8); c9:=Coefficient(f2, 9); m:=elt; n:=elt; if m*n ne zeromat then continue; end if; G, R:= GaloisGroup(f); if G eq G1 then print(f); end if; end for; end for; end for; Output: Magma V2.10-22 Thu Apr 1 2004 16:11:13 on modular [Seed = 2376157396] ------------------------------------- Permutation group GA acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) Total time: 2.690 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host client-146-186-121-68.mobility-up.psu.edu. (146.186.121.68) Time: Thu Apr 1 16:15:11 2004 Input: T := PolynomialRing(RationalField()); GA, RA := GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1); print(GA); p:=5; P:= FunctionField(GF(p)); Q:= PolynomialRing(P); S := [ P | ]; for r in [0..p-1] do for s in [0..p-1] do Append(~S, r*t+s); end for; end for; zeromat := elt; for b in S do for c in S do for d in S do f := x^6 + (2*c)*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); fp:=f^((p-1)/2); c12:=Coefficient(f2, p-2); c11:=Coefficient(f2, p-1); c22:=Coefficient(f2, 2*p-2); c21:=Coefficient(f2, 2*p-1); m:=elt; n:=elt; if m*n ne zeromat then continue; end if; if not IsIrreducible(f) then continue; end if; G, R:= GaloisGroup(f); if G eq GA then print(f); end if; end for; end for; end for; Output: Magma V2.10-22 Thu Apr 1 2004 16:15:09 on modular [Seed = 2595642607] ------------------------------------- Permutation group GA acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) >> c12:=Coefficient(f2, p-2); ^ User error: Identifier 'f2' has not been declared or assigned Total time: 2.649 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host client-146-186-121-68.mobility-up.psu.edu. (146.186.121.68) Time: Thu Apr 1 16:15:32 2004 Input: T := PolynomialRing(RationalField()); GA, RA := GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1); print(GA); p:=5; P:= FunctionField(GF(p)); Q:= PolynomialRing(P); S := [ P | ]; for r in [0..p-1] do for s in [0..p-1] do Append(~S, r*t+s); end for; end for; zeromat := elt; for b in S do for c in S do for d in S do f := x^6 + (2*c)*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); fp:=f^((p-1)/2); c12:=Coefficient(fp, p-2); c11:=Coefficient(fp, p-1); c22:=Coefficient(fp, 2*p-2); c21:=Coefficient(fp, 2*p-1); m:=elt; n:=elt; if m*n ne zeromat then continue; end if; if not IsIrreducible(f) then continue; end if; G, R:= GaloisGroup(f); if G eq GA then print(f); end if; end for; end for; end for; Output: Magma V2.10-22 Thu Apr 1 2004 16:15:29 on modular [Seed = 2461947083] ------------------------------------- Permutation group GA acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) >> fp:=f^((p-1)/2); ^ Runtime error in '^': Bad argument types Argument types given: RngUPolElt, RngUPolElt Total time: 2.649 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host client-146-186-121-68.mobility-up.psu.edu. (146.186.121.68) Time: Thu Apr 1 16:16:35 2004 Input: T := PolynomialRing(RationalField()); GA, RA := GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1); print(GA); p:=5; hp:=(p-1)/2; P:= FunctionField(GF(p)); Q:= PolynomialRing(P); S := [ P | ]; for r in [0..p-1] do for s in [0..p-1] do Append(~S, r*t+s); end for; end for; zeromat := elt; for b in S do for c in S do for d in S do f := x^6 + (2*c)*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); fp:=f^hp; c12:=Coefficient(fp, p-2); c11:=Coefficient(fp, p-1); c22:=Coefficient(fp, 2*p-2); c21:=Coefficient(fp, 2*p-1); m:=elt; n:=elt; if m*n ne zeromat then continue; end if; if not IsIrreducible(f) then continue; end if; G, R:= GaloisGroup(f); if G eq GA then print(f); end if; end for; end for; end for; Output: Magma V2.10-22 Thu Apr 1 2004 16:16:33 on modular [Seed = 3938856051] ------------------------------------- Permutation group GA acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) >> fp:=f^hp; ^ Runtime error in '^': Bad argument types Argument types given: RngUPolElt, RngUPolElt Total time: 2.690 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host client-146-186-121-68.mobility-up.psu.edu. (146.186.121.68) Time: Thu Apr 1 16:19:03 2004 Input: T := PolynomialRing(RationalField()); GA, RA := GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1); print(GA); p:=5; hp:=Integers((p-1)/2); P:= FunctionField(GF(p)); Q:= PolynomialRing(P); S := [ P | ]; for r in [0..p-1] do for s in [0..p-1] do Append(~S, r*t+s); end for; end for; zeromat := elt; for b in S do for c in S do for d in S do f := x^6 + (2*c)*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); fp:=f^hp; c12:=Coefficient(fp, p-2); c11:=Coefficient(fp, p-1); c22:=Coefficient(fp, 2*p-2); c21:=Coefficient(fp, 2*p-1); m:=elt; n:=elt; if m*n ne zeromat then continue; end if; if not IsIrreducible(f) then continue; end if; G, R:= GaloisGroup(f); if G eq GA then print(f); end if; end for; end for; end for; Output: Magma V2.10-22 Thu Apr 1 2004 16:19:00 on modular [Seed = 3822003343] ------------------------------------- Permutation group GA acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) >> hp:=Integers((p-1)/2); ^ Runtime error in 'Integers': Bad argument types Argument types given: FldRatElt >> fp:=f^hp; ^ User error: Identifier 'hp' has not been declared or assigned Total time: 2.759 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host client-146-186-121-68.mobility-up.psu.edu. (146.186.121.68) Time: Thu Apr 1 16:19:14 2004 Input: T := PolynomialRing(RationalField()); GA, RA := GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1); print(GA); p:=5; hp:=Integers(|(p-1)/2); P:= FunctionField(GF(p)); Q:= PolynomialRing(P); S := [ P | ]; for r in [0..p-1] do for s in [0..p-1] do Append(~S, r*t+s); end for; end for; zeromat := elt; for b in S do for c in S do for d in S do f := x^6 + (2*c)*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); fp:=f^hp; c12:=Coefficient(fp, p-2); c11:=Coefficient(fp, p-1); c22:=Coefficient(fp, 2*p-2); c21:=Coefficient(fp, 2*p-1); m:=elt; n:=elt; if m*n ne zeromat then continue; end if; if not IsIrreducible(f) then continue; end if; G, R:= GaloisGroup(f); if G eq GA then print(f); end if; end for; end for; end for; Output: Magma V2.10-22 Thu Apr 1 2004 16:19:12 on modular [Seed = 4225186947] ------------------------------------- Permutation group GA acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) >> hp:=Integers(|(p-1)/2); ^ User error: bad syntax >> fp:=f^hp; ^ User error: Identifier 'hp' has not been declared or assigned Total time: 2.679 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host client-146-186-121-68.mobility-up.psu.edu. (146.186.121.68) Time: Thu Apr 1 16:20:37 2004 Input: T := PolynomialRing(RationalField()); GA, RA := GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1); print(GA); Z=Integers(); p:=5; hp:=Integers(|(p-1)/2); P:= FunctionField(GF(p)); Q:= PolynomialRing(P); S := [ P | ]; for r in [0..p-1] do for s in [0..p-1] do Append(~S, r*t+s); end for; end for; zeromat := elt; for b in S do for c in S do for d in S do f := x^6 + (2*c)*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); fp:=f^hp; c12:=Coefficient(fp, p-2); c11:=Coefficient(fp, p-1); c22:=Coefficient(fp, 2*p-2); c21:=Coefficient(fp, 2*p-1); m:=elt; n:=elt; if m*n ne zeromat then continue; end if; if not IsIrreducible(f) then continue; end if; G, R:= GaloisGroup(f); if G eq GA then print(f); end if; end for; end for; end for; Output: Magma V2.10-22 Thu Apr 1 2004 16:20:34 on modular [Seed = 3404074304] ------------------------------------- Permutation group GA acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) >> Z=Integers(); ^ User error: Identifier 'Z' has not been declared or assigned >> hp:=Integers(|(p-1)/2); ^ User error: bad syntax >> fp:=f^hp; ^ User error: Identifier 'hp' has not been declared or assigned Total time: 2.669 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host client-146-186-121-68.mobility-up.psu.edu. (146.186.121.68) Time: Thu Apr 1 16:20:48 2004 Input: T := PolynomialRing(RationalField()); GA, RA := GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1); print(GA); Z := Integers(); p:=5; hp:=Integers(|(p-1)/2); P:= FunctionField(GF(p)); Q:= PolynomialRing(P); S := [ P | ]; for r in [0..p-1] do for s in [0..p-1] do Append(~S, r*t+s); end for; end for; zeromat := elt; for b in S do for c in S do for d in S do f := x^6 + (2*c)*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); fp:=f^hp; c12:=Coefficient(fp, p-2); c11:=Coefficient(fp, p-1); c22:=Coefficient(fp, 2*p-2); c21:=Coefficient(fp, 2*p-1); m:=elt; n:=elt; if m*n ne zeromat then continue; end if; if not IsIrreducible(f) then continue; end if; G, R:= GaloisGroup(f); if G eq GA then print(f); end if; end for; end for; end for; Output: Magma V2.10-22 Thu Apr 1 2004 16:20:45 on modular [Seed = 3270378823] ------------------------------------- Permutation group GA acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) >> hp:=Integers(|(p-1)/2); ^ User error: bad syntax >> fp:=f^hp; ^ User error: Identifier 'hp' has not been declared or assigned Total time: 2.740 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host client-146-186-121-68.mobility-up.psu.edu. (146.186.121.68) Time: Thu Apr 1 16:21:42 2004 Input: T := PolynomialRing(RationalField()); GA, RA := GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1); print(GA); Z := Integers(); p:=5; hp:=Z ! ((p-1)/2); P:= FunctionField(GF(p)); Q:= PolynomialRing(P); S := [ P | ]; for r in [0..p-1] do for s in [0..p-1] do Append(~S, r*t+s); end for; end for; zeromat := elt; for b in S do for c in S do for d in S do f := x^6 + (2*c)*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); fp:=f^hp; c12:=Coefficient(fp, p-2); c11:=Coefficient(fp, p-1); c22:=Coefficient(fp, 2*p-2); c21:=Coefficient(fp, 2*p-1); m:=elt; n:=elt; if m*n ne zeromat then continue; end if; if not IsIrreducible(f) then continue; end if; G, R:= GaloisGroup(f); if G eq GA then print(f); end if; end for; end for; end for; Output: Magma V2.10-22 Thu Apr 1 2004 16:21:19 on modular [Seed = 3673562429] ------------------------------------- Permutation group GA acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + t*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + 2*t*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + 3*t*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + 4*t*x^3 + 3*x + 1 x^6 + 4*x^5 + (4*t + 4)*x^3 + (2*t + 2)*x^2 + 2*t*x + 4*t + 1 x^6 + 2*t*x^5 + (t + 2)*x^4 + (3*t + 1)*x^3 + (4*t + 1)*x + 4*t + 1 x^6 + (2*t + 3)*x^5 + (4*t + 1)*x^4 + (4*t + 1)*x^3 + (3*t + 2)*x^2 + (4*t + 4)*x + 4*t + 1 x^6 + (3*t + 1)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t + 1 x^6 + 4*x^5 + (4*t + 3)*x^3 + (2*t + 4)*x^2 + (2*t + 2)*x + 4*t x^6 + 2*t*x^5 + 4*t*x^4 + 4*t*x^3 + 3*t*x^2 + (4*t + 3)*x + 4*t x^6 + (2*t + 2)*x^5 + (t + 3)*x^4 + (3*t + 4)*x^3 + 4*t*x + 4*t x^6 + (3*t + 4)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t x^6 + 4*x^5 + (4*t + 2)*x^3 + (2*t + 1)*x^2 + (2*t + 4)*x + 4*t + 4 x^6 + (2*t + 2)*x^5 + (4*t + 4)*x^4 + (4*t + 4)*x^3 + (3*t + 3)*x^2 + (4*t + 2)*x + 4*t + 4 x^6 + (2*t + 4)*x^5 + (t + 4)*x^4 + (3*t + 2)*x^3 + (4*t + 4)*x + 4*t + 4 x^6 + (3*t + 2)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t + 4 x^6 + 4*x^5 + (4*t + 1)*x^3 + (2*t + 3)*x^2 + (2*t + 1)*x + 4*t + 3 x^6 + (2*t + 4)*x^5 + (4*t + 3)*x^4 + (4*t + 3)*x^3 + (3*t + 1)*x^2 + (4*t + 1)*x + 4*t + 3 x^6 + (2*t + 1)*x^5 + t*x^4 + 3*t*x^3 + (4*t + 3)*x + 4*t + 3 x^6 + 3*t*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t + 3 x^6 + 4*x^5 + 4*t*x^3 + 2*t*x^2 + (2*t + 3)*x + 4*t + 2 x^6 + (2*t + 1)*x^5 + (4*t + 2)*x^4 + (4*t + 2)*x^3 + (3*t + 4)*x^2 + 4*t*x + 4*t + 2 x^6 + (2*t + 3)*x^5 + (t + 1)*x^4 + (3*t + 3)*x^3 + (4*t + 2)*x + 4*t + 2 x^6 + (3*t + 3)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t + 2 x^6 + 4*x^5 + (3*t + 4)*x^3 + (4*t + 2)*x^2 + 4*t*x + 3*t + 1 x^6 + 4*t*x^5 + (2*t + 2)*x^4 + (t + 1)*x^3 + (3*t + 1)*x + 3*t + 1 x^6 + (4*t + 3)*x^5 + (3*t + 1)*x^4 + (3*t + 1)*x^3 + (t + 2)*x^2 + (3*t + 4)*x + 3*t + 1 x^6 + (t + 1)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 3*t + 1 x^6 + 4*x^5 + (3*t + 3)*x^3 + (4*t + 4)*x^2 + (4*t + 2)*x + 3*t x^6 + 4*t*x^5 + 3*t*x^4 + 3*t*x^3 + t*x^2 + (3*t + 3)*x + 3*t x^6 + (4*t + 2)*x^5 + (2*t + 3)*x^4 + (t + 4)*x^3 + 3*t*x + 3*t x^6 + (t + 4)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 3*t x^6 + 4*x^5 + (3*t + 2)*x^3 + (4*t + 1)*x^2 + (4*t + 4)*x + 3*t + 4 x^6 + (4*t + 2)*x^5 + (3*t + 4)*x^4 + (3*t + 4)*x^3 + (t + 3)*x^2 + (3*t + 2)*x + 3*t + 4 x^6 + (4*t + 4)*x^5 + (2*t + 4)*x^4 + (t + 2)*x^3 + (3*t + 4)*x + 3*t + 4 x^6 + (t + 2)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 3*t + 4 ************** MAGMA ***************** Host client-146-186-121-68.mobility-up.psu.edu. (146.186.121.68) Time: Thu Apr 1 16:24:07 2004 Input: T := PolynomialRing(RationalField()); GA, RA := GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1); print(GA); Z := Integers(); p:=3; hp:=Z ! ((p-1)/2); P:= FunctionField(GF(p)); Q:= PolynomialRing(P); S := [ P | ]; for r in [0..p-1] do for s in [0..p-1] do Append(~S, r*t+s); end for; end for; zeromat := elt; for b in S do for c in S do for d in S do f := x^6 + (2*c)*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); fp:=f^hp; c12:=Coefficient(fp, p-2); c11:=Coefficient(fp, p-1); c22:=Coefficient(fp, 2*p-2); c21:=Coefficient(fp, 2*p-1); m:=elt; n:=elt; if m*n ne zeromat then continue; end if; if not IsIrreducible(f) then continue; end if; G, R:= GaloisGroup(f); if G eq GA then print(f); end if; end for; end for; end for; Output: Magma V2.10-22 Thu Apr 1 2004 16:24:03 on modular [Seed = 3623559052] ------------------------------------- Permutation group GA acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) Total time: 3.689 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host client-146-186-121-68.mobility-up.psu.edu. (146.186.121.68) Time: Thu Apr 1 16:24:35 2004 Input: T := PolynomialRing(RationalField()); GA, RA := GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1); print(GA); Z := Integers(); p:=7; hp:=Z ! ((p-1)/2); P:= FunctionField(GF(p)); Q:= PolynomialRing(P); S := [ P | ]; for r in [0..p-1] do for s in [0..p-1] do Append(~S, r*t+s); end for; end for; zeromat := elt; for b in S do for c in S do for d in S do f := x^6 + (2*c)*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); fp:=f^hp; c12:=Coefficient(fp, p-2); c11:=Coefficient(fp, p-1); c22:=Coefficient(fp, 2*p-2); c21:=Coefficient(fp, 2*p-1); m:=elt; n:=elt; if m*n ne zeromat then continue; end if; if not IsIrreducible(f) then continue; end if; G, R:= GaloisGroup(f); if G eq GA then print(f); end if; end for; end for; end for; Output: Magma V2.10-22 Thu Apr 1 2004 16:24:12 on modular [Seed = 771942011] ------------------------------------- Permutation group GA acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) ************** MAGMA ***************** Host client-146-186-121-68.mobility-up.psu.edu. (146.186.121.68) Time: Thu Apr 1 16:25:11 2004 Input: T := PolynomialRing(RationalField()); GA, RA := GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1); print(GA); Z := Integers(); p:=11; hp:=Z ! ((p-1)/2); P:= FunctionField(GF(p)); Q:= PolynomialRing(P); S := [ P | ]; for r in [0..p-1] do for s in [0..p-1] do Append(~S, r*t+s); end for; end for; zeromat := elt; for b in S do for c in S do for d in S do f := x^6 + (2*c)*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); fp:=f^hp; c12:=Coefficient(fp, p-2); c11:=Coefficient(fp, p-1); c22:=Coefficient(fp, 2*p-2); c21:=Coefficient(fp, 2*p-1); m:=elt; n:=elt; if m*n ne zeromat then continue; end if; if not IsIrreducible(f) then continue; end if; G, R:= GaloisGroup(f); if G eq GA then print(f); end if; end for; end for; end for; Output: Magma V2.10-22 Thu Apr 1 2004 16:24:49 on modular [Seed = 638250670] ------------------------------------- Permutation group GA acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) ************** MAGMA ***************** Host client-146-186-121-68.mobility-up.psu.edu. (146.186.121.68) Time: Thu Apr 1 16:29:26 2004 Input: T := PolynomialRing(RationalField()); GA, RA := GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1); print(GA); Z := Integers(); p:=11; hp:=Z ! ((p-1)/2); P:= FunctionField(GF(p)); Q:= PolynomialRing(P); S := [ P | ]; for q in [0..p-1] do for r in [0..p-1] do for s in [0..p-1] do Append(~S, q*t^2+r*t+s); end for; end for; zeromat := elt; for b in S do for c in S do for d in S do f := x^6 + (2*c)*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); fp:=f^hp; c12:=Coefficient(fp, p-2); c11:=Coefficient(fp, p-1); c22:=Coefficient(fp, 2*p-2); c21:=Coefficient(fp, 2*p-1); m:=elt; n:=elt; if m*n ne zeromat then continue; end if; if not IsIrreducible(f) then continue; end if; G, R:= GaloisGroup(f); if G eq GA then print(f); end if; end for; end for; end for; Output: Magma V2.10-22 Thu Apr 1 2004 16:29:24 on modular [Seed = 890895528] ------------------------------------- Permutation group GA acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) User error: syntax error at end of input Total time: 2.680 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host client-146-186-121-68.mobility-up.psu.edu. (146.186.121.68) Time: Thu Apr 1 16:30:07 2004 Input: T := PolynomialRing(RationalField()); GA, RA := GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1); print(GA); Z := Integers(); p:=11; hp:=Z ! ((p-1)/2); P:= FunctionField(GF(p)); Q:= PolynomialRing(P); S := [ P | ]; for q in [0..p-1] do for r in [0..p-1] do for s in [0..p-1] do Append(~S, q*t^2+r*t+s); end for; end for; end for; zeromat := elt; for b in S do for c in S do for d in S do f := x^6 + (2*c)*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); fp:=f^hp; c12:=Coefficient(fp, p-2); c11:=Coefficient(fp, p-1); c22:=Coefficient(fp, 2*p-2); c21:=Coefficient(fp, 2*p-1); m:=elt; n:=elt; if m*n ne zeromat then continue; end if; if not IsIrreducible(f) then continue; end if; G, R:= GaloisGroup(f); if G eq GA then print(f); end if; end for; end for; end for; Output: Magma V2.10-22 Thu Apr 1 2004 16:29:44 on modular [Seed = 220316908] ------------------------------------- Permutation group GA acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) ************** MAGMA ***************** Host client-146-186-121-68.mobility-up.psu.edu. (146.186.121.68) Time: Thu Apr 1 16:30:45 2004 Input: T := PolynomialRing(RationalField()); GA, RA := GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1); print(GA); Z := Integers(); p:=5; hp:=Z ! ((p-1)/2); P:= FunctionField(GF(p)); Q:= PolynomialRing(P); S := [ P | ]; for q in [0..p-1] do for r in [0..p-1] do for s in [0..p-1] do Append(~S, q*t^2+r*t+s); end for; end for; end for; zeromat := elt; for b in S do for c in S do for d in S do f := x^6 + (2*c)*x^5 +(2+2*c+c^2-4*b*d)*x^4 +(2+4*b+2*c+2*c^2-4*d-8*b*d)*x^3 +(5+12*b+4*c+c^2-4*b*d)*x^2 +(6+12*b+2*c)*x +(4*b+1); fp:=f^hp; c12:=Coefficient(fp, p-2); c11:=Coefficient(fp, p-1); c22:=Coefficient(fp, 2*p-2); c21:=Coefficient(fp, 2*p-1); m:=elt; n:=elt; if m*n ne zeromat then continue; end if; if not IsIrreducible(f) then continue; end if; G, R:= GaloisGroup(f); if G eq GA then print(f); end if; end for; end for; end for; Output: Magma V2.10-22 Thu Apr 1 2004 16:30:22 on modular [Seed = 439800797] ------------------------------------- Permutation group GA acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + t*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + 2*t*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + 3*t*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + 4*t*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + t^2*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + t)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + 2*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + 2*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + 2*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + 2*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + 2*t)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + 3*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + 3*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + 3*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + 3*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + 3*t)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + 4*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + 4*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + 4*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + 4*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + 4*t)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + 2*t^2*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + t)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + 2*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + 2*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + 2*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + 2*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + 2*t)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + 3*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + 3*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + 3*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + 3*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + 3*t)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + 4*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + 4*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + 4*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + 4*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + 4*t)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + 3*t^2*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + t)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + 2*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + 2*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + 2*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + 2*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + 2*t)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + 3*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + 3*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + 3*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + 3*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + 3*t)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + 4*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + 4*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + 4*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + 4*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + 4*t)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + 4*t^2*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + t)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + 2*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + 2*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + 2*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + 2*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + 2*t)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + 3*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + 3*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + 3*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + 3*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + 3*t)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + 4*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + 4*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + 4*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + 4*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + 4*t)*x^3 + 3*x + 1 ************** MAGMA ***************** Host client-146-186-121-68.mobility-up.psu.edu. (146.186.121.68) Time: Thu Apr 1 16:50:58 2004 Input: T := PolynomialRing(RationalField()); GA, RA := GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1); print(GA); Z := Integers(); p:=5; hp:=Z ! ((p-1)/2); P:= FunctionField(GF(p)); Q:= PolynomialRing(P); S := [ P | ]; for q in [0..p-1] do for r in [0..p-1] do for s in [0..p-1] do Append(~S, q*t^2+r*t+s); end for; end for; end for; zeromat := elt; for b in S do for c in S do for d in S do a5 := 2*c; a4 := 2+2*c+c^2-4*b*d; a3 := 2+4*b+2*c+2*c^2-4*d-8*b*d; a2 := 5+12*b+4*c+c^2-4*b*d; a1 := 6+12*b+2*c; a0 := 4*b+1; f := x^6 + a5*x^5 + a4*x^4 + a3*x^3 + a2*x^2 + a1*x +a0; fp:=f^hp; c12:=Coefficient(fp, p-2); c11:=Coefficient(fp, p-1); c22:=Coefficient(fp, 2*p-2); c21:=Coefficient(fp, 2*p-1); m:=elt; if m nq zeromat then n:=elt; if m*n ne zeromat then continue; end if; end if; if not IsIrreducible(f) then continue; end if; G, R:= GaloisGroup(f); if G eq GA then print(f); end if; end for; end for; end for; Output: Magma V2.10-22 Thu Apr 1 2004 16:50:55 on modular [Seed = 1968815075] ------------------------------------- Permutation group GA acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) >> if m nq zeromat then ^ User error: bad syntax >> n:=elt; ^ User error: Identifier 'c11' has not been declared or assigned >> if m*n ne zeromat then ^ User error: Identifier 'm' has not been declared or assigned >> end if; ^ User error: bad syntax >> if not IsIrreducible(f) then ^ User error: Identifier 'f' has not been declared or assigned >> G, R:= GaloisGroup(f); ^ User error: Identifier 'f' has not been declared or assigned >> if G eq GA then ^ User error: Identifier 'G' has not been declared or assigned >> end for; ^ User error: bad syntax >> end for; ^ User error: bad syntax >> end for;; ^ User error: bad syntax Total time: 2.709 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host client-146-186-121-68.mobility-up.psu.edu. (146.186.121.68) Time: Thu Apr 1 16:51:53 2004 Input: T := PolynomialRing(RationalField()); GA, RA := GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1); print(GA); Z := Integers(); p:=5; hp:=Z ! ((p-1)/2); P:= FunctionField(GF(p)); Q:= PolynomialRing(P); S := [ P | ]; for q in [0..p-1] do for r in [0..p-1] do for s in [0..p-1] do Append(~S, q*t^2+r*t+s); end for; end for; end for; zeromat := elt; for b in S do for c in S do for d in S do a5 := 2*c; a4 := 2+2*c+c^2-4*b*d; a3 := 2+4*b+2*c+2*c^2-4*d-8*b*d; a2 := 5+12*b+4*c+c^2-4*b*d; a1 := 6+12*b+2*c; a0 := 4*b+1; f := x^6 + a5*x^5 + a4*x^4 + a3*x^3 + a2*x^2 + a1*x + a0; fp:=f^hp; c12:=Coefficient(fp, p-2); c11:=Coefficient(fp, p-1); c22:=Coefficient(fp, 2*p-2); c21:=Coefficient(fp, 2*p-1); m:=elt; if m ne zeromat then n:=elt; if m*n ne zeromat then continue; end if; end if; if not IsIrreducible(f) then continue; end if; G, R:= GaloisGroup(f); if G eq GA then print(f); end if; end for; end for; end for; Output: Magma V2.10-22 Thu Apr 1 2004 16:51:31 on modular [Seed = 1298236295] ------------------------------------- Permutation group GA acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + t*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + 2*t*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + 3*t*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + 4*t*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + t^2*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + t)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + 2*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + 2*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + 2*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + 2*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + 2*t)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + 3*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + 3*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + 3*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + 3*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + 3*t)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + 4*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + 4*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + 4*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + 4*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t^2 + 4*t)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + 2*t^2*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + t)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + 2*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + 2*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + 2*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + 2*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + 2*t)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + 3*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + 3*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + 3*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + 3*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + 3*t)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + 4*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + 4*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + 4*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + 4*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t^2 + 4*t)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + 3*t^2*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + t)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + 2*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + 2*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + 2*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + 2*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + 2*t)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + 3*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + 3*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + 3*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + 3*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + 3*t)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + 4*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + 4*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + 4*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + 4*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t^2 + 4*t)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + 4*t^2*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + t)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + 2*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + 2*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + 2*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + 2*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + 2*t)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + 3*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + 3*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + 3*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + 3*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + 3*t)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + 4*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + 4*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + 4*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + 4*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t^2 + 4*t)*x^3 + 3*x + 1 ************** MAGMA ***************** Host client-146-186-121-68.mobility-up.psu.edu. (146.186.121.68) Time: Thu Apr 1 16:53:04 2004 Input: T := PolynomialRing(RationalField()); GA, RA := GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1); print(GA); Z := Integers(); p:=5; hp:=Z ! ((p-1)/2); P:= FunctionField(GF(p)); Q:= PolynomialRing(P); S := [ P | ]; // for q in [0..p-1] do q:=0; for r in [0..p-1] do for s in [0..p-1] do Append(~S, q*t^2+r*t+s); end for; end for; //end for; zeromat := elt; for b in S do for c in S do for d in S do a5 := 2*c; a4 := 2+2*c+c^2-4*b*d; a3 := 2+4*b+2*c+2*c^2-4*d-8*b*d; a2 := 5+12*b+4*c+c^2-4*b*d; a1 := 6+12*b+2*c; a0 := 4*b+1; f := x^6 + a5*x^5 + a4*x^4 + a3*x^3 + a2*x^2 + a1*x + a0; fp:=f^hp; c12:=Coefficient(fp, p-2); c11:=Coefficient(fp, p-1); c22:=Coefficient(fp, 2*p-2); c21:=Coefficient(fp, 2*p-1); m:=elt; if m ne zeromat then n:=elt; if m*n ne zeromat then continue; end if; end if; if not IsIrreducible(f) then continue; end if; G, R:= GaloisGroup(f); if G eq GA then print(f); end if; end for; end for; end for; Output: Magma V2.10-22 Thu Apr 1 2004 16:52:41 on modular [Seed = 1164544581] ------------------------------------- Permutation group GA acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + t*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + 2*t*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + 3*t*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + 4*t*x^3 + 3*x + 1 x^6 + 4*x^5 + (4*t + 4)*x^3 + (2*t + 2)*x^2 + 2*t*x + 4*t + 1 x^6 + 2*t*x^5 + (t + 2)*x^4 + (3*t + 1)*x^3 + (4*t + 1)*x + 4*t + 1 x^6 + (2*t + 3)*x^5 + (4*t + 1)*x^4 + (4*t + 1)*x^3 + (3*t + 2)*x^2 + (4*t + 4)*x + 4*t + 1 x^6 + (3*t + 1)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t + 1 x^6 + 4*x^5 + (4*t + 3)*x^3 + (2*t + 4)*x^2 + (2*t + 2)*x + 4*t x^6 + 2*t*x^5 + 4*t*x^4 + 4*t*x^3 + 3*t*x^2 + (4*t + 3)*x + 4*t x^6 + (2*t + 2)*x^5 + (t + 3)*x^4 + (3*t + 4)*x^3 + 4*t*x + 4*t x^6 + (3*t + 4)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t x^6 + 4*x^5 + (4*t + 2)*x^3 + (2*t + 1)*x^2 + (2*t + 4)*x + 4*t + 4 x^6 + (2*t + 2)*x^5 + (4*t + 4)*x^4 + (4*t + 4)*x^3 + (3*t + 3)*x^2 + (4*t + 2)*x + 4*t + 4 x^6 + (2*t + 4)*x^5 + (t + 4)*x^4 + (3*t + 2)*x^3 + (4*t + 4)*x + 4*t + 4 x^6 + (3*t + 2)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t + 4 x^6 + 4*x^5 + (4*t + 1)*x^3 + (2*t + 3)*x^2 + (2*t + 1)*x + 4*t + 3 x^6 + (2*t + 4)*x^5 + (4*t + 3)*x^4 + (4*t + 3)*x^3 + (3*t + 1)*x^2 + (4*t + 1)*x + 4*t + 3 x^6 + (2*t + 1)*x^5 + t*x^4 + 3*t*x^3 + (4*t + 3)*x + 4*t + 3 x^6 + 3*t*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t + 3 x^6 + 4*x^5 + 4*t*x^3 + 2*t*x^2 + (2*t + 3)*x + 4*t + 2 x^6 + (2*t + 1)*x^5 + (4*t + 2)*x^4 + (4*t + 2)*x^3 + (3*t + 4)*x^2 + 4*t*x + 4*t + 2 x^6 + (2*t + 3)*x^5 + (t + 1)*x^4 + (3*t + 3)*x^3 + (4*t + 2)*x + 4*t + 2 x^6 + (3*t + 3)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t + 2 x^6 + 4*x^5 + (3*t + 4)*x^3 + (4*t + 2)*x^2 + 4*t*x + 3*t + 1 x^6 + 4*t*x^5 + (2*t + 2)*x^4 + (t + 1)*x^3 + (3*t + 1)*x + 3*t + 1 x^6 + (4*t + 3)*x^5 + (3*t + 1)*x^4 + (3*t + 1)*x^3 + (t + 2)*x^2 + (3*t + 4)*x + 3*t + 1 x^6 + (t + 1)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 3*t + 1 x^6 + 4*x^5 + (3*t + 3)*x^3 + (4*t + 4)*x^2 + (4*t + 2)*x + 3*t x^6 + 4*t*x^5 + 3*t*x^4 + 3*t*x^3 + t*x^2 + (3*t + 3)*x + 3*t x^6 + (4*t + 2)*x^5 + (2*t + 3)*x^4 + (t + 4)*x^3 + 3*t*x + 3*t x^6 + (t + 4)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 3*t x^6 + 4*x^5 + (3*t + 2)*x^3 + (4*t + 1)*x^2 + (4*t + 4)*x + 3*t + 4 x^6 + (4*t + 2)*x^5 + (3*t + 4)*x^4 + (3*t + 4)*x^3 + (t + 3)*x^2 + (3*t + 2)*x + 3*t + 4 x^6 + (4*t + 4)*x^5 + (2*t + 4)*x^4 + (t + 2)*x^3 + (3*t + 4)*x + 3*t + 4 x^6 + (t + 2)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 3*t + 4 ************** MAGMA ***************** Host client-146-186-121-68.mobility-up.psu.edu. (146.186.121.68) Time: Thu Apr 1 16:54:02 2004 Input: T := PolynomialRing(RationalField()); GA, RA := GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1); print(GA); Z := Integers(); p:=7; hp:=Z ! ((p-1)/2); P:= FunctionField(GF(p)); Q:= PolynomialRing(P); S := [ P | ]; // for q in [0..p-1] do q:=0; for r in [0..p-1] do for s in [0..p-1] do Append(~S, q*t^2+r*t+s); end for; end for; //end for; zeromat := elt; for b in S do for c in S do for d in S do a5 := 2*c; a4 := 2+2*c+c^2-4*b*d; a3 := 2+4*b+2*c+2*c^2-4*d-8*b*d; a2 := 5+12*b+4*c+c^2-4*b*d; a1 := 6+12*b+2*c; a0 := 4*b+1; f := x^6 + a5*x^5 + a4*x^4 + a3*x^3 + a2*x^2 + a1*x + a0; fp:=f^hp; c12:=Coefficient(fp, p-2); c11:=Coefficient(fp, p-1); c22:=Coefficient(fp, 2*p-2); c21:=Coefficient(fp, 2*p-1); m:=elt; if m ne zeromat then n:=elt; if m*n ne zeromat then continue; end if; end if; if not IsIrreducible(f) then continue; end if; G, R:= GaloisGroup(f); if G eq GA then print(f); end if; end for; end for; end for; Output: Magma V2.10-22 Thu Apr 1 2004 16:53:40 on modular [Seed = 1550881553] ------------------------------------- Permutation group GA acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) ************** MAGMA ***************** Host client-146-186-121-68.mobility-up.psu.edu. (146.186.121.68) Time: Thu Apr 1 16:54:58 2004 Input: T := PolynomialRing(RationalField()); GA, RA := GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1); p:=7; hp:= Integers() ! ((p-1)/2); P:= FunctionField(GF(p)); Q:= PolynomialRing(P); S := [ P | ]; // for q in [0..p-1] do q:=0; for r in [0..p-1] do for s in [0..p-1] do Append(~S, q*t^2+r*t+s); end for; end for; //end for; zeromat := elt; for b in S do for c in S do for d in S do a5 := 2*c; a4 := 2+2*c+c^2-4*b*d; a3 := 2+4*b+2*c+2*c^2-4*d-8*b*d; a2 := 5+12*b+4*c+c^2-4*b*d; a1 := 6+12*b+2*c; a0 := 4*b+1; f := x^6 + a5*x^5 + a4*x^4 + a3*x^3 + a2*x^2 + a1*x + a0; fp:=f^hp; c12:=Coefficient(fp, p-2); c11:=Coefficient(fp, p-1); c22:=Coefficient(fp, 2*p-2); c21:=Coefficient(fp, 2*p-1); m:=elt; if m ne zeromat then n:=elt; if m*n ne zeromat then continue; end if; end if; if not IsIrreducible(f) then continue; end if; G, R:= GaloisGroup(f); if G eq GA then print(f); end if; end for; end for; end for; Output: Magma V2.10-22 Thu Apr 1 2004 16:54:36 on modular [Seed = 1417190369] ------------------------------------- ************** MAGMA ***************** Host client-146-186-121-68.mobility-up.psu.edu. (146.186.121.68) Time: Thu Apr 1 16:55:27 2004 Input: T := PolynomialRing(RationalField()); GA, RA := GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1); p:=5; hp:= Integers() ! ((p-1)/2); P:= FunctionField(GF(p)); Q:= PolynomialRing(P); S := [ P | ]; // for q in [0..p-1] do q:=0; for r in [0..p-1] do for s in [0..p-1] do Append(~S, q*t^2+r*t+s); end for; end for; //end for; zeromat := elt; for b in S do for c in S do for d in S do a5 := 2*c; a4 := 2+2*c+c^2-4*b*d; a3 := 2+4*b+2*c+2*c^2-4*d-8*b*d; a2 := 5+12*b+4*c+c^2-4*b*d; a1 := 6+12*b+2*c; a0 := 4*b+1; f := x^6 + a5*x^5 + a4*x^4 + a3*x^3 + a2*x^2 + a1*x + a0; fp:=f^hp; c12:=Coefficient(fp, p-2); c11:=Coefficient(fp, p-1); c22:=Coefficient(fp, 2*p-2); c21:=Coefficient(fp, 2*p-1); m:=elt; if m ne zeromat then n:=elt; if m*n ne zeromat then continue; end if; end if; if not IsIrreducible(f) then continue; end if; G, R:= GaloisGroup(f); if G eq GA then print(f); end if; end for; end for; end for; Output: Magma V2.10-22 Thu Apr 1 2004 16:55:05 on modular [Seed = 2693558064] ------------------------------------- x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + t*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + 2*t*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + 3*t*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + 4*t*x^3 + 3*x + 1 x^6 + 4*x^5 + (4*t + 4)*x^3 + (2*t + 2)*x^2 + 2*t*x + 4*t + 1 x^6 + 2*t*x^5 + (t + 2)*x^4 + (3*t + 1)*x^3 + (4*t + 1)*x + 4*t + 1 x^6 + (2*t + 3)*x^5 + (4*t + 1)*x^4 + (4*t + 1)*x^3 + (3*t + 2)*x^2 + (4*t + 4)*x + 4*t + 1 x^6 + (3*t + 1)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t + 1 x^6 + 4*x^5 + (4*t + 3)*x^3 + (2*t + 4)*x^2 + (2*t + 2)*x + 4*t x^6 + 2*t*x^5 + 4*t*x^4 + 4*t*x^3 + 3*t*x^2 + (4*t + 3)*x + 4*t x^6 + (2*t + 2)*x^5 + (t + 3)*x^4 + (3*t + 4)*x^3 + 4*t*x + 4*t x^6 + (3*t + 4)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t x^6 + 4*x^5 + (4*t + 2)*x^3 + (2*t + 1)*x^2 + (2*t + 4)*x + 4*t + 4 x^6 + (2*t + 2)*x^5 + (4*t + 4)*x^4 + (4*t + 4)*x^3 + (3*t + 3)*x^2 + (4*t + 2)*x + 4*t + 4 x^6 + (2*t + 4)*x^5 + (t + 4)*x^4 + (3*t + 2)*x^3 + (4*t + 4)*x + 4*t + 4 x^6 + (3*t + 2)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t + 4 x^6 + 4*x^5 + (4*t + 1)*x^3 + (2*t + 3)*x^2 + (2*t + 1)*x + 4*t + 3 x^6 + (2*t + 4)*x^5 + (4*t + 3)*x^4 + (4*t + 3)*x^3 + (3*t + 1)*x^2 + (4*t + 1)*x + 4*t + 3 x^6 + (2*t + 1)*x^5 + t*x^4 + 3*t*x^3 + (4*t + 3)*x + 4*t + 3 x^6 + 3*t*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t + 3 x^6 + 4*x^5 + 4*t*x^3 + 2*t*x^2 + (2*t + 3)*x + 4*t + 2 x^6 + (2*t + 1)*x^5 + (4*t + 2)*x^4 + (4*t + 2)*x^3 + (3*t + 4)*x^2 + 4*t*x + 4*t + 2 x^6 + (2*t + 3)*x^5 + (t + 1)*x^4 + (3*t + 3)*x^3 + (4*t + 2)*x + 4*t + 2 x^6 + (3*t + 3)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t + 2 x^6 + 4*x^5 + (3*t + 4)*x^3 + (4*t + 2)*x^2 + 4*t*x + 3*t + 1 x^6 + 4*t*x^5 + (2*t + 2)*x^4 + (t + 1)*x^3 + (3*t + 1)*x + 3*t + 1 x^6 + (4*t + 3)*x^5 + (3*t + 1)*x^4 + (3*t + 1)*x^3 + (t + 2)*x^2 + (3*t + 4)*x + 3*t + 1 x^6 + (t + 1)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 3*t + 1 x^6 + 4*x^5 + (3*t + 3)*x^3 + (4*t + 4)*x^2 + (4*t + 2)*x + 3*t x^6 + 4*t*x^5 + 3*t*x^4 + 3*t*x^3 + t*x^2 + (3*t + 3)*x + 3*t x^6 + (4*t + 2)*x^5 + (2*t + 3)*x^4 + (t + 4)*x^3 + 3*t*x + 3*t x^6 + (t + 4)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 3*t x^6 + 4*x^5 + (3*t + 2)*x^3 + (4*t + 1)*x^2 + (4*t + 4)*x + 3*t + 4 x^6 + (4*t + 2)*x^5 + (3*t + 4)*x^4 + (3*t + 4)*x^3 + (t + 3)*x^2 + (3*t + 2)*x + 3*t + 4 x^6 + (4*t + 4)*x^5 + (2*t + 4)*x^4 + (t + 2)*x^3 + (3*t + 4)*x + 3*t + 4 x^6 + (t + 2)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 3*t + 4 ************** MAGMA ***************** Host client-146-186-121-68.mobility-up.psu.edu. (146.186.121.68) Time: Thu Apr 1 16:57:10 2004 Input: T := PolynomialRing(RationalField()); GA, RA := GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1); p:=5; hp:= Integers() ! ((p-1)/2); P:= FunctionField(GF(p)); Q:= PolynomialRing(P); S := [ P | ]; // for q in [0..p-1] do q:=0; for r in [0..p-1] do for s in [0..p-1] do Append(~S, q*t^2+r*t+s); end for; end for; //end for; zeromat := elt; for b in S do for c in S do for d in S do a5 := 2*c; a4 := 2+2*c+c^2-4*b*d; a3 := 2+4*b+2*c+2*c^2-4*d-8*b*d; a2 := 5+12*b+4*c+c^2-4*b*d; a1 := 6+12*b+2*c; a0 := 4*b+1; f := x^6 + a5*x^5 + a4*x^4 + a3*x^3 + a2*x^2 + a1*x + a0; fp:=f^hp; c12:=Coefficient(fp, p-2); c11:=Coefficient(fp, p-1); c22:=Coefficient(fp, 2*p-2); c21:=Coefficient(fp, 2*p-1); m:=elt; if m ne zeromat then n:=elt; if m*n ne zeromat then continue; end if; end if; if not IsIrreducible(f) then continue; end if; G, R:= GaloisGroup(f); if G eq GA then print(f); end if; end for; end for; end for; Output: Magma V2.10-22 Thu Apr 1 2004 16:56:47 on modular [Seed = 3096733838] ------------------------------------- x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + t*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (2*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + 2*t*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (3*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + 3*t*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t + 1)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t + 2)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t + 3)*x^3 + 3*x + 1 x^6 + 2*x^5 + (4*t + 4)*x^3 + 3*x + 1 x^6 + 2*x^5 + 4*t*x^3 + 3*x + 1 x^6 + 4*x^5 + (4*t + 4)*x^3 + (2*t + 2)*x^2 + 2*t*x + 4*t + 1 x^6 + 2*t*x^5 + (t + 2)*x^4 + (3*t + 1)*x^3 + (4*t + 1)*x + 4*t + 1 x^6 + (2*t + 3)*x^5 + (4*t + 1)*x^4 + (4*t + 1)*x^3 + (3*t + 2)*x^2 + (4*t + 4)*x + 4*t + 1 x^6 + (3*t + 1)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t + 1 x^6 + 4*x^5 + (4*t + 3)*x^3 + (2*t + 4)*x^2 + (2*t + 2)*x + 4*t x^6 + 2*t*x^5 + 4*t*x^4 + 4*t*x^3 + 3*t*x^2 + (4*t + 3)*x + 4*t x^6 + (2*t + 2)*x^5 + (t + 3)*x^4 + (3*t + 4)*x^3 + 4*t*x + 4*t x^6 + (3*t + 4)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t x^6 + 4*x^5 + (4*t + 2)*x^3 + (2*t + 1)*x^2 + (2*t + 4)*x + 4*t + 4 x^6 + (2*t + 2)*x^5 + (4*t + 4)*x^4 + (4*t + 4)*x^3 + (3*t + 3)*x^2 + (4*t + 2)*x + 4*t + 4 x^6 + (2*t + 4)*x^5 + (t + 4)*x^4 + (3*t + 2)*x^3 + (4*t + 4)*x + 4*t + 4 x^6 + (3*t + 2)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t + 4 x^6 + 4*x^5 + (4*t + 1)*x^3 + (2*t + 3)*x^2 + (2*t + 1)*x + 4*t + 3 x^6 + (2*t + 4)*x^5 + (4*t + 3)*x^4 + (4*t + 3)*x^3 + (3*t + 1)*x^2 + (4*t + 1)*x + 4*t + 3 x^6 + (2*t + 1)*x^5 + t*x^4 + 3*t*x^3 + (4*t + 3)*x + 4*t + 3 x^6 + 3*t*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t + 3 x^6 + 4*x^5 + 4*t*x^3 + 2*t*x^2 + (2*t + 3)*x + 4*t + 2 x^6 + (2*t + 1)*x^5 + (4*t + 2)*x^4 + (4*t + 2)*x^3 + (3*t + 4)*x^2 + 4*t*x + 4*t + 2 x^6 + (2*t + 3)*x^5 + (t + 1)*x^4 + (3*t + 3)*x^3 + (4*t + 2)*x + 4*t + 2 x^6 + (3*t + 3)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t + 2 x^6 + 4*x^5 + (3*t + 4)*x^3 + (4*t + 2)*x^2 + 4*t*x + 3*t + 1 x^6 + 4*t*x^5 + (2*t + 2)*x^4 + (t + 1)*x^3 + (3*t + 1)*x + 3*t + 1 x^6 + (4*t + 3)*x^5 + (3*t + 1)*x^4 + (3*t + 1)*x^3 + (t + 2)*x^2 + (3*t + 4)*x + 3*t + 1 x^6 + (t + 1)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 3*t + 1 x^6 + 4*x^5 + (3*t + 3)*x^3 + (4*t + 4)*x^2 + (4*t + 2)*x + 3*t x^6 + 4*t*x^5 + 3*t*x^4 + 3*t*x^3 + t*x^2 + (3*t + 3)*x + 3*t x^6 + (4*t + 2)*x^5 + (2*t + 3)*x^4 + (t + 4)*x^3 + 3*t*x + 3*t x^6 + (t + 4)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 3*t x^6 + 4*x^5 + (3*t + 2)*x^3 + (4*t + 1)*x^2 + (4*t + 4)*x + 3*t + 4 x^6 + (4*t + 2)*x^5 + (3*t + 4)*x^4 + (3*t + 4)*x^3 + (t + 3)*x^2 + (3*t + 2)*x + 3*t + 4 x^6 + (4*t + 4)*x^5 + (2*t + 4)*x^4 + (t + 2)*x^3 + (3*t + 4)*x + 3*t + 4 x^6 + (t + 2)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 3*t + 4 ************** MAGMA ***************** Host client-146-186-121-68.mobility-up.psu.edu. (146.186.121.68) Time: Thu Apr 1 16:57:25 2004 Input: T := PolynomialRing(RationalField()); GA, RA := GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1); p:=5; hp:= Integers() ! ((p-1)/2); P:= FunctionField(GF(p)); Q:= PolynomialRing(P); S := [ P | ]; // for q in [0..p-1] do q:=0; for r in [0..p-1] do for s in [0..p-1] do Append(~S, q*t^2+r*t+s); end for; end for; //end for; zeromat := elt; for b in S do for c in S do for d in S do a5 := 2*c; a4 := 2+2*c+c^2-4*b*d; a3 := 2+4*b+2*c+2*c^2-4*d-8*b*d; a2 := 5+12*b+4*c+c^2-4*b*d; a1 := 6+12*b+2*c; a0 := 4*b+1; f := x^6 + a5*x^5 + a4*x^4 + a3*x^3 + a2*x^2 + a1*x + a0; fp:=f^hp; c12:=Coefficient(fp, p-2); c11:=Coefficient(fp, p-1); c22:=Coefficient(fp, 2*p-2); c21:=Coefficient(fp, 2*p-1); m:=elt; if m ne zeromat then n:=elt; if m*n ne zeromat then continue; end if; end if; if not IsIrreducible(f) then continue; end if; G, R:= GaloisGroup(f); if G eq GA then print b c d f; end if; end for; end for; end for; Output: Magma V2.10-22 Thu Apr 1 2004 16:57:22 on modular [Seed = 2963038427] ------------------------------------- >> print b c d f; ^ User error: bad syntax >> end if; ^ User error: bad syntax >> end for; ^ User error: bad syntax >> end for; ^ User error: bad syntax >> end for;; ^ User error: bad syntax Total time: 2.650 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host client-146-186-121-68.mobility-up.psu.edu. (146.186.121.68) Time: Thu Apr 1 16:58:01 2004 Input: T := PolynomialRing(RationalField()); GA, RA := GaloisGroup(u^6 + 2*u^4 + 2*u^3 + 5*u^2 + 6*u +1); p:=5; hp:= Integers() ! ((p-1)/2); P:= FunctionField(GF(p)); Q:= PolynomialRing(P); S := [ P | ]; // for q in [0..p-1] do q:=0; for r in [0..p-1] do for s in [0..p-1] do Append(~S, q*t^2+r*t+s); end for; end for; //end for; zeromat := elt; for b in S do for c in S do for d in S do a5 := 2*c; a4 := 2+2*c+c^2-4*b*d; a3 := 2+4*b+2*c+2*c^2-4*d-8*b*d; a2 := 5+12*b+4*c+c^2-4*b*d; a1 := 6+12*b+2*c; a0 := 4*b+1; f := x^6 + a5*x^5 + a4*x^4 + a3*x^3 + a2*x^2 + a1*x + a0; fp:=f^hp; c12:=Coefficient(fp, p-2); c11:=Coefficient(fp, p-1); c22:=Coefficient(fp, 2*p-2); c21:=Coefficient(fp, 2*p-1); m:=elt; if m ne zeromat then n:=elt; if m*n ne zeromat then continue; end if; end if; if not IsIrreducible(f) then continue; end if; G, R:= GaloisGroup(f); if G eq GA then print b, c, d, f; end if; end for; end for; end for; Output: Magma V2.10-22 Thu Apr 1 2004 16:57:38 on modular [Seed = 2292472051] ------------------------------------- 0 1 t x^6 + 2*x^5 + (t + 1)*x^3 + 3*x + 1 0 1 t + 1 x^6 + 2*x^5 + (t + 2)*x^3 + 3*x + 1 0 1 t + 2 x^6 + 2*x^5 + (t + 3)*x^3 + 3*x + 1 0 1 t + 3 x^6 + 2*x^5 + (t + 4)*x^3 + 3*x + 1 0 1 t + 4 x^6 + 2*x^5 + t*x^3 + 3*x + 1 0 1 2*t x^6 + 2*x^5 + (2*t + 1)*x^3 + 3*x + 1 0 1 2*t + 1 x^6 + 2*x^5 + (2*t + 2)*x^3 + 3*x + 1 0 1 2*t + 2 x^6 + 2*x^5 + (2*t + 3)*x^3 + 3*x + 1 0 1 2*t + 3 x^6 + 2*x^5 + (2*t + 4)*x^3 + 3*x + 1 0 1 2*t + 4 x^6 + 2*x^5 + 2*t*x^3 + 3*x + 1 0 1 3*t x^6 + 2*x^5 + (3*t + 1)*x^3 + 3*x + 1 0 1 3*t + 1 x^6 + 2*x^5 + (3*t + 2)*x^3 + 3*x + 1 0 1 3*t + 2 x^6 + 2*x^5 + (3*t + 3)*x^3 + 3*x + 1 0 1 3*t + 3 x^6 + 2*x^5 + (3*t + 4)*x^3 + 3*x + 1 0 1 3*t + 4 x^6 + 2*x^5 + 3*t*x^3 + 3*x + 1 0 1 4*t x^6 + 2*x^5 + (4*t + 1)*x^3 + 3*x + 1 0 1 4*t + 1 x^6 + 2*x^5 + (4*t + 2)*x^3 + 3*x + 1 0 1 4*t + 2 x^6 + 2*x^5 + (4*t + 3)*x^3 + 3*x + 1 0 1 4*t + 3 x^6 + 2*x^5 + (4*t + 4)*x^3 + 3*x + 1 0 1 4*t + 4 x^6 + 2*x^5 + 4*t*x^3 + 3*x + 1 t 2 0 x^6 + 4*x^5 + (4*t + 4)*x^3 + (2*t + 2)*x^2 + 2*t*x + 4*t + 1 t t 4*t + 4 x^6 + 2*t*x^5 + (t + 2)*x^4 + (3*t + 1)*x^3 + (4*t + 1)*x + 4*t + 1 t t + 4 4*t + 4 x^6 + (2*t + 3)*x^5 + (4*t + 1)*x^4 + (4*t + 1)*x^3 + (3*t + 2)*x^2 + (4*t + 4)*x + 4*t + 1 t 4*t + 3 4*t + 3 x^6 + (3*t + 1)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t + 1 t + 1 2 0 x^6 + 4*x^5 + (4*t + 3)*x^3 + (2*t + 4)*x^2 + (2*t + 2)*x + 4*t t + 1 t 4*t + 3 x^6 + 2*t*x^5 + 4*t*x^4 + 4*t*x^3 + 3*t*x^2 + (4*t + 3)*x + 4*t t + 1 t + 1 4*t + 3 x^6 + (2*t + 2)*x^5 + (t + 3)*x^4 + (3*t + 4)*x^3 + 4*t*x + 4*t t + 1 4*t + 2 4*t + 2 x^6 + (3*t + 4)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t t + 2 2 0 x^6 + 4*x^5 + (4*t + 2)*x^3 + (2*t + 1)*x^2 + (2*t + 4)*x + 4*t + 4 t + 2 t + 1 4*t + 2 x^6 + (2*t + 2)*x^5 + (4*t + 4)*x^4 + (4*t + 4)*x^3 + (3*t + 3)*x^2 + (4*t + 2)*x + 4*t + 4 t + 2 t + 2 4*t + 2 x^6 + (2*t + 4)*x^5 + (t + 4)*x^4 + (3*t + 2)*x^3 + (4*t + 4)*x + 4*t + 4 t + 2 4*t + 1 4*t + 1 x^6 + (3*t + 2)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t + 4 t + 3 2 0 x^6 + 4*x^5 + (4*t + 1)*x^3 + (2*t + 3)*x^2 + (2*t + 1)*x + 4*t + 3 t + 3 t + 2 4*t + 1 x^6 + (2*t + 4)*x^5 + (4*t + 3)*x^4 + (4*t + 3)*x^3 + (3*t + 1)*x^2 + (4*t + 1)*x + 4*t + 3 t + 3 t + 3 4*t + 1 x^6 + (2*t + 1)*x^5 + t*x^4 + 3*t*x^3 + (4*t + 3)*x + 4*t + 3 t + 3 4*t 4*t x^6 + 3*t*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t + 3 t + 4 2 0 x^6 + 4*x^5 + 4*t*x^3 + 2*t*x^2 + (2*t + 3)*x + 4*t + 2 t + 4 t + 3 4*t x^6 + (2*t + 1)*x^5 + (4*t + 2)*x^4 + (4*t + 2)*x^3 + (3*t + 4)*x^2 + 4*t*x + 4*t + 2 t + 4 t + 4 4*t x^6 + (2*t + 3)*x^5 + (t + 1)*x^4 + (3*t + 3)*x^3 + (4*t + 2)*x + 4*t + 2 t + 4 4*t + 4 4*t + 4 x^6 + (3*t + 3)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4*t + 2 2*t 2 0 x^6 + 4*x^5 + (3*t + 4)*x^3 + (4*t + 2)*x^2 + 4*t*x + 3*t + 1 2*t 2*t 3*t + 4 x^6 + 4*t*x^5 + (2*t + 2)*x^4 + (t + 1)*x^3 + (3*t + 1)*x + 3*t + 1 2*t 2*t + 4 3*t + 4 x^6 + (4*t + 3)*x^5 + (3*t + 1)*x^4 + (3*t + 1)*x^3 + (t + 2)*x^2 + (3*t + 4)*x + 3*t + 1 2*t 3*t + 3 3*t + 3 x^6 + (t + 1)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 3*t + 1 2*t + 1 2 0 x^6 + 4*x^5 + (3*t + 3)*x^3 + (4*t + 4)*x^2 + (4*t + 2)*x + 3*t 2*t + 1 2*t 3*t + 3 x^6 + 4*t*x^5 + 3*t*x^4 + 3*t*x^3 + t*x^2 + (3*t + 3)*x + 3*t 2*t + 1 2*t + 1 3*t + 3 x^6 + (4*t + 2)*x^5 + (2*t + 3)*x^4 + (t + 4)*x^3 + 3*t*x + 3*t 2*t + 1 3*t + 2 3*t + 2 x^6 + (t + 4)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 3*t 2*t + 2 2 0 x^6 + 4*x^5 + (3*t + 2)*x^3 + (4*t + 1)*x^2 + (4*t + 4)*x + 3*t + 4 2*t + 2 2*t + 1 3*t + 2 x^6 + (4*t + 2)*x^5 + (3*t + 4)*x^4 + (3*t + 4)*x^3 + (t + 3)*x^2 + (3*t + 2)*x + 3*t + 4 2*t + 2 2*t + 2 3*t + 2 x^6 + (4*t + 4)*x^5 + (2*t + 4)*x^4 + (t + 2)*x^3 + (3*t + 4)*x + 3*t + 4 2*t + 2 3*t + 1 3*t + 1 x^6 + (t + 2)*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 3*t + 4 ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Thu Apr 1 17:56:55 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > ( (17*x+19*y)^15+15*(17*x+19*y)^7*(17*x-19*y)^8 ) div 16 in I > Output: Magma V2.10-22 Thu Apr 1 2004 17:56:53 on modular [Seed = 874048043] ------------------------------------- [ 17*x^2*y + 361*y^3, 289*x^2 + 361*y^2, 2*x*y^3, 34*x*y, 722*y^3 ] true Total time: 2.510 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Thu Apr 1 17:57:27 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > ( (17*x+19*y)^15+15*(17*x+19*y)^7*(17*x-19*y)^8 ) div 16 in I > Output: Magma V2.10-22 Thu Apr 1 2004 17:57:24 on modular [Seed = 203477618] ------------------------------------- >> I := ideal; ^ User error: bad syntax >> GroebnerBasis(I); ^ User error: Identifier 'I' has not been declared or assigned >> ( (17*x+19*y)^15+15*(17*x+19*y)^7*(17*x-19*y)^8 ) div 16 in I ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.549 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Thu Apr 1 17:57:43 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > ( (17*x+19*y)^15+15*(17*x+19*y)^7*(17*x-19*y)^8 ) div 16 in I > Output: Magma V2.10-22 Thu Apr 1 2004 17:57:40 on modular [Seed = 69786186] ------------------------------------- [ 17*x^2*y + 3249*y^3, 289*x^2 + 361*y^2, 38*x*y^3, 646*x*y, 13718*y^3 ] true Total time: 2.539 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Thu Apr 1 17:58:16 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > ( (17*x+19*y)^15+15*(17*x+19*y)^7*(17*x-19*y)^8 ) div 16 in I > Output: Magma V2.10-22 Thu Apr 1 2004 17:58:13 on modular [Seed = 289263550] ------------------------------------- [ 17*x^2*y + 3249*y^3 + 137*y*z^2, 289*x^2 + 361*y^2 + 961*z^2, 38*x*y^3, 38*x*y*z, 646*x*y, 38*y^3*z + 950*y*z^3, 13718*y^3 + 38*y*z^2, 1216*y*z ] false Total time: 2.549 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Thu Apr 1 17:58:52 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > ( (17*x+19*y+31*z)^15+15*(17*x+19*y+31*z)^7*(17*x-19*y-31*z)^8 ) div 16 in I > Output: Magma V2.10-22 Thu Apr 1 2004 17:58:50 on modular [Seed = 1766176745] ------------------------------------- [ 17*x^2*y + 3249*y^3 + 137*y*z^2, 289*x^2 + 361*y^2 + 961*z^2, 38*x*y^3, 38*x*y*z, 646*x*y, 38*y^3*z + 950*y*z^3, 13718*y^3 + 38*y*z^2, 1216*y*z ] false Total time: 2.549 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Thu Apr 1 17:59:34 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > ( (17*x+19*y+31*z)^31+31*(17*x+19*y+31*z)^15*(17*x-19*y-31*z)^16 ) div 32 in I > Output: Magma V2.10-22 Thu Apr 1 2004 17:59:32 on modular [Seed = 1632485279] ------------------------------------- [ x^2*y*z + 19*y^3*z + 31*y*z^3, 17*x^2*y + 3249*y^3 + 403*y*z^2, 17*x^2*z + 437*y^2*z + 10571*z^3, 289*x^2 + 361*y^2 + 961*z^2, 38*x*y^3, 2*x*y*z, 646*x*y, 62*x*z^3, 1054*x*z, 38*y^3*z, 13718*y^3, 62*y*z^3, 1178*y*z, 59582*z^3 ] true Total time: 2.580 seconds, Total memory usage: 2.50MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Thu Apr 1 17:59:56 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > ( (17*x+19*y+31*z)^15+15*(17*x+19*y+31*z)^7*(17*x-19*y-31*z)^15 ) div 16 in I > Output: Magma V2.10-22 Thu Apr 1 2004 17:59:54 on modular [Seed = 2035656633] ------------------------------------- [ x^2*y*z + 19*y^3*z + 31*y*z^3, 17*x^2*y + 3249*y^3 + 403*y*z^2, 17*x^2*z + 437*y^2*z + 10571*z^3, 289*x^2 + 361*y^2 + 961*z^2, 38*x*y^3, 2*x*y*z, 646*x*y, 62*x*z^3, 1054*x*z, 38*y^3*z, 13718*y^3, 62*y*z^3, 1178*y*z, 59582*z^3 ] >> ( (17*x+19*y+31*z)^15+15*(17*x+19*y+31*z)^7*(17*x-19*y-31*z)^15 ) div 16 ^ Runtime error in 'div': Argument 2 does not divide argument 1 Total time: 2.529 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Thu Apr 1 18:00:10 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > ( (17*x+19*y+31*z)^15+15*(17*x+19*y+31*z)^7*(17*x-19*y-31*z)^8 ) div 16 in I > Output: Magma V2.10-22 Thu Apr 1 2004 18:00:08 on modular [Seed = 1214551706] ------------------------------------- [ x^2*y*z + 19*y^3*z + 31*y*z^3, 17*x^2*y + 3249*y^3 + 403*y*z^2, 17*x^2*z + 437*y^2*z + 10571*z^3, 289*x^2 + 361*y^2 + 961*z^2, 38*x*y^3, 2*x*y*z, 646*x*y, 62*x*z^3, 1054*x*z, 38*y^3*z, 13718*y^3, 62*y*z^3, 1178*y*z, 59582*z^3 ] true Total time: 2.519 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Fri Apr 2 02:24:19 2004 Input: F := PolynomialRing(FiniteField(5^4)); C := HyperellipticCurve(x^3-1); Points(C : Bound:=4); Output: Magma V2.10-22 Fri Apr 2 2004 02:24:16 on modular [Seed = 638284596] ------------------------------------- {@ (1 : 0 : 0), (1 : 0 : 1), ($.1^2 : $.1^103 : 1), ($.1^2 : $.1^415 : 1), ($.1^3 : $.1^226 : 1), ($.1^3 : $.1^538 : 1), ($.1^7 : $.1^243 : 1), ($.1^7 : $.1^555 : 1), ($.1^8 : $.1^253 : 1), ($.1^8 : $.1^565 : 1), ($.1^9 : $.1^311 : 1), ($.1^9 : $.1^623 : 1), ($.1^10 : $.1^203 : 1), ($.1^10 : $.1^515 : 1), ($.1^12 : $.1^106 : 1), ($.1^12 : $.1^418 : 1), ($.1^13 : $.1^61 : 1), ($.1^13 : $.1^373 : 1), ($.1^15 : $.1^194 : 1), ($.1^15 : $.1^506 : 1), ($.1^17 : $.1^287 : 1), ($.1^17 : $.1^599 : 1), ($.1^18 : $.1^73 : 1), ($.1^18 : $.1^385 : 1), ($.1^23 : $.1^304 : 1), ($.1^23 : $.1^616 : 1), ($.1^24 : $.1^122 : 1), ($.1^24 : $.1^434 : 1), ($.1^26 : $.1^182 : 1), ($.1^26 : $.1^494 : 1), ($.1^27 : $.1^124 : 1), ($.1^27 : $.1^436 : 1), ($.1^29 : $.1^245 : 1), ($.1^29 : $.1^557 : 1), ($.1^34 : $.1^265 : 1), ($.1^34 : $.1^577 : 1), ($.1^35 : $.1^279 : 1), ($.1^35 : $.1^591 : 1), ($.1^38 : $.1^290 : 1), ($.1^38 : $.1^602 : 1), ($.1^40 : $.1^17 : 1), ($.1^40 : $.1^329 : 1), ($.1^42 : $.1^83 : 1), ($.1^42 : $.1^395 : 1), ($.1^43 : $.1^111 : 1), ($.1^43 : $.1^423 : 1), ($.1^44 : $.1^146 : 1), ($.1^44 : $.1^458 : 1), ($.1^45 : $.1^307 : 1), ($.1^45 : $.1^619 : 1), ($.1^47 : $.1^212 : 1), ($.1^47 : $.1^524 : 1), ($.1^50 : $.1^79 : 1), ($.1^50 : $.1^391 : 1), ($.1^51 : $.1^292 : 1), ($.1^51 : $.1^604 : 1), ($.1^52 : 1 : 1), ($.1^52 : 4 : 1), ($.1^53 : $.1^69 : 1), ($.1^53 : $.1^381 : 1), ($.1^56 : $.1^55 : 1), ($.1^56 : $.1^367 : 1), ($.1^57 : $.1^33 : 1), ($.1^57 : $.1^345 : 1), ($.1^60 : $.1^218 : 1), ($.1^60 : $.1^530 : 1), ($.1^61 : $.1^255 : 1), ($.1^61 : $.1^567 : 1), ($.1^65 : $.1^305 : 1), ($.1^65 : $.1^617 : 1), ($.1^69 : $.1^135 : 1), ($.1^69 : $.1^447 : 1), ($.1^72 : $.1^275 : 1), ($.1^72 : $.1^587 : 1), ($.1^75 : $.1^34 : 1), ($.1^75 : $.1^346 : 1), ($.1^77 : $.1^165 : 1), ($.1^77 : $.1^477 : 1), ($.1^78 : $.1^247 : 1), ($.1^78 : $.1^559 : 1), ($.1^79 : $.1^285 : 1), ($.1^79 : $.1^597 : 1), ($.1^81 : $.1^204 : 1), ($.1^81 : $.1^516 : 1), ($.1^83 : $.1^155 : 1), ($.1^83 : $.1^467 : 1), ($.1^85 : $.1^187 : 1), ($.1^85 : $.1^499 : 1), ($.1^88 : $.1^274 : 1), ($.1^88 : $.1^586 : 1), ($.1^89 : $.1^49 : 1), ($.1^89 : $.1^361 : 1), ($.1^90 : $.1^53 : 1), ($.1^90 : $.1^365 : 1), ($.1^92 : $.1^154 : 1), ($.1^92 : $.1^466 : 1), ($.1^97 : $.1^27 : 1), ($.1^97 : $.1^339 : 1), ($.1^99 : $.1^57 : 1), ($.1^99 : $.1^369 : 1), ($.1^101 : $.1^197 : 1), ($.1^101 : $.1^509 : 1), ($.1^103 : $.1^261 : 1), ($.1^103 : $.1^573 : 1), ($.1^104 : $.1^234 : 1), ($.1^104 : $.1^546 : 1), ($.1^113 : $.1^230 : 1), ($.1^113 : $.1^542 : 1), ($.1^115 : $.1^272 : 1), ($.1^115 : $.1^584 : 1), ($.1^116 : $.1^172 : 1), ($.1^116 : $.1^484 : 1), ($.1^117 : $.1^277 : 1), ($.1^117 : $.1^589 : 1), ($.1^118 : $.1^74 : 1), ($.1^118 : $.1^386 : 1), ($.1^120 : $.1^298 : 1), ($.1^120 : $.1^610 : 1), ($.1^121 : $.1^134 : 1), ($.1^121 : $.1^446 : 1), ($.1^130 : $.1^286 : 1), ($.1^130 : $.1^598 : 1), ($.1^135 : $.1^308 : 1), ($.1^135 : $.1^620 : 1), ($.1^136 : $.1^11 : 1), ($.1^136 : $.1^323 : 1), ($.1^137 : $.1^51 : 1), ($.1^137 : $.1^363 : 1), ($.1^141 : $.1^228 : 1), ($.1^141 : $.1^540 : 1), ($.1^145 : $.1^289 : 1), ($.1^145 : $.1^601 : 1), ($.1^148 : $.1^284 : 1), ($.1^148 : $.1^596 : 1), ($.1^149 : $.1^214 : 1), ($.1^149 : $.1^526 : 1), ($.1^152 : $.1^127 : 1), ($.1^152 : $.1^439 : 1), ($.1^153 : $.1^108 : 1), ($.1^153 : $.1^420 : 1), (2 : $.1^78 : 1), (2 : $.1^390 : 1), ($.1^158 : $.1^160 : 1), ($.1^158 : $.1^472 : 1), ($.1^159 : $.1^112 : 1), ($.1^159 : $.1^424 : 1), ($.1^164 : $.1^236 : 1), ($.1^164 : $.1^548 : 1), ($.1^166 : $.1^176 : 1), ($.1^166 : $.1^488 : 1), ($.1^167 : $.1^170 : 1), ($.1^167 : $.1^482 : 1), ($.1^168 : $.1^113 : 1), ($.1^168 : $.1^425 : 1), ($.1^169 : $.1^137 : 1), ($.1^169 : $.1^449 : 1), ($.1^170 : $.1^77 : 1), ($.1^170 : $.1^389 : 1), ($.1^171 : $.1^248 : 1), ($.1^171 : $.1^560 : 1), ($.1^174 : $.1^58 : 1), ($.1^174 : $.1^370 : 1), ($.1^175 : $.1^147 : 1), ($.1^175 : $.1^459 : 1), ($.1^177 : $.1^201 : 1), ($.1^177 : $.1^513 : 1), ($.1^182 : $.1^299 : 1), ($.1^182 : $.1^611 : 1), ($.1^183 : $.1^31 : 1), ($.1^183 : $.1^343 : 1), ($.1^184 : $.1^242 : 1), ($.1^184 : $.1^554 : 1), ($.1^187 : $.1^177 : 1), ($.1^187 : $.1^489 : 1), ($.1^189 : $.1^46 : 1), ($.1^189 : $.1^358 : 1), ($.1^190 : $.1^202 : 1), ($.1^190 : $.1^514 : 1), ($.1^196 : $.1^244 : 1), ($.1^196 : $.1^556 : 1), ($.1^197 : $.1^84 : 1), ($.1^197 : $.1^396 : 1), ($.1^198 : $.1^32 : 1), ($.1^198 : $.1^344 : 1), ($.1^200 : $.1^85 : 1), ($.1^200 : $.1^397 : 1), ($.1^203 : $.1^131 : 1), ($.1^203 : $.1^443 : 1), ($.1^206 : $.1^256 : 1), ($.1^206 : $.1^568 : 1), ($.1^207 : $.1^151 : 1), ($.1^207 : $.1^463 : 1), ($.1^208 : 0 : 1), ($.1^210 : $.1^103 : 1), ($.1^210 : $.1^415 : 1), ($.1^211 : $.1^226 : 1), ($.1^211 : $.1^538 : 1), ($.1^215 : $.1^243 : 1), ($.1^215 : $.1^555 : 1), ($.1^216 : $.1^253 : 1), ($.1^216 : $.1^565 : 1), ($.1^217 : $.1^311 : 1), ($.1^217 : $.1^623 : 1), ($.1^218 : $.1^203 : 1), ($.1^218 : $.1^515 : 1), ($.1^220 : $.1^106 : 1), ($.1^220 : $.1^418 : 1), ($.1^221 : $.1^61 : 1), ($.1^221 : $.1^373 : 1), ($.1^223 : $.1^194 : 1), ($.1^223 : $.1^506 : 1), ($.1^225 : $.1^287 : 1), ($.1^225 : $.1^599 : 1), ($.1^226 : $.1^73 : 1), ($.1^226 : $.1^385 : 1), ($.1^231 : $.1^304 : 1), ($.1^231 : $.1^616 : 1), ($.1^232 : $.1^122 : 1), ($.1^232 : $.1^434 : 1), ($.1^234 : $.1^182 : 1), ($.1^234 : $.1^494 : 1), ($.1^235 : $.1^124 : 1), ($.1^235 : $.1^436 : 1), ($.1^237 : $.1^245 : 1), ($.1^237 : $.1^557 : 1), ($.1^242 : $.1^265 : 1), ($.1^242 : $.1^577 : 1), ($.1^243 : $.1^279 : 1), ($.1^243 : $.1^591 : 1), ($.1^246 : $.1^290 : 1), ($.1^246 : $.1^602 : 1), ($.1^248 : $.1^17 : 1), ($.1^248 : $.1^329 : 1), ($.1^250 : $.1^83 : 1), ($.1^250 : $.1^395 : 1), ($.1^251 : $.1^111 : 1), ($.1^251 : $.1^423 : 1), ($.1^252 : $.1^146 : 1), ($.1^252 : $.1^458 : 1), ($.1^253 : $.1^307 : 1), ($.1^253 : $.1^619 : 1), ($.1^255 : $.1^212 : 1), ($.1^255 : $.1^524 : 1), ($.1^258 : $.1^79 : 1), ($.1^258 : $.1^391 : 1), ($.1^259 : $.1^292 : 1), ($.1^259 : $.1^604 : 1), ($.1^260 : 1 : 1), ($.1^260 : 4 : 1), ($.1^261 : $.1^69 : 1), ($.1^261 : $.1^381 : 1), ($.1^264 : $.1^55 : 1), ($.1^264 : $.1^367 : 1), ($.1^265 : $.1^33 : 1), ($.1^265 : $.1^345 : 1), ($.1^268 : $.1^218 : 1), ($.1^268 : $.1^530 : 1), ($.1^269 : $.1^255 : 1), ($.1^269 : $.1^567 : 1), ($.1^273 : $.1^305 : 1), ($.1^273 : $.1^617 : 1), ($.1^277 : $.1^135 : 1), ($.1^277 : $.1^447 : 1), ($.1^280 : $.1^275 : 1), ($.1^280 : $.1^587 : 1), ($.1^283 : $.1^34 : 1), ($.1^283 : $.1^346 : 1), ($.1^285 : $.1^165 : 1), ($.1^285 : $.1^477 : 1), ($.1^286 : $.1^247 : 1), ($.1^286 : $.1^559 : 1), ($.1^287 : $.1^285 : 1), ($.1^287 : $.1^597 : 1), ($.1^289 : $.1^204 : 1), ($.1^289 : $.1^516 : 1), ($.1^291 : $.1^155 : 1), ($.1^291 : $.1^467 : 1), ($.1^293 : $.1^187 : 1), ($.1^293 : $.1^499 : 1), ($.1^296 : $.1^274 : 1), ($.1^296 : $.1^586 : 1), ($.1^297 : $.1^49 : 1), ($.1^297 : $.1^361 : 1), ($.1^298 : $.1^53 : 1), ($.1^298 : $.1^365 : 1), ($.1^300 : $.1^154 : 1), ($.1^300 : $.1^466 : 1), ($.1^305 : $.1^27 : 1), ($.1^305 : $.1^339 : 1), ($.1^307 : $.1^57 : 1), ($.1^307 : $.1^369 : 1), ($.1^309 : $.1^197 : 1), ($.1^309 : $.1^509 : 1), ($.1^311 : $.1^261 : 1), ($.1^311 : $.1^573 : 1), (4 : $.1^234 : 1), (4 : $.1^546 : 1), ($.1^321 : $.1^230 : 1), ($.1^321 : $.1^542 : 1), ($.1^323 : $.1^272 : 1), ($.1^323 : $.1^584 : 1), ($.1^324 : $.1^172 : 1), ($.1^324 : $.1^484 : 1), ($.1^325 : $.1^277 : 1), ($.1^325 : $.1^589 : 1), ($.1^326 : $.1^74 : 1), ($.1^326 : $.1^386 : 1), ($.1^328 : $.1^298 : 1), ($.1^328 : $.1^610 : 1), ($.1^329 : $.1^134 : 1), ($.1^329 : $.1^446 : 1), ($.1^338 : $.1^286 : 1), ($.1^338 : $.1^598 : 1), ($.1^343 : $.1^308 : 1), ($.1^343 : $.1^620 : 1), ($.1^344 : $.1^11 : 1), ($.1^344 : $.1^323 : 1), ($.1^345 : $.1^51 : 1), ($.1^345 : $.1^363 : 1), ($.1^349 : $.1^228 : 1), ($.1^349 : $.1^540 : 1), ($.1^353 : $.1^289 : 1), ($.1^353 : $.1^601 : 1), ($.1^356 : $.1^284 : 1), ($.1^356 : $.1^596 : 1), ($.1^357 : $.1^214 : 1), ($.1^357 : $.1^526 : 1), ($.1^360 : $.1^127 : 1), ($.1^360 : $.1^439 : 1), ($.1^361 : $.1^108 : 1), ($.1^361 : $.1^420 : 1), ($.1^364 : $.1^78 : 1), ($.1^364 : $.1^390 : 1), ($.1^366 : $.1^160 : 1), ($.1^366 : $.1^472 : 1), ($.1^367 : $.1^112 : 1), ($.1^367 : $.1^424 : 1), ($.1^372 : $.1^236 : 1), ($.1^372 : $.1^548 : 1), ($.1^374 : $.1^176 : 1), ($.1^374 : $.1^488 : 1), ($.1^375 : $.1^170 : 1), ($.1^375 : $.1^482 : 1), ($.1^376 : $.1^113 : 1), ($.1^376 : $.1^425 : 1), ($.1^377 : $.1^137 : 1), ($.1^377 : $.1^449 : 1), ($.1^378 : $.1^77 : 1), ($.1^378 : $.1^389 : 1), ($.1^379 : $.1^248 : 1), ($.1^379 : $.1^560 : 1), ($.1^382 : $.1^58 : 1), ($.1^382 : $.1^370 : 1), ($.1^383 : $.1^147 : 1), ($.1^383 : $.1^459 : 1), ($.1^385 : $.1^201 : 1), ($.1^385 : $.1^513 : 1), ($.1^390 : $.1^299 : 1), ($.1^390 : $.1^611 : 1), ($.1^391 : $.1^31 : 1), ($.1^391 : $.1^343 : 1), ($.1^392 : $.1^242 : 1), ($.1^392 : $.1^554 : 1), ($.1^395 : $.1^177 : 1), ($.1^395 : $.1^489 : 1), ($.1^397 : $.1^46 : 1), ($.1^397 : $.1^358 : 1), ($.1^398 : $.1^202 : 1), ($.1^398 : $.1^514 : 1), ($.1^404 : $.1^244 : 1), ($.1^404 : $.1^556 : 1), ($.1^405 : $.1^84 : 1), ($.1^405 : $.1^396 : 1), ($.1^406 : $.1^32 : 1), ($.1^406 : $.1^344 : 1), ($.1^408 : $.1^85 : 1), ($.1^408 : $.1^397 : 1), ($.1^411 : $.1^131 : 1), ($.1^411 : $.1^443 : 1), ($.1^414 : $.1^256 : 1), ($.1^414 : $.1^568 : 1), ($.1^415 : $.1^151 : 1), ($.1^415 : $.1^463 : 1), ($.1^416 : 0 : 1), ($.1^418 : $.1^103 : 1), ($.1^418 : $.1^415 : 1), ($.1^419 : $.1^226 : 1), ($.1^419 : $.1^538 : 1), ($.1^423 : $.1^243 : 1), ($.1^423 : $.1^555 : 1), ($.1^424 : $.1^253 : 1), ($.1^424 : $.1^565 : 1), ($.1^425 : $.1^311 : 1), ($.1^425 : $.1^623 : 1), ($.1^426 : $.1^203 : 1), ($.1^426 : $.1^515 : 1), ($.1^428 : $.1^106 : 1), ($.1^428 : $.1^418 : 1), ($.1^429 : $.1^61 : 1), ($.1^429 : $.1^373 : 1), ($.1^4 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Fri Apr 2 02:24:37 2004 Input: F := PolynomialRing(FiniteField(3^2)); C := HyperellipticCurve(x^3-1); Points(C : Bound:=4); Output: Magma V2.10-22 Fri Apr 2 2004 02:24:34 on modular [Seed = 771980078] ------------------------------------- HyperellipticCurve( f: x^3 + 2 ) In file "/usr/local/magma/package/Geometry/CrvHyp/curve.m", line 257, column 30: >> return HyperellipticCurve(f, Parent(f)!0); ^ Runtime error in 'HyperellipticCurve': Curve has a finite singularity >> Points(C : Bound:=4);; ^ User error: Identifier 'C' has not been declared or assigned Total time: 2.539 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Fri Apr 2 02:24:53 2004 Input: F := PolynomialRing(FiniteField(3^2)); C := HyperellipticCurve(x^3+1); Points(C : Bound:=4); Output: Magma V2.10-22 Fri Apr 2 2004 02:24:50 on modular [Seed = 372982630] ------------------------------------- HyperellipticCurve( f: x^3 + 1 ) In file "/usr/local/magma/package/Geometry/CrvHyp/curve.m", line 257, column 30: >> return HyperellipticCurve(f, Parent(f)!0); ^ Runtime error in 'HyperellipticCurve': Curve has a finite singularity >> Points(C : Bound:=4);; ^ User error: Identifier 'C' has not been declared or assigned Total time: 2.569 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Fri Apr 2 02:25:01 2004 Input: F := PolynomialRing(FiniteField(3^2)); C := HyperellipticCurve(x^3+x+1); Points(C : Bound:=4); Output: Magma V2.10-22 Fri Apr 2 2004 02:24:58 on modular [Seed = 506678118] ------------------------------------- {@ (1 : 0 : 0), (1 : 0 : 1), ($.1 : $.1^2 : 1), ($.1 : $.1^6 : 1), ($.1^2 : 1 : 1), ($.1^2 : 2 : 1), ($.1^3 : $.1^2 : 1), ($.1^3 : $.1^6 : 1), (2 : $.1^2 : 1), (2 : $.1^6 : 1), ($.1^5 : 0 : 1), ($.1^6 : 1 : 1), ($.1^6 : 2 : 1), ($.1^7 : 0 : 1), (0 : 1 : 1), (0 : 2 : 1) @} Total time: 2.509 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host c-24-6-41-32.client.comcast.net. (24.6.41.32) Time: Fri Apr 2 11:07:10 2004 Input: factor(498384049428333414764928632140399662108495887457206674968055822617263669621523687568865802302210999132601412697613279391058654527145340515840099290478026350382802884371712359337984274122861159800280019110197888555893671151) Output: Magma V2.10-22 Fri Apr 2 2004 11:07:08 on modular [Seed = 1024520874] ------------------------------------- >> factor(49838404942833341476492863214039966210849588745720667496805582261726 ^ User error: Identifier 'factor' has not been declared or assigned Total time: 2.659 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host user-0c90hdq.cable.mindspring.com. (24.144.69.186) Time: Fri Apr 2 19:27:27 2004 Input: 495,594 Output: Magma V2.10-22 Fri Apr 2 2004 19:27:24 on modular [Seed = 356209071] ------------------------------------- 495 594 Total time: 2.589 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 66-50-75-116.prtc.net. (66.50.75.116) Time: Fri Apr 2 22:00:20 2004 Input: (((a^2)(61^2)/((((61^2)-1)/8)^2))+(((((61^2)-1)/8)^2)/(61^2)))/(2+((((a^2)(61^4))-((2a)((((61^2)-1)/8)^2)(61^2))+((((61^2)-1)/8)^4))/(a(61^2)((((61^2)-1)/8)^2)))) Output: Magma V2.10-22 Fri Apr 2 2004 22:00:18 on modular [Seed = 1833108983] ------------------------------------- >> 61^2)))/(2+((((a^2)(61^4))-((2a)((((61^2)-1)/8)^2)(61^2))+((((61^2)-1)/8)^4 ^ User error: bad syntax Total time: 2.579 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 66-50-75-116.prtc.net. (66.50.75.116) Time: Fri Apr 2 22:01:13 2004 Input: (((a^2)(61^2))/((((61^2)-1)/8)^2))+(((((61^2)-1)/8)^2)/(61^2)))/(2+((((a^2)(61^4))-((2a)((((61^2)-1)/8)^2)(61^2))+((((61^2)-1)/8)^4))/(a(61^2)((((61^2)-1)/8)^2)))) Output: Magma V2.10-22 Fri Apr 2 2004 22:01:10 on modular [Seed = 36465324] ------------------------------------- >> (((a^2)(61^2))/((((61^2)-1)/8)^2))+(((((61^2)-1)/8)^2)/(61^2)))/(2+((((a^2) ^ User error: bad syntax Total time: 2.559 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 66-50-75-116.prtc.net. (66.50.75.116) Time: Fri Apr 2 22:07:42 2004 Input: (2+3)/5 Output: Magma V2.10-22 Fri Apr 2 2004 22:07:39 on modular [Seed = 924409108] ------------------------------------- 1 Total time: 2.659 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 66-50-75-116.prtc.net. (66.50.75.116) Time: Fri Apr 2 22:09:15 2004 Input: (((a^2)(61^2)/((((61^2)-1)/8)^2))+(((((61^2)-1)/8)^2)/(61^2)))/(2+((((a^2)(61^4))-((2a)((((61^2)-1)/8)^2)(61^2))+((((61^2)-1)/8)^4))/(a(61^2)((((61^2)-1)/8)^2))))=a Output: Magma V2.10-22 Fri Apr 2 2004 22:09:13 on modular [Seed = 3673469019] ------------------------------------- >> 61^2)))/(2+((((a^2)(61^4))-((2a)((((61^2)-1)/8)^2)(61^2))+((((61^2)-1)/8)^4 ^ User error: bad syntax Total time: 2.549 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 66-50-75-116.prtc.net. (66.50.75.116) Time: Fri Apr 2 22:09:53 2004 Input: (((a^2)(61^2)/((((61^2)-1)/8)^2))+(((((61^2)-1)/8)^2)/(61^2)))/(2+((((a^2)(61^4))-((2*a)((((61^2)-1)/8)^2)(61^2))+((((61^2)-1)/8)^4))/(a(61^2)((((61^2)-1)/8)^2))))=a Output: Magma V2.10-22 Fri Apr 2 2004 22:09:51 on modular [Seed = 3539777653] ------------------------------------- >> 2))+((((61^2)-1)/8)^4))/(a(61^2)((((61^2)-1)/8)^2))))=a ^ User error: Identifier 'a' has not been declared or assigned Total time: 2.579 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 66-50-75-116.prtc.net. (66.50.75.116) Time: Fri Apr 2 22:10:22 2004 Input: (((a^2)(61^2)/((((61^2)-1)/8)^2))+(((((61^2)-1)/8)^2)/(61^2)))/(2+((((a^2)(61^4))-((2*a)((((61^2)-1)/8)^2)(61^2))+((((61^2)-1)/8)^4))/(a(61^2)((((61^2)-1)/8)^2)))) Output: Magma V2.10-22 Fri Apr 2 2004 22:10:19 on modular [Seed = 3270289793] ------------------------------------- >> (((a^2)(61^2)/((((61^2)-1)/8)^2))+(((((61^2)-1)/8)^2)/(61^2)))/(2+((((a^2)( ^ User error: Identifier 'a' has not been declared or assigned Total time: 2.559 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 66-50-75-116.prtc.net. (66.50.75.116) Time: Fri Apr 2 22:11:37 2004 Input: (((x^2)(61^2)/((((61^2)-1)/8)^2))+(((((61^2)-1)/8)^2)/(61^2)))/(2+((((x^2)(61^4))-((2*x)((((61^2)-1)/8)^2)(61^2))+((((61^2)-1)/8)^4))/(x(61^2)((((61^2)-1)/8)^2))))=x Output: Magma V2.10-22 Fri Apr 2 2004 22:11:34 on modular [Seed = 4241659842] ------------------------------------- >> 2))+((((61^2)-1)/8)^4))/(x(61^2)((((61^2)-1)/8)^2))))=x ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.589 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 66-50-75-116.prtc.net. (66.50.75.116) Time: Fri Apr 2 22:13:06 2004 Input: (((x^2)(61^2)/((((61^2)-1)/8)^2))+(((((61^2)-1)/8)^2)/(61^2)))/(2+((((x^2)(61^4))-((2*x)((((61^2)-1)/8)^2)(61^2))+((((61^2)-1)/8)^4))/(x(61^2)((((61^2)-1)/8)^2))))=x Output: Magma V2.10-22 Fri Apr 2 2004 22:13:03 on modular [Seed = 4005594377] ------------------------------------- >> 2))+((((61^2)-1)/8)^4))/(x(61^2)((((61^2)-1)/8)^2))))=x ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.549 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 66-50-75-116.prtc.net. (66.50.75.116) Time: Fri Apr 2 22:27:48 2004 Input: (((x^2)(61^2)/((((61^2)-1)/8)^2))+(((((61^2)-1)/8)^2)/(61^2)))/(2+((((x^2)(61^4))-((2*x)((((61^2)-1)/8)^2)(61^2))+((((61^2)-1)/8)^4))/(x(61^2)((((61^2)-1)/8)^2))))=x >x:=x Output: Magma V2.10-22 Fri Apr 2 2004 22:27:46 on modular [Seed = 2392908260] ------------------------------------- >> x:=x ^ User error: bad syntax Total time: 2.510 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 66-50-75-116.prtc.net. (66.50.75.116) Time: Fri Apr 2 22:28:40 2004 Input: x:=x; (((x^2)(61^2)/((((61^2)-1)/8)^2))+(((((61^2)-1)/8)^2)/(61^2)))/(2+((((x^2)(61^4))-((2*x)((((61^2)-1)/8)^2)(61^2))+((((61^2)-1)/8)^4))/(x(61^2)((((61^2)-1)/8)^2))))=x; Output: Magma V2.10-22 Fri Apr 2 2004 22:28:38 on modular [Seed = 2276059321] ------------------------------------- >> x:=x; ^ User error: Identifier 'x' has not been declared or assigned >> 2))+((((61^2)-1)/8)^4))/(x(61^2)((((61^2)-1)/8)^2))))=x; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.579 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 66-50-75-116.prtc.net. (66.50.75.116) Time: Fri Apr 2 22:29:05 2004 Input: x:=3; (((x^2)(61^2)/((((61^2)-1)/8)^2))+(((((61^2)-1)/8)^2)/(61^2)))/(2+((((x^2)(61^4))-((2*x)((((61^2)-1)/8)^2)(61^2))+((((61^2)-1)/8)^4))/(x(61^2)((((61^2)-1)/8)^2))))=x; Output: Magma V2.10-22 Fri Apr 2 2004 22:29:02 on modular [Seed = 3214004377] ------------------------------------- >> (((x^2)(61^2)/((((61^2)-1)/8)^2))+(((((61^2)-1)/8)^2)/(61^2)))/(2+((((x^2)( ^ Runtime error: Bad argument types Argument types given: RngIntElt, RngIntElt Total time: 2.509 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 66-50-75-116.prtc.net. (66.50.75.116) Time: Fri Apr 2 22:29:47 2004 Input: (((x^2)(61^2)/((((61^2)-1)/8)^2))+(((((61^2)-1)/8)^2)/(61^2)))/(2+((((x^2)(61^4))-((2*x)((((61^2)-1)/8)^2)(61^2))+((((61^2)-1)/8)^4))/(x(61^2)((((61^2)-1)/8)^2))))=x Output: Magma V2.10-22 Fri Apr 2 2004 22:29:45 on modular [Seed = 3080312902] ------------------------------------- >> 2))+((((61^2)-1)/8)^4))/(x(61^2)((((61^2)-1)/8)^2))))=x ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.500 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 66-50-75-116.prtc.net. (66.50.75.116) Time: Fri Apr 2 23:56:33 2004 Input: (((a^2)(61^2)/((((61^2)-1)/8)^2))+(((((61^2)-1)/8)^2)/(61^2)))/(2+((((a^2)(61^4))-((2a)((((61^2)-1)/8)^2)(61^2))+((((61^2)-1)/8)^4))/(a(61^2)((((61^2)-1)/8)^2)))) Output: Magma V2.10-22 Fri Apr 2 2004 23:56:31 on modular [Seed = 236981675] ------------------------------------- >> 61^2)))/(2+((((a^2)(61^4))-((2a)((((61^2)-1)/8)^2)(61^2))+((((61^2)-1)/8)^4 ^ User error: bad syntax Total time: 2.529 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 66-50-75-116.prtc.net. (66.50.75.116) Time: Fri Apr 2 23:56:47 2004 Input: (((a^2)(61^2)/((((61^2)-1)/8)^2))+(((((61^2)-1)/8)^2)/(61^2)))/(2+((((a^2)(61^4))-((2*a)((((61^2)-1)/8)^2)(61^2))+((((61^2)-1)/8)^4))/(a(61^2)((((61^2)-1)/8)^2)))) Output: Magma V2.10-22 Fri Apr 2 2004 23:56:44 on modular [Seed = 103285328] ------------------------------------- >> (((a^2)(61^2)/((((61^2)-1)/8)^2))+(((((61^2)-1)/8)^2)/(61^2)))/(2+((((a^2)( ^ User error: Identifier 'a' has not been declared or assigned Total time: 2.549 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 66-50-75-116.prtc.net. (66.50.75.116) Time: Fri Apr 2 23:57:15 2004 Input: a:=a;(((a^2)(61^2)/((((61^2)-1)/8)^2))+(((((61^2)-1)/8)^2)/(61^2)))/(2+((((a^2)(61^4))-((2*a)((((61^2)-1)/8)^2)(61^2))+((((61^2)-1)/8)^4))/(a(61^2)((((61^2)-1)/8)^2)))) Output: Magma V2.10-22 Fri Apr 2 2004 23:57:12 on modular [Seed = 1041250892] ------------------------------------- >> a:=a;(((a^2)(61^2)/((((61^2)-1)/8)^2))+(((((61^2)-1)/8)^2)/(61^2)))/(2+(((( ^ User error: Identifier 'a' has not been declared or assigned >> a:=a;(((a^2)(61^2)/((((61^2)-1)/8)^2))+(((((61^2)-1)/8)^2)/(61^2)))/(2+(((( ^ User error: Identifier 'a' has not been declared or assigned Total time: 2.579 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 66-50-75-116.prtc.net. (66.50.75.116) Time: Fri Apr 2 23:57:32 2004 Input: a:=a+0;(((a^2)(61^2)/((((61^2)-1)/8)^2))+(((((61^2)-1)/8)^2)/(61^2)))/(2+((((a^2)(61^4))-((2*a)((((61^2)-1)/8)^2)(61^2))+((((61^2)-1)/8)^4))/(a(61^2)((((61^2)-1)/8)^2)))) Output: Magma V2.10-22 Fri Apr 2 2004 23:57:30 on modular [Seed = 907555414] ------------------------------------- >> a:=a+0;(((a^2)(61^2)/((((61^2)-1)/8)^2))+(((((61^2)-1)/8)^2)/(61^2)))/(2+(( ^ User error: Identifier 'a' has not been declared or assigned >> a:=a+0;(((a^2)(61^2)/((((61^2)-1)/8)^2))+(((((61^2)-1)/8)^2)/(61^2)))/(2+(( ^ User error: Identifier 'a' has not been declared or assigned Total time: 2.560 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 66-50-75-116.prtc.net. (66.50.75.116) Time: Fri Apr 2 23:58:06 2004 Input: a:=0;(((a^2)(61^2)/((((61^2)-1)/8)^2))+(((((61^2)-1)/8)^2)/(61^2)))/(2+((((a^2)(61^4))-((2*a)((((61^2)-1)/8)^2)(61^2))+((((61^2)-1)/8)^4))/(a(61^2)((((61^2)-1)/8)^2)))) Output: Magma V2.10-22 Fri Apr 2 2004 23:58:03 on modular [Seed = 788605742] ------------------------------------- >> a:=0;(((a^2)(61^2)/((((61^2)-1)/8)^2))+(((((61^2)-1)/8)^2)/(61^2)))/(2+(((( ^ Runtime error: Bad argument types Argument types given: RngIntElt, RngIntElt Total time: 2.539 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 66-50-75-116.prtc.net. (66.50.75.116) Time: Fri Apr 2 23:58:49 2004 Input: a:=0;(((a^2)61^2/((((61^2)-1)/8)^2))+(((((61^2)-1)/8)^2)/(61^2)))/(2+((((a^2)(61^4))-((2*a)((((61^2)-1)/8)^2)(61^2))+((((61^2)-1)/8)^4))/(a(61^2)((((61^2)-1)/8)^2)))) Output: Magma V2.10-22 Fri Apr 2 2004 23:58:47 on modular [Seed = 604643577] ------------------------------------- >> a:=0;(((a^2)61^2/((((61^2)-1)/8)^2))+(((((61^2)-1)/8)^2)/(61^2)))/(2+((((a^ ^ User error: bad syntax Total time: 2.559 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 66-50-75-116.prtc.net. (66.50.75.116) Time: Fri Apr 2 23:59:19 2004 Input: a:=0;(((a^2)(61^2)/((((61^2)-1)/8)^2))+(((((61^2)-1)/8)^2)/(61^2)))/(2+((((a^2)(61^4))-((2*a)((((61^2)-1)/8)^2)(61^2))+((((61^2)-1)/8)^4))/(a(61^2)((((61^2)-1)/8)^2)))) Output: Magma V2.10-22 Fri Apr 2 2004 23:59:16 on modular [Seed = 3706902562] ------------------------------------- >> a:=0;(((a^2)(61^2)/((((61^2)-1)/8)^2))+(((((61^2)-1)/8)^2)/(61^2)))/(2+(((( ^ Runtime error: Bad argument types Argument types given: RngIntElt, RngIntElt Total time: 2.549 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host adsl-ull-171-143.41-151.net24.it. (151.41.143.171) Time: Sat Apr 3 15:14:06 2004 Input: K := GaloisField(5); Output: Magma V2.10-22 Sat Apr 3 2004 15:14:03 on modular [Seed = 4174881685] ------------------------------------- Total time: 2.580 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host adsl-ull-171-143.41-151.net24.it. (151.41.143.171) Time: Sat Apr 3 15:14:16 2004 Input: K := GaloisField(5); Output: Magma V2.10-22 Sat Apr 3 2004 15:14:14 on modular [Seed = 3236928432] ------------------------------------- Total time: 2.539 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host adsl-ull-171-143.41-151.net24.it. (151.41.143.171) Time: Sat Apr 3 15:14:23 2004 Input: K := GaloisField(5) Output: Magma V2.10-22 Sat Apr 3 2004 15:14:20 on modular [Seed = 3370619826] ------------------------------------- Total time: 2.579 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host adsl-ull-171-143.41-151.net24.it. (151.41.143.171) Time: Sat Apr 3 15:14:48 2004 Input: K Output: Magma V2.10-22 Sat Apr 3 2004 15:14:46 on modular [Seed = 3506408320] ------------------------------------- >> K; ^ User error: Identifier 'K' has not been declared or assigned Total time: 2.499 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 21:24:35 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > p:=2 > Output: Magma V2.10-22 Sat Apr 3 2004 21:24:31 on modular [Seed = 1601203946] ------------------------------------- [ x^2*y*z + 19*y^3*z + 31*y*z^3, 17*x^2*y + 3249*y^3 + 403*y*z^2, 17*x^2*z + 437*y^2*z + 10571*z^3, 289*x^2 + 361*y^2 + 961*z^2, 38*x*y^3, 2*x*y*z, 646*x*y, 62*x*z^3, 1054*x*z, 38*y^3*z, 13718*y^3, 62*y*z^3, 1178*y*z, 59582*z^3 ] Total time: 2.609 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 21:26:39 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2+x^2)*(5^2+y^2)+ 4*15*x*y; > P2 := 2*3*x(5^2+y^2) + 2*5*y*(3^2+x^2); > I := ideal; > GroebnerBasis(I); > p:=2; > Output: Magma V2.10-22 Sat Apr 3 2004 21:26:37 on modular [Seed = 671554079] ------------------------------------- >> P2 := 2*3*x(5^2+y^2) + 2*5*y*(3^2+x^2); ^ Runtime error: Bad argument types Argument types given: RngMPolElt, RngMPolElt >> I := ideal; ^ User error: Identifier 'P2' has not been declared or assigned >> GroebnerBasis(I); ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.529 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 21:26:49 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2+x^2)*(5^2+y^2)+ 4*15*x*y; > P2 := 2*3*x*(5^2+y^2) + 2*5*y*(3^2+x^2); > I := ideal; > GroebnerBasis(I); > p:=2; > Output: Magma V2.10-22 Sat Apr 3 2004 21:26:47 on modular [Seed = 537858605] ------------------------------------- [ x^2*y^2 + 25*x^2 + 60*x*y + 9*y^2 + 225, 10*x^2*y + 6*x*y^2 + 150*x + 90*y, 250*x^2 - 6*x*y^3 + 450*x*y + 2250, 6*x*y^4 - 300*x*y^2 + 3750*x, 54*y^4 - 2700*y^2 + 33750 ] Total time: 2.520 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 21:28:18 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2+x^2)*(5^2+y^2)+ 4*15*x*y; > P2 := 2*3*x*(5^2+y^2) + 2*5*y*(3^2+x^2); > I := ideal; > GroebnerBasis(I); > n=16; > P = ((X+Y)^(n-1)+(n-1)*(X+Y)^(n/2-1)(X-Y)^(n/2))/n Output: Magma V2.10-22 Sat Apr 3 2004 21:28:16 on modular [Seed = 941034130] ------------------------------------- [ x^2*y^2 + 25*x^2 + 60*x*y + 9*y^2 + 225, 10*x^2*y + 6*x*y^2 + 150*x + 90*y, 250*x^2 - 6*x*y^3 + 450*x*y + 2250, 6*x*y^4 - 300*x*y^2 + 3750*x, 54*y^4 - 2700*y^2 + 33750 ] >> n=16; ^ User error: Identifier 'n' has not been declared or assigned >> P = ((X+Y)^(n-1)+(n-1)*(X+Y)^(n/2-1)(X-Y)^(n/2))/n; ^ User error: Identifier 'X' has not been declared or assigned Total time: 2.579 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 21:28:39 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2+x^2)*(5^2+y^2)+ 4*15*x*y; > P2 := 2*3*x*(5^2+y^2) + 2*5*y*(3^2+x^2); > I := ideal; > GroebnerBasis(I); > n: =16; > P = ((X+Y)^(n-1)+(n-1)*(X+Y)^(n/2-1)(X-Y)^(n/2))/n Output: Magma V2.10-22 Sat Apr 3 2004 21:28:36 on modular [Seed = 907609224] ------------------------------------- [ x^2*y^2 + 25*x^2 + 60*x*y + 9*y^2 + 225, 10*x^2*y + 6*x*y^2 + 150*x + 90*y, 250*x^2 - 6*x*y^3 + 450*x*y + 2250, 6*x*y^4 - 300*x*y^2 + 3750*x, 54*y^4 - 2700*y^2 + 33750 ] >> n: =16; ^ User error: bad syntax >> P = ((X+Y)^(n-1)+(n-1)*(X+Y)^(n/2-1)(X-Y)^(n/2))/n; ^ User error: Identifier 'X' has not been declared or assigned Total time: 2.609 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 21:28:44 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2+x^2)*(5^2+y^2)+ 4*15*x*y; > P2 := 2*3*x*(5^2+y^2) + 2*5*y*(3^2+x^2); > I := ideal; > GroebnerBasis(I); > n :=16; > P = ((X+Y)^(n-1)+(n-1)*(X+Y)^(n/2-1)(X-Y)^(n/2))/n Output: Magma V2.10-22 Sat Apr 3 2004 21:28:42 on modular [Seed = 153500601] ------------------------------------- [ x^2*y^2 + 25*x^2 + 60*x*y + 9*y^2 + 225, 10*x^2*y + 6*x*y^2 + 150*x + 90*y, 250*x^2 - 6*x*y^3 + 450*x*y + 2250, 6*x*y^4 - 300*x*y^2 + 3750*x, 54*y^4 - 2700*y^2 + 33750 ] >> P = ((X+Y)^(n-1)+(n-1)*(X+Y)^(n/2-1)(X-Y)^(n/2))/n; ^ User error: Identifier 'X' has not been declared or assigned Total time: 2.559 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 21:29:53 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2+x^2)*(5^2+y^2)+ 4*15*x*y; > P2 := 2*3*x*(5^2+y^2) + 2*5*y*(3^2+x^2); > I := ideal; > GroebnerBasis(I); > n :=16; X: = 3; Y:= x; > Pd1 = ((X+Y)^(n-1)+(n-1)*(X+Y)^(n/2-1)(X-Y)^(n/2))/n Output: Magma V2.10-22 Sat Apr 3 2004 21:29:51 on modular [Seed = 103363955] ------------------------------------- [ x^2*y^2 + 25*x^2 + 60*x*y + 9*y^2 + 225, 10*x^2*y + 6*x*y^2 + 150*x + 90*y, 250*x^2 - 6*x*y^3 + 450*x*y + 2250, 6*x*y^4 - 300*x*y^2 + 3750*x, 54*y^4 - 2700*y^2 + 33750 ] >> n :=16; X: = 3; Y:= x; ^ User error: bad syntax >> Pd1 = ((X+Y)^(n-1)+(n-1)*(X+Y)^(n/2-1)(X-Y)^(n/2))/n; ^ User error: Identifier 'X' has not been declared or assigned Total time: 2.569 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 21:30:05 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2+x^2)*(5^2+y^2)+ 4*15*x*y; > P2 := 2*3*x*(5^2+y^2) + 2*5*y*(3^2+x^2); > I := ideal; > GroebnerBasis(I); > n :=16; X := 3; Y:= x; > Pd1 = ((X+Y)^(n-1)+(n-1)*(X+Y)^(n/2-1)(X-Y)^(n/2))/n Output: Magma V2.10-22 Sat Apr 3 2004 21:30:03 on modular [Seed = 289284688] ------------------------------------- [ x^2*y^2 + 25*x^2 + 60*x*y + 9*y^2 + 225, 10*x^2*y + 6*x*y^2 + 150*x + 90*y, 250*x^2 - 6*x*y^3 + 450*x*y + 2250, 6*x*y^4 - 300*x*y^2 + 3750*x, 54*y^4 - 2700*y^2 + 33750 ] >> Pd1 = ((X+Y)^(n-1)+(n-1)*(X+Y)^(n/2-1)(X-Y)^(n/2))/n; ^ User error: Identifier 'Pd1' has not been declared or assigned Total time: 2.430 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 21:30:16 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2+x^2)*(5^2+y^2)+ 4*15*x*y; > P2 := 2*3*x*(5^2+y^2) + 2*5*y*(3^2+x^2); > I := ideal; > GroebnerBasis(I); > n :=16; X := 3; Y:= x; > Pd1 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n/2-1)(X-Y)^(n/2))/n Output: Magma V2.10-22 Sat Apr 3 2004 21:30:14 on modular [Seed = 3922123445] ------------------------------------- [ x^2*y^2 + 25*x^2 + 60*x*y + 9*y^2 + 225, 10*x^2*y + 6*x*y^2 + 150*x + 90*y, 250*x^2 - 6*x*y^3 + 450*x*y + 2250, 6*x*y^4 - 300*x*y^2 + 3750*x, 54*y^4 - 2700*y^2 + 33750 ] >> Pd1 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n/2-1)(X-Y)^(n/2))/n; ^ Runtime error: Bad argument types Argument types given: RngMPolElt, FldRatElt Total time: 2.549 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 21:30:27 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2+x^2)*(5^2+y^2)+ 4*15*x*y; > P2 := 2*3*x*(5^2+y^2) + 2*5*y*(3^2+x^2); > I := ideal; > GroebnerBasis(I); > n :=16; X := 3; Y:= x; > Pd1 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n/2-1)*(X-Y)^(n/2))/n Output: Magma V2.10-22 Sat Apr 3 2004 21:30:24 on modular [Seed = 3788427979] ------------------------------------- [ x^2*y^2 + 25*x^2 + 60*x*y + 9*y^2 + 225, 10*x^2*y + 6*x*y^2 + 150*x + 90*y, 250*x^2 - 6*x*y^3 + 450*x*y + 2250, 6*x*y^4 - 300*x*y^2 + 3750*x, 54*y^4 - 2700*y^2 + 33750 ] >> Pd1 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n/2-1)*(X-Y)^(n/2))/n; ^ Runtime error in '^': Bad argument types Argument types given: RngMPolElt, FldRatElt Total time: 2.569 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 21:30:55 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2+x^2)*(5^2+y^2)+ 4*15*x*y; > P2 := 2*3*x*(5^2+y^2) + 2*5*y*(3^2+x^2); > I := ideal; > GroebnerBasis(I); > n :=16; X := 3; Y:= x; > 3^2 Output: Magma V2.10-22 Sat Apr 3 2004 21:30:52 on modular [Seed = 4241739722] ------------------------------------- [ x^2*y^2 + 25*x^2 + 60*x*y + 9*y^2 + 225, 10*x^2*y + 6*x*y^2 + 150*x + 90*y, 250*x^2 - 6*x*y^3 + 450*x*y + 2250, 6*x*y^4 - 300*x*y^2 + 3750*x, 54*y^4 - 2700*y^2 + 33750 ] 9 Total time: 2.780 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 21:31:19 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2+x^2)*(5^2+y^2)+ 4*15*x*y; > P2 := 2*3*x*(5^2+y^2) + 2*5*y*(3^2+x^2); > I := ideal; > GroebnerBasis(I); > n :=16; X := 3; Y:= x; > Pd1 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n/2-1)*(X-Y)^(n/2))/n Output: Magma V2.10-22 Sat Apr 3 2004 21:31:17 on modular [Seed = 4124755690] ------------------------------------- [ x^2*y^2 + 25*x^2 + 60*x*y + 9*y^2 + 225, 10*x^2*y + 6*x*y^2 + 150*x + 90*y, 250*x^2 - 6*x*y^3 + 450*x*y + 2250, 6*x*y^4 - 300*x*y^2 + 3750*x, 54*y^4 - 2700*y^2 + 33750 ] >> Pd1 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n/2-1)*(X-Y)^(n/2))/n; ^ Runtime error in '^': Bad argument types Argument types given: RngMPolElt, FldRatElt Total time: 2.519 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 21:31:50 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2+x^2)*(5^2+y^2)+ 4*15*x*y; > P2 := 2*3*x*(5^2+y^2) + 2*5*y*(3^2+x^2); > I := ideal; > GroebnerBasis(I); > n :=16; X := 3; Y:= x; > Pd1 := ((X+Y)^(31)+(31)*(X+Y)^(15)*(X-Y)^(16))/32 Output: Magma V2.10-22 Sat Apr 3 2004 21:31:47 on modular [Seed = 3454205492] ------------------------------------- [ x^2*y^2 + 25*x^2 + 60*x*y + 9*y^2 + 225, 10*x^2*y + 6*x*y^2 + 150*x + 90*y, 250*x^2 - 6*x*y^3 + 450*x*y + 2250, 6*x*y^4 - 300*x*y^2 + 3750*x, 54*y^4 - 2700*y^2 + 33750 ] >> Pd1 := ((X+Y)^(31)+(31)*(X+Y)^(15)*(X-Y)^(16))/32; ^ Runtime error in '/': Coefficient ring of argument 1 is not a field Total time: 2.649 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 21:32:18 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2+x^2)*(5^2+y^2)+ 4*15*x*y; > P2 := 2*3*x*(5^2+y^2) + 2*5*y*(3^2+x^2); > I := ideal; > GroebnerBasis(I); > n :=16; X := 3; Y:= x; > Pd1 := ((X+Y)^(31)+(31)*(X+Y)^(15)*(X-Y)^(16)) div 32 Output: Magma V2.10-22 Sat Apr 3 2004 21:32:15 on modular [Seed = 3673549087] ------------------------------------- [ x^2*y^2 + 25*x^2 + 60*x*y + 9*y^2 + 225, 10*x^2*y + 6*x*y^2 + 150*x + 90*y, 250*x^2 - 6*x*y^3 + 450*x*y + 2250, 6*x*y^4 - 300*x*y^2 + 3750*x, 54*y^4 - 2700*y^2 + 33750 ] Total time: 2.579 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 21:33:39 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2+x^2)*(5^2+y^2)+ 4*15*x*y; > P2 := 2*3*x*(5^2+y^2) + 2*5*y*(3^2+x^2); > I := ideal; > GroebnerBasis(I); > n :=16; X := 3; Y:= x; > Pd1 := ((X+Y)^(31)+(31)*(X+Y)^(15)*(X-Y)^(16)) div 32; > Po1 := ((X+Y)^(31)-(1)*(X+Y)^(15)*(X-Y)^(16)) div 32; > n :=16; X := 5^2+y^2; Y:= 10*y; > Pd2 := ((X+Y)^(31)+(31)*(X+Y)^(15)*(X-Y)^(16)) div 32; > Pd2 := ((X+Y)^(31)-(1)*(X+Y)^(15)*(X-Y)^(16)) div 32; > Pd1*Pd1-31*Po1*Po2 in I Output: Magma V2.10-22 Sat Apr 3 2004 21:33:36 on modular [Seed = 3506431162] ------------------------------------- [ x^2*y^2 + 25*x^2 + 60*x*y + 9*y^2 + 225, 10*x^2*y + 6*x*y^2 + 150*x + 90*y, 250*x^2 - 6*x*y^3 + 450*x*y + 2250, 6*x*y^4 - 300*x*y^2 + 3750*x, 54*y^4 - 2700*y^2 + 33750 ] >> Pd1*Pd1-31*Po1*Po2 in I ^ User error: Identifier 'Po2' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 21:33:57 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2+x^2)*(5^2+y^2)+ 4*15*x*y; > P2 := 2*3*x*(5^2+y^2) + 2*5*y*(3^2+x^2); > I := ideal; > GroebnerBasis(I); > n :=16; X := 3; Y:= x; > Pd1 := ((X+Y)^(31)+(31)*(X+Y)^(15)*(X-Y)^(16)) div 32; > Po1 := ((X+Y)^(31)-(1)*(X+Y)^(15)*(X-Y)^(16)) div 32; > n :=16; X := 5^2+y^2; Y:= 10*y; > Pd2 := ((X+Y)^(31)+(31)*(X+Y)^(15)*(X-Y)^(16)) div 32; > Po2 := ((X+Y)^(31)-(1)*(X+Y)^(15)*(X-Y)^(16)) div 32; > Pd1*Pd1-31*Po1*Po2 in I Output: Magma V2.10-22 Sat Apr 3 2004 21:33:54 on modular [Seed = 2827459792] ------------------------------------- [ x^2*y^2 + 25*x^2 + 60*x*y + 9*y^2 + 225, 10*x^2*y + 6*x*y^2 + 150*x + 90*y, 250*x^2 - 6*x*y^3 + 450*x*y + 2250, 6*x*y^4 - 300*x*y^2 + 3750*x, 54*y^4 - 2700*y^2 + 33750 ] false Total time: 2.729 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 21:39:06 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2+x^2)*(5^2+y^2)+ 4*15*x*y; > P2 := 2*3*x*(5^2+y^2) + 2*5*y*(3^2+x^2); > I := ideal; > GroebnerBasis(I); > X := 3; Y:= x; > Pd1 := ((X+Y)^(31)+(31)*(X+Y)^(15)*(X-Y)^(16)) div 32; > Po1 := ((X+Y)^(31)-(1)*(X+Y)^(15)*(X-Y)^(16)) div 32; > n :=16; X := 5^2+y^2; Y:= 10*y; > Pd2 := ((X+Y)^(31)+(31)*(X+Y)^(15)*(X-Y)^(16)) div 32; > Po2 := ((X+Y)^(31)-(1)*(X+Y)^(15)*(X-Y)^(16)) div 32; > Pd1*Pd2-31*Po1*Po2 in I Output: Magma V2.10-22 Sat Apr 3 2004 21:39:03 on modular [Seed = 1632523341] ------------------------------------- [ x^2*y^2 + 25*x^2 + 60*x*y + 9*y^2 + 225, 10*x^2*y + 6*x*y^2 + 150*x + 90*y, 250*x^2 - 6*x*y^3 + 450*x*y + 2250, 6*x*y^4 - 300*x*y^2 + 3750*x, 54*y^4 - 2700*y^2 + 33750 ] true Total time: 2.640 seconds, Total memory usage: 2.29MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 21:39:16 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2+x^2)*(5^2+y^2)+ 4*15*x*y; > P2 := 2*3*x*(5^2+y^2) + 2*5*y*(3^2+x^2); > I := ideal; > GroebnerBasis(I); > X := 3; Y:= x; > Pd1 := ((X+Y)^(31)+(31)*(X+Y)^(15)*(X-Y)^(16)) div 32; > Po1 := ((X+Y)^(31)-(1)*(X+Y)^(15)*(X-Y)^(16)) div 32; > n :=16; X := 5^2+y^2; Y:= 10*y; > Pd2 := ((X+Y)^(31)+(31)*(X+Y)^(15)*(X-Y)^(16)) div 32; > Po2 := ((X+Y)^(31)-(1)*(X+Y)^(15)*(X-Y)^(16)) div 32; > Pd1*Pd2+31*Po1*Po2 in I Output: Magma V2.10-22 Sat Apr 3 2004 21:39:14 on modular [Seed = 2035698752] ------------------------------------- [ x^2*y^2 + 25*x^2 + 60*x*y + 9*y^2 + 225, 10*x^2*y + 6*x*y^2 + 150*x + 90*y, 250*x^2 - 6*x*y^3 + 450*x*y + 2250, 6*x*y^4 - 300*x*y^2 + 3750*x, 54*y^4 - 2700*y^2 + 33750 ] true Total time: 2.630 seconds, Total memory usage: 2.29MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 21:40:02 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2+x^2)*(5^2+y^2)+ 4*15*x*y; > P2 := 2*3*x*(5^2+y^2) + 2*5*y*(3^2+x^2); > I := ideal; > GroebnerBasis(I); > X := 3; Y:= x; > Pd1 := ((X+Y)^(31)+(31)*(X+Y)^(15)*(X-Y)^(16)) div 32; > Po1 := ((X+Y)^(31)-(1)*(X+Y)^(15)*(X-Y)^(16)) div 32; > n :=16; X := 5^2+y^2; Y:= 10*y; > Pd2 := ((X+Y)^(31)+(31)*(X+Y)^(15)*(X-Y)^(16)) div 32; > Po2 := ((X+Y)^(31)-(1)*(X+Y)^(15)*(X-Y)^(16)) div 32; > Pd1*Pd2+31*Po1*Po2 in I Output: Magma V2.10-22 Sat Apr 3 2004 21:39:59 on modular [Seed = 1885291876] ------------------------------------- [ x^2*y^2 + 25*x^2 + 60*x*y + 9*y^2 + 225, 10*x^2*y + 6*x*y^2 + 150*x + 90*y, 250*x^2 - 6*x*y^3 + 450*x*y + 2250, 6*x*y^4 - 300*x*y^2 + 3750*x, 54*y^4 - 2700*y^2 + 33750 ] true Total time: 2.789 seconds, Total memory usage: 2.29MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 21:41:11 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2+x^2)*(5^2+y^2)+ 4*15*x*y; > P2 := 2*3*x*(5^2+y^2) + 2*5*y*(3^2+x^2); > I := ideal; > GroebnerBasis(I); > X := 3; Y:= x; > Pd1 := ((X+Y)^(15)+(15)*(X+Y)^(7)*(X-Y)^(8)) div 16; > Po1 := ((X+Y)^(15)-(1)*(X+Y)^(7)*(X-Y)^(8)) div 16; > n :=16; X := 5^2+y^2; Y:= 10*y; > Pd2 := ((X+Y)^(15)+(15)*(X+Y)^(7)*(X-Y)^(8)) div 16; > Po2 := ((X+Y)^(15)-(1)*(X+Y)^(7)*(X-Y)^(8)) div 16; > Pd1*Pd2+31*Po1*Po2 in I Output: Magma V2.10-22 Sat Apr 3 2004 21:41:08 on modular [Seed = 1097757934] ------------------------------------- [ x^2*y^2 + 25*x^2 + 60*x*y + 9*y^2 + 225, 10*x^2*y + 6*x*y^2 + 150*x + 90*y, 250*x^2 - 6*x*y^3 + 450*x*y + 2250, 6*x*y^4 - 300*x*y^2 + 3750*x, 54*y^4 - 2700*y^2 + 33750 ] true Total time: 2.569 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 21:42:39 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2+x^2)*(5^2+y^2)+ 4*15*x*y; > P2 := 2*3*x*(5^2+y^2) + 2*5*y*(3^2+x^2); > I := ideal; > GroebnerBasis(I); > X := 3; Y:= x; > Pd1 := ((X+Y)^(7)+(7)*(X+Y)^(3)*(X-Y)^(4)) div 8; > Po1 := ((X+Y)^(7)-(7)*(X+Y)^(3)*(X-Y)^(4)) div 8; > n :=16; X := 5^2+y^2; Y:= 10*y; > Pd2 := ((X+Y)^(7)+(7)*(X+Y)^(3)*(X-Y)^(4)) div 8; > Po2 := ((X+Y)^(7)-(7)*(X+Y)^(3)*(X-Y)^(4)) div 8; > Pd1*Pd2+7*Po1*Po2 in I Output: Magma V2.10-22 Sat Apr 3 2004 21:42:37 on modular [Seed = 1500933935] ------------------------------------- [ x^2*y^2 + 25*x^2 + 60*x*y + 9*y^2 + 225, 10*x^2*y + 6*x*y^2 + 150*x + 90*y, 250*x^2 - 6*x*y^3 + 450*x*y + 2250, 6*x*y^4 - 300*x*y^2 + 3750*x, 54*y^4 - 2700*y^2 + 33750 ] >> Po1 := ((X+Y)^(7)-(7)*(X+Y)^(3)*(X-Y)^(4)) div 8; ^ Runtime error in 'div': Argument 2 does not divide argument 1 >> Po2 := ((X+Y)^(7)-(7)*(X+Y)^(3)*(X-Y)^(4)) div 8; ^ Runtime error in 'div': Argument 2 does not divide argument 1 >> Pd1*Pd2+7*Po1*Po2 in I ^ User error: Identifier 'Po1' has not been declared or assigned Total time: 2.520 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 21:42:56 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2+x^2)*(5^2+y^2)+ 4*15*x*y; > P2 := 2*3*x*(5^2+y^2) + 2*5*y*(3^2+x^2); > I := ideal; > GroebnerBasis(I); > X := 3; Y:= x; > Pd1 := ((X+Y)^(7)+(7)*(X+Y)^(3)*(X-Y)^(4)) div 8; > Po1 := ((X+Y)^(7)-(1)*(X+Y)^(3)*(X-Y)^(4)) div 8; > n :=16; X := 5^2+y^2; Y:= 10*y; > Pd2 := ((X+Y)^(7)+(7)*(X+Y)^(3)*(X-Y)^(4)) div 8; > Po2 := ((X+Y)^(7)-(1)*(X+Y)^(3)*(X-Y)^(4)) div 8; > Pd1*Pd2+7*Po1*Po2 in I Output: Magma V2.10-22 Sat Apr 3 2004 21:42:54 on modular [Seed = 1367238420] ------------------------------------- [ x^2*y^2 + 25*x^2 + 60*x*y + 9*y^2 + 225, 10*x^2*y + 6*x*y^2 + 150*x + 90*y, 250*x^2 - 6*x*y^3 + 450*x*y + 2250, 6*x*y^4 - 300*x*y^2 + 3750*x, 54*y^4 - 2700*y^2 + 33750 ] true Total time: 2.569 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 21:45:06 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2+x^2)* 17 + 6*x*y; > P2 := 2*3*x*17 + y*(3^2+x^2); > I := ideal; > GroebnerBasis(I); > X := 3; Y:= x; > Pd1 := ((X+Y)^(7)+(7)*(X+Y)^(3)*(X-Y)^(4)) div 8; > Po1 := ((X+Y)^(7)-(1)*(X+Y)^(3)*(X-Y)^(4)) div 8; > n :=16; X := 17; Y:= y; > Pd2 := ((X+Y)^(7)+(7)*(X+Y)^(3)*(X-Y)^(4)) div 8; > Po2 := ((X+Y)^(7)-(1)*(X+Y)^(3)*(X-Y)^(4)) div 8; > Pd1*Pd2+7*Po1*Po2 in I Output: Magma V2.10-22 Sat Apr 3 2004 21:45:04 on modular [Seed = 587994616] ------------------------------------- [ x^2*y + 102*x + 9*y, 17*x^2 + 6*x*y + 153, 6*x*y^2 - 1734*x, 54*y^2 - 15606 ] true Total time: 2.579 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 21:46:02 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2+121*x^2)* 17 + 11*13*6*x*y; > P2 := 11*2*3*x*17 + 13*y*(3^2+121*x^2); > I := ideal; > GroebnerBasis(I); > X := 3; Y:= 11*x; > Pd1 := ((X+Y)^(7)+(7)*(X+Y)^(3)*(X-Y)^(4)) div 8; > Po1 := ((X+Y)^(7)-(1)*(X+Y)^(3)*(X-Y)^(4)) div 8; > n :=16; X := 17; Y:= 13*y; > Pd2 := ((X+Y)^(7)+(7)*(X+Y)^(3)*(X-Y)^(4)) div 8; > Po2 := ((X+Y)^(7)-(1)*(X+Y)^(3)*(X-Y)^(4)) div 8; > Pd1*Pd2+7*Po1*Po2 in I Output: Magma V2.10-22 Sat Apr 3 2004 21:46:00 on modular [Seed = 991169976] ------------------------------------- [ 11*x^2*y^2 + 748*x^2 + 780*x*y^3 - 1014*x*y + 4149*y^2 - 7038, 121*x^2*y + 468*x*y^2 - 714*x + 9*y, 2057*x^2 + 858*x*y + 153, 1014*x*y^2 - 1734*x, 9126*y^2 - 15606 ] false Total time: 2.520 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 21:50:03 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2+121*x^2)* 17 + 11*13*6*x*y; > P2 := 11*2*3*x*17 + 13*y*(3^2+121*x^2); > I := ideal; > GroebnerBasis(I); > n:=8; X := 3; Y:= 11*x; > Pd1 := ((X+Y)^(n-1)+(7)*(X+Y)^(3)*(X-Y)^(4)) div 8; > Po1 := ((X+Y)^(7)-(1)*(X+Y)^(3)*(X-Y)^(4)) div 8; > n :=16; X := 17; Y:= 13*y; > Pd2 := ((X+Y)^(7)+(7)*(X+Y)^(3)*(X-Y)^(4)) div 8; > Po2 := ((X+Y)^(7)-(1)*(X+Y)^(3)*(X-Y)^(4)) div 8; > Pd1*Pd2+7*Po1*Po2 in I Output: Magma V2.10-22 Sat Apr 3 2004 21:50:01 on modular [Seed = 203635646] ------------------------------------- [ 11*x^2*y^2 + 748*x^2 + 780*x*y^3 - 1014*x*y + 4149*y^2 - 7038, 121*x^2*y + 468*x*y^2 - 714*x + 9*y, 2057*x^2 + 858*x*y + 153, 1014*x*y^2 - 1734*x, 9126*y^2 - 15606 ] false Total time: 2.520 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 21:50:48 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2+121*x^2)* 17 + 11*13*6*x*y; > P2 := 11*2*3*x*17 + 13*y*(3^2+121*x^2); > I := ideal; > GroebnerBasis(I); > n:=8; X := 3; Y:= 11*x; n2:= n div 2; > Pd1 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po1 := ((X+Y)^(7)-(1)*(X+Y)^(3)*(X-Y)^(4)) div 8; > n :=16; X := 17; Y:= 13*y; > Pd2 := ((X+Y)^(7)+(7)*(X+Y)^(3)*(X-Y)^(4)) div 8; > Po2 := ((X+Y)^(7)-(1)*(X+Y)^(3)*(X-Y)^(4)) div 8; > Pd1*Pd2+7*Po1*Po2 in I Output: Magma V2.10-22 Sat Apr 3 2004 21:50:45 on modular [Seed = 523249521] ------------------------------------- [ 11*x^2*y^2 + 748*x^2 + 780*x*y^3 - 1014*x*y + 4149*y^2 - 7038, 121*x^2*y + 468*x*y^2 - 714*x + 9*y, 2057*x^2 + 858*x*y + 153, 1014*x*y^2 - 1734*x, 9126*y^2 - 15606 ] false Total time: 2.569 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 21:58:14 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2+121*x^2)* 17 + 11*13*6*x*y; > P2 := 11*2*3*x*17 + 13*y*(3^2+121*x^2); > I := ideal; > GroebnerBasis(I); > n:=16; X := 3; Y:= 11*x; n2:= n div 2; > Pd1 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po1 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > X := 17; Y:= 13*y; > Pd1 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po1 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Pd1*Pd2+7*Po1*Po2 in I Output: Magma V2.10-22 Sat Apr 3 2004 21:58:12 on modular [Seed = 3905409351] ------------------------------------- [ 11*x^2*y^2 + 748*x^2 + 780*x*y^3 - 1014*x*y + 4149*y^2 - 7038, 121*x^2*y + 468*x*y^2 - 714*x + 9*y, 2057*x^2 + 858*x*y + 153, 1014*x*y^2 - 1734*x, 9126*y^2 - 15606 ] >> Pd1*Pd2+7*Po1*Po2 in I ^ User error: Identifier 'Pd2' has not been declared or assigned Total time: 2.550 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 21:58:34 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2+121*x^2)* 17 + 11*13*6*x*y; > P2 := 11*2*3*x*17 + 13*y*(3^2+121*x^2); > I := ideal; > GroebnerBasis(I); > n:=16; X := 3; Y:= 11*x; n2:= n div 2; > Pd1 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po1 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > X := 17; Y:= 13*y; > Pd2 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po2 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Pd1*Pd2+(n-1)*Po1*Po2 in I Output: Magma V2.10-22 Sat Apr 3 2004 21:58:32 on modular [Seed = 3888701012] ------------------------------------- [ 11*x^2*y^2 + 748*x^2 + 780*x*y^3 - 1014*x*y + 4149*y^2 - 7038, 121*x^2*y + 468*x*y^2 - 714*x + 9*y, 2057*x^2 + 858*x*y + 153, 1014*x*y^2 - 1734*x, 9126*y^2 - 15606 ] true Total time: 2.559 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 21:58:45 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2+121*x^2)* 17 + 11*13*6*x*y; > P2 := 11*2*3*x*17 + 13*y*(3^2+121*x^2); > I := ideal; > GroebnerBasis(I); > n:=8; X := 3; Y:= 11*x; n2:= n div 2; > Pd1 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po1 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > X := 17; Y:= 13*y; > Pd2 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po2 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Pd1*Pd2+(n-1)*Po1*Po2 in I Output: Magma V2.10-22 Sat Apr 3 2004 21:58:42 on modular [Seed = 4291872374] ------------------------------------- [ 11*x^2*y^2 + 748*x^2 + 780*x*y^3 - 1014*x*y + 4149*y^2 - 7038, 121*x^2*y + 468*x*y^2 - 714*x + 9*y, 2057*x^2 + 858*x*y + 153, 1014*x*y^2 - 1734*x, 9126*y^2 - 15606 ] false Total time: 2.560 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 21:59:21 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2+121*x^2)* 17 + 11*13*6*x*y; > P2 := 11*2*3*x*17 + 13*y*(3^2+121*x^2); > I := ideal; > GroebnerBasis(I); > n:=32; X := 3; Y:= 11*x; n2:= n div 2; > Pd1 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po1 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > X := 17; Y:= 13*y; > Pd2 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po2 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Pd1*Pd2+(n-1)*Po1*Po2 in I Output: Magma V2.10-22 Sat Apr 3 2004 21:59:18 on modular [Seed = 4158180762] ------------------------------------- [ 11*x^2*y^2 + 748*x^2 + 780*x*y^3 - 1014*x*y + 4149*y^2 - 7038, 121*x^2*y + 468*x*y^2 - 714*x + 9*y, 2057*x^2 + 858*x*y + 153, 1014*x*y^2 - 1734*x, 9126*y^2 - 15606 ] true Total time: 2.589 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 21:59:33 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2+121*x^2)* 17 + 11*13*6*x*y; > P2 := 11*2*3*x*17 + 13*y*(3^2+121*x^2); > I := ideal; > GroebnerBasis(I); > n:=8; X := 3; Y:= 11*x; n2:= n div 2; > Pd1 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po1 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > X := 17; Y:= 13*y; > Pd2 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po2 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Pd1*Pd2+(n-1)*Po1*Po2 in I Output: Magma V2.10-22 Sat Apr 3 2004 21:59:30 on modular [Seed = 3487626678] ------------------------------------- [ 11*x^2*y^2 + 748*x^2 + 780*x*y^3 - 1014*x*y + 4149*y^2 - 7038, 121*x^2*y + 468*x*y^2 - 714*x + 9*y, 2057*x^2 + 858*x*y + 153, 1014*x*y^2 - 1734*x, 9126*y^2 - 15606 ] false Total time: 2.550 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 22:09:06 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2+121*x^2)* 17 + 11*13*6*x*y; > P2 := 11*2*3*x*17 + 13*y*(3^2+121*x^2); > I := ideal; > GroebnerBasis(I); > n:=8; X := 3; Y:= 11*x; n2:= n div 2; > Pd1 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po1 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > X := 17; Y:= 13*y; > Pd2 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po2 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Pd1*Pd2+(n-1)*Po1*Po2 in I > Pd1*Po2 + Pd1*Po1 in I Output: Magma V2.10-22 Sat Apr 3 2004 22:09:03 on modular [Seed = 2777323905] ------------------------------------- [ 11*x^2*y^2 + 748*x^2 + 780*x*y^3 - 1014*x*y + 4149*y^2 - 7038, 121*x^2*y + 468*x*y^2 - 714*x + 9*y, 2057*x^2 + 858*x*y + 153, 1014*x*y^2 - 1734*x, 9126*y^2 - 15606 ] >> Pd1*Po2 + Pd1*Po1 in I ^ User error: bad syntax Total time: 2.549 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 22:09:42 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2+121*x^2)* 17 + 11*13*6*x*y; > P2 := 11*2*3*x*17 + 13*y*(3^2+121*x^2); > I := ideal; > GroebnerBasis(I); > n:=8; X := 3; Y:= 11*x; n2:= n div 2; > Pd1 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po1 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > X := 17; Y:= 13*y; > Pd2 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po2 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Pd1*Pd2+(n-1)*Po1*Po2 in I; > Pd1*Po2 + Pd2*Po1 in I Output: Magma V2.10-22 Sat Apr 3 2004 22:09:40 on modular [Seed = 3180495266] ------------------------------------- [ 11*x^2*y^2 + 748*x^2 + 780*x*y^3 - 1014*x*y + 4149*y^2 - 7038, 121*x^2*y + 468*x*y^2 - 714*x + 9*y, 2057*x^2 + 858*x*y + 153, 1014*x*y^2 - 1734*x, 9126*y^2 - 15606 ] false false Total time: 2.590 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 22:09:53 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2+121*x^2)* 17 + 11*13*6*x*y; > P2 := 11*2*3*x*17 + 13*y*(3^2+121*x^2); > I := ideal; > GroebnerBasis(I); > n:=16; X := 3; Y:= 11*x; n2:= n div 2; > Pd1 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po1 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > X := 17; Y:= 13*y; > Pd2 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po2 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Pd1*Pd2+(n-1)*Po1*Po2 in I; > Pd1*Po2 + Pd2*Po1 in I Output: Magma V2.10-22 Sat Apr 3 2004 22:09:50 on modular [Seed = 3046803872] ------------------------------------- [ 11*x^2*y^2 + 748*x^2 + 780*x*y^3 - 1014*x*y + 4149*y^2 - 7038, 121*x^2*y + 468*x*y^2 - 714*x + 9*y, 2057*x^2 + 858*x*y + 153, 1014*x*y^2 - 1734*x, 9126*y^2 - 15606 ] true true Total time: 2.519 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 22:12:13 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2+121*x^2)* 117 + 11*117*6*x*y; > P2 := 11*2*3*x*117 + 13*y*(3^2+121*x^2); > I := ideal; > GroebnerBasis(I); > n:=8; X := 3; Y:= 11*x; n2:= n div 2; > Pd1 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po1 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > X := 1; Y:= 117*y; > Pd2 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po2 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Pd1*Pd2+(n-1)*Po1*Po2 in I; > Pd1*Po2 + Pd2*Po1 in I Output: Magma V2.10-22 Sat Apr 3 2004 22:12:11 on modular [Seed = 2259270630] ------------------------------------- [ 143*x^2*y^2 + 12870*x^2 + 7722*x*y + 585*y^2 - 4212, 1573*x^2*y + 7722*x + 117*y, 14157*x^2 + 7722*x*y + 1053, 702*x*y^2 - 6318*x, 6318*y^2 - 56862 ] false false Total time: 2.629 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 22:13:05 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2+121*x^2)* 117 + 11*31*6*x*y; > P2 := 11*2*3*x*117 + 31*y*(3^2+121*x^2); > I := ideal; > GroebnerBasis(I); > n:=8; X := 3; Y:= 11*x; n2:= n div 2; > Pd1 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po1 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > X := 117; Y:= 31*y; > Pd2 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po2 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Pd1*Pd2+(n-1)*Po1*Po2 in I; > Pd1*Po2 + Pd2*Po1 in I Output: Magma V2.10-22 Sat Apr 3 2004 22:13:03 on modular [Seed = 2645729481] ------------------------------------- [ 11*x^2*y^2 + 1287*x^2 + 4092*x*y^3 - 58080*x*y + 23589*y^2 - 335907, 121*x^2*y + 4650*x*y^2 - 65988*x + 9*y, 14157*x^2 + 2046*x*y + 1053, 5766*x*y^2 - 82134*x, 51894*y^2 - 739206 ] false false Total time: 2.519 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 22:17:30 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 117*(9+121*x^2)+2036*x*y; > P2 := 7722*x+31*(9+121*x^2)*y; > I := ideal; > GroebnerBasis(I); > n:=8; X := 117; Y:= 31*y; n2:= n div 2; > Pd1 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po1 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > X := 3; Y:= 11*x; > Pd2 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po2 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Pd1*Pd2+(n-1)*Po1*Po2 in I; > Pd1*Po2 + Pd2*Po1 in I Output: Magma V2.10-22 Sat Apr 3 2004 22:17:27 on modular [Seed = 1766217549] ------------------------------------- [ x^2*y^2 + 12870*x^2 + 6108*x*y^3 - 85580*x*y + 234729*y^2 - 3359070, 121*x^2*y + 44792*x*y^2 - 640926*x + 9*y, 14157*x^2 + 2036*x*y + 1053, 63116*x*y^2 - 903474*x, 568044*y^2 - 8131266 ] false false Total time: 2.549 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 22:17:48 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 117*(9+121*x^2)+2036*x*y; > P2 := 7722*x+31*(9+121*x^2)*y; > I := ideal; > GroebnerBasis(I); > n:=16; X := 117; Y:= 31*y; n2:= n div 2; > Pd1 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po1 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > X := 3; Y:= 11*x; > Pd2 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po2 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Pd1*Pd2+(n-1)*Po1*Po2 in I; > Pd1*Po2 + Pd2*Po1 in I Output: Magma V2.10-22 Sat Apr 3 2004 22:17:45 on modular [Seed = 1632526164] ------------------------------------- [ x^2*y^2 + 12870*x^2 + 6108*x*y^3 - 85580*x*y + 234729*y^2 - 3359070, 121*x^2*y + 44792*x*y^2 - 640926*x + 9*y, 14157*x^2 + 2036*x*y + 1053, 63116*x*y^2 - 903474*x, 568044*y^2 - 8131266 ] false false Total time: 2.519 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 22:17:58 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 117*(9+121*x^2)+2036*x*y; > P2 := 7722*x+31*(9+121*x^2)*y; > I := ideal; > GroebnerBasis(I); > n:=32; X := 117; Y:= 31*y; n2:= n div 2; > Pd1 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po1 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > X := 3; Y:= 11*x; > Pd2 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po2 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Pd1*Pd2+(n-1)*Po1*Po2 in I; > Pd1*Po2 + Pd2*Po1 in I Output: Magma V2.10-22 Sat Apr 3 2004 22:17:55 on modular [Seed = 2035697526] ------------------------------------- [ x^2*y^2 + 12870*x^2 + 6108*x*y^3 - 85580*x*y + 234729*y^2 - 3359070, 121*x^2*y + 44792*x*y^2 - 640926*x + 9*y, 14157*x^2 + 2036*x*y + 1053, 63116*x*y^2 - 903474*x, 568044*y^2 - 8131266 ] false false Total time: 2.559 seconds, Total memory usage: 2.16MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 22:18:26 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 117*(9+121*x^2)+2036*x*y; > P2 := 7722*x+31*(9+121*x^2)*y; > I := ideal; > GroebnerBasis(I); > n:=64; X := 117; Y:= 31*y; n2:= n div 2; > Pd1 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po1 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > X := 3; Y:= 11*x; > Pd2 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po2 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Pd1*Pd2+(n-1)*Po1*Po2 in I; > Pd1*Po2 + Pd2*Po1 in I Output: Magma V2.10-22 Sat Apr 3 2004 22:18:23 on modular [Seed = 1902006114] ------------------------------------- [ x^2*y^2 + 12870*x^2 + 6108*x*y^3 - 85580*x*y + 234729*y^2 - 3359070, 121*x^2*y + 44792*x*y^2 - 640926*x + 9*y, 14157*x^2 + 2036*x*y + 1053, 63116*x*y^2 - 903474*x, 568044*y^2 - 8131266 ] false false Total time: 2.920 seconds, Total memory usage: 3.90MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 22:26:55 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 117*(9+121*x^2)+2046*x*y; > P2 := 7722*x+31*(9+121*x^2)*y; > I := ideal; > GroebnerBasis(I); > n:=8; X := 117; Y:= 31*y; n2:= n div 2; > Pd1 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po1 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > X := 3; Y:= 11*x; > Pd2 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po2 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Pd1*Pd2+(n-1)*Po1*Po2 in I; > Pd1*Po2 + Pd2*Po1 in I Output: Magma V2.10-22 Sat Apr 3 2004 22:26:53 on modular [Seed = 1517656651] ------------------------------------- [ 11*x^2*y^2 + 1287*x^2 + 4092*x*y^3 - 58080*x*y + 23589*y^2 - 335907, 121*x^2*y + 4650*x*y^2 - 65988*x + 9*y, 14157*x^2 + 2046*x*y + 1053, 5766*x*y^2 - 82134*x, 51894*y^2 - 739206 ] false false Total time: 2.569 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 22:27:05 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 117*(9+121*x^2)+2046*x*y; > P2 := 7722*x+31*(9+121*x^2)*y; > I := ideal; > GroebnerBasis(I); > n:=16; X := 117; Y:= 31*y; n2:= n div 2; > Pd1 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po1 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > X := 3; Y:= 11*x; > Pd2 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po2 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Pd1*Pd2+(n-1)*Po1*Po2 in I; > Pd1*Po2 + Pd2*Po1 in I Output: Magma V2.10-22 Sat Apr 3 2004 22:27:03 on modular [Seed = 1383961273] ------------------------------------- [ 11*x^2*y^2 + 1287*x^2 + 4092*x*y^3 - 58080*x*y + 23589*y^2 - 335907, 121*x^2*y + 4650*x*y^2 - 65988*x + 9*y, 14157*x^2 + 2046*x*y + 1053, 5766*x*y^2 - 82134*x, 51894*y^2 - 739206 ] true true Total time: 2.530 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 22:27:19 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 117*(9+121*x^2)+2046*x*y; > P2 := 7722*x+31*(9+121*x^2)*y; > I := ideal; > GroebnerBasis(I); > n:=32; X := 117; Y:= 31*y; n2:= n div 2; > Pd1 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po1 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > X := 3; Y:= 11*x; > Pd2 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po2 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Pd1*Pd2+(n-1)*Po1*Po2 in I; > Pd1*Po2 + Pd2*Po1 in I Output: Magma V2.10-22 Sat Apr 3 2004 22:27:16 on modular [Seed = 705030866] ------------------------------------- [ 11*x^2*y^2 + 1287*x^2 + 4092*x*y^3 - 58080*x*y + 23589*y^2 - 335907, 121*x^2*y + 4650*x*y^2 - 65988*x + 9*y, 14157*x^2 + 2046*x*y + 1053, 5766*x*y^2 - 82134*x, 51894*y^2 - 739206 ] true true Total time: 2.620 seconds, Total memory usage: 2.20MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 22:29:38 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 117*(2601+121*x^2)+347826*x*y; > P2 := 131274*x+31*(2601+121*x^2)*y; > I := ideal; > GroebnerBasis(I); > n:=16; X := 117; Y:= 31*y; n2:= n div 2; > Pd1 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po1 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > X := 3; Y:= 11*x; > Pd2 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po2 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Pd1*Pd2+(n-1)*Po1*Po2 in I; > Pd1*Po2 + Pd2*Po1 in I Output: Magma V2.10-22 Sat Apr 3 2004 22:29:35 on modular [Seed = 588046928] ------------------------------------- [ x^2*y^2 + 12870*x^2 + 1043478*x*y^3 - 1170120*x*y + 12979762497*y^2 - 18488475018, 121*x^2*y + 7652172*x*y^2 - 10895742*x + 2601*y, 14157*x^2 + 347826*x*y + 304317, 10782606*x*y^2 - 15359058*x, 28045558206*y^2 - 39948909858 ] false false Total time: 2.530 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 22:30:31 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 117*(2601+121*x^2)+347826*x*y; > P2 := 131274*x+31*(2601+121*x^2)*y; > I := ideal; > GroebnerBasis(I); > n:=16; X := 117; Y:= 31*y; n2:= n div 2; > Pd1 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po1 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > X := 51; Y:= 11*x; > Pd2 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po2 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Pd1*Pd2+(n-1)*Po1*Po2 in I; > Pd1*Po2 + Pd2*Po1 in I Output: Magma V2.10-22 Sat Apr 3 2004 22:30:28 on modular [Seed = 857534987] ------------------------------------- [ x^2*y^2 + 12870*x^2 + 1043478*x*y^3 - 1170120*x*y + 12979762497*y^2 - 18488475018, 121*x^2*y + 7652172*x*y^2 - 10895742*x + 2601*y, 14157*x^2 + 347826*x*y + 304317, 10782606*x*y^2 - 15359058*x, 28045558206*y^2 - 39948909858 ] false false Total time: 2.529 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 22:32:19 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 117*(2601+121*x^2)+34782*x*y; > P2 := 131274*x+31*(2601+121*x^2)*y; > I := ideal; > GroebnerBasis(I); > n:=16; X := 117; Y:= 31*y; n2:= n div 2; > Pd1 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po1 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > X := 51; Y:= 11*x; > Pd2 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po2 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Pd1*Pd2+(n-1)*Po1*Po2 in I; > Pd1*Po2 + Pd2*Po1 in I Output: Magma V2.10-22 Sat Apr 3 2004 22:32:16 on modular [Seed = 186960551] ------------------------------------- [ 11*x^2*y^2 + 1287*x^2 + 69564*x*y^3 - 987360*x*y + 231777711*y^2 - 3301535133, 121*x^2*y + 79050*x*y^2 - 1121796*x + 2601*y, 14157*x^2 + 34782*x*y + 304317, 98022*x*y^2 - 1396278*x, 254955222*y^2 - 3631719078 ] true true Total time: 2.480 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 22:36:37 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 : = (304317 + 14157*x^2 + 34782*x*y + 11934*z + 682*x*y*z + 117*z^2); > P2 := 131274*x + 80631*y + 3751*x^2*y + 2574*x*z + 3162*y*z + 31*y*z^2; > I := ideal; > GroebnerBasis(I); > n:=16; X := 117; Y:= 31*y; n2:= n div 2; > Pd1 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po1 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > X := 51+z; Y:= 11*x; > Pd2 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po2 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Pd1*Pd2+(n-1)*Po1*Po2 in I; > Pd1*Po2 + Pd2*Po1 in I Output: Magma V2.10-22 Sat Apr 3 2004 22:36:35 on modular [Seed = 423025590] ------------------------------------- >> P1 : = (304317 + 14157*x^2 + 34782*x*y + 11934*z + 682*x*y*z + 117*z^2); ^ User error: bad syntax >> I := ideal; ^ User error: Identifier 'P1' has not been declared or assigned >> GroebnerBasis(I); ^ User error: Identifier 'I' has not been declared or assigned >> Pd1*Pd2+(n-1)*Po1*Po2 in I; ^ User error: Identifier 'I' has not been declared or assigned >> Pd1*Po2 + Pd2*Po1 in I ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.649 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 22:36:57 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (304317 + 14157*x^2 + 34782*x*y + 11934*z + 682*x*y*z + 117*z^2); > P2 := 131274*x + 80631*y + 3751*x^2*y + 2574*x*z + 3162*y*z + 31*y*z^2; > I := ideal; > GroebnerBasis(I); > n:=16; X := 117; Y:= 31*y; n2:= n div 2; > Pd1 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po1 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > X := 51+z; Y:= 11*x; > Pd2 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po2 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Pd1*Pd2+(n-1)*Po1*Po2 in I; > Pd1*Po2 + Pd2*Po1 in I Output: Magma V2.10-22 Sat Apr 3 2004 22:36:54 on modular [Seed = 289330091] ------------------------------------- [ 99*x^2*y^2*z + 88*x^2*y^2 + 11583*x^2*z + 10296*x^2 + 12276*x*y^3*z^2 + 2728*x*y^3*z - 31790748*x*y^3 - 174240*x*y*z^2 - 6380*x*y*z + 452872860*x*y + 525*y^2*z^3 + 80284*y^2*z^2 + 4092393*y^2*z + 69535134*y^2 - 7371*z^3 - 1132560*z^2 - 58005207*z - 990247518, 121*x^2*y + 15004*x*y^2*z + 765204*x*y^2 - 213642*x*z - 10895742*x + y*z^2 + 102*y*z + 2601*y, 14157*x^2 + 682*x*y*z + 34782*x*y + 117*z^2 + 11934*z + 304317, 21142*x*y^2*z + 1078242*x*y^2 - 301158*x*z - 15359058*x, 1922*y^2*z^3 + 294066*y^2*z^2 + 14997366*y^2*z + 254955222*y^2 - 27378*z^3 - 4188834*z^2 - 213630534*z - 3631719078 ] true true Total time: 2.879 seconds, Total memory usage: 2.52MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 22:37:52 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (304317 + 14157*x^2 + 34782*x*y + 11934*z*x + 682*x*y*z*x + 117*z^2*x^2); > P2 := 131274*x + 80631*y + 3751*x^2*y + 2574*x*z*x + 3162*y*z*x + 31*y*z^2*x^2; > I := ideal; > GroebnerBasis(I); > n:=16; X := 117; Y:= 31*y; n2:= n div 2; > Pd1 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po1 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > X := 51+z*x; Y:= 11*x; > Pd2 := ((X+Y)^(n-1)+(n-1)*(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Po2 := ((X+Y)^(n-1)-(X+Y)^(n2 -1)*(X-Y)^(n2)) div 8; > Pd1*Pd2+(n-1)*Po1*Po2 in I; > Pd1*Po2 + Pd2*Po1 in I Output: Magma V2.10-22 Sat Apr 3 2004 22:37:48 on modular [Seed = 3938789770] ------------------------------------- [ x^2*y*z^4 + 6*x^2*y*z^2 + 44649*x^2*y + 20592*x^2*z + 313038*x*y^2*z^2 + 6615953784*x*y^2 + 102*x*y*z^3 + 12954*x*y*z - 4463316*x*z^2 - 94239635490*x + 15964938*y^2*z + 2601*y*z^2 + 959769*y - 227629116*z, 31*x^2*y*z^2 + 3751*x^2*y + 2574*x^2*z + 3162*x*y*z + 131274*x + 80631*y, 682*x^2*y*z + 117*x^2*z^2 + 14157*x^2 + 34782*x*y + 11934*x*z + 304317, 82522*x^2*y - 117*x^2*z^3 + 42471*x^2*z + 34782*x*y*z - 11934*x*z^2 + 2888028*x + 1773882*y - 304317*z, 117*x^2*z^4 - 28314*x^2*z^2 + 1712997*x^2 - 34782*x*y*z^2 + 4208622*x*y + 11934*x*z^3 - 1444014*x*z - 1773882*y*z + 304317*z^2 + 36822357, 1078242*x*y^2*z^2 + 6523364100*x*y^2 - 15359058*x*z^2 - 92922300900*x + 54990342*y^2*z - 783311958*z, 54990342*x*y^2*z - 783311958*x*z + 2804507442*y^2 - 39948909858, 6653831382*x*y^2 - 94780746918*x, 339345400482*y^2 - 4833818092818 ] true true Total time: 2.769 seconds, Total memory usage: 2.34MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 22:53:07 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 184977 + 14157*x^2 + 27962*x*y - 2340*z - 117*z^2 > P2 := 105534*x + 49011*y + 3751*x^2*y - 620*y*z - 31*y*z^2; > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-22 Sat Apr 3 2004 22:53:05 on modular [Seed = 3337158667] ------------------------------------- >> P2 := 105534*x + 49011*y + 3751*x^2*y - 620*y*z - 31*y*z^2; ^ User error: bad syntax >> I := ideal; ^ User error: Identifier 'P1' has not been declared or assigned >> GroebnerBasis(I); ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.599 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 22:53:20 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 184977 + 14157*x^2 + 27962*x*y - 2340*z - 117*z^2; > P2 := 105534*x + 49011*y + 3751*x^2*y - 620*y*z - 31*y*z^2; > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-22 Sat Apr 3 2004 22:53:18 on modular [Seed = 3740342300] ------------------------------------- [ 11*x^2*y^2 + 1287*x^2 + 55924*x*y^3 - 793760*x*y + 35819*y^2*z^2 + 716380*y^2*z - 56629839*y^2 - 510237*z^2 - 10204740*z + 806684697, 121*x^2*y + 615164*x*y^2 - 8759322*x - y*z^2 - 20*y*z + 1581*y, 14157*x^2 + 27962*x*y - 117*z^2 - 2340*z + 184977, 866822*x*y^2 - 12347478*x, 78802*y^2*z^2 + 1576040*y^2*z - 124585962*y^2 - 1122498*z^2 - 22449960*z + 1774669338 ] Total time: 2.540 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 23:18:36 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-22 Sat Apr 3 2004 23:18:33 on modular [Seed = 1315013306] ------------------------------------- >> 21*(289*Power(x,2) + (12 - z)*(13 + z)) , >; ^ User error: bad syntax >> GroebnerBasis(I); ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.530 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 23:18:45 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-22 Sat Apr 3 2004 23:18:42 on modular [Seed = 1181321865] ------------------------------------- >> I := ideal> GroebnerBasis(I); ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.569 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 23:19:08 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1: = 11*y*(17*x*(12 - z) + 17*x*(13 + z)) + 21*(289*x^2 + (12 - z)*(13 + z)) > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-22 Sat Apr 3 2004 23:19:06 on modular [Seed = 1500943758] ------------------------------------- >> P1: = 11*y*(17*x*(12 - z) + 17*x*(13 + z)) + 21*(289*x^2 + (12 - z)*(13 + ^ User error: bad syntax >> I := ideal; ^ User error: Identifier 'P1' has not been declared or assigned >> GroebnerBasis(I); ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.559 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 23:19:30 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 11*y*(17*x*(12 - z) + 17*x*(13 + z)) + 21*(289*x^2 + (12 - z)*(13 + z)); > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-22 Sat Apr 3 2004 23:19:27 on modular [Seed = 1367252467] ------------------------------------- [ 6069*x^2 + 4675*x*y - 21*z^2 - 21*z + 3276 ] Total time: 2.510 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 048.c.011.mel.iprimus.net.au. (210.50.218.48) Time: Sat Apr 3 23:21:00 2004 Input: ModInv(18,101) Output: Magma V2.10-22 Sat Apr 3 2004 23:20:57 on modular [Seed = 638184290] ------------------------------------- >> ModInv(18,101) ^ User error: Identifier 'ModInv' has not been declared or assigned Total time: 2.529 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 048.c.011.mel.iprimus.net.au. (210.50.218.48) Time: Sat Apr 3 23:21:17 2004 Input: ModInverse(18,101) Output: Magma V2.10-22 Sat Apr 3 2004 23:21:14 on modular [Seed = 1041363817] ------------------------------------- >> ModInverse(18,101) ^ User error: Identifier 'ModInverse' has not been declared or assigned Total time: 2.589 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 048.c.011.mel.iprimus.net.au. (210.50.218.48) Time: Sat Apr 3 23:21:40 2004 Input: ModNInv(18,101) Output: Magma V2.10-22 Sat Apr 3 2004 23:21:37 on modular [Seed = 907672330] ------------------------------------- >> ModNInv(18,101) ^ User error: Identifier 'ModNInv' has not been declared or assigned Total time: 2.529 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 23:21:46 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 11*y*(17*x*(12 - z) + 17*x*(13 + z)) + 21*(289*x**2 + (12 - z)*(13 + z)); > P2 := 21*(17*x*(12 - z) + 17*x*(13 + z)) + 11*y*(289*Power(x,2) + (12 - z)*(13 + z)); > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-22 Sat Apr 3 2004 23:21:43 on modular [Seed = 237093684] ------------------------------------- >> P1 := 11*y*(17*x*(12 - z) + 17*x*(13 + z)) + 21*(289*x**2 + (12 - z)*(13 ^ User error: bad syntax >> P2 := 21*(17*x*(12 - z) + 17*x*(13 + z)) + 11*y*(289*Power(x,2) + (12 - z ^ Runtime error in 'Power': Bad argument types Argument types given: RngMPolElt, RngIntElt >> I := ideal; ^ User error: Identifier 'P1' has not been declared or assigned >> GroebnerBasis(I); ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.510 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 23:21:59 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 11*y*(17*x*(12 - z) + 17*x*(13 + z)) + 21*(289*x^22 + (12 - z)*(13 + z)); > P2 := 21*(17*x*(12 - z) + 17*x*(13 + z)) + 11*y*(289*x^2 + (12 - z)*(13 + z)); > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-22 Sat Apr 3 2004 23:21:56 on modular [Seed = 3132681] ------------------------------------- [ 6069*x^22 + 4675*x*y - 21*z^2 - 21*z + 3276 ] Total time: 2.520 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 23:22:42 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 11*y*(17*x*(12 - z) + 17*x*(13 + z)) + 21*(289*x^22 + (12 - z)*(13 + z)); > P2 := 21*(17*x*(12 - z) + 17*x*(13 + z)) + 11*y*(289*x^2 + (12 - z)*(13 + z)); > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-22 Sat Apr 3 2004 23:22:19 on modular [Seed = 439736076] ------------------------------------- ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 23:23:33 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 11*y*(17*x*(12 - z) + 17*x*(13 + z)) + 21*(289*x^22 + (12 - z)*(13 + z)); > P2 := 21*(17*x*(12 - z) + 17*x*(13 + z)) + 11*y*(289*x^2 + (12 - z)*(13 + z)); > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-22 Sat Apr 3 2004 23:23:10 on modular [Seed = 306044881] ------------------------------------- ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 23:24:15 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 11*y*(17*x*(13 - z) + 17*x*(13 + z)) + 21*(289*x^2) + (13 - z)*(13 + z)); > P2 := 21*(17*x*(13 - z) + 17*x*(13 + z)) + 11*y*(289*x^2 + (13 - z)*(13 + z)); > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-22 Sat Apr 3 2004 23:24:13 on modular [Seed = 3855231077] ------------------------------------- >> x^2) + (13 - z)*(13 + z)); ^ User error: bad syntax >> I := ideal; ^ User error: Identifier 'P1' has not been declared or assigned >> GroebnerBasis(I); ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.569 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 23:24:29 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 11*y*(17*x*(13 - z) + 17*x*(13 + z)) + 21*(289*x^2 + (13 - z)*(13 + z)); > P2 := 21*(17*x*(13 - z) + 17*x*(13 + z)) + 11*y*(289*x^2 + (13 - z)*(13 + z)); > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-22 Sat Apr 3 2004 23:24:27 on modular [Seed = 4258410603] ------------------------------------- [ 17*x^2*y^2 + 5355*x^2 + 43758*x*y^3 - 155142*x*y + 185*y^2*z^2 - 31265*y^2 - 693*z^2 + 117117, 289*x^2*y + 48620*x*y^2 - 176358*x - y*z^2 + 169*y, 6069*x^2 + 4862*x*y - 21*z^2 + 3549, 53482*x*y^2 - 194922*x, 3146*y^2*z^2 - 531674*y^2 - 11466*z^2 + 1937754 ] Total time: 2.559 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 23:32:03 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 11*y*(17*x*(13 - z) + 17*x*(13 + z)) + 21*(289*x^2 + (13 - z)*(13 + z)); > P2 := 21*(17*x*(13 - z) + 17*x*(13 + z)) + 11*y*(289*x^2 + (13 - z)*(13 + z)); > I := ideal; > 51185893014090757 + 4006222227236220355*x^3 + 15716717968388249085*x^4 + 32884209903089259624*x^5 + 71670713891348386360*x^6 + 145605749787505856355*x^7 + 190407518952892273695*x^8 + 160272288278650260440*x^9 + 125752103110940973576*x^10 + 102778161196442141865*x^11 + 44800736931782472095*x^12 + 2862423051509815793*x^15 + 19686881928496445*z + 1232683762226529340*x^3*z + 4432920452622326665*x^4*z + 8431848693099810160*x^5*z + 16539395513388089160*x^6*z + 29867846110257611560*x^7*z + 34175708530006305535*x^8*z + 24657275119792347760*x^9*z + 16122064501402688920*x^10*z + 10541349866301758140*x^11*z + 3446210533214036315*x^12*z + 1514375532961265*z^2 + 74502864749955070*x^3*z^2 + 243567057836391575*x^4*z^2 + 416959550757682920*x^5*z^2 + 727006396192883040*x^6*z^2 + 1148763311932985060*x^7*z^2 + 1126671709780427655*x^8*z^2 + 677397668126163400*x^9*z^2 + 354331087942916240*x^10*z^2 + 173758514279699310*x^11*z^2 + 37870445419934465*x^12*z^2 - 349471276837215*z^3 - 13545975409082740*x^3*z^3 - 38493814734982165*x^4*z^3 - 57020109505324160*x^5*z^3 - 93205948229856800*x^6*z^3 - 127978936607918760*x^7*z^3 - 92644092846666465*x^8*z^3 - 41686010346225440*x^9*z^3 - 27256237534070480*x^10*z^3 - 8910693039984580*x^11*z^3 + 2913111186148805*x^12*z^3 - 62725613791295*z^4 - 1903650390329675*x^3*z^4 - 4475659330656878*x^4*z^4 - 5592356893791408*x^5*z^4 - 9033807289970736*x^6*z^4 - 10102366607694686*x^7*z^4 - 4398487121090699*x^8*z^4 - 1763638899263384*x^9*z^4 - 1467643559526872*x^10*z^4 + 34271896307633*x^11*z^4 + 137858491849*z^5 - 12331338560840*x^3*z^5 + 36282592304010*x^4*z^5 + 50609564649696*x^5*z^5 - 99272607582096*x^6*z^5 - 7212112516648*x^7*z^5 + 109637979700197*x^8*z^5 - 24666278311376*x^9*z^5 - 16127951203592*x^10*z^5 + 689292459245*z^6 + 9959927299140*x^3*z^6 + 21521469281182*x^4*z^6 + 16221014310800*x^5*z^6 + 11878773556832*x^6*z^6 + 15811169748036*x^7*z^6 + 5169036263781*x^8*z^6 - 948703011976*x^9*z^6 + 36707882445*z^7 + 510765502520*x^3*z^7 + 548651954630*x^4*z^7 + 391607919456*x^6*z^7 + 384076997928*x^7*z^7 - 20927272323*x^8*z^7 - 2823683265*z^8 - 4911206755*x^3*z^8 - 35781649215*x^4*z^8 - 28794699960*x^5*z^8 + 7530921528*x^6*z^8 + 1231016019*x^7*z^8 - 313742585*z^9 - 1079386100*x^3*z^9 - 1961991811*x^4*z^9 - 295330256*x^5*z^9 + 193100552*x^6*z^9 - 371293*z^10 - 41514850*x^3*z^10 - 27144325*x^4*z^10 + 11358856*x^5*z^10 + 999635*z^11 - 1277380*x^3*z^11 - 83521*x^4*z^11 + 32955*z^12 - 24565*x^3*z^12 - 845*z^13 - 65*z^14 - z^15 in I; Output: Magma V2.10-22 Sat Apr 3 2004 23:32:00 on modular [Seed = 3337161067] ------------------------------------- false Total time: 2.529 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 23:32:50 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 11*y*(17*x*(13 - z) + 17*x*(13 + z)) + 21*(289*x^2 + (13 - z)*(13 + z)); > P2 := 21*(17*x*(13 - z) + 17*x*(13 + z)) + 11*y*(289*x^2 + (13 - z)*(13 + z)); > I := ideal; > 51185893014090757 + 4006222227236220355*x^3 + 15716717968388249085*x^4 + 32884209903089259624*x^5 + 71670713891348386360*x^6 + 145605749787505856355*x^7 + 190407518952892273695*x^8 + 160272288278650260440*x^9 + 125752103110940973576*x^10 + 102778161196442141865*x^11 + 44800736931782472095*x^12 + 2862423051509815793*x^15 + 19686881928496445*z + 1232683762226529340*x^3*z + 4432920452622326665*x^4*z + 8431848693099810160*x^5*z + 16539395513388089160*x^6*z + 29867846110257611560*x^7*z + 34175708530006305535*x^8*z + 24657275119792347760*x^9*z + 16122064501402688920*x^10*z + 10541349866301758140*x^11*z + 3446210533214036315*x^12*z + 1514375532961265*z^2 + 74502864749955070*x^3*z^2 + 243567057836391575*x^4*z^2 + 416959550757682920*x^5*z^2 + 727006396192883040*x^6*z^2 + 1148763311932985060*x^7*z^2 + 1126671709780427655*x^8*z^2 + 677397668126163400*x^9*z^2 + 354331087942916240*x^10*z^2 + 173758514279699310*x^11*z^2 + 37870445419934465*x^12*z^2 - 349471276837215*z^3 - 13545975409082740*x^3*z^3 - 38493814734982165*x^4*z^3 - 57020109505324160*x^5*z^3 - 93205948229856800*x^6*z^3 - 127978936607918760*x^7*z^3 - 92644092846666465*x^8*z^3 - 41686010346225440*x^9*z^3 - 27256237534070480*x^10*z^3 - 8910693039984580*x^11*z^3 + 2913111186148805*x^12*z^3 - 62725613791295*z^4 - 1903650390329675*x^3*z^4 - 4475659330656878*x^4*z^4 - 5592356893791408*x^5*z^4 - 9033807289970736*x^6*z^4 - 10102366607694686*x^7*z^4 - 4398487121090699*x^8*z^4 - 1763638899263384*x^9*z^4 - 1467643559526872*x^10*z^4 + 34271896307633*x^11*z^4 + 137858491849*z^5 - 12331338560840*x^3*z^5 + 36282592304010*x^4*z^5 + 50609564649696*x^5*z^5 - 99272607582096*x^6*z^5 - 7212112516648*x^7*z^5 + 109637979700197*x^8*z^5 - 24666278311376*x^9*z^5 - 16127951203592*x^10*z^5 + 689292459245*z^6 + 9959927299140*x^3*z^6 + 21521469281182*x^4*z^6 + 16221014310800*x^5*z^6 + 11878773556832*x^6*z^6 + 15811169748036*x^7*z^6 + 5169036263781*x^8*z^6 - 948703011976*x^9*z^6 + 36707882445*z^7 + 510765502520*x^3*z^7 + 548651954630*x^4*z^7 + 391607919456*x^6*z^7 + 384076997928*x^7*z^7 - 20927272323*x^8*z^7 - 2823683265*z^8 - 4911206755*x^3*z^8 - 35781649215*x^4*z^8 - 28794699960*x^5*z^8 + 7530921528*x^6*z^8 + 1231016019*x^7*z^8 - 313742585*z^9 - 1079386100*x^3*z^9 - 1961991811*x^4*z^9 - 295330256*x^5*z^9 + 193100552*x^6*z^9 - 371293*z^10 - 41514850*x^3*z^10 - 27144325*x^4*z^10 + 11358856*x^5*z^10 + 999635*z^11 - 1277380*x^3*z^11 - 83521*x^4*z^11 + 32955*z^12 - 24565*x^3*z^12 - 845*z^13 - 65*z^14 - z^15 in I; Output: Magma V2.10-22 Sat Apr 3 2004 23:32:47 on modular [Seed = 3740340572] ------------------------------------- false Total time: 2.579 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 23:33:17 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 11*y*(17*x*(13 - z) + 17*x*(13 + z)) + 21*(289*x^2 + (13 - z)*(13 + z)); > P2 := 21*(17*x*(13 - z) + 17*x*(13 + z)) + 11*y*(289*x^2 + (13 - z)*(13 + z)); > I := ideal; > 51185893014090757 + 4006222227236220355*x^3 + 15716717968388249085*x^4 + 32884209903089259624*x^5 + 71670713891348386360*x^6 + 145605749787505856355*x^7 + 190407518952892273695*x^8 + 160272288278650260440*x^9 + 125752103110940973576*x^10 + 102778161196442141865*x^11 + 44800736931782472095*x^12 + 2862423051509815793*x^15 + 11812129157097867*z + 739610257335917604*x^3*z + 2659752271573395999*x^4*z + 5059109215859886096*x^5*z + 9923637308032853496*x^6*z + 17920707666154566936*x^7*z + 20505425118003783321*x^8*z + 14794365071875408656*x^9*z + 9673238700841613352*x^10*z + 6324809919781054884*x^11*z + 2067726319928421789*x^12*z - 908625319776759*z^2 - 44701718849973042*x^3*z^2 - 146140234701834945*x^4*z^2 - 250175730454609752*x^5*z^2 - 436203837715729824*x^6*z^2 - 689257987159791036*x^7*z^2 - 676003025868256593*x^8*z^2 - 406438600875698040*x^9*z^2 - 212598652765749744*x^10*z^2 - 104255108567819586*x^11*z^2 - 22722267251960679*x^12*z^2 - 396067447082177*z^3 - 15213172382508308*x^3*z^3 - 43808005087776163*x^4*z^3 - 65573125931122784*x^5*z^3 - 104390662017439616*x^6*z^3 - 142605100791680904*x^7*z^3 - 108184392291913743*x^8*z^3 - 50023212415470528*x^9*z^3 - 27256237534070480*x^10*z^3 - 8910693039984580*x^11*z^3 + 1747866711689283*x^12*z^3 - 5376481182111*z^4 - 204391936645923*x^3*z^4 - 366857322184990*x^4*z^4 - 219308113482016*x^5*z^4 - 860362599044832*x^6*z^4 - 1476680037783678*x^7*z^4 - 229886086468155*x^8*z^4 + 480992427071832*x^9*z^4 - 209663365646696*x^10*z^4 - 239903274153431*x^11*z^4 + 5376481182111*z^5 + 110982047047560*x^3*z^5 + 247527907496246*x^4*z^5 + 303657387898176*x^5*z^5 + 330908691940320*x^6*z^5 + 237999713049384*x^7*z^5 + 145005069926067*x^8*z^5 + 73998834934128*x^9*z^5 - 16127951203592*x^10*z^5 + 265112484325*z^6 + 4647966072932*x^3*z^6 + 6636303207742*x^4*z^6 + 6488405724320*x^5*z^6 + 6787870603904*x^6*z^6 + 2496500486532*x^7*z^6 + 2992599942189*x^8*z^6 + 948703011976*x^9*z^6 - 36707882445*z^7 - 306459301512*x^3*z^7 - 548651954630*x^4*z^7 - 499108132640*x^5*z^7 - 391607919456*x^6*z^7 - 128025665976*x^7*z^7 + 20927272323*x^8*z^7 - 2823683265*z^8 - 20627068371*x^3*z^8 - 15230137871*x^4*z^8 - 17276819976*x^5*z^8 - 7530921528*x^6*z^8 + 1231016019*x^7*z^8 + 120670225*z^9 + 43175444*x^3*z^9 + 494026715*x^4*z^9 - 295330256*x^5*z^9 + 193100552*x^6*z^9 + 14480427*z^10 + 24908910*x^3*z^10 - 1085773*x^4*z^10 - 11358856*x^5*z^10 - 85683*z^11 + 766428*x^3*z^11 - 584647*x^4*z^11 - 37349*z^12 + 14739*x^3*z^12 - 507*z^13 + 39*z^14 + z^15 Output: Magma V2.10-22 Sat Apr 3 2004 23:33:15 on modular [Seed = 3606644400] ------------------------------------- 2862423051509815793*x^15 + 1747866711689283*x^12*z^3 - 22722267251960679*x^12*z^2 + 2067726319928421789*x^12*z + 44800736931782472095*x^12 - 239903274153431*x^11*z^4 - 8910693039984580*x^11*z^3 - 104255108567819586*x^11*z^2 + 6324809919781054884*x^11*z + 102778161196442141865*x^11 - 16127951203592*x^10*z^5 - 209663365646696*x^10*z^4 - 27256237534070480*x^10*z^3 - 212598652765749744*x^10*z^2 + 9673238700841613352*x^10*z + 125752103110940973576*x^10 + 948703011976*x^9*z^6 + 73998834934128*x^9*z^5 + 480992427071832*x^9*z^4 - 50023212415470528*x^9*z^3 - 406438600875698040*x^9*z^2 + 14794365071875408656*x^9*z + 160272288278650260440*x^9 + 20927272323*x^8*z^7 + 2992599942189*x^8*z^6 + 145005069926067*x^8*z^5 - 229886086468155*x^8*z^4 - 108184392291913743*x^8*z^3 - 676003025868256593*x^8*z^2 + 20505425118003783321*x^8*z + 190407518952892273695*x^8 + 1231016019*x^7*z^8 - 128025665976*x^7*z^7 + 2496500486532*x^7*z^6 + 237999713049384*x^7*z^5 - 1476680037783678*x^7*z^4 - 142605100791680904*x^7*z^3 - 689257987159791036*x^7*z^2 + 17920707666154566936*x^7*z + 145605749787505856355*x^7 + 193100552*x^6*z^9 - 7530921528*x^6*z^8 - 391607919456*x^6*z^7 + 6787870603904*x^6*z^6 + 330908691940320*x^6*z^5 - 860362599044832*x^6*z^4 - 104390662017439616*x^6*z^3 - 436203837715729824*x^6*z^2 + 9923637308032853496*x^6*z + 71670713891348386360*x^6 - 11358856*x^5*z^10 - 295330256*x^5*z^9 - 17276819976*x^5*z^8 - 499108132640*x^5*z^7 + 6488405724320*x^5*z^6 + 303657387898176*x^5*z^5 - 219308113482016*x^5*z^4 - 65573125931122784*x^5*z^3 - 250175730454609752*x^5*z^2 + 5059109215859886096*x^5*z + 32884209903089259624*x^5 - 584647*x^4*z^11 - 1085773*x^4*z^10 + 494026715*x^4*z^9 - 15230137871*x^4*z^8 - 548651954630*x^4*z^7 + 6636303207742*x^4*z^6 + 247527907496246*x^4*z^5 - 366857322184990*x^4*z^4 - 43808005087776163*x^4*z^3 - 146140234701834945*x^4*z^2 + 2659752271573395999*x^4*z + 15716717968388249085*x^4 + 14739*x^3*z^12 + 766428*x^3*z^11 + 24908910*x^3*z^10 + 43175444*x^3*z^9 - 20627068371*x^3*z^8 - 306459301512*x^3*z^7 + 4647966072932*x^3*z^6 + 110982047047560*x^3*z^5 - 204391936645923*x^3*z^4 - 15213172382508308*x^3*z^3 - 44701718849973042*x^3*z^2 + 739610257335917604*x^3*z + 4006222227236220355*x^3 + z^15 + 39*z^14 - 507*z^13 - 37349*z^12 - 85683*z^11 + 14480427*z^10 + 120670225*z^9 - 2823683265*z^8 - 36707882445*z^7 + 265112484325*z^6 + 5376481182111*z^5 - 5376481182111*z^4 - 396067447082177*z^3 - 908625319776759*z^2 + 11812129157097867*z + 51185893014090757 Total time: 2.589 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 23:33:29 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 11*y*(17*x*(13 - z) + 17*x*(13 + z)) + 21*(289*x^2 + (13 - z)*(13 + z)); > P2 := 21*(17*x*(13 - z) + 17*x*(13 + z)) + 11*y*(289*x^2 + (13 - z)*(13 + z)); > I := ideal; > 51185893014090757 + 4006222227236220355*x^3 + 15716717968388249085*x^4 + 32884209903089259624*x^5 + 71670713891348386360*x^6 + 145605749787505856355*x^7 + 190407518952892273695*x^8 + 160272288278650260440*x^9 + 125752103110940973576*x^10 + 102778161196442141865*x^11 + 44800736931782472095*x^12 + 2862423051509815793*x^15 + 11812129157097867*z + 739610257335917604*x^3*z + 2659752271573395999*x^4*z + 5059109215859886096*x^5*z + 9923637308032853496*x^6*z + 17920707666154566936*x^7*z + 20505425118003783321*x^8*z + 14794365071875408656*x^9*z + 9673238700841613352*x^10*z + 6324809919781054884*x^11*z + 2067726319928421789*x^12*z - 908625319776759*z^2 - 44701718849973042*x^3*z^2 - 146140234701834945*x^4*z^2 - 250175730454609752*x^5*z^2 - 436203837715729824*x^6*z^2 - 689257987159791036*x^7*z^2 - 676003025868256593*x^8*z^2 - 406438600875698040*x^9*z^2 - 212598652765749744*x^10*z^2 - 104255108567819586*x^11*z^2 - 22722267251960679*x^12*z^2 - 396067447082177*z^3 - 15213172382508308*x^3*z^3 - 43808005087776163*x^4*z^3 - 65573125931122784*x^5*z^3 - 104390662017439616*x^6*z^3 - 142605100791680904*x^7*z^3 - 108184392291913743*x^8*z^3 - 50023212415470528*x^9*z^3 - 27256237534070480*x^10*z^3 - 8910693039984580*x^11*z^3 + 1747866711689283*x^12*z^3 - 5376481182111*z^4 - 204391936645923*x^3*z^4 - 366857322184990*x^4*z^4 - 219308113482016*x^5*z^4 - 860362599044832*x^6*z^4 - 1476680037783678*x^7*z^4 - 229886086468155*x^8*z^4 + 480992427071832*x^9*z^4 - 209663365646696*x^10*z^4 - 239903274153431*x^11*z^4 + 5376481182111*z^5 + 110982047047560*x^3*z^5 + 247527907496246*x^4*z^5 + 303657387898176*x^5*z^5 + 330908691940320*x^6*z^5 + 237999713049384*x^7*z^5 + 145005069926067*x^8*z^5 + 73998834934128*x^9*z^5 - 16127951203592*x^10*z^5 + 265112484325*z^6 + 4647966072932*x^3*z^6 + 6636303207742*x^4*z^6 + 6488405724320*x^5*z^6 + 6787870603904*x^6*z^6 + 2496500486532*x^7*z^6 + 2992599942189*x^8*z^6 + 948703011976*x^9*z^6 - 36707882445*z^7 - 306459301512*x^3*z^7 - 548651954630*x^4*z^7 - 499108132640*x^5*z^7 - 391607919456*x^6*z^7 - 128025665976*x^7*z^7 + 20927272323*x^8*z^7 - 2823683265*z^8 - 20627068371*x^3*z^8 - 15230137871*x^4*z^8 - 17276819976*x^5*z^8 - 7530921528*x^6*z^8 + 1231016019*x^7*z^8 + 120670225*z^9 + 43175444*x^3*z^9 + 494026715*x^4*z^9 - 295330256*x^5*z^9 + 193100552*x^6*z^9 + 14480427*z^10 + 24908910*x^3*z^10 - 1085773*x^4*z^10 - 11358856*x^5*z^10 - 85683*z^11 + 766428*x^3*z^11 - 584647*x^4*z^11 - 37349*z^12 + 14739*x^3*z^12 - 507*z^13 + 39*z^14 + z^15 in I Output: Magma V2.10-22 Sat Apr 3 2004 23:33:26 on modular [Seed = 2844162514] ------------------------------------- false Total time: 2.529 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 23:34:41 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 11*y*(17*x*(13 - z) + 17*x*(13 + z)) + 21*(289*x^2 + (13 - z)*(13 + z)); > P2 := 21*(17*x*(13 - z) + 17*x*(13 + z)) + 11*y*(289*x^2 + (13 - z)*(13 + z)); > I := ideal; > 51185893014090757 + 4006222227236220355*x^3 + 15716717968388249085*x^4 + 32884209903089259624*x^5 + 71670713891348386360*x^6 + 145605749787505856355*x^7 + 190407518952892273695*x^8 + 160272288278650260440*x^9 + 125752103110940973576*x^10 + 102778161196442141865*x^11 + 44800736931782472095*x^12 + 2862423051509815793*x^15 + 35436387471293601*z + 2218830772007752812*x^3*z + 7979256814720187997*x^4*z + 15177327647579658288*x^5*z + 29770911924098560488*x^6*z + 53762122998463700808*x^7*z + 61516275354011349963*x^8*z + 44383095215626225968*x^9*z + 29019716102524840056*x^10*z + 18974429759343164652*x^11*z + 6203178959785265367*x^12*z + 9994878517544349*z^2 + 491718907349703462*x^3*z^2 + 1607542581720184395*x^4*z^2 + 2751933035000707272*x^5*z^2 + 4798242214873028064*x^6*z^2 + 7581837858757701396*x^7*z^2 + 7436033284550822523*x^8*z^2 + 4470824609632678440*x^9*z^2 + 2338585180423247184*x^10*z^2 + 1146806194246015446*x^11*z^2 + 249944939771567469*x^12*z^2 + 1327990851981417*z^3 + 50224308824445236*x^3*z^3 + 147911631486099611*x^4*z^3 + 225229432546030432*x^5*z^3 + 342997889485873024*x^6*z^3 + 464380712834448072*x^7*z^3 + 380737336408558311*x^8*z^3 + 183418445523391936*x^9*z^3 + 70866217588583248*x^10*z^3 + 23167801903959908*x^11*z^3 + 2913111186148805*x^12*z^3 + 37635368274777*z^4 + 1046005793423253*x^3*z^4 + 2819560561936066*x^4*z^4 + 3837891985935280*x^5*z^4 + 4731994294746576*x^6*z^4 + 5273857277798850*x^7*z^4 + 3816109035371373*x^8*z^4 + 1442977281215496*x^9*z^4 + 209663365646696*x^10*z^4 + 34271896307633*x^11*z^4 - 13647990693051*z^5 - 288553322323656*x^3*z^5 - 637767344721598*x^4*z^5 - 708533905095744*x^5*z^5 - 827271729850800*x^6*z^5 - 757271814248040*x^7*z^5 - 328913939100591*x^8*z^5 - 73998834934128*x^9*z^5 - 16127951203592*x^10*z^5 - 1983041382751*z^6 - 29879781897420*x^3*z^6 - 55137135997034*x^4*z^6 - 49960724077264*x^5*z^6 - 49212061878304*x^6*z^6 - 34118839982604*x^7*z^6 - 8977799826567*x^8*z^6 - 948703011976*x^9*z^6 - 80757341379*z^7 - 919377904536*x^3*z^7 - 1168867207690*x^4*z^7 - 698751385696*x^5*z^7 - 783215838912*x^6*z^7 - 384076997928*x^7*z^7 - 20927272323*x^8*z^7 + 6212103183*z^8 + 26520516477*x^3*z^8 + 55232186737*x^4*z^8 + 40312579944*x^5*z^8 + 7530921528*x^6*z^8 + 1231016019*x^7*z^8 + 902613283*z^9 + 2547351196*x^3*z^9 + 3288806417*x^4*z^9 + 1476651280*x^5*z^9 + 193100552*x^6*z^9 + 36758007*z^10 + 44836038*x^3*z^10 + 46688239*x^4*z^10 + 11358856*x^5*z^10 - 599781*z^11 - 766428*x^3*z^11 - 83521*x^4*z^11 - 125229*z^12 - 24565*x^3*z^12 - 5577*z^13 - 117*z^14 - z^15 in I Output: Magma V2.10-22 Sat Apr 3 2004 23:34:39 on modular [Seed = 2693755026] ------------------------------------- false Total time: 2.610 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 23:39:51 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 17*x*(13 - z) + 17*x*(13 + z); > P2 := 289*x^2 + (13 - z)*(13 + z); > I := ideal; > 51185893014090757 + 4006222227236220355*x^3 + 15716717968388249085*x^4 + 32884209903089259624*x^5 + 71670713891348386360*x^6 + 145605749787505856355*x^7 + 190407518952892273695*x^8 + 160272288278650260440*x^9 + 125752103110940973576*x^10 + 102778161196442141865*x^11 + 44800736931782472095*x^12 + 2862423051509815793*x^15 + 19686881928496445*z + 1232683762226529340*x^3*z + 4432920452622326665*x^4*z + 8431848693099810160*x^5*z + 16539395513388089160*x^6*z + 29867846110257611560*x^7*z + 34175708530006305535*x^8*z + 24657275119792347760*x^9*z + 16122064501402688920*x^10*z + 10541349866301758140*x^11*z + 3446210533214036315*x^12*z + 1514375532961265*z^2 + 74502864749955070*x^3*z^2 + 243567057836391575*x^4*z^2 + 416959550757682920*x^5*z^2 + 727006396192883040*x^6*z^2 + 1148763311932985060*x^7*z^2 + 1126671709780427655*x^8*z^2 + 677397668126163400*x^9*z^2 + 354331087942916240*x^10*z^2 + 173758514279699310*x^11*z^2 + 37870445419934465*x^12*z^2 - 349471276837215*z^3 - 13129176165726348*x^3*z^3 - 39038859899371293*x^4*z^3 - 59871114980590368*x^5*z^3 - 89477710300662528*x^6*z^3 - 120665854516037688*x^7*z^3 - 102207354043741713*x^8*z^3 - 50023212415470528*x^9*z^3 - 16353742520442288*x^10*z^3 - 5346415823990748*x^11*z^3 - 1747866711689283*x^12*z^3 - 62725613791295*z^4 - 1743342989038755*x^3*z^4 - 4727218637298014*x^4*z^4 - 6359935290978464*x^5*z^4 - 7743263391403488*x^6*z^4 - 8977277055097598*x^7*z^4 - 6605393551184987*x^8*z^4 - 2084300517311272*x^9*z^4 - 209663365646696*x^10*z^4 - 239903274153431*x^11*z^4 + 137858491849*z^5 + 7398803136504*x^3*z^5 - 8869078118758*x^4*z^5 + 66181738388064*x^6*z^5 - 7212112516648*x^7*z^5 - 60124053383979*x^8*z^5 + 24666278311376*x^9*z^5 + 16127951203592*x^10*z^5 + 689292459245*z^6 + 9959927299140*x^3*z^6 + 18048263864046*x^4*z^6 + 19465217172960*x^5*z^6 + 20363611811712*x^6*z^6 + 9153835117284*x^7*z^6 + 816163620597*x^8*z^6 + 948703011976*x^9*z^6 + 36707882445*z^7 + 306459301512*x^3*z^7 + 548651954630*x^4*z^7 + 499108132640*x^5*z^7 + 391607919456*x^6*z^7 + 128025665976*x^7*z^7 - 20927272323*x^8*z^7 - 2823683265*z^8 - 20627068371*x^3*z^8 - 15230137871*x^4*z^8 - 17276819976*x^5*z^8 - 7530921528*x^6*z^8 + 1231016019*x^7*z^8 - 313742585*z^9 - 1079386100*x^3*z^9 - 381106323*x^4*z^9 - 885990768*x^5*z^9 - 193100552*x^6*z^9 - 371293*z^10 + 11624158*x^3*z^10 + 24972779*x^4*z^10 - 11358856*x^5*z^10 + 999635*z^11 + 1277380*x^3*z^11 + 584647*x^4*z^11 + 32955*z^12 + 14739*x^3*z^12 - 845*z^13 - 65*z^14 - z^15 in I Output: Magma V2.10-22 Sat Apr 3 2004 23:39:48 on modular [Seed = 3063506767] ------------------------------------- true Total time: 2.569 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 23:40:19 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 17*x*(13 - z) + 17*x*(13 + z); > P2 := 289*x^2 + (13 - z)*(13 + z); > I := ideal; > 51185893014090757 + 4006222227236220355*x^3 + 15716717968388249085*x^4 + 32884209903089259624*x^5 + 71670713891348386360*x^6 + 145605749787505856355*x^7 + 190407518952892273695*x^8 + 160272288278650260440*x^9 + 125752103110940973576*x^10 + 102778161196442141865*x^11 + 44800736931782472095*x^12 + 2862423051509815793*x^15 - 3937376385699289*z - 246536752445305868*x^3*z - 886584090524465333*x^4*z - 1686369738619962032*x^5*z - 3307879102677617832*x^6*z - 5973569222051522312*x^7*z - 6835141706001261107*x^8*z - 4931455023958469552*x^9*z - 3224412900280537784*x^10*z - 2108269973260351628*x^11*z - 689242106642807263*x^12*z - 2120125746145771*z^2 - 104304010649937098*x^3*z^2 - 340993880970948205*x^4*z^2 - 583743371060756088*x^5*z^2 - 1017808954670036256*x^6*z^2 - 1608268636706179084*x^7*z^2 - 1577340393692598717*x^8*z^2 - 948356735376628760*x^9*z^2 - 496063523120082736*x^10*z^2 - 243261919991579034*x^11*z^2 - 53018623587908251*x^12*z^2 + 163086595857367*z^3 + 6460388272024076*x^3*z^3 + 17782098488195301*x^4*z^3 + 25659049277395872*x^5*z^3 + 44738855150331264*x^6*z^3 + 62161197780989112*x^7*z^3 + 40046156262752601*x^8*z^3 + 16674404138490176*x^9*z^3 + 16353742520442288*x^10*z^3 + 5346415823990748*x^11*z^3 - 2913111186148805*x^12*z^3 + 37635368274777*z^4 + 1046005793423253*x^3*z^4 + 2819560561936066*x^4*z^4 + 3837891985935280*x^5*z^4 + 4731994294746576*x^6*z^4 + 5273857277798850*x^7*z^4 + 3816109035371373*x^8*z^4 + 1442977281215496*x^9*z^4 + 209663365646696*x^10*z^4 + 34271896307633*x^11*z^4 - 2895028328829*z^5 - 66589228228536*x^3*z^5 - 129811052465458*x^4*z^5 - 134958839065856*x^5*z^5 - 187514925432848*x^6*z^5 - 165878587882904*x^7*z^5 - 76628695489385*x^8*z^5 - 24666278311376*x^9*z^5 + 16127951203592*x^10*z^5 - 371157478055*z^6 - 4837678973868*x^3*z^6 - 10977809979162*x^4*z^6 - 11030289731344*x^5*z^6 - 8484838254880*x^6*z^6 - 5270389916012*x^7*z^6 - 997533314063*x^8*z^6 - 948703011976*x^9*z^6 + 28550575235*z^7 + 335645901656*x^3*z^7 + 405525357770*x^4*z^7 + 299464879584*x^5*z^7 + 261071946304*x^6*z^7 + 42675221992*x^7*z^7 + 20927272323*x^8*z^7 + 2196198095*z^8 + 8559531773*x^3*z^8 + 20001024433*x^4*z^8 + 9598233320*x^5*z^8 + 7530921528*x^6*z^8 + 1231016019*x^7*z^8 - 168938315*z^9 - 820333436*x^3*z^9 - 465796617*x^4*z^9 - 295330256*x^5*z^9 - 193100552*x^6*z^9 - 7797153*z^10 + 4981782*x^3*z^10 - 14115049*x^4*z^10 + 11358856*x^5*z^10 + 599781*z^11 + 766428*x^3*z^11 + 83521*x^4*z^11 + 15379*z^12 - 24565*x^3*z^12 - 1183*z^13 - 13*z^14 + z^15 in I Output: Magma V2.10-22 Sat Apr 3 2004 23:40:17 on modular [Seed = 2259244890] ------------------------------------- true Total time: 2.530 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 23:42:31 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 17*x*(12 - z) + 17*x*(13 + z) > P2 := 289*x^2 + (12 - z)*(13 + z) > I := ideal; > 51185893014090757 + 4006222227236220355*x^3 + 15716717968388249085*x^4 + 32884209903089259624*x^5 + 71670713891348386360*x^6 + 145605749787505856355*x^7 + 190407518952892273695*x^8 + 160272288278650260440*x^9 + 125752103110940973576*x^10 + 102778161196442141865*x^11 + 44800736931782472095*x^12 + 2862423051509815793*x^15 + 736289384125767043*z + 46102372707272197316*x^3*z + 165791224928075017271*x^4*z + 315351141121932899984*x^5*z + 618573392200714534584*x^6*z + 1117057444523634672344*x^7*z + 1278171499022235827009*x^8*z + 922182089480233806224*x^9*z + 602965212352460565608*x^10*z + 394246484999685754436*x^11*z + 128888273942204958181*x^12*z + 4938075737880092912*z^2 + 242886112072558069570*x^3*z^2 + 793970152452755800522*x^4*z^2 + 1359019428204002479096*x^5*z^2 + 2369204794233176894904*x^6*z^2 + 3742900622940051922492*x^7*z^2 + 3669945315991446348220*x^8*z^2 + 2205688095138963170008*x^9*z^2 + 1153099659492632319832*x^10*z^2 + 564935265527110376626*x^11*z^2 + 122897169476771325818*x^12*z^2 + 20476989889255143153*z^3 + 774303584354795283100*x^3*z^3 + 2277352876468653358583*x^4*z^3 + 3463712210950193495072*x^5*z^3 + 5281073260250226050768*x^6*z^3 + 7146688753891517282296*x^7*z^3 + 5834209149082236719511*x^8*z^3 + 2801266546458072587648*x^9*z^3 + 1095733456354674180576*x^10*z^3 + 356112283065767745868*x^11*z^3 + 38118059870757113425*x^12*z^3 + 58689283269438958045*z^4 + 1662346027377969405797*x^3*z^4 + 4343182073262375293067*x^4*z^4 + 5775106707985034887389*x^5*z^4 + 7538597244414613046475*x^6*z^4 + 8487205707548345673571*x^7*z^4 + 5528338523264719587698*x^8*z^4 + 1981623845516942014687*x^9*z^4 + 511581678504660822929*x^10*z^4 + 80304673639778570812*x^11*z^4 - 739930241281796470*x^12*z^4 + 123069578487350018342*z^5 + 2528930451063016850980*x^3*z^5 + 5773487632376641001682*x^4*z^5 + 6567808197578297583446*x^5*z^5 + 7124561371547250721987*x^6*z^5 + 6388319714087588263844*x^7*z^5 + 3095756115732891220259*x^8*z^5 + 726363730102480186470*x^9*z^5 + 87614879202166191957*x^10*z^5 - 2563126581055256804*x^11*z^5 - 48357645690070163*x^12*z^5 + 194857435097671742305*z^6 + 2789344817984088915174*x^3*z^6 + 5442325595150680824263*x^4*z^6 + 5136665807318318568555*x^5*z^6 + 4425796995125952036981*x^6*z^6 + 2936667308696926080822*x^7*z^6 + 919160766291745136003*x^8*z^6 + 94918344348241600119*x^9*z^6 - 4546959330810393907*x^10*z^6 - 220916643599002318*x^11*z^6 + 1747866711689283*x^12*z^6 + 236807196257998765529*z^7 + 2238092572720862024856*x^3*z^7 + 3614840012539890209439*x^4*z^7 + 2699250622300284189202*x^5*z^7 + 1707108408760018076774*x^6*z^7 + 715833893338937123556*x^7*z^7 + 87962019156157117322*x^8*z^7 - 8034020541368610794*x^9*z^7 - 420810502804122464*x^10*z^7 + 1233788267074788*x^11*z^7 + 222069126820424226967*z^8 + 1284966611076716076561*x^3*z^8 + 1632537209311135473086*x^4*z^8 + 883965499568897350631*x^5*z^8 + 340872259089218817740*x^6*z^8 + 43724004236204524752*x^7*z^8 - 12833600705529182329*x^8*z^8 - 697030246843871241*x^9*z^8 + 6838251310323008*x^10*z^8 - 239903274153431*x^11*z^8 + 159842936433008919220*z^9 + 503382915054975131332*x^3*z^9 + 455153573829187568803*x^4*z^9 + 141487580768693187496*x^5*z^9 + 7515146915227791294*x^6*z^9 - 12761382577531421148*x^7*z^9 - 1026853964229917461*x^8*z^9 + 28769418838172200*x^9*z^9 + 564478292125720*x^10*z^9 + 86660413405383273729*z^10 + 118622672912309281976*x^3*z^10 + 55041354260262199921*x^4*z^10 - 4070816308659511502*x^5*z^10 - 7798256417374288644*x^6*z^10 - 897745784211014834*x^7*z^10 + 55943579610191874*x^8*z^10 + 1550180721568784*x^9*z^10 - 16127951203592*x^10*z^10 + 33910576458818606547*z^11 + 9276999477759373984*x^3*z^11 - 6100127593083647188*x^4*z^11 - 4234014310837629864*x^5*z^11 - 431306575465320906*x^6*z^11 + 71135956177311836*x^7*z^11 + 2477837873345287*x^8*z^11 - 20871466263472*x^9*z^11 + 8632551825178963318*z^12 - 2719299606987207842*x^3*z^12 - 2312114434307428699*x^4*z^12 - 155040479182868945*x^5*z^12 + 59812570438606897*x^6*z^12 + 3770757584554067*x^7*z^12 - 62809719998764*x^8*z^12 + 948703011976*x^9*z^12 + 944057392334028427*z^13 - 637424163828170368*x^3*z^13 - 36782588886693845*x^4*z^13 + 41935352243313930*x^5*z^13 + 3094803309261507*x^6*z^13 - 145469983642576*x^7*z^13 - 2281072683207*x^8*z^13 - 179675891055560965*z^14 + 8122880936188720*x^3*z^14 + 28500242913215286*x^4*z^14 + 1689322191003667*x^5*z^14 - 202934028647617*x^6*z^14 - 4305273357116*x^7*z^14 + 20927272323*x^8*z^14 - 75785411180435450*z^15 + 10102029513627324*x^3*z^15 + 921473814856783*x^4*z^15 - 194988771549162*x^5*z^15 - 7675746942000*x^6*z^15 + 128025665976*x^7*z^15 - 5286063756216217*z^16 + 212737904740449*x^3*z^16 - 162109983137901*x^4*z^16 - 6326262314491*x^5*z^16 + 255278929744*x^6*z^16 + 1231016019*x^7*z^16 + 1507744265277523*z^17 - 76149457135296*x^3*z^17 - 4925560605278*x^4*z^17 + 426445530808*x^5*z^17 + 3282709384*x^6*z^17 + 226043828849566*z^18 - 2279142321290*x^3*z^18 + 413252470127*x^4*z^18 + 10722760064*x^5*z^18 + 193100552*x^6*z^18 - 14090636383005*z^19 + 298632322604*x^3*z^19 + 8530417335*x^4*z^19 - 340765680*x^5*z^19 - 3563554148427*z^20 + 9412232053*x^3*z^20 - 210974046*x^4*z^20 - 11358856*x^5*z^20 + 60748081108*z^21 - 558332972*x^3*z^21 - 83521*x^4*z^21 + 31797152011*z^22 - 18109318*x^3*z^22 - 584647*x^4*z^22 - 10316935*z^23 + 334084*x^3*z^23 - 175569275*z^24 + 14739*x^3*z^24 - 1022602*z^25 + 599305*z^26 + 3969*z^27 - 1168*z^28 - 5*z^29 + z^30 in I Output: Magma V2.10-22 Sat Apr 3 2004 23:42:28 on modular [Seed = 2662419655] ------------------------------------- >> P2 := 289*x^2 + (12 - z)*(13 + z) ^ User error: bad syntax >> I := ideal; ^ User error: Identifier 'P1' has not been declared or assigned >> 599305*z^26 + 3969*z^27 - 1168*z^28 - 5*z^29 + z^30 in I; ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.529 seconds, Total memory usage: 2.10MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 23:42:44 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 17*x*(12 - z) + 17*x*(13 + z); > P2 := 289*x^2 + (12 - z)*(13 + z); > I := ideal; > 51185893014090757 + 4006222227236220355*x^3 + 15716717968388249085*x^4 + 32884209903089259624*x^5 + 71670713891348386360*x^6 + 145605749787505856355*x^7 + 190407518952892273695*x^8 + 160272288278650260440*x^9 + 125752103110940973576*x^10 + 102778161196442141865*x^11 + 44800736931782472095*x^12 + 2862423051509815793*x^15 + 736289384125767043*z + 46102372707272197316*x^3*z + 165791224928075017271*x^4*z + 315351141121932899984*x^5*z + 618573392200714534584*x^6*z + 1117057444523634672344*x^7*z + 1278171499022235827009*x^8*z + 922182089480233806224*x^9*z + 602965212352460565608*x^10*z + 394246484999685754436*x^11*z + 128888273942204958181*x^12*z + 4938075737880092912*z^2 + 242886112072558069570*x^3*z^2 + 793970152452755800522*x^4*z^2 + 1359019428204002479096*x^5*z^2 + 2369204794233176894904*x^6*z^2 + 3742900622940051922492*x^7*z^2 + 3669945315991446348220*x^8*z^2 + 2205688095138963170008*x^9*z^2 + 1153099659492632319832*x^10*z^2 + 564935265527110376626*x^11*z^2 + 122897169476771325818*x^12*z^2 + 20476989889255143153*z^3 + 774303584354795283100*x^3*z^3 + 2277352876468653358583*x^4*z^3 + 3463712210950193495072*x^5*z^3 + 5281073260250226050768*x^6*z^3 + 7146688753891517282296*x^7*z^3 + 5834209149082236719511*x^8*z^3 + 2801266546458072587648*x^9*z^3 + 1095733456354674180576*x^10*z^3 + 356112283065767745868*x^11*z^3 + 38118059870757113425*x^12*z^3 + 58689283269438958045*z^4 + 1662346027377969405797*x^3*z^4 + 4343182073262375293067*x^4*z^4 + 5775106707985034887389*x^5*z^4 + 7538597244414613046475*x^6*z^4 + 8487205707548345673571*x^7*z^4 + 5528338523264719587698*x^8*z^4 + 1981623845516942014687*x^9*z^4 + 511581678504660822929*x^10*z^4 + 80304673639778570812*x^11*z^4 - 739930241281796470*x^12*z^4 + 123069578487350018342*z^5 + 2528930451063016850980*x^3*z^5 + 5773487632376641001682*x^4*z^5 + 6567808197578297583446*x^5*z^5 + 7124561371547250721987*x^6*z^5 + 6388319714087588263844*x^7*z^5 + 3095756115732891220259*x^8*z^5 + 726363730102480186470*x^9*z^5 + 87614879202166191957*x^10*z^5 - 2563126581055256804*x^11*z^5 - 48357645690070163*x^12*z^5 + 194857435097671742305*z^6 + 2789344817984088915174*x^3*z^6 + 5442325595150680824263*x^4*z^6 + 5136665807318318568555*x^5*z^6 + 4425796995125952036981*x^6*z^6 + 2936667308696926080822*x^7*z^6 + 919160766291745136003*x^8*z^6 + 94918344348241600119*x^9*z^6 - 4546959330810393907*x^10*z^6 - 220916643599002318*x^11*z^6 + 1747866711689283*x^12*z^6 + 236807196257998765529*z^7 + 2238092572720862024856*x^3*z^7 + 3614840012539890209439*x^4*z^7 + 2699250622300284189202*x^5*z^7 + 1707108408760018076774*x^6*z^7 + 715833893338937123556*x^7*z^7 + 87962019156157117322*x^8*z^7 - 8034020541368610794*x^9*z^7 - 420810502804122464*x^10*z^7 + 1233788267074788*x^11*z^7 + 222069126820424226967*z^8 + 1284966611076716076561*x^3*z^8 + 1632537209311135473086*x^4*z^8 + 883965499568897350631*x^5*z^8 + 340872259089218817740*x^6*z^8 + 43724004236204524752*x^7*z^8 - 12833600705529182329*x^8*z^8 - 697030246843871241*x^9*z^8 + 6838251310323008*x^10*z^8 - 239903274153431*x^11*z^8 + 159842936433008919220*z^9 + 503382915054975131332*x^3*z^9 + 455153573829187568803*x^4*z^9 + 141487580768693187496*x^5*z^9 + 7515146915227791294*x^6*z^9 - 12761382577531421148*x^7*z^9 - 1026853964229917461*x^8*z^9 + 28769418838172200*x^9*z^9 + 564478292125720*x^10*z^9 + 86660413405383273729*z^10 + 118622672912309281976*x^3*z^10 + 55041354260262199921*x^4*z^10 - 4070816308659511502*x^5*z^10 - 7798256417374288644*x^6*z^10 - 897745784211014834*x^7*z^10 + 55943579610191874*x^8*z^10 + 1550180721568784*x^9*z^10 - 16127951203592*x^10*z^10 + 33910576458818606547*z^11 + 9276999477759373984*x^3*z^11 - 6100127593083647188*x^4*z^11 - 4234014310837629864*x^5*z^11 - 431306575465320906*x^6*z^11 + 71135956177311836*x^7*z^11 + 2477837873345287*x^8*z^11 - 20871466263472*x^9*z^11 + 8632551825178963318*z^12 - 2719299606987207842*x^3*z^12 - 2312114434307428699*x^4*z^12 - 155040479182868945*x^5*z^12 + 59812570438606897*x^6*z^12 + 3770757584554067*x^7*z^12 - 62809719998764*x^8*z^12 + 948703011976*x^9*z^12 + 944057392334028427*z^13 - 637424163828170368*x^3*z^13 - 36782588886693845*x^4*z^13 + 41935352243313930*x^5*z^13 + 3094803309261507*x^6*z^13 - 145469983642576*x^7*z^13 - 2281072683207*x^8*z^13 - 179675891055560965*z^14 + 8122880936188720*x^3*z^14 + 28500242913215286*x^4*z^14 + 1689322191003667*x^5*z^14 - 202934028647617*x^6*z^14 - 4305273357116*x^7*z^14 + 20927272323*x^8*z^14 - 75785411180435450*z^15 + 10102029513627324*x^3*z^15 + 921473814856783*x^4*z^15 - 194988771549162*x^5*z^15 - 7675746942000*x^6*z^15 + 128025665976*x^7*z^15 - 5286063756216217*z^16 + 212737904740449*x^3*z^16 - 162109983137901*x^4*z^16 - 6326262314491*x^5*z^16 + 255278929744*x^6*z^16 + 1231016019*x^7*z^16 + 1507744265277523*z^17 - 76149457135296*x^3*z^17 - 4925560605278*x^4*z^17 + 426445530808*x^5*z^17 + 3282709384*x^6*z^17 + 226043828849566*z^18 - 2279142321290*x^3*z^18 + 413252470127*x^4*z^18 + 10722760064*x^5*z^18 + 193100552*x^6*z^18 - 14090636383005*z^19 + 298632322604*x^3*z^19 + 8530417335*x^4*z^19 - 340765680*x^5*z^19 - 3563554148427*z^20 + 9412232053*x^3*z^20 - 210974046*x^4*z^20 - 11358856*x^5*z^20 + 60748081108*z^21 - 558332972*x^3*z^21 - 83521*x^4*z^21 + 31797152011*z^22 - 18109318*x^3*z^22 - 584647*x^4*z^22 - 10316935*z^23 + 334084*x^3*z^23 - 175569275*z^24 + 14739*x^3*z^24 - 1022602*z^25 + 599305*z^26 + 3969*z^27 - 1168*z^28 - 5*z^29 + z^30 in I Output: Magma V2.10-22 Sat Apr 3 2004 23:42:41 on modular [Seed = 2528724154] ------------------------------------- false Total time: 2.550 seconds, Total memory usage: 2.21MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 23:43:58 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 17*x*(12 - z) + 17*x*(13 + z); > P2 := 289*x^2 + (12 - z)*(13 + z); > I := ideal; > 51185893014090757 + 4006222227236220355*x^3 + 15716717968388249085*x^4 + 32884209903089259624*x^5 + 71670713891348386360*x^6 + 145605749787505856355*x^7 + 190407518952892273695*x^8 + 160272288278650260440*x^9 + 125752103110940973576*x^10 + 102778161196442141865*x^11 + 44800736931782472095*x^12 + 2862423051509815793*x^15 + 736289384125767043*z + 46102372707272197316*x^3*z + 165791224928075017271*x^4*z + 315351141121932899984*x^5*z + 618573392200714534584*x^6*z + 1117057444523634672344*x^7*z + 1278171499022235827009*x^8*z + 922182089480233806224*x^9*z + 602965212352460565608*x^10*z + 394246484999685754436*x^11*z + 128888273942204958181*x^12*z + 4938075737880092912*z^2 + 242886112072558069570*x^3*z^2 + 793970152452755800522*x^4*z^2 + 1359019428204002479096*x^5*z^2 + 2369204794233176894904*x^6*z^2 + 3742900622940051922492*x^7*z^2 + 3669945315991446348220*x^8*z^2 + 2205688095138963170008*x^9*z^2 + 1153099659492632319832*x^10*z^2 + 564935265527110376626*x^11*z^2 + 122897169476771325818*x^12*z^2 + 20476989889255143153*z^3 + 774303584354795283100*x^3*z^3 + 2277352876468653358583*x^4*z^3 + 3463712210950193495072*x^5*z^3 + 5281073260250226050768*x^6*z^3 + 7146688753891517282296*x^7*z^3 + 5834209149082236719511*x^8*z^3 + 2801266546458072587648*x^9*z^3 + 1095733456354674180576*x^10*z^3 + 356112283065767745868*x^11*z^3 + 38118059870757113425*x^12*z^3 + 58689283269438958045*z^4 + 1662346027377969405797*x^3*z^4 + 4343182073262375293067*x^4*z^4 + 5775106707985034887389*x^5*z^4 + 7538597244414613046475*x^6*z^4 + 8487205707548345673571*x^7*z^4 + 5528338523264719587698*x^8*z^4 + 1981623845516942014687*x^9*z^4 + 511581678504660822929*x^10*z^4 + 80304673639778570812*x^11*z^4 - 739930241281796470*x^12*z^4 + 123069578487350018342*z^5 + 2528930451063016850980*x^3*z^5 + 5773487632376641001682*x^4*z^5 + 6567808197578297583446*x^5*z^5 + 7124561371547250721987*x^6*z^5 + 6388319714087588263844*x^7*z^5 + 3095756115732891220259*x^8*z^5 + 726363730102480186470*x^9*z^5 + 87614879202166191957*x^10*z^5 - 2563126581055256804*x^11*z^5 - 48357645690070163*x^12*z^5 + 194857435097671742305*z^6 + 2789344817984088915174*x^3*z^6 + 5442325595150680824263*x^4*z^6 + 5136665807318318568555*x^5*z^6 + 4425796995125952036981*x^6*z^6 + 2936667308696926080822*x^7*z^6 + 919160766291745136003*x^8*z^6 + 94918344348241600119*x^9*z^6 - 4546959330810393907*x^10*z^6 - 220916643599002318*x^11*z^6 + 1747866711689283*x^12*z^6 + 236807196257998765529*z^7 + 2238092572720862024856*x^3*z^7 + 3614840012539890209439*x^4*z^7 + 2699250622300284189202*x^5*z^7 + 1707108408760018076774*x^6*z^7 + 715833893338937123556*x^7*z^7 + 87962019156157117322*x^8*z^7 - 8034020541368610794*x^9*z^7 - 420810502804122464*x^10*z^7 + 1233788267074788*x^11*z^7 + 222069126820424226967*z^8 + 1284966611076716076561*x^3*z^8 + 1632537209311135473086*x^4*z^8 + 883965499568897350631*x^5*z^8 + 340872259089218817740*x^6*z^8 + 43724004236204524752*x^7*z^8 - 12833600705529182329*x^8*z^8 - 697030246843871241*x^9*z^8 + 6838251310323008*x^10*z^8 - 239903274153431*x^11*z^8 + 159842936433008919220*z^9 + 503382915054975131332*x^3*z^9 + 455153573829187568803*x^4*z^9 + 141487580768693187496*x^5*z^9 + 7515146915227791294*x^6*z^9 - 12761382577531421148*x^7*z^9 - 1026853964229917461*x^8*z^9 + 28769418838172200*x^9*z^9 + 564478292125720*x^10*z^9 + 86660413405383273729*z^10 + 118622672912309281976*x^3*z^10 + 55041354260262199921*x^4*z^10 - 4070816308659511502*x^5*z^10 - 7798256417374288644*x^6*z^10 - 897745784211014834*x^7*z^10 + 55943579610191874*x^8*z^10 + 1550180721568784*x^9*z^10 - 16127951203592*x^10*z^10 + 33910576458818606547*z^11 + 9276999477759373984*x^3*z^11 - 6100127593083647188*x^4*z^11 - 4234014310837629864*x^5*z^11 - 431306575465320906*x^6*z^11 + 71135956177311836*x^7*z^11 + 2477837873345287*x^8*z^11 - 20871466263472*x^9*z^11 + 8632551825178963318*z^12 - 2719299606987207842*x^3*z^12 - 2312114434307428699*x^4*z^12 - 155040479182868945*x^5*z^12 + 59812570438606897*x^6*z^12 + 3770757584554067*x^7*z^12 - 62809719998764*x^8*z^12 + 948703011976*x^9*z^12 + 944057392334028427*z^13 - 637424163828170368*x^3*z^13 - 36782588886693845*x^4*z^13 + 41935352243313930*x^5*z^13 + 3094803309261507*x^6*z^13 - 145469983642576*x^7*z^13 - 2281072683207*x^8*z^13 - 179675891055560965*z^14 + 8122880936188720*x^3*z^14 + 28500242913215286*x^4*z^14 + 1689322191003667*x^5*z^14 - 202934028647617*x^6*z^14 - 4305273357116*x^7*z^14 + 20927272323*x^8*z^14 - 75785411180435450*z^15 + 10102029513627324*x^3*z^15 + 921473814856783*x^4*z^15 - 194988771549162*x^5*z^15 - 7675746942000*x^6*z^15 + 128025665976*x^7*z^15 - 5286063756216217*z^16 + 212737904740449*x^3*z^16 - 162109983137901*x^4*z^16 - 6326262314491*x^5*z^16 + 255278929744*x^6*z^16 + 1231016019*x^7*z^16 + 1507744265277523*z^17 - 76149457135296*x^3*z^17 - 4925560605278*x^4*z^17 + 426445530808*x^5*z^17 + 3282709384*x^6*z^17 + 226043828849566*z^18 - 2279142321290*x^3*z^18 + 413252470127*x^4*z^18 + 10722760064*x^5*z^18 + 193100552*x^6*z^18 - 14090636383005*z^19 + 298632322604*x^3*z^19 + 8530417335*x^4*z^19 - 340765680*x^5*z^19 - 3563554148427*z^20 + 9412232053*x^3*z^20 - 210974046*x^4*z^20 - 11358856*x^5*z^20 + 60748081108*z^21 - 558332972*x^3*z^21 - 83521*x^4*z^21 + 31797152011*z^22 - 18109318*x^3*z^22 - 584647*x^4*z^22 - 10316935*z^23 + 334084*x^3*z^23 - 175569275*z^24 + 14739*x^3*z^24 - 1022602*z^25 + 599305*z^26 + 3969*z^27 - 1168*z^28 - 5*z^29 + z^30 in I Output: Magma V2.10-22 Sat Apr 3 2004 23:43:55 on modular [Seed = 1782954127] ------------------------------------- false Total time: 2.549 seconds, Total memory usage: 2.21MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 23:44:41 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 17*x*(12 - z) + 17*x*(13 + z); > P2 := 289*x^2 + (12 - z)*(13 + z); > I := ideal; > 34303604243770368 + 2913989020099554384*x^3 + 11745632989244862864*x^4 + 25247612495380587156*x^5 + 56526361173262973629*x^6 + 117955343397673097199*x^7 + 158419065718747755259*x^8 + 136937840998418696184*x^9 + 110326514102295902931*x^10 + 92580318546831789284*x^11 + 41429684667171074949*x^12 + 2862423051509815793*x^15 + 12094219444919040*z + 843507381241572216*x^3*z + 3142659713328863208*x^4*z + 6192140455405934445*x^5*z + 12581441671762911597*x^6*z + 23526771420459564959*x^7*z + 27867122129305784351*x^8*z + 20811216388351057683*x^9*z + 14084771625395445235*x^10*z + 9527895620588742697*x^11*z + 3221318349643348569*x^12*z + 521545593778560*z^2 + 34598687826164501*x^3*z^2 + 122956016036064705*x^4*z^2 + 228898928567438805*x^5*z^2 + 436933134039231726*x^6*z^2 + 747605807119616263*x^7*z^2 + 786114087486587331*x^8*z^2 + 509476642067028915*x^9*z^2 + 292036876419042140*x^10*z^2 + 152578482361582116*x^11*z^2 + 33792089759326138*x^12*z^2 - 298271310648480*z^3 - 11737818522897285*x^3*z^3 - 35689343569763520*x^4*z^3 - 55507286360150690*x^5*z^3 - 83256862233482262*x^6*z^3 - 114520764116031873*x^7*z^3 - 99248670234230855*x^8*z^3 - 48262893976749060*x^9*z^3 - 15482833155448320*x^10*z^3 - 5620590994451812*x^11*z^3 - 1747866711689283*x^12*z^3 - 38589469129380*z^4 - 1229248282001220*x^3*z^4 - 3552200924041705*x^4*z^4 - 4962085248121690*x^5*z^4 - 6153528507927111*x^6*z^4 - 7657561818203245*x^7*z^4 - 6008289641507710*x^8*z^4 - 1864201418532840*x^9*z^4 - 161279512035920*x^10*z^4 - 239903274153431*x^11*z^4 + 1669842370703*z^5 + 30428428039971*x^3*z^5 + 39858549849001*x^4*z^5 + 52127688532809*x^5*z^5 + 112730581590753*x^6*z^5 + 19633064148358*x^7*z^5 - 53343617151327*x^8*z^5 + 26563684335328*x^9*z^5 + 16127951203592*x^10*z^5 + 560549896010*z^6 + 8619739227099*x^3*z^6 + 16377669388677*x^4*z^6 + 18071009889665*x^5*z^6 + 19317682671804*x^6*z^6 + 8902707849408*x^7*z^6 + 711527258982*x^8*z^6 + 948703011976*x^9*z^6 + 16021172115*z^7 + 172909561509*x^3*z^7 + 412032896485*x^4*z^7 + 371974136860*x^5*z^7 + 331360547232*x^6*z^7 + 128025665976*x^7*z^7 - 20927272323*x^8*z^7 - 3246503520*z^8 - 21803476395*x^3*z^8 - 14842934515*x^4*z^8 - 19934792280*x^5*z^8 - 8110223184*x^6*z^8 + 1231016019*x^7*z^8 - 236965170*z^9 - 888540615*x^3*z^9 - 224253885*x^4*z^9 - 908708480*x^5*z^9 - 193100552*x^6*z^9 + 4845996*z^10 + 17745756*x^3*z^10 + 27227846*x^4*z^10 - 11358856*x^5*z^10 + 1012110*z^11 + 1316684*x^3*z^11 + 584647*x^4*z^11 + 22740*z^12 + 14739*x^3*z^12 - 1245*z^13 - 70*z^14 - z^15 in I Output: Magma V2.10-22 Sat Apr 3 2004 23:44:39 on modular [Seed = 1665970618] ------------------------------------- true Total time: 2.569 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 23:45:12 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 17*x*(12 - z) + 17*x*(13 + z); > P2 := 289*x^2 + (12 - z)*(13 + z); > I := ideal; > 37162237930751232 + 3105987961491833184*x^3 + 12452437238042873136*x^4 + 26623573213868324681*x^5 + 59287613586510593271*x^6 + 123057349556911194074*x^7 + 164392812469722764291*x^8 + 141346899705517294659*x^9 + 113274223775764213669*x^10 + 94551809381928377609*x^11 + 42089213039715164401*x^12 + 2862423051509815793*x^15 + 19057557913205760*z + 1294450203943920816*x^3*z + 4782218209551919292*x^4*z + 9342878846920499270*x^5*z + 18817513653078651303*x^6*z + 34891266386972118084*x^7*z + 40990670953227692749*x^8*z + 30357525622874995558*x^9*z + 20367959335107830065*x^10*z + 13667083897143118272*x^11*z + 4585819629235448831*x^12*z + 3160989173103840*z^2 + 174798573800691126*x^3*z^2 + 594992339148555920*x^4*z^2 + 1059273395319053655*x^5*z^2 + 1913560011047843574*x^6*z^2 + 3138335089144100638*x^7*z^2 + 3202906535453573169*x^8*z^2 + 1999177546622342915*x^9*z^2 + 1077024581375873760*x^10*z^2 + 548418884714743266*x^11*z^2 + 126429025478858137*x^12*z^2 - 16249355962320*z^3 + 498470647209340*x^3*z^3 + 3830831073823520*x^4*z^3 + 9194008522844860*x^5*z^3 + 14019326920073462*x^6*z^3 + 23128626050171252*x^7*z^3 + 29895689755808855*x^8*z^3 + 18324198676316440*x^9*z^3 + 2983670972664520*x^10*z^3 + 1233788267074788*x^11*z^3 + 1747866711689283*x^12*z^3 - 68015313774395*z^4 - 2100897082427845*x^3*z^4 - 5268257908435795*x^4*z^4 - 6746479422490665*x^5*z^4 - 9908225412682389*x^6*z^4 - 11722479297609495*x^7*z^4 - 6529762389009665*x^8*z^4 - 1982789295029840*x^9*z^4 - 1048316828233480*x^10*z^4 - 239903274153431*x^11*z^4 - 7074736007053*z^5 - 182574532077704*x^3*z^5 - 390103946870001*x^4*z^5 - 403543433338266*x^5*z^5 - 570820607343453*x^6*z^5 - 603568795470392*x^7*z^5 - 219757286663823*x^8*z^5 - 20871466263472*x^9*z^5 - 16127951203592*x^10*z^5 + 156854584315*z^6 - 308877126376*x^3*z^6 + 1204231920073*x^4*z^6 + 6128876634065*x^5*z^6 - 328657139504*x^6*z^6 - 6484992388092*x^7*z^6 - 188345450907*x^8*z^6 + 948703011976*x^9*z^6 + 77139976485*z^7 + 736533220384*x^3*z^7 + 1113060563515*x^4*z^7 + 1168655899560*x^5*z^7 + 812760223368*x^6*z^7 + 128025665976*x^7*z^7 + 20927272323*x^8*z^7 + 4246383570*z^8 + 38268388730*x^3*z^8 + 25909467015*x^4*z^8 + 25216660320*x^5*z^8 + 22592764584*x^6*z^8 + 1231016019*x^7*z^8 - 173388930*z^9 + 464376760*x^3*z^9 - 1237363615*x^4*z^9 - 340765680*x^5*z^9 + 193100552*x^6*z^9 - 28946346*z^10 - 6082294*x^3*z^10 - 58548221*x^4*z^10 - 11358856*x^5*z^10 - 911910*z^11 + 334084*x^3*z^11 - 584647*x^4*z^11 + 32985*z^12 + 14739*x^3*z^12 + 3295*z^13 + 95*z^14 + z^15 in I Output: Magma V2.10-22 Sat Apr 3 2004 23:45:10 on modular [Seed = 2002298319] ------------------------------------- true Total time: 2.599 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 23:45:50 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 289*x^2 + (13 - y)*(13 + z); > P2 := 17*x*(13 - y) + 17*x*(13 + z); > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-22 Sat Apr 3 2004 23:45:47 on modular [Seed = 1331731930] ------------------------------------- [ 289*x^2 - y*z - 13*y + 13*z + 169, 17*x*y - 17*x*z - 442*x, y^2*z + 13*y^2 - y*z^2 - 52*y*z - 507*y + 13*z^2 + 507*z + 4394 ] Total time: 2.529 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 23:47:01 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 289*x^2 + (13 - y)*(13 + z); > P2 := 17*x*(13 - y) + 17*x*(13 + z); > I := ideal; > 51185893014090757 + 4006222227236220355*x^3 + 15716717968388249085*x^4 + 32884209903089259624*x^5 + 71670713891348386360*x^6 + 145605749787505856355*x^7 + 190407518952892273695*x^8 + 160272288278650260440*x^9 + 125752103110940973576*x^10 + 102778161196442141865*x^11 + 44800736931782472095*x^12 + 2862423051509815793*x^15 - 51185893014090757*y - 3204977781788976284*x^3*y - 11525593176818049329*x^4*y - 21922806602059506416*x^5*y - 43002428334809031816*x^6*y - 77656399886669790056*x^7*y - 88856842178016394391*x^8*y - 64108915311460104176*x^9*y - 41917367703646991192*x^10*y - 27407509652384571164*x^11*y - 8960147386356494419*x^12*y + 23624258314195734*y^2 + 1162244690099299092*x^3*y^2 + 3799646102247708570*x^4*y^2 + 6504568991819853552*x^5*y^2 + 11341299780608975424*x^6*y^2 + 17920707666154566936*x^7*y^2 + 17576078672574671418*x^8*y^2 + 10567403622768149040*x^9*y^2 + 5527564971909493344*x^10*y^2 + 2710632822763309236*x^11*y^2 + 590778948550977654*x^12*y^2 - 6663252345029566*y^3 - 252163542230617160*x^3*y^3 - 741942730024700490*x^4*y^3 - 1128998168205418368*x^5*y^3 - 1722445923287753664*x^6*y^3 - 2332873187310061968*x^7*y^3 - 1906675201166877570*x^8*y^3 - 917092227616959680*x^9*y^3 - 359782335449730336*x^10*y^3 - 117621148127796456*x^11*y^3 - 12817689219054742*x^12*y^3 + 1281394681736455*y^4 + 36369741667877475*x^3*y^4 + 95120862823679550*x^4*y^4 + 126650435535864240*x^5*y^4 + 165619800316130160*x^6*y^4 + 186928941290870350*x^7*y^4 + 122222769305569075*x^8*y^4 + 44090972481584600*x^9*y^4 + 11531485110568280*x^10*y^4 + 1884954296919815*x^11*y^4 - 177423879009663*y^5 - 3662407552569480*x^3*y^5 - 8381278822226310*x^4*y^5 - 9565207718792544*x^5*y^5 - 10423623796120080*x^6*y^5 - 9411806834225640*x^7*y^5 - 4615405274476035*x^8*y^5 - 1109982524011920*x^9*y^5 - 145151560832328*x^10*y^5 + 18197320924068*y^6 + 262942080697296*x^3*y^6 + 515771004444696*x^4*y^6 + 490523472758592*x^5*y^6 + 427635848045952*x^6*y^6 + 289594056437712*x^7*y^6 + 94674979989252*x^8*y^6 + 11384436143712*x^9*y^6 - 1399793917236*y^7 - 13484209266528*x^3*y^7 - 22041495916440*x^4*y^7 - 16770033256704*x^5*y^7 - 10965021744768*x^6*y^7 - 4950325751072*x^7*y^7 - 809187863156*x^8*y^7 + 80757341379*y^8 + 486209468745*x^3*y^8 + 635812382205*x^4*y^8 + 362813219496*x^5*y^8 + 158149352088*x^6*y^8 + 35699464551*x^7*y^8 - 3451168435*y^9 - 11873247100*x^3*y^9 - 11644915425*x^4*y^9 - 4429953840*x^5*y^9 - 965502760*x^6*y^9 + 106189798*y^10 + 182665340*x^3*y^10 + 119435030*x^4*y^10 + 22717712*x^5*y^10 - 2227758*y^11 - 1532856*x^3*y^11 - 501126*x^4*y^11 + 28561*y^12 + 4913*x^3*y^12 - 169*y^13 + 7874752771398578*z + 493073504890611736*x^3*z + 1773168181048930666*x^4*z + 3372739477239924064*x^5*z + 6615758205355235664*x^6*z + 11947138444103044624*x^7*z + 13670283412002522214*x^8*z + 9862910047916939104*x^9*z + 6448825800561075568*x^10*z + 4216539946520703256*x^11*z + 1378484213285614526*x^12*z - 7874752771398578*y*z - 387414896699766364*x^3*y*z - 1266548700749236190*x^4*y*z - 2168189663939951184*x^5*y*z - 3780433260202991808*x^6*y*z - 5973569222051522312*x^7*y*z - 5858692890858223806*x^8*y*z - 3522467874256049680*x^9*y*z - 1842521657303164448*x^10*y*z - 903544274254436412*x^11*y*z - 196926316183659218*x^12*y*z + 3634501279107036*y^2*z + 137543750307609360*x^3*y^2*z + 404696034558927540*x^4*y^2*z + 615817182657500928*x^5*y^2*z + 939515958156956544*x^6*y^2*z + 1272476283987306528*x^7*y^2*z + 1040004655181933220*x^8*y^2*z + 500232124154705280*x^9*y^2*z + 196244910245307456*x^10*y^2*z + 64156989887888976*x^11*y^2*z + 6991466846757132*x^12*y^2*z - 1025115745389164*y^3*z - 29095793334301980*x^3*y^3*z - 76096690258943640*x^4*y^3*z - 101320348428691392*x^5*y^3*z - 132495840252904128*x^6*y^3*z - 149543153032696280*x^7*y^3*z - 97778215444455260*x^8*y^3*z - 35272777985267680*x^9*y^3*z - 9225188088454624*x^10*y^3*z - 1507963437535852*x^11*y^3*z + 197137643344070*y^4*z + 4069341725077200*x^3*y^4*z + 9312532024695900*x^4*y^4*z + 10628008576436160*x^5*y^4*z + 11581804217911200*x^6*y^4*z + 10457563149139600*x^7*y^4*z + 5128228082751150*x^8*y^4*z + 1233313915568800*x^9*y^4*z + 161279512035920*x^10*y^4*z - 27295981386102*y^5*z - 394413121045944*x^3*y^5*z - 773656506667044*x^4*y^5*z - 735785209137888*x^5*y^5*z - 641453772068928*x^6*y^5*z - 434391084656568*x^7*y^5*z - 142012469983878*x^8*y^5*z - 17076654215568*x^9*y^5*z + 2799587834472*y^6*z + 26968418533056*x^3*y^6*z + 44082991832880*x^4*y^6*z + 33540066513408*x^5*y^6*z + 21930043489536*x^6*y^6*z + 9900651502144*x^7*y^6*z + 1618375726312*x^8*y^6*z - 215352910344*y^7*z - 1296558583320*x^3*y^7*z - 1695499685880*x^4*y^7*z - 967501918656*x^5*y^7*z - 421731605568*x^6*y^7*z - 95198572136*x^7*y^7*z + 12424206366*y^8*z + 42743689560*x^3*y^8*z + 41921695530*x^4*y^8*z + 15947833824*x^5*y^8*z + 3475809936*x^6*y^8*z - 530948990*y^9*z - 913326700*x^3*y^9*z - 597175150*x^4*y^9*z - 113588560*x^5*y^9*z + 16336892*y^10*z + 11240944*x^3*y^10*z + 3674924*x^4*y^10*z - 342732*y^11*z - 58956*x^3*y^11*z + 4394*y^12*z - 26*y^13*z + 302875106592253*z^2 + 14900572949991014*x^3*z^2 + 48713411567278315*x^4*z^2 + 83391910151536584*x^5*z^2 + 145401279238576608*x^6*z^2 + 229752662386597012*x^7*z^2 + 225334341956085531*x^8*z^2 + 135479533625232680*x^9*z^2 + 70866217588583248*x^10*z^2 + 34751702855939862*x^11*z^2 + 7574089083986893*x^12*z^2 - 302875106592253*y*z^2 - 11461979192300780*x^3*y*z^2 - 33724669546577295*x^4*y*z^2 - 51318098554791744*x^5*y*z^2 - 78292996513079712*x^6*y*z^2 - 106039690332275544*x^7*y*z^2 - 86667054598494435*x^8*y*z^2 - 41686010346225440*x^9*y*z^2 - 16353742520442288*x^10*y*z^2 - 5346415823990748*x^11*y*z^2 - 582622237229761*x^12*y*z^2 + 139788510734886*y^2*z^2 + 3967608181950270*x^3*y^2*z^2 + 10376821398946860*x^4*y^2*z^2 + 13816411149367008*x^5*y^2*z^2 + 18067614579941472*x^6*y^2*z^2 + 20392248140822220*x^7*y^2*z^2 + 13333393015152990*x^8*y^2*z^2 + 4809924270718320*x^9*y^2*z^2 + 1257980193880176*x^10*y^2*z^2 + 205631377845798*x^11*y^2*z^2 - 39427528668814*y^3*z^2 - 813868345015440*x^3*y^3*z^2 - 1862506404939180*x^4*y^3*z^2 - 2125601715287232*x^5*y^3*z^2 - 2316360843582240*x^6*y^3*z^2 - 2091512629827920*x^7*y^3*z^2 - 1025645616550230*x^8*y^3*z^2 - 246662783113760*x^9*y^3*z^2 - 32255902407184*x^10*y^3*z^2 + 7582217051695*y^4*z^2 + 109559200290540*x^3*y^4*z^2 + 214904585185290*x^4*y^4*z^2 + 204384780316080*x^5*y^4*z^2 + 178181603352480*x^6*y^4*z^2 + 120664190182380*x^7*y^4*z^2 + 39447908328855*x^8*y^4*z^2 + 4743515059880*x^9*y^4*z^2 - 1049845437927*y^5*z^2 - 10113156949896*x^3*y^5*z^2 - 16531121937330*x^4*y^5*z^2 - 12577524942528*x^5*y^5*z^2 - 8223766308576*x^6*y^5*z^2 - 3712744313304*x^7*y^5*z^2 - 606890897367*x^8*y^5*z^2 + 107676455172*y^6*z^2 + 648279291660*x^3*y^6*z^2 + 847749842940*x^4*y^6*z^2 + 483750959328*x^5*y^6*z^2 + 210865802784*x^6*y^6*z^2 + 47599286068*x^7*y^6*z^2 - 8282804244*y^7*z^2 - 28495793040*x^3*y^7*z^2 - 27947797020*x^4*y^7*z^2 - 10631889216*x^5*y^7*z^2 - 2317206624*x^6*y^7*z^2 + 477854091*y^8*z^2 + 821994030*x^3*y^8*z^2 + 537457635*x^4*y^8*z^2 + 102229704*x^5*y^8*z^2 - 20421115*y^9*z^2 - 14051180*x^3*y^9*z^2 - 4593655*x^4*y^9*z^2 + 628342*y^10*z^2 + 108086*x^3*y^10*z^2 - 13182*y^11*z^2 + 169*y^12*z^2 - y^13*z^2 in I; Output: Magma V2.10-22 Sat Apr 3 2004 23:46:58 on modular [Seed = 1114476910] ------------------------------------- true Total time: 2.619 seconds, Total memory usage: 2.40MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 23:47:51 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 289*x^2 + (13 - y)*(13 + z); > P2 := 17*x*(13 - y) + 17*x*(13 + z); > I := ideal; > 51185893014090757 + 4006222227236220355*x^3 + 15716717968388249085*x^4 + 32884209903089259624*x^5 + 71670713891348386360*x^6 + 145605749787505856355*x^7 + 190407518952892273695*x^8 + 160272288278650260440*x^9 + 125752103110940973576*x^10 + 102778161196442141865*x^11 + 44800736931782472095*x^12 + 2862423051509815793*x^15 - 39373763856992890*y - 2465367524453058680*x^3*y - 8865840905244653330*x^4*y - 16863697386199620320*x^5*y - 33078791026776178320*x^6*y - 59735692220515223120*x^7*y - 68351417060012611070*x^8*y - 49314550239584695520*x^9*y - 32244129002805377840*x^10*y - 21082699732603516280*x^11*y - 6892421066428072630*x^12*y + 13629379796651385*y^2 + 670525782749595630*x^3*y^2 + 2192103520527524175*x^4*y^2 + 3752635956819146280*x^5*y^2 + 6543057565735947360*x^6*y^2 + 10338869807396865540*x^7*y^2 + 10140045388023848895*x^8*y^2 + 6096579013135470600*x^9*y^2 + 3188979791486246160*x^10*y^2 + 1563826628517293790*x^11*y^2 + 340834008779410185*x^12*y^2 - 2795770214697720*y^3 - 105762808001684470*x^3*y^3 - 311357050157289370*x^4*y^3 - 473979660263007080*x^5*y^3 - 722346098781390200*x^6*y^3 - 978124729789093380*x^7*y^3 - 800923125255052020*x^8*y^3 - 385595595702585320*x^9*y^3 - 149909306437387640*x^10*y^3 - 49008811719915190*x^11*y^3 - 5826222372297610*x^12*y^3 + 376353682747770*y^4 + 10660442185846180*x^3*y^4 + 27965009588272952*x^4*y^4 + 37309792806127972*x^5*y^4 + 48502941521152404*x^6*y^4 + 54707479495033404*x^7*y^4 + 36138092792793966*x^8*y^4 + 13066960935451436*x^9*y^4 + 3249782167523788*x^10*y^4 + 548350340922128*x^11*y^4 - 34740339945948*y^5 - 712134801888510*x^3*y^5 - 1647229690602054*x^4*y^5 - 1891532478782388*x^5*y^5 - 2018543020835952*x^6*y^5 - 1822861438582782*x^7*y^5 - 926617763917794*x^8*y^5 - 221996504802384*x^9*y^5 - 24191926805388*x^10*y^5 + 2226944868330*y^6 + 31539769780610*x^3*y^6 + 63882171065180*x^4*y^6 + 61639854381040*x^5*y^6 + 50484787616536*x^6*y^6 + 34534923397026*x^7*y^6 + 12514508849154*x^8*y^6 + 1423054517964*x^9*y^6 - 97887686520*y^7 - 893839629410*x^3*y^7 - 1598246998270*x^4*y^7 - 1247770331600*x^5*y^7 - 685313859048*x^6*y^7 - 330732970438*x^7*y^7 - 69757574410*x^8*y^7 + 2823683265*y^8 + 14733620265*x^3*y^8 + 24771910995*x^4*y^8 + 14397349980*x^5*y^8 + 3765460764*x^6*y^8 + 1231016019*x^7*y^8 - 48268090*y^9 - 107938610*x^3*y^9 - 225840784*x^4*y^9 - 73832564*x^5*y^9 + 371293*y^10 + 1085773*x^4*y^10 + 19686881928496445*z + 1232683762226529340*x^3*z + 4432920452622326665*x^4*z + 8431848693099810160*x^5*z + 16539395513388089160*x^6*z + 29867846110257611560*x^7*z + 34175708530006305535*x^8*z + 24657275119792347760*x^9*z + 16122064501402688920*x^10*z + 10541349866301758140*x^11*z + 3446210533214036315*x^12*z - 15143755329612650*y*z - 745028647499550700*x^3*y*z - 2435670578363915750*x^4*y*z - 4169595507576829200*x^5*y*z - 7270063961928830400*x^6*y*z - 11487633119329850600*x^7*y*z - 11266717097804276550*x^8*y*z - 6773976681261634000*x^9*y*z - 3543310879429162400*x^10*y*z - 1737585142796993100*x^11*y*z - 378704454199344650*x^12*y*z + 5242069152558225*y^2*z + 198500639648481690*x^3*y^2*z + 583538979124110165*x^4*y^2*z + 887375454176607240*x^5*y^2*z + 1356146546744416440*x^6*y^2*z + 1837411875585119340*x^7*y^2*z + 1497248081167093515*x^8*y^2*z + 719083678472388840*x^9*y^2*z + 286190494107740040*x^10*y^2*z + 93562276919838090*x^11*y^2*z + 8739333558446415*x^12*y^2*z - 1075296236422200*y^3*z - 30578636796242990*x^3*y^3*z - 79744300205240112*x^4*y^3*z - 105980645840184232*x^5*y^3*z - 139378741045262784*x^6*y^3*z - 157371901169517684*x^7*y^3*z - 101885513522686296*x^8*y^3*z - 36715755266483176*x^9*y^3*z - 10063841551041408*x^10*y^3*z - 1576507230151118*x^11*y^3*z + 144751416441450*y^4*z + 2999598104924330*x^3*y^4*z + 6821933632982858*x^4*y^4*z + 7762241978147124*x^5*y^4*z + 8562262403955780*x^6*y^4*z + 7718763420942522*x^7*y^4*z + 3706471055671176*x^8*y^4*z + 900319158365224*x^9*y^4*z + 129023609628736*x^10*y^4*z - 13361669209980*y^5*z - 194218582333230*x^3*y^5*z - 376966830809868*x^4*y^5*z - 357673365553140*x^5*y^5*z - 318181434558000*x^6*y^5*z - 213450791598486*x^7*y^5*z - 67469525969352*x^8*y^5*z - 8538327107784*x^9*y^5*z + 856517257050*y^6*z + 8299939415950*x^3*y^6*z + 13382336806410*x^4*y^6*z + 10231716719120*x^5*y^6*z + 6853138590480*x^6*y^6*z + 2997934344938*x^7*y^6*z + 474351505988*x^8*y^6*z - 37649110200*y^7*z - 225915510730*x^3*y^7*z - 293593019200*x^4*y^7*z - 172768199760*x^5*y^7*z - 75309215280*x^6*y^7*z - 15592869574*x^7*y^7*z + 1086032025*y^8*z + 3561974130*x^3*y^8*z + 3684027789*x^4*y^8*z + 1550483844*x^5*y^8*z + 289650828*x^6*y^8*z - 18564650*y^9*z - 24908910*x^3*y^9*z - 23887006*x^4*y^9*z - 5679428*x^5*y^9*z + 142805*y^10*z + 83521*x^4*y^10*z + 3028751065922530*z^2 + 149005729499910140*x^3*z^2 + 487134115672783150*x^4*z^2 + 833919101515365840*x^5*z^2 + 1454012792385766080*x^6*z^2 + 2297526623865970120*x^7*z^2 + 2253343419560855310*x^8*z^2 + 1354795336252326800*x^9*z^2 + 708662175885832480*x^10*z^2 + 347517028559398620*x^11*z^2 + 75740890839868930*x^12*z^2 - 2329808512248100*y*z^2 - 88048840159037810*x^3*y*z^2 - 259577759540322210*x^4*y*z^2 - 395577009693186360*x^5*y*z^2 - 601178366082576360*x^6*y*z^2 - 813580382721769260*x^7*y*z^2 - 669428283795267360*x^8*y*z^2 - 323066580183247160*x^9*y*z^2 - 122653068903317160*x^10*y*z^2 - 40098118679930610*x^11*y*z^2 - 5826222372297610*x^12*y*z^2 + 806472177316650*y^2*z^2 + 22843804683956100*x^3*y^2*z^2 + 59934004807250652*x^4*y^2*z^2 + 79937807364194832*x^5*y^2*z^2 + 103888783834663464*x^6*y^2*z^2 + 117290585858246424*x^7*y^2*z^2 + 77517588357061866*x^8*y^2*z^2 + 27897560770166256*x^9*y^2*z^2 + 6918891066340968*x^10*y^2*z^2 + 1233788267074788*x^11*y^2*z^2 - 165430190218800*y^3*z^2 - 3409615112072260*x^3*y^3*z^2 - 7825752020060468*x^4*y^3*z^2 - 8932588160671344*x^5*y^3*z^2 - 9679079239254360*x^6*y^3*z^2 - 8773534876502292*x^7*y^3*z^2 - 4343078679736836*x^8*y^3*z^2 - 1023650549922104*x^9*y^3*z^2 - 129023609628736*x^10*y^3*z^2 + 22269448683300*y^4*z^2 + 322037649338860*x^3*y^4*z^2 + 631875299817528*x^4*y^4*z^2 + 598555428068520*x^5*y^4*z^2 + 521817552675120*x^6*y^4*z^2 + 356999569574076*x^7*y^4*z^2 + 116439343205172*x^8*y^4*z^2 + 13281842167664*x^9*y^4*z^2 - 2055641416920*y^5*z^2 - 19919854598280*x^3*y^5*z^2 - 32346610890360*x^4*y^5*z^2 - 24331521466200*x^5*y^5*z^2 - 16153826677560*x^6*y^5*z^2 - 7425488626608*x^7*y^5*z^2 - 1171927250088*x^8*y^5*z^2 + 131771885700*y^6*z^2 + 805437907820*x^3*y^6*z^2 + 1031245479940*x^4*y^6*z^2 + 575893999200*x^5*y^6*z^2 + 263582253480*x^6*y^6*z^2 + 60730123604*x^7*y^6*z^2 - 5792170800*y^7*z^2 - 20508335900*x^3*y^7*z^2 - 19140006444*x^4*y^7*z^2 - 7087926144*x^5*y^7*z^2 - 1737904968*x^6*y^7*z^2 + 167081850*y^8*z^2 + 298906920*x^3*y^8*z^2 + 175895226*x^4*y^8*z^2 + 34076568*x^5*y^8*z^2 - 2856100*y^9*z^2 - 1916070*x^3*y^9*z^2 - 501126*x^4*y^9*z^2 + 21970*y^10*z^2 + 232980851224810*z^3 + 8856983921323330*x^3*z^3 + 25889645308483580*x^4*z^3 + 39201325284910360*x^5*z^3 + 60583866349406920*x^6*z^3 + 82272173533662060*x^7*z^3 + 65747420729892330*x^8*z^3 + 31264507759669080*x^9*z^3 + 13628118767035240*x^10*z^3 + 4455346519992290*x^11*z^3 - 179216039403700*y*z^3 - 5089759990986710*x^3*y*z^3 - 13290716700873352*x^4*y*z^3 - 17709130163672792*x^5*y*z^3 - 23229790174210464*x^6*y*z^3 - 26111453366524084*x^7*y*z^3 - 16980918920447716*x^8*y*z^3 - 6252901551933816*x^9*y*z^3 - 1677306925173568*x^10*y*z^3 - 205631377845798*x^11*y*z^3 + 62036321332050*y^2*z^3 + 1276293541046940*x^3*y^2*z^3 + 2931633458164008*x^4*y^2*z^3 + 3365536049204784*x^5*y^2*z^3 + 3639995611343520*x^6*y^2*z^3 + 3256268801266572*x^7*y^2*z^3 + 1619812732344846*x^8*y^2*z^3 + 406993592137704*x^9*y^2*z^3 + 48383853610776*x^10*y^2*z^3 - 12725399247600*y^3*z^3 - 182598667150900*x^3*y^3*z^3 - 361461449483368*x^4*y^3*z^3 - 347129706251120*x^5*y^3*z^3 - 296969338920800*x^6*y^3*z^3 - 198887872093716*x^7*y^3*z^3 - 67469525969352*x^8*y^3*z^3 - 8538327107784*x^9*y^3*z^3 + 1713034514100*y^4*z^3 + 16344496080640*x^3*y^4*z^3 + 27098635672160*x^4*y^4*z^3 + 20837764537720*x^5*y^4*z^3 + 13216767281640*x^6*y^4*z^3 + 5931855856888*x^7*y^4*z^3 + 1032412101268*x^8*y^4*z^3 - 158126262840*y^5*z^3 - 942951696960*x^3*y^5*z^3 - 1255110157080*x^4*y^5*z^3 - 719867499000*x^5*y^5*z^3 - 301236861120*x^6*y^5*z^3 - 68936897064*x^7*y^5*z^3 + 10136298900*y^6*z^3 + 34756232420*x^3*y^6*z^3 + 34666560344*x^4*y^6*z^3 + 12994531264*x^5*y^6*z^3 + 2703407728*x^6*y^6*z^3 - 445551600*y^7*z^3 - 780479180*x^3*y^7*z^3 - 512484856*x^4*y^7*z^3 - 90870848*x^5*y^7*z^3 + 12852450*y^8*z^3 + 9580350*x^3*y^8*z^3 + 3006756*x^4*y^8*z^3 - 219700*y^9*z^3 - 49130*x^3*y^9*z^3 + 1690*y^10*z^3 + 8960801970185*z^4 + 260499527097745*x^3*z^4 + 660343179932982*x^4*z^4 + 849818939742812*x^5*z^4 + 1182998573686644*x^6*z^4 + 1382922575067254*x^7*z^4 + 812264172187481*x^8*z^4 + 240496213535916*x^9*z^4 + 104831682823348*x^10*z^4 + 34271896307633*x^11*z^4 - 6892924592450*y*z^4 - 144893228089870*x^3*y*z^4 - 323318211420178*x^4*y*z^4 - 360593148129084*x^5*y*z^4 - 413635864925400*x^6*y*z^4 - 380438935253182*x^7*y*z^4 - 169762033084176*x^8*y*z^4 - 36999417467064*x^9*y*z^4 - 8063975601796*x^10*y*z^4 + 2386012358925*y^2*z^4 + 34859745546990*x^3*y^2*z^4 + 67169311906398*x^4*y^2*z^4 + 63261955812120*x^5*y^2*z^4 + 57272658220440*x^6*y^2*z^4 + 38695757541246*x^7*y^2*z^4 + 11698345228557*x^8*y^2*z^4 + 1423054517964*x^9*y^2*z^4 - 489438432600*y^3*z^4 - 4724580898310*x^3*y^3*z^4 - 7657272932010*x^4*y^3*z^4 - 5864520558520*x^5*y^3*z^4 - 3916079194560*x^6*y^3*z^4 - 1717677685178*x^7*y^3*z^4 - 265078782758*x^8*y^3*z^4 + 65885942850*y^4*z^4 + 392896540400*x^3*y^4*z^4 + 515622739970*x^4*y^4*z^4 + 302344349580*x^5*y^4*z^4 + 131791126740*x^6*y^4*z^4 + 27903029764*x^7*y^4*z^4 - 6081779340*y^5*z^4 - 20400397290*x^3*y^5*z^4 - 20410360854*x^4*y^5*z^4 - 8195414604*x^5*y^5*z^4 - 1737904968*x^6*y^5*z^4 + 389857650*y^6*z^4 + 639328690*x^3*y^6*z^4 + 436480746*x^4*y^6*z^4 + 90870848*x^5*y^6*z^4 - 17136600*y^7*z^4 - 10857730*x^3*y^7*z^4 - 3841966*x^4*y^7*z^4 + 494325*y^8*z^4 + 73695*x^3*y^8*z^4 - 8450*y^9*z^4 + 65*y^10*z^4 + 137858491849*z^5 + 3082834640210*x^3*z^5 + 6450238631824*x^4*z^5 + 6326195581212*x^5*z^5 + 8272717298508*x^6*z^5 + 9015140645810*x^7*z^5 + 3536709022587*x^8*z^5 - 106044993730*y*z^5 - 1659987883190*x^3*y*z^5 - 2977033214688*x^4*y*z^5 - 2433152146620*x^5*y*z^5 - 2545451476464*x^6*y*z^5 - 2080417072110*x^7*y*z^5 - 544109080398*x^8*y*z^5 + 36707882445*y^2*z^5 + 383074126890*x^3*y^2*z^5 + 572506387440*x^4*y^2*z^5 + 374331099480*x^5*y^2*z^5 + 293705939592*x^6*y^2*z^5 + 160032082470*x^7*y^2*z^5 + 20927272323*x^8*y^2*z^5 - 7529822040*y^3*z^5 - 49112067550*x^3*y^3*z^5 - 58718603840*x^4*y^3*z^5 - 28794699960*x^5*y^3*z^5 - 15061843056*x^6*y^3*z^5 - 4103386730*x^7*y^3*z^5 + 1013629890*y^4*z^5 + 3777851350*x^3*y^4*z^5 + 3387611760*x^4*y^4*z^5 + 1107488460*x^5*y^4*z^5 + 289650828*x^6*y^4*z^5 - 93565836*y^5*z^5 - 174362370*x^3*y^5*z^5 - 104234208*x^4*y^5*z^5 - 17038284*x^5*y^5*z^5 + 5997810*y^6*z^5 + 4470830*x^3*y^6*z^5 + 1336336*x^4*y^6*z^5 - 263640*y^7*z^5 - 49130*x^3*y^7*z^5 + 7605*y^8*z^5 - 130*y^9*z^5 + y^10*z^5 Output: Magma V2.10-22 Sat Apr 3 2004 23:47:49 on modular [Seed = 1517652289] ------------------------------------- 2862423051509815793*x^15 - 5826222372297610*x^12*y^3 + 8739333558446415*x^12*y^2*z + 340834008779410185*x^12*y^2 - 5826222372297610*x^12*y*z^2 - 378704454199344650*x^12*y*z - 6892421066428072630*x^12*y + 75740890839868930*x^12*z^2 + 3446210533214036315*x^12*z + 44800736931782472095*x^12 + 548350340922128*x^11*y^4 - 1576507230151118*x^11*y^3*z - 49008811719915190*x^11*y^3 + 1233788267074788*x^11*y^2*z^2 + 93562276919838090*x^11*y^2*z + 1563826628517293790*x^11*y^2 - 205631377845798*x^11*y*z^3 - 40098118679930610*x^11*y*z^2 - 1737585142796993100*x^11*y*z - 21082699732603516280*x^11*y + 34271896307633*x^11*z^4 + 4455346519992290*x^11*z^3 + 347517028559398620*x^11*z^2 + 10541349866301758140*x^11*z + 102778161196442141865*x^11 - 24191926805388*x^10*y^5 + 129023609628736*x^10*y^4*z + 3249782167523788*x^10*y^4 - 129023609628736*x^10*y^3*z^2 - 10063841551041408*x^10*y^3*z - 149909306437387640*x^10*y^3 + 48383853610776*x^10*y^2*z^3 + 6918891066340968*x^10*y^2*z^2 + 286190494107740040*x^10*y^2*z + 3188979791486246160*x^10*y^2 - 8063975601796*x^10*y*z^4 - 1677306925173568*x^10*y*z^3 - 122653068903317160*x^10*y*z^2 - 3543310879429162400*x^10*y*z - 32244129002805377840*x^10*y + 104831682823348*x^10*z^4 + 13628118767035240*x^10*z^3 + 708662175885832480*x^10*z^2 + 16122064501402688920*x^10*z + 125752103110940973576*x^10 + 1423054517964*x^9*y^6 - 8538327107784*x^9*y^5*z - 221996504802384*x^9*y^5 + 13281842167664*x^9*y^4*z^2 + 900319158365224*x^9*y^4*z + 13066960935451436*x^9*y^4 - 8538327107784*x^9*y^3*z^3 - 1023650549922104*x^9*y^3*z^2 - 36715755266483176*x^9*y^3*z - 385595595702585320*x^9*y^3 + 1423054517964*x^9*y^2*z^4 + 406993592137704*x^9*y^2*z^3 + 27897560770166256*x^9*y^2*z^2 + 719083678472388840*x^9*y^2*z + 6096579013135470600*x^9*y^2 - 36999417467064*x^9*y*z^4 - 6252901551933816*x^9*y*z^3 - 323066580183247160*x^9*y*z^2 - 6773976681261634000*x^9*y*z - 49314550239584695520*x^9*y + 240496213535916*x^9*z^4 + 31264507759669080*x^9*z^3 + 1354795336252326800*x^9*z^2 + 24657275119792347760*x^9*z + 160272288278650260440*x^9 - 69757574410*x^8*y^7 + 474351505988*x^8*y^6*z + 12514508849154*x^8*y^6 - 1171927250088*x^8*y^5*z^2 - 67469525969352*x^8*y^5*z - 926617763917794*x^8*y^5 + 1032412101268*x^8*y^4*z^3 + 116439343205172*x^8*y^4*z^2 + 3706471055671176*x^8*y^4*z + 36138092792793966*x^8*y^4 - 265078782758*x^8*y^3*z^4 - 67469525969352*x^8*y^3*z^3 - 4343078679736836*x^8*y^3*z^2 - 101885513522686296*x^8*y^3*z - 800923125255052020*x^8*y^3 + 20927272323*x^8*y^2*z^5 + 11698345228557*x^8*y^2*z^4 + 1619812732344846*x^8*y^2*z^3 + 77517588357061866*x^8*y^2*z^2 + 1497248081167093515*x^8*y^2*z + 10140045388023848895*x^8*y^2 - 544109080398*x^8*y*z^5 - 169762033084176*x^8*y*z^4 - 16980918920447716*x^8*y*z^3 - 669428283795267360*x^8*y*z^2 - 11266717097804276550*x^8*y*z - 68351417060012611070*x^8*y + 3536709022587*x^8*z^5 + 812264172187481*x^8*z^4 + 65747420729892330*x^8*z^3 + 2253343419560855310*x^8*z^2 + 34175708530006305535*x^8*z + 190407518952892273695*x^8 + 1231016019*x^7*y^8 - 15592869574*x^7*y^7*z - 330732970438*x^7*y^7 + 60730123604*x^7*y^6*z^2 + 2997934344938*x^7*y^6*z + 34534923397026*x^7*y^6 - 68936897064*x^7*y^5*z^3 - 7425488626608*x^7*y^5*z^2 - 213450791598486*x^7*y^5*z - 1822861438582782*x^7*y^5 + 27903029764*x^7*y^4*z^4 + 5931855856888*x^7*y^4*z^3 + 356999569574076*x^7*y^4*z^2 + 7718763420942522*x^7*y^4*z + 54707479495033404*x^7*y^4 - 4103386730*x^7*y^3*z^5 - 1717677685178*x^7*y^3*z^4 - 198887872093716*x^7*y^3*z^3 - 8773534876502292*x^7*y^3*z^2 - 157371901169517684*x^7*y^3*z - 978124729789093380*x^7*y^3 + 160032082470*x^7*y^2*z^5 + 38695757541246*x^7*y^2*z^4 + 3256268801266572*x^7*y^2*z^3 + 117290585858246424*x^7*y^2*z^2 + 1837411875585119340*x^7*y^2*z + 10338869807396865540*x^7*y^2 - 2080417072110*x^7*y*z^5 - 380438935253182*x^7*y*z^4 - 26111453366524084*x^7*y*z^3 - 813580382721769260*x^7*y*z^2 - 11487633119329850600*x^7*y*z - 59735692220515223120*x^7*y + 9015140645810*x^7*z^5 + 1382922575067254*x^7*z^4 + 82272173533662060*x^7*z^3 + 2297526623865970120*x^7*z^2 + 29867846110257611560*x^7*z + 145605749787505856355*x^7 + 289650828*x^6*y^8*z + 3765460764*x^6*y^8 - 1737904968*x^6*y^7*z^2 - 75309215280*x^6*y^7*z - 685313859048*x^6*y^7 + 2703407728*x^6*y^6*z^3 + 263582253480*x^6*y^6*z^2 + 6853138590480*x^6*y^6*z + 50484787616536*x^6*y^6 - 1737904968*x^6*y^5*z^4 - 301236861120*x^6*y^5*z^3 - 16153826677560*x^6*y^5*z^2 - 318181434558000*x^6*y^5*z - 2018543020835952*x^6*y^5 + 289650828*x^6*y^4*z^5 + 131791126740*x^6*y^4*z^4 + 13216767281640*x^6*y^4*z^3 + 521817552675120*x^6*y^4*z^2 + 8562262403955780*x^6*y^4*z + 48502941521152404*x^6*y^4 - 15061843056*x^6*y^3*z^5 - 3916079194560*x^6*y^3*z^4 - 296969338920800*x^6*y^3*z^3 - 9679079239254360*x^6*y^3*z^2 - 139378741045262784*x^6*y^3*z - 722346098781390200*x^6*y^3 + 293705939592*x^6*y^2*z^5 + 57272658220440*x^6*y^2*z^4 + 3639995611343520*x^6*y^2*z^3 + 103888783834663464*x^6*y^2*z^2 + 1356146546744416440*x^6*y^2*z + 6543057565735947360*x^6*y^2 - 2545451476464*x^6*y*z^5 - 413635864925400*x^6*y*z^4 - 23229790174210464*x^6*y*z^3 - 601178366082576360*x^6*y*z^2 - 7270063961928830400*x^6*y*z - 33078791026776178320*x^6*y + 8272717298508*x^6*z^5 + 1182998573686644*x^6*z^4 + 60583866349406920*x^6*z^3 + 1454012792385766080*x^6*z^2 + 16539395513388089160*x^6*z + 71670713891348386360*x^6 - 5679428*x^5*y^9*z - 73832564*x^5*y^9 + 34076568*x^5*y^8*z^2 + 1550483844*x^5*y^8*z + 14397349980*x^5*y^8 - 90870848*x^5*y^7*z^3 - 7087926144*x^5*y^7*z^2 - 172768199760*x^5*y^7*z - 1247770331600*x^5*y^7 + 90870848*x^5*y^6*z^4 + 12994531264*x^5*y^6*z^3 + 575893999200*x^5*y^6*z^2 + 10231716719120*x^5*y^6*z + 61639854381040*x^5*y^6 - 17038284*x^5*y^5*z^5 - 8195414604*x^5*y^5*z^4 - 719867499000*x^5*y^5*z^3 - 24331521466200*x^5*y^5*z^2 - 357673365553140*x^5*y^5*z - 1891532478782388*x^5*y^5 + 1107488460*x^5*y^4*z^5 + 302344349580*x^5*y^4*z^4 + 20837764537720*x^5*y^4*z^3 + 598555428068520*x^5*y^4*z^2 + 7762241978147124*x^5*y^4*z + 37309792806127972*x^5*y^4 - 28794699960*x^5*y^3*z^5 - 5864520558520*x^5*y^3*z^4 - 347129706251120*x^5*y^3*z^3 - 8932588160671344*x^5*y^3*z^2 - 105980645840184232*x^5*y^3*z - 473979660263007080*x^5*y^3 + 374331099480*x^5*y^2*z^5 + 63261955812120*x^5*y^2*z^4 + 3365536049204784*x^5*y^2*z^3 + 79937807364194832*x^5*y^2*z^2 + 887375454176607240*x^5*y^2*z + 3752635956819146280*x^5*y^2 - 2433152146620*x^5*y*z^5 - 360593148129084*x^5*y*z^4 - 17709130163672792*x^5*y*z^3 - 395577009693186360*x^5*y*z^2 - 4169595507576829200*x^5*y*z - 16863697386199620320*x^5*y + 6326195581212*x^5*z^5 + 849818939742812*x^5*z^4 + 39201325284910360*x^5*z^3 + 833919101515365840*x^5*z^2 + 8431848693099810160*x^5*z + 32884209903089259624*x^5 + 83521*x^4*y^10*z + 1085773*x^4*y^10 - 501126*x^4*y^9*z^2 - 23887006*x^4*y^9*z - 225840784*x^4*y^9 + 3006756*x^4*y^8*z^3 + 175895226*x^4*y^8*z^2 + 3684027789*x^4*y^8*z + 24771910995*x^4*y^8 - 3841966*x^4*y^7*z^4 - 512484856*x^4*y^7*z^3 - 19140006444*x^4*y^7*z^2 - 293593019200*x^4*y^7*z - 1598246998270*x^4*y^7 + 1336336*x^4*y^6*z^5 + 436480746*x^4*y^6*z^4 + 34666560344*x^4*y^6*z^3 + 1031245479940*x^4*y^6*z^2 + 13382336806410*x^4*y^6*z + 63882171065180*x^4*y^6 - 104234208*x^4*y^5*z^5 - 20410360854*x^4*y^5*z^4 - 1255110157080*x^4*y^5*z^3 - 32346610890360*x^4*y^5*z^2 - 376966830809868*x^4*y^5*z - 1647229690602054*x^4*y^5 + 3387611760*x^4*y^4*z^5 + 515622739970*x^4*y^4*z^4 + 27098635672160*x^4*y^4*z^3 + 631875299817528*x^4*y^4*z^2 + 6821933632982858*x^4*y^4*z + 27965009588272952*x^4*y^4 - 58718603840*x^4*y^3*z^5 - 7657272932010*x^4*y^3*z^4 - 361461449483368*x^4*y^3*z^3 - 7825752020060468*x^4*y^3*z^2 - 79744300205240112*x^4*y^3*z - 311357050157289370*x^4*y^3 + 572506387440*x^4*y^2*z^5 + 67169311906398*x^4*y^2*z^4 + 2931633458164008*x^4*y^2*z^3 + 59934004807250652*x^4*y^2*z^2 + 583538979124110165*x^4*y^2*z + 2192103520527524175*x^4*y^2 - 2977033214688*x^4*y*z^5 - 323318211420178*x^4*y*z^4 - 13290716700873352*x^4*y*z^3 - 259577759540322210*x^4*y*z^2 - 2435670578363915750*x^4*y*z - 8865840905244653330*x^4*y + 6450238631824*x^4*z^5 + 660343179932982*x^4*z^4 + 25889645308483580*x^4*z^3 + 487134115672783150*x^4*z^2 + 4432920452622326665*x^4*z + 15716717968388249085*x^4 - 49130*x^3*y^9*z^3 - 1916070*x^3*y^9*z^2 - 24908910*x^3*y^9*z - 107938610*x^3*y^9 + 73695*x^3*y^8*z^4 + 9580350*x^3*y^8*z^3 + 298906920*x^3*y^8*z^2 + 3561974130*x^3*y^8*z + 14733620265*x^3*y^8 - 49130*x^3*y^7*z^5 - 10857730*x^3*y^7*z^4 - 780479180*x^3*y^7*z^3 - 20508335900*x^3*y^7*z^2 - 225915510730*x^3*y^7*z - 893839629410*x^3*y^7 + 4470830*x^3*y^6*z^5 + 639328690*x^3*y^6*z^4 + 34756232420*x^3*y^6*z^3 + 805437907820*x^3*y^6*z^2 + 8299939415950*x^3*y^6*z + 31539769780610*x^3*y^6 - 174362370*x^3*y^5*z^5 - 20400397290*x^3*y^5*z^4 - 942951696960*x^3*y^5*z^3 - 19919854598280*x^3*y^5*z^2 - 194218582333230*x^3*y^5*z - 712134801888510*x^3*y^5 + 3777851350*x^3*y^4*z^5 + 392896540400*x^3*y^4*z^4 + 16344496080640*x^3*y^4*z^3 + 322037649338860*x^3*y^4*z^2 + 2999598104924330*x^3*y^4*z + 10660442185846180*x^3*y^4 - 49112067550*x^3*y^3*z^5 - 4724580898310*x^3*y^3*z^4 - 182598667150900*x^3*y^3*z^3 - 3409615112072260*x^3*y^3*z^2 - 30578636796242990*x^3*y^3*z - 105762808001684470*x^3*y^3 + 383074126890*x^3*y^2*z^5 + 34859745546990*x^3*y^2 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 23:48:02 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 289*x^2 + (13 - y)*(13 + z); > P2 := 17*x*(13 - y) + 17*x*(13 + z); > I := ideal; > 51185893014090757 + 4006222227236220355*x^3 + 15716717968388249085*x^4 + 32884209903089259624*x^5 + 71670713891348386360*x^6 + 145605749787505856355*x^7 + 190407518952892273695*x^8 + 160272288278650260440*x^9 + 125752103110940973576*x^10 + 102778161196442141865*x^11 + 44800736931782472095*x^12 + 2862423051509815793*x^15 - 39373763856992890*y - 2465367524453058680*x^3*y - 8865840905244653330*x^4*y - 16863697386199620320*x^5*y - 33078791026776178320*x^6*y - 59735692220515223120*x^7*y - 68351417060012611070*x^8*y - 49314550239584695520*x^9*y - 32244129002805377840*x^10*y - 21082699732603516280*x^11*y - 6892421066428072630*x^12*y + 13629379796651385*y^2 + 670525782749595630*x^3*y^2 + 2192103520527524175*x^4*y^2 + 3752635956819146280*x^5*y^2 + 6543057565735947360*x^6*y^2 + 10338869807396865540*x^7*y^2 + 10140045388023848895*x^8*y^2 + 6096579013135470600*x^9*y^2 + 3188979791486246160*x^10*y^2 + 1563826628517293790*x^11*y^2 + 340834008779410185*x^12*y^2 - 2795770214697720*y^3 - 105762808001684470*x^3*y^3 - 311357050157289370*x^4*y^3 - 473979660263007080*x^5*y^3 - 722346098781390200*x^6*y^3 - 978124729789093380*x^7*y^3 - 800923125255052020*x^8*y^3 - 385595595702585320*x^9*y^3 - 149909306437387640*x^10*y^3 - 49008811719915190*x^11*y^3 - 5826222372297610*x^12*y^3 + 376353682747770*y^4 + 10660442185846180*x^3*y^4 + 27965009588272952*x^4*y^4 + 37309792806127972*x^5*y^4 + 48502941521152404*x^6*y^4 + 54707479495033404*x^7*y^4 + 36138092792793966*x^8*y^4 + 13066960935451436*x^9*y^4 + 3249782167523788*x^10*y^4 + 548350340922128*x^11*y^4 - 34740339945948*y^5 - 712134801888510*x^3*y^5 - 1647229690602054*x^4*y^5 - 1891532478782388*x^5*y^5 - 2018543020835952*x^6*y^5 - 1822861438582782*x^7*y^5 - 926617763917794*x^8*y^5 - 221996504802384*x^9*y^5 - 24191926805388*x^10*y^5 + 2226944868330*y^6 + 31539769780610*x^3*y^6 + 63882171065180*x^4*y^6 + 61639854381040*x^5*y^6 + 50484787616536*x^6*y^6 + 34534923397026*x^7*y^6 + 12514508849154*x^8*y^6 + 1423054517964*x^9*y^6 - 97887686520*y^7 - 893839629410*x^3*y^7 - 1598246998270*x^4*y^7 - 1247770331600*x^5*y^7 - 685313859048*x^6*y^7 - 330732970438*x^7*y^7 - 69757574410*x^8*y^7 + 2823683265*y^8 + 14733620265*x^3*y^8 + 24771910995*x^4*y^8 + 14397349980*x^5*y^8 + 3765460764*x^6*y^8 + 1231016019*x^7*y^8 - 48268090*y^9 - 107938610*x^3*y^9 - 225840784*x^4*y^9 - 73832564*x^5*y^9 + 371293*y^10 + 1085773*x^4*y^10 + 19686881928496445*z + 1232683762226529340*x^3*z + 4432920452622326665*x^4*z + 8431848693099810160*x^5*z + 16539395513388089160*x^6*z + 29867846110257611560*x^7*z + 34175708530006305535*x^8*z + 24657275119792347760*x^9*z + 16122064501402688920*x^10*z + 10541349866301758140*x^11*z + 3446210533214036315*x^12*z - 15143755329612650*y*z - 745028647499550700*x^3*y*z - 2435670578363915750*x^4*y*z - 4169595507576829200*x^5*y*z - 7270063961928830400*x^6*y*z - 11487633119329850600*x^7*y*z - 11266717097804276550*x^8*y*z - 6773976681261634000*x^9*y*z - 3543310879429162400*x^10*y*z - 1737585142796993100*x^11*y*z - 378704454199344650*x^12*y*z + 5242069152558225*y^2*z + 198500639648481690*x^3*y^2*z + 583538979124110165*x^4*y^2*z + 887375454176607240*x^5*y^2*z + 1356146546744416440*x^6*y^2*z + 1837411875585119340*x^7*y^2*z + 1497248081167093515*x^8*y^2*z + 719083678472388840*x^9*y^2*z + 286190494107740040*x^10*y^2*z + 93562276919838090*x^11*y^2*z + 8739333558446415*x^12*y^2*z - 1075296236422200*y^3*z - 30578636796242990*x^3*y^3*z - 79744300205240112*x^4*y^3*z - 105980645840184232*x^5*y^3*z - 139378741045262784*x^6*y^3*z - 157371901169517684*x^7*y^3*z - 101885513522686296*x^8*y^3*z - 36715755266483176*x^9*y^3*z - 10063841551041408*x^10*y^3*z - 1576507230151118*x^11*y^3*z + 144751416441450*y^4*z + 2999598104924330*x^3*y^4*z + 6821933632982858*x^4*y^4*z + 7762241978147124*x^5*y^4*z + 8562262403955780*x^6*y^4*z + 7718763420942522*x^7*y^4*z + 3706471055671176*x^8*y^4*z + 900319158365224*x^9*y^4*z + 129023609628736*x^10*y^4*z - 13361669209980*y^5*z - 194218582333230*x^3*y^5*z - 376966830809868*x^4*y^5*z - 357673365553140*x^5*y^5*z - 318181434558000*x^6*y^5*z - 213450791598486*x^7*y^5*z - 67469525969352*x^8*y^5*z - 8538327107784*x^9*y^5*z + 856517257050*y^6*z + 8299939415950*x^3*y^6*z + 13382336806410*x^4*y^6*z + 10231716719120*x^5*y^6*z + 6853138590480*x^6*y^6*z + 2997934344938*x^7*y^6*z + 474351505988*x^8*y^6*z - 37649110200*y^7*z - 225915510730*x^3*y^7*z - 293593019200*x^4*y^7*z - 172768199760*x^5*y^7*z - 75309215280*x^6*y^7*z - 15592869574*x^7*y^7*z + 1086032025*y^8*z + 3561974130*x^3*y^8*z + 3684027789*x^4*y^8*z + 1550483844*x^5*y^8*z + 289650828*x^6*y^8*z - 18564650*y^9*z - 24908910*x^3*y^9*z - 23887006*x^4*y^9*z - 5679428*x^5*y^9*z + 142805*y^10*z + 83521*x^4*y^10*z + 3028751065922530*z^2 + 149005729499910140*x^3*z^2 + 487134115672783150*x^4*z^2 + 833919101515365840*x^5*z^2 + 1454012792385766080*x^6*z^2 + 2297526623865970120*x^7*z^2 + 2253343419560855310*x^8*z^2 + 1354795336252326800*x^9*z^2 + 708662175885832480*x^10*z^2 + 347517028559398620*x^11*z^2 + 75740890839868930*x^12*z^2 - 2329808512248100*y*z^2 - 88048840159037810*x^3*y*z^2 - 259577759540322210*x^4*y*z^2 - 395577009693186360*x^5*y*z^2 - 601178366082576360*x^6*y*z^2 - 813580382721769260*x^7*y*z^2 - 669428283795267360*x^8*y*z^2 - 323066580183247160*x^9*y*z^2 - 122653068903317160*x^10*y*z^2 - 40098118679930610*x^11*y*z^2 - 5826222372297610*x^12*y*z^2 + 806472177316650*y^2*z^2 + 22843804683956100*x^3*y^2*z^2 + 59934004807250652*x^4*y^2*z^2 + 79937807364194832*x^5*y^2*z^2 + 103888783834663464*x^6*y^2*z^2 + 117290585858246424*x^7*y^2*z^2 + 77517588357061866*x^8*y^2*z^2 + 27897560770166256*x^9*y^2*z^2 + 6918891066340968*x^10*y^2*z^2 + 1233788267074788*x^11*y^2*z^2 - 165430190218800*y^3*z^2 - 3409615112072260*x^3*y^3*z^2 - 7825752020060468*x^4*y^3*z^2 - 8932588160671344*x^5*y^3*z^2 - 9679079239254360*x^6*y^3*z^2 - 8773534876502292*x^7*y^3*z^2 - 4343078679736836*x^8*y^3*z^2 - 1023650549922104*x^9*y^3*z^2 - 129023609628736*x^10*y^3*z^2 + 22269448683300*y^4*z^2 + 322037649338860*x^3*y^4*z^2 + 631875299817528*x^4*y^4*z^2 + 598555428068520*x^5*y^4*z^2 + 521817552675120*x^6*y^4*z^2 + 356999569574076*x^7*y^4*z^2 + 116439343205172*x^8*y^4*z^2 + 13281842167664*x^9*y^4*z^2 - 2055641416920*y^5*z^2 - 19919854598280*x^3*y^5*z^2 - 32346610890360*x^4*y^5*z^2 - 24331521466200*x^5*y^5*z^2 - 16153826677560*x^6*y^5*z^2 - 7425488626608*x^7*y^5*z^2 - 1171927250088*x^8*y^5*z^2 + 131771885700*y^6*z^2 + 805437907820*x^3*y^6*z^2 + 1031245479940*x^4*y^6*z^2 + 575893999200*x^5*y^6*z^2 + 263582253480*x^6*y^6*z^2 + 60730123604*x^7*y^6*z^2 - 5792170800*y^7*z^2 - 20508335900*x^3*y^7*z^2 - 19140006444*x^4*y^7*z^2 - 7087926144*x^5*y^7*z^2 - 1737904968*x^6*y^7*z^2 + 167081850*y^8*z^2 + 298906920*x^3*y^8*z^2 + 175895226*x^4*y^8*z^2 + 34076568*x^5*y^8*z^2 - 2856100*y^9*z^2 - 1916070*x^3*y^9*z^2 - 501126*x^4*y^9*z^2 + 21970*y^10*z^2 + 232980851224810*z^3 + 8856983921323330*x^3*z^3 + 25889645308483580*x^4*z^3 + 39201325284910360*x^5*z^3 + 60583866349406920*x^6*z^3 + 82272173533662060*x^7*z^3 + 65747420729892330*x^8*z^3 + 31264507759669080*x^9*z^3 + 13628118767035240*x^10*z^3 + 4455346519992290*x^11*z^3 - 179216039403700*y*z^3 - 5089759990986710*x^3*y*z^3 - 13290716700873352*x^4*y*z^3 - 17709130163672792*x^5*y*z^3 - 23229790174210464*x^6*y*z^3 - 26111453366524084*x^7*y*z^3 - 16980918920447716*x^8*y*z^3 - 6252901551933816*x^9*y*z^3 - 1677306925173568*x^10*y*z^3 - 205631377845798*x^11*y*z^3 + 62036321332050*y^2*z^3 + 1276293541046940*x^3*y^2*z^3 + 2931633458164008*x^4*y^2*z^3 + 3365536049204784*x^5*y^2*z^3 + 3639995611343520*x^6*y^2*z^3 + 3256268801266572*x^7*y^2*z^3 + 1619812732344846*x^8*y^2*z^3 + 406993592137704*x^9*y^2*z^3 + 48383853610776*x^10*y^2*z^3 - 12725399247600*y^3*z^3 - 182598667150900*x^3*y^3*z^3 - 361461449483368*x^4*y^3*z^3 - 347129706251120*x^5*y^3*z^3 - 296969338920800*x^6*y^3*z^3 - 198887872093716*x^7*y^3*z^3 - 67469525969352*x^8*y^3*z^3 - 8538327107784*x^9*y^3*z^3 + 1713034514100*y^4*z^3 + 16344496080640*x^3*y^4*z^3 + 27098635672160*x^4*y^4*z^3 + 20837764537720*x^5*y^4*z^3 + 13216767281640*x^6*y^4*z^3 + 5931855856888*x^7*y^4*z^3 + 1032412101268*x^8*y^4*z^3 - 158126262840*y^5*z^3 - 942951696960*x^3*y^5*z^3 - 1255110157080*x^4*y^5*z^3 - 719867499000*x^5*y^5*z^3 - 301236861120*x^6*y^5*z^3 - 68936897064*x^7*y^5*z^3 + 10136298900*y^6*z^3 + 34756232420*x^3*y^6*z^3 + 34666560344*x^4*y^6*z^3 + 12994531264*x^5*y^6*z^3 + 2703407728*x^6*y^6*z^3 - 445551600*y^7*z^3 - 780479180*x^3*y^7*z^3 - 512484856*x^4*y^7*z^3 - 90870848*x^5*y^7*z^3 + 12852450*y^8*z^3 + 9580350*x^3*y^8*z^3 + 3006756*x^4*y^8*z^3 - 219700*y^9*z^3 - 49130*x^3*y^9*z^3 + 1690*y^10*z^3 + 8960801970185*z^4 + 260499527097745*x^3*z^4 + 660343179932982*x^4*z^4 + 849818939742812*x^5*z^4 + 1182998573686644*x^6*z^4 + 1382922575067254*x^7*z^4 + 812264172187481*x^8*z^4 + 240496213535916*x^9*z^4 + 104831682823348*x^10*z^4 + 34271896307633*x^11*z^4 - 6892924592450*y*z^4 - 144893228089870*x^3*y*z^4 - 323318211420178*x^4*y*z^4 - 360593148129084*x^5*y*z^4 - 413635864925400*x^6*y*z^4 - 380438935253182*x^7*y*z^4 - 169762033084176*x^8*y*z^4 - 36999417467064*x^9*y*z^4 - 8063975601796*x^10*y*z^4 + 2386012358925*y^2*z^4 + 34859745546990*x^3*y^2*z^4 + 67169311906398*x^4*y^2*z^4 + 63261955812120*x^5*y^2*z^4 + 57272658220440*x^6*y^2*z^4 + 38695757541246*x^7*y^2*z^4 + 11698345228557*x^8*y^2*z^4 + 1423054517964*x^9*y^2*z^4 - 489438432600*y^3*z^4 - 4724580898310*x^3*y^3*z^4 - 7657272932010*x^4*y^3*z^4 - 5864520558520*x^5*y^3*z^4 - 3916079194560*x^6*y^3*z^4 - 1717677685178*x^7*y^3*z^4 - 265078782758*x^8*y^3*z^4 + 65885942850*y^4*z^4 + 392896540400*x^3*y^4*z^4 + 515622739970*x^4*y^4*z^4 + 302344349580*x^5*y^4*z^4 + 131791126740*x^6*y^4*z^4 + 27903029764*x^7*y^4*z^4 - 6081779340*y^5*z^4 - 20400397290*x^3*y^5*z^4 - 20410360854*x^4*y^5*z^4 - 8195414604*x^5*y^5*z^4 - 1737904968*x^6*y^5*z^4 + 389857650*y^6*z^4 + 639328690*x^3*y^6*z^4 + 436480746*x^4*y^6*z^4 + 90870848*x^5*y^6*z^4 - 17136600*y^7*z^4 - 10857730*x^3*y^7*z^4 - 3841966*x^4*y^7*z^4 + 494325*y^8*z^4 + 73695*x^3*y^8*z^4 - 8450*y^9*z^4 + 65*y^10*z^4 + 137858491849*z^5 + 3082834640210*x^3*z^5 + 6450238631824*x^4*z^5 + 6326195581212*x^5*z^5 + 8272717298508*x^6*z^5 + 9015140645810*x^7*z^5 + 3536709022587*x^8*z^5 - 106044993730*y*z^5 - 1659987883190*x^3*y*z^5 - 2977033214688*x^4*y*z^5 - 2433152146620*x^5*y*z^5 - 2545451476464*x^6*y*z^5 - 2080417072110*x^7*y*z^5 - 544109080398*x^8*y*z^5 + 36707882445*y^2*z^5 + 383074126890*x^3*y^2*z^5 + 572506387440*x^4*y^2*z^5 + 374331099480*x^5*y^2*z^5 + 293705939592*x^6*y^2*z^5 + 160032082470*x^7*y^2*z^5 + 20927272323*x^8*y^2*z^5 - 7529822040*y^3*z^5 - 49112067550*x^3*y^3*z^5 - 58718603840*x^4*y^3*z^5 - 28794699960*x^5*y^3*z^5 - 15061843056*x^6*y^3*z^5 - 4103386730*x^7*y^3*z^5 + 1013629890*y^4*z^5 + 3777851350*x^3*y^4*z^5 + 3387611760*x^4*y^4*z^5 + 1107488460*x^5*y^4*z^5 + 289650828*x^6*y^4*z^5 - 93565836*y^5*z^5 - 174362370*x^3*y^5*z^5 - 104234208*x^4*y^5*z^5 - 17038284*x^5*y^5*z^5 + 5997810*y^6*z^5 + 4470830*x^3*y^6*z^5 + 1336336*x^4*y^6*z^5 - 263640*y^7*z^5 - 49130*x^3*y^7*z^5 + 7605*y^8*z^5 - 130*y^9*z^5 + y^10*z^5 in I Output: Magma V2.10-22 Sat Apr 3 2004 23:47:59 on modular [Seed = 1383956803] ------------------------------------- true Total time: 2.749 seconds, Total memory usage: 2.85MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 23:49:51 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 221*x + 17*x*(x + 13*y); > P2 := 289*x^2 + 13*(x + 13*y); > I := ideal; > 6685838345500704*x^9 + 924870005458296768*x^10 + 1444844648155824864*x^11 + 2622697047413149824*x^12 + 1432934469020152800*x^13 + 133120811052725184*x^14 + 2866822682655126816*x^15 + 184138638474872016*x^8*y + 2943223398707990112*x^9*y + 7892679375051672240*x^10*y + 20618475737132190528*x^11*y + 22259753926962452784*x^12*y + 3731780053540098144*x^13*y + 175938759364854096*x^14*y + 1406841752355290784*x^7*y^2 + 9512670787815738816*x^8*y^2 + 27626231672555499360*x^9*y^2 + 46734567855744053376*x^10*y^2 + 52388337644423535456*x^11*y^2 + 29766996495664219584*x^12*y^2 + 2402811816273427104*x^13*y^2 + 1984173688776051448*x^6*y^3 + 14696726058509480128*x^7*y^3 + 53131838689406622392*x^8*y^3 + 79989274197663957568*x^9*y^3 + 73536840864848829416*x^10*y^3 + 51955301522716603648*x^11*y^3 + 11969402235441937000*x^12*y^3 + 1763703368432545722*x^5*y^4 + 13942559889136346988*x^6*y^4 + 55089854868616400742*x^7*y^4 + 97437228318034266792*x^8*y^4 + 86246859141446323398*x^9*y^4 + 43633624498924459116*x^10*y^4 + 10862669312227847322*x^11*y^4 + 1717178195310885957*x^4*y^5 + 11854083080488305774*x^5*y^5 + 34548020382662556939*x^6*y^5 + 68418253057297039572*x^7*y^5 + 70891000579595296971*x^8*y^5 + 29634762705897506430*x^9*y^5 + 6239430227266782117*x^10*y^5 + 803201484597532475*x^3*y^6 + 7061516980754832362*x^4*y^6 + 16681191417514940173*x^5*y^6 + 28863972801295180588*x^6*y^6 + 33456302933761198101*x^7*y^6 + 17282973378905957034*x^8*y^6 + 4141489802158399587*x^9*y^6 + 10903503837321108*x^2*y^7 + 1716952383101237295*x^3*y^7 + 6682906968070969779*x^4*y^7 + 9627124723235103318*x^5*y^7 + 8433620089884074826*x^6*y^7 + 5535138036308240763*x^7*y^7 + 1313155303123394991*x^8*y^7 + 35436387471293601*x*y^8 + 1373561906480989836*x^3*y^8 + 2324489380198598184*x^4*y^8 + 1278062779846956519*x^5*y^8 + 903412359974979660*x^6*y^8 + 51185893014090757*y^9 + 114463492206749153*x^3*y^9 + 149683028270364277*x^4*y^9 + 195739344661245593*x^5*y^9 in I Output: Magma V2.10-22 Sat Apr 3 2004 23:49:48 on modular [Seed = 604764070] ------------------------------------- true Total time: 2.730 seconds, Total memory usage: 1.91MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 23:51:05 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 289*x^2 + (x + 13*y)*(13 + x*y); > P2 := 17*x*(x + 13*y) + 17*x*(13 + x*y); > I := ideal; > 28983269932682832*x^8 + 129541660146128880*x^9 + 2056337622715298832*x^10 + 3954030970704944688*x^11 + 4421108115312331248*x^12 + 1761089458761152208*x^13 + 113096080963874736*x^14 + 2865511798316814096*x^15 + 421897025243289024*x^7*y + 2094098049331000128*x^8*y + 9009605128180728240*x^9*y + 16433647309631451744*x^10*y + 29072901033275480784*x^11*y + 28133568632064654720*x^12*y + 4162131539224590672*x^13*y + 393740082818915040*x^14*y + 8699698535682672*x^15*y + 631451150610916324*x^6*y^2 + 5881341907821143868*x^7*y^2 + 25063602236420939620*x^8*y^2 + 47407995673090941980*x^9*y^2 + 62948764167076118812*x^10*y^2 + 61943025902411982692*x^11*y^2 + 31148642986073224716*x^12*y^2 + 5939594004622103540*x^13*y^2 + 320163964555737744*x^14*y^2 + 10420647684977232*x^15*y^2 + 655632929875148160*x^5*y^3 + 7726207574097438504*x^6*y^3 + 33888760362421902028*x^7*y^3 + 79724811757778560464*x^8*y^3 + 98699927507693289284*x^9*y^3 + 78645257193326985512*x^10*y^3 + 52311827623777726212*x^11*y^3 + 17340886260549426016*x^12*y^3 + 2396049460467171132*x^13*y^3 + 166470820308074880*x^14*y^3 + 2012338696091184*x^15*y^3 + 968662692976998500*x^4*y^4 + 7788935860222575500*x^5*y^4 + 26273778060420636720*x^6*y^4 + 70845515512463246568*x^7*y^4 + 103599465823828913016*x^8*y^4 + 84569314704693228384*x^9*y^4 + 49856907011745221648*x^10*y^4 + 17118704325183358456*x^11*y^4 + 4023986740290594324*x^12*y^4 + 366526780487644868*x^13*y^4 + 13233000015145872*x^14*y^4 + 138441615164208*x^15*y^4 + 573622153800604701*x^3*y^5 + 5326954829621787505*x^4*y^5 + 16371056131307951437*x^5*y^5 + 37718716426685469981*x^6*y^5 + 61300970098617456311*x^7*y^5 + 62629008676367921307*x^8*y^5 + 38250867616208079859*x^9*y^5 + 14152338955272986351*x^10*y^5 + 3835146693211170896*x^11*y^5 + 465356551439804648*x^12*y^5 + 28652145729210796*x^13*y^5 + 575387672337504*x^14*y^5 + 5538315084624*x^15*y^5 + 8480502984583084*x^2*y^6 + 1488025398687738989*x^3*y^6 + 7969122561267384309*x^4*y^6 + 15150496196288590553*x^5*y^6 + 21588497097596338793*x^6*y^6 + 26357867158489066863*x^7*y^6 + 19602186610604929123*x^8*y^6 + 10184353653262255727*x^9*y^6 + 2942374432016006143*x^10*y^6 + 500410146181616736*x^11*y^6 + 44924864591576372*x^12*y^6 + 1659885706841180*x^13*y^6 + 24265486093680*x^14*y^6 + 26837950320*x^15*y^6 + 31499011085594312*x*y^7 + 1721518807785243571*x^3*y^7 + 3971002691172605231*x^4*y^7 + 6034216867562320957*x^5*y^7 + 7178585468232558965*x^6*y^7 + 5504873997484781517*x^7*y^7 + 4053490097640704201*x^8*y^7 + 1507860508508071471*x^9*y^7 + 370585850156023203*x^10*y^7 + 47154968513349528*x^11*y^7 + 2791387267875024*x^12*y^7 + 67503567900340*x^13*y^7 + 433847299392*x^14*y^7 + 461895696*x^15*y^7 + 51185893014090757*y^8 + 16961005969166168*x^2*y^8 + 228926984413498306*x^3*y^8 + 1110469176315570162*x^4*y^8 + 1534081715078620305*x^5*y^8 + 1158566381633282193*x^6*y^8 + 929951250258691466*x^7*y^8 + 423451845960367809*x^8*y^8 + 155963710996976727*x^9*y^8 + 27902125670740763*x^10*y^8 + 2480498424861288*x^11*y^8 + 91272284590396*x^12*y^8 + 1218474132252*x^13*y^8 + 6723617472*x^14*y^8 + 27561634699895023*x*y^9 + 3914078300576808*x^3*y^9 + 70439072127230248*x^4*y^9 + 205356628769615531*x^5*y^9 + 190373054403032046*x^6*y^9 + 89120490894867861*x^7*y^9 + 42476837090133485*x^8*y^9 + 9826352798177669*x^9*y^9 + 1320637107478221*x^10*y^9 + 70762923245040*x^11*y^9 + 1600686410856*x^12*y^9 + 10063204372*x^13*y^9 + 6360377238437313*x^2*y^10 + 501804910330360*x^4*y^10 + 8127585245449644*x^5*y^10 + 15796663751508887*x^6*y^10 + 9077406598098345*x^7*y^10 + 2746571173219081*x^8*y^10 + 530460985129673*x^9*y^10 + 44092013938609*x^10*y^10 + 1613682219500*x^11*y^10 + 10448580480*x^12*y^10 + 815432979286835*x^3*y^11 + 38600377717720*x^5*y^11 + 416799243356392*x^6*y^11 + 505447963730346*x^7*y^11 + 139035842273471*x^8*y^11 + 21463164027513*x^9*y^11 + 1103618317945*x^10*y^11 + 15437220500*x^11*y^11 + 62725613791295*x^4*y^12 + 1781555894664*x^6*y^12 + 8015370064546*x^7*y^12 + 4636550669647*x^8*y^12 + 308283464021*x^9*y^12 + 9141604953*x^10*y^12 + 2895028328829*x^5*y^13 + 45680920376*x^7*y^13 + 135150652*x^9*y^13 + 74231495611*x^6*y^14 + 501988136*x^8*y^14 + 815730721*x^7*y^15 in I Output: Magma V2.10-22 Sat Apr 3 2004 23:51:02 on modular [Seed = 103404126] ------------------------------------- true Total time: 2.579 seconds, Total memory usage: 2.10MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 23:52:28 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 289*x^2 + (x + 13*y)*(13 + x*z); > P2 := 17*x*(x + 13*y) + 17*x*(13 + x*z); > I := ideal; > 677436628945986*x^5 + 309473438192121060*x^6 + 1270572416521638282*x^7 + 4226151958752265776*x^8 + 9656060446309240548*x^9 + 14727345355888048728*x^10 + 19321452431855240004*x^11 + 15386941084693274928*x^12 + 1971892115543381850*x^13 + 57108600860413284*x^14 + 2863005673747045554*x^15 + 17618728833777747*x^4*y + 808694731922239578*x^5*y + 3885767245906223067*x^6*y + 16579023502987204584*x^7*y + 40269267913066419318*x^8*y + 51839914797308015820*x^9*y + 53633767653218699934*x^10*y + 54770203237590691656*x^11*y + 28341506170226489175*x^12*y + 1539055518523094442*x^13*y + 22722267251960679*x^14*y + 114696473057973963*x^3*y^2 + 1532049818767257894*x^4*y^2 + 5910786369753253599*x^5*y^2 + 20310210329513625768*x^6*y^2 + 55019447857969428678*x^7*y^2 + 87154168251834753732*x^8*y^2 + 83925198949739383782*x^9*y^2 + 61762634806981593576*x^10*y^2 + 36697221732301812591*x^11*y^2 + 11075451873862771590*x^12*y^2 + 295389474275488827*x^13*y^2 + 3028751065922530*x^2*y^3 + 801244445447244071*x^3*y^3 + 5573491582067093373*x^4*y^3 + 15927357885999485692*x^5*y^3 + 34230471459130405784*x^6*y^3 + 61842050703210338418*x^7*y^3 + 69959219666977640870*x^8*y^3 + 43439098202265910924*x^9*y^3 + 20155768380485719566*x^10*y^3 + 9534372178875749855*x^11*y^3 + 1280021055193784917*x^12*y^3 + 19686881928496445*x*y^4 + 2060342859721484754*x^3*y^4 + 7431322109422791164*x^4*y^4 + 11882529628847379528*x^5*y^4 + 18790977087479576928*x^6*y^4 + 25951099150768454182*x^7*y^4 + 18847640821300492812*x^8*y^4 + 7373872086769833411*x^9*y^4 + 2465727511979234776*x^10*y^4 + 51185893014090757*y^5 + 1030171429860742377*x^3*y^5 + 2394928452325828432*x^4*y^5 + 2936090169918683895*x^5*y^5 + 3071602023914930844*x^6*y^5 + 2343081031063312631*x^7*y^5 + 1313155303123394991*x^8*y^5 + 572401029566608073*x^9*y^5 + 521105099189220*x^6*y*z + 214250841825314580*x^7*y*z + 781890717859469712*x^8*y*z + 2275620285481989264*x^9*y*z + 4456643282911957176*x^10*y*z + 5664363598418480280*x^11*y*z + 5945062286724689232*x^12*y*z + 3550832558006140368*x^13*y*z + 303368017775904900*x^14*y*z + 4392969296954868*x^15*y*z + 13552868333675190*x^5*y^2*z + 559865583638473554*x^6*y^2*z + 2391241382096137272*x^7*y^2*z + 8927166501608494776*x^8*y^2*z + 18585815959876808916*x^9*y^2*z + 19938428768195390700*x^10*y^2*z + 16502697739451907672*x^11*y^2*z + 12639277670213236536*x^12*y^2*z + 4360231718496382950*x^13*y^2*z + 118388886040238034*x^14*y^2*z + 88228056198441510*x^4*y^3*z + 1060649874531178542*x^5*y^3*z + 3637406996771232984*x^6*y^3*z + 10936267100507336952*x^7*y^3*z + 25393591319062813236*x^8*y^3*z + 33520833943013366820*x^9*y^3*z + 25823138138381348856*x^10*y^3*z + 14252915724688060056*x^11*y^3*z + 5645726420354125014*x^12*y^3*z + 851957836450982430*x^13*y^3*z + 2329808512248100*x^3*y^4*z + 554707693001938203*x^4*y^4*z + 3429840973579749768*x^5*y^4*z + 8576269630922799988*x^6*y^4*z + 15798679134983264208*x^7*y^4*z + 23785404116619360930*x^8*y^4*z + 21525913743685427960*x^9*y^4*z + 10024407277445979444*x^10*y^4*z + 3100887443151649164*x^11*y^4*z + 733413244528903835*x^12*y^4*z + 15143755329612650*x^2*y^5*z + 1267903298290144464*x^4*y^5*z + 4001481135843041396*x^5*y^5*z + 5484244444083405936*x^6*y^5*z + 7227298879799837280*x^7*y^5*z + 7984953584851832056*x^8*y^5*z + 4349455574146267572*x^9*y^5*z + 1134441859503051294*x^10*y^5*z + 189671347075325752*x^11*y^5*z + 39373763856992890*x*y^6*z + 554707693001938203*x^4*y^6*z + 1105351593381151584*x^5*y^6*z + 1129265449968724575*x^6*y^6*z + 945108315050747952*x^7*y^6*z + 540711007168456761*x^8*y^6*z + 202023892788214614*x^9*y^6*z + 44030848428200621*x^10*y^6*z + 180382534334730*x^7*y^2*z^2 + 65923335946250640*x^8*y^2*z^2 + 210509039423703384*x^9*y^2*z^2 + 525143142803535984*x^10*y^2*z^2 + 857046785175376380*x^11*y^2*z^2 + 871440553602843120*x^12*y^2*z^2 + 685968725391310296*x^13*y^2*z^2 + 273140966000472336*x^14*y^2*z^2 + 11668000683688650*x^15*y^2*z^2 + 4691377500118335*x^6*y^3*z^2 + 172266333427222632*x^7*y^3*z^2 + 643795756718190804*x^8*y^3*z^2 + 2060115346525037256*x^9*y^3*z^2 + 3574195376899386330*x^10*y^3*z^2 + 3067450579722367800*x^11*y^3*z^2 + 1904157431475220116*x^12*y^3*z^2 + 972252128477941272*x^13*y^3*z^2 + 167701219942168575*x^14*y^3*z^2 + 30540480991768215*x^5*y^4*z^2 + 326353807548054936*x^6*y^4*z^2 + 979301883746101188*x^7*y^4*z^2 + 2523753946270923912*x^8*y^4*z^2 + 4883382945973617930*x^9*y^4*z^2 + 5157051375848210280*x^10*y^4*z^2 + 2979592862120924868*x^11*y^4*z^2 + 1096378132668312312*x^12*y^4*z^2 + 217143323859774039*x^13*y^4*z^2 + 806472177316650*x^4*y^5*z^2 + 170679290154442524*x^5*y^5*z^2 + 923418723656086476*x^6*y^5*z^2 + 1979139145597569228*x^7*y^5*z^2 + 3038207525958320040*x^8*y^5*z^2 + 3659292941018363220*x^9*y^5*z^2 + 2483759278117549380*x^10*y^5*z^2 + 771108252111229188*x^11*y^5*z^2 + 119264901659678814*x^12*y^5*z^2 + 5242069152558225*x^3*y^6*z^2 + 341358580308885048*x^5*y^6*z^2 + 923418723656086476*x^6*y^6*z^2 + 1054662393092962680*x^7*y^6*z^2 + 1111892135353821120*x^8*y^6*z^2 + 921340798252134468*x^9*y^6*z^2 + 334573505703559044*x^10*y^6*z^2 + 43632379211655819*x^11*y^6*z^2 + 13629379796651385*x^2*y^7*z^2 + 128009467615831893*x^5*y^7*z^2 + 212567614111759920*x^6*y^7*z^2 + 173733146149034550*x^7*y^7*z^2 + 109050959428932456*x^8*y^7*z^2 + 41593154397573597*x^9*y^7*z^2 + 7770149722623639*x^10*y^7*z^2 + 37001545504560*x^8*y^3*z^3 + 11832393631378320*x^9*y^3*z^3 + 32386006065185136*x^10*y^3*z^3 + 67326043949171280*x^11*y^3*z^3 + 87902234376961680*x^12*y^3*z^3 + 67033888738680240*x^13*y^3*z^3 + 35177883353400528*x^14*y^3*z^3 + 7003614512832624*x^15*y^3*z^3 + 962333846178120*x^7*y^4*z^3 + 30919598307450216*x^8*y^4*z^3 + 99045501033567816*x^9*y^4*z^3 + 264117352118594520*x^10*y^4*z^3 + 366584141220449880*x^11*y^4*z^3 + 235957736901720600*x^12*y^4*z^3 + 97649099050011288*x^13*y^4*z^3 + 24929541755844648*x^14*y^4*z^3 + 6264714049593480*x^6*y^5*z^3 + 58576324431702168*x^7*y^5*z^3 + 150661828268630952*x^8*y^5*z^3 + 323558198239862040*x^9*y^5*z^3 + 500859789330627480*x^10*y^5*z^3 + 396696259680631560*x^11*y^5*z^3 + 152799633954919224*x^12*y^5*z^3 + 28112259812008008*x^13*y^5*z^3 + 165430190218800*x^5*y^6*z^3 + 30634744386694812*x^6*y^6*z^3 + 142064419024013304*x^7*y^6*z^3 + 253735787897124260*x^8*y^6*z^3 + 311611028303417440*x^9*y^6*z^3 + 281484072386027940*x^10*y^6*z^3 + 127372270672694840*x^11*y^6*z^3 + 19772006464390492*x^12*y^6*z^3 + 1075296236422200*x^4*y^7*z^3 + 52516704662905392*x^6*y^7*z^3 + 118387015853344420*x^7*y^7*z^3 + 108170501855688480*x^8*y^7*z^3 + 85530164257986240*x^9*y^7*z^3 + 47248246064212024*x^10*y^7*z^3 + 8578807838552796*x^11*y^7*z^3 + 2795770214697720*x^3*y^8*z^3 + 16411470207157935*x^6*y^8*z^3 + 21801806575565120*x^7*y^8*z^3 + 13364088165310350*x^8*y^8*z^3 + 5592356893791408*x^9*y^8*z^3 + 1066491138399323*x^10*y^8*z^3 + 4980977279460*x^9*y^4*z^4 + 1365276188235960*x^10*y^4*z^4 + 3114039044729340*x^11*y^4*z^4 + 5178926457628560*x^12*y^4*z^4 + 5071282752517020*x^13*y^4*z^4 + 2578226489949240*x^14*y^4*z^4 + 676497756796164*x^15*y^4*z^4 + 129544940831670*x^8*y^5*z^4 + 3567645958551948*x^9*y^5*z^4 + 9523605868612290*x^10*y^5*z^4 + 20316719393738040*x^11*y^5*z^4 + 21149085070410570*x^12*y^5*z^4 + 9075297573143100*x^13*y^5*z^4 + 1877867289423294*x^14*y^5*z^4 + 843326891291430*x^7*y^6*z^4 + 6758806665196404*x^8*y^6*z^4 + 14486714256599130*x^9*y^6*z^4 + 24889092172297080*x^10*y^6*z^4 + 28895757076766970*x^11*y^6*z^4 + 15257548449255060*x^12*y^6*z^4 + 2938454499133062*x^13*y^6*z^4 + 22269448683300*x^6*y^7*z^4 + 3534778198464786*x^7*y^7*z^4 + 13660040290770510*x^8*y^7*z^4 + 19518137530548020*x^9*y^7*z^4 + 17977559325197160*x^10*y^7*z^4 + 10826310476385690*x^11*y^7*z^4 + 2449466743705670*x^12*y^7*z^4 + 144751416441450*x^5*y^8*z^4 + 5049683140663980*x^7*y^8*z^4 + 9106693527180340*x^8*y^8*z^4 + 6240605876289720*x^9*y^8*z^4 + 3289621702230240*x^10*y^8*z^4 + 908620116619462*x^11*y^8*z^4 + 376353682747770*x^4*y^9*z^4 + 1262420785165995*x^7*y^9*z^4 + 1257796533205680*x^8*y^9*z^4 + 514003390973475*x^9*y^9*z^4 + 107545324880604*x^10*y^9*z^4 + 459782518104*x^10*y^5*z^5 + 105021245248920*x^11*y^5*z^5 + 191633171983344*x^12*y^5*z^5 + 239027374967472*x^13*y^5*z^5 + 156039469308216*x^14*y^5*z^5 + 39665022922296*x^15*y^5*z^5 + 11957994538308*x^9*y^6*z^5 + 274434304503996*x^10*y^6*z^5 + 586068053453064*x^11*y^6*z^5 + 937694741249448*x^12*y^6*z^5 + 650741079089556*x^13*y^6*z^5 + 139619962663740*x^14*y^6*z^5 + 77845559196132*x^8*y^7*z^5 + 519908205015108*x^9*y^7*z^5 + 891490108098408*x^10*y^7*z^5 + 1148727331029096*x^11*y^7*z^5 + 889100217746676*x^12*y^7*z^5 + 234731514603924*x^13*y^7*z^5 + 2055641416920*x^7*y^8*z^5 + 271906015266522*x^8*y^8*z^5 + 840617864047416*x^9*y^8*z^5 + 900837116794524*x^10*y^8*z^5 + 553155671544528*x^11*y^8*z^5 + 166558622713626*x^12*y^8*z^5 + 13361669209980*x^6*y^9*z^5 + 310749731733168*x^8*y^9*z^5 + 420308932023708*x^9*y^9*z^5 + 192018642347376*x^10*y^9*z^5 + 50609564649696*x^11*y^9*z^5 + 34740339945948*x^5*y^10*z^5 + 58265574699969*x^8*y^10*z^5 + 38701431790944*x^9*y^10*z^5 + 7907744476515*x^10*y^10*z^5 + 29473238340*x^11*y^6*z^6 + 5385704884560*x^12*y^6*z^6 + 7370506614744*x^13*y^6*z^6 + 6128907050448*x^14*y^6*z^6 + 2000506016772*x^15*y^6*z^6 + 766538111430*x^10*y^7*z^6 + 14073554077128*x^11*y^7*z^6 + 22541078978964*x^12*y^7*z^6 + 24043454903832*x^13*y^7*z^6 + 8342834347302*x^14*y^7*z^6 + 4990099948470*x^9*y^8*z^6 + 26661959231544*x^10*y^8*z^6 + 34288081080708*x^11*y^8*z^6 + 29454546949464*x^12*y^8*z^6 + 11398720740342*x^13*y^8*z^6 + 131771885700*x^8*y^9*z^6 + 13943898218796*x^9*y^9*z^6 + 32331456309516*x^10*y^9*z^6 + 23098387610116*x^11*y^9*z^6 + 7091739378776*x^12*y^9*z^6 + 856517257050*x^7*y^10*z^6 + 11951912758968*x^9*y^10*z^6 + 10777152103172*x^10*y^10*z^6 + 2461777465992*x^11*y^10*z^6 + 2226944868330*x^6*y^11*z^6 + 1493989094871*x^9*y^11*z^6 + 496172202448*x^10*y^11*z^6 + 1295526960*x^12*y^7*z^7 + 177550710480*x^13*y^7*z^7 + 161989156368*x^14*y^7*z^7 + 67350626928*x^15*y^7*z^7 + 33693982920*x^11*y^8*z^7 + 463963321224*x^12*y^8*z^7 + 495408329208*x^13*y^8*z^7 + 264213790152*x^14*y^8*z^7 + 219345052680*x^10*y^9*z^7 + 878965688952*x^11*y^9*z^7 + 753584199576*x^12*y^9*z^7 + 323676340104*x^13*y^9*z^7 + 5792170800*x^9*y^10*z^7 + 459688952268*x^10*y^10*z^7 + 710581457352*x^11*y^10*z^7 + 253828435276*x^12*y^10*z^7 + 37649110200*x^8*y^11*z^7 + 262679401296*x^10*y^11*z^7 + 118430242892*x^11*y^11*z^7 + 97887686520*x^7*y^12*z^7 + 16417462581*x^10*y^12*z^7 + 37370970*x^13*y^8*z^8 + 3414436740*x^14*y^8*z^8 + 1557588042*x^15*y^8*z^8 + 971941815*x^12*y^9*z^8 + 8922371562*x^13*y^9*z^8 + 4763541627*x^14*y^9*z^8 + 6327261135*x^11*y^10*z^8 + 16903186326*x^12*y^10*z^8 + 7246001919*x^13*y^10*z^8 + 167081850*x^10*y^11*z^8 + 8840172159*x^11*y^11*z^8 + 6832514013*x^12*y^11*z^8 + 1086032025*x^9*y^12*z^8 + 2525763474*x^11*y^12*z^8 + 2823683265*x^8*y^13*z^8 + 638820*x^14*y^9*z^9 + 29183220*x^15*y^9*z^9 + 16614390*x^13*y^10*z^9 + 76259586*x^14*y^10*z^9 + 108158310*x^12*y^11*z^9 + 144471678*x^13*y^11*z^9 + 2856100*x^11*y^12*z^9 + 75557027*x^12*y^12*z^9 + 18564650*x^10*y^13*z^9 + 48268090*x^9*y^14*z^9 + 4914*x^15*y^10*z^10 + 127803*x^14*y^11*z^10 + 831987*x^13*y^12*z^10 + 21970*x^12*y^13*z^10 + 142805*x^11*y^14*z^10 + 371293*x^10*y^15*z^10 in I Output: Magma V2.10-22 Sat Apr 3 2004 23:52:26 on modular [Seed = 523291643] ------------------------------------- false Total time: 2.679 seconds, Total memory usage: 2.85MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 23:53:39 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 289*x^2 + (x + 13*y)*(13 + x*z); > P2 := 17*x*(x + 13*y) + 17*x*(13 + x*z); > I := ideal; > 3413006292925008*x^8 + 737327157429603312*x^9 + 1217360629327978512*x^10 + 3096920854536221232*x^11 + 5917114022214266352*x^12 + 1449788252847354576*x^13 + 136129856312554416*x^14 + 2864933201091627792*x^15 + 94100451083615808*x^7*y + 2572475064924802752*x^8*y + 7790256736295342400*x^9*y + 18039076039067069376*x^10*y + 30947511994647258816*x^11*y + 22683539282010085440*x^12*y + 3743023738873199040*x^13*y + 100342420170677568*x^14*y + 721271387554218800*x^6*y^2 + 6064044253072405392*x^7*y^2 + 24524699308255049072*x^8*y^2 + 47480439156873011536*x^9*y^2 + 57459279956638326416*x^10*y^2 + 54751240547441080240*x^11*y^2 + 28428464997200473296*x^12*y^2 + 1369545770682529648*x^13*y^2 + 1040338631493097976*x^5*y^3 + 6925119428366453080*x^6*y^3 + 34319089390564026360*x^7*y^3 + 76509047754150417432*x^8*y^3 + 86790737618922920232*x^9*y^3 + 68066612789312377032*x^10*y^3 + 37815611073280217320*x^11*y^3 + 6813578391090548168*x^12*y^3 + 924638272897479595*x^4*y^4 + 6898287977075385345*x^5*y^4 + 27456389656575225255*x^6*y^4 + 66858466050421420245*x^7*y^4 + 90540203686594439505*x^8*y^4 + 63343824690685359795*x^9*y^4 + 23682063075885437405*x^10*y^4 + 6147383838244932855*x^11*y^4 + 459158661593855548*x^3*y^5 + 5635125770178419840*x^4*y^5 + 16382502659744665756*x^5*y^5 + 32977989732844447824*x^6*y^5 + 51196364813652987604*x^7*y^5 + 41456470615845930528*x^8*y^5 + 14449252124333550420*x^9*y^5 + 3522467874256049680*x^10*y^5 + 8480502984583084*x^2*y^6 + 1831415875307986448*x^3*y^6 + 7026297444691217238*x^4*y^6 + 12561182996842424802*x^5*y^6 + 16070111626849049952*x^6*y^6 + 14524091018059288380*x^7*y^6 + 6891414797245037150*x^8*y^6 + 1144802059133216146*x^9*y^6 + 31499011085594312*x*y^7 + 1373561906480989836*x^3*y^7 + 3803709894870433392*x^4*y^7 + 3316054780143454752*x^5*y^7 + 2168189663939951184*x^6*y^7 + 1496421498830350924*x^7*y^7 + 51185893014090757*y^8 + 343390476620247459*x^3*y^8 + 299366056540728554*x^4*y^8 + 195739344661245593*x^5*y^8 + 255966835326244237*x^6*y^8 + 1837772619267312*x^9*z + 340304841890586144*x^10*z + 468215626664607120*x^11*z + 952898724472683456*x^12*z + 1365487851280215312*x^13*z + 223044346591900704*x^14*z + 10471527408658032*x^15*z + 50669473660408512*x^8*y*z + 1187296183811447424*x^9*y*z + 2996252590882824000*x^10*y*z + 5550484935097559808*x^11*y*z + 7141733537226290496*x^12*y*z + 3489775274155397760*x^13*y*z + 287924902990246080*x^14*y*z + 388376900990733200*x^7*y^2*z + 2798789655264187104*x^8*y^2*z + 9432576657021172720*x^9*y^2*z + 14609365894422465088*x^10*y^2*z + 13259833836147306096*x^11*y^2*z + 8423267776529396960*x^12*y^2*z + 2186804999784651792*x^13*y^2*z + 560182340034745064*x^6*y^3*z + 3196208966938362960*x^7*y^3*z + 13199649765601548600*x^8*y^3*z + 23541245462815513056*x^9*y^3*z + 20028631758212981592*x^10*y^3*z + 10471786582971134928*x^11*y^3*z + 2908893159483093640*x^12*y^3*z + 497882146944796705*x^5*y^4*z + 3183825220188639390*x^6*y^4*z + 10560149867913548175*x^7*y^4*z + 20571835707821975460*x^8*y^4*z + 20893893158444870655*x^9*y^4*z + 9745203798566978430*x^10*y^4*z + 1821697159683495185*x^11*y^4*z + 247239279319768372*x^4*y^5*z + 2600827278543886080*x^5*y^5*z + 6300962561440256060*x^6*y^5*z + 10147073763952137792*x^7*y^5*z + 11814545726227612524*x^8*y^5*z + 6377918556283989312*x^9*y^5*z + 1111480932641042340*x^10*y^5*z + 4566424684006276*x^3*y^6*z + 845268865526762976*x^4*y^6*z + 2702422094112006630*x^5*y^6*z + 3864979383643823016*x^6*y^6*z + 3708487298503626912*x^7*y^6*z + 2234475541239890520*x^8*y^6*z + 530108830557310550*x^9*y^6*z + 16961005969166168*x^2*y^7*z + 528293040954226860*x^4*y^7*z + 1170372275344748736*x^5*y^7*z + 765243410802335712*x^6*y^7*z + 333567640606146336*x^7*y^7*z + 115109346063873148*x^8*y^7*z + 27561634699895023*x*y^8*z + 105658608190845372*x^4*y^8*z + 69084474586321974*x^5*y^8*z + 30113745332499322*x^6*y^8*z + 19689756563557249*x^7*y^8*z + 424101373677072*x^10*z^2 + 65443238825112720*x^11*z^2 + 72033173333016480*x^12*z^2 + 109949852823771168*x^13*z^2 + 105037527021555024*x^14*z^2 + 8578628715073104*x^15*z^2 + 11692955460094272*x^9*y*z^2 + 228326189194509120*x^10*y*z^2 + 460961937058896000*x^11*y*z^2 + 640440569434333824*x^12*y*z^2 + 549364118248176192*x^13*y*z^2 + 134222125929053760*x^14*y*z^2 + 89625438690169200*x^8*y^2*z^2 + 538228779858497520*x^9*y^2*z^2 + 1451165639541718880*x^10*y^2*z^2 + 1685696064741053664*x^11*y^2*z^2 + 1019987218165177392*x^12*y^2*z^2 + 323971837558822960*x^13*y^2*z^2 + 129272847700325784*x^7*y^3*z^2 + 614655570565069800*x^8*y^3*z^2 + 2030715348554084400*x^9*y^3*z^2 + 2716297553401789968*x^10*y^3*z^2 + 1540663981400998584*x^11*y^3*z^2 + 402761022421966728*x^12*y^3*z^2 + 114895880064183855*x^6*y^4*z^2 + 612274080805507575*x^7*y^4*z^2 + 1624638441217468950*x^8*y^4*z^2 + 2373673350902535630*x^9*y^4*z^2 + 1607222550649605435*x^10*y^4*z^2 + 374815530714114555*x^11*y^4*z^2 + 57055218304561932*x^5*y^5*z^2 + 500159092027670400*x^6*y^5*z^2 + 969378855606193240*x^7*y^5*z^2 + 1170816203532938976*x^8*y^5*z^2 + 908811209709816348*x^9*y^5*z^2 + 245304559857076512*x^10*y^5*z^2 + 1053790311693756*x^4*y^6*z^2 + 162551704908992880*x^5*y^6*z^2 + 415757245248001020*x^6*y^6*z^2 + 445959159651210348*x^7*y^6*z^2 + 285268253731048224*x^8*y^6*z^2 + 85941366970765020*x^9*y^6*z^2 + 3914078300576808*x^3*y^7*z^2 + 81275852454496440*x^5*y^7*z^2 + 135042954847471008*x^6*y^7*z^2 + 58864877754025824*x^7*y^7*z^2 + 12829524638697936*x^8*y^7*z^2 + 6360377238437313*x^2*y^8*z^2 + 12191377868174466*x^5*y^8*z^2 + 5314190352793998*x^6*y^8*z^2 + 1158220974326897*x^7*y^8*z^2 + 54371970984240*x^11*z^3 + 6712127058985920*x^12*z^3 + 5541013333308960*x^13*z^3 + 5638453990962624*x^14*z^3 + 2693269923629616*x^15*z^3 + 1499096853858240*x^10*y*z^3 + 23418070686616320*x^11*y*z^3 + 35458610542992000*x^12*y*z^3 + 32843106124837632*x^13*y*z^3 + 14086259442260928*x^14*y*z^3 + 11490440857714000*x^9*y^2*z^3 + 55202951780358720*x^10*y^2*z^3 + 111628126118593760*x^11*y^2*z^3 + 86445952038002752*x^12*y^2*z^3 + 26153518414491728*x^13*y^2*z^3 + 16573442012862280*x^8*y^3*z^3 + 63041596981032800*x^9*y^3*z^3 + 156208872965698800*x^10*y^3*z^3 + 139297310430861024*x^11*y^3*z^3 + 39504204651307656*x^12*y^3*z^3 + 14730241033869725*x^7*y^4*z^3 + 62797341621077700*x^8*y^4*z^3 + 124972187785959150*x^9*y^4*z^3 + 121726838507822340*x^10*y^4*z^3 + 41210834632041165*x^11*y^4*z^3 + 7314771577507940*x^6*y^5*z^3 + 51298368413094400*x^7*y^5*z^3 + 74567604277399480*x^8*y^5*z^3 + 60041856591432768*x^9*y^5*z^3 + 23302851531020932*x^10*y^5*z^3 + 135101322012020*x^5*y^6*z^3 + 16671969734255680*x^6*y^6*z^3 + 31981326557538540*x^7*y^6*z^3 + 22869700494933864*x^8*y^6*z^3 + 7314570608488416*x^9*y^6*z^3 + 501804910330360*x^4*y^7*z^3 + 6251988650345880*x^6*y^7*z^3 + 6925279735767744*x^7*y^7*z^3 + 1509355839846816*x^8*y^7*z^3 + 815432979286835*x^3*y^8*z^3 + 625198865034588*x^6*y^8*z^3 + 136261291097282*x^7*y^8*z^3 + 4182459306480*x^12*z^4 + 387238099556880*x^13*z^4 + 213115897434960*x^14*z^4 + 108431807518512*x^15*z^4 + 115315142604480*x^11*y*z^4 + 1351042539612480*x^12*y*z^4 + 1363792713192000*x^13*y*z^4 + 631598194708416*x^14*y*z^4 + 883880065978000*x^10*y^2*z^4 + 3184785679636080*x^11*y^2*z^4 + 4293389466099760*x^12*y^2*z^4 + 1662422154576976*x^13*y^2*z^4 + 1274880154835560*x^9*y^3*z^4 + 3637015210444200*x^10*y^3*z^4 + 6008033575603800*x^11*y^3*z^4 + 2678794431362712*x^12*y^3*z^4 + 1133095464143825*x^8*y^4*z^4 + 3622923555062175*x^9*y^4*z^4 + 4806622607152275*x^10*y^4*z^4 + 2340900740535045*x^11*y^4*z^4 + 562674736731380*x^7*y^5*z^4 + 2959521254601600*x^8*y^5*z^4 + 2867984779899980*x^9*y^5*z^4 + 1154651088296784*x^10*y^5*z^4 + 10392409385540*x^6*y^6*z^4 + 961844407745520*x^7*y^6*z^4 + 1230051021443790*x^8*y^6*z^4 + 439801932594882*x^9*y^6*z^4 + 38600377717720*x^5*y^7*z^4 + 240461101936380*x^7*y^7*z^4 + 133178456457072*x^8*y^7*z^4 + 62725613791295*x^4*y^8*z^4 + 12023055096819*x^7*y^8*z^4 + 193036583376*x^13*z^5 + 11915018447904*x^14*z^5 + 3278706114384*x^15*z^5 + 5322237350976*x^12*y*z^5 + 41570539680384*x^13*y*z^5 + 20981426356800*x^14*y*z^5 + 40794464583600*x^11*y^2*z^5 + 97993405527264*x^12*y^2*z^5 + 66052145632304*x^13*y^2*z^5 + 58840622530872*x^10*y^3*z^5 + 111908160321360*x^11*y^3*z^5 + 92431285778520*x^12*y^3*z^5 + 52296713729715*x^9*y^4*z^5 + 111474570924990*x^10*y^4*z^5 + 73948040110035*x^11*y^4*z^5 + 25969603233756*x^8*y^5*z^5 + 91062192449280*x^9*y^5*z^5 + 44122842767692*x^10*y^5*z^5 + 479649663948*x^7*y^6*z^5 + 29595212546016*x^8*y^6*z^5 + 18923861868366*x^9*y^6*z^5 + 1781555894664*x^6*y^7*z^5 + 3699401568252*x^8*y^7*z^5 + 2895028328829*x^5*y^8*z^5 + 4949655984*x^14*z^6 + 152756646768*x^15*z^6 + 136467624384*x^13*y*z^6 + 532955636928*x^14*y*z^6 + 1046011912400*x^12*y^2*z^6 + 1256325711888*x^13*y^2*z^6 + 1508733911048*x^11*y^3*z^6 + 1434720004120*x^12*y^3*z^6 + 1340941377685*x^10*y^4*z^6 + 1429161165705*x^11*y^4*z^6 + 665887262404*x^9*y^5*z^6 + 1167464005760*x^10*y^5*z^6 + 12298709332*x^8*y^6*z^6 + 379425801872*x^9*y^6*z^6 + 45680920376*x^7*y^7*z^6 + 74231495611*x^6*y^8*z^6 + 54391824*x^15*z^7 + 1499644224*x^14*y*z^7 + 11494636400*x^13*y^2*z^7 + 16579493528*x^12*y^3*z^7 + 14735619535*x^11*y^4*z^7 + 7317442444*x^10*y^5*z^7 + 135150652*x^9*y^6*z^7 + 501988136*x^8*y^7*z^7 + 815730721*x^7*y^8*z^7 in I Output: Magma V2.10-22 Sat Apr 3 2004 23:53:36 on modular [Seed = 3972216914] ------------------------------------- true Total time: 2.629 seconds, Total memory usage: 2.61MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 23:57:32 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 289*x*z + (x + 13*y)*(13 + x*z) > P2 := 17*(x + 13*y)*z + 17*x*(13 + x*z); > I := ideal; > 989908807470804*x^6 + 27092777969116574*x^5*y + 202539214771697518*x^4*y^2 + 229392946115947926*x^3*y^3 + 4543126598883795*x^2*y^4 + 23624258314195734*x*y^5 + 51185893014090757*y^6 + 423740553832288836*x^6*z + 685321482095172*x^7*z + 1303852233029633274*x^5*y*z + 18756538594003782*x^6*y*z + 2086080212998741960*x^4*y^2*z + 140219456380405974*x^5*y^2*z + 2412538220357635994*x^3*y^3*z + 158810501157194718*x^4*y^3*z + 1030171429860742377*x^2*y^4*z + 3145241491534935*x^3*y^4*z + 16355255755981662*x^2*y^5*z + 35436387471293601*x*y^6*z + 1282109000312232144*x^6*z^2 + 260763417742946976*x^7*z^2 + 210868148336976*x^8*z^2 + 5939581586710135104*x^5*y*z^2 + 802370604941312784*x^6*y*z^2 + 5771242644308856*x^7*y*z^2 + 9206470086877664692*x^4*y^2*z^2 + 1283741669537687360*x^5*y^2*z^2 + 43144448117047992*x^6*y^2*z^2 + 9885852853548583652*x^3*y^3*z^2 + 1484638904835468304*x^4*y^3*z^2 + 48864769586829144*x^5*y^3*z^2 + 7079126748786639924*x^2*y^4*z^2 + 633951649145072232*x^3*y^4*z^2 + 967766612779980*x^4*y^4*z^2 + 2060342859721484754*x*y^5*z^2 + 5032386386455896*x^3*y^5*z^2 + 10903503837321108*x^2*y^6*z^2 + 3616433666434055376*x^6*z^3 + 690366384783509616*x^7*z^3 + 70205535546178032*x^8*z^3 + 37848129188688*x^9*z^3 + 19773977139660074032*x^5*y*z^3 + 3198236238997765056*x^6*y*z^3 + 216022855176507288*x^7*y*z^3 + 1035864064363128*x^8*y*z^3 + 34983675784095793404*x^4*y^2*z^3 + 4957330046780280988*x^5*y^2*z^3 + 345622757183223520*x^6*y^2*z^3 + 7743875303059896*x^7*y^2*z^3 + 29252012896859981540*x^3*y^3*z^3 + 5323151536526160428*x^4*y^3*z^3 + 399710474378779928*x^5*y^3*z^3 + 8770599669430872*x^6*y^3*z^3 + 16341864733517417536*x^2*y^4*z^3 + 3811837480115883036*x^3*y^4*z^3 + 170679290154442524*x^4*y^4*z^3 + 173701699729740*x^5*y^4*z^3 + 6004930898846378642*x*y^5*z^3 + 1109415386003876406*x^2*y^5*z^3 + 903248838594648*x^4*y^5*z^3 + 686780953240494918*y^6*z^3 + 1957039150288404*x^3*y^6*z^3 + 8288808449286582360*x^6*z^4 + 1669123230661871712*x^7*z^4 + 159315319565425296*x^8*z^4 + 10800851622488928*x^9*z^4 + 4367091829464*x^10*z^4 + 34988111651145478956*x^5*y*z^4 + 9126450987535418784*x^6*y*z^4 + 738054516691791936*x^7*y*z^4 + 33234285411770352*x^8*y*z^4 + 119522776657284*x^9*y*z^4 + 70861992647048240976*x^4*y^2*z^4 + 16146311900351904648*x^5*y^2*z^4 + 1143999241564680228*x^6*y^2*z^4 + 53172731874342080*x^7*y^2*z^4 + 893524073429988*x^8*y^2*z^4 + 64901797994799805728*x^3*y^3*z^4 + 13500929029319991480*x^4*y^3*z^4 + 1228419585352190868*x^5*y^3*z^4 + 61493919135196912*x^6*y^3*z^4 + 1011992269549716*x^7*y^3*z^4 + 29764780165999182798*x^2*y^4*z^4 + 7542399107777269632*x^3*y^4*z^4 + 879654803103665316*x^4*y^4*z^4 + 26258352331452696*x^5*y^4*z^4 + 20042503814970*x^6*y^4*z^4 + 8520418532313043460*x*y^5*z^4 + 2771506568698328604*x^2*y^5*z^4 + 256018935231663786*x^3*y^5*z^4 + 104221019837844*x^5*y^5*z^4 + 1496830282703642770*y^6*z^4 + 316975824572536116*x*y^6*z^4 + 225812209648662*x^4*y^6*z^4 + 12478820794153574328*x^6*z^5 + 3188003249725608600*x^7*z^5 + 320985236665744560*x^8*z^5 + 20425040969926320*x^9*z^5 + 1038543425239320*x^10*z^5 + 335930140728*x^11*z^5 + 40486000582710103668*x^5*y*z^5 + 13456966019671338060*x^6*y*z^5 + 1755086728372195920*x^7*y*z^5 + 94622373934845120*x^8*y*z^5 + 3195604366516380*x^9*y*z^5 + 9194059742868*x^10*y*z^5 + 78096688337999122428*x^4*y^2*z^5 + 27254612556557015760*x^5*y^2*z^5 + 3105059980836904740*x^6*y^2*z^5 + 146666569431369260*x^7*y^2*z^5 + 5112762680225200*x^8*y^2*z^5 + 68732621033076*x^9*y^2*z^5 + 87606408995348855976*x^3*y^3*z^5 + 24962229997999925280*x^4*y^3*z^5 + 2596332505638459900*x^5*y^3*z^5 + 157489690429768060*x^6*y^3*z^5 + 5912876839922780*x^7*y^3*z^5 + 77845559196132*x^8*y^3*z^5 + 47985094966363342710*x^2*y^4*z^5 + 11447992371538147230*x^3*y^4*z^5 + 1450461366880244160*x^4*y^4*z^5 + 112776256808162220*x^5*y^4*z^5 + 2524841570331990*x^6*y^4*z^5 + 1541731062690*x^7*y^4*z^5 + 11985270642334730156*x*y^5*z^5 + 3277084050889632100*x^2*y^5*z^5 + 532982032441986270*x^3*y^5*z^5 + 32822940414315870*x^4*y^5*z^5 + 8017001525988*x^6*y^5*z^5 + 1565914757289964744*y^6*z^5 + 575703954886016450*x*y^6*z^5 + 60956889340872330*x^2*y^6*z^5 + 17370169972974*x^5*y^6*z^5 + 10886608328819687568*x^6*z^6 + 3839637167431869024*x^7*z^6 + 490462038419324400*x^8*z^6 + 32921562734948160*x^9*z^6 + 1571156997686640*x^10*z^6 + 63910364630112*x^11*z^6 + 17227186704*x^12*z^6 + 46533251653536574576*x^5*y*z^6 + 12457230948526185744*x^6*y*z^6 + 2070302464564821240*x^7*y*z^6 + 180008895217661120*x^8*y*z^6 + 7278644148834240*x^9*y*z^6 + 196652576401008*x^10*y*z^6 + 471490243224*x^11*y*z^6 + 67963447300505832140*x^4*y^2*z^6 + 24029750257845883824*x^5*y^2*z^6 + 4193017316393387040*x^6*y^2*z^6 + 318467690342246640*x^7*y^2*z^6 + 11282043802413020*x^8*y^2*z^6 + 314631549552320*x^9*y^2*z^6 + 3524749796568*x^10*y^2*z^6 + 67215935595702380604*x^3*y^3*z^6 + 26955818152415032608*x^4*y^3*z^6 + 3840343076615373120*x^5*y^3*z^6 + 266290513398816400*x^6*y^3*z^6 + 12114591571520620*x^7*y^3*z^6 + 363869343995248*x^8*y^3*z^6 + 3992079958776*x^9*y^3*z^6 + 42111845499472750092*x^2*y^4*z^6 + 14764644605034874680*x^3*y^4*z^6 + 1761229595621253420*x^4*y^4*z^6 + 148765268397973760*x^5*y^4*z^6 + 8675096677550940*x^6*y^4*z^6 + 155374865866584*x^7*y^4*z^6 + 79063131420*x^8*y^4*z^6 + 11853233451261463898*x*y^5*z^6 + 3687775582256840048*x^2*y^5*z^6 + 504166777059943400*x^3*y^5*z^6 + 54664823840203720*x^4*y^5*z^6 + 2524841570331990*x^5*y^5*z^6 + 411128283384*x^7*y^5*z^6 + 1023867341304976948*y^6*z^6 + 481819925319989152*x*y^6*z^6 + 88569839213233300*x^2*y^6*z^6 + 6251988650345880*x^3*y^6*z^6 + 890777947332*x^6*y^6*z^6 + 2029804685579707920*x^6*z^7 + 2512294229727620208*x^7*z^7 + 443035057780600272*x^8*z^7 + 37727849109178800*x^9*z^7 + 1899320927016240*x^10*z^7 + 72514938354768*x^11*z^7 + 2458090947312*x^12*z^7 + 567929232*x^13*z^7 + 29926949372331541920*x^5*y*z^7 + 10738442689277671056*x^6*y*z^7 + 1437372801753021432*x^7*y*z^7 + 159254035735755480*x^8*y*z^7 + 10385128570249680*x^9*y*z^7 + 335937422253888*x^10*y*z^7 + 7563560630808*x^11*y*z^7 + 15543634392*x^12*y*z^7 + 48617979170333023412*x^4*y^2*z^7 + 15683872453962884340*x^5*y^2*z^7 + 2772663491289909672*x^6*y^2*z^7 + 322539793568722080*x^7*y^2*z^7 + 18373135981283460*x^8*y^2*z^7 + 520709713957524*x^9*y^2*z^7 + 12101213444320*x^10*y^2*z^7 + 116200542744*x^11*y^2*z^7 + 35241133177267229212*x^3*y^3*z^7 + 15511369752854395524*x^4*y^3*z^7 + 3110286709894042224*x^5*y^3*z^7 + 295411005893490240*x^6*y^3*z^7 + 15362914234547100*x^7*y^3*z^7 + 559134995608644*x^8*y^3*z^7 + 13994974769048*x^9*y^3*z^7 + 131607031608*x^10*y^3*z^7 + 18443593035724063584*x^2*y^4*z^7 + 9718118192186019252*x^3*y^4*z^7 + 1703612839042485540*x^4*y^4*z^7 + 135479199663173340*x^5*y^4*z^7 + 8582611638344640*x^6*y^4*z^7 + 400389077425428*x^7*y^4*z^7 + 5975956379484*x^8*y^4*z^7 + 2606476860*x^9*y^4*z^7 + 6437035799624485250*x*y^5*z^7 + 2735361565675722438*x^2*y^5*z^7 + 425512567183481544*x^3*y^5*z^7 + 38782059773841800*x^4*y^5*z^7 + 3153739836934830*x^5*y^5*z^7 + 116531149399938*x^6*y^5*z^7 + 13553679672*x^8*y^5*z^7 + 669451723160946466*y^6*z^7 + 236277078762686988*x*y^6*z^7 + 55594606767691056*x^2*y^6*z^7 + 6813064554864100*x^3*y^6*z^7 + 360691652904570*x^4*y^6*z^7 + 29366305956*x^7*y^6*z^7 + 74620207503942516*x^6*z^8 + 312277643935339680*x^7*z^8 + 193253402286740016*x^8*z^8 + 22719746552851296*x^9*z^8 + 1451071119583800*x^10*z^8 + 58440643908192*x^11*z^8 + 1859357393712*x^12*z^8 + 54023976864*x^13*z^8 + 10921716*x^14*z^8 + 2026909161098745222*x^5*y*z^8 + 4604146057281775680*x^6*y*z^8 + 826034053021359312*x^7*y*z^8 + 73711425730924176*x^8*y*z^8 + 6125155220605980*x^9*y*z^8 + 319542417546144*x^10*y*z^8 + 8613780057792*x^11*y*z^8 + 166232101776*x^12*y*z^8 + 298916046*x^13*y*z^8 + 14905844498073365954*x^4*y^2*z^8 + 7479689103128157448*x^5*y^2*z^8 + 1206451727227914180*x^6*y^2*z^8 + 142187871348200496*x^7*y^2*z^8 + 12405376675720080*x^8*y^2*z^8 + 565327260962568*x^9*y^2*z^8 + 13351531127116*x^10*y^2*z^8 + 265960735040*x^11*y^2*z^8 + 2234625822*x^12*y^2*z^8 + 15685740709286130730*x^3*y^3*z^8 + 5421712796502650648*x^4*y^3*z^8 + 1193182288681107348*x^5*y^3*z^8 + 159501882558668832*x^6*y^3*z^8 + 11361961765134240*x^7*y^3*z^8 + 472705053370680*x^8*y^3*z^8 + 14336794759196*x^9*y^3*z^8 + 307581863056*x^10*y^3*z^8 + 2530904454*x^11*y^3*z^8 + 6907663103412415071*x^2*y^4*z^8 + 2837475851649855936*x^3*y^4*z^8 + 747547553245078404*x^4*y^4*z^8 + 87364760976537720*x^5*y^4*z^8 + 5210738448583590*x^6*y^4*z^8 + 264080358102912*x^7*y^4*z^8 + 10266386600652*x^8*y^4*z^8 + 131339700648*x^9*y^4*z^8 + 50124555*x^10*y^4*z^8 + 2491628011054646906*x*y^5*z^8 + 990313199942228500*x^2*y^5*z^8 + 210412428128901726*x^3*y^5*z^8 + 21821157291460592*x^4*y^5*z^8 + 1491617683609300*x^5*y^5*z^8 + 97038148828764*x^6*y^5*z^8 + 2987978189742*x^7*y^5*z^8 + 260647686*x^9*y^5*z^8 + 437718434374464997*y^6*z^8 + 102992572793991764*x*y^6*z^8 + 18175159904822076*x^2*y^6*z^8 + 2851005475266208*x^3*y^6*z^8 + 262040944417850*x^4*y^6*z^8 + 11098204704756*x^5*y^6*z^8 + 564736653*x^8*y^6*z^8 + 2863622567880582948*x^6*z^9 + 5740015961841732*x^7*z^9 + 12010678612897680*x^8*z^9 + 4955215443249744*x^9*z^9 + 436918202939448*x^10*z^9 + 22324171070520*x^11*z^9 + 749239024464*x^12*z^9 + 20432498832*x^13*z^9 + 519461316*x^14*z^9 + 93348*x^15*z^9 + 47226673111918274*x^5*y*z^9 + 155916089315288094*x^6*y*z^9 + 177082540664683680*x^7*y*z^9 + 21180360333881008*x^8*y*z^9 + 1417527417902388*x^9*y*z^9 + 94233157240092*x^10*y*z^9 + 4096697660848*x^11*y*z^9 + 94656923712*x^12*y*z^9 + 1598385594*x^13*y*z^9 + 2554838*x^14*y*z^9 + 625530651406917516*x^4*y^2*z^9 + 1146603422928720458*x^5*y^2*z^9 + 287680350120313748*x^6*y^2*z^9 + 30934659672510620*x^7*y^2*z^9 + 2734382141311548*x^8*y^2*z^9 + 190851948857232*x^9*y^2*z^9 + 7247785396956*x^10*y^2*z^9 + 146720122276*x^11*y^2*z^9 + 2557314760*x^12*y^2*z^9 + 19099366*x^13*y^2*z^9 + 2861223535139048638*x^3*y^3*z^9 + 1206595439175856210*x^4*y^3*z^9 + 208527415250101948*x^5*y^3*z^9 + 30594417658489932*x^6*y^3*z^9 + 3067343895359016*x^7*y^3*z^9 + 174799411771296*x^8*y^3*z^9 + 6060321197060*x^9*y^3*z^9 + 157547195156*x^10*y^3*z^9 + 2957517914*x^11*y^3*z^9 + 21631662*x^12*y^3*z^9 + 978839630442306113*x^2*y^4*z^9 + 531358700262493467*x^3*y^4*z^9 + 109133686601917536*x^4*y^4*z^9 + 19167885980643036*x^5*y^4*z^9 + 1680091557241110*x^6*y^4*z^9 + 80165206901286*x^7*y^4*z^9 + 3385645616704*x^8*y^4*z^9 + 112817435172*x^9*y^4*z^9 + 1262881737*x^10*y^4*z^9 + 428415*x^11*y^4*z^9 + 191663693158049762*x^2*y^5*z^9 + 38088969228547250*x^3*y^5*z^9 + 5395190464843634*x^4*y^5*z^9 + 419637640220396*x^5*y^5*z^9 + 22947964363220*x^6*y^5*z^9 + 1244078831138*x^7*y^5*z^9 + 32834925162*x^8*y^5*z^9 + 2227758*x^10*y^5*z^9 + 33670648798035769*x*y^6*z^9 + 3961252799768914*x^2*y^6*z^9 + 466029741149284*x^3*y^6*z^9 + 54827028370504*x^4*y^6*z^9 + 4031399144890*x^5*y^6*z^9 + 142284675702*x^6*y^6*z^9 + 4826809*x^9*y^6*z^9 in I Output: Magma V2.10-22 Sat Apr 3 2004 23:57:30 on modular [Seed = 3788387381] ------------------------------------- >> P2 := 17*(x + 13*y)*z + 17*x*(13 + x*z); ^ User error: bad syntax >> I := ideal; ^ User error: Identifier 'P1' has not been declared or assigned >> 4826809*x^9*y^6*z^9 in I; ^ User error: Identifier 'I' has not been declared or assigned Total time: 2.630 seconds, Total memory usage: 2.60MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 23:57:43 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 289*x*z + (x + 13*y)*(13 + x*z); > P2 := 17*(x + 13*y)*z + 17*x*(13 + x*z); > I := ideal; > 989908807470804*x^6 + 27092777969116574*x^5*y + 202539214771697518*x^4*y^2 + 229392946115947926*x^3*y^3 + 4543126598883795*x^2*y^4 + 23624258314195734*x*y^5 + 51185893014090757*y^6 + 423740553832288836*x^6*z + 685321482095172*x^7*z + 1303852233029633274*x^5*y*z + 18756538594003782*x^6*y*z + 2086080212998741960*x^4*y^2*z + 140219456380405974*x^5*y^2*z + 2412538220357635994*x^3*y^3*z + 158810501157194718*x^4*y^3*z + 1030171429860742377*x^2*y^4*z + 3145241491534935*x^3*y^4*z + 16355255755981662*x^2*y^5*z + 35436387471293601*x*y^6*z + 1282109000312232144*x^6*z^2 + 260763417742946976*x^7*z^2 + 210868148336976*x^8*z^2 + 5939581586710135104*x^5*y*z^2 + 802370604941312784*x^6*y*z^2 + 5771242644308856*x^7*y*z^2 + 9206470086877664692*x^4*y^2*z^2 + 1283741669537687360*x^5*y^2*z^2 + 43144448117047992*x^6*y^2*z^2 + 9885852853548583652*x^3*y^3*z^2 + 1484638904835468304*x^4*y^3*z^2 + 48864769586829144*x^5*y^3*z^2 + 7079126748786639924*x^2*y^4*z^2 + 633951649145072232*x^3*y^4*z^2 + 967766612779980*x^4*y^4*z^2 + 2060342859721484754*x*y^5*z^2 + 5032386386455896*x^3*y^5*z^2 + 10903503837321108*x^2*y^6*z^2 + 3616433666434055376*x^6*z^3 + 690366384783509616*x^7*z^3 + 70205535546178032*x^8*z^3 + 37848129188688*x^9*z^3 + 19773977139660074032*x^5*y*z^3 + 3198236238997765056*x^6*y*z^3 + 216022855176507288*x^7*y*z^3 + 1035864064363128*x^8*y*z^3 + 34983675784095793404*x^4*y^2*z^3 + 4957330046780280988*x^5*y^2*z^3 + 345622757183223520*x^6*y^2*z^3 + 7743875303059896*x^7*y^2*z^3 + 29252012896859981540*x^3*y^3*z^3 + 5323151536526160428*x^4*y^3*z^3 + 399710474378779928*x^5*y^3*z^3 + 8770599669430872*x^6*y^3*z^3 + 16341864733517417536*x^2*y^4*z^3 + 3811837480115883036*x^3*y^4*z^3 + 170679290154442524*x^4*y^4*z^3 + 173701699729740*x^5*y^4*z^3 + 6004930898846378642*x*y^5*z^3 + 1109415386003876406*x^2*y^5*z^3 + 903248838594648*x^4*y^5*z^3 + 686780953240494918*y^6*z^3 + 1957039150288404*x^3*y^6*z^3 + 8288808449286582360*x^6*z^4 + 1669123230661871712*x^7*z^4 + 159315319565425296*x^8*z^4 + 10800851622488928*x^9*z^4 + 4367091829464*x^10*z^4 + 34988111651145478956*x^5*y*z^4 + 9126450987535418784*x^6*y*z^4 + 738054516691791936*x^7*y*z^4 + 33234285411770352*x^8*y*z^4 + 119522776657284*x^9*y*z^4 + 70861992647048240976*x^4*y^2*z^4 + 16146311900351904648*x^5*y^2*z^4 + 1143999241564680228*x^6*y^2*z^4 + 53172731874342080*x^7*y^2*z^4 + 893524073429988*x^8*y^2*z^4 + 64901797994799805728*x^3*y^3*z^4 + 13500929029319991480*x^4*y^3*z^4 + 1228419585352190868*x^5*y^3*z^4 + 61493919135196912*x^6*y^3*z^4 + 1011992269549716*x^7*y^3*z^4 + 29764780165999182798*x^2*y^4*z^4 + 7542399107777269632*x^3*y^4*z^4 + 879654803103665316*x^4*y^4*z^4 + 26258352331452696*x^5*y^4*z^4 + 20042503814970*x^6*y^4*z^4 + 8520418532313043460*x*y^5*z^4 + 2771506568698328604*x^2*y^5*z^4 + 256018935231663786*x^3*y^5*z^4 + 104221019837844*x^5*y^5*z^4 + 1496830282703642770*y^6*z^4 + 316975824572536116*x*y^6*z^4 + 225812209648662*x^4*y^6*z^4 + 12478820794153574328*x^6*z^5 + 3188003249725608600*x^7*z^5 + 320985236665744560*x^8*z^5 + 20425040969926320*x^9*z^5 + 1038543425239320*x^10*z^5 + 335930140728*x^11*z^5 + 40486000582710103668*x^5*y*z^5 + 13456966019671338060*x^6*y*z^5 + 1755086728372195920*x^7*y*z^5 + 94622373934845120*x^8*y*z^5 + 3195604366516380*x^9*y*z^5 + 9194059742868*x^10*y*z^5 + 78096688337999122428*x^4*y^2*z^5 + 27254612556557015760*x^5*y^2*z^5 + 3105059980836904740*x^6*y^2*z^5 + 146666569431369260*x^7*y^2*z^5 + 5112762680225200*x^8*y^2*z^5 + 68732621033076*x^9*y^2*z^5 + 87606408995348855976*x^3*y^3*z^5 + 24962229997999925280*x^4*y^3*z^5 + 2596332505638459900*x^5*y^3*z^5 + 157489690429768060*x^6*y^3*z^5 + 5912876839922780*x^7*y^3*z^5 + 77845559196132*x^8*y^3*z^5 + 47985094966363342710*x^2*y^4*z^5 + 11447992371538147230*x^3*y^4*z^5 + 1450461366880244160*x^4*y^4*z^5 + 112776256808162220*x^5*y^4*z^5 + 2524841570331990*x^6*y^4*z^5 + 1541731062690*x^7*y^4*z^5 + 11985270642334730156*x*y^5*z^5 + 3277084050889632100*x^2*y^5*z^5 + 532982032441986270*x^3*y^5*z^5 + 32822940414315870*x^4*y^5*z^5 + 8017001525988*x^6*y^5*z^5 + 1565914757289964744*y^6*z^5 + 575703954886016450*x*y^6*z^5 + 60956889340872330*x^2*y^6*z^5 + 17370169972974*x^5*y^6*z^5 + 10886608328819687568*x^6*z^6 + 3839637167431869024*x^7*z^6 + 490462038419324400*x^8*z^6 + 32921562734948160*x^9*z^6 + 1571156997686640*x^10*z^6 + 63910364630112*x^11*z^6 + 17227186704*x^12*z^6 + 46533251653536574576*x^5*y*z^6 + 12457230948526185744*x^6*y*z^6 + 2070302464564821240*x^7*y*z^6 + 180008895217661120*x^8*y*z^6 + 7278644148834240*x^9*y*z^6 + 196652576401008*x^10*y*z^6 + 471490243224*x^11*y*z^6 + 67963447300505832140*x^4*y^2*z^6 + 24029750257845883824*x^5*y^2*z^6 + 4193017316393387040*x^6*y^2*z^6 + 318467690342246640*x^7*y^2*z^6 + 11282043802413020*x^8*y^2*z^6 + 314631549552320*x^9*y^2*z^6 + 3524749796568*x^10*y^2*z^6 + 67215935595702380604*x^3*y^3*z^6 + 26955818152415032608*x^4*y^3*z^6 + 3840343076615373120*x^5*y^3*z^6 + 266290513398816400*x^6*y^3*z^6 + 12114591571520620*x^7*y^3*z^6 + 363869343995248*x^8*y^3*z^6 + 3992079958776*x^9*y^3*z^6 + 42111845499472750092*x^2*y^4*z^6 + 14764644605034874680*x^3*y^4*z^6 + 1761229595621253420*x^4*y^4*z^6 + 148765268397973760*x^5*y^4*z^6 + 8675096677550940*x^6*y^4*z^6 + 155374865866584*x^7*y^4*z^6 + 79063131420*x^8*y^4*z^6 + 11853233451261463898*x*y^5*z^6 + 3687775582256840048*x^2*y^5*z^6 + 504166777059943400*x^3*y^5*z^6 + 54664823840203720*x^4*y^5*z^6 + 2524841570331990*x^5*y^5*z^6 + 411128283384*x^7*y^5*z^6 + 1023867341304976948*y^6*z^6 + 481819925319989152*x*y^6*z^6 + 88569839213233300*x^2*y^6*z^6 + 6251988650345880*x^3*y^6*z^6 + 890777947332*x^6*y^6*z^6 + 2029804685579707920*x^6*z^7 + 2512294229727620208*x^7*z^7 + 443035057780600272*x^8*z^7 + 37727849109178800*x^9*z^7 + 1899320927016240*x^10*z^7 + 72514938354768*x^11*z^7 + 2458090947312*x^12*z^7 + 567929232*x^13*z^7 + 29926949372331541920*x^5*y*z^7 + 10738442689277671056*x^6*y*z^7 + 1437372801753021432*x^7*y*z^7 + 159254035735755480*x^8*y*z^7 + 10385128570249680*x^9*y*z^7 + 335937422253888*x^10*y*z^7 + 7563560630808*x^11*y*z^7 + 15543634392*x^12*y*z^7 + 48617979170333023412*x^4*y^2*z^7 + 15683872453962884340*x^5*y^2*z^7 + 2772663491289909672*x^6*y^2*z^7 + 322539793568722080*x^7*y^2*z^7 + 18373135981283460*x^8*y^2*z^7 + 520709713957524*x^9*y^2*z^7 + 12101213444320*x^10*y^2*z^7 + 116200542744*x^11*y^2*z^7 + 35241133177267229212*x^3*y^3*z^7 + 15511369752854395524*x^4*y^3*z^7 + 3110286709894042224*x^5*y^3*z^7 + 295411005893490240*x^6*y^3*z^7 + 15362914234547100*x^7*y^3*z^7 + 559134995608644*x^8*y^3*z^7 + 13994974769048*x^9*y^3*z^7 + 131607031608*x^10*y^3*z^7 + 18443593035724063584*x^2*y^4*z^7 + 9718118192186019252*x^3*y^4*z^7 + 1703612839042485540*x^4*y^4*z^7 + 135479199663173340*x^5*y^4*z^7 + 8582611638344640*x^6*y^4*z^7 + 400389077425428*x^7*y^4*z^7 + 5975956379484*x^8*y^4*z^7 + 2606476860*x^9*y^4*z^7 + 6437035799624485250*x*y^5*z^7 + 2735361565675722438*x^2*y^5*z^7 + 425512567183481544*x^3*y^5*z^7 + 38782059773841800*x^4*y^5*z^7 + 3153739836934830*x^5*y^5*z^7 + 116531149399938*x^6*y^5*z^7 + 13553679672*x^8*y^5*z^7 + 669451723160946466*y^6*z^7 + 236277078762686988*x*y^6*z^7 + 55594606767691056*x^2*y^6*z^7 + 6813064554864100*x^3*y^6*z^7 + 360691652904570*x^4*y^6*z^7 + 29366305956*x^7*y^6*z^7 + 74620207503942516*x^6*z^8 + 312277643935339680*x^7*z^8 + 193253402286740016*x^8*z^8 + 22719746552851296*x^9*z^8 + 1451071119583800*x^10*z^8 + 58440643908192*x^11*z^8 + 1859357393712*x^12*z^8 + 54023976864*x^13*z^8 + 10921716*x^14*z^8 + 2026909161098745222*x^5*y*z^8 + 4604146057281775680*x^6*y*z^8 + 826034053021359312*x^7*y*z^8 + 73711425730924176*x^8*y*z^8 + 6125155220605980*x^9*y*z^8 + 319542417546144*x^10*y*z^8 + 8613780057792*x^11*y*z^8 + 166232101776*x^12*y*z^8 + 298916046*x^13*y*z^8 + 14905844498073365954*x^4*y^2*z^8 + 7479689103128157448*x^5*y^2*z^8 + 1206451727227914180*x^6*y^2*z^8 + 142187871348200496*x^7*y^2*z^8 + 12405376675720080*x^8*y^2*z^8 + 565327260962568*x^9*y^2*z^8 + 13351531127116*x^10*y^2*z^8 + 265960735040*x^11*y^2*z^8 + 2234625822*x^12*y^2*z^8 + 15685740709286130730*x^3*y^3*z^8 + 5421712796502650648*x^4*y^3*z^8 + 1193182288681107348*x^5*y^3*z^8 + 159501882558668832*x^6*y^3*z^8 + 11361961765134240*x^7*y^3*z^8 + 472705053370680*x^8*y^3*z^8 + 14336794759196*x^9*y^3*z^8 + 307581863056*x^10*y^3*z^8 + 2530904454*x^11*y^3*z^8 + 6907663103412415071*x^2*y^4*z^8 + 2837475851649855936*x^3*y^4*z^8 + 747547553245078404*x^4*y^4*z^8 + 87364760976537720*x^5*y^4*z^8 + 5210738448583590*x^6*y^4*z^8 + 264080358102912*x^7*y^4*z^8 + 10266386600652*x^8*y^4*z^8 + 131339700648*x^9*y^4*z^8 + 50124555*x^10*y^4*z^8 + 2491628011054646906*x*y^5*z^8 + 990313199942228500*x^2*y^5*z^8 + 210412428128901726*x^3*y^5*z^8 + 21821157291460592*x^4*y^5*z^8 + 1491617683609300*x^5*y^5*z^8 + 97038148828764*x^6*y^5*z^8 + 2987978189742*x^7*y^5*z^8 + 260647686*x^9*y^5*z^8 + 437718434374464997*y^6*z^8 + 102992572793991764*x*y^6*z^8 + 18175159904822076*x^2*y^6*z^8 + 2851005475266208*x^3*y^6*z^8 + 262040944417850*x^4*y^6*z^8 + 11098204704756*x^5*y^6*z^8 + 564736653*x^8*y^6*z^8 + 2863622567880582948*x^6*z^9 + 5740015961841732*x^7*z^9 + 12010678612897680*x^8*z^9 + 4955215443249744*x^9*z^9 + 436918202939448*x^10*z^9 + 22324171070520*x^11*z^9 + 749239024464*x^12*z^9 + 20432498832*x^13*z^9 + 519461316*x^14*z^9 + 93348*x^15*z^9 + 47226673111918274*x^5*y*z^9 + 155916089315288094*x^6*y*z^9 + 177082540664683680*x^7*y*z^9 + 21180360333881008*x^8*y*z^9 + 1417527417902388*x^9*y*z^9 + 94233157240092*x^10*y*z^9 + 4096697660848*x^11*y*z^9 + 94656923712*x^12*y*z^9 + 1598385594*x^13*y*z^9 + 2554838*x^14*y*z^9 + 625530651406917516*x^4*y^2*z^9 + 1146603422928720458*x^5*y^2*z^9 + 287680350120313748*x^6*y^2*z^9 + 30934659672510620*x^7*y^2*z^9 + 2734382141311548*x^8*y^2*z^9 + 190851948857232*x^9*y^2*z^9 + 7247785396956*x^10*y^2*z^9 + 146720122276*x^11*y^2*z^9 + 2557314760*x^12*y^2*z^9 + 19099366*x^13*y^2*z^9 + 2861223535139048638*x^3*y^3*z^9 + 1206595439175856210*x^4*y^3*z^9 + 208527415250101948*x^5*y^3*z^9 + 30594417658489932*x^6*y^3*z^9 + 3067343895359016*x^7*y^3*z^9 + 174799411771296*x^8*y^3*z^9 + 6060321197060*x^9*y^3*z^9 + 157547195156*x^10*y^3*z^9 + 2957517914*x^11*y^3*z^9 + 21631662*x^12*y^3*z^9 + 978839630442306113*x^2*y^4*z^9 + 531358700262493467*x^3*y^4*z^9 + 109133686601917536*x^4*y^4*z^9 + 19167885980643036*x^5*y^4*z^9 + 1680091557241110*x^6*y^4*z^9 + 80165206901286*x^7*y^4*z^9 + 3385645616704*x^8*y^4*z^9 + 112817435172*x^9*y^4*z^9 + 1262881737*x^10*y^4*z^9 + 428415*x^11*y^4*z^9 + 191663693158049762*x^2*y^5*z^9 + 38088969228547250*x^3*y^5*z^9 + 5395190464843634*x^4*y^5*z^9 + 419637640220396*x^5*y^5*z^9 + 22947964363220*x^6*y^5*z^9 + 1244078831138*x^7*y^5*z^9 + 32834925162*x^8*y^5*z^9 + 2227758*x^10*y^5*z^9 + 33670648798035769*x*y^6*z^9 + 3961252799768914*x^2*y^6*z^9 + 466029741149284*x^3*y^6*z^9 + 54827028370504*x^4*y^6*z^9 + 4031399144890*x^5*y^6*z^9 + 142284675702*x^6*y^6*z^9 + 4826809*x^9*y^6*z^9 in I Output: Magma V2.10-22 Sat Apr 3 2004 23:57:40 on modular [Seed = 4141425500] ------------------------------------- true Total time: 2.680 seconds, Total memory usage: 2.83MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sat Apr 3 23:59:16 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 289*x*z + (x + 13*y)*(13 + x*z); > P2 := 17*(x + 13*y)*z + 17*x*(13 + x*z); > I := ideal; > 26142129528265296*x^8 + 350592293149087808*x^7*y + 219445098553122832*x^6*y^2 + 1125678276570319238*x^5*y^3 + 1179979909358689244*x^4*y^4 + 344695169387106395*x^3*y^5 + 8480502984583084*x^2*y^6 + 31499011085594312*x*y^7 + 51185893014090757*y^8 + 256518781297404912*x^8*z + 14076531284450544*x^9*z + 3647215343462525120*x^7*y*z + 188780465541816512*x^8*y*z + 4642951202108657776*x^6*y^2*z + 118162745374758448*x^7*y^2*z + 8070796348542335590*x^5*y^3*z + 606134456614787282*x^6*y^3*z + 7112991687309346774*x^4*y^4*z + 635373797346986516*x^5*y^4*z + 4745832484572137959*x^3*y^5*z + 185605091208441905*x^4*y^5*z + 2174806351928233907*x^2*y^6*z + 4566424684006276*x^3*y^6*z + 16961005969166168*x^2*y^7*z + 27561634699895023*x*y^8*z + 627882835597230096*x^8*z^2 + 118393283675725344*x^9*z^2 + 3248430296411664*x^10*z^2 + 9649346032462863168*x^7*y*z^2 + 1683330158521165440*x^8*y*z^2 + 43564722817342272*x^9*y*z^2 + 21985854269853369168*x^6*y^2*z^2 + 2142900554819380512*x^7*y^2*z^2 + 27268325855713488*x^8*y^2*z^2 + 36502596426697324950*x^5*y^3*z^2 + 3724982930096462580*x^6*y^3*z^2 + 139877182295720142*x^7*y^3*z^2 + 26712246707467806888*x^4*y^4*z^2 + 3282919240296621588*x^5*y^4*z^2 + 146624722464689196*x^6*y^4*z^2 + 15395678351192988147*x^3*y^5*z^2 + 2190384223648679058*x^4*y^5*z^2 + 42831944125025055*x^5*y^5*z^2 + 8188542134790516330*x^2*y^6*z^2 + 1003756777813031034*x^3*y^6*z^2 + 1053790311693756*x^4*y^6*z^2 + 1030171429860742377*x*y^7*z^2 + 3914078300576808*x^3*y^7*z^2 + 6360377238437313*x^2*y^8*z^2 + 4063162057454326320*x^8*z^3 + 241493398306626960*x^9*z^3 + 22767939168408720*x^10*z^3 + 416465422616880*x^11*z^3 + 17723260214027306432*x^7*y*z^3 + 3711286935562639680*x^8*y*z^3 + 323717338177147200*x^9*y*z^3 + 5585220874018240*x^10*y*z^3 + 45648934875353188912*x^6*y^2*z^3 + 8456097796097449680*x^7*y^2*z^3 + 412096260542188560*x^8*y^2*z^3 + 3495939212270960*x^9*y^2*z^3 + 78295461025947546342*x^5*y^3*z^3 + 14039460164114355750*x^6*y^3*z^3 + 716342871172396650*x^7*y^3*z^3 + 17932972089194890*x^8*y^3*z^3 + 65612160166770194978*x^4*y^4*z^3 + 10273941041333771880*x^5*y^4*z^3 + 631330623133965690*x^6*y^4*z^3 + 18798041341626820*x^7*y^4*z^3 + 33429956412359035399*x^3*y^5*z^3 + 5921414750458841595*x^4*y^5*z^3 + 421227735317053665*x^5*y^5*z^3 + 5491274887823725*x^6*y^5*z^3 + 13351590661962402681*x^2*y^6*z^3 + 3149439282611737050*x^3*y^6*z^3 + 193030149579429045*x^4*y^6*z^3 + 135101322012020*x^5*y^6*z^3 + 3125733825645842255*x*y^7*z^3 + 396219780715670145*x^2*y^7*z^3 + 501804910330360*x^4*y^7*z^3 + 457853968826996612*y^8*z^3 + 815432979286835*x^3*y^8*z^3 + 6847176120740892144*x^8*z^4 + 1250203709985946560*x^9*z^4 + 37152830508711840*x^10*z^4 + 2335173248041920*x^11*z^4 + 32035801739760*x^12*z^4 + 26741348175911994560*x^7*y*z^4 + 5453310835085325056*x^8*y*z^4 + 570967220855790720*x^9*y*z^4 + 33201778274579200*x^10*y*z^4 + 429632374924480*x^11*y*z^4 + 61895346234056461360*x^6*y^2*z^4 + 14045826115493288896*x^7*y^2*z^4 + 1300938122476530720*x^8*y^2*z^4 + 42266283132532160*x^9*y^2*z^4 + 268918400943920*x^10*y^2*z^4 + 86341740539160796482*x^5*y^3*z^4 + 24090911084906937336*x^6*y^3*z^4 + 2159916948325285500*x^7*y^3*z^4 + 73471063709989400*x^8*y^3*z^4 + 1379459391476530*x^9*y^3*z^4 + 89342524586857102652*x^4*y^4*z^4 + 20188356974390829224*x^5*y^4*z^4 + 1580606314051349520*x^6*y^4*z^4 + 64751858782970840*x^7*y^4*z^4 + 1446003180125140*x^8*y^4*z^4 + 52401255280180703689*x^3*y^5*z^4 + 10286140434572010892*x^4*y^5*z^4 + 910986884685975630*x^5*y^5*z^4 + 43202844647902940*x^6*y^5*z^4 + 422405760601825*x^7*y^5*z^4 + 15071043840523778328*x^2*y^6*z^4 + 4108181742142277748*x^3*y^6*z^4 + 484529120401805700*x^4*y^6*z^4 + 19797964059428620*x^5*y^6*z^4 + 10392409385540*x^6*y^6*z^4 + 3408167412925217384*x*y^7*z^4 + 961764254044874540*x^2*y^7*z^4 + 60956889340872330*x^3*y^7*z^4 + 38600377717720*x^5*y^7*z^4 + 449049084811092831*y^8*z^4 + 140878144254460496*x*y^8*z^4 + 62725613791295*x^4*y^8*z^4 + 1203788450718683856*x^8*z^5 + 1580117566324821264*x^9*z^5 + 144254274229147680*x^10*z^5 + 2857910039131680*x^11*z^5 + 134721533540880*x^12*z^5 + 1478575464912*x^13*z^5 + 20091951048337856064*x^7*y*z^5 + 6171080348287383360*x^8*y*z^5 + 629228173279075968*x^9*y*z^5 + 43920555450445440*x^10*y*z^5 + 1915487208148800*x^11*y*z^5 + 19829186534976*x^12*y*z^5 + 62171356677831679824*x^6*y^2*z^5 + 14283541438628414160*x^7*y^2*z^5 + 1620672244095379488*x^8*y^2*z^5 + 100072163267425440*x^9*y^2*z^5 + 2438439411492240*x^10*y^2*z^5 + 12411618505104*x^11*y^2*z^5 + 62063492853335083266*x^5*y^3*z^5 + 19925017047498645342*x^6*y^3*z^5 + 2779720509796954308*x^7*y^3*z^5 + 166147457563483500*x^8*y^3*z^5 + 4238715214037850*x^9*y^3*z^5 + 63667356529686*x^10*y^3*z^5 + 63757761901504118682*x^4*y^4*z^5 + 20617505673890100612*x^5*y^4*z^5 + 2329425804737403372*x^6*y^4*z^5 + 121585101080873040*x^7*y^4*z^5 + 3735684160556010*x^8*y^4*z^5 + 66738608313468*x^9*y^4*z^5 + 43561314501882310653*x^3*y^5*z^5 + 12092597372349393159*x^4*y^5*z^5 + 1186862357835232026*x^5*y^5*z^5 + 70075914206613510*x^6*y^5*z^5 + 2492471806609785*x^7*y^5*z^5 + 19495650489315*x^8*y^5*z^5 + 12699892983494425605*x^2*y^6*z^5 + 3477933193967025768*x^3*y^6*z^5 + 474020970247185894*x^4*y^6*z^5 + 37271470800138900*x^5*y^6*z^5 + 1142190234197805*x^6*y^6*z^5 + 479649663948*x^7*y^6*z^5 + 3071602023914930844*x*y^7*z^5 + 786500172213511704*x^2*y^7*z^5 + 110972798543639370*x^3*y^7*z^5 + 4688991487759410*x^4*y^7*z^5 + 1781555894664*x^6*y^7*z^5 + 103626711879482961*x*y^8*z^5 + 16255170490899288*x^2*y^8*z^5 + 2895028328829*x^5*y^8*z^5 + 155817733597402032*x^8*z^6 + 185198223187489824*x^9*z^6 + 121547505101909328*x^10*z^6 + 7397655088674240*x^11*z^6 + 109919616889680*x^12*z^6 + 4145277955104*x^13*z^6 + 37912191408*x^14*z^6 + 4216627046648788928*x^7*y*z^6 + 3091069392051977856*x^8*y*z^6 + 474698488329798720*x^9*y*z^6 + 32268111450209024*x^10*y*z^6 + 1689252132709440*x^11*y*z^6 + 58938067943040*x^12*y*z^6 + 508440680384*x^13*y*z^6 + 30776377560317310064*x^6*y^2*z^6 + 9564824104281796896*x^7*y^2*z^6 + 1098733956817570320*x^8*y^2*z^6 + 83111397133096384*x^9*y^2*z^6 + 3848929356439440*x^10*y^2*z^6 + 75028904968992*x^11*y^2*z^6 + 318246628336*x^12*y^2*z^6 + 31771427315154847138*x^5*y^3*z^6 + 9548229669743858964*x^6*y^3*z^6 + 1532693619038357334*x^7*y^3*z^6 + 142549769733177144*x^8*y^3*z^6 + 6390286829364750*x^9*y^3*z^6 + 130422006585780*x^10*y^3*z^6 + 1632496321274*x^11*y^3*z^6 + 26629369590569610176*x^4*y^4*z^6 + 9808886446385249028*x^5*y^4*z^6 + 1585961974914623124*x^6*y^4*z^6 + 119457733576277096*x^7*y^4*z^6 + 4676350041572040*x^8*y^4*z^6 + 114944128017108*x^9*y^4*z^6 + 1711246367012*x^10*y^4*z^6 + 15846991825475540457*x^3*y^5*z^6 + 6701740692597278562*x^4*y^5*z^6 + 930199797873030243*x^5*y^5*z^6 + 60864736299242668*x^6*y^5*z^6 + 2695227469485135*x^7*y^5*z^6 + 76691440203378*x^8*y^5*z^6 + 499888474085*x^9*y^5*z^6 + 5201124926096584082*x^2*y^6*z^6 + 1953829689768373170*x^3*y^6*z^6 + 267533322612848136*x^4*y^6*z^6 + 24308767704983892*x^5*y^6*z^6 + 1433518107697650*x^6*y^6*z^6 + 35144314898394*x^7*y^6*z^6 + 12298709332*x^8*y^6*z^6 + 2343081031063312631*x*y^7*z^6 + 472554157525373976*x^2*y^7*z^6 + 60500013247193208*x^3*y^7*z^6 + 5690912745827660*x^4*y^7*z^6 + 180345826452285*x^5*y^7*z^6 + 45680920376*x^7*y^7*z^6 + 7971285529190997*x^2*y^8*z^6 + 833598486712784*x^3*y^8*z^6 + 74231495611*x^6*y^8*z^6 + 2864418892447017744*x^8*z^7 + 11985979507492464*x^9*z^7 + 7123008584134224*x^10*z^7 + 3116602694920752*x^11*z^7 + 142262597859120*x^12*z^7 + 1691071029072*x^13*z^7 + 53144589168*x^14*z^7 + 416617488*x^15*z^7 + 81166565219904320*x^7*y*z^7 + 324355926665291456*x^8*y*z^7 + 118887284309691456*x^9*y*z^7 + 12171756111020480*x^10*y*z^7 + 620540604811712*x^11*y*z^7 + 25988494349376*x^12*y*z^7 + 755616255680*x^13*y*z^7 + 5587260224*x^14*y*z^7 + 1143083218548238864*x^6*y^2*z^7 + 2367413658485946928*x^7*y^2*z^7 + 367877850164684496*x^8*y^2*z^7 + 28172665559424880*x^9*y^2*z^7 + 1598296098713392*x^10*y^2*z^7 + 59214297791376*x^11*y^2*z^7 + 961909038064*x^12*y^2*z^7 + 3497215696*x^13*y^2*z^7 + 6126035083681590194*x^5*y^3*z^7 + 2443955947319603626*x^6*y^3*z^7 + 367239602682456114*x^7*y^3*z^7 + 39299836385598906*x^8*y^3*z^7 + 2741341725638022*x^9*y^3*z^7 + 98312105067150*x^10*y^3*z^7 + 1672077007510*x^11*y^3*z^7 + 17939520014*x^12*y^3*z^7 + 8010426660200154606*x^4*y^4*z^7 + 2048413045428431552*x^5*y^4*z^7 + 377264863322509578*x^6*y^4*z^7 + 40665691664477516*x^7*y^4*z^7 + 2297264107236098*x^8*y^4*z^7 + 71943846793416*x^9*y^4*z^7 + 1473642666886*x^10*y^4*z^7 + 18804905132*x^11*y^4*z^7 + 3048488741176007701*x^3*y^5*z^7 + 1218999371190426189*x^4*y^5*z^7 + 257759257407587637*x^5*y^5*z^7 + 23851276868539237*x^6*y^5*z^7 + 1170475698062359*x^7*y^5*z^7 + 41465037992079*x^8*y^5*z^7 + 983223592351*x^9*y^5*z^7 + 5493279935*x^10*y^5*z^7 + 235694541586250383*x^2*y^6*z^7 + 400086532776660314*x^3*y^6*z^7 + 75147295760322045*x^4*y^6*z^7 + 6859828784944824*x^5*y^6*z^7 + 467476302018921*x^6*y^6*z^7 + 22054124733810*x^7*y^6*z^7 + 450568139723*x^8*y^6*z^7 + 135150652*x^9*y^6*z^7 + 437718434374464997*x*y^7*z^7 + 180237002389485587*x^2*y^7*z^7 + 18175159904822076*x^3*y^7*z^7 + 1551282390953672*x^4*y^7*z^7 + 109440629727455*x^5*y^7*z^7 + 2774551176189*x^6*y^7*z^7 + 501988136*x^8*y^7*z^7 + 204391936645923*x^3*y^8*z^7 + 16030740129092*x^4*y^8*z^7 + 815730721*x^7*y^8*z^7 in I Output: Magma V2.10-22 Sat Apr 3 2004 23:59:14 on modular [Seed = 3404012678] ------------------------------------- true Total time: 2.589 seconds, Total memory usage: 2.60MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sun Apr 4 00:07:38 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2-(x*y)^2); > P2 := (5^2-x^2); > P3 := (7^2-y^2); > I := ideal; > GroebnerBasis(I) Output: Magma V2.10-22 Sun Apr 4 2004 00:07:35 on modular [Seed = 3213912006] ------------------------------------- [ x^2 - 25, 25*y^2 - 9 ] Total time: 2.519 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sun Apr 4 00:07:57 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2-(x*y)^2); > P2 := (5^2-121*x^2); > P3 := (7^2-17^2*y^2); > I := ideal; > GroebnerBasis(I) Output: Magma V2.10-22 Sun Apr 4 2004 00:07:55 on modular [Seed = 3080220658] ------------------------------------- [ x^2*y^2 - 9, 121*x^2 - 25, 25*y^2 - 1089 ] Total time: 2.520 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sun Apr 4 00:08:22 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2-(x*y)^2); > P2 := (5^2-121*x^2); > P3 := (7^2-17^2*y^2); > I := ideal; > GroebnerBasis(I) > (3+x*y)(5-11*x)(7+17*y) Output: Magma V2.10-22 Sun Apr 4 2004 00:08:20 on modular [Seed = 2409650085] ------------------------------------- >> (3+x*y)(5-11*x)(7+17*y) ^ Runtime error: Bad argument types Argument types given: RngMPolElt, SeqEnum[RngMPolElt] Total time: 2.509 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sun Apr 4 00:08:35 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2-(x*y)^2); > P2 := (5^2-121*x^2); > P3 := (7^2-17^2*y^2); > I := ideal; > GroebnerBasis(I) > (3*x*y)(5-11*x)*(7+17*y) in I Output: Magma V2.10-22 Sun Apr 4 2004 00:08:32 on modular [Seed = 2275958713] ------------------------------------- >> (3*x*y)(5-11*x)*(7+17*y) in I ^ Runtime error: Bad argument types Argument types given: RngMPolElt, SeqEnum[RngMPolElt] Total time: 2.569 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sun Apr 4 00:08:44 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2-(x*y)^2); > P2 := (5^2-121*x^2); > P3 := (7^2-17^2*y^2); > I := ideal; > GroebnerBasis(I) > (3*x*y)*(5-11*x)*(7+17*y) in I Output: Magma V2.10-22 Sun Apr 4 2004 00:08:41 on modular [Seed = 2645706154] ------------------------------------- >> (3*x*y)*(5-11*x)*(7+17*y) in I ^ Runtime error: Bad argument types Argument types given: RngMPolElt, SeqEnum[RngMPolElt] Total time: 2.589 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sun Apr 4 00:08:54 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2-(x*y)^2); > P2 := (5^2-121*x^2); > P3 := (7^2-17^2*y^2); > I := ideal; > (3*x*y)*(5-11*x)*(7+17*y) in I Output: Magma V2.10-22 Sun Apr 4 2004 00:08:52 on modular [Seed = 2512014751] ------------------------------------- false Total time: 2.599 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sun Apr 4 00:09:04 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2-(x*y)^2); > P2 := (5^2-121*x^2); > P3 := (7^2-17^2*y^2); > I := ideal; > (3+x*y)*(5-11*x)*(7+17*y) in I Output: Magma V2.10-22 Sun Apr 4 2004 00:09:02 on modular [Seed = 1816376429] ------------------------------------- false Total time: 2.609 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sun Apr 4 00:09:11 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2-(x*y)^2); > P2 := (5^2-121*x^2); > P3 := (7^2-17^2*y^2); > I := ideal; > (3-x*y)*(5-11*x)*(7+17*y) in I Output: Magma V2.10-22 Sun Apr 4 2004 00:09:08 on modular [Seed = 1682685055] ------------------------------------- false Total time: 2.559 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sun Apr 4 00:09:21 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2-(x*y)^2); > P2 := (5^2-121*x^2); > P3 := (7^2-17^2*y^2); > I := ideal; > (3-x*y)*(5+11*x)*(7-17*y) in I Output: Magma V2.10-22 Sun Apr 4 2004 00:09:18 on modular [Seed = 2085856365] ------------------------------------- false Total time: 2.560 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sun Apr 4 00:09:30 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2-(x*y)^2); > P2 := (5^2-121*x^2); > P3 := (7^2-17^2*y^2); > I := ideal; > (3-x*y)*(5-11*x)*(7-17*y) in I Output: Magma V2.10-22 Sun Apr 4 2004 00:09:27 on modular [Seed = 1952165020] ------------------------------------- false Total time: 2.500 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sun Apr 4 00:09:42 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2-(x*y)^2); > P2 := (5^2-121*x^2); > P3 := (7^2-17^2*y^2); > I := ideal; > (3-x*y)*(5-11*x)*(7-17*y) in I Output: Magma V2.10-22 Sun Apr 4 2004 00:09:39 on modular [Seed = 1281594544] ------------------------------------- false Total time: 2.519 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sun Apr 4 00:09:52 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2-(x*y)^2); > P2 := (5^2-121*x^2); > P3 := (7^2-17^2*y^2); > I := ideal; > (3-x*y)*(5-11*x)*(7+17*y) in I Output: Magma V2.10-22 Sun Apr 4 2004 00:09:49 on modular [Seed = 1147903158] ------------------------------------- false Total time: 2.579 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sun Apr 4 00:09:59 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2-(x*y)^2); > P2 := (5^2-121*x^2); > P3 := (7^2-17^2*y^2); > I := ideal; > (3-x*y)*(5+11*x)*(7+17*y) in I Output: Magma V2.10-22 Sun Apr 4 2004 00:09:56 on modular [Seed = 1551074455] ------------------------------------- false Total time: 2.569 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sun Apr 4 00:10:22 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (3^2-(x*y)^2); > P2 := (5^2-121*x^2); > P3 := (7^2-17^2*y^2); > I := ideal; > GroebnerBasis(I); > (3-x*y)*(5+11*x)*(7+17*y) in I Output: Magma V2.10-22 Sun Apr 4 2004 00:10:20 on modular [Seed = 738456831] ------------------------------------- [ x^2 + 204679, y^2 + 112815, 313496 ] false Total time: 2.569 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sun Apr 4 00:13:36 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (9 + 289*x^2 + 121*z^2); > P2 := (102*x); > P3 := (66*z); > P4 := 374*x*z; > I := ideal; > GroebnerBasis(I); Output: Magma V2.10-22 Sun Apr 4 2004 00:13:33 on modular [Seed = 554629171] ------------------------------------- [ x^2*z + 3*z^3 + 3*z, 5*x^2 + 5*z^2 + 45, 2*x*z, 6*x, 4*z^3, 6*z, 54 ] Total time: 2.579 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sun Apr 4 00:21:45 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (9 + 289*x^2 + 121*z^2); > P2 := (102*x); > P3 := (66*z); > P4 := 374*x*z; > I := ideal; > GroebnerBasis(I); > 2303796735*x^2 + 75718119357*x^3 + 1257617039895*x^4 + 15342927886719*x^5 + 150131527518132*x^6 + 1125352990025154*x^7 + 6254952424621470*x^8 + 26108069713826526*x^9 + 84750367580975511*x^10 + 224857911674380113*x^11 + 519116413371717051*x^12 + 980553225257687763*x^13 + 1010266959356405574*x^14 + 105225318*z + 4472076015*x*z + 138534976998*x^2*z + 3187993921893*x^3*z + 51754640065326*x^4*z + 591471267385284*x^5*z + 4898595368344788*x^6*z + 30976821778060818*x^7*z + 155621182193712378*x^8*z + 608294970848967039*x^9*z + 1727993043818656758*x^10*z + 3430239829534679337*x^11*z + 4960445727774185154*x^12*z + 4575915051202542894*x^13*z + 1736217747*z^2 + 97292498193*x*z^2 + 3165467909373*x^2*z^2 + 65010822999804*x^3*z^2 + 927153092518983*x^4*z^2 + 9599213867564772*x^5*z^2 + 72727533843493518*x^6*z^2 + 406982921690851308*x^7*z^2 + 1711217679542722989*x^8*z^2 + 5417386043147019117*x^9*z^2 + 12428257661311108221*x^10*z^2 + 19108912680454316544*x^11*z^2 + 17553825385495469169*x^12*z^2 + 7190723651889710262*x^13*z^2 + 19805743188*z^3 + 1366832062629*x*z^3 + 42202109022678*x^2*z^3 + 796721911097310*x^3*z^3 + 10203789559303890*x^4*z^3 + 92935930534158294*x^5*z^3 + 616712794450365492*x^6*z^3 + 2999405737351643400*x^7*z^3 + 10564986439105753248*x^8*z^3 + 26239240831310746173*x^9*z^3 + 44097153044531870646*x^10*z^3 + 46254516501255956322*x^11*z^3 + 23264105932584356730*x^12*z^3 + 223050393522*z^4 + 14065142838021*x*z^4 + 389101325241024*x^2*z^4 + 6623217463852242*x^3*z^4 + 75357307701279846*x^4*z^4 + 596846564821521432*x^5*z^4 + 3377836746493714098*x^6*z^4 + 13727811126218118930*x^7*z^4 + 39179494129531130496*x^8*z^4 + 74177599398438267171*x^9*z^4 + 83766881084592669942*x^10*z^4 + 46163284713285037276*x^11*z^4 + 1844920696806*z^5 + 102066592088934*x*z^5 + 2587734798160446*x^2*z^5 + 39146232486340782*x^3*z^5 + 388038341778521148*x^4*z^5 + 2633304097906179390*x^5*z^5 + 12393588225300575040*x^6*z^5 + 40143344462887955058*x^7*z^5 + 85923910290923212662*x^8*z^5 + 107945830344304097244*x^9*z^5 + 61688788395630260810*x^10*z^5 + 10565499454389*z^6 + 547732229140404*x*z^6 + 12601134513550242*x^2*z^6 + 166923789920684676*x^3*z^6 + 1420434229870656198*x^4*z^6 + 8060536990469205594*x^5*z^6 + 30246946710625585314*x^6*z^6 + 72909173224859351688*x^7*z^6 + 103325069341367887761*x^8*z^6 + 61765183180021134198*x^9*z^6 + 48073603678056*z^7 + 2302504000275402*x*z^7 + 46031725662732612*x^2*z^7 + 520017815561534928*x^3*z^7 + 3706662421551807036*x^4*z^7 + 16903045088805071394*x^5*z^7 + 47870794302889473828*x^6*z^7 + 76860819009839165796*x^7*z^7 + 53831360130486606756*x^8*z^7 + 189396360589788*z^8 + 7549913997966186*x*z^8 + 127610902689761799*x^2*z^8 + 1192645846352660733*x^3*z^8 + 6779595782767878675*x^4*z^8 + 23275242572193400041*x^5*z^8 + 44424842183809881354*x^6*z^8 + 37294929240729283112*x^7*z^8 + 587878802424738*z^9 + 18497554949978379*x*z^9 + 261303532958462346*x^2*z^9 + 1965848188913315685*x^3*z^9 + 8227681993100259558*x^4*z^9 + 19023043574166462534*x^5*z^9 + 17985179528409404564*x^6*z^9 + 1254256041430557*z^10 + 33180009484611033*x*z^10 + 377861615009712801*x^2*z^10 + 2156125194734943960*x^3*z^10 + 5881557822871828515*x^4*z^10 + 6555283230942966146*x^5*z^10 + 1756378644281316*z^11 + 44132865145121313*x*z^11 + 381437166803234454*x^2*z^11 + 1387718875334724570*x^3*z^11 + 2049338379534714466*x^4*z^11 + 1864226455772274*z^12 + 42735979205809857*x*z^12 + 255775635846008058*x^2*z^12 + 431734761215247644*x^3*z^12 + 1864226455772274*z^13 + 28170533109447696*x*z^13 + 59862382857576354*x^2*z^13 + 1139249500749723*z^14 + 12911494341830194*x*z^14 in I Output: Magma V2.10-22 Sun Apr 4 2004 00:21:42 on modular [Seed = 136827649] ------------------------------------- [ x^2*z + 3*z^3 + 3*z, 5*x^2 + 5*z^2 + 45, 2*x*z, 6*x, 4*z^3, 6*z, 54 ] false Total time: 2.609 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Sun Apr 4 00:48:18 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2-2,x^2-3, x^2-5,x^2-7]); FrobeniusAutomosphism(K, 37); Output: Magma V2.10-22 Sun Apr 4 2004 00:48:16 on modular [Seed = 3437440259] ------------------------------------- >> FrobeniusAutomosphism(K, 37); ^ User error: Identifier 'FrobeniusAutomosphism' has not been declared or assigned Total time: 2.679 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sun Apr 4 00:48:56 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (9 + 289*x^2 + 121*z^2); > P2 := (102*x); > P3 := (66*z); > P4 := 374*x*z; > I := ideal; > GroebnerBasis(I); > 4801302120177*x + 353695922853039*x^2 + 20659469545108278*x^3 + 718147829411301186*x^4 + 16679027021035463433*x^5 + 308287234083377662047*x^6 + 4771115963790324163164*x^7 + 61038023292058870540548*x^8 + 650813404085138594804130*x^9 + 5901923144016174544512318*x^10 + 45749156283784022888601684*x^11 + 302197001593228999140913596*x^12 + 1708101860441241852547307802*x^13 + 8305025451991277487962904342*x^14 + 34567276516804559796948386784*x^15 + 122230380156119644082507319168*x^16 + 366971136820427943781761026061*x^17 + 927876729102901024019952389427*x^18 + 1922350375927662733423727143110*x^19 + 3229478918036227602025536170610*x^20 + 4460367977622104768587562647869*x^21 + 4598413661580296216883455427435*x^22 + 3594162402154714284460631828340*x^23 + 4073384055775342855722049405452*x^24 + 774610075388556*x*z + 42098883945738642*x^2*z + 1775635154858298789*x^3*z + 53221568700824386434*x^4*z + 1206028808692895549142*x^5*z + 21666101757105606755526*x^6*z + 315218330711655722772597*x^7*z + 3791484372324652773922350*x^8*z + 38238853206236526292954032*x^9*z + 325269963220175184685702932*x^10*z + 2344351550532551137054358442*x^11*z + 14385514338085518739759662036*x^12*z + 75267573978302733636865969812*x^13*z + 335156379117277844439074301804*x^14*z + 1266327701803812653310174513138*x^15*z + 4038168050094464634357426458844*x^16*z + 10760267685242084034982065873588*x^17*z + 23676454992726471653274100851450*x^18*z + 42443160897487559184763993421073*x^19*z + 60250027790127859660296593157258*x^20*z + 64803121207292628795982748331942*x^21*z + 51396522350812414267787035145262*x^22*z + 27016120722862935704862415909689*x^23*z + 7467870768921461902157090576662*x^24*z + 205043843485206*z^2 + 28402369430913720*x*z^2 + 1726154002163781333*x^2*z^2 + 69200400731655243105*x^3*z^2 + 1955615554191758142618*x^4*z^2 + 41930597560136800507344*x^5*z^2 + 713334999231897615698103*x^6*z^2 + 9828665825361618882910923*x^7*z^2 + 111363617054265794554809132*x^8*z^2 + 1051460299992775492491769152*x^9*z^2 + 8342728602274007444681716626*x^10*z^2 + 55871686632390592802199851754*x^11*z^2 + 316583670229510350197310618564*x^12*z^2 + 1518123805066052121917306620656*x^13*z^2 + 6144568104515084130088742385582*x^14*z^2 + 20887982939165739917287571903286*x^15*z^2 + 59198779044490478129970383317662*x^16*z^2 + 138160299135489569183808478722312*x^17*z^2 + 260792063764441569258921240711273*x^18*z^2 + 389105656482399070637497571537733*x^19*z^2 + 440479197039041506993578374712258*x^20*z^2 + 351526494098077135220935761270336*x^21*z^2 + 191438479555552423882805555492043*x^22*z^2 + 55569744251092054742521879879279*x^23*z^2 + 6348764931616008*z^3 + 755976399686153514*x*z^3 + 44804895568207676154*x^2*z^3 + 1680220690977479540274*x^3*z^3 + 45253439286152308708860*x^4*z^3 + 924038013589871615164620*x^5*z^3 + 14834337577545511962151578*x^6*z^3 + 192121783211978643501535464*x^7*z^3 + 2041283155339696849332478848*x^8*z^3 + 17993507834052143140506500412*x^9*z^3 + 132560166303450086071071180276*x^10*z^3 + 819471735030158649402736628988*x^11*z^3 + 4256256948619753914009315128712*x^12*z^3 + 18552424685018350117241370954240*x^13*z^3 + 67593375202059970063916022931716*x^14*z^3 + 204294870026903614447559229435144*x^15*z^3 + 506414764417886114202788374634328*x^16*z^3 + 1012801482587717662399605523252170*x^17*z^3 + 1594179576654241233011501155389138*x^18*z^3 + 1899779861415808087133748277539042*x^19*z^3 + 1611877150893816928407561354571932*x^20*z^3 + 875104340187650356887049841769732*x^21*z^3 + 234501478297447289834171615858850*x^22*z^3 + 120069624496176432*z^4 + 14302170917877886560*x*z^4 + 816313472858029137453*x^2*z^4 + 29283197772631317267852*x^3*z^4 + 747218032959879548335818*x^4*z^4 + 14400481869952660344413133*x^5*z^4 + 217536755830913784447496908*x^6*z^4 + 2641478259315855524792582520*x^7*z^4 + 26198934383077421937477680592*x^8*z^4 + 214436690691792763137395153724*x^9*z^4 + 1458039634610028742436433872526*x^10*z^4 + 8262403497849958945511389502400*x^11*z^4 + 39018678647820992724706894605924*x^12*z^4 + 153072937745842706390739011316894*x^13*z^4 + 495653416457995117334018392385868*x^14*z^4 + 1310699302906591971030140745995304*x^15*z^4 + 2785370536792177060578799965578352*x^16*z^4 + 4642253527155758004019858600571388*x^17*z^4 + 5845864360264257394049983920185517*x^18*z^4 + 5237578346416480160628411578012820*x^19*z^4 + 2940112998141766470536807726307810*x^20*z^4 + 773854878381576056452766332334205*x^21*z^4 + 1868838781273820928*z^5 + 210719808656970269580*x*z^5 + 11366974912949669174238*x^2*z^5 + 386924803415030971413081*x^3*z^5 + 9315939788152110116672922*x^4*z^5 + 168907679855061299678047896*x^5*z^5 + 2393133308191235111349843864*x^6*z^5 + 27123009849147572186778062892*x^7*z^5 + 249743534888888256634672816584*x^8*z^5 + 1886901278483969004138173731296*x^9*z^5 + 11762072782530387816327153692004*x^10*z^5 + 60594248409606347201198988375942*x^11*z^5 + 257516089489893435185921716160172*x^12*z^5 + 897971096261808802735197584507784*x^13*z^5 + 2544414728021699198887913442909048*x^14*z^5 + 5767541779492054599214594661558028*x^15*z^5 + 10212603799933886773341168114889320*x^16*z^5 + 13621366255984350041458919097030132*x^17*z^5 + 12867477427213195054385996488506798*x^18*z^5 + 7656023164856525796528989185261929*x^19*z^5 + 2135137312271258135919889391527562*x^20*z^5 + 22867443765334295622*z^6 + 2459004491366212527936*x*z^6 + 125190050122488511875231*x^2*z^6 + 4018932806622995698007373*x^3*z^6 + 91085186286970958553439320*x^4*z^6 + 1548440755841257669627906032*x^5*z^6 + 20474680324357085637757011516*x^6*z^6 + 215466190588658760809502943620*x^7*z^6 + 1831438919951176243676896288548*x^8*z^6 + 12684679482463484254050464469792*x^9*z^6 + 71879696731446057087874084418706*x^10*z^6 + 333254400517473772466022677695494*x^11*z^6 + 1258963846622506340212608820659672*x^12*z^6 + 3841529096570389151021754200983728*x^13*z^6 + 9329583006389541903004697229050796*x^14*z^6 + 17622062639651660422888601232065460*x^15*z^6 + 24963911416845168230343040470208998*x^16*z^6 + 24967730182182130607948947033727616*x^17*z^6 + 15735412397159445392235566116053351*x^18*z^6 + 4715175112213277402877293153868789*x^19*z^6 + 225948299030499213432*z^7 + 23144867949092647119318*x*z^7 + 1114386159412637966916270*x^2*z^7 + 33677163662768261124477912*x^3*z^7 + 715697319066562243773937872*x^4*z^7 + 11355855442444512107198606736*x^5*z^7 + 139417288990039179925046498664*x^6*z^7 + 1354347215800631287261048871640*x^7*z^7 + 10552766084725633689491466442272*x^8*z^7 + 66442514023205478119406447902988*x^9*z^7 + 338857207842386159686062393025716*x^10*z^7 + 1396531503336015143115517269887688*x^11*z^7 + 4616248511632711622908595621235696*x^12*z^7 + 12072873728347184996193454297976160*x^13*z^7 + 24434189169575143779126105065601192*x^14*z^7 + 36919024419463453090424318257237896*x^15*z^7 + 39224948586004904881295152946106792*x^16*z^7 + 26170943330094450084558783055311150*x^17*z^7 + 8285619582318694918575474574026126*x^18*z^7 + 1870994052209827911564*z^8 + 180167091927707211541929*x*z^8 + 8170826469478229619463302*x^2*z^8 + 231550079625404724821709204*x^3*z^8 + 4592154330391687354751464404*x^4*z^8 + 67658593401695094463430858466*x^5*z^8 + 766800106786053524506250016594*x^6*z^8 + 6828201570872327254419216241440*x^7*z^8 + 48366613099415553577807708945728*x^8*z^8 + 274077850492495469050215569314704*x^9*z^8 + 1242493155201264340204030967000586*x^10*z^8 + 4480433373391608323651835911447268*x^11*z^8 + 12694356130589004629192540239968372*x^12*z^8 + 27667436012242665862307904773488854*x^13*z^8 + 44797664312108797124698098691205214*x^14*z^8 + 50755292334348293147756761913626152*x^15*z^8 + 35964401603994431214657523539123372*x^16*z^8 + 11972894237427157552035830610260303*x^17*z^8 + 12985749174896342450496*z^9 + 1175234931459828921050424*x*z^9 + 49945163937450380825871348*x^2*z^9 + 1320640547970378825296862426*x^3*z^9 + 24321494445136058010652125732*x^4*z^9 + 330773457946509872016700335732*x^5*z^9 + 3436458472947318681798002085876*x^6*z^9 + 27818711155653192382576976464446*x^7*z^9 + 177345083319755138248640946398676*x^8*z^9 + 893284980577540024612411405774224*x^9*z^9 + 3543356246118613030571384566572156*x^10*z^9 + 10952460116331565768050293112018294*x^11*z^9 + 25859585674601159950821683855808108*x^12*z^9 + 45090057619852660397392493648150916*x^13*z^9 + 54752436406523256050259686894050332*x^14*z^9 + 41358796407375533786933741369329842*x^15*z^9 + 14615650625225478683352368034517980*x^16*z^9 + 75948741268681775583276*z^10 + 6463648712099194843830768*x*z^10 + 256368333655381566442214754*x^2*z^10 + 6294617271985831256872870290*x^3*z^10 + 107021049386112399981136755996*x^4*z^10 + 1334146920895324620595308588912*x^5*z^10 + 12600360673147871019643352216562*x^6*z^10 + 91802038240363686236599964861682*x^7*z^10 + 520210977845268842454515145745716*x^8*z^10 + 2292800994016250163026228898519456*x^9*z^10 + 7795636807098732945382433496185478*x^10*z^10 + 20079782888267590103077815873267990*x^11*z^10 + 37925414585414723079089502665472900*x^12*z^10 + 49609159830482197049462114764457472*x^13*z^10 + 40139727744753250780708370804130342*x^14*z^10 + 15171143350908385477565729904040806*x^15*z^10 + 379980408812423527980432*z^11 + 30153061897133171561799300*x*z^11 + 1110838387866796888325859492*x^2*z^11 + 25181465733684060837624463788*x^3*z^11 + 392403946030500691684538424360*x^4*z^11 + 4447217611377154940636046856680*x^5*z^11 + 37800809298022215886195651801740*x^6*z^11 + 244806503234456354544027426883032*x^7*z^11 + 1213835917440157761512521196102016*x^8*z^11 + 4585523677775030176156028682508500*x^9*z^11 + 12992276553630418448476104184671420*x^10*z^11 + 26771607537117612835903864115869116*x^11*z^11 + 37926816529934941700234902877963592*x^12*z^11 + 33065374522038588002870962466226048*x^13*z^11 + 13394172808183787758780872880948628*x^14*z^11 + 1629114419509357966626672*z^12 + 119798886407186548095281352*x*z^12 + 4073550003327192265288266570*x^2*z^12 + 84642343786131616293091056576*x^3*z^12 + 1198921540801702867422032621268*x^4*z^12 + 12229730198476624681367804606322*x^5*z^12 + 92399346275378490583992697440060*x^6*z^12 + 523603614598955308072066990969512*x^7*z^12 + 2225264386012820869820758921823040*x^8*z^12 + 7005372038874099392377578314025348*x^9*z^12 + 15880395179950646452520369447102634*x^10*z^12 + 24535785526637089639568349965656968*x^11*z^12 + 23182940660566595840912038316305740*x^12*z^12 + 10102873694411402128504699022450770*x^13*z^12 + 5959035659024024668660800*z^13 + 405609492243408874506696600*x*z^13 + 12637452014547154817569026876*x^2*z^13 + 238693136212745604446637814794*x^3*z^13 + 3043458967365362021165131794660*x^4*z^13 + 27594243230119824646534739450616*x^5*z^13 + 182430873485354689951978767154104*x^6*z^13 + 886102257882737442539284798730796*x^7*z^13 + 3138352574654860542944122451276808*x^8*z^13 + 7904069820798681523698921240760032*x^9*z^13 + 13436566420261463060823926835055884*x^10*z^13 + 13844526955587463304562693080078298*x^11*z^13 + 6537998342363034247167381943560532*x^12*z^13 + 18699605564770615801690044*z^14 + 1168330553531626628423402496*x*z^14 + 33093872586557564644423087758*x^2*z^14 + 562628786553497267628907500882*x^3*z^14 + 6377516430143922402433744137048*x^4*z^14 + 50591478879124415195877962299152*x^5*z^14 + 286701770269281605152794247545804*x^6*z^14 + 1160466888673093692731332150711908*x^7*z^14 + 3287613157810655146824522688623612*x^8*z^14 + 6211455042411194648642642085361920*x^9*z^14 + 7037669275387574531157300670719702*x^10*z^14 + 3625934521240273364519160443222906*x^11*z^14 + 50488818420871461729214512*z^15 + 2854072232977045456146285900*x*z^15 + 72828123922789532861439289788*x^2*z^15 + 1100479043086510953754778244696*x^3*z^15 + 10912511580490500801370777027152*x^4*z^15 + 74203450704446944330265635782864*x^5*z^15 + 350386018378796612043477798415560*x^6*z^15 + 1134552779032530812267197582688232*x^7*z^15 + 2411078074753681687135082962576608*x^8*z^15 + 3035956408678916900147172013180644*x^9*z^15 + 1718653983135292606440013677289116*x^10*z^15 + 115788558496590140735543112*z^16 + 5887724534023542821674165971*x*z^16 + 133534229446797611364356593851*x^2*z^16 + 1765200309302378767322191596678*x^3*z^16 + 15001916881678336907317192260330*x^4*z^16 + 85013266825100975920522611149205*x^5*z^16 + 321188111842963664233430111982663*x^6*z^16 + 779954890842209896950619407280356*x^7*z^16 + 1104662038644440724841897042646316*x^8*z^16 + 695640564596006884119455796970254*x^9*z^16 + 223487908194880726553737152*z^17 + 10176477506281816552932457788*x*z^17 + 201478652240665710942881533530*x^2*z^17 + 2284180826296659805053767531457*x^3*z^17 + 16179138027752092877201585012442*x^4*z^17 + 73357292131740016147428498262566*x^5*z^17 + 207807779224786049841166941463542*x^6*z^17 + 336396557608634171840151237343605*x^7*z^17 + 239005021729601304324809785945646*x^8*z^17 + 364324112449970222078950014*z^18 + 14492452136010221021962972824*x*z^18 + 246241664359886609266278547737*x^2*z^18 + 2325987433364626880301494316429*x^3*z^18 + 13186726530914457913180722433434*x^4*z^18 + 44793576765965321499691212864192*x^5*z^18 + 84830047979909086265675994245967*x^6*z^18 + 68559826675956632342018781990363*x^7*z^18 + 493288184829797475779281896*z^19 + 16703583269499666043998991794*x*z^19 + 237803773280078702428560007938*x^2*z^19 + 1795090014721934315293177080306*x^3*z^19 + 7634580317509720116399604447932*x^4*z^19 + 17342770783159851163403396890092*x^5*z^19 + 16223787104777559098212745303210*x^6*z^19 + 544055611901941009680885504*z^20 + 15496430157274276499300029656*x*z^20 + 174256097246178729130848402585*x^2*z^20 + 995810120942133306406916494692*x^3*z^20 + 2776286252465327443152034784610*x^4*z^20 + 3179890060428461363900083071553*x^5*z^20 + 498717644243445925540811712*z^21 + 10855900259228727574712893404*x*z^21 + 91813199000923812998901598470*x^2*z^21 + 338233152462033588390153428829*x^3*z^21 + 498169478129074946589474608386*x^4*z^21 + 303306644215364949908234046*z^22 + 4782574331975609644929835392*x*z^22 + 31124097019810022142394944387*x^2*z^22 + 54790643960043493249915212001*x^3*z^22 + 64470977514377090801750232*z^23 + 2100679350676786875290361726*x*z^23 + 4658028125413744810426454262*x^2*z^23 + 118196792109691333136542092*z^24 + 502336366466188165830303891*x*z^24 Output: Magma V2.10-22 Sun Apr 4 2004 00:48:54 on modular [Seed = 3287032426] ------------------------------------- [ x^2*z + 3*z^3 + 3*z, 5*x^2 + 5*z^2 + 45, 2*x*z, 6*x, 4*z^3, 6*z, 54 ] 7467870768921461902157090576662*x^24*z + 4073384055775342855722049405452*x^24 + 55569744251092054742521879879279*x^23*z^2 + 27016120722862935704862415909689*x^23*z + 3594162402154714284460631828340*x^23 + 234501478297447289834171615858850*x^22*z^3 + 191438479555552423882805555492043*x^22*z^2 + 51396522350812414267787035145262*x^22*z + 4598413661580296216883455427435*x^22 + 773854878381576056452766332334205*x^21*z^4 + 875104340187650356887049841769732*x^21*z^3 + 351526494098077135220935761270336*x^21*z^2 + 64803121207292628795982748331942*x^21*z + 4460367977622104768587562647869*x^21 + 2135137312271258135919889391527562*x^20*z^5 + 2940112998141766470536807726307810*x^20*z^4 + 1611877150893816928407561354571932*x^20*z^3 + 440479197039041506993578374712258*x^20*z^2 + 60250027790127859660296593157258*x^20*z + 3229478918036227602025536170610*x^20 + 4715175112213277402877293153868789*x^19*z^6 + 7656023164856525796528989185261929*x^19*z^5 + 5237578346416480160628411578012820*x^19*z^4 + 1899779861415808087133748277539042*x^19*z^3 + 389105656482399070637497571537733*x^19*z^2 + 42443160897487559184763993421073*x^19*z + 1922350375927662733423727143110*x^19 + 8285619582318694918575474574026126*x^18*z^7 + 15735412397159445392235566116053351*x^18*z^6 + 12867477427213195054385996488506798*x^18*z^5 + 5845864360264257394049983920185517*x^18*z^4 + 1594179576654241233011501155389138*x^18*z^3 + 260792063764441569258921240711273*x^18*z^2 + 23676454992726471653274100851450*x^18*z + 927876729102901024019952389427*x^18 + 11972894237427157552035830610260303*x\ ^17*z^8 + 26170943330094450084558783055311150*x^17*z^7 + 24967730182182130607948947033727616*x^17*z^6 + 13621366255984350041458919097030132*x^17*z^5 + 4642253527155758004019858600571388*x^17*z^4 + 1012801482587717662399605523252170*x^17*z^3 + 138160299135489569183808478722312*x^17*z^2 + 10760267685242084034982065873588*x^17*z + 366971136820427943781761026061*x^17 + 14615650625225478683352368034517980*x\ ^16*z^9 + 35964401603994431214657523539123372*x^16*z^8 + 39224948586004904881295152946106792*x^16*z^7 + 24963911416845168230343040470208998*x^16*z^6 + 10212603799933886773341168114889320*x^16*z^5 + 2785370536792177060578799965578352*x^16*z^4 + 506414764417886114202788374634328*x^16*z^3 + 59198779044490478129970383317662*x^16*z^2 + 4038168050094464634357426458844*x^16*z + 122230380156119644082507319168*x^16 + 15171143350908385477565729904040806*x^15*z^10 + 41358796407375533786933741369329842*x^15*z^9 + 50755292334348293147756761913626152*x^15*z^8 + 36919024419463453090424318257237896*x^15*z^7 + 17622062639651660422888601232065460*x^15*z^6 + 5767541779492054599214594661558028*x^15*z^5 + 1310699302906591971030140745995304*x^15*z^4 + 204294870026903614447559229435144*x^15*z^3 + 20887982939165739917287571903286*x^15*z^2 + 1266327701803812653310174513138*x^15*z + 34567276516804559796948386784*x^15 + 13394172808183787758780872880948628*x^14*z^11 + 40139727744753250780708370804130342*x^14*z^10 + 54752436406523256050259686894050332*x^14*z^9 + 44797664312108797124698098691205214*x^14*z^8 + 24434189169575143779126105065601192*x^14*z^7 + 9329583006389541903004697229050796*x^14*z^6 + 2544414728021699198887913442909048*x^14*z^5 + 495653416457995117334018392385868*x^14*z^4 + 67593375202059970063916022931716*x^14*z^3 + 6144568104515084130088742385582*x^14*z^2 + 335156379117277844439074301804*x^14*z + 8305025451991277487962904342*x^14 + 10102873694411402128504699022450770*x^13*z^12 + 33065374522038588002870962466226048*x^13*z^11 + 49609159830482197049462114764457472*x^13*z^10 + 45090057619852660397392493648150916*x^13*z^9 + 27667436012242665862307904773488854*x^13*z^8 + 12072873728347184996193454297976160*x^13*z^7 + 3841529096570389151021754200983728*x^13*z^6 + 897971096261808802735197584507784*x^13*z^5 + 153072937745842706390739011316894*x^13*z^4 + 18552424685018350117241370954240*x^13*z^3 + 1518123805066052121917306620656*x^13*z^2 + 75267573978302733636865969812*x^13*z + 1708101860441241852547307802*x^13 + 6537998342363034247167381943560532*x^12*z^13 + 23182940660566595840912038316305740*x^12*z^12 + 37926816529934941700234902877963592*x^12*z^11 + 37925414585414723079089502665472900*x^12*z^10 + 25859585674601159950821683855808108*x^12*z^9 + 12694356130589004629192540239968372*x^12*z^8 + 4616248511632711622908595621235696*x^12*z^7 + 1258963846622506340212608820659672*x^12*z^6 + 257516089489893435185921716160172*x^12*z^5 + 39018678647820992724706894605924*x^12*z^4 + 4256256948619753914009315128712*x^12*z^3 + 316583670229510350197310618564*x^12*z^2 + 14385514338085518739759662036*x^12*z + 302197001593228999140913596*x^12 + 3625934521240273364519160443222906*x^11*z^14 + 13844526955587463304562693080078298*x^11*z^13 + 24535785526637089639568349965656968*x^11*z^12 + 26771607537117612835903864115869116*x^11*z^11 + 20079782888267590103077815873267990*x^11*z^10 + 10952460116331565768050293112018294*x^11*z^9 + 4480433373391608323651835911447268*x^11*z^8 + 1396531503336015143115517269887688*x^11*z^7 + 333254400517473772466022677695494*x^11*z^6 + 60594248409606347201198988375942*x^11*z^5 + 8262403497849958945511389502400*x^11*z^4 + 819471735030158649402736628988*x^11*z^3 + 55871686632390592802199851754*x^11*z^2 + 2344351550532551137054358442*x^11*z + 45749156283784022888601684*x^11 + 1718653983135292606440013677289116*x^10\ *z^15 + 7037669275387574531157300670719702*x^10*z^14 + 13436566420261463060823926835055884*x^10*z^13 + 15880395179950646452520369447102634*x^10*z^12 + 12992276553630418448476104184671420*x^10*z^11 + 7795636807098732945382433496185478*x^10*z^10 + 3543356246118613030571384566572156*x^10*z^9 + 1242493155201264340204030967000586*x^10*z^8 + 338857207842386159686062393025716*x^10*z^7 + 71879696731446057087874084418706*x^10*z^6 + 11762072782530387816327153692004*x^10*z^5 + 1458039634610028742436433872526*x^10*z^4 + 132560166303450086071071180276*x^10*z^3 + 8342728602274007444681716626*x^10*z^2 + 325269963220175184685702932*x^10*z + 5901923144016174544512318*x^10 + 695640564596006884119455796970254*x^9*z^16 + 3035956408678916900147172013180644*x^9*z^15 + 6211455042411194648642642085361920*x^9*z^14 + 7904069820798681523698921240760032*x^9*z^13 + 7005372038874099392377578314025348*x^9*z^12 + 4585523677775030176156028682508500*x^9*z^11 + 2292800994016250163026228898519456*x^9*z^10 + 893284980577540024612411405774224*x^9*z^9 + 274077850492495469050215569314704*x^9*z^8 + 66442514023205478119406447902988*x^9*z^7 + 12684679482463484254050464469792*x^9*z^6 + 1886901278483969004138173731296*x^9*z^5 + 214436690691792763137395153724*x^9*z^4 + 17993507834052143140506500412*x^9*z^3 + 1051460299992775492491769152*x^9*z^2 + 38238853206236526292954032*x^9*z + 650813404085138594804130*x^9 + 239005021729601304324809785945646*x^8*z^17 + 1104662038644440724841897042646316*x^8*z^16 + 2411078074753681687135082962576608*x^8*z^15 + 3287613157810655146824522688623612*x^8*z^14 + 3138352574654860542944122451276808*x^8*z^13 + 2225264386012820869820758921823040*x^8*z^12 + 1213835917440157761512521196102016*x^8*z^11 + 520210977845268842454515145745716*x^8*z^10 + 177345083319755138248640946398676*x^8*z^9 + 48366613099415553577807708945728*x^8*z^8 + 10552766084725633689491466442272*x^8*z^7 + 1831438919951176243676896288548*x^8*z^6 + 249743534888888256634672816584*x^8*z^5 + 26198934383077421937477680592*x^8*z^4 + 2041283155339696849332478848*x^8*z^3 + 111363617054265794554809132*x^8*z^2 + 3791484372324652773922350*x^8*z + 61038023292058870540548*x^8 + 68559826675956632342018781990363*x^7*z^18 + 336396557608634171840151237343605*x^7*z^17 + 779954890842209896950619407280356*x^7*z^16 + 1134552779032530812267197582688232*x^7*z^15 + 1160466888673093692731332150711908*x^7*z^14 + 886102257882737442539284798730796*x^7*z^13 + 523603614598955308072066990969512*x^7*z^12 + 244806503234456354544027426883032*x^7*z^11 + 91802038240363686236599964861682*x^7*z^10 + 27818711155653192382576976464446*x^7*z^9 + 6828201570872327254419216241440*x^7*z^8 + 1354347215800631287261048871640*x^7*z^7 + 215466190588658760809502943620*x^7*z^6 + 27123009849147572186778062892*x^7*z^5 + 2641478259315855524792582520*x^7*z^4 + 192121783211978643501535464*x^7*z^3 + 9828665825361618882910923*x^7*z^2 + 315218330711655722772597*x^7*z + 4771115963790324163164*x^7 + 16223787104777559098212745303210*x^6*z^19 + 84830047979909086265675994245967*x^6*z^18 + 207807779224786049841166941463542*x^6*z^17 + 321188111842963664233430111982663*x^6*z^16 + 350386018378796612043477798415560*x^6*z^15 + 286701770269281605152794247545804*x^6*z^14 + 182430873485354689951978767154104*x^6*z^13 + 92399346275378490583992697440060*x^6*z^12 + 37800809298022215886195651801740*x^6*z^11 + 12600360673147871019643352216562*x^6*z^10 + 3436458472947318681798002085876*x^6*z^9 + 766800106786053524506250016594*x^6*z^8 + 139417288990039179925046498664*x^6*z^7 + 20474680324357085637757011516*x^6*z^6 + 239313330 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sun Apr 4 00:49:10 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := (9 + 289*x^2 + 121*z^2); > P2 := (102*x); > P3 := (66*z); > P4 := 374*x*z; > I := ideal; > GroebnerBasis(I); > 4801302120177*x + 353695922853039*x^2 + 20659469545108278*x^3 + 718147829411301186*x^4 + 16679027021035463433*x^5 + 308287234083377662047*x^6 + 4771115963790324163164*x^7 + 61038023292058870540548*x^8 + 650813404085138594804130*x^9 + 5901923144016174544512318*x^10 + 45749156283784022888601684*x^11 + 302197001593228999140913596*x^12 + 1708101860441241852547307802*x^13 + 8305025451991277487962904342*x^14 + 34567276516804559796948386784*x^15 + 122230380156119644082507319168*x^16 + 366971136820427943781761026061*x^17 + 927876729102901024019952389427*x^18 + 1922350375927662733423727143110*x^19 + 3229478918036227602025536170610*x^20 + 4460367977622104768587562647869*x^21 + 4598413661580296216883455427435*x^22 + 3594162402154714284460631828340*x^23 + 4073384055775342855722049405452*x^24 + 774610075388556*x*z + 42098883945738642*x^2*z + 1775635154858298789*x^3*z + 53221568700824386434*x^4*z + 1206028808692895549142*x^5*z + 21666101757105606755526*x^6*z + 315218330711655722772597*x^7*z + 3791484372324652773922350*x^8*z + 38238853206236526292954032*x^9*z + 325269963220175184685702932*x^10*z + 2344351550532551137054358442*x^11*z + 14385514338085518739759662036*x^12*z + 75267573978302733636865969812*x^13*z + 335156379117277844439074301804*x^14*z + 1266327701803812653310174513138*x^15*z + 4038168050094464634357426458844*x^16*z + 10760267685242084034982065873588*x^17*z + 23676454992726471653274100851450*x^18*z + 42443160897487559184763993421073*x^19*z + 60250027790127859660296593157258*x^20*z + 64803121207292628795982748331942*x^21*z + 51396522350812414267787035145262*x^22*z + 27016120722862935704862415909689*x^23*z + 7467870768921461902157090576662*x^24*z + 205043843485206*z^2 + 28402369430913720*x*z^2 + 1726154002163781333*x^2*z^2 + 69200400731655243105*x^3*z^2 + 1955615554191758142618*x^4*z^2 + 41930597560136800507344*x^5*z^2 + 713334999231897615698103*x^6*z^2 + 9828665825361618882910923*x^7*z^2 + 111363617054265794554809132*x^8*z^2 + 1051460299992775492491769152*x^9*z^2 + 8342728602274007444681716626*x^10*z^2 + 55871686632390592802199851754*x^11*z^2 + 316583670229510350197310618564*x^12*z^2 + 1518123805066052121917306620656*x^13*z^2 + 6144568104515084130088742385582*x^14*z^2 + 20887982939165739917287571903286*x^15*z^2 + 59198779044490478129970383317662*x^16*z^2 + 138160299135489569183808478722312*x^17*z^2 + 260792063764441569258921240711273*x^18*z^2 + 389105656482399070637497571537733*x^19*z^2 + 440479197039041506993578374712258*x^20*z^2 + 351526494098077135220935761270336*x^21*z^2 + 191438479555552423882805555492043*x^22*z^2 + 55569744251092054742521879879279*x^23*z^2 + 6348764931616008*z^3 + 755976399686153514*x*z^3 + 44804895568207676154*x^2*z^3 + 1680220690977479540274*x^3*z^3 + 45253439286152308708860*x^4*z^3 + 924038013589871615164620*x^5*z^3 + 14834337577545511962151578*x^6*z^3 + 192121783211978643501535464*x^7*z^3 + 2041283155339696849332478848*x^8*z^3 + 17993507834052143140506500412*x^9*z^3 + 132560166303450086071071180276*x^10*z^3 + 819471735030158649402736628988*x^11*z^3 + 4256256948619753914009315128712*x^12*z^3 + 18552424685018350117241370954240*x^13*z^3 + 67593375202059970063916022931716*x^14*z^3 + 204294870026903614447559229435144*x^15*z^3 + 506414764417886114202788374634328*x^16*z^3 + 1012801482587717662399605523252170*x^17*z^3 + 1594179576654241233011501155389138*x^18*z^3 + 1899779861415808087133748277539042*x^19*z^3 + 1611877150893816928407561354571932*x^20*z^3 + 875104340187650356887049841769732*x^21*z^3 + 234501478297447289834171615858850*x^22*z^3 + 120069624496176432*z^4 + 14302170917877886560*x*z^4 + 816313472858029137453*x^2*z^4 + 29283197772631317267852*x^3*z^4 + 747218032959879548335818*x^4*z^4 + 14400481869952660344413133*x^5*z^4 + 217536755830913784447496908*x^6*z^4 + 2641478259315855524792582520*x^7*z^4 + 26198934383077421937477680592*x^8*z^4 + 214436690691792763137395153724*x^9*z^4 + 1458039634610028742436433872526*x^10*z^4 + 8262403497849958945511389502400*x^11*z^4 + 39018678647820992724706894605924*x^12*z^4 + 153072937745842706390739011316894*x^13*z^4 + 495653416457995117334018392385868*x^14*z^4 + 1310699302906591971030140745995304*x^15*z^4 + 2785370536792177060578799965578352*x^16*z^4 + 4642253527155758004019858600571388*x^17*z^4 + 5845864360264257394049983920185517*x^18*z^4 + 5237578346416480160628411578012820*x^19*z^4 + 2940112998141766470536807726307810*x^20*z^4 + 773854878381576056452766332334205*x^21*z^4 + 1868838781273820928*z^5 + 210719808656970269580*x*z^5 + 11366974912949669174238*x^2*z^5 + 386924803415030971413081*x^3*z^5 + 9315939788152110116672922*x^4*z^5 + 168907679855061299678047896*x^5*z^5 + 2393133308191235111349843864*x^6*z^5 + 27123009849147572186778062892*x^7*z^5 + 249743534888888256634672816584*x^8*z^5 + 1886901278483969004138173731296*x^9*z^5 + 11762072782530387816327153692004*x^10*z^5 + 60594248409606347201198988375942*x^11*z^5 + 257516089489893435185921716160172*x^12*z^5 + 897971096261808802735197584507784*x^13*z^5 + 2544414728021699198887913442909048*x^14*z^5 + 5767541779492054599214594661558028*x^15*z^5 + 10212603799933886773341168114889320*x^16*z^5 + 13621366255984350041458919097030132*x^17*z^5 + 12867477427213195054385996488506798*x^18*z^5 + 7656023164856525796528989185261929*x^19*z^5 + 2135137312271258135919889391527562*x^20*z^5 + 22867443765334295622*z^6 + 2459004491366212527936*x*z^6 + 125190050122488511875231*x^2*z^6 + 4018932806622995698007373*x^3*z^6 + 91085186286970958553439320*x^4*z^6 + 1548440755841257669627906032*x^5*z^6 + 20474680324357085637757011516*x^6*z^6 + 215466190588658760809502943620*x^7*z^6 + 1831438919951176243676896288548*x^8*z^6 + 12684679482463484254050464469792*x^9*z^6 + 71879696731446057087874084418706*x^10*z^6 + 333254400517473772466022677695494*x^11*z^6 + 1258963846622506340212608820659672*x^12*z^6 + 3841529096570389151021754200983728*x^13*z^6 + 9329583006389541903004697229050796*x^14*z^6 + 17622062639651660422888601232065460*x^15*z^6 + 24963911416845168230343040470208998*x^16*z^6 + 24967730182182130607948947033727616*x^17*z^6 + 15735412397159445392235566116053351*x^18*z^6 + 4715175112213277402877293153868789*x^19*z^6 + 225948299030499213432*z^7 + 23144867949092647119318*x*z^7 + 1114386159412637966916270*x^2*z^7 + 33677163662768261124477912*x^3*z^7 + 715697319066562243773937872*x^4*z^7 + 11355855442444512107198606736*x^5*z^7 + 139417288990039179925046498664*x^6*z^7 + 1354347215800631287261048871640*x^7*z^7 + 10552766084725633689491466442272*x^8*z^7 + 66442514023205478119406447902988*x^9*z^7 + 338857207842386159686062393025716*x^10*z^7 + 1396531503336015143115517269887688*x^11*z^7 + 4616248511632711622908595621235696*x^12*z^7 + 12072873728347184996193454297976160*x^13*z^7 + 24434189169575143779126105065601192*x^14*z^7 + 36919024419463453090424318257237896*x^15*z^7 + 39224948586004904881295152946106792*x^16*z^7 + 26170943330094450084558783055311150*x^17*z^7 + 8285619582318694918575474574026126*x^18*z^7 + 1870994052209827911564*z^8 + 180167091927707211541929*x*z^8 + 8170826469478229619463302*x^2*z^8 + 231550079625404724821709204*x^3*z^8 + 4592154330391687354751464404*x^4*z^8 + 67658593401695094463430858466*x^5*z^8 + 766800106786053524506250016594*x^6*z^8 + 6828201570872327254419216241440*x^7*z^8 + 48366613099415553577807708945728*x^8*z^8 + 274077850492495469050215569314704*x^9*z^8 + 1242493155201264340204030967000586*x^10*z^8 + 4480433373391608323651835911447268*x^11*z^8 + 12694356130589004629192540239968372*x^12*z^8 + 27667436012242665862307904773488854*x^13*z^8 + 44797664312108797124698098691205214*x^14*z^8 + 50755292334348293147756761913626152*x^15*z^8 + 35964401603994431214657523539123372*x^16*z^8 + 11972894237427157552035830610260303*x^17*z^8 + 12985749174896342450496*z^9 + 1175234931459828921050424*x*z^9 + 49945163937450380825871348*x^2*z^9 + 1320640547970378825296862426*x^3*z^9 + 24321494445136058010652125732*x^4*z^9 + 330773457946509872016700335732*x^5*z^9 + 3436458472947318681798002085876*x^6*z^9 + 27818711155653192382576976464446*x^7*z^9 + 177345083319755138248640946398676*x^8*z^9 + 893284980577540024612411405774224*x^9*z^9 + 3543356246118613030571384566572156*x^10*z^9 + 10952460116331565768050293112018294*x^11*z^9 + 25859585674601159950821683855808108*x^12*z^9 + 45090057619852660397392493648150916*x^13*z^9 + 54752436406523256050259686894050332*x^14*z^9 + 41358796407375533786933741369329842*x^15*z^9 + 14615650625225478683352368034517980*x^16*z^9 + 75948741268681775583276*z^10 + 6463648712099194843830768*x*z^10 + 256368333655381566442214754*x^2*z^10 + 6294617271985831256872870290*x^3*z^10 + 107021049386112399981136755996*x^4*z^10 + 1334146920895324620595308588912*x^5*z^10 + 12600360673147871019643352216562*x^6*z^10 + 91802038240363686236599964861682*x^7*z^10 + 520210977845268842454515145745716*x^8*z^10 + 2292800994016250163026228898519456*x^9*z^10 + 7795636807098732945382433496185478*x^10*z^10 + 20079782888267590103077815873267990*x^11*z^10 + 37925414585414723079089502665472900*x^12*z^10 + 49609159830482197049462114764457472*x^13*z^10 + 40139727744753250780708370804130342*x^14*z^10 + 15171143350908385477565729904040806*x^15*z^10 + 379980408812423527980432*z^11 + 30153061897133171561799300*x*z^11 + 1110838387866796888325859492*x^2*z^11 + 25181465733684060837624463788*x^3*z^11 + 392403946030500691684538424360*x^4*z^11 + 4447217611377154940636046856680*x^5*z^11 + 37800809298022215886195651801740*x^6*z^11 + 244806503234456354544027426883032*x^7*z^11 + 1213835917440157761512521196102016*x^8*z^11 + 4585523677775030176156028682508500*x^9*z^11 + 12992276553630418448476104184671420*x^10*z^11 + 26771607537117612835903864115869116*x^11*z^11 + 37926816529934941700234902877963592*x^12*z^11 + 33065374522038588002870962466226048*x^13*z^11 + 13394172808183787758780872880948628*x^14*z^11 + 1629114419509357966626672*z^12 + 119798886407186548095281352*x*z^12 + 4073550003327192265288266570*x^2*z^12 + 84642343786131616293091056576*x^3*z^12 + 1198921540801702867422032621268*x^4*z^12 + 12229730198476624681367804606322*x^5*z^12 + 92399346275378490583992697440060*x^6*z^12 + 523603614598955308072066990969512*x^7*z^12 + 2225264386012820869820758921823040*x^8*z^12 + 7005372038874099392377578314025348*x^9*z^12 + 15880395179950646452520369447102634*x^10*z^12 + 24535785526637089639568349965656968*x^11*z^12 + 23182940660566595840912038316305740*x^12*z^12 + 10102873694411402128504699022450770*x^13*z^12 + 5959035659024024668660800*z^13 + 405609492243408874506696600*x*z^13 + 12637452014547154817569026876*x^2*z^13 + 238693136212745604446637814794*x^3*z^13 + 3043458967365362021165131794660*x^4*z^13 + 27594243230119824646534739450616*x^5*z^13 + 182430873485354689951978767154104*x^6*z^13 + 886102257882737442539284798730796*x^7*z^13 + 3138352574654860542944122451276808*x^8*z^13 + 7904069820798681523698921240760032*x^9*z^13 + 13436566420261463060823926835055884*x^10*z^13 + 13844526955587463304562693080078298*x^11*z^13 + 6537998342363034247167381943560532*x^12*z^13 + 18699605564770615801690044*z^14 + 1168330553531626628423402496*x*z^14 + 33093872586557564644423087758*x^2*z^14 + 562628786553497267628907500882*x^3*z^14 + 6377516430143922402433744137048*x^4*z^14 + 50591478879124415195877962299152*x^5*z^14 + 286701770269281605152794247545804*x^6*z^14 + 1160466888673093692731332150711908*x^7*z^14 + 3287613157810655146824522688623612*x^8*z^14 + 6211455042411194648642642085361920*x^9*z^14 + 7037669275387574531157300670719702*x^10*z^14 + 3625934521240273364519160443222906*x^11*z^14 + 50488818420871461729214512*z^15 + 2854072232977045456146285900*x*z^15 + 72828123922789532861439289788*x^2*z^15 + 1100479043086510953754778244696*x^3*z^15 + 10912511580490500801370777027152*x^4*z^15 + 74203450704446944330265635782864*x^5*z^15 + 350386018378796612043477798415560*x^6*z^15 + 1134552779032530812267197582688232*x^7*z^15 + 2411078074753681687135082962576608*x^8*z^15 + 3035956408678916900147172013180644*x^9*z^15 + 1718653983135292606440013677289116*x^10*z^15 + 115788558496590140735543112*z^16 + 5887724534023542821674165971*x*z^16 + 133534229446797611364356593851*x^2*z^16 + 1765200309302378767322191596678*x^3*z^16 + 15001916881678336907317192260330*x^4*z^16 + 85013266825100975920522611149205*x^5*z^16 + 321188111842963664233430111982663*x^6*z^16 + 779954890842209896950619407280356*x^7*z^16 + 1104662038644440724841897042646316*x^8*z^16 + 695640564596006884119455796970254*x^9*z^16 + 223487908194880726553737152*z^17 + 10176477506281816552932457788*x*z^17 + 201478652240665710942881533530*x^2*z^17 + 2284180826296659805053767531457*x^3*z^17 + 16179138027752092877201585012442*x^4*z^17 + 73357292131740016147428498262566*x^5*z^17 + 207807779224786049841166941463542*x^6*z^17 + 336396557608634171840151237343605*x^7*z^17 + 239005021729601304324809785945646*x^8*z^17 + 364324112449970222078950014*z^18 + 14492452136010221021962972824*x*z^18 + 246241664359886609266278547737*x^2*z^18 + 2325987433364626880301494316429*x^3*z^18 + 13186726530914457913180722433434*x^4*z^18 + 44793576765965321499691212864192*x^5*z^18 + 84830047979909086265675994245967*x^6*z^18 + 68559826675956632342018781990363*x^7*z^18 + 493288184829797475779281896*z^19 + 16703583269499666043998991794*x*z^19 + 237803773280078702428560007938*x^2*z^19 + 1795090014721934315293177080306*x^3*z^19 + 7634580317509720116399604447932*x^4*z^19 + 17342770783159851163403396890092*x^5*z^19 + 16223787104777559098212745303210*x^6*z^19 + 544055611901941009680885504*z^20 + 15496430157274276499300029656*x*z^20 + 174256097246178729130848402585*x^2*z^20 + 995810120942133306406916494692*x^3*z^20 + 2776286252465327443152034784610*x^4*z^20 + 3179890060428461363900083071553*x^5*z^20 + 498717644243445925540811712*z^21 + 10855900259228727574712893404*x*z^21 + 91813199000923812998901598470*x^2*z^21 + 338233152462033588390153428829*x^3*z^21 + 498169478129074946589474608386*x^4*z^21 + 303306644215364949908234046*z^22 + 4782574331975609644929835392*x*z^22 + 31124097019810022142394944387*x^2*z^22 + 54790643960043493249915212001*x^3*z^22 + 64470977514377090801750232*z^23 + 2100679350676786875290361726*x*z^23 + 4658028125413744810426454262*x^2*z^23 + 118196792109691333136542092*z^24 + 502336366466188165830303891*x*z^24 in I Output: Magma V2.10-22 Sun Apr 4 2004 00:49:07 on modular [Seed = 3690216039] ------------------------------------- [ x^2*z + 3*z^3 + 3*z, 5*x^2 + 5*z^2 + 45, 2*x*z, 6*x, 4*z^3, 6*z, 54 ] false Total time: 2.620 seconds, Total memory usage: 2.51MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Sun Apr 4 00:50:00 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2-2,x^2-3, x^2-5,x^2-7]); F:=FrobeniusAutomosphism(K, 37); F; Output: Magma V2.10-22 Sun Apr 4 2004 00:49:57 on modular [Seed = 3539808440] ------------------------------------- >> F:=FrobeniusAutomosphism(K, 37); ^ User error: Identifier 'FrobeniusAutomosphism' has not been declared or assigned >> F; ^ User error: Identifier 'F' has not been declared or assigned Total time: 2.660 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sun Apr 4 00:51:32 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > GroebnerBasis(I); > 4801302120177*x + 353695922853039*x^2 + 20659469545108278*x^3 + 718147829411301186*x^4 + 16679027021035463433*x^5 + 308287234083377662047*x^6 + 4771115963790324163164*x^7 + 61038023292058870540548*x^8 + 650813404085138594804130*x^9 + 5901923144016174544512318*x^10 + 45749156283784022888601684*x^11 + 302197001593228999140913596*x^12 + 1708101860441241852547307802*x^13 + 8305025451991277487962904342*x^14 + 34567276516804559796948386784*x^15 + 122230380156119644082507319168*x^16 + 366971136820427943781761026061*x^17 + 927876729102901024019952389427*x^18 + 1922350375927662733423727143110*x^19 + 3229478918036227602025536170610*x^20 + 4460367977622104768587562647869*x^21 + 4598413661580296216883455427435*x^22 + 3594162402154714284460631828340*x^23 + 4073384055775342855722049405452*x^24 + 774610075388556*x*z + 42098883945738642*x^2*z + 1775635154858298789*x^3*z + 53221568700824386434*x^4*z + 1206028808692895549142*x^5*z + 21666101757105606755526*x^6*z + 315218330711655722772597*x^7*z + 3791484372324652773922350*x^8*z + 38238853206236526292954032*x^9*z + 325269963220175184685702932*x^10*z + 2344351550532551137054358442*x^11*z + 14385514338085518739759662036*x^12*z + 75267573978302733636865969812*x^13*z + 335156379117277844439074301804*x^14*z + 1266327701803812653310174513138*x^15*z + 4038168050094464634357426458844*x^16*z + 10760267685242084034982065873588*x^17*z + 23676454992726471653274100851450*x^18*z + 42443160897487559184763993421073*x^19*z + 60250027790127859660296593157258*x^20*z + 64803121207292628795982748331942*x^21*z + 51396522350812414267787035145262*x^22*z + 27016120722862935704862415909689*x^23*z + 7467870768921461902157090576662*x^24*z + 205043843485206*z^2 + 28402369430913720*x*z^2 + 1726154002163781333*x^2*z^2 + 69200400731655243105*x^3*z^2 + 1955615554191758142618*x^4*z^2 + 41930597560136800507344*x^5*z^2 + 713334999231897615698103*x^6*z^2 + 9828665825361618882910923*x^7*z^2 + 111363617054265794554809132*x^8*z^2 + 1051460299992775492491769152*x^9*z^2 + 8342728602274007444681716626*x^10*z^2 + 55871686632390592802199851754*x^11*z^2 + 316583670229510350197310618564*x^12*z^2 + 1518123805066052121917306620656*x^13*z^2 + 6144568104515084130088742385582*x^14*z^2 + 20887982939165739917287571903286*x^15*z^2 + 59198779044490478129970383317662*x^16*z^2 + 138160299135489569183808478722312*x^17*z^2 + 260792063764441569258921240711273*x^18*z^2 + 389105656482399070637497571537733*x^19*z^2 + 440479197039041506993578374712258*x^20*z^2 + 351526494098077135220935761270336*x^21*z^2 + 191438479555552423882805555492043*x^22*z^2 + 55569744251092054742521879879279*x^23*z^2 + 6348764931616008*z^3 + 755976399686153514*x*z^3 + 44804895568207676154*x^2*z^3 + 1680220690977479540274*x^3*z^3 + 45253439286152308708860*x^4*z^3 + 924038013589871615164620*x^5*z^3 + 14834337577545511962151578*x^6*z^3 + 192121783211978643501535464*x^7*z^3 + 2041283155339696849332478848*x^8*z^3 + 17993507834052143140506500412*x^9*z^3 + 132560166303450086071071180276*x^10*z^3 + 819471735030158649402736628988*x^11*z^3 + 4256256948619753914009315128712*x^12*z^3 + 18552424685018350117241370954240*x^13*z^3 + 67593375202059970063916022931716*x^14*z^3 + 204294870026903614447559229435144*x^15*z^3 + 506414764417886114202788374634328*x^16*z^3 + 1012801482587717662399605523252170*x^17*z^3 + 1594179576654241233011501155389138*x^18*z^3 + 1899779861415808087133748277539042*x^19*z^3 + 1611877150893816928407561354571932*x^20*z^3 + 875104340187650356887049841769732*x^21*z^3 + 234501478297447289834171615858850*x^22*z^3 + 120069624496176432*z^4 + 14302170917877886560*x*z^4 + 816313472858029137453*x^2*z^4 + 29283197772631317267852*x^3*z^4 + 747218032959879548335818*x^4*z^4 + 14400481869952660344413133*x^5*z^4 + 217536755830913784447496908*x^6*z^4 + 2641478259315855524792582520*x^7*z^4 + 26198934383077421937477680592*x^8*z^4 + 214436690691792763137395153724*x^9*z^4 + 1458039634610028742436433872526*x^10*z^4 + 8262403497849958945511389502400*x^11*z^4 + 39018678647820992724706894605924*x^12*z^4 + 153072937745842706390739011316894*x^13*z^4 + 495653416457995117334018392385868*x^14*z^4 + 1310699302906591971030140745995304*x^15*z^4 + 2785370536792177060578799965578352*x^16*z^4 + 4642253527155758004019858600571388*x^17*z^4 + 5845864360264257394049983920185517*x^18*z^4 + 5237578346416480160628411578012820*x^19*z^4 + 2940112998141766470536807726307810*x^20*z^4 + 773854878381576056452766332334205*x^21*z^4 + 1868838781273820928*z^5 + 210719808656970269580*x*z^5 + 11366974912949669174238*x^2*z^5 + 386924803415030971413081*x^3*z^5 + 9315939788152110116672922*x^4*z^5 + 168907679855061299678047896*x^5*z^5 + 2393133308191235111349843864*x^6*z^5 + 27123009849147572186778062892*x^7*z^5 + 249743534888888256634672816584*x^8*z^5 + 1886901278483969004138173731296*x^9*z^5 + 11762072782530387816327153692004*x^10*z^5 + 60594248409606347201198988375942*x^11*z^5 + 257516089489893435185921716160172*x^12*z^5 + 897971096261808802735197584507784*x^13*z^5 + 2544414728021699198887913442909048*x^14*z^5 + 5767541779492054599214594661558028*x^15*z^5 + 10212603799933886773341168114889320*x^16*z^5 + 13621366255984350041458919097030132*x^17*z^5 + 12867477427213195054385996488506798*x^18*z^5 + 7656023164856525796528989185261929*x^19*z^5 + 2135137312271258135919889391527562*x^20*z^5 + 22867443765334295622*z^6 + 2459004491366212527936*x*z^6 + 125190050122488511875231*x^2*z^6 + 4018932806622995698007373*x^3*z^6 + 91085186286970958553439320*x^4*z^6 + 1548440755841257669627906032*x^5*z^6 + 20474680324357085637757011516*x^6*z^6 + 215466190588658760809502943620*x^7*z^6 + 1831438919951176243676896288548*x^8*z^6 + 12684679482463484254050464469792*x^9*z^6 + 71879696731446057087874084418706*x^10*z^6 + 333254400517473772466022677695494*x^11*z^6 + 1258963846622506340212608820659672*x^12*z^6 + 3841529096570389151021754200983728*x^13*z^6 + 9329583006389541903004697229050796*x^14*z^6 + 17622062639651660422888601232065460*x^15*z^6 + 24963911416845168230343040470208998*x^16*z^6 + 24967730182182130607948947033727616*x^17*z^6 + 15735412397159445392235566116053351*x^18*z^6 + 4715175112213277402877293153868789*x^19*z^6 + 225948299030499213432*z^7 + 23144867949092647119318*x*z^7 + 1114386159412637966916270*x^2*z^7 + 33677163662768261124477912*x^3*z^7 + 715697319066562243773937872*x^4*z^7 + 11355855442444512107198606736*x^5*z^7 + 139417288990039179925046498664*x^6*z^7 + 1354347215800631287261048871640*x^7*z^7 + 10552766084725633689491466442272*x^8*z^7 + 66442514023205478119406447902988*x^9*z^7 + 338857207842386159686062393025716*x^10*z^7 + 1396531503336015143115517269887688*x^11*z^7 + 4616248511632711622908595621235696*x^12*z^7 + 12072873728347184996193454297976160*x^13*z^7 + 24434189169575143779126105065601192*x^14*z^7 + 36919024419463453090424318257237896*x^15*z^7 + 39224948586004904881295152946106792*x^16*z^7 + 26170943330094450084558783055311150*x^17*z^7 + 8285619582318694918575474574026126*x^18*z^7 + 1870994052209827911564*z^8 + 180167091927707211541929*x*z^8 + 8170826469478229619463302*x^2*z^8 + 231550079625404724821709204*x^3*z^8 + 4592154330391687354751464404*x^4*z^8 + 67658593401695094463430858466*x^5*z^8 + 766800106786053524506250016594*x^6*z^8 + 6828201570872327254419216241440*x^7*z^8 + 48366613099415553577807708945728*x^8*z^8 + 274077850492495469050215569314704*x^9*z^8 + 1242493155201264340204030967000586*x^10*z^8 + 4480433373391608323651835911447268*x^11*z^8 + 12694356130589004629192540239968372*x^12*z^8 + 27667436012242665862307904773488854*x^13*z^8 + 44797664312108797124698098691205214*x^14*z^8 + 50755292334348293147756761913626152*x^15*z^8 + 35964401603994431214657523539123372*x^16*z^8 + 11972894237427157552035830610260303*x^17*z^8 + 12985749174896342450496*z^9 + 1175234931459828921050424*x*z^9 + 49945163937450380825871348*x^2*z^9 + 1320640547970378825296862426*x^3*z^9 + 24321494445136058010652125732*x^4*z^9 + 330773457946509872016700335732*x^5*z^9 + 3436458472947318681798002085876*x^6*z^9 + 27818711155653192382576976464446*x^7*z^9 + 177345083319755138248640946398676*x^8*z^9 + 893284980577540024612411405774224*x^9*z^9 + 3543356246118613030571384566572156*x^10*z^9 + 10952460116331565768050293112018294*x^11*z^9 + 25859585674601159950821683855808108*x^12*z^9 + 45090057619852660397392493648150916*x^13*z^9 + 54752436406523256050259686894050332*x^14*z^9 + 41358796407375533786933741369329842*x^15*z^9 + 14615650625225478683352368034517980*x^16*z^9 + 75948741268681775583276*z^10 + 6463648712099194843830768*x*z^10 + 256368333655381566442214754*x^2*z^10 + 6294617271985831256872870290*x^3*z^10 + 107021049386112399981136755996*x^4*z^10 + 1334146920895324620595308588912*x^5*z^10 + 12600360673147871019643352216562*x^6*z^10 + 91802038240363686236599964861682*x^7*z^10 + 520210977845268842454515145745716*x^8*z^10 + 2292800994016250163026228898519456*x^9*z^10 + 7795636807098732945382433496185478*x^10*z^10 + 20079782888267590103077815873267990*x^11*z^10 + 37925414585414723079089502665472900*x^12*z^10 + 49609159830482197049462114764457472*x^13*z^10 + 40139727744753250780708370804130342*x^14*z^10 + 15171143350908385477565729904040806*x^15*z^10 + 379980408812423527980432*z^11 + 30153061897133171561799300*x*z^11 + 1110838387866796888325859492*x^2*z^11 + 25181465733684060837624463788*x^3*z^11 + 392403946030500691684538424360*x^4*z^11 + 4447217611377154940636046856680*x^5*z^11 + 37800809298022215886195651801740*x^6*z^11 + 244806503234456354544027426883032*x^7*z^11 + 1213835917440157761512521196102016*x^8*z^11 + 4585523677775030176156028682508500*x^9*z^11 + 12992276553630418448476104184671420*x^10*z^11 + 26771607537117612835903864115869116*x^11*z^11 + 37926816529934941700234902877963592*x^12*z^11 + 33065374522038588002870962466226048*x^13*z^11 + 13394172808183787758780872880948628*x^14*z^11 + 1629114419509357966626672*z^12 + 119798886407186548095281352*x*z^12 + 4073550003327192265288266570*x^2*z^12 + 84642343786131616293091056576*x^3*z^12 + 1198921540801702867422032621268*x^4*z^12 + 12229730198476624681367804606322*x^5*z^12 + 92399346275378490583992697440060*x^6*z^12 + 523603614598955308072066990969512*x^7*z^12 + 2225264386012820869820758921823040*x^8*z^12 + 7005372038874099392377578314025348*x^9*z^12 + 15880395179950646452520369447102634*x^10*z^12 + 24535785526637089639568349965656968*x^11*z^12 + 23182940660566595840912038316305740*x^12*z^12 + 10102873694411402128504699022450770*x^13*z^12 + 5959035659024024668660800*z^13 + 405609492243408874506696600*x*z^13 + 12637452014547154817569026876*x^2*z^13 + 238693136212745604446637814794*x^3*z^13 + 3043458967365362021165131794660*x^4*z^13 + 27594243230119824646534739450616*x^5*z^13 + 182430873485354689951978767154104*x^6*z^13 + 886102257882737442539284798730796*x^7*z^13 + 3138352574654860542944122451276808*x^8*z^13 + 7904069820798681523698921240760032*x^9*z^13 + 13436566420261463060823926835055884*x^10*z^13 + 13844526955587463304562693080078298*x^11*z^13 + 6537998342363034247167381943560532*x^12*z^13 + 18699605564770615801690044*z^14 + 1168330553531626628423402496*x*z^14 + 33093872586557564644423087758*x^2*z^14 + 562628786553497267628907500882*x^3*z^14 + 6377516430143922402433744137048*x^4*z^14 + 50591478879124415195877962299152*x^5*z^14 + 286701770269281605152794247545804*x^6*z^14 + 1160466888673093692731332150711908*x^7*z^14 + 3287613157810655146824522688623612*x^8*z^14 + 6211455042411194648642642085361920*x^9*z^14 + 7037669275387574531157300670719702*x^10*z^14 + 3625934521240273364519160443222906*x^11*z^14 + 50488818420871461729214512*z^15 + 2854072232977045456146285900*x*z^15 + 72828123922789532861439289788*x^2*z^15 + 1100479043086510953754778244696*x^3*z^15 + 10912511580490500801370777027152*x^4*z^15 + 74203450704446944330265635782864*x^5*z^15 + 350386018378796612043477798415560*x^6*z^15 + 1134552779032530812267197582688232*x^7*z^15 + 2411078074753681687135082962576608*x^8*z^15 + 3035956408678916900147172013180644*x^9*z^15 + 1718653983135292606440013677289116*x^10*z^15 + 115788558496590140735543112*z^16 + 5887724534023542821674165971*x*z^16 + 133534229446797611364356593851*x^2*z^16 + 1765200309302378767322191596678*x^3*z^16 + 15001916881678336907317192260330*x^4*z^16 + 85013266825100975920522611149205*x^5*z^16 + 321188111842963664233430111982663*x^6*z^16 + 779954890842209896950619407280356*x^7*z^16 + 1104662038644440724841897042646316*x^8*z^16 + 695640564596006884119455796970254*x^9*z^16 + 223487908194880726553737152*z^17 + 10176477506281816552932457788*x*z^17 + 201478652240665710942881533530*x^2*z^17 + 2284180826296659805053767531457*x^3*z^17 + 16179138027752092877201585012442*x^4*z^17 + 73357292131740016147428498262566*x^5*z^17 + 207807779224786049841166941463542*x^6*z^17 + 336396557608634171840151237343605*x^7*z^17 + 239005021729601304324809785945646*x^8*z^17 + 364324112449970222078950014*z^18 + 14492452136010221021962972824*x*z^18 + 246241664359886609266278547737*x^2*z^18 + 2325987433364626880301494316429*x^3*z^18 + 13186726530914457913180722433434*x^4*z^18 + 44793576765965321499691212864192*x^5*z^18 + 84830047979909086265675994245967*x^6*z^18 + 68559826675956632342018781990363*x^7*z^18 + 493288184829797475779281896*z^19 + 16703583269499666043998991794*x*z^19 + 237803773280078702428560007938*x^2*z^19 + 1795090014721934315293177080306*x^3*z^19 + 7634580317509720116399604447932*x^4*z^19 + 17342770783159851163403396890092*x^5*z^19 + 16223787104777559098212745303210*x^6*z^19 + 544055611901941009680885504*z^20 + 15496430157274276499300029656*x*z^20 + 174256097246178729130848402585*x^2*z^20 + 995810120942133306406916494692*x^3*z^20 + 2776286252465327443152034784610*x^4*z^20 + 3179890060428461363900083071553*x^5*z^20 + 498717644243445925540811712*z^21 + 10855900259228727574712893404*x*z^21 + 91813199000923812998901598470*x^2*z^21 + 338233152462033588390153428829*x^3*z^21 + 498169478129074946589474608386*x^4*z^21 + 303306644215364949908234046*z^22 + 4782574331975609644929835392*x*z^22 + 31124097019810022142394944387*x^2*z^22 + 54790643960043493249915212001*x^3*z^22 + 64470977514377090801750232*z^23 + 2100679350676786875290361726*x*z^23 + 4658028125413744810426454262*x^2*z^23 + 118196792109691333136542092*z^24 + 502336366466188165830303891*x*z^24 in I Output: Magma V2.10-22 Sun Apr 4 2004 00:51:29 on modular [Seed = 2743878061] ------------------------------------- [ x^2*z + 3*z^3 + 3*z, 5*x^2 + 5*z^2 + 45, 2*x*z, 6*x, 4*z^3, 6*z, 54 ] false Total time: 2.630 seconds, Total memory usage: 2.51MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sun Apr 4 01:08:17 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > 275573750405290386156*x + 17177430441929767403724*x^2 + 1291950980511202505940696*x^3 + 71568332483763548406999069*x^4 + 2933002060899381069228645912*x^5 + 96694114364841635947146176766*x^6 + 2658053466027253803681878061708*x^7 + 62109462904914230956593041593401*x^8 + 1251609559311431425713553664769168*x^9 + 21991590820796269937289124980924576*x^10 + 339874528606848103579134147488680128*x^11 + 4654026031226274102693081032154096516*x^12 + 56801409394762285311633922332217353600*x^13 + 620770532721078411713098345209265341864*x^14 + 6097456834004194955480660618053741035024*x^15 + 53987934247818304475156697719045285693796*x^16 + 431899431419641327846058269926722954630088*x^17 + 3127249750515556304176353645072789494350584*x^18 + 20519223977129947710225260098905240932075760*x^19 + 122090416162149246895308268001813372348103702*x^20 + 658900225567898031947473915900074743078980656*x^21 + 3224592191327204316990397911940987002079789716*x^22 + 14300367515641454048978476849108478504680345992*x^23 + 57400451693893534478325151250855145167883714510*x^24 + 208171412665872532941127001273787505392125274384*x^25 + 680557440907355495456217907040251678802415826560*x^26 + 1999703759524094125195693668464837454569737422720*x^27 + 5261152461969601583290677713952014651700824222484*x^28 + 12335604798454205588965973570184471884788998461376*x^29 + 25629910383456630695709698944761765360645003932904*x^30 + 46860929955092484657379858243622139248061088083600*x^31 + 74697758228167981052469534838842040243897235551764*x^32 + 102551000907319343546873515233031719460536147365292*x^33 + 119536192741689256717272905440585639510921919857692*x^34 + 116266905241756572785108148359746736516657964039672*x^35 + 91839208096405022857172933664731867078794672188213*x^36 + 55918378230452549529642128108440729812729682374264*x^37 + 23662430614834358080184060703896456013828253039326*x^38 + 11659748418903886590235624114963471079277689903436*x^39 + 16517976926780506002833800829531584028976727363201*x^40 + 24250490035665553981728*x*z + 2708308199677593327320484*x^2*z + 185965724869405316873949978*x^3*z + 9446560232542184898725758938*x^4*z + 374833372709513310969631240854*x^5*z + 12038896134723137149519284869370*x^6*z + 321606369640715339865668708845296*x^7*z + 7289962021587165411775199840852400*x^8*z + 142293161575424443092248116938507408*x^9*z + 2418938185907234199673011434215372704*x^10*z + 36136740027070924449065961714034928856*x^11*z + 477811029745193728538166008188884320664*x^12*z + 5623536831215179112397946824729248223720*x^13*z + 59180957599185729922006047847199225929272*x^14*z + 558927233667570416451242568971215445973648*x^15*z + 4750878761361244583792220045412446030682704*x^16*z + 36423564892007624175774554157873815154892080*x^17*z + 252267212463326592215194562285703658764876840*x^18*z + 1579984888847646191802159943453081444663907484*x^19*z + 8953235042103492321181581093013602155769051612*x^20*z + 45903181479775065685746052620589410081998731524*x^21*z + 212824169916940053786033181936625696969521713660*x^22*z + 891392832702671559852449634740368405988291154576*x^23*z + 3367478276531373587105438940780372630636177196752*x^24*z + 11449435585574619285981935439477146954818804880112*x^25*z + 34935528499554504685253316363689474984388242818752*x^26*z + 95317892340744767224896692668255805803325768161752*x^27*z + 231485665082691309511503545714991895032671262644760*x^28*z + 497560801755520178970056212349142432013282965491688*x^29*z + 939840996417932148185674193085533589140914345757304*x^30*z + 1546197412122515582506898752925041825121169239926512*x^31*z + 2190449751731184517705071896277054264595772555710512*x^32*z + 2632902875335051927821246423225939508411350031304496*x^33*z + 2632452245401035714299054555506473029495846016234708*x^34*z + 2130958730852612957996086501629287342380238549530266*x^35*z + 1346387674158018214620227794644620177276669936326554*x^36*z + 623756195261119510824698500447725759934853718865302*x^37*z + 169752219628159525357842174614909358360072250064730*x^38*z + 9643730412467490523371*z^2 + 1751508483444024959631681*x*z^2 + 180916037470323574417460781*x^2*z^2 + 12233407143306482256457577232*x^3*z^2 + 606118551048335019634649146107*x^4*z^2 + 23367473975046034208061025711911*x^5*z^2 + 728421126124038027914198607293817*x^6*z^2 + 18868752321588740210322789303668064*x^7*z^2 + 414308451729930813185694749573131260*x^8*z^2 + 7825833236785378088088541177710286500*x^9*z^2 + 128606153173224855814637756267582780100*x^10*z^2 + 1855051313833448119668449319118667226144*x^11*z^2 + 23651798888503668012425878793329093994316*x^12*z^2 + 268053120097636202152862712811264334823660*x^13*z^2 + 2712446938606718806914465313418525436055908*x^14*z^2 + 24592891641134888395019327537830483012319712*x^15*z^2 + 200329471000092472634559667088086162644503034*x^16*z^2 + 1469081104905246707248850519426796600825460350*x^17*z^2 + 9712259663051622035756481607475766318900968694*x^18*z^2 + 57932825783353442937754995850599570761534690880*x^19*z^2 + 311871752669677894681341719409199844667357685482*x^20*z^2 + 1514804669394469909743434970510837176423644472994*x^21*z^2 + 6633006505988272084744115348483570998893557632590*x^22*z^2 + 26147518920242847558373144438530469629205441249824*x^23*z^2 + 92605827724522886122699851554931070431436969686828*x^24*z^2 + 293868939116730390556145423872799672728059885903828*x^25*z^2 + 832628374118471953013760679702380937055811671891796*x^26*z^2 + 2096993653802535947088435222344004038514578837331168*x^27*z^2 + 4668309788359972208217093338322979087260119258263452*x^28*z^2 + 9121934877513245906129022129440154179483931791374620*x^29*z^2 + 15507243382046238606774064102966507272115701064901652*x^30*z^2 + 22677615122299555101271309965832575195383030752749216*x^31*z^2 + 28111325531206383405154326247231776793069269312841203*x^32*z^2 + 28962929405996491059899824597548995685882889678576329*x^33*z^2 + 24134320054203597812361190704593444755766618423081157*x^34*z^2 + 15621709739973357383625054788685193267178784889408944*x^35*z^2 + 7371534190697021547710669575085297427277061353243443*x^36*z^2 + 2261476792601814121156141859591959118596962531417903*x^37*z^2 + 283549077971481281245877113893793039334787351034049*x^38*z^2 + 342216218761063886877363*z^3 + 76247891165136585238075017*x*z^3 + 7900491927292055387627684760*x^2*z^3 + 523423319831841499759193824242*x^3*z^3 + 25208128013123300679123783506919*x^4*z^3 + 942604050647503773602266819194459*x^5*z^3 + 28486466706334994716272337611139392*x^6*z^3 + 714888056920772762652913527624186384*x^7*z^3 + 15191552673031244868346296925948277628*x^8*z^3 + 277386071766831376373149739089646019300*x^9*z^3 + 4401177198207987600932726465579721392928*x^10*z^3 + 61216350729494417188416842710952114743896*x^11*z^3 + 751601551512798238314882821390537965330140*x^12*z^3 + 8190533662655483498951061355277406250784988*x^13*z^3 + 79565159229370130726630526679180141627237824*x^14*z^3 + 691332571241415444592014409222903331311618224*x^15*z^3 + 5386633154954873898016398855766238231995385610*x^16*z^3 + 37706441909655498989199727326488589068414979534*x^17*z^3 + 237410948819741182128583361537690173328718756624*x^18*z^3 + 1345328488141384647812489150978159106661679762700*x^19*z^3 + 6861174417941368179223190277768151650698736476850*x^20*z^3 + 31474278495337897889481906128202239891328383840922*x^21*z^3 + 129712195267969818280228890674598696122343832432320*x^22*z^3 + 479371179226166129129042782787289468854984356989168*x^23*z^3 + 1584587966452281379330468964959620463005653681905260*x^24*z^3 + 4669251547371105506086517598456206910248301772471380*x^25*z^3 + 12211885942828029339427593796868733804207587339878944*x^26*z^3 + 28192884115946756732781391530027654068914075937600280*x^27*z^3 + 57057094983342569431062100563499054566043670890616748*x^28*z^3 + 100341758582959633960950649590749146584574341954511500*x^29*z^3 + 151626854198223527379825060122520385779927813689914944*x^30*z^3 + 194016570806273602044640576365703540145063769649949520*x^31* z^3 + 206146703836682632840215191656611539932782869503245915*x^32*z^3 + 177001087190786570521091635763164992989673921351249777* x^33*z^3 + 117982303460122404914358699007442107624981770461595672*x^34*z^3 + 57271519598998921957280188771746329896902501735072402*x^35*z^3 + 18086430043190782419136861912719629110996113184587999*x^36*z^3 + 2868442681172043779145881678716118680558946358882467*x^37*z^3 + 12741311150112745228992678*z^4 + 2571906247574770454933951586*x*z^4 + 253982468482258302269922247974*x^2*z^4 + 16304993653056933011183451422352*x^3*z^4 + 762343600149242634985513381020933*x^4*z^4 + 27649388978070973457017554083210832*x^5*z^4 + 809520414810735464625948600846100608*x^6*z^4 + 19659630596045126816939038688043173952*x^7*z^4 + 403839644078034093724274266327300754016*x^8*z^4 + 7119547083509018381452024338536385518808*x^9*z^4 + 108929239643071926805758911508580857383544*x^10*z^4 + 1458992033222818844159493206552705588754816*x^11*z^4 + 17224202978930354252753220620452207735716252*x^12*z^4 + 180191614049158907715152023283858857449405936*x^13*z^4 + 1677498369500012938825651910413077130443315936*x^14*z^4 + 13941877987322130657269119936294001722976161344*x^15*z^4 + 103692715562900381704349393944711177595984096172*x^16*z^4 + 691284680914383463141363459795134728910280910316*x^17*z^4 + 4134906348764220850823008029350315148529827272628*x^18*z^4 + 22197920061839158666973289148682682670360326925344*x^19*z^4 + 106919989865345093606934330574596567312751999422798*x^20*z^4 + 461622801594484033896560027833695805380220168563120*x^21*z^4 + 1783542464577829765297843362295179528527585173664064*x^22*z^4 + 6151928762467408432767884432542976298588266277143232*x^23*z^4 + 18883005288525385309841496051859934786331963291015984*x^24*z^4 + 51361783227141637008875498424579896016519967554266136*x^25*z^4 + 123136586013563889190416308653580054084454058774217112*x^26*z^4 + 258434724746553375570151807374691909229035243226111232*x^27* z^4 + 470720156638654018409421319303555916211908338219586556*x^28*z^4 + 735838781312920044555927576926285381276397677810815248* x^29*z^4 + 972944565390857464965683817636861637138337102502150240*x^30*z^4 + 1067096764997074070908498386969699657388613891366616768*x^31*z^4 + 944811163730939089911288120180399428010517623859697310*x^32* z^4 + 649004925226402301589956294019754766907238943044347330*x^33*z^4 + 324588758185787327474749894056820750690071076168409622* x^34*z^4 + 105033043579231769755317496651393722459318721745938128*x^35*z^4 + 16600220317771184440146529898584435381489293771699093*x^36*z^4 + 332312791708775912732854794*z^5 + 65740127318065123122105552294*x*z^5 + 6331112506265092145068098404808*x^2*z^5 + 394660641171724329210939981524124*x^3*z^5 + 17891047637304395373594843816407616*x^4*z^5 + 628561492033131562156955047282520736*x^5*z^5 + 17809200633325096882362152562020253360*x^6*z^5 + 418093243425619011981624433368569119632*x^7*z^5 + 8292194209040025463570036931978051183880*x^8*z^5 + 140967274531631952447936450367408580548248*x^9*z^5 + 2076916789546416165853805266946009732069808*x^10*z^5 + 26748168089899447618313946543365101776315936*x^11*z^5 + 303145957212485629991928382524357213415061472*x^12*z^5 + 3039232855907900431944461015983070778122845056*x^13*z^5 + 27063643626211301796957481656976547640980760624*x^14*z^5 + 214704889859889669584988205398992944641575820240*x^15*z^5 + 1520826299536621592083553384065512389584973911980*x^16*z^5 + 9631900401161558873643979553354660337587808417876*x^17*z^5 + 54580770576594420819800499584100670311415844686080*x^18*z^5 + 276734074153305476039534373645142002580113258080184*x^19*z^5 + 1254527741301725585349306889278876887704199877364992*x^20*z^5 + 5077850375643790067352350488160442605966434207567776*x^21*z^5 + 18311037303635484100693269584698573710567081373536912*x^22*z^5 + 58648398162102180656280634802789892446023468987920816*x^23*z^5 + 166170454360414414902421270371411647129758295273298024*x^24*z^5 + 414318264752290865554753100113977871584945085645411320*x^25* z^5 + 903001266083503138991153681164423273444417014081308880*x^26*z^5 + 1705669646562197001578586455734311281362422684528361152* x^27*z^5 + 2761562176036700005774703575128615883365401285972698080*x^28*z^5 + 3777307871890990732740158013618256256463863527182550848*x^29*z^5 + 4280936986972444661877046433046000337309812992623028880*x^30* z^5 + 3912673049604395904622715596659579018483800913545847024*x^31*z^5 + 2771510186736665040704531168173399003596092243589940698* x^32*z^5 + 1427818770723150459054664467261570222114220075124804214*x^33*z^5 + 475878092246793337453326680846839628421291755063824056*x^34*z^5 + 76929802779825090695114781235516217609130364196197580*x^35*z^5 + 7074140179699768467882758751*z^6 + 1364979631893772484777289508593*x*z^6 + 127677463055642373688810949509809*x^2*z^6 + 7717618628353231755656667898213440*x^3*z^6 + 338931491807121289074311070522558024*x^4*z^6 + 11523651647862048076290967188187542408*x^5*z^6 + 315619662906015102672852958758092992536*x^6*z^6 + 7154044127271192967771270094096624686368*x^7*z^6 + 136821108285222759822997207422350672289444*x^8*z^6 + 2239812397817969894270766304987380250673772*x^9*z^6 + 31730676809558954012162924757357624346281852*x^10*z^6 + 392306550471785345505510663802963855211928192*x^11*z^6 + 4260884921340158557791786732850332994772094840*x^12*z^6 + 40860792965311022278208675547234136199007267480*x^13*z^6 + 347316742661854788899505521512195000951164877416*x^14*z^6 + 2624171002495562769395941336896146549917484923104*x^15*z^6 + 17658484158487211996524442505393915198380880243258*x^16*z^6 + 105950903229655744927872597820231569891556919857974*x^17*z^6 + 567033527630836897208151048925601780787461959892742*x^18*z^6 + 2705844216563860316490951440635108438221449779085376*x^19*z^6 + 11499838234853837474061749037326883919761319868854008*x^20*z^6 + 43443834047022922865437105434337106009651986165758072*x^21*z^6 + 145471015351498890682427244677048312978102552620479528*x^22*z^6 + 430088191689823454232615799348065247182401334922472160*x^23*z^6 + 1117034620582697502706786385573388723184774471557331236*x^24* z^6 + 2531945566116465268042087554848299668307972111478315148*x^25*z^6 + 4966509287191533485866705887411261007708875207689667516* x^26*z^6 + 8338827171089650343804988258897810270903344803352794368*x^27*z^6 + 11813328613191566364102061312251666204965518204176634824*x^28*z^6 + 13850125223530401597128066007588020074534260693323617512*x^29* z^6 + 13080739856100979280416222945031720711002220565228300504*x^30*z^6 + 9564309340637587431711641644070531366009564207635653408* x^31*z^6 + 5080718804917499771606379545191333047699711583965631263*x^32*z^6 + 1745072394630523109129087572728715306188634309303762785*x^33*z^6 + 290813985597689820336642384477701962349579968813542289*x^34* z^6 + 126298796322161844433301385411*z^7 + 23607581505510789544991615955441*x*z^7 + 2140215513102492405278223198155328*x^2*z^7 + 125318031581952661777948160405390160*x^3*z^7 + 5326030221874122866502279432003600168*x^4*z^7 + 175049510378644116455682578354416911240*x^5*z^7 + 4629090251593548767969227075198334560128*x^6*z^7 + 101178657858236909404611848774815951520400*x^7*z^7 + 1863373299468195505207274537852681577540756*x^8*z^7 + 29330876383378586018150551016680654691720364*x^9*z^7 + 398899928305818224368416119779578240362997696*x^10*z^7 + 4726359707794654056074257027008238065798012432*x^11*z^7 + 49101625713775087550835831030033628597580482968*x^12*z^7 + 449468734192278345099798949977368514868135365912*x^13*z^7 + 3638556438248884831592229590552183637954902896128*x^14*z^7 + 26116749198256483791971561364133495861393889096016*x^15*z^7 + 166494274333758441485748929753066901447334901082258*x^16*z^7 + 943467563307431866673931926735281378384878589098486*x^17*z^7 + 4752281143958747287076561762298592517636136820850112*x^18*z^7 + 21260205086764354489770101847030069769425809132379888*x^19*z^7 + 84332144656661442544480957523999087880012759143097624*x^20*z^7 + 295831804365271554323157880791849837115178976619171704*x^21*z^7 + 914389243296340004831876603308260096634932636704179584*x^22* z^7 + 2478127510423692766674163104163599417010487796593906352*x^23*z^7 + 5851134281310205989158910470561144675327766467644874004* x^24*z^7 + 11936312104442496156894796391907635820840409379023275084*x^25*z^7 + 20812029601606519619849719102835789467612267947420692544*x^26*z^7 + 30575708379630987295550991481705324307914657715719076784*x^27* z^7 + 37127664994942787679286664540287880551963982699016321192*x^28*z^7 + 36274138330087119670717236415330016290845196841553382248*x^29*z^7 + 27407086718212074466187405728692067019541440114772712704*x^30* z^7 + 15029667436237215884863348018312305765870764159567641968*x^31*z^7 + 5322985898519730715161784458782168730304791565804025475* x^32*z^7 + 913945012098706230667813847792368321204727850808641441*x^33*z^7 + 1908921407361667514961102741168*z^8 + 346191633438160246866555636199968*x*z^8 + 30408012266243193412984502820770112*x^2*z^8 + 1723138606092104700640474384775129472*x^3*z^8 + 70792181252745480626399334602145402804*x^4*z^8 + 2246469001339816851147965790382995727344*x^5*z^8 + 57284958422463742820015716583369699064504*x^6*z^8 + 1205712174223801157641529999552699347743696*x^7*z^8 + 21351153504938839183436405964239617871700204*x^8*z^8 + 322639644741153901635261305690036582874716736*x^9*z^8 + 4205070037203033499180135874202876494769458928*x^10*z^8 + 47657460972236394244156207822198082378893523616*x^11*z^8 + 472603153844482663281990062738381704267818240564*x^12*z^8 + 4120130018431430405137608848988681742435257386832*x^13*z^8 + 31685761754628025930882360759416196684054849896648*x^14*z^8 + 215463181709518679427479279851520137940304274911024*x^15*z^8 + 1297267914142920821239247823969662590684626249264492*x^16*z^8 + 6918762172776641621195338166013151067828987986503456*x^17*z^8 + 32671932141363715033361851309187154237268756862419296*x^18*z^8 + 136419646306039207498945509725388173091995900314907712*x^19*z^8 + 502479038141001559889354300430958153695819888160626108*x^20* z^8 + 1627075008576331460361673907556067296933418322403594384*x^21*z^8 + 4610045791216823406294871495163939000616070054776913608* x^22*z^8 + 11358083188914360002194490910466900251620459226683866416*x^23*z^8 + 24135926258294995966685406689837113830885751443801091428*x^24*z^8 + 43766486111756890999583502770633711858248312639436706432*x^25* z^8 + 66771962364519129334519948447868894675852885286504634224*x^26*z^8 + 84083181016469409685079801364595487786281702017358278048*x^27*z^8 + 85084047541538130009085923342056191256846465051443122780*x^28* z^8 + 66502622521158386298767207931825174799573950290801524272*x^29*z^8 + 37685448727451866074617500254148992835875752801367821496*x^30*z^8 + 13777260717649052942017159002439996360530923934222850512*x^31* z^8 + 2439786446152216550995326348683945199342052475693261716*x^32*z^8 + 24887510231216342800061240341776*z^9 + 4372451597448148105811656800763920*x*z^9 + 371656781455105480324275202302353232*x^2*z^9 + 20358522283769244865961696727057800664*x^3*z^9 + 807554454362146334167439454565686832680*x^4*z^9 + 24711163574142939808528648320859947503448*x^5*z^9 + 606796324045853848159459672179587993908536*x^6*z^9 + 12280401695822241286719473185086698669416848*x^7*z^9 + 208766830405313115006287538086848696979279232*x^8*z^9 + 3023252988769349780506929287752788734208063264*x^9*z^9 + 37689887101600570240028529052921574853976897632*x^10*z^9 + 407736050868929350956551180684775844559692859496*x^11*z^9 + 3850840489739176406470512560137335650100569183352*x^12*z^9 + 31892858530144729219318321595352616278408022761864*x^13*z^9 + 232362255186235343609223927747121030654653528220776*x^14*z^9 + 1492282032716820170582574823660215978862158883112064*x^15*z^9 + 8456264812339214641497247601807076841417591974978768*x^16*z^9 + 42281324162583266558999220253970874806893116607605648*x^17*z^9 + 186351023090789191253427173742057134388733545491528784*x^18*z^9 + 722518881438356749661595461791224908857569046161499176*x^19*z^9 + 2456564158921818010623766616158153144706883951520114968*x^20* z^9 + 7291706170840948930935607704249484841252054701556088168*x^21*z^9 + 18781667753089246003186342510992206565581805133731628296* x^22*z^9 + 41646309390619935103228110127120826465048096561203036752*x^23*z^9 + 78665251472679669368743148655729704244249760337428799904*x^24*z^9 + 124815510513408876964763617634038772350837279479841147968*x^25* z^9 + 163220262074960010877906055908855576420469249605295782656*x^26*z^9 + 171280599718606165943478426018947761317980915169448425624*x^27*z^9 + 138655763810690924941111235358705013049560666190415858504* x^28*z^9 + 81280821313625900777278743083728210015099190733860758200*x^29*z^9 + 30706210461836332080702772557016958294721922228943622744*x^30*z^9 + 5613480648292009109861196392151734138797490289919825056*x^31* z^9 + 282956170734983678739488904995388*z^10 + 48097728106939595701804487177594772*x*z^10 + 3951961234817517290399974191342025668*x^2*z^10 + 209013973341944116621755636208919123136*x^3*z^10 + 7994785570372862279538275746173505018356*x^4*z^10 + 235579749026634686233405246785162216503076*x^5*z^10 + 5562299714805589302683024703028917487024284*x^6*z^10 + 108067534925024855131847332035117664748882400*x^7*z^10 + 1760600261333043126598300496719884967701709980*x^8*z^10 + 24387574114821283525294896785024383798909311972*x^9*z^10 + 290212131728693309261073540218844963104123265348*x^10*z^10 + 2990064384794771523310849485480320763727713386592*x^11*z^10 + 26827522114964654549633610315003057718799721499764*x^12*z^10 + 210492865479814485758622214310571409186490694796596*x^13*z^10 + 1448391382255458122836313815327034429900051155967676*x^14*z^10 + 8754721265356689724352124214972515510048292424389824*x^15*z^10 + 46509456894362947304909541456087456691081377015488724*x^16*z^10 + 217044131928396812709282546245371941889068525195061308*x^17* z^10 + 888273200260550391907863153003447659917027886499405420*x^18*z^10 + 3179083018446745010488282732552687918027223200709563776* x^19*z^10 + 9908142173844611500293572759988091619809422384863910012*x^20*z^10 + 26736257217031469013971083596159906328729879567952664300*x^21*z^10 + 61979505213827235142774548291951199145510262040423239540*x^22* z^10 + 122162495418796730679317463385981864385212592820686817120*x^23*z^10 + 201907444099826682016395981928835261578020710119223236692*x^24*z^10 + 274594162617810449167381155152254505640036104408182749516* x^25*z^10 + 299237362232047149732307772779497112512941772626614578828*x^26*z^10 + 251211461823928964887418222044341995895482509203836170080*x^27*z^10 + 152520459009026512696939366941540931988252460884587208988* x^28*z^10 + 59605831671480908966529599777708644799933862456628791228*x^29*z^10 + 11258611628807781397598747987473580307653170749574819636*x^30*z^10 + 2829190614455711406539947462522236*z^11 + 464925557498655806328691701833949396*x*z^11 + 36884697419091626350366083471470023776*x^2*z^11 + 1881126204978879834319339898152799945880*x^3*z^11 + 69288169959391663728776583373778249443524*x^4*z^11 + 1963164598088936768796874086083084976432468*x^5*z^11 + 44498396764454209707994210917231479598116160*x^6*z^11 + 828517772502261526554799734972491183017596240*x^7*z^11 + 12911068602217795503325508634179743160981903100*x^8*z^11 + 170713018238300714623606230878062558032512964996*x^9*z^11 + 1934747542094910086282807925311556457149547967136*x^10*z^11 + 18937074419701511527536289102730772390588814099080*x^11*z^11 + 160965132537172291729464905267076966474346614148260*x^12*z^11 + 1192792906747170634733202158508982273960664532839940*x^13*z^11 + 7724754070980983016529450860667663954227446866471296*x^14*z^11 + 43773606330188206736992073800224084329648146193745120*x^15*z^11 + 217044130630811862135491138120241966598450567588683348*x^16* z^11 + 940524566083461824941616908279856846504117771949678396*x^17*z^11 + 3553092831243041336280162874919379490558770353966455200* x^18*z^11 + 11656637963799610374373533638508151012136863466157894696*x^19*z^11 + 33027140521371199253486369275493922006557764271529500844*x^20*z^11 + 80208767589004113306954744077331787234926666166515026364*x^21* z^11 + 165278673522925261407943219848925836901386540112361802048*x^22*z^11 + 285045853072347955460472427626010864446722939067005831376*x^23*z^11 + 403814976406489434035898111682266595313973514551317050164* x^24*z^11 + 457656854683683854213565717739097800951730634488316367212*x^25*z^11 + 398982860442621908490940723767175736459554234442102898528*x^26*z^11 + 251211743154574868024378029498329799639838154707689548216* x^27*z^11 + 101680808097125491798195549800734743109554294809398021100*x^28*z^11 + 19867860395742170767264334984898541892343463702698833900*x^29*z^11 + 25069584304539692013997416959944776*z^12 + 3977781302711917010721915911801836728*x*z^12 + 304299816407929307329527058158575238696*x^2*z^12 + 14944504543496654648957745602145518431008*x^3*z^12 + 529284564342218218111329554966016871995780*x^4*z^12 + 14396540184239933954010894321027269212999056*x^5*z^12 + 312724845923927416687579980903420775282730784*x^6*z^12 + 5569480591359078276364772970701202138063365952*x^7*z^12 + 82846023676496217728358840500358687466842906048*x^8*z^12 + 1043246223471200888115087606366571570514013075816*x^9*z^12 + 11232284341597200904877215000658757061183759528872*x^10*z^12 + 104153909380893636981295095192212108677449806967648*x^11*z^12 + 836124439181508128824884403698425231587849294778316*x^12*z^12 + 5831431980795475797424349172950661713505457535542368*x^13*z^12 + 35405122704568296358709282156506907508983080060945152*x^14*z^12 + 187253760286881678918213649840721447677700914082822016*x^15*z^12 + 862147524148431728151936802611226836280807094121994536*x^16* z^12 + 3448590099543321435437823546543335146359508807868139528*x^17*z^12 + 11942339713240443481854709749573542309399003100329637240*x^18*z^12 + 35617504095060533441276931256379023013999945659838915040*x^19* z^12 + 90824636007699818902638395289723849605952310312164871068*x^20*z^12 + 196065887104517561564339369415956291348752472242998455568*x^21*z^12 + 353512743413118516317961695019124370419266855672733164768* x^22*z^12 + 522584020056742297417722977475600857788691542220086718784*x^23*z^12 + 616939373049980104666044445602329934142024861696259573328*x^24*z^12 + 559358478726037606646083157270756641834355177461119503064* x^25*z^12 + 365735069478342831781999795234853394926534116358520777144*x^26*z^12 + 153518402442763405689286938678035601852888883148743126944*x^27*z^12 + 31069725463820313097573706901119215807314850811408237972* x^28*z^12 + 197991115362552741348103140284622648*z^13 + 30292624634658874467495240575237542056*x*z^13 + 2231537684077460154936184089091049706336*x^2*z^13 + 105377951740893391471701354750403661500992*x^3*z^13 + 3582849273921232459427480544302766662963232*x^4*z^13 + 93392939834952550381842668775074693658024576*x^5*z^13 + 1940497761914494626790936001051838307338361488*x^6*z^13 + 32988461932191420679307933724274608914163156048*x^7*z^13 + 467336543841568798167269723193513789810946955640*x^8*z^13 + 5590729761808762277623614734018028139723396388424*x^9*z^13 + 57025443567203556140463279553814791067004750944688*x^10*z^13 + 499404642123512723977228679120891820339730000740240*x^11*z^13 + 3773279517930682117442039692517253652340780422801536*x^12*z^13 + 24671443019445621354273576449867538812526205735862976*x^13*z^13 + 139804843938553538035906746619926136756620891179631648*x^14*z^13 + 686597121966080685275476188129981187101189346874173344*x^15* z^13 + 2918037757580417336889906144621281982962802135246139944*x^16*z^13 + 10699471754113790768304599519099885446389160880823407928*x^17*z^13 + 33683522438350717556703775975912152249025102695334222656*x^18* z^13 + 90413666764248454506739455529061367336296510933311277280*x^19*z^13 + 204937643349770146844408054912615652083637830464764524640*x^20*z^13 + 387104418728547879810159140896092255018876778768895374272* x^21*z^13 + 598252270536118304486247466177137770699100341706623038800*x^22*z^13 + 736977541962726668066816795743572229170044409190160465424*x^23*z^13 + 696034378710719462706064689765691197098340016609184414760* x^24*z^13 + 473303042323078224878142920217131906694567697689803789016*x^25*z^13 + 206311648307273040432260708861193296379794407660310807472*x^26*z^13 + 43300714495648429818811640476029081541298584258220301136* x^27*z^13 + 1400038283931642888514436853397415196*z^14 + 206274625629707757576488326543639673604*x*z^14 + 14611211454807085123315645074816944584068*x^2*z^14 + 662375513500743961644435255926911877362368*x^3*z^14 + 21582402496043676379790148823205001086307576*x^4*z^14 + 538121225080814373075897552446375103052317432*x^5*z^14 + 10672737637983780987512948323803400347893013864*x^6*z^14 + 172796705068955002796289106835148304250673172128*x^7*z^14 + 2325555657961455762406010258955180877753398970980*x^8*z^14 + 26356297456613043237521225941615368692261209514700*x^9*z^14 + 253898998792501506183819303682941004593003108066396*x^10*z^14 + 2092743263054323120244936891919816036314428984744704*x^11*z^14 + 14823598115572563688448687636556027900199238093035152*x^12*z^14 + 90461957670196985627068633314553502263522401738995664*x^13* z^14 + 476002205179745458600689577515572563965579599710427184*x^14*z^14 + 2157876664077625561712311460436289432989239584542512064* x^15*z^14 + 8406727871392457296955097363560479515433893732210272676*x^16*z^14 + 28022426351504418794996990295311591907555645030316243164*x^17*z^14 + 79396874160588634085830132570321018559364600232855874172*x^18* z^14 + 189438152160174273880418954366158577062353559061805354816*x^19*z^14 + 375718998777288562095795861199864517512851245716058114040*x^20*z^14 + 608306975856207308726502663887152274812694797165174536888* x^21*z^14 + 783425699973673639535341540444691966153540330902768993512*x^22*z^14 + 772071639900183357752295209878295659483960773411282034848*x^23*z^14 + 546883645907139025021484366545643553080264709795353860956* x^24*z^14 + 247920547596707986871026937070787365304266500158182560724*x^25*z^14 + 54033350890112773096977655856734479912494767732298391844*x^26*z^14 + 8898218766696128949968423924579180364*z^15 + 1260572544585234590244260368880927316132*x*z^15 + 85719101074875271814831265788624548931904*x^2*z^15 + 3724021566561433325883718583984098683933936*x^3*z^15 + 116065362427771637889174762862092782871988248*x^4*z^15 + 2762355633108726634686813711503140086778323192*x^5*z^15 + 52177828520294895640454173034608659858668211840*x^6*z^15 + 802544695728794407021148344142726045342037245136*x^7*z^15 + 10232444883186876556814030680897077556559390471412*x^8*z^15 + 109525058249923992944009935662931270811679934229676*x^9*z^15 + 993027194939692391265673365813330766082010698892672*x^10*z^15 + 7673391959955274761747031098253881726567808629775968*x^11*z^15 + 50729646838345372329382465562990057240030477237118288*x^12*z^15 + 287467998939912146038522342111082183755785946272353232*x^13*z^15 + 1396273140318208758253830154023583295629090595668396032*x^14* z^15 + 5802290607360151424136203840115503944109430827034861216*x^15*z^15 + 20549779124374910542246785866798356888739977129843594740*x^16*z^15 + 61649336868686008465940842498206055134234599361673599804*x^17* z^15 + 155264997568096985568936807464465093350988940314809945920*x^18*z^15 + 324149742067877794543635982132061707057092558940031169456*x^19*z^15 + 551054569619269926705916139314396203625794082166332664856* x^20*z^15 + 743486257650398688092074767693982365301644993528221731512*x^21*z^15 + 766016119559089680470645169175448290123283954100989262720*x^22*z^15 + 566186050618524327359227432024512015724185214134127005072* x^23*z^15 + 267365639585810517517451005006086241642495926752128166988*x^24*z^15 + 60602437683591894210217783544472470829875944707199588340*x^25*z^15 + 50980283032856002647975290394542728080*z^16 + 6933213732786427461247479736739370583416*x*z^16 + 451811960119271176750060256559365987211288*x^2*z^16 + 18775280435952747317861512628281773743220720*x^3*z^16 + 558564561530666079559234633417214277716454342*x^4*z^16 + 12660796782853516585307986908929833832138740896*x^5*z^16 + 227190963575387722199622376196913341705903477412*x^6*z^16 + 3310496885067053312114784238655729930099098443912*x^7*z^16 + 39863899933142922125018813599424407717740732651318*x^8*z^16 + 401591880675462216852347973352248761649316399700304*x^9*z^16 + 3413530985394046322391141473548872149605495954186944*x^10*z^16 + 24618799230712783096008049408572379696364412131476992*x^11*z^16 + 151132073103006232085946364245847447145127099842122380*x^12* z^16 + 790536997232079347264061627690316284252300795894661920*x^13*z^16 + 3519771859370105291916652417516003547741746650006677688* x^14*z^16 + 13296915890721187318049142136280323359680728677895443696*x^15*z^16 + 42383919672083399058024730510331498979882252857038265772*x^16*z^16 + 113023787475219822034227361012152375317141800434622283256* x^17*z^16 + 249070940021901602426511050587255345943505454143955743048*x^18*z^16 + 445705877814719797753608921077731670353296521859667170384*x^19*z^16 + 631416638715171431874012410641299171726533928553254764526* x^20*z^16 + 681529096564736542829131198440402192253516195055431015296*x^21*z^16 + 526636337638517739687336993055451766294146659859702234244*x^22*z^16 + 259502006637288639265049868427112110296551626452051130440* x^23*z^16 + 61271792888361956378252332622589154861362446079827821902*x^24*z^16 + 263888740156078110512123314571452111920*z^17 + 34393917363664944840127939881057077699760*x*z^17 + 2143890376269105720759899985619028117143992*x^2*z^17 + 85040978194736986251948608432834230658697180*x^3*z^17 + 2409494137719684254747637555035410271071942572*x^4*z^17 + 51884440873503084183037130307706518027194123124*x^5*z^17 + 882035498617862684173823048293563594905720292732*x^6*z^17 + 12138488555318113352434756117502306608809266976432*x^7*z^17 + 137569536884955555861049928945616585809147952228720*x^8*z^17 + 1299267848445480370605878014799459854084494112431120*x^9*z^17 + 10307524928561315223178812927049574602796524561901280*x^10*z^17 + 69029182082884994367691769385767344987178413881393576*x^11*z^17 + 391165364849618846815311913927542916447517872976270088*x^12* z^17 + 1875587776451937491568141997392831449067914940393126648*x^13*z^17 + 7591664841331792183499008537302701311412351854186800648*x^14*z^17 + 25811660600386300592120551735595374141692127339896056208*x^15* z^17 + 73133037825498027914196678375189021562283191476691592448*x^16*z^17 + 170643750504806022227478384248961256674804451365343709088*x^17*z^17 + 322327079998851027037784715869632999961455539631560488904* x^18*z^17 + 480663220229919701675965634181517848209106911416018682076*x^19*z^17 + 544751664891646968045900079974939407541135340976052729516*x^20*z^17 + 440989349288768154577433935799304822043343299013282354484* x^21*z^17 + 227176300518722588946897955926760569584084252680943962140*x^22*z^17 + 55971132978837534944541783051008969162090351404972005728*x^23*z^17 + 1236366691619624991600504188141931088122*z^18 + 154135283781776631029894718077876931092238*x*z^18 + 9171079378385651366886909605711936183362038*x^2*z^18 + 346463202510987577846202868986311474840770528*x^3*z^18 + 9325634849480671990914328868385566783364415842*x^4*z^18 + 190242949807464351293286269194609709390962966986*x^5*z^18 + 3054456253991132340806945167397341523653490155638*x^6*z^18 + 39562481115362879408535012026293379884967366035488*x^7*z^18 + 420351362243361580237541182717611164630595256362516*x^8*z^18 + 3705319417660170941667251949047469925670520498156300*x^9*z^18 + 27295853050574516933373284579346131760768208995874668*x^10*z^18 + 168738000799513769330471501754634619085249348798560736*x^11*z^18 + 876500171930240836153436727409615556480238755830645620*x^12* z^18 + 3820641774804138079764556079167786798987947821546495892*x^13*z^18 + 13918052077651604974553679196198318452748552867095231516*x^14*z^18 + 42063445721367443080697215382305668552528157570459938144*x^15* z^18 + 104282292286543026549891055757221735631241207355078996338*x^16*z^18 + 208564591717137853327387539784262893083402109822458776646*x^17*z^18 + 328296125805491285632093811189354009507797512719137103070* x^18*z^18 + 391651512053189885850891150340836476544801781732488394944*x^19*z^18 + 332903688362547467659816283163777549339076388096361599658*x^20*z^18 + 179662279549995055762323025326457439577352259111910113346* x^21*z^18 + 46276375500949644388973764086156722652538077297789203758*x^22*z^18 + 5249293597722989862331337857834519205706*z^19 + 624657539119445018615862813568569444099486*x*z^19 + 35397176259851800888221297250706681895645648*x^2*z^19 + 1270365100787693785417345910867760289834649676*x^3*z^19 + 32394311556261264452770219529476890942289415274*x^4*z^19 + 624130389967625012779046310508554858039780938946*x^5*z^19 + 9431303620416193778134595712761681962211480283072*x^6*z^19 + 114522972018544370900421761888555869906598078247984*x^7*z^19 + 1135686139059957283888321363148759989905638326041300*x^8*z^19 + 9295801348992442312785441282724722725770167021581196*x^9*z^19 + 63211449168793187175597697042281197023140585144512352*x^10*z^19 + 358198211306506748384592636777166958707278936165287400*x^11*z^19 + 1691491548208570778422317387072858845559964796178029412*x^12* z^19 + 6635851435267206759730656803851252556278312634410101924*x^13*z^19 + 21487519150582200018792569940469883483149037059232196288*x^14*z^19 + 56822552165862645985250301103221556201684273546089415536*x^15* z^19 + 120747925193484393600501499516075872423290903881486099362*x^16*z^19 + 201246530407424234537107591920072122025861518933153436918*x^17*z^19 + 253421548586164899736373974477191295659277085289198397008* x^18*z^19 + 226745616988284361180603658511001644766913147264115552300*x^19*z^19 + 128489209405322963039640211175227883684303163800207920242*x^20*z^19 + 34671672435780205789595367494985430114130467937057757818* x^21*z^19 + 20209544173097942520319942615958813371524*z^20 + 2290408163361829924513393961689382267470476*x*z^20 + 123300168236127078471277152187296697819021476*x^2*z^20 + 4192204623846684968915062148855725178009484096*x^3*z^20 + 100962264585882123796195183734278148256282857510*x^4*z^20 + 1830782439290629988948478476885462951873589820656*x^5*z^20 + 25936084738979738937952897263490112434409871011520*x^6*z^20 + 293942293953355785795245094826482260398452992940480*x^7*z^20 + 2706718626986502283439452315767237029439350850427296*x^8*z^20 + 20450762960599157636182947455164226814511640488676520*x^9*z^20 + 127476422611703041614379739662296412533027760179955272*x^10*z^20 + 656696723994253431388751575650517654595443219811722560*x^11* z^20 + 2790961103996526660526237852780883932317263387384380308*x^12*z^20 + 9732582438346609713479198390722881705903703233522086064*x^13*z^20 + 27575650252786610422429992436077088304243847188927904288*x^14* z^20 + 62504804411956707446571091657644995936893066691072206656*x^15*z^20 + 110685587394021889439214632949533850150653941026312112332*x^16*z^20 + 147580783247993821453871708338016322652424731019104417068* x^17*z^20 + 139381893430286176384074809085431121522405029961659837748*x^18*z^20 + 83140092267724100303967821126163773361475470050225106048*x^19*z^20 + 23556468484499236606356200318160777881663175374952073302*x^20* z^20 + 70571820359255968090488736841210962046172*z^21 + 7598313097372719043853302279886240402148708*x*z^21 + 387514706738157183407949832992448082709496176*x^2*z^21 + 12443529512497443677954530846849403569134842616*x^3*z^21 + 282053316797045111358542168917110604037864490624*x^4*z^21 + 4794906456263681896797775890720480288176697315744*x^5*z^21 + 63399318550683183177224095823451358197075634282320*x^6*z^21 + 667202355153869228237587324057539071342095692306864*x^7*z^21 + 5671220012589169759066713629799269597183159691400440*x^8*z^21 + 39278449812853039138078715904663351010257175425072168*x^9*z^21 + 222577882272408686294597172692110277883035459143669776*x^10*z^21 + 1031951999647551035087818918123186960232476153177147392*x^11* z^21 + 3898485266708543647168337770079739718984893978683413920*x^12*z^21 + 11895377707468737647388316819861795826779304805514593984*x^13*z^21 + 28888773827365211765795419784203162325739148825103304624*x^14* z^21 + 54567687710724842996832249711326237775292766262213626256*x^15*z^21 + 77304228131059731039450919844449702171855639044943314444*x^16*z^21 + 77304229066811253434983342940046422023137757693537363476*x^17* z^21 + 48673018015811615528432378404532016888059102815754789760*x^18*z^21 + 14516498699056317117963198283885148393947895143294163400*x^19*z^21 + 223481288881004776389911958097047943836834*z^22 + 22795001451325115168691509974426703673565278*x*z^22 + 1097958642714910307079051830916357926359272222*x^2*z^22 + 33182749216777355567355905455314356613255886272*x^3*z^22 + 705133344716343120810963789259708470981221461752*x^4*z^22 + 11188115243976506678521067823852771370489984184376*x^5*z^22 + 137365190266560523528020339433174268732815144732200*x^6*z^22 + 1334404696841442063546724141400268638310740494243680*x^7*z^22 + 10397236519768549384215372099004643124403642599092748*x^8*z^22 + 65464081425997125557462204763758770450437134578507620*x^9*z^22 + 333866810786350428493143295771156320417060499990940820*x^10* z^22 + 1375935931676941986608473843877978934962788452187540608*x^11*z^22 + 4548232685556639685738836789018138929887421833050174072*x^12*z^22 + 11895378698122881557054705031682427701784853586090639896*x^13* z^22 + 24073981920778656656382851869104881124999382935495634920*x^14*z^22 + 36378462253798400640737393082229542393108505886363232096*x^15*z^22 + 38652097889805629022860274155260095997466288790077758434*x^16* z^22 + 25768057903601904736717146112655111793462552839710371054*x^17*z^22 + 8112136422783000401263288152378900867648600723181186622*x^18*z^22 + 641292680691182275163826100991692814010042*z^23 + 61777683758990813434995674560347134580988926*x*z^23 + 2800588308009556995404512692010166012527279296*x^2*z^23 + 79350016471153140369852904498328374443168968880*x^3*z^23 + 1573775646300165106155953023725558898214734414104*x^4*z^23 + 23186961673833147058435932002663461887595019692344*x^5*z^23 + 262785573483667890418616270851242616037925249751680*x^6*z^23 + 2340042975402636089935743050113229187103419974924208*x^7*z^23 + 16575304635319704537534030468834877392489545712750108*x^8*z^23 + 93926727318529818994658308850746426266206885186420580*x^9*z^23 + 425801177937111393695381586421348794901808536765172928*x^10* z^23 + 1535464937155255356389767650752721248063916360919595664*x^11*z^23 + 4350484127151669103418556478725654613522953422119990680*x^12*z^23 + 9481823272869098669348934326238182466892854713472578712*x^13* z^23 + 15351521845113293765973226292122955076880185074347336704*x^14*z^23 + 17398389083494177655534724001654368708737334641845026576*x^15*z^23 + 12323865928606266011815479854101364768029081142142438522*x^16* z^23 + 4107966357481382207265757787740409835876609387925284046*x^17*z^23 + 1665560036067176966550921434008112128265808*z^24 + 151011951100159525903553063670245900029057920*x*z^24 + 6418015612854903586705653441073289147055444576*x^2*z^24 + 169720893652840662927614080939082825978431900224*x^3*z^24 + 3125693501664967674313047857539250678450078509860*x^4*z^24 + 42509433945014070701687025708071829197994461547408*x^5*z^24 + 441625793459402736195947324247280779373699432836504*x^6*z^24 + 3575065982667819103758807080345026315555353916164432*x^7*z^24 + 22791045924045466831052506556259818649106542698539116*x^8*z^24 + 114799342046118090501139611903890600187541283212524768*x^9*z^24 + 455370712678158669881148001542749483356586601556709040*x^10* z^24 + 1407509250437057475788431532741171319550261947294874272*x^11*z^24 + 3323285458106093808635530249973067973139039410504017084*x^12*z^24 + 5794446151556052496070370734856482659973636283833949456*x^13* z^24 + 7036120000860107515618262282211317157472599700462356696*x^14*z^24 + 5316182378141792338347280173250455249444985286530605264*x^15*z^24 + 1882819333970796780382285351639177807448835852660429284*x^16* z^24 + 3908613365102054033059613140607786073730800*z^25 + 332228584506036260847372746982876409967202672*x*z^25 + 13178349991366034165646716363462899747304628240*x^2*z^25 + 323601438820350966194700509226768095898306891096*x^3*z^25 + 5501221669949352959932091182985703554222762991048*x^4*z^25 + 68581889660004480964987378467473985260109232490424*x^5*z^25 + 647717784257668377624803817720921780278091945826680*x^6*z^25 + 4719086458542458724807497958026854078467876394040112*x^7*z^25 + 26741487938188282597972679549767241159826316803178080*x^8*z^25 + 117860620916984732905648815509235686053624493682401088*x^9*z^25 + 400726093470792927583404817706112877144552680927361824*x^10*z^25 + 1032173534811051801782989313370258215260484308888347672*x^11* z^25 + 1949661619399519348409862559716734793922026226357674216*x^12*z^25 + 2549558268087851856446209335946260063306035091719572632*x^13*z^25 + 2063925386424915319544923336267604937633055145893057368*x^14* z^25 + 779701337854277004017003469709606978426326937214569056*x^15*z^25 + 8268084017089004517641253354978115118579052*z^26 + 655934444277971695258995064882351385624757348*x*z^26 + 24160264581708724445832476119159059509059934292*x^2*z^26 + 547632596521017000432254273285786763546183499200*x^3*z^26 + 8533942388994276125446256704727284512312263904372*x^4*z^26 + 96718013362626108048175343206108996190547179825508*x^5*z^26 + 822103162920406618283723528926045471505556538599516*x^6*z^26 + 5324097139237945329979892023634900025440269378777248*x^7*z^26 + 26398650845304304096512963719362357467574281457900884*x^8*z^26 + 99728276928628788474757387408428314605044938054452332*x^9*z^26 + 282563485627311392428730550776737484050966311111547020*x^10* z^26 + 582252086016013054771339548486565344710818132057565088*x^11*z^26 + 824855106569599137915697553536138920802791189431840844* x^12*z^26 + 719103671338202744974481262118004489386549574134339020*x^13*z^26 + 291065811465911589569990903851165537519812577420280132*x^14*z^26 + 15718977933121165839135526604922982723419372*z^27 + 1157993359382647112841352483702796845616049252*x*z^27 + 39372204730519247075800804815066671391933598944*x^2*z^27 + 818068170502938932648288439083716923816083861976*x^3*z^27 + 11589310576460281247047894820245555256008288600644*x^4*z^27 + 118210994150426448970171327624805333893990963270164*x^5*z^27 + 893149905658910077739307775586261225012680635509184*x^6*z^27 + 5061183497044372072688194711554971403501868660109424*x^7*z^27 + 21510029783325164441870809979857527980863617337301172*x^8*z^27 + 67716713338257793638869274435097184246117320359023628*x^9*z^27 + 153491094753245605262116627019613668831932322233164000*x^10* z^27 + 237213407315166288620605998060701698193353967239648824*x^11*z^27 + 224035756538295651243574366028397594377789297389016220* x^12*z^27 + 97657398828946375547743799765429181849250936017829628*x^13*z^27 + 26762109729186209033249510286678567154406280*z^28 + 1819747169329357958795607451581181897502396472*x*z^28 + 56714984748244074785221067942292096384597817512*x^2*z^28 + 1071282360763620347819893030466215915810316292576*x^3*z^28 + 13658834374207498223832970545796351283265026162388*x^4*z^28 + 123840044748653232573914238747184253820771344434992*x^5*z^28 + 818719918066754829609243820017490729030383209875104*x^6*z^28 + 3976635100514236224454579548915549051186817560155328*x^7*z^28 + 14083915012959706835522046699906070375420978718466240*x^8*z^28 + 35470599381587449661339962721864280290077249945448472*x^9*z^28 + 60300466202815670405709539696850018492001958460545688*x^10*z^28 + 62127884247131143741305415283937027307905777669728736*x^11*z^28 + 29337931969301905539240530326963803621001515460007428*x^12* z^28 + 40602920653480590033286781623530586571418744*z^29 + 2530939770070162386078969647222197399284140712*x*z^29 + 71708201716470323982805712799263835456599176416*x^2*z^29 + 1219040247314396191231113238368520910610793407072*x^3*z^29 + 13815770990088737128314708976055056441843213553184*x^4*z^29 + 109605174349546310633656012354844488464581326083648*x^5*z^29 + 621096349288639898206694026869714079301750673380976*x^6*z^29 + 2513967306436901799394982864719955549443611947397744*x^7*z^29 + 7122929061630634931307969808686951996353917656128904*x^8*z^29 + 13454415808990914023935019438041910901428837134327800*x^9*z^29 + 15248124316717150971467383461788948491878728925332112*x^10*z^29 + 7855010522753815957024183970175373363611928907741008*x^11*z^29 + 54576802383951465515471671645346977558614828*z^30 + 3093209205370167092372703937341821548966573620*x*z^30 + 78879310850781400152487671421049733850540617012*x^2*z^30 + 1191955224564832110903874515955654087839681512256*x^3*z^30 + 11820270436331276940105398639748004584327871558728*x^4*z^30 + 80378015449124121339696484655947617069386916108744*x^5*z^30 + 379562552830379710545884638351383357292260500764632*x^6*z^30 + 1229057835429592266149501815199027670322859288655072*x^7*z^30 + 2611675982563862133919612657859715643040783800545516*x^8*z^30 + 3288772166588869331853083608803359294827090896425316*x^9*z^30 + 1863700473202891884957278562170720865562556904072084*x^10*z^30 + 64588814616622938540534210557785409271965916*z^31 + 3292827912669952101493217210126416291269260820*x*z^31 + 74641572976634122390886195208744827028978377664*x^2*z^31 + 986903137989881812482392235639966694026242682384*x^3*z^31 + 8388650369771808334424946695218932812526208913448*x^4*z^31 + 47535155272878171787696453128269649649936336583880*x^5*z^31 + 179574641326144251096064971909967830121116797831040*x^6*z^31 + 436114488457186592469361691672520639780821640533232*x^7*z^31 + 617866681329170382696112543649021205765126861664860*x^8*z^31 + 389024944092041444127931530594796823256227785847620*x^9*z^31 + 66608228055657372382276923624876763274919024*z^32 + 3018522061775202900051060914177115010295852796*x*z^32 + 59861677340994200948852403406716243683127623292*x^2*z^32 + 678450693801035238353602046964974089581220075896*x^3*z^32 + 4805714397337412170979830836835487567970206158149*x^4*z^32 + 21786368968848831738958130329199971445366513280456*x^5*z^32 + 61736111612584072306231187341279070116362767144718*x^6*z^32 + 99950365734964066012880528711324300657335241658828*x^7*z^32 + 70789817328720566511448490357982713388281298806969*x^8*z^32 + 59051202582058953212447864109067840923544272*z^33 + 2347623586765533912473255708304142393653734832*x*z^33 + 39905144993078151512313813906876730903645134660*x^2*z^33 + 376928722893603475551902865898957782842063491290*x^3*z^33 + 2136119443615728051505459766978828908111320784266*x^4*z^33 + 7261998608638431401580911705052919997220441947622*x^5*z^33 + 13712630420030146331374919720652752987110565921754*x^6*z^33 + 11102887311578604966049745540038157524811180650912*x^7*z^33 + 44734520480431430700875487399376628727050355*z^34 + 1519682973636709832758620346971686938939486137*x*z^34 + 21531147591551692123348581593808560520774012357*x^2*z^34 + 162626598289570262481128673027689795874865119888*x^3*z^34 + 690565225248625282315603880662244850104627494587*x^4*z^34 + 1566138477841640425503257210345186479969682679303*x^5*z^34 + 1479592250846869356951891915180009895395077080473*x^6*z^34 + 28300977754152136955251928734592063209318299*z^35 + 795715943947926106675506132506779247691386529*x*z^35 + 9011842528608681472666089363246368287739407704*x^2*z^35 + 51138433214952224861471056731420554450174930514*x^3*z^35 + 145199233828905359472552139127211520424503268391*x^4*z^35 + 164238324081686120453791927814376827924174322427*x^5*z^35 + 14117141120390313037914035472511888425994758*z^36 + 323365495108952286879451032465134263502610210*x*z^36 + 2775381201154071312777287444152926380414109798*x^2*z^36 + 10388181562926763242679921715758679192001361200*x^3*z^36 + 14739827269396654283506059097653904848264738429*x^4*z^36 + 5820795918978481915952021011310033692969578*z^37 + 94999551481035770575700649964819172395984038*x*z^37 + 530665621635577688867550180526372156866942600*x^2*z^37 + 1022415764351213013884813347814143688896976076*x^3*z^37 + 1312892454911550337509682972582547031695031*z^38 + 20411550217812906529317207924167974791908217*x*z^38 + 52968290752143773018446212463650850472459641*x^2*z^38 + 370303000103257787502731094830974803811419*z^39 + 2098383667251794129182142870708857221598041*x*z^39 in I Output: Magma V2.10-22 Sun Apr 4 2004 01:08:14 on modular [Seed = 2428466865] ------------------------------------- false Total time: 2.819 seconds, Total memory usage: 3.72MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Sun Apr 4 01:15:19 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2-2,x^2-3, x^2-5,x^2-7]); OK:=MaximalOrder(K); I:=37*OK; Factorization(I); Output: Magma V2.10-22 Sun Apr 4 2004 01:14:57 on modular [Seed = 1665959154] ------------------------------------- ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Sun Apr 4 01:15:53 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2-2,x^2-3, x^2-5,x^2-7]); OK:=MaximalOrder(K); I:=37*OK; Factorization(I); Output: Magma V2.10-22 Sun Apr 4 2004 01:15:30 on modular [Seed = 1350547490] ------------------------------------- ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sun Apr 4 01:24:39 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > 275573750405290386156*x + 17177430441929767403724*x^2 + 1291950980511202505940696*x^3 + 71568332483763548406999069*x^4 + 2933002060899381069228645912*x^5 + 96694114364841635947146176766*x^6 + 2658053466027253803681878061708*x^7 + 62109462904914230956593041593401*x^8 + 1251609559311431425713553664769168*x^9 + 21991590820796269937289124980924576*x^10 + 339874528606848103579134147488680128*x^11 + 4654026031226274102693081032154096516*x^12 + 56801409394762285311633922332217353600*x^13 + 620770532721078411713098345209265341864*x^14 + 6097456834004194955480660618053741035024*x^15 + 53987934247818304475156697719045285693796*x^16 + 431899431419641327846058269926722954630088*x^17 + 3127249750515556304176353645072789494350584*x^18 + 20519223977129947710225260098905240932075760*x^19 + 122090416162149246895308268001813372348103702*x^20 + 658900225567898031947473915900074743078980656*x^21 + 3224592191327204316990397911940987002079789716*x^22 + 14300367515641454048978476849108478504680345992*x^23 + 57400451693893534478325151250855145167883714510*x^24 + 208171412665872532941127001273787505392125274384*x^25 + 680557440907355495456217907040251678802415826560*x^26 + 1999703759524094125195693668464837454569737422720*x^27 + 5261152461969601583290677713952014651700824222484*x^28 + 12335604798454205588965973570184471884788998461376*x^29 + 25629910383456630695709698944761765360645003932904*x^30 + 46860929955092484657379858243622139248061088083600*x^31 + 74697758228167981052469534838842040243897235551764*x^32 + 102551000907319343546873515233031719460536147365292*x^33 + 119536192741689256717272905440585639510921919857692*x^34 + 116266905241756572785108148359746736516657964039672*x^35 + 91839208096405022857172933664731867078794672188213*x^36 + 55918378230452549529642128108440729812729682374264*x^37 + 23662430614834358080184060703896456013828253039326*x^38 + 11659748418903886590235624114963471079277689903436*x^39 + 16517976926780506002833800829531584028976727363201*x^40 + 24250490035665553981728*x*z + 2708308199677593327320484*x^2*z + 185965724869405316873949978*x^3*z + 9446560232542184898725758938*x^4*z + 374833372709513310969631240854*x^5*z + 12038896134723137149519284869370*x^6*z + 321606369640715339865668708845296*x^7*z + 7289962021587165411775199840852400*x^8*z + 142293161575424443092248116938507408*x^9*z + 2418938185907234199673011434215372704*x^10*z + 36136740027070924449065961714034928856*x^11*z + 477811029745193728538166008188884320664*x^12*z + 5623536831215179112397946824729248223720*x^13*z + 59180957599185729922006047847199225929272*x^14*z + 558927233667570416451242568971215445973648*x^15*z + 4750878761361244583792220045412446030682704*x^16*z + 36423564892007624175774554157873815154892080*x^17*z + 252267212463326592215194562285703658764876840*x^18*z + 1579984888847646191802159943453081444663907484*x^19*z + 8953235042103492321181581093013602155769051612*x^20*z + 45903181479775065685746052620589410081998731524*x^21*z + 212824169916940053786033181936625696969521713660*x^22*z + 891392832702671559852449634740368405988291154576*x^23*z + 3367478276531373587105438940780372630636177196752*x^24*z + 11449435585574619285981935439477146954818804880112*x^25*z + 34935528499554504685253316363689474984388242818752*x^26*z + 95317892340744767224896692668255805803325768161752*x^27*z + 231485665082691309511503545714991895032671262644760*x^28*z + 497560801755520178970056212349142432013282965491688*x^29*z + 939840996417932148185674193085533589140914345757304*x^30*z + 1546197412122515582506898752925041825121169239926512*x^31*z + 2190449751731184517705071896277054264595772555710512*x^32*z + 2632902875335051927821246423225939508411350031304496*x^33*z + 2632452245401035714299054555506473029495846016234708*x^34*z + 2130958730852612957996086501629287342380238549530266*x^35*z + 1346387674158018214620227794644620177276669936326554*x^36*z + 623756195261119510824698500447725759934853718865302*x^37*z + 169752219628159525357842174614909358360072250064730*x^38*z + 9643730412467490523371*z^2 + 1751508483444024959631681*x*z^2 + 180916037470323574417460781*x^2*z^2 + 12233407143306482256457577232*x^3*z^2 + 606118551048335019634649146107*x^4*z^2 + 23367473975046034208061025711911*x^5*z^2 + 728421126124038027914198607293817*x^6*z^2 + 18868752321588740210322789303668064*x^7*z^2 + 414308451729930813185694749573131260*x^8*z^2 + 7825833236785378088088541177710286500*x^9*z^2 + 128606153173224855814637756267582780100*x^10*z^2 + 1855051313833448119668449319118667226144*x^11*z^2 + 23651798888503668012425878793329093994316*x^12*z^2 + 268053120097636202152862712811264334823660*x^13*z^2 + 2712446938606718806914465313418525436055908*x^14*z^2 + 24592891641134888395019327537830483012319712*x^15*z^2 + 200329471000092472634559667088086162644503034*x^16*z^2 + 1469081104905246707248850519426796600825460350*x^17*z^2 + 9712259663051622035756481607475766318900968694*x^18*z^2 + 57932825783353442937754995850599570761534690880*x^19*z^2 + 311871752669677894681341719409199844667357685482*x^20*z^2 + 1514804669394469909743434970510837176423644472994*x^21*z^2 + 6633006505988272084744115348483570998893557632590*x^22*z^2 + 26147518920242847558373144438530469629205441249824*x^23*z^2 + 92605827724522886122699851554931070431436969686828*x^24*z^2 + 293868939116730390556145423872799672728059885903828*x^25*z^2 + 832628374118471953013760679702380937055811671891796*x^26*z^2 + 2096993653802535947088435222344004038514578837331168*x^27*z^2 + 4668309788359972208217093338322979087260119258263452*x^28*z^2 + 9121934877513245906129022129440154179483931791374620*x^29*z^2 + 15507243382046238606774064102966507272115701064901652*x^30*z^2 + 22677615122299555101271309965832575195383030752749216*x^31*z^2 + 28111325531206383405154326247231776793069269312841203*x^32*z^2 + 28962929405996491059899824597548995685882889678576329*x^33*z^2 + 24134320054203597812361190704593444755766618423081157*x^34*z^2 + 15621709739973357383625054788685193267178784889408944*x^35*z^2 + 7371534190697021547710669575085297427277061353243443*x^36*z^2 + 2261476792601814121156141859591959118596962531417903*x^37*z^2 + 283549077971481281245877113893793039334787351034049*x^38*z^2 + 342216218761063886877363*z^3 + 76247891165136585238075017*x*z^3 + 7900491927292055387627684760*x^2*z^3 + 523423319831841499759193824242*x^3*z^3 + 25208128013123300679123783506919*x^4*z^3 + 942604050647503773602266819194459*x^5*z^3 + 28486466706334994716272337611139392*x^6*z^3 + 714888056920772762652913527624186384*x^7*z^3 + 15191552673031244868346296925948277628*x^8*z^3 + 277386071766831376373149739089646019300*x^9*z^3 + 4401177198207987600932726465579721392928*x^10*z^3 + 61216350729494417188416842710952114743896*x^11*z^3 + 751601551512798238314882821390537965330140*x^12*z^3 + 8190533662655483498951061355277406250784988*x^13*z^3 + 79565159229370130726630526679180141627237824*x^14*z^3 + 691332571241415444592014409222903331311618224*x^15*z^3 + 5386633154954873898016398855766238231995385610*x^16*z^3 + 37706441909655498989199727326488589068414979534*x^17*z^3 + 237410948819741182128583361537690173328718756624*x^18*z^3 + 1345328488141384647812489150978159106661679762700*x^19*z^3 + 6861174417941368179223190277768151650698736476850*x^20*z^3 + 31474278495337897889481906128202239891328383840922*x^21*z^3 + 129712195267969818280228890674598696122343832432320*x^22*z^3 + 479371179226166129129042782787289468854984356989168*x^23*z^3 + 1584587966452281379330468964959620463005653681905260*x^24*z^3 + 4669251547371105506086517598456206910248301772471380*x^25*z^3 + 12211885942828029339427593796868733804207587339878944*x^26*z^3 + 28192884115946756732781391530027654068914075937600280*x^27*z^3 + 57057094983342569431062100563499054566043670890616748*x^28*z^3 + 100341758582959633960950649590749146584574341954511500*x^29*z^3 + 151626854198223527379825060122520385779927813689914944*x^30*z^3 + 194016570806273602044640576365703540145063769649949520*x^31* z^3 + 206146703836682632840215191656611539932782869503245915*x^32*z^3 + 177001087190786570521091635763164992989673921351249777* x^33*z^3 + 117982303460122404914358699007442107624981770461595672*x^34*z^3 + 57271519598998921957280188771746329896902501735072402*x^35*z^3 + 18086430043190782419136861912719629110996113184587999*x^36*z^3 + 2868442681172043779145881678716118680558946358882467*x^37*z^3 + 12741311150112745228992678*z^4 + 2571906247574770454933951586*x*z^4 + 253982468482258302269922247974*x^2*z^4 + 16304993653056933011183451422352*x^3*z^4 + 762343600149242634985513381020933*x^4*z^4 + 27649388978070973457017554083210832*x^5*z^4 + 809520414810735464625948600846100608*x^6*z^4 + 19659630596045126816939038688043173952*x^7*z^4 + 403839644078034093724274266327300754016*x^8*z^4 + 7119547083509018381452024338536385518808*x^9*z^4 + 108929239643071926805758911508580857383544*x^10*z^4 + 1458992033222818844159493206552705588754816*x^11*z^4 + 17224202978930354252753220620452207735716252*x^12*z^4 + 180191614049158907715152023283858857449405936*x^13*z^4 + 1677498369500012938825651910413077130443315936*x^14*z^4 + 13941877987322130657269119936294001722976161344*x^15*z^4 + 103692715562900381704349393944711177595984096172*x^16*z^4 + 691284680914383463141363459795134728910280910316*x^17*z^4 + 4134906348764220850823008029350315148529827272628*x^18*z^4 + 22197920061839158666973289148682682670360326925344*x^19*z^4 + 106919989865345093606934330574596567312751999422798*x^20*z^4 + 461622801594484033896560027833695805380220168563120*x^21*z^4 + 1783542464577829765297843362295179528527585173664064*x^22*z^4 + 6151928762467408432767884432542976298588266277143232*x^23*z^4 + 18883005288525385309841496051859934786331963291015984*x^24*z^4 + 51361783227141637008875498424579896016519967554266136*x^25*z^4 + 123136586013563889190416308653580054084454058774217112*x^26*z^4 + 258434724746553375570151807374691909229035243226111232*x^27* z^4 + 470720156638654018409421319303555916211908338219586556*x^28*z^4 + 735838781312920044555927576926285381276397677810815248* x^29*z^4 + 972944565390857464965683817636861637138337102502150240*x^30*z^4 + 1067096764997074070908498386969699657388613891366616768*x^31*z^4 + 944811163730939089911288120180399428010517623859697310*x^32* z^4 + 649004925226402301589956294019754766907238943044347330*x^33*z^4 + 324588758185787327474749894056820750690071076168409622* x^34*z^4 + 105033043579231769755317496651393722459318721745938128*x^35*z^4 + 16600220317771184440146529898584435381489293771699093*x^36*z^4 + 332312791708775912732854794*z^5 + 65740127318065123122105552294*x*z^5 + 6331112506265092145068098404808*x^2*z^5 + 394660641171724329210939981524124*x^3*z^5 + 17891047637304395373594843816407616*x^4*z^5 + 628561492033131562156955047282520736*x^5*z^5 + 17809200633325096882362152562020253360*x^6*z^5 + 418093243425619011981624433368569119632*x^7*z^5 + 8292194209040025463570036931978051183880*x^8*z^5 + 140967274531631952447936450367408580548248*x^9*z^5 + 2076916789546416165853805266946009732069808*x^10*z^5 + 26748168089899447618313946543365101776315936*x^11*z^5 + 303145957212485629991928382524357213415061472*x^12*z^5 + 3039232855907900431944461015983070778122845056*x^13*z^5 + 27063643626211301796957481656976547640980760624*x^14*z^5 + 214704889859889669584988205398992944641575820240*x^15*z^5 + 1520826299536621592083553384065512389584973911980*x^16*z^5 + 9631900401161558873643979553354660337587808417876*x^17*z^5 + 54580770576594420819800499584100670311415844686080*x^18*z^5 + 276734074153305476039534373645142002580113258080184*x^19*z^5 + 1254527741301725585349306889278876887704199877364992*x^20*z^5 + 5077850375643790067352350488160442605966434207567776*x^21*z^5 + 18311037303635484100693269584698573710567081373536912*x^22*z^5 + 58648398162102180656280634802789892446023468987920816*x^23*z^5 + 166170454360414414902421270371411647129758295273298024*x^24*z^5 + 414318264752290865554753100113977871584945085645411320*x^25* z^5 + 903001266083503138991153681164423273444417014081308880*x^26*z^5 + 1705669646562197001578586455734311281362422684528361152* x^27*z^5 + 2761562176036700005774703575128615883365401285972698080*x^28*z^5 + 3777307871890990732740158013618256256463863527182550848*x^29*z^5 + 4280936986972444661877046433046000337309812992623028880*x^30* z^5 + 3912673049604395904622715596659579018483800913545847024*x^31*z^5 + 2771510186736665040704531168173399003596092243589940698* x^32*z^5 + 1427818770723150459054664467261570222114220075124804214*x^33*z^5 + 475878092246793337453326680846839628421291755063824056*x^34*z^5 + 76929802779825090695114781235516217609130364196197580*x^35*z^5 + 7074140179699768467882758751*z^6 + 1364979631893772484777289508593*x*z^6 + 127677463055642373688810949509809*x^2*z^6 + 7717618628353231755656667898213440*x^3*z^6 + 338931491807121289074311070522558024*x^4*z^6 + 11523651647862048076290967188187542408*x^5*z^6 + 315619662906015102672852958758092992536*x^6*z^6 + 7154044127271192967771270094096624686368*x^7*z^6 + 136821108285222759822997207422350672289444*x^8*z^6 + 2239812397817969894270766304987380250673772*x^9*z^6 + 31730676809558954012162924757357624346281852*x^10*z^6 + 392306550471785345505510663802963855211928192*x^11*z^6 + 4260884921340158557791786732850332994772094840*x^12*z^6 + 40860792965311022278208675547234136199007267480*x^13*z^6 + 347316742661854788899505521512195000951164877416*x^14*z^6 + 2624171002495562769395941336896146549917484923104*x^15*z^6 + 17658484158487211996524442505393915198380880243258*x^16*z^6 + 105950903229655744927872597820231569891556919857974*x^17*z^6 + 567033527630836897208151048925601780787461959892742*x^18*z^6 + 2705844216563860316490951440635108438221449779085376*x^19*z^6 + 11499838234853837474061749037326883919761319868854008*x^20*z^6 + 43443834047022922865437105434337106009651986165758072*x^21*z^6 + 145471015351498890682427244677048312978102552620479528*x^22*z^6 + 430088191689823454232615799348065247182401334922472160*x^23*z^6 + 1117034620582697502706786385573388723184774471557331236*x^24* z^6 + 2531945566116465268042087554848299668307972111478315148*x^25*z^6 + 4966509287191533485866705887411261007708875207689667516* x^26*z^6 + 8338827171089650343804988258897810270903344803352794368*x^27*z^6 + 11813328613191566364102061312251666204965518204176634824*x^28*z^6 + 13850125223530401597128066007588020074534260693323617512*x^29* z^6 + 13080739856100979280416222945031720711002220565228300504*x^30*z^6 + 9564309340637587431711641644070531366009564207635653408* x^31*z^6 + 5080718804917499771606379545191333047699711583965631263*x^32*z^6 + 1745072394630523109129087572728715306188634309303762785*x^33*z^6 + 290813985597689820336642384477701962349579968813542289*x^34* z^6 + 126298796322161844433301385411*z^7 + 23607581505510789544991615955441*x*z^7 + 2140215513102492405278223198155328*x^2*z^7 + 125318031581952661777948160405390160*x^3*z^7 + 5326030221874122866502279432003600168*x^4*z^7 + 175049510378644116455682578354416911240*x^5*z^7 + 4629090251593548767969227075198334560128*x^6*z^7 + 101178657858236909404611848774815951520400*x^7*z^7 + 1863373299468195505207274537852681577540756*x^8*z^7 + 29330876383378586018150551016680654691720364*x^9*z^7 + 398899928305818224368416119779578240362997696*x^10*z^7 + 4726359707794654056074257027008238065798012432*x^11*z^7 + 49101625713775087550835831030033628597580482968*x^12*z^7 + 449468734192278345099798949977368514868135365912*x^13*z^7 + 3638556438248884831592229590552183637954902896128*x^14*z^7 + 26116749198256483791971561364133495861393889096016*x^15*z^7 + 166494274333758441485748929753066901447334901082258*x^16*z^7 + 943467563307431866673931926735281378384878589098486*x^17*z^7 + 4752281143958747287076561762298592517636136820850112*x^18*z^7 + 21260205086764354489770101847030069769425809132379888*x^19*z^7 + 84332144656661442544480957523999087880012759143097624*x^20*z^7 + 295831804365271554323157880791849837115178976619171704*x^21*z^7 + 914389243296340004831876603308260096634932636704179584*x^22* z^7 + 2478127510423692766674163104163599417010487796593906352*x^23*z^7 + 5851134281310205989158910470561144675327766467644874004* x^24*z^7 + 11936312104442496156894796391907635820840409379023275084*x^25*z^7 + 20812029601606519619849719102835789467612267947420692544*x^26*z^7 + 30575708379630987295550991481705324307914657715719076784*x^27* z^7 + 37127664994942787679286664540287880551963982699016321192*x^28*z^7 + 36274138330087119670717236415330016290845196841553382248*x^29*z^7 + 27407086718212074466187405728692067019541440114772712704*x^30* z^7 + 15029667436237215884863348018312305765870764159567641968*x^31*z^7 + 5322985898519730715161784458782168730304791565804025475* x^32*z^7 + 913945012098706230667813847792368321204727850808641441*x^33*z^7 + 1908921407361667514961102741168*z^8 + 346191633438160246866555636199968*x*z^8 + 30408012266243193412984502820770112*x^2*z^8 + 1723138606092104700640474384775129472*x^3*z^8 + 70792181252745480626399334602145402804*x^4*z^8 + 2246469001339816851147965790382995727344*x^5*z^8 + 57284958422463742820015716583369699064504*x^6*z^8 + 1205712174223801157641529999552699347743696*x^7*z^8 + 21351153504938839183436405964239617871700204*x^8*z^8 + 322639644741153901635261305690036582874716736*x^9*z^8 + 4205070037203033499180135874202876494769458928*x^10*z^8 + 47657460972236394244156207822198082378893523616*x^11*z^8 + 472603153844482663281990062738381704267818240564*x^12*z^8 + 4120130018431430405137608848988681742435257386832*x^13*z^8 + 31685761754628025930882360759416196684054849896648*x^14*z^8 + 215463181709518679427479279851520137940304274911024*x^15*z^8 + 1297267914142920821239247823969662590684626249264492*x^16*z^8 + 6918762172776641621195338166013151067828987986503456*x^17*z^8 + 32671932141363715033361851309187154237268756862419296*x^18*z^8 + 136419646306039207498945509725388173091995900314907712*x^19*z^8 + 502479038141001559889354300430958153695819888160626108*x^20* z^8 + 1627075008576331460361673907556067296933418322403594384*x^21*z^8 + 4610045791216823406294871495163939000616070054776913608* x^22*z^8 + 11358083188914360002194490910466900251620459226683866416*x^23*z^8 + 24135926258294995966685406689837113830885751443801091428*x^24*z^8 + 43766486111756890999583502770633711858248312639436706432*x^25* z^8 + 66771962364519129334519948447868894675852885286504634224*x^26*z^8 + 84083181016469409685079801364595487786281702017358278048*x^27*z^8 + 85084047541538130009085923342056191256846465051443122780*x^28* z^8 + 66502622521158386298767207931825174799573950290801524272*x^29*z^8 + 37685448727451866074617500254148992835875752801367821496*x^30*z^8 + 13777260717649052942017159002439996360530923934222850512*x^31* z^8 + 2439786446152216550995326348683945199342052475693261716*x^32*z^8 + 24887510231216342800061240341776*z^9 + 4372451597448148105811656800763920*x*z^9 + 371656781455105480324275202302353232*x^2*z^9 + 20358522283769244865961696727057800664*x^3*z^9 + 807554454362146334167439454565686832680*x^4*z^9 + 24711163574142939808528648320859947503448*x^5*z^9 + 606796324045853848159459672179587993908536*x^6*z^9 + 12280401695822241286719473185086698669416848*x^7*z^9 + 208766830405313115006287538086848696979279232*x^8*z^9 + 3023252988769349780506929287752788734208063264*x^9*z^9 + 37689887101600570240028529052921574853976897632*x^10*z^9 + 407736050868929350956551180684775844559692859496*x^11*z^9 + 3850840489739176406470512560137335650100569183352*x^12*z^9 + 31892858530144729219318321595352616278408022761864*x^13*z^9 + 232362255186235343609223927747121030654653528220776*x^14*z^9 + 1492282032716820170582574823660215978862158883112064*x^15*z^9 + 8456264812339214641497247601807076841417591974978768*x^16*z^9 + 42281324162583266558999220253970874806893116607605648*x^17*z^9 + 186351023090789191253427173742057134388733545491528784*x^18*z^9 + 722518881438356749661595461791224908857569046161499176*x^19*z^9 + 2456564158921818010623766616158153144706883951520114968*x^20* z^9 + 7291706170840948930935607704249484841252054701556088168*x^21*z^9 + 18781667753089246003186342510992206565581805133731628296* x^22*z^9 + 41646309390619935103228110127120826465048096561203036752*x^23*z^9 + 78665251472679669368743148655729704244249760337428799904*x^24*z^9 + 124815510513408876964763617634038772350837279479841147968*x^25* z^9 + 163220262074960010877906055908855576420469249605295782656*x^26*z^9 + 171280599718606165943478426018947761317980915169448425624*x^27*z^9 + 138655763810690924941111235358705013049560666190415858504* x^28*z^9 + 81280821313625900777278743083728210015099190733860758200*x^29*z^9 + 30706210461836332080702772557016958294721922228943622744*x^30*z^9 + 5613480648292009109861196392151734138797490289919825056*x^31* z^9 + 282956170734983678739488904995388*z^10 + 48097728106939595701804487177594772*x*z^10 + 3951961234817517290399974191342025668*x^2*z^10 + 209013973341944116621755636208919123136*x^3*z^10 + 7994785570372862279538275746173505018356*x^4*z^10 + 235579749026634686233405246785162216503076*x^5*z^10 + 5562299714805589302683024703028917487024284*x^6*z^10 + 108067534925024855131847332035117664748882400*x^7*z^10 + 1760600261333043126598300496719884967701709980*x^8*z^10 + 24387574114821283525294896785024383798909311972*x^9*z^10 + 290212131728693309261073540218844963104123265348*x^10*z^10 + 2990064384794771523310849485480320763727713386592*x^11*z^10 + 26827522114964654549633610315003057718799721499764*x^12*z^10 + 210492865479814485758622214310571409186490694796596*x^13*z^10 + 1448391382255458122836313815327034429900051155967676*x^14*z^10 + 8754721265356689724352124214972515510048292424389824*x^15*z^10 + 46509456894362947304909541456087456691081377015488724*x^16*z^10 + 217044131928396812709282546245371941889068525195061308*x^17* z^10 + 888273200260550391907863153003447659917027886499405420*x^18*z^10 + 3179083018446745010488282732552687918027223200709563776* x^19*z^10 + 9908142173844611500293572759988091619809422384863910012*x^20*z^10 + 26736257217031469013971083596159906328729879567952664300*x^21*z^10 + 61979505213827235142774548291951199145510262040423239540*x^22* z^10 + 122162495418796730679317463385981864385212592820686817120*x^23*z^10 + 201907444099826682016395981928835261578020710119223236692*x^24*z^10 + 274594162617810449167381155152254505640036104408182749516* x^25*z^10 + 299237362232047149732307772779497112512941772626614578828*x^26*z^10 + 251211461823928964887418222044341995895482509203836170080*x^27*z^10 + 152520459009026512696939366941540931988252460884587208988* x^28*z^10 + 59605831671480908966529599777708644799933862456628791228*x^29*z^10 + 11258611628807781397598747987473580307653170749574819636*x^30*z^10 + 2829190614455711406539947462522236*z^11 + 464925557498655806328691701833949396*x*z^11 + 36884697419091626350366083471470023776*x^2*z^11 + 1881126204978879834319339898152799945880*x^3*z^11 + 69288169959391663728776583373778249443524*x^4*z^11 + 1963164598088936768796874086083084976432468*x^5*z^11 + 44498396764454209707994210917231479598116160*x^6*z^11 + 828517772502261526554799734972491183017596240*x^7*z^11 + 12911068602217795503325508634179743160981903100*x^8*z^11 + 170713018238300714623606230878062558032512964996*x^9*z^11 + 1934747542094910086282807925311556457149547967136*x^10*z^11 + 18937074419701511527536289102730772390588814099080*x^11*z^11 + 160965132537172291729464905267076966474346614148260*x^12*z^11 + 1192792906747170634733202158508982273960664532839940*x^13*z^11 + 7724754070980983016529450860667663954227446866471296*x^14*z^11 + 43773606330188206736992073800224084329648146193745120*x^15*z^11 + 217044130630811862135491138120241966598450567588683348*x^16* z^11 + 940524566083461824941616908279856846504117771949678396*x^17*z^11 + 3553092831243041336280162874919379490558770353966455200* x^18*z^11 + 11656637963799610374373533638508151012136863466157894696*x^19*z^11 + 33027140521371199253486369275493922006557764271529500844*x^20*z^11 + 80208767589004113306954744077331787234926666166515026364*x^21* z^11 + 165278673522925261407943219848925836901386540112361802048*x^22*z^11 + 285045853072347955460472427626010864446722939067005831376*x^23*z^11 + 403814976406489434035898111682266595313973514551317050164* x^24*z^11 + 457656854683683854213565717739097800951730634488316367212*x^25*z^11 + 398982860442621908490940723767175736459554234442102898528*x^26*z^11 + 251211743154574868024378029498329799639838154707689548216* x^27*z^11 + 101680808097125491798195549800734743109554294809398021100*x^28*z^11 + 19867860395742170767264334984898541892343463702698833900*x^29*z^11 + 25069584304539692013997416959944776*z^12 + 3977781302711917010721915911801836728*x*z^12 + 304299816407929307329527058158575238696*x^2*z^12 + 14944504543496654648957745602145518431008*x^3*z^12 + 529284564342218218111329554966016871995780*x^4*z^12 + 14396540184239933954010894321027269212999056*x^5*z^12 + 312724845923927416687579980903420775282730784*x^6*z^12 + 5569480591359078276364772970701202138063365952*x^7*z^12 + 82846023676496217728358840500358687466842906048*x^8*z^12 + 1043246223471200888115087606366571570514013075816*x^9*z^12 + 11232284341597200904877215000658757061183759528872*x^10*z^12 + 104153909380893636981295095192212108677449806967648*x^11*z^12 + 836124439181508128824884403698425231587849294778316*x^12*z^12 + 5831431980795475797424349172950661713505457535542368*x^13*z^12 + 35405122704568296358709282156506907508983080060945152*x^14*z^12 + 187253760286881678918213649840721447677700914082822016*x^15*z^12 + 862147524148431728151936802611226836280807094121994536*x^16* z^12 + 3448590099543321435437823546543335146359508807868139528*x^17*z^12 + 11942339713240443481854709749573542309399003100329637240*x^18*z^12 + 35617504095060533441276931256379023013999945659838915040*x^19* z^12 + 90824636007699818902638395289723849605952310312164871068*x^20*z^12 + 196065887104517561564339369415956291348752472242998455568*x^21*z^12 + 353512743413118516317961695019124370419266855672733164768* x^22*z^12 + 522584020056742297417722977475600857788691542220086718784*x^23*z^12 + 616939373049980104666044445602329934142024861696259573328*x^24*z^12 + 559358478726037606646083157270756641834355177461119503064* x^25*z^12 + 365735069478342831781999795234853394926534116358520777144*x^26*z^12 + 153518402442763405689286938678035601852888883148743126944*x^27*z^12 + 31069725463820313097573706901119215807314850811408237972* x^28*z^12 + 197991115362552741348103140284622648*z^13 + 30292624634658874467495240575237542056*x*z^13 + 2231537684077460154936184089091049706336*x^2*z^13 + 105377951740893391471701354750403661500992*x^3*z^13 + 3582849273921232459427480544302766662963232*x^4*z^13 + 93392939834952550381842668775074693658024576*x^5*z^13 + 1940497761914494626790936001051838307338361488*x^6*z^13 + 32988461932191420679307933724274608914163156048*x^7*z^13 + 467336543841568798167269723193513789810946955640*x^8*z^13 + 5590729761808762277623614734018028139723396388424*x^9*z^13 + 57025443567203556140463279553814791067004750944688*x^10*z^13 + 499404642123512723977228679120891820339730000740240*x^11*z^13 + 3773279517930682117442039692517253652340780422801536*x^12*z^13 + 24671443019445621354273576449867538812526205735862976*x^13*z^13 + 139804843938553538035906746619926136756620891179631648*x^14*z^13 + 686597121966080685275476188129981187101189346874173344*x^15* z^13 + 2918037757580417336889906144621281982962802135246139944*x^16*z^13 + 10699471754113790768304599519099885446389160880823407928*x^17*z^13 + 33683522438350717556703775975912152249025102695334222656*x^18* z^13 + 90413666764248454506739455529061367336296510933311277280*x^19*z^13 + 204937643349770146844408054912615652083637830464764524640*x^20*z^13 + 387104418728547879810159140896092255018876778768895374272* x^21*z^13 + 598252270536118304486247466177137770699100341706623038800*x^22*z^13 + 736977541962726668066816795743572229170044409190160465424*x^23*z^13 + 696034378710719462706064689765691197098340016609184414760* x^24*z^13 + 473303042323078224878142920217131906694567697689803789016*x^25*z^13 + 206311648307273040432260708861193296379794407660310807472*x^26*z^13 + 43300714495648429818811640476029081541298584258220301136* x^27*z^13 + 1400038283931642888514436853397415196*z^14 + 206274625629707757576488326543639673604*x*z^14 + 14611211454807085123315645074816944584068*x^2*z^14 + 662375513500743961644435255926911877362368*x^3*z^14 + 21582402496043676379790148823205001086307576*x^4*z^14 + 538121225080814373075897552446375103052317432*x^5*z^14 + 10672737637983780987512948323803400347893013864*x^6*z^14 + 172796705068955002796289106835148304250673172128*x^7*z^14 + 2325555657961455762406010258955180877753398970980*x^8*z^14 + 26356297456613043237521225941615368692261209514700*x^9*z^14 + 253898998792501506183819303682941004593003108066396*x^10*z^14 + 2092743263054323120244936891919816036314428984744704*x^11*z^14 + 14823598115572563688448687636556027900199238093035152*x^12*z^14 + 90461957670196985627068633314553502263522401738995664*x^13* z^14 + 476002205179745458600689577515572563965579599710427184*x^14*z^14 + 2157876664077625561712311460436289432989239584542512064* x^15*z^14 + 8406727871392457296955097363560479515433893732210272676*x^16*z^14 + 28022426351504418794996990295311591907555645030316243164*x^17*z^14 + 79396874160588634085830132570321018559364600232855874172*x^18* z^14 + 189438152160174273880418954366158577062353559061805354816*x^19*z^14 + 375718998777288562095795861199864517512851245716058114040*x^20*z^14 + 608306975856207308726502663887152274812694797165174536888* x^21*z^14 + 783425699973673639535341540444691966153540330902768993512*x^22*z^14 + 772071639900183357752295209878295659483960773411282034848*x^23*z^14 + 546883645907139025021484366545643553080264709795353860956* x^24*z^14 + 247920547596707986871026937070787365304266500158182560724*x^25*z^14 + 54033350890112773096977655856734479912494767732298391844*x^26*z^14 + 8898218766696128949968423924579180364*z^15 + 1260572544585234590244260368880927316132*x*z^15 + 85719101074875271814831265788624548931904*x^2*z^15 + 3724021566561433325883718583984098683933936*x^3*z^15 + 116065362427771637889174762862092782871988248*x^4*z^15 + 2762355633108726634686813711503140086778323192*x^5*z^15 + 52177828520294895640454173034608659858668211840*x^6*z^15 + 802544695728794407021148344142726045342037245136*x^7*z^15 + 10232444883186876556814030680897077556559390471412*x^8*z^15 + 109525058249923992944009935662931270811679934229676*x^9*z^15 + 993027194939692391265673365813330766082010698892672*x^10*z^15 + 7673391959955274761747031098253881726567808629775968*x^11*z^15 + 50729646838345372329382465562990057240030477237118288*x^12*z^15 + 287467998939912146038522342111082183755785946272353232*x^13*z^15 + 1396273140318208758253830154023583295629090595668396032*x^14* z^15 + 5802290607360151424136203840115503944109430827034861216*x^15*z^15 + 20549779124374910542246785866798356888739977129843594740*x^16*z^15 + 61649336868686008465940842498206055134234599361673599804*x^17* z^15 + 155264997568096985568936807464465093350988940314809945920*x^18*z^15 + 324149742067877794543635982132061707057092558940031169456*x^19*z^15 + 551054569619269926705916139314396203625794082166332664856* x^20*z^15 + 743486257650398688092074767693982365301644993528221731512*x^21*z^15 + 766016119559089680470645169175448290123283954100989262720*x^22*z^15 + 566186050618524327359227432024512015724185214134127005072* x^23*z^15 + 267365639585810517517451005006086241642495926752128166988*x^24*z^15 + 60602437683591894210217783544472470829875944707199588340*x^25*z^15 + 50980283032856002647975290394542728080*z^16 + 6933213732786427461247479736739370583416*x*z^16 + 451811960119271176750060256559365987211288*x^2*z^16 + 18775280435952747317861512628281773743220720*x^3*z^16 + 558564561530666079559234633417214277716454342*x^4*z^16 + 12660796782853516585307986908929833832138740896*x^5*z^16 + 227190963575387722199622376196913341705903477412*x^6*z^16 + 3310496885067053312114784238655729930099098443912*x^7*z^16 + 39863899933142922125018813599424407717740732651318*x^8*z^16 + 401591880675462216852347973352248761649316399700304*x^9*z^16 + 3413530985394046322391141473548872149605495954186944*x^10*z^16 + 24618799230712783096008049408572379696364412131476992*x^11*z^16 + 151132073103006232085946364245847447145127099842122380*x^12* z^16 + 790536997232079347264061627690316284252300795894661920*x^13*z^16 + 3519771859370105291916652417516003547741746650006677688* x^14*z^16 + 13296915890721187318049142136280323359680728677895443696*x^15*z^16 + 42383919672083399058024730510331498979882252857038265772*x^16*z^16 + 113023787475219822034227361012152375317141800434622283256* x^17*z^16 + 249070940021901602426511050587255345943505454143955743048*x^18*z^16 + 445705877814719797753608921077731670353296521859667170384*x^19*z^16 + 631416638715171431874012410641299171726533928553254764526* x^20*z^16 + 681529096564736542829131198440402192253516195055431015296*x^21*z^16 + 526636337638517739687336993055451766294146659859702234244*x^22*z^16 + 259502006637288639265049868427112110296551626452051130440* x^23*z^16 + 61271792888361956378252332622589154861362446079827821902*x^24*z^16 + 263888740156078110512123314571452111920*z^17 + 34393917363664944840127939881057077699760*x*z^17 + 2143890376269105720759899985619028117143992*x^2*z^17 + 85040978194736986251948608432834230658697180*x^3*z^17 + 2409494137719684254747637555035410271071942572*x^4*z^17 + 51884440873503084183037130307706518027194123124*x^5*z^17 + 882035498617862684173823048293563594905720292732*x^6*z^17 + 12138488555318113352434756117502306608809266976432*x^7*z^17 + 137569536884955555861049928945616585809147952228720*x^8*z^17 + 1299267848445480370605878014799459854084494112431120*x^9*z^17 + 10307524928561315223178812927049574602796524561901280*x^10*z^17 + 69029182082884994367691769385767344987178413881393576*x^11*z^17 + 391165364849618846815311913927542916447517872976270088*x^12* z^17 + 1875587776451937491568141997392831449067914940393126648*x^13*z^17 + 7591664841331792183499008537302701311412351854186800648*x^14*z^17 + 25811660600386300592120551735595374141692127339896056208*x^15* z^17 + 73133037825498027914196678375189021562283191476691592448*x^16*z^17 + 170643750504806022227478384248961256674804451365343709088*x^17*z^17 + 322327079998851027037784715869632999961455539631560488904* x^18*z^17 + 480663220229919701675965634181517848209106911416018682076*x^19*z^17 + 544751664891646968045900079974939407541135340976052729516*x^20*z^17 + 440989349288768154577433935799304822043343299013282354484* x^21*z^17 + 227176300518722588946897955926760569584084252680943962140*x^22*z^17 + 55971132978837534944541783051008969162090351404972005728*x^23*z^17 + 1236366691619624991600504188141931088122*z^18 + 154135283781776631029894718077876931092238*x*z^18 + 9171079378385651366886909605711936183362038*x^2*z^18 + 346463202510987577846202868986311474840770528*x^3*z^18 + 9325634849480671990914328868385566783364415842*x^4*z^18 + 190242949807464351293286269194609709390962966986*x^5*z^18 + 3054456253991132340806945167397341523653490155638*x^6*z^18 + 39562481115362879408535012026293379884967366035488*x^7*z^18 + 420351362243361580237541182717611164630595256362516*x^8*z^18 + 3705319417660170941667251949047469925670520498156300*x^9*z^18 + 27295853050574516933373284579346131760768208995874668*x^10*z^18 + 168738000799513769330471501754634619085249348798560736*x^11*z^18 + 876500171930240836153436727409615556480238755830645620*x^12* z^18 + 3820641774804138079764556079167786798987947821546495892*x^13*z^18 + 13918052077651604974553679196198318452748552867095231516*x^14*z^18 + 42063445721367443080697215382305668552528157570459938144*x^15* z^18 + 104282292286543026549891055757221735631241207355078996338*x^16*z^18 + 208564591717137853327387539784262893083402109822458776646*x^17*z^18 + 328296125805491285632093811189354009507797512719137103070* x^18*z^18 + 391651512053189885850891150340836476544801781732488394944*x^19*z^18 + 332903688362547467659816283163777549339076388096361599658*x^20*z^18 + 179662279549995055762323025326457439577352259111910113346* x^21*z^18 + 46276375500949644388973764086156722652538077297789203758*x^22*z^18 + 5249293597722989862331337857834519205706*z^19 + 624657539119445018615862813568569444099486*x*z^19 + 35397176259851800888221297250706681895645648*x^2*z^19 + 1270365100787693785417345910867760289834649676*x^3*z^19 + 32394311556261264452770219529476890942289415274*x^4*z^19 + 624130389967625012779046310508554858039780938946*x^5*z^19 + 9431303620416193778134595712761681962211480283072*x^6*z^19 + 114522972018544370900421761888555869906598078247984*x^7*z^19 + 1135686139059957283888321363148759989905638326041300*x^8*z^19 + 9295801348992442312785441282724722725770167021581196*x^9*z^19 + 63211449168793187175597697042281197023140585144512352*x^10*z^19 + 358198211306506748384592636777166958707278936165287400*x^11*z^19 + 1691491548208570778422317387072858845559964796178029412*x^12* z^19 + 6635851435267206759730656803851252556278312634410101924*x^13*z^19 + 21487519150582200018792569940469883483149037059232196288*x^14*z^19 + 56822552165862645985250301103221556201684273546089415536*x^15* z^19 + 120747925193484393600501499516075872423290903881486099362*x^16*z^19 + 201246530407424234537107591920072122025861518933153436918*x^17*z^19 + 253421548586164899736373974477191295659277085289198397008* x^18*z^19 + 226745616988284361180603658511001644766913147264115552300*x^19*z^19 + 128489209405322963039640211175227883684303163800207920242*x^20*z^19 + 34671672435780205789595367494985430114130467937057757818* x^21*z^19 + 20209544173097942520319942615958813371524*z^20 + 2290408163361829924513393961689382267470476*x*z^20 + 123300168236127078471277152187296697819021476*x^2*z^20 + 4192204623846684968915062148855725178009484096*x^3*z^20 + 100962264585882123796195183734278148256282857510*x^4*z^20 + 1830782439290629988948478476885462951873589820656*x^5*z^20 + 25936084738979738937952897263490112434409871011520*x^6*z^20 + 293942293953355785795245094826482260398452992940480*x^7*z^20 + 2706718626986502283439452315767237029439350850427296*x^8*z^20 + 20450762960599157636182947455164226814511640488676520*x^9*z^20 + 127476422611703041614379739662296412533027760179955272*x^10*z^20 + 656696723994253431388751575650517654595443219811722560*x^11* z^20 + 2790961103996526660526237852780883932317263387384380308*x^12*z^20 + 9732582438346609713479198390722881705903703233522086064*x^13*z^20 + 27575650252786610422429992436077088304243847188927904288*x^14* z^20 + 62504804411956707446571091657644995936893066691072206656*x^15*z^20 + 110685587394021889439214632949533850150653941026312112332*x^16*z^20 + 147580783247993821453871708338016322652424731019104417068* x^17*z^20 + 139381893430286176384074809085431121522405029961659837748*x^18*z^20 + 83140092267724100303967821126163773361475470050225106048*x^19*z^20 + 23556468484499236606356200318160777881663175374952073302*x^20* z^20 + 70571820359255968090488736841210962046172*z^21 + 7598313097372719043853302279886240402148708*x*z^21 + 387514706738157183407949832992448082709496176*x^2*z^21 + 12443529512497443677954530846849403569134842616*x^3*z^21 + 282053316797045111358542168917110604037864490624*x^4*z^21 + 4794906456263681896797775890720480288176697315744*x^5*z^21 + 63399318550683183177224095823451358197075634282320*x^6*z^21 + 667202355153869228237587324057539071342095692306864*x^7*z^21 + 5671220012589169759066713629799269597183159691400440*x^8*z^21 + 39278449812853039138078715904663351010257175425072168*x^9*z^21 + 222577882272408686294597172692110277883035459143669776*x^10*z^21 + 1031951999647551035087818918123186960232476153177147392*x^11* z^21 + 3898485266708543647168337770079739718984893978683413920*x^12*z^21 + 11895377707468737647388316819861795826779304805514593984*x^13*z^21 + 28888773827365211765795419784203162325739148825103304624*x^14* z^21 + 54567687710724842996832249711326237775292766262213626256*x^15*z^21 + 77304228131059731039450919844449702171855639044943314444*x^16*z^21 + 77304229066811253434983342940046422023137757693537363476*x^17* z^21 + 48673018015811615528432378404532016888059102815754789760*x^18*z^21 + 14516498699056317117963198283885148393947895143294163400*x^19*z^21 + 223481288881004776389911958097047943836834*z^22 + 22795001451325115168691509974426703673565278*x*z^22 + 1097958642714910307079051830916357926359272222*x^2*z^22 + 33182749216777355567355905455314356613255886272*x^3*z^22 + 705133344716343120810963789259708470981221461752*x^4*z^22 + 11188115243976506678521067823852771370489984184376*x^5*z^22 + 137365190266560523528020339433174268732815144732200*x^6*z^22 + 1334404696841442063546724141400268638310740494243680*x^7*z^22 + 10397236519768549384215372099004643124403642599092748*x^8*z^22 + 65464081425997125557462204763758770450437134578507620*x^9*z^22 + 333866810786350428493143295771156320417060499990940820*x^10* z^22 + 1375935931676941986608473843877978934962788452187540608*x^11*z^22 + 4548232685556639685738836789018138929887421833050174072*x^12*z^22 + 11895378698122881557054705031682427701784853586090639896*x^13* z^22 + 24073981920778656656382851869104881124999382935495634920*x^14*z^22 + 36378462253798400640737393082229542393108505886363232096*x^15*z^22 + 38652097889805629022860274155260095997466288790077758434*x^16* z^22 + 25768057903601904736717146112655111793462552839710371054*x^17*z^22 + 8112136422783000401263288152378900867648600723181186622*x^18*z^22 + 641292680691182275163826100991692814010042*z^23 + 61777683758990813434995674560347134580988926*x*z^23 + 2800588308009556995404512692010166012527279296*x^2*z^23 + 79350016471153140369852904498328374443168968880*x^3*z^23 + 1573775646300165106155953023725558898214734414104*x^4*z^23 + 23186961673833147058435932002663461887595019692344*x^5*z^23 + 262785573483667890418616270851242616037925249751680*x^6*z^23 + 2340042975402636089935743050113229187103419974924208*x^7*z^23 + 16575304635319704537534030468834877392489545712750108*x^8*z^23 + 93926727318529818994658308850746426266206885186420580*x^9*z^23 + 425801177937111393695381586421348794901808536765172928*x^10* z^23 + 1535464937155255356389767650752721248063916360919595664*x^11*z^23 + 4350484127151669103418556478725654613522953422119990680*x^12*z^23 + 9481823272869098669348934326238182466892854713472578712*x^13* z^23 + 15351521845113293765973226292122955076880185074347336704*x^14*z^23 + 17398389083494177655534724001654368708737334641845026576*x^15*z^23 + 12323865928606266011815479854101364768029081142142438522*x^16* z^23 + 4107966357481382207265757787740409835876609387925284046*x^17*z^23 + 1665560036067176966550921434008112128265808*z^24 + 151011951100159525903553063670245900029057920*x*z^24 + 6418015612854903586705653441073289147055444576*x^2*z^24 + 169720893652840662927614080939082825978431900224*x^3*z^24 + 3125693501664967674313047857539250678450078509860*x^4*z^24 + 42509433945014070701687025708071829197994461547408*x^5*z^24 + 441625793459402736195947324247280779373699432836504*x^6*z^24 + 3575065982667819103758807080345026315555353916164432*x^7*z^24 + 22791045924045466831052506556259818649106542698539116*x^8*z^24 + 114799342046118090501139611903890600187541283212524768*x^9*z^24 + 455370712678158669881148001542749483356586601556709040*x^10* z^24 + 1407509250437057475788431532741171319550261947294874272*x^11*z^24 + 3323285458106093808635530249973067973139039410504017084*x^12*z^24 + 5794446151556052496070370734856482659973636283833949456*x^13* z^24 + 7036120000860107515618262282211317157472599700462356696*x^14*z^24 + 5316182378141792338347280173250455249444985286530605264*x^15*z^24 + 1882819333970796780382285351639177807448835852660429284*x^16* z^24 + 3908613365102054033059613140607786073730800*z^25 + 332228584506036260847372746982876409967202672*x*z^25 + 13178349991366034165646716363462899747304628240*x^2*z^25 + 323601438820350966194700509226768095898306891096*x^3*z^25 + 5501221669949352959932091182985703554222762991048*x^4*z^25 + 68581889660004480964987378467473985260109232490424*x^5*z^25 + 647717784257668377624803817720921780278091945826680*x^6*z^25 + 4719086458542458724807497958026854078467876394040112*x^7*z^25 + 26741487938188282597972679549767241159826316803178080*x^8*z^25 + 117860620916984732905648815509235686053624493682401088*x^9*z^25 + 400726093470792927583404817706112877144552680927361824*x^10*z^25 + 1032173534811051801782989313370258215260484308888347672*x^11* z^25 + 1949661619399519348409862559716734793922026226357674216*x^12*z^25 + 2549558268087851856446209335946260063306035091719572632*x^13*z^25 + 2063925386424915319544923336267604937633055145893057368*x^14* z^25 + 779701337854277004017003469709606978426326937214569056*x^15*z^25 + 8268084017089004517641253354978115118579052*z^26 + 655934444277971695258995064882351385624757348*x*z^26 + 24160264581708724445832476119159059509059934292*x^2*z^26 + 547632596521017000432254273285786763546183499200*x^3*z^26 + 8533942388994276125446256704727284512312263904372*x^4*z^26 + 96718013362626108048175343206108996190547179825508*x^5*z^26 + 822103162920406618283723528926045471505556538599516*x^6*z^26 + 5324097139237945329979892023634900025440269378777248*x^7*z^26 + 26398650845304304096512963719362357467574281457900884*x^8*z^26 + 99728276928628788474757387408428314605044938054452332*x^9*z^26 + 282563485627311392428730550776737484050966311111547020*x^10* z^26 + 582252086016013054771339548486565344710818132057565088*x^11*z^26 + 824855106569599137915697553536138920802791189431840844* x^12*z^26 + 719103671338202744974481262118004489386549574134339020*x^13*z^26 + 291065811465911589569990903851165537519812577420280132*x^14*z^26 + 15718977933121165839135526604922982723419372*z^27 + 1157993359382647112841352483702796845616049252*x*z^27 + 39372204730519247075800804815066671391933598944*x^2*z^27 + 818068170502938932648288439083716923816083861976*x^3*z^27 + 11589310576460281247047894820245555256008288600644*x^4*z^27 + 118210994150426448970171327624805333893990963270164*x^5*z^27 + 893149905658910077739307775586261225012680635509184*x^6*z^27 + 5061183497044372072688194711554971403501868660109424*x^7*z^27 + 21510029783325164441870809979857527980863617337301172*x^8*z^27 + 67716713338257793638869274435097184246117320359023628*x^9*z^27 + 153491094753245605262116627019613668831932322233164000*x^10* z^27 + 237213407315166288620605998060701698193353967239648824*x^11*z^27 + 224035756538295651243574366028397594377789297389016220* x^12*z^27 + 97657398828946375547743799765429181849250936017829628*x^13*z^27 + 26762109729186209033249510286678567154406280*z^28 + 1819747169329357958795607451581181897502396472*x*z^28 + 56714984748244074785221067942292096384597817512*x^2*z^28 + 1071282360763620347819893030466215915810316292576*x^3*z^28 + 13658834374207498223832970545796351283265026162388*x^4*z^28 + 123840044748653232573914238747184253820771344434992*x^5*z^28 + 818719918066754829609243820017490729030383209875104*x^6*z^28 + 3976635100514236224454579548915549051186817560155328*x^7*z^28 + 14083915012959706835522046699906070375420978718466240*x^8*z^28 + 35470599381587449661339962721864280290077249945448472*x^9*z^28 + 60300466202815670405709539696850018492001958460545688*x^10*z^28 + 62127884247131143741305415283937027307905777669728736*x^11*z^28 + 29337931969301905539240530326963803621001515460007428*x^12* z^28 + 40602920653480590033286781623530586571418744*z^29 + 2530939770070162386078969647222197399284140712*x*z^29 + 71708201716470323982805712799263835456599176416*x^2*z^29 + 1219040247314396191231113238368520910610793407072*x^3*z^29 + 13815770990088737128314708976055056441843213553184*x^4*z^29 + 109605174349546310633656012354844488464581326083648*x^5*z^29 + 621096349288639898206694026869714079301750673380976*x^6*z^29 + 2513967306436901799394982864719955549443611947397744*x^7*z^29 + 7122929061630634931307969808686951996353917656128904*x^8*z^29 + 13454415808990914023935019438041910901428837134327800*x^9*z^29 + 15248124316717150971467383461788948491878728925332112*x^10*z^29 + 7855010522753815957024183970175373363611928907741008*x^11*z^29 + 54576802383951465515471671645346977558614828*z^30 + 3093209205370167092372703937341821548966573620*x*z^30 + 78879310850781400152487671421049733850540617012*x^2*z^30 + 1191955224564832110903874515955654087839681512256*x^3*z^30 + 11820270436331276940105398639748004584327871558728*x^4*z^30 + 80378015449124121339696484655947617069386916108744*x^5*z^30 + 379562552830379710545884638351383357292260500764632*x^6*z^30 + 1229057835429592266149501815199027670322859288655072*x^7*z^30 + 2611675982563862133919612657859715643040783800545516*x^8*z^30 + 3288772166588869331853083608803359294827090896425316*x^9*z^30 + 1863700473202891884957278562170720865562556904072084*x^10*z^30 + 64588814616622938540534210557785409271965916*z^31 + 3292827912669952101493217210126416291269260820*x*z^31 + 74641572976634122390886195208744827028978377664*x^2*z^31 + 986903137989881812482392235639966694026242682384*x^3*z^31 + 8388650369771808334424946695218932812526208913448*x^4*z^31 + 47535155272878171787696453128269649649936336583880*x^5*z^31 + 179574641326144251096064971909967830121116797831040*x^6*z^31 + 436114488457186592469361691672520639780821640533232*x^7*z^31 + 617866681329170382696112543649021205765126861664860*x^8*z^31 + 389024944092041444127931530594796823256227785847620*x^9*z^31 + 66608228055657372382276923624876763274919024*z^32 + 3018522061775202900051060914177115010295852796*x*z^32 + 59861677340994200948852403406716243683127623292*x^2*z^32 + 678450693801035238353602046964974089581220075896*x^3*z^32 + 4805714397337412170979830836835487567970206158149*x^4*z^32 + 21786368968848831738958130329199971445366513280456*x^5*z^32 + 61736111612584072306231187341279070116362767144718*x^6*z^32 + 99950365734964066012880528711324300657335241658828*x^7*z^32 + 70789817328720566511448490357982713388281298806969*x^8*z^32 + 59051202582058953212447864109067840923544272*z^33 + 2347623586765533912473255708304142393653734832*x*z^33 + 39905144993078151512313813906876730903645134660*x^2*z^33 + 376928722893603475551902865898957782842063491290*x^3*z^33 + 2136119443615728051505459766978828908111320784266*x^4*z^33 + 7261998608638431401580911705052919997220441947622*x^5*z^33 + 13712630420030146331374919720652752987110565921754*x^6*z^33 + 11102887311578604966049745540038157524811180650912*x^7*z^33 + 44734520480431430700875487399376628727050355*z^34 + 1519682973636709832758620346971686938939486137*x*z^34 + 21531147591551692123348581593808560520774012357*x^2*z^34 + 162626598289570262481128673027689795874865119888*x^3*z^34 + 690565225248625282315603880662244850104627494587*x^4*z^34 + 1566138477841640425503257210345186479969682679303*x^5*z^34 + 1479592250846869356951891915180009895395077080473*x^6*z^34 + 28300977754152136955251928734592063209318299*z^35 + 795715943947926106675506132506779247691386529*x*z^35 + 9011842528608681472666089363246368287739407704*x^2*z^35 + 51138433214952224861471056731420554450174930514*x^3*z^35 + 145199233828905359472552139127211520424503268391*x^4*z^35 + 164238324081686120453791927814376827924174322427*x^5*z^35 + 14117141120390313037914035472511888425994758*z^36 + 323365495108952286879451032465134263502610210*x*z^36 + 2775381201154071312777287444152926380414109798*x^2*z^36 + 10388181562926763242679921715758679192001361200*x^3*z^36 + 14739827269396654283506059097653904848264738429*x^4*z^36 + 5820795918978481915952021011310033692969578*z^37 + 94999551481035770575700649964819172395984038*x*z^37 + 530665621635577688867550180526372156866942600*x^2*z^37 + 1022415764351213013884813347814143688896976076*x^3*z^37 + 1312892454911550337509682972582547031695031*z^38 + 20411550217812906529317207924167974791908217*x*z^38 + 52968290752143773018446212463650850472459641*x^2*z^38 + 370303000103257787502731094830974803811419*z^39 + 2098383667251794129182142870708857221598041*x*z^39 in I Output: Magma V2.10-22 Sun Apr 4 2004 01:24:36 on modular [Seed = 1231463197] ------------------------------------- false Total time: 2.709 seconds, Total memory usage: 3.72MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sun Apr 4 01:36:56 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > 18912730482171158765495432783759748*x + 4072541297160856187503349859436265736*x^2 + 490098193471489351196126813347422189756*x^3 + 46199295485496137760120146591615851370694*x^4 + 3425803916841864025859317034271559769449560*x^5 + 207087464356940090159659771495414464508349328*x^6 + 10556740308670001853459257103410876261572356264*x^7 + 463598075298097174901066800670013675928188773760*x^8 + 17805883968885052565017583921240683394515989818520*x^9 + 605399830694221249740855850539665723812990009208304*x^10 + 18400526314248558665351722279706707786526357808683688*x^11 + 503971019362295949824092264354879181457997045719536976*x^12 + 12521732810506876302250934229449971951280016381720610008*x^13 + 283825711368914266321172167490429922638564156740099553616*x^14 + 5897268091490843424174205436735595514586422844115443589288*x^15 + 112785279557149492718447224687310713690436938797006018474240*x^16 + 1992539959267351392524696869073642514640167613207427707099176* x^17 + 32618615157348812707678433839771828476189587516923320519775440*x^18 + 496146298342812560729691380617712194405263614710826009295331992*x^19 + 7028739300151041849321625127649322228281610666695621799637256552*x^20 + 92935553395498747880498358013068778410745884016601205425408566968*x^21 + 1149021388289350914959366713915422945481117759518640686564413062992*x^22 + 13305334619061654197218130524978731268813521558183324282593004808008*x^23 + 144510717355551554219293633194415182212110829582392529809105946570112*x^24 + 1474009315783992459006580003114359777728686050887433830485441946244792*x^25 + 14135371409191905543659561306392488326968202846131496637133176343191216*x^26 + 127567364333947015592555181716121227189589724348502704343309494502591112*x^27 + 1084322595955712002240977895477815882268719335082797883353835593053435056*x^28 + 8687044238611132563103926598680131797366132315993368260586361084625370552*x^29 + 65635445378733575666188334180909045972209256917876699672570360517589703440*x^30 + 467917207588597413992439572385093561407335365048119175110663208609809322696*x^31 + 3148692875936763370213155362848432047241711500848221795755993325171608917760*x^32 + 20005331503726557771312025833925556732793224165443345668000762922193616684336*x^33 + 120031989017800600886557734567255446192574194918628162537779053342134343540320*x^34 + 680181270851257788559455583115712285838255830647136879576087580855895671814160*x^35 + 3640229393796590078403827988713079034889879434033476987236936345056601497436004*x^36 + 18397916140217091153608721400708926007030707747312578761694455693487434503423240*x^37 + 87793564770063956690170470401140197445774704624305209794228279614079489122130864*x^38 + 395446227133222027324267583392657257323831583444624861962198012211356551184119800*x^39 + 1680646463744984686852588839812376093513397374646731846156620224096554787031234688*x^40 + 6736249659361894759262703318912355121416941497768358074983794751564223443148443464*x^41 + 25448054319081689038399074987427054965381659733417772183704097867235551124711563728*x^42 + 90547727958726703620128316799218401014777105888521745191034516375495898147017841784*x^43 + 303197693997224853198886929128959742718195959265667880261298645733956401265941045808*x^44 + 954511261009680121334432380942436401576310248304297093247178384454322068800931493768*x^45 + 2822033311809961041045974405085475981689645664919425299773202877017058215479905485552*x^46 + 7825638467011103584054345647174089396833578628725773039869084463130361372394768965368*x^47 + 20324921927321708313771578349215266403751105306353286334525301841701871189812475409152*x^48 + 49360524505801344254053661275845182665911251788398248288772860515792042205501294097048*x^49 + 111883856732293225730768370412561336234061509775619567166422080284463723306981468837808*x^50 + 236199256444388001746328361303260536098735371799542318317787464656080123089821464937896*x^51 + 463313929434063366214549136280823024371707332198009498116333064336682548815825338305512*x^52 + 842124037956176243980567729586447323309365163537773428421789156708473192184818627784168*x^53 + 1413936519977564039701102150559011385468736776464090890580254445914921665563587761100144*x^54 + 2185174574262823243618887777498143402722205651930218885425165209594758490790142443956760*x^55 + 3095665110022860034929649403307884919885992274201392792585223437510992591141351101334656*x^56 + 4000832197822462019084136417904309399131741056848657098342803837639192882365082118476136*x^57 + 4690628853438141637452805959326361323880574134606565560311894455621332706436506787631504*x^58 + 4955627072755784211242271994719526363592137367613910520391819901222788779236557796178520*x^59 + 4680280152907199177365803848707394042912189468517992566040205392684834909645872622594256*x^60 + 3912978950958891995988071606736362409742226002608903669280292924116244519701437514156008*x^61 + 2861370000763690366626496449326099085577667989389171158702644097496089516135749671513264*x^62 + 1802201979919654610812051060384925066406171062914086027576929421798920265764475989506968*x^63 + 956760010096976753698669686444493341391895673643723784367222446160810237060258226746624*x^64 + 415165348666818937787684336859062666715334697019446925821078109512805558629575800554124*x^65 + 143154785354479013833111120740958750361859810477632198925535277117832678675466316608536*x^66 + 36692893230630521475561081885111268939531304315578913253529620744546354884624414485236*x^67 + 2809816148291526419299722486697709783657802582724511375270286273231027175849617325446*x^68 + 12237649135522514495320574154197484*z + 5929141006160658272982818177708680998*x*z + 972095959406739894142109902303377947445*x^2*z + 120227655915300720264538083404619616410285*x^3*z + 11086290882645948586906644130879774376753190*x^4*z + 803666999036017493883051220491062857829497224*x^5*z + 47811250721109903077852437643538245280500584320*x^6*z + 2399806040152137877280783802576136535645060667096*x^7*z + 103693801257626292820899007155689529922151517425808*x^8*z + 3917314595526891286830097750973711242925718125047608*x^9*z + 130968611409443120082167627348705953885673101068523368*x^10*z + 3913181148959808267771339014651827807398650291704157184*x^11*z + 105329792264513234847119328959446001211307830009804604128*x^12*z + 2571127686274327082756704612633415165185143145140085657608*x^13* z + 57238204493747404803730826949060993095805272763401092229856*x^14*z + 1167659337173364828159707114954727411460531760273912897680632*x^15*z + 21917938067407272585925619041680864435426912192304874123943552*x^16*z + 379910926670857054877264428903886379216537954601923076201978320*x^17*z + 6099681047733908256906131069232028148412618356874690099924687708*x^18*z + 90960156193625562603385292879682730947028461196217690367836596116*x^19*z + 1262830166313237776226220332356360760405932154040198648345841240376*x^20*z + 16356657369775490764116628065494489892334755516182911765357115230632*x^21*z + 198014685373344751395142501239582409075301310450266234182898646352320*x^22*z + 2244166435291386049732059956961922012639434851342475572354120282909688*x^23*z + 23844268388822985351713808679948487856421505493070516840590922993467024*x^24*z + 237806836725195482899165046989480142594744890476307518016656042501376056*x^25*z + 2228676891883453733866305873983480351130649217020301911570833402064506552*x^26*z + 19645374081170551037284254113547886479585156016829529881963114707957554096*x^27*z + 163009830219529196791945428067759104212142154596941251698205975499346923520*x^28*z + 1274099822636136759429400892742024185252689692761683464108499379477126047656*x^29*z + 9385868692069990626374451159356973300199950267783408180147213687765110727840*x^30*z + 65196464237785162328166880203546301310243924209508851580506053442880004255000*x^31*z + 427172666744973351827389192126679899631825706646546785682439851521176818267512*x^32*z + 2640703758351190692786701299739792167279154208093012714984281961757792140657324*x^33*z + 15404105257264138488625293672045400274016876729194085945068897680501940180292174*x^34*z + 84795931793201015074718083382377801362759701645408973486869661467895873512471190*x^35*z + 440467756794310127222162257411605496685979657119298067656575842621216069773381300*x^36*z + 2158688826020973696694930170558101407605911060413157986891755131069847669733137048*x^37*z + 9979201854089983515469377483499179577445510164323850736617287123583677605554707456*x^38*z + 43499085010636052007317260684577950646966808146186631605361699971593725045655683336*x^39*z + 178708740918637471685467652210779907655457501291820080035107720630080617852894717744*x^40*z + 691588298019920728829145995208825140047928978620074310036627463724545727220854170088*x^41*z + 2519357371031428431962983544488770465639303014864785776428768853362877695121667762584*x^42*z + 8632216731736765888099742131312303175141013219072303389243537846815664198983513415520*x^43*z + 27793122064483707147887450308160938414233353215171220731229873536103058732788865806304*x^44*z + 83996991097300271253449148207038720359127665190020723802332934922326516639462973692184*x^45*z + 237991474544838645306365351541082023884485494651756084121250928142061469015061759837728*x^46*z + 631268166471549780088305426295122812208856824951874854268560691361413959085306924174440*x^47*z + 1565018998957136384133679305185843081149146915500927713497587178102779011970500220566752*x^48*z + 3619771842141153378659312878404394159189173448278385250446729687103254084536950857633056*x^49*z + 7794575347357980727680397390980827990105346589217238524361931960911099527303568591766140*x^50*z + 15589150547177224870169066437705093319864800605994371778877148874483580337547111353879780*x^51*z + 28879900645941776081773794209943644021645412935313119893721640132061115600900413630582104*x^52*z + 49404611507569373412153377144374435453778638606767880141207407594965898274748275072728120*x^53*z + 77766520718525343645896236012366927533950760487872317051404863570816112300405762625705664*x^54*z + 112172303914812022180075677264859837980212353538393808423541189544566547252752357743719976*x^55*z + 147559966337984141896370815724823980533744381947662410591635698656809601047672286965647280*x^56*z + 176036494070576283145198668558286174475393270827388342580728551656888156213328692241722792*x^57*z + 189188808217623206762702303333236858615619646992216391542103535462744652059164915123259848*x^58*z + 181706670630957495147791409441260717118461362609532669899528281779286926589206050721924208*x^59*z + 154450230257200319476467874665211333031923290499061640103997865899670989149544355897425472*x^60*z + 114783079024539360820589673151167097398633128324782885262623163711572100445475951501415736*x^61*z + 73436958503444809407246191112187571664431755326263458545015243491553459673984611872613984*x^62*z + 39629365320243968620033166102776110851568392525822709053098910587323831339433545443628936*x^63*z + 17540540235010352617950076117255002431305041391184064428665050430304634189612027364501308*x^64*z + 6125271666332505202379622613487363202731478449802909749028225648239012636582327694026814*x^65*z + 1600209741546476140264681919651762314940410320360451612378194608980663270952072289106725*x^66*z + 280898973177732302917639903890750457489790322902371004839520677726831216785672037917381*x^67*z + 10302659210402263537432315784558269206745276136656541709324383001847099644781930193302*x^68*z + 1839726586706884679129859647847688428*z^2 + 608216600990640313757208233496572375904*x*z^2 + 116546921074763137062190803266199627260382*x^2*z^2 + 14336940179727590490120756130256991985276797*x^3*z^2 + 1299837187453396199876731398775187816259713460*x^4*z^2 + 92818565788869057969748180762685255115635732100*x^5*z^2 + 5435036377292386304667373000324377202782965314452*x^6*z^2 + 268382681139489019853708248613074161337774068942588*x^7*z^2 + 11406250553681671565813885480833225616952040119657396*x^8*z^2 + 423721790309593017544658562620427007089919128605461524*x^9*z^2 + 13926325495621799884575936624306895914664433229005769252*x^10*z^2 + 408927516495870863336053389186510119618223720602707781748*x^11* z^2 + 10813861057122130742443334023911861321308277878000882995860*x^12*z^2 + 259255384516952752823193575666551745993970562322535426451140*x^13*z^2 + 5666581885160584175230265030415191413344614915330456063704884*x^14*z^2 + 113457562358584122698589843798371758694589065255663413127609052*x^15*z^2 + 2089510123144501937416811783869285852873034298031863306636740292*x^16*z^2 + 35521672047013386528971755287433136340817483215449849962979512788*x^17*z^2 + 559137428694146574967827392623769176933111133320503120924875812668*x^18*z^2 + 8171254002955097827974704333270218160490475136121839417456189605128*x^19*z^2 + 111129054551500357354950328534980373098580721345407530852473294606916*x^20*z^2 + 1409398644294830766635027762185999655413943702838849226587020580067860*x^21*z^2 + 16699238477776353624328581735077549886073832383410672352421214476325924*x^22*z^2 + 185143730945827437606237084228984685282820560304503264440814712388990252*x^23*z^2 + 1923437649344645387710815215435098380197927904445826687894452467261285252*x^24*z^2 + 18747105621840337497884572732825408740791724477759245472947752452086875620*x^25*z^2 + 171608120696783811757221535285589989680613219245305608237564361122583429268*x^26*z^2 + 1476677285573330630069517351480248747209474690666972914734976027526764818292*x^27*z^2 + 11954054216146002159578408227713145333162392126576852297988614143758808035428*x^28*z^2 + 91098137297055200584714687350892172580000038574722335083362888205901705159188*x^29*z^2 + 653882185502751707924133115791075952538603369379297501111985796456280341702148*x^30*z^2 + 4422493491455109479089600055157149454851787926676415421901681504715365883475916*x^31*z^2 + 28193396007783427224995591859397864493894159293430096774477878442169071535455436*x^32*z^2 + 169445157815551390760165472864761633127675198170499903829521202017995533065985572*x^33*z^2 + 960189227616423935905283060890099883887155823893518081875648010180093655552093432*x^34*z^2 + 5130153873485455673483580669795106574840613243983584009081711392478663621272836922*x^35*z^2 + 25840775066888635174324374955308437436726173568555659349812361727469854108173800604*x^36*z^2 + 122685481620542585583210252915961742981963962380692007932960055536799577111507788684*x^37*z^2 + 548856101972585125904225252224968103882025967349940121907176317751816849914480448828*x^38*z^2 + 2312701352762555437141222307860616047964171002118666215839010780647937561686093144948*x^39*z^2 + 9173715366205281020959221876500543356373763750203672791020964965216169302456223093020*x^40*z^2 + 34233620758036044855594437238182332212736886482714446434420427538099215240872330790972*x^41*z^2 + 120089368054448132520097659770939032333969052322908775191195168776432276677684611567148*x^42*z^2 + 395643266808259665878595619469441424838982282702542674945333426822590287814821636854972*x^43*z^2 + 1222897370092430765217976656204325719767271178639308199326266749470061781022401657910972*x^44*z^2 + 3541873124402106281100293539615767492540189873680296049477996010285225872775931850354124*x^45*z^2 + 9598989483422798144544677274169921724055099988176370664320329124794302194599354400138140*x^46*z^2 + 24303824429413482859581221149583587122159993460942387783647997085569358738432977821924756*x^47*z^2 + 57384029885581743995158765704819434758833407983959206002458505697713295868659725365153708*x^48*z^2 + 126088718783325395723901336587482359523080690471672042541573873940338876035974941888909308*x^49*z^2 + 257220986371193917346184232419832088574731136063217946050602936379752823416116584632800292*x^50*z^2 + 485861862784312691160054338254692792027430058164851177659254725959512990322584629293421888*x^51*z^2 + 847143762587378237399973210168775616986418814660686502335178499273521443687730631298577516*x^52*z^2 + 1358626793602782772061222641287912297990084855425521694694796712538426821692533517449789660*x^53*z^2 + 1996007229986463409320985024886840544397094599459166403081456591635075092353603659983411212*x^54*z^2 + 2673439916615179737635092349170043087180024097453993585266117615818522172296183685054127972*x^55*z^2 + 3246320205807243556677534967715342327486973969848130258804701231948892746678228919892958892*x^56*z^2 + 3550070171037871217167253463934631762679892644850361462585005283276839278655389994523776716*x^57*z^2 + 3468457846850568885558024275737137155507704220810869342757379654670768625136859397066196252*x^58*z^2 + 2998154429390919411867160332533905720959684263289212779197485680539681361938825261449103324*x^59*z^2 + 2265276199404644668401792124607498610250957176253584995032485019804719224239356242321895756*x^60*z^2 + 1473059660809600884897569654437866301588642948265663028634363105984835633905897164970679388*x^61*z^2 + 807800174928732493825035285894104851003669525477880594584719976221714115152645293791969836*x^62*z^2 + 363290336259404575997235871175235579417637880714418342243084393650208099753488900648800452*x^63*z^2 + 128688660087735373995018245458636162894465458466460198766082564487860428875428375832497368*x^64*z^2 + 33639895587295142668179788504931208985657747691537495999197014637182318927717538380127148*x^65*z^2 + 5739793257748225762530674282091256921004971193545535678177131259440816513866450638868426*x^66*z^2 + 509981630914912045102899631335634325733891168764498814611556958591431432416705544568449*x^67*z^2 + 127715165790596841901789342016743492395*z^3 + 50661514506393773667909627630578399401155*x*z^3 + 9277070822856244306576075171016110452607539*x^2*z^3 + 1121404121451035238604472699975366993825468868*x^3*z^3 + 100099112727719951905970194954476145768556084232*x^4*z^3 + 7033445582897624187368863093109789245519165090356*x^5*z^3 + 405203798211226963507954551618418672454339396827152*x^6*z^3 + 19681422848767332682811308206465628201685274483185508*x^7*z^3 + 822519348681575362457922316494731821777689777991378032*x^8*z^3 + 30037165796118366067218017767607001277302152341758278508*x^9* z^3 + 970200483622919010824796913328630111682818802452505089592*x^10*z^3 + 27988816957359635440858054170399777147497508117950758464420*x^11*z^3 + 726931767434557759774774835724894559002466563403329896898696*x^12*z^3 + 17110855199883662445057947144914754267304111112119101451913140*x^13*z^3 + 367068585667494607106773767420171397165453271229457482448114896*x^14*z^3 + 7210858450250078476020270489819076556640239883914690145435679428*x^15*z^3 + 130246130503977963767571105669304550170632861568022960435727060828*x^16*z^3 + 2170768841567106643418190046749115934458763724653263094124342322104*x^17*z^3 + 33486119381505151265834091814765363952231357666158853696418162851460*x^18*z^3 + 479380235341149333319421521432194450371823632549172118055314476850836*x^19*z^3 + 6383746798272224834365631963733998653397525408142813583404093335972520*x^20*z^3 + 79239523751051017625141482981149411756628170396151488418490001994280580*x^21*z^3 + 918458116340157017770116951467790695042783290893015287753564809329016656*x^22*z^3 + 9956618420555742649383061107065746376128411996490446295105237362166680500*x^23*z^3 + 101087334236755106676402919575153433577061166052469371965730237360683735104*x^24*z^3 + 962351421941073883119988304492438103920890688602304484099270453217759433388*x^25*z^3 + 8599473603870002305808452810740906029310330907310007836060739365881248864552*x^26*z^3 + 72193111735398581957047855571276340203502143537419363054282650957979863880884*x^27*z^3 + 569809917626766839211132587707682553307202512944473134336124735341941515085480*x^28*z^3 + 4231002376919941999429678246287924270533903481098195007253639255694869374613956*x^29*z^3 + 29570005500726930358641568693847412616297810141124189106501726899619530578327056*x^30*z^3 + 194589713614606594954714092672543961830219733538751697523715393642433138245830484*x^31*z^3 + 1206050829182379394634898556391200857908400213485267167615796428272899642207241546*x^32*z^3 + 7041387669484500659106170527969423920428541945054638577445906973745795210472473030*x^33*z^3 + 38727632181930438540927575845168965614575814989209761958581042851516920924855008994*x^34*z^3 + 200646018158391638700698384625043822504769561495049553034546942801729243120314644684*x^35*z^3 + 979078255277622311518492098493875643456180681465115479612802475731280448384204008216*x^36*z^3 + 4498467659446204117951371817588387326393762409643265859882255440707026363151993238684*x^37*z^3 + 19453899614881551878487005820839858694590687971011308273394396908288249408466446810160*x^38*z^3 + 79145779629076113979259849819004867190225954908634302270574363156212263823307107317676*x^39*z^3 + 302732607083688047901575814597825195130632294805912035074716321608310080539430427934832*x^40*z^3 + 1087868392933442529441080552332189677282371627608243388247993704441929210840151433690468*x^41*z^3 + 3669397357040600506120382055425960416674703822038764734264176386447613571812796434493896*x^42*z^3 + 11605535827150176491279535546777981677948507308252538445099121590111963568993782901130220*x^43*z^3 + 34377003853547635112503671733493580653626355432776458166707001173859837817630870359451544*x^44*z^3 + 95237032893191363483052627433525094918741421464051028739929090443598674837380864433101980*x^45*z^3 + 246374063319180024257799119905763360632669015769886694197878524691683526457192125703523440*x^46*z^3 + 594093486070192340479117099274323000636507097485659383622922975690339346609431565416725324*x^47*z^3 + 1332584694891464352553029030328133178932372143066456967781587014434496135504782537736400940*x^48*z^3 + 2773951813590873370280916573842816949222723715640314762824997061756596140830321824647079296*x^49*z^3 + 5344480490676367208578296712921079164729144447497215729713062094495158388080145523078364132*x^50*z^3 + 9501298649684534269646865155295632110066426485513043520769801377231851960554487893518720988*x^51*z^3 + 15530968957169622901963481265632279031015356648147796695031061691793407362934073768589613112*x^52*z^3 + 23247613916095195142480868021623968047564448152194150318301987137469342563389779677118022572*x^53*z^3 + 31714337602440500246177237026944328750694089010423770607453291254899555404562913904827996272*x^54*z^3 + 39210453929196155994854509058919283460753049094233650736271155586419471452506130002876712508*x^55*z^3 + 43644968256108995736891233568950700902298634793877889601890114619239362429381946892071803744*x^56*z^3 + 43389731875015577329069961947199584330883477328186820047956644256854008800790524832963525636*x^57*z^3 + 38153045560761086361930264241965008715655122954001327986862522879850384954230733581260658008*x^58*z^3 + 29315349109203821876965185517332885775867405800686497286130017206973326865669011549649236668*x^59*z^3 + 19380698667573412499935456742630720933050418328244812141258601762811578407729657338449454904*x^60*z^3 + 10802334945741809501333358323264521619431536047791075513106328822743269030160199049636630764*x^61*z^3 + 4936542498721115858143315641498219706949550953161022472145560978647880732080889733343141040*x^62*z^3 + 1776060818040379488039876573366122564201162277192372701963891992248964902372062473956221340*x^63*z^3 + 471667197817950459502271465241055728067025539737123403872200724634841840601542148099872643*x^64*z^3 + 82202056456023435670811196597791563776657072862001421150894983068704012468836269751670975*x^65*z^3 + 7076411780603648834989907956376154728974189224098241721701538713003979941311541641299459*x^66*z^3 + 8250783609658399970921426180441207581641*z^4 + 2996911175423029659215649386348435237605734*x*z^4 + 544347147105815141998425693130690988769807960*x^2*z^4 + 64773492712574718306811470237723542183833290588*x^3*z^4 + 5688794571323302187924263496476612165110262704084*x^4*z^4 + 393286571091553820124399634686870021902226164893872*x^5*z^4 + 22286315123392665229481394109869758775434710635009840*x^6*z^4 + 1064436116697724418938703515663323520690836963451210236*x^7*z^4 + 43730578985370672760859600100532503905255300862293734692*x^8*z^4 + 1569442139268933548192467362041051412925296179990271087360*x^9* z^4 + 49803630542757209538266346223232859185464962492614410661640*x^10*z^4 + 1411102820328331622423997773639488118985479017211598260610588*x^11*z^4 + 35983121942087855727894876797543133597887910814755416164659684*x^12*z^4 + 831302386244920764082831718903070100517833037393056073748194448*x^13*z^4 + 17496935933681915157837278399257724843042905753760191507080084384*x^14*z^4 + 337107631977900697470709829443998170334718712614308415373614970364*x^15*z^4 + 5969614317562379137625806062761714378736823640544682110334032347736*x^16*z^4 + 97503700533586816681555044433837567457730724148530942104052858261560*x^17*z^4 + 1473389252305474417528676458118934719797000960757789265933329525841048*x^18*z^4 + 20653298466494149860412403524776469126290387557616392103234390774258636*x^19*z^4 + 269181323367396830000101203129508535079514159540669680017334905621612100*x^20*z^4 + 3268630355143334260978056836521860865189625481423774217222615489405378224*x^21*z^4 + 37044477356817441501728492975601830749009935712400951629342569522683952720*x^22*z^4 + 392456709391437705016348265389896135232394706124727013281582282899789058412*x^23*z^4 + 3891862368205661916552629835354798653053757432096350130632780743398601150084*x^24*z^4 + 36168374275041481879633357948375852345149805641502782809640414410368926930144*x^25*z^4 + 315314032138844594080062383148571907446893306429710559844212879113265374416776*x^26*z^4 + 2580903744552966039302282656363231305723970654908331289196427500467212988288460*x^27*z^4 + 19848378797445968655507540353576160321356481724951587018552183278233456800109908*x^28*z^4 + 143501497282141847445174787055592076438855509406069623969248498574234366270233616*x^29*z^4 + 975810181518666573754023064631670664531690141526620571991970891872698029030819968*x^30*z^4 + 6243086645227246550661043624748337181021762090610910608566574033129111260563207084*x^31*z^4 + 37588584176425603512666490815189701620047537527547740151056676826777867184482308450*x^32*z^4 + 213001976998687969711333793908873173916904080881557946869132383715717744935638513012*x^33*z^4 + 1136010543994810019748687128536303656528259753464687686913875777139079926460382468424*x^34*z^4 + 5701691016081018907656738124862018431374724002484235418033416290943517601901892789012*x^35*z^4 + 26924652020340125937397662495746464677269561864377664710480204267673227797324309344316*x^36*z^4 + 119584265278878064629270187361440166313589991033888881214692628751916328076950037524880*x^37*z^4 + 499316756779289688331816359945129840354843687425687386228828997125335664012181684103888*x^38*z^4 + 1958858045835264931450737849274096326852216416881104346351879537052203202813516137241076*x^39*z^4 + 7215127135474470854657963522677183591022314612258412125634431927186707292548670179851916*x^40*z^4 + 24930317337983898286818378255787301075248712369711133212444616705065324834025707678514624*x^41*z^4 + 80726741856858692049138486668800273526711993592152282499986333132160730752880985842514520*x^42*z^4 + 244683380355451970833662337612159204482072080030929911537226005059142931400340806139385812*x^43*z^4 + 693269577660703721175678233360483656931749240826509149717483793464809863120029269439709164*x^44*z^4 + 1833312883185177593572269181398022140234658501519245226532296744548127603538809944836781360*x^45*z^4 + 4516857828372757776366527192875187705031483580038949945178082742536813541727865537040574496*x^46*z^4 + 10347128216256127029030832167506941395455899182987833285150077255326549503663217815677325940*x^47*z^4 + 21987647456682397968248554745021843951874030941396331857934507326555758510249826751717290448*x^48*z^4 + 43227415752655450575936317213388313523139911090421242954866236923982519800771135695845354456*x^49*z^4 + 78385713918598157146043722976516037202800716071415176169651337969350434529604504753542706120*x^50*z^4 + 130642856497329372241474595049418038930553660402956285712672091538013870061076458280311082180*x^51*z^4 + 199314101548213024056085110216657033816151316895680933378025270153656384612755938626992191660*x^52*z^4 + 277034066024032664934016767513758817750444944027628205151043921924842413166399957597434158864*x^53*z^4 + 348857711858166490818085862131206473988513529728139664591335285499300371301535323671622028720*x^54*z^4 + 395372069453815958819659996707946524254131093985792733659850738986887809203920289149369851300*x^55*z^4 + 400078888924080772683911155660317343640324146661323593299417094400806584475834854211672158796*x^56*z^4 + 357965352047703224314645395621472906994615750254145379201998674237030864154416974511865380704*x^57*z^4 + 279788973373167031186300948135995056594245431249404858935649074089248307343758332317782150936*x^58*z^4 + 188106588377868284606195885904848448836663654123466877831538416112391833669162846207723446596*x^59*z^4 + 106593807129922677770414006700466536182647122179973977337301054864474882539689738324021666268*x^60*z^4 + 49510957301072613264566033873642878396172532225014038233760085905853893298118918200185655856*x^61*z^4 + 18100600240034049752974540236503919836504683260971091800385489996291976260896084944438166976*x^62*z^4 + 4884430055604590293819442058499402025542050952313021163714456889308301418386173276084105444*x^63*z^4 + 865458700750987717133165550164298933014625211053311531400668690788038417625787211428436525*x^64*z^4 + 75235006364913311860397033135712274160119474905113188650989287200790471789396297913243670*x^65*z^4 + 387687139157920812628211173228369204868184*z^5 + 140891065697889676055095261372958008827360564*x*z^5 + 25144939313356212411642026166315218598190894788*x^2*z^5 + 2944753944042759813071934366595289606452883448360*x^3*z^5 + 254480390309518590592489999842360251711195038568676*x^4*z^5 + 17304677820900536312663683867068252042536339662707876*x^5*z^5 + 964253892635568438821639517261733057552186064363430564*x^6*z^5 + 45274013786389392704215071682108937011746941972773752072*x^7* z^5 + 1827938463856855387089112224008805311102913104938424099076*x^8*z^5 + 64451755586147367047611939902130691467946120536363396778964*x^9*z^5 + 2008746370232887177508657739914701363371770846199841657046820*x^10*z^5 + 55879672037940071153578184237178501685866257088145618871002056*x^11*z^5 + 1398544014800838002240861703552089818709876509671101104318422852*x^12*z^5 + 31700330953143796099254664576030975594371411478023107711119602564*x^13*z^5 + 654385403205851130102237523942010823697357984733747680349501566596*x^14*z^5 + 12360613176692443797931711020976446364907362739664362418511057198824*x^15*z^5 + 214508141168867593484133370923550013663410619272352912576376542359620*x^16*z^5 + 3432130258362105790622979903699203074209078124600193543451413882336196*x^17*z^5 + 50782816231226253773109243802155422278782453975729402651869691097714836*x^18*z^5 + 696704601643736535892828457805348805377684835510116090813613953926436744*x^19*z^5 + 8882983670802169287747588628179148257380475763031215721712154720394108724*x^20*z^5 + 105467806122756391587035401301146841377090621777653306841463347168981979508*x^21*z^5 + 1168135852676986555499277532480717273058103213934465151249984293742076766452*x^22*z^5 + 12087666649441532534569045489603588779741679607994835034003841871735670238312*x^23*z^5 + 117015328536038010457765292666028997336249019353570473906924636889567574764884*x^24*z^5 + 1060938978727422269621681662746488874870482051405639791770062919173996682936228*x^25*z^5 + 9017981319225883059828772371222163894193162530659883134612058232045806704580404*x^26*z^5 + 71921184348330607347170492549175638134500633107311046835461458546967649420838440*x^27*z^5 + 538552678035419190359674990110230435489201659887519052346973600541183887248044500*x^28*z^5 + 3788439528253496180189760329486695474544871499976202789142949544582132417140207508*x^29*z^5 + 25045794659047523440492728271811799117403993921317126543131484195704562637547942676*x^30*z^5 + 155660960353846157183381118819879377515207744408445617390675599702222481348365285960*x^31*z^5 + 909643737067064326361325383232461608544190248313893735854538936490070471958256896964*x^32*z^5 + 4998446393590389209984739661255629781495972049170653204157373586351213600508943641884*x^33*z^5 + 25825306366893430857375519994549394925283109661651752011924580547019774952468781465036*x^34*z^5 + 125437202353173205245752931906571850009939562859817942021538246992952953929297639091448*x^35*z^5 + 572597599630612193696170024878941889848664154511047078480603259811454243497413075645484*x^36*z^5 + 2455463580405293409789159860008255514731412294223876163997434116229052216704758707983980*x^37*z^5 + 9886471784262216887809535205508492506299945991179117069082622511161119265251674080104300*x^38*z^5 + 37348893407085606148284068721749659323430209989985469592824506527679214728955255397380248*x^39*z^5 + 132277330816870297737748778526829457813495304292611154622789310399456721671708876717409164*x^40*z^5 + 438773585150123343083666334386574249923171205726809005251253437322471480401760128397919868*x^41*z^5 + 1361591045977384557751540406996323238927044413419856508911361302868626745436957293642159212*x^42*z^5 + 3947558536390804555476405361461959009637498580641938844516056606508941686654379918105043672*x^43*z^5 + 10676351496262309925282898129131950583194701730490217658999369736031890140357389058738514124*x^44*z^5 + 26888588953517093082244994088405819590878868665590827122461864243360868715061043935944979084*x^45*z^5 + 62934885736958206025530151411132503742269045583991298848971906959935495851642221453889950860*x^46*z^5 + 136582092451499493597741619420783178371191271396713222884295176670329258347870376831666901816*x^47*z^5 + 274112671681615600893234602591762969248372479703445194020935172060540360652237870508627723916*x^48*z^5 + 507201678204787654043619674599188998744869114533937897057167741159042438438506682054210662124*x^49*z^5 + 862242852749166478868377869505830405702605054823791159011045937472984902592930665473931615196*x^50*z^5 + 1341266659899659445849185085625106887982537118205971300802468012137268163591090087182961614680*x^51*z^5 + 1900127768953303921764473590629993561048268729475073935765261077751752061872767835114524163260*x^52*z^5 + 2437899777750327783511416525285518744681817449666991747306187153640418991507835307345305437308*x^53*z^5 + 2814118880253878080784562624016256295120967486417079003972909371510137344855549296452880926204*x^54*z^5 + 2899395228046234428587126040658991814359461805672299061755759646965182942270935908736416984056*x^55*z^5 + 2640520634578149332399192212066479658197406740843213345402035056406996391672404490258178501404*x^56*z^5 + 2100063067413117497495458450359163378356364261988896012332241268541321968282756627846833301772*x^57*z^5 + 1436250053081536714184647246030209307235817632564679198358331162772592405865051703623810208828*x^58*z^5 + 827669895488697691629382454313934432415682595627810800673741649413602611290361141544197139768*x^59*z^5 + 390844298205264442316446202826951995735455351044590000370184378100284590933347813043914024220*x^60*z^5 + 145231655901113049799119339652857576753014775197214951946874805182015866651718199105750344028*x^61*z^5 + 39821531124644615367471199165988162608094864162375514217897664497009344742476684591911807196*x^62*z^5 + 7163581388923129505672510020017830738598582397298104907884616517814088913019225145953729944*x^63*z^5 + 634677841008382652321732098082427284927761011732302326978924635074662740621963586059439124*x^64*z^5 + 15193078801014173823363927507610427346366864*z^6 + 5423813817579596617929857451527369536618480860*x*z^6 + 952717937418211065294117299116089497568381182880*x^2*z^6 + 109775731160109485678932601856015531511054283266032*x^3*z^6 + 9330944633583499218484631651805581424036269320174644*x^4*z^6 + 623928868665037596225221934938191559724128480527345272*x^5*z^6 + 34177443814007756122963744921144336133782408697855445372*x^6*z^6 + 1577044982468013102877158412576137729099321304171608770508*x^7* z^6 + 62556115694491935452086744213366366315881175157648932741224*x^8*z^6 + 2166295107400882200621361686268799987402863357838113902948900*x^9*z^6 + 66288630524333695131974671602270316509562398812734806270531624*x^10*z^6 + 1809880487686353086678569850372533928142908550563821548799656120*x^11*z^6 + 44442620847316343632492180038886258345612791831683445958294066380*x^12*z^6 + 987993648361793547403394823253216580708786059247818402157035344192*x^13*z^6 + 19995109550948977712228306703378164524557496547623670019238912387332*x^14*z^6 + 370131694527542053989583594482747263708689073149732253994071853981780*x^15*z^6 + 6292238806962365332380850120672379509904843713914905733086611521183744*x^16*z^6 + 98578407980437428489152481654832967908084363704630706851024460140167772*x^17*z^6 + 1427561389637116722761460936178554808260329272595694122249087573440386864*x^18*z^6 + 19159376544822310779794080978188101290201643313680581950760770812633413440*x^19*z^6 + 238853560926438329816941667759753128000265103587430778838110663844618079156*x^20*z^6 + 2771459572034095136192549865195921664790571888484525980465983233013980924776*x^21*z^6 + 29982153551902264665801362206635430453224848476464022042828899022919921094012*x^22*z^6 + 302863203270148476362625787384370530987309762491475732961659237270816393853964*x^23*z^6 + 2860374697558794946804284261187209956062108622783356992110703372178818471271992*x^24*z^6 + 25285712326432296292138242720268957061097583334131224295446714697677528158336772*x^25*z^6 + 209417566190322083915106043162700061824906533581395575658766696003991555291429848*x^26*z^6 + 1626217890539606049351321500689902016014388728451366566247131041824568444734350888*x^27*z^6 + 11848158916803661180731711282409562213028096913430337823319872517945586935666283372*x^28*z^6 + 81030512132145712367929453133043072917207619350152891856053480838475621050470741200*x^29*z^6 + 520395955692666582028159333343333418251547476358054506791062763549144567218161718372*x^30*z^6 + 3139162700469991190270640164568793782616821816583085981504051833571583798450233783028*x^31*z^6 + 17788588636006685720340134428662902404734830676258686119560043673331511420920126269520*x^32*z^6 + 94692790011811819710223582422511285541380337029543397560157420839824213617755761025908*x^33*z^6 + 473463950058886653568684844607593433025130641537077815272968017737582036017600612779712*x^34*z^6 + 2223025975040482816651382491491626096435437762557497758087767589195612156183468566862512*x^35*z^6 + 9797781149254637796521280666535593958056473483497198996870507808434634136187887949874748*x^36*z^6 + 40515149076595825874594517323579514349875146938009450270584725845767780813511353431160648*x^37*z^6 + 157085051682932421709973075558158432338623103574461149422404630625479511396445299186176852*x^38*z^6 + 570608093720980723548375231628197108096371148746942630760750707569835238372184273451794500*x^39*z^6 + 1940067518650718201800539026794663168332121090055680521686964266085167896273497611525583576*x^40*z^6 + 6167206502366111922247653053374465460100505896604451578289366191333863170535931029794579916*x^41*z^6 + 18305835173718453843395982635451177252115637347609571750714904731252156555330004434329931352*x^42*z^6 + 50660334550603430944873966450670797470365978783538784254371222323710581158141701926887926024*x^43*z^6 + 130488740508388663115123208826336359321498334545373015504445433461555040600514164279840879492*x^44*z^6 + 312206393957056734342274706634113040621304543467231767161603280396051147093734072557918587040*x^45*z^6 + 692283743135044271915486787337421981405971442263146625079129344579021105157767619008011050604*x^46*z^6 + 1418936182733139494947483547914551273381784867697851351722760804121819462139129264666867512412*x^47*z^6 + 2680212789457346933747837606282783964854525812868513336678618571180205828387956590493677185824*x^48*z^6 + 4649348716451014054088842826307701399815223225471617567561862860462509826933133455401931543380*x^49*z^6 + 7376966631179485054192395020188551822176017502939654108254204402565905152300467785817315910000*x^50*z^6 + 10655618466793886174485150515679690171345725307553956610630896873790442869366955504762135512352*x^51*z^6 + 13934270299231352177907365628936890003890049368691204836732645215357524748870225556665050176476*x^52*z^6 + 16388104070845873362723017521880488127583737256022507278143168813425649724676159553289852258264*x^53*z^6 + 17197393152391001604960720100585944705516256257375539424791007057919514509024817298542636268468*x^54*z^6 + 15946673555294083502560695601505102090197370070654401465297466287099554600377013303377831831012*x^55*z^6 + 12909212029828580999998561294349468732913233952574101003682690061754291970275642984023389677960*x^56*z^6 + 8983604230251327180366706943057131929061696562650884713767882431106796075209810979065686061836*x^57*z^6 + 5266250514322172088298730932504721018918623125945781667268939433780121895963329950584616647336*x^58*z^6 + 2528989249312090822341729412618047082616030741587320823445648528945177543561660780839169884440*x^59*z^6 + 955396363912677254555349447655551146047289466867057365658143082262203546194144517486005566020*x^60*z^6 + 266257576144055990362763880893909383899140692990051754616113867941395289172099984098071150672*x^61*z^6 + 48668354584660487571207238020931234610641700295463801700544681292524338864054804472397430316*x^62*z^6 + 4378362764288356829976846234190384090691213640941768999100771905323025411349697202191191644*x^63*z^6 + 501424000577910245165651377580720374922087784*z^7 + 176130877925658696278287247784492149754360501300*x*z^7 + 30442226735459534875127380136747620236913550035380*x^2*z^7 + 3450101390994576692624093839031253276670155430857180*x^3*z^7 + 288370495549543383038081406773908712005436653039447704*x^4*z^7 + 18955556870419936416207924307704408097592035524128627160*x^5* z^7 + 1020440843628017372813925882129468969702546888195793377036*x^6*z^7 + 46259984346809129575667132447417339994942871419453308360520*x^7*z^7 + 1802211900946607907396968047648060140917399193286131066526920*x^8*z^7 + 61275204762189632606276081517195624483565954521221085407744940*x^9*z^7 + 1840298647011885535554787369544716423122382684607788422815528868*x^10*z^7 + 49297697074110256327862122339320602488143312009322651338455063076*x^11*z^7 + 1187252871512005480787447088605905726861353503369742484836706430136*x^12*z^7 + 25876024122920135464036317713947328953894185303491830688431902737424*x^13*z^7 + 513207811746440848480379085341634263730213844115112688305261281409852*x^14*z^7 + 9306168319856896316790349633108501496960275552072916201958099015096720*x^15*z^7 + 154908926825914599278718424364939546172335968070799898702799695182741192*x^16*z^7 + 2375270211300791564094773653811461706703255387011475556442208835610804340*x^17*z^7 + 33649661326674931369162887129030193603224495095934934542838055230888528740*x^18*z^7 + 441578011798271395635044160517276066159347056747117077440054138341385159132*x^19*z^7 + 5379892110411017193979737900925476924906192550564129605889947002323441359672*x^20*z^7 + 60972110584501358429694772053057814584146293268121696632834051572924087337256*x^21*z^7 + 643902440566828055386332569572266676864749022622892613023390483782749997089692*x^22*z^7 + 6345705211390300242620805024774836325569827157408019754616537103661146611382264*x^23*z^7 + 58433368821522645316039347827978337002810363262696212679292051344761496604796712*x^24*z^7 + 503306083449135043671597323878332483381994961782669682186383835528704971141477516*x^25*z^7 + 4058711878072692822147237137839767020821572879008728938418657415593187775863270100*x^26*z^7 + 30665823078777794170449791674061889675220601449955452827977488601330160484026154116*x^27*z^7 + 217216246807908749404330404121306798405153904891593414994784509329707014980487800920*x^28*z^7 + 1443114835114540556462449839673148417630026999824998497906060652490005048053176641472*x^29*z^7 + 8995415805550851761752858815487437456793809200370253613461819015332557999441063018700*x^30*z^7 + 52618346217411850110620158207135456020530268344594694891021075487974479778703353827040*x^31*z^7 + 288852796422570623483562125496107282091965560603899456509239986491280238492225408180920*x^32*z^7 + 1488029557328705564179521658244230866260031249321235869842789908496545742644840746090684*x^33*z^7 + 7192142860424173528706949696109043014968924251898102652943238436099844698161310983846492*x^34*z^7 + 32604380967243651951049235914629523331518813154058333300187270955489920471061663895397236*x^35*z^7 + 138568619110748363539606701624263298821552815903636768021880449632649947277949221254490440*x^36*z^7 + 551777744567472297693095704023565539580657831603734734315821482545884467598112814648177576*x^37*z^7 + 2057066152993274814494100908200429549999812944695588701888727209767605254662237749673258340*x^38*z^7 + 7173358892482448379332930128230356226903912116460613068231321384585627025854131841440788152*x^39*z^7 + 23373194391335608542838610945898489064682299245935369177165079213577791157517107572258967512*x^40*z^7 + 71069713027412305052111187404848876580268541870737948384629804899764130763010144785006536356*x^41*z^7 + 201364186910911180420984680204861509425224901514031126866176368856100476158328562124579864492*x^42*z^7 + 530727314337824412250761341460786303174738781520988427500137770858219286695291018098161633484*x^43*z^7 + 1298673655542403169422626603561173343276087551999115626234250990103445412433886756518833107112*x^44*z^7 + 2943660285903591826314851380613503756991476154441389921349527714873536687345986024149689583440*x^45*z^7 + 6164621903018719066780884968438189196143120005130272384402253604131529939987364835949503259252*x^46*z^7 + 11892036578825545765480677811671556374943853652091577822321624576822604367330196369932416600720*x^47*z^7 + 21058814775815064150336515284601354436619026823072321630256442567647446628942394034812810729240*x^48*z^7 + 34095223923039974734546291675301734566148519790058411230480986295798894979641094663192825747612*x^49*z^7 + 50233629907534400236860932805628388424572235428721171759315240066196885307198377642439783717772*x^50*z^7 + 66978173210163241146950646322984540236420546107030741401324778744939459459785219866371935561428*x^51*z^7 + 80287938419659892974238478817751425503927551909478581878042288683843316757217701097571664275176*x^52*z^7 + 85842449844475556377554855169851035030346632254237908675630380038173290314435267676133661500504*x^53*z^7 + 81073424843269344342352997214543044311218720517057707351600920526859484022595400403594144979188*x^54*z^7 + 66824156667642787896924804973353829503381106045885672678948898805922478389455269718233356144392*x^55*z^7 + 47333777631647054206314651873851391814028943266193431241692476879007778184033517252794079028792*x^56*z^7 + 28234181283314781656200332587566819626485731146150550326256836634271884774759934550902914081572*x^57*z^7 + 13792558921469619465152031358481173065586614504037076671785703559864003535548513276176534254300*x^58*z^7 + 5298838107204157812533216627669234094796131589380409575128175145441171803441959772311010069132*x^59*z^7 + 1501339103310576911726204112265117436103398288164953672704878276470571603547607359253413830728*x^60*z^7 + 278938054104006803271857188908227370620681067781880909106534869653370837887113476047497419232*x^61*z^7 + 25491916673667495925992896485493444949656146688755946135660414649279670676241781581763657860*x^62*z^7 + 14244618790182164140190486982628498062608148672*z^8 + 4924477290267571636117965014640822480416579271708*x*z^8 + 837155549715080722600052802115241531262200003430888*x^2*z^8 + 93296313774431612112510298518968049280289190672743412*x^3*z^8 + 7665850960203229615259775623152548842896654988292024516*x^4*z^8 + 495213952044920618950235875146843184722775483877593994124*x^5* z^8 + 26191314708481686109274041254216208193746899093731915717136*x^6*z^8 + 1166137111904310918257432925068535754539206238214879971532272*x^7*z^8 + 44604744595134563275058398288375754757410766384232834129578312*x^8*z^8 + 1488476846264753715662017479503198901284544797132383814271369444*x^9*z^8 + 43860451080448587116617346928462031574676348692833040982061594680*x^10*z^8 + 1152333669518506865798670079482329261025534156029453987407068788340*x^11*z^8 + 27207878305341158566923463827011498095909014721131651830954401370412*x^12*z^8 + 581132375060930960251253657120026117566436626405596471545068118627908*x^13*z^8 + 11290571858645844598835067195077102053159327552302262977534940427108256*x^14*z^8 + 200470375891502733797762468857699640794493219507094004067032484701251840*x^15*z^8 + 3265996540539488811059194499266522848848319052762028008285094043652693392*x^16*z^8 + 48989948108116894922116405288671930011246614094396313336141192297725189244*x^17*z^8 + 678601503425257825077919132731564369549615338435263593308010132499775851944*x^18*z^8 + 8702766649180281578894679018895060217128018464328796236815651112627607248356*x^19*z^8 + 103562923125159304770703961164799081856673367198247161871545342651208675008100*x^20*z^8 + 1145767578068185961096442475320490154921538847255402865111855879825956902101388*x^21*z^8 + 11804878077068776121931774191708765603624426364111562600553760635597030272653552*x^22*z^8 + 113429480653518810762528754668485471543470311885272560939470120404071949016519408*x^23*z^8 + 1017714506974650518509263250380126089900670310593671265178135518213085795576293816*x^24*z^8 + 8535232331829757296083207840721730342841707869267283790025862430629261787392030308*x^25*z^8 + 66968745988194421246860094849297309008311750207260451413277838925767815555491547064*x^26*z^8 + 491930911888512031487147517890706621072623300820766774992047077410069397417485046884*x^27*z^8 + 3384953179423881591053267375596427521809273051561559687141731188047386642173749870764*x^28*z^8 + 21827111881114361310138344542032664275106034353688679340322697186069847352152404119076*x^29*z^8 + 131932765148046144482163912710195054186773634177894731010551942505183677020092402591424*x^30*z^8 + 747619002505581267855441859204006947570791444991950391104736785267411441686952936993664*x^31*z^8 + 3971725950811596564682850302499822460783277936758007413115839333081158916974336054465952*x^32*z^8 + 19778392866161788240916091604882709764466536500241548528101181155710410715814153124387828*x^33*z^8 + 92299166708738634349827987176133007129991350179017373622782469467875770592418121240433016*x^34*z^8 + 403479214469688055972233684770705931472138142245027334940633746017557247392501994747520028*x^35*z^8 + 1651276044404029030447261218468930805221175377690329425827479952033447714960290831190787884*x^36*z^8 + 6322453323166748768320316036105226489969964989396734360697386090474922127838915752931646084*x^37*z^8 + 22627727682908227567694354754961001404367018826644864263289600313376549584217144558862222064*x^38*z^8 + 75619158324970799834483652728982372478326902789664303451917530830362493359378241900363409616*x^39*z^8 + 235679710112859834761505942921953640985602331402929105045382419680762078061350253021958849080*x^40*z^8 + 684045987887983667906656671305348980432782627723350601548866450870918337955254829411653580108*x^41*z^8 + 1845838380015558238542696720047759388082790889407375926926606177768550868529369694256344615272*x^42*z^8 + 4621750362370418833330876186526335382083902151665637982916080025294638064117462394769649971868*x^43*z^8 + 10714057658203376376665532053809588523139224436450783523643460186959401145482713108442943505636*x^44*z^8 + 22936019727514503289897033799873164475632220221728554170291586623057213586352868232581469911980*x^45*z^8 + 45207227289370483194326016461275936872494329976839805527991967106738012514812640038295769581472*x^46*z^8 + 81757751481119916074212020100936554333385422223743534388692349258516149837360117876337532168064*x^47*z^8 + 135127394805150590313687852063014483110274006266560866038929892395703582499712072935463816243984*x^48*z^8 + 203150709194412620873901129716385033781157675343072010643972262005448330753224526405491695456116*x^49*z^8 + 276284964529439812622057473536305604461060942010187935191583222906942539438083976394166982835960*x^50*z^8 + 337681623320592469460002415491753930919019409513374469001327385439773967919776915205765588925708*x^51*z^8 + 367986384314615657925025985149071222689710643587490517313192107069392976894658268200179669385644*x^52*z^8 + 354100105775693341457738411258015678312467502461952011047102684183617429650449655857490916911716*x^53*z^8 + 297269224588098529893205216143318862498391740391132527868923114270105341270974763610075801508880*x^54*z^8 + 214394166747535222284199073673767790868330580513668773226242766862818943732522910201354148045392*x^55*z^8 + 130167887163308104960327235089611308279399516483106969772009098970453155920262127912305940284360*x^56*z^8 + 64703339715046816878010495789502575125164466257924228852921894833685125748459609471520706170732*x^57*z^8 + 25286363028023990647829907210878966810187974285773148621880878715603063198075881304037956570792*x^58*z^8 + 7285901311245398537436812207095967550429910171110785356545897005025213020192265229648210085772*x^59*z^8 + 1376231839146988481888178093502212093795518300446910234195516068458717516134501585341087193412*x^60*z^8 + 127845547376317400244988927029973671179398903013332786009264225940969548965311453017761015276*x^61*z^8 + 354051615559540288964643264768819726917622769848*z^9 + 120375196545823477284386724027160477249549481627844*x*z^9 + 20122725392517574316907827672536342108914743940590124*x^2*z^9 + 2204558296517124819314082092223277804630547427380741064*x^3*z^9 + 178018079742590772953581794881108188770782073852806709492*x^4*z^9 + 11298214128025153056295657624542625290295566123087866534928* x^5*z^9 + 586879463810688486267963045509641063245114513039748418383320*x^6*z^9 + 25655016524105011426400155151702649960032348307129289131649032*x^7*z^9 + 963132076965068533337092082452075516512175917575189177533960176*x^8*z^9 + 31533657638757154809435182138589160163365860148165314849870182532*x^9*z^9 + 911322705903914402294120881348386835156273816551465925828167834276*x^10*z^9 + 23473463635380930252384197874774071729977111749991547170805211397440*x^11*z^9 + 543149866896060527726134480468420949797911555966191934328550103035724*x^12*z^9 + 11364366446051569471235755696262093283291141860753844145300382404147392*x^13*z^9 + 216193542627320335346575935123912268411425036526719890369269586959306992*x^14*z^9 + 3756963340747358390721243355579196262153853447802340171113932599407999664*x^15*z^9 + 59876603243303716779377313019195820479887859365895914885539930393891824200*x^16*z^9 + 878190180902844563875721822827871380839247677120291633318927227839855092084*x^17*z^9 + 11888093004432786654100061454616724304967259161935850709307816478835363077644*x^18*z^9 + 148914007108148179772261436513705548678681031770803763086551488819955862376952*x^19*z^9 + 1729884382573658266014112855877007374065793435044989513960636272525677250861748*x^20*z^9 + 18671767938887317478627779896216306029773255633522901133346655026466951552016720*x^21*z^9 + 187566396113339336981924260401837020998673932786118026378736505574364849344214184*x^22*z^9 + 1756056404191831724092964758083650914464816166772666776197304656233964340101020952*x^23*z^9 + 15341103864398728496823052504677624814000219223128061582625561567612364241100907872*x^24*z^9 + 125183407533478638590674498601977081538256507678784790740592584280649956500568692788*x^25*z^9 + 954924711313090126201413756338314916513713487513899925150740588465624826746078512420*x^26*z^9 + 6814154112827321026467312033126228245917339738096479150321043538965007723905502778384*x^27*z^9 + 45508814967808763632630519291387474733501831132937451876488224346474721937217420319404*x^28*z^9 + 284560866005592436737103796236237185295105031603264886649939340364923235844093208658432*x^29*z^9 + 1666261959832864941534563864182233862642929959450199568219114894793099233367724457815840*x^30*z^9 + 9137565586180516828615139689514159237303946705786738586689742393660437487747863002656800*x^31*z^9 + 46925206604027105839157017798831450292938894291498057386699153128727582160929605960022984*x^32*z^9 + 225620185288049797771610819463681749939147130219844680254532382710309503441111002268008332*x^33*z^9 + 1015290833796330598492692589769807120697446574961513414755352797978864904288856924827009572*x^34*z^9 + 4273890938456707396998777048050184536739864382198800687334575217552271364874041558192080568*x^35*z^9 + 16818552304109855906976182128150423452948869815901216176062671704986574148072328169626721020*x^36*z^9 + 61819543604304472624526050958909803279011143802467538582229287801342565723997893032507590064*x^37*z^9 + 212030189028833706677368323040364710143937751303863477008524161510911867849719909499607578024*x^38*z^9 + 677771715356924822969847358149813172159381211210404915695493737378895656243406506448126231992*x^39*z^9 + 2016370853186471596198800982351168535446449952642875051306575553752998530034547970880227673968*x^40*z^9 + 5573708049461725069289518364240678400102221338974485052115088506301191988271046321367417262540*x^41*z^9 + 14288156349017732611821838154245150224046322019193039625234950968405489910826451368149308072204*x^42*z^9 + 33892835990656594808271195764435111831084807307016485725366881475058846234703378232242586792352*x^43*z^9 + 74204769706883328738658321061757190652183092185883251683581185298839692004288015261600452313732*x^44*z^9 + 149508869335682064781606217833568794605959128029987823111397748765711599080789524648970613146944*x^45*z^9 + 276266388988379936886035916959536738423901560085869504566782468758262929152056369738756915236080*x^46*z^9 + 466321989921031826042207725575679942548447756878691254467789383145417876491555026527020483426864*x^47*z^9 + 715674720658626096594553582416908630746060024860699439350312938965483760160954671745832540684344*x^48*z^9 + 993181245011647297976103554403427690932455122643040922299336962695215354096360873249356943174972*x^49*z^9 + 1238165952020204913710171997219163621660220344712641399875394169215643051020635085296838969230756*x^50*z^9 + 1375739946668254341207507927354226904484579098432722986998518096506190687265774261359553124070536*x^51*z^9 + 1349283409497055642940875037082282396145872838397263866433139317611430284251316195739235005405020*x^52*z^9 + 1154104047693372966950936614608985480961193558644933718193338983192646522889918898210141664918768*x^53*z^9 + 847767787694530307680444326887433023584705870863258892171812470788606664981889341505940439161560*x^54*z^9 + 524074637436245615860964578719299403379604183363685531509943870798812035775356209999022678175784*x^55*z^9 + 265156813509759599389451064201161373372464763069243772070484266196863757052548902499409066966080*x^56*z^9 + 105442466844051089772394579096507972452642028336172084782166883344325719122830291783811034398332*x^57*z^9 + 30905543674258687234767809903164233864620631759123780609962980507145697820596405501443104501548*x^58*z^9 + 5936656541270232997901958868509667189282604788789570271812509330873559191172028691516042128400*x^59*z^9 + 560690931353858044260576524234082859558583294753197627422554847613087692760537989139400320388*x^60*z^9 + 7789085193205830857853130062792520271546586273264*z^10 + 2604117573598650761394943051535549391024909877071132*x*z^10 + 427943814915949345007126159830419476901453304745689056*x^2*z^10 + 46075270182635506907942240989842769892716516444534203120*x^3* z^10 + 3655304562157458443174041622526590562619401221890265480532*x^4*z^10 + 227847320564810766608158424697450990899245353653623070202300*x^5*z^10 + 11620213349214378093277580011030826561230957132366164401739300*x^6*z^10 + 498562486838191806393919913926697993240661042728830401840447468*x^7*z^10 + 18363718275517206771532862630395501989981024494061335164309168380*x^8*z^10 + 589679397965032434766073017565829976122375749273479440821216196672*x^9*z^10 + 16707582940353142675445956673643224296658429770742982170240990685372*x^10*z^10 + 421739896647695907620464167849646347128498790605486655906333648316980*x^11*z^10 + 9559437657528579059729741139444180635031149127009462857344165595344536*x^12*z^10 + 195845915085564751120080484483235833589131959358787261530723183962066984*x^13*z^10 + 3646464418965705867232833023074574906780641465009744702982686420871268600*x^14*z^10 + 61989895122528355428535105030733333385968354935507185440325230069062875432*x^15*z^10 + 966009198992738916074370886875609845377109157485964857815733261232965708088*x^16*z^10 + 13846131852220001399557674537231304665678132559322420896110920098018012613700*x^17*z^10 + 183076632268276053944496908743268904053502115067274084588743565797636497052616*x^18*z^10 + 2238673906859864745977437714175886797271201078999585454349270928581543827222728*x^19*z^10 + 25371637611075128633747164403976171887382597819173280849747767926535179397378076*x^20*z^10 + 267006281526072109507719527935239497050349152769192157882060177782098752530356404*x^21*z^10 + 2613425119179632192054374610043777366740182474357138768086555836480588540891373324*x^22*z^10 + 23823831883535251163648705451825213821954033522715378668850608232147414687251403492*x^23*z^10 + 202502571010042111527205092866583772862265442428917664463418221103259913065059244372*x^24*z^10 + 1606520396679737020402127219152076190056432463085450299949227783772894078626688599192*x^25*z^10 + 11904728067703809025229238357261163679787286197664869124181955289035582862672836660084*x^26*z^10 + 82451264765204527834278579334236594196326997248753801666131374909235191926002842943676*x^27*z^10 + 533970095622282478909392666916504262661747775192586409317986957471379286996624413119248*x^28*z^10 + 3234508510263822354534437300578269788190011876204944187594109976871785027872224604948720*x^29*z^10 + 18328881558161171320238424655799622418486651854841411407796727987517243226769105328287568*x^30*z^10 + 97162780733045407023005485308774107123612988822562401576892832550360488365992364883466864*x^31*z^10 + 481765454468037039199030908194573386868824053230077074880466410493154449362374896485681920*x^32*z^10 + 2233639834351834720865248573702613617356245397681416572866212970158279124957713252384628516*x^33*z^10 + 9679105948857371951469349226459485372461648273501825478700263292348473411450036957221249552*x^34*z^10 + 39177333602518516677785117395536964750801190124669402176946070620832686928010382594101359200*x^35*z^10 + 148003260276193572240829335899682120341842115408623372830243548977064345293654338815736111180*x^36*z^10 + 521344817729619501968983520815163053934330780257569366974419022726739373509945385969485789540*x^37*z^10 + 1710376858165388427105249204482965448023514391830989824761356977261037325860680528004212442620*x^38*z^10 + 5218842208249132344987615188689845563282207044493744615148491047271324462098875536167454007540*x^39*z^10 + 14786719590041485079129557543438438458742583064984770771275622903806330888342161309653541423972*x^40*z^10 + 38830166077899199481436339187729995326149223356783419060314800197337669873775933874828660646224*x^41*z^10 + 94301831903462196918572556821336190493158995235522637278876128183881115832791557304660986944228*x^42*z^10 + 211265344342036269612841450232968931285130093032515706342545771578680291837281974354463509977580*x^43*z^10 + 435334648946936559788498748634426362431677223868567252017638680422506413710996128355165717880024*x^44*z^10 + 822298781342603765032120443728240052551750402490638184572424840991292367080641452265476349858920*x^45*z^10 + 1418167463481213613624770626781507526870909959898566378686052970823092655196121326907082014664760*x^46*z^10 + 2222801485327857067801869345259894136676795293845517368474560055904883332916374298346496498603496*x^47*z^10 + 3148968770818897742180147873414981585631405782615226802573309401465487140322944293626096010356056*x^48*z^10 + 4005831021296863216105783639243441476725723431998868938007953010292832452076202382745199049003772*x^49*z^10 + 4539941824451028752585555857952923518655880123224116123749522751379177839583575360326280940064712*x^50*z^10 + 4539941824656824725156233913887813599997577697758996418927800811104707748879195453544410898553960*x^51*z^10 + 3957898000310494083668488016466538722425095894182362458436789457531973172455448219588220791854020*x^52*z^10 + 2962200391645496007568389620850805537297425186883553109373829482216868163718329797846607297390252*x^53*z^10 + 1865089136419440775075548438056612137889975201985229186330951654271135545074047847862491411932244*x^54*z^10 + 960803485390383073618472649472657143441905092880842584493149921698080786599232499630593366434492*x^55*z^10 + 388896643724204949959338819102497433885202408481951937530685143617667806247097339289469599992524*x^56*z^10 + 115986721572312764872635336164027412406231814384543695043449018188226456391212629855945407272536*x^57*z^10 + 22664063917817455653819631316033687469765441066991717758685191101379668809625572138960880118636*x^58*z^10 + 2176772691385416739968185595376864758201953345916496230368888952541452339327493570276978350244*x^59*z^10 + 153182435999885075537219271168073316657788168988160*z^11 + 50346353220357900874239387789464406691191812252504940*x*z^11 + 8130929808229964750672509031108103083437073164861898316*x^2*z^11 + 860071659748495573485662299819216287951600881383361892180*x^3* z^11 + 67013918468422498841153106961117744137843252292349021902536*x^4*z^11 + 4101251776720615749731313742417721647026035643641565055551660*x^5*z^11 + 205290435694570002430655801071986741213403988783346146916443736*x^6*z^11 + 8641749775661215735078569439842645169500759999441724050573994476*x^7*z^11 + 312183210670995445493900779206519910054130363944824593622738240264*x^8*z^11 + 9827989964852985209033148903515777776547879249124362586851795978736*x^9*z^11 + 272890521363665627984083301889534363550071791001123768216651141049812*x^10*z^11 + 6747838346511515558581478669718353562772390235908618214386170826714008*x^11*z^11 + 149764523300523701017031345092799769186483759207552884249384658509296944*x^12*z^11 + 3002970697971384225875597877413550140428854223864906945170868218980991240*x^13*z^11 + 54696966284579751180024014056204112840964537937600286608862704713650517552*x^14*z^11 + 909185128463535196563277749838414625841506706117686462046532043772900402120*x^15*z^11 + 13846131852221474586442879725492049828844565735558434949466217232059791129200*x^16*z^11 + 193845845931138767331276779313019367933957806478736480642775293833963528229204*x^17*z^11 + 2502047307666770243818077867893769067222612344926830489212553974885134048076492*x^18*z^11 + 29848985424793629675403520388948595521177280752145037862659838859646608768165404*x^19*z^11 + 329831288943980786565204351622653080636155002227176483387335212049572228680401624*x^20*z^11 + 3382079565997117054131231168415920060683698257707210329228341587260555293555553476*x^21*z^11 + 32232243136547261062214647758446308190790680888463017672452488830073028211118933864*x^22*z^11 + 285885982602419132340817549644455037954175210490928659994926232484550022419627312964*x^23*z^11 + 2362529995117264189930476277414215166647757294841607539652750428555002346802569925336*x^24*z^11 + 18207231162370149803761985774501573411074020631197579413836376537015211826889479351176*x^25*z^11 + 130952008744737751811647250685961841514349263638467834395832384361671505817149601737652*x^26*z^11 + 879480157495538073734415425334945426437994769429671537190820205439929211785514846683408*x^27*z^11 + 5517690988097010253355416971580443876225258905967265001697268629430376821573412247963936*x^28*z^11 + 32345085102637041053067648135460737397450173237429084297648059203979039574430432695059760*x^29*z^11 + 177179188395557889255739088780779681665905342868987562015939804363422587368114290514884000*x^30*z^11 + 906852620175129447131942277318643166033146248094207487415672823374841162641409350237492912*x^31*z^11 + 4335889090212248907087673537862208133141285283012188791886159265206715899316008733975981472*x^32*z^11 + 19358211897715048585370625325327825372107899524517956089880423215988721870132049101911384596*x^33*z^11 + 80659216240482208203025105741762950003488782901117941848696284429172114523488961645878298692*x^34*z^11 + 313418668820159141419383724535968937283045150766510339400644067849173793204048947471139217996*x^35*z^11 + 1134691662117362269583525472699113059760016903232011631964760277626225434446156351878946050552*x^36*z^11 + 3823195330017187644591693396200514836482277953566672113755803917369584793841751496647162569588*x^37*z^11 + 11972638007160225491504775489677640263668056060284482455288862217229369581568049164122398469544*x^38*z^11 + 34792281388325075540204113987766053283195121006446243235697028111841023894631908710913771860404*x^39*z^11 + 93649224070228057356605223563101779720407426761297422042091156510577650852574463328625625258552*x^40*z^11 + 232980996467461674417289411540965866774312746928110621513958089532071691923270477071188629507680*x^41*z^11 + 534377047453219243818598262060103361992628553223062699247521448648954412188880311971704332681564*x^42*z^11 + 1126748503156386657931099692853517389094674875431464776001058278629661378323240412818354824026584*x^43*z^11 + 2176673244734766777391979373627367200476209993376757679030791896052540065098699807846577129358000*x^44*z^11 + 3837394312947378502264452160658719369043841622920359919554975202287795480934337179082939203390792*x^45*z^11 + 6145392341727175595044082042686749015821474598136110317172997329613805578776344798513181423104304*x^46*z^11 + 8891205941162927698869022858151535359327684996258655970415403847643700330129821136518332749905160*x^47*z^11 + 11546218826574838140869398153645679062535674113298887962981277928294960051344871957847499488024304*x^48*z^11 + 13352770071847876083430481677286841947279756315488269844547281901649180426607153931182502328034476*x^49*z^11 + 13619825472385953642346759161703096540267568953133685222003957645578350074386605546571662005698724*x^50*z^11 + 12106511530980866909903351241199460578146975123865650775900723137100817641660033636248140159574468*x^51*z^11 + 9235095336531749641779198303983136722063456079480012589498584888990625418457064501171862221165416*x^52*z^11 + 5924400773903707328235415561214836539329002068619374678710839926670118694059598896085959779093404*x^53*z^11 + 3108481880375220657071482188080093144995101986317909237441026485366362848785183234712551919454104*x^54*z^11 + 1281071343409273465716890901231308917589723313030477698230389509026166462502526623333133034857884*x^55*z^11 + 388896676232505313415808304131740788148251399337784058057597836280678816723345499181187321572072*x^56*z^11 + 77324485022163454673540945320720428232788488199630535517210824128686027763049834691226221138088*x^57*z^11 + 7554680772128777880287317528805794507300646735534954001300489938530721920545132460174353054492*x^58*z^11 + 2714753547354189175487409949113132284401924552727496*z^12 + 876864804010884108577300758749203521557380132545979500*x*z^12 + 139129230823661427954305786982656390971656220601497208760*x^2*z^12 + 14453982288160937565389597930432467710795282984816205417836* x^3*z^12 + 1105729643015734364681688020471125070713583105418254103994932*x^4*z^12 + 66417493916020116394819954742989983415835055667234417461404376*x^5*z^12 + 3261836926389240639749366914357172390580294287106287661233675760*x^6*z^12 + 134667267354019613158899175333756002628538099273326328964415739844*x^7*z^12 + 4769465718147183946810197039574747266463920596575627231075950520140*x^8*z^12 + 147146849754234509601150076685071964004904526290322228398801243306836*x^9*z^12 + 4002394313360817521459549871672993053046260010532274756317937956113456*x^10*z^12 + 96906456253224139328240312167459315042428628913866677045410294833279464*x^11*z^12 + 2105023577501597806272645453549974406849016224994557893841698657621427192*x^12*z^12 + 41290847097193118503590238620614937016442302473437289497520710994853748592*x^13*z^12 + 735370324492460213779082774266396631497468608149471333802253413592393194240*x^14*z^12 + 11945682382308750457112947250193616070761929291439585518446590538940398553816*x^15*z^12 + 177692025436875647061508102837295627353466444028634701844128041073315852808992*x^16*z^12 + 2428457680970603556208896822417980575818682776493959174106302119142511339665900*x^17*z^12 + 30580578204813681732882467795301668733757969883346567927140040938289561726232200*x^18*z^12 + 355700409645475246894558883598576188973290595011475158026740512754797240861852580*x^19*z^12 + 3829707743849622932432196126906392679169156231982733309290303757967824051648264156*x^20*z^12 + 38236288426688415003566709356348902403112608945331523805834392736612363782952359848*x^21*z^12 + 354554674502022897277436354645918725329183089013849375964987040053755630919555564080*x^22*z^12 + 3057391758387025396589806591511898008505439462431705583447251646411918089724283684556*x^23*z^12 + 24544061615940059684807624529839638326396191885140547335386107737441764043042956055380*x^24*z^12 + 183589580887232104604111945756308040161192087978565585586837889588305308755400847925044*x^25*z^12 + 1280419641059678653230436468602847832951724078566363324737293659019379552218953015904672*x^26*z^12 + 8330631491832664827651297390065197356424792303334121554226363854513953741271673728065008*x^27*z^12 + 50578834057555332177469261585046110297353711903487601213085103326163115033031880661052624*x^28*z^12 + 286613392992816396763382742937269236533873457665493101261906535383972335684412787551576608*x^29*z^12 + 1515866389606446988837615965882838074891533450787543167131874903273066853823224347386161792*x^30*z^12 + 7481534116444636585686239558955695469081484932910461653834487641739148692257701173036796176*x^31*z^12 + 34446229994464195257369498730264925653484156184805419098690640538450397025209009559072259368*x^32*z^12 + 147875229774216565216506449092886671472124561566568328162235566763917492634107130690527294116*x^33*z^12 + 591500919096853695781722526014500450872171443138404232698529896066681291683933347576068949576*x^34*z^12 + 2202636755874940749768463555594831665967610601430750490814906727894223690692049755123655135220*x^35*z^12 + 7627649506456120091016750729792559510574108026579433886620285400282596010847911607487899313580*x^36*z^12 + 24532170034277400358144714845345032511960881780837628795438537503330713392888111122835103760040*x^37*z^12 + 73166121154857020394506634187287792626979788435161736473916059432869735532543513875365240108112*x^38*z^12 + 201988522504448556695642268913150572816159837764615783672502557253348144331314178703542237789980*x^39*z^12 + 515070732386407924668470977600785637469998841567371900062243435109992905360319545476429066507380*x^40*z^12 + 1210206842761304291964251394856541426589095823721609835709818132939172499302821704013078062086876*x^41*z^12 + 2612510009770090550009550008032755373792278558254205910321447626992608107876332127048023050047792*x^42*z^12 + 5164263972804509542866743638149871205236256783916272216454787582615085569580954101508691324321192*x^43*z^12 + 9311324435811016510449330095062624768425380047899739628517960857925600736275600900060669541547448*x^44*z^12 + 15242982965259455555198028461345902547829484580512260671183734740177085593915948335659854428934000*x^45*z^12 + 22533105253070442378255758952854670880416137005556897639134260285894066762197298879412937559848064*x^46*z^12 + 29884331080559128115916669345592708131187963144103060307477633293155464057723203515684108250683032*x^47*z^12 + 35280113080594355491869839890546855605101294950913460806996617191212672847073237159966118753211504*x^48*z^12 + 36720117694927680973703132129730711432569147514559735205669996014624040999976181056429267852538116*x^49*z^12 + 33292906712193128341562498064249779501025364510142140325194193716022656170301647294976987432068216*x^50*z^12 + 25894482999371399696001619523086623927751792663287277648158794885147390973971120515442369327632764*x^51*z^12 + 16931008110991347348107294730007783220522709020845751540513935937840168437678149404656290567197124*x^52*z^12 + 9051167871234595347843542947922820222859404062411576680130646593293843043445982045902372236359128*x^53*z^12 + 3799255665986945604628303715891846540304970299553236810125375635902731841657120009908620627964304*x^54*z^12 + 1174315375645649778384853087648164824621288785422088775083945631496508653473773541885909656942548*x^55*z^12 + 237659064601910837116430962341729591796685331925480998609637405584162073863047563529547471261804*x^56*z^12 + 23626937630694900609540712890906555232183889735326211490174806422707767235370962039110315976860*x^57*z^12 + 43644903226430371152284061944336743386943655196389016*z^13 + 13849968045160088925211051799825197063445895104405654484*x*z^13 + 2158287006260108693123336616477842993454320212408077053892*x^2*z^13 + 220145268539023962781298562972716303259612274254583416012792* x^3*z^13 + 16529240538496535102025303873883511672816474245938623312285412*x^4*z^13 + 974123244678492597165699079427083932054515473127374825010047020*x^5*z^13 + 46920269619404305986426915308612378698505254852475448483950479548*x^6*z^13 + 1899153770139928505707909563302034667452760551434900602577697250296*x^7*z^13 + 65916462108081335116095273985992211387134452899631138575142168415924*x^8*z^13 + 1992141965930920539969383205607121929270734324272006860168537093439448*x^9*z^13 + 53057381025463610889523762879500935112398603293316011209226831290165432*x^10*z^13 + 1257299150362602375086617784298823111797151914955930221044886226496739216*x^11*z^13 + 26717606945237471289851144180409636126817374217254471112239484511184857400*x^12*z^13 + 512429999872535907858626186846920667432306428089776692346617146231977205384*x^13*z^13 + 8918722140638539615957769564987586224264097436375442437867103073751974710952*x^14*z^13 + 141510391298149644749258556473540836988758250479674871056745456008843592131024*x^15*z^13 + 2054848806975091230886606369650320179672284289886661451632250073003069930115360*x^16*z^13 + 27397984093000526526648580172252910088413362805327949498994733227370048518623836*x^17*z^13 + 336386360252960389561299932349206786979099649622727381181609027520693808592563180*x^18*z^13 + 3812378749533539851952813402351475383507772401779134337688141702760785253566203176*x^19*z^13 + 39966437224276289609418758338869477778403350387641001325544930035448987561101944716*x^20*z^13 + 388245390178686456865302762582449904985050817495687047100731822558606095804326134468*x^21*z^13 + 3500091017519974704927316268270331523749484764267963103311149243802307636210908970164*x^22*z^13 + 29319603016326638218188117675059981549427180956440011177567000696998010744285806564328*x^23*z^13 + 228448573502212498328207812781669692573305646515540037814350342217643102398761690778892*x^24*z^13 + 1657013653136048211392542903871847725383042293695897782198114458851428888126398339721104*x^25*z^13 + 11195464041060182101892692249271138238691551351801841480678737946828949817703772411911632*x^26*z^13 + 70489958777045792301777018503547261102914359384640162721186617933904648356721171861445728*x^27*z^13 + 413708924727186398153771608586951038560777708638101854658555186425388040049272744761027536*x^28*z^13 + 2263510898507352487896678752142625091140433249060499671399518654225364269808649745478421552*x^29*z^13 + 11543905582387502222505797070249577100488871862045150481589043874189586877143897536025144304*x^30*z^13 + 54864583520594775657000592019134881538032986399305572527906125246944492350569253108175657696*x^31*z^13 + 242890083294298540499299746556162665852672083938797099029001747295094850425714309959877034936*x^32*z^13 + 1001001555394676396736910823222911011001983756220742664797176425586347961402470704749808258892*x^33*z^13 + 3837172629012978372396620268937533337266533175232394509315186279229029010342942078939944521564*x^34*z^13 + 13667643459532022802406144347188068164935187650109993026659311234381829314760036060582864402632*x^35*z^13 + 45179154769007280280226051058000135745086207783527691642790722474073323519891968280584565622716*x^36*z^13 + 138386600193356635704429634041096936746863105783469949693908600422001794537414315290844479585012*x^37*z^13 + 392095367214534847069063270245521802264529380149353703625297792928772059641056729156402481055332*x^38*z^13 + 1025480191176424906366924571737471493831655896699395353656291568353797431914900264253730942769736*x^39*z^13 + 2469698127082931244562653073177536813825070319976713997692822943647075914843242370774497376974924*x^40*z^13 + 5461446264769718215084504397071295128632322992819981105848122959519975934413187782370696271923992*x^41*z^13 + 11052926964416583663355423216439834694512991929797323990535147994098834380038474306317593281928696*x^42*z^13 + 20392221841314707642998427665945600513418034269910533299751251479966139757301831631968664199171856*x^43*z^13 + 34141522931301035616843306896625813280659921821857470745209933717840519115795188764832456997033848*x^44*z^13 + 51591634651859493599642811080261893008919191334268823849508941111820480234052560999425384864710856*x^45*z^13 + 69910403477280604997884573918142831681091200109521985182670116022893690558168523547253016648576744*x^46*z^13 + 84289138943432337484154493097759028935426568541570905373948882951578040850000984523734113267071568*x^47*z^13 + 89557210129039403905953119239025462284977880964217607740610063799860474776884292255475379446664208*x^48*z^13 + 82855650190020413074668037949297797325464377750695450192172513759058080538672070917797507244826628*x^49*z^13 + 65732149145908687691024869626015445318822748518743252279888687075734275040381487127945111261327476*x^50*z^13 + 43821432769728063958508211400361465397698742973724129517572532274378229613535348128873547145494296*x^51*z^13 + 23877062740942685490664696119765016894783908058112401170030958013801392529661067948957591169733972*x^52*z^13 + 10211573961794741928862631755530070280225354230825853271649819533761504646540604077648020804071068*x^53*z^13 + 3214754729080009505046794457388385723410200736301848855561784796778384141606507038896462622149292*x^54*z^13 + 662434317522224622185677476931805335694380119968691551451317168482270869366029985844031133089496*x^55*z^13 + 67032050012530574840747811281264985313073767992992870111192169223218483389842775170512963935348*x^56*z^13 + 640124343970784541213620111712035049236940417541918608*z^14 + 199505537686739703832946137006255485388032865867655627580*x*z^14 + 30524344149331527056435505983013167288517615896407750693248*x^2*z^14 + 3055825988104983368873244060015544750503992226645638203304640*x^3*z^14 + 225112514775509807129948769135626085807381402409978766156597076*x^4*z^14 + 13011503339710072258144475764427161498100337597687248736859358640*x^5*z^14 + 614432102057919744188735828418149878240056671168094684554964507852*x^6*z^14 + 24372473384312857858591288989489355980102801078330937021780138822332*x^7*z^14 + 828664095071033827480117296868578682950835557580222802432779774835088*x^8*z^14 + 24522318961344401130985047128092960925657200839649487771193087399641688*x^9*z^14 + 639215114260595397062128945777665188234365380565991232483585229892005584*x^10*z^14 + 14818168557866141766916486330032321005021034803225006945956913637555783312*x^11*z^14 + 307888613368764693384813737501447220044727748204018816089806018859298768776*x^12*z^14 + 5770937855707178124767418421837132052940062364899929567508654467668561976080*x^13*z^14 + 98105943547034456230591014821252817350056327367558798779198342514248185516600*x^14*z^14 + 1519552058939548822672762625888219669374384754312744998580951946215089413149208*x^15*z^14 + 21526987501643533068844273660937146783830799034755810855622995545386797575244896*x^16*z^14 + 279850837521371104088704507294316667744156592666009470029420976949787891838943140*x^17*z^14 + 3347845204422300085507393139109439948607400290251825106876248457544921832485554256*x^18*z^14 + 36943765501431919292101876120428184539685886751742879407168465407174795036664900432*x^19*z^14 + 376826408114607285771673475791717070119261130533640743432376601205322668304859364236*x^20*z^14 + 3558916076637952912103371251939611457885092251791819495412395050370736175907389141184*x^21*z^14 + 31167477156011136235076432625277587281292506019547249788099428671232673046875305155668*x^22*z^14 + 253405140355395322670805142157319250020504893889136880041378661705487708359978890827876*x^23*z^14 + 1914616616018540211481591846701527113095031108161974668973275399031717978716945230736800*x^24*z^14 + 13453372755223602325303352480619156482275279958375395167051064159674984889949326640024400*x^25*z^14 + 87964360322616033738317261307689687805988264081761127708477614084490963944558205015567008*x^26*z^14 + 535388020235180922664243041489561129386651561668653087381862079220953671934668550139867168*x^27*z^14 + 3033865447999353259998523642906489199897801233539089322219801412092117435000952842637924848*x^28*z^14 + 16006255639444912224185686128606781834937026531741946166487480575442387214015505836684793504*x^29*z^14 + 78608499918162823598812367163903935990789336163081567349657853596665636094704908447674554000*x^30*z^14 + 359232392099129365798781488617058856675988675499884773053030517796469805208436564911554662608*x^31*z^14 + 1526737666421303865879013256245776520375524471720269881109184667851146558930515350517966476240*x^32*z^14 + 6029842702734685546644326067073135167605768482763685793850533749951011574445159965987449574468*x^33*z^14 + 22109423243360310985348582210887072204095205094105217149602770416474729962745878466741462299552*x^34*z^14 + 75172039027424578725248326088073206667618336925251522484543846244132874875614797109563944384736*x^35*z^14 + 236652715456712526565823739414505334588596342374692586656269344464618968226447781451905335949228*x^36*z^14 + 688638081914576395345356931597283626661525687805942555973634628562696475925393409076163702281136*x^37*z^14 + 1848449588296920703340878660335276449663024659515029249734828924479617104683882749811538469906484*x^38*z^14 + 4565828470237860113803146347532041765941440198629650000817161251235421755681670658770938324377924*x^39*z^14 + 10349211199206980724008584472450947096681381273336036354700238193262151653132010943341449444176080*x^40*z^14 + 21455681754450139439667186327984521079080160206017625803199853672315763534223656201955157357205464*x^41*z^14 + 40527398869510688174803428276792261213653538830276867767879745307258757162639644041919704699655312*x^42*z^14 + 69430660078817163775612824923883479097176046830425297161669149103552186079183646193960250973560656*x^43*z^14 + 107301929212686655162510717039115242725916430953190791402203724630408383418047139881140539028439816*x^44*z^14 + 148633042686786477762489166177932377100513111395760524796529150286640748599277214456450271002982480*x^45*z^14 + 183098675774259372686892752630519096162527919848440307181720649929359420306224279354289714330645176*x^46*z^14 + 198681541800335198052899274109409941073115201166279445921353944365239362422502690762854881427902104*x^47*z^14 + 187643678363438622842993197458019385397106111833032056358700912706626700207500468075157240517089344*x^48*z^14 + 151902025334121507275977956523936941351556073528223522471423976160797947912170266787331952365740892*x^49*z^14 + 103293377235067068674545067344334127573045196623756020461410465203008404885369996189702296404042896*x^50*z^14 + 57385209566244965583477074394944142321369515091175995523720218303991493471217757420367755405458192*x^51*z^14 + 25014065676782801261604943572622337202725551785613839418590667915208231571125985873911824135749876*x^52*z^14 + 8023379580553799877932587382458576437408907698540979701812752841836721097773090780442815555873760*x^53*z^14 + 1683919195009408286389665263485672303609339687387182388663407269292302857635275754085061471740716*x^54*z^14 + 173494670186264156715722067958216845246197728519043347705229367078175495254092167495269284719132*x^55*z^14 + 8606120794169377248388463169888543107234144132172002376*z^15 + 2633472773115762626396610775067406213656557026443697453876*x*z^15 + 395459830002269839044040885944444725113090499528158145519604*x^2*z^15 + 38842943716142092906359826359402328038324684290827154085555756*x^3*z^15 + 2806402681589175632770170466685286697897281289725844270528017048*x^4*z^15 + 159029485248778708775279252811229921958702548103073822447261101328*x^5*z^15 + 7359531179011477466489723923832849883381015944974619597729282612052*x^6*z^15 + 285970354377701266520116618789405702521849973884914243178526424800464*x^7*z^15 + 9520429714379595279502686911017266490605332391559783665645869920003824*x^8*z^15 + 275739853210310645046974731338345011136484576276831997820911576150430216*x^9*z^15 + 7031366256868436532637302775614655769758990820930281042774382915076522168*x^10*z^15 + 159377635155592920614808929603867234066445768412058545752234560631128961912*x^11*z^15 + 3236251424965481172792070384859557368756953120043280206930493273762352922768*x^12*z^15 + 59248295318602387976869097345616459617491283911065809284673473247297210207664*x^13*z^15 + 983239567549111352751171793556338638573795897219968119154692707900484618680024*x^14*z^15 + 14857842354075518178641016540061268224684276551349721991839944532713468952444880*x^15*z^15 + 205223947515671589290837292458459671055416391347183034852827971856901860598224152*x^16*z^15 + 2599503335198489252735643145490590105853010916752034397574410686523414756341945452*x^17*z^15 + 30279399959997190935185465727455582247449212303332248714250787838396216274178684764*x^18*z^15 + 325105136412602296323437898012606258635138447984894872435905729078293106809065870452*x^19*z^15 + 3223959269424968396224024178937377044814649131340968259446078094265728687877919924808*x^20*z^15 + 29578546948057643979663015849933974618630694992945281501957302524201327956152474461376*x^21*z^15 + 251417649058490128241838474567669070077567364211452147822142109779881741884414292444188*x^22*z^15 + 1982191320113312058076146317292695428452973801814021200440858836963348273421107189106336*x^23*z^15 + 14508539245829386934385496988299494367101346586988589347411569025486763439059510075885728*x^24*z^15 + 98658066871639873496047713085479441800978590381053256605340282633332943645331753759936496*x^25*z^15 + 623569576509210326388712334322217481945923209190198480316592193543331295655029226854529104*x^26*z^15 + 3664433560720793235045211601348924256488025532963131048466188841863923076698353511101597200*x^27*z^15 + 20023511956795788056769391628649494190190764654108693557840486152071655549126826511014546784*x^28*z^15 + 101728646952916349004304980851469748758358233791210498554735773377021115125372796651830023392*x^29*z^15 + 480385277277660227790296977709144049565895592027130028461631223408800995547185587659926650000*x^30*z^15 + 2107496700314904051065650333382563607551474950564179211802882718847395390851465215324714741024*x^31*z^15 + 8583658435657565856364277387339207869363365654939938741385324137975681043863469414764909783544*x^32*z^15 + 32427154090261734547449346130469100104518187339381068903469156675760812500836670039105224133964*x^33*z^15 + 113495039315916825666113481392489254409752757873233232393486351344872499492997033158237612824684*x^34*z^15 + 367507746356304433291413415615117169677702285035678675653890083334685198435950056316708091131860*x^35*z^15 + 1099120389565592616462924145151615684273708616930061578111641173919034803450091502913410837050792*x^36*z^15 + 3030007560424064239618289571978458168134012115954910402056929040793046075392735203806685989062672*x^37*z^15 + 7681334955812273283931536111632315043538949965963756565190591028862607730565019494999491584288588*x^38*z^15 + 17857462461375018379936160718591730894639625816225425999913151695482827069147284224377201572737680*x^39*z^15 + 37947107730417533938294613480037970889535542342148772923393491472975180867594320818021945585770864*x^40*z^15 + 73426110893014109522225901403411739649077579877397996586772764729844037402182517256136899499599496*x^41*z^15 + 128787067518720943862874543929237431651234409170846822983127090372432962111653975277437684537431416*x^42*z^15 + 203663269564347435676096504276821064742508870084853437650154879246661774990091831113206493010433528*x^43*z^15 + 288522965216258208448771763285730664252910677047181717321342725850783722131421353579309270987100432*x^44*z^15 + 363325215458788891880360856197301374832846791237163884248131185817210321621749743621445698579233648*x^45*z^15 + 402817086702523628029845485781921859371017511277522322335796924801587591030300228408628199941154072*x^46*z^15 + 388532792841239571234891106412650088949756161291251039143989394252792609432401802153331509701451024*x^47*z^15 + 321079182980338408306852080757134447302827472932958357823583085235191863700583642749239403519933352*x^48*z^15 + 222789637175792174188623126254660982189399104512603860653142124210032990164290860674237591421500052*x^49*z^15 + 126247461045883051785865223225902155376839329956633639116740066830374223962550772368009982552965572*x^50*z^15 + 56109982735968497529935730393474512390573407310359125037820059524215472500794676806172177008645644*x^51*z^15 + 18343648260472541550462952746437462423980958420697159088549227708561848448260209122762239036610168*x^52*z^15 + 3922541109127774467718893817338234856882364410376337925880380992966712031511513113995072833169440*x^53*z^15 + 411624696108980403142666226029002657120612177169102401512303331528433855091494456245957618180292*x^54*z^15 + 106500748265181680852099606055933079760858717024143221408*z^16 + 31985720933937868221756552906127558292530071777411552139596*x* z^16 + 4712563029266529253032490062311356049884656861971848008837864*x^2*z^16 + 453976904016482152494525692111187620476733858639563424421663924*x^3*z^16 + 32156697373619911514434521131489155137876737763409535018442938940*x^4*z^16 + 1785768594911061865374622045681800066541675720318228275486667355988*x^5*z^16 + 80954842967798853307458389503109708173836100824267659289707697981648*x^6*z^16 + 3080139025241640496216198297218538683101909286920894848894311475976088*x^7*z^16 + 100361196573035314760275133368341383626296288253281916292854488732062928*x^8*z^16 + 2843567236234506735301775817524045669244949583086268036905299826689656544*x^9*z^16 + 70899609756703043258647469746973517634220551797700012250674703501913513504*x^10*z^16 + 1570533779762574047768479481282708876499214049058419879287495184627718000240*x^11*z^16 + 31148919965294131434602981753368546491709086358779492642766495317818218495608*x^12*z^16 + 556687108097657574728749123521518506635918174175026416340567023968917616221168*x^13*z^16 + 9013029369200299429412995312137162167579323633952856369310148115449572368131760*x^14*z^16 + 132791966039552406765162706806211928125980532215879046156908498144844880448806088*x^15*z^16 + 1787158542948959711886586451239668545534481455094828285129274365561507737630323248*x^16*z^16 + 22041622029703842832486617671446495033729952504820064257670959378291561089177677452*x^17*z^16 + 249805049669977402179937564837167183223853498217269911819328356728061827298882593672*x^18*z^16 + 2607614114976077185076562274873879638881176950301490844106903095776546375712444983364*x^19*z^16 + 25120015974269547576021285619217170797396168304575603479664825915896632767741779728068*x^20*z^16 + 223687761294686021989695100126650154422053928641323511315340279091866312611713862166276*x^21*z^16 + 1843729426428926637426238064869832140155771398044150630939470947717929493649465325906464*x^22*z^16 + 14081817503304994672728109736287668181880770203732205898911369526111988164419168889835120*x^23*z^16 + 99746207315077032978402386781702315623771093876812611660664527699183892003200815015853216*x^24*z^16 + 655665069417772832040187981569427449466392546283617423545769387226201596084478647684518304*x^25*z^16 + 4001238115934103353461544637604921690666454045547447822513762226817868816088955911460088192*x^26*z^16 + 22673682656959914990536449974120425518124470427139915529040103632844110190921536096126991360*x^27*z^16 + 119306758742574682214996996835591704376133361556265366671429537731623201851909330510089841552*x^28*z^16 + 582820373167750552586704695968788691123081654184025589812450280015097656195389102745294865024*x^29*z^16 + 2642119025027137648924541042312748454115198114312905734420419050592473334579018815047296857440*x^30*z^16 + 11108263857909763671950861846240948428272805385969739693222342345806714089649049294305767921680*x^31*z^16 + 43275944613106819409388733649984896283922209172515416938066928116701430060809789856215079340416*x^32*z^16 + 156055679059385949786132645692918341871701610629188946359228331279221739545229676008948559891364*x^33*z^16 + 520185596864617143685150774001874722566681110521126875779412499984478263417600456164841509026168*x^34*z^16 + 1600189978926383390750741735462453648411249563756818654384228781424318127510680692350228954485628*x^35*z^16 + 4533871606958166426863957291288382302171407797998298762075775386081115479070172556636299900816004*x^36*z^16 + 11804404454152375266693196629601296992551002026494104554807652165235736881714749296355194683685148*x^37*z^16 + 28164894837976163805062640757784984139482316251125266595542231614893854313097265546573610292142096*x^38*z^16 + 61385027210975241020516879822805886363490461550633494534499569316036918393602977101962462139683704*x^39*z^16 + 121746970635116019313701467485343905146775300792190559842178288615588536701535733248908318866925200*x^40*z^16 + 218748622035416751822444832647053617604448835943323986145419166233322151064096143095672145558497152*x^41*z^16 + 354164435676323215213190769975531998536851955371759448893791907976208993665398242475517521193302624*x^42*z^16 + 513401158694047618481616775413870286698523526507392611447861886661716975973996756447484965163599760*x^43*z^16 + 661198461954179462581917109937817036103200535459257030125255061292043371491578017910376020222973816*x^44*z^16 + 749358256877435258916620102962691001466627746768430932274203322399547789866873541176111541146090128*x^45*z^16 + 738497992288505970584670790423881451244621195126979020235048383021151030345417788046130747354337520*x^46*z^16 + 623271355210847479624183594524927105701919859765214187347189490024943328436220108091830001869623720*x^47*z^16 + 441483876598331601746052813381433287516269512735603697567991809424969273787736329175522306767817136*x^48*z^16 + 255279792581733266675705418556578819228876450109356608478675786897744591794841863474331153924344964*x^49*z^16 + 115726839345665412280792390978431062166081919801960091763085220527368561752564491904877320114910744*x^50*z^16 + 38575613085000198304108986710863691309095424770319139221862826612869799985609994503127602545794444*x^51*z^16 + 8407505355277820856621623032684980471894286427674143616011542517056909823114579082948536843477756*x^52*z^16 + 898915727026754183562530728780941590325573948955472153210114801351855380169883855692144464080780*x^53*z^16 + 1217449532028448801269558537668932880056902682670169010344*z^17 + 358741827974399356345223953180466407525653215492811777598716*x* z^17 + 51838193319343084751818361065942159525907148592145795636194368*x^2*z^17 + 4895829358868709902401138989894630147339205701584007280763143500*x^3*z^17 + 339852154758432219499347419629953180762905148855006904205608941900*x^4*z^17 + 18487957217213853417988736131249900702747603170127985237138611560888*x^5*z^17 + 820659878689316805093231302828375401475928899922779803655193817950384*x^6*z^17 + 30559810721185103145025168487203620167505382665565559221469346423372504*x^7*z^17 + 974093966737688980598011130950773312177837009703098238010045473263571056*x^8*z^17 + 26986010634040158254600055083068427697721195829305419175110998136255714528*x^9*z^17 + 657559125783043329148905665539195616937135692528069374552104788166620343792*x^10*z^17 + 14227188357850954173885136933222651607412243082967265743596178711438595852384*x^11*z^17 + 275454174595030484373782117012274579747250350894980607291027782754177630977832*x^12*z^17 + 4802790736528861128308158915506879812279552568870713598219944440010181291622056*x^13*z^17 + 75815482340920781000273576947552472189290795106160680204635851344106229872142800*x^14*z^17 + 1088373368716321221840399953088216030213082129850606530946284776673063367719789320*x^15*z^17 + 14262226019220145433820900296627777603118420570635804367213192661460005270124505816*x^16*z^17 + 171146712230641953002759471193172472738757949806257821233452985745797669803043459036*x^17*z^17 + 1885783218096886291779292143101766632192643501523119147622088911870598768508909112656*x^18*z^17 + 19122503509824570245013794951183333583078355942269023686788032731131838099430738307756*x^19*z^17 + 178795407816859746483137761672719528782126439736042677752099661072964844243458261508004*x^20*z^17 + 1543884156386852197438622767372029730593402991422672569718346975582487861902530806873520*x^21*z^17 + 12327681066907139779241589914897030793670345111932903755677561357876042271853912103977696*x^22*z^17 + 91117642668444064202964025497697871316169692110600048896145170381159116178383400665721584*x^23*z^17 + 623902747715873965341046486006120079426482287400974126257596035549050854958813911011579936*x^24*z^17 + 3959702772170080926182639653718193367339667284209113320078701979956524275148747286193737120*x^25*z^17 + 23301327851616236468542337091563839380813958466522058343692970538488493870004165225754405728*x^26*z^17 + 127150455684128112287711688598162381975934722913655306460549246849477707355553099132301163296*x^27*z^17 + 643320757925648632547789192303152089297631794279832873083931855187491898995921410072519238896*x^28*z^17 + 3016952519927177428543813679305565728034879684150959296630736709929023270146256721361375804880*x^29*z^17 + 13106982614350284247799367300033854609977805899146941649927130984594146561403514917363189790112*x^30*z^17 + 52709801051258247415884310484419891488648293374489097313488905215864575404962259714861959721104*x^31*z^17 + 196014572659366536773942914103179564351074302535761730418972845965203963718390711037388398276696*x^32*z^17 + 673181360648326567657381974995969547677544979630122025929447859012818460353148877928139474290804*x^33*z^17 + 2131740975386376783644890211819991602519031647485415856822742389985671732424166243832080198163168*x^34*z^17 + 6212502271126053596490268887798495257683502857540020576500000315483746060864780822321904426833764*x^35*z^17 + 16624195892179616440496018754382521674691557485063897114116169507468995565169911835781462419303508*x^36*z^17 + 40736768312367893655830395704720939038186766843561487899402877895935927421644774285002947713867800*x^37*z^17 + 91121718593459453150749108527256154163234202441834263559445806636049690389696511901066996733954416*x^38*z^17 + 185358709617460131825732894008673530168228971114406422460237356084202676837761063851121121467876280*x^39*z^17 + 341368956878774766600039549530301938075979371729348975846152119969081830681620177849512698390115696*x^40*z^17 + 566172904091733552326187608836686982241273406574693220779808972197802980231018895778484912085444736*x^41*z^17 + 840272484644242872222346064945433754252693132856374026209849652977323283491588053714186955297805232*x^42*z^17 + 1107335832475559470886094929213796215015733173325780591671052712375637660534833354643780213617193856*x^43*z^17 + 1283502896733921768789729326626051804961386702249811853662660485852485258991829438889239065862805096*x^44*z^17 + 1293010325608381323899466221634494936999264503859610764344841808737995815664124688054424244611007496*x^45*z^17 + 1114987164829079811310626387927182021736654473534721563061268369009387571695941291567532258690493328*x^46*z^17 + 806586459639618418285088816879093658620538571270464842335294258565472331638613890099122368904430312*x^47*z^17 + 476110063003469860116873997037521828797457121586197053229012473979873881290685206151140608763393576*x^48*z^17 + 220241389652673865226489956867841738361584901589946084047358981985749737487816940212008198113605556*x^49*z^17 + 74882072406782740900817223333342924408539262550007189784812026365915649700425203210904760928222864*x^50*z^17 + 16640460584702986279920094696277986242126894477883049188162833365127124506990043255302476195168676*x^51*z^17 + 1813383486038190109832265818744811382184217580188867772710068364588094017627686615858054691053628*x^52*z^17 + 12895947969881194622486132375644267491740916084575057947296*z^18 + 3726928935023465369800576501606192211142758262341319328834428*x* z^18 + 527981597042144368070710492961153851805148990862078508835564600*x^2*z^18 + 48867630112183199096691953986073551415076980524741088189868725940*x^3*z^18 + 3322998846502441886648571258084256402312516908981672200718297500100*x^4*z^18 + 177005071874300787409227980973498527646722074441577233868339343767556*x^5*z^18 + 7689887011565760684113469945446217556289965092924550890221025721644804*x^6*z^18 + 280131598277591208424523433336170288158162333252135680362825906023371660*x^7*z^18 + 8730768146301594732635135309917342003176047196646115237599031612111428308*x^8*z^18 + 236377463516751243895119392397260536684631400061945498857887646464073381708*x^9*z^18 + 5625783631699228809520391048308170693635924811241263168758622637186125694500*x^10*z^18 + 118823369433150900288893426623745083030091364124749982924436004313917220060356*x^11*z^18 + 2244441422626256029365340312610189143581964885264366126677631015938072712318812*x^12*z^18 + 38155504184646491411217221443252476939066389381053728737678828556710544674987868*x^13*z^18 + 586867992935270686550692438347842007733901552088612997345329200480954685104080092*x^14*z^18 + 8203110390139689814317812800872372121449897104263010765664638093623219322520217044*x^15*z^18 + 104589657474281169529386155153607146638299790876233386107643597028512658882635174604*x^16*z^18 + 1220212670533279342739100988894207687829085053900674805678328829261007054715674187792*x^17*z^18 + 13060794880893252679280625149056432181999770169949454410970572344711730233867426901780*x^18*z^18 + 128545718038265174232433656467712325697541117930224122990919065276866436360580000689104*x^19*z^18 + 1165481176880270817733597263867413878719735002579608397050565777815751538466359895057320*x^20*z^18 + 9749342543109567680055660315306703117074167651477149919252940088112057334266911116651048*x^21*z^18 + 75335828742210290683913123592348586394577528452931036596611583443602646780336349725141800*x^22*z^18 + 538269037245067766397307071773993817643281788644266469600865810624020484484004830627379320*x^23*z^18 + 3558556412897947966670089159323751504418721890123651872461422031080957221387188714677719752*x^24*z^18 + 21778365246935438282102753304728025630306234404204235182836520251303367572966297143723890136*x^25*z^18 + 123410736399300848968422696226687659148032204410024985867961132204610573799686272114613012136*x^26*z^18 + 647525468761763712625654748729051761952181968915238195852715374895865053329096680472422932296*x^27*z^18 + 3145123705414279135939959423324997898937461447762523674616068265323971940693694360563554340664*x^28*z^18 + 14134981250769929371535236681433702692538886933445508101569405692336515347742010284928987875128*x^29*z^18 + 58738699864310634028753969578867524837883691214955995574162327171760229012488272149411225369400*x^30*z^18 + 225480815608159749307941673710341155741918641547661341881377056612029905964487646310508338911784*x^31*z^18 + 798577888612232551365721076799521846106956102998834819728074294758893032292746125062206166876984*x^32*z^18 + 2605461192138911244491806492657045982675978792504047702948903992415084444164161553209367686422236*x^33*z^18 + 7816383576416702238606685408859377412873470587887861477680336922958020782089821086655887953335520*x^34*z^18 + 21513665272232481963063682248432687716925511204586318224247281588491433025123157382696862516143380*x^35*z^18 + 54182564389327238131642679412690948544784497656368968158991556706081091549727153701077518439226452*x^36*z^18 + 124473458732239012685001728574164656376304878361333648619589763003406400057425204227155956282421652*x^37*z^18 + 259865641914658088051150785182507782816188527419726873550934636872443950459001900475005690306262420*x^38*z^18 + 490857323616588793741444710130979603398191341826565355572246163777551984721662480767931031165379900*x^39*z^18 + 834457450148342702888953772122964765334598912250757114682246918885795101590359929274085632954266660*x^40*z^18 + 1268646692501624432119453398629115769899219497734000332178907171470538347128505029328506098005097244*x^41*z^18 + 1711666172422421578510258687749309755816770911691454509390602315889416463183577288514737631019516404*x^42*z^18 + 2030115692877097613061911584116781294574585592106214449380834140460158600473653184261837640151162036*x^43*z^18 + 2091634350235602487389855957349041390183982909806478068680745757984545391876705219875584778693765036*x^44*z^18 + 1843736945739272368641926451424418615392209717768423998557967833469555044089413426880669680040433068*x^45*z^18 + 1362762090334704790159093433062611209406450896315033133112162972385152914092977108927574764305627180*x^46*z^18 + 821523245982577593133917088757834623208196530939946834290656237102894847967448613280616230316834500*x^47*z^18 + 387941532787094499657210613888201287122819126087822479374009906364876433009741458306761003452681628*x^48*z^18 + 134591960377622111288692451063478010969976672845468747119142152230503101525777494777468793643273560*x^49*z^18 + 30507511112506229584114956967250180917157134490406996554294602080169058015090101078504825159102740*x^50*z^18 + 3389723381580010511506750076852163865426006128835320286099502645080595539420243504534860077412264*x^51*z^18 + 126923278670430884462150077249265871253336743270994546603212*z^19 + 35961594609512277491645962776802576063930709462925964710820920* x*z^19 + 4992668089582649927317087542167846869038437975719310915269349400*x^2*z^19 + 452668573438928594215103560888580309002680140798134208190406538100*x^3*z^19 + 30140182516069156143034290384441683680415609869042605538208628404520*x^4*z^19 + 1571308181940130691819009496831229975549607593142481693362539796651124*x^5*z^19 + 66780597731908785639462820948590362204928905332218468056315020289746656*x^6*z^19 + 2378661290633703588879917049763410819484712704113319754013974463974943684*x^7*z^19 + 72450058477297601221022300764665253817097200188307545142208766778510356032*x^8*z^19 + 1915901546399163405454704462989141546984947268841276410274283542290716898388*x^9*z^19 + 44512779261332950198180428944926703262495924086372671023036467584484543694144*x^10*z^19 + 917233027203292958254347306992016310428755448550749861813592822791845705703852*x^11*z^19 + 16892374917660819088129883111278790070193151118495604860330381357912740699384088*x^12*z^19 + 279807030687404539616047557738357048768868906302851586407076407457008749360294380*x^13*z^19 + 4190443388151857505944686232235140159117939567586398152138985376667573871400844224*x^14*z^19 + 56990030078865289655994381796653262798117082539428951072914130090289335354419183292*x^15*z^19 + 706438914519266981604940144092105728032488807970109786974146585605744026731654416556*x^16*z^19 + 8006307697885028060781847084177163613735834344370782456949431505626419344929133435876*x^17*z^19 + 83176641083583346196541575151566813366243439358812346599493447218106950068410593464376*x^18*z^19 + 793826188587181367879927518436424165105051263606607074784404347297465202570060293485192*x^19*z^19 + 6972440023090743344264531392028897397169220473570185600787542294738665856359387189385360*x^20*z^19 + 56443562091686968129427754792828786205997148438443652922590160052826107246860762698560904*x^21*z^19 + 421616304715176912984085829393212311951010227654093079822968372274255611656405931391629888*x^22*z^19 + 2908541464411944962139945390975562857087462923932528334851453591205246688833260361309770536*x^23*z^19 + 18541951835626149163566911196581333646195524436541340397234177547272233941935313835528314464*x^24*z^19 + 109273902817956784987753226501246964192160190306688035878162208520515376849491738947901700744*x^25*z^19 + 595402675610661856355652374680559747468998234156376147005968502087577278144688877161468438976*x^26*z^19 + 2999065329001852239868823022180587810186690822265347869136715320522577395821456763523692538840*x^27*z^19 + 13959935043330056997570368915493166059917528851869594577205749725867587811730076857490040820272*x^28*z^19 + 60011674783970561871940992617226721725686044792533308537691866379730384780715912937213326284632*x^29*z^19 + 238046309976416404549019182152914513804640747971280628777536944025691171659515028186278350433280*x^30*z^19 + 870276832171846455444619018166395683374405835325174402412629226204455244034354479904709557282936*x^31*z^19 + 2928118924911525094382436919145609795993078707408039716384062162843681938116684822382944080675940*x^32*z^19 + 9050549404271946832767798403858338131544219493030760776368453369111157815785986446360271448358528*x^33*z^19 + 25643223312103954019646124156461393509799571530301132501304898276951306534645414482652083583981960*x^34*z^19 + 66428159437069835269144394087770155260727931355912217734048227778012585289162996692388621965708484*x^35*z^19 + 156844265337522738178424020411261768531274700513977964863202780974617562987668672350602141824458696*x^36*z^19 + 336296713066036982308105321422559441670749118246055343944961662554505061017577232266186525777395396*x^37*z^19 + 651943627961402224633262306256282870791489555638412868250617066042388920871726565179673360339904480*x^38*z^19 + 1136722223112154254508921218624246188347705647057620011938865451650542250515019038120269563741279188*x^39*z^19 + 1771392131016077847900360420067494780064630816658520630951906322999143094960765192395632587035180384*x^40*z^19 + 2448265546933721156755903590011054990279919800917287328037134578239250728223289213306929379681781988*x^41*z^19 + 2972893878420124416032249894862836609478034573780443642254665150791207868705038256245350363291280384*x^42*z^19 + 3134213701270136301815277080006437877450241606311264810593485286403648901141272635343156557318836156*x^43*z^19 + 2825541139784767486504413324163990469835504349053954119236330232531042304353090474562984796121234232*x^44*z^19 + 2134853305654563301552680270321426638778084271075447187319447567406163197480349910988996755693256188*x^45*z^19 + 1314945876656897640799802816901222220689586544084439663128984998901926717135881907808747309314142016*x^46*z^19 + 634158295128872228851724780535926602584635707571670388917807123249585175382504459380962319597205004*x^47*z^19 + 224597729602299622673962721635334749216084177801911653811807711288554437107481039419002876998063140*x^48*z^19 + 51947774131105705718148527012269293386675852209700885644121556091614458996839446682106573387489700*x^49*z^19 + 5887414464748819701217051128264100051913506712850615514692215302820554157062692145225621690389288*x^50*z^19 + 1163463346604081101329605569819650249984263327558238910060428*z^20 + 323054994719990641862373018384229649510953733980191376557887268*x*z^20 + 43935479200793004923705104906732481664220128943987033779181709688*x^2*z^20 + 3900494207532709405953688761198156574101339992269458435063823303788*x^3*z^20 + 254182205900165105005190674868900002125247025894068917018191356193508*x^4*z^20 + 12963292500867971410525555157808058360538296483207283934615291844838208*x^5*z^20 + 538696821700902831799623302546112190561793327071403955071392151625903216*x^6*z^20 + 18751779841179390241969759649652962474725270226691018539279893536999593148*x^7*z^20 + 557865450275110293325787893847261318348991840658724909823795367126536765636*x^8*z^20 + 14401193290431652374657454744335511472802712569413758428615039151118396748792*x^9*z^20 + 326427047916473153199051320380271934570729016714971599278652454178723360258584*x^10*z^20 + 6558216144503633379555975535084292705975818261824777050577086807700499372462356*x^11*z^20 + 117683545259702200400854196568603647251608360537073128591885547643265159234826188*x^12*z^20 + 1898024358162899045770661245013394719017531481352995385868667310392478306204795072*x^13*z^20 + 27656926361802267311984720830087822992281744557347563790455259753480073777911391008*x^14*z^20 + 365686026339385246317519500231651716615759583144363192101154590326142525368646208292*x^15*z^20 + 4403469233836765570482993432214770409817919994315135590645729693501812115002791571640*x^16*z^20 + 48438161572204419215556613484488145797835508517302600348831821613065753171759078520396*x^17*z^20 + 487969627690355610480716380149878050990933121986995183426440332324891567498378709441136*x^18*z^20 + 4511578838470480975259110402256854786425419160645201690343027444176432672442220632359096*x^19*z^20 + 38348420126999087457605870435265785444760389758499290380854526802628261933872540436762280*x^20*z^20 + 300091605120802387579564822445392627692067149237326303304183044722987147365384308736202368*x^21*z^20 + 2164297030871241415208310136118117421542519296406610863598912289846612014922714806964755744*x^22*z^20 + 14397280248839128063891270745602805059559967542200055088437058950400517681101667736448150360*x^23*z^20 + 88383303749817980873284736536485595649788390098662858669422289602780642935404378882743527624*x^24*z^20 + 500838721248968510926810386596752296822925906377680115678124565298082134351181940145436200528*x^25*z^20 + 2619771772686912607962926658600418607268046310627752767391814073101321434166123781527914875504*x^26*z^20 + 12646058803957813208613694424576202152514078016046067512252335332841825273908818057693705359656*x^27*z^20 + 56305071341431191087480410898463694685501176898679096363314930232205989140402313303476029859672*x^28*z^20 + 231044947918286706324791763908374356628589540145065339893372350694215204087523760786330929124736*x^29*z^20 + 872836469913528165244665236103329181167416649895914061666314472562858127523832231196972301901440*x^30*z^20 + 3031464298731925754346267622414095002880105113327496007990324778355135842534026582841174226263496*x^31*z^20 + 9662792452208012144678139399185136282460760641648389977519954464421087927254948742365255863782268*x^32*z^20 + 28207545643314435787910013320312333673093127313955999997985727324446902542316456281165844103387772*x^33*z^20 + 75220121715504817109835499967653253642660959411382619735947391420949499565243705704706975585610776*x^34*z^20 + 182677438451938455059658457495627514302794781225714931379365313768834999806670941173509398664709404*x^35*z^20 + 402566947699652651769316847453370210558643255255922149616039967955310675427140478870071886714028980*x^36*z^20 + 801507166140758968490707805301016383034898851822935217587940827629269150516992912067506320633706048*x^37*z^20 + 1434275981514896285343279160054731718577069625704668400025532904233478371726838237269918771644530928*x^38*z^20 + 2292389816609380628160449465921918800728704462249118633281026879303139210778488626519940175918154284*x^39*z^20 + 3247552240197524516380064828337065919151636287593047875059210126795375087860546536305309905483568820*x^40*z^20 + 4039638152438087480510694244350343367072144260117239919759295813620915361032353992276245528853868600*x^41*z^20 + 4360244355010949810691404760062523790715692483162748999393624790625324825595004234804871899042872184*x^42*z^20 + 4022240916662303284300720899647860424989077013071730393368424827038472869579776964401269966502650756*x^43*z^20 + 3108095253786760373903858639378194286863818295663553163470845932993246958797006428848156826784418716*x^44*z^20 + 1956948863436603007770700152605550693209917299639849462903855868466051904067771302180465496296839616*x^45*z^20 + 964293642871571138881640543934384070507264019193912409493768189632330830463537209119673907754107872*x^46*z^20 + 348787062312250447613004063283513576158662093139079180135664060375897471347498749973334747218183380*x^47*z^20 + 82352500719076290479174307725574051207120430471646422890284608646992072612568527712950782398254080*x^48*z^20 + 9523758656784123936914218211143368435880516649842437700305544857489735123765952902669867489504660*x^49*z^20 + 9954075455738685447697121709493998897390536657412041494346808*z^21 + 2707508527036036214039857643966047918732524093507391616383218756*x*z^21 + 360549884757560205610361641221610719028041068701471398341113970004*x^2*z^21 + 31327778882171723805249052565088515269388955213802855589082210888552*x^3*z^21 + 1997145903524784028273404759627512007260495026681721608855690219041780*x^4*z^21 + 99591009053826857276371280195256371126841357977800759612483511345308740*x^5*z^21 + 4044501534375570128978226304519123988809099998593410501249603609906272996*x^6*z^21 + 137513052168637819560998973974149537598142944550662144346483794522510939592*x^7*z^21 + 3993608223396159584716348380126589099001687045718503007953149462628541930708*x^8*z^21 + 100579762663337872496419532528465165347574055300782875495363302818600692433244*x^9*z^21 + 2222812754859786790350390764280429866493140187194240588654956936476800068948812*x^10*z^21 + 43513243625436104540344047735987709545813576571398253392960716760011411645855160*x^11*z^21 + 760273062233319444213545529998868607492457221620951761550102011566190752605122412*x^12*z^21 + 11930438822738237992483428787870926519402986157815262540295682433895603250694143484*x^13*z^21 + 169014549988791485328885012877099925053237017444840577110690394402843661540114336796*x^14*z^21 + 2170897997633811607060664900102137481710755341167401854811016482403042600982604643416*x^15*z^21 + 25372370347345171565819862508547760676650513221125548754527893277137216685226348037220*x^16*z^21 + 270638617038348488614954675033619373582305435983814207360202168462055165545858761896872*x^17*z^21 + 2641232429244623305065162313306626246807955333718303943247689706873889820362546512952136*x^18*z^21 + 23632079630083471287614749807202078125526386734711808273652875336257569609822774254921104*x^19*z^21 + 194176920960519191095724202651773765327155560072290402539343017352799326686771102292919432*x^20*z^21 + 1467114513923922762807017883664779863739398728322254501990831442715087866737938531145587240*x^21*z^21 + 10203114574107281186819466520955549531643840848260481064651941179086357430354080324142357608*x^22*z^21 + 65359081764571278189065598672397726361331478506636597243873269235640906806369464965744814928*x^23*z^21 + 385800135415872126246073373290682672504794018723498784163373286880826249929655557500156998536*x^24*z^21 + 2098752736662344542214113043272613070832257425896347886424225756425831552205200137301841528376*x^25*z^21 + 10520670769679187279072351156601767107819243229628698019774288362478989563561714451472113560856*x^26*z^21 + 48576924294568096867505738247988010814717559442695540321404526793131762459041611340149928828144*x^27*z^21 + 206451928251914502019940897041108154635774840101634543012499889384640909323030006205789448531544*x^28*z^21 + 806823627651159804221348378456971231063515406616208725472365446083875684321472480979336953842424*x^29*z^21 + 2895600352570271285571344414804143650136262962969555732798463299208162977914122558937594098101560*x^30*z^21 + 9527459224586072436321448161063910492900805370149989704857899499941461548593499386540339471319088*x^31*z^21 + 28681622040680994874279329154502450854290352133800122171050336304310979328150136922866635893119872*x^32*z^21 + 78802032273385712684022630591155263298153017027819424943545688496320449570676203081595713450478036*x^33*z^21 + 197005080683465403574557965396854797999752082822780448757229169036272628393831045991861828670756900*x^34*z^21 + 446544849549193882248711132428057755305951961841006696859728362818467123154129604661335629165221256*x^35*z^21 + 913763071762670395083187276386125987448665770847177868829644174052101314462590615687893556940412996*x^36*z^21 + 1679348348104340917599950768776662637184135580852744250531150839791242591916151249522731783590414932*x^37*z^21 + 2754720535925920794735800513533612155166274600060214927516019594124447003657241117778833756827938164*x^38*z^21 + 4002585394080089291089742703185266116566115062902665150228300361450256840629519815617930546158923624*x^39*z^21 + 5103296377450389106470080187607707091389620321153602144789078294180982658496035584563407715135518564*x^40*z^21 + 5642669165318186665633176041278869772910803486358496550958444924053781199014986573782042477770610348*x^41*z^21 + 5329187545024600664628259336810435125413697594105732553397627262784027521427775051940888662250028764*x^42*z^21 + 4213776198348171312344482358349628906724608653111184020498739234185090844709543901550197000588805848*x^43*z^21 + 2713416491361215778825568491506629455794179697600881391546302913281288655485629064146262812040733052*x^44*z^21 + 1366757936421339126784295722707687913305462067207595718914320118954751356917830819516268020478123596*x^45*z^21 + 505106193833131219204052960183879615345523952234934985265077805657848190067312204672511355685573100*x^46*z^21 + 121798656727887262503580200620425051969055999904079574938007777313741430911344735058079006114304760*x^47*z^21 + 14379008014259372185841647424793815007111610355893977579084296251114610148827361057771948671437860*x^48*z^21 + 79632604027708693512021406410015567822644331908130173695246800*z^22 + 21208816716178585053552086505206026294108550029457487795901947660*x*z^22 + 2764215783577138624978341658276936229948285835072711254672512251360*x^2*z^22 + 234958341594383133390447220609451363020031091427146833040689578562640*x^3*z^22 + 14645736625477663195663580544062748824975198829881409948567278674961220*x^4*z^22 + 713735564891278611188618444823886196147393574705153030478693059732055752*x^5*z^22 + 28311510740631818214757864067636816197965422433212493830168509698504260364*x^6*z^22 + 939672523152164019529064162785967378652714475785674669366012887004507691036*x^7*z^22 + 26624054822649651471656985240366744763087695253360220267266518329797923415320*x^8*z^22 + 653768457311700196276917398889360670705630849844957141613086648477809864652844*x^9*z^22 + 14077814114111535186919320912537437474238435883304955454000694558474214215601432*x^10*z^22 + 268331669023524100280588568717685512078326327084896359644912701744949402083961256*x^11*z^22 + 4561638373399913137278591325909796841863445482182852111258729500945990244739718756*x^12*z^22 + 69594226465972958144982551157074044574558624662875373257673567978440609086310431760*x^13*z^22 + 957749116603152260746572668440677561114707123693553602884500556538694522016532875116*x^14*z^22 + 11939938986985963217468157675186413005271006209520715312673279840382467224680323520028*x^15*z^22 + 135319308519174245343832084228691086609058993613301356323720152419932837960673754643328*x^16*z^22 + 1398299521364800578207090020470392786116361154045042194259252834675492011191168055197208*x^17*z^22 + 13206162146223116338215423818738308290424019393474744352974812147081816213322584001917152*x^18*z^22 + 114221718212070112375100260580028161403107674019408966930465057309548915320146736225518400*x^19*z^22 + 906158964482422885684048860359719658787289593314930741872453122633034581699557287343712648*x^20*z^22 + 6602015312657652498681232236351344615817228370939211332511097196213375589075972326387124592*x^21*z^22 + 44213496487798217724822622894918632460963792202182861198863616520935742075579653668552075288*x^22*z^22 + 272329507352380330973207355759829014120561066481912057100484077925805375237023926607257597880*x^23*z^22 + 1543200541663488552020159999203845233386683876779872692098284605755085551322129179934196937040*x^24*z^22 + 8045218823872319676103325947693534749197608997033497227832337795519557012528010889696720929208*x^25*z^22 + 38575792822157024828025259211508099731081028360157557845746868398809845353705901907003955220880*x^26*z^22 + 170019235030988378932067059902770997621183949114350550482152526969259881597792870136792203027120*x^27*z^22 + 688173094173047878932182048249614400202686173245791612493135075483952938744180131187157145297640*x^28*z^22 + 2554941487562006417218296084756917846548675210141068818925459505945909011121939876560315594835200*x^29*z^22 + 8686801057710829683013833719603269900206272891667709362714449762678166316028948301502462547952696*x^30*z^22 + 26994467802993806362027680850836897614699972983346271686889177967410781440121506904454956813310616*x^31*z^22 + 76484325441815764019939724004329755698673219867790351723584526098634480397260229580218180935786864*x^32*z^22 + 197005080683466295012872752260115313994559738083381425049322031408850030785655749363735687353769564*x^33*z^22 + 459678521594751033227649664320646783691770151011619268876849954631591320818369179229278652322995328*x^34*z^22 + 967513840689887869355887123180612264130062349039312302889684649136473092272202758102433916692285616*x^35*z^22 + 1827526143525438123503504718870524002648195064909369673338188849189547557941137755586452739066850228*x^36*z^22 + 3078805304858239550450746191215014300732360622454618158905509102429147368691102487519015318048545672*x^37*z^22 + 4591200893208711056993839196258263979387253413290660145385092895992806929222946014719141251557190236*x^38*z^22 + 6003878091120114271333100462299773359732541622032314276554153722593298015684890688914388309059175084*x^39*z^22 + 6804395169939773971597317259897186465678573299100301334237765292145430783102539415870749885207868120*x^40*z^22 + 6583114026183769385815113389417451531183463974485217093692895742426965615004301011708376864180482716*x^41*z^22 + 5329187544995814709889574748032390681724977207731135624278578854963166643435487002958145580194043416*x^42*z^22 + 3511480165372502226482300060736259320567945877164333604063351135632392699536525945930729939605171048*x^43*z^22 + 1808944327622567472959615496375294228974057674600270126307525580837192288964716242990948456059199028*x^44*z^22 + 683378968194285113759065892725672958829289183882335649857990942665610296921430266031845328882469680*x^45*z^22 + 168368731383305635616529047968374838474691779762465275401273723577721392609450912153102983901540060*x^46*z^22 + 20299776077221287148953787753870893552078014889761276271695345714361180928362584841947012516177100*x^47*z^22 + 596667476226385430119057494449684676935822568875771389533017928*z^23 + 155531322855347306653124372237158092776459788426043879295646229892*x*z^23 + 19830243663039884611706757859337582178538839940188567821714653287300*x^2*z^23 + 1648113584347233519996805461916306610262711295318452910666986610966380*x^3*z^23 + 100397585854056727550206195423787451442537876686897989519562390359401080*x^4*z^23 + 4778925086648632010432696341244634852855565339147912542489863454162957096*x^5*z^23 + 185050599188350371272126072401748965614556429613380946384965303673722607820*x^6*z^23 + 5992114640392147302278535593864608674765442631741590433883521717922824069304*x^7*z^23 + 165532166940824453042109728919104874293057491925439863193288994601745709249176*x^8*z^23 + 3960510364583822661510083286784014313817487138118923847781400823979985476497092*x^9*z^23 + 83038700644108954688043599232289028112732877740439573760903188195460906381801676*x^10*z^23 + 1539990448308923826454879496746791225948520799355245672563307762079970567645973196*x^11*z^23 + 25452619909550201342860812324257987238009092030537740376596633321903911503086762344*x^12*z^23 + 377220879685129015914042245621054862456462767026335063014334416706043712277683709888*x^13*z^23 + 5038593178651365370245331294640571409815610507115104826932605076117476825200235764388*x^14*z^23 + 60910993093029838155001063398970628684310892690788417214976547580915901062280862517536*x^15*z^23 + 668751945000556795563615842132190599975230462129521075037964323106230856084104041419856*x^16*z^23 + 6687519450005567847703019445625663270802984242898533003393418129352868913423136003336072*x^17*z^23 + 61054575719495277348017842958809400895831567322398115759088729856272559244889902837508712*x^18*z^23 + 509859263903153541743068933285167305743420197598749752602313508116951736058115280719270616*x^19*z^23 + 3900423368859124612448309596491742404854050794388832438988457251911336145552004729481774640*x^20*z^23 + 27364875064059255066466648994436778400812593978637198595868551765823027531143926946819099376*x^21*z^23 + 176213210639775507922779087427522040114430977967672417369695004867411098244426377262222545592*x^22*z^23 + 1041956375956933422956903675699601940205108524972366130598159567462945503875330617930940537296*x^23*z^23 + 5658401986099457851335464219553593657450373110276371433757546859715969666581377517025743292592*x^24*z^23 + 28216564570682632140774240865246348176071976621542597280756241071630679232943479659780190693928*x^25*z^23 + 129145045535047414821638312083773669027338466364223067244098706629155401321713413769404366654424*x^26*z^23 + 542090314591557010265216305039672839863604180841000215109714692047045566446156547333644191289336*x^27*z^23 + 2084466328727059625348565274136797018441063238695494771998567029001029300355685496952840716602960*x^28*z^23 + 7331571225177930223833251327406558240822752535691228391831886106825605301432501234376704940239776*x^29*z^23 + 23542489823071327223815484979274769588798710976769361016992648160189990493164249030804804766196488*x^30*z^23 + 68855454106187311173609883173011680662819719522617125224267092067120021936368107885778452464464416*x^31*z^23 + 182897299969560095879663741927319578635481281663296400956976789289817809898292583257581296073825000*x^32*z^23 + 439692498916715852629694796882828675147878418816362517728379653340429597972604894236612219331933812*x^33*z^23 + 952667080986229285539391191103577131793088840268656653369619083590632367855023558996283286993571924*x^34*z^23 + 1850896043059005661449539288540223222722042127628988884681662251809534082832402982530008674925018940*x^35*z^23 + 3204792222703765648122968271710452863062388783059108870604020235449603354910953890342734098409998040*x^36*z^23 + 4908240341077693049221824103072305855741191077772864258914443911326597214673201010129704821915555112*x^37*z^23 + 6587375194606181633457497826977976552743991075138024026930161549633649109309407085021939959073046332*x^38*z^23 + 7657119884325289185925960475737685040782743943723119223801114252731422416575683053492057302179037752*x^39*z^23 + 7593310551950447902751246498214928999584836553496889651070904120551024731151820693531526865152384568*x^40*z^23 + 6296891677262285511722543718127996023688349300353153652826388207646200651657913662921851909903326100*x^41*z^23 + 4247903115625825376455033797670877813203005115075722681883562963862306813842405693781983361861815580*x^42*z^23 + 2239204743068061990664575192724638071609488802713263946819401285461317123370709482576907778473515964*x^43*z^23 + 865147287128603055899075267720102743942549586328713693047675301188882448746241687945747621121648840*x^44*z^23 + 217888946346559647080159405268100788394239922899956366152589240321294406755773227350500238075076960*x^45*z^23 + 26841392003792453115406851806449702005103816186792902569199268561623784556582088899808360958506900*x^46*z^23 + 4193246449816064900303569588912297029555462565028098199798668032*z^24 + 1069277845381090258786498426895687160896711333510184999754577244300*x*z^24 + 133303304614831487005981750597763594191969783793264111470148457998280*x^2*z^24 + 10827190631516006465580790467470379732674673031445865493392672692957220*x^3*z^24 + 644217842565859002845681560167166205329917944812218427478314274008588980*x^4*z^24 + 29934655751032316203962246976898622698512888513153194222433949777848859532*x^5*z^24 + 1130864772818916542595981860559649712752980508097813073699122232777766778448*x^6*z^24 + 35703016398997144348647823110678142077522824911536645768719801092999308469248*x^7*z^24 + 961006191406313073826564994477629818125672665500798111724560868516229001147192*x^8*z^24 + 22387884977578319459208493461870835536515743815823579112039901145684248851779452*x^9*z^24 + 456712853542597489934719120173562616280071069666860939374815694738072479797127880*x^10*z^24 + 8234671147207417867074022334820224659040054919625548232678738675044886141424783436*x^11*z^24 + 132212220085719291521991464592129229303821206986966794491315291766959968232137957668*x^12*z^24 + 1901821935079191945852999566704866146192797695224540259703967869339939675527365168556*x^13*z^24 + 24633122206740008632370348804559072602882295449804290612063408786025240219310436591296*x^14*z^24 + 288481231176710779311682517391303537363888390338494459977633850145256784017045356282304*x^15*z^24 + 3065113081252551943694568709562680968279671887723986000103221121812341594226319939048608*x^16*z^24 + 29629426452108002331175500036160197722823253593918076406613443527936452684343749855800856*x^17*z^24 + 261177907244507574588064176994659778517188134665381309199685200788858178070352917458977424*x^18*z^24 + 2103169463600508370966199429826874027884294368485235706269264817476334915729274824737299944*x^19*z^24 + 15493348381857078273007314823778699106670921706979949555851557844398336748725588138556282792*x^20*z^24 + 104518620036337433308233414685198800504804632156979153980106129691052354277142176172499425368*x^21*z^24 + 646115105679176854071931072068291362189643377772085091220901330302474885563598754934284550880*x^22*z^24 + 3661318932182002226283604260929438727953808253218010416733235148143256688726111871590191059904*x^23*z^24 + 19018517786612067291459678298491672032697982982884475397123035798794756647620902519633528662096*x^24*z^24 + 90528144664273431992535914136869797877336822742121850206680694167176322474847558466830142105304*x^25*z^24 + 394609861357089378004834349417387811779917163047819501167924991697748837603553608299911288483536*x^26*z^24 + 1573567718744936798089741583856648145006078967826289845187591262854287265822191235482720742200600*x^27*z^24 + 5732282403999408787862434086245615391571055014085297856393997123937119067905200417079631764059816*x^28*z^24 + 19041719709837128905553722895498882497505109602324294790916926604567534525507548961017498325260792*x^29*z^24 + 57548308456396741757746009075652862875680330292143113494599975967167401216462390578175134566241472*x^30*z^24 + 157793748993345255714030804731829175475645640453881480275485872765790219153077226970467986128003392*x^31*z^24 + 391197002712668405773043064784291590012999969944587265607557169826979683041900059603820953305345440*x^32*z^24 + 873278157570716886137743512924467446473215608119042081711712160714501006434347647370415993571580252*x^33*z^24 + 1746556315141397087029234837161346246145127672533503834464947982628681831598157184119220088251951272*x^34*z^24 + 3110533627918367050357461287019020611741853160452427576103314224699425361392617565265853134192288820*x^35*z^24 + 4896210340242521976491957799478529736097041078489593292625311188526152156880120018199311605461208484*x^36*z^24 + 6748830468983131027539372164770443432552697968248085282304144376685380998172586921087549422067502236*x^37*z^24 + 8051236348958465448531591614209725251072463485141016866491397881622247933186799669859310622020795216*x^38*z^24 + 8188864320745051227414686216737560181568465998803624828200698690530230494350387586228087596331169088*x^39*z^24 + 6960534672647047108912132582336136307428192474171774257703414226948080247502212636018594235590508344*x^40*z^24 + 4810125586734307970306585268036334946397648425526037924911774721400127100980625560770218770105334188*x^41*z^24 + 2595940792815617444442062160216967071192377061466540901039980012986114487661428431501961586337833832*x^42*z^24 + 1026302173934589180010313789598426420782759529477286955081644109633616696195879821852381251246594140*x^43*z^24 + 264350559895294806043455963916650288716064362561841170891226590533890066159681446253843906628118580*x^44*z^24 + 33288589042393354036836291457371825682847143166182283964575077291062371729022446062306236899905500*x^45*z^24 + 27675426649187211585958976637238552930666790965179671949545297496*z^25 + 6900406353779764807798499179405739104911218388748778882842597301556*x*z^25 + 840699507911313471482116527957893149508146149229184148497974716467916*x^2*z^25 + 66695494290848645944545854887591198787305324034615832235278571874153976*x^3*z^25 + 3873896626598356668491128319241792685170658470876779159968592289309055716*x^4*z^25 + 175616647073350227122351436252314591427851377423071639980574546873473043936*x^5*z^25 + 6468546500528036562656497714545567257541464343204351960240082950143223847272*x^6*z^25 + 198984811397072624537013723137481777955216860601890369808350441688960174720200*x^7*z^25 + 5215060265365364163304285464314247394196209853193255767825207344993228900999440*x^8*z^25 + 118208032681613445059171119424120220038312999369643495933010607441207122855730748*x^9*z^25 + 2344459314851986177584904557554970916423936749832254495486887193602690952600659580*x^10*z^25 + 41063560120741029746889464527286335685926070960334165078560971065236564824205620896*x^11*z^25 + 639907145214880895910456427401445558808961983028266260417701276022840034709074107812*x^12*z^25 + 8925884281971672732564149400549243616635185648615454683321321371387172878691853431616*x^13*z^25 + 111998595633311240693790263687888588624064550302402519904008747444247701082526838373344*x^14*z^25 + 1269317417177527371221803315057635966235352138146655952397823550083815170640797544203168*x^15*z^25 + 13036947638927520926967101008769693788103091030385624161551738083865815212758809251750480*x^16*z^25 + 121678177963323528263461267926897636775962810449501059758156291805571269334793654113168520*x^17*z^25 + 1034264512688249995492052429967799009669495292771817778608816391330113026325874597191594456*x^18*z^25 + 8020086221196605207739983154689594812377222590835268101052521987444587557858931581539210768*x^19*z^25 + 56808944066809287099355819214015921263357537142260679365170970010043768736414303355468387016*x^20*z^25 + 367905542527907762289390160315615998022982108165246490680641593002609897768062244113258457088*x^21*z^25 + 2179561623157756614478588020428059882326847530446290494895605779963742817235948634262042254960*x^22*z^25 + 11813855754507260300393982015008303157256369584820254980212127949008255836416567880330467338736*x^23*z^25 + 58577034782765165000860908562094781863856052482408201379140537099901752627637830921664417771968*x^24*z^25 + 265549224348535444101679082980993462257078005791514121250751797269059034366176740965113910430968*x^25*z^25 + 1099646146981755542121424296192204353432201207842284139126293076904466405101281236154653863225880*x^26*z^25 + 4154218777486631566500236761927349674581692424293733586217211362321415801228815588494099572315360*x^27*z^25 + 14292490793971876166616693498165196755891595007456032065555139327680000060578776662875082094198632*x^28*z^25 + 44684568919084444065297149693883003044892532749414964438129912120937876300786136492598253379560640*x^29*z^25 + 126606278604072328162671411109708625360119652861689580429226356176832665380211499084899804139962848*x^30*z^25 + 324003164599670961579879662018732938697683085301635508599251586665784908656685547254207705110790176*x^31*z^25 + 745882285172158737310689337846108749264269372454141183768001018729872531984740971484476224984699288*x^32*z^25 + 1536969557324413773795938029637705038845844028537479244309175035566521106674315740819055664507420548*x^33*z^25 + 2817777521761533273238781029371418376717949643989812921584051819766105970113843029394128217662294620*x^34*z^25 + 4562115987614201922801649200900898560021611718450784878848722233960172223783991649458432144249497016*x^35*z^25 + 6462997649118743397570358965391834070889160716120942701012183190097996896518259885229696594347739092*x^36*z^25 + 7918627750271912528839742844267016418767342942317023698799216978988090502893316633815621107284300320*x^37*z^25 + 8265935984938992898167342449543446189754696799242901010963101802681851560983228312012822163260953192*x^38*z^25 + 7206200602233442673994360029052013074804606096608890921949455017693688092667318508053170043272279432*x^39*z^25 + 5104392093230060789358807494113233369103297786560221354032097123584997230717418427154319308065262320*x^40*z^25 + 2821940344276710977994787053794774231378589751528075516111097195770852260080328065388153159889562508*x^41*z^25 + 1142213948866836174125096050678258910603206973038615417392017344115536093701328750121461004320088172*x^42*z^25 + 301048637705948393011214474866000676540413509465645861826575982144475641286061979479637503515957952*x^43*z^25 + 38771415418503281645478226585601767464489503815202686425744819263153914146053199412328765592192372*x^44*z^25 + 171729569622116591732533445968922469916569948559215140198144682480*z^26 + 41844771879152400047207647459249040562573633891279658996183644787020*x*z^26 + 4979527854296351950910329332314282852116015485519795919524184191011520*x^2*z^26 + 385636768250402950596574958826501463492738593492946869667589427597585600*x^3*z^26 + 21852750201392370674746319084763913445879932086645168158603306662262308260*x^4*z^26 + 965891558902071922926708247062714380453679216912912611842024664274703077084*x^5*z^26 + 34664774836137000390817560292886883810952823593378993394097665703510087596436*x^6*z^26 + 1038292541520788044622716311275796407458775458058389191006666915547357635884028*x^7*z^26 + 26476459808778320701142572093649768020478764559545213234821061036017390143069820*x^8*z^26 + 583462725415655836005899290214817849205516361479300817981722469625768037779547656*x^9*z^26 + 11241381843008329931554185079644953463077457234653696180180871544500180429724123356*x^10*z^26 + 191103491331141025262738630604010278487991665949825624689029949838015803545796784004*x^11*z^26 + 2887786091226130012965598738829078037252378569353471219262877900049758451817154866448*x^12*z^26 + 39022135130158219418611991215319360458319018329098917443066378846561445655326647516080*x^13*z^26 + 473840212294778333546434509768160867626676279739043410313930284274579650376117543104208*x^14*z^26 + 5191182770251682649527144087402424436898854558287236910381510030485038084766352317122032*x^15*z^26 + 51479229138329185561110879198117498049956613964766382442988094878740547556156488917304912*x^16*z^26 + 463313062244962670960922235890977892159742776451476522795689856441755231704658738680798920*x^17*z^26 + 3792303213190249992258290571851890475231019983826214258517107844784004123268626502303967792*x^18*z^26 + 28275945010629057028096848784452024141288355320560626928083072187635681554804381554072858064*x^19*z^26 + 192276426072277587045941815852215554950047134064659355623185886715183946436115880298251233720*x^20*z^26 + 1193334644353341856270977047414999991597716572491349651996434005794472703389037968875347379464*x^21*z^26 + 6762229651335603770768281678793273338435809637746150782401117403139906331820728525012937362392*x^22*z^26 + 34987188196040733244306776995976001122830577397448695548377140230636662902210359496908097252488*x^23*z^26 + 165217277592414576052647965188357422668534563694761180188184824401381214177188551682667159995400*x^24*z^26 + 711535742164665337958879872493157984092867786157771314014800254211526888603713922824734068836672*x^25*z^26 + 2791409450030610901147026441236741830619958934473247309655057364266567747775011352899590055842056*x^26*z^26 + 9959473222948724358392681021620715199023784548825721699563780918532164057591694036490789139486904*x^27*z^26 + 32249722817167256302695507594098892369802802407336314413382426718200573481891589069571917869717968*x^28*z^26 + 94525049636524862452134453223492996249824505979579936784585349040854869570387457637580327626558064*x^29*z^26 + 249966242372144297242455740546680686600292614462925859372486050645069429404975856322748580594283664*x^30*z^26 + 594005801766057480771088204440475899772916481729726871641831738663969835336156770039426019874655792*x^31*z^26 + 1262262328752876141609106378169342063550508313966291164509281058797475695627143860836729011816138848*x^32*z^26 + 2384273287644412550906353214271067001600112203128068011557865212521680990155531861765729930272258444*x^33*z^26 + 3973788812740387995878815472068964855228942300673808303463546273704961636290843412820152706757222704*x^34*z^26 + 5790377984278224117116332865385623897711927928024233499528164799865179312267997161725572423398406224*x^35*z^26 + 7291587091316094068215413693926871059121733354975831527592952651648665167997154844263663869719289284*x^36*z^26 + 7817106881678498856384940933652116465545373631851761106253175922715717151210849423690290369823715836*x^37*z^26 + 6994253525699867999365373270827908471200831550244202459708425898494742725820310710552214565799617332*x^38*z^26 + 5081295296483456955818871861604012027317748048381972529773887307377067730845428213540197600711137116*x^39*z^26 + 2879400668038255763682725281721744418470106051077445090121280697266494290644061356576770133861832924*x^40*z^26 + 1193897837937167014499077136492004821907001922133017287147899731446390914454331436605348201623051032*x^41*z^26 + 322162908676093873557829496793537114697008382872095510569009860234339582565854617355944331682204668*x^42*z^26 + 42455577114736556831925923982515262181644321087996203184146440467069898257341451878586959616301284*x^43*z^26 + 1002815882998218242366218437429326685244781887260671735853489244368*z^27 + 238670180467309002272090666716871093600568140144382880949638953850284*x*z^27 + 27725519284304960262095139797711773483670057487038629101831867446918028*x^2*z^27 + 2094817012764158736432526901927582237252069048357523884232096307330992900*x^3*z^27 + 115738639955746688252916283035111024019580896221331088203798418074895332200*x^4*z^27 + 4984477427411814856869076413822584285006232147023133472497175379686595615628*x^5*z^27 + 174179794547015685994799432432592936321410780678516917074406067458454843043144*x^6*z^27 + 5076096869656541182862706580360088029336400444665500292417817488315577719282092*x^7*z^27 + 125844901560235592953030570705081442392284407952782919949917268397482494889755384*x^8*z^27 + 2694013077845123112814218642611385838103402153437901646398468195613249014942253192*x^9*z^27 + 50378044555703787840801768630601816922875080697601821470295566349849970224809264300*x^10*z^27 + 830474431463723372776435447603091387254234052979780753006959693848226429263413359760*x^11*z^27 + 12157222927260621508111385006550236971753057803582789809778956395829062065332743090464*x^12*z^27 + 158979069048792727748397531572636405616785339407032074719285418306915593582581766351344*x^13*z^27 + 1866111453358448014801449422637246763102136471573208310617908444110031246237560611795168*x^14*z^27 + 19739312262191583124383548024483750504927100061815320517313803471999686914997492948442096*x^15*z^27 + 188757173507207014377914565479971377141504324206413267839861024490020453331859065979594304*x^16*z^27 + 1635895503729127448173849560435651026792564635069169838123373709065649126987314896001619592*x^17*z^27 + 12875103501571836429888768609418241281677450985515373449531438673975854247052346252565817496*x^18*z^27 + 92158635590198407756910235534131547770904141780236474862136359781421954763941631659076086520*x^19*z^27 + 600567108596126292801119066880653528856178407435399806875622784626823410193443961867982359216*x^20*z^27 + 3565271406586527490672079967455353381489085461729090384865246809897367761742758920648063676968*x^21*z^27 + 19284877153808944452362678317294424229136526124801746093390811757451088137280109625028149501232*x^22*z^27 + 95026930902826680305502388983140197803673582969701728921875229645788510068256658786945803908456*x^23*z^27 + 426301370577958571892708929377821219698053818133828420194267565738648961303262945456017896508880*x^24*z^27 + 1739309591958071332709470722666007348334376857818901234941616000596802369098485184119136869198912*x^25*z^27 + 6444365026613877138236555764464808793873193554929742163224132189875163556548656739771343132288312*x^26*z^27 + 21640336879493509223004597048621583893757623424400052181045709500353244078897294079001984205497168*x^27*z^27 + 65693879812748285090090560292432916891457545642938992162573973465378824377531276390295108353426336*x^28*z^27 + 179714291901540793043182392599083367425733606773613589078879588929388271458244684762762341431872176*x^29*z^27 + 441298427891559184118051911027504045910705346127117105819979243103045075497710306698340873277006304*x^30*z^27 + 968009454729887977616644529794077321699247124137815860974510910452033007388696460084289828048394672*x^31*z^27 + 1885601750359240495218112126600371738991514255180597034516719263247404464674527512787340002396166064*x^32*z^27 + 3237901995566146054435022931964157201637070980846142664531698348117767743061878112579741564672024684*x^33*z^27 + 4856852993349909011080994596207984088725252731487827915480792692063579881923949865631643185330264924*x^34*z^27 + 6290781019958932944856779724615430905937958798194996135834647521795433215416217190124713441366470180*x^35*z^27 + 6931508716431791462970282083679517100502853690518974616447126914038327282624418231517873309754400040*x^36*z^27 + 6369494496189351848855150046215452013965196409889071556600859282204644947339980387031859381422371244*x^37*z^27 + 4749184492790050550487780913690566797282315076736305810038434586727261960864376639204780330908066504*x^38*z^27 + 2760209790643932440399760485250350461123952605066163658167043855128386237087355320184709360016441164*x^39*z^27 + 1173089161013841015916506785943801771060863850470891396801855894008690402510750895971056965326215288*x^40*z^27 + 324268548568697783924302015315295522600093938119205196823206445783912683916335948055090846323364504*x^41*z^27 + 43750518482474074574797916044169079496947449591407025883358666011112588309967158651914726851057308*x^42*z^27 + 5515487372506373589013883960242098111449557858765097704246560754008*z^28 + 1281431563449509604761459452694467070362424908221844825928835218298492*x*z^28 + 145228910552140027348341551428038374271574413250474782818767248667221720*x^2*z^28 + 10698529743962312911270407439762081565813216995051851617476406039762523900*x^3*z^28 + 575937517873656449921279694579351025696147599351949955420037435305285964420*x^4*z^28 + 24150979916206218821211937044010105242227301973720375840219362350507478198792*x^5*z^28 + 821133317150453462401714499729070237422178089219270788951246826181134409665328*x^6*z^28 + 23265443985925574751364943881411291672515186193112122626834236789842367466575460*x^7*z^28 + 560309442661067672793136373243391237103507572282136051800637750160880906817291212*x^8*z^28 + 11641985086402090629989672498530595678132001745754389372876460730968261245371727932*x^9*z^28 + 211107996233425065543553677043367898164052675550554624837021877956659158631269146912*x^10*z^28 + 3371330727727733098773591520050292362426407885217719911566648528599473324112752359024*x^11*z^28 + 47760518642809560562827856192763535407956925302325720810675760407857785995443866506064*x^12*z^28 + 603741940792438952055123493314224176474464387059837152260470070507900090166958358032736*x^13*z^28 + 6842408662314308526817772302386595072396206645036235248618186721047229913252652780883200*x^14*z^28 + 69792568355605950583823908496641459301220207083062157945003652263715575461332687463196496*x^15*z^28 + 642673233607871470350568427259045220675890509193230169782141934495163617381404867544231936*x^16*z^28 + 5355610280065595671330746368926518578048821237919178617281073409197050113610740194939135352*x^17*z^28 + 40464611004940056256328233302165944657905517756028026501127396542272288858087190819428997520*x^18*z^28 + 277573033384764247644380647247837515275008960454299597198310403309908847152415359176656160520*x^19*z^28 + 1730205241431697136471636678705585529783651799831768272052786519110960683774094177970080051768*x^20*z^28 + 9804496368112950532140152542306033769611125619454829456420237455568766044944820765520648111920*x^21*z^28 + 50508011593309137898531287948520579064813988135646247331243794849217281301577641387121900609632*x^22*z^28 + 236436054270128291683547989977479449973738230774700485036860957573006280532886858573858955304568*x^23*z^28 + 1004853230648045257156048337193927038806362250400592361755978297079084822911447471178996767483912*x^24*z^28 + 3872034448763799780517457030937680474162226588552687159958488719731749844244791533031213252556760*x^25*z^28 + 13502479103381464237809426427139851617989341375963265567677127449235966078296839082355539881550368*x^26*z^28 + 42507804584719431861697452020251534636796495390047909980603174737980119204646943828427852517133232*x^27*z^28 + 120438779656704642734756963291576894035436991322755925350874016201633670656108823133946681107578000*x^28*z^28 + 305942187403814518255338260654281828475994284847397268714296868939324635457724374511481858028521824*x^29*z^28 + 693468958115317781929008414015797237686238563351677921928025951217128528362973333600529671191367040*x^30*z^28 + 1394394571694197646093615942722584184129227889946885767613759135306546622892415209209890039448284304*x^31*z^28 + 2469240387375221046755497907070877444260136914694144831199718221866496772305876995617859138753139976*x^32*z^28 + 3816098780489504305306546748419375570928681501647882088915243772147438676582713515243738296442858124*x^33*z^28 + 5088131707317904927683663276546755577807696814264084683198081882354028695516348971775517405181352024*x^34*z^28 + 5766549268292986114124890365422523175248185445110014968048635869271586422784043421152428492621904860*x^35*z^28 + 5446185420062953021903029635841125287965165862494202908613615721885575350155893557120499389092625252*x^36*z^28 + 4170502348679917490468121020846531882185421797748770780312361298358453561353444242376870167027971080*x^37*z^28 + 2487668067607514885002146629991278784993387361142347049416906997821297002034740891101289245394216432*x^38*z^28 + 1084368132055168935989609889392293126828866277874645197955794071316922865562491854239726449879292740*x^39*z^28 + 307237637409722113885545734367089212361807002805632204172641484792434889224840894530886346389566924*x^40*z^28 + 42463738492698184205979808037793477807097755454653662433681145084875860128563527696080471678533996*x^41*z^28 + 28591779298263468707761117637519340740728708866296398376886129790968*z^29 + 6480803309274991538230449497070586633634132870709175467588207409469220*x*z^29 + 716128765852669917450855927423680724917423543924704175462298899447737620*x^2*z^29 + 51402131412256703447089524152452370565391309597095104160266944485422820600*x^3*z^29 + 2694328388216532157122800369383771874918869013222034280378676796400815433140*x^4*z^29 + 109928598239275771078429177226681154475080310299513234010810893340627011504300*x^5*z^29 + 3633750886240183309463257468102239377797488805749200243831968667473918857679644*x^6*z^29 + 100014667249853282062789672961740865428039403275440518821091045307068690572601976*x^7*z^29 + 2337842846965184697649189443036177169003085484894454315299533720488698717101572548*x^8*z^29 + 47103204027742287336744960555396061152832877323203113956478313651034112329542344592*x^9*z^29 + 827446284087337117094330792444031520213034658848765726796253664987007142394911161552*x^10*z^29 + 12787806208622455556418806050639086022259244113707178168608063737325497788281033292256*x^11*z^29 + 175121901690301880701754381323595749294208862968183583656487169706727594127863675042000*x^12*z^29 + 2137385261655991574119432777501657253718384354593349606624968055662188363879993704490608*x^13*z^29 + 23358567502383334614187660520101102258565001988088754171636837352920003501334516445507760*x^14*z^29 + 229433040801187406031410073281274688360176800946171072570008884407877652493318434121993312*x^15*z^29 + 2031438382093846791423117967548127161623999425365443361894511669682899081397161679191618656*x^16*z^29 + 16251507056750774023531266515382100844164249982731733511464114856094482778447805599330074936*x^17*z^29 + 117672949244250974790595473245277427326687967709392169762547465979043939041643426294155152600*x^18*z^29 + 772099702058769546986815747358136313749747667919643827354300241170018157812122663292277550608*x^19*z^29 + 4593993227249678843482539096772266610820135230769497434279509244232347914834440973089737379608*x^20*z^29 + 24792979321664933153504318522553482340906739743897863907192048701167377594754542207005194753512*x^21*z^29 + 121335338195420814366787860301710640845667486904800274980406177242985119806543483605670908771208*x^22*z^29 + 538095847649257496260458370873061834337090703111353085092833571175212280483037338170232256038800*x^23*z^29 + 2159856944036602995179853560625755577145695544904578887125796466197008989271431296067501697837784*x^24*z^29 + 7833081183706084708356572377705768355917277654137016091744490408412774186578808771226000584592720*x^25*z^29 + 25608150023654479267353034555546600737648589320841698554065694530279476011220673618311594832722576*x^26*z^29 + 75243700069503290301427385054663200344150036030247453922948308836656582642637741467402494425016416*x^27*z^29 + 197962591849527783034448435579574548038643550875116004971226869401366418507394885171925708469592976*x^28*z^29 + 464188146405784627211837471730015401104264406707620059223528512026669616214398649938468149684763952*x^29*z^29 + 964479815309788928127937908933885316457420391901286897764633167570919723041018979837659966159349104*x^30*z^29 + 1763027619383598714668736215216994634544935282217853983181338137215006168473082065144571022927207392*x^31*z^29 + 2809825268392385696787396895594065417702042407090411377168360734433558335788431205049559446082762056*x^32*z^29 + 3859961984861282567776839586869069288445332412129172509964912159371140337947010052086724675346687684*x^33*z^29 + 4503288982340543713567542652302364341053343215757105739778713696616559927466113806045586473051232948*x^34*z^29 + 4374623582843380881440054147475949724757158964478292990996573227000728952647307738942827399438582456*x^35*z^29 + 3442990782781562496559618937129604893444192149477089879618368606432207466111969930552067563993590484*x^36*z^29 + 2109219578661455543767020454161624883762473035763855715050425761971016518274565336179941955180876236*x^37*z^29 + 943598232573888993795066991828853417930357207915726758659096405198853055938205457408081311652007740*x^38*z^29 + 274208033394300015481270155138980380049356251803338494228757541747966433705654703506893503883208120*x^39*z^29 + 38846138052555165554825933987138622306732769244594077172507588153035816576964797626151944017812932*x^40*z^29 + 139782032024020978155077713376171706900922105573636229896835514999504*z^30 + 30891829120482520789278878844893417729202267645388325496903698048911404*x*z^30 + 3326020267724011048876536843854066694724232284749321558591450148117687104*x^2*z^30 + 232451860942943560930336378421220520428456296331207912376353631955454025824*x^3*z^30 + 11855044908146298033677473007165570603953860112795416920967357251223305252004*x^4*z^30 + 470250114689381044428464171673417136822703533760061184322120518325088083127648*x^5*z^30 + 15100253682819182414538926185777954981247831700444450933655159075364514599559900*x^6*z^30 + 403392491241029422644302562898092530786234772608301843582423768388920366291071628*x^7*z^30 + 9143563134796864326314037714472954014634745226525688566015054437902903221573788640*x^8*z^30 + 178468806371778113602855855830217330653608971810029671707769452344921863285492903184*x^9*z^30 + 3033969708320225472021461582735487321858488777421464346923939324531889355458501411936*x^10*z^30 + 45325668672784005384872481422815450272559356262849250286077527248511399231764022526304*x^11*z^30 + 599306063562366190128760698768092630724640422715612699451911941295888261159067866319664*x^12*z^30 + 7053371363464771523285830848497185371658581963038823823046910653758999335644856856562208*x^13*z^30 + 74228336729795924247305343319456210422624770254518805239417012491374815164916135977008080*x^14*z^30 + 701045402448072617747909182277976283139198382157229091015996684372863375187637477478615568*x^15*z^30 + 5958885920808617096694566266442432155917664489701887520868756929523652126822920879573680960*x^16*z^30 + 45684792059532731193206256353507458916927388299506126931384809188409661571678970081232624712*x^17*z^30 + 316409485745652614856067381175474337229057808828506665181041282692855534636446278540942813600*x^18*z^30 + 1981722568617508496755925447487291015458531882624205117573248310484196803888882401995869599456*x^19*z^30 + 11229761222165881275166923292921273123949490908548252169742567035069719066372540497069467092248*x^20*z^30 + 57574807535866344969125458121229864244621128704663619200657494041681755633403280877349587312544*x^21*z^30 + 266937744029925762357441813082235047281742435302940643239651140034765225163408625817555335493608*x^22*z^30 + 1118043594560123970023801177734106677766039797533700272707771092311967717502986245710428837232904*x^23*z^30 + 4223720246116023864768928451872785649693141634815220803622246969970988423836649791427593582424992*x^24*z^30 + 14360648836794466623297203519007378899313905059417897505732094703221960784724413682677881168885648*x^25*z^30 + 43818390040475521993747973127365886346684036141129557873244731101642348723194455039040352961907104*x^26*z^30 + 119553878999321998897411189805414820698453726713987059597627527608552771047181794118640160202985376*x^27*z^30 + 290345134712635568814652362654299735584635744982006690784598619345129535273400429418686161694803376*x^28*z^30 + 624075174612229935099882195224128240746351413718611908723936887115612310164813574959047740505889248*x^29*z^30 + 1178808663156437844304073457527948267188490656061032340533470965700547214918205063143215612836262224*x^30*z^30 + 1939330381321599889625367462318352616129697197378027507821062525587556983293871373209163418187193744*x^31*z^30 + 2747384706872782539730270751355124020063166487711503890061504994339185349755900671416408018238445680*x^32*z^30 + 3302411920383798463997391934943863567053813672537261465829073441861226843914449835912095038925008108*x^33*z^30 + 3302411920379362890239178969460251669958066454613181240245431443234555052249341582367123533701803808*x^34*z^30 + 2673381078408044612425866362095972075236400315973552244492242420044128019598208244592810057265988032*x^35*z^30 + 1683239938273896147560814565071803487423192740372034102681788306627582229036568833910282435316508516*x^36*z^30 + 773380512168560417038329766453428392809667770596403201706560698228438228010816773947206062307285248*x^37*z^30 + 230657345731670584723314830911995183606929440432444355217799518704131155229575443141623980972008988*x^38*z^30 + 33514315202462291738503626118018526105173770754905896022753836982669278722028365517306975182191308*x^39*z^30 + 644800987853345656852423202425957932862512860669154929870486979554088*z^31 + 138847145910109616443153557242596621770012331045942001533441755002426436*x*z^31 + 14555809129039907810795211520723254425133438558753849591178487242041441924*x^2*z^31 + 989795020804247908427200494752963075399416848819581025716423282520056708412*x^3*z^31 + 49077336447656088094005941107782976738878610568131689822581389165429696629240*x^4*z^31 + 1891113364451936354413814929473495563015205579746672149912413286029082072413888*x^5*z^31 + 58939699858745238402483291764672139018655701557319829434400388111181231174291060*x^6*z^31 + 1526818891578915494079149284459239886643096040031012967688747993994937367385971552*x^7*z^31 + 33526398160921795544580682460827329185921276980099770059549402907682391844243513504*x^8*z^31 + 633276409706303299831233084346096229279035475175068770126713432212115979988706125616*x^9*z^31 + 10406842332840311439895772721937121936584868413826981903166103724744554332790213631184*x^10*z^31 + 150110816679757440533583950402438441922921594328405763751316525057869971632892640923472*x^11*z^31 + 1913912912666909418706370675039106342271433229257890908783204938071767548036519477377632*x^12*z^31 + 21691013010224980640376451981242001423336462542923735323709343110823134727601222307519712*x^13*z^31 + 219492393555848076454568459244447039725849532648681657372521996855153401577727212274536016*x^14*z^31 + 1990064368239689389403238622239358453119921451832076722740541491155250030431804136040828448*x^15*z^31 + 16210732666285804556853346096335989953669561106773211455170671692971443175475759601417654448*x^16*z^31 + 118878706219429235114187397810011915661843044703679783873682883662528201696003348140474708568*x^17*z^31 + 785920335561782194853572460931139486578957747640155559865906600469290208434355360998491229880*x^18*z^31 + 4687945861245718273033193338966903674972125263353639401308839893643086071947733654478044977960*x^19*z^31 + 25236775219706117367553497208685741923253309767348614664448174793418248705145943155245821197200*x^20*z^31 + 122578622495715418486747502699951982817492917923061869791073238992451432260129460023931272077728*x^21*z^31 + 536745786382753932862749583225657294605262575753867377749814442803167719506053744605785628984984*x^22*z^31 + 2115867447769695986683874694130553841035166014572144302295018414459004855773660041290474250211488*x^23*z^31 + 7493697210851006378057581262985779231773541133110817148645361812590775024533675739855542848065056*x^24*z^31 + 23779999149100566408564346373367367943889364761247390446656899751624832626012236247949026349786288*x^25*z^31 + 67376664255784579251619825233032439740955846278656940250249230950551763694845708014393944439969552*x^26*z^31 + 169689376644198675398353531605512219073653873407018900906247310104622488809168554101376815770765008*x^27*z^31 + 377760874196022085190327440659481442135834360880086006759771151822709170975412997308065537796622304*x^28*z^31 + 738153432337016609312015884746075799832578727832934663089655841463002858773025755772591587734721056*x^29*z^31 + 1254860834972954439370340746439292953489911104221129466538946169456712011402359954712187314957331728*x^30*z^31 + 1835065307057812279263239198348202245548637784566959272378263236836573511956640359448052071019644896*x^31*z^31 + 2274716370206156374952067185118388881736465104432931569292748649648818439773314279013945119494270312*x^32*z^31 + 2343647169302504689920749205003520170948103484275264380255420705257042392945388728378132534044934020*x^33*z^31 + 1953039307758353255717794056202229775580052117849978757629870434335290050989077507340686332420339428*x^34*z^31 + 1264825456444695249930369839047228175820244229695647918186462119601265273076436725160779817480130428*x^35*z^31 + 597278687753355088415969631868514196523096985621843852804135305517305559368866053981807487784640568*x^36*z^31 + 182950228685695168646674548798475068788362800457690387573488221840755068774939581941580039720494752*x^37*z^31 + 27282051650707541095559870685354358832596509523312561319570677418424616407973795630334618059536276*x^38*z^31 + 2807570965677336523212612405078044175683986059574916475602091114465888*z^32 + 588654045573712177108989086156575453893882840284083827313124689114949604*x*z^32 + 60042712661483206903642187329722754006479291836676364577352636179765940888*x^2*z^32 + 3969490447962808689865519094548191514123075451573142835967190738221230530300*x^3*z^32 + 191197123244556566773021119182599677112173374625363177921302410184807908352520*x^4*z^32 + 7150772409339189969500183566652489291311366306580133524942581656427759480701732*x^5*z^32 + 216112232815423388370648327284795224661571816798709177975611368986556241531093168*x^6*z^32 + 5423387937796722117462051043305800774063985776067269147794461757280300209698444888*x^7*z^32 + 115246993678172087809603113017024136341346221530228917867587061511194455136418687200*x^8*z^32 + 2104324736419943047917111714856466690360237530201877689241037872499523381086157056696*x^9*z^32 + 33388619151196210708705668434046012657709247400258451644993290986678649616061106445168*x^10*z^32 + 464405339103001297351524612576025698374744375356123034297222379319480152093795501082728*x^11*z^32 + 5701865552320176820386545471088899325879168699221638854418613215897201179118785331485024*x^12*z^32 + 62135714352207043072182914562434959629820623522505960345374373770459180146297746539773208*x^13*z^32 + 603604082278582561376974483425242937694173758199912825862414345204149373138079968742755248*x^14*z^32 + 5244648803798350580947590667024107693881294142022961550585526612302965707441610035310361144*x^15*z^32 + 40864555262928811583557034348873853667078671320144277137632966717689124862749618420845792864*x^16*z^32 + 286051886840501687725301648258318387514445685432036366889668095428813492692615171082877338432*x^17*z^32 + 1801067435662417957590469999704131251448086247302939907141963504899386046699177540230717603936*x^18*z^32 + 10206048802087035744586628897865542721095876052831990727718977461522648122927260761193167140832*x^19*z^32 + 52050848890643880186333030625078499891555052098577740448392120228176807194079024133755909650288*x^20*z^32 + 238772941736445780889869821561976826727556328560153052114355167200648635027490012301754206755360*x^21*z^32 + 984033941701715744232016950698554628288150689112942110952863814611765588675274352028833651420048*x^22*z^32 + 3636647175854170006751774032907083334866643026702684451182067213492033388010895829428255560135944*x^23*z^32 + 12021139275740172660672921197802211692019425053098276230991306306814877458005686359171282292229920*x^24*z^32 + 35422290399180947848892290477174880178141314584861175943918136924553082267638017055457253689539400*x^25*z^32 + 92642913351705254020545555513359837042412929935423376554359793010728684444937533351660480011301776*x^26*z^32 + 213879318478626391059624959941861036726445683900397490777177207544440606669529910907257346075587736*x^27*z^32 + 432851001682919384549551872711963406582381669672143519145322434463284724221533620809437653530224864*x^28*z^32 + 761220727097653091900843175944740460182851997138651604551636721018572622755529164909071922338572136*x^29*z^32 + 1150289098725241584280547556574327170037231982223804626135812142753855806438667244311922039737277456*x^30*z^32 + 1471875298367888985685474522066720074378201237124105133057482107396641294168138975049704717167472232*x^31*z^32 + 1563867504517659136371529588736667705971407316358457920211894829841948815878751825226239371626811200*x^32*z^32 + 1342714524080050385110629391028454465263050413736926229408827293859297799865523319698563138442570972*x^33*z^32 + 895143016044537340938312992469369975946145451889525307822533095395435897329062122973150386813929992*x^34*z^32 + 434783750654779815545807126489690678245376018296039497320539795704064196003161512404150439472429092*x^35*z^32 + 136876365951027628031584916941073207477974752735743125558339552084909174164470630802914985040088136*x^36*z^32 + 20963047030767447244478362088918650240795645507619134617117249616515766719332052294621006425014332*x^37*z^32 + 11542236177878506896113437401617659274370062236133491756144934242773696*z^33 + 2354616182884166202670030204548548568854388141534452008138840151216406024*x*z^33 + 233499438112622434987761312321164656295792668578482944026391161725618365890*x^2*z^33 + 14995852803374065787376529086888245826114967882542786517072083129583485934350*x^3*z^33 + 701056118562390482519809101384777455722749084448750267873981789197997954844760*x^4*z^33 + 25424968566504747920230416423947820330737305651764907210721646563124474311725176*x^5*z^33 + 744386579697575533453040244422857064234299752040938835031534342149043012253577248*x^6*z^33 + 18077959792654047824076078438275753524726222022979260525878915715301428412751325256*x^7*z^33 + 371351424074108771683853582252140352923572765523319474678233140394379114116135671024*x^8*z^33 + 6546788068862011514276047325660029487992256294593502070101577645942248065818296426328*x^9*z^33 + 100165857453588712884735424146295342988385545937765085113374160855806380261733293165224*x^10*z^33 + 1341615424075337113855637656877036397828171863549702409628793535761931028535847890937024*x^11*z^33 + 15838515423111611838579133421786329985420022196181720580187873429462545929822698597265232*x^12*z^33 + 165695238272552152104279381994474724797386656652957951588232958013383012427381539675459160*x^13*z^33 + 1542543765823044838392160641811223698339287588485151780353197895308893633047334612517324032*x^14*z^33 + 12820252631507080975979232533700551504475516614754082789667445152787331167770806263034486152*x^15*z^33 + 95350628946833913596009013288170398919702967435446573005332509990988692327570826752711641008*x^16*z^33 + 635670859645559347649152091284571207993766624373348525648145692567161459889947395558079601032*x^17*z^33 + 3802253475287327407101982263235115776226749816111853901418385982273171783134802704106023324604*x^18*z^33 + 20412097604174070885330338293328529874786878896955056394423273891884252080265163129127274323308*x^19*z^33 + 98318270126771790071969531329838865840015391786240536133221406577719319124705752603964384979584*x^20*z^33 + 424485229753681234972664395862151895991336926355089595293005495193520071474601748563192547388776*x^21*z^33 + 1640056569502860538400312983874490352283013917125344706357149727322799537858853823318722233033504*x^22*z^33 + 5657006717995362739687646287730757049686924775518685769103509265377052861296039969892872412196632*x^23*z^33 + 17363867842735792762547461773204403231706258619509435551708662933828732864193325502696595045343184*x^24*z^33 + 47229720532241578920124643788120764435727074684124664572670423869774209882013983005930019585259080*x^25*z^33 + 113230227429857691095607346589151591247775613785006184589993525843436441706393282169403508398795400*x^26*z^33 + 237643687198473814743763539911045514396454324783424604144329025603687947551635442665901573544325168*x^27*z^33 + 432851001682953371134591038625470797952793079783079938406754006336660570230063491115946607704525488*x^28*z^33 + 676640646308735935802885924886787848047815702519935665241995100640165141914082126210995481294421448*x^29*z^33 + 894669299008445695078467778836744421200226085831724990130338058151068092821640367491105717432335040*x^30*z^33 + 981250198913495714491328262474352954843353943101245808973008200651240111384750895626014749992974872*x^31*z^33 + 868815280285422780269989714592030733511517400658684852039211078846091962896795790696373611482007760*x^32*z^33 + 596762010703298515611438796024848620851311757598483601826213365526048174487193611846049524272990416*x^33*z^33 + 298381005359003178409480607651653452789112849409449760012159639652043627419436717575820340224460370*x^34*z^33 + 96618611255989197725748697145898140175513418818771210936583565598393896082705495033852368558605206*x^35*z^33 + 15208485103521693085792880348564303785791550537614111307752119230649718969159378224328114552202024*x^36*z^33 + 44811034644307810715111948995590516689038498956469841102270548388781720*z^34 + 8887521866440680953616539029478274197503136779414434309008665067523690540*x*z^34 + 856164606397765622531565205839564345247664710023820191341872790840651938980*x^2*z^34 + 53367593800968721189069606551079445892094918072795749747247112452954427143350*x^3*z^34 + 2419330918951861947574134300791634852352020541362842469462810372202867891125660*x^4*z^34 + 84999159619418242506741128928720463640976339398093561435031848231339810062698924*x^5*z^34 + 2408309522550364812280835876290837206615611680777478196435042930654366347728195452*x^6*z^34 + 56537933077021162440762883664749448194434560361376621262104918427373031995695830452*x^7*z^34 + 1121335672694319114578144827923507339403203801426004621817615053751041954859188373628*x^8*z^34 + 19062706435803677157559659017842527835112391946024679775158970329651720430699776706348*x^9*z^34 + 280857208154177042596327188701672133898024665312534624931659994398033877831961381818764*x^10*z^34 + 3617100408046229109799258182342093201055391534071393230173162858004082348464449335949916*x^11*z^34 + 40993804624524020222478967689771270269864052967668660952885769248672248159674856898861068*x^12*z^34 + 410989169440741091704835515372700453525043509595832416837022420845540528202034768007282108*x^13*z^34 + 3659760699305649054023214199599825083853338092913547188362228572064870735688291987014286508*x^14*z^34 + 29034101547824821543905338397037400804194154093478144426485610534115633647589781997073117380*x^15*z^34 + 205658219297092518600703529513097573787183751365414041582583245441427145059213592893399666332*x^16*z^34 + 1302502055548252694184922676077161112699745112464306501367572649318183931100258806210626448692*x^17*z^34 + 7380844981440098136050682538699777185385703422358633279378613482615915071708585829545097502372*x^18*z^34 + 37422178940985762021633643563102990971611913214653194035658533656857692094662580260202544695656*x^19*z^34 + 169647211199135381780771719723549254567676655857718737033448712405704885611699535231075508296148*x^20*z^34 + 686667283425072034831680171484038085967974637906498636585151830473595982441811123865589088035396*x^21*z^34 + 2476163840229799250103125876689339583514693707079720254048094826280404884524967579516985091437044*x^22*z^34 + 7930901575228812562058170532214161159657290637934264159217385270041699183218556930319888294131740*x^23*z^34 + 22470887796481436240313673165493852675180961780339531187965771658011762950759758169240710041830580*x^24*z^34 + 56027413572559895691542472465518547611096244717704863229876567170436827517657995650765923678852388*x^25*z^34 + 122111029581228224031226305440629390670506562062191752115358015788157611517617284407160216039089476*x^26*z^34 + 230654166986738504697941977620592013630281553940953991296277221318180483459118464519273619758026884*x^27*z^34 + 373440079883276500916931048420964531191739467660805921140601905785006386226046699291084488439390084*x^28*z^34 + 510797350645402212477514005510771658105435521136388094618591942439246181246900517943718946202637652*x^29*z^34 + 578903664064280192811002779228611407511178836213881900648016255028760638555966362233202460537600740*x^30*z^34 + 529105499413056124253985411223985424257132194411344545280826761021786801978643922155168939808473452*x^31*z^34 + 374783062087952859883440366833865166091122060548491247773059902060244163906179346116448663785846428*x^32*z^34 + 193070062286469245452553898335079910770108122904458422911225926992777996202386496617628774622488400*x^33*z^34 + 64356687426032638595240760899582852378927665719893175695686519441672998736204961682215695948264680*x^34*z^34 + 10419654157892861490761313674731036791921987463022462187642376744723147893797608294002684694525698*x^35*z^34 + 164307127030785745248116679626252560740744312619336796390302595791949370*z^35 + 31656506452842852780161822424045671357672170703430304353540547087533198150*x*z^35 + 2959883353765465433294836350515994268951638673613567535671673213097880244870*x^2*z^35 + 178908504931459631617447397733691950041759223376474053202874358290235662247180*x^3*z^35 + 7857065174918829896944469457044088380223328772704816241657645284924952445620760*x^4*z^35 + 267140215946974090816386681307248829877743750689733544040458708769018306750424764*x^5*z^35 + 7316673692321342252707832317194216460819700173502748500115110269655876017325894928*x^6*z^35 + 165844603692621198296744506899227382487591297793513893733069667169463548044877811340*x^7*z^35 + 3171778045621168845205249080270078528508056977149475214291857935864648771975240117680*x^8*z^35 + 51923181339428496094103926463439543711824710774447250069955852559878535143489410517012*x^9*z^35 + 735578402308563204887810071702764488883650034925785254222034196482849900030280452534936*x^10*z^35 + 9094423883087717246353878128551059345755622291868694415775607170758171514475117905791420*x^11*z^35 + 98775548285758046417161355635720721098010265393884895465371897690675156379114732837577272*x^12*z^35 + 947232180996757768711533327764740456917812145204579552725405071016666392054596385882696908*x^13*z^35 + 8051473538472434632784959768075414753704777764550009976323462088964821565531852552694923472*x^14*z^35 + 60833355624013989860133868572605741035779720359855383510967677115907040256396160717039491196*x^15*z^35 + 409357788886593964632018674503815333894234644589629000884605299413907874668860403912337167988*x^16*z^35 + 2456146733319565018229006832950021682453129800265925770466488268815983972350719998139006124032*x^17*z^35 + 13144933443136187313323445629485442988210723682248781573523711164154027732959977537703681769268*x^18*z^35 + 62726699939176223845290808415156246682491527171244496196797290246782072368652573528976769103140*x^19*z^35 + 266588474741499017989735739790068765623036022595521585975022437963885573391359609705684720984136*x^20*z^35 + 1007112015690107402575799077617477081226464998704515000729055620194761898125925795565414383040372*x^21*z^35 + 3372299325265376871431397201510654658105944572721447819544438368599553925658736337012102608339120*x^22*z^35 + 9970276266001872854824724891492613064603935687072913475510706936643271627170579337201437390989348*x^23*z^35 + 25895023079755696124662310844191831636711360172226241197927227082331897783120299449958376425740960*x^24*z^35 + 58695385647446694339249276835402002732092912703639173625725487958439937524481256723594974558533484*x^25*z^35 + 115133256462285057226348705119642310739933376544915296567748110462434496446308048876584141315152568*x^26*z^35 + 193310158998480373496858642284961922525868051155917067869726889014673726454845714070736930116084500*x^27*z^35 + 273856058581172002946964370435020043635287915118123183317495063742630382386118921513410483556770408*x^28*z^35 + 321072620404933199825896840271964176609665709672394816595298754721751514403157748424308351741718788*x^29*z^35 + 303235252605440126147605583600626269581369004162822243695095156927388748387770022758190413796952176*x^30*z^35 + 221720399754435269586533121831965269060832136566063223955188902601698092865438862311248491024722388*x^31*z^35 + 117788962366063366074435199820171264279650730055996185008814287298089241180268748801923148544760834*x^32*z^35 + 40452774955544284074574013581532263920353140684358114722530966817284780219588291685768295547566394*x^33*z^35 + 6742129159776894719183740459561393348969695727421223637015256254900434209118798463294911968111094*x^34*z^35 + 568989494506740997102771851511849594279095145540738981218159264493685958*z^36 + 106401035597661372265879617208012635490075966351696271760524403874330765776*x*z^36 + 9647027226698345230924133538621165713323872745053339390023877756440118726024*x^2*z^36 + 564887038715425573975446967089189155352588703389022462294937177917300685682132*x^3*z^36 + 24007699145623202944013116540081694954139174728647940401112440734723919869746940*x^4*z^36 + 789053045250130867600625017977078227125414310106497769305814594078248594644688496*x^5*z^36 + 20866069418848207007957446301280640109145672101278859275750914189272499473774085264*x^6*z^36 + 456072660154698912203188256170506708962857190228825793648479446839879853217003248212*x^7*z^36 + 8399338157849151009647928977157703662496342280952570110809608863023975601475300894540*x^8*z^36 + 132211804336508904158868287877489950640042765143959006500488704346445206656551948475344*x^9*z^36 + 1798080538976519808492559251564661446486217184535912530973033811447264201358674595622072*x^10*z^36 + 21304530022418550976655373046984997489018353631884021885800396130026131603681739364406148*x^11*z^36 + 221330395232903886885197049605768070444575686811190494475731072801526755604487709037070140*x^12*z^36 + 2026024387131959085286745791624404061805319606119348728342535440489806949435879996604160144*x^13*z^36 + 16401149800592061933584106051937331120500084665236010738229685843437788494436737462063991264*x^14*z^36 + 117723808568693910901798900477553701108274177510501749876251011085810664466796581201754637572*x^15*z^36 + 750489279625424508435771824534014448059896154828787001062915685084666416136500971198585413960*x^16*z^36 + 4252772584544065783990696197989050045823471339507797765377246098190247386498158157642448461648*x^17*z^36 + 21421373018444219257925441744897772784241964401698339037146426001628257856495325547944257457272*x^18*z^36 + 95832458240408176670351881439814794613664600800417590104806483117162037957944196821506210136636*x^19*z^36 + 380135417686953419059263732668128461974242601210434423209190816808816653796809490829050530309332*x^20*z^36 + 1333490909663755095632682694534668029482985041038914070154035994105747812419501960947057259348496*x^21*z^36 + 4121699175324314109827128559514138791988419078188660332598234666376228980889897959102229596088208*x^22*z^36 + 11170402112835801677814338034993294025284828766144558338813095016677563390086920545259732057932476*x^23*z^36 + 26374560544193233626418686791438982535758192466270837798986938622333757949858871379827142554483636*x^24*z^36 + 53804103510156815918604596676622536297995974009492892278176550459144592838025057369147621396862256*x^25*z^36 + 93812283043371334838513260007744429987137558332033516662957315933619140768342996176975616441240136*x^26*z^36 + 137822983730223563851409353153042046885657528089070055345386734742057119505636052446782486594373484*x^27*z^36 + 167356480243918437746135267687820740193104094054393532209699640223994319670539204847273817946621428*x^28*z^36 + 163509204836506041716283103441967803054014131614424527203361869869326431693197311645307110550744304*x^29*z^36 + 123540288097455296207397743987638872752175618969648037779910621144249298389094362798220852935866624*x^30*z^36 + 67747899924540069067275734732657951371786664037296957758202585717430394169574964629413681854171884*x^31*z^36 + 23994047891266347767798495306983859221575498505495307357523855535095028720780306344472580061601266*x^32*z^36 + 4120190040792719170744634249155408571070521907476013582573101644944651049169137733031766274826208*x^33*z^36 + 1860749430242083755027606544395263807390535059314150075860297113124418056*z^37 + 337415896651216188719459533335190157866803670456801648828929759909147015708*x*z^37 + 29636362920256136102142263052847873580761943893570466310195430036914246464076*x^2*z^37 + 1679393898902265364307978028972500954735241653832073116860854297871586675445560*x^3*z^37 + 68995099345912329751035570083127941460697426752428418823723526343991795142724780*x^4*z^37 + 2189444485919237657865201412775105562625677183250279255332970065067254152683051212*x^5*z^37 + 55830834390933387519754540803078562179533341151183136772583381013433156454958681996*x^6*z^37 + 1175106133371420204366492564262088341000812431477392495864648653673314991472077151448*x^7*z^37 + 20809171111786061650137597912609303281917170167637907087327264723423596703468292838156*x^8*z^37 + 314449696800333992845844964102005761233366475456995882194528375558862969734658801519948*x^9*z^37 + 4098327714964376410683246670581782006955886927861733950629343781739015973957062662965116*x^10*z^37 + 46447714102929948332112420128226495757358528152231117108045208220807571873583520791933880*x^11*z^37 + 460606498187388895873920182544575741065212625769350422629790044272223794083370987558984668*x^12*z^37 + 4015543830351606975331283358749975233727251933948309929451778816777201918362664245745325756*x^13*z^37 + 30881444219132564361516407322395797356657097615071603656418336500684730672915761781917248764*x^14*z^37 + 209993820690101863028394688618177885884223928624531603325894118588829713731430863620686274328*x^15*z^37 + 1264337795404985386818411975356200571667189863738337937612974398229903616790677829203484560716*x^16*z^37 + 6743134908826605829873374620374054865110141348103818652412864110772193047956457391046205147732*x^17*z^37 + 31842581513903257926318837838830360810773876647130968453739787809813108247406663413679801103844*x^18*z^37 + 132956743865070408551026101918460797069483242024017814701276524186786610035073944772404902494440*x^19*z^37 + 489724006569669873683791078000225056642080075448796322468827039641990217865742297518557356439044*x^20*z^37 + 1585772973654185950603548737638814834442043647886867460736566423028297317063379930581905909754724*x^21*z^37 + 4493023425353463397013096542568421908039402238982233000140094669554266512023746591132367003876388*x^22*z^37 + 11069767859565698414704333406018528773983445025466327088358562847522234748082822895182978354695496*x^23*z^37 + 23523256701582450912114242594278825785961934861307776693102457405915367241491952787245293633771236*x^24*z^37 + 42655505485520827192162998209188607610840682990290428612099930717213008551435621021588196603109700*x^25*z^37 + 65076989138143087687422378212952752143851371518386584576689037414705176018867714408953752751050580*x^26*z^37 + 81948801137152648700129000361925403616180538880185281277362902301647279373056496136240444375510056*x^27*z^37 + 82924382102923936880824444326194150651564040316613711209055811147291509337092635635293107040097396*x^28*z^37 + 64814459574414897276542911432249931184498835642011050438911222826067862681061163625567377383420436*x^29*z^37 + 36728193760153209918605622424208321360014036469206081283643769141520939038264944192748470369503316*x^30*z^37 + 13427511696679878879548827540231610684475644802615826468259822403237493658054850601647923910051528*x^31*z^37 + 2377788529443645869329216803941528941302847358918506858824535160497708808714758471665629733561276*x^32*z^37 + 5745471931108404301022149481365849281326168168096217848409749166518391984*z^38 + 1009287901161493289906078845466994726391023198738143576391486099578523306516*x*z^38 + 85789471619118724238906096393183989972372592681618517351256902888110094330720*x^2*z^38 + 4699356611810484284335993541092203698446652161046114946268561590631854776311440*x^3*z^38 + 186407812268510714210182631369801102031697265305180660205417667215441677324796700*x^4*z^38 + 5704079055424061265169735728042724028457132512925761256538684284204301856883640968*x^5*z^38 + 140066830138673930720903025480067188631963909854471969659591762020909353310119994932*x^6*z^38 + 2834685848045293916760501368597354559452898762885162285194624378821036453991987038500*x^7*z^38 + 48189659416767314401232671432608343920867091158012631044736172830383263023078635239448*x^8*z^38 + 697857660442851458869738585767588890861161798095751386191375300270322706634978832872508*x^9*z^38 + 8699958833520805451021948288254051884900672990585599094662121679380029094414226111892952*x^10*z^38 + 94117736471726433649643833890321142122746614372738666120339115826418573875653770001149320*x^11*z^38 + 888889733344080861034627851372698618792132059382437488762710600630477170229806742778216660*x^12*z^38 + 7361830355644604005550501799974305528687171030676762500033321342316344785855032758846195680*x^13*z^38 + 53636192591124938054873932248097655390922923463684397400240784781747860190385699071796946588*x^14*z^38 + 344463547974113975057700268938592075446277336770604816688223129079762348782705878919818170188*x^15*z^38 + 1951960105186648367592657599942216538184877036109500586839855419424591090647848332881696675200*x^16*z^38 + 9759800525933221254706296356700480285664473857772975575291677380449500032818866000545756925644*x^17*z^38 + 43015417132817101353641584969746962899389142564932584896494385345386420985969334197242388141296*x^18*z^38 + 166779073444780039960084736388393945288665861413256016931620604265648800584587151978720200316672*x^19*z^38 + 567048849712270889587306099598473822727215073518661126141060678899271181686724502366627165934724*x^20*z^38 + 1683144998352208473592498457129922440861590955034434993244338678155286722609538035460829517511784*x^21*z^38 + 4335373480604588691674725866782129647691786946834498102106006404800836197026948693823357331429164*x^22*z^38 + 9613219456993736582103668528798405406725482149361864673077696831171378836849721969100335089967356*x^23*z^38 + 18158303418756496397208564919655889834699454539820950792911487632390664821961619619252226123032376*x^24*z^38 + 28811174757801980403902681967759572883237254948614770697938854114242246962120854256065124134297700*x^25*z^38 + 37676151606372128605781458068621302031369954054890645644289636505647642134250602902930400499986008*x^26*z^38 + 39536702302743081369755668247530955837326084455223522329158754796960291641698211168288518604741480*x^27*z^38 + 32005901864439386064473620659572573612422308218544197562863501230918759241305455854834796455026188*x^28*z^38 + 18762080403380817618360168185589489301659575842787887878416455853642205423474234907867277789742000*x^29*z^38 + 7087897040797188865185934529315885588074281780910283543118059107185834843810387925595622764388228*x^30*z^38 + 1295637093767684436910994652632346165387585054631611336527982872794332827526916997537234016274452*x^31*z^38 + 16745349780394471119917735274424720837669317505291224369275985867878338488*z^39 + 2846709465773800356109460970427828844028720680888990246929563829119318073500*x*z^39 + 233904627742980619425186384469121876130371548758014455543191116373839061957660*x^2*z^39 + 12370955866940148085447247800580502470150145415460159765554007143590051423184980*x^3*z^39 + 473189061915927031075155392745619826928603734629200835444614842537083092387251400*x^4*z^39 + 13943304357697187269278802784285453582923502304684728399599607735542419280717385640*x^5*z^39 + 329216908445980556198824083715756546021552388349501884492051354762963577688179245316*x^6*z^39 + 6396214221230748665605370655615277375048524921403268926622183580295991143412280767544*x^7*z^39 + 104204990020898851465046533035869889537398464264393423763409506462251943798568848040312*x^8*z^39 + 1443432083992958012017494939335887089497222339587850580635625004302174909690782875505268*x^9*z^39 + 17176841799516815916473198927248472184562484555613724246164126853580511077099989663219452*x^10*z^39 + 176973521570770882508042839369489852753360820928982053207410363667792192359621835886664316*x^11*z^39 + 1587845762982221586654931649487961181435045722880447615178944677226030877711743119560469512*x^12*z^39 + 12458482140321782116914522722574355495014959268212215801054187171308850805318540972795938064*x^13*z^39 + 85726222346500973497685953966259691201023281318709579718626517823209811541045311649266828356*x^14*z^39 + 518167388405510220391054651255349517864637794888780702584084955566514187422236568662939646288*x^15*z^39 + 2752764250904305957552177754555531526272317606583550014983683218990152500330800155652821031784*x^16*z^39 + 12846233170886662065016143376946880734420319576720492666988326528911770162386927631111963342020*x^17*z^39 + 52574398717888396759435575620153886903490609933970144999386366992028013634903797291229463322868*x^18*z^39 + 188161005937708800987730656997170862343058078785360401896139773034755366555534377459149715083788*x^19*z^39 + 586435135172496777534089524106851592987532012562049499162454220397410858635207173171936535024920*x^20*z^39 + 1582444015545119259413357799794381694427387192133808529514555972766199875065848872635492085755688*x^21*z^39 + 3668392945126050873345479179621164790201774667725291250686071617369369708033749463372856401090604*x^22*z^39 + 7230455659959735436488259624805673199694487921689748572289925778752866328649545335215334781624056*x^23*z^39 + 11950336438002193944596195909164392598747640464301042049396744154642545305597771637271454299840872*x^24*z^39 + 16252457555613674157269594018564398728021886323334694767270531582305931911491913596327017497485484*x^25*z^39 + 17711011438806512063935750364917176898737566511541574504991602405927914852835075654068813783438836*x^26*z^39 + 14868503430293100446289730037757378881624231309775210351101556163376937477910143955405264735444644*x^27*z^39 + 9027305653709302877290664882105747071502136055305204039912057597375296794860662973175921564240920*x^28*z^39 + 3527912554487720234378071590019087781180520000905577723136583172497207196375856174786521693336480*x^29*z^39 + 666383482577435827380390475288912804453412884867022161142833254178532033212200107290254192144524*x^30*z^39 + 46049711905111177705868625548782938874668250361532842775244251453033322944*z^40 + 7567502663692919813552958135588323605254973311018062442157338127406479011924*x*z^40 + 600355211139129072783884651535772681170013915620559699892819552034674424840504*x^2*z^40 + 30618115771214972784776028687497660145781165886503945448194823107293249571671324*x^3*z^40 + 1127767264221395161007831313942299725895641811459666899299803037437281995745654284*x^4*z^40 + 31953405819744548572714204859927934651873667979567413816544047053008952873819851268*x^5*z^40 + 724277198580249627469009904268799234279003270092627531077318790181015201808933365296*x^6*z^40 + 13485351649762011201225651141383890162969091163452569191027988699907734898197439162928*x^7*z^40 + 210146729875426932561477573435986749731890501366689193332521490047344611859143849143096*x^8*z^40 + 2778606761686467370883267163916522981582171355319683118044405345193342185597817373434972*x^9*z^40 + 31490876632444875676640960851244025294520867369169485378373632419930423640173708521953224*x^10*z^40 + 308228883402427687076072028011844471480857593306418164475012271751921946731119066528313356*x^11*z^40 + 2619945508920544185827542973498615379770711416331153387799990695095581768991278329438988084*x^12*z^40 + 19414468002001541156645428721821715417177408511763804312401237133151913824438078054842795932*x^13*z^40 + 125731792774862945370698370101799880884590823590613791466835617210004037888065238667290723232*x^14*z^40 + 712480159057580046254165227005160348224843516340147930792598792230152100497924833579791553088*x^15*z^40 + 3532714121993675052370798682358365535516083779715922652207484884968137935470236857413768671952*x^16*z^40 + 15308427861973284979336410242690951607052645755331557776498451475439056987076684842783087956396*x^17*z^40 + 57831838589672675414273246426406240669078887452816025870379891136525186716325017769579371515976*x^18*z^40 + 189729014320512641382450711604222314944390135348102839414686186630135814768002086326120711275636*x^19*z^40 + 537565540574777500399457230763638866089357823896489147008746957781209164993006602871347109921460*x^20*z^40 + 1305516312823895359091585467583071238299290859928067835038043024971519483498187709232883932102300*x^21*z^40 + 2690154826427691330962541406909414905325949367401589551130096348575804304008861984327948811169584*x^22*z^40 + 4639542381802844890962008320034176570276313959977359901545537635477688903337447346414422592968336*x^23*z^40 + 6572685040871848990033821598815650662192740497475861437437535359603888456894848019989925216720056*x^24*z^40 + 7449043046404980928752144656738440241863034089040744591794979990710072769965604527855536922116900*x^25*z^40 + 6494037527584131349921731046182975756284828423088343394862502452592053869231516557340024715591096*x^26*z^40 + 4088838443229211486658922030269847663244750638055722023840126352328953425096598503275691058416484*x^27*z^40 + 1655006036677921216373819436306054416187534033009822986385532053881467997971595098782690629964684*x^28*z^40 + 323391984142076527837694673877167062166117616436054817509888298471008757982790084885421653157444*x^29*z^40 + 119429740907794822840430708726086106507124854005460033828758388725212980136*z^41 + 18949518853450238686236549130977620531728375752106075598667517114960453044492*x*z^41 + 1449638192946559640057702181980476459830772573034803957963980496604669434139748*x^2*z^41 + 71193342360991726131479527290516939270155637865902557206290178028777057429292024*x^3*z^41 + 2521430875288852309903622043273583484657496053035092782678612921493365214897316380*x^4*z^41 + 68582919808173799485675253097434264444230095436448814702430247292640401695313548560*x^5*z^41 + 1489773424720723831355102303741850905546908610272175534853132364448776427746668290856*x^6*z^41 + 26532155278387869075710226913509050836656961643165125203326819390435726853676280960472*x^7*z^41 + 394665809765945149209429426374086722070874398285137317070167796203407375889476833233808*x^8*z^41 + 4969865752609448503832071743868132764272031328198008090053283743610346330197201276815484*x^9*z^41 + 53508887936425861734854287403871823166268220002614843667516618640938772137020033890401948*x^10*z^41 + 496173324501438126564745428304293669427159914020474707475196604523324908787750375611612032*x^11*z^41 + 3983169188358731913431795975717320393365277077029040023323595500738671063262420279933436628*x^12*z^41 + 27780051775220195766796655602041032087199747116640352259799043221285685606987948563966223104*x^13*z^41 + 168664600063839614646162509573617603825117500646990886511212129539071446325967510875906250032*x^14*z^41 + 892048329226501067833064109981542587836749424497100002679034726258798170491565164549142334128*x^15*z^41 + 4107139182480615016991004931278006213599998392132788699319094604509761158579916444012177146856*x^16*z^41 + 16428556729920502492491887667015219142445117389550904535290887814311849010429138190248068491716*x^17*z^41 + 56891483490662531983697767445107454154988574408225848927534622086850810775974809912935459129180*x^18*z^41 + 169676354270342282935979066011041583781588668658874462663119021323403720605872683574365911208184*x^19*z^41 + 432674703389543064466126706724338871878330049443375014399311328664244056120212465167884929712964*x^20*z^41 + 934027931127130300677323513237351919885417664108944627729435693194997165935678257854140537035248*x^21*z^41 + 1684080663694538529297807660241122024408756102648780277004549399596233570249900190933783188794664*x^22*z^41 + 2489510546346442199186650565049631025383492099759834972235344160482213657275632119142740845990648*x^23*z^41 + 2939005506118804533018006590051704960243525153918273722655611420856937608689251763824761678987872*x^24*z^41 + 2664698325475178294393754839353976878024193405161952826082427052423577007295514129422612054225588*x^25*z^41 + 1742302751364124657187282116353627465443116536257528393679540650571894661359128269649255874428964*x^26*z^41 + 731336957330900629570413553365512780294250415010466295913072470265718232572354883732665372277776*x^27*z^41 + 148008669914582990434394934870049785403554384224441090412719107833097230875376349642695131750988*x^28*z^41 + 291939366097456392763789855164595574518348390361675688203222158692118833744*z^42 + 44666723028838872148515552525136761831831135522521612052811428165358181232852*x*z^42 + 3290448596883479597823482178915759351376088503654839404305299340125886578071904*x^2*z^42 + 155382294833291378737348073741519744700807718103717061066186893833981551682327920*x^3*z^42 + 5282998024495496304899977715814036481134984307093707826473417073343208107601117180*x^4*z^42 + 137710148503519001936714062380371544753146338333251700271627655859930914806475128532*x^5*z^42 + 2861310863361004839624211341942725717489767274647495476983114129299963772299948432044*x^6*z^42 + 48642284677037077609748356789807678949261115950709373419487972281842890340012910305796*x^7*z^42 + 689099032925226184999118336057410931323626998743627514069693361702375414423701837106900*x^8*z^42 + 8243666208693370046922436028768699105660365481610981200871239637522249398323418898411504*x^9*z^42 + 84085395328696864779025945019012287575237843603110882471672635670358141958899670858295508*x^10*z^42 + 736384219696592250233762034722043755717761447011165732978015047625198757703978768851626396*x^11*z^42 + 5563791882152941200643747049175474171490720900207969017028750744275287128823778745453257432*x^12*z^42 + 36378639229456577812022387959573553866398071575083914601524360315689496582130260695855766184*x^13*z^42 + 206145622300277792620229343059907437283294497153341894418886578595957143202827890104479420088*x^14*z^42 + 1012404056185742615629910656462099082084007826009607217657062330823898215200414280593695942248*x^15*z^42 + 4302717238789592663469150654434215863368636716258548470757656236919629848120507694715793006072*x^16*z^42 + 15776629875564187101360183421279807639916539328539059736696370723107138933215022014220297252020*x^17*z^42 + 49667168126759079575538720976821373583619561217919830084327726287748030042751190226897203902856*x^18*z^42 + 133317135498295392819760358419108886313720716200993550640674579322479436340256633925137681697384*x^19*z^42 + 302185507128957453894107116824526482069722060489471106514570052714007028844699547903938260035180*x^20*z^42 + 570794846799615502131798184218535910921578664424172950876494446702656550170669847786105834238916*x^21*z^42 + 882137490514623872525884252276996251620295871606631072846161055876865122484560310835908790920156*x^22*z^42 + 1086691111481397506197958985546598307716534228231624545420923562541257670694522881089385236138708*x^23*z^42 + 1026319383065662084768354879956561291609473176457046290156101875075663422263864735008885747568548*x^24*z^42 + 697897180509679961345326564515457619621398697291348606177564714232304675503461726511443768911176*x^25*z^42 + 304211591478099607920920747537657568775737678932484906540661695554952616529379331508617287075588*x^26*z^42 + 63846877215545075418817722735355226406271452069762050127284992873002746677718146397329472152396*x^27*z^42 + 672139470201121866234511289383590995932897651493387223281881346739026666400*z^43 + 99028548799098085852907848594843624902650639986838844904159120860822923298660*x*z^43 + 7014522200704839002809808521913666388789206605936147807015339105616071968732420*x^2*z^43 + 317991673165100375060201826048068070434244813453507255475766526866837486207811900*x^3*z^43 + 10361228683539712182807396136562832649455712595566596872856070076826316912285083480*x^4*z^43 + 258339968511889130588677891619162928743056468333535053957926215586175648441515657636*x^5*z^43 + 5123742708800302647079331933558201961390412570809124184397288329003020922885350953960*x^6*z^43 + 82955834333027045063085496364214353539654931639601813602296044605103026632431897963684*x^7*z^43 + 1116447270397744381228349176012878593024070173754116717985147629224816475599261372703736*x^8*z^43 + 12653069064511768353359999766574033518155463308109933678670420365303314973179563787237472*x^9*z^43 + 121891231988082235148149827961059319874074415866948568392091025875101500795484974772928940*x^10*z^43 + 1004679245477791942897940373026192535904453533123671506034565982838782383439331728852465752*x^11*z^43 + 7116477988798744417982711176040955251694528288140197245196269125964918726495406919021794992*x^12*z^43 + 43428763111143838128778293768367006253004846875469308627511765133895562657756288887688678792*x^13*z^43 + 228518015418076107043823308524611294014695539163066497861091805717349732061764022571105394928*x^14*z^43 + 1035948336562349935763884034465658346368469326663634130010601206036444145509132590696946322632*x^15*z^43 + 4035882061188854410065044747713527084916461770341261905918847393266100760712359980791727813968*x^16*z^43 + 13452940203966752766439975134824281914666926199966824001962243142913738042188587700447758095332*x^17*z^43 + 38116663911241319732780154104338456120780404627056786696515218158122186353620392024773630309852*x^18*z^43 + 90945022665181479676654931366498623659145739871867356173345528496040951815503839749369559419052*x^19*z^43 + 180374294953622068395224477814990373684820056661816367877823254956392079377328211853873059786488*x^20*z^43 + 292034572779738255561740029609438610808316018909255098760601014123548816421438192554113483109780*x^21*z^43 + 376105131603273694037963103647637934931686242582490014530702769080405988930079043165695679371560*x^22*z^43 + 370654332615445204428933231812664680228658216708975235813787679463257134971480824669174309565524*x^23*z^43 + 262546818921446584526432275933043290024912922958873869315552291667444767940372847959057408615960*x^24*z^43 + 119021224579836661326697703600914986048390672978318762749491835362253890108746993490709524508568*x^25*z^43 + 25940523312069166721022123224011928771309979310430666446822926508129459215973107785585041290612*x^26*z^43 + 1456302190201893551405002117038597042481287234594823331278421398691820685368*z^44 + 206309476415151479933584442336160707998517350808702845308564485972061879766020*x*z^44 + 14029044403536195282624691410020903616912729135739414788276658746153255137214120*x^2*z^44 + 609484040214267535014195974533623392028844927343525697888814126133147298012238980*x^3*z^44 + 18995585919719252118008399618235238562742671126460428288516194177052939224096637340*x^4*z^44 + 452094944894248633746875669501259853623427181516809173229257345573421647613664898792*x^5*z^44 + 8539571181308075962801755330044517171961346959272606813832045042965559654230967339728*x^6*z^44 + 131346737693810309397799290376412565925126181633911175149880172272014346195398472690988*x^7*z^44 + 1674670905594791144528749499436534227171031161613985371268927763309975690639443449178692*x^8*z^44 + 17925181174713202450557622645962591211958057010832882050228312935130654535742411367112332*x^9*z^44 + 162521642650705445316131493903090176807500990378023263174265694557989915104686848772531120*x^10*z^44 + 1255849056846510082780999640924802686151691651093088816232880673922363086192836745419834152*x^11*z^44 + 8302557653597406596555443457885281994773368171995624390283929557313235223825386725014677816*x^12*z^44 + 47047826703704203254274908324819970423930341698698999530156665812376214151455571774018318128*x^13*z^44 + 228518015418115238001734982814186214122407784763045103759591171043294002567878449841065233408*x^14*z^44 + 949619308514290724578501533903893170910484946669225157449695102401878265978693176513453644120*x^15*z^44 + 3363235050993187883762227192918655209487675554328870619064021921009937933839084946531463285984*x^16*z^44 + 10089705152954879533379443298816437193829089652609007475683908546735943558727600212701096943836*x^17*z^44 + 25411109274163035795174996757829334123387117372290384125473916859900690763446695205734060997736*x^18*z^44 + 53051263221668296841015685357422626648528753247823531443989892259523312152066599247372525278868*x^19*z^44 + 90187147475202033625116001430297245299492252880925850495165819424544894693676887787389972393004*x^20*z^44 + 121681071994798729109239763688818094052832974795056961354374106477532893795468728079357765550568*x^21*z^44 + 125368377210165617976537457027141143274750876632433343417716918422358927017792885133782541498992*x^22*z^44 + 92663583148500135952193485636134480895104065194877507786005002660283758162186470614263522620220*x^23*z^44 + 43757803155964349310654476192209789893178237127786990334065800823202541217662365481900952893860*x^24*z^44 + 9918435388750579708431752122314002525165850110161541683065985945815014977444606989150029229204*x^25*z^44 + 2966541488282268091319867171249797439424196062622603752196401610080164948424*z^45 + 403449642761517591665824040985024029142772505562601012381984076510528601877884*x*z^45 + 26291468409945936831010350851429085689087447843299569628607305931856848971031244*x^2*z^45 + 1092556575705865449012856060381169983116365411416751577368754777246473171269207464*x^3*z^45 + 32503558130561984776473729331291177522632176663416694557091003798282099664308293164*x^4*z^45 + 736747317597291001571062697239779288026394538162529642355695150465753082081810737892*x^5*z^45 + 13220521310421481454597685121591027793716620987304760960288395684046541271807445585748*x^6*z^45 + 192641881950447034913868888115110616195992006660052091017981815093328460769046518221736*x^7*z^45 + 2319729328496377739330828657545731350724911930363270621222159045660110261382413554702876*x^8*z^45 + 23369125087015165158097570697069919508415896194176906814388035320450126564957774615735064*x^9*z^45 + 198637563240003067421217785474970267330429751552462496180107883227496271114663081335678712*x^10*z^45 + 1432598183365393663226992543152115804080477848839262736155654814484179401212910336605849488*x^11*z^45 + 8794561070114022138945861762673729946131175310405793927033245495467280419871612619052779128*x^12*z^45 + 46002319443644985653534877062437847384003222008084788013122833399979864669261822340646779272*x^13*z^45 + 204819850856291287221664861789695010450792438795934075292210251635857213065151922795233641256*x^14*z^45 + 773763881013571057402111995426940323263779230322840079660962652390827241288181267220038846672*x^15*z^45 + 2466372370723986103356775978936239806235502758497718886909275565008727973046577356350892824448*x^16*z^45 + 6576992988652600816132796234553194603074915028947603598958140273657730281977748575408982526636*x^17*z^45 + 14493743808164555195775964800456595578200864310232578060415627749838188742229686879166675842428*x^18*z^45 + 25936173130539129969853754650937148236349196068251734327147615384943086687865674188111320063688*x^19*z^45 + 36742911936958408973621374636675148557661360105246025520658329697387590735709678667941264416668*x^20*z^45 + 39659016054384053515669299660448614682853664459312483845225625164561894604647906044025762691156*x^21*z^45 + 30645603315452692043596564869263643541201492086881459282711324370450819650676804442272783703620*x^22*z^45 + 15100732069705579789071469338817988203530146034361280590803615396267971654545449574847385599880*x^23*z^45 + 3565450626168839469936732988898043324365489183013998597145186843242691858344895241046540075100*x^24*z^45 + 5675122839859648320880591054684998140382698616452600718787565026776152286384*z^46 + 739657679981965583776499986613655802996516538292106671233803996179279170765748*x*z^46 + 46105328632264085664807302836810464454428673433219972893779431561753922149559552*x^2*z^46 + 1828844703090849868267456131532554437092163335986868491679809167401946913179410176*x^3*z^46 + 51817266582461147790534005366468376035279406020700203108311707272087777700206316540*x^4*z^46 + 1115798473781261815663651446865916213533884529179705491489941885748679017222224168752*x^5*z^46 + 18968574053959622556495329198633964947259827460023956376093946960039026780269286983332*x^6*z^46 + 261043709601715804973545307045704518912098465497915118268145216249863802470446254026612*x^7*z^46 + 2958495375467644906413262716996301476969309883846096661554994355901964776180208359058832*x^8*z^46 + 27941345212861313377180203969208225538262634619088166988122503497627543651584592710125336*x^9*z^46 + 221668005354464388145067112590075655689488403760828190871638460965903782042786844333369296*x^10*z^46 + 1484503914651958395763021978107644242285560985643642224671018234538948301321023191254840592*x^11*z^46 + 8412188849660877778428652628900555964333674714221470460737354607121254369698000735891189960*x^12*z^46 + 40335367048545888837879267376157236698532804773623798765767054806783291753515145226550010576*x^13*z^46 + 163262199957672011778505482512912427582295502338411939319916871759164533354362477449129345144*x^14*z^46 + 555091479857967211932459388614359772916821002957256123229747039731351911836854968371573866072*x^15*z^46 + 1572759192932314398959601770241161092726454225811700707424026718149335683150905211458256691040*x^16*z^46 + 3669771450104615421373596486247557670280738979035110590442442063222734039696859767483886445780*x^17*z^46 + 6931790517181307300744270147414388342567536825210455487599097119093717059519781791907274617104*x^18*z^46 + 10336880595158196179028688386387844604269061813646874840530759148320233459311369600913115176016*x^19*z^46 + 11715131339827451825518612418553722247941639203221310323487099323284660426237955773768620123548*x^20*z^46 + 9483677752653534327461704366647712310156985502293653002355063910783129338400232974802500478560*x^21*z^46 + 4885530963996319680208442466263668294495074235505053299334539273461162821105272728189847723780*x^22*z^46 + 1203681539507725889433864827089833770798739493077520147969970922200120150531235509218596790740*x^23*z^46 + 10183021949864983919651668644044473666163146461454740458368878837070957882200*z^47 + 1269483390778899379202253602144737983477897880016567683153413546934640646839580*x*z^47 + 75534261799987498203980781392182006408065504352691850190013004883338137119241820*x^2*z^47 + 2853516557903093732465524487993599924776070245646054462958068041223381229034170820*x^3*z^47 + 76807154010267242649629974263008797098722607042976042987372884588197431752456836040*x^4*z^47 + 1566865941894593205952775989344454737128456054819042112573179561622446280943906012752*x^5*z^47 + 25156903177749778977898499663273113843037974023093826228652149217593185089105302042716*x^6*z^47 + 325841793543702718527735744742292394685021812991083386576483600787122265011501012100816*x^7*z^47 + 3462069056390177090575214125819037115263872558710269445561736638673770665598351847162224*x^8*z^47 + 30517497608212990462637543128043997561619161209704539125471037023638007666777745453304392*x^9*z^47 + 224812232380775083381314254490555257446326885001650847727907470956996470477503912330766072*x^10*z^47 + 1389748345621753846421311200370711464654435764605672936024127622911370441198815289375949752*x^11*z^47 + 7218970573131133103536354214216541918633987950040783309923354897827922638099112550900589584*x^12*z^47 + 31467307626138796952857290428934015602642082588583583324850797138242408767888228963774747504*x^13*z^47 + 114630906353990148289956148084889210153543122125393503550429186124282381141433753348963511384*x^14*z^47 + 346440072528405937177382840082202766458681048253313052289714700428451728698020225975184782864*x^15*z^47 + 858882679825461952277518673864376346115940651943189237111771780403420857555171118372316785592*x^16*z^47 + 1717765359687857689776520040644655585954093268536384268465255983132226348646605321771604143228*x^17*z^47 + 2703889917597376281362295717778015323557986552690357441935046043489633806273230112689124791084*x^18*z^47 + 3225693235757710320772281301503333634318158543538486535437527424440390341005797705136693070244*x^19*z^47 + 2741839250815965375522673998441581067623943642721691954424933524808890297198587133279948458920*x^20*z^47 + 1479722769671564782050943715844813990434364541655777282700868229788402300108483945930420422240*x^21*z^47 + 381140713614930456592215912909358837872141778936423277265876728094796335741893874534657609420*x^22*z^47 + 17113133910885622343884693667576951690276226503678569719542874256972707764064*z^48 + 2036462936585317600273750274366028902825384960682475726825587705164895794488836*x*z^48 + 115399566785911339271948052264452862792034188371853681181794853821931362393976440*x^2*z^48 + 4141562225167487324344598886943500445552825940563060718486816997961592074848433980*x^3*z^48 + 105609836782519879705088209414589239237438216779145003167683349435119090856917385060*x^4*z^48 + 2034749521622127783070719739305361581565179296230634706075394199156159948788126994844*x^5*z^48 + 30747326107292753565690612969813554188361313169446323785180323641026612982047535955696*x^6*z^48 + 373360388426235386362029375289120752121372315653581327971606221737552565636090167497320*x^7*z^48 + 3702490518687975382410359230125011430083315432658715027900109834778957855543281207147472*x^8*z^48 + 30305570541149654880066345794055968438503832426378911013301556589304783147429798208137552*x^9*z^48 + 206077879683556435366798935812204577583261643870138806053487023940353574898659901731031424*x^10*z^48 + 1167774651526254962664853972447182783838868754738661712710654044948851505474485426061904896*x^11*z^48 + 5514491410022594475455597872059606419627682647806147839774540083760123418311737138566028376*x^12*z^48 + 21633773993314865213164335012529532548453952327481664864700580001192751536392194994731765664*x^13*z^48 + 70052220548043238078534711923874417679473652544905736496269623824038194881764942183236545104*x^14*z^48 + 185249205463731893420291062323667044865069032360498732987805166243066945112641080109357214552*x^15*z^48 + 393654561566394831917940293302893248343806327040631029720938155371450627168037666877449234800*x^16*z^48 + 656090935994406684803549376755975998842947498880753201783375369231100823272583552585848064460*x^17*z^48 + 826188586402804667994571148010673172265971299604876044958982651707737312325081938125309241032*x^18*z^48 + 739221366595326659510948987531758615339493712992155085102489544548381258333504721299343539460*x^19*z^48 + 418892107422326189374974460047961091949808087181948961345207026878246719721993314613539970980*x^20*z^48 + 113034378746290428707143149557636732810648612642178452818392653264580714426992462724693051300*x^21*z^48 + 26892067084390348605148901259741900683654489714940980405842704673251562270296*z^49 + 3047767685647694107917095377507361048757106495567574465386678418280903960238500*x*z^49 + 164071492665523887032802627255046885232465034847360122219914568014057904866643240*x^2*z^49 + 5578430755753378294636508078769176947019334167359812676338669495058111377563147340*x^3*z^49 + 134347207310526811359901187155773884212888318073172003416086576818308065328062170900*x^4*z^49 + 2436162692915010446733326858541227648724125494783164847786306181603214598186027010376*x^5*z^49 + 34512304812655584446693281391878100084599727986270741495856809309837623739795962493104*x^6*z^49 + 391139454568673514116490419595235487404932541245663966745074305345866502045504117805576*x^7*z^49 + 3601742477274359094722357797434369434158990679756648866258465149358596938974619263311888*x^8*z^49 + 27213165385257415161221920760105169833251060256974063786182233905970723924496054339846672*x^9*z^49 + 169628730892562748309029460680098317991745839023151271272320822951731263122863001692917632*x^10*z^49 + 873844977374663296436191518319364495951326504723241814581998671653286103324579350356474592*x^11*z^49 + 3713841153637418780946562909179991305481150154404025635778278668918597242864461566002756136*x^12*z^49 + 12950830690271780948777591302482483078626296813768745801610942495935438443906262007716590584*x^13*z^49 + 36694020289120187979291964207709910995367259714987242573323344955575107716619793180472009808*x^14*z^49 + 83173112641715035638019508073402367856449730729975978351566474660096935131729836183057105272*x^15*z^49 + 147285720371032106530058113461595204498019103251347123680371954030649364540725992220546737784*x^16*z^49 + 196380960419496097664474663577814233743985135326049800090119944885313798311261350578684065036*x^17*z^49 + 185470906896164904414673689046086419101589531620673905947171699601868763735083694006932145240*x^18*z^49 + 110631769191819870131975997341039568448764895496172704036815325000798362464391156367874230100*x^19*z^49 + 31345667927030893805906728900385125359672464954433040142918005859183543865067708793745476580*x^20*z^49 + 39441700359659481033761764247305250210129697201449371577101349488962626281536*z^50 + 4246556274543086721750733953026062411686893090691544594846755764340036561303924*x*z^50 + 216574370116802752553689125433660777238617735796224223709310840201876819734066072*x^2*z^50 + 6954443674431404899288492744246473026826138958454628342889727657293032167362654212*x^3*z^50 + 157634056542909986348436697677517753568703962195630509380469928939559508546284723180*x^4*z^50 + 2679778962207396292079555757212779383397568426313723911592022796744331438240512553420*x^5*z^50 + 35432632939577004723193144255822313209834645282193958938959278494876809477035061064940*x^6*z^50 + 372886280013597946667960786986614954488675395399321732774580865227347419803383116290244*x^7*z^50 + 3169533380026177804441079049332791163573193080847300202613976628025187341116610399324412*x^8*z^50 + 21951953409548125164193256978144301628100960352021397433854512676449931232294143240439796*x^9*z^50 + 124394402659621577821941896239054917524326855564339386537422934709709451124326204231015468*x^10*z^50 + 576737684996631731108534882409628168582028449285500274202580327002688997111948024174901100*x^11*z^50 + 2178786810325408705654988792467860255822987878032757724046308346198913104498895774246619012*x^12*z^50 + 6648093086048003512799230190418801009881285802338825490970177050193650392278809791294322084*x^13*z^50 + 16145368927135466681676562514285896531721032683094480963202307697496470597504231855067592900*x^14*z^50 + 30496807976244843272157638185304340237664468960761026702327675167171183379731828726888073484*x^15*z^50 + 43203811239240699653352890605477556384447133687129577750304353699836476926251809145966291540*x^16*z^50 + 43203811250608259860909842160010916236799378029457892223037935112911805710668545059935338792*x^17*z^50 + 27202399763529536955082194002926765016216596697164439252042950173987227524474872008524172172*x^18*z^50 + 8112996327601388084052262210709524882516156650374805778619549593958175451862280636430716096*x^19*z^50 + 53877877955923548548901546566655031810127207543687391847676240298262345169148*z^51 + 5495543339895910480802415165207759868782638266567728694385408161347689076132096*x*z^51 + 264702009298438081552660433186783906184918621347012420242321423359833154437190432*x^2*z^51 + 7999882903788220865706346206800342770200246582624487132616271617134064053025425596*x^3*z^51 + 169997512112209288375851435605110172763905866725850847900597878159262889375533451960*x^4*z^51 + 2697293855780967506652249926713946050231464777683550766775258409835777319651999588508*x^5*z^51 + 33116774585791786956870612914568286703400856053977003164570566405533777026534454668032*x^6*z^51 + 321705810120278472807011467183035446437603107776965750612323979724532437729710982289996*x^7*z^51 + 2506624438012922008013864983298425246242604875607637872033647508486646312308064049629856*x^8*z^51 + 15782450161585286508522537975647056930581972711512548324998503340763204120269263840805804*x^9*z^51 + 80490495835910925271267371819505989025088880133064108054158766001830090872629609024895344*x^10*z^51 + 331718407081111144644401467057160235221275257147608383715789148191661658483106865041035380*x^11*z^51 + 1096513623132831120802432672435384793586213395867109482303985359846668729092119341011277608*x^12*z^51 + 2867804862899224543124278338336235829725585300568305428454467274567998105255903044251355412*x^13*z^51 + 5803890786201931335349804349554427998406917615963452437826418653759019453485193610188146336*x^14*z^51 + 8770323856329859289790565778854406533266727805896998191706305684340378205453269270538355076*x^15*z^51 + 9318469133732516300709746257288738027703548806012255001428920974981321875606775913326443396*x^16*z^51 + 6212312723961693144448893188678905309575389292107263971248278910530225237856375718911866020*x^17*z^51 + 1955728074588525242733614956400520959367931184531688034441502811229036798595343453680992464*x^18*z^51 + 68383452595648869536562841373788998464684647359053797112356400568433708124844*z^52 + 6587606732662063184672662665967743142022806346333526013599627827833585562687772*x*z^52 + 298638162647927931609037509714566611194140063267664291937822522342302108380544168*x^2*z^52 + 8461414643322969660322404387075970300089260654705735562535240076951145898065051492*x^3*z^52 + 167818056665928826100569050352962518626780950169453639437526538093983760178855582540*x^4*z^52 + 2472519370521258267601087848672634499171928943595025535196875322804176330567382958240*x^5*z^52 + 28021886175716769584864511391958437668060196205638043864442900456691415790692645256144*x^6*z^52 + 249528224690495095408376101781943037744179679205159478880237419224583891583354613350644*x^7*z^52 + 1767491590326843352338874406721351335907653406250110243904735917611244493180863476040396*x^8*z^52 + 10015785686488184323549140966602331829079109728202113251118758967575337113097096568033720*x^9*z^52 + 45404895077115816041157003624672973125301901158421483468134938026974481755684834431490344*x^10*z^52 + 163732803602739908792852730263094703909474302485409822999570340298629761049563981469485516*x^11*z^52 + 463909610120313021127331655062861177005367643173314598540127681806184445239674704105510548*x^12*z^52 + 1011085046088200063435979263772353116778234153106384822068620022876591727163680831160771104*x^13*z^52 + 1636994844554290668884754797435722840478801770793779375912135358569650309953894295648854880*x^14*z^52 + 1855260825722473675734890233195439746309104233981363671815873403213452492740581594849676892*x^15*z^52 + 1314143068263245803896339376988398658722866045410070752142624561963882232722186989974076328*x^16*z^52 + 438047699958855506052538209721834082404413518074227907417487517567528969487570285726181868*x^17*z^52 + 80425834547018997110392654403669843810904696037400292125269322423349511611240*z^53 + 7291941879365386413155925785551772332596743395420998166469955028815583959259500*x*z^53 + 309907525297230651089495852181538587658755814670105393137890663606873430791403164*x^2*z^53 + 8195332427648800649923681888048028851396367984312368442181362603593148257542622008*x^3*z^53 + 150930704907292547370644825243546772042853296766267229312452448975142297014336246652*x^4*z^53 + 2052657591507339348631003063699003115871335782324851660481280943278859467030022540876*x^5*z^53 + 21324831623253311481703253863166944546710292783440267717810459600076137040609381857516*x^6*z^53 + 172629589365399583436275705480925391080750297863808387215375419359480819513797036783704*x^7*z^53 + 1100513632642288588875641262629408938551523172131696121577741058560286788118239676095516*x^8*z^53 + 5543327920080244698053424226755269671445527776893391038903828625771743690369098469956356*x^9*z^53 + 21988534130073849793130726669695718924823810779929177226966921442003291550077640255000980*x^10*z^53 + 67964559771706838786517884281120570393282702786945940496488989437745341723231771372263880*x^11*z^53 + 160471877798690755724916391599061695006728219541820700677686385408340589097392998081801460*x^12*z^53 + 279797121338149166679069825832522395020293609200254862279585301363775495905931954172598596*x^13*z^53 + 339753641827444073177185647728971406616605117260201310497071279603497430619902648476693988*x^14*z^53 + 256702756085450384628912775830527799228016770074559529457511667556345616612392994717126312*x^15*z^53 + 90915561344532202192640612924357532978439364871548340618199537372452707100009601806147852*x^16*z^53 + 87376218646806216370163983683563446607924644261966178397484756944099859508208*z^54 + 7426976950090193077842070507095183103777779143256233611307284175040881488390404*x*z^54 + 294603459166511861074215767267820411072246809487773957384420233815425385104328480*x^2*z^54 + 7234151342961156219263559566990564077564159759503807379200507289796346917017409328*x^3*z^54 + 122980575161465796946984755481425200458924969527911280572582395505334341162668141164*x^4*z^54 + 1533157821780648365323639058005039237195313282002387531909516443579064920082848262968*x^5*z^54 + 14479823966524480081645300341008522685509338622376737602870867380310157202987585232452*x^6*z^54 + 105495859830396562843590828291911628143838994410713966379124120240577833166575162936308*x^7*z^54 + 597809874032615315488187543393824514422569944321044505866955062520997592334504245409640*x^8*z^54 + 2634791664122088274651679803958414470587787103703195029584734254838196818458097807502068*x^9*z^54 + 8958291627601044945760109707494256564601542413918535872027326966113426051050078051217896*x^10*z^54 + 23074387799047242417194382244871604881639955997634383000548996882441496887283278765828888*x^11*z^54 + 43584953977250829174629298248032298519173696967379877226905598105726769181438943645419644*x^12*z^54 + 56995708349012849817812309257055748844318519395709001968411990605648949144206817074070224*x^13*z^54 + 46139385286960687052267461230991496044956311178331834819152103854903939968152243644865140*x^14*z^54 + 17430433896747896019398536572660171489079212413253365526011421113814012813452132933902276*x^15*z^54 + 87376167398073777005729464361120813804310265244532391972962710217071098577304*z^55 + 6931847247113924686999112098259002459170510750647085468722240804240503909525164*x*z^55 + 255322987924906618934561639555956996427719805632599947163578784045191841860124588*x^2*z^55 + 5787321255114445174455986417396776995027851759893720212743641731174022547004204900*x^3*z^55 + 90185753778242477914407552671146850917007961861819108772500105317785138288142729256*x^4*z^55 + 1022105226392829798940929661587721892451800403002718921000735843794686235706328299096*x^5*z^55 + 8687894294616367561507593911340686665333668804845460621056881691137348797935097368868*x^6*z^55 + 56264459193214030436065405771497371954986645329551173272726163044836028040320055702728*x^7*z^55 + 278977939346163283075969297499809654632166827232056131132801163639018184301809124705832*x^8*z^55 + 1053916677923465297338053233463127892712741515331567434653033815910421760503615069857692*x^9*z^55 + 2986097243892497555779190760341476997618881952682009800368281083485567278996831479335956*x^10*z^55 + 6153169846091759871510903811968549428668543032796948161155205407829138401645930929240596*x^11*z^55 + 8716991207424501290691930615811390458651400273356700449739190270534650675366184423837400*x^12*z^55 + 7599427785473188044897154255436344986819579201392144011012334264335555791750473468375328*x^13*z^55 + 3075958495272945358357029856646010755242513051168726800202900482095993162394273767986268*x^14*z^55 + 80094922309063084586465027571050253051340450991858212892590773707173784610432*z^56 + 5900322001833961036684346397532805035865178027342337429489061337504933885396996*x*z^56 + 200610909629959241115603874786443110871743083509919498504876617820743953452220184*x^2*z^56 + 4168249257826600628407097441170894556629254350547349122917107380587761376783620044*x^3*z^56 + 59050196279819558076068415498638422622852662881492060616517406005547342897252608124*x^4*z^56 + 602312008360283965460618044293961758095863425468515718742164853563704112071523422436*x^5*z^56 + 4550801886160835808400463881040583304537157742265675538623118459619308326185040835952*x^6*z^56 + 25787876738026185912612117101610239991691432369309058676988450101037497737523210857184*x^7*z^56 + 109598481058111102141399424753140538735718127245430429890197348828467750968509963614536*x^8*z^56 + 345032227597172258831057352060933711230527771968190338462834428619968451635883930338244*x^9*z^56 + 782073091526531773993984201872096505751361337997086717420994041930928374790997184304184*x^10*z^56 + 1208658530998024538678968776306638157087245492669330996332210652349622192654200704699316*x^11*z^56 + 1141510593261499792983298561598897918102706916137879499762760008553791043051021968973052*x^12*z^56 + 497581483629155930661249526325501559100934258838685016747661585678609102190486260090612*x^13*z^56 + 66979969331200622032343451557464642962756080716721897264635533152544049483080*z^57 + 4554628226893910157512901782863771885142872975858551738031115019283612545194748*x*z^57 + 141952793227923412153824670292245789437136200443567405464862553559500424928989476*x^2*z^57 + 2681329429235321480561997178526742955372906662731262124804611966355671311743955400*x^3*z^57 + 34186959075509878907435988177726361998508625265666192649046788518170239956580795404*x^4*z^57 + 309961712460817420246016682607353719351034516933197645363456183094386731349425867776*x^5*z^57 + 2049191499950360700026692757663750001653223638481187872274660176472509161971385316504*x^6*z^57 + 9953215328883260610880552806654609651162887091978342721599450665108808845882300428632*x^7*z^57 + 35250968141411037591613562008844776985965202672537760665831259902319943010281637260656*x^8*z^57 + 88780242653696011242771088582158483111808058426481597933912609992883413986548090960708*x^9*z^57 + 150926370718502008721148058210348033684315840094455450498639355359580887426865257914564*x^10*z^57 + 155499923949682363992305316036207772823692039496676970760651294709596171678597593502880*x^11*z^57 + 73430568604691191675986010309422408032931549197840357309938300681366823078950813303996*x^12*z^57 + 50812011935356377358330767678963257868340801567526640036989693352740674212816*z^58 + 3167309029003641030240024877914746087248833046331018517294573855246917204957124*x*z^58 + 89740221353820649864217817058413222672217309674453184529324189144567038007217408*x^2*z^58 + 1525584726852245008110282337818893581263933447580962568615613671772631824488805472*x^3*z^58 + 17289949410218187126372962013837135843149024084485789387253765012006066217514788876*x^4*z^58 + 137166998305279206607941160936785485079673886553733554564163536933649965517786543764*x^5*z^58 + 777279290778765151136269704405918979944458034099035613901639396616082087382944130716*x^6*z^58 + 3146132134646757690714122024845272584138109483554155997158759261796048722308713128212*x^7*z^58 + 8914040900643750134557710283681361410618305970659923193520795656772431490936211923380*x^8*z^58 + 16837619993496783911206855733893514496660531400707026861976102050108691031741892386632*x^9*z^58 + 19082653247436306514248700656616943939015467850651335550169959151508675385923447123860*x^10*z^58 + 9830473730891669103339853473174722282139696906795762048199829483739298876428789867948*x^11*z^58 + 34736400482489842549043563009738928555147477465865933563280026298322866675216*z^59 + 1968386857175642845501835067267421271958661620962697232830102214443168715400964*x*z^59 + 50193661374061679163208927543987535890633392220474274916282777793868187548754084*x^2*z^59 + 758482757305812831406772302894868057376895881675740612871914321758524260870451564*x^3*z^59 + 7521620873753747867695904057675283524472808000981071570273718230313340690076828792*x^4*z^59 + 51147002261332398832866292483320997053394871861540748249915443976794787223471408164*x^5*z^59 + 241527853784671153358134405374693752252753993828778840889057242922820255713170022776*x^6*z^59 + 782088345995273719938136990944577715349283786636872613852086579120013608026315744196*x^7*z^59 + 1661939029766813341344127694405104347293061541328214877618096653862876622979660286728*x^8*z^59 + 2092811971915002365267299833323399564378523935043932947682363188743140336251983528360*x^9*z^59 + 1185922265826920993225657442861229579154543392311564072959081719985994895776326468692*x^10*z^59 + 21227981622454937031940192204808445546709300311747889594115896901559647306280*z^60 + 1082590383676487024323210367665616957477813555588305574204228296133861352041748*x*z^60 + 24539255936553772240182211681561642641834343986329783427772089635332514200410312*x^2*z^60 + 324461179569136750190968456043928139152293539365114041069877124561828022889350676*x^3*z^60 + 2757932764636562563587851747180558360009507261931058564755045455623508099265330348*x^4*z^60 + 15628240263538899052570150997289990170533103859366506917549775298862840536100804920*x^5*z^60 + 59039816102913542461068148226695659157060150690236945261206381232012856429442680848*x^6*z^60 + 143383364946476648446770165161967325556570752098739223520082259295740830346888669868*x^7*z^60 + 203125747699724658866555320802818132905800917826456339678517262983297915258426755748*x^8*z^60 + 127892258908867019387406746386677548065110461200814875284802291029501665208054559076*x^9*z^60 + 11482939431830092022568160834909581930557941522269353552750999520534217331112*z^61 + 520609767687352976528194865823003555584722545776043064128689411668377729954444*x*z^61 + 10325101357074156617974529192655498521438822251437111207479643555934808695540572*x^2*z^61 + 117019676355763594947356272973493094497697104372399371945942572889804140332623208*x^3*z^61 + 828872069892959818594325898921841143206051292560352340606291762327796975725418556*x^4*z^61 + 3757620069824376532711877084477747947811713579133744224309990263328515109870517316*x^5*z^61 + 10646669507169008252302394443986235747211557494888237343192959274782372923304627924*x^6*z^61 + 17237321764436269620930326681507820686863520523703366363977045055898468764643735016*x^7*z^61 + 12210048618088861966853592661470469724315154385160817798971907794192526984781375596*x^8*z^61 + 5434261587814353684241125727866067835560080697029918194608323779084826375408*z^62 + 215517659822338535205014089436833770890602068948368391076928839911014474504676*x*z^62 + 3663784537804289397366907440648775291974925500387249453194759688351441792977472*x^2*z^62 + 34601574874107865520484216761316985908813199974888151881178874922479342088270816*x^3*z^62 + 196093178042339370447192727121391767157618111691202646013050951125199110952825612*x^4*z^62 + 666672608060730905652077278026292452141951521991026488642191604949729494165799616*x^5*z^62 + 1259265661978433212081010331539933900313589185507726587556281911687202311491023028*x^6*z^62 + 1019502220771691708676883996119579460452228430893737573186974832899900691374497348*x^7*z^62 + 2212820527907619704148800480979412127978207530531603612217937971931803402040*z^63 + 75251802373593740557111461905019833510013285278114115994517798919798444298860*x*z^63 + 1066345335756237929578873271600078139091856993321043782835544464764064684118572*x^2*z^63 + 8056952633923753382867184661818600908701235810361385137323323955530019588297172*x^3*z^63 + 34230329146900893815991667380210115666542801856614148242951726924246203707578792*x^4*z^63 + 77602219143723978134336731602732236375132930399739334831980895748597211988282080*x^5*z^63 + 73280902648636545920369685512678063060778617511600819269759930817318254681922524*x^6*z^63 + 759262071004016453214251891023984394725986573960976529437635731945441900448*z^64 + 21597137333700571420604886903611798268074602003912238319630570836383314405960*x*z^64 + 244094673163032013056644422368283921511230067758795525337145882643170374131968*x^2*z^64 + 1383964802825674916564235985563965580554507773946187466158477456636234895100760*x^3*z^64 + 3923514498987964455904012480176467195781861595632894087439345041264578815279506*x^4*z^64 + 4445229402653598224166495610767004205417420143097364438823178375265101374694804*x^5*z^64 + 218348942039694294696613289507085773835988160574279598085261734513895144532*z^65 + 4809918065390720449182048646574308537997835049072502524786027167870650501682*x*z^65 + 41477134694242187136394752194820803977640566702095561330027212518830054918945*x^2*z^65 + 156182817434881540883371689973300126485118990827094424664506626682591708543277*x^3*z^65 + 221384931845126058048257226605959788346456653405172702684891999244019639123234*x^4*z^65 + 45497968931165288649702994740483006694922852542958500743420494341576880028*z^66 + 829585459115796968162168859713262709779683817109573243815478847104782710916*x*z^66 + 4584067628143709775591419477697964530489051372205751025001608376722985881774*x^2*z^66 + 8514805070966386848009893330998453397940640515583565487880461509385370735509*x^3*z^66 + 8170409913695175074418495534382511765637554505953815274346638068381763667*z^67 + 89269293501484320257535414171957072994928836268754648367861415932319269695*x*z^67 + 255501831004813314364222829488776571634073155105938445554568323792728486031*x^2*z^67 + 587415091834293632801329744302010649817079082127398483776555678118950329*z^68 + 11095618401314435286247339614593534496544827106850860249112718364469061770*x*z^68 in I Output: Magma V2.10-22 Sun Apr 4 2004 01:36:51 on modular [Seed = 654887508] ------------------------------------- true Total time: 4.279 seconds, Total memory usage: 7.64MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sun Apr 4 03:25:39 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > (275573750405290386156*x + 17177430441929767403724*x^2 + 1291950980511202505940696*x^3 + 71568332483763548406999069*x^4 + 2933002060899381069228645912*x^5 + 96694114364841635947146176766*x^6 + 2658053466027253803681878061708*x^7 + 62109462904914230956593041593401*x^8 + 1251609559311431425713553664769168*x^9 + 21991590820796269937289124980924576*x^10 + 339874528606848103579134147488680128*x^11 + 4654026031226274102693081032154096516*x^12 + 56801409394762285311633922332217353600*x^13 + 620770532721078411713098345209265341864*x^14 + 6097456834004194955480660618053741035024*x^15 + 53987934247818304475156697719045285693796*x^16 + 431899431419641327846058269926722954630088*x^17 + 3127249750515556304176353645072789494350584*x^18 + 20519223977129947710225260098905240932075760*x^19 + 122090416162149246895308268001813372348103702*x^20 + 658900225567898031947473915900074743078980656*x^21 + 3224592191327204316990397911940987002079789716*x^22 + 14300367515641454048978476849108478504680345992*x^23 + 57400451693893534478325151250855145167883714510*x^24 + 208171412665872532941127001273787505392125274384*x^25 + 680557440907355495456217907040251678802415826560*x^26 + 1999703759524094125195693668464837454569737422720*x^27 + 5261152461969601583290677713952014651700824222484*x^28 + 12335604798454205588965973570184471884788998461376*x^29 + 25629910383456630695709698944761765360645003932904*x^30 + 46860929955092484657379858243622139248061088083600*x^31 + 74697758228167981052469534838842040243897235551764*x^32 + 102551000907319343546873515233031719460536147365292*x^33 + 119536192741689256717272905440585639510921919857692*x^34 + 116266905241756572785108148359746736516657964039672*x^35 + 91839208096405022857172933664731867078794672188213*x^36 + 55918378230452549529642128108440729812729682374264*x^37 + 23662430614834358080184060703896456013828253039326*x^38 + 11659748418903886590235624114963471079277689903436*x^39 + 16517976926780506002833800829531584028976727363201*x^40 + 24250490035665553981728*x*z + 2708308199677593327320484*x^2*z + 185965724869405316873949978*x^3*z + 9446560232542184898725758938*x^4*z + 374833372709513310969631240854*x^5*z + 12038896134723137149519284869370*x^6*z + 321606369640715339865668708845296*x^7*z + 7289962021587165411775199840852400*x^8*z + 142293161575424443092248116938507408*x^9*z + 2418938185907234199673011434215372704*x^10*z + 36136740027070924449065961714034928856*x^11*z + 477811029745193728538166008188884320664*x^12*z + 5623536831215179112397946824729248223720*x^13*z + 59180957599185729922006047847199225929272*x^14*z + 558927233667570416451242568971215445973648*x^15*z + 4750878761361244583792220045412446030682704*x^16*z + 36423564892007624175774554157873815154892080*x^17*z + 252267212463326592215194562285703658764876840*x^18*z + 1579984888847646191802159943453081444663907484*x^19*z + 8953235042103492321181581093013602155769051612*x^20*z + 45903181479775065685746052620589410081998731524*x^21*z + 212824169916940053786033181936625696969521713660*x^22*z + 891392832702671559852449634740368405988291154576*x^23*z + 3367478276531373587105438940780372630636177196752*x^24*z + 11449435585574619285981935439477146954818804880112*x^25*z + 34935528499554504685253316363689474984388242818752*x^26*z + 95317892340744767224896692668255805803325768161752*x^27*z + 231485665082691309511503545714991895032671262644760*x^28*z + 497560801755520178970056212349142432013282965491688*x^29*z + 939840996417932148185674193085533589140914345757304*x^30*z + 1546197412122515582506898752925041825121169239926512*x^31*z + 2190449751731184517705071896277054264595772555710512*x^32*z + 2632902875335051927821246423225939508411350031304496*x^33*z + 2632452245401035714299054555506473029495846016234708*x^34*z + 2130958730852612957996086501629287342380238549530266*x^35*z + 1346387674158018214620227794644620177276669936326554*x^36*z + 623756195261119510824698500447725759934853718865302*x^37*z + 169752219628159525357842174614909358360072250064730*x^38*z + 9643730412467490523371*z^2 + 1751508483444024959631681*x*z^2 + 180916037470323574417460781*x^2*z^2 + 12233407143306482256457577232*x^3*z^2 + 606118551048335019634649146107*x^4*z^2 + 23367473975046034208061025711911*x^5*z^2 + 728421126124038027914198607293817*x^6*z^2 + 18868752321588740210322789303668064*x^7*z^2 + 414308451729930813185694749573131260*x^8*z^2 + 7825833236785378088088541177710286500*x^9*z^2 + 128606153173224855814637756267582780100*x^10*z^2 + 1855051313833448119668449319118667226144*x^11*z^2 + 23651798888503668012425878793329093994316*x^12*z^2 + 268053120097636202152862712811264334823660*x^13*z^2 + 2712446938606718806914465313418525436055908*x^14*z^2 + 24592891641134888395019327537830483012319712*x^15*z^2 + 200329471000092472634559667088086162644503034*x^16*z^2 + 1469081104905246707248850519426796600825460350*x^17*z^2 + 9712259663051622035756481607475766318900968694*x^18*z^2 + 57932825783353442937754995850599570761534690880*x^19*z^2 + 311871752669677894681341719409199844667357685482*x^20*z^2 + 1514804669394469909743434970510837176423644472994*x^21*z^2 + 6633006505988272084744115348483570998893557632590*x^22*z^2 + 26147518920242847558373144438530469629205441249824*x^23*z^2 + 92605827724522886122699851554931070431436969686828*x^24*z^2 + 293868939116730390556145423872799672728059885903828*x^25*z^2 + 832628374118471953013760679702380937055811671891796*x^26*z^2 + 2096993653802535947088435222344004038514578837331168*x^27*z^2 + 4668309788359972208217093338322979087260119258263452*x^28*z^2 + 9121934877513245906129022129440154179483931791374620*x^29*z^2 + 15507243382046238606774064102966507272115701064901652*x^30*z^2 + 22677615122299555101271309965832575195383030752749216*x^31*z^2 + 28111325531206383405154326247231776793069269312841203*x^32*z^2 + 28962929405996491059899824597548995685882889678576329*x^33*z^2 + 24134320054203597812361190704593444755766618423081157*x^34*z^2 + 15621709739973357383625054788685193267178784889408944*x^35*z^2 + 7371534190697021547710669575085297427277061353243443*x^36*z^2 + 2261476792601814121156141859591959118596962531417903*x^37*z^2 + 283549077971481281245877113893793039334787351034049*x^38*z^2 + 342216218761063886877363*z^3 + 76247891165136585238075017*x*z^3 + 7900491927292055387627684760*x^2*z^3 + 523423319831841499759193824242*x^3*z^3 + 25208128013123300679123783506919*x^4*z^3 + 942604050647503773602266819194459*x^5*z^3 + 28486466706334994716272337611139392*x^6*z^3 + 714888056920772762652913527624186384*x^7*z^3 + 15191552673031244868346296925948277628*x^8*z^3 + 277386071766831376373149739089646019300*x^9*z^3 + 4401177198207987600932726465579721392928*x^10*z^3 + 61216350729494417188416842710952114743896*x^11*z^3 + 751601551512798238314882821390537965330140*x^12*z^3 + 8190533662655483498951061355277406250784988*x^13*z^3 + 79565159229370130726630526679180141627237824*x^14*z^3 + 691332571241415444592014409222903331311618224*x^15*z^3 + 5386633154954873898016398855766238231995385610*x^16*z^3 + 37706441909655498989199727326488589068414979534*x^17*z^3 + 237410948819741182128583361537690173328718756624*x^18*z^3 + 1345328488141384647812489150978159106661679762700*x^19*z^3 + 6861174417941368179223190277768151650698736476850*x^20*z^3 + 31474278495337897889481906128202239891328383840922*x^21*z^3 + 129712195267969818280228890674598696122343832432320*x^22*z^3 + 479371179226166129129042782787289468854984356989168*x^23*z^3 + 1584587966452281379330468964959620463005653681905260*x^24*z^3 + 4669251547371105506086517598456206910248301772471380*x^25*z^3 + 12211885942828029339427593796868733804207587339878944*x^26*z^3 + 28192884115946756732781391530027654068914075937600280*x^27*z^3 + 57057094983342569431062100563499054566043670890616748*x^28*z^3 + 100341758582959633960950649590749146584574341954511500*x^29*z^3 + 151626854198223527379825060122520385779927813689914944*x^30*z^3 + 194016570806273602044640576365703540145063769649949520*x^31* z^3 + 206146703836682632840215191656611539932782869503245915*x^32*z^3 + 177001087190786570521091635763164992989673921351249777* x^33*z^3 + 117982303460122404914358699007442107624981770461595672*x^34*z^3 + 57271519598998921957280188771746329896902501735072402*x^35*z^3 + 18086430043190782419136861912719629110996113184587999*x^36*z^3 + 2868442681172043779145881678716118680558946358882467*x^37*z^3 + 12741311150112745228992678*z^4 + 2571906247574770454933951586*x*z^4 + 253982468482258302269922247974*x^2*z^4 + 16304993653056933011183451422352*x^3*z^4 + 762343600149242634985513381020933*x^4*z^4 + 27649388978070973457017554083210832*x^5*z^4 + 809520414810735464625948600846100608*x^6*z^4 + 19659630596045126816939038688043173952*x^7*z^4 + 403839644078034093724274266327300754016*x^8*z^4 + 7119547083509018381452024338536385518808*x^9*z^4 + 108929239643071926805758911508580857383544*x^10*z^4 + 1458992033222818844159493206552705588754816*x^11*z^4 + 17224202978930354252753220620452207735716252*x^12*z^4 + 180191614049158907715152023283858857449405936*x^13*z^4 + 1677498369500012938825651910413077130443315936*x^14*z^4 + 13941877987322130657269119936294001722976161344*x^15*z^4 + 103692715562900381704349393944711177595984096172*x^16*z^4 + 691284680914383463141363459795134728910280910316*x^17*z^4 + 4134906348764220850823008029350315148529827272628*x^18*z^4 + 22197920061839158666973289148682682670360326925344*x^19*z^4 + 106919989865345093606934330574596567312751999422798*x^20*z^4 + 461622801594484033896560027833695805380220168563120*x^21*z^4 + 1783542464577829765297843362295179528527585173664064*x^22*z^4 + 6151928762467408432767884432542976298588266277143232*x^23*z^4 + 18883005288525385309841496051859934786331963291015984*x^24*z^4 + 51361783227141637008875498424579896016519967554266136*x^25*z^4 + 123136586013563889190416308653580054084454058774217112*x^26*z^4 + 258434724746553375570151807374691909229035243226111232*x^27* z^4 + 470720156638654018409421319303555916211908338219586556*x^28*z^4 + 735838781312920044555927576926285381276397677810815248* x^29*z^4 + 972944565390857464965683817636861637138337102502150240*x^30*z^4 + 1067096764997074070908498386969699657388613891366616768*x^31*z^4 + 944811163730939089911288120180399428010517623859697310*x^32* z^4 + 649004925226402301589956294019754766907238943044347330*x^33*z^4 + 324588758185787327474749894056820750690071076168409622* x^34*z^4 + 105033043579231769755317496651393722459318721745938128*x^35*z^4 + 16600220317771184440146529898584435381489293771699093*x^36*z^4 + 332312791708775912732854794*z^5 + 65740127318065123122105552294*x*z^5 + 6331112506265092145068098404808*x^2*z^5 + 394660641171724329210939981524124*x^3*z^5 + 17891047637304395373594843816407616*x^4*z^5 + 628561492033131562156955047282520736*x^5*z^5 + 17809200633325096882362152562020253360*x^6*z^5 + 418093243425619011981624433368569119632*x^7*z^5 + 8292194209040025463570036931978051183880*x^8*z^5 + 140967274531631952447936450367408580548248*x^9*z^5 + 2076916789546416165853805266946009732069808*x^10*z^5 + 26748168089899447618313946543365101776315936*x^11*z^5 + 303145957212485629991928382524357213415061472*x^12*z^5 + 3039232855907900431944461015983070778122845056*x^13*z^5 + 27063643626211301796957481656976547640980760624*x^14*z^5 + 214704889859889669584988205398992944641575820240*x^15*z^5 + 1520826299536621592083553384065512389584973911980*x^16*z^5 + 9631900401161558873643979553354660337587808417876*x^17*z^5 + 54580770576594420819800499584100670311415844686080*x^18*z^5 + 276734074153305476039534373645142002580113258080184*x^19*z^5 + 1254527741301725585349306889278876887704199877364992*x^20*z^5 + 5077850375643790067352350488160442605966434207567776*x^21*z^5 + 18311037303635484100693269584698573710567081373536912*x^22*z^5 + 58648398162102180656280634802789892446023468987920816*x^23*z^5 + 166170454360414414902421270371411647129758295273298024*x^24*z^5 + 414318264752290865554753100113977871584945085645411320*x^25* z^5 + 903001266083503138991153681164423273444417014081308880*x^26*z^5 + 1705669646562197001578586455734311281362422684528361152* x^27*z^5 + 2761562176036700005774703575128615883365401285972698080*x^28*z^5 + 3777307871890990732740158013618256256463863527182550848*x^29*z^5 + 4280936986972444661877046433046000337309812992623028880*x^30* z^5 + 3912673049604395904622715596659579018483800913545847024*x^31*z^5 + 2771510186736665040704531168173399003596092243589940698* x^32*z^5 + 1427818770723150459054664467261570222114220075124804214*x^33*z^5 + 475878092246793337453326680846839628421291755063824056*x^34*z^5 + 76929802779825090695114781235516217609130364196197580*x^35*z^5 + 7074140179699768467882758751*z^6 + 1364979631893772484777289508593*x*z^6 + 127677463055642373688810949509809*x^2*z^6 + 7717618628353231755656667898213440*x^3*z^6 + 338931491807121289074311070522558024*x^4*z^6 + 11523651647862048076290967188187542408*x^5*z^6 + 315619662906015102672852958758092992536*x^6*z^6 + 7154044127271192967771270094096624686368*x^7*z^6 + 136821108285222759822997207422350672289444*x^8*z^6 + 2239812397817969894270766304987380250673772*x^9*z^6 + 31730676809558954012162924757357624346281852*x^10*z^6 + 392306550471785345505510663802963855211928192*x^11*z^6 + 4260884921340158557791786732850332994772094840*x^12*z^6 + 40860792965311022278208675547234136199007267480*x^13*z^6 + 347316742661854788899505521512195000951164877416*x^14*z^6 + 2624171002495562769395941336896146549917484923104*x^15*z^6 + 17658484158487211996524442505393915198380880243258*x^16*z^6 + 105950903229655744927872597820231569891556919857974*x^17*z^6 + 567033527630836897208151048925601780787461959892742*x^18*z^6 + 2705844216563860316490951440635108438221449779085376*x^19*z^6 + 11499838234853837474061749037326883919761319868854008*x^20*z^6 + 43443834047022922865437105434337106009651986165758072*x^21*z^6 + 145471015351498890682427244677048312978102552620479528*x^22*z^6 + 430088191689823454232615799348065247182401334922472160*x^23*z^6 + 1117034620582697502706786385573388723184774471557331236*x^24* z^6 + 2531945566116465268042087554848299668307972111478315148*x^25*z^6 + 4966509287191533485866705887411261007708875207689667516* x^26*z^6 + 8338827171089650343804988258897810270903344803352794368*x^27*z^6 + 11813328613191566364102061312251666204965518204176634824*x^28*z^6 + 13850125223530401597128066007588020074534260693323617512*x^29* z^6 + 13080739856100979280416222945031720711002220565228300504*x^30*z^6 + 9564309340637587431711641644070531366009564207635653408* x^31*z^6 + 5080718804917499771606379545191333047699711583965631263*x^32*z^6 + 1745072394630523109129087572728715306188634309303762785*x^33*z^6 + 290813985597689820336642384477701962349579968813542289*x^34* z^6 + 126298796322161844433301385411*z^7 + 23607581505510789544991615955441*x*z^7 + 2140215513102492405278223198155328*x^2*z^7 + 125318031581952661777948160405390160*x^3*z^7 + 5326030221874122866502279432003600168*x^4*z^7 + 175049510378644116455682578354416911240*x^5*z^7 + 4629090251593548767969227075198334560128*x^6*z^7 + 101178657858236909404611848774815951520400*x^7*z^7 + 1863373299468195505207274537852681577540756*x^8*z^7 + 29330876383378586018150551016680654691720364*x^9*z^7 + 398899928305818224368416119779578240362997696*x^10*z^7 + 4726359707794654056074257027008238065798012432*x^11*z^7 + 49101625713775087550835831030033628597580482968*x^12*z^7 + 449468734192278345099798949977368514868135365912*x^13*z^7 + 3638556438248884831592229590552183637954902896128*x^14*z^7 + 26116749198256483791971561364133495861393889096016*x^15*z^7 + 166494274333758441485748929753066901447334901082258*x^16*z^7 + 943467563307431866673931926735281378384878589098486*x^17*z^7 + 4752281143958747287076561762298592517636136820850112*x^18*z^7 + 21260205086764354489770101847030069769425809132379888*x^19*z^7 + 84332144656661442544480957523999087880012759143097624*x^20*z^7 + 295831804365271554323157880791849837115178976619171704*x^21*z^7 + 914389243296340004831876603308260096634932636704179584*x^22* z^7 + 2478127510423692766674163104163599417010487796593906352*x^23*z^7 + 5851134281310205989158910470561144675327766467644874004* x^24*z^7 + 11936312104442496156894796391907635820840409379023275084*x^25*z^7 + 20812029601606519619849719102835789467612267947420692544*x^26*z^7 + 30575708379630987295550991481705324307914657715719076784*x^27* z^7 + 37127664994942787679286664540287880551963982699016321192*x^28*z^7 + 36274138330087119670717236415330016290845196841553382248*x^29*z^7 + 27407086718212074466187405728692067019541440114772712704*x^30* z^7 + 15029667436237215884863348018312305765870764159567641968*x^31*z^7 + 5322985898519730715161784458782168730304791565804025475* x^32*z^7 + 913945012098706230667813847792368321204727850808641441*x^33*z^7 + 1908921407361667514961102741168*z^8 + 346191633438160246866555636199968*x*z^8 + 30408012266243193412984502820770112*x^2*z^8 + 1723138606092104700640474384775129472*x^3*z^8 + 70792181252745480626399334602145402804*x^4*z^8 + 2246469001339816851147965790382995727344*x^5*z^8 + 57284958422463742820015716583369699064504*x^6*z^8 + 1205712174223801157641529999552699347743696*x^7*z^8 + 21351153504938839183436405964239617871700204*x^8*z^8 + 322639644741153901635261305690036582874716736*x^9*z^8 + 4205070037203033499180135874202876494769458928*x^10*z^8 + 47657460972236394244156207822198082378893523616*x^11*z^8 + 472603153844482663281990062738381704267818240564*x^12*z^8 + 4120130018431430405137608848988681742435257386832*x^13*z^8 + 31685761754628025930882360759416196684054849896648*x^14*z^8 + 215463181709518679427479279851520137940304274911024*x^15*z^8 + 1297267914142920821239247823969662590684626249264492*x^16*z^8 + 6918762172776641621195338166013151067828987986503456*x^17*z^8 + 32671932141363715033361851309187154237268756862419296*x^18*z^8 + 136419646306039207498945509725388173091995900314907712*x^19*z^8 + 502479038141001559889354300430958153695819888160626108*x^20* z^8 + 1627075008576331460361673907556067296933418322403594384*x^21*z^8 + 4610045791216823406294871495163939000616070054776913608* x^22*z^8 + 11358083188914360002194490910466900251620459226683866416*x^23*z^8 + 24135926258294995966685406689837113830885751443801091428*x^24*z^8 + 43766486111756890999583502770633711858248312639436706432*x^25* z^8 + 66771962364519129334519948447868894675852885286504634224*x^26*z^8 + 84083181016469409685079801364595487786281702017358278048*x^27*z^8 + 85084047541538130009085923342056191256846465051443122780*x^28* z^8 + 66502622521158386298767207931825174799573950290801524272*x^29*z^8 + 37685448727451866074617500254148992835875752801367821496*x^30*z^8 + 13777260717649052942017159002439996360530923934222850512*x^31* z^8 + 2439786446152216550995326348683945199342052475693261716*x^32*z^8 + 24887510231216342800061240341776*z^9 + 4372451597448148105811656800763920*x*z^9 + 371656781455105480324275202302353232*x^2*z^9 + 20358522283769244865961696727057800664*x^3*z^9 + 807554454362146334167439454565686832680*x^4*z^9 + 24711163574142939808528648320859947503448*x^5*z^9 + 606796324045853848159459672179587993908536*x^6*z^9 + 12280401695822241286719473185086698669416848*x^7*z^9 + 208766830405313115006287538086848696979279232*x^8*z^9 + 3023252988769349780506929287752788734208063264*x^9*z^9 + 37689887101600570240028529052921574853976897632*x^10*z^9 + 407736050868929350956551180684775844559692859496*x^11*z^9 + 3850840489739176406470512560137335650100569183352*x^12*z^9 + 31892858530144729219318321595352616278408022761864*x^13*z^9 + 232362255186235343609223927747121030654653528220776*x^14*z^9 + 1492282032716820170582574823660215978862158883112064*x^15*z^9 + 8456264812339214641497247601807076841417591974978768*x^16*z^9 + 42281324162583266558999220253970874806893116607605648*x^17*z^9 + 186351023090789191253427173742057134388733545491528784*x^18*z^9 + 722518881438356749661595461791224908857569046161499176*x^19*z^9 + 2456564158921818010623766616158153144706883951520114968*x^20* z^9 + 7291706170840948930935607704249484841252054701556088168*x^21*z^9 + 18781667753089246003186342510992206565581805133731628296* x^22*z^9 + 41646309390619935103228110127120826465048096561203036752*x^23*z^9 + 78665251472679669368743148655729704244249760337428799904*x^24*z^9 + 124815510513408876964763617634038772350837279479841147968*x^25* z^9 + 163220262074960010877906055908855576420469249605295782656*x^26*z^9 + 171280599718606165943478426018947761317980915169448425624*x^27*z^9 + 138655763810690924941111235358705013049560666190415858504* x^28*z^9 + 81280821313625900777278743083728210015099190733860758200*x^29*z^9 + 30706210461836332080702772557016958294721922228943622744*x^30*z^9 + 5613480648292009109861196392151734138797490289919825056*x^31* z^9 + 282956170734983678739488904995388*z^10 + 48097728106939595701804487177594772*x*z^10 + 3951961234817517290399974191342025668*x^2*z^10 + 209013973341944116621755636208919123136*x^3*z^10 + 7994785570372862279538275746173505018356*x^4*z^10 + 235579749026634686233405246785162216503076*x^5*z^10 + 5562299714805589302683024703028917487024284*x^6*z^10 + 108067534925024855131847332035117664748882400*x^7*z^10 + 1760600261333043126598300496719884967701709980*x^8*z^10 + 24387574114821283525294896785024383798909311972*x^9*z^10 + 290212131728693309261073540218844963104123265348*x^10*z^10 + 2990064384794771523310849485480320763727713386592*x^11*z^10 + 26827522114964654549633610315003057718799721499764*x^12*z^10 + 210492865479814485758622214310571409186490694796596*x^13*z^10 + 1448391382255458122836313815327034429900051155967676*x^14*z^10 + 8754721265356689724352124214972515510048292424389824*x^15*z^10 + 46509456894362947304909541456087456691081377015488724*x^16*z^10 + 217044131928396812709282546245371941889068525195061308*x^17* z^10 + 888273200260550391907863153003447659917027886499405420*x^18*z^10 + 3179083018446745010488282732552687918027223200709563776* x^19*z^10 + 9908142173844611500293572759988091619809422384863910012*x^20*z^10 + 26736257217031469013971083596159906328729879567952664300*x^21*z^10 + 61979505213827235142774548291951199145510262040423239540*x^22* z^10 + 122162495418796730679317463385981864385212592820686817120*x^23*z^10 + 201907444099826682016395981928835261578020710119223236692*x^24*z^10 + 274594162617810449167381155152254505640036104408182749516* x^25*z^10 + 299237362232047149732307772779497112512941772626614578828*x^26*z^10 + 251211461823928964887418222044341995895482509203836170080*x^27*z^10 + 152520459009026512696939366941540931988252460884587208988* x^28*z^10 + 59605831671480908966529599777708644799933862456628791228*x^29*z^10 + 11258611628807781397598747987473580307653170749574819636*x^30*z^10 + 2829190614455711406539947462522236*z^11 + 464925557498655806328691701833949396*x*z^11 + 36884697419091626350366083471470023776*x^2*z^11 + 1881126204978879834319339898152799945880*x^3*z^11 + 69288169959391663728776583373778249443524*x^4*z^11 + 1963164598088936768796874086083084976432468*x^5*z^11 + 44498396764454209707994210917231479598116160*x^6*z^11 + 828517772502261526554799734972491183017596240*x^7*z^11 + 12911068602217795503325508634179743160981903100*x^8*z^11 + 170713018238300714623606230878062558032512964996*x^9*z^11 + 1934747542094910086282807925311556457149547967136*x^10*z^11 + 18937074419701511527536289102730772390588814099080*x^11*z^11 + 160965132537172291729464905267076966474346614148260*x^12*z^11 + 1192792906747170634733202158508982273960664532839940*x^13*z^11 + 7724754070980983016529450860667663954227446866471296*x^14*z^11 + 43773606330188206736992073800224084329648146193745120*x^15*z^11 + 217044130630811862135491138120241966598450567588683348*x^16* z^11 + 940524566083461824941616908279856846504117771949678396*x^17*z^11 + 3553092831243041336280162874919379490558770353966455200* x^18*z^11 + 11656637963799610374373533638508151012136863466157894696*x^19*z^11 + 33027140521371199253486369275493922006557764271529500844*x^20*z^11 + 80208767589004113306954744077331787234926666166515026364*x^21* z^11 + 165278673522925261407943219848925836901386540112361802048*x^22*z^11 + 285045853072347955460472427626010864446722939067005831376*x^23*z^11 + 403814976406489434035898111682266595313973514551317050164* x^24*z^11 + 457656854683683854213565717739097800951730634488316367212*x^25*z^11 + 398982860442621908490940723767175736459554234442102898528*x^26*z^11 + 251211743154574868024378029498329799639838154707689548216* x^27*z^11 + 101680808097125491798195549800734743109554294809398021100*x^28*z^11 + 19867860395742170767264334984898541892343463702698833900*x^29*z^11 + 25069584304539692013997416959944776*z^12 + 3977781302711917010721915911801836728*x*z^12 + 304299816407929307329527058158575238696*x^2*z^12 + 14944504543496654648957745602145518431008*x^3*z^12 + 529284564342218218111329554966016871995780*x^4*z^12 + 14396540184239933954010894321027269212999056*x^5*z^12 + 312724845923927416687579980903420775282730784*x^6*z^12 + 5569480591359078276364772970701202138063365952*x^7*z^12 + 82846023676496217728358840500358687466842906048*x^8*z^12 + 1043246223471200888115087606366571570514013075816*x^9*z^12 + 11232284341597200904877215000658757061183759528872*x^10*z^12 + 104153909380893636981295095192212108677449806967648*x^11*z^12 + 836124439181508128824884403698425231587849294778316*x^12*z^12 + 5831431980795475797424349172950661713505457535542368*x^13*z^12 + 35405122704568296358709282156506907508983080060945152*x^14*z^12 + 187253760286881678918213649840721447677700914082822016*x^15*z^12 + 862147524148431728151936802611226836280807094121994536*x^16* z^12 + 3448590099543321435437823546543335146359508807868139528*x^17*z^12 + 11942339713240443481854709749573542309399003100329637240*x^18*z^12 + 35617504095060533441276931256379023013999945659838915040*x^19* z^12 + 90824636007699818902638395289723849605952310312164871068*x^20*z^12 + 196065887104517561564339369415956291348752472242998455568*x^21*z^12 + 353512743413118516317961695019124370419266855672733164768* x^22*z^12 + 522584020056742297417722977475600857788691542220086718784*x^23*z^12 + 616939373049980104666044445602329934142024861696259573328*x^24*z^12 + 559358478726037606646083157270756641834355177461119503064* x^25*z^12 + 365735069478342831781999795234853394926534116358520777144*x^26*z^12 + 153518402442763405689286938678035601852888883148743126944*x^27*z^12 + 31069725463820313097573706901119215807314850811408237972* x^28*z^12 + 197991115362552741348103140284622648*z^13 + 30292624634658874467495240575237542056*x*z^13 + 2231537684077460154936184089091049706336*x^2*z^13 + 105377951740893391471701354750403661500992*x^3*z^13 + 3582849273921232459427480544302766662963232*x^4*z^13 + 93392939834952550381842668775074693658024576*x^5*z^13 + 1940497761914494626790936001051838307338361488*x^6*z^13 + 32988461932191420679307933724274608914163156048*x^7*z^13 + 467336543841568798167269723193513789810946955640*x^8*z^13 + 5590729761808762277623614734018028139723396388424*x^9*z^13 + 57025443567203556140463279553814791067004750944688*x^10*z^13 + 499404642123512723977228679120891820339730000740240*x^11*z^13 + 3773279517930682117442039692517253652340780422801536*x^12*z^13 + 24671443019445621354273576449867538812526205735862976*x^13*z^13 + 139804843938553538035906746619926136756620891179631648*x^14*z^13 + 686597121966080685275476188129981187101189346874173344*x^15* z^13 + 2918037757580417336889906144621281982962802135246139944*x^16*z^13 + 10699471754113790768304599519099885446389160880823407928*x^17*z^13 + 33683522438350717556703775975912152249025102695334222656*x^18* z^13 + 90413666764248454506739455529061367336296510933311277280*x^19*z^13 + 204937643349770146844408054912615652083637830464764524640*x^20*z^13 + 387104418728547879810159140896092255018876778768895374272* x^21*z^13 + 598252270536118304486247466177137770699100341706623038800*x^22*z^13 + 736977541962726668066816795743572229170044409190160465424*x^23*z^13 + 696034378710719462706064689765691197098340016609184414760* x^24*z^13 + 473303042323078224878142920217131906694567697689803789016*x^25*z^13 + 206311648307273040432260708861193296379794407660310807472*x^26*z^13 + 43300714495648429818811640476029081541298584258220301136* x^27*z^13 + 1400038283931642888514436853397415196*z^14 + 206274625629707757576488326543639673604*x*z^14 + 14611211454807085123315645074816944584068*x^2*z^14 + 662375513500743961644435255926911877362368*x^3*z^14 + 21582402496043676379790148823205001086307576*x^4*z^14 + 538121225080814373075897552446375103052317432*x^5*z^14 + 10672737637983780987512948323803400347893013864*x^6*z^14 + 172796705068955002796289106835148304250673172128*x^7*z^14 + 2325555657961455762406010258955180877753398970980*x^8*z^14 + 26356297456613043237521225941615368692261209514700*x^9*z^14 + 253898998792501506183819303682941004593003108066396*x^10*z^14 + 2092743263054323120244936891919816036314428984744704*x^11*z^14 + 14823598115572563688448687636556027900199238093035152*x^12*z^14 + 90461957670196985627068633314553502263522401738995664*x^13* z^14 + 476002205179745458600689577515572563965579599710427184*x^14*z^14 + 2157876664077625561712311460436289432989239584542512064* x^15*z^14 + 8406727871392457296955097363560479515433893732210272676*x^16*z^14 + 28022426351504418794996990295311591907555645030316243164*x^17*z^14 + 79396874160588634085830132570321018559364600232855874172*x^18* z^14 + 189438152160174273880418954366158577062353559061805354816*x^19*z^14 + 375718998777288562095795861199864517512851245716058114040*x^20*z^14 + 608306975856207308726502663887152274812694797165174536888* x^21*z^14 + 783425699973673639535341540444691966153540330902768993512*x^22*z^14 + 772071639900183357752295209878295659483960773411282034848*x^23*z^14 + 546883645907139025021484366545643553080264709795353860956* x^24*z^14 + 247920547596707986871026937070787365304266500158182560724*x^25*z^14 + 54033350890112773096977655856734479912494767732298391844*x^26*z^14 + 8898218766696128949968423924579180364*z^15 + 1260572544585234590244260368880927316132*x*z^15 + 85719101074875271814831265788624548931904*x^2*z^15 + 3724021566561433325883718583984098683933936*x^3*z^15 + 116065362427771637889174762862092782871988248*x^4*z^15 + 2762355633108726634686813711503140086778323192*x^5*z^15 + 52177828520294895640454173034608659858668211840*x^6*z^15 + 802544695728794407021148344142726045342037245136*x^7*z^15 + 10232444883186876556814030680897077556559390471412*x^8*z^15 + 109525058249923992944009935662931270811679934229676*x^9*z^15 + 993027194939692391265673365813330766082010698892672*x^10*z^15 + 7673391959955274761747031098253881726567808629775968*x^11*z^15 + 50729646838345372329382465562990057240030477237118288*x^12*z^15 + 287467998939912146038522342111082183755785946272353232*x^13*z^15 + 1396273140318208758253830154023583295629090595668396032*x^14* z^15 + 5802290607360151424136203840115503944109430827034861216*x^15*z^15 + 20549779124374910542246785866798356888739977129843594740*x^16*z^15 + 61649336868686008465940842498206055134234599361673599804*x^17* z^15 + 155264997568096985568936807464465093350988940314809945920*x^18*z^15 + 324149742067877794543635982132061707057092558940031169456*x^19*z^15 + 551054569619269926705916139314396203625794082166332664856* x^20*z^15 + 743486257650398688092074767693982365301644993528221731512*x^21*z^15 + 766016119559089680470645169175448290123283954100989262720*x^22*z^15 + 566186050618524327359227432024512015724185214134127005072* x^23*z^15 + 267365639585810517517451005006086241642495926752128166988*x^24*z^15 + 60602437683591894210217783544472470829875944707199588340*x^25*z^15 + 50980283032856002647975290394542728080*z^16 + 6933213732786427461247479736739370583416*x*z^16 + 451811960119271176750060256559365987211288*x^2*z^16 + 18775280435952747317861512628281773743220720*x^3*z^16 + 558564561530666079559234633417214277716454342*x^4*z^16 + 12660796782853516585307986908929833832138740896*x^5*z^16 + 227190963575387722199622376196913341705903477412*x^6*z^16 + 3310496885067053312114784238655729930099098443912*x^7*z^16 + 39863899933142922125018813599424407717740732651318*x^8*z^16 + 401591880675462216852347973352248761649316399700304*x^9*z^16 + 3413530985394046322391141473548872149605495954186944*x^10*z^16 + 24618799230712783096008049408572379696364412131476992*x^11*z^16 + 151132073103006232085946364245847447145127099842122380*x^12* z^16 + 790536997232079347264061627690316284252300795894661920*x^13*z^16 + 3519771859370105291916652417516003547741746650006677688* x^14*z^16 + 13296915890721187318049142136280323359680728677895443696*x^15*z^16 + 42383919672083399058024730510331498979882252857038265772*x^16*z^16 + 113023787475219822034227361012152375317141800434622283256* x^17*z^16 + 249070940021901602426511050587255345943505454143955743048*x^18*z^16 + 445705877814719797753608921077731670353296521859667170384*x^19*z^16 + 631416638715171431874012410641299171726533928553254764526* x^20*z^16 + 681529096564736542829131198440402192253516195055431015296*x^21*z^16 + 526636337638517739687336993055451766294146659859702234244*x^22*z^16 + 259502006637288639265049868427112110296551626452051130440* x^23*z^16 + 61271792888361956378252332622589154861362446079827821902*x^24*z^16 + 263888740156078110512123314571452111920*z^17 + 34393917363664944840127939881057077699760*x*z^17 + 2143890376269105720759899985619028117143992*x^2*z^17 + 85040978194736986251948608432834230658697180*x^3*z^17 + 2409494137719684254747637555035410271071942572*x^4*z^17 + 51884440873503084183037130307706518027194123124*x^5*z^17 + 882035498617862684173823048293563594905720292732*x^6*z^17 + 12138488555318113352434756117502306608809266976432*x^7*z^17 + 137569536884955555861049928945616585809147952228720*x^8*z^17 + 1299267848445480370605878014799459854084494112431120*x^9*z^17 + 10307524928561315223178812927049574602796524561901280*x^10*z^17 + 69029182082884994367691769385767344987178413881393576*x^11*z^17 + 391165364849618846815311913927542916447517872976270088*x^12* z^17 + 1875587776451937491568141997392831449067914940393126648*x^13*z^17 + 7591664841331792183499008537302701311412351854186800648*x^14*z^17 + 25811660600386300592120551735595374141692127339896056208*x^15* z^17 + 73133037825498027914196678375189021562283191476691592448*x^16*z^17 + 170643750504806022227478384248961256674804451365343709088*x^17*z^17 + 322327079998851027037784715869632999961455539631560488904* x^18*z^17 + 480663220229919701675965634181517848209106911416018682076*x^19*z^17 + 544751664891646968045900079974939407541135340976052729516*x^20*z^17 + 440989349288768154577433935799304822043343299013282354484* x^21*z^17 + 227176300518722588946897955926760569584084252680943962140*x^22*z^17 + 55971132978837534944541783051008969162090351404972005728*x^23*z^17 + 1236366691619624991600504188141931088122*z^18 + 154135283781776631029894718077876931092238*x*z^18 + 9171079378385651366886909605711936183362038*x^2*z^18 + 346463202510987577846202868986311474840770528*x^3*z^18 + 9325634849480671990914328868385566783364415842*x^4*z^18 + 190242949807464351293286269194609709390962966986*x^5*z^18 + 3054456253991132340806945167397341523653490155638*x^6*z^18 + 39562481115362879408535012026293379884967366035488*x^7*z^18 + 420351362243361580237541182717611164630595256362516*x^8*z^18 + 3705319417660170941667251949047469925670520498156300*x^9*z^18 + 27295853050574516933373284579346131760768208995874668*x^10*z^18 + 168738000799513769330471501754634619085249348798560736*x^11*z^18 + 876500171930240836153436727409615556480238755830645620*x^12* z^18 + 3820641774804138079764556079167786798987947821546495892*x^13*z^18 + 13918052077651604974553679196198318452748552867095231516*x^14*z^18 + 42063445721367443080697215382305668552528157570459938144*x^15* z^18 + 104282292286543026549891055757221735631241207355078996338*x^16*z^18 + 208564591717137853327387539784262893083402109822458776646*x^17*z^18 + 328296125805491285632093811189354009507797512719137103070* x^18*z^18 + 391651512053189885850891150340836476544801781732488394944*x^19*z^18 + 332903688362547467659816283163777549339076388096361599658*x^20*z^18 + 179662279549995055762323025326457439577352259111910113346* x^21*z^18 + 46276375500949644388973764086156722652538077297789203758*x^22*z^18 + 5249293597722989862331337857834519205706*z^19 + 624657539119445018615862813568569444099486*x*z^19 + 35397176259851800888221297250706681895645648*x^2*z^19 + 1270365100787693785417345910867760289834649676*x^3*z^19 + 32394311556261264452770219529476890942289415274*x^4*z^19 + 624130389967625012779046310508554858039780938946*x^5*z^19 + 9431303620416193778134595712761681962211480283072*x^6*z^19 + 114522972018544370900421761888555869906598078247984*x^7*z^19 + 1135686139059957283888321363148759989905638326041300*x^8*z^19 + 9295801348992442312785441282724722725770167021581196*x^9*z^19 + 63211449168793187175597697042281197023140585144512352*x^10*z^19 + 358198211306506748384592636777166958707278936165287400*x^11*z^19 + 1691491548208570778422317387072858845559964796178029412*x^12* z^19 + 6635851435267206759730656803851252556278312634410101924*x^13*z^19 + 21487519150582200018792569940469883483149037059232196288*x^14*z^19 + 56822552165862645985250301103221556201684273546089415536*x^15* z^19 + 120747925193484393600501499516075872423290903881486099362*x^16*z^19 + 201246530407424234537107591920072122025861518933153436918*x^17*z^19 + 253421548586164899736373974477191295659277085289198397008* x^18*z^19 + 226745616988284361180603658511001644766913147264115552300*x^19*z^19 + 128489209405322963039640211175227883684303163800207920242*x^20*z^19 + 34671672435780205789595367494985430114130467937057757818* x^21*z^19 + 20209544173097942520319942615958813371524*z^20 + 2290408163361829924513393961689382267470476*x*z^20 + 123300168236127078471277152187296697819021476*x^2*z^20 + 4192204623846684968915062148855725178009484096*x^3*z^20 + 100962264585882123796195183734278148256282857510*x^4*z^20 + 1830782439290629988948478476885462951873589820656*x^5*z^20 + 25936084738979738937952897263490112434409871011520*x^6*z^20 + 293942293953355785795245094826482260398452992940480*x^7*z^20 + 2706718626986502283439452315767237029439350850427296*x^8*z^20 + 20450762960599157636182947455164226814511640488676520*x^9*z^20 + 127476422611703041614379739662296412533027760179955272*x^10*z^20 + 656696723994253431388751575650517654595443219811722560*x^11* z^20 + 2790961103996526660526237852780883932317263387384380308*x^12*z^20 + 9732582438346609713479198390722881705903703233522086064*x^13*z^20 + 27575650252786610422429992436077088304243847188927904288*x^14* z^20 + 62504804411956707446571091657644995936893066691072206656*x^15*z^20 + 110685587394021889439214632949533850150653941026312112332*x^16*z^20 + 147580783247993821453871708338016322652424731019104417068* x^17*z^20 + 139381893430286176384074809085431121522405029961659837748*x^18*z^20 + 83140092267724100303967821126163773361475470050225106048*x^19*z^20 + 23556468484499236606356200318160777881663175374952073302*x^20* z^20 + 70571820359255968090488736841210962046172*z^21 + 7598313097372719043853302279886240402148708*x*z^21 + 387514706738157183407949832992448082709496176*x^2*z^21 + 12443529512497443677954530846849403569134842616*x^3*z^21 + 282053316797045111358542168917110604037864490624*x^4*z^21 + 4794906456263681896797775890720480288176697315744*x^5*z^21 + 63399318550683183177224095823451358197075634282320*x^6*z^21 + 667202355153869228237587324057539071342095692306864*x^7*z^21 + 5671220012589169759066713629799269597183159691400440*x^8*z^21 + 39278449812853039138078715904663351010257175425072168*x^9*z^21 + 222577882272408686294597172692110277883035459143669776*x^10*z^21 + 1031951999647551035087818918123186960232476153177147392*x^11* z^21 + 3898485266708543647168337770079739718984893978683413920*x^12*z^21 + 11895377707468737647388316819861795826779304805514593984*x^13*z^21 + 28888773827365211765795419784203162325739148825103304624*x^14* z^21 + 54567687710724842996832249711326237775292766262213626256*x^15*z^21 + 77304228131059731039450919844449702171855639044943314444*x^16*z^21 + 77304229066811253434983342940046422023137757693537363476*x^17* z^21 + 48673018015811615528432378404532016888059102815754789760*x^18*z^21 + 14516498699056317117963198283885148393947895143294163400*x^19*z^21 + 223481288881004776389911958097047943836834*z^22 + 22795001451325115168691509974426703673565278*x*z^22 + 1097958642714910307079051830916357926359272222*x^2*z^22 + 33182749216777355567355905455314356613255886272*x^3*z^22 + 705133344716343120810963789259708470981221461752*x^4*z^22 + 11188115243976506678521067823852771370489984184376*x^5*z^22 + 137365190266560523528020339433174268732815144732200*x^6*z^22 + 1334404696841442063546724141400268638310740494243680*x^7*z^22 + 10397236519768549384215372099004643124403642599092748*x^8*z^22 + 65464081425997125557462204763758770450437134578507620*x^9*z^22 + 333866810786350428493143295771156320417060499990940820*x^10* z^22 + 1375935931676941986608473843877978934962788452187540608*x^11*z^22 + 4548232685556639685738836789018138929887421833050174072*x^12*z^22 + 11895378698122881557054705031682427701784853586090639896*x^13* z^22 + 24073981920778656656382851869104881124999382935495634920*x^14*z^22 + 36378462253798400640737393082229542393108505886363232096*x^15*z^22 + 38652097889805629022860274155260095997466288790077758434*x^16* z^22 + 25768057903601904736717146112655111793462552839710371054*x^17*z^22 + 8112136422783000401263288152378900867648600723181186622*x^18*z^22 + 641292680691182275163826100991692814010042*z^23 + 61777683758990813434995674560347134580988926*x*z^23 + 2800588308009556995404512692010166012527279296*x^2*z^23 + 79350016471153140369852904498328374443168968880*x^3*z^23 + 1573775646300165106155953023725558898214734414104*x^4*z^23 + 23186961673833147058435932002663461887595019692344*x^5*z^23 + 262785573483667890418616270851242616037925249751680*x^6*z^23 + 2340042975402636089935743050113229187103419974924208*x^7*z^23 + 16575304635319704537534030468834877392489545712750108*x^8*z^23 + 93926727318529818994658308850746426266206885186420580*x^9*z^23 + 425801177937111393695381586421348794901808536765172928*x^10* z^23 + 1535464937155255356389767650752721248063916360919595664*x^11*z^23 + 4350484127151669103418556478725654613522953422119990680*x^12*z^23 + 9481823272869098669348934326238182466892854713472578712*x^13* z^23 + 15351521845113293765973226292122955076880185074347336704*x^14*z^23 + 17398389083494177655534724001654368708737334641845026576*x^15*z^23 + 12323865928606266011815479854101364768029081142142438522*x^16* z^23 + 4107966357481382207265757787740409835876609387925284046*x^17*z^23 + 1665560036067176966550921434008112128265808*z^24 + 151011951100159525903553063670245900029057920*x*z^24 + 6418015612854903586705653441073289147055444576*x^2*z^24 + 169720893652840662927614080939082825978431900224*x^3*z^24 + 3125693501664967674313047857539250678450078509860*x^4*z^24 + 42509433945014070701687025708071829197994461547408*x^5*z^24 + 441625793459402736195947324247280779373699432836504*x^6*z^24 + 3575065982667819103758807080345026315555353916164432*x^7*z^24 + 22791045924045466831052506556259818649106542698539116*x^8*z^24 + 114799342046118090501139611903890600187541283212524768*x^9*z^24 + 455370712678158669881148001542749483356586601556709040*x^10* z^24 + 1407509250437057475788431532741171319550261947294874272*x^11*z^24 + 3323285458106093808635530249973067973139039410504017084*x^12*z^24 + 5794446151556052496070370734856482659973636283833949456*x^13* z^24 + 7036120000860107515618262282211317157472599700462356696*x^14*z^24 + 5316182378141792338347280173250455249444985286530605264*x^15*z^24 + 1882819333970796780382285351639177807448835852660429284*x^16* z^24 + 3908613365102054033059613140607786073730800*z^25 + 332228584506036260847372746982876409967202672*x*z^25 + 13178349991366034165646716363462899747304628240*x^2*z^25 + 323601438820350966194700509226768095898306891096*x^3*z^25 + 5501221669949352959932091182985703554222762991048*x^4*z^25 + 68581889660004480964987378467473985260109232490424*x^5*z^25 + 647717784257668377624803817720921780278091945826680*x^6*z^25 + 4719086458542458724807497958026854078467876394040112*x^7*z^25 + 26741487938188282597972679549767241159826316803178080*x^8*z^25 + 117860620916984732905648815509235686053624493682401088*x^9*z^25 + 400726093470792927583404817706112877144552680927361824*x^10*z^25 + 1032173534811051801782989313370258215260484308888347672*x^11* z^25 + 1949661619399519348409862559716734793922026226357674216*x^12*z^25 + 2549558268087851856446209335946260063306035091719572632*x^13*z^25 + 2063925386424915319544923336267604937633055145893057368*x^14* z^25 + 779701337854277004017003469709606978426326937214569056*x^15*z^25 + 8268084017089004517641253354978115118579052*z^26 + 655934444277971695258995064882351385624757348*x*z^26 + 24160264581708724445832476119159059509059934292*x^2*z^26 + 547632596521017000432254273285786763546183499200*x^3*z^26 + 8533942388994276125446256704727284512312263904372*x^4*z^26 + 96718013362626108048175343206108996190547179825508*x^5*z^26 + 822103162920406618283723528926045471505556538599516*x^6*z^26 + 5324097139237945329979892023634900025440269378777248*x^7*z^26 + 26398650845304304096512963719362357467574281457900884*x^8*z^26 + 99728276928628788474757387408428314605044938054452332*x^9*z^26 + 282563485627311392428730550776737484050966311111547020*x^10* z^26 + 582252086016013054771339548486565344710818132057565088*x^11*z^26 + 824855106569599137915697553536138920802791189431840844* x^12*z^26 + 719103671338202744974481262118004489386549574134339020*x^13*z^26 + 291065811465911589569990903851165537519812577420280132*x^14*z^26 + 15718977933121165839135526604922982723419372*z^27 + 1157993359382647112841352483702796845616049252*x*z^27 + 39372204730519247075800804815066671391933598944*x^2*z^27 + 818068170502938932648288439083716923816083861976*x^3*z^27 + 11589310576460281247047894820245555256008288600644*x^4*z^27 + 118210994150426448970171327624805333893990963270164*x^5*z^27 + 893149905658910077739307775586261225012680635509184*x^6*z^27 + 5061183497044372072688194711554971403501868660109424*x^7*z^27 + 21510029783325164441870809979857527980863617337301172*x^8*z^27 + 67716713338257793638869274435097184246117320359023628*x^9*z^27 + 153491094753245605262116627019613668831932322233164000*x^10* z^27 + 237213407315166288620605998060701698193353967239648824*x^11*z^27 + 224035756538295651243574366028397594377789297389016220* x^12*z^27 + 97657398828946375547743799765429181849250936017829628*x^13*z^27 + 26762109729186209033249510286678567154406280*z^28 + 1819747169329357958795607451581181897502396472*x*z^28 + 56714984748244074785221067942292096384597817512*x^2*z^28 + 1071282360763620347819893030466215915810316292576*x^3*z^28 + 13658834374207498223832970545796351283265026162388*x^4*z^28 + 123840044748653232573914238747184253820771344434992*x^5*z^28 + 818719918066754829609243820017490729030383209875104*x^6*z^28 + 3976635100514236224454579548915549051186817560155328*x^7*z^28 + 14083915012959706835522046699906070375420978718466240*x^8*z^28 + 35470599381587449661339962721864280290077249945448472*x^9*z^28 + 60300466202815670405709539696850018492001958460545688*x^10*z^28 + 62127884247131143741305415283937027307905777669728736*x^11*z^28 + 29337931969301905539240530326963803621001515460007428*x^12* z^28 + 40602920653480590033286781623530586571418744*z^29 + 2530939770070162386078969647222197399284140712*x*z^29 + 71708201716470323982805712799263835456599176416*x^2*z^29 + 1219040247314396191231113238368520910610793407072*x^3*z^29 + 13815770990088737128314708976055056441843213553184*x^4*z^29 + 109605174349546310633656012354844488464581326083648*x^5*z^29 + 621096349288639898206694026869714079301750673380976*x^6*z^29 + 2513967306436901799394982864719955549443611947397744*x^7*z^29 + 7122929061630634931307969808686951996353917656128904*x^8*z^29 + 13454415808990914023935019438041910901428837134327800*x^9*z^29 + 15248124316717150971467383461788948491878728925332112*x^10*z^29 + 7855010522753815957024183970175373363611928907741008*x^11*z^29 + 54576802383951465515471671645346977558614828*z^30 + 3093209205370167092372703937341821548966573620*x*z^30 + 78879310850781400152487671421049733850540617012*x^2*z^30 + 1191955224564832110903874515955654087839681512256*x^3*z^30 + 11820270436331276940105398639748004584327871558728*x^4*z^30 + 80378015449124121339696484655947617069386916108744*x^5*z^30 + 379562552830379710545884638351383357292260500764632*x^6*z^30 + 1229057835429592266149501815199027670322859288655072*x^7*z^30 + 2611675982563862133919612657859715643040783800545516*x^8*z^30 + 3288772166588869331853083608803359294827090896425316*x^9*z^30 + 1863700473202891884957278562170720865562556904072084*x^10*z^30 + 64588814616622938540534210557785409271965916*z^31 + 3292827912669952101493217210126416291269260820*x*z^31 + 74641572976634122390886195208744827028978377664*x^2*z^31 + 986903137989881812482392235639966694026242682384*x^3*z^31 + 8388650369771808334424946695218932812526208913448*x^4*z^31 + 47535155272878171787696453128269649649936336583880*x^5*z^31 + 179574641326144251096064971909967830121116797831040*x^6*z^31 + 436114488457186592469361691672520639780821640533232*x^7*z^31 + 617866681329170382696112543649021205765126861664860*x^8*z^31 + 389024944092041444127931530594796823256227785847620*x^9*z^31 + 66608228055657372382276923624876763274919024*z^32 + 3018522061775202900051060914177115010295852796*x*z^32 + 59861677340994200948852403406716243683127623292*x^2*z^32 + 678450693801035238353602046964974089581220075896*x^3*z^32 + 4805714397337412170979830836835487567970206158149*x^4*z^32 + 21786368968848831738958130329199971445366513280456*x^5*z^32 + 61736111612584072306231187341279070116362767144718*x^6*z^32 + 99950365734964066012880528711324300657335241658828*x^7*z^32 + 70789817328720566511448490357982713388281298806969*x^8*z^32 + 59051202582058953212447864109067840923544272*z^33 + 2347623586765533912473255708304142393653734832*x*z^33 + 39905144993078151512313813906876730903645134660*x^2*z^33 + 376928722893603475551902865898957782842063491290*x^3*z^33 + 2136119443615728051505459766978828908111320784266*x^4*z^33 + 7261998608638431401580911705052919997220441947622*x^5*z^33 + 13712630420030146331374919720652752987110565921754*x^6*z^33 + 11102887311578604966049745540038157524811180650912*x^7*z^33 + 44734520480431430700875487399376628727050355*z^34 + 1519682973636709832758620346971686938939486137*x*z^34 + 21531147591551692123348581593808560520774012357*x^2*z^34 + 162626598289570262481128673027689795874865119888*x^3*z^34 + 690565225248625282315603880662244850104627494587*x^4*z^34 + 1566138477841640425503257210345186479969682679303*x^5*z^34 + 1479592250846869356951891915180009895395077080473*x^6*z^34 + 28300977754152136955251928734592063209318299*z^35 + 795715943947926106675506132506779247691386529*x*z^35 + 9011842528608681472666089363246368287739407704*x^2*z^35 + 51138433214952224861471056731420554450174930514*x^3*z^35 + 145199233828905359472552139127211520424503268391*x^4*z^35 + 164238324081686120453791927814376827924174322427*x^5*z^35 + 14117141120390313037914035472511888425994758*z^36 + 323365495108952286879451032465134263502610210*x*z^36 + 2775381201154071312777287444152926380414109798*x^2*z^36 + 10388181562926763242679921715758679192001361200*x^3*z^36 + 14739827269396654283506059097653904848264738429*x^4*z^36 + 5820795918978481915952021011310033692969578*z^37 + 94999551481035770575700649964819172395984038*x*z^37 + 530665621635577688867550180526372156866942600*x^2*z^37 + 1022415764351213013884813347814143688896976076*x^3*z^37 + 1312892454911550337509682972582547031695031*z^38 + 20411550217812906529317207924167974791908217*x*z^38 + 52968290752143773018446212463650850472459641*x^2*z^38 + 370303000103257787502731094830974803811419*z^39 + 2098383667251794129182142870708857221598041*x*z^39)^2 in I Output: Magma V2.10-22 Sun Apr 4 2004 03:25:34 on modular [Seed = 2760596666] ------------------------------------- false Total time: 4.909 seconds, Total memory usage: 19.24MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Sun Apr 4 03:26:07 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > (275573750405290386156*x + 17177430441929767403724*x^2 + 1291950980511202505940696*x^3 + 71568332483763548406999069*x^4 + 2933002060899381069228645912*x^5 + 96694114364841635947146176766*x^6 + 2658053466027253803681878061708*x^7 + 62109462904914230956593041593401*x^8 + 1251609559311431425713553664769168*x^9 + 21991590820796269937289124980924576*x^10 + 339874528606848103579134147488680128*x^11 + 4654026031226274102693081032154096516*x^12 + 56801409394762285311633922332217353600*x^13 + 620770532721078411713098345209265341864*x^14 + 6097456834004194955480660618053741035024*x^15 + 53987934247818304475156697719045285693796*x^16 + 431899431419641327846058269926722954630088*x^17 + 3127249750515556304176353645072789494350584*x^18 + 20519223977129947710225260098905240932075760*x^19 + 122090416162149246895308268001813372348103702*x^20 + 658900225567898031947473915900074743078980656*x^21 + 3224592191327204316990397911940987002079789716*x^22 + 14300367515641454048978476849108478504680345992*x^23 + 57400451693893534478325151250855145167883714510*x^24 + 208171412665872532941127001273787505392125274384*x^25 + 680557440907355495456217907040251678802415826560*x^26 + 1999703759524094125195693668464837454569737422720*x^27 + 5261152461969601583290677713952014651700824222484*x^28 + 12335604798454205588965973570184471884788998461376*x^29 + 25629910383456630695709698944761765360645003932904*x^30 + 46860929955092484657379858243622139248061088083600*x^31 + 74697758228167981052469534838842040243897235551764*x^32 + 102551000907319343546873515233031719460536147365292*x^33 + 119536192741689256717272905440585639510921919857692*x^34 + 116266905241756572785108148359746736516657964039672*x^35 + 91839208096405022857172933664731867078794672188213*x^36 + 55918378230452549529642128108440729812729682374264*x^37 + 23662430614834358080184060703896456013828253039326*x^38 + 11659748418903886590235624114963471079277689903436*x^39 + 16517976926780506002833800829531584028976727363201*x^40 + 24250490035665553981728*x*z + 2708308199677593327320484*x^2*z + 185965724869405316873949978*x^3*z + 9446560232542184898725758938*x^4*z + 374833372709513310969631240854*x^5*z + 12038896134723137149519284869370*x^6*z + 321606369640715339865668708845296*x^7*z + 7289962021587165411775199840852400*x^8*z + 142293161575424443092248116938507408*x^9*z + 2418938185907234199673011434215372704*x^10*z + 36136740027070924449065961714034928856*x^11*z + 477811029745193728538166008188884320664*x^12*z + 5623536831215179112397946824729248223720*x^13*z + 59180957599185729922006047847199225929272*x^14*z + 558927233667570416451242568971215445973648*x^15*z + 4750878761361244583792220045412446030682704*x^16*z + 36423564892007624175774554157873815154892080*x^17*z + 252267212463326592215194562285703658764876840*x^18*z + 1579984888847646191802159943453081444663907484*x^19*z + 8953235042103492321181581093013602155769051612*x^20*z + 45903181479775065685746052620589410081998731524*x^21*z + 212824169916940053786033181936625696969521713660*x^22*z + 891392832702671559852449634740368405988291154576*x^23*z + 3367478276531373587105438940780372630636177196752*x^24*z + 11449435585574619285981935439477146954818804880112*x^25*z + 34935528499554504685253316363689474984388242818752*x^26*z + 95317892340744767224896692668255805803325768161752*x^27*z + 231485665082691309511503545714991895032671262644760*x^28*z + 497560801755520178970056212349142432013282965491688*x^29*z + 939840996417932148185674193085533589140914345757304*x^30*z + 1546197412122515582506898752925041825121169239926512*x^31*z + 2190449751731184517705071896277054264595772555710512*x^32*z + 2632902875335051927821246423225939508411350031304496*x^33*z + 2632452245401035714299054555506473029495846016234708*x^34*z + 2130958730852612957996086501629287342380238549530266*x^35*z + 1346387674158018214620227794644620177276669936326554*x^36*z + 623756195261119510824698500447725759934853718865302*x^37*z + 169752219628159525357842174614909358360072250064730*x^38*z + 9643730412467490523371*z^2 + 1751508483444024959631681*x*z^2 + 180916037470323574417460781*x^2*z^2 + 12233407143306482256457577232*x^3*z^2 + 606118551048335019634649146107*x^4*z^2 + 23367473975046034208061025711911*x^5*z^2 + 728421126124038027914198607293817*x^6*z^2 + 18868752321588740210322789303668064*x^7*z^2 + 414308451729930813185694749573131260*x^8*z^2 + 7825833236785378088088541177710286500*x^9*z^2 + 128606153173224855814637756267582780100*x^10*z^2 + 1855051313833448119668449319118667226144*x^11*z^2 + 23651798888503668012425878793329093994316*x^12*z^2 + 268053120097636202152862712811264334823660*x^13*z^2 + 2712446938606718806914465313418525436055908*x^14*z^2 + 24592891641134888395019327537830483012319712*x^15*z^2 + 200329471000092472634559667088086162644503034*x^16*z^2 + 1469081104905246707248850519426796600825460350*x^17*z^2 + 9712259663051622035756481607475766318900968694*x^18*z^2 + 57932825783353442937754995850599570761534690880*x^19*z^2 + 311871752669677894681341719409199844667357685482*x^20*z^2 + 1514804669394469909743434970510837176423644472994*x^21*z^2 + 6633006505988272084744115348483570998893557632590*x^22*z^2 + 26147518920242847558373144438530469629205441249824*x^23*z^2 + 92605827724522886122699851554931070431436969686828*x^24*z^2 + 293868939116730390556145423872799672728059885903828*x^25*z^2 + 832628374118471953013760679702380937055811671891796*x^26*z^2 + 2096993653802535947088435222344004038514578837331168*x^27*z^2 + 4668309788359972208217093338322979087260119258263452*x^28*z^2 + 9121934877513245906129022129440154179483931791374620*x^29*z^2 + 15507243382046238606774064102966507272115701064901652*x^30*z^2 + 22677615122299555101271309965832575195383030752749216*x^31*z^2 + 28111325531206383405154326247231776793069269312841203*x^32*z^2 + 28962929405996491059899824597548995685882889678576329*x^33*z^2 + 24134320054203597812361190704593444755766618423081157*x^34*z^2 + 15621709739973357383625054788685193267178784889408944*x^35*z^2 + 7371534190697021547710669575085297427277061353243443*x^36*z^2 + 2261476792601814121156141859591959118596962531417903*x^37*z^2 + 283549077971481281245877113893793039334787351034049*x^38*z^2 + 342216218761063886877363*z^3 + 76247891165136585238075017*x*z^3 + 7900491927292055387627684760*x^2*z^3 + 523423319831841499759193824242*x^3*z^3 + 25208128013123300679123783506919*x^4*z^3 + 942604050647503773602266819194459*x^5*z^3 + 28486466706334994716272337611139392*x^6*z^3 + 714888056920772762652913527624186384*x^7*z^3 + 15191552673031244868346296925948277628*x^8*z^3 + 277386071766831376373149739089646019300*x^9*z^3 + 4401177198207987600932726465579721392928*x^10*z^3 + 61216350729494417188416842710952114743896*x^11*z^3 + 751601551512798238314882821390537965330140*x^12*z^3 + 8190533662655483498951061355277406250784988*x^13*z^3 + 79565159229370130726630526679180141627237824*x^14*z^3 + 691332571241415444592014409222903331311618224*x^15*z^3 + 5386633154954873898016398855766238231995385610*x^16*z^3 + 37706441909655498989199727326488589068414979534*x^17*z^3 + 237410948819741182128583361537690173328718756624*x^18*z^3 + 1345328488141384647812489150978159106661679762700*x^19*z^3 + 6861174417941368179223190277768151650698736476850*x^20*z^3 + 31474278495337897889481906128202239891328383840922*x^21*z^3 + 129712195267969818280228890674598696122343832432320*x^22*z^3 + 479371179226166129129042782787289468854984356989168*x^23*z^3 + 1584587966452281379330468964959620463005653681905260*x^24*z^3 + 4669251547371105506086517598456206910248301772471380*x^25*z^3 + 12211885942828029339427593796868733804207587339878944*x^26*z^3 + 28192884115946756732781391530027654068914075937600280*x^27*z^3 + 57057094983342569431062100563499054566043670890616748*x^28*z^3 + 100341758582959633960950649590749146584574341954511500*x^29*z^3 + 151626854198223527379825060122520385779927813689914944*x^30*z^3 + 194016570806273602044640576365703540145063769649949520*x^31* z^3 + 206146703836682632840215191656611539932782869503245915*x^32*z^3 + 177001087190786570521091635763164992989673921351249777* x^33*z^3 + 117982303460122404914358699007442107624981770461595672*x^34*z^3 + 57271519598998921957280188771746329896902501735072402*x^35*z^3 + 18086430043190782419136861912719629110996113184587999*x^36*z^3 + 2868442681172043779145881678716118680558946358882467*x^37*z^3 + 12741311150112745228992678*z^4 + 2571906247574770454933951586*x*z^4 + 253982468482258302269922247974*x^2*z^4 + 16304993653056933011183451422352*x^3*z^4 + 762343600149242634985513381020933*x^4*z^4 + 27649388978070973457017554083210832*x^5*z^4 + 809520414810735464625948600846100608*x^6*z^4 + 19659630596045126816939038688043173952*x^7*z^4 + 403839644078034093724274266327300754016*x^8*z^4 + 7119547083509018381452024338536385518808*x^9*z^4 + 108929239643071926805758911508580857383544*x^10*z^4 + 1458992033222818844159493206552705588754816*x^11*z^4 + 17224202978930354252753220620452207735716252*x^12*z^4 + 180191614049158907715152023283858857449405936*x^13*z^4 + 1677498369500012938825651910413077130443315936*x^14*z^4 + 13941877987322130657269119936294001722976161344*x^15*z^4 + 103692715562900381704349393944711177595984096172*x^16*z^4 + 691284680914383463141363459795134728910280910316*x^17*z^4 + 4134906348764220850823008029350315148529827272628*x^18*z^4 + 22197920061839158666973289148682682670360326925344*x^19*z^4 + 106919989865345093606934330574596567312751999422798*x^20*z^4 + 461622801594484033896560027833695805380220168563120*x^21*z^4 + 1783542464577829765297843362295179528527585173664064*x^22*z^4 + 6151928762467408432767884432542976298588266277143232*x^23*z^4 + 18883005288525385309841496051859934786331963291015984*x^24*z^4 + 51361783227141637008875498424579896016519967554266136*x^25*z^4 + 123136586013563889190416308653580054084454058774217112*x^26*z^4 + 258434724746553375570151807374691909229035243226111232*x^27* z^4 + 470720156638654018409421319303555916211908338219586556*x^28*z^4 + 735838781312920044555927576926285381276397677810815248* x^29*z^4 + 972944565390857464965683817636861637138337102502150240*x^30*z^4 + 1067096764997074070908498386969699657388613891366616768*x^31*z^4 + 944811163730939089911288120180399428010517623859697310*x^32* z^4 + 649004925226402301589956294019754766907238943044347330*x^33*z^4 + 324588758185787327474749894056820750690071076168409622* x^34*z^4 + 105033043579231769755317496651393722459318721745938128*x^35*z^4 + 16600220317771184440146529898584435381489293771699093*x^36*z^4 + 332312791708775912732854794*z^5 + 65740127318065123122105552294*x*z^5 + 6331112506265092145068098404808*x^2*z^5 + 394660641171724329210939981524124*x^3*z^5 + 17891047637304395373594843816407616*x^4*z^5 + 628561492033131562156955047282520736*x^5*z^5 + 17809200633325096882362152562020253360*x^6*z^5 + 418093243425619011981624433368569119632*x^7*z^5 + 8292194209040025463570036931978051183880*x^8*z^5 + 140967274531631952447936450367408580548248*x^9*z^5 + 2076916789546416165853805266946009732069808*x^10*z^5 + 26748168089899447618313946543365101776315936*x^11*z^5 + 303145957212485629991928382524357213415061472*x^12*z^5 + 3039232855907900431944461015983070778122845056*x^13*z^5 + 27063643626211301796957481656976547640980760624*x^14*z^5 + 214704889859889669584988205398992944641575820240*x^15*z^5 + 1520826299536621592083553384065512389584973911980*x^16*z^5 + 9631900401161558873643979553354660337587808417876*x^17*z^5 + 54580770576594420819800499584100670311415844686080*x^18*z^5 + 276734074153305476039534373645142002580113258080184*x^19*z^5 + 1254527741301725585349306889278876887704199877364992*x^20*z^5 + 5077850375643790067352350488160442605966434207567776*x^21*z^5 + 18311037303635484100693269584698573710567081373536912*x^22*z^5 + 58648398162102180656280634802789892446023468987920816*x^23*z^5 + 166170454360414414902421270371411647129758295273298024*x^24*z^5 + 414318264752290865554753100113977871584945085645411320*x^25* z^5 + 903001266083503138991153681164423273444417014081308880*x^26*z^5 + 1705669646562197001578586455734311281362422684528361152* x^27*z^5 + 2761562176036700005774703575128615883365401285972698080*x^28*z^5 + 3777307871890990732740158013618256256463863527182550848*x^29*z^5 + 4280936986972444661877046433046000337309812992623028880*x^30* z^5 + 3912673049604395904622715596659579018483800913545847024*x^31*z^5 + 2771510186736665040704531168173399003596092243589940698* x^32*z^5 + 1427818770723150459054664467261570222114220075124804214*x^33*z^5 + 475878092246793337453326680846839628421291755063824056*x^34*z^5 + 76929802779825090695114781235516217609130364196197580*x^35*z^5 + 7074140179699768467882758751*z^6 + 1364979631893772484777289508593*x*z^6 + 127677463055642373688810949509809*x^2*z^6 + 7717618628353231755656667898213440*x^3*z^6 + 338931491807121289074311070522558024*x^4*z^6 + 11523651647862048076290967188187542408*x^5*z^6 + 315619662906015102672852958758092992536*x^6*z^6 + 7154044127271192967771270094096624686368*x^7*z^6 + 136821108285222759822997207422350672289444*x^8*z^6 + 2239812397817969894270766304987380250673772*x^9*z^6 + 31730676809558954012162924757357624346281852*x^10*z^6 + 392306550471785345505510663802963855211928192*x^11*z^6 + 4260884921340158557791786732850332994772094840*x^12*z^6 + 40860792965311022278208675547234136199007267480*x^13*z^6 + 347316742661854788899505521512195000951164877416*x^14*z^6 + 2624171002495562769395941336896146549917484923104*x^15*z^6 + 17658484158487211996524442505393915198380880243258*x^16*z^6 + 105950903229655744927872597820231569891556919857974*x^17*z^6 + 567033527630836897208151048925601780787461959892742*x^18*z^6 + 2705844216563860316490951440635108438221449779085376*x^19*z^6 + 11499838234853837474061749037326883919761319868854008*x^20*z^6 + 43443834047022922865437105434337106009651986165758072*x^21*z^6 + 145471015351498890682427244677048312978102552620479528*x^22*z^6 + 430088191689823454232615799348065247182401334922472160*x^23*z^6 + 1117034620582697502706786385573388723184774471557331236*x^24* z^6 + 2531945566116465268042087554848299668307972111478315148*x^25*z^6 + 4966509287191533485866705887411261007708875207689667516* x^26*z^6 + 8338827171089650343804988258897810270903344803352794368*x^27*z^6 + 11813328613191566364102061312251666204965518204176634824*x^28*z^6 + 13850125223530401597128066007588020074534260693323617512*x^29* z^6 + 13080739856100979280416222945031720711002220565228300504*x^30*z^6 + 9564309340637587431711641644070531366009564207635653408* x^31*z^6 + 5080718804917499771606379545191333047699711583965631263*x^32*z^6 + 1745072394630523109129087572728715306188634309303762785*x^33*z^6 + 290813985597689820336642384477701962349579968813542289*x^34* z^6 + 126298796322161844433301385411*z^7 + 23607581505510789544991615955441*x*z^7 + 2140215513102492405278223198155328*x^2*z^7 + 125318031581952661777948160405390160*x^3*z^7 + 5326030221874122866502279432003600168*x^4*z^7 + 175049510378644116455682578354416911240*x^5*z^7 + 4629090251593548767969227075198334560128*x^6*z^7 + 101178657858236909404611848774815951520400*x^7*z^7 + 1863373299468195505207274537852681577540756*x^8*z^7 + 29330876383378586018150551016680654691720364*x^9*z^7 + 398899928305818224368416119779578240362997696*x^10*z^7 + 4726359707794654056074257027008238065798012432*x^11*z^7 + 49101625713775087550835831030033628597580482968*x^12*z^7 + 449468734192278345099798949977368514868135365912*x^13*z^7 + 3638556438248884831592229590552183637954902896128*x^14*z^7 + 26116749198256483791971561364133495861393889096016*x^15*z^7 + 166494274333758441485748929753066901447334901082258*x^16*z^7 + 943467563307431866673931926735281378384878589098486*x^17*z^7 + 4752281143958747287076561762298592517636136820850112*x^18*z^7 + 21260205086764354489770101847030069769425809132379888*x^19*z^7 + 84332144656661442544480957523999087880012759143097624*x^20*z^7 + 295831804365271554323157880791849837115178976619171704*x^21*z^7 + 914389243296340004831876603308260096634932636704179584*x^22* z^7 + 2478127510423692766674163104163599417010487796593906352*x^23*z^7 + 5851134281310205989158910470561144675327766467644874004* x^24*z^7 + 11936312104442496156894796391907635820840409379023275084*x^25*z^7 + 20812029601606519619849719102835789467612267947420692544*x^26*z^7 + 30575708379630987295550991481705324307914657715719076784*x^27* z^7 + 37127664994942787679286664540287880551963982699016321192*x^28*z^7 + 36274138330087119670717236415330016290845196841553382248*x^29*z^7 + 27407086718212074466187405728692067019541440114772712704*x^30* z^7 + 15029667436237215884863348018312305765870764159567641968*x^31*z^7 + 5322985898519730715161784458782168730304791565804025475* x^32*z^7 + 913945012098706230667813847792368321204727850808641441*x^33*z^7 + 1908921407361667514961102741168*z^8 + 346191633438160246866555636199968*x*z^8 + 30408012266243193412984502820770112*x^2*z^8 + 1723138606092104700640474384775129472*x^3*z^8 + 70792181252745480626399334602145402804*x^4*z^8 + 2246469001339816851147965790382995727344*x^5*z^8 + 57284958422463742820015716583369699064504*x^6*z^8 + 1205712174223801157641529999552699347743696*x^7*z^8 + 21351153504938839183436405964239617871700204*x^8*z^8 + 322639644741153901635261305690036582874716736*x^9*z^8 + 4205070037203033499180135874202876494769458928*x^10*z^8 + 47657460972236394244156207822198082378893523616*x^11*z^8 + 472603153844482663281990062738381704267818240564*x^12*z^8 + 4120130018431430405137608848988681742435257386832*x^13*z^8 + 31685761754628025930882360759416196684054849896648*x^14*z^8 + 215463181709518679427479279851520137940304274911024*x^15*z^8 + 1297267914142920821239247823969662590684626249264492*x^16*z^8 + 6918762172776641621195338166013151067828987986503456*x^17*z^8 + 32671932141363715033361851309187154237268756862419296*x^18*z^8 + 136419646306039207498945509725388173091995900314907712*x^19*z^8 + 502479038141001559889354300430958153695819888160626108*x^20* z^8 + 1627075008576331460361673907556067296933418322403594384*x^21*z^8 + 4610045791216823406294871495163939000616070054776913608* x^22*z^8 + 11358083188914360002194490910466900251620459226683866416*x^23*z^8 + 24135926258294995966685406689837113830885751443801091428*x^24*z^8 + 43766486111756890999583502770633711858248312639436706432*x^25* z^8 + 66771962364519129334519948447868894675852885286504634224*x^26*z^8 + 84083181016469409685079801364595487786281702017358278048*x^27*z^8 + 85084047541538130009085923342056191256846465051443122780*x^28* z^8 + 66502622521158386298767207931825174799573950290801524272*x^29*z^8 + 37685448727451866074617500254148992835875752801367821496*x^30*z^8 + 13777260717649052942017159002439996360530923934222850512*x^31* z^8 + 2439786446152216550995326348683945199342052475693261716*x^32*z^8 + 24887510231216342800061240341776*z^9 + 4372451597448148105811656800763920*x*z^9 + 371656781455105480324275202302353232*x^2*z^9 + 20358522283769244865961696727057800664*x^3*z^9 + 807554454362146334167439454565686832680*x^4*z^9 + 24711163574142939808528648320859947503448*x^5*z^9 + 606796324045853848159459672179587993908536*x^6*z^9 + 12280401695822241286719473185086698669416848*x^7*z^9 + 208766830405313115006287538086848696979279232*x^8*z^9 + 3023252988769349780506929287752788734208063264*x^9*z^9 + 37689887101600570240028529052921574853976897632*x^10*z^9 + 407736050868929350956551180684775844559692859496*x^11*z^9 + 3850840489739176406470512560137335650100569183352*x^12*z^9 + 31892858530144729219318321595352616278408022761864*x^13*z^9 + 232362255186235343609223927747121030654653528220776*x^14*z^9 + 1492282032716820170582574823660215978862158883112064*x^15*z^9 + 8456264812339214641497247601807076841417591974978768*x^16*z^9 + 42281324162583266558999220253970874806893116607605648*x^17*z^9 + 186351023090789191253427173742057134388733545491528784*x^18*z^9 + 722518881438356749661595461791224908857569046161499176*x^19*z^9 + 2456564158921818010623766616158153144706883951520114968*x^20* z^9 + 7291706170840948930935607704249484841252054701556088168*x^21*z^9 + 18781667753089246003186342510992206565581805133731628296* x^22*z^9 + 41646309390619935103228110127120826465048096561203036752*x^23*z^9 + 78665251472679669368743148655729704244249760337428799904*x^24*z^9 + 124815510513408876964763617634038772350837279479841147968*x^25* z^9 + 163220262074960010877906055908855576420469249605295782656*x^26*z^9 + 171280599718606165943478426018947761317980915169448425624*x^27*z^9 + 138655763810690924941111235358705013049560666190415858504* x^28*z^9 + 81280821313625900777278743083728210015099190733860758200*x^29*z^9 + 30706210461836332080702772557016958294721922228943622744*x^30*z^9 + 5613480648292009109861196392151734138797490289919825056*x^31* z^9 + 282956170734983678739488904995388*z^10 + 48097728106939595701804487177594772*x*z^10 + 3951961234817517290399974191342025668*x^2*z^10 + 209013973341944116621755636208919123136*x^3*z^10 + 7994785570372862279538275746173505018356*x^4*z^10 + 235579749026634686233405246785162216503076*x^5*z^10 + 5562299714805589302683024703028917487024284*x^6*z^10 + 108067534925024855131847332035117664748882400*x^7*z^10 + 1760600261333043126598300496719884967701709980*x^8*z^10 + 24387574114821283525294896785024383798909311972*x^9*z^10 + 290212131728693309261073540218844963104123265348*x^10*z^10 + 2990064384794771523310849485480320763727713386592*x^11*z^10 + 26827522114964654549633610315003057718799721499764*x^12*z^10 + 210492865479814485758622214310571409186490694796596*x^13*z^10 + 1448391382255458122836313815327034429900051155967676*x^14*z^10 + 8754721265356689724352124214972515510048292424389824*x^15*z^10 + 46509456894362947304909541456087456691081377015488724*x^16*z^10 + 217044131928396812709282546245371941889068525195061308*x^17* z^10 + 888273200260550391907863153003447659917027886499405420*x^18*z^10 + 3179083018446745010488282732552687918027223200709563776* x^19*z^10 + 9908142173844611500293572759988091619809422384863910012*x^20*z^10 + 26736257217031469013971083596159906328729879567952664300*x^21*z^10 + 61979505213827235142774548291951199145510262040423239540*x^22* z^10 + 122162495418796730679317463385981864385212592820686817120*x^23*z^10 + 201907444099826682016395981928835261578020710119223236692*x^24*z^10 + 274594162617810449167381155152254505640036104408182749516* x^25*z^10 + 299237362232047149732307772779497112512941772626614578828*x^26*z^10 + 251211461823928964887418222044341995895482509203836170080*x^27*z^10 + 152520459009026512696939366941540931988252460884587208988* x^28*z^10 + 59605831671480908966529599777708644799933862456628791228*x^29*z^10 + 11258611628807781397598747987473580307653170749574819636*x^30*z^10 + 2829190614455711406539947462522236*z^11 + 464925557498655806328691701833949396*x*z^11 + 36884697419091626350366083471470023776*x^2*z^11 + 1881126204978879834319339898152799945880*x^3*z^11 + 69288169959391663728776583373778249443524*x^4*z^11 + 1963164598088936768796874086083084976432468*x^5*z^11 + 44498396764454209707994210917231479598116160*x^6*z^11 + 828517772502261526554799734972491183017596240*x^7*z^11 + 12911068602217795503325508634179743160981903100*x^8*z^11 + 170713018238300714623606230878062558032512964996*x^9*z^11 + 1934747542094910086282807925311556457149547967136*x^10*z^11 + 18937074419701511527536289102730772390588814099080*x^11*z^11 + 160965132537172291729464905267076966474346614148260*x^12*z^11 + 1192792906747170634733202158508982273960664532839940*x^13*z^11 + 7724754070980983016529450860667663954227446866471296*x^14*z^11 + 43773606330188206736992073800224084329648146193745120*x^15*z^11 + 217044130630811862135491138120241966598450567588683348*x^16* z^11 + 940524566083461824941616908279856846504117771949678396*x^17*z^11 + 3553092831243041336280162874919379490558770353966455200* x^18*z^11 + 11656637963799610374373533638508151012136863466157894696*x^19*z^11 + 33027140521371199253486369275493922006557764271529500844*x^20*z^11 + 80208767589004113306954744077331787234926666166515026364*x^21* z^11 + 165278673522925261407943219848925836901386540112361802048*x^22*z^11 + 285045853072347955460472427626010864446722939067005831376*x^23*z^11 + 403814976406489434035898111682266595313973514551317050164* x^24*z^11 + 457656854683683854213565717739097800951730634488316367212*x^25*z^11 + 398982860442621908490940723767175736459554234442102898528*x^26*z^11 + 251211743154574868024378029498329799639838154707689548216* x^27*z^11 + 101680808097125491798195549800734743109554294809398021100*x^28*z^11 + 19867860395742170767264334984898541892343463702698833900*x^29*z^11 + 25069584304539692013997416959944776*z^12 + 3977781302711917010721915911801836728*x*z^12 + 304299816407929307329527058158575238696*x^2*z^12 + 14944504543496654648957745602145518431008*x^3*z^12 + 529284564342218218111329554966016871995780*x^4*z^12 + 14396540184239933954010894321027269212999056*x^5*z^12 + 312724845923927416687579980903420775282730784*x^6*z^12 + 5569480591359078276364772970701202138063365952*x^7*z^12 + 82846023676496217728358840500358687466842906048*x^8*z^12 + 1043246223471200888115087606366571570514013075816*x^9*z^12 + 11232284341597200904877215000658757061183759528872*x^10*z^12 + 104153909380893636981295095192212108677449806967648*x^11*z^12 + 836124439181508128824884403698425231587849294778316*x^12*z^12 + 5831431980795475797424349172950661713505457535542368*x^13*z^12 + 35405122704568296358709282156506907508983080060945152*x^14*z^12 + 187253760286881678918213649840721447677700914082822016*x^15*z^12 + 862147524148431728151936802611226836280807094121994536*x^16* z^12 + 3448590099543321435437823546543335146359508807868139528*x^17*z^12 + 11942339713240443481854709749573542309399003100329637240*x^18*z^12 + 35617504095060533441276931256379023013999945659838915040*x^19* z^12 + 90824636007699818902638395289723849605952310312164871068*x^20*z^12 + 196065887104517561564339369415956291348752472242998455568*x^21*z^12 + 353512743413118516317961695019124370419266855672733164768* x^22*z^12 + 522584020056742297417722977475600857788691542220086718784*x^23*z^12 + 616939373049980104666044445602329934142024861696259573328*x^24*z^12 + 559358478726037606646083157270756641834355177461119503064* x^25*z^12 + 365735069478342831781999795234853394926534116358520777144*x^26*z^12 + 153518402442763405689286938678035601852888883148743126944*x^27*z^12 + 31069725463820313097573706901119215807314850811408237972* x^28*z^12 + 197991115362552741348103140284622648*z^13 + 30292624634658874467495240575237542056*x*z^13 + 2231537684077460154936184089091049706336*x^2*z^13 + 105377951740893391471701354750403661500992*x^3*z^13 + 3582849273921232459427480544302766662963232*x^4*z^13 + 93392939834952550381842668775074693658024576*x^5*z^13 + 1940497761914494626790936001051838307338361488*x^6*z^13 + 32988461932191420679307933724274608914163156048*x^7*z^13 + 467336543841568798167269723193513789810946955640*x^8*z^13 + 5590729761808762277623614734018028139723396388424*x^9*z^13 + 57025443567203556140463279553814791067004750944688*x^10*z^13 + 499404642123512723977228679120891820339730000740240*x^11*z^13 + 3773279517930682117442039692517253652340780422801536*x^12*z^13 + 24671443019445621354273576449867538812526205735862976*x^13*z^13 + 139804843938553538035906746619926136756620891179631648*x^14*z^13 + 686597121966080685275476188129981187101189346874173344*x^15* z^13 + 2918037757580417336889906144621281982962802135246139944*x^16*z^13 + 10699471754113790768304599519099885446389160880823407928*x^17*z^13 + 33683522438350717556703775975912152249025102695334222656*x^18* z^13 + 90413666764248454506739455529061367336296510933311277280*x^19*z^13 + 204937643349770146844408054912615652083637830464764524640*x^20*z^13 + 387104418728547879810159140896092255018876778768895374272* x^21*z^13 + 598252270536118304486247466177137770699100341706623038800*x^22*z^13 + 736977541962726668066816795743572229170044409190160465424*x^23*z^13 + 696034378710719462706064689765691197098340016609184414760* x^24*z^13 + 473303042323078224878142920217131906694567697689803789016*x^25*z^13 + 206311648307273040432260708861193296379794407660310807472*x^26*z^13 + 43300714495648429818811640476029081541298584258220301136* x^27*z^13 + 1400038283931642888514436853397415196*z^14 + 206274625629707757576488326543639673604*x*z^14 + 14611211454807085123315645074816944584068*x^2*z^14 + 662375513500743961644435255926911877362368*x^3*z^14 + 21582402496043676379790148823205001086307576*x^4*z^14 + 538121225080814373075897552446375103052317432*x^5*z^14 + 10672737637983780987512948323803400347893013864*x^6*z^14 + 172796705068955002796289106835148304250673172128*x^7*z^14 + 2325555657961455762406010258955180877753398970980*x^8*z^14 + 26356297456613043237521225941615368692261209514700*x^9*z^14 + 253898998792501506183819303682941004593003108066396*x^10*z^14 + 2092743263054323120244936891919816036314428984744704*x^11*z^14 + 14823598115572563688448687636556027900199238093035152*x^12*z^14 + 90461957670196985627068633314553502263522401738995664*x^13* z^14 + 476002205179745458600689577515572563965579599710427184*x^14*z^14 + 2157876664077625561712311460436289432989239584542512064* x^15*z^14 + 8406727871392457296955097363560479515433893732210272676*x^16*z^14 + 28022426351504418794996990295311591907555645030316243164*x^17*z^14 + 79396874160588634085830132570321018559364600232855874172*x^18* z^14 + 189438152160174273880418954366158577062353559061805354816*x^19*z^14 + 375718998777288562095795861199864517512851245716058114040*x^20*z^14 + 608306975856207308726502663887152274812694797165174536888* x^21*z^14 + 783425699973673639535341540444691966153540330902768993512*x^22*z^14 + 772071639900183357752295209878295659483960773411282034848*x^23*z^14 + 546883645907139025021484366545643553080264709795353860956* x^24*z^14 + 247920547596707986871026937070787365304266500158182560724*x^25*z^14 + 54033350890112773096977655856734479912494767732298391844*x^26*z^14 + 8898218766696128949968423924579180364*z^15 + 1260572544585234590244260368880927316132*x*z^15 + 85719101074875271814831265788624548931904*x^2*z^15 + 3724021566561433325883718583984098683933936*x^3*z^15 + 116065362427771637889174762862092782871988248*x^4*z^15 + 2762355633108726634686813711503140086778323192*x^5*z^15 + 52177828520294895640454173034608659858668211840*x^6*z^15 + 802544695728794407021148344142726045342037245136*x^7*z^15 + 10232444883186876556814030680897077556559390471412*x^8*z^15 + 109525058249923992944009935662931270811679934229676*x^9*z^15 + 993027194939692391265673365813330766082010698892672*x^10*z^15 + 7673391959955274761747031098253881726567808629775968*x^11*z^15 + 50729646838345372329382465562990057240030477237118288*x^12*z^15 + 287467998939912146038522342111082183755785946272353232*x^13*z^15 + 1396273140318208758253830154023583295629090595668396032*x^14* z^15 + 5802290607360151424136203840115503944109430827034861216*x^15*z^15 + 20549779124374910542246785866798356888739977129843594740*x^16*z^15 + 61649336868686008465940842498206055134234599361673599804*x^17* z^15 + 155264997568096985568936807464465093350988940314809945920*x^18*z^15 + 324149742067877794543635982132061707057092558940031169456*x^19*z^15 + 551054569619269926705916139314396203625794082166332664856* x^20*z^15 + 743486257650398688092074767693982365301644993528221731512*x^21*z^15 + 766016119559089680470645169175448290123283954100989262720*x^22*z^15 + 566186050618524327359227432024512015724185214134127005072* x^23*z^15 + 267365639585810517517451005006086241642495926752128166988*x^24*z^15 + 60602437683591894210217783544472470829875944707199588340*x^25*z^15 + 50980283032856002647975290394542728080*z^16 + 6933213732786427461247479736739370583416*x*z^16 + 451811960119271176750060256559365987211288*x^2*z^16 + 18775280435952747317861512628281773743220720*x^3*z^16 + 558564561530666079559234633417214277716454342*x^4*z^16 + 12660796782853516585307986908929833832138740896*x^5*z^16 + 227190963575387722199622376196913341705903477412*x^6*z^16 + 3310496885067053312114784238655729930099098443912*x^7*z^16 + 39863899933142922125018813599424407717740732651318*x^8*z^16 + 401591880675462216852347973352248761649316399700304*x^9*z^16 + 3413530985394046322391141473548872149605495954186944*x^10*z^16 + 24618799230712783096008049408572379696364412131476992*x^11*z^16 + 151132073103006232085946364245847447145127099842122380*x^12* z^16 + 790536997232079347264061627690316284252300795894661920*x^13*z^16 + 3519771859370105291916652417516003547741746650006677688* x^14*z^16 + 13296915890721187318049142136280323359680728677895443696*x^15*z^16 + 42383919672083399058024730510331498979882252857038265772*x^16*z^16 + 113023787475219822034227361012152375317141800434622283256* x^17*z^16 + 249070940021901602426511050587255345943505454143955743048*x^18*z^16 + 445705877814719797753608921077731670353296521859667170384*x^19*z^16 + 631416638715171431874012410641299171726533928553254764526* x^20*z^16 + 681529096564736542829131198440402192253516195055431015296*x^21*z^16 + 526636337638517739687336993055451766294146659859702234244*x^22*z^16 + 259502006637288639265049868427112110296551626452051130440* x^23*z^16 + 61271792888361956378252332622589154861362446079827821902*x^24*z^16 + 263888740156078110512123314571452111920*z^17 + 34393917363664944840127939881057077699760*x*z^17 + 2143890376269105720759899985619028117143992*x^2*z^17 + 85040978194736986251948608432834230658697180*x^3*z^17 + 2409494137719684254747637555035410271071942572*x^4*z^17 + 51884440873503084183037130307706518027194123124*x^5*z^17 + 882035498617862684173823048293563594905720292732*x^6*z^17 + 12138488555318113352434756117502306608809266976432*x^7*z^17 + 137569536884955555861049928945616585809147952228720*x^8*z^17 + 1299267848445480370605878014799459854084494112431120*x^9*z^17 + 10307524928561315223178812927049574602796524561901280*x^10*z^17 + 69029182082884994367691769385767344987178413881393576*x^11*z^17 + 391165364849618846815311913927542916447517872976270088*x^12* z^17 + 1875587776451937491568141997392831449067914940393126648*x^13*z^17 + 7591664841331792183499008537302701311412351854186800648*x^14*z^17 + 25811660600386300592120551735595374141692127339896056208*x^15* z^17 + 73133037825498027914196678375189021562283191476691592448*x^16*z^17 + 170643750504806022227478384248961256674804451365343709088*x^17*z^17 + 322327079998851027037784715869632999961455539631560488904* x^18*z^17 + 480663220229919701675965634181517848209106911416018682076*x^19*z^17 + 544751664891646968045900079974939407541135340976052729516*x^20*z^17 + 440989349288768154577433935799304822043343299013282354484* x^21*z^17 + 227176300518722588946897955926760569584084252680943962140*x^22*z^17 + 55971132978837534944541783051008969162090351404972005728*x^23*z^17 + 1236366691619624991600504188141931088122*z^18 + 154135283781776631029894718077876931092238*x*z^18 + 9171079378385651366886909605711936183362038*x^2*z^18 + 346463202510987577846202868986311474840770528*x^3*z^18 + 9325634849480671990914328868385566783364415842*x^4*z^18 + 190242949807464351293286269194609709390962966986*x^5*z^18 + 3054456253991132340806945167397341523653490155638*x^6*z^18 + 39562481115362879408535012026293379884967366035488*x^7*z^18 + 420351362243361580237541182717611164630595256362516*x^8*z^18 + 3705319417660170941667251949047469925670520498156300*x^9*z^18 + 27295853050574516933373284579346131760768208995874668*x^10*z^18 + 168738000799513769330471501754634619085249348798560736*x^11*z^18 + 876500171930240836153436727409615556480238755830645620*x^12* z^18 + 3820641774804138079764556079167786798987947821546495892*x^13*z^18 + 13918052077651604974553679196198318452748552867095231516*x^14*z^18 + 42063445721367443080697215382305668552528157570459938144*x^15* z^18 + 104282292286543026549891055757221735631241207355078996338*x^16*z^18 + 208564591717137853327387539784262893083402109822458776646*x^17*z^18 + 328296125805491285632093811189354009507797512719137103070* x^18*z^18 + 391651512053189885850891150340836476544801781732488394944*x^19*z^18 + 332903688362547467659816283163777549339076388096361599658*x^20*z^18 + 179662279549995055762323025326457439577352259111910113346* x^21*z^18 + 46276375500949644388973764086156722652538077297789203758*x^22*z^18 + 5249293597722989862331337857834519205706*z^19 + 624657539119445018615862813568569444099486*x*z^19 + 35397176259851800888221297250706681895645648*x^2*z^19 + 1270365100787693785417345910867760289834649676*x^3*z^19 + 32394311556261264452770219529476890942289415274*x^4*z^19 + 624130389967625012779046310508554858039780938946*x^5*z^19 + 9431303620416193778134595712761681962211480283072*x^6*z^19 + 114522972018544370900421761888555869906598078247984*x^7*z^19 + 1135686139059957283888321363148759989905638326041300*x^8*z^19 + 9295801348992442312785441282724722725770167021581196*x^9*z^19 + 63211449168793187175597697042281197023140585144512352*x^10*z^19 + 358198211306506748384592636777166958707278936165287400*x^11*z^19 + 1691491548208570778422317387072858845559964796178029412*x^12* z^19 + 6635851435267206759730656803851252556278312634410101924*x^13*z^19 + 21487519150582200018792569940469883483149037059232196288*x^14*z^19 + 56822552165862645985250301103221556201684273546089415536*x^15* z^19 + 120747925193484393600501499516075872423290903881486099362*x^16*z^19 + 201246530407424234537107591920072122025861518933153436918*x^17*z^19 + 253421548586164899736373974477191295659277085289198397008* x^18*z^19 + 226745616988284361180603658511001644766913147264115552300*x^19*z^19 + 128489209405322963039640211175227883684303163800207920242*x^20*z^19 + 34671672435780205789595367494985430114130467937057757818* x^21*z^19 + 20209544173097942520319942615958813371524*z^20 + 2290408163361829924513393961689382267470476*x*z^20 + 123300168236127078471277152187296697819021476*x^2*z^20 + 4192204623846684968915062148855725178009484096*x^3*z^20 + 100962264585882123796195183734278148256282857510*x^4*z^20 + 1830782439290629988948478476885462951873589820656*x^5*z^20 + 25936084738979738937952897263490112434409871011520*x^6*z^20 + 293942293953355785795245094826482260398452992940480*x^7*z^20 + 2706718626986502283439452315767237029439350850427296*x^8*z^20 + 20450762960599157636182947455164226814511640488676520*x^9*z^20 + 127476422611703041614379739662296412533027760179955272*x^10*z^20 + 656696723994253431388751575650517654595443219811722560*x^11* z^20 + 2790961103996526660526237852780883932317263387384380308*x^12*z^20 + 9732582438346609713479198390722881705903703233522086064*x^13*z^20 + 27575650252786610422429992436077088304243847188927904288*x^14* z^20 + 62504804411956707446571091657644995936893066691072206656*x^15*z^20 + 110685587394021889439214632949533850150653941026312112332*x^16*z^20 + 147580783247993821453871708338016322652424731019104417068* x^17*z^20 + 139381893430286176384074809085431121522405029961659837748*x^18*z^20 + 83140092267724100303967821126163773361475470050225106048*x^19*z^20 + 23556468484499236606356200318160777881663175374952073302*x^20* z^20 + 70571820359255968090488736841210962046172*z^21 + 7598313097372719043853302279886240402148708*x*z^21 + 387514706738157183407949832992448082709496176*x^2*z^21 + 12443529512497443677954530846849403569134842616*x^3*z^21 + 282053316797045111358542168917110604037864490624*x^4*z^21 + 4794906456263681896797775890720480288176697315744*x^5*z^21 + 63399318550683183177224095823451358197075634282320*x^6*z^21 + 667202355153869228237587324057539071342095692306864*x^7*z^21 + 5671220012589169759066713629799269597183159691400440*x^8*z^21 + 39278449812853039138078715904663351010257175425072168*x^9*z^21 + 222577882272408686294597172692110277883035459143669776*x^10*z^21 + 1031951999647551035087818918123186960232476153177147392*x^11* z^21 + 3898485266708543647168337770079739718984893978683413920*x^12*z^21 + 11895377707468737647388316819861795826779304805514593984*x^13*z^21 + 28888773827365211765795419784203162325739148825103304624*x^14* z^21 + 54567687710724842996832249711326237775292766262213626256*x^15*z^21 + 77304228131059731039450919844449702171855639044943314444*x^16*z^21 + 77304229066811253434983342940046422023137757693537363476*x^17* z^21 + 48673018015811615528432378404532016888059102815754789760*x^18*z^21 + 14516498699056317117963198283885148393947895143294163400*x^19*z^21 + 223481288881004776389911958097047943836834*z^22 + 22795001451325115168691509974426703673565278*x*z^22 + 1097958642714910307079051830916357926359272222*x^2*z^22 + 33182749216777355567355905455314356613255886272*x^3*z^22 + 705133344716343120810963789259708470981221461752*x^4*z^22 + 11188115243976506678521067823852771370489984184376*x^5*z^22 + 137365190266560523528020339433174268732815144732200*x^6*z^22 + 1334404696841442063546724141400268638310740494243680*x^7*z^22 + 10397236519768549384215372099004643124403642599092748*x^8*z^22 + 65464081425997125557462204763758770450437134578507620*x^9*z^22 + 333866810786350428493143295771156320417060499990940820*x^10* z^22 + 1375935931676941986608473843877978934962788452187540608*x^11*z^22 + 4548232685556639685738836789018138929887421833050174072*x^12*z^22 + 11895378698122881557054705031682427701784853586090639896*x^13* z^22 + 24073981920778656656382851869104881124999382935495634920*x^14*z^22 + 36378462253798400640737393082229542393108505886363232096*x^15*z^22 + 38652097889805629022860274155260095997466288790077758434*x^16* z^22 + 25768057903601904736717146112655111793462552839710371054*x^17*z^22 + 8112136422783000401263288152378900867648600723181186622*x^18*z^22 + 641292680691182275163826100991692814010042*z^23 + 61777683758990813434995674560347134580988926*x*z^23 + 2800588308009556995404512692010166012527279296*x^2*z^23 + 79350016471153140369852904498328374443168968880*x^3*z^23 + 1573775646300165106155953023725558898214734414104*x^4*z^23 + 23186961673833147058435932002663461887595019692344*x^5*z^23 + 262785573483667890418616270851242616037925249751680*x^6*z^23 + 2340042975402636089935743050113229187103419974924208*x^7*z^23 + 16575304635319704537534030468834877392489545712750108*x^8*z^23 + 93926727318529818994658308850746426266206885186420580*x^9*z^23 + 425801177937111393695381586421348794901808536765172928*x^10* z^23 + 1535464937155255356389767650752721248063916360919595664*x^11*z^23 + 4350484127151669103418556478725654613522953422119990680*x^12*z^23 + 9481823272869098669348934326238182466892854713472578712*x^13* z^23 + 15351521845113293765973226292122955076880185074347336704*x^14*z^23 + 17398389083494177655534724001654368708737334641845026576*x^15*z^23 + 12323865928606266011815479854101364768029081142142438522*x^16* z^23 + 4107966357481382207265757787740409835876609387925284046*x^17*z^23 + 1665560036067176966550921434008112128265808*z^24 + 151011951100159525903553063670245900029057920*x*z^24 + 6418015612854903586705653441073289147055444576*x^2*z^24 + 169720893652840662927614080939082825978431900224*x^3*z^24 + 3125693501664967674313047857539250678450078509860*x^4*z^24 + 42509433945014070701687025708071829197994461547408*x^5*z^24 + 441625793459402736195947324247280779373699432836504*x^6*z^24 + 3575065982667819103758807080345026315555353916164432*x^7*z^24 + 22791045924045466831052506556259818649106542698539116*x^8*z^24 + 114799342046118090501139611903890600187541283212524768*x^9*z^24 + 455370712678158669881148001542749483356586601556709040*x^10* z^24 + 1407509250437057475788431532741171319550261947294874272*x^11*z^24 + 3323285458106093808635530249973067973139039410504017084*x^12*z^24 + 5794446151556052496070370734856482659973636283833949456*x^13* z^24 + 7036120000860107515618262282211317157472599700462356696*x^14*z^24 + 5316182378141792338347280173250455249444985286530605264*x^15*z^24 + 1882819333970796780382285351639177807448835852660429284*x^16* z^24 + 3908613365102054033059613140607786073730800*z^25 + 332228584506036260847372746982876409967202672*x*z^25 + 13178349991366034165646716363462899747304628240*x^2*z^25 + 323601438820350966194700509226768095898306891096*x^3*z^25 + 5501221669949352959932091182985703554222762991048*x^4*z^25 + 68581889660004480964987378467473985260109232490424*x^5*z^25 + 647717784257668377624803817720921780278091945826680*x^6*z^25 + 4719086458542458724807497958026854078467876394040112*x^7*z^25 + 26741487938188282597972679549767241159826316803178080*x^8*z^25 + 117860620916984732905648815509235686053624493682401088*x^9*z^25 + 400726093470792927583404817706112877144552680927361824*x^10*z^25 + 1032173534811051801782989313370258215260484308888347672*x^11* z^25 + 1949661619399519348409862559716734793922026226357674216*x^12*z^25 + 2549558268087851856446209335946260063306035091719572632*x^13*z^25 + 2063925386424915319544923336267604937633055145893057368*x^14* z^25 + 779701337854277004017003469709606978426326937214569056*x^15*z^25 + 8268084017089004517641253354978115118579052*z^26 + 655934444277971695258995064882351385624757348*x*z^26 + 24160264581708724445832476119159059509059934292*x^2*z^26 + 547632596521017000432254273285786763546183499200*x^3*z^26 + 8533942388994276125446256704727284512312263904372*x^4*z^26 + 96718013362626108048175343206108996190547179825508*x^5*z^26 + 822103162920406618283723528926045471505556538599516*x^6*z^26 + 5324097139237945329979892023634900025440269378777248*x^7*z^26 + 26398650845304304096512963719362357467574281457900884*x^8*z^26 + 99728276928628788474757387408428314605044938054452332*x^9*z^26 + 282563485627311392428730550776737484050966311111547020*x^10* z^26 + 582252086016013054771339548486565344710818132057565088*x^11*z^26 + 824855106569599137915697553536138920802791189431840844* x^12*z^26 + 719103671338202744974481262118004489386549574134339020*x^13*z^26 + 291065811465911589569990903851165537519812577420280132*x^14*z^26 + 15718977933121165839135526604922982723419372*z^27 + 1157993359382647112841352483702796845616049252*x*z^27 + 39372204730519247075800804815066671391933598944*x^2*z^27 + 818068170502938932648288439083716923816083861976*x^3*z^27 + 11589310576460281247047894820245555256008288600644*x^4*z^27 + 118210994150426448970171327624805333893990963270164*x^5*z^27 + 893149905658910077739307775586261225012680635509184*x^6*z^27 + 5061183497044372072688194711554971403501868660109424*x^7*z^27 + 21510029783325164441870809979857527980863617337301172*x^8*z^27 + 67716713338257793638869274435097184246117320359023628*x^9*z^27 + 153491094753245605262116627019613668831932322233164000*x^10* z^27 + 237213407315166288620605998060701698193353967239648824*x^11*z^27 + 224035756538295651243574366028397594377789297389016220* x^12*z^27 + 97657398828946375547743799765429181849250936017829628*x^13*z^27 + 26762109729186209033249510286678567154406280*z^28 + 1819747169329357958795607451581181897502396472*x*z^28 + 56714984748244074785221067942292096384597817512*x^2*z^28 + 1071282360763620347819893030466215915810316292576*x^3*z^28 + 13658834374207498223832970545796351283265026162388*x^4*z^28 + 123840044748653232573914238747184253820771344434992*x^5*z^28 + 818719918066754829609243820017490729030383209875104*x^6*z^28 + 3976635100514236224454579548915549051186817560155328*x^7*z^28 + 14083915012959706835522046699906070375420978718466240*x^8*z^28 + 35470599381587449661339962721864280290077249945448472*x^9*z^28 + 60300466202815670405709539696850018492001958460545688*x^10*z^28 + 62127884247131143741305415283937027307905777669728736*x^11*z^28 + 29337931969301905539240530326963803621001515460007428*x^12* z^28 + 40602920653480590033286781623530586571418744*z^29 + 2530939770070162386078969647222197399284140712*x*z^29 + 71708201716470323982805712799263835456599176416*x^2*z^29 + 1219040247314396191231113238368520910610793407072*x^3*z^29 + 13815770990088737128314708976055056441843213553184*x^4*z^29 + 109605174349546310633656012354844488464581326083648*x^5*z^29 + 621096349288639898206694026869714079301750673380976*x^6*z^29 + 2513967306436901799394982864719955549443611947397744*x^7*z^29 + 7122929061630634931307969808686951996353917656128904*x^8*z^29 + 13454415808990914023935019438041910901428837134327800*x^9*z^29 + 15248124316717150971467383461788948491878728925332112*x^10*z^29 + 7855010522753815957024183970175373363611928907741008*x^11*z^29 + 54576802383951465515471671645346977558614828*z^30 + 3093209205370167092372703937341821548966573620*x*z^30 + 78879310850781400152487671421049733850540617012*x^2*z^30 + 1191955224564832110903874515955654087839681512256*x^3*z^30 + 11820270436331276940105398639748004584327871558728*x^4*z^30 + 80378015449124121339696484655947617069386916108744*x^5*z^30 + 379562552830379710545884638351383357292260500764632*x^6*z^30 + 1229057835429592266149501815199027670322859288655072*x^7*z^30 + 2611675982563862133919612657859715643040783800545516*x^8*z^30 + 3288772166588869331853083608803359294827090896425316*x^9*z^30 + 1863700473202891884957278562170720865562556904072084*x^10*z^30 + 64588814616622938540534210557785409271965916*z^31 + 3292827912669952101493217210126416291269260820*x*z^31 + 74641572976634122390886195208744827028978377664*x^2*z^31 + 986903137989881812482392235639966694026242682384*x^3*z^31 + 8388650369771808334424946695218932812526208913448*x^4*z^31 + 47535155272878171787696453128269649649936336583880*x^5*z^31 + 179574641326144251096064971909967830121116797831040*x^6*z^31 + 436114488457186592469361691672520639780821640533232*x^7*z^31 + 617866681329170382696112543649021205765126861664860*x^8*z^31 + 389024944092041444127931530594796823256227785847620*x^9*z^31 + 66608228055657372382276923624876763274919024*z^32 + 3018522061775202900051060914177115010295852796*x*z^32 + 59861677340994200948852403406716243683127623292*x^2*z^32 + 678450693801035238353602046964974089581220075896*x^3*z^32 + 4805714397337412170979830836835487567970206158149*x^4*z^32 + 21786368968848831738958130329199971445366513280456*x^5*z^32 + 61736111612584072306231187341279070116362767144718*x^6*z^32 + 99950365734964066012880528711324300657335241658828*x^7*z^32 + 70789817328720566511448490357982713388281298806969*x^8*z^32 + 59051202582058953212447864109067840923544272*z^33 + 2347623586765533912473255708304142393653734832*x*z^33 + 39905144993078151512313813906876730903645134660*x^2*z^33 + 376928722893603475551902865898957782842063491290*x^3*z^33 + 2136119443615728051505459766978828908111320784266*x^4*z^33 + 7261998608638431401580911705052919997220441947622*x^5*z^33 + 13712630420030146331374919720652752987110565921754*x^6*z^33 + 11102887311578604966049745540038157524811180650912*x^7*z^33 + 44734520480431430700875487399376628727050355*z^34 + 1519682973636709832758620346971686938939486137*x*z^34 + 21531147591551692123348581593808560520774012357*x^2*z^34 + 162626598289570262481128673027689795874865119888*x^3*z^34 + 690565225248625282315603880662244850104627494587*x^4*z^34 + 1566138477841640425503257210345186479969682679303*x^5*z^34 + 1479592250846869356951891915180009895395077080473*x^6*z^34 + 28300977754152136955251928734592063209318299*z^35 + 795715943947926106675506132506779247691386529*x*z^35 + 9011842528608681472666089363246368287739407704*x^2*z^35 + 51138433214952224861471056731420554450174930514*x^3*z^35 + 145199233828905359472552139127211520424503268391*x^4*z^35 + 164238324081686120453791927814376827924174322427*x^5*z^35 + 14117141120390313037914035472511888425994758*z^36 + 323365495108952286879451032465134263502610210*x*z^36 + 2775381201154071312777287444152926380414109798*x^2*z^36 + 10388181562926763242679921715758679192001361200*x^3*z^36 + 14739827269396654283506059097653904848264738429*x^4*z^36 + 5820795918978481915952021011310033692969578*z^37 + 94999551481035770575700649964819172395984038*x*z^37 + 530665621635577688867550180526372156866942600*x^2*z^37 + 1022415764351213013884813347814143688896976076*x^3*z^37 + 1312892454911550337509682972582547031695031*z^38 + 20411550217812906529317207924167974791908217*x*z^38 + 52968290752143773018446212463650850472459641*x^2*z^38 + 370303000103257787502731094830974803811419*z^39 + 2098383667251794129182142870708857221598041*x*z^39)^3 in I Output: Magma V2.10-22 Sun Apr 4 2004 03:25:51 on modular [Seed = 2894288035] ------------------------------------- false Total time: 15.370 seconds, Total memory usage: 24.43MB ************** MAGMA ***************** Host modemcable030.75-201-24.mc.videotron.ca. (24.201.75.30) Time: Sun Apr 4 16:49:09 2004 Input: yvon Output: Magma V2.10-22 Sun Apr 4 2004 16:49:06 on modular [Seed = 756881883] ------------------------------------- >> yvon; ^ User error: Identifier 'yvon' has not been declared or assigned Total time: 2.559 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host modemcable030.75-201-24.mc.videotron.ca. (24.201.75.30) Time: Sun Apr 4 16:49:24 2004 Input: yvon Output: Magma V2.10-22 Sun Apr 4 2004 16:49:22 on modular [Seed = 506342136] ------------------------------------- >> yvon; ^ User error: Identifier 'yvon' has not been declared or assigned Total time: 2.529 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host w-102034.wireless.wisc.edu. (128.104.102.34) Time: Sun Apr 4 23:27:23 2004 Input: G:=PSL(2,7); numRx = 1; //G := DegreeReduction(CosetImage(G, sub)); G:= DegreeReduction(CosetImage(G, sub)); //G:=CosetImage(G, sub); //T := CharacterTable(G); pi := PowerMap(G); C := Classes(G); fTable := []; Expo := Exponent(G); usedExp := Expo + 1; while not IsPrime(usedExp) do usedExp:=usedExp+Expo; end while; print usedExp; F := GF(usedExp); ComF := ComplexField(); P := PolynomialAlgebra(ComplexField()); I := IrreducibleModules(G,F); e := PrimitiveElement(F); // iterate for each character //for n in [1..#T] do for n in [1..#I] do NumRow := []; injective := Booleans(); injective := true; f := elt

; Rep := Representation(I[n]); // iterate for each class except identity //for m in [2..#T] do for m in [2..#I] do NumOneEval := 0; for k in [1..C[m][1]] do //NumOneEval +:= T[n, pi(m,k)]; NumOneEval +:= Trace(Rep(C[pi(m,k)][3])); end for; NumOneEval := NumOneEval / C[m][1]; if m ne 1 then if Trace(Rep(C[m][3])) eq Trace(Rep(C[1][3])) then //if T[n,m] eq T[n,1] then injective := false; end if; end if; // Calculate the coefficient CharPol:=CharacteristicPolynomial(Rep(C[m][3])); R:=Roots(CharPol); Coeff:=ComplexField() ! 1; for i in [1..#R] do if R[i][1] ne 1 then Coeff := Coeff*(1 - Exp(2*Pi(ComF)*j*Log(F!R[i][1])/Expo) )^(IntegerRing()!R[i][2]); end if; end for; if injective then //f := f + C[m][2]*(Coeff)^(-2*numRx) * x^((IntegerRing() ! numRx)*((IntegerRing()!T[n,1])-(IntegerRing() ! NumOneEval))); f := f + C[m][2]*(Coeff)^(-2*numRx) * x^((IntegerRing() ! numRx)*((IntegerRing()!Trace(Rep(C[1][3]))) - (IntegerRing() ! NumOneEval))); else f := elt

; end if; end for; fTable[n] := f*0.5; end for; print fTable; Output: Magma V2.10-22 Sun Apr 4 2004 23:27:20 on modular [Seed = 2085416541] ------------------------------------- >> numRx = 1; ^ User error: Identifier 'numRx' has not been declared or assigned 337 >> f := f + C[m][2]*(Coeff)^(-2*numRx) * x^((I ^ User error: Identifier 'numRx' has not been declared or assigned [] Total time: 2.660 seconds, Total memory usage: 2.20MB ************** MAGMA ***************** Host w-102034.wireless.wisc.edu. (128.104.102.34) Time: Sun Apr 4 23:29:03 2004 Input: G:=PSL(2,7); numRx := 1; //G := DegreeReduction(CosetImage(G, sub)); G:= DegreeReduction(CosetImage(G, sub)); //G:=CosetImage(G, sub); //T := CharacterTable(G); pi := PowerMap(G); C := Classes(G); fTable := []; Expo := Exponent(G); usedExp := Expo + 1; while not IsPrime(usedExp) do usedExp:=usedExp+Expo; end while; print usedExp; F := GF(usedExp); ComF := ComplexField(); P := PolynomialAlgebra(ComplexField()); I := IrreducibleModules(G,F); e := PrimitiveElement(F); // iterate for each character //for n in [1..#T] do for n in [1..#I] do NumRow := []; injective := Booleans(); injective := true; f := elt

; Rep := Representation(I[n]); // iterate for each class except identity //for m in [2..#T] do for m in [2..#I] do NumOneEval := 0; for k in [1..C[m][1]] do //NumOneEval +:= T[n, pi(m,k)]; NumOneEval +:= Trace(Rep(C[pi(m,k)][3])); end for; NumOneEval := NumOneEval / C[m][1]; if m ne 1 then if Trace(Rep(C[m][3])) eq Trace(Rep(C[1][3])) then //if T[n,m] eq T[n,1] then injective := false; end if; end if; // Calculate the coefficient CharPol:=CharacteristicPolynomial(Rep(C[m][3])); R:=Roots(CharPol); Coeff:=ComplexField() ! 1; for i in [1..#R] do if R[i][1] ne 1 then Coeff := Coeff*(1 - Exp(2*Pi(ComF)*j*Log(F!R[i][1])/Expo) )^(IntegerRing()!R[i][2]); end if; end for; if injective then //f := f + C[m][2]*(Coeff)^(-2*numRx) * x^((IntegerRing() ! numRx)*((IntegerRing()!T[n,1])-(IntegerRing() ! NumOneEval))); f := f + C[m][2]*(Coeff)^(-2*numRx) * x^((IntegerRing() ! numRx)*((IntegerRing()!Trace(Rep(C[1][3]))) - (IntegerRing() ! NumOneEval))); else f := elt

; end if; end for; fTable[n] := f*0.5; end for; print fTable; Output: Magma V2.10-22 Sun Apr 4 2004 23:29:00 on modular [Seed = 1984357427] ------------------------------------- 337 [ 0, (-3.428571428571428571428571428831 - 1.027809259787280275603 E-27*j)*x^3 + (1.89386473874881911496426205226 E112 + 1.28610342617241100982 E102*j)*x^2, (-3.428571428571428571428571428831 - 1.027809259787280275603 E-27*j)*x^3 + (1.89386473874881911496426205226 E112 + 1.28610342617241100982 E102*j)*x^2, (0.489795918367346938775510204154 + 2.94190552280441616110 E-28*j)*x^6 + (7.59094952100768863172405646461 E222 + 9.94165685392642591369 E212*j)*x^4 + (6.312882462496063716553555796132 E111 + 3.67458121763546002760 E101*j)*x^2, (4.56388305760593645346704207893 E333 + 9.29785351130458151587 E323*j)*x^6 + (3.79547476050384431587066825497 E222 + 4.41851415730063373874 E212*j)*x^4, (4.56388305760593645346704207893 E333 + 9.29785351130458151587 E323*j)*x^6 + (3.79547476050384431587066825497 E222 + 4.41851415730063373874 E212*j)*x^4 ] Total time: 2.730 seconds, Total memory usage: 21.69MB ************** MAGMA ***************** Host w-102034.wireless.wisc.edu. (128.104.102.34) Time: Sun Apr 4 23:33:21 2004 Input: G:=Sym(5); numRx:=1; G:= DegreeReduction(CosetImage(G, sub)); pi := PowerMap(G); C := Classes(G); fTable := []; Expo := Exponent(G); usedExp := Expo + 1; while not IsPrime(usedExp) do usedExp:=usedExp+Expo; end while; F := GF(usedExp); ComF := ComplexField(); P := PolynomialAlgebra(ComplexField()); I := IrreducibleModules(G,F); e := PrimitiveElement(F); // iterate for each character for n in [1..#I] do NumRow := []; injective := Booleans(); injective := true; f := elt

; Rep := Representation(I[n]); // iterate for each class except identity for m in [2..#I] do NumOneEval := 0; for k in [1..C[m][1]] do NumOneEval +:= Trace(Rep(C[pi(m,k)][3])); end for; NumOneEval := NumOneEval / C[m][1]; if m ne 1 then if Trace(Rep(C[m][3])) eq Trace(Rep(C[1][3])) then injective := false; end if; end if; // Calculate the coefficient CharPol:=CharacteristicPolynomial(Rep(C[m][3])); R:=Roots(CharPol); Coeff:=ComplexField() ! 1; for i in [1..#R] do if R[i][1] ne 1 then Coeff := Coeff*(1 - Exp(2*Pi(ComF)*j*Log(F!R[i][1])/Expo) )^(IntegerRing()!R[i][2]); end if; end for; if injective then f := f + C[m][2]*(Coeff)^(-2*numRx) * x^((IntegerRing() ! numRx)*((IntegerRing()!Trace(Rep(C[1][3]))) - (IntegerRing() ! NumOneEval))); else f := elt

; end if; end for; fTable[n] := f*0.5; end for; print fTable; Output: Magma V2.10-22 Sun Apr 4 2004 23:33:18 on modular [Seed = 1716974881] ------------------------------------- [ 0, 0, (0.479999999999999999999999999958 + 9.97614520221533949799 E-29*j)*x^4 + (1.215277777777777777777777777679 + 2.199513460284987706413641823841 E-28*j)*x^3 + (1.57986111111111111111111111107 + 2.083971025423976427019 E-28*j)*x^2 + (1.250000000000000000000000000000 + 6.310887241768094443037243110069 E-29*j)*x, (0.479999999999999999999999999958 + 9.97614520221533949799 E-29*j)*x^4 + (3.51562499999999999999999999954 + 5.83170361196070570356 E-28*j)*x^3 + (1.57986111111111111111111111107 + 2.083971025423976427019 E-28*j)*x^2, (0.277777777777777777777777777730 + 8.53415462251091996165 E-29*j)*x^5 + (0.60345679012345679012345679007 + 1.35553773851280484868 E-28*j)*x^4 + (1.0156249999999999999999999999242 + 1.77493703677482721096658947026 E-28*j)*x^3 + (0.468750000000000000000000000000 + 4.73316543132607083224585915600 E-29*j)*x^2, (1.94894290123456790123456790097 + 4.74071294372441284651 E-28*j)*x^4 + (0.78125000000000000000000000000 + 7.88860905221011805374309859333 E-29*j)*x^2, (0.51215277777777777777777777769 + 1.56339027696377794542 E-28*j)*x^5 + (0.63275366512345679012345679007 + 1.41470230640438073411 E-28*j)*x^4 + (0.078125000000000000000000000000 + 1.183291357831517708058792024275 E-29*j)*x^3 ] Total time: 2.659 seconds, Total memory usage: 2.22MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Mon Apr 5 02:48:03 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=16; m2 :=m div 2; > ((tx - ty - tz)^(m2)*(tx + ty - tz)^(-1 + m2))/2 - ((tx - ty - tz)^(m2)*(tx + ty - tz)^(-1 + m2))/(2*m) + (tx + ty - tz)^(-1 + m)/(2*m) + ((tx - ty + tz)^(m/2)*(tx + ty + tz)^(-1 + m2))/2 - ((tx - ty + tz)^(m2)*(tx + ty + tz)^(-1 + m2))/(2*m) + (tx + ty + tz)^(-1 + m)/(2*m) in I Output: Magma V2.10-22 Mon Apr 5 2004 02:48:01 on modular [Seed = 1081147738] ------------------------------------- >> ((tx - ty - tz)^(m2)*(tx + ty - tz)^(-1 + m2))/2 - ((tx - ty - tz)^(m2)*( ^ Runtime error in '/': Coefficient ring of argument 1 is not a field Total time: 2.519 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Mon Apr 5 02:49:52 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=16; m2 :=m div 2; > ((-1 + m)*(tx - ty - tz)^(m2)*(tx + ty - tz)^(-1 + m2) + (tx + ty - tz)^(-1 + m) + (-1 + m)*(tx - ty + tz)^(m2)*(tx + ty + tz)^(-1 + m2) + (tx + ty + tz)^(-1 + m))/(2*m) in I Output: Magma V2.10-22 Mon Apr 5 2004 02:49:49 on modular [Seed = 3163421962] ------------------------------------- >> (tx + ty + tz)^(-1 + m))/(2*m) in I ^ Runtime error in '/': Coefficient ring of argument 1 is not a field Total time: 2.569 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Mon Apr 5 02:50:03 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=16; m2 :=m div 2; > ((-1 + m)*(tx - ty - tz)^(m2)*(tx + ty - tz)^(-1 + m2) + (tx + ty - tz)^(-1 + m) + (-1 + m)*(tx - ty + tz)^(m2)*(tx + ty + tz)^(-1 + m2) + (tx + ty + tz)^(-1 + m)) div (2*m) in I Output: Magma V2.10-22 Mon Apr 5 2004 02:50:01 on modular [Seed = 2912742415] ------------------------------------- false Total time: 2.529 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Mon Apr 5 02:50:11 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=32; m2 :=m div 2; > ((-1 + m)*(tx - ty - tz)^(m2)*(tx + ty - tz)^(-1 + m2) + (tx + ty - tz)^(-1 + m) + (-1 + m)*(tx - ty + tz)^(m2)*(tx + ty + tz)^(-1 + m2) + (tx + ty + tz)^(-1 + m)) div (2*m) in I Output: Magma V2.10-22 Mon Apr 5 2004 02:50:09 on modular [Seed = 2777998399] ------------------------------------- false Total time: 2.689 seconds, Total memory usage: 2.44MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Mon Apr 5 02:50:23 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=64; m2 :=m div 2; > ((-1 + m)*(tx - ty - tz)^(m2)*(tx + ty - tz)^(-1 + m2) + (tx + ty - tz)^(-1 + m) + (-1 + m)*(tx - ty + tz)^(m2)*(tx + ty + tz)^(-1 + m2) + (tx + ty + tz)^(-1 + m)) div (2*m) in I Output: Magma V2.10-22 Mon Apr 5 2004 02:50:19 on modular [Seed = 2645351437] ------------------------------------- false Total time: 4.570 seconds, Total memory usage: 9.18MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Mon Apr 5 02:50:51 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=128; m2 :=m div 2; > ((-1 + m)*(tx - ty - tz)^(m2)*(tx + ty - tz)^(-1 + m2) + (tx + ty - tz)^(-1 + m) + (-1 + m)*(tx - ty + tz)^(m2)*(tx + ty + tz)^(-1 + m2) + (tx + ty + tz)^(-1 + m)) div (2*m) in I Output: Magma V2.10-22 Mon Apr 5 2004 02:50:29 on modular [Seed = 2510607387] ------------------------------------- ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Mon Apr 5 05:01:51 2004 Input: K := GF(2); R := PolynomialRing(K, [7, 6, 4, 1016, 1008, 992, 960, 896, 768, 512]); R; P := [a, b, c, d, e, f, g , x*(a- b*z^2 -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) +d*z^(2^2)*y^(2^3) -d*z^(2^3 +2^2 +2) + e*(x^(2^4)*z^2 +x^(2^3)*z^(2^4) +y^(2^4)*y^(2^2) -y^(2^4)*z^(2^2 +2) -y^(2^2)*z^(2^4 +2^3)-y^(2^3)*z^(2^4 +2) +z^(2^4 + 2^3 + 2^2 +2) ) + f*(x^(2^5)*y^(2^2)+x^(2^3)*y^(2^5) - x^(2^5)*z^(2^2 +2)- x^(2^4)*z^(2^5 +2)- x^(2^3)*z^(2^5 +2^4) - y^(2^5 +2^3)*z^(2)- y^(2^5 +2^2)*z^(2^3)- y^(2^3 +2)*z^(2^5) + y^(2^5)*z^( 2^3 + 2^2 +2)+ y^(2^4)*z^( 2^5 + 2^2 +2) + y^(2^3)*z^( 2^5 + 2^4 +2)+ y^(2^2)*z^( 2^5 + 2^4 +2^3) -z^(2^5 +2^4 + 2^3 + 2^2 +2) ) + g*(x^(2^6 +2^3) -x^(2^6)*y^(2^3)*z^2 -x^(2^4)*y^(2^6)*z^2 -x^(2^3)*y^(2^6)*z^(2^4) -x^(2^3)*y^(2^5)*z^(2^6) + x^(2^6)*z^(2^3 +2^2 +2)+ x^(2^5)*z^(2^6 +2^2 +2)+ x^(2^4)*z^(2^6 +2^5 +2)+ x^(2^3)*z^(2^6 +2^5 +2^4) -y^(2^6 + 2^4 + 2^2 ) + y^(2^6 +2^4)*z^(2^2 +2)+ y^(2^6 +2^3)*z^(2^4 +2)+ y^(2^5 +2^3)*z^(2^6 +2)+ y^(2^4 +2^2)*z^(2^6 +2^5) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2)- y^(2^5)*z^( 2^6 +2^3 + 2^2 +2)- y^(2^4)*z^( 2^6 +2^5 + 2^2 +2)- y^(2^3)*z^( 2^6 +2^5 + 2^4 +2)- y^(2^2)*z^( 2^6 +2^5 + 2^4 +2^3) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2) ) - (x^(2^7 +2^4)*z^2 +x^(2^7 +2^3)*z^(2^4)+x^(2^6 +2^3)*z^(2^7) + x^(2^7)*z^(2^4 +2^3 +2^2)*z^2+ x^(2^6)*z^(2^7 +2^3 +2^2)*z^2 + x^(2^5)*z^(2^7 +2^6 +2^2)*z^2+ x^(2^4)*z^(2^7 +2^6 +2^5)*z^2+ x^(2^3)*z^(2^7 +2^6 +2^5)*z^(2^4) - y^(2^7 + 2^5 + 2^3)*z^2 -y^(2^7 + 2^5 + 2^2)*z^(2^3) -y^(2^7 + 2^4 + 2^2)*z^(2^5)-y^(2^6 + 2^4 + 2^2)*z^(2^7) + y^(2^7 +2^5)*z^(2^3 +2^2)*z^2 + y^(2^7 +2^4)*z^(2^5 +2^2)*z^2 + y^(2^7 +2^3)*z^(2^5 +2^4)*z^2 + y^(2^7 +2^2)*z^(2^5 +2^4)*z^(2^3) + y^(2^6 +2^4)*z^(2^7 +2^2+2)+ y^(2^6 +2^3)*z^(2^7 +2^4+2) + y^(2^6 +2^2)*z^(2^7 +2^4+2^3) + y^(2^5 +2^3)*z^(2^7 +2^6+2) + y^(2^5 +2^2)*z^(2^7 +2^6+2^3)+ y^(2^3 +2)*z^(2^7 +2^6+2^5) - y^(2^7)*z^(2^5 + 2^4 +2^3 + 2^2 +2) - y^(2^6)*z^(2^7 + 2^4 +2^3 + 2^2 +2) - y^(2^5)*z^(2^7 + 2^6 +2^3 + 2^2 +2) - y^(2^4)*z^(2^7 + 2^6 +2^5 + 2^2 +2) - y^(2^3)*z^(2^7 + 2^6 +2^5 + 2^4 +2) - y^(2^2)*z^(2^7 + 2^6 +2^5 + 2^4 +2^3) + z^(2^7 +2^6 +2^5 +2^4 + 2^3 + 2^2 )*z^2 )- x^(2^7)*y^(2^2 +2^4)-x^(2^5)*y^(2^7 +2^2)-x^(2^3)*y^(2^7 +2^5) + x^(2^7)*y^(2^4)*z^(2^2 +2) + x^(2^7)*y^(2^3)*z^(2^4 +2) + x^(2^7)*y^(2^2)*z^(2^4 +2^3) + x^(2^5)*y^(2^7)*z^(2^2 +2)+ x^(2^5)*y^(2^2)*z^(2^7 +2^6) + x^(2^4)*y^(2^6)*z^(2^7 +2)+ x^(2^4)*y^(2^7)*z^(2^5 +2) + x^(2^3)*y^(2^7)*z^(2^5 +2^4) + x^(2^3)*y^(2^5)*z^(2^7 +2^6) ), y*(a- b*z^2 -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) +d*z^(2^2)*y^(2^3) -d*z^(2^3 +2^2 +2) + e*(x^(2^4)*z^2 +x^(2^3)*z^(2^4) +y^(2^4)*y^(2^2) -y^(2^4)*z^(2^2 +2) -y^(2^2)*z^(2^4 +2^3)-y^(2^3)*z^(2^4 +2) +z^(2^4 + 2^3 + 2^2 +2) ) + f*(x^(2^5)*y^(2^2)+x^(2^3)*y^(2^5) - x^(2^5)*z^(2^2 +2)- x^(2^4)*z^(2^5 +2)- x^(2^3)*z^(2^5 +2^4) - y^(2^5 +2^3)*z^(2)- y^(2^5 +2^2)*z^(2^3)- y^(2^3 +2)*z^(2^5) + y^(2^5)*z^( 2^3 + 2^2 +2)+ y^(2^4)*z^( 2^5 + 2^2 +2) + y^(2^3)*z^( 2^5 + 2^4 +2)+ y^(2^2)*z^( 2^5 + 2^4 +2^3) -z^(2^5 +2^4 + 2^3 + 2^2 +2) ) + g*(x^(2^6 +2^3) -x^(2^6)*y^(2^3)*z^2 -x^(2^4)*y^(2^6)*z^2 -x^(2^3)*y^(2^6)*z^(2^4) -x^(2^3)*y^(2^5)*z^(2^6) + x^(2^6)*z^(2^3 +2^2 +2)+ x^(2^5)*z^(2^6 +2^2 +2)+ x^(2^4)*z^(2^6 +2^5 +2)+ x^(2^3)*z^(2^6 +2^5 +2^4) -y^(2^6 + 2^4 + 2^2 ) + y^(2^6 +2^4)*z^(2^2 +2)+ y^(2^6 +2^3)*z^(2^4 +2)+ y^(2^5 +2^3)*z^(2^6 +2)+ y^(2^4 +2^2)*z^(2^6 +2^5) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2)- y^(2^5)*z^( 2^6 +2^3 + 2^2 +2)- y^(2^4)*z^( 2^6 +2^5 + 2^2 +2)- y^(2^3)*z^( 2^6 +2^5 + 2^4 +2)- y^(2^2)*z^( 2^6 +2^5 + 2^4 +2^3) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2) ) - (x^(2^7 +2^4)*z^2 +x^(2^7 +2^3)*z^(2^4)+x^(2^6 +2^3)*z^(2^7) + x^(2^7)*z^(2^4 +2^3 +2^2)*z^2+ x^(2^6)*z^(2^7 +2^3 +2^2)*z^2 + x^(2^5)*z^(2^7 +2^6 +2^2)*z^2+ x^(2^4)*z^(2^7 +2^6 +2^5)*z^2+ x^(2^3)*z^(2^7 +2^6 +2^5)*z^(2^4) - y^(2^7 + 2^5 + 2^3)*z^2 -y^(2^7 + 2^5 + 2^2)*z^(2^3) -y^(2^7 + 2^4 + 2^2)*z^(2^5)-y^(2^6 + 2^4 + 2^2)*z^(2^7) + y^(2^7 +2^5)*z^(2^3 +2^2)*z^2 + y^(2^7 +2^4)*z^(2^5 +2^2)*z^2 + y^(2^7 +2^3)*z^(2^5 +2^4)*z^2 + y^(2^7 +2^2)*z^(2^5 +2^4)*z^(2^3) + y^(2^6 +2^4)*z^(2^7 +2^2+2)+ y^(2^6 +2^3)*z^(2^7 +2^4+2) + y^(2^6 +2^2)*z^(2^7 +2^4+2^3) + y^(2^5 +2^3)*z^(2^7 +2^6+2) + y^(2^5 +2^2)*z^(2^7 +2^6+2^3)+ y^(2^3 +2)*z^(2^7 +2^6+2^5) - y^(2^7)*z^(2^5 + 2^4 +2^3 + 2^2 +2) - y^(2^6)*z^(2^7 + 2^4 +2^3 + 2^2 +2) - y^(2^5)*z^(2^7 + 2^6 +2^3 + 2^2 +2) - y^(2^4)*z^(2^7 + 2^6 +2^5 + 2^2 +2) - y^(2^3)*z^(2^7 + 2^6 +2^5 + 2^4 +2) - y^(2^2)*z^(2^7 + 2^6 +2^5 + 2^4 +2^3) + z^(2^7 +2^6 +2^5 +2^4 + 2^3 + 2^2 )*z^2 )- x^(2^7)*y^(2^2 +2^4)-x^(2^5)*y^(2^7 +2^2)-x^(2^3)*y^(2^7 +2^5) + x^(2^7)*y^(2^4)*z^(2^2 +2) + x^(2^7)*y^(2^3)*z^(2^4 +2) + x^(2^7)*y^(2^2)*z^(2^4 +2^3) + x^(2^5)*y^(2^7)*z^(2^2 +2)+ x^(2^5)*y^(2^2)*z^(2^7 +2^6) + x^(2^4)*y^(2^6)*z^(2^7 +2)+ x^(2^4)*y^(2^7)*z^(2^5 +2) + x^(2^3)*y^(2^7)*z^(2^5 +2^4) + x^(2^3)*y^(2^5)*z^(2^7 +2^6) ) + x^2 *(b- c*z^(2^2) -d*y^(2^3) +d*z^(2^3 +2^2) -e*x^(2^4) +e*z^(2^4)*y^(2^3) +e*z^(2^2)*y^(2^4) -e*z^(2^4 +2^3 +2^2) + f*( x^(2^5)*z^(2^2) +x^(2^4)*z^(2^5) +y^(2^5)*y^(2^3) -y^(2^5)*z^(2^2 +2^3) -y^(2^4)*z^(2^2 +2^5) -y^(2^3)*z^(2^4 +2^5) +z^(2^4 + 2^3 + 2^2 +2^5)) + g*( x^(2^6)*y^(2^3) + x^(2^4)*y^(2^6) - x^(2^6)*z^(2^2 +2^3) - x^(2^5)*z^(2^2 +2^6) - x^(2^4)*z^(2^6 +2^5) - y^(2^6 +2^4)*z^(2^2) - y^(2^6 +2^3)*z^(2^4) - y^(2^5 +2^3)*z^(2^6) + y^(2^6)*z^( 2^3 + 2^2 +2^4)+ y^(2^5)*z^( 2^3 + 2^2 +2^6) + y^(2^4)*z^( 2^5 + 2^2 +2^6)+ y^(2^3)*z^( 2^6 + 2^5 +2^4) -z^(2^5 +2^4 + 2^3 + 2^2 +2^6))+ x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) -x^(2^7)*y^(2^3)*z^(2^4) -x^(2^6)*y^(2^3)*z^(2^7) -x^(2^4)*y^(2^6)*z^(2^7) + x^(2^7)*z^(2^3 +2^2 +2^4) + x^(2^6)*z^(2^3 +2^2 +2^7) + x^(2^5)*z^(2^7 +2^2 +2^6) + x^(2^4)*z^(2^7 +2^6 +2^5) - y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^2 +2^3) + y^(2^7 +2^4)*z^(2^2 +2^5)+ y^(2^7 +2^3)*z^(2^4 +2^5)+ y^(2^3 +2^5)*z^(2^7 +2^6) + y^(2^3 +2^6)*z^(2^7 +2^4) + y^(2^6 +2^4)*z^(2^7 +2^2) - y^(2^7)*z^( 2^4 +2^3 + 2^2 +2^5) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2^7) - y^(2^5)*z^( 2^6 +2^3 + 2^2 +2^7) - y^(2^4)*z^( 2^6 +2^5 + 2^2 +2^7) - y^(2^4)*z^( 2^6 +2^5 + 2^2 +2^7) - y^(2^3)*z^( 2^7 +2^6 + 2^5 +2^4) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2^7) ), z*(a- b*z^2 -c*y^(2^2) +c*z^(2^2 +2) -d*x^(2^3) +d*z^(2^3)*y^(2^2) +d*z^(2^2)*y^(2^3) -d*z^(2^3 +2^2 +2) + e*(x^(2^4)*z^2 +x^(2^3)*z^(2^4) +y^(2^4)*y^(2^2) -y^(2^4)*z^(2^2 +2) -y^(2^2)*z^(2^4 +2^3)-y^(2^3)*z^(2^4 +2) +z^(2^4 + 2^3 + 2^2 +2) ) + f*(x^(2^5)*y^(2^2)+x^(2^3)*y^(2^5) - x^(2^5)*z^(2^2 +2)- x^(2^4)*z^(2^5 +2)- x^(2^3)*z^(2^5 +2^4) - y^(2^5 +2^3)*z^(2)- y^(2^5 +2^2)*z^(2^3)- y^(2^3 +2)*z^(2^5) + y^(2^5)*z^( 2^3 + 2^2 +2)+ y^(2^4)*z^( 2^5 + 2^2 +2) + y^(2^3)*z^( 2^5 + 2^4 +2)+ y^(2^2)*z^( 2^5 + 2^4 +2^3) -z^(2^5 +2^4 + 2^3 + 2^2 +2) ) + g*(x^(2^6 +2^3) -x^(2^6)*y^(2^3)*z^2 -x^(2^4)*y^(2^6)*z^2 -x^(2^3)*y^(2^6)*z^(2^4) -x^(2^3)*y^(2^5)*z^(2^6) + x^(2^6)*z^(2^3 +2^2 +2)+ x^(2^5)*z^(2^6 +2^2 +2)+ x^(2^4)*z^(2^6 +2^5 +2)+ x^(2^3)*z^(2^6 +2^5 +2^4) -y^(2^6 + 2^4 + 2^2 ) + y^(2^6 +2^4)*z^(2^2 +2)+ y^(2^6 +2^3)*z^(2^4 +2)+ y^(2^5 +2^3)*z^(2^6 +2)+ y^(2^4 +2^2)*z^(2^6 +2^5) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2)- y^(2^5)*z^( 2^6 +2^3 + 2^2 +2)- y^(2^4)*z^( 2^6 +2^5 + 2^2 +2)- y^(2^3)*z^( 2^6 +2^5 + 2^4 +2)- y^(2^2)*z^( 2^6 +2^5 + 2^4 +2^3) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2) ) - (x^(2^7 +2^4)*z^2 +x^(2^7 +2^3)*z^(2^4)+x^(2^6 +2^3)*z^(2^7) + x^(2^7)*z^(2^4 +2^3 +2^2)*z^2+ x^(2^6)*z^(2^7 +2^3 +2^2)*z^2 + x^(2^5)*z^(2^7 +2^6 +2^2)*z^2+ x^(2^4)*z^(2^7 +2^6 +2^5)*z^2+ x^(2^3)*z^(2^7 +2^6 +2^5)*z^(2^4) - y^(2^7 + 2^5 + 2^3)*z^2 -y^(2^7 + 2^5 + 2^2)*z^(2^3) -y^(2^7 + 2^4 + 2^2)*z^(2^5)-y^(2^6 + 2^4 + 2^2)*z^(2^7) + y^(2^7 +2^5)*z^(2^3 +2^2)*z^2 + y^(2^7 +2^4)*z^(2^5 +2^2)*z^2 + y^(2^7 +2^3)*z^(2^5 +2^4)*z^2 + y^(2^7 +2^2)*z^(2^5 +2^4)*z^(2^3) + y^(2^6 +2^4)*z^(2^7 +2^2+2)+ y^(2^6 +2^3)*z^(2^7 +2^4+2) + y^(2^6 +2^2)*z^(2^7 +2^4+2^3) + y^(2^5 +2^3)*z^(2^7 +2^6+2) + y^(2^5 +2^2)*z^(2^7 +2^6+2^3)+ y^(2^3 +2)*z^(2^7 +2^6+2^5) - y^(2^7)*z^(2^5 + 2^4 +2^3 + 2^2 +2) - y^(2^6)*z^(2^7 + 2^4 +2^3 + 2^2 +2) - y^(2^5)*z^(2^7 + 2^6 +2^3 + 2^2 +2) - y^(2^4)*z^(2^7 + 2^6 +2^5 + 2^2 +2) - y^(2^3)*z^(2^7 + 2^6 +2^5 + 2^4 +2) - y^(2^2)*z^(2^7 + 2^6 +2^5 + 2^4 +2^3) + z^(2^7 +2^6 +2^5 +2^4 + 2^3 + 2^2 )*z^2 )- x^(2^7)*y^(2^2 +2^4)-x^(2^5)*y^(2^7 +2^2)-x^(2^3)*y^(2^7 +2^5) + x^(2^7)*y^(2^4)*z^(2^2 +2) + x^(2^7)*y^(2^3)*z^(2^4 +2) + x^(2^7)*y^(2^2)*z^(2^4 +2^3) + x^(2^5)*y^(2^7)*z^(2^2 +2)+ x^(2^5)*y^(2^2)*z^(2^7 +2^6) + x^(2^4)*y^(2^6)*z^(2^7 +2)+ x^(2^4)*y^(2^7)*z^(2^5 +2) + x^(2^3)*y^(2^7)*z^(2^5 +2^4) + x^(2^3)*y^(2^5)*z^(2^7 +2^6) )+ y^2 *(b- c*z^(2^2) -d*y^(2^3) +d*z^(2^3 +2^2) -e*x^(2^4) +e*z^(2^4)*y^(2^3) +e*z^(2^2)*y^(2^4) -e*z^(2^4 +2^3 +2^2) + f*( x^(2^5)*z^(2^2) +x^(2^4)*z^(2^5) +y^(2^5)*y^(2^3) -y^(2^5)*z^(2^2 +2^3) -y^(2^4)*z^(2^2 +2^5) -y^(2^3)*z^(2^4 +2^5) +z^(2^4 + 2^3 + 2^2 +2^5)) + g*( x^(2^6)*y^(2^3) + x^(2^4)*y^(2^6) - x^(2^6)*z^(2^2 +2^3) - x^(2^5)*z^(2^2 +2^6) - x^(2^4)*z^(2^6 +2^5) - y^(2^6 +2^4)*z^(2^2) - y^(2^6 +2^3)*z^(2^4) - y^(2^5 +2^3)*z^(2^6) + y^(2^6)*z^( 2^3 + 2^2 +2^4)+ y^(2^5)*z^( 2^3 + 2^2 +2^6) + y^(2^4)*z^( 2^5 + 2^2 +2^6)+ y^(2^3)*z^( 2^6 + 2^5 +2^4) -z^(2^5 +2^4 + 2^3 + 2^2 +2^6))+ x^(2^7 +2^4) -x^(2^7)*y^(2^4)*z^(2^2) -x^(2^7)*y^(2^3)*z^(2^4) -x^(2^6)*y^(2^3)*z^(2^7) -x^(2^4)*y^(2^6)*z^(2^7) + x^(2^7)*z^(2^3 +2^2 +2^4) + x^(2^6)*z^(2^3 +2^2 +2^7) + x^(2^5)*z^(2^7 +2^2 +2^6) + x^(2^4)*z^(2^7 +2^6 +2^5) - y^(2^7 + 2^5 + 2^3 ) + y^(2^7 +2^5)*z^(2^2 +2^3) + y^(2^7 +2^4)*z^(2^2 +2^5)+ y^(2^7 +2^3)*z^(2^4 +2^5)+ y^(2^3 +2^5)*z^(2^7 +2^6) + y^(2^3 +2^6)*z^(2^7 +2^4) + y^(2^6 +2^4)*z^(2^7 +2^2) - y^(2^7)*z^( 2^4 +2^3 + 2^2 +2^5) - y^(2^6)*z^( 2^4 +2^3 + 2^2 +2^7) - y^(2^5)*z^( 2^6 +2^3 + 2^2 +2^7) - y^(2^4)*z^( 2^6 +2^5 + 2^2 +2^7) - y^(2^4)*z^( 2^6 +2^5 + 2^2 +2^7) - y^(2^3)*z^( 2^7 +2^6 + 2^5 +2^4) +z^(2^6 +2^5 +2^4 + 2^3 + 2^2 +2^7) )+ x^(2^2) *(c- d*z^(2^3) -e*y^(2^4) +e*z^(2^4 +2^3) -f*x^(2^5) +f*z^(2^5)*y^(2^4) +f*z^(2^3)*y^(2^5) -f*z^(2^5 +2^4 +2^3) + g*(x^(2^6)*z^(2^3) +x^(2^5)*z^(2^6) +y^(2^6)*y^(2^4) -y^(2^6)*z^(2^4 +2^3) -y^(2^5)*z^(2^6 +2^3) -y^(2^4)*z^(2^6 +2^5) +z^(2^4 + 2^3 + 2^6 +2^5) ) + x^(2^7)*y^(2^4) + x^(2^5)*y^(2^7) - x^(2^7)*z^(2^4 +2^3) - x^(2^6)*z^(2^7 +2^3) - x^(2^5)*z^(2^7 +2^6) - y^(2^7 +2^5)*z^(2^3) - y^(2^7 +2^4)*z^(2^5) - y^(2^6 +2^4)*z^(2^7) + y^(2^7)*z^( 2^3 + 2^5 +2^4)+ y^(2^6)*z^( 2^3 + 2^7 +2^4)+ y^(2^5)*z^( 2^3 + 2^7 +2^6)+ y^(2^4)*z^( 2^7 + 2^6 +2^5) -z^(2^5 +2^4 + 2^3 + 2^7 +2^6)) ] ; [IsHomogeneous(f): f in P]; P; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S; Output: Magma V2.10-22 Mon Apr 5 2004 05:01:27 on modular [Seed = 588399476] ------------------------------------- Graded Polynomial ring of rank 10 over GF(2) Lexicographical Order Variables: x, y, z, a, b, c, d, e, f, g Variable weights: 7 6 4 1016 1008 992 960 896 768 512 [ true, true, true, true, true, true, true, false, false, false ] [ a, b, c, d, e, f, g, x^145*z^2 + x^137*z^16 + x^129*y^20 + x^129*y^16*z^6 + x^129*y^8*z^18 + x^129*y^4*z^24 + x^129*z^30 + x^73*z^128 + x^73*g + x^65*y^8*z^2*g + x^65*z^142 + x^65*z^14*g + x^33*y^132 + x^33*y^128*z^6 + x^33*y^4*z^192 + x^33*y^4*f + x^33*z^198 + x^33*z^70*g + x^33*z^6*f + x^17*y^128*z^34 + x^17*y^64*z^130 + x^17*y^64*z^2*g + x^17*z^226 + x^17*z^98*g + x^17*z^34*f + x^17*z^2*e + x^9*y^160 + x^9*y^128*z^48 + x^9*y^64*z^16*g + x^9*y^32*z^192 + x^9*y^32*z^64*g + x^9*y^32*f + x^9*z^240 + x^9*z^112*g + x^9*z^48*f + x^9*z^16*e + x^9*d + x*y^168*z^2 + x*y^164*z^8 + x*y^160*z^14 + x*y^148*z^32 + x*y^144*z^38 + x*y^136*z^50 + x*y^132*z^56 + x*y^128*z^62 + x*y^84*z^128 + x*y^84*g + x*y^80*z^134 + x*y^80*z^6*g + x*y^72*z^146 + x*y^72*z^18*g + x*y^68*z^152 + x*y^64*z^158 + x*y^64*z^30*g + x*y^40*z^194 + x*y^40*z^66*g + x*y^40*z^2*f + x*y^36*z^200 + x*y^36*z^8*f + x*y^32*z^206 + x*y^32*z^78*g + x*y^32*z^14*f + x*y^20*z^96*g + x*y^20*e + x*y^16*z^230 + x*y^16*z^102*g + x*y^16*z^38*f + x*y^16*z^6*e + x*y^10*z^224 + x*y^10*z^32*f + x*y^8*z^242 + x*y^8*z^114*g + x*y^8*z^50*f + x*y^8*z^18*e + x*y^8*z^4*d + x*y^4*z^248 + x*y^4*z^120*g + x*y^4*z^56*f + x*y^4*z^24*e + x*y^4*z^8*d + x*y^4*c + x*z^254 + x*z^126*g + x*z^62*f + x*z^30*e + x*z^14*d + x*z^6*c + x*z^2*b + x*a, x^146 + x^144*y*z^2 + x^136*y*z^16 + x^130*y^16*z^4 + x^130*y^8*z^16 + x^130*z^28 + x^128*y^21 + x^128*y^17*z^6 + x^128*y^9*z^18 + x^128*y^5*z^24 + x^128*y*z^30 + x^72*y*z^128 + x^72*y*g + x^66*y^8*z^128 + x^66*y^8*g + x^66*z^140 + x^66*z^12*g + x^64*y^9*z^2*g + x^64*y*z^142 + x^64*y*z^14*g + x^34*z^196 + x^34*z^68*g + x^34*z^4*f + x^32*y^133 + x^32*y^129*z^6 + x^32*y^5*z^192 + x^32*y^5*f + x^32*y*z^198 + x^32*y*z^70*g + x^32*y*z^6*f + x^18*y^64*z^128 + x^18*y^64*g + x^18*z^224 + x^18*z^96*g + x^18*z^32*f + x^18*e + x^16*y^129*z^34 + x^16*y^65*z^130 + x^16*y^65*z^2*g + x^16*y*z^226 + x^16*y*z^98*g + x^16*y*z^34*f + x^16*y*z^2*e + x^8*y^161 + x^8*y^129*z^48 + x^8*y^65*z^16*g + x^8*y^33*z^192 + x^8*y^33*z^64*g + x^8*y^33*f + x^8*y*z^240 + x^8*y*z^112*g + x^8*y*z^48*f + x^8*y*z^16*e + x^8*y*d + x^2*y^168 + x^2*y^160*z^12 + x^2*y^144*z^36 + x^2*y^136*z^48 + x^2*y^128*z^60 + x^2*y^80*z^132 + x^2*y^80*z^4*g + x^2*y^72*z^144 + x^2*y^72*z^16*g + x^2*y^64*z^156 + x^2*y^64*z^28*g + x^2*y^40*z^192 + x^2*y^40*z^64*g + x^2*y^40*f + x^2*y^32*z^204 + x^2*y^32*z^76*g + x^2*y^32*z^12*f + x^2*y^16*z^100*g + x^2*y^16*z^36*f + x^2*y^16*z^4*e + x^2*y^8*z^240 + x^2*y^8*z^112*g + x^2*y^8*z^48*f + x^2*y^8*z^16*e + x^2*y^8*d + x^2*z^252 + x^2*z^124*g + x^2*z^60*f + x^2*z^28*e + x^2*z^12*d + x^2*z^4*c + x^2*b + y^169*z^2 + y^165*z^8 + y^161*z^14 + y^149*z^32 + y^145*z^38 + y^137*z^50 + y^133*z^56 + y^129*z^62 + y^85*z^128 + y^85*g + y^81*z^134 + y^81*z^6*g + y^73*z^146 + y^73*z^18*g + y^69*z^152 + y^65*z^158 + y^65*z^30*g + y^41*z^194 + y^41*z^66*g + y^41*z^2*f + y^37*z^200 + y^37*z^8*f + y^33*z^206 + y^33*z^78*g + y^33*z^14*f + y^21*z^96*g + y^21*e + y^17*z^230 + y^17*z^102*g + y^17*z^38*f + y^17*z^6*e + y^11*z^224 + y^11*z^32*f + y^9*z^242 + y^9*z^114*g + y^9*z^50*f + y^9*z^18*e + y^9*z^4*d + y^5*z^248 + y^5*z^120*g + y^5*z^56*f + y^5*z^24*e + y^5*z^8*d + y^5*c + y*z^254 + y*z^126*g + y*z^62*f + y*z^30*e + y*z^14*d + y*z^6*c + y*z^2*b + y*a, x^144*y^2 + x^144*z^3 + x^136*z^17 + x^132*y^16 + x^132*z^24 + x^128*y^20*z + x^128*y^18*z^4 + x^128*y^16*z^7 + x^128*y^10*z^16 + x^128*y^8*z^19 + x^128*y^4*z^25 + x^128*y^2*z^28 + x^128*z^31 + x^72*z^129 + x^72*z*g + x^68*z^136 + x^68*z^8*g + x^64*y^10*z^128 + x^64*y^10*g + x^64*y^8*z^3*g + x^64*y^2*z^140 + x^64*y^2*z^12*g + x^64*z^143 + x^64*z^15*g + x^36*y^128 + x^36*z^192 + x^36*z^64*g + x^36*f + x^32*y^132*z + x^32*y^128*z^7 + x^32*y^4*z^193 + x^32*y^4*z*f + x^32*y^2*z^196 + x^32*y^2*z^68*g + x^32*y^2*z^4*f + x^32*z^199 + x^32*z^71*g + x^32*z^7*f + x^16*y^128*z^35 + x^16*y^66*z^128 + x^16*y^66*g + x^16*y^64*z^131 + x^16*y^64*z^3*g + x^16*y^2*z^224 + x^16*y^2*z^96*g + x^16*y^2*z^32*f + x^16*y^2*e + x^16*z^227 + x^16*z^99*g + x^16*z^35*f + x^16*z^3*e + x^8*y^160*z + x^8*y^128*z^49 + x^8*y^64*z^17*g + x^8*y^32*z^193 + x^8*y^32*z^65*g + x^8*y^32*z*f + x^8*z^241 + x^8*z^113*g + x^8*z^49*f + x^8*z^17*e + x^8*z*d + x^4*y^160*z^8 + x^4*y^144*z^32 + x^4*y^128*z^56 + x^4*y^80*z^128 + x^4*y^80*g + x^4*y^64*z^152 + x^4*y^64*z^24*g + x^4*y^32*z^200 + x^4*y^32*z^72*g + x^4*y^32*z^8*f + x^4*y^16*z^224 + x^4*y^16*z^96*g + x^4*y^16*z^32*f + x^4*y^16*e + x^4*z^248 + x^4*z^120*g + x^4*z^56*f + x^4*z^24*e + x^4*z^8*d + x^4*c + y^170 + y^168*z^3 + y^164*z^9 + y^162*z^12 + y^160*z^15 + y^148*z^33 + y^146*z^36 + y^144*z^39 + y^138*z^48 + y^136*z^51 + y^132*z^57 + y^130*z^60 + y^128*z^63 + y^84*z^129 + y^84*z*g + y^82*z^132 + y^82*z^4*g + y^80*z^135 + y^80*z^7*g + y^74*z^144 + y^74*z^16*g + y^72*z^147 + y^72*z^19*g + y^68*z^153 + y^66*z^156 + y^66*z^28*g + y^64*z^159 + y^64*z^31*g + y^42*z^192 + y^42*z^64*g + y^42*f + y^40*z^195 + y^40*z^67*g + y^40*z^3*f + y^36*z^201 + y^36*z^9*f + y^34*z^204 + y^34*z^76*g + y^34*z^12*f + y^32*z^207 + y^32*z^79*g + y^32*z^15*f + y^20*z^97*g + y^20*z*e + y^18*z^100*g + y^18*z^36*f + y^18*z^4*e + y^16*z^231 + y^16*z^103*g + y^16*z^39*f + y^16*z^7*e + y^10*z^240 + y^10*z^225 + y^10*z^112*g + y^10*z^48*f + y^10*z^33*f + y^10*z^16*e + y^10*d + y^8*z^243 + y^8*z^115*g + y^8*z^51*f + y^8*z^19*e + y^8*z^5*d + y^4*z^249 + y^4*z^121*g + y^4*z^57*f + y^4*z^25*e + y^4*z^9*d + y^4*z*c + y^2*z^252 + y^2*z^124*g + y^2*z^60*f + y^2*z^28*e + y^2*z^12*d + y^2*z^4*c + y^2*b + z^255 + z^127*g + z^63*f + z^31*e + z^15*d + z^7*c + z^3*b + z*a ] ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Mon Apr 5 05:20:39 2004 Input: K := GF(2); R := PolynomialRing(K, [7, 6, 4, 1016, 1008, 992, 960, 896, 768, 512]); R; P := [ 7^145*4^2 , 7^137*4^16 , 7^129*6^20 , 7^129*6^16*4^6 , 7^129*6^8*4^18 , 7^129*6^4*4^24 , 7^129*4^30 , 7^73*4^128 , 7^73*512 , 7^65*6^8*4^2*512 , 7^65*4^142 , 7^65*4^14*512 , 7^33*6^132 , 7^33*6^128*4^6 , 7^33*6^4*4^192 , 7^33*6^4*768 , 7^33*4^198 , 7^33*4^70*512 , 7^33*4^6*768 , 7^17*6^128*4^34 , 7^17*6^64*4^130 , 7^17*6^64*4^2*512 , 7^17*4^226 , 7^17*4^98*512 , x^17*4^34*768 , 7^17*4^2*896 , 7^9*6^160 , 7^9*6^128*4^48 , 7^9*6^64*4^16*512 , 7^9*6^32*4^192 , 7^9*6^32*4^64*512 , 7^9*6^32*768 , 7^9*4^240 , 7^9*4^112*512 , 7^9*4^48*768 , 7^9*4^16*896 , 7^9*960 , 7*6^168*4^2 , 7*6^164*4^8 , 7*6^160*4^14 , 7*6^148*4^32 , 7*6^144*4^38 , 7*6^136*4^50 , 7*6^132*4^56 , 7*6^128*4^62 , 7*6^84*4^128 , 7*6^84*512 , 7*6^80*4^134 , 7*6^80*4^6*512 , 7*6^72*4^146 , 7*6^72*4^18*512 , 7*6^68*4^152 , 7*6^64*4^158 , 7*6^64*4^30*512 , 7*6^40*4^194 , 7*6^40*4^66*512 , 7*6^40*4^2*768 , 7*6^36*4^200 , 7*6^36*4^8*768 , 7*6^32*4^206 , 7*6^32*4^78*512 , 7*6^32*4^14*768 , 7*6^20*4^96*512 , 7*6^20*896 , 7*6^16*4^230 , 7*6^16*4^102*512 , 7*6^16*4^38*768 , 7*6^16*4^6*896 , 7*6^10*4^224 , 7*6^10*4^32*768 , 7*6^8*4^242 , 7*6^8*4^114*512 , 7*6^8*4^50*768 , 7*6^8*4^18*896 , 7*6^8*4^4*960 , 7*6^4*4^248 , 7*6^4*4^120*512 , 7*6^4*4^56*768 , 7*6^4*4^24*896 , 7*6^4*4^8*960 , 7*6^4*992 , 7*4^254 , 7*4^126*512 , 7*4^62*768 , 7*4^30*896 , 7*4^14*960 , 7*4^6*992 , 7*4^2*1008 , 7*1016, 7^146 , 7^144*6*4^2 , 7^136*6*4^16 , 7^130*6^16*4^4 , 7^130*6^8*4^16 , 7^130*4^28 , 7^128*6^21 , 7^128*6^17*4^6 , 7^128*6^9*4^18 , 7^128*6^5*4^24 , 7^128*6*4^30 , 7^72*6*4^128 , 7^72*6*512 , 7^66*6^8*4^128 , 7^66*6^8*512 , 7^66*4^140 , 7^66*4^12*512 , 7^64*6^9*4^2*512 , 7^64*6*4^142 , 7^64*6*4^14*512 , 7^34*4^196 , 7^34*4^68*512 , 7^34*4^4*768 , 7^32*6^133 , 7^32*6^129*4^6 , 7^32*6^5*4^192 , 7^32*6^5*768 , 7^32*6*4^198 , 7^32*6*4^70*512 , 7^32*6*4^6*768 , 7^18*6^64*4^128 , 7^18*6^64*512 , 7^18*4^224 , 7^18*4^96*512 , 7^18*4^32*768 , 7^18*896 , 7^16*6^129*4^34 , 7^16*6^65*4^130 , 7^16*6^65*4^2*512 , 7^16*6*4^226 , 7^16*6*4^98*512 , 7^16*6*4^34*768 , 7^16*6*4^2*896 , 7^8*6^161 , 7^8*6^129*4^48 , 7^8*6^65*4^16*512 , 7^8*6^33*4^192 , 7^8*6^33*4^64*512 , 7^8*6^33*768 , 7^8*6*4^240 , 7^8*6*4^112*512 , 7^8*6*4^48*768 , 7^8*6*4^16*896 , 7^8*6*960 , 7^2*6^168 , 7^2*6^160*4^12 , 7^2*6^144*4^36 , 7^2*6^136*4^48 , 7^2*6^128*4^60 , 7^2*6^80*4^132 , 7^2*6^80*4^4*512 , 7^2*6^72*4^144 , 7^2*6^72*4^16*512 , 7^2*6^64*4^156 , 7^2*6^64*4^28*512 , 7^2*6^40*4^192 , 7^2*6^40*4^64*512 , 7^2*6^40*768 , 7^2*6^32*4^204 , 7^2*6^32*4^76*512 , 7^2*6^32*4^12*768 , 7^2*6^16*4^100*512 , 7^2*6^16*4^36*768 , 7^2*6^16*4^4*896 , 7^2*6^8*4^240 , 7^2*6^8*4^112*512 , 7^2*6^8*4^48*768 , 7^2*6^8*4^16*896 , 7^2*6^8*960 , 7^2*4^252 , 7^2*4^124*512 , 7^2*4^60*768 , 7^2*4^28*896 , 7^2*4^12*960 , 7^2*4^4*992 , 7^2*1008 , 6^169*4^2 , 6^165*4^8 , 6^161*4^14 , 6^149*4^32 , 6^145*4^38 , 6^137*4^50 , 6^133*4^56 , 6^129*4^62 , 6^85*4^128 , 6^85*512 , 6^81*4^134 , 6^81*4^6*512 , 6^73*4^146 , 6^73*4^18*512 , 6^69*4^152 , 6^65*4^158 , 6^65*4^30*512 , 6^41*4^194 , 6^41*4^66*512 , 6^41*4^2*768 , 6^37*4^200 , 6^37*4^8*768 , 6^33*4^206 , 6^33*4^78*512 , 6^33*4^14*768 , 6^21*4^96*512 , 6^21*896 , 6^17*4^230 , 6^17*4^102*512 , 6^17*4^38*768 , 6^17*4^6*896 , 6^11*4^224 , 6^11*4^32*768 , 6^9*4^242 , 6^9*4^114*512 , 6^9*4^50*768 , 6^9*4^18*896 , 6^9*4^4*960 , 6^5*4^248 , 6^5*4^120*512 , 6^5*4^56*768 , 6^5*4^24*896 , 6^5*4^8*960 , 6^5*992 , 6*4^254 , 6*4^126*512 , 6*4^62*768 , 6*4^30*896 , 6*4^14*960 , 6*4^6*992 , 6*4^2*1008 , 6*1016, 7^144*6^2 , 7^144*4^3 , 7^136*4^17 , 7^132*6^16 , 7^132*4^24 , 7^128*6^20*4 , 7^128*6^18*4^4 , 7^128*6^16*4^7 , 7^128*6^10*4^16 , 7^128*6^8*4^19 , 7^128*6^4*4^25 , 7^128*6^2*4^28 , 7^128*4^31 , 7^72*4^129 , 7^72*4*512 , 7^68*4^136 , 7^68*4^8*512 , 7^64*6^10*4^128 , 7^64*6^10*512 , 7^64*6^8*4^3*512 , 7^64*6^2*4^140 , 7^64*6^2*4^12*512 , 7^64*4^143 , 7^64*4^15*512 , 7^36*6^128 , 7^36*4^192 , 7^36*4^64*512 , 7^36*768 , 7^32*6^132*4 , 7^32*6^128*4^7 , 7^32*6^4*4^193 , 7^32*6^4*4*768 , 7^32*6^2*4^196 , 7^32*6^2*4^68*512 , 7^32*6^2*4^4*768 , 7^32*4^199 , 7^32*4^71*512 , 7^32*4^7*768 , 7^16*6^128*4^35 , 7^16*6^66*4^128 , 7^16*6^66*512 , 7^16*6^64*4^131 , 7^16*6^64*4^3*512 , 7^16*6^2*4^224 , 7^16*6^2*4^96*512 , 7^16*6^2*4^32*768 , 7^16*6^2*896 , 7^16*4^227 , 7^16*4^99*512 , 7^16*4^35*768 , 7^16*4^3*896 , 7^8*6^160*4 , 7^8*6^128*4^49 , 7^8*6^64*4^17*512 , 7^8*6^32*4^193 , 7^8*6^32*4^65*512 , 7^8*6^32*4*768 , 7^8*4^241 , 7^8*4^113*512 , 7^8*4^49*768 , 7^8*4^17*896 , 7^8*4*960 , 7^4*6^160*4^8 , 7^4*6^144*4^32 , 7^4*6^128*4^56 , 7^4*6^80*4^128 , 7^4*6^80*512 , 7^4*6^64*4^152 , 7^4*6^64*4^24*512 , 7^4*6^32*4^200 , 7^4*6^32*4^72*512 , 7^4*6^32*4^8*768 , 7^4*6^16*4^224 , 7^4*6^16*4^96*512 , 7^4*6^16*4^32*768 , 7^4*6^16*896 , 7^4*4^248 , 7^4*4^120*512 , 7^4*4^56*768 , 7^4*4^24*896 , 7^4*4^8*960 , 7^4*992 , 6^170 , 6^168*4^3 , 6^164*4^9 , 6^162*4^12 , 6^160*4^15 , 6^148*4^33 , 6^146*4^36 , 6^144*4^39 , 6^138*4^48 , 6^136*4^51 , 6^132*4^57 , 6^130*4^60 , 6^128*4^63 , 6^84*4^129 , 6^84*4*512 , 6^82*4^132 , 6^82*4^4*512 , 6^80*4^135 , 6^80*4^7*512 , 6^74*4^144 , 6^74*4^16*512 , 6^72*4^147 , 6^72*4^19*512 , 6^68*4^153 , 6^66*4^156 , 6^66*4^28*512 , 6^64*4^159 , 6^64*4^31*512 , 6^42*4^192 , 6^42*4^64*512 , 6^42*768 , 6^40*4^195 , 6^40*4^67*512 , 6^40*4^3*768 , 6^36*4^201 , 6^36*4^9*768 , 6^34*4^204 , 6^34*4^76*512 , 6^34*4^12*768 , 6^32*4^207 , 6^32*4^79*512 , 6^32*4^15*768 , 6^20*4^97*512 , 6^20*4*896 , 6^18*4^100*512 , 6^18*4^36*768 , 6^18*4^4*896 , 6^16*4^231 , 6^16*4^103*512 , 6^16*4^39*768 , 6^16*4^7*896 , 6^10*4^240 , 6^10*4^225 , 6^10*4^112*512 , 6^10*4^48*768 , 6^10*4^33*768 , 6^10*4^16*896 , 6^10*960 , 6^8*4^243 , 6^8*4^115*512 , 6^8*4^51*768 , 6^8*4^19*896 , 6^8*4^5*960 , 6^4*4^249 , 6^4*4^121*512 , 6^4*4^57*768 , 6^4*4^25*896 , 6^4*4^9*960 , 6^4*4*992 , 6^2*4^252 , 6^2*4^124*512 , 6^2*4^60*768 , 6^2*4^28*896 , 6^2*4^12*960 , 6^2*4^4*992 , 6^2*1008 , 4^255 , 4^127*512 , 4^63*768 , 4^31*896 , 4^15*960 , 4^7*992 , 4^3*1008 , 4*1016 ] ; P; [IsHomogeneous(f): f in P]; P; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S; Output: Magma V2.10-22 Mon Apr 5 2004 05:20:37 on modular [Seed = 1967395247] ------------------------------------- Graded Polynomial ring of rank 10 over GF(2) Lexicographical Order Variables: x, y, z, a, b, c, d, e, f, g Variable weights: 7 6 4 1016 1008 992 960 896 768 512 [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] [ true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] -1 [] Total time: 2.659 seconds, Total memory usage: 2.55MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Mon Apr 5 05:21:26 2004 Input: R := PolynomialRing(K, [7, 6, 4, 1016, 1008, 992, 960, 896, 768, 512]); R; P := [ 7^145*4^2 , 7^137*4^16 , 7^129*6^20 , 7^129*6^16*4^6 , 7^129*6^8*4^18 , 7^129*6^4*4^24 , 7^129*4^30 , 7^73*4^128 , 7^73*512 , 7^65*6^8*4^2*512 , 7^65*4^142 , 7^65*4^14*512 , 7^33*6^132 , 7^33*6^128*4^6 , 7^33*6^4*4^192 , 7^33*6^4*768 , 7^33*4^198 , 7^33*4^70*512 , 7^33*4^6*768 , 7^17*6^128*4^34 , 7^17*6^64*4^130 , 7^17*6^64*4^2*512 , 7^17*4^226 , 7^17*4^98*512 , x^17*4^34*768 , 7^17*4^2*896 , 7^9*6^160 , 7^9*6^128*4^48 , 7^9*6^64*4^16*512 , 7^9*6^32*4^192 , 7^9*6^32*4^64*512 , 7^9*6^32*768 , 7^9*4^240 , 7^9*4^112*512 , 7^9*4^48*768 , 7^9*4^16*896 , 7^9*960 , 7*6^168*4^2 , 7*6^164*4^8 , 7*6^160*4^14 , 7*6^148*4^32 , 7*6^144*4^38 , 7*6^136*4^50 , 7*6^132*4^56 , 7*6^128*4^62 , 7*6^84*4^128 , 7*6^84*512 , 7*6^80*4^134 , 7*6^80*4^6*512 , 7*6^72*4^146 , 7*6^72*4^18*512 , 7*6^68*4^152 , 7*6^64*4^158 , 7*6^64*4^30*512 , 7*6^40*4^194 , 7*6^40*4^66*512 , 7*6^40*4^2*768 , 7*6^36*4^200 , 7*6^36*4^8*768 , 7*6^32*4^206 , 7*6^32*4^78*512 , 7*6^32*4^14*768 , 7*6^20*4^96*512 , 7*6^20*896 , 7*6^16*4^230 , 7*6^16*4^102*512 , 7*6^16*4^38*768 , 7*6^16*4^6*896 , 7*6^10*4^224 , 7*6^10*4^32*768 , 7*6^8*4^242 , 7*6^8*4^114*512 , 7*6^8*4^50*768 , 7*6^8*4^18*896 , 7*6^8*4^4*960 , 7*6^4*4^248 , 7*6^4*4^120*512 , 7*6^4*4^56*768 , 7*6^4*4^24*896 , 7*6^4*4^8*960 , 7*6^4*992 , 7*4^254 , 7*4^126*512 , 7*4^62*768 , 7*4^30*896 , 7*4^14*960 , 7*4^6*992 , 7*4^2*1008 , 7*1016, 7^146 , 7^144*6*4^2 , 7^136*6*4^16 , 7^130*6^16*4^4 , 7^130*6^8*4^16 , 7^130*4^28 , 7^128*6^21 , 7^128*6^17*4^6 , 7^128*6^9*4^18 , 7^128*6^5*4^24 , 7^128*6*4^30 , 7^72*6*4^128 , 7^72*6*512 , 7^66*6^8*4^128 , 7^66*6^8*512 , 7^66*4^140 , 7^66*4^12*512 , 7^64*6^9*4^2*512 , 7^64*6*4^142 , 7^64*6*4^14*512 , 7^34*4^196 , 7^34*4^68*512 , 7^34*4^4*768 , 7^32*6^133 , 7^32*6^129*4^6 , 7^32*6^5*4^192 , 7^32*6^5*768 , 7^32*6*4^198 , 7^32*6*4^70*512 , 7^32*6*4^6*768 , 7^18*6^64*4^128 , 7^18*6^64*512 , 7^18*4^224 , 7^18*4^96*512 , 7^18*4^32*768 , 7^18*896 , 7^16*6^129*4^34 , 7^16*6^65*4^130 , 7^16*6^65*4^2*512 , 7^16*6*4^226 , 7^16*6*4^98*512 , 7^16*6*4^34*768 , 7^16*6*4^2*896 , 7^8*6^161 , 7^8*6^129*4^48 , 7^8*6^65*4^16*512 , 7^8*6^33*4^192 , 7^8*6^33*4^64*512 , 7^8*6^33*768 , 7^8*6*4^240 , 7^8*6*4^112*512 , 7^8*6*4^48*768 , 7^8*6*4^16*896 , 7^8*6*960 , 7^2*6^168 , 7^2*6^160*4^12 , 7^2*6^144*4^36 , 7^2*6^136*4^48 , 7^2*6^128*4^60 , 7^2*6^80*4^132 , 7^2*6^80*4^4*512 , 7^2*6^72*4^144 , 7^2*6^72*4^16*512 , 7^2*6^64*4^156 , 7^2*6^64*4^28*512 , 7^2*6^40*4^192 , 7^2*6^40*4^64*512 , 7^2*6^40*768 , 7^2*6^32*4^204 , 7^2*6^32*4^76*512 , 7^2*6^32*4^12*768 , 7^2*6^16*4^100*512 , 7^2*6^16*4^36*768 , 7^2*6^16*4^4*896 , 7^2*6^8*4^240 , 7^2*6^8*4^112*512 , 7^2*6^8*4^48*768 , 7^2*6^8*4^16*896 , 7^2*6^8*960 , 7^2*4^252 , 7^2*4^124*512 , 7^2*4^60*768 , 7^2*4^28*896 , 7^2*4^12*960 , 7^2*4^4*992 , 7^2*1008 , 6^169*4^2 , 6^165*4^8 , 6^161*4^14 , 6^149*4^32 , 6^145*4^38 , 6^137*4^50 , 6^133*4^56 , 6^129*4^62 , 6^85*4^128 , 6^85*512 , 6^81*4^134 , 6^81*4^6*512 , 6^73*4^146 , 6^73*4^18*512 , 6^69*4^152 , 6^65*4^158 , 6^65*4^30*512 , 6^41*4^194 , 6^41*4^66*512 , 6^41*4^2*768 , 6^37*4^200 , 6^37*4^8*768 , 6^33*4^206 , 6^33*4^78*512 , 6^33*4^14*768 , 6^21*4^96*512 , 6^21*896 , 6^17*4^230 , 6^17*4^102*512 , 6^17*4^38*768 , 6^17*4^6*896 , 6^11*4^224 , 6^11*4^32*768 , 6^9*4^242 , 6^9*4^114*512 , 6^9*4^50*768 , 6^9*4^18*896 , 6^9*4^4*960 , 6^5*4^248 , 6^5*4^120*512 , 6^5*4^56*768 , 6^5*4^24*896 , 6^5*4^8*960 , 6^5*992 , 6*4^254 , 6*4^126*512 , 6*4^62*768 , 6*4^30*896 , 6*4^14*960 , 6*4^6*992 , 6*4^2*1008 , 6*1016, 7^144*6^2 , 7^144*4^3 , 7^136*4^17 , 7^132*6^16 , 7^132*4^24 , 7^128*6^20*4 , 7^128*6^18*4^4 , 7^128*6^16*4^7 , 7^128*6^10*4^16 , 7^128*6^8*4^19 , 7^128*6^4*4^25 , 7^128*6^2*4^28 , 7^128*4^31 , 7^72*4^129 , 7^72*4*512 , 7^68*4^136 , 7^68*4^8*512 , 7^64*6^10*4^128 , 7^64*6^10*512 , 7^64*6^8*4^3*512 , 7^64*6^2*4^140 , 7^64*6^2*4^12*512 , 7^64*4^143 , 7^64*4^15*512 , 7^36*6^128 , 7^36*4^192 , 7^36*4^64*512 , 7^36*768 , 7^32*6^132*4 , 7^32*6^128*4^7 , 7^32*6^4*4^193 , 7^32*6^4*4*768 , 7^32*6^2*4^196 , 7^32*6^2*4^68*512 , 7^32*6^2*4^4*768 , 7^32*4^199 , 7^32*4^71*512 , 7^32*4^7*768 , 7^16*6^128*4^35 , 7^16*6^66*4^128 , 7^16*6^66*512 , 7^16*6^64*4^131 , 7^16*6^64*4^3*512 , 7^16*6^2*4^224 , 7^16*6^2*4^96*512 , 7^16*6^2*4^32*768 , 7^16*6^2*896 , 7^16*4^227 , 7^16*4^99*512 , 7^16*4^35*768 , 7^16*4^3*896 , 7^8*6^160*4 , 7^8*6^128*4^49 , 7^8*6^64*4^17*512 , 7^8*6^32*4^193 , 7^8*6^32*4^65*512 , 7^8*6^32*4*768 , 7^8*4^241 , 7^8*4^113*512 , 7^8*4^49*768 , 7^8*4^17*896 , 7^8*4*960 , 7^4*6^160*4^8 , 7^4*6^144*4^32 , 7^4*6^128*4^56 , 7^4*6^80*4^128 , 7^4*6^80*512 , 7^4*6^64*4^152 , 7^4*6^64*4^24*512 , 7^4*6^32*4^200 , 7^4*6^32*4^72*512 , 7^4*6^32*4^8*768 , 7^4*6^16*4^224 , 7^4*6^16*4^96*512 , 7^4*6^16*4^32*768 , 7^4*6^16*896 , 7^4*4^248 , 7^4*4^120*512 , 7^4*4^56*768 , 7^4*4^24*896 , 7^4*4^8*960 , 7^4*992 , 6^170 , 6^168*4^3 , 6^164*4^9 , 6^162*4^12 , 6^160*4^15 , 6^148*4^33 , 6^146*4^36 , 6^144*4^39 , 6^138*4^48 , 6^136*4^51 , 6^132*4^57 , 6^130*4^60 , 6^128*4^63 , 6^84*4^129 , 6^84*4*512 , 6^82*4^132 , 6^82*4^4*512 , 6^80*4^135 , 6^80*4^7*512 , 6^74*4^144 , 6^74*4^16*512 , 6^72*4^147 , 6^72*4^19*512 , 6^68*4^153 , 6^66*4^156 , 6^66*4^28*512 , 6^64*4^159 , 6^64*4^31*512 , 6^42*4^192 , 6^42*4^64*512 , 6^42*768 , 6^40*4^195 , 6^40*4^67*512 , 6^40*4^3*768 , 6^36*4^201 , 6^36*4^9*768 , 6^34*4^204 , 6^34*4^76*512 , 6^34*4^12*768 , 6^32*4^207 , 6^32*4^79*512 , 6^32*4^15*768 , 6^20*4^97*512 , 6^20*4*896 , 6^18*4^100*512 , 6^18*4^36*768 , 6^18*4^4*896 , 6^16*4^231 , 6^16*4^103*512 , 6^16*4^39*768 , 6^16*4^7*896 , 6^10*4^240 , 6^10*4^225 , 6^10*4^112*512 , 6^10*4^48*768 , 6^10*4^33*768 , 6^10*4^16*896 , 6^10*960 , 6^8*4^243 , 6^8*4^115*512 , 6^8*4^51*768 , 6^8*4^19*896 , 6^8*4^5*960 , 6^4*4^249 , 6^4*4^121*512 , 6^4*4^57*768 , 6^4*4^25*896 , 6^4*4^9*960 , 6^4*4*992 , 6^2*4^252 , 6^2*4^124*512 , 6^2*4^60*768 , 6^2*4^28*896 , 6^2*4^12*960 , 6^2*4^4*992 , 6^2*1008 , 4^255 , 4^127*512 , 4^63*768 , 4^31*896 , 4^15*960 , 4^7*992 , 4^3*1008 , 4*1016 ] ; P; [IsHomogeneous(f): f in P]; P; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S; Output: Magma V2.10-22 Mon Apr 5 2004 05:21:23 on modular [Seed = 1834747969] ------------------------------------- >> R := PolynomialRing(K, [7, 6, 4, 1016, 1008, ^ User error: Identifier 'K' has not been declared or assigned >> R; ^ User error: Identifier 'R' has not been declared or assigned >> x^17*4^34*768 , 7^17*4^2*896 , 7^9*6^160 , 7^9*6^128*4^48 , 7^9*6^6 ^ User error: Identifier 'x' has not been declared or assigned >> P; ^ User error: Identifier 'P' has not been declared or assigned >> [IsHomogeneous(f): f in P]; ^ User error: Identifier 'P' has not been declared or assigned >> P; ^ User error: Identifier 'P' has not been declared or assigned >> I:=ideal; ^ User error: Identifier 'R' has not been declared or assigned >> Dimension(I); ^ User error: Identifier 'I' has not been declared or assigned >> V,phi:=VectorSpace(quo); ^ User error: Identifier 'R' has not been declared or assigned >> S:=[R!(v@@phi ): v in Basis(V)]; ^ User error: Identifier 'V' has not been declared or assigned >> S; ^ User error: Identifier 'S' has not been declared or assigned Total time: 2.599 seconds, Total memory usage: 2.11MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Mon Apr 5 05:24:00 2004 Input: K := GF(2, 50); R := PolynomialRing(K, [7, 6, 4, 1016, 1008, 992, 960, 896, 768, 512]); R; P := [ 7^145*4^2 , 7^137*4^16 , 7^129*6^20 , 7^129*6^16*4^6 , 7^129*6^8*4^18 , 7^129*6^4*4^24 , 7^129*4^30 , 7^73*4^128 , 7^73*512 , 7^65*6^8*4^2*512 , 7^65*4^142 , 7^65*4^14*512 , 7^33*6^132 , 7^33*6^128*4^6 , 7^33*6^4*4^192 , 7^33*6^4*768 , 7^33*4^198 , 7^33*4^70*512 , 7^33*4^6*768 , 7^17*6^128*4^34 , 7^17*6^64*4^130 , 7^17*6^64*4^2*512 , 7^17*4^226 , 7^17*4^98*512 , x^17*4^34*768 , 7^17*4^2*896 , 7^9*6^160 , 7^9*6^128*4^48 , 7^9*6^64*4^16*512 , 7^9*6^32*4^192 , 7^9*6^32*4^64*512 , 7^9*6^32*768 , 7^9*4^240 , 7^9*4^112*512 , 7^9*4^48*768 , 7^9*4^16*896 , 7^9*960 , 7*6^168*4^2 , 7*6^164*4^8 , 7*6^160*4^14 , 7*6^148*4^32 , 7*6^144*4^38 , 7*6^136*4^50 , 7*6^132*4^56 , 7*6^128*4^62 , 7*6^84*4^128 , 7*6^84*512 , 7*6^80*4^134 , 7*6^80*4^6*512 , 7*6^72*4^146 , 7*6^72*4^18*512 , 7*6^68*4^152 , 7*6^64*4^158 , 7*6^64*4^30*512 , 7*6^40*4^194 , 7*6^40*4^66*512 , 7*6^40*4^2*768 , 7*6^36*4^200 , 7*6^36*4^8*768 , 7*6^32*4^206 , 7*6^32*4^78*512 , 7*6^32*4^14*768 , 7*6^20*4^96*512 , 7*6^20*896 , 7*6^16*4^230 , 7*6^16*4^102*512 , 7*6^16*4^38*768 , 7*6^16*4^6*896 , 7*6^10*4^224 , 7*6^10*4^32*768 , 7*6^8*4^242 , 7*6^8*4^114*512 , 7*6^8*4^50*768 , 7*6^8*4^18*896 , 7*6^8*4^4*960 , 7*6^4*4^248 , 7*6^4*4^120*512 , 7*6^4*4^56*768 , 7*6^4*4^24*896 , 7*6^4*4^8*960 , 7*6^4*992 , 7*4^254 , 7*4^126*512 , 7*4^62*768 , 7*4^30*896 , 7*4^14*960 , 7*4^6*992 , 7*4^2*1008 , 7*1016, 7^146 , 7^144*6*4^2 , 7^136*6*4^16 , 7^130*6^16*4^4 , 7^130*6^8*4^16 , 7^130*4^28 , 7^128*6^21 , 7^128*6^17*4^6 , 7^128*6^9*4^18 , 7^128*6^5*4^24 , 7^128*6*4^30 , 7^72*6*4^128 , 7^72*6*512 , 7^66*6^8*4^128 , 7^66*6^8*512 , 7^66*4^140 , 7^66*4^12*512 , 7^64*6^9*4^2*512 , 7^64*6*4^142 , 7^64*6*4^14*512 , 7^34*4^196 , 7^34*4^68*512 , 7^34*4^4*768 , 7^32*6^133 , 7^32*6^129*4^6 , 7^32*6^5*4^192 , 7^32*6^5*768 , 7^32*6*4^198 , 7^32*6*4^70*512 , 7^32*6*4^6*768 , 7^18*6^64*4^128 , 7^18*6^64*512 , 7^18*4^224 , 7^18*4^96*512 , 7^18*4^32*768 , 7^18*896 , 7^16*6^129*4^34 , 7^16*6^65*4^130 , 7^16*6^65*4^2*512 , 7^16*6*4^226 , 7^16*6*4^98*512 , 7^16*6*4^34*768 , 7^16*6*4^2*896 , 7^8*6^161 , 7^8*6^129*4^48 , 7^8*6^65*4^16*512 , 7^8*6^33*4^192 , 7^8*6^33*4^64*512 , 7^8*6^33*768 , 7^8*6*4^240 , 7^8*6*4^112*512 , 7^8*6*4^48*768 , 7^8*6*4^16*896 , 7^8*6*960 , 7^2*6^168 , 7^2*6^160*4^12 , 7^2*6^144*4^36 , 7^2*6^136*4^48 , 7^2*6^128*4^60 , 7^2*6^80*4^132 , 7^2*6^80*4^4*512 , 7^2*6^72*4^144 , 7^2*6^72*4^16*512 , 7^2*6^64*4^156 , 7^2*6^64*4^28*512 , 7^2*6^40*4^192 , 7^2*6^40*4^64*512 , 7^2*6^40*768 , 7^2*6^32*4^204 , 7^2*6^32*4^76*512 , 7^2*6^32*4^12*768 , 7^2*6^16*4^100*512 , 7^2*6^16*4^36*768 , 7^2*6^16*4^4*896 , 7^2*6^8*4^240 , 7^2*6^8*4^112*512 , 7^2*6^8*4^48*768 , 7^2*6^8*4^16*896 , 7^2*6^8*960 , 7^2*4^252 , 7^2*4^124*512 , 7^2*4^60*768 , 7^2*4^28*896 , 7^2*4^12*960 , 7^2*4^4*992 , 7^2*1008 , 6^169*4^2 , 6^165*4^8 , 6^161*4^14 , 6^149*4^32 , 6^145*4^38 , 6^137*4^50 , 6^133*4^56 , 6^129*4^62 , 6^85*4^128 , 6^85*512 , 6^81*4^134 , 6^81*4^6*512 , 6^73*4^146 , 6^73*4^18*512 , 6^69*4^152 , 6^65*4^158 , 6^65*4^30*512 , 6^41*4^194 , 6^41*4^66*512 , 6^41*4^2*768 , 6^37*4^200 , 6^37*4^8*768 , 6^33*4^206 , 6^33*4^78*512 , 6^33*4^14*768 , 6^21*4^96*512 , 6^21*896 , 6^17*4^230 , 6^17*4^102*512 , 6^17*4^38*768 , 6^17*4^6*896 , 6^11*4^224 , 6^11*4^32*768 , 6^9*4^242 , 6^9*4^114*512 , 6^9*4^50*768 , 6^9*4^18*896 , 6^9*4^4*960 , 6^5*4^248 , 6^5*4^120*512 , 6^5*4^56*768 , 6^5*4^24*896 , 6^5*4^8*960 , 6^5*992 , 6*4^254 , 6*4^126*512 , 6*4^62*768 , 6*4^30*896 , 6*4^14*960 , 6*4^6*992 , 6*4^2*1008 , 6*1016, 7^144*6^2 , 7^144*4^3 , 7^136*4^17 , 7^132*6^16 , 7^132*4^24 , 7^128*6^20*4 , 7^128*6^18*4^4 , 7^128*6^16*4^7 , 7^128*6^10*4^16 , 7^128*6^8*4^19 , 7^128*6^4*4^25 , 7^128*6^2*4^28 , 7^128*4^31 , 7^72*4^129 , 7^72*4*512 , 7^68*4^136 , 7^68*4^8*512 , 7^64*6^10*4^128 , 7^64*6^10*512 , 7^64*6^8*4^3*512 , 7^64*6^2*4^140 , 7^64*6^2*4^12*512 , 7^64*4^143 , 7^64*4^15*512 , 7^36*6^128 , 7^36*4^192 , 7^36*4^64*512 , 7^36*768 , 7^32*6^132*4 , 7^32*6^128*4^7 , 7^32*6^4*4^193 , 7^32*6^4*4*768 , 7^32*6^2*4^196 , 7^32*6^2*4^68*512 , 7^32*6^2*4^4*768 , 7^32*4^199 , 7^32*4^71*512 , 7^32*4^7*768 , 7^16*6^128*4^35 , 7^16*6^66*4^128 , 7^16*6^66*512 , 7^16*6^64*4^131 , 7^16*6^64*4^3*512 , 7^16*6^2*4^224 , 7^16*6^2*4^96*512 , 7^16*6^2*4^32*768 , 7^16*6^2*896 , 7^16*4^227 , 7^16*4^99*512 , 7^16*4^35*768 , 7^16*4^3*896 , 7^8*6^160*4 , 7^8*6^128*4^49 , 7^8*6^64*4^17*512 , 7^8*6^32*4^193 , 7^8*6^32*4^65*512 , 7^8*6^32*4*768 , 7^8*4^241 , 7^8*4^113*512 , 7^8*4^49*768 , 7^8*4^17*896 , 7^8*4*960 , 7^4*6^160*4^8 , 7^4*6^144*4^32 , 7^4*6^128*4^56 , 7^4*6^80*4^128 , 7^4*6^80*512 , 7^4*6^64*4^152 , 7^4*6^64*4^24*512 , 7^4*6^32*4^200 , 7^4*6^32*4^72*512 , 7^4*6^32*4^8*768 , 7^4*6^16*4^224 , 7^4*6^16*4^96*512 , 7^4*6^16*4^32*768 , 7^4*6^16*896 , 7^4*4^248 , 7^4*4^120*512 , 7^4*4^56*768 , 7^4*4^24*896 , 7^4*4^8*960 , 7^4*992 , 6^170 , 6^168*4^3 , 6^164*4^9 , 6^162*4^12 , 6^160*4^15 , 6^148*4^33 , 6^146*4^36 , 6^144*4^39 , 6^138*4^48 , 6^136*4^51 , 6^132*4^57 , 6^130*4^60 , 6^128*4^63 , 6^84*4^129 , 6^84*4*512 , 6^82*4^132 , 6^82*4^4*512 , 6^80*4^135 , 6^80*4^7*512 , 6^74*4^144 , 6^74*4^16*512 , 6^72*4^147 , 6^72*4^19*512 , 6^68*4^153 , 6^66*4^156 , 6^66*4^28*512 , 6^64*4^159 , 6^64*4^31*512 , 6^42*4^192 , 6^42*4^64*512 , 6^42*768 , 6^40*4^195 , 6^40*4^67*512 , 6^40*4^3*768 , 6^36*4^201 , 6^36*4^9*768 , 6^34*4^204 , 6^34*4^76*512 , 6^34*4^12*768 , 6^32*4^207 , 6^32*4^79*512 , 6^32*4^15*768 , 6^20*4^97*512 , 6^20*4*896 , 6^18*4^100*512 , 6^18*4^36*768 , 6^18*4^4*896 , 6^16*4^231 , 6^16*4^103*512 , 6^16*4^39*768 , 6^16*4^7*896 , 6^10*4^240 , 6^10*4^225 , 6^10*4^112*512 , 6^10*4^48*768 , 6^10*4^33*768 , 6^10*4^16*896 , 6^10*960 , 6^8*4^243 , 6^8*4^115*512 , 6^8*4^51*768 , 6^8*4^19*896 , 6^8*4^5*960 , 6^4*4^249 , 6^4*4^121*512 , 6^4*4^57*768 , 6^4*4^25*896 , 6^4*4^9*960 , 6^4*4*992 , 6^2*4^252 , 6^2*4^124*512 , 6^2*4^60*768 , 6^2*4^28*896 , 6^2*4^12*960 , 6^2*4^4*992 , 6^2*1008 , 4^255 , 4^127*512 , 4^63*768 , 4^31*896 , 4^15*960 , 4^7*992 , 4^3*1008 , 4*1016 ] ; P; [IsHomogeneous(f): f in P]; P; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S; Output: Magma V2.10-22 Mon Apr 5 2004 05:23:58 on modular [Seed = 1666320114] ------------------------------------- Graded Polynomial ring of rank 10 over GF(2^50) Lexicographical Order Variables: x, y, z, a, b, c, d, e, f, g Variable weights: 7 6 4 1016 1008 992 960 896 768 512 [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] [ true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] -1 [] Total time: 2.649 seconds, Total memory usage: 2.56MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Mon Apr 5 05:24:31 2004 Input: K := GF(5, 50); R := PolynomialRing(K, [7, 6, 4, 1016, 1008, 992, 960, 896, 768, 512]); R; P := [ 7^145*4^2 , 7^137*4^16 , 7^129*6^20 , 7^129*6^16*4^6 , 7^129*6^8*4^18 , 7^129*6^4*4^24 , 7^129*4^30 , 7^73*4^128 , 7^73*512 , 7^65*6^8*4^2*512 , 7^65*4^142 , 7^65*4^14*512 , 7^33*6^132 , 7^33*6^128*4^6 , 7^33*6^4*4^192 , 7^33*6^4*768 , 7^33*4^198 , 7^33*4^70*512 , 7^33*4^6*768 , 7^17*6^128*4^34 , 7^17*6^64*4^130 , 7^17*6^64*4^2*512 , 7^17*4^226 , 7^17*4^98*512 , x^17*4^34*768 , 7^17*4^2*896 , 7^9*6^160 , 7^9*6^128*4^48 , 7^9*6^64*4^16*512 , 7^9*6^32*4^192 , 7^9*6^32*4^64*512 , 7^9*6^32*768 , 7^9*4^240 , 7^9*4^112*512 , 7^9*4^48*768 , 7^9*4^16*896 , 7^9*960 , 7*6^168*4^2 , 7*6^164*4^8 , 7*6^160*4^14 , 7*6^148*4^32 , 7*6^144*4^38 , 7*6^136*4^50 , 7*6^132*4^56 , 7*6^128*4^62 , 7*6^84*4^128 , 7*6^84*512 , 7*6^80*4^134 , 7*6^80*4^6*512 , 7*6^72*4^146 , 7*6^72*4^18*512 , 7*6^68*4^152 , 7*6^64*4^158 , 7*6^64*4^30*512 , 7*6^40*4^194 , 7*6^40*4^66*512 , 7*6^40*4^2*768 , 7*6^36*4^200 , 7*6^36*4^8*768 , 7*6^32*4^206 , 7*6^32*4^78*512 , 7*6^32*4^14*768 , 7*6^20*4^96*512 , 7*6^20*896 , 7*6^16*4^230 , 7*6^16*4^102*512 , 7*6^16*4^38*768 , 7*6^16*4^6*896 , 7*6^10*4^224 , 7*6^10*4^32*768 , 7*6^8*4^242 , 7*6^8*4^114*512 , 7*6^8*4^50*768 , 7*6^8*4^18*896 , 7*6^8*4^4*960 , 7*6^4*4^248 , 7*6^4*4^120*512 , 7*6^4*4^56*768 , 7*6^4*4^24*896 , 7*6^4*4^8*960 , 7*6^4*992 , 7*4^254 , 7*4^126*512 , 7*4^62*768 , 7*4^30*896 , 7*4^14*960 , 7*4^6*992 , 7*4^2*1008 , 7*1016, 7^146 , 7^144*6*4^2 , 7^136*6*4^16 , 7^130*6^16*4^4 , 7^130*6^8*4^16 , 7^130*4^28 , 7^128*6^21 , 7^128*6^17*4^6 , 7^128*6^9*4^18 , 7^128*6^5*4^24 , 7^128*6*4^30 , 7^72*6*4^128 , 7^72*6*512 , 7^66*6^8*4^128 , 7^66*6^8*512 , 7^66*4^140 , 7^66*4^12*512 , 7^64*6^9*4^2*512 , 7^64*6*4^142 , 7^64*6*4^14*512 , 7^34*4^196 , 7^34*4^68*512 , 7^34*4^4*768 , 7^32*6^133 , 7^32*6^129*4^6 , 7^32*6^5*4^192 , 7^32*6^5*768 , 7^32*6*4^198 , 7^32*6*4^70*512 , 7^32*6*4^6*768 , 7^18*6^64*4^128 , 7^18*6^64*512 , 7^18*4^224 , 7^18*4^96*512 , 7^18*4^32*768 , 7^18*896 , 7^16*6^129*4^34 , 7^16*6^65*4^130 , 7^16*6^65*4^2*512 , 7^16*6*4^226 , 7^16*6*4^98*512 , 7^16*6*4^34*768 , 7^16*6*4^2*896 , 7^8*6^161 , 7^8*6^129*4^48 , 7^8*6^65*4^16*512 , 7^8*6^33*4^192 , 7^8*6^33*4^64*512 , 7^8*6^33*768 , 7^8*6*4^240 , 7^8*6*4^112*512 , 7^8*6*4^48*768 , 7^8*6*4^16*896 , 7^8*6*960 , 7^2*6^168 , 7^2*6^160*4^12 , 7^2*6^144*4^36 , 7^2*6^136*4^48 , 7^2*6^128*4^60 , 7^2*6^80*4^132 , 7^2*6^80*4^4*512 , 7^2*6^72*4^144 , 7^2*6^72*4^16*512 , 7^2*6^64*4^156 , 7^2*6^64*4^28*512 , 7^2*6^40*4^192 , 7^2*6^40*4^64*512 , 7^2*6^40*768 , 7^2*6^32*4^204 , 7^2*6^32*4^76*512 , 7^2*6^32*4^12*768 , 7^2*6^16*4^100*512 , 7^2*6^16*4^36*768 , 7^2*6^16*4^4*896 , 7^2*6^8*4^240 , 7^2*6^8*4^112*512 , 7^2*6^8*4^48*768 , 7^2*6^8*4^16*896 , 7^2*6^8*960 , 7^2*4^252 , 7^2*4^124*512 , 7^2*4^60*768 , 7^2*4^28*896 , 7^2*4^12*960 , 7^2*4^4*992 , 7^2*1008 , 6^169*4^2 , 6^165*4^8 , 6^161*4^14 , 6^149*4^32 , 6^145*4^38 , 6^137*4^50 , 6^133*4^56 , 6^129*4^62 , 6^85*4^128 , 6^85*512 , 6^81*4^134 , 6^81*4^6*512 , 6^73*4^146 , 6^73*4^18*512 , 6^69*4^152 , 6^65*4^158 , 6^65*4^30*512 , 6^41*4^194 , 6^41*4^66*512 , 6^41*4^2*768 , 6^37*4^200 , 6^37*4^8*768 , 6^33*4^206 , 6^33*4^78*512 , 6^33*4^14*768 , 6^21*4^96*512 , 6^21*896 , 6^17*4^230 , 6^17*4^102*512 , 6^17*4^38*768 , 6^17*4^6*896 , 6^11*4^224 , 6^11*4^32*768 , 6^9*4^242 , 6^9*4^114*512 , 6^9*4^50*768 , 6^9*4^18*896 , 6^9*4^4*960 , 6^5*4^248 , 6^5*4^120*512 , 6^5*4^56*768 , 6^5*4^24*896 , 6^5*4^8*960 , 6^5*992 , 6*4^254 , 6*4^126*512 , 6*4^62*768 , 6*4^30*896 , 6*4^14*960 , 6*4^6*992 , 6*4^2*1008 , 6*1016, 7^144*6^2 , 7^144*4^3 , 7^136*4^17 , 7^132*6^16 , 7^132*4^24 , 7^128*6^20*4 , 7^128*6^18*4^4 , 7^128*6^16*4^7 , 7^128*6^10*4^16 , 7^128*6^8*4^19 , 7^128*6^4*4^25 , 7^128*6^2*4^28 , 7^128*4^31 , 7^72*4^129 , 7^72*4*512 , 7^68*4^136 , 7^68*4^8*512 , 7^64*6^10*4^128 , 7^64*6^10*512 , 7^64*6^8*4^3*512 , 7^64*6^2*4^140 , 7^64*6^2*4^12*512 , 7^64*4^143 , 7^64*4^15*512 , 7^36*6^128 , 7^36*4^192 , 7^36*4^64*512 , 7^36*768 , 7^32*6^132*4 , 7^32*6^128*4^7 , 7^32*6^4*4^193 , 7^32*6^4*4*768 , 7^32*6^2*4^196 , 7^32*6^2*4^68*512 , 7^32*6^2*4^4*768 , 7^32*4^199 , 7^32*4^71*512 , 7^32*4^7*768 , 7^16*6^128*4^35 , 7^16*6^66*4^128 , 7^16*6^66*512 , 7^16*6^64*4^131 , 7^16*6^64*4^3*512 , 7^16*6^2*4^224 , 7^16*6^2*4^96*512 , 7^16*6^2*4^32*768 , 7^16*6^2*896 , 7^16*4^227 , 7^16*4^99*512 , 7^16*4^35*768 , 7^16*4^3*896 , 7^8*6^160*4 , 7^8*6^128*4^49 , 7^8*6^64*4^17*512 , 7^8*6^32*4^193 , 7^8*6^32*4^65*512 , 7^8*6^32*4*768 , 7^8*4^241 , 7^8*4^113*512 , 7^8*4^49*768 , 7^8*4^17*896 , 7^8*4*960 , 7^4*6^160*4^8 , 7^4*6^144*4^32 , 7^4*6^128*4^56 , 7^4*6^80*4^128 , 7^4*6^80*512 , 7^4*6^64*4^152 , 7^4*6^64*4^24*512 , 7^4*6^32*4^200 , 7^4*6^32*4^72*512 , 7^4*6^32*4^8*768 , 7^4*6^16*4^224 , 7^4*6^16*4^96*512 , 7^4*6^16*4^32*768 , 7^4*6^16*896 , 7^4*4^248 , 7^4*4^120*512 , 7^4*4^56*768 , 7^4*4^24*896 , 7^4*4^8*960 , 7^4*992 , 6^170 , 6^168*4^3 , 6^164*4^9 , 6^162*4^12 , 6^160*4^15 , 6^148*4^33 , 6^146*4^36 , 6^144*4^39 , 6^138*4^48 , 6^136*4^51 , 6^132*4^57 , 6^130*4^60 , 6^128*4^63 , 6^84*4^129 , 6^84*4*512 , 6^82*4^132 , 6^82*4^4*512 , 6^80*4^135 , 6^80*4^7*512 , 6^74*4^144 , 6^74*4^16*512 , 6^72*4^147 , 6^72*4^19*512 , 6^68*4^153 , 6^66*4^156 , 6^66*4^28*512 , 6^64*4^159 , 6^64*4^31*512 , 6^42*4^192 , 6^42*4^64*512 , 6^42*768 , 6^40*4^195 , 6^40*4^67*512 , 6^40*4^3*768 , 6^36*4^201 , 6^36*4^9*768 , 6^34*4^204 , 6^34*4^76*512 , 6^34*4^12*768 , 6^32*4^207 , 6^32*4^79*512 , 6^32*4^15*768 , 6^20*4^97*512 , 6^20*4*896 , 6^18*4^100*512 , 6^18*4^36*768 , 6^18*4^4*896 , 6^16*4^231 , 6^16*4^103*512 , 6^16*4^39*768 , 6^16*4^7*896 , 6^10*4^240 , 6^10*4^225 , 6^10*4^112*512 , 6^10*4^48*768 , 6^10*4^33*768 , 6^10*4^16*896 , 6^10*960 , 6^8*4^243 , 6^8*4^115*512 , 6^8*4^51*768 , 6^8*4^19*896 , 6^8*4^5*960 , 6^4*4^249 , 6^4*4^121*512 , 6^4*4^57*768 , 6^4*4^25*896 , 6^4*4^9*960 , 6^4*4*992 , 6^2*4^252 , 6^2*4^124*512 , 6^2*4^60*768 , 6^2*4^28*896 , 6^2*4^12*960 , 6^2*4^4*992 , 6^2*1008 , 4^255 , 4^127*512 , 4^63*768 , 4^31*896 , 4^15*960 , 4^7*992 , 4^3*1008 , 4*1016 ] ; P; [IsHomogeneous(f): f in P]; P; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S; Output: Magma V2.10-22 Mon Apr 5 2004 05:24:28 on modular [Seed = 1516978089] ------------------------------------- Graded Polynomial ring of rank 10 over GF(5^50) Lexicographical Order Variables: x, y, z, a, b, c, d, e, f, g Variable weights: 7 6 4 1016 1008 992 960 896 768 512 [ 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 2, 4, 2, 2, 2, 1, 2, 4, 1, 2, 2, 4, 2, 4, 3*x^17, 2, 2, 2, 4, 2, 4, 1, 2, 4, 1, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 4, 2, 4, 2, 2, 4, 2, 4, 1, 2, 1, 2, 4, 1, 4, 2, 2, 4, 1, 2, 2, 1, 2, 4, 1, 2, 0, 2, 4, 1, 2, 0, 4, 2, 4, 1, 2, 0, 4, 1, 2, 4, 1, 1, 4, 4, 4, 1, 1, 1, 1, 1, 1, 2, 4, 3, 4, 3, 2, 1, 2, 4, 3, 2, 1, 1, 1, 3, 1, 2, 3, 4, 3, 4, 3, 2, 4, 1, 1, 2, 1, 2, 3, 1, 1, 1, 2, 1, 2, 3, 1, 2, 3, 1, 0, 4, 4, 4, 4, 4, 4, 3, 4, 3, 4, 3, 4, 3, 2, 4, 3, 2, 3, 2, 4, 4, 3, 2, 4, 0, 4, 3, 2, 4, 0, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 3, 1, 3, 1, 2, 3, 2, 1, 1, 2, 3, 1, 1, 3, 1, 2, 3, 1, 0, 1, 2, 3, 1, 0, 2, 1, 2, 3, 1, 0, 2, 3, 1, 1, 4, 4, 1, 1, 4, 1, 4, 1, 4, 4, 1, 4, 4, 3, 1, 2, 1, 2, 3, 1, 2, 4, 3, 1, 1, 2, 3, 4, 4, 4, 2, 1, 2, 3, 4, 3, 2, 4, 1, 2, 4, 3, 1, 2, 3, 1, 4, 3, 2, 4, 4, 4, 3, 4, 3, 2, 4, 3, 2, 4, 0, 1, 1, 1, 1, 2, 1, 2, 1, 2, 3, 1, 2, 3, 1, 1, 2, 3, 1, 0, 2, 1, 4, 4, 1, 4, 4, 1, 4, 1, 4, 4, 1, 4, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 4, 1, 2, 4, 3, 1, 2, 3, 4, 3, 2, 4, 2, 1, 2, 3, 4, 3, 2, 3, 4, 2, 3, 1, 4, 3, 2, 4, 1, 4, 2, 3, 2, 1, 0, 4, 3, 2, 4, 0, 4, 3, 2, 4, 0, 3, 1, 2, 3, 1, 0, 2, 3, 4, 3, 2, 4, 0, 3, 2, 4 ] [ true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true ] [ 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 2, 4, 2, 2, 2, 1, 2, 4, 1, 2, 2, 4, 2, 4, 3*x^17, 2, 2, 2, 4, 2, 4, 1, 2, 4, 1, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 4, 2, 4, 2, 2, 4, 2, 4, 1, 2, 1, 2, 4, 1, 4, 2, 2, 4, 1, 2, 2, 1, 2, 4, 1, 2, 0, 2, 4, 1, 2, 0, 4, 2, 4, 1, 2, 0, 4, 1, 2, 4, 1, 1, 4, 4, 4, 1, 1, 1, 1, 1, 1, 2, 4, 3, 4, 3, 2, 1, 2, 4, 3, 2, 1, 1, 1, 3, 1, 2, 3, 4, 3, 4, 3, 2, 4, 1, 1, 2, 1, 2, 3, 1, 1, 1, 2, 1, 2, 3, 1, 2, 3, 1, 0, 4, 4, 4, 4, 4, 4, 3, 4, 3, 4, 3, 4, 3, 2, 4, 3, 2, 3, 2, 4, 4, 3, 2, 4, 0, 4, 3, 2, 4, 0, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 3, 1, 3, 1, 2, 3, 2, 1, 1, 2, 3, 1, 1, 3, 1, 2, 3, 1, 0, 1, 2, 3, 1, 0, 2, 1, 2, 3, 1, 0, 2, 3, 1, 1, 4, 4, 1, 1, 4, 1, 4, 1, 4, 4, 1, 4, 4, 3, 1, 2, 1, 2, 3, 1, 2, 4, 3, 1, 1, 2, 3, 4, 4, 4, 2, 1, 2, 3, 4, 3, 2, 4, 1, 2, 4, 3, 1, 2, 3, 1, 4, 3, 2, 4, 4, 4, 3, 4, 3, 2, 4, 3, 2, 4, 0, 1, 1, 1, 1, 2, 1, 2, 1, 2, 3, 1, 2, 3, 1, 1, 2, 3, 1, 0, 2, 1, 4, 4, 1, 4, 4, 1, 4, 1, 4, 4, 1, 4, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 4, 1, 2, 4, 3, 1, 2, 3, 4, 3, 2, 4, 2, 1, 2, 3, 4, 3, 2, 3, 4, 2, 3, 1, 4, 3, 2, 4, 1, 4, 2, 3, 2, 1, 0, 4, 3, 2, 4, 0, 4, 3, 2, 4, 0, 3, 1, 2, 3, 1, 0, 2, 3, 4, 3, 2, 4, 0, 3, 2, 4 ] -1 [] Total time: 2.699 seconds, Total memory usage: 2.63MB ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Mon Apr 5 05:27:10 2004 Input: K := (RationalField()); ; R := PolynomialRing(K, [7, 6, 4, 1016, 1008, 992, 960, 896, 768, 512]); R; P := [ 7^145*4^2 , 7^137*4^16 , 7^129*6^20 , 7^129*6^16*4^6 , 7^129*6^8*4^18 , 7^129*6^4*4^24 , 7^129*4^30 , 7^73*4^128 , 7^73*512 , 7^65*6^8*4^2*512 , 7^65*4^142 , 7^65*4^14*512 , 7^33*6^132 , 7^33*6^128*4^6 , 7^33*6^4*4^192 , 7^33*6^4*768 , 7^33*4^198 , 7^33*4^70*512 , 7^33*4^6*768 , 7^17*6^128*4^34 , 7^17*6^64*4^130 , 7^17*6^64*4^2*512 , 7^17*4^226 , 7^17*4^98*512 , x^17*4^34*768 , 7^17*4^2*896 , 7^9*6^160 , 7^9*6^128*4^48 , 7^9*6^64*4^16*512 , 7^9*6^32*4^192 , 7^9*6^32*4^64*512 , 7^9*6^32*768 , 7^9*4^240 , 7^9*4^112*512 , 7^9*4^48*768 , 7^9*4^16*896 , 7^9*960 , 7*6^168*4^2 , 7*6^164*4^8 , 7*6^160*4^14 , 7*6^148*4^32 , 7*6^144*4^38 , 7*6^136*4^50 , 7*6^132*4^56 , 7*6^128*4^62 , 7*6^84*4^128 , 7*6^84*512 , 7*6^80*4^134 , 7*6^80*4^6*512 , 7*6^72*4^146 , 7*6^72*4^18*512 , 7*6^68*4^152 , 7*6^64*4^158 , 7*6^64*4^30*512 , 7*6^40*4^194 , 7*6^40*4^66*512 , 7*6^40*4^2*768 , 7*6^36*4^200 , 7*6^36*4^8*768 , 7*6^32*4^206 , 7*6^32*4^78*512 , 7*6^32*4^14*768 , 7*6^20*4^96*512 , 7*6^20*896 , 7*6^16*4^230 , 7*6^16*4^102*512 , 7*6^16*4^38*768 , 7*6^16*4^6*896 , 7*6^10*4^224 , 7*6^10*4^32*768 , 7*6^8*4^242 , 7*6^8*4^114*512 , 7*6^8*4^50*768 , 7*6^8*4^18*896 , 7*6^8*4^4*960 , 7*6^4*4^248 , 7*6^4*4^120*512 , 7*6^4*4^56*768 , 7*6^4*4^24*896 , 7*6^4*4^8*960 , 7*6^4*992 , 7*4^254 , 7*4^126*512 , 7*4^62*768 , 7*4^30*896 , 7*4^14*960 , 7*4^6*992 , 7*4^2*1008 , 7*1016, 7^146 , 7^144*6*4^2 , 7^136*6*4^16 , 7^130*6^16*4^4 , 7^130*6^8*4^16 , 7^130*4^28 , 7^128*6^21 , 7^128*6^17*4^6 , 7^128*6^9*4^18 , 7^128*6^5*4^24 , 7^128*6*4^30 , 7^72*6*4^128 , 7^72*6*512 , 7^66*6^8*4^128 , 7^66*6^8*512 , 7^66*4^140 , 7^66*4^12*512 , 7^64*6^9*4^2*512 , 7^64*6*4^142 , 7^64*6*4^14*512 , 7^34*4^196 , 7^34*4^68*512 , 7^34*4^4*768 , 7^32*6^133 , 7^32*6^129*4^6 , 7^32*6^5*4^192 , 7^32*6^5*768 , 7^32*6*4^198 , 7^32*6*4^70*512 , 7^32*6*4^6*768 , 7^18*6^64*4^128 , 7^18*6^64*512 , 7^18*4^224 , 7^18*4^96*512 , 7^18*4^32*768 , 7^18*896 , 7^16*6^129*4^34 , 7^16*6^65*4^130 , 7^16*6^65*4^2*512 , 7^16*6*4^226 , 7^16*6*4^98*512 , 7^16*6*4^34*768 , 7^16*6*4^2*896 , 7^8*6^161 , 7^8*6^129*4^48 , 7^8*6^65*4^16*512 , 7^8*6^33*4^192 , 7^8*6^33*4^64*512 , 7^8*6^33*768 , 7^8*6*4^240 , 7^8*6*4^112*512 , 7^8*6*4^48*768 , 7^8*6*4^16*896 , 7^8*6*960 , 7^2*6^168 , 7^2*6^160*4^12 , 7^2*6^144*4^36 , 7^2*6^136*4^48 , 7^2*6^128*4^60 , 7^2*6^80*4^132 , 7^2*6^80*4^4*512 , 7^2*6^72*4^144 , 7^2*6^72*4^16*512 , 7^2*6^64*4^156 , 7^2*6^64*4^28*512 , 7^2*6^40*4^192 , 7^2*6^40*4^64*512 , 7^2*6^40*768 , 7^2*6^32*4^204 , 7^2*6^32*4^76*512 , 7^2*6^32*4^12*768 , 7^2*6^16*4^100*512 , 7^2*6^16*4^36*768 , 7^2*6^16*4^4*896 , 7^2*6^8*4^240 , 7^2*6^8*4^112*512 , 7^2*6^8*4^48*768 , 7^2*6^8*4^16*896 , 7^2*6^8*960 , 7^2*4^252 , 7^2*4^124*512 , 7^2*4^60*768 , 7^2*4^28*896 , 7^2*4^12*960 , 7^2*4^4*992 , 7^2*1008 , 6^169*4^2 , 6^165*4^8 , 6^161*4^14 , 6^149*4^32 , 6^145*4^38 , 6^137*4^50 , 6^133*4^56 , 6^129*4^62 , 6^85*4^128 , 6^85*512 , 6^81*4^134 , 6^81*4^6*512 , 6^73*4^146 , 6^73*4^18*512 , 6^69*4^152 , 6^65*4^158 , 6^65*4^30*512 , 6^41*4^194 , 6^41*4^66*512 , 6^41*4^2*768 , 6^37*4^200 , 6^37*4^8*768 , 6^33*4^206 , 6^33*4^78*512 , 6^33*4^14*768 , 6^21*4^96*512 , 6^21*896 , 6^17*4^230 , 6^17*4^102*512 , 6^17*4^38*768 , 6^17*4^6*896 , 6^11*4^224 , 6^11*4^32*768 , 6^9*4^242 , 6^9*4^114*512 , 6^9*4^50*768 , 6^9*4^18*896 , 6^9*4^4*960 , 6^5*4^248 , 6^5*4^120*512 , 6^5*4^56*768 , 6^5*4^24*896 , 6^5*4^8*960 , 6^5*992 , 6*4^254 , 6*4^126*512 , 6*4^62*768 , 6*4^30*896 , 6*4^14*960 , 6*4^6*992 , 6*4^2*1008 , 6*1016, 7^144*6^2 , 7^144*4^3 , 7^136*4^17 , 7^132*6^16 , 7^132*4^24 , 7^128*6^20*4 , 7^128*6^18*4^4 , 7^128*6^16*4^7 , 7^128*6^10*4^16 , 7^128*6^8*4^19 , 7^128*6^4*4^25 , 7^128*6^2*4^28 , 7^128*4^31 , 7^72*4^129 , 7^72*4*512 , 7^68*4^136 , 7^68*4^8*512 , 7^64*6^10*4^128 , 7^64*6^10*512 , 7^64*6^8*4^3*512 , 7^64*6^2*4^140 , 7^64*6^2*4^12*512 , 7^64*4^143 , 7^64*4^15*512 , 7^36*6^128 , 7^36*4^192 , 7^36*4^64*512 , 7^36*768 , 7^32*6^132*4 , 7^32*6^128*4^7 , 7^32*6^4*4^193 , 7^32*6^4*4*768 , 7^32*6^2*4^196 , 7^32*6^2*4^68*512 , 7^32*6^2*4^4*768 , 7^32*4^199 , 7^32*4^71*512 , 7^32*4^7*768 , 7^16*6^128*4^35 , 7^16*6^66*4^128 , 7^16*6^66*512 , 7^16*6^64*4^131 , 7^16*6^64*4^3*512 , 7^16*6^2*4^224 , 7^16*6^2*4^96*512 , 7^16*6^2*4^32*768 , 7^16*6^2*896 , 7^16*4^227 , 7^16*4^99*512 , 7^16*4^35*768 , 7^16*4^3*896 , 7^8*6^160*4 , 7^8*6^128*4^49 , 7^8*6^64*4^17*512 , 7^8*6^32*4^193 , 7^8*6^32*4^65*512 , 7^8*6^32*4*768 , 7^8*4^241 , 7^8*4^113*512 , 7^8*4^49*768 , 7^8*4^17*896 , 7^8*4*960 , 7^4*6^160*4^8 , 7^4*6^144*4^32 , 7^4*6^128*4^56 , 7^4*6^80*4^128 , 7^4*6^80*512 , 7^4*6^64*4^152 , 7^4*6^64*4^24*512 , 7^4*6^32*4^200 , 7^4*6^32*4^72*512 , 7^4*6^32*4^8*768 , 7^4*6^16*4^224 , 7^4*6^16*4^96*512 , 7^4*6^16*4^32*768 , 7^4*6^16*896 , 7^4*4^248 , 7^4*4^120*512 , 7^4*4^56*768 , 7^4*4^24*896 , 7^4*4^8*960 , 7^4*992 , 6^170 , 6^168*4^3 , 6^164*4^9 , 6^162*4^12 , 6^160*4^15 , 6^148*4^33 , 6^146*4^36 , 6^144*4^39 , 6^138*4^48 , 6^136*4^51 , 6^132*4^57 , 6^130*4^60 , 6^128*4^63 , 6^84*4^129 , 6^84*4*512 , 6^82*4^132 , 6^82*4^4*512 , 6^80*4^135 , 6^80*4^7*512 , 6^74*4^144 , 6^74*4^16*512 , 6^72*4^147 , 6^72*4^19*512 , 6^68*4^153 , 6^66*4^156 , 6^66*4^28*512 , 6^64*4^159 , 6^64*4^31*512 , 6^42*4^192 , 6^42*4^64*512 , 6^42*768 , 6^40*4^195 , 6^40*4^67*512 , 6^40*4^3*768 , 6^36*4^201 , 6^36*4^9*768 , 6^34*4^204 , 6^34*4^76*512 , 6^34*4^12*768 , 6^32*4^207 , 6^32*4^79*512 , 6^32*4^15*768 , 6^20*4^97*512 , 6^20*4*896 , 6^18*4^100*512 , 6^18*4^36*768 , 6^18*4^4*896 , 6^16*4^231 , 6^16*4^103*512 , 6^16*4^39*768 , 6^16*4^7*896 , 6^10*4^240 , 6^10*4^225 , 6^10*4^112*512 , 6^10*4^48*768 , 6^10*4^33*768 , 6^10*4^16*896 , 6^10*960 , 6^8*4^243 , 6^8*4^115*512 , 6^8*4^51*768 , 6^8*4^19*896 , 6^8*4^5*960 , 6^4*4^249 , 6^4*4^121*512 , 6^4*4^57*768 , 6^4*4^25*896 , 6^4*4^9*960 , 6^4*4*992 , 6^2*4^252 , 6^2*4^124*512 , 6^2*4^60*768 , 6^2*4^28*896 , 6^2*4^12*960 , 6^2*4^4*992 , 6^2*1008 , 4^255 , 4^127*512 , 4^63*768 , 4^31*896 , 4^15*960 , 4^7*992 , 4^3*1008 , 4*1016 ] ; P; [IsHomogeneous(f): f in P]; P; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S; Output: Magma V2.10-22 Mon Apr 5 2004 05:27:08 on modular [Seed = 1316956189] ------------------------------------- >> K := (RationalField()); ^ Runtime error in 'Name': Bad argument types Graded Polynomial ring of rank 10 over Rational Field Lexicographical Order Variables: x, y, z, a, b, c, d, e, f, g Variable weights: 7 6 4 1016 1008 992 960 896 768 512 [ 553778109961263108507885905005456408869624289852498652478378504918917770836\ 8519779203036551812183740457502339379278755276912, 257864372890356154303143911656468928594482343441224854973170911031461337244\ 935015618992994445145837423615366617571612554166272, 380778281503151491963018399198432737837544264261702302465585063809526841915\ 84751150869937249674173458683993374272455607058432, 120344740820749113509299642215800964057297940309871344976777501648443051272\ 169090057070418961933190190408670417453686856876032, 120209006773793840922808433962120591075431760648494565834447345649022463163\ 7383552199385303625857880249751962273776074051551232, 379919823877669423163443939435837917472969515135982825353315067730243834196\ 5064066210402934916291572147364226445514505644408832, 120073425818127620160298331476017909719852093672606917642529206591286940190\ 50079024072384584426798055181793110741379178332946432, 569948757231575212015999448718318746333057130324182287201638896697569130530\ 5819599745471996873521042701156860951927209360368632434578685952, 25201528500318654955500469857453146934705429822751437238918352384, 117482329033987380897936639075925846784670472315475876470277013504, 265394164593177092558462107039688808382566056751348919229119793003000213963\ 153785136974070642850324828746129085316071538888857078617721536512, 1173498234350159578498273979344593247200146940049844084797450747904, 401976228461706718713941919868722703569257817805922718452950057084545624504\ 18336401740937089081724576856264519294585062135747837952, 127044338871848049371319915415300014955222223899155822128339771127955160337\ 124618751181233269196561625619798974560663900083351191552, 394783194532866594457038361637185107104520454738045914540252414945601941424\ 24341007340464522225124884580474724493656637089890325969888309910123315\ 2, 7694874517048971343320325901930496, 124770984938782528618520766147060972121922514090049079163339034847005058030\ 37816417134764095913125889447656209222686542092607312899125194243199467\ 52, 5517021474388358259559864819405945158134307703164580287700031874724265984, 24319603411907860048024733714743296, 275465005292624870738146523044200261028285218773995842334641267202385380393\ 099404121869230432869589285600111304057852997614355687145472, 272989270156149540604790328139848738370686692629791802143162635592401161000\ 56428366877961761622271134404753327134592757250297330421241397379072, 120708165160996913756322665579785467547315133943406155244971359207424, 270535785629908593744827585329001999658731208800582495547989103641877427718\ 87348924331154265060947683054673014237275464733543839895385019932530672\ 92672, 119623303418101151526439362404746175531199131418228274794308216014481118986\ 24, 226673591177742970257408*x^17, 3334991048520599552, 128849406217056419256800915159217449780344646085011288542451429071912528213\ 8357746176797499515657232306253490109385277139505834360832, 128269083889917744972524495655937482012729965179469915577664403607149949969\ 74760759093374852595332534186831446836677349278071607506501632, 5620723309948690329253541903362356543311163656091391442027344658694144, 126543752088758925839878158672801474038091726868711604585315511872709120496\ 42748587355310862882901545330892790742591091381628895508163806803664044\ 032, 55954082438789467216636873562774665817782724438254010983475709039549087744, 246651404295905934607261147632500736, 125973814152271276320226041643362124387820770250032178488108132300037118377\ 23946566644612520272565105183899016648931214752010969950755750495390839\ 0264832, 557020719384144244773147352414546420474418476354275432170224647310353675321\ 344, 2455405158476355819544472301378402779136, 155292410417210458112, 38739462720, 600659136085127475342669211765857454244164481871890656184712983479011838884\ 7351044249368979630665864503701722348619525004795777646592, 189837949182460041589781874335875936156180379455807417263316696013119791054\ 92862559602943935622845201394415320015390103718860729352192, 599981666551972477123261232468941230320767619020823442214926841720477364321\ 74973027880909228635165080950250887949874895704053663137792, 189409963020964085848702157371328902218633256186821554752142684658170151801\ 1724485470507613084435618928083915996934463652981949796974592, 598629018930454394781083361568644431703334735602794049587018855215945171124\ 6931707166048752464389116612215833274262008582263940099080192, 597953839119436964127009284922461232679618125780593062547399294245270274879\ 25455930625540472718519302895622138311543209030216366153531392, 188982941746389954094462193753271698229607703950409659274239776946653321443\ 319959484446152605135073352361472437132778537181918391793876992, 597279420828096645039287920997994503046661385324751515730930653065966052956\ 665550963187840332278750348204159801308534636031742077768302592, 187707645515510522645917592615599134915318153277808673124197190051974564586\ 600694687197219116004573492310752368551212443589361789109815520264192, 829990331264955759979087582192527209229828368727311879051409006526464, 593248854962601157992035848266584920226190706655790374318450378435870228816\ 910837529907260416014454494216698843816177599492303926075466335649792, 2623179318565786105612918778287493402010321757952985691816798835441664, 592579743313961735865966489132737529826911052452276756155067276347709058310\ 3958032062185980585874605964484922333232283975053746395257089128660992, 26202206953441145895053840124043464044223204805548981908078909995352064, 187284462084412598002083236071581243994678061021954135278638546598782122132\ 66830323554563099135603692924791853300092156760663692310935985394286592\ , 591911386340859568994238375732404919291822020020003192979400838633187941555\ 09982257160100658996475868996873017837328297910245743599995213097992192\ , 261726540908507687452865183107653171711966460926148160086550746144702464, 589910834967764991668500732933889292949993518017549359839950898675162461654\ 38161175171535836944040391229443168958395277941551839053150484891583905\ 792, 260841953446815762815857849111567481624294607193087702869942012608369393664\ , 1149818410253182629579226175521161216, 186440955249071404774242206951945258018763383472213131011144975383755049609\ 28604025733226141058857210067577100312776779201280581231612992755858617\ 1392, 3633993987960675965089900011523670016, 589245488194596044718592654070345506824733656406006932578433502447423366666\ 38550994909949285321820318238268366420627845376886775250529952413577851\ 6992, 260547755846525191768024081685348063949546888843258583985436972082031650406\ 4, 11485215566888062309419930900618018816, 822530813044611912090629422953202425869167274683612933021316935465313123696\ 64, 22931425736074985472, 587917045089530534973223389623097014806952626699325292017863299720882182709\ 88452471435976423262480573612488386617866010207995515847984879564869328\ 699392, 259960355727679814191606336143234346941366447307413470189453253677926123044\ 864, 1145932235983649674774736871334153814016, 72474629486854275072, 307644107588115495895377050341223893241177273293391983606714371481521136913\ 055987529131814374583473643092237279538053924434936669159902981128192, 5996412300683636003526898876416, 587253947065805108062874075024223227593178590814921236666402822900590378388\ 58393860204666222754609463073739352315020070797000367727686893265710658\ 8270592, 259667152461045942735270733813184059764508329381780966046883225621651675047\ 5264, 11446397655452593367784965035780384751616, 723928870301856694272, 2889476997120, 185601247467711244029747855810124871930683604010641773563702620571050786256\ 14504726188141423487876571045527499003265602622261844615170178612372751\ 43176192, 820676432469478535064559356249075546910051016317727497629655626656084306323\ 0464, 36176269133282270396950012952589857980416, 2287972725892287823872, 570760888320, 8999424, 586591596934988623106363593671505768077222254650917210275405813162827176315\ 71768023508200054480202496143889379565876472485173237302266243515647214\ 40161792, 259374279891588277748799006419460913591324765651034863448384988177725410393\ 45664, 114334875285435323723693868097074119049216, 7231123676894144233472, 1803886264320, 28442624, 112896, 7112, 242277923108052609972200083439887178880460626810468160459290595902026524741\ 1227403401328491417830386450157273478434455433649, 474666951395368378721045061433248350459677962730713130695753004216215232145\ 8731239316888472981871777535002005182238933094496, 221026605334590989402694781419830510223842008663907018548432209455538289067\ 087156244851138095839289220241742815061382189285376, 526508241090777371603185934694129217750678488855687134273401569711938349315\ 7397689996830829584577070830379330763598 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host pc43.math.uoi.gr. (195.130.112.43) Time: Mon Apr 5 05:27:23 2004 Input: K := (RationalField()); ; R := PolynomialRing(K, [7, 6, 4, 1016, 1008, 992, 960, 896, 768, 512]); R; P := [ 7^145*4^2 , 7^137*4^16 , 7^129*6^20 , 7^129*6^16*4^6 , 7^129*6^8*4^18 , 7^129*6^4*4^24 , 7^129*4^30 , 7^73*4^128 , 7^73*512 , 7^65*6^8*4^2*512 , 7^65*4^142 , 7^65*4^14*512 , 7^33*6^132 , 7^33*6^128*4^6 , 7^33*6^4*4^192 , 7^33*6^4*768 , 7^33*4^198 , 7^33*4^70*512 , 7^33*4^6*768 , 7^17*6^128*4^34 , 7^17*6^64*4^130 , 7^17*6^64*4^2*512 , 7^17*4^226 , 7^17*4^98*512 , x^17*4^34*768 , 7^17*4^2*896 , 7^9*6^160 , 7^9*6^128*4^48 , 7^9*6^64*4^16*512 , 7^9*6^32*4^192 , 7^9*6^32*4^64*512 , 7^9*6^32*768 , 7^9*4^240 , 7^9*4^112*512 , 7^9*4^48*768 , 7^9*4^16*896 , 7^9*960 , 7*6^168*4^2 , 7*6^164*4^8 , 7*6^160*4^14 , 7*6^148*4^32 , 7*6^144*4^38 , 7*6^136*4^50 , 7*6^132*4^56 , 7*6^128*4^62 , 7*6^84*4^128 , 7*6^84*512 , 7*6^80*4^134 , 7*6^80*4^6*512 , 7*6^72*4^146 , 7*6^72*4^18*512 , 7*6^68*4^152 , 7*6^64*4^158 , 7*6^64*4^30*512 , 7*6^40*4^194 , 7*6^40*4^66*512 , 7*6^40*4^2*768 , 7*6^36*4^200 , 7*6^36*4^8*768 , 7*6^32*4^206 , 7*6^32*4^78*512 , 7*6^32*4^14*768 , 7*6^20*4^96*512 , 7*6^20*896 , 7*6^16*4^230 , 7*6^16*4^102*512 , 7*6^16*4^38*768 , 7*6^16*4^6*896 , 7*6^10*4^224 , 7*6^10*4^32*768 , 7*6^8*4^242 , 7*6^8*4^114*512 , 7*6^8*4^50*768 , 7*6^8*4^18*896 , 7*6^8*4^4*960 , 7*6^4*4^248 , 7*6^4*4^120*512 , 7*6^4*4^56*768 , 7*6^4*4^24*896 , 7*6^4*4^8*960 , 7*6^4*992 , 7*4^254 , 7*4^126*512 , 7*4^62*768 , 7*4^30*896 , 7*4^14*960 , 7*4^6*992 , 7*4^2*1008 , 7*1016, 7^146 , 7^144*6*4^2 , 7^136*6*4^16 , 7^130*6^16*4^4 , 7^130*6^8*4^16 , 7^130*4^28 , 7^128*6^21 , 7^128*6^17*4^6 , 7^128*6^9*4^18 , 7^128*6^5*4^24 , 7^128*6*4^30 , 7^72*6*4^128 , 7^72*6*512 , 7^66*6^8*4^128 , 7^66*6^8*512 , 7^66*4^140 , 7^66*4^12*512 , 7^64*6^9*4^2*512 , 7^64*6*4^142 , 7^64*6*4^14*512 , 7^34*4^196 , 7^34*4^68*512 , 7^34*4^4*768 , 7^32*6^133 , 7^32*6^129*4^6 , 7^32*6^5*4^192 , 7^32*6^5*768 , 7^32*6*4^198 , 7^32*6*4^70*512 , 7^32*6*4^6*768 , 7^18*6^64*4^128 , 7^18*6^64*512 , 7^18*4^224 , 7^18*4^96*512 , 7^18*4^32*768 , 7^18*896 , 7^16*6^129*4^34 , 7^16*6^65*4^130 , 7^16*6^65*4^2*512 , 7^16*6*4^226 , 7^16*6*4^98*512 , 7^16*6*4^34*768 , 7^16*6*4^2*896 , 7^8*6^161 , 7^8*6^129*4^48 , 7^8*6^65*4^16*512 , 7^8*6^33*4^192 , 7^8*6^33*4^64*512 , 7^8*6^33*768 , 7^8*6*4^240 , 7^8*6*4^112*512 , 7^8*6*4^48*768 , 7^8*6*4^16*896 , 7^8*6*960 , 7^2*6^168 , 7^2*6^160*4^12 , 7^2*6^144*4^36 , 7^2*6^136*4^48 , 7^2*6^128*4^60 , 7^2*6^80*4^132 , 7^2*6^80*4^4*512 , 7^2*6^72*4^144 , 7^2*6^72*4^16*512 , 7^2*6^64*4^156 , 7^2*6^64*4^28*512 , 7^2*6^40*4^192 , 7^2*6^40*4^64*512 , 7^2*6^40*768 , 7^2*6^32*4^204 , 7^2*6^32*4^76*512 , 7^2*6^32*4^12*768 , 7^2*6^16*4^100*512 , 7^2*6^16*4^36*768 , 7^2*6^16*4^4*896 , 7^2*6^8*4^240 , 7^2*6^8*4^112*512 , 7^2*6^8*4^48*768 , 7^2*6^8*4^16*896 , 7^2*6^8*960 , 7^2*4^252 , 7^2*4^124*512 , 7^2*4^60*768 , 7^2*4^28*896 , 7^2*4^12*960 , 7^2*4^4*992 , 7^2*1008 , 6^169*4^2 , 6^165*4^8 , 6^161*4^14 , 6^149*4^32 , 6^145*4^38 , 6^137*4^50 , 6^133*4^56 , 6^129*4^62 , 6^85*4^128 , 6^85*512 , 6^81*4^134 , 6^81*4^6*512 , 6^73*4^146 , 6^73*4^18*512 , 6^69*4^152 , 6^65*4^158 , 6^65*4^30*512 , 6^41*4^194 , 6^41*4^66*512 , 6^41*4^2*768 , 6^37*4^200 , 6^37*4^8*768 , 6^33*4^206 , 6^33*4^78*512 , 6^33*4^14*768 , 6^21*4^96*512 , 6^21*896 , 6^17*4^230 , 6^17*4^102*512 , 6^17*4^38*768 , 6^17*4^6*896 , 6^11*4^224 , 6^11*4^32*768 , 6^9*4^242 , 6^9*4^114*512 , 6^9*4^50*768 , 6^9*4^18*896 , 6^9*4^4*960 , 6^5*4^248 , 6^5*4^120*512 , 6^5*4^56*768 , 6^5*4^24*896 , 6^5*4^8*960 , 6^5*992 , 6*4^254 , 6*4^126*512 , 6*4^62*768 , 6*4^30*896 , 6*4^14*960 , 6*4^6*992 , 6*4^2*1008 , 6*1016, 7^144*6^2 , 7^144*4^3 , 7^136*4^17 , 7^132*6^16 , 7^132*4^24 , 7^128*6^20*4 , 7^128*6^18*4^4 , 7^128*6^16*4^7 , 7^128*6^10*4^16 , 7^128*6^8*4^19 , 7^128*6^4*4^25 , 7^128*6^2*4^28 , 7^128*4^31 , 7^72*4^129 , 7^72*4*512 , 7^68*4^136 , 7^68*4^8*512 , 7^64*6^10*4^128 , 7^64*6^10*512 , 7^64*6^8*4^3*512 , 7^64*6^2*4^140 , 7^64*6^2*4^12*512 , 7^64*4^143 , 7^64*4^15*512 , 7^36*6^128 , 7^36*4^192 , 7^36*4^64*512 , 7^36*768 , 7^32*6^132*4 , 7^32*6^128*4^7 , 7^32*6^4*4^193 , 7^32*6^4*4*768 , 7^32*6^2*4^196 , 7^32*6^2*4^68*512 , 7^32*6^2*4^4*768 , 7^32*4^199 , 7^32*4^71*512 , 7^32*4^7*768 , 7^16*6^128*4^35 , 7^16*6^66*4^128 , 7^16*6^66*512 , 7^16*6^64*4^131 , 7^16*6^64*4^3*512 , 7^16*6^2*4^224 , 7^16*6^2*4^96*512 , 7^16*6^2*4^32*768 , 7^16*6^2*896 , 7^16*4^227 , 7^16*4^99*512 , 7^16*4^35*768 , 7^16*4^3*896 , 7^8*6^160*4 , 7^8*6^128*4^49 , 7^8*6^64*4^17*512 , 7^8*6^32*4^193 , 7^8*6^32*4^65*512 , 7^8*6^32*4*768 , 7^8*4^241 , 7^8*4^113*512 , 7^8*4^49*768 , 7^8*4^17*896 , 7^8*4*960 , 7^4*6^160*4^8 , 7^4*6^144*4^32 , 7^4*6^128*4^56 , 7^4*6^80*4^128 , 7^4*6^80*512 , 7^4*6^64*4^152 , 7^4*6^64*4^24*512 , 7^4*6^32*4^200 , 7^4*6^32*4^72*512 , 7^4*6^32*4^8*768 , 7^4*6^16*4^224 , 7^4*6^16*4^96*512 , 7^4*6^16*4^32*768 , 7^4*6^16*896 , 7^4*4^248 , 7^4*4^120*512 , 7^4*4^56*768 , 7^4*4^24*896 , 7^4*4^8*960 , 7^4*992 , 6^170 , 6^168*4^3 , 6^164*4^9 , 6^162*4^12 , 6^160*4^15 , 6^148*4^33 , 6^146*4^36 , 6^144*4^39 , 6^138*4^48 , 6^136*4^51 , 6^132*4^57 , 6^130*4^60 , 6^128*4^63 , 6^84*4^129 , 6^84*4*512 , 6^82*4^132 , 6^82*4^4*512 , 6^80*4^135 , 6^80*4^7*512 , 6^74*4^144 , 6^74*4^16*512 , 6^72*4^147 , 6^72*4^19*512 , 6^68*4^153 , 6^66*4^156 , 6^66*4^28*512 , 6^64*4^159 , 6^64*4^31*512 , 6^42*4^192 , 6^42*4^64*512 , 6^42*768 , 6^40*4^195 , 6^40*4^67*512 , 6^40*4^3*768 , 6^36*4^201 , 6^36*4^9*768 , 6^34*4^204 , 6^34*4^76*512 , 6^34*4^12*768 , 6^32*4^207 , 6^32*4^79*512 , 6^32*4^15*768 , 6^20*4^97*512 , 6^20*4*896 , 6^18*4^100*512 , 6^18*4^36*768 , 6^18*4^4*896 , 6^16*4^231 , 6^16*4^103*512 , 6^16*4^39*768 , 6^16*4^7*896 , 6^10*4^240 , 6^10*4^225 , 6^10*4^112*512 , 6^10*4^48*768 , 6^10*4^33*768 , 6^10*4^16*896 , 6^10*960 , 6^8*4^243 , 6^8*4^115*512 , 6^8*4^51*768 , 6^8*4^19*896 , 6^8*4^5*960 , 6^4*4^249 , 6^4*4^121*512 , 6^4*4^57*768 , 6^4*4^25*896 , 6^4*4^9*960 , 6^4*4*992 , 6^2*4^252 , 6^2*4^124*512 , 6^2*4^60*768 , 6^2*4^28*896 , 6^2*4^12*960 , 6^2*4^4*992 , 6^2*1008 , 4^255 , 4^127*512 , 4^63*768 , 4^31*896 , 4^15*960 , 4^7*992 , 4^3*1008 , 4*1016 ] ; P; [IsHomogeneous(f): f in P]; P; I:=ideal; Dimension(I); V,phi:=VectorSpace(quo); S:=[R!(v@@phi ): v in Basis(V)]; S; Output: Magma V2.10-22 Mon Apr 5 2004 05:27:20 on modular [Seed = 1182212097] ------------------------------------- Graded Polynomial ring of rank 10 over Rational Field Lexicographical Order Variables: x, y, z, a, b, c, d, e, f, g Variable weights: 7 6 4 1016 1008 992 960 896 768 512 [ 553778109961263108507885905005456408869624289852498652478378504918917770836\ 8519779203036551812183740457502339379278755276912, 257864372890356154303143911656468928594482343441224854973170911031461337244\ 935015618992994445145837423615366617571612554166272, 380778281503151491963018399198432737837544264261702302465585063809526841915\ 84751150869937249674173458683993374272455607058432, 120344740820749113509299642215800964057297940309871344976777501648443051272\ 169090057070418961933190190408670417453686856876032, 120209006773793840922808433962120591075431760648494565834447345649022463163\ 7383552199385303625857880249751962273776074051551232, 379919823877669423163443939435837917472969515135982825353315067730243834196\ 5064066210402934916291572147364226445514505644408832, 120073425818127620160298331476017909719852093672606917642529206591286940190\ 50079024072384584426798055181793110741379178332946432, 569948757231575212015999448718318746333057130324182287201638896697569130530\ 5819599745471996873521042701156860951927209360368632434578685952, 25201528500318654955500469857453146934705429822751437238918352384, 117482329033987380897936639075925846784670472315475876470277013504, 265394164593177092558462107039688808382566056751348919229119793003000213963\ 153785136974070642850324828746129085316071538888857078617721536512, 1173498234350159578498273979344593247200146940049844084797450747904, 401976228461706718713941919868722703569257817805922718452950057084545624504\ 18336401740937089081724576856264519294585062135747837952, 127044338871848049371319915415300014955222223899155822128339771127955160337\ 124618751181233269196561625619798974560663900083351191552, 394783194532866594457038361637185107104520454738045914540252414945601941424\ 24341007340464522225124884580474724493656637089890325969888309910123315\ 2, 7694874517048971343320325901930496, 124770984938782528618520766147060972121922514090049079163339034847005058030\ 37816417134764095913125889447656209222686542092607312899125194243199467\ 52, 5517021474388358259559864819405945158134307703164580287700031874724265984, 24319603411907860048024733714743296, 275465005292624870738146523044200261028285218773995842334641267202385380393\ 099404121869230432869589285600111304057852997614355687145472, 272989270156149540604790328139848738370686692629791802143162635592401161000\ 56428366877961761622271134404753327134592757250297330421241397379072, 120708165160996913756322665579785467547315133943406155244971359207424, 270535785629908593744827585329001999658731208800582495547989103641877427718\ 87348924331154265060947683054673014237275464733543839895385019932530672\ 92672, 119623303418101151526439362404746175531199131418228274794308216014481118986\ 24, 226673591177742970257408*x^17, 3334991048520599552, 128849406217056419256800915159217449780344646085011288542451429071912528213\ 8357746176797499515657232306253490109385277139505834360832, 128269083889917744972524495655937482012729965179469915577664403607149949969\ 74760759093374852595332534186831446836677349278071607506501632, 5620723309948690329253541903362356543311163656091391442027344658694144, 126543752088758925839878158672801474038091726868711604585315511872709120496\ 42748587355310862882901545330892790742591091381628895508163806803664044\ 032, 55954082438789467216636873562774665817782724438254010983475709039549087744, 246651404295905934607261147632500736, 125973814152271276320226041643362124387820770250032178488108132300037118377\ 23946566644612520272565105183899016648931214752010969950755750495390839\ 0264832, 557020719384144244773147352414546420474418476354275432170224647310353675321\ 344, 2455405158476355819544472301378402779136, 155292410417210458112, 38739462720, 600659136085127475342669211765857454244164481871890656184712983479011838884\ 7351044249368979630665864503701722348619525004795777646592, 189837949182460041589781874335875936156180379455807417263316696013119791054\ 92862559602943935622845201394415320015390103718860729352192, 599981666551972477123261232468941230320767619020823442214926841720477364321\ 74973027880909228635165080950250887949874895704053663137792, 189409963020964085848702157371328902218633256186821554752142684658170151801\ 1724485470507613084435618928083915996934463652981949796974592, 598629018930454394781083361568644431703334735602794049587018855215945171124\ 6931707166048752464389116612215833274262008582263940099080192, 597953839119436964127009284922461232679618125780593062547399294245270274879\ 25455930625540472718519302895622138311543209030216366153531392, 188982941746389954094462193753271698229607703950409659274239776946653321443\ 319959484446152605135073352361472437132778537181918391793876992, 597279420828096645039287920997994503046661385324751515730930653065966052956\ 665550963187840332278750348204159801308534636031742077768302592, 187707645515510522645917592615599134915318153277808673124197190051974564586\ 600694687197219116004573492310752368551212443589361789109815520264192, 829990331264955759979087582192527209229828368727311879051409006526464, 593248854962601157992035848266584920226190706655790374318450378435870228816\ 910837529907260416014454494216698843816177599492303926075466335649792, 2623179318565786105612918778287493402010321757952985691816798835441664, 592579743313961735865966489132737529826911052452276756155067276347709058310\ 3958032062185980585874605964484922333232283975053746395257089128660992, 26202206953441145895053840124043464044223204805548981908078909995352064, 187284462084412598002083236071581243994678061021954135278638546598782122132\ 66830323554563099135603692924791853300092156760663692310935985394286592\ , 591911386340859568994238375732404919291822020020003192979400838633187941555\ 09982257160100658996475868996873017837328297910245743599995213097992192\ , 261726540908507687452865183107653171711966460926148160086550746144702464, 589910834967764991668500732933889292949993518017549359839950898675162461654\ 38161175171535836944040391229443168958395277941551839053150484891583905\ 792, 260841953446815762815857849111567481624294607193087702869942012608369393664\ , 1149818410253182629579226175521161216, 186440955249071404774242206951945258018763383472213131011144975383755049609\ 28604025733226141058857210067577100312776779201280581231612992755858617\ 1392, 3633993987960675965089900011523670016, 589245488194596044718592654070345506824733656406006932578433502447423366666\ 38550994909949285321820318238268366420627845376886775250529952413577851\ 6992, 260547755846525191768024081685348063949546888843258583985436972082031650406\ 4, 11485215566888062309419930900618018816, 822530813044611912090629422953202425869167274683612933021316935465313123696\ 64, 22931425736074985472, 587917045089530534973223389623097014806952626699325292017863299720882182709\ 88452471435976423262480573612488386617866010207995515847984879564869328\ 699392, 259960355727679814191606336143234346941366447307413470189453253677926123044\ 864, 1145932235983649674774736871334153814016, 72474629486854275072, 307644107588115495895377050341223893241177273293391983606714371481521136913\ 055987529131814374583473643092237279538053924434936669159902981128192, 5996412300683636003526898876416, 587253947065805108062874075024223227593178590814921236666402822900590378388\ 58393860204666222754609463073739352315020070797000367727686893265710658\ 8270592, 259667152461045942735270733813184059764508329381780966046883225621651675047\ 5264, 11446397655452593367784965035780384751616, 723928870301856694272, 2889476997120, 185601247467711244029747855810124871930683604010641773563702620571050786256\ 14504726188141423487876571045527499003265602622261844615170178612372751\ 43176192, 820676432469478535064559356249075546910051016317727497629655626656084306323\ 0464, 36176269133282270396950012952589857980416, 2287972725892287823872, 570760888320, 8999424, 586591596934988623106363593671505768077222254650917210275405813162827176315\ 71768023508200054480202496143889379565876472485173237302266243515647214\ 40161792, 259374279891588277748799006419460913591324765651034863448384988177725410393\ 45664, 114334875285435323723693868097074119049216, 7231123676894144233472, 1803886264320, 28442624, 112896, 7112, 242277923108052609972200083439887178880460626810468160459290595902026524741\ 1227403401328491417830386450157273478434455433649, 474666951395368378721045061433248350459677962730713130695753004216215232145\ 8731239316888472981871777535002005182238933094496, 221026605334590989402694781419830510223842008663907018548432209455538289067\ 087156244851138095839289220241742815061382189285376, 526508241090777371603185934694129217750678488855687134273401569711938349315\ 73976899968308295845770708303793307635987999883264, 525914404635348054037286898584277585955013952837163725525707137214 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 72-236-ADSL.red.retevision.es. (80.224.236.72) Time: Mon Apr 5 08:13:03 2004 Input: /***************************************/ /* Practica 2 teoria de la codificacio */ /***************************************/ /* ALUMNES: */ /* JAUME PERNAS VALLES ORIOL ORELLANA QUINTILLA */ /********************/ /* 1) cossos finits */ /********************/ /* i */ Z2:=GF(2); Z3:=GF(3); Z5:=GF(5); {i:i in Z2}; {i:i in Z3}; {i:i in Z5}; primitiusG5 := [b: b in Z5 |IsPrimitive(b)]; /* ii */ /* NO HO ES PQ 9 NO ES PRIMER I PER TANT TOTS ELS ELEMENTS NO TENEN INVERS JA QUE NO TOTS SON PRIMERS AMB 9 EL 3 PER EXEMPLE NO TE INVERS A Z9 */ Z9:=GF(9); IsInvertible(Z9!3); /*false*/ /* iii */ P2:=PolynomialRing(Z2); p:=1+x+x^4; IsIrreducible(p); G16:= ext< Z2 | p >; P3:=PolynomialRing(Z3); q:=2+2*x+x^2; IsIrreducible(q); G9:= ext< Z3 | q >; qq:=1+2*x+x^2; IsIrreducible(qq); /*G9b:= ext< Z3 | qq >;*//*NO funciona perque qq no es irreductible*/ P5:=PolynomialRing(Z5); r:=3+2*x+x^2; IsIrreducible(r); G25:= ext< Z5 | r >; /* iv */ [Order(a) :a in G25 | not a eq 0 ]; primitiusG25 := [a: a in G25 | IsPrimitive(a)]; [a: a in G25 | IsPrimitive(a)]; #[a: a in G25 | IsPrimitive(a)]; /* Hi haurá tants elements com f(p^n -1) on f es la funció multiplicativa d Euler Donat que si b es primitiu b^i es primitiu sii mcd(i,p^n -1)=1 i aquests son precisament tots els que busca la fi d Euler */ /* v */ pm:=MinimalPolynomial(a); /* el grau dun element es el grau del seu polinomi minim */ /* el polinomi minim esta definit dintre de Zp */ Roots(pm,Z5); Roots(pm,G25); /* vi */ calculeu:=2*a^(-3)-a^5+((a^6)/(a+2)); IsInvertible(calculeu); /* tots perque G25 es un cos*/ /* vii */ taula25:=[ : i in [0..23]]; taula16:=[ : i in [0..14]]; /* viii */ /* Quina Estructura de Subcos hi ha entre els cossos de 2,4,8,16 elements? */ G2 := GF(2); G4 := GF(4); G8 := GF(8); G166 := GF(16); {i:i in G2}; {i:i in G4}; {i:i in G8}; {i:i in G166}; /*************************************/ /* 2) Polinomis sobre cossos Finits */ /*************************************/ /* i */ G25x:=PolynomialRing(G25); IsFinite(G25x); /* false */ /* Efectivament no es finit, pq estem definint un anell de polynomis sobre un camp de coeficients finits pero els polynomis poden tenir el grau que vulguin */ /* ii */ alpha := primitiusG25[1]; beta := primitiusG5[1]; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; /* iii */ suma := p1 + p2; producte := p1 * p2; Output: Magma V2.10-22 Mon Apr 5 2004 08:13:01 on modular [Seed = 1057894961] ------------------------------------- { 0, 1 } { 0, 1, 2 } { 0, 1, 2, 3, 4 } false true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ a, a^5, a^7, a^11, a^13, a^17, a^19, a^23 ] 8 [] [ , ] true a^16 >> taula16:=[ : i in [0..14]]; ^ User error: Identifier 'b' has not been declared or assigned { 0, 1 } { 1, G4.1, G4.1^2, 0 } { 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 } { 1, G166.1, G166.1^2, G166.1^3, G166.1^4, G166.1^5, G166.1^6, G166.1^7, G166.1^8, G166.1^9, G166.1^10, G166.1^11, G166.1^12, G166.1^13, G166.1^14, 0 } false Total time: 2.639 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 72-236-ADSL.red.retevision.es. (80.224.236.72) Time: Mon Apr 5 08:13:32 2004 Input: /***************************************/ /* Practica 2 teoria de la codificacio */ /***************************************/ /* ALUMNES: */ /* JAUME PERNAS VALLES ORIOL ORELLANA QUINTILLA */ /********************/ /* 1) cossos finits */ /********************/ /* i */ Z2:=GF(2); Z3:=GF(3); Z5:=GF(5); {i:i in Z2}; {i:i in Z3}; {i:i in Z5}; primitiusG5 := [b: b in Z5 |IsPrimitive(b)]; /* ii */ /* NO HO ES PQ 9 NO ES PRIMER I PER TANT TOTS ELS ELEMENTS NO TENEN INVERS JA QUE NO TOTS SON PRIMERS AMB 9 EL 3 PER EXEMPLE NO TE INVERS A Z9 */ Z9:=GF(9); IsInvertible(Z9!3); /*false*/ /* iii */ P2:=PolynomialRing(Z2); p:=1+x+x^4; IsIrreducible(p); G16:= ext< Z2 | p >; P3:=PolynomialRing(Z3); q:=2+2*x+x^2; IsIrreducible(q); G9:= ext< Z3 | q >; qq:=1+2*x+x^2; IsIrreducible(qq); /*G9b:= ext< Z3 | qq >;*//*NO funciona perque qq no es irreductible*/ P5:=PolynomialRing(Z5); r:=3+2*x+x^2; IsIrreducible(r); G25:= ext< Z5 | r >; /* iv */ [Order(a) :a in G25 | not a eq 0 ]; primitiusG25 := [a: a in G25 | IsPrimitive(a)]; [a: a in G25 | IsPrimitive(a)]; #[a: a in G25 | IsPrimitive(a)]; /* Hi haurá tants elements com f(p^n -1) on f es la funció multiplicativa d Euler Donat que si b es primitiu b^i es primitiu sii mcd(i,p^n -1)=1 i aquests son precisament tots els que busca la fi d Euler */ /* v */ pm:=MinimalPolynomial(a); /* el grau dun element es el grau del seu polinomi minim */ /* el polinomi minim esta definit dintre de Zp */ Roots(pm,Z5); Roots(pm,G25); /* vi */ calculeu:=2*a^(-3)-a^5+((a^6)/(a+2)); IsInvertible(calculeu); /* tots perque G25 es un cos*/ /* vii */ taula25:=[ : i in [0..23]]; taula16:=[ : i in [0..14]]; /* viii */ /* Quina Estructura de Subcos hi ha entre els cossos de 2,4,8,16 elements? */ G2 := GF(2); G4 := GF(4); G8 := GF(8); G166 := GF(16); {i:i in G2}; {i:i in G4}; {i:i in G8}; {i:i in G166}; /*************************************/ /* 2) Polinomis sobre cossos Finits */ /*************************************/ /* i */ G25x:=PolynomialRing(G25); IsFinite(G25x); /* false */ /* Efectivament no es finit, pq estem definint un anell de polynomis sobre un camp de coeficients finits pero els polynomis poden tenir el grau que vulguin */ /* ii */ alpha := primitiusG25[1]; beta := primitiusG5[1]; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; /* iii */ suma := p1 + p2; producte := p1 * p2; suma; producte; Output: Magma V2.10-22 Mon Apr 5 2004 08:13:29 on modular [Seed = 3354839789] ------------------------------------- { 0, 1 } { 0, 1, 2 } { 0, 1, 2, 3, 4 } false true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ a, a^5, a^7, a^11, a^13, a^17, a^19, a^23 ] 8 [] [ , ] true a^16 >> taula16:=[ : i in [0..14]]; ^ User error: Identifier 'b' has not been declared or assigned { 0, 1 } { 1, G4.1, G4.1^2, 0 } { 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 } { 1, G166.1, G166.1^2, G166.1^3, G166.1^4, G166.1^5, G166.1^6, G166.1^7, G166.1^8, G166.1^9, G166.1^10, G166.1^11, G166.1^12, G166.1^13, G166.1^14, 0 } false 2*x^2 + a^19*x + a^9 a^19*x^3 + a^22*x^2 + a^10*x + a^2 Total time: 2.530 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 72-236-ADSL.red.retevision.es. (80.224.236.72) Time: Mon Apr 5 08:17:07 2004 Input: /***************************************/ /* Practica 2 teoria de la codificacio */ /***************************************/ /* ALUMNES: */ /* JAUME PERNAS VALLES ORIOL ORELLANA QUINTILLA */ /********************/ /* 1) cossos finits */ /********************/ /* i */ Z2:=GF(2); Z3:=GF(3); Z5:=GF(5); {i:i in Z2}; {i:i in Z3}; {i:i in Z5}; primitiusG5 := [b: b in Z5 |IsPrimitive(b)]; /* ii */ /* NO HO ES PQ 9 NO ES PRIMER I PER TANT TOTS ELS ELEMENTS NO TENEN INVERS JA QUE NO TOTS SON PRIMERS AMB 9 EL 3 PER EXEMPLE NO TE INVERS A Z9 */ Z9:=GF(9); IsInvertible(Z9!3); /*false*/ /* iii */ P2:=PolynomialRing(Z2); p:=1+x+x^4; IsIrreducible(p); G16:= ext< Z2 | p >; P3:=PolynomialRing(Z3); q:=2+2*x+x^2; IsIrreducible(q); G9:= ext< Z3 | q >; qq:=1+2*x+x^2; IsIrreducible(qq); /*G9b:= ext< Z3 | qq >;*//*NO funciona perque qq no es irreductible*/ P5:=PolynomialRing(Z5); r:=3+2*x+x^2; IsIrreducible(r); G25:= ext< Z5 | r >; /* iv */ [Order(a) :a in G25 | not a eq 0 ]; primitiusG25 := [a: a in G25 | IsPrimitive(a)]; [a: a in G25 | IsPrimitive(a)]; #[a: a in G25 | IsPrimitive(a)]; /* Hi haurá tants elements com f(p^n -1) on f es la funció multiplicativa d Euler Donat que si b es primitiu b^i es primitiu sii mcd(i,p^n -1)=1 i aquests son precisament tots els que busca la fi d Euler */ /* v */ pm:=MinimalPolynomial(a); /* el grau dun element es el grau del seu polinomi minim */ /* el polinomi minim esta definit dintre de Zp */ Roots(pm,Z5); Roots(pm,G25); /* vi */ calculeu:=2*a^(-3)-a^5+((a^6)/(a+2)); IsInvertible(calculeu); /* tots perque G25 es un cos*/ /* vii */ taula25:=[ : i in [0..23]]; taula16:=[ : i in [0..14]]; /* viii */ /* Quina Estructura de Subcos hi ha entre els cossos de 2,4,8,16 elements? */ G2 := GF(2); G4 := GF(4); G8 := GF(8); G166 := GF(16); {i:i in G2}; {i:i in G4}; {i:i in G8}; {i:i in G166}; /*************************************/ /* 2) Polinomis sobre cossos Finits */ /*************************************/ /* i */ G25x:=PolynomialRing(G25); IsFinite(G25x); /* false */ /* Efectivament no es finit, pq estem definint un anell de polynomis sobre un camp de coeficients finits pero els polynomis poden tenir el grau que vulguin */ /* ii */ alpha := primitiusG25[1]; beta := primitiusG5[1]; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; /* iii */ suma := p1 + p2; producte := p1 * p2; suma; producte; /* iv */ quocient := p1 div p2; quocient; residu := p1 mod p2; residu; Output: Magma V2.10-22 Mon Apr 5 2004 08:17:05 on modular [Seed = 3504463570] ------------------------------------- { 0, 1 } { 0, 1, 2 } { 0, 1, 2, 3, 4 } false true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ a, a^5, a^7, a^11, a^13, a^17, a^19, a^23 ] 8 [] [ , ] true a^16 >> taula16:=[ : i in [0..14]]; ^ User error: Identifier 'b' has not been declared or assigned { 0, 1 } { 1, G4.1, G4.1^2, 0 } { 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 } { 1, G166.1, G166.1^2, G166.1^3, G166.1^4, G166.1^5, G166.1^6, G166.1^7, G166.1^8, G166.1^9, G166.1^10, G166.1^11, G166.1^12, G166.1^13, G166.1^14, 0 } false 2*x^2 + a^19*x + a^9 a^19*x^3 + a^22*x^2 + a^10*x + a^2 a^17*x + a^5 a^15 Total time: 2.569 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 72-236-ADSL.red.retevision.es. (80.224.236.72) Time: Mon Apr 5 08:19:12 2004 Input: /***************************************/ /* Practica 2 teoria de la codificacio */ /***************************************/ /* ALUMNES: */ /* JAUME PERNAS VALLES ORIOL ORELLANA QUINTILLA */ /********************/ /* 1) cossos finits */ /********************/ /* i */ Z2:=GF(2); Z3:=GF(3); Z5:=GF(5); {i:i in Z2}; {i:i in Z3}; {i:i in Z5}; primitiusG5 := [b: b in Z5 |IsPrimitive(b)]; /* ii */ /* NO HO ES PQ 9 NO ES PRIMER I PER TANT TOTS ELS ELEMENTS NO TENEN INVERS JA QUE NO TOTS SON PRIMERS AMB 9 EL 3 PER EXEMPLE NO TE INVERS A Z9 */ Z9:=GF(9); IsInvertible(Z9!3); /*false*/ /* iii */ P2:=PolynomialRing(Z2); p:=1+x+x^4; IsIrreducible(p); G16:= ext< Z2 | p >; P3:=PolynomialRing(Z3); q:=2+2*x+x^2; IsIrreducible(q); G9:= ext< Z3 | q >; qq:=1+2*x+x^2; IsIrreducible(qq); /*G9b:= ext< Z3 | qq >;*//*NO funciona perque qq no es irreductible*/ P5:=PolynomialRing(Z5); r:=3+2*x+x^2; IsIrreducible(r); G25:= ext< Z5 | r >; /* iv */ [Order(a) :a in G25 | not a eq 0 ]; primitiusG25 := [a: a in G25 | IsPrimitive(a)]; [a: a in G25 | IsPrimitive(a)]; #[a: a in G25 | IsPrimitive(a)]; /* Hi haurá tants elements com f(p^n -1) on f es la funció multiplicativa d Euler Donat que si b es primitiu b^i es primitiu sii mcd(i,p^n -1)=1 i aquests son precisament tots els que busca la fi d Euler */ /* v */ pm:=MinimalPolynomial(a); /* el grau dun element es el grau del seu polinomi minim */ /* el polinomi minim esta definit dintre de Zp */ Roots(pm,Z5); Roots(pm,G25); /* vi */ calculeu:=2*a^(-3)-a^5+((a^6)/(a+2)); IsInvertible(calculeu); /* tots perque G25 es un cos*/ /* vii */ taula25:=[ : i in [0..23]]; taula16:=[ : i in [0..14]]; /* viii */ /* Quina Estructura de Subcos hi ha entre els cossos de 2,4,8,16 elements? */ G2 := GF(2); G4 := GF(4); G8 := GF(8); G166 := GF(16); {i:i in G2}; {i:i in G4}; {i:i in G8}; {i:i in G166}; /*************************************/ /* 2) Polinomis sobre cossos Finits */ /*************************************/ /* i */ G25x:=PolynomialRing(G25); IsFinite(G25x); /* false */ /* Efectivament no es finit, pq estem definint un anell de polynomis sobre un camp de coeficients finits pero els polynomis poden tenir el grau que vulguin */ /* ii */ alpha := primitiusG25[1]; beta := primitiusG5[1]; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; /* iii */ suma := p1 + p2; producte := p1 * p2; suma; producte; /* iv */ quocient := p1 div p2; quocient; residu := p1 mod p2; residu; /* v */ mcm := LCM(p1,p2); mcm; mcd := GCD(p1,p2); mcd; Output: Magma V2.10-22 Mon Apr 5 2004 08:19:10 on modular [Seed = 3756970274] ------------------------------------- { 0, 1 } { 0, 1, 2 } { 0, 1, 2, 3, 4 } false true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ a, a^5, a^7, a^11, a^13, a^17, a^19, a^23 ] 8 [] [ , ] true a^16 >> taula16:=[ : i in [0..14]]; ^ User error: Identifier 'b' has not been declared or assigned { 0, 1 } { 1, G4.1, G4.1^2, 0 } { 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 } { 1, G166.1, G166.1^2, G166.1^3, G166.1^4, G166.1^5, G166.1^6, G166.1^7, G166.1^8, G166.1^9, G166.1^10, G166.1^11, G166.1^12, G166.1^13, G166.1^14, 0 } false 2*x^2 + a^19*x + a^9 a^19*x^3 + a^22*x^2 + a^10*x + a^2 a^17*x + a^5 a^15 x^3 + a^3*x^2 + a^15*x + a^7 1 Total time: 2.579 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 72-236-ADSL.red.retevision.es. (80.224.236.72) Time: Mon Apr 5 08:23:12 2004 Input: /***************************************/ /* Practica 2 teoria de la codificacio */ /***************************************/ /* ALUMNES: */ /* JAUME PERNAS VALLES ORIOL ORELLANA QUINTILLA */ /********************/ /* 1) cossos finits */ /********************/ /* i */ Z2:=GF(2); Z3:=GF(3); Z5:=GF(5); {i:i in Z2}; {i:i in Z3}; {i:i in Z5}; primitiusG5 := [b: b in Z5 |IsPrimitive(b)]; /* ii */ /* NO HO ES PQ 9 NO ES PRIMER I PER TANT TOTS ELS ELEMENTS NO TENEN INVERS JA QUE NO TOTS SON PRIMERS AMB 9 EL 3 PER EXEMPLE NO TE INVERS A Z9 */ Z9:=GF(9); IsInvertible(Z9!3); /*false*/ /* iii */ P2:=PolynomialRing(Z2); p:=1+x+x^4; IsIrreducible(p); G16:= ext< Z2 | p >; P3:=PolynomialRing(Z3); q:=2+2*x+x^2; IsIrreducible(q); G9:= ext< Z3 | q >; qq:=1+2*x+x^2; IsIrreducible(qq); /*G9b:= ext< Z3 | qq >;*//*NO funciona perque qq no es irreductible*/ P5:=PolynomialRing(Z5); r:=3+2*x+x^2; IsIrreducible(r); G25:= ext< Z5 | r >; /* iv */ [Order(a) :a in G25 | not a eq 0 ]; primitiusG25 := [a: a in G25 | IsPrimitive(a)]; [a: a in G25 | IsPrimitive(a)]; #[a: a in G25 | IsPrimitive(a)]; /* Hi haurá tants elements com f(p^n -1) on f es la funció multiplicativa d Euler Donat que si b es primitiu b^i es primitiu sii mcd(i,p^n -1)=1 i aquests son precisament tots els que busca la fi d Euler */ /* v */ pm:=MinimalPolynomial(a); /* el grau dun element es el grau del seu polinomi minim */ /* el polinomi minim esta definit dintre de Zp */ Roots(pm,Z5); Roots(pm,G25); /* vi */ calculeu:=2*a^(-3)-a^5+((a^6)/(a+2)); IsInvertible(calculeu); /* tots perque G25 es un cos*/ /* vii */ taula25:=[ : i in [0..23]]; taula16:=[ : i in [0..14]]; /* viii */ /* Quina Estructura de Subcos hi ha entre els cossos de 2,4,8,16 elements? */ G2 := GF(2); G4 := GF(4); G8 := GF(8); G166 := GF(16); {i:i in G2}; {i:i in G4}; {i:i in G8}; {i:i in G166}; /*************************************/ /* 2) Polinomis sobre cossos Finits */ /*************************************/ /* i */ G25x:=PolynomialRing(G25); IsFinite(G25x); /* false */ /* Efectivament no es finit, pq estem definint un anell de polynomis sobre un camp de coeficients finits pero els polynomis poden tenir el grau que vulguin */ /* ii */ alpha := primitiusG25[1]; beta := primitiusG5[1]; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; /* iii */ suma := p1 + p2; producte := p1 * p2; suma; producte; /* iv */ quocient := p1 div p2; quocient; residu := p1 mod p2; residu; /* v */ mcm := LCM(p1,p2); mcm; mcd := GCD(p1,p2); mcd; /* vi */ XGCD(p1,p2); Output: Magma V2.10-22 Mon Apr 5 2004 08:23:09 on modular [Seed = 3990675971] ------------------------------------- { 0, 1 } { 0, 1, 2 } { 0, 1, 2, 3, 4 } false true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ a, a^5, a^7, a^11, a^13, a^17, a^19, a^23 ] 8 [] [ , ] true a^16 >> taula16:=[ : i in [0..14]]; ^ User error: Identifier 'b' has not been declared or assigned { 0, 1 } { 1, G4.1, G4.1^2, 0 } { 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 } { 1, G166.1, G166.1^2, G166.1^3, G166.1^4, G166.1^5, G166.1^6, G166.1^7, G166.1^8, G166.1^9, G166.1^10, G166.1^11, G166.1^12, G166.1^13, G166.1^14, 0 } false 2*x^2 + a^19*x + a^9 a^19*x^3 + a^22*x^2 + a^10*x + a^2 a^17*x + a^5 a^15 x^3 + a^3*x^2 + a^15*x + a^7 1 1 a^9 a^14*x + a^2 Total time: 2.619 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 72-236-ADSL.red.retevision.es. (80.224.236.72) Time: Mon Apr 5 08:23:49 2004 Input: /***************************************/ /* Practica 2 teoria de la codificacio */ /***************************************/ /* ALUMNES: */ /* JAUME PERNAS VALLES ORIOL ORELLANA QUINTILLA */ /********************/ /* 1) cossos finits */ /********************/ /* i */ Z2:=GF(2); Z3:=GF(3); Z5:=GF(5); {i:i in Z2}; {i:i in Z3}; {i:i in Z5}; primitiusG5 := [b: b in Z5 |IsPrimitive(b)]; /* ii */ /* NO HO ES PQ 9 NO ES PRIMER I PER TANT TOTS ELS ELEMENTS NO TENEN INVERS JA QUE NO TOTS SON PRIMERS AMB 9 EL 3 PER EXEMPLE NO TE INVERS A Z9 */ Z9:=GF(9); IsInvertible(Z9!3); /*false*/ /* iii */ P2:=PolynomialRing(Z2); p:=1+x+x^4; IsIrreducible(p); G16:= ext< Z2 | p >; P3:=PolynomialRing(Z3); q:=2+2*x+x^2; IsIrreducible(q); G9:= ext< Z3 | q >; qq:=1+2*x+x^2; IsIrreducible(qq); /*G9b:= ext< Z3 | qq >;*//*NO funciona perque qq no es irreductible*/ P5:=PolynomialRing(Z5); r:=3+2*x+x^2; IsIrreducible(r); G25:= ext< Z5 | r >; /* iv */ [Order(a) :a in G25 | not a eq 0 ]; primitiusG25 := [a: a in G25 | IsPrimitive(a)]; [a: a in G25 | IsPrimitive(a)]; #[a: a in G25 | IsPrimitive(a)]; /* Hi haurá tants elements com f(p^n -1) on f es la funció multiplicativa d Euler Donat que si b es primitiu b^i es primitiu sii mcd(i,p^n -1)=1 i aquests son precisament tots els que busca la fi d Euler */ /* v */ pm:=MinimalPolynomial(a); /* el grau dun element es el grau del seu polinomi minim */ /* el polinomi minim esta definit dintre de Zp */ Roots(pm,Z5); Roots(pm,G25); /* vi */ calculeu:=2*a^(-3)-a^5+((a^6)/(a+2)); IsInvertible(calculeu); /* tots perque G25 es un cos*/ /* vii */ taula25:=[ : i in [0..23]]; taula16:=[ : i in [0..14]]; /* viii */ /* Quina Estructura de Subcos hi ha entre els cossos de 2,4,8,16 elements? */ G2 := GF(2); G4 := GF(4); G8 := GF(8); G166 := GF(16); {i:i in G2}; {i:i in G4}; {i:i in G8}; {i:i in G166}; /*************************************/ /* 2) Polinomis sobre cossos Finits */ /*************************************/ /* i */ G25x:=PolynomialRing(G25); IsFinite(G25x); /* false */ /* Efectivament no es finit, pq estem definint un anell de polynomis sobre un camp de coeficients finits pero els polynomis poden tenir el grau que vulguin */ /* ii */ alpha := primitiusG25[1]; beta := primitiusG5[1]; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; /* iii */ suma := p1 + p2; producte := p1 * p2; suma; producte; /* iv */ quocient := p1 div p2; quocient; residu := p1 mod p2; residu; /* v */ mcm := LCM(p1,p2); mcm; mcd := GCD(p1,p2); mcd; /* vi */ [d,a,b]:=XGCD(p1,p2); d; a; b; Output: Magma V2.10-22 Mon Apr 5 2004 08:23:47 on modular [Seed = 4123327077] ------------------------------------- { 0, 1 } { 0, 1, 2 } { 0, 1, 2, 3, 4 } false true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ a, a^5, a^7, a^11, a^13, a^17, a^19, a^23 ] 8 [] [ , ] true a^16 >> taula16:=[ : i in [0..14]]; ^ User error: Identifier 'b' has not been declared or assigned { 0, 1 } { 1, G4.1, G4.1^2, 0 } { 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 } { 1, G166.1, G166.1^2, G166.1^3, G166.1^4, G166.1^5, G166.1^6, G166.1^7, G166.1^8, G166.1^9, G166.1^10, G166.1^11, G166.1^12, G166.1^13, G166.1^14, 0 } false 2*x^2 + a^19*x + a^9 a^19*x^3 + a^22*x^2 + a^10*x + a^2 a^17*x + a^5 a^15 x^3 + a^3*x^2 + a^15*x + a^7 1 >> [d,a,b]:=XGCD(p1,p2); ^ User error: Illegal left hand side of an assignment statement >> d; ^ User error: Identifier 'd' has not been declared or assigned a >> b;; ^ User error: Identifier 'b' has not been declared or assigned Total time: 2.579 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host kalgan.topologie.math.uni-siegen.de. (141.99.112.122) Time: Mon Apr 5 09:06:48 2004 Input: ?galois Output: Magma V2.10-22 Mon Apr 5 2004 09:06:45 on modular [Seed = 87301287] ------------------------------------- 21 matches: 1 O /magma/ring-field-algebra 2 O /system/database/galpols 3 S /magma/ring-field-algebra/abelian-extension/\ galois-module-structure 4 S /magma/ring-field-algebra/algebraic-field/galois 5 S /magma/ring-field-algebra/finite-Galois-field 6 S /magma/ring-field-algebra/function-field/structure-invar/galois 7 S /magma/ring-field-algebra/galois-ring 8 I /magma/group/character/element/conjugate/GaloisConjugate 9 I /magma/group/character/element/conjugate/GaloisOrbit 10 I /magma/ring-field-algebra/algebraic-field/galois/GaloisGroup 11 I /magma/ring-field-algebra/algebraic-field/galois/GaloisGroup 12 I /magma/ring-field-algebra/finite-Galois-field/creation/structure/\ FiniteField 13 I /magma/ring-field-algebra/finite-Galois-field/creation/structure/\ FiniteField 14 I /magma/ring-field-algebra/function-field/structure-invar/galois/\ GaloisGroup 15 I /magma/ring-field-algebra/galois-ring/creation/structure/\ GaloisRing 16 I /magma/ring-field-algebra/galois-ring/creation/structure/\ GaloisRing 17 I /magma/ring-field-algebra/galois-ring/creation/structure/\ GaloisRing 18 I /magma/ring-field-algebra/galois-ring/creation/structure/\ GaloisRing 19 I /magma/ring-field-algebra/local/operation-element/norm-trace/\ GaloisImage 20 I /magma/ring-field-algebra/local/operation-element/norm-trace/\ GaloisImage 21 I /magma/ring-field-algebra/local/operation-element/norm-trace/\ GaloisImage To view an entry, type ? followed by the number next to it Total time: 2.559 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host kalgan.topologie.math.uni-siegen.de. (141.99.112.122) Time: Mon Apr 5 09:07:16 2004 Input: galois(x^3+x+1) Output: Magma V2.10-22 Mon Apr 5 2004 09:07:14 on modular [Seed = 239014984] ------------------------------------- >> galois(x^3+x+1); ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.609 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host kalgan.topologie.math.uni-siegen.de. (141.99.112.122) Time: Mon Apr 5 09:09:12 2004 Input: galoisgroup(x^3+x+1) Output: Magma V2.10-22 Mon Apr 5 2004 09:09:09 on modular [Seed = 655768854] ------------------------------------- >> galoisgroup(x^3+x+1); ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.599 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host kalgan.topologie.math.uni-siegen.de. (141.99.112.122) Time: Mon Apr 5 09:09:30 2004 Input: galoisgroup(x->x^3+x+1) Output: Magma V2.10-22 Mon Apr 5 2004 09:09:27 on modular [Seed = 790509036] ------------------------------------- >> galoisgroup(x->x^3+x+1); ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.569 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 72-236-ADSL.red.retevision.es. (80.224.236.72) Time: Mon Apr 5 09:14:51 2004 Input: /***************************************/ /* Practica 2 teoria de la codificacio */ /***************************************/ /* ALUMNES: */ /* JAUME PERNAS VALLES ORIOL ORELLANA QUINTILLA */ /********************/ /* 1) cossos finits */ /********************/ /* i */ Z2:=GF(2); Z3:=GF(3); Z5:=GF(5); {i:i in Z2}; {i:i in Z3}; {i:i in Z5}; primitiusG5 := [b: b in Z5 |IsPrimitive(b)]; /* ii */ /* NO HO ES PQ 9 NO ES PRIMER I PER TANT TOTS ELS ELEMENTS NO TENEN INVERS JA QUE NO TOTS SON PRIMERS AMB 9 EL 3 PER EXEMPLE NO TE INVERS A Z9 */ Z9:=GF(9); IsInvertible(Z9!3); /*false*/ /* iii */ P2:=PolynomialRing(Z2); p:=1+x+x^4; IsIrreducible(p); G16:= ext< Z2 | p >; P3:=PolynomialRing(Z3); q:=2+2*x+x^2; IsIrreducible(q); G9:= ext< Z3 | q >; qq:=1+2*x+x^2; IsIrreducible(qq); /*G9b:= ext< Z3 | qq >;*//*NO funciona perque qq no es irreductible*/ P5:=PolynomialRing(Z5); r:=3+2*x+x^2; IsIrreducible(r); G25:= ext< Z5 | r >; /* iv */ [Order(a) :a in G25 | not a eq 0 ]; primitiusG25 := [a: a in G25 | IsPrimitive(a)]; [a: a in G25 | IsPrimitive(a)]; #[a: a in G25 | IsPrimitive(a)]; /* Hi haurá tants elements com f(p^n -1) on f es la funció multiplicativa d Euler Donat que si b es primitiu b^i es primitiu sii mcd(i,p^n -1)=1 i aquests son precisament tots els que busca la fi d Euler */ /* v */ pm:=MinimalPolynomial(a); /* el grau dun element es el grau del seu polinomi minim */ /* el polinomi minim esta definit dintre de Zp */ Roots(pm,Z5); Roots(pm,G25); /* vi */ calculeu:=2*a^(-3)-a^5+((a^6)/(a+2)); IsInvertible(calculeu); /* tots perque G25 es un cos*/ /* vii */ taula25:=[ : i in [0..23]]; taula16:=[ : i in [0..14]]; /* viii */ /* Quina Estructura de Subcos hi ha entre els cossos de 2,4,8,16 elements? */ G2 := GF(2); G4 := GF(4); G8 := GF(8); G166 := GF(16); {i:i in G2}; {i:i in G4}; {i:i in G8}; {i:i in G166}; /*************************************/ /* 2) Polinomis sobre cossos Finits */ /*************************************/ /* i */ G25x:=PolynomialRing(G25); IsFinite(G25x); /* false */ /* Efectivament no es finit, pq estem definint un anell de polynomis sobre un camp de coeficients finits pero els polynomis poden tenir el grau que vulguin */ /* ii */ alpha := primitiusG25[1]; beta := primitiusG5[1]; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; /* iii */ suma := p1 + p2; producte := p1 * p2; suma; producte; /* iv */ quocient := p1 div p2; quocient; residu := p1 mod p2; residu; /* v */ mcm := LCM(p1,p2); mcm; mcd := GCD(p1,p2); mcd; /* vi */ XGCD(p1,p2); Output: Magma V2.10-22 Mon Apr 5 2004 09:14:48 on modular [Seed = 973808054] ------------------------------------- { 0, 1 } { 0, 1, 2 } { 0, 1, 2, 3, 4 } false true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ a, a^5, a^7, a^11, a^13, a^17, a^19, a^23 ] 8 [] [ , ] true a^16 >> taula16:=[ : i in [0..14]]; ^ User error: Identifier 'b' has not been declared or assigned { 0, 1 } { 1, G4.1, G4.1^2, 0 } { 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 } { 1, G166.1, G166.1^2, G166.1^3, G166.1^4, G166.1^5, G166.1^6, G166.1^7, G166.1^8, G166.1^9, G166.1^10, G166.1^11, G166.1^12, G166.1^13, G166.1^14, 0 } false 2*x^2 + a^19*x + a^9 a^19*x^3 + a^22*x^2 + a^10*x + a^2 a^17*x + a^5 a^15 x^3 + a^3*x^2 + a^15*x + a^7 1 1 a^9 a^14*x + a^2 Total time: 2.559 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 72-236-ADSL.red.retevision.es. (80.224.236.72) Time: Mon Apr 5 09:24:18 2004 Input: /***************************************/ /* Practica 2 teoria de la codificacio */ /***************************************/ /* ALUMNES: */ /* JAUME PERNAS VALLES ORIOL ORELLANA QUINTILLA */ /********************/ /* 1) cossos finits */ /********************/ /* i */ Z2:=GF(2); Z3:=GF(3); Z5:=GF(5); {i:i in Z2}; {i:i in Z3}; {i:i in Z5}; primitiusG5 := [b: b in Z5 |IsPrimitive(b)]; /* ii */ /* NO HO ES PQ 9 NO ES PRIMER I PER TANT TOTS ELS ELEMENTS NO TENEN INVERS JA QUE NO TOTS SON PRIMERS AMB 9 EL 3 PER EXEMPLE NO TE INVERS A Z9 */ Z9:=GF(9); IsInvertible(Z9!3); /*false*/ /* iii */ P2:=PolynomialRing(Z2); p:=1+x+x^4; IsIrreducible(p); G16:= ext< Z2 | p >; P3:=PolynomialRing(Z3); q:=2+2*x+x^2; IsIrreducible(q); G9:= ext< Z3 | q >; qq:=1+2*x+x^2; IsIrreducible(qq); /*G9b:= ext< Z3 | qq >;*//*NO funciona perque qq no es irreductible*/ P5:=PolynomialRing(Z5); r:=3+2*x+x^2; IsIrreducible(r); G25:= ext< Z5 | r >; /* iv */ [Order(a) :a in G25 | not a eq 0 ]; primitiusG25 := [a: a in G25 | IsPrimitive(a)]; [a: a in G25 | IsPrimitive(a)]; #[a: a in G25 | IsPrimitive(a)]; /* Hi haurá tants elements com f(p^n -1) on f es la funció multiplicativa d Euler Donat que si b es primitiu b^i es primitiu sii mcd(i,p^n -1)=1 i aquests son precisament tots els que busca la fi d Euler */ /* v */ pm:=MinimalPolynomial(a); /* el grau dun element es el grau del seu polinomi minim */ /* el polinomi minim esta definit dintre de Zp */ Roots(pm,Z5); Roots(pm,G25); /* vi */ calculeu:=2*a^(-3)-a^5+((a^6)/(a+2)); IsInvertible(calculeu); /* tots perque G25 es un cos*/ /* vii */ taula25:=[ : i in [0..23]]; taula16:=[ : i in [0..14]]; /* viii */ /* Quina Estructura de Subcos hi ha entre els cossos de 2,4,8,16 elements? */ G2 := GF(2); G4 := GF(4); G8 := GF(8); G166 := GF(16); {i:i in G2}; {i:i in G4}; {i:i in G8}; {i:i in G166}; /*************************************/ /* 2) Polinomis sobre cossos Finits */ /*************************************/ /* i */ G25x:=PolynomialRing(G25); IsFinite(G25x); /* false */ /* Efectivament no es finit, pq estem definint un anell de polynomis sobre un camp de coeficients finits pero els polynomis poden tenir el grau que vulguin */ /* ii */ alpha := primitiusG25[1]; beta := primitiusG5[1]; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; /* iii */ suma := p1 + p2; producte := p1 * p2; suma; producte; /* iv */ quocient := p1 div p2; quocient; residu := p1 mod p2; residu; /* v */ mcm := LCM(p1,p2); mcm; mcd := GCD(p1,p2); mcd; /* vi */ XGCD(p1,p2); /* Id Bezout 1 = (a^9)p1 + (a^14*x + a^2)p2 */ /* vii */ p3:= (1/alpha^4) - ((alpha^3)*x) + (alpha^5)*(x^2) + (alpha^11)*(x^3); Output: Magma V2.10-22 Mon Apr 5 2004 09:24:15 on modular [Seed = 3639199075] ------------------------------------- { 0, 1 } { 0, 1, 2 } { 0, 1, 2, 3, 4 } false true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ a, a^5, a^7, a^11, a^13, a^17, a^19, a^23 ] 8 [] [ , ] true a^16 >> taula16:=[ : i in [0..14]]; ^ User error: Identifier 'b' has not been declared or assigned { 0, 1 } { 1, G4.1, G4.1^2, 0 } { 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 } { 1, G166.1, G166.1^2, G166.1^3, G166.1^4, G166.1^5, G166.1^6, G166.1^7, G166.1^8, G166.1^9, G166.1^10, G166.1^11, G166.1^12, G166.1^13, G166.1^14, 0 } false 2*x^2 + a^19*x + a^9 a^19*x^3 + a^22*x^2 + a^10*x + a^2 a^17*x + a^5 a^15 x^3 + a^3*x^2 + a^15*x + a^7 1 1 a^9 a^14*x + a^2 Total time: 2.609 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 72-236-ADSL.red.retevision.es. (80.224.236.72) Time: Mon Apr 5 09:25:37 2004 Input: /***************************************/ /* Practica 2 teoria de la codificacio */ /***************************************/ /* ALUMNES: */ /* JAUME PERNAS VALLES ORIOL ORELLANA QUINTILLA */ /********************/ /* 1) cossos finits */ /********************/ /* i */ Z2:=GF(2); Z3:=GF(3); Z5:=GF(5); {i:i in Z2}; {i:i in Z3}; {i:i in Z5}; primitiusG5 := [b: b in Z5 |IsPrimitive(b)]; /* ii */ /* NO HO ES PQ 9 NO ES PRIMER I PER TANT TOTS ELS ELEMENTS NO TENEN INVERS JA QUE NO TOTS SON PRIMERS AMB 9 EL 3 PER EXEMPLE NO TE INVERS A Z9 */ Z9:=GF(9); IsInvertible(Z9!3); /*false*/ /* iii */ P2:=PolynomialRing(Z2); p:=1+x+x^4; IsIrreducible(p); G16:= ext< Z2 | p >; P3:=PolynomialRing(Z3); q:=2+2*x+x^2; IsIrreducible(q); G9:= ext< Z3 | q >; qq:=1+2*x+x^2; IsIrreducible(qq); /*G9b:= ext< Z3 | qq >;*//*NO funciona perque qq no es irreductible*/ P5:=PolynomialRing(Z5); r:=3+2*x+x^2; IsIrreducible(r); G25:= ext< Z5 | r >; /* iv */ [Order(a) :a in G25 | not a eq 0 ]; primitiusG25 := [a: a in G25 | IsPrimitive(a)]; [a: a in G25 | IsPrimitive(a)]; #[a: a in G25 | IsPrimitive(a)]; /* Hi haurá tants elements com f(p^n -1) on f es la funció multiplicativa d Euler Donat que si b es primitiu b^i es primitiu sii mcd(i,p^n -1)=1 i aquests son precisament tots els que busca la fi d Euler */ /* v */ pm:=MinimalPolynomial(a); /* el grau dun element es el grau del seu polinomi minim */ /* el polinomi minim esta definit dintre de Zp */ Roots(pm,Z5); Roots(pm,G25); /* vi */ calculeu:=2*a^(-3)-a^5+((a^6)/(a+2)); IsInvertible(calculeu); /* tots perque G25 es un cos*/ /* vii */ taula25:=[ : i in [0..23]]; taula16:=[ : i in [0..14]]; /* viii */ /* Quina Estructura de Subcos hi ha entre els cossos de 2,4,8,16 elements? */ G2 := GF(2); G4 := GF(4); G8 := GF(8); G166 := GF(16); {i:i in G2}; {i:i in G4}; {i:i in G8}; {i:i in G166}; /*************************************/ /* 2) Polinomis sobre cossos Finits */ /*************************************/ /* i */ G25x:=PolynomialRing(G25); IsFinite(G25x); /* false */ /* Efectivament no es finit, pq estem definint un anell de polynomis sobre un camp de coeficients finits pero els polynomis poden tenir el grau que vulguin */ /* ii */ alpha := primitiusG25[1]; beta := primitiusG5[1]; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; /* iii */ suma := p1 + p2; producte := p1 * p2; suma; producte; /* iv */ quocient := p1 div p2; quocient; residu := p1 mod p2; residu; /* v */ mcm := LCM(p1,p2); mcm; mcd := GCD(p1,p2); mcd; /* vi */ XGCD(p1,p2); /* Id Bezout 1 = (a^9)p1 + (a^14*x + a^2)p2 */ /* vii */ p3:= (1/alpha^4) - ((alpha^3)*x) + (alpha^5)*(x^2) + (alpha^11)*(x^3); f:=Factoritzation(p3); f; Output: Magma V2.10-22 Mon Apr 5 2004 09:25:34 on modular [Seed = 3990680551] ------------------------------------- { 0, 1 } { 0, 1, 2 } { 0, 1, 2, 3, 4 } false true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ a, a^5, a^7, a^11, a^13, a^17, a^19, a^23 ] 8 [] [ , ] true a^16 >> taula16:=[ : i in [0..14]]; ^ User error: Identifier 'b' has not been declared or assigned { 0, 1 } { 1, G4.1, G4.1^2, 0 } { 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 } { 1, G166.1, G166.1^2, G166.1^3, G166.1^4, G166.1^5, G166.1^6, G166.1^7, G166.1^8, G166.1^9, G166.1^10, G166.1^11, G166.1^12, G166.1^13, G166.1^14, 0 } false 2*x^2 + a^19*x + a^9 a^19*x^3 + a^22*x^2 + a^10*x + a^2 a^17*x + a^5 a^15 x^3 + a^3*x^2 + a^15*x + a^7 1 1 a^9 a^14*x + a^2 >> f:=Factoritzation(p3); ^ User error: Identifier 'Factoritzation' has not been declared or assigned >> f; ^ User error: Identifier 'f' has not been declared or assigned Total time: 2.529 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 72-236-ADSL.red.retevision.es. (80.224.236.72) Time: Mon Apr 5 09:26:05 2004 Input: /***************************************/ /* Practica 2 teoria de la codificacio */ /***************************************/ /* ALUMNES: */ /* JAUME PERNAS VALLES ORIOL ORELLANA QUINTILLA */ /********************/ /* 1) cossos finits */ /********************/ /* i */ Z2:=GF(2); Z3:=GF(3); Z5:=GF(5); {i:i in Z2}; {i:i in Z3}; {i:i in Z5}; primitiusG5 := [b: b in Z5 |IsPrimitive(b)]; /* ii */ /* NO HO ES PQ 9 NO ES PRIMER I PER TANT TOTS ELS ELEMENTS NO TENEN INVERS JA QUE NO TOTS SON PRIMERS AMB 9 EL 3 PER EXEMPLE NO TE INVERS A Z9 */ Z9:=GF(9); IsInvertible(Z9!3); /*false*/ /* iii */ P2:=PolynomialRing(Z2); p:=1+x+x^4; IsIrreducible(p); G16:= ext< Z2 | p >; P3:=PolynomialRing(Z3); q:=2+2*x+x^2; IsIrreducible(q); G9:= ext< Z3 | q >; qq:=1+2*x+x^2; IsIrreducible(qq); /*G9b:= ext< Z3 | qq >;*//*NO funciona perque qq no es irreductible*/ P5:=PolynomialRing(Z5); r:=3+2*x+x^2; IsIrreducible(r); G25:= ext< Z5 | r >; /* iv */ [Order(a) :a in G25 | not a eq 0 ]; primitiusG25 := [a: a in G25 | IsPrimitive(a)]; [a: a in G25 | IsPrimitive(a)]; #[a: a in G25 | IsPrimitive(a)]; /* Hi haurá tants elements com f(p^n -1) on f es la funció multiplicativa d Euler Donat que si b es primitiu b^i es primitiu sii mcd(i,p^n -1)=1 i aquests son precisament tots els que busca la fi d Euler */ /* v */ pm:=MinimalPolynomial(a); /* el grau dun element es el grau del seu polinomi minim */ /* el polinomi minim esta definit dintre de Zp */ Roots(pm,Z5); Roots(pm,G25); /* vi */ calculeu:=2*a^(-3)-a^5+((a^6)/(a+2)); IsInvertible(calculeu); /* tots perque G25 es un cos*/ /* vii */ taula25:=[ : i in [0..23]]; taula16:=[ : i in [0..14]]; /* viii */ /* Quina Estructura de Subcos hi ha entre els cossos de 2,4,8,16 elements? */ G2 := GF(2); G4 := GF(4); G8 := GF(8); G166 := GF(16); {i:i in G2}; {i:i in G4}; {i:i in G8}; {i:i in G166}; /*************************************/ /* 2) Polinomis sobre cossos Finits */ /*************************************/ /* i */ G25x:=PolynomialRing(G25); IsFinite(G25x); /* false */ /* Efectivament no es finit, pq estem definint un anell de polynomis sobre un camp de coeficients finits pero els polynomis poden tenir el grau que vulguin */ /* ii */ alpha := primitiusG25[1]; beta := primitiusG5[1]; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; /* iii */ suma := p1 + p2; producte := p1 * p2; suma; producte; /* iv */ quocient := p1 div p2; quocient; residu := p1 mod p2; residu; /* v */ mcm := LCM(p1,p2); mcm; mcd := GCD(p1,p2); mcd; /* vi */ XGCD(p1,p2); /* Id Bezout 1 = (a^9)p1 + (a^14*x + a^2)p2 */ /* vii */ p3:= (1/alpha^4) - ((alpha^3)*x) + (alpha^5)*(x^2) + (alpha^11)*(x^3); f:=Factorization(p3); f; Output: Magma V2.10-22 Mon Apr 5 2004 09:26:03 on modular [Seed = 4123323354] ------------------------------------- { 0, 1 } { 0, 1, 2 } { 0, 1, 2, 3, 4 } false true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ a, a^5, a^7, a^11, a^13, a^17, a^19, a^23 ] 8 [] [ , ] true a^16 >> taula16:=[ : i in [0..14]]; ^ User error: Identifier 'b' has not been declared or assigned { 0, 1 } { 1, G4.1, G4.1^2, 0 } { 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 } { 1, G166.1, G166.1^2, G166.1^3, G166.1^4, G166.1^5, G166.1^6, G166.1^7, G166.1^8, G166.1^9, G166.1^10, G166.1^11, G166.1^12, G166.1^13, G166.1^14, 0 } false 2*x^2 + a^19*x + a^9 a^19*x^3 + a^22*x^2 + a^10*x + a^2 a^17*x + a^5 a^15 x^3 + a^3*x^2 + a^15*x + a^7 1 1 a^9 a^14*x + a^2 [ , ] Total time: 2.529 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 72-236-ADSL.red.retevision.es. (80.224.236.72) Time: Mon Apr 5 09:27:29 2004 Input: /***************************************/ /* Practica 2 teoria de la codificacio */ /***************************************/ /* ALUMNES: */ /* JAUME PERNAS VALLES ORIOL ORELLANA QUINTILLA */ /********************/ /* 1) cossos finits */ /********************/ /* i */ Z2:=GF(2); Z3:=GF(3); Z5:=GF(5); {i:i in Z2}; {i:i in Z3}; {i:i in Z5}; primitiusG5 := [b: b in Z5 |IsPrimitive(b)]; /* ii */ /* NO HO ES PQ 9 NO ES PRIMER I PER TANT TOTS ELS ELEMENTS NO TENEN INVERS JA QUE NO TOTS SON PRIMERS AMB 9 EL 3 PER EXEMPLE NO TE INVERS A Z9 */ Z9:=GF(9); IsInvertible(Z9!3); /*false*/ /* iii */ P2:=PolynomialRing(Z2); p:=1+x+x^4; IsIrreducible(p); G16:= ext< Z2 | p >; P3:=PolynomialRing(Z3); q:=2+2*x+x^2; IsIrreducible(q); G9:= ext< Z3 | q >; qq:=1+2*x+x^2; IsIrreducible(qq); /*G9b:= ext< Z3 | qq >;*//*NO funciona perque qq no es irreductible*/ P5:=PolynomialRing(Z5); r:=3+2*x+x^2; IsIrreducible(r); G25:= ext< Z5 | r >; /* iv */ [Order(a) :a in G25 | not a eq 0 ]; primitiusG25 := [a: a in G25 | IsPrimitive(a)]; [a: a in G25 | IsPrimitive(a)]; #[a: a in G25 | IsPrimitive(a)]; /* Hi haurá tants elements com f(p^n -1) on f es la funció multiplicativa d Euler Donat que si b es primitiu b^i es primitiu sii mcd(i,p^n -1)=1 i aquests son precisament tots els que busca la fi d Euler */ /* v */ pm:=MinimalPolynomial(a); /* el grau dun element es el grau del seu polinomi minim */ /* el polinomi minim esta definit dintre de Zp */ Roots(pm,Z5); Roots(pm,G25); /* vi */ calculeu:=2*a^(-3)-a^5+((a^6)/(a+2)); IsInvertible(calculeu); /* tots perque G25 es un cos*/ /* vii */ taula25:=[ : i in [0..23]]; taula16:=[ : i in [0..14]]; /* viii */ /* Quina Estructura de Subcos hi ha entre els cossos de 2,4,8,16 elements? */ G2 := GF(2); G4 := GF(4); G8 := GF(8); G166 := GF(16); {i:i in G2}; {i:i in G4}; {i:i in G8}; {i:i in G166}; /*************************************/ /* 2) Polinomis sobre cossos Finits */ /*************************************/ /* i */ G25x:=PolynomialRing(G25); IsFinite(G25x); /* false */ /* Efectivament no es finit, pq estem definint un anell de polynomis sobre un camp de coeficients finits pero els polynomis poden tenir el grau que vulguin */ /* ii */ alpha := primitiusG25[1]; beta := primitiusG5[1]; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; /* iii */ suma := p1 + p2; producte := p1 * p2; suma; producte; /* iv */ quocient := p1 div p2; quocient; residu := p1 mod p2; residu; /* v */ mcm := LCM(p1,p2); mcm; mcd := GCD(p1,p2); mcd; /* vi */ XGCD(p1,p2); /* Id Bezout 1 = (a^9)p1 + (a^14*x + a^2)p2 */ /* vii */ p3:= (1/alpha^4) - ((alpha^3)*x) + (alpha^5)*(x^2) + (alpha^11)*(x^3); f:=Factorization(p3); f; Evaluate(p3,f[1]); Output: Magma V2.10-22 Mon Apr 5 2004 09:27:26 on modular [Seed = 4275036164] ------------------------------------- { 0, 1 } { 0, 1, 2 } { 0, 1, 2, 3, 4 } false true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ a, a^5, a^7, a^11, a^13, a^17, a^19, a^23 ] 8 [] [ , ] true a^16 >> taula16:=[ : i in [0..14]]; ^ User error: Identifier 'b' has not been declared or assigned { 0, 1 } { 1, G4.1, G4.1^2, 0 } { 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 } { 1, G166.1, G166.1^2, G166.1^3, G166.1^4, G166.1^5, G166.1^6, G166.1^7, G166.1^8, G166.1^9, G166.1^10, G166.1^11, G166.1^12, G166.1^13, G166.1^14, 0 } false 2*x^2 + a^19*x + a^9 a^19*x^3 + a^22*x^2 + a^10*x + a^2 a^17*x + a^5 a^15 x^3 + a^3*x^2 + a^15*x + a^7 1 1 a^9 a^14*x + a^2 [ , ] >> Evaluate(p3,f[1]);; ^ Runtime error in 'Evaluate': Bad argument types Argument types given: RngUPolElt, Tup Total time: 2.529 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host reached (203.255.11.105) Time: Mon Apr 5 09:29:20 2004 Input: 2+3 Output: Magma V2.10-22 Mon Apr 5 2004 09:29:03 on modular [Seed = 2159124443] ------------------------------------- 5 Total time: 2.499 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host reached (203.255.11.105) Time: Mon Apr 5 09:47:21 2004 Input: Factorization(x^8-1); Output: Magma V2.10-22 Mon Apr 5 2004 09:47:04 on modular [Seed = 2994966958] ------------------------------------- >> Factorization(x^8-1); ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.580 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host reached (203.255.11.105) Time: Mon Apr 5 09:48:47 2004 Input: P :=PolynomialRing(IntegerRing()); Factorization(x^8-1); Output: Magma V2.10-22 Mon Apr 5 2004 09:48:30 on modular [Seed = 1165256366] ------------------------------------- [ , , , ] Total time: 2.649 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host reached (203.255.11.105) Time: Mon Apr 5 09:50:02 2004 Input: P :=PolynomialRing(IntegerRing()); Factorization(x^8-1); Factorial(5); Output: Magma V2.10-22 Mon Apr 5 2004 09:49:45 on modular [Seed = 1232628470] ------------------------------------- [ , , , ] 120 Total time: 2.589 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host kalgan.topologie.math.uni-siegen.de. (141.99.112.122) Time: Mon Apr 5 11:10:42 2004 Input: polgalois(x^3+x+1) Output: Magma V2.10-22 Mon Apr 5 2004 11:10:40 on modular [Seed = 1533701612] ------------------------------------- >> polgalois(x^3+x+1); ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.589 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host kalgan.topologie.math.uni-siegen.de. (141.99.112.122) Time: Mon Apr 5 11:12:09 2004 Input: f := x^3 - x - 1; GaloisGroup(f); Output: Magma V2.10-22 Mon Apr 5 2004 11:12:06 on modular [Seed = 1615943521] ------------------------------------- >> f := x^3 - x - 1; ^ User error: Identifier 'x' has not been declared or assigned >> GaloisGroup(f);; ^ User error: Identifier 'f' has not been declared or assigned Total time: 2.519 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host kalgan.topologie.math.uni-siegen.de. (141.99.112.122) Time: Mon Apr 5 11:12:40 2004 Input: R := PolynomialRing(RationalField()); f := x^3 - x - 1; GaloisGroup(f); Output: Magma V2.10-22 Mon Apr 5 2004 11:12:37 on modular [Seed = 1917011280] ------------------------------------- Permutation group acting on a set of cardinality 3 (1, 3) (1, 2) [ 2, 3*w + 4, 2*w + 4 ] 5 Total time: 2.569 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host kalgan.topologie.math.uni-siegen.de. (141.99.112.122) Time: Mon Apr 5 11:15:42 2004 Input: R := PolynomialRing(RationalField()); f := x^3 - x - 1; GaloisGroup(f); ?GaloisGroup Output: Magma V2.10-22 Mon Apr 5 2004 11:15:39 on modular [Seed = 53623647] ------------------------------------- Permutation group acting on a set of cardinality 3 (1, 3) (1, 2) [ 2, 2*w + 4, 3*w + 4 ] 5 2 matches: 1 I /magma/ring-field-algebra/algebraic-field/galois/GaloisGroup 2 I /magma/ring-field-algebra/function-field/structure-invar/galois/\ GaloisGroup To view an entry, type ? followed by the number next to it Total time: 2.579 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host kalgan.topologie.math.uni-siegen.de. (141.99.112.122) Time: Mon Apr 5 11:16:01 2004 Input: R := PolynomialRing(RationalField()); f := x^3 - x - 1; GaloisGroup(f); ?GaloisGroup ?2 Output: Magma V2.10-22 Mon Apr 5 2004 11:15:59 on modular [Seed = 171651682] ------------------------------------- Permutation group acting on a set of cardinality 3 (1, 3) (1, 2) [ 2, 3*w + 4, 2*w + 4 ] 5 2 matches: 1 I /magma/ring-field-algebra/algebraic-field/galois/GaloisGroup 2 I /magma/ring-field-algebra/function-field/structure-invar/galois/\ GaloisGroup To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/ring-field-algebra/function-field/structure-invar/galois/\ GaloisGroup KIND: Intrinsic =============================================================================== GaloisGroup(f) : RngUPolElt -> GrpPerm, [ FldPrElt ], Any SetVerbose("GaloisGroup", n): Maximum: 5 Given a separable, irreducible polynomial f(t, x) of degree n over the rational function field k(t), K in {Q, F_q}, q != 2, this function returns a permutation group that forms the Galois group of the normal closure of F=k[t][x]/f(t, x)k[t][x] in some algebraic closure of k(t). The permutation group acts on the points 1, 2, ..., n. The roots of f are calculated in the process, expressed as power series and returned as the second argument: For a prime polynomial p(t) in k(t) denote by bar(N) the splitting field of the polynomial f(t, x) mod p(t). It is well known that the roots of the polynomial f(t, x) can be expressed as power series in bar(N)[[t]]. In the case k=Q we embed bar(N) in an unramified p-adic extension, in the case k=F_q the splitting field is easily computed. The prime polynomial, which is used for the series computations is returned as a third argument. Currently this function is restricted to polynomials of degree n le23. The required precision increases linearly with the index of the subgroups, which are passed traversing the subgroup lattice. Therefore computations may slow down considerably for higher degrees and large indices. The default version employs series computations over either unramified p-adic fields (k=Q) or finite fields (k=F_q) and returns proven results. The prime polynomial is determined during a Galois group computation in such a way that f is squarefree modulo p. There are no optional parameters. =============================================================================== Total time: 2.529 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host kalgan.topologie.math.uni-siegen.de. (141.99.112.122) Time: Mon Apr 5 11:16:55 2004 Input: R := PolynomialRing(RationalField()); f := x^5 - x - 1; GaloisGroup(f); ?GaloisGroup ?2 Output: Magma V2.10-22 Mon Apr 5 2004 11:16:53 on modular [Seed = 287320371] ------------------------------------- Permutation group acting on a set of cardinality 5 (1, 2, 3, 4, 5) (1, 2) [ 8, 6, w^2519, w^3527, w^1015 ] 17 2 matches: 1 I /magma/ring-field-algebra/algebraic-field/galois/GaloisGroup 2 I /magma/ring-field-algebra/function-field/structure-invar/galois/\ GaloisGroup To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/ring-field-algebra/function-field/structure-invar/galois/\ GaloisGroup KIND: Intrinsic =============================================================================== GaloisGroup(f) : RngUPolElt -> GrpPerm, [ FldPrElt ], Any SetVerbose("GaloisGroup", n): Maximum: 5 Given a separable, irreducible polynomial f(t, x) of degree n over the rational function field k(t), K in {Q, F_q}, q != 2, this function returns a permutation group that forms the Galois group of the normal closure of F=k[t][x]/f(t, x)k[t][x] in some algebraic closure of k(t). The permutation group acts on the points 1, 2, ..., n. The roots of f are calculated in the process, expressed as power series and returned as the second argument: For a prime polynomial p(t) in k(t) denote by bar(N) the splitting field of the polynomial f(t, x) mod p(t). It is well known that the roots of the polynomial f(t, x) can be expressed as power series in bar(N)[[t]]. In the case k=Q we embed bar(N) in an unramified p-adic extension, in the case k=F_q the splitting field is easily computed. The prime polynomial, which is used for the series computations is returned as a third argument. Currently this function is restricted to polynomials of degree n le23. The required precision increases linearly with the index of the subgroups, which are passed traversing the subgroup lattice. Therefore computations may slow down considerably for higher degrees and large indices. The default version employs series computations over either unramified p-adic fields (k=Q) or finite fields (k=F_q) and returns proven results. The prime polynomial is determined during a Galois group computation in such a way that f is squarefree modulo p. There are no optional parameters. =============================================================================== Total time: 2.579 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Apr 5 14:22:51 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^3-2); OK:=MaximalOrder(K); Factorization(2*OK); Output: Magma V2.10-22 Mon Apr 5 2004 14:22:48 on modular [Seed = 2327537976] ------------------------------------- [ ] Total time: 2.520 seconds, Total memory usage: 1.86MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Apr 5 14:23:42 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^3-2); OK:=MaximalOrder(K); Factorization(2*OK); Factorization(3*OK); Factorization(5*OK); Factorization(7*OK); Factorization(11*OK); Factorization(13*OK); Factorization(17*OK); Factorization(19*OK); Factorization(23*OK); Factorization(29*OK); Output: Magma V2.10-22 Mon Apr 5 2004 14:23:39 on modular [Seed = 2192795363] ------------------------------------- [ ] [ ] [ , ] [ ] [ , ] [ ] [ , ] [ ] [ , ] [ , ] Total time: 2.580 seconds, Total memory usage: 1.87MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Apr 5 14:25:56 2004 Input: R:=PolynomialRing(Rationals()); K:=SplittingField(x^3-2); OK:=MaximalOrder(K); OK: Output: Magma V2.10-22 Mon Apr 5 2004 14:25:53 on modular [Seed = 2679012196] ------------------------------------- >> OK:; ^ User error: bad syntax Total time: 2.840 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Apr 5 14:26:05 2004 Input: R:=PolynomialRing(Rationals()); K:=SplittingField(x^3-2); OK:=MaximalOrder(K); OK; Output: Magma V2.10-22 Mon Apr 5 2004 14:26:02 on modular [Seed = 2544268135] ------------------------------------- Maximal Equation Order with defining polynomial x^6 - 3*x^5 + 5*x^3 - 3*x + 1 over its ground order Total time: 2.809 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Apr 5 14:26:14 2004 Input: R:=PolynomialRing(Rationals()); K:=SplittingField(x^3-2); OK:=MaximalOrder(K); Factorization(2*OK); Factorization(3*OK); Factorization(5*OK); Factorization(7*OK); Factorization(11*OK); Factorization(13*OK); Factorization(17*OK); Factorization(19*OK); Factorization(23*OK); Factorization(29*OK); Output: Magma V2.10-22 Mon Apr 5 2004 14:26:11 on modular [Seed = 2946386726] ------------------------------------- [ ] [ ] [ , , ] [ , ] [ , , ] [ , ] [ , , ] [ , ] [ , , ] [ , , ] Total time: 2.799 seconds, Total memory usage: 1.91MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Apr 5 14:27:21 2004 Input: R:=PolynomialRing(Rationals()); K:=SplittingField(x^3-2); OK:=MaximalOrder(K); Factorization(31*OK); Factorization(37*OK); Factorization(41*OK); Factorization(43*OK); Factorization(47*OK); Factorization(53*OK); Output: Magma V2.10-22 Mon Apr 5 2004 14:27:18 on modular [Seed = 2811642603] ------------------------------------- [ , , , , , ] [ , ] [ , , ] [ , , , , , ] [ , , ] [ , , ] Total time: 2.780 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Apr 5 14:28:50 2004 Input: R:=PolynomialRing(Rationals()); K:=SplittingField(x^3-2); OK:=MaximalOrder(K); Factorization(2*OK); Factorization(3*OK); Factorization(5*OK); Factorization(7*OK); Factorization(11*OK); Factorization(13*OK); Output: Magma V2.10-22 Mon Apr 5 2004 14:28:47 on modular [Seed = 3011663526] ------------------------------------- [ ] [ ] [ , , ] [ , ] [ , , ] [ , ] Total time: 2.909 seconds, Total memory usage: 1.91MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Apr 5 18:34:51 2004 Input: R:=PolynomialRing(Rationals()); K:=SplittingField(x^3-2); K; OK:=MaximalOrder(K); OK; [K!OK.i : i in [1..6]]; Factorization(2*OK); Factorization(3*OK); Factorization(5*OK); Factorization(7*OK); Factorization(11*OK); Factorization(13*OK); Output: Magma V2.10-22 Mon Apr 5 2004 18:34:48 on modular [Seed = 3554823318] ------------------------------------- Number Field with defining polynomial x^6 - 3*x^5 + 5*x^3 - 3*x + 1 over the Rational Field Maximal Equation Order with defining polynomial x^6 - 3*x^5 + 5*x^3 - 3*x + 1 over its ground order [ 1, a, a^2, a^3, a^4, a^5 ] [ ] [ ] [ , , ] [ , ] [ , , ] [ , ] Total time: 2.809 seconds, Total memory usage: 1.91MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Apr 5 18:41:29 2004 Input: Q:=Rationals(); Q; Output: Magma V2.10-22 Mon Apr 5 2004 18:41:26 on modular [Seed = 2693857403] ------------------------------------- Rational Field Total time: 2.630 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Apr 5 18:42:14 2004 Input: Q:=Rationals(); Q; R:=PolynomialRing(Q); K:=NumberField(x^3-2); Output: Magma V2.10-22 Mon Apr 5 2004 18:42:11 on modular [Seed = 3095992374] ------------------------------------- Rational Field Total time: 2.509 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Apr 5 18:42:56 2004 Input: Q:=Rationals(); R:=PolynomialRing(Q); K:=NumberField(x^3-2); OK:=MaximalOrder(K); Q!OK.1; Q!OK.2; Output: Magma V2.10-22 Mon Apr 5 2004 18:42:54 on modular [Seed = 2961248275] ------------------------------------- 1 >> Q!OK.2;; ^ Runtime error in '!': Illegal coercion LHS: FldRat RHS: FldOrdElt Total time: 2.580 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Apr 5 18:43:33 2004 Input: Q:=Rationals(); R:=PolynomialRing(Q); K:=NumberField(x^3-2); OK:=MaximalOrder(K); Q!OK.1; Q!K.2; Output: Magma V2.10-22 Mon Apr 5 2004 18:43:31 on modular [Seed = 1266346518] ------------------------------------- 1 >> Q!K.2;; ^ Runtime error in '.': Value for name index (2) should be in the range [1..1] Total time: 2.560 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Apr 5 18:43:47 2004 Input: Q:=Rationals(); R:=PolynomialRing(Q); K:=NumberField(x^3-2); OK:=MaximalOrder(K); Q!OK.1; Q!K.1; Output: Magma V2.10-22 Mon Apr 5 2004 18:43:44 on modular [Seed = 1131602477] ------------------------------------- 1 >> Q!K.1;; ^ Runtime error in '!': Illegal coercion LHS: FldRat RHS: FldNumElt Total time: 2.559 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Apr 5 19:09:36 2004 Input: R:=PolynomialRing(Rationals()); K:=SplittingField(x^3-2); K; OK:=MaximalOrder(K); OK; [K!OK.i : i in [1..6]]; Factorization(2*OK); Factorization(3*OK); Factorization(5*OK); Factorization(7*OK); Factorization(11*OK); Factorization(13*OK); Output: Magma V2.10-22 Mon Apr 5 2004 19:09:33 on modular [Seed = 3254115] ------------------------------------- Number Field with defining polynomial x^6 - 3*x^5 + 5*x^3 - 3*x + 1 over the Rational Field Maximal Equation Order with defining polynomial x^6 - 3*x^5 + 5*x^3 - 3*x + 1 over its ground order [ 1, a, a^2, a^3, a^4, a^5 ] [ ] [ ] [ , , ] [ , ] [ , , ] [ , ] Total time: 2.820 seconds, Total memory usage: 1.91MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Apr 5 19:09:39 2004 Input: R:=PolynomialRing(Rationals()); K:=SplittingField(x^3-2); OK:=MaximalOrder(K); Factorization(2*OK); Factorization(3*OK); Factorization(5*OK); Factorization(7*OK); Factorization(11*OK); Factorization(13*OK); Output: Magma V2.10-22 Mon Apr 5 2004 19:09:36 on modular [Seed = 506444128] ------------------------------------- [ ] [ ] [ , , ] [ , ] [ , , ] [ , ] Total time: 2.849 seconds, Total memory usage: 1.91MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Apr 5 19:09:43 2004 Input: R:=PolynomialRing(Rationals()); K:=SplittingField(x^3-2); K; OK:=MaximalOrder(K); OK; [K!OK.i : i in [1..6]]; Factorization(2*OK); Factorization(3*OK); Factorization(5*OK); Factorization(7*OK); Factorization(11*OK); Factorization(13*OK); Output: Magma V2.10-22 Mon Apr 5 2004 19:09:40 on modular [Seed = 304330088] ------------------------------------- Number Field with defining polynomial x^6 - 3*x^5 + 5*x^3 - 3*x + 1 over the Rational Field Maximal Equation Order with defining polynomial x^6 - 3*x^5 + 5*x^3 - 3*x + 1 over its ground order [ 1, a, a^2, a^3, a^4, a^5 ] [ ] [ ] [ , , ] [ , ] [ , , ] [ , ] Total time: 2.870 seconds, Total memory usage: 1.91MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Apr 5 19:10:32 2004 Input: R:=PolynomialRing(Rationals()); K:=SplittingField([x^2-2, x^2-3, x^2-5, x^2-7]); K; Output: Magma V2.10-22 Mon Apr 5 2004 19:10:29 on modular [Seed = 605389583] ------------------------------------- >> K:=SplittingField([x^2-2, x^2-3, x^2-5, x^2-7]); ^ Runtime error in 'SplittingField': Bad argument types Argument types given: SeqEnum[RngUPolElt] >> K;; ^ User error: Identifier 'K' has not been declared or assigned Total time: 2.549 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Apr 5 19:10:44 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2-2, x^2-3, x^2-5, x^2-7]); K; Output: Magma V2.10-22 Mon Apr 5 2004 19:10:41 on modular [Seed = 1007524611] ------------------------------------- Number Field with defining polynomial $.1^2 - 2 over its ground field Total time: 2.579 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Apr 5 19:11:14 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2-2, x^2-3, x^2-5, x^2-7]); K; Output: Magma V2.10-22 Mon Apr 5 2004 19:11:11 on modular [Seed = 872780789] ------------------------------------- Number Field with defining polynomial $.1^2 - 2 over its ground field Total time: 2.580 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Apr 5 19:12:29 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2-2, x^2-3]); K; Output: Magma V2.10-22 Mon Apr 5 2004 19:12:26 on modular [Seed = 3439160152] ------------------------------------- Number Field with defining polynomial $.1^2 - 2 over its ground field Total time: 2.559 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Apr 5 19:12:35 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2-2, x^2-3]); K; Output: Magma V2.10-22 Mon Apr 5 2004 19:12:32 on modular [Seed = 3304416106] ------------------------------------- Number Field with defining polynomial $.1^2 - 2 over its ground field Total time: 2.579 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Apr 5 19:13:14 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2+5, x^2+10]); OK:=MaximalOrder(K); Output: Magma V2.10-22 Mon Apr 5 2004 19:13:11 on modular [Seed = 3756947350] ------------------------------------- Total time: 2.999 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Apr 5 19:13:23 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2+5, x^2+10]); OK:=MaximalOrder(K); K; OK; Output: Magma V2.10-22 Mon Apr 5 2004 19:13:20 on modular [Seed = 3622207369] ------------------------------------- Number Field with defining polynomial $.1^2 + 5 over its ground field Maximal Order of Equation Order with defining polynomial x^2 + [5, 0] over its ground order Total time: 3.029 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam169-183.student.harvard.edu. (140.247.169.183) Time: Mon Apr 5 19:15:17 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-2, x^2-3, x^2-5, x^2-7]); OK:=MaximalOrder(K); Factorization(11*OK); Output: Magma V2.10-22 Mon Apr 5 2004 19:14:54 on modular [Seed = 3973924044] ------------------------------------- ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Mon Apr 5 22:14:00 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=64; m2 :=m div 2; > ((-1 + m)*(tx - ty - tz)^(m2)*(tx + ty - tz)^(-1 + m2) + (tx + ty - tz)^(-1 + m) + (-1 + m)*(tx - ty + tz)^(m2)*(tx + ty + tz)^(-1 + m2) + (tx + ty + tz)^(-1 + m)) div (2*m) in I Output: Magma V2.10-22 Mon Apr 5 2004 22:13:55 on modular [Seed = 1834958686] ------------------------------------- false Total time: 4.569 seconds, Total memory usage: 9.18MB ************** MAGMA ***************** Host pi.wien.rhno.columbia.edu. (160.39.208.120) Time: Mon Apr 5 22:16:21 2004 Input: A := AlgebraicClosure(); x := Sqrt(A!2) + Sqrt(A!-3); y := Sqrt(A ! (-1 + 2*Sqrt(A!-6))); A; [ r4^2 - 2*r3 + 1, r3^2 + 6, r2^2 + 3, r1^2 - 2 ] x; Output: Magma V2.10-22 Mon Apr 5 2004 22:16:19 on modular [Seed = 438847673] ------------------------------------- Algebraically closed field with 4 variables Defining relations: [ r4^2 - 2*r3 + 1, r3^2 + 6, r2^2 + 3, r1^2 - 2 ] >> x;; ^ User error: bad syntax Total time: 2.579 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pi.wien.rhno.columbia.edu. (160.39.208.120) Time: Mon Apr 5 22:16:50 2004 Input: A := AlgebraicClosure(); x := Sqrt(A!2) + Sqrt(A!-3); y := Sqrt(A ! (-1 + 2*Sqrt(A!-6))); A; Output: Magma V2.10-22 Mon Apr 5 2004 22:16:48 on modular [Seed = 36720962] ------------------------------------- Algebraically closed field with 4 variables Defining relations: [ r4^2 - 2*r3 + 1, r3^2 + 6, r2^2 + 3, r1^2 - 2 ] Total time: 2.619 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pi.wien.rhno.columbia.edu. (160.39.208.120) Time: Mon Apr 5 22:17:30 2004 Input: A := AlgebraicClosure(); x := Sqrt(A!2) + Sqrt(A!-3); y := Sqrt(A ! (-1 + 2*Sqrt(A!-6))); A; x; Output: Magma V2.10-22 Mon Apr 5 2004 22:17:27 on modular [Seed = 188307564] ------------------------------------- Algebraically closed field with 4 variables Defining relations: [ r4^2 - 2*r3 + 1, r3^2 + 6, r2^2 + 3, r1^2 - 2 ] r2 + r1 Total time: 2.559 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pi.wien.rhno.columbia.edu. (160.39.208.120) Time: Mon Apr 5 22:18:48 2004 Input: A := AlgebraicClosure(); x := Sqrt(A!2) + Sqrt(A!-3); y := Sqrt(A ! (-1 + 2*Sqrt(A!-6))); A; x; y; Output: Magma V2.10-22 Mon Apr 5 2004 22:18:45 on modular [Seed = 872835041] ------------------------------------- Algebraically closed field with 4 variables Defining relations: [ r4^2 - 2*r3 + 1, r3^2 + 6, r2^2 + 3, r1^2 - 2 ] r2 + r1 r4 Total time: 2.549 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pi.wien.rhno.columbia.edu. (160.39.208.120) Time: Mon Apr 5 22:19:19 2004 Input: A := AlgebraicClosure(); x := Sqrt(A!2) + Sqrt(A!-3); y := Sqrt(A ! (-1 + 2*Sqrt(A!-6))); A; x; y; Output: Magma V2.10-22 Mon Apr 5 2004 22:19:16 on modular [Seed = 1024421577] ------------------------------------- Algebraically closed field with 4 variables Defining relations: [ r4^2 - 2*r3 + 1, r3^2 + 6, r2^2 + 3, r1^2 - 2 ] r2 + r1 r4 Total time: 2.509 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pi.wien.rhno.columbia.edu. (160.39.208.120) Time: Mon Apr 5 22:19:41 2004 Input: A := AlgebraicClosure(); x := Cubert(A!2); A; Output: Magma V2.10-22 Mon Apr 5 2004 22:19:39 on modular [Seed = 622294734] ------------------------------------- >> x := Cubert(A!2); ^ User error: Identifier 'Cubert' has not been declared or assigned Algebraically closed field with no variables Total time: 2.529 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pi.wien.rhno.columbia.edu. (160.39.208.120) Time: Mon Apr 5 22:21:42 2004 Input: A := AlgebraicClosure(); x := Sqrt(A!2); A; Output: Magma V2.10-22 Mon Apr 5 2004 22:21:39 on modular [Seed = 3588719030] ------------------------------------- Algebraically closed field with 1 variable Defining relations: [ r1^2 - 2 ] Total time: 2.499 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Mon Apr 5 22:22:35 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=64; m2 :=m div 2; > ((-1 + m)*(tx - ty - tz)^(m2)*(tx + ty - tz)^(-1 + m2) + (tx + ty - tz)^(-1 + m) + (-1 + m)*(tx - ty + tz)^(m2)*(tx + ty + tz)^(-1 + m2) + (tx + ty + tz)^(-1 + m)) div (2*m) in I Output: Magma V2.10-22 Mon Apr 5 2004 22:22:31 on modular [Seed = 3723463146] ------------------------------------- false Total time: 4.629 seconds, Total memory usage: 9.18MB ************** MAGMA ***************** Host cs662550-194.houston.rr.com. (66.25.50.194) Time: Mon Apr 5 22:29:42 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=64; m2 :=m div 2; Output: Magma V2.10-22 Mon Apr 5 2004 22:29:39 on modular [Seed = 3472660621] ------------------------------------- Total time: 2.589 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host cs662550-194.houston.rr.com. (66.25.50.194) Time: Mon Apr 5 22:29:45 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=64; m2 :=m div 2; Output: Magma V2.10-22 Mon Apr 5 2004 22:29:42 on modular [Seed = 4123501491] ------------------------------------- Total time: 2.540 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host cs662550-194.houston.rr.com. (66.25.50.194) Time: Mon Apr 5 22:30:29 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=64; m2 :=m div 2; ((-1 + m)*(tx - ty - tz)^(m2)*(tx + ty - tz)^(-1 + m2) + (tx + ty - tz)^(-1 + m) + (-1 + m)*(tx - ty + tz)^(m2)*(tx + ty + tz)^(-1 + m2) + (tx + ty + tz)^(-1 + m)) div (2*m) in I Output: Magma V2.10-22 Mon Apr 5 2004 22:30:24 on modular [Seed = 3839275764] ------------------------------------- false Total time: 4.589 seconds, Total memory usage: 9.18MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Mon Apr 5 22:32:49 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=64; m2 :=m div 2; > ((-1 + m)*(tx - ty - tz)^(m div 2)*(tx + ty - tz)^(-1 + (m div 2)) + (tx + ty - tz)^(-1 + m) + (-1 + m)*(tx - ty + tz)^(m div 2)*(tx + ty + tz)^(-1 + (m div 2)) + (tx + ty + tz)^(-1 + m)) dic (2*m) Output: Magma V2.10-22 Mon Apr 5 2004 22:32:47 on modular [Seed = 3990862706] ------------------------------------- >> + (m div 2)) + (tx + ty + tz)^(-1 + m)) dic (2*m); ^ User error: bad syntax Total time: 2.559 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Mon Apr 5 22:33:13 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=64; m2 :=m div 2; > ((-1 + m)*(tx - ty - tz)^(m div 2)*(tx + ty - tz)^(-1 + (m div 2)) + (tx + ty - tz)^(-1 + m) + (-1 + m)*(tx - ty + tz)^(m div 2)*(tx + ty + tz)^(-1 + (m div 2)) + (tx + ty + tz)^(-1 + m)) div (2*m) Output: Magma V2.10-22 Mon Apr 5 2004 22:33:09 on modular [Seed = 2510799648] ------------------------------------- 329823842388297603127136803999476682470817199986161913402815245153916577027313*\ x^63 + 47593117239755203432393494543168125339747338681251707861974035636916\ 845959936139*x^60*z^2 + 117999464230798025038992135230995352082018195077483\ 5732115058734799591222147177*x^60 + 564585018236311726992118905855229722167\ 590978473672220715574344320288074622771845*x^59*z^4 + 251963561857527547583259676993243016504544734194861982798686071018971537434\ 956030*x^59*z^2 + 312351522963877125103214475611458284922989339910985929089\ 2802533293035588036645*x^59 + 557942841551178647851035154021638784259736966\ 9622172534130381755635788031566215880*x^58*z^4 + 829997615530678980274267171271859348485559124406604178630965881003670946844\ 561040*x^58*z^2 + 617353598328604200204000375326176374906614224765242777494\ 1068536390940926943016*x^58 + 255924370065762859517553249079990914244106799\ 61704841074854260889576444709497845128*x^57*z^6 + 285535454205603190370823872940485730768218330151252359099613654553125622791\ 91810680*x^57*z^4 + 2123817427975560920113565997077993038771871877158075398\ 261589166097628599278729720*x^57*z^2 + 105313260891350128270094181673288911013481250107012003219582933856080756989\ 02792*x^57 + 25863953407591433523302308922254123801917557973903600418190424\ 7918713208561007109219*x^56*z^6 + 96188256474513595747818504256316989345974\ 389159145621389964389721835490787151404255*x^56*z^4 + 429269904927581336395223076846373340882860910297013516946948516113976570455\ 0558537*x^56*z^2 + 15204364991531806483892198707663754694788461993991033658\ 097350039456076875621813*x^56 + 6136349730036398933959959567828919568690244\ 14674967774627655176434594083056507063049*x^55*z^8 + 127798358013981200938670232321726258785945580576935437360470334265717114818\ 3799833788*x^55*z^6 + 23764157481938653067108101051560667956064260851083035\ 8728147315783358271356491704630*x^55*z^4 + 707032784586604554062720361864614914395300322842139910265562261834784939573\ 0331708*x^55*z^2 + 18781862636598113891866833697702285211209276580812453342\ 355550048739859669885769*x^55 + 5952323394105631453686577189329675571280010\ 114945431096206628212286922630341774339640*x^54*z^8 + 413219144714771109181547507358423758667372603021005133951534520522397934668\ 3545822560*x^54*z^6 + 46102962426854627883891664044121659024872149923831151\ 3086422812153088604795271641360*x^54*z^4 + 979755990181090084899704784880979766762336125890154337137616365850719585161\ 1439840*x^54*z^2 + 20242892359113431506192247621507846420709424088639552420\ 198685244849578205808760*x^54 + 8473307419844487128189127528339891107351543\ 810687025442835317808079031038486525824664*x^53*z^10 + 283610702895621263381536913138649247808047540770929363995727579526612195916\ 28454206520*x^53*z^8 + 9844338447616605836383925910597742485899170836676887\ 014727734165386539031804917989040*x^53*z^6 + 732223520897102913450044075994873408042087087025553579607847995772552489968\ 960842160*x^53*z^4 + 116706228242159260113053069963763766334925332642797796\ 04139253769692395058537156280*x^53*z^2 + 192902856598610347294302594981427712950289806021153381886599235862684215843\ 58936*x^53 + 79258361800676351620817129462208534647924503248648808740823088\ 941418460969792198276747*x^52*z^10 + 88428750769349648502564565928910348574\ 130644120393299008356338901582580420842535267445*x^52*z^8 + 184165662759306705972283228215581882980834068746604226033932209943791820380\ 59767675534*x^52*z^6 + 9784480311887605394041021569895141362618102825970708\ 58503772071720263508515572072490*x^52*z^4 + 121295210477945521413731672354072000363034332553355891550054389056231013452\ 34364535*x^52*z^2 + 1640355964389946946241299851520132236314513888775661944\ 3283087926462496184389073*x^52 + 740780767156648253710905196934367349977333\ 59245469148038808507964855162867191401003757*x^51*z^12 + 363656012967809142730808005767780335443418309023212181281423584554743526802\ 575968563898*x^51*z^10 + 20286595764733154656470694536632374084653500709972\ 5803607405718656571802141932875025315*x^51*z^8 + 281665131278939667957609643153242879853040340435982933934249262266975725287\ 97291739052*x^51*z^6 + 1122337447540048854022352474193854450417958853567228\ 337695503258737949318591391494915*x^51*z^4 + 111306193144467654944365534630795482686078563990138347540049909957482577050\ 38593338*x^51*z^2 + 1254389855121724135360994004103630533652275326710800310\ 3687067237883085317473997*x^51 + 666688147116684549411646365943121178801177\ 234802775631616042472331145488882918981943152*x^50*z^12 + 109094424073639289903723950790692556531101729331363285173534222745096534544\ 4776515906976*x^50*z^10 + 3651507582630075405868446286795907883892247965223\ 31656985796365386480136285235114828368*x^50*z^8 + 362132983401329792317531863153313178567826244484957015192525321044443110365\ 52242792896*x^50*z^6 + 1122312965086765885281607013904896214569709435387263\ 476836338804889803027992321574160*x^50*z^4 + 910667169266496736366743482357090842776323208278170214112130660616819887476\ 8649888*x^50*z^2 + 86840480222488563544190414719366577505688799263652595115\ 58779344724919460999984*x^50 + 43454678841369764317393455224691695019900046\ 0090152183934179805818081254874128403442800*x^49*z^14 + 294127123727949065916902808504318167118166427118871602183548149557858303918\ 9348449749200*x^49*z^12 + 2406494648683219630229204796853512276421361676427\ 131290592666678200658850245830549794800*x^49*z^10 + 536986409210305206745359748058221747631212936062252436743818184391882553360\ 639874747600*x^49*z^8 + 399411378751466682703160143183801299890984828476055\ 53146234410409313578349138503080400*x^49*z^6 + 990276145664793428189653247563143718737978913576997185443828357255708554110\ 871977200*x^49*z^4 + 669608212695953482622605501733155031453178829616301628\ 0236254857476616819682830800*x^49*z^2 + 547313950982070778639855554953991034699719323090247448207486093154931898802\ 5200*x^49 + 375757338768008748432987951761304584986200920342883510789848763\ 9009966434355701499443475*x^48*z^14 + 8477830866418709778694686845523648900\ 928334814347702350878405995452238318835590986347675*x^48*z^12 + 416184424351463934590466445143888218772845527249796297224939930685837153833\ 7471938752495*x^48*z^10 + 6633399915873392109765403789188301007595530835740\ 55491444709452686989560419785964263975*x^48*z^8 + 383750408356311940234362202680314934323708395456065160339914559405696439912\ 27287188825*x^48*z^6 + 7784568764553285038563320415002632026100771357861577\ 25708316536735822981039171115025*x^48*z^4 + 445398085702349430051302503083430948727952588815983441282571445049104057810\ 0788325*x^48*z^2 + 31551222127675284301154840832356383617092273115654080846\ 46314840961776088383085*x^48 + 17830054114089826886428055750242295993462867\ 20058388423747909820863552700223685809539845*x^47*z^16 + 159144284654686058159853720745964294817685095674633016334524182358069166631\ 53559291760600*x^47*z^14 + 179530535994749148254711015552265506137305913715\ 59840272448389166840034086945957382853900*x^47*z^12 + 587554481437360848833599687261959838267546626705594772552856372732946570118\ 2313325297640*x^47*z^10 + 7023599910924768116222192247375848125689385590784\ 11696823810008727400711032714550397150*x^47*z^8 + 325059169431228937610283277564502062015376523209843429934986450320119337337\ 45466795240*x^47*z^6 + 5494989716155260027221167351766563783129956252608172\ 18147046967107639751321767845900*x^47*z^4 + 269484556055203016501628405226949817717752826846645443465085244063323463548\ 9552600*x^47*z^2 + 16703588185239856394729033381835732503166497531816866330\ 48049033450352046791045*x^47 + 14788429332520687085509936803566041397075563\ 263214031979518375470852236913564890054138960*x^46*z^16 + 439986327248549367833353491676345033301421716922070372944348361116264899907\ 71573714793600*x^46*z^14 + 297808927286414820045881412961096348986664781949\ 73193011687711384646359754084230473071040*x^46*z^12 + 696176713137073605302060445883082374254541048713659057416076370030694124121\ 4495435263360*x^46*z^10 + 6472717374208328974915851253045187363936848593412\ 11933548004889491347842674901435096800*x^46*z^8 + 245097637610893899576077312662267049693776986557453654777005608041802639149\ 62458549120*x^46*z^6 + 3505846691827789409066585845455186661226943545799559\ 58835513425361764741313830462400*x^46*z^4 + 149008832238253150798579799806832018658996419892307137167396497202166832199\ 5029120*x^46*z^2 + 81494864495884683834906307624057375299645586961033315174\ 1959452369653311737680*x^46 + 527440712961746407266104756174859582315279925\ 1765301935024944115773647998263627966252560*x^45*z^18 + 600236249378780828764815082027092268469537567742216592109863474993414321785\ 86906690328720*x^45*z^16 + 892913428827938422955923262519641391111708778459\ 49575685764814461830229687154076068257600*x^45*z^14 + 402917960446325933003251323417953883923134704990813787805186683439333102555\ 25723581213760*x^45*z^12 + 706414605977324687732973099499010056228872534724\ 1540435545480813546749200644120368134880*x^45*z^10 + 525432351553381999140227925247197562484285356406395569586027498528270601700\ 802341431520*x^45*z^8 + 165801343089722343830875829153886533616378549730042\ 17823150379367533707942474604312640*x^45*z^6 + 203280186332871822878650775912947798003915214000142530753364927310603085299\ 615982400*x^45*z^4 + 756000 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Mon Apr 5 22:33:46 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=64; m2 :=m div 2; > ((-1 + m)*(tx - ty - tz)^(m div 2)*(tx + ty - tz)^(-1 + (m div 2)) + (tx + ty - tz)^(-1 + m) + (-1 + m)*(tx - ty + tz)^(m div 2)*(tx + ty + tz)^(-1 + (m div 2)) + (tx + ty + tz)^(-1 + m)) div (2*m) in I Output: Magma V2.10-22 Mon Apr 5 2004 22:33:42 on modular [Seed = 2645543627] ------------------------------------- false Total time: 4.659 seconds, Total memory usage: 9.09MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Mon Apr 5 22:35:00 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=128; m2 :=m div 2; > ((-1 + m)*(tx - ty - tz)^(m div 2)*(tx + ty - tz)^(-1 + (m div 2)) + (tx + ty - tz)^(-1 + m) + (-1 + m)*(tx - ty + tz)^(m div 2)*(tx + ty + tz)^(-1 + (m div 2)) + (tx + ty + tz)^(-1 + m)) div (2*m) in I Output: Magma V2.10-22 Mon Apr 5 2004 22:34:38 on modular [Seed = 2259997160] ------------------------------------- ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Mon Apr 5 22:37:06 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=128; m2 :=m div 2; > ((-1 + m)*(tx - ty - tz)^(m div 2)*(tx + ty - tz)^(-1 + (m div 2)) + (tx + ty - tz)^(-1 + m) + (-1 + m)*(tx - ty + tz)^(m div 2)*(tx + ty + tz)^(-1 + (m div 2)) + (tx + ty + tz)^(-1 + m)) div (2*m) in I; > (3^2 +(11*z)^2 + (17*x)^2)(x+y*z)+2*3*17*x*(y-y^2) in I Output: Magma V2.10-22 Mon Apr 5 2004 22:36:43 on modular [Seed = 3028738911] ------------------------------------- ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Mon Apr 5 22:37:31 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=128; m2 :=m div 2; > ((-1 + m)*(tx - ty - tz)^(m div 2)*(tx + ty - tz)^(-1 + (m div 2)) + (tx + ty - tz)^(-1 + m) + (-1 + m)*(tx - ty + tz)^(m div 2)*(tx + ty + tz)^(-1 + (m div 2)) + (tx + ty + tz)^(-1 + m)) div (2*m) in I; > (3^2 +(11*z)^2 + (17*x)^2)(x+y*z)+2*3*17*x*(y-y^2) in I Output: Magma V2.10-22 Mon Apr 5 2004 22:37:08 on modular [Seed = 3163482937] ------------------------------------- ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Mon Apr 5 22:37:45 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=64; m2 :=m div 2; > ((-1 + m)*(tx - ty - tz)^(m div 2)*(tx + ty - tz)^(-1 + (m div 2)) + (tx + ty - tz)^(-1 + m) + (-1 + m)*(tx - ty + tz)^(m div 2)*(tx + ty + tz)^(-1 + (m div 2)) + (tx + ty + tz)^(-1 + m)) div (2*m) in I; > (3^2 +(11*z)^2 + (17*x)^2)(x+y*z)+2*3*17*x*(y-y^2) in I Output: Magma V2.10-22 Mon Apr 5 2004 22:37:40 on modular [Seed = 2761356032] ------------------------------------- false >> (3^2 +(11*z)^2 + (17*x)^2)(x+y*z)+2*3*17*x*(y-y^2) in I; ^ Runtime error: Bad argument types Argument types given: RngMPolElt, RngMPolElt Total time: 4.649 seconds, Total memory usage: 9.09MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Mon Apr 5 22:38:00 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=64; m2 :=m div 2; > ((-1 + m)*(tx - ty - tz)^(m div 2)*(tx + ty - tz)^(-1 + (m div 2)) + (tx + ty - tz)^(-1 + m) + (-1 + m)*(tx - ty + tz)^(m div 2)*(tx + ty + tz)^(-1 + (m div 2)) + (tx + ty + tz)^(-1 + m)) div (2*m) in I; > (3^2 +(11*z)^2 + (17*x)^2)*(x+y*z)+2*3*17*x*(y-y^2) in I Output: Magma V2.10-22 Mon Apr 5 2004 22:37:55 on modular [Seed = 2896098559] ------------------------------------- false false Total time: 4.529 seconds, Total memory usage: 9.09MB ************** MAGMA ***************** Host cs662550-194.houston.rr.com. (66.25.50.194) Time: Mon Apr 5 22:39:48 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=64; m2 :=m div 2; ((-1 + m)*(tx - ty - tz)^(m2)*(tx + ty - tz)^(-1 + m2) + (tx + ty - tz)^(-1 + m) + (-1 + m)*(tx - ty + tz)^(m2)*(tx + ty + tz)^(-1 + m2) + (tx + ty + tz)^(-1 + m)) div (2*m) in I (3^2 +(11*z)^2 + (17*x)^2)*(x+y*z)+2*3*17*x*(y-y^2) in I Output: Magma V2.10-22 Mon Apr 5 2004 22:39:45 on modular [Seed = 1466240887] ------------------------------------- >> (3^2 +(11*z)^2 + (17*x)^2)*(x+y*z)+2*3*17*x*(y-y^2) in I ^ User error: bad syntax Total time: 2.550 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Apr 5 22:40:48 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^3-2); OK:=MaximalOrder(K); I:=5*OK; Factorization(I); Output: Magma V2.10-22 Mon Apr 5 2004 22:40:45 on modular [Seed = 1198858168] ------------------------------------- [ , ] Total time: 2.530 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cs662550-194.houston.rr.com. (66.25.50.194) Time: Mon Apr 5 22:42:08 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=64; m2 :=m div 2; ((-1 + m)*(tx - ty - tz)^(m2)*(tx + ty - tz)^(-1 + m2) + (tx + ty - tz)^(-1 + m) + (-1 + m)*(tx - ty + tz)^(m2)*(tx + ty + tz)^(-1 + m2) + (tx + ty + tz)^(-1 + m)) div (2*m) in I; (3^2 +(11*z)^2 + (17*x)^2)*(x+y*z)+2*3*17*x*(y-y^2) in I Output: Magma V2.10-22 Mon Apr 5 2004 22:42:03 on modular [Seed = 1316755172] ------------------------------------- false false Total time: 4.579 seconds, Total memory usage: 9.18MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Mon Apr 5 22:43:52 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=64; m2 :=m div 2; > (3^2 +(11*z)^2 + (17*x)^2)*(x+y*z)+2*3*17*x*(y-y^2) in I Output: Magma V2.10-22 Mon Apr 5 2004 22:43:50 on modular [Seed = 1984180033] ------------------------------------- false Total time: 2.560 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Mon Apr 5 22:44:04 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > I := ideal; > (3^2 +(11*z)^2 + (17*x)^2)*(x+y*z)+2*3*17*x*(y-y^2) in I Output: Magma V2.10-22 Mon Apr 5 2004 22:44:01 on modular [Seed = 1616001344] ------------------------------------- false Total time: 2.889 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host cs662550-194.houston.rr.com. (66.25.50.194) Time: Mon Apr 5 22:44:04 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=64; m2 :=m div 2; ((-1 + m)*(tx - ty - tz)^(m2)*(tx + ty - tz)^(-1 + m2) + (tx + ty - tz)^(-1 + m) + (-1 + m)*(tx - ty + tz)^(m2)*(tx + ty + tz)^(-1 + m2) + (tx + ty + tz)^(-1 + m)) div (2*m) in I; (3^2 +(11*z)^2 + (17*x)^2)*(x+y*z)+2*3*17*x*(y-y^2) in I Output: Magma V2.10-22 Mon Apr 5 2004 22:43:59 on modular [Seed = 2118920000] ------------------------------------- false false Total time: 4.989 seconds, Total memory usage: 9.18MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Apr 5 22:45:18 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^3-2); OK:=MaximalOrder(K); I:=5*OK; F:=Factorization(I); print IntegralBasis(K); Output: Magma V2.10-22 Mon Apr 5 2004 22:45:15 on modular [Seed = 338054654] ------------------------------------- [ 1, a, a^2 ] Total time: 2.559 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Apr 5 22:47:12 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^3-2); OK:=MaximalOrder(K); I:=5*OK; F:=Factorization(I); print IntegralBasis(K); PrimitiveElement(K); Output: Magma V2.10-22 Mon Apr 5 2004 22:47:10 on modular [Seed = 506217569] ------------------------------------- [ 1, a, a^2 ] a Total time: 2.549 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Mon Apr 5 22:47:29 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > I := ideal; > (3^2 +(11*z)^2 + (17*x)^2)*(x+y*z) in I Output: Magma V2.10-22 Mon Apr 5 2004 22:47:26 on modular [Seed = 104094825] ------------------------------------- >> I := ideal; ^ User error: Identifier 'P1' has not been declared or assigned false Total time: 2.560 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Mon Apr 5 22:47:37 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > (3^2 +(11*z)^2 + (17*x)^2)*(x+y*z) in I Output: Magma V2.10-22 Mon Apr 5 2004 22:47:35 on modular [Seed = 238834712] ------------------------------------- false Total time: 2.519 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Mon Apr 5 22:50:17 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); [ x^2 - 1, x*z - 2*y, 2*x - y*z, y^2 - 1, z^2 - 4 ] Output: Magma V2.10-22 Mon Apr 5 2004 22:50:14 on modular [Seed = 554924950] ------------------------------------- [ x^2 - 1, x*z - 2*y, 2*x - y*z, y^2 - 1, z^2 - 4 ] [ x^2 - 1, x*z - 2*y, 2*x - y*z, y^2 - 1, z^2 - 4 ] Total time: 2.570 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Mon Apr 5 22:51:21 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); (x^2-1)*y+(2*x*y-z)*3 in I; Output: Magma V2.10-22 Mon Apr 5 2004 22:51:18 on modular [Seed = 689664606] ------------------------------------- [ x^2 - 1, x*z - 2*y, 2*x - y*z, y^2 - 1, z^2 - 4 ] true Total time: 2.549 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Apr 5 22:52:11 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^3-2); OK:=MaximalOrder(K); I:=5*OK; F:=Factorization(I); print IntegralBasis(K); PrimitiveElement(K); F; Output: Magma V2.10-22 Mon Apr 5 2004 22:52:08 on modular [Seed = 3504507865] ------------------------------------- [ 1, a, a^2 ] a [ , ] Total time: 2.549 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Mon Apr 5 22:52:38 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); (x^2-1)*y+(2*x*y-z)*3 in I; Output: Magma V2.10-22 Mon Apr 5 2004 22:52:35 on modular [Seed = 3639247866] ------------------------------------- [ x^2 - 1, x*z - 2*y, 2*x - y*z, y^2 - 1, z^2 - 4 ] true Total time: 2.559 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host cs662550-194.houston.rr.com. (66.25.50.194) Time: Mon Apr 5 22:53:17 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=64; m2 :=m div 2; ((-1 + m)*(tx - ty - tz)^(m2)*(tx + ty - tz)^(-1 + m2) + (tx + ty - tz)^(-1 + m) + (-1 + m)*(tx - ty + tz)^(m2)*(tx + ty + tz)^(-1 + m2) + (tx + ty + tz)^(-1 + m)) div (2*m) in I; 2*3*17*x*(z-z^2) in I Output: Magma V2.10-22 Mon Apr 5 2004 22:53:12 on modular [Seed = 3287390218] ------------------------------------- false true Total time: 4.540 seconds, Total memory usage: 9.18MB ************** MAGMA ***************** Host cs662550-194.houston.rr.com. (66.25.50.194) Time: Mon Apr 5 22:53:40 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=64; m2 :=m div 2; ((-1 + m)*(tx - ty - tz)^(m2)*(tx + ty - tz)^(-1 + m2) + (tx + ty - tz)^(-1 + m) + (-1 + m)*(tx - ty + tz)^(m2)*(tx + ty + tz)^(-1 + m2) + (tx + ty + tz)^(-1 + m)) div (2*m) in I; 2*ty*(z-z^2) in I Output: Magma V2.10-22 Mon Apr 5 2004 22:53:35 on modular [Seed = 3422130229] ------------------------------------- false true Total time: 4.629 seconds, Total memory usage: 9.18MB ************** MAGMA ***************** Host cs662550-194.houston.rr.com. (66.25.50.194) Time: Mon Apr 5 22:54:18 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=64; m2 :=m div 2; ((-1 + m)*(tx - ty - tz)^(m2)*(tx + ty - tz)^(-1 + m2) + (tx + ty - tz)^(-1 + m) + (-1 + m)*(tx - ty + tz)^(m2)*(tx + ty + tz)^(-1 + m2) + (tx + ty + tz)^(-1 + m)) div (2*m) in I; 2*ty*(z-z^2)+(ty^2+3*11*z) in I Output: Magma V2.10-22 Mon Apr 5 2004 22:54:13 on modular [Seed = 4072712566] ------------------------------------- false false Total time: 4.569 seconds, Total memory usage: 9.18MB ************** MAGMA ***************** Host cs662550-194.houston.rr.com. (66.25.50.194) Time: Mon Apr 5 22:54:33 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=64; m2 :=m div 2; ((-1 + m)*(tx - ty - tz)^(m2)*(tx + ty - tz)^(-1 + m2) + (tx + ty - tz)^(-1 + m) + (-1 + m)*(tx - ty + tz)^(m2)*(tx + ty + tz)^(-1 + m2) + (tx + ty + tz)^(-1 + m)) div (2*m) in I; 2*ty*(z-z^2)+(ty^2+2*3*11*z) in I Output: Magma V2.10-22 Mon Apr 5 2004 22:54:28 on modular [Seed = 4207452495] ------------------------------------- false false Total time: 4.929 seconds, Total memory usage: 9.18MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Apr 5 22:54:34 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^3-2); OK:=MaximalOrder(K); I:=5*OK; F:=Factorization(I); print IntegralBasis(K); PrimitiveElement(K); F; #(OK/I); Output: Magma V2.10-22 Mon Apr 5 2004 22:54:30 on modular [Seed = 4241401675] ------------------------------------- [ 1, a, a^2 ] a [ , ] >> #(OK/I);; ^ Runtime error in '/': Bad argument types Argument types given: RngOrd, RngOrdIdl Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Mon Apr 5 22:54:36 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > ((3*x+5*y)^7 + 7(3*x+5*y)^3(3*x+5*y)^4) div 16 in I; Output: Magma V2.10-22 Mon Apr 5 2004 22:54:32 on modular [Seed = 4274824519] ------------------------------------- [ 3*x^2*y + 175*y^3, 9*x^2 + 25*y^2, 10*x*y^3, 30*x*y, 250*y^3 ] >> ((3*x+5*y)^7 + 7(3*x+5*y)^3(3*x+5*y)^4) div 16 in I; ^ Runtime error: Bad argument types Argument types given: RngMPolElt, RngIntElt Total time: 2.729 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Mon Apr 5 22:54:45 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > ((3*x+5*y)^7 + 7*(3*x+5*y)^3(3*x+5*y)^4) div 16 in I; Output: Magma V2.10-22 Mon Apr 5 2004 22:54:42 on modular [Seed = 2460010801] ------------------------------------- [ 3*x^2*y + 175*y^3, 9*x^2 + 25*y^2, 10*x*y^3, 30*x*y, 250*y^3 ] >> ((3*x+5*y)^7 + 7*(3*x+5*y)^3(3*x+5*y)^4) div 16 in I; ^ Runtime error: Bad argument types Argument types given: RngMPolElt, RngIntElt Total time: 2.519 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Apr 5 22:54:49 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^3-2); OK:=MaximalOrder(K); I:=5*OK; F:=Factorization(I); print IntegralBasis(K); PrimitiveElement(K); F; #(OKI); Output: Magma V2.10-22 Mon Apr 5 2004 22:54:47 on modular [Seed = 2594750780] ------------------------------------- [ 1, a, a^2 ] a [ , ] >> #(OKI);; ^ User error: Identifier 'OKI' has not been declared or assigned Total time: 2.599 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Mon Apr 5 22:54:54 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > ((3*x+5*y)^7 + 7*(3*x+5*y)^3*(3*x+5*y)^4) div 16 in I; Output: Magma V2.10-22 Mon Apr 5 2004 22:54:52 on modular [Seed = 2192628015] ------------------------------------- [ 3*x^2*y + 175*y^3, 9*x^2 + 25*y^2, 10*x*y^3, 30*x*y, 250*y^3 ] >> ((3*x+5*y)^7 + 7*(3*x+5*y)^3*(3*x+5*y)^4) div 16 in I; ^ Runtime error in 'div': Argument 2 does not divide argument 1 Total time: 2.570 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Apr 5 22:55:04 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^3-2); OK:=MaximalOrder(K); I:=5*OK; F:=Factorization(I); print IntegralBasis(K); PrimitiveElement(K); F; #(OKI); Output: Magma V2.10-22 Mon Apr 5 2004 22:54:58 on modular [Seed = 2411582428] ------------------------------------- [ 1, a, a^2 ] a [ , ] >> #(OKI);; ^ User error: Identifier 'OKI' has not been declared or assigned Total time: 3.139 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cs662550-194.houston.rr.com. (66.25.50.194) Time: Mon Apr 5 22:55:04 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=64; m2 :=m div 2; ((-1 + m)*(tx - ty - tz)^(m2)*(tx + ty - tz)^(-1 + m2) + (tx + ty - tz)^(-1 + m) + (-1 + m)*(tx - ty + tz)^(m2)*(tx + ty + tz)^(-1 + m2) + (tx + ty + tz)^(-1 + m)) div (2*m) in I; 2*ty*(z-z^2)+((ty)^2+2*3*11*z) in I Output: Magma V2.10-22 Mon Apr 5 2004 22:54:58 on modular [Seed = 2361315551] ------------------------------------- false false Total time: 5.360 seconds, Total memory usage: 9.18MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Mon Apr 5 22:55:05 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > ((3*x+5*y)^7 + 7*(3*x+5*y)^3*(3*x-5*y)^4) div 16 in I; Output: Magma V2.10-22 Mon Apr 5 2004 22:55:01 on modular [Seed = 3045583329] ------------------------------------- [ 3*x^2*y + 175*y^3, 9*x^2 + 25*y^2, 10*x*y^3, 30*x*y, 250*y^3 ] >> ((3*x+5*y)^7 + 7*(3*x+5*y)^3*(3*x-5*y)^4) div 16 in I; ^ Runtime error in 'div': Argument 2 does not divide argument 1 Total time: 2.679 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Mon Apr 5 22:55:25 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > ((3*x+5*y)^7 + 7*(3*x+5*y)^3*(3*x-5*y)^4) div 8 in I; Output: Magma V2.10-22 Mon Apr 5 2004 22:55:22 on modular [Seed = 2845570530] ------------------------------------- [ 3*x^2*y + 175*y^3, 9*x^2 + 25*y^2, 10*x*y^3, 30*x*y, 250*y^3 ] true Total time: 2.849 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host cs662550-194.houston.rr.com. (66.25.50.194) Time: Mon Apr 5 22:55:29 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=64; m2 :=m div 2; ((-1 + m)*(tx - ty - tz)^(m2)*(tx + ty - tz)^(-1 + m2) + (tx + ty - tz)^(-1 + m) + (-1 + m)*(tx - ty + tz)^(m2)*(tx + ty + tz)^(-1 + m2) + (tx + ty + tz)^(-1 + m)) div (2*m) in I; 2*ty*(z-z^2)*((ty)^2 + 2*3*11*z) in I Output: Magma V2.10-22 Mon Apr 5 2004 22:55:24 on modular [Seed = 2878994406] ------------------------------------- false true Total time: 4.999 seconds, Total memory usage: 9.18MB ************** MAGMA ***************** Host cs662550-194.houston.rr.com. (66.25.50.194) Time: Mon Apr 5 22:55:54 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=64; m2 :=m div 2; ((-1 + m)*(tx - ty - tz)^(m2)*(tx + ty - tz)^(-1 + m2) + (tx + ty - tz)^(-1 + m) + (-1 + m)*(tx - ty + tz)^(m2)*(tx + ty + tz)^(-1 + m2) + (tx + ty + tz)^(-1 + m)) div (2*m) in I; 2*ty*(z-z^2)+((ty)^2 + 2*3*11*z) in I; ty Output: Magma V2.10-22 Mon Apr 5 2004 22:55:49 on modular [Seed = 1516766781] ------------------------------------- false false 17*x Total time: 4.629 seconds, Total memory usage: 9.18MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Mon Apr 5 22:56:18 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > ((3+5*y)^7 + 7*(3+5*y)^3*(3-5*y)^4) div 8 in I; Output: Magma V2.10-22 Mon Apr 5 2004 22:56:16 on modular [Seed = 1114644032] ------------------------------------- [ 5*y^2 + 45, 6*y, 54 ] true Total time: 2.499 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Mon Apr 5 22:56:38 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > ((3+5*y)^7 + 7*(3+5*y)^3*(-3+5*y)^4) div 8 in I; Output: Magma V2.10-22 Mon Apr 5 2004 22:56:35 on modular [Seed = 1249384059] ------------------------------------- [ 5*y^2 + 45, 6*y, 54 ] true Total time: 2.769 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host cs662550-194.houston.rr.com. (66.25.50.194) Time: Mon Apr 5 22:56:42 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=64; m2 :=m div 2; ((-1 + m)*(tx - ty - tz)^(m2)*(tx + ty - tz)^(-1 + m2) + (tx + ty - tz)^(-1 + m) + (-1 + m)*(tx - ty + tz)^(m2)*(tx + ty + tz)^(-1 + m2) + (tx + ty + tz)^(-1 + m)) div (2*m) in I; 2*ty*(z-z^2)+((ty)^2+tx^2+tz^2)*7 + 2*3*11*z) in I Output: Magma V2.10-22 Mon Apr 5 2004 22:56:37 on modular [Seed = 1215960191] ------------------------------------- false >> 2*ty*(z-z^2)+((ty)^2+tx^2+tz^2)*7 + 2*3*11*z) in I ^ User error: bad syntax Total time: 4.799 seconds, Total memory usage: 9.18MB ************** MAGMA ***************** Host pool-141-151-191-61.pitt.east.verizon.net. (141.151.191.61) Time: Mon Apr 5 22:56:56 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > I := ideal; > GroebnerBasis(I); > ((3+5*y)^3 + 3*(3+5*y)^1*(-3+5*y)^2) div 4 in I; Output: Magma V2.10-22 Mon Apr 5 2004 22:56:53 on modular [Seed = 2018124895] ------------------------------------- [ 5*y^2 + 45, 6*y, 54 ] false Total time: 2.999 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host cs662550-194.houston.rr.com. (66.25.50.194) Time: Mon Apr 5 22:56:57 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=64; m2 :=m div 2; ((-1 + m)*(tx - ty - tz)^(m2)*(tx + ty - tz)^(-1 + m2) + (tx + ty - tz)^(-1 + m) + (-1 + m)*(tx - ty + tz)^(m2)*(tx + ty + tz)^(-1 + m2) + (tx + ty + tz)^(-1 + m)) div (2*m) in I; 2*ty*(z-z^2)+((ty)^2+tx^2+tz^2)*7 + 2*3*11*z in I Output: Magma V2.10-22 Mon Apr 5 2004 22:56:52 on modular [Seed = 2051548764] ------------------------------------- false false Total time: 5.040 seconds, Total memory usage: 9.18MB ************** MAGMA ***************** Host cs662550-194.houston.rr.com. (66.25.50.194) Time: Mon Apr 5 22:57:17 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=64; m2 :=m div 2; ((-1 + m)*(tx - ty - tz)^(m2)*(tx + ty - tz)^(-1 + m2) + (tx + ty - tz)^(-1 + m) + (-1 + m)*(tx - ty + tz)^(m2)*(tx + ty + tz)^(-1 + m2) + (tx + ty + tz)^(-1 + m)) div (2*m) in I; 2*17*ty*(z-z^2)+((ty)^2+tx^2+tz^2)*7 + 2*3*11*z in I Output: Magma V2.10-22 Mon Apr 5 2004 22:57:12 on modular [Seed = 1784166064] ------------------------------------- false false Total time: 4.559 seconds, Total memory usage: 9.18MB ************** MAGMA ***************** Host cs662550-194.houston.rr.com. (66.25.50.194) Time: Mon Apr 5 22:57:56 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=64; m2 :=m div 2; ((-1 + m)*(tx - ty - tz)^(m2)*(tx + ty - tz)^(-1 + m2) + (tx + ty - tz)^(-1 + m) + (-1 + m)*(tx - ty + tz)^(m2)*(tx + ty + tz)^(-1 + m2) + (tx + ty + tz)^(-1 + m)) div (2*m) in I; 2*17*ty*(z-z^2)+((ty)^2+(tx)^2+(tz)^2)*7 + 2*3*11*z in I Output: Magma V2.10-22 Mon Apr 5 2004 22:57:51 on modular [Seed = 304107247] ------------------------------------- false false Total time: 4.589 seconds, Total memory usage: 9.18MB ************** MAGMA ***************** Host cs662550-194.houston.rr.com. (66.25.50.194) Time: Mon Apr 5 22:58:21 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=64; m2 :=m div 2; ((-1 + m)*(tx - ty - tz)^(m2)*(tx + ty - tz)^(-1 + m2) + (tx + ty - tz)^(-1 + m) + (-1 + m)*(tx - ty + tz)^(m2)*(tx + ty + tz)^(-1 + m2) + (tx + ty + tz)^(-1 + m)) div (2*m) in I; 2*11*(ty)*(z-z^2)+((ty)^2+(tx)^2+(tz)^2)*7 + 2*3*11*z in I Output: Magma V2.10-22 Mon Apr 5 2004 22:58:16 on modular [Seed = 438847104] ------------------------------------- false false Total time: 4.540 seconds, Total memory usage: 9.18MB ************** MAGMA ***************** Host cs662550-194.houston.rr.com. (66.25.50.194) Time: Mon Apr 5 22:59:37 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=64; m2 :=m div 2; ((-1 + m)*(tx - ty - tz)^(m2)*(tx + ty - tz)^(-1 + m2) + (tx + ty - tz)^(-1 + m) + (-1 + m)*(tx - ty + tz)^(m2)*(tx + ty + tz)^(-1 + m2) + (tx + ty + tz)^(-1 + m)) div (2*m) in I; (ty^2+tx^2+tz^2)*7 in I Output: Magma V2.10-22 Mon Apr 5 2004 22:59:32 on modular [Seed = 3300678] ------------------------------------- false false Total time: 4.609 seconds, Total memory usage: 9.18MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Apr 5 23:00:09 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^3-2); OK:=MaximalOrder(K); I:=5*OK; F:=Factorization(I); print IntegralBasis(K); PrimitiveElement(K); F; #(quo); Output: Magma V2.10-22 Mon Apr 5 2004 23:00:07 on modular [Seed = 855731798] ------------------------------------- [ 1, a, a^2 ] a [ , ] 125 Total time: 2.570 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cs662550-194.houston.rr.com. (66.25.50.194) Time: Mon Apr 5 23:00:18 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=64; m2 :=m div 2; ((-1 + m)*(tx - ty - tz)^(m2)*(tx + ty - tz)^(-1 + m2) + (tx + ty - tz)^(-1 + m) + (-1 + m)*(tx - ty + tz)^(m2)*(tx + ty + tz)^(-1 + m2) + (tx + ty + tz)^(-1 + m)) div (2*m) in I; (ty^2+tx^2+tz^2) in I Output: Magma V2.10-22 Mon Apr 5 2004 23:00:13 on modular [Seed = 990471764] ------------------------------------- false false Total time: 4.569 seconds, Total memory usage: 9.18MB ************** MAGMA ***************** Host cs662550-194.houston.rr.com. (66.25.50.194) Time: Mon Apr 5 23:00:51 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=64; m2 :=m div 2; ((-1 + m)*(tx - ty - tz)^(m2)*(tx + ty - tz)^(-1 + m2) + (tx + ty - tz)^(-1 + m) + (-1 + m)*(tx - ty + tz)^(m2)*(tx + ty + tz)^(-1 + m2) + (tx + ty + tz)^(-1 + m)) div (2*m) in I; (ty^2+tx^2+tz^2) in I; ty^2+tx^2+tz^2 Output: Magma V2.10-22 Mon Apr 5 2004 23:00:46 on modular [Seed = 588348975] ------------------------------------- false false 289*x^2 + 121*z^2 + 9 Total time: 4.549 seconds, Total memory usage: 9.18MB ************** MAGMA ***************** Host cs662550-194.houston.rr.com. (66.25.50.194) Time: Mon Apr 5 23:01:20 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=64; m2 :=m div 2; ((-1 + m)*(tx - ty - tz)^(m2)*(tx + ty - tz)^(-1 + m2) + (tx + ty - tz)^(-1 + m) + (-1 + m)*(tx - ty + tz)^(m2)*(tx + ty + tz)^(-1 + m2) + (tx + ty + tz)^(-1 + m)) div (2*m) in I; 289*x^2 + 121*z^2 + 9 in I Output: Magma V2.10-22 Mon Apr 5 2004 23:01:16 on modular [Seed = 3656090871] ------------------------------------- false false Total time: 4.559 seconds, Total memory usage: 9.18MB ************** MAGMA ***************** Host cs662550-194.houston.rr.com. (66.25.50.194) Time: Mon Apr 5 23:01:50 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=64; m2 :=m div 2; ((-1 + m)*(tx - ty - tz)^(m2)*(tx + ty - tz)^(-1 + m2) + (tx + ty - tz)^(-1 + m) + (-1 + m)*(tx - ty + tz)^(m2)*(tx + ty + tz)^(-1 + m2) + (tx + ty + tz)^(-1 + m)) div (2*m) in I; 289*x^2 + 121*z^2 + 9 in I Output: Magma V2.10-22 Mon Apr 5 2004 23:01:45 on modular [Seed = 3253967882] ------------------------------------- false false Total time: 4.670 seconds, Total memory usage: 9.18MB ************** MAGMA ***************** Host cs662550-194.houston.rr.com. (66.25.50.194) Time: Mon Apr 5 23:02:38 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=64; m2 :=m div 2; ((-1 + m)*(tx - ty - tz)^(m2)*(tx + ty - tz)^(-1 + m2) + (tx + ty - tz)^(-1 + m) + (-1 + m)*(tx - ty + tz)^(m2)*(tx + ty + tz)^(-1 + m2) + (tx + ty + tz)^(-1 + m)) div (2*m) in I; (289*x^2 + 121*z^2 + 9)*2*3*11*z in I Output: Magma V2.10-22 Mon Apr 5 2004 23:02:34 on modular [Seed = 3388707921] ------------------------------------- false true Total time: 4.639 seconds, Total memory usage: 9.18MB ************** MAGMA ***************** Host cs662550-194.houston.rr.com. (66.25.50.194) Time: Mon Apr 5 23:02:52 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=64; m2 :=m div 2; ((-1 + m)*(tx - ty - tz)^(m2)*(tx + ty - tz)^(-1 + m2) + (tx + ty - tz)^(-1 + m) + (-1 + m)*(tx - ty + tz)^(m2)*(tx + ty + tz)^(-1 + m2) + (tx + ty + tz)^(-1 + m)) div (2*m) in I; (289*x^2 + 121*z^2 + 9)^2 in I Output: Magma V2.10-22 Mon Apr 5 2004 23:02:47 on modular [Seed = 4056132724] ------------------------------------- false false Total time: 4.680 seconds, Total memory usage: 9.18MB ************** MAGMA ***************** Host cs662550-194.houston.rr.com. (66.25.50.194) Time: Mon Apr 5 23:03:24 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=64; m2 :=m div 2; ((-1 + m)*(tx - ty - tz)^(m2)*(tx + ty - tz)^(-1 + m2) + (tx + ty - tz)^(-1 + m) + (-1 + m)*(tx - ty + tz)^(m2)*(tx + ty + tz)^(-1 + m2) + (tx + ty + tz)^(-1 + m)) div (2*m) in I; 3^2 +(11*z)^2 + (17*x)^2 in I Output: Magma V2.10-22 Mon Apr 5 2004 23:03:19 on modular [Seed = 4274824027] ------------------------------------- false false Total time: 4.589 seconds, Total memory usage: 9.18MB ************** MAGMA ***************** Host cs662550-194.houston.rr.com. (66.25.50.194) Time: Mon Apr 5 23:03:45 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=64; m2 :=m div 2; ((-1 + m)*(tx - ty - tz)^(m2)*(tx + ty - tz)^(-1 + m2) + (tx + ty - tz)^(-1 + m) + (-1 + m)*(tx - ty + tz)^(m2)*(tx + ty + tz)^(-1 + m2) + (tx + ty + tz)^(-1 + m)) div (2*m) in I; 3^2 +(11*z)^2 + (17*x)^2 in I; I Output: Magma V2.10-22 Mon Apr 5 2004 23:03:41 on modular [Seed = 3889543608] ------------------------------------- false false Ideal of Polynomial ring of rank 3 over Integer Ring Lexicographical Order Variables: x, y, z Groebner basis: [ x^2*z + 3*z^3 + 3*z, 5*x^2 + 5*z^2 + 45, 2*x*z, 6*x, 4*z^3, 6*z, 54 ] Total time: 4.589 seconds, Total memory usage: 9.18MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Apr 5 23:04:35 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^3-2); OK:=MaximalOrder(K); I:=5*OK; F:=Factorization(I); print IntegralBasis(K); PrimitiveElement(K); F; #(quo); K; Output: Magma V2.10-22 Mon Apr 5 2004 23:04:32 on modular [Seed = 3974017790] ------------------------------------- [ 1, a, a^2 ] a [ , ] 125 Number Field with defining polynomial x^3 - 2 over the Rational Field Total time: 2.569 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cs662550-194.houston.rr.com. (66.25.50.194) Time: Mon Apr 5 23:04:57 2004 Input: > P := PolynomialRing(IntegerRing(), 3); > P1 := 9 + 289*x^2 + 121*z^2; > P2 := 102*x; > P3 := 66*z; > P4 := 374*x*z; > I := ideal; > I := ideal; > tx :=3; ty := 17*x; tz :=11*z; m:=64; m2 :=m div 2; ((-1 + m)*(tx - ty - tz)^(m2)*(tx + ty - tz)^(-1 + m2) + (tx + ty - tz)^(-1 + m) + (-1 + m)*(tx - ty + tz)^(m2)*(tx + ty + tz)^(-1 + m2) + (tx + ty + tz)^(-1 + m)) div (2*m) in I; 3^2 +(11*z)^2 + (17*x)^2 in I; I Output: Magma V2.10-22 Mon Apr 5 2004 23:04:53 on modular [Seed = 2493958803] ------------------------------------- false false Ideal of Polynomial ring of rank 3 over Integer Ring Lexicographical Order Variables: x, y, z Groebner basis: [ x^2*z + 3*z^3 + 3*z, 5*x^2 + 5*z^2 + 45, 2*x*z, 6*x, 4*z^3, 6*z, 54 ] Total time: 4.630 seconds, Total memory usage: 9.18MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Apr 5 23:09:01 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^3-2); M:=NumberField(x^3-1); L:=CompositeField(K,M); L; OK:=MaximalOrder(K); I:=5*OK; F:=Factorization(I); print IntegralBasis(K); PrimitiveElement(K); F; #(quo); K; Output: Magma V2.10-22 Mon Apr 5 2004 23:08:58 on modular [Seed = 3045583533] ------------------------------------- >> M:=NumberField(x^3-1); ^ Runtime error in 'NumberField': Argument 1 is not irreducible >> L:=CompositeField(K,M); ^ User error: Identifier 'M' has not been declared or assigned >> L; ^ User error: Identifier 'L' has not been declared or assigned [ 1, a, a^2 ] a [ , ] 125 Number Field with defining polynomial x^3 - 2 over the Rational Field Total time: 2.629 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Apr 5 23:14:33 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^3-2); M:=NumberField(x^3-1); L:=CompositeFields(K,M); L; OK:=MaximalOrder(K); I:=5*OK; F:=Factorization(I); print IntegralBasis(K); PrimitiveElement(K); F; #(quo); K; Output: Magma V2.10-22 Mon Apr 5 2004 23:14:30 on modular [Seed = 2929512042] ------------------------------------- >> M:=NumberField(x^3-1); ^ Runtime error in 'NumberField': Argument 1 is not irreducible >> L:=CompositeFields(K,M); ^ User error: Identifier 'M' has not been declared or assigned >> L; ^ User error: Identifier 'L' has not been declared or assigned [ 1, a, a^2 ] a [ , ] 125 Number Field with defining polynomial x^3 - 2 over the Rational Field Total time: 2.629 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Apr 5 23:14:50 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^3-2); M:=NumberField(x^2+x+1); L:=CompositeFields(K,M); L; OK:=MaximalOrder(K); I:=5*OK; F:=Factorization(I); print IntegralBasis(K); PrimitiveElement(K); F; #(quo); K; Output: Magma V2.10-22 Mon Apr 5 2004 23:14:47 on modular [Seed = 1466251171] ------------------------------------- [ Number Field with defining polynomial x^6 + 3*x^5 + 6*x^4 + 3*x^3 + 9*x + 9 over the Rational Field ] [ 1, a, a^2 ] a [ , ] 125 Number Field with defining polynomial x^3 - 2 over the Rational Field Total time: 2.579 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Apr 5 23:15:11 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^3-2); M:=NumberField(x^2+x+1); L:=CompositeFields(K,M); L; OK:=MaximalOrder(L); I:=5*OK; F:=Factorization(I); print IntegralBasis(L); PrimitiveElement(L); F; #(quo); K; Output: Magma V2.10-22 Mon Apr 5 2004 23:15:08 on modular [Seed = 1131488172] ------------------------------------- [ Number Field with defining polynomial x^6 + 3*x^5 + 6*x^4 + 3*x^3 + 9*x + 9 over the Rational Field ] >> OK:=MaximalOrder(L); ^ Runtime error in 'MaximalOrder': Bad argument types Argument types given: SeqEnum[FldNum] >> I:=5*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> F:=Factorization(I); ^ User error: Identifier 'I' has not been declared or assigned >> print IntegralBasis(L); ^ Runtime error in 'IntegralBasis': Bad argument types Argument types given: SeqEnum[FldNum] >> PrimitiveElement(L); ^ Runtime error in 'PrimitiveElement': Bad argument types Argument types given: SeqEnum[FldNum] >> F; ^ User error: Identifier 'F' has not been declared or assigned >> #(quo); ^ User error: Identifier 'OK' has not been declared or assigned Number Field with defining polynomial x^3 - 2 over the Rational Field Total time: 2.589 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Apr 5 23:15:21 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^3-2); M:=NumberField(x^2+x+1); L:=CompositeFields(K,M); L; OL:=MaximalOrder(L); I:=5*OK; F:=Factorization(I); print IntegralBasis(L); PrimitiveElement(L); F; #(quo); K; Output: Magma V2.10-22 Mon Apr 5 2004 23:15:18 on modular [Seed = 1266232286] ------------------------------------- [ Number Field with defining polynomial x^6 + 3*x^5 + 6*x^4 + 3*x^3 + 9*x + 9 over the Rational Field ] >> OL:=MaximalOrder(L); ^ Runtime error in 'MaximalOrder': Bad argument types Argument types given: SeqEnum[FldNum] >> I:=5*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> F:=Factorization(I); ^ User error: Identifier 'I' has not been declared or assigned >> print IntegralBasis(L); ^ Runtime error in 'IntegralBasis': Bad argument types Argument types given: SeqEnum[FldNum] >> PrimitiveElement(L); ^ Runtime error in 'PrimitiveElement': Bad argument types Argument types given: SeqEnum[FldNum] >> F; ^ User error: Identifier 'F' has not been declared or assigned >> #(quo); ^ User error: Identifier 'OK' has not been declared or assigned Number Field with defining polynomial x^3 - 2 over the Rational Field Total time: 2.579 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Apr 5 23:15:46 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^3-2); M:=NumberField(x^2+x+1); L:=CompositeFields(K,M); L; OL:=MaximalOrder(L); I:=5*OL; F:=Factorization(I); print IntegralBasis(L); PrimitiveElement(L); F; #(quo); K; Output: Magma V2.10-22 Mon Apr 5 2004 23:15:44 on modular [Seed = 1933644736] ------------------------------------- [ Number Field with defining polynomial x^6 + 3*x^5 + 6*x^4 + 3*x^3 + 9*x + 9 over the Rational Field ] >> OL:=MaximalOrder(L); ^ Runtime error in 'MaximalOrder': Bad argument types Argument types given: SeqEnum[FldNum] >> I:=5*OL; ^ User error: Identifier 'OL' has not been declared or assigned >> F:=Factorization(I); ^ User error: Identifier 'I' has not been declared or assigned >> print IntegralBasis(L); ^ Runtime error in 'IntegralBasis': Bad argument types Argument types given: SeqEnum[FldNum] >> PrimitiveElement(L); ^ Runtime error in 'PrimitiveElement': Bad argument types Argument types given: SeqEnum[FldNum] >> F; ^ User error: Identifier 'F' has not been declared or assigned >> #(quo); ^ User error: Identifier 'OK' has not been declared or assigned Number Field with defining polynomial x^3 - 2 over the Rational Field Total time: 2.589 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Apr 5 23:16:54 2004 Input: R:=PolynomialRing(Rationals()); L:=NumberField(x^6 + 3*x^5 + 6*x^4 + 3*x^3 + 9*x + 9 ); OL:=MaximalOrder(L); I:=5*OL; F:=Factorization(I); print IntegralBasis(L); PrimitiveElement(L); F; #(quo); Output: Magma V2.10-22 Mon Apr 5 2004 23:16:51 on modular [Seed = 2051545866] ------------------------------------- [ 1, a, a^2, 1/3*a^3, 1/9*(a^4 + 3*a^2 + 6*a), 1/9*(a^5 + 6*a^2) ] a [ , , ] 15625 Total time: 2.630 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Apr 5 23:18:16 2004 Input: R:=PolynomialRing(Rationals()); L:=NumberField(x^6 + 3*x^5 + 6*x^4 + 3*x^3 + 9*x + 9 ); OL:=MaximalOrder(L); I:=5*OL; F:=Factorization(I); print IntegralBasis(L); PrimitiveElement(L); F; #(quo); a^15625; Output: Magma V2.10-22 Mon Apr 5 2004 23:18:13 on modular [Seed = 1649410884] ------------------------------------- [ 1, a, a^2, 1/3*a^3, 1/9*(a^4 + 3*a^2 + 6*a), 1/9*(a^5 + 6*a^2) ] a [ , , ] 15625 4103191886927983683810463812369159552998394934005156268717075331422354179144278\ 221229992764790458980455405374277986754869979223629253441482222987379301439\ 384021675779802270566168376906128196548703274755872097587160123930003302310\ 064127786922421614971783646299072532844835398573872614266415901677528604233\ 667836105479100343932785697806677741839699536764935111804343523832962486254\ 534125830377002572739003678823983159124806087153058437182624693632376599236\ 374878589377789061250751930104576147340266194740289369128536110379616690656\ 871910432899462069733594878454194390636601257483278044385578505556810246967\ 137039634042113489748045398337232557768760118100395945758541808551352883164\ 091989979356327879722180061949888456403588289330846655234713035392978306645\ 229426560844812724252944870128075851947156140837629437729015330329497183204\ 430546556881251085938361662181499074839370556792748749361401122392718244469\ 346382943251698917719290574199514568625697654312827406979208473711549309132\ 686742865917411234756240091736683981458749247768183846102705733230716694768\ 769375213144796180261341404893171641012636765206620357627361369708155410527\ 359408690507265683450159541965153632087646238302332305355639798094737108251\ 762411684009628945036509163707381139062213870633039280256892846561707139032\ 018921936264835451664505770839426504284358495714879411588482151037594833889\ 520789369626800084162671526633136454994174417474137203187992960413684159559\ 098097865576029575458285583538034796964622477023744875984008171595589902441\ 678027260766745717288005589551655203535447655723213060207748914028005932249\ 095444478213888873376278239641035945663164877311311560871819566690216610138\ 960838052469096556823710445353365212957937923702840693015737618997355389718\ 431808697641032675431135987668063062786011328806004081212976175322128110120\ 301805800854840251943636986616186021883375168003836165678687679185208701672\ 811705119177633801476196117990065232929418422811838401342338313686185600770\ 177843229785723449107580624606503624872749551939782060047537768965224335927\ 145204262529210813314135273622781804394263670769528906335477223666612205240\ 399580548121135214738827576451001199760189279782814236414594254843599197564\ 657920610194460628802139490590025836033932401795640738678004200108782639117\ 613967666876096650026754708638006031457896606071689032279113970647089106252\ 404301735779256910014355692163961664574462980325266659273959659497499995144\ 002598597089281009647461020126497235600037213275792706642087928876571054232\ 200326005001614982640936279243172487290680688803984128654794381883402494098\ 439478281892886792168220589829543833191310548792714987032307075923579553853\ 741411987202008773661630200959060157171014444766764138716789187461938603949\ 095504511482442414837371113877824962168348227748769166330292167690814554386\ 861777056936648044613765117928218990139119636751562980442437584240833876105\ 994742486453613807392179502240074586337117110592793527364849433767775071983\ 124177666862968525071787676347528643029395087263262379555175926115284530812\ 994639988973883640271401359373437742247909239819134776053402574283989421032\ 989037248731441519884513722180052758316308790380690463745572462802040131977\ 331486849001335135306753213113531180234939806610096525928843447745839239888\ 885208260071022778273572363652502756421888344221341530165416826602702538536\ 316850223382718908001313432523895412271689861573210893452884417788057051831\ 307112255800352782610544153228288578887496978271376834040908403379970086420\ 549711820378131500465247511656162399531349816201033019394604136667308045231\ 732014054590198165532681325381876845857129283993874788907922024524874451056\ 646289905619348644723240724761760439249920927866123275120816585917907789668\ 773728122848586181670038120313079127428181812568134223044426931925673372498\ 595925361240257513541004362273579403442989492492229058676354784679706793215\ 444053208876872357894629355629271244445571356685304094268983144171138844162\ 297769103606296764265292085115870395006438489106565473056886706753913788575\ 721115534919843149411302866564066292025830877728669933646345011049051071313\ 089876324187001914196041994553784720026064962110556411478987499267022133352\ 152068057001333661674955638938382386046114696111426534608007930505825850119\ 061999243138763786949447449569736994192837704869617332365765086068261951397\ 010968685376995729174194125871707410427593325211307080128805295188856486815\ 847965785888689976284436287316072150552389503636801106671582009232376482694\ 517070839328317844771973011001345670224748942658526452211188567092316705117\ 853242583393970596993965178289491977863470604114360289925347592478216659260\ 134779202012758230563581991973835766553783437184091199517787762343718422683\ 898738684542849394784017799486576729222669852752059833498144627137750707095\ 379800480779942574142210134355099974844990797906973455138924984532312857883\ 861502159443999866196061326770386307183443153983305647161584152531127722960\ 435989266958565848618034302238616003755585581803888085793023741461713566902\ 635423754668744378235665961257490245503428591320133834478793685727423709654\ 410287785180846380256019556674221566742671519261019000829782622354223552956\ 458326586434101541878692640774686879212983557739011114908328024136461374814\ 041491937745501734470437049807057125256657886126899262511939375933903708840\ 457924035517931375933187229892649936823114226774892910890703516953327666499\ 756254822935031865437329941338672249938428411728503174122501807830249749168\ 896636428962330110861590310874760575792810367242908884346769801487672960173\ 2073128506818880054416095486630128738708078822220940*a^5 + 239926846086192446420158583589034255245054826315040897694888567958819941001\ 250644065909106515032390138404645664339886320192461676960195157496886813072\ 030005323919413398302922531094804755483428675124428033267569678780353070581\ 915376243130555376283523521504874964016337374026157161374608081559427556218\ 269768105017242595513029819833273289691645994647505137232971952029223763507\ 135334438113464482890624423574602891243419686534429633758711148927071843522\ 849272586771695101132490987641136326055270967977134063464904881000153530117\ 425981170370913858138876057619427773046270150627993591886558081571676134250\ 485420550647528731828197792868942622819197287236533663386887949972643455976\ 657713825847832905528901403090144365284486822142439725365571041524848267716\ 948722131220767291439632544462884116416273480343463843582684073420925589135\ 837579982324527669849079533075825390121581664647427743457274436637545254250\ 843401660581262654360180240201257417070911271324976236162946857382503317359\ 973335947804091313919831259715517577691943219491528864548482124236224167077\ 545490695515231584232807042753690224304958804753412508997474225383673373822\ 055475379837494445075800982000270285964883499089937785015690838119295243494\ 324580106641178091646458953798616221256369563707545701023729117598740389924\ 954680606624991311410672144178202998976333117250726553993766140759042502868\ 382949314233031790690636124292124889917705611803550845064840391636099461933\ 597107106658449137174541989408783784779309469406843450979985992021049159808\ 240903036053492364112682185340312254623118182458073226950194245968341116859\ 093010616856969505097250568729132586517332460860695913390507282542402985163\ 132365016982109969319234779791085772975068663863167380914882175421935067359\ 335991061825301441058746527661352259372642209194378623744287893277012557237\ 104753542730883919217049561236000676981279333133822446669136041986704337868\ 287443545476591124608086022453651380259620984427401204598985783483461464921\ 025560073607612273870556504835921470178128144506029632741250722220587053692\ 334494808643029955191846732317230229203710494761082249161995460685431508341\ 790126070912508826049733564374412246121590996121292072632944582385913562324\ 446601313493403112253521933919648228693023319684971733889447495434329725950\ 131451018455232467488266000569852450162485489052355722490825596005072826471\ 285535082849488232511603620406312265442528177430301930372672001560912241126\ 138926206772352252714940329625714838296536469529231890874712390119492429080\ 483276968275736720766711230307319495805530329675980818671354831122349447084\ 728650837463238034525551381992582497813262822731040921941114110956806080878\ 019351726740866534432698576264944641405157658887802558447255246260438008768\ 797738534941172185056584722579446400964901948660901550840857029371697017034\ 058081109947221516262322607635481429420336354754996610253938756192549007162\ 305320476588343067401289152819146094904922944025170738666241687693878124378\ 246031090058603682981040036843007133918474058756162392613409613993696557542\ 831659997553991666882181462543016389291475986028612537749460069240822775716\ 277640543486568982409461912838592338052975805955694316143238960834090604115\ 18655867754279108429354979249514660785282150247955437321444878742381 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Apr 5 23:21:11 2004 Input: R:=PolynomialRing(Rationals()); L:=NumberField(x^6 + 3*x^5 + 6*x^4 + 3*x^3 + 9*x + 9 ); OL:=MaximalOrder(L); I:=5*OL; F:=Factorization(I); print IntegralBasis(L); PrimitiveElement(L); F; #(quo); a^15625 mod F[1][1]; Output: Magma V2.10-22 Mon Apr 5 2004 23:21:08 on modular [Seed = 287535974] ------------------------------------- [ 1, a, a^2, 1/3*a^3, 1/9*(a^4 + 3*a^2 + 6*a), 1/9*(a^5 + 6*a^2) ] a [ , , ] 15625 >> a^15625 mod F[1][1]; ^ Runtime error in 'mod': Bad argument types Argument types given: FldNumElt, RngOrdIdl Total time: 2.600 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Apr 5 23:35:42 2004 Input: R:=PolynomialRing(Rationals()); L:=NumberField(x^6 + 3*x^5 + 6*x^4 + 3*x^3 + 9*x + 9 ); OL:=MaximalOrder(L); I:=5*OL; F:=Factorization(I); print IntegralBasis(L); PrimitiveElement(L); F; #(quo); ResideClassField(OL,F[1][1]); Output: Magma V2.10-22 Mon Apr 5 2004 23:35:39 on modular [Seed = 822301929] ------------------------------------- [ 1, a, a^2, 1/3*a^3, 1/9*(a^4 + 3*a^2 + 6*a), 1/9*(a^5 + 6*a^2) ] a [ , , ] 15625 >> ResideClassField(OL,F[1][1]); ^ User error: Identifier 'ResideClassField' has not been declared or assigned Total time: 2.689 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Apr 5 23:35:54 2004 Input: R:=PolynomialRing(Rationals()); L:=NumberField(x^6 + 3*x^5 + 6*x^4 + 3*x^3 + 9*x + 9 ); OL:=MaximalOrder(L); I:=5*OL; F:=Factorization(I); print IntegralBasis(L); PrimitiveElement(L); F; #(quo); ResidueClassField(OL,F[1][1]); Output: Magma V2.10-22 Mon Apr 5 2004 23:35:51 on modular [Seed = 940203516] ------------------------------------- [ 1, a, a^2, 1/3*a^3, 1/9*(a^4 + 3*a^2 + 6*a), 1/9*(a^5 + 6*a^2) ] a [ , , ] 15625 Finite field of size 5^2 Mapping from: RngOrd: OL to GF(5^2) given by the ideal Prime Ideal of OL Two element generators: [5, 0, 0, 0, 0, 0] [7, 0, 1, 0, 0, 0] Total time: 2.659 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Apr 5 23:38:44 2004 Input: R:=PolynomialRing(Rationals()); L:=NumberField(x^6 + 3*x^5 + 6*x^4 + 3*x^3 + 9*x + 9 ); OL:=MaximalOrder(L); I:=5*OL; F:=Factorization(I); print IntegralBasis(L); PrimitiveElement(L); F; #(quo); R:=ResidueClassField(OL,F[1][1]); a^15625!R; Output: Magma V2.10-22 Mon Apr 5 2004 23:38:41 on modular [Seed = 538068530] ------------------------------------- [ 1, a, a^2, 1/3*a^3, 1/9*(a^4 + 3*a^2 + 6*a), 1/9*(a^5 + 6*a^2) ] a [ , , ] 15625 >> a^15625!R; ^ Runtime error in '!': Illegal coercion Total time: 2.639 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Mon Apr 5 23:42:29 2004 Input: R:=PolynomialRing(Rationals()); L:=NumberField(x^6 + 3*x^5 + 6*x^4 + 3*x^3 + 9*x + 9 ); OL:=MaximalOrder(L); I:=5*OL; F:=Factorization(I); print IntegralBasis(L); PrimitiveElement(L); F; #(quo); R:=ResidueClassField(OL,F[1][1]); R; Output: Magma V2.10-22 Mon Apr 5 2004 23:42:26 on modular [Seed = 3689528490] ------------------------------------- [ 1, a, a^2, 1/3*a^3, 1/9*(a^4 + 3*a^2 + 6*a), 1/9*(a^5 + 6*a^2) ] a [ , , ] 15625 Finite field of size 5^2 Total time: 2.580 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 3(NXDOMAIN) (137.205.234.204) Time: Tue Apr 6 10:05:49 2004 Input: #AutomorphismGroup(DirectProduct(Sym(4),PSL(2,37))); Output: Magma V2.10-22 Tue Apr 6 2004 10:05:45 on modular [Seed = 2645517560] ------------------------------------- 1214784 Total time: 3.039 seconds, Total memory usage: 18.97MB ************** MAGMA ***************** Host w186.z066088156.lax-ca.dsl.cnc.net. (66.88.156.186) Time: Tue Apr 6 13:01:22 2004 Input: cos(3*acos(1/sqrt(2))) Output: Magma V2.10-22 Tue Apr 6 2004 13:01:19 on modular [Seed = 1148642885] ------------------------------------- >> cos(3*acos(1/sqrt(2))); ^ User error: Identifier 'sqrt' has not been declared or assigned Total time: 2.619 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pr10-ts.telepac.pt. (194.65.14.72) Time: Tue Apr 6 18:51:34 2004 Input: 36! Output: Magma V2.10-22 Tue Apr 6 2004 18:51:31 on modular [Seed = 1165373781] ------------------------------------- >> 36!; ^ User error: bad syntax Total time: 2.579 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 3(NXDOMAIN) (218.4.236.250) Time: Tue Apr 6 20:25:26 2004 Input: 123412341234 Output: Magma V2.10-22 Tue Apr 6 2004 20:25:23 on modular [Seed = 2378074013] ------------------------------------- 123412341234 Total time: 2.559 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Apr 6 21:16:41 2004 Input: R:=PolynomialRing(Rationals()); L:=NumberField(x^6 + 3*x^5 + 6*x^4 + 3*x^3 + 9*x + 9 ); OL:=MaximalOrder(L); I:=5*OL; F:=Factorization(I); print IntegralBasis(L); PrimitiveElement(L); F; l:=#(quo); R:=ResidueClassField(OL,F[1][1]); b:=a^l; R!a; R; Output: Magma V2.10-22 Tue Apr 6 2004 21:16:38 on modular [Seed = 4190826475] ------------------------------------- [ 1, a, a^2, 1/3*a^3, 1/9*(a^4 + 3*a^2 + 6*a), 1/9*(a^5 + 6*a^2) ] a [ , , ] >> R!a; ^ Runtime error in '!': Illegal coercion Finite field of size 5^2 Total time: 2.660 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Apr 6 22:11:27 2004 Input: R:=PolynomialRing(Rationals()); L:=NumberField(x^6 + 3*x^5 + 6*x^4 + 3*x^3 + 9*x + 9 ); OL:=MaximalOrder(L); I:=5*OL; F:=Factorization(I); print IntegralBasis(L); PrimitiveElement(L); F; l:=#(quo); R:=ResidueClassField(OL,F[1][1]); function factormod(f, p) R := PolynomialRing(GF(p)); return Factorization(R!f); end function; factormod(x^6 + 3*x^5 + 6*x^4 + 3*x^3 + 9*x + 9, 5); Output: Magma V2.10-22 Tue Apr 6 2004 22:11:24 on modular [Seed = 1466201214] ------------------------------------- [ 1, a, a^2, 1/3*a^3, 1/9*(a^4 + 3*a^2 + 6*a), 1/9*(a^5 + 6*a^2) ] a [ , , ] [ <$.1^2 + 2, 1>, <$.1^2 + 4*$.1 + 1, 1>, <$.1^2 + 4*$.1 + 2, 1> ] 1 Total time: 2.749 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Apr 6 22:16:51 2004 Input: R:=PolynomialRing(Rationals()); L:=NumberField(x^6 + 3*x^5 + 6*x^4 + 3*x^3 + 9*x + 9 ); OL:=MaximalOrder(L); I:=5*OL; F:=Factorization(I); print IntegralBasis(L); PrimitiveElement(L); F; l:=#(quo); R:=ResidueClassField(OL,F[1][1]); function factormod(f, p) R := PolynomialRing(GF(p)); return Factorization(R!f); end function; factormod(x^6 + 3*x^5 + 6*x^4 + 3*x^3 + 9*x + 9, F[1][1]); Output: Magma V2.10-22 Tue Apr 6 2004 22:16:48 on modular [Seed = 622199248] ------------------------------------- [ 1, a, a^2, 1/3*a^3, 1/9*(a^4 + 3*a^2 + 6*a), 1/9*(a^5 + 6*a^2) ] a [ , , ] factormod( f: x^6 + 3*x^5 + 6*x^4 + 3*x^3 + 9*x + 9, p: p ) >> R := PolynomialRing(GF(p)); ^ Runtime error in 'GF': Bad argument types Argument types given: RngOrdIdl Total time: 2.719 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 05:13:37 2004 Input: knapsack := function(Q, t) > R := [IntegerRing() | x : x in Q | x le t]; > if &+R lt t then > return [ ]; > elif t in R then > return [t]; > else > for x in R do > RR := Exclude(R, x); > s := $$(RR, t - x); > if not IsEmpty(s) then > return Append(s, x); > end if; > end for; > return [ ]; > end if; > end function; Output: Magma V2.10-22 Wed Apr 7 2004 05:13:33 on modular [Seed = 2378042330] ------------------------------------- Total time: 2.619 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 05:15:24 2004 Input: > G := GeneralLinearGroup(20, GF(16)); > RP := RandomProcess(G); > [ FactoredOrder(Random(RP)) : i in [1..10] ]; Output: Magma V2.10-22 Wed Apr 7 2004 05:15:21 on modular [Seed = 2662144093] ------------------------------------- [ [ <5, 2>, <11, 1>, <17, 1>, <31, 1>, <41, 1>, <257, 1>, <61681, 1>, <4278255361, 1> ], [ <3, 3>, <5, 1>, <7, 1>, <13, 1>, <19, 1>, <37, 1>, <73, 1>, <109, 1> ], [ <3, 1>, <5, 1>, <17, 1>, <29, 1>, <43, 1>, <113, 1>, <127, 1>, <15790321, 1> ], [ <3, 3>, <5, 1>, <7, 1>, <13, 1>, <19, 1>, <23, 1>, <37, 1>, <73, 1>, <89, 1>, <109, 1>, <397, 1>, <683, 1>, <2113, 1> ], [ <3, 1>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <31, 1>, <41, 1>, <61, 1>, <151, 1>, <257, 1>, <331, 1>, <1321, 1> ], [ <3, 2>, <5, 1>, <7, 1>, <13, 1>, <137, 1>, <953, 1>, <26317, 1>, <43691, 1>, <131071, 1> ], [ <3, 1>, <5, 1>, <11, 1>, <17, 1>, <29, 1>, <31, 1>, <41, 1>, <43, 1>, <113, 1>, <127, 1>, <15790321, 1> ], [ <3, 3>, <5, 1>, <7, 1>, <13, 1>, <17, 1>, <19, 1>, <37, 1>, <73, 1>, <109, 1>, <257, 1>, <65537, 1> ], [ <3, 2>, <5, 2>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <31, 1>, <41, 1>, <97, 1>, <241, 1>, <257, 1>, <673, 1> ], [ <3, 1>, <5, 1>, <229, 1>, <457, 1>, <174763, 1>, <524287, 1>, <525313, 1> ] ] Total time: 2.599 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 05:15:52 2004 Input: > G := GeneralLinearGroup(20, GF(16)); > RP := RandomProcess(G); Output: Magma V2.10-22 Wed Apr 7 2004 05:15:49 on modular [Seed = 2527399993] ------------------------------------- Total time: 2.529 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 05:20:40 2004 Input: > R := RealField(); > V := VectorSpace(R,5); > a1 := V![1,1,1,0,0]; > a2 := V![1,0,-1,0,-1]; > a3 := V![2,-1,1,1,0]; > a4 := V![4,0,0,1,-1]; > u1 := a1; > u2 := a2 - Projection( sub< V | u1 >, a2 ); > u3 := a3 - Projection( sub< V | u1,u2 >, a3 ); > u4 := a4 - Projection( sub< V | u1,u2,u3 >, a4 ); > print u1, u2, u3, u4; Output: Magma V2.10-22 Wed Apr 7 2004 05:20:38 on modular [Seed = 2051669495] ------------------------------------- >> u2 := a2 - Projection( sub< V | u1 >, a2 ); ^ Runtime error in 'Projection': Bad argument types Argument types given: ModTupFld, ModTupFldElt >> u3 := a3 - Projection( sub< V | u1,u2 >, a3 ); ^ User error: Identifier 'u2' has not been declared or assigned >> u4 := a4 - Projection( sub< V | u1,u2,u3 >, a4 ); ^ User error: Identifier 'u2' has not been declared or assigned >> print u1, u2, u3, u4;; ^ User error: Identifier 'u2' has not been declared or assigned Total time: 2.509 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 05:22:03 2004 Input: > R := RealField(); > R:=RealField(); > V := VectorSpace(R,5); > a1 := V![1,1,1,0,0]; > a2 := V![1,0,-1,0,-1]; > a3 := V![2,-1,1,1,0]; > a4 := V![4,0,0,1,-1]; > u1 := a1; > u2 := a2 - Projection( sub< V | u1 >, a2 ); > u3 := a3 - Projection( sub< V | u1,u2 >, a3 ); > u4 := a4 - Projection( sub< V | u1,u2,u3 >, a4 ); > print u1, u2, u3, u4; Output: Magma V2.10-22 Wed Apr 7 2004 05:22:00 on modular [Seed = 1916926497] ------------------------------------- >> u2 := a2 - Projection( sub< V | u1 >, a2 ); ^ Runtime error in 'Projection': Bad argument types Argument types given: ModTupFld, ModTupFldElt >> u3 := a3 - Projection( sub< V | u1,u2 >, a3 ); ^ User error: Identifier 'u2' has not been declared or assigned >> u4 := a4 - Projection( sub< V | u1,u2,u3 >, a4 ); ^ User error: Identifier 'u2' has not been declared or assigned >> print u1, u2, u3, u4;; ^ User error: Identifier 'u2' has not been declared or assigned Total time: 2.509 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 05:22:23 2004 Input: > R := RealField(); > R:=RealField(); > V := VectorSpace(R,5); > a1 := V![1,1,1,0,0]; > a2 := V![1,0,-1,0,-1]; > a3 := V![2,-1,1,1,0]; > a4 := V![4,0,0,1,-1]; > u1 := a1; > u2 := a2-Projection( sub< V | u1 >, a2 ); > u3 := a3 - Projection( sub< V | u1,u2 >, a3 ); > u4 := a4 - Projection( sub< V | u1,u2,u3 >, a4 ); > print u1, u2, u3, u4; Output: Magma V2.10-22 Wed Apr 7 2004 05:22:20 on modular [Seed = 1249493613] ------------------------------------- >> u2 := a2-Projection( sub< V | u1 >, a2 ); ^ Runtime error in 'Projection': Bad argument types Argument types given: ModTupFld, ModTupFldElt >> u3 := a3 - Projection( sub< V | u1,u2 >, a3 ); ^ User error: Identifier 'u2' has not been declared or assigned >> u4 := a4 - Projection( sub< V | u1,u2,u3 >, a4 ); ^ User error: Identifier 'u2' has not been declared or assigned >> print u1, u2, u3, u4;; ^ User error: Identifier 'u2' has not been declared or assigned Total time: 2.539 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 05:23:06 2004 Input: > R := RealField(); > R:=RealField(); > V := VectorSpace(R,5); > a1 := V![1,1,1,0,0]; > a2 := V![1,0,-1,0,-1]; > a3 := V![2,-1,1,1,0]; > a4 := V![4,0,0,1,-1]; > u1 := a1; > u2 := a2-Projection(sub,a2); > u3 := a3 - Projection( sub< V | u1,u2 >, a3 ); > u4 := a4 - Projection( sub< V | u1,u2,u3 >, a4 ); > print u1, u2, u3, u4; Output: Magma V2.10-22 Wed Apr 7 2004 05:23:03 on modular [Seed = 1114753630] ------------------------------------- >> u2 := a2-Projection(sub,a2); ^ Runtime error in 'Projection': Bad argument types Argument types given: ModTupFld, ModTupFldElt >> u3 := a3 - Projection( sub< V | u1,u2 >, a3 ); ^ User error: Identifier 'u2' has not been declared or assigned >> u4 := a4 - Projection( sub< V | u1,u2,u3 >, a4 ); ^ User error: Identifier 'u2' has not been declared or assigned >> print u1, u2, u3, u4;; ^ User error: Identifier 'u2' has not been declared or assigned Total time: 2.570 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 05:23:52 2004 Input: > R := RealField(); > R:=RealField(); > V := VectorSpace(R,5); > a1 := V![1,1,1,0,0]; > a2 := V![1,0,-1,0,-1]; > a3 := V![2,-1,1,1,0]; > a4 := V![4,0,0,1,-1]; > print a1; Output: Magma V2.10-22 Wed Apr 7 2004 05:23:50 on modular [Seed = 1500172692] ------------------------------------- (1 1 1 0 0) Total time: 2.589 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 05:24:10 2004 Input: > R := RealField(); > R:=RealField(); > V := VectorSpace(R,5); > a1 := V![1,1,1,0,0]; > a2 := V![1,0,-1,0,-1]; > a3 := V![2,-1,1,1,0]; > a4 := V![4,0,0,1,-1]; > print a1+a2; Output: Magma V2.10-22 Wed Apr 7 2004 05:24:07 on modular [Seed = 1365432717] ------------------------------------- ( 2 1 0 0 -1) Total time: 2.559 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 05:24:48 2004 Input: > a1:=2^25; > print a1; Output: Magma V2.10-22 Wed Apr 7 2004 05:24:46 on modular [Seed = 672899229] ------------------------------------- 33554432 Total time: 2.569 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 05:25:01 2004 Input: > a1:=2^52; > print a1; Output: Magma V2.10-22 Wed Apr 7 2004 05:24:58 on modular [Seed = 538159265] ------------------------------------- 4503599627370496 Total time: 2.739 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 05:25:13 2004 Input: > a1:=2^100; > print a1; Output: Magma V2.10-22 Wed Apr 7 2004 05:25:11 on modular [Seed = 1007662240] ------------------------------------- 1267650600228229401496703205376 Total time: 2.589 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 05:25:30 2004 Input: > a1:=2^155; > print a1; Output: Magma V2.10-22 Wed Apr 7 2004 05:25:28 on modular [Seed = 872922455] ------------------------------------- 45671926166590716193865151022383844364247891968 Total time: 2.549 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 05:27:08 2004 Input: > knapsack := function(Q, t) > R := [IntegerRing() | x : x in Q | x le t]; > if &+R lt t then > return [ ]; > elif t in R then > return [t]; > else > for x in R do > RR := Exclude(R, x); > s := $$(RR, t - x); > if not IsEmpty(s) then > return Append(s, x); > end if; > end for; > return [ ]; > end if; > end function; > primes := [ p : p in [1..100] | IsPrime(p) ]; > k := knapsack(primes, 151); > k, &+k; Output: Magma V2.10-22 Wed Apr 7 2004 05:27:05 on modular [Seed = 205489422] ------------------------------------- [ 43, 31, 19, 17, 13, 11, 7, 5, 3, 2 ] 151 Total time: 2.519 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 05:28:07 2004 Input: > knapsack := function(Q, t) > R := [IntegerRing() | x : x in Q | x le t]; > if &+R lt t then > return [ ]; > elif t in R then > return [t]; > else > for x in R do > RR := Exclude(R, x); > s := $$(RR, t - x); > if not IsEmpty(s) then > return Append(s, x); > end if; > end for; > return [ ]; > end if; > end function; > primes := [ p : p in [1..100] | IsPrime(p) ]; > k := knapsack(primes, 1510); > k, &+k; Output: Magma V2.10-22 Wed Apr 7 2004 05:28:04 on modular [Seed = 70749643] ------------------------------------- >> k, &+k; ^ Runtime error in '&+': Illegal null sequence Total time: 2.569 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 05:28:34 2004 Input: > knapsack := function(Q, t) > R := [IntegerRing() | x : x in Q | x le t]; > if &+R lt t then > return [ ]; > elif t in R then > return [t]; > else > for x in R do > RR := Exclude(R, x); > s := $$(RR, t - x); > if not IsEmpty(s) then > return Append(s, x); > end if; > end for; > return [ ]; > end if; > end function; > primes := [ p : p in [1..100] | IsPrime(p) ]; > k := knapsack(primes, 2043); > k, &+k; Output: Magma V2.10-22 Wed Apr 7 2004 05:28:31 on modular [Seed = 472880584] ------------------------------------- >> k, &+k; ^ Runtime error in '&+': Illegal null sequence Total time: 2.579 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 05:28:48 2004 Input: > knapsack := function(Q, t) > R := [IntegerRing() | x : x in Q | x le t]; > if &+R lt t then > return [ ]; > elif t in R then > return [t]; > else > for x in R do > RR := Exclude(R, x); > s := $$(RR, t - x); > if not IsEmpty(s) then > return Append(s, x); > end if; > end for; > return [ ]; > end if; > end function; > primes := [ p : p in [1..100] | IsPrime(p) ]; > k := knapsack(primes, 151); > k, &+k; Output: Magma V2.10-22 Wed Apr 7 2004 05:28:46 on modular [Seed = 338140593] ------------------------------------- [ 43, 31, 19, 17, 13, 11, 7, 5, 3, 2 ] 151 Total time: 2.549 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 05:29:15 2004 Input: > knapsack := function(Q, t) > R := [IntegerRing() | x : x in Q | x le t]; > if &+R lt t then > return [ ]; > elif t in R then > return [t]; > else > for x in R do > RR := Exclude(R, x); > s := $$(RR, t - x); > if not IsEmpty(s) then > return Append(s, x); > end if; > end for; > return [ ]; > end if; > end function; > primes := [ p : p in [1..100] | IsPrime(p) ]; > k := knapsack(primes, 151); > k, &+k; >Isprime(151); Output: Magma V2.10-22 Wed Apr 7 2004 05:29:12 on modular [Seed = 3974063470] ------------------------------------- [ 43, 31, 19, 17, 13, 11, 7, 5, 3, 2 ] 151 >> Isprime(151); ^ User error: Identifier 'Isprime' has not been declared or assigned Total time: 2.509 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 05:29:59 2004 Input: > knapsack := function(Q, t) > R := [IntegerRing() | x : x in Q | x le t]; > if &+R lt t then > return [ ]; > elif t in R then > return [t]; > else > for x in R do > RR := Exclude(R, x); > s := $$(RR, t - x); > if not IsEmpty(s) then > return Append(s, x); > end if; > end for; > return [ ]; > end if; > end function; > primes := [ p : p in [1..100] | IsPrime(p) ]; > k := knapsack(primes, 151); > k, &+k; >a:=Isprime(151); >a; Output: Magma V2.10-22 Wed Apr 7 2004 05:29:56 on modular [Seed = 4224217476] ------------------------------------- [ 43, 31, 19, 17, 13, 11, 7, 5, 3, 2 ] 151 >> a:=Isprime(151); ^ User error: Identifier 'Isprime' has not been declared or assigned >> a; ^ User error: Identifier 'a' has not been declared or assigned Total time: 2.509 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 05:31:49 2004 Input: > knapsack := function(Q, t) > R := [IntegerRing() | x : x in Q | x le t]; > if &+R lt t then > return [ ]; > elif t in R then > return [t]; > else > for x in R do > RR := Exclude(R, x); > s := $$(RR, t - x); > if not IsEmpty(s) then > return Append(s, x); > end if; > end for; > return [ ]; > end if; > end function; > primes := [ p : p in [1..1000] | IsPrime(p) ]; > k := knapsack(primes, 1510); > k, &+k; Output: Magma V2.10-22 Wed Apr 7 2004 05:31:46 on modular [Seed = 3422044450] ------------------------------------- [ 719, 79, 73, 71, 67, 61, 59, 53, 47, 43, 41, 37, 31, 29, 23, 19, 17, 13, 11, 7, 5, 3, 2 ] 1510 Total time: 2.560 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 06:26:01 2004 Input: a:=[1 2 3]; a; Output: Magma V2.10-22 Wed Apr 7 2004 06:25:56 on modular [Seed = 1883498281] ------------------------------------- >> a:=[1 2 3]; ^ User error: bad syntax >> a;; ^ User error: Identifier 'a' has not been declared or assigned Total time: 2.649 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 06:26:24 2004 Input: a:=3; a; Output: Magma V2.10-22 Wed Apr 7 2004 06:26:22 on modular [Seed = 1216077674] ------------------------------------- 3 Total time: 2.500 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 06:29:50 2004 Input: > Factorization(n); Output: Magma V2.10-22 Wed Apr 7 2004 06:29:47 on modular [Seed = 1516880429] ------------------------------------- >> Factorization(n);; ^ User error: Identifier 'n' has not been declared or assigned Total time: 2.519 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 06:30:07 2004 Input: > Factorization(1558); Output: Magma V2.10-22 Wed Apr 7 2004 06:30:04 on modular [Seed = 689615209] ------------------------------------- [ <2, 1>, <19, 1>, <41, 1> ] Total time: 2.569 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 06:30:52 2004 Input: > Factorization(1558); >2*19*1*41; Output: Magma V2.10-22 Wed Apr 7 2004 06:30:49 on modular [Seed = 571587095] ------------------------------------- [ <2, 1>, <19, 1>, <41, 1> ] 1558 Total time: 2.499 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 06:32:29 2004 Input: >GCD(12,569); Output: Magma V2.10-22 Wed Apr 7 2004 06:32:26 on modular [Seed = 973710060] ------------------------------------- 1 Total time: 2.549 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 06:32:52 2004 Input: >GCD(124545454,5454545569); Output: Magma V2.10-22 Wed Apr 7 2004 06:32:49 on modular [Seed = 838969999] ------------------------------------- 11 Total time: 2.550 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 06:33:12 2004 Input: >GCD(124545465498732165498754,5454546554554545569); Output: Magma V2.10-22 Wed Apr 7 2004 06:33:10 on modular [Seed = 171545216] ------------------------------------- 11 Total time: 2.529 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 06:33:30 2004 Input: >GCD(124545465498732165498754,54545465545545455690); Output: Magma V2.10-22 Wed Apr 7 2004 06:33:27 on modular [Seed = 36805273] ------------------------------------- 22 Total time: 2.579 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 06:35:32 2004 Input: > K := GF(2); > P := PolynomialRing(K); > time Factorization(x^100 + x + 1); Output: Magma V2.10-22 Wed Apr 7 2004 06:35:30 on modular [Seed = 388271625] ------------------------------------- [ , , ] Time: 0.010 Total time: 2.509 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 06:35:57 2004 Input: > K := GF(2); > P := PolynomialRing(K); > time Factorization(x^2+ x + 1); Output: Magma V2.10-22 Wed Apr 7 2004 06:35:54 on modular [Seed = 3906695438] ------------------------------------- [ ] Time: 0.000 Total time: 2.560 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 06:36:21 2004 Input: > K := GF(9); > P := PolynomialRing(K); > time Factorization(x^2+ x + 1); Output: Magma V2.10-22 Wed Apr 7 2004 06:36:19 on modular [Seed = 3771955503] ------------------------------------- [ ] Time: 0.000 Total time: 2.509 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 06:37:46 2004 Input: > input = a; >a; Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed. ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 06:40:46 2004 Input: > K := GF(2, 4); > X := FunctionField(K); > Y := PolynomialRing(X); > f := y^4+y+x^5; > F := FunctionField(f); > F; Global function field defined over Finite field of size 2^4 by y^4 + y + x^5 > Signature(F); [ <4, 1> ] DimensionOfExactConstantField(F); 1 > Genus(F); 6 Output: Magma V2.10-22 Wed Apr 7 2004 06:40:43 on modular [Seed = 3489420552] ------------------------------------- Algebraic function field defined over Univariate rational function field over GF(2^4) by y^4 + y + x^5 >> Global function field defined over ^ User error: bad syntax >> Finite field of size 2^4 by ^ User error: bad syntax >> Signature(F); ^ User error: bad syntax >> DimensionOfExactConstantField(F); ^ User error: bad syntax >> Genus(F); ^ User error: bad syntax 6 Total time: 2.589 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 06:41:50 2004 Input: > K := GF(2, 4); > X := FunctionField(K); > Y := PolynomialRing(X); > f := y^4+y+x^5; > F := FunctionField(f); > F; Output: Magma V2.10-22 Wed Apr 7 2004 06:41:47 on modular [Seed = 3237173831] ------------------------------------- Algebraic function field defined over Univariate rational function field over GF(2^4) by y^4 + y + x^5 Total time: 2.609 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 06:42:20 2004 Input: > K := GF(2, 4); > X := FunctionField(K); > Y := PolynomialRing(X); > f := y^4+y+x^5; > F := FunctionField(f); > F; > Genus(F); Output: Magma V2.10-22 Wed Apr 7 2004 06:42:17 on modular [Seed = 3639296957] ------------------------------------- Algebraic function field defined over Univariate rational function field over GF(2^4) by y^4 + y + x^5 6 Total time: 2.669 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 06:49:30 2004 Input: > function KnapsackLattice(Q, s) > n := #Q; > X := RMatrixSpace(IntegerRing(), n + 1, n + 2) ! 0; > for i := 1 to n do > X[i][i] := 2; > X[i][n + 1] := n * Q[i]; > X[n + 1][i] := 1; > end for; > X[n + 1][n + 1] := n * s; > X[n + 1][n + 2] := 1; > return Lattice(X); > end function; > function KnapsackSolutions(L) > n := Rank(L) - 1; > M := n + 1; > S := ShortVectors(L, M, M); > return [ > [i: i in [1 .. n] | v[i] ne v[n + 2]]: t in S | > forall{i: i in [1 .. n] cat [n + 2] | Abs(v[i]) eq 1} and > v[n + 1] eq 0 where v is t[1] > ]; > end function; > Q := [ 52, 218, 755, 221, 574, 593, 172, 771, 183, 810, 437, 137 ]; > s := 2676; > L := KnapsackLattice(Q, s); > L; Output: Magma V2.10-22 Wed Apr 7 2004 06:49:28 on modular [Seed = 2828743804] ------------------------------------- Lattice of rank 13 and degree 14 Basis: ( 0 0 0 0 2 0 0 0 0 0 -2 -2 0 0) ( 1 1 1 1 -1 -1 -1 -1 1 1 1 -1 0 -1) ( 1 1 -1 -1 -1 1 -1 -1 -1 1 1 1 0 1) ( 0 2 0 0 0 0 -2 0 -2 0 0 2 0 0) ( 2 0 0 2 0 -2 0 0 2 0 0 2 0 0) ( 0 0 2 0 0 -2 2 -2 0 0 2 0 0 0) ( 3 -1 1 1 -1 1 -1 -1 -1 -1 1 1 0 1) ( 1 1 1 -1 -1 1 1 -1 1 -1 -1 3 0 1) ( 1 -1 -1 3 -1 -1 1 1 -1 1 -1 -1 0 1) ( 1 -1 -1 1 1 1 1 -1 -3 1 1 -1 0 -1) ( 1 3 -3 1 -1 1 1 1 1 -1 1 1 0 1) ( 1 1 1 -3 1 -1 3 1 1 -1 -1 -1 0 -1) ( 1 -1 -1 1 -1 1 1 1 -1 -1 1 -1 -12 1) Total time: 2.530 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 06:50:23 2004 Input: > function KnapsackLattice(Q, s) > n := #Q; > X := RMatrixSpace(IntegerRing(), n + 1, n + 2) ! 0; > for i := 1 to n do > X[i][i] := 2; > X[i][n + 1] := n * Q[i]; > X[n + 1][i] := 1; > end for; > X[n + 1][n + 1] := n * s; > X[n + 1][n + 2] := 1; > return Lattice(X); > end function; > function KnapsackSolutions(L) > n := Rank(L) - 1; > M := n + 1; > S := ShortVectors(L, M, M); > return [ > [i: i in [1 .. n] | v[i] ne v[n + 2]]: t in S | > forall{i: i in [1 .. n] cat [n + 2] | Abs(v[i]) eq 1} and > v[n + 1] eq 0 where v is t[1] > ]; > end function; > Q := [ 52, 218, 755, 221, 574, 593, 172, 771, 183, 810, 437]; > s := 2676; > L := KnapsackLattice(Q, s); > L; Output: Magma V2.10-22 Wed Apr 7 2004 06:50:21 on modular [Seed = 3096126521] ------------------------------------- Lattice of rank 12 and degree 13 Basis: ( 1 1 1 1 -1 -1 -1 -1 1 1 1 0 -1) ( 1 1 -1 -1 -1 1 -1 -1 -1 1 1 0 1) ( 2 -2 2 2 0 0 0 0 0 -2 0 0 0) ( 1 -1 -1 1 1 1 1 -1 -3 1 1 0 -1) ( 0 2 0 0 2 0 -2 0 -2 0 -2 0 0) ( 0 0 2 0 0 -2 2 -2 0 0 2 0 0) ( 2 0 0 2 2 -2 0 0 2 0 -2 0 0) ( 0 2 2 -2 -2 2 0 -2 0 0 0 0 0) ( 2 2 0 -4 0 0 2 0 0 0 0 0 0) ( 2 2 0 0 0 -2 2 2 -2 0 -2 0 0) ( 0 2 -2 2 0 0 2 2 2 -2 0 0 0) ( 0 0 0 2 0 -2 0 0 0 2 -2 11 0) Total time: 2.509 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 06:50:49 2004 Input: > function KnapsackLattice(Q, s) > n := #Q; > X := RMatrixSpace(IntegerRing(), n + 1, n + 2) ! 0; > for i := 1 to n do > X[i][i] := 2; > X[i][n + 1] := n * Q[i]; > X[n + 1][i] := 1; > end for; > X[n + 1][n + 1] := n * s; > X[n + 1][n + 2] := 1; > return Lattice(X); > end function; > function KnapsackSolutions(L) > n := Rank(L) - 1; > M := n + 1; > S := ShortVectors(L, M, M); > return [ > [i: i in [1 .. n] | v[i] ne v[n + 2]]: t in S | > forall{i: i in [1 .. n] cat [n + 2] | Abs(v[i]) eq 1} and > v[n + 1] eq 0 where v is t[1] > ]; > end function; > Q := [ 52, 218, 755, 221, 574, 593, 172, 771, 183, 810, 437,137]; > s := 2676; > L := KnapsackLattice(Q, s); > L; Output: Magma V2.10-22 Wed Apr 7 2004 06:50:46 on modular [Seed = 2961386970] ------------------------------------- Lattice of rank 13 and degree 14 Basis: ( 0 0 0 0 2 0 0 0 0 0 -2 -2 0 0) ( 1 1 1 1 -1 -1 -1 -1 1 1 1 -1 0 -1) ( 1 1 -1 -1 -1 1 -1 -1 -1 1 1 1 0 1) ( 0 2 0 0 0 0 -2 0 -2 0 0 2 0 0) ( 2 0 0 2 0 -2 0 0 2 0 0 2 0 0) ( 0 0 2 0 0 -2 2 -2 0 0 2 0 0 0) ( 3 -1 1 1 -1 1 -1 -1 -1 -1 1 1 0 1) ( 1 1 1 -1 -1 1 1 -1 1 -1 -1 3 0 1) ( 1 -1 -1 3 -1 -1 1 1 -1 1 -1 -1 0 1) ( 1 -1 -1 1 1 1 1 -1 -3 1 1 -1 0 -1) ( 1 3 -3 1 -1 1 1 1 1 -1 1 1 0 1) ( 1 1 1 -3 1 -1 3 1 1 -1 -1 -1 0 -1) ( 1 -1 -1 1 -1 1 1 1 -1 -1 1 -1 -12 1) Total time: 2.509 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 06:55:57 2004 Input: > function KnapsackLattice(Q, s) > n := #Q; > X := RMatrixSpace(IntegerRing(), n + 1, n + 2) ! 0; > for i := 1 to n do > X[i][i] := 2; > X[i][n + 1] := n * Q[i]; > X[n + 1][i] := 1; > end for; > X[n + 1][n + 1] := n * s; > X[n + 1][n + 2] := 1; > return Lattice(X); > end function; > function KnapsackSolutions(L) > n := Rank(L) - 1; > M := n + 1; > S := ShortVectors(L, M, M); > return [ > [i: i in [1 .. n] | v[i] ne v[n + 2]]: t in S | > forall{i: i in [1 .. n] cat [n + 2] | Abs(v[i]) eq 1} and > v[n + 1] eq 0 where v is t[1] > ]; > end function; > Q := [ 52, 218, 755, 221, 574, 593, 172, 771, 183, 810, 437,137]; > s := 2676; > L := KnapsackLattice(Q, s); > L; > S := KnapsackSolutions(L); > S; Output: Magma V2.10-22 Wed Apr 7 2004 06:55:54 on modular [Seed = 2276727249] ------------------------------------- Lattice of rank 13 and degree 14 Basis: ( 0 0 0 0 2 0 0 0 0 0 -2 -2 0 0) ( 1 1 1 1 -1 -1 -1 -1 1 1 1 -1 0 -1) ( 1 1 -1 -1 -1 1 -1 -1 -1 1 1 1 0 1) ( 0 2 0 0 0 0 -2 0 -2 0 0 2 0 0) ( 2 0 0 2 0 -2 0 0 2 0 0 2 0 0) ( 0 0 2 0 0 -2 2 -2 0 0 2 0 0 0) ( 3 -1 1 1 -1 1 -1 -1 -1 -1 1 1 0 1) ( 1 1 1 -1 -1 1 1 -1 1 -1 -1 3 0 1) ( 1 -1 -1 3 -1 -1 1 1 -1 1 -1 -1 0 1) ( 1 -1 -1 1 1 1 1 -1 -3 1 1 -1 0 -1) ( 1 3 -3 1 -1 1 1 1 1 -1 1 1 0 1) ( 1 1 1 -3 1 -1 3 1 1 -1 -1 -1 0 -1) ( 1 -1 -1 1 -1 1 1 1 -1 -1 1 -1 -12 1) [ [ 2, 3, 4, 5, 8, 12 ], [ 3, 4, 5, 7, 8, 9 ], [ 3, 4, 7, 8, 9, 11, 12 ], [ 1, 2, 3, 4, 9, 10, 11 ] ] Total time: 2.519 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 06:57:47 2004 Input: n:=50; b:=10; > Q := [Random(1, 2^b): i in [1 .. n]]; Output: Magma V2.10-22 Wed Apr 7 2004 06:57:44 on modular [Seed = 2678849883] ------------------------------------- Total time: 2.549 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 06:58:22 2004 Input: >n:=50; >b:=10; > Q := [Random(1, 2^b): i in [1 .. n]]; Output: Magma V2.10-22 Wed Apr 7 2004 06:58:19 on modular [Seed = 2544109872] ------------------------------------- Total time: 2.559 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 06:59:10 2004 Input: > b := 1000; > n := 50; > SetSeed(1); > Q := [Random(1, 2^b): i in [1 .. n]]; Output: Magma V2.10-22 Wed Apr 7 2004 06:59:07 on modular [Seed = 1767569407] ------------------------------------- Total time: 2.519 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 06:59:46 2004 Input: > b := 1000; > n := 50; > SetSeed(1); > Q := [Random(1, 2^b): i in [1 .. n]]; >Q; Output: Magma V2.10-22 Wed Apr 7 2004 06:59:43 on modular [Seed = 1616117522] ------------------------------------- [ 68674622439477790754770292079103262950710364759234845474454192585815149637815\ 5531598234814194769307352242281634683387658772641693430298977641051014182249630\ 8460188568610710660880012920877182990881099932014686853843546532242915529903517\ 181375117595161626000410161619744719046184298090205835924998829152, 7357701981853634460982224773242534601716551222379455341659498674659190525681286\ 9222095124349639293017691088631067617971055541838941487229868776723189291238251\ 3355734067923891482097378385597921588393126557961014926249114534152302821930755\ 8562834622641622854913458799510347043149568032011215915341106366, 9823732626613392275196296558667106420197858588504812619549322499156510389406402\ 6083699912092090627963736961776637055006363350344081958645131020934305501496911\ 8902967917214840719895616302374991238469037437919909197735566283871131833444488\ 8875639659110812523275985826007815128697091746881797897030650899, 8831484794487819199274712270048994841181493604966885118572965045923656011349258\ 4690265492731646249165339739836042975243787762233662447150305254987545114622584\ 9385306045304286827613578393056278133869761821938021835026085749853608716866178\ 6090165946754768596555232317664849314586155354821379728892585197, 9584402059548586273800969012535160338496760062065512420216573938287112723256971\ 9834798803191300581463474035099032361988886939766556766623831246888166492752681\ 2608917442640927371743998182665576373020979200298048335379459304285965588000011\ 3245872328100963638927578744051901885402151940112851807760549311, 2593429030331521790296770310372302932757652645086345435885330527903796192375558\ 4487600982275758202909799880469961869329508088704345202922575790141807078315321\ 7931514075307625090023359771928346000427394701608268604523781316339565264245264\ 0300373317872749348323123185139844777582402538537911610857126526, 2821884009498234954487151045486620993118803215440298959478933999612229642600248\ 6289262613824890144436254250129464830357603753631919431057055734948277268409277\ 2334012893730861254170006075594495447869952274523981953114409704100272409294798\ 7978936689925307700183763775062764724210159839533805915928742620, 4477281046153050916566599659838088193951446210292185248347002079480612801856644\ 1713578211504284239474601043947462331168002114562707406381022459465338659723597\ 9889350130911854771759268934889956937152025872898863940055089673571324684581921\ 5078739226594701714640219251662805744991390291369991310539361334, 8176326695605211987163436279065217971283046488767901855218124220665273725109628\ 4884564632439034816955841521457824619156865881319377669302368759982596588443808\ 0195331205702790128568490924618338263959872298034380190117832115407848243444266\ 8823433600947396690956465697507900085569957724368698859342292109, 6973717540784856272219916109310844608585484176854641827010361611539005371285609\ 2023599113932147462240789315453433453514670179347154457462003920138174117707517\ 8263644828275783097640077785102985907970621658355853047430374485755198360311091\ 2628991433708222510806696897086802801306907708909033709356600103, 1718788410600164441179227714766043441243798735185634975534476227427785467099236\ 7336110691954769950777737390713282944731733959077054217656995159290724133485690\ 7817485103913134506444229782634347778335793356282480367043640981693350868991881\ 4017576251908878940885930567152513647973784451764327881200104651, 5247120497454415864317113053388779645127338720101332555102600103616182916567701\ 9682067467859823018095798615833307620270694609022752834741035942570576329497042\ 2859782313139230082620614288770844975104136739393501366544274619212625434009435\ 9156326419321373191381424415660765891845965567482127266397627567, 7246862102443771663000146221685537887530590599228958679010173750996208435095430\ 2476547883747281039584530641867797011985765127592178565427888757952512796850194\ 0244556118195813754319172542280725869766028215416592142724419194012936284179232\ 0673839231575132698575046893463034092334774547114376318347398956, 7967779277615664956839336189314349939576247136992716242183497505940541898431811\ 0696281861493799529318897420322182936320057221525773670568800110967335025575157\ 8893150825207822598338424223815983421584383268159995637983639688260111124820597\ 7929317865623475817335461519095373123961641209163674857667002106, 2998276315504187967389336499665756999503885501906741733039303949264734064469413\ 5432342722834483980306547237885844699540355705343171724650965053616722104435774\ 2939995227908530360930257449357464402859241066950098941651028174684877080206072\ 7765856780553569763137134536809319867580656459240881368119611411, 2283806118400719415293788124290345886895379519728637495521113567584021613518806\ 2442635945308367599079898715082372496731071456643741761854384996664842256145260\ 8300054356384177818307285369045213386226545137706107012435772332491425822340293\ 4014376330784020706362149206706922608850720554846385922323004562, 4735284368732716418267773801281106203651529101222012167938879047137905221582815\ 1857817727673747954814012566644569267367765500250035657313075028637401289693002\ 3064057507810042711021646874266054537301781092810402248813788895031209121347651\ 6192874623754668397039714149952731406912599716804914523664751641, 8007797450668068315764626376945942251365955351509422913557057510597122972132997\ 9463830171062877925481061509158894552832077100636610882474645220246115338727147\ 2683569038017978290594917724644830129812432833620939809878117765177764233858671\ 7465065363347310929498158925197718724316156685497518573836335514, 9476947361586446903675853010987039161571658069271537462204969719399149453272320\ 4820388877335956755036377914231325288615507255772009790568937022594835719213097\ 8018826536174453154971763926312980100581552893431720025532839726482568027338878\ 4936102705525030729576491236836265460702436284917428775778635211, 7993071958651151522334059737225652436340560873073608992932749400814484984713788\ 0493225770178789093369456849860007876692491264566781882864051859043244098528231\ 6054859769758219286689018660294739321682219752863472450768013946665124967729330\ 3237966721789912686534221284156836559304206931987980049579943407, 1446792557439205990250731169119945079917865420789455096374508024371495543030048\ 7531522536638733966680887857398372859158986472329995630536981017561567084100646\ 5527118868146105415262141357716746835178747776691171415120920731025876034625197\ 1433583589956083142304287268366568625637420623911946765915560887, 1179052488036106447538510015704451005378385921048308797361106894706250880165531\ 3501765835938473106065848987592743154430048499452096778607082375697019052538653\ 7667447943171177483613251833581341695627083249819014911614757093125382245080228\ 4317405443279975754265077726342795180952568938124681779543129904, 6401163058874351426364839097209717155514541565813346562997120587248155566263066\ 5570788457329403354763721089502232800473633645808387835247130498726652915245733\ 4107236687111559305523897211987642946590398306490472488905334164748451685294400\ 9026128641710397264663559645861234176025036684511607100815208145, 2019037333634507497538676612742354715882632953793508723165452851884468141300577\ 5073406997328750262749603280072226531806631729161153200348300924961452655103934\ 1011058701800420665682603492386598854293361920005823413159581080044636519628816\ 5161429993269875570214831235245460683797108499329606577404718728, 9348193273178504687749121311904046490894526501168965198383493396474522789943435\ 0032141871187676979068586232769364854218750871353875586440643848446117955967422\ 2907071530385608688912464334478629022217185683986588187782930288753823427077393\ 1454794726037396845938995448064565941097085861091315921101709234, 3602700326915582816357277565623069318471201484425831327617379174543252707969727\ 1599169399988397879516209445386941232884697413252475141142574431153046883679580\ 6975974613644414824823458968083856469781385552890034076694406292785201043158177\ 5940152707189250835896543946698434552349328067129304490983084461, 3783331943860399118817300898400691602655215056566576431327079450991317178315023\ 9478380793606502902744857373273910913011999529635675280607340573953511082605198\ 3373862427704216472714479451960410344081924192063022537483730521585578895256608\ 5419964187497327902398327602623159733770034844676116610931845874, 3892451897833353809355358732479558937138095245501629622601080475732507005280487\ 2547188683201080239336380983135779465673359277503917661950693520467477701051484\ 7996705134331769617498194987353380644187089653322060663605204068440137318848182\ 9398340532854122345357045779665907148280867002001525453970356891, 2583479850115341496221396499066105844444826208158719586424889844819766957104907\ 5160463458006560569830707484709653599303174618894244463206812119929426472126225\ 6868386298283709555596991546302028759330943037645676019992693561187955974269128\ 3390380502224468271242066428972428947358564587215943546701245877, 8652431196355551614391800748759958372464334703687594820642128621203692101251757\ 6925185072286253135144986157104551640377348140468926830582194323151151549605135\ 6030166407073051549824048549312494169526348082305014757731674338155254364435156\ 2016933415442869541924592980547887576418702537503986572198948109, 3423526364883310804180828702839203319777895429879015841201578796071055339189911\ 5248201712397342167689941191639989198890560646487537042435034253920546392201340\ 6918989813843244708916370749771548104665099062041741636054201367433473996435039\ 7942484525759421051385646085732553842592942944325495586943124570, 4705444800115669183322793844177301090815336515099843598899863814905385547700175\ 9551828289080755359547971166459468650670130631785905219239778851134848833697345\ 5496877082116096282809614397405739573277543393772411197120011935565985495277707\ 3330081347314181282661799825 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 07:03:52 2004 Input: > b := 2; > n := 5; > SetSeed(1); > Q := [Random(1, 2^b): i in [1 .. n]]; >Q; Output: Magma V2.10-22 Wed Apr 7 2004 07:03:50 on modular [Seed = 1600978724] ------------------------------------- [ 4, 1, 1, 2, 4 ] Total time: 2.529 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 07:05:10 2004 Input: > b := 10; > n := 50; > SetSeed(1); > Q := [Random(1, 2^b): i in [1 .. n]]; >Q; Output: Magma V2.10-22 Wed Apr 7 2004 07:05:07 on modular [Seed = 756976932] ------------------------------------- [ 96, 21, 885, 446, 700, 236, 153, 29, 398, 329, 932, 368, 349, 440, 838, 320, 477, 648, 765, 80, 464, 67, 747, 821, 370, 759, 565, 460, 570, 282, 148, 933, 190, 311, 376, 270, 336, 900, 799, 655, 347, 642, 472, 38, 1, 755, 716, 470, 259, 32 ] Total time: 2.559 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 07:05:28 2004 Input: > b := 10; > n := 50; > SetSeed(1); > Q := [Random(1, 2^b): i in [1 .. n]]; >Q(1); Output: Magma V2.10-22 Wed Apr 7 2004 07:05:25 on modular [Seed = 622232893] ------------------------------------- >> Q(1);; ^ Runtime error: Bad argument types Argument types given: RngIntElt, SeqEnum[RngIntElt] Total time: 2.559 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 07:06:01 2004 Input: > b := 10; > n := 5; > SetSeed(1); > Q := [Random(1, 2^b): i in [1 .. n]]; >Q[1]; Output: Magma V2.10-22 Wed Apr 7 2004 07:05:58 on modular [Seed = 1024368070] ------------------------------------- 96 Total time: 2.509 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 07:06:20 2004 Input: > b := 10; > n := 5; > SetSeed(1); > Q := [Random(1, 2^b): i in [1 .. n]]; >Q; >Q[1]; Output: Magma V2.10-22 Wed Apr 7 2004 07:06:18 on modular [Seed = 889624050] ------------------------------------- [ 96, 21, 885, 446, 700 ] 96 Total time: 2.509 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 07:11:40 2004 Input: function KnapsackParamGeneration (n) max_increment := 2^n; /* generate b_1 : the first element of the vector */ b_i := 2^n + Random (1, max_increment); b_vec := [b_i]; sum := b_i; for i in [2..n] do b_i := sum + Random (1, max_increment); sum +:= b_i; Append (~b_vec, b_i); end for; M := NextPrime (sum); W := Random (1, M); aprime_vec := [(b * W) mod M : b in b_vec]; pi := Random(Sym(n)); /* The public weights are... */ a_vec := [ aprime_vec[Image(pi, i)] : i in [1..n] ]; return a_vec, b_vec, M, W, pi; end function; Output: Magma V2.10-22 Wed Apr 7 2004 07:11:38 on modular [Seed = 70755715] ------------------------------------- Total time: 2.519 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host genoa.ucc.usyd.edu.au. (129.78.228.114) Time: Wed Apr 7 07:12:19 2004 Input: rounds:=[100000000000000000000..100000000000000000100]; yr:=1997; for i in rounds do if IsPrime(i*yr-1) then if IsPrime(i*yr+1) then print i*yr; Factorization(i*yr); end if; end if; end for; Output: Magma V2.10-22 Wed Apr 7 2004 07:12:16 on modular [Seed = 472890977] ------------------------------------- Total time: 2.619 seconds, Total memory usage: 2.96MB ************** MAGMA ***************** Host genoa.ucc.usyd.edu.au. (129.78.228.114) Time: Wed Apr 7 07:12:49 2004 Input: rounds:=[100000000000000000000..100000000000000001000]; yr:=1997; for i in rounds do if IsPrime(i*yr-1) then if IsPrime(i*yr+1) then print i*yr; Factorization(i*yr); end if; end if; end for; Output: Magma V2.10-22 Wed Apr 7 2004 07:12:45 on modular [Seed = 338146900] ------------------------------------- Total time: 3.599 seconds, Total memory usage: 2.96MB ************** MAGMA ***************** Host genoa.ucc.usyd.edu.au. (129.78.228.114) Time: Wed Apr 7 07:12:58 2004 Input: rounds:=[100000000000000000000..100000000000000001000]; yr:=1997; for i in rounds do if IsPrime(i*yr-1) then if IsPrime(i*yr+1) then print i*yr; Factorization(i*yr); end if; end if; end for; Output: Magma V2.10-22 Wed Apr 7 2004 07:12:55 on modular [Seed = 3974057654] ------------------------------------- Total time: 3.499 seconds, Total memory usage: 2.96MB ************** MAGMA ***************** Host genoa.ucc.usyd.edu.au. (129.78.228.114) Time: Wed Apr 7 07:13:15 2004 Input: rounds:=[100000000000000009000..100000000000000010000]; yr:=1997; for i in rounds do if IsPrime(i*yr-1) then if IsPrime(i*yr+1) then print i*yr; Factorization(i*yr); end if; end if; end for; Output: Magma V2.10-22 Wed Apr 7 2004 07:13:12 on modular [Seed = 3839313601] ------------------------------------- Total time: 3.589 seconds, Total memory usage: 2.96MB ************** MAGMA ***************** Host genoa.ucc.usyd.edu.au. (129.78.228.114) Time: Wed Apr 7 07:13:30 2004 Input: rounds:=[100000000000000009000..100000000000000010000]; yr:=1997; for i in rounds do if IsPrime(i*yr-1) then if IsPrime(i*yr+1) then print i*yr; end if; end if; end for; Output: Magma V2.10-22 Wed Apr 7 2004 07:13:26 on modular [Seed = 4241448647] ------------------------------------- Total time: 3.619 seconds, Total memory usage: 2.96MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 07:13:42 2004 Input: function KnapsackParamGeneration (n) max_increment := 2^n; /* generate b_1 : the first element of the vector */ b_i := 2^n + Random (1, max_increment); b_vec := [b_i]; sum := b_i; for i in [2..n] do b_i := sum + Random (1, max_increment); sum +:= b_i; Append (~b_vec, b_i); end for; M := NextPrime (sum); W := Random (1, M); aprime_vec := [(b * W) mod M : b in b_vec]; pi := Random(Sym(n)); /* The public weights are... */ a_vec := [ aprime_vec[Image(pi, i)] : i in [1..n] ]; return a_vec, b_vec, M, W, pi; end function; function KnapsackEncrypt (bit_stream, a_vec) n := #bit_stream; if n ne #a_vec then print "ERROR: bit_stream must be same length as a_vec"; return 0; end if; /* assume bit_stream was entered properly (contains only 1's and 0's) */ return &+[a_vec[i]*bit_stream[i] : i in [1..n]]; end function; function KnapsackDecrypt (s, b_vec, M, W, pi) c := (s * Modinv (W, M)) mod M; n := #b_vec; pi_inv := pi^-1; bit_stream := [0 : i in [1..n]]; for j in [n..1 by -1] do if c ge b_vec[j] then bit_stream[Image (pi_inv, j)] := 1; c -:= b_vec[j]; end if; end for; return bit_stream; end function; > n := 50; > a_vec, b_vec, M, W, pi := KnapsackParamGeneration (n); > a_vec; > bit_stream := [Random(0,1): i in [1..n]]; > bit_stream; > s := KnapsackEncrypt (bit_stream, a_vec); > s; > KnapsackDecrypt (s, b_vec, M, W, pi); Output: WARNING: MAGMA command contains unsafe command 'save', so it will not be executed. ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 07:15:36 2004 Input: >function KnapsackParamGeneration (n) >max_increment := 2^n; /* generate b_1 : the first element of the vector */ >b_i := 2^n + Random (1, max_increment); b_vec := [b_i]; sum := b_i; for i in [2..n] do b_i := sum + Random (1, max_increment); sum +:= b_i; Append (~b_vec, b_i); end for; M := NextPrime (sum); W := Random (1, M); aprime_vec := [(b * W) mod M : b in b_vec]; pi := Random(Sym(n)); /* The public weights are... */ a_vec := [ aprime_vec[Image(pi, i)] : i in [1..n] ]; return a_vec, b_vec, M, W, pi; end function; function KnapsackEncrypt (bit_stream, a_vec) n := #bit_stream; if n ne #a_vec then print "ERROR: bit_stream must be same length as a_vec"; return 0; end if; /* assume bit_stream was entered properly (contains only 1's and 0's) */ return &+[a_vec[i]*bit_stream[i] : i in [1..n]]; end function; function KnapsackDecrypt (s, b_vec, M, W, pi) c := (s * Modinv (W, M)) mod M; n := #b_vec; pi_inv := pi^-1; bit_stream := [0 : i in [1..n]]; for j in [n..1 by -1] do if c ge b_vec[j] then bit_stream[Image (pi_inv, j)] := 1; c -:= b_vec[j]; end if; end for; return bit_stream; end function; > n := 50; > a_vec, b_vec, M, W, pi := KnapsackParamGeneration (n); > a_vec; > bit_stream := [Random(0,1): i in [1..n]]; > bit_stream; > s := KnapsackEncrypt (bit_stream, a_vec); > s; > KnapsackDecrypt (s, b_vec, M, W, pi); Output: WARNING: MAGMA command contains unsafe command 'save', so it will not be executed. ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 07:20:16 2004 Input: >function KnapsackParamGeneration (n) >max_increment := 2^n; /* generate b_1 : the first element of the vector */ >b_i := 2^n + Random (1, max_increment); b_vec := [b_i]; sum := b_i; for i in [2..n] do b_i := sum + Random (1, max_increment); sum +:= b_i; Append (~b_vec, b_i); end for; M := NextPrime (sum); W := Random (1, M); aprime_vec := [(b * W) mod M : b in b_vec]; pi := Random(Sym(n)); /* The public weights are... */ a_vec := [ aprime_vec[Image(pi, i)] : i in [1..n] ]; return a_vec, b_vec, M, W, pi; end function; function KnapsackEncrypt (bit_stream, a_vec) n := #bit_stream; if n ne #a_vec then print "ERROR: bit_stream must be same length as a_vec"; return 0; end if; /* assume bit_stream was entered properly (contains only 1's and 0's) */ return &+[a_vec[i]*bit_stream[i] : i in [1..n]]; end function; function KnapsackDecrypt (s, b_vec, M, W, pi) c := (s * Modinv (W, M)) mod M; n := #b_vec; pi_inv := pi^-1; bit_stream := [0 : i in [1..n]]; for j in [n..1 by -1] do if c ge b_vec[j] then bit_stream[Image (pi_inv, j)] := 1; c -:= b_vec[j]; end if; end for; return bit_stream; end function; > n := 50; > a_vec, b_vec, M, W, pi := KnapsackParamGeneration (n); > a_vec; > bit_stream := [Random(0,1): i in [1..n]]; > bit_stream; > s := KnapsackEncrypt (bit_stream, a_vec); > s; > KnapsackDecrypt (s, b_vec, M, W, pi); Output: WARNING: MAGMA command contains unsafe command 'save', so it will not be executed. ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 07:21:21 2004 Input: >function KnapsackParamGeneration (n) >max_increment := 2^n; >/* generate b_1 : the first element of the vector */ >b_i := 2^n + Random (1, max_increment); >b_vec := [b_i]; >sum := b_i; >for i in [2..n] do >b_i := sum + Random (1, max_increment); >sum +:= b_i; >Append (~b_vec, b_i); >end for; >M := NextPrime (sum); >W := Random (1, M); >aprime_vec := [(b * W) mod M : b in b_vec]; >pi := Random(Sym(n)); >/* The public weights are... */ >a_vec := [ aprime_vec[Image(pi, i)] : i in [1..n] ]; >return a_vec, b_vec, M, W, pi; >end function; >function KnapsackEncrypt (bit_stream, a_vec) >n := #bit_stream; >if n ne #a_vec then >print "ERROR: bit_stream must be same length as a_vec"; >return 0; >end if; >/* assume bit_stream was entered properly (contains only 1's and 0's) */ >return &+[a_vec[i]*bit_stream[i] : i in [1..n]]; >end function; >function KnapsackDecrypt (s, b_vec, M, W, pi) >c := (s * Modinv (W, M)) mod M; >n := #b_vec; >pi_inv := pi^-1; >bit_stream := [0 : i in [1..n]]; >for j in [n..1 by -1] do >if c ge b_vec[j] then >bit_stream[Image (pi_inv, j)] := 1; >c -:= b_vec[j]; >end if; >end for; >return bit_stream; >end function; > n := 50; > a_vec, b_vec, M, W, pi := KnapsackParamGeneration (n); > a_vec; > bit_stream := [Random(0,1): i in [1..n]]; > bit_stream; > s := KnapsackEncrypt (bit_stream, a_vec); > s; > KnapsackDecrypt (s, b_vec, M, W, pi); Output: WARNING: MAGMA command contains unsafe command 'save', so it will not be executed. ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 07:23:16 2004 Input: >function KnapsackParamGeneration (n) >max_increment := 2^n; >/* generate b_1 : the first element of the vector */ >b_i := 2^n + Random (1, max_increment); >b_vec := [b_i]; >sum := b_i; >for i in [2..n] do >b_i := sum + Random (1, max_increment); >sum +:= b_i; >Append (~b_vec, b_i); >end for; >M := NextPrime (sum); >W := Random (1, M); >aprime_vec := [(b * W) mod M : b in b_vec]; >pi := Random(Sym(n)); >/* The public weights are... */ >a_vec := [ aprime_vec[Image(pi, i)] : i in [1..n] ]; >return a_vec, b_vec, M, W, pi; >end function; >function KnapsackEncrypt (bit_stream, a_vec) >n := #bit_stream; >if n ne #a_vec then >print "ERROR: bit_stream must be same length as a_vec"; >return 0; >end if; >/* assume bit_stream was entered properly (contains only 1's and 0's) */ >return &+[a_vec[i]*bit_stream[i] : i in [1..n]]; >end function; >function KnapsackDecrypt (s, b_vec, M, W, pi) >c := (s * Modinv (W, M)) mod M; >n := #b_vec; >pi_inv := pi^-1; >bit_stream := [0 : i in [1..n]]; >for j in [n..1 by -1] do >if c ge b_vec[j] then >bit_stream[Image (pi_inv, j)] := 1; >c -:= b_vec[j]; >end if; >end for; >return bit_stream; >end function; > n := 50; > a_vec, b_vec, M, W, pi := KnapsackParamGeneration (n); > a_vec; > bit_stream := [Random(0,1): i in [1..n]]; > bit_stream; > s := KnapsackEncrypt (bit_stream, a_vec); > s; > KnapsackDecrypt (s, b_vec, M, W, pi); Output: WARNING: MAGMA command contains unsafe command 'save', so it will not be executed. ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 07:23:41 2004 Input: >function KnapsackParamGeneration (n) >max_increment := 2^n; >/* generate b_1 : the first element of the vector */ >b_i := 2^n + Random (1, max_increment); >b_vec := [b_i]; >sum := b_i; >for i in [2..n] do >b_i := sum + Random (1, max_increment); >sum +:= b_i; >end for; >M := NextPrime (sum); >W := Random (1, M); >aprime_vec := [(b * W) mod M : b in b_vec]; >pi := Random(Sym(n)); >/* The public weights are... */ >a_vec := [ aprime_vec[Image(pi, i)] : i in [1..n] ]; >return a_vec, b_vec, M, W, pi; >end function; >function KnapsackEncrypt (bit_stream, a_vec) >n := #bit_stream; >if n ne #a_vec then >print "ERROR: bit_stream must be same length as a_vec"; >return 0; >end if; >/* assume bit_stream was entered properly (contains only 1's and 0's) */ >return &+[a_vec[i]*bit_stream[i] : i in [1..n]]; >end function; >function KnapsackDecrypt (s, b_vec, M, W, pi) >c := (s * Modinv (W, M)) mod M; >n := #b_vec; >pi_inv := pi^-1; >bit_stream := [0 : i in [1..n]]; >for j in [n..1 by -1] do >if c ge b_vec[j] then >bit_stream[Image (pi_inv, j)] := 1; >c -:= b_vec[j]; >end if; >end for; >return bit_stream; >end function; > n := 50; > a_vec, b_vec, M, W, pi := KnapsackParamGeneration (n); > a_vec; > bit_stream := [Random(0,1): i in [1..n]]; > bit_stream; > s := KnapsackEncrypt (bit_stream, a_vec); > s; > KnapsackDecrypt (s, b_vec, M, W, pi); Output: WARNING: MAGMA command contains unsafe command 'save', so it will not be executed. ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 07:31:18 2004 Input: >function KnapsackParamGeneration (n) >max_increment := 2^n; >/* generate b_1 : the first element of the vector */ >b_i := 2^n + Random (1, max_increment); >b_vec := [b_i]; >sum := b_i; >for i in [2..n] do >b_i := sum + Random (1, max_increment); >sum +:= b_i; >Append (~b_vec, b_i); >end for; >M := NextPrime (sum); >W := Random (1, M); >aprime_vec := [(b * W) mod M : b in b_vec]; >pi := Random(Sym(n)); >/* The public weights are... */ >a_vec := [ aprime_vec[Image(pi, i)] : i in [1..n] ]; >return a_vec, b_vec, M, W, pi; >end function; >function KnapsackEncrypt (bit_stream, a_vec) >n := #bit_stream; >if n ne #a_vec then >print "ERROR: bit_stream must be same length as a_vec"; >return 0; >end if; >/* assume bit_stream was entered properly (contains only 1's and 0's) */ >return &+[a_vec[i]*bit_stream[i] : i in [1..n]]; >end function; >function KnapsackDecrypt (s, b_vec, M, W, pi) >c := (s * Modinv (W, M)) mod M; >n := #b_vec; >pi_inv := pi^-1; >bit_stream := [0 : i in [1..n]]; >for j in [n..1 by -1] do >if c ge b_vec[j] then >bit_stream[Image (pi_inv, j)] := 1; >c -:= b_vec[j]; >end if; >end for; >return bit_stream; >end function; > n := 50; n; > a_vec, b_vec, M, W, pi := KnapsackParamGeneration (n); > a_vec; > bit_stream := [Random(0,1): i in [1..n]]; > bit_stream; > s := KnapsackEncrypt (bit_stream, a_vec); > s; > KnapsackDecrypt (s, b_vec, M, W, pi); Output: WARNING: MAGMA command contains unsafe command 'save', so it will not be executed. ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 07:32:32 2004 Input: a:=10; a; Output: Magma V2.10-22 Wed Apr 7 2004 07:32:29 on modular [Seed = 2662152254] ------------------------------------- 10 Total time: 2.550 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 07:32:57 2004 Input: /*laya */ a:=10; a; Output: Magma V2.10-22 Wed Apr 7 2004 07:32:55 on modular [Seed = 2527408156] ------------------------------------- 10 Total time: 2.549 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 07:33:20 2004 Input: /*laya * a:=10; a; Output: Magma V2.10-22 Wed Apr 7 2004 07:33:18 on modular [Seed = 1834929149] ------------------------------------- >> /*laya * ^ User error: Unterminated /* comment Total time: 2.509 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 07:33:33 2004 Input: >function KnapsackParamGeneration (n) >max_increment := 2^n; >b_i := 2^n + Random (1, max_increment); >b_vec := [b_i]; >sum := b_i; >for i in [2..n] do >b_i := sum + Random (1, max_increment); >sum +:= b_i; >Append (~b_vec, b_i); >end for; >M := NextPrime (sum); >W := Random (1, M); >aprime_vec := [(b * W) mod M : b in b_vec]; >pi := Random(Sym(n)); >a_vec := [ aprime_vec[Image(pi, i)] : i in [1..n] ]; >return a_vec, b_vec, M, W, pi; >end function; >function KnapsackEncrypt (bit_stream, a_vec) >n := #bit_stream; >if n ne #a_vec then >print "ERROR: bit_stream must be same length as a_vec"; >return 0; >end if; >return &+[a_vec[i]*bit_stream[i] : i in [1..n]]; >end function; >function KnapsackDecrypt (s, b_vec, M, W, pi) >c := (s * Modinv (W, M)) mod M; >n := #b_vec; >pi_inv := pi^-1; >bit_stream := [0 : i in [1..n]]; >for j in [n..1 by -1] do >if c ge b_vec[j] then >bit_stream[Image (pi_inv, j)] := 1; >c -:= b_vec[j]; >end if; >end for; >return bit_stream; >end function; > n := 50; n; > a_vec, b_vec, M, W, pi := KnapsackParamGeneration (n); > a_vec; > bit_stream := [Random(0,1): i in [1..n]]; > bit_stream; > s := KnapsackEncrypt (bit_stream, a_vec); > s; > KnapsackDecrypt (s, b_vec, M, W, pi); Output: WARNING: MAGMA command contains unsafe command 'save', so it will not be executed. ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 07:34:25 2004 Input: /*laya * a:=10; a; print "ERROR: bit_stream must be same length as a_vec"; Output: WARNING: MAGMA command contains unsafe command 'save', so it will not be executed. ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 07:36:00 2004 Input: function KnapsackParamGeneration (n) max_increment := 2^n; b_i := 2^n + Random (1, max_increment); b_vec := [b_i]; sum := b_i; for i in [2..n] do b_i := sum + Random (1, max_increment); sum +:= b_i; /*Append (~b_vec, b_i);*/ end for; M := NextPrime (sum); W := Random (1, M); aprime_vec := [(b * W) mod M : b in b_vec]; pi := Random(Sym(n)); a_vec := [ aprime_vec[Image(pi, i)] : i in [1..n] ]; return a_vec, b_vec, M, W, pi; end function; function KnapsackEncrypt (bit_stream, a_vec) n := #bit_stream; if n ne #a_vec then return 0; end if; return &+[a_vec[i]*bit_stream[i] : i in [1..n]]; end function; function KnapsackDecrypt (s, b_vec, M, W, pi) c := (s * Modinv (W, M)) mod M; n := #b_vec; pi_inv := pi^-1; bit_stream := [0 : i in [1..n]]; for j in [n..1 by -1] do if c ge b_vec[j] then bit_stream[Image (pi_inv, j)] := 1; c -:= b_vec[j]; end if; end for; return bit_stream; end function; n := 50; a_vec, b_vec, M, W, pi := KnapsackParamGeneration (n); a_vec; bit_stream := [Random(0,1): i in [1..n]]; bit_stream; s := KnapsackEncrypt (bit_stream, a_vec); s; > KnapsackDecrypt (s, b_vec, M, W, pi); Output: Magma V2.10-22 Wed Apr 7 2004 07:35:57 on modular [Seed = 1283451839] ------------------------------------- KnapsackParamGeneration( n: 50 ) >> a_vec := [ aprime_vec[Image(pi, i)] : i in [1..n] ]; ^ Runtime error in '[]': Sequence element 38 not defined >> a_vec; ^ User error: Identifier 'a_vec' has not been declared or assigned [ 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0 ] >> s := KnapsackEncrypt (bit_stream, a_vec); ^ User error: Identifier 'a_vec' has not been declared or assigned >> s; ^ User error: Identifier 's' has not been declared or assigned >> KnapsackDecrypt (s, b_vec, M, W, pi);; ^ User error: Identifier 's' has not been declared or assigned Total time: 2.630 seconds, Total memory usage: 2.98MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 07:36:58 2004 Input: function KnapsackParamGeneration (n) max_increment := 2^n; b_i := 2^n + Random (1, max_increment); b_vec := [b_i]; sum := b_i; for i in [2..n] do b_i := sum + Random (1, max_increment); sum +:= b_i; Append (~b_vec, b_i); end for; M := NextPrime (sum); W := Random (1, M); aprime_vec := [(b * W) mod M : b in b_vec]; pi := Random(Sym(n)); a_vec := [ aprime_vec[Image(pi, i)] : i in [1..n] ]; return a_vec, b_vec, M, W, pi; end function; function KnapsackEncrypt (bit_stream, a_vec) n := #bit_stream; if n ne #a_vec then return 0; end if; return &+[a_vec[i]*bit_stream[i] : i in [1..n]]; end function; function KnapsackDecrypt (s, b_vec, M, W, pi) c := (s * Modinv (W, M)) mod M; n := #b_vec; pi_inv := pi^-1; bit_stream := [0 : i in [1..n]]; for j in [n..1 by -1] do if c ge b_vec[j] then bit_stream[Image (pi_inv, j)] := 1; c -:= b_vec[j]; end if; end for; return bit_stream; end function; n := 50; a_vec, b_vec, M, W, pi := KnapsackParamGeneration (n); a_vec; bit_stream := [Random(0,1): i in [1..n]]; bit_stream; s := KnapsackEncrypt (bit_stream, a_vec); s; KnapsackDecrypt (s, b_vec, M, W, pi); Output: Magma V2.10-22 Wed Apr 7 2004 07:36:55 on modular [Seed = 1165419260] ------------------------------------- [ 1463314945879959113763461342745, 1260474734041962430255758960121, 1077120172078782521821702269934, 536812333623158097645548648016, 1180875455218399468440166093380, 1115064658712827356158520290718, 815589399708163778593758595411, 104472177149709985316496695291, 860144872174943239719275758090, 732894799305926556997951394736, 1186774047125330101695531142187, 1106374556741877026650196199022, 742228236675194765620973680411, 1103315468873059268374443443041, 583952969965708451739002849159, 667012380013210681038707822916, 769813090135914490218940028085, 1489157042547337558341505243797, 318696441278373390145591752679, 961505082097329558076424511831, 1070370010779205231297863870605, 703064910612565086769280210674, 481224288856480488853605403758, 935929133921112443937106611787, 152325696808389270025012545161, 724473018290196079397443042823, 329488353724364294680447368137, 935112409132079878718064637966, 1144512006760781355050884097155, 163154662210827030271092590758, 1166750336593563683043550215361, 257819255796566930617057367187, 334447022148206488963791726999, 371289939902838527804782982049, 595261802030273634631918455584, 551589588063651706218900851414, 1308743893234633487414393778814, 1490273329851405972276307766968, 953038777347148982229310173857, 1054173084525764894456628361201, 1110279532680337599515866825504, 394983386597100728618427197080, 1444827282284523326336644773065, 87676548017984104943412941705, 1219579131885529181396705386454, 229827027440001780281854248033, 1337948394073036122921634703631, 1247246534778169733020591275985, 1028615126509954603010965623876, 1408589128032280312732435700360 ] [ 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1 ] 31012780458354161159586862624121 [ 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1 ] Total time: 2.649 seconds, Total memory usage: 2.98MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 07:38:11 2004 Input: function KnapsackParamGeneration (n) max_increment := 2^n; b_i := 2^n + Random (1, max_increment); b_vec := [b_i]; sum := b_i; for i in [2..n] do b_i := sum + Random (1, max_increment); sum +:= b_i; Append (~b_vec, b_i); end for; M := NextPrime (sum); W := Random (1, M); aprime_vec := [(b * W) mod M : b in b_vec]; pi := Random(Sym(n)); a_vec := [ aprime_vec[Image(pi, i)] : i in [1..n] ]; return a_vec, b_vec, M, W, pi; end function; function KnapsackEncrypt (bit_stream, a_vec) n := #bit_stream; if n ne #a_vec then return 0; end if; return &+[a_vec[i]*bit_stream[i] : i in [1..n]]; end function; function KnapsackDecrypt (s, b_vec, M, W, pi) c := (s * Modinv (W, M)) mod M; n := #b_vec; pi_inv := pi^-1; bit_stream := [0 : i in [1..n]]; for j in [n..1 by -1] do if c ge b_vec[j] then bit_stream[Image (pi_inv, j)] := 1; c -:= b_vec[j]; end if; end for; return bit_stream; end function; n := 50; n; a_vec, b_vec, M, W, pi := KnapsackParamGeneration (n); a_vec; bit_stream := [Random(0,1): i in [1..n]]; bit_stream; s := KnapsackEncrypt (bit_stream, a_vec); s; KnapsackDecrypt (s, b_vec, M, W, pi); Output: Magma V2.10-22 Wed Apr 7 2004 07:38:08 on modular [Seed = 1567552787] ------------------------------------- 50 [ 28396762283700512628143411555, 14507040122991338772799236301, 411313112392839649872536576821, 756432356078459985206584774176, 66900104694363842958158357710, 347089275506495261779828762023, 543562343105460216281458639673, 214564472165005644295094206222, 142497826503507283206372886417, 311385255667678161761459097178, 746624702890673506568879469854, 94135102537102871750732737217, 318652299599642157148936253065, 636924491369569341051524754219, 153707546876972418367130004512, 372728836715660378290237625270, 526968660427350523719760718262, 392889373972926950600183793218, 708058590265770826956897709243, 502443794881804928294981103320, 291011438129878476139864909817, 142642243643959095057881425872, 97602986663290898557577976073, 379948147205873713616171945844, 159982054106981794844581934727, 220050583962244688511901658996, 503029619865919869105156921043, 487166330955696880006367059467, 785779557766120273531069211144, 133272963384677108843743978818, 82859707420658572844236172762, 453244551159733455818353685376, 484149961490122174283869361966, 50605575263531769204324746296, 724947150440667096333381436141, 596315940294136529911974785007, 312799900438463995654855507086, 128443985433980462542859124989, 17828941382345868682635629640, 88585520414868986044560073017, 102442367706910256600166739605, 618128742561081906885958231702, 769055363917452884481751341389, 784070942892441667488862890954, 435469054407328800253020087847, 752525994380543064138696441431, 280102597215442409111739416215, 375585912203369125331076814196, 80351492114076306725367902920, 741718792164711032330406119305 ] [ 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0 ] 9421449051273768520513839366167 [ 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0 ] Total time: 2.619 seconds, Total memory usage: 2.88MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 07:38:49 2004 Input: function KnapsackParamGeneration (n) max_increment := 2^n; b_i := 2^n + Random (1, max_increment); b_vec := [b_i]; sum := b_i; for i in [2..n] do b_i := sum + Random (1, max_increment); sum +:= b_i; Append (~b_vec, b_i); end for; M := NextPrime (sum); W := Random (1, M); aprime_vec := [(b * W) mod M : b in b_vec]; pi := Random(Sym(n)); a_vec := [ aprime_vec[Image(pi, i)] : i in [1..n] ]; return a_vec, b_vec, M, W, pi; end function; function KnapsackEncrypt (bit_stream, a_vec) n := #bit_stream; if n ne #a_vec then return 0; end if; return &+[a_vec[i]*bit_stream[i] : i in [1..n]]; end function; function KnapsackDecrypt (s, b_vec, M, W, pi) c := (s * Modinv (W, M)) mod M; n := #b_vec; pi_inv := pi^-1; bit_stream := [0 : i in [1..n]]; for j in [n..1 by -1] do if c ge b_vec[j] then bit_stream[Image (pi_inv, j)] := 1; c -:= b_vec[j]; end if; end for; return bit_stream; end function; n := 50; n; a_vec, b_vec, M, W, pi := KnapsackParamGeneration (n); a_vec; n; bit_stream := [Random(0,1): i in [1..n]]; bit_stream; n; s := KnapsackEncrypt (bit_stream, a_vec); s; KnapsackDecrypt (s, b_vec, M, W, pi); Output: Magma V2.10-22 Wed Apr 7 2004 07:38:46 on modular [Seed = 1432812925] ------------------------------------- 50 [ 417740274523981320227651638257, 74891988558673770299112534496, 235472534253030545861126159131, 680487024547738386959725639651, 176149204281001548966790117717, 14845431126376740115314439832, 863700797736833083137199377591, 327787576132837632521887219522, 447357647225727150750357029224, 66538874000256122619250115824, 704754897906622883916321261056, 864155053210594022511529340002, 286498932353550002801065870266, 283624200130945274416422128501, 748226741423813071048304956331, 795444182436224578758949001094, 664944584285166948362088173666, 732786111076416302976086028885, 638783822164578508719065508465, 324792903352557455469385879993, 654937633158052767975583434503, 176856047052125818940517796685, 281608415169571772114662605602, 211039088030002934359315157002, 280982699686742620964590104643, 375868708321728989413108702536, 248987459663041918513029758602, 364636076433135291606423899181, 505560644717772278161808132873, 793608702378009952991777794793, 111617863943154606050094329026, 452692671930742546364658390245, 860939153855019818431842615797, 187023979817980900208663735239, 368743596707773891036525683531, 685109594262786599733794309606, 844913249021069651444518745996, 331180318075101996235940856020, 562278538461322748518057777436, 239994342393967025576299170336, 100668460954523781209408123719, 646878119359776330078195304997, 51412585100948405136439318647, 762784226627968700254800602743, 10321304115042783982852532026, 694802473550389125049379661770, 459287628152520704213965925940, 639419680771224322311246497139, 392846604207682739401557686406, 174886939674778429581288372488 ] 50 [ 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0 ] 50 9862739982646456711123647414319 [ 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0 ] Total time: 2.609 seconds, Total memory usage: 2.98MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 07:40:09 2004 Input: function KnapsackParamGeneration (n) max_increment := 2^n; b_i := 2^n + Random (1, max_increment); b_vec := [b_i]; sum := b_i; for i in [2..n] do b_i := sum + Random (1, max_increment); sum +:= b_i; Append (~b_vec, b_i); end for; M := NextPrime (sum); W := Random (1, M); aprime_vec := [(b * W) mod M : b in b_vec]; pi := Random(Sym(n)); a_vec := [ aprime_vec[Image(pi, i)] : i in [1..n] ]; return a_vec, b_vec, M, W, pi; end function; function KnapsackEncrypt (bit_stream, a_vec) n := #bit_stream; if n ne #a_vec then return 0; end if; return &+[a_vec[i]*bit_stream[i] : i in [1..n]]; end function; function KnapsackDecrypt (s, b_vec, M, W, pi) c := (s * Modinv (W, M)) mod M; n := #b_vec; pi_inv := pi^-1; bit_stream := [0 : i in [1..n]]; for j in [n..1 by -1] do if c ge b_vec[j] then bit_stream[Image (pi_inv, j)] := 1; c -:= b_vec[j]; end if; end for; return bit_stream; end function; n := 5; n; a_vec, b_vec, M, W, pi := KnapsackParamGeneration (n); a_vec; n; bit_stream := [Random(0,1): i in [1..n]]; bit_stream; n; s := KnapsackEncrypt (bit_stream, a_vec); s; KnapsackDecrypt (s, b_vec, M, W, pi); Output: Magma V2.10-22 Wed Apr 7 2004 07:40:07 on modular [Seed = 622235100] ------------------------------------- 5 [ 680, 227, 395, 743, 577 ] 5 [ 0, 1, 0, 0, 1 ] 5 804 [ 0, 1, 0, 0, 1 ] Total time: 2.569 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 07:42:19 2004 Input: function KnapsackParamGeneration (n) max_increment := 2^n; b_i := 2^n + Random (1, max_increment); b_vec := [b_i]; sum := b_i; for i in [2..n] do b_i := sum + Random (1, max_increment); sum +:= b_i; Append (~b_vec, b_i); end for; M := NextPrime (sum); W := Random (1, M); aprime_vec := [(b * W) mod M : b in b_vec]; pi := Random(Sym(n)); a_vec := [ aprime_vec[Image(pi, i)] : i in [1..n] ]; return a_vec, b_vec, M, W, pi; end function; function KnapsackEncrypt (bit_stream, a_vec) n := #bit_stream; if n ne #a_vec then return 0; end if; return &+[a_vec[i]*bit_stream[i] : i in [1..n]]; end function; function KnapsackDecrypt (s, b_vec, M, W, pi) c := (s * Modinv (W, M)) mod M; n := #b_vec; pi_inv := pi^-1; bit_stream := [0 : i in [1..n]]; for j in [n..1 by -1] do if c ge b_vec[j] then bit_stream[Image (pi_inv, j)] := 1; c -:= b_vec[j]; end if; end for; return bit_stream; end function; n := 32; n; a_vec, b_vec, M, W, pi := KnapsackParamGeneration (n); a_vec; n; bit_stream := [Random(0,1): i in [1..n]]; bit_stream; n; s := KnapsackEncrypt (bit_stream, a_vec); s; KnapsackDecrypt (s, b_vec, M, W, pi); Output: Magma V2.10-22 Wed Apr 7 2004 07:42:17 on modular [Seed = 973706061] ------------------------------------- 32 [ 14318916599771025695, 12952588988303984010, 10880410492154800703, 12260991175227874261, 4858818008546809075, 10256933748215261955, 16319411949639925398, 8189400787577031850, 6089329977125996359, 1087438545384007426, 1776236753704418848, 44618260901065820, 12780627332464214730, 10846229630263611086, 4733806331483345808, 1391655253953866170, 2941486258312847799, 5993095511910027458, 4332490238764697078, 8961156792833113635, 13394192052715579145, 11556064343559282326, 8445723303982484637, 10950020483301292089, 12691648040478871492, 16231432962271155408, 11593992841134288650, 14125876289871443665, 2334444125134984545, 2405402938381861675, 5291133487196713615, 15461523855517316631 ] 32 [ 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ] 32 99967703877793629472 [ 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ] Total time: 2.600 seconds, Total memory usage: 2.88MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 07:45:25 2004 Input: function KnapsackParamGeneration (n) max_increment := 2^n; b_i := 2^n + Random (1, max_increment); b_vec := [b_i]; sum := b_i; for i in [2..n] do b_i := sum + Random (1, max_increment); sum +:= b_i; Append (~b_vec, b_i); end for; M := NextPrime (sum); W := Random (1, M); aprime_vec := [(b * W) mod M : b in b_vec]; pi := Random(Sym(n)); a_vec := [ aprime_vec[Image(pi, i)] : i in [1..n] ]; return a_vec, b_vec, M, W, pi; end function; function KnapsackEncrypt (bit_stream, a_vec) n := #bit_stream; if n ne #a_vec then return 0; end if; return &+[a_vec[i]*bit_stream[i] : i in [1..n]]; end function; function KnapsackDecrypt (s, b_vec, M, W, pi) c := (s * Modinv (W, M)) mod M; n := #b_vec; pi_inv := pi^-1; bit_stream := [0 : i in [1..n]]; for j in [n..1 by -1] do if c ge b_vec[j] then bit_stream[Image (pi_inv, j)] := 1; c -:= b_vec[j]; end if; end for; return bit_stream; end function; n := 32; n; a_vec, b_vec, M, W, pi := KnapsackParamGeneration (n); a_vec; n; bit_stream := [Random(0,1): i in [1..n]]; bit_stream; n; s := KnapsackEncrypt (bit_stream, a_vec); s; KnapsackDecrypt (s, b_vec, M, W, pi); b_vec; Output: Magma V2.10-22 Wed Apr 7 2004 07:45:22 on modular [Seed = 255633075] ------------------------------------- 32 [ 8368358207619572103, 11338213030478682204, 1603476977662336819, 5074665584591468726, 14252437603065287388, 10082687325911339688, 9973328930446829886, 5595965976278112340, 6169672123095347136, 13651807905243218083, 1169809268610627537, 6953306729519215797, 648192026033419134, 7773349644540384020, 8464395675896277231, 9797710116751927546, 12182331808530542371, 6769950483066688785, 12672379557157773436, 9674466824742649407, 8728292676752104805, 11933633527183219642, 15435538871229319062, 7205843172360722795, 4959947915473661159, 15223806639013610070, 2547470255529414398, 14431180883261051210, 6565374342922842005, 11382439605705117829, 5306507766953150784, 13250149471325463414 ] 32 [ 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1 ] 32 178549964037629622479 [ 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1 ] [ 6348392848, 6634309093, 15156705122, 28671194560, 58841259297, 116144888968, 235805630329, 471496358142, 939925919534, 1882918598900, 3764783900941, 7528278604083, 15056678936703, 30115751903070, 60229155312776, 120457305379066, 240915003307547, 481830415070609, 963662243564834, 1927325343223612, 3854649702082754, 7709298572358418, 15418596067117680, 30837194514615656, 61674388642614034, 123348777212099375, 246697552388672548, 493395105732783227, 986790211045997055, 1973580425070148370, 3947160845978024363, 7894321693318984092 ] Total time: 2.639 seconds, Total memory usage: 2.88MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 07:51:52 2004 Input: n:=20; max_increment:=2^n; b_i := 2^n + Random (1, max_increment); b_i; Output: Magma V2.10-22 Wed Apr 7 2004 07:51:50 on modular [Seed = 438939938] ------------------------------------- 1807565 Total time: 2.539 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 07:53:09 2004 Input: n:=20; max_increment:=2^n; max_increment; b_i := 2^n + Random (1, max_increment); b_i; Output: Magma V2.10-22 Wed Apr 7 2004 07:53:06 on modular [Seed = 304200158] ------------------------------------- 1048576 1919214 Total time: 2.590 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 07:54:37 2004 Input: function KnapsackParamGeneration (n) max_increment := 2^n; b_i := 2^n + Random (1, max_increment); b_vec := [b_i]; sum := b_i; for i in [2..n] do b_i := sum + Random (1, max_increment); sum +:= b_i; Append (~b_vec, b_i); end for; M := NextPrime (sum); W := Random (1, M); aprime_vec := [(b * W) mod M : b in b_vec]; pi := Random(Sym(n)); a_vec := [ aprime_vec[Image(pi, i)] : i in [1..n] ]; return a_vec, b_vec, M, W, pi; end function; function KnapsackEncrypt (bit_stream, a_vec) n := #bit_stream; if n ne #a_vec then return 0; end if; return &+[a_vec[i]*bit_stream[i] : i in [1..n]]; end function; function KnapsackDecrypt (s, b_vec, M, W, pi) c := (s * Modinv (W, M)) mod M; n := #b_vec; pi_inv := pi^-1; bit_stream := [0 : i in [1..n]]; for j in [n..1 by -1] do if c ge b_vec[j] then bit_stream[Image (pi_inv, j)] := 1; c -:= b_vec[j]; end if; end for; return bit_stream; end function; n := 32; n; a_vec, b_vec, M, W, pi := KnapsackParamGeneration (n); a_vec; n; bit_stream := [Random(0,1): i in [1..n]]; bit_stream; n; s := KnapsackEncrypt (bit_stream, a_vec); s; KnapsackDecrypt (s, b_vec, M, W, pi); b_vec; Output: Magma V2.10-22 Wed Apr 7 2004 07:54:34 on modular [Seed = 3906683772] ------------------------------------- 32 [ 3924621789675265125, 7254566886504390925, 9358117225038469176, 5247826807633145519, 5332011822879507021, 7482097301151168916, 10557574356498720092, 5785059933151291870, 11268338884471722495, 9523807847360583975, 11646136373688823703, 3527390077118722686, 527613786862360701, 3725432473451699763, 6333713797496976303, 5750439551945947040, 7654209897349341302, 4810471274043095824, 2743346099961155380, 464359505495246373, 3232726897441584813, 2039498613231531115, 4881771205458354844, 2261719483376098448, 11561503355830882039, 12460298411859462617, 4890669417788679329, 5072677799350345857, 1544174478654811249, 1772362783926254941, 4366593083460488581, 9646030411387604273 ] 32 [ 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1 ] 32 92712022833445808379 [ 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1 ] [ 4782256589, 5059542262, 11660715838, 22466759985, 46739174066, 94605944621, 188638817883, 376648511700, 754848013438, 1509223242227, 3018801629101, 6035323859049, 12070835850481, 24142947408496, 48285597763826, 96569413586454, 193140127961390, 386281542100656, 772559296058504, 1545120166581488, 3090242004852152, 6180481732380607, 12360964518487749, 24721928774207233, 49443859159162855, 98887715848428613, 197775434303352813, 395550867157222489, 791101732280628733, 1582203467275913901, 3164406935429390037, 6328813867526780254 ] Total time: 2.609 seconds, Total memory usage: 2.88MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 07:56:05 2004 Input: n=10; max_increment := 2^n; b_i := 2^n + Random (1, max_increment); b_vec := [b_i]; sum := b_i; for i in [2..n] do b_i := sum + Random (1, max_increment); sum +:= b_i; Append (~b_vec, b_i); end for; Output: Magma V2.10-22 Wed Apr 7 2004 07:56:02 on modular [Seed = 4241445056] ------------------------------------- >> n=10; ^ User error: Identifier 'n' has not been declared or assigned >> max_increment := 2^n; ^ User error: Identifier 'n' has not been declared or assigned >> b_i := 2^n + Random (1, max_increment); ^ User error: Identifier 'n' has not been declared or assigned >> b_vec := [b_i]; ^ User error: Identifier 'b_i' has not been declared or assigned >> sum := b_i; ^ User error: Identifier 'b_i' has not been declared or assigned >> for i in [2..n] do ^ User error: Identifier 'n' has not been declared or assigned Total time: 2.529 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 07:56:19 2004 Input: n:=10; max_increment := 2^n; b_i := 2^n + Random (1, max_increment); b_vec := [b_i]; sum := b_i; for i in [2..n] do b_i := sum + Random (1, max_increment); sum +:= b_i; Append (~b_vec, b_i); end for; Output: Magma V2.10-22 Wed Apr 7 2004 07:56:16 on modular [Seed = 4106705146] ------------------------------------- Total time: 2.540 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 07:56:40 2004 Input: n:=10; max_increment := 2^n; b_i := 2^n + Random (1, max_increment); b_vec := [b_i]; sum := b_i; for i in [2..n] do b_i := sum + Random (1, max_increment); sum +:= b_i; Append (~b_vec, b_i); end for; b_vec; Output: Magma V2.10-22 Wed Apr 7 2004 07:56:38 on modular [Seed = 3439288532] ------------------------------------- [ 1406, 1636, 4002, 7940, 15280, 30294, 60966, 121623, 243638, 487487 ] Total time: 2.599 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 07:56:55 2004 Input: n:=32; max_increment := 2^n; b_i := 2^n + Random (1, max_increment); b_vec := [b_i]; sum := b_i; for i in [2..n] do b_i := sum + Random (1, max_increment); sum +:= b_i; Append (~b_vec, b_i); end for; b_vec; Output: Magma V2.10-22 Wed Apr 7 2004 07:56:52 on modular [Seed = 3304548398] ------------------------------------- [ 7593866246, 9701795460, 18276206027, 39217859372, 76479612800, 155034693640, 308616980374, 615437667989, 1233818679242, 2465818407771, 4933636068466, 9866229214320, 19733554650719, 39467048785849, 78930992051746, 157865327386356, 315728608616648, 631458591920589, 1262915290468921, 2525833148171673, 5051665424853687, 10103332013352480, 20206663344600643, 40413327314742812, 80826654166882440, 161653308667994106, 323306614542245817, 646613229372532292, 1293226457499246540, 2586452916362468004, 5172905832877468636, 10345811667722262999 ] Total time: 2.630 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 07:58:20 2004 Input: n:=10; max_increment := 2^n; b_i := 2^n + Random (1, max_increment); b_vec := [b_i]; sum := b_i; for i in [2..n] do b_i := sum + Random (1, 2^(n+i)); sum +:= b_i; Append (~b_vec, b_i); end for; b_vec; Output: Magma V2.10-22 Wed Apr 7 2004 07:58:17 on modular [Seed = 3706679403] ------------------------------------- [ 1634, 4645, 6691, 20540, 34562, 119246, 265399, 573165, 1549389, 3259713 ] Total time: 2.560 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 07:58:43 2004 Input: n:=10; max_increment := 2^n; b_i := 2^n + Random (1, max_increment); b_vec := [b_i]; sum := b_i; for i in [2..n] do b_i := sum + Random (2^n, 2^(n+i)); sum +:= b_i; Append (~b_vec, b_i); end for; b_vec; Output: Magma V2.10-22 Wed Apr 7 2004 07:58:40 on modular [Seed = 3571939403] ------------------------------------- [ 1405, 4535, 9154, 31235, 64115, 153468, 270952, 761693, 1312826, 2762078 ] Total time: 2.489 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 07:58:56 2004 Input: n:=32; max_increment := 2^n; b_i := 2^n + Random (1, max_increment); b_vec := [b_i]; sum := b_i; for i in [2..n] do b_i := sum + Random (2^n, 2^(n+i)); sum +:= b_i; Append (~b_vec, b_i); end for; b_vec; Output: Magma V2.10-22 Wed Apr 7 2004 07:58:54 on modular [Seed = 2896101436] ------------------------------------- [ 8428291532, 19382992871, 36927674798, 124864334198, 299853239622, 516561683838, 1229593891106, 2764960087633, 6067753864399, 11710635806114, 23343204154648, 60137517850329, 117147617747758, 257701462592980, 485196089498590, 1042662766117390, 2268475925102711, 5092900190918926, 10596619428062741, 23690858721708760, 45243652900990419, 104241451605324110, 195206300541422940, 416142674464033649, 828635982198159352, 1903912971260957100, 3952841852413498781, 8431806347468186183, 17300804264357872464, 33776730428048246435, 75190330610884316907, 154399170883338619213 ] Total time: 2.549 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 07:59:58 2004 Input: n:=32; max_increment := 2^n; b_i := 2^n + Random (1, max_increment); b_vec := [b_i]; sum := b_i; for i in [2..n] do b_i := sum + Random (2^(n+i-1), 2^(n+i)); sum +:= b_i; Append (~b_vec, b_i); end for; b_vec; Output: Magma V2.10-22 Wed Apr 7 2004 07:59:56 on modular [Seed = 2727415792] ------------------------------------- [ 7681903278, 19931862987, 53247286540, 122514779946, 318508170237, 770021664034, 1691120623425, 3599263319933, 8395341878270, 18980892592820, 38932421973561, 83938938919985, 185223923413772, 396890169787589, 832611963031480, 1782742312055860, 3818925634690565, 8045575898642573, 17434440418656752, 36031536917578292, 73944746601821193, 158367535408840367, 330738538671834565, 685832446972523499, 1431798618704618482, 2943588353475296821, 6238788929143928679, 12874523143028273192, 26218602803911984276, 54445107248788371202, 114529935186889962334, 236943217023833767060 ] Total time: 2.599 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 08:02:36 2004 Input: n:=32; max_increment := 2^n; b_i := 2^n + Random (1, max_increment); b_vec := [b_i]; sum := b_i; for i in [2..n] do b_i := sum + Random (2^(n+i-2), 2^(n+i-1)); sum +:= b_i; Append (~b_vec, b_i); end for; b_vec; Output: Magma V2.10-22 Wed Apr 7 2004 08:02:34 on modular [Seed = 2175937589] ------------------------------------- [ 4774876492, 9879763666, 29441716648, 76309477658, 188183881681, 400565923879, 936146800337, 2030175839730, 4469187320117, 9313877330475, 20101470006496, 46179366522651, 101261069372989, 213712592880365, 442148664899769, 941380579674118, 2056433241638509, 4271343069949548, 8916346639111018, 19030742058670293, 39474196555437714, 82128538282343325, 172182319618711844, 357027522442194224, 724282450604435088, 1502952813969939934, 3177553570381204359, 6432337766022163587, 13595629396467880716, 27455128625610819612, 56972414254416325021, 116654739127631058487 ] Total time: 2.559 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host ns.icbank.ru. (195.5.134.194) Time: Wed Apr 7 08:09:39 2004 Input: CanonicalModularPolynomial(N) Output: Magma V2.10-22 Wed Apr 7 2004 08:09:36 on modular [Seed = 1666239628] ------------------------------------- >> CanonicalModularPolynomial(N); ^ User error: Identifier 'N' has not been declared or assigned Total time: 2.500 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host ns.icbank.ru. (195.5.134.194) Time: Wed Apr 7 08:10:18 2004 Input: CanonicalModularPolynomial(7) Output: Magma V2.10-22 Wed Apr 7 2004 08:10:15 on modular [Seed = 1933630651] ------------------------------------- $.1^8 + 28*$.1^7 + 322*$.1^6 + 1904*$.1^5 + 5915*$.1^4 + 8624*$.1^3 + 4018*$.1^2 - $.1*$.2 + 748*$.1 + 49 Total time: 2.490 seconds, Total memory usage: 2.50MB ************** MAGMA ***************** Host ns.icbank.ru. (195.5.134.194) Time: Wed Apr 7 08:12:08 2004 Input: CanonicalModularPolynomial(11) Output: Magma V2.10-22 Wed Apr 7 2004 08:12:05 on modular [Seed = 1249507888] ------------------------------------- $.1^12 - 5940*$.1^11 + 14701434*$.1^10 - 139755*$.1^9*$.2 - 19264518900*$.1^9 + 723797800*$.1^8*$.2 + 13849401061815*$.1^8 + 67496*$.1^7*$.2^2 - 1327909897380*$.1^7*$.2 - 4875351166521000*$.1^7 + 2291468355*$.1^6*$.2^2 + 1036871615940600*$.1^6*$.2 + 400050977713074380*$.1^6 - 5346*$.1^5*$.2^3 + 4231762569540*$.1^5*$.2^2 - 310557763459301490*$.1^5*$.2 + 122471154456433615800*$.1^5 + 161201040*$.1^4*$.2^3 + 755793774757450*$.1^4*$.2^2 + 17309546645642506200*$.1^4*$.2 + 6513391734069824031615*$.1^4 + 132*$.1^3*$.2^4 - 49836805205*$.1^3*$.2^3 + 6941543075967060*$.1^3*$.2^2 - 64815179429761398660*$.1^3*$.2 + 104264884483130180036700*$.1^3 + 468754*$.1^2*$.2^4 + 51801406800*$.1^2*$.2^3 + 214437541826475*$.1^2*$.2^2 + 77380735840203400*$.1^2*$.2 + 804140494949359194*$.1^2 - $.1*$.2^5 + 3732*$.1*$.2^4 - 4586706*$.1*$.2^3 + 2059075976*$.1*$.2^2 - 253478654715*$.1*$.2 + 2067305393340*$.1 + 1771561 Total time: 2.509 seconds, Total memory usage: 2.50MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 08:13:38 2004 Input: n:=32; max_increment := 2^n; b_i := 2^n + Random (1, max_increment); b_vec := [b_i]; sum := b_i; for i in [2..n] do b_i := Random (2^(n+i-2), 2^(n+i-1)); sum +:= b_i; Append (~b_vec, b_i); end for; b_vec; Output: Magma V2.10-22 Wed Apr 7 2004 08:13:35 on modular [Seed = 1081339968] ------------------------------------- [ 5166713318, 7570920955, 16977795090, 24617050276, 39232593661, 129048202322, 143840975239, 442971244483, 636748046808, 1910912997146, 2299111146579, 4965639258313, 17135695675542, 23608845937830, 68749021708310, 135904518550889, 216793247384383, 352774478488901, 791481582596098, 1594585311818378, 4398020239935546, 8339476487390593, 15719560552498702, 26022111459843324, 40353934437121623, 137655326519172682, 190680876025627265, 385492176204363003, 725550771241880872, 1900152996588428022, 2642860447355468319, 9044696301197246942 ] Total time: 2.539 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 08:15:15 2004 Input: n:=32; max_increment := 2^n; b_i := 2^n + Random (1, max_increment); b_vec := [b_i]; sum := b_i; for i in [2..n] do b_i := sum+Random (2^(n+i-2), 2^(n+i-1)); sum +:= b_i; Append (~b_vec, b_i); end for; b_vec; Output: Magma V2.10-22 Wed Apr 7 2004 08:15:12 on modular [Seed = 1398858732] ------------------------------------- [ 5388072263, 12457009451, 31315123081, 66396724250, 166898561359, 381673756113, 878198248698, 1902251623523, 4192460474494, 9113116261738, 19500575369840, 41904145285725, 94265576287049, 196842528815523, 406613551834713, 862462357044497, 1866498140396440, 3892864119827165, 8256043760483143, 17510682331205179, 36312620236176912, 78410033500848448, 163243651556757667, 332344493163891903, 690568986528664331, 1419968890089700644, 3014568087390816321, 6255698065569467941, 12674471855663191808, 25988534879254114831, 54808686374860193537, 113678123865839742554 ] Total time: 2.529 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host ns.icbank.ru. (195.5.134.194) Time: Wed Apr 7 08:18:50 2004 Input: CanonicalModularPolynomial(7) Output: Magma V2.10-22 Wed Apr 7 2004 08:18:47 on modular [Seed = 104183758] ------------------------------------- $.1^8 + 28*$.1^7 + 322*$.1^6 + 1904*$.1^5 + 5915*$.1^4 + 8624*$.1^3 + 4018*$.1^2 - $.1*$.2 + 748*$.1 + 49 Total time: 2.559 seconds, Total memory usage: 2.50MB ************** MAGMA ***************** Host ns.icbank.ru. (195.5.134.194) Time: Wed Apr 7 08:20:46 2004 Input: CanonicalModularPolynomial(5) Output: Magma V2.10-22 Wed Apr 7 2004 08:20:44 on modular [Seed = 338142823] ------------------------------------- $.1^6 + 30*$.1^5 + 315*$.1^4 + 1300*$.1^3 + 1575*$.1^2 - $.1*$.2 + 750*$.1 + 125 Total time: 2.579 seconds, Total memory usage: 2.50MB ************** MAGMA ***************** Host ns.icbank.ru. (195.5.134.194) Time: Wed Apr 7 08:23:12 2004 Input: CanonicalModularPolynomial(3) Output: Magma V2.10-22 Wed Apr 7 2004 08:23:08 on modular [Seed = 4224207160] ------------------------------------- $.1^4 + 36*$.1^3 + 270*$.1^2 - $.1*$.2 + 756*$.1 + 729 Total time: 2.559 seconds, Total memory usage: 2.50MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 08:37:04 2004 Input: n := #12; n; Output: Magma V2.10-22 Wed Apr 7 2004 08:37:01 on modular [Seed = 3723389023] ------------------------------------- >> n := #12; ^ Runtime error in '#': Bad argument types Argument types given: RngIntElt >> n;; ^ User error: Identifier 'n' has not been declared or assigned Total time: 2.549 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 08:38:28 2004 Input: n :=[1 2 3]; n; Output: Magma V2.10-22 Wed Apr 7 2004 08:38:26 on modular [Seed = 3588645880] ------------------------------------- >> n :=[1 2 3]; ^ User error: bad syntax >> n;; ^ User error: Identifier 'n' has not been declared or assigned Total time: 2.509 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 08:38:41 2004 Input: n :=(1 2 3); n; Output: Magma V2.10-22 Wed Apr 7 2004 08:38:39 on modular [Seed = 2912820109] ------------------------------------- >> n :=(1 2 3); ^ User error: bad syntax >> n;; ^ User error: Identifier 'n' has not been declared or assigned Total time: 2.580 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 08:39:26 2004 Input: n[1] :=3; n[2] :=43; n; Output: Magma V2.10-22 Wed Apr 7 2004 08:39:24 on modular [Seed = 2778076086] ------------------------------------- >> n[1] :=3; ^ User error: Identifier 'n' has not been declared or assigned >> n[2] :=43; ^ User error: Identifier 'n' has not been declared or assigned >> n;; ^ User error: Identifier 'n' has not been declared or assigned Total time: 2.539 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 08:40:54 2004 Input: n:=3; n:=43; n; Output: Magma V2.10-22 Wed Apr 7 2004 08:40:51 on modular [Seed = 3028746760] ------------------------------------- 43 Total time: 2.560 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 08:41:48 2004 Input: n(1):=3; n(2):=43; n; Output: Magma V2.10-22 Wed Apr 7 2004 08:41:46 on modular [Seed = 2361342953] ------------------------------------- >> n(1):=3; ^ User error: Illegal left hand side of an assignment statement >> n(2):=43; ^ User error: Illegal left hand side of an assignment statement >> n;; ^ User error: Identifier 'n' has not been declared or assigned Total time: 2.519 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 08:42:20 2004 Input: a:=(1 2 3); a; Output: Magma V2.10-22 Wed Apr 7 2004 08:42:18 on modular [Seed = 2226598849] ------------------------------------- >> a:=(1 2 3); ^ User error: bad syntax >> a;; ^ User error: Identifier 'a' has not been declared or assigned Total time: 2.499 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 08:43:32 2004 Input: a:=[1, 2, 3]; a; Output: Magma V2.10-22 Wed Apr 7 2004 08:43:30 on modular [Seed = 2628725633] ------------------------------------- [ 1, 2, 3 ] Total time: 2.569 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 08:43:47 2004 Input: a:=[1, 2, 3]; a(1); Output: Magma V2.10-22 Wed Apr 7 2004 08:43:45 on modular [Seed = 2493981562] ------------------------------------- >> a(1);; ^ Runtime error: Bad argument types Argument types given: RngIntElt, SeqEnum[RngIntElt] Total time: 2.530 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 08:44:05 2004 Input: a:=[1, 2, 3]; a[1]; Output: Magma V2.10-22 Wed Apr 7 2004 08:44:02 on modular [Seed = 1933624465] ------------------------------------- 1 Total time: 2.529 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 08:46:50 2004 Input: > K := GF(2); > P := PolynomialRing (K); > P; > C := 1 + D + D^4; > S := [K| 0,1,1,0]; > LFSRSequence (C, S, 15); Output: Magma V2.10-22 Wed Apr 7 2004 08:46:48 on modular [Seed = 1733615407] ------------------------------------- Univariate Polynomial Ring in D over GF(2) [ 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1 ] Total time: 2.559 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 08:47:15 2004 Input: > K := GF(2); > P := PolynomialRing (K); > P; > C := 1 + D + D^4; > S := [K| 0,1,1,0]; > LFSRSequence (C, S, 15); P; Output: Magma V2.10-22 Wed Apr 7 2004 08:47:12 on modular [Seed = 1868355407] ------------------------------------- Univariate Polynomial Ring in D over GF(2) [ 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1 ] Univariate Polynomial Ring in D over GF(2) Total time: 2.579 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 08:47:38 2004 Input: > K := GF(2); > P := PolynomialRing (K); > P; > C := 1 + D + D^4; > S := [K| 0,1,1,0,1,1]; > LFSRSequence (C, S, 15); Output: Magma V2.10-22 Wed Apr 7 2004 08:47:35 on modular [Seed = 1466232640] ------------------------------------- Univariate Polynomial Ring in D over GF(2) [ 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1 ] Total time: 2.529 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 08:47:56 2004 Input: > K := GF(2); > P := PolynomialRing (K); > P; > C := 1 + D + D^6; > S := [K| 0,1,1,0,1,1]; > LFSRSequence (C, S, 15); Output: Magma V2.10-22 Wed Apr 7 2004 08:47:54 on modular [Seed = 1600972629] ------------------------------------- Univariate Polynomial Ring in D over GF(2) [ 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1 ] Total time: 2.529 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 08:48:36 2004 Input: > K := GF(2); > P := PolynomialRing (K); > P; > C := 1 + D + D^12; > S := [K| 0,1,1,0,1,1]; > LFSRSequence (C, S, 15); Output: Magma V2.10-22 Wed Apr 7 2004 08:48:34 on modular [Seed = 1198849941] ------------------------------------- Univariate Polynomial Ring in D over GF(2) >> LFSRSequence (C, S, 15); ^ Runtime error in 'LFSRSequence': Sequence must have at least as many terms as the degree of the polynomial Total time: 2.580 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Wed Apr 7 08:49:13 2004 Input: > K := GF(2); > P := PolynomialRing (K); > P; > C := 1 + D + D^12; > S := [K| 0,1,1,0,1,1,1,1,1,0,1,0]; > LFSRSequence (C, S, 15); Output: Magma V2.10-22 Wed Apr 7 2004 08:49:10 on modular [Seed = 838961796] ------------------------------------- Univariate Polynomial Ring in D over GF(2) [ 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0 ] Total time: 2.509 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 3(NXDOMAIN) (145.253.130.115) Time: Wed Apr 7 09:29:30 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-22 Wed Apr 7 2004 09:29:28 on modular [Seed = 3045193724] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.509 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Apr 7 10:32:36 2004 Input: R:=PolynomialRing(Rationals()); L:=SplittingField([x^2-2,x^2-3,x^2-5,x^2-7]); OL:MaximalOrder(L); I:=37*OK Factorization(I); Output: Magma V2.10-22 Wed Apr 7 2004 10:32:32 on modular [Seed = 839279425] ------------------------------------- >> L:=SplittingField([x^2-2,x^2-3,x^2-5,x^2-7]); ^ Runtime error in 'SplittingField': Bad argument types Argument types given: SeqEnum[RngUPolElt] >> OL:MaximalOrder(L); ^ User error: bad syntax >> Factorization(I); ^ User error: bad syntax Total time: 3.239 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Apr 7 10:33:26 2004 Input: R:=PolynomialRing(Rationals()); L:=NumberField([x^2-2,x^2-3,x^2-5,x^2-7]); OL:MaximalOrder(L); I:=37*OK Factorization(I); Output: Magma V2.10-22 Wed Apr 7 2004 10:33:20 on modular [Seed = 321339984] ------------------------------------- >> OL:MaximalOrder(L); ^ User error: bad syntax >> Factorization(I); ^ User error: bad syntax Total time: 3.439 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Apr 7 10:33:49 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2-2,x^2-3,x^2-5,x^2-7]); OK:MaximalOrder(K); I:=37*OK Factorization(I); Output: Magma V2.10-22 Wed Apr 7 2004 10:33:46 on modular [Seed = 120804926] ------------------------------------- >> OK:MaximalOrder(K); ^ User error: bad syntax >> Factorization(I); ^ User error: bad syntax Total time: 3.469 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Apr 7 10:34:32 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField([x^2-2,x^2-3,x^2-5,x^2-7]); OK:=MaximalOrder(K); I:=37*OK Factorization(I); Output: Magma V2.10-22 Wed Apr 7 2004 10:34:08 on modular [Seed = 4139952101] ------------------------------------- ************** MAGMA ***************** Host c-24-13-251-235.client.comcast.net. (24.13.251.235) Time: Wed Apr 7 16:58:13 2004 Input: Generators(Gamma0(5)) Output: Magma V2.10-22 Wed Apr 7 2004 16:58:10 on modular [Seed = 2611982479] ------------------------------------- [ [1 1] [0 1], [ 2 -1] [ 5 -2], [ 3 -2] [ 5 -3] ] Total time: 2.579 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host euclides.mat.ufc.br. (200.19.178.22) Time: Wed Apr 7 17:54:17 2004 Input: Pi Output: Magma V2.10-22 Wed Apr 7 2004 17:54:06 on modular [Seed = 337652765] ------------------------------------- Intrinsic 'Pi' Signatures: ( R) -> FldReElt ( R) -> FldReElt ( R) -> FldPrElt Create pi to the precision of R as a real number. ( R, p) -> FldPrElt Create pi to the precision p as an element of R. Total time: 2.579 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 2(SERVFAIL) (209.53.95.77) Time: Wed Apr 7 20:48:25 2004 Input: (-1)^7-21*(-1)^5+126*(-1)^3-189*(-1)+92; Output: Magma V2.10-22 Wed Apr 7 2004 20:48:22 on modular [Seed = 255585824] ------------------------------------- 175 Total time: 2.559 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 2(SERVFAIL) (209.53.95.77) Time: Wed Apr 7 20:49:21 2004 Input: m:=(-1)^7-21*(-1)^5+126*(-1)^3-189*(-1)+92;m;m/7; Output: Magma V2.10-22 Wed Apr 7 2004 20:49:18 on modular [Seed = 120841968] ------------------------------------- 175 25 Total time: 2.530 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 2(SERVFAIL) (209.53.95.77) Time: Wed Apr 7 20:50:11 2004 Input: m:=2^7-35*2^5+350*2^3-875*2+558;m;m/7; Output: Magma V2.10-22 Wed Apr 7 2004 20:50:08 on modular [Seed = 4156757583] ------------------------------------- 616 88 Total time: 2.609 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 2(SERVFAIL) (209.53.95.77) Time: Wed Apr 7 20:51:14 2004 Input: m:=2^7-133*2^5+5054*2^3-48013*2+10316;m;m/7; Output: Magma V2.10-22 Wed Apr 7 2004 20:51:11 on modular [Seed = 4024110697] ------------------------------------- -49406 -7058 Total time: 2.559 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 2(SERVFAIL) (209.53.95.77) Time: Wed Apr 7 21:04:16 2004 Input: m:=(-3)^2+6*(-3)+9;m;m/11; Output: Magma V2.10-22 Wed Apr 7 2004 21:04:13 on modular [Seed = 2411424504] ------------------------------------- 0 0 Total time: 2.520 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 2(SERVFAIL) (209.53.95.77) Time: Wed Apr 7 21:05:13 2004 Input: m:=(-3)^2+2*(-3)-47;m;m/11; Output: Magma V2.10-22 Wed Apr 7 2004 21:05:11 on modular [Seed = 2035129412] ------------------------------------- -44 -4 Total time: 2.549 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Wed Apr 7 21:17:43 2004 Input: P:=PolynomialRing(RationalField()); N:=NumberField(x^2-5); M:=NumberField(x^2+1); O:=NumberField([x^2-5,x^2+1]); ON:=MaximalIdeal(N); OM:=MaximalIdeal(M); OO:=MaximalIdeal(O); Factorization(3*ON); Factorization(3*OM); Factorization(3*OO); Output: Magma V2.10-22 Wed Apr 7 2004 21:17:41 on modular [Seed = 1616152623] ------------------------------------- >> ON:=MaximalIdeal(N); ^ User error: Identifier 'MaximalIdeal' has not been declared or assigned >> OM:=MaximalIdeal(M); ^ User error: Identifier 'MaximalIdeal' has not been declared or assigned >> OO:=MaximalIdeal(O); ^ User error: Identifier 'MaximalIdeal' has not been declared or assigned >> Factorization(3*ON); ^ User error: Identifier 'ON' has not been declared or assigned >> Factorization(3*OM); ^ User error: Identifier 'OM' has not been declared or assigned >> Factorization(3*OO); ^ User error: Identifier 'OO' has not been declared or assigned Total time: 2.579 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Wed Apr 7 21:18:05 2004 Input: P:=PolynomialRing(RationalField()); N:=NumberField(x^2-5); M:=NumberField(x^2+1); O:=NumberField([x^2-5,x^2+1]); ON:=MaximalOrder(N); OM:=MaximalOrder(M); OO:=MaximalOrder(O); Factorization(3*ON); Factorization(3*OM); Factorization(3*OO); Output: Magma V2.10-22 Wed Apr 7 2004 21:18:02 on modular [Seed = 1483518056] ------------------------------------- [ ] [ ] [ , ] Total time: 2.929 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Wed Apr 7 21:26:47 2004 Input: P:=PolynomialRing(RationalField()); N:=NumberField([x^3-2,x^3-1]); ON:=MaximalOrder(N); Factorization(5*ON); Factorization(7*ON); Factorization(11*ON); Factorization(13*ON); Output: Magma V2.10-22 Wed Apr 7 2004 21:26:45 on modular [Seed = 1131915628] ------------------------------------- >> N:=NumberField([x^3-2,x^3-1]); ^ Runtime error in 'NumberField': Argument 2 is not irreducible >> ON:=MaximalOrder(N); ^ User error: Identifier 'N' has not been declared or assigned >> Factorization(5*ON); ^ User error: Identifier 'ON' has not been declared or assigned >> Factorization(7*ON); ^ User error: Identifier 'ON' has not been declared or assigned >> Factorization(11*ON); ^ User error: Identifier 'ON' has not been declared or assigned >> Factorization(13*ON);; ^ User error: Identifier 'ON' has not been declared or assigned Total time: 2.500 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Wed Apr 7 21:27:06 2004 Input: P:=PolynomialRing(RationalField()); N:=NumberField([x^3-2,x^2+x+1]); ON:=MaximalOrder(N); Factorization(5*ON); Factorization(7*ON); Factorization(11*ON); Factorization(13*ON); Output: Magma V2.10-22 Wed Apr 7 2004 21:27:03 on modular [Seed = 990892326] ------------------------------------- [ , , ] [ , ] [ , , ] [ , ] Total time: 3.199 seconds, Total memory usage: 2.20MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Wed Apr 7 21:28:03 2004 Input: P:=PolynomialRing(RationalField()); N:=NumberField([x^3-2,x^2+x+1]); ON:=MaximalOrder(N); 5; Factorization(5*ON); 7; Factorization(7*ON); 11; Factorization(11*ON); 13; Factorization(13*ON); Output: Magma V2.10-22 Wed Apr 7 2004 21:27:59 on modular [Seed = 856152534] ------------------------------------- 5 [ , , ] 7 [ , ] 11 [ , , ] 13 [ , ] Total time: 3.260 seconds, Total memory usage: 2.20MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Wed Apr 7 21:32:03 2004 Input: P:=PolynomialRing(RationalField()); N:=NumberField([x^2-2,x^2-3,x^2-5,x^2-7]); ON:=MaximalOrder(N); Factorization(37*ON); Output: Magma V2.10-22 Wed Apr 7 2004 21:31:40 on modular [Seed = 538233638] ------------------------------------- ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Wed Apr 7 21:32:30 2004 Input: P:=PolynomialRing(RationalField()); N:=NumberField([x^2-2,x^2-3,x^2-5,x^2-7]); ON:=MaximalOrder(N); Factorization(37*ON); Output: Magma V2.10-22 Wed Apr 7 2004 21:32:08 on modular [Seed = 405599226] ------------------------------------- ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Wed Apr 7 21:33:04 2004 Input: P:=PolynomialRing(RationalField()); N:=NumberField([x^2-2,x^2-3,x^2-5,x^2-7]); ON:=MaximalOrder(N); Factorization(37*ON); Output: Magma V2.10-22 Wed Apr 7 2004 21:32:41 on modular [Seed = 287701714] ------------------------------------- ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Wed Apr 7 21:37:35 2004 Input: P:=PolynomialRing(RationalField()); N:=NumberField([x^2-2,x^2-3,x^2-5,x^2-7]); ON:=MaximalOrder(N); Discriminant(ON); Output: Magma V2.10-22 Wed Apr 7 2004 21:37:12 on modular [Seed = 37154480] ------------------------------------- ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Wed Apr 7 21:41:07 2004 Input: P:=PolynomialRing(RationalField()); N:=NumberField([x^2-2,x^2-3,x^2-5,x^2-7]); ON:=MaximalOrder(N); Discriminant(ON); Output: Magma V2.10-22 Wed Apr 7 2004 21:40:44 on modular [Seed = 4089912853] ------------------------------------- ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Apr 7 23:55:39 2004 Input: R:=PolynomialRing(Rationals()); K:=SplittingField(x^3-2); OK:=MaximalOrder(K); I:=5*OK Factorization(I); Output: Magma V2.10-22 Wed Apr 7 2004 23:55:36 on modular [Seed = 3605158805] ------------------------------------- >> Factorization(I); ^ User error: bad syntax Total time: 2.829 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Wed Apr 7 23:55:50 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2+x+1,x^3-2] : Abs := true); OK:=MaximalOrder(K); [Factorization(n*OK): n in {2,3,5,7,11,13}] Output: Magma V2.10-22 Wed Apr 7 2004 23:55:47 on modular [Seed = 3472507894] ------------------------------------- [ [ , , ], [ ], [ , ], [ ], [ , , ], [ , ] ] Total time: 3.240 seconds, Total memory usage: 2.63MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Apr 7 23:55:56 2004 Input: R:=PolynomialRing(Rationals()); K:=SplittingField(x^3-2); OK:=MaximalOrder(K); I:=5*OK; Factorization(I); Output: Magma V2.10-22 Wed Apr 7 2004 23:55:53 on modular [Seed = 3337767924] ------------------------------------- [ , , ] Total time: 2.899 seconds, Total memory usage: 1.91MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Wed Apr 7 23:56:13 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([CyclotomicPolynomial(3),x^3-2] : Abs := true); OK:=MaximalOrder(K); [Factorization(n*OK): n in {2,3,5,7,11,13}] Output: Magma V2.10-22 Wed Apr 7 2004 23:56:09 on modular [Seed = 3196728220] ------------------------------------- [ [ , , ], [ ], [ , ], [ ], [ , , ], [ , ] ] Total time: 3.269 seconds, Total memory usage: 2.63MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Wed Apr 7 23:56:53 2004 Input: R:=PolynomialRing(Rationals()); K:=SplittingField(x^3-2); OK:=MaximalOrder(K); Factorization(5*OK); Factorization(7*OK); Factorization(11*OK); Factorization(13*OK); Output: Magma V2.10-22 Wed Apr 7 2004 23:56:49 on modular [Seed = 3061988172] ------------------------------------- [ , , ] [ , ] [ , , ] [ , ] Total time: 3.319 seconds, Total memory usage: 1.91MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Wed Apr 7 23:56:53 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([CyclotomicPolynomial(3),x^3-2] : Abs := true); OK:=MaximalOrder(K); Factorization(2*OK) [Factorization(n*OK): n in {2,3,5,7,11,13}] Output: Magma V2.10-22 Wed Apr 7 2004 23:56:50 on modular [Seed = 3028302157] ------------------------------------- >> [Factorization(n*OK): n in {2,3,5,7,11,13}]; ^ User error: bad syntax Total time: 3.159 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Wed Apr 7 23:57:04 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([CyclotomicPolynomial(3),x^3-2] : Abs := true); OK:=MaximalOrder(K); Factorization(2*OK) Output: Magma V2.10-22 Wed Apr 7 2004 23:57:02 on modular [Seed = 2794597203] ------------------------------------- [ ] Total time: 2.599 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Wed Apr 7 23:58:17 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([CyclotomicPolynomial(3),x^3-2] : Abs := true); OK:=MaximalOrder(K); Factorization(2*OK) Factorization(3*OK) Factorization(5*OK) Factorization(7*OK) Factorization(11*OK) Factorization(13*OK) Output: Magma V2.10-22 Wed Apr 7 2004 23:58:15 on modular [Seed = 2645102641] ------------------------------------- >> Factorization(3*OK) ^ User error: bad syntax >> Factorization(7*OK) ^ User error: bad syntax >> Factorization(13*OK); ^ User error: bad syntax Total time: 2.629 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Wed Apr 7 23:58:31 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([CyclotomicPolynomial(3),x^3-2] : Abs := true); OK:=MaximalOrder(K); Factorization(2*OK) Output: Magma V2.10-22 Wed Apr 7 2004 23:58:29 on modular [Seed = 2510362635] ------------------------------------- [ ] Total time: 2.629 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Wed Apr 7 23:59:54 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([CyclotomicPolynomial(3),x^3-2] : Abs := true); OK:=MaximalOrder(K); Factorization(5*OK) Output: Magma V2.10-22 Wed Apr 7 2004 23:59:52 on modular [Seed = 2360869583] ------------------------------------- [ , , ] Total time: 2.730 seconds, Total memory usage: 2.13MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Apr 8 00:00:49 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([CyclotomicPolynomial(3),x^3-2] : Abs := true); OK:=MaximalOrder(K); Factorization(7*OK) Output: Magma V2.10-22 Thu Apr 8 2004 00:00:46 on modular [Seed = 2051994728] ------------------------------------- [ , ] Total time: 2.800 seconds, Total memory usage: 2.13MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Apr 8 00:13:47 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([CyclotomicPolynomial(3),x^3-2] : Abs := true); OK:=MaximalOrder(K); Factorization(9*OK) Output: Magma V2.10-22 Thu Apr 8 2004 00:13:44 on modular [Seed = 1399308886] ------------------------------------- [ ] Total time: 2.649 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Apr 8 00:14:49 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([CyclotomicPolynomial(3),x^3-2] : Abs := true); OK:=MaximalOrder(K); Factorization(7*OK) Output: Magma V2.10-22 Thu Apr 8 2004 00:14:47 on modular [Seed = 1165087886] ------------------------------------- [ , ] Total time: 2.640 seconds, Total memory usage: 2.13MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Apr 8 00:15:17 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([CyclotomicPolynomial(3),x^3-2] : Abs := true); OK:=MaximalOrder(K); Factorization(11*OK) Output: Magma V2.10-22 Thu Apr 8 2004 00:15:14 on modular [Seed = 957196439] ------------------------------------- [ , , ] Total time: 2.869 seconds, Total memory usage: 2.33MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Apr 8 00:16:11 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([CyclotomicPolynomial(3),x^3-2] : Abs := true); OK:=MaximalOrder(K); Factorization(13*OK) Output: Magma V2.10-22 Thu Apr 8 2004 00:16:08 on modular [Seed = 822453061] ------------------------------------- [ , ] Total time: 2.779 seconds, Total memory usage: 2.36MB ************** MAGMA ***************** Host roam141-131.student.harvard.edu. (140.247.141.131) Time: Thu Apr 8 00:37:12 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField([x^2-2,x^2-3,x^2-5,x^2-7] : Abs := true); OK:=MaximalOrder(K); Factorization(37*OK) Output: Magma V2.10-22 Thu Apr 8 2004 00:37:08 on modular [Seed = 138190464] ------------------------------------- [ , , , , , , , ] Total time: 4.000 seconds, Total memory usage: 2.81MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Apr 8 00:43:40 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2-2); OK:=MaximalOrder(K); Factorization(37*OK); Output: Magma V2.10-22 Thu Apr 8 2004 00:43:37 on modular [Seed = 3855711712] ------------------------------------- [ ] Total time: 2.509 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Apr 8 00:44:11 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2-5); OK:=MaximalOrder(K); Factorization(37*OK); Output: Magma V2.10-22 Thu Apr 8 2004 00:44:09 on modular [Seed = 3723052344] ------------------------------------- [ ] Total time: 2.529 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Apr 8 00:44:26 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2-7); OK:=MaximalOrder(K); Factorization(37*OK); Output: Magma V2.10-22 Thu Apr 8 2004 00:44:23 on modular [Seed = 3588312334] ------------------------------------- [ , ] Total time: 2.509 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Apr 8 00:44:50 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2-3); OK:=MaximalOrder(K); Factorization(37*OK); Output: Magma V2.10-22 Thu Apr 8 2004 00:44:48 on modular [Seed = 3472512626] ------------------------------------- [ , ] Total time: 2.509 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Apr 8 00:44:59 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2-2); OK:=MaximalOrder(K); Factorization(37*OK); Output: Magma V2.10-22 Thu Apr 8 2004 00:44:56 on modular [Seed = 3337772658] ------------------------------------- [ ] Total time: 2.579 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Apr 8 00:45:08 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2-5); OK:=MaximalOrder(K); Factorization(37*OK); Output: Magma V2.10-22 Thu Apr 8 2004 00:45:06 on modular [Seed = 3129877012] ------------------------------------- [ ] Total time: 2.569 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Apr 8 00:46:36 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2-5); OK:=MaximalOrder(K); Factorization(37*OK); function factormod(f, p) R := PolynomialRing(GF(p)); return Factorization(R!f); end function; factormod(x^2-5,37); Output: Magma V2.10-22 Thu Apr 8 2004 00:46:34 on modular [Seed = 2895656442] ------------------------------------- [ ] [ <$.1^2 + 32, 1> ] 1 Total time: 2.569 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Apr 8 00:46:48 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2-5); OK:=MaximalOrder(K); Factorization(37*OK); function factormod(f, p) R := PolynomialRing(GF(p)); return Factorization(R!f); end function; factormod(x^2-2,37); Output: Magma V2.10-22 Thu Apr 8 2004 00:46:45 on modular [Seed = 2777758956] ------------------------------------- [ ] [ <$.1^2 + 35, 1> ] 1 Total time: 2.569 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Apr 8 01:11:55 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2-3); OK:=MaximalOrder(K); Factorization(37*OK); Output: Magma V2.10-22 Thu Apr 8 2004 01:11:52 on modular [Seed = 1600897082] ------------------------------------- [ , ] Total time: 2.519 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Apr 8 01:12:22 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2-7); OK:=MaximalOrder(K); Factorization(37*OK); Output: Magma V2.10-22 Thu Apr 8 2004 01:12:19 on modular [Seed = 1466157081] ------------------------------------- [ , ] Total time: 2.509 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Thu Apr 8 01:13:16 2004 Input: R:=PolynomialRing(Rationals()); K:=NumberField(x^2-2); OK:=MaximalOrder(K); Factorization(37*OK); Output: Magma V2.10-22 Thu Apr 8 2004 01:13:14 on modular [Seed = 1333514328] ------------------------------------- [ ] Total time: 2.499 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host cache6.syd.ops.aspac.uu.net. (203.166.96.240) Time: Thu Apr 8 04:44:44 2004 Input: IsPrime(2^1000-1); Output: Magma V2.10-22 Thu Apr 8 2004 04:44:41 on modular [Seed = 405620960] ------------------------------------- false Total time: 2.599 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host cache6.syd.ops.aspac.uu.net. (203.166.96.240) Time: Thu Apr 8 04:45:08 2004 Input: IsPrime(2^5000-1); Output: Magma V2.10-22 Thu Apr 8 2004 04:45:06 on modular [Seed = 655521332] ------------------------------------- false Total time: 2.600 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam159-43.student.harvard.edu. (140.247.159.43) Time: Thu Apr 8 05:04:43 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-22 Thu Apr 8 2004 05:04:40 on modular [Seed = 1632908488] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.589 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam159-43.student.harvard.edu. (140.247.159.43) Time: Thu Apr 8 05:10:27 2004 Input: A := Matrix(3, 3, [ 4,7,2, 2,4,6, 0,0,0]); Output: Magma V2.10-22 Thu Apr 8 2004 05:10:24 on modular [Seed = 2000822391] ------------------------------------- Total time: 2.549 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam159-43.student.harvard.edu. (140.247.159.43) Time: Thu Apr 8 05:10:45 2004 Input: A := Matrix(3, 3, [ 4,7,2, 2,4,6, 0,0,0]); Output: Magma V2.10-22 Thu Apr 8 2004 05:10:42 on modular [Seed = 2135566444] ------------------------------------- Total time: 2.669 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam159-43.student.harvard.edu. (140.247.159.43) Time: Thu Apr 8 05:11:57 2004 Input: A := Matrix(3, 3, [ 4,7,2, 2,4,6, 0,0,0]); SmithForm(A); Output: Magma V2.10-22 Thu Apr 8 2004 05:11:54 on modular [Seed = 2276643036] ------------------------------------- [1 0 0] [0 2 0] [0 0 0] [ 1 0 0] [14 1 0] [ 0 0 1] [ 0 10 -17] [ 1 -6 10] [ -3 1 -1] Total time: 2.749 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam159-43.student.harvard.edu. (140.247.159.43) Time: Thu Apr 8 05:21:33 2004 Input: A := Matrix(3, 3, [ 4,7,2, 2,4,6, 0,0,0]); SmithForm(A); CoKernel(A); Output: Magma V2.10-22 Thu Apr 8 2004 05:21:30 on modular [Seed = 2662057733] ------------------------------------- [1 0 0] [0 2 0] [0 0 0] [ 1 0 0] [14 1 0] [ 0 0 1] [ 0 10 -17] [ 1 -6 10] [ -3 1 -1] >> CoKernel(A);; ^ User error: Identifier 'CoKernel' has not been declared or assigned Total time: 2.580 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam159-43.student.harvard.edu. (140.247.159.43) Time: Thu Apr 8 05:21:49 2004 Input: A := Matrix(3, 3, [ 4,7,2, 2,4,6, 0,0,0]); SmithForm(A); Cokernel(A); Output: Magma V2.10-22 Thu Apr 8 2004 05:21:47 on modular [Seed = 2794716940] ------------------------------------- [1 0 0] [0 2 0] [0 0 0] [ 1 0 0] [14 1 0] [ 0 0 1] [ 0 10 -17] [ 1 -6 10] [ -3 1 -1] >> Cokernel(A);; ^ Runtime error in 'Cokernel': Bad argument types Argument types given: AlgMatElt Total time: 2.590 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam159-43.student.harvard.edu. (140.247.159.43) Time: Thu Apr 8 05:28:42 2004 Input: A := Matrix(3, 3, [ 4,7,2, 2,4,6, 0,0,0]); SmithForm(A); G := Group(Z,3); Output: Magma V2.10-22 Thu Apr 8 2004 05:28:39 on modular [Seed = 3028414450] ------------------------------------- [1 0 0] [0 2 0] [0 0 0] [ 1 0 0] [14 1 0] [ 0 0 1] [ 0 10 -17] [ 1 -6 10] [ -3 1 -1] >> G := Group(Z,3);; ^ User error: Identifier 'Z' has not been declared or assigned Total time: 2.539 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam159-43.student.harvard.edu. (140.247.159.43) Time: Thu Apr 8 05:34:55 2004 Input: A := Matrix(3, 3, [ 4,7,2, 2,4,6, 0,0,0]); SmithForm(A); G := MatrixGroup<3,Z>; Output: Magma V2.10-22 Thu Apr 8 2004 05:34:53 on modular [Seed = 3388773749] ------------------------------------- [1 0 0] [0 2 0] [0 0 0] [ 1 0 0] [14 1 0] [ 0 0 1] [ 0 10 -17] [ 1 -6 10] [ -3 1 -1] >> G := MatrixGroup<3,Z>;; ^ User error: bad syntax Total time: 2.610 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam159-43.student.harvard.edu. (140.247.159.43) Time: Thu Apr 8 05:36:55 2004 Input: A := Matrix(3, 3, [ 4,7,2, 2,4,6, 0,0,0]); SmithForm(A); G := MatrixGroup<3,Z | [1,0,0,0,1,0,0,0,1] >; Output: Magma V2.10-22 Thu Apr 8 2004 05:36:52 on modular [Seed = 3588262112] ------------------------------------- [1 0 0] [0 2 0] [0 0 0] [ 1 0 0] [14 1 0] [ 0 0 1] [ 0 10 -17] [ 1 -6 10] [ -3 1 -1] >> G := MatrixGroup<3,Z | [1,0,0,0,1,0,0,0,1] >;; ^ User error: Identifier 'Z' has not been declared or assigned Total time: 2.509 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam159-43.student.harvard.edu. (140.247.159.43) Time: Thu Apr 8 05:39:01 2004 Input: A := Matrix(3, 3, [ 4,7,2, 2,4,6, 0,0,0]); SmithForm(A); G := MatrixGroup<3, IntegerRing() | [1,0,0,0,1,0,0,0,1] >; Output: Magma V2.10-22 Thu Apr 8 2004 05:38:58 on modular [Seed = 3723001966] ------------------------------------- [1 0 0] [0 2 0] [0 0 0] [ 1 0 0] [14 1 0] [ 0 0 1] [ 0 10 -17] [ 1 -6 10] [ -3 1 -1] Total time: 2.509 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam159-43.student.harvard.edu. (140.247.159.43) Time: Thu Apr 8 05:42:29 2004 Input: A := Matrix(3, 3, [ 4,7,2, 2,4,6, 0,0,0]); SmithForm(A); G := MatrixGroup<3, IntegerRing() | [1,0,0,0,1,0,0,0,1] >; B := Hom(G,G) ! A; Output: Magma V2.10-22 Thu Apr 8 2004 05:42:26 on modular [Seed = 70343300] ------------------------------------- [1 0 0] [0 2 0] [0 0 0] [ 1 0 0] [14 1 0] [ 0 0 1] [ 0 10 -17] [ 1 -6 10] [ -3 1 -1] >> B := Hom(G,G) ! A;; ^ Runtime error in 'Hom': Bad argument types Argument types given: GrpMat, GrpMat Total time: 2.580 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam159-43.student.harvard.edu. (140.247.159.43) Time: Thu Apr 8 05:45:10 2004 Input: A := Matrix(3, 3, [ 4,7,2, 2,4,6, 0,0,0]); SmithForm(A); G := MatrixGroup<3, IntegerRing() | [1,0,0,0,1,0,0,0,1] >; B := Hom(IntegerRing(3),IntegerRing(3)) ! A; Output: Magma V2.10-22 Thu Apr 8 2004 05:45:08 on modular [Seed = 371411248] ------------------------------------- [1 0 0] [0 2 0] [0 0 0] [ 1 0 0] [14 1 0] [ 0 0 1] [ 0 10 -17] [ 1 -6 10] [ -3 1 -1] >> B := Hom(IntegerRing(3),IntegerRing(3)) ! A;; ^ Runtime error in 'Hom': Bad argument types Argument types given: RngIntRes, RngIntRes Total time: 2.509 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Thu Apr 8 05:58:55 2004 Input: a:=[1,2,3]; a; Output: Magma V2.10-22 Thu Apr 8 2004 05:58:45 on modular [Seed = 756567930] ------------------------------------- [ 1, 2, 3 ] Total time: 2.609 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Thu Apr 8 05:59:25 2004 Input: a:=[1,2,3]; a^2; Output: Magma V2.10-22 Thu Apr 8 2004 05:59:23 on modular [Seed = 889214796] ------------------------------------- >> a^2;; ^ Runtime error in '^': Bad argument types Argument types given: SeqEnum[RngIntElt], RngIntElt Total time: 2.549 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Thu Apr 8 05:59:42 2004 Input: a:=[1,2,3]; a.^2; Output: Magma V2.10-22 Thu Apr 8 2004 05:59:39 on modular [Seed = 1023958963] ------------------------------------- >> a.^2;; ^ User error: bad syntax Total time: 2.569 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Thu Apr 8 06:00:08 2004 Input: a:=2^34; Output: Magma V2.10-22 Thu Apr 8 2004 06:00:06 on modular [Seed = 1365521397] ------------------------------------- Total time: 2.670 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Thu Apr 8 06:00:21 2004 Input: a:=2^34; a; Output: Magma V2.10-22 Thu Apr 8 2004 06:00:18 on modular [Seed = 1500265449] ------------------------------------- 17179869184 Total time: 2.829 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Thu Apr 8 06:24:58 2004 Input: > b := 10; > n := 5; > SetSeed(1); > Q := [Random(1, 2^b): i in [1 .. n]]; >Q; >Q[1]; Output: Magma V2.10-22 Thu Apr 8 2004 06:24:56 on modular [Seed = 2678781925] ------------------------------------- [ 96, 21, 885, 446, 700 ] 96 Total time: 2.529 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Thu Apr 8 06:25:29 2004 Input: > b := 10; > n := 50; > SetSeed(1); > Q := [Random(0, 1): i in [1 .. n]]; >Q; >Q[1]; Output: Magma V2.10-22 Thu Apr 8 2004 06:25:27 on modular [Seed = 2879308606] ------------------------------------- [ 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1 ] 1 Total time: 2.639 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Thu Apr 8 06:25:47 2004 Input: > b := 10; > n := 5000; > SetSeed(1); > Q := [Random(0, 1): i in [1 .. n]]; >Q; >Q[1]; Output: Magma V2.10-22 Thu Apr 8 2004 06:25:44 on modular [Seed = 3011959577] ------------------------------------- [ 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Thu Apr 8 06:45:05 2004 Input: K := GF(2, 4); X := FunctionField(K); Y := PolynomialRing(X); f := y^4+y+x^5; F := FunctionField(f); F; Signature(F); Genus(F); Output: Magma V2.10-22 Thu Apr 8 2004 06:45:03 on modular [Seed = 3639457269] ------------------------------------- Algebraic function field defined over Univariate rational function field over GF(2^4) by y^4 + y + x^5 >> Signature(F); ^ Runtime error in 'Signature': Bad argument types Argument types given: FldFun 6 Total time: 2.620 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Thu Apr 8 06:46:15 2004 Input: K := GF(3, 2); X := FunctionField(K); Y := PolynomialRing(X); f := y^4+y+x^5; F := FunctionField(f); F; Signature(F); Genus(F); Output: Magma V2.10-22 Thu Apr 8 2004 06:46:12 on modular [Seed = 3772091798] ------------------------------------- Algebraic function field defined over Univariate rational function field over GF(3^2) by y^4 + y + x^5 >> Signature(F); ^ Runtime error in 'Signature': Bad argument types Argument types given: FldFun 2 Total time: 3.089 seconds, Total memory usage: 8.26MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Thu Apr 8 06:46:51 2004 Input: K := GF(3, 2); X := FunctionField(K); Y := PolynomialRing(X); f := y^4+y+x^5; F := FunctionField(f); F; Genus(F); Output: Magma V2.10-22 Thu Apr 8 2004 06:46:48 on modular [Seed = 4007363444] ------------------------------------- Algebraic function field defined over Univariate rational function field over GF(3^2) by y^4 + y + x^5 2 Total time: 3.190 seconds, Total memory usage: 8.26MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Thu Apr 8 06:47:27 2004 Input: K := GF(3, 2); X := FunctionField(K); Y := PolynomialRing(X); f := y^4+y+x^5; F := FunctionField(f); F; Genus(F); Place(F); Output: Magma V2.10-22 Thu Apr 8 2004 06:47:24 on modular [Seed = 4156725833] ------------------------------------- Algebraic function field defined over Univariate rational function field over GF(3^2) by y^4 + y + x^5 2 >> Place(F); ^ Runtime error in 'Place': Bad argument types Argument types given: FldFun Total time: 3.209 seconds, Total memory usage: 8.26MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Thu Apr 8 06:49:02 2004 Input: K := GF(3, 2); X := FunctionField(K); Y := PolynomialRing(X); f := y^2-x*(x+1)*(x-1); F := FunctionField(f); F; Genus(F); Place(F); Output: Magma V2.10-22 Thu Apr 8 2004 06:48:59 on modular [Seed = 4291465702] ------------------------------------- Algebraic function field defined over Univariate rational function field over GF(3^2) by y^2 + 2*x^3 + x 1 >> Place(F); ^ Runtime error in 'Place': Bad argument types Argument types given: FldFun Total time: 2.599 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Thu Apr 8 07:22:45 2004 Input: R:=PolynomialRing(Integers()); F:=FieldofFractions(R); F!x+3; Output: Magma V2.10-22 Thu Apr 8 2004 07:22:42 on modular [Seed = 2193093763] ------------------------------------- >> F:=FieldofFractions(R); ^ User error: Identifier 'FieldofFractions' has not been declared or assigned >> F!x+3;; ^ User error: Identifier 'F' has not been declared or assigned Total time: 2.569 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Thu Apr 8 07:23:08 2004 Input: R:=PolynomialRing(Integers()); F:=FieldOfFractions(R); F!x+3; Output: Magma V2.10-22 Thu Apr 8 2004 07:23:05 on modular [Seed = 2327837840] ------------------------------------- w + 3 Total time: 2.549 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Thu Apr 8 07:38:55 2004 Input: "mdmdf"; Output: Magma V2.10-22 Thu Apr 8 2004 07:38:53 on modular [Seed = 2845626471] ------------------------------------- mdmdf Total time: 2.560 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Thu Apr 8 07:39:20 2004 Input: "mdmdf is " Factorial(12); Output: Magma V2.10-22 Thu Apr 8 2004 07:39:17 on modular [Seed = 2978269271] ------------------------------------- >> "mdmdf is " Factorial(12);; ^ User error: bad syntax Total time: 2.560 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Thu Apr 8 07:39:50 2004 Input: "mdmdf is" Factorial(12); Output: Magma V2.10-22 Thu Apr 8 2004 07:39:48 on modular [Seed = 3213542840] ------------------------------------- >> "mdmdf is" Factorial(12);; ^ User error: bad syntax Total time: 2.549 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Thu Apr 8 07:40:03 2004 Input: "mdmdf is ", Factorial(12); Output: Magma V2.10-22 Thu Apr 8 2004 07:40:00 on modular [Seed = 3372069595] ------------------------------------- mdmdf is 479001600 Total time: 2.599 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Thu Apr 8 07:58:14 2004 Input: "Murat Cenk ", Factorial(12); Output: Magma V2.10-22 Thu Apr 8 2004 07:58:12 on modular [Seed = 3923548094] ------------------------------------- Murat Cenk 479001600 Total time: 2.519 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Thu Apr 8 07:58:43 2004 Input: "Murat Cenk ", Factorial(120); Output: Magma V2.10-22 Thu Apr 8 2004 07:58:41 on modular [Seed = 4056190851] ------------------------------------- Murat Cenk 6689502913449127057588118054090372586752746333138029810295671352301\ 6335572449629893668741652719849813081576378932140905525344085894081218598984811\ 14389650005964960521256960000000000000000000000000000 Total time: 2.549 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Thu Apr 8 08:01:43 2004 Input: primes(100); Output: Magma V2.10-22 Thu Apr 8 2004 08:01:40 on modular [Seed = 506159422] ------------------------------------- >> primes(100);; ^ User error: Identifier 'primes' has not been declared or assigned Total time: 2.639 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Thu Apr 8 08:02:53 2004 Input: isprime(100); Output: Magma V2.10-22 Thu Apr 8 2004 08:02:51 on modular [Seed = 638802249] ------------------------------------- >> isprime(100);; ^ User error: Identifier 'isprime' has not been declared or assigned Total time: 2.549 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Thu Apr 8 08:03:06 2004 Input: Isprime(100); Output: Magma V2.10-22 Thu Apr 8 2004 08:03:03 on modular [Seed = 773542237] ------------------------------------- >> Isprime(100);; ^ User error: Identifier 'Isprime' has not been declared or assigned Total time: 2.539 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Thu Apr 8 08:04:16 2004 Input: IsPrime(100); Output: Magma V2.10-22 Thu Apr 8 2004 08:04:13 on modular [Seed = 906185103] ------------------------------------- false Total time: 2.569 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Thu Apr 8 08:04:39 2004 Input: IsPrime(100021215454545454545514252525252541); Output: Magma V2.10-22 Thu Apr 8 2004 08:04:37 on modular [Seed = 1040925167] ------------------------------------- false Total time: 2.560 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Thu Apr 8 08:04:56 2004 Input: IsPrime(100021215454545454545514252525252542121212121111131); Output: Magma V2.10-22 Thu Apr 8 2004 08:04:53 on modular [Seed = 1198667942] ------------------------------------- false Total time: 2.549 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Thu Apr 8 08:05:48 2004 Input: NextPrime(100021215454545454545514252525252542121212121111131); Output: Magma V2.10-22 Thu Apr 8 2004 08:05:45 on modular [Seed = 1266568022] ------------------------------------- 100021215454545454545514252525252542121212121111181 Total time: 2.779 seconds, Total memory usage: 2.96MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Thu Apr 8 08:07:32 2004 Input: NextPrime(10002121545454545454551422152525252542121212121111131); Output: Magma V2.10-22 Thu Apr 8 2004 08:07:29 on modular [Seed = 1550408921] ------------------------------------- 10002121545454545454551422152525252542121212121111343 Total time: 2.800 seconds, Total memory usage: 2.96MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Thu Apr 8 08:07:44 2004 Input: NextPrime(1000212154545454545455142215232154525252542121212121111131); Output: Magma V2.10-22 Thu Apr 8 2004 08:07:41 on modular [Seed = 1683055853] ------------------------------------- 1000212154545454545455142215232154525252542121212121111297 Total time: 3.049 seconds, Total memory usage: 2.96MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Thu Apr 8 08:07:58 2004 Input: NextPrime(100021215454545454545514221321654988875232154525252542121212121111131); Output: Magma V2.10-22 Thu Apr 8 2004 08:07:55 on modular [Seed = 1817799923] ------------------------------------- 100021215454545454545514221321654988875232154525252542121212121111191 Total time: 3.479 seconds, Total memory usage: 2.96MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Thu Apr 8 08:08:36 2004 Input: NextPrime(100021215454545454545514221321654988875232132132132154525252542121212121111131); Output: Magma V2.10-22 Thu Apr 8 2004 08:08:33 on modular [Seed = 1950446769] ------------------------------------- 100021215454545454545514221321654988875232132132132154525252542121212121111453 Total time: 3.239 seconds, Total memory usage: 2.96MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Thu Apr 8 08:09:18 2004 Input: NextPrime(10002121545454545454551422321321321654654654654656541321654988875232132132132154525252542121212121111131); Output: Magma V2.10-22 Thu Apr 8 2004 08:09:11 on modular [Seed = 2085190815] ------------------------------------- 1000212154545454545455142232132132165465465465465654132165498887523213213213215\ 4525252542121212121111619 Total time: 6.919 seconds, Total memory usage: 2.96MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Thu Apr 8 08:11:27 2004 Input: NextPrime(10002121545454545454551321654654422321321321654654654654656541321654988875232132132132154525252542121212121111131); Output: Magma V2.10-22 Thu Apr 8 2004 08:11:11 on modular [Seed = 2360970711] ------------------------------------- 1000212154545454545455132165465442232132132165465465465465654132165498887523213\ 2132132154525252542121212121111189 Total time: 16.679 seconds, Total memory usage: 2.96MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Thu Apr 8 08:22:15 2004 Input: NextPrime(35435432165498765432165498765465432132132132321654654654165498765432132132132132132132132132132165498765465432165498798798798798798732165474136546548689) Output: Magma V2.10-22 Thu Apr 8 2004 08:21:52 on modular [Seed = 2761008960] ------------------------------------- ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Thu Apr 8 08:22:53 2004 Input: NextPrime(3543543216549876543216549876546543213213213232165465465416549876543213213213213213213213213213216549876546543216549879889) Output: Magma V2.10-22 Thu Apr 8 2004 08:22:31 on modular [Seed = 2895751343] ------------------------------------- ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Thu Apr 8 08:23:20 2004 Input: NextPrime(5416549876543213213213213213213213213213216549876546543216549879889) Output: Magma V2.10-22 Thu Apr 8 2004 08:23:17 on modular [Seed = 3045110148] ------------------------------------- 5416549876543213213213213213213213213213216549876546543216549880011 Total time: 3.039 seconds, Total memory usage: 2.96MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Thu Apr 8 08:42:16 2004 Input: P:=PolynomialRing(RationalField()); N:=NumberField([x^4-2*x^2-3]); ON:=MaximalOrder(N); Factorization(5 * ON); Output: Magma V2.10-22 Thu Apr 8 2004 08:42:13 on modular [Seed = 3872648775] ------------------------------------- >> N:=NumberField([x^4-2*x^2-3]); ^ Runtime error in 'NumberField': Argument 1 is not irreducible >> ON:=MaximalOrder(N); ^ User error: Identifier 'N' has not been declared or assigned >> Factorization(5 * ON);; ^ User error: Identifier 'ON' has not been declared or assigned Total time: 2.499 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Thu Apr 8 08:42:33 2004 Input: P:=PolynomialRing(RationalField()); N:=NumberField([x^5-2*x^2-3]); ON:=MaximalOrder(N); Factorization(5 * ON); Output: Magma V2.10-22 Thu Apr 8 2004 08:42:30 on modular [Seed = 4007388765] ------------------------------------- [ , ] Total time: 2.559 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Thu Apr 8 08:43:17 2004 Input: P:=PolynomialRing(RationalField()); N:=NumberField([x^5-2*x^2-3]); ON:=MaximalOrder(N); 2; Factorization(2 * ON);3 Factorization(3 * ON); 5; Factorization(5 * ON); 7; Factorization(7 * ON); 11; Factorization(11 * ON); Output: Magma V2.10-22 Thu Apr 8 2004 08:43:15 on modular [Seed = 4140039697] ------------------------------------- 2 [ , ] >> Factorization(3 * ON); 5; ^ User error: bad syntax [ , ] 7 [ , ] 11 [ , ] Total time: 2.600 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Thu Apr 8 08:43:38 2004 Input: P:=PolynomialRing(RationalField()); N:=NumberField([x^5-2*x^2-3]); ON:=MaximalOrder(N); 2; Factorization(2 * ON);3; Factorization(3 * ON); 5; Factorization(5 * ON); 7; Factorization(7 * ON); 11; Factorization(11 * ON); Output: Magma V2.10-22 Thu Apr 8 2004 08:43:36 on modular [Seed = 4274779650] ------------------------------------- 2 [ , ] 3 [ , ] 5 [ , ] 7 [ , ] 11 [ , ] Total time: 2.600 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Thu Apr 8 08:44:12 2004 Input: P:=PolynomialRing(RationalField()); N:=NumberField([x^5-2*x^2-3]); ON:=MaximalOrder(N); 3; Factorization(3 * ON); Output: Magma V2.10-22 Thu Apr 8 2004 08:44:10 on modular [Seed = 104009497] ------------------------------------- 3 [ , ] Total time: 2.580 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host txplano-nat209.nextlink.net. (205.158.160.209) Time: Thu Apr 8 08:47:12 2004 Input: 5*6 Output: Magma V2.10-22 Thu Apr 8 2004 08:47:10 on modular [Seed = 554969322] ------------------------------------- 30 Total time: 2.509 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host Donnelly.iuhb02.iu-bremen.de. (212.201.48.249) Time: Thu Apr 8 12:31:42 2004 Input: P:=PolynomialRing(Rationals()); NF:=NumberField(u^5-666); ClassNumber(NF); Output: Magma V2.10-22 Thu Apr 8 2004 12:31:19 on modular [Seed = 2561517256] ------------------------------------- ************** MAGMA ***************** Host Donnelly.iuhb02.iu-bremen.de. (212.201.48.249) Time: Thu Apr 8 12:32:04 2004 Input: P:=PolynomialRing(Rationals()); NF:=NumberField(u^5-6); ClassNumber(NF); Output: Magma V2.10-22 Thu Apr 8 2004 12:32:01 on modular [Seed = 2694159910] ------------------------------------- 1 Total time: 2.889 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host Donnelly.iuhb02.iu-bremen.de. (212.201.48.249) Time: Thu Apr 8 12:32:22 2004 Input: P:=PolynomialRing(Rationals()); NF:=NumberField(u^5-65); ClassNumber(NF); Output: Magma V2.10-22 Thu Apr 8 2004 12:32:11 on modular [Seed = 2828899876] ------------------------------------- 2 Total time: 10.389 seconds, Total memory usage: 2.60MB ************** MAGMA ***************** Host Donnelly.iuhb02.iu-bremen.de. (212.201.48.249) Time: Thu Apr 8 12:32:51 2004 Input: P:=PolynomialRing(Rationals()); NF:=NumberField(u^5-666); ClassNumber(NF); Output: Magma V2.10-22 Thu Apr 8 2004 12:32:29 on modular [Seed = 3213525285] ------------------------------------- ************** MAGMA ***************** Host Donnelly.iuhb02.iu-bremen.de. (212.201.48.249) Time: Thu Apr 8 12:34:50 2004 Input: D2:=Scheme(A4,[ y^2-(x^3-x), s^2-x, t^2-(x-1) ]); K2:=NumberField([u^2-6,u^2+7]); D2:=BaseChange(D2,K2); P2:=BaseChange(P2,K2); D2crv:=Curve(Image(map< D2->P2 | [s,t+y,1] >)); D2map:=map< D2->D2crv | [s,t+y,1] >; DivD2:=DivisorGroup(D2crv); Output: Magma V2.10-22 Thu Apr 8 2004 12:34:47 on modular [Seed = 3354589415] ------------------------------------- >> D2:=Scheme(A4,[ y^2-(x^3-x), s^2-x, t^2-(x-1) ]); ^ User error: Identifier 'A4' has not been declared or assigned >> K2:=NumberField([u^2-6,u^2+7]); D2:=BaseChange(D2,K2); ^ User error: Identifier 'u' has not been declared or assigned >> K2:=NumberField([u^2-6,u^2+7]); D2:=BaseChange(D2,K2); ^ User error: Identifier 'D2' has not been declared or assigned >> P2:=BaseChange(P2,K2); ^ User error: Identifier 'P2' has not been declared or assigned >> D2crv:=Curve(Image(map< D2->P2 | [s,t+y,1] >)); ^ User error: Identifier 'D2' has not been declared or assigned >> D2map:=map< D2->D2crv | [s,t+y,1] >; ^ User error: Identifier 'D2' has not been declared or assigned >> DivD2:=DivisorGroup(D2crv);; ^ User error: Identifier 'D2crv' has not been declared or assigned Total time: 2.569 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host Donnelly.iuhb02.iu-bremen.de. (212.201.48.249) Time: Thu Apr 8 12:35:17 2004 Input: P2:=ProjectivePlane(Rationals()); A4:=AffineSpace(Rationals(),4); D2:=Scheme(A4,[ y^2-(x^3-x), s^2-x, t^2-(x-1) ]); K2:=NumberField([u^2-6,u^2+7]); D2:=BaseChange(D2,K2); P2:=BaseChange(P2,K2); D2crv:=Curve(Image(map< D2->P2 | [s,t+y,1] >)); D2map:=map< D2->D2crv | [s,t+y,1] >; DivD2:=DivisorGroup(D2crv); Output: Magma V2.10-22 Thu Apr 8 2004 12:35:14 on modular [Seed = 3405772175] ------------------------------------- >> K2:=NumberField([u^2-6,u^2+7]); D2:=BaseChange(D2,K2); ^ User error: Identifier 'u' has not been declared or assigned >> K2:=NumberField([u^2-6,u^2+7]); D2:=BaseChange(D2,K2); ^ User error: Identifier 'K2' has not been declared or assigned >> P2:=BaseChange(P2,K2); ^ User error: Identifier 'K2' has not been declared or assigned Total time: 2.559 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host Donnelly.iuhb02.iu-bremen.de. (212.201.48.249) Time: Thu Apr 8 12:35:57 2004 Input: P2:=ProjectivePlane(Rationals()); A4:=AffineSpace(Rationals(),4); D2:=Scheme(A4,[ y^2-(x^3-x), s^2-x, t^2-(x-1) ]); Pu:=PolynomialRing(Rationals()); K2:=NumberField([u^2-6,u^2+7]); D2:=BaseChange(D2,K2); P2:=BaseChange(P2,K2); D2crv:=Curve(Image(map< D2->P2 | [s,t+y,1] >)); D2map:=map< D2->D2crv | [s,t+y,1] >; DivD2:=DivisorGroup(D2crv); Output: Magma V2.10-22 Thu Apr 8 2004 12:35:34 on modular [Seed = 3538414979] ------------------------------------- ************** MAGMA ***************** Host Donnelly.iuhb02.iu-bremen.de. (212.201.48.249) Time: Thu Apr 8 12:36:09 2004 Input: P2:=ProjectivePlane(Rationals()); A4:=AffineSpace(Rationals(),4); D2:=Scheme(A4,[ y^2-(x^3-x), s^2-x, t^2-(x-1) ]); Pu:=PolynomialRing(Rationals()); K2:=NumberField([u^2-6,u^2+7]); D2:=BaseChange(D2,K2); P2:=BaseChange(P2,K2); D2crv:=Curve(Image(map< D2->P2 | [s,t+y,1] >)); D2map:=map< D2->D2crv | [s,t+y,1] >; //DivD2:=DivisorGroup(D2crv); Output: Magma V2.10-22 Thu Apr 8 2004 12:36:07 on modular [Seed = 3673154986] ------------------------------------- Total time: 2.639 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host Donnelly.iuhb02.iu-bremen.de. (212.201.48.249) Time: Thu Apr 8 12:36:29 2004 Input: P2:=ProjectivePlane(Rationals()); A4:=AffineSpace(Rationals(),4); D2:=Scheme(A4,[ y^2-(x^3-x), s^2-x, t^2-(x-1) ]); Pu:=PolynomialRing(Rationals()); K2:=NumberField([u^2-6,u^2+7]); D2:=BaseChange(D2,K2); P2:=BaseChange(P2,K2); D2crv:=Curve(Image(map< D2->P2 | [s,t+y,1] >)); D2map:=map< D2->D2crv | [s,t+y,1] >; D2map([9/16,15*b7/64,3/4,b7/4]); //DivD2:=DivisorGroup(D2crv); Output: Magma V2.10-22 Thu Apr 8 2004 12:36:27 on modular [Seed = 3805797742] ------------------------------------- (3/4 : 31/64*b7 : 1) Total time: 2.660 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host Donnelly.iuhb02.iu-bremen.de. (212.201.48.249) Time: Thu Apr 8 12:37:45 2004 Input: P2:=ProjectivePlane(Rationals()); A4:=AffineSpace(Rationals(),4); D2:=Scheme(A4,[ y^2-(x^3-x), s^2-x, t^2-(x-1) ]); //Pu:=PolynomialRing(Rationals()); //K2:=NumberField([u^2-6,u^2+7]); D2:=BaseChange(D2,K2); //P2:=BaseChange(P2,K2); D2crv:=Curve(Image(map< D2->P2 | [s,t+y,1] >)); D2map:=map< D2->D2crv | [s,t+y,1] >; // D2map([9/16,15*b7/64,3/4,b7/4]); DivD2:=DivisorGroup(D2crv); Output: Magma V2.10-22 Thu Apr 8 2004 12:37:42 on modular [Seed = 4089891874] ------------------------------------- Total time: 2.570 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ws14.fas.harvard.edu. (140.247.31.114) Time: Thu Apr 8 13:09:06 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^3-2); R := RingOfIntegers(F); Output: Magma V2.10-22 Thu Apr 8 2004 13:09:03 on modular [Seed = 3889307840] ------------------------------------- >> R := RingOfIntegers(F);; ^ User error: Identifier 'F' has not been declared or assigned Total time: 2.589 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host ws14.fas.harvard.edu. (140.247.31.114) Time: Thu Apr 8 13:09:18 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^3-2); R := RingOfIntegers(K); Output: Magma V2.10-22 Thu Apr 8 2004 13:09:15 on modular [Seed = 4291442892] ------------------------------------- Total time: 2.559 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ws14.fas.harvard.edu. (140.247.31.114) Time: Thu Apr 8 13:10:41 2004 Input: Q := PolynomialRing(Rationals()); Ka := NumberField(x^2-2); OKa := RingOfIntegers(Ka); Kb := NumberField(x^2+2); OKb := RingOfIntegers(Kb); OK = OKa*OKb; Output: Magma V2.10-22 Thu Apr 8 2004 13:10:38 on modular [Seed = 255510664] ------------------------------------- >> OK = OKa*OKb;; ^ User error: Identifier 'OK' has not been declared or assigned Total time: 2.570 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host ws14.fas.harvard.edu. (140.247.31.114) Time: Thu Apr 8 13:10:52 2004 Input: Q := PolynomialRing(Rationals()); Ka := NumberField(x^2-2); OKa := RingOfIntegers(Ka); Kb := NumberField(x^2+2); OKb := RingOfIntegers(Kb); OK := OKa*OKb; Output: Magma V2.10-22 Thu Apr 8 2004 13:10:50 on modular [Seed = 70370199] ------------------------------------- >> OK := OKa*OKb;; ^ Runtime error in '*': Bad argument types Argument types given: RngOrd, RngOrd Total time: 2.579 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host ws14.fas.harvard.edu. (140.247.31.114) Time: Thu Apr 8 13:11:47 2004 Input: Q := PolynomialRing(Rationals()); Ka := NumberField(x^2-2); OKa := RingOfIntegers(Ka); Kb := NumberField(x^2+2); OKa := RingOfIntegers(Ka); K := Ka*Kb; OK := RingOfIntegers(K); Output: Magma V2.10-22 Thu Apr 8 2004 13:11:45 on modular [Seed = 489216709] ------------------------------------- >> K := Ka*Kb; ^ Runtime error in '*': Bad argument types Argument types given: FldNum, FldNum >> OK := RingOfIntegers(K);; ^ User error: Identifier 'K' has not been declared or assigned Total time: 2.510 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host ws14.fas.harvard.edu. (140.247.31.114) Time: Thu Apr 8 13:12:29 2004 Input: Q := PolynomialRing(Rationals()); Ka := NumberField(x^2-2); OKa := RingOfIntegers(Ka); Kb := NumberField(x^2+2); OKa := RingOfIntegers(Ka); K := (Ka)(Kb); OK := RingOfIntegers(K); Output: Magma V2.10-22 Thu Apr 8 2004 13:12:27 on modular [Seed = 739896286] ------------------------------------- >> K := (Ka)(Kb); ^ Runtime error: Bad argument types Argument types given: FldNum, FldNum >> OK := RingOfIntegers(K);; ^ User error: Identifier 'K' has not been declared or assigned Total time: 2.659 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host ws14.fas.harvard.edu. (140.247.31.114) Time: Thu Apr 8 13:12:44 2004 Input: Q := PolynomialRing(Rationals()); Ka := NumberField(x^2-2); OKa := RingOfIntegers(Ka); Kb := NumberField(x^2+2); OKa := RingOfIntegers(Ka); Output: Magma V2.10-22 Thu Apr 8 2004 13:12:42 on modular [Seed = 621866278] ------------------------------------- Total time: 2.579 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host ws14.fas.harvard.edu. (140.247.31.114) Time: Thu Apr 8 13:19:52 2004 Input: R = PolynomialRing(RationalField()); Ka := NumberField(x^2 - 2); Kb := NumberField(x^2 + 2); K := NumberField((X^2 - 2)(x^2 + 2)); OKa := RingOfIntegers(Ka); OKb := RingOfIntegers(Kb); OK := RingOfIntegers(K); Output: Magma V2.10-22 Thu Apr 8 2004 13:19:49 on modular [Seed = 839383950] ------------------------------------- >> R = PolynomialRing(RationalField()); ^ User error: bad syntax >> Ka := NumberField(x^2 - 2); ^ User error: Identifier 'x' has not been declared or assigned >> Kb := NumberField(x^2 + 2); ^ User error: Identifier 'x' has not been declared or assigned >> K := NumberField((X^2 - 2)(x^2 + 2)); ^ User error: Identifier 'x' has not been declared or assigned >> OKa := RingOfIntegers(Ka); ^ User error: Identifier 'Ka' has not been declared or assigned >> OKb := RingOfIntegers(Kb); ^ User error: Identifier 'Kb' has not been declared or assigned >> OK := RingOfIntegers(K);; ^ User error: Identifier 'K' has not been declared or assigned Total time: 2.559 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host ws14.fas.harvard.edu. (140.247.31.114) Time: Thu Apr 8 13:20:03 2004 Input: R := PolynomialRing(RationalField()); Ka := NumberField(x^2 - 2); Kb := NumberField(x^2 + 2); K := NumberField((X^2 - 2)(x^2 + 2)); OKa := RingOfIntegers(Ka); OKb := RingOfIntegers(Kb); OK := RingOfIntegers(K); Output: Magma V2.10-22 Thu Apr 8 2004 13:20:00 on modular [Seed = 1299743876] ------------------------------------- >> K := NumberField((X^2 - 2)(x^2 + 2)); ^ User error: Identifier 'X' has not been declared or assigned >> OK := RingOfIntegers(K);; ^ User error: Identifier 'K' has not been declared or assigned Total time: 2.710 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host ws14.fas.harvard.edu. (140.247.31.114) Time: Thu Apr 8 13:20:15 2004 Input: R := PolynomialRing(RationalField()); Ka := NumberField(x^2 - 2); Kb := NumberField(x^2 + 2); K := NumberField((x^2 - 2)(x^2 + 2)); OKa := RingOfIntegers(Ka); OKb := RingOfIntegers(Kb); OK := RingOfIntegers(K); Output: Magma V2.10-22 Thu Apr 8 2004 13:20:12 on modular [Seed = 1533973150] ------------------------------------- >> K := NumberField((x^2 - 2)(x^2 + 2)); ^ Runtime error: Bad argument types Argument types given: RngUPolElt, RngUPolElt >> OK := RingOfIntegers(K);; ^ User error: Identifier 'K' has not been declared or assigned Total time: 2.559 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host ws14.fas.harvard.edu. (140.247.31.114) Time: Thu Apr 8 13:20:26 2004 Input: R := PolynomialRing(RationalField()); Ka := NumberField(x^2 - 2); Kb := NumberField(x^2 + 2); K := NumberField((x^2 - 2)*(x^2 + 2)); OKa := RingOfIntegers(Ka); OKb := RingOfIntegers(Kb); OK := RingOfIntegers(K); Output: Magma V2.10-22 Thu Apr 8 2004 13:20:23 on modular [Seed = 1348835726] ------------------------------------- >> K := NumberField((x^2 - 2)*(x^2 + 2)); ^ Runtime error in 'NumberField': Argument 1 is not irreducible >> OK := RingOfIntegers(K);; ^ User error: Identifier 'K' has not been declared or assigned Total time: 2.509 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host k19067.kenyon.edu. (138.28.42.22) Time: Thu Apr 8 13:58:36 2004 Input: int sum=0; for(int i=0; i<10000;i++) sum=sum+i*i; cout<> int sum=0; ^ User error: bad syntax >> for(int i=0; i<10000;i++) ^ User error: bad syntax >> sum=sum+i*i; ^ User error: Identifier 'sum' has not been declared or assigned >> cout< := PolynomialRing(RationalField()); K := NumberField({x^2-2},{x^2+2}); OK := RingOfIntegers(K); Output: Magma V2.10-22 Thu Apr 8 2004 14:40:10 on modular [Seed = 4106299510] ------------------------------------- >> K := NumberField({x^2-2},{x^2+2}); ^ Runtime error in 'NumberField': Bad argument types Argument types given: SetEnum[RngUPolElt], SetEnum[RngUPolElt] >> OK := RingOfIntegers(K);; ^ User error: Identifier 'K' has not been declared or assigned Total time: 2.549 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 3(NXDOMAIN) (140.247.129.19) Time: Thu Apr 8 14:40:36 2004 Input: R := PolynomialRing(RationalField()); K := NumberField({x^2-2,x^2+2}); OK := RingOfIntegers(K); Output: Magma V2.10-22 Thu Apr 8 2004 14:40:33 on modular [Seed = 255513508] ------------------------------------- >> K := NumberField({x^2-2,x^2+2}); ^ Runtime error in 'NumberField': Bad argument types Argument types given: SetEnum[RngUPolElt] >> OK := RingOfIntegers(K);; ^ User error: Identifier 'K' has not been declared or assigned Total time: 2.559 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 3(NXDOMAIN) (140.247.129.19) Time: Thu Apr 8 14:40:40 2004 Input: R := PolynomialRing(RationalField()); K := NumberField({x^2-2,x^2+2}); OK := RingOfIntegers(K); Output: Magma V2.10-22 Thu Apr 8 2004 14:40:37 on modular [Seed = 120773544] ------------------------------------- >> K := NumberField({x^2-2,x^2+2}); ^ Runtime error in 'NumberField': Bad argument types Argument types given: SetEnum[RngUPolElt] >> OK := RingOfIntegers(K);; ^ User error: Identifier 'K' has not been declared or assigned Total time: 2.539 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host k19067.kenyon.edu. (138.28.42.22) Time: Thu Apr 8 14:58:23 2004 Input: MinimumWeight(RandomLinearCode(GF(2),32,16)); Output: Magma V2.10-22 Thu Apr 8 2004 14:58:20 on modular [Seed = 1007279354] ------------------------------------- 4 Total time: 2.589 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host k19067.kenyon.edu. (138.28.42.22) Time: Thu Apr 8 14:59:37 2004 Input: MinimumWeightBounds(C) : Code -> RngIntElt, RngIntElt Output: Magma V2.10-22 Thu Apr 8 2004 14:59:35 on modular [Seed = 889246760] ------------------------------------- >> MinimumWeightBounds(C) : Code -> RngIntElt, RngIntElt ^ User error: bad syntax Total time: 2.569 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host k19067.kenyon.edu. (138.28.42.22) Time: Thu Apr 8 15:00:23 2004 Input: C:=RandomLinearCode(GF(2),32,16); MinimumWeightBounds(C) : Code -> RngIntElt, RngIntElt Output: Magma V2.10-22 Thu Apr 8 2004 15:00:20 on modular [Seed = 1165009931] ------------------------------------- >> MinimumWeightBounds(C) : Code -> RngIntElt, RngIntElt ^ User error: bad syntax Total time: 2.499 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host k19067.kenyon.edu. (138.28.42.22) Time: Thu Apr 8 15:00:52 2004 Input: C:=RandomLinearCode(GF(2),32,16); MinimumWeightBounds(C); Output: Magma V2.10-22 Thu Apr 8 2004 15:00:50 on modular [Seed = 1567145013] ------------------------------------- 1 17 Total time: 2.549 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host k19067.kenyon.edu. (138.28.42.22) Time: Thu Apr 8 15:02:19 2004 Input: a := BKLC(GF(2),77,34); ResetMinimumWeightBounds(a); MinimumWeightBounds(a); Output: Magma V2.10-22 Thu Apr 8 2004 15:02:16 on modular [Seed = 2068749001] ------------------------------------- 1 44 Total time: 2.600 seconds, Total memory usage: 2.28MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:16:16 2004 Input: R := PolynomialRing(RationalField()); K := NumberField({x^2-2,x^2+2}); OK := RingOfIntegers(K); Output: Magma V2.10-22 Thu Apr 8 2004 15:16:14 on modular [Seed = 3689824047] ------------------------------------- >> K := NumberField({x^2-2,x^2+2}); ^ Runtime error in 'NumberField': Bad argument types Argument types given: SetEnum[RngUPolElt] >> OK := RingOfIntegers(K);; ^ User error: Identifier 'K' has not been declared or assigned Total time: 2.540 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:16:53 2004 Input: R := PolynomialRing(RationalField()); K := NumberField([x^2-2,x^2+2]); OK := RingOfIntegers(K); Output: Magma V2.10-22 Thu Apr 8 2004 15:16:50 on modular [Seed = 3555079931] ------------------------------------- Total time: 2.940 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:17:02 2004 Input: R := PolynomialRing(RationalField()); K := NumberField([x^2-2,x^2+2]); OK := RingOfIntegers(K) Output: Magma V2.10-22 Thu Apr 8 2004 15:16:59 on modular [Seed = 3957198538] ------------------------------------- Total time: 2.950 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:17:08 2004 Input: R := PolynomialRing(RationalField()); K := NumberField([x^2-2,x^2+2]); OK := RingOfIntegers(K) Output: Magma V2.10-22 Thu Apr 8 2004 15:17:05 on modular [Seed = 3822454488] ------------------------------------- Total time: 2.949 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:18:25 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-2); L := NumberField(x^2+2); M := NumberField([x^2-2,x^2+2]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Output: Magma V2.10-22 Thu Apr 8 2004 15:18:22 on modular [Seed = 4224589455] ------------------------------------- Total time: 3.029 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:19:18 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-2); L := NumberField(x^2+2); M := NumberField([x^2-2,x^2+2]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Factorization(3*OK); Factorization(3*OL); Factorization(3*OM); Output: Magma V2.10-22 Thu Apr 8 2004 15:19:15 on modular [Seed = 4089845322] ------------------------------------- [ ] [ , ] [ , ] Total time: 3.039 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:19:49 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-2); L := NumberField(x^2+2); M := NumberField([x^2-2,x^2+2]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Factorization(2*OK); Factorization(2*OL); Factorization(2*OM); Output: Magma V2.10-22 Thu Apr 8 2004 15:19:46 on modular [Seed = 154987728] ------------------------------------- [ ] [ ] [ ] Total time: 3.229 seconds, Total memory usage: 1.92MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:20:52 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-2); L := NumberField(x^2+2); M := NumberField([x^2-2,x^2+2]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Factorization(a*OK); Factorization(a*OL); Factorization(a*OM); Output: Magma V2.10-22 Thu Apr 8 2004 15:20:49 on modular [Seed = 422379267] ------------------------------------- [ ] >> Factorization(a*OL); ^ Runtime error in '*': Rhs argument 1 is invalid for this constructor >> Factorization(a*OM);; ^ Runtime error in '*': Rhs argument 1 is invalid for this constructor Total time: 2.970 seconds, Total memory usage: 1.92MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:20:57 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-2); L := NumberField(x^2+2); M := NumberField([x^2-2,x^2+2]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Factorization(a*OK); Factorization(a*OL); Factorization(a*OM); Output: Magma V2.10-22 Thu Apr 8 2004 15:20:54 on modular [Seed = 287635212] ------------------------------------- [ ] >> Factorization(a*OL); ^ Runtime error in '*': Rhs argument 1 is invalid for this constructor >> Factorization(a*OM);; ^ Runtime error in '*': Rhs argument 1 is invalid for this constructor Total time: 2.950 seconds, Total memory usage: 1.92MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:21:10 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-2); L := NumberField(x^2+2); M := NumberField([x^2-2,x^2+2]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Factorization(2*OK); Factorization(2*OL); Factorization(2*OM); Output: Magma V2.10-22 Thu Apr 8 2004 15:21:07 on modular [Seed = 689753857] ------------------------------------- [ ] [ ] [ ] Total time: 3.170 seconds, Total memory usage: 1.92MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:23:22 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-2); L := NumberField(x^2+2); M := NumberField([x^2-2,x^2+2]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Factorization(5*OK); Factorization(5*OL); Factorization(5*OM); Output: Magma V2.10-22 Thu Apr 8 2004 15:23:19 on modular [Seed = 555009933] ------------------------------------- [ ] [ ] [ , ] Total time: 2.920 seconds, Total memory usage: 1.92MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:25:55 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-2); L := NumberField(x^2+2); M := NumberField([x^2-2,x^2+2]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Factorization(7*OK); Factorization(7*OL); Factorization(7*OM); Output: Magma V2.10-22 Thu Apr 8 2004 15:25:52 on modular [Seed = 856085624] ------------------------------------- [ , ] [ ] [ , ] Total time: 2.919 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:26:32 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-2); L := NumberField(x^2+3); M := NumberField([x^2-2,x^2+2]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Factorization(7*OK); Factorization(7*OL); Factorization(7*OM); Output: Magma V2.10-22 Thu Apr 8 2004 15:26:29 on modular [Seed = 1266592805] ------------------------------------- [ , ] [ , ] [ , ] Total time: 2.969 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:26:39 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-2); L := NumberField(x^2+3); M := NumberField([x^2-2,x^2+3]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Factorization(7*OK); Factorization(7*OL); Factorization(7*OM); Output: Magma V2.10-22 Thu Apr 8 2004 15:26:37 on modular [Seed = 1131848741] ------------------------------------- [ , ] [ , ] [ , , , ] Total time: 2.619 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:27:01 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-2); L := NumberField(x^2+3); M := NumberField([x^2-2,x^2+3]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Factorization(2*OK); Factorization(2*OL); Factorization(2*OM); Output: Magma V2.10-22 Thu Apr 8 2004 15:26:58 on modular [Seed = 1533983954] ------------------------------------- [ ] [ ] [ ] Total time: 2.620 seconds, Total memory usage: 1.91MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:27:24 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-2); L := NumberField(x^2+3); M := NumberField([x^2-2,x^2+3]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Factorization(3*OK); Factorization(3*OL); Factorization(3*OM); Output: Magma V2.10-22 Thu Apr 8 2004 15:27:21 on modular [Seed = 1399239873] ------------------------------------- [ ] [ ] [ ] Total time: 2.589 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:27:34 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-3); L := NumberField(x^2+3); M := NumberField([x^2-2,x^2+3]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Factorization(3*OK); Factorization(3*OL); Factorization(3*OM); Output: Magma V2.10-22 Thu Apr 8 2004 15:27:31 on modular [Seed = 1801358531] ------------------------------------- [ ] [ ] [ ] Total time: 2.629 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:27:53 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-3); L := NumberField(x^2-7); M := NumberField([x^2-2,x^2+3]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Factorization(3*OK); Factorization(3*OL); Factorization(3*OM); Output: Magma V2.10-22 Thu Apr 8 2004 15:27:50 on modular [Seed = 1666614494] ------------------------------------- [ ] [ , ] [ ] Total time: 2.639 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:28:18 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-3); L := NumberField(x^2-7); M := NumberField([x^2-2,x^2+3]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Factorization(2*OK); Factorization(2*OL); Factorization(2*OM); Output: Magma V2.10-22 Thu Apr 8 2004 15:28:16 on modular [Seed = 2068749472] ------------------------------------- [ ] [ ] [ ] Total time: 2.609 seconds, Total memory usage: 1.91MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:28:29 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-5); L := NumberField(x^2-7); M := NumberField([x^2-2,x^2+3]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Factorization(2*OK); Factorization(2*OL); Factorization(2*OM); Output: Magma V2.10-22 Thu Apr 8 2004 15:28:27 on modular [Seed = 1934005411] ------------------------------------- [ ] [ ] [ ] Total time: 2.649 seconds, Total memory usage: 1.91MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:28:49 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-5); L := NumberField(x^2-1); M := NumberField([x^2-2,x^2+3]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Factorization(2*OK); Factorization(2*OL); Factorization(2*OM); Output: Magma V2.10-22 Thu Apr 8 2004 15:28:46 on modular [Seed = 2344512622] ------------------------------------- >> L := NumberField(x^2-1); ^ Runtime error in 'NumberField': Argument 1 is not irreducible >> OL := RingOfIntegers(L); ^ User error: Identifier 'L' has not been declared or assigned [ ] >> Factorization(2*OL); ^ User error: Identifier 'OL' has not been declared or assigned [ ] Total time: 2.590 seconds, Total memory usage: 1.91MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:28:59 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-5); L := NumberField(x^2-1); M := NumberField([x^2-2,x^2-1]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Factorization(2*OK); Factorization(2*OL); Factorization(2*OM); Output: Magma V2.10-22 Thu Apr 8 2004 15:28:57 on modular [Seed = 2209768561] ------------------------------------- >> L := NumberField(x^2-1); ^ Runtime error in 'NumberField': Argument 1 is not irreducible >> M := NumberField([x^2-2,x^2-1]); ^ Runtime error in 'NumberField': Argument 2 is not irreducible >> OL := RingOfIntegers(L); ^ User error: Identifier 'L' has not been declared or assigned >> OM := RingOfIntegers(M); ^ User error: Identifier 'M' has not been declared or assigned [ ] >> Factorization(2*OL); ^ User error: Identifier 'OL' has not been declared or assigned >> Factorization(2*OM);; ^ User error: Identifier 'OM' has not been declared or assigned Total time: 2.589 seconds, Total memory usage: 1.87MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:29:14 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-5); L := NumberField(x^2+1); M := NumberField([x^2-2,x^2+1]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Factorization(2*OK); Factorization(2*OL); Factorization(2*OM); Output: Magma V2.10-22 Thu Apr 8 2004 15:29:10 on modular [Seed = 2611901334] ------------------------------------- [ ] [ ] [ ] Total time: 3.019 seconds, Total memory usage: 1.92MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:29:28 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-3); L := NumberField(x^2+1); M := NumberField([x^2-2,x^2+1]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Factorization(2*OK); Factorization(2*OL); Factorization(2*OM); Output: Magma V2.10-22 Thu Apr 8 2004 15:29:24 on modular [Seed = 2477161357] ------------------------------------- [ ] [ ] [ ] Total time: 3.049 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:29:41 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-5); L := NumberField(x^2+3); M := NumberField([x^2-2,x^2+1]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Factorization(2*OK); Factorization(2*OL); Factorization(2*OM); Output: Magma V2.10-22 Thu Apr 8 2004 15:29:38 on modular [Seed = 2879275906] ------------------------------------- [ ] [ ] [ ] Total time: 3.109 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:30:44 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+1); L := NumberField(x^2+5); M := NumberField([x^2-2,x^2+1]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Factorization(2*OK); Factorization(2*OL); Factorization(2*OM); Output: Magma V2.10-22 Thu Apr 8 2004 15:30:41 on modular [Seed = 3129955024] ------------------------------------- [ ] [ ] [ ] Total time: 2.999 seconds, Total memory usage: 1.92MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:31:03 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+1); L := NumberField(x^2+5); M := NumberField([x^2+1,x^2+5]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Factorization(2*OK); Factorization(2*OL); Factorization(2*OM); Output: Magma V2.10-22 Thu Apr 8 2004 15:31:00 on modular [Seed = 2995215053] ------------------------------------- [ ] [ ] [ ] Total time: 3.119 seconds, Total memory usage: 1.92MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:31:37 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-3); L := NumberField(x^2+5); M := NumberField([x^2-3,x^2+5]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Factorization(2*OK); Factorization(2*OL); Factorization(2*OM); Output: Magma V2.10-22 Thu Apr 8 2004 15:31:34 on modular [Seed = 3388744020] ------------------------------------- [ ] [ ] [ , ] Total time: 3.079 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:34:26 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-3); L := NumberField(x^2+5); M := NumberField([x^2-3,x^2+5]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Factorization(3*OK); Factorization(3*OL); Factorization(3*OM); Output: Magma V2.10-22 Thu Apr 8 2004 15:34:23 on modular [Seed = 3254003957] ------------------------------------- [ ] [ , ] [ , ] Total time: 2.880 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:41:29 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-3); L := NumberField(x^2+5); M := NumberField([x^2-3,x^2+5]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Factorization(7*OK); Factorization(7*OL); Factorization(7*OM); Output: Magma V2.10-22 Thu Apr 8 2004 15:41:26 on modular [Seed = 3923510020] ------------------------------------- [ ] [ , ] [ , ] Total time: 2.920 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:42:15 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-3); L := NumberField(x^2+5); M := NumberField([x^2+1,x^2+7]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Factorization(7*OK); Factorization(7*OL); Factorization(7*OM); Output: Magma V2.10-22 Thu Apr 8 2004 15:42:12 on modular [Seed = 3788770046] ------------------------------------- [ ] [ , ] [ ] Total time: 2.629 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:42:36 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-3); L := NumberField(x^2+5); M := NumberField([x^2+1,x^2+7]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Factorization(11*OK); Factorization(11*OL); Factorization(11*OM); Output: Magma V2.10-22 Thu Apr 8 2004 15:42:34 on modular [Seed = 4190900952] ------------------------------------- [ , ] [ ] [ , ] Total time: 2.659 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:42:59 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-3); L := NumberField(x^2+5); M := NumberField([x^2+1,x^2+7]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Factorization(13*OK); Factorization(13*OL); Factorization(13*OM); Output: Magma V2.10-22 Thu Apr 8 2004 15:42:56 on modular [Seed = 4056160954] ------------------------------------- [ , ] [ ] [ , ] Total time: 2.659 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:43:17 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2-3); L := NumberField(x^2+5); M := NumberField([x^2+1,x^2+7]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Factorization(2*OK); Factorization(2*OL); Factorization(2*OM); Output: Magma V2.10-22 Thu Apr 8 2004 15:43:14 on modular [Seed = 238806352] ------------------------------------- [ ] [ ] [ , ] Total time: 2.689 seconds, Total memory usage: 1.91MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:44:38 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+1); L := NumberField(x^2+7); M := NumberField([x^2+1,x^2+7]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Factorization(2*OK); Factorization(2*OL); Factorization(2*OM); Output: Magma V2.10-22 Thu Apr 8 2004 15:44:35 on modular [Seed = 104066473] ------------------------------------- [ ] [ , ] [ , ] Total time: 2.700 seconds, Total memory usage: 1.91MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:44:51 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+3); L := NumberField(x^2+7); M := NumberField([x^2+1,x^2+7]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Factorization(2*OK); Factorization(2*OL); Factorization(2*OM); Output: Magma V2.10-22 Thu Apr 8 2004 15:44:48 on modular [Seed = 506197410] ------------------------------------- [ ] [ , ] [ , ] Total time: 2.749 seconds, Total memory usage: 1.92MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:45:31 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+1); L := NumberField(x^2+5); M := NumberField([x^2+1,x^2+5]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Factorization(2*OK); Factorization(2*OL); Factorization(2*OM); Output: Magma V2.10-22 Thu Apr 8 2004 15:45:28 on modular [Seed = 321321159] ------------------------------------- [ ] [ ] [ ] Total time: 3.119 seconds, Total memory usage: 1.92MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:49:12 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+1); L := NumberField(x^2+5); M := NumberField([x^2+1,x^2+5]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Factorization(3*OK); Factorization(3*OL); Factorization(3*OM); Output: Magma V2.10-22 Thu Apr 8 2004 15:49:09 on modular [Seed = 638831263] ------------------------------------- [ ] [ , ] [ , ] Total time: 2.929 seconds, Total memory usage: 2.02MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:49:34 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+1); L := NumberField(x^2+5); M := NumberField([x^2+1,x^2+5]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Factorization(5*OK); Factorization(5*OL); Factorization(5*OM); Output: Magma V2.10-22 Thu Apr 8 2004 15:49:31 on modular [Seed = 1040962297] ------------------------------------- [ , ] [ ] [ , ] Total time: 2.879 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:49:59 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+3); L := NumberField(x^2+5); M := NumberField([x^2+3,x^2+5]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Factorization(5*OK); Factorization(5*OL); Factorization(5*OM); Output: Magma V2.10-22 Thu Apr 8 2004 15:49:56 on modular [Seed = 922934239] ------------------------------------- [ ] [ ] [ ] Total time: 2.839 seconds, Total memory usage: 1.98MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:50:15 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+3); L := NumberField(x^2+7); M := NumberField([x^2+3,x^2+7]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Factorization(5*OK); Factorization(5*OL); Factorization(5*OM); Output: Magma V2.10-22 Thu Apr 8 2004 15:50:12 on modular [Seed = 1181985470] ------------------------------------- [ ] [ ] [ , ] Total time: 2.930 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:50:45 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+3); L := NumberField(x^2+7); M := NumberField([x^2+3,x^2+7]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Factorization(2*OK); Factorization(2*OL); Factorization(2*OM); Output: Magma V2.10-22 Thu Apr 8 2004 15:50:41 on modular [Seed = 1584116547] ------------------------------------- [ ] [ , ] [ , ] Total time: 3.479 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:50:54 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+3); L := NumberField(x^2+7); M := NumberField([x^2+3,x^2+7]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Factorization(3*OK); Factorization(3*OL); Factorization(3*OM); Output: Magma V2.10-22 Thu Apr 8 2004 15:50:51 on modular [Seed = 1449376577] ------------------------------------- [ ] [ ] [ ] Total time: 2.880 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:51:21 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+3); L := NumberField(x^2+1); M := NumberField([x^2+3,x^2+1]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Factorization(3*OK); Factorization(3*OL); Factorization(3*OM); Output: Magma V2.10-22 Thu Apr 8 2004 15:51:18 on modular [Seed = 1851491156] ------------------------------------- [ ] [ ] [ ] Total time: 2.949 seconds, Total memory usage: 1.98MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:51:38 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+3); L := NumberField(x^2-3); M := NumberField([x^2+3,x^2-3]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Factorization(3*OK); Factorization(3*OL); Factorization(3*OM); Output: Magma V2.10-22 Thu Apr 8 2004 15:51:35 on modular [Seed = 1716751149] ------------------------------------- [ ] [ ] [ ] Total time: 3.029 seconds, Total memory usage: 2.13MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:51:49 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+3); L := NumberField(x^2-5); M := NumberField([x^2+3,x^2-5]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Factorization(3*OK); Factorization(3*OL); Factorization(3*OM); Output: Magma V2.10-22 Thu Apr 8 2004 15:51:46 on modular [Seed = 2118882080] ------------------------------------- [ ] [ ] [ ] Total time: 2.609 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:52:01 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+5); L := NumberField(x^2-5); M := NumberField([x^2+3,x^2-5]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Factorization(3*OK); Factorization(3*OL); Factorization(3*OM); Output: Magma V2.10-22 Thu Apr 8 2004 15:51:58 on modular [Seed = 2000853541] ------------------------------------- [ , ] [ ] [ ] Total time: 2.669 seconds, Total memory usage: 1.98MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:52:09 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+5); L := NumberField(x^2-5); M := NumberField([x^2+5,x^2-5]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Factorization(3*OK); Factorization(3*OL); Factorization(3*OM); Output: Magma V2.10-22 Thu Apr 8 2004 15:52:07 on modular [Seed = 2411356900] ------------------------------------- [ , ] [ ] [ , ] Total time: 2.660 seconds, Total memory usage: 2.04MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Thu Apr 8 15:52:33 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+5); L := NumberField(x^2-5); M := NumberField([x^2+5,x^2-5]); OK := RingOfIntegers(K); OL := RingOfIntegers(L); OM := RingOfIntegers(M); Factorization(5*OK); Factorization(5*OL); Factorization(5*OM); Output: Magma V2.10-22 Thu Apr 8 2004 15:52:30 on modular [Seed = 2276616949] ------------------------------------- [ ] [ ] [ , ] Total time: 2.670 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host gw1.btc.transwitch.com. (63.149.68.2) Time: Thu Apr 8 16:49:37 2004 Input: R := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 555615421240*x^14 + 27406433638578514502920*x^12 - 13726572204638324273630700*x^10 + 3588427787776363269109190*x^8 - 195353042686112443470900*x^6 + 2091417622303284637675*x^4 - 5278681730835445500*x^2 + 166802520192025)); Output: Magma V2.10-22 Thu Apr 8 2004 16:49:19 on modular [Seed = 221837263] ------------------------------------- 103 16 Total time: 9.529 seconds, Total memory usage: 14.82MB ************** MAGMA ***************** Host gw1.btc.transwitch.com. (63.149.68.2) Time: Thu Apr 8 16:50:27 2004 Input: R := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 96*x^14 + 2568*x^12 - 28560*x^10 + 145548*x^8 - 371520*x^6 + 471600*x^4 - 252000*x^2 + 22500)); Output: Magma V2.10-22 Thu Apr 8 2004 16:50:18 on modular [Seed = 638836000] ------------------------------------- 103 16 Total time: 8.240 seconds, Total memory usage: 3.66MB ************** MAGMA ***************** Host dialup-74.106.220.203.acc02-beau-nwc.comindico.com.au. (203.220.106.74) Time: Fri Apr 9 06:51:23 2004 Input: Factorisation(2454356456); Output: Magma V2.10-22 Fri Apr 9 2004 06:51:18 on modular [Seed = 1165198709] ------------------------------------- [ <2, 3>, <661, 1>, <464137, 1> ] Total time: 2.649 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host dialup-74.106.220.203.acc02-beau-nwc.comindico.com.au. (203.220.106.74) Time: Fri Apr 9 06:52:14 2004 Input: Factorisation(24543564566455867957891); Output: Magma V2.10-22 Fri Apr 9 2004 06:52:12 on modular [Seed = 1299942663] ------------------------------------- [ <1637, 1>, <541759, 1>, <27674693721977, 1> ] Total time: 2.499 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host dialup-74.106.220.203.acc02-beau-nwc.comindico.com.au. (203.220.106.74) Time: Fri Apr 9 06:52:33 2004 Input: ??; Output: Magma V2.10-22 Fri Apr 9 2004 06:52:31 on modular [Seed = 1917104651] ------------------------------------- No references for word "?;" Total time: 2.549 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host dialup-74.106.220.203.acc02-beau-nwc.comindico.com.au. (203.220.106.74) Time: Fri Apr 9 06:52:50 2004 Input: ?Goldbach; Output: Magma V2.10-22 Fri Apr 9 2004 06:52:48 on modular [Seed = 2051848940] ------------------------------------- No references for word "Goldbach;" Total time: 2.589 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host dialup-74.106.220.203.acc02-beau-nwc.comindico.com.au. (203.220.106.74) Time: Fri Apr 9 07:12:16 2004 Input: G:=Group<4|>; Output: Magma V2.10-22 Fri Apr 9 2004 07:12:13 on modular [Seed = 3011868328] ------------------------------------- >> G:=Group<4|>;; ^ User error: bad syntax Total time: 2.569 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host dialup-74.106.220.203.acc02-beau-nwc.comindico.com.au. (203.220.106.74) Time: Fri Apr 9 07:15:08 2004 Input: G:=quo; Output: Magma V2.10-22 Fri Apr 9 2004 07:15:05 on modular [Seed = 2761056523] ------------------------------------- Total time: 2.569 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host dialup-74.106.220.203.acc02-beau-nwc.comindico.com.au. (203.220.106.74) Time: Fri Apr 9 07:18:20 2004 Input: G:=quo; G; G:Magma; Output: Magma V2.10-22 Fri Apr 9 2004 07:18:17 on modular [Seed = 2912644034] ------------------------------------- Finitely presented group G on 4 generators Relations G.1 * G.2 * G.3 * G.4 = Id(G) quo< FreeGroup(4) | $.1 * $.2 * $.3 * $.4 = Id($) > Total time: 2.579 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host dialup-74.106.220.203.acc02-beau-nwc.comindico.com.au. (203.220.106.74) Time: Fri Apr 9 07:19:52 2004 Input: F:=FreeGroup(4) G:=quo; G; G:Magma; Output: Magma V2.10-22 Fri Apr 9 2004 07:19:50 on modular [Seed = 3588428565] ------------------------------------- >> G:=quo; ^ User error: bad syntax >> G; ^ User error: Identifier 'G' has not been declared or assigned >> G:Magma;; ^ User error: Identifier 'G' has not been declared or assigned Total time: 2.560 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host dialup-74.106.220.203.acc02-beau-nwc.comindico.com.au. (203.220.106.74) Time: Fri Apr 9 07:20:19 2004 Input: F:=FreeGroup(4); G:=quo; G; G:Magma; Output: Magma V2.10-22 Fri Apr 9 2004 07:20:17 on modular [Seed = 3321037602] ------------------------------------- Finitely presented group G on 4 generators Relations G.1 * G.2 * G.3 * G.4 = Id(G) quo Total time: 2.560 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host dialup-74.106.220.203.acc02-beau-nwc.comindico.com.au. (203.220.106.74) Time: Fri Apr 9 07:26:28 2004 Input: F; G; G:Magma; Output: Magma V2.10-22 Fri Apr 9 2004 07:26:25 on modular [Seed = 4156637056] ------------------------------------- >> F> G:=quo; ^ User error: Identifier 'F' has not been declared or assigned >> G; ^ User error: Identifier 'G' has not been declared or assigned >> G:Magma;; ^ User error: Identifier 'G' has not been declared or assigned Total time: 2.569 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host dialup-74.106.220.203.acc02-beau-nwc.comindico.com.au. (203.220.106.74) Time: Fri Apr 9 07:27:49 2004 Input: F:=FreeGroup(4); G:=quo; G; Output: Magma V2.10-22 Fri Apr 9 2004 07:27:46 on modular [Seed = 4291376987] ------------------------------------- Finitely presented group G on 4 generators Relations G.1 * G.2 * G.3 * G.4 = Id(G) Total time: 2.550 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host dialup-74.106.220.203.acc02-beau-nwc.comindico.com.au. (203.220.106.74) Time: Fri Apr 9 07:28:40 2004 Input: F:=FreeGroup(4); G:=quo; G; Output: Magma V2.10-22 Fri Apr 9 2004 07:28:38 on modular [Seed = 3838979092] ------------------------------------- Finitely presented group G on 4 generators Relations G.1 * G.3 * G.1 * G.3^-1 = Id(G) Total time: 2.569 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host dialup-74.106.220.203.acc02-beau-nwc.comindico.com.au. (203.220.106.74) Time: Fri Apr 9 07:29:31 2004 Input: F:=FreeGroup(4); G:=quo; G; Output: Magma V2.10-22 Fri Apr 9 2004 07:29:29 on modular [Seed = 3973719523] ------------------------------------- Finitely presented group G on 4 generators Relations G.1 * G.3 * G.1 * G.3^-1 = Id(G) G.1 * G.4 * G.1 * G.4^-1 = Id(G) Total time: 2.569 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host dialup-74.106.220.203.acc02-beau-nwc.comindico.com.au. (203.220.106.74) Time: Fri Apr 9 07:30:42 2004 Input: F:=FreeGroup(4); G:=quo; G; Output: Magma V2.10-22 Fri Apr 9 2004 07:30:40 on modular [Seed = 489411690] ------------------------------------- Finitely presented group G on 4 generators Relations G.1 * G.3 * G.1 * G.3^-1 = Id(G) G.1 * G.4 * G.1 * G.4^-1 = Id(G) G.2 * G.3 * G.2 * G.3^-1 = Id(G) G.2 * G.4 * G.2 * G.4^-1 = Id(G) Total time: 2.549 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host dialup-74.106.220.203.acc02-beau-nwc.comindico.com.au. (203.220.106.74) Time: Fri Apr 9 07:32:41 2004 Input: F:=FreeGroup(4); G:=quo; AbelianQuotientInvariants(G); Output: Magma V2.10-22 Fri Apr 9 2004 07:32:39 on modular [Seed = 70438340] ------------------------------------- [ 2, 2, 0, 0 ] Total time: 2.559 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host dialup-74.106.220.203.acc02-beau-nwc.comindico.com.au. (203.220.106.74) Time: Fri Apr 9 07:33:09 2004 Input: F:=FreeGroup(4); G:=quo; AbelianQuotientInvariants(G); LowIndexSubgroups; Output: Magma V2.10-22 Fri Apr 9 2004 07:33:06 on modular [Seed = 205178345] ------------------------------------- [ 2, 2, 0, 0 ] Intrinsic 'LowIndexSubgroups' Signatures: ( G, R) -> SeqEnum, BoolElt [ ColumnMajor: BoolElt, GeneratingSets: BoolElt, Limit: RngIntElt, Long: SeqEnum, Print: RngIntElt, Subgroup: GrpFP, TimeLimit: RngIntElt ] ( G, R) -> SeqEnum, BoolElt [ ColumnMajor: BoolElt, GeneratingSets: BoolElt, Limit: RngIntElt, Long: SeqEnum, Print: RngIntElt, Subgroup: GrpFP, TimeLimit: RngIntElt ] Determine the conjugacy classes of subgroups of the FP group G whose indices in G satisfy the bounds specified in range R. ( G, n) -> SeqEnum Return representatives of the conjugacy classes of subgroups of G having index less than or equal to n. ( G, maxind) -> SeqEnum [ Presentation, Print, Algorithm, Limit ] Find subgroups of index up to maxind in permutation group G. ( G, T) -> SeqEnum [ Presentation, Print, Algorithm, Limit ] Find subgroups of index up to maxind in permutation group G. ( G, R) -> SeqEnum [ Print, Limit ] Subgroups of index lying in range specified by R. ( G, n) -> SeqEnum [ Print, Limit ] Subgroups of index at most n in G. Total time: 2.519 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dialup-74.106.220.203.acc02-beau-nwc.comindico.com.au. (203.220.106.74) Time: Fri Apr 9 07:33:45 2004 Input: F:=FreeGroup(4); G:=quo; AbelianQuotientInvariants(G); LowIndexSubgroups(G,5); Output: Magma V2.10-22 Fri Apr 9 2004 07:33:42 on modular [Seed = 872611381] ------------------------------------- [ 2, 2, 0, 0 ] [ Finitely presented group on 4 generators Index in group G is 1 Generators as words in group G $.1 = G.1 $.2 = G.2 $.3 = G.3 $.4 = G.4, Finitely presented group on 5 generators Index in group G is 2 Generators as words in group G $.1 = G.2 * G.1^-1 $.2 = G.3 * G.1^-1 $.3 = G.4 * G.1^-1 $.4 = G.1^-2 $.5 = G.2^-1 * G.1^-1, Finitely presented group on 4 generators Index in group G is 2 Generators as words in group G $.1 = G.2 * G.1^-1 $.2 = G.3 * G.1^-1 $.3 = G.4 $.4 = G.1^-2, Finitely presented group on 4 generators Index in group G is 2 Generators as words in group G $.1 = G.2 * G.1^-1 $.2 = G.3 $.3 = G.4 * G.1^-1 $.4 = G.1^-2, Finitely presented group on 4 generators Index in group G is 2 Generators as words in group G $.1 = G.2 * G.1^-1 $.2 = G.3 $.3 = G.4 $.4 = G.1^-2, Finitely presented group on 4 generators Index in group G is 2 Generators as words in group G $.1 = G.2 $.2 = G.3 * G.1^-1 $.3 = G.4 * G.1^-1 $.4 = G.1^-2, Finitely presented group on 4 generators Index in group G is 2 Generators as words in group G $.1 = G.2 $.2 = G.3 * G.1^-1 $.3 = G.4 $.4 = G.1^-2, Finitely presented group on 4 generators Index in group G is 2 Generators as words in group G $.1 = G.2 $.2 = G.3 $.3 = G.4 * G.1^-1 $.4 = G.1^-2, Finitely presented group on 5 generators Index in group G is 2 Generators as words in group G $.1 = G.2 $.2 = G.3 $.3 = G.4 $.4 = G.1^-2 $.5 = G.1 * G.2 * G.1^-1, Finitely presented group on 4 generators Index in group G is 2 Generators as words in group G $.1 = G.1 $.2 = G.3 * G.2^-1 $.3 = G.4 * G.2^-1 $.4 = G.2^-2, Finitely presented group on 4 generators Index in group G is 2 Generators as words in group G $.1 = G.1 $.2 = G.3 * G.2^-1 $.3 = G.4 $.4 = G.2^-2, Finitely presented group on 4 generators Index in group G is 2 Generators as words in group G $.1 = G.1 $.2 = G.3 $.3 = G.4 * G.2^-1 $.4 = G.2^-2, Finitely presented group on 5 generators Index in group G is 2 Generators as words in group G $.1 = G.1 $.2 = G.3 $.3 = G.4 $.4 = G.2^-2 $.5 = G.2 * G.1 * G.2^-1, Finitely presented group on 5 generators Index in group G is 2 Generators as words in group G $.1 = G.1 $.2 = G.2 $.3 = G.4 * G.3^-1 $.4 = G.3^-2 $.5 = G.4^-1 * G.3^-1, Finitely presented group on 5 generators Index in group G is 2 Generators as words in group G $.1 = G.1 $.2 = G.2 $.3 = G.4 $.4 = G.3^-2 $.5 = G.3 * G.4 * G.3^-1, Finitely presented group on 5 generators Index in group G is 2 Generators as words in group G $.1 = G.1 $.2 = G.2 $.3 = G.3 $.4 = G.4^-2 $.5 = G.4 * G.3 * G.4^-1, Finitely presented group on 4 generators Index in group G is 3 Generators as words in group G $.1 = G.3 $.2 = G.4 * G.2^-1 $.3 = G.1^-1 * G.2^-1 $.4 = G.1^2 * G.2^-1, Finitely presented group on 4 generators Index in group G is 3 Generators as words in group G $.1 = G.3 $.2 = G.4 * G.1^-1 $.3 = G.1^-1 * G.2^-1 $.4 = G.1^2 * G.2^-1, Finitely presented group on 5 generators Index in group G is 3 Generators as words in group G $.1 = G.3 $.2 = G.4 $.3 = G.1^-1 * G.2^-1 $.4 = G.1^2 * G.2^-1 $.5 = G.1 * G.2^-2, Finitely presented group on 4 generators Index in group G is 3 Generators as words in group G $.1 = G.2 * G.1^-1 $.2 = G.3 $.3 = G.1^-1 * G.4^-1 $.4 = G.1^2 * G.4^-1, Finitely presented group on 4 generators Index in group G is 3 Generators as words in group G $.1 = G.2 * G.1^-1 $.2 = G.3 $.3 = G.4 * G.1^-1 $.4 = G.1^3, Finitely presented group on 5 generators Index in group G is 3 Generators as words in group G $.1 = G.2 * G.1^-1 $.2 = G.3 $.3 = G.4 $.4 = G.1^3 $.5 = G.1 * G.2 * G.1, Finitely presented group on 4 generators Index in group G is 3 Generators as words in group G $.1 = G.2 $.2 = G.3 $.3 = G.1^-1 * G.4^-1 $.4 = G.1^2 * G.4^-1, Finitely presented group on 4 generators Index in group G is 3 Generators as words in group G $.1 = G.2 $.2 = G.3 $.3 = G.4 * G.1^-1 $.4 = G.1^3, Finitely presented group on 6 generators Index in group G is 3 Generators as words in group G $.1 = G.2 $.2 = G.3 $.3 = G.4 $.4 = G.1^3 $.5 = G.1 * G.2 * G.1 $.6 = G.1 * G.2^-1 * G.1, Finitely presented group on 5 generators Index in group G is 3 Generators as words in group G $.1 = G.2 $.2 = G.3 $.3 = G.4 $.4 = G.1^3 $.5 = G.1 * G.2 * G.1^-1, Finitely presented group on 4 generators Index in group G is 3 Generators as words in group G $.1 = G.1 $.2 = G.3 $.3 = G.2^-1 * G.4^-1 $.4 = G.2^2 * G.4^-1, Finitely presented group on 4 generators Index in group G is 3 Generators as words in group G $.1 = G.1 $.2 = G.3 $.3 = G.4 * G.2^-1 $.4 = G.2^3, Finitely presented group on 6 generators Index in group G is 3 Generators as words in group G $.1 = G.1 $.2 = G.3 $.3 = G.4 $.4 = G.2 * G.1 * G.2 $.5 = G.2^3 $.6 = G.2 * G.1^-1 * G.2, Finitely presented group on 5 generators Index in group G is 3 Generators as words in group G $.1 = G.1 $.2 = G.3 $.3 = G.4 $.4 = G.2 * G.1 * G.2^-1 $.5 = G.2^3, Finitely presented group on 6 generators Index in group G is 3 Generators as words in group G $.1 = G.1 $.2 = G.3 $.3 = G.4 $.4 = G.2^-2 $.5 = (G.2 * G.1^-1 * G.2^-1)^2 $.6 = G.2 * G.1 * G.2 * G.1^-1 * G.2^-1, Finitely presented group on 6 generators Index in group G is 3 Generators as words in group G $.1 = G.1 $.2 = G.2 $.3 = G.3^-1 * G.4^-1 $.4 = G.4^-1 * G.3^-1 $.5 = G.3^2 * G.4^-1 $.6 = G.3 * G.4^-2, Finitely presented group on 6 generators Index in group G is 3 Generators as words in group G $.1 = G.1 $.2 = G.2 $.3 = G.4 * G.3^-1 $.4 = G.4^-1 * G.3 $.5 = G.3^3 $.6 = G.3 * G.4 * G.3, Finitely presented group on 6 generators Index in group G is 3 Generators as words in group G $.1 = G.1 $.2 = G.2 $.3 = G.4 $.4 = G.3^3 $.5 = G.3 * G.4 * G.3 $.6 = G.3 * G.4^-1 * G.3, Finitely presented group on 6 generators Index in group G is 3 Generators as words in group G $.1 = G.1 $.2 = G.2 $.3 = G.4 $.4 = G.3^3 $.5 = G.3 * G.4 * G.3^-1 $.6 = G.4^G.3, Finitely presented group on 6 generators Index in group G is 3 Generators as words in group G $.1 = G.1 $.2 = G.2 $.3 = G.3 $.4 = G.4 * G.3 * G.4 $.5 = G.4^3 $.6 = G.4 * G.3^-1 * G.4, Finitely presented group on 6 generators Index in group G is 3 Generators as words in group G $.1 = G.1 $.2 = G.2 $.3 = G.3 $.4 = G.4 * G.3 * G.4^-1 $.5 = G.4^3 $.6 = G.3^G.4, Finitely presented group on 6 generators Index in group G is 3 Generators as words in group G $.1 = G.1 $.2 = G.2 $.3 = G.3 $.4 = G.4^-2 $.5 = (G.4 * G.3^-1 * G.4^-1)^2 $.6 = G.4 * G.3 * G.4 * G.3^-1 * G.4^-1, Finitely presented group on 6 generators Index in group G is 4 = 2^2 Generators as words in group G $.1 = G.4 * G.3^-1 $.2 = G.1^-2 $.3 = G.2^-2 $.4 = G.3^-2 $.5 = G.4^-1 * G.3^-1 $.6 = G.1 * G.2 * G.3^-1, Finitely presented group on 5 generators Index in group G is 4 = 2^2 Generators as words in group G $.1 = G.4 * G.2^-1 $.2 = G.1^-2 $.3 = G.2^-2 $.4 = G.3^-2 $.5 = G.1 * G.2 * G.3^-1, Finitely presented group on 5 generators Index in group G is 4 = 2^2 Generators as words in group G $.1 = G.4 * G.1^-1 $.2 = G.1^-2 $.3 = G.2^-2 $.4 = G.3^-2 $.5 = G.1 * G.2 * G.3^-1, Finitely presented group on 5 generators Index in group G is 4 = 2^2 Generators as words in group G $.1 = G.4 $.2 = G.1^-2 $.3 = G.2^-2 $.4 = G.3^-2 $.5 = G.1 * G.2 * G.3^-1, Finitely presented group on 4 generators Index in group G is 4 = 2^2 Generators as words in group G $.1 = G.3 * G.2^-1 $.2 = G.1^-2 $.3 = G.2^-1 * G.4^-1 $.4 = G.1 * G.2 * G.4^-1, Finitely presented group on 5 generators Index in group G is 4 = 2^2 Generators as words in group G $.1 = G.3 * G.2^-1 $.2 = G.1^-2 $.3 = G.2^-2 $.4 = G.4^-2 $.5 = G.1 * G.2 * G.4^-1, Finitely presented group on 5 generators Index in group G is 4 = 2^2 Generators as words in group G $.1 = G.3 * G.2^-1 $.2 = G.4 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host dialup-74.106.220.203.acc02-beau-nwc.comindico.com.au. (203.220.106.74) Time: Fri Apr 9 07:35:35 2004 Input: F:=FreeGroup(4); G:=quo; AbelianQuotientInvariants(G); #LowIndexSubgroups(G,5); Output: Magma V2.10-22 Fri Apr 9 2004 07:35:33 on modular [Seed = 655486389] ------------------------------------- [ 2, 2, 0, 0 ] 425 Total time: 2.650 seconds, Total memory usage: 2.30MB ************** MAGMA ***************** Host dialup-74.106.220.203.acc02-beau-nwc.comindico.com.au. (203.220.106.74) Time: Fri Apr 9 07:37:30 2004 Input: F:=FreeGroup(4); G:=quo; AbelianQuotientInvariants(G); [#LowIndexSubgroups(G,):i in [1..7]]; Output: Magma V2.10-22 Fri Apr 9 2004 07:37:19 on modular [Seed = 790226391] ------------------------------------- [ 2, 2, 0, 0 ] [ 1, 15, 22, 181, 206, 1697, 5618 ] Total time: 11.389 seconds, Total memory usage: 8.74MB ************** MAGMA ***************** Host dialup-74.106.220.203.acc02-beau-nwc.comindico.com.au. (203.220.106.74) Time: Fri Apr 9 07:38:40 2004 Input: F:=FreeGroup(4); G:=quo; AbelianQuotientInvariants(G); [#LowIndexSubgroups(G,):i in [1..8]]; Output: Magma V2.10-22 Fri Apr 9 2004 07:38:17 on modular [Seed = 1466014825] ------------------------------------- [ 2, 2, 0, 0 ] ************** MAGMA ***************** Host dialup-74.106.220.203.acc02-beau-nwc.comindico.com.au. (203.220.106.74) Time: Fri Apr 9 07:41:45 2004 Input: F:=FreeGroup(4); G:=quo; AbelianQuotientInvariants(G); //[#LowIndexSubgroups(G,):i in [1..8]]; LISILInvariants := function( G: LowerIndexLimit := 1, UpperIndexLimit := 4, aqi := true ) p := LowIndexProcess( G, < LowerIndexLimit, UpperIndexLimit > ); lisc := {**}; if LowerIndexLimit eq 1 then if aqi then Include( ~lisc, <1,1,AQI(G)> ); else Include( ~lisc, <1,1> ); end if; end if; // t := Cputime(); while not IsEmpty( p ) do // print "IsEmpty done in", Cputime(t), "seconds."; // t := Cputime(); H := ExtractGroup( p ); // print "ExtractGroup done in", Cputime(t), "seconds."; // t := Cputime(); if aqi then Include( ~lisc, < Index( G, H ), #Conjugates( G, H ), AQI( H ) > ); else Include( ~lisc, < Index( G, H ), #Conjugates( G, H ) > ); end if; // print "Inclusion done in", Cputime(t), "seconds."; // t := Cputime(); NextSubgroup( ~p ); // print "NextSubgroup done in", Cputime(t), "seconds."; // t := Cputime(); end while; if aqi then return Sort([ < index_length_aqi[1], index_length_aqi[2], index_length_aqi[3], Multiplicity( lisc, index_length_aqi ) >: index_length_aqi in Set( lisc ) ]) ; else return Sort([ < index_length[1], index_length[2], Multiplicity( lisc, index_length ) >: index_length in Set( lisc ) ]) ; end if; end function ; Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed. ************** MAGMA ***************** Host dialup-74.106.220.203.acc02-beau-nwc.comindico.com.au. (203.220.106.74) Time: Fri Apr 9 07:42:39 2004 Input: F:=FreeGroup(4); G:=quo; AbelianQuotientInvariants(G); //[#LowIndexSubgroups(G,):i in [1..8]]; LISILInvariants := function( G: LowerIndexLimit := 1, UpperIndexLimit := 4, aqi := true ) p := LowIndexProcess( G, < LowerIndexLimit, UpperIndexLimit > ); lisc := {**}; if LowerIndexLimit eq 1 then if aqi then Include( ~lisc, <1,1,AQI(G)> ); else Include( ~lisc, <1,1> ); end if; end if; while not IsEmpty( p ) do H := ExtractGroup( p ); if aqi then Include( ~lisc, < Index( G, H ), #Conjugates( G, H ), AQI( H ) > ); else Include( ~lisc, < Index( G, H ), #Conjugates( G, H ) > ); end if; NextSubgroup( ~p ); end while; if aqi then return Sort([ < index_length_aqi[1], index_length_aqi[2], index_length_aqi[3], Multiplicity( lisc, index_length_aqi ) >: index_length_aqi in Set( lisc ) ]) ; else return Sort([ < index_length[1], index_length[2], Multiplicity( lisc, index_length ) >: index_length in Set( lisc ) ]) ; end if; end function ; Output: Magma V2.10-22 Fri Apr 9 2004 07:42:37 on modular [Seed = 1316520564] ------------------------------------- [ 2, 2, 0, 0 ] >> : ^ User error: bad syntax >> ]) ^ User error: bad syntax >> else ^ User error: bad syntax >> : ^ User error: bad syntax >> ]) ^ User error: bad syntax >> end if; ^ User error: bad syntax >> end function ^ User error: bad syntax Total time: 2.620 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host dialup-74.106.220.203.acc02-beau-nwc.comindico.com.au. (203.220.106.74) Time: Fri Apr 9 07:44:34 2004 Input: F:=FreeGroup(4); G:=quo; AbelianQuotientInvariants(G); LISILInvariants := function( G: LowerIndexLimit := 1, UpperIndexLimit := 4, aqi := true ) p := LowIndexProcess( G, < LowerIndexLimit, UpperIndexLimit > ); lisc := {**}; if LowerIndexLimit eq 1 then if aqi then Include( ~lisc, <1,1,AQI(G)> ); else Include( ~lisc, <1,1> ); end if; end if; while not IsEmpty( p ) do H := ExtractGroup( p ); if aqi then Include( ~lisc, < Index( G, H ), #Conjugates( G, H ), AQI( H ) > ); else Include( ~lisc, < Index( G, H ), #Conjugates( G, H ) > ); end if; NextSubgroup( ~p ); end while; if aqi then return Sort([ < index_length_aqi[1], index_length_aqi[2], index_length_aqi[3], Multiplicity( lisc, index_length_aqi ) >: index_length_aqi in Set( lisc ) ]) ; else return Sort([ < index_length[1], index_length[2], Multiplicity( lisc, index_length ) >: index_length in Set( lisc ) ]) ; end if; end function ; Output: Magma V2.10-22 Fri Apr 9 2004 07:44:32 on modular [Seed = 1983953601] ------------------------------------- [ 2, 2, 0, 0 ] >> : ^ User error: bad syntax >> ]) ^ User error: bad syntax >> else ^ User error: bad syntax >> : ^ User error: bad syntax >> ]) ^ User error: bad syntax >> end if; ^ User error: bad syntax >> end function ^ User error: bad syntax Total time: 2.550 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host dialup-74.106.220.203.acc02-beau-nwc.comindico.com.au. (203.220.106.74) Time: Fri Apr 9 07:45:59 2004 Input: F:=FreeGroup(4); G:=quo; AbelianQuotientInvariants(G); LISILInvariants := function( G: LowerIndexLimit := 1, UpperIndexLimit := 4, aqi := true ) p := LowIndexProcess( G, < LowerIndexLimit, UpperIndexLimit > ); lisc := {**}; if LowerIndexLimit eq 1 then if aqi then Include( ~lisc, <1,1,AQI(G)> ); else Include( ~lisc, <1,1> ); end if; end if; while not IsEmpty( p ) do H := ExtractGroup( p ); if aqi then Include( ~lisc, < Index( G, H ), #Conjugates( G, H ), AQI( H ) > ); else Include( ~lisc, < Index( G, H ), #Conjugates( G, H ) > ); end if; NextSubgroup( ~p ); end while; if aqi then return Sort([ < index_length_aqi[1], index_length_aqi[2], index_length_aqi[3], Multiplicity( lisc, index_length_aqi ) >: index_length_aqi in Set( lisc ) ]) ; else return Sort([ < index_length[1], index_length[2], Multiplicity( lisc, index_length ) >: index_length in Set( lisc ) ]) ; end if; end function ; Output: Magma V2.10-22 Fri Apr 9 2004 07:45:57 on modular [Seed = 2035266971] ------------------------------------- [ 2, 2, 0, 0 ] >> : ^ User error: bad syntax >> ]) ^ User error: bad syntax >> else ^ User error: bad syntax >> : ^ User error: bad syntax >> ]) ^ User error: bad syntax >> end if; ^ User error: bad syntax >> end function ^ User error: bad syntax Total time: 2.589 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host dialup-74.106.220.203.acc02-beau-nwc.comindico.com.au. (203.220.106.74) Time: Fri Apr 9 07:47:30 2004 Input: F:=FreeGroup(4); G:=quo; AbelianQuotientInvariants(G); [#LowIndexSubgroups(G,):i in [1..8]]; Output: Magma V2.10-22 Fri Apr 9 2004 07:47:07 on modular [Seed = 1868145219] ------------------------------------- [ 2, 2, 0, 0 ] ************** MAGMA ***************** Host dialup-74.106.220.203.acc02-beau-nwc.comindico.com.au. (203.220.106.74) Time: Fri Apr 9 07:48:18 2004 Input: F:=FreeGroup(4); G:=quo; AbelianQuotientInvariants(G); #LowIndexSubgroups(G,8); Output: Magma V2.10-22 Fri Apr 9 2004 07:47:56 on modular [Seed = 2543934188] ------------------------------------- [ 2, 2, 0, 0 ] ************** MAGMA ***************** Host dialup-74.106.220.203.acc02-beau-nwc.comindico.com.au. (203.220.106.74) Time: Fri Apr 9 07:51:09 2004 Input: F:=FreeGroup(4); G:=quo; AbelianQuotientInvariants(G); #LowIndexSubgroups(G,7); Output: Magma V2.10-22 Fri Apr 9 2004 07:50:48 on modular [Seed = 2259699848] ------------------------------------- [ 2, 2, 0, 0 ] 7740 Total time: 20.089 seconds, Total memory usage: 11.12MB ************** MAGMA ***************** Host dialup-74.106.220.203.acc02-beau-nwc.comindico.com.au. (203.220.106.74) Time: Fri Apr 9 07:55:34 2004 Input: F:=FreeGroup(4); G:=quo; AbelianQuotientInvariants(G); [#LowIndexSubgroups(G,):i in [1..6]]; Output: Magma V2.10-22 Fri Apr 9 2004 07:55:31 on modular [Seed = 2294171564] ------------------------------------- [ 2, 2, 0, 0 ] [ 1, 15, 22, 181, 206, 1697 ] Total time: 3.050 seconds, Total memory usage: 3.75MB ************** MAGMA ***************** Host dialup-74.106.220.203.acc02-beau-nwc.comindico.com.au. (203.220.106.74) Time: Fri Apr 9 07:56:50 2004 Input: F:=FreeGroup(4); G:=quo; AbelianQuotientInvariants(G); [#LowIndexSubgroups(G,):i in [1..7]]; Output: Magma V2.10-22 Fri Apr 9 2004 07:56:39 on modular [Seed = 2961604560] ------------------------------------- [ 2, 2, 0, 0 ] [ 1, 15, 22, 181, 206, 1697, 5618 ] Total time: 11.459 seconds, Total memory usage: 8.74MB ************** MAGMA ***************** Host dialup-74.106.220.203.acc02-beau-nwc.comindico.com.au. (203.220.106.74) Time: Fri Apr 9 07:57:27 2004 Input: F:=FreeGroup(4); G:=quo; AbelianQuotientInvariants(G); [#LowIndexSubgroups(G,):i in [1..8]]; Output: Magma V2.10-22 Fri Apr 9 2004 07:57:04 on modular [Seed = 3096344383] ------------------------------------- [ 2, 2, 0, 0 ] ************** MAGMA ***************** Host dialup-74.106.220.203.acc02-beau-nwc.comindico.com.au. (203.220.106.74) Time: Fri Apr 9 07:58:59 2004 Input: F:=FreeGroup(4); G:=quo; AbelianQuotientInvariants(G); [#LowIndexSubgroups(G,):i in [8]]; Output: Magma V2.10-22 Fri Apr 9 2004 07:58:37 on modular [Seed = 3588430383] ------------------------------------- [ 2, 2, 0, 0 ] ************** MAGMA ***************** Host dialup-74.106.220.203.acc02-beau-nwc.comindico.com.au. (203.220.106.74) Time: Fri Apr 9 08:00:06 2004 Input: F:=FreeGroup(4); G:=quo; AbelianQuotientInvariants(G); LowIndexSubgroups(G,7):Magma; Output: Magma V2.10-22 Fri Apr 9 2004 07:59:46 on modular [Seed = 3723169272] ------------------------------------- [ 2, 2, 0, 0 ] [ PowerStructure(GrpFP) | sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub, sub:=FreeGroup(4); G:=quo; AbelianQuotientInvariants(G); LowIndexProcess; Output: Magma V2.10-22 Fri Apr 9 2004 08:00:46 on modular [Seed = 3422362546] ------------------------------------- [ 2, 2, 0, 0 ] Intrinsic 'LowIndexProcess' Signatures: ( G, R) -> GrpFPLixProc [ ColumnMajor: BoolElt, GeneratingSets: BoolElt, Long: SeqEnum, Print: RngIntElt, Subgroup: GrpFP, TimeLimit: RngIntElt ] ( G, R) -> GrpFPLixProc [ ColumnMajor: BoolElt, GeneratingSets: BoolElt, Long: SeqEnum, Print: RngIntElt, Subgroup: GrpFP, TimeLimit: RngIntElt ] Create a low index subgroups process for the FP group G whose indices in G satisfy the bounds specified in range R. Total time: 2.570 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host dialup-74.106.220.203.acc02-beau-nwc.comindico.com.au. (203.220.106.74) Time: Fri Apr 9 08:02:56 2004 Input: F:=FreeGroup(4); G:=quo; AbelianQuotientInvariants(G); LowIndexProcess(G,7); Output: Magma V2.10-22 Fri Apr 9 2004 08:02:53 on modular [Seed = 3772133402] ------------------------------------- [ 2, 2, 0, 0 ] Low Index Subgroups Process Total time: 2.499 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host dialup-74.106.220.203.acc02-beau-nwc.comindico.com.au. (203.220.106.74) Time: Fri Apr 9 08:03:44 2004 Input: F:=FreeGroup(4); G:=quo; AbelianQuotientInvariants(G); lip:=LowIndexProcess(G,7); ?LowIndexProcess; Output: Magma V2.10-22 Fri Apr 9 2004 08:03:41 on modular [Seed = 3906877922] ------------------------------------- [ 2, 2, 0, 0 ] =============================================================================== PATH: /magma/group/finitely-presented/subgroup/low-index-subgroup/\ LowIndexProcess KIND: Intrinsic =============================================================================== LowIndexProcess(G, R : parameters) : GrpFP, RngIntElt -> Process(Lix) LowIndexProcess(G, R: parameters) : GrpFP, < RngIntElt, RngIntElt > -> Process(Lix) ColumnMajor: BoolElt Default: false GeneratingSets: BoolElt Default: false Long: [ RngIntElt ] Default: [] Print: RngIntElt Default: 0 Subgroup: GrpFP Default: sub< G | > TimeLimit: RngIntElt Default: 0 (no limit) Create a low index subgroups process. This process may be used to create the conjugacy classes of proper subgroups one at at time, with control being handed back to the Magma language processor each time a new class of subgroups is found. This function returns a process which is used by the function NextSubgroup to actually produce the subgroups. The arguments and parameters have the same interpretation as for the function LowIndexSubgroups, except that Limit is not available (since the same effect can be achieved by limiting the number of calls to NextSubgroup). Setting a time limit for a process P limits the total amount of time spent in calls to NextSubgroup. If the time limit is exceeded in a call to NextSubgroup, this call is aborted and P becomes invalid. Further attempts to access P will cause a runtime error. The function IsValid can be used to check whether a process is valid in order to avoid runtime errors in loops or user written functions. =============================================================================== Total time: 2.590 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host dialup-74.106.220.203.acc02-beau-nwc.comindico.com.au. (203.220.106.74) Time: Fri Apr 9 08:06:21 2004 Input: F:=FreeGroup(4); G:=quo; AbelianQuotientInvariants(G); lip:=LowIndexProcess(G,7); ?NextSubgroup; Output: Magma V2.10-22 Fri Apr 9 2004 08:06:19 on modular [Seed = 238608301] ------------------------------------- [ 2, 2, 0, 0 ] =============================================================================== PATH: /magma/group/finitely-presented/subgroup/low-index-subgroup/NextSubgroup KIND: Intrinsic =============================================================================== NextSubgroup(~P) : Process(Lix) -> NextSubgroup(~P, ~G) : Process(Lix), GrpFP -> Given a low index subgroups process P, construct the next conjugacy class of proper subgroups. The process P must have been previously created using the function LowIndexProcess and must be valid. Calling NextSubgroup for an empty process has no effect. =============================================================================== Total time: 2.500 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host dialup-74.106.220.203.acc02-beau-nwc.comindico.com.au. (203.220.106.74) Time: Fri Apr 9 08:08:45 2004 Input: F:=FreeGroup(4); G:=quo; AbelianQuotientInvariants(G); lip:=LowIndexProcess(G,7); NextSubgroup(~lip); Output: Magma V2.10-22 Fri Apr 9 2004 08:08:42 on modular [Seed = 103863380] ------------------------------------- [ 2, 2, 0, 0 ] Total time: 2.539 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host dialup-74.106.220.203.acc02-beau-nwc.comindico.com.au. (203.220.106.74) Time: Fri Apr 9 08:10:11 2004 Input: F:=FreeGroup(4); G:=quo; AbelianQuotientInvariants(G); lip:=LowIndexProcess(G,5); NextSubgroup(~lip); Output: Magma V2.10-22 Fri Apr 9 2004 08:10:09 on modular [Seed = 922871182] ------------------------------------- [ 2, 2, 0, 0 ] Total time: 2.510 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host dialup-74.106.220.203.acc02-beau-nwc.comindico.com.au. (203.220.106.74) Time: Fri Apr 9 08:10:25 2004 Input: F:=FreeGroup(4); G:=quo; lip:=LowIndexProcess(G,5); NextSubgroup(~lip); Output: Magma V2.10-22 Fri Apr 9 2004 08:10:22 on modular [Seed = 790232473] ------------------------------------- Total time: 2.510 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host dialup-74.106.220.203.acc02-beau-nwc.comindico.com.au. (203.220.106.74) Time: Fri Apr 9 08:11:02 2004 Input: F:=FreeGroup(4); G:=quo; lip:=LowIndexProcess(G,3); NextSubgroup(~lip); Output: Magma V2.10-22 Fri Apr 9 2004 08:11:00 on modular [Seed = 655488491] ------------------------------------- Total time: 2.509 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host carens.lip6.fr. (132.227.66.11) Time: Fri Apr 9 11:11:40 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-22 Fri Apr 9 2004 11:11:37 on modular [Seed = 255455804] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.579 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host carens.lip6.fr. (132.227.66.11) Time: Fri Apr 9 11:16:12 2004 Input: n:= 15 Factorisation(n) Output: Magma V2.10-22 Fri Apr 9 2004 11:16:09 on modular [Seed = 839175185] ------------------------------------- >> Factorisation(n); ^ User error: bad syntax Total time: 2.539 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host carens.lip6.fr. (132.227.66.11) Time: Fri Apr 9 11:16:26 2004 Input: n:= 15; Factorisation(n); Output: Magma V2.10-22 Fri Apr 9 2004 11:16:24 on modular [Seed = 706532472] ------------------------------------- [ <3, 1>, <5, 1> ] Total time: 2.509 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host carens.lip6.fr. (132.227.66.11) Time: Fri Apr 9 11:24:50 2004 Input: Q := RationalField(); P := PolynomialRing(Q, 6); I := ideal

; time B := GroebnerBasis(I); B; Output: Magma V2.10-22 Fri Apr 9 2004 11:24:47 on modular [Seed = 1365758324] ------------------------------------- Time: 0.530 [ x + y + z + t + u + v, y^2 + 4*y*v + t^2 + 4*t*v + u^5*v^3 - 4*u^4*v^4 + 6*u^3*v^5 + 52*u^2*v^6 + 58*u^2 - 729705987316687/3968379498283200*u*v^43 + 266238213838172203/566911356897600*u*v^37 + 2627701385330910851/35751166651200*u*v^31 + 10789720711596719/117216939840*u*v^25 + 330307018515863/2383411110080*u*v^19 - 156605921938553599/1702436507200*u*v^13 - 292382820431504027669/3968379498283200*u*v^7 - 37244237174292877/65055401611200*u*v - 3988812642545399/3968379498283200*v^44 + 10187423878429609997/3968379498283200*v^38 + 43091284416873352801/107253499953600*v^32 + 10782374640215763449/21450699990720*v^26 + 8631568043527799/21450699990720*v^20 - 53878219413544922849/107253499953600*v^14 - 532016580763229938351/1322793166094400*v^8 - 11488171330159667449/3968379498283200*v^2, y*z - y*v + z^2 + 3*z*v - t^2 - 4*t*v - 7/3*u^5*v^3 + 22/3*u^4*v^4 - 22/3*u^3*v^5 - 102*u^2*v^6 - 329/3*u^2 + 8305444561289527/23810276989699200*u*v^43 - 573299652755282693/643520999721600*u*v^37 - 9969417066346700857/71502333302400*u*v^31 - 832370699952283711/4766822220160*u*v^25 - 10941840734253629/42901399981440*u*v^19 + 37432312694022164159/214506999907200*u*v^13 + 3327761311138587096749/23810276989699200*u*v^7 + 699603800224076801/643520999721600*u*v + 45815897629010329/23810276989699200*v^44 - 117013765582151891207/23810276989699200*v^38 - 164983485125863649317/214506999907200*v^32 - 5897032494118223279/6128771425920*v^26 - 29068920290639923/42901399981440*v^20 + 206282034753479083393/214506999907200*v^14 + 18329944781867242497923/23810276989699200*v^8 + 18608361571717202957/3401468141385600*v^2, y*t - y*v - t*v - u^5*v^3 + 3*u^4*v^4 - 3*u^3*v^5 - 85/2*u^2*v^6 - 93/2*u^2 + 168049341234353/1133822713795200*u*v^43 - 1001461194297157691/2645586332188800*u*v^37 - 4236067591957172123/71502333302400*u*v^31 - 1061005735860620447/14300466660480*u*v^25 - 220576398616091/2042923808640*u*v^19 + 5301555623804869607/71502333302400*u*v^13 + 471313241958371103517/7936758996566400*u*v^7 + 1219914183026184127/2645586332188800*u*v + 6423170513956901/7936758996566400*v^44 - 16404772137036480803/7936758996566400*v^38 - 9912815309758798357/30643857129600*v^32 - 17361827517976660391/42901399981440*v^26 - 12597245041608581/42901399981440*v^20 + 86759462417425807151/214506999907200*v^14 + 122374205495007743707/377940904598400*v^8 + 18326089487427735751/7936758996566400*v^2, y*u - y*v - 1/3*u^5*v^3 + 4/3*u^4*v^4 - 7/3*u^3*v^5 - 35/2*u^2*v^6 - 121/6*u^2 + 7145727134101/108228531771360*u*v^43 - 521433508618765/3092243764896*u*v^37 - 25732028084199329/975031817760*u*v^31 - 6444286118557405/195006363552*u*v^25 - 1001600001191/21667373728*u*v^19 + 511155842503399/15476695520*u*v^13 + 2862657934537968143/108228531771360*u*v^7 + 21903513774060623/108228531771360*u*v + 596805506678261/1700734070692800*v^44 - 10669685294602576381/11905138494849600*v^38 - 1671524504924874399/11917055550400*v^32 - 1254700935308050553/7150233330240*v^26 - 404092603238167/3064385712960*v^20 + 18809585827558698859/107253499953600*v^14 + 1671496085945199577969/11905138494849600*v^8 + 11940257226216280177/11905138494849600*v^2, y*v^6 - y - 4/3*u^5*v^2 + 10/3*u^4*v^3 - 10/3*u^3*v^4 - 173/3*u^2*v^11 - 51*u^2*v^5 + 4071533206669/744071155928100*u*v^42 - 5942188603610309/425183517673200*u*v^36 - 14658465373012547/6703343747100*u*v^30 - 14277594407144437/5362674997680*u*v^24 + 36467420914699/446889583140*u*v^18 + 1151869191823659/425609126800*u*v^12 + 1595386104129408113/744071155928100*u*v^6 + 34650817088937311/2976284623712400*u + 167620036074811/11905138494849600*v^43 - 428102417974791473/11905138494849600*v^37 - 28741846332574723/5107309521600*v^31 - 50106136169458709/7150233330240*v^25 + 366979991657623/21450699990720*v^19 + 752459966900994887/107253499953600*v^13 + 9570827091462580991/1700734070692800*v^7 + 478592855549587901/11905138494849600*v, z^3 + 3*z^2*v - 3*z*v^2 - 13752945467/801692827936*v^45 + 35125117815561/801692827936*v^39 + 148566133995309/21667373728*v^33 + 184720525614841/21667373728*v^27 - 1202294066553/21667373728*v^21 - 185767735948461/21667373728*v^15 - 5450844938762633/801692827936*v^9 + 1216586044571/801692827936*v^3, z*t - z*v + t^2 + 3*t*v + 1/3*u^5*v^3 - 4/3*u^4*v^4 + 4/3*u^3*v^5 + 17*u^2*v^6 + 50/3*u^2 - 1247372229446701/23810276989699200*u*v^43 + 3185785654596621203/23810276989699200*u*v^37 + 499093960810785537/23834111100800*u*v^31 + 375100628135610239/14300466660480*u*v^25 + 1677631992377807/42901399981440*u*v^19 - 5622978951192946517/214506999907200*u*v^13 - 499881859388360475647/23810276989699200*u*v^7 - 3926885313819527351/23810276989699200*u*v - 7026011547118141/23810276989699200*v^44 + 2563489578850098749/3401468141385600*v^38 + 25300752455801681113/214506999907200*v^32 + 6330854310549202757/42901399981440*v^26 + 5154517129199167/42901399981440*v^20 - 4519120637892137371/30643857129600*v^14 - 2811332494697103819887/23810276989699200*v^8 - 20315011631522847311/23810276989699200*v^2, z*u - z*v - 4418748183673/7936758996566400*u*v^43 + 3761856235818853/2645586332188800*u*v^37 + 47729692359309487/214506999907200*u*v^31 + 11749996127689763/42901399981440*u*v^25 - 301558336191367/42901399981440*u*v^19 - 59872741129413323/214506999907200*u*v^13 - 1718142665347430851/7936758996566400*u*v^7 + 30256569458230237/7936758996566400*u*v + 4418748183673/7936758996566400*v^44 - 3761856235818853/2645586332188800*v^38 - 47729692359309487/214506999907200*v^32 - 11749996127689763/42901399981440*v^26 + 301558336191367/42901399981440*v^20 + 59872741129413323/214506999907200*v^14 + 1718142665347430851/7936758996566400*v^8 - 30256569458230237/7936758996566400*v^2, z*v^6 - z + 13650286483/24050784838080*v^43 - 104588980990367/72152354514240*v^37 - 147452499059237/650021211840*v^31 - 36519862011761/130004242368*v^25 + 796765769837/130004242368*v^19 + 185369909331433/650021211840*v^13 + 1777459310774507/8016928279360*v^7 - 275099892785581/72152354514240*v, t^3 + 3*t^2*v - 3*t*v^2 - 2*u^5*v^4 + 8*u^4*v^5 + 9*u^3 - 75*u^2*v^7 - 82*u^2*v - 195000457339439/992094874570800*u*v^44 + 498031352296878217/992094874570800*u*v^38 + 702190648522679387/8937791662800*u*v^32 + 175446807336923803/1787558332560*u*v^26 + 5590159996013/1787558332560*u*v^20 - 876560867807653463/8937791662800*u*v^14 - 77898448970378461333/992094874570800*u*v^8 - 518187879538660489/992094874570800*u*v^2 - 28846048464307/152629980703200*v^45 + 10524693479070923/21804282957600*v^39 + 103873288681056751/1375044871200*v^33 + 25939594101662459/275008974240*v^27 - 17620099158191/275008974240*v^21 - 18536930327998717/196434981600*v^15 - 11516921812921271849/152629980703200*v^9 - 64358006249203697/152629980703200*v^3, t*u - t*v - 2/3*u^5*v^3 + 5/3*u^4*v^4 - 2/3*u^3*v^5 - 25*u^2*v^6 - 76/3*u^2 + 492558110242553/5952569247424800*u*v^43 - 1257992359608074599/5952569247424800*u*v^37 - 1773721572426743369/53626749976800*u*v^31 - 444256064406730501/10725349995360*u*v^25 - 586844508097091/10725349995360*u*v^19 + 2219979908861728001/53626749976800*u*v^13 + 197327352068200652911/5952569247424800*u*v^7 + 1523373796389332143/5952569247424800*u*v + 36209203808149/80440124965200*v^44 - 427712043463869163/372035577964050*v^38 - 1608138828292262633/8937791662800*v^32 - 28738506428400713/127682738040*v^26 - 768240316135811/5362674997680*v^20 + 377000310239830631/1675835936775*v^14 + 14485139050793418713/80440124965200*v^8 + 269829966859740277/212591758836600*v^2, t*v^6 - t - 2/3*u^5*v^2 + 8/3*u^4*v^3 - 8/3*u^3*v^4 - 106/3*u^2*v^11 - 34*u^2*v^5 + 15336187600889/11905138494849600*u*v^42 - 5595677080737301/1700734070692800*u*v^36 - 55199784932339557/107253499953600*u*v^30 - 13004880616775693/21450699990720*u*v^24 + 107833530308453/2383411110080*u*v^18 + 3220422288221153/5107309521600*u*v^12 + 5886160769782607203/11905138494849600*u*v^6 + 63576108396535879/11905138494849600*u + 35868890888533/5952569247424800*v^43 - 91609428103778969/5952569247424800*v^37 - 43052363770468883/17875583325600*v^31 - 10698265371453397/3575116665120*v^25 + 148496702373049/10725349995360*v^19 + 160919641545374111/53626749976800*v^13 + 14313511289332455311/5952569247424800*v^7 + 93729993514840253/5952569247424800*v, u^6 - 3*u^5*v + 3*u^4*v^2 - 4*u^3*v^3 - 174*u^2*v^10 - 171*u^2*v^4 - 10158357640696259/88186211072960*u*v^47 + 2103603384134350759/7150233330240*u*v^41 + 329222150493840859391/7150233330240*u*v^3 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 3(NXDOMAIN) (82.100.96.3) Time: Fri Apr 9 14:16:02 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; i := 18; for n in [1..521] do for m in [1..521] do C := 1 + X^m + X^n + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: Magma V2.10-22 Fri Apr 9 2004 14:15:39 on modular [Seed = 388087616] ------------------------------------- X^9 + X^4 + 1 X + 1 ************** MAGMA ***************** Host 3(NXDOMAIN) (82.100.96.3) Time: Fri Apr 9 14:17:03 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; i := 18; for m in [1..521] do C := 1 + X^m + X^521; if IsPrimitive(C) then C; end if; end for; Output: Magma V2.10-22 Fri Apr 9 2004 14:17:00 on modular [Seed = 255436687] ------------------------------------- X^9 + X^4 + 1 X^521 + X^32 + 1 X^521 + X^48 + 1 X^521 + X^158 + 1 X^521 + X^168 + 1 X^521 + X^353 + 1 X^521 + X^363 + 1 X^521 + X^473 + 1 X^521 + X^489 + 1 >> if IsPrimitive(C) then ^ Runtime error in 'IsPrimitive': Degree of argument 1 must be >= 1 Total time: 2.979 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host infovia16.upc.es. (147.83.116.16) Time: Fri Apr 9 17:56:48 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-22 Fri Apr 9 2004 17:56:45 on modular [Seed = 4089753587] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.679 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host infovia16.upc.es. (147.83.116.16) Time: Fri Apr 9 17:57:25 2004 Input: "sin(8)" Output: Magma V2.10-22 Fri Apr 9 2004 17:57:22 on modular [Seed = 3957110708] ------------------------------------- sin(8) Total time: 2.630 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host c-24-13-251-235.client.comcast.net. (24.13.251.235) Time: Sat Apr 10 02:18:49 2004 Input: Generators(Gamma1(6)) Output: Magma V2.10-22 Sat Apr 10 2004 02:18:46 on modular [Seed = 756743375] ------------------------------------- [ [1 1] [0 1], [ 1 -1] [ 6 -5], [ 5 -3] [12 -7] ] Total time: 2.649 seconds, Total memory usage: 2.10MB ************** MAGMA ***************** Host c-24-13-251-235.client.comcast.net. (24.13.251.235) Time: Sat Apr 10 05:07:58 2004 Input: Generators(Gamma0(25)) Output: Magma V2.10-22 Sat Apr 10 2004 05:07:54 on modular [Seed = 120651338] ------------------------------------- [ [1 1] [0 1], [ 4 -1] [25 -6], [ 7 -2] [25 -7], [ 9 -4] [ 25 -11], [ 14 -9] [ 25 -16], [ 18 -13] [ 25 -18], [ 19 -16] [ 25 -21] ] Total time: 2.719 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host c-24-13-251-235.client.comcast.net. (24.13.251.235) Time: Sat Apr 10 05:09:14 2004 Input: Generators(Gamma0(125)) Output: Magma V2.10-22 Sat Apr 10 2004 05:09:12 on modular [Seed = 255391376] ------------------------------------- [ [1 1] [0 1], [ 13 -5] [125 -48], [ 17 -3] [125 -22], [ 19 -7] [125 -46], [ 23 -7] [125 -38], [ 27 -8] [125 -37], [ 57 -13] [250 -57], [ 29 -13] [125 -56], [ 33 -14] [125 -53], [ 103 -64] [ 375 -233], [ 174 -49] [ 625 -176], [ 44 -25] [125 -71], [ 224 -81] [ 625 -226], [ 142 -103] [ 375 -272], [ 49 -20] [125 -51], [ 54 -35] [125 -81], [ 274 -121] [ 625 -276], [ 68 -37] [125 -68], [ 69 -53] [125 -96], [ 72 -53] [125 -92], [ 74 -45] [125 -76], [ 463 -292] [ 750 -473], [ 232 -159] [ 375 -257], [ 79 -67] [ 125 -106], [ 87 -71] [ 125 -102], [ 88 -69] [125 -98], [ 449 -324] [ 625 -451] ] Total time: 2.619 seconds, Total memory usage: 2.10MB ************** MAGMA ***************** Host c-24-13-251-235.client.comcast.net. (24.13.251.235) Time: Sat Apr 10 05:10:03 2004 Input: Generators(Gamma0(625)) Output: Magma V2.10-22 Sat Apr 10 2004 05:10:00 on modular [Seed = 388034264] ------------------------------------- [ [1 1] [0 1], [ 53 -24] [ 625 -283], [ 59 -27] [ 625 -286], [ 64 -17] [ 625 -166], [ 73 -57] [ 625 -488], [ 74 -9] [625 -76], [ 82 -37] [ 625 -282], [ 84 -25] [ 625 -186], [ 93 -25] [ 625 -168], [ 94 -37] [ 625 -246], [ 98 -53] [ 625 -338], [ 99 -16] [ 625 -101], [ 108 -61] [ 625 -353], [ 219 -65] [1250 -371], [ 111 -46] [ 625 -259], [ 116 -49] [ 625 -264], [ 118 -27] [ 625 -143], [ 358 -139] [1875 -728], [ 241 -75] [1250 -389], [ 131 -48] [ 625 -229], [ 132 -49] [ 625 -232], [ 941 -288] [ 4375 -1339], [ 539 -246] [ 2500 -1141], [ 1484 -855] [ 6875 -3961], [ 3374 -729] [15625 -3376], [ 271 -80] [1250 -369], [ 136 -89] [ 625 -409], [ 683 -252] [ 3125 -1153], [ 137 -121] [ 625 -552], [ 549 -121] [2500 -551], [ 141 -37] [ 625 -164], [ 707 -488] [ 3125 -2157], [ 1274 -289] [ 5625 -1276], [ 146 -57] [ 625 -244], [ 738 -401] [ 3125 -1698], [ 1183 -746] [ 5000 -3153], [ 593 -366] [ 2500 -1543], [ 149 -36] [ 625 -151], [ 1484 -1045] [ 5625 -3961], [ 4124 -1089] [15625 -4126], [ 661 -280] [ 2500 -1059], [ 663 -205] [2500 -773], [ 337 -196] [1250 -727], [ 169 -53] [ 625 -196], [ 172 -101] [ 625 -367], [ 173 -142] [ 625 -513], [ 174 -49] [ 625 -176], [ 182 -53] [ 625 -182], [ 183 -118] [ 625 -403], [ 189 -88] [ 625 -291], [ 379 -161] [1250 -531], [ 381 -146] [1250 -479], [ 1911 -706] [ 6250 -2309], [ 383 -292] [1250 -953], [ 387 -287] [1250 -927], [ 971 -371] [ 3125 -1194], [ 216 -169] [ 625 -489], [ 653 -412] [ 1875 -1183], [ 219 -130] [ 625 -371], [ 222 -157] [ 625 -442], [ 224 -81] [ 625 -226], [ 459 -206] [1250 -561], [ 1608 -727] [ 4375 -1978], [ 1379 -563] [ 3750 -1531], [ 3004 -1629] [ 8125 -4406], [ 1618 -885] [ 4375 -2393], [ 3699 -1369] [10000 -3701], [ 236 -145] [ 625 -384], [ 949 -361] [2500 -951], [ 1669 -647] [ 4375 -1696], [ 477 -224] [1250 -587], [ 241 -150] [ 625 -389], [ 1697 -666] [ 4375 -1717], [ 1224 -725] [ 3125 -1851], [ 6124 -2401] [15625 -6126], [ 254 -165] [ 625 -406], [ 1274 -775] [ 3125 -1901], [ 6374 -2601] [15625 -6376], [ 256 -145] [ 625 -354], [ 258 -187] [ 625 -453], [ 523 -382] [1250 -913], [ 262 -179] [ 625 -427], [ 1049 -441] [ 2500 -1051], [ 271 -160] [ 625 -369], [ 272 -225] [ 625 -517], [ 818 -575] [ 1875 -1318], [ 274 -121] [ 625 -276], [ 1982 -1249] [ 4375 -2757], [ 287 -242] [ 625 -527], [ 328 -201] [ 625 -383], [ 663 -410] [1250 -773], [ 334 -233] [ 625 -436], [ 339 -307] [ 625 -566], [ 2039 -1436] [ 3750 -2641], [ 1027 -568] [ 1875 -1037], [ 343 -298] [ 625 -543], [ 689 -436] [1250 -791], [ 1381 -817] [ 2500 -1479], [ 349 -196] [ 625 -351], [ 719 -501] [1250 -871], [ 1441 -1060] [ 2500 -1839], [ 361 -294] [ 625 -509], [ 1449 -841] [ 2500 -1451], [ 378 -277] [ 625 -458], [ 2658 -1627] [ 4375 -2678], [ 381 -292] [ 625 -479], [ 1529 -1181] [ 2500 -1931], [ 771 -536] [1250 -869], [ 1931 -1331] [ 3125 -2154], [ 3863 -2981] [ 6250 -4823], [ 1549 -961] [ 2500 -1551], [ 393 -310] [ 625 -493], [ 6299 -3969] [10000 -6301], [ 396 -313] [ 625 -494], [ 399 -256] [ 625 -401], [ 1727 -1269] [ 2500 -1837], [ 439 -380] [ 625 -541], [ 881 -690] [1250 -979], [ 443 -314] [ 625 -443], [ 449 -324] [ 625 -451], [ 457 -389] [ 625 -532], [ 459 -412] [ 625 -561], [ 461 -357] [ 625 -484], [ 1849 -1369] [ 2500 -1851], [ 474 -361] [ 625 -476], [ 482 -391] [ 625 -507], [ 524 -441] [ 625 -526] ] Total time: 2.859 seconds, Total memory usage: 2.10MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Sat Apr 10 09:48:53 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3-2); OK := RingOfIntegers(K); Factorization(5); Factorization(7); Factorization(11); Factorization(13); Output: Magma V2.10-22 Sat Apr 10 2004 09:48:50 on modular [Seed = 1465969724] ------------------------------------- [ <5, 1> ] [ <7, 1> ] [ <11, 1> ] [ <13, 1> ] Total time: 2.569 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Sat Apr 10 09:49:20 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3-2); OK := RingOfIntegers(K); Factorization(5*OK); Factorization(7*OK); Factorization(11*OK); Factorization(13*OK); Output: Magma V2.10-22 Sat Apr 10 2004 09:49:17 on modular [Seed = 2945979611] ------------------------------------- [ , ] [ ] [ , ] [ ] Total time: 2.640 seconds, Total memory usage: 1.86MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Sat Apr 10 09:57:15 2004 Input: R := PolynomialRing(RationalField()); K := NumberField({x^3-2,x^2+x-1}); OK := RingOfIntegers(K); Factorization(5*OK); Factorization(7*OK); Factorization(11*OK); Factorization(13*OK); Output: Magma V2.10-22 Sat Apr 10 2004 09:57:13 on modular [Seed = 3078621863] ------------------------------------- >> K := NumberField({x^3-2,x^2+x-1}); ^ Runtime error in 'NumberField': Bad argument types Argument types given: SetEnum[RngUPolElt] >> OK := RingOfIntegers(K); ^ User error: Identifier 'K' has not been declared or assigned >> Factorization(5*OK); ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(7*OK); ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(11*OK); ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(13*OK);; ^ User error: Identifier 'OK' has not been declared or assigned Total time: 2.549 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Sat Apr 10 09:58:49 2004 Input: R := PolynomialRing(RationalField()); K := NumberField{x^3-2,x^2+x-1}; OK := RingOfIntegers(K); Factorization(5*OK); Factorization(7*OK); Factorization(11*OK); Factorization(13*OK); Output: Magma V2.10-22 Sat Apr 10 2004 09:58:46 on modular [Seed = 2411213360] ------------------------------------- >> K := NumberField{x^3-2,x^2+x-1}; ^ User error: bad syntax >> OK := RingOfIntegers(K); ^ User error: Identifier 'K' has not been declared or assigned >> Factorization(5*OK); ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(7*OK); ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(11*OK); ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(13*OK);; ^ User error: Identifier 'OK' has not been declared or assigned Total time: 2.570 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Sat Apr 10 09:58:59 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3-2,x^2+x-1); OK := RingOfIntegers(K); Factorization(5*OK); Factorization(7*OK); Factorization(11*OK); Factorization(13*OK); Output: Magma V2.10-22 Sat Apr 10 2004 09:58:56 on modular [Seed = 2276473358] ------------------------------------- >> K := NumberField(x^3-2,x^2+x-1); ^ Runtime error in 'NumberField': Bad argument types Argument types given: RngUPolElt, RngUPolElt >> OK := RingOfIntegers(K); ^ User error: Identifier 'K' has not been declared or assigned >> Factorization(5*OK); ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(7*OK); ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(11*OK); ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(13*OK);; ^ User error: Identifier 'OK' has not been declared or assigned Total time: 2.629 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Sat Apr 10 09:59:20 2004 Input: R := PolynomialRing(RationalField()); K := NumberField([x^3-2,x^2+x-1]); OK := RingOfIntegers(K); Factorization(5*OK); Factorization(7*OK); Factorization(11*OK); Factorization(13*OK); Output: Magma V2.10-22 Sat Apr 10 2004 09:59:18 on modular [Seed = 2678596096] ------------------------------------- [ , ] [ ] [ , , , ] [ ] Total time: 2.649 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Sat Apr 10 10:03:56 2004 Input: R := PolynomialRing(RationalField()); K := NumberField([x^3-2,x^2+x-1]); OK := RingOfIntegers(K); Factorization(5*OK); Factorization(7*OK); Factorization(11*OK); Factorization(13*OK); K OK Output: Magma V2.10-22 Sat Apr 10 2004 10:03:53 on modular [Seed = 4039593488] ------------------------------------- [ , ] [ ] [ , , , ] [ ] >> OK; ^ User error: bad syntax Total time: 2.639 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Sat Apr 10 10:04:11 2004 Input: R := PolynomialRing(RationalField()); K := NumberField([x^3-2,x^2+x-1]); OK := RingOfIntegers(K); Factorization(5*OK); Factorization(7*OK); Factorization(11*OK); Factorization(13*OK); K; OK; Output: Magma V2.10-22 Sat Apr 10 2004 10:04:09 on modular [Seed = 3372185144] ------------------------------------- [ , ] [ ] [ , , , ] [ ] Number Field with defining polynomial $.1^3 - 2 over its ground field Maximal Equation Order with defining polynomial x^3 + [-2, 0] over its ground order Total time: 2.649 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Sat Apr 10 10:28:12 2004 Input: R := PolynomialRing(RationalField()); K := NumberField([x^3-2,x^2+x-1]); OK := RingOfIntegers(K); Factorization(5*OK); Factorization(7*OK); Factorization(11*OK); Factorization(13*OK); K; Degree(K); OK; Output: Magma V2.10-22 Sat Apr 10 2004 10:28:09 on modular [Seed = 805860451] ------------------------------------- [ , ] [ ] [ , , , ] [ ] Number Field with defining polynomial $.1^3 - 2 over its ground field 3 Maximal Equation Order with defining polynomial x^3 + [-2, 0] over its ground order Total time: 2.610 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host roam23-82.fas.harvard.edu. (140.247.23.82) Time: Sat Apr 10 10:36:25 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^4-34*x^2+9); OK:=MaximalOrder(K); [K!x : x in Basis(OK)]; Output: Magma V2.10-22 Sat Apr 10 2004 10:36:23 on modular [Seed = 455302486] ------------------------------------- [ 1, a, 1/2*(a^2 + 1), 1/12*(a^3 + 3*a^2 + 11*a + 9) ] Total time: 2.560 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam23-82.fas.harvard.edu. (140.247.23.82) Time: Sat Apr 10 10:37:38 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^4-34*x^2+9); OK:=MaximalOrder(K); Factorization(37*OK); Output: Magma V2.10-22 Sat Apr 10 2004 10:37:35 on modular [Seed = 321607062] ------------------------------------- [ , , , ] Total time: 2.569 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam23-82.fas.harvard.edu. (140.247.23.82) Time: Sat Apr 10 10:40:31 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^4-34*x^2+9); OK:=MaximalOrder(K); [K!x : x in Basis(OK)]; Factorization(37*OK); Output: Magma V2.10-22 Sat Apr 10 2004 10:40:28 on modular [Seed = 1666917397] ------------------------------------- [ 1, a, 1/2*(a^2 + 1), 1/12*(a^3 + 3*a^2 + 11*a + 9) ] [ , , , ] Total time: 2.609 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam23-82.fas.harvard.edu. (140.247.23.82) Time: Sat Apr 10 10:48:50 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^4-74*x^2+529); OK:=MaximalOrder(K); [K!x : x in Basis(OK)]; Factorization(37*OK); Output: Magma V2.10-22 Sat Apr 10 2004 10:48:47 on modular [Seed = 1883781397] ------------------------------------- [ 1, a, 1/2*(a^2 + 1), 1/92*(a^3 + 23*a^2 + 87*a + 69) ] [ , , , ] Total time: 2.570 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Sat Apr 10 10:50:24 2004 Input: R := PolynomialRing(RationalField()); K := NumberField([x^2+x-1,x^3-2]); OK := RingOfIntegers(K); Factorization(5*OK); Factorization(7*OK); Factorization(11*OK); Factorization(13*OK); K; Degree(K); OK; Output: Magma V2.10-22 Sat Apr 10 2004 10:50:22 on modular [Seed = 1081608644] ------------------------------------- [ , ] [ ] [ , , , ] [ ] Number Field with defining polynomial $.1^2 + $.1 - 1 over its ground field 2 Maximal Equation Order with defining polynomial x^2 + x + [-1, 0, 0] over its ground order Total time: 2.609 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host roam23-82.fas.harvard.edu. (140.247.23.82) Time: Sat Apr 10 10:56:22 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-7,y^-10); OK:=MaximalOrder(K); [K!x : x in Basis(OK)]; Factorization(37*OK); Output: Magma V2.10-22 Sat Apr 10 2004 10:56:20 on modular [Seed = 1399527533] ------------------------------------- >> R:=PolynomialRing(RationalField()); ^ Runtime error in 'AssignNames': Argument 2 must have length 1 >> K:=NumberField(x^2-7,y^-10); ^ User error: Identifier 'x' has not been declared or assigned >> OK:=MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> [K!x : x in Basis(OK)]; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(37*OK);; ^ User error: Identifier 'OK' has not been declared or assigned Total time: 2.559 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam23-82.fas.harvard.edu. (140.247.23.82) Time: Sat Apr 10 10:58:28 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-7); L:=NumberField(x^2-30); OL:=MaximalOrder(L); [L!x : x in Basis(OL)]; Factorization(37*OL); Output: Magma V2.10-22 Sat Apr 10 2004 10:58:26 on modular [Seed = 2878595091] ------------------------------------- >> L:=NumberField(x^2-30); ^ Runtime error in 'AssignNames': Argument 2 must have length 2 [ 1, L.1 ] [ , ] Total time: 2.559 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam23-82.fas.harvard.edu. (140.247.23.82) Time: Sat Apr 10 10:58:54 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-7); L:=NumberField(x^2-30); OL:=MaximalOrder(L); [L!x : x in Basis(OL)]; Factorization(37*OL); Output: Magma V2.10-22 Sat Apr 10 2004 10:58:51 on modular [Seed = 2744903714] ------------------------------------- >> L:=NumberField(x^2-30); ^ User error: bad syntax >> OL:=MaximalOrder(L); ^ User error: Identifier 'L' has not been declared or assigned >> [L!x : x in Basis(OL)]; ^ User error: Identifier 'OL' has not been declared or assigned >> Factorization(37*OL);; ^ User error: Identifier 'OL' has not been declared or assigned Total time: 2.499 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam23-82.fas.harvard.edu. (140.247.23.82) Time: Sat Apr 10 10:59:00 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-7); L:=NumberField(x^2-30); OL:=MaximalOrder(L); [L!x : x in Basis(OL)]; Factorization(37*OL); Output: Magma V2.10-22 Sat Apr 10 2004 10:58:57 on modular [Seed = 3145986080] ------------------------------------- >> L:=NumberField(x^2-30); ^ User error: bad syntax >> OL:=MaximalOrder(L); ^ User error: Identifier 'L' has not been declared or assigned >> [L!x : x in Basis(OL)]; ^ User error: Identifier 'OL' has not been declared or assigned >> Factorization(37*OL);; ^ User error: Identifier 'OL' has not been declared or assigned Total time: 2.550 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam23-82.fas.harvard.edu. (140.247.23.82) Time: Sat Apr 10 11:05:33 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField((x^-7)(x^2-10); OK:=MaximalOrder(K); [K!x : x in Basis(OK)]; Factorization(37*OK); Output: Magma V2.10-22 Sat Apr 10 2004 11:05:30 on modular [Seed = 2528041862] ------------------------------------- >> K:=NumberField((x^-7)(x^2-10); ^ User error: bad syntax >> OK:=MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> [K!x : x in Basis(OK)]; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(37*OK); ^ User error: Identifier 'OK' has not been declared or assigned Total time: 2.499 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam23-82.fas.harvard.edu. (140.247.23.82) Time: Sat Apr 10 11:05:47 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField((x^-7)(x^2-10)); OK:=MaximalOrder(K); [K!x : x in Basis(OK)]; Factorization(37*OK); Output: Magma V2.10-22 Sat Apr 10 2004 11:05:44 on modular [Seed = 4007043980] ------------------------------------- >> K:=NumberField((x^-7)(x^2-10)); ^ Runtime error in '^': Argument 2 (-7) should be >= 0 >> OK:=MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> [K!x : x in Basis(OK)]; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(37*OK); ^ User error: Identifier 'OK' has not been declared or assigned Total time: 2.520 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam23-82.fas.harvard.edu. (140.247.23.82) Time: Sat Apr 10 11:06:03 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField((x^2-7)(x^2-10)); OK:=MaximalOrder(K); [K!x : x in Basis(OK)]; Factorization(37*OK); Output: Magma V2.10-22 Sat Apr 10 2004 11:06:00 on modular [Seed = 3890195093] ------------------------------------- >> K:=NumberField((x^2-7)(x^2-10)); ^ Runtime error: Bad argument types Argument types given: RngUPolElt, RngUPolElt >> OK:=MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> [K!x : x in Basis(OK)]; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(37*OK); ^ User error: Identifier 'OK' has not been declared or assigned Total time: 2.499 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam23-82.fas.harvard.edu. (140.247.23.82) Time: Sat Apr 10 11:11:52 2004 Input: R:=PolynomialRing(RationalField()); L:=NumberField(x^2-7); S:=PolynomialRing(L); K:=NumberField(x^2-10); OK:=MaximalOrder(K); [K!x : x in Basis(OK)]; Factorization(37*OK); Output: Magma V2.10-22 Sat Apr 10 2004 11:11:50 on modular [Seed = 4107057768] ------------------------------------- [ 1, b ] [ , ] Total time: 2.569 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam23-82.fas.harvard.edu. (140.247.23.82) Time: Sat Apr 10 11:15:13 2004 Input: Qbar:=AlgebraicClosure(RationalField()); Qbar; S:=PolynomialRing(Qbar); r:=roots(x^2-2); s:=roots(x^2-3); t:=roots(x^2-5); u:=roots(x^2-7); r; s; t; u; Output: Magma V2.10-22 Sat Apr 10 2004 11:15:10 on modular [Seed = 3254357653] ------------------------------------- >> Qbar:=AlgebraicClosure(RationalField()); ^ Runtime error in 'AlgebraicClosure': Bad argument types Argument types given: FldRat >> Qbar; ^ User error: Identifier 'Qbar' has not been declared or assigned >> S:=PolynomialRing(Qbar); ^ User error: Identifier 'Qbar' has not been declared or assigned >> r:=roots(x^2-2); ^ User error: Identifier 'x' has not been declared or assigned >> s:=roots(x^2-3); ^ User error: Identifier 'x' has not been declared or assigned >> t:=roots(x^2-5); ^ User error: Identifier 'x' has not been declared or assigned >> u:=roots(x^2-7); ^ User error: Identifier 'x' has not been declared or assigned >> r; ^ User error: Identifier 'r' has not been declared or assigned >> s; ^ User error: Identifier 's' has not been declared or assigned >> t; ^ User error: Identifier 't' has not been declared or assigned >> u;; ^ User error: Identifier 'u' has not been declared or assigned Total time: 2.559 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam23-82.fas.harvard.edu. (140.247.23.82) Time: Sat Apr 10 11:17:43 2004 Input: Qbar:=AlgebraicClosure(FldRat()); Qbar; S:=PolynomialRing(Qbar); r:=roots(x^2-2); s:=roots(x^2-3); t:=roots(x^2-5); u:=roots(x^2-7); r; s; t; u; Output: Magma V2.10-22 Sat Apr 10 2004 11:17:40 on modular [Seed = 3739651808] ------------------------------------- >> Qbar:=AlgebraicClosure(FldRat()); ^ Runtime error: Attempting to call something that is not callable >> Qbar; ^ User error: Identifier 'Qbar' has not been declared or assigned >> S:=PolynomialRing(Qbar); ^ User error: Identifier 'Qbar' has not been declared or assigned >> r:=roots(x^2-2); ^ User error: Identifier 'x' has not been declared or assigned >> s:=roots(x^2-3); ^ User error: Identifier 'x' has not been declared or assigned >> t:=roots(x^2-5); ^ User error: Identifier 'x' has not been declared or assigned >> u:=roots(x^2-7); ^ User error: Identifier 'x' has not been declared or assigned >> r; ^ User error: Identifier 'r' has not been declared or assigned >> s; ^ User error: Identifier 's' has not been declared or assigned >> t; ^ User error: Identifier 't' has not been declared or assigned >> u;; ^ User error: Identifier 'u' has not been declared or assigned Total time: 2.520 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam23-82.fas.harvard.edu. (140.247.23.82) Time: Sat Apr 10 11:17:55 2004 Input: Qbar:=AlgebraicClosure(FldRat); Qbar; S:=PolynomialRing(Qbar); r:=roots(x^2-2); s:=roots(x^2-3); t:=roots(x^2-5); u:=roots(x^2-7); r; s; t; u; Output: Magma V2.10-22 Sat Apr 10 2004 11:17:52 on modular [Seed = 3605956316] ------------------------------------- >> Qbar:=AlgebraicClosure(FldRat); ^ Runtime error in 'AlgebraicClosure': Bad argument types Argument types given: Cat >> Qbar; ^ User error: Identifier 'Qbar' has not been declared or assigned >> S:=PolynomialRing(Qbar); ^ User error: Identifier 'Qbar' has not been declared or assigned >> r:=roots(x^2-2); ^ User error: Identifier 'x' has not been declared or assigned >> s:=roots(x^2-3); ^ User error: Identifier 'x' has not been declared or assigned >> t:=roots(x^2-5); ^ User error: Identifier 'x' has not been declared or assigned >> u:=roots(x^2-7); ^ User error: Identifier 'x' has not been declared or assigned >> r; ^ User error: Identifier 'r' has not been declared or assigned >> s; ^ User error: Identifier 's' has not been declared or assigned >> t; ^ User error: Identifier 't' has not been declared or assigned >> u;; ^ User error: Identifier 'u' has not been declared or assigned Total time: 2.519 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam23-82.fas.harvard.edu. (140.247.23.82) Time: Sat Apr 10 11:18:13 2004 Input: Qbar:=AlgebraicClosure(RationalField); Qbar; S:=PolynomialRing(Qbar); r:=roots(x^2-2); s:=roots(x^2-3); t:=roots(x^2-5); u:=roots(x^2-7); r; s; t; u; Output: Magma V2.10-22 Sat Apr 10 2004 11:18:11 on modular [Seed = 790069047] ------------------------------------- >> Qbar:=AlgebraicClosure(RationalField); ^ Runtime error in 'AlgebraicClosure': Bad argument types Argument types given: Intrinsic >> Qbar; ^ User error: Identifier 'Qbar' has not been declared or assigned >> S:=PolynomialRing(Qbar); ^ User error: Identifier 'Qbar' has not been declared or assigned >> r:=roots(x^2-2); ^ User error: Identifier 'x' has not been declared or assigned >> s:=roots(x^2-3); ^ User error: Identifier 'x' has not been declared or assigned >> t:=roots(x^2-5); ^ User error: Identifier 'x' has not been declared or assigned >> u:=roots(x^2-7); ^ User error: Identifier 'x' has not been declared or assigned >> r; ^ User error: Identifier 'r' has not been declared or assigned >> s; ^ User error: Identifier 's' has not been declared or assigned >> t; ^ User error: Identifier 't' has not been declared or assigned >> u;; ^ User error: Identifier 'u' has not been declared or assigned Total time: 2.560 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam23-82.fas.harvard.edu. (140.247.23.82) Time: Sat Apr 10 11:18:32 2004 Input: Qbar:=AlgebraicClosure(RationalField()); Qbar; S:=PolynomialRing(Qbar); r:=roots(x^2-2); s:=roots(x^2-3); t:=roots(x^2-5); u:=roots(x^2-7); r; s; t; u; Output: Magma V2.10-22 Sat Apr 10 2004 11:18:30 on modular [Seed = 656373578] ------------------------------------- >> Qbar:=AlgebraicClosure(RationalField()); ^ Runtime error in 'AlgebraicClosure': Bad argument types Argument types given: FldRat >> Qbar; ^ User error: Identifier 'Qbar' has not been declared or assigned >> S:=PolynomialRing(Qbar); ^ User error: Identifier 'Qbar' has not been declared or assigned >> r:=roots(x^2-2); ^ User error: Identifier 'x' has not been declared or assigned >> s:=roots(x^2-3); ^ User error: Identifier 'x' has not been declared or assigned >> t:=roots(x^2-5); ^ User error: Identifier 'x' has not been declared or assigned >> u:=roots(x^2-7); ^ User error: Identifier 'x' has not been declared or assigned >> r; ^ User error: Identifier 'r' has not been declared or assigned >> s; ^ User error: Identifier 's' has not been declared or assigned >> t; ^ User error: Identifier 't' has not been declared or assigned >> u;; ^ User error: Identifier 'u' has not been declared or assigned Total time: 2.550 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam23-82.fas.harvard.edu. (140.247.23.82) Time: Sat Apr 10 11:19:49 2004 Input: Qbar:=AlgebraicClosure(); Qbar; S:=PolynomialRing(Qbar); r:=roots(x^2-2); s:=roots(x^2-3); t:=roots(x^2-5); u:=roots(x^2-7); r; s; t; u; Output: Magma V2.10-22 Sat Apr 10 2004 11:19:46 on modular [Seed = 1040608903] ------------------------------------- Algebraically closed field with no variables >> r:=roots(x^2-2); ^ User error: Identifier 'roots' has not been declared or assigned >> s:=roots(x^2-3); ^ User error: Identifier 'roots' has not been declared or assigned >> t:=roots(x^2-5); ^ User error: Identifier 'roots' has not been declared or assigned >> u:=roots(x^2-7); ^ User error: Identifier 'roots' has not been declared or assigned >> r; ^ User error: Identifier 'r' has not been declared or assigned >> s; ^ User error: Identifier 's' has not been declared or assigned >> t; ^ User error: Identifier 't' has not been declared or assigned >> u;; ^ User error: Identifier 'u' has not been declared or assigned Total time: 2.509 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam23-82.fas.harvard.edu. (140.247.23.82) Time: Sat Apr 10 11:20:40 2004 Input: Qbar:=AlgebraicClosure(); S:=PolynomialRing(Qbar); r:=Roots(x^2-2); s:=Roots(x^2-3); t:=Roots(x^2-5); u:=Roots(x^2-7); r; s; t; u; Output: Magma V2.10-22 Sat Apr 10 2004 11:20:38 on modular [Seed = 238444259] ------------------------------------- [ , ] [ , ] [ , ] [ , ] Total time: 2.570 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam23-82.fas.harvard.edu. (140.247.23.82) Time: Sat Apr 10 11:22:37 2004 Input: Qbar:=AlgebraicClosure(); S:=PolynomialRing(Qbar); r:=Roots(x^2-2); s:=Roots(x^2-3); t:=Roots(x^2-5); u:=Roots(x^2-7); a:=r[1][1]; b:=r[3][1]; c:=r[5][1]; d:=r[7][1]; MinimalPolynomial(a+b+c+d); Output: Magma V2.10-22 Sat Apr 10 2004 11:22:34 on modular [Seed = 87905300] ------------------------------------- >> b:=r[3][1]; ^ Runtime error in '[]': Sequence element 3 not defined >> c:=r[5][1]; ^ Runtime error in '[]': Sequence element 5 not defined >> d:=r[7][1]; ^ Runtime error in '[]': Sequence element 7 not defined >> MinimalPolynomial(a+b+c+d);; ^ User error: Identifier 'b' has not been declared or assigned Total time: 2.629 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam23-82.fas.harvard.edu. (140.247.23.82) Time: Sat Apr 10 11:23:38 2004 Input: Qbar:=AlgebraicClosure(); S:=PolynomialRing(Qbar); r:=Roots(x^2-2); s:=Roots(x^2-3); t:=Roots(x^2-5); u:=Roots(x^2-7); r;s;t;u; MinimalPolynomial(a); Output: Magma V2.10-22 Sat Apr 10 2004 11:23:36 on modular [Seed = 488983630] ------------------------------------- [ , ] [ , ] [ , ] [ , ] >> MinimalPolynomial(a);; ^ User error: Identifier 'a' has not been declared or assigned Total time: 2.520 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam23-82.fas.harvard.edu. (140.247.23.82) Time: Sat Apr 10 11:24:33 2004 Input: Qbar:=AlgebraicClosure(); S:=PolynomialRing(Qbar); r:=Roots(x^2-2); s:=Roots(x^2-3); t:=Roots(x^2-5); u:=Roots(x^2-7); a:=r[1][1]; b:=s[1][1]; c:=t[1][1]; d:=u[1][1]; MinimalPolynomial(a+b+c+d); Output: Magma V2.10-22 Sat Apr 10 2004 11:24:30 on modular [Seed = 355288208] ------------------------------------- $.1^16 - 136*$.1^14 + 6476*$.1^12 - 141912*$.1^10 + 1513334*$.1^8 - 7453176*$.1^6 + 13950764*$.1^4 - 5596840*$.1^2 + 46225 Total time: 2.579 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam23-82.fas.harvard.edu. (140.247.23.82) Time: Sat Apr 10 11:26:29 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^16 - 136*x^14 + 6476*x^12 - 141912*x^10 + 1513334*x^8 - 7453176*x^6 + 13950764*x^4 - 5596840*x^2 + 46225); OK:=MaximalOrder(K); [K!x : x in Basis(OK)]; Factorization(37*OK); Output: Magma V2.10-22 Sat Apr 10 2004 11:26:20 on modular [Seed = 1616392791] ------------------------------------- [ 1, a, 1/4*(a^2 + 2*a + 3), 1/4*(a^3 + 3*a + 2), 1/32*(a^4 + 2*a^2 + 16*a + 25), 1/32*(a^5 + 2*a^3 + 25*a + 16), 1/128*(a^6 + 2*a^5 + a^4 + 20*a^3 + 23*a^2 + 98*a + 7), 1/128*(a^7 + a^5 + 2*a^4 + 23*a^3 + 20*a^2 + 7*a + 98), 1/1024*(a^8 + 4*a^6 + 22*a^4 + 36*a^2 + 593), 1/2048*(a^9 + a^8 + 4*a^7 + 4*a^6 + 22*a^5 + 22*a^4 + 36*a^3 + 36*a^2 + 1617*a + 1617), 1/20480*(a^10 + 5*a^8 + 122*a^6 + 320*a^5 + 410*a^4 + 3200*a^3 + 1301*a^2 + 5440*a + 7665), 1/40960*(a^11 + a^10 + 5*a^9 + 25*a^8 + 282*a^7 + 42*a^6 + 1210*a^5 + 690*a^4 + 6261*a^3 + 3461*a^2 + 24785*a + 33765), 1/491520*(a^12 + 22*a^10 + 87*a^8 + 404*a^6 + 12351*a^4 + 82102*a^2 + 342985), 1/4915200*(a^13 + 5*a^12 + 22*a^11 + 110*a^10 + 1047*a^9 + 2835*a^8 + 27284*a^7 + 11620*a^6 + 148671*a^5 + 37755*a^4 + 339382*a^3 + 957710*a^2 + 3869065*a + 603725), 1/1739980800*(a^14 + 987*a^12 + 45797*a^10 + 411239*a^8 + 9244771*a^6 + 27187200*a^5 + 52832497*a^4 + 271872000*a^3 + 29447415*a^2 + 1332172800*a + 911686925), 1/149638348800*(a^15 + 43*a^14 + 23643*a^13 + 194661*a^12 + 34469*a^11 + 1664831*a^10 + 47071271*a^9 + 85725617*a^8 + 653558755*a^7 + 305584273*a^6 + 333676273*a^5 + 1923365791*a^4 + 31693688247*a^3 + 6965051205*a^2 + 78855746765*a + 48284744075) ] [ , , , , , , , ] Total time: 9.259 seconds, Total memory usage: 2.10MB ************** MAGMA ***************** Host roam23-82.fas.harvard.edu. (140.247.23.82) Time: Sat Apr 10 11:28:25 2004 Input: Qbar:=AlgebraicClosure(); S:=PolynomialRing(Qbar); s:=Roots(x^2-3); t:=Roots(x^2-5); u:=Roots(x^2-7); b:=s[1][1]; c:=t[1][1]; d:=u[1][1]; MinimalPolynomial(b+c+d); Output: Magma V2.10-22 Sat Apr 10 2004 11:28:23 on modular [Seed = 2135371203] ------------------------------------- $.1^8 - 60*$.1^6 + 782*$.1^4 - 3180*$.1^2 + 3481 Total time: 2.519 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam23-82.fas.harvard.edu. (140.247.23.82) Time: Sat Apr 10 11:30:37 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^8 - 60*x^6 + 782*x^4 - 3180*x^2 + 3481); OK:=MaximalOrder(K); [K!x : x in Basis(OK)]; Factorization(37*OK); Output: Magma V2.10-22 Sat Apr 10 2004 11:30:35 on modular [Seed = 1333206143] ------------------------------------- [ 1, 1/2*(a + 1), 1/4*(a^2 + 3), 1/8*(a^3 + a^2 + 3*a + 3), 1/32*(a^4 + 6*a^2 + 25), 1/64*(a^5 + a^4 + 6*a^3 + 6*a^2 + 25*a + 25), 1/128*(a^6 + a^4 + 27*a^2 + 99), 1/15104*(a^7 + 59*a^6 + 117*a^5 + 295*a^4 + 723*a^3 + 3009*a^2 + 183*a + 11741) ] [ , , , ] Total time: 2.730 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Sat Apr 10 11:42:25 2004 Input: R := PolynomialRing(RationalField()); K := NumberField([x^2+x-1,x^3-2]); OK := RingOfIntegers(K); Factorization(2*OK); Factorization(5*OK); Factorization(7*OK); Factorization(11*OK); Factorization(13*OK); K; Degree(K); OK; Output: Magma V2.10-22 Sat Apr 10 2004 11:42:22 on modular [Seed = 1433206944] ------------------------------------- [ ] [ , ] [ ] [ , , , ] [ ] Number Field with defining polynomial $.1^2 + $.1 - 1 over its ground field 2 Maximal Equation Order with defining polynomial x^2 + x + [-1, 0, 0] over its ground order Total time: 2.619 seconds, Total memory usage: 1.92MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Sat Apr 10 11:44:16 2004 Input: R := PolynomialRing(RationalField()); K := NumberField([x^2+x-1,x^3-2]); OK := RingOfIntegers(K); Factorization(5*OK); Factorization(7*OK); Factorization(11*OK); Factorization(13*OK); K; Degree(K); OK; Output: Magma V2.10-22 Sat Apr 10 2004 11:44:14 on modular [Seed = 2912287688] ------------------------------------- [ , ] [ ] [ , , , ] [ ] Number Field with defining polynomial $.1^2 + $.1 - 1 over its ground field 2 Maximal Equation Order with defining polynomial x^2 + x + [-1, 0, 0] over its ground order Total time: 2.619 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Sat Apr 10 11:44:49 2004 Input: R := PolynomialRing(RationalField()); K := NumberField([x^2+x-1,x^3-2]: Abs=true); OK := RingOfIntegers(K); Factorization(5*OK); Factorization(7*OK); Factorization(11*OK); Factorization(13*OK); K; Degree(K); OK; Output: Magma V2.10-22 Sat Apr 10 2004 11:44:46 on modular [Seed = 2778592224] ------------------------------------- >> K := NumberField([x^2+x-1,x^3-2]: Abs=true); ^ User error: bad syntax >> OK := RingOfIntegers(K); ^ User error: Identifier 'K' has not been declared or assigned >> Factorization(5*OK); ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(7*OK); ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(11*OK); ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(13*OK); ^ User error: Identifier 'OK' has not been declared or assigned >> K; ^ User error: Identifier 'K' has not been declared or assigned >> Degree(K); ^ User error: Identifier 'K' has not been declared or assigned >> OK;; ^ User error: Identifier 'OK' has not been declared or assigned Total time: 2.629 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Sat Apr 10 11:44:58 2004 Input: R := PolynomialRing(RationalField()); K := NumberField([x^2+x-1,x^3-2]: Abs = true); OK := RingOfIntegers(K); Factorization(5*OK); Factorization(7*OK); Factorization(11*OK); Factorization(13*OK); K; Degree(K); OK; Output: Magma V2.10-22 Sat Apr 10 2004 11:44:55 on modular [Seed = 3179670497] ------------------------------------- >> K := NumberField([x^2+x-1,x^3-2]: Abs = true); ^ User error: bad syntax >> OK := RingOfIntegers(K); ^ User error: Identifier 'K' has not been declared or assigned >> Factorization(5*OK); ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(7*OK); ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(11*OK); ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(13*OK); ^ User error: Identifier 'OK' has not been declared or assigned >> K; ^ User error: Identifier 'K' has not been declared or assigned >> Degree(K); ^ User error: Identifier 'K' has not been declared or assigned >> OK;; ^ User error: Identifier 'OK' has not been declared or assigned Total time: 2.509 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Sat Apr 10 11:45:16 2004 Input: R := PolynomialRing(RationalField()); K := NumberField([x^2+x-1,x^3-2]: Abs := true); OK := RingOfIntegers(K); Factorization(5*OK); Factorization(7*OK); Factorization(11*OK); Factorization(13*OK); K; Degree(K); OK; Output: Magma V2.10-22 Sat Apr 10 2004 11:45:13 on modular [Seed = 2293292586] ------------------------------------- [ , ] [ ] [ , , , ] [ ] Number Field with defining polynomial [ x^2 + x - 1, x^3 - 2] over the Rational Field 6 Non-simple Equation Order defined by x^2 + x - 1, x^3 - 2 over its ground order Total time: 3.030 seconds, Total memory usage: 2.55MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Sat Apr 10 11:49:20 2004 Input: R := PolynomialRing(RationalField()); K := NumberField([x^2+x-1,x^3-2]: Abs := true); OK := MaximalOrder(K); Factorization(5*OK); Factorization(7*OK); Factorization(11*OK); Factorization(13*OK); K; Degree(K); OK; Output: Magma V2.10-22 Sat Apr 10 2004 11:49:17 on modular [Seed = 2226967506] ------------------------------------- [ , ] [ ] [ , , , ] [ ] Number Field with defining polynomial [ x^2 + x - 1, x^3 - 2] over the Rational Field 6 Non-simple Equation Order defined by x^2 + x - 1, x^3 - 2 over its ground order Total time: 3.059 seconds, Total memory usage: 2.59MB ************** MAGMA ***************** Host roam23-82.fas.harvard.edu. (140.247.23.82) Time: Sat Apr 10 11:52:20 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-2); OK:=MaximalOrder(K); [K!x : x in Basis(OK)]; Factorization(37*OK); Output: Magma V2.10-22 Sat Apr 10 2004 11:52:17 on modular [Seed = 3956519921] ------------------------------------- [ 1, a ] [ ] Total time: 2.609 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam23-82.fas.harvard.edu. (140.247.23.82) Time: Sat Apr 10 11:52:55 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-3); OK:=MaximalOrder(K); [K!x : x in Basis(OK)]; Factorization(37*OK); Output: Magma V2.10-22 Sat Apr 10 2004 11:52:53 on modular [Seed = 3822828445] ------------------------------------- [ 1, a ] [ , ] Total time: 2.739 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Sat Apr 10 11:52:58 2004 Input: R := PolynomialRing(RationalField()); K := NumberField([CyclotomicPolynomial(3),x^3-2]: Abs := true); OK := MaximalOrder(K); Factorization(5*OK); Factorization(7*OK); Factorization(11*OK); Factorization(13*OK); K; Degree(K); OK; Output: Magma V2.10-22 Sat Apr 10 2004 11:52:55 on modular [Seed = 3789142429] ------------------------------------- [ , , ] [ , ] [ , , ] [ , ] Number Field with defining polynomial [ x^2 + x + 1, x^3 - 2] over the Rational Field 6 Maximal Order of Equation Order with defining polynomials x^2 + x + 1, x^3 - 2 over its ground order Total time: 3.329 seconds, Total memory usage: 2.80MB ************** MAGMA ***************** Host roam23-82.fas.harvard.edu. (140.247.23.82) Time: Sat Apr 10 11:54:16 2004 Input: Qbar:=AlgebraicClosure(); S:=PolynomialRing(Qbar); r:=Roots(x^2-2); s:=Roots(x^2-3); t:=Roots(x^2-5); u:=Roots(x^2-7); a:=r[1][1]; b:=s[1][1]; c:=t[1][1]; d:=u[1][1]; MinimalPolynomial(a+b); Output: Magma V2.10-22 Sat Apr 10 2004 11:54:14 on modular [Seed = 4090211198] ------------------------------------- $.1^4 - 10*$.1^2 + 1 Total time: 2.519 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam23-82.fas.harvard.edu. (140.247.23.82) Time: Sat Apr 10 11:55:35 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^4 - 10*x^2 + 1); OK:=MaximalOrder(K); [K!x : x in Basis(OK)]; Factorization(37*OK); Output: Magma V2.10-22 Sat Apr 10 2004 11:55:32 on modular [Seed = 3472266769] ------------------------------------- [ 1, a, 1/2*(a^2 - 1), 1/4*(a^3 + a^2 - a - 1) ] [ , ] Total time: 2.569 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam23-82.fas.harvard.edu. (140.247.23.82) Time: Sat Apr 10 11:58:18 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-7); OK:=MaximalOrder(K); [K!x : x in Basis(OK)]; Factorization(37*OK); Output: Magma V2.10-22 Sat Apr 10 2004 11:58:15 on modular [Seed = 3321732217] ------------------------------------- [ 1, a ] [ , ] Total time: 2.559 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam23-82.fas.harvard.edu. (140.247.23.82) Time: Sat Apr 10 11:58:33 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^2-5); OK:=MaximalOrder(K); [K!x : x in Basis(OK)]; Factorization(37*OK); Output: Magma V2.10-22 Sat Apr 10 2004 11:58:31 on modular [Seed = 3722806353] ------------------------------------- [ 1, 1/2*(a + 1) ] [ ] Total time: 2.509 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam23-82.fas.harvard.edu. (140.247.23.82) Time: Sat Apr 10 11:59:58 2004 Input: Qbar:=AlgebraicClosure(); S:=PolynomialRing(Qbar); r:=Roots(x^2-2); s:=Roots(x^2-3); t:=Roots(x^2-5); u:=Roots(x^2-7); a:=r[1][1]; b:=s[1][1]; c:=t[1][1]; d:=u[1][1]; MinimalPolynomial(a+b); R:=PolynomialRing(RationalField()); K:=NumberField(x^2-3); OK:=MaximalOrder(K); [K!x : x in Basis(OK)]; Factorization(37*OK); Output: Magma V2.10-22 Sat Apr 10 2004 11:59:55 on modular [Seed = 3589114885] ------------------------------------- $.1^4 - 10*$.1^2 + 1 [ 1, a ] [ , ] Total time: 2.520 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam23-82.fas.harvard.edu. (140.247.23.82) Time: Sat Apr 10 12:00:15 2004 Input: Qbar:=AlgebraicClosure(); S:=PolynomialRing(Qbar); r:=Roots(x^2-2); s:=Roots(x^2-3); t:=Roots(x^2-5); u:=Roots(x^2-7); a:=r[1][1]; b:=s[1][1]; c:=t[1][1]; d:=u[1][1]; MinimalPolynomial(b+d); R:=PolynomialRing(RationalField()); K:=NumberField(x^2-3); OK:=MaximalOrder(K); [K!x : x in Basis(OK)]; Factorization(37*OK); Output: Magma V2.10-22 Sat Apr 10 2004 12:00:12 on modular [Seed = 1006921244] ------------------------------------- $.1^4 - 20*$.1^2 + 16 [ 1, a ] [ , ] Total time: 2.529 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam23-82.fas.harvard.edu. (140.247.23.82) Time: Sat Apr 10 12:00:38 2004 Input: Qbar:=AlgebraicClosure(); S:=PolynomialRing(Qbar); r:=Roots(x^2-2); s:=Roots(x^2-3); t:=Roots(x^2-5); u:=Roots(x^2-7); a:=r[1][1]; b:=s[1][1]; c:=t[1][1]; d:=u[1][1]; MinimalPolynomial(b+d); R:=PolynomialRing(RationalField()); K:=NumberField(x^4 - 20*x^2 + 16); OK:=MaximalOrder(K); [K!x : x in Basis(OK)]; Factorization(37*OK); Output: Magma V2.10-22 Sat Apr 10 2004 12:00:36 on modular [Seed = 873229884] ------------------------------------- $.1^4 - 20*$.1^2 + 16 [ 1, 1/2*a, 1/4*a^2, 1/8*a^3 ] [ , , , ] Total time: 2.580 seconds, Total memory usage: 1.88MB ************** MAGMA ***************** Host roam23-82.fas.harvard.edu. (140.247.23.82) Time: Sat Apr 10 12:07:14 2004 Input: Qbar:=AlgebraicClosure(); S:=PolynomialRing(Qbar); s:=Roots(x^2-3); u:=Roots(x^2-7); b:=s[1][1]; d:=u[1][1]; MinimalPolynomial(b+d); Output: Magma V2.10-22 Sat Apr 10 2004 12:07:11 on modular [Seed = 355290774] ------------------------------------- $.1^4 - 20*$.1^2 + 16 Total time: 2.569 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam23-82.fas.harvard.edu. (140.247.23.82) Time: Sat Apr 10 12:07:52 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^4 - 20*x^2 + 16); OK:=MaximalOrder(K); [K!x : x in Basis(OK)]; Factorization(37*OK); Output: Magma V2.10-22 Sat Apr 10 2004 12:07:49 on modular [Seed = 1834301079] ------------------------------------- [ 1, 1/2*a, 1/4*a^2, 1/8*a^3 ] [ , , , ] Total time: 2.609 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host roam23-82.fas.harvard.edu. (140.247.23.82) Time: Sat Apr 10 12:09:27 2004 Input: Qbar:=AlgebraicClosure(); S:=PolynomialRing(Qbar); s:=Roots(x^2-3); u:=Roots(x^2-7); b:=s[1][1]; d:=u[1][1]; MinimalPolynomial(b+d); Output: Magma V2.10-22 Sat Apr 10 2004 12:09:24 on modular [Seed = 1700608381] ------------------------------------- $.1^4 - 20*$.1^2 + 16 Total time: 2.569 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam23-82.fas.harvard.edu. (140.247.23.82) Time: Sat Apr 10 12:10:45 2004 Input: Qbar:=AlgebraicClosure(); S:=PolynomialRing(Qbar); r:=Roots(x^2-2); s:=Roots(x^2-3); t:=Roots(x^2-5); u:=Roots(x^2-7); a:=r[1][1]; b:=s[1][1]; c:=t[1][1]; d:=u[1][1]; MinimalPolynomial(a*c+b+d); Output: Magma V2.10-22 Sat Apr 10 2004 12:10:43 on modular [Seed = 1967991258] ------------------------------------- $.1^8 - 80*$.1^6 + 1432*$.1^4 - 6720*$.1^2 + 7056 Total time: 2.599 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam23-82.fas.harvard.edu. (140.247.23.82) Time: Sat Apr 10 12:11:49 2004 Input: R:=PolynomialRing(RationalField()); K:=NumberField(x^8 - 80*x^6 + 1432*x^4 - 6720*x^2 + 7056); OK:=MaximalOrder(K); [K!x : x in Basis(OK)]; Factorization(37*OK); Output: Magma V2.10-22 Sat Apr 10 2004 12:11:47 on modular [Seed = 1299517858] ------------------------------------- [ 1, a, 1/4*(a^2 + 2), 1/4*(a^3 + 2*a), 1/32*(a^4 + 4*a^3 + 8*a + 12), 1/32*(a^5 + 12*a), 1/2688*(a^6 + 46*a^4 + 172*a^2 + 1344*a + 1512), 1/56448*(a^7 + 1642*a^5 + 13612*a^3 + 7224*a) ] [ , , , , , , , ] Total time: 2.699 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host pD9590BA5.dip.t-dialin.net. (217.89.11.165) Time: Sat Apr 10 12:12:11 2004 Input: P<[X]> := PolynomialRing(RationalField(), 5); Output: Magma V2.10-22 Sat Apr 10 2004 12:12:08 on modular [Seed = 1165826481] ------------------------------------- Total time: 2.559 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pD9590BA5.dip.t-dialin.net. (217.89.11.165) Time: Sat Apr 10 12:12:51 2004 Input: P<[X]> := PolynomialRing(RationalField(), 5); P; Output: Magma V2.10-22 Sat Apr 10 2004 12:12:48 on modular [Seed = 1566900337] ------------------------------------- Polynomial ring of rank 5 over Rational Field Lexicographical Order Variables: X[1], X[2], X[3], X[4], X[5] Total time: 2.569 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host pD9590BA5.dip.t-dialin.net. (217.89.11.165) Time: Sat Apr 10 12:15:31 2004 Input: P := PolynomialRing(FiniteField(2)); F := Factorization(x^23 - 1); F; Output: Magma V2.10-22 Sat Apr 10 2004 12:15:28 on modular [Seed = 1382682590] ------------------------------------- [ , , ] Total time: 2.519 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host roam129-19.student.harvard.edu. (140.247.129.19) Time: Sat Apr 10 15:10:09 2004 Input: R := PolynomialRing(RationalField()); K:=NumberField([x^2-2,x^2-3,x^2-5,x^2-7] : Abs := true); OK := MaximalOrder(K); Factorization(37*OK); K; Degree(K); OK; Output: Magma V2.10-22 Sat Apr 10 2004 15:10:04 on modular [Seed = 739519118] ------------------------------------- [ , , , , , , , ] Number Field with defining polynomial [ x^2 - 2, x^2 - 3, x^2 - 5, x^2 - 7] over the Rational Field 16 Maximal Order of Equation Order with defining polynomials x^2 - 2, x^2 - 3, x^2 - 5, x^2 - 7 over its ground order Total time: 4.079 seconds, Total memory usage: 2.84MB ************** MAGMA ***************** Host 2(SERVFAIL) (202.113.25.81) Time: Sat Apr 10 22:32:03 2004 Input: SetVerbose("Factorization", true); SetVerbose("MPQS", true); n := 279227912220351686582028455516412641158896790659830288566001946957408; time Factorization(n); Output: Magma V2.10-22 Sat Apr 10 2004 22:31:48 on modular [Seed = 1482733181] ------------------------------------- Integer main factorization (primality of factors will be proved) Effort: 3 Seed: 1 Number: 2792279122203516865820284555164126411588967906598302885660019469574\ 08 Trial Division Number: 2792279122203516865820284555164126411588967906598302885660019469574\ 08 Minimum: 2 Maximum: 10000 Factors found: <2, 5> <3, 2> <61, 1> Time: 0.000 Pollard Rho Trials: 8191 Number: 15894120686495428425661911174659189501303323694207097482126704631 (65 digits) Factor: 1234577 (7 digits) Cofactor: 12874142873628318384079657384399020475274789417109744861703 (59 digits) Time: 0.040 Pollard Rho Trials: 8191 Number: 12874142873628318384079657384399020475274789417109744861703 (59 digits) No factor found Time: 0.060 1 composite number remaining ECM x: 12874142873628318384079657384399020475274789417109744861703 (59 digits) Initial smoothness: 500, steps: 14, step size: 285 Step 1/14; smoothness: 500, digits: 59, elapsed time: 0.000 Step 2/14; smoothness: 785, digits: 59, elapsed time: 0.330 Factor: 51030885799 (11 digits) Cofactor: 252281391397689588517339571105707909275219700897 (48 digits) Time: 0.780 ECM x: 252281391397689588517339571105707909275219700897 (48 digits) Initial smoothness: 785, steps: 10, step size: 100 Step 1/10; smoothness: 785, digits: 48, elapsed time: 0.000 Step 2/10; smoothness: 885, digits: 48, elapsed time: 0.339 Step 3/10; smoothness: 985, digits: 48, elapsed time: 0.689 Step 4/10; smoothness: 1085, digits: 48, elapsed time: 1.059 Step 5/10; smoothness: 1185, digits: 48, elapsed time: 1.449 Step 6/10; smoothness: 1285, digits: 48, elapsed time: 1.879 Step 7/10; smoothness: 1385, digits: 48, elapsed time: 2.329 Step 8/10; smoothness: 1485, digits: 48, elapsed time: 2.799 Step 9/10; smoothness: 1585, digits: 48, elapsed time: 3.299 Step 10/10; smoothness: 1685, digits: 48, elapsed time: 3.829 No factor found Time: 4.379 MPQS MPQS: 252281391397689588517339571105707909275219700897 (48d) 1042 factor base elements created in 0.010 seconds master completed initialization for /tmp/mqs29033: multiplier=1 sievelength=62464, sievesize=124928 one large prime will be used initialized global data in 0.000 seconds master ready to sieve master made own task 0 interrupt sieving: collect, count, try to factor if appropriate cycles: 8 total 100 fulls, 8 cycles, rate 0.018, need 966 more fulls+cycles another 894 fulls and 3872 partials and double partials should suffice 533 relations: 100 fulls, 433 partials, 0 double partials initialized global data in -0.000 seconds master ready to resume sieving with task 0 interrupt sieving: collect, count, try to factor if appropriate cycles: 35 new, 43 total 200 fulls, 43 cycles, rate 0.094, need 831 more fulls+cycles another 602 fulls and 2433 partials and double partials should suffice 1007 relations: 200 fulls, 807 partials, 0 double partials initialized global data in -0.000 seconds master ready to resume sieving with task 0 interrupt sieving: collect, count, try to factor if appropriate cycles: 47 new, 90 total 302 fulls, 90 cycles, rate 0.118, need 682 more fulls+cycles another 463 fulls and 1852 partials and double partials should suffice 1508 relations: 302 fulls, 1206 partials, 0 double partials initialized global data in 0.000 seconds master ready to resume sieving with task 0 interrupt sieving: collect, count, try to factor if appropriate cycles: 57 new, 147 total 402 fulls, 147 cycles, rate 0.148, need 525 more fulls+cycles another 330 fulls and 1310 partials and double partials should suffice 1993 relations: 402 fulls, 1591 partials, 0 double partials initialized global data in -0.000 seconds master ready to resume sieving with task 0 interrupt sieving: collect, count, try to factor if appropriate cycles: 104 new, 251 total 503 fulls, 251 cycles, rate 0.223, need 320 more fulls+cycles another 167 fulls and 684 partials and double partials should suffice 2560 relations: 503 fulls, 2057 partials, 0 double partials initialized global data in 0.000 seconds master ready to resume sieving with task 0 interrupt sieving: collect, count, try to factor if appropriate cycles: 78 new, 329 total 603 fulls, 329 cycles, rate 0.222, need 142 more fulls+cycles another 75 fulls and 300 partials and double partials should suffice 3012 relations: 603 fulls, 2409 partials, 0 double partials initialized global data in 0.000 seconds master ready to resume sieving with task 0 interrupt sieving: collect, count, try to factor if appropriate cycles: 76 new, 405 total 663 fulls, 405 cycles, rate 0.256, need 6 more fulls+cycles another 2 fulls and 11 partials and double partials should suffice 3369 relations: 663 fulls, 2706 partials, 0 double partials initialized global data in 0.000 seconds master ready to resume sieving with task 0 interrupt sieving: collect, count, try to factor if appropriate no need to count cycles sent termination signal to slaves, start factoring attempt made 405 cycle descriptions making combinations: 405 made used partials: 405 combined relations formed collecting from /tmp/mqs29033/f777mas: accepted 405 Lanczos call with seed 12 first scan: 1074 rows, 1028 columns>16, weight 9326 second scan complete, matrix read into memory Removed 59 singletons Removed 3 singletons all 62 singletons removed Got 947 by 1012 matrix with 8779 nonzeros in 0.040 seconds average of 9 nonzero entries per column Lanczos iteration 0, sum = 32, 915 to go Lanczos iterations done at i=31, sum=946, after 0.030 seconds Lanczos complete in 0.030 seconds, 17 dependencies factoring attempt dependency 1 produced 21905534578936053246671913391051 (32d) dependency 2 produced 6756504442031587 (16d) dependency 3 produced 11516787708996547 (17d) dependency 4 failed to produce a factor dependency 5 produced 11516787708996547 (17d) dependency 6 failed to produce a factor dependency 7 produced 6756504442031587 (16d) dependency 8 produced 3242140187559673 (16d) dependency 9 produced 37339040262931001600391513449131 (32d) dependency 10 produced 3242140187559673 (16d) dependency 11 produced 37339040262931001600391513449131 (32d) dependency 12 produced 6756504442031587 (16d) dependency 13 failed to produce a factor dependency 14 produced 77813227313769953941525847930089 (32d) dependency 15 failed to produce a factor dependency 16 produced 77813227313769953941525847930089 (32d) dependency 17 produced 37339040262931001600391513449131 (32d) done at 1065: 3803(1074,2729,0)(3398(669,2729,0)), 5.84(3.21,2.63), 0.002s/r MPQS time: 6.579 Factor 1: 6756504442031587 (16 digits) Factor 2: 3242140187559673 (16 digits) Factor 3: 11516787708996547 (17 digits) Total MPQS Time: 6.689 Total time: 11.960 [ <2, 5>, <3, 2>, <61, 1>, <1234577, 1>, <51030885799, 1>, <3242140187559673, 1>, <6756504442031587, 1>, <11516787708996547, 1> ] Time: 11.970 Total time: 14.549 seconds, Total memory usage: 2.96MB ************** MAGMA ***************** Host 2(SERVFAIL) (202.113.25.81) Time: Sat Apr 10 22:33:50 2004 Input: SetVerbose("Factorization", true); SetVerbose("MPQS", true); n := 1745264755423825474573924809951949066708882319246693921995410289; time Factorization(n); Output: Magma V2.10-22 Sat Apr 10 2004 22:33:28 on modular [Seed = 1115335691] ------------------------------------- Integer main factorization (primality of factors will be proved) Effort: 3 Seed: 1 Number: 1745264755423825474573924809951949066708882319246693921995410289 Trial Division Number: 1745264755423825474573924809951949066708882319246693921995410289 Minimum: 2 Maximum: 10000 No factors found Time: 0.000 Pollard Rho Trials: 8191 Number: 1745264755423825474573924809951949066708882319246693921995410289 (64 digits) No factor found Time: 0.069 1 composite number remaining ECM x: 1745264755423825474573924809951949066708882319246693921995410289 (64 digits) Initial smoothness: 500, steps: 43, step size: 132 Step 1/43; smoothness: 500, digits: 64, elapsed time: 0.000 Step 2/43; smoothness: 632, digits: 64, elapsed time: 0.360 Step 3/43; smoothness: 764, digits: 64, elapsed time: 0.750 Step 4/43; smoothness: 896, digits: 64, elapsed time: 1.200 Step 5/43; smoothness: 1028, digits: 64, elapsed time: 1.680 Step 6/43; smoothness: 1160, digits: 64, elapsed time: 2.230 Step 7/43; smoothness: 1292, digits: 64, elapsed time: 2.790 Step 8/43; smoothness: 1424, digits: 64, elapsed time: 3.410 Step 9/43; smoothness: 1556, digits: 64, elapsed time: 4.060 Step 10/43; smoothness: 1688, digits: 64, elapsed time: 4.770 Step 11/43; smoothness: 1820, digits: 64, elapsed time: 5.530 Step 12/43; smoothness: 1952, digits: 64, elapsed time: 6.330 Step 13/43; smoothness: 2084, digits: 64, elapsed time: 7.190 Step 14/43; smoothness: 2216, digits: 64, elapsed time: 8.100 Step 15/43; smoothness: 2348, digits: 64, elapsed time: 9.050 Step 16/43; smoothness: 2480, digits: 64, elapsed time: 10.050 Step 17/43; smoothness: 2612, digits: 64, elapsed time: 11.130 Step 18/43; smoothness: 2744, digits: 64, elapsed time: 12.220 Step 19/43; smoothness: 2876, digits: 64, elapsed time: 13.360 Step 20/43; smoothness: 3008, digits: 64, elapsed time: 14.560 Step 21/43; smoothness: 3140, digits: 64, elapsed time: 15.800 Step 22/43; smoothness: 3272, digits: 64, elapsed time: 17.080 Step 23/43; smoothness: 3404, digits: 64, elapsed time: 18.370 Step 24/43; smoothness: 3536, digits: 64, elapsed time: 19.750 ************** MAGMA ***************** Host 3(NXDOMAIN) (210.44.181.59) Time: Sun Apr 11 10:14:56 2004 Input: 24 dfdf 23 er Output: Magma V2.10-22 Sun Apr 11 2004 10:14:51 on modular [Seed = 1232100323] ------------------------------------- >> dfdf ^ User error: bad syntax >> er ^ User error: bad syntax Total time: 2.709 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 105-BAR2-X114.libre.retevision.es. (62.82.171.105) Time: Sun Apr 11 14:41:05 2004 Input: K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; Output: Magma V2.10-22 Sun Apr 11 2004 14:41:02 on modular [Seed = 3404929927] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Total time: 2.559 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 105-BAR2-X114.libre.retevision.es. (62.82.171.105) Time: Sun Apr 11 14:41:37 2004 Input: K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); Output: Magma V2.10-22 Sun Apr 11 2004 14:41:34 on modular [Seed = 2995479455] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true Total time: 2.549 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 105-BAR2-X114.libre.retevision.es. (62.82.171.105) Time: Sun Apr 11 14:42:01 2004 Input: K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); Z3:=GF(3); P3:=PolynomialRing(Z3); Z2:=GF(2); P2:=PolynomialRing(Z2); Z5:=GF(5); P5:=PolynomialRing(Z5); f1:=P3![2,2,1]; f1; f2:=P2![1,1,0,0,1]; f2; f3:=P5![3,2,1]; f3; f4:=P3![1,2,1]; f4; IsIrreducible(f1); IsIrreducible(f2); IsIrreducible(f3); IsIrreducible(f4); G9:=ext; G16:=ext; G25:=ext; G9b:=ext; /* L'ultim cas dona error perque el polinomi NO es irreductible*/ /** iv **/ list:=[G25!x : x in [1..5]]; [Order(G25!x):x in list| x ne 0]; primitiu:=PrimitiveElement(G25); /* Hem repetit bastantes vegades aquesta comanda i sempre ens ha donat l'1. Per tant la llista es la [1] Un cos de p^n te p elements primitius*/ /** v **/ polmin:=MinimalPolynomial(primitiu); grau:=Degree(polmin); polmin; grau; MinimalPolynomial(primitiu,Z5); MinimalPolynomial(primitiu,G25); /*Veiem que esta definit sobre Z5*/ Roots(polmin,Z5); Roots(polmin,G25); Output: Magma V2.10-22 Sun Apr 11 2004 14:41:58 on modular [Seed = 3129174975] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 true true true false >> G9b:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 4, 4, 2 ] x^2 + 2*x + 3 2 x^2 + 2*x + 3 $.1 + alpha^13 [] [ , ] Total time: 2.559 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 105-BAR2-X114.libre.retevision.es. (62.82.171.105) Time: Sun Apr 11 14:43:01 2004 Input: K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); Z3:=GF(3); P3:=PolynomialRing(Z3); Z2:=GF(2); P2:=PolynomialRing(Z2); Z5:=GF(5); P5:=PolynomialRing(Z5); f1:=P3![2,2,1]; f1; f2:=P2![1,1,0,0,1]; f2; f3:=P5![3,2,1]; f3; f4:=P3![1,2,1]; f4; IsIrreducible(f1); IsIrreducible(f2); IsIrreducible(f3); IsIrreducible(f4); G9:=ext; G16:=ext; G25:=ext; G9b:=ext; /* L'ultim cas dona error perque el polinomi NO es irreductible*/ /** iv **/ list:=[G25!x : x in [1..5]]; [Order(G25!x):x in list| x ne 0]; primitiu:=PrimitiveElement(G25); /* Hem repetit bastantes vegades aquesta comanda i sempre ens ha donat l'1. Per tant la llista es la [1] Un cos de p^n te p elements primitius*/ /** v **/ polmin:=MinimalPolynomial(primitiu); grau:=Degree(polmin); polmin; grau; MinimalPolynomial(primitiu,Z5); MinimalPolynomial(primitiu,G25); /*Veiem que esta definit sobre Z5*/ Roots(polmin,Z5); Roots(polmin,G25); 1/alpha^3; Output: Magma V2.10-22 Sun Apr 11 2004 14:42:58 on modular [Seed = 2728096611] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 true true true false >> G9b:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 4, 4, 2 ] x^2 + 2*x + 3 2 x^2 + 2*x + 3 $.1 + alpha^13 [] [ , ] alpha^21 Total time: 2.620 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 105-BAR2-X114.libre.retevision.es. (62.82.171.105) Time: Sun Apr 11 14:43:37 2004 Input: K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); Z3:=GF(3); P3:=PolynomialRing(Z3); Z2:=GF(2); P2:=PolynomialRing(Z2); Z5:=GF(5); P5:=PolynomialRing(Z5); f1:=P3![2,2,1]; f1; f2:=P2![1,1,0,0,1]; f2; f3:=P5![3,2,1]; f3; f4:=P3![1,2,1]; f4; IsIrreducible(f1); IsIrreducible(f2); IsIrreducible(f3); IsIrreducible(f4); G9:=ext; G16:=ext; G25:=ext; G9b:=ext; /* L'ultim cas dona error perque el polinomi NO es irreductible*/ /** iv **/ list:=[G25!x : x in [1..5]]; [Order(G25!x):x in list| x ne 0]; primitiu:=PrimitiveElement(G25); /* Hem repetit bastantes vegades aquesta comanda i sempre ens ha donat l'1. Per tant la llista es la [1] Un cos de p^n te p elements primitius*/ /** v **/ polmin:=MinimalPolynomial(primitiu); grau:=Degree(polmin); polmin; grau; MinimalPolynomial(primitiu,Z5); MinimalPolynomial(primitiu,G25); /*Veiem que esta definit sobre Z5*/ Roots(polmin,Z5); Roots(polmin,G25); ra:=1/alpha^3; ra; Output: Magma V2.10-22 Sun Apr 11 2004 14:43:35 on modular [Seed = 2844817421] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 true true true false >> G9b:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 4, 4, 2 ] x^2 + 2*x + 3 2 x^2 + 2*x + 3 $.1 + alpha^13 [] [ , ] alpha^21 Total time: 2.559 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 105-BAR2-X114.libre.retevision.es. (62.82.171.105) Time: Sun Apr 11 14:43:57 2004 Input: K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); Z3:=GF(3); P3:=PolynomialRing(Z3); Z2:=GF(2); P2:=PolynomialRing(Z2); Z5:=GF(5); P5:=PolynomialRing(Z5); f1:=P3![2,2,1]; f1; f2:=P2![1,1,0,0,1]; f2; f3:=P5![3,2,1]; f3; f4:=P3![1,2,1]; f4; IsIrreducible(f1); IsIrreducible(f2); IsIrreducible(f3); IsIrreducible(f4); G9:=ext; G16:=ext; G25:=ext; G9b:=ext; /* L'ultim cas dona error perque el polinomi NO es irreductible*/ /** iv **/ list:=[G25!x : x in [1..5]]; [Order(G25!x):x in list| x ne 0]; primitiu:=PrimitiveElement(G25); /* Hem repetit bastantes vegades aquesta comanda i sempre ens ha donat l'1. Per tant la llista es la [1] Un cos de p^n te p elements primitius*/ /** v **/ polmin:=MinimalPolynomial(primitiu); grau:=Degree(polmin); polmin; grau; MinimalPolynomial(primitiu,Z5); MinimalPolynomial(primitiu,G25); /*Veiem que esta definit sobre Z5*/ Roots(polmin,Z5); Roots(polmin,G25); /*ra:=1/alpha^3; ra; */ Output: Magma V2.10-22 Sun Apr 11 2004 14:43:54 on modular [Seed = 2443722760] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 true true true false >> G9b:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 4, 4, 2 ] x^2 + 2*x + 3 2 x^2 + 2*x + 3 $.1 + alpha^13 [] [ , ] Total time: 2.550 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 105-BAR2-X114.libre.retevision.es. (62.82.171.105) Time: Sun Apr 11 14:45:06 2004 Input: K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); Z3:=GF(3); P3:=PolynomialRing(Z3); Z2:=GF(2); P2:=PolynomialRing(Z2); Z5:=GF(5); P5:=PolynomialRing(Z5); f1:=P3![2,2,1]; f1; f2:=P2![1,1,0,0,1]; f2; f3:=P5![3,2,1]; f3; f4:=P3![1,2,1]; f4; IsIrreducible(f1); IsIrreducible(f2); IsIrreducible(f3); IsIrreducible(f4); G9:=ext; G16:=ext; G25:=ext; G9b:=ext; /* L'ultim cas dona error perque el polinomi NO es irreductible*/ /** iv **/ list:=[G25!x : x in [1..5]]; [Order(G25!x):x in list| x ne 0]; primitiu:=PrimitiveElement(G25); /* Hem repetit bastantes vegades aquesta comanda i sempre ens ha donat l'1. Per tant la llista es la [1] Un cos de p^n te p elements primitius*/ /** v **/ polmin:=MinimalPolynomial(primitiu); grau:=Degree(polmin); polmin; grau; MinimalPolynomial(primitiu,Z5); MinimalPolynomial(primitiu,G25); /*Veiem que esta definit sobre Z5*/ Roots(polmin,Z5); Roots(polmin,G25); vi:=1/alpha^3-alpha^5+(1/alpha+2)*alpha^6; Output: Magma V2.10-22 Sun Apr 11 2004 14:45:04 on modular [Seed = 2644791262] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 true true true false >> G9b:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 4, 4, 2 ] x^2 + 2*x + 3 2 x^2 + 2*x + 3 $.1 + alpha^13 [] [ , ] Total time: 2.560 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 105-BAR2-X114.libre.retevision.es. (62.82.171.105) Time: Sun Apr 11 14:45:22 2004 Input: K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); Z3:=GF(3); P3:=PolynomialRing(Z3); Z2:=GF(2); P2:=PolynomialRing(Z2); Z5:=GF(5); P5:=PolynomialRing(Z5); f1:=P3![2,2,1]; f1; f2:=P2![1,1,0,0,1]; f2; f3:=P5![3,2,1]; f3; f4:=P3![1,2,1]; f4; IsIrreducible(f1); IsIrreducible(f2); IsIrreducible(f3); IsIrreducible(f4); G9:=ext; G16:=ext; G25:=ext; G9b:=ext; /* L'ultim cas dona error perque el polinomi NO es irreductible*/ /** iv **/ list:=[G25!x : x in [1..5]]; [Order(G25!x):x in list| x ne 0]; primitiu:=PrimitiveElement(G25); /* Hem repetit bastantes vegades aquesta comanda i sempre ens ha donat l'1. Per tant la llista es la [1] Un cos de p^n te p elements primitius*/ /** v **/ polmin:=MinimalPolynomial(primitiu); grau:=Degree(polmin); polmin; grau; MinimalPolynomial(primitiu,Z5); MinimalPolynomial(primitiu,G25); /*Veiem que esta definit sobre Z5*/ Roots(polmin,Z5); Roots(polmin,G25); vi:=1/alpha^3-alpha^5+(1/alpha+2)*alpha^6; vi; Output: Magma V2.10-22 Sun Apr 11 2004 14:45:20 on modular [Seed = 2227001015] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 true true true false >> G9b:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 4, 4, 2 ] x^2 + 2*x + 3 2 x^2 + 2*x + 3 $.1 + alpha^13 [] [ , ] alpha^14 Total time: 2.509 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 105-BAR2-X114.libre.retevision.es. (62.82.171.105) Time: Sun Apr 11 14:49:16 2004 Input: K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); Z3:=GF(3); P3:=PolynomialRing(Z3); Z2:=GF(2); P2:=PolynomialRing(Z2); Z5:=GF(5); P5:=PolynomialRing(Z5); f1:=P3![2,2,1]; f1; f2:=P2![1,1,0,0,1]; f2; f3:=P5![3,2,1]; f3; f4:=P3![1,2,1]; f4; IsIrreducible(f1); IsIrreducible(f2); IsIrreducible(f3); IsIrreducible(f4); G9:=ext; G16:=ext; G25:=ext; G9b:=ext; /* L'ultim cas dona error perque el polinomi NO es irreductible*/ /** iv **/ list:=[G25!x : x in [1..5]]; [Order(G25!x):x in list| x ne 0]; primitiu:=PrimitiveElement(G25); /* Hem repetit bastantes vegades aquesta comanda i sempre ens ha donat l'1. Per tant la llista es la [1] Un cos de p^n te p elements primitius*/ /** v **/ polmin:=MinimalPolynomial(primitiu); grau:=Degree(polmin); polmin; grau; MinimalPolynomial(primitiu,Z5); MinimalPolynomial(primitiu,G25); /*Veiem que esta definit sobre Z5*/ Roots(polmin,Z5); Roots(polmin,G25); vi:=1/alpha^3-alpha^5+(1/alpha+2)*alpha^6; vi; IsInvertible(vi); Output: Magma V2.10-22 Sun Apr 11 2004 14:49:13 on modular [Seed = 1984931115] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 true true true false >> G9b:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 4, 4, 2 ] x^2 + 2*x + 3 2 x^2 + 2*x + 3 $.1 + alpha^13 [] [ , ] alpha^14 true alpha^10 Total time: 2.550 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.36.42.proxycache.rima-tde.net. (80.58.36.42) Time: Sun Apr 11 17:17:44 2004 Input: G2:=GF(2); G3:=GF(3); G5:=GF(5); ElementsG2:=[i : i in G2 ]; ElementsG3:=[i : i in G3 ]; ElementsG5:=[i : i in G5 ]; Output: Magma V2.10-22 Sun Apr 11 2004 17:17:41 on modular [Seed = 873316788] ------------------------------------- Total time: 2.639 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 80.58.36.42.proxycache.rima-tde.net. (80.58.36.42) Time: Sun Apr 11 17:18:16 2004 Input: G2:=GF(2); G3:=GF(3); G5:=GF(5); ElementsG2:=[i : i in G2 ]; ElementsG3:=[i : i in G3 ]; ElementsG5:=[i : i in G5 ]; ElementsG2; ElementsG3; ElementsG5; Output: Magma V2.10-22 Sun Apr 11 2004 17:18:13 on modular [Seed = 1007012444] ------------------------------------- [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 2, 3, 4 ] Total time: 2.490 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 80.58.36.42.proxycache.rima-tde.net. (80.58.36.42) Time: Sun Apr 11 17:19:30 2004 Input: G2:=GF(2); G4:=GF(4); G8:=GF(8); G16:=GF(16); [i : i in G2 ]; [i : i in G4 ]; [i : i in G8 ]; [i: i in G16]; Output: Magma V2.10-22 Sun Apr 11 2004 17:19:28 on modular [Seed = 605934129] ------------------------------------- [ 0, 1 ] [ 1, G4.1, G4.1^2, 0 ] [ 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 ] [ 1, G16.1, G16.1^2, G16.1^3, G16.1^4, G16.1^5, G16.1^6, G16.1^7, G16.1^8, G16.1^9, G16.1^10, G16.1^11, G16.1^12, G16.1^13, G16.1^14, 0 ] Total time: 2.559 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 80.58.36.42.proxycache.rima-tde.net. (80.58.36.42) Time: Sun Apr 11 17:26:08 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); IsFinite(p2); Output: Magma V2.10-22 Sun Apr 11 2004 17:26:06 on modular [Seed = 488958598] ------------------------------------- false Total time: 2.599 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 80.58.36.42.proxycache.rima-tde.net. (80.58.36.42) Time: Sun Apr 11 17:32:34 2004 Input: G5:=GF(5); G25:=ext; [Order(b^i) : i in [0..23]] Output: Magma V2.10-22 Sun Apr 11 2004 17:32:32 on modular [Seed = 3756402394] ------------------------------------- >> G25:=ext; ^ User error: Identifier 'z' has not been declared or assigned >> [Order(b^i) : i in [0..23]]; ^ User error: Identifier 'b' has not been declared or assigned Total time: 2.549 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 80.58.36.42.proxycache.rima-tde.net. (80.58.36.42) Time: Sun Apr 11 17:33:20 2004 Input: G5:=GF(5); p5:=PolynomialRing(GF(5)); G25:=ext; [Order(b^i) : i in [0..23]] Output: Magma V2.10-22 Sun Apr 11 2004 17:33:17 on modular [Seed = 3355328047] ------------------------------------- [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] Total time: 2.489 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 80.58.36.42.proxycache.rima-tde.net. (80.58.36.42) Time: Sun Apr 11 17:34:06 2004 Input: G5:=GF(5); p5:=PolynomialRing(GF(5)); G25:=ext; [b^i : i in [0..23] | IsPrimitive(b^i)] #[b^i : i in [0..23] | IsPrimitive(b^i)]; Output: Magma V2.10-22 Sun Apr 11 2004 17:34:04 on modular [Seed = 3489019510] ------------------------------------- >> #[b^i : i in [0..23] | IsPrimitive(b^i)];; ^ User error: bad syntax Total time: 2.500 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 80.58.36.42.proxycache.rima-tde.net. (80.58.36.42) Time: Sun Apr 11 17:34:33 2004 Input: G5:=GF(5); p5:=PolynomialRing(GF(5)); G25:=ext; [b^i : i in [0..23] | IsPrimitive(b^i)]; #[b^i : i in [0..23] | IsPrimitive(b^i)]; Output: Magma V2.10-22 Sun Apr 11 2004 17:34:31 on modular [Seed = 3079556645] ------------------------------------- [ b, b^5, b^7, b^11, b^13, b^17, b^19, b^23 ] 8 Total time: 2.499 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 80.58.36.42.proxycache.rima-tde.net. (80.58.36.42) Time: Sun Apr 11 17:35:16 2004 Input: G5:=GF(5); p5:=PolynomialRing(GF(5)); G25:=ext; MinimalPolynomial(b); Output: Magma V2.10-22 Sun Apr 11 2004 17:35:13 on modular [Seed = 2778488769] ------------------------------------- z^2 + 2*z + 3 Total time: 2.500 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 80.58.36.42.proxycache.rima-tde.net. (80.58.36.42) Time: Sun Apr 11 17:36:13 2004 Input: G5:=GF(5); p5:=PolynomialRing(GF(5)); G25:=ext; Roots(MinimalPolynomial(b), G5); Roots(MinimalPolynomial(b), G25); Output: Magma V2.10-22 Sun Apr 11 2004 17:36:11 on modular [Seed = 2912180115] ------------------------------------- [] [ , ] Total time: 2.590 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 80.58.36.42.proxycache.rima-tde.net. (80.58.36.42) Time: Sun Apr 11 17:37:23 2004 Input: G5:=GF(5); p5:=PolynomialRing(GF(5)); G25:=ext; 2*b^(-3) - b^5+ (b^6)/(b + 2); b^17; Output: Magma V2.10-22 Sun Apr 11 2004 17:37:20 on modular [Seed = 2511105904] ------------------------------------- b^8 b^17 Total time: 2.489 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 80.58.36.42.proxycache.rima-tde.net. (80.58.36.42) Time: Sun Apr 11 17:38:00 2004 Input: G5:=GF(5); p5:=PolynomialRing(GF(5)); G25:=ext; 2*b^(-3) - b^5+ (b^6)/(b + 2); 1/(b^8); Output: Magma V2.10-22 Sun Apr 11 2004 17:37:57 on modular [Seed = 2644797278] ------------------------------------- b^8 b^16 Total time: 2.510 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 80.58.36.42.proxycache.rima-tde.net. (80.58.36.42) Time: Sun Apr 11 17:38:54 2004 Input: G5:=GF(5); p5:=PolynomialRing(GF(5)); G25:=ext; [b^i : i in [0..23] | IsInvertible(b^i)] Output: Magma V2.10-22 Sun Apr 11 2004 17:38:52 on modular [Seed = 2243723036] ------------------------------------- [ 1, b, b^2, b^3, b^4, b^5, 3, b^7, b^8, b^9, b^10, b^11, 4, b^13, b^14, b^15, b^16, b^17, 2, b^19, b^20, b^21, b^22, b^23 ] Total time: 2.530 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 80.58.36.42.proxycache.rima-tde.net. (80.58.36.42) Time: Sun Apr 11 17:40:11 2004 Input: G5:=GF(5); p5:=PolynomialRing(GF(5)); G25:=ext; [ : i in [0..23] ]; Output: Magma V2.10-22 Sun Apr 11 2004 17:40:09 on modular [Seed = 1934264380] ------------------------------------- [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , ] Total time: 2.539 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 80.58.36.42.proxycache.rima-tde.net. (80.58.36.42) Time: Sun Apr 11 17:41:32 2004 Input: G5:=GF(5); p5:=PolynomialRing(GF(5)); G25:=ext; p2:=PolynomialRing(G25); IsFinite(p2); Output: Magma V2.10-22 Sun Apr 11 2004 17:41:30 on modular [Seed = 2067955847] ------------------------------------- false Total time: 2.579 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 80.58.36.42.proxycache.rima-tde.net. (80.58.36.42) Time: Sun Apr 11 17:45:59 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=y^2+z*y+z*x^2; pol1:=1+y*x; pol2:=pol1+pol; pol2; pol3:=pol1*pol; pol3; Output: Magma V2.10-22 Sun Apr 11 2004 17:45:56 on modular [Seed = 1834258831] ------------------------------------- y^3 + 3*y^2 + 1 y^5 + 2*y^4 + y^3 + 2*y^2 Total time: 2.509 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.36.42.proxycache.rima-tde.net. (80.58.36.42) Time: Sun Apr 11 17:46:51 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=y^2+z*y+z*x^2; pol1:=1+y*x; pol2:=pol1+pol; pol3:=pol1*pol; pol4:=pol/pol1; pol4; pol5:=(pol)mod(pol1); pol5; Output: Magma V2.10-22 Sun Apr 11 2004 17:46:48 on modular [Seed = 1399500781] ------------------------------------- y^2/(y + 3) 4*y + 3 Total time: 2.560 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.36.42.proxycache.rima-tde.net. (80.58.36.42) Time: Sun Apr 11 17:47:48 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=y^2+z*y+z*x^2; pol1:=1+y*x; pol2:=pol1+pol; pol3:=pol1*pol; pol4:=pol/pol1; pol5:=(pol)mod(pol1); pol6:=GCD(pol1,pol); pol6; pol7:=LCM(pol1,pol); pol7; Output: Magma V2.10-22 Sun Apr 11 2004 17:47:45 on modular [Seed = 1482794287] ------------------------------------- y + 2 y^4 + y^2 Total time: 2.539 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.36.42.proxycache.rima-tde.net. (80.58.36.42) Time: Sun Apr 11 17:48:23 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=y^2+z*y+z*x^2; pol1:=1+y*x; pol2:=pol1+pol; pol3:=pol1*pol; pol4:=pol/pol1; pol5:=(pol)mod(pol1); pol6:=GCD(pol1,pol); pol7:=LCM(pol1,pol); a, b, c :=XGCD(pol1,pol); pol8:=b*pol1 + c*pol; pol8; b; c; Output: Magma V2.10-22 Sun Apr 11 2004 17:48:21 on modular [Seed = 1081720083] ------------------------------------- y + 2 y + 2 4 Total time: 2.509 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.36.42.proxycache.rima-tde.net. (80.58.36.42) Time: Sun Apr 11 17:49:50 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=1/alpha^4-(x/(alpha^3))+(alpha^5)*(x^2)+(alpha^11)*(x^3); pol; Evaluate(pol,6); Output: Magma V2.10-22 Sun Apr 11 2004 17:49:47 on modular [Seed = 1215411525] ------------------------------------- (alpha^18 + alpha^11 + 4*alpha^2 + 1)/alpha^4 2 Total time: 2.559 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.36.42.proxycache.rima-tde.net. (80.58.36.42) Time: Sun Apr 11 17:51:22 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=1/alpha^4-(x/(alpha^3))+(alpha^5)*(x^2); pol; Evaluate(pol,6); Output: Magma V2.10-22 Sun Apr 11 2004 17:51:19 on modular [Seed = 956351640] ------------------------------------- (alpha^11 + 4*alpha^2 + 1)/alpha^4 1 Total time: 2.559 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.36.42.proxycache.rima-tde.net. (80.58.36.42) Time: Sun Apr 11 17:54:41 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=1/alpha^4-(x/(alpha^3))+(alpha^5)*(x^2); pol; Factorization(pol); Evaluate(pol,6); Output: Magma V2.10-22 Sun Apr 11 2004 17:54:39 on modular [Seed = 555278280] ------------------------------------- (alpha^11 + 4*alpha^2 + 1)/alpha^4 >> Factorization(pol); ^ Runtime error in 'Factorization': Bad argument types Argument types given: FldFunRatUElt 1 Total time: 2.549 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.36.42.proxycache.rima-tde.net. (80.58.36.42) Time: Sun Apr 11 17:55:54 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=1/alpha^4-(x/(alpha^3))+(alpha^5)*(x^2); pol; Terms(pol); Evaluate(pol,6); Output: Magma V2.10-22 Sun Apr 11 2004 17:55:51 on modular [Seed = 321580418] ------------------------------------- (alpha^11 + 4*alpha^2 + 1)/alpha^4 >> Terms(pol); ^ Runtime error in 'Terms': Bad argument types Argument types given: FldFunRatUElt 1 Total time: 2.499 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.36.42.proxycache.rima-tde.net. (80.58.36.42) Time: Sun Apr 11 17:56:42 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=1/alpha^4-(x/(alpha^3))+(alpha^5)*(x^2); pol; Roots(pol); Evaluate(pol,6); Output: Magma V2.10-22 Sun Apr 11 2004 17:56:40 on modular [Seed = 455271541] ------------------------------------- (alpha^11 + 4*alpha^2 + 1)/alpha^4 >> Roots(pol); ^ Runtime error in 'Roots': Bad argument types Argument types given: FldFunRatUElt 1 Total time: 2.489 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.36.42.proxycache.rima-tde.net. (80.58.36.42) Time: Sun Apr 11 17:57:16 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=1/alpha^4-(x/(alpha^3))+(alpha^5)*(x^2); pol; Roots(pol,G25); Evaluate(pol,6); Output: Magma V2.10-22 Sun Apr 11 2004 17:57:14 on modular [Seed = 54197327] ------------------------------------- (alpha^11 + 4*alpha^2 + 1)/alpha^4 >> Roots(pol,G25); ^ Runtime error in 'Roots': Bad argument types Argument types given: FldFunRatUElt, FldFin 1 Total time: 2.490 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.36.42.proxycache.rima-tde.net. (80.58.36.42) Time: Sun Apr 11 17:58:51 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=1/alpha^4-(x/(alpha^3))+(alpha^5)*(x^2); pol; Factorization(pol,G25); Evaluate(pol,6); Output: Magma V2.10-22 Sun Apr 11 2004 17:58:48 on modular [Seed = 4157474840] ------------------------------------- (alpha^11 + 4*alpha^2 + 1)/alpha^4 >> Factorization(pol,G25); ^ Runtime error in 'Factorization': Bad argument types Argument types given: FldFunRatUElt, FldFin 1 Total time: 2.549 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.36.42.proxycache.rima-tde.net. (80.58.36.42) Time: Sun Apr 11 17:59:22 2004 Input: G5:=GF(5); p1:=PolynomialRing(G5); G25:=ext; p2:=PolynomialRing(G25); p3:=PolynomialRing(Integers()); pol:=1/alpha^4-(x/(alpha^3))+(alpha^5)*(x^2); pol; Factorization(pol); Evaluate(pol,6); Output: Magma V2.10-22 Sun Apr 11 2004 17:59:19 on modular [Seed = 4291166270] ------------------------------------- (alpha^11 + 4*alpha^2 + 1)/alpha^4 >> Factorization(pol); ^ Runtime error in 'Factorization': Bad argument types Argument types given: FldFunRatUElt 1 Total time: 2.549 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 72-236-ADSL.red.retevision.es. (80.224.236.72) Time: Sun Apr 11 18:20:28 2004 Input: /*******************************************************************/ Z2:=GF(2); Z3:=GF(3); Z5:=GF(5); {i:i in Z2}; {i:i in Z3}; {i:i in Z5}; /*******************************************************************/ P2:=PolynomialRing(Z2); p:=1+x+x^4; IsIrreducible(p); G16

:= ext< Z2 | p >; P3:=PolynomialRing(Z3); q:=2+2*x+x^2; IsIrreducible(q); G9:= ext< Z3 | q >; qq:=1+2*x+x^2; IsIrreducible(qq); /*G9b:= ext< Z3 | qq >;*//*NO funciona perque qq no es irreductible*/ P5:=PolynomialRing(Z5); r:=3+2*x+x^2; IsIrreducible(r); G25

:= ext< Z5 | r >; /*******************************************************************/ [Order(a) :a in G25 | not a eq 0 ]; Output: Magma V2.10-22 Sun Apr 11 2004 18:20:25 on modular [Seed = 2661751361] ------------------------------------- { 0, 1 } { 0, 1, 2 } { 0, 1, 2, 3, 4 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] Total time: 2.539 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 72-236-ADSL.red.retevision.es. (80.224.236.72) Time: Sun Apr 11 18:21:42 2004 Input: /*******************************************************************/ Z2:=GF(2); Z3:=GF(3); Z5:=GF(5); {i:i in Z2}; {i:i in Z3}; {i:i in Z5}; /*******************************************************************/ P2:=PolynomialRing(Z2); p:=1+x+x^4; IsIrreducible(p); G16

:= ext< Z2 | p >; P3:=PolynomialRing(Z3); q:=2+2*x+x^2; IsIrreducible(q); G9:= ext< Z3 | q >; qq:=1+2*x+x^2; IsIrreducible(qq); /*G9b:= ext< Z3 | qq >;*//*NO funciona perque qq no es irreductible*/ P5:=PolynomialRing(Z5); r:=3+2*x+x^2; IsIrreducible(r); G25

:= ext< Z5 | r >; /*******************************************************************/ [Order(a) :a in G25 | not a eq 0 ]; primitiusG25 := [a: a in G25 | IsPrimitive(a)]; [a: a in G25 | IsPrimitive(a)]; #[a: a in G25 | IsPrimitive(a)]; Output: Magma V2.10-22 Sun Apr 11 2004 18:21:40 on modular [Seed = 2193294848] ------------------------------------- { 0, 1 } { 0, 1, 2 } { 0, 1, 2, 3, 4 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ p, p^5, p^7, p^11, p^13, p^17, p^19, p^23 ] 8 Total time: 2.549 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 72-236-ADSL.red.retevision.es. (80.224.236.72) Time: Sun Apr 11 18:23:18 2004 Input: /*******************************************************************/ Z2:=GF(2); Z3:=GF(3); Z5:=GF(5); {i:i in Z2}; {i:i in Z3}; {i:i in Z5}; /*******************************************************************/ P2:=PolynomialRing(Z2); p:=1+x+x^4; IsIrreducible(p); G16

:= ext< Z2 | p >; P3:=PolynomialRing(Z3); q:=2+2*x+x^2; IsIrreducible(q); G9:= ext< Z3 | q >; qq:=1+2*x+x^2; IsIrreducible(qq); /*G9b:= ext< Z3 | qq >;*//*NO funciona perque qq no es irreductible*/ P5:=PolynomialRing(Z5); r:=3+2*x+x^2; IsIrreducible(r); G25

:= ext< Z5 | r >; /*******************************************************************/ [Order(a) :a in G25 | not a eq 0 ]; primitiusG25 := [a: a in G25 | IsPrimitive(a)]; [a: a in G25 | IsPrimitive(a)]; #[a: a in G25 | IsPrimitive(a)]; /*******************************************************************/ pm:=MinimalPolynomial(a); /* el grau dun element es el grau del seu polinomi minim */ /* el polinomi minim esta definit dintre de Zp */ Roots(pm,Z5); Roots(pm,G25); Output: Magma V2.10-22 Sun Apr 11 2004 18:23:16 on modular [Seed = 2343702185] ------------------------------------- { 0, 1 } { 0, 1, 2 } { 0, 1, 2, 3, 4 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ p, p^5, p^7, p^11, p^13, p^17, p^19, p^23 ] 8 >> pm:=MinimalPolynomial(a); ^ User error: Identifier 'a' has not been declared or assigned >> Roots(pm,Z5); ^ User error: Identifier 'pm' has not been declared or assigned >> Roots(pm,G25);; ^ User error: Identifier 'pm' has not been declared or assigned Total time: 2.519 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 72-236-ADSL.red.retevision.es. (80.224.236.72) Time: Sun Apr 11 18:24:46 2004 Input: /*******************************************************************/ Z2:=GF(2); Z3:=GF(3); Z5:=GF(5); {i:i in Z2}; {i:i in Z3}; {i:i in Z5}; /*******************************************************************/ P2:=PolynomialRing(Z2); p:=1+x+x^4; IsIrreducible(p); G16

:= ext< Z2 | p >; P3:=PolynomialRing(Z3); q:=2+2*x+x^2; IsIrreducible(q); G9:= ext< Z3 | q >; qq:=1+2*x+x^2; IsIrreducible(qq); /*G9b:= ext< Z3 | qq >;*//*NO funciona perque qq no es irreductible*/ P5:=PolynomialRing(Z5); r:=3+2*x+x^2; IsIrreducible(r); G25

:= ext< Z5 | r >; /*******************************************************************/ [Order(a) :a in G25 | not a eq 0 ]; primitiusG25 := [a: a in G25 | IsPrimitive(a)]; [a: a in G25 | IsPrimitive(a)]; #[a: a in G25 | IsPrimitive(a)]; /*******************************************************************/ pm:=MinimalPolynomial(p); /* el grau dun element es el grau del seu polinomi minim */ /* el polinomi minim esta definit dintre de Zp */ Roots(pm,Z5); Roots(pm,G25); Output: Magma V2.10-22 Sun Apr 11 2004 18:24:43 on modular [Seed = 1917581225] ------------------------------------- { 0, 1 } { 0, 1, 2 } { 0, 1, 2, 3, 4 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ p, p^5, p^7, p^11, p^13, p^17, p^19, p^23 ] 8 [] [ , ] Total time: 2.500 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 72-236-ADSL.red.retevision.es. (80.224.236.72) Time: Sun Apr 11 18:26:43 2004 Input: /*******************************************************************/ Z2:=GF(2); Z3:=GF(3); Z5:=GF(5); {i:i in Z2}; {i:i in Z3}; {i:i in Z5}; /*******************************************************************/ P2:=PolynomialRing(Z2); p:=1+x+x^4; IsIrreducible(p); G16

:= ext< Z2 | p >; P3:=PolynomialRing(Z3); q:=2+2*x+x^2; IsIrreducible(q); G9:= ext< Z3 | q >; qq:=1+2*x+x^2; IsIrreducible(qq); /*G9b:= ext< Z3 | qq >;*//*NO funciona perque qq no es irreductible*/ P5:=PolynomialRing(Z5); r:=3+2*x+x^2; IsIrreducible(r); G25

:= ext< Z5 | r >; /*******************************************************************/ [Order(a) :a in G25 | not a eq 0 ]; primitiusG25 := [a: a in G25 | IsPrimitive(a)]; [a: a in G25 | IsPrimitive(a)]; #[a: a in G25 | IsPrimitive(a)]; /*******************************************************************/ pm:=MinimalPolynomial(p); /* el grau dun element es el grau del seu polinomi minim */ /* el polinomi minim esta definit dintre de Zp */ Roots(pm,Z5); Roots(pm,G25); calculeu:=2*a^(-3)-a^5+((a^6)/(a+2)); IsInvertible(calculeu); Output: Magma V2.10-22 Sun Apr 11 2004 18:26:40 on modular [Seed = 1700586290] ------------------------------------- { 0, 1 } { 0, 1, 2 } { 0, 1, 2, 3, 4 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ p, p^5, p^7, p^11, p^13, p^17, p^19, p^23 ] 8 [] [ , ] >> calculeu:=2*a^(-3)-a^5+((a^6)/(a+2)); ^ User error: Identifier 'a' has not been declared or assigned >> IsInvertible(calculeu);; ^ User error: Identifier 'calculeu' has not been declared or assigned Total time: 2.510 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 72-236-ADSL.red.retevision.es. (80.224.236.72) Time: Sun Apr 11 18:27:06 2004 Input: /*******************************************************************/ Z2:=GF(2); Z3:=GF(3); Z5:=GF(5); {i:i in Z2}; {i:i in Z3}; {i:i in Z5}; /*******************************************************************/ P2:=PolynomialRing(Z2); p:=1+x+x^4; IsIrreducible(p); G16

:= ext< Z2 | p >; P3:=PolynomialRing(Z3); q:=2+2*x+x^2; IsIrreducible(q); G9:= ext< Z3 | q >; qq:=1+2*x+x^2; IsIrreducible(qq); /*G9b:= ext< Z3 | qq >;*//*NO funciona perque qq no es irreductible*/ P5:=PolynomialRing(Z5); r:=3+2*x+x^2; IsIrreducible(r); G25

:= ext< Z5 | r >; /*******************************************************************/ [Order(a) :a in G25 | not a eq 0 ]; primitiusG25 := [a: a in G25 | IsPrimitive(a)]; [a: a in G25 | IsPrimitive(a)]; #[a: a in G25 | IsPrimitive(a)]; /*******************************************************************/ pm:=MinimalPolynomial(p); /* el grau dun element es el grau del seu polinomi minim */ /* el polinomi minim esta definit dintre de Zp */ Roots(pm,Z5); Roots(pm,G25); calculeu:=2*p^(-3)-p^5+((p^6)/(p+2)); IsInvertible(calculeu); Output: Magma V2.10-22 Sun Apr 11 2004 18:27:03 on modular [Seed = 1834281773] ------------------------------------- { 0, 1 } { 0, 1, 2 } { 0, 1, 2, 3, 4 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ p, p^5, p^7, p^11, p^13, p^17, p^19, p^23 ] 8 [] [ , ] true p^16 Total time: 2.550 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 72-236-ADSL.red.retevision.es. (80.224.236.72) Time: Sun Apr 11 18:27:44 2004 Input: /*******************************************************************/ Z2:=GF(2); Z3:=GF(3); Z5:=GF(5); {i:i in Z2}; {i:i in Z3}; {i:i in Z5}; /*******************************************************************/ P2:=PolynomialRing(Z2); p:=1+x+x^4; IsIrreducible(p); G16

:= ext< Z2 | p >; P3:=PolynomialRing(Z3); q:=2+2*x+x^2; IsIrreducible(q); G9:= ext< Z3 | q >; qq:=1+2*x+x^2; IsIrreducible(qq); /*G9b:= ext< Z3 | qq >;*//*NO funciona perque qq no es irreductible*/ P5:=PolynomialRing(Z5); r:=3+2*x+x^2; IsIrreducible(r); G25

:= ext< Z5 | r >; /*******************************************************************/ [Order(a) :a in G25 | not a eq 0 ]; primitiusG25 := [a: a in G25 | IsPrimitive(a)]; [a: a in G25 | IsPrimitive(a)]; #[a: a in G25 | IsPrimitive(a)]; /*******************************************************************/ pm:=MinimalPolynomial(p); /* el grau dun element es el grau del seu polinomi minim */ /* el polinomi minim esta definit dintre de Zp */ Roots(pm,Z5); Roots(pm,G25); calculeu:=2*p^(-3)-p^5+((p^6)/(p+2)); IsInvertible(calculeu); calculeu; Output: Magma V2.10-22 Sun Apr 11 2004 18:27:41 on modular [Seed = 1433195391] ------------------------------------- { 0, 1 } { 0, 1, 2 } { 0, 1, 2, 3, 4 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ p, p^5, p^7, p^11, p^13, p^17, p^19, p^23 ] 8 [] [ , ] true p^16 p^8 Total time: 2.520 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 72-236-ADSL.red.retevision.es. (80.224.236.72) Time: Sun Apr 11 18:30:14 2004 Input: /*******************************************************************/ Z2:=GF(2); Z3:=GF(3); Z5:=GF(5); {i:i in Z2}; {i:i in Z3}; {i:i in Z5}; /*******************************************************************/ P2:=PolynomialRing(Z2); p:=1+x+x^4; IsIrreducible(p); G16

:= ext< Z2 | p >; P3:=PolynomialRing(Z3); q:=2+2*x+x^2; IsIrreducible(q); G9:= ext< Z3 | q >; qq:=1+2*x+x^2; IsIrreducible(qq); /*G9b:= ext< Z3 | qq >;*//*NO funciona perque qq no es irreductible*/ P5:=PolynomialRing(Z5); r:=3+2*x+x^2; IsIrreducible(r); G25

:= ext< Z5 | r >; /*******************************************************************/ [Order(a) :a in G25 | not a eq 0 ]; primitiusG25 := [a: a in G25 | IsPrimitive(a)]; [a: a in G25 | IsPrimitive(a)]; #[a: a in G25 | IsPrimitive(a)]; /*******************************************************************/ pm:=MinimalPolynomial(p); /* el grau dun element es el grau del seu polinomi minim */ /* el polinomi minim esta definit dintre de Zp */ Roots(pm,Z5); Roots(pm,G25); calculeu:=2*p^(-3)-p^5+((p^6)/(p+2)); IsInvertible(calculeu); calculeu; taula25:=[ : i in [0..23]]; taula16:=[ : i in [0..14]]; taula25; taula16; Output: Magma V2.10-22 Sun Apr 11 2004 18:30:12 on modular [Seed = 1149092551] ------------------------------------- { 0, 1 } { 0, 1, 2 } { 0, 1, 2, 3, 4 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ p, p^5, p^7, p^11, p^13, p^17, p^19, p^23 ] 8 [] [ , ] true p^16 p^8 >> taula25:=[ : i in [0..23]]; ^ User error: Identifier 'a' has not been declared or assigned >> taula16:=[ : i in [0..14]]; ^ User error: Identifier 'b' has not been declared or assigned >> taula25; ^ User error: Identifier 'taula25' has not been declared or assigned >> taula16;; ^ User error: Identifier 'taula16' has not been declared or assigned Total time: 2.539 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 72-236-ADSL.red.retevision.es. (80.224.236.72) Time: Sun Apr 11 18:31:26 2004 Input: /*******************************************************************/ Z2:=GF(2); Z3:=GF(3); Z5:=GF(5); {i:i in Z2}; {i:i in Z3}; {i:i in Z5}; /*******************************************************************/ P2:=PolynomialRing(Z2); p:=1+x+x^4; IsIrreducible(p); G16

:= ext< Z2 | p >; P3:=PolynomialRing(Z3); q:=2+2*x+x^2; IsIrreducible(q); G9:= ext< Z3 | q >; qq:=1+2*x+x^2; IsIrreducible(qq); /*G9b:= ext< Z3 | qq >;*//*NO funciona perque qq no es irreductible*/ P5:=PolynomialRing(Z5); r:=3+2*x+x^2; IsIrreducible(r); G25

:= ext< Z5 | r >; /*******************************************************************/ [Order(a) :a in G25 | not a eq 0 ]; primitiusG25 := [a: a in G25 | IsPrimitive(a)]; [a: a in G25 | IsPrimitive(a)]; #[a: a in G25 | IsPrimitive(a)]; /*******************************************************************/ pm:=MinimalPolynomial(p); /* el grau dun element es el grau del seu polinomi minim */ /* el polinomi minim esta definit dintre de Zp */ Roots(pm,Z5); Roots(pm,G25); calculeu:=2*p^(-3)-p^5+((p^6)/(p+2)); IsInvertible(calculeu); calculeu; taula25:=[ : i in [0..23]]; taula16:=[ : i in [0..14]]; taula25; taula16; Output: Magma V2.10-22 Sun Apr 11 2004 18:31:24 on modular [Seed = 1282788103] ------------------------------------- { 0, 1 } { 0, 1, 2 } { 0, 1, 2, 3, 4 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ p, p^5, p^7, p^11, p^13, p^17, p^19, p^23 ] 8 [] [ , ] true p^16 p^8 [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , ] [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , ] Total time: 2.559 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 72-236-ADSL.red.retevision.es. (80.224.236.72) Time: Sun Apr 11 18:33:44 2004 Input: /*******************************************************************/ Z2:=GF(2); Z3:=GF(3); Z5:=GF(5); {i:i in Z2}; {i:i in Z3}; {i:i in Z5}; /*******************************************************************/ P2:=PolynomialRing(Z2); p:=1+x+x^4; IsIrreducible(p); G16

:= ext< Z2 | p >; P3:=PolynomialRing(Z3); q:=2+2*x+x^2; IsIrreducible(q); G9:= ext< Z3 | q >; qq:=1+2*x+x^2; IsIrreducible(qq); /*G9b:= ext< Z3 | qq >;*//*NO funciona perque qq no es irreductible*/ P5:=PolynomialRing(Z5); r:=3+2*x+x^2; IsIrreducible(r); G25

:= ext< Z5 | r >; /*******************************************************************/ [Order(a) :a in G25 | not a eq 0 ]; primitiusG25 := [a: a in G25 | IsPrimitive(a)]; [a: a in G25 | IsPrimitive(a)]; #[a: a in G25 | IsPrimitive(a)]; /*******************************************************************/ pm:=MinimalPolynomial(p); /* el grau dun element es el grau del seu polinomi minim */ /* el polinomi minim esta definit dintre de Zp */ Roots(pm,Z5); Roots(pm,G25); calculeu:=2*p^(-3)-p^5+((p^6)/(p+2)); IsInvertible(calculeu); calculeu; taula25:=[ : i in [0..23]]; taula16:=[ : i in [0..14]]; taula25; taula16; G2 := GF(2); G4 := GF(4); G8 := GF(8); G166 := GF(16); {i:i in G2}; {i:i in G4}; {i:i in G8}; {i:i in G166}; G2 subset G4; G2 subset G8; G2 subset G16; G4 subset G8; G4 subset G16; G8 subset G16; Output: Magma V2.10-22 Sun Apr 11 2004 18:33:41 on modular [Seed = 856339585] ------------------------------------- { 0, 1 } { 0, 1, 2 } { 0, 1, 2, 3, 4 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ p, p^5, p^7, p^11, p^13, p^17, p^19, p^23 ] 8 [] [ , ] true p^16 p^8 [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , ] [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , ] { 0, 1 } { 1, G4.1, G4.1^2, 0 } { 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 } { 1, G166.1, G166.1^2, G166.1^3, G166.1^4, G166.1^5, G166.1^6, G166.1^7, G166.1^8, G166.1^9, G166.1^10, G166.1^11, G166.1^12, G166.1^13, G166.1^14, 0 } true true true false >> G4 subset G16; ^ Runtime error in 'subset': Arguments have no covering field >> G8 subset G16;; ^ Runtime error in 'subset': Arguments have no covering field Total time: 2.559 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 72-236-ADSL.red.retevision.es. (80.224.236.72) Time: Sun Apr 11 18:34:16 2004 Input: /*******************************************************************/ Z2:=GF(2); Z3:=GF(3); Z5:=GF(5); {i:i in Z2}; {i:i in Z3}; {i:i in Z5}; /*******************************************************************/ P2:=PolynomialRing(Z2); p:=1+x+x^4; IsIrreducible(p); G16

:= ext< Z2 | p >; P3:=PolynomialRing(Z3); q:=2+2*x+x^2; IsIrreducible(q); G9:= ext< Z3 | q >; qq:=1+2*x+x^2; IsIrreducible(qq); /*G9b:= ext< Z3 | qq >;*//*NO funciona perque qq no es irreductible*/ P5:=PolynomialRing(Z5); r:=3+2*x+x^2; IsIrreducible(r); G25

:= ext< Z5 | r >; /*******************************************************************/ [Order(a) :a in G25 | not a eq 0 ]; primitiusG25 := [a: a in G25 | IsPrimitive(a)]; [a: a in G25 | IsPrimitive(a)]; #[a: a in G25 | IsPrimitive(a)]; /*******************************************************************/ pm:=MinimalPolynomial(p); /* el grau dun element es el grau del seu polinomi minim */ /* el polinomi minim esta definit dintre de Zp */ Roots(pm,Z5); Roots(pm,G25); calculeu:=2*p^(-3)-p^5+((p^6)/(p+2)); IsInvertible(calculeu); calculeu; taula25:=[ : i in [0..23]]; taula16:=[ : i in [0..14]]; taula25; taula16; G2 := GF(2); G4 := GF(4); G8 := GF(8); G166 := GF(16); {i:i in G2}; {i:i in G4}; {i:i in G8}; {i:i in G166}; G2 subset G4; G2 subset G8; G2 subset G166; G4 subset G8; G4 subset G166; G8 subset G166; Output: Magma V2.10-22 Sun Apr 11 2004 18:34:14 on modular [Seed = 990035114] ------------------------------------- { 0, 1 } { 0, 1, 2 } { 0, 1, 2, 3, 4 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ p, p^5, p^7, p^11, p^13, p^17, p^19, p^23 ] 8 [] [ , ] true p^16 p^8 [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , ] [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , ] { 0, 1 } { 1, G4.1, G4.1^2, 0 } { 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 } { 1, G166.1, G166.1^2, G166.1^3, G166.1^4, G166.1^5, G166.1^6, G166.1^7, G166.1^8, G166.1^9, G166.1^10, G166.1^11, G166.1^12, G166.1^13, G166.1^14, 0 } true true true false true false Total time: 2.659 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 72-236-ADSL.red.retevision.es. (80.224.236.72) Time: Sun Apr 11 18:38:51 2004 Input: /*******************************************************************/ Z2:=GF(2); Z3:=GF(3); Z5:=GF(5); {i:i in Z2}; {i:i in Z3}; {i:i in Z5}; /*******************************************************************/ P2:=PolynomialRing(Z2); p:=1+x+x^4; IsIrreducible(p); G16

:= ext< Z2 | p >; P3:=PolynomialRing(Z3); q:=2+2*x+x^2; IsIrreducible(q); G9:= ext< Z3 | q >; qq:=1+2*x+x^2; IsIrreducible(qq); /*G9b:= ext< Z3 | qq >;*//*NO funciona perque qq no es irreductible*/ P5:=PolynomialRing(Z5); r:=3+2*x+x^2; IsIrreducible(r); G25

:= ext< Z5 | r >; /*******************************************************************/ [Order(a) :a in G25 | not a eq 0 ]; primitiusG25 := [a: a in G25 | IsPrimitive(a)]; [a: a in G25 | IsPrimitive(a)]; #[a: a in G25 | IsPrimitive(a)]; /*******************************************************************/ pm:=MinimalPolynomial(p); /* el grau dun element es el grau del seu polinomi minim */ /* el polinomi minim esta definit dintre de Zp */ Roots(pm,Z5); Roots(pm,G25); calculeu:=2*p^(-3)-p^5+((p^6)/(p+2)); IsInvertible(calculeu); calculeu; taula25:=[ : i in [0..23]]; taula16:=[ : i in [0..14]]; taula25; taula16; G2 := GF(2); G4 := GF(4); G8 := GF(8); G166 := GF(16); {i:i in G2}; {i:i in G4}; {i:i in G8}; {i:i in G166}; G2 subset G4; G2 subset G8; G2 subset G166; G4 subset G8; G4 subset G166; G8 subset G166; /*******************************************************************/ G25x:=PolynomialRing(G25); IsFinite(G25x); /* false */ /* Efectivament no es finit, pq estem definint un anell de polynomis sobre un camp de coeficients finits pero els polynomis poden tenir el grau que vulguin */ /* ii */ /*******************************************************************/ alpha := primitiusG25[1]; beta := primitiusG5[1]; p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; /* iii */ /*******************************************************************/ suma := p1 + p2; producte := p1 * p2; suma; producte; Output: Magma V2.10-22 Sun Apr 11 2004 18:38:48 on modular [Seed = 756327842] ------------------------------------- { 0, 1 } { 0, 1, 2 } { 0, 1, 2, 3, 4 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ p, p^5, p^7, p^11, p^13, p^17, p^19, p^23 ] 8 [] [ , ] true p^16 p^8 [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , ] [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , ] { 0, 1 } { 1, G4.1, G4.1^2, 0 } { 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 } { 1, G166.1, G166.1^2, G166.1^3, G166.1^4, G166.1^5, G166.1^6, G166.1^7, G166.1^8, G166.1^9, G166.1^10, G166.1^11, G166.1^12, G166.1^13, G166.1^14, 0 } true true true false true false false >> beta := primitiusG5[1]; ^ User error: Identifier 'primitiusG5' has not been declared or assigned >> p1 := alpha^2 + alpha*x + beta*x^2; ^ User error: Identifier 'beta' has not been declared or assigned >> suma := p1 + p2; ^ User error: Identifier 'p1' has not been declared or assigned >> producte := p1 * p2; ^ User error: Identifier 'p1' has not been declared or assigned >> suma; ^ User error: Identifier 'suma' has not been declared or assigned >> producte; ^ User error: Identifier 'producte' has not been declared or assigned Total time: 2.520 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 72-236-ADSL.red.retevision.es. (80.224.236.72) Time: Sun Apr 11 18:40:11 2004 Input: /*******************************************************************/ Z2:=GF(2); Z3:=GF(3); Z5:=GF(5); {i:i in Z2}; {i:i in Z3}; {i:i in Z5}; /*******************************************************************/ P2:=PolynomialRing(Z2); p:=1+x+x^4; IsIrreducible(p); G16

:= ext< Z2 | p >; P3:=PolynomialRing(Z3); q:=2+2*x+x^2; IsIrreducible(q); G9:= ext< Z3 | q >; qq:=1+2*x+x^2; IsIrreducible(qq); /*G9b:= ext< Z3 | qq >;*//*NO funciona perque qq no es irreductible*/ P5:=PolynomialRing(Z5); r:=3+2*x+x^2; IsIrreducible(r); G25

:= ext< Z5 | r >; /*******************************************************************/ [Order(a) :a in G25 | not a eq 0 ]; primitiusG25 := [a: a in G25 | IsPrimitive(a)]; [a: a in G25 | IsPrimitive(a)]; #[a: a in G25 | IsPrimitive(a)]; /*******************************************************************/ pm:=MinimalPolynomial(p); /* el grau dun element es el grau del seu polinomi minim */ /* el polinomi minim esta definit dintre de Zp */ Roots(pm,Z5); Roots(pm,G25); calculeu:=2*p^(-3)-p^5+((p^6)/(p+2)); IsInvertible(calculeu); calculeu; taula25:=[ : i in [0..23]]; taula16:=[ : i in [0..14]]; taula25; taula16; G2 := GF(2); G4 := GF(4); G8 := GF(8); G166 := GF(16); {i:i in G2}; {i:i in G4}; {i:i in G8}; {i:i in G166}; G2 subset G4; G2 subset G8; G2 subset G166; G4 subset G8; G4 subset G166; G8 subset G166; /*******************************************************************/ G25x:=PolynomialRing(G25); IsFinite(G25x); /* false */ /* Efectivament no es finit, pq estem definint un anell de polynomis sobre un camp de coeficients finits pero els polynomis poden tenir el grau que vulguin */ /* ii */ /*******************************************************************/ alpha := PrimitiveElement(G25); beta := PrimitiveElement(G5); p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; /* iii */ /*******************************************************************/ suma := p1 + p2; producte := p1 * p2; suma; producte; Output: Magma V2.10-22 Sun Apr 11 2004 18:40:08 on modular [Seed = 505911072] ------------------------------------- { 0, 1 } { 0, 1, 2 } { 0, 1, 2, 3, 4 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ p, p^5, p^7, p^11, p^13, p^17, p^19, p^23 ] 8 [] [ , ] true p^16 p^8 [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , ] [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , ] { 0, 1 } { 1, G4.1, G4.1^2, 0 } { 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 } { 1, G166.1, G166.1^2, G166.1^3, G166.1^4, G166.1^5, G166.1^6, G166.1^7, G166.1^8, G166.1^9, G166.1^10, G166.1^11, G166.1^12, G166.1^13, G166.1^14, 0 } true true true false true false false >> beta := PrimitiveElement(G5); ^ User error: Identifier 'G5' has not been declared or assigned >> p1 := alpha^2 + alpha*x + beta*x^2; ^ User error: Identifier 'beta' has not been declared or assigned >> suma := p1 + p2; ^ User error: Identifier 'p1' has not been declared or assigned >> producte := p1 * p2; ^ User error: Identifier 'p1' has not been declared or assigned >> suma; ^ User error: Identifier 'suma' has not been declared or assigned >> producte; ^ User error: Identifier 'producte' has not been declared or assigned Total time: 2.559 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 72-236-ADSL.red.retevision.es. (80.224.236.72) Time: Sun Apr 11 18:40:46 2004 Input: /*******************************************************************/ Z2:=GF(2); Z3:=GF(3); Z5:=GF(5); {i:i in Z2}; {i:i in Z3}; {i:i in Z5}; /*******************************************************************/ P2:=PolynomialRing(Z2); p:=1+x+x^4; IsIrreducible(p); G16

:= ext< Z2 | p >; P3:=PolynomialRing(Z3); q:=2+2*x+x^2; IsIrreducible(q); G9:= ext< Z3 | q >; qq:=1+2*x+x^2; IsIrreducible(qq); /*G9b:= ext< Z3 | qq >;*//*NO funciona perque qq no es irreductible*/ P5:=PolynomialRing(Z5); r:=3+2*x+x^2; IsIrreducible(r); G25

:= ext< Z5 | r >; /*******************************************************************/ [Order(a) :a in G25 | not a eq 0 ]; primitiusG25 := [a: a in G25 | IsPrimitive(a)]; [a: a in G25 | IsPrimitive(a)]; #[a: a in G25 | IsPrimitive(a)]; /*******************************************************************/ pm:=MinimalPolynomial(p); /* el grau dun element es el grau del seu polinomi minim */ /* el polinomi minim esta definit dintre de Zp */ Roots(pm,Z5); Roots(pm,G25); calculeu:=2*p^(-3)-p^5+((p^6)/(p+2)); IsInvertible(calculeu); calculeu; taula25:=[ : i in [0..23]]; taula16:=[ : i in [0..14]]; taula25; taula16; G2 := GF(2); G4 := GF(4); G8 := GF(8); G166 := GF(16); {i:i in G2}; {i:i in G4}; {i:i in G8}; {i:i in G166}; G2 subset G4; G2 subset G8; G2 subset G166; G4 subset G8; G4 subset G166; G8 subset G166; /*******************************************************************/ G25x:=PolynomialRing(G25); IsFinite(G25x); /* false */ /* Efectivament no es finit, pq estem definint un anell de polynomis sobre un camp de coeficients finits pero els polynomis poden tenir el grau que vulguin */ /* ii */ /*******************************************************************/ alpha := PrimitiveElement(G25); beta := PrimitiveElement(Z5); p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; /* iii */ /*******************************************************************/ suma := p1 + p2; producte := p1 * p2; suma; producte; Output: Magma V2.10-22 Sun Apr 11 2004 18:40:43 on modular [Seed = 87854105] ------------------------------------- { 0, 1 } { 0, 1, 2 } { 0, 1, 2, 3, 4 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ p, p^5, p^7, p^11, p^13, p^17, p^19, p^23 ] 8 [] [ , ] true p^16 p^8 [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , ] [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , ] { 0, 1 } { 1, G4.1, G4.1^2, 0 } { 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 } { 1, G166.1, G166.1^2, G166.1^3, G166.1^4, G166.1^5, G166.1^6, G166.1^7, G166.1^8, G166.1^9, G166.1^10, G166.1^11, G166.1^12, G166.1^13, G166.1^14, 0 } true true true false true false false 2*x^2 + p^19*x + p^9 p^19*x^3 + p^22*x^2 + p^10*x + p^2 Total time: 2.569 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 72-236-ADSL.red.retevision.es. (80.224.236.72) Time: Sun Apr 11 18:42:53 2004 Input: /*******************************************************************/ Z2:=GF(2); Z3:=GF(3); Z5:=GF(5); {i:i in Z2}; {i:i in Z3}; {i:i in Z5}; /*******************************************************************/ P2:=PolynomialRing(Z2); p:=1+x+x^4; IsIrreducible(p); G16

:= ext< Z2 | p >; P3:=PolynomialRing(Z3); q:=2+2*x+x^2; IsIrreducible(q); G9:= ext< Z3 | q >; qq:=1+2*x+x^2; IsIrreducible(qq); /*G9b:= ext< Z3 | qq >;*//*NO funciona perque qq no es irreductible*/ P5:=PolynomialRing(Z5); r:=3+2*x+x^2; IsIrreducible(r); G25

:= ext< Z5 | r >; /*******************************************************************/ [Order(a) :a in G25 | not a eq 0 ]; primitiusG25 := [a: a in G25 | IsPrimitive(a)]; [a: a in G25 | IsPrimitive(a)]; #[a: a in G25 | IsPrimitive(a)]; /*******************************************************************/ pm:=MinimalPolynomial(p); /* el grau dun element es el grau del seu polinomi minim */ /* el polinomi minim esta definit dintre de Zp */ Roots(pm,Z5); Roots(pm,G25); calculeu:=2*p^(-3)-p^5+((p^6)/(p+2)); IsInvertible(calculeu); calculeu; taula25:=[ : i in [0..23]]; taula16:=[ : i in [0..14]]; taula25; taula16; G2 := GF(2); G4 := GF(4); G8 := GF(8); G166 := GF(16); {i:i in G2}; {i:i in G4}; {i:i in G8}; {i:i in G166}; G2 subset G4; G2 subset G8; G2 subset G166; G4 subset G8; G4 subset G166; G8 subset G166; /*******************************************************************/ G25x:=PolynomialRing(G25); IsFinite(G25x); /* false */ /* Efectivament no es finit, pq estem definint un anell de polynomis sobre un camp de coeficients finits pero els polynomis poden tenir el grau que vulguin */ /* ii */ /*******************************************************************/ alpha := PrimitiveElement(G25); beta := PrimitiveElement(Z5); p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; /* iii */ /*******************************************************************/ suma := p1 + p2; producte := p1 * p2; suma; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; Output: Magma V2.10-22 Sun Apr 11 2004 18:42:50 on modular [Seed = 221545616] ------------------------------------- { 0, 1 } { 0, 1, 2 } { 0, 1, 2, 3, 4 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ p, p^5, p^7, p^11, p^13, p^17, p^19, p^23 ] 8 [] [ , ] true p^16 p^8 [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , ] [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , ] { 0, 1 } { 1, G4.1, G4.1^2, 0 } { 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 } { 1, G166.1, G166.1^2, G166.1^3, G166.1^4, G166.1^5, G166.1^6, G166.1^7, G166.1^8, G166.1^9, G166.1^10, G166.1^11, G166.1^12, G166.1^13, G166.1^14, 0 } true true true false true false false 2*x^2 + p^19*x + p^9 p^19*x^3 + p^22*x^2 + p^10*x + p^2 p^17*x + p^5 p^15 Total time: 2.519 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 72-236-ADSL.red.retevision.es. (80.224.236.72) Time: Sun Apr 11 18:45:12 2004 Input: /*******************************************************************/ Z2:=GF(2); Z3:=GF(3); Z5:=GF(5); {i:i in Z2}; {i:i in Z3}; {i:i in Z5}; /*******************************************************************/ P2:=PolynomialRing(Z2); p:=1+x+x^4; IsIrreducible(p); G16

:= ext< Z2 | p >; P3:=PolynomialRing(Z3); q:=2+2*x+x^2; IsIrreducible(q); G9:= ext< Z3 | q >; qq:=1+2*x+x^2; IsIrreducible(qq); /*G9b:= ext< Z3 | qq >;*//*NO funciona perque qq no es irreductible*/ P5:=PolynomialRing(Z5); r:=3+2*x+x^2; IsIrreducible(r); G25

:= ext< Z5 | r >; /*******************************************************************/ [Order(a) :a in G25 | not a eq 0 ]; primitiusG25 := [a: a in G25 | IsPrimitive(a)]; [a: a in G25 | IsPrimitive(a)]; #[a: a in G25 | IsPrimitive(a)]; /*******************************************************************/ pm:=MinimalPolynomial(p); /* el grau dun element es el grau del seu polinomi minim */ /* el polinomi minim esta definit dintre de Zp */ Roots(pm,Z5); Roots(pm,G25); calculeu:=2*p^(-3)-p^5+((p^6)/(p+2)); IsInvertible(calculeu); calculeu; taula25:=[ : i in [0..23]]; taula16:=[ : i in [0..14]]; taula25; taula16; G2 := GF(2); G4 := GF(4); G8 := GF(8); G166 := GF(16); {i:i in G2}; {i:i in G4}; {i:i in G8}; {i:i in G166}; G2 subset G4; G2 subset G8; G2 subset G166; G4 subset G8; G4 subset G166; G8 subset G166; /*******************************************************************/ G25x:=PolynomialRing(G25); IsFinite(G25x); /* false */ /* Efectivament no es finit, pq estem definint un anell de polynomis sobre un camp de coeficients finits pero els polynomis poden tenir el grau que vulguin */ /* ii */ /*******************************************************************/ alpha := PrimitiveElement(G25); beta := PrimitiveElement(Z5); p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; /* iii */ /*******************************************************************/ suma := p1 + p2; producte := p1 * p2; suma; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; mcm := LCM(p1,p2); mcm; mcd := GCD(p1,p2); mcd; Output: Magma V2.10-22 Sun Apr 11 2004 18:45:09 on modular [Seed = 4291196413] ------------------------------------- { 0, 1 } { 0, 1, 2 } { 0, 1, 2, 3, 4 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ p, p^5, p^7, p^11, p^13, p^17, p^19, p^23 ] 8 [] [ , ] true p^16 p^8 [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , ] [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , ] { 0, 1 } { 1, G4.1, G4.1^2, 0 } { 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 } { 1, G166.1, G166.1^2, G166.1^3, G166.1^4, G166.1^5, G166.1^6, G166.1^7, G166.1^8, G166.1^9, G166.1^10, G166.1^11, G166.1^12, G166.1^13, G166.1^14, 0 } true true true false true false false 2*x^2 + p^19*x + p^9 p^19*x^3 + p^22*x^2 + p^10*x + p^2 p^17*x + p^5 p^15 x^3 + p^3*x^2 + p^15*x + p^7 1 Total time: 2.549 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 72-236-ADSL.red.retevision.es. (80.224.236.72) Time: Sun Apr 11 18:48:37 2004 Input: /*******************************************************************/ Z2:=GF(2); Z3:=GF(3); Z5:=GF(5); {i:i in Z2}; {i:i in Z3}; {i:i in Z5}; /*******************************************************************/ P2:=PolynomialRing(Z2); p:=1+x+x^4; IsIrreducible(p); G16

:= ext< Z2 | p >; P3:=PolynomialRing(Z3); q:=2+2*x+x^2; IsIrreducible(q); G9:= ext< Z3 | q >; qq:=1+2*x+x^2; IsIrreducible(qq); /*G9b:= ext< Z3 | qq >;*//*NO funciona perque qq no es irreductible*/ P5:=PolynomialRing(Z5); r:=3+2*x+x^2; IsIrreducible(r); G25

:= ext< Z5 | r >; /*******************************************************************/ [Order(a) :a in G25 | not a eq 0 ]; primitiusG25 := [a: a in G25 | IsPrimitive(a)]; [a: a in G25 | IsPrimitive(a)]; #[a: a in G25 | IsPrimitive(a)]; /*******************************************************************/ pm:=MinimalPolynomial(p); /* el grau dun element es el grau del seu polinomi minim */ /* el polinomi minim esta definit dintre de Zp */ Roots(pm,Z5); Roots(pm,G25); calculeu:=2*p^(-3)-p^5+((p^6)/(p+2)); IsInvertible(calculeu); calculeu; taula25:=[ : i in [0..23]]; taula16:=[ : i in [0..14]]; taula25; taula16; G2 := GF(2); G4 := GF(4); G8 := GF(8); G166 := GF(16); {i:i in G2}; {i:i in G4}; {i:i in G8}; {i:i in G166}; G2 subset G4; G2 subset G8; G2 subset G166; G4 subset G8; G4 subset G166; G8 subset G166; /*******************************************************************/ G25x:=PolynomialRing(G25); IsFinite(G25x); /* false */ /* Efectivament no es finit, pq estem definint un anell de polynomis sobre un camp de coeficients finits pero els polynomis poden tenir el grau que vulguin */ /* ii */ /*******************************************************************/ alpha := PrimitiveElement(G25); beta := PrimitiveElement(Z5); p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; /* iii */ /*******************************************************************/ suma := p1 + p2; producte := p1 * p2; suma; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; mcm := LCM(p1,p2); mcm; mcd := GCD(p1,p2); mcd; p3:= (1/alpha^4) - ((alpha^3)*x) + (alpha^5)*(x^2) + (alpha^11)*(x^3); f:=Factorization(p3); f; Evaluate(p3,f[1]); Output: Magma V2.10-22 Sun Apr 11 2004 18:48:34 on modular [Seed = 3839717329] ------------------------------------- { 0, 1 } { 0, 1, 2 } { 0, 1, 2, 3, 4 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ p, p^5, p^7, p^11, p^13, p^17, p^19, p^23 ] 8 [] [ , ] true p^16 p^8 [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , ] [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , ] { 0, 1 } { 1, G4.1, G4.1^2, 0 } { 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 } { 1, G166.1, G166.1^2, G166.1^3, G166.1^4, G166.1^5, G166.1^6, G166.1^7, G166.1^8, G166.1^9, G166.1^10, G166.1^11, G166.1^12, G166.1^13, G166.1^14, 0 } true true true false true false false 2*x^2 + p^19*x + p^9 p^19*x^3 + p^22*x^2 + p^10*x + p^2 p^17*x + p^5 p^15 x^3 + p^3*x^2 + p^15*x + p^7 1 [ , ] >> Evaluate(p3,f[1]);; ^ Runtime error in 'Evaluate': Bad argument types Argument types given: RngUPolElt, Tup Total time: 2.539 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 72-236-ADSL.red.retevision.es. (80.224.236.72) Time: Sun Apr 11 18:50:34 2004 Input: /*******************************************************************/ Z2:=GF(2); Z3:=GF(3); Z5:=GF(5); {i:i in Z2}; {i:i in Z3}; {i:i in Z5}; /*******************************************************************/ P2:=PolynomialRing(Z2); p:=1+x+x^4; IsIrreducible(p); G16

:= ext< Z2 | p >; P3:=PolynomialRing(Z3); q:=2+2*x+x^2; IsIrreducible(q); G9:= ext< Z3 | q >; qq:=1+2*x+x^2; IsIrreducible(qq); /*G9b:= ext< Z3 | qq >;*//*NO funciona perque qq no es irreductible*/ P5:=PolynomialRing(Z5); r:=3+2*x+x^2; IsIrreducible(r); G25

:= ext< Z5 | r >; /*******************************************************************/ [Order(a) :a in G25 | not a eq 0 ]; primitiusG25 := [a: a in G25 | IsPrimitive(a)]; [a: a in G25 | IsPrimitive(a)]; #[a: a in G25 | IsPrimitive(a)]; /*******************************************************************/ pm:=MinimalPolynomial(p); /* el grau dun element es el grau del seu polinomi minim */ /* el polinomi minim esta definit dintre de Zp */ Roots(pm,Z5); Roots(pm,G25); calculeu:=2*p^(-3)-p^5+((p^6)/(p+2)); IsInvertible(calculeu); calculeu; taula25:=[ : i in [0..23]]; taula16:=[ : i in [0..14]]; taula25; taula16; G2 := GF(2); G4 := GF(4); G8 := GF(8); G166 := GF(16); {i:i in G2}; {i:i in G4}; {i:i in G8}; {i:i in G166}; G2 subset G4; G2 subset G8; G2 subset G166; G4 subset G8; G4 subset G166; G8 subset G166; /*******************************************************************/ G25x:=PolynomialRing(G25); IsFinite(G25x); /* false */ /* Efectivament no es finit, pq estem definint un anell de polynomis sobre un camp de coeficients finits pero els polynomis poden tenir el grau que vulguin */ /* ii */ /*******************************************************************/ alpha := PrimitiveElement(G25); beta := PrimitiveElement(Z5); p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; /* iii */ /*******************************************************************/ suma := p1 + p2; producte := p1 * p2; suma; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; mcm := LCM(p1,p2); mcm; mcd := GCD(p1,p2); mcd; p3:= (1/alpha^4) - ((alpha^3)*x) + (alpha^5)*(x^2) + (alpha^11)*(x^3); f:=Factorization(p3); f; Evaluate(p3, -p^16); Output: Magma V2.10-22 Sun Apr 11 2004 18:50:31 on modular [Seed = 3572326164] ------------------------------------- { 0, 1 } { 0, 1, 2 } { 0, 1, 2, 3, 4 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ p, p^5, p^7, p^11, p^13, p^17, p^19, p^23 ] 8 [] [ , ] true p^16 p^8 [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , ] [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , ] { 0, 1 } { 1, G4.1, G4.1^2, 0 } { 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 } { 1, G166.1, G166.1^2, G166.1^3, G166.1^4, G166.1^5, G166.1^6, G166.1^7, G166.1^8, G166.1^9, G166.1^10, G166.1^11, G166.1^12, G166.1^13, G166.1^14, 0 } true true true false true false false 2*x^2 + p^19*x + p^9 p^19*x^3 + p^22*x^2 + p^10*x + p^2 p^17*x + p^5 p^15 x^3 + p^3*x^2 + p^15*x + p^7 1 [ , ] 0 Total time: 2.559 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 72-236-ADSL.red.retevision.es. (80.224.236.72) Time: Sun Apr 11 18:52:59 2004 Input: /*******************************************************************/ Z2:=GF(2); Z3:=GF(3); Z5:=GF(5); {i:i in Z2}; {i:i in Z3}; {i:i in Z5}; /*******************************************************************/ P2:=PolynomialRing(Z2); p:=1+x+x^4; IsIrreducible(p); G16

:= ext< Z2 | p >; P3:=PolynomialRing(Z3); q:=2+2*x+x^2; IsIrreducible(q); G9:= ext< Z3 | q >; qq:=1+2*x+x^2; IsIrreducible(qq); /*G9b:= ext< Z3 | qq >;*//*NO funciona perque qq no es irreductible*/ P5:=PolynomialRing(Z5); r:=3+2*x+x^2; IsIrreducible(r); G25

:= ext< Z5 | r >; /*******************************************************************/ [Order(a) :a in G25 | not a eq 0 ]; primitiusG25 := [a: a in G25 | IsPrimitive(a)]; [a: a in G25 | IsPrimitive(a)]; #[a: a in G25 | IsPrimitive(a)]; /*******************************************************************/ pm:=MinimalPolynomial(p); /* el grau dun element es el grau del seu polinomi minim */ /* el polinomi minim esta definit dintre de Zp */ Roots(pm,Z5); Roots(pm,G25); calculeu:=2*p^(-3)-p^5+((p^6)/(p+2)); IsInvertible(calculeu); calculeu; taula25:=[ : i in [0..23]]; taula16:=[ : i in [0..14]]; taula25; taula16; G2 := GF(2); G4 := GF(4); G8 := GF(8); G166 := GF(16); {i:i in G2}; {i:i in G4}; {i:i in G8}; {i:i in G166}; G2 subset G4; G2 subset G8; G2 subset G166; G4 subset G8; G4 subset G166; G8 subset G166; /*******************************************************************/ G25x:=PolynomialRing(G25); IsFinite(G25x); /* false */ /* Efectivament no es finit, pq estem definint un anell de polynomis sobre un camp de coeficients finits pero els polynomis poden tenir el grau que vulguin */ /* ii */ /*******************************************************************/ alpha := PrimitiveElement(G25); beta := PrimitiveElement(Z5); p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; /* iii */ /*******************************************************************/ suma := p1 + p2; producte := p1 * p2; suma; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; mcm := LCM(p1,p2); mcm; mcd := GCD(p1,p2); mcd; p3:= (1/alpha^4) - ((alpha^3)*x) + (alpha^5)*(x^2) + (alpha^11)*(x^3); f:=Factorization(p3); f; Evaluate(p3, f(1)); Output: Magma V2.10-22 Sun Apr 11 2004 18:52:56 on modular [Seed = 3689043940] ------------------------------------- { 0, 1 } { 0, 1, 2 } { 0, 1, 2, 3, 4 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ p, p^5, p^7, p^11, p^13, p^17, p^19, p^23 ] 8 [] [ , ] true p^16 p^8 [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , ] [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , ] { 0, 1 } { 1, G4.1, G4.1^2, 0 } { 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 } { 1, G166.1, G166.1^2, G166.1^3, G166.1^4, G166.1^5, G166.1^6, G166.1^7, G166.1^8, G166.1^9, G166.1^10, G166.1^11, G166.1^12, G166.1^13, G166.1^14, 0 } true true true false true false false 2*x^2 + p^19*x + p^9 p^19*x^3 + p^22*x^2 + p^10*x + p^2 p^17*x + p^5 p^15 x^3 + p^3*x^2 + p^15*x + p^7 1 [ , ] >> Evaluate(p3, f(1));; ^ Runtime error: Bad argument types Argument types given: RngIntElt, SeqEnum[Tup] Total time: 2.519 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 72-236-ADSL.red.retevision.es. (80.224.236.72) Time: Sun Apr 11 18:53:31 2004 Input: /*******************************************************************/ Z2:=GF(2); Z3:=GF(3); Z5:=GF(5); {i:i in Z2}; {i:i in Z3}; {i:i in Z5}; /*******************************************************************/ P2:=PolynomialRing(Z2); p:=1+x+x^4; IsIrreducible(p); G16

:= ext< Z2 | p >; P3:=PolynomialRing(Z3); q:=2+2*x+x^2; IsIrreducible(q); G9:= ext< Z3 | q >; qq:=1+2*x+x^2; IsIrreducible(qq); /*G9b:= ext< Z3 | qq >;*//*NO funciona perque qq no es irreductible*/ P5:=PolynomialRing(Z5); r:=3+2*x+x^2; IsIrreducible(r); G25

:= ext< Z5 | r >; /*******************************************************************/ [Order(a) :a in G25 | not a eq 0 ]; primitiusG25 := [a: a in G25 | IsPrimitive(a)]; [a: a in G25 | IsPrimitive(a)]; #[a: a in G25 | IsPrimitive(a)]; /*******************************************************************/ pm:=MinimalPolynomial(p); /* el grau dun element es el grau del seu polinomi minim */ /* el polinomi minim esta definit dintre de Zp */ Roots(pm,Z5); Roots(pm,G25); calculeu:=2*p^(-3)-p^5+((p^6)/(p+2)); IsInvertible(calculeu); calculeu; taula25:=[ : i in [0..23]]; taula16:=[ : i in [0..14]]; taula25; taula16; G2 := GF(2); G4 := GF(4); G8 := GF(8); G166 := GF(16); {i:i in G2}; {i:i in G4}; {i:i in G8}; {i:i in G166}; G2 subset G4; G2 subset G8; G2 subset G166; G4 subset G8; G4 subset G166; G8 subset G166; /*******************************************************************/ G25x:=PolynomialRing(G25); IsFinite(G25x); /* false */ /* Efectivament no es finit, pq estem definint un anell de polynomis sobre un camp de coeficients finits pero els polynomis poden tenir el grau que vulguin */ /* ii */ /*******************************************************************/ alpha := PrimitiveElement(G25); beta := PrimitiveElement(Z5); p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; /* iii */ /*******************************************************************/ suma := p1 + p2; producte := p1 * p2; suma; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; mcm := LCM(p1,p2); mcm; mcd := GCD(p1,p2); mcd; p3:= (1/alpha^4) - ((alpha^3)*x) + (alpha^5)*(x^2) + (alpha^11)*(x^3); f:=Factorization(p3); f; f(1); f[1]; Output: Magma V2.10-22 Sun Apr 11 2004 18:53:28 on modular [Seed = 3287961564] ------------------------------------- { 0, 1 } { 0, 1, 2 } { 0, 1, 2, 3, 4 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ p, p^5, p^7, p^11, p^13, p^17, p^19, p^23 ] 8 [] [ , ] true p^16 p^8 [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , ] [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , ] { 0, 1 } { 1, G4.1, G4.1^2, 0 } { 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 } { 1, G166.1, G166.1^2, G166.1^3, G166.1^4, G166.1^5, G166.1^6, G166.1^7, G166.1^8, G166.1^9, G166.1^10, G166.1^11, G166.1^12, G166.1^13, G166.1^14, 0 } true true true false true false false 2*x^2 + p^19*x + p^9 p^19*x^3 + p^22*x^2 + p^10*x + p^2 p^17*x + p^5 p^15 x^3 + p^3*x^2 + p^15*x + p^7 1 [ , ] >> f(1); ^ Runtime error: Bad argument types Argument types given: RngIntElt, SeqEnum[Tup] Total time: 2.579 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 72-236-ADSL.red.retevision.es. (80.224.236.72) Time: Sun Apr 11 18:54:05 2004 Input: /*******************************************************************/ Z2:=GF(2); Z3:=GF(3); Z5:=GF(5); {i:i in Z2}; {i:i in Z3}; {i:i in Z5}; /*******************************************************************/ P2:=PolynomialRing(Z2); p:=1+x+x^4; IsIrreducible(p); G16

:= ext< Z2 | p >; P3:=PolynomialRing(Z3); q:=2+2*x+x^2; IsIrreducible(q); G9:= ext< Z3 | q >; qq:=1+2*x+x^2; IsIrreducible(qq); /*G9b:= ext< Z3 | qq >;*//*NO funciona perque qq no es irreductible*/ P5:=PolynomialRing(Z5); r:=3+2*x+x^2; IsIrreducible(r); G25

:= ext< Z5 | r >; /*******************************************************************/ [Order(a) :a in G25 | not a eq 0 ]; primitiusG25 := [a: a in G25 | IsPrimitive(a)]; [a: a in G25 | IsPrimitive(a)]; #[a: a in G25 | IsPrimitive(a)]; /*******************************************************************/ pm:=MinimalPolynomial(p); /* el grau dun element es el grau del seu polinomi minim */ /* el polinomi minim esta definit dintre de Zp */ Roots(pm,Z5); Roots(pm,G25); calculeu:=2*p^(-3)-p^5+((p^6)/(p+2)); IsInvertible(calculeu); calculeu; taula25:=[ : i in [0..23]]; taula16:=[ : i in [0..14]]; taula25; taula16; G2 := GF(2); G4 := GF(4); G8 := GF(8); G166 := GF(16); {i:i in G2}; {i:i in G4}; {i:i in G8}; {i:i in G166}; G2 subset G4; G2 subset G8; G2 subset G166; G4 subset G8; G4 subset G166; G8 subset G166; /*******************************************************************/ G25x:=PolynomialRing(G25); IsFinite(G25x); /* false */ /* Efectivament no es finit, pq estem definint un anell de polynomis sobre un camp de coeficients finits pero els polynomis poden tenir el grau que vulguin */ /* ii */ /*******************************************************************/ alpha := PrimitiveElement(G25); beta := PrimitiveElement(Z5); p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; /* iii */ /*******************************************************************/ suma := p1 + p2; producte := p1 * p2; suma; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; mcm := LCM(p1,p2); mcm; mcd := GCD(p1,p2); mcd; p3:= (1/alpha^4) - ((alpha^3)*x) + (alpha^5)*(x^2) + (alpha^11)*(x^3); f:=Factorization(p3); f; f(1); f[1](1); Output: Magma V2.10-22 Sun Apr 11 2004 18:54:02 on modular [Seed = 3421652790] ------------------------------------- { 0, 1 } { 0, 1, 2 } { 0, 1, 2, 3, 4 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ p, p^5, p^7, p^11, p^13, p^17, p^19, p^23 ] 8 [] [ , ] true p^16 p^8 [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , ] [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , ] { 0, 1 } { 1, G4.1, G4.1^2, 0 } { 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 } { 1, G166.1, G166.1^2, G166.1^3, G166.1^4, G166.1^5, G166.1^6, G166.1^7, G166.1^8, G166.1^9, G166.1^10, G166.1^11, G166.1^12, G166.1^13, G166.1^14, 0 } true true true false true false false 2*x^2 + p^19*x + p^9 p^19*x^3 + p^22*x^2 + p^10*x + p^2 p^17*x + p^5 p^15 x^3 + p^3*x^2 + p^15*x + p^7 1 [ , ] >> f(1); ^ Runtime error: Bad argument types Argument types given: RngIntElt, SeqEnum[Tup] >> f[1](1); ^ Runtime error: Bad argument types Argument types given: RngIntElt, Tup Total time: 2.580 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 72-236-ADSL.red.retevision.es. (80.224.236.72) Time: Sun Apr 11 18:54:24 2004 Input: /*******************************************************************/ Z2:=GF(2); Z3:=GF(3); Z5:=GF(5); {i:i in Z2}; {i:i in Z3}; {i:i in Z5}; /*******************************************************************/ P2:=PolynomialRing(Z2); p:=1+x+x^4; IsIrreducible(p); G16

:= ext< Z2 | p >; P3:=PolynomialRing(Z3); q:=2+2*x+x^2; IsIrreducible(q); G9:= ext< Z3 | q >; qq:=1+2*x+x^2; IsIrreducible(qq); /*G9b:= ext< Z3 | qq >;*//*NO funciona perque qq no es irreductible*/ P5:=PolynomialRing(Z5); r:=3+2*x+x^2; IsIrreducible(r); G25

:= ext< Z5 | r >; /*******************************************************************/ [Order(a) :a in G25 | not a eq 0 ]; primitiusG25 := [a: a in G25 | IsPrimitive(a)]; [a: a in G25 | IsPrimitive(a)]; #[a: a in G25 | IsPrimitive(a)]; /*******************************************************************/ pm:=MinimalPolynomial(p); /* el grau dun element es el grau del seu polinomi minim */ /* el polinomi minim esta definit dintre de Zp */ Roots(pm,Z5); Roots(pm,G25); calculeu:=2*p^(-3)-p^5+((p^6)/(p+2)); IsInvertible(calculeu); calculeu; taula25:=[ : i in [0..23]]; taula16:=[ : i in [0..14]]; taula25; taula16; G2 := GF(2); G4 := GF(4); G8 := GF(8); G166 := GF(16); {i:i in G2}; {i:i in G4}; {i:i in G8}; {i:i in G166}; G2 subset G4; G2 subset G8; G2 subset G166; G4 subset G8; G4 subset G166; G8 subset G166; /*******************************************************************/ G25x:=PolynomialRing(G25); IsFinite(G25x); /* false */ /* Efectivament no es finit, pq estem definint un anell de polynomis sobre un camp de coeficients finits pero els polynomis poden tenir el grau que vulguin */ /* ii */ /*******************************************************************/ alpha := PrimitiveElement(G25); beta := PrimitiveElement(Z5); p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; /* iii */ /*******************************************************************/ suma := p1 + p2; producte := p1 * p2; suma; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; mcm := LCM(p1,p2); mcm; mcd := GCD(p1,p2); mcd; p3:= (1/alpha^4) - ((alpha^3)*x) + (alpha^5)*(x^2) + (alpha^11)*(x^3); f:=Factorization(p3); f; f[1][1]; Output: Magma V2.10-22 Sun Apr 11 2004 18:54:22 on modular [Seed = 3012181850] ------------------------------------- { 0, 1 } { 0, 1, 2 } { 0, 1, 2, 3, 4 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ p, p^5, p^7, p^11, p^13, p^17, p^19, p^23 ] 8 [] [ , ] true p^16 p^8 [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , ] [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , ] { 0, 1 } { 1, G4.1, G4.1^2, 0 } { 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 } { 1, G166.1, G166.1^2, G166.1^3, G166.1^4, G166.1^5, G166.1^6, G166.1^7, G166.1^8, G166.1^9, G166.1^10, G166.1^11, G166.1^12, G166.1^13, G166.1^14, 0 } true true true false true false false 2*x^2 + p^19*x + p^9 p^19*x^3 + p^22*x^2 + p^10*x + p^2 p^17*x + p^5 p^15 x^3 + p^3*x^2 + p^15*x + p^7 1 [ , ] x + p^16 Total time: 2.569 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 72-236-ADSL.red.retevision.es. (80.224.236.72) Time: Sun Apr 11 18:55:02 2004 Input: /*******************************************************************/ Z2:=GF(2); Z3:=GF(3); Z5:=GF(5); {i:i in Z2}; {i:i in Z3}; {i:i in Z5}; /*******************************************************************/ P2:=PolynomialRing(Z2); p:=1+x+x^4; IsIrreducible(p); G16

:= ext< Z2 | p >; P3:=PolynomialRing(Z3); q:=2+2*x+x^2; IsIrreducible(q); G9:= ext< Z3 | q >; qq:=1+2*x+x^2; IsIrreducible(qq); /*G9b:= ext< Z3 | qq >;*//*NO funciona perque qq no es irreductible*/ P5:=PolynomialRing(Z5); r:=3+2*x+x^2; IsIrreducible(r); G25

:= ext< Z5 | r >; /*******************************************************************/ [Order(a) :a in G25 | not a eq 0 ]; primitiusG25 := [a: a in G25 | IsPrimitive(a)]; [a: a in G25 | IsPrimitive(a)]; #[a: a in G25 | IsPrimitive(a)]; /*******************************************************************/ pm:=MinimalPolynomial(p); /* el grau dun element es el grau del seu polinomi minim */ /* el polinomi minim esta definit dintre de Zp */ Roots(pm,Z5); Roots(pm,G25); calculeu:=2*p^(-3)-p^5+((p^6)/(p+2)); IsInvertible(calculeu); calculeu; taula25:=[ : i in [0..23]]; taula16:=[ : i in [0..14]]; taula25; taula16; G2 := GF(2); G4 := GF(4); G8 := GF(8); G166 := GF(16); {i:i in G2}; {i:i in G4}; {i:i in G8}; {i:i in G166}; G2 subset G4; G2 subset G8; G2 subset G166; G4 subset G8; G4 subset G166; G8 subset G166; /*******************************************************************/ G25x:=PolynomialRing(G25); IsFinite(G25x); /* false */ /* Efectivament no es finit, pq estem definint un anell de polynomis sobre un camp de coeficients finits pero els polynomis poden tenir el grau que vulguin */ /* ii */ /*******************************************************************/ alpha := PrimitiveElement(G25); beta := PrimitiveElement(Z5); p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; /* iii */ /*******************************************************************/ suma := p1 + p2; producte := p1 * p2; suma; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; mcm := LCM(p1,p2); mcm; mcd := GCD(p1,p2); mcd; p3:= (1/alpha^4) - ((alpha^3)*x) + (alpha^5)*(x^2) + (alpha^11)*(x^3); f:=Factorization(p3); f; Evaluate(p3,f[1][1]); Output: Magma V2.10-22 Sun Apr 11 2004 18:54:59 on modular [Seed = 3145873167] ------------------------------------- { 0, 1 } { 0, 1, 2 } { 0, 1, 2, 3, 4 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ p, p^5, p^7, p^11, p^13, p^17, p^19, p^23 ] 8 [] [ , ] true p^16 p^8 [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , ] [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , ] { 0, 1 } { 1, G4.1, G4.1^2, 0 } { 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 } { 1, G166.1, G166.1^2, G166.1^3, G166.1^4, G166.1^5, G166.1^6, G166.1^7, G166.1^8, G166.1^9, G166.1^10, G166.1^11, G166.1^12, G166.1^13, G166.1^14, 0 } true true true false true false false 2*x^2 + p^19*x + p^9 p^19*x^3 + p^22*x^2 + p^10*x + p^2 p^17*x + p^5 p^15 x^3 + p^3*x^2 + p^15*x + p^7 1 [ , ] p^11*x^3 + p^10*x^2 + p^5*x + 3 Total time: 2.609 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 72-236-ADSL.red.retevision.es. (80.224.236.72) Time: Sun Apr 11 18:55:23 2004 Input: /*******************************************************************/ Z2:=GF(2); Z3:=GF(3); Z5:=GF(5); {i:i in Z2}; {i:i in Z3}; {i:i in Z5}; /*******************************************************************/ P2:=PolynomialRing(Z2); p:=1+x+x^4; IsIrreducible(p); G16

:= ext< Z2 | p >; P3:=PolynomialRing(Z3); q:=2+2*x+x^2; IsIrreducible(q); G9:= ext< Z3 | q >; qq:=1+2*x+x^2; IsIrreducible(qq); /*G9b:= ext< Z3 | qq >;*//*NO funciona perque qq no es irreductible*/ P5:=PolynomialRing(Z5); r:=3+2*x+x^2; IsIrreducible(r); G25

:= ext< Z5 | r >; /*******************************************************************/ [Order(a) :a in G25 | not a eq 0 ]; primitiusG25 := [a: a in G25 | IsPrimitive(a)]; [a: a in G25 | IsPrimitive(a)]; #[a: a in G25 | IsPrimitive(a)]; /*******************************************************************/ pm:=MinimalPolynomial(p); /* el grau dun element es el grau del seu polinomi minim */ /* el polinomi minim esta definit dintre de Zp */ Roots(pm,Z5); Roots(pm,G25); calculeu:=2*p^(-3)-p^5+((p^6)/(p+2)); IsInvertible(calculeu); calculeu; taula25:=[ : i in [0..23]]; taula16:=[ : i in [0..14]]; taula25; taula16; G2 := GF(2); G4 := GF(4); G8 := GF(8); G166 := GF(16); {i:i in G2}; {i:i in G4}; {i:i in G8}; {i:i in G166}; G2 subset G4; G2 subset G8; G2 subset G166; G4 subset G8; G4 subset G166; G8 subset G166; /*******************************************************************/ G25x:=PolynomialRing(G25); IsFinite(G25x); /* false */ /* Efectivament no es finit, pq estem definint un anell de polynomis sobre un camp de coeficients finits pero els polynomis poden tenir el grau que vulguin */ /* ii */ /*******************************************************************/ alpha := PrimitiveElement(G25); beta := PrimitiveElement(Z5); p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; /* iii */ /*******************************************************************/ suma := p1 + p2; producte := p1 * p2; suma; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; mcm := LCM(p1,p2); mcm; mcd := GCD(p1,p2); mcd; p3:= (1/alpha^4) - ((alpha^3)*x) + (alpha^5)*(x^2) + (alpha^11)*(x^3); f:=Factorization(p3); f; Evaluate(p3,x-f[1][1]); Output: Magma V2.10-22 Sun Apr 11 2004 18:55:20 on modular [Seed = 2929140225] ------------------------------------- { 0, 1 } { 0, 1, 2 } { 0, 1, 2, 3, 4 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ p, p^5, p^7, p^11, p^13, p^17, p^19, p^23 ] 8 [] [ , ] true p^16 p^8 [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , ] [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , ] { 0, 1 } { 1, G4.1, G4.1^2, 0 } { 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 } { 1, G166.1, G166.1^2, G166.1^3, G166.1^4, G166.1^5, G166.1^6, G166.1^7, G166.1^8, G166.1^9, G166.1^10, G166.1^11, G166.1^12, G166.1^13, G166.1^14, 0 } true true true false true false false 2*x^2 + p^19*x + p^9 p^19*x^3 + p^22*x^2 + p^10*x + p^2 p^17*x + p^5 p^15 x^3 + p^3*x^2 + p^15*x + p^7 1 [ , ] 0 Total time: 2.509 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 72-236-ADSL.red.retevision.es. (80.224.236.72) Time: Sun Apr 11 18:55:51 2004 Input: /*******************************************************************/ Z2:=GF(2); Z3:=GF(3); Z5:=GF(5); {i:i in Z2}; {i:i in Z3}; {i:i in Z5}; /*******************************************************************/ P2:=PolynomialRing(Z2); p:=1+x+x^4; IsIrreducible(p); G16

:= ext< Z2 | p >; P3:=PolynomialRing(Z3); q:=2+2*x+x^2; IsIrreducible(q); G9:= ext< Z3 | q >; qq:=1+2*x+x^2; IsIrreducible(qq); /*G9b:= ext< Z3 | qq >;*//*NO funciona perque qq no es irreductible*/ P5:=PolynomialRing(Z5); r:=3+2*x+x^2; IsIrreducible(r); G25

:= ext< Z5 | r >; /*******************************************************************/ [Order(a) :a in G25 | not a eq 0 ]; primitiusG25 := [a: a in G25 | IsPrimitive(a)]; [a: a in G25 | IsPrimitive(a)]; #[a: a in G25 | IsPrimitive(a)]; /*******************************************************************/ pm:=MinimalPolynomial(p); /* el grau dun element es el grau del seu polinomi minim */ /* el polinomi minim esta definit dintre de Zp */ Roots(pm,Z5); Roots(pm,G25); calculeu:=2*p^(-3)-p^5+((p^6)/(p+2)); IsInvertible(calculeu); calculeu; taula25:=[ : i in [0..23]]; taula16:=[ : i in [0..14]]; taula25; taula16; G2 := GF(2); G4 := GF(4); G8 := GF(8); G166 := GF(16); {i:i in G2}; {i:i in G4}; {i:i in G8}; {i:i in G166}; G2 subset G4; G2 subset G8; G2 subset G166; G4 subset G8; G4 subset G166; G8 subset G166; /*******************************************************************/ G25x:=PolynomialRing(G25); IsFinite(G25x); /* false */ /* Efectivament no es finit, pq estem definint un anell de polynomis sobre un camp de coeficients finits pero els polynomis poden tenir el grau que vulguin */ /* ii */ /*******************************************************************/ alpha := PrimitiveElement(G25); beta := PrimitiveElement(Z5); p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; /* iii */ /*******************************************************************/ suma := p1 + p2; producte := p1 * p2; suma; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; mcm := LCM(p1,p2); mcm; mcd := GCD(p1,p2); mcd; p3:= (1/alpha^4) - ((alpha^3)*x) + (alpha^5)*(x^2) + (alpha^11)*(x^3); f:=Factorization(p3); f; Evaluate(p3,x-f[1][1]); Evaluate(p3,x-f[2][2]); Output: Magma V2.10-22 Sun Apr 11 2004 18:55:49 on modular [Seed = 2528057876] ------------------------------------- { 0, 1 } { 0, 1, 2 } { 0, 1, 2, 3, 4 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ p, p^5, p^7, p^11, p^13, p^17, p^19, p^23 ] 8 [] [ , ] true p^16 p^8 [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , ] [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , ] { 0, 1 } { 1, G4.1, G4.1^2, 0 } { 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 } { 1, G166.1, G166.1^2, G166.1^3, G166.1^4, G166.1^5, G166.1^6, G166.1^7, G166.1^8, G166.1^9, G166.1^10, G166.1^11, G166.1^12, G166.1^13, G166.1^14, 0 } true true true false true false false 2*x^2 + p^19*x + p^9 p^19*x^3 + p^22*x^2 + p^10*x + p^2 p^17*x + p^5 p^15 x^3 + p^3*x^2 + p^15*x + p^7 1 [ , ] 0 p^11*x^3 + p^23*x^2 + p^19*x + p^15 Total time: 2.509 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 72-236-ADSL.red.retevision.es. (80.224.236.72) Time: Sun Apr 11 18:57:33 2004 Input: /*******************************************************************/ Z2:=GF(2); Z3:=GF(3); Z5:=GF(5); {i:i in Z2}; {i:i in Z3}; {i:i in Z5}; /*******************************************************************/ P2:=PolynomialRing(Z2); p:=1+x+x^4; IsIrreducible(p); G16

:= ext< Z2 | p >; P3:=PolynomialRing(Z3); q:=2+2*x+x^2; IsIrreducible(q); G9:= ext< Z3 | q >; qq:=1+2*x+x^2; IsIrreducible(qq); /*G9b:= ext< Z3 | qq >;*//*NO funciona perque qq no es irreductible*/ P5:=PolynomialRing(Z5); r:=3+2*x+x^2; IsIrreducible(r); G25

:= ext< Z5 | r >; /*******************************************************************/ [Order(a) :a in G25 | not a eq 0 ]; primitiusG25 := [a: a in G25 | IsPrimitive(a)]; [a: a in G25 | IsPrimitive(a)]; #[a: a in G25 | IsPrimitive(a)]; /*******************************************************************/ pm:=MinimalPolynomial(p); /* el grau dun element es el grau del seu polinomi minim */ /* el polinomi minim esta definit dintre de Zp */ Roots(pm,Z5); Roots(pm,G25); calculeu:=2*p^(-3)-p^5+((p^6)/(p+2)); IsInvertible(calculeu); calculeu; taula25:=[ : i in [0..23]]; taula16:=[ : i in [0..14]]; taula25; taula16; G2 := GF(2); G4 := GF(4); G8 := GF(8); G166 := GF(16); {i:i in G2}; {i:i in G4}; {i:i in G8}; {i:i in G166}; G2 subset G4; G2 subset G8; G2 subset G166; G4 subset G8; G4 subset G166; G8 subset G166; /*******************************************************************/ G25x:=PolynomialRing(G25); IsFinite(G25x); /* false */ /* Efectivament no es finit, pq estem definint un anell de polynomis sobre un camp de coeficients finits pero els polynomis poden tenir el grau que vulguin */ /* ii */ /*******************************************************************/ alpha := PrimitiveElement(G25); beta := PrimitiveElement(Z5); p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; /* iii */ /*******************************************************************/ suma := p1 + p2; producte := p1 * p2; suma; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; mcm := LCM(p1,p2); mcm; mcd := GCD(p1,p2); mcd; p3:= (1/alpha^4) - ((alpha^3)*x) + (alpha^5)*(x^2) + (alpha^11)*(x^3); f:=Factorization(p3); f; Evaluate(p3,Roots(f[1][1],G25)); Evaluate(p3,x-f[2][2]); Output: Magma V2.10-22 Sun Apr 11 2004 18:57:31 on modular [Seed = 2661749682] ------------------------------------- { 0, 1 } { 0, 1, 2 } { 0, 1, 2, 3, 4 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ p, p^5, p^7, p^11, p^13, p^17, p^19, p^23 ] 8 [] [ , ] true p^16 p^8 [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , ] [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , ] { 0, 1 } { 1, G4.1, G4.1^2, 0 } { 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 } { 1, G166.1, G166.1^2, G166.1^3, G166.1^4, G166.1^5, G166.1^6, G166.1^7, G166.1^8, G166.1^9, G166.1^10, G166.1^11, G166.1^12, G166.1^13, G166.1^14, 0 } true true true false true false false 2*x^2 + p^19*x + p^9 p^19*x^3 + p^22*x^2 + p^10*x + p^2 p^17*x + p^5 p^15 x^3 + p^3*x^2 + p^15*x + p^7 1 [ , ] >> Evaluate(p3,Roots(f[1][1],G25)); ^ Runtime error in 'Evaluate': Bad argument types Argument types given: RngUPolElt, SeqEnum[Tup] p^11*x^3 + p^23*x^2 + p^19*x + p^15 Total time: 2.520 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 72-236-ADSL.red.retevision.es. (80.224.236.72) Time: Sun Apr 11 18:58:14 2004 Input: /*******************************************************************/ Z2:=GF(2); Z3:=GF(3); Z5:=GF(5); {i:i in Z2}; {i:i in Z3}; {i:i in Z5}; /*******************************************************************/ P2:=PolynomialRing(Z2); p:=1+x+x^4; IsIrreducible(p); G16

:= ext< Z2 | p >; P3:=PolynomialRing(Z3); q:=2+2*x+x^2; IsIrreducible(q); G9:= ext< Z3 | q >; qq:=1+2*x+x^2; IsIrreducible(qq); /*G9b:= ext< Z3 | qq >;*//*NO funciona perque qq no es irreductible*/ P5:=PolynomialRing(Z5); r:=3+2*x+x^2; IsIrreducible(r); G25

:= ext< Z5 | r >; /*******************************************************************/ [Order(a) :a in G25 | not a eq 0 ]; primitiusG25 := [a: a in G25 | IsPrimitive(a)]; [a: a in G25 | IsPrimitive(a)]; #[a: a in G25 | IsPrimitive(a)]; /*******************************************************************/ pm:=MinimalPolynomial(p); /* el grau dun element es el grau del seu polinomi minim */ /* el polinomi minim esta definit dintre de Zp */ Roots(pm,Z5); Roots(pm,G25); calculeu:=2*p^(-3)-p^5+((p^6)/(p+2)); IsInvertible(calculeu); calculeu; taula25:=[ : i in [0..23]]; taula16:=[ : i in [0..14]]; taula25; taula16; G2 := GF(2); G4 := GF(4); G8 := GF(8); G166 := GF(16); {i:i in G2}; {i:i in G4}; {i:i in G8}; {i:i in G166}; G2 subset G4; G2 subset G8; G2 subset G166; G4 subset G8; G4 subset G166; G8 subset G166; /*******************************************************************/ G25x:=PolynomialRing(G25); IsFinite(G25x); /* false */ /* Efectivament no es finit, pq estem definint un anell de polynomis sobre un camp de coeficients finits pero els polynomis poden tenir el grau que vulguin */ /* ii */ /*******************************************************************/ alpha := PrimitiveElement(G25); beta := PrimitiveElement(Z5); p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; /* iii */ /*******************************************************************/ suma := p1 + p2; producte := p1 * p2; suma; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; mcm := LCM(p1,p2); mcm; mcd := GCD(p1,p2); mcd; p3:= (1/alpha^4) - ((alpha^3)*x) + (alpha^5)*(x^2) + (alpha^11)*(x^3); f:=Factorization(p3); f; Roots(f[1][1],G25); /*Evaluate(p3,Roots(f[1][1],G25));*/ Evaluate(p3,x-f[2][2]); Output: Magma V2.10-22 Sun Apr 11 2004 18:58:11 on modular [Seed = 2243692657] ------------------------------------- { 0, 1 } { 0, 1, 2 } { 0, 1, 2, 3, 4 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ p, p^5, p^7, p^11, p^13, p^17, p^19, p^23 ] 8 [] [ , ] true p^16 p^8 [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , ] [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , ] { 0, 1 } { 1, G4.1, G4.1^2, 0 } { 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 } { 1, G166.1, G166.1^2, G166.1^3, G166.1^4, G166.1^5, G166.1^6, G166.1^7, G166.1^8, G166.1^9, G166.1^10, G166.1^11, G166.1^12, G166.1^13, G166.1^14, 0 } true true true false true false false 2*x^2 + p^19*x + p^9 p^19*x^3 + p^22*x^2 + p^10*x + p^2 p^17*x + p^5 p^15 x^3 + p^3*x^2 + p^15*x + p^7 1 [ , ] [ ] p^11*x^3 + p^23*x^2 + p^19*x + p^15 Total time: 2.579 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 72-236-ADSL.red.retevision.es. (80.224.236.72) Time: Sun Apr 11 18:58:57 2004 Input: /*******************************************************************/ Z2:=GF(2); Z3:=GF(3); Z5:=GF(5); {i:i in Z2}; {i:i in Z3}; {i:i in Z5}; /*******************************************************************/ P2:=PolynomialRing(Z2); p:=1+x+x^4; IsIrreducible(p); G16

:= ext< Z2 | p >; P3:=PolynomialRing(Z3); q:=2+2*x+x^2; IsIrreducible(q); G9:= ext< Z3 | q >; qq:=1+2*x+x^2; IsIrreducible(qq); /*G9b:= ext< Z3 | qq >;*//*NO funciona perque qq no es irreductible*/ P5:=PolynomialRing(Z5); r:=3+2*x+x^2; IsIrreducible(r); G25

:= ext< Z5 | r >; /*******************************************************************/ [Order(a) :a in G25 | not a eq 0 ]; primitiusG25 := [a: a in G25 | IsPrimitive(a)]; [a: a in G25 | IsPrimitive(a)]; #[a: a in G25 | IsPrimitive(a)]; /*******************************************************************/ pm:=MinimalPolynomial(p); /* el grau dun element es el grau del seu polinomi minim */ /* el polinomi minim esta definit dintre de Zp */ Roots(pm,Z5); Roots(pm,G25); calculeu:=2*p^(-3)-p^5+((p^6)/(p+2)); IsInvertible(calculeu); calculeu; taula25:=[ : i in [0..23]]; taula16:=[ : i in [0..14]]; taula25; taula16; G2 := GF(2); G4 := GF(4); G8 := GF(8); G166 := GF(16); {i:i in G2}; {i:i in G4}; {i:i in G8}; {i:i in G166}; G2 subset G4; G2 subset G8; G2 subset G166; G4 subset G8; G4 subset G166; G8 subset G166; /*******************************************************************/ G25x:=PolynomialRing(G25); IsFinite(G25x); /* false */ /* Efectivament no es finit, pq estem definint un anell de polynomis sobre un camp de coeficients finits pero els polynomis poden tenir el grau que vulguin */ /* ii */ /*******************************************************************/ alpha := PrimitiveElement(G25); beta := PrimitiveElement(Z5); p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; /* iii */ /*******************************************************************/ suma := p1 + p2; producte := p1 * p2; suma; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; mcm := LCM(p1,p2); mcm; mcd := GCD(p1,p2); mcd; p3:= (1/alpha^4) - ((alpha^3)*x) + (alpha^5)*(x^2) + (alpha^11)*(x^3); f:=Factorization(p3); f; Roots(f[1][1],G25); Evaluate(p3,p^4); Evaluate(p3,x-f[2][2]); Output: Magma V2.10-22 Sun Apr 11 2004 18:58:54 on modular [Seed = 2377384020] ------------------------------------- { 0, 1 } { 0, 1, 2 } { 0, 1, 2, 3, 4 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ p, p^5, p^7, p^11, p^13, p^17, p^19, p^23 ] 8 [] [ , ] true p^16 p^8 [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , ] [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , ] { 0, 1 } { 1, G4.1, G4.1^2, 0 } { 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 } { 1, G166.1, G166.1^2, G166.1^3, G166.1^4, G166.1^5, G166.1^6, G166.1^7, G166.1^8, G166.1^9, G166.1^10, G166.1^11, G166.1^12, G166.1^13, G166.1^14, 0 } true true true false true false false 2*x^2 + p^19*x + p^9 p^19*x^3 + p^22*x^2 + p^10*x + p^2 p^17*x + p^5 p^15 x^3 + p^3*x^2 + p^15*x + p^7 1 [ , ] [ ] 0 p^11*x^3 + p^23*x^2 + p^19*x + p^15 Total time: 2.600 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 72-236-ADSL.red.retevision.es. (80.224.236.72) Time: Sun Apr 11 19:00:15 2004 Input: /*******************************************************************/ Z2:=GF(2); Z3:=GF(3); Z5:=GF(5); {i:i in Z2}; {i:i in Z3}; {i:i in Z5}; /*******************************************************************/ P2:=PolynomialRing(Z2); p:=1+x+x^4; IsIrreducible(p); G16

:= ext< Z2 | p >; P3:=PolynomialRing(Z3); q:=2+2*x+x^2; IsIrreducible(q); G9:= ext< Z3 | q >; qq:=1+2*x+x^2; IsIrreducible(qq); /*G9b:= ext< Z3 | qq >;*//*NO funciona perque qq no es irreductible*/ P5:=PolynomialRing(Z5); r:=3+2*x+x^2; IsIrreducible(r); G25

:= ext< Z5 | r >; /*******************************************************************/ [Order(a) :a in G25 | not a eq 0 ]; primitiusG25 := [a: a in G25 | IsPrimitive(a)]; [a: a in G25 | IsPrimitive(a)]; #[a: a in G25 | IsPrimitive(a)]; /*******************************************************************/ pm:=MinimalPolynomial(p); /* el grau dun element es el grau del seu polinomi minim */ /* el polinomi minim esta definit dintre de Zp */ Roots(pm,Z5); Roots(pm,G25); calculeu:=2*p^(-3)-p^5+((p^6)/(p+2)); IsInvertible(calculeu); calculeu; taula25:=[ : i in [0..23]]; taula16:=[ : i in [0..14]]; taula25; taula16; G2 := GF(2); G4 := GF(4); G8 := GF(8); G166 := GF(16); {i:i in G2}; {i:i in G4}; {i:i in G8}; {i:i in G166}; G2 subset G4; G2 subset G8; G2 subset G166; G4 subset G8; G4 subset G166; G8 subset G166; /*******************************************************************/ G25x:=PolynomialRing(G25); IsFinite(G25x); /* false */ /* Efectivament no es finit, pq estem definint un anell de polynomis sobre un camp de coeficients finits pero els polynomis poden tenir el grau que vulguin */ /* ii */ /*******************************************************************/ alpha := PrimitiveElement(G25); beta := PrimitiveElement(Z5); p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; /* iii */ /*******************************************************************/ suma := p1 + p2; producte := p1 * p2; suma; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; mcm := LCM(p1,p2); mcm; mcd := GCD(p1,p2); mcd; p3:= (1/alpha^4) - ((alpha^3)*x) + (alpha^5)*(x^2) + (alpha^11)*(x^3); f:=Factorization(p3); f; r = Roots(f[1][1],G25); arrel1 = r[1][1]; arrel1; Evaluate(p3,arrel1); /*Evaluate(p3,x-f[2][2]);*/ Output: Magma V2.10-22 Sun Apr 11 2004 19:00:12 on modular [Seed = 1917583350] ------------------------------------- { 0, 1 } { 0, 1, 2 } { 0, 1, 2, 3, 4 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ p, p^5, p^7, p^11, p^13, p^17, p^19, p^23 ] 8 [] [ , ] true p^16 p^8 [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , ] [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , ] { 0, 1 } { 1, G4.1, G4.1^2, 0 } { 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 } { 1, G166.1, G166.1^2, G166.1^3, G166.1^4, G166.1^5, G166.1^6, G166.1^7, G166.1^8, G166.1^9, G166.1^10, G166.1^11, G166.1^12, G166.1^13, G166.1^14, 0 } true true true false true false false 2*x^2 + p^19*x + p^9 p^19*x^3 + p^22*x^2 + p^10*x + p^2 p^17*x + p^5 p^15 x^3 + p^3*x^2 + p^15*x + p^7 1 [ , ] >> r = Roots(f[1][1],G25); ^ Runtime error in elt< ... >: LHS and RHS of relation constructor are not compatible >> arrel1 = r[1][1]; ^ User error: Identifier 'arrel1' has not been declared or assigned >> arrel1; ^ User error: Identifier 'arrel1' has not been declared or assigned >> Evaluate(p3,arrel1); ^ User error: Identifier 'arrel1' has not been declared or assigned Total time: 2.509 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 72-236-ADSL.red.retevision.es. (80.224.236.72) Time: Sun Apr 11 19:00:32 2004 Input: /*******************************************************************/ Z2:=GF(2); Z3:=GF(3); Z5:=GF(5); {i:i in Z2}; {i:i in Z3}; {i:i in Z5}; /*******************************************************************/ P2:=PolynomialRing(Z2); p:=1+x+x^4; IsIrreducible(p); G16

:= ext< Z2 | p >; P3:=PolynomialRing(Z3); q:=2+2*x+x^2; IsIrreducible(q); G9:= ext< Z3 | q >; qq:=1+2*x+x^2; IsIrreducible(qq); /*G9b:= ext< Z3 | qq >;*//*NO funciona perque qq no es irreductible*/ P5:=PolynomialRing(Z5); r:=3+2*x+x^2; IsIrreducible(r); G25

:= ext< Z5 | r >; /*******************************************************************/ [Order(a) :a in G25 | not a eq 0 ]; primitiusG25 := [a: a in G25 | IsPrimitive(a)]; [a: a in G25 | IsPrimitive(a)]; #[a: a in G25 | IsPrimitive(a)]; /*******************************************************************/ pm:=MinimalPolynomial(p); /* el grau dun element es el grau del seu polinomi minim */ /* el polinomi minim esta definit dintre de Zp */ Roots(pm,Z5); Roots(pm,G25); calculeu:=2*p^(-3)-p^5+((p^6)/(p+2)); IsInvertible(calculeu); calculeu; taula25:=[ : i in [0..23]]; taula16:=[ : i in [0..14]]; taula25; taula16; G2 := GF(2); G4 := GF(4); G8 := GF(8); G166 := GF(16); {i:i in G2}; {i:i in G4}; {i:i in G8}; {i:i in G166}; G2 subset G4; G2 subset G8; G2 subset G166; G4 subset G8; G4 subset G166; G8 subset G166; /*******************************************************************/ G25x:=PolynomialRing(G25); IsFinite(G25x); /* false */ /* Efectivament no es finit, pq estem definint un anell de polynomis sobre un camp de coeficients finits pero els polynomis poden tenir el grau que vulguin */ /* ii */ /*******************************************************************/ alpha := PrimitiveElement(G25); beta := PrimitiveElement(Z5); p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; /* iii */ /*******************************************************************/ suma := p1 + p2; producte := p1 * p2; suma; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; mcm := LCM(p1,p2); mcm; mcd := GCD(p1,p2); mcd; p3:= (1/alpha^4) - ((alpha^3)*x) + (alpha^5)*(x^2) + (alpha^11)*(x^3); f:=Factorization(p3); f; r := Roots(f[1][1],G25); arrel1 := r[1][1]; arrel1; Evaluate(p3,arrel1); /*Evaluate(p3,x-f[2][2]);*/ Output: Magma V2.10-22 Sun Apr 11 2004 19:00:29 on modular [Seed = 1783882783] ------------------------------------- { 0, 1 } { 0, 1, 2 } { 0, 1, 2, 3, 4 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ p, p^5, p^7, p^11, p^13, p^17, p^19, p^23 ] 8 [] [ , ] true p^16 p^8 [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , ] [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , ] { 0, 1 } { 1, G4.1, G4.1^2, 0 } { 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 } { 1, G166.1, G166.1^2, G166.1^3, G166.1^4, G166.1^5, G166.1^6, G166.1^7, G166.1^8, G166.1^9, G166.1^10, G166.1^11, G166.1^12, G166.1^13, G166.1^14, 0 } true true true false true false false 2*x^2 + p^19*x + p^9 p^19*x^3 + p^22*x^2 + p^10*x + p^2 p^17*x + p^5 p^15 x^3 + p^3*x^2 + p^15*x + p^7 1 [ , ] p^4 0 Total time: 2.509 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 72-236-ADSL.red.retevision.es. (80.224.236.72) Time: Sun Apr 11 19:01:19 2004 Input: /*******************************************************************/ Z2:=GF(2); Z3:=GF(3); Z5:=GF(5); {i:i in Z2}; {i:i in Z3}; {i:i in Z5}; /*******************************************************************/ P2:=PolynomialRing(Z2); p:=1+x+x^4; IsIrreducible(p); G16

:= ext< Z2 | p >; P3:=PolynomialRing(Z3); q:=2+2*x+x^2; IsIrreducible(q); G9:= ext< Z3 | q >; qq:=1+2*x+x^2; IsIrreducible(qq); /*G9b:= ext< Z3 | qq >;*//*NO funciona perque qq no es irreductible*/ P5:=PolynomialRing(Z5); r:=3+2*x+x^2; IsIrreducible(r); G25

:= ext< Z5 | r >; /*******************************************************************/ [Order(a) :a in G25 | not a eq 0 ]; primitiusG25 := [a: a in G25 | IsPrimitive(a)]; [a: a in G25 | IsPrimitive(a)]; #[a: a in G25 | IsPrimitive(a)]; /*******************************************************************/ pm:=MinimalPolynomial(p); /* el grau dun element es el grau del seu polinomi minim */ /* el polinomi minim esta definit dintre de Zp */ Roots(pm,Z5); Roots(pm,G25); calculeu:=2*p^(-3)-p^5+((p^6)/(p+2)); IsInvertible(calculeu); calculeu; taula25:=[ : i in [0..23]]; taula16:=[ : i in [0..14]]; taula25; taula16; G2 := GF(2); G4 := GF(4); G8 := GF(8); G166 := GF(16); {i:i in G2}; {i:i in G4}; {i:i in G8}; {i:i in G166}; G2 subset G4; G2 subset G8; G2 subset G166; G4 subset G8; G4 subset G166; G8 subset G166; /*******************************************************************/ G25x:=PolynomialRing(G25); IsFinite(G25x); /* false */ /* Efectivament no es finit, pq estem definint un anell de polynomis sobre un camp de coeficients finits pero els polynomis poden tenir el grau que vulguin */ /* ii */ /*******************************************************************/ alpha := PrimitiveElement(G25); beta := PrimitiveElement(Z5); p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; /* iii */ /*******************************************************************/ suma := p1 + p2; producte := p1 * p2; suma; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; mcm := LCM(p1,p2); mcm; mcd := GCD(p1,p2); mcd; p3:= (1/alpha^4) - ((alpha^3)*x) + (alpha^5)*(x^2) + (alpha^11)*(x^3); f:=Factorization(p3); f; r := Roots(f[1][1],G25); arrel1 := r[1][1]; Evaluate(p3,arrel1); Roots(f[2][2],G25); /*Evaluate(p3,x-f[2][2]);*/ Output: Magma V2.10-22 Sun Apr 11 2004 19:01:16 on modular [Seed = 1416485392] ------------------------------------- { 0, 1 } { 0, 1, 2 } { 0, 1, 2, 3, 4 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ p, p^5, p^7, p^11, p^13, p^17, p^19, p^23 ] 8 [] [ , ] true p^16 p^8 [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , ] [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , ] { 0, 1 } { 1, G4.1, G4.1^2, 0 } { 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 } { 1, G166.1, G166.1^2, G166.1^3, G166.1^4, G166.1^5, G166.1^6, G166.1^7, G166.1^8, G166.1^9, G166.1^10, G166.1^11, G166.1^12, G166.1^13, G166.1^14, 0 } true true true false true false false 2*x^2 + p^19*x + p^9 p^19*x^3 + p^22*x^2 + p^10*x + p^2 p^17*x + p^5 p^15 x^3 + p^3*x^2 + p^15*x + p^7 1 [ , ] 0 >> Roots(f[2][2],G25); ^ Runtime error in 'Roots': Bad argument types Argument types given: RngIntElt, FldFin Total time: 2.559 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 72-236-ADSL.red.retevision.es. (80.224.236.72) Time: Sun Apr 11 19:02:53 2004 Input: /*******************************************************************/ Z2:=GF(2); Z3:=GF(3); Z5:=GF(5); {i:i in Z2}; {i:i in Z3}; {i:i in Z5}; /*******************************************************************/ P2:=PolynomialRing(Z2); p:=1+x+x^4; IsIrreducible(p); G16

:= ext< Z2 | p >; P3:=PolynomialRing(Z3); q:=2+2*x+x^2; IsIrreducible(q); G9:= ext< Z3 | q >; qq:=1+2*x+x^2; IsIrreducible(qq); /*G9b:= ext< Z3 | qq >;*//*NO funciona perque qq no es irreductible*/ P5:=PolynomialRing(Z5); r:=3+2*x+x^2; IsIrreducible(r); G25

:= ext< Z5 | r >; /*******************************************************************/ [Order(a) :a in G25 | not a eq 0 ]; primitiusG25 := [a: a in G25 | IsPrimitive(a)]; [a: a in G25 | IsPrimitive(a)]; #[a: a in G25 | IsPrimitive(a)]; /*******************************************************************/ pm:=MinimalPolynomial(p); /* el grau dun element es el grau del seu polinomi minim */ /* el polinomi minim esta definit dintre de Zp */ Roots(pm,Z5); Roots(pm,G25); calculeu:=2*p^(-3)-p^5+((p^6)/(p+2)); IsInvertible(calculeu); calculeu; taula25:=[ : i in [0..23]]; taula16:=[ : i in [0..14]]; taula25; taula16; G2 := GF(2); G4 := GF(4); G8 := GF(8); G166 := GF(16); {i:i in G2}; {i:i in G4}; {i:i in G8}; {i:i in G166}; G2 subset G4; G2 subset G8; G2 subset G166; G4 subset G8; G4 subset G166; G8 subset G166; /*******************************************************************/ G25x:=PolynomialRing(G25); IsFinite(G25x); /* false */ /* Efectivament no es finit, pq estem definint un anell de polynomis sobre un camp de coeficients finits pero els polynomis poden tenir el grau que vulguin */ /* ii */ /*******************************************************************/ alpha := PrimitiveElement(G25); beta := PrimitiveElement(Z5); p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; /* iii */ /*******************************************************************/ suma := p1 + p2; producte := p1 * p2; suma; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; mcm := LCM(p1,p2); mcm; mcd := GCD(p1,p2); mcd; p3:= (1/alpha^4) - ((alpha^3)*x) + (alpha^5)*(x^2) + (alpha^11)*(x^3); f:=Factorization(p3); f; r := Roots(f[1][1],G25); arrel1 := r[1][1]; Evaluate(p3,arrel1); a := f[2][2]; a; Roots(a,G25); /*Evaluate(p3,x-f[2][2]);*/ Output: Magma V2.10-22 Sun Apr 11 2004 19:02:51 on modular [Seed = 1282785967] ------------------------------------- { 0, 1 } { 0, 1, 2 } { 0, 1, 2, 3, 4 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ p, p^5, p^7, p^11, p^13, p^17, p^19, p^23 ] 8 [] [ , ] true p^16 p^8 [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , ] [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , ] { 0, 1 } { 1, G4.1, G4.1^2, 0 } { 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 } { 1, G166.1, G166.1^2, G166.1^3, G166.1^4, G166.1^5, G166.1^6, G166.1^7, G166.1^8, G166.1^9, G166.1^10, G166.1^11, G166.1^12, G166.1^13, G166.1^14, 0 } true true true false true false false 2*x^2 + p^19*x + p^9 p^19*x^3 + p^22*x^2 + p^10*x + p^2 p^17*x + p^5 p^15 x^3 + p^3*x^2 + p^15*x + p^7 1 [ , ] 0 1 >> Roots(a,G25); ^ Runtime error in 'Roots': Bad argument types Argument types given: RngIntElt, FldFin Total time: 2.520 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 72-236-ADSL.red.retevision.es. (80.224.236.72) Time: Sun Apr 11 19:03:35 2004 Input: /*******************************************************************/ Z2:=GF(2); Z3:=GF(3); Z5:=GF(5); {i:i in Z2}; {i:i in Z3}; {i:i in Z5}; /*******************************************************************/ P2:=PolynomialRing(Z2); p:=1+x+x^4; IsIrreducible(p); G16

:= ext< Z2 | p >; P3:=PolynomialRing(Z3); q:=2+2*x+x^2; IsIrreducible(q); G9:= ext< Z3 | q >; qq:=1+2*x+x^2; IsIrreducible(qq); /*G9b:= ext< Z3 | qq >;*//*NO funciona perque qq no es irreductible*/ P5:=PolynomialRing(Z5); r:=3+2*x+x^2; IsIrreducible(r); G25

:= ext< Z5 | r >; /*******************************************************************/ [Order(a) :a in G25 | not a eq 0 ]; primitiusG25 := [a: a in G25 | IsPrimitive(a)]; [a: a in G25 | IsPrimitive(a)]; #[a: a in G25 | IsPrimitive(a)]; /*******************************************************************/ pm:=MinimalPolynomial(p); /* el grau dun element es el grau del seu polinomi minim */ /* el polinomi minim esta definit dintre de Zp */ Roots(pm,Z5); Roots(pm,G25); calculeu:=2*p^(-3)-p^5+((p^6)/(p+2)); IsInvertible(calculeu); calculeu; taula25:=[ : i in [0..23]]; taula16:=[ : i in [0..14]]; taula25; taula16; G2 := GF(2); G4 := GF(4); G8 := GF(8); G166 := GF(16); {i:i in G2}; {i:i in G4}; {i:i in G8}; {i:i in G166}; G2 subset G4; G2 subset G8; G2 subset G166; G4 subset G8; G4 subset G166; G8 subset G166; /*******************************************************************/ G25x:=PolynomialRing(G25); IsFinite(G25x); /* false */ /* Efectivament no es finit, pq estem definint un anell de polynomis sobre un camp de coeficients finits pero els polynomis poden tenir el grau que vulguin */ /* ii */ /*******************************************************************/ alpha := PrimitiveElement(G25); beta := PrimitiveElement(Z5); p1 := alpha^2 + alpha*x + beta*x^2; p2 := 1 + alpha*x; /* iii */ /*******************************************************************/ suma := p1 + p2; producte := p1 * p2; suma; producte; quocient := p1 div p2; quocient; residu := p1 mod p2; residu; mcm := LCM(p1,p2); mcm; mcd := GCD(p1,p2); mcd; p3:= (1/alpha^4) - ((alpha^3)*x) + (alpha^5)*(x^2) + (alpha^11)*(x^3); f:=Factorization(p3); f; r := Roots(f[1][1],G25); arrel1 := r[1][1]; Evaluate(p3,arrel1); a := f[2][1]; a; Roots(a,G25); /*Evaluate(p3,x-f[2][2]);*/ Output: Magma V2.10-22 Sun Apr 11 2004 19:03:32 on modular [Seed = 1165806585] ------------------------------------- { 0, 1 } { 0, 1, 2 } { 0, 1, 2, 3, 4 } true true false true [ 1, 24, 12, 8, 6, 24, 4, 24, 3, 8, 12, 24, 2, 24, 12, 8, 3, 24, 4, 24, 6, 8, 12, 24 ] [ p, p^5, p^7, p^11, p^13, p^17, p^19, p^23 ] 8 [] [ , ] true p^16 p^8 [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , , , , , <2, [ 2, 0 ]>, , , , , ] [ <1, [ 1, 0 ]>, , , , , , <3, [ 3, 0 ]>, , , , , , <4, [ 4, 0 ]>, , ] { 0, 1 } { 1, G4.1, G4.1^2, 0 } { 1, G8.1, G8.1^2, G8.1^3, G8.1^4, G8.1^5, G8.1^6, 0 } { 1, G166.1, G166.1^2, G166.1^3, G166.1^4, G166.1^5, G166.1^6, G166.1^7, G166.1^8, G166.1^9, G166.1^10, G166.1^11, G166.1^12, G166.1^13, G166.1^14, 0 } true true true false true false false 2*x^2 + p^19*x + p^9 p^19*x^3 + p^22*x^2 + p^10*x + p^2 p^17*x + p^5 p^15 x^3 + p^3*x^2 + p^15*x + p^7 1 [ , ] 0 x^2 + p^15*x + p^17 [] Total time: 2.569 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.185.74.31) Time: Sun Apr 11 20:03:37 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-22 Sun Apr 11 2004 20:03:32 on modular [Seed = 1583858370] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.700 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host c-24-13-251-235.client.comcast.net. (24.13.251.235) Time: Sun Apr 11 21:49:57 2004 Input: Generators(Gamma(5)); Output: Magma V2.10-22 Sun Apr 11 2004 21:49:54 on modular [Seed = 3145862705] ------------------------------------- >> Generators(Gamma(5));; ^ Runtime error in 'Generators': Bad argument types Argument types given: FldPrElt Total time: 2.539 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host c-24-13-251-235.client.comcast.net. (24.13.251.235) Time: Sun Apr 11 21:50:13 2004 Input: Generators(Gamma0(5)); Output: Magma V2.10-22 Sun Apr 11 2004 21:50:10 on modular [Seed = 1265827536] ------------------------------------- [ [1 1] [0 1], [ 2 -1] [ 5 -2], [ 3 -2] [ 5 -3] ] Total time: 2.569 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host c-24-13-251-235.client.comcast.net. (24.13.251.235) Time: Sun Apr 11 21:51:51 2004 Input: G:=CongruenceSubgroup(2,N); Generators(G); Output: Magma V2.10-22 Sun Apr 11 2004 21:51:49 on modular [Seed = 1115419710] ------------------------------------- >> G:=CongruenceSubgroup(2,N); ^ User error: Identifier 'N' has not been declared or assigned >> Generators(G);; ^ User error: Identifier 'G' has not been declared or assigned Total time: 2.539 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host c-24-13-251-235.client.comcast.net. (24.13.251.235) Time: Sun Apr 11 21:52:03 2004 Input: G:=CongruenceSubgroup(2,5); Generators(G); Output: Magma V2.10-22 Sun Apr 11 2004 21:51:59 on modular [Seed = 1516497964] ------------------------------------- [ [11 -5] [20 -9], [-1 0] [ 5 -1], [ 16 -5] [ 45 -14], [ 41 -25] [105 -64], [ 31 -20] [ 45 -29], [ 6 -5] [ 5 -4], [ 71 -15] [ 90 -19], [ 21 -5] [ 80 -19], [ 66 -25] [235 -89], [ 76 -55] [ 275 -199], [ 61 -45] [ 80 -59] ] Total time: 3.580 seconds, Total memory usage: 2.60MB ************** MAGMA ***************** Host 3(NXDOMAIN) (163.152.39.238) Time: Mon Apr 12 00:51:16 2004 Input: nfinit(x^2+x+1) Output: Magma V2.10-22 Mon Apr 12 2004 00:51:14 on modular [Seed = 3572413660] ------------------------------------- >> nfinit(x^2+x+1) ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.539 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 3(NXDOMAIN) (163.152.39.238) Time: Mon Apr 12 01:20:14 2004 Input: C := HyperellipticCurve(x^6+x^2+1); Output: Magma V2.10-22 Mon Apr 12 2004 01:20:11 on modular [Seed = 2727921123] ------------------------------------- >> C := HyperellipticCurve(x^6+x^2+1);; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.550 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 3(NXDOMAIN) (163.152.39.238) Time: Mon Apr 12 01:22:58 2004 Input: C := HyperellipticCurve(x^6+x^2+1) Output: Magma V2.10-22 Mon Apr 12 2004 01:22:55 on modular [Seed = 3145849950] ------------------------------------- >> C := HyperellipticCurve(x^6+x^2+1) ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.489 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 3(NXDOMAIN) (163.152.39.238) Time: Mon Apr 12 01:23:20 2004 Input: x=13 Output: Magma V2.10-22 Mon Apr 12 2004 01:23:18 on modular [Seed = 3012154431] ------------------------------------- >> x=13; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.489 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 3(NXDOMAIN) (163.152.39.238) Time: Mon Apr 12 01:23:31 2004 Input: x:=13 Output: Magma V2.10-22 Mon Apr 12 2004 01:23:29 on modular [Seed = 1248865744] ------------------------------------- Total time: 2.489 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 3(NXDOMAIN) (163.152.39.238) Time: Mon Apr 12 01:26:06 2004 Input: P := PolynomialRing(RationalField()); C := HyperellipticCurve(x^6+x^2+1); C; Output: Magma V2.10-22 Mon Apr 12 2004 01:26:03 on modular [Seed = 1516253818] ------------------------------------- Hyperelliptic Curve defined by y^2 = x^6 + x^2 + 1 over Rational Field Total time: 2.570 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (163.152.39.238) Time: Mon Apr 12 01:28:42 2004 Input: P := PolynomialRing(RationalField(GF(2^5)); C := HyperellipticCurve(x^6+x^2+1); C; Output: Magma V2.10-22 Mon Apr 12 2004 01:28:40 on modular [Seed = 1382562577] ------------------------------------- >> P := PolynomialRing(RationalField(GF(2^5)); ^ User error: bad syntax >> C := HyperellipticCurve(x^6+x^2+1); ^ User error: Identifier 'x' has not been declared or assigned >> C; ^ User error: Identifier 'C' has not been declared or assigned Total time: 2.499 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 3(NXDOMAIN) (163.152.39.238) Time: Mon Apr 12 01:29:29 2004 Input: P := PolynomialRing(GF(2^5)); C := HyperellipticCurve(x^6+x^2+1); C; Output: Magma V2.10-22 Mon Apr 12 2004 01:29:27 on modular [Seed = 1767047189] ------------------------------------- HyperellipticCurve( f: x^6 + x^2 + 1 ) In file "/usr/local/magma/package/Geometry/CrvHyp/curve.m", line 257, column 30: >> return HyperellipticCurve(f, Parent(f)!0); ^ Runtime error in 'HyperellipticCurve': Curve is not reduced >> C;; ^ User error: Identifier 'C' has not been declared or assigned Total time: 2.499 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (163.152.39.238) Time: Mon Apr 12 01:30:02 2004 Input: P := PolynomialRing(GF(7)); > C := HyperellipticCurve(x^6+x^2+1); > C; Output: Magma V2.10-22 Mon Apr 12 2004 01:29:59 on modular [Seed = 1633355901] ------------------------------------- Hyperelliptic Curve defined by y^2 = x^6 + x^2 + 1 over GF(7) Total time: 2.580 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (163.152.39.238) Time: Mon Apr 12 01:30:15 2004 Input: P := PolynomialRing(GF(2^5)); > C := HyperellipticCurve(x^6+x^2+1); > C; Output: Magma V2.10-22 Mon Apr 12 2004 01:30:12 on modular [Seed = 1917328221] ------------------------------------- HyperellipticCurve( f: x^6 + x^2 + 1 ) In file "/usr/local/magma/package/Geometry/CrvHyp/curve.m", line 257, column 30: >> return HyperellipticCurve(f, Parent(f)!0); ^ Runtime error in 'HyperellipticCurve': Curve is not reduced >> C; ^ User error: Identifier 'C' has not been declared or assigned Total time: 2.549 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (163.152.39.238) Time: Mon Apr 12 01:30:46 2004 Input: P := PolynomialRing(GF(2^5)); > C := HyperellipticCurve(x^5+x^3+1,x^2x); > C; Output: Magma V2.10-22 Mon Apr 12 2004 01:30:43 on modular [Seed = 170943426] ------------------------------------- >> C := HyperellipticCurve(x^5+x^3+1,x^2x); ^ User error: bad syntax >> C; ^ User error: Identifier 'C' has not been declared or assigned Total time: 2.489 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 3(NXDOMAIN) (163.152.39.238) Time: Mon Apr 12 01:31:00 2004 Input: P := PolynomialRing(GF(2^5)); > C := HyperellipticCurve(x^5+x^3+1,x^2+x); > C; Output: Magma V2.10-22 Mon Apr 12 2004 01:30:58 on modular [Seed = 20670680] ------------------------------------- Hyperelliptic Curve defined by y^2 + (x^2 + x)*y = x^5 + x^3 + 1 over GF(2^5) Total time: 2.499 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 3(NXDOMAIN) (163.152.39.238) Time: Mon Apr 12 01:41:57 2004 Input: P := PolynomialRing(GF(2^5)); C := HyperellipticCurve(x^5+x^3+1,x^2+x); C; C![0,1] Output: Magma V2.10-22 Mon Apr 12 2004 01:41:55 on modular [Seed = 705709634] ------------------------------------- Hyperelliptic Curve defined by y^2 + (x^2 + x)*y = x^5 + x^3 + 1 over GF(2^5) (0 : 1 : 1) Total time: 2.549 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 3(NXDOMAIN) (163.152.39.238) Time: Mon Apr 12 01:42:21 2004 Input: P := PolynomialRing(GF(2^5)); C := HyperellipticCurve(x^5+x^3+1,x^2+x); C; C![0,1]; C![x^5,x^15] Output: Magma V2.10-22 Mon Apr 12 2004 01:42:18 on modular [Seed = 572018259] ------------------------------------- Hyperelliptic Curve defined by y^2 + (x^2 + x)*y = x^5 + x^3 + 1 over GF(2^5) (0 : 1 : 1) >> C![x^5,x^15]; ^ Runtime error in '!': Cannot coerce element into ring Total time: 2.539 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 3(NXDOMAIN) (163.152.39.238) Time: Mon Apr 12 01:42:42 2004 Input: P := PolynomialRing(GF(2^5)); C := HyperellipticCurve(x^5+x^3+1,x^2+x); C; C![0,1]; C![y^5,y^15] Output: Magma V2.10-22 Mon Apr 12 2004 01:42:39 on modular [Seed = 973100606] ------------------------------------- Hyperelliptic Curve defined by y^2 + (x^2 + x)*y = x^5 + x^3 + 1 over GF(2^5) (0 : 1 : 1) >> C![y^5,y^15]; ^ User error: Identifier 'y' has not been declared or assigned Total time: 2.500 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 3(NXDOMAIN) (163.152.39.238) Time: Mon Apr 12 01:47:36 2004 Input: P := PolynomialRing(GF(2^5)); C := HyperellipticCurve(x^5+x^3+1,x^2+x); C; C![0,1]; C![1,1] Output: Magma V2.10-22 Mon Apr 12 2004 01:47:33 on modular [Seed = 873355530] ------------------------------------- Hyperelliptic Curve defined by y^2 + (x^2 + x)*y = x^5 + x^3 + 1 over GF(2^5) (0 : 1 : 1) (1 : 1 : 1) Total time: 2.480 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 3(NXDOMAIN) (163.152.39.238) Time: Mon Apr 12 01:48:27 2004 Input: P := PolynomialRing(GF(2^5)); C := HyperellipticCurve(x^5+x^3+1,x^2+x); C; C![0,1]; C![1,1]; C! DivisorGroup(C) Output: Magma V2.10-22 Mon Apr 12 2004 01:48:24 on modular [Seed = 3438715183] ------------------------------------- Hyperelliptic Curve defined by y^2 + (x^2 + x)*y = x^5 + x^3 + 1 over GF(2^5) (0 : 1 : 1) (1 : 1 : 1) >> C! ^ Runtime error in '!': Illegal coercion LHS: CrvHyp RHS: DivCrv Total time: 2.539 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 3(NXDOMAIN) (163.152.39.238) Time: Mon Apr 12 01:56:55 2004 Input: P := PolynomialRing(GF(2^5)); C := HyperellipticCurve(x^5+x^3+1,x^2+x); C; Genrate(P) Output: Magma V2.10-22 Mon Apr 12 2004 01:56:52 on modular [Seed = 3589257786] ------------------------------------- Hyperelliptic Curve defined by y^2 + (x^2 + x)*y = x^5 + x^3 + 1 over GF(2^5) >> Genrate(P) ^ User error: Identifier 'Genrate' has not been declared or assigned Total time: 2.520 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 3(NXDOMAIN) (163.152.39.238) Time: Mon Apr 12 01:57:03 2004 Input: P := PolynomialRing(GF(2^5)); Genrate(P) Output: Magma V2.10-22 Mon Apr 12 2004 01:57:01 on modular [Seed = 3990323723] ------------------------------------- >> Genrate(P) ^ User error: Identifier 'Genrate' has not been declared or assigned Total time: 2.500 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 3(NXDOMAIN) (163.152.39.238) Time: Mon Apr 12 01:57:22 2004 Input: P := PolynomialRing(GF(2^5)); Genrator(P) Output: Magma V2.10-22 Mon Apr 12 2004 01:57:19 on modular [Seed = 3856632337] ------------------------------------- >> Genrator(P) ^ User error: Identifier 'Genrator' has not been declared or assigned Total time: 2.489 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 3(NXDOMAIN) (163.152.39.238) Time: Mon Apr 12 01:57:30 2004 Input: P := PolynomialRing(GF(2^5)); Generator(P) Output: Magma V2.10-22 Mon Apr 12 2004 01:57:28 on modular [Seed = 4257714814] ------------------------------------- 1 Total time: 2.470 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 3(NXDOMAIN) (163.152.39.238) Time: Mon Apr 12 01:58:24 2004 Input: P := PolynomialRing(GF(2^5)); Generator(P); P.1. Output: Magma V2.10-22 Mon Apr 12 2004 01:58:22 on modular [Seed = 4124023360] ------------------------------------- 1 >> P.1. ^ User error: Real literal has no digits after decimal point Total time: 2.500 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 3(NXDOMAIN) (163.152.39.238) Time: Mon Apr 12 01:59:34 2004 Input: P := PolynomialRing(GF(2^5)); Generator(P); P.1 Output: Magma V2.10-22 Mon Apr 12 2004 01:59:31 on modular [Seed = 2360802436] ------------------------------------- 1 x Total time: 2.540 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 3(NXDOMAIN) (163.152.39.238) Time: Mon Apr 12 02:01:26 2004 Input: P := PolynomialRing(GF(2^5)); Generator(P); P.1 NormalElement(P) Output: Magma V2.10-22 Mon Apr 12 2004 02:01:24 on modular [Seed = 2727924317] ------------------------------------- 1 >> NormalElement(P); ^ User error: bad syntax Total time: 2.499 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 3(NXDOMAIN) (163.152.39.238) Time: Mon Apr 12 02:01:36 2004 Input: P := PolynomialRing(GF(2^5)); Generator(P); P.1; NormalElement(P) Output: Magma V2.10-22 Mon Apr 12 2004 02:01:34 on modular [Seed = 3129002575] ------------------------------------- 1 x >> NormalElement(P); ^ Runtime error in 'NormalElement': Bad argument types Argument types given: RngUPol Total time: 2.550 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 3(NXDOMAIN) (163.152.39.238) Time: Mon Apr 12 02:02:18 2004 Input: P := PolynomialRing(GF(2^5)); Generator(P); P.1; NormalElement(P); Output: Magma V2.10-22 Mon Apr 12 2004 02:02:16 on modular [Seed = 2995307025] ------------------------------------- 1 x >> NormalElement(P);; ^ Runtime error in 'NormalElement': Bad argument types Argument types given: RngUPol Total time: 2.550 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 3(NXDOMAIN) (163.152.39.238) Time: Mon Apr 12 02:02:26 2004 Input: P := PolynomialRing(GF(2^5)); NormalElement(P); Output: Magma V2.10-22 Mon Apr 12 2004 02:02:23 on modular [Seed = 1299660270] ------------------------------------- >> NormalElement(P);; ^ Runtime error in 'NormalElement': Bad argument types Argument types given: RngUPol Total time: 2.539 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 3(NXDOMAIN) (163.152.39.238) Time: Mon Apr 12 02:03:02 2004 Input: P := PolynomialRing(GF(2^5)); NormalElement(P,GF(2)); Output: Magma V2.10-22 Mon Apr 12 2004 02:03:00 on modular [Seed = 1165964317] ------------------------------------- >> NormalElement(P,GF(2));; ^ Runtime error in 'NormalElement': Bad argument types Argument types given: RngUPol, FldFin Total time: 2.539 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 3(NXDOMAIN) (163.152.39.238) Time: Mon Apr 12 02:10:23 2004 Input: P := PolynomialRing(GF(2^5)); C:= HyperellipticCurve(x^5+x^3+1,x^2+x); Output: Magma V2.10-22 Mon Apr 12 2004 02:10:21 on modular [Seed = 1399398866] ------------------------------------- Total time: 2.489 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 3(NXDOMAIN) (163.152.39.238) Time: Mon Apr 12 02:10:38 2004 Input: P := PolynomialRing(GF(2^5)); C:= HyperellipticCurve(x^5+x^3+1,x^2+x); #C; Output: Magma V2.10-22 Mon Apr 12 2004 02:10:35 on modular [Seed = 1800477180] ------------------------------------- 33 Total time: 2.489 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 3(NXDOMAIN) (163.152.39.238) Time: Mon Apr 12 02:11:41 2004 Input: P := PolynomialRing(GF(2^5)); C:= HyperellipticCurve(x^5+x^3+1,x^2+x); #C; Points(C); Output: Magma V2.10-22 Mon Apr 12 2004 02:11:38 on modular [Seed = 2084966186] ------------------------------------- 33 {@ (1 : 0 : 0), (1 : 1 : 1), ($.1^5 : $.1^15 : 1), ($.1^5 : $.1^27 : 1), ($.1^7 : $.1^4 : 1), ($.1^7 : $.1^25 : 1), ($.1^9 : $.1^27 : 1), ($.1^9 : $.1^30 : 1), ($.1^10 : $.1^23 : 1), ($.1^10 : $.1^30 : 1), ($.1^14 : $.1^8 : 1), ($.1^14 : $.1^19 : 1), ($.1^15 : 0 : 1), ($.1^15 : $.1^8 : 1), ($.1^18 : $.1^23 : 1), ($.1^18 : $.1^29 : 1), ($.1^19 : $.1^2 : 1), ($.1^19 : $.1^28 : 1), ($.1^20 : $.1^15 : 1), ($.1^20 : $.1^29 : 1), ($.1^23 : 0 : 1), ($.1^23 : $.1^4 : 1), ($.1^25 : $.1 : 1), ($.1^25 : $.1^14 : 1), ($.1^27 : 0 : 1), ($.1^27 : $.1^2 : 1), ($.1^28 : $.1^7 : 1), ($.1^28 : $.1^16 : 1), ($.1^29 : 0 : 1), ($.1^29 : $.1 : 1), ($.1^30 : 0 : 1), ($.1^30 : $.1^16 : 1), (0 : 1 : 1) @} Total time: 2.539 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 3(NXDOMAIN) (163.152.39.238) Time: Mon Apr 12 02:12:30 2004 Input: P := PolynomialRing(GF(2^5)); C:= HyperellipticCurve(x^5+x^3+1,x^2+x); #C; P.1 Output: Magma V2.10-22 Mon Apr 12 2004 02:12:28 on modular [Seed = 1951270772] ------------------------------------- 33 x Total time: 2.490 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 3(NXDOMAIN) (163.152.39.238) Time: Mon Apr 12 02:12:42 2004 Input: P := PolynomialRing(GF(2^5)); C:= HyperellipticCurve(x^5+x^3+1,x^2+x); #C; P.3 Output: Magma V2.10-22 Mon Apr 12 2004 02:12:39 on modular [Seed = 204898071] ------------------------------------- 33 >> P.3 ^ Runtime error in '.': Value for name index (3) should be in the range [1..1] Total time: 2.500 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 3(NXDOMAIN) (163.152.39.238) Time: Mon Apr 12 02:13:12 2004 Input: P := PolynomialRing(GF(2^5)); C:= HyperellipticCurve(x^5+x^3+1,x^2+x); #C; Points(C); Output: Magma V2.10-22 Mon Apr 12 2004 02:13:10 on modular [Seed = 71202622] ------------------------------------- 33 {@ (1 : 0 : 0), (1 : 1 : 1), ($.1^5 : $.1^15 : 1), ($.1^5 : $.1^27 : 1), ($.1^7 : $.1^4 : 1), ($.1^7 : $.1^25 : 1), ($.1^9 : $.1^27 : 1), ($.1^9 : $.1^30 : 1), ($.1^10 : $.1^23 : 1), ($.1^10 : $.1^30 : 1), ($.1^14 : $.1^8 : 1), ($.1^14 : $.1^19 : 1), ($.1^15 : 0 : 1), ($.1^15 : $.1^8 : 1), ($.1^18 : $.1^23 : 1), ($.1^18 : $.1^29 : 1), ($.1^19 : $.1^2 : 1), ($.1^19 : $.1^28 : 1), ($.1^20 : $.1^15 : 1), ($.1^20 : $.1^29 : 1), ($.1^23 : 0 : 1), ($.1^23 : $.1^4 : 1), ($.1^25 : $.1 : 1), ($.1^25 : $.1^14 : 1), ($.1^27 : 0 : 1), ($.1^27 : $.1^2 : 1), ($.1^28 : $.1^7 : 1), ($.1^28 : $.1^16 : 1), ($.1^29 : 0 : 1), ($.1^29 : $.1 : 1), ($.1^30 : 0 : 1), ($.1^30 : $.1^16 : 1), (0 : 1 : 1) @} Total time: 2.559 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 3(NXDOMAIN) (163.152.39.238) Time: Mon Apr 12 02:13:36 2004 Input: P := PolynomialRing(GF(2^5)); C:= HyperellipticCurve(x^5+x^3+1,x^2+x); #C; Points(C); P.1^5 Output: Magma V2.10-22 Mon Apr 12 2004 02:13:33 on modular [Seed = 472281053] ------------------------------------- 33 {@ (1 : 0 : 0), (1 : 1 : 1), ($.1^5 : $.1^15 : 1), ($.1^5 : $.1^27 : 1), ($.1^7 : $.1^4 : 1), ($.1^7 : $.1^25 : 1), ($.1^9 : $.1^27 : 1), ($.1^9 : $.1^30 : 1), ($.1^10 : $.1^23 : 1), ($.1^10 : $.1^30 : 1), ($.1^14 : $.1^8 : 1), ($.1^14 : $.1^19 : 1), ($.1^15 : 0 : 1), ($.1^15 : $.1^8 : 1), ($.1^18 : $.1^23 : 1), ($.1^18 : $.1^29 : 1), ($.1^19 : $.1^2 : 1), ($.1^19 : $.1^28 : 1), ($.1^20 : $.1^15 : 1), ($.1^20 : $.1^29 : 1), ($.1^23 : 0 : 1), ($.1^23 : $.1^4 : 1), ($.1^25 : $.1 : 1), ($.1^25 : $.1^14 : 1), ($.1^27 : 0 : 1), ($.1^27 : $.1^2 : 1), ($.1^28 : $.1^7 : 1), ($.1^28 : $.1^16 : 1), ($.1^29 : 0 : 1), ($.1^29 : $.1 : 1), ($.1^30 : 0 : 1), ($.1^30 : $.1^16 : 1), (0 : 1 : 1) @} x^5 Total time: 2.489 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 3(NXDOMAIN) (163.152.39.238) Time: Mon Apr 12 02:24:53 2004 Input: P := PolynomialRing(GF(2^5)); C:= HyperellipticCurve(x^5+x^3+1,x^2+x); #C; J!0; Output: Magma V2.10-22 Mon Apr 12 2004 02:24:51 on modular [Seed = 605966939] ------------------------------------- 33 >> J!0;; ^ User error: Identifier 'J' has not been declared or assigned Total time: 2.559 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 3(NXDOMAIN) (163.152.39.238) Time: Mon Apr 12 02:25:41 2004 Input: P := PolynomialRing(GF(2^5)); C:= HyperellipticCurve(x^5+x^3+1,x^2+x); #C; Jacobian(C); J!0; Output: Magma V2.10-22 Mon Apr 12 2004 02:25:39 on modular [Seed = 890192666] ------------------------------------- 33 Jacobian of Hyperelliptic Curve defined by y^2 + (x^2 + x)*y = x^5 + x^3 + 1 over GF(2^5) >> J!0;; ^ User error: Identifier 'J' has not been declared or assigned Total time: 2.489 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 3(NXDOMAIN) (163.152.39.238) Time: Mon Apr 12 02:26:29 2004 Input: P := PolynomialRing(GF(2^5)); C:= HyperellipticCurve(x^5+x^3+1,x^2+x); #C; J:=Jacobian(C); J!0; Output: Magma V2.10-22 Mon Apr 12 2004 02:26:27 on modular [Seed = 3472144401] ------------------------------------- 33 (1, 0, 0) Total time: 2.509 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 3(NXDOMAIN) (163.152.39.238) Time: Mon Apr 12 02:26:44 2004 Input: P := PolynomialRing(GF(2^5)); C:= HyperellipticCurve(x^5+x^3+1,x^2+x); #C; J:=Jacobian(C); Output: Magma V2.10-22 Mon Apr 12 2004 02:26:41 on modular [Seed = 3338448939] ------------------------------------- 33 Total time: 2.539 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 3(NXDOMAIN) (163.152.39.238) Time: Mon Apr 12 02:26:51 2004 Input: P := PolynomialRing(GF(2^5)); C:= HyperellipticCurve(x^5+x^3+1,x^2+x); #C; J:=Jacobian(C); J Output: Magma V2.10-22 Mon Apr 12 2004 02:26:48 on modular [Seed = 3739527226] ------------------------------------- 33 Jacobian of Hyperelliptic Curve defined by y^2 + (x^2 + x)*y = x^5 + x^3 + 1 over GF(2^5) Total time: 2.539 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host dsl-roigw2fe4.dial.inet.fi. (80.223.133.228) Time: Mon Apr 12 04:02:13 2004 Input: (a+b)^2 Output: Magma V2.10-22 Mon Apr 12 2004 04:02:11 on modular [Seed = 505680723] ------------------------------------- >> (a+b)^2; ^ User error: Identifier 'a' has not been declared or assigned Total time: 2.599 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host c-24-13-251-235.client.comcast.net. (24.13.251.235) Time: Mon Apr 12 06:34:36 2004 Input: Generators(Gamma1(7)); Output: Magma V2.10-22 Mon Apr 12 2004 06:34:34 on modular [Seed = 1057296341] ------------------------------------- [ [1 1] [0 1], [ 1 -1] [ 7 -6], [ 13 -4] [ 49 -15], [ 8 -5] [ 21 -13], [ 20 -9] [ 49 -22] ] Total time: 2.589 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Mon Apr 12 08:27:56 2004 Input: function KnapsackLattice(Q, s) > n := #Q; > X := RMatrixSpace(IntegerRing(), n + 1, n + 2) ! 0; > for i := 1 to n do > X[i][i] := 2; > X[i][n + 1] := n * Q[i]; > X[n + 1][i] := 1; > end for; > X[n + 1][n + 1] := n * s; > X[n + 1][n + 2] := 1; > return Lattice(X); > end function; > function KnapsackSolutions(L) > n := Rank(L) - 1; > M := n + 1; > S := ShortVectors(L, M, M); > return [ > [i: i in [1 .. n] | v[i] ne v[n + 2]]: t in S | > forall{i: i in [1 .. n] cat [n + 2] | Abs(v[i]) eq 1} and > v[n + 1] eq 0 where v is t[1] > ]; > end function; > Q := [ 52, 218, 755, 221, 574, 593, 172, 771, 183, 810, 437,137]; > s := 2676; > L := KnapsackLattice(Q, s); > L; > S := KnapsackSolutions(L); > S; Output: Magma V2.10-22 Mon Apr 12 2004 08:27:45 on modular [Seed = 1800511611] ------------------------------------- Lattice of rank 13 and degree 14 Basis: ( 0 0 0 0 2 0 0 0 0 0 -2 -2 0 0) ( 1 1 1 1 -1 -1 -1 -1 1 1 1 -1 0 -1) ( 1 1 -1 -1 -1 1 -1 -1 -1 1 1 1 0 1) ( 0 2 0 0 0 0 -2 0 -2 0 0 2 0 0) ( 2 0 0 2 0 -2 0 0 2 0 0 2 0 0) ( 0 0 2 0 0 -2 2 -2 0 0 2 0 0 0) ( 3 -1 1 1 -1 1 -1 -1 -1 -1 1 1 0 1) ( 1 1 1 -1 -1 1 1 -1 1 -1 -1 3 0 1) ( 1 -1 -1 3 -1 -1 1 1 -1 1 -1 -1 0 1) ( 1 -1 -1 1 1 1 1 -1 -3 1 1 -1 0 -1) ( 1 3 -3 1 -1 1 1 1 1 -1 1 1 0 1) ( 1 1 1 -3 1 -1 3 1 1 -1 -1 -1 0 -1) ( 1 -1 -1 1 -1 1 1 1 -1 -1 1 -1 -12 1) [ [ 2, 3, 4, 5, 8, 12 ], [ 3, 4, 5, 7, 8, 9 ], [ 3, 4, 7, 8, 9, 11, 12 ], [ 1, 2, 3, 4, 9, 10, 11 ] ] Total time: 2.520 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Mon Apr 12 08:33:37 2004 Input: function KnapsackParamGeneration (n) max_increment := 2^n; b_i := 2^n + Random (1, max_increment); b_vec := [b_i]; sum := b_i; for i in [2..n] do b_i := sum + Random (1, max_increment); sum +:= b_i; Append (~b_vec, b_i); end for; M := NextPrime (sum); W := Random (1, M); aprime_vec := [(b * W) mod M : b in b_vec]; pi := Random(Sym(n)); a_vec := [ aprime_vec[Image(pi, i)] : i in [1..n] ]; return a_vec, b_vec, M, W, pi; end function; function KnapsackEncrypt (bit_stream, a_vec) n := #bit_stream; if n ne #a_vec then return 0; end if; return &+[a_vec[i]*bit_stream[i] : i in [1..n]]; end function; function KnapsackDecrypt (s, b_vec, M, W, pi) c := (s * Modinv (W, M)) mod M; n := #b_vec; pi_inv := pi^-1; bit_stream := [0 : i in [1..n]]; for j in [n..1 by -1] do if c ge b_vec[j] then bit_stream[Image (pi_inv, j)] := 1; c -:= b_vec[j]; end if; end for; return bit_stream; end function; n := 5; n; a_vec, b_vec, M, W, pi := KnapsackParamGeneration (n); a_vec; n; bit_stream := [Random(0,1): i in [1..n]]; bit_stream; n; s := KnapsackEncrypt (bit_stream, a_vec); s; KnapsackDecrypt (s, b_vec, M, W, pi); Output: Magma V2.10-22 Mon Apr 12 2004 08:33:34 on modular [Seed = 455202772] ------------------------------------- 5 [ 185, 121, 729, 432, 177 ] 5 [ 0, 1, 0, 0, 1 ] 5 298 [ 0, 1, 0, 0, 1 ] Total time: 2.519 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host wwwcache.cankaya.edu.tr. (194.27.200.8) Time: Mon Apr 12 08:35:54 2004 Input: function KnapsackParamGeneration (n) max_increment := 2^n; b_i := 2^n + Random (1, max_increment); b_vec := [b_i]; sum := b_i; for i in [2..n] do b_i := sum + Random (1, max_increment); sum +:= b_i; Append (~b_vec, b_i); end for; M := NextPrime (sum); W := Random (1, M); aprime_vec := [(b * W) mod M : b in b_vec]; pi := Random(Sym(n)); a_vec := [ aprime_vec[Image(pi, i)] : i in [1..n] ]; return a_vec, b_vec, M, W, pi; end function; function KnapsackEncrypt (bit_stream, a_vec) n := #bit_stream; if n ne #a_vec then return 0; end if; return &+[a_vec[i]*bit_stream[i] : i in [1..n]]; end function; function KnapsackDecrypt (s, b_vec, M, W, pi) c := (s * Modinv (W, M)) mod M; n := #b_vec; pi_inv := pi^-1; bit_stream := [0 : i in [1..n]]; for j in [n..1 by -1] do if c ge b_vec[j] then bit_stream[Image (pi_inv, j)] := 1; c -:= b_vec[j]; end if; end for; return bit_stream; end function; n := 32; n; a_vec, b_vec, M, W, pi := KnapsackParamGeneration (n); a_vec; n; bit_stream := [Random(0,1): i in [1..n]]; bit_stream; n; s := KnapsackEncrypt (bit_stream, a_vec); s; KnapsackDecrypt (s, b_vec, M, W, pi); Output: Magma V2.10-22 Mon Apr 12 2004 08:35:51 on modular [Seed = 121490033] ------------------------------------- 32 [ 1629591823897072440, 12957972572655120217, 12256614068120344453, 13818059772999658789, 536099374056403247, 7472022889778356602, 10399222563727522985, 4379635146247568303, 8709560703800263924, 9948501457915496708, 10765692871655626596, 12110640763444328960, 6651449711115481497, 9036100337854068621, 2989117429846963844, 828758680646901269, 15267356843161620567, 6535179365992399085, 13978382144374032839, 4650046402499818872, 12654015600974912958, 16172585478920179357, 14861220607526695167, 6001073458098697395, 5895278703930821218, 12785090153558234303, 11949009241849961858, 10366643794264148588, 911369066857574892, 10043541627555416759, 11449963130149752473, 10244881442144861115 ] 32 [ 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0 ] 32 111639221396331275891 [ 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0 ] Total time: 2.549 seconds, Total memory usage: 2.88MB ************** MAGMA ***************** Host 94-BARC-X53.libre.retevision.es. (62.82.23.94) Time: Mon Apr 12 12:35:17 2004 Input: /** i **/ K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; /** ii **/ K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); /*Provem amb Z2 */ Z2:=Integers(2); IsField(Z2); /** iii**/ Z3:=GF(3); P3:=PolynomialRing(Z3); Z2:=GF(2); P2:=PolynomialRing(Z2); Z5:=GF(5); P5:=PolynomialRing(Z5); f1:=P3![2,2,1]; f1; f2:=P2![1,1,0,0,1]; f2; f3:=P5![3,2,1]; f3; f4:=P3![1,2,1]; f4; IsIrreducible(f1); IsIrreducible(f2); IsIrreducible(f3); IsIrreducible(f4); G9:=ext; G16:=ext; G25:=ext; G9b:=ext; /* L'ultim cas dona error perque el polinomi NO es irreductible*/ /** iv **/ list:=[G25!x : x in [1..5]]; [Order(G25!x):x in list| x ne 0]; primitiu:=PrimitiveElement(G25); /* Hem repetit bastantes vegades aquesta comanda i sempre ens ha donat l'1. Per tant la llista es la [1] Un cos de p^n te p elements primitius*/ /** v **/ polmin:=MinimalPolynomial(primitiu); grau:=Degree(polmin); polmin; grau; MinimalPolynomial(primitiu,Z5); MinimalPolynomial(primitiu,G25); /*Veiem que esta definit sobre Z5*/ Roots(polmin,Z5); Roots(polmin,G25); /** vi **/ vi:=1/alpha^3-alpha^5+(1/alpha+2)*alpha^6; vi; IsInvertible(vi); Output: Magma V2.10-22 Mon Apr 12 2004 12:35:14 on modular [Seed = 3371322841] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true true x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 true true true false >> G9b:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 4, 4, 2 ] x^2 + 2*x + 3 2 x^2 + 2*x + 3 $.1 + alpha^13 [] [ , ] alpha^14 true alpha^10 Total time: 2.629 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 94-BARC-X53.libre.retevision.es. (62.82.23.94) Time: Mon Apr 12 12:36:09 2004 Input: /** i **/ K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; /** ii **/ K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); /*Provem amb Z2 */ Z2:=Integers(2); IsField(Z2); /** iii**/ Z3:=GF(3); P3:=PolynomialRing(Z3); Z2:=GF(2); P2:=PolynomialRing(Z2); Z5:=GF(5); P5:=PolynomialRing(Z5); f1:=P3![2,2,1]; f1; f2:=P2![1,1,0,0,1]; f2; f3:=P5![3,2,1]; f3; f4:=P3![1,2,1]; f4; IsIrreducible(f1); IsIrreducible(f2); IsIrreducible(f3); IsIrreducible(f4); G9:=ext; G16:=ext; G25:=ext; G9b:=ext; /* L'ultim cas dona error perque el polinomi NO es irreductible*/ /** iv **/ list:=[G25!x : x in [1..5]]; [Order(G25!x):x in list| x ne 0]; primitiu:=PrimitiveElement(G25); /* Hem repetit bastantes vegades aquesta comanda i sempre ens ha donat l'1. Per tant la llista es la [1] Un cos de p^n te p elements primitius*/ /** v **/ polmin:=MinimalPolynomial(primitiu); grau:=Degree(polmin); polmin; grau; MinimalPolynomial(primitiu,Z5); MinimalPolynomial(primitiu,G25); /*Veiem que esta definit sobre Z5*/ Roots(polmin,Z5); Roots(polmin,G25); /** vi **/ vi:=1/alpha^3-alpha^5+(1/alpha+2)*alpha^6; vi; IsInvertible(vi); [x:x in G25|IsInvertible(x)]; Output: Magma V2.10-22 Mon Apr 12 2004 12:36:07 on modular [Seed = 4039800276] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true true x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 true true true false >> G9b:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 4, 4, 2 ] x^2 + 2*x + 3 2 x^2 + 2*x + 3 $.1 + alpha^13 [] [ , ] alpha^14 true alpha^10 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] Total time: 2.630 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 94-BARC-X53.libre.retevision.es. (62.82.23.94) Time: Mon Apr 12 12:42:18 2004 Input: /** i **/ K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; /** ii **/ K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); /*Provem amb Z2 */ Z2:=Integers(2); IsField(Z2); /** iii**/ Z3:=GF(3); P3:=PolynomialRing(Z3); Z2:=GF(2); P2:=PolynomialRing(Z2); Z5:=GF(5); P5:=PolynomialRing(Z5); f1:=P3![2,2,1]; f1; f2:=P2![1,1,0,0,1]; f2; f3:=P5![3,2,1]; f3; f4:=P3![1,2,1]; f4; IsIrreducible(f1); IsIrreducible(f2); IsIrreducible(f3); IsIrreducible(f4); G9:=ext; G16:=ext; G25:=ext; G9b:=ext; /* L'ultim cas dona error perque el polinomi NO es irreductible*/ /** iv **/ list:=[G25!x : x in [1..5]]; [Order(G25!x):x in list| x ne 0]; primitiu:=PrimitiveElement(G25); /* Hem repetit bastantes vegades aquesta comanda i sempre ens ha donat l'1. Per tant la llista es la [1] Un cos de p^n te p elements primitius*/ /** v **/ polmin:=MinimalPolynomial(primitiu); grau:=Degree(polmin); polmin; grau; MinimalPolynomial(primitiu,Z5); MinimalPolynomial(primitiu,G25); /*Veiem que esta definit sobre Z5*/ Roots(polmin,Z5); Roots(polmin,G25); /** vi **/ vi:=1/alpha^3-alpha^5+(1/alpha+2)*alpha^6; vi; IsInvertible(vi); [x:x in G25|IsInvertible(x)]; [y:y in G25 |ElementToSequence(x)]; Output: Magma V2.10-22 Mon Apr 12 2004 12:42:15 on modular [Seed = 3873202258] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true true x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 true true true false >> G9b:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 4, 4, 2 ] x^2 + 2*x + 3 2 x^2 + 2*x + 3 $.1 + alpha^13 [] [ , ] alpha^14 true alpha^10 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] >> [y:y in G25 |ElementToSequence(x)];; ^ Runtime error in sequence construction: Logical expected Total time: 2.539 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 94-BARC-X53.libre.retevision.es. (62.82.23.94) Time: Mon Apr 12 12:42:38 2004 Input: /** i **/ K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; /** ii **/ K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); /*Provem amb Z2 */ Z2:=Integers(2); IsField(Z2); /** iii**/ Z3:=GF(3); P3:=PolynomialRing(Z3); Z2:=GF(2); P2:=PolynomialRing(Z2); Z5:=GF(5); P5:=PolynomialRing(Z5); f1:=P3![2,2,1]; f1; f2:=P2![1,1,0,0,1]; f2; f3:=P5![3,2,1]; f3; f4:=P3![1,2,1]; f4; IsIrreducible(f1); IsIrreducible(f2); IsIrreducible(f3); IsIrreducible(f4); G9:=ext; G16:=ext; G25:=ext; G9b:=ext; /* L'ultim cas dona error perque el polinomi NO es irreductible*/ /** iv **/ list:=[G25!x : x in [1..5]]; [Order(G25!x):x in list| x ne 0]; primitiu:=PrimitiveElement(G25); /* Hem repetit bastantes vegades aquesta comanda i sempre ens ha donat l'1. Per tant la llista es la [1] Un cos de p^n te p elements primitius*/ /** v **/ polmin:=MinimalPolynomial(primitiu); grau:=Degree(polmin); polmin; grau; MinimalPolynomial(primitiu,Z5); MinimalPolynomial(primitiu,G25); /*Veiem que esta definit sobre Z5*/ Roots(polmin,Z5); Roots(polmin,G25); /** vi **/ vi:=1/alpha^3-alpha^5+(1/alpha+2)*alpha^6; vi; IsInvertible(vi); [x:x in G25|IsInvertible(x)]; [y:y in G25 |ElementToSequence(y)]; Output: Magma V2.10-22 Mon Apr 12 2004 12:42:36 on modular [Seed = 4006897729] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true true x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 true true true false >> G9b:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 4, 4, 2 ] x^2 + 2*x + 3 2 x^2 + 2*x + 3 $.1 + alpha^13 [] [ , ] alpha^14 true alpha^10 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] >> [y:y in G25 |ElementToSequence(y)];; ^ Runtime error in sequence construction: Logical expected Total time: 2.519 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 94-BARC-X53.libre.retevision.es. (62.82.23.94) Time: Mon Apr 12 12:43:07 2004 Input: /** i **/ K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; /** ii **/ K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); /*Provem amb Z2 */ Z2:=Integers(2); IsField(Z2); /** iii**/ Z3:=GF(3); P3:=PolynomialRing(Z3); Z2:=GF(2); P2:=PolynomialRing(Z2); Z5:=GF(5); P5:=PolynomialRing(Z5); f1:=P3![2,2,1]; f1; f2:=P2![1,1,0,0,1]; f2; f3:=P5![3,2,1]; f3; f4:=P3![1,2,1]; f4; IsIrreducible(f1); IsIrreducible(f2); IsIrreducible(f3); IsIrreducible(f4); G9:=ext; G16:=ext; G25:=ext; G9b:=ext; /* L'ultim cas dona error perque el polinomi NO es irreductible*/ /** iv **/ list:=[G25!x : x in [1..5]]; [Order(G25!x):x in list| x ne 0]; primitiu:=PrimitiveElement(G25); /* Hem repetit bastantes vegades aquesta comanda i sempre ens ha donat l'1. Per tant la llista es la [1] Un cos de p^n te p elements primitius*/ /** v **/ polmin:=MinimalPolynomial(primitiu); grau:=Degree(polmin); polmin; grau; MinimalPolynomial(primitiu,Z5); MinimalPolynomial(primitiu,G25); /*Veiem que esta definit sobre Z5*/ Roots(polmin,Z5); Roots(polmin,G25); /** vi **/ vi:=1/alpha^3-alpha^5+(1/alpha+2)*alpha^6; vi; IsInvertible(vi); [x:x in G25|IsInvertible(x)]; ElementToSequence(G25); Output: Magma V2.10-22 Mon Apr 12 2004 12:43:05 on modular [Seed = 2527859164] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true true x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 true true true false >> G9b:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 4, 4, 2 ] x^2 + 2*x + 3 2 x^2 + 2*x + 3 $.1 + alpha^13 [] [ , ] alpha^14 true alpha^10 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] >> ElementToSequence(G25);; ^ Runtime error in 'ElementToSequence': Bad argument types Argument types given: FldFin Total time: 2.509 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 94-BARC-X53.libre.retevision.es. (62.82.23.94) Time: Mon Apr 12 12:45:30 2004 Input: /** i **/ K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; /** ii **/ K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); /*Provem amb Z2 */ Z2:=Integers(2); IsField(Z2); /** iii**/ Z3:=GF(3); P3:=PolynomialRing(Z3); Z2:=GF(2); P2:=PolynomialRing(Z2); Z5:=GF(5); P5:=PolynomialRing(Z5); f1:=P3![2,2,1]; f1; f2:=P2![1,1,0,0,1]; f2; f3:=P5![3,2,1]; f3; f4:=P3![1,2,1]; f4; IsIrreducible(f1); IsIrreducible(f2); IsIrreducible(f3); IsIrreducible(f4); G9:=ext; G16:=ext; G25:=ext; G9b:=ext; /* L'ultim cas dona error perque el polinomi NO es irreductible*/ /** iv **/ list:=[G25!x : x in [1..5]]; [Order(G25!x):x in list| x ne 0]; primitiu:=PrimitiveElement(G25); /* Hem repetit bastantes vegades aquesta comanda i sempre ens ha donat l'1. Per tant la llista es la [1] Un cos de p^n te p elements primitius*/ /** v **/ polmin:=MinimalPolynomial(primitiu); grau:=Degree(polmin); polmin; grau; MinimalPolynomial(primitiu,Z5); MinimalPolynomial(primitiu,G25); /*Veiem que esta definit sobre Z5*/ Roots(polmin,Z5); Roots(polmin,G25); /** vi **/ vi:=1/alpha^3-alpha^5+(1/alpha+2)*alpha^6; vi; IsInvertible(vi); [x:x in G25|IsInvertible(x)]; [x:x in G25|ElementToSequence(x)]; Output: Magma V2.10-22 Mon Apr 12 2004 12:45:27 on modular [Seed = 2176517749] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true true x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 true true true false >> G9b:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 4, 4, 2 ] x^2 + 2*x + 3 2 x^2 + 2*x + 3 $.1 + alpha^13 [] [ , ] alpha^14 true alpha^10 [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, 3, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, 4, alpha^13, alpha^14, alpha^15, alpha^16, alpha^17, 2, alpha^19, alpha^20, alpha^21, alpha^22, alpha^23 ] >> [x:x in G25|ElementToSequence(x)]; ^ Runtime error in sequence construction: Logical expected Total time: 2.569 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 94-BARC-X53.libre.retevision.es. (62.82.23.94) Time: Mon Apr 12 12:47:21 2004 Input: /** i **/ K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; /** ii **/ K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); /*Provem amb Z2 */ Z2:=Integers(2); IsField(Z2); /** iii**/ Z3:=GF(3); P3:=PolynomialRing(Z3); Z2:=GF(2); P2:=PolynomialRing(Z2); Z5:=GF(5); P5:=PolynomialRing(Z5); f1:=P3![2,2,1]; f1; f2:=P2![1,1,0,0,1]; f2; f3:=P5![3,2,1]; f3; f4:=P3![1,2,1]; f4; IsIrreducible(f1); IsIrreducible(f2); IsIrreducible(f3); IsIrreducible(f4); G9:=ext; G16:=ext; G25:=ext; G9b:=ext; /* L'ultim cas dona error perque el polinomi NO es irreductible*/ /** iv **/ list:=[G25!x : x in [1..5]]; [Order(G25!x):x in list| x ne 0]; primitiu:=PrimitiveElement(G25); /* Hem repetit bastantes vegades aquesta comanda i sempre ens ha donat l'1. Per tant la llista es la [1] Un cos de p^n te p elements primitius*/ /** v **/ polmin:=MinimalPolynomial(primitiu); grau:=Degree(polmin); polmin; grau; MinimalPolynomial(primitiu,Z5); MinimalPolynomial(primitiu,G25); /*Veiem que esta definit sobre Z5*/ Roots(polmin,Z5); Roots(polmin,G25); /** vi **/ vi:=1/alpha^3-alpha^5+(1/alpha+2)*alpha^6; vi; IsInvertible(vi); /*[x:x in G25|IsInvertible(x)];*/ [x:x in G25|ElementToSequence(x)]; Output: Magma V2.10-22 Mon Apr 12 2004 12:47:18 on modular [Seed = 2293366989] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true true x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 true true true false >> G9b:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 4, 4, 2 ] x^2 + 2*x + 3 2 x^2 + 2*x + 3 $.1 + alpha^13 [] [ , ] alpha^14 true alpha^10 >> [x:x in G25|ElementToSequence(x)]; ^ Runtime error in sequence construction: Logical expected Total time: 2.570 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 94-BARC-X53.libre.retevision.es. (62.82.23.94) Time: Mon Apr 12 12:47:59 2004 Input: /** i **/ K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; /** ii **/ K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); /*Provem amb Z2 */ Z2:=Integers(2); IsField(Z2); /** iii**/ Z3:=GF(3); P3:=PolynomialRing(Z3); Z2:=GF(2); P2:=PolynomialRing(Z2); Z5:=GF(5); P5:=PolynomialRing(Z5); f1:=P3![2,2,1]; f1; f2:=P2![1,1,0,0,1]; f2; f3:=P5![3,2,1]; f3; f4:=P3![1,2,1]; f4; IsIrreducible(f1); IsIrreducible(f2); IsIrreducible(f3); IsIrreducible(f4); G9:=ext; G16:=ext; G25:=ext; G9b:=ext; /* L'ultim cas dona error perque el polinomi NO es irreductible*/ /** iv **/ list:=[G25!x : x in [1..5]]; [Order(G25!x):x in list| x ne 0]; primitiu:=PrimitiveElement(G25); /* Hem repetit bastantes vegades aquesta comanda i sempre ens ha donat l'1. Per tant la llista es la [1] Un cos de p^n te p elements primitius*/ /** v **/ polmin:=MinimalPolynomial(primitiu); grau:=Degree(polmin); polmin; grau; MinimalPolynomial(primitiu,Z5); MinimalPolynomial(primitiu,G25); /*Veiem que esta definit sobre Z5*/ Roots(polmin,Z5); Roots(polmin,G25); /** vi **/ vi:=1/alpha^3-alpha^5+(1/alpha+2)*alpha^6; vi; IsInvertible(vi); /*[x:x in G25|IsInvertible(x)];*/ [ElementToSequence(x):x in G25|ElementToSequence(x)]; Output: Magma V2.10-22 Mon Apr 12 2004 12:47:57 on modular [Seed = 2961848542] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true true x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 true true true false >> G9b:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 4, 4, 2 ] x^2 + 2*x + 3 2 x^2 + 2*x + 3 $.1 + alpha^13 [] [ , ] alpha^14 true alpha^10 >> [ElementToSequence(x):x in G25|ElementToSequence(x)]; ^ Runtime error in sequence construction: Logical expected Total time: 2.519 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 94-BARC-X53.libre.retevision.es. (62.82.23.94) Time: Mon Apr 12 12:48:19 2004 Input: /** i **/ K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; /** ii **/ K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); /*Provem amb Z2 */ Z2:=Integers(2); IsField(Z2); /** iii**/ Z3:=GF(3); P3:=PolynomialRing(Z3); Z2:=GF(2); P2:=PolynomialRing(Z2); Z5:=GF(5); P5:=PolynomialRing(Z5); f1:=P3![2,2,1]; f1; f2:=P2![1,1,0,0,1]; f2; f3:=P5![3,2,1]; f3; f4:=P3![1,2,1]; f4; IsIrreducible(f1); IsIrreducible(f2); IsIrreducible(f3); IsIrreducible(f4); G9:=ext; G16:=ext; G25:=ext; G9b:=ext; /* L'ultim cas dona error perque el polinomi NO es irreductible*/ /** iv **/ list:=[G25!x : x in [1..5]]; [Order(G25!x):x in list| x ne 0]; primitiu:=PrimitiveElement(G25); /* Hem repetit bastantes vegades aquesta comanda i sempre ens ha donat l'1. Per tant la llista es la [1] Un cos de p^n te p elements primitius*/ /** v **/ polmin:=MinimalPolynomial(primitiu); grau:=Degree(polmin); polmin; grau; MinimalPolynomial(primitiu,Z5); MinimalPolynomial(primitiu,G25); /*Veiem que esta definit sobre Z5*/ Roots(polmin,Z5); Roots(polmin,G25); /** vi **/ vi:=1/alpha^3-alpha^5+(1/alpha+2)*alpha^6; vi; IsInvertible(vi); /*[x:x in G25|IsInvertible(x)];*/ [ElementToSequence(x):x in G25]; Output: Magma V2.10-22 Mon Apr 12 2004 12:48:17 on modular [Seed = 3095539898] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true true x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 true true true false >> G9b:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 4, 4, 2 ] x^2 + 2*x + 3 2 x^2 + 2*x + 3 $.1 + alpha^13 [] [ , ] alpha^14 true alpha^10 [ [ 1, 0 ], [ 0, 1 ], [ 2, 3 ], [ 1, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 0 ], [ 0, 3 ], [ 1, 4 ], [ 3, 3 ], [ 1, 2 ], [ 4, 2 ], [ 4, 0 ], [ 0, 4 ], [ 3, 2 ], [ 4, 4 ], [ 3, 1 ], [ 2, 1 ], [ 2, 0 ], [ 0, 2 ], [ 4, 1 ], [ 2, 2 ], [ 4, 3 ], [ 1, 3 ], [ 0, 0 ] ] Total time: 2.519 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 94-BARC-X53.libre.retevision.es. (62.82.23.94) Time: Mon Apr 12 12:51:29 2004 Input: /** i **/ K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; /** ii **/ K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); /*Provem amb Z2 */ Z2:=Integers(2); IsField(Z2); /** iii**/ Z3:=GF(3); P3:=PolynomialRing(Z3); Z2:=GF(2); P2:=PolynomialRing(Z2); Z5:=GF(5); P5:=PolynomialRing(Z5); f1:=P3![2,2,1]; f1; f2:=P2![1,1,0,0,1]; f2; f3:=P5![3,2,1]; f3; f4:=P3![1,2,1]; f4; IsIrreducible(f1); IsIrreducible(f2); IsIrreducible(f3); IsIrreducible(f4); G9:=ext; G16:=ext; G25:=ext; G9b:=ext; /* L'ultim cas dona error perque el polinomi NO es irreductible*/ /** iv **/ list:=[G25!x : x in [1..5]]; [Order(G25!x):x in list| x ne 0]; primitiu:=PrimitiveElement(G25); /* Hem repetit bastantes vegades aquesta comanda i sempre ens ha donat l'1. Per tant la llista es la [1] Un cos de p^n te p elements primitius*/ /** v **/ polmin:=MinimalPolynomial(primitiu); grau:=Degree(polmin); polmin; grau; MinimalPolynomial(primitiu,Z5); MinimalPolynomial(primitiu,G25); /*Veiem que esta definit sobre Z5*/ Roots(polmin,Z5); Roots(polmin,G25); /** vi **/ vi:=1/alpha^3-alpha^5+(1/alpha+2)*alpha^6; vi; IsInvertible(vi); /*[x:x in G25|IsInvertible(x)];*/ [ElementToSequence(x):x in G25]; [ElementToSequence(x):x in G16]; Output: Magma V2.10-22 Mon Apr 12 2004 12:51:26 on modular [Seed = 2895521265] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true true x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 true true true false >> G9b:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 4, 4, 2 ] x^2 + 2*x + 3 2 x^2 + 2*x + 3 $.1 + alpha^13 [] [ , ] alpha^14 true alpha^10 [ [ 1, 0 ], [ 0, 1 ], [ 2, 3 ], [ 1, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 0 ], [ 0, 3 ], [ 1, 4 ], [ 3, 3 ], [ 1, 2 ], [ 4, 2 ], [ 4, 0 ], [ 0, 4 ], [ 3, 2 ], [ 4, 4 ], [ 3, 1 ], [ 2, 1 ], [ 2, 0 ], [ 0, 2 ], [ 4, 1 ], [ 2, 2 ], [ 4, 3 ], [ 1, 3 ], [ 0, 0 ] ] [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 1, 1, 0, 0 ], [ 0, 1, 1, 0 ], [ 0, 0, 1, 1 ], [ 1, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 0, 1, 0, 1 ], [ 1, 1, 1, 0 ], [ 0, 1, 1, 1 ], [ 1, 1, 1, 1 ], [ 1, 0, 1, 1 ], [ 1, 0, 0, 1 ], [ 0, 0, 0, 0 ] ] Total time: 2.510 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 94-BARC-X53.libre.retevision.es. (62.82.23.94) Time: Mon Apr 12 12:59:27 2004 Input: /** i **/ K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; /** ii **/ K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); /*Provem amb Z2 */ Z2:=Integers(2); IsField(Z2); /** iii**/ Z3:=GF(3); P3:=PolynomialRing(Z3); Z2:=GF(2); P2:=PolynomialRing(Z2); Z5:=GF(5); P5:=PolynomialRing(Z5); f1:=P3![2,2,1]; f1; f2:=P2![1,1,0,0,1]; f2; f3:=P5![3,2,1]; f3; f4:=P3![1,2,1]; f4; IsIrreducible(f1); IsIrreducible(f2); IsIrreducible(f3); IsIrreducible(f4); G9:=ext; G16:=ext; G25:=ext; G9b:=ext; /* L'ultim cas dona error perque el polinomi NO es irreductible*/ /** iv **/ list:=[G25!x : x in [1..5]]; [Order(G25!x):x in list| x ne 0]; primitiu:=PrimitiveElement(G25); /* Hem repetit bastantes vegades aquesta comanda i sempre ens ha donat l'1. Per tant la llista es la [1] Un cos de p^n te p elements primitius*/ /** v **/ polmin:=MinimalPolynomial(primitiu); grau:=Degree(polmin); polmin; grau; MinimalPolynomial(primitiu,Z5); MinimalPolynomial(primitiu,G25); /*Veiem que esta definit sobre Z5*/ Roots(polmin,Z5); Roots(polmin,G25); /** vi **/ vi:=1/alpha^3-alpha^5+(1/alpha+2)*alpha^6; vi; IsInvertible(vi); /*[x:x in G25|IsInvertible(x)];*/ [ElementToSequence(x):x in G25]; [ElementToSequence(x):x in G16]; [x:x in K2]; Output: Magma V2.10-22 Mon Apr 12 2004 12:59:24 on modular [Seed = 1516294370] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true true x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 true true true false >> G9b:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 4, 4, 2 ] x^2 + 2*x + 3 2 x^2 + 2*x + 3 $.1 + alpha^13 [] [ , ] alpha^14 true alpha^10 [ [ 1, 0 ], [ 0, 1 ], [ 2, 3 ], [ 1, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 0 ], [ 0, 3 ], [ 1, 4 ], [ 3, 3 ], [ 1, 2 ], [ 4, 2 ], [ 4, 0 ], [ 0, 4 ], [ 3, 2 ], [ 4, 4 ], [ 3, 1 ], [ 2, 1 ], [ 2, 0 ], [ 0, 2 ], [ 4, 1 ], [ 2, 2 ], [ 4, 3 ], [ 1, 3 ], [ 0, 0 ] ] [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 1, 1, 0, 0 ], [ 0, 1, 1, 0 ], [ 0, 0, 1, 1 ], [ 1, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 0, 1, 0, 1 ], [ 1, 1, 1, 0 ], [ 0, 1, 1, 1 ], [ 1, 1, 1, 1 ], [ 1, 0, 1, 1 ], [ 1, 0, 0, 1 ], [ 0, 0, 0, 0 ] ] [ 0, 1 ] Total time: 2.520 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 94-BARC-X53.libre.retevision.es. (62.82.23.94) Time: Mon Apr 12 13:00:13 2004 Input: /** i **/ K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; /** ii **/ K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); /*Provem amb Z2 */ Z2:=Integers(2); IsField(Z2); /** iii**/ Z3:=GF(3); P3:=PolynomialRing(Z3); Z2:=GF(2); P2:=PolynomialRing(Z2); Z5:=GF(5); P5:=PolynomialRing(Z5); f1:=P3![2,2,1]; f1; f2:=P2![1,1,0,0,1]; f2; f3:=P5![3,2,1]; f3; f4:=P3![1,2,1]; f4; IsIrreducible(f1); IsIrreducible(f2); IsIrreducible(f3); IsIrreducible(f4); G9:=ext; G16:=ext; G25:=ext; G9b:=ext; /* L'ultim cas dona error perque el polinomi NO es irreductible*/ /** iv **/ list:=[G25!x : x in [1..5]]; [Order(G25!x):x in list| x ne 0]; primitiu:=PrimitiveElement(G25); /* Hem repetit bastantes vegades aquesta comanda i sempre ens ha donat l'1. Per tant la llista es la [1] Un cos de p^n te p elements primitius*/ /** v **/ polmin:=MinimalPolynomial(primitiu); grau:=Degree(polmin); polmin; grau; MinimalPolynomial(primitiu,Z5); MinimalPolynomial(primitiu,G25); /*Veiem que esta definit sobre Z5*/ Roots(polmin,Z5); Roots(polmin,G25); /** vi **/ vi:=1/alpha^3-alpha^5+(1/alpha+2)*alpha^6; vi; IsInvertible(vi); /*[x:x in G25|IsInvertible(x)];*/ [ElementToSequence(x):x in G25]; [ElementToSequence(x):x in G16]; [x:x in K2]; [x:x in K4]; [x:x in K8]; [x:x in K16]; Output: Magma V2.10-22 Mon Apr 12 2004 13:00:10 on modular [Seed = 1232323079] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true true x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 true true true false >> G9b:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 4, 4, 2 ] x^2 + 2*x + 3 2 x^2 + 2*x + 3 $.1 + alpha^13 [] [ , ] alpha^14 true alpha^10 [ [ 1, 0 ], [ 0, 1 ], [ 2, 3 ], [ 1, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 0 ], [ 0, 3 ], [ 1, 4 ], [ 3, 3 ], [ 1, 2 ], [ 4, 2 ], [ 4, 0 ], [ 0, 4 ], [ 3, 2 ], [ 4, 4 ], [ 3, 1 ], [ 2, 1 ], [ 2, 0 ], [ 0, 2 ], [ 4, 1 ], [ 2, 2 ], [ 4, 3 ], [ 1, 3 ], [ 0, 0 ] ] [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 1, 1, 0, 0 ], [ 0, 1, 1, 0 ], [ 0, 0, 1, 1 ], [ 1, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 0, 1, 0, 1 ], [ 1, 1, 1, 0 ], [ 0, 1, 1, 1 ], [ 1, 1, 1, 1 ], [ 1, 0, 1, 1 ], [ 1, 0, 0, 1 ], [ 0, 0, 0, 0 ] ] [ 0, 1 ] >> [x:x in K4]; ^ User error: Identifier 'K4' has not been declared or assigned >> [x:x in K8]; ^ User error: Identifier 'K8' has not been declared or assigned >> [x:x in K16]; ^ User error: Identifier 'K16' has not been declared or assigned Total time: 2.529 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 94-BARC-X53.libre.retevision.es. (62.82.23.94) Time: Mon Apr 12 13:00:47 2004 Input: /** i **/ K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; /** ii **/ K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); /*Provem amb Z2 */ Z2:=Integers(2); IsField(Z2); /** iii**/ Z3:=GF(3); P3:=PolynomialRing(Z3); Z2:=GF(2); P2:=PolynomialRing(Z2); Z5:=GF(5); P5:=PolynomialRing(Z5); f1:=P3![2,2,1]; f1; f2:=P2![1,1,0,0,1]; f2; f3:=P5![3,2,1]; f3; f4:=P3![1,2,1]; f4; IsIrreducible(f1); IsIrreducible(f2); IsIrreducible(f3); IsIrreducible(f4); G9:=ext; G16:=ext; G25:=ext; G9b:=ext; /* L'ultim cas dona error perque el polinomi NO es irreductible*/ /** iv **/ list:=[G25!x : x in [1..5]]; [Order(G25!x):x in list| x ne 0]; primitiu:=PrimitiveElement(G25); /* Hem repetit bastantes vegades aquesta comanda i sempre ens ha donat l'1. Per tant la llista es la [1] Un cos de p^n te p elements primitius*/ /** v **/ polmin:=MinimalPolynomial(primitiu); grau:=Degree(polmin); polmin; grau; MinimalPolynomial(primitiu,Z5); MinimalPolynomial(primitiu,G25); /*Veiem que esta definit sobre Z5*/ Roots(polmin,Z5); Roots(polmin,G25); /** vi **/ vi:=1/alpha^3-alpha^5+(1/alpha+2)*alpha^6; vi; IsInvertible(vi); /*[x:x in G25|IsInvertible(x)];*/ [ElementToSequence(x):x in G25]; [ElementToSequence(x):x in G16]; K8:=GF(8); K16:=GF(16); [x:x in K2]; [x:x in K4]; [x:x in K8]; [x:x in K16]; Output: Magma V2.10-22 Mon Apr 12 2004 13:00:44 on modular [Seed = 1900804633] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true true x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 true true true false >> G9b:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 4, 4, 2 ] x^2 + 2*x + 3 2 x^2 + 2*x + 3 $.1 + alpha^13 [] [ , ] alpha^14 true alpha^10 [ [ 1, 0 ], [ 0, 1 ], [ 2, 3 ], [ 1, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 0 ], [ 0, 3 ], [ 1, 4 ], [ 3, 3 ], [ 1, 2 ], [ 4, 2 ], [ 4, 0 ], [ 0, 4 ], [ 3, 2 ], [ 4, 4 ], [ 3, 1 ], [ 2, 1 ], [ 2, 0 ], [ 0, 2 ], [ 4, 1 ], [ 2, 2 ], [ 4, 3 ], [ 1, 3 ], [ 0, 0 ] ] [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 1, 1, 0, 0 ], [ 0, 1, 1, 0 ], [ 0, 0, 1, 1 ], [ 1, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 0, 1, 0, 1 ], [ 1, 1, 1, 0 ], [ 0, 1, 1, 1 ], [ 1, 1, 1, 1 ], [ 1, 0, 1, 1 ], [ 1, 0, 0, 1 ], [ 0, 0, 0, 0 ] ] [ 0, 1 ] >> [x:x in K4]; ^ User error: Identifier 'K4' has not been declared or assigned [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, alpha^12, alpha^13, alpha^14, 0 ] Total time: 2.519 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 94-BARC-X53.libre.retevision.es. (62.82.23.94) Time: Mon Apr 12 13:01:51 2004 Input: /** i **/ K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; /** ii **/ K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); /*Provem amb Z2 */ Z2:=Integers(2); IsField(Z2); /** iii**/ Z3:=GF(3); P3:=PolynomialRing(Z3); Z2:=GF(2); P2:=PolynomialRing(Z2); Z5:=GF(5); P5:=PolynomialRing(Z5); f1:=P3![2,2,1]; f1; f2:=P2![1,1,0,0,1]; f2; f3:=P5![3,2,1]; f3; f4:=P3![1,2,1]; f4; IsIrreducible(f1); IsIrreducible(f2); IsIrreducible(f3); IsIrreducible(f4); G9:=ext; G16:=ext; G25:=ext; G9b:=ext; /* L'ultim cas dona error perque el polinomi NO es irreductible*/ /** iv **/ list:=[G25!x : x in [1..5]]; [Order(G25!x):x in list| x ne 0]; primitiu:=PrimitiveElement(G25); /* Hem repetit bastantes vegades aquesta comanda i sempre ens ha donat l'1. Per tant la llista es la [1] Un cos de p^n te p elements primitius*/ /** v **/ polmin:=MinimalPolynomial(primitiu); grau:=Degree(polmin); polmin; grau; MinimalPolynomial(primitiu,Z5); MinimalPolynomial(primitiu,G25); /*Veiem que esta definit sobre Z5*/ Roots(polmin,Z5); Roots(polmin,G25); /** vi **/ vi:=1/alpha^3-alpha^5+(1/alpha+2)*alpha^6; vi; IsInvertible(vi); /*[x:x in G25|IsInvertible(x)];*/ [ElementToSequence(x):x in G25]; [ElementToSequence(x):x in G16]; K8:=GF(8); K16:=GF(16); K4:=GF(4); [x:x in K2]; [x:x in K4]; [x:x in K8]; [x:x in K16]; Output: Magma V2.10-22 Mon Apr 12 2004 13:01:48 on modular [Seed = 338599740] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true true x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 true true true false >> G9b:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 4, 4, 2 ] x^2 + 2*x + 3 2 x^2 + 2*x + 3 $.1 + alpha^13 [] [ , ] alpha^14 true alpha^10 [ [ 1, 0 ], [ 0, 1 ], [ 2, 3 ], [ 1, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 0 ], [ 0, 3 ], [ 1, 4 ], [ 3, 3 ], [ 1, 2 ], [ 4, 2 ], [ 4, 0 ], [ 0, 4 ], [ 3, 2 ], [ 4, 4 ], [ 3, 1 ], [ 2, 1 ], [ 2, 0 ], [ 0, 2 ], [ 4, 1 ], [ 2, 2 ], [ 4, 3 ], [ 1, 3 ], [ 0, 0 ] ] [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 1, 1, 0, 0 ], [ 0, 1, 1, 0 ], [ 0, 0, 1, 1 ], [ 1, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 0, 1, 0, 1 ], [ 1, 1, 1, 0 ], [ 0, 1, 1, 1 ], [ 1, 1, 1, 1 ], [ 1, 0, 1, 1 ], [ 1, 0, 0, 1 ], [ 0, 0, 0, 0 ] ] [ 0, 1 ] [ 1, alpha, alpha^2, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, alpha^12, alpha^13, alpha^14, 0 ] Total time: 2.579 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 94-BARC-X53.libre.retevision.es. (62.82.23.94) Time: Mon Apr 12 13:05:37 2004 Input: /** i **/ K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; /** ii **/ K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); /*Provem amb Z2 */ Z2:=Integers(2); IsField(Z2); /** iii**/ Z3:=GF(3); P3:=PolynomialRing(Z3); Z2:=GF(2); P2:=PolynomialRing(Z2); Z5:=GF(5); P5:=PolynomialRing(Z5); f1:=P3![2,2,1]; f1; f2:=P2![1,1,0,0,1]; f2; f3:=P5![3,2,1]; f3; f4:=P3![1,2,1]; f4; IsIrreducible(f1); IsIrreducible(f2); IsIrreducible(f3); IsIrreducible(f4); G9:=ext; G16:=ext; G25:=ext; G9b:=ext; /* L'ultim cas dona error perque el polinomi NO es irreductible*/ /** iv **/ list:=[G25!x : x in [1..5]]; [Order(G25!x):x in list| x ne 0]; primitiu:=PrimitiveElement(G25); /* Hem repetit bastantes vegades aquesta comanda i sempre ens ha donat l'1. Per tant la llista es la [1] Un cos de p^n te p elements primitius*/ /** v **/ polmin:=MinimalPolynomial(primitiu); grau:=Degree(polmin); polmin; grau; MinimalPolynomial(primitiu,Z5); MinimalPolynomial(primitiu,G25); /*Veiem que esta definit sobre Z5*/ Roots(polmin,Z5); Roots(polmin,G25); /** vi **/ vi:=1/alpha^3-alpha^5+(1/alpha+2)*alpha^6; vi; IsInvertible(vi); /*[x:x in G25|IsInvertible(x)];*/ [ElementToSequence(x):x in G25]; [ElementToSequence(x):x in G16]; K8:=GF(8); K16:=GF(16); K4:=GF(4); [x:x in K2]; [x:x in K4]; [x:x in K8]; [x:x in K16]; CoefficientRing(G25); Output: Magma V2.10-22 Mon Apr 12 2004 13:05:34 on modular [Seed = 572042792] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true true x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 true true true false >> G9b:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 4, 4, 2 ] x^2 + 2*x + 3 2 x^2 + 2*x + 3 $.1 + alpha^13 [] [ , ] alpha^14 true alpha^10 [ [ 1, 0 ], [ 0, 1 ], [ 2, 3 ], [ 1, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 0 ], [ 0, 3 ], [ 1, 4 ], [ 3, 3 ], [ 1, 2 ], [ 4, 2 ], [ 4, 0 ], [ 0, 4 ], [ 3, 2 ], [ 4, 4 ], [ 3, 1 ], [ 2, 1 ], [ 2, 0 ], [ 0, 2 ], [ 4, 1 ], [ 2, 2 ], [ 4, 3 ], [ 1, 3 ], [ 0, 0 ] ] [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 1, 1, 0, 0 ], [ 0, 1, 1, 0 ], [ 0, 0, 1, 1 ], [ 1, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 0, 1, 0, 1 ], [ 1, 1, 1, 0 ], [ 0, 1, 1, 1 ], [ 1, 1, 1, 1 ], [ 1, 0, 1, 1 ], [ 1, 0, 0, 1 ], [ 0, 0, 0, 0 ] ] [ 0, 1 ] [ 1, alpha, alpha^2, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, alpha^12, alpha^13, alpha^14, 0 ] >> CoefficientRing(G25); ^ Runtime error in 'CoefficientRing': Bad argument types Argument types given: FldFin Total time: 2.589 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 94-BARC-X53.libre.retevision.es. (62.82.23.94) Time: Mon Apr 12 13:10:11 2004 Input: /** i **/ K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; /** ii **/ K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); /*Provem amb Z2 */ Z2:=Integers(2); IsField(Z2); /** iii**/ Z3:=GF(3); P3:=PolynomialRing(Z3); Z2:=GF(2); P2:=PolynomialRing(Z2); Z5:=GF(5); P5:=PolynomialRing(Z5); f1:=P3![2,2,1]; f1; f2:=P2![1,1,0,0,1]; f2; f3:=P5![3,2,1]; f3; f4:=P3![1,2,1]; f4; IsIrreducible(f1); IsIrreducible(f2); IsIrreducible(f3); IsIrreducible(f4); G9:=ext; G16:=ext; G25:=ext; G9b:=ext; /* L'ultim cas dona error perque el polinomi NO es irreductible*/ /** iv **/ list:=[G25!x : x in [1..5]]; [Order(G25!x):x in list| x ne 0]; primitiu:=PrimitiveElement(G25); /* Hem repetit bastantes vegades aquesta comanda i sempre ens ha donat l'1. Per tant la llista es la [1] Un cos de p^n te p elements primitius*/ /** v **/ polmin:=MinimalPolynomial(primitiu); grau:=Degree(polmin); polmin; grau; MinimalPolynomial(primitiu,Z5); MinimalPolynomial(primitiu,G25); /*Veiem que esta definit sobre Z5*/ Roots(polmin,Z5); Roots(polmin,G25); /** vi **/ vi:=1/alpha^3-alpha^5+(1/alpha+2)*alpha^6; vi; IsInvertible(vi); /*[x:x in G25|IsInvertible(x)];*/ [ElementToSequence(x):x in G25]; [ElementToSequence(x):x in G16]; K8:=GF(8); K16:=GF(16); K4:=GF(4); [x:x in K2]; [x:x in K4]; [x:x in K8]; [x:x in K16]; G25b:=PolynomialRing(G25); Output: Magma V2.10-22 Mon Apr 12 2004 13:10:09 on modular [Seed = 3739505659] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true true x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 true true true false >> G9b:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 4, 4, 2 ] x^2 + 2*x + 3 2 x^2 + 2*x + 3 $.1 + alpha^13 [] [ , ] alpha^14 true alpha^10 [ [ 1, 0 ], [ 0, 1 ], [ 2, 3 ], [ 1, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 0 ], [ 0, 3 ], [ 1, 4 ], [ 3, 3 ], [ 1, 2 ], [ 4, 2 ], [ 4, 0 ], [ 0, 4 ], [ 3, 2 ], [ 4, 4 ], [ 3, 1 ], [ 2, 1 ], [ 2, 0 ], [ 0, 2 ], [ 4, 1 ], [ 2, 2 ], [ 4, 3 ], [ 1, 3 ], [ 0, 0 ] ] [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 1, 1, 0, 0 ], [ 0, 1, 1, 0 ], [ 0, 0, 1, 1 ], [ 1, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 0, 1, 0, 1 ], [ 1, 1, 1, 0 ], [ 0, 1, 1, 1 ], [ 1, 1, 1, 1 ], [ 1, 0, 1, 1 ], [ 1, 0, 0, 1 ], [ 0, 0, 0, 0 ] ] [ 0, 1 ] [ 1, alpha, alpha^2, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, alpha^12, alpha^13, alpha^14, 0 ] Total time: 2.580 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host ACB134B9.ipt.aol.com. (172.177.52.185) Time: Mon Apr 12 13:11:04 2004 Input: 13407807929942597099574024998205846127601533213795056077209462877025034368196627761240552786569937831201077590982462638461210895540034428529412103952374939 Output: Magma V2.10-22 Mon Apr 12 2004 13:11:01 on modular [Seed = 3488956990] ------------------------------------- 1340780792994259709957402499820584612760153321379505607720946287702503436819662\ 7761240552786569937831201077590982462638461210895540034428529412103952374939 Total time: 2.519 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 94-BARC-X53.libre.retevision.es. (62.82.23.94) Time: Mon Apr 12 13:11:13 2004 Input: /** i **/ K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; /** ii **/ K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); /*Provem amb Z2 */ Z2:=Integers(2); IsField(Z2); /** iii**/ Z3:=GF(3); P3:=PolynomialRing(Z3); Z2:=GF(2); P2:=PolynomialRing(Z2); Z5:=GF(5); P5:=PolynomialRing(Z5); f1:=P3![2,2,1]; f1; f2:=P2![1,1,0,0,1]; f2; f3:=P5![3,2,1]; f3; f4:=P3![1,2,1]; f4; IsIrreducible(f1); IsIrreducible(f2); IsIrreducible(f3); IsIrreducible(f4); G9:=ext; G16:=ext; G25:=ext; G9b:=ext; /* L'ultim cas dona error perque el polinomi NO es irreductible*/ /** iv **/ list:=[G25!x : x in [1..5]]; [Order(G25!x):x in list| x ne 0]; primitiu:=PrimitiveElement(G25); /* Hem repetit bastantes vegades aquesta comanda i sempre ens ha donat l'1. Per tant la llista es la [1] Un cos de p^n te p elements primitius*/ /** v **/ polmin:=MinimalPolynomial(primitiu); grau:=Degree(polmin); polmin; grau; MinimalPolynomial(primitiu,Z5); MinimalPolynomial(primitiu,G25); /*Veiem que esta definit sobre Z5*/ Roots(polmin,Z5); Roots(polmin,G25); /** vi **/ vi:=1/alpha^3-alpha^5+(1/alpha+2)*alpha^6; vi; IsInvertible(vi); /*[x:x in G25|IsInvertible(x)];*/ [ElementToSequence(x):x in G25]; [ElementToSequence(x):x in G16]; K8:=GF(8); K16:=GF(16); K4:=GF(4); [x:x in K2]; [x:x in K4]; [x:x in K8]; [x:x in K16]; G25b:=PolynomialRing(G25); Coefficients(G25); Output: Magma V2.10-22 Mon Apr 12 2004 13:11:10 on modular [Seed = 4157438477] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true true x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 true true true false >> G9b:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 4, 4, 2 ] x^2 + 2*x + 3 2 x^2 + 2*x + 3 $.1 + alpha^13 [] [ , ] alpha^14 true alpha^10 [ [ 1, 0 ], [ 0, 1 ], [ 2, 3 ], [ 1, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 0 ], [ 0, 3 ], [ 1, 4 ], [ 3, 3 ], [ 1, 2 ], [ 4, 2 ], [ 4, 0 ], [ 0, 4 ], [ 3, 2 ], [ 4, 4 ], [ 3, 1 ], [ 2, 1 ], [ 2, 0 ], [ 0, 2 ], [ 4, 1 ], [ 2, 2 ], [ 4, 3 ], [ 1, 3 ], [ 0, 0 ] ] [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 1, 1, 0, 0 ], [ 0, 1, 1, 0 ], [ 0, 0, 1, 1 ], [ 1, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 0, 1, 0, 1 ], [ 1, 1, 1, 0 ], [ 0, 1, 1, 1 ], [ 1, 1, 1, 1 ], [ 1, 0, 1, 1 ], [ 1, 0, 0, 1 ], [ 0, 0, 0, 0 ] ] [ 0, 1 ] [ 1, alpha, alpha^2, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, alpha^12, alpha^13, alpha^14, 0 ] >> Coefficients(G25);; ^ Runtime error in 'Coefficients': Bad argument types Argument types given: FldFin Total time: 2.559 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 94-BARC-X53.libre.retevision.es. (62.82.23.94) Time: Mon Apr 12 13:12:50 2004 Input: /** i **/ K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; /** ii **/ K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); /*Provem amb Z2 */ Z2:=Integers(2); IsField(Z2); /** iii**/ Z3:=GF(3); P3:=PolynomialRing(Z3); Z2:=GF(2); P2:=PolynomialRing(Z2); Z5:=GF(5); P5:=PolynomialRing(Z5); f1:=P3![2,2,1]; f1; f2:=P2![1,1,0,0,1]; f2; f3:=P5![3,2,1]; f3; f4:=P3![1,2,1]; f4; IsIrreducible(f1); IsIrreducible(f2); IsIrreducible(f3); IsIrreducible(f4); G9:=ext; G16:=ext; G25:=ext; G9b:=ext; /* L'ultim cas dona error perque el polinomi NO es irreductible*/ /** iv **/ list:=[G25!x : x in [1..5]]; [Order(G25!x):x in list| x ne 0]; primitiu:=PrimitiveElement(G25); /* Hem repetit bastantes vegades aquesta comanda i sempre ens ha donat l'1. Per tant la llista es la [1] Un cos de p^n te p elements primitius*/ /** v **/ polmin:=MinimalPolynomial(primitiu); grau:=Degree(polmin); polmin; grau; MinimalPolynomial(primitiu,Z5); MinimalPolynomial(primitiu,G25); /*Veiem que esta definit sobre Z5*/ Roots(polmin,Z5); Roots(polmin,G25); /** vi **/ vi:=1/alpha^3-alpha^5+(1/alpha+2)*alpha^6; vi; IsInvertible(vi); /*[x:x in G25|IsInvertible(x)];*/ [ElementToSequence(x):x in G25]; [ElementToSequence(x):x in G16]; K8:=GF(8); K16:=GF(16); K4:=GF(4); [x:x in K2]; [x:x in K4]; [x:x in K8]; [x:x in K16]; G25b:=PolynomialRing(G25); G25; Output: Magma V2.10-22 Mon Apr 12 2004 13:12:48 on modular [Seed = 3789254565] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true true x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 true true true false >> G9b:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 4, 4, 2 ] x^2 + 2*x + 3 2 x^2 + 2*x + 3 $.1 + alpha^13 [] [ , ] alpha^14 true alpha^10 [ [ 1, 0 ], [ 0, 1 ], [ 2, 3 ], [ 1, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 0 ], [ 0, 3 ], [ 1, 4 ], [ 3, 3 ], [ 1, 2 ], [ 4, 2 ], [ 4, 0 ], [ 0, 4 ], [ 3, 2 ], [ 4, 4 ], [ 3, 1 ], [ 2, 1 ], [ 2, 0 ], [ 0, 2 ], [ 4, 1 ], [ 2, 2 ], [ 4, 3 ], [ 1, 3 ], [ 0, 0 ] ] [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 1, 1, 0, 0 ], [ 0, 1, 1, 0 ], [ 0, 0, 1, 1 ], [ 1, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 0, 1, 0, 1 ], [ 1, 1, 1, 0 ], [ 0, 1, 1, 1 ], [ 1, 1, 1, 1 ], [ 1, 0, 1, 1 ], [ 1, 0, 0, 1 ], [ 0, 0, 0, 0 ] ] [ 0, 1 ] [ 1, alpha, alpha^2, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, alpha^12, alpha^13, alpha^14, 0 ] Finite field of size 5^2 Total time: 2.529 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 94-BARC-X53.libre.retevision.es. (62.82.23.94) Time: Mon Apr 12 13:13:10 2004 Input: /** i **/ K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; /** ii **/ K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); /*Provem amb Z2 */ Z2:=Integers(2); IsField(Z2); /** iii**/ Z3:=GF(3); P3:=PolynomialRing(Z3); Z2:=GF(2); P2:=PolynomialRing(Z2); Z5:=GF(5); P5:=PolynomialRing(Z5); f1:=P3![2,2,1]; f1; f2:=P2![1,1,0,0,1]; f2; f3:=P5![3,2,1]; f3; f4:=P3![1,2,1]; f4; IsIrreducible(f1); IsIrreducible(f2); IsIrreducible(f3); IsIrreducible(f4); G9:=ext; G16:=ext; G25:=ext; G9b:=ext; /* L'ultim cas dona error perque el polinomi NO es irreductible*/ /** iv **/ list:=[G25!x : x in [1..5]]; [Order(G25!x):x in list| x ne 0]; primitiu:=PrimitiveElement(G25); /* Hem repetit bastantes vegades aquesta comanda i sempre ens ha donat l'1. Per tant la llista es la [1] Un cos de p^n te p elements primitius*/ /** v **/ polmin:=MinimalPolynomial(primitiu); grau:=Degree(polmin); polmin; grau; MinimalPolynomial(primitiu,Z5); MinimalPolynomial(primitiu,G25); /*Veiem que esta definit sobre Z5*/ Roots(polmin,Z5); Roots(polmin,G25); /** vi **/ vi:=1/alpha^3-alpha^5+(1/alpha+2)*alpha^6; vi; IsInvertible(vi); /*[x:x in G25|IsInvertible(x)];*/ [ElementToSequence(x):x in G25]; [ElementToSequence(x):x in G16]; K8:=GF(8); K16:=GF(16); K4:=GF(4); [x:x in K2]; [x:x in K4]; [x:x in K8]; [x:x in K16]; G25b:=PolynomialRing(G25); G25b; Output: Magma V2.10-22 Mon Apr 12 2004 13:13:07 on modular [Seed = 3922945950] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true true x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 true true true false >> G9b:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 4, 4, 2 ] x^2 + 2*x + 3 2 x^2 + 2*x + 3 $.1 + alpha^13 [] [ , ] alpha^14 true alpha^10 [ [ 1, 0 ], [ 0, 1 ], [ 2, 3 ], [ 1, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 0 ], [ 0, 3 ], [ 1, 4 ], [ 3, 3 ], [ 1, 2 ], [ 4, 2 ], [ 4, 0 ], [ 0, 4 ], [ 3, 2 ], [ 4, 4 ], [ 3, 1 ], [ 2, 1 ], [ 2, 0 ], [ 0, 2 ], [ 4, 1 ], [ 2, 2 ], [ 4, 3 ], [ 1, 3 ], [ 0, 0 ] ] [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 1, 1, 0, 0 ], [ 0, 1, 1, 0 ], [ 0, 0, 1, 1 ], [ 1, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 0, 1, 0, 1 ], [ 1, 1, 1, 0 ], [ 0, 1, 1, 1 ], [ 1, 1, 1, 1 ], [ 1, 0, 1, 1 ], [ 1, 0, 0, 1 ], [ 0, 0, 0, 0 ] ] [ 0, 1 ] [ 1, alpha, alpha^2, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, alpha^12, alpha^13, alpha^14, 0 ] Univariate Polynomial Ring over GF(5^2) Total time: 2.549 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 94-BARC-X53.libre.retevision.es. (62.82.23.94) Time: Mon Apr 12 13:13:43 2004 Input: /** i **/ K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; /** ii **/ K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); /*Provem amb Z2 */ Z2:=Integers(2); IsField(Z2); /** iii**/ Z3:=GF(3); P3:=PolynomialRing(Z3); Z2:=GF(2); P2:=PolynomialRing(Z2); Z5:=GF(5); P5:=PolynomialRing(Z5); f1:=P3![2,2,1]; f1; f2:=P2![1,1,0,0,1]; f2; f3:=P5![3,2,1]; f3; f4:=P3![1,2,1]; f4; IsIrreducible(f1); IsIrreducible(f2); IsIrreducible(f3); IsIrreducible(f4); G9:=ext; G16:=ext; G25:=ext; G9b:=ext; /* L'ultim cas dona error perque el polinomi NO es irreductible*/ /** iv **/ list:=[G25!x : x in [1..5]]; [Order(G25!x):x in list| x ne 0]; primitiu:=PrimitiveElement(G25); /* Hem repetit bastantes vegades aquesta comanda i sempre ens ha donat l'1. Per tant la llista es la [1] Un cos de p^n te p elements primitius*/ /** v **/ polmin:=MinimalPolynomial(primitiu); grau:=Degree(polmin); polmin; grau; MinimalPolynomial(primitiu,Z5); MinimalPolynomial(primitiu,G25); /*Veiem que esta definit sobre Z5*/ Roots(polmin,Z5); Roots(polmin,G25); /** vi **/ vi:=1/alpha^3-alpha^5+(1/alpha+2)*alpha^6; vi; IsInvertible(vi); /*[x:x in G25|IsInvertible(x)];*/ [ElementToSequence(x):x in G25]; [ElementToSequence(x):x in G16]; K8:=GF(8); K16:=GF(16); K4:=GF(4); [x:x in K2]; [x:x in K4]; [x:x in K8]; [x:x in K16]; G25b:=CoefficientRing(G25); G25b; Output: Magma V2.10-22 Mon Apr 12 2004 13:13:40 on modular [Seed = 2443911041] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true true x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 true true true false >> G9b:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 4, 4, 2 ] x^2 + 2*x + 3 2 x^2 + 2*x + 3 $.1 + alpha^13 [] [ , ] alpha^14 true alpha^10 [ [ 1, 0 ], [ 0, 1 ], [ 2, 3 ], [ 1, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 0 ], [ 0, 3 ], [ 1, 4 ], [ 3, 3 ], [ 1, 2 ], [ 4, 2 ], [ 4, 0 ], [ 0, 4 ], [ 3, 2 ], [ 4, 4 ], [ 3, 1 ], [ 2, 1 ], [ 2, 0 ], [ 0, 2 ], [ 4, 1 ], [ 2, 2 ], [ 4, 3 ], [ 1, 3 ], [ 0, 0 ] ] [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 1, 1, 0, 0 ], [ 0, 1, 1, 0 ], [ 0, 0, 1, 1 ], [ 1, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 0, 1, 0, 1 ], [ 1, 1, 1, 0 ], [ 0, 1, 1, 1 ], [ 1, 1, 1, 1 ], [ 1, 0, 1, 1 ], [ 1, 0, 0, 1 ], [ 0, 0, 0, 0 ] ] [ 0, 1 ] [ 1, alpha, alpha^2, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, alpha^12, alpha^13, alpha^14, 0 ] >> G25b:=CoefficientRing(G25); ^ Runtime error in 'CoefficientRing': Bad argument types Argument types given: FldFin >> G25b;; ^ User error: Identifier 'G25b' has not been declared or assigned Total time: 2.560 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 94-BARC-X53.libre.retevision.es. (62.82.23.94) Time: Mon Apr 12 13:16:28 2004 Input: /** i **/ K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; /** ii **/ K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); /*Provem amb Z2 */ Z2:=Integers(2); IsField(Z2); /** iii**/ Z3:=GF(3); P3:=PolynomialRing(Z3); Z2:=GF(2); P2:=PolynomialRing(Z2); Z5:=GF(5); P5:=PolynomialRing(Z5); f1:=P3![2,2,1]; f1; f2:=P2![1,1,0,0,1]; f2; f3:=P5![3,2,1]; f3; f4:=P3![1,2,1]; f4; IsIrreducible(f1); IsIrreducible(f2); IsIrreducible(f3); IsIrreducible(f4); G9:=ext; G16:=ext; G25:=ext; G9b:=ext; /* L'ultim cas dona error perque el polinomi NO es irreductible*/ /** iv **/ list:=[G25!x : x in [1..5]]; [Order(G25!x):x in list| x ne 0]; primitiu:=PrimitiveElement(G25); /* Hem repetit bastantes vegades aquesta comanda i sempre ens ha donat l'1. Per tant la llista es la [1] Un cos de p^n te p elements primitius*/ /** v **/ polmin:=MinimalPolynomial(primitiu); grau:=Degree(polmin); polmin; grau; MinimalPolynomial(primitiu,Z5); MinimalPolynomial(primitiu,G25); /*Veiem que esta definit sobre Z5*/ Roots(polmin,Z5); Roots(polmin,G25); /** vi **/ vi:=1/alpha^3-alpha^5+(1/alpha+2)*alpha^6; vi; IsInvertible(vi); /*[x:x in G25|IsInvertible(x)];*/ [ElementToSequence(x):x in G25]; [ElementToSequence(x):x in G16]; K8:=GF(8); K16:=GF(16); K4:=GF(4); [x:x in K2]; [x:x in K4]; [x:x in K8]; [x:x in K16]; G25b:=PolynomialRing(G25); G25b; alpa:=PrimitiveElement(G25b); beta:=PrimitiveElement(Z5); Output: Magma V2.10-22 Mon Apr 12 2004 13:16:25 on modular [Seed = 2260469819] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true true x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 true true true false >> G9b:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 4, 4, 2 ] x^2 + 2*x + 3 2 x^2 + 2*x + 3 $.1 + alpha^13 [] [ , ] alpha^14 true alpha^10 [ [ 1, 0 ], [ 0, 1 ], [ 2, 3 ], [ 1, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 0 ], [ 0, 3 ], [ 1, 4 ], [ 3, 3 ], [ 1, 2 ], [ 4, 2 ], [ 4, 0 ], [ 0, 4 ], [ 3, 2 ], [ 4, 4 ], [ 3, 1 ], [ 2, 1 ], [ 2, 0 ], [ 0, 2 ], [ 4, 1 ], [ 2, 2 ], [ 4, 3 ], [ 1, 3 ], [ 0, 0 ] ] [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 1, 1, 0, 0 ], [ 0, 1, 1, 0 ], [ 0, 0, 1, 1 ], [ 1, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 0, 1, 0, 1 ], [ 1, 1, 1, 0 ], [ 0, 1, 1, 1 ], [ 1, 1, 1, 1 ], [ 1, 0, 1, 1 ], [ 1, 0, 0, 1 ], [ 0, 0, 0, 0 ] ] [ 0, 1 ] [ 1, alpha, alpha^2, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, alpha^12, alpha^13, alpha^14, 0 ] Univariate Polynomial Ring over GF(5^2) >> alpa:=PrimitiveElement(G25b); ^ Runtime error in 'PrimitiveElement': Bad argument types Argument types given: RngUPol Total time: 2.569 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 94-BARC-X53.libre.retevision.es. (62.82.23.94) Time: Mon Apr 12 13:16:47 2004 Input: /** i **/ K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; /** ii **/ K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); /*Provem amb Z2 */ Z2:=Integers(2); IsField(Z2); /** iii**/ Z3:=GF(3); P3:=PolynomialRing(Z3); Z2:=GF(2); P2:=PolynomialRing(Z2); Z5:=GF(5); P5:=PolynomialRing(Z5); f1:=P3![2,2,1]; f1; f2:=P2![1,1,0,0,1]; f2; f3:=P5![3,2,1]; f3; f4:=P3![1,2,1]; f4; IsIrreducible(f1); IsIrreducible(f2); IsIrreducible(f3); IsIrreducible(f4); G9:=ext; G16:=ext; G25:=ext; G9b:=ext; /* L'ultim cas dona error perque el polinomi NO es irreductible*/ /** iv **/ list:=[G25!x : x in [1..5]]; [Order(G25!x):x in list| x ne 0]; primitiu:=PrimitiveElement(G25); /* Hem repetit bastantes vegades aquesta comanda i sempre ens ha donat l'1. Per tant la llista es la [1] Un cos de p^n te p elements primitius*/ /** v **/ polmin:=MinimalPolynomial(primitiu); grau:=Degree(polmin); polmin; grau; MinimalPolynomial(primitiu,Z5); MinimalPolynomial(primitiu,G25); /*Veiem que esta definit sobre Z5*/ Roots(polmin,Z5); Roots(polmin,G25); /** vi **/ vi:=1/alpha^3-alpha^5+(1/alpha+2)*alpha^6; vi; IsInvertible(vi); /*[x:x in G25|IsInvertible(x)];*/ [ElementToSequence(x):x in G25]; [ElementToSequence(x):x in G16]; K8:=GF(8); K16:=GF(16); K4:=GF(4); [x:x in K2]; [x:x in K4]; [x:x in K8]; [x:x in K16]; G25b:=PolynomialRing(G25); G25b; alpa:=PrimitiveElement(G25); beta:=PrimitiveElement(Z5); Output: Magma V2.10-22 Mon Apr 12 2004 13:16:44 on modular [Seed = 2394161190] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true true x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 true true true false >> G9b:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 4, 4, 2 ] x^2 + 2*x + 3 2 x^2 + 2*x + 3 $.1 + alpha^13 [] [ , ] alpha^14 true alpha^10 [ [ 1, 0 ], [ 0, 1 ], [ 2, 3 ], [ 1, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 0 ], [ 0, 3 ], [ 1, 4 ], [ 3, 3 ], [ 1, 2 ], [ 4, 2 ], [ 4, 0 ], [ 0, 4 ], [ 3, 2 ], [ 4, 4 ], [ 3, 1 ], [ 2, 1 ], [ 2, 0 ], [ 0, 2 ], [ 4, 1 ], [ 2, 2 ], [ 4, 3 ], [ 1, 3 ], [ 0, 0 ] ] [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 1, 1, 0, 0 ], [ 0, 1, 1, 0 ], [ 0, 0, 1, 1 ], [ 1, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 0, 1, 0, 1 ], [ 1, 1, 1, 0 ], [ 0, 1, 1, 1 ], [ 1, 1, 1, 1 ], [ 1, 0, 1, 1 ], [ 1, 0, 0, 1 ], [ 0, 0, 0, 0 ] ] [ 0, 1 ] [ 1, alpha, alpha^2, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, alpha^12, alpha^13, alpha^14, 0 ] Univariate Polynomial Ring over GF(5^2) Total time: 2.589 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 94-BARC-X53.libre.retevision.es. (62.82.23.94) Time: Mon Apr 12 13:19:02 2004 Input: /** i **/ K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; /** ii **/ K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); /*Provem amb Z2 */ Z2:=Integers(2); IsField(Z2); /** iii**/ Z3:=GF(3); P3:=PolynomialRing(Z3); Z2:=GF(2); P2:=PolynomialRing(Z2); Z5:=GF(5); P5:=PolynomialRing(Z5); f1:=P3![2,2,1]; f1; f2:=P2![1,1,0,0,1]; f2; f3:=P5![3,2,1]; f3; f4:=P3![1,2,1]; f4; IsIrreducible(f1); IsIrreducible(f2); IsIrreducible(f3); IsIrreducible(f4); G9:=ext; G16:=ext; G25:=ext; G9b:=ext; /* L'ultim cas dona error perque el polinomi NO es irreductible*/ /** iv **/ list:=[G25!x : x in [1..5]]; [Order(G25!x):x in list| x ne 0]; primitiu:=PrimitiveElement(G25); /* Hem repetit bastantes vegades aquesta comanda i sempre ens ha donat l'1. Per tant la llista es la [1] Un cos de p^n te p elements primitius*/ /** v **/ polmin:=MinimalPolynomial(primitiu); grau:=Degree(polmin); polmin; grau; MinimalPolynomial(primitiu,Z5); MinimalPolynomial(primitiu,G25); /*Veiem que esta definit sobre Z5*/ Roots(polmin,Z5); Roots(polmin,G25); /** vi **/ vi:=1/alpha^3-alpha^5+(1/alpha+2)*alpha^6; vi; IsInvertible(vi); /*[x:x in G25|IsInvertible(x)];*/ [ElementToSequence(x):x in G25]; [ElementToSequence(x):x in G16]; K8:=GF(8); K16:=GF(16); K4:=GF(4); [x:x in K2]; [x:x in K4]; [x:x in K8]; [x:x in K16]; G25b:=PolynomialRing(G25); G25b; alpa:=PrimitiveElement(G25); beta:=PrimitiveElement(Z5); p1:=alpa*alpa+alpa*x+beta*x^2; Output: Magma V2.10-22 Mon Apr 12 2004 13:18:59 on modular [Seed = 3062643041] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true true x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 true true true false >> G9b:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 4, 4, 2 ] x^2 + 2*x + 3 2 x^2 + 2*x + 3 $.1 + alpha^13 [] [ , ] alpha^14 true alpha^10 [ [ 1, 0 ], [ 0, 1 ], [ 2, 3 ], [ 1, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 0 ], [ 0, 3 ], [ 1, 4 ], [ 3, 3 ], [ 1, 2 ], [ 4, 2 ], [ 4, 0 ], [ 0, 4 ], [ 3, 2 ], [ 4, 4 ], [ 3, 1 ], [ 2, 1 ], [ 2, 0 ], [ 0, 2 ], [ 4, 1 ], [ 2, 2 ], [ 4, 3 ], [ 1, 3 ], [ 0, 0 ] ] [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 1, 1, 0, 0 ], [ 0, 1, 1, 0 ], [ 0, 0, 1, 1 ], [ 1, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 0, 1, 0, 1 ], [ 1, 1, 1, 0 ], [ 0, 1, 1, 1 ], [ 1, 1, 1, 1 ], [ 1, 0, 1, 1 ], [ 1, 0, 0, 1 ], [ 0, 0, 0, 0 ] ] [ 0, 1 ] [ 1, alpha, alpha^2, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, alpha^12, alpha^13, alpha^14, 0 ] Univariate Polynomial Ring over GF(5^2) >> p1:=alpa*alpa+alpa*x+beta*x^2;; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt Total time: 2.499 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 94-BARC-X53.libre.retevision.es. (62.82.23.94) Time: Mon Apr 12 13:19:45 2004 Input: /** i **/ K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; /** ii **/ K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); /*Provem amb Z2 */ Z2:=Integers(2); IsField(Z2); /** iii**/ Z3:=GF(3); P3:=PolynomialRing(Z3); Z2:=GF(2); P2:=PolynomialRing(Z2); Z5:=GF(5); P5:=PolynomialRing(Z5); f1:=P3![2,2,1]; f1; f2:=P2![1,1,0,0,1]; f2; f3:=P5![3,2,1]; f3; f4:=P3![1,2,1]; f4; IsIrreducible(f1); IsIrreducible(f2); IsIrreducible(f3); IsIrreducible(f4); G9:=ext; G16:=ext; G25:=ext; G9b:=ext; /* L'ultim cas dona error perque el polinomi NO es irreductible*/ /** iv **/ list:=[G25!x : x in [1..5]]; [Order(G25!x):x in list| x ne 0]; primitiu:=PrimitiveElement(G25); /* Hem repetit bastantes vegades aquesta comanda i sempre ens ha donat l'1. Per tant la llista es la [1] Un cos de p^n te p elements primitius*/ /** v **/ polmin:=MinimalPolynomial(primitiu); grau:=Degree(polmin); polmin; grau; MinimalPolynomial(primitiu,Z5); MinimalPolynomial(primitiu,G25); /*Veiem que esta definit sobre Z5*/ Roots(polmin,Z5); Roots(polmin,G25); /** vi **/ vi:=1/alpha^3-alpha^5+(1/alpha+2)*alpha^6; vi; IsInvertible(vi); /*[x:x in G25|IsInvertible(x)];*/ [ElementToSequence(x):x in G25]; [ElementToSequence(x):x in G16]; K8:=GF(8); K16:=GF(16); K4:=GF(4); [x:x in K2]; [x:x in K4]; [x:x in K8]; [x:x in K16]; G25b:=PolynomialRing(G25); G25b; alpa:=PrimitiveElement(G25); beta:=PrimitiveElement(Z5); /*p1:=alpa*alpa+alpa*x+beta*x^2;*/ p1:=beta*x^2; Output: Magma V2.10-22 Mon Apr 12 2004 13:19:42 on modular [Seed = 2812094557] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true true x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 true true true false >> G9b:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 4, 4, 2 ] x^2 + 2*x + 3 2 x^2 + 2*x + 3 $.1 + alpha^13 [] [ , ] alpha^14 true alpha^10 [ [ 1, 0 ], [ 0, 1 ], [ 2, 3 ], [ 1, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 0 ], [ 0, 3 ], [ 1, 4 ], [ 3, 3 ], [ 1, 2 ], [ 4, 2 ], [ 4, 0 ], [ 0, 4 ], [ 3, 2 ], [ 4, 4 ], [ 3, 1 ], [ 2, 1 ], [ 2, 0 ], [ 0, 2 ], [ 4, 1 ], [ 2, 2 ], [ 4, 3 ], [ 1, 3 ], [ 0, 0 ] ] [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 1, 1, 0, 0 ], [ 0, 1, 1, 0 ], [ 0, 0, 1, 1 ], [ 1, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 0, 1, 0, 1 ], [ 1, 1, 1, 0 ], [ 0, 1, 1, 1 ], [ 1, 1, 1, 1 ], [ 1, 0, 1, 1 ], [ 1, 0, 0, 1 ], [ 0, 0, 0, 0 ] ] [ 0, 1 ] [ 1, alpha, alpha^2, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, alpha^12, alpha^13, alpha^14, 0 ] Univariate Polynomial Ring over GF(5^2) Total time: 2.519 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 94-BARC-X53.libre.retevision.es. (62.82.23.94) Time: Mon Apr 12 13:20:38 2004 Input: /** i **/ K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; /** ii **/ K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); /*Provem amb Z2 */ Z2:=Integers(2); IsField(Z2); /** iii**/ Z3:=GF(3); P3:=PolynomialRing(Z3); Z2:=GF(2); P2:=PolynomialRing(Z2); Z5:=GF(5); P5:=PolynomialRing(Z5); f1:=P3![2,2,1]; f1; f2:=P2![1,1,0,0,1]; f2; f3:=P5![3,2,1]; f3; f4:=P3![1,2,1]; f4; IsIrreducible(f1); IsIrreducible(f2); IsIrreducible(f3); IsIrreducible(f4); G9:=ext; G16:=ext; G25:=ext; G9b:=ext; /* L'ultim cas dona error perque el polinomi NO es irreductible*/ /** iv **/ list:=[G25!x : x in [1..5]]; [Order(G25!x):x in list| x ne 0]; primitiu:=PrimitiveElement(G25); /* Hem repetit bastantes vegades aquesta comanda i sempre ens ha donat l'1. Per tant la llista es la [1] Un cos de p^n te p elements primitius*/ /** v **/ polmin:=MinimalPolynomial(primitiu); grau:=Degree(polmin); polmin; grau; MinimalPolynomial(primitiu,Z5); MinimalPolynomial(primitiu,G25); /*Veiem que esta definit sobre Z5*/ Roots(polmin,Z5); Roots(polmin,G25); /** vi **/ vi:=1/alpha^3-alpha^5+(1/alpha+2)*alpha^6; vi; IsInvertible(vi); /*[x:x in G25|IsInvertible(x)];*/ [ElementToSequence(x):x in G25]; [ElementToSequence(x):x in G16]; K8:=GF(8); K16:=GF(16); K4:=GF(4); [x:x in K2]; [x:x in K4]; [x:x in K8]; [x:x in K16]; G25b:=PolynomialRing(G25); G25b; alpa:=PrimitiveElement(G25); beta:=PrimitiveElement(Z5); /*p1:=alpa*alpa+alpa*x+beta*x^2;*/ p1:=beta*x^2 + alpa*x + alpa^2; Output: Magma V2.10-22 Mon Apr 12 2004 13:20:35 on modular [Seed = 1466816737] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true true x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 true true true false >> G9b:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 4, 4, 2 ] x^2 + 2*x + 3 2 x^2 + 2*x + 3 $.1 + alpha^13 [] [ , ] alpha^14 true alpha^10 [ [ 1, 0 ], [ 0, 1 ], [ 2, 3 ], [ 1, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 0 ], [ 0, 3 ], [ 1, 4 ], [ 3, 3 ], [ 1, 2 ], [ 4, 2 ], [ 4, 0 ], [ 0, 4 ], [ 3, 2 ], [ 4, 4 ], [ 3, 1 ], [ 2, 1 ], [ 2, 0 ], [ 0, 2 ], [ 4, 1 ], [ 2, 2 ], [ 4, 3 ], [ 1, 3 ], [ 0, 0 ] ] [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 1, 1, 0, 0 ], [ 0, 1, 1, 0 ], [ 0, 0, 1, 1 ], [ 1, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 0, 1, 0, 1 ], [ 1, 1, 1, 0 ], [ 0, 1, 1, 1 ], [ 1, 1, 1, 1 ], [ 1, 0, 1, 1 ], [ 1, 0, 0, 1 ], [ 0, 0, 0, 0 ] ] [ 0, 1 ] [ 1, alpha, alpha^2, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, alpha^12, alpha^13, alpha^14, 0 ] Univariate Polynomial Ring over GF(5^2) >> p1:=beta*x^2 + alpa*x + alpa^2;; ^ Runtime error in '*': Bad argument types Argument types given: FldFinElt, RngUPolElt Total time: 2.569 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 94-BARC-X53.libre.retevision.es. (62.82.23.94) Time: Mon Apr 12 13:23:35 2004 Input: /** i **/ K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; /** ii **/ K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); /*Provem amb Z2 */ Z2:=Integers(2); IsField(Z2); /** iii**/ Z3:=GF(3); P3:=PolynomialRing(Z3); Z2:=GF(2); P2:=PolynomialRing(Z2); Z5:=GF(5); P5:=PolynomialRing(Z5); f1:=P3![2,2,1]; f1; f2:=P2![1,1,0,0,1]; f2; f3:=P5![3,2,1]; f3; f4:=P3![1,2,1]; f4; IsIrreducible(f1); IsIrreducible(f2); IsIrreducible(f3); IsIrreducible(f4); G9:=ext; G16:=ext; G25:=ext; G9b:=ext; /* L'ultim cas dona error perque el polinomi NO es irreductible*/ /** iv **/ list:=[G25!x : x in [1..5]]; [Order(G25!x):x in list| x ne 0]; primitiu:=PrimitiveElement(G25); /* Hem repetit bastantes vegades aquesta comanda i sempre ens ha donat l'1. Per tant la llista es la [1] Un cos de p^n te p elements primitius*/ /** v **/ polmin:=MinimalPolynomial(primitiu); grau:=Degree(polmin); polmin; grau; MinimalPolynomial(primitiu,Z5); MinimalPolynomial(primitiu,G25); /*Veiem que esta definit sobre Z5*/ Roots(polmin,Z5); Roots(polmin,G25); /** vi **/ vi:=1/alpha^3-alpha^5+(1/alpha+2)*alpha^6; vi; IsInvertible(vi); /*[x:x in G25|IsInvertible(x)];*/ [ElementToSequence(x):x in G25]; [ElementToSequence(x):x in G16]; K8:=GF(8); K16:=GF(16); K4:=GF(4); [x:x in K2]; [x:x in K4]; [x:x in K8]; [x:x in K16]; G25b:=PolynomialRing(G25); G25b; alpa:=PrimitiveElement(G25); beta:=PrimitiveElement(Z5); /*p1:=alpa*alpa+alpa*x+beta*x^2;*/ p1:=G25b![alpa*alpa,alpa,beta]; Output: Magma V2.10-22 Mon Apr 12 2004 13:23:33 on modular [Seed = 1098633601] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true true x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 true true true false >> G9b:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 4, 4, 2 ] x^2 + 2*x + 3 2 x^2 + 2*x + 3 $.1 + alpha^13 [] [ , ] alpha^14 true alpha^10 [ [ 1, 0 ], [ 0, 1 ], [ 2, 3 ], [ 1, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 0 ], [ 0, 3 ], [ 1, 4 ], [ 3, 3 ], [ 1, 2 ], [ 4, 2 ], [ 4, 0 ], [ 0, 4 ], [ 3, 2 ], [ 4, 4 ], [ 3, 1 ], [ 2, 1 ], [ 2, 0 ], [ 0, 2 ], [ 4, 1 ], [ 2, 2 ], [ 4, 3 ], [ 1, 3 ], [ 0, 0 ] ] [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 1, 1, 0, 0 ], [ 0, 1, 1, 0 ], [ 0, 0, 1, 1 ], [ 1, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 0, 1, 0, 1 ], [ 1, 1, 1, 0 ], [ 0, 1, 1, 1 ], [ 1, 1, 1, 1 ], [ 1, 0, 1, 1 ], [ 1, 0, 0, 1 ], [ 0, 0, 0, 0 ] ] [ 0, 1 ] [ 1, alpha, alpha^2, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, alpha^12, alpha^13, alpha^14, 0 ] Univariate Polynomial Ring in x over GF(5^2) Total time: 2.529 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 94-BARC-X53.libre.retevision.es. (62.82.23.94) Time: Mon Apr 12 13:24:18 2004 Input: /** i **/ K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; /** ii **/ K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); /*Provem amb Z2 */ Z2:=Integers(2); IsField(Z2); /** iii**/ Z3:=GF(3); P3:=PolynomialRing(Z3); Z2:=GF(2); P2:=PolynomialRing(Z2); Z5:=GF(5); P5:=PolynomialRing(Z5); f1:=P3![2,2,1]; f1; f2:=P2![1,1,0,0,1]; f2; f3:=P5![3,2,1]; f3; f4:=P3![1,2,1]; f4; IsIrreducible(f1); IsIrreducible(f2); IsIrreducible(f3); IsIrreducible(f4); G9:=ext; G16:=ext; G25:=ext; G9b:=ext; /* L'ultim cas dona error perque el polinomi NO es irreductible*/ /** iv **/ list:=[G25!x : x in [1..5]]; [Order(G25!x):x in list| x ne 0]; primitiu:=PrimitiveElement(G25); /* Hem repetit bastantes vegades aquesta comanda i sempre ens ha donat l'1. Per tant la llista es la [1] Un cos de p^n te p elements primitius*/ /** v **/ polmin:=MinimalPolynomial(primitiu); grau:=Degree(polmin); polmin; grau; MinimalPolynomial(primitiu,Z5); MinimalPolynomial(primitiu,G25); /*Veiem que esta definit sobre Z5*/ Roots(polmin,Z5); Roots(polmin,G25); /** vi **/ vi:=1/alpha^3-alpha^5+(1/alpha+2)*alpha^6; vi; IsInvertible(vi); /*[x:x in G25|IsInvertible(x)];*/ [ElementToSequence(x):x in G25]; [ElementToSequence(x):x in G16]; K8:=GF(8); K16:=GF(16); K4:=GF(4); [x:x in K2]; [x:x in K4]; [x:x in K8]; [x:x in K16]; G25b:=PolynomialRing(G25); G25b; alpa:=PrimitiveElement(G25); beta:=PrimitiveElement(Z5); /*p1:=alpa*alpa+alpa*x+beta*x^2;*/ p1:=G25b![alpa*alpa,alpa,beta]; p2:=G25b![1,alpa]; p1+p2; Output: Magma V2.10-22 Mon Apr 12 2004 13:24:15 on modular [Seed = 1232329123] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true true x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 true true true false >> G9b:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 4, 4, 2 ] x^2 + 2*x + 3 2 x^2 + 2*x + 3 $.1 + alpha^13 [] [ , ] alpha^14 true alpha^10 [ [ 1, 0 ], [ 0, 1 ], [ 2, 3 ], [ 1, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 0 ], [ 0, 3 ], [ 1, 4 ], [ 3, 3 ], [ 1, 2 ], [ 4, 2 ], [ 4, 0 ], [ 0, 4 ], [ 3, 2 ], [ 4, 4 ], [ 3, 1 ], [ 2, 1 ], [ 2, 0 ], [ 0, 2 ], [ 4, 1 ], [ 2, 2 ], [ 4, 3 ], [ 1, 3 ], [ 0, 0 ] ] [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 1, 1, 0, 0 ], [ 0, 1, 1, 0 ], [ 0, 0, 1, 1 ], [ 1, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 0, 1, 0, 1 ], [ 1, 1, 1, 0 ], [ 0, 1, 1, 1 ], [ 1, 1, 1, 1 ], [ 1, 0, 1, 1 ], [ 1, 0, 0, 1 ], [ 0, 0, 0, 0 ] ] [ 0, 1 ] [ 1, alpha, alpha^2, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, alpha^12, alpha^13, alpha^14, 0 ] Univariate Polynomial Ring in x over GF(5^2) 2*x^2 + alpha^19*x + alpha^9 Total time: 2.569 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 94-BARC-X53.libre.retevision.es. (62.82.23.94) Time: Mon Apr 12 13:26:36 2004 Input: /** i **/ K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; /** ii **/ K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); /*Provem amb Z2 */ Z2:=Integers(2); IsField(Z2); /** iii**/ Z3:=GF(3); P3:=PolynomialRing(Z3); Z2:=GF(2); P2:=PolynomialRing(Z2); Z5:=GF(5); P5:=PolynomialRing(Z5); f1:=P3![2,2,1]; f1; f2:=P2![1,1,0,0,1]; f2; f3:=P5![3,2,1]; f3; f4:=P3![1,2,1]; f4; IsIrreducible(f1); IsIrreducible(f2); IsIrreducible(f3); IsIrreducible(f4); G9:=ext; G16:=ext; G25:=ext; G9b:=ext; /* L'ultim cas dona error perque el polinomi NO es irreductible*/ /** iv **/ list:=[G25!x : x in [1..5]]; [Order(G25!x):x in list| x ne 0]; primitiu:=PrimitiveElement(G25); /* Hem repetit bastantes vegades aquesta comanda i sempre ens ha donat l'1. Per tant la llista es la [1] Un cos de p^n te p elements primitius*/ /** v **/ polmin:=MinimalPolynomial(primitiu); grau:=Degree(polmin); polmin; grau; MinimalPolynomial(primitiu,Z5); MinimalPolynomial(primitiu,G25); /*Veiem que esta definit sobre Z5*/ Roots(polmin,Z5); Roots(polmin,G25); /** vi **/ vi:=1/alpha^3-alpha^5+(1/alpha+2)*alpha^6; vi; IsInvertible(vi); /*[x:x in G25|IsInvertible(x)];*/ [ElementToSequence(x):x in G25]; [ElementToSequence(x):x in G16]; K8:=GF(8); K16:=GF(16); K4:=GF(4); [x:x in K2]; [x:x in K4]; [x:x in K8]; [x:x in K16]; G25b:=PolynomialRing(G25); G25b; alpa:=PrimitiveElement(G25); beta:=PrimitiveElement(Z5); /*p1:=alpa*alpa+alpa*x+beta*x^2;*/ p1:=G25b![alpa*alpa,alpa,beta]; p2:=G25b![1,alpa]; p1+p2; p1*p2; p1 div p2; p1 mod p2; Output: Magma V2.10-22 Mon Apr 12 2004 13:26:33 on modular [Seed = 1633415293] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true true x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 true true true false >> G9b:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 4, 4, 2 ] x^2 + 2*x + 3 2 x^2 + 2*x + 3 $.1 + alpha^13 [] [ , ] alpha^14 true alpha^10 [ [ 1, 0 ], [ 0, 1 ], [ 2, 3 ], [ 1, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 0 ], [ 0, 3 ], [ 1, 4 ], [ 3, 3 ], [ 1, 2 ], [ 4, 2 ], [ 4, 0 ], [ 0, 4 ], [ 3, 2 ], [ 4, 4 ], [ 3, 1 ], [ 2, 1 ], [ 2, 0 ], [ 0, 2 ], [ 4, 1 ], [ 2, 2 ], [ 4, 3 ], [ 1, 3 ], [ 0, 0 ] ] [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 1, 1, 0, 0 ], [ 0, 1, 1, 0 ], [ 0, 0, 1, 1 ], [ 1, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 0, 1, 0, 1 ], [ 1, 1, 1, 0 ], [ 0, 1, 1, 1 ], [ 1, 1, 1, 1 ], [ 1, 0, 1, 1 ], [ 1, 0, 0, 1 ], [ 0, 0, 0, 0 ] ] [ 0, 1 ] [ 1, alpha, alpha^2, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, alpha^12, alpha^13, alpha^14, 0 ] Univariate Polynomial Ring in x over GF(5^2) 2*x^2 + alpha^19*x + alpha^9 alpha^19*x^3 + alpha^22*x^2 + alpha^10*x + alpha^2 alpha^17*x + alpha^5 alpha^15 Total time: 2.509 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 94-BARC-X53.libre.retevision.es. (62.82.23.94) Time: Mon Apr 12 13:30:33 2004 Input: /** i **/ K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; /** ii **/ K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); /*Provem amb Z2 */ Z2:=Integers(2); IsField(Z2); /** iii**/ Z3:=GF(3); P3:=PolynomialRing(Z3); Z2:=GF(2); P2:=PolynomialRing(Z2); Z5:=GF(5); P5:=PolynomialRing(Z5); f1:=P3![2,2,1]; f1; f2:=P2![1,1,0,0,1]; f2; f3:=P5![3,2,1]; f3; f4:=P3![1,2,1]; f4; IsIrreducible(f1); IsIrreducible(f2); IsIrreducible(f3); IsIrreducible(f4); G9:=ext; G16:=ext; G25:=ext; G9b:=ext; /* L'ultim cas dona error perque el polinomi NO es irreductible*/ /** iv **/ list:=[G25!x : x in [1..5]]; [Order(G25!x):x in list| x ne 0]; primitiu:=PrimitiveElement(G25); /* Hem repetit bastantes vegades aquesta comanda i sempre ens ha donat l'1. Per tant la llista es la [1] Un cos de p^n te p elements primitius*/ /** v **/ polmin:=MinimalPolynomial(primitiu); grau:=Degree(polmin); polmin; grau; MinimalPolynomial(primitiu,Z5); MinimalPolynomial(primitiu,G25); /*Veiem que esta definit sobre Z5*/ Roots(polmin,Z5); Roots(polmin,G25); /** vi **/ vi:=1/alpha^3-alpha^5+(1/alpha+2)*alpha^6; vi; IsInvertible(vi); /*[x:x in G25|IsInvertible(x)];*/ [ElementToSequence(x):x in G25]; [ElementToSequence(x):x in G16]; K8:=GF(8); K16:=GF(16); K4:=GF(4); [x:x in K2]; [x:x in K4]; [x:x in K8]; [x:x in K16]; G25b:=PolynomialRing(G25); G25b; alpa:=PrimitiveElement(G25); beta:=PrimitiveElement(Z5); /*p1:=alpa*alpa+alpa*x+beta*x^2;*/ p1:=G25b![alpa*alpa,alpa,beta]; p2:=G25b![1,alpa]; p1+p2; p1*p2; p1 div p2; p1 mod p2; Output: Magma V2.10-22 Mon Apr 12 2004 13:30:30 on modular [Seed = 3838563] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true true x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 true true true false >> G9b:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 4, 4, 2 ] x^2 + 2*x + 3 2 x^2 + 2*x + 3 $.1 + alpha^13 [] [ , ] alpha^14 true alpha^10 [ [ 1, 0 ], [ 0, 1 ], [ 2, 3 ], [ 1, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 0 ], [ 0, 3 ], [ 1, 4 ], [ 3, 3 ], [ 1, 2 ], [ 4, 2 ], [ 4, 0 ], [ 0, 4 ], [ 3, 2 ], [ 4, 4 ], [ 3, 1 ], [ 2, 1 ], [ 2, 0 ], [ 0, 2 ], [ 4, 1 ], [ 2, 2 ], [ 4, 3 ], [ 1, 3 ], [ 0, 0 ] ] [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 1, 1, 0, 0 ], [ 0, 1, 1, 0 ], [ 0, 0, 1, 1 ], [ 1, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 0, 1, 0, 1 ], [ 1, 1, 1, 0 ], [ 0, 1, 1, 1 ], [ 1, 1, 1, 1 ], [ 1, 0, 1, 1 ], [ 1, 0, 0, 1 ], [ 0, 0, 0, 0 ] ] [ 0, 1 ] [ 1, alpha, alpha^2, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, alpha^12, alpha^13, alpha^14, 0 ] Univariate Polynomial Ring in x over GF(5^2) 2*x^2 + alpha^19*x + alpha^9 alpha^19*x^3 + alpha^22*x^2 + alpha^10*x + alpha^2 alpha^17*x + alpha^5 alpha^15 Total time: 2.579 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 94-BARC-X53.libre.retevision.es. (62.82.23.94) Time: Mon Apr 12 13:44:17 2004 Input: /** i **/ K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; /** ii **/ K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); /*Provem amb Z2 */ Z2:=Integers(2); IsField(Z2); /** iii**/ Z3:=GF(3); P3:=PolynomialRing(Z3); Z2:=GF(2); P2:=PolynomialRing(Z2); Z5:=GF(5); P5:=PolynomialRing(Z5); f1:=P3![2,2,1]; f1; f2:=P2![1,1,0,0,1]; f2; f3:=P5![3,2,1]; f3; f4:=P3![1,2,1]; f4; IsIrreducible(f1); IsIrreducible(f2); IsIrreducible(f3); IsIrreducible(f4); G9:=ext; G16:=ext; G25:=ext; G9b:=ext; /* L'ultim cas dona error perque el polinomi NO es irreductible*/ /** iv **/ list:=[G25!x : x in [1..5]]; [Order(G25!x):x in list| x ne 0]; primitiu:=PrimitiveElement(G25); /* Hem repetit bastantes vegades aquesta comanda i sempre ens ha donat l'1. Per tant la llista es la [1] Un cos de p^n te p elements primitius*/ /** v **/ polmin:=MinimalPolynomial(primitiu); grau:=Degree(polmin); polmin; grau; MinimalPolynomial(primitiu,Z5); MinimalPolynomial(primitiu,G25); /*Veiem que esta definit sobre Z5*/ Roots(polmin,Z5); Roots(polmin,G25); /** vi **/ vi:=1/alpha^3-alpha^5+(1/alpha+2)*alpha^6; vi; IsInvertible(vi); /*[x:x in G25|IsInvertible(x)];*/ [ElementToSequence(x):x in G25]; [ElementToSequence(x):x in G16]; K8:=GF(8); K16:=GF(16); K4:=GF(4); [x:x in K2]; [x:x in K4]; [x:x in K8]; [x:x in K16]; G25b:=PolynomialRing(G25); G25b; alpa:=PrimitiveElement(G25); beta:=PrimitiveElement(Z5); /*p1:=alpa*alpa+alpa*x+beta*x^2;*/ p1:=G25b![alpa*alpa,alpa,beta]; p2:=G25b![1,alpa]; p1+p2; p1*p2; p1 div p2; p1 mod p2; GCD(p1,p2); LCM(p1,p2); Output: Magma V2.10-22 Mon Apr 12 2004 13:44:15 on modular [Seed = 4006902740] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true true x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 true true true false >> G9b:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 4, 4, 2 ] x^2 + 2*x + 3 2 x^2 + 2*x + 3 $.1 + alpha^13 [] [ , ] alpha^14 true alpha^10 [ [ 1, 0 ], [ 0, 1 ], [ 2, 3 ], [ 1, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 0 ], [ 0, 3 ], [ 1, 4 ], [ 3, 3 ], [ 1, 2 ], [ 4, 2 ], [ 4, 0 ], [ 0, 4 ], [ 3, 2 ], [ 4, 4 ], [ 3, 1 ], [ 2, 1 ], [ 2, 0 ], [ 0, 2 ], [ 4, 1 ], [ 2, 2 ], [ 4, 3 ], [ 1, 3 ], [ 0, 0 ] ] [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 1, 1, 0, 0 ], [ 0, 1, 1, 0 ], [ 0, 0, 1, 1 ], [ 1, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 0, 1, 0, 1 ], [ 1, 1, 1, 0 ], [ 0, 1, 1, 1 ], [ 1, 1, 1, 1 ], [ 1, 0, 1, 1 ], [ 1, 0, 0, 1 ], [ 0, 0, 0, 0 ] ] [ 0, 1 ] [ 1, alpha, alpha^2, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, alpha^12, alpha^13, alpha^14, 0 ] Univariate Polynomial Ring in x over GF(5^2) 2*x^2 + alpha^19*x + alpha^9 alpha^19*x^3 + alpha^22*x^2 + alpha^10*x + alpha^2 alpha^17*x + alpha^5 alpha^15 1 x^3 + alpha^3*x^2 + alpha^15*x + alpha^7 Total time: 2.559 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 94-BARC-X53.libre.retevision.es. (62.82.23.94) Time: Mon Apr 12 13:45:59 2004 Input: /** i **/ K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; /** ii **/ K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); /*Provem amb Z2 */ Z2:=Integers(2); IsField(Z2); /** iii**/ Z3:=GF(3); P3:=PolynomialRing(Z3); Z2:=GF(2); P2:=PolynomialRing(Z2); Z5:=GF(5); P5:=PolynomialRing(Z5); f1:=P3![2,2,1]; f1; f2:=P2![1,1,0,0,1]; f2; f3:=P5![3,2,1]; f3; f4:=P3![1,2,1]; f4; IsIrreducible(f1); IsIrreducible(f2); IsIrreducible(f3); IsIrreducible(f4); G9:=ext; G16:=ext; G25:=ext; G9b:=ext; /* L'ultim cas dona error perque el polinomi NO es irreductible*/ /** iv **/ list:=[G25!x : x in [1..5]]; [Order(G25!x):x in list| x ne 0]; primitiu:=PrimitiveElement(G25); /* Hem repetit bastantes vegades aquesta comanda i sempre ens ha donat l'1. Per tant la llista es la [1] Un cos de p^n te p elements primitius*/ /** v **/ polmin:=MinimalPolynomial(primitiu); grau:=Degree(polmin); polmin; grau; MinimalPolynomial(primitiu,Z5); MinimalPolynomial(primitiu,G25); /*Veiem que esta definit sobre Z5*/ Roots(polmin,Z5); Roots(polmin,G25); /** vi **/ vi:=1/alpha^3-alpha^5+(1/alpha+2)*alpha^6; vi; IsInvertible(vi); /*[x:x in G25|IsInvertible(x)];*/ [ElementToSequence(x):x in G25]; [ElementToSequence(x):x in G16]; K8:=GF(8); K16:=GF(16); K4:=GF(4); [x:x in K2]; [x:x in K4]; [x:x in K8]; [x:x in K16]; G25b:=PolynomialRing(G25); G25b; alpa:=PrimitiveElement(G25); beta:=PrimitiveElement(Z5); /*p1:=alpa*alpa+alpa*x+beta*x^2;*/ p1:=G25b![alpa*alpa,alpa,beta]; p2:=G25b![1,alpa]; p1+p2; p1*p2; p1 div p2; p1 mod p2; GCD(p1,p2); LCM(p1,p2); vii:=1/alpha^4-alpha^(-3)x+alpha^5x^2+alpha^11x^3; Factoritzation(vii); Roots(vii); Evaluate(vii); Output: Magma V2.10-22 Mon Apr 12 2004 13:45:56 on modular [Seed = 2460485395] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true true x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 true true true false >> G9b:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 4, 4, 2 ] x^2 + 2*x + 3 2 x^2 + 2*x + 3 $.1 + alpha^13 [] [ , ] alpha^14 true alpha^10 [ [ 1, 0 ], [ 0, 1 ], [ 2, 3 ], [ 1, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 0 ], [ 0, 3 ], [ 1, 4 ], [ 3, 3 ], [ 1, 2 ], [ 4, 2 ], [ 4, 0 ], [ 0, 4 ], [ 3, 2 ], [ 4, 4 ], [ 3, 1 ], [ 2, 1 ], [ 2, 0 ], [ 0, 2 ], [ 4, 1 ], [ 2, 2 ], [ 4, 3 ], [ 1, 3 ], [ 0, 0 ] ] [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 1, 1, 0, 0 ], [ 0, 1, 1, 0 ], [ 0, 0, 1, 1 ], [ 1, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 0, 1, 0, 1 ], [ 1, 1, 1, 0 ], [ 0, 1, 1, 1 ], [ 1, 1, 1, 1 ], [ 1, 0, 1, 1 ], [ 1, 0, 0, 1 ], [ 0, 0, 0, 0 ] ] [ 0, 1 ] [ 1, alpha, alpha^2, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, alpha^12, alpha^13, alpha^14, 0 ] Univariate Polynomial Ring in x over GF(5^2) 2*x^2 + alpha^19*x + alpha^9 alpha^19*x^3 + alpha^22*x^2 + alpha^10*x + alpha^2 alpha^17*x + alpha^5 alpha^15 1 x^3 + alpha^3*x^2 + alpha^15*x + alpha^7 >> vii:=1/alpha^4-alpha^(-3)x+alpha^5x^2+alpha^11x^3; ^ User error: bad syntax >> Factoritzation(vii); ^ User error: Identifier 'vii' has not been declared or assigned >> Roots(vii); ^ User error: Identifier 'vii' has not been declared or assigned >> Evaluate(vii); ^ User error: Identifier 'vii' has not been declared or assigned Total time: 2.579 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 94-BARC-X53.libre.retevision.es. (62.82.23.94) Time: Mon Apr 12 13:47:02 2004 Input: /** i **/ K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; /** ii **/ K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); /*Provem amb Z2 */ Z2:=Integers(2); IsField(Z2); /** iii**/ Z3:=GF(3); P3:=PolynomialRing(Z3); Z2:=GF(2); P2:=PolynomialRing(Z2); Z5:=GF(5); P5:=PolynomialRing(Z5); f1:=P3![2,2,1]; f1; f2:=P2![1,1,0,0,1]; f2; f3:=P5![3,2,1]; f3; f4:=P3![1,2,1]; f4; IsIrreducible(f1); IsIrreducible(f2); IsIrreducible(f3); IsIrreducible(f4); G9:=ext; G16:=ext; G25:=ext; G9b:=ext; /* L'ultim cas dona error perque el polinomi NO es irreductible*/ /** iv **/ list:=[G25!x : x in [1..5]]; [Order(G25!x):x in list| x ne 0]; primitiu:=PrimitiveElement(G25); /* Hem repetit bastantes vegades aquesta comanda i sempre ens ha donat l'1. Per tant la llista es la [1] Un cos de p^n te p elements primitius*/ /** v **/ polmin:=MinimalPolynomial(primitiu); grau:=Degree(polmin); polmin; grau; MinimalPolynomial(primitiu,Z5); MinimalPolynomial(primitiu,G25); /*Veiem que esta definit sobre Z5*/ Roots(polmin,Z5); Roots(polmin,G25); /** vi **/ vi:=1/alpha^3-alpha^5+(1/alpha+2)*alpha^6; vi; IsInvertible(vi); /*[x:x in G25|IsInvertible(x)];*/ [ElementToSequence(x):x in G25]; [ElementToSequence(x):x in G16]; K8:=GF(8); K16:=GF(16); K4:=GF(4); [x:x in K2]; [x:x in K4]; [x:x in K8]; [x:x in K16]; G25b:=PolynomialRing(G25); G25b; alpa:=PrimitiveElement(G25); beta:=PrimitiveElement(Z5); /*p1:=alpa*alpa+alpa*x+beta*x^2;*/ p1:=G25b![alpa*alpa,alpa,beta]; p2:=G25b![1,alpa]; p1+p2; p1*p2; p1 div p2; p1 mod p2; GCD(p1,p2); LCM(p1,p2); vii:=1/alpha^4-alpha^(-3)x+alpha^5x^2+alpha^11x^3; Factoritzation(vii); Roots(vii); Evaluate(vii,alpha); Output: Magma V2.10-22 Mon Apr 12 2004 13:46:59 on modular [Seed = 2243892163] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true true x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 true true true false >> G9b:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 4, 4, 2 ] x^2 + 2*x + 3 2 x^2 + 2*x + 3 $.1 + alpha^13 [] [ , ] alpha^14 true alpha^10 [ [ 1, 0 ], [ 0, 1 ], [ 2, 3 ], [ 1, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 0 ], [ 0, 3 ], [ 1, 4 ], [ 3, 3 ], [ 1, 2 ], [ 4, 2 ], [ 4, 0 ], [ 0, 4 ], [ 3, 2 ], [ 4, 4 ], [ 3, 1 ], [ 2, 1 ], [ 2, 0 ], [ 0, 2 ], [ 4, 1 ], [ 2, 2 ], [ 4, 3 ], [ 1, 3 ], [ 0, 0 ] ] [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 1, 1, 0, 0 ], [ 0, 1, 1, 0 ], [ 0, 0, 1, 1 ], [ 1, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 0, 1, 0, 1 ], [ 1, 1, 1, 0 ], [ 0, 1, 1, 1 ], [ 1, 1, 1, 1 ], [ 1, 0, 1, 1 ], [ 1, 0, 0, 1 ], [ 0, 0, 0, 0 ] ] [ 0, 1 ] [ 1, alpha, alpha^2, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, alpha^12, alpha^13, alpha^14, 0 ] Univariate Polynomial Ring in x over GF(5^2) 2*x^2 + alpha^19*x + alpha^9 alpha^19*x^3 + alpha^22*x^2 + alpha^10*x + alpha^2 alpha^17*x + alpha^5 alpha^15 1 x^3 + alpha^3*x^2 + alpha^15*x + alpha^7 >> vii:=1/alpha^4-alpha^(-3)x+alpha^5x^2+alpha^11x^3; ^ User error: bad syntax >> Factoritzation(vii); ^ User error: Identifier 'vii' has not been declared or assigned >> Roots(vii); ^ User error: Identifier 'vii' has not been declared or assigned >> Evaluate(vii,alpha); ^ User error: Identifier 'vii' has not been declared or assigned Total time: 2.520 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 94-BARC-X53.libre.retevision.es. (62.82.23.94) Time: Mon Apr 12 13:51:25 2004 Input: /** i **/ K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; /** ii **/ K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); /*Provem amb Z2 */ Z2:=Integers(2); IsField(Z2); /** iii**/ Z3:=GF(3); P3:=PolynomialRing(Z3); Z2:=GF(2); P2:=PolynomialRing(Z2); Z5:=GF(5); P5:=PolynomialRing(Z5); f1:=P3![2,2,1]; f1; f2:=P2![1,1,0,0,1]; f2; f3:=P5![3,2,1]; f3; f4:=P3![1,2,1]; f4; IsIrreducible(f1); IsIrreducible(f2); IsIrreducible(f3); IsIrreducible(f4); G9:=ext; G16:=ext; G25:=ext; G9b:=ext; /* L'ultim cas dona error perque el polinomi NO es irreductible*/ /** iv **/ list:=[G25!x : x in [1..5]]; [Order(G25!x):x in list| x ne 0]; primitiu:=PrimitiveElement(G25); /* Hem repetit bastantes vegades aquesta comanda i sempre ens ha donat l'1. Per tant la llista es la [1] Un cos de p^n te p elements primitius*/ /** v **/ polmin:=MinimalPolynomial(primitiu); grau:=Degree(polmin); polmin; grau; MinimalPolynomial(primitiu,Z5); MinimalPolynomial(primitiu,G25); /*Veiem que esta definit sobre Z5*/ Roots(polmin,Z5); Roots(polmin,G25); /** vi **/ vi:=1/alpha^3-alpha^5+(1/alpha+2)*alpha^6; vi; IsInvertible(vi); /*[x:x in G25|IsInvertible(x)];*/ [ElementToSequence(x):x in G25]; [ElementToSequence(x):x in G16]; K8:=GF(8); K16:=GF(16); K4:=GF(4); [x:x in K2]; [x:x in K4]; [x:x in K8]; [x:x in K16]; G25b:=PolynomialRing(G25); G25b; alpa:=PrimitiveElement(G25); beta:=PrimitiveElement(Z5); /*p1:=alpa*alpa+alpa*x+beta*x^2;*/ p1:=G25b![alpa*alpa,alpa,beta]; p2:=G25b![1,alpa]; p1+p2; p1*p2; p1 div p2; p1 mod p2; GCD(p1,p2); LCM(p1,p2); vii:=G25b![1/alpha^4,-alpha^(-3),alpha^5,alpha^11]; Factoritzation(vii); Roots(vii); Evaluate(vii,alpha); Output: Magma V2.10-22 Mon Apr 12 2004 13:51:23 on modular [Seed = 3046056699] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true true x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 true true true false >> G9b:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 4, 4, 2 ] x^2 + 2*x + 3 2 x^2 + 2*x + 3 $.1 + alpha^13 [] [ , ] alpha^14 true alpha^10 [ [ 1, 0 ], [ 0, 1 ], [ 2, 3 ], [ 1, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 0 ], [ 0, 3 ], [ 1, 4 ], [ 3, 3 ], [ 1, 2 ], [ 4, 2 ], [ 4, 0 ], [ 0, 4 ], [ 3, 2 ], [ 4, 4 ], [ 3, 1 ], [ 2, 1 ], [ 2, 0 ], [ 0, 2 ], [ 4, 1 ], [ 2, 2 ], [ 4, 3 ], [ 1, 3 ], [ 0, 0 ] ] [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 1, 1, 0, 0 ], [ 0, 1, 1, 0 ], [ 0, 0, 1, 1 ], [ 1, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 0, 1, 0, 1 ], [ 1, 1, 1, 0 ], [ 0, 1, 1, 1 ], [ 1, 1, 1, 1 ], [ 1, 0, 1, 1 ], [ 1, 0, 0, 1 ], [ 0, 0, 0, 0 ] ] [ 0, 1 ] [ 1, alpha, alpha^2, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, alpha^12, alpha^13, alpha^14, 0 ] Univariate Polynomial Ring in x over GF(5^2) 2*x^2 + alpha^19*x + alpha^9 alpha^19*x^3 + alpha^22*x^2 + alpha^10*x + alpha^2 alpha^17*x + alpha^5 alpha^15 1 x^3 + alpha^3*x^2 + alpha^15*x + alpha^7 >> vii:=G25b![1/alpha^4,-alpha^(-3),alpha^5,alpha^11]; ^ Runtime error in '!': Can't coerce sequence element 3 into the coefficient ring >> Factoritzation(vii); ^ User error: Identifier 'vii' has not been declared or assigned >> Roots(vii); ^ User error: Identifier 'vii' has not been declared or assigned >> Evaluate(vii,alpha); ^ User error: Identifier 'vii' has not been declared or assigned Total time: 2.569 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 94-BARC-X53.libre.retevision.es. (62.82.23.94) Time: Mon Apr 12 13:53:31 2004 Input: /** i **/ K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; /** ii **/ K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); /*Provem amb Z2 */ Z2:=Integers(2); IsField(Z2); /** iii**/ Z3:=GF(3); P3:=PolynomialRing(Z3); Z2:=GF(2); P2:=PolynomialRing(Z2); Z5:=GF(5); P5:=PolynomialRing(Z5); f1:=P3![2,2,1]; f1; f2:=P2![1,1,0,0,1]; f2; f3:=P5![3,2,1]; f3; f4:=P3![1,2,1]; f4; IsIrreducible(f1); IsIrreducible(f2); IsIrreducible(f3); IsIrreducible(f4); G9:=ext; G16:=ext; G25:=ext; G9b:=ext; /* L'ultim cas dona error perque el polinomi NO es irreductible*/ /** iv **/ list:=[G25!x : x in [1..5]]; [Order(G25!x):x in list| x ne 0]; primitiu:=PrimitiveElement(G25); /* Hem repetit bastantes vegades aquesta comanda i sempre ens ha donat l'1. Per tant la llista es la [1] Un cos de p^n te p elements primitius*/ /** v **/ polmin:=MinimalPolynomial(primitiu); grau:=Degree(polmin); polmin; grau; MinimalPolynomial(primitiu,Z5); MinimalPolynomial(primitiu,G25); /*Veiem que esta definit sobre Z5*/ Roots(polmin,Z5); Roots(polmin,G25); /** vi **/ vi:=1/alpha^3-alpha^5+(1/alpha+2)*alpha^6; vi; IsInvertible(vi); /*[x:x in G25|IsInvertible(x)];*/ [ElementToSequence(x):x in G25]; [ElementToSequence(x):x in G16]; K8:=GF(8); K16:=GF(16); K4:=GF(4); [x:x in K2]; [x:x in K4]; [x:x in K8]; [x:x in K16]; G25b:=PolynomialRing(G25); G25b; alpa:=PrimitiveElement(G25); beta:=PrimitiveElement(Z5); /*p1:=alpa*alpa+alpa*x+beta*x^2;*/ p1:=G25b![alpa*alpa,alpa,beta]; p2:=G25b![1,alpa]; p1+p2; p1*p2; p1 div p2; p1 mod p2; GCD(p1,p2); LCM(p1,p2); vii:=G25b![1/alpa^4,-alpa^(-3),alpa^5,alpa^11]; Factoritzation(vii); Roots(vii); Evaluate(vii,alpha); Output: Magma V2.10-22 Mon Apr 12 2004 13:53:28 on modular [Seed = 3179752048] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true true x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 true true true false >> G9b:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 4, 4, 2 ] x^2 + 2*x + 3 2 x^2 + 2*x + 3 $.1 + alpha^13 [] [ , ] alpha^14 true alpha^10 [ [ 1, 0 ], [ 0, 1 ], [ 2, 3 ], [ 1, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 0 ], [ 0, 3 ], [ 1, 4 ], [ 3, 3 ], [ 1, 2 ], [ 4, 2 ], [ 4, 0 ], [ 0, 4 ], [ 3, 2 ], [ 4, 4 ], [ 3, 1 ], [ 2, 1 ], [ 2, 0 ], [ 0, 2 ], [ 4, 1 ], [ 2, 2 ], [ 4, 3 ], [ 1, 3 ], [ 0, 0 ] ] [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 1, 1, 0, 0 ], [ 0, 1, 1, 0 ], [ 0, 0, 1, 1 ], [ 1, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 0, 1, 0, 1 ], [ 1, 1, 1, 0 ], [ 0, 1, 1, 1 ], [ 1, 1, 1, 1 ], [ 1, 0, 1, 1 ], [ 1, 0, 0, 1 ], [ 0, 0, 0, 0 ] ] [ 0, 1 ] [ 1, alpha, alpha^2, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, alpha^12, alpha^13, alpha^14, 0 ] Univariate Polynomial Ring in x over GF(5^2) 2*x^2 + alpha^19*x + alpha^9 alpha^19*x^3 + alpha^22*x^2 + alpha^10*x + alpha^2 alpha^17*x + alpha^5 alpha^15 1 x^3 + alpha^3*x^2 + alpha^15*x + alpha^7 >> Factoritzation(vii); ^ User error: Identifier 'Factoritzation' has not been declared or assigned [ <4, 1>, , ] >> Evaluate(vii,alpha); ^ Runtime error in 'Evaluate': Incompatible rings Total time: 2.499 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 94-BARC-X53.libre.retevision.es. (62.82.23.94) Time: Mon Apr 12 13:55:02 2004 Input: /** i **/ K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; /** ii **/ K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); /*Provem amb Z2 */ Z2:=Integers(2); IsField(Z2); /** iii**/ Z3:=GF(3); P3:=PolynomialRing(Z3); Z2:=GF(2); P2:=PolynomialRing(Z2); Z5:=GF(5); P5:=PolynomialRing(Z5); f1:=P3![2,2,1]; f1; f2:=P2![1,1,0,0,1]; f2; f3:=P5![3,2,1]; f3; f4:=P3![1,2,1]; f4; IsIrreducible(f1); IsIrreducible(f2); IsIrreducible(f3); IsIrreducible(f4); G9:=ext; G16:=ext; G25:=ext; G9b:=ext; /* L'ultim cas dona error perque el polinomi NO es irreductible*/ /** iv **/ list:=[G25!x : x in [1..5]]; [Order(G25!x):x in list| x ne 0]; primitiu:=PrimitiveElement(G25); /* Hem repetit bastantes vegades aquesta comanda i sempre ens ha donat l'1. Per tant la llista es la [1] Un cos de p^n te p elements primitius*/ /** v **/ polmin:=MinimalPolynomial(primitiu); grau:=Degree(polmin); polmin; grau; MinimalPolynomial(primitiu,Z5); MinimalPolynomial(primitiu,G25); /*Veiem que esta definit sobre Z5*/ Roots(polmin,Z5); Roots(polmin,G25); /** vi **/ vi:=1/alpha^3-alpha^5+(1/alpha+2)*alpha^6; vi; IsInvertible(vi); /*[x:x in G25|IsInvertible(x)];*/ [ElementToSequence(x):x in G25]; [ElementToSequence(x):x in G16]; K8:=GF(8); K16:=GF(16); K4:=GF(4); [x:x in K2]; [x:x in K4]; [x:x in K8]; [x:x in K16]; G25b:=PolynomialRing(G25); G25b; alpa:=PrimitiveElement(G25); beta:=PrimitiveElement(Z5); /*p1:=alpa*alpa+alpa*x+beta*x^2;*/ p1:=G25b![alpa*alpa,alpa,beta]; p2:=G25b![1,alpa]; p1+p2; p1*p2; p1 div p2; p1 mod p2; GCD(p1,p2); LCM(p1,p2); vii:=G25b![1/alpa^4,-alpa^(-3),alpa^5,alpa^11]; fact:=Factoritzation(vii); fact; Roots(vii); Evaluate(vii,alpha); Output: Magma V2.10-22 Mon Apr 12 2004 13:54:59 on modular [Seed = 2778673667] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true true x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 true true true false >> G9b:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 4, 4, 2 ] x^2 + 2*x + 3 2 x^2 + 2*x + 3 $.1 + alpha^13 [] [ , ] alpha^14 true alpha^10 [ [ 1, 0 ], [ 0, 1 ], [ 2, 3 ], [ 1, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 0 ], [ 0, 3 ], [ 1, 4 ], [ 3, 3 ], [ 1, 2 ], [ 4, 2 ], [ 4, 0 ], [ 0, 4 ], [ 3, 2 ], [ 4, 4 ], [ 3, 1 ], [ 2, 1 ], [ 2, 0 ], [ 0, 2 ], [ 4, 1 ], [ 2, 2 ], [ 4, 3 ], [ 1, 3 ], [ 0, 0 ] ] [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 1, 1, 0, 0 ], [ 0, 1, 1, 0 ], [ 0, 0, 1, 1 ], [ 1, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 0, 1, 0, 1 ], [ 1, 1, 1, 0 ], [ 0, 1, 1, 1 ], [ 1, 1, 1, 1 ], [ 1, 0, 1, 1 ], [ 1, 0, 0, 1 ], [ 0, 0, 0, 0 ] ] [ 0, 1 ] [ 1, alpha, alpha^2, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, alpha^12, alpha^13, alpha^14, 0 ] Univariate Polynomial Ring in x over GF(5^2) 2*x^2 + alpha^19*x + alpha^9 alpha^19*x^3 + alpha^22*x^2 + alpha^10*x + alpha^2 alpha^17*x + alpha^5 alpha^15 1 x^3 + alpha^3*x^2 + alpha^15*x + alpha^7 >> fact:=Factoritzation(vii); ^ User error: Identifier 'Factoritzation' has not been declared or assigned >> fact; ^ User error: Identifier 'fact' has not been declared or assigned [ <4, 1>, , ] >> Evaluate(vii,alpha); ^ Runtime error in 'Evaluate': Incompatible rings Total time: 2.689 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 94-BARC-X53.libre.retevision.es. (62.82.23.94) Time: Mon Apr 12 13:55:42 2004 Input: /** i **/ K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; /** ii **/ K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); /*Provem amb Z2 */ Z2:=Integers(2); IsField(Z2); /** iii**/ Z3:=GF(3); P3:=PolynomialRing(Z3); Z2:=GF(2); P2:=PolynomialRing(Z2); Z5:=GF(5); P5:=PolynomialRing(Z5); f1:=P3![2,2,1]; f1; f2:=P2![1,1,0,0,1]; f2; f3:=P5![3,2,1]; f3; f4:=P3![1,2,1]; f4; IsIrreducible(f1); IsIrreducible(f2); IsIrreducible(f3); IsIrreducible(f4); G9:=ext; G16:=ext; G25:=ext; G9b:=ext; /* L'ultim cas dona error perque el polinomi NO es irreductible*/ /** iv **/ list:=[G25!x : x in [1..5]]; [Order(G25!x):x in list| x ne 0]; primitiu:=PrimitiveElement(G25); /* Hem repetit bastantes vegades aquesta comanda i sempre ens ha donat l'1. Per tant la llista es la [1] Un cos de p^n te p elements primitius*/ /** v **/ polmin:=MinimalPolynomial(primitiu); grau:=Degree(polmin); polmin; grau; MinimalPolynomial(primitiu,Z5); MinimalPolynomial(primitiu,G25); /*Veiem que esta definit sobre Z5*/ Roots(polmin,Z5); Roots(polmin,G25); /** vi **/ vi:=1/alpha^3-alpha^5+(1/alpha+2)*alpha^6; vi; IsInvertible(vi); /*[x:x in G25|IsInvertible(x)];*/ [ElementToSequence(x):x in G25]; [ElementToSequence(x):x in G16]; K8:=GF(8); K16:=GF(16); K4:=GF(4); [x:x in K2]; [x:x in K4]; [x:x in K8]; [x:x in K16]; G25b:=PolynomialRing(G25); G25b; alpa:=PrimitiveElement(G25); beta:=PrimitiveElement(Z5); /*p1:=alpa*alpa+alpa*x+beta*x^2;*/ p1:=G25b![alpa*alpa,alpa,beta]; p2:=G25b![1,alpa]; p1+p2; p1*p2; p1 div p2; p1 mod p2; GCD(p1,p2); LCM(p1,p2); vii:=G25b![1/alpa^4,-alpa^(-3),alpa^5,alpa^11]; fact:=Factorization(vii); fact; Roots(vii); Evaluate(vii,alpha); Output: Magma V2.10-22 Mon Apr 12 2004 13:55:39 on modular [Seed = 2844996071] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true true x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 true true true false >> G9b:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 4, 4, 2 ] x^2 + 2*x + 3 2 x^2 + 2*x + 3 $.1 + alpha^13 [] [ , ] alpha^14 true alpha^10 [ [ 1, 0 ], [ 0, 1 ], [ 2, 3 ], [ 1, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 0 ], [ 0, 3 ], [ 1, 4 ], [ 3, 3 ], [ 1, 2 ], [ 4, 2 ], [ 4, 0 ], [ 0, 4 ], [ 3, 2 ], [ 4, 4 ], [ 3, 1 ], [ 2, 1 ], [ 2, 0 ], [ 0, 2 ], [ 4, 1 ], [ 2, 2 ], [ 4, 3 ], [ 1, 3 ], [ 0, 0 ] ] [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 1, 1, 0, 0 ], [ 0, 1, 1, 0 ], [ 0, 0, 1, 1 ], [ 1, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 0, 1, 0, 1 ], [ 1, 1, 1, 0 ], [ 0, 1, 1, 1 ], [ 1, 1, 1, 1 ], [ 1, 0, 1, 1 ], [ 1, 0, 0, 1 ], [ 0, 0, 0, 0 ] ] [ 0, 1 ] [ 1, alpha, alpha^2, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, alpha^12, alpha^13, alpha^14, 0 ] Univariate Polynomial Ring in x over GF(5^2) 2*x^2 + alpha^19*x + alpha^9 alpha^19*x^3 + alpha^22*x^2 + alpha^10*x + alpha^2 alpha^17*x + alpha^5 alpha^15 1 x^3 + alpha^3*x^2 + alpha^15*x + alpha^7 [ , , ] [ <4, 1>, , ] >> Evaluate(vii,alpha); ^ Runtime error in 'Evaluate': Incompatible rings Total time: 2.510 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host 94-BARC-X53.libre.retevision.es. (62.82.23.94) Time: Mon Apr 12 13:56:05 2004 Input: /** i **/ K2:=GF(2); K3:=GF(3); K5:=GF(5); [K2!x : x in [1..2]]; [K3!x : x in [1..3]]; [K5!x : x in [1..5]]; /** ii **/ K9:=GF(9); K9; Z9:=Integers(9); [Z9!x : x in [1..9]| IsInvertible(x) ne true]; [Z9!x : x in [1..9]| IsInvertible(x) ne false]; [K9!x : x in [1..9]| IsInvertible(x) ne false]; IsField(Z9); IsField(K9); /*Provem amb Z2 */ Z2:=Integers(2); IsField(Z2); /** iii**/ Z3:=GF(3); P3:=PolynomialRing(Z3); Z2:=GF(2); P2:=PolynomialRing(Z2); Z5:=GF(5); P5:=PolynomialRing(Z5); f1:=P3![2,2,1]; f1; f2:=P2![1,1,0,0,1]; f2; f3:=P5![3,2,1]; f3; f4:=P3![1,2,1]; f4; IsIrreducible(f1); IsIrreducible(f2); IsIrreducible(f3); IsIrreducible(f4); G9:=ext; G16:=ext; G25:=ext; G9b:=ext; /* L'ultim cas dona error perque el polinomi NO es irreductible*/ /** iv **/ list:=[G25!x : x in [1..5]]; [Order(G25!x):x in list| x ne 0]; primitiu:=PrimitiveElement(G25); /* Hem repetit bastantes vegades aquesta comanda i sempre ens ha donat l'1. Per tant la llista es la [1] Un cos de p^n te p elements primitius*/ /** v **/ polmin:=MinimalPolynomial(primitiu); grau:=Degree(polmin); polmin; grau; MinimalPolynomial(primitiu,Z5); MinimalPolynomial(primitiu,G25); /*Veiem que esta definit sobre Z5*/ Roots(polmin,Z5); Roots(polmin,G25); /** vi **/ vi:=1/alpha^3-alpha^5+(1/alpha+2)*alpha^6; vi; IsInvertible(vi); /*[x:x in G25|IsInvertible(x)];*/ [ElementToSequence(x):x in G25]; [ElementToSequence(x):x in G16]; K8:=GF(8); K16:=GF(16); K4:=GF(4); [x:x in K2]; [x:x in K4]; [x:x in K8]; [x:x in K16]; G25b:=PolynomialRing(G25); G25b; alpa:=PrimitiveElement(G25); beta:=PrimitiveElement(Z5); /*p1:=alpa*alpa+alpa*x+beta*x^2;*/ p1:=G25b![alpa*alpa,alpa,beta]; p2:=G25b![1,alpa]; p1+p2; p1*p2; p1 div p2; p1 mod p2; GCD(p1,p2); LCM(p1,p2); vii:=G25b![1/alpa^4,-alpa^(-3),alpa^5,alpa^11]; fact:=Factorization(vii); fact; Roots(vii); Evaluate(vii,alpa); Output: Magma V2.10-22 Mon Apr 12 2004 13:56:03 on modular [Seed = 1382599223] ------------------------------------- [ 1, 0 ] [ 1, 2, 0 ] [ 1, 2, 3, 4, 0 ] Finite field of size 3^2 [ 2, 3, 4, 5, 6, 7, 8, 0 ] [ 1 ] [ 1 ] false true true x^2 + 2*x + 2 x^4 + x + 1 x^2 + 2*x + 3 x^2 + 2*x + 1 true true true false >> G9b:=ext; ^ Runtime error in ext< ... >: Argument is not irreducible [ 1, 4, 4, 2 ] x^2 + 2*x + 3 2 x^2 + 2*x + 3 $.1 + alpha^13 [] [ , ] alpha^14 true alpha^10 [ [ 1, 0 ], [ 0, 1 ], [ 2, 3 ], [ 1, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 0 ], [ 0, 3 ], [ 1, 4 ], [ 3, 3 ], [ 1, 2 ], [ 4, 2 ], [ 4, 0 ], [ 0, 4 ], [ 3, 2 ], [ 4, 4 ], [ 3, 1 ], [ 2, 1 ], [ 2, 0 ], [ 0, 2 ], [ 4, 1 ], [ 2, 2 ], [ 4, 3 ], [ 1, 3 ], [ 0, 0 ] ] [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 1, 1, 0, 0 ], [ 0, 1, 1, 0 ], [ 0, 0, 1, 1 ], [ 1, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 0, 1, 0, 1 ], [ 1, 1, 1, 0 ], [ 0, 1, 1, 1 ], [ 1, 1, 1, 1 ], [ 1, 0, 1, 1 ], [ 1, 0, 0, 1 ], [ 0, 0, 0, 0 ] ] [ 0, 1 ] [ 1, alpha, alpha^2, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, 0 ] [ 1, alpha, alpha^2, alpha^3, alpha^4, alpha^5, alpha^6, alpha^7, alpha^8, alpha^9, alpha^10, alpha^11, alpha^12, alpha^13, alpha^14, 0 ] Univariate Polynomial Ring in x over GF(5^2) 2*x^2 + alpha^19*x + alpha^9 alpha^19*x^3 + alpha^22*x^2 + alpha^10*x + alpha^2 alpha^17*x + alpha^5 alpha^15 1 x^3 + alpha^3*x^2 + alpha^15*x + alpha^7 [ , , ] [ <4, 1>, , ] alpha^9 Total time: 2.509 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host ACB3DD8B.ipt.aol.com. (172.179.221.139) Time: Mon Apr 12 14:19:14 2004 Input: 13407807929942597099574024998205846127601533213795056077209462877025034368196627761240552786569937831201077590982462638461210895540034428529412103952374939 Output: Magma V2.10-22 Mon Apr 12 2004 14:19:12 on modular [Seed = 3046058051] ------------------------------------- 1340780792994259709957402499820584612760153321379505607720946287702503436819662\ 7761240552786569937831201077590982462638461210895540034428529412103952374939 Total time: 2.489 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 3(NXDOMAIN) (203.130.237.66) Time: Tue Apr 13 01:07:13 2004 Input: 1+1 Output: Magma V2.10-22 Tue Apr 13 2004 01:07:10 on modular [Seed = 3079438996] ------------------------------------- 2 Total time: 2.609 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host 3(NXDOMAIN) (203.130.237.66) Time: Tue Apr 13 01:11:02 2004 Input: 1km + 1km Output: Magma V2.10-22 Tue Apr 13 2004 01:11:00 on modular [Seed = 1516334176] ------------------------------------- >> 1km + 1km ^ User error: bad syntax Total time: 2.550 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217) Time: Thu Apr 22 21:36:30 2004 Input: 2+2 Output: Magma V2.10-22 Thu Apr 22 2004 21:36:26 on modular [Seed = 416295689] ------------------------------------- [PC] While attempting to compile /usr/local/magma/package/Group/GrpCoh/strongpr\ [PC] es.m (Source file newer than data file): [PC] Can't open lock file /usr/local/magma/package/Group/GrpCoh/strongpres.lck [PC] for writing (Permission denied) [PC] While attempting to compile /usr/local/magma/package/Group/GrpCoh/strongpr\ [PC] esab.m (Source file newer than data file): [PC] Can't open lock file /usr/local/magma/package/Group/GrpCoh/strongpresab.lc\ [PC] k for writing (Permission denied) [PC] While attempting to compile /usr/local/magma/package/LieThry/RootDtm.m [PC] (Source file newer than data file): [PC] Can't open lock file /usr/local/magma/package/LieThry/RootDtm.lck for [PC] writing (Permission denied) 4 Total time: 2.609 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host beta.wwwcache.cam.ac.uk. (131.111.8.97) Time: Thu Apr 22 21:43:31 2004 Input: 9+0 Output: Magma V2.10-22 Thu Apr 22 2004 21:43:28 on modular [Seed = 1772182946] ------------------------------------- [PC] While attempting to compile /usr/local/magma/package/Group/GrpCoh/strongpr\ [PC] es.m (Source file newer than data file): [PC] Can't open lock file /usr/local/magma/package/Group/GrpCoh/strongpres.lck [PC] for writing (Permission denied) [PC] While attempting to compile /usr/local/magma/package/Group/GrpCoh/strongpr\ [PC] esab.m (Source file newer than data file): [PC] Can't open lock file /usr/local/magma/package/Group/GrpCoh/strongpresab.lc\ [PC] k for writing (Permission denied) [PC] While attempting to compile /usr/local/magma/package/LieThry/RootDtm.m [PC] (Source file newer than data file): [PC] Can't open lock file /usr/local/magma/package/LieThry/RootDtm.lck for [PC] writing (Permission denied) 9 Total time: 2.499 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host beta.wwwcache.cam.ac.uk. (131.111.8.97) Time: Thu Apr 22 21:43:48 2004 Input: 9+9 Output: Magma V2.10-22 Thu Apr 22 2004 21:43:46 on modular [Seed = 1958494381] ------------------------------------- [PC] While attempting to compile /usr/local/magma/package/Group/GrpCoh/strongpr\ [PC] es.m (Source file newer than data file): [PC] Can't open lock file /usr/local/magma/package/Group/GrpCoh/strongpres.lck [PC] for writing (Permission denied) [PC] While attempting to compile /usr/local/magma/package/Group/GrpCoh/strongpr\ [PC] esab.m (Source file newer than data file): [PC] Can't open lock file /usr/local/magma/package/Group/GrpCoh/strongpresab.lc\ [PC] k for writing (Permission denied) [PC] While attempting to compile /usr/local/magma/package/LieThry/RootDtm.m [PC] (Source file newer than data file): [PC] Can't open lock file /usr/local/magma/package/LieThry/RootDtm.lck for [PC] writing (Permission denied) 18 Total time: 2.499 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217) Time: Thu Apr 22 21:44:12 2004 Input: factor(omitted) Output: Magma V2.10-22 Thu Apr 22 2004 21:44:10 on modular [Seed = 2572266872] ------------------------------------- [PC] While attempting to compile /usr/local/magma/package/Group/GrpCoh/strongpr\ [PC] es.m (Source file newer than data file): [PC] Can't open lock file /usr/local/magma/package/Group/GrpCoh/strongpres.lck [PC] for writing (Permission denied) [PC] While attempting to compile /usr/local/magma/package/Group/GrpCoh/strongpr\ [PC] esab.m (Source file newer than data file): [PC] Can't open lock file /usr/local/magma/package/Group/GrpCoh/strongpresab.lc\ [PC] k for writing (Permission denied) [PC] While attempting to compile /usr/local/magma/package/LieThry/RootDtm.m [PC] (Source file newer than data file): [PC] Can't open lock file /usr/local/magma/package/LieThry/RootDtm.lck for [PC] writing (Permission denied) >> factor(omitted) ^ User error: Identifier 'factor' has not been declared or assigned Total time: 2.509 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217) Time: Thu Apr 22 21:55:17 2004 Input: 1+2; Output: Magma V2.10-22 Thu Apr 22 2004 21:55:14 on modular [Seed = 4030252921] ------------------------------------- [PC] While attempting to compile /usr/local/magma/package/Group/GrpCoh/strongpr\ [PC] es.m (Source file newer than data file): [PC] Can't open lock file /usr/local/magma/package/Group/GrpCoh/strongpres.lck [PC] for writing (Permission denied) [PC] While attempting to compile /usr/local/magma/package/Group/GrpCoh/strongpr\ [PC] esab.m (Source file newer than data file): [PC] Can't open lock file /usr/local/magma/package/Group/GrpCoh/strongpresab.lc\ [PC] k for writing (Permission denied) [PC] While attempting to compile /usr/local/magma/package/LieThry/RootDtm.m [PC] (Source file newer than data file): [PC] Can't open lock file /usr/local/magma/package/LieThry/RootDtm.lck for [PC] writing (Permission denied) 3 Total time: 2.499 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217) Time: Thu Apr 22 22:13:58 2004 Input: 1+2; Output: Magma V2.10-22 Thu Apr 22 2004 22:13:55 on modular [Seed = 2024817559] ------------------------------------- 3 Total time: 2.479 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217) Time: Thu Apr 22 22:14:29 2004 Input: 1+2; Output: Magma V2.10-22 Thu Apr 22 2004 22:14:27 on modular [Seed = 2285941895] ------------------------------------- 3 Total time: 2.489 seconds, Total memory usage: 1.70MB ************** MAGMA ***************** Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217) Time: Thu Apr 22 22:14:42 2004 Input: Basis(ModularForms(37)); Output: Magma V2.10-22 Thu Apr 22 2004 22:14:39 on modular [Seed = 2152250499] ------------------------------------- [ 1 - 2*q^3 + 10*q^4 + 2*q^5 + 14*q^6 + 6*q^7 + O(q^8), q + q^3 - 2*q^4 - q^7 + O(q^8), q^2 + 2*q^3 - 2*q^4 + q^5 - 3*q^6 + O(q^8) ] Total time: 2.719 seconds, Total memory usage: 2.90MB